LMFDB - Embedded newform 256.2.m.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [256,2,Mod(5,256)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(256, base_ring=CyclotomicField(64))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("256.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 256 = 2^{8} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	256.m (of order $64$, degree $32$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.04417029174$
Analytic rank:	$0$
Dimension:	$992$
Relative dimension:	$31$ over $\Q(\zeta_{64})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{64}]$

Embedding invariants

Embedding label			5.5
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.5

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.32340 - 0.498599i) q^{2} +(-0.0465769 + 0.313996i) q^{3} +(1.50280 + 1.31970i) q^{4} +(-2.22226 - 0.109173i) q^{5} +(0.218198 - 0.392320i) q^{6} +(-0.0426083 - 0.0227746i) q^{7} +(-1.33081 - 2.49578i) q^{8} +(2.77440 + 0.841604i) q^{9} +O(q^{10})$	\(q+(-1.32340 - 0.498599i) q^{2} +(-0.0465769 + 0.313996i) q^{3} +(1.50280 + 1.31970i) q^{4} +(-2.22226 - 0.109173i) q^{5} +(0.218198 - 0.392320i) q^{6} +(-0.0426083 - 0.0227746i) q^{7} +(-1.33081 - 2.49578i) q^{8} +(2.77440 + 0.841604i) q^{9} +(2.88652 + 1.25250i) q^{10} +(1.29469 + 2.16006i) q^{11} +(-0.484375 + 0.410405i) q^{12} +(-2.91521 + 3.21644i) q^{13} +(0.0450326 + 0.0513844i) q^{14} +(0.137786 - 0.692696i) q^{15} +(0.516809 + 3.96647i) q^{16} +(0.0943461 + 0.474310i) q^{17} +(-3.25203 - 2.49709i) q^{18} +(3.49676 + 7.39328i) q^{19} +(-3.19554 - 3.09677i) q^{20} +(0.00913569 - 0.0123180i) q^{21} +(-0.636397 - 3.50417i) q^{22} +(0.0750285 + 0.0615743i) q^{23} +(0.845651 - 0.301624i) q^{24} +(-0.0493910 - 0.00486459i) q^{25} +(5.46171 - 2.80313i) q^{26} +(-0.800642 + 1.69281i) q^{27} +(-0.0339761 - 0.0904555i) q^{28} +(-0.180324 + 0.0451687i) q^{29} +(-0.527724 + 0.848018i) q^{30} +(5.77436 + 2.39182i) q^{31} +(1.29373 - 5.50693i) q^{32} +(-0.738554 + 0.305919i) q^{33} +(0.111632 - 0.674744i) q^{34} +(0.0922004 + 0.0552628i) q^{35} +(3.05870 + 4.92612i) q^{36} +(2.19518 + 6.13512i) q^{37} +(-0.941349 - 11.5278i) q^{38} +(-0.874167 - 1.06518i) q^{39} +(2.68494 + 5.69158i) q^{40} +(-2.60996 + 0.257058i) q^{41} +(-0.0182320 + 0.0117467i) q^{42} +(6.27828 - 0.931294i) q^{43} +(-0.904963 + 4.95474i) q^{44} +(-6.07356 - 2.17315i) q^{45} +(-0.0685922 - 0.118897i) q^{46} +(2.14756 - 3.21406i) q^{47} +(-1.26953 - 0.0224702i) q^{48} +(-3.88769 - 5.81835i) q^{49} +(0.0629388 + 0.0310641i) q^{50} +(-0.153326 + 0.00753241i) q^{51} +(-8.62569 + 0.986471i) q^{52} +(-8.67705 - 2.17349i) q^{53} +(1.90361 - 1.84108i) q^{54} +(-2.64133 - 4.94157i) q^{55} +(-0.000136855 + 0.136650i) q^{56} +(-2.48433 + 0.753612i) q^{57} +(0.261162 + 0.0301326i) q^{58} +(-4.61943 - 5.09676i) q^{59} +(1.12121 - 0.859148i) q^{60} +(-8.42035 - 11.3535i) q^{61} +(-6.44926 - 6.04444i) q^{62} +(-0.0990450 - 0.0990450i) q^{63} +(-4.45788 + 6.64284i) q^{64} +(6.82951 - 6.82951i) q^{65} +(1.12994 - 0.0366127i) q^{66} +(7.13867 - 5.29440i) q^{67} +(-0.484161 + 0.837300i) q^{68} +(-0.0228287 + 0.0206907i) q^{69} +(-0.0944644 - 0.119106i) q^{70} +(1.66828 + 5.49957i) q^{71} +(-1.59174 - 8.04431i) q^{72} +(-4.64786 + 2.48433i) q^{73} +(0.153850 - 9.21375i) q^{74} +(0.00382794 - 0.0152820i) q^{75} +(-4.50195 + 15.7253i) q^{76} +(-0.00597002 - 0.121523i) q^{77} +(0.625781 + 1.84552i) q^{78} +(5.85192 - 3.91013i) q^{79} +(-0.715454 - 8.87097i) q^{80} +(6.73764 + 4.50195i) q^{81} +(3.58220 + 0.961129i) q^{82} +(-4.54588 + 12.7049i) q^{83} +(0.0299852 - 0.00645523i) q^{84} +(-0.157880 - 1.06434i) q^{85} +(-8.77304 - 1.89786i) q^{86} +(-0.00578388 - 0.0587247i) q^{87} +(3.66806 - 6.10591i) q^{88} +(-4.91740 + 4.03560i) q^{89} +(6.95424 + 5.90423i) q^{90} +(0.197465 - 0.0706541i) q^{91} +(0.0314934 + 0.191548i) q^{92} +(-1.01997 + 1.70172i) q^{93} +(-4.44462 + 3.18272i) q^{94} +(-6.96357 - 16.8116i) q^{95} +(1.66890 + 0.662722i) q^{96} +(3.55813 - 8.59008i) q^{97} +(2.24397 + 9.63843i) q^{98} +(1.77407 + 7.08249i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) $ 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{1}{64}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.32340	−	0.498599i	−0.935788	−	0.352562i
$2$	−1.32340	−	0.498599i	−0.935788	−	0.352562i
$3$	−0.0465769	+	0.313996i	−0.0268912	+	0.181286i	−0.998460	−	0.0554703i	$-0.982334\pi$
$3$	−0.0465769	+	0.313996i	−0.0268912	+	0.181286i	0.971569	+	0.236756i	$0.0760842\pi$
$4$	1.50280	+	1.31970i	0.751399	+	0.659848i
$5$	−2.22226	−	0.109173i	−0.993826	−	0.0488235i	−0.454349	−	0.890824i	$-0.650128\pi$
$5$	−2.22226	−	0.109173i	−0.993826	−	0.0488235i	−0.539477	+	0.842000i	$0.681378\pi$
$6$	0.218198	−	0.392320i	0.0890790	−	0.160164i
$7$	−0.0426083	−	0.0227746i	−0.0161044	−	0.00860799i	0.463325	−	0.886188i	$-0.346656\pi$
$7$	−0.0426083	−	0.0227746i	−0.0161044	−	0.00860799i	−0.479429	+	0.877581i	$0.659156\pi$
$8$	−1.33081	−	2.49578i	−0.470513	−	0.882393i
$9$	2.77440	+	0.841604i	0.924799	+	0.280535i
$10$	2.88652	+	1.25250i	0.912797	+	0.396074i
$11$	1.29469	+	2.16006i	0.390364	+	0.651283i	0.988691	−	0.149969i	$-0.0479174\pi$
$11$	1.29469	+	2.16006i	0.390364	+	0.651283i	−0.598326	+	0.801252i	$0.704167\pi$
$12$	−0.484375	+	0.410405i	−0.139827	+	0.118474i
$13$	−2.91521	+	3.21644i	−0.808533	+	0.892079i	−0.995923	−	0.0902065i	$-0.971247\pi$
$13$	−2.91521	+	3.21644i	−0.808533	+	0.892079i	0.187390	+	0.982286i	$0.439997\pi$
$14$	0.0450326	+	0.0513844i	0.0120355	+	0.0137331i
$15$	0.137786	−	0.692696i	0.0355762	−	0.178853i
$16$	0.516809	+	3.96647i	0.129202	+	0.991618i
$17$	0.0943461	+	0.474310i	0.0228823	+	0.115037i	0.990538	−	0.137236i	$-0.0438219\pi$
$17$	0.0943461	+	0.474310i	0.0228823	+	0.115037i	−0.967656	+	0.252273i	$0.918822\pi$
$18$	−3.25203	−	2.49709i	−0.766510	−	0.588571i
$19$	3.49676	+	7.39328i	0.802212	+	1.69613i	0.714122	+	0.700021i	$0.246826\pi$
$19$	3.49676	+	7.39328i	0.802212	+	1.69613i	0.0880895	+	0.996113i	$0.471924\pi$
$20$	−3.19554	−	3.09677i	−0.714544	−	0.692460i
$21$	0.00913569	−	0.0123180i	0.00199357	−	0.00268802i
$22$	−0.636397	−	3.50417i	−0.135680	−	0.747091i
$23$	0.0750285	+	0.0615743i	0.0156445	+	0.0128391i	0.642183	−	0.766551i	$-0.278029\pi$
$23$	0.0750285	+	0.0615743i	0.0156445	+	0.0128391i	−0.626539	+	0.779390i	$0.715529\pi$
$24$	0.845651	−	0.301624i	0.172618	−	0.0615687i
$25$	−0.0493910	−	0.00486459i	−0.00987820	−	0.000972918i
$26$	5.46171	−	2.80313i	1.07113	−	0.549739i
$27$	−0.800642	+	1.69281i	−0.154084	+	0.325782i
$28$	−0.0339761	−	0.0904555i	−0.00642088	−	0.0170945i
$29$	−0.180324	+	0.0451687i	−0.0334853	+	0.00838763i	−0.259687	−	0.965693i	$-0.583619\pi$
$29$	−0.180324	+	0.0451687i	−0.0334853	+	0.00838763i	0.226201	+	0.974081i	$0.427369\pi$
$30$	−0.527724	+	0.848018i	−0.0963488	+	0.154826i
$31$	5.77436	+	2.39182i	1.03711	+	0.429584i	0.835272	−	0.549836i	$-0.185310\pi$
$31$	5.77436	+	2.39182i	1.03711	+	0.429584i	0.201834	+	0.979420i	$0.435310\pi$
$32$	1.29373	−	5.50693i	0.228702	−	0.973497i
$33$	−0.738554	+	0.305919i	−0.128566	+	0.0532536i
$34$	0.111632	−	0.674744i	0.0191448	−	0.115718i
$35$	0.0922004	+	0.0552628i	0.0155847	+	0.00934111i
$36$	3.05870	+	4.92612i	0.509783	+	0.821020i
$37$	2.19518	+	6.13512i	0.360885	+	1.00861i	0.975542	+	0.219812i	$0.0705445\pi$
$37$	2.19518	+	6.13512i	0.360885	+	1.00861i	−0.614657	+	0.788795i	$0.710706\pi$
$38$	−0.941349	−	11.5278i	−0.152707	−	1.87005i
$39$	−0.874167	−	1.06518i	−0.139979	−	0.170565i
$40$	2.68494	+	5.69158i	0.424527	+	0.899917i
$41$	−2.60996	+	0.257058i	−0.407607	+	0.0401458i	−0.299743	−	0.954020i	$-0.596901\pi$
$41$	−2.60996	+	0.257058i	−0.407607	+	0.0401458i	−0.107864	+	0.994166i	$0.534401\pi$
$42$	−0.0182320	+	0.0117467i	−0.00281325	+	0.00181256i
$43$	6.27828	−	0.931294i	0.957428	−	0.142021i	0.350311	−	0.936633i	$-0.386076\pi$
$43$	6.27828	−	0.931294i	0.957428	−	0.142021i	0.607117	+	0.794612i	$0.292326\pi$
$44$	−0.904963	+	4.95474i	−0.136428	+	0.746955i
$45$	−6.07356	−	2.17315i	−0.905393	−	0.323955i
$46$	−0.0685922	−	0.118897i	−0.0101134	−	0.0175304i
$47$	2.14756	−	3.21406i	0.313254	−	0.468818i	−0.641116	−	0.767444i	$-0.721528\pi$
$47$	2.14756	−	3.21406i	0.313254	−	0.468818i	0.954370	+	0.298626i	$0.0965283\pi$
$48$	−1.26953	−	0.0224702i	−0.183241	−	0.00324329i
$49$	−3.88769	−	5.81835i	−0.555385	−	0.831192i
$50$	0.0629388	+	0.0310641i	0.00890089	+	0.00439313i
$51$	−0.153326	+	0.00753241i	−0.0214699	+	0.00105475i
$52$	−8.62569	+	0.986471i	−1.19617	+	0.136799i
$53$	−8.67705	−	2.17349i	−1.19188	−	0.298552i	−0.404223	−	0.914660i	$-0.632458\pi$
$53$	−8.67705	−	2.17349i	−1.19188	−	0.298552i	−0.787661	+	0.616109i	$0.788708\pi$
$54$	1.90361	−	1.84108i	0.259048	−	0.250539i
$55$	−2.64133	−	4.94157i	−0.356156	−	0.666321i
$56$	−0.000136855		0.136650i	−1.82881e−5		0.0182606i
$57$	−2.48433	+	0.753612i	−0.329057	+	0.0998184i
$58$	0.261162	+	0.0301326i	0.0342923	+	0.00395661i
$59$	−4.61943	−	5.09676i	−0.601399	−	0.663542i	0.361823	−	0.932247i	$-0.382154\pi$
$59$	−4.61943	−	5.09676i	−0.601399	−	0.663542i	−0.963223	+	0.268705i	$0.913404\pi$
$60$	1.12121	−	0.859148i	0.144748	−	0.110916i
$61$	−8.42035	−	11.3535i	−1.07812	−	1.45367i	−0.880895	−	0.473312i	$-0.843058\pi$
$61$	−8.42035	−	11.3535i	−1.07812	−	1.45367i	−0.197221	−	0.980359i	$-0.563192\pi$
$62$	−6.44926	−	6.04444i	−0.819057	−	0.767644i
$63$	−0.0990450	−	0.0990450i	−0.0124785	−	0.0124785i
$64$	−4.45788	+	6.64284i	−0.557235	+	0.830355i
$65$	6.82951	−	6.82951i	0.847096	−	0.847096i
$66$	1.12994	−	0.0366127i	0.139085	−	0.00450671i
$67$	7.13867	−	5.29440i	0.872128	−	0.646814i	−0.0642015	−	0.997937i	$-0.520450\pi$
$67$	7.13867	−	5.29440i	0.872128	−	0.646814i	0.936329	+	0.351123i	$0.114200\pi$
$68$	−0.484161	+	0.837300i	−0.0587132	+	0.101538i
$69$	−0.0228287	+	0.0206907i	−0.00274825	+	0.00249087i
$70$	−0.0944644	−	0.119106i	−0.0112907	−	0.0142359i
$71$	1.66828	+	5.49957i	0.197988	+	0.652679i	0.998570	+	0.0534559i	$0.0170237\pi$
$71$	1.66828	+	5.49957i	0.197988	+	0.652679i	−0.800582	+	0.599223i	$0.795476\pi$
$72$	−1.59174	−	8.04431i	−0.187588	−	0.948031i
$73$	−4.64786	+	2.48433i	−0.543991	+	0.290769i	−0.720413	−	0.693545i	$-0.756048\pi$
$73$	−4.64786	+	2.48433i	−0.543991	+	0.290769i	0.176422	+	0.984315i	$0.443548\pi$
$74$	0.153850	−	9.21375i	0.0178847	−	1.07108i
$75$	0.00382794	−	0.0152820i	0.000442013	−	0.00176461i
$76$	−4.50195	+	15.7253i	−0.516409	+	1.80381i
$77$	−0.00597002	−	0.121523i	−0.000680347	−	0.0138488i
$78$	0.625781	+	1.84552i	0.0708558	+	0.208964i
$79$	5.85192	−	3.91013i	0.658392	−	0.439924i	−0.180975	−	0.983488i	$-0.557925\pi$
$79$	5.85192	−	3.91013i	0.658392	−	0.439924i	0.839368	+	0.543564i	$0.182925\pi$
$80$	−0.715454	−	8.87097i	−0.0799902	−	0.991804i
$81$	6.73764	+	4.50195i	0.748626	+	0.500216i
$82$	3.58220	+	0.961129i	0.395588	+	0.106139i
$83$	−4.54588	+	12.7049i	−0.498975	+	1.39454i	0.383219	+	0.923657i	$0.374815\pi$
$83$	−4.54588	+	12.7049i	−0.498975	+	1.39454i	−0.882195	+	0.470885i	$0.843935\pi$
$84$	0.0299852	−	0.00645523i	0.00327165	−	0.000704323i
$85$	−0.157880	−	1.06434i	−0.0171245	−	0.115444i
$86$	−8.77304	−	1.89786i	−0.946021	−	0.204652i
$87$	−0.00578388	−	0.0587247i	−0.000620097	−	0.00629595i
$88$	3.66806	−	6.10591i	0.391016	−	0.650892i
$89$	−4.91740	+	4.03560i	−0.521243	+	0.427773i	−0.857871	−	0.513864i	$-0.828213\pi$
$89$	−4.91740	+	4.03560i	−0.521243	+	0.427773i	0.336628	+	0.941638i	$0.390713\pi$
$90$	6.95424	+	5.90423i	0.733042	+	0.622360i
$91$	0.197465	−	0.0706541i	0.0207000	−	0.00740656i
$92$	0.0314934	+	0.191548i	0.00328342	+	0.0199703i
$93$	−1.01997	+	1.70172i	−0.105766	+	0.176460i
$94$	−4.44462	+	3.18272i	−0.458427	+	0.328273i
$95$	−6.96357	−	16.8116i	−0.714447	−	1.72483i
$96$	1.66890	+	0.662722i	0.170331	+	0.0676388i
$97$	3.55813	−	8.59008i	0.361273	−	0.872191i	−0.633841	−	0.773463i	$-0.718523\pi$
$97$	3.55813	−	8.59008i	0.361273	−	0.872191i	0.995114	−	0.0987277i	$-0.0314773\pi$
$98$	2.24397	+	9.63843i	0.226676	+	0.973628i
$99$	1.77407	+	7.08249i	0.178301	+	0.711817i
$100$	−0.0678050	−	0.0724916i	−0.00678050	−	0.00724916i
$101$	11.0390	+	5.22104i	1.09842	+	0.519513i	0.888812	−	0.458273i	$-0.151532\pi$
$101$	11.0390	+	5.22104i	1.09842	+	0.519513i	0.209607	+	0.977786i	$0.432782\pi$
$102$	0.206667	+	0.0664795i	0.0204631	+	0.00658245i
$103$	−0.156073	+	1.58463i	−0.0153783	+	0.156139i	−0.999807	−	0.0196457i	$-0.993746\pi$
$103$	−0.156073	+	1.58463i	−0.0153783	+	0.156139i	0.984429	+	0.175784i	$0.0562462\pi$
$104$	11.9071	+	2.99526i	1.16759	+	0.293709i
$105$	−0.0216467	+	0.0263766i	−0.00211250	+	0.00257409i
$106$	10.3995	+	7.20277i	1.01009	+	0.699595i
$107$	−8.23298	−	6.10599i	−0.795912	−	0.590289i	0.119487	−	0.992836i	$-0.461875\pi$
$107$	−8.23298	−	6.10599i	−0.795912	−	0.590289i	−0.915399	+	0.402547i	$0.868125\pi$
$108$	−3.43720	+	1.48736i	−0.330745	+	0.143121i
$109$	0.141518	−	0.0669329i	0.0135549	−	0.00641101i	−0.420766	−	0.907169i	$-0.638239\pi$
$109$	0.141518	−	0.0669329i	0.0135549	−	0.00641101i	0.434321	+	0.900758i	$0.356989\pi$
$110$	1.03168	+	7.85666i	0.0983669	+	0.749103i
$111$	−2.02865	+	0.403523i	−0.192551	+	0.0383007i
$112$	0.0683145	−	0.180775i	0.00645511	−	0.0170816i
$113$	18.2267	+	3.62552i	1.71463	+	0.341061i	0.952075	−	0.305865i	$-0.0989457\pi$
$113$	18.2267	+	3.62552i	1.71463	+	0.341061i	0.762553	+	0.646926i	$0.223946\pi$
$114$	3.66352	+	0.241348i	0.343120	+	0.0226043i
$115$	−0.160011	−	0.145025i	−0.0149211	−	0.0135237i
$116$	−0.330599	−	0.170093i	−0.0306954	−	0.0157927i
$117$	−10.7949	+	6.47022i	−0.997990	+	0.598172i
$118$	3.57214	+	9.04832i	0.328842	+	0.832965i
$119$	0.00678229	−	0.0223582i	0.000621731	−	0.00204957i
$120$	−1.91219	+	0.577965i	−0.174558	+	0.0527608i
$121$	2.19572	−	4.10790i	0.199611	−	0.373446i
$122$	5.48268	+	19.2237i	0.496378	+	1.74043i
$123$	0.0408484	−	0.831489i	0.00368318	−	0.0749729i
$124$	5.52123	+	11.2148i	0.495821	+	1.00712i
$125$	11.1135	+	1.64854i	0.994025	+	0.147450i
$126$	0.0816929	+	0.180460i	0.00727778	+	0.0160767i
$127$		−	4.85413i		−	0.430734i	−0.976533	−	0.215367i	$-0.930905\pi$
$127$		−	4.85413i		−	0.430734i	0.976533	−	0.215367i	$-0.0690948\pi$
$128$	9.21169	−	6.56847i	0.814206	−	0.580577i
$129$			2.01473i			0.177387i
$130$	−12.4434	+	5.63302i	−1.09136	+	0.494048i
$131$	19.8431	+	2.94344i	1.73370	+	0.257170i	0.937529	−	0.347907i	$-0.113107\pi$
$131$	19.8431	+	2.94344i	1.73370	+	0.257170i	0.796167	+	0.605076i	$0.206857\pi$
$132$	−1.51362	−	0.514931i	−0.131743	−	0.0448190i
$133$	0.0193880	−	0.394652i	0.00168115	−	0.0342207i
$134$	−12.0871	+	3.44730i	−1.04417	+	0.297802i
$135$	1.96405	−	3.67447i	0.169038	−	0.316248i
$136$	1.05822	−	0.866685i	0.0907414	−	0.0743176i
$137$	0.888256	−	2.92819i	0.0758888	−	0.250172i	−0.910785	−	0.412880i	$-0.864523\pi$
$137$	0.888256	−	2.92819i	0.0758888	−	0.250172i	0.986674	+	0.162708i	$0.0520229\pi$
$138$	0.0405279	−	0.0159998i	0.00344996	−	0.00136199i
$139$	−7.73000	+	4.63319i	−0.655650	+	0.392982i	−0.802897	−	0.596118i	$-0.796709\pi$
$139$	−7.73000	+	4.63319i	−0.655650	+	0.392982i	0.147246	+	0.989100i	$0.452959\pi$
$140$	0.0656286	+	0.204725i	0.00554663	+	0.0173024i
$141$	0.909173	+	0.824027i	0.0765662	+	0.0693956i
$142$	0.534274	−	8.10995i	0.0448352	−	0.680572i
$143$	−10.7220	−	2.13274i	−0.896619	−	0.178349i
$144$	−1.90437	+	11.4395i	−0.158697	+	0.953293i
$145$	0.405658	−	0.0806904i	0.0336881	−	0.00670097i
$146$	7.38969	−	0.970362i	0.611575	−	0.0803077i
$147$	2.00801	−	0.949720i	0.165618	−	0.0783316i
$148$	−4.79757	+	12.1168i	−0.394358	+	0.995996i
$149$	−3.51244	−	2.60500i	−0.287750	−	0.213410i	0.442190	−	0.896922i	$-0.354202\pi$
$149$	−3.51244	−	2.60500i	−0.287750	−	0.213410i	−0.729940	+	0.683512i	$0.760452\pi$
$150$	−0.0126855	+	0.0183157i	−0.00103577	+	0.00149547i
$151$	−5.76237	+	7.02146i	−0.468935	+	0.571399i	−0.952744	−	0.303775i	$-0.901753\pi$
$151$	−5.76237	+	7.02146i	−0.468935	+	0.571399i	0.483809	+	0.875174i	$0.339253\pi$
$152$	13.7985	−	18.5662i	1.11921	−	1.50592i
$153$	−0.137428	+	1.39533i	−0.0111104	+	0.112805i
$154$	−0.0526902	+	0.163800i	−0.00424590	+	0.0131994i
$155$	−12.5710	−	5.94566i	−1.00973	−	0.477567i
$156$	0.0920100	−	2.75438i	0.00736670	−	0.220527i
$157$	−5.38428	−	21.4953i	−0.429713	−	1.71551i	−0.667866	−	0.744281i	$-0.732792\pi$
$157$	−5.38428	−	21.4953i	−0.429713	−	1.71551i	0.238153	−	0.971228i	$-0.423458\pi$
$158$	−9.69404	+	2.25692i	−0.771216	+	0.179551i
$159$	1.08662	−	2.62332i	0.0861743	−	0.208043i
$160$	−3.47622	+	12.0966i	−0.274819	+	0.956320i
$161$	−0.00179450	−	0.00433231i	−0.000141427	−	0.000341434i
$162$	−6.67196	−	9.31727i	−0.524198	−	0.732034i
$163$	2.10023	−	3.50402i	0.164503	−	0.274456i	−0.764429	−	0.644708i	$-0.776979\pi$
$163$	2.10023	−	3.50402i	0.164503	−	0.274456i	0.928931	+	0.370252i	$0.120729\pi$
$164$	−4.26148	−	3.05804i	−0.332766	−	0.238793i
$165$	1.67466	−	0.599202i	0.130372	−	0.0466478i
$166$	12.3507	−	14.5471i	0.958598	−	1.12908i
$167$	−13.3312	+	10.9406i	−1.03160	+	0.846610i	−0.988311	−	0.152453i	$-0.951283\pi$
$167$	−13.3312	+	10.9406i	−1.03160	+	0.846610i	−0.0432863	+	0.999063i	$0.513783\pi$
$168$	−0.0429011	−	0.00640769i	−0.00330989	−	0.000494364i
$169$	−0.572803	−	5.81577i	−0.0440618	−	0.447367i
$170$	−0.321740	+	1.48727i	−0.0246763	+	0.114069i
$171$	3.47919	+	23.4548i	0.266060	+	1.79363i
$172$	10.6640	+	6.88586i	0.813123	+	0.525042i
$173$	−0.798148	+	2.23068i	−0.0606821	+	0.169595i	−0.968059	−	0.250723i	$-0.919332\pi$
$173$	−0.798148	+	2.23068i	−0.0606821	+	0.169595i	0.907377	+	0.420318i	$0.138082\pi$
$174$	−0.0216257	+	0.0806004i	−0.00163944	+	0.00611030i
$175$	0.00199368	+	0.00133213i	0.000150708	+	0.000100700i
$176$	−7.89872	+	6.25170i	−0.595389	+	0.471240i
$177$	1.81552	−	1.21309i	0.136463	−	0.0911816i
$178$	8.51985	−	2.88893i	0.638590	−	0.216534i
$179$	−0.483967	−	9.85137i	−0.0361734	−	0.736326i	−0.946552	−	0.322550i	$-0.895460\pi$
$179$	−0.483967	−	9.85137i	−0.0361734	−	0.736326i	0.910379	−	0.413776i	$-0.135790\pi$
$180$	−6.25944	−	11.2811i	−0.466551	−	0.840841i
$181$	−5.58677	+	22.3036i	−0.415261	+	1.65782i	0.296226	+	0.955118i	$0.404272\pi$
$181$	−5.58677	+	22.3036i	−0.415261	+	1.65782i	−0.711488	+	0.702699i	$0.751978\pi$
$182$	−0.296554	−	0.00495182i	−0.0219821	−	0.000367053i
$183$	3.95716	−	2.11514i	0.292521	−	0.156356i
$184$	0.0538273	−	0.269199i	0.00396820	−	0.0198456i
$185$	−4.20848	−	13.8735i	−0.309413	−	1.02000i
$186$	2.19831	−	1.74351i	0.161188	−	0.127840i
$187$	−0.902389	+	0.817878i	−0.0659893	+	0.0598092i
$188$	7.46893	−	1.99595i	0.544728	−	0.145570i
$189$	0.0726671	−	0.0538936i	0.00528575	−	0.00392018i
$190$	0.833407	+	25.7205i	0.0604617	+	1.86596i
$191$	17.0548	−	17.0548i	1.23404	−	1.23404i	0.271646	−	0.962397i	$-0.412432\pi$
$191$	17.0548	−	17.0548i	1.23404	−	1.23404i	0.962397	−	0.271646i	$-0.0875680\pi$
$192$	−1.87819	−	1.70916i	−0.135547	−	0.123348i
$193$	7.45994	+	7.45994i	0.536978	+	0.536978i	0.922640	−	0.385662i	$-0.126027\pi$
$193$	7.45994	+	7.45994i	0.536978	+	0.536978i	−0.385662	+	0.922640i	$0.626027\pi$
$194$	−8.99185	+	9.59408i	−0.645577	+	0.688815i
$195$	1.82634	+	2.46253i	0.130787	+	0.176346i
$196$	1.83602	−	13.8744i	0.131144	−	0.991027i
$197$	2.49746	+	2.75552i	0.177937	+	0.196323i	0.823388	−	0.567478i	$-0.192081\pi$
$197$	2.49746	+	2.75552i	0.177937	+	0.196323i	−0.645452	+	0.763801i	$0.723331\pi$
$198$	1.18351	−	10.2575i	0.0841081	−	0.728972i
$199$	13.6063	−	4.12743i	0.964526	−	0.292586i	0.231537	−	0.972826i	$-0.425625\pi$
$199$	13.6063	−	4.12743i	0.964526	−	0.292586i	0.732989	+	0.680240i	$0.238125\pi$
$200$	0.0535892	+	0.129743i	0.00378933	+	0.00917423i
$201$	1.32992	+	2.48811i	0.0938056	+	0.175498i
$202$	−12.0058	−	12.4136i	−0.844726	−	0.873415i
$203$	0.00871198	+	0.00218224i	0.000611461	+	0.000153163i
$204$	−0.240358	−	0.191023i	−0.0168284	−	0.0133743i
$205$	5.82808	−	0.286315i	0.407051	−	0.0199971i
$206$	0.996644	−	2.01930i	0.0694395	−	0.140691i
$207$	0.156338	+	0.233976i	0.0108662	+	0.0162624i
$208$	−14.2645	−	9.90081i	−0.989066	−	0.686498i
$209$	−11.4427	+	17.1252i	−0.791509	+	1.18458i
$210$	0.0417987	−	0.0241139i	0.00288438	−	0.00166401i
$211$	−5.31184	−	1.90061i	−0.365682	−	0.130843i	0.147636	−	0.989042i	$-0.452834\pi$
$211$	−5.31184	−	1.90061i	−0.365682	−	0.130843i	−0.513318	+	0.858199i	$0.671584\pi$
$212$	−10.1715	−	14.7174i	−0.698583	−	1.01079i
$213$	−1.80455	+	0.267679i	−0.123645	+	0.0183411i
$214$	7.85112	+	12.1857i	0.536692	+	0.832994i
$215$	−14.0537	+	1.38416i	−0.958451	+	0.0943992i
$216$	5.29040	−	0.254590i	0.359966	−	0.0173227i
$217$	−0.191563	−	0.233420i	−0.0130041	−	0.0158456i
$218$	−0.220658	+	0.0180188i	−0.0149448	+	0.00122038i
$219$	−0.563588	−	1.57512i	−0.0380837	−	0.106437i
$220$	2.55199	−	10.9119i	0.172055	−	0.735682i
$221$	−1.80063	−	1.07925i	−0.121123	−	0.0725984i
$222$	2.88592	+	0.477456i	0.193690	+	0.0320448i
$223$	−3.72308	+	1.54215i	−0.249316	+	0.103270i	−0.503842	−	0.863796i	$-0.668081\pi$
$223$	−3.72308	+	1.54215i	−0.249316	+	0.103270i	0.254526	+	0.967066i	$0.418081\pi$
$224$	−0.180542	+	0.205176i	−0.0120629	+	0.0137089i
$225$	−0.132936	−	0.0550640i	−0.00886241	−	0.00367093i
$226$	−22.3137	−	13.8859i	−1.48428	−	0.923674i
$227$	−6.64566	+	1.66465i	−0.441088	+	0.110487i	−0.457161	−	0.889384i	$-0.651134\pi$
$227$	−6.64566	+	1.66465i	−0.441088	+	0.110487i	0.0160730	+	0.999871i	$0.494884\pi$
$228$	−4.72798	−	2.14603i	−0.313118	−	0.142124i
$229$	4.41578	−	9.33639i	0.291803	−	0.616966i	−0.703825	−	0.710374i	$-0.748526\pi$
$229$	4.41578	−	9.33639i	0.291803	−	0.616966i	0.995628	+	0.0934076i	$0.0297760\pi$
$230$	0.139449	+	0.271708i	0.00919503	+	0.0179159i
$231$	0.0384357	+	0.00378558i	0.00252888	+	0.000249073i
$232$	0.352709	+	0.389938i	0.0231564	+	0.0256007i
$233$	15.2643	+	12.5271i	1.00000	+	0.820679i	0.983815	−	0.179190i	$-0.0573475\pi$
$233$	15.2643	+	12.5271i	1.00000	+	0.820679i	0.0161862	+	0.999869i	$0.494848\pi$
$234$	17.5121	−	3.18039i	1.14480	−	0.207909i
$235$	−5.12334	+	6.90802i	−0.334210	+	0.450630i
$236$	−0.215910	−	13.7557i	−0.0140545	−	0.895417i
$237$	0.955200	+	2.01960i	0.0620469	+	0.131187i
$238$	−0.0201235	+	0.0262073i	−0.00130441	+	0.00169877i
$239$	−1.26255	−	6.34728i	−0.0816677	−	0.410571i	−0.999895	−	0.0145167i	$-0.995379\pi$
$239$	−1.26255	−	6.34728i	−0.0816677	−	0.410571i	0.918227	−	0.396055i	$-0.129621\pi$
$240$	2.81877	+	0.188533i	0.181951	+	0.0121697i
$241$	1.54196	−	7.75196i	0.0993264	−	0.499347i	−0.898811	−	0.438337i	$-0.855568\pi$
$241$	1.54196	−	7.75196i	0.0993264	−	0.499347i	0.998137	−	0.0610105i	$-0.0194323\pi$
$242$	−4.95402	+	4.34163i	−0.318456	+	0.279091i
$243$	−5.50010	+	6.06843i	−0.352832	+	0.389290i
$244$	2.32911	−	28.1744i	0.149106	−	1.80368i
$245$	8.00427	+	13.3543i	0.511374	+	0.853177i
$246$	−0.468638	+	1.08003i	−0.0298793	+	0.0688602i
$247$	−33.9738	−	10.3058i	−2.16170	−	0.655745i
$248$	−1.71513	−	17.5946i	−0.108911	−	1.11726i
$249$	−3.77755	−	2.01914i	−0.239392	−	0.127958i
$250$	−13.8857	−	7.72287i	−0.878211	−	0.488437i
$251$	−16.3169	−	0.801598i	−1.02991	−	0.0505964i	−0.472913	−	0.881109i	$-0.656798\pi$
$251$	−16.3169	−	0.801598i	−1.02991	−	0.0505964i	−0.557000	+	0.830512i	$0.688048\pi$
$252$	−0.0181355	−	0.279554i	−0.00114243	−	0.0176102i
$253$	−0.0358655	+	0.241786i	−0.00225485	+	0.0152009i
$254$	−2.42026	+	6.42397i	−0.151861	+	0.403076i
$255$	0.341552			0.0213888
$256$	−15.4658	+	4.09982i	−0.966614	+	0.256238i
$257$	8.39857			0.523889			0.261944	−	0.965083i	$-0.415636\pi$
$257$	8.39857			0.523889			0.261944	+	0.965083i	$0.415636\pi$
$258$	1.00454	−	2.66630i	0.0625400	−	0.165997i
$259$	0.0461920	−	0.311401i	0.00287023	−	0.0193495i
$260$	19.2762	−	1.25051i	1.19546	−	0.0775531i
$261$	−0.538304	−	0.0264452i	−0.0333202	−	0.00163692i
$262$	−24.7928	−	13.7891i	−1.53170	−	0.851893i
$263$	7.37538	+	3.94222i	0.454785	+	0.243088i	0.682851	−	0.730558i	$-0.260740\pi$
$263$	7.37538	+	3.94222i	0.454785	+	0.243088i	−0.228065	+	0.973646i	$0.573240\pi$
$264$	1.74638	+	1.43615i	0.107482	+	0.0883889i
$265$	19.0454	+	5.77736i	1.16995	+	0.354900i
$266$	−0.222431	+	0.512617i	−0.0136381	+	0.0314306i
$267$	−1.03813	−	1.73201i	−0.0635323	−	0.105997i
$268$	17.7150	+	1.46445i	1.08212	+	0.0894558i
$269$	6.82221	−	7.52715i	0.415958	−	0.458938i	−0.496544	−	0.868012i	$-0.665398\pi$
$269$	6.82221	−	7.52715i	0.415958	−	0.458938i	0.912502	+	0.409073i	$0.134148\pi$
$270$	−4.43131	+	3.88354i	−0.269681	+	0.236345i
$271$	−5.00353	+	25.1545i	−0.303943	+	1.52802i	0.463029	+	0.886343i	$0.346763\pi$
$271$	−5.00353	+	25.1545i	−0.303943	+	1.52802i	−0.766972	+	0.641681i	$0.778237\pi$
$272$	−1.83258	+	0.619348i	−0.111116	+	0.0375535i
$273$	0.0129878	+	0.0652941i	0.000786057	+	0.00395178i
$274$	−2.63551	+	3.43229i	−0.159217	+	0.207352i
$275$	−0.0534383	−	0.112986i	−0.00322245	−	0.00681330i
$276$	−0.0616123		0.000967071i	−0.00370862		5.82109e-5i
$277$	10.5902	−	14.2792i	0.636301	−	0.857953i	−0.360909	−	0.932601i	$-0.617533\pi$
$277$	10.5902	−	14.2792i	0.636301	−	0.857953i	0.997210	+	0.0746484i	$0.0237834\pi$
$278$	12.5400	−	2.27741i	0.752101	−	0.136590i
$279$	14.0074	+	11.4956i	0.838602	+	0.688223i
$280$	0.0152226	−	0.303657i	0.000909722	−	0.0181470i
$281$	−18.1125	−	1.78392i	−1.08050	−	0.106420i	−0.457932	−	0.888987i	$-0.651410\pi$
$281$	−18.1125	−	1.78392i	−1.08050	−	0.106420i	−0.622566	+	0.782567i	$0.713910\pi$
$282$	−0.792346	−	1.54383i	−0.0471835	−	0.0919339i
$283$	8.41019	−	17.7818i	0.499934	−	1.05702i	−0.483432	−	0.875382i	$-0.660610\pi$
$283$	8.41019	−	17.7818i	0.499934	−	1.05702i	0.983365	−	0.181639i	$-0.0581402\pi$
$284$	−4.75067	+	10.4664i	−0.281901	+	0.621064i
$285$	5.60310	−	1.40350i	0.331899	−	0.0831364i
$286$	13.1262	+	8.16845i	0.776166	+	0.483011i
$287$	0.117060	+	0.0484879i	0.00690984	+	0.00286215i
$288$	8.22398	−	14.1896i	0.484603	−	0.836130i
$289$	15.4899	−	6.41612i	0.911170	−	0.377419i
$290$	−0.577082	−	0.0954745i	−0.0338874	−	0.00560645i
$291$	2.53152	+	1.51734i	0.148401	+	0.0889479i
$292$	−10.2634	−	2.40031i	−0.600618	−	0.140467i
$293$	5.87431	+	16.4176i	0.343181	+	0.959127i	0.981852	+	0.189647i	$0.0607344\pi$
$293$	5.87431	+	16.4176i	0.343181	+	0.959127i	−0.638671	+	0.769480i	$0.720516\pi$
$294$	−3.13094	+	0.255671i	−0.182600	+	0.0149110i
$295$	9.70917	+	11.8307i	0.565290	+	0.688807i
$296$	12.3906	−	13.6434i	0.720186	−	0.793006i
$297$	−4.69317	+	0.462237i	−0.272325	+	0.0268217i
$298$	3.34952	+	5.19876i	0.194033	+	0.301156i
$299$	−0.416773	+	0.0618225i	−0.0241026	+	0.00357529i
$300$	0.0259202	−	0.0179141i	0.00149650	−	0.00103427i
$301$	−0.288716	−	0.103304i	−0.0166413	−	0.00595436i
$302$	11.1268	−	6.41913i	0.640277	−	0.369379i
$303$	−2.15355	+	3.22301i	−0.123718	+	0.185157i
$304$	−27.5181	+	17.6907i	−1.57827	+	1.01463i
$305$	17.4727	+	26.1498i	1.00049	+	1.49733i
$306$	0.877579	−	1.77806i	0.0501679	−	0.101645i
$307$	−0.273355	+	0.0134291i	−0.0156012	+	0.000766436i	−0.0568668	−	0.998382i	$-0.518111\pi$
$307$	−0.273355	+	0.0134291i	−0.0156012	+	0.000766436i	0.0412656	+	0.999148i	$0.486861\pi$
$308$	0.151401	−	0.190503i	0.00862687	−	0.0108549i
$309$	−0.490300	−	0.122814i	−0.0278922	−	0.00698662i
$310$	13.6721	+	14.1364i	0.776521	+	0.802894i
$311$	−1.79549	−	3.35913i	−0.101813	−	0.190479i	0.825857	−	0.563879i	$-0.190692\pi$
$311$	−1.79549	−	3.35913i	−0.101813	−	0.190479i	−0.927670	+	0.373401i	$0.878192\pi$
$312$	−1.49510	+	3.59928i	−0.0846431	+	0.203769i
$313$	−16.0658	+	4.87352i	−0.908095	+	0.275468i	−0.709576	−	0.704629i	$-0.751113\pi$
$313$	−16.0658	+	4.87352i	−0.908095	+	0.275468i	−0.198519	+	0.980097i	$0.563613\pi$
$314$	−3.59192	+	31.1315i	−0.202704	+	1.75685i
$315$	0.209291	+	0.230917i	0.0117922	+	0.0130107i
$316$	13.9544	+	1.84662i	0.784998	+	0.103880i
$317$	−5.58761	−	7.53402i	−0.313832	−	0.423153i	0.617925	−	0.786237i	$-0.287974\pi$
$317$	−5.58761	−	7.53402i	−0.313832	−	0.423153i	−0.931756	+	0.363084i	$0.881724\pi$
$318$	−2.74602	+	2.92993i	−0.153989	+	0.164303i
$319$	−0.331031	−	0.331031i	−0.0185342	−	0.0185342i
$320$	10.6318	−	14.2755i	0.594335	−	0.798022i
$321$	2.30072	−	2.30072i	0.128414	−	0.128414i
$322$	0.000214768		0.00662814i	1.19685e−5		0.000369372i
$323$	−3.17680	+	2.35607i	−0.176762	+	0.131095i
$324$	4.18412	+	15.6571i	0.232451	+	0.869841i
$325$	0.159632	−	0.144682i	0.00885478	−	0.00802550i
$326$	−4.52655	+	3.59006i	−0.250702	+	0.198835i
$327$	0.0144252	+	0.0475535i	0.000797716	+	0.00262972i
$328$	4.11493	+	6.17180i	0.227209	+	0.340780i
$329$	−0.164703	+	0.0880354i	−0.00908035	+	0.00485355i
$330$	−2.51501	−	0.0419953i	−0.138447	−	0.00231176i
$331$	6.62948	−	26.4664i	0.364389	−	1.45472i	−0.459604	−	0.888124i	$-0.652009\pi$
$331$	6.62948	−	26.4664i	0.364389	−	1.45472i	0.823993	−	0.566599i	$-0.191741\pi$
$332$	−23.5981	+	13.0937i	−1.29512	+	0.718611i
$333$	0.926961	+	18.8687i	0.0507971	+	1.03400i
$334$	23.0975	−	7.83195i	1.26384	−	0.428545i
$335$	−16.4420	+	10.9862i	−0.898323	+	0.600240i
$336$	0.0535806	+	0.0298704i	0.00292306	+	0.00162956i
$337$	−22.1895	−	14.8266i	−1.20874	−	0.807654i	−0.222818	−	0.974860i	$-0.571525\pi$
$337$	−22.1895	−	14.8266i	−1.20874	−	0.807654i	−0.985922	+	0.167206i	$0.946525\pi$
$338$	−2.14168	+	7.98222i	−0.116492	+	0.434175i
$339$	−1.98734	+	5.55426i	−0.107938	+	0.301666i
$340$	1.16734	−	1.80784i	0.0633081	−	0.0980441i
$341$	2.30954	+	15.5697i	0.125069	+	0.843144i
$342$	7.09014	−	32.7749i	0.383391	−	1.77226i
$343$	0.0662860	+	0.673013i	0.00357911	+	0.0363393i
$344$	−10.6795	−	14.4298i	−0.575801	−	0.778005i
$345$	0.0529901	−	0.0434879i	0.00285289	−	0.00234131i
$346$	2.16848	−	2.55413i	0.116578	−	0.137311i
$347$	10.5250	−	3.76592i	0.565014	−	0.202165i	−0.0388608	−	0.999245i	$-0.512373\pi$
$347$	10.5250	−	3.76592i	0.565014	−	0.202165i	0.603874	+	0.797080i	$0.293623\pi$
$348$	0.0688068	−	0.0958844i	0.00368843	−	0.00513995i
$349$	−6.17841	+	10.3081i	−0.330723	+	0.551777i	−0.977509	−	0.210894i	$-0.932363\pi$
$349$	−6.17841	+	10.3081i	−0.330723	+	0.551777i	0.646786	+	0.762671i	$0.276113\pi$
$350$	−0.00197424	−	0.00275699i	−0.000105528	−	0.000147367i
$351$	−3.11079	−	7.51012i	−0.166042	−	0.400861i
$352$	13.5703	−	4.33523i	0.723299	−	0.231069i
$353$	13.6696	−	33.0012i	0.727557	−	1.75648i	0.0769879	−	0.997032i	$-0.475470\pi$
$353$	13.6696	−	33.0012i	0.727557	−	1.75648i	0.650569	−	0.759447i	$-0.274530\pi$
$354$	−3.00751	+	0.700196i	−0.159848	+	0.0372150i
$355$	−3.10694	−	12.4036i	−0.164899	−	0.658316i
$356$	−12.7156	−	0.424766i	−0.673927	−	0.0225125i
$357$	0.00670449	+	0.00317099i	0.000354839	+	0.000167826i
$358$	−4.27140	+	13.2787i	−0.225750	+	0.701799i
$359$	−1.95255	+	19.8246i	−0.103052	+	1.04630i	0.795059	+	0.606533i	$0.207440\pi$
$359$	−1.95255	+	19.8246i	−0.103052	+	1.04630i	−0.898110	+	0.439770i	$0.855060\pi$
$360$	2.65904	+	18.0504i	0.140144	+	0.951337i
$361$	−30.3797	+	37.0178i	−1.59893	+	1.94831i
$362$	18.5141	−	26.7312i	0.973081	−	1.40496i
$363$	1.18759	+	0.880780i	0.0623326	+	0.0462290i
$364$	0.389992	+	0.154415i	0.0204411	+	0.00809353i
$365$	10.6000	−	5.01342i	0.554829	−	0.262415i
$366$	−6.29153	+	0.826159i	−0.328863	+	0.0431840i
$367$	25.4420	−	5.06072i	1.32806	−	0.264167i	0.520453	−	0.853890i	$-0.325763\pi$
$367$	25.4420	−	5.06072i	1.32806	−	0.264167i	0.807606	+	0.589723i	$0.200763\pi$
$368$	−0.205457	+	0.329420i	−0.0107102	+	0.0171722i
$369$	−7.45740	−	1.48337i	−0.388217	−	0.0772211i
$370$	−1.34779	+	20.4586i	−0.0700680	+	1.06359i
$371$	0.320214	+	0.290225i	0.0166247	+	0.0150677i
$372$	−3.77857	+	1.21129i	−0.195910	+	0.0628026i
$373$	17.7085	−	10.6141i	0.916910	−	0.549575i	0.0239514	−	0.999713i	$-0.492375\pi$
$373$	17.7085	−	10.6141i	0.916910	−	0.549575i	0.892959	+	0.450138i	$0.148625\pi$
$374$	1.60202	−	0.632453i	0.0828384	−	0.0327034i
$375$	−1.03527	+	3.41282i	−0.0534610	+	0.176237i
$376$	−10.8796	−	1.08255i	−0.561072	−	0.0558282i
$377$	0.380399	−	0.711676i	0.0195915	−	0.0366532i
$378$	−0.123039	+	0.0350913i	−0.00632846	+	0.00180490i
$379$	1.30379	−	26.5393i	0.0669713	−	1.36323i	−0.696578	−	0.717481i	$-0.745295\pi$
$379$	1.30379	−	26.5393i	0.0669713	−	1.36323i	0.763549	−	0.645750i	$-0.223455\pi$
$380$	11.7213	−	34.4542i	0.601289	−	1.76746i
$381$	1.52418	+	0.226090i	0.0780859	+	0.0115829i
$382$	−31.0739	+	14.0669i	−1.58988	+	0.719726i
$383$			19.5009i			0.996447i	0.867049	+	0.498223i	$0.166014\pi$
$383$			19.5009i			0.996447i	−0.867049	+	0.498223i	$0.833986\pi$
$384$	1.63342	+	3.19837i	0.0833552	+	0.163216i
$385$			0.270707i			0.0137965i
$386$	−6.15300	−	13.5920i	−0.313180	−	0.691816i
$387$	18.2022	+	2.70004i	0.925271	+	0.137251i
$388$	16.6834	−	8.21352i	0.846974	−	0.416978i
$389$	0.0659541	−	1.34253i	0.00334401	−	0.0680688i	−0.996543	−	0.0830736i	$-0.973526\pi$
$389$	0.0659541	−	1.34253i	0.00334401	−	0.0680688i	0.999887	+	0.0150048i	$0.00477635\pi$
$390$	−1.18917	−	4.16954i	−0.0602160	−	0.211133i
$391$	−0.0221266	+	0.0413960i	−0.00111899	+	0.00209349i
$392$	−9.34754	+	17.4460i	−0.472122	+	0.881155i
$393$	−1.84846	+	6.09355i	−0.0932423	+	0.307379i
$394$	−1.93125	−	4.89190i	−0.0972950	−	0.246450i
$395$	−13.4314	+	8.05046i	−0.675806	+	0.405063i
$396$	−6.68066	+	12.9848i	−0.335716	+	0.652510i
$397$	−1.66385	−	1.50803i	−0.0835064	−	0.0756858i	0.628739	−	0.777617i	$-0.283572\pi$
$397$	−1.66385	−	1.50803i	−0.0835064	−	0.0756858i	−0.712245	+	0.701931i	$0.752322\pi$
$398$	−20.0646	−	1.32183i	−1.00575	−	0.0662573i
$399$	0.123016	+	0.0244694i	0.00615850	+	0.00122500i
$400$	−0.00623044	−	0.198422i	−0.000311522	−	0.00992111i
$401$	−36.5269	+	7.26566i	−1.82407	+	0.362830i	−0.983790	−	0.179325i	$-0.942609\pi$
$401$	−36.5269	+	7.26566i	−1.82407	+	0.362830i	−0.840279	+	0.542155i	$0.817609\pi$
$402$	−0.519458	−	3.95588i	−0.0259082	−	0.197301i
$403$	−24.5266	+	11.6002i	−1.22176	+	0.577848i
$404$	9.69916	+	22.4142i	0.482551	+	1.11515i
$405$	−14.4813	−	10.7401i	−0.719582	−	0.533678i
$406$	−0.0104414	−	0.00723176i	−0.000518199	−	0.000358906i
$407$	−10.4102	+	12.6848i	−0.516012	+	0.628763i
$408$	0.222847	+	0.372643i	0.0110326	+	0.0184486i
$409$	0.978117	−	9.93099i	0.0483648	−	0.491056i	−0.940239	−	0.340515i	$-0.889399\pi$
$409$	0.978117	−	9.93099i	0.0483648	−	0.491056i	0.988604	−	0.150541i	$-0.0481014\pi$
$410$	−7.85566	−	2.52696i	−0.387963	−	0.124798i
$411$	0.878067	+	0.415295i	0.0433118	+	0.0204850i
$412$	−2.32578	+	2.17542i	−0.114583	+	0.107175i
$413$	0.0807494	+	0.322370i	0.00397342	+	0.0158628i
$414$	−0.0902379	−	0.387594i	−0.00443495	−	0.0190492i
$415$	11.4892	−	27.7373i	0.563981	−	1.36157i
$416$	13.9412	+	20.2151i	0.683523	+	0.991124i
$417$	−1.09476	−	2.64299i	−0.0536107	−	0.129428i
$418$	23.6820	−	16.9583i	1.15832	−	0.829457i
$419$	13.1358	−	21.9157i	0.641724	−	1.07065i	−0.349305	−	0.937009i	$-0.613582\pi$
$419$	13.1358	−	21.9157i	0.641724	−	1.07065i	0.991029	−	0.133643i	$-0.0426677\pi$
$420$	−0.0673397	+	0.0110716i	−0.00328584	+	0.000540241i
$421$	38.3970	−	13.7387i	1.87136	−	0.669582i	0.898134	−	0.439722i	$-0.144923\pi$
$421$	38.3970	−	13.7387i	1.87136	−	0.669582i	0.973224	−	0.229860i	$-0.0738269\pi$
$422$	6.08207	+	5.16375i	0.296071	+	0.251367i
$423$	8.66315	−	7.10967i	0.421217	−	0.345684i
$424$	6.12297	+	24.5485i	0.297358	+	1.19218i
$425$	−0.00235253	−	0.0238856i	−0.000114114	−	0.00115862i
$426$	2.52161	+	0.545496i	0.122172	+	0.0264294i
$427$	0.100205	+	0.675524i	0.00484924	+	0.0326909i
$428$	−4.31446	−	20.0411i	−0.208547	−	0.968723i
$429$	1.16907	−	3.26733i	0.0564432	−	0.157748i
$430$	19.2888	+	5.17532i	0.930189	+	0.249576i
$431$	29.8724	+	19.9601i	1.43890	+	0.961445i	0.997956	+	0.0639120i	$0.0203577\pi$
$431$	29.8724	+	19.9601i	1.43890	+	0.961445i	0.440948	+	0.897533i	$0.354642\pi$
$432$	−7.12828	−	2.30086i	−0.342960	−	0.110700i
$433$	−23.4779	+	15.6874i	−1.12828	+	0.753890i	−0.972269	−	0.233866i	$-0.924862\pi$
$433$	−23.4779	+	15.6874i	−1.12828	+	0.753890i	−0.156007	+	0.987756i	$0.549862\pi$
$434$	0.137132	+	0.404422i	0.00658256	+	0.0194129i
$435$	0.00644216	+	0.131133i	0.000308878	+	0.00628736i
$436$	0.301004	+	0.0861736i	0.0144155	+	0.00412697i
$437$	−0.192879	+	0.770016i	−0.00922666	+	0.0368349i
$438$	−0.0394992	+	2.36553i	−0.00188735	+	0.113029i
$439$	−9.79756	+	5.23691i	−0.467612	+	0.249944i	−0.688335	−	0.725393i	$-0.741658\pi$
$439$	−9.79756	+	5.23691i	−0.467612	+	0.249944i	0.220723	+	0.975336i	$0.429158\pi$
$440$	−8.81799	+	13.1685i	−0.420381	+	0.627783i
$441$	−5.88926	−	19.4143i	−0.280441	−	0.924491i
$442$	1.84484	+	2.32608i	0.0877502	+	0.110640i
$443$	−18.8455	+	17.0806i	−0.895378	+	0.811524i	−0.982805	−	0.184647i	$-0.940886\pi$
$443$	−18.8455	+	17.0806i	−0.895378	+	0.811524i	0.0874264	+	0.996171i	$0.472136\pi$
$444$	−3.58117	−	2.07078i	−0.169955	−	0.0982749i
$445$	11.3683	−	8.43133i	0.538911	−	0.399683i
$446$	5.69606	−	0.184566i	0.269716	−	0.00873945i
$447$	0.981558	−	0.981558i	0.0464261	−	0.0464261i
$448$	0.341230	−	0.181514i	0.0161216	−	0.00857571i
$449$	14.5039	+	14.5039i	0.684481	+	0.684481i	0.961007	−	0.276525i	$-0.0891830\pi$
$449$	14.5039	+	14.5039i	0.684481	+	0.684481i	−0.276525	+	0.961007i	$0.589183\pi$
$450$	0.148474	+	0.139154i	0.00699911	+	0.00655977i
$451$	−3.93435	−	5.30486i	−0.185262	−	0.249796i
$452$	22.6065	+	29.5022i	1.06332	+	1.38767i
$453$	−1.93632	−	2.13640i	−0.0909762	−	0.100377i
$454$	9.62489	+	1.11051i	0.451718	+	0.0521188i
$455$	−0.446533	+	0.135454i	−0.0209338	+	0.00635019i
$456$	5.18703	+	5.19743i	0.242905	+	0.243392i
$457$	−10.4153	−	19.4856i	−0.487206	−	0.911497i	−0.998638	−	0.0521739i	$-0.983385\pi$
$457$	−10.4153	−	19.4856i	−0.487206	−	0.911497i	0.511433	−	0.859323i	$-0.329115\pi$
$458$	−10.4990	+	10.1541i	−0.490585	+	0.474471i
$459$	−0.878456	−	0.220042i	−0.0410028	−	0.0102707i
$460$	−0.0490748	−	0.429109i	−0.00228812	−	0.0200073i
$461$	−1.03436	+	0.0508147i	−0.0481748	+	0.00236668i	−0.0731408	−	0.997322i	$-0.523302\pi$
$461$	−1.03436	+	0.0508147i	−0.0481748	+	0.00236668i	0.0249660	+	0.999688i	$0.492052\pi$
$462$	−0.0489784	−	0.0241738i	−0.00227868	−	0.00112467i
$463$	14.1153	+	21.1251i	0.655995	+	0.981766i	0.999098	+	0.0424680i	$0.0135221\pi$
$463$	14.1153	+	21.1251i	0.655995	+	0.981766i	−0.343103	+	0.939298i	$0.611478\pi$
$464$	−0.272353	−	0.691906i	−0.0126437	−	0.0321209i
$465$	2.45243	−	3.67032i	0.113729	−	0.170207i
$466$	−13.9549	−	24.1892i	−0.646448	−	1.12054i
$467$	21.2575	+	7.60607i	0.983682	+	0.351967i	0.779112	−	0.626885i	$-0.215670\pi$
$467$	21.2575	+	7.60607i	0.983682	+	0.351967i	0.204570	+	0.978852i	$0.434420\pi$
$468$	−24.7613	−	4.52255i	−1.14459	−	0.209055i
$469$	−0.424744	+	0.0630049i	−0.0196129	+	0.00290929i
$470$	10.2246	−	6.58762i	0.471625	−	0.303864i
$471$	7.00021	−	0.689460i	0.322553	−	0.0317687i
$472$	−6.57281	+	18.3119i	−0.302538	+	0.842875i
$473$	10.1401	+	12.3557i	0.466242	+	0.568117i
$474$	−0.257146	−	3.14901i	−0.0118111	−	0.144639i
$475$	−0.136743	−	0.382172i	−0.00627421	−	0.0175352i
$476$	0.0396984	−	0.0246493i	0.00181957	−	0.00112980i
$477$	−22.2444	−	13.3328i	−1.01850	−	0.610465i
$478$	−1.49388	+	9.02953i	−0.0683284	+	0.413001i
$479$	2.93654	−	1.21636i	0.134174	−	0.0555767i	−0.314586	−	0.949229i	$-0.601866\pi$
$479$	2.93654	−	1.21636i	0.134174	−	0.0555767i	0.448760	+	0.893652i	$0.351866\pi$
$480$	−3.63637	−	1.65494i	−0.165977	−	0.0755373i
$481$	−26.1326	−	10.8245i	−1.19155	−	0.493554i
$482$	−5.90575	+	9.49016i	−0.269000	+	0.432265i
$483$	0.00144391		0.000361681i	6.57002e−5		1.64571e-5i
$484$	8.72091	−	3.27567i	0.396405	−	0.148894i
$485$	−8.84490	+	18.7010i	−0.401626	+	0.849167i
$486$	10.3046	−	5.28864i	0.467425	−	0.239898i
$487$	32.6202	+	3.21281i	1.47816	+	0.145586i	0.804721	−	0.593653i	$-0.202315\pi$
$487$	32.6202	+	3.21281i	1.47816	+	0.145586i	0.673443	+	0.739239i	$0.264815\pi$
$488$	−17.1301	+	36.1248i	−0.775441	+	1.63529i
$489$	1.00243	+	0.822669i	0.0453313	+	0.0372024i
$490$	−3.93444	−	21.6641i	−0.177740	−	0.978684i
$491$	15.6256	−	21.0686i	0.705172	−	0.950814i	−0.294817	−	0.955554i	$-0.595259\pi$
$491$	15.6256	−	21.0686i	0.705172	−	0.950814i	0.999989	+	0.00473934i	$0.00150859\pi$
$492$	1.15870	−	1.19565i	0.0522382	−	0.0539042i
$493$	−0.0384368	−	0.0812678i	−0.00173111	−	0.00366012i
$494$	39.8226	+	30.5781i	1.79170	+	1.37577i
$495$	−3.16924	−	15.9328i	−0.142447	−	0.716128i
$496$	−6.50285	+	24.1400i	−0.291987	+	1.08392i
$497$	0.0541681	−	0.272321i	0.00242977	−	0.0122153i
$498$	3.99248	+	4.55562i	0.178907	+	0.204142i
$499$	24.5835	−	27.1237i	1.10051	−	1.21422i	0.125489	−	0.992095i	$-0.459950\pi$
$499$	24.5835	−	27.1237i	1.10051	−	1.21422i	0.975018	−	0.222127i	$-0.0713000\pi$
$500$	14.5258	+	17.1439i	0.649615	+	0.766698i
$501$	−2.81438	−	4.69551i	−0.125737	−	0.209780i
$502$	21.1942	+	9.19642i	0.945943	+	0.410456i
$503$	−21.6727	−	6.57435i	−0.966339	−	0.293136i	−0.232604	−	0.972572i	$-0.574725\pi$
$503$	−21.6727	−	6.57435i	−0.966339	−	0.293136i	−0.733735	+	0.679436i	$0.762225\pi$
$504$	−0.115385	+	0.379005i	−0.00513964	+	0.0168822i
$505$	−23.9615	−	12.8077i	−1.06627	−	0.569934i
$506$	0.168019	−	0.302098i	0.00746934	−	0.0134299i
$507$	1.85281	+	0.0910226i	0.0822861	+	0.00404246i
$508$	6.40597	−	7.29477i	0.284219	−	0.323653i
$509$	5.16684	−	34.8320i	0.229016	−	1.54390i	−0.504008	−	0.863699i	$-0.668142\pi$
$509$	5.16684	−	34.8320i	0.229016	−	1.54390i	0.733024	−	0.680202i	$-0.238108\pi$
$510$	−0.452012	−	0.170297i	−0.0200154	−	0.00754090i
$511$	0.254617			0.0112636
$512$	22.5117	+	2.28552i	0.994886	+	0.101007i
$513$	−15.3151			−0.676178
$514$	−11.1147	−	4.18752i	−0.490249	−	0.184703i
$515$	0.519834	−	3.50444i	0.0229066	−	0.154424i
$516$	−2.65883	+	3.02773i	−0.117048	+	0.133289i
$517$	9.72299	+	0.477660i	0.427617	+	0.0210075i
$518$	−0.216395	+	0.389078i	−0.00950784	+	0.0170951i
$519$	−0.663248	−	0.354513i	−0.0291133	−	0.0155614i
$520$	−26.1338	−	7.95618i	−1.14604	−	0.348902i
$521$	21.4863	+	6.51779i	0.941330	+	0.285549i	0.723411	−	0.690417i	$-0.242573\pi$
$521$	21.4863	+	6.51779i	0.941330	+	0.285549i	0.217919	+	0.975967i	$0.430073\pi$
$522$	0.699208	+	0.303395i	0.0306035	+	0.0132792i
$523$	1.82865	+	3.05091i	0.0799611	+	0.133407i	0.895112	−	0.445842i	$-0.147096\pi$
$523$	1.82865	+	3.05091i	0.0799611	+	0.133407i	−0.815150	+	0.579249i	$0.803346\pi$
$524$	25.9357	+	30.6102i	1.13301	+	1.33721i
$525$	−0.000511143	0	0.000563960i	−2.23081e−5	0	2.46132e-5i
$526$	−7.79502	−	8.89451i	−0.339879	−	0.387819i
$527$	−0.589675	+	2.96450i	−0.0256866	+	0.129135i
$528$	−1.59511	−	2.77135i	−0.0694183	−	0.120608i
$529$	−4.48524	−	22.5488i	−0.195010	−	0.980384i
$530$	−22.3242	−	17.1418i	−0.969701	−	0.744592i
$531$	−8.52669	−	18.0282i	−0.370027	−	0.782356i
$532$	0.549956	−	0.567496i	0.0238436	−	0.0246041i
$533$	6.78176	−	9.14415i	0.293751	−	0.396077i
$534$	0.510284	+	2.80976i	0.0220821	+	0.121590i
$535$	17.6292	+	14.4679i	0.762178	+	0.625504i
$536$	−22.7139	−	10.7707i	−0.981092	−	0.465225i
$537$	3.11583	+	0.306883i	0.134458	+	0.0132430i
$538$	−12.7816	+	6.55992i	−0.551053	+	0.282818i
$539$	7.53463	−	15.9306i	0.324539	−	0.686181i
$540$	7.80075	−	2.93005i	0.335691	−	0.126089i
$541$	−0.0261298	+	0.00654518i	−0.00112341	+	0.000281399i	−0.243542	−	0.969890i	$-0.578309\pi$
$541$	−0.0261298	+	0.00654518i	−0.00112341	+	0.000281399i	0.242418	+	0.970172i	$0.422059\pi$
$542$	19.1637	−	30.7948i	0.823150	−	1.32275i
$543$	−6.74304	−	2.79306i	−0.289371	−	0.119862i
$544$	2.73405	+	0.0940722i	0.117221	+	0.00403331i
$545$	−0.321797	+	0.133293i	−0.0137843	+	0.00570963i
$546$	0.0153674	−	0.0928861i	0.000657665	−	0.00397516i
$547$	−8.04309	−	4.82084i	−0.343898	−	0.206124i	0.331717	−	0.943379i	$-0.392372\pi$
$547$	−8.04309	−	4.82084i	−0.343898	−	0.206124i	−0.675615	+	0.737254i	$0.736122\pi$
$548$	5.19918	−	3.22825i	0.222098	−	0.137904i
$549$	−13.8062	−	38.5858i	−0.589235	−	1.64680i
$550$	0.0143859	+	0.176170i	0.000613418	+	0.00751192i
$551$	−0.964494	−	1.17524i	−0.0410888	−	0.0500669i
$552$	0.0820202	+	0.0294400i	0.00349101	+	0.00125305i
$553$	−0.338392	+	0.0333287i	−0.0143899	+	0.00141728i
$554$	−21.1346	+	13.6169i	−0.897925	+	0.578526i
$555$	4.55224	−	0.675261i	0.193232	−	0.0286632i
$556$	−17.7310	−	3.23850i	−0.751963	−	0.137343i
$557$	−28.1309	−	10.0654i	−1.19195	−	0.426485i	−0.335162	−	0.942160i	$-0.608791\pi$
$557$	−28.1309	−	10.0654i	−1.19195	−	0.426485i	−0.856784	+	0.515675i	$0.827541\pi$
$558$	−12.8058	−	22.1974i	−0.542112	−	0.939690i
$559$	−15.3070	+	22.9086i	−0.647419	+	0.968931i
$560$	−0.171548	+	0.394271i	−0.00724924	+	0.0166610i
$561$	−0.214780	−	0.321441i	−0.00906801	−	0.0135712i
$562$	23.0806	+	11.3917i	0.973598	+	0.480530i
$563$	−26.9115	+	1.32208i	−1.13418	+	0.0557188i	−0.607483	−	0.794333i	$-0.707821\pi$
$563$	−26.9115	+	1.32208i	−1.13418	+	0.0557188i	−0.526700	+	0.850051i	$0.676571\pi$
$564$	0.278841	+	2.43818i	0.0117413	+	0.102666i
$565$	−40.1088	−	10.0467i	−1.68739	−	0.422669i
$566$	−19.9961	+	19.3393i	−0.840498	+	0.812890i
$567$	−0.184549	−	0.345267i	−0.00775033	−	0.0144999i
$568$	11.5056	−	11.4826i	0.482763	−	0.481797i
$569$	−9.45714	+	2.86879i	−0.396464	+	0.120266i	−0.482220	−	0.876050i	$-0.660169\pi$
$569$	−9.45714	+	2.86879i	−0.396464	+	0.120266i	0.0857560	+	0.996316i	$0.472669\pi$
$570$	−8.11495	−	0.936295i	−0.339898	−	0.0392171i
$571$	−9.62344	−	10.6178i	−0.402729	−	0.444342i	0.505494	−	0.862830i	$-0.331310\pi$
$571$	−9.62344	−	10.6178i	−0.402729	−	0.444342i	−0.908222	+	0.418488i	$0.862560\pi$
$572$	−13.2984	−	17.3549i	−0.556036	−	0.725643i
$573$	4.56078	+	6.14950i	0.190529	+	0.256899i
$574$	−0.130742	−	0.122535i	−0.00545706	−	0.00511452i
$575$	−0.00340620	−	0.00340620i	−0.000142048	−	0.000142048i
$576$	−17.9586	+	14.6781i	−0.748273	+	0.611588i
$577$	−10.6482	+	10.6482i	−0.443290	+	0.443290i	−0.893116	−	0.449826i	$-0.851486\pi$
$577$	−10.6482	+	10.6482i	−0.443290	+	0.443290i	0.449826	+	0.893116i	$0.351486\pi$
$578$	−23.6984	+	0.767887i	−0.985726	+	0.0319399i
$579$	−2.68985	+	1.99493i	−0.111786	+	0.0829065i
$580$	0.716109	+	0.414083i	0.0297348	+	0.0171939i
$581$	0.483041	−	0.437802i	0.0200399	−	0.0181631i
$582$	−2.59369	−	3.27027i	−0.107512	−	0.135557i
$583$	−6.53924	−	21.5570i	−0.270827	−	0.892798i
$584$	12.3858	+	8.29388i	0.512528	+	0.343203i
$585$	24.6955	−	13.2000i	1.02103	−	0.545754i
$586$	0.411703	−	24.6561i	0.0170073	−	1.01853i
$587$	−0.726520	+	2.90043i	−0.0299867	+	0.119713i	−0.983176	−	0.182660i	$-0.941529\pi$
$587$	−0.726520	+	2.90043i	−0.0299867	+	0.119713i	0.953189	+	0.302374i	$0.0977791\pi$
$588$	4.27098	+	1.22273i	0.176132	+	0.0504245i
$589$	2.50818	+	51.0551i	0.103348	+	2.10369i
$590$	−6.95041	−	20.4977i	−0.286144	−	0.843878i
$591$	−0.981547	+	0.655849i	−0.0403755	+	0.0269780i
$592$	−23.2003	+	11.8778i	−0.953526	+	0.488175i
$593$	9.75801	+	6.52010i	0.400714	+	0.267748i	0.739556	−	0.673095i	$-0.235035\pi$
$593$	9.75801	+	6.52010i	0.400714	+	0.267748i	−0.338843	+	0.940843i	$0.610035\pi$
$594$	6.44143	+	1.72828i	0.264295	+	0.0709122i
$595$	−0.0175129	+	0.0489454i	−0.000717960	+	0.00200656i
$596$	−1.84068	−	8.55014i	−0.0753971	−	0.350227i
$597$	0.662256	+	4.46457i	0.0271043	+	0.182723i
$598$	0.582384	+	0.125986i	0.0238155	+	0.00515197i
$599$	−2.98241	−	30.2810i	−0.121858	−	1.23725i	−0.840479	−	0.541844i	$-0.817726\pi$
$599$	−2.98241	−	30.2810i	−0.121858	−	1.23725i	0.718621	−	0.695402i	$-0.244774\pi$
$600$	−0.0432348	+	0.0107838i	−0.00176506	+	0.000440245i
$601$	1.44344	−	1.18460i	0.0588790	−	0.0483207i	−0.604494	−	0.796610i	$-0.706624\pi$
$601$	1.44344	−	1.18460i	0.0588790	−	0.0483207i	0.663373	+	0.748289i	$0.269124\pi$
$602$	0.330581	+	0.280667i	0.0134735	+	0.0114391i
$603$	24.2613	−	8.68083i	0.987997	−	0.353511i
$604$	−17.9259	+	2.94728i	−0.729393	+	0.119923i
$605$	−5.32794	+	8.88913i	−0.216611	+	0.361394i
$606$	4.45700	−	3.19159i	0.181053	−	0.129650i
$607$	6.24954	+	15.0877i	0.253661	+	0.612392i	0.998494	−	0.0548591i	$-0.0174710\pi$
$607$	6.24954	+	15.0877i	0.253661	+	0.612392i	−0.744833	+	0.667251i	$0.767471\pi$
$608$	45.2381	−	9.69149i	1.83465	−	0.393042i
$609$	−0.00109099	+	0.00263388i	−4.42092e−5	+	0.000106730i
$610$	−10.0852	−	43.3187i	−0.408340	−	1.75392i
$611$	4.07721	+	16.2771i	0.164946	+	0.658503i
$612$	−2.04793	+	1.91553i	−0.0827827	+	0.0774307i
$613$	31.4150	+	14.8582i	1.26884	+	0.600117i	0.938999	−	0.343919i	$-0.111755\pi$
$613$	31.4150	+	14.8582i	1.26884	+	0.600117i	0.329842	+	0.944036i	$0.393005\pi$
$614$	0.368454	+	0.118522i	0.0148696	+	0.00478317i
$615$	−0.181552	+	1.84333i	−0.00732088	+	0.0743302i
$616$	−0.295349	+	0.176624i	−0.0119000	+	0.00711637i
$617$	−12.9307	+	15.7561i	−0.520572	+	0.634318i	−0.965236	−	0.261379i	$-0.915823\pi$
$617$	−12.9307	+	15.7561i	−0.520572	+	0.634318i	0.444665	+	0.895697i	$0.353323\pi$
$618$	0.587630	+	0.406995i	0.0236379	+	0.0163717i
$619$	28.9459	+	21.4678i	1.16343	+	0.862862i	0.992479	−	0.122417i	$-0.0390644\pi$
$619$	28.9459	+	21.4678i	1.16343	+	0.862862i	0.170956	+	0.985279i	$0.445314\pi$
$620$	−11.0453	−	25.5251i	−0.443589	−	1.02511i
$621$	−0.164305	+	0.0777103i	−0.00659332	+	0.00311841i
$622$	0.701304	+	5.34071i	0.0281197	+	0.214143i
$623$	0.301431	−	0.0599584i	0.0120766	−	0.00240218i
$624$	3.77321	−	4.01785i	0.151049	−	0.160843i
$625$	−24.2738	−	4.82837i	−0.970953	−	0.193135i
$626$	23.6915	+	1.56077i	0.946904	+	0.0623809i
$627$	−4.84429	−	4.39061i	−0.193462	−	0.175344i
$628$	20.2757	−	39.4087i	0.809089	−	1.57258i
$629$	−2.70284	+	1.62002i	−0.107769	+	0.0645944i
$630$	−0.161842	−	0.409949i	−0.00644793	−	0.0163328i
$631$	−6.83508	+	22.5322i	−0.272100	+	0.896994i	0.709282	+	0.704925i	$0.249020\pi$
$631$	−6.83508	+	22.5322i	−0.272100	+	0.896994i	−0.981382	+	0.192068i	$0.938480\pi$
$632$	−17.5466	−	9.40148i	−0.697968	−	0.373971i
$633$	0.844192	−	1.57937i	0.0335536	−	0.0627744i
$634$	3.63822	+	12.7565i	0.144492	+	0.506627i
$635$	−0.529938	+	10.7871i	−0.0210300	+	0.428075i
$636$	5.09495	−	2.50833i	0.202028	−	0.0994616i
$637$	30.0478	+	4.45717i	1.19054	+	0.176599i
$638$	0.273036	+	0.603140i	0.0108096	+	0.0238785i
$639$			16.6620i			0.659139i
$640$	−21.1879	+	13.5912i	−0.837525	+	0.537240i
$641$		−	1.87201i		−	0.0739401i	−0.999316	−	0.0369700i	$-0.988229\pi$
$641$		−	1.87201i		−	0.0739401i	0.999316	−	0.0369700i	$-0.0117706\pi$
$642$	−4.19193	+	1.89765i	−0.165442	+	0.0748943i
$643$	15.6597	+	2.32290i	0.617559	+	0.0916062i	0.448178	−	0.893944i	$-0.352073\pi$
$643$	15.6597	+	2.32290i	0.617559	+	0.0916062i	0.169381	+	0.985551i	$0.445823\pi$
$644$	0.00302056	−	0.00887879i	0.000119027	−	0.000349874i
$645$	0.219954	−	4.47726i	0.00866067	−	0.176292i
$646$	5.37892	−	1.53409i	0.211631	−	0.0603580i
$647$	18.1582	−	33.9716i	0.713872	−	1.33556i	−0.219132	−	0.975695i	$-0.570322\pi$
$647$	18.1582	−	33.9716i	0.713872	−	1.33556i	0.933004	−	0.359866i	$-0.117178\pi$
$648$	2.26935	−	22.8069i	0.0891486	−	0.895941i
$649$	5.02858	−	16.5770i	0.197389	−	0.650704i
$650$	−0.283396	+	0.111880i	−0.0111157	+	0.00438831i
$651$	0.0822154	−	0.0492780i	0.00322227	−	0.00193136i
$652$	7.78046	−	2.49417i	0.304706	−	0.0976794i
$653$	22.0494	+	19.9844i	0.862860	+	0.782051i	0.977407	−	0.211367i	$-0.0677916\pi$
$653$	22.0494	+	19.9844i	0.862860	+	0.782051i	−0.114547	+	0.993418i	$0.536542\pi$
$654$	0.00461974	−	0.0701249i	0.000180646	−	0.00274210i
$655$	−43.7752	−	8.70742i	−1.71044	−	0.340227i
$656$	−2.36846	−	10.2195i	−0.0924730	−	0.399004i
$657$	−14.9858	+	2.98087i	−0.584654	+	0.116295i
$658$	0.261863	−	0.0343859i	0.0102085	−	0.00134050i
$659$	−29.2650	+	13.8413i	−1.14000	+	0.539181i	−0.901851	−	0.432047i	$-0.857791\pi$
$659$	−29.2650	+	13.8413i	−1.14000	+	0.539181i	−0.238151	+	0.971228i	$0.576541\pi$
$660$	3.30744	+	1.30956i	0.128742	+	0.0509745i
$661$	−14.7048	−	10.9058i	−0.571952	−	0.424188i	0.270687	−	0.962667i	$-0.412749\pi$
$661$	−14.7048	−	10.9058i	−0.571952	−	0.424188i	−0.842639	+	0.538479i	$0.818999\pi$
$662$	−21.9696	+	31.7203i	−0.853872	+	1.23284i
$663$	0.422749	−	0.515121i	0.0164182	−	0.0200056i
$664$	37.7584	−	5.56228i	1.46531	−	0.215858i
$665$	−0.0861705	+	0.874903i	−0.00334155	+	0.0339273i
$666$	8.18117	−	25.4331i	0.317014	−	0.985514i
$667$	−0.0163106	−	0.00771436i	−0.000631551	−	0.000298701i
$668$	−34.4723	−	1.15155i	−1.33377	−	0.0445548i
$669$	−0.310819	−	1.24086i	−0.0120170	−	0.0479744i
$670$	27.2371	−	6.34122i	1.05226	−	0.244983i
$671$	13.6226	−	32.8878i	0.525894	−	1.26962i
$672$	−0.0560155	−	0.0662458i	−0.00216084	−	0.00255549i
$673$	6.16399	+	14.8812i	0.237604	+	0.573628i	0.997034	−	0.0769616i	$-0.0245219\pi$
$673$	6.16399	+	14.8812i	0.237604	+	0.573628i	−0.759430	+	0.650589i	$0.774522\pi$
$674$	21.9732	+	30.6852i	0.846376	+	1.18195i
$675$	0.0477793	−	0.0797150i	0.00183903	−	0.00306823i
$676$	6.81424	−	9.49586i	0.262086	−	0.365225i
$677$	−27.9838	+	10.0128i	−1.07550	+	0.384821i	−0.814289	−	0.580459i	$-0.802873\pi$
$677$	−27.9838	+	10.0128i	−1.07550	+	0.384821i	−0.261215	+	0.965281i	$0.584123\pi$
$678$	5.39941	−	6.35964i	0.207363	−	0.244241i
$679$	−0.347241	+	0.284974i	−0.0133259	+	0.0109363i
$680$	−2.44626	+	1.81047i	−0.0938096	+	0.0694284i
$681$	−0.213159	−	2.16424i	−0.00816829	−	0.0829340i
$682$	4.70655	−	21.7565i	0.180223	−	0.833099i
$683$	6.88243	+	46.3975i	0.263349	+	1.77535i	0.568138	+	0.822933i	$0.307664\pi$
$683$	6.88243	+	46.3975i	0.263349	+	1.77535i	−0.304790	+	0.952420i	$0.598586\pi$
$684$	−25.7246	+	39.8393i	−0.983606	+	1.52329i
$685$	−2.29362	+	6.41023i	−0.0876346	+	0.244922i
$686$	0.247840	−	0.923718i	0.00946258	−	0.0352677i
$687$	2.72591	+	1.82140i	0.104000	+	0.0694907i
$688$	6.93862	+	24.4213i	0.264532	+	0.931054i
$689$	32.2863	−	21.5730i	1.23001	−	0.821867i
$690$	−0.0918104	+	0.0311312i	−0.00349516	+	0.00118515i
$691$	0.241058	+	4.90685i	0.00917027	+	0.186665i	0.999010	+	0.0444796i	$0.0141630\pi$
$691$	0.241058	+	4.90685i	0.00917027	+	0.186665i	−0.989840	+	0.142186i	$0.954587\pi$
$692$	−4.14327	+	2.29894i	−0.157503	+	0.0873927i
$693$	0.0857107	−	0.342176i	0.00325588	−	0.0129982i
$694$	−15.8066	−	0.263936i	−0.600009	−	0.0100189i
$695$	17.6839	−	9.45225i	0.670789	−	0.358544i
$696$	−0.138867	+	0.0925869i	−0.00526374	+	0.00350950i
$697$	−0.368165	−	1.21368i	−0.0139452	−	0.0459713i
$698$	13.3161	−	10.5612i	0.504022	−	0.399746i
$699$	−4.64443	+	4.20947i	−0.175669	+	0.159217i
$700$	0.00123809	+	0.00463297i	4.67953e−5	+	0.000175110i
$701$	1.15577	−	0.857180i	0.0436530	−	0.0323753i	−0.573653	−	0.819099i	$-0.694474\pi$
$701$	1.15577	−	0.857180i	0.0436530	−	0.0323753i	0.617306	+	0.786723i	$0.288224\pi$
$702$	0.372303	+	11.4900i	0.0140517	+	0.433661i
$703$	−37.6826	+	37.6826i	−1.42123	+	1.42123i
$704$	−20.1205	−	1.02886i	−0.758321	−	0.0387767i
$705$	−1.93046	−	1.93046i	−0.0727054	−	0.0727054i
$706$	−34.5447	+	36.8584i	−1.30011	+	1.38718i
$707$	−0.351444	−	0.473867i	−0.0132174	−	0.0178216i
$708$	4.32927	+	0.572901i	0.162704	+	0.0215309i
$709$	−22.7003	−	25.0459i	−0.852527	−	0.940619i	0.146290	−	0.989242i	$-0.453267\pi$
$709$	−22.7003	−	25.0459i	−0.852527	−	0.940619i	−0.998817	+	0.0486230i	$0.984517\pi$
$710$	−2.07268	+	17.9641i	−0.0777864	+	0.674181i
$711$	19.5263	−	5.92325i	0.732294	−	0.222139i
$712$	16.6161	+	6.90213i	0.622716	+	0.258668i
$713$	0.285967	+	0.535007i	0.0107096	+	0.0200362i
$714$	−0.00729170	−	0.00753934i	−0.000272885	−	0.000282153i
$715$	23.5943	+	5.91006i	0.882376	+	0.221024i
$716$	12.2735	−	15.4433i	0.458682	−	0.577144i
$717$	2.05183	−	0.100800i	0.0766268	−	0.00376444i
$718$	12.4685	−	25.2624i	0.465322	−	0.942786i
$719$	−17.8273	−	26.6804i	−0.664845	−	0.995011i	−0.998628	−	0.0523611i	$-0.983325\pi$
$719$	−17.8273	−	26.6804i	−0.664845	−	0.995011i	0.333783	−	0.942650i	$-0.391675\pi$
$720$	5.48089	−	25.2137i	0.204261	−	0.939660i
$721$	0.0427394	−	0.0639640i	0.00159170	−	0.00238215i
$722$	58.6617	−	33.8422i	2.18316	−	1.25948i
$723$	2.36226	+	0.845231i	0.0878535	+	0.0314345i
$724$	−37.8298	+	26.1450i	−1.40593	+	0.971673i
$725$	0.00912610	−	0.00135373i	0.000338935	−	5.02762e-5i
$726$	−1.13251	−	1.75776i	−0.0420315	−	0.0652367i
$727$	39.4588	−	3.88635i	1.46345	−	0.144137i	0.665289	−	0.746586i	$-0.268308\pi$
$727$	39.4588	−	3.88635i	1.46345	−	0.144137i	0.798157	+	0.602449i	$0.205808\pi$
$728$	−0.439126	−	0.398803i	−0.0162751	−	0.0147806i
$729$	13.7727	+	16.7821i	0.510101	+	0.621560i
$730$	−16.5278	+	1.34965i	−0.611720	+	0.0499526i
$731$	1.03405	+	2.88998i	0.0382458	+	0.106890i
$732$	8.73816	+	2.04360i	0.322972	+	0.0755338i
$733$	27.4684	+	16.4639i	1.01457	+	0.608109i	0.921835	−	0.387582i	$-0.126690\pi$
$733$	27.4684	+	16.4639i	1.01457	+	0.608109i	0.0927334	+	0.995691i	$0.470440\pi$
$734$	−36.1933	−	5.98794i	−1.33592	−	0.221019i
$735$	−4.56602	+	1.89131i	−0.168420	+	0.0697619i
$736$	0.436152	−	0.333516i	0.0160768	−	0.0122936i
$737$	20.6786	+	8.56537i	0.761707	+	0.315509i
$738$	9.12955	+	5.68135i	0.336064	+	0.209133i
$739$	−41.4462	+	10.3817i	−1.52462	+	0.381898i	−0.912570	−	0.408920i	$-0.865906\pi$
$739$	−41.4462	+	10.3817i	−1.52462	+	0.381898i	−0.612052	+	0.790818i	$0.709656\pi$
$740$	11.9843	−	26.4030i	0.440551	−	0.970593i
$741$	4.81838	−	10.1876i	0.177008	−	0.374251i
$742$	−0.279067	−	0.543743i	−0.0102449	−	0.0199614i
$743$	−27.1241	−	2.67149i	−0.995087	−	0.0980076i	−0.412656	−	0.910887i	$-0.635399\pi$
$743$	−27.1241	−	2.67149i	−0.995087	−	0.0980076i	−0.582432	+	0.812880i	$0.697899\pi$
$744$	5.60453	+	0.280960i	0.205472	+	0.0103005i
$745$	7.52116	+	6.17246i	0.275554	+	0.226141i
$746$	−28.7276	+	5.21726i	−1.05179	+	0.191018i
$747$	−23.3046	+	31.4226i	−0.852669	+	1.14969i
$748$	−2.43546	+	0.0382272i	−0.0890492	+	0.00139772i
$749$	0.211731	+	0.447668i	0.00773650	+	0.0163575i
$750$	3.07171	−	4.00036i	0.112163	−	0.146072i
$751$	9.65455	+	48.5367i	0.352300	+	1.77113i	0.597712	+	0.801711i	$0.296077\pi$
$751$	9.65455	+	48.5367i	0.352300	+	1.77113i	−0.245412	+	0.969419i	$0.578923\pi$
$752$	13.8583	+	6.85720i	0.505362	+	0.250056i
$753$	1.01169	−	5.08610i	0.0368680	−	0.185348i
$754$	−0.858263	+	0.752169i	−0.0312561	+	0.0273924i
$755$	13.5720	−	14.9744i	0.493937	−	0.544976i
$756$	0.180327	+	0.0149072i	0.00655844	+	0.000542170i
$757$	17.6496	+	29.4465i	0.641485	+	1.07025i	0.991069	+	0.133348i	$0.0425728\pi$
$757$	17.6496	+	29.4465i	0.641485	+	1.07025i	−0.349584	+	0.936905i	$0.613677\pi$
$758$	−14.9579	+	34.4721i	−0.543295	+	1.25208i
$759$	−0.0742493	−	0.0225233i	−0.00269508	−	0.000817543i
$760$	−32.6908	+	39.7526i	−1.18582	+	1.44198i
$761$	−14.2706	−	7.62781i	−0.517310	−	0.276508i	0.192012	−	0.981393i	$-0.438499\pi$
$761$	−14.2706	−	7.62781i	−0.517310	−	0.276508i	−0.709322	+	0.704885i	$0.750999\pi$
$762$	−1.90437	−	1.05916i	−0.0689881	−	0.0383693i
$763$	−0.00755419		0.000371114i	−0.000273480		1.34352e-5i
$764$	48.1371	−	3.12280i	1.74154	−	0.112979i
$765$	0.457732	−	3.08578i	0.0165493	−	0.111566i
$766$	9.72310	−	25.8075i	0.351310	−	0.932463i
$767$	29.8600			1.07818
$768$	−0.566975	−	5.04716i	−0.0204590	−	0.182124i
$769$	−51.6674			−1.86318			−0.931588	−	0.363516i	$-0.881576\pi$
$769$	−51.6674			−1.86318			−0.931588	+	0.363516i	$0.881576\pi$
$770$	0.134974	−	0.358255i	0.00486413	−	0.0129106i
$771$	−0.391180	+	2.63712i	−0.0140880	+	0.0949735i
$772$	1.36594	+	21.0556i	0.0491613	+	0.757809i
$773$	14.4780	+	0.711260i	0.520739	+	0.0255823i	0.307740	−	0.951470i	$-0.400427\pi$
$773$	14.4780	+	0.711260i	0.520739	+	0.0255823i	0.212998	+	0.977053i	$0.431677\pi$
$774$	−22.7427	−	12.6488i	−0.817468	−	0.454653i
$775$	−0.273566	−	0.146224i	−0.00982680	−	0.00525253i
$776$	−26.1742	+	2.55147i	−0.939599	+	0.0915924i
$777$	0.0956271	+	0.0290082i	0.00343060	+	0.00104066i
$778$	−0.756666	+	1.74382i	−0.0271278	+	0.0625190i
$779$	−11.0269	−	18.3973i	−0.395080	−	0.659151i
$780$	−0.505174	+	6.11091i	−0.0180881	+	0.218806i
$781$	−9.71951	+	10.7238i	−0.347791	+	0.383729i
$782$	0.0499225	−	0.0437514i	0.00178522	−	0.00156455i
$783$	0.0679124	−	0.341419i	0.00242699	−	0.0122013i
$784$	21.0691	−	18.4274i	0.752469	−	0.658122i
$785$	9.61860	+	48.3559i	0.343302	+	1.72590i
$786$	5.48449	−	7.14259i	0.195625	−	0.254768i
$787$	8.09397	+	17.1133i	0.288519	+	0.610022i	0.995238	−	0.0974722i	$-0.0310757\pi$
$787$	8.09397	+	17.1133i	0.288519	+	0.610022i	−0.706719	+	0.707494i	$0.749826\pi$
$788$	0.116730	+	7.43688i	0.00415833	+	0.264928i
$789$	−1.58136	+	2.13222i	−0.0562980	+	0.0759091i
$790$	21.7891	−	3.95715i	0.775221	−	0.140789i
$791$	−0.694040	−	0.569584i	−0.0246772	−	0.0202521i
$792$	15.3154	−	13.8532i	0.544209	−	0.492251i
$793$	61.0650	+	6.01438i	2.16848	+	0.213577i
$794$	1.45005	+	2.82533i	0.0514603	+	0.100267i
$795$	−2.70114	+	5.71109i	−0.0957997	+	0.202551i
$796$	25.8945	+	11.7535i	0.917806	+	0.416591i
$797$	−44.5042	+	11.1477i	−1.57642	+	0.394872i	−0.929837	−	0.367972i	$-0.880052\pi$
$797$	−44.5042	+	11.1477i	−1.57642	+	0.394872i	−0.646582	+	0.762845i	$0.723802\pi$
$798$	−0.150600	−	0.0937186i	−0.00533117	−	0.00331760i
$799$	1.72707	+	0.715376i	0.0610994	+	0.0253082i
$800$	−0.0906876	+	0.265699i	−0.00320629	+	0.00939389i
$801$	−17.0392	+	7.05787i	−0.602050	+	0.249377i
$802$	51.9626	+	8.59688i	1.83486	+	0.303566i
$803$	−11.3839	−	6.82323i	−0.401728	−	0.240787i
$804$	−1.28494	+	5.49422i	−0.0453164	+	0.193766i
$805$	0.00351489	+	0.00982345i	0.000123883	+	0.000346231i
$806$	38.2425	−	3.12285i	1.34703	−	0.109998i
$807$	2.04574	+	2.49274i	0.0720134	+	0.0877485i
$808$	−1.66020	−	34.4991i	−0.0584056	−	1.21367i
$809$	32.5003	−	3.20100i	1.14265	−	0.112541i	0.491070	−	0.871120i	$-0.336606\pi$
$809$	32.5003	−	3.20100i	1.14265	−	0.112541i	0.651581	+	0.758579i	$0.274106\pi$
$810$	13.8096	+	21.4338i	0.485221	+	0.753108i
$811$	45.0905	−	6.68855i	1.58334	−	0.234867i	0.703699	−	0.710499i	$-0.251531\pi$
$811$	45.0905	−	6.68855i	1.58334	−	0.234867i	0.879644	+	0.475632i	$0.157781\pi$
$812$	0.0102125	+	0.0147766i	0.000358387	+	0.000518558i
$813$	−7.66535	−	2.74270i	−0.268835	−	0.0961909i
$814$	20.1015	−	11.5966i	0.704556	−	0.406462i
$815$	−5.04980	+	7.55756i	−0.176887	+	0.264730i
$816$	−0.109117	−	0.604269i	−0.00381986	−	0.0211537i
$817$	28.8389	+	43.1605i	1.00895	+	1.51000i
$818$	−6.24602	+	12.6550i	−0.218387	+	0.442472i
$819$	0.607309	−	0.0298352i	0.0212211	−	0.00104253i
$820$	9.13628	+	7.26101i	0.319053	+	0.253566i
$821$	−24.6879	−	6.18400i	−0.861614	−	0.215823i	−0.213104	−	0.977030i	$-0.568357\pi$
$821$	−24.6879	−	6.18400i	−0.861614	−	0.215823i	−0.648509	+	0.761207i	$0.724607\pi$
$822$	−0.954972	−	0.987405i	−0.0333085	−	0.0344397i
$823$	9.73587	+	18.2145i	0.339371	+	0.634918i	0.992488	−	0.122338i	$-0.0390392\pi$
$823$	9.73587	+	18.2145i	0.339371	+	0.634918i	−0.653118	+	0.757257i	$0.726539\pi$
$824$	4.16261	−	1.71933i	0.145011	−	0.0598956i
$825$	0.0379661	−	0.0115169i	0.00132181	−	0.000400966i
$826$	0.0538690	−	0.466887i	0.00187434	−	0.0162451i
$827$	11.8805	+	13.1081i	0.413125	+	0.455813i	0.911592	−	0.411095i	$-0.134854\pi$
$827$	11.8805	+	13.1081i	0.413125	+	0.455813i	−0.498467	+	0.866908i	$0.666104\pi$
$828$	−0.0738327	+	0.557936i	−0.00256586	+	0.0193896i
$829$	10.0977	+	13.6152i	0.350709	+	0.472876i	0.942974	−	0.332867i	$-0.108016\pi$
$829$	10.0977	+	13.6152i	0.350709	+	0.472876i	−0.592265	+	0.805743i	$0.701766\pi$
$830$	−29.0346	+	30.9792i	−1.00781	+	1.07530i
$831$	3.99035	+	3.99035i	0.138424	+	0.138424i
$832$	−8.37064	−	33.7037i	−0.290200	−	1.16847i
$833$	2.39291	−	2.39291i	0.0829094	−	0.0829094i
$834$	0.131022	+	4.04359i	0.00453693	+	0.140018i
$835$	30.8198	−	22.8575i	1.06656	−	0.791017i
$836$	−39.7962	+	10.6349i	−1.37638	+	0.367815i
$837$	−8.67210	+	7.85994i	−0.299752	+	0.271679i
$838$	−28.3111	+	22.4539i	−0.977990	+	0.775656i
$839$	7.22631	+	23.8220i	0.249480	+	0.822425i	0.988823	+	0.149096i	$0.0476364\pi$
$839$	7.22631	+	23.8220i	0.249480	+	0.822425i	−0.739343	+	0.673329i	$0.764864\pi$
$840$	0.0946379	+	0.0189232i	0.00326532	+	0.000652913i
$841$	−25.5452	+	13.6542i	−0.880870	+	0.470835i
$842$	−57.6649	−	0.962880i	−1.98726	−	0.0331830i
$843$	1.40377	−	5.60415i	0.0483483	−	0.193017i
$844$	−5.47440	−	9.86624i	−0.188437	−	0.339610i
$845$	0.637996	+	12.9867i	0.0219477	+	0.446756i
$846$	−15.0097	+	5.08953i	−0.516045	+	0.174982i
$847$	−0.187112	+	0.125024i	−0.00642923	+	0.00429587i
$848$	4.13671	−	35.5406i	0.142055	−	1.22047i
$849$	5.19171	+	3.46899i	0.178179	+	0.119055i
$850$	−0.00879598	+	0.0327833i	−0.000301700	+	0.00112446i
$851$	−0.213064	+	0.595475i	−0.00730375	+	0.0204126i
$852$	−3.06512	−	1.97918i	−0.105009	−	0.0678057i
$853$	−3.93223	−	26.5090i	−0.134637	−	0.907650i	−0.946246	−	0.323448i	$-0.895158\pi$
$853$	−3.93223	−	26.5090i	−0.134637	−	0.907650i	0.811609	−	0.584201i	$-0.198592\pi$
$854$	0.204204	−	0.943954i	0.00698773	−	0.0323014i
$855$	−5.17104	−	52.5025i	−0.176846	−	1.79555i
$856$	−4.28269	+	28.6737i	−0.146379	+	0.980046i
$857$	−14.8226	+	12.1646i	−0.506330	+	0.415534i	−0.852571	−	0.522611i	$-0.824958\pi$
$857$	−14.8226	+	12.1646i	−0.506330	+	0.415534i	0.346241	+	0.938146i	$0.387458\pi$
$858$	−3.17624	+	3.74110i	−0.108435	+	0.127719i
$859$	−0.916638	+	0.327978i	−0.0312753	+	0.0111905i	−0.352481	−	0.935819i	$-0.614662\pi$
$859$	−0.916638	+	0.327978i	−0.0312753	+	0.0111905i	0.321206	+	0.947009i	$0.395912\pi$
$860$	−22.9465	−	16.4664i	−0.782469	−	0.561500i
$861$	−0.0206773	+	0.0344980i	−0.000704681	+	0.00117569i
$862$	−29.5812	−	41.3096i	−1.00754	−	1.40701i
$863$	−10.1862	−	24.5916i	−0.346741	−	0.837106i	−0.997001	−	0.0773944i	$-0.975340\pi$
$863$	−10.1862	−	24.5916i	−0.346741	−	0.837106i	0.650260	−	0.759712i	$-0.274660\pi$
$864$	8.28639	+	6.59912i	0.281909	+	0.224507i
$865$	2.01722	−	4.87001i	0.0685877	−	0.165585i
$866$	38.8925	−	9.05477i	1.32162	−	0.307693i
$867$	1.29316	+	5.16260i	0.0439182	+	0.175331i
$868$	0.0201629	−	0.603588i	0.000684372	−	0.0204871i
$869$	16.0226	+	7.57810i	0.543528	+	0.257070i
$870$	0.0568573	−	0.176754i	0.00192764	−	0.00599253i
$871$	−3.78162	+	38.3954i	−0.128135	+	1.30098i
$872$	−0.355384	−	0.264123i	−0.0120348	−	0.00894432i
$873$	17.1011	−	20.8378i	0.578785	−	0.705252i
$874$	0.639186	−	0.922874i	0.0216208	−	0.0312167i
$875$	−0.435984	−	0.323347i	−0.0147389	−	0.0109311i
$876$	1.23172	−	3.11086i	0.0416161	−	0.105106i
$877$	20.2209	−	9.56377i	0.682811	−	0.322945i	−0.0544859	−	0.998515i	$-0.517352\pi$
$877$	20.2209	−	9.56377i	0.682811	−	0.322945i	0.737297	+	0.675569i	$0.236102\pi$
$878$	15.5772	−	2.04549i	0.525707	−	0.0690321i
$879$	−5.42867	+	1.07983i	−0.183104	+	0.0364217i
$880$	18.2356	−	13.0306i	0.614720	−	0.439261i
$881$	−3.35785	−	0.667918i	−0.113129	−	0.0225027i	0.138201	−	0.990404i	$-0.455868\pi$
$881$	−3.35785	−	0.667918i	−0.113129	−	0.0225027i	−0.251330	+	0.967901i	$0.580868\pi$
$882$	−1.88607	+	28.6294i	−0.0635071	+	0.964001i
$883$	−39.1477	−	35.4814i	−1.31743	−	1.19405i	−0.966212	−	0.257750i	$-0.917019\pi$
$883$	−39.1477	−	35.4814i	−1.31743	−	1.19405i	−0.351214	−	0.936295i	$-0.614231\pi$
$884$	−1.28169	−	3.99818i	−0.0431080	−	0.134473i
$885$	−4.16700	+	2.49760i	−0.140072	+	0.0839560i
$886$	33.4566	−	13.2082i	1.12400	−	0.443738i
$887$	11.8302	−	38.9989i	0.397218	−	1.30945i	−0.499293	−	0.866433i	$-0.666407\pi$
$887$	11.8302	−	38.9989i	0.397218	−	1.30945i	0.896511	−	0.443020i	$-0.146093\pi$
$888$	3.70685	+	4.52605i	0.124394	+	0.151884i
$889$	−0.110551	+	0.206826i	−0.00370775	+	0.00693672i
$890$	−19.2487	+	5.48982i	−0.645219	+	0.184019i
$891$	−1.00132	+	20.3824i	−0.0335455	+	0.682834i
$892$	−7.63021	−	2.59579i	−0.255478	−	0.0869135i
$893$	31.2719	+	4.63875i	1.04647	+	0.155230i
$894$	−1.78840	+	0.809595i	−0.0598131	+	0.0270769i
$895$			21.9452i			0.733546i
$896$	−0.542088	+	0.0700789i	−0.0181099	+	0.00234117i
$897$		−	0.133745i		−	0.00446560i
$898$	−11.9629	−	26.4261i	−0.399207	−	0.881852i
$899$	−1.14929	−	0.170481i	−0.0383310	−	0.00568586i
$900$	−0.127109	−	0.258185i	−0.00423696	−	0.00860618i
$901$	0.212261	−	4.32067i	0.00707143	−	0.143942i
$902$	2.56174	+	8.98214i	0.0852968	+	0.299073i
$903$	0.0458847	−	0.0858441i	0.00152695	−	0.00285671i
$904$	−15.2078	−	50.3149i	−0.505806	−	1.67345i
$905$	14.8502	−	48.9546i	0.493638	−	1.62731i
$906$	1.49733	+	3.79276i	0.0497454	+	0.126006i
$907$	−6.49477	+	3.89281i	−0.215655	+	0.129259i	−0.617852	−	0.786295i	$-0.711997\pi$
$907$	−6.49477	+	3.89281i	−0.215655	+	0.129259i	0.402197	+	0.915553i	$0.368247\pi$
$908$	−12.1839	−	6.26861i	−0.404338	−	0.208031i
$909$	26.2324	+	23.7757i	0.870075	+	0.788590i
$910$	0.658481	+	0.0433799i	0.0218284	+	0.00143803i
$911$	−43.7402	−	8.70047i	−1.44918	−	0.288260i	−0.593110	−	0.805122i	$-0.702100\pi$
$911$	−43.7402	−	8.70047i	−1.44918	−	0.288260i	−0.856069	+	0.516862i	$0.827100\pi$
$912$	−4.27310	−	9.46454i	−0.141497	−	0.313402i
$913$	−33.3289	+	6.62952i	−1.10302	+	0.219405i
$914$	4.06812	+	30.9804i	0.134561	+	1.02474i
$915$	−9.02476	+	4.26839i	−0.298349	+	0.141109i
$916$	18.9572	−	8.20323i	0.626364	−	0.271042i
$917$	−0.778443	−	0.577333i	−0.0257064	−	0.0190652i
$918$	1.05284	+	0.729201i	0.0347489	+	0.0240672i
$919$	0.429229	−	0.523017i	0.0141590	−	0.0172528i	−0.765883	−	0.642980i	$-0.777698\pi$
$919$	0.429229	−	0.523017i	0.0141590	−	0.0172528i	0.780042	+	0.625727i	$0.215198\pi$
$920$	−0.149007	+	0.592354i	−0.00491263	+	0.0195293i
$921$	0.00851534	−	0.0864577i	0.000280590	−	0.00284888i
$922$	1.39421	+	0.448481i	0.0459158	+	0.0147699i
$923$	−22.5524	−	10.6665i	−0.742321	−	0.351092i
$924$	0.0527653	+	0.0564123i	0.00173585	+	0.00185583i
$925$	−0.0785773	−	0.313698i	−0.00258361	−	0.0103143i
$926$	−8.14735	−	34.9949i	−0.267739	−	1.15000i
$927$	−1.76664	+	4.26505i	−0.0580242	+	0.140083i
$928$	0.0154506	+	1.05147i	0.000507191	+	0.0345161i
$929$	−6.02119	−	14.5364i	−0.197549	−	0.476925i	0.793800	−	0.608179i	$-0.208100\pi$
$929$	−6.02119	−	14.5364i	−0.197549	−	0.476925i	−0.991349	+	0.131254i	$0.958100\pi$
$930$	−5.07558	+	3.63454i	−0.166435	+	0.119181i
$931$	29.4223	−	49.0882i	0.964277	−	1.60880i
$932$	6.40725	+	38.9700i	0.209877	+	1.27651i
$933$	1.13838	−	0.407319i	0.0372689	−	0.0133350i
$934$	−24.3400	−	20.6649i	−0.796428	−	0.676176i
$935$	2.09464	−	1.71902i	0.0685019	−	0.0562181i
$936$	30.5143	+	18.3311i	0.997391	+	0.599171i
$937$	1.00641	+	10.2182i	0.0328780	+	0.333816i	0.997527	+	0.0702790i	$0.0223890\pi$
$937$	1.00641	+	10.2182i	0.0328780	+	0.333816i	−0.964649	+	0.263537i	$0.915111\pi$
$938$	0.593523	+	0.128396i	0.0193792	+	0.00419228i
$939$	−0.781968	−	5.27160i	−0.0255186	−	0.172032i
$940$	−16.8158	+	3.62012i	−0.548472	+	0.118075i
$941$	9.28400	−	25.9470i	0.302650	−	0.845849i	−0.689889	−	0.723916i	$-0.742341\pi$
$941$	9.28400	−	25.9470i	0.302650	−	0.845849i	0.992538	−	0.121934i	$-0.0389095\pi$
$942$	−9.60787	−	2.57786i	−0.313041	−	0.0839912i
$943$	−0.211649	−	0.141420i	−0.00689225	−	0.00460525i
$944$	17.8288	−	20.9569i	0.580278	−	0.682089i
$945$	−0.167369	+	0.111832i	−0.00544452	+	0.00363791i
$946$	−7.25889	−	21.4075i	−0.236007	−	0.696017i
$947$	2.59035	+	52.7279i	0.0841752	+	1.71343i	0.555542	+	0.831488i	$0.312511\pi$
$947$	2.59035	+	52.7279i	0.0841752	+	1.71343i	−0.471367	+	0.881937i	$0.656239\pi$
$948$	−1.22978	+	4.29563i	−0.0399415	+	0.139515i
$949$	5.55879	−	22.1919i	0.180446	−	0.720380i
$950$	−0.00958369	+	0.573948i	−0.000310936	+	0.0186213i
$951$	2.62591	−	1.40358i	0.0851508	−	0.0455141i
$952$	−0.0648272	+	0.0128274i	−0.00210106	+	0.000415740i
$953$	−5.73346	−	18.9007i	−0.185725	−	0.612254i	−0.999516	−	0.0310963i	$-0.990100\pi$
$953$	−5.73346	−	18.9007i	−0.185725	−	0.612254i	0.813791	−	0.581157i	$-0.197400\pi$
$954$	22.7906	+	28.7356i	0.737873	+	0.930351i
$955$	−39.7622	+	36.0384i	−1.28667	+	1.16617i
$956$	6.47911	−	11.2049i	0.209550	−	0.362391i
$957$	0.119361	−	0.0885240i	0.00385839	−	0.00286157i
$958$	−4.49271	+	0.145575i	−0.145153	+	0.00470330i
$959$	−0.104535	+	0.104535i	−0.00337562	+	0.00337562i
$960$	3.98724	+	4.00325i	0.128688	+	0.129204i
$961$	5.70217	+	5.70217i	0.183941	+	0.183941i
$962$	29.1870	+	27.3549i	0.941025	+	0.881956i
$963$	−17.7027	−	23.8694i	−0.570462	−	0.769179i
$964$	12.5475	−	9.61471i	0.404127	−	0.309669i
$965$	−15.7635	−	17.3924i	−0.507446	−	0.559880i
$966$	−0.00209121		0.000241282i	−6.72837e−5		7.76312e-6i
$967$	−45.5360	+	13.8132i	−1.46434	+	0.444203i	−0.919082	−	0.394066i	$-0.871068\pi$
$967$	−45.5360	+	13.8132i	−1.46434	+	0.444203i	−0.545258	+	0.838269i	$0.683568\pi$
$968$	−13.1745	−	0.0131944i	−0.423445	−	0.000424083i
$969$	−0.591832	−	1.10724i	−0.0190124	−	0.0355697i
$970$	21.0297	−	20.3389i	0.675222	−	0.653043i
$971$	−46.7418	−	11.7082i	−1.50001	−	0.375734i	−0.595912	−	0.803050i	$-0.703209\pi$
$971$	−46.7418	−	11.7082i	−1.50001	−	0.375734i	−0.904103	+	0.427316i	$0.859459\pi$
$972$	−16.2740	+	1.86117i	−0.521990	+	0.0596970i
$973$	0.434881	−	0.0213643i	0.0139416	−	0.000684909i
$974$	−41.5679	−	20.5163i	−1.33192	−	0.657383i
$975$	0.0379943	+	0.0568626i	0.00121679	+	0.00182106i
$976$	40.6818	−	39.2667i	1.30219	−	1.25690i
$977$	30.2429	−	45.2618i	0.967558	−	1.44805i	0.0749661	−	0.997186i	$-0.476115\pi$
$977$	30.2429	−	45.2618i	0.967558	−	1.44805i	0.892592	−	0.450866i	$-0.148885\pi$
$978$	−0.916433	−	1.58853i	−0.0293043	−	0.0507957i
$979$	−15.0837	−	5.39703i	−0.482076	−	0.172490i
$980$	−5.59483	+	30.6321i	−0.178720	+	0.978505i
$981$	0.448957	−	0.0665965i	0.0143341	−	0.00212626i
$982$	−31.1837	+	20.0914i	−0.995113	+	0.641144i
$983$	−0.177857	+	0.0175173i	−0.00567274	+	0.000558716i	−0.100853	−	0.994901i	$-0.532157\pi$
$983$	−0.177857	+	0.0175173i	−0.00567274	+	0.000558716i	0.0951804	+	0.995460i	$0.469657\pi$
$984$	−2.12958	+	1.00461i	−0.0678885	+	0.0320257i
$985$	−5.24919	−	6.39615i	−0.167253	−	0.203798i
$986$	0.0103474	+	0.126715i	0.000329529	+	0.00403542i
$987$	−0.0199714	−	0.0558164i	−0.000635698	−	0.00177666i
$988$	−37.4552	−	60.3227i	−1.19161	−	1.91912i
$989$	0.528393	+	0.316707i	0.0168019	+	0.0100707i
$990$	−3.74991	+	22.6658i	−0.119180	+	0.720365i
$991$	−29.9227	+	12.3944i	−0.950526	+	0.393721i	−0.803429	−	0.595401i	$-0.796993\pi$
$991$	−29.9227	+	12.3944i	−0.950526	+	0.393721i	−0.147098	+	0.989122i	$0.546993\pi$
$992$	20.6421	−	28.7046i	0.655386	−	0.911373i
$993$	8.00155	+	3.31435i	0.253922	+	0.105178i
$994$	−0.207465	+	0.333383i	−0.00658040	+	0.0105743i
$995$	−30.6874	+	7.68679i	−0.972856	+	0.243688i
$996$	−3.01224	−	8.01958i	−0.0954466	−	0.254110i
$997$	−7.47296	+	15.8002i	−0.236671	+	0.500399i	−0.987011	−	0.160653i	$-0.948640\pi$
$997$	−7.47296	+	15.8002i	−0.236671	+	0.500399i	0.750340	+	0.661052i	$0.229890\pi$
$998$	−46.0577	+	23.6383i	−1.45793	+	0.748257i
$999$	−12.1432	−	1.19600i	−0.384193	−	0.0378397i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.5	✓	992
256.205	even	64	inner	256.2.m.a.205.5	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.5	✓	992	1.1	even	1	trivial
256.2.m.a.205.5	yes	992	256.205	even	64	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 256 = 2^{8} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	256.m (of order \(64\), degree \(32\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.32340 - 0.498599i) q^{2} +(-0.0465769 + 0.313996i) q^{3} +(1.50280 + 1.31970i) q^{4} +(-2.22226 - 0.109173i) q^{5} +(0.218198 - 0.392320i) q^{6} +(-0.0426083 - 0.0227746i) q^{7} +(-1.33081 - 2.49578i) q^{8} +(2.77440 + 0.841604i) q^{9} +O(q^{10})\)	\(q+(-1.32340 - 0.498599i) q^{2} +(-0.0465769 + 0.313996i) q^{3} +(1.50280 + 1.31970i) q^{4} +(-2.22226 - 0.109173i) q^{5} +(0.218198 - 0.392320i) q^{6} +(-0.0426083 - 0.0227746i) q^{7} +(-1.33081 - 2.49578i) q^{8} +(2.77440 + 0.841604i) q^{9} +(2.88652 + 1.25250i) q^{10} +(1.29469 + 2.16006i) q^{11} +(-0.484375 + 0.410405i) q^{12} +(-2.91521 + 3.21644i) q^{13} +(0.0450326 + 0.0513844i) q^{14} +(0.137786 - 0.692696i) q^{15} +(0.516809 + 3.96647i) q^{16} +(0.0943461 + 0.474310i) q^{17} +(-3.25203 - 2.49709i) q^{18} +(3.49676 + 7.39328i) q^{19} +(-3.19554 - 3.09677i) q^{20} +(0.00913569 - 0.0123180i) q^{21} +(-0.636397 - 3.50417i) q^{22} +(0.0750285 + 0.0615743i) q^{23} +(0.845651 - 0.301624i) q^{24} +(-0.0493910 - 0.00486459i) q^{25} +(5.46171 - 2.80313i) q^{26} +(-0.800642 + 1.69281i) q^{27} +(-0.0339761 - 0.0904555i) q^{28} +(-0.180324 + 0.0451687i) q^{29} +(-0.527724 + 0.848018i) q^{30} +(5.77436 + 2.39182i) q^{31} +(1.29373 - 5.50693i) q^{32} +(-0.738554 + 0.305919i) q^{33} +(0.111632 - 0.674744i) q^{34} +(0.0922004 + 0.0552628i) q^{35} +(3.05870 + 4.92612i) q^{36} +(2.19518 + 6.13512i) q^{37} +(-0.941349 - 11.5278i) q^{38} +(-0.874167 - 1.06518i) q^{39} +(2.68494 + 5.69158i) q^{40} +(-2.60996 + 0.257058i) q^{41} +(-0.0182320 + 0.0117467i) q^{42} +(6.27828 - 0.931294i) q^{43} +(-0.904963 + 4.95474i) q^{44} +(-6.07356 - 2.17315i) q^{45} +(-0.0685922 - 0.118897i) q^{46} +(2.14756 - 3.21406i) q^{47} +(-1.26953 - 0.0224702i) q^{48} +(-3.88769 - 5.81835i) q^{49} +(0.0629388 + 0.0310641i) q^{50} +(-0.153326 + 0.00753241i) q^{51} +(-8.62569 + 0.986471i) q^{52} +(-8.67705 - 2.17349i) q^{53} +(1.90361 - 1.84108i) q^{54} +(-2.64133 - 4.94157i) q^{55} +(-0.000136855 + 0.136650i) q^{56} +(-2.48433 + 0.753612i) q^{57} +(0.261162 + 0.0301326i) q^{58} +(-4.61943 - 5.09676i) q^{59} +(1.12121 - 0.859148i) q^{60} +(-8.42035 - 11.3535i) q^{61} +(-6.44926 - 6.04444i) q^{62} +(-0.0990450 - 0.0990450i) q^{63} +(-4.45788 + 6.64284i) q^{64} +(6.82951 - 6.82951i) q^{65} +(1.12994 - 0.0366127i) q^{66} +(7.13867 - 5.29440i) q^{67} +(-0.484161 + 0.837300i) q^{68} +(-0.0228287 + 0.0206907i) q^{69} +(-0.0944644 - 0.119106i) q^{70} +(1.66828 + 5.49957i) q^{71} +(-1.59174 - 8.04431i) q^{72} +(-4.64786 + 2.48433i) q^{73} +(0.153850 - 9.21375i) q^{74} +(0.00382794 - 0.0152820i) q^{75} +(-4.50195 + 15.7253i) q^{76} +(-0.00597002 - 0.121523i) q^{77} +(0.625781 + 1.84552i) q^{78} +(5.85192 - 3.91013i) q^{79} +(-0.715454 - 8.87097i) q^{80} +(6.73764 + 4.50195i) q^{81} +(3.58220 + 0.961129i) q^{82} +(-4.54588 + 12.7049i) q^{83} +(0.0299852 - 0.00645523i) q^{84} +(-0.157880 - 1.06434i) q^{85} +(-8.77304 - 1.89786i) q^{86} +(-0.00578388 - 0.0587247i) q^{87} +(3.66806 - 6.10591i) q^{88} +(-4.91740 + 4.03560i) q^{89} +(6.95424 + 5.90423i) q^{90} +(0.197465 - 0.0706541i) q^{91} +(0.0314934 + 0.191548i) q^{92} +(-1.01997 + 1.70172i) q^{93} +(-4.44462 + 3.18272i) q^{94} +(-6.96357 - 16.8116i) q^{95} +(1.66890 + 0.662722i) q^{96} +(3.55813 - 8.59008i) q^{97} +(2.24397 + 9.63843i) q^{98} +(1.77407 + 7.08249i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9}+O(q^{10}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9	\( 992 q - 32 q^{2} - 32 q^{3} - 32 q^{4} - 32 q^{5} - 32 q^{6} - 32 q^{7} - 32 q^{8} - 32 q^{9} - 32 q^{10} - 32 q^{11} - 32 q^{12} - 32 q^{13} - 32 q^{14} - 32 q^{15} - 32 q^{16} - 32 q^{17} - 32 q^{18} - 32 q^{19} - 32 q^{20} - 32 q^{21} - 32 q^{22} - 32 q^{23} - 32 q^{24} - 32 q^{25} - 32 q^{26} - 32 q^{27} - 32 q^{28} - 32 q^{29} - 32 q^{30} - 32 q^{31} - 32 q^{32} - 32 q^{33} - 32 q^{34} - 32 q^{35} - 32 q^{36} - 32 q^{37} - 32 q^{38} - 32 q^{39} - 32 q^{40} - 32 q^{41} - 32 q^{42} - 32 q^{43} - 32 q^{44} - 32 q^{45} - 32 q^{46} - 32 q^{47} - 32 q^{48} - 32 q^{49} - 32 q^{50} - 32 q^{51} - 32 q^{52} - 32 q^{53} - 32 q^{54} - 32 q^{55} - 32 q^{56} - 32 q^{57} - 32 q^{58} - 32 q^{59} - 32 q^{60} - 32 q^{61} - 32 q^{62} - 32 q^{63} - 32 q^{64} - 32 q^{65} - 32 q^{66} - 32 q^{67} - 32 q^{68} - 32 q^{69} - 32 q^{70} - 32 q^{71} - 32 q^{72} - 32 q^{73} - 32 q^{74} - 32 q^{75} - 32 q^{76} - 32 q^{77} - 32 q^{78} - 32 q^{79} - 32 q^{80} - 32 q^{81} - 32 q^{82} - 32 q^{83} - 32 q^{84} - 32 q^{85} - 32 q^{86} - 32 q^{87} - 32 q^{88} - 32 q^{89} - 32 q^{90} - 32 q^{91} - 32 q^{92} - 32 q^{93} - 32 q^{94} - 32 q^{95} - 32 q^{96} - 32 q^{97} - 32 q^{98} - 32 q^{99}+O(q^{100}) \) 992 * q - 32 * q^2 - 32 * q^3 - 32 * q^4 - 32 * q^5 - 32 * q^6 - 32 * q^7 - 32 * q^8 - 32 * q^9 - 32 * q^10 - 32 * q^11 - 32 * q^12 - 32 * q^13 - 32 * q^14 - 32 * q^15 - 32 * q^16 - 32 * q^17 - 32 * q^18 - 32 * q^19 - 32 * q^20 - 32 * q^21 - 32 * q^22 - 32 * q^23 - 32 * q^24 - 32 * q^25 - 32 * q^26 - 32 * q^27 - 32 * q^28 - 32 * q^29 - 32 * q^30 - 32 * q^31 - 32 * q^32 - 32 * q^33 - 32 * q^34 - 32 * q^35 - 32 * q^36 - 32 * q^37 - 32 * q^38 - 32 * q^39 - 32 * q^40 - 32 * q^41 - 32 * q^42 - 32 * q^43 - 32 * q^44 - 32 * q^45 - 32 * q^46 - 32 * q^47 - 32 * q^48 - 32 * q^49 - 32 * q^50 - 32 * q^51 - 32 * q^52 - 32 * q^53 - 32 * q^54 - 32 * q^55 - 32 * q^56 - 32 * q^57 - 32 * q^58 - 32 * q^59 - 32 * q^60 - 32 * q^61 - 32 * q^62 - 32 * q^63 - 32 * q^64 - 32 * q^65 - 32 * q^66 - 32 * q^67 - 32 * q^68 - 32 * q^69 - 32 * q^70 - 32 * q^71 - 32 * q^72 - 32 * q^73 - 32 * q^74 - 32 * q^75 - 32 * q^76 - 32 * q^77 - 32 * q^78 - 32 * q^79 - 32 * q^80 - 32 * q^81 - 32 * q^82 - 32 * q^83 - 32 * q^84 - 32 * q^85 - 32 * q^86 - 32 * q^87 - 32 * q^88 - 32 * q^89 - 32 * q^90 - 32 * q^91 - 32 * q^92 - 32 * q^93 - 32 * q^94 - 32 * q^95 - 32 * q^96 - 32 * q^97 - 32 * q^98 - 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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