LMFDB - Embedded newform 256.2.m.a.5.11

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			5.11
Character	$\chi$	$=$	256.5
Dual form			256.2.m.a.205.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.731994 - 1.21004i) q^{2} +(0.434101 - 2.92647i) q^{3} +(-0.928370 + 1.77148i) q^{4} +(-4.11288 - 0.202053i) q^{5} +(-3.85889 + 1.61688i) q^{6} +(2.18104 + 1.16579i) q^{7} +(2.82311 - 0.173349i) q^{8} +(-5.50497 - 1.66991i) q^{9} +O(q^{10})$	\(q+(-0.731994 - 1.21004i) q^{2} +(0.434101 - 2.92647i) q^{3} +(-0.928370 + 1.77148i) q^{4} +(-4.11288 - 0.202053i) q^{5} +(-3.85889 + 1.61688i) q^{6} +(2.18104 + 1.16579i) q^{7} +(2.82311 - 0.173349i) q^{8} +(-5.50497 - 1.66991i) q^{9} +(2.76611 + 5.12463i) q^{10} +(-1.66629 - 2.78003i) q^{11} +(4.78117 + 3.48585i) q^{12} +(-3.02549 + 3.33812i) q^{13} +(-0.185861 - 3.49248i) q^{14} +(-2.37671 + 11.9485i) q^{15} +(-2.27626 - 3.28917i) q^{16} +(-0.411225 - 2.06737i) q^{17} +(2.00895 + 7.88357i) q^{18} +(-0.0395570 - 0.0836362i) q^{19} +(4.17621 - 7.09829i) q^{20} +(4.35844 - 5.87668i) q^{21} +(-2.14422 + 4.05123i) q^{22} +(0.455301 + 0.373656i) q^{23} +(0.718213 - 8.33700i) q^{24} +(11.8991 + 1.17195i) q^{25} +(6.25389 + 1.21747i) q^{26} +(-3.48191 + 7.36189i) q^{27} +(-4.08998 + 2.78137i) q^{28} +(4.31512 - 1.08088i) q^{29} +(16.1979 - 5.87034i) q^{30} +(-6.52371 - 2.70221i) q^{31} +(-2.31381 + 5.16201i) q^{32} +(-8.85902 + 3.66953i) q^{33} +(-2.20057 + 2.01090i) q^{34} +(-8.73480 - 5.23544i) q^{35} +(8.06886 - 8.20163i) q^{36} +(-3.38716 - 9.46647i) q^{37} +(-0.0722473 + 0.109087i) q^{38} +(8.45554 + 10.3031i) q^{39} +(-11.6461 + 0.142547i) q^{40} +(-5.96215 + 0.587220i) q^{41} +(-10.3013 - 0.972175i) q^{42} +(-4.68082 + 0.694334i) q^{43} +(6.47169 - 0.370890i) q^{44} +(22.3039 + 7.98046i) q^{45} +(0.118859 - 0.824444i) q^{46} +(0.250196 - 0.374445i) q^{47} +(-10.6138 + 5.23357i) q^{48} +(-0.491127 - 0.735023i) q^{49} +(-7.29193 - 15.2561i) q^{50} +(-6.22861 + 0.305992i) q^{51} +(-3.10462 - 8.45860i) q^{52} +(-9.04507 - 2.26567i) q^{53} +(11.4569 - 1.17562i) q^{54} +(6.29153 + 11.7706i) q^{55} +(6.35940 + 2.91307i) q^{56} +(-0.261931 + 0.0794558i) q^{57} +(-4.46655 - 4.43025i) q^{58} +(-1.26931 - 1.40047i) q^{59} +(-18.9601 - 15.3029i) q^{60} +(2.67022 + 3.60038i) q^{61} +(1.50555 + 9.87192i) q^{62} +(-10.0598 - 10.0598i) q^{63} +(7.93990 - 0.978768i) q^{64} +(13.1180 - 13.1180i) q^{65} +(10.9250 + 8.03366i) q^{66} +(1.95056 - 1.44663i) q^{67} +(4.04406 + 1.19081i) q^{68} +(1.29114 - 1.17022i) q^{69} +(0.0587558 + 14.4017i) q^{70} +(-0.562586 - 1.85460i) q^{71} +(-15.8306 - 3.76007i) q^{72} +(9.18918 - 4.91172i) q^{73} +(-8.97538 + 11.0280i) q^{74} +(8.59508 - 34.3135i) q^{75} +(0.184883 + 0.00757110i) q^{76} +(-0.393304 - 8.00590i) q^{77} +(6.27772 - 17.7733i) q^{78} +(9.34299 - 6.24278i) q^{79} +(8.69739 + 13.9879i) q^{80} +(5.68332 + 3.79747i) q^{81} +(5.07481 + 6.78457i) q^{82} +(0.676540 - 1.89080i) q^{83} +(6.36415 + 13.1766i) q^{84} +(1.27360 + 8.58593i) q^{85} +(4.26650 + 5.15571i) q^{86} +(-1.28997 - 13.0973i) q^{87} +(-5.18603 - 7.55949i) q^{88} +(-2.23466 + 1.83394i) q^{89} +(-6.66967 - 32.8301i) q^{90} +(-10.4903 + 3.75348i) q^{91} +(-1.08461 + 0.459664i) q^{92} +(-10.7399 + 17.9184i) q^{93} +(-0.636233 - 0.0286547i) q^{94} +(0.145794 + 0.351979i) q^{95} +(14.1020 + 9.01212i) q^{96} +(1.18715 - 2.86605i) q^{97} +(-0.529902 + 1.13231i) q^{98} +(4.53044 + 18.0865i) 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 $

$2$	−0.731994	−	1.21004i	−0.517598	−	0.855624i
$2$	−0.731994	−	1.21004i	−0.517598	−	0.855624i
$3$	0.434101	−	2.92647i	0.250628	−	1.68960i	−0.389257	−	0.921129i	$-0.627268\pi$
$3$	0.434101	−	2.92647i	0.250628	−	1.68960i	0.639886	−	0.768470i	$-0.278982\pi$
$4$	−0.928370	+	1.77148i	−0.464185	+	0.885738i
$5$	−4.11288	−	0.202053i	−1.83934	−	0.0903608i	−0.900528	−	0.434799i	$-0.856820\pi$
$5$	−4.11288	−	0.202053i	−1.83934	−	0.0903608i	−0.938809	+	0.344438i	$0.888070\pi$
$6$	−3.85889	+	1.61688i	−1.57539	+	0.660089i
$7$	2.18104	+	1.16579i	0.824355	+	0.440627i	0.828923	−	0.559363i	$-0.188954\pi$
$7$	2.18104	+	1.16579i	0.824355	+	0.440627i	−0.00456797	+	0.999990i	$0.501454\pi$
$8$	2.82311	−	0.173349i	0.998120	−	0.0612882i
$9$	−5.50497	−	1.66991i	−1.83499	−	0.556638i
$10$	2.76611	+	5.12463i	0.874722	+	1.62055i
$11$	−1.66629	−	2.78003i	−0.502404	−	0.838211i	0.497162	−	0.867658i	$-0.334375\pi$
$11$	−1.66629	−	2.78003i	−0.502404	−	0.838211i	−0.999566	+	0.0294467i	$0.990625\pi$
$12$	4.78117	+	3.48585i	1.38020	+	1.00628i
$13$	−3.02549	+	3.33812i	−0.839121	+	0.925828i	−0.998110	−	0.0614527i	$-0.980427\pi$
$13$	−3.02549	+	3.33812i	−0.839121	+	0.925828i	0.158989	+	0.987280i	$0.449177\pi$
$14$	−0.185861	−	3.49248i	−0.0496733	−	0.933406i
$15$	−2.37671	+	11.9485i	−0.613664	+	3.08509i
$16$	−2.27626	−	3.28917i	−0.569064	−	0.822293i
$17$	−0.411225	−	2.06737i	−0.0997367	−	0.501410i	−0.998070	−	0.0620962i	$-0.980221\pi$
$17$	−0.411225	−	2.06737i	−0.0997367	−	0.501410i	0.898333	−	0.439314i	$-0.144779\pi$
$18$	2.00895	+	7.88357i	0.473514	+	1.85818i
$19$	−0.0395570	−	0.0836362i	−0.00907500	−	0.0191875i	0.899401	−	0.437125i	$-0.144003\pi$
$19$	−0.0395570	−	0.0836362i	−0.00907500	−	0.0191875i	−0.908476	+	0.417937i	$0.862753\pi$
$20$	4.17621	−	7.09829i	0.933829	−	1.58723i
$21$	4.35844	−	5.87668i	0.951090	−	1.28240i
$22$	−2.14422	+	4.05123i	−0.457150	+	0.863726i
$23$	0.455301	+	0.373656i	0.0949368	+	0.0779126i	0.680664	−	0.732595i	$-0.261691\pi$
$23$	0.455301	+	0.373656i	0.0949368	+	0.0779126i	−0.585728	+	0.810508i	$0.699191\pi$
$24$	0.718213	−	8.33700i	0.146605	−	1.70178i
$25$	11.8991	+	1.17195i	2.37981	+	0.234391i
$26$	6.25389	+	1.21747i	1.22649	+	0.238766i
$27$	−3.48191	+	7.36189i	−0.670095	+	1.41680i
$28$	−4.08998	+	2.78137i	−0.772934	+	0.525630i
$29$	4.31512	−	1.08088i	0.801298	−	0.200715i	0.179362	−	0.983783i	$-0.442597\pi$
$29$	4.31512	−	1.08088i	0.801298	−	0.200715i	0.621935	+	0.783069i	$0.286347\pi$
$30$	16.1979	−	5.87034i	2.95731	−	1.07177i
$31$	−6.52371	−	2.70221i	−1.17169	−	0.485331i	−0.289941	−	0.957044i	$-0.593636\pi$
$31$	−6.52371	−	2.70221i	−1.17169	−	0.485331i	−0.881752	+	0.471713i	$0.843636\pi$
$32$	−2.31381	+	5.16201i	−0.409027	+	0.912522i
$33$	−8.85902	+	3.66953i	−1.54216	+	0.638783i
$34$	−2.20057	+	2.01090i	−0.377395	+	0.344866i
$35$	−8.73480	−	5.23544i	−1.47645	−	0.884951i
$36$	8.06886	−	8.20163i	1.34481	−	1.36694i
$37$	−3.38716	−	9.46647i	−0.556845	−	1.55628i	−0.808522	−	0.588466i	$-0.799732\pi$
$37$	−3.38716	−	9.46647i	−0.556845	−	1.55628i	0.251677	−	0.967811i	$-0.419018\pi$
$38$	−0.0722473	+	0.109087i	−0.0117201	+	0.0176962i
$39$	8.45554	+	10.3031i	1.35397	+	1.64982i
$40$	−11.6461	+	0.142547i	−1.84142	+	0.0225387i
$41$	−5.96215	+	0.587220i	−0.931131	+	0.0917084i	−0.552195	−	0.833715i	$-0.686210\pi$
$41$	−5.96215	+	0.587220i	−0.931131	+	0.0917084i	−0.378935	+	0.925423i	$0.623710\pi$
$42$	−10.3013	−	0.972175i	−1.58953	−	0.150010i
$43$	−4.68082	+	0.694334i	−0.713818	+	0.105885i	−0.493755	−	0.869601i	$-0.664376\pi$
$43$	−4.68082	+	0.694334i	−0.713818	+	0.105885i	−0.220063	+	0.975486i	$0.570626\pi$
$44$	6.47169	−	0.370890i	0.975644	−	0.0559137i
$45$	22.3039	+	7.98046i	3.32487	+	1.18966i
$46$	0.118859	−	0.824444i	0.0175248	−	0.121558i
$47$	0.250196	−	0.374445i	0.0364949	−	0.0546184i	−0.812774	−	0.582580i	$-0.802043\pi$
$47$	0.250196	−	0.374445i	0.0364949	−	0.0546184i	0.849268	+	0.527961i	$0.177043\pi$
$48$	−10.6138	+	5.23357i	−1.53197	+	0.755401i
$49$	−0.491127	−	0.735023i	−0.0701610	−	0.105003i
$50$	−7.29193	−	15.2561i	−1.03123	−	2.15754i
$51$	−6.22861	+	0.305992i	−0.872180	+	0.0428474i
$52$	−3.10462	−	8.45860i	−0.430533	−	1.17300i
$53$	−9.04507	−	2.26567i	−1.24244	−	0.311214i	−0.434601	−	0.900623i	$-0.643111\pi$
$53$	−9.04507	−	2.26567i	−1.24244	−	0.311214i	−0.807835	+	0.589409i	$0.799361\pi$
$54$	11.4569	−	1.17562i	1.55908	−	0.159981i
$55$	6.29153	+	11.7706i	0.848349	+	1.58715i
$56$	6.35940	+	2.91307i	0.849811	+	0.389275i
$57$	−0.261931	+	0.0794558i	−0.0346936	+	0.0105242i
$58$	−4.46655	−	4.43025i	−0.586486	−	0.581720i
$59$	−1.26931	−	1.40047i	−0.165250	−	0.182326i	0.652696	−	0.757620i	$-0.273638\pi$
$59$	−1.26931	−	1.40047i	−0.165250	−	0.182326i	−0.817947	+	0.575294i	$0.804888\pi$
$60$	−18.9601	−	15.3029i	−2.44773	−	1.97560i
$61$	2.67022	+	3.60038i	0.341887	+	0.460981i	0.940370	−	0.340154i	$-0.110479\pi$
$61$	2.67022	+	3.60038i	0.341887	+	0.460981i	−0.598482	+	0.801136i	$0.704229\pi$
$62$	1.50555	+	9.87192i	0.191205	+	1.25374i
$63$	−10.0598	−	10.0598i	−1.26741	−	1.26741i
$64$	7.93990	−	0.978768i	0.992488	−	0.122346i
$65$	13.1180	−	13.1180i	1.62709	−	1.62709i
$66$	10.9250	+	8.03366i	1.34478	+	0.988875i
$67$	1.95056	−	1.44663i	0.238298	−	0.176734i	−0.469959	−	0.882688i	$-0.655731\pi$
$67$	1.95056	−	1.44663i	0.238298	−	0.176734i	0.708258	+	0.705954i	$0.249481\pi$
$68$	4.04406	+	1.19081i	0.490415	+	0.144407i
$69$	1.29114	−	1.17022i	0.155435	−	0.140878i
$70$	0.0587558	+	14.4017i	0.00702267	+	1.72134i
$71$	−0.562586	−	1.85460i	−0.0667666	−	0.220100i	0.917208	−	0.398409i	$-0.130437\pi$
$71$	−0.562586	−	1.85460i	−0.0667666	−	0.220100i	−0.983975	+	0.178309i	$0.942937\pi$
$72$	−15.8306	−	3.76007i	−1.86566	−	0.443128i
$73$	9.18918	−	4.91172i	1.07551	−	0.574873i	0.164131	−	0.986438i	$-0.447518\pi$
$73$	9.18918	−	4.91172i	1.07551	−	0.574873i	0.911380	+	0.411566i	$0.135018\pi$
$74$	−8.97538	+	11.0280i	−1.04337	+	1.28198i
$75$	8.59508	−	34.3135i	0.992474	−	3.96218i
$76$	0.184883	+	0.00757110i	0.0212076	+	0.000868465i
$77$	−0.393304	−	8.00590i	−0.0448212	−	0.912357i
$78$	6.27772	−	17.7733i	0.710811	−	2.01243i
$79$	9.34299	−	6.24278i	1.05117	−	0.702368i	0.0950865	−	0.995469i	$-0.469687\pi$
$79$	9.34299	−	6.24278i	1.05117	−	0.702368i	0.956081	+	0.293101i	$0.0946872\pi$
$80$	8.69739	+	13.9879i	0.972398	+	1.56389i
$81$	5.68332	+	3.79747i	0.631480	+	0.421942i
$82$	5.07481	+	6.78457i	0.560419	+	0.749230i
$83$	0.676540	−	1.89080i	0.0742599	−	0.207543i	−0.898678	−	0.438609i	$-0.855471\pi$
$83$	0.676540	−	1.89080i	0.0742599	−	0.207543i	0.972938	+	0.231066i	$0.0742214\pi$
$84$	6.36415	+	13.1766i	0.694386	+	1.43769i
$85$	1.27360	+	8.58593i	0.138142	+	0.931275i
$86$	4.26650	+	5.15571i	0.460068	+	0.555954i
$87$	−1.28997	−	13.0973i	−0.138299	−	1.40418i
$88$	−5.18603	−	7.55949i	−0.552832	−	0.805844i
$89$	−2.23466	+	1.83394i	−0.236874	+	0.194397i	−0.745340	−	0.666685i	$-0.767713\pi$
$89$	−2.23466	+	1.83394i	−0.236874	+	0.194397i	0.508466	+	0.861082i	$0.330213\pi$
$90$	−6.66967	−	32.8301i	−0.703045	−	3.46060i
$91$	−10.4903	+	3.75348i	−1.09968	+	0.393471i
$92$	−1.08461	+	0.459664i	−0.113078	+	0.0479233i
$93$	−10.7399	+	17.9184i	−1.11367	+	1.85805i
$94$	−0.636233	−	0.0286547i	−0.0656225	−	0.00295551i
$95$	0.145794	+	0.351979i	0.0149582	+	0.0361122i
$96$	14.1020	+	9.01212i	1.43928	+	0.919796i
$97$	1.18715	−	2.86605i	0.120537	−	0.291003i	−0.852081	−	0.523409i	$-0.824660\pi$
$97$	1.18715	−	2.86605i	0.120537	−	0.291003i	0.972619	+	0.232406i	$0.0746599\pi$
$98$	−0.529902	+	1.13231i	−0.0535282	+	0.114381i
$99$	4.53044	+	18.0865i	0.455327	+	1.81777i
$100$	−13.1228	+	19.9909i	−1.31228	+	1.99909i
$101$	6.23609	+	2.94945i	0.620514	+	0.293481i	0.711842	−	0.702340i	$-0.247861\pi$
$101$	6.23609	+	2.94945i	0.620514	+	0.293481i	−0.0913281	+	0.995821i	$0.529111\pi$
$102$	4.92956	+	7.31285i	0.488099	+	0.724080i
$103$	−0.649937	+	6.59892i	−0.0640402	+	0.650211i	0.908564	+	0.417745i	$0.137179\pi$
$103$	−0.649937	+	6.59892i	−0.0640402	+	0.650211i	−0.972605	+	0.232466i	$0.925321\pi$
$104$	−7.96264	+	9.94835i	−0.780802	+	0.975515i
$105$	−19.1132	+	23.2894i	−1.86525	+	2.27282i
$106$	3.87939	+	12.6033i	0.376800	+	1.22414i
$107$	11.0756	+	8.21424i	1.07072	+	0.794101i	0.979442	−	0.201724i	$-0.0646545\pi$
$107$	11.0756	+	8.21424i	1.07072	+	0.794101i	0.0912788	+	0.995825i	$0.470905\pi$
$108$	−9.80891	−	13.0027i	−0.943863	−	1.25118i
$109$	16.8868	−	7.98686i	1.61746	−	0.765003i	0.617692	−	0.786420i	$-0.288068\pi$
$109$	16.8868	−	7.98686i	1.61746	−	0.765003i	0.999771	+	0.0214172i	$0.00681782\pi$
$110$	9.63751	−	16.2290i	0.918900	−	1.54737i
$111$	−29.1737	+	5.80301i	−2.76905	+	0.550798i
$112$	−1.13012	−	9.82745i	−0.106787	−	0.928607i
$113$	−8.64275	−	1.71915i	−0.813042	−	0.161724i	−0.228978	−	0.973432i	$-0.573538\pi$
$113$	−8.64275	−	1.71915i	−0.813042	−	0.161724i	−0.584064	+	0.811708i	$0.698538\pi$
$114$	0.287876	+	0.258784i	0.0269621	+	0.0242374i
$115$	−1.79710	−	1.62880i	−0.167580	−	0.151886i
$116$	−2.09127	+	8.64759i	−0.194170	+	0.802909i
$117$	22.2296	−	13.3239i	2.05513	−	1.23180i
$118$	−0.765489	+	2.56105i	−0.0704690	+	0.235764i
$119$	1.51322	−	4.98841i	0.138716	−	0.457287i
$120$	−4.63844	+	34.1440i	−0.423430	+	3.11691i
$121$	0.233300	−	0.436473i	0.0212091	−	0.0396793i
$122$	2.40200	−	5.86652i	0.217467	−	0.531130i
$123$	−0.869691	+	17.7030i	−0.0784174	+	1.59622i
$124$	10.8433	−	9.04795i	0.973759	−	0.812530i
$125$	−28.3362	−	4.20328i	−2.53447	−	0.375953i
$126$	−4.80899	+	19.5364i	−0.428419	+	1.74044i
$127$			5.54401i			0.491951i	0.969276	+	0.245975i	$0.0791083\pi$
$127$			5.54401i			0.491951i	−0.969276	+	0.245975i	$0.920892\pi$
$128$	−6.99630	−	8.89111i	−0.618392	−	0.785870i
$129$			13.9997i			1.23260i
$130$	−25.4755	−	6.27094i	−2.23435	−	0.549998i
$131$	19.5363	+	2.89793i	1.70689	+	0.253193i	0.927629	−	0.373504i	$-0.121844\pi$
$131$	19.5363	+	2.89793i	1.70689	+	0.253193i	0.779263	+	0.626697i	$0.215594\pi$
$132$	1.72397	−	19.1002i	0.150052	−	1.66246i
$133$	0.0112269	−	0.228529i	0.000973497	−	0.0198160i
$134$	−3.17827	−	1.30132i	−0.274561	−	0.112417i
$135$	15.8082	−	29.5751i	1.36055	−	2.54542i
$136$	−1.51931	−	5.76512i	−0.130280	−	0.494355i
$137$	5.55204	−	18.3026i	0.474343	−	1.56370i	−0.314596	−	0.949226i	$-0.601869\pi$
$137$	5.55204	−	18.3026i	0.474343	−	1.56370i	0.788938	−	0.614472i	$-0.210631\pi$
$138$	−2.36111	−	0.705730i	−0.200991	−	0.0600757i
$139$	3.10928	−	1.86363i	0.263725	−	0.158071i	−0.376128	−	0.926568i	$-0.622745\pi$
$139$	3.10928	−	1.86363i	0.263725	−	0.158071i	0.639854	+	0.768497i	$0.278995\pi$
$140$	17.3836	−	10.6131i	1.46918	−	0.896968i
$141$	−0.987192	−	0.894739i	−0.0831366	−	0.0753506i
$142$	−1.83232	+	2.03830i	−0.153765	+	0.171050i
$143$	14.3214	+	2.84871i	1.19762	+	0.238221i
$144$	7.03810	+	21.9079i	0.586508	+	1.82566i
$145$	−17.9660	+	3.57365i	−1.49199	+	0.296776i
$146$	−12.6698	−	7.52388i	−1.04856	−	0.622681i
$147$	−2.36422	+	1.11819i	−0.194998	+	0.0922271i
$148$	19.9142	+	2.78812i	1.63693	+	0.229182i
$149$	−8.84050	−	6.55656i	−0.724242	−	0.537135i	0.169602	−	0.985513i	$-0.445752\pi$
$149$	−8.84050	−	6.55656i	−0.724242	−	0.537135i	−0.893844	+	0.448378i	$0.852002\pi$
$150$	−47.8121	+	14.7169i	−3.90384	+	1.20163i
$151$	−0.336640	+	0.410197i	−0.0273954	+	0.0333814i	−0.786528	−	0.617555i	$-0.788123\pi$
$151$	−0.336640	+	0.410197i	−0.0273954	+	0.0333814i	0.759133	+	0.650936i	$0.225623\pi$
$152$	−0.126172	−	0.229257i	−0.0102339	−	0.0185952i
$153$	−1.18855	+	12.0675i	−0.0960883	+	0.975600i
$154$	−9.39952	+	6.33618i	−0.757435	+	0.510584i
$155$	26.2853	+	12.4320i	2.11128	+	0.998563i
$156$	−26.1016	+	5.41369i	−2.08980	+	0.433442i
$157$	−2.46338	−	9.83438i	−0.196599	−	0.784869i	−0.985405	−	0.170226i	$-0.945550\pi$
$157$	−2.46338	−	9.83438i	−0.196599	−	0.784869i	0.788806	−	0.614643i	$-0.210700\pi$
$158$	−14.3930	−	6.73566i	−1.14505	−	0.535860i
$159$	−10.5569	+	25.4866i	−0.837216	+	2.02122i
$160$	10.5594	−	20.7632i	0.834795	−	1.64148i
$161$	0.557425	+	1.34574i	0.0439312	+	0.106059i
$162$	0.434921	−	9.65675i	0.0341706	−	0.758706i
$163$	−2.77042	+	4.62217i	−0.216996	+	0.362037i	−0.946908	−	0.321505i	$-0.895811\pi$
$163$	−2.77042	+	4.62217i	−0.216996	+	0.362037i	0.729911	+	0.683542i	$0.239561\pi$
$164$	4.49483	−	11.1070i	0.350987	−	0.867308i
$165$	37.1775	−	13.3023i	2.89427	−	1.03559i
$166$	−2.78316	+	0.565419i	−0.216015	+	0.0438850i
$167$	−2.33822	+	1.91893i	−0.180937	+	0.148491i	−0.720502	−	0.693453i	$-0.756089\pi$
$167$	−2.33822	+	1.91893i	−0.180937	+	0.148491i	0.539565	+	0.841944i	$0.318589\pi$
$168$	11.2856	−	17.3460i	0.870706	−	1.33828i
$169$	−0.715198	−	7.26152i	−0.0550152	−	0.558579i
$170$	9.45701	−	7.82595i	0.725320	−	0.600223i
$171$	0.0780947	+	0.526472i	0.00597205	+	0.0402603i
$172$	3.11554	−	8.93656i	0.237557	−	0.681406i
$173$	−3.83416	+	10.7158i	−0.291506	+	0.814704i	0.703111	+	0.711080i	$0.251794\pi$
$173$	−3.83416	+	10.7158i	−0.291506	+	0.814704i	−0.994617	+	0.103623i	$0.966956\pi$
$174$	−14.9039	+	11.1480i	−1.12986	+	0.845131i
$175$	24.5860	+	16.4279i	1.85853	+	1.24183i
$176$	−5.35110	+	11.8088i	−0.403355	+	0.890120i
$177$	−4.64944	+	3.10666i	−0.349474	+	0.233511i
$178$	3.85489	+	1.36159i	0.288936	+	0.102055i
$179$	−0.246575	−	5.01915i	−0.0184299	−	0.375149i	−0.990239	−	0.139380i	$-0.955489\pi$
$179$	−0.246575	−	5.01915i	−0.0184299	−	0.375149i	0.971809	−	0.235769i	$-0.0757609\pi$
$180$	−34.8434	+	32.1020i	−2.59708	+	2.39274i
$181$	−1.65749	+	6.61709i	−0.123201	+	0.491844i	0.876740	+	0.480964i	$0.159713\pi$
$181$	−1.65749	+	6.61709i	−0.123201	+	0.491844i	−0.999941	+	0.0108800i	$0.996537\pi$
$182$	12.2206	+	9.94607i	0.905855	+	0.737252i
$183$	11.6956	−	6.25141i	0.864560	−	0.462117i
$184$	1.35014	+	0.975945i	0.0995334	+	0.0719476i
$185$	12.0182	+	39.6189i	0.883599	+	2.91284i
$186$	29.5435	−	0.120531i	2.16623	−	0.00883774i
$187$	−5.06213	+	4.58805i	−0.370180	+	0.335511i
$188$	0.431046	+	0.790840i	0.0314372	+	0.0576779i
$189$	−16.1766	+	11.9974i	−1.17667	+	0.872681i
$190$	0.319186	−	0.434062i	0.0231562	−	0.0314902i
$191$	11.1408	−	11.1408i	0.806121	−	0.806121i	−0.177923	−	0.984044i	$-0.556938\pi$
$191$	11.1408	−	11.1408i	0.806121	−	0.806121i	0.984044	+	0.177923i	$0.0569379\pi$
$192$	0.582382	−	23.6608i	0.0420298	−	1.70757i
$193$	−8.86173	−	8.86173i	−0.637881	−	0.637881i	0.312151	−	0.950032i	$-0.398950\pi$
$193$	−8.86173	−	8.86173i	−0.637881	−	0.637881i	−0.950032	+	0.312151i	$0.898950\pi$
$194$	−4.33701	+	0.661428i	−0.311379	+	0.0474878i
$195$	−32.6949	−	44.0839i	−2.34133	−	3.15692i
$196$	1.75802	−	0.187646i	0.125573	−	0.0134033i
$197$	0.0766077	+	0.0845236i	0.00545808	+	0.00602206i	0.743674	−	0.668542i	$-0.233081\pi$
$197$	0.0766077	+	0.0845236i	0.00545808	+	0.00602206i	−0.738216	+	0.674564i	$0.764331\pi$
$198$	18.5691	−	18.7212i	1.31965	−	1.33046i
$199$	−21.7736	+	6.60495i	−1.54349	+	0.468212i	−0.943382	−	0.331707i	$-0.892375\pi$
$199$	−21.7736	+	6.60495i	−1.54349	+	0.468212i	−0.600107	+	0.799920i	$0.704875\pi$
$200$	33.7955	+	1.24586i	2.38970	+	0.0880959i
$201$	−3.38679	−	6.33623i	−0.238886	−	0.446923i
$202$	−0.995839	−	9.70486i	−0.0700670	−	0.682832i
$203$	10.6715	+	2.67308i	0.748994	+	0.187613i
$204$	5.24040	−	11.3179i	0.366901	−	0.792412i
$205$	24.6403	−	1.21050i	1.72095	−	0.0845449i
$206$	8.46068	−	4.04392i	0.589483	−	0.281753i
$207$	−1.88244	−	2.81728i	−0.130839	−	0.195814i
$208$	17.8665	+	2.35295i	1.23882	+	0.163148i
$209$	−0.166598	+	0.249332i	−0.0115238	+	0.0172466i
$210$	42.1718	+	6.07986i	2.91013	+	0.419550i
$211$	11.7726	+	4.21232i	0.810462	+	0.289988i	0.709322	−	0.704884i	$-0.249001\pi$
$211$	11.7726	+	4.21232i	0.810462	+	0.289988i	0.101140	+	0.994872i	$0.467751\pi$
$212$	12.4108	−	13.9197i	0.852374	−	0.956012i
$213$	−5.67164	+	0.841309i	−0.388615	+	0.0576455i
$214$	1.83223	−	19.4147i	0.125249	−	1.32716i
$215$	19.3919	−	1.90994i	1.32252	−	0.130257i
$216$	−8.55365	+	21.3870i	−0.582002	+	1.45520i
$217$	−11.0783	−	13.4989i	−0.752041	−	0.916365i
$218$	−22.0254	−	14.5873i	−1.49175	−	0.987976i
$219$	−10.3850	−	29.0240i	−0.701751	−	1.96126i
$220$	−26.6922	+	0.217800i	−1.79959	+	0.0146841i
$221$	8.14528	+	4.88209i	0.547911	+	0.328405i
$222$	28.3768	+	31.0535i	1.90453	+	2.08417i
$223$	−20.1618	+	8.35130i	−1.35014	+	0.559244i	−0.936330	−	0.351121i	$-0.885801\pi$
$223$	−20.1618	+	8.35130i	−1.35014	+	0.559244i	−0.413805	+	0.910365i	$0.635801\pi$
$224$	−11.0643	+	8.56112i	−0.739266	+	0.572014i
$225$	−63.5469	−	26.3220i	−4.23646	−	1.75480i
$226$	4.24621	+	11.7164i	0.282454	+	0.779366i
$227$	−17.7529	+	4.44686i	−1.17830	+	0.295148i	−0.782181	−	0.623051i	$-0.785893\pi$
$227$	−17.7529	+	4.44686i	−1.17830	+	0.295148i	−0.396118	+	0.918200i	$0.629643\pi$
$228$	0.102415	−	0.537769i	0.00678257	−	0.0356146i
$229$	3.50293	−	7.40632i	0.231480	−	0.489424i	−0.754497	−	0.656303i	$-0.772119\pi$
$229$	3.50293	−	7.40632i	0.231480	−	0.489424i	0.985977	+	0.166880i	$0.0533692\pi$
$230$	−0.655435	+	3.36682i	−0.0432181	+	0.222002i
$231$	−23.5998	−	2.32437i	−1.55275	−	0.152933i
$232$	11.9947	−	3.79947i	0.787490	−	0.249447i
$233$	−4.97739	−	4.08484i	−0.326079	−	0.267606i	0.457082	−	0.889424i	$-0.348894\pi$
$233$	−4.97739	−	4.08484i	−0.326079	−	0.267606i	−0.783162	+	0.621818i	$0.786394\pi$
$234$	−32.3944	−	17.1456i	−2.11769	−	1.12084i
$235$	−1.10468	+	1.48949i	−0.0720617	+	0.0971639i
$236$	3.65929	−	0.948402i	0.238200	−	0.0617357i
$237$	−14.2135	−	30.0520i	−0.923268	−	1.95209i
$238$	−7.14382	+	1.82044i	−0.463065	+	0.118002i
$239$	4.05467	+	20.3842i	0.262275	+	1.31854i	0.857292	+	0.514831i	$0.172145\pi$
$239$	4.05467	+	20.3842i	0.262275	+	1.31854i	−0.595017	+	0.803713i	$0.702855\pi$
$240$	44.7107	−	19.3805i	2.88607	−	1.25101i
$241$	−1.48208	+	7.45093i	−0.0954693	+	0.479957i	0.903239	+	0.429139i	$0.141183\pi$
$241$	−1.48208	+	7.45093i	−0.0954693	+	0.479957i	−0.998708	+	0.0508181i	$0.983817\pi$
$242$	−0.698921	+	0.0371947i	−0.0449284	+	0.00239097i
$243$	−2.82675	+	3.11883i	−0.181336	+	0.200073i
$244$	−8.85695	+	1.38775i	−0.567008	+	0.0888418i
$245$	1.87143	+	3.12230i	0.119562	+	0.199476i
$246$	22.0578	−	11.9061i	1.40636	−	0.759105i
$247$	0.398867	+	0.120995i	0.0253793	+	0.00769873i
$248$	−18.8856	−	6.49776i	−1.19924	−	0.412608i
$249$	−5.23969	−	2.80067i	−0.332052	−	0.177486i
$250$	15.6558	+	37.3646i	0.990161	+	2.36315i
$251$	10.1006	+	0.496208i	0.637541	+	0.0313204i	0.365272	−	0.930901i	$-0.380976\pi$
$251$	10.1006	+	0.496208i	0.637541	+	0.0313204i	0.272269	+	0.962221i	$0.412226\pi$
$252$	27.1599	−	8.48147i	1.71091	−	0.534282i
$253$	0.280113	−	1.88837i	0.0176105	−	0.118721i
$254$	6.70844	−	4.05818i	0.420925	−	0.254633i
$255$	25.6794			1.60810
$256$	−5.63730	+	14.9740i	−0.352331	+	0.935875i
$257$	−17.9028			−1.11674			−0.558372	−	0.829591i	$-0.688574\pi$
$257$	−17.9028			−1.11674			−0.558372	+	0.829591i	$0.688574\pi$
$258$	16.9401	−	10.2477i	1.05465	−	0.637993i
$259$	3.64839	−	24.5954i	0.226700	−	1.52829i
$260$	11.0599	+	35.4165i	0.685903	+	2.19644i
$261$	−25.5596	−	1.25566i	−1.58210	−	0.0777235i
$262$	−10.7938	−	25.7608i	−0.666845	−	1.59151i
$263$	−9.57907	−	5.12012i	−0.590671	−	0.315720i	0.148844	−	0.988861i	$-0.452445\pi$
$263$	−9.57907	−	5.12012i	−0.590671	−	0.315720i	−0.739515	+	0.673141i	$0.764945\pi$
$264$	−24.3739	+	11.8952i	−1.50011	+	0.732098i
$265$	36.7435	+	11.1460i	2.25714	+	0.684695i
$266$	−0.284746	+	0.153697i	−0.0174589	+	0.00942376i
$267$	4.39690	+	7.33579i	0.269086	+	0.448943i
$268$	0.751835	+	4.79838i	0.0459256	+	0.293107i
$269$	−8.28743	+	9.14377i	−0.505294	+	0.557506i	−0.939164	−	0.343470i	$-0.888398\pi$
$269$	−8.28743	+	9.14377i	−0.505294	+	0.557506i	0.433870	+	0.900975i	$0.357148\pi$
$270$	−47.3584	+	2.52028i	−2.88214	+	0.153380i
$271$	5.27391	−	26.5137i	0.320367	−	1.61060i	−0.399670	−	0.916659i	$-0.630875\pi$
$271$	5.27391	−	26.5137i	0.320367	−	1.61060i	0.720037	−	0.693936i	$-0.244125\pi$
$272$	−5.86388	+	6.05845i	−0.355550	+	0.367348i
$273$	6.43061	+	32.3289i	0.389198	+	1.95663i
$274$	−26.2109	+	6.67924i	−1.58346	+	0.403508i
$275$	−16.5692	−	35.0326i	−0.999158	−	2.11254i
$276$	0.874363	+	3.37362i	0.0526304	+	0.203068i
$277$	−0.576282	+	0.777026i	−0.0346254	+	0.0466870i	−0.820181	−	0.572104i	$-0.806127\pi$
$277$	−0.576282	+	0.777026i	−0.0346254	+	0.0466870i	0.785556	+	0.618791i	$0.212377\pi$
$278$	−4.53103	−	2.39817i	−0.271753	−	0.143833i
$279$	31.4004	+	25.7696i	1.87989	+	1.54279i
$280$	−25.5669	−	13.2661i	−1.52791	−	0.792798i
$281$	9.50929	+	0.936583i	0.567276	+	0.0558719i	0.377590	−	0.925973i	$-0.376753\pi$
$281$	9.50929	+	0.936583i	0.567276	+	0.0558719i	0.189686	+	0.981845i	$0.439253\pi$
$282$	−0.360047	+	1.84948i	−0.0214405	+	0.110135i
$283$	−9.12832	+	19.3002i	−0.542623	+	1.14728i	0.427355	+	0.904084i	$0.359445\pi$
$283$	−9.12832	+	19.3002i	−0.542623	+	1.14728i	−0.969977	+	0.243195i	$0.921805\pi$
$284$	3.80766	+	0.725145i	0.225943	+	0.0430294i
$285$	1.09334	−	0.273869i	0.0647642	−	0.0162226i
$286$	−7.03615	−	19.4147i	−0.416057	−	1.14801i
$287$	−13.6882	−	5.66986i	−0.807992	−	0.334681i
$288$	21.3575	−	24.5528i	1.25851	−	1.44679i
$289$	11.6010	−	4.80531i	0.682414	−	0.282665i
$290$	17.4752	+	19.1236i	1.02618	+	1.12297i
$291$	−7.87206	−	4.71833i	−0.461468	−	0.276593i
$292$	0.170034	+	20.8383i	0.00995049	+	1.21947i
$293$	−0.892113	−	2.49329i	−0.0521178	−	0.145659i	0.912664	−	0.408710i	$-0.134021\pi$
$293$	−0.892113	−	2.49329i	−0.0521178	−	0.145659i	−0.964782	+	0.263051i	$0.915271\pi$
$294$	3.08365	+	2.04228i	0.179842	+	0.119108i
$295$	4.93756	+	6.01644i	0.287476	+	0.350290i
$296$	−11.2033	−	26.1377i	−0.651180	−	1.51922i
$297$	26.2682	−	2.58719i	1.52423	−	0.150124i
$298$	−1.46248	+	15.4967i	−0.0847192	+	0.897699i
$299$	−2.62482	+	0.389355i	−0.151797	+	0.0225170i
$300$	52.8061	+	47.0816i	3.04876	+	2.71826i
$301$	−11.0185	−	3.94248i	−0.635095	−	0.227241i
$302$	0.742771	+	0.107085i	0.0427417	+	0.00616202i
$303$	11.3386	−	16.9694i	0.651384	−	0.974865i
$304$	−0.185052	+	0.320487i	−0.0106135	+	0.0183812i
$305$	−10.2548	−	15.3475i	−0.587191	−	0.878793i
$306$	15.4721	−	7.39516i	0.884482	−	0.422753i
$307$	26.6547	−	1.30946i	1.52126	−	0.0747349i	0.728830	−	0.684694i	$-0.240064\pi$
$307$	26.6547	−	1.30946i	1.52126	−	0.0747349i	0.792433	+	0.609959i	$0.208814\pi$
$308$	14.5474	+	6.73571i	0.828914	+	0.383802i
$309$	19.0294	+	4.76662i	1.08255	+	0.271164i
$310$	−4.19749	−	40.9063i	−0.238401	−	2.32332i
$311$	−13.8864	−	25.9796i	−0.787423	−	1.47317i	−0.878718	−	0.477341i	$-0.841601\pi$
$311$	−13.8864	−	25.9796i	−0.787423	−	1.47317i	0.0912947	−	0.995824i	$-0.470899\pi$
$312$	25.6570	+	27.6210i	1.45254	+	1.56373i
$313$	11.3775	−	3.45131i	0.643092	−	0.195080i	0.0481394	−	0.998841i	$-0.484671\pi$
$313$	11.3775	−	3.45131i	0.643092	−	0.195080i	0.594953	+	0.803761i	$0.297171\pi$
$314$	−10.0968	+	10.1795i	−0.569793	+	0.574462i
$315$	39.3421	+	43.4073i	2.21668	+	2.44573i
$316$	2.38519	+	22.3465i	0.134178	+	1.25709i
$317$	−2.85243	−	3.84606i	−0.160208	−	0.216016i	0.715808	−	0.698297i	$-0.246058\pi$
$317$	−2.85243	−	3.84606i	−0.160208	−	0.216016i	−0.876017	+	0.482281i	$0.839808\pi$
$318$	38.5673	−	5.88182i	2.16274	−	0.329836i
$319$	−10.1951	−	10.1951i	−0.570817	−	0.570817i
$320$	−32.8536	+	2.42128i	−1.83657	+	0.135354i
$321$	28.8467	−	28.8467i	1.61007	−	1.61007i
$322$	1.22036	−	1.65958i	0.0680082	−	0.0924847i
$323$	−0.156640	+	0.116172i	−0.00871569	+	0.00646400i
$324$	−12.0034	+	6.54241i	−0.666854	+	0.363467i
$325$	−39.9126	+	36.1747i	−2.21396	+	2.00661i
$326$	7.62093	−	0.0310917i	0.422084	−	0.00172201i
$327$	−16.0428	−	52.8859i	−0.887166	−	2.92459i
$328$	−16.7300	+	2.69132i	−0.923760	+	0.148603i
$329$	0.982211	−	0.525003i	0.0541511	−	0.0289443i
$330$	−43.3100	−	35.2489i	−2.38414	−	1.94039i
$331$	−5.71358	+	22.8099i	−0.314047	+	1.25374i	0.583242	+	0.812299i	$0.301784\pi$
$331$	−5.71358	+	22.8099i	−0.314047	+	1.25374i	−0.897288	+	0.441445i	$0.854466\pi$
$332$	2.72143	+	2.95384i	0.149358	+	0.162113i
$333$	2.83800	+	57.7689i	0.155522	+	3.16572i
$334$	4.03353	+	1.42468i	0.220705	+	0.0779553i
$335$	−8.31471	+	5.55571i	−0.454281	+	0.303541i
$336$	−29.2503	−	0.958829i	−1.59574	−	0.0523084i
$337$	23.9158	+	15.9800i	1.30278	+	0.870488i	0.996673	−	0.0815094i	$-0.0259741\pi$
$337$	23.9158	+	15.9800i	1.30278	+	0.870488i	0.306105	+	0.951998i	$0.400974\pi$
$338$	−8.26318	+	6.18081i	−0.449458	+	0.336191i
$339$	−8.78287	+	24.5465i	−0.477020	+	1.33318i
$340$	−16.3922	−	5.71477i	−0.888989	−	0.309927i
$341$	3.35815	+	22.6388i	0.181854	+	1.22596i
$342$	0.579885	−	0.479871i	0.0313566	−	0.0259485i
$343$	−1.91110	−	19.4037i	−0.103189	−	1.04770i
$344$	−13.0941	+	2.77160i	−0.705987	+	0.149435i
$345$	−5.54675	+	4.55210i	−0.298627	+	0.245077i
$346$	15.7730	−	3.20440i	0.847963	−	0.172270i
$347$	−6.72065	+	2.40469i	−0.360783	+	0.129090i	−0.511041	−	0.859557i	$-0.670740\pi$
$347$	−6.72065	+	2.40469i	−0.360783	+	0.129090i	0.150257	+	0.988647i	$0.451990\pi$
$348$	24.3991	+	9.87398i	1.30793	+	0.529301i
$349$	−16.6390	+	27.7606i	−0.890668	+	1.48599i	−0.0167812	+	0.999859i	$0.505342\pi$
$349$	−16.6390	+	27.7606i	−0.890668	+	1.48599i	−0.873886	+	0.486130i	$0.838408\pi$
$350$	1.88147	−	41.7751i	0.100569	−	2.23297i
$351$	−14.0403	−	33.8964i	−0.749418	−	1.80926i
$352$	18.2060	−	2.16892i	0.970383	−	0.115604i
$353$	−7.55540	+	18.2404i	−0.402133	+	0.970836i	0.585014	+	0.811023i	$0.301089\pi$
$353$	−7.55540	+	18.2404i	−0.402133	+	0.970836i	−0.987147	+	0.159813i	$0.948911\pi$
$354$	7.16253	+	3.35194i	0.380684	+	0.178153i
$355$	1.93912	+	7.74141i	0.102918	+	0.410871i
$356$	−1.17419	−	5.66123i	−0.0622318	−	0.300044i
$357$	−13.9416	−	6.59386i	−0.737865	−	0.348984i
$358$	−5.89286	+	3.97235i	−0.311447	+	0.209945i
$359$	−0.364848	+	3.70436i	−0.0192559	+	0.195509i	0.980744	+	0.195298i	$0.0625673\pi$
$359$	−0.364848	+	3.70436i	−0.0192559	+	0.195509i	−1.00000		0.000211290i	$0.999933\pi$
$360$	64.3497	+	18.6633i	3.39153	+	0.983645i
$361$	12.0480	−	14.6806i	0.634107	−	0.772662i
$362$	9.22018	−	2.83804i	0.484602	−	0.149164i
$363$	−1.17605	−	0.872218i	−0.0617266	−	0.0457796i
$364$	3.08965	−	22.0679i	0.161942	−	1.15667i
$365$	−38.7864	+	18.3446i	−2.03017	+	0.960201i
$366$	−16.1255	−	9.57605i	−0.842893	−	0.500548i
$367$	18.0108	−	3.58257i	0.940157	−	0.187009i	0.298856	−	0.954298i	$-0.403395\pi$
$367$	18.0108	−	3.58257i	0.940157	−	0.187009i	0.641301	+	0.767289i	$0.278395\pi$
$368$	0.192636	−	2.34810i	0.0100418	−	0.122403i
$369$	33.8020	+	6.72365i	1.75966	+	0.350019i
$370$	39.1429	−	43.5433i	2.03494	−	2.26371i
$371$	−17.0863	−	15.4862i	−0.887079	−	0.804001i
$372$	−21.7715	−	35.6604i	−1.12880	−	1.84891i
$373$	−4.49816	+	2.69609i	−0.232906	+	0.139598i	−0.625795	−	0.779987i	$-0.715226\pi$
$373$	−4.49816	+	2.69609i	−0.232906	+	0.139598i	0.392889	+	0.919586i	$0.371476\pi$
$374$	9.25715	+	2.76693i	0.478676	+	0.143075i
$375$	−24.6016	+	81.1005i	−1.27042	+	4.18801i
$376$	0.641421	−	1.10047i	0.0330788	−	0.0567524i
$377$	−9.44726	+	17.6746i	−0.486559	+	0.910287i
$378$	26.3584	+	10.7922i	1.35573	+	0.555093i
$379$	1.76947	−	36.0184i	0.0908915	−	1.85014i	−0.331168	−	0.943572i	$-0.607443\pi$
$379$	1.76947	−	36.0184i	0.0908915	−	1.85014i	0.422060	−	0.906568i	$-0.361307\pi$
$380$	−0.758873	−	0.0684953i	−0.0389294	−	0.00351373i
$381$	16.2244	+	2.40666i	0.831200	+	0.123297i
$382$	−21.6358	−	5.32577i	−1.10698	−	0.272490i
$383$			13.6010i			0.694978i	0.937684	+	0.347489i	$0.112966\pi$
$383$			13.6010i			0.694978i	−0.937684	+	0.347489i	$0.887034\pi$
$384$	−29.0567	+	16.6148i	−1.48279	+	0.847872i
$385$			33.0068i			1.68218i
$386$	−4.23627	+	17.2097i	−0.215621	+	0.875952i
$387$	26.9272	+	3.99428i	1.36879	+	0.203041i
$388$	3.97501	+	4.76377i	0.201801	+	0.241844i
$389$	0.302391	−	6.15531i	0.0153318	−	0.312087i	−0.978865	−	0.204508i	$-0.934440\pi$
$389$	0.302391	−	6.15531i	0.0153318	−	0.312087i	0.994197	−	0.107578i	$-0.0343096\pi$
$390$	−29.4107	+	71.8311i	−1.48927	+	3.63731i
$391$	0.585253	−	1.09493i	0.0295975	−	0.0553730i
$392$	−1.51392	−	1.98992i	−0.0764646	−	0.100506i
$393$	16.9614	−	55.9143i	0.855591	−	2.82050i
$394$	0.0462002	−	0.154569i	0.00232753	−	0.00778706i
$395$	−39.6880	+	23.7881i	−1.99692	+	1.19691i
$396$	−36.2458	−	8.76544i	−1.82142	−	0.440480i
$397$	−24.5811	−	22.2790i	−1.23369	−	1.11815i	−0.988902	−	0.148572i	$-0.952532\pi$
$397$	−24.5811	−	22.2790i	−1.23369	−	1.11815i	−0.244786	−	0.969577i	$-0.578718\pi$
$398$	23.9304	+	21.5120i	1.19952	+	1.07830i
$399$	−0.663910	−	0.132060i	−0.0332371	−	0.00661127i
$400$	−23.2305	−	41.8057i	−1.16153	−	2.09028i
$401$	20.1025	−	3.99863i	1.00387	−	0.199682i	0.334328	−	0.942457i	$-0.391491\pi$
$401$	20.1025	−	3.99863i	1.00387	−	0.199682i	0.669541	+	0.742775i	$0.266491\pi$
$402$	−5.18796	+	8.73622i	−0.258752	+	0.435723i
$403$	28.7578	−	13.6014i	1.43253	−	0.677534i
$404$	−11.0143	+	8.30890i	−0.547981	+	0.413383i
$405$	−22.6075	−	16.7669i	−1.12338	−	0.833154i
$406$	−4.57697	−	14.8696i	−0.227151	−	0.737966i
$407$	−20.6731	+	25.1903i	−1.02473	+	1.24863i
$408$	−17.5310	+	1.94357i	−0.867914	+	0.0962212i
$409$	3.08714	−	31.3443i	0.152649	−	1.54987i	−0.548067	−	0.836434i	$-0.684636\pi$
$409$	3.08714	−	31.3443i	0.152649	−	1.54987i	0.700717	−	0.713440i	$-0.252864\pi$
$410$	−19.5013	−	28.9295i	−0.963099	−	1.42873i
$411$	−51.1519	−	24.1931i	−2.52314	−	1.19336i
$412$	−11.0865	−	7.27759i	−0.546190	−	0.358541i
$413$	−1.13577	−	4.53423i	−0.0558874	−	0.223115i
$414$	−2.03107	+	4.34005i	−0.0998215	+	0.213302i
$415$	−3.16457	+	7.63995i	−0.155343	+	0.375030i
$416$	−10.2310	−	23.3414i	−0.501615	−	1.14441i
$417$	−4.10412	−	9.90821i	−0.200979	−	0.485207i
$418$	0.423649	+	0.0190803i	0.0207213	+	0.000933249i
$419$	12.3384	−	20.5855i	0.602773	−	1.00567i	−0.393493	−	0.919328i	$-0.628734\pi$
$419$	12.3384	−	20.5855i	0.602773	−	1.00567i	0.996266	−	0.0863379i	$-0.0275165\pi$
$420$	−23.5126	−	55.4797i	−1.14730	−	2.70713i
$421$	6.05918	−	2.16801i	0.295306	−	0.105662i	−0.185068	−	0.982726i	$-0.559251\pi$
$421$	6.05918	−	2.16801i	0.295306	−	0.105662i	0.480375	+	0.877063i	$0.340501\pi$
$422$	−3.52045	−	17.3287i	−0.171373	−	0.843548i
$423$	−2.00261	+	1.64350i	−0.0973704	+	0.0799098i
$424$	−25.9280	−	4.82828i	−1.25917	−	0.234482i
$425$	−2.47033	−	25.0817i	−0.119828	−	1.21664i
$426$	5.16962	+	6.24705i	0.250469	+	0.302671i
$427$	1.62658	+	10.9655i	0.0787156	+	0.530657i
$428$	−24.8336	+	11.9944i	−1.20038	+	0.579769i
$429$	14.5536	−	40.6746i	0.702655	−	1.96379i
$430$	−16.5059	−	22.0669i	−0.795984	−	1.06416i
$431$	27.0182	+	18.0530i	1.30142	+	0.869580i	0.996565	−	0.0828189i	$-0.0263923\pi$
$431$	27.0182	+	18.0530i	1.30142	+	0.869580i	0.304854	+	0.952399i	$0.401392\pi$
$432$	32.1403	−	5.30494i	1.54635	−	0.255234i
$433$	−21.1069	+	14.1032i	−1.01433	+	0.677754i	−0.947416	−	0.320004i	$-0.896316\pi$
$433$	−21.1069	+	14.1032i	−1.01433	+	0.677754i	−0.0669150	+	0.997759i	$0.521316\pi$
$434$	−8.22493	+	23.2862i	−0.394809	+	1.11777i
$435$	2.65915	+	54.1282i	0.127496	+	2.59525i
$436$	−1.52866	+	37.3293i	−0.0732098	+	1.78775i
$437$	0.0132408	−	0.0528603i	0.000633395	−	0.00252865i
$438$	−27.5184	+	33.8116i	−1.31488	+	1.61558i
$439$	26.2197	−	14.0147i	1.25140	−	0.668886i	0.293490	−	0.955962i	$-0.405183\pi$
$439$	26.2197	−	14.0147i	1.25140	−	0.668886i	0.957908	+	0.287076i	$0.0926831\pi$
$440$	19.8021	+	32.1391i	0.944028	+	1.53217i
$441$	1.47621	+	4.86642i	0.0702959	+	0.231734i
$442$	−0.0547903	−	13.4297i	−0.00260611	−	0.638788i
$443$	−16.8791	+	15.2984i	−0.801952	+	0.726847i	−0.965701	−	0.259655i	$-0.916391\pi$
$443$	−16.8791	+	15.2984i	−0.801952	+	0.726847i	0.163750	+	0.986502i	$0.447641\pi$
$444$	16.8041	−	57.0679i	0.797488	−	2.70832i
$445$	9.56146	−	7.09126i	0.453257	−	0.336158i
$446$	24.8637	+	18.2834i	1.17733	+	0.865745i
$447$	−23.0253	+	23.0253i	−1.08906	+	1.08906i
$448$	18.4583	+	7.12152i	0.872071	+	0.336460i
$449$	11.4510	+	11.4510i	0.540407	+	0.540407i	0.923648	−	0.383241i	$-0.125192\pi$
$449$	11.4510	+	11.4510i	0.540407	+	0.540407i	−0.383241	+	0.923648i	$0.625192\pi$
$450$	14.6654	+	96.1614i	0.691333	+	4.53309i
$451$	11.5671	+	15.5965i	0.544675	+	0.734410i
$452$	11.0691	−	13.7144i	0.520647	−	0.645072i
$453$	1.05429	+	1.16323i	0.0495351	+	0.0546535i
$454$	18.3758	+	18.2265i	0.862421	+	0.855412i
$455$	43.9036	−	13.3180i	2.05823	−	0.624358i
$456$	−0.725686	+	0.269718i	−0.0339834	+	0.0126307i
$457$	0.149779	+	0.280218i	0.00700638	+	0.0131080i	0.885400	−	0.464830i	$-0.153884\pi$
$457$	0.149779	+	0.280218i	0.00700638	+	0.0131080i	−0.878394	+	0.477938i	$0.841384\pi$
$458$	−11.5260	+	1.18271i	−0.538576	+	0.0552646i
$459$	16.6516	+	4.17101i	0.777229	+	0.194686i
$460$	4.55375	−	1.67139i	0.212320	−	0.0779292i
$461$	−19.7797	+	0.971715i	−0.921233	+	0.0452573i	−0.504155	−	0.863613i	$-0.668196\pi$
$461$	−19.7797	+	0.971715i	−0.921233	+	0.0452573i	−0.417078	+	0.908871i	$0.636946\pi$
$462$	14.4623	+	30.2580i	0.672847	+	1.40773i
$463$	−4.09682	−	6.13132i	−0.190395	−	0.284947i	0.723974	−	0.689827i	$-0.242313\pi$
$463$	−4.09682	−	6.13132i	−0.190395	−	0.284947i	−0.914370	+	0.404880i	$0.867313\pi$
$464$	−13.3775	−	11.7328i	−0.621036	−	0.544682i
$465$	47.7924	−	71.5264i	2.21632	−	3.31696i
$466$	−1.29938	+	9.01289i	−0.0601925	+	0.417514i
$467$	32.8915	+	11.7688i	1.52204	+	0.544594i	0.959385	−	0.282100i	$-0.0910310\pi$
$467$	32.8915	+	11.7688i	1.52204	+	0.544594i	0.562652	+	0.826694i	$0.309781\pi$
$468$	2.96570	+	51.7488i	0.137089	+	2.39209i
$469$	5.94071	−	0.881221i	0.274316	−	0.0406910i
$470$	2.61096	+	0.246406i	0.120435	+	0.0113659i
$471$	−29.8494	+	2.93991i	−1.37539	+	0.135464i
$472$	−3.82618	−	3.73365i	−0.176114	−	0.171855i
$473$	9.72986	+	11.8559i	0.447379	+	0.545133i
$474$	−25.9597	+	39.1967i	−1.19237	+	1.80037i
$475$	−0.372673	−	1.04155i	−0.0170994	−	0.0477896i
$476$	7.43203	+	7.31172i	0.340646	+	0.335132i
$477$	46.0093	+	27.5769i	2.10662	+	1.26266i
$478$	21.6976	−	19.8274i	0.992425	−	0.906884i
$479$	−34.1760	+	14.1562i	−1.56154	+	0.646812i	−0.985357	−	0.170507i	$-0.945460\pi$
$479$	−34.1760	+	14.1562i	−1.56154	+	0.646812i	−0.576186	+	0.817319i	$0.695460\pi$
$480$	−56.1791	−	39.9152i	−2.56421	−	1.82187i
$481$	41.8480	+	17.3340i	1.90811	+	0.790363i
$482$	10.1008	−	3.66066i	0.460077	−	0.166739i
$483$	4.18025	−	1.04710i	0.190208	−	0.0476447i
$484$	0.556613	+	0.818493i	0.0253006	+	0.0372042i
$485$	−5.46172	+	11.5478i	−0.248004	+	0.524360i
$486$	5.84306	+	1.13750i	0.265047	+	0.0515978i
$487$	10.9615	+	1.07961i	0.496711	+	0.0489218i	0.343272	−	0.939236i	$-0.388465\pi$
$487$	10.9615	+	1.07961i	0.496711	+	0.0489218i	0.153440	+	0.988158i	$0.450965\pi$
$488$	8.16246	+	9.70139i	0.369497	+	0.439161i
$489$	12.3240	+	10.1141i	0.557311	+	0.457374i
$490$	2.40821	−	4.55000i	0.108792	−	0.205548i
$491$	2.22065	−	2.99420i	0.100216	−	0.135126i	−0.750253	−	0.661151i	$-0.770068\pi$
$491$	2.22065	−	2.99420i	0.100216	−	0.135126i	0.850469	+	0.526025i	$0.176318\pi$
$492$	−30.5530	−	17.9755i	−1.37744	−	0.810400i
$493$	−4.00907	−	8.47646i	−0.180559	−	0.381760i
$494$	−0.145560	−	0.571211i	−0.00654906	−	0.0257000i
$495$	−14.9787	−	75.3032i	−0.673244	−	3.38463i
$496$	5.96162	+	27.6085i	0.267685	+	1.23966i
$497$	0.935048	−	4.70080i	0.0419426	−	0.210860i
$498$	0.446508	+	8.39029i	0.0200085	+	0.375978i
$499$	−23.9009	+	26.3705i	−1.06995	+	1.18051i	−0.0870811	+	0.996201i	$0.527754\pi$
$499$	−23.9009	+	26.3705i	−1.06995	+	1.18051i	−0.982869	+	0.184307i	$0.940996\pi$
$500$	33.7525	−	46.2948i	1.50946	−	2.07036i
$501$	4.60066	+	7.67574i	0.205542	+	0.342927i
$502$	−6.79311	−	12.5852i	−0.303191	−	0.561707i
$503$	−5.05829	−	1.53441i	−0.225538	−	0.0684162i	0.175493	−	0.984481i	$-0.443848\pi$
$503$	−5.05829	−	1.53441i	−0.225538	−	0.0684162i	−0.401031	+	0.916064i	$0.631348\pi$
$504$	−30.1437	−	26.6560i	−1.34271	−	1.18735i
$505$	−25.0523	−	13.3908i	−1.11481	−	0.595881i
$506$	−2.49003	+	1.04333i	−0.110695	+	0.0463816i
$507$	−21.5611	−	1.05923i	−0.957563	−	0.0470420i
$508$	−9.82108	−	5.14689i	−0.435740	−	0.228356i
$509$	3.47424	−	23.4214i	0.153993	−	1.03814i	−0.765047	−	0.643974i	$-0.777285\pi$
$509$	3.47424	−	23.4214i	0.153993	−	1.03814i	0.919041	−	0.394163i	$-0.128965\pi$
$510$	−18.7971	−	31.0729i	−0.832351	−	1.37593i
$511$	25.7680			1.13991
$512$	22.2455	−	4.13955i	0.983123	−	0.182944i
$513$	0.753455			0.0332658
$514$	13.1047	+	21.6630i	0.578024	+	0.955513i
$515$	4.00645	−	27.0093i	0.176545	−	1.19017i
$516$	−24.8001	−	12.9969i	−1.09176	−	0.572157i
$517$	−1.45787	−	0.0716204i	−0.0641169	−	0.00314986i
$518$	−32.4319	+	13.5890i	−1.42498	+	0.597068i
$519$	29.6949	+	15.8723i	1.30346	+	0.696715i
$520$	34.7595	−	39.3075i	1.52431	−	1.72375i
$521$	21.9254	+	6.65099i	0.960568	+	0.291385i	0.731360	−	0.681992i	$-0.238886\pi$
$521$	21.9254	+	6.65099i	0.960568	+	0.291385i	0.229209	+	0.973377i	$0.426386\pi$
$522$	17.1901	+	31.8471i	0.752389	+	1.39391i
$523$	1.77280	+	2.95773i	0.0775190	+	0.129333i	0.894047	−	0.447973i	$-0.147854\pi$
$523$	1.77280	+	2.95773i	0.0775190	+	0.129333i	−0.816528	+	0.577306i	$0.804104\pi$
$524$	−23.2705	+	31.9177i	−1.01658	+	1.39433i
$525$	58.7485	−	64.8190i	2.56399	−	2.82893i
$526$	0.816295	+	15.3389i	0.0355922	+	0.668808i
$527$	−2.90375	+	14.5981i	−0.126489	+	0.635905i
$528$	32.2351	+	20.7861i	1.40285	+	0.904597i
$529$	−4.41940	−	22.2178i	−0.192148	−	0.965992i
$530$	−13.4089	−	52.6198i	−0.582447	−	2.28566i
$531$	4.64886	+	9.82919i	0.201743	+	0.426550i
$532$	0.394411	+	0.232048i	0.0170999	+	0.0100605i
$533$	16.0782	−	21.6790i	0.696426	−	0.939021i
$534$	5.65806	−	10.6902i	0.244848	−	0.462609i
$535$	−43.8930	−	36.0221i	−1.89766	−	1.55737i
$536$	5.25586	−	4.42213i	0.227019	−	0.191007i
$537$	−14.7954	−	1.45722i	−0.638470	−	0.0628838i
$538$	17.1306	+	3.33490i	0.738554	+	0.143778i
$539$	−1.22503	+	2.59011i	−0.0527658	+	0.111564i
$540$	37.7156	+	55.4604i	1.62302	+	2.38664i
$541$	−3.54947	+	0.889095i	−0.152603	+	0.0382252i	−0.318529	−	0.947913i	$-0.603189\pi$
$541$	−3.54947	+	0.889095i	−0.152603	+	0.0382252i	0.165926	+	0.986138i	$0.446939\pi$
$542$	−35.9430	+	13.0263i	−1.54389	+	0.559527i
$543$	18.6452	+	7.72309i	0.800142	+	0.331430i
$544$	11.6233	+	2.66075i	0.498343	+	0.114079i
$545$	−71.0672	+	29.4370i	−3.04419	+	1.26094i
$546$	34.4119	−	31.4458i	1.47269	−	1.34576i
$547$	−16.6113	−	9.95643i	−0.710248	−	0.425706i	0.112845	−	0.993613i	$-0.464004\pi$
$547$	−16.6113	−	9.95643i	−0.710248	−	0.425706i	−0.823093	+	0.567906i	$0.807754\pi$
$548$	27.2683	+	26.8269i	1.16484	+	1.14599i
$549$	−8.68718	−	24.2790i	−0.370760	−	1.03620i
$550$	−30.2621	+	45.6929i	−1.29038	+	1.94835i
$551$	−0.261094	−	0.318144i	−0.0111230	−	0.0135534i
$552$	3.44217	−	3.52748i	0.146509	−	0.150139i
$553$	27.6552	−	2.72380i	1.17602	−	0.115828i
$554$	1.36206	+	0.128543i	0.0578685	+	0.00546127i
$555$	121.161	−	17.9725i	5.14298	−	0.762889i
$556$	0.414815	+	7.23815i	0.0175921	+	0.306966i
$557$	4.52865	+	1.62038i	0.191885	+	0.0686575i	0.431079	−	0.902314i	$-0.358133\pi$
$557$	4.52865	+	1.62038i	0.191885	+	0.0686575i	−0.239194	+	0.970972i	$0.576883\pi$
$558$	8.19727	−	56.8588i	0.347018	−	2.40702i
$559$	11.8440	−	17.7258i	0.500949	−	0.749723i
$560$	2.66240	+	40.6475i	0.112507	+	1.71767i
$561$	11.2293	+	16.8059i	0.474102	+	0.709544i
$562$	−5.82744	−	12.1921i	−0.245816	−	0.514295i
$563$	1.31762	−	0.0647306i	0.0555311	−	0.00272807i	−0.0212832	−	0.999773i	$-0.506775\pi$
$563$	1.31762	−	0.0647306i	0.0555311	−	0.00272807i	0.0768143	+	0.997045i	$0.475525\pi$
$564$	2.50149	−	0.918139i	0.105332	−	0.0386606i
$565$	35.1993	+	8.81696i	1.48084	+	0.370932i
$566$	30.0358	−	3.08205i	1.26250	−	0.129548i
$567$	7.96849	+	14.9080i	0.334645	+	0.626077i
$568$	−1.90973	−	5.13821i	−0.0801307	−	0.215594i
$569$	−27.0631	+	8.20950i	−1.13454	+	0.344160i	−0.801053	−	0.598593i	$-0.795727\pi$
$569$	−27.0631	+	8.20950i	−1.13454	+	0.344160i	−0.333491	+	0.942753i	$0.608227\pi$
$570$	−1.13171	−	1.12252i	−0.0474022	−	0.0470170i
$571$	3.30934	+	3.65129i	0.138492	+	0.152802i	0.806247	−	0.591578i	$-0.201495\pi$
$571$	3.30934	+	3.65129i	0.138492	+	0.152802i	−0.667756	+	0.744380i	$0.732745\pi$
$572$	−18.3420	+	22.7254i	−0.766917	+	0.950197i
$573$	−27.7670	−	37.4395i	−1.15998	−	1.56406i
$574$	3.15899	+	20.7136i	0.131853	+	0.864567i
$575$	4.97974	+	4.97974i	0.207669	+	0.207669i
$576$	−45.3434	−	7.87086i	−1.88931	−	0.327953i
$577$	−19.5884	+	19.5884i	−0.815476	+	0.815476i	−0.985449	−	0.169972i	$-0.945632\pi$
$577$	−19.5884	+	19.5884i	−0.815476	+	0.815476i	0.169972	+	0.985449i	$0.445632\pi$
$578$	−14.3065	−	10.5202i	−0.595071	−	0.437583i
$579$	−29.7805	+	22.0867i	−1.23763	+	0.917892i
$580$	10.3484	−	35.1440i	0.429695	−	1.45927i
$581$	3.67984	−	3.33521i	0.152665	−	0.138368i
$582$	0.0529525	+	12.9793i	0.00219495	+	0.538007i
$583$	8.77304	+	28.9208i	0.363342	+	1.19778i
$584$	25.0906	−	15.4593i	1.03826	−	0.639708i
$585$	−94.1200	+	50.3082i	−3.89138	+	2.07999i
$586$	−2.36395	+	2.90456i	−0.0976537	+	0.119986i
$587$	6.65489	−	26.5678i	0.274677	−	1.09657i	−0.662877	−	0.748729i	$-0.730665\pi$
$587$	6.65489	−	26.5678i	0.274677	−	1.09657i	0.937553	−	0.347842i	$-0.113085\pi$
$588$	0.214019	−	5.22627i	0.00882601	−	0.215528i
$589$	0.0320558	+	0.652510i	0.00132084	+	0.0268862i
$590$	3.66583	−	10.3786i	0.150920	−	0.427281i
$591$	0.280611	−	0.187499i	0.0115428	−	0.00771266i
$592$	−23.4268	+	32.6891i	−0.962835	+	1.34351i
$593$	−34.5092	−	23.0583i	−1.41712	−	0.946892i	−0.999263	−	0.0383809i	$-0.987780\pi$
$593$	−34.5092	−	23.0583i	−1.41712	−	0.946892i	−0.417861	−	0.908511i	$-0.637220\pi$
$594$	−22.3587	−	29.8916i	−0.917389	−	1.22647i
$595$	−7.23161	+	20.2110i	−0.296467	+	0.828570i
$596$	19.8221	−	9.57383i	0.811943	−	0.392159i
$597$	9.87725	+	66.5870i	0.404249	+	2.72523i
$598$	2.39248	+	2.89112i	0.0978359	+	0.118227i
$599$	2.10097	+	21.3315i	0.0858435	+	0.871583i	0.937616	+	0.347672i	$0.113028\pi$
$599$	2.10097	+	21.3315i	0.0858435	+	0.871583i	−0.851773	+	0.523911i	$0.824472\pi$
$600$	18.3166	−	98.3607i	0.747774	−	4.01556i
$601$	13.9593	−	11.4561i	0.569411	−	0.467304i	−0.305092	−	0.952323i	$-0.598687\pi$
$601$	13.9593	−	11.4561i	0.569411	−	0.467304i	0.874504	+	0.485019i	$0.161187\pi$
$602$	3.29493	+	16.2186i	0.134291	+	0.661022i
$603$	−13.1535	+	4.70640i	−0.535652	+	0.191659i
$604$	−0.414128	−	0.977164i	−0.0168506	−	0.0397603i
$605$	−1.04772	+	1.74802i	−0.0425960	+	0.0710672i
$606$	−28.8333	−	1.29860i	−1.17127	−	0.0527518i
$607$	−0.618383	−	1.49291i	−0.0250994	−	0.0605953i	0.910833	−	0.412775i	$-0.135441\pi$
$607$	−0.618383	−	1.49291i	−0.0250994	−	0.0605953i	−0.935932	+	0.352180i	$0.885441\pi$
$608$	0.523258	−	0.0106753i	0.0212209	−	0.000432941i
$609$	12.4552	−	30.0695i	0.504710	−	1.21848i
$610$	−11.0645	+	23.6430i	−0.447988	+	0.957276i
$611$	0.492975	+	1.96807i	0.0199436	+	0.0796194i
$612$	−20.2739	−	13.3086i	−0.819524	−	0.537968i
$613$	−24.3401	−	11.5120i	−0.983086	−	0.464965i	−0.132718	−	0.991154i	$-0.542371\pi$
$613$	−24.3401	−	11.5120i	−0.983086	−	0.464965i	−0.850368	+	0.526189i	$0.823621\pi$
$614$	−21.0956	−	31.2946i	−0.851347	−	1.26295i
$615$	7.15387	−	72.6345i	0.288472	−	2.92891i
$616$	−2.49816	−	22.5333i	−0.100654	−	0.907894i
$617$	10.1945	−	12.4220i	0.410414	−	0.500091i	−0.526245	−	0.850333i	$-0.676401\pi$
$617$	10.1945	−	12.4220i	0.410414	−	0.500091i	0.936659	+	0.350242i	$0.113901\pi$
$618$	−8.16164	−	26.5154i	−0.328309	−	1.06661i
$619$	6.29877	+	4.67148i	0.253169	+	0.187763i	0.714839	−	0.699289i	$-0.246500\pi$
$619$	6.29877	+	4.67148i	0.253169	+	0.187763i	−0.461671	+	0.887051i	$0.652750\pi$
$620$	−46.4255	+	35.0222i	−1.86449	+	1.40653i
$621$	−4.33613	+	2.05084i	−0.174003	+	0.0822972i
$622$	−21.2714	+	35.8199i	−0.852907	+	1.43625i
$623$	−7.01187	+	1.39475i	−0.280925	+	0.0558794i
$624$	14.6417	−	51.2642i	0.586137	−	2.05221i
$625$	57.0599	+	11.3499i	2.28240	+	0.453997i
$626$	−12.5044	−	11.2408i	−0.499778	−	0.449272i
$627$	0.657342	+	0.595780i	0.0262517	+	0.0237932i
$628$	19.7083	+	4.76612i	0.786447	+	0.190189i
$629$	−18.1778	+	10.8953i	−0.724796	+	0.434426i
$630$	23.7262	−	79.3792i	0.945275	−	3.16254i
$631$	−11.9511	+	39.3975i	−0.475766	+	1.56839i	0.310544	+	0.950559i	$0.399489\pi$
$631$	−11.9511	+	39.3975i	−0.475766	+	1.56839i	−0.786310	+	0.617832i	$0.788011\pi$
$632$	25.2941	−	19.2437i	1.00614	−	0.765472i
$633$	17.4377	−	32.6237i	0.693088	−	1.29668i
$634$	−2.56590	+	6.26683i	−0.101905	+	0.248888i
$635$	1.12018	−	22.8018i	0.0444531	−	0.904864i
$636$	−35.3482	−	42.3623i	−1.40165	−	1.67977i
$637$	3.93950	+	0.584369i	0.156089	+	0.0231536i
$638$	−4.87368	+	19.7992i	−0.192951	+	0.783858i
$639$			11.1490i			0.441046i
$640$	26.9785	+	37.9817i	1.06642	+	1.50136i
$641$		−	10.5849i		−	0.418078i	−0.977907	−	0.209039i	$-0.932966\pi$
$641$		−	10.5849i		−	0.418078i	0.977907	−	0.209039i	$-0.0670335\pi$
$642$	−56.0211	−	13.7899i	−2.21098	−	0.544244i
$643$	0.491111	+	0.0728494i	0.0193675	+	0.00287290i	0.156407	−	0.987693i	$-0.450009\pi$
$643$	0.491111	+	0.0728494i	0.0193675	+	0.00287290i	−0.137040	+	0.990566i	$0.543759\pi$
$644$	−2.90145	−	0.261882i	−0.114333	−	0.0103196i
$645$	2.82868	−	57.5791i	0.111379	−	2.26717i
$646$	0.255232	+	0.104503i	0.0100420	+	0.00411160i
$647$	11.4082	−	21.3432i	0.448502	−	0.839089i	−0.551486	−	0.834184i	$-0.685939\pi$
$647$	11.4082	−	21.3432i	0.448502	−	0.839089i	0.999988	−	0.00490448i	$-0.00156115\pi$
$648$	16.7029	+	9.73549i	0.656153	+	0.382446i
$649$	−1.77831	+	5.86231i	−0.0698049	+	0.230116i
$650$	72.9885	+	21.8160i	2.86284	+	0.855695i
$651$	−44.3132	+	26.5603i	−1.73677	+	1.04098i
$652$	−5.61609	−	9.19883i	−0.219943	−	0.360254i
$653$	18.4495	+	16.7217i	0.721986	+	0.654370i	0.947458	−	0.319879i	$-0.103642\pi$
$653$	18.4495	+	16.7217i	0.721986	+	0.654370i	−0.225472	+	0.974250i	$0.572392\pi$
$654$	−52.2506	+	58.1244i	−2.04316	+	2.27284i
$655$	−79.7648	−	15.8662i	−3.11667	−	0.619944i
$656$	15.5029	+	18.2739i	0.605285	+	0.713474i
$657$	−58.7883	+	11.6937i	−2.29355	+	0.456215i
$658$	−1.35424	−	0.804211i	−0.0527939	−	0.0313514i
$659$	17.0147	−	8.04737i	0.662800	−	0.313481i	−0.0663888	−	0.997794i	$-0.521148\pi$
$659$	17.0147	−	8.04737i	0.662800	−	0.313481i	0.729188	+	0.684313i	$0.239898\pi$
$660$	−10.9497	+	78.2086i	−0.426218	+	3.04427i
$661$	−38.5011	−	28.5544i	−1.49752	−	1.11064i	−0.964351	−	0.264626i	$-0.914752\pi$
$661$	−38.5011	−	28.5544i	−1.49752	−	1.11064i	−0.533168	−	0.846010i	$-0.678998\pi$
$662$	31.7831	−	9.78306i	1.23528	−	0.380229i
$663$	17.8232	−	21.7176i	0.692195	−	0.843442i
$664$	1.58218	−	5.45522i	0.0614004	−	0.211704i
$665$	−0.0923499	+	0.937645i	−0.00358118	+	0.0363603i
$666$	67.8250	−	45.7205i	2.62816	−	1.77164i
$667$	2.36855	+	1.12024i	0.0917108	+	0.0433760i
$668$	−1.22860	−	5.92357i	−0.0475360	−	0.229190i
$669$	15.6876	+	62.6283i	0.606516	+	2.42135i
$670$	12.8089	+	5.99434i	0.494852	+	0.231582i
$671$	5.55981	−	13.4226i	0.214634	−	0.518173i
$672$	20.2508	+	36.0958i	0.781193	+	1.39243i
$673$	−5.91019	−	14.2685i	−0.227821	−	0.550009i	0.768090	−	0.640341i	$-0.221207\pi$
$673$	−5.91019	−	14.2685i	−0.227821	−	0.550009i	−0.995912	+	0.0903322i	$0.971207\pi$
$674$	1.83018	−	40.6363i	0.0704958	−	1.56525i
$675$	−50.0593	+	83.5188i	−1.92678	+	3.21464i
$676$	13.5276	+	5.47443i	0.520292	+	0.210555i
$677$	24.6800	−	8.83064i	0.948529	−	0.339389i	0.183234	−	0.983069i	$-0.441343\pi$
$677$	24.6800	−	8.83064i	0.948529	−	0.339389i	0.765294	+	0.643680i	$0.222593\pi$
$678$	36.1311	−	7.34029i	1.38761	−	0.281902i
$679$	5.93044	−	4.86698i	0.227589	−	0.186778i
$680$	5.08389	+	24.0183i	0.194958	+	0.921058i
$681$	5.30707	+	53.8836i	0.203367	+	2.06482i
$682$	24.9356	−	20.6349i	0.954833	−	0.790152i
$683$	−4.98021	−	33.5738i	−0.190562	−	1.28467i	−0.847530	−	0.530748i	$-0.821911\pi$
$683$	−4.98021	−	33.5738i	−0.190562	−	1.28467i	0.656967	−	0.753919i	$-0.271839\pi$
$684$	−1.00513	−	0.350418i	−0.0384322	−	0.0133986i
$685$	−26.5330	+	74.1547i	−1.01377	+	2.83331i
$686$	−22.0802	+	16.5159i	−0.843027	+	0.630579i
$687$	−20.1538	−	13.4663i	−0.768914	−	0.513772i
$688$	12.9385	+	13.8155i	0.493277	+	0.526712i
$689$	34.9289	−	23.3387i	1.33068	−	0.889135i
$690$	9.56839	+	3.37965i	0.364262	+	0.128661i
$691$	−1.75995	−	35.8247i	−0.0669518	−	1.36283i	−0.763724	−	0.645543i	$-0.776631\pi$
$691$	−1.75995	−	35.8247i	−0.0669518	−	1.36283i	0.696773	−	0.717292i	$-0.254619\pi$
$692$	−15.4232	−	16.7403i	−0.586301	−	0.636371i
$693$	−11.2040	+	44.7290i	−0.425606	+	1.69911i
$694$	7.82923	+	6.37201i	0.297193	+	0.241878i
$695$	−13.1646	+	7.03665i	−0.499363	+	0.266915i
$696$	−5.91213	−	36.7515i	−0.224099	−	1.39306i
$697$	3.66579	+	12.0845i	0.138852	+	0.457732i
$698$	45.7709	−	0.186735i	1.73246	−	0.00706803i
$699$	−14.1148	+	12.7929i	−0.533872	+	0.483874i
$700$	−51.9265	+	28.3024i	−1.96264	+	1.06973i
$701$	8.96581	−	6.64950i	0.338634	−	0.251148i	−0.412996	−	0.910733i	$-0.635518\pi$
$701$	8.96581	−	6.64950i	0.338634	−	0.251148i	0.751630	+	0.659585i	$0.229268\pi$
$702$	−30.7384	+	41.8013i	−1.16015	+	1.57769i
$703$	−0.657754	+	0.657754i	−0.0248077	+	0.0248077i
$704$	−15.9512	−	20.4423i	−0.601182	−	0.770447i
$705$	3.87942	+	3.87942i	0.146107	+	0.146107i
$706$	27.6020	−	4.20952i	1.03881	−	0.158428i
$707$	10.1627	+	13.7028i	0.382208	+	0.515348i
$708$	−1.18697	−	11.1205i	−0.0446090	−	0.417934i
$709$	−3.85250	−	4.25058i	−0.144684	−	0.159634i	0.664298	−	0.747468i	$-0.268731\pi$
$709$	−3.85250	−	4.25058i	−0.144684	−	0.159634i	−0.808981	+	0.587834i	$0.799981\pi$
$710$	7.94795	−	8.01307i	0.298281	−	0.300725i
$711$	−61.8578	+	18.7643i	−2.31985	+	0.703718i
$712$	−5.99079	+	5.56479i	−0.224514	+	0.208549i
$713$	−1.96056	−	3.66794i	−0.0734234	−	0.137365i
$714$	2.22632	+	21.6964i	0.0833181	+	0.811969i
$715$	−58.3267	−	14.6101i	−2.18130	−	0.546386i
$716$	9.12022	+	4.22283i	0.340839	+	0.157814i
$717$	61.4139	−	3.01707i	2.29354	−	0.112675i
$718$	4.74948	−	2.27009i	0.177249	−	0.0847191i
$719$	16.8415	+	25.2050i	0.628080	+	0.939989i	0.999932	+	0.0116963i	$0.00372312\pi$
$719$	16.8415	+	25.2050i	0.628080	+	0.939989i	−0.371851	+	0.928292i	$0.621277\pi$
$720$	−24.5203	−	91.5269i	−0.913817	−	3.41101i
$721$	−9.11049	+	13.6348i	−0.339292	+	0.507787i
$722$	−26.5831	−	3.83246i	−0.989321	−	0.142629i
$723$	21.1616	+	7.57173i	0.787007	+	0.281596i
$724$	−10.1832	−	9.07932i	−0.378457	−	0.337430i
$725$	52.6126	−	7.80434i	1.95398	−	0.289846i
$726$	−0.194553	+	2.06152i	−0.00722055	+	0.0765102i
$727$	43.0172	−	4.23683i	1.59542	−	0.157135i	0.739106	−	0.673590i	$-0.235248\pi$
$727$	43.0172	−	4.23683i	1.59542	−	0.157135i	0.856315	+	0.516454i	$0.172748\pi$
$728$	−28.9645	+	12.4150i	−1.07350	+	0.460129i
$729$	20.9088	+	25.4775i	0.774401	+	0.943611i
$730$	50.5890	+	33.5048i	1.87238	+	1.24007i
$731$	3.36031	+	9.39145i	0.124286	+	0.347355i
$732$	0.216411	+	26.5220i	0.00799880	+	0.980282i
$733$	−25.8952	−	15.5210i	−0.956461	−	0.573281i	−0.0514531	−	0.998675i	$-0.516385\pi$
$733$	−25.8952	−	15.5210i	−0.956461	−	0.573281i	−0.905008	+	0.425395i	$0.860135\pi$
$734$	−17.5188	−	19.1713i	−0.646632	−	0.707625i
$735$	9.94971	−	4.12130i	0.367001	−	0.152017i
$736$	−2.98229	+	1.48570i	−0.109929	+	0.0547635i
$737$	−7.27187	−	3.01211i	−0.267863	−	0.110952i
$738$	−16.6070	−	45.8233i	−0.611314	−	1.68678i
$739$	−20.9406	+	5.24534i	−0.770311	+	0.192953i	−0.608161	−	0.793813i	$-0.708093\pi$
$739$	−20.9406	+	5.24534i	−0.770311	+	0.192953i	−0.162149	+	0.986766i	$0.551843\pi$
$740$	−81.3412	−	15.4909i	−2.99016	−	0.569457i
$741$	0.527237	−	1.11475i	0.0193685	−	0.0409513i
$742$	−6.23170	+	32.0109i	−0.228773	+	1.17516i
$743$	24.5039	+	2.41342i	0.898959	+	0.0885398i	0.536930	−	0.843627i	$-0.319584\pi$
$743$	24.5039	+	2.41342i	0.898959	+	0.0885398i	0.362029	+	0.932167i	$0.382084\pi$
$744$	−27.2137	+	52.4474i	−0.997704	+	1.92282i
$745$	35.0352	+	28.7526i	1.28359	+	1.05341i
$746$	6.55499	+	3.46941i	0.239995	+	0.127024i
$747$	−6.88181	+	9.27905i	−0.251792	+	0.339503i
$748$	−3.42809	−	13.2269i	−0.125343	−	0.483622i
$749$	14.5803	+	30.8274i	0.532752	+	1.12641i
$750$	116.143	−	29.5963i	4.24093	−	1.08070i
$751$	−2.37456	−	11.9377i	−0.0866488	−	0.435613i	−0.999619	−	0.0275875i	$-0.991218\pi$
$751$	−2.37456	−	11.9377i	−0.0866488	−	0.435613i	0.912971	−	0.408025i	$-0.133782\pi$
$752$	−1.80112	+	0.0293952i	−0.0656802	+	0.00107193i
$753$	5.83680	−	29.3436i	0.212705	−	1.06934i
$754$	28.3022	−	1.50617i	1.03071	−	0.0548514i
$755$	1.46744	−	1.61907i	0.0534057	−	0.0589241i
$756$	−6.23521	−	39.7945i	−0.226772	−	1.44731i
$757$	−10.4092	−	17.3667i	−0.378329	−	0.631204i	0.608390	−	0.793638i	$-0.291816\pi$
$757$	−10.4092	−	17.3667i	−0.378329	−	0.631204i	−0.986719	+	0.162434i	$0.948066\pi$
$758$	−44.8787	+	24.2241i	−1.63007	+	0.879859i
$759$	−5.40466	−	1.63948i	−0.196177	−	0.0595095i
$760$	0.472609	+	0.968401i	0.0171433	+	0.0351276i
$761$	5.74291	+	3.06965i	0.208180	+	0.111275i	0.572192	−	0.820120i	$-0.306093\pi$
$761$	5.74291	+	3.06965i	0.208180	+	0.111275i	−0.364012	+	0.931394i	$0.618593\pi$
$762$	−8.96400	−	21.3937i	−0.324731	−	0.775013i
$763$	46.1418	+	2.26680i	1.67044	+	0.0820637i
$764$	9.39289	+	30.0785i	0.339823	+	1.08820i
$765$	7.32663	−	49.3921i	0.264895	−	1.78578i
$766$	16.4577	−	9.95584i	0.594640	−	0.359719i
$767$	8.51523			0.307467
$768$	41.3738	+	22.9976i	1.49295	+	0.829856i
$769$	51.7425			1.86588			0.932940	−	0.360031i	$-0.117234\pi$
$769$	51.7425			1.86588			0.932940	+	0.360031i	$0.117234\pi$
$770$	39.9394	−	24.1608i	1.43931	−	0.870693i
$771$	−7.77161	+	52.3920i	−0.279888	+	1.88685i
$772$	23.9253	−	7.47138i	0.861090	−	0.268901i
$773$	19.6146	+	0.963603i	0.705488	+	0.0346584i	0.398650	−	0.917103i	$-0.369479\pi$
$773$	19.6146	+	0.963603i	0.705488	+	0.0346584i	0.306838	+	0.951762i	$0.400729\pi$
$774$	−14.8774	−	35.5067i	−0.534756	−	1.27626i
$775$	−74.4591	−	39.7992i	−2.67465	−	1.42963i
$776$	2.85464	−	8.29695i	0.102476	−	0.297843i
$777$	−70.3941	−	21.3538i	−2.52537	−	0.766064i
$778$	−7.66949	+	4.13975i	−0.274965	+	0.148417i
$779$	0.284958	+	0.475423i	0.0102097	+	0.0170338i
$780$	108.447	−	16.9920i	3.88301	−	0.608411i
$781$	−4.21841	+	4.65430i	−0.150946	+	0.166544i
$782$	−1.75331	+	0.0933062i	−0.0626981	+	0.00333662i
$783$	−7.06755	+	35.5310i	−0.252574	+	1.26977i
$784$	−1.29969	+	3.28850i	−0.0464174	+	0.117447i
$785$	8.14454	+	40.9454i	0.290691	+	1.46140i
$786$	−80.0740	+	20.4050i	−2.85614	+	0.727823i
$787$	20.4686	+	43.2772i	0.729626	+	1.54266i	0.836240	+	0.548364i	$0.184749\pi$
$787$	20.4686	+	43.2772i	0.729626	+	1.54266i	−0.106614	+	0.994300i	$0.534001\pi$
$788$	−0.220852	+	0.0572396i	−0.00786752	+	0.00203908i
$789$	−19.1422	+	25.8102i	−0.681479	+	0.918868i
$790$	57.8357	+	30.6111i	2.05770	+	1.08910i
$791$	−16.8460	−	13.8252i	−0.598975	−	0.491566i
$792$	15.9252	+	50.2750i	0.565878	+	1.78644i
$793$	−20.0972	−	1.97941i	−0.713674	−	0.0702908i
$794$	−8.96516	+	46.0520i	−0.318161	+	1.63432i
$795$	48.5689	−	102.690i	1.72256	−	3.64205i
$796$	8.51345	−	44.7032i	0.301751	−	1.58446i
$797$	18.0946	−	4.53246i	0.640943	−	0.160548i	0.0911345	−	0.995839i	$-0.470951\pi$
$797$	18.0946	−	4.53246i	0.640943	−	0.160548i	0.549809	+	0.835291i	$0.314701\pi$
$798$	0.326181	+	0.900022i	0.0115467	+	0.0318604i
$799$	−0.877002	−	0.363266i	−0.0310261	−	0.0128514i
$800$	−33.5817	+	58.7113i	−1.18729	+	2.07576i
$801$	15.3643	−	6.36409i	0.542870	−	0.224864i
$802$	−19.5534	−	21.3977i	−0.690453	−	0.755580i
$803$	−28.9665	−	17.3619i	−1.02221	−	0.612687i
$804$	14.3687	−	0.117244i	0.506744	−	0.00413488i
$805$	−2.02071	−	5.64751i	−0.0712207	−	0.199049i
$806$	−37.5087	−	24.8418i	−1.32119	−	0.875013i
$807$	23.1614	+	28.2222i	0.815320	+	0.993470i
$808$	18.1164	+	7.24560i	0.637334	+	0.254899i
$809$	−55.5567	+	5.47186i	−1.95327	+	0.192380i	−0.995471	−	0.0950609i	$-0.969695\pi$
$809$	−55.5567	+	5.47186i	−1.95327	+	0.192380i	−0.957798	+	0.287441i	$0.907195\pi$
$810$	−3.73995	+	39.6292i	−0.131409	+	1.39243i
$811$	−37.7745	+	5.60332i	−1.32644	+	0.196759i	−0.772085	−	0.635520i	$-0.780786\pi$
$811$	−37.7745	+	5.60332i	−1.32644	+	0.196759i	−0.554357	+	0.832279i	$0.687036\pi$
$812$	−14.6424	+	16.4227i	−0.513848	+	0.576325i
$813$	−75.3023	−	26.9436i	−2.64097	−	0.944953i
$814$	45.6137	+	6.57608i	1.59876	+	0.230491i
$815$	12.3284	−	18.4507i	0.431843	−	0.646299i
$816$	15.1844	+	19.7904i	0.531559	+	0.692804i
$817$	0.243231	+	0.364020i	0.00850956	+	0.0127355i
$818$	−40.1874	+	19.2083i	−1.40512	+	0.671601i
$819$	64.0166	−	3.14493i	2.23692	−	0.109893i
$820$	−20.7309	+	44.7734i	−0.723955	+	1.56356i
$821$	−2.93766	−	0.735845i	−0.102525	−	0.0256812i	0.191378	−	0.981516i	$-0.438704\pi$
$821$	−2.93766	−	0.735845i	−0.102525	−	0.0256812i	−0.293903	+	0.955835i	$0.594954\pi$
$822$	8.16844	+	79.6048i	0.284907	+	2.77654i
$823$	−17.4239	−	32.5978i	−0.607358	−	1.13629i	−0.978214	−	0.207597i	$-0.933436\pi$
$823$	−17.4239	−	32.5978i	−0.607358	−	1.13629i	0.370856	−	0.928690i	$-0.379064\pi$
$824$	−0.690926	+	18.7421i	−0.0240695	+	0.652914i
$825$	−109.714	+	33.2815i	−3.81977	+	1.15871i
$826$	−4.65520	+	4.69334i	−0.161975	+	0.163302i
$827$	8.81285	+	9.72348i	0.306453	+	0.338119i	0.874633	−	0.484786i	$-0.161102\pi$
$827$	8.81285	+	9.72348i	0.306453	+	0.338119i	−0.568180	+	0.822904i	$0.692352\pi$
$828$	6.73834	−	0.719230i	0.234174	−	0.0249950i
$829$	6.52350	+	8.79593i	0.226571	+	0.305495i	0.901835	−	0.432081i	$-0.142220\pi$
$829$	6.52350	+	8.79593i	0.226571	+	0.305495i	−0.675264	+	0.737576i	$0.735970\pi$
$830$	11.5611	−	1.76315i	0.401290	−	0.0612000i
$831$	2.02378	+	2.02378i	0.0702041	+	0.0702041i
$832$	−20.7549	+	29.4656i	−0.719546	+	1.02154i
$833$	−1.31760	+	1.31760i	−0.0456522	+	0.0456522i
$834$	−8.98510	+	12.2189i	−0.311129	+	0.423105i
$835$	10.0045	−	7.41988i	0.346222	−	0.256775i
$836$	−0.287021	−	0.526597i	−0.00992681	−	0.0182127i
$837$	42.6084	−	38.6180i	1.47276	−	1.33483i
$838$	−33.9408	+	0.138471i	−1.17247	+	0.00478340i
$839$	7.66734	+	25.2758i	0.264706	+	0.872619i	0.984039	+	0.177953i	$0.0569476\pi$
$839$	7.66734	+	25.2758i	0.264706	+	0.872619i	−0.719333	+	0.694665i	$0.755552\pi$
$840$	−49.9213	+	69.0619i	−1.72245	+	2.38286i
$841$	−8.12376	+	4.34224i	−0.280130	+	0.149732i
$842$	−7.05865	−	5.74485i	−0.243257	−	0.197981i
$843$	6.86887	−	27.4221i	0.236577	−	0.944467i
$844$	−18.3914	+	16.9444i	−0.633058	+	0.583249i
$845$	1.47431	+	30.0103i	0.0507179	+	1.03239i
$846$	3.45460	+	1.22020i	0.118771	+	0.0419513i
$847$	1.01767	−	0.679986i	0.0349676	−	0.0233646i
$848$	13.1367	+	34.9080i	0.451117	+	1.19875i
$849$	52.5189	+	35.0920i	1.80244	+	1.20436i
$850$	−28.5414	+	21.3488i	−0.978963	+	0.732258i
$851$	1.99502	−	5.57572i	0.0683886	−	0.191133i
$852$	3.77502	−	10.8282i	0.129330	−	0.370969i
$853$	0.820811	+	5.53346i	0.0281040	+	0.189462i	0.998682	−	0.0513251i	$-0.0163445\pi$
$853$	0.820811	+	5.53346i	0.0281040	+	0.189462i	−0.970578	+	0.240787i	$0.922594\pi$
$854$	12.0780	−	9.99488i	0.413300	−	0.342018i
$855$	−0.214819	−	2.18110i	−0.00734666	−	0.0745919i
$856$	32.6916	+	21.2698i	1.11738	+	0.726986i
$857$	−9.82124	+	8.06009i	−0.335487	+	0.275327i	−0.787020	−	0.616927i	$-0.788377\pi$
$857$	−9.82124	+	8.06009i	−0.335487	+	0.275327i	0.451533	+	0.892254i	$0.350877\pi$
$858$	−59.8708	+	12.1632i	−2.04396	+	0.415244i
$859$	4.47804	−	1.60227i	0.152789	−	0.0546687i	−0.259385	−	0.965774i	$-0.583520\pi$
$859$	4.47804	−	1.60227i	0.152789	−	0.0546687i	0.412173	+	0.911105i	$0.364770\pi$
$860$	−14.6195	+	36.1255i	−0.498521	+	1.23187i
$861$	−22.5348	+	37.5970i	−0.767983	+	1.28130i
$862$	2.06759	−	45.9076i	0.0704223	−	1.56362i
$863$	3.71221	+	8.96207i	0.126365	+	0.305072i	0.974383	−	0.224895i	$-0.0722040\pi$
$863$	3.71221	+	8.96207i	0.126365	+	0.305072i	−0.848018	+	0.529968i	$0.822204\pi$
$864$	−29.9456	−	35.0076i	−1.01877	−	1.19098i
$865$	17.9346	−	43.2979i	0.609794	−	1.47217i
$866$	32.5154	+	15.2166i	1.10492	+	0.517082i
$867$	−9.02658	−	36.0361i	−0.306559	−	1.22385i
$868$	34.1977	−	7.09290i	1.16075	−	0.240749i
$869$	−32.9232	−	15.5715i	−1.11684	−	0.528228i
$870$	63.5506	−	42.8392i	2.15457	−	1.45238i
$871$	−1.07237	+	10.8880i	−0.0363359	+	0.368925i
$872$	46.2888	−	25.4751i	1.56754	−	0.862696i
$873$	−11.3213	+	13.7950i	−0.383168	+	0.466892i
$874$	−0.0736551	+	0.0226716i	−0.00249142	+	0.000766878i
$875$	−56.9023	−	42.2016i	−1.92365	−	1.42667i
$876$	61.0565	+	8.54833i	2.06291	+	0.288821i
$877$	18.0405	−	8.53251i	0.609184	−	0.288122i	−0.0979621	−	0.995190i	$-0.531232\pi$
$877$	18.0405	−	8.53251i	0.609184	−	0.288122i	0.707146	+	0.707068i	$0.249982\pi$
$878$	−36.1510	−	21.4681i	−1.22004	−	0.724512i
$879$	−7.68381	+	1.52840i	−0.259168	+	0.0515518i
$880$	24.3945	−	47.4869i	0.822337	−	1.60078i
$881$	−29.3644	−	5.84094i	−0.989311	−	0.196786i	−0.326194	−	0.945303i	$-0.605766\pi$
$881$	−29.3644	−	5.84094i	−0.989311	−	0.196786i	−0.663116	+	0.748517i	$0.730766\pi$
$882$	4.80796	−	5.34846i	0.161893	−	0.180092i
$883$	2.98793	+	2.70810i	0.100552	+	0.0911348i	0.720287	−	0.693676i	$-0.244010\pi$
$883$	2.98793	+	2.70810i	0.100552	+	0.0911348i	−0.619735	+	0.784811i	$0.712760\pi$
$884$	−16.2104	+	9.89678i	−0.545213	+	0.332865i
$885$	19.7503	−	11.8379i	0.663900	−	0.397926i
$886$	30.8670	+	9.22604i	1.03700	+	0.309955i
$887$	−5.64705	+	18.6158i	−0.189609	+	0.625059i	0.809662	+	0.586896i	$0.199650\pi$
$887$	−5.64705	+	18.6158i	−0.189609	+	0.625059i	−0.999272	+	0.0381623i	$0.987850\pi$
$888$	−81.3547	+	21.4398i	−2.73008	+	0.719472i
$889$	−6.46314	+	12.0917i	−0.216767	+	0.405542i
$890$	−15.5796	−	6.37894i	−0.522229	−	0.213823i
$891$	1.08705	−	22.1275i	0.0364177	−	0.741299i
$892$	3.92350	−	43.4693i	0.131369	−	1.45546i
$893$	−0.0412142	−	0.00611355i	−0.00137918	−	0.000204582i
$894$	44.7157	+	11.0070i	1.49552	+	0.368130i
$895$			20.6930i			0.691690i
$896$	−4.89405	−	27.5481i	−0.163499	−	0.920316i
$897$			7.85047i			0.262120i
$898$	5.47406	−	22.2382i	0.182672	−	0.742098i
$899$	−31.0714	−	4.60900i	−1.03629	−	0.153719i
$900$	105.624	−	88.1352i	3.52079	−	2.93784i
$901$	−0.964418	+	19.6312i	−0.0321294	+	0.654010i
$902$	10.4052	−	25.4132i	0.346456	−	0.846166i
$903$	−16.3207	+	30.5339i	−0.543119	+	1.01610i
$904$	−24.6975	−	3.35514i	−0.821425	−	0.111590i
$905$	8.15408	−	26.8804i	0.271051	−	0.893535i
$906$	0.635818	−	2.12721i	0.0211236	−	0.0706719i
$907$	33.1263	−	19.8552i	1.09994	−	0.659280i	0.155459	−	0.987842i	$-0.450314\pi$
$907$	33.1263	−	19.8552i	1.09994	−	0.659280i	0.944482	+	0.328563i	$0.106564\pi$
$908$	8.60372	−	35.5771i	0.285524	−	1.18067i
$909$	−29.4041	−	26.6504i	−0.975274	−	0.883937i
$910$	−48.2525	−	43.3762i	−1.59955	−	1.43791i
$911$	11.4068	+	2.26895i	0.377923	+	0.0751736i	0.380397	−	0.924823i	$-0.375787\pi$
$911$	11.4068	+	2.26895i	0.377923	+	0.0751736i	−0.00247374	+	0.999997i	$0.500787\pi$
$912$	0.857566	+	0.680673i	0.0283968	+	0.0225394i
$913$	−6.38380	+	1.26982i	−0.211273	+	0.0420248i
$914$	0.229435	−	0.386356i	0.00758905	−	0.0127795i
$915$	−49.3656	+	23.3482i	−1.63198	+	0.771867i
$916$	9.86811	+	13.0812i	0.326052	+	0.432214i
$917$	39.2310	+	29.0957i	1.29552	+	0.960824i
$918$	−7.14179	−	23.2022i	−0.235714	−	0.765785i
$919$	7.76269	−	9.45887i	0.256068	−	0.312019i	−0.629070	−	0.777349i	$-0.716564\pi$
$919$	7.76269	−	9.45887i	0.256068	−	0.312019i	0.885138	+	0.465329i	$0.154064\pi$
$920$	−5.35576	−	4.28675i	−0.176574	−	0.141330i
$921$	7.73873	−	78.5726i	0.255000	−	2.58906i
$922$	15.6544	+	23.2229i	0.515551	+	0.764804i
$923$	7.89296	+	3.73309i	0.259800	+	0.122876i
$924$	26.0269	−	39.6485i	0.856222	−	1.30434i
$925$	−29.2097	−	116.612i	−0.960408	−	3.83416i
$926$	−4.42027	+	9.44539i	−0.145259	+	0.310395i
$927$	14.5975	−	35.2415i	0.479445	−	1.15748i
$928$	−4.40484	+	24.7756i	−0.144596	+	0.813300i
$929$	−5.03285	−	12.1504i	−0.165123	−	0.398641i	0.819561	−	0.572992i	$-0.194217\pi$
$929$	−5.03285	−	12.1504i	−0.165123	−	0.398641i	−0.984684	+	0.174351i	$0.944217\pi$
$930$	−121.533	−	5.47361i	−3.98523	−	0.179487i
$931$	−0.0420471	+	0.0701513i	−0.00137804	+	0.00229912i
$932$	11.8570	−	5.02508i	0.388390	−	0.164602i
$933$	−82.0565	+	29.3603i	−2.68641	+	0.961213i
$934$	−9.83575	−	48.4145i	−0.321836	−	1.58417i
$935$	21.7470	−	17.8473i	0.711202	−	0.583669i
$936$	60.4470	−	41.4684i	1.97577	−	1.35544i
$937$	0.397426	+	4.03513i	0.0129833	+	0.131822i	0.999491	−	0.0318909i	$-0.0101529\pi$
$937$	0.397426	+	4.03513i	0.0129833	+	0.131822i	−0.986508	+	0.163713i	$0.947653\pi$
$938$	−5.41487	−	6.54342i	−0.176802	−	0.213650i
$939$	−5.16121	−	34.7940i	−0.168430	−	1.13546i
$940$	−1.61305	−	3.33973i	−0.0526119	−	0.108930i
$941$	15.6604	−	43.7678i	0.510514	−	1.42679i	−0.359213	−	0.933256i	$-0.616955\pi$
$941$	15.6604	−	43.7678i	0.510514	−	1.42679i	0.869726	−	0.493534i	$-0.164295\pi$
$942$	25.4070	+	33.9668i	0.827804	+	1.10670i
$943$	−2.93399	−	1.96043i	−0.0955438	−	0.0638403i
$944$	−1.71710	+	7.36281i	−0.0558870	+	0.239639i
$945$	68.9566	−	46.0753i	2.24316	−	1.49883i
$946$	7.22382	−	20.4519i	0.234867	−	0.664948i
$947$	0.513532	+	10.4532i	0.0166876	+	0.339683i	0.992593	+	0.121488i	$0.0387667\pi$
$947$	0.513532	+	10.4532i	0.0166876	+	0.339683i	−0.975905	+	0.218195i	$0.929983\pi$
$948$	66.4318	+	2.72043i	2.15760	+	0.0883555i
$949$	−11.4059	+	45.5349i	−0.370251	+	1.47813i
$950$	−0.987519	+	1.21336i	−0.0320393	+	0.0393665i
$951$	−12.4936	+	6.67798i	−0.405133	+	0.216548i
$952$	3.40724	−	14.3452i	0.110429	−	0.464929i
$953$	−1.42292	−	4.69074i	−0.0460929	−	0.151948i	0.930873	−	0.365342i	$-0.119048\pi$
$953$	−1.42292	−	4.69074i	−0.0460929	−	0.151948i	−0.976966	+	0.213394i	$0.931548\pi$
$954$	−0.309488	−	75.8591i	−0.0100200	−	2.45603i
$955$	−48.0719	+	43.5698i	−1.55557	+	1.40989i
$956$	−39.8744	−	11.7413i	−1.28963	−	0.379742i
$957$	−34.2614	+	25.4100i	−1.10751	+	0.821388i
$958$	42.1461	+	30.9920i	1.36168	+	1.00130i
$959$	33.4462	−	33.4462i	1.08003	−	1.08003i
$960$	−7.17600	+	97.1963i	−0.231604	+	3.13700i
$961$	13.3366	+	13.3366i	0.430212	+	0.430212i
$962$	−9.65772	−	63.3260i	−0.311377	−	2.04171i
$963$	−47.2539	−	63.7145i	−1.52274	−	2.05317i
$964$	−11.8232	−	9.54270i	−0.380801	−	0.307350i
$965$	34.6567	+	38.2378i	1.11564	+	1.23092i
$966$	−4.32695	−	4.29179i	−0.139217	−	0.138086i
$967$	−34.0211	+	10.3202i	−1.09404	+	0.331875i	−0.785203	−	0.619239i	$-0.787441\pi$
$967$	−34.0211	+	10.3202i	−1.09404	+	0.331875i	−0.308841	+	0.951114i	$0.599941\pi$
$968$	0.582968	−	1.27265i	0.0187373	−	0.0409046i
$969$	0.271977	+	0.508833i	0.00873716	+	0.0163461i
$970$	17.9712	−	1.84407i	0.577022	−	0.0592096i
$971$	35.5975	+	8.91670i	1.14238	+	0.286151i	0.767578	−	0.640956i	$-0.221462\pi$
$971$	35.5975	+	8.91670i	1.14238	+	0.286151i	0.374799	+	0.927106i	$0.377712\pi$
$972$	−2.90067	−	7.90295i	−0.0930391	−	0.253487i
$973$	8.95405	−	0.439884i	0.287054	−	0.0141020i
$974$	−6.71736	−	14.0540i	−0.215238	−	0.450320i
$975$	88.5381	+	132.507i	2.83549	+	4.24361i
$976$	5.76415	−	16.9782i	0.184506	−	0.543460i
$977$	−27.7521	+	41.5340i	−0.887869	+	1.32879i	0.0559870	+	0.998432i	$0.482169\pi$
$977$	−27.7521	+	41.5340i	−0.887869	+	1.32879i	−0.943856	+	0.330358i	$0.892831\pi$
$978$	3.21726	−	22.3159i	0.102877	−	0.713584i
$979$	8.82200	+	3.15656i	0.281952	+	0.100884i
$980$	−7.26846	+	0.416552i	−0.232182	+	0.0133063i
$981$	−106.299	+	15.7679i	−3.39386	+	0.503431i
$982$	−5.24859	−	0.495329i	−0.167489	−	0.0158066i
$983$	−21.9571	+	2.16258i	−0.700322	+	0.0689757i	−0.441910	−	0.897059i	$-0.645699\pi$
$983$	−21.9571	+	2.16258i	−0.700322	+	0.0689757i	−0.258412	+	0.966035i	$0.583199\pi$
$984$	0.613563	+	50.1282i	0.0195597	+	1.59803i
$985$	−0.298000	−	0.363114i	−0.00949508	−	0.0115698i
$986$	−7.32220	+	11.0558i	−0.233186	+	0.352089i
$987$	−1.11003	−	3.10232i	−0.0353325	−	0.0987479i
$988$	−0.584636	+	0.594256i	−0.0185998	+	0.0189058i
$989$	−2.39062	−	1.43288i	−0.0760174	−	0.0455631i
$990$	−80.1552	+	73.2463i	−2.54750	+	2.32792i
$991$	43.3346	−	17.9498i	1.37657	−	0.570193i	0.433007	−	0.901391i	$-0.357453\pi$
$991$	43.3346	−	17.9498i	1.37657	−	0.570193i	0.943561	+	0.331198i	$0.107453\pi$
$992$	29.0434	−	27.4230i	0.922130	−	0.870683i
$993$	64.2722	+	26.6224i	2.03962	+	0.844837i
$994$	−6.37259	+	2.30952i	−0.202126	+	0.0732535i
$995$	90.8868	−	22.7660i	2.88130	−	0.721729i
$996$	9.82570	−	6.68193i	0.311339	−	0.211725i
$997$	5.65728	−	11.9613i	0.179168	−	0.378818i	−0.794340	−	0.607474i	$-0.792183\pi$
$997$	5.65728	−	11.9613i	0.179168	−	0.378818i	0.973507	+	0.228656i	$0.0734330\pi$
$998$	49.4046	+	9.61782i	1.56387	+	0.304447i
$999$	81.4849	+	8.02556i	2.57807	+	0.253917i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.5.11	✓	992
256.205	even	64	inner	256.2.m.a.205.11	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.5.11	✓	992	1.1	even	1	trivial
256.2.m.a.205.11	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)

\(f(q)\)	\(=\)	\(q+(-0.731994 - 1.21004i) q^{2} +(0.434101 - 2.92647i) q^{3} +(-0.928370 + 1.77148i) q^{4} +(-4.11288 - 0.202053i) q^{5} +(-3.85889 + 1.61688i) q^{6} +(2.18104 + 1.16579i) q^{7} +(2.82311 - 0.173349i) q^{8} +(-5.50497 - 1.66991i) q^{9} +O(q^{10})\)	\(q+(-0.731994 - 1.21004i) q^{2} +(0.434101 - 2.92647i) q^{3} +(-0.928370 + 1.77148i) q^{4} +(-4.11288 - 0.202053i) q^{5} +(-3.85889 + 1.61688i) q^{6} +(2.18104 + 1.16579i) q^{7} +(2.82311 - 0.173349i) q^{8} +(-5.50497 - 1.66991i) q^{9} +(2.76611 + 5.12463i) q^{10} +(-1.66629 - 2.78003i) q^{11} +(4.78117 + 3.48585i) q^{12} +(-3.02549 + 3.33812i) q^{13} +(-0.185861 - 3.49248i) q^{14} +(-2.37671 + 11.9485i) q^{15} +(-2.27626 - 3.28917i) q^{16} +(-0.411225 - 2.06737i) q^{17} +(2.00895 + 7.88357i) q^{18} +(-0.0395570 - 0.0836362i) q^{19} +(4.17621 - 7.09829i) q^{20} +(4.35844 - 5.87668i) q^{21} +(-2.14422 + 4.05123i) q^{22} +(0.455301 + 0.373656i) q^{23} +(0.718213 - 8.33700i) q^{24} +(11.8991 + 1.17195i) q^{25} +(6.25389 + 1.21747i) q^{26} +(-3.48191 + 7.36189i) q^{27} +(-4.08998 + 2.78137i) q^{28} +(4.31512 - 1.08088i) q^{29} +(16.1979 - 5.87034i) q^{30} +(-6.52371 - 2.70221i) q^{31} +(-2.31381 + 5.16201i) q^{32} +(-8.85902 + 3.66953i) q^{33} +(-2.20057 + 2.01090i) q^{34} +(-8.73480 - 5.23544i) q^{35} +(8.06886 - 8.20163i) q^{36} +(-3.38716 - 9.46647i) q^{37} +(-0.0722473 + 0.109087i) q^{38} +(8.45554 + 10.3031i) q^{39} +(-11.6461 + 0.142547i) q^{40} +(-5.96215 + 0.587220i) q^{41} +(-10.3013 - 0.972175i) q^{42} +(-4.68082 + 0.694334i) q^{43} +(6.47169 - 0.370890i) q^{44} +(22.3039 + 7.98046i) q^{45} +(0.118859 - 0.824444i) q^{46} +(0.250196 - 0.374445i) q^{47} +(-10.6138 + 5.23357i) q^{48} +(-0.491127 - 0.735023i) q^{49} +(-7.29193 - 15.2561i) q^{50} +(-6.22861 + 0.305992i) q^{51} +(-3.10462 - 8.45860i) q^{52} +(-9.04507 - 2.26567i) q^{53} +(11.4569 - 1.17562i) q^{54} +(6.29153 + 11.7706i) q^{55} +(6.35940 + 2.91307i) q^{56} +(-0.261931 + 0.0794558i) q^{57} +(-4.46655 - 4.43025i) q^{58} +(-1.26931 - 1.40047i) q^{59} +(-18.9601 - 15.3029i) q^{60} +(2.67022 + 3.60038i) q^{61} +(1.50555 + 9.87192i) q^{62} +(-10.0598 - 10.0598i) q^{63} +(7.93990 - 0.978768i) q^{64} +(13.1180 - 13.1180i) q^{65} +(10.9250 + 8.03366i) q^{66} +(1.95056 - 1.44663i) q^{67} +(4.04406 + 1.19081i) q^{68} +(1.29114 - 1.17022i) q^{69} +(0.0587558 + 14.4017i) q^{70} +(-0.562586 - 1.85460i) q^{71} +(-15.8306 - 3.76007i) q^{72} +(9.18918 - 4.91172i) q^{73} +(-8.97538 + 11.0280i) q^{74} +(8.59508 - 34.3135i) q^{75} +(0.184883 + 0.00757110i) q^{76} +(-0.393304 - 8.00590i) q^{77} +(6.27772 - 17.7733i) q^{78} +(9.34299 - 6.24278i) q^{79} +(8.69739 + 13.9879i) q^{80} +(5.68332 + 3.79747i) q^{81} +(5.07481 + 6.78457i) q^{82} +(0.676540 - 1.89080i) q^{83} +(6.36415 + 13.1766i) q^{84} +(1.27360 + 8.58593i) q^{85} +(4.26650 + 5.15571i) q^{86} +(-1.28997 - 13.0973i) q^{87} +(-5.18603 - 7.55949i) q^{88} +(-2.23466 + 1.83394i) q^{89} +(-6.66967 - 32.8301i) q^{90} +(-10.4903 + 3.75348i) q^{91} +(-1.08461 + 0.459664i) q^{92} +(-10.7399 + 17.9184i) q^{93} +(-0.636233 - 0.0286547i) q^{94} +(0.145794 + 0.351979i) q^{95} +(14.1020 + 9.01212i) q^{96} +(1.18715 - 2.86605i) q^{97} +(-0.529902 + 1.13231i) q^{98} +(4.53044 + 18.0865i) 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

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