LMFDB - Embedded newform 256.2.m.a.101.2

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			101.2
Character	$\chi$	$=$	256.101
Dual form			256.2.m.a.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40949 + 0.115540i) q^{2} +(-2.53419 + 0.634783i) q^{3} +(1.97330 - 0.325703i) q^{4} +(-0.285312 - 0.134943i) q^{5} +(3.49857 - 1.18752i) q^{6} +(0.865145 + 2.85200i) q^{7} +(-2.74371 + 0.687069i) q^{8} +(3.37343 - 1.80313i) q^{9} +O(q^{10})$	\(q+(-1.40949 + 0.115540i) q^{2} +(-2.53419 + 0.634783i) q^{3} +(1.97330 - 0.325703i) q^{4} +(-0.285312 - 0.134943i) q^{5} +(3.49857 - 1.18752i) q^{6} +(0.865145 + 2.85200i) q^{7} +(-2.74371 + 0.687069i) q^{8} +(3.37343 - 1.80313i) q^{9} +(0.417735 + 0.157235i) q^{10} +(-1.76730 + 0.262154i) q^{11} +(-4.79398 + 2.07801i) q^{12} +(0.330990 - 0.925056i) q^{13} +(-1.54893 - 3.91989i) q^{14} +(0.808696 + 0.160860i) q^{15} +(3.78783 - 1.28542i) q^{16} +(-0.771882 + 0.153537i) q^{17} +(-4.54646 + 2.93126i) q^{18} +(-5.55801 - 5.03748i) q^{19} +(-0.606959 - 0.173355i) q^{20} +(-4.00284 - 6.67834i) q^{21} +(2.46069 - 0.573695i) q^{22} +(-6.61818 + 0.651834i) q^{23} +(6.51695 - 3.48283i) q^{24} +(-3.10877 - 3.78805i) q^{25} +(-0.359645 + 1.34210i) q^{26} +(-1.59715 + 1.44757i) q^{27} +(2.63610 + 5.34607i) q^{28} +(-4.99613 - 6.73650i) q^{29} +(-1.15843 - 0.133293i) q^{30} +(5.49781 + 2.27727i) q^{31} +(-5.19038 + 2.24943i) q^{32} +(4.31226 - 1.78620i) q^{33} +(1.07022 - 0.305591i) q^{34} +(0.138020 - 0.930456i) q^{35} +(6.06950 - 4.65686i) q^{36} +(-0.0749570 + 1.52579i) q^{37} +(8.41596 + 6.45809i) q^{38} +(-0.251584 + 2.55438i) q^{39} +(0.875529 + 0.174214i) q^{40} +(0.0557099 - 0.0678828i) q^{41} +(6.41357 + 8.95054i) q^{42} +(-1.80551 + 7.20799i) q^{43} +(-3.40203 + 1.09292i) q^{44} +(-1.20580 + 0.0592372i) q^{45} +(9.25292 - 1.68341i) q^{46} +(-3.66273 - 2.44736i) q^{47} +(-8.78314 + 5.66196i) q^{48} +(-1.56514 + 1.04579i) q^{49} +(4.81944 + 4.98002i) q^{50} +(1.85864 - 0.879069i) q^{51} +(0.351850 - 1.93322i) q^{52} +(1.78218 - 2.40299i) q^{53} +(2.08390 - 2.22486i) q^{54} +(0.539608 + 0.163688i) q^{55} +(-4.33323 - 7.23064i) q^{56} +(17.2828 + 9.23784i) q^{57} +(7.82031 + 8.91776i) q^{58} +(1.17678 + 3.28887i) q^{59} +(1.64819 + 0.0540295i) q^{60} +(-5.50741 + 9.18855i) q^{61} +(-8.01220 - 2.57456i) q^{62} +(8.06104 + 8.06104i) q^{63} +(7.05587 - 3.77024i) q^{64} +(-0.219265 + 0.219265i) q^{65} +(-5.87170 + 3.01586i) q^{66} +(-2.97870 - 1.78537i) q^{67} +(-1.47315 + 0.554379i) q^{68} +(16.3580 - 5.85298i) q^{69} +(-0.0870327 + 1.32741i) q^{70} +(1.06420 - 1.99097i) q^{71} +(-8.01682 + 7.26505i) q^{72} +(-0.0290936 + 0.0959087i) q^{73} +(-0.0706380 - 2.15923i) q^{74} +(10.2828 + 7.62626i) q^{75} +(-12.6083 - 8.13021i) q^{76} +(-2.27663 - 4.81353i) q^{77} +(0.0594722 - 3.62943i) q^{78} +(-9.18123 - 13.7407i) q^{79} +(-1.25417 - 0.144394i) q^{80} +(-3.24673 + 4.85908i) q^{81} +(-0.0706792 + 0.102117i) q^{82} +(-0.710645 - 14.4655i) q^{83} +(-10.0740 - 11.8746i) q^{84} +(0.240946 + 0.0603539i) q^{85} +(1.71203 - 10.3682i) q^{86} +(16.9374 + 13.9002i) q^{87} +(4.66883 - 1.93353i) q^{88} +(1.76295 + 0.173635i) q^{89} +(1.69271 - 0.222812i) q^{90} +(2.92461 + 0.143677i) q^{91} +(-12.8474 + 3.44183i) q^{92} +(-15.3781 - 2.28112i) q^{93} +(5.44534 + 3.02633i) q^{94} +(0.905997 + 2.18727i) q^{95} +(11.7255 - 8.99526i) q^{96} +(-5.09916 + 12.3105i) q^{97} +(2.08521 - 1.65487i) q^{98} +(-5.48915 + 4.07103i) 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 $\left(\mathbb{Z}/256\mathbb{Z}\right)^\times$.

$n$	$5$	$255$
$\chi(n)$	$e\left(\frac{9}{64}\right)$	$1$

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 $

$2$	−1.40949	+	0.115540i	−0.996657	+	0.0816990i
$2$	−1.40949	+	0.115540i	−0.996657	+	0.0816990i
$3$	−2.53419	+	0.634783i	−1.46312	+	0.366492i	−0.891122	−	0.453765i	$-0.850081\pi$
$3$	−2.53419	+	0.634783i	−1.46312	+	0.366492i	−0.571996	+	0.820256i	$0.693831\pi$
$4$	1.97330	−	0.325703i	0.986651	−	0.162852i
$5$	−0.285312	−	0.134943i	−0.127596	−	0.0603482i	0.362691	−	0.931909i	$-0.381858\pi$
$5$	−0.285312	−	0.134943i	−0.127596	−	0.0603482i	−0.490287	+	0.871561i	$0.663108\pi$
$6$	3.49857	−	1.18752i	1.42828	−	0.484802i
$7$	0.865145	+	2.85200i	0.326994	+	1.07795i	0.954217	+	0.299115i	$0.0966914\pi$
$7$	0.865145	+	2.85200i	0.326994	+	1.07795i	−0.627223	+	0.778840i	$0.715809\pi$
$8$	−2.74371	+	0.687069i	−0.970047	+	0.242916i
$9$	3.37343	−	1.80313i	1.12448	−	0.601045i
$10$	0.417735	+	0.157235i	0.132099	+	0.0497221i
$11$	−1.76730	+	0.262154i	−0.532860	+	0.0790424i	−0.407738	−	0.913099i	$-0.633682\pi$
$11$	−1.76730	+	0.262154i	−0.532860	+	0.0790424i	−0.125122	+	0.992141i	$0.539932\pi$
$12$	−4.79398	+	2.07801i	−1.38390	+	0.599871i
$13$	0.330990	−	0.925056i	0.0918002	−	0.256564i	−0.886864	−	0.462031i	$-0.847121\pi$
$13$	0.330990	−	0.925056i	0.0918002	−	0.256564i	0.978664	+	0.205466i	$0.0658711\pi$
$14$	−1.54893	−	3.91989i	−0.413969	−	1.04764i
$15$	0.808696	+	0.160860i	0.208805	+	0.0415338i
$16$	3.78783	−	1.28542i	0.946959	−	0.321355i
$17$	−0.771882	+	0.153537i	−0.187209	+	0.0372381i	−0.287804	−	0.957689i	$-0.592925\pi$
$17$	−0.771882	+	0.153537i	−0.187209	+	0.0372381i	0.100595	+	0.994927i	$0.467925\pi$
$18$	−4.54646	+	2.93126i	−1.07161	+	0.690904i
$19$	−5.55801	−	5.03748i	−1.27509	−	1.15568i	−0.979736	−	0.200292i	$-0.935811\pi$
$19$	−5.55801	−	5.03748i	−1.27509	−	1.15568i	−0.295358	−	0.955387i	$-0.595439\pi$
$20$	−0.606959	−	0.173355i	−0.135720	−	0.0387634i
$21$	−4.00284	−	6.67834i	−0.873492	−	1.45733i
$22$	2.46069	−	0.573695i	0.524621	−	0.122312i
$23$	−6.61818	+	0.651834i	−1.37999	+	0.135917i	−0.760626	−	0.649190i	$-0.775108\pi$
$23$	−6.61818	+	0.651834i	−1.37999	+	0.135917i	−0.619360	+	0.785107i	$0.712608\pi$
$24$	6.51695	−	3.48283i	1.33027	−	0.710929i
$25$	−3.10877	−	3.78805i	−0.621755	−	0.757610i
$26$	−0.359645	+	1.34210i	−0.0705323	+	0.263207i
$27$	−1.59715	+	1.44757i	−0.307371	+	0.278585i
$28$	2.63610	+	5.34607i	0.498176	+	1.01031i
$29$	−4.99613	−	6.73650i	−0.927758	−	1.25094i	−0.967795	−	0.251739i	$-0.918997\pi$
$29$	−4.99613	−	6.73650i	−0.927758	−	1.25094i	0.0400367	−	0.999198i	$-0.487253\pi$
$30$	−1.15843	−	0.133293i	−0.211500	−	0.0243358i
$31$	5.49781	+	2.27727i	0.987436	+	0.409009i	0.817175	−	0.576390i	$-0.195539\pi$
$31$	5.49781	+	2.27727i	0.987436	+	0.409009i	0.170261	+	0.985399i	$0.445539\pi$
$32$	−5.19038	+	2.24943i	−0.917539	+	0.397647i
$33$	4.31226	−	1.78620i	0.750669	−	0.310937i
$34$	1.07022	−	0.305591i	0.183541	−	0.0524084i
$35$	0.138020	−	0.930456i	0.0233297	−	0.157276i
$36$	6.06950	−	4.65686i	1.01158	−	0.776144i
$37$	−0.0749570	+	1.52579i	−0.0123229	+	0.250838i	0.984728	+	0.174098i	$0.0557010\pi$
$37$	−0.0749570	+	1.52579i	−0.0123229	+	0.250838i	−0.997051	+	0.0767395i	$0.975549\pi$
$38$	8.41596	+	6.45809i	1.36525	+	1.04764i
$39$	−0.251584	+	2.55438i	−0.0402857	+	0.409028i
$40$	0.875529	+	0.174214i	0.138433	+	0.0275457i
$41$	0.0557099	−	0.0678828i	0.00870043	−	0.0106015i	−0.768642	−	0.639679i	$-0.779067\pi$
$41$	0.0557099	−	0.0678828i	0.00870043	−	0.0106015i	0.777342	+	0.629078i	$0.216567\pi$
$42$	6.41357	+	8.95054i	0.989635	+	1.38110i
$43$	−1.80551	+	7.20799i	−0.275337	+	1.09921i	0.661641	+	0.749820i	$0.269860\pi$
$43$	−1.80551	+	7.20799i	−0.275337	+	1.09921i	−0.936978	+	0.349387i	$0.886390\pi$
$44$	−3.40203	+	1.09292i	−0.512875	+	0.164764i
$45$	−1.20580	+	0.0592372i	−0.179750	+	0.00883056i
$46$	9.25292	−	1.68341i	1.36427	−	0.248206i
$47$	−3.66273	−	2.44736i	−0.534264	−	0.356984i	0.258985	−	0.965881i	$-0.416612\pi$
$47$	−3.66273	−	2.44736i	−0.534264	−	0.356984i	−0.793249	+	0.608897i	$0.791612\pi$
$48$	−8.78314	+	5.66196i	−1.26774	+	0.817234i
$49$	−1.56514	+	1.04579i	−0.223591	+	0.149399i
$50$	4.81944	+	4.98002i	0.681572	+	0.704281i
$51$	1.85864	−	0.879069i	0.260261	−	0.123094i
$52$	0.351850	−	1.93322i	0.0487928	−	0.268089i
$53$	1.78218	−	2.40299i	0.244801	−	0.330076i	−0.663669	−	0.748026i	$-0.731002\pi$
$53$	1.78218	−	2.40299i	0.244801	−	0.330076i	0.908470	+	0.417951i	$0.137252\pi$
$54$	2.08390	−	2.22486i	0.283583	−	0.302765i
$55$	0.539608	+	0.163688i	0.0727607	+	0.0220717i
$56$	−4.33323	−	7.23064i	−0.579052	−	0.966235i
$57$	17.2828	+	9.23784i	2.28916	+	1.22358i
$58$	7.82031	+	8.91776i	1.02686	+	1.17096i
$59$	1.17678	+	3.28887i	0.153203	+	0.428175i	0.993483	−	0.113978i	$-0.0363594\pi$
$59$	1.17678	+	3.28887i	0.153203	+	0.428175i	−0.840280	+	0.542153i	$0.817609\pi$
$60$	1.64819	+	0.0540295i	0.212781	+	0.00697517i
$61$	−5.50741	+	9.18855i	−0.705151	+	1.17647i	0.271665	+	0.962392i	$0.412426\pi$
$61$	−5.50741	+	9.18855i	−0.705151	+	1.17647i	−0.976816	+	0.214081i	$0.931324\pi$
$62$	−8.01220	−	2.57456i	−1.01755	−	0.326970i
$63$	8.06104	+	8.06104i	1.01560	+	1.01560i
$64$	7.05587	−	3.77024i	0.881984	−	0.471279i
$65$	−0.219265	+	0.219265i	−0.0271965	+	0.0271965i
$66$	−5.87170	+	3.01586i	−0.722756	+	0.371227i
$67$	−2.97870	−	1.78537i	−0.363906	−	0.218117i	0.320449	−	0.947266i	$-0.396166\pi$
$67$	−2.97870	−	1.78537i	−0.363906	−	0.218117i	−0.684355	+	0.729149i	$0.739916\pi$
$68$	−1.47315	+	0.554379i	−0.178645	+	0.0672283i
$69$	16.3580	−	5.85298i	1.96927	−	0.704616i
$70$	−0.0870327	+	1.32741i	−0.0104024	+	0.158656i
$71$	1.06420	−	1.99097i	0.126297	−	0.236285i	−0.810824	−	0.585290i	$-0.800981\pi$
$71$	1.06420	−	1.99097i	0.126297	−	0.236285i	0.937121	+	0.349006i	$0.113481\pi$
$72$	−8.01682	+	7.26505i	−0.944792	+	0.856195i
$73$	−0.0290936	+	0.0959087i	−0.00340515	+	0.0112253i	−0.958626	−	0.284667i	$-0.908117\pi$
$73$	−0.0290936	+	0.0959087i	−0.00340515	+	0.0112253i	0.955221	+	0.295892i	$0.0956170\pi$
$74$	−0.0706380	−	2.15923i	−0.00821151	−	0.251006i
$75$	10.2828	+	7.62626i	1.18736	+	0.880605i
$76$	−12.6083	−	8.13021i	−1.44628	−	0.932599i
$77$	−2.27663	−	4.81353i	−0.259446	−	0.548553i
$78$	0.0594722	−	3.62943i	0.00673390	−	0.410952i
$79$	−9.18123	−	13.7407i	−1.03297	−	1.54595i	−0.822840	−	0.568273i	$-0.807612\pi$
$79$	−9.18123	−	13.7407i	−1.03297	−	1.54595i	−0.210129	−	0.977674i	$-0.567388\pi$
$80$	−1.25417	−	0.144394i	−0.140221	−	0.0161437i
$81$	−3.24673	+	4.85908i	−0.360748	+	0.539897i
$82$	−0.0706792	+	0.102117i	−0.00780521	+	0.0112769i
$83$	−0.710645	−	14.4655i	−0.0780034	−	1.58780i	−0.645070	−	0.764124i	$-0.723172\pi$
$83$	−0.710645	−	14.4655i	−0.0780034	−	1.58780i	0.567066	−	0.823672i	$-0.308078\pi$
$84$	−10.0740	−	11.8746i	−1.09916	−	1.29563i
$85$	0.240946	+	0.0603539i	0.0261343	+	0.00654630i
$86$	1.71203	−	10.3682i	0.184613	−	1.11803i
$87$	16.9374	+	13.9002i	1.81588	+	1.49025i
$88$	4.66883	−	1.93353i	0.497699	−	0.206115i
$89$	1.76295	+	0.173635i	0.186872	+	0.0184053i	0.191020	−	0.981586i	$-0.438820\pi$
$89$	1.76295	+	0.173635i	0.186872	+	0.0184053i	−0.00414827	+	0.999991i	$0.501320\pi$
$90$	1.69271	−	0.222812i	0.178428	−	0.0234864i
$91$	2.92461	+	0.143677i	0.306583	+	0.0150614i
$92$	−12.8474	+	3.44183i	−1.33943	+	0.358835i
$93$	−15.3781	−	2.28112i	−1.59463	−	0.236542i
$94$	5.44534	+	3.02633i	0.561644	+	0.312142i
$95$	0.905997	+	2.18727i	0.0929533	+	0.224409i
$96$	11.7255	−	8.99526i	1.19673	−	0.918074i
$97$	−5.09916	+	12.3105i	−0.517741	+	1.24994i	0.421547	+	0.906807i	$0.361487\pi$
$97$	−5.09916	+	12.3105i	−0.517741	+	1.24994i	−0.939288	+	0.343131i	$0.888513\pi$
$98$	2.08521	−	1.65487i	0.210638	−	0.167167i
$99$	−5.48915	+	4.07103i	−0.551680	+	0.409154i
$100$	−7.36833	−	6.46243i	−0.736833	−	0.646243i
$101$	6.57670	+	7.25627i	0.654406	+	0.722026i	0.974257	−	0.225442i	$-0.0723827\pi$
$101$	6.57670	+	7.25627i	0.654406	+	0.722026i	−0.319851	+	0.947468i	$0.603633\pi$
$102$	−2.51815	+	1.45378i	−0.249334	+	0.143946i
$103$	12.5785	−	10.3229i	1.23940	−	1.01715i	0.240477	−	0.970655i	$-0.422696\pi$
$103$	12.5785	−	10.3229i	1.23940	−	1.01715i	0.998919	−	0.0464910i	$-0.0148039\pi$
$104$	−0.272563	+	2.76550i	−0.0267270	+	0.271179i
$105$	0.240868	+	2.44557i	0.0235063	+	0.238663i
$106$	−2.23431	+	3.59289i	−0.217016	+	0.348972i
$107$	−14.2303	+	8.52930i	−1.37569	+	0.824558i	−0.994974	−	0.100133i	$-0.968073\pi$
$107$	−14.2303	+	8.52930i	−1.37569	+	0.824558i	−0.380718	+	0.924691i	$0.624323\pi$
$108$	−2.68017	+	3.37668i	−0.257900	+	0.324921i
$109$	3.10368	−	3.42439i	0.297279	−	0.327997i	−0.573935	−	0.818901i	$-0.694584\pi$
$109$	3.10368	−	3.42439i	0.297279	−	0.327997i	0.871213	+	0.490905i	$0.163334\pi$
$110$	−0.779482	−	0.168370i	−0.0743207	−	0.0160535i
$111$	−0.778586	−	3.91422i	−0.0739001	−	0.371521i
$112$	6.94305	+	9.69083i	0.656056	+	0.915697i
$113$	−3.98085	+	20.0131i	−0.374486	+	1.88267i	0.0881252	+	0.996109i	$0.471912\pi$
$113$	−3.98085	+	20.0131i	−0.374486	+	1.88267i	−0.462612	+	0.886561i	$0.653088\pi$
$114$	−25.4272	−	11.0238i	−2.38147	−	1.03247i
$115$	1.97621	+	0.707099i	0.184282	+	0.0659373i
$116$	−12.0530	−	11.6659i	−1.11909	−	1.08315i
$117$	−0.551428	−	3.71743i	−0.0509796	−	0.343676i
$118$	−2.03865	−	4.49965i	−0.187673	−	0.414227i
$119$	−1.10568	−	2.06857i	−0.101357	−	0.189626i
$120$	−2.32935	+	0.114278i	−0.212639	+	0.0104321i
$121$	−7.47173	+	2.26652i	−0.679248	+	0.206048i
$122$	6.70097	−	13.5875i	0.606677	−	1.23015i
$123$	−0.0980890	+	0.207392i	−0.00884439	+	0.0186999i
$124$	11.5905	+	2.70308i	1.04086	+	0.242744i
$125$	0.759242	+	3.03107i	0.0679087	+	0.271107i
$126$	−12.2933	−	10.4306i	−1.09517	−	0.929228i
$127$		−	11.7986i		−	1.04695i	−0.852040	−	0.523477i	$-0.824635\pi$
$127$		−	11.7986i		−	1.04695i	0.852040	−	0.523477i	$-0.175365\pi$
$128$	−9.50954	+	6.12933i	−0.840533	+	0.541761i
$129$		−	19.4125i		−	1.70918i
$130$	0.283717	−	0.334385i	0.0248837	−	0.0293275i
$131$	1.40581	+	5.61233i	0.122827	+	0.490351i	0.999949	+	0.0100846i	$0.00321008\pi$
$131$	1.40581	+	5.61233i	0.122827	+	0.490351i	−0.877123	+	0.480267i	$0.840540\pi$
$132$	7.92763	−	4.92923i	0.690011	−	0.429034i
$133$	9.55842	−	20.2096i	0.828820	−	1.75239i
$134$	4.40472	+	2.17229i	0.380510	+	0.187657i
$135$	0.651024	−	0.197486i	0.0560312	−	0.0169969i
$136$	2.01233	−	0.951596i	0.172556	−	0.0815987i
$137$	−2.21018	−	4.13496i	−0.188829	−	0.353274i	0.769637	−	0.638482i	$-0.220437\pi$
$137$	−2.21018	−	4.13496i	−0.188829	−	0.353274i	−0.958466	+	0.285208i	$0.907937\pi$
$138$	−22.3801	+	10.1397i	−1.90512	+	0.863148i
$139$	2.81458	+	18.9744i	0.238730	+	1.60939i	0.694638	+	0.719360i	$0.255565\pi$
$139$	2.81458	+	18.9744i	0.238730	+	1.60939i	−0.455908	+	0.890027i	$0.650685\pi$
$140$	−0.0306975	−	1.88102i	−0.00259441	−	0.158975i
$141$	10.8356	+	3.87705i	0.912524	+	0.326506i
$142$	−1.26993	+	2.92920i	−0.106570	+	0.245813i
$143$	−0.342451	+	1.72162i	−0.0286372	+	0.143969i
$144$	10.4602	−	11.1663i	0.871683	−	0.930521i
$145$	0.516416	+	2.59620i	0.0428860	+	0.215603i
$146$	0.0299257	−	0.138543i	0.00247667	−	0.0114659i
$147$	3.30252	−	3.64377i	0.272387	−	0.300533i
$148$	0.349041	+	3.03525i	0.0286910	+	0.249496i
$149$	5.88155	−	3.52526i	0.481835	−	0.288801i	−0.252489	−	0.967600i	$-0.581249\pi$
$149$	5.88155	−	3.52526i	0.481835	−	0.288801i	0.734324	+	0.678799i	$0.237499\pi$
$150$	−15.3746	−	9.56103i	−1.25533	−	0.780655i
$151$	−0.260390	−	2.64379i	−0.0211903	−	0.215148i	−0.999949	−	0.0101314i	$-0.996775\pi$
$151$	−0.260390	−	2.64379i	−0.0211903	−	0.215148i	0.978758	−	0.205017i	$-0.0657250\pi$
$152$	18.7107	+	10.0027i	1.51763	+	0.811322i
$153$	−2.32704	+	1.90975i	−0.188130	+	0.154394i
$154$	3.76503	+	6.52156i	0.303395	+	0.525523i
$155$	−1.26129	−	1.39162i	−0.101309	−	0.111778i
$156$	0.335518	+	5.12250i	0.0268630	+	0.410128i
$157$	−10.3950	+	7.70949i	−0.829615	+	0.615284i	−0.924919	−	0.380164i	$-0.875868\pi$
$157$	−10.3950	+	7.70949i	−0.829615	+	0.615284i	0.0953042	+	0.995448i	$0.469618\pi$
$158$	14.5284	+	18.3065i	1.15582	+	1.45639i
$159$	−2.99101	+	7.22093i	−0.237202	+	0.572657i
$160$	1.78442	+	0.0586141i	0.141071	+	0.00463385i
$161$	−7.58471	−	18.3111i	−0.597759	−	1.44312i
$162$	4.01481	−	7.22393i	0.315433	−	0.567565i
$163$	−21.5592	−	3.19801i	−1.68865	−	0.250487i	−0.767878	−	0.640596i	$-0.778687\pi$
$163$	−21.5592	−	3.19801i	−1.68865	−	0.250487i	−0.920769	+	0.390109i	$0.872437\pi$
$164$	0.0878228	−	0.152098i	0.00685781	−	0.0118769i
$165$	−1.47138	−	0.0722841i	−0.114547	−	0.00562731i
$166$	2.67299	+	20.3068i	0.207464	+	1.57612i
$167$	16.9112	+	1.66560i	1.30862	+	0.128888i	0.728166	−	0.685401i	$-0.240373\pi$
$167$	16.9112	+	1.66560i	1.30862	+	0.128888i	0.580459	+	0.814289i	$0.302873\pi$
$168$	15.5711	+	15.5732i	1.20134	+	1.20150i
$169$	9.30296	+	7.63474i	0.715612	+	0.587288i
$170$	−0.346583	−	0.0572290i	−0.0265817	−	0.00438927i
$171$	−27.8328	−	6.97175i	−2.12843	−	0.533143i
$172$	−1.21514	+	14.8116i	−0.0926537	+	1.12937i
$173$	−0.174983	−	3.56187i	−0.0133037	−	0.270804i	−0.996227	−	0.0867873i	$-0.972340\pi$
$173$	−0.174983	−	3.56187i	−0.0133037	−	0.270804i	0.982923	−	0.184017i	$-0.0589100\pi$
$174$	−25.4790	−	17.6351i	−1.93156	−	1.33692i
$175$	8.11398	−	12.1434i	0.613359	−	0.917957i
$176$	−6.35725	+	3.26472i	−0.479196	+	0.246087i
$177$	−5.06990	−	7.58764i	−0.381077	−	0.570322i
$178$	−2.50491	−	0.0410457i	−0.187751	−	0.00307650i
$179$	8.18074	+	17.2967i	0.611458	+	1.29282i	0.937672	+	0.347522i	$0.112977\pi$
$179$	8.18074	+	17.2967i	0.611458	+	1.29282i	−0.326214	+	0.945296i	$0.605773\pi$
$180$	−2.36011	+	0.509626i	−0.175913	+	0.0379853i
$181$	3.24053	+	2.40334i	0.240867	+	0.178639i	0.709398	−	0.704808i	$-0.248967\pi$
$181$	3.24053	+	2.40334i	0.240867	+	0.178639i	−0.468531	+	0.883447i	$0.655217\pi$
$182$	−4.13880	+	0.135398i	−0.306788	+	0.0100364i
$183$	8.12410	−	26.7816i	0.600551	−	1.97975i
$184$	17.7105	−	6.33559i	1.30564	−	0.467066i
$185$	0.227280	−	0.425211i	0.0167099	−	0.0312621i
$186$	21.9388	+	1.43843i	1.60863	+	0.105471i
$187$	1.32389	−	0.473697i	0.0968127	−	0.0346402i
$188$	−8.02479	−	3.63641i	−0.585268	−	0.265213i
$189$	−5.51022	−	3.30270i	−0.400810	−	0.240236i
$190$	−1.52971	−	2.97825i	−0.110977	−	0.216065i
$191$	−11.3405	+	11.3405i	−0.820570	+	0.820570i	−0.986190	−	0.165619i	$-0.947038\pi$
$191$	−11.3405	+	11.3405i	−0.820570	+	0.820570i	0.165619	+	0.986190i	$0.447038\pi$
$192$	−15.4877	+	14.0335i	−1.11773	+	1.01278i
$193$	−8.21463	−	8.21463i	−0.591302	−	0.591302i	0.346681	−	0.937983i	$-0.387309\pi$
$193$	−8.21463	−	8.21463i	−0.591302	−	0.591302i	−0.937983	+	0.346681i	$0.887309\pi$
$194$	5.76484	−	17.9406i	0.413892	−	1.28806i
$195$	0.416475	−	0.694846i	0.0298244	−	0.0497590i
$196$	−2.74787	+	2.57344i	−0.196277	+	0.183817i
$197$	1.48535	+	4.15128i	0.105827	+	0.295767i	0.982771	−	0.184825i	$-0.0591719\pi$
$197$	1.48535	+	4.15128i	0.105827	+	0.295767i	−0.876944	+	0.480592i	$0.840422\pi$
$198$	7.26652	−	6.37228i	0.516409	−	0.452858i
$199$	−22.7835	−	12.1780i	−1.61508	−	0.863278i	−0.997020	−	0.0771476i	$-0.975419\pi$
$199$	−22.7835	−	12.1780i	−1.61508	−	0.863278i	−0.618060	−	0.786131i	$-0.712081\pi$
$200$	11.1322	+	8.25736i	0.787167	+	0.583884i
$201$	8.68193	+	2.63363i	0.612376	+	0.185762i
$202$	−10.1082	−	9.46774i	−0.711207	−	0.666148i
$203$	14.8901	−	20.0770i	1.04508	−	1.40913i
$204$	3.38133	−	2.34003i	0.236741	−	0.163835i
$205$	−0.0250550	+	0.0118501i	−0.00174992	+	0.000827650i
$206$	−16.5365	+	16.0033i	−1.15215	+	1.11500i
$207$	−21.1506	+	14.1324i	−1.47007	+	0.982268i
$208$	0.0646494	−	3.92942i	0.00448263	−	0.272456i
$209$	11.1433	+	7.44568i	0.770795	+	0.515029i
$210$	−0.622060	−	3.41917i	−0.0429262	−	0.235945i
$211$	12.9536	−	0.636370i	0.891763	−	0.0438095i	0.401974	−	0.915651i	$-0.368324\pi$
$211$	12.9536	−	0.636370i	0.891763	−	0.0438095i	0.489788	+	0.871841i	$0.337074\pi$
$212$	2.73411	−	5.32228i	0.187779	−	0.365535i
$213$	−1.43305	+	5.72104i	−0.0981907	+	0.391999i
$214$	19.0719	−	13.6661i	1.30373	−	0.934194i
$215$	1.48780	−	1.81289i	0.101467	−	0.123638i
$216$	3.38752	−	5.06905i	0.230492	−	0.344905i
$217$	−1.73837	+	17.6499i	−0.118008	+	1.19815i
$218$	−3.97894	+	5.18522i	−0.269488	+	0.351188i
$219$	0.0128476	−	0.261519i	0.000868161	−	0.0176718i
$220$	1.11812	+	0.147254i	0.0753838	+	0.00992787i
$221$	−0.113455	+	0.764853i	−0.00763182	+	0.0514496i
$222$	1.54965	+	5.42708i	0.104006	+	0.364241i
$223$	0.553492	−	0.229264i	0.0370646	−	0.0153526i	−0.364074	−	0.931370i	$-0.618615\pi$
$223$	0.553492	−	0.229264i	0.0370646	−	0.0153526i	0.401139	+	0.916017i	$0.368615\pi$
$224$	−10.9058	−	12.8569i	−0.728675	−	0.859037i
$225$	−17.3176	−	7.17318i	−1.15451	−	0.478212i
$226$	3.29864	−	28.6681i	0.219422	−	1.90697i
$227$	7.35426	+	9.91607i	0.488119	+	0.658153i	0.976761	−	0.214332i	$-0.0687574\pi$
$227$	7.35426	+	9.91607i	0.488119	+	0.658153i	−0.488641	+	0.872485i	$0.662507\pi$
$228$	37.1129	+	12.6000i	2.45786	+	0.834454i
$229$	−13.5411	+	12.2730i	−0.894822	+	0.811020i	−0.982718	−	0.185110i	$-0.940736\pi$
$229$	−13.5411	+	12.2730i	−0.894822	+	0.811020i	0.0878956	+	0.996130i	$0.471986\pi$
$230$	−2.86714	−	0.768315i	−0.189053	−	0.0506612i
$231$	8.82497	+	10.7533i	0.580640	+	0.707512i
$232$	18.3364	+	15.0503i	1.20384	+	0.988102i
$233$	−8.41063	+	0.828375i	−0.550999	+	0.0542686i	−0.369686	−	0.929157i	$-0.620535\pi$
$233$	−8.41063	+	0.828375i	−0.550999	+	0.0542686i	−0.181313	+	0.983425i	$0.558035\pi$
$234$	1.20674	+	5.17595i	0.0788872	+	0.338363i
$235$	0.714770	+	1.19252i	0.0466264	+	0.0777915i
$236$	3.39333	+	6.10666i	0.220887	+	0.397509i
$237$	31.9894	+	28.9935i	2.07793	+	1.88333i
$238$	1.79744	+	2.78788i	0.116511	+	0.180711i
$239$	9.13037	−	1.81614i	0.590595	−	0.117477i	0.109260	−	0.994013i	$-0.465152\pi$
$239$	9.13037	−	1.81614i	0.590595	−	0.117477i	0.481335	+	0.876537i	$0.340152\pi$
$240$	3.26998	−	0.430206i	0.211076	−	0.0277697i
$241$	9.19230	+	1.82846i	0.592128	+	0.117782i	0.482053	−	0.876142i	$-0.339891\pi$
$241$	9.19230	+	1.82846i	0.592128	+	0.117782i	0.110074	+	0.993923i	$0.464891\pi$
$242$	10.2694	−	4.05792i	0.660143	−	0.260853i
$243$	7.32192	−	20.4634i	0.469702	−	1.31273i
$244$	−7.87503	+	19.9256i	−0.504147	+	1.27560i
$245$	0.587676	−	0.0871735i	0.0375452	−	0.00556931i
$246$	0.114293	−	0.303649i	0.00728706	−	0.0193600i
$247$	−6.49960	+	3.47411i	−0.413560	+	0.221052i
$248$	−16.6490	−	2.47078i	−1.05721	−	0.156895i
$249$	10.9834	+	36.2073i	0.696043	+	2.29455i
$250$	−1.42035	−	4.18452i	−0.0898308	−	0.264652i
$251$	20.9014	+	9.88561i	1.31928	+	0.623974i	0.951989	−	0.306131i	$-0.0990345\pi$
$251$	20.9014	+	9.88561i	1.31928	+	0.623974i	0.367293	+	0.930105i	$0.380285\pi$
$252$	18.5324	+	13.2814i	1.16743	+	0.836647i
$253$	11.5254	−	2.88697i	0.724596	−	0.181502i
$254$	1.36321	+	16.6299i	0.0855351	+	1.04345i
$255$	−0.648916			−0.0406367
$256$	12.6954	−	9.73793i	0.793461	−	0.608621i
$257$	8.08693			0.504449			0.252224	−	0.967669i	$-0.418838\pi$
$257$	8.08693			0.504449			0.252224	+	0.967669i	$0.418838\pi$
$258$	2.24292	+	27.3617i	0.139638	+	1.70347i
$259$	−4.41639	+	1.10625i	−0.274421	+	0.0687389i
$260$	−0.361261	+	0.504092i	−0.0224044	+	0.0312624i
$261$	−29.0009	−	13.7164i	−1.79511	−	0.849024i
$262$	−2.62992	−	7.74807i	−0.162477	−	0.478677i
$263$	−2.20923	−	7.28287i	−0.136227	−	0.449081i	0.862110	−	0.506721i	$-0.169142\pi$
$263$	−2.20923	−	7.28287i	−0.136227	−	0.449081i	−0.998337	+	0.0576399i	$0.981642\pi$
$264$	−10.6044	+	7.86363i	−0.652653	+	0.483973i
$265$	−0.832743	+	0.445110i	−0.0511550	+	0.0273429i
$266$	−11.1375	+	29.5895i	−0.682881	+	1.81425i
$267$	−4.57787	+	0.679062i	−0.280161	+	0.0415579i
$268$	−6.45937	−	2.55289i	−0.394569	−	0.155943i
$269$	−4.01066	+	11.2091i	−0.244535	+	0.683428i	0.755079	+	0.655634i	$0.227598\pi$
$269$	−4.01066	+	11.2091i	−0.244535	+	0.683428i	−0.999614	+	0.0277946i	$0.991152\pi$
$270$	−0.894792	+	0.353573i	−0.0544553	+	0.0215178i
$271$	−14.7305	−	2.93007i	−0.894812	−	0.177989i	−0.273796	−	0.961788i	$-0.588279\pi$
$271$	−14.7305	−	2.93007i	−0.894812	−	0.177989i	−0.621015	+	0.783799i	$0.713279\pi$
$272$	−2.72640	+	1.57377i	−0.165312	+	0.0954236i
$273$	−7.50274	+	1.49239i	−0.454087	+	0.0903234i
$274$	3.59297	+	5.57281i	0.217060	+	0.336666i
$275$	6.48718	+	5.87964i	0.391192	+	0.354555i
$276$	30.3729	−	16.8775i	1.82823	−	1.01591i
$277$	−4.63198	−	7.72800i	−0.278309	−	0.464331i	0.686556	−	0.727077i	$-0.259122\pi$
$277$	−4.63198	−	7.72800i	−0.278309	−	0.464331i	−0.964865	+	0.262747i	$0.915372\pi$
$278$	−6.15941	−	26.4189i	−0.369417	−	1.58450i
$279$	22.6527	−	2.23109i	1.35618	−	0.133572i
$280$	0.260601	+	2.64773i	0.0155739	+	0.158232i
$281$	−16.8246	−	20.5009i	−1.00367	−	1.22298i	−0.974727	−	0.223398i	$-0.928285\pi$
$281$	−16.8246	−	20.5009i	−1.00367	−	1.22298i	−0.0289458	−	0.999581i	$-0.509215\pi$
$282$	−15.7206	−	4.21270i	−0.936148	−	0.250862i
$283$	17.6967	−	16.0393i	1.05196	−	0.953439i	0.0529774	−	0.998596i	$-0.483129\pi$
$283$	17.6967	−	16.0393i	1.05196	−	0.953439i	0.998980	+	0.0451572i	$0.0143789\pi$
$284$	1.45151	−	4.27540i	0.0861314	−	0.253698i
$285$	−3.68441	−	4.96786i	−0.218246	−	0.294270i
$286$	0.283765	−	2.46617i	0.0167794	−	0.145827i
$287$	0.241799	+	0.100156i	0.0142729	+	0.00591204i
$288$	−13.4534	+	16.9472i	−0.792746	+	0.998626i
$289$	−15.1337	+	6.26859i	−0.890219	+	0.368741i
$290$	−1.02785	−	3.59964i	−0.0603572	−	0.211378i
$291$	5.10779	−	34.4339i	0.299424	−	2.01855i
$292$	−0.0261726	+	0.198733i	−0.00153164	+	0.0116299i
$293$	1.19138	−	24.2511i	0.0696012	−	1.41676i	−0.669321	−	0.742973i	$-0.733415\pi$
$293$	1.19138	−	24.2511i	0.0696012	−	1.41676i	0.738922	−	0.673791i	$-0.235335\pi$
$294$	−4.23385	+	5.51741i	−0.246923	+	0.321782i
$295$	0.108060	−	1.09715i	0.00629151	−	0.0638788i
$296$	−0.842660	−	4.23781i	−0.0489786	−	0.246318i
$297$	2.44315	−	2.97698i	0.141766	−	0.172742i
$298$	−7.88265	+	5.64836i	−0.456630	+	0.327201i
$299$	−1.58757	+	6.33794i	−0.0918116	+	0.366532i
$300$	22.7750	+	11.6998i	1.31492	+	0.675486i
$301$	−22.1192	+	1.08665i	−1.27493	+	0.0626333i
$302$	0.672479	+	3.69630i	0.0386968	+	0.212698i
$303$	−21.2728	−	14.2140i	−1.22209	−	0.816574i
$304$	−27.5281	−	11.9368i	−1.57885	−	0.684621i
$305$	2.81126	−	1.87842i	0.160972	−	0.107558i
$306$	3.05928	−	2.96063i	0.174887	−	0.169248i
$307$	−17.8485	+	8.44170i	−1.01867	+	0.481793i	−0.862564	−	0.505947i	$-0.831143\pi$
$307$	−17.8485	+	8.44170i	−1.01867	+	0.481793i	−0.156102	+	0.987741i	$0.549893\pi$
$308$	−6.06026	−	8.75704i	−0.345315	−	0.498979i
$309$	−25.3235	+	34.1448i	−1.44061	+	1.94243i
$310$	1.93856	+	1.81574i	0.110103	+	0.103127i
$311$	14.3515	+	4.35349i	0.813800	+	0.246864i	0.669635	−	0.742690i	$-0.266450\pi$
$311$	14.3515	+	4.35349i	0.813800	+	0.246864i	0.144165	+	0.989554i	$0.453950\pi$
$312$	−1.06476	−	7.18132i	−0.0602802	−	0.406562i
$313$	−4.12794	−	2.20643i	−0.233325	−	0.124715i	0.350592	−	0.936528i	$-0.385981\pi$
$313$	−4.12794	−	2.20643i	−0.233325	−	0.124715i	−0.583917	+	0.811814i	$0.698481\pi$
$314$	13.7609	−	12.0675i	0.776574	−	0.681006i
$315$	−1.21214	−	3.38769i	−0.0682961	−	0.190875i
$316$	−22.5927	−	24.1241i	−1.27094	−	1.35709i
$317$	5.54688	−	9.25440i	0.311544	−	0.519779i	−0.661636	−	0.749825i	$-0.730138\pi$
$317$	5.54688	−	9.25440i	0.311544	−	0.519779i	0.973180	+	0.230046i	$0.0738877\pi$
$318$	3.38148	−	10.5234i	0.189624	−	0.590122i
$319$	10.5957	+	10.5957i	0.593243	+	0.593243i
$320$	−2.52189	+	0.123556i	−0.140978	+	0.00690701i
$321$	30.6480	−	30.6480i	1.71061	−	1.71061i
$322$	12.8062	+	24.9329i	0.713662	+	1.38946i
$323$	5.06356	+	3.03498i	0.281744	+	0.168871i
$324$	−4.82416	+	10.6459i	−0.268009	+	0.591439i
$325$	−4.53313	+	1.62198i	−0.251453	+	0.0899713i
$326$	30.7569	+	2.01660i	1.70347	+	0.111689i
$327$	−5.69159	+	10.6482i	−0.314746	+	0.588848i
$328$	−0.106212	+	0.224527i	−0.00586456	+	0.0123974i
$329$	3.81108	−	12.5634i	0.210111	−	0.692644i
$330$	2.08224	−	0.0681192i	0.114623	−	0.00374984i
$331$	−17.6200	−	13.0679i	−0.968484	−	0.718276i	−0.00897623	−	0.999960i	$-0.502857\pi$
$331$	−17.6200	−	13.0679i	−0.968484	−	0.718276i	−0.959507	+	0.281683i	$0.909107\pi$
$332$	−6.11378	−	28.3134i	−0.335537	−	1.55390i
$333$	2.49833	+	5.28228i	0.136908	+	0.289467i
$334$	−24.0285	−	0.393733i	−1.31478	−	0.0215441i
$335$	0.608939	+	0.911341i	0.0332699	+	0.0497919i
$336$	−23.7466	−	20.1511i	−1.29548	−	1.09933i
$337$	−1.45794	+	2.18196i	−0.0794191	+	0.118859i	−0.869053	−	0.494720i	$-0.835271\pi$
$337$	−1.45794	+	2.18196i	−0.0794191	+	0.118859i	0.789633	+	0.613579i	$0.210271\pi$
$338$	−13.9945	−	9.68620i	−0.761201	−	0.526860i
$339$	−2.61571	−	53.2440i	−0.142066	−	2.89181i
$340$	0.495117	+	0.0406194i	0.0268515	+	0.00220289i
$341$	−10.3133	−	2.58334i	−0.558494	−	0.139896i
$342$	40.0354	+	6.61079i	2.16487	+	0.357471i
$343$	11.7901	+	9.67590i	0.636607	+	0.522450i
$344$	0.00139813	−	21.0171i	7.53822e−5	−	1.13317i
$345$	−5.45695	−	0.537463i	−0.293792	−	0.0289360i
$346$	0.658174	+	5.00019i	0.0353837	+	0.268812i
$347$	−22.3077	−	1.09591i	−1.19754	−	0.0588314i	−0.559498	−	0.828832i	$-0.689006\pi$
$347$	−22.3077	−	1.09591i	−1.19754	−	0.0588314i	−0.638043	+	0.770000i	$0.720256\pi$
$348$	37.9499	+	21.9126i	2.03433	+	1.17464i
$349$	−23.6267	−	3.50469i	−1.26471	−	0.187602i	−0.519521	−	0.854458i	$-0.673890\pi$
$349$	−23.6267	−	3.50469i	−1.26471	−	0.187602i	−0.745187	+	0.666856i	$0.767640\pi$
$350$	−10.0335	+	18.0535i	−0.536313	+	0.964999i
$351$	0.810442	+	1.95658i	0.0432582	+	0.104434i
$352$	8.58325	−	5.33609i	0.457489	−	0.284415i
$353$	−3.37393	+	8.14538i	−0.179576	+	0.433535i	−0.987878	−	0.155233i	$-0.950387\pi$
$353$	−3.37393	+	8.14538i	−0.179576	+	0.433535i	0.808302	+	0.588768i	$0.200387\pi$
$354$	8.02263	+	10.1089i	0.426398	+	0.537282i
$355$	−0.572295	+	0.424443i	−0.0303743	+	0.0225271i
$356$	3.53538	−	0.231563i	0.187375	−	0.0122728i
$357$	4.11509	+	4.54031i	0.217794	+	0.240298i
$358$	−13.5291	−	23.4343i	−0.715035	−	1.23854i
$359$	−27.9117	+	22.9066i	−1.47313	+	1.20896i	−0.544060	+	0.839046i	$0.683114\pi$
$359$	−27.9117	+	22.9066i	−1.47313	+	1.20896i	−0.929065	+	0.369916i	$0.879386\pi$
$360$	3.26767	−	0.990998i	0.172221	−	0.0522302i
$361$	3.65287	+	37.0882i	0.192257	+	1.95201i
$362$	−4.84517	−	3.01307i	−0.254656	−	0.158363i
$363$	17.4961	−	10.4867i	0.918305	−	0.550411i
$364$	5.81794	−	0.669039i	0.304943	−	0.0350672i
$365$	0.0212429	−	0.0234380i	0.00111191	−	0.00122680i
$366$	−8.35647	+	38.6869i	−0.436800	+	2.02220i
$367$	−3.03444	−	15.2552i	−0.158397	−	0.796314i	−0.975530	−	0.219865i	$-0.929438\pi$
$367$	−3.03444	−	15.2552i	−0.158397	−	0.796314i	0.817134	−	0.576448i	$-0.195562\pi$
$368$	−24.2307	+	10.9762i	−1.26311	+	0.572173i
$369$	0.0655317	−	0.329450i	0.00341144	−	0.0171505i
$370$	−0.271219	+	0.625588i	−0.0141000	+	0.0325228i
$371$	8.39516	+	3.00384i	0.435855	+	0.155951i
$372$	−31.0886	+	0.507352i	−1.61187	+	0.0263050i
$373$	0.108728	+	0.732986i	0.00562973	+	0.0379526i	0.991809	−	0.127727i	$-0.0407682\pi$
$373$	0.108728	+	0.732986i	0.00562973	+	0.0379526i	−0.986180	+	0.165680i	$0.947018\pi$
$374$	−1.81128	+	0.820632i	−0.0936590	+	0.0424339i
$375$	−3.84814	−	7.19935i	−0.198717	−	0.371773i
$376$	11.7310	+	4.19829i	0.604979	+	0.216510i
$377$	−7.88531	+	2.39198i	−0.406114	+	0.123193i
$378$	8.14818	+	4.01846i	0.419097	+	0.206687i
$379$	4.45715	−	9.42385i	0.228948	−	0.484071i	−0.756511	−	0.653981i	$-0.773098\pi$
$379$	4.45715	−	9.42385i	0.228948	−	0.484071i	0.985460	+	0.169910i	$0.0543477\pi$
$380$	2.50021	+	4.02106i	0.128258	+	0.206276i
$381$	7.48953	+	29.8999i	0.383700	+	1.53182i
$382$	14.6740	−	17.2946i	0.750788	−	0.884867i
$383$		−	11.7238i		−	0.599060i	−0.954087	−	0.299530i	$-0.903170\pi$
$383$		−	11.7238i		−	0.599060i	0.954087	−	0.299530i	$-0.0968298\pi$
$384$	20.2082	−	21.5694i	1.03125	−	1.10071i
$385$			1.68058i			0.0856500i
$386$	12.5275	+	10.6293i	0.637634	+	0.541017i
$387$	6.90622	+	27.5712i	0.351063	+	1.40152i
$388$	−6.05262	+	25.9531i	−0.307275	+	1.31757i
$389$	9.42512	−	19.9277i	0.477873	−	1.01038i	−0.510718	−	0.859748i	$-0.670620\pi$
$389$	9.42512	−	19.9277i	0.477873	−	1.01038i	0.988590	−	0.150628i	$-0.0481296\pi$
$390$	−0.506733	+	1.02750i	−0.0256594	+	0.0520293i
$391$	5.00837	−	1.51927i	0.253284	−	0.0768329i
$392$	3.57576	−	3.94471i	0.180603	−	0.199238i
$393$	−7.12521	−	13.3303i	−0.359419	−	0.672427i
$394$	−2.57322	−	5.67956i	−0.129637	−	0.286132i
$395$	0.765314	+	5.15933i	0.0385071	+	0.259594i
$396$	−9.50580	+	9.82121i	−0.477684	+	0.493534i
$397$	13.3812	+	4.78786i	0.671581	+	0.240296i	0.650528	−	0.759483i	$-0.274548\pi$
$397$	13.3812	+	4.78786i	0.671581	+	0.240296i	0.0210539	+	0.999778i	$0.493298\pi$
$398$	33.5201	+	14.5324i	1.68021	+	0.728442i
$399$	−11.3942	+	57.2825i	−0.570424	+	2.86771i
$400$	−16.6448	−	10.3524i	−0.832238	−	0.517621i
$401$	−4.79575	−	24.1098i	−0.239488	−	1.20399i	−0.894046	−	0.447976i	$-0.852145\pi$
$401$	−4.79575	−	24.1098i	−0.239488	−	1.20399i	0.654558	−	0.756012i	$-0.272855\pi$
$402$	−12.5413	−	2.70896i	−0.625505	−	0.135111i
$403$	3.92632	−	4.33203i	0.195584	−	0.215794i
$404$	15.3412	+	12.1767i	0.763253	+	0.605816i
$405$	1.58203	−	0.948232i	0.0786117	−	0.0471180i
$406$	−18.6677	+	30.0187i	−0.926464	+	1.48980i
$407$	−0.267519	−	2.71617i	−0.0132604	−	0.134635i
$408$	−4.49557	+	3.68892i	−0.222564	+	0.182629i
$409$	17.7108	−	14.5349i	0.875742	−	0.718703i	−0.0849308	−	0.996387i	$-0.527067\pi$
$409$	17.7108	−	14.5349i	0.875742	−	0.718703i	0.960672	+	0.277684i	$0.0895669\pi$
$410$	0.0339455	−	0.0195975i	0.00167645	−	0.000967850i
$411$	8.22584	+	9.07581i	0.405751	+	0.447677i
$412$	21.4590	−	24.4671i	1.05721	−	1.20541i
$413$	−8.36178	+	6.20152i	−0.411456	+	0.305157i
$414$	28.1786	−	22.3631i	1.38490	−	1.09909i
$415$	−1.74926	+	4.22309i	−0.0858678	+	0.207303i
$416$	0.362882	+	5.54593i	0.0177918	+	0.271912i
$417$	−19.1773	−	46.2981i	−0.939117	−	2.26723i
$418$	−16.5665	−	9.20709i	−0.810295	−	0.450334i
$419$	16.8026	+	2.49244i	0.820862	+	0.121763i	0.543935	−	0.839127i	$-0.316934\pi$
$419$	16.8026	+	2.49244i	0.820862	+	0.121763i	0.276927	+	0.960891i	$0.410684\pi$
$420$	1.27183	+	4.74739i	0.0620592	+	0.231649i
$421$	22.4679	+	1.10378i	1.09502	+	0.0537949i	0.588548	−	0.808462i	$-0.299700\pi$
$421$	22.4679	+	1.10378i	1.09502	+	0.0537949i	0.506471	+	0.862257i	$0.330950\pi$
$422$	−18.1844	+	2.39361i	−0.885202	+	0.116519i
$423$	−16.7689	−	1.65159i	−0.815331	−	0.0803031i
$424$	−3.23875	+	7.81757i	−0.157288	+	0.379655i
$425$	2.98121	+	2.44662i	0.144610	+	0.118678i
$426$	1.35885	−	8.22930i	0.0658365	−	0.398711i
$427$	−30.9704	−	7.75769i	−1.49876	−	0.375421i
$428$	−25.3026	+	21.4657i	−1.22305	+	1.03758i
$429$	−0.225016	−	4.58030i	−0.0108639	−	0.221139i
$430$	−1.88757	+	2.72714i	−0.0910267	+	0.131514i
$431$	5.04438	−	7.54945i	0.242979	−	0.363644i	−0.689856	−	0.723946i	$-0.742326\pi$
$431$	5.04438	−	7.54945i	0.242979	−	0.363644i	0.932836	+	0.360302i	$0.117326\pi$
$432$	−4.18899	+	7.53615i	−0.201543	+	0.362583i
$433$	−11.1263	−	16.6517i	−0.534697	−	0.800231i	0.461520	−	0.887130i	$-0.347304\pi$
$433$	−11.1263	−	16.6517i	−0.534697	−	0.800231i	−0.996217	+	0.0868991i	$0.972304\pi$
$434$	0.410933	−	25.0782i	0.0197254	−	1.20379i
$435$	−2.95672	−	6.25146i	−0.141764	−	0.299735i
$436$	5.00917	−	7.76822i	0.239896	−	0.372030i
$437$	40.0675	+	29.7161i	1.91669	+	1.42151i
$438$	0.0121073	+	0.370092i	0.000578511	+	0.0176837i
$439$	0.437099	−	1.44092i	0.0208616	−	0.0687714i	−0.945892	−	0.324483i	$-0.894810\pi$
$439$	0.437099	−	1.44092i	0.0208616	−	0.0687714i	0.966753	+	0.255711i	$0.0823097\pi$
$440$	−1.59299	−	0.0783649i	−0.0759429	−	0.00373590i
$441$	−3.39418	+	6.35006i	−0.161628	+	0.302384i
$442$	0.0715426	−	1.09116i	0.00340293	−	0.0519011i
$443$	34.4411	−	12.3232i	1.63635	−	0.585494i	0.651457	−	0.758685i	$-0.274158\pi$
$443$	34.4411	−	12.3232i	1.63635	−	0.585494i	0.984888	+	0.173192i	$0.0554080\pi$
$444$	−2.81126	−	7.47034i	−0.133416	−	0.354527i
$445$	−0.479559	−	0.287437i	−0.0227333	−	0.0136258i
$446$	−0.753650	+	0.387095i	−0.0356864	+	0.0183295i
$447$	−12.6672	+	12.6672i	−0.599138	+	0.599138i
$448$	16.8571	+	16.8615i	0.796421	+	0.796633i
$449$	16.1123	+	16.1123i	0.760385	+	0.760385i	0.976392	−	0.216007i	$-0.0693034\pi$
$449$	16.1123	+	16.1123i	0.760385	+	0.760385i	−0.216007	+	0.976392i	$0.569303\pi$
$450$	25.2377	+	8.10962i	1.18972	+	0.382291i
$451$	−0.0806603	+	0.134574i	−0.00379815	+	0.00633682i
$452$	−1.33708	+	40.7884i	−0.0628911	+	1.91852i
$453$	2.33811	+	6.53458i	0.109854	+	0.307021i
$454$	−11.5114	−	13.1269i	−0.540258	−	0.616074i
$455$	−0.815040	−	0.435648i	−0.0382097	−	0.0204235i
$456$	−53.7659	−	13.4715i	−2.51782	−	0.630859i
$457$	4.91634	+	1.49136i	0.229977	+	0.0697627i	0.403170	−	0.915125i	$-0.367908\pi$
$457$	4.91634	+	1.49136i	0.229977	+	0.0697627i	−0.173193	+	0.984888i	$0.555408\pi$
$458$	17.6680	−	18.8631i	0.825571	−	0.881414i
$459$	1.01055	−	1.36257i	0.0471685	−	0.0635994i
$460$	4.12996	+	0.751661i	0.192560	+	0.0350464i
$461$	−0.153130	+	0.0724249i	−0.00713195	+	0.00337316i	−0.431118	−	0.902296i	$-0.641881\pi$
$461$	−0.153130	+	0.0724249i	−0.00713195	+	0.00337316i	0.423986	+	0.905669i	$0.360631\pi$
$462$	−13.6811	−	14.1369i	−0.636502	−	0.657710i
$463$	−6.07333	+	4.05807i	−0.282252	+	0.188595i	−0.688635	−	0.725108i	$-0.741790\pi$
$463$	−6.07333	+	4.05807i	−0.282252	+	0.188595i	0.406383	+	0.913703i	$0.366790\pi$
$464$	−27.5838	−	19.0946i	−1.28054	−	0.886446i
$465$	4.07974	+	2.72599i	0.189193	+	0.126415i
$466$	11.7590	−	2.13934i	0.544723	−	0.0991032i
$467$	−20.4668	+	1.00547i	−0.947090	+	0.0465276i	−0.516747	−	0.856138i	$-0.672857\pi$
$467$	−20.4668	+	1.00547i	−0.947090	+	0.0465276i	−0.430343	+	0.902666i	$0.641607\pi$
$468$	−2.29891	−	7.15600i	−0.106267	−	0.330786i
$469$	2.51485	−	10.0399i	0.116125	−	0.463597i
$470$	−1.14524	−	1.59826i	−0.0528261	−	0.0737221i
$471$	21.4492	−	26.1359i	0.988328	−	1.20428i
$472$	−5.48842	−	8.21518i	−0.252625	−	0.378134i
$473$	1.30127	−	13.2120i	0.0598323	−	0.607487i
$474$	−48.4384	−	37.1698i	−2.22485	−	1.70727i
$475$	−1.80366	+	36.7144i	−0.0827577	+	1.68457i
$476$	−2.85557	−	3.72180i	−0.130885	−	0.170588i
$477$	1.67913	−	11.3198i	0.0768823	−	0.518298i
$478$	−12.6593	+	3.61475i	−0.579023	+	0.165335i
$479$	−11.2115	+	4.64397i	−0.512268	+	0.212188i	−0.623817	−	0.781571i	$-0.714419\pi$
$479$	−11.2115	+	4.64397i	−0.512268	+	0.212188i	0.111549	+	0.993759i	$0.464419\pi$
$480$	−4.55929	+	0.984182i	−0.208102	+	0.0449216i
$481$	1.38663	+	0.574359i	0.0632247	+	0.0261885i
$482$	−13.1677	−	1.51511i	−0.599771	−	0.0690116i
$483$	30.8447	+	41.5893i	1.40348	+	1.89238i
$484$	−14.0058	+	6.90610i	−0.636625	+	0.313914i
$485$	3.11606	−	2.82423i	0.141493	−	0.128242i
$486$	−7.95581	+	29.6889i	−0.360883	+	1.34671i
$487$	9.40195	+	11.4563i	0.426043	+	0.519135i	0.941149	−	0.337991i	$-0.109747\pi$
$487$	9.40195	+	11.4563i	0.426043	+	0.519135i	−0.515106	+	0.857126i	$0.672247\pi$
$488$	8.79754	−	28.9947i	0.398246	−	1.31253i
$489$	56.6652	−	5.58104i	2.56249	−	0.252383i
$490$	−0.818249	+	0.190770i	−0.0369647	+	0.00861810i
$491$	8.94539	+	14.9245i	0.403700	+	0.673533i	0.990702	−	0.136053i	$-0.0434418\pi$
$491$	8.94539	+	14.9245i	0.403700	+	0.673533i	−0.587002	+	0.809586i	$0.699692\pi$
$492$	−0.126011	+	0.441194i	−0.00568101	+	0.0198906i
$493$	4.89072	+	4.43269i	0.220267	+	0.199638i
$494$	8.75970	−	5.64767i	0.394117	−	0.254101i
$495$	2.11548	−	0.420795i	0.0950837	−	0.0189133i
$496$	23.7520	+	1.55891i	1.06650	+	0.0699970i
$497$	6.59893	+	1.31261i	0.296002	+	0.0588786i
$498$	−19.6643	−	49.7647i	−0.881178	−	2.23001i
$499$	−4.66953	+	13.0505i	−0.209037	+	0.584219i	−0.999604	−	0.0281572i	$-0.991036\pi$
$499$	−4.66953	+	13.0505i	−0.209037	+	0.584219i	0.790567	+	0.612376i	$0.209786\pi$
$500$	2.48544	+	5.73392i	0.111152	+	0.256429i
$501$	−43.9135	+	6.51395i	−1.96191	+	0.291022i
$502$	−30.6024	−	11.5187i	−1.36585	−	0.514104i
$503$	−29.6337	+	15.8395i	−1.32130	+	0.706251i	−0.972929	−	0.231105i	$-0.925766\pi$
$503$	−29.6337	+	15.8395i	−1.32130	+	0.706251i	−0.348373	+	0.937356i	$0.613266\pi$
$504$	−27.6556	−	16.5787i	−1.23188	−	0.738472i
$505$	−0.897233	−	2.95778i	−0.0399263	−	0.131620i
$506$	−15.9113	+	5.40078i	−0.707346	+	0.240094i
$507$	−28.4219	−	13.4426i	−1.26226	−	0.597005i
$508$	−3.84284	−	23.2821i	−0.170498	−	1.03298i
$509$	36.1903	−	9.06521i	1.60411	−	0.401808i	0.665391	−	0.746495i	$-0.268265\pi$
$509$	36.1903	−	9.06521i	1.60411	−	0.401808i	0.938718	+	0.344687i	$0.112015\pi$
$510$	0.914638	−	0.0749756i	0.0405008	−	0.00331998i
$511$	−0.298702			−0.0132138
$512$	−16.7688	+	15.1923i	−0.741085	+	0.671411i
$513$	16.1690			0.713881
$514$	−11.3984	+	0.934362i	−0.502763	+	0.0412130i
$515$	−4.98180	+	1.24788i	−0.219524	+	0.0549880i
$516$	−6.32273	−	38.3068i	−0.278343	−	1.68636i
$517$	7.11472	+	3.36501i	0.312905	+	0.147993i
$518$	6.09702	−	2.06951i	0.267888	−	0.0909290i
$519$	2.70445	+	8.91539i	0.118712	+	0.391342i
$520$	0.450949	−	0.752250i	0.0197754	−	0.0329884i
$521$	4.34472	−	2.32230i	0.190346	−	0.101742i	−0.373471	−	0.927642i	$-0.621832\pi$
$521$	4.34472	−	2.32230i	0.190346	−	0.101742i	0.563817	+	0.825900i	$0.309332\pi$
$522$	42.4612	+	15.9823i	1.85847	+	0.699527i
$523$	−2.07305	+	0.307508i	−0.0906483	+	0.0134464i	−0.191900	−	0.981414i	$-0.561465\pi$
$523$	−2.07305	+	0.307508i	−0.0906483	+	0.0134464i	0.101252	+	0.994861i	$0.467715\pi$
$524$	4.60205	+	10.6169i	0.201041	+	0.463803i
$525$	−12.8540	+	35.9244i	−0.560993	+	1.56787i
$526$	3.95534	+	10.0098i	0.172461	+	0.436450i
$527$	−4.59330	−	0.913665i	−0.200087	−	0.0397999i
$528$	14.0381	−	12.3089i	0.610931	−	0.535676i
$529$	20.8173	−	4.14083i	0.905102	−	0.180036i
$530$	1.12231	−	0.723591i	0.0487501	−	0.0314308i
$531$	9.90005	+	8.97288i	0.429626	+	0.389390i
$532$	12.2793	−	42.9928i	0.532376	−	1.86398i
$533$	−0.0443559	−	0.0740033i	−0.00192127	−	0.00320544i
$534$	6.37398	−	1.48605i	0.275829	−	0.0643079i
$535$	5.21104	−	0.513243i	0.225293	−	0.0221894i
$536$	9.39936	+	2.85195i	0.405990	+	0.123185i
$537$	−31.7113	−	38.6403i	−1.36844	−	1.66745i
$538$	4.35788	−	16.2624i	0.187882	−	0.701122i
$539$	2.49191	−	2.25854i	0.107334	−	0.0972820i
$540$	1.22034	−	0.601740i	0.0525153	−	0.0258948i
$541$	−1.06307	−	1.43338i	−0.0457049	−	0.0616259i	0.779764	−	0.626074i	$-0.215339\pi$
$541$	−1.06307	−	1.43338i	−0.0457049	−	0.0616259i	−0.825469	+	0.564448i	$0.809089\pi$
$542$	21.1009	+	2.42794i	0.906362	+	0.104289i
$543$	−9.73774	−	4.03350i	−0.417887	−	0.173094i
$544$	3.66099	−	2.53321i	0.156964	−	0.108610i
$545$	−1.34762	+	0.558200i	−0.0577255	+	0.0239107i
$546$	10.4026	−	2.97037i	0.445189	−	0.127120i
$547$	1.00155	−	6.75188i	0.0428230	−	0.288689i	−0.957177	−	0.289505i	$-0.906509\pi$
$547$	1.00155	−	6.75188i	0.0428230	−	0.288689i	1.00000		0.000815138i	$0.000259467\pi$
$548$	−5.70813	−	7.43966i	−0.243839	−	0.317807i
$549$	−2.01064	+	40.9275i	−0.0858120	+	1.74674i
$550$	−9.82292	−	7.53774i	−0.418851	−	0.321410i
$551$	−6.16650	+	62.6095i	−0.262702	+	2.66725i
$552$	−40.8601	+	27.2979i	−1.73912	+	1.16188i
$553$	31.2453	−	38.0725i	1.32869	−	1.61901i
$554$	7.42161	+	10.3573i	0.315314	+	0.440041i
$555$	−0.306055	+	1.22184i	−0.0129913	+	0.0518642i
$556$	11.7340	+	36.5255i	0.497634	+	1.54902i
$557$	14.0470	−	0.690087i	0.595192	−	0.0292399i	0.250757	−	0.968050i	$-0.419320\pi$
$557$	14.0470	−	0.690087i	0.595192	−	0.0292399i	0.344435	+	0.938810i	$0.388070\pi$
$558$	−31.6709	+	5.76198i	−1.34073	+	0.243924i
$559$	6.07019	+	4.05597i	0.256741	+	0.171549i
$560$	−0.673231	−	3.70183i	−0.0284492	−	0.156431i
$561$	−3.05431	+	2.04083i	−0.128953	+	0.0861637i
$562$	26.0827	+	26.9518i	1.10023	+	1.13689i
$563$	−0.124154	+	0.0587206i	−0.00523248	+	0.00247478i	−0.430170	−	0.902748i	$-0.641546\pi$
$563$	−0.124154	+	0.0587206i	−0.00523248	+	0.00247478i	0.424937	+	0.905223i	$0.360296\pi$
$564$	22.6447	+	4.12138i	0.953514	+	0.173541i
$565$	3.83640	−	5.17279i	0.161399	−	0.217621i
$566$	−23.0900	+	24.6519i	−0.970546	+	1.03620i
$567$	−16.6670	−	5.05587i	−0.699947	−	0.212327i
$568$	−1.55191	+	6.19382i	−0.0651166	+	0.259887i
$569$	−33.9084	−	18.1244i	−1.42151	−	0.759815i	−0.431678	−	0.902028i	$-0.642078\pi$
$569$	−33.9084	−	18.1244i	−1.42151	−	0.759815i	−0.989836	+	0.142212i	$0.954578\pi$
$570$	5.76711	+	6.57643i	0.241558	+	0.275456i
$571$	12.8880	+	36.0196i	0.539347	+	1.50738i	0.833997	+	0.551770i	$0.186047\pi$
$571$	12.8880	+	36.0196i	0.539347	+	1.50738i	−0.294649	+	0.955606i	$0.595203\pi$
$572$	−0.115022	+	3.50881i	−0.00480933	+	0.146711i
$573$	21.5403	−	35.9378i	0.899859	−	1.50132i
$574$	−0.352384	−	0.113232i	−0.0147082	−	0.00472619i
$575$	23.0436	+	23.0436i	0.960984	+	0.960984i
$576$	17.0042	−	25.4413i	0.708510	−	1.06005i
$577$	−11.8267	+	11.8267i	−0.492353	+	0.492353i	−0.909047	−	0.416694i	$-0.863189\pi$
$577$	−11.8267	+	11.8267i	−0.492353	+	0.492353i	0.416694	+	0.909047i	$0.363189\pi$
$578$	20.6065	−	10.5840i	0.857117	−	0.440238i
$579$	26.0320	+	15.6030i	1.08185	+	0.648437i
$580$	1.86464	+	4.95489i	0.0774248	+	0.205740i
$581$	40.6408	−	14.5415i	1.68607	−	0.603284i
$582$	−3.22087	+	49.1243i	−0.133509	+	2.03627i
$583$	−2.51968	+	4.71400i	−0.104355	+	0.195234i
$584$	0.0139284	−	0.283135i	0.000576361	−	0.0117162i
$585$	−0.344311	+	1.13504i	−0.0142355	+	0.0469281i
$586$	1.12273	+	34.3192i	0.0463797	+	1.41771i
$587$	15.2322	+	11.2969i	0.628699	+	0.466275i	0.862532	−	0.506002i	$-0.168877\pi$
$587$	15.2322	+	11.2969i	0.628699	+	0.466275i	−0.233833	+	0.972277i	$0.575127\pi$
$588$	5.33007	−	8.26589i	0.219809	−	0.340880i
$589$	−19.0852	−	40.3522i	−0.786391	−	1.66268i
$590$	−0.0255444	+	1.55891i	−0.00105165	+	0.0641792i
$591$	−6.39933	−	9.57728i	−0.263233	−	0.393957i
$592$	1.67735	+	5.87577i	0.0689388	+	0.241493i
$593$	2.98879	−	4.47305i	0.122735	−	0.183686i	−0.765014	−	0.644014i	$-0.777268\pi$
$593$	2.98879	−	4.47305i	0.122735	−	0.183686i	0.887749	+	0.460328i	$0.152268\pi$
$594$	−3.09962	+	4.47829i	−0.127179	+	0.183747i
$595$	0.0363241	+	0.739393i	0.00148914	+	0.0303122i
$596$	10.4579	−	8.87205i	0.428371	−	0.363413i
$597$	65.4682	+	16.3989i	2.67944	+	0.671164i
$598$	1.50537	−	9.11666i	0.0615593	−	0.372808i
$599$	−13.1981	−	10.8314i	−0.539261	−	0.442560i	0.324920	−	0.945742i	$-0.394663\pi$
$599$	−13.1981	−	10.8314i	−0.539261	−	0.442560i	−0.864181	+	0.503182i	$0.832163\pi$
$600$	−33.4528	−	13.8592i	−1.36571	−	0.565800i
$601$	−9.28917	−	0.914904i	−0.378913	−	0.0373197i	−0.0932320	−	0.995644i	$-0.529720\pi$
$601$	−9.28917	−	0.914904i	−0.378913	−	0.0373197i	−0.285681	+	0.958325i	$0.592220\pi$
$602$	31.0511	−	4.08726i	1.26555	−	0.166584i
$603$	−13.2677	−	0.651800i	−0.540302	−	0.0265433i
$604$	−1.37492	−	5.13218i	−0.0559447	−	0.208825i
$605$	2.43763	+	0.361588i	0.0991037	+	0.0147006i
$606$	31.6260	+	17.5766i	1.28472	+	0.714001i
$607$	−3.24566	−	7.83572i	−0.131737	−	0.318042i	0.844222	−	0.535993i	$-0.180063\pi$
$607$	−3.24566	−	7.83572i	−0.131737	−	0.318042i	−0.975960	+	0.217951i	$0.930063\pi$
$608$	40.1797	+	13.6441i	1.62950	+	0.553342i
$609$	−24.9899	+	60.3311i	−1.01264	+	2.44474i
$610$	−3.74540	+	2.97242i	−0.151647	+	0.120350i
$611$	−3.47627	+	2.57818i	−0.140635	+	0.104302i
$612$	−3.96994	+	4.52644i	−0.160475	+	0.182970i
$613$	−30.7992	−	33.9817i	−1.24397	−	1.37251i	−0.901384	−	0.433021i	$-0.857448\pi$
$613$	−30.7992	−	33.9817i	−1.24397	−	1.37251i	−0.342584	−	0.939487i	$-0.611302\pi$
$614$	24.1818	−	13.9607i	0.975899	−	0.563407i
$615$	0.0559720	−	0.0459351i	0.00225701	−	0.00185228i
$616$	9.55364	+	11.6427i	0.384927	+	0.469099i
$617$	−0.347467	−	3.52789i	−0.0139885	−	0.142028i	0.985654	−	0.168781i	$-0.0539831\pi$
$617$	−0.347467	−	3.52789i	−0.0139885	−	0.142028i	−0.999642	+	0.0267535i	$0.991483\pi$
$618$	31.7481	−	51.0526i	1.27710	−	2.05364i
$619$	29.0481	−	17.4108i	1.16754	−	0.699799i	0.207113	−	0.978317i	$-0.433593\pi$
$619$	29.0481	−	17.4108i	1.16754	−	0.699799i	0.960431	+	0.278519i	$0.0898434\pi$
$620$	−2.94217	−	2.33528i	−0.118160	−	0.0937872i
$621$	9.62662	−	10.6213i	0.386303	−	0.426220i
$622$	−20.7313	−	4.47801i	−0.831248	−	0.179552i
$623$	1.03000	+	5.17814i	0.0412659	+	0.207458i
$624$	2.33049	+	9.99895i	0.0932944	+	0.400278i
$625$	−4.58769	+	23.0639i	−0.183508	+	0.922555i
$626$	6.07320	+	2.63299i	0.242734	+	0.105235i
$627$	−32.9655	−	11.7953i	−1.31652	−	0.471057i
$628$	−18.0015	+	18.5989i	−0.718340	+	0.742175i
$629$	−0.176406	−	1.18923i	−0.00703378	−	0.0474179i
$630$	2.09990	+	4.63486i	0.0836621	+	0.184657i
$631$	−12.7953	−	23.9382i	−0.509371	−	0.952966i	−0.996810	−	0.0798094i	$-0.974569\pi$
$631$	−12.7953	−	23.9382i	−0.509371	−	0.952966i	0.487439	−	0.873157i	$-0.337931\pi$
$632$	34.6314	+	31.3923i	1.37756	+	1.24872i
$633$	−32.4230	+	9.83540i	−1.28870	+	0.390922i
$634$	−6.74899	+	13.6848i	−0.268037	+	0.543494i
$635$	−1.59213	+	3.36628i	−0.0631818	+	0.133587i
$636$	−3.55028	+	15.2232i	−0.140778	+	0.603641i
$637$	0.449371	+	1.79399i	0.0178047	+	0.0710804i
$638$	−16.1586	−	13.7102i	−0.639727	−	0.542792i
$639$		−	8.63528i		−	0.341606i
$640$	3.54030	−	0.465530i	0.139943	−	0.0184017i
$641$		−	1.59539i		−	0.0630142i	−0.999504	−	0.0315071i	$-0.989969\pi$
$641$		−	1.59539i		−	0.0630142i	0.999504	−	0.0315071i	$-0.0100307\pi$
$642$	−39.6569	+	46.7390i	−1.56513	+	1.84464i
$643$	−1.86860	−	7.45985i	−0.0736902	−	0.294188i	0.921969	−	0.387264i	$-0.126580\pi$
$643$	−1.86860	−	7.45985i	−0.0736902	−	0.294188i	−0.995659	+	0.0930764i	$0.970330\pi$
$644$	−20.9309	−	33.6630i	−0.824794	−	1.32651i
$645$	−2.61958	+	5.53864i	−0.103146	+	0.218084i
$646$	−7.48768	−	3.69272i	−0.294599	−	0.145288i
$647$	5.76818	−	1.74976i	0.226771	−	0.0687901i	−0.174855	−	0.984594i	$-0.555946\pi$
$647$	5.76818	−	1.74976i	0.226771	−	0.0687901i	0.401625	+	0.915804i	$0.368446\pi$
$648$	5.56956	−	15.5626i	0.218793	−	0.611357i
$649$	−2.94191	−	5.50392i	−0.115480	−	0.216048i
$650$	6.20198	−	2.80992i	0.243262	−	0.110214i
$651$	−6.79851	−	45.8318i	−0.266454	−	1.79629i
$652$	−43.5844	+	0.711278i	−1.70690	+	0.0278558i
$653$	9.32083	+	3.33505i	0.364752	+	0.130510i	0.512886	−	0.858457i	$-0.328576\pi$
$653$	9.32083	+	3.33505i	0.364752	+	0.130510i	−0.148133	+	0.988967i	$0.547326\pi$
$654$	6.79193	−	15.6661i	0.265585	−	0.612594i
$655$	0.356246	−	1.79097i	0.0139197	−	0.0699790i
$656$	0.123762	−	0.328739i	0.00483210	−	0.0128351i
$657$	0.0747911	+	0.376000i	0.00291788	+	0.0146692i
$658$	−3.92008	+	18.1483i	−0.152821	+	0.707495i
$659$	−9.29084	+	10.2509i	−0.361920	+	0.399317i	−0.894504	−	0.447060i	$-0.852471\pi$
$659$	−9.29084	+	10.2509i	−0.361920	+	0.399317i	0.532584	+	0.846377i	$0.321221\pi$
$660$	−2.92701	+	0.336594i	−0.113934	+	0.0131019i
$661$	0.397594	−	0.238309i	0.0154646	−	0.00926914i	−0.506350	−	0.862328i	$-0.669005\pi$
$661$	0.397594	−	0.238309i	0.0154646	−	0.00926914i	0.521814	+	0.853059i	$0.325255\pi$
$662$	26.3450	+	16.3832i	1.02393	+	0.636751i
$663$	−0.197998	−	2.01031i	−0.00768960	−	0.0780738i
$664$	11.8886	+	39.2009i	0.461368	+	1.52129i
$665$	−5.45427	+	4.47621i	−0.211508	+	0.173580i
$666$	−4.13168	−	7.15665i	−0.160099	−	0.277314i
$667$	37.4564	+	41.3267i	1.45032	+	1.60018i
$668$	33.9133	−	2.22129i	1.31215	−	0.0859441i
$669$	−1.25712	+	0.932346i	−0.0486032	+	0.0360466i
$670$	−0.963587	−	1.21417i	−0.0372266	−	0.0469073i
$671$	7.32441	−	17.6827i	0.282756	−	0.682633i
$672$	35.7988	+	25.6590i	1.38097	+	0.989819i
$673$	16.1138	+	38.9022i	0.621143	+	1.49957i	0.850363	+	0.526197i	$0.176382\pi$
$673$	16.1138	+	38.9022i	0.621143	+	1.49957i	−0.229220	+	0.973375i	$0.573618\pi$
$674$	1.80284	−	3.24389i	0.0694429	−	0.124950i
$675$	10.4486	+	1.54991i	0.402168	+	0.0596559i
$676$	20.8442	+	12.0356i	0.801700	+	0.462909i
$677$	14.8773	+	0.730876i	0.571782	+	0.0280898i	0.332906	−	0.942960i	$-0.391971\pi$
$677$	14.8773	+	0.730876i	0.571782	+	0.0280898i	0.238876	+	0.971050i	$0.423221\pi$
$678$	9.83860	+	74.7444i	0.377849	+	2.87054i
$679$	−39.5209	−	3.89247i	−1.51667	−	0.149379i
$680$	−0.702553		4.67363e-5i	−0.0269417		1.79225e-6i
$681$	−24.9317	−	20.4609i	−0.955384	−	0.784063i
$682$	14.8349	+	2.44959i	0.568057	+	0.0937995i
$683$	−34.0036	−	8.51746i	−1.30111	−	0.325912i	−0.470321	−	0.882495i	$-0.655862\pi$
$683$	−34.0036	−	8.51746i	−1.30111	−	0.325912i	−0.830791	+	0.556584i	$0.812112\pi$
$684$	−57.1932	−	4.69213i	−2.18684	−	0.179408i
$685$	0.0726097	+	1.47800i	0.00277427	+	0.0564716i
$686$	−17.7360	−	12.2758i	−0.677162	−	0.468693i
$687$	26.5252	−	39.6977i	1.01200	−	1.51456i
$688$	2.42634	+	29.6235i	0.0925035	+	1.12939i
$689$	−1.63301	−	2.44398i	−0.0622129	−	0.0931081i
$690$	7.75359	+	0.127051i	0.295174	+	0.00483676i
$691$	11.2306	+	23.7451i	0.427231	+	0.903305i	0.996691	+	0.0812853i	$0.0259025\pi$
$691$	11.2306	+	23.7451i	0.427231	+	0.903305i	−0.569460	+	0.822019i	$0.692847\pi$
$692$	−1.50541	−	6.97165i	−0.0572270	−	0.265022i
$693$	−16.3595	−	12.1330i	−0.621446	−	0.460896i
$694$	31.5690	−	1.03276i	1.19834	−	0.0392031i
$695$	1.75742	−	5.79344i	0.0666627	−	0.219758i
$696$	−56.0216	−	26.5008i	−2.12349	−	1.00451i
$697$	−0.0325790	+	0.0609510i	−0.00123402	+	0.00230868i
$698$	33.7064	+	2.20999i	1.27581	+	0.0836492i
$699$	20.7883	−	7.43818i	0.786287	−	0.281338i
$700$	12.0562	−	26.6054i	0.455680	−	1.00559i
$701$	−23.5271	−	14.1016i	−0.888606	−	0.532610i	−0.00454963	−	0.999990i	$-0.501448\pi$
$701$	−23.5271	−	14.1016i	−0.888606	−	0.532610i	−0.884057	+	0.467379i	$0.845198\pi$
$702$	−1.36837	−	2.66413i	−0.0516458	−	0.100551i
$703$	8.10273	−	8.10273i	0.305600	−	0.305600i
$704$	−11.4814	+	8.51285i	−0.432723	+	0.320840i
$705$	−2.56836	−	2.56836i	−0.0967299	−	0.0967299i
$706$	3.81439	−	11.8706i	0.143556	−	0.446757i
$707$	−15.0051	+	25.0345i	−0.564324	+	0.941518i
$708$	−12.4758	−	13.3214i	−0.468868	−	0.500650i
$709$	−3.11075	−	8.69397i	−0.116827	−	0.326509i	0.868869	−	0.495042i	$-0.164847\pi$
$709$	−3.11075	−	8.69397i	−0.116827	−	0.326509i	−0.985696	+	0.168533i	$0.946097\pi$
$710$	0.757602	−	0.664369i	0.0284323	−	0.0249333i
$711$	−55.7485	−	29.7982i	−2.09073	−	1.11752i
$712$	−4.95631	+	0.734862i	−0.185745	+	0.0275401i
$713$	−37.8699	−	11.4877i	−1.41824	−	0.430218i
$714$	−6.32475	−	5.92404i	−0.236698	−	0.221702i
$715$	0.330026	−	0.444988i	0.0123423	−	0.0166416i
$716$	21.7767	+	31.4672i	0.813833	+	1.17598i
$717$	−21.9853	+	10.3983i	−0.821055	+	0.388330i
$718$	36.6946	−	35.5114i	1.36943	−	1.32527i
$719$	40.3632	−	26.9699i	1.50530	−	1.00581i	0.516540	−	0.856263i	$-0.327220\pi$
$719$	40.3632	−	26.9699i	1.50530	−	1.00581i	0.988755	−	0.149543i	$-0.0477803\pi$
$720$	−4.49123	+	1.77434i	−0.167378	+	0.0661259i
$721$	40.3231	+	26.9431i	1.50171	+	1.00341i
$722$	−9.43384	−	51.8533i	−0.351091	−	1.92978i
$723$	−24.4557	+	1.20143i	−0.909519	+	0.0446818i
$724$	7.17733	+	3.68707i	0.266743	+	0.137029i
$725$	−9.98638	+	39.8679i	−0.370885	+	1.48066i
$726$	−23.4488	+	16.8024i	−0.870267	+	0.623595i
$727$	22.5458	−	27.4722i	0.836179	−	1.01889i	−0.163299	−	0.986577i	$-0.552214\pi$
$727$	22.5458	−	27.4722i	0.836179	−	1.01889i	0.999478	−	0.0323102i	$-0.0102865\pi$
$728$	−8.12300	+	1.61520i	−0.301059	+	0.0598634i
$729$	−3.84694	+	39.0586i	−0.142479	+	1.44661i
$730$	−0.0272336	+	0.0354899i	−0.00100796	+	0.00131354i
$731$	0.286946	−	5.84092i	0.0106131	−	0.216034i
$732$	7.30845	−	55.4942i	0.270128	−	2.05112i
$733$	1.31710	−	8.87914i	0.0486480	−	0.327958i	−0.951166	−	0.308679i	$-0.900113\pi$
$733$	1.31710	−	8.87914i	0.0486480	−	0.327958i	0.999814	−	0.0192789i	$-0.00613705\pi$
$734$	6.03958	+	21.1514i	0.222925	+	0.780711i
$735$	−1.43395	+	0.593961i	−0.0528920	+	0.0219086i
$736$	32.8846	−	18.2704i	1.21214	−	0.673456i
$737$	5.73229	+	2.37439i	0.211152	+	0.0874619i
$738$	−0.0543014	+	0.471927i	−0.00199886	+	0.0173719i
$739$	−15.9159	−	21.4602i	−0.585477	−	0.789425i	0.406793	−	0.913520i	$-0.366647\pi$
$739$	−15.9159	−	21.4602i	−0.585477	−	0.789425i	−0.992270	+	0.124096i	$0.960397\pi$
$740$	0.309999	−	0.913094i	0.0113958	−	0.0335660i
$741$	14.2659	−	12.9299i	0.524073	−	0.474992i
$742$	−12.1799	−	3.26389i	−0.447139	−	0.119821i
$743$	3.34980	+	4.08174i	0.122892	+	0.149744i	0.830822	−	0.556538i	$-0.187871\pi$
$743$	3.34980	+	4.08174i	0.122892	+	0.149744i	−0.707930	+	0.706283i	$0.750371\pi$
$744$	43.7603	−	4.30707i	1.60433	−	0.157905i
$745$	−2.15379	+	0.212130i	−0.0789087	+	0.00777182i
$746$	−0.237940	−	1.02057i	−0.00871160	−	0.0373657i
$747$	−28.4806	−	47.5170i	−1.04205	−	1.73855i
$748$	2.45816	−	1.36594i	0.0898791	−	0.0499438i
$749$	−36.6368	−	33.2057i	−1.33868	−	1.21331i
$750$	6.25570	+	9.70278i	0.228426	+	0.354295i
$751$	38.1584	−	7.59017i	1.39242	−	0.276969i	0.558796	−	0.829305i	$-0.311263\pi$
$751$	38.1584	−	7.59017i	1.39242	−	0.276969i	0.833622	+	0.552336i	$0.186263\pi$
$752$	−17.0197	−	4.56204i	−0.620645	−	0.166360i
$753$	−59.2433	−	11.7842i	−2.15895	−	0.429441i
$754$	10.8379	−	4.28254i	0.394692	−	0.155961i
$755$	−0.282467	+	0.789443i	−0.0102800	+	0.0287308i
$756$	−11.9490	−	4.72253i	−0.434582	−	0.171757i
$757$	−21.4319	+	3.17913i	−0.778957	+	0.115547i	−0.524356	−	0.851499i	$-0.675694\pi$
$757$	−21.4319	+	3.17913i	−0.778957	+	0.115547i	−0.254601	+	0.967046i	$0.581944\pi$
$758$	−5.19346	+	13.7978i	−0.188635	+	0.501158i
$759$	−27.3750	+	14.6323i	−0.993651	+	0.531117i
$760$	−3.98860	−	5.37875i	−0.144682	−	0.195108i
$761$	−11.3355	−	37.3680i	−0.410910	−	1.35459i	−0.881478	−	0.472226i	$-0.843451\pi$
$761$	−11.3355	−	37.3680i	−0.410910	−	1.35459i	0.470567	−	0.882364i	$-0.344049\pi$
$762$	−14.0110	−	41.2781i	−0.507566	−	1.49535i
$763$	12.4515	+	5.88911i	0.450774	+	0.213200i
$764$	−18.6846	+	26.0719i	−0.675985	+	0.943248i
$765$	0.921640	−	0.230859i	0.0333220	−	0.00834672i
$766$	1.35457	+	16.5246i	0.0489426	+	0.597057i
$767$	3.43189			0.123918
$768$	−25.9911	+	32.7366i	−0.937873	+	1.18128i
$769$	−28.8632			−1.04083			−0.520417	−	0.853912i	$-0.674223\pi$
$769$	−28.8632			−1.04083			−0.520417	+	0.853912i	$0.674223\pi$
$770$	−0.194173	−	2.36875i	−0.00699752	−	0.0853637i
$771$	−20.4939	+	5.13344i	−0.738068	+	0.184876i
$772$	−18.8855	−	13.5344i	−0.679703	−	0.487114i
$773$	−48.1638	−	22.7798i	−1.73233	−	0.819331i	−0.988548	−	0.150909i	$-0.951780\pi$
$773$	−48.1638	−	22.7798i	−1.73233	−	0.819331i	−0.743782	−	0.668422i	$-0.766970\pi$
$774$	−12.9198	−	38.0633i	−0.464392	−	1.36816i
$775$	−8.46504	−	27.9055i	−0.304073	−	1.00239i
$776$	5.53247	−	37.2798i	0.198604	−	1.33827i
$777$	10.4898	−	5.60689i	0.376318	−	0.201146i
$778$	−10.9821	+	29.1768i	−0.393728	+	1.04604i
$779$	−0.651595	+	0.0966549i	−0.0233458	+	0.00346302i
$780$	0.595517	−	1.50679i	0.0213229	−	0.0539517i
$781$	−1.35881	+	3.79762i	−0.0486221	+	0.135890i
$782$	−6.88369	+	2.72006i	−0.246160	+	0.0972691i
$783$	17.7311	+	3.52693i	0.633658	+	0.126042i
$784$	−4.58421	+	5.97316i	−0.163722	+	0.213327i
$785$	4.00618	−	0.796878i	0.142987	−	0.0284418i
$786$	11.5831	+	17.9657i	0.413155	+	0.640814i
$787$	−28.4168	−	25.7555i	−1.01295	−	0.918084i	−0.0162995	−	0.999867i	$-0.505189\pi$
$787$	−28.4168	−	25.7555i	−1.01295	−	0.918084i	−0.996650	+	0.0817831i	$0.973939\pi$
$788$	4.28314	+	7.70795i	0.152580	+	0.274584i
$789$	10.2217	+	17.0538i	0.363901	+	0.607132i
$790$	−1.67481	−	7.18357i	−0.0595869	−	0.255580i
$791$	−60.5213	+	5.96082i	−2.15189	+	0.211942i
$792$	12.2635	−	14.9412i	0.435766	−	0.530911i
$793$	6.67703	+	8.13598i	0.237108	+	0.288917i
$794$	−19.4138	−	5.20236i	−0.688968	−	0.184625i
$795$	1.82778	−	1.65661i	0.0648248	−	0.0587538i
$796$	−48.9252	−	16.6103i	−1.73411	−	0.588735i
$797$	−0.854358	−	1.15197i	−0.0302629	−	0.0408048i	0.787817	−	0.615909i	$-0.211211\pi$
$797$	−0.854358	−	1.15197i	−0.0302629	−	0.0408048i	−0.818080	+	0.575105i	$0.804961\pi$
$798$	9.44156	−	82.0554i	0.334228	−	2.90473i
$799$	3.20296	+	1.32671i	0.113312	+	0.0469355i
$800$	24.6567	+	12.6685i	0.871745	+	0.447898i
$801$	6.26025	−	2.59308i	0.221195	−	0.0916221i
$802$	9.54518	+	33.4284i	0.337052	+	1.18040i
$803$	0.0262742	−	0.177126i	0.000927196	−	0.00625065i
$804$	17.9898	+	2.36922i	0.634453	+	0.0835559i
$805$	−0.306939	+	6.24789i	−0.0108182	+	0.220209i
$806$	−5.03357	+	6.55958i	−0.177300	+	0.231051i
$807$	3.04849	−	30.9518i	0.107312	−	1.08956i
$808$	−23.0301	−	15.3904i	−0.810196	−	0.541434i
$809$	27.6248	−	33.6610i	0.971237	−	1.18346i	−0.0117776	−	0.999931i	$-0.503749\pi$
$809$	27.6248	−	33.6610i	0.971237	−	1.18346i	0.983015	−	0.183526i	$-0.0587510\pi$
$810$	−2.12029	+	1.51931i	−0.0744994	+	0.0533830i
$811$	−5.36326	+	21.4113i	−0.188329	+	0.751853i	0.800061	+	0.599918i	$0.204800\pi$
$811$	−5.36326	+	21.4113i	−0.188329	+	0.751853i	−0.988391	+	0.151935i	$0.951450\pi$
$812$	22.8436	−	44.4678i	0.801652	−	1.56051i
$813$	39.1898	−	1.92527i	1.37445	−	0.0675222i
$814$	0.690890	+	3.79749i	0.0242157	+	0.133102i
$815$	5.71956	+	3.82169i	0.200347	+	0.133868i
$816$	5.91023	−	5.71890i	0.206899	−	0.200202i
$817$	46.3451	−	30.9668i	1.62141	−	1.08339i
$818$	−23.2837	+	22.5330i	−0.814097	+	0.787847i
$819$	10.1250	−	4.78879i	0.353798	−	0.167334i
$820$	−0.0455815	+	0.0315444i	−0.00159177	+	0.00110158i
$821$	−25.5969	+	34.5134i	−0.893338	+	1.20453i	0.0847646	+	0.996401i	$0.472986\pi$
$821$	−25.5969	+	34.5134i	−0.893338	+	1.20453i	−0.978102	+	0.208125i	$0.933264\pi$
$822$	−12.6428	−	11.8418i	−0.440969	−	0.413031i
$823$	53.5852	+	16.2549i	1.86786	+	0.566610i	0.997204	+	0.0747239i	$0.0238076\pi$
$823$	53.5852	+	16.2549i	1.86786	+	0.566610i	0.870659	+	0.491886i	$0.163692\pi$
$824$	−27.4192	+	36.9653i	−0.955192	+	1.28775i
$825$	−20.1721	−	10.7822i	−0.702301	−	0.375388i
$826$	11.0693	−	9.70707i	0.385150	−	0.337752i
$827$	−13.2706	−	37.0887i	−0.461463	−	1.28970i	−0.916787	−	0.399376i	$-0.869227\pi$
$827$	−13.2706	−	37.0887i	−0.461463	−	1.28970i	0.455325	−	0.890325i	$-0.349523\pi$
$828$	−37.1335	+	34.7763i	−1.29048	+	1.20856i
$829$	−13.7416	+	22.9264i	−0.477264	+	0.796267i	−0.998361	−	0.0572307i	$-0.981773\pi$
$829$	−13.7416	+	22.9264i	−0.477264	+	0.796267i	0.521097	+	0.853497i	$0.325523\pi$
$830$	1.97762	−	6.15449i	0.0686443	−	0.213625i
$831$	16.6439	+	16.6439i	0.577372	+	0.577372i
$832$	−1.15225	−	7.77499i	−0.0399472	−	0.269549i
$833$	1.04754	−	1.04754i	0.0362949	−	0.0362949i
$834$	32.3794	+	63.0408i	1.12121	+	2.18292i
$835$	−4.60020	−	2.75726i	−0.159197	−	0.0954188i
$836$	24.4141	+	11.0632i	0.844378	+	0.382628i
$837$	−12.0773	+	4.32133i	−0.417453	+	0.149367i
$838$	−23.9711	−	1.57168i	−0.828066	−	0.0542928i
$839$	−23.5842	+	44.1229i	−0.814217	+	1.52329i	0.0375037	+	0.999296i	$0.488059\pi$
$839$	−23.5842	+	44.1229i	−0.814217	+	1.52329i	−0.851721	+	0.523996i	$0.824441\pi$
$840$	−2.34115	−	6.54444i	−0.0807772	−	0.225804i
$841$	−12.0009	+	39.5617i	−0.413824	+	1.36420i
$842$	−31.7958	+	1.04018i	−1.09575	+	0.0358469i
$843$	55.6505	+	41.2732i	1.91670	+	1.42152i
$844$	25.3541	−	5.47478i	0.872724	−	0.188450i
$845$	−1.62400	−	3.43365i	−0.0558672	−	0.118121i
$846$	23.8263	+	0.390421i	0.819166	+	0.0134229i
$847$	−12.9282	−	19.3485i	−0.444220	−	0.664822i
$848$	3.66174	−	11.3930i	0.125745	−	0.391236i
$849$	−34.6653	+	51.8803i	−1.18971	+	1.78053i
$850$	−4.48465	−	3.10402i	−0.153822	−	0.106467i
$851$	−0.498479	−	10.1468i	−0.0170876	−	0.347827i
$852$	−0.964468	+	11.7561i	−0.0330421	+	0.402757i
$853$	21.1047	+	5.28645i	0.722611	+	0.181005i	0.586802	−	0.809730i	$-0.300387\pi$
$853$	21.1047	+	5.28645i	0.722611	+	0.181005i	0.135809	+	0.990735i	$0.456637\pi$
$854$	44.5487	+	7.35604i	1.52443	+	0.251718i
$855$	7.00026	+	5.74496i	0.239404	+	0.196474i
$856$	33.1835	−	33.1791i	1.13419	−	1.13404i
$857$	1.32476	+	0.130477i	0.0452529	+	0.00445703i	0.120618	−	0.992699i	$-0.461512\pi$
$857$	1.32476	+	0.130477i	0.0452529	+	0.00445703i	−0.0753653	+	0.997156i	$0.524012\pi$
$858$	0.846363	+	6.42987i	0.0288944	+	0.219512i
$859$	−41.7604	−	2.05156i	−1.42485	−	0.0699982i	−0.678032	−	0.735032i	$-0.737167\pi$
$859$	−41.7604	−	2.05156i	−1.42485	−	0.0699982i	−0.746813	+	0.665034i	$0.768417\pi$
$860$	2.34541	−	4.06196i	0.0799779	−	0.138512i
$861$	−0.676343	−	0.100326i	−0.0230497	−	0.00341910i
$862$	−6.23772	+	11.2237i	−0.212458	+	0.382280i
$863$	0.544622	+	1.31483i	0.0185392	+	0.0447575i	0.932878	−	0.360192i	$-0.117289\pi$
$863$	0.544622	+	1.31483i	0.0185392	+	0.0447575i	−0.914339	+	0.404950i	$0.867289\pi$
$864$	5.03359	−	11.1061i	0.171246	−	0.377837i
$865$	−0.430723	+	1.03986i	−0.0146450	+	0.0353562i
$866$	17.6063	+	22.1848i	0.598288	+	0.753871i
$867$	34.3726	−	25.4925i	1.16735	−	0.865769i
$868$	2.31832	+	35.3948i	0.0786889	+	1.20138i
$869$	19.8281	+	21.8770i	0.672623	+	0.742125i
$870$	4.88975	+	8.46973i	0.165778	+	0.287151i
$871$	−2.63748	+	2.16453i	−0.0893677	+	0.0733422i
$872$	−6.16281	+	11.5280i	−0.208699	+	0.390386i
$873$	4.99577	+	50.7229i	0.169081	+	1.71671i
$874$	−59.9080	−	37.2550i	−2.02642	−	1.26017i
$875$	−7.98774	+	4.78767i	−0.270035	+	0.161853i
$876$	−0.0598255	−	0.520241i	−0.00202132	−	0.0175773i
$877$	14.6354	−	16.1477i	0.494203	−	0.545269i	−0.441868	−	0.897080i	$-0.645684\pi$
$877$	14.6354	−	16.1477i	0.494203	−	0.545269i	0.936071	+	0.351811i	$0.114434\pi$
$878$	−0.449601	+	2.08146i	−0.0151733	+	0.0702459i
$879$	12.3750	+	62.2132i	0.417398	+	2.09840i
$880$	2.25435	−	0.0735997i	0.0759942	−	0.00248105i
$881$	4.29107	−	21.5727i	0.144570	−	0.726802i	−0.838692	−	0.544606i	$-0.816679\pi$
$881$	4.29107	−	21.5727i	0.144570	−	0.726802i	0.983262	−	0.182197i	$-0.0583207\pi$
$882$	4.05036	−	9.34249i	0.136383	−	0.314578i
$883$	15.3811	+	5.50344i	0.517615	+	0.185206i	0.582720	−	0.812673i	$-0.301988\pi$
$883$	15.3811	+	5.50344i	0.517615	+	0.185206i	−0.0651054	+	0.997878i	$0.520738\pi$
$884$	0.0252339	+	1.54624i	0.000848709	+	0.0520056i
$885$	0.422609	+	2.84900i	0.0142058	+	0.0957679i
$886$	−47.1204	+	21.3487i	−1.58304	+	0.717224i
$887$	10.8460	+	20.2914i	0.364173	+	0.681320i	0.995558	−	0.0941495i	$-0.0300132\pi$
$887$	10.8460	+	20.2914i	0.364173	+	0.681320i	−0.631385	+	0.775470i	$0.717513\pi$
$888$	4.82555	+	10.2045i	0.161935	+	0.342442i
$889$	33.6495	−	10.2075i	1.12857	−	0.342348i
$890$	0.709143	+	0.349730i	0.0237705	+	0.0117230i
$891$	4.46412	−	9.43858i	0.149553	−	0.316204i
$892$	1.01753	−	0.632681i	0.0340696	−	0.0211837i
$893$	8.02896	+	32.0534i	0.268679	+	1.07263i
$894$	16.3907	−	19.3178i	0.548186	−	0.646084i
$895$		−	6.03890i		−	0.201858i
$896$	−25.7080	−	21.8184i	−0.858843	−	0.728903i
$897$		−	17.0693i		−	0.569928i
$898$	−24.5716	−	20.8484i	−0.819965	−	0.695720i
$899$	−12.1270	−	48.4136i	−0.404457	−	1.61468i
$900$	−36.5091	−	8.51444i	−1.21697	−	0.283815i
$901$	−1.00668	+	2.12845i	−0.0335374	+	0.0709090i
$902$	0.0981410	−	0.198999i	0.00326774	−	0.00662595i
$903$	55.3646	−	16.7947i	1.84242	−	0.558891i
$904$	−2.82808	−	57.6451i	−0.0940605	−	1.91725i
$905$	−0.600251	−	1.12299i	−0.0199530	−	0.0373295i
$906$	−4.05054	−	8.94026i	−0.134570	−	0.297020i
$907$	−1.47567	−	9.94816i	−0.0489988	−	0.330323i	−0.999790	−	0.0204909i	$-0.993477\pi$
$907$	−1.47567	−	9.94816i	−0.0489988	−	0.330323i	0.950791	−	0.309832i	$-0.100273\pi$
$908$	17.7419	+	17.1721i	0.588785	+	0.569876i
$909$	35.2700	+	12.6198i	1.16983	+	0.418573i
$910$	1.19912	+	0.519870i	0.0397505	+	0.0172335i
$911$	2.49583	−	12.5474i	0.0826907	−	0.415714i	−0.917161	−	0.398516i	$-0.869525\pi$
$911$	2.49583	−	12.5474i	0.0826907	−	0.415714i	0.999852	−	0.0171982i	$-0.00547463\pi$
$912$	77.3388	+	12.7757i	2.56094	+	0.423047i
$913$	5.04811	+	25.3786i	0.167068	+	0.839908i
$914$	−7.10183	−	1.53401i	−0.234907	−	0.0507406i
$915$	−5.93189	+	6.54483i	−0.196102	+	0.216365i
$916$	−22.7234	+	28.6286i	−0.750801	+	0.945916i
$917$	−14.7901	+	8.86486i	−0.488413	+	0.292743i
$918$	−1.26693	+	2.03728i	−0.0418148	+	0.0672404i
$919$	1.54474	+	15.6840i	0.0509562	+	0.517367i	0.986454	+	0.164036i	$0.0524512\pi$
$919$	1.54474	+	15.6840i	0.0509562	+	0.517367i	−0.935498	+	0.353332i	$0.885049\pi$
$920$	−5.90797	−	0.582281i	−0.194780	−	0.0191972i
$921$	39.8729	−	32.7228i	1.31386	−	1.07825i
$922$	0.207466	−	0.119774i	0.00683253	−	0.00394456i
$923$	−1.48952	−	1.64343i	−0.0490282	−	0.0540942i
$924$	20.9167	+	18.3451i	0.688109	+	0.603509i
$925$	6.01278	−	4.45938i	0.197699	−	0.146623i
$926$	8.09141	−	6.42151i	0.265900	−	0.211024i
$927$	23.8190	−	57.5043i	0.782320	−	1.88869i
$928$	41.0851	+	23.7266i	1.34869	+	0.778863i
$929$	0.803899	+	1.94078i	0.0263751	+	0.0636750i	0.936518	−	0.350619i	$-0.114029\pi$
$929$	0.803899	+	1.94078i	0.0263751	+	0.0636750i	−0.910143	+	0.414294i	$0.864029\pi$
$930$	−6.06529	−	3.37088i	−0.198889	−	0.110535i
$931$	13.9672	+	2.07184i	0.457757	+	0.0679019i
$932$	−16.3269	+	4.37400i	−0.534805	+	0.143275i
$933$	−39.1331	−	1.92248i	−1.28116	−	0.0629393i
$934$	28.7315	−	3.78192i	0.940123	−	0.123748i
$935$	−0.441646	−	0.0434983i	−0.0144434	−	0.00142255i
$936$	4.06709	+	9.82067i	0.132937	+	0.320999i
$937$	−18.4342	−	15.1285i	−0.602218	−	0.494228i	0.283176	−	0.959068i	$-0.408612\pi$
$937$	−18.4342	−	15.1285i	−0.602218	−	0.494228i	−0.885395	+	0.464840i	$0.846112\pi$
$938$	−2.38465	+	14.4416i	−0.0778615	+	0.471535i
$939$	11.8616	+	2.97118i	0.387089	+	0.0969607i
$940$	1.79886	+	2.12040i	0.0586725	+	0.0691598i
$941$	−1.53576	−	31.2611i	−0.0500643	−	1.01908i	−0.884078	−	0.467339i	$-0.845213\pi$
$941$	−1.53576	−	31.2611i	−0.0500643	−	1.01908i	0.834014	−	0.551744i	$-0.186037\pi$
$942$	−27.2126	+	39.3165i	−0.886635	+	1.28100i
$943$	−0.324450	+	0.485574i	−0.0105655	+	0.0158125i
$944$	8.68503	+	10.9450i	0.282674	+	0.356231i
$945$	1.12646	+	1.68587i	0.0366438	+	0.0548412i
$946$	−0.307607	+	18.7724i	−0.0100012	+	0.610345i
$947$	12.9624	+	27.4067i	0.421222	+	0.890598i	0.997316	+	0.0732151i	$0.0233260\pi$
$947$	12.9624	+	27.4067i	0.421222	+	0.890598i	−0.576095	+	0.817383i	$0.695424\pi$
$948$	72.5679	+	46.7938i	2.35690	+	1.51979i
$949$	0.0790912	+	0.0586580i	0.00256741	+	0.00190412i
$950$	−1.69974	−	51.9568i	−0.0551468	−	1.68570i
$951$	−8.18233	+	26.9735i	−0.265330	+	0.874676i
$952$	4.45491	+	4.91589i	0.144384	+	0.159325i
$953$	−6.12904	+	11.4666i	−0.198539	+	0.371441i	−0.961414	−	0.275105i	$-0.911287\pi$
$953$	−6.12904	+	11.4666i	−0.198539	+	0.371441i	0.762875	+	0.646546i	$0.223787\pi$
$954$	−1.05883	+	16.1491i	−0.0342808	+	0.522847i
$955$	4.76591	−	1.70527i	0.154221	−	0.0551812i
$956$	17.4254	−	6.55759i	0.563579	−	0.212088i
$957$	−33.5774	−	20.1255i	−1.08540	−	0.650565i
$958$	15.2659	−	7.84098i	0.493220	−	0.253331i
$959$	9.88078	−	9.88078i	0.319067	−	0.319067i
$960$	6.31254	−	1.91397i	0.203736	−	0.0617731i
$961$	3.11966	+	3.11966i	0.100634	+	0.100634i
$962$	−2.02079	−	0.649341i	−0.0651529	−	0.0209356i
$963$	−32.6253	+	54.4320i	−1.05134	+	1.75405i
$964$	18.7347	+	0.614142i	0.603404	+	0.0197802i
$965$	1.23523	+	3.45224i	0.0397635	+	0.111132i
$966$	−48.2804	−	55.0557i	−1.55340	−	1.77139i
$967$	8.33608	+	4.45573i	0.268070	+	0.143287i	0.599956	−	0.800033i	$-0.295185\pi$
$967$	8.33608	+	4.45573i	0.268070	+	0.143287i	−0.331886	+	0.943320i	$0.607685\pi$
$968$	18.9430	−	11.3523i	0.608851	−	0.364876i
$969$	−14.7586	−	4.47697i	−0.474115	−	0.143821i
$970$	−4.06573	+	4.34074i	−0.130543	+	0.139373i
$971$	−2.63337	+	3.55069i	−0.0845089	+	0.113947i	−0.843439	−	0.537225i	$-0.819473\pi$
$971$	−2.63337	+	3.55069i	−0.0845089	+	0.113947i	0.758930	+	0.651172i	$0.225723\pi$
$972$	7.78336	−	42.7652i	0.249651	−	1.37170i
$973$	−51.6799	+	24.4428i	−1.65678	+	0.783600i
$974$	−14.5756	−	15.0612i	−0.467032	−	0.482592i
$975$	10.4582	−	6.98797i	0.334931	−	0.223794i
$976$	−9.04998	+	41.8840i	−0.289683	+	1.34068i
$977$	19.7699	+	13.2098i	0.632496	+	0.422620i	0.830063	−	0.557669i	$-0.188304\pi$
$977$	19.7699	+	13.2098i	0.632496	+	0.422620i	−0.197568	+	0.980289i	$0.563304\pi$
$978$	−79.2240	+	14.4135i	−2.53330	+	0.460892i
$979$	−3.16117	+	0.155298i	−0.101031	+	0.00496335i
$980$	1.13127	−	0.363428i	0.0361371	−	0.0116093i
$981$	4.29542	−	17.1483i	0.137142	−	0.547502i
$982$	−14.3328	−	20.0023i	−0.457377	−	0.638299i
$983$	−10.7043	+	13.0432i	−0.341413	+	0.416013i	−0.915205	−	0.402988i	$-0.867972\pi$
$983$	−10.7043	+	13.0432i	−0.341413	+	0.416013i	0.573792	+	0.819001i	$0.305472\pi$
$984$	0.126635	−	0.636417i	0.00403698	−	0.0202882i
$985$	0.136396	−	1.38485i	0.00434593	−	0.0441250i
$986$	−7.40556	−	5.68275i	−0.235841	−	0.180976i
$987$	−1.68296	+	34.2574i	−0.0535691	+	1.09042i
$988$	−11.6941	+	8.97241i	−0.372040	+	0.285450i
$989$	7.25076	−	48.8806i	0.230561	−	1.55431i
$990$	−2.93312	+	0.837527i	−0.0932207	+	0.0266183i
$991$	−31.1486	+	12.9022i	−0.989468	+	0.409851i	−0.817925	−	0.575325i	$-0.804875\pi$
$991$	−31.1486	+	12.9022i	−0.989468	+	0.409851i	−0.171544	+	0.985177i	$0.554875\pi$
$992$	−33.6583	+	0.547049i	−1.06865	+	0.0173688i
$993$	52.9478	+	21.9317i	1.68025	+	0.695982i
$994$	−9.45276	−	1.08766i	−0.299823	−	0.0344986i
$995$	4.85708	+	6.54901i	0.153980	+	0.207618i
$996$	33.4663	+	67.8706i	1.06042	+	2.15056i
$997$	23.4778	−	21.2790i	0.743550	−	0.673914i	−0.209131	−	0.977888i	$-0.567063\pi$
$997$	23.4778	−	21.2790i	0.743550	−	0.673914i	0.952680	+	0.303974i	$0.0983135\pi$
$998$	5.07379	−	18.9340i	0.160608	−	0.599344i
$999$	−2.08896	−	2.54541i	−0.0660918	−	0.0805331i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	256.2.m.a.101.2	✓	992
256.109	even	64	inner	256.2.m.a.109.2	yes	992

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
256.2.m.a.101.2	✓	992	1.1	even	1	trivial
256.2.m.a.109.2	yes	992	256.109	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)

\(f(q)\)	\(=\)	\(q+(-1.40949 + 0.115540i) q^{2} +(-2.53419 + 0.634783i) q^{3} +(1.97330 - 0.325703i) q^{4} +(-0.285312 - 0.134943i) q^{5} +(3.49857 - 1.18752i) q^{6} +(0.865145 + 2.85200i) q^{7} +(-2.74371 + 0.687069i) q^{8} +(3.37343 - 1.80313i) q^{9} +O(q^{10})\)	\(q+(-1.40949 + 0.115540i) q^{2} +(-2.53419 + 0.634783i) q^{3} +(1.97330 - 0.325703i) q^{4} +(-0.285312 - 0.134943i) q^{5} +(3.49857 - 1.18752i) q^{6} +(0.865145 + 2.85200i) q^{7} +(-2.74371 + 0.687069i) q^{8} +(3.37343 - 1.80313i) q^{9} +(0.417735 + 0.157235i) q^{10} +(-1.76730 + 0.262154i) q^{11} +(-4.79398 + 2.07801i) q^{12} +(0.330990 - 0.925056i) q^{13} +(-1.54893 - 3.91989i) q^{14} +(0.808696 + 0.160860i) q^{15} +(3.78783 - 1.28542i) q^{16} +(-0.771882 + 0.153537i) q^{17} +(-4.54646 + 2.93126i) q^{18} +(-5.55801 - 5.03748i) q^{19} +(-0.606959 - 0.173355i) q^{20} +(-4.00284 - 6.67834i) q^{21} +(2.46069 - 0.573695i) q^{22} +(-6.61818 + 0.651834i) q^{23} +(6.51695 - 3.48283i) q^{24} +(-3.10877 - 3.78805i) q^{25} +(-0.359645 + 1.34210i) q^{26} +(-1.59715 + 1.44757i) q^{27} +(2.63610 + 5.34607i) q^{28} +(-4.99613 - 6.73650i) q^{29} +(-1.15843 - 0.133293i) q^{30} +(5.49781 + 2.27727i) q^{31} +(-5.19038 + 2.24943i) q^{32} +(4.31226 - 1.78620i) q^{33} +(1.07022 - 0.305591i) q^{34} +(0.138020 - 0.930456i) q^{35} +(6.06950 - 4.65686i) q^{36} +(-0.0749570 + 1.52579i) q^{37} +(8.41596 + 6.45809i) q^{38} +(-0.251584 + 2.55438i) q^{39} +(0.875529 + 0.174214i) q^{40} +(0.0557099 - 0.0678828i) q^{41} +(6.41357 + 8.95054i) q^{42} +(-1.80551 + 7.20799i) q^{43} +(-3.40203 + 1.09292i) q^{44} +(-1.20580 + 0.0592372i) q^{45} +(9.25292 - 1.68341i) q^{46} +(-3.66273 - 2.44736i) q^{47} +(-8.78314 + 5.66196i) q^{48} +(-1.56514 + 1.04579i) q^{49} +(4.81944 + 4.98002i) q^{50} +(1.85864 - 0.879069i) q^{51} +(0.351850 - 1.93322i) q^{52} +(1.78218 - 2.40299i) q^{53} +(2.08390 - 2.22486i) q^{54} +(0.539608 + 0.163688i) q^{55} +(-4.33323 - 7.23064i) q^{56} +(17.2828 + 9.23784i) q^{57} +(7.82031 + 8.91776i) q^{58} +(1.17678 + 3.28887i) q^{59} +(1.64819 + 0.0540295i) q^{60} +(-5.50741 + 9.18855i) q^{61} +(-8.01220 - 2.57456i) q^{62} +(8.06104 + 8.06104i) q^{63} +(7.05587 - 3.77024i) q^{64} +(-0.219265 + 0.219265i) q^{65} +(-5.87170 + 3.01586i) q^{66} +(-2.97870 - 1.78537i) q^{67} +(-1.47315 + 0.554379i) q^{68} +(16.3580 - 5.85298i) q^{69} +(-0.0870327 + 1.32741i) q^{70} +(1.06420 - 1.99097i) q^{71} +(-8.01682 + 7.26505i) q^{72} +(-0.0290936 + 0.0959087i) q^{73} +(-0.0706380 - 2.15923i) q^{74} +(10.2828 + 7.62626i) q^{75} +(-12.6083 - 8.13021i) q^{76} +(-2.27663 - 4.81353i) q^{77} +(0.0594722 - 3.62943i) q^{78} +(-9.18123 - 13.7407i) q^{79} +(-1.25417 - 0.144394i) q^{80} +(-3.24673 + 4.85908i) q^{81} +(-0.0706792 + 0.102117i) q^{82} +(-0.710645 - 14.4655i) q^{83} +(-10.0740 - 11.8746i) q^{84} +(0.240946 + 0.0603539i) q^{85} +(1.71203 - 10.3682i) q^{86} +(16.9374 + 13.9002i) q^{87} +(4.66883 - 1.93353i) q^{88} +(1.76295 + 0.173635i) q^{89} +(1.69271 - 0.222812i) q^{90} +(2.92461 + 0.143677i) q^{91} +(-12.8474 + 3.44183i) q^{92} +(-15.3781 - 2.28112i) q^{93} +(5.44534 + 3.02633i) q^{94} +(0.905997 + 2.18727i) q^{95} +(11.7255 - 8.99526i) q^{96} +(-5.09916 + 12.3105i) q^{97} +(2.08521 - 1.65487i) q^{98} +(-5.48915 + 4.07103i) 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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