LMFDB - Embedded newform 546.2.cg.b.271.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(145,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 10, 1]))

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

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

chi := DirichletCharacter("546.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.cg (of order $12$, 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:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$10$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			271.10
Character	$\chi$	$=$	546.271
Dual form			546.2.cg.b.409.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(1.04742 + 3.90903i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.49243 + 0.887573i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(1.04742 + 3.90903i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.49243 + 0.887573i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.02346 + 3.50474i) q^{10} +(-1.31252 - 4.89839i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.15689 - 2.88926i) q^{13} +(1.13481 + 2.39002i) q^{14} +(-1.04742 + 3.90903i) q^{15} -1.00000 q^{16} -4.96234 q^{17} +(-0.258819 + 0.965926i) q^{18} +(1.40177 + 0.375603i) q^{19} +(-3.90903 + 1.04742i) q^{20} +(1.71472 + 2.01488i) q^{21} +(2.53559 - 4.39177i) q^{22} -5.43264i q^{23} +(-0.965926 + 0.258819i) q^{24} +(-9.85327 + 5.68879i) q^{25} +(3.56817 - 0.517865i) q^{26} +1.00000i q^{27} +(-0.887573 + 2.49243i) q^{28} +(-4.24486 - 7.35231i) q^{29} +(-3.50474 + 2.02346i) q^{30} +(3.97807 + 1.06592i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.31252 - 4.89839i) q^{33} +(-3.50891 - 3.50891i) q^{34} +(-0.858922 + 10.6726i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.552475 + 0.552475i) q^{37} +(0.725610 + 1.25679i) q^{38} +(3.31255 - 1.42373i) q^{39} +(-3.50474 - 2.02346i) q^{40} +(3.46045 + 0.927225i) q^{41} +(-0.212241 + 2.63722i) q^{42} +(8.45709 + 4.88270i) q^{43} +(4.89839 - 1.31252i) q^{44} +(-2.86161 + 2.86161i) q^{45} +(3.84146 - 3.84146i) q^{46} +(-2.84109 + 0.761269i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(5.42443 + 4.42443i) q^{49} +(-10.9899 - 2.94473i) q^{50} +(-4.29751 - 2.48117i) q^{51} +(2.88926 + 2.15689i) q^{52} +(2.08448 + 3.61043i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(17.7732 - 10.2613i) q^{55} +(-2.39002 + 1.13481i) q^{56} +(1.02617 + 1.02617i) q^{57} +(2.19730 - 8.20043i) q^{58} +(-0.661436 - 0.661436i) q^{59} +(-3.90903 - 1.04742i) q^{60} +(-10.4863 + 6.05427i) q^{61} +(2.05920 + 3.56664i) q^{62} +(0.477555 + 2.60230i) q^{63} -1.00000i q^{64} +(13.5534 + 5.40507i) q^{65} +(4.39177 - 2.53559i) q^{66} +(-8.88378 + 2.38040i) q^{67} -4.96234i q^{68} +(2.71632 - 4.70481i) q^{69} +(-8.15405 + 6.93935i) q^{70} +(-4.28503 + 1.14817i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(3.43906 - 12.8347i) q^{73} -0.781318 q^{74} -11.3776 q^{75} +(-0.375603 + 1.40177i) q^{76} +(1.07631 - 13.3739i) q^{77} +(3.34906 + 1.33560i) q^{78} +(1.32924 - 2.30231i) q^{79} +(-1.04742 - 3.90903i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.79126 + 3.10255i) q^{82} +(-1.02375 + 1.02375i) q^{83} +(-2.01488 + 1.71472i) q^{84} +(-5.19766 - 19.3979i) q^{85} +(2.52747 + 9.43266i) q^{86} -8.48971i q^{87} +(4.39177 + 2.53559i) q^{88} +(4.52554 + 4.52554i) q^{89} -4.04692 q^{90} +(7.94033 - 5.28689i) q^{91} +5.43264 q^{92} +(2.91215 + 2.91215i) q^{93} +(-2.54726 - 1.47066i) q^{94} +5.87297i q^{95} +(-0.258819 - 0.965926i) q^{96} +(-2.62347 - 9.79094i) q^{97} +(0.707107 + 6.96419i) q^{98} +(3.58587 - 3.58587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 40 * q + 4 * q^7 + 20 * q^9	$ 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$			1.00000i			0.500000i
$5$	1.04742	+	3.90903i	0.468421	+	1.74817i	0.645292	+	0.763936i	$0.276736\pi$
$5$	1.04742	+	3.90903i	0.468421	+	1.74817i	−0.176872	+	0.984234i	$0.556598\pi$
$6$	0.258819	+	0.965926i	0.105662	+	0.394338i
$7$	2.49243	+	0.887573i	0.942051	+	0.335471i
$7$	2.49243	+	0.887573i	0.942051	+	0.335471i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$	−2.02346	+	3.50474i	−0.639874	+	1.10830i
$11$	−1.31252	−	4.89839i	−0.395739	−	1.47692i	−0.820517	−	0.571622i	$-0.806314\pi$
$11$	−1.31252	−	4.89839i	−0.395739	−	1.47692i	0.424778	−	0.905298i	$-0.360352\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	2.15689	−	2.88926i	0.598213	−	0.801337i
$13$	2.15689	−	2.88926i	0.598213	−	0.801337i
$14$	1.13481	+	2.39002i	0.303290	+	0.638761i
$15$	−1.04742	+	3.90903i	−0.270443	+	1.00931i
$16$	−1.00000			−0.250000
$17$	−4.96234			−1.20354			−0.601772	−	0.798668i	$-0.705539\pi$
$17$	−4.96234			−1.20354			−0.601772	+	0.798668i	$0.705539\pi$
$18$	−0.258819	+	0.965926i	−0.0610042	+	0.227671i
$19$	1.40177	+	0.375603i	0.321588	+	0.0861693i	0.416002	−	0.909364i	$-0.363431\pi$
$19$	1.40177	+	0.375603i	0.321588	+	0.0861693i	−0.0944137	+	0.995533i	$0.530098\pi$
$20$	−3.90903	+	1.04742i	−0.874085	+	0.234210i
$21$	1.71472	+	2.01488i	0.374183	+	0.439682i
$22$	2.53559	−	4.39177i	0.540590	−	0.936330i
$23$		−	5.43264i		−	1.13278i	−0.824136	−	0.566392i	$-0.808339\pi$
$23$		−	5.43264i		−	1.13278i	0.824136	−	0.566392i	$-0.191661\pi$
$24$	−0.965926	+	0.258819i	−0.197169	+	0.0528312i
$25$	−9.85327	+	5.68879i	−1.97065	+	1.13776i
$26$	3.56817	−	0.517865i	0.699775	−	0.101562i
$27$			1.00000i			0.192450i
$28$	−0.887573	+	2.49243i	−0.167736	+	0.471025i
$29$	−4.24486	−	7.35231i	−0.788250	−	1.36529i	−0.927038	−	0.374967i	$-0.877654\pi$
$29$	−4.24486	−	7.35231i	−0.788250	−	1.36529i	0.138788	−	0.990322i	$-0.455679\pi$
$30$	−3.50474	+	2.02346i	−0.639874	+	0.369432i
$31$	3.97807	+	1.06592i	0.714483	+	0.191445i	0.597709	−	0.801714i	$-0.296078\pi$
$31$	3.97807	+	1.06592i	0.714483	+	0.191445i	0.116774	+	0.993159i	$0.462745\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	1.31252	−	4.89839i	0.228480	−	0.852700i
$34$	−3.50891	−	3.50891i	−0.601772	−	0.601772i
$35$	−0.858922	+	10.6726i	−0.145184	+	1.80401i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−0.552475	+	0.552475i	−0.0908264	+	0.0908264i	−0.751060	−	0.660234i	$-0.770457\pi$
$37$	−0.552475	+	0.552475i	−0.0908264	+	0.0908264i	0.660234	+	0.751060i	$0.270457\pi$
$38$	0.725610	+	1.25679i	0.117709	+	0.203879i
$39$	3.31255	−	1.42373i	0.530433	−	0.227979i
$40$	−3.50474	−	2.02346i	−0.554148	−	0.319937i
$41$	3.46045	+	0.927225i	0.540431	+	0.144808i	0.518701	−	0.854956i	$-0.326416\pi$
$41$	3.46045	+	0.927225i	0.540431	+	0.144808i	0.0217304	+	0.999764i	$0.493082\pi$
$42$	−0.212241	+	2.63722i	−0.0327495	+	0.406933i
$43$	8.45709	+	4.88270i	1.28969	+	0.744605i	0.978600	−	0.205773i	$-0.0659710\pi$
$43$	8.45709	+	4.88270i	1.28969	+	0.744605i	0.311095	+	0.950379i	$0.399304\pi$
$44$	4.89839	−	1.31252i	0.738460	−	0.197870i
$45$	−2.86161	+	2.86161i	−0.426583	+	0.426583i
$46$	3.84146	−	3.84146i	0.566392	−	0.566392i
$47$	−2.84109	+	0.761269i	−0.414416	+	0.111043i	−0.460002	−	0.887918i	$-0.652151\pi$
$47$	−2.84109	+	0.761269i	−0.414416	+	0.111043i	0.0455856	+	0.998960i	$0.485485\pi$
$48$	−0.866025	−	0.500000i	−0.125000	−	0.0721688i
$49$	5.42443	+	4.42443i	0.774918	+	0.632061i
$50$	−10.9899	−	2.94473i	−1.55421	−	0.416448i
$51$	−4.29751	−	2.48117i	−0.601772	−	0.347433i
$52$	2.88926	+	2.15689i	0.400668	+	0.299107i
$53$	2.08448	+	3.61043i	0.286325	+	0.495930i	0.972930	−	0.231101i	$-0.0742328\pi$
$53$	2.08448	+	3.61043i	0.286325	+	0.495930i	−0.686604	+	0.727031i	$0.740899\pi$
$54$	−0.707107	+	0.707107i	−0.0962250	+	0.0962250i
$55$	17.7732	−	10.2613i	2.39653	−	1.38364i
$56$	−2.39002	+	1.13481i	−0.319380	+	0.151645i
$57$	1.02617	+	1.02617i	0.135919	+	0.135919i
$58$	2.19730	−	8.20043i	0.288519	−	1.07677i
$59$	−0.661436	−	0.661436i	−0.0861117	−	0.0861117i	0.662739	−	0.748851i	$-0.269394\pi$
$59$	−0.661436	−	0.661436i	−0.0861117	−	0.0861117i	−0.748851	+	0.662739i	$0.769394\pi$
$60$	−3.90903	−	1.04742i	−0.504653	−	0.135221i
$61$	−10.4863	+	6.05427i	−1.34263	+	0.775170i	−0.987193	−	0.159529i	$-0.949002\pi$
$61$	−10.4863	+	6.05427i	−1.34263	+	0.775170i	−0.355441	+	0.934699i	$0.615669\pi$
$62$	2.05920	+	3.56664i	0.261519	+	0.452964i
$63$	0.477555	+	2.60230i	0.0601663	+	0.327858i
$64$		−	1.00000i		−	0.125000i
$65$	13.5534	+	5.40507i	1.68109	+	0.670416i
$66$	4.39177	−	2.53559i	0.540590	−	0.312110i
$67$	−8.88378	+	2.38040i	−1.08533	+	0.290812i	−0.756776	−	0.653674i	$-0.773227\pi$
$67$	−8.88378	+	2.38040i	−1.08533	+	0.290812i	−0.328550	+	0.944486i	$0.606560\pi$
$68$		−	4.96234i		−	0.601772i
$69$	2.71632	−	4.70481i	0.327007	−	0.566392i
$70$	−8.15405	+	6.93935i	−0.974595	+	0.829411i
$71$	−4.28503	+	1.14817i	−0.508540	+	0.136263i	−0.503960	−	0.863727i	$-0.668124\pi$
$71$	−4.28503	+	1.14817i	−0.508540	+	0.136263i	−0.00457912	+	0.999990i	$0.501458\pi$
$72$	−0.965926	−	0.258819i	−0.113835	−	0.0305021i
$73$	3.43906	−	12.8347i	0.402511	−	1.50219i	−0.406089	−	0.913833i	$-0.633108\pi$
$73$	3.43906	−	12.8347i	0.402511	−	1.50219i	0.808600	−	0.588358i	$-0.200226\pi$
$74$	−0.781318			−0.0908264
$75$	−11.3776			−1.31377
$76$	−0.375603	+	1.40177i	−0.0430847	+	0.160794i
$77$	1.07631	−	13.3739i	0.122657	−	1.52409i
$78$	3.34906	+	1.33560i	0.379206	+	0.151227i
$79$	1.32924	−	2.30231i	0.149551	−	0.259030i	−0.781511	−	0.623892i	$-0.785551\pi$
$79$	1.32924	−	2.30231i	0.149551	−	0.259030i	0.931062	+	0.364862i	$0.118884\pi$
$80$	−1.04742	−	3.90903i	−0.117105	−	0.437042i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	1.79126	+	3.10255i	0.197812	+	0.342620i
$83$	−1.02375	+	1.02375i	−0.112371	+	0.112371i	−0.761056	−	0.648686i	$-0.775319\pi$
$83$	−1.02375	+	1.02375i	−0.112371	+	0.112371i	0.648686	+	0.761056i	$0.275319\pi$
$84$	−2.01488	+	1.71472i	−0.219841	+	0.187092i
$85$	−5.19766	−	19.3979i	−0.563765	−	2.10400i
$86$	2.52747	+	9.43266i	0.272545	+	1.01715i
$87$		−	8.48971i		−	0.910193i
$88$	4.39177	+	2.53559i	0.468165	+	0.270295i
$89$	4.52554	+	4.52554i	0.479706	+	0.479706i	0.905038	−	0.425331i	$-0.139842\pi$
$89$	4.52554	+	4.52554i	0.479706	+	0.479706i	−0.425331	+	0.905038i	$0.639842\pi$
$90$	−4.04692			−0.426583
$91$	7.94033	−	5.28689i	0.832373	−	0.554216i
$92$	5.43264			0.566392
$93$	2.91215	+	2.91215i	0.301976	+	0.301976i
$94$	−2.54726	−	1.47066i	−0.262729	−	0.151687i
$95$			5.87297i			0.602554i
$96$	−0.258819	−	0.965926i	−0.0264156	−	0.0985844i
$97$	−2.62347	−	9.79094i	−0.266374	−	0.994119i	−0.961404	−	0.275139i	$-0.911276\pi$
$97$	−2.62347	−	9.79094i	−0.266374	−	0.994119i	0.695031	−	0.718980i	$-0.255391\pi$
$98$	0.707107	+	6.96419i	0.0714286	+	0.703490i
$99$	3.58587	−	3.58587i	0.360393	−	0.360393i
$100$	−5.68879	−	9.85327i	−0.568879	−	0.985327i
$101$	1.96266	−	3.39942i	0.195292	−	0.338255i	−0.751704	−	0.659500i	$-0.770768\pi$
$101$	1.96266	−	3.39942i	0.195292	−	0.338255i	0.946996	+	0.321245i	$0.104101\pi$
$102$	−1.28435	−	4.79325i	−0.127169	−	0.474603i
$103$	3.52526	−	6.10594i	0.347355	−	0.601636i	−0.638424	−	0.769685i	$-0.720413\pi$
$103$	3.52526	−	6.10594i	0.347355	−	0.601636i	0.985779	+	0.168049i	$0.0537467\pi$
$104$	0.517865	+	3.56817i	0.0507808	+	0.349888i
$105$	−6.08017	+	8.81332i	−0.593364	+	0.860092i
$106$	−1.07901	+	4.02691i	−0.104802	+	0.391128i
$107$	−7.93596			−0.767199			−0.383599	−	0.923500i	$-0.625316\pi$
$107$	−7.93596			−0.767199			−0.383599	+	0.923500i	$0.625316\pi$
$108$	−1.00000			−0.0962250
$109$	−0.743535	+	2.77491i	−0.0712177	+	0.265788i	−0.992349	−	0.123464i	$-0.960600\pi$
$109$	−0.743535	+	2.77491i	−0.0712177	+	0.265788i	0.921131	+	0.389252i	$0.127266\pi$
$110$	19.8234	+	5.31166i	1.89009	+	0.506447i
$111$	−0.754695	+	0.202220i	−0.0716325	+	0.0191939i
$112$	−2.49243	−	0.887573i	−0.235513	−	0.0838678i
$113$	−4.74902	+	8.22554i	−0.446750	+	0.773793i	−0.998172	−	0.0604327i	$-0.980752\pi$
$113$	−4.74902	+	8.22554i	−0.446750	+	0.773793i	0.551422	+	0.834226i	$0.314085\pi$
$114$			1.45122i			0.135919i
$115$	21.2363	−	5.69026i	1.98030	−	0.530619i
$116$	7.35231	−	4.24486i	0.682644	−	0.394125i
$117$	3.58062	+	0.423290i	0.331028	+	0.0391332i
$118$		−	0.935412i		−	0.0861117i
$119$	−12.3683	−	4.40444i	−1.13380	−	0.403754i
$120$	−2.02346	−	3.50474i	−0.184716	−	0.319937i
$121$	−12.7452	+	7.35846i	−1.15866	+	0.668951i
$122$	−11.6960	−	3.13392i	−1.05890	−	0.283732i
$123$	2.53322	+	2.53322i	0.228413	+	0.228413i
$124$	−1.06592	+	3.97807i	−0.0957225	+	0.357241i
$125$	−18.2501	−	18.2501i	−1.63234	−	1.63234i
$126$	−1.50242	+	2.17778i	−0.133846	+	0.194012i
$127$	−12.2743	+	7.08657i	−1.08917	+	0.628831i	−0.933355	−	0.358955i	$-0.883133\pi$
$127$	−12.2743	+	7.08657i	−1.08917	+	0.628831i	−0.155813	+	0.987787i	$0.549800\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	4.88270	+	8.45709i	0.429898	+	0.744605i
$130$	5.76172	+	13.4056i	0.505336	+	1.17575i
$131$	8.60736	+	4.96946i	0.752029	+	0.434184i	0.826427	−	0.563045i	$-0.190370\pi$
$131$	8.60736	+	4.96946i	0.752029	+	0.434184i	−0.0743977	+	0.997229i	$0.523703\pi$
$132$	4.89839	+	1.31252i	0.426350	+	0.114240i
$133$	3.16044	+	2.18034i	0.274045	+	0.189059i
$134$	−7.96498	−	4.59858i	−0.688069	−	0.397257i
$135$	−3.90903	+	1.04742i	−0.336435	+	0.0901476i
$136$	3.50891	−	3.50891i	0.300886	−	0.300886i
$137$	−12.4912	+	12.4912i	−1.06719	+	1.06719i	−0.0696180	+	0.997574i	$0.522178\pi$
$137$	−12.4912	+	12.4912i	−1.06719	+	1.06719i	−0.997574	+	0.0696180i	$0.977822\pi$
$138$	5.24753	−	1.40607i	0.446699	−	0.119693i
$139$	11.0687	+	6.39049i	0.938831	+	0.542035i	0.889594	−	0.456752i	$-0.150987\pi$
$139$	11.0687	+	6.39049i	0.938831	+	0.542035i	0.0492377	+	0.998787i	$0.484321\pi$
$140$	−10.6726	−	0.858922i	−0.902003	−	0.0725922i
$141$	−2.84109	−	0.761269i	−0.239263	−	0.0641104i
$142$	−3.84185	−	2.21809i	−0.322401	−	0.186138i
$143$	−16.9837	−	6.77307i	−1.42025	−	0.566393i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	24.2942	−	24.2942i	2.01752	−	2.01752i
$146$	11.5073	−	6.64375i	0.952351	−	0.549840i
$147$	2.48548	+	6.54388i	0.204999	+	0.539730i
$148$	−0.552475	−	0.552475i	−0.0454132	−	0.0454132i
$149$	3.01906	−	11.2673i	0.247331	−	0.923051i	−0.724867	−	0.688889i	$-0.758099\pi$
$149$	3.01906	−	11.2673i	0.247331	−	0.923051i	0.972198	−	0.234162i	$-0.0752346\pi$
$150$	−8.04516	−	8.04516i	−0.656884	−	0.656884i
$151$	16.0351	+	4.29660i	1.30492	+	0.349652i	0.843308	−	0.537430i	$-0.180605\pi$
$151$	16.0351	+	4.29660i	1.30492	+	0.349652i	0.461611	+	0.887082i	$0.347271\pi$
$152$	−1.25679	+	0.725610i	−0.101939	+	0.0588547i
$153$	−2.48117	−	4.29751i	−0.200591	−	0.347433i
$154$	10.2178	−	8.69567i	0.823375	−	0.700717i
$155$			16.6668i			1.33871i
$156$	1.42373	+	3.31255i	0.113990	+	0.265216i
$157$	19.4589	−	11.2346i	1.55299	−	0.896620i	0.555095	−	0.831787i	$-0.312682\pi$
$157$	19.4589	−	11.2346i	1.55299	−	0.896620i	0.997896	−	0.0648334i	$-0.0206516\pi$
$158$	2.56789	−	0.688065i	0.204291	−	0.0547395i
$159$			4.16896i			0.330620i
$160$	2.02346	−	3.50474i	0.159969	−	0.277074i
$161$	4.82187	−	13.5405i	0.380016	−	1.06714i
$162$	−0.965926	+	0.258819i	−0.0758903	+	0.0203347i
$163$	0.737570	+	0.197631i	0.0577710	+	0.0154797i	0.287589	−	0.957754i	$-0.407146\pi$
$163$	0.737570	+	0.197631i	0.0577710	+	0.0154797i	−0.229818	+	0.973234i	$0.573813\pi$
$164$	−0.927225	+	3.46045i	−0.0724041	+	0.270216i
$165$	20.5227			1.59769
$166$	−1.44779			−0.112371
$167$	0.00377911	−	0.0141038i	0.000292436	−	0.00109139i	−0.965779	−	0.259365i	$-0.916487\pi$
$167$	0.00377911	−	0.0141038i	0.000292436	−	0.00109139i	0.966072	+	0.258273i	$0.0831535\pi$
$168$	−2.63722	−	0.212241i	−0.203466	−	0.0163747i
$169$	−3.69566	−	12.4636i	−0.284281	−	0.958741i
$170$	10.0411	−	17.3917i	0.770117	−	1.33388i
$171$	0.375603	+	1.40177i	0.0287231	+	0.107196i
$172$	−4.88270	+	8.45709i	−0.372303	+	0.644847i
$173$	3.61727	+	6.26529i	0.275016	+	0.476341i	0.970139	−	0.242549i	$-0.0779837\pi$
$173$	3.61727	+	6.26529i	0.275016	+	0.476341i	−0.695123	+	0.718890i	$0.744650\pi$
$174$	6.00313	−	6.00313i	0.455096	−	0.455096i
$175$	−29.6078	+	5.43342i	−2.23814	+	0.410728i
$176$	1.31252	+	4.89839i	0.0989349	+	0.369230i
$177$	−0.242102	−	0.903539i	−0.0181975	−	0.0679141i
$178$			6.40008i			0.479706i
$179$	13.9618	+	8.06082i	1.04355	+	0.602494i	0.920837	−	0.389948i	$-0.127507\pi$
$179$	13.9618	+	8.06082i	1.04355	+	0.602494i	0.122713	+	0.992442i	$0.460840\pi$
$180$	−2.86161	−	2.86161i	−0.213291	−	0.213291i
$181$	−6.35633			−0.472462			−0.236231	−	0.971697i	$-0.575912\pi$
$181$	−6.35633			−0.472462			−0.236231	+	0.971697i	$0.575912\pi$
$182$	9.35305	+	1.87627i	0.693295	+	0.139078i
$183$	−12.1085			−0.895089
$184$	3.84146	+	3.84146i	0.283196	+	0.283196i
$185$	−2.73831	−	1.58097i	−0.201325	−	0.116235i
$186$			4.11840i			0.301976i
$187$	6.51317	+	24.3075i	0.476290	+	1.77754i
$188$	−0.761269	−	2.84109i	−0.0555213	−	0.207208i
$189$	−0.887573	+	2.49243i	−0.0645614	+	0.181298i
$190$	−4.15282	+	4.15282i	−0.301277	+	0.301277i
$191$	10.4189	+	18.0461i	0.753888	+	1.30577i	0.945925	+	0.324384i	$0.105157\pi$
$191$	10.4189	+	18.0461i	0.753888	+	1.30577i	−0.192038	+	0.981388i	$0.561510\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	−2.78045	−	10.3768i	−0.200141	−	0.746937i	−0.990876	−	0.134778i	$-0.956968\pi$
$193$	−2.78045	−	10.3768i	−0.200141	−	0.746937i	0.790735	−	0.612159i	$-0.209699\pi$
$194$	5.06816	−	8.77832i	0.363873	−	0.630246i
$195$	9.03503	+	11.4576i	0.647012	+	0.820496i
$196$	−4.42443	+	5.42443i	−0.316031	+	0.387459i
$197$	3.04663	−	11.3702i	0.217063	−	0.810092i	−0.768367	−	0.640010i	$-0.778930\pi$
$197$	3.04663	−	11.3702i	0.217063	−	0.810092i	0.985430	−	0.170082i	$-0.0544032\pi$
$198$	5.07118			0.360393
$199$	−19.4226			−1.37683			−0.688417	−	0.725316i	$-0.741694\pi$
$199$	−19.4226			−1.37683			−0.688417	+	0.725316i	$0.741694\pi$
$200$	2.94473	−	10.9899i	0.208224	−	0.777103i
$201$	−8.88378	−	2.38040i	−0.626613	−	0.167901i
$202$	3.79157	−	1.01595i	0.266774	−	0.0714818i
$203$	−4.05430	−	22.0927i	−0.284556	−	1.55061i
$204$	2.48117	−	4.29751i	0.173717	−	0.300886i
$205$			14.4982i			1.01260i
$206$	6.81029	−	1.82481i	0.474495	−	0.127141i
$207$	4.70481	−	2.71632i	0.327007	−	0.188797i
$208$	−2.15689	+	2.88926i	−0.149553	+	0.200334i
$209$		−	7.35940i		−	0.509061i
$210$	−10.5313	+	1.93263i	−0.726728	+	0.133364i
$211$	−1.69854	−	2.94196i	−0.116932	−	0.202533i	0.801618	−	0.597836i	$-0.203973\pi$
$211$	−1.69854	−	2.94196i	−0.116932	−	0.202533i	−0.918551	+	0.395304i	$0.870639\pi$
$212$	−3.61043	+	2.08448i	−0.247965	+	0.143163i
$213$	−4.28503	−	1.14817i	−0.293605	−	0.0786713i
$214$	−5.61157	−	5.61157i	−0.383599	−	0.383599i
$215$	−10.2285	+	38.1732i	−0.697577	+	2.60339i
$216$	−0.707107	−	0.707107i	−0.0481125	−	0.0481125i
$217$	8.96898	+	6.18756i	0.608854	+	0.420039i
$218$	−2.48792	+	1.43640i	−0.168503	+	0.0972852i
$219$	9.39568	−	9.39568i	0.634901	−	0.634901i
$220$	10.2613	+	17.7732i	0.691820	+	1.19827i
$221$	−10.7032	+	14.3375i	−0.719977	+	0.964445i
$222$	−0.676641	−	0.390659i	−0.0454132	−	0.0262193i
$223$	−18.6599	−	4.99990i	−1.24956	−	0.334818i	−0.427393	−	0.904066i	$-0.640568\pi$
$223$	−18.6599	−	4.99990i	−1.24956	−	0.334818i	−0.822166	+	0.569248i	$0.807235\pi$
$224$	−1.13481	−	2.39002i	−0.0758224	−	0.159690i
$225$	−9.85327	−	5.68879i	−0.656884	−	0.379252i
$226$	−9.17439	+	2.45827i	−0.610272	+	0.163522i
$227$	−0.494349	+	0.494349i	−0.0328111	+	0.0328111i	−0.723322	−	0.690511i	$-0.757386\pi$
$227$	−0.494349	+	0.494349i	−0.0328111	+	0.0328111i	0.690511	+	0.723322i	$0.257386\pi$
$228$	−1.02617	+	1.02617i	−0.0679596	+	0.0679596i
$229$	−13.8280	+	3.70519i	−0.913778	+	0.244846i	−0.684924	−	0.728615i	$-0.740164\pi$
$229$	−13.8280	+	3.70519i	−0.913778	+	0.244846i	−0.228854	+	0.973461i	$0.573498\pi$
$230$	19.0400	+	10.9927i	1.25546	+	0.724840i
$231$	7.61904	−	11.0439i	0.501296	−	0.726638i
$232$	8.20043	+	2.19730i	0.538385	+	0.144260i
$233$	−14.6943	−	8.48375i	−0.962655	−	0.555789i	−0.0656657	−	0.997842i	$-0.520917\pi$
$233$	−14.6943	−	8.48375i	−0.962655	−	0.555789i	−0.896989	+	0.442053i	$0.854250\pi$
$234$	2.23257	+	2.83119i	0.145948	+	0.185081i
$235$	−5.95164	−	10.3085i	−0.388242	−	0.672455i
$236$	0.661436	−	0.661436i	0.0430558	−	0.0430558i
$237$	2.30231	−	1.32924i	0.149551	−	0.0863433i
$238$	−5.63130	−	11.8601i	−0.365023	−	0.768777i
$239$	−10.9179	−	10.9179i	−0.706219	−	0.706219i	0.259519	−	0.965738i	$-0.416436\pi$
$239$	−10.9179	−	10.9179i	−0.706219	−	0.706219i	−0.965738	+	0.259519i	$0.916436\pi$
$240$	1.04742	−	3.90903i	0.0676107	−	0.252327i
$241$	−0.246303	−	0.246303i	−0.0158658	−	0.0158658i	0.699129	−	0.714995i	$-0.253571\pi$
$241$	−0.246303	−	0.246303i	−0.0158658	−	0.0158658i	−0.714995	+	0.699129i	$0.753571\pi$
$242$	−14.2154	−	3.80902i	−0.913804	−	0.244853i
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	−6.05427	−	10.4863i	−0.387585	−	0.671317i
$245$	−11.6136	+	25.8385i	−0.741963	+	1.65076i
$246$			3.58252i			0.228413i
$247$	4.10868	−	3.23995i	0.261429	−	0.206153i
$248$	−3.56664	+	2.05920i	−0.226482	+	0.130759i
$249$	−1.39846	+	0.374717i	−0.0886239	+	0.0237467i
$250$		−	25.8095i		−	1.63234i
$251$	−0.267758	+	0.463770i	−0.0169007	+	0.0292729i	−0.874352	−	0.485292i	$-0.838713\pi$
$251$	−0.267758	+	0.463770i	−0.0169007	+	0.0292729i	0.857451	+	0.514565i	$0.172047\pi$
$252$	−2.60230	+	0.477555i	−0.163929	+	0.0300831i
$253$	−26.6112	+	7.13045i	−1.67303	+	0.448287i
$254$	−13.6902	−	3.66828i	−0.858999	−	0.230168i
$255$	5.19766	−	19.3979i	0.325490	−	1.21474i
$256$	1.00000			0.0625000
$257$	21.2389			1.32484			0.662422	−	0.749131i	$-0.269529\pi$
$257$	21.2389			1.32484			0.662422	+	0.749131i	$0.269529\pi$
$258$	−2.52747	+	9.43266i	−0.157354	+	0.587252i
$259$	−1.86737	+	0.886644i	−0.116033	+	0.0550934i
$260$	−5.40507	+	13.5534i	−0.335208	+	0.840544i
$261$	4.24486	−	7.35231i	0.262750	−	0.455096i
$262$	2.57238	+	9.60027i	0.158922	+	0.593106i
$263$	6.21578	−	10.7660i	0.383281	−	0.663863i	−0.608248	−	0.793747i	$-0.708127\pi$
$263$	6.21578	−	10.7660i	0.383281	−	0.663863i	0.991529	+	0.129885i	$0.0414607\pi$
$264$	2.53559	+	4.39177i	0.156055	+	0.270295i
$265$	−11.9299	+	11.9299i	−0.732849	+	0.732849i
$266$	0.693037	+	3.77650i	0.0424928	+	0.231552i
$267$	1.65646	+	6.18200i	0.101374	+	0.378332i
$268$	−2.38040	−	8.88378i	−0.145406	−	0.542663i
$269$		−	10.0427i		−	0.612317i	−0.951981	−	0.306158i	$-0.900956\pi$
$269$		−	10.0427i		−	0.612317i	0.951981	−	0.306158i	$-0.0990437\pi$
$270$	−3.50474	−	2.02346i	−0.213291	−	0.123144i
$271$	13.7004	+	13.7004i	0.832238	+	0.832238i	0.987823	−	0.155585i	$-0.0497262\pi$
$271$	13.7004	+	13.7004i	0.832238	+	0.832238i	−0.155585	+	0.987823i	$0.549726\pi$
$272$	4.96234			0.300886
$273$	9.51997	−	0.608415i	0.576175	−	0.0368230i
$274$	−17.6652			−1.06719
$275$	40.7985	+	40.7985i	2.46024	+	2.46024i
$276$	4.70481	+	2.71632i	0.283196	+	0.163503i
$277$			22.3378i			1.34215i	0.741391	+	0.671073i	$0.234166\pi$
$277$			22.3378i			1.34215i	−0.741391	+	0.671073i	$0.765834\pi$
$278$	3.30796	+	12.3455i	0.198398	+	0.740433i
$279$	1.06592	+	3.97807i	0.0638150	+	0.238161i
$280$	−6.93935	−	8.15405i	−0.414705	−	0.487297i
$281$	−19.3688	+	19.3688i	−1.15545	+	1.15545i	−0.170002	+	0.985444i	$0.554378\pi$
$281$	−19.3688	+	19.3688i	−1.15545	+	1.15545i	−0.985444	+	0.170002i	$0.945622\pi$
$282$	−1.47066	−	2.54726i	−0.0875765	−	0.151687i
$283$	−5.58662	+	9.67632i	−0.332090	+	0.575197i	−0.982922	−	0.184025i	$-0.941087\pi$
$283$	−5.58662	+	9.67632i	−0.332090	+	0.575197i	0.650831	+	0.759222i	$0.274421\pi$
$284$	−1.14817	−	4.28503i	−0.0681314	−	0.254270i
$285$	−2.93649	+	5.08614i	−0.173942	+	0.301277i
$286$	−7.21999	−	16.7986i	−0.426927	−	0.993320i
$287$	7.80195	+	5.38244i	0.460535	+	0.317716i
$288$	0.258819	−	0.965926i	0.0152511	−	0.0569177i
$289$	7.62483			0.448519
$290$	34.3572			2.01752
$291$	2.62347	−	9.79094i	0.153791	−	0.573955i
$292$	12.8347	+	3.43906i	0.751096	+	0.201256i
$293$	19.1845	−	5.14048i	1.12077	−	0.300310i	0.349577	−	0.936908i	$-0.386325\pi$
$293$	19.1845	−	5.14048i	1.12077	−	0.300310i	0.771196	+	0.636598i	$0.219659\pi$
$294$	−2.86972	+	6.38472i	−0.167366	+	0.372365i
$295$	1.89277	−	3.27837i	0.110201	−	0.190874i
$296$		−	0.781318i		−	0.0454132i
$297$	4.89839	−	1.31252i	0.284233	−	0.0761601i
$298$	10.1020	−	5.83237i	0.585191	−	0.337860i
$299$	−15.6963	−	11.7176i	−0.907742	−	0.677647i
$300$		−	11.3776i		−	0.656884i
$301$	16.7450	+	19.6761i	0.965164	+	1.13411i
$302$	8.30039	+	14.3767i	0.477634	+	0.827286i
$303$	3.39942	−	1.96266i	0.195292	−	0.112752i
$304$	−1.40177	−	0.375603i	−0.0803971	−	0.0215423i
$305$	−34.6499	−	34.6499i	−1.98405	−	1.98405i
$306$	1.28435	−	4.79325i	0.0734213	−	0.274012i
$307$	2.00335	+	2.00335i	0.114337	+	0.114337i	0.761961	−	0.647623i	$-0.224237\pi$
$307$	2.00335	+	2.00335i	0.114337	+	0.114337i	−0.647623	+	0.761961i	$0.724237\pi$
$308$	13.3739	+	1.07631i	0.762046	+	0.0613286i
$309$	6.10594	−	3.52526i	0.347355	−	0.200545i
$310$	−11.7852	+	11.7852i	−0.669357	+	0.669357i
$311$	10.4635	+	18.1233i	0.593332	+	1.02768i	0.993780	+	0.111361i	$0.0355211\pi$
$311$	10.4635	+	18.1233i	0.593332	+	1.02768i	−0.400448	+	0.916319i	$0.631146\pi$
$312$	−1.33560	+	3.34906i	−0.0756134	+	0.189603i
$313$	−22.2663	−	12.8554i	−1.25856	−	0.726632i	−0.285769	−	0.958299i	$-0.592249\pi$
$313$	−22.2663	−	12.8554i	−1.25856	−	0.726632i	−0.972795	+	0.231666i	$0.925582\pi$
$314$	21.7036	+	5.81547i	1.22481	+	0.328186i
$315$	−9.67224	+	4.59247i	−0.544969	+	0.258756i
$316$	2.30231	+	1.32924i	0.129515	+	0.0747755i
$317$	−31.4472	+	8.42624i	−1.76625	+	0.473265i	−0.987969	−	0.154653i	$-0.950574\pi$
$317$	−31.4472	+	8.42624i	−1.76625	+	0.473265i	−0.778280	+	0.627918i	$0.783907\pi$
$318$	−2.94790	+	2.94790i	−0.165310	+	0.165310i
$319$	−30.4430	+	30.4430i	−1.70448	+	1.70448i
$320$	3.90903	−	1.04742i	0.218521	−	0.0585526i
$321$	−6.87275	−	3.96798i	−0.383599	−	0.221471i
$322$	12.9841	−	6.16500i	0.723578	−	0.343562i
$323$	−6.95606	−	1.86387i	−0.387046	−	0.103709i
$324$	−0.866025	−	0.500000i	−0.0481125	−	0.0277778i
$325$	−4.81602	+	40.7387i	−0.267145	+	2.25978i
$326$	0.381795	+	0.661288i	0.0211456	+	0.0366253i
$327$	−2.03137	+	2.03137i	−0.112335	+	0.112335i
$328$	−3.10255	+	1.79126i	−0.171310	+	0.0989058i
$329$	−7.75692	−	0.624268i	−0.427653	−	0.0344170i
$330$	14.5117	+	14.5117i	0.798844	+	0.798844i
$331$	4.70948	−	17.5760i	0.258857	−	0.966066i	−0.707048	−	0.707166i	$-0.749973\pi$
$331$	4.70948	−	17.5760i	0.258857	−	0.966066i	0.965904	−	0.258900i	$-0.0833600\pi$
$332$	−1.02375	−	1.02375i	−0.0561853	−	0.0561853i
$333$	−0.754695	−	0.202220i	−0.0413570	−	0.0110816i
$334$	0.0126452	−	0.00730068i	0.000691912	−	0.000399476i
$335$	−18.6101	−	32.2336i	−1.01678	−	1.76111i
$336$	−1.71472	−	2.01488i	−0.0935458	−	0.109921i
$337$		−	6.02776i		−	0.328353i	−0.986431	−	0.164177i	$-0.947503\pi$
$337$		−	6.02776i		−	0.328353i	0.986431	−	0.164177i	$-0.0524967\pi$
$338$	6.19989	−	11.4263i	0.337230	−	0.621511i
$339$	−8.22554	+	4.74902i	−0.446750	+	0.257931i
$340$	19.3979	−	5.19766i	1.05200	−	0.281883i
$341$		−	20.8852i		−	1.13100i
$342$	−0.725610	+	1.25679i	−0.0392365	+	0.0679596i
$343$	9.59301	+	15.8422i	0.517974	+	0.855396i
$344$	−9.43266	+	2.52747i	−0.508575	+	0.136272i
$345$	21.2363	+	5.69026i	1.14333	+	0.306353i
$346$	−1.87243	+	6.98802i	−0.100663	+	0.375678i
$347$	30.2037			1.62142			0.810710	−	0.585448i	$-0.199082\pi$
$347$	30.2037			1.62142			0.810710	+	0.585448i	$0.199082\pi$
$348$	8.48971			0.455096
$349$	−4.66318	+	17.4032i	−0.249614	+	0.931573i	0.721394	+	0.692525i	$0.243502\pi$
$349$	−4.66318	+	17.4032i	−0.249614	+	0.931573i	−0.971008	+	0.239048i	$0.923165\pi$
$350$	−24.7779	−	17.0939i	−1.32443	−	0.913706i
$351$	2.88926	+	2.15689i	0.154217	+	0.115126i
$352$	−2.53559	+	4.39177i	−0.135148	+	0.234082i
$353$	0.434096	+	1.62007i	0.0231046	+	0.0862276i	0.976515	−	0.215447i	$-0.0691209\pi$
$353$	0.434096	+	1.62007i	0.0231046	+	0.0862276i	−0.953411	+	0.301675i	$0.902454\pi$
$354$	0.467706	−	0.810091i	0.0248583	−	0.0430558i
$355$	−8.97646	−	15.5477i	−0.476421	−	0.825185i
$356$	−4.52554	+	4.52554i	−0.239853	+	0.239853i
$357$	−8.50904	−	9.99850i	−0.450346	−	0.529177i
$358$	4.17259	+	15.5723i	0.220528	+	0.823022i
$359$	−0.0574832	−	0.214530i	−0.00303385	−	0.0113225i	0.964392	−	0.264476i	$-0.0851989\pi$
$359$	−0.0574832	−	0.214530i	−0.00303385	−	0.0113225i	−0.967426	+	0.253153i	$0.918532\pi$
$360$		−	4.04692i		−	0.213291i
$361$	−14.6306	−	8.44698i	−0.770032	−	0.444578i
$362$	−4.49460	−	4.49460i	−0.236231	−	0.236231i
$363$	−14.7169			−0.772438
$364$	5.28689	+	7.94033i	0.277108	+	0.416186i
$365$	53.7734			2.81463
$366$	−8.56203	−	8.56203i	−0.447545	−	0.447545i
$367$	7.30853	+	4.21958i	0.381502	+	0.220261i	0.678472	−	0.734627i	$-0.262643\pi$
$367$	7.30853	+	4.21958i	0.381502	+	0.220261i	−0.296969	+	0.954887i	$0.595976\pi$
$368$			5.43264i			0.283196i
$369$	0.927225	+	3.46045i	0.0482694	+	0.180144i
$370$	−0.818368	−	3.05419i	−0.0425449	−	0.158780i
$371$	1.99091	+	10.8489i	0.103363	+	0.563245i
$372$	−2.91215	+	2.91215i	−0.150988	+	0.150988i
$373$	5.14263	+	8.90730i	0.266275	+	0.461203i	0.967897	−	0.251347i	$-0.0808736\pi$
$373$	5.14263	+	8.90730i	0.266275	+	0.461203i	−0.701622	+	0.712550i	$0.747540\pi$
$374$	−12.5825	+	21.7935i	−0.650624	+	1.12691i
$375$	−6.68000	−	24.9301i	−0.344954	−	1.28738i
$376$	1.47066	−	2.54726i	0.0758434	−	0.131365i
$377$	−30.3984	−	3.59361i	−1.56560	−	0.185081i
$378$	−2.39002	+	1.13481i	−0.122930	+	0.0583681i
$379$	6.02799	−	22.4968i	0.309637	−	1.15558i	−0.619243	−	0.785199i	$-0.712560\pi$
$379$	6.02799	−	22.4968i	0.309637	−	1.15558i	0.928880	−	0.370381i	$-0.120773\pi$
$380$	−5.87297			−0.301277
$381$	−14.1731			−0.726112
$382$	−5.39324	+	20.1278i	−0.275942	+	1.02983i
$383$	−7.44533	−	1.99497i	−0.380439	−	0.101938i	0.0635314	−	0.997980i	$-0.479764\pi$
$383$	−7.44533	−	1.99497i	−0.380439	−	0.101938i	−0.443970	+	0.896042i	$0.646430\pi$
$384$	0.965926	−	0.258819i	0.0492922	−	0.0132078i
$385$	53.4061	−	9.80071i	2.72183	−	0.499491i
$386$	5.37141	−	9.30356i	0.273398	−	0.473539i
$387$			9.76541i			0.496404i
$388$	9.79094	−	2.62347i	0.497060	−	0.133187i
$389$	22.8006	−	13.1639i	1.15604	−	0.667438i	0.205686	−	0.978618i	$-0.434057\pi$
$389$	22.8006	−	13.1639i	1.15604	−	0.667438i	0.950351	+	0.311180i	$0.100724\pi$
$390$	−1.71302	+	14.4905i	−0.0867423	+	0.733754i
$391$			26.9586i			1.36336i
$392$	−6.96419	+	0.707107i	−0.351745	+	0.0357143i
$393$	4.96946	+	8.60736i	0.250676	+	0.434184i
$394$	10.1942	−	5.88564i	0.513578	−	0.296514i
$395$	10.3921	+	2.78454i	0.522881	+	0.140106i
$396$	3.58587	+	3.58587i	0.180197	+	0.180197i
$397$	−2.70592	+	10.0986i	−0.135806	+	0.506835i	0.864187	+	0.503170i	$0.167833\pi$
$397$	−2.70592	+	10.0986i	−0.135806	+	0.506835i	−0.999993	+	0.00366458i	$0.998834\pi$
$398$	−13.7339	−	13.7339i	−0.688417	−	0.688417i
$399$	1.64685	+	3.46845i	0.0824458	+	0.173640i
$400$	9.85327	−	5.68879i	0.492663	−	0.284439i
$401$	−7.25103	+	7.25103i	−0.362099	+	0.362099i	−0.864585	−	0.502486i	$-0.832419\pi$
$401$	−7.25103	+	7.25103i	−0.362099	+	0.362099i	0.502486	+	0.864585i	$0.332419\pi$
$402$	−4.59858	−	7.96498i	−0.229356	−	0.397257i
$403$	11.6600	−	9.19461i	0.580825	−	0.458016i
$404$	3.39942	+	1.96266i	0.169128	+	0.0976459i
$405$	−3.90903	−	1.04742i	−0.194241	−	0.0520467i
$406$	12.7551	−	18.4887i	0.633025	−	0.917581i
$407$	3.43137	+	1.98110i	0.170087	+	0.0981997i
$408$	4.79325	−	1.28435i	0.237301	−	0.0635847i
$409$	11.0226	−	11.0226i	0.545031	−	0.545031i	−0.379969	−	0.924999i	$-0.624065\pi$
$409$	11.0226	−	11.0226i	0.545031	−	0.545031i	0.924999	+	0.379969i	$0.124065\pi$
$410$	−10.2518	+	10.2518i	−0.506298	+	0.506298i
$411$	−17.0632	+	4.57208i	−0.841668	+	0.225524i
$412$	6.10594	+	3.52526i	0.300818	+	0.173677i
$413$	−1.06151	−	2.23566i	−0.0522336	−	0.110010i
$414$	5.24753	+	1.40607i	0.257902	+	0.0691046i
$415$	−5.07414	−	2.92955i	−0.249080	−	0.143806i
$416$	−3.56817	+	0.517865i	−0.174944	+	0.0253904i
$417$	6.39049	+	11.0687i	0.312944	+	0.542035i
$418$	5.20388	−	5.20388i	0.254530	−	0.254530i
$419$	14.7689	−	8.52681i	0.721506	−	0.416562i	−0.0938005	−	0.995591i	$-0.529902\pi$
$419$	14.7689	−	8.52681i	0.721506	−	0.416562i	0.815307	+	0.579029i	$0.196568\pi$
$420$	−8.81332	−	6.08017i	−0.430046	−	0.296682i
$421$	−22.4757	−	22.4757i	−1.09540	−	1.09540i	−0.994941	−	0.100458i	$-0.967969\pi$
$421$	−22.4757	−	22.4757i	−1.09540	−	1.09540i	−0.100458	−	0.994941i	$-0.532031\pi$
$422$	0.879229	−	3.28133i	0.0428002	−	0.159733i
$423$	−2.07983	−	2.07983i	−0.101125	−	0.101125i
$424$	−4.02691	−	1.07901i	−0.195564	−	0.0524012i
$425$	48.8953	−	28.2297i	2.37177	−	1.36934i
$426$	−2.21809	−	3.84185i	−0.107467	−	0.186138i
$427$	−31.5100	+	5.78250i	−1.52488	+	0.279835i
$428$		−	7.93596i		−	0.383599i
$429$	−11.3218	−	14.3575i	−0.546620	−	0.693186i
$430$	−34.2252	+	19.7599i	−1.65049	+	0.952908i
$431$	−25.9933	+	6.96488i	−1.25205	+	0.335486i	−0.823129	−	0.567855i	$-0.807774\pi$
$431$	−25.9933	+	6.96488i	−1.25205	+	0.335486i	−0.428923	+	0.903341i	$0.641107\pi$
$432$		−	1.00000i		−	0.0481125i
$433$	−10.8841	+	18.8518i	−0.523055	+	0.905958i	0.476585	+	0.879128i	$0.341874\pi$
$433$	−10.8841	+	18.8518i	−0.523055	+	0.905958i	−0.999640	+	0.0268294i	$0.991459\pi$
$434$	1.96676	+	10.7173i	0.0944077	+	0.514447i
$435$	33.1865	−	8.89230i	1.59117	−	0.426353i
$436$	−2.77491	−	0.743535i	−0.132894	−	0.0356089i
$437$	2.04052	−	7.61532i	0.0976112	−	0.364290i
$438$	13.2875			0.634901
$439$	−1.65543			−0.0790096			−0.0395048	−	0.999219i	$-0.512578\pi$
$439$	−1.65543			−0.0790096			−0.0395048	+	0.999219i	$0.512578\pi$
$440$	−5.31166	+	19.8234i	−0.253224	+	0.945043i
$441$	−1.11945	+	6.90991i	−0.0533073	+	0.329043i
$442$	−17.7065	+	2.56982i	−0.842211	+	0.122234i
$443$	−14.7088	+	25.4763i	−0.698835	+	1.21042i	0.270036	+	0.962850i	$0.412965\pi$
$443$	−14.7088	+	25.4763i	−0.698835	+	1.21042i	−0.968871	+	0.247567i	$0.920369\pi$
$444$	−0.202220	−	0.754695i	−0.00959693	−	0.0358162i
$445$	−12.9503	+	22.4306i	−0.613903	+	1.06331i
$446$	−9.65907	−	16.7300i	−0.457370	−	0.792189i
$447$	8.24822	−	8.24822i	0.390127	−	0.390127i
$448$	0.887573	−	2.49243i	0.0419339	−	0.117756i
$449$	−8.91712	−	33.2791i	−0.420825	−	1.57054i	−0.772875	−	0.634559i	$-0.781182\pi$
$449$	−8.91712	−	33.2791i	−0.420825	−	1.57054i	0.352050	−	0.935981i	$-0.385485\pi$
$450$	−2.94473	−	10.9899i	−0.138816	−	0.518068i
$451$		−	18.1676i		−	0.855480i
$452$	−8.22554	−	4.74902i	−0.386897	−	0.223375i
$453$	11.7385	+	11.7385i	0.551524	+	0.551524i
$454$	−0.699115			−0.0328111
$455$	28.9834	+	25.5014i	1.35876	+	1.19552i
$456$	−1.45122			−0.0679596
$457$	0.744924	+	0.744924i	0.0348461	+	0.0348461i	0.724315	−	0.689469i	$-0.242156\pi$
$457$	0.744924	+	0.744924i	0.0348461	+	0.0348461i	−0.689469	+	0.724315i	$0.742156\pi$
$458$	−12.3978	−	7.15788i	−0.579312	−	0.334466i
$459$		−	4.96234i		−	0.231622i
$460$	5.69026	+	21.2363i	0.265310	+	0.990149i
$461$	−5.12435	−	19.1243i	−0.238665	−	0.890709i	−0.976462	−	0.215687i	$-0.930801\pi$
$461$	−5.12435	−	19.1243i	−0.238665	−	0.890709i	0.737798	−	0.675022i	$-0.235866\pi$
$462$	13.1967	−	2.42177i	0.613967	−	0.112671i
$463$	1.31618	−	1.31618i	0.0611683	−	0.0611683i	−0.675861	−	0.737029i	$-0.736228\pi$
$463$	1.31618	−	1.31618i	0.0611683	−	0.0611683i	0.737029	+	0.675861i	$0.236228\pi$
$464$	4.24486	+	7.35231i	0.197062	+	0.341322i
$465$	−8.33342	+	14.4339i	−0.386453	+	0.669357i
$466$	−4.39151	−	16.3893i	−0.203433	−	0.759222i
$467$	−11.3114	+	19.5920i	−0.523431	+	0.906609i	0.476197	+	0.879339i	$0.342015\pi$
$467$	−11.3114	+	19.5920i	−0.523431	+	0.906609i	−0.999628	+	0.0272707i	$0.991318\pi$
$468$	−0.423290	+	3.58062i	−0.0195666	+	0.165514i
$469$	−24.2550	−	1.95201i	−1.11999	−	0.0901356i
$470$	3.08080	−	11.4977i	0.142107	−	0.530349i
$471$	22.4692			1.03533
$472$	0.935412			0.0430558
$473$	12.8173	−	47.8348i	0.589339	−	2.19944i
$474$	2.56789	+	0.688065i	0.117947	+	0.0316039i
$475$	−15.9487	+	4.27345i	−0.731779	+	0.196080i
$476$	4.40444	−	12.3683i	0.201877	−	0.566900i
$477$	−2.08448	+	3.61043i	−0.0954418	+	0.165310i
$478$		−	15.4402i		−	0.706219i
$479$	25.1486	−	6.73856i	1.14907	−	0.307892i	0.366478	−	0.930427i	$-0.380564\pi$
$479$	25.1486	−	6.73856i	1.14907	−	0.307892i	0.782592	+	0.622534i	$0.213897\pi$
$480$	3.50474	−	2.02346i	0.159969	−	0.0923579i
$481$	0.404617	+	2.78787i	0.0184490	+	0.127116i
$482$		−	0.348325i		−	0.0158658i
$483$	10.9461	−	9.31547i	0.498065	−	0.423869i
$484$	−7.35846	−	12.7452i	−0.334475	−	0.579328i
$485$	35.5252	−	20.5105i	1.61311	−	0.931332i
$486$	−0.965926	−	0.258819i	−0.0438153	−	0.0117403i
$487$	1.90641	+	1.90641i	0.0863877	+	0.0863877i	0.748980	−	0.662592i	$-0.230544\pi$
$487$	1.90641	+	1.90641i	0.0863877	+	0.0863877i	−0.662592	+	0.748980i	$0.730544\pi$
$488$	3.13392	−	11.6960i	0.141866	−	0.529451i
$489$	0.539939	+	0.539939i	0.0244169	+	0.0244169i
$490$	−26.4826	+	10.0585i	−1.19636	+	0.454398i
$491$	27.0819	−	15.6357i	1.22219	−	0.705631i	0.256804	−	0.966463i	$-0.417330\pi$
$491$	27.0819	−	15.6357i	1.22219	−	0.705631i	0.965384	+	0.260832i	$0.0839970\pi$
$492$	−2.53322	+	2.53322i	−0.114207	+	0.114207i
$493$	21.0644	+	36.4846i	0.948694	+	1.64319i
$494$	5.19626	+	0.614287i	0.233791	+	0.0276381i
$495$	17.7732	+	10.2613i	0.798844	+	0.461213i
$496$	−3.97807	−	1.06592i	−0.178621	−	0.0478613i
$497$	−11.6992	−	0.941541i	−0.524782	−	0.0422339i
$498$	−1.25383	−	0.723897i	−0.0561853	−	0.0324386i
$499$	−2.53849	+	0.680186i	−0.113638	+	0.0304493i	−0.315190	−	0.949029i	$-0.602068\pi$
$499$	−2.53849	+	0.680186i	−0.113638	+	0.0304493i	0.201552	+	0.979478i	$0.435402\pi$
$500$	18.2501	−	18.2501i	0.816169	−	0.816169i
$501$	0.0103247	−	0.0103247i	0.000461275	−	0.000461275i
$502$	−0.517268	+	0.138602i	−0.0230868	+	0.00618609i
$503$	−28.0460	−	16.1924i	−1.25051	−	0.721982i	−0.279299	−	0.960204i	$-0.590102\pi$
$503$	−28.0460	−	16.1924i	−1.25051	−	0.721982i	−0.971211	+	0.238222i	$0.923435\pi$
$504$	−2.17778	−	1.50242i	−0.0970062	−	0.0669230i
$505$	15.3442	+	4.11146i	0.682807	+	0.182957i
$506$	−23.8589	−	13.7750i	−1.06066	−	0.612372i
$507$	3.03128	−	12.6417i	0.134624	−	0.561435i
$508$	−7.08657	−	12.2743i	−0.314416	−	0.544584i
$509$	−16.7170	+	16.7170i	−0.740967	+	0.740967i	−0.972764	−	0.231797i	$-0.925539\pi$
$509$	−16.7170	+	16.7170i	−0.740967	+	0.740967i	0.231797	+	0.972764i	$0.425539\pi$
$510$	17.3917	−	10.0411i	0.770117	−	0.444627i
$511$	19.9634	−	28.9373i	0.883128	−	1.28011i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.375603	+	1.40177i	−0.0165833	+	0.0618897i
$514$	15.0181	+	15.0181i	0.662422	+	0.662422i
$515$	27.5607	+	7.38487i	1.21447	+	0.325416i
$516$	−8.45709	+	4.88270i	−0.372303	+	0.214949i
$517$	7.45798	+	12.9176i	0.328002	+	0.568116i
$518$	−1.94738	−	0.693476i	−0.0855630	−	0.0304696i
$519$			7.23453i			0.317561i
$520$	−13.4056	+	5.76172i	−0.587876	+	0.252668i
$521$	−5.65413	+	3.26442i	−0.247712	+	0.143017i	−0.618716	−	0.785615i	$-0.712347\pi$
$521$	−5.65413	+	3.26442i	−0.247712	+	0.143017i	0.371004	+	0.928631i	$0.379014\pi$
$522$	8.20043	−	2.19730i	0.358923	−	0.0961732i
$523$			7.60819i			0.332683i	0.986068	+	0.166341i	$0.0531954\pi$
$523$			7.60819i			0.332683i	−0.986068	+	0.166341i	$0.946805\pi$
$524$	−4.96946	+	8.60736i	−0.217092	+	0.376014i
$525$	−28.3578	−	10.0984i	−1.23764	−	0.440731i
$526$	12.0080	−	3.21752i	0.523572	−	0.140291i
$527$	−19.7405	−	5.28946i	−0.859912	−	0.230413i
$528$	−1.31252	+	4.89839i	−0.0571201	+	0.213175i
$529$	−6.51360			−0.283200
$530$	−16.8715			−0.732849
$531$	0.242102	−	0.903539i	0.0105064	−	0.0392102i
$532$	−2.18034	+	3.16044i	−0.0945297	+	0.137023i
$533$	10.1428	−	7.99822i	0.439333	−	0.346441i
$534$	−3.20004	+	5.54263i	−0.138479	+	0.239853i
$535$	−8.31229	−	31.0219i	−0.359372	−	1.34119i
$536$	4.59858	−	7.96498i	0.198629	−	0.344035i
$537$	8.06082	+	13.9618i	0.347850	+	0.602494i
$538$	7.10129	−	7.10129i	0.306158	−	0.306158i
$539$	14.5529	−	32.3781i	0.626838	−	1.39462i
$540$	−1.04742	−	3.90903i	−0.0450738	−	0.168218i
$541$	−2.24023	−	8.36067i	−0.0963152	−	0.359453i	0.900900	−	0.434026i	$-0.142907\pi$
$541$	−2.24023	−	8.36067i	−0.0963152	−	0.359453i	−0.997216	+	0.0745728i	$0.976241\pi$
$542$			19.3752i			0.832238i
$543$	−5.50474	−	3.17816i	−0.236231	−	0.136388i
$544$	3.50891	+	3.50891i	0.150443	+	0.150443i
$545$	−11.6260			−0.498003
$546$	7.16185	+	6.30142i	0.306499	+	0.269676i
$547$	5.06040			0.216367			0.108184	−	0.994131i	$-0.465497\pi$
$547$	5.06040			0.216367			0.108184	+	0.994131i	$0.465497\pi$
$548$	−12.4912	−	12.4912i	−0.533596	−	0.533596i
$549$	−10.4863	−	6.05427i	−0.447545	−	0.258390i
$550$			57.6978i			2.46024i
$551$	−3.18876	−	11.9006i	−0.135846	−	0.506984i
$552$	1.40607	+	5.24753i	0.0598464	+	0.223350i
$553$	5.35650	−	4.55855i	0.227782	−	0.193849i
$554$	−15.7952	+	15.7952i	−0.671073	+	0.671073i
$555$	−1.58097	−	2.73831i	−0.0671083	−	0.116235i
$556$	−6.39049	+	11.0687i	−0.271017	+	0.469416i
$557$	−1.22339	−	4.56575i	−0.0518367	−	0.193457i	0.935152	−	0.354247i	$-0.115263\pi$
$557$	−1.22339	−	4.56575i	−0.0518367	−	0.193457i	−0.986989	+	0.160789i	$0.948596\pi$
$558$	−2.05920	+	3.56664i	−0.0871729	+	0.150988i
$559$	32.3484	−	13.9033i	1.36819	−	0.588047i
$560$	0.858922	−	10.6726i	0.0362961	−	0.451001i
$561$	−6.51317	+	24.3075i	−0.274986	+	1.02626i
$562$	−27.3916			−1.15545
$563$	1.45990			0.0615276			0.0307638	−	0.999527i	$-0.490206\pi$
$563$	1.45990			0.0615276			0.0307638	+	0.999527i	$0.490206\pi$
$564$	0.761269	−	2.84109i	0.0320552	−	0.119632i
$565$	−37.1281	−	9.94843i	−1.56199	−	0.418534i
$566$	−10.7925	+	2.89185i	−0.453644	+	0.121553i
$567$	−2.01488	+	1.71472i	−0.0846169	+	0.0720116i
$568$	2.21809	−	3.84185i	0.0930692	−	0.161201i
$569$			4.03815i			0.169288i	0.996411	+	0.0846440i	$0.0269753\pi$
$569$			4.03815i			0.169288i	−0.996411	+	0.0846440i	$0.973025\pi$
$570$	−5.67286	+	1.52004i	−0.237610	+	0.0636673i
$571$	25.0701	−	14.4742i	1.04915	−	0.605727i	0.126739	−	0.991936i	$-0.459549\pi$
$571$	25.0701	−	14.4742i	1.04915	−	0.605727i	0.922411	+	0.386209i	$0.126216\pi$
$572$	6.77307	−	16.9837i	0.283196	−	0.710123i
$573$			20.8379i			0.870515i
$574$	1.71085	+	9.32278i	0.0714095	+	0.389125i
$575$	30.9051	+	53.5293i	1.28883	+	2.23233i
$576$	0.866025	−	0.500000i	0.0360844	−	0.0208333i
$577$	−5.29341	−	1.41837i	−0.220368	−	0.0590474i	0.146946	−	0.989145i	$-0.453056\pi$
$577$	−5.29341	−	1.41837i	−0.220368	−	0.0590474i	−0.367314	+	0.930097i	$0.619722\pi$
$578$	5.39157	+	5.39157i	0.224260	+	0.224260i
$579$	2.78045	−	10.3768i	0.115552	−	0.431244i
$580$	24.2942	+	24.2942i	1.00876	+	1.00876i
$581$	−3.46026	+	1.64297i	−0.143556	+	0.0681617i
$582$	8.77832	−	5.06816i	0.363873	−	0.210082i
$583$	14.9494	−	14.9494i	0.619139	−	0.619139i
$584$	6.64375	+	11.5073i	0.274920	+	0.476176i
$585$	2.09576	+	14.4401i	0.0866490	+	0.597024i
$586$	17.2004	+	9.93065i	0.710542	+	0.410231i
$587$	39.3764	+	10.5509i	1.62524	+	0.435481i	0.952534	−	0.304432i	$-0.0984667\pi$
$587$	39.3764	+	10.5509i	1.62524	+	0.435481i	0.672703	+	0.739913i	$0.265133\pi$
$588$	−6.54388	+	2.48548i	−0.269865	+	0.102499i
$589$	5.17598	+	2.98835i	0.213272	+	0.123133i
$590$	3.65655	−	0.979770i	0.150538	−	0.0403365i
$591$	8.32355	−	8.32355i	0.342385	−	0.342385i
$592$	0.552475	−	0.552475i	0.0227066	−	0.0227066i
$593$	−9.21264	+	2.46852i	−0.378318	+	0.101370i	−0.442967	−	0.896538i	$-0.646074\pi$
$593$	−9.21264	+	2.46852i	−0.378318	+	0.101370i	0.0646487	+	0.997908i	$0.479407\pi$
$594$	4.39177	+	2.53559i	0.180197	+	0.104037i
$595$	4.26226	−	52.9613i	0.174736	−	2.17120i
$596$	11.2673	+	3.01906i	0.461526	+	0.123665i
$597$	−16.8205	−	9.71131i	−0.688417	−	0.397457i
$598$	−2.81337	−	19.3846i	−0.115047	−	0.792694i
$599$	−17.6775	−	30.6183i	−0.722282	−	1.25103i	−0.960083	−	0.279716i	$-0.909760\pi$
$599$	−17.6775	−	30.6183i	−0.722282	−	1.25103i	0.237800	−	0.971314i	$-0.423574\pi$
$600$	8.04516	−	8.04516i	0.328442	−	0.328442i
$601$	39.6382	−	22.8851i	1.61688	−	0.933503i	0.629154	−	0.777281i	$-0.283402\pi$
$601$	39.6382	−	22.8851i	1.61688	−	0.933503i	0.987722	−	0.156222i	$-0.0499317\pi$
$602$	−2.07262	+	25.7536i	−0.0844736	+	1.04964i
$603$	−6.50338	−	6.50338i	−0.264838	−	0.264838i
$604$	−4.29660	+	16.0351i	−0.174826	+	0.652460i
$605$	−42.1140	−	42.1140i	−1.71218	−	1.71218i
$606$	3.79157	+	1.01595i	0.154022	+	0.0412700i
$607$	−30.0021	+	17.3217i	−1.21775	+	0.703066i	−0.964435	−	0.264319i	$-0.914853\pi$
$607$	−30.0021	+	17.3217i	−1.21775	+	0.703066i	−0.253311	+	0.967385i	$0.581520\pi$
$608$	−0.725610	−	1.25679i	−0.0294274	−	0.0509697i
$609$	7.53524	−	21.1600i	0.305343	−	0.857447i
$610$		−	49.0023i		−	1.98405i
$611$	−3.92842	+	9.85064i	−0.158927	+	0.398514i
$612$	4.29751	−	2.48117i	0.173717	−	0.100295i
$613$	23.4774	−	6.29074i	0.948242	−	0.254081i	0.248626	−	0.968600i	$-0.420021\pi$
$613$	23.4774	−	6.29074i	0.948242	−	0.254081i	0.699616	+	0.714519i	$0.253354\pi$
$614$			2.83317i			0.114337i
$615$	−7.24909	+	12.5558i	−0.292311	+	0.506298i
$616$	8.69567	+	10.2178i	0.350359	+	0.411687i
$617$	−6.04046	+	1.61854i	−0.243180	+	0.0651599i	−0.378350	−	0.925663i	$-0.623509\pi$
$617$	−6.04046	+	1.61854i	−0.243180	+	0.0651599i	0.135170	+	0.990822i	$0.456842\pi$
$618$	6.81029	+	1.82481i	0.273950	+	0.0734047i
$619$	−5.04055	+	18.8116i	−0.202597	+	0.756102i	0.787572	+	0.616223i	$0.211338\pi$
$619$	−5.04055	+	18.8116i	−0.202597	+	0.756102i	−0.990169	+	0.139879i	$0.955329\pi$
$620$	−16.6668			−0.669357
$621$	5.43264			0.218004
$622$	−5.41632	+	20.2140i	−0.217174	+	0.810506i
$623$	7.26285	+	15.2963i	0.290980	+	0.612835i
$624$	−3.31255	+	1.42373i	−0.132608	+	0.0569948i
$625$	23.7806	−	41.1893i	0.951226	−	1.64757i
$626$	−6.65447	−	24.8348i	−0.265966	−	0.992598i
$627$	3.67970	−	6.37343i	0.146953	−	0.254530i
$628$	11.2346	+	19.4589i	0.448310	+	0.776496i
$629$	2.74157	−	2.74157i	0.109314	−	0.109314i
$630$	−10.0867	−	3.59194i	−0.401863	−	0.143106i
$631$	−2.64586	−	9.87448i	−0.105330	−	0.393097i	0.893052	−	0.449953i	$-0.148559\pi$
$631$	−2.64586	−	9.87448i	−0.105330	−	0.393097i	−0.998382	+	0.0568558i	$0.981892\pi$
$632$	0.688065	+	2.56789i	0.0273697	+	0.102145i
$633$		−	3.39708i		−	0.135022i
$634$	−28.1948	−	16.2783i	−1.11976	−	0.646492i
$635$	−40.5579	−	40.5579i	−1.60949	−	1.60949i
$636$	−4.16896			−0.165310
$637$	24.4832	−	6.12959i	0.970061	−	0.242863i
$638$	−43.0529			−1.70448
$639$	−3.13686	−	3.13686i	−0.124092	−	0.124092i
$640$	3.50474	+	2.02346i	0.138537	+	0.0799843i
$641$			12.7428i			0.503310i	0.967817	+	0.251655i	$0.0809749\pi$
$641$			12.7428i			0.503310i	−0.967817	+	0.251655i	$0.919025\pi$
$642$	−2.05398	−	7.66555i	−0.0810641	−	0.302535i
$643$	0.166808	+	0.622537i	0.00657828	+	0.0245505i	0.969137	−	0.246523i	$-0.0792881\pi$
$643$	0.166808	+	0.622537i	0.00657828	+	0.0245505i	−0.962559	+	0.271073i	$0.912621\pi$
$644$	13.5405	+	4.82187i	0.533570	+	0.190008i
$645$	−27.9447	+	27.9447i	−1.10032	+	1.10032i
$646$	−3.60072	−	6.23664i	−0.141669	−	0.245377i
$647$	−8.41643	+	14.5777i	−0.330884	+	0.573108i	−0.982685	−	0.185282i	$-0.940680\pi$
$647$	−8.41643	+	14.5777i	−0.330884	+	0.573108i	0.651801	+	0.758390i	$0.274014\pi$
$648$	−0.258819	−	0.965926i	−0.0101674	−	0.0379452i
$649$	−2.37182	+	4.10812i	−0.0931022	+	0.161258i
$650$	−32.2121	+	25.4012i	−1.26346	+	0.996317i
$651$	4.67359	+	9.84308i	0.183172	+	0.385781i
$652$	−0.197631	+	0.737570i	−0.00773984	+	0.0288855i
$653$	−7.20923			−0.282119			−0.141060	−	0.990001i	$-0.545051\pi$
$653$	−7.20923			−0.282119			−0.141060	+	0.990001i	$0.545051\pi$
$654$	−2.87280			−0.112335
$655$	−10.4102	+	38.8515i	−0.406762	+	1.51805i
$656$	−3.46045	−	0.927225i	−0.135108	−	0.0362020i
$657$	12.8347	−	3.43906i	0.500731	−	0.134170i
$658$	−5.04354	−	5.92639i	−0.196618	−	0.231035i
$659$	4.22306	−	7.31455i	0.164507	−	0.284934i	−0.771973	−	0.635655i	$-0.780730\pi$
$659$	4.22306	−	7.31455i	0.164507	−	0.284934i	0.936480	+	0.350721i	$0.114063\pi$
$660$			20.5227i			0.798844i
$661$	−2.48435	+	0.665680i	−0.0966301	+	0.0258920i	−0.306810	−	0.951771i	$-0.599262\pi$
$661$	−2.48435	+	0.665680i	−0.0966301	+	0.0258920i	0.210180	+	0.977663i	$0.432595\pi$
$662$	15.7582	−	9.09802i	0.612461	−	0.353605i
$663$	−16.4380	+	7.06503i	−0.638399	+	0.274383i
$664$		−	1.44779i		−	0.0561853i
$665$	−5.21269	+	14.6380i	−0.202139	+	0.567637i
$666$	−0.390659	−	0.676641i	−0.0151377	−	0.0262193i
$667$	−39.9424	+	23.0608i	−1.54658	+	0.892917i
$668$	0.0141038	+	0.00377911i	0.000545694	+	0.000146218i
$669$	−13.6600	−	13.6600i	−0.528126	−	0.528126i
$670$	9.63330	−	35.9520i	0.372167	−	1.38895i
$671$	43.4196	+	43.4196i	1.67620	+	1.67620i
$672$	0.212241	−	2.63722i	0.00818737	−	0.101733i
$673$	−12.2144	+	7.05201i	−0.470832	+	0.271835i	−0.716588	−	0.697497i	$-0.754297\pi$
$673$	−12.2144	+	7.05201i	−0.470832	+	0.271835i	0.245756	+	0.969332i	$0.420964\pi$
$674$	4.26227	−	4.26227i	0.164177	−	0.164177i
$675$	−5.68879	−	9.85327i	−0.218961	−	0.379252i
$676$	12.4636	−	3.69566i	0.479370	−	0.142141i
$677$	6.31593	+	3.64650i	0.242741	+	0.140146i	0.616436	−	0.787405i	$-0.288576\pi$
$677$	6.31593	+	3.64650i	0.242741	+	0.140146i	−0.373695	+	0.927552i	$0.621909\pi$
$678$	−9.17439	−	2.45827i	−0.352340	−	0.0944094i
$679$	2.15134	−	26.7318i	0.0825610	−	1.02587i
$680$	17.3917	+	10.0411i	0.666941	+	0.385059i
$681$	−0.675293	+	0.180944i	−0.0258773	+	0.00693380i
$682$	14.7680	−	14.7680i	0.565498	−	0.565498i
$683$	32.9710	−	32.9710i	1.26160	−	1.26160i	0.311281	−	0.950318i	$-0.399242\pi$
$683$	32.9710	−	32.9710i	1.26160	−	1.26160i	0.950318	−	0.311281i	$-0.100758\pi$
$684$	−1.40177	+	0.375603i	−0.0535980	+	0.0143616i
$685$	−61.9118	−	35.7448i	−2.36553	−	1.36574i
$686$	−4.41881	+	17.9854i	−0.168711	+	0.686685i
$687$	−13.8280	−	3.70519i	−0.527570	−	0.141362i
$688$	−8.45709	−	4.88270i	−0.322424	−	0.186151i
$689$	14.9275	+	1.76468i	0.568691	+	0.0672290i
$690$	10.9927	+	19.0400i	0.418486	+	0.724840i
$691$	20.5970	−	20.5970i	0.783545	−	0.783545i	−0.196882	−	0.980427i	$-0.563082\pi$
$691$	20.5970	−	20.5970i	0.783545	−	0.783545i	0.980427	+	0.196882i	$0.0630815\pi$
$692$	−6.26529	+	3.61727i	−0.238170	+	0.137508i
$693$	12.1203	−	5.75481i	0.460410	−	0.218607i
$694$	21.3572	+	21.3572i	0.810710	+	0.810710i
$695$	−13.3871	+	49.9612i	−0.507800	+	1.89514i
$696$	6.00313	+	6.00313i	0.227548	+	0.227548i
$697$	−17.1719	−	4.60120i	−0.650433	−	0.174283i
$698$	−15.6033	+	9.00857i	−0.590593	+	0.340979i
$699$	−8.48375	−	14.6943i	−0.320885	−	0.555789i
$700$	−5.43342	−	29.6078i	−0.205364	−	1.11907i
$701$			52.2166i			1.97219i	0.166172	+	0.986097i	$0.446859\pi$
$701$			52.2166i			1.97219i	−0.166172	+	0.986097i	$0.553141\pi$
$702$	0.517865	+	3.56817i	0.0195456	+	0.134672i
$703$	−0.981955	+	0.566932i	−0.0370351	+	0.0213822i
$704$	−4.89839	+	1.31252i	−0.184615	+	0.0494674i
$705$		−	11.9033i		−	0.448304i
$706$	−0.838610	+	1.45252i	−0.0315615	+	0.0546661i
$707$	7.90903	−	6.73083i	0.297450	−	0.253139i
$708$	0.903539	−	0.242102i	0.0339571	−	0.00909877i
$709$	9.96077	+	2.66898i	0.374084	+	0.100236i	0.440963	−	0.897526i	$-0.354637\pi$
$709$	9.96077	+	2.66898i	0.374084	+	0.100236i	−0.0668780	+	0.997761i	$0.521304\pi$
$710$	4.64656	−	17.3412i	0.174382	−	0.650803i
$711$	2.65848			0.0997007
$712$	−6.40008			−0.239853
$713$	5.79077	−	21.6114i	0.216866	−	0.809355i
$714$	1.05321	−	13.0868i	0.0394154	−	0.489762i
$715$	8.68706	−	73.4839i	0.324878	−	2.74814i
$716$	−8.06082	+	13.9618i	−0.301247	+	0.521775i
$717$	−3.99622	−	14.9141i	−0.149242	−	0.556978i
$718$	0.111049	−	0.192342i	0.00414431	−	0.00717816i
$719$	−12.0706	−	20.9070i	−0.450159	−	0.779698i	0.548237	−	0.836323i	$-0.315299\pi$
$719$	−12.0706	−	20.9070i	−0.450159	−	0.779698i	−0.998396	+	0.0566252i	$0.981966\pi$
$720$	2.86161	−	2.86161i	0.106646	−	0.106646i
$721$	14.2059	−	12.0897i	0.529057	−	0.450244i
$722$	−4.37248	−	16.3183i	−0.162727	−	0.607305i
$723$	−0.0901532	−	0.336456i	−0.00335283	−	0.0125129i
$724$		−	6.35633i		−	0.236231i
$725$	83.6514	+	48.2962i	3.10673	+	1.79367i
$726$	−10.4064	−	10.4064i	−0.386219	−	0.386219i
$727$	−50.2420			−1.86337			−0.931686	−	0.363265i	$-0.881662\pi$
$727$	−50.2420			−1.86337			−0.931686	+	0.363265i	$0.881662\pi$
$728$	−1.87627	+	9.35305i	−0.0695390	+	0.346647i
$729$	−1.00000			−0.0370370
$730$	38.0236	+	38.0236i	1.40732	+	1.40732i
$731$	−41.9670	−	24.2296i	−1.55220	−	0.896166i
$732$		−	12.1085i		−	0.447545i
$733$	−6.17205	−	23.0344i	−0.227970	−	0.850796i	−0.981193	−	0.193030i	$-0.938168\pi$
$733$	−6.17205	−	23.0344i	−0.227970	−	0.850796i	0.753223	−	0.657765i	$-0.228498\pi$
$734$	2.18422	+	8.15161i	0.0806209	+	0.300881i
$735$	−22.9769	+	16.5700i	−0.847514	+	0.611193i
$736$	−3.84146	+	3.84146i	−0.141598	+	0.141598i
$737$	23.3203	+	40.3919i	0.859013	+	1.48785i
$738$	−1.79126	+	3.10255i	−0.0659372	+	0.114207i
$739$	−10.5865	−	39.5095i	−0.389432	−	1.45338i	−0.831061	−	0.556182i	$-0.812266\pi$
$739$	−10.5865	−	39.5095i	−0.389432	−	1.45338i	0.441629	−	0.897198i	$-0.354401\pi$
$740$	1.58097	−	2.73831i	0.0581175	−	0.100662i
$741$	5.17819	−	0.751536i	0.190226	−	0.0276084i
$742$	−6.26352	+	9.07910i	−0.229941	+	0.333304i
$743$	−4.35552	+	16.2550i	−0.159789	+	0.596339i	0.838859	+	0.544349i	$0.183223\pi$
$743$	−4.35552	+	16.2550i	−0.159789	+	0.596339i	−0.998648	+	0.0519903i	$0.983443\pi$
$744$	−4.11840			−0.150988
$745$	47.2063			1.72950
$746$	−2.66202	+	9.93480i	−0.0974636	+	0.363739i
$747$	−1.39846	−	0.374717i	−0.0511670	−	0.0137102i
$748$	−24.3075	+	6.51317i	−0.888769	+	0.238145i
$749$	−19.7798	−	7.04375i	−0.722740	−	0.257373i
$750$	12.9048	−	22.3517i	0.471215	−	0.816169i
$751$		−	18.5938i		−	0.678496i	−0.940697	−	0.339248i	$-0.889827\pi$
$751$		−	18.5938i		−	0.678496i	0.940697	−	0.339248i	$-0.110173\pi$
$752$	2.84109	−	0.761269i	0.103604	−	0.0277606i
$753$	−0.463770	+	0.267758i	−0.0169007	+	0.00975763i
$754$	−18.9539	−	24.0360i	−0.690259	−	0.875339i
$755$			67.1821i			2.44501i
$756$	−2.49243	−	0.887573i	−0.0906489	−	0.0322807i
$757$	24.4862	+	42.4113i	0.889964	+	1.54146i	0.839916	+	0.542717i	$0.182604\pi$
$757$	24.4862	+	42.4113i	0.889964	+	1.54146i	0.0500485	+	0.998747i	$0.484062\pi$
$758$	20.1700	−	11.6452i	0.732609	−	0.422972i
$759$	−26.6112	−	7.13045i	−0.965925	−	0.258819i
$760$	−4.15282	−	4.15282i	−0.150639	−	0.150639i
$761$	−11.5453	+	43.0875i	−0.418515	+	1.56192i	0.359174	+	0.933270i	$0.383058\pi$
$761$	−11.5453	+	43.0875i	−0.418515	+	1.56192i	−0.777689	+	0.628649i	$0.783608\pi$
$762$	−10.0219	−	10.0219i	−0.363056	−	0.363056i
$763$	−4.31614	+	6.25633i	−0.156255	+	0.226494i
$764$	−18.0461	+	10.4189i	−0.652886	+	0.376944i
$765$	14.2003	−	14.2003i	0.513412	−	0.513412i
$766$	−3.85399	−	6.67530i	−0.139250	−	0.241188i
$767$	−3.33771	+	0.484417i	−0.120518	+	0.0174913i
$768$	0.866025	+	0.500000i	0.0312500	+	0.0180422i
$769$	17.1234	+	4.58821i	0.617487	+	0.165455i	0.553985	−	0.832527i	$-0.313106\pi$
$769$	17.1234	+	4.58821i	0.617487	+	0.165455i	0.0635019	+	0.997982i	$0.479773\pi$
$770$	44.6940	+	30.8337i	1.61066	+	1.11117i
$771$	18.3934	+	10.6194i	0.662422	+	0.382449i
$772$	10.3768	−	2.78045i	0.373468	−	0.100071i
$773$	5.72064	−	5.72064i	0.205757	−	0.205757i	−0.596704	−	0.802461i	$-0.703523\pi$
$773$	5.72064	−	5.72064i	0.205757	−	0.205757i	0.802461	+	0.596704i	$0.203523\pi$
$774$	−6.90519	+	6.90519i	−0.248202	+	0.248202i
$775$	−45.2608	+	12.1276i	−1.62582	+	0.435636i
$776$	8.77832	+	5.06816i	0.315123	+	0.181936i
$777$	−2.06051	−	0.165828i	−0.0739204	−	0.00594903i
$778$	25.4308	+	6.81416i	0.911738	+	0.244299i
$779$	4.50249	+	2.59951i	0.161318	+	0.0931372i
$780$	−11.4576	+	9.03503i	−0.410248	+	0.323506i
$781$	11.2484	+	19.4827i	0.402498	+	0.697147i
$782$	−19.0626	+	19.0626i	−0.681678	+	0.681678i
$783$	7.35231	−	4.24486i	0.262750	−	0.151699i
$784$	−5.42443	−	4.42443i	−0.193730	−	0.158015i
$785$	64.2981	+	64.2981i	2.29490	+	2.29490i
$786$	−2.57238	+	9.60027i	−0.0917539	+	0.342430i
$787$	20.3065	+	20.3065i	0.723849	+	0.723849i	0.969387	−	0.245538i	$-0.0789647\pi$
$787$	20.3065	+	20.3065i	0.723849	+	0.723849i	−0.245538	+	0.969387i	$0.578965\pi$
$788$	11.3702	+	3.04663i	0.405046	+	0.108532i
$789$	10.7660	−	6.21578i	0.383281	−	0.221288i
$790$	5.37932	+	9.31726i	0.191388	+	0.331493i
$791$	−19.1374	+	16.2865i	−0.680446	+	0.579081i
$792$			5.07118i			0.180197i
$793$	−5.12543	+	43.3561i	−0.182009	+	1.53962i
$794$	−9.05417	+	5.22743i	−0.321320	+	0.185514i
$795$	−16.2966	+	4.36666i	−0.577980	+	0.154869i
$796$		−	19.4226i		−	0.688417i
$797$	−8.46866	+	14.6682i	−0.299975	+	0.519573i	−0.976130	−	0.217187i	$-0.930312\pi$
$797$	−8.46866	+	14.6682i	−0.299975	+	0.519573i	0.676155	+	0.736760i	$0.263645\pi$
$798$	−1.28806	+	3.61707i	−0.0455969	+	0.128043i
$799$	14.0985	−	3.77768i	0.498768	−	0.133645i
$800$	10.9899	+	2.94473i	0.388551	+	0.104112i
$801$	−1.65646	+	6.18200i	−0.0585282	+	0.218430i
$802$	−10.2545			−0.362099
$803$	−67.3833			−2.37791
$804$	2.38040	−	8.88378i	0.0839503	−	0.313307i
$805$	57.9806	+	4.66622i	2.04355	+	0.164462i
$806$	14.7464	+	1.74328i	0.519421	+	0.0614044i
$807$	5.02137	−	8.69727i	0.176761	−	0.306158i
$808$	1.01595	+	3.79157i	0.0357409	+	0.133387i
$809$	−22.2160	+	38.4792i	−0.781072	+	1.35286i	0.150246	+	0.988649i	$0.451993\pi$
$809$	−22.2160	+	38.4792i	−0.781072	+	1.35286i	−0.931318	+	0.364208i	$0.881340\pi$
$810$	−2.02346	−	3.50474i	−0.0710972	−	0.123144i
$811$	−8.45727	+	8.45727i	−0.296975	+	0.296975i	−0.839828	−	0.542853i	$-0.817344\pi$
$811$	−8.45727	+	8.45727i	−0.296975	+	0.296975i	0.542853	+	0.839828i	$0.317344\pi$
$812$	22.0927	−	4.05430i	0.775303	−	0.142278i
$813$	5.01468	+	18.7150i	0.175873	+	0.656365i
$814$	1.02549	+	3.82720i	0.0359436	+	0.134143i
$815$			3.09019i			0.108244i
$816$	4.29751	+	2.48117i	0.150443	+	0.0868583i
$817$	10.0209	+	10.0209i	0.350588	+	0.350588i
$818$	15.5883			0.545031
$819$	8.54874	+	4.23308i	0.298717	+	0.147916i
$820$	−14.4982			−0.506298
$821$	−7.21936	−	7.21936i	−0.251957	−	0.251957i	0.569815	−	0.821773i	$-0.307015\pi$
$821$	−7.21936	−	7.21936i	−0.251957	−	0.251957i	−0.821773	+	0.569815i	$0.807015\pi$
$822$	−15.2985	−	8.83258i	−0.533596	−	0.308072i
$823$			6.11047i			0.212998i	0.994313	+	0.106499i	$0.0339640\pi$
$823$			6.11047i			0.212998i	−0.994313	+	0.106499i	$0.966036\pi$
$824$	1.82481	+	6.81029i	0.0635703	+	0.237248i
$825$	14.9333	+	55.7318i	0.519910	+	1.94033i
$826$	0.830246	−	2.33145i	0.0288880	−	0.0811215i
$827$	10.6347	−	10.6347i	0.369805	−	0.369805i	−0.497601	−	0.867406i	$-0.665786\pi$
$827$	10.6347	−	10.6347i	0.369805	−	0.369805i	0.867406	+	0.497601i	$0.165786\pi$
$828$	2.71632	+	4.70481i	0.0943987	+	0.163503i
$829$	23.5052	−	40.7122i	0.816369	−	1.41399i	−0.0919723	−	0.995762i	$-0.529317\pi$
$829$	23.5052	−	40.7122i	0.816369	−	1.41399i	0.908341	−	0.418230i	$-0.137350\pi$
$830$	−1.51645	−	5.65946i	−0.0526367	−	0.196443i
$831$	−11.1689	+	19.3451i	−0.387444	+	0.671073i
$832$	−2.88926	−	2.15689i	−0.100167	−	0.0747767i
$833$	−26.9179	−	21.9555i	−0.932649	−	0.760714i
$834$	−3.30796	+	12.3455i	−0.114545	+	0.427489i
$835$	0.0590906			0.00204491
$836$	7.35940			0.254530
$837$	−1.06592	+	3.97807i	−0.0368436	+	0.137502i
$838$	16.4725	+	4.41380i	0.569034	+	0.152472i
$839$	46.1618	−	12.3690i	1.59368	−	0.427026i	0.650556	−	0.759458i	$-0.274536\pi$
$839$	46.1618	−	12.3690i	1.59368	−	0.427026i	0.943127	+	0.332432i	$0.107869\pi$
$840$	−1.93263	−	10.5313i	−0.0666820	−	0.363364i
$841$	−21.5376	+	37.3042i	−0.742676	+	1.28635i
$842$		−	31.7855i		−	1.09540i
$843$	−26.4583	+	7.08947i	−0.911272	+	0.244174i
$844$	2.94196	−	1.69854i	0.101266	−	0.0584662i
$845$	44.8498	−	27.5011i	1.54288	−	0.946066i
$846$		−	2.94132i		−	0.101125i
$847$	−38.2978	+	7.02814i	−1.31593	+	0.241490i
$848$	−2.08448	−	3.61043i	−0.0715814	−	0.123983i
$849$	−9.67632	+	5.58662i	−0.332090	+	0.191732i
$850$	54.5356	+	14.6128i	1.87056	+	0.501214i
$851$	3.00140	+	3.00140i	0.102887	+	0.102887i
$852$	1.14817	−	4.28503i	0.0393357	−	0.146803i
$853$	27.3996	+	27.3996i	0.938143	+	0.938143i	0.998195	−	0.0600519i	$-0.0191266\pi$
$853$	27.3996	+	27.3996i	0.938143	+	0.938143i	−0.0600519	+	0.998195i	$0.519127\pi$
$854$	−26.3698	−	18.1921i	−0.902355	−	0.622521i
$855$	−5.08614	+	2.93649i	−0.173942	+	0.100426i
$856$	5.61157	−	5.61157i	0.191800	−	0.191800i
$857$	24.0598	+	41.6729i	0.821869	+	1.42352i	0.904289	+	0.426921i	$0.140402\pi$
$857$	24.0598	+	41.6729i	0.821869	+	1.42352i	−0.0824204	+	0.996598i	$0.526265\pi$
$858$	2.14658	−	18.1580i	0.0732832	−	0.619903i
$859$	39.5475	+	22.8327i	1.34934	+	0.779043i	0.988156	−	0.153451i	$-0.0490387\pi$
$859$	39.5475	+	22.8327i	1.34934	+	0.779043i	0.361186	+	0.932494i	$0.382372\pi$
$860$	−38.1732	−	10.2285i	−1.30170	−	0.348789i
$861$	4.06547	+	8.56231i	0.138551	+	0.291803i
$862$	−23.3049	−	13.4551i	−0.793769	−	0.458283i
$863$	−24.9708	+	6.69091i	−0.850016	+	0.227761i	−0.657427	−	0.753518i	$-0.728355\pi$
$863$	−24.9708	+	6.69091i	−0.850016	+	0.227761i	−0.192589	+	0.981279i	$0.561688\pi$
$864$	0.707107	−	0.707107i	0.0240563	−	0.0240563i
$865$	−20.7024	+	20.7024i	−0.703902	+	0.703902i
$866$	−21.0264	+	5.63401i	−0.714506	+	0.191451i
$867$	6.60330	+	3.81242i	0.224260	+	0.129476i
$868$	−6.18756	+	8.96898i	−0.210020	+	0.304427i
$869$	−13.0223	−	3.48930i	−0.441750	−	0.118366i
$870$	29.7542	+	17.1786i	1.00876	+	0.582409i
$871$	−12.2837	+	30.8018i	−0.416218	+	1.04368i
$872$	−1.43640	−	2.48792i	−0.0486426	−	0.0842515i
$873$	7.16747	−	7.16747i	0.242582	−	0.242582i
$874$	6.82771	−	3.94198i	0.230951	−	0.133339i
$875$	−29.2888	−	61.6854i	−0.990143	−	2.08535i
$876$	9.39568	+	9.39568i	0.317450	+	0.317450i
$877$	−0.298652	+	1.11459i	−0.0100848	+	0.0376369i	−0.970785	−	0.239951i	$-0.922868\pi$
$877$	−0.298652	+	1.11459i	−0.0100848	+	0.0376369i	0.960700	+	0.277588i	$0.0895351\pi$
$878$	−1.17057	−	1.17057i	−0.0395048	−	0.0395048i
$879$	19.1845	+	5.14048i	0.647079	+	0.173384i
$880$	−17.7732	+	10.2613i	−0.599133	+	0.345910i
$881$	−15.2953	−	26.4923i	−0.515312	−	0.892547i	−0.999842	−	0.0177724i	$-0.994343\pi$
$881$	−15.2953	−	26.4923i	−0.515312	−	0.892547i	0.484530	−	0.874775i	$-0.338991\pi$
$882$	−5.67762	+	4.09447i	−0.191175	+	0.137868i
$883$		−	7.60820i		−	0.256036i	−0.991772	−	0.128018i	$-0.959138\pi$
$883$		−	7.60820i		−	0.256036i	0.991772	−	0.128018i	$-0.0408616\pi$
$884$	−14.3375	−	10.7032i	−0.482222	−	0.359988i
$885$	3.27837	−	1.89277i	0.110201	−	0.0636248i
$886$	−28.4152	+	7.61382i	−0.954626	+	0.255791i
$887$			21.4217i			0.719270i	0.933093	+	0.359635i	$0.117099\pi$
$887$			21.4217i			0.719270i	−0.933093	+	0.359635i	$0.882901\pi$
$888$	0.390659	−	0.676641i	0.0131097	−	0.0227066i
$889$	−36.8827	+	6.76845i	−1.23701	+	0.227007i
$890$	−25.0181	+	6.70357i	−0.838608	+	0.224704i
$891$	4.89839	+	1.31252i	0.164102	+	0.0439710i
$892$	4.99990	−	18.6599i	0.167409	−	0.624779i
$893$	−4.26850			−0.142840
$894$	11.6647			0.390127
$895$	−16.8861	+	63.0199i	−0.564441	+	2.10652i
$896$	2.39002	−	1.13481i	0.0798451	−	0.0379112i
$897$	−7.73461	−	17.9959i	−0.258251	−	0.600866i
$898$	17.2266	−	29.8373i	0.574857	−	0.995682i
$899$	−9.04936	−	33.7727i	−0.301813	−	1.12638i
$900$	5.68879	−	9.85327i	0.189626	−	0.328442i
$901$	−10.3439	−	17.9162i	−0.344605	−	0.596874i
$902$	12.8464	−	12.8464i	0.427740	−	0.427740i
$903$	4.66352	+	25.4125i	0.155192	+	0.845674i
$904$	−2.45827	−	9.17439i	−0.0817609	−	0.305136i
$905$	−6.65775	−	24.8471i	−0.221311	−	0.825944i
$906$			16.6008i			0.551524i
$907$	24.9248	+	14.3904i	0.827615	+	0.477824i	0.853035	−	0.521853i	$-0.174759\pi$
$907$	24.9248	+	14.3904i	0.827615	+	0.477824i	−0.0254203	+	0.999677i	$0.508092\pi$
$908$	−0.494349	−	0.494349i	−0.0164056	−	0.0164056i
$909$	3.92532			0.130195
$910$	2.46221	+	38.5266i	0.0816214	+	1.27714i
$911$	13.0247			0.431529			0.215764	−	0.976445i	$-0.430776\pi$
$911$	13.0247			0.431529			0.215764	+	0.976445i	$0.430776\pi$
$912$	−1.02617	−	1.02617i	−0.0339798	−	0.0339798i
$913$	6.35839	+	3.67102i	0.210432	+	0.121493i
$914$			1.05348i			0.0348461i
$915$	−12.6827	−	47.3326i	−0.419278	−	1.56477i
$916$	−3.70519	−	13.8280i	−0.122423	−	0.456889i
$917$	17.0425	+	20.0257i	0.562793	+	0.661307i
$918$	3.50891	−	3.50891i	0.115811	−	0.115811i
$919$	−27.7681	−	48.0958i	−0.915986	−	1.58653i	−0.805451	−	0.592663i	$-0.798077\pi$
$919$	−27.7681	−	48.0958i	−0.915986	−	1.58653i	−0.110536	−	0.993872i	$-0.535257\pi$
$920$	−10.9927	+	19.0400i	−0.362420	+	0.627730i
$921$	0.733279	+	2.73663i	0.0241624	+	0.0901751i
$922$	9.89949	−	17.1464i	0.326022	−	0.564687i
$923$	−5.92497	+	14.8570i	−0.195023	+	0.489026i
$924$	11.0439	+	7.61904i	0.363319	+	0.250648i
$925$	2.30077	−	8.58660i	0.0756489	−	0.282326i
$926$	1.86137			0.0611683
$927$	7.05053			0.231570
$928$	−2.19730	+	8.20043i	−0.0721299	+	0.269192i
$929$	26.6859	+	7.15046i	0.875536	+	0.234599i	0.668480	−	0.743730i	$-0.266945\pi$
$929$	26.6859	+	7.15046i	0.875536	+	0.234599i	0.207056	+	0.978329i	$0.433612\pi$
$930$	−16.0989	+	4.31370i	−0.527905	+	0.141452i
$931$	5.94197	+	8.23947i	0.194740	+	0.270038i
$932$	8.48375	−	14.6943i	0.277894	−	0.481327i
$933$			20.9270i			0.685121i
$934$	−21.8520	+	5.85523i	−0.715020	+	0.191589i
$935$	−88.1965	+	50.9203i	−2.88433	+	1.66527i
$936$	−2.83119	+	2.23257i	−0.0925404	+	0.0729738i
$937$			3.19610i			0.104412i	0.998636	+	0.0522060i	$0.0166253\pi$
$937$			3.19610i			0.104412i	−0.998636	+	0.0522060i	$0.983375\pi$
$938$	−15.7706	−	18.5311i	−0.514928	−	0.605063i
$939$	−12.8554	−	22.2663i	−0.419521	−	0.726632i
$940$	10.3085	−	5.95164i	0.336228	−	0.194121i
$941$	−15.6799	−	4.20141i	−0.511149	−	0.136962i	−0.00597943	−	0.999982i	$-0.501903\pi$
$941$	−15.6799	−	4.20141i	−0.511149	−	0.136962i	−0.505169	+	0.863020i	$0.668570\pi$
$942$	15.8881	+	15.8881i	0.517664	+	0.517664i
$943$	5.03728	−	18.7994i	0.164036	−	0.612192i
$944$	0.661436	+	0.661436i	0.0215279	+	0.0215279i
$945$	−10.6726	−	0.858922i	−0.347181	−	0.0279407i
$946$	42.8875	−	24.7611i	1.39439	−	0.805053i
$947$	6.50608	−	6.50608i	0.211419	−	0.211419i	−0.593451	−	0.804870i	$-0.702235\pi$
$947$	6.50608	−	6.50608i	0.211419	−	0.211419i	0.804870	+	0.593451i	$0.202235\pi$
$948$	1.32924	+	2.30231i	0.0431717	+	0.0747755i
$949$	−29.6652	−	37.6194i	−0.962974	−	1.22118i
$950$	−14.2993	−	8.25568i	−0.463929	−	0.267850i
$951$	−31.4472	−	8.42624i	−1.01974	−	0.273240i
$952$	11.8601	−	5.63130i	0.384389	−	0.182511i
$953$	−13.0704	−	7.54618i	−0.423391	−	0.244445i	0.273136	−	0.961975i	$-0.411939\pi$
$953$	−13.0704	−	7.54618i	−0.423391	−	0.244445i	−0.696527	+	0.717531i	$0.745272\pi$
$954$	−4.02691	+	1.07901i	−0.130376	+	0.0349341i
$955$	−59.6298	+	59.6298i	−1.92957	+	1.92957i
$956$	10.9179	−	10.9179i	0.353110	−	0.353110i
$957$	−41.5859	+	11.1429i	−1.34428	+	0.360199i
$958$	22.5476	+	13.0179i	0.728481	+	0.420589i
$959$	−42.2202	+	20.0465i	−1.36336	+	0.647337i
$960$	3.90903	+	1.04742i	0.126163	+	0.0338053i
$961$	−12.1579	−	7.01939i	−0.392191	−	0.226432i
$962$	−1.68522	+	2.25743i	−0.0543335	+	0.0727825i
$963$	−3.96798	−	6.87275i	−0.127866	−	0.221471i
$964$	0.246303	−	0.246303i	0.00793289	−	0.00793289i
$965$	37.6508	−	21.7377i	1.21202	−	0.699761i
$966$	14.3271	+	1.15303i	0.460967	+	0.0370981i
$967$	39.3450	+	39.3450i	1.26525	+	1.26525i	0.948514	+	0.316735i	$0.102587\pi$
$967$	39.3450	+	39.3450i	1.26525	+	1.26525i	0.316735	+	0.948514i	$0.397413\pi$
$968$	3.80902	−	14.2154i	0.122426	−	0.456902i
$969$	−5.09219	−	5.09219i	−0.163585	−	0.163585i
$970$	39.6232	+	10.6170i	1.27222	+	0.340891i
$971$	33.8550	−	19.5462i	1.08646	−	0.627267i	0.153827	−	0.988098i	$-0.450840\pi$
$971$	33.8550	−	19.5462i	1.08646	−	0.627267i	0.932631	+	0.360831i	$0.117507\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	21.9158	+	25.7521i	0.702590	+	0.825575i
$974$			2.69607i			0.0863877i
$975$	−24.5402	+	32.8728i	−0.785914	+	1.05277i
$976$	10.4863	−	6.05427i	0.335658	−	0.193792i
$977$	6.69510	−	1.79395i	0.214195	−	0.0573935i	−0.150126	−	0.988667i	$-0.547968\pi$
$977$	6.69510	−	1.79395i	0.214195	−	0.0573935i	0.364321	+	0.931273i	$0.381301\pi$
$978$			0.763589i			0.0244169i
$979$	16.2280	−	28.1077i	0.518649	−	0.898326i
$980$	−25.8385	−	11.6136i	−0.825380	−	0.370981i
$981$	−2.77491	+	0.743535i	−0.0885960	+	0.0237392i
$982$	30.2059	+	8.09365i	0.963910	+	0.258279i
$983$	−0.442972	+	1.65319i	−0.0141286	+	0.0527287i	−0.972630	−	0.232358i	$-0.925356\pi$
$983$	−0.442972	+	1.65319i	−0.0141286	+	0.0527287i	0.958502	+	0.285087i	$0.0920225\pi$
$984$	−3.58252			−0.114207
$985$	47.6374			1.51785
$986$	−10.9037	+	40.6933i	−0.347246	+	1.29594i
$987$	−6.40555	−	4.41909i	−0.203891	−	0.140661i
$988$	3.23995	+	4.10868i	0.103076	+	0.130715i
$989$	26.5260	−	45.9444i	0.843477	−	1.46095i
$990$	5.31166	+	19.8234i	0.168816	+	0.630029i
$991$	14.1382	−	24.4881i	0.449115	−	0.777890i	−0.549214	−	0.835682i	$-0.685073\pi$
$991$	14.1382	−	24.4881i	0.449115	−	0.777890i	0.998329	+	0.0577920i	$0.0184060\pi$
$992$	−2.05920	−	3.56664i	−0.0653797	−	0.113241i
$993$	12.8665	−	12.8665i	0.408307	−	0.408307i
$994$	−7.60683	−	8.93837i	−0.241274	−	0.283508i
$995$	−20.3436	−	75.9235i	−0.644937	−	2.40694i
$996$	−0.374717	−	1.39846i	−0.0118734	−	0.0443120i
$997$		−	0.0426085i		−	0.00134943i	−1.00000		0.000674713i	$-0.999785\pi$
$997$		−	0.0426085i		−	0.00134943i	1.00000		0.000674713i	$-0.000214768\pi$
$998$	−2.27595	−	1.31402i	−0.0720438	−	0.0415945i
$999$	−0.552475	−	0.552475i	−0.0174795	−	0.0174795i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.cg.b.271.10	yes	40
7.3	odd	6		546.2.by.b.115.5	yes	40
13.6	odd	12		546.2.by.b.19.5	✓	40
91.45	even	12	inner	546.2.cg.b.409.10	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.5	✓	40	13.6	odd	12
546.2.by.b.115.5	yes	40	7.3	odd	6
546.2.cg.b.271.10	yes	40	1.1	even	1	trivial
546.2.cg.b.409.10	yes	40	91.45	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.cg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(1.04742 + 3.90903i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.49243 + 0.887573i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +(0.866025 + 0.500000i) q^{3} +1.00000i q^{4} +(1.04742 + 3.90903i) q^{5} +(0.258819 + 0.965926i) q^{6} +(2.49243 + 0.887573i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(0.500000 + 0.866025i) q^{9} +(-2.02346 + 3.50474i) q^{10} +(-1.31252 - 4.89839i) q^{11} +(-0.500000 + 0.866025i) q^{12} +(2.15689 - 2.88926i) q^{13} +(1.13481 + 2.39002i) q^{14} +(-1.04742 + 3.90903i) q^{15} -1.00000 q^{16} -4.96234 q^{17} +(-0.258819 + 0.965926i) q^{18} +(1.40177 + 0.375603i) q^{19} +(-3.90903 + 1.04742i) q^{20} +(1.71472 + 2.01488i) q^{21} +(2.53559 - 4.39177i) q^{22} -5.43264i q^{23} +(-0.965926 + 0.258819i) q^{24} +(-9.85327 + 5.68879i) q^{25} +(3.56817 - 0.517865i) q^{26} +1.00000i q^{27} +(-0.887573 + 2.49243i) q^{28} +(-4.24486 - 7.35231i) q^{29} +(-3.50474 + 2.02346i) q^{30} +(3.97807 + 1.06592i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(1.31252 - 4.89839i) q^{33} +(-3.50891 - 3.50891i) q^{34} +(-0.858922 + 10.6726i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.552475 + 0.552475i) q^{37} +(0.725610 + 1.25679i) q^{38} +(3.31255 - 1.42373i) q^{39} +(-3.50474 - 2.02346i) q^{40} +(3.46045 + 0.927225i) q^{41} +(-0.212241 + 2.63722i) q^{42} +(8.45709 + 4.88270i) q^{43} +(4.89839 - 1.31252i) q^{44} +(-2.86161 + 2.86161i) q^{45} +(3.84146 - 3.84146i) q^{46} +(-2.84109 + 0.761269i) q^{47} +(-0.866025 - 0.500000i) q^{48} +(5.42443 + 4.42443i) q^{49} +(-10.9899 - 2.94473i) q^{50} +(-4.29751 - 2.48117i) q^{51} +(2.88926 + 2.15689i) q^{52} +(2.08448 + 3.61043i) q^{53} +(-0.707107 + 0.707107i) q^{54} +(17.7732 - 10.2613i) q^{55} +(-2.39002 + 1.13481i) q^{56} +(1.02617 + 1.02617i) q^{57} +(2.19730 - 8.20043i) q^{58} +(-0.661436 - 0.661436i) q^{59} +(-3.90903 - 1.04742i) q^{60} +(-10.4863 + 6.05427i) q^{61} +(2.05920 + 3.56664i) q^{62} +(0.477555 + 2.60230i) q^{63} -1.00000i q^{64} +(13.5534 + 5.40507i) q^{65} +(4.39177 - 2.53559i) q^{66} +(-8.88378 + 2.38040i) q^{67} -4.96234i q^{68} +(2.71632 - 4.70481i) q^{69} +(-8.15405 + 6.93935i) q^{70} +(-4.28503 + 1.14817i) q^{71} +(-0.965926 - 0.258819i) q^{72} +(3.43906 - 12.8347i) q^{73} -0.781318 q^{74} -11.3776 q^{75} +(-0.375603 + 1.40177i) q^{76} +(1.07631 - 13.3739i) q^{77} +(3.34906 + 1.33560i) q^{78} +(1.32924 - 2.30231i) q^{79} +(-1.04742 - 3.90903i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(1.79126 + 3.10255i) q^{82} +(-1.02375 + 1.02375i) q^{83} +(-2.01488 + 1.71472i) q^{84} +(-5.19766 - 19.3979i) q^{85} +(2.52747 + 9.43266i) q^{86} -8.48971i q^{87} +(4.39177 + 2.53559i) q^{88} +(4.52554 + 4.52554i) q^{89} -4.04692 q^{90} +(7.94033 - 5.28689i) q^{91} +5.43264 q^{92} +(2.91215 + 2.91215i) q^{93} +(-2.54726 - 1.47066i) q^{94} +5.87297i q^{95} +(-0.258819 - 0.965926i) q^{96} +(-2.62347 - 9.79094i) q^{97} +(0.707107 + 6.96419i) q^{98} +(3.58587 - 3.58587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 40 * q + 4 * q^7 + 20 * q^9	\( 40 q + 4 q^{7} + 20 q^{9} + 8 q^{11} - 20 q^{12} + 4 q^{14} - 40 q^{16} + 16 q^{17} + 4 q^{19} + 4 q^{21} - 4 q^{22} - 24 q^{25} + 8 q^{26} - 4 q^{28} - 12 q^{29} - 8 q^{33} - 8 q^{34} - 32 q^{35} + 40 q^{37} + 8 q^{38} + 20 q^{39} + 20 q^{41} + 12 q^{42} - 24 q^{43} - 4 q^{44} + 32 q^{46} + 4 q^{47} + 32 q^{49} - 16 q^{50} + 24 q^{51} + 16 q^{52} - 4 q^{53} + 24 q^{55} + 12 q^{56} + 8 q^{57} + 12 q^{58} + 24 q^{59} + 60 q^{61} + 32 q^{62} - 4 q^{63} + 44 q^{65} - 12 q^{67} - 8 q^{69} - 24 q^{70} - 28 q^{71} + 60 q^{73} - 40 q^{74} - 72 q^{75} + 4 q^{76} - 12 q^{77} + 4 q^{78} - 20 q^{81} - 24 q^{82} + 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{89} - 16 q^{92} - 24 q^{93} - 48 q^{97} - 88 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q + 4 * q^7 + 20 * q^9 + 8 * q^11 - 20 * q^12 + 4 * q^14 - 40 * q^16 + 16 * q^17 + 4 * q^19 + 4 * q^21 - 4 * q^22 - 24 * q^25 + 8 * q^26 - 4 * q^28 - 12 * q^29 - 8 * q^33 - 8 * q^34 - 32 * q^35 + 40 * q^37 + 8 * q^38 + 20 * q^39 + 20 * q^41 + 12 * q^42 - 24 * q^43 - 4 * q^44 + 32 * q^46 + 4 * q^47 + 32 * q^49 - 16 * q^50 + 24 * q^51 + 16 * q^52 - 4 * q^53 + 24 * q^55 + 12 * q^56 + 8 * q^57 + 12 * q^58 + 24 * q^59 + 60 * q^61 + 32 * q^62 - 4 * q^63 + 44 * q^65 - 12 * q^67 - 8 * q^69 - 24 * q^70 - 28 * q^71 + 60 * q^73 - 40 * q^74 - 72 * q^75 + 4 * q^76 - 12 * q^77 + 4 * q^78 - 20 * q^81 - 24 * q^82 + 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^89 - 16 * q^92 - 24 * q^93 - 48 * q^97 - 88 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more