LMFDB - Embedded newform 625.2.h.a.449.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(24,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([11]))

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

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

chi := DirichletCharacter("625.24");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.h (of order $50$, degree $20$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{50})$
Twist minimal:	no (minimal twist has level 125)
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			449.11
Character	$\chi$	$=$	625.449
Dual form			625.2.h.a.174.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.285704 + 2.26158i) q^{2} +(-1.43951 - 1.19086i) q^{3} +(-3.09594 + 0.794901i) q^{4} +(2.28196 - 3.59579i) q^{6} +(1.01659 + 0.330310i) q^{7} +(-1.00393 - 2.53564i) q^{8} +(0.0918805 + 0.481654i) q^{9} +O(q^{10})$	\(q+(0.285704 + 2.26158i) q^{2} +(-1.43951 - 1.19086i) q^{3} +(-3.09594 + 0.794901i) q^{4} +(2.28196 - 3.59579i) q^{6} +(1.01659 + 0.330310i) q^{7} +(-1.00393 - 2.53564i) q^{8} +(0.0918805 + 0.481654i) q^{9} +(1.56186 - 0.197308i) q^{11} +(5.40324 + 2.54257i) q^{12} +(3.41636 - 0.651706i) q^{13} +(-0.456579 + 2.39347i) q^{14} +(-0.154251 + 0.0848005i) q^{16} +(1.57081 - 6.11789i) q^{17} +(-1.06305 + 0.345405i) q^{18} +(0.707051 + 0.854677i) q^{19} +(-1.07004 - 1.68611i) q^{21} +(0.892455 + 3.47588i) q^{22} +(5.21894 + 5.55761i) q^{23} +(-1.57444 + 4.84562i) q^{24} +(2.44995 + 7.54017i) q^{26} +(-2.25878 + 4.10870i) q^{27} +(-3.40986 - 0.214530i) q^{28} +(-0.566426 + 9.00309i) q^{29} +(3.33058 + 0.855147i) q^{31} +(-3.44181 - 4.73725i) q^{32} +(-2.48327 - 1.57593i) q^{33} +(14.2849 + 1.80460i) q^{34} +(-0.667324 - 1.41813i) q^{36} +(3.04110 + 5.53175i) q^{37} +(-1.73091 + 1.84323i) q^{38} +(-5.69397 - 3.13029i) q^{39} +(2.67790 + 2.51471i) q^{41} +(3.50754 - 2.90169i) q^{42} +(-2.82164 + 3.88365i) q^{43} +(-4.67856 + 1.85237i) q^{44} +(-11.0779 + 13.3909i) q^{46} +(2.28738 - 5.77726i) q^{47} +(0.323032 + 0.0616216i) q^{48} +(-4.73877 - 3.44292i) q^{49} +(-9.54677 + 6.93614i) q^{51} +(-10.0588 + 4.73331i) q^{52} +(4.97994 - 3.16036i) q^{53} +(-9.93749 - 3.93453i) q^{54} +(-0.183039 - 2.90932i) q^{56} -2.07232i q^{57} +(-20.5230 + 1.29120i) q^{58} +(4.73910 - 10.0711i) q^{59} +(-0.277999 + 0.261059i) q^{61} +(-0.982423 + 7.77668i) q^{62} +(-0.0656906 + 0.519994i) q^{63} +(9.47368 - 8.89638i) q^{64} +(2.85461 - 6.06635i) q^{66} +(13.2091 - 0.831045i) q^{67} +20.1892i q^{68} +(-0.894349 - 14.2153i) q^{69} +(7.25236 + 2.87141i) q^{71} +(1.12906 - 0.716524i) q^{72} +(0.650260 - 0.305989i) q^{73} +(-11.6416 + 8.45813i) q^{74} +(-2.86837 - 2.08399i) q^{76} +(1.65294 + 0.315315i) q^{77} +(5.45260 - 13.7717i) q^{78} +(4.42134 - 5.34448i) q^{79} +(9.51216 - 3.76613i) q^{81} +(-4.92213 + 6.77473i) q^{82} +(-5.71826 + 4.73056i) q^{83} +(4.65305 + 4.36950i) q^{84} +(-9.58933 - 5.27178i) q^{86} +(11.5368 - 12.2855i) q^{87} +(-2.06830 - 3.76222i) q^{88} +(-1.50344 - 3.19497i) q^{89} +(3.68831 + 0.465942i) q^{91} +(-20.5753 - 13.0575i) q^{92} +(-3.77603 - 5.19726i) q^{93} +(13.7192 + 3.52250i) q^{94} +(-0.686905 + 10.9180i) q^{96} +(-13.1975 - 0.830318i) q^{97} +(6.43253 - 11.7007i) q^{98} +(0.238538 + 0.734146i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) $ 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9	$ 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) $ 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9 - 25 * q^11 - 60 * q^12 + 20 * q^13 - 30 * q^14 - 40 * q^16 + 15 * q^17 + 25 * q^18 - 10 * q^19 - 35 * q^21 + 25 * q^22 - 70 * q^23 + 15 * q^24 - 45 * q^26 + 20 * q^27 + 10 * q^28 - 10 * q^29 - 30 * q^31 + 25 * q^32 + 35 * q^33 - 20 * q^34 + 170 * q^36 + 55 * q^37 + 40 * q^38 - 35 * q^41 + 10 * q^42 + 25 * q^43 + 15 * q^44 - 40 * q^46 - 100 * q^47 - 5 * q^48 + 35 * q^49 - 55 * q^51 + 15 * q^52 + 15 * q^53 + 30 * q^54 + 65 * q^56 - 255 * q^58 + 5 * q^59 - 40 * q^61 - 5 * q^62 + 35 * q^63 + 25 * q^64 - 95 * q^66 - 105 * q^67 - 10 * q^69 + 45 * q^71 + 30 * q^72 + 40 * q^73 + 35 * q^74 - 65 * q^76 + 35 * q^77 - 100 * q^78 - 95 * q^81 - 175 * q^82 - 20 * q^83 + 45 * q^84 - 80 * q^86 + 5 * q^87 + 5 * q^88 + 30 * q^89 + 65 * q^91 + 55 * q^92 - 275 * q^93 + 60 * q^94 - 135 * q^96 - 35 * q^97 + 15 * q^98 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{23}{50}\right)$

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 $

$2$	0.285704	+	2.26158i	0.202023	+	1.59918i	0.688336	+	0.725392i	$0.258341\pi$
$2$	0.285704	+	2.26158i	0.202023	+	1.59918i	−0.486313	+	0.873784i	$0.661659\pi$
$3$	−1.43951	−	1.19086i	−0.831100	−	0.687546i	0.121227	−	0.992625i	$-0.461317\pi$
$3$	−1.43951	−	1.19086i	−0.831100	−	0.687546i	−0.952327	+	0.305079i	$0.901317\pi$
$4$	−3.09594	+	0.794901i	−1.54797	+	0.397451i
$5$		0			0
$5$		0			0
$6$	2.28196	−	3.59579i	0.931606	−	1.46798i
$7$	1.01659	+	0.330310i	0.384235	+	0.124846i	0.494764	−	0.869027i	$-0.335254\pi$
$7$	1.01659	+	0.330310i	0.384235	+	0.124846i	−0.110529	+	0.993873i	$0.535254\pi$
$8$	−1.00393	−	2.53564i	−0.354944	−	0.896485i
$9$	0.0918805	+	0.481654i	0.0306268	+	0.160551i
$10$		0			0
$11$	1.56186	−	0.197308i	0.470917	−	0.0594907i	0.113706	−	0.993514i	$-0.463728\pi$
$11$	1.56186	−	0.197308i	0.470917	−	0.0594907i	0.357211	+	0.934024i	$0.383728\pi$
$12$	5.40324	+	2.54257i	1.55978	+	0.733978i
$13$	3.41636	−	0.651706i	0.947529	−	0.180751i	0.309618	−	0.950861i	$-0.399799\pi$
$13$	3.41636	−	0.651706i	0.947529	−	0.180751i	0.637911	+	0.770110i	$0.279799\pi$
$14$	−0.456579	+	2.39347i	−0.122026	+	0.639681i
$15$		0			0
$16$	−0.154251	+	0.0848005i	−0.0385629	+	0.0212001i
$17$	1.57081	−	6.11789i	0.380977	−	1.48381i	−0.432193	−	0.901781i	$-0.642260\pi$
$17$	1.57081	−	6.11789i	0.380977	−	1.48381i	0.813170	−	0.582026i	$-0.197740\pi$
$18$	−1.06305	+	0.345405i	−0.250563	+	0.0814127i
$19$	0.707051	+	0.854677i	0.162209	+	0.196076i	0.845355	−	0.534205i	$-0.179389\pi$
$19$	0.707051	+	0.854677i	0.162209	+	0.196076i	−0.683146	+	0.730281i	$0.739389\pi$
$20$		0			0
$21$	−1.07004	−	1.68611i	−0.233501	−	0.367938i
$22$	0.892455	+	3.47588i	0.190272	+	0.741061i
$23$	5.21894	+	5.55761i	1.08822	+	1.15884i	0.986455	+	0.164034i	$0.0524505\pi$
$23$	5.21894	+	5.55761i	1.08822	+	1.15884i	0.101770	+	0.994808i	$0.467549\pi$
$24$	−1.57444	+	4.84562i	−0.321381	+	0.989109i
$25$		0			0
$26$	2.44995	+	7.54017i	0.480475	+	1.47875i
$27$	−2.25878	+	4.10870i	−0.434702	+	0.790721i
$28$	−3.40986	−	0.214530i	−0.644404	−	0.0405424i
$29$	−0.566426	+	9.00309i	−0.105183	+	1.67183i	0.492663	+	0.870220i	$0.336023\pi$
$29$	−0.566426	+	9.00309i	−0.105183	+	1.67183i	−0.597846	+	0.801611i	$0.703977\pi$
$30$		0			0
$31$	3.33058	+	0.855147i	0.598190	+	0.153589i	0.535631	−	0.844452i	$-0.320074\pi$
$31$	3.33058	+	0.855147i	0.598190	+	0.153589i	0.0625588	+	0.998041i	$0.480074\pi$
$32$	−3.44181	−	4.73725i	−0.608432	−	0.837435i
$33$	−2.48327	−	1.57593i	−0.432282	−	0.274334i
$34$	14.2849	+	1.80460i	2.44984	+	0.309486i
$35$		0			0
$36$	−0.667324	−	1.41813i	−0.111221	−	0.236356i
$37$	3.04110	+	5.53175i	0.499954	+	0.909414i	0.999080	+	0.0428841i	$0.0136546\pi$
$37$	3.04110	+	5.53175i	0.499954	+	0.909414i	−0.499126	+	0.866530i	$0.666345\pi$
$38$	−1.73091	+	1.84323i	−0.280791	+	0.299012i
$39$	−5.69397	−	3.13029i	−0.911766	−	0.501247i
$40$		0			0
$41$	2.67790	+	2.51471i	0.418217	+	0.392732i	0.864887	−	0.501967i	$-0.167390\pi$
$41$	2.67790	+	2.51471i	0.418217	+	0.392732i	−0.446670	+	0.894699i	$0.647390\pi$
$42$	3.50754	−	2.90169i	0.541226	−	0.447741i
$43$	−2.82164	+	3.88365i	−0.430296	+	0.592251i	−0.968021	−	0.250869i	$-0.919284\pi$
$43$	−2.82164	+	3.88365i	−0.430296	+	0.592251i	0.537725	+	0.843120i	$0.319284\pi$
$44$	−4.67856	+	1.85237i	−0.705320	+	0.279256i
$45$		0			0
$46$	−11.0779	+	13.3909i	−1.63335	+	1.97438i
$47$	2.28738	−	5.77726i	0.333648	−	0.842700i	−0.661999	−	0.749504i	$-0.730292\pi$
$47$	2.28738	−	5.77726i	0.333648	−	0.842700i	0.995648	−	0.0931954i	$-0.0297081\pi$
$48$	0.323032	+	0.0616216i	0.0466256	+	0.00889432i
$49$	−4.73877	−	3.44292i	−0.676967	−	0.491845i
$50$		0			0
$51$	−9.54677	+	6.93614i	−1.33682	+	0.971253i
$52$	−10.0588	+	4.73331i	−1.39490	+	0.656392i
$53$	4.97994	−	3.16036i	0.684047	−	0.434109i	−0.147872	−	0.989006i	$-0.547242\pi$
$53$	4.97994	−	3.16036i	0.684047	−	0.434109i	0.831919	+	0.554897i	$0.187242\pi$
$54$	−9.93749	−	3.93453i	−1.35232	−	0.535422i
$55$		0			0
$56$	−0.183039	−	2.90932i	−0.0244596	−	0.388774i
$57$		−	2.07232i		−	0.274485i
$58$	−20.5230	+	1.29120i	−2.69480	+	0.169543i
$59$	4.73910	−	10.0711i	0.616979	−	1.31115i	−0.315158	−	0.949039i	$-0.602057\pi$
$59$	4.73910	−	10.0711i	0.616979	−	1.31115i	0.932136	−	0.362107i	$-0.117943\pi$
$60$		0			0
$61$	−0.277999	+	0.261059i	−0.0355942	+	0.0334251i	−0.702140	−	0.712039i	$-0.747772\pi$
$61$	−0.277999	+	0.261059i	−0.0355942	+	0.0334251i	0.666546	+	0.745464i	$0.267772\pi$
$62$	−0.982423	+	7.77668i	−0.124768	+	0.987639i
$63$	−0.0656906	+	0.519994i	−0.00827623	+	0.0655131i
$64$	9.47368	−	8.89638i	1.18421	−	1.11205i
$65$		0			0
$66$	2.85461	−	6.06635i	0.351378	−	0.746717i
$67$	13.2091	−	0.831045i	1.61375	−	0.101528i	0.769918	−	0.638142i	$-0.220297\pi$
$67$	13.2091	−	0.831045i	1.61375	−	0.101528i	0.843828	+	0.536614i	$0.180297\pi$
$68$			20.1892i			2.44831i
$69$	−0.894349	−	14.2153i	−0.107667	−	1.71132i
$70$		0			0
$71$	7.25236	+	2.87141i	0.860697	+	0.340774i	0.756667	−	0.653800i	$-0.226826\pi$
$71$	7.25236	+	2.87141i	0.860697	+	0.340774i	0.104029	+	0.994574i	$0.466826\pi$
$72$	1.12906	−	0.716524i	0.133061	−	0.0844432i
$73$	0.650260	−	0.305989i	0.0761072	−	0.0358133i	−0.387349	−	0.921933i	$-0.626609\pi$
$73$	0.650260	−	0.305989i	0.0761072	−	0.0358133i	0.463456	+	0.886120i	$0.346609\pi$
$74$	−11.6416	+	8.45813i	−1.35331	+	0.983238i
$75$		0			0
$76$	−2.86837	−	2.08399i	−0.329024	−	0.239050i
$77$	1.65294	+	0.315315i	0.188370	+	0.0359335i
$78$	5.45260	−	13.7717i	0.617385	−	1.55934i
$79$	4.42134	−	5.34448i	0.497440	−	0.601301i	−0.460717	−	0.887547i	$-0.652408\pi$
$79$	4.42134	−	5.34448i	0.497440	−	0.601301i	0.958156	+	0.286246i	$0.0924075\pi$
$80$		0			0
$81$	9.51216	−	3.76613i	1.05691	−	0.418459i
$82$	−4.92213	+	6.77473i	−0.543558	+	0.748144i
$83$	−5.71826	+	4.73056i	−0.627661	+	0.519246i	−0.895986	−	0.444082i	$-0.853530\pi$
$83$	−5.71826	+	4.73056i	−0.627661	+	0.519246i	0.268325	+	0.963328i	$0.413530\pi$
$84$	4.65305	+	4.36950i	0.507689	+	0.476752i
$85$		0			0
$86$	−9.58933	−	5.27178i	−1.03404	−	0.568471i
$87$	11.5368	−	12.2855i	1.23688	−	1.31714i
$88$	−2.06830	−	3.76222i	−0.220482	−	0.401054i
$89$	−1.50344	−	3.19497i	−0.159364	−	0.338666i	0.809159	−	0.587590i	$-0.199923\pi$
$89$	−1.50344	−	3.19497i	−0.159364	−	0.338666i	−0.968523	+	0.248924i	$0.919923\pi$
$90$		0			0
$91$	3.68831	+	0.465942i	0.386640	+	0.0488440i
$92$	−20.5753	−	13.0575i	−2.14512	−	1.36133i
$93$	−3.77603	−	5.19726i	−0.391556	−	0.538930i
$94$	13.7192	+	3.52250i	1.41503	+	0.363318i
$95$		0			0
$96$	−0.686905	+	10.9180i	−0.0701069	+	1.11432i
$97$	−13.1975	−	0.830318i	−1.34001	−	0.0843060i	−0.623465	−	0.781851i	$-0.714276\pi$
$97$	−13.1975	−	0.830318i	−1.34001	−	0.0843060i	−0.716541	+	0.697545i	$0.754276\pi$
$98$	6.43253	−	11.7007i	0.649784	−	1.18195i
$99$	0.238538	+	0.734146i	0.0239740	+	0.0737844i
$100$		0			0
$101$	4.81951	−	14.8329i	0.479559	−	1.47593i	−0.360149	−	0.932895i	$-0.617274\pi$
$101$	4.81951	−	14.8329i	0.479559	−	1.47593i	0.839709	−	0.543037i	$-0.182726\pi$
$102$	−18.4141	−	19.6091i	−1.82327	−	1.94159i
$103$	2.62145	+	10.2099i	0.258300	+	1.00601i	0.956881	+	0.290480i	$0.0938149\pi$
$103$	2.62145	+	10.2099i	0.258300	+	1.00601i	−0.698582	+	0.715530i	$0.746185\pi$
$104$	−5.08229	−	8.00841i	−0.498360	−	0.785289i
$105$		0			0
$106$	8.57019	+	10.3596i	0.832410	+	1.00621i
$107$	7.65390	−	2.48690i	0.739930	−	0.240418i	0.0852877	−	0.996356i	$-0.472819\pi$
$107$	7.65390	−	2.48690i	0.739930	−	0.240418i	0.654643	+	0.755938i	$0.272819\pi$
$108$	3.72702	−	14.5158i	0.358633	−	1.39678i
$109$	−7.70272	+	4.23461i	−0.737787	+	0.405602i	−0.805881	−	0.592077i	$-0.798308\pi$
$109$	−7.70272	+	4.23461i	−0.737787	+	0.405602i	0.0680944	+	0.997679i	$0.478308\pi$
$110$		0			0
$111$	2.20987	−	11.5845i	0.209751	−	1.09956i
$112$	−0.184821	+	0.0352565i	−0.0174640	+	0.00333143i
$113$	−16.3958	−	7.71530i	−1.54239	−	0.725794i	−0.548499	−	0.836151i	$-0.684801\pi$
$113$	−16.3958	−	7.71530i	−1.54239	−	0.725794i	−0.993892	+	0.110357i	$0.964801\pi$
$114$	4.68670	−	0.592068i	0.438950	−	0.0554522i
$115$		0			0
$116$	−5.40295	−	28.3232i	−0.501651	−	2.62975i
$117$	0.627794	+	1.58563i	0.0580396	+	0.146591i
$118$	24.1306	+	7.84050i	2.22140	+	0.721776i
$119$	3.61767	−	5.70054i	0.331632	−	0.522568i
$120$		0			0
$121$	−8.25395	+	2.11925i	−0.750359	+	0.192660i
$122$	−0.669829	−	0.554131i	−0.0606435	−	0.0501687i
$123$	−0.860172	−	6.80896i	−0.0775591	−	0.613943i
$124$	−10.9910			−0.987022
$125$		0			0
$126$	−1.19478			−0.106439
$127$	2.26628	+	17.9395i	0.201100	+	1.59187i	0.692816	+	0.721115i	$0.256370\pi$
$127$	2.26628	+	17.9395i	0.201100	+	1.59187i	−0.491716	+	0.870756i	$0.663630\pi$
$128$	13.8029	+	11.4188i	1.22002	+	1.00929i
$129$	8.68667	−	2.23036i	0.764819	−	0.196372i
$130$		0			0
$131$	0.416170	−	0.655779i	0.0363610	−	0.0572957i	−0.825661	−	0.564166i	$-0.809198\pi$
$131$	0.416170	−	0.655779i	0.0363610	−	0.0572957i	0.862022	+	0.506870i	$0.169198\pi$
$132$	8.94075	+	2.90503i	0.778193	+	0.252850i
$133$	0.436472	+	1.10240i	0.0378470	+	0.0955905i
$134$	5.65335	+	29.6359i	0.488375	+	2.56015i
$135$		0			0
$136$	−17.0898	+	2.15894i	−1.46544	+	0.185128i
$137$	−15.9572	−	7.50891i	−1.36332	−	0.641529i	−0.401663	−	0.915788i	$-0.631568\pi$
$137$	−15.9572	−	7.50891i	−1.36332	−	0.641529i	−0.961656	+	0.274259i	$0.911568\pi$
$138$	31.8934	−	6.08399i	2.71495	−	0.517904i
$139$	−1.23113	+	6.45379i	−0.104423	+	0.547403i	0.891174	+	0.453662i	$0.149883\pi$
$139$	−1.23113	+	6.45379i	−0.104423	+	0.547403i	−0.995597	+	0.0937413i	$0.970117\pi$
$140$		0			0
$141$	−10.1726	+	5.59245i	−0.856690	+	0.470969i
$142$	−4.42189	+	17.2221i	−0.371077	+	1.44525i
$143$	5.20728	−	1.69195i	0.435455	−	0.141488i
$144$	−0.0550172	−	0.0665044i	−0.00458477	−	0.00554203i
$145$		0			0
$146$	0.877800	+	1.38319i	0.0726472	+	0.114474i
$147$	2.72145	+	10.5993i	0.224461	+	0.874218i
$148$	−13.8123	−	14.7086i	−1.13536	−	1.20904i
$149$	−0.389344	+	1.19828i	−0.0318963	+	0.0981667i	−0.965737	−	0.259522i	$-0.916435\pi$
$149$	−0.389344	+	1.19828i	−0.0318963	+	0.0981667i	0.933841	+	0.357689i	$0.116435\pi$
$150$		0			0
$151$	−1.47032	−	4.52518i	−0.119653	−	0.368254i	0.873236	−	0.487297i	$-0.162017\pi$
$151$	−1.47032	−	4.52518i	−0.119653	−	0.368254i	−0.992889	+	0.119044i	$0.962017\pi$
$152$	1.45733	−	2.65087i	0.118205	−	0.215014i
$153$	3.09104	+	0.194472i	0.249895	+	0.0157221i
$154$	−0.240859	+	3.82834i	−0.0194089	+	0.308496i
$155$		0			0
$156$	20.1164	+	5.16503i	1.61060	+	0.413533i
$157$	−0.776241	−	1.06840i	−0.0619508	−	0.0852680i	0.776917	−	0.629602i	$-0.216782\pi$
$157$	−0.776241	−	1.06840i	−0.0619508	−	0.0852680i	−0.838868	+	0.544335i	$0.816782\pi$
$158$	13.3501	+	8.47226i	1.06208	+	0.674017i
$159$	−10.9322	−	1.38106i	−0.866981	−	0.109525i
$160$		0			0
$161$	3.46979	+	7.37368i	0.273458	+	0.581128i
$162$	11.2350	+	20.4365i	0.882709	+	1.60564i
$163$	−1.27382	+	1.35648i	−0.0997731	+	0.106248i	−0.776917	−	0.629603i	$-0.783217\pi$
$163$	−1.27382	+	1.35648i	−0.0997731	+	0.106248i	0.677144	+	0.735851i	$0.263217\pi$
$164$	−10.2895	−	5.65672i	−0.803478	−	0.441716i
$165$		0			0
$166$	−12.3322	−	11.5807i	−0.957168	−	0.898840i
$167$	6.05522	−	5.00932i	0.468567	−	0.387632i	−0.372960	−	0.927847i	$-0.621657\pi$
$167$	6.05522	−	5.00932i	0.468567	−	0.387632i	0.841527	+	0.540215i	$0.181657\pi$
$168$	−3.20112	+	4.40596i	−0.246972	+	0.339927i
$169$	−0.840276	+	0.332689i	−0.0646366	+	0.0255914i
$170$		0			0
$171$	−0.346695	+	0.419082i	−0.0265124	+	0.0320480i
$172$	5.64849	−	14.2665i	0.430694	−	1.08781i
$173$	−1.29725	−	0.247464i	−0.0986283	−	0.0188143i	0.137831	−	0.990456i	$-0.455987\pi$
$173$	−1.29725	−	0.247464i	−0.0986283	−	0.0188143i	−0.236459	+	0.971641i	$0.575987\pi$
$174$	31.0807	+	22.5814i	2.35622	+	1.71189i
$175$		0			0
$176$	−0.224187	+	0.162881i	−0.0168987	+	0.0122776i
$177$	−18.8153	+	8.85381i	−1.41424	+	0.665493i
$178$	6.79613	−	4.31296i	0.509392	−	0.323270i
$179$	7.78280	+	3.08143i	0.581714	+	0.230317i	0.640506	−	0.767954i	$-0.278725\pi$
$179$	7.78280	+	3.08143i	0.581714	+	0.230317i	−0.0587919	+	0.998270i	$0.518725\pi$
$180$		0			0
$181$	−0.0690838	−	1.09805i	−0.00513496	−	0.0816178i	0.994625	−	0.103547i	$-0.0330192\pi$
$181$	−0.0690838	−	1.09805i	−0.00513496	−	0.0816178i	−0.999760	+	0.0219291i	$0.993019\pi$
$182$			8.47451i			0.628173i
$183$	0.711067	−	0.0447366i	0.0525636	−	0.00330702i
$184$	8.85265	−	18.8128i	0.652626	−	1.38690i
$185$		0			0
$186$	10.6752	−	10.0247i	0.782741	−	0.735043i
$187$	1.24626	−	9.86520i	0.0911359	−	0.721415i
$188$	−2.48923	+	19.7043i	−0.181546	+	1.43708i
$189$	−3.65340	+	3.43077i	−0.265746	+	0.249552i
$190$		0			0
$191$	−1.20147	+	2.55325i	−0.0869353	+	0.184747i	−0.943567	−	0.331181i	$-0.892553\pi$
$191$	−1.20147	+	2.55325i	−0.0869353	+	0.184747i	0.856632	+	0.515928i	$0.172553\pi$
$192$	−24.2318	+	1.52454i	−1.74878	+	0.110024i
$193$			7.28514i			0.524396i	0.965014	+	0.262198i	$0.0844474\pi$
$193$			7.28514i			0.524396i	−0.965014	+	0.262198i	$0.915553\pi$
$194$	−1.89275	−	30.0844i	−0.135892	−	2.15994i
$195$		0			0
$196$	17.4077	+	6.89219i	1.24341	+	0.492300i
$197$	22.3510	−	14.1844i	1.59245	−	1.01060i	0.617943	−	0.786223i	$-0.287966\pi$
$197$	22.3510	−	14.1844i	1.59245	−	1.01060i	0.974503	−	0.224374i	$-0.0720337\pi$
$198$	−1.59218	+	0.749221i	−0.113151	+	0.0532448i
$199$	−5.70507	+	4.14497i	−0.404421	+	0.293829i	−0.771339	−	0.636424i	$-0.780413\pi$
$199$	−5.70507	+	4.14497i	−0.404421	+	0.293829i	0.366918	+	0.930253i	$0.380413\pi$
$200$		0			0
$201$	−20.0042	−	14.5339i	−1.41099	−	1.02514i
$202$	34.9228	+	6.66187i	2.45716	+	0.468728i
$203$	−3.54964	+	8.96536i	−0.249136	+	0.629245i
$204$	24.0426	−	29.0626i	1.68332	−	2.03479i
$205$		0			0
$206$	−22.3415	+	8.84562i	−1.55661	+	0.616304i
$207$	−2.19733	+	3.02436i	−0.152725	+	0.210208i
$208$	−0.471714	+	0.390236i	−0.0327075	+	0.0270580i
$209$	1.27295	+	1.19538i	0.0880515	+	0.0826859i
$210$		0			0
$211$	5.97883	+	3.28689i	0.411600	+	0.226279i	0.674080	−	0.738659i	$-0.264540\pi$
$211$	5.97883	+	3.28689i	0.411600	+	0.226279i	−0.262480	+	0.964937i	$0.584540\pi$
$212$	−12.9054	+	13.7428i	−0.886345	+	0.943862i
$213$	−7.02036	−	12.7700i	−0.481027	−	0.874985i
$214$	7.81107	+	16.5994i	0.533954	+	1.13471i
$215$		0			0
$216$	12.6859	+	1.60260i	0.863164	+	0.109043i
$217$	3.10337	+	1.96946i	0.210671	+	0.133696i
$218$	−11.7776	−	16.2105i	−0.797679	−	1.09791i
$219$	−1.30045	−	0.333898i	−0.0878760	−	0.0225627i
$220$		0			0
$221$	1.37938	−	21.9247i	0.0927873	−	1.47481i
$222$	26.8307	+	1.68804i	1.80076	+	0.113294i
$223$	−0.331068	+	0.602210i	−0.0221699	+	0.0403270i	−0.887160	−	0.461463i	$-0.847325\pi$
$223$	−0.331068	+	0.602210i	−0.0221699	+	0.0403270i	0.864990	+	0.501790i	$0.167325\pi$
$224$	−1.93415	−	5.95271i	−0.129231	−	0.397732i
$225$		0			0
$226$	12.7644	−	39.2847i	0.849074	−	2.61318i
$227$	−15.0160	−	15.9904i	−0.996646	−	1.06132i	−0.998118	−	0.0613215i	$-0.980468\pi$
$227$	−15.0160	−	15.9904i	−0.996646	−	1.06132i	0.00147183	−	0.999999i	$-0.499532\pi$
$228$	1.64729	+	6.41576i	0.109094	+	0.424894i
$229$	6.28846	+	9.90902i	0.415553	+	0.654807i	0.986042	−	0.166499i	$-0.0532462\pi$
$229$	6.28846	+	9.90902i	0.415553	+	0.654807i	−0.570489	+	0.821305i	$0.693246\pi$
$230$		0			0
$231$	−2.00392	−	2.42233i	−0.131848	−	0.159377i
$232$	23.3973	−	7.60223i	1.53611	−	0.499111i
$233$	4.24526	−	16.5342i	0.278116	−	1.08319i	−0.663954	−	0.747774i	$-0.731123\pi$
$233$	4.24526	−	16.5342i	0.278116	−	1.08319i	0.942070	−	0.335417i	$-0.108877\pi$
$234$	−3.40665	+	1.87282i	−0.222700	+	0.122430i
$235$		0			0
$236$	−6.66643	+	34.9466i	−0.433947	+	2.27483i
$237$	−12.7291	+	2.42821i	−0.826844	+	0.157729i
$238$	13.9258	+	6.55298i	0.902675	+	0.424767i
$239$	−28.3476	+	3.58114i	−1.83366	+	0.231645i	−0.964720	−	0.263279i	$-0.915196\pi$
$239$	−28.3476	+	3.58114i	−1.83366	+	0.231645i	−0.868936	+	0.494924i	$0.835196\pi$
$240$		0			0
$241$	2.17872	+	11.4213i	0.140344	+	0.735708i	0.980980	+	0.194108i	$0.0621813\pi$
$241$	2.17872	+	11.4213i	0.140344	+	0.735708i	−0.840636	+	0.541600i	$0.817819\pi$
$242$	−7.15104	−	18.0615i	−0.459686	−	1.16104i
$243$	−4.80023	−	1.55969i	−0.307935	−	0.100054i
$244$	0.653152	−	1.02920i	0.0418138	−	0.0658880i
$245$		0			0
$246$	15.1532	−	3.89069i	0.966134	−	0.248061i
$247$	2.97254	+	2.45910i	0.189138	+	0.156469i
$248$	−1.17533	−	9.30367i	−0.0746333	−	0.590783i
$249$	13.8649			0.878654
$250$		0			0
$251$	5.45773			0.344489			0.172244	−	0.985054i	$-0.444898\pi$
$251$	5.45773			0.344489			0.172244	+	0.985054i	$0.444898\pi$
$252$	−0.209970	−	1.66209i	−0.0132269	−	0.104702i
$253$	9.24780	+	7.65044i	0.581404	+	0.480979i
$254$	−39.9240	+	10.2507i	−2.50505	+	0.643189i
$255$		0			0
$256$	−7.95367	+	12.5330i	−0.497105	+	0.783312i
$257$	−1.91131	−	0.621022i	−0.119224	−	0.0387383i	0.248797	−	0.968556i	$-0.419965\pi$
$257$	−1.91131	−	0.621022i	−0.119224	−	0.0387383i	−0.368021	+	0.929817i	$0.619965\pi$
$258$	7.52594	+	19.0084i	0.468545	+	1.18341i
$259$	1.26436	+	6.62803i	0.0785638	+	0.411846i
$260$		0			0
$261$	−4.38842	+	0.554386i	−0.271636	+	0.0343156i
$262$	1.60200	+	0.753842i	0.0989717	+	0.0465725i
$263$	−25.4906	+	4.86260i	−1.57182	+	0.299841i	−0.898318	−	0.439345i	$-0.855211\pi$
$263$	−25.4906	+	4.86260i	−1.57182	+	0.299841i	−0.673502	+	0.739186i	$0.735211\pi$
$264$	−1.50296	+	7.87881i	−0.0925010	+	0.484907i
$265$		0			0
$266$	−2.36847	+	1.30208i	−0.145220	+	0.0798354i
$267$	−1.64056	+	6.38958i	−0.100401	+	0.391036i
$268$	−40.2339	+	13.0728i	−2.45767	+	0.798547i
$269$	−0.363519	−	0.439419i	−0.0221642	−	0.0267919i	0.759315	−	0.650724i	$-0.225534\pi$
$269$	−0.363519	−	0.439419i	−0.0221642	−	0.0267919i	−0.781479	+	0.623932i	$0.785534\pi$
$270$		0			0
$271$	0.178819	+	0.281774i	0.0108625	+	0.0171166i	0.849716	−	0.527241i	$-0.176773\pi$
$271$	0.178819	+	0.281774i	0.0108625	+	0.0171166i	−0.838853	+	0.544358i	$0.816773\pi$
$272$	0.276501	+	1.07690i	0.0167653	+	0.0652966i
$273$	−4.75448	−	5.06300i	−0.287754	−	0.306427i
$274$	12.4229	−	38.2338i	0.750496	−	2.30979i
$275$		0			0
$276$	14.0686	+	43.2986i	0.846829	+	2.60627i
$277$	−1.41470	+	2.57334i	−0.0850013	+	0.154617i	−0.915391	−	0.402567i	$-0.868118\pi$
$277$	−1.41470	+	2.57334i	−0.0850013	+	0.154617i	0.830389	+	0.557184i	$0.188118\pi$
$278$	−14.9475	−	0.940416i	−0.896490	−	0.0564024i
$279$	−0.105870	+	1.68276i	−0.00633828	+	0.100744i
$280$		0			0
$281$	−15.3531	−	3.94200i	−0.915888	−	0.235160i	−0.238806	−	0.971067i	$-0.576756\pi$
$281$	−15.3531	−	3.94200i	−0.915888	−	0.235160i	−0.677082	+	0.735907i	$0.736756\pi$
$282$	−15.5541	−	21.4084i	−0.926234	−	1.27485i
$283$	−6.41016	−	4.06801i	−0.381044	−	0.241818i	0.331485	−	0.943461i	$-0.392450\pi$
$283$	−6.41016	−	4.06801i	−0.381044	−	0.241818i	−0.712529	+	0.701642i	$0.752450\pi$
$284$	−24.7353	−	3.12480i	−1.46777	−	0.185423i
$285$		0			0
$286$	5.31421	+	11.2933i	0.314236	+	0.667785i
$287$	1.89169	+	3.44097i	0.111663	+	0.203114i
$288$	1.96548	−	2.09302i	0.115817	−	0.123333i
$289$	−20.0640	−	11.0303i	−1.18023	−	0.648839i
$290$		0			0
$291$	18.0091	+	16.9117i	1.05571	+	0.991382i
$292$	−1.76993	+	1.46422i	−0.103577	+	0.0856867i
$293$	9.90014	−	13.6264i	0.578372	−	0.796061i	−0.415143	−	0.909756i	$-0.636269\pi$
$293$	9.90014	−	13.6264i	0.578372	−	0.796061i	0.993516	+	0.113695i	$0.0362686\pi$
$294$	−23.1937	+	9.18302i	−1.35268	+	0.535565i
$295$		0			0
$296$	10.9735	−	13.2647i	0.637820	−	0.770992i
$297$	−2.71721	+	6.86288i	−0.157668	+	0.398225i
$298$	−2.82123	−	0.538179i	−0.163430	−	0.0311759i
$299$	21.4517	+	15.5856i	1.24059	+	0.901338i
$300$		0			0
$301$	−4.15126	+	3.01607i	−0.239275	+	0.173843i
$302$	9.81396	−	4.61810i	0.564730	−	0.265742i
$303$	−24.6017	+	15.6127i	−1.41333	+	0.896928i
$304$	−0.181541	−	0.0718770i	−0.0104121	−	0.00412243i
$305$		0			0
$306$	0.443308	+	7.04618i	0.0253422	+	0.402803i
$307$		−	21.1073i		−	1.20466i	−0.798248	−	0.602329i	$-0.794240\pi$
$307$		−	21.1073i		−	1.20466i	0.798248	−	0.602329i	$-0.205760\pi$
$308$	−5.36804	+	0.337729i	−0.305873	+	0.0192439i
$309$	8.38499	−	17.8190i	0.477005	−	1.01369i
$310$		0			0
$311$	−19.5841	+	18.3907i	−1.11051	+	1.04284i	−0.111718	+	0.993740i	$0.535635\pi$
$311$	−19.5841	+	18.3907i	−1.11051	+	1.04284i	−0.998794	+	0.0491006i	$0.984365\pi$
$312$	−2.22093	+	17.5805i	−0.125735	+	0.995299i
$313$	1.14592	−	9.07092i	0.0647714	−	0.512719i	−0.926036	−	0.377436i	$-0.876806\pi$
$313$	1.14592	−	9.07092i	0.0647714	−	0.512719i	0.990807	−	0.135282i	$-0.0431942\pi$
$314$	2.19450	−	2.06078i	0.123843	−	0.116296i
$315$		0			0
$316$	−9.43985	+	20.0607i	−0.531033	+	1.12850i
$317$	−26.0025	+	1.63594i	−1.46045	+	0.0918834i	−0.773025	−	0.634376i	$-0.781257\pi$
$317$	−26.0025	+	1.63594i	−1.46045	+	0.0918834i	−0.687421	+	0.726259i	$0.741257\pi$
$318$		−	25.1186i		−	1.40858i
$319$	0.891707	+	14.1733i	0.0499260	+	0.793551i
$320$		0			0
$321$	−13.9794	−	5.53484i	−0.780255	−	0.308925i
$322$	−15.6848	+	9.95389i	−0.874081	+	0.554709i
$323$	6.33947	−	2.98313i	0.352737	−	0.165986i
$324$	−26.4553	+	19.2209i	−1.46974	+	1.06783i
$325$		0			0
$326$	−3.43171	−	2.49328i	−0.190065	−	0.138090i
$327$	16.1310	+	3.07715i	0.892045	+	0.170167i
$328$	3.68799	−	9.31479i	0.203635	−	0.514323i
$329$	4.23362	−	5.11756i	0.233407	−	0.282140i
$330$		0			0
$331$	−5.74683	+	2.27533i	−0.315874	+	0.125063i	−0.520712	−	0.853733i	$-0.674333\pi$
$331$	−5.74683	+	2.27533i	−0.315874	+	0.125063i	0.204838	+	0.978796i	$0.434333\pi$
$332$	13.9430	−	19.1909i	0.765224	−	1.05324i
$333$	−2.38497	+	1.97302i	−0.130696	+	0.108121i
$334$	13.0589	+	12.2632i	0.714554	+	0.671011i
$335$		0			0
$336$	0.308037	+	0.169345i	0.0168048	+	0.00923852i
$337$	5.54779	−	5.90779i	0.302207	−	0.321818i	−0.559884	−	0.828571i	$-0.689154\pi$
$337$	5.54779	−	5.90779i	0.302207	−	0.321818i	0.862091	+	0.506753i	$0.169154\pi$
$338$	−0.992471	−	1.80530i	−0.0539833	−	0.0981953i
$339$	14.4141	+	30.6314i	0.782865	+	1.66367i
$340$		0			0
$341$	5.37061	+	0.678466i	0.290835	+	0.0367410i
$342$	−1.04684	−	0.664344i	−0.0566065	−	0.0359236i
$343$	−8.07817	−	11.1186i	−0.436180	−	0.600351i
$344$	12.6803	+	3.25574i	0.683675	+	0.175538i
$345$		0			0
$346$	0.189029	−	3.00454i	0.0101623	−	0.161525i
$347$	−20.1065	−	1.26499i	−1.07937	−	0.0679085i	−0.486869	−	0.873475i	$-0.661861\pi$
$347$	−20.1065	−	1.26499i	−1.07937	−	0.0679085i	−0.592505	+	0.805566i	$0.701861\pi$
$348$	−25.9515	+	47.2057i	−1.39115	+	2.53049i
$349$	−3.11943	−	9.60061i	−0.166979	−	0.513909i	0.832198	−	0.554479i	$-0.187083\pi$
$349$	−3.11943	−	9.60061i	−0.166979	−	0.513909i	−0.999177	+	0.0405703i	$0.987083\pi$
$350$		0			0
$351$	−5.03914	+	15.5089i	−0.268970	+	0.827803i
$352$	−6.31031	−	6.71980i	−0.336341	−	0.358167i
$353$	1.98748	+	7.74072i	0.105783	+	0.411997i	0.999315	−	0.0370018i	$-0.0117807\pi$
$353$	1.98748	+	7.74072i	0.105783	+	0.411997i	−0.893532	+	0.448999i	$0.851781\pi$
$354$	−25.3992	−	40.0227i	−1.34995	−	2.12718i
$355$		0			0
$356$	7.19424	+	8.69634i	0.381294	+	0.460905i
$357$	−11.9962	+	3.89781i	−0.634908	+	0.206294i
$358$	−4.74531	+	18.4818i	−0.250798	+	0.976792i
$359$	−10.6972	+	5.88083i	−0.564576	+	0.310379i	−0.738362	−	0.674405i	$-0.764400\pi$
$359$	−10.6972	+	5.88083i	−0.564576	+	0.310379i	0.173785	+	0.984784i	$0.444400\pi$
$360$		0			0
$361$	3.32969	−	17.4549i	0.175247	−	0.918677i
$362$	2.46360	−	0.469956i	0.129484	−	0.0247004i
$363$	14.4054	+	6.77865i	0.756086	+	0.355787i
$364$	−11.7891	+	1.48932i	−0.617919	+	0.0780613i
$365$		0			0
$366$	0.304330	+	1.59535i	0.0159076	+	0.0833904i
$367$	8.06640	+	20.3734i	0.421063	+	1.06348i	0.973247	+	0.229761i	$0.0737945\pi$
$367$	8.06640	+	20.3734i	0.421063	+	1.06348i	−0.552184	+	0.833722i	$0.686206\pi$
$368$	−1.27632	−	0.414701i	−0.0665326	−	0.0216178i
$369$	−0.965175	+	1.52087i	−0.0502450	+	0.0791735i
$370$		0			0
$371$	6.10646	−	1.56787i	0.317032	−	0.0813999i
$372$	15.8216	+	13.0888i	0.820314	+	0.678623i
$373$	−0.258262	−	2.04435i	−0.0133723	−	0.105852i	0.984016	−	0.178081i	$-0.0569889\pi$
$373$	−0.258262	−	2.04435i	−0.0133723	−	0.105852i	−0.997388	+	0.0722285i	$0.976989\pi$
$374$	22.6670			1.17208
$375$		0			0
$376$	−16.9454			−0.873894
$377$	3.93225	+	31.1270i	0.202521	+	1.60312i
$378$	−8.80275	−	7.28227i	−0.452764	−	0.374559i
$379$	0.568420	−	0.145945i	0.0291978	−	0.00749672i	−0.234063	−	0.972221i	$-0.575202\pi$
$379$	0.568420	−	0.145945i	0.0291978	−	0.00749672i	0.263261	+	0.964725i	$0.415202\pi$
$380$		0			0
$381$	18.1011	−	28.5228i	0.927350	−	1.46127i
$382$	−6.11764	−	1.98774i	−0.313006	−	0.101702i
$383$	9.66012	+	24.3987i	0.493609	+	1.24671i	0.936667	+	0.350221i	$0.113893\pi$
$383$	9.66012	+	24.3987i	0.493609	+	1.24671i	−0.443058	+	0.896493i	$0.646107\pi$
$384$	−6.27121	−	32.8748i	−0.320026	−	1.67764i
$385$		0			0
$386$	−16.4759	+	2.08139i	−0.838602	+	0.105940i
$387$	−2.12983	−	1.00222i	−0.108265	−	0.0509458i
$388$	41.5187	−	7.92012i	2.10779	−	0.402083i
$389$	−0.989866	+	5.18906i	−0.0501882	+	0.263096i	−0.998533	−	0.0541456i	$-0.982757\pi$
$389$	−0.989866	+	5.18906i	−0.0501882	+	0.263096i	0.948345	+	0.317241i	$0.102757\pi$
$390$		0			0
$391$	42.1988	−	23.1990i	2.13409	−	1.17322i
$392$	−3.97260	+	15.4723i	−0.200647	+	0.781468i
$393$	−1.38002	+	0.448397i	−0.0696130	+	0.0226186i
$394$	38.4649	+	46.4961i	1.93783	+	2.34244i
$395$		0			0
$396$	−1.32207	−	2.08325i	−0.0664366	−	0.104687i
$397$	4.93393	+	19.2164i	0.247627	+	0.964443i	0.963823	+	0.266544i	$0.0858816\pi$
$397$	4.93393	+	19.2164i	0.247627	+	0.964443i	−0.716196	+	0.697899i	$0.754118\pi$
$398$	−11.0041	−	11.7182i	−0.551587	−	0.587381i
$399$	0.684507	−	2.10670i	0.0342682	−	0.105467i
$400$		0			0
$401$	1.24374	+	3.82783i	0.0621092	+	0.191153i	0.977296	−	0.211876i	$-0.0679574\pi$
$401$	1.24374	+	3.82783i	0.0621092	+	0.191153i	−0.915187	+	0.403029i	$0.867957\pi$
$402$	27.1543	−	49.3935i	1.35433	−	2.46352i
$403$	11.9358	+	0.750935i	0.594563	+	0.0374067i
$404$	−3.13018	+	49.7528i	−0.155732	+	2.47530i
$405$		0			0
$406$	−21.2900	−	5.46634i	−1.05660	−	0.271290i
$407$	5.84122	+	8.03976i	0.289539	+	0.398516i
$408$	27.1719	+	17.2438i	1.34521	+	0.853695i
$409$	−35.5527	−	4.49135i	−1.75797	−	0.222083i	−0.820862	−	0.571126i	$-0.806507\pi$
$409$	−35.5527	−	4.49135i	−1.75797	−	0.222083i	−0.937107	+	0.349043i	$0.886507\pi$
$410$		0			0
$411$	14.0285	+	29.8120i	0.691974	+	1.47052i
$412$	−16.2317	−	29.5254i	−0.799679	−	1.45461i
$413$	8.14432	−	8.67282i	0.400756	−	0.426762i
$414$	−7.46761	−	4.10535i	−0.367013	−	0.201767i
$415$		0			0
$416$	−14.8458	−	13.9411i	−0.727874	−	0.683519i
$417$	9.45780	−	7.82418i	0.463151	−	0.383152i
$418$	−2.33975	+	3.22039i	−0.114441	+	0.157514i
$419$	8.15524	−	3.22889i	0.398410	−	0.157742i	−0.160371	−	0.987057i	$-0.551269\pi$
$419$	8.15524	−	3.22889i	0.398410	−	0.157742i	0.558781	+	0.829315i	$0.311269\pi$
$420$		0			0
$421$	−11.0513	+	13.3588i	−0.538609	+	0.651067i	−0.967673	−	0.252207i	$-0.918844\pi$
$421$	−11.0513	+	13.3588i	−0.538609	+	0.651067i	0.429064	+	0.903274i	$0.358844\pi$
$422$	−5.72538	+	14.4607i	−0.278707	+	0.703934i
$423$	2.99281	+	0.570908i	0.145515	+	0.0277585i
$424$	−13.0131	−	9.45455i	−0.631970	−	0.459153i
$425$		0			0
$426$	26.8746	−	19.5255i	1.30208	−	0.946015i
$427$	−0.368842	+	0.173564i	−0.0178495	+	0.00839934i
$428$	−21.7191	+	13.7834i	−1.04983	+	0.666245i
$429$	−9.51080	−	3.76559i	−0.459186	−	0.181804i
$430$		0			0
$431$	−2.26037	−	35.9275i	−0.108878	−	1.73057i	−0.551772	−	0.833995i	$-0.686048\pi$
$431$	−2.26037	−	35.9275i	−0.108878	−	1.73057i	0.442894	−	0.896574i	$-0.353952\pi$
$432$		−	0.825319i		−	0.0397082i
$433$	10.0875	−	0.634652i	0.484775	−	0.0304994i	0.181477	−	0.983395i	$-0.441912\pi$
$433$	10.0875	−	0.634652i	0.484775	−	0.0304994i	0.303298	+	0.952896i	$0.401912\pi$
$434$	−3.56744	+	7.58119i	−0.171243	+	0.363909i
$435$		0			0
$436$	20.4810	−	19.2330i	0.980864	−	0.921092i
$437$	−1.05991	+	8.39002i	−0.0507022	+	0.401349i
$438$	0.383593	−	3.03645i	0.0183288	−	0.145087i
$439$	18.4853	−	17.3588i	0.882255	−	0.828492i	−0.103854	−	0.994593i	$-0.533118\pi$
$439$	18.4853	−	17.3588i	0.882255	−	0.828492i	0.986109	+	0.166100i	$0.0531175\pi$
$440$		0			0
$441$	1.22289	−	2.59878i	0.0582331	−	0.123752i
$442$	49.9784	−	3.14437i	2.37723	−	0.149563i
$443$		−	30.5458i		−	1.45128i	−0.688077	−	0.725638i	$-0.741545\pi$
$443$		−	30.5458i		−	1.45128i	0.688077	−	0.725638i	$-0.258455\pi$
$444$	2.36695	+	37.6216i	0.112330	+	1.78544i
$445$		0			0
$446$	−1.45653	−	0.576681i	−0.0689687	−	0.0273067i
$447$	1.98745	−	1.26127i	0.0940031	−	0.0596562i
$448$	12.5694	−	5.91472i	0.593850	−	0.279444i
$449$	24.4297	−	17.7492i	1.15291	−	0.837638i	0.164045	−	0.986453i	$-0.447546\pi$
$449$	24.4297	−	17.7492i	1.15291	−	0.837638i	0.988865	+	0.148814i	$0.0475457\pi$
$450$		0			0
$451$	4.67866	+	3.39925i	0.220310	+	0.160064i
$452$	56.8934	+	10.8530i	2.67604	+	0.510482i
$453$	−3.27234	+	8.26498i	−0.153748	+	0.388323i
$454$	31.8734	−	38.5283i	1.49589	−	1.80822i
$455$		0			0
$456$	−5.25465	+	2.08046i	−0.246072	+	0.0974266i
$457$	0.490978	−	0.675773i	0.0229670	−	0.0316113i	−0.797379	−	0.603479i	$-0.793781\pi$
$457$	0.490978	−	0.675773i	0.0229670	−	0.0316113i	0.820346	+	0.571867i	$0.193781\pi$
$458$	−20.6134	+	17.0529i	−0.963200	+	0.796828i
$459$	21.5885	+	20.2730i	1.00767	+	0.946261i
$460$		0			0
$461$	−11.1026	−	6.10371i	−0.517100	−	0.284278i	0.201757	−	0.979436i	$-0.435335\pi$
$461$	−11.1026	−	6.10371i	−0.517100	−	0.284278i	−0.718858	+	0.695157i	$0.755335\pi$
$462$	4.90575	−	5.22409i	0.228236	−	0.243047i
$463$	−10.4957	−	19.0916i	−0.487777	−	0.887263i	−0.999603	−	0.0281742i	$-0.991031\pi$
$463$	−10.4957	−	19.0916i	−0.487777	−	0.887263i	0.511826	−	0.859089i	$-0.328969\pi$
$464$	−0.676094	−	1.43677i	−0.0313869	−	0.0667005i
$465$		0			0
$466$	38.6062	+	4.87710i	1.78840	+	0.225927i
$467$	17.6082	+	11.1745i	0.814812	+	0.517096i	0.876728	−	0.480986i	$-0.159721\pi$
$467$	17.6082	+	11.1745i	0.814812	+	0.517096i	−0.0619162	+	0.998081i	$0.519721\pi$
$468$	−3.20403	−	4.40996i	−0.148106	−	0.203851i
$469$	13.7027	+	3.51826i	0.632733	+	0.162458i
$470$		0			0
$471$	−0.154919	+	2.46237i	−0.00713831	+	0.113460i
$472$	−30.2945	−	1.90597i	−1.39442	−	0.0877292i
$473$	−3.64072	+	6.62244i	−0.167400	+	0.304500i
$474$	−9.12833	−	28.0941i	−0.419278	−	1.29040i
$475$		0			0
$476$	−6.66872	+	20.5242i	−0.305660	+	0.940725i
$477$	1.97976	+	2.10823i	0.0906470	+	0.0965293i
$478$	−16.1980	−	63.0872i	−0.740881	−	2.88554i
$479$	6.53134	+	10.2917i	0.298425	+	0.470242i	0.960143	−	0.279511i	$-0.0901723\pi$
$479$	6.53134	+	10.2917i	0.298425	+	0.470242i	−0.661718	+	0.749753i	$0.730172\pi$
$480$		0			0
$481$	13.9946	+	16.9166i	0.638098	+	0.771328i
$482$	−25.2076	+	8.19044i	−1.14817	+	0.373064i
$483$	3.78626	−	14.7465i	0.172281	−	0.670990i
$484$	23.8691	−	13.1222i	1.08496	−	0.596462i
$485$		0			0
$486$	2.15591	−	11.3017i	0.0977942	−	0.512655i
$487$	−6.97324	+	1.33022i	−0.315988	+	0.0602779i	−0.342935	−	0.939359i	$-0.611421\pi$
$487$	−6.97324	+	1.33022i	−0.315988	+	0.0602779i	0.0269478	+	0.999637i	$0.491421\pi$
$488$	0.941044	+	0.442822i	0.0425990	+	0.0200456i
$489$	3.44905	−	0.435716i	0.155971	−	0.0197038i
$490$		0			0
$491$	3.95370	+	20.7260i	0.178428	+	0.935352i	0.953024	+	0.302895i	$0.0979533\pi$
$491$	3.95370	+	20.7260i	0.178428	+	0.935352i	−0.774596	+	0.632457i	$0.782047\pi$
$492$	8.07548	+	20.3963i	0.364071	+	0.919538i
$493$	54.1902	+	17.6075i	2.44060	+	0.793000i
$494$	−4.71218	+	7.42520i	−0.212011	+	0.334076i
$495$		0			0
$496$	−0.586263	+	0.150527i	−0.0263240	+	0.00675886i
$497$	6.42422	+	5.31458i	0.288166	+	0.238392i
$498$	3.96126	+	31.3566i	0.177508	+	1.40512i
$499$	−38.9862			−1.74526			−0.872632	−	0.488378i	$-0.837589\pi$
$499$	−38.9862			−1.74526			−0.872632	+	0.488378i	$0.837589\pi$
$500$		0			0
$501$	−14.6820			−0.655941
$502$	1.55929	+	12.3431i	0.0695946	+	0.550898i
$503$	28.9755	+	23.9706i	1.29195	+	1.06880i	0.993436	+	0.114393i	$0.0364925\pi$
$503$	28.9755	+	23.9706i	1.29195	+	1.06880i	0.298519	+	0.954404i	$0.403508\pi$
$504$	1.38447	−	0.355471i	0.0616691	−	0.0158339i
$505$		0			0
$506$	−14.6599	+	23.1004i	−0.651713	+	1.02694i
$507$	1.60577	+	0.521747i	0.0713148	+	0.0231716i
$508$	−21.2764	−	53.7380i	−0.943986	−	2.38424i
$509$	0.949844	+	4.97926i	0.0421011	+	0.220702i	0.997120	−	0.0758443i	$-0.0241652\pi$
$509$	0.949844	+	4.97926i	0.0421011	+	0.220702i	−0.955019	+	0.296546i	$0.904165\pi$
$510$		0			0
$511$	0.762120	−	0.0962781i	0.0337142	−	0.00425909i
$512$	1.80134	+	0.847647i	0.0796088	+	0.0374611i
$513$	−5.10869	+	0.974534i	−0.225554	+	0.0430267i
$514$	0.858421	−	4.50000i	0.0378633	−	0.198487i
$515$		0			0
$516$	−25.1205	+	13.8101i	−1.10587	+	0.607955i
$517$	2.43265	−	9.47456i	0.106988	−	0.416691i
$518$	−14.6286	+	4.75311i	−0.642742	+	0.208840i
$519$	1.57271	+	1.90108i	0.0690342	+	0.0834480i
$520$		0			0
$521$	−13.9130	−	21.9234i	−0.609540	−	0.960481i	−0.999218	−	0.0395303i	$-0.987414\pi$
$521$	−13.9130	−	21.9234i	−0.609540	−	0.960481i	0.389678	−	0.920951i	$-0.372586\pi$
$522$	−2.50757	−	9.76635i	−0.109754	−	0.427462i
$523$	−11.1917	−	11.9179i	−0.489379	−	0.521135i	0.436119	−	0.899889i	$-0.356353\pi$
$523$	−11.1917	−	11.9179i	−0.489379	−	0.521135i	−0.925498	+	0.378754i	$0.876353\pi$
$524$	−0.767156	+	2.36106i	−0.0335134	+	0.103144i
$525$		0			0
$526$	−18.2799	−	56.2598i	−0.797042	−	2.45304i
$527$	10.4634	−	19.0329i	0.455793	−	0.829084i
$528$	0.516688	+	0.0325072i	0.0224859	+	0.00141470i
$529$	−2.20548	+	35.0551i	−0.0958903	+	1.52413i
$530$		0			0
$531$	5.28622	+	1.35727i	0.229403	+	0.0589006i
$532$	−2.22759	−	3.06602i	−0.0965784	−	0.132929i
$533$	10.7875	+	6.84597i	0.467259	+	0.296532i
$534$	−14.9192	−	1.88474i	−0.645618	−	0.0815606i
$535$		0			0
$536$	−15.3683	−	32.6592i	−0.663807	−	1.41066i
$537$	−7.53383	−	13.7040i	−0.325109	−	0.591371i
$538$	0.889922	−	0.947670i	0.0383672	−	0.0408570i
$539$	−8.08059	−	4.44234i	−0.348055	−	0.191345i
$540$		0			0
$541$	22.1004	+	20.7537i	0.950173	+	0.892271i	0.994285	−	0.106755i	$-0.0340461\pi$
$541$	22.1004	+	20.7537i	0.950173	+	0.892271i	−0.0441128	+	0.999027i	$0.514046\pi$
$542$	−0.586165	+	0.484918i	−0.0251779	+	0.0208290i
$543$	−1.20819	+	1.66293i	−0.0518483	+	0.0713631i
$544$	−34.3884	+	13.6153i	−1.47439	+	0.583753i
$545$		0			0
$546$	10.0920	−	12.1991i	0.431898	−	0.522074i
$547$	−6.16710	+	15.5763i	−0.263686	+	0.665995i	−0.999943	−	0.0107073i	$-0.996592\pi$
$547$	−6.16710	+	15.5763i	−0.263686	+	0.665995i	0.736256	+	0.676703i	$0.236592\pi$
$548$	55.3714	+	10.5627i	2.36535	+	0.451215i
$549$	−0.151283	−	0.109913i	−0.00645659	−	0.00469099i
$550$		0			0
$551$	−8.09523	+	5.88153i	−0.344868	+	0.250561i
$552$	−35.1470	+	16.5389i	−1.49595	+	0.703943i
$553$	6.26003	−	3.97274i	0.266204	−	0.168938i
$554$	−6.22398	−	2.46425i	−0.264432	−	0.104696i
$555$		0			0
$556$	−1.31864	−	20.9591i	−0.0559227	−	0.888866i
$557$			14.7747i			0.626023i	0.949749	+	0.313011i	$0.101338\pi$
$557$			14.7747i			0.626023i	−0.949749	+	0.313011i	$0.898662\pi$
$558$	−3.83593	+	0.241337i	−0.162388	+	0.0102166i
$559$	−7.10874	+	15.1068i	−0.300668	+	0.638952i
$560$		0			0
$561$	−13.5421	+	12.7169i	−0.571749	+	0.536908i
$562$	4.52871	−	35.8484i	0.191032	−	1.51217i
$563$	−2.59783	+	20.5639i	−0.109485	+	0.866666i	0.837734	+	0.546079i	$0.183880\pi$
$563$	−2.59783	+	20.5639i	−0.109485	+	0.866666i	−0.947219	+	0.320587i	$0.896120\pi$
$564$	27.0484	−	25.4001i	1.13894	−	1.06954i
$565$		0			0
$566$	7.36871	−	15.6593i	0.309730	−	0.658210i
$567$	10.9140	−	0.686648i	0.458343	−	0.0288365i
$568$		−	21.2721i		−	0.892557i
$569$	−2.55506	−	40.6115i	−0.107114	−	1.70252i	−0.574528	−	0.818485i	$-0.694814\pi$
$569$	−2.55506	−	40.6115i	−0.107114	−	1.70252i	0.467414	−	0.884038i	$-0.345186\pi$
$570$		0			0
$571$	16.1747	+	6.40403i	0.676891	+	0.268000i	0.681315	−	0.731990i	$-0.261408\pi$
$571$	16.1747	+	6.40403i	0.676891	+	0.268000i	−0.00442398	+	0.999990i	$0.501408\pi$
$572$	−14.7765	+	9.37743i	−0.617835	+	0.392090i
$573$	4.77010	−	2.24464i	0.199274	−	0.0937712i
$574$	−7.24156	+	5.26130i	−0.302257	+	0.219602i
$575$		0			0
$576$	5.15543	+	3.74564i	0.214809	+	0.156068i
$577$	−45.3702	−	8.65482i	−1.88878	−	0.360305i	−0.892848	−	0.450359i	$-0.851296\pi$
$577$	−45.3702	−	8.65482i	−1.88878	−	0.360305i	−0.995937	+	0.0900537i	$0.971296\pi$
$578$	19.2134	−	48.5276i	0.799174	−	2.01848i
$579$	8.67562	−	10.4870i	0.360546	−	0.435826i
$580$		0			0
$581$	−7.37568	+	2.92024i	−0.305995	+	0.121152i
$582$	−33.1019	+	45.5608i	−1.37212	+	1.88856i
$583$	7.15437	−	5.91861i	0.296304	−	0.245124i
$584$	−1.42870	−	1.34164i	−0.0591199	−	0.0555173i
$585$		0			0
$586$	33.6456	+	18.4968i	1.38989	+	0.764097i
$587$	5.28879	−	5.63198i	0.218292	−	0.232457i	−0.610497	−	0.792018i	$-0.709030\pi$
$587$	5.28879	−	5.63198i	0.218292	−	0.232457i	0.828789	+	0.559561i	$0.189030\pi$
$588$	−16.8508	−	30.6516i	−0.694917	−	1.26405i
$589$	1.62401	+	3.45120i	0.0669163	+	0.142204i
$590$		0			0
$591$	−49.0662	−	6.19850i	−2.01831	−	0.254972i
$592$	−0.938190	−	0.595393i	−0.0385594	−	0.0244705i
$593$	26.2209	+	36.0899i	1.07676	+	1.48204i	0.863037	+	0.505142i	$0.168560\pi$
$593$	26.2209	+	36.0899i	1.07676	+	1.48204i	0.213725	+	0.976894i	$0.431440\pi$
$594$	−16.2972	−	4.18442i	−0.668684	−	0.171689i
$595$		0			0
$596$	0.252872	−	4.01928i	0.0103580	−	0.164636i
$597$	13.1486	+	0.827239i	0.538136	+	0.0338566i
$598$	−29.1192	+	52.9676i	−1.19077	+	2.16601i
$599$	3.55544	+	10.9425i	0.145271	+	0.447099i	0.997046	−	0.0768094i	$-0.0244733\pi$
$599$	3.55544	+	10.9425i	0.145271	+	0.447099i	−0.851774	+	0.523909i	$0.824473\pi$
$600$		0			0
$601$	−4.92573	+	15.1598i	−0.200925	+	0.618383i	0.798931	+	0.601422i	$0.205399\pi$
$601$	−4.92573	+	15.1598i	−0.200925	+	0.618383i	−0.999856	+	0.0169606i	$0.994601\pi$
$602$	−8.00710	−	8.52670i	−0.326345	−	0.347522i
$603$	1.61393	+	6.28585i	0.0657244	+	0.255980i
$604$	8.14908	+	12.8409i	0.331582	+	0.522489i
$605$		0			0
$606$	−42.3382	−	51.1781i	−1.71987	−	2.07897i
$607$	−2.78973	+	0.906439i	−0.113232	+	0.0367912i	−0.365085	−	0.930974i	$-0.618960\pi$
$607$	−2.78973	+	0.906439i	−0.113232	+	0.0367912i	0.251853	+	0.967765i	$0.418960\pi$
$608$	1.61528	−	6.29112i	0.0655084	−	0.255138i
$609$	15.7863	−	8.67857i	0.639691	−	0.351673i
$610$		0			0
$611$	4.04944	−	21.2279i	0.163823	−	0.858789i
$612$	−9.72424	+	1.85500i	−0.393079	+	0.0749838i
$613$	15.8665	+	7.46620i	0.640842	+	0.301557i	0.718609	−	0.695414i	$-0.244779\pi$
$613$	15.8665	+	7.46620i	0.640842	+	0.301557i	−0.0777674	+	0.996972i	$0.524779\pi$
$614$	47.7358	−	6.03043i	1.92646	−	0.243368i
$615$		0			0
$616$	−0.859913	−	4.50782i	−0.0346469	−	0.181625i
$617$	−13.5309	−	34.1750i	−0.544732	−	1.37583i	−0.897869	−	0.440263i	$-0.854885\pi$
$617$	−13.5309	−	34.1750i	−0.544732	−	1.37583i	0.353137	−	0.935572i	$-0.385115\pi$
$618$	42.6947	+	13.8723i	1.71743	+	0.558027i
$619$	−6.36133	+	10.0238i	−0.255683	+	0.402892i	−0.947786	−	0.318906i	$-0.896684\pi$
$619$	−6.36133	+	10.0238i	−0.255683	+	0.402892i	0.692103	+	0.721799i	$0.256684\pi$
$620$		0			0
$621$	−34.6230	+	8.88968i	−1.38937	+	0.356731i
$622$	−47.1872	−	39.0367i	−1.89203	−	1.56523i
$623$	−0.473050	−	3.74458i	−0.0189524	−	0.150023i
$624$	1.14375			0.0457868
$625$		0			0
$626$	20.8420			0.833013
$627$	−0.408885	−	3.23666i	−0.0163293	−	0.129260i
$628$	3.25247	+	2.69068i	0.129788	+	0.107370i
$629$	38.6196	−	9.91584i	1.53987	−	0.395370i
$630$		0			0
$631$	3.67739	−	5.79464i	0.146395	−	0.230681i	−0.763215	−	0.646144i	$-0.776380\pi$
$631$	3.67739	−	5.79464i	0.146395	−	0.230681i	0.909610	+	0.415463i	$0.136380\pi$
$632$	−17.9904	−	5.84544i	−0.715620	−	0.232519i
$633$	−4.69233	−	11.8515i	−0.186503	−	0.471054i
$634$	−11.1288	−	58.3392i	−0.441981	−	2.31695i
$635$		0			0
$636$	34.9433	−	4.41436i	1.38559	−	0.175041i
$637$	−18.4331	−	8.67397i	−0.730347	−	0.343675i
$638$	−31.7992	+	6.06602i	−1.25894	+	0.240156i
$639$	−0.716678	+	3.75696i	−0.0283513	+	0.148623i
$640$		0			0
$641$	−11.5450	+	6.34689i	−0.455998	+	0.250687i	−0.693161	−	0.720783i	$-0.743783\pi$
$641$	−11.5450	+	6.34689i	−0.455998	+	0.250687i	0.237163	+	0.971470i	$0.423783\pi$
$642$	8.52350	−	33.1968i	0.336396	−	1.31017i
$643$	6.20839	−	2.01723i	0.244835	−	0.0795517i	−0.184029	−	0.982921i	$-0.558914\pi$
$643$	6.20839	−	2.01723i	0.244835	−	0.0795517i	0.428864	+	0.903369i	$0.358914\pi$
$644$	−16.6036	−	20.0703i	−0.654274	−	0.790881i
$645$		0			0
$646$	8.55778	+	13.4849i	0.336701	+	0.530556i
$647$	−9.92632	−	38.6605i	−0.390244	−	1.51990i	−0.795646	−	0.605761i	$-0.792869\pi$
$647$	−9.92632	−	38.6605i	−0.390244	−	1.51990i	0.405402	−	0.914138i	$-0.367131\pi$
$648$	−19.0991	−	20.3385i	−0.750284	−	0.798972i
$649$	5.41468	−	16.6647i	0.212545	−	0.654146i
$650$		0			0
$651$	−2.12197	−	6.53075i	−0.0831665	−	0.255960i
$652$	2.86539	−	5.21213i	0.112217	−	0.204123i
$653$	−27.4931	−	1.72972i	−1.07589	−	0.0676893i	−0.485056	−	0.874483i	$-0.661201\pi$
$653$	−27.4931	−	1.72972i	−1.07589	−	0.0676893i	−0.590833	+	0.806794i	$0.701201\pi$
$654$	−2.35053	+	37.3606i	−0.0919129	+	1.46091i
$655$		0			0
$656$	−0.626318	−	0.160811i	−0.0244536	−	0.00627862i
$657$	0.207127	+	0.285086i	0.00808080	+	0.0111223i
$658$	12.7833	+	8.11254i	0.498346	+	0.316260i
$659$	−2.70371	−	0.341559i	−0.105322	−	0.0133052i	0.0724957	−	0.997369i	$-0.476904\pi$
$659$	−2.70371	−	0.341559i	−0.105322	−	0.0133052i	−0.177817	+	0.984063i	$0.556904\pi$
$660$		0			0
$661$	0.512507	+	1.08913i	0.0199342	+	0.0423623i	0.914546	−	0.404481i	$-0.132548\pi$
$661$	0.512507	+	1.08913i	0.0199342	+	0.0423623i	−0.894612	+	0.446844i	$0.852548\pi$
$662$	−6.78772	−	12.3468i	−0.263812	−	0.479873i
$663$	−28.0949	+	29.9181i	−1.09112	+	1.16192i
$664$	17.7357	+	9.75031i	0.688280	+	0.378385i
$665$		0			0
$666$	−5.14353	−	4.83010i	−0.199308	−	0.187162i
$667$	−52.9918	+	43.8386i	−2.05185	+	1.69744i
$668$	−14.7647	+	20.3218i	−0.571262	+	0.786275i
$669$	1.19372	−	0.472629i	0.0461521	−	0.0182729i
$670$		0			0
$671$	−0.382686	+	0.462587i	−0.0147734	+	0.0178580i
$672$	−4.30464	+	10.8723i	−0.166055	+	0.419408i
$673$	18.5614	+	3.54077i	0.715489	+	0.136487i	0.532257	−	0.846583i	$-0.321344\pi$
$673$	18.5614	+	3.54077i	0.715489	+	0.136487i	0.183232	+	0.983070i	$0.441344\pi$
$674$	14.9459	+	10.8589i	0.575696	+	0.418268i
$675$		0			0
$676$	2.33699	−	1.69792i	0.0898841	−	0.0653046i
$677$	−12.8740	+	6.05804i	−0.494788	+	0.232829i	−0.656949	−	0.753935i	$-0.728153\pi$
$677$	−12.8740	+	6.05804i	−0.494788	+	0.232829i	0.162162	+	0.986764i	$0.448153\pi$
$678$	−65.1572	+	41.3500i	−2.50235	+	1.58804i
$679$	−13.1422	−	5.20337i	−0.504352	−	0.199687i
$680$		0			0
$681$	2.57323	+	40.9003i	0.0986064	+	1.56730i
$682$			12.3399i			0.472519i
$683$	22.2780	−	1.40161i	0.852443	−	0.0536312i	0.369445	−	0.929253i	$-0.379548\pi$
$683$	22.2780	−	1.40161i	0.852443	−	0.0536312i	0.482998	+	0.875621i	$0.339548\pi$
$684$	0.740216	−	1.57304i	0.0283029	−	0.0601467i
$685$		0			0
$686$	22.8377	−	21.4460i	0.871948	−	0.818814i
$687$	2.74802	−	21.7528i	0.104843	−	0.829922i
$688$	0.105906	−	0.838335i	0.00403764	−	0.0319612i
$689$	14.9536	−	14.0424i	0.569688	−	0.534973i
$690$		0			0
$691$	−14.1510	+	30.0723i	−0.538328	+	1.14400i	0.431925	+	0.901910i	$0.357835\pi$
$691$	−14.1510	+	30.0723i	−0.538328	+	1.14400i	−0.970253	+	0.242095i	$0.922165\pi$
$692$	4.21292	−	0.265054i	0.160151	−	0.0100759i
$693$			0.825117i			0.0313436i
$694$	−2.88362	−	45.8338i	−0.109461	−	1.73983i
$695$		0			0
$696$	−42.7338	−	16.9195i	−1.61982	−	0.641332i
$697$	19.5912	−	12.4330i	0.742070	−	0.470932i
$698$	20.8213	−	9.79775i	0.788097	−	0.370850i
$699$	−25.8010	+	18.7456i	−0.975885	+	0.709022i
$700$		0			0
$701$	39.8432	+	28.9478i	1.50486	+	1.09334i	0.968396	+	0.249418i	$0.0802394\pi$
$701$	39.8432	+	28.9478i	1.50486	+	1.09334i	0.536462	+	0.843925i	$0.319761\pi$
$702$	−36.5142	−	6.96546i	−1.37814	−	0.262895i
$703$	−2.57764	+	6.51039i	−0.0972177	+	0.245544i
$704$	13.0412	−	15.7641i	0.491508	−	0.594132i
$705$		0			0
$706$	−16.9384	+	6.70639i	−0.637485	+	0.252398i
$707$	9.79894	−	13.4871i	0.368527	−	0.507234i
$708$	51.2131	−	42.3671i	1.92470	−	1.59225i
$709$	−1.57455	−	1.47860i	−0.0591335	−	0.0555300i	0.654417	−	0.756134i	$-0.272914\pi$
$709$	−1.57455	−	1.47860i	−0.0591335	−	0.0555300i	−0.713551	+	0.700604i	$0.752914\pi$
$710$		0			0
$711$	2.98043	+	1.63850i	0.111775	+	0.0614487i
$712$	−6.59195	+	7.01972i	−0.247044	+	0.263075i
$713$	12.6295	+	22.9730i	0.472979	+	0.860346i
$714$	−12.2426	−	26.0168i	−0.458167	−	0.973654i
$715$		0			0
$716$	−26.5445	−	3.35335i	−0.992013	−	0.125320i
$717$	45.0713	+	28.6031i	1.68322	+	1.06820i
$718$	−16.3562	−	22.5124i	−0.610407	−	0.840154i
$719$	21.5474	+	5.53242i	0.803581	+	0.206325i	0.628074	−	0.778154i	$-0.283843\pi$
$719$	21.5474	+	5.53242i	0.803581	+	0.206325i	0.175507	+	0.984478i	$0.443843\pi$
$720$		0			0
$721$	−0.707486	+	11.2452i	−0.0263482	+	0.418792i
$722$	40.4268	+	2.54344i	1.50453	+	0.0946570i
$723$	10.4649	−	19.0356i	0.389193	−	0.707940i
$724$	1.08672	+	3.34459i	0.0403878	+	0.124301i
$725$		0			0
$726$	−11.2148	+	34.5155i	−0.416219	+	1.28099i
$727$	−3.70615	−	3.94665i	−0.137454	−	0.146373i	0.656559	−	0.754275i	$-0.272011\pi$
$727$	−3.70615	−	3.94665i	−0.137454	−	0.146373i	−0.794012	+	0.607902i	$0.792011\pi$
$728$	−2.52135	−	9.82001i	−0.0934474	−	0.363954i
$729$	−11.3929	−	17.9523i	−0.421958	−	0.664900i
$730$		0			0
$731$	19.3275	+	23.3630i	0.714854	+	0.864110i
$732$	−2.16586	+	0.703730i	−0.0800524	+	0.0260106i
$733$	2.92419	−	11.3890i	0.108008	−	0.420661i	−0.891467	−	0.453086i	$-0.850323\pi$
$733$	2.92419	−	11.3890i	0.108008	−	0.420661i	0.999474	+	0.0324248i	$0.0103229\pi$
$734$	−43.7714	+	24.0635i	−1.61563	+	0.888202i
$735$		0			0
$736$	8.36516	−	43.8517i	0.308344	−	1.61639i
$737$	20.4667	−	3.90423i	0.753901	−	0.143814i
$738$	−3.71533	−	1.74830i	−0.136763	−	0.0643558i
$739$	21.1183	−	2.66786i	0.776848	−	0.0981387i	0.273096	−	0.961987i	$-0.411952\pi$
$739$	21.1183	−	2.66786i	0.776848	−	0.0981387i	0.503752	+	0.863848i	$0.331952\pi$
$740$		0			0
$741$	−1.35054	−	7.07978i	−0.0496134	−	0.260082i
$742$	5.29050	+	13.3623i	0.194220	+	0.490545i
$743$	−26.6442	−	8.65722i	−0.977480	−	0.317603i	−0.223648	−	0.974670i	$-0.571797\pi$
$743$	−26.6442	−	8.65722i	−0.977480	−	0.317603i	−0.753832	+	0.657067i	$0.771797\pi$
$744$	−9.38751	+	14.7924i	−0.344163	+	0.542314i
$745$		0			0
$746$	4.54967	−	1.16816i	0.166575	−	0.0427693i
$747$	−2.80389	−	2.31958i	−0.102589	−	0.0848689i
$748$	3.98350	+	31.5327i	0.145651	+	1.15295i
$749$	8.60234			0.314322
$750$		0			0
$751$	6.02192			0.219743			0.109872	−	0.993946i	$-0.464956\pi$
$751$	6.02192			0.219743			0.109872	+	0.993946i	$0.464956\pi$
$752$	0.137083	+	1.08512i	0.00499889	+	0.0395703i
$753$	−7.85644	−	6.49941i	−0.286305	−	0.236852i
$754$	−69.2725	+	17.7862i	−2.52276	+	0.647734i
$755$		0			0
$756$	8.58357	−	13.5255i	0.312182	−	0.491919i
$757$	0.810253	+	0.263267i	0.0294492	+	0.00956861i	0.323705	−	0.946158i	$-0.395072\pi$
$757$	0.810253	+	0.263267i	0.0294492	+	0.00956861i	−0.294255	+	0.955727i	$0.595072\pi$
$758$	0.492467	+	1.24383i	0.0178872	+	0.0451779i
$759$	−4.20163	−	22.0257i	−0.152510	−	0.799484i
$760$		0			0
$761$	7.86865	−	0.994042i	0.285238	−	0.0360340i	0.0185877	−	0.999827i	$-0.494083\pi$
$761$	7.86865	−	0.994042i	0.285238	−	0.0360340i	0.266651	+	0.963793i	$0.414083\pi$
$762$	69.6781	+	32.7880i	2.52417	+	1.18779i
$763$	−9.22925	+	1.76057i	−0.334121	+	0.0637371i
$764$	1.69009	−	8.85976i	0.0611453	−	0.320535i
$765$		0			0
$766$	−52.4195	+	28.8179i	−1.89399	+	1.04123i
$767$	9.62710	−	37.4951i	0.347614	−	1.35387i
$768$	26.3745	−	8.56958i	0.951706	−	0.309228i
$769$	−34.4923	−	41.6940i	−1.24382	−	1.50352i	−0.790864	−	0.611992i	$-0.790369\pi$
$769$	−34.4923	−	41.6940i	−1.24382	−	1.50352i	−0.452958	−	0.891532i	$-0.649631\pi$
$770$		0			0
$771$	2.01179	+	3.17008i	0.0724529	+	0.114168i
$772$	−5.79097	−	22.5543i	−0.208422	−	0.811748i
$773$	−16.3423	−	17.4028i	−0.587793	−	0.625936i	0.364470	−	0.931215i	$-0.381250\pi$
$773$	−16.3423	−	17.4028i	−0.587793	−	0.625936i	−0.952263	+	0.305279i	$0.901250\pi$
$774$	1.65810	−	5.10312i	0.0595993	−	0.183428i
$775$		0			0
$776$	11.1440	+	34.2978i	0.400047	+	1.23122i
$777$	6.07302	−	11.0468i	0.217869	−	0.396301i
$778$	−12.0183	−	0.756125i	−0.430876	−	0.0271084i
$779$	−0.255859	+	4.06677i	−0.00916711	+	0.145707i
$780$		0			0
$781$	11.8937	+	3.05378i	0.425590	+	0.109273i
$782$	64.5227	+	88.8078i	2.30733	+	3.17576i
$783$	−35.7116	−	22.6633i	−1.27623	−	0.809919i
$784$	1.02292	+	0.129225i	0.0365329	+	0.00461518i
$785$		0			0
$786$	−1.40836	−	2.99292i	−0.0502346	−	0.106754i
$787$	−0.925837	−	1.68409i	−0.0330025	−	0.0600314i	0.859291	−	0.511487i	$-0.170905\pi$
$787$	−0.925837	−	1.68409i	−0.0330025	−	0.0600314i	−0.892294	+	0.451455i	$0.850905\pi$
$788$	−57.9222	+	61.6809i	−2.06339	+	2.19729i
$789$	42.4847	+	23.3561i	1.51249	+	0.831501i
$790$		0			0
$791$	−14.1194	−	13.2590i	−0.502029	−	0.471436i
$792$	1.62205	−	1.34188i	0.0576372	−	0.0476816i
$793$	−0.779613	+	1.07305i	−0.0276849	+	0.0381049i
$794$	−42.0497	+	16.6486i	−1.49229	+	0.590838i
$795$		0			0
$796$	14.3677	−	17.3675i	0.509249	−	0.615576i
$797$	6.25007	−	15.7859i	0.221389	−	0.559164i	−0.776052	−	0.630670i	$-0.782780\pi$
$797$	6.25007	−	15.7859i	0.221389	−	0.559164i	0.997440	+	0.0715055i	$0.0227804\pi$
$798$	4.96002	+	0.946175i	0.175583	+	0.0334942i
$799$	−31.7516	−	23.0689i	−1.12329	−	0.816119i
$800$		0			0
$801$	1.40073	−	1.01769i	0.0494925	−	0.0359584i
$802$	−8.30159	+	3.90643i	−0.293139	+	0.137941i
$803$	0.955238	−	0.606213i	0.0337096	−	0.0213928i
$804$	73.4849	+	29.0947i	2.59161	+	1.02609i
$805$		0			0
$806$	1.71180	+	27.2082i	0.0602954	+	0.958368i
$807$			1.06545i			0.0375056i
$808$	−42.4495	+	2.67069i	−1.49337	+	0.0939547i
$809$	5.86516	−	12.4641i	0.206208	−	0.438215i	−0.774793	−	0.632215i	$-0.782146\pi$
$809$	5.86516	−	12.4641i	0.206208	−	0.438215i	0.981002	+	0.194000i	$0.0621461\pi$
$810$		0			0
$811$	9.89940	−	9.29615i	0.347615	−	0.326432i	−0.490997	−	0.871161i	$-0.663367\pi$
$811$	9.89940	−	9.29615i	0.347615	−	0.326432i	0.838612	+	0.544729i	$0.183367\pi$
$812$	3.86287	−	30.5778i	0.135560	−	1.07307i
$813$	0.0781430	−	0.618566i	0.00274060	−	0.0216940i
$814$	−16.5137	+	15.5074i	−0.578804	+	0.543533i
$815$		0			0
$816$	0.884416	−	1.87948i	0.0309608	−	0.0657950i
$817$	−5.31431	+	0.334348i	−0.185924	+	0.0116974i
$818$		−	81.6884i		−	2.85617i
$819$	0.114461	+	1.81930i	0.00399958	+	0.0635715i
$820$		0			0
$821$	19.9768	+	7.90936i	0.697194	+	0.276038i	0.689869	−	0.723935i	$-0.257668\pi$
$821$	19.9768	+	7.90936i	0.697194	+	0.276038i	0.00732510	+	0.999973i	$0.497668\pi$
$822$	−63.4142	+	40.2439i	−2.21182	+	1.40367i
$823$	16.5303	−	7.77858i	0.576211	−	0.271144i	−0.115513	−	0.993306i	$-0.536851\pi$
$823$	16.5303	−	7.77858i	0.576211	−	0.271144i	0.691724	+	0.722162i	$0.256851\pi$
$824$	23.2569	−	16.8971i	0.810191	−	0.588638i
$825$		0			0
$826$	21.9411	+	15.9412i	0.763429	+	0.554664i
$827$	−2.37026	−	0.452152i	−0.0824222	−	0.0157229i	0.146005	−	0.989284i	$-0.453358\pi$
$827$	−2.37026	−	0.452152i	−0.0824222	−	0.0157229i	−0.228427	+	0.973561i	$0.573358\pi$
$828$	4.39871	−	11.1099i	0.152866	−	0.386095i
$829$	−7.08789	+	8.56779i	−0.246173	+	0.297572i	−0.879098	−	0.476641i	$-0.841854\pi$
$829$	−7.08789	+	8.56779i	−0.246173	+	0.297572i	0.632925	+	0.774213i	$0.281854\pi$
$830$		0			0
$831$	5.10097	−	2.01962i	0.176951	−	0.0700597i
$832$	26.5677	−	36.5673i	0.921070	−	1.26774i
$833$	−28.5071	+	23.5831i	−0.987712	+	0.817107i
$834$	20.3971	+	19.1542i	0.706294	+	0.663254i
$835$		0			0
$836$	−4.89116	−	2.68894i	−0.169164	−	0.0929989i
$837$	−11.0366	+	11.7528i	−0.381480	+	0.406235i
$838$	9.63236	+	17.5212i	0.332744	+	0.605260i
$839$	6.24218	+	13.2653i	0.215504	+	0.457969i	0.983125	−	0.182935i	$-0.0585597\pi$
$839$	6.24218	+	13.2653i	0.215504	+	0.457969i	−0.767621	+	0.640904i	$0.778560\pi$
$840$		0			0
$841$	−51.9634	−	6.56450i	−1.79184	−	0.226362i
$842$	−33.3693	−	21.1768i	−1.14998	−	0.729801i
$843$	17.4065	+	23.9580i	0.599511	+	0.825156i
$844$	−21.1228	−	5.42342i	−0.727078	−	0.186682i
$845$		0			0
$846$	−0.436097	+	6.93157i	−0.0149933	+	0.238312i
$847$	−9.09090	−	0.571951i	−0.312367	−	0.0196525i
$848$	−0.500162	+	0.909792i	−0.0171756	+	0.0312424i
$849$	4.38302	+	13.4896i	0.150425	+	0.462961i
$850$		0			0
$851$	−14.8719	+	45.7711i	−0.509804	+	1.56901i
$852$	31.8855	+	33.9546i	1.09238	+	1.16326i
$853$	−7.23940	−	28.1956i	−0.247872	−	0.965399i	−0.963671	−	0.267092i	$-0.913937\pi$
$853$	−7.23940	−	28.1956i	−0.247872	−	0.965399i	0.715799	−	0.698307i	$-0.246063\pi$
$854$	−0.497907	−	0.784576i	−0.0170380	−	0.0268476i
$855$		0			0
$856$	−13.9899	−	16.9109i	−0.478165	−	0.578002i
$857$	−5.99102	+	1.94660i	−0.204649	+	0.0664946i	−0.409548	−	0.912289i	$-0.634314\pi$
$857$	−5.99102	+	1.94660i	−0.204649	+	0.0664946i	0.204899	+	0.978783i	$0.434314\pi$
$858$	5.79890	−	22.5852i	0.197971	−	0.771047i
$859$	34.3487	−	18.8834i	1.17196	−	0.644293i	0.227781	−	0.973713i	$-0.426853\pi$
$859$	34.3487	−	18.8834i	1.17196	−	0.644293i	0.944184	+	0.329420i	$0.106853\pi$
$860$		0			0
$861$	1.37463	−	7.20605i	0.0468472	−	0.245581i
$862$	80.6071	−	15.3766i	2.74549	−	0.523730i
$863$	−40.9862	−	19.2867i	−1.39519	−	0.656526i	−0.426427	−	0.904522i	$-0.640228\pi$
$863$	−40.9862	−	19.2867i	−1.39519	−	0.656526i	−0.968761	+	0.247996i	$0.920228\pi$
$864$	27.2383	−	3.44099i	0.926664	−	0.117065i
$865$		0			0
$866$	4.31735	+	22.6323i	0.146710	+	0.769078i
$867$	15.7467	+	39.7716i	0.534786	+	1.35072i
$868$	−11.1734	−	3.63045i	−0.379249	−	0.123225i
$869$	5.85098	−	9.21968i	0.198481	−	0.312756i
$870$		0			0
$871$	44.5854	−	11.4476i	1.51072	−	0.387887i
$872$	18.4705	+	15.2801i	0.625489	+	0.517449i
$873$	−0.812669	−	6.43294i	−0.0275047	−	0.217722i
$874$	−19.2775			−0.652071
$875$		0			0
$876$	4.29151			0.144997
$877$	1.82061	+	14.4116i	0.0614775	+	0.486644i	0.992553	+	0.121817i	$0.0388720\pi$
$877$	1.82061	+	14.4116i	0.0614775	+	0.486644i	−0.931075	+	0.364828i	$0.881128\pi$
$878$	44.5397	+	36.8464i	1.50314	+	1.24351i
$879$	−30.4785	+	7.82555i	−1.02801	+	0.263949i
$880$		0			0
$881$	1.44251	−	2.27303i	0.0485994	−	0.0765804i	−0.819160	−	0.573566i	$-0.805560\pi$
$881$	1.44251	−	2.27303i	0.0485994	−	0.0765804i	0.867759	+	0.496985i	$0.165560\pi$
$882$	6.22673	+	2.02319i	0.209665	+	0.0681243i
$883$	6.08537	+	15.3699i	0.204789	+	0.517238i	0.995479	−	0.0949782i	$-0.0302781\pi$
$883$	6.08537	+	15.3699i	0.204789	+	0.517238i	−0.790690	+	0.612216i	$0.790278\pi$
$884$	13.1575	+	68.9738i	0.442533	+	2.31984i
$885$		0			0
$886$	69.0817	−	8.72705i	2.32085	−	0.293191i
$887$	−3.45723	−	1.62685i	−0.116082	−	0.0546243i	0.366861	−	0.930276i	$-0.380432\pi$
$887$	−3.45723	−	1.62685i	−0.116082	−	0.0546243i	−0.482944	+	0.875651i	$0.660432\pi$
$888$	−31.5928	+	6.02665i	−1.06018	+	0.202241i
$889$	−3.62171	+	18.9857i	−0.121468	+	0.636759i
$890$		0			0
$891$	14.1135	−	7.75898i	0.472821	−	0.259936i
$892$	0.546267	−	2.12757i	0.0182904	−	0.0712363i
$893$	6.55498	−	2.12984i	0.219354	−	0.0712725i
$894$	3.42029	+	4.13442i	0.114392	+	0.138276i
$895$		0			0
$896$	10.2602	+	16.1675i	0.342769	+	0.540117i
$897$	−12.3196	−	47.9817i	−0.411340	−	1.60206i
$898$	47.1209	+	50.1787i	1.57245	+	1.67448i
$899$	−9.58549	+	29.5011i	−0.319694	+	0.983917i
$900$		0			0
$901$	−11.5122	−	35.4310i	−0.383528	−	1.18038i
$902$	−6.35095	+	11.5523i	−0.211463	+	0.384650i
$903$	9.56750	+	0.601936i	0.318387	+	0.0200312i
$904$	−3.10293	+	49.3196i	−0.103202	+	1.64035i
$905$		0			0
$906$	−19.6268	−	5.03931i	−0.652057	−	0.167420i
$907$	15.4750	+	21.2995i	0.513838	+	0.707237i	0.984561	−	0.175044i	$-0.0560068\pi$
$907$	15.4750	+	21.2995i	0.513838	+	0.707237i	−0.470723	+	0.882281i	$0.656007\pi$
$908$	59.1993	+	37.5690i	1.96460	+	1.24677i
$909$	7.58716	+	0.958482i	0.251650	+	0.0317908i
$910$		0			0
$911$	−21.0287	−	44.6883i	−0.696713	−	1.48059i	−0.868621	−	0.495477i	$-0.834993\pi$
$911$	−21.0287	−	44.6883i	−0.696713	−	1.48059i	0.171909	−	0.985113i	$-0.445007\pi$
$912$	0.175733	+	0.319658i	0.00581911	+	0.0105849i
$913$	−7.99772	+	8.51670i	−0.264686	+	0.281862i
$914$	1.66859	+	0.917313i	0.0551919	+	0.0303420i
$915$		0			0
$916$	−27.3454	−	25.6790i	−0.903516	−	0.848458i
$917$	0.639685	−	0.529194i	0.0211243	−	0.0174755i
$918$	−39.6809	+	54.6161i	−1.30967	+	1.80260i
$919$	31.9999	−	12.6697i	1.05558	−	0.417934i	0.224725	−	0.974422i	$-0.427852\pi$
$919$	31.9999	−	12.6697i	1.05558	−	0.417934i	0.830855	+	0.556489i	$0.187852\pi$
$920$		0			0
$921$	−25.1359	+	30.3841i	−0.828257	+	1.00119i
$922$	10.6320	−	26.8533i	0.350145	−	0.884365i
$923$	26.6480	+	5.08338i	0.877130	+	0.167321i
$924$	8.12953	+	5.90645i	0.267442	+	0.194308i
$925$		0			0
$926$	40.1785	−	29.1914i	1.32035	−	0.959289i
$927$	−4.67678	+	2.20072i	−0.153605	+	0.0722812i
$928$	44.5994	−	28.3036i	1.46405	−	0.929113i
$929$	44.6009	+	17.6587i	1.46331	+	0.579365i	0.958810	−	0.284048i	$-0.0916777\pi$
$929$	44.6009	+	17.6587i	1.46331	+	0.579365i	0.504498	+	0.863413i	$0.331678\pi$
$930$		0			0
$931$	−0.407966	−	6.48443i	−0.0133705	−	0.212519i
$932$			54.5633i			1.78728i
$933$	50.0923	−	3.15154i	1.63995	−	0.103177i
$934$	−20.2413	+	43.0150i	−0.662316	+	1.40749i
$935$		0			0
$936$	3.39032	−	3.18372i	0.110816	−	0.104063i
$937$	−6.30906	+	49.9414i	−0.206108	+	1.63151i	0.461599	+	0.887089i	$0.347276\pi$
$937$	−6.30906	+	49.9414i	−0.206108	+	1.63151i	−0.667707	+	0.744424i	$0.732724\pi$
$938$	−4.04190	+	31.9950i	−0.131973	+	1.04467i
$939$	−12.4518	+	11.6930i	−0.406349	+	0.381587i
$940$		0			0
$941$	18.1738	−	38.6213i	0.592449	−	1.25902i	−0.353722	−	0.935351i	$-0.615084\pi$
$941$	18.1738	−	38.6213i	0.592449	−	1.25902i	0.946171	−	0.323667i	$-0.104916\pi$
$942$	−5.61311	+	0.353147i	−0.182885	+	0.0115061i
$943$			28.0068i			0.912028i
$944$	0.123021	+	1.95536i	0.00400399	+	0.0636416i
$945$		0			0
$946$	−16.0173	−	6.34170i	−0.520768	−	0.206187i
$947$	13.0088	−	8.25565i	0.422730	−	0.268272i	−0.307401	−	0.951580i	$-0.599459\pi$
$947$	13.0088	−	8.25565i	0.422730	−	0.268272i	0.730131	+	0.683308i	$0.239459\pi$
$948$	37.4783	−	17.6360i	1.21724	−	0.572789i
$949$	2.02211	−	1.46915i	0.0656405	−	0.0476906i
$950$		0			0
$951$	39.3790	+	28.6105i	1.27695	+	0.927759i
$952$	−18.0864	−	3.45017i	−0.586185	−	0.111821i
$953$	11.2351	−	28.3765i	0.363940	−	0.919207i	−0.626268	−	0.779607i	$-0.715419\pi$
$953$	11.2351	−	28.3765i	0.363940	−	0.919207i	0.990208	−	0.139599i	$-0.0445814\pi$
$954$	−4.20230	+	5.07971i	−0.136055	+	0.164462i
$955$		0			0
$956$	84.9158	−	33.6205i	2.74637	−	1.08737i
$957$	15.5948	−	21.4644i	0.504109	−	0.693847i
$958$	−21.4095	+	17.7115i	−0.691711	+	0.572233i
$959$	−13.7417	−	12.9043i	−0.443743	−	0.416702i
$960$		0			0
$961$	−16.8040	−	9.23809i	−0.542066	−	0.298003i
$962$	−34.2598	+	36.4830i	−1.10458	+	1.17626i
$963$	1.90107	+	3.45804i	0.0612612	+	0.111434i
$964$	−15.8240	−	33.6276i	−0.509655	−	1.08307i
$965$		0			0
$966$	34.4321	+	4.34979i	1.10784	+	0.139952i
$967$	33.4912	+	21.2541i	1.07700	+	0.683487i	0.951202	−	0.308568i	$-0.0998498\pi$
$967$	33.4912	+	21.2541i	1.07700	+	0.683487i	0.125801	+	0.992055i	$0.459850\pi$
$968$	13.6601	+	18.8015i	0.439052	+	0.604303i
$969$	−12.6782	−	3.25521i	−0.407283	−	0.104572i
$970$		0			0
$971$	2.39800	−	38.1151i	0.0769555	−	1.22317i	−0.750204	−	0.661206i	$-0.770045\pi$
$971$	2.39800	−	38.1151i	0.0769555	−	1.22317i	0.827160	−	0.561967i	$-0.189955\pi$
$972$	16.1010	+	1.01299i	0.516440	+	0.0324916i
$973$	−3.38331	+	6.15421i	−0.108464	+	0.197295i
$974$	−5.00066	−	15.3905i	−0.160232	−	0.493142i
$975$		0			0
$976$	0.0207439	−	0.0638431i	0.000663996	−	0.00204357i
$977$	29.9007	+	31.8411i	0.956610	+	1.01869i	0.999808	+	0.0196193i	$0.00624543\pi$
$977$	29.9007	+	31.8411i	0.956610	+	1.01869i	−0.0431978	+	0.999067i	$0.513755\pi$
$978$	1.97081	+	7.67581i	0.0630196	+	0.245445i
$979$	−2.97855	−	4.69344i	−0.0951948	−	0.150003i
$980$		0			0
$981$	−2.74735	−	3.32097i	−0.0877160	−	0.106030i
$982$	−45.7439	+	14.8631i	−1.45975	+	0.474300i
$983$	3.55875	−	13.8604i	0.113507	−	0.442079i	−0.886271	−	0.463167i	$-0.846713\pi$
$983$	3.55875	−	13.8604i	0.113507	−	0.442079i	0.999778	+	0.0210882i	$0.00671307\pi$
$984$	−16.4015	+	9.01682i	−0.522862	+	0.287446i
$985$		0			0
$986$	−24.3383	+	127.586i	−0.775089	+	4.06316i
$987$	−12.1886	+	2.32511i	−0.387969	+	0.0740090i
$988$	−11.1575	−	5.25034i	−0.354968	−	0.167035i
$989$	−36.3098	+	4.58699i	−1.15458	+	0.145858i
$990$		0			0
$991$	0.576032	+	3.01967i	0.0182983	+	0.0959229i	0.990265	−	0.139196i	$-0.0444519\pi$
$991$	0.576032	+	3.01967i	0.0182983	+	0.0959229i	−0.971967	+	0.235119i	$0.924452\pi$
$992$	−7.41218	−	18.7210i	−0.235337	−	0.594394i
$993$	10.9822	+	3.56834i	0.348510	+	0.113238i
$994$	−10.1839	+	16.0473i	−0.323014	+	0.508988i
$995$		0			0
$996$	−42.9249	+	11.0212i	−1.36013	+	0.349222i
$997$	5.93224	+	4.90757i	0.187876	+	0.155424i	0.726607	−	0.687053i	$-0.241096\pi$
$997$	5.93224	+	4.90757i	0.187876	+	0.155424i	−0.538731	+	0.842478i	$0.681096\pi$
$998$	−11.1385	−	88.1704i	−0.352583	−	2.79098i
$999$	−29.5975			−0.936424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.h.a.449.11		240
5.2	odd	4		625.2.g.b.176.4		480
5.3	odd	4		625.2.g.b.176.21		480
5.4	even	2		125.2.h.a.39.2	✓	240
125.16	even	25		125.2.h.a.109.2	yes	240
125.37	odd	100		625.2.g.b.451.4		480
125.88	odd	100		625.2.g.b.451.21		480
125.109	even	50	inner	625.2.h.a.174.11		240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
125.2.h.a.39.2	✓	240	5.4	even	2
125.2.h.a.109.2	yes	240	125.16	even	25
625.2.g.b.176.4		480	5.2	odd	4
625.2.g.b.176.21		480	5.3	odd	4
625.2.g.b.451.4		480	125.37	odd	100
625.2.g.b.451.21		480	125.88	odd	100
625.2.h.a.174.11		240	125.109	even	50	inner
625.2.h.a.449.11		240	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.h (of order \(50\), degree \(20\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.285704 + 2.26158i) q^{2} +(-1.43951 - 1.19086i) q^{3} +(-3.09594 + 0.794901i) q^{4} +(2.28196 - 3.59579i) q^{6} +(1.01659 + 0.330310i) q^{7} +(-1.00393 - 2.53564i) q^{8} +(0.0918805 + 0.481654i) q^{9} +O(q^{10})\)	\(q+(0.285704 + 2.26158i) q^{2} +(-1.43951 - 1.19086i) q^{3} +(-3.09594 + 0.794901i) q^{4} +(2.28196 - 3.59579i) q^{6} +(1.01659 + 0.330310i) q^{7} +(-1.00393 - 2.53564i) q^{8} +(0.0918805 + 0.481654i) q^{9} +(1.56186 - 0.197308i) q^{11} +(5.40324 + 2.54257i) q^{12} +(3.41636 - 0.651706i) q^{13} +(-0.456579 + 2.39347i) q^{14} +(-0.154251 + 0.0848005i) q^{16} +(1.57081 - 6.11789i) q^{17} +(-1.06305 + 0.345405i) q^{18} +(0.707051 + 0.854677i) q^{19} +(-1.07004 - 1.68611i) q^{21} +(0.892455 + 3.47588i) q^{22} +(5.21894 + 5.55761i) q^{23} +(-1.57444 + 4.84562i) q^{24} +(2.44995 + 7.54017i) q^{26} +(-2.25878 + 4.10870i) q^{27} +(-3.40986 - 0.214530i) q^{28} +(-0.566426 + 9.00309i) q^{29} +(3.33058 + 0.855147i) q^{31} +(-3.44181 - 4.73725i) q^{32} +(-2.48327 - 1.57593i) q^{33} +(14.2849 + 1.80460i) q^{34} +(-0.667324 - 1.41813i) q^{36} +(3.04110 + 5.53175i) q^{37} +(-1.73091 + 1.84323i) q^{38} +(-5.69397 - 3.13029i) q^{39} +(2.67790 + 2.51471i) q^{41} +(3.50754 - 2.90169i) q^{42} +(-2.82164 + 3.88365i) q^{43} +(-4.67856 + 1.85237i) q^{44} +(-11.0779 + 13.3909i) q^{46} +(2.28738 - 5.77726i) q^{47} +(0.323032 + 0.0616216i) q^{48} +(-4.73877 - 3.44292i) q^{49} +(-9.54677 + 6.93614i) q^{51} +(-10.0588 + 4.73331i) q^{52} +(4.97994 - 3.16036i) q^{53} +(-9.93749 - 3.93453i) q^{54} +(-0.183039 - 2.90932i) q^{56} -2.07232i q^{57} +(-20.5230 + 1.29120i) q^{58} +(4.73910 - 10.0711i) q^{59} +(-0.277999 + 0.261059i) q^{61} +(-0.982423 + 7.77668i) q^{62} +(-0.0656906 + 0.519994i) q^{63} +(9.47368 - 8.89638i) q^{64} +(2.85461 - 6.06635i) q^{66} +(13.2091 - 0.831045i) q^{67} +20.1892i q^{68} +(-0.894349 - 14.2153i) q^{69} +(7.25236 + 2.87141i) q^{71} +(1.12906 - 0.716524i) q^{72} +(0.650260 - 0.305989i) q^{73} +(-11.6416 + 8.45813i) q^{74} +(-2.86837 - 2.08399i) q^{76} +(1.65294 + 0.315315i) q^{77} +(5.45260 - 13.7717i) q^{78} +(4.42134 - 5.34448i) q^{79} +(9.51216 - 3.76613i) q^{81} +(-4.92213 + 6.77473i) q^{82} +(-5.71826 + 4.73056i) q^{83} +(4.65305 + 4.36950i) q^{84} +(-9.58933 - 5.27178i) q^{86} +(11.5368 - 12.2855i) q^{87} +(-2.06830 - 3.76222i) q^{88} +(-1.50344 - 3.19497i) q^{89} +(3.68831 + 0.465942i) q^{91} +(-20.5753 - 13.0575i) q^{92} +(-3.77603 - 5.19726i) q^{93} +(13.7192 + 3.52250i) q^{94} +(-0.686905 + 10.9180i) q^{96} +(-13.1975 - 0.830318i) q^{97} +(6.43253 - 11.7007i) q^{98} +(0.238538 + 0.734146i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9}+O(q^{10}) \) 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9	\( 240 q + 20 q^{2} + 20 q^{3} - 20 q^{4} - 20 q^{6} + 25 q^{7} + 35 q^{8} - 20 q^{9} - 25 q^{11} - 60 q^{12} + 20 q^{13} - 30 q^{14} - 40 q^{16} + 15 q^{17} + 25 q^{18} - 10 q^{19} - 35 q^{21} + 25 q^{22} - 70 q^{23} + 15 q^{24} - 45 q^{26} + 20 q^{27} + 10 q^{28} - 10 q^{29} - 30 q^{31} + 25 q^{32} + 35 q^{33} - 20 q^{34} + 170 q^{36} + 55 q^{37} + 40 q^{38} - 35 q^{41} + 10 q^{42} + 25 q^{43} + 15 q^{44} - 40 q^{46} - 100 q^{47} - 5 q^{48} + 35 q^{49} - 55 q^{51} + 15 q^{52} + 15 q^{53} + 30 q^{54} + 65 q^{56} - 255 q^{58} + 5 q^{59} - 40 q^{61} - 5 q^{62} + 35 q^{63} + 25 q^{64} - 95 q^{66} - 105 q^{67} - 10 q^{69} + 45 q^{71} + 30 q^{72} + 40 q^{73} + 35 q^{74} - 65 q^{76} + 35 q^{77} - 100 q^{78} - 95 q^{81} - 175 q^{82} - 20 q^{83} + 45 q^{84} - 80 q^{86} + 5 q^{87} + 5 q^{88} + 30 q^{89} + 65 q^{91} + 55 q^{92} - 275 q^{93} + 60 q^{94} - 135 q^{96} - 35 q^{97} + 15 q^{98} + 45 q^{99}+O(q^{100}) \) 240 * q + 20 * q^2 + 20 * q^3 - 20 * q^4 - 20 * q^6 + 25 * q^7 + 35 * q^8 - 20 * q^9 - 25 * q^11 - 60 * q^12 + 20 * q^13 - 30 * q^14 - 40 * q^16 + 15 * q^17 + 25 * q^18 - 10 * q^19 - 35 * q^21 + 25 * q^22 - 70 * q^23 + 15 * q^24 - 45 * q^26 + 20 * q^27 + 10 * q^28 - 10 * q^29 - 30 * q^31 + 25 * q^32 + 35 * q^33 - 20 * q^34 + 170 * q^36 + 55 * q^37 + 40 * q^38 - 35 * q^41 + 10 * q^42 + 25 * q^43 + 15 * q^44 - 40 * q^46 - 100 * q^47 - 5 * q^48 + 35 * q^49 - 55 * q^51 + 15 * q^52 + 15 * q^53 + 30 * q^54 + 65 * q^56 - 255 * q^58 + 5 * q^59 - 40 * q^61 - 5 * q^62 + 35 * q^63 + 25 * q^64 - 95 * q^66 - 105 * q^67 - 10 * q^69 + 45 * q^71 + 30 * q^72 + 40 * q^73 + 35 * q^74 - 65 * q^76 + 35 * q^77 - 100 * q^78 - 95 * q^81 - 175 * q^82 - 20 * q^83 + 45 * q^84 - 80 * q^86 + 5 * q^87 + 5 * q^88 + 30 * q^89 + 65 * q^91 + 55 * q^92 - 275 * q^93 + 60 * q^94 - 135 * q^96 - 35 * q^97 + 15 * q^98 + 45 * q^99

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