LMFDB - Embedded newform 224.2.u.c.29.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,2,Mod(29,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 3, 0]))

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

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

chi := DirichletCharacter("224.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	224.u (of order $8$, degree $4$, 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:	$1.78864900528$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			29.8
Character	$\chi$	$=$	224.29
Dual form			224.2.u.c.85.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.171231 + 1.40381i) q^{2} +(-0.380077 - 0.157433i) q^{3} +(-1.94136 + 0.480752i) q^{4} +(-1.58477 - 3.82598i) q^{5} +(0.155925 - 0.560513i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.00731 - 2.64298i) q^{8} +(-2.00165 - 2.00165i) q^{9} +O(q^{10})$	\(q+(0.171231 + 1.40381i) q^{2} +(-0.380077 - 0.157433i) q^{3} +(-1.94136 + 0.480752i) q^{4} +(-1.58477 - 3.82598i) q^{5} +(0.155925 - 0.560513i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.00731 - 2.64298i) q^{8} +(-2.00165 - 2.00165i) q^{9} +(5.09958 - 2.87984i) q^{10} +(-2.23049 + 0.923900i) q^{11} +(0.813552 + 0.122911i) q^{12} +(0.305188 - 0.736788i) q^{13} +(1.11372 + 0.871564i) q^{14} +1.70366i q^{15} +(3.53776 - 1.86662i) q^{16} +2.91159i q^{17} +(2.46719 - 3.15267i) q^{18} +(1.73982 - 4.20029i) q^{19} +(4.91596 + 6.66571i) q^{20} +(-0.380077 + 0.157433i) q^{21} +(-1.67891 - 2.97298i) q^{22} +(0.788947 + 0.788947i) q^{23} +(-0.0332386 + 1.16312i) q^{24} +(-8.59105 + 8.59105i) q^{25} +(1.08657 + 0.302264i) q^{26} +(0.917954 + 2.21614i) q^{27} +(-1.03281 + 1.71269i) q^{28} +(-4.16405 - 1.72481i) q^{29} +(-2.39161 + 0.291720i) q^{30} +10.1873 q^{31} +(3.22616 + 4.64671i) q^{32} +0.993211 q^{33} +(-4.08731 + 0.498555i) q^{34} +(-3.82598 - 1.58477i) q^{35} +(4.84821 + 2.92362i) q^{36} +(-3.18556 - 7.69062i) q^{37} +(6.19431 + 1.72315i) q^{38} +(-0.231990 + 0.231990i) q^{39} +(-8.51562 + 8.04244i) q^{40} +(-4.33451 - 4.33451i) q^{41} +(-0.286087 - 0.506598i) q^{42} +(-1.35347 + 0.560626i) q^{43} +(3.88602 - 2.86594i) q^{44} +(-4.48610 + 10.8304i) q^{45} +(-0.972439 + 1.24262i) q^{46} -1.49721i q^{47} +(-1.63849 + 0.152502i) q^{48} -1.00000i q^{49} +(-13.5313 - 10.5891i) q^{50} +(0.458380 - 1.10663i) q^{51} +(-0.238267 + 1.57709i) q^{52} +(7.13162 - 2.95402i) q^{53} +(-2.95385 + 1.66810i) q^{54} +(7.06964 + 7.06964i) q^{55} +(-2.58114 - 1.15660i) q^{56} +(-1.32253 + 1.32253i) q^{57} +(1.70828 - 6.14088i) q^{58} +(-4.61370 - 11.1385i) q^{59} +(-0.819038 - 3.30742i) q^{60} +(8.94680 + 3.70589i) q^{61} +(1.74438 + 14.3010i) q^{62} -2.83076 q^{63} +(-5.97067 + 5.32457i) q^{64} -3.30259 q^{65} +(0.170069 + 1.39428i) q^{66} +(8.16996 + 3.38411i) q^{67} +(-1.39975 - 5.65244i) q^{68} +(-0.175654 - 0.424067i) q^{69} +(1.56959 - 5.64230i) q^{70} +(-2.34721 + 2.34721i) q^{71} +(-3.27404 + 7.30658i) q^{72} +(-2.55659 - 2.55659i) q^{73} +(10.2507 - 5.78879i) q^{74} +(4.61778 - 1.91275i) q^{75} +(-1.35831 + 8.99069i) q^{76} +(-0.923900 + 2.23049i) q^{77} +(-0.365393 - 0.285945i) q^{78} +14.2511i q^{79} +(-12.7482 - 10.5772i) q^{80} +7.50545i q^{81} +(5.34263 - 6.82703i) q^{82} +(-1.74047 + 4.20187i) q^{83} +(0.662180 - 0.488357i) q^{84} +(11.1397 - 4.61420i) q^{85} +(-1.01877 - 1.80402i) q^{86} +(1.31112 + 1.31112i) q^{87} +(4.68863 + 4.96449i) q^{88} +(2.67017 - 2.67017i) q^{89} +(-15.9720 - 4.44312i) q^{90} +(-0.305188 - 0.736788i) q^{91} +(-1.91092 - 1.15234i) q^{92} +(-3.87195 - 1.60381i) q^{93} +(2.10180 - 0.256369i) q^{94} -18.8274 q^{95} +(-0.494643 - 2.27401i) q^{96} +3.18567 q^{97} +(1.40381 - 0.171231i) q^{98} +(6.31398 + 2.61534i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 20 q^{6}+O(q^{10}) $ 52 * q - 20 * q^6	$ 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) $ 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	0.171231	+	1.40381i	0.121079	+	0.992643i
$2$	0.171231	+	1.40381i	0.121079	+	0.992643i
$3$	−0.380077	−	0.157433i	−0.219438	−	0.0908940i	0.270256	−	0.962788i	$-0.412892\pi$
$3$	−0.380077	−	0.157433i	−0.219438	−	0.0908940i	−0.489694	+	0.871894i	$0.662892\pi$
$4$	−1.94136	+	0.480752i	−0.970680	+	0.240376i
$5$	−1.58477	−	3.82598i	−0.708731	−	1.71103i	−0.703148	−	0.711044i	$-0.748223\pi$
$5$	−1.58477	−	3.82598i	−0.708731	−	1.71103i	−0.00558334	−	0.999984i	$-0.501777\pi$
$6$	0.155925	−	0.560513i	0.0636561	−	0.228828i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	−1.00731	−	2.64298i	−0.356136	−	0.934434i
$9$	−2.00165	−	2.00165i	−0.667216	−	0.667216i
$10$	5.09958	−	2.87984i	1.61263	−	0.910686i
$11$	−2.23049	+	0.923900i	−0.672519	+	0.278566i	−0.692696	−	0.721230i	$-0.743577\pi$
$11$	−2.23049	+	0.923900i	−0.672519	+	0.278566i	0.0201769	+	0.999796i	$0.493577\pi$
$12$	0.813552	+	0.122911i	0.234852	+	0.0354815i
$13$	0.305188	−	0.736788i	0.0846438	−	0.204348i	−0.875890	−	0.482510i	$-0.839725\pi$
$13$	0.305188	−	0.736788i	0.0846438	−	0.204348i	0.960534	+	0.278162i	$0.0897252\pi$
$14$	1.11372	+	0.871564i	0.297655	+	0.232935i
$15$			1.70366i			0.439883i
$16$	3.53776	−	1.86662i	0.884439	−	0.466656i
$17$			2.91159i			0.706164i	0.935592	+	0.353082i	$0.114866\pi$
$17$			2.91159i			0.706164i	−0.935592	+	0.353082i	$0.885134\pi$
$18$	2.46719	−	3.15267i	0.581521	−	0.743093i
$19$	1.73982	−	4.20029i	0.399141	−	0.963612i	−0.588729	−	0.808331i	$-0.700371\pi$
$19$	1.73982	−	4.20029i	0.399141	−	0.963612i	0.987870	−	0.155282i	$-0.0496285\pi$
$20$	4.91596	+	6.66571i	1.09924	+	1.49050i
$21$	−0.380077	+	0.157433i	−0.0829396	+	0.0343547i
$22$	−1.67891	−	2.97298i	−0.357945	−	0.633842i
$23$	0.788947	+	0.788947i	0.164507	+	0.164507i	0.784560	−	0.620053i	$-0.212889\pi$
$23$	0.788947	+	0.788947i	0.164507	+	0.164507i	−0.620053	+	0.784560i	$0.712889\pi$
$24$	−0.0332386	+	1.16312i	−0.00678480	+	0.237421i
$25$	−8.59105	+	8.59105i	−1.71821	+	1.71821i
$26$	1.08657	+	0.302264i	0.213093	+	0.0592789i
$27$	0.917954	+	2.21614i	0.176660	+	0.426496i
$28$	−1.03281	+	1.71269i	−0.195182	+	0.323668i
$29$	−4.16405	−	1.72481i	−0.773245	−	0.320289i	−0.0390591	−	0.999237i	$-0.512436\pi$
$29$	−4.16405	−	1.72481i	−0.773245	−	0.320289i	−0.734186	+	0.678948i	$0.762436\pi$
$30$	−2.39161	+	0.291720i	−0.436647	+	0.0532605i
$31$	10.1873			1.82969			0.914844	−	0.403807i	$-0.132313\pi$
$31$	10.1873			1.82969			0.914844	+	0.403807i	$0.132313\pi$
$32$	3.22616	+	4.64671i	0.570310	+	0.821430i
$33$	0.993211			0.172896
$34$	−4.08731	+	0.498555i	−0.700968	+	0.0855014i
$35$	−3.82598	−	1.58477i	−0.646708	−	0.267875i
$36$	4.84821	+	2.92362i	0.808035	+	0.487270i
$37$	−3.18556	−	7.69062i	−0.523703	−	1.26433i	−0.935588	−	0.353095i	$-0.885129\pi$
$37$	−3.18556	−	7.69062i	−0.523703	−	1.26433i	0.411885	−	0.911236i	$-0.364871\pi$
$38$	6.19431	+	1.72315i	1.00485	+	0.279532i
$39$	−0.231990	+	0.231990i	−0.0371481	+	0.0371481i
$40$	−8.51562	+	8.04244i	−1.34644	+	1.27162i
$41$	−4.33451	−	4.33451i	−0.676937	−	0.676937i	0.282369	−	0.959306i	$-0.408880\pi$
$41$	−4.33451	−	4.33451i	−0.676937	−	0.676937i	−0.959306	+	0.282369i	$0.908880\pi$
$42$	−0.286087	−	0.506598i	−0.0441442	−	0.0781698i
$43$	−1.35347	+	0.560626i	−0.206402	+	0.0854947i	−0.483490	−	0.875350i	$-0.660631\pi$
$43$	−1.35347	+	0.560626i	−0.206402	+	0.0854947i	0.277087	+	0.960845i	$0.410631\pi$
$44$	3.88602	−	2.86594i	0.585840	−	0.432056i
$45$	−4.48610	+	10.8304i	−0.668748	+	1.61450i
$46$	−0.972439	+	1.24262i	−0.143378	+	0.183215i
$47$		−	1.49721i		−	0.218391i	−0.994020	−	0.109195i	$-0.965173\pi$
$47$		−	1.49721i		−	0.218391i	0.994020	−	0.109195i	$-0.0348274\pi$
$48$	−1.63849	+	0.152502i	−0.236495	+	0.0220117i
$49$		−	1.00000i		−	0.142857i
$50$	−13.5313	−	10.5891i	−1.91361	−	1.49753i
$51$	0.458380	−	1.10663i	0.0641861	−	0.154959i
$52$	−0.238267	+	1.57709i	−0.0330416	+	0.218703i
$53$	7.13162	−	2.95402i	0.979604	−	0.405765i	0.165325	−	0.986239i	$-0.447133\pi$
$53$	7.13162	−	2.95402i	0.979604	−	0.405765i	0.814279	+	0.580474i	$0.197133\pi$
$54$	−2.95385	+	1.66810i	−0.401968	+	0.227000i
$55$	7.06964	+	7.06964i	0.953270	+	0.953270i
$56$	−2.58114	−	1.15660i	−0.344919	−	0.154557i
$57$	−1.32253	+	1.32253i	−0.175173	+	0.175173i
$58$	1.70828	−	6.14088i	0.224309	−	0.806337i
$59$	−4.61370	−	11.1385i	−0.600653	−	1.45010i	−0.872910	−	0.487880i	$-0.837770\pi$
$59$	−4.61370	−	11.1385i	−0.600653	−	1.45010i	0.272257	−	0.962224i	$-0.412230\pi$
$60$	−0.819038	−	3.30742i	−0.105737	−	0.426986i
$61$	8.94680	+	3.70589i	1.14552	+	0.474490i	0.873029	−	0.487668i	$-0.162152\pi$
$61$	8.94680	+	3.70589i	1.14552	+	0.474490i	0.272492	+	0.962158i	$0.412152\pi$
$62$	1.74438	+	14.3010i	0.221536	+	1.81623i
$63$	−2.83076			−0.356642
$64$	−5.97067	+	5.32457i	−0.746334	+	0.665572i
$65$	−3.30259			−0.409635
$66$	0.170069	+	1.39428i	0.0209340	+	0.171624i
$67$	8.16996	+	3.38411i	0.998119	+	0.413434i	0.821107	−	0.570774i	$-0.193357\pi$
$67$	8.16996	+	3.38411i	0.998119	+	0.413434i	0.177012	+	0.984209i	$0.443357\pi$
$68$	−1.39975	−	5.65244i	−0.169745	−	0.685459i
$69$	−0.175654	−	0.424067i	−0.0211463	−	0.0510517i
$70$	1.56959	−	5.64230i	0.187602	−	0.674384i
$71$	−2.34721	+	2.34721i	−0.278562	+	0.278562i	−0.832535	−	0.553973i	$-0.813111\pi$
$71$	−2.34721	+	2.34721i	−0.278562	+	0.278562i	0.553973	+	0.832535i	$0.313111\pi$
$72$	−3.27404	+	7.30658i	−0.385849	+	0.861089i
$73$	−2.55659	−	2.55659i	−0.299226	−	0.299226i	0.541485	−	0.840711i	$-0.317862\pi$
$73$	−2.55659	−	2.55659i	−0.299226	−	0.299226i	−0.840711	+	0.541485i	$0.817862\pi$
$74$	10.2507	−	5.78879i	1.19162	−	0.672934i
$75$	4.61778	−	1.91275i	0.533215	−	0.220865i
$76$	−1.35831	+	8.99069i	−0.155809	+	1.03130i
$77$	−0.923900	+	2.23049i	−0.105288	+	0.254188i
$78$	−0.365393	−	0.285945i	−0.0413726	−	0.0323769i
$79$			14.2511i			1.60337i	0.597746	+	0.801686i	$0.296063\pi$
$79$			14.2511i			1.60337i	−0.597746	+	0.801686i	$0.703937\pi$
$80$	−12.7482	−	10.5772i	−1.42529	−	1.18257i
$81$			7.50545i			0.833939i
$82$	5.34263	−	6.82703i	0.589994	−	0.753920i
$83$	−1.74047	+	4.20187i	−0.191041	+	0.461215i	−0.990157	−	0.139963i	$-0.955302\pi$
$83$	−1.74047	+	4.20187i	−0.191041	+	0.461215i	0.799115	+	0.601178i	$0.205302\pi$
$84$	0.662180	−	0.488357i	0.0722497	−	0.0532841i
$85$	11.1397	−	4.61420i	1.20827	−	0.500480i
$86$	−1.01877	−	1.80402i	−0.109857	−	0.194532i
$87$	1.31112	+	1.31112i	0.140567	+	0.140567i
$88$	4.68863	+	4.96449i	0.499810	+	0.529217i
$89$	2.67017	−	2.67017i	0.283037	−	0.283037i	−0.551282	−	0.834319i	$-0.685861\pi$
$89$	2.67017	−	2.67017i	0.283037	−	0.283037i	0.834319	+	0.551282i	$0.185861\pi$
$90$	−15.9720	−	4.44312i	−1.68359	−	0.468346i
$91$	−0.305188	−	0.736788i	−0.0319924	−	0.0772364i
$92$	−1.91092	−	1.15234i	−0.199227	−	0.120140i
$93$	−3.87195	−	1.60381i	−0.401502	−	0.166308i
$94$	2.10180	−	0.256369i	0.216784	−	0.0264425i
$95$	−18.8274			−1.93165
$96$	−0.494643	−	2.27401i	−0.0504843	−	0.232090i
$97$	3.18567			0.323455			0.161728	−	0.986835i	$-0.448293\pi$
$97$	3.18567			0.323455			0.161728	+	0.986835i	$0.448293\pi$
$98$	1.40381	−	0.171231i	0.141806	−	0.0172970i
$99$	6.31398	+	2.61534i	0.634579	+	0.262851i
$100$	12.5482	−	20.8085i	1.25482	−	2.08085i
$101$	1.56095	+	3.76847i	0.155320	+	0.374976i	0.982316	−	0.187232i	$-0.0599517\pi$
$101$	1.56095	+	3.76847i	0.155320	+	0.374976i	−0.826995	+	0.562209i	$0.809952\pi$
$102$	1.63198	+	0.453989i	0.161590	+	0.0449516i
$103$	8.24025	−	8.24025i	0.811936	−	0.811936i	−0.172988	−	0.984924i	$-0.555342\pi$
$103$	8.24025	−	8.24025i	0.811936	−	0.811936i	0.984924	+	0.172988i	$0.0553421\pi$
$104$	−2.25473	−	0.0644338i	−0.221095	−	0.00631825i
$105$	1.20467	+	1.20467i	0.117564	+	0.117564i
$106$	5.36803	+	9.50562i	0.521389	+	0.923267i
$107$	4.35513	−	1.80395i	0.421026	−	0.174395i	−0.162104	−	0.986774i	$-0.551828\pi$
$107$	4.35513	−	1.80395i	0.421026	−	0.174395i	0.583130	+	0.812379i	$0.301828\pi$
$108$	−2.84749	−	3.86101i	−0.274000	−	0.371526i
$109$	5.55056	−	13.4002i	0.531647	−	1.28351i	−0.398784	−	0.917045i	$-0.630568\pi$
$109$	5.55056	−	13.4002i	0.531647	−	1.28351i	0.930432	−	0.366465i	$-0.119432\pi$
$110$	−8.71388	+	11.1350i	−0.830836	+	1.06168i
$111$			3.42454i			0.325043i
$112$	1.18167	−	3.82147i	0.111657	−	0.361095i
$113$		−	21.0444i		−	1.97969i	−0.142146	−	0.989846i	$-0.545400\pi$
$113$		−	21.0444i		−	1.97969i	0.142146	−	0.989846i	$-0.454600\pi$
$114$	−2.08304	−	1.63012i	−0.195094	−	0.152675i
$115$	1.76819	−	4.26879i	0.164885	−	0.398067i
$116$	8.91313	+	1.34659i	0.827563	+	0.125028i
$117$	−2.08567	+	0.863912i	−0.192820	+	0.0798687i
$118$	14.8463	−	8.38401i	1.36671	−	0.771811i
$119$	2.05880	+	2.05880i	0.188730	+	0.188730i
$120$	4.50274	−	1.71611i	0.411042	−	0.156658i
$121$	−3.65667	+	3.65667i	−0.332425	+	0.332425i
$122$	−3.67039	+	13.1942i	−0.332301	+	1.19454i
$123$	0.965053	+	2.32984i	0.0870159	+	0.210075i
$124$	−19.7772	+	4.89755i	−1.77604	+	0.439813i
$125$	27.3541	+	11.3305i	2.44663	+	1.01343i
$126$	−0.484714	−	3.97384i	−0.0431817	−	0.354018i
$127$	15.0163			1.33248			0.666240	−	0.745738i	$-0.267903\pi$
$127$	15.0163			1.33248			0.666240	+	0.745738i	$0.267903\pi$
$128$	−8.49705	−	7.46995i	−0.751040	−	0.660257i
$129$	0.602684			0.0530634
$130$	−0.565506	−	4.63620i	−0.0495982	−	0.406622i
$131$	6.72747	+	2.78661i	0.587782	+	0.243467i	0.656696	−	0.754155i	$-0.271953\pi$
$131$	6.72747	+	2.78661i	0.587782	+	0.243467i	−0.0689141	+	0.997623i	$0.521953\pi$
$132$	−1.92818	+	0.477488i	−0.167827	+	0.0415600i
$133$	−1.73982	−	4.20029i	−0.150861	−	0.364211i
$134$	−3.35169	+	12.0485i	−0.289542	+	1.04083i
$135$	7.02414	−	7.02414i	0.604541	−	0.604541i
$136$	7.69526	−	2.93286i	0.659863	−	0.251491i
$137$	3.03206	+	3.03206i	0.259046	+	0.259046i	0.824666	−	0.565620i	$-0.191363\pi$
$137$	3.03206	+	3.03206i	0.259046	+	0.259046i	−0.565620	+	0.824666i	$0.691363\pi$
$138$	0.565232	−	0.319199i	0.0481157	−	0.0271720i
$139$	−15.8280	+	6.55615i	−1.34251	+	0.556086i	−0.934197	−	0.356757i	$-0.883882\pi$
$139$	−15.8280	+	6.55615i	−1.34251	+	0.556086i	−0.408312	+	0.912842i	$0.633882\pi$
$140$	8.18948	+	1.23727i	0.692137	+	0.104568i
$141$	−0.235710	+	0.569055i	−0.0198504	+	0.0479231i
$142$	−3.69695	−	2.89312i	−0.310241	−	0.242785i
$143$			1.92536i			0.161007i
$144$	−10.8177	−	3.34501i	−0.901472	−	0.278751i
$145$			18.6650i			1.55004i
$146$	3.15119	−	4.02673i	0.260795	−	0.333254i
$147$	−0.157433	+	0.380077i	−0.0129849	+	0.0313482i
$148$	9.88160	+	13.3988i	0.812263	+	1.10137i
$149$	−3.09755	+	1.28305i	−0.253761	+	0.105111i	−0.505938	−	0.862570i	$-0.668854\pi$
$149$	−3.09755	+	1.28305i	−0.253761	+	0.105111i	0.252177	+	0.967681i	$0.418854\pi$
$150$	3.47584	+	6.15496i	0.283801	+	0.502550i
$151$	−5.90592	−	5.90592i	−0.480617	−	0.480617i	0.424712	−	0.905329i	$-0.360375\pi$
$151$	−5.90592	−	5.90592i	−0.480617	−	0.480617i	−0.905329	+	0.424712i	$0.860375\pi$
$152$	−12.8538	−	0.367325i	−1.04258	−	0.0297940i
$153$	5.82797	−	5.82797i	0.471164	−	0.471164i
$154$	−3.28939	−	0.915049i	−0.265066	−	0.0737368i
$155$	−16.1445	−	38.9763i	−1.29676	−	3.13065i
$156$	0.338846	−	0.561905i	0.0271294	−	0.0449884i
$157$	−15.8936	−	6.58334i	−1.26845	−	0.525408i	−0.355955	−	0.934503i	$-0.615844\pi$
$157$	−15.8936	−	6.58334i	−1.26845	−	0.525408i	−0.912492	+	0.409096i	$0.865844\pi$
$158$	−20.0058	+	2.44023i	−1.59158	+	0.194134i
$159$	−3.17563			−0.251843
$160$	12.6655	−	19.7072i	1.00129	−	1.55799i
$161$	1.11574			0.0879326
$162$	−10.5362	+	1.28517i	−0.827804	+	0.100972i
$163$	−9.15222	−	3.79097i	−0.716857	−	0.296932i	−0.00571828	−	0.999984i	$-0.501820\pi$
$163$	−9.15222	−	3.79097i	−0.716857	−	0.296932i	−0.711139	+	0.703052i	$0.751820\pi$
$164$	10.4987	+	6.33103i	0.819809	+	0.494370i
$165$	−1.57401	−	3.80000i	−0.122537	−	0.295830i
$166$	−6.19664	−	1.72380i	−0.480952	−	0.133793i
$167$	11.7702	−	11.7702i	0.910807	−	0.910807i	−0.0855287	−	0.996336i	$-0.527258\pi$
$167$	11.7702	−	11.7702i	0.910807	−	0.910807i	0.996336	+	0.0855287i	$0.0272579\pi$
$168$	0.798946	+	0.845952i	0.0616400	+	0.0652666i
$169$	8.74267	+	8.74267i	0.672513	+	0.672513i
$170$	8.38491	+	14.8479i	0.643094	+	1.13878i
$171$	−11.8900	+	4.92500i	−0.909251	+	0.376624i
$172$	2.35805	−	1.73906i	0.179800	−	0.132602i
$173$	5.45770	−	13.1761i	0.414941	−	1.00176i	−0.568850	−	0.822441i	$-0.692612\pi$
$173$	5.45770	−	13.1761i	0.414941	−	1.00176i	0.983792	−	0.179316i	$-0.0573884\pi$
$174$	−1.61606	+	2.06507i	−0.122513	+	0.156552i
$175$			12.1496i			0.918422i
$176$	−6.16636	+	7.43202i	−0.464807	+	0.560210i
$177$			4.95982i			0.372803i
$178$	4.20562	+	3.29119i	0.315225	+	0.246685i
$179$	−9.60664	+	23.1925i	−0.718034	+	1.73349i	−0.0391592	+	0.999233i	$0.512468\pi$
$179$	−9.60664	+	23.1925i	−0.718034	+	1.73349i	−0.678875	+	0.734254i	$0.737532\pi$
$180$	3.50240	−	23.1824i	0.261053	−	1.72791i
$181$	−4.67610	+	1.93691i	−0.347572	+	0.143969i	−0.549638	−	0.835403i	$-0.685234\pi$
$181$	−4.67610	+	1.93691i	−0.347572	+	0.143969i	0.202066	+	0.979372i	$0.435234\pi$
$182$	0.982052	−	0.554586i	0.0727946	−	0.0411087i
$183$	−2.81705	−	2.81705i	−0.208242	−	0.208242i
$184$	1.29046	−	2.87988i	0.0951340	−	0.212308i
$185$	−24.3758	+	24.3758i	−1.79214	+	1.79214i
$186$	1.58845	−	5.71010i	0.116471	−	0.418685i
$187$	−2.69002	−	6.49427i	−0.196713	−	0.474908i
$188$	0.719787	+	2.90663i	0.0524959	+	0.211987i
$189$	2.21614	+	0.917954i	0.161200	+	0.0667713i
$190$	−3.22384	−	26.4301i	−0.233882	−	1.91744i
$191$	−24.7308			−1.78946			−0.894728	−	0.446611i	$-0.852631\pi$
$191$	−24.7308			−1.78946			−0.894728	+	0.446611i	$0.852631\pi$
$192$	3.10758	−	1.08377i	0.224270	−	0.0782141i
$193$	−5.75563			−0.414299			−0.207149	−	0.978309i	$-0.566419\pi$
$193$	−5.75563			−0.414299			−0.207149	+	0.978309i	$0.566419\pi$
$194$	0.545486	+	4.47207i	0.0391636	+	0.321076i
$195$	1.25524	+	0.519936i	0.0898894	+	0.0372334i
$196$	0.480752	+	1.94136i	0.0343394	+	0.138669i
$197$	1.02531	+	2.47532i	0.0730504	+	0.176359i	0.956187	−	0.292757i	$-0.0945726\pi$
$197$	1.02531	+	2.47532i	0.0730504	+	0.176359i	−0.883137	+	0.469116i	$0.844573\pi$
$198$	−2.59028	+	9.31145i	−0.184083	+	0.661736i
$199$	11.7785	−	11.7785i	0.834955	−	0.834955i	−0.153235	−	0.988190i	$-0.548969\pi$
$199$	11.7785	−	11.7785i	0.834955	−	0.834955i	0.988190	+	0.153235i	$0.0489690\pi$
$200$	31.3598	+	14.0522i	2.21747	+	0.993638i
$201$	−2.57244	−	2.57244i	−0.181446	−	0.181446i
$202$	−5.02292	+	2.83655i	−0.353412	+	0.199579i
$203$	−4.16405	+	1.72481i	−0.292259	+	0.121058i
$204$	−0.357867	+	2.36873i	−0.0250557	+	0.165844i
$205$	−9.71453	+	23.4530i	−0.678492	+	1.63803i
$206$	12.9787	+	10.1568i	0.904271	+	0.707654i
$207$		−	3.15839i		−	0.219523i
$208$	−0.295628	−	3.17625i	−0.0204981	−	0.220233i
$209$			10.9761i			0.759235i
$210$	−1.48485	+	1.89740i	−0.102464	+	0.130933i
$211$	−8.51412	+	20.5549i	−0.586136	+	1.41506i	0.301033	+	0.953614i	$0.402669\pi$
$211$	−8.51412	+	20.5549i	−0.586136	+	1.41506i	−0.887169	+	0.461444i	$0.847331\pi$
$212$	−12.4249	+	9.16335i	−0.853345	+	0.629341i
$213$	1.26165	−	0.522592i	0.0864467	−	0.0358074i
$214$	3.27814	+	5.80487i	0.224089	+	0.396813i
$215$	4.28988	+	4.28988i	0.292568	+	0.292568i
$216$	4.93254	−	4.65846i	0.335617	−	0.316968i
$217$	7.20349	−	7.20349i	0.489005	−	0.489005i
$218$	19.7618	+	5.49739i	1.33844	+	0.372330i
$219$	0.569209	+	1.37419i	0.0384636	+	0.0928592i
$220$	−17.1235	−	10.3260i	−1.15446	−	0.696177i
$221$	2.14522	+	0.888581i	0.144303	+	0.0597724i
$222$	−4.80740	+	0.586388i	−0.322652	+	0.0393558i
$223$	−11.4519			−0.766878			−0.383439	−	0.923566i	$-0.625260\pi$
$223$	−11.4519			−0.766878			−0.383439	+	0.923566i	$0.625260\pi$
$224$	5.56696	+	1.00448i	0.371958	+	0.0671146i
$225$	34.3925			2.29283
$226$	29.5423	−	3.60346i	1.96513	−	0.239699i
$227$	10.6172	+	4.39777i	0.704686	+	0.291890i	0.706104	−	0.708109i	$-0.250451\pi$
$227$	10.6172	+	4.39777i	0.704686	+	0.291890i	−0.00141775	+	0.999999i	$0.500451\pi$
$228$	1.93170	−	3.20331i	0.127930	−	0.212144i
$229$	−8.46390	−	20.4337i	−0.559310	−	1.35029i	−0.910313	−	0.413920i	$-0.864159\pi$
$229$	−8.46390	−	20.4337i	−0.559310	−	1.35029i	0.351003	−	0.936374i	$-0.385841\pi$
$230$	6.29534	+	1.75125i	0.415102	+	0.115474i
$231$	0.702306	−	0.702306i	0.0462084	−	0.0462084i
$232$	−0.364156	+	12.7429i	−0.0239080	+	0.836613i
$233$	6.09827	+	6.09827i	0.399511	+	0.399511i	0.878061	−	0.478550i	$-0.158837\pi$
$233$	6.09827	+	6.09827i	0.399511	+	0.399511i	−0.478550	+	0.878061i	$0.658837\pi$
$234$	−1.56990	−	2.77995i	−0.102628	−	0.181731i
$235$	−5.72829	+	2.37274i	−0.373673	+	0.154780i
$236$	14.3117	+	19.4057i	0.931612	+	1.26321i
$237$	2.24359	−	5.41651i	0.145737	−	0.351840i
$238$	−2.53764	+	3.24270i	−0.164490	+	0.210193i
$239$			2.99774i			0.193908i	0.995289	+	0.0969540i	$0.0309100\pi$
$239$			2.99774i			0.193908i	−0.995289	+	0.0969540i	$0.969090\pi$
$240$	3.18009	+	6.02713i	0.205274	+	0.389050i
$241$		−	19.9724i		−	1.28654i	−0.765641	−	0.643268i	$-0.777578\pi$
$241$		−	19.9724i		−	1.28654i	0.765641	−	0.643268i	$-0.222422\pi$
$242$	−5.75940	−	4.50713i	−0.370229	−	0.289729i
$243$	3.93547	−	9.50106i	0.252460	−	0.609493i
$244$	−19.1506	−	2.89327i	−1.22599	−	0.185222i
$245$	−3.82598	+	1.58477i	−0.244433	+	0.101247i
$246$	−3.10541	+	1.75369i	−0.197994	+	0.111811i
$247$	−2.56375	−	2.56375i	−0.163128	−	0.163128i
$248$	−10.2617	−	26.9247i	−0.651618	−	1.70972i
$249$	1.32302	−	1.32302i	0.0838433	−	0.0838433i
$250$	−11.2219	+	40.3401i	−0.709736	+	2.55133i
$251$	1.20442	+	2.90774i	0.0760225	+	0.183535i	0.957322	−	0.289024i	$-0.0933306\pi$
$251$	1.20442	+	2.90774i	0.0760225	+	0.183535i	−0.881299	+	0.472558i	$0.843331\pi$
$252$	5.49552	−	1.36089i	0.346185	−	0.0857281i
$253$	−2.48865	−	1.03083i	−0.156460	−	0.0648079i
$254$	2.57126	+	21.0800i	0.161335	+	1.32268i
$255$	−4.96036			−0.310630
$256$	9.03142	−	13.2073i	0.564464	−	0.825458i
$257$	9.29055			0.579529			0.289764	−	0.957098i	$-0.406423\pi$
$257$	9.29055			0.579529			0.289764	+	0.957098i	$0.406423\pi$
$258$	0.103198	+	0.846054i	0.00642485	+	0.0526730i
$259$	−7.69062	−	3.18556i	−0.477872	−	0.197941i
$260$	6.41151	−	1.58772i	0.397625	−	0.0984665i
$261$	4.88251	+	11.7874i	0.302220	+	0.729623i
$262$	−2.75992	+	9.92124i	−0.170508	+	0.612936i
$263$	−1.67985	+	1.67985i	−0.103584	+	0.103584i	−0.757000	−	0.653415i	$-0.773336\pi$
$263$	−1.67985	+	1.67985i	−0.103584	+	0.103584i	0.653415	+	0.757000i	$0.273336\pi$
$264$	−1.00047	−	2.62504i	−0.0615745	−	0.161560i
$265$	−22.6040	−	22.6040i	−1.38855	−	1.38855i
$266$	5.59849	−	3.16159i	0.343266	−	0.193850i
$267$	−1.43524	+	0.594496i	−0.0878353	+	0.0363826i
$268$	−17.4877	−	2.64205i	−1.06823	−	0.161389i
$269$	−3.11902	+	7.52997i	−0.190170	+	0.459111i	−0.989991	−	0.141127i	$-0.954927\pi$
$269$	−3.11902	+	7.52997i	−0.190170	+	0.459111i	0.799822	+	0.600238i	$0.204927\pi$
$270$	11.0633	+	8.65779i	0.673291	+	0.526897i
$271$			14.6934i			0.892558i	0.894894	+	0.446279i	$0.147251\pi$
$271$			14.6934i			0.892558i	−0.894894	+	0.446279i	$0.852749\pi$
$272$	5.43484	+	10.3005i	0.329536	+	0.624559i
$273$			0.328083i			0.0198565i
$274$	−3.73725	+	4.77561i	−0.225775	+	0.288505i
$275$	11.2250	−	27.0996i	0.676893	−	1.63416i
$276$	0.544879	+	0.738820i	0.0327979	+	0.0444718i
$277$	16.8633	−	6.98503i	1.01322	−	0.419690i	0.186592	−	0.982438i	$-0.440256\pi$
$277$	16.8633	−	6.98503i	1.01322	−	0.419690i	0.826629	+	0.562748i	$0.190256\pi$
$278$	−11.9138	−	21.0968i	−0.714544	−	1.26530i
$279$	−20.3913	−	20.3913i	−1.22080	−	1.22080i
$280$	−0.334590	+	11.7083i	−0.0199956	+	0.699706i
$281$	−1.57732	+	1.57732i	−0.0940951	+	0.0940951i	−0.752587	−	0.658492i	$-0.771194\pi$
$281$	−1.57732	+	1.57732i	−0.0940951	+	0.0940951i	0.658492	+	0.752587i	$0.271194\pi$
$282$	−0.839206	−	0.233452i	−0.0499740	−	0.0139019i
$283$	8.55092	+	20.6437i	0.508299	+	1.22714i	0.944862	+	0.327469i	$0.106196\pi$
$283$	8.55092	+	20.6437i	0.508299	+	1.22714i	−0.436563	+	0.899674i	$0.643804\pi$
$284$	3.42835	−	5.68520i	0.203435	−	0.337355i
$285$	7.15586	+	2.96406i	0.423877	+	0.175576i
$286$	−2.70284	+	0.329682i	−0.159822	+	0.0194945i
$287$	−6.12993			−0.361838
$288$	2.84344	−	15.7587i	0.167551	−	0.928590i
$289$	8.52266			0.501333
$290$	−26.2021	+	3.19603i	−1.53864	+	0.187677i
$291$	−1.21080	−	0.501529i	−0.0709783	−	0.0294002i
$292$	6.19234	+	3.73417i	0.362379	+	0.218526i
$293$	−2.58595	−	6.24303i	−0.151073	−	0.364722i	0.830167	−	0.557515i	$-0.188245\pi$
$293$	−2.58595	−	6.24303i	−0.151073	−	0.364722i	−0.981239	+	0.192794i	$0.938245\pi$
$294$	−0.560513	−	0.155925i	−0.0326898	−	0.00909372i
$295$	−35.3038	+	35.3038i	−2.05547	+	2.05547i
$296$	−17.1173	+	16.1662i	−0.994924	+	0.939640i
$297$	−4.09498	−	4.09498i	−0.237615	−	0.237615i
$298$	−2.33155	−	4.12867i	−0.135063	−	0.239168i
$299$	0.822064	−	0.340510i	0.0475412	−	0.0196922i
$300$	−8.04521	+	5.93333i	−0.464490	+	0.342561i
$301$	−0.560626	+	1.35347i	−0.0323140	+	0.0780128i
$302$	7.27950	−	9.30206i	0.418888	−	0.535273i
$303$		−	1.67805i		−	0.0964016i
$304$	−1.68532	−	18.1072i	−0.0966596	−	1.03852i
$305$		−	40.1032i		−	2.29630i
$306$	9.17929	+	7.18343i	0.524745	+	0.410649i
$307$	1.20890	−	2.91855i	0.0689958	−	0.166571i	−0.885620	−	0.464411i	$-0.846266\pi$
$307$	1.20890	−	2.91855i	0.0689958	−	0.166571i	0.954616	+	0.297840i	$0.0962662\pi$
$308$	0.721309	−	4.77435i	0.0411004	−	0.272044i
$309$	−4.42922	+	1.83464i	−0.251969	+	0.104369i
$310$	51.9508	−	29.3377i	2.95061	−	1.66627i
$311$	−3.45753	−	3.45753i	−0.196058	−	0.196058i	0.602249	−	0.798308i	$-0.294271\pi$
$311$	−3.45753	−	3.45753i	−0.196058	−	0.196058i	−0.798308	+	0.602249i	$0.794271\pi$
$312$	0.846828	+	0.379459i	0.0479422	+	0.0214826i
$313$	21.8063	−	21.8063i	1.23256	−	1.23256i	0.269586	−	0.962976i	$-0.413113\pi$
$313$	21.8063	−	21.8063i	1.23256	−	1.23256i	0.962976	−	0.269586i	$-0.0868869\pi$
$314$	6.52027	−	23.4388i	0.367960	−	1.32273i
$315$	4.48610	+	10.8304i	0.252763	+	0.610224i
$316$	−6.85123	−	27.6665i	−0.385412	−	1.55636i
$317$	−2.05083	−	0.849480i	−0.115186	−	0.0477115i	0.324346	−	0.945938i	$-0.394856\pi$
$317$	−2.05083	−	0.849480i	−0.115186	−	0.0477115i	−0.439532	+	0.898227i	$0.644856\pi$
$318$	−0.543766	−	4.45797i	−0.0304929	−	0.249991i
$319$	10.8814			0.609243
$320$	29.8338	+	14.4054i	1.66776	+	0.805287i
$321$	−1.93928			−0.108240
$322$	0.191050	+	1.56629i	0.0106468	+	0.0872857i
$323$	12.2295	+	5.06563i	0.680468	+	0.281859i
$324$	−3.60826	−	14.5708i	−0.200459	−	0.809488i
$325$	3.70790	+	8.95167i	0.205678	+	0.496549i
$326$	3.75466	−	13.4971i	0.207951	−	0.747535i
$327$	−4.21928	+	4.21928i	−0.233327	+	0.233327i
$328$	−7.08985	+	15.8222i	−0.391471	+	0.873635i
$329$	−1.05869	−	1.05869i	−0.0583674	−	0.0583674i
$330$	5.06496	−	2.86029i	0.278817	−	0.157454i
$331$	14.4315	−	5.97771i	0.793225	−	0.328565i	0.0509857	−	0.998699i	$-0.483764\pi$
$331$	14.4315	−	5.97771i	0.793225	−	0.328565i	0.742239	+	0.670135i	$0.233764\pi$
$332$	1.35882	−	8.99407i	0.0745751	−	0.493613i
$333$	−9.01754	+	21.7703i	−0.494158	+	1.19300i
$334$	18.5386	+	14.5077i	1.01439	+	0.793827i
$335$		−	36.6211i		−	2.00082i
$336$	−1.05075	+	1.26642i	−0.0573232	+	0.0690889i
$337$			6.70028i			0.364987i	0.983207	+	0.182494i	$0.0584169\pi$
$337$			6.70028i			0.364987i	−0.983207	+	0.182494i	$0.941583\pi$
$338$	−10.7760	+	13.7701i	−0.586138	+	0.748992i
$339$	−3.31308	+	7.99849i	−0.179942	+	0.434419i
$340$	−19.4078	+	14.3132i	−1.05254	+	0.776244i
$341$	−22.7226	+	9.41202i	−1.23050	+	0.509690i
$342$	−8.94969	−	15.8480i	−0.483944	−	0.856960i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	2.84508	+	3.01247i	0.153397	+	0.162422i
$345$	−1.34410	+	1.34410i	−0.0723638	+	0.0723638i
$346$	19.4312	+	5.40542i	1.04463	+	0.290597i
$347$	−0.753539	−	1.81920i	−0.0404521	−	0.0976600i	0.902362	−	0.430979i	$-0.141832\pi$
$347$	−0.753539	−	1.81920i	−0.0404521	−	0.0976600i	−0.942814	+	0.333319i	$0.891832\pi$
$348$	−3.17568	−	1.91503i	−0.170234	−	0.102656i
$349$	1.23750	+	0.512589i	0.0662418	+	0.0274383i	0.415558	−	0.909567i	$-0.363586\pi$
$349$	1.23750	+	0.512589i	0.0662418	+	0.0274383i	−0.349317	+	0.937005i	$0.613586\pi$
$350$	−17.0557	+	2.08039i	−0.911665	+	0.111201i
$351$	1.91297			0.102107
$352$	−11.4890	−	7.38380i	−0.612367	−	0.393558i
$353$	−5.15658			−0.274457			−0.137229	−	0.990539i	$-0.543819\pi$
$353$	−5.15658			−0.274457			−0.137229	+	0.990539i	$0.543819\pi$
$354$	−6.96265	+	0.849277i	−0.370060	+	0.0451386i
$355$	12.7001	+	5.26057i	0.674054	+	0.279202i
$356$	−3.90007	+	6.46744i	−0.206703	+	0.342774i
$357$	−0.458380	−	1.10663i	−0.0242600	−	0.0585689i
$358$	−34.2028	−	9.51461i	−1.80767	−	0.502863i
$359$	11.2858	−	11.2858i	0.595642	−	0.595642i	−0.343508	−	0.939150i	$-0.611615\pi$
$359$	11.2858	−	11.2858i	0.595642	−	0.595642i	0.939150	+	0.343508i	$0.111615\pi$
$360$	33.1434	+	0.947143i	1.74681	+	0.0499188i
$361$	−1.18043	−	1.18043i	−0.0621281	−	0.0621281i
$362$	−3.51974	−	6.23270i	−0.184993	−	0.327583i
$363$	1.96550	−	0.814136i	0.103162	−	0.0427310i
$364$	0.946691	+	1.28365i	0.0496201	+	0.0672816i
$365$	−5.72983	+	13.8330i	−0.299913	+	0.724055i
$366$	3.47223	−	4.43696i	0.181496	−	0.231924i
$367$		−	29.5014i		−	1.53996i	−0.638067	−	0.769981i	$-0.720266\pi$
$367$		−	29.5014i		−	1.53996i	0.638067	−	0.769981i	$-0.279734\pi$
$368$	4.26377	+	1.31843i	0.222264	+	0.0687281i
$369$			17.3523i			0.903326i
$370$	−38.3928	−	30.0450i	−1.99595	−	1.56197i
$371$	2.95402	−	7.13162i	0.153365	−	0.370255i
$372$	8.28788	+	1.25213i	0.429707	+	0.0649200i
$373$	−19.2237	+	7.96270i	−0.995364	+	0.412293i	−0.820095	−	0.572228i	$-0.806079\pi$
$373$	−19.2237	+	7.96270i	−0.995364	+	0.412293i	−0.175269	+	0.984521i	$0.556079\pi$
$374$	8.65611	−	4.88829i	0.447597	−	0.252768i
$375$	−8.61289	−	8.61289i	−0.444768	−	0.444768i
$376$	−3.95710	+	1.50815i	−0.204072	+	0.0777768i
$377$	−2.54164	+	2.54164i	−0.130901	+	0.130901i
$378$	−0.909160	+	3.26821i	−0.0467621	+	0.168099i
$379$	8.62374	+	20.8195i	0.442972	+	1.06943i	0.974901	+	0.222639i	$0.0714672\pi$
$379$	8.62374	+	20.8195i	0.442972	+	1.06943i	−0.531929	+	0.846789i	$0.678533\pi$
$380$	36.5508	−	9.05131i	1.87502	−	0.464323i
$381$	−5.70734	−	2.36406i	−0.292396	−	0.121114i
$382$	−4.23468	−	34.7173i	−0.216665	−	1.77629i
$383$	9.27333			0.473845			0.236922	−	0.971529i	$-0.423861\pi$
$383$	9.27333			0.473845			0.236922	+	0.971529i	$0.423861\pi$
$384$	2.05352	+	4.17687i	0.104793	+	0.213150i
$385$	9.99798			0.509544
$386$	−0.985543	−	8.07980i	−0.0501628	−	0.411251i
$387$	3.83135	+	1.58700i	0.194758	+	0.0806716i
$388$	−6.18452	+	1.53152i	−0.313972	+	0.0777509i
$389$	3.98472	+	9.61998i	0.202034	+	0.487752i	0.992127	−	0.125234i	$-0.0399681\pi$
$389$	3.98472	+	9.61998i	0.202034	+	0.487752i	−0.790094	+	0.612986i	$0.789968\pi$
$390$	−0.514955	+	1.85114i	−0.0260758	+	0.0937362i
$391$	−2.29709	+	2.29709i	−0.116169	+	0.116169i
$392$	−2.64298	+	1.00731i	−0.133491	+	0.0508766i
$393$	−2.11825	−	2.11825i	−0.106852	−	0.106852i
$394$	−3.29931	+	1.86319i	−0.166217	+	0.0938664i
$395$	54.5243	−	22.5847i	2.74341	−	1.13636i
$396$	−13.5150	−	2.04185i	−0.679156	−	0.102607i
$397$	−8.82563	+	21.3070i	−0.442946	+	1.06937i	0.531965	+	0.846767i	$0.321454\pi$
$397$	−8.82563	+	21.3070i	−0.442946	+	1.06937i	−0.974910	+	0.222599i	$0.928546\pi$
$398$	18.5516	+	14.5179i	0.929908	+	0.727717i
$399$			1.87034i			0.0936340i
$400$	−14.3568	+	46.4293i	−0.717839	+	2.32147i
$401$			8.55052i			0.426993i	0.976944	+	0.213496i	$0.0684851\pi$
$401$			8.55052i			0.426993i	−0.976944	+	0.213496i	$0.931515\pi$
$402$	3.17073	−	4.05170i	0.158142	−	0.202080i
$403$	3.10903	−	7.50586i	0.154872	−	0.373894i
$404$	−4.84206	−	6.56552i	−0.240902	−	0.326647i
$405$	28.7157	−	11.8944i	1.42689	−	0.591038i
$406$	−3.13432	−	5.55019i	−0.155553	−	0.275452i
$407$	14.2107	+	14.2107i	0.704400	+	0.704400i
$408$	−3.38652	−	0.0967770i	−0.167658	−	0.00479118i
$409$	−4.54403	+	4.54403i	−0.224688	+	0.224688i	−0.810469	−	0.585781i	$-0.800788\pi$
$409$	−4.54403	+	4.54403i	−0.224688	+	0.224688i	0.585781	+	0.810469i	$0.300788\pi$
$410$	−34.5869	−	9.62147i	−1.70813	−	0.475171i
$411$	−0.675069	−	1.62976i	−0.0332987	−	0.0803902i
$412$	−12.0358	+	19.9588i	−0.592960	+	0.983300i
$413$	−11.1385	−	4.61370i	−0.548088	−	0.227026i
$414$	4.43377	−	0.540815i	0.217908	−	0.0265796i
$415$	18.8345			0.924548
$416$	4.40822	−	0.958878i	0.216131	−	0.0470129i
$417$	7.04799			0.345142
$418$	−15.4084	+	1.87946i	−0.753649	+	0.0919272i
$419$	0.322992	+	0.133788i	0.0157792	+	0.00653595i	0.390559	−	0.920578i	$-0.372282\pi$
$419$	0.322992	+	0.133788i	0.0157792	+	0.00653595i	−0.374780	+	0.927114i	$0.622282\pi$
$420$	−2.91784	−	1.75955i	−0.142376	−	0.0858572i
$421$	−1.09888	−	2.65293i	−0.0535560	−	0.129296i	0.894837	−	0.446393i	$-0.147292\pi$
$421$	−1.09888	−	2.65293i	−0.0535560	−	0.129296i	−0.948393	+	0.317098i	$0.897292\pi$
$422$	−30.3130	−	8.43256i	−1.47562	−	0.410490i
$423$	−2.99689	+	2.99689i	−0.145714	+	0.145714i
$424$	−14.9911	−	15.8731i	−0.728033	−	0.770867i
$425$	−25.0136	−	25.0136i	−1.21334	−	1.21334i
$426$	0.949652	+	1.68163i	0.0460108	+	0.0814752i
$427$	8.94680	−	3.70589i	0.432966	−	0.179340i
$428$	−7.58761	+	5.59586i	−0.366761	+	0.270486i
$429$	0.303116	−	0.731786i	0.0146346	−	0.0353310i
$430$	−5.28762	+	6.75674i	−0.254992	+	0.325839i
$431$			31.9632i			1.53961i	0.638278	+	0.769806i	$0.279647\pi$
$431$			31.9632i			1.53961i	−0.638278	+	0.769806i	$0.720353\pi$
$432$	7.38419	+	6.12667i	0.355272	+	0.294770i
$433$		−	2.92548i		−	0.140590i	−0.997526	−	0.0702949i	$-0.977606\pi$
$433$		−	2.92548i		−	0.140590i	0.997526	−	0.0702949i	$-0.0223940\pi$
$434$	11.3458	+	8.87886i	0.544615	+	0.426199i
$435$	2.93849	−	7.09413i	0.140890	−	0.340138i
$436$	−4.33344	+	28.6831i	−0.207534	+	1.37367i
$437$	4.68643	−	1.94118i	0.224182	−	0.0928593i
$438$	−1.83164	+	1.03436i	−0.0875189	+	0.0494239i
$439$	10.9461	+	10.9461i	0.522431	+	0.522431i	0.918305	−	0.395874i	$-0.129558\pi$
$439$	10.9461	+	10.9461i	0.522431	+	0.522431i	−0.395874	+	0.918305i	$0.629558\pi$
$440$	11.5636	−	25.8062i	0.551274	−	1.23026i
$441$	−2.00165	+	2.00165i	−0.0953165	+	0.0953165i
$442$	−0.880068	+	3.16364i	−0.0418606	+	0.150479i
$443$	0.912309	+	2.20251i	0.0433451	+	0.104644i	0.944069	−	0.329747i	$-0.106963\pi$
$443$	0.912309	+	2.20251i	0.0433451	+	0.104644i	−0.900724	+	0.434391i	$0.856963\pi$
$444$	−1.64635	−	6.64827i	−0.0781325	−	0.315513i
$445$	−14.4476	−	5.98439i	−0.684882	−	0.283687i
$446$	−1.96093	−	16.0763i	−0.0928527	−	0.761236i
$447$	1.37930			0.0652388
$448$	−0.456861	+	7.98694i	−0.0215846	+	0.377348i
$449$	10.3640			0.489109			0.244555	−	0.969636i	$-0.421358\pi$
$449$	10.3640			0.489109			0.244555	+	0.969636i	$0.421358\pi$
$450$	5.88907	+	48.2805i	0.277614	+	2.27597i
$451$	13.6728	+	5.66344i	0.643825	+	0.266681i
$452$	10.1171	+	40.8548i	0.475870	+	1.92165i
$453$	1.31492	+	3.17449i	0.0617802	+	0.149151i
$454$	−4.35564	+	15.6575i	−0.204420	+	0.734843i
$455$	−2.33528	+	2.33528i	−0.109480	+	0.109480i
$456$	4.82760	+	2.16322i	0.226073	+	0.101302i
$457$	17.7126	+	17.7126i	0.828561	+	0.828561i	0.987318	−	0.158756i	$-0.0507484\pi$
$457$	17.7126	+	17.7126i	0.828561	+	0.828561i	−0.158756	+	0.987318i	$0.550748\pi$
$458$	27.2357	−	15.3806i	1.27264	−	0.718687i
$459$	−6.45247	+	2.67270i	−0.301176	+	0.124751i
$460$	−1.38047	+	9.13732i	−0.0643646	+	0.426030i
$461$	1.14895	−	2.77381i	0.0535120	−	0.129189i	−0.894863	−	0.446342i	$-0.852727\pi$
$461$	1.14895	−	2.77381i	0.0535120	−	0.129189i	0.948375	+	0.317152i	$0.102727\pi$
$462$	1.10616	+	0.865647i	0.0514633	+	0.0402735i
$463$		−	13.6044i		−	0.632248i	−0.948718	−	0.316124i	$-0.897618\pi$
$463$		−	13.6044i		−	0.632248i	0.948718	−	0.316124i	$-0.102382\pi$
$464$	−17.9510	+	1.67078i	−0.833353	+	0.0775640i
$465$			17.3557i			0.804849i
$466$	−7.51659	+	9.60502i	−0.348199	+	0.444944i
$467$	−7.39496	+	17.8530i	−0.342198	+	0.826139i	0.655295	+	0.755373i	$0.272544\pi$
$467$	−7.39496	+	17.8530i	−0.342198	+	0.826139i	−0.997493	+	0.0707658i	$0.977456\pi$
$468$	3.63370	−	2.67985i	0.167968	−	0.123876i
$469$	8.16996	−	3.38411i	0.377253	−	0.156264i
$470$	−4.31173	−	7.63514i	−0.198885	−	0.352183i
$471$	5.00435	+	5.00435i	0.230588	+	0.230588i
$472$	−24.7913	+	23.4138i	−1.14111	+	1.07771i
$473$	2.50095	−	2.50095i	0.114994	−	0.114994i
$474$	7.98791	+	2.22210i	0.366897	+	0.102064i
$475$	21.1380	+	51.0318i	0.969880	+	2.34150i
$476$	−4.98665	−	3.00710i	−0.228563	−	0.137830i
$477$	−20.1879	−	8.36210i	−0.924340	−	0.382874i
$478$	−4.20826	+	0.513307i	−0.192481	+	0.0234781i
$479$	24.3713			1.11355			0.556776	−	0.830663i	$-0.312038\pi$
$479$	24.3713			1.11355			0.556776	+	0.830663i	$0.312038\pi$
$480$	−7.91641	+	5.49628i	−0.361333	+	0.250870i
$481$	−6.63855			−0.302692
$482$	28.0375	−	3.41990i	1.27707	−	0.155772i
$483$	−0.424067	−	0.175654i	−0.0192957	−	0.00799255i
$484$	5.34096	−	8.85686i	0.242771	−	0.402585i
$485$	−5.04855	−	12.1883i	−0.229243	−	0.553441i
$486$	14.0115	+	3.89777i	0.635577	+	0.176806i
$487$	26.0865	−	26.0865i	1.18209	−	1.18209i	0.202892	−	0.979201i	$-0.434966\pi$
$487$	26.0865	−	26.0865i	1.18209	−	1.18209i	0.979201	−	0.202892i	$-0.0650341\pi$
$488$	0.782418	−	27.3792i	0.0354184	−	1.23940i
$489$	2.88172	+	2.88172i	0.130316	+	0.130316i
$490$	−2.87984	−	5.09958i	−0.130098	−	0.230375i
$491$	−16.6186	+	6.88366i	−0.749988	+	0.310655i	−0.724737	−	0.689026i	$-0.758039\pi$
$491$	−16.6186	+	6.88366i	−0.749988	+	0.310655i	−0.0252512	+	0.999681i	$0.508039\pi$
$492$	−2.99359	−	4.05912i	−0.134962	−	0.182999i
$493$	5.02193	−	12.1240i	0.226176	−	0.546038i
$494$	3.16002	−	4.03801i	0.142176	−	0.181679i
$495$		−	28.3018i		−	1.27207i
$496$	36.0401	−	19.0158i	1.61825	−	0.853835i
$497$			3.31945i			0.148898i
$498$	2.08382	+	1.63073i	0.0933781	+	0.0730748i
$499$	−0.598414	+	1.44470i	−0.0267887	+	0.0646736i	−0.936708	−	0.350112i	$-0.886143\pi$
$499$	−0.598414	+	1.44470i	−0.0267887	+	0.0646736i	0.909919	+	0.414786i	$0.136143\pi$
$500$	−58.5514	−	8.84593i	−2.61850	−	0.395602i
$501$	−6.32661	+	2.62057i	−0.282652	+	0.117078i
$502$	−3.87567	+	2.18868i	−0.172980	+	0.0976854i
$503$	−7.83172	−	7.83172i	−0.349199	−	0.349199i	0.510612	−	0.859811i	$-0.329419\pi$
$503$	−7.83172	−	7.83172i	−0.349199	−	0.349199i	−0.859811	+	0.510612i	$0.829419\pi$
$504$	2.85144	+	7.48163i	0.127013	+	0.333258i
$505$	11.9443	−	11.9443i	0.531515	−	0.531515i
$506$	1.02096	−	3.67010i	0.0453871	−	0.163156i
$507$	−1.94650	−	4.69927i	−0.0864472	−	0.208702i
$508$	−29.1520	+	7.21910i	−1.29341	+	0.320296i
$509$	23.1209	+	9.57699i	1.02482	+	0.424493i	0.830839	−	0.556514i	$-0.187861\pi$
$509$	23.1209	+	9.57699i	1.02482	+	0.424493i	0.193977	+	0.981006i	$0.437861\pi$
$510$	−0.849368	−	6.96339i	−0.0376106	−	0.308344i
$511$	−3.61556			−0.159943
$512$	20.0870	+	10.4169i	0.887729	+	0.460366i
$513$	10.9055			0.481489
$514$	1.59083	+	13.0422i	0.0701686	+	0.575265i
$515$	−44.5859	−	18.4681i	−1.96469	−	0.813801i
$516$	−1.17003	+	0.289742i	−0.0515076	+	0.0127552i
$517$	1.38327	+	3.33952i	0.0608363	+	0.146872i
$518$	3.15504	−	11.3416i	0.138625	−	0.498323i
$519$	−4.14869	+	4.14869i	−0.182107	+	0.182107i
$520$	3.32671	+	8.72866i	0.145886	+	0.382777i
$521$	17.7171	+	17.7171i	0.776202	+	0.776202i	0.979183	−	0.202981i	$-0.0650629\pi$
$521$	17.7171	+	17.7171i	0.776202	+	0.776202i	−0.202981	+	0.979183i	$0.565063\pi$
$522$	−15.7112	+	8.87248i	−0.687663	+	0.388338i
$523$	−26.8020	+	11.1017i	−1.17197	+	0.485445i	−0.881843	−	0.471544i	$-0.843697\pi$
$523$	−26.8020	+	11.1017i	−1.17197	+	0.485445i	−0.290125	+	0.956989i	$0.593697\pi$
$524$	−14.4001	−	2.17557i	−0.629072	−	0.0950401i
$525$	1.91275	−	4.61778i	0.0834791	−	0.201536i
$526$	−2.64584	−	2.07055i	−0.115364	−	0.0902803i
$527$			29.6611i			1.29206i
$528$	3.51374	−	1.85395i	0.152916	−	0.0806829i
$529$		−	21.7551i		−	0.945875i
$530$	27.8612	−	35.6022i	1.21021	−	1.54646i
$531$	−13.0603	+	31.5303i	−0.566768	+	1.36830i
$532$	5.39691	+	7.31785i	0.233986	+	0.317269i
$533$	−4.51646	+	1.87078i	−0.195630	+	0.0810324i
$534$	−1.08032	−	1.91301i	−0.0467499	−	0.0827840i
$535$	−13.8038	−	13.8038i	−0.596788	−	0.596788i
$536$	0.714481	−	25.0018i	0.0308609	−	1.07992i
$537$	7.30252	−	7.30252i	0.315127	−	0.315127i
$538$	−11.1047	−	3.08914i	−0.478758	−	0.133182i
$539$	0.923900	+	2.23049i	0.0397952	+	0.0960741i
$540$	−10.2595	+	17.0132i	−0.441499	+	0.732133i
$541$	−26.5886	−	11.0134i	−1.14313	−	0.473501i	−0.270908	−	0.962605i	$-0.587324\pi$
$541$	−26.5886	−	11.0134i	−1.14313	−	0.473501i	−0.872225	+	0.489104i	$0.837324\pi$
$542$	−20.6267	+	2.51596i	−0.885991	+	0.108070i
$543$	2.08221			0.0893563
$544$	−13.5293	+	9.39325i	−0.580064	+	0.402732i
$545$	−60.0653			−2.57292
$546$	−0.460566	+	0.0561780i	−0.0197104	+	0.00240420i
$547$	9.70118	+	4.01836i	0.414793	+	0.171813i	0.580313	−	0.814394i	$-0.302930\pi$
$547$	9.70118	+	4.01836i	0.414793	+	0.171813i	−0.165520	+	0.986206i	$0.552930\pi$
$548$	−7.34398	−	4.42865i	−0.313719	−	0.189182i
$549$	−10.4905	−	25.3262i	−0.447722	−	1.08090i
$550$	39.9647	+	11.1175i	1.70410	+	0.474051i
$551$	−14.4894	+	14.4894i	−0.617268	+	0.617268i
$552$	−0.943862	+	0.891415i	−0.0401735	+	0.0379412i
$553$	10.0770	+	10.0770i	0.428519	+	0.428519i
$554$	12.6932	+	22.4769i	0.539281	+	0.954950i
$555$	13.1022	−	5.42711i	0.556158	−	0.230368i
$556$	27.5759	−	20.3372i	1.16948	−	0.862488i
$557$	1.64719	−	3.97666i	0.0697935	−	0.168496i	−0.885133	−	0.465337i	$-0.845933\pi$
$557$	1.64719	−	3.97666i	0.0697935	−	0.168496i	0.954927	+	0.296841i	$0.0959331\pi$
$558$	25.1339	−	32.1172i	1.06400	−	1.35963i
$559$			1.16832i			0.0494146i
$560$	−16.4935	+	1.53513i	−0.696979	+	0.0648711i
$561$			2.89182i			0.122093i
$562$	−2.48434	−	1.94417i	−0.104796	−	0.0820099i
$563$	−0.566229	+	1.36700i	−0.0238637	+	0.0576121i	−0.935362	−	0.353691i	$-0.884926\pi$
$563$	−0.566229	+	1.36700i	−0.0238637	+	0.0576121i	0.911498	+	0.411303i	$0.134926\pi$
$564$	0.184024	−	1.21806i	0.00774882	−	0.0512896i
$565$	−80.5154	+	33.3506i	−3.38731	+	1.40307i
$566$	−27.5157	+	15.5387i	−1.15657	+	0.653141i
$567$	5.30716	+	5.30716i	0.222880	+	0.222880i
$568$	8.56798	+	3.83927i	0.359504	+	0.161092i
$569$	18.7623	−	18.7623i	0.786556	−	0.786556i	−0.194372	−	0.980928i	$-0.562267\pi$
$569$	18.7623	−	18.7623i	0.786556	−	0.786556i	0.980928	+	0.194372i	$0.0622670\pi$
$570$	−2.93566	+	10.5530i	−0.122961	+	0.442017i
$571$	13.6201	+	32.8818i	0.569982	+	1.37606i	0.901570	+	0.432634i	$0.142416\pi$
$571$	13.6201	+	32.8818i	0.569982	+	1.37606i	−0.331588	+	0.943424i	$0.607584\pi$
$572$	−0.925622	−	3.73782i	−0.0387022	−	0.156286i
$573$	9.39960	+	3.89344i	0.392674	+	0.162651i
$574$	−1.04964	−	8.60525i	−0.0438109	−	0.359176i
$575$	−13.5558			−0.565315
$576$	22.6091	+	1.29326i	0.942046	+	0.0538859i
$577$	−34.0596			−1.41792			−0.708959	−	0.705250i	$-0.750835\pi$
$577$	−34.0596			−1.41792			−0.708959	+	0.705250i	$0.750835\pi$
$578$	1.45934	+	11.9642i	0.0607007	+	0.497644i
$579$	2.18758	+	0.906126i	0.0909127	+	0.0376573i
$580$	−8.97323	−	36.2355i	−0.372593	−	1.50460i
$581$	1.74047	+	4.20187i	0.0722068	+	0.174323i
$582$	0.496725	−	1.78561i	0.0205899	−	0.0740158i
$583$	−13.1778	+	13.1778i	−0.545769	+	0.545769i
$584$	−4.18174	+	9.33227i	−0.173042	+	0.386172i
$585$	6.61061	+	6.61061i	0.273315	+	0.273315i
$586$	8.32123	−	4.69918i	0.343747	−	0.194121i
$587$	4.51655	−	1.87082i	0.186418	−	0.0772169i	−0.287522	−	0.957774i	$-0.592831\pi$
$587$	4.51655	−	1.87082i	0.186418	−	0.0772169i	0.473940	+	0.880557i	$0.342831\pi$
$588$	0.122911	−	0.813552i	0.00506878	−	0.0335503i
$589$	17.7240	−	42.7895i	0.730304	−	1.76311i
$590$	−55.6050	−	43.5147i	−2.28922	−	1.79147i
$591$		−	1.10223i		−	0.0453397i
$592$	−25.6252	−	21.2613i	−1.05319	−	0.873834i
$593$			17.3682i			0.713228i	0.934252	+	0.356614i	$0.116069\pi$
$593$			17.3682i			0.713228i	−0.934252	+	0.356614i	$0.883931\pi$
$594$	5.04738	−	6.44975i	0.207096	−	0.264637i
$595$	4.61420	−	11.1397i	0.189164	−	0.456682i
$596$	5.39664	−	3.98001i	0.221055	−	0.163028i
$597$	−6.33106	+	2.62241i	−0.259113	+	0.107328i
$598$	0.618774	+	1.09571i	0.0253036	+	0.0448071i
$599$	15.9325	+	15.9325i	0.650983	+	0.650983i	0.953230	−	0.302247i	$-0.0977367\pi$
$599$	15.9325	+	15.9325i	0.650983	+	0.650983i	−0.302247	+	0.953230i	$0.597737\pi$
$600$	−9.70686	−	10.2780i	−0.396281	−	0.419596i
$601$	−16.5480	+	16.5480i	−0.675007	+	0.675007i	−0.958866	−	0.283859i	$-0.908385\pi$
$601$	−16.5480	+	16.5480i	−0.675007	+	0.675007i	0.283859	+	0.958866i	$0.408385\pi$
$602$	−1.99601	−	0.555256i	−0.0813514	−	0.0226305i
$603$	−9.57958	−	23.1272i	−0.390111	−	0.941811i
$604$	14.3048	+	8.62623i	0.582054	+	0.350996i
$605$	19.7853	+	8.19535i	0.804388	+	0.333188i
$606$	2.35566	−	0.287335i	0.0956923	−	0.0116722i
$607$	16.6570			0.676086			0.338043	−	0.941131i	$-0.390235\pi$
$607$	16.6570			0.676086			0.338043	+	0.941131i	$0.390235\pi$
$608$	25.1304	−	5.46638i	1.01917	−	0.221691i
$609$	1.85420			0.0751361
$610$	56.2973	−	6.86693i	2.27941	−	0.278034i
$611$	−1.10313	−	0.456930i	−0.0446278	−	0.0184854i
$612$	−8.51238	+	14.1160i	−0.344093	+	0.570605i
$613$	14.8792	+	35.9215i	0.600964	+	1.45086i	0.872590	+	0.488453i	$0.162439\pi$
$613$	14.8792	+	35.9215i	0.600964	+	1.45086i	−0.271626	+	0.962403i	$0.587561\pi$
$614$	4.30409	+	1.19732i	0.173699	+	0.0483200i
$615$	7.38454	−	7.38454i	0.297773	−	0.297773i
$616$	6.82579	+	0.195062i	0.275019	+	0.00785925i
$617$	−9.62603	−	9.62603i	−0.387529	−	0.387529i	0.486276	−	0.873805i	$-0.338355\pi$
$617$	−9.62603	−	9.62603i	−0.387529	−	0.387529i	−0.873805	+	0.486276i	$0.838355\pi$
$618$	−3.33391	−	5.90363i	−0.134109	−	0.237479i
$619$	−20.3134	+	8.41409i	−0.816465	+	0.338191i	−0.751530	−	0.659699i	$-0.770684\pi$
$619$	−20.3134	+	8.41409i	−0.816465	+	0.338191i	−0.0649347	+	0.997890i	$0.520684\pi$
$620$	50.0802	+	67.9054i	2.01127	+	2.72715i
$621$	−1.02420	+	2.47263i	−0.0410996	+	0.0992233i
$622$	4.26167	−	5.44575i	0.170878	−	0.218355i
$623$		−	3.77619i		−	0.151290i
$624$	−0.387685	+	1.25376i	−0.0155198	+	0.0501906i
$625$		−	61.8645i		−	2.47458i
$626$	34.3457	+	26.8779i	1.37273	+	1.07426i
$627$	1.72800	−	4.17177i	0.0690099	−	0.166605i
$628$	34.0201	+	5.13976i	1.35755	+	0.205099i
$629$	22.3919	−	9.27504i	0.892825	−	0.369820i
$630$	−14.4357	+	8.15213i	−0.575130	+	0.324789i
$631$	−30.5951	−	30.5951i	−1.21797	−	1.21797i	−0.968341	−	0.249631i	$-0.919691\pi$
$631$	−30.5951	−	30.5951i	−1.21797	−	1.21797i	−0.249631	−	0.968341i	$-0.580309\pi$
$632$	37.6653	−	14.3552i	1.49824	−	0.571019i
$633$	6.47204	−	6.47204i	0.257241	−	0.257241i
$634$	0.841342	−	3.02443i	0.0334140	−	0.120115i
$635$	−23.7974	−	57.4519i	−0.944369	−	2.27991i
$636$	6.16503	−	1.52669i	0.244459	−	0.0605371i
$637$	−0.736788	−	0.305188i	−0.0291926	−	0.0120920i
$638$	1.86324	+	15.2755i	0.0737665	+	0.604761i
$639$	9.39656			0.371722
$640$	−15.1140	+	44.3477i	−0.597432	+	1.75300i
$641$	−1.32098			−0.0521756			−0.0260878	−	0.999660i	$-0.508305\pi$
$641$	−1.32098			−0.0521756			−0.0260878	+	0.999660i	$0.508305\pi$
$642$	−0.332066	−	2.72239i	−0.0131056	−	0.107444i
$643$	19.6168	+	8.12555i	0.773611	+	0.320440i	0.734334	−	0.678788i	$-0.237495\pi$
$643$	19.6168	+	8.12555i	0.773611	+	0.320440i	0.0392770	+	0.999228i	$0.487495\pi$
$644$	−2.16605	+	0.536394i	−0.0853544	+	0.0211369i
$645$	−0.955117	−	2.30586i	−0.0376077	−	0.0907930i
$646$	−5.01710	+	18.0353i	−0.197395	+	0.709589i
$647$	16.9786	−	16.9786i	0.667498	−	0.667498i	−0.289638	−	0.957136i	$-0.593535\pi$
$647$	16.9786	−	16.9786i	0.667498	−	0.667498i	0.957136	+	0.289638i	$0.0935349\pi$
$648$	19.8367	−	7.56028i	0.779261	−	0.296996i
$649$	20.5817	+	20.5817i	0.807901	+	0.807901i
$650$	−11.9315	+	6.73800i	−0.467993	+	0.264286i
$651$	−3.87195	+	1.60381i	−0.151754	+	0.0628584i
$652$	19.5903	+	2.95970i	0.767214	+	0.115911i
$653$	4.68030	−	11.2993i	0.183154	−	0.442174i	−0.805459	−	0.592652i	$-0.798081\pi$
$653$	4.68030	−	11.2993i	0.183154	−	0.442174i	0.988613	+	0.150478i	$0.0480811\pi$
$654$	−6.64554	−	5.20059i	−0.259861	−	0.203359i
$655$		−	30.1553i		−	1.17826i
$656$	−23.4254	−	7.24354i	−0.914607	−	0.282813i
$657$			10.2348i			0.399296i
$658$	1.30492	−	1.66748i	0.0508709	−	0.0650050i
$659$	13.7273	−	33.1407i	0.534741	−	1.29098i	−0.393611	−	0.919277i	$-0.628774\pi$
$659$	13.7273	−	33.1407i	0.534741	−	1.29098i	0.928352	−	0.371702i	$-0.121226\pi$
$660$	4.88258	+	6.62046i	0.190054	+	0.257701i
$661$	5.52795	−	2.28975i	0.215012	−	0.0890610i	−0.272578	−	0.962134i	$-0.587876\pi$
$661$	5.52795	−	2.28975i	0.215012	−	0.0890610i	0.487590	+	0.873073i	$0.337876\pi$
$662$	10.8627	+	19.2355i	0.422190	+	0.747607i
$663$	−0.675458	−	0.675458i	−0.0262326	−	0.0262326i
$664$	12.8586	+	0.367462i	0.499011	+	0.0142603i
$665$	−13.3130	+	13.3130i	−0.516256	+	0.516256i
$666$	−32.1054	−	8.93116i	−1.24406	−	0.346075i
$667$	−1.92444	−	4.64600i	−0.0745145	−	0.179894i
$668$	−17.1917	+	28.5088i	−0.665166	+	1.10304i
$669$	4.35262	+	1.80291i	0.168282	+	0.0697046i
$670$	51.4090	−	6.27067i	1.98610	−	0.242257i
$671$	−23.3796			−0.902561
$672$	−1.95773	−	1.25820i	−0.0755212	−	0.0485362i
$673$	−29.6929			−1.14458			−0.572289	−	0.820052i	$-0.693944\pi$
$673$	−29.6929			−1.14458			−0.572289	+	0.820052i	$0.693944\pi$
$674$	−9.40591	+	1.14730i	−0.362302	+	0.0441922i
$675$	−26.9251	−	11.1528i	−1.03635	−	0.429270i
$676$	−21.1757	−	12.7696i	−0.814451	−	0.491139i
$677$	11.5832	+	27.9643i	0.445179	+	1.07476i	0.974106	+	0.226090i	$0.0725943\pi$
$677$	11.5832	+	27.9643i	0.445179	+	1.07476i	−0.528928	+	0.848667i	$0.677406\pi$
$678$	−11.7957	−	3.28135i	−0.453010	−	0.126019i
$679$	2.25261	−	2.25261i	0.0864471	−	0.0864471i
$680$	−23.4163	−	24.7940i	−0.897973	−	0.950806i
$681$	−3.34298	−	3.34298i	−0.128103	−	0.128103i
$682$	−17.1035	−	30.2866i	−0.654927	−	1.15973i
$683$	4.08563	−	1.69232i	0.156332	−	0.0647549i	−0.303145	−	0.952944i	$-0.598037\pi$
$683$	4.08563	−	1.69232i	0.156332	−	0.0647549i	0.459477	+	0.888189i	$0.348037\pi$
$684$	20.7151	−	15.2773i	0.792060	−	0.584143i
$685$	6.79546	−	16.4057i	0.259641	−	0.626829i
$686$	0.871564	−	1.11372i	0.0332765	−	0.0425221i
$687$			9.09886i			0.347143i
$688$	−3.74177	+	4.50978i	−0.142654	+	0.171934i
$689$		−	6.15603i		−	0.234526i
$690$	−2.11701	−	1.65671i	−0.0805931	−	0.0630697i
$691$	4.27972	−	10.3322i	0.162808	−	0.393054i	−0.821331	−	0.570452i	$-0.806768\pi$
$691$	4.27972	−	10.3322i	0.162808	−	0.393054i	0.984139	+	0.177398i	$0.0567681\pi$
$692$	−4.26095	+	28.2033i	−0.161977	+	1.07213i
$693$	6.31398	−	2.61534i	0.239848	−	0.0993484i
$694$	2.42479	−	1.36933i	0.0920436	−	0.0519791i
$695$	50.1674	+	50.1674i	1.90296	+	1.90296i
$696$	2.14456	−	4.78596i	0.0812894	−	0.181411i
$697$	12.6203	−	12.6203i	0.478029	−	0.478029i
$698$	−0.507679	+	1.82498i	−0.0192159	+	0.0690767i
$699$	−1.35774	−	3.27788i	−0.0513545	−	0.123981i
$700$	−5.84094	−	23.5867i	−0.220767	−	0.891494i
$701$	−6.63620	−	2.74880i	−0.250646	−	0.103821i	0.253823	−	0.967251i	$-0.418312\pi$
$701$	−6.63620	−	2.74880i	−0.250646	−	0.103821i	−0.504469	+	0.863430i	$0.668312\pi$
$702$	0.327560	+	2.68545i	0.0123630	+	0.101356i
$703$	−37.8451			−1.42736
$704$	8.39816	−	17.3927i	0.316518	−	0.655513i
$705$	2.55074			0.0960664
$706$	−0.882967	−	7.23885i	−0.0332309	−	0.272438i
$707$	3.76847	+	1.56095i	0.141728	+	0.0587056i
$708$	−2.38444	−	9.62880i	−0.0896129	−	0.361873i
$709$	6.04328	+	14.5898i	0.226960	+	0.547930i	0.995805	−	0.0915057i	$-0.0291680\pi$
$709$	6.04328	+	14.5898i	0.226960	+	0.547930i	−0.768844	+	0.639436i	$0.779168\pi$
$710$	−5.21018	+	18.7294i	−0.195535	+	0.702900i
$711$	28.5256	−	28.5256i	1.06979	−	1.06979i
$712$	−9.74687	−	4.36752i	−0.365279	−	0.163680i
$713$	8.03722	+	8.03722i	0.300996	+	0.300996i
$714$	1.47500	−	0.832967i	0.0552007	−	0.0311730i
$715$	7.36639	−	3.05126i	0.275487	−	0.114111i
$716$	7.50011	−	49.6434i	0.280292	−	1.85526i
$717$	0.471944	−	1.13937i	0.0176251	−	0.0425507i
$718$	17.7756	+	13.9106i	0.663380	+	0.519141i
$719$		−	27.4250i		−	1.02278i	−0.859349	−	0.511390i	$-0.829131\pi$
$719$		−	27.4250i		−	1.02278i	0.859349	−	0.511390i	$-0.170869\pi$
$720$	4.34558	+	46.6892i	0.161950	+	1.74000i
$721$		−	11.6535i		−	0.433998i
$722$	1.45498	−	1.85923i	0.0541486	−	0.0691934i
$723$	−3.14432	+	7.59106i	−0.116938	+	0.282314i
$724$	8.14683	−	6.00828i	0.302775	−	0.223296i
$725$	50.5915	−	20.9557i	1.87892	−	0.778275i
$726$	1.47945	+	2.61978i	0.0549074	+	0.0972290i
$727$	−14.4494	−	14.4494i	−0.535897	−	0.535897i	0.386424	−	0.922321i	$-0.373710\pi$
$727$	−14.4494	−	14.4494i	−0.535897	−	0.535897i	−0.922321	+	0.386424i	$0.873710\pi$
$728$	−1.63990	+	1.54878i	−0.0607787	+	0.0574014i
$729$	12.9299	−	12.9299i	0.478885	−	0.478885i
$730$	−20.4001	−	5.67494i	−0.755041	−	0.210039i
$731$	−1.63231	−	3.94075i	−0.0603733	−	0.145754i
$732$	6.82320	+	4.11460i	0.252193	+	0.152080i
$733$	−25.3709	−	10.5090i	−0.937094	−	0.388157i	−0.138729	−	0.990330i	$-0.544302\pi$
$733$	−25.3709	−	10.5090i	−0.937094	−	0.388157i	−0.798365	+	0.602173i	$0.794302\pi$
$734$	41.4144	−	5.05157i	1.52863	−	0.186457i
$735$	1.70366			0.0628405
$736$	−1.12074	+	6.21128i	−0.0413110	+	0.228951i
$737$	−21.3496			−0.786423
$738$	−24.3594	+	2.97126i	−0.896681	+	0.109374i
$739$	−1.72549	−	0.714723i	−0.0634733	−	0.0262915i	0.350721	−	0.936480i	$-0.385937\pi$
$739$	−1.72549	−	0.714723i	−0.0634733	−	0.0262915i	−0.414194	+	0.910189i	$0.635937\pi$
$740$	35.6034	−	59.0408i	1.30881	−	2.17038i
$741$	0.570804	+	1.37804i	0.0209690	+	0.0506237i
$742$	10.5173	+	2.92572i	0.386101	+	0.107406i
$743$	−15.2878	+	15.2878i	−0.560856	+	0.560856i	−0.929551	−	0.368695i	$-0.879805\pi$
$743$	−15.2878	+	15.2878i	−0.560856	+	0.560856i	0.368695	+	0.929551i	$0.379805\pi$
$744$	−0.338610	+	11.8490i	−0.0124141	+	0.434406i
$745$	9.81782	+	9.81782i	0.359697	+	0.359697i
$746$	−14.4698	−	25.6229i	−0.529777	−	0.938121i
$747$	11.8945	−	4.92685i	0.435195	−	0.180264i
$748$	8.34442	+	11.3145i	0.305102	+	0.413699i
$749$	1.80395	−	4.35513i	0.0659150	−	0.159133i
$750$	10.6161	−	13.5656i	0.387644	−	0.495347i
$751$		−	9.94247i		−	0.362806i	−0.983409	−	0.181403i	$-0.941936\pi$
$751$		−	9.94247i		−	0.362806i	0.983409	−	0.181403i	$-0.0580638\pi$
$752$	−2.79473	−	5.29677i	−0.101913	−	0.193153i
$753$		−	1.29478i		−	0.0471844i
$754$	−4.00318	−	3.13276i	−0.145787	−	0.114089i
$755$	−13.2364	+	31.9554i	−0.481721	+	1.16298i
$756$	−4.74363	−	0.716666i	−0.172524	−	0.0260649i
$757$	−40.2504	+	16.6722i	−1.46292	+	0.605963i	−0.965233	−	0.261391i	$-0.915819\pi$
$757$	−40.2504	+	16.6722i	−1.46292	+	0.605963i	−0.497691	+	0.867354i	$0.665819\pi$
$758$	−27.7500	+	15.6710i	−1.00793	+	0.569198i
$759$	0.783591	+	0.783591i	0.0284426	+	0.0284426i
$760$	18.9650	+	49.7604i	0.687931	+	1.80500i
$761$	−5.99015	+	5.99015i	−0.217143	+	0.217143i	−0.807293	−	0.590151i	$-0.799068\pi$
$761$	−5.99015	+	5.99015i	−0.217143	+	0.217143i	0.590151	+	0.807293i	$0.299068\pi$
$762$	2.34141	−	8.41682i	0.0848204	−	0.304909i
$763$	−5.55056	−	13.4002i	−0.200944	−	0.485121i
$764$	48.0113	−	11.8894i	1.73699	−	0.430142i
$765$	−31.5337	−	13.0617i	−1.14010	−	0.472246i
$766$	1.58788	+	13.0180i	0.0573726	+	0.470359i
$767$	−9.61474			−0.347168
$768$	−5.51190	+	3.59795i	−0.198894	+	0.129830i
$769$	0.0761973			0.00274775			0.00137387	−	0.999999i	$-0.499563\pi$
$769$	0.0761973			0.00274775			0.00137387	+	0.999999i	$0.499563\pi$
$770$	1.71197	+	14.0353i	0.0616950	+	0.505795i
$771$	−3.53113	−	1.46264i	−0.127170	−	0.0526757i
$772$	11.1737	−	2.76703i	0.402152	−	0.0995875i
$773$	19.7130	+	47.5915i	0.709029	+	1.71175i	0.702414	+	0.711768i	$0.252105\pi$
$773$	19.7130	+	47.5915i	0.709029	+	1.71175i	0.00661410	+	0.999978i	$0.497895\pi$
$774$	−1.57179	+	5.65022i	−0.0564969	+	0.203093i
$775$	−87.5194	+	87.5194i	−3.14379	+	3.14379i
$776$	−3.20894	−	8.41965i	−0.115194	−	0.302248i
$777$	2.42152	+	2.42152i	0.0868714	+	0.0868714i
$778$	−12.8223	+	7.24103i	−0.459702	+	0.259604i
$779$	−25.7475	+	10.6650i	−0.922499	+	0.382112i
$780$	−2.68683	−	0.405926i	−0.0962038	−	0.0145345i
$781$	3.06684	−	7.40401i	0.109740	−	0.264936i
$782$	−3.61801	−	2.83134i	−0.129380	−	0.101249i
$783$		−	10.8114i		−	0.386368i
$784$	−1.86662	−	3.53776i	−0.0666652	−	0.126348i
$785$			71.2415i			2.54272i
$786$	2.61091	−	3.33633i	0.0931281	−	0.119003i
$787$	11.6675	−	28.1677i	0.415900	−	1.00407i	−0.567623	−	0.823289i	$-0.692137\pi$
$787$	11.6675	−	28.1677i	0.415900	−	1.00407i	0.983523	−	0.180783i	$-0.0578632\pi$
$788$	−3.18051	−	4.31257i	−0.113301	−	0.153629i
$789$	0.902938	−	0.374009i	0.0321455	−	0.0133151i
$790$	41.0409	+	72.6745i	1.46017	+	2.58564i
$791$	−14.8806	−	14.8806i	−0.529095	−	0.529095i
$792$	0.552172	−	19.3222i	0.0196206	−	0.686583i
$793$	5.46091	−	5.46091i	0.193923	−	0.193923i
$794$	−31.4221	−	8.74108i	−1.11513	−	0.310209i
$795$	5.03264	+	12.1499i	0.178489	+	0.430911i
$796$	−17.2038	+	28.5288i	−0.609771	+	1.01118i
$797$	32.4721	+	13.4504i	1.15022	+	0.476437i	0.874607	−	0.484832i	$-0.161119\pi$
$797$	32.4721	+	13.4504i	1.15022	+	0.476437i	0.275613	+	0.961269i	$0.411119\pi$
$798$	−2.62560	+	0.320260i	−0.0929451	+	0.0113371i
$799$	4.35926			0.154220
$800$	−67.6362	−	12.2040i	−2.39130	−	0.431477i
$801$	−10.6895			−0.377694
$802$	−12.0033	+	1.46412i	−0.423851	+	0.0516997i
$803$	8.06448	+	3.34042i	0.284589	+	0.117881i
$804$	6.23074	+	3.75733i	0.219741	+	0.132511i
$805$	−1.76819	−	4.26879i	−0.0623206	−	0.150455i
$806$	11.0692	+	3.07925i	0.389895	+	0.108462i
$807$	2.37093	−	2.37093i	0.0834608	−	0.0834608i
$808$	8.38762	−	7.92155i	0.295076	−	0.278679i
$809$	16.2669	+	16.2669i	0.571914	+	0.571914i	0.932663	−	0.360749i	$-0.117479\pi$
$809$	16.2669	+	16.2669i	0.571914	+	0.571914i	−0.360749	+	0.932663i	$0.617479\pi$
$810$	21.6145	+	38.2746i	0.759457	+	1.34483i
$811$	3.72880	−	1.54452i	0.130936	−	0.0542354i	−0.316253	−	0.948675i	$-0.602425\pi$
$811$	3.72880	−	1.54452i	0.130936	−	0.0542354i	0.447189	+	0.894439i	$0.352425\pi$
$812$	7.25472	−	5.35035i	0.254591	−	0.187760i
$813$	2.31322	−	5.58461i	0.0811282	−	0.195861i
$814$	−17.5158	+	22.3825i	−0.613930	+	0.784505i
$815$			41.0240i			1.43701i
$816$	−0.444022	−	4.77060i	−0.0155439	−	0.167004i
$817$			6.66036i			0.233016i
$818$	−7.15703	−	5.60087i	−0.250240	−	0.195830i
$819$	−0.863912	+	2.08567i	−0.0301875	+	0.0728791i
$820$	7.58435	−	50.2009i	0.264857	−	1.75309i
$821$	32.1703	−	13.3254i	1.12275	−	0.465059i	0.257441	−	0.966294i	$-0.417121\pi$
$821$	32.1703	−	13.3254i	1.12275	−	0.465059i	0.865311	+	0.501235i	$0.167121\pi$
$822$	2.17228	−	1.22673i	0.0757670	−	0.0427873i
$823$	4.50895	+	4.50895i	0.157172	+	0.157172i	0.781312	−	0.624140i	$-0.214551\pi$
$823$	4.50895	+	4.50895i	0.157172	+	0.157172i	−0.624140	+	0.781312i	$0.714551\pi$
$824$	−30.0793	−	13.4784i	−1.04786	−	0.469541i
$825$	−8.53273	+	8.53273i	−0.297072	+	0.297072i
$826$	4.56951	−	16.4263i	0.158993	−	0.571544i
$827$	13.3550	+	32.2419i	0.464401	+	1.12116i	0.966572	+	0.256394i	$0.0825345\pi$
$827$	13.3550	+	32.2419i	0.464401	+	1.12116i	−0.502172	+	0.864768i	$0.667465\pi$
$828$	1.51840	+	6.13157i	0.0527681	+	0.213087i
$829$	−7.03715	−	2.91488i	−0.244410	−	0.101238i	0.257116	−	0.966381i	$-0.417228\pi$
$829$	−7.03715	−	2.91488i	−0.244410	−	0.101238i	−0.501526	+	0.865143i	$0.667228\pi$
$830$	3.22505	+	26.4400i	0.111943	+	0.917746i
$831$	−7.50904			−0.260486
$832$	2.10091	+	6.02411i	0.0728359	+	0.208849i
$833$	2.91159			0.100881
$834$	1.20684	+	9.89404i	0.0417893	+	0.342603i
$835$	−63.6857	−	26.3795i	−2.20393	−	0.912899i
$836$	−5.27679	−	21.3086i	−0.182502	−	0.736974i
$837$	9.35144	+	22.5764i	0.323233	+	0.780354i
$838$	−0.132506	+	0.476328i	−0.00457734	+	0.0164545i
$839$	−23.9535	+	23.9535i	−0.826967	+	0.826967i	−0.987096	−	0.160129i	$-0.948809\pi$
$839$	−23.9535	+	23.9535i	−0.826967	+	0.826967i	0.160129	+	0.987096i	$0.448809\pi$
$840$	1.97045	−	4.39739i	0.0679868	−	0.151724i
$841$	−6.14172	−	6.14172i	−0.211783	−	0.211783i
$842$	3.53604	−	1.99688i	0.121860	−	0.0688170i
$843$	0.847826	−	0.351181i	0.0292007	−	0.0120953i
$844$	6.64716	−	43.9976i	0.228805	−	1.51446i
$845$	19.5941	−	47.3044i	0.674058	−	1.62732i
$846$	−4.72022	−	3.69390i	−0.162284	−	0.126999i
$847$			5.17131i			0.177688i
$848$	19.7159	−	23.7626i	0.677047	−	0.816013i
$849$		−	9.19241i		−	0.315483i
$850$	30.8312	−	39.3974i	1.05750	−	1.35132i
$851$	3.55426	−	8.58073i	0.121838	−	0.294144i
$852$	−2.19808	+	1.62108i	−0.0753048	+	0.0555372i
$853$	−6.33625	+	2.62456i	−0.216949	+	0.0898632i	−0.488511	−	0.872558i	$-0.662460\pi$
$853$	−6.33625	+	2.62456i	−0.216949	+	0.0898632i	0.271562	+	0.962421i	$0.412460\pi$
$854$	6.73433	+	11.9250i	0.230444	+	0.408067i
$855$	37.6858	+	37.6858i	1.28883	+	1.28883i
$856$	−9.15475	−	9.69337i	−0.312903	−	0.331313i
$857$	9.97241	−	9.97241i	0.340651	−	0.340651i	−0.515961	−	0.856612i	$-0.672565\pi$
$857$	9.97241	−	9.97241i	0.340651	−	0.340651i	0.856612	+	0.515961i	$0.172565\pi$
$858$	1.07919	+	0.300212i	0.0368430	+	0.0102491i
$859$	−12.3141	−	29.7288i	−0.420150	−	1.01433i	−0.982303	−	0.187299i	$-0.940027\pi$
$859$	−12.3141	−	29.7288i	−0.420150	−	1.01433i	0.562153	−	0.827034i	$-0.309973\pi$
$860$	−10.3906	−	6.26584i	−0.354316	−	0.213663i
$861$	2.32984	+	0.965053i	0.0794009	+	0.0328889i
$862$	−44.8702	+	5.47309i	−1.52828	+	0.186414i
$863$	−16.9726			−0.577755			−0.288877	−	0.957366i	$-0.593282\pi$
$863$	−16.9726			−0.577755			−0.288877	+	0.957366i	$0.593282\pi$
$864$	−7.33627	+	11.4151i	−0.249585	+	0.388349i
$865$	−59.0605			−2.00812
$866$	4.10682	−	0.500934i	0.139555	−	0.0170224i
$867$	−3.23926	−	1.34175i	−0.110011	−	0.0455681i
$868$	−10.5215	+	17.4477i	−0.357122	+	0.592212i
$869$	−13.1666	−	31.7869i	−0.446645	−	1.07830i
$870$	10.4620	+	2.91034i	0.354694	+	0.0986696i
$871$	4.98674	−	4.98674i	0.168969	−	0.168969i
$872$	−41.0077	−	1.17188i	−1.38869	−	0.0396849i
$873$	−6.37658	−	6.37658i	−0.215815	−	0.215815i
$874$	3.52751	+	6.24646i	0.119320	+	0.211290i
$875$	27.3541	−	11.3305i	0.924739	−	0.383039i
$876$	−1.76568	−	2.39415i	−0.0596569	−	0.0808909i
$877$	13.8347	−	33.3998i	0.467163	−	1.12783i	−0.498233	−	0.867043i	$-0.666018\pi$
$877$	13.8347	−	33.3998i	0.467163	−	1.12783i	0.965396	−	0.260788i	$-0.0839825\pi$
$878$	−13.4920	+	17.2406i	−0.455332	+	0.581843i
$879$			2.77995i			0.0937653i
$880$	38.2070	+	11.8143i	1.28796	+	0.398260i
$881$			0.767974i			0.0258737i	0.999916	+	0.0129368i	$0.00411804\pi$
$881$			0.767974i			0.0258737i	−0.999916	+	0.0129368i	$0.995882\pi$
$882$	−3.15267	−	2.46719i	−0.106156	−	0.0830745i
$883$	−0.413268	+	0.997718i	−0.0139076	+	0.0335759i	−0.930681	−	0.365832i	$-0.880784\pi$
$883$	−0.413268	+	0.997718i	−0.0139076	+	0.0335759i	0.916773	+	0.399408i	$0.130784\pi$
$884$	−4.59184	−	0.693734i	−0.154440	−	0.0233328i
$885$	18.9762	−	7.86018i	0.637877	−	0.264217i
$886$	−2.93569	+	1.65785i	−0.0986263	+	0.0556964i
$887$	0.534590	+	0.534590i	0.0179498	+	0.0179498i	0.716025	−	0.698075i	$-0.245960\pi$
$887$	0.534590	+	0.534590i	0.0179498	+	0.0179498i	−0.698075	+	0.716025i	$0.745960\pi$
$888$	9.05099	−	3.44956i	0.303731	−	0.115760i
$889$	10.6181	−	10.6181i	0.356120	−	0.356120i
$890$	5.92706	−	21.3064i	0.198676	−	0.714191i
$891$	−6.93429	−	16.7408i	−0.232307	−	0.560840i
$892$	22.2323	−	5.50554i	0.744393	−	0.184339i
$893$	−6.28872	−	2.60487i	−0.210444	−	0.0871687i
$894$	0.236180	+	1.93628i	0.00789903	+	0.0647588i
$895$	103.958			3.47494
$896$	−11.2904	+	0.726269i	−0.377185	+	0.0242629i
$897$	−0.366055			−0.0122222
$898$	1.77465	+	14.5491i	0.0592207	+	0.485511i
$899$	−42.4203	−	17.5711i	−1.41480	−	0.586028i
$900$	−66.7682	+	16.5343i	−2.22561	+	0.551142i
$901$	8.60087	+	20.7643i	0.286537	+	0.691761i
$902$	−5.60919	+	20.1637i	−0.186766	+	0.671378i
$903$	0.426162	−	0.426162i	0.0141818	−	0.0141818i
$904$	−55.6199	+	21.1981i	−1.84989	+	0.705040i
$905$	14.8211	+	14.8211i	0.492670	+	0.492670i
$906$	−4.23122	+	2.38946i	−0.140573	+	0.0793846i
$907$	37.3481	−	15.4701i	1.24012	−	0.513676i	0.336370	−	0.941730i	$-0.390801\pi$
$907$	37.3481	−	15.4701i	1.24012	−	0.513676i	0.903753	+	0.428054i	$0.140801\pi$
$908$	−22.7260	−	3.43344i	−0.754188	−	0.113943i
$909$	4.41867	−	10.6676i	0.146558	−	0.353822i
$910$	−3.67816	−	2.87842i	−0.121930	−	0.0954185i
$911$			21.9128i			0.726003i	0.931789	+	0.363001i	$0.118248\pi$
$911$			21.9128i			0.726003i	−0.931789	+	0.363001i	$0.881752\pi$
$912$	−2.21012	+	7.14745i	−0.0731843	+	0.236676i
$913$		−	10.9802i		−	0.363393i
$914$	−21.8322	+	27.8981i	−0.722144	+	0.922787i
$915$	−6.31357	+	15.2423i	−0.208720	+	0.503895i
$916$	26.2550	+	35.6000i	0.867489	+	1.17626i
$917$	6.72747	−	2.78661i	0.222161	−	0.0920220i
$918$	−4.85683	−	8.60039i	−0.160299	−	0.283855i
$919$	−29.2978	−	29.2978i	−0.966444	−	0.966444i	0.0330114	−	0.999455i	$-0.489490\pi$
$919$	−29.2978	−	29.2978i	−0.966444	−	0.966444i	−0.999455	+	0.0330114i	$0.989490\pi$
$920$	−13.0634	−	0.373315i	−0.430689	−	0.0123078i
$921$	−0.918953	+	0.918953i	−0.0302805	+	0.0302805i
$922$	4.09064	+	1.13794i	0.134718	+	0.0374762i
$923$	1.01306	+	2.44573i	0.0333452	+	0.0805023i
$924$	−1.02579	+	1.70106i	−0.0337461	+	0.0559609i
$925$	93.4379	+	38.7032i	3.07222	+	1.27255i
$926$	19.0979	−	2.32949i	0.627597	−	0.0765519i
$927$	−32.9882			−1.08347
$928$	−5.41922	−	24.9136i	−0.177895	−	0.817830i
$929$	−12.8838			−0.422704			−0.211352	−	0.977410i	$-0.567787\pi$
$929$	−12.8838			−0.422704			−0.211352	+	0.977410i	$0.567787\pi$
$930$	−24.3640	+	2.97183i	−0.798928	+	0.0974501i
$931$	−4.20029	−	1.73982i	−0.137659	−	0.0570202i
$932$	−14.7707	−	8.90718i	−0.483830	−	0.291764i
$933$	0.769798	+	1.85846i	0.0252020	+	0.0608431i
$934$	−26.3285	−	7.32412i	−0.861494	−	0.239652i
$935$	−20.5839	+	20.5839i	−0.673165	+	0.673165i
$936$	4.38421	+	4.64215i	0.143302	+	0.151734i
$937$	5.27729	+	5.27729i	0.172401	+	0.172401i	0.788034	−	0.615632i	$-0.211099\pi$
$937$	5.27729	+	5.27729i	0.172401	+	0.172401i	−0.615632	+	0.788034i	$0.711099\pi$
$938$	6.14959	+	10.8896i	0.200791	+	0.355558i
$939$	−11.7211	+	4.85503i	−0.382503	+	0.158438i
$940$	9.97998	−	7.36022i	0.325511	−	0.240064i
$941$	−4.00127	+	9.65993i	−0.130438	+	0.314905i	−0.975583	−	0.219633i	$-0.929514\pi$
$941$	−4.00127	+	9.65993i	−0.130438	+	0.314905i	0.845145	+	0.534537i	$0.179514\pi$
$942$	−6.16825	+	7.88205i	−0.200972	+	0.256811i
$943$		−	6.83941i		−	0.222722i
$944$	−37.1135	−	30.7931i	−1.20794	−	1.00223i
$945$		−	9.93363i		−	0.323141i
$946$	3.93909	+	3.08261i	0.128071	+	0.100224i
$947$	18.3351	−	44.2649i	0.595812	−	1.43842i	−0.282002	−	0.959414i	$-0.590998\pi$
$947$	18.3351	−	44.2649i	0.595812	−	1.43842i	0.877813	−	0.479003i	$-0.159002\pi$
$948$	−1.75162	+	11.5940i	−0.0568900	+	0.376555i
$949$	−2.66390	+	1.10342i	−0.0864739	+	0.0358187i
$950$	−68.0194	+	38.4120i	−2.20684	+	1.24625i
$951$	0.645735	+	0.645735i	0.0209394	+	0.0209394i
$952$	3.36753	−	7.51522i	0.109142	−	0.243570i
$953$	35.6779	−	35.6779i	1.15572	−	1.15572i	0.170334	−	0.985386i	$-0.445515\pi$
$953$	35.6779	−	35.6779i	1.15572	−	1.15572i	0.985386	−	0.170334i	$-0.0544848\pi$
$954$	8.28199	−	29.7718i	0.268139	−	0.963897i
$955$	39.1926	+	94.6193i	1.26824	+	3.06181i
$956$	−1.44117	−	5.81970i	−0.0466108	−	0.188223i
$957$	−4.13578	−	1.71310i	−0.133691	−	0.0553766i
$958$	4.17312	+	34.2126i	0.134828	+	1.10536i
$959$	4.28798			0.138466
$960$	−9.07126	−	10.1720i	−0.292774	−	0.328300i
$961$	72.7805			2.34776
$962$	−1.13673	−	9.31926i	−0.0366496	−	0.300465i
$963$	−12.3283	−	5.10655i	−0.397274	−	0.164556i
$964$	9.60178	+	38.7737i	0.309253	+	1.24882i
$965$	9.12135	+	22.0209i	0.293627	+	0.708877i
$966$	0.173972	−	0.625387i	0.00559744	−	0.0201215i
$967$	21.8408	−	21.8408i	0.702353	−	0.702353i	−0.262562	−	0.964915i	$-0.584567\pi$
$967$	21.8408	−	21.8408i	0.702353	−	0.702353i	0.964915	+	0.262562i	$0.0845675\pi$
$968$	13.3479	+	5.98112i	0.429017	+	0.192240i
$969$	−3.85066	−	3.85066i	−0.123701	−	0.123701i
$970$	16.2455	−	9.17422i	0.521613	−	0.294566i
$971$	−51.4800	+	21.3237i	−1.65207	+	0.684311i	−0.997431	−	0.0716292i	$-0.977180\pi$
$971$	−51.4800	+	21.3237i	−1.65207	+	0.684311i	−0.654641	+	0.755940i	$0.727180\pi$
$972$	−3.07250	+	20.3370i	−0.0985506	+	0.652308i
$973$	−6.55615	+	15.8280i	−0.210181	+	0.507421i
$974$	41.0873	+	32.1537i	1.31652	+	1.03027i
$975$		−	3.98607i		−	0.127656i
$976$	38.5691	−	3.58980i	1.23457	−	0.114907i
$977$			31.2813i			1.00078i	0.865801	+	0.500389i	$0.166810\pi$
$977$			31.2813i			1.00078i	−0.865801	+	0.500389i	$0.833190\pi$
$978$	−3.55195	+	4.53883i	−0.113579	+	0.145136i
$979$	−3.48882	+	8.42275i	−0.111503	+	0.269192i
$980$	6.66571	−	4.91596i	0.212928	−	0.157034i
$981$	−37.9328	+	15.7123i	−1.21110	+	0.501655i
$982$	−12.5090	−	22.1507i	−0.399177	−	0.706856i
$983$	25.0573	+	25.0573i	0.799203	+	0.799203i	0.982970	−	0.183767i	$-0.0588292\pi$
$983$	25.0573	+	25.0573i	0.799203	+	0.799203i	−0.183767	+	0.982970i	$0.558829\pi$
$984$	5.18563	−	4.89748i	0.165312	−	0.156126i
$985$	7.84563	−	7.84563i	0.249983	−	0.249983i
$986$	17.8797	+	4.97382i	0.569406	+	0.158399i
$987$	0.235710	+	0.569055i	0.00750275	+	0.0181132i
$988$	6.20970	+	3.74464i	0.197557	+	0.119133i
$989$	−1.51012	−	0.625513i	−0.0480191	−	0.0198902i
$990$	39.7304	−	4.84616i	1.26271	−	0.154021i
$991$	12.2428			0.388905			0.194452	−	0.980912i	$-0.437707\pi$
$991$	12.2428			0.388905			0.194452	+	0.980912i	$0.437707\pi$
$992$	32.8658	+	47.3373i	1.04349	+	1.50296i
$993$	−6.42616			−0.203928
$994$	−4.65988	+	0.568394i	−0.147802	+	0.0180284i
$995$	−63.7304	−	26.3980i	−2.02039	−	0.836873i
$996$	−1.93242	+	3.20451i	−0.0612311	+	0.101539i
$997$	−5.18330	−	12.5136i	−0.164157	−	0.396310i	0.820301	−	0.571932i	$-0.193806\pi$
$997$	−5.18330	−	12.5136i	−0.164157	−	0.396310i	−0.984458	+	0.175623i	$0.943806\pi$
$998$	−2.13055	−	0.592681i	−0.0674413	−	0.0187610i
$999$	14.1193	−	14.1193i	0.446714	−	0.446714i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.2.u.c.29.8	✓	52
4.3	odd	2		896.2.u.c.337.8		52
32.11	odd	8		896.2.u.c.561.8		52
32.21	even	8	inner	224.2.u.c.85.8	yes	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
224.2.u.c.29.8	✓	52	1.1	even	1	trivial
224.2.u.c.85.8	yes	52	32.21	even	8	inner
896.2.u.c.337.8		52	4.3	odd	2
896.2.u.c.561.8		52	32.11	odd	8

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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	224.u (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.171231 + 1.40381i) q^{2} +(-0.380077 - 0.157433i) q^{3} +(-1.94136 + 0.480752i) q^{4} +(-1.58477 - 3.82598i) q^{5} +(0.155925 - 0.560513i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.00731 - 2.64298i) q^{8} +(-2.00165 - 2.00165i) q^{9} +O(q^{10})\)	\(q+(0.171231 + 1.40381i) q^{2} +(-0.380077 - 0.157433i) q^{3} +(-1.94136 + 0.480752i) q^{4} +(-1.58477 - 3.82598i) q^{5} +(0.155925 - 0.560513i) q^{6} +(0.707107 - 0.707107i) q^{7} +(-1.00731 - 2.64298i) q^{8} +(-2.00165 - 2.00165i) q^{9} +(5.09958 - 2.87984i) q^{10} +(-2.23049 + 0.923900i) q^{11} +(0.813552 + 0.122911i) q^{12} +(0.305188 - 0.736788i) q^{13} +(1.11372 + 0.871564i) q^{14} +1.70366i q^{15} +(3.53776 - 1.86662i) q^{16} +2.91159i q^{17} +(2.46719 - 3.15267i) q^{18} +(1.73982 - 4.20029i) q^{19} +(4.91596 + 6.66571i) q^{20} +(-0.380077 + 0.157433i) q^{21} +(-1.67891 - 2.97298i) q^{22} +(0.788947 + 0.788947i) q^{23} +(-0.0332386 + 1.16312i) q^{24} +(-8.59105 + 8.59105i) q^{25} +(1.08657 + 0.302264i) q^{26} +(0.917954 + 2.21614i) q^{27} +(-1.03281 + 1.71269i) q^{28} +(-4.16405 - 1.72481i) q^{29} +(-2.39161 + 0.291720i) q^{30} +10.1873 q^{31} +(3.22616 + 4.64671i) q^{32} +0.993211 q^{33} +(-4.08731 + 0.498555i) q^{34} +(-3.82598 - 1.58477i) q^{35} +(4.84821 + 2.92362i) q^{36} +(-3.18556 - 7.69062i) q^{37} +(6.19431 + 1.72315i) q^{38} +(-0.231990 + 0.231990i) q^{39} +(-8.51562 + 8.04244i) q^{40} +(-4.33451 - 4.33451i) q^{41} +(-0.286087 - 0.506598i) q^{42} +(-1.35347 + 0.560626i) q^{43} +(3.88602 - 2.86594i) q^{44} +(-4.48610 + 10.8304i) q^{45} +(-0.972439 + 1.24262i) q^{46} -1.49721i q^{47} +(-1.63849 + 0.152502i) q^{48} -1.00000i q^{49} +(-13.5313 - 10.5891i) q^{50} +(0.458380 - 1.10663i) q^{51} +(-0.238267 + 1.57709i) q^{52} +(7.13162 - 2.95402i) q^{53} +(-2.95385 + 1.66810i) q^{54} +(7.06964 + 7.06964i) q^{55} +(-2.58114 - 1.15660i) q^{56} +(-1.32253 + 1.32253i) q^{57} +(1.70828 - 6.14088i) q^{58} +(-4.61370 - 11.1385i) q^{59} +(-0.819038 - 3.30742i) q^{60} +(8.94680 + 3.70589i) q^{61} +(1.74438 + 14.3010i) q^{62} -2.83076 q^{63} +(-5.97067 + 5.32457i) q^{64} -3.30259 q^{65} +(0.170069 + 1.39428i) q^{66} +(8.16996 + 3.38411i) q^{67} +(-1.39975 - 5.65244i) q^{68} +(-0.175654 - 0.424067i) q^{69} +(1.56959 - 5.64230i) q^{70} +(-2.34721 + 2.34721i) q^{71} +(-3.27404 + 7.30658i) q^{72} +(-2.55659 - 2.55659i) q^{73} +(10.2507 - 5.78879i) q^{74} +(4.61778 - 1.91275i) q^{75} +(-1.35831 + 8.99069i) q^{76} +(-0.923900 + 2.23049i) q^{77} +(-0.365393 - 0.285945i) q^{78} +14.2511i q^{79} +(-12.7482 - 10.5772i) q^{80} +7.50545i q^{81} +(5.34263 - 6.82703i) q^{82} +(-1.74047 + 4.20187i) q^{83} +(0.662180 - 0.488357i) q^{84} +(11.1397 - 4.61420i) q^{85} +(-1.01877 - 1.80402i) q^{86} +(1.31112 + 1.31112i) q^{87} +(4.68863 + 4.96449i) q^{88} +(2.67017 - 2.67017i) q^{89} +(-15.9720 - 4.44312i) q^{90} +(-0.305188 - 0.736788i) q^{91} +(-1.91092 - 1.15234i) q^{92} +(-3.87195 - 1.60381i) q^{93} +(2.10180 - 0.256369i) q^{94} -18.8274 q^{95} +(-0.494643 - 2.27401i) q^{96} +3.18567 q^{97} +(1.40381 - 0.171231i) q^{98} +(6.31398 + 2.61534i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 20 q^{6}+O(q^{10}) \) 52 * q - 20 * q^6	\( 52 q - 20 q^{6} - 8 q^{10} + 12 q^{12} - 12 q^{16} - 20 q^{18} + 20 q^{22} - 20 q^{23} - 8 q^{24} + 20 q^{26} - 24 q^{27} - 8 q^{28} + 20 q^{30} + 60 q^{32} - 48 q^{33} + 48 q^{34} + 8 q^{36} - 60 q^{38} - 24 q^{39} + 20 q^{40} - 44 q^{43} + 32 q^{44} + 40 q^{45} - 32 q^{46} - 84 q^{48} - 124 q^{50} + 16 q^{51} - 32 q^{52} - 36 q^{53} + 96 q^{54} + 32 q^{55} + 16 q^{56} + 4 q^{58} - 92 q^{60} - 32 q^{61} + 12 q^{62} + 68 q^{63} + 48 q^{64} + 80 q^{65} + 16 q^{66} + 28 q^{67} - 4 q^{68} - 32 q^{69} + 8 q^{70} - 88 q^{72} + 36 q^{74} + 32 q^{75} + 96 q^{76} - 12 q^{77} + 12 q^{78} - 108 q^{80} - 96 q^{82} + 64 q^{85} + 76 q^{86} - 56 q^{87} + 104 q^{88} - 132 q^{90} + 32 q^{92} - 4 q^{94} - 64 q^{95} + 8 q^{96} - 72 q^{97} - 64 q^{99}+O(q^{100}) \) 52 * q - 20 * q^6 - 8 * q^10 + 12 * q^12 - 12 * q^16 - 20 * q^18 + 20 * q^22 - 20 * q^23 - 8 * q^24 + 20 * q^26 - 24 * q^27 - 8 * q^28 + 20 * q^30 + 60 * q^32 - 48 * q^33 + 48 * q^34 + 8 * q^36 - 60 * q^38 - 24 * q^39 + 20 * q^40 - 44 * q^43 + 32 * q^44 + 40 * q^45 - 32 * q^46 - 84 * q^48 - 124 * q^50 + 16 * q^51 - 32 * q^52 - 36 * q^53 + 96 * q^54 + 32 * q^55 + 16 * q^56 + 4 * q^58 - 92 * q^60 - 32 * q^61 + 12 * q^62 + 68 * q^63 + 48 * q^64 + 80 * q^65 + 16 * q^66 + 28 * q^67 - 4 * q^68 - 32 * q^69 + 8 * q^70 - 88 * q^72 + 36 * q^74 + 32 * q^75 + 96 * q^76 - 12 * q^77 + 12 * q^78 - 108 * q^80 - 96 * q^82 + 64 * q^85 + 76 * q^86 - 56 * q^87 + 104 * q^88 - 132 * q^90 + 32 * q^92 - 4 * q^94 - 64 * q^95 + 8 * q^96 - 72 * q^97 - 64 * q^99

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