LMFDB - Embedded newform 546.2.by.b.115.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(19,546)]

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, 5]))

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

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

chi := DirichletCharacter("546.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.by (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			115.5
Character	$\chi$	$=$	546.115
Dual form			546.2.by.b.19.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(3.90903 + 1.04742i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.71472 + 2.01488i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(3.90903 + 1.04742i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.71472 + 2.01488i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -4.04692 q^{10} +(-3.58587 + 3.58587i) 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} +(0.500000 - 0.866025i) q^{16} +(-2.48117 - 4.29751i) q^{17} +(0.965926 - 0.258819i) q^{18} +(1.02617 - 1.02617i) q^{19} +(3.90903 - 1.04742i) q^{20} +(-2.01488 - 1.71472i) q^{21} +(2.53559 - 4.39177i) q^{22} +(4.70481 + 2.71632i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(9.85327 + 5.68879i) q^{25} +(1.33560 - 3.34906i) q^{26} -1.00000i q^{27} +(-0.477555 + 2.60230i) q^{28} +(-4.24486 - 7.35231i) q^{29} -4.04692i q^{30} +(1.06592 + 3.97807i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-3.58587 - 3.58587i) q^{33} +(3.50891 + 3.50891i) q^{34} +(-8.81332 + 6.08017i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.202220 - 0.754695i) q^{37} +(-0.725610 + 1.25679i) q^{38} +(-2.88926 - 2.15689i) q^{39} +(-3.50474 + 2.02346i) q^{40} +(-3.46045 - 0.927225i) q^{41} +(2.39002 + 1.13481i) q^{42} +(8.45709 + 4.88270i) q^{43} +(-1.31252 + 4.89839i) q^{44} +(-3.90903 - 1.04742i) q^{45} +(-5.24753 - 1.40607i) q^{46} +(-0.761269 + 2.84109i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-1.11945 - 6.90991i) q^{49} +(-10.9899 - 2.94473i) q^{50} +(4.29751 - 2.48117i) q^{51} +(-0.423290 + 3.58062i) q^{52} +(2.08448 - 3.61043i) q^{53} +(0.258819 + 0.965926i) q^{54} +(-17.7732 + 10.2613i) q^{55} +(-0.212241 - 2.63722i) q^{56} +(1.02617 + 1.02617i) q^{57} +(6.00313 + 6.00313i) q^{58} +(0.242102 - 0.903539i) q^{59} +(1.04742 + 3.90903i) q^{60} +12.1085i q^{61} +(-2.05920 - 3.56664i) q^{62} +(1.71472 - 2.01488i) q^{63} -1.00000i q^{64} +(-11.4576 + 9.03503i) q^{65} +(4.39177 + 2.53559i) q^{66} +(6.50338 + 6.50338i) q^{67} +(-4.29751 - 2.48117i) q^{68} +(-2.71632 + 4.70481i) q^{69} +(6.93935 - 8.15405i) q^{70} +(-4.28503 + 1.14817i) q^{71} +(0.707107 - 0.707107i) q^{72} +(12.8347 - 3.43906i) q^{73} +(0.390659 + 0.676641i) q^{74} +(-5.68879 + 9.85327i) 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} +(2.86161 - 2.86161i) q^{80} +1.00000 q^{81} +3.58252 q^{82} +(1.02375 - 1.02375i) q^{83} +(-2.60230 - 0.477555i) q^{84} +(-5.19766 - 19.3979i) q^{85} +(-9.43266 - 2.52747i) q^{86} +(7.35231 - 4.24486i) q^{87} -5.07118i q^{88} +(6.18200 - 1.65646i) q^{89} +4.04692 q^{90} +(-2.12304 - 9.30015i) q^{91} +5.43264 q^{92} +(-3.97807 + 1.06592i) q^{93} -2.94132i q^{94} +(5.08614 - 2.93649i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(2.62347 + 9.79094i) q^{97} +(2.86972 + 6.38472i) q^{98} +(3.58587 - 3.58587i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) $ 40 * q - 4 * q^7 - 40 * q^9	$ 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) $ 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	3.90903	+	1.04742i	1.74817	+	0.468421i	0.984234	−	0.176872i	$-0.0565978\pi$
$5$	3.90903	+	1.04742i	1.74817	+	0.468421i	0.763936	+	0.645292i	$0.223264\pi$
$6$	−0.258819	−	0.965926i	−0.105662	−	0.394338i
$7$	−1.71472	+	2.01488i	−0.648104	+	0.761552i
$7$	−1.71472	+	2.01488i	−0.648104	+	0.761552i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−1.00000			−0.333333
$10$	−4.04692			−1.27975
$11$	−3.58587	+	3.58587i	−1.08118	+	1.08118i	−0.0847806	+	0.996400i	$0.527019\pi$
$11$	−3.58587	+	3.58587i	−1.08118	+	1.08118i	−0.996400	+	0.0847806i	$0.972981\pi$
$12$	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
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.48117	−	4.29751i	−0.601772	−	1.04230i	−0.992553	−	0.121816i	$-0.961128\pi$
$17$	−2.48117	−	4.29751i	−0.601772	−	1.04230i	0.390780	−	0.920484i	$-0.372205\pi$
$18$	0.965926	−	0.258819i	0.227671	−	0.0610042i
$19$	1.02617	−	1.02617i	0.235419	−	0.235419i	−0.579531	−	0.814950i	$-0.696764\pi$
$19$	1.02617	−	1.02617i	0.235419	−	0.235419i	0.814950	+	0.579531i	$0.196764\pi$
$20$	3.90903	−	1.04742i	0.874085	−	0.234210i
$21$	−2.01488	−	1.71472i	−0.439682	−	0.374183i
$22$	2.53559	−	4.39177i	0.540590	−	0.936330i
$23$	4.70481	+	2.71632i	0.981020	+	0.566392i	0.902578	−	0.430527i	$-0.141672\pi$
$23$	4.70481	+	2.71632i	0.981020	+	0.566392i	0.0784420	+	0.996919i	$0.475005\pi$
$24$	−0.707107	−	0.707107i	−0.144338	−	0.144338i
$25$	9.85327	+	5.68879i	1.97065	+	1.13776i
$26$	1.33560	−	3.34906i	0.261933	−	0.656804i
$27$		−	1.00000i		−	0.192450i
$28$	−0.477555	+	2.60230i	−0.0902494	+	0.491788i
$29$	−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	$-0.455679\pi$
$30$		−	4.04692i		−	0.738863i
$31$	1.06592	+	3.97807i	0.191445	+	0.714483i	0.993159	+	0.116774i	$0.0372553\pi$
$31$	1.06592	+	3.97807i	0.191445	+	0.714483i	−0.801714	+	0.597709i	$0.796078\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−3.58587	−	3.58587i	−0.624220	−	0.624220i
$34$	3.50891	+	3.50891i	0.601772	+	0.601772i
$35$	−8.81332	+	6.08017i	−1.48972	+	1.02774i
$36$	−0.866025	+	0.500000i	−0.144338	+	0.0833333i
$37$	−0.202220	−	0.754695i	−0.0332448	−	0.124071i	0.947309	−	0.320320i	$-0.103791\pi$
$37$	−0.202220	−	0.754695i	−0.0332448	−	0.124071i	−0.980554	+	0.196249i	$0.937124\pi$
$38$	−0.725610	+	1.25679i	−0.117709	+	0.203879i
$39$	−2.88926	−	2.15689i	−0.462652	−	0.345379i
$40$	−3.50474	+	2.02346i	−0.554148	+	0.319937i
$41$	−3.46045	−	0.927225i	−0.540431	−	0.144808i	−0.0217304	−	0.999764i	$-0.506918\pi$
$41$	−3.46045	−	0.927225i	−0.540431	−	0.144808i	−0.518701	+	0.854956i	$0.673584\pi$
$42$	2.39002	+	1.13481i	0.368789	+	0.175104i
$43$	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	$0.399304\pi$
$44$	−1.31252	+	4.89839i	−0.197870	+	0.738460i
$45$	−3.90903	−	1.04742i	−0.582723	−	0.156140i
$46$	−5.24753	−	1.40607i	−0.773706	−	0.207314i
$47$	−0.761269	+	2.84109i	−0.111043	+	0.414416i	−0.998960	−	0.0455856i	$-0.985485\pi$
$47$	−0.761269	+	2.84109i	−0.111043	+	0.414416i	0.887918	+	0.460002i	$0.152151\pi$
$48$	0.866025	+	0.500000i	0.125000	+	0.0721688i
$49$	−1.11945	−	6.90991i	−0.159922	−	0.987130i
$50$	−10.9899	−	2.94473i	−1.55421	−	0.416448i
$51$	4.29751	−	2.48117i	0.601772	−	0.347433i
$52$	−0.423290	+	3.58062i	−0.0586998	+	0.496542i
$53$	2.08448	−	3.61043i	0.286325	−	0.495930i	−0.686604	−	0.727031i	$-0.740899\pi$
$53$	2.08448	−	3.61043i	0.286325	−	0.495930i	0.972930	+	0.231101i	$0.0742328\pi$
$54$	0.258819	+	0.965926i	0.0352208	+	0.131446i
$55$	−17.7732	+	10.2613i	−2.39653	+	1.38364i
$56$	−0.212241	−	2.63722i	−0.0283619	−	0.352414i
$57$	1.02617	+	1.02617i	0.135919	+	0.135919i
$58$	6.00313	+	6.00313i	0.788250	+	0.788250i
$59$	0.242102	−	0.903539i	0.0315191	−	0.117631i	−0.948374	−	0.317154i	$-0.897273\pi$
$59$	0.242102	−	0.903539i	0.0315191	−	0.117631i	0.979893	+	0.199523i	$0.0639394\pi$
$60$	1.04742	+	3.90903i	0.135221	+	0.504653i
$61$			12.1085i			1.55034i	0.631753	+	0.775170i	$0.282336\pi$
$61$			12.1085i			1.55034i	−0.631753	+	0.775170i	$0.717664\pi$
$62$	−2.05920	−	3.56664i	−0.261519	−	0.452964i
$63$	1.71472	−	2.01488i	0.216035	−	0.253851i
$64$		−	1.00000i		−	0.125000i
$65$	−11.4576	+	9.03503i	−1.42114	+	1.12066i
$66$	4.39177	+	2.53559i	0.540590	+	0.312110i
$67$	6.50338	+	6.50338i	0.794514	+	0.794514i	0.982224	−	0.187710i	$-0.0601066\pi$
$67$	6.50338	+	6.50338i	0.794514	+	0.794514i	−0.187710	+	0.982224i	$0.560107\pi$
$68$	−4.29751	−	2.48117i	−0.521150	−	0.300886i
$69$	−2.71632	+	4.70481i	−0.327007	+	0.566392i
$70$	6.93935	−	8.15405i	0.829411	−	0.974595i
$71$	−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	$0.501458\pi$
$72$	0.707107	−	0.707107i	0.0833333	−	0.0833333i
$73$	12.8347	−	3.43906i	1.50219	−	0.402511i	0.588358	−	0.808600i	$-0.299774\pi$
$73$	12.8347	−	3.43906i	1.50219	−	0.402511i	0.913833	+	0.406089i	$0.133108\pi$
$74$	0.390659	+	0.676641i	0.0454132	+	0.0786579i
$75$	−5.68879	+	9.85327i	−0.656884	+	1.13776i
$76$	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	0.931062	−	0.364862i	$-0.118884\pi$
$79$	1.32924	+	2.30231i	0.149551	+	0.259030i	−0.781511	+	0.623892i	$0.785551\pi$
$80$	2.86161	−	2.86161i	0.319937	−	0.319937i
$81$	1.00000			0.111111
$82$	3.58252			0.395623
$83$	1.02375	−	1.02375i	0.112371	−	0.112371i	−0.648686	−	0.761056i	$-0.724681\pi$
$83$	1.02375	−	1.02375i	0.112371	−	0.112371i	0.761056	+	0.648686i	$0.224681\pi$
$84$	−2.60230	−	0.477555i	−0.283934	−	0.0521055i
$85$	−5.19766	−	19.3979i	−0.563765	−	2.10400i
$86$	−9.43266	−	2.52747i	−1.01715	−	0.272545i
$87$	7.35231	−	4.24486i	0.788250	−	0.455096i
$88$		−	5.07118i		−	0.540590i
$89$	6.18200	−	1.65646i	0.655291	−	0.175585i	0.0841709	−	0.996451i	$-0.473176\pi$
$89$	6.18200	−	1.65646i	0.655291	−	0.175585i	0.571120	+	0.820867i	$0.306509\pi$
$90$	4.04692			0.426583
$91$	−2.12304	−	9.30015i	−0.222555	−	0.974920i
$92$	5.43264			0.566392
$93$	−3.97807	+	1.06592i	−0.412507	+	0.110531i
$94$		−	2.94132i		−	0.303374i
$95$	5.08614	−	2.93649i	0.521827	−	0.301277i
$96$	−0.965926	−	0.258819i	−0.0985844	−	0.0264156i
$97$	2.62347	+	9.79094i	0.266374	+	0.994119i	0.961404	+	0.275139i	$0.0887240\pi$
$97$	2.62347	+	9.79094i	0.266374	+	0.994119i	−0.695031	+	0.718980i	$0.744609\pi$
$98$	2.86972	+	6.38472i	0.289886	+	0.644954i
$99$	3.58587	−	3.58587i	0.360393	−	0.360393i
$100$	11.3776			1.13776
$101$	3.92532			0.390584			0.195292	−	0.980745i	$-0.437435\pi$
$101$	3.92532			0.390584			0.195292	+	0.980745i	$0.437435\pi$
$102$	−3.50891	+	3.50891i	−0.347433	+	0.347433i
$103$	−3.52526	−	6.10594i	−0.347355	−	0.601636i	0.638424	−	0.769685i	$-0.279587\pi$
$103$	−3.52526	−	6.10594i	−0.347355	−	0.601636i	−0.985779	+	0.168049i	$0.946253\pi$
$104$	−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
$107$	3.96798	−	6.87275i	0.383599	−	0.664413i	−0.607975	−	0.793957i	$-0.708018\pi$
$107$	3.96798	−	6.87275i	0.383599	−	0.664413i	0.991574	+	0.129543i	$0.0413511\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	2.77491	−	0.743535i	0.265788	−	0.0712177i	−0.123464	−	0.992349i	$-0.539400\pi$
$109$	2.77491	−	0.743535i	0.265788	−	0.0712177i	0.389252	+	0.921131i	$0.372734\pi$
$110$	14.5117	−	14.5117i	1.38364	−	1.38364i
$111$	0.754695	−	0.202220i	0.0716325	−	0.0191939i
$112$	0.887573	+	2.49243i	0.0838678	+	0.235513i
$113$	−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	$0.314085\pi$
$114$	−1.25679	−	0.725610i	−0.117709	−	0.0679596i
$115$	15.5461	+	15.5461i	1.44968	+	1.44968i
$116$	−7.35231	−	4.24486i	−0.682644	−	0.394125i
$117$	2.15689	−	2.88926i	0.199404	−	0.267112i
$118$			0.935412i			0.0861117i
$119$	12.9135	+	2.36979i	1.18378	+	0.217238i
$120$	−2.02346	−	3.50474i	−0.184716	−	0.319937i
$121$		−	14.7169i		−	1.33790i
$122$	−3.13392	−	11.6960i	−0.283732	−	1.05890i
$123$	0.927225	−	3.46045i	0.0836050	−	0.312018i
$124$	2.91215	+	2.91215i	0.261519	+	0.261519i
$125$	18.2501	+	18.2501i	1.63234	+	1.63234i
$126$	−1.13481	+	2.39002i	−0.101097	+	0.212920i
$127$	−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	$0.549800\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	−4.88270	+	8.45709i	−0.429898	+	0.744605i
$130$	8.72876	−	11.6926i	0.765563	−	1.02551i
$131$	8.60736	−	4.96946i	0.752029	−	0.434184i	−0.0743977	−	0.997229i	$-0.523703\pi$
$131$	8.60736	−	4.96946i	0.752029	−	0.434184i	0.826427	+	0.563045i	$0.190370\pi$
$132$	−4.89839	−	1.31252i	−0.426350	−	0.114240i
$133$	0.308008	+	3.82719i	0.0267077	+	0.331860i
$134$	−7.96498	−	4.59858i	−0.688069	−	0.397257i
$135$	1.04742	−	3.90903i	0.0901476	−	0.336435i
$136$	4.79325	+	1.28435i	0.411018	+	0.110132i
$137$	17.0632	+	4.57208i	1.45781	+	0.390619i	0.898733	−	0.438496i	$-0.144489\pi$
$137$	17.0632	+	4.57208i	1.45781	+	0.390619i	0.559078	+	0.829115i	$0.311155\pi$
$138$	1.40607	−	5.24753i	0.119693	−	0.446699i
$139$	−11.0687	−	6.39049i	−0.938831	−	0.542035i	−0.0492377	−	0.998787i	$-0.515679\pi$
$139$	−11.0687	−	6.39049i	−0.938831	−	0.542035i	−0.889594	+	0.456752i	$0.849013\pi$
$140$	−4.59247	+	9.67224i	−0.388135	+	0.817453i
$141$	−2.84109	−	0.761269i	−0.239263	−	0.0641104i
$142$	3.84185	−	2.21809i	0.322401	−	0.186138i
$143$	−2.62619	−	18.0948i	−0.219613	−	1.51317i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−8.89230	−	33.1865i	−0.738465	−	2.75599i
$146$	−11.5073	+	6.64375i	−0.952351	+	0.549840i
$147$	6.90991	−	1.11945i	0.569920	−	0.0923310i
$148$	−0.552475	−	0.552475i	−0.0454132	−	0.0454132i
$149$	8.24822	+	8.24822i	0.675720	+	0.675720i	0.959029	−	0.283309i	$-0.0914320\pi$
$149$	8.24822	+	8.24822i	0.675720	+	0.675720i	−0.283309	+	0.959029i	$0.591432\pi$
$150$	2.94473	−	10.9899i	0.240436	−	0.897321i
$151$	−4.29660	−	16.0351i	−0.349652	−	1.30492i	−0.887082	−	0.461611i	$-0.847271\pi$
$151$	−4.29660	−	16.0351i	−0.349652	−	1.30492i	0.537430	−	0.843308i	$-0.319395\pi$
$152$			1.45122i			0.117709i
$153$	2.48117	+	4.29751i	0.200591	+	0.347433i
$154$	4.50105	+	12.6396i	0.362705	+	1.01853i
$155$			16.6668i			1.33871i
$156$	−3.58062	−	0.423290i	−0.286679	−	0.0338904i
$157$	19.4589	+	11.2346i	1.55299	+	0.896620i	0.997896	+	0.0648334i	$0.0206516\pi$
$157$	19.4589	+	11.2346i	1.55299	+	0.896620i	0.555095	+	0.831787i	$0.312682\pi$
$158$	−1.87983	−	1.87983i	−0.149551	−	0.149551i
$159$	3.61043	+	2.08448i	0.286325	+	0.165310i
$160$	−2.02346	+	3.50474i	−0.159969	+	0.277074i
$161$	−13.5405	+	4.82187i	−1.06714	+	0.380016i
$162$	−0.965926	+	0.258819i	−0.0758903	+	0.0203347i
$163$	−0.539939	+	0.539939i	−0.0422913	+	0.0422913i	−0.727936	−	0.685645i	$-0.759520\pi$
$163$	−0.539939	+	0.539939i	−0.0422913	+	0.0422913i	0.685645	+	0.727936i	$0.259520\pi$
$164$	−3.46045	+	0.927225i	−0.270216	+	0.0724041i
$165$	−10.2613	−	17.7732i	−0.798844	−	1.38364i
$166$	−0.723897	+	1.25383i	−0.0561853	+	0.0973158i
$167$	−0.00377911	+	0.0141038i	−0.000292436	+	0.00109139i	−0.966072	−	0.258273i	$-0.916846\pi$
$167$	−0.00377911	+	0.0141038i	−0.000292436	+	0.00109139i	0.965779	+	0.259365i	$0.0835132\pi$
$168$	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
$171$	−1.02617	+	1.02617i	−0.0784730	+	0.0784730i
$172$	9.76541			0.744605
$173$	7.23453			0.550031			0.275016	−	0.961440i	$-0.411317\pi$
$173$	7.23453			0.550031			0.275016	+	0.961440i	$0.411317\pi$
$174$	−6.00313	+	6.00313i	−0.455096	+	0.455096i
$175$	−28.3578	+	10.0984i	−2.14365	+	0.763369i
$176$	1.31252	+	4.89839i	0.0989349	+	0.369230i
$177$	0.903539	+	0.242102i	0.0679141	+	0.0181975i
$178$	−5.54263	+	3.20004i	−0.415438	+	0.239853i
$179$		−	16.1216i		−	1.20499i	−0.798123	−	0.602494i	$-0.794174\pi$
$179$		−	16.1216i		−	1.20499i	0.798123	−	0.602494i	$-0.205826\pi$
$180$	−3.90903	+	1.04742i	−0.291362	+	0.0780701i
$181$	6.35633			0.472462			0.236231	−	0.971697i	$-0.424088\pi$
$181$	6.35633			0.472462			0.236231	+	0.971697i	$0.424088\pi$
$182$	4.45775	+	8.43377i	0.330430	+	0.625153i
$183$	−12.1085			−0.895089
$184$	−5.24753	+	1.40607i	−0.386853	+	0.103657i
$185$		−	3.16193i		−	0.232470i
$186$	3.56664	−	2.05920i	0.261519	−	0.150988i
$187$	24.3075	+	6.51317i	1.77754	+	0.476290i
$188$	0.761269	+	2.84109i	0.0555213	+	0.207208i
$189$	2.01488	+	1.71472i	0.146561	+	0.124728i
$190$	−4.15282	+	4.15282i	−0.301277	+	0.301277i
$191$	−20.8379			−1.50778			−0.753888	−	0.657003i	$-0.771824\pi$
$191$	−20.8379			−1.50778			−0.753888	+	0.657003i	$0.771824\pi$
$192$	1.00000			0.0721688
$193$	−7.59633	+	7.59633i	−0.546796	+	0.546796i	−0.925513	−	0.378717i	$-0.876365\pi$
$193$	−7.59633	+	7.59633i	−0.546796	+	0.546796i	0.378717	+	0.925513i	$0.376365\pi$
$194$	−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	$-0.0544032\pi$
$198$	−2.53559	+	4.39177i	−0.180197	+	0.312110i
$199$	−9.71131	−	16.8205i	−0.688417	−	1.19237i	−0.972350	−	0.233528i	$-0.924973\pi$
$199$	−9.71131	−	16.8205i	−0.688417	−	1.19237i	0.283933	−	0.958844i	$-0.408361\pi$
$200$	−10.9899	+	2.94473i	−0.777103	+	0.208224i
$201$	−6.50338	+	6.50338i	−0.458713	+	0.458713i
$202$	−3.79157	+	1.01595i	−0.266774	+	0.0714818i
$203$	22.0927	+	4.05430i	1.55061	+	0.284556i
$204$	2.48117	−	4.29751i	0.173717	−	0.300886i
$205$	−12.5558	−	7.24909i	−0.876934	−	0.506298i
$206$	4.98548	+	4.98548i	0.347355	+	0.347355i
$207$	−4.70481	−	2.71632i	−0.327007	−	0.188797i
$208$	1.42373	+	3.31255i	0.0987178	+	0.229684i
$209$			7.35940i			0.509061i
$210$	8.15405	+	6.93935i	0.562683	+	0.478860i
$211$	−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	$0.870639\pi$
$212$		−	4.16896i		−	0.286325i
$213$	−1.14817	−	4.28503i	−0.0786713	−	0.293605i
$214$	−2.05398	+	7.66555i	−0.140407	+	0.524006i
$215$	27.9447	+	27.9447i	1.90582	+	1.90582i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−9.84308	−	4.67359i	−0.668192	−	0.317264i
$218$	−2.48792	+	1.43640i	−0.168503	+	0.0972852i
$219$	3.43906	+	12.8347i	0.232390	+	0.867291i
$220$	−10.2613	+	17.7732i	−0.691820	+	1.19827i
$221$	17.7682	+	2.10051i	1.19522	+	0.141296i
$222$	−0.676641	+	0.390659i	−0.0454132	+	0.0262193i
$223$	18.6599	+	4.99990i	1.24956	+	0.334818i	0.822166	−	0.569248i	$-0.192765\pi$
$223$	18.6599	+	4.99990i	1.24956	+	0.334818i	0.427393	+	0.904066i	$0.359432\pi$
$224$	−1.50242	−	2.17778i	−0.100385	−	0.145509i
$225$	−9.85327	−	5.68879i	−0.656884	−	0.379252i
$226$	2.45827	−	9.17439i	0.163522	−	0.610272i
$227$	−0.675293	−	0.180944i	−0.0448208	−	0.0120097i	0.236339	−	0.971671i	$-0.424052\pi$
$227$	−0.675293	−	0.180944i	−0.0448208	−	0.0120097i	−0.281160	+	0.959661i	$0.590719\pi$
$228$	1.40177	+	0.375603i	0.0928345	+	0.0248749i
$229$	−3.70519	+	13.8280i	−0.244846	+	0.913778i	0.728615	+	0.684924i	$0.240164\pi$
$229$	−3.70519	+	13.8280i	−0.244846	+	0.913778i	−0.973461	+	0.228854i	$0.926502\pi$
$230$	−19.0400	−	10.9927i	−1.25546	−	0.724840i
$231$	13.3739	−	1.07631i	0.879935	−	0.0708162i
$232$	8.20043	+	2.19730i	0.538385	+	0.144260i
$233$	14.6943	−	8.48375i	0.962655	−	0.555789i	0.0656657	−	0.997842i	$-0.479083\pi$
$233$	14.6943	−	8.48375i	0.962655	−	0.555789i	0.896989	+	0.442053i	$0.145750\pi$
$234$	−1.33560	+	3.34906i	−0.0873109	+	0.218935i
$235$	−5.95164	+	10.3085i	−0.388242	+	0.672455i
$236$	−0.242102	−	0.903539i	−0.0157595	−	0.0588154i
$237$	−2.30231	+	1.32924i	−0.149551	+	0.0863433i
$238$	−13.0868	+	1.05321i	−0.848292	+	0.0682696i
$239$	−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	$0.916436\pi$
$240$	2.86161	+	2.86161i	0.184716	+	0.184716i
$241$	0.0901532	−	0.336456i	0.00580728	−	0.0216731i	−0.962961	−	0.269639i	$-0.913096\pi$
$241$	0.0901532	−	0.336456i	0.00580728	−	0.0216731i	0.968769	+	0.247966i	$0.0797622\pi$
$242$	3.80902	+	14.2154i	0.244853	+	0.913804i
$243$			1.00000i			0.0641500i
$244$	6.05427	+	10.4863i	0.387585	+	0.671317i
$245$	2.86161	−	28.1835i	0.182821	−	1.80058i
$246$			3.58252i			0.228413i
$247$	0.751536	+	5.17819i	0.0478191	+	0.329481i
$248$	−3.56664	−	2.05920i	−0.226482	−	0.130759i
$249$	1.02375	+	1.02375i	0.0648772	+	0.0648772i
$250$	−22.3517	−	12.9048i	−1.41365	−	0.816169i
$251$	0.267758	−	0.463770i	0.0169007	−	0.0292729i	−0.857451	−	0.514565i	$-0.827953\pi$
$251$	0.267758	−	0.463770i	0.0169007	−	0.0292729i	0.874352	+	0.485292i	$0.161287\pi$
$252$	0.477555	−	2.60230i	0.0300831	−	0.163929i
$253$	−26.6112	+	7.13045i	−1.67303	+	0.448287i
$254$	10.0219	−	10.0219i	0.628831	−	0.628831i
$255$	19.3979	−	5.19766i	1.21474	−	0.325490i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	10.6194	−	18.3934i	0.662422	−	1.14735i	−0.317556	−	0.948240i	$-0.602862\pi$
$257$	10.6194	−	18.3934i	0.662422	−	1.14735i	0.979978	−	0.199108i	$-0.0638045\pi$
$258$	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
$262$	−7.02788	+	7.02788i	−0.434184	+	0.434184i
$263$	−12.4316			−0.766563			−0.383281	−	0.923632i	$-0.625206\pi$
$263$	−12.4316			−0.766563			−0.383281	+	0.923632i	$0.625206\pi$
$264$	5.07118			0.312110
$265$	11.9299	−	11.9299i	0.732849	−	0.732849i
$266$	−1.28806	−	3.61707i	−0.0789762	−	0.221777i
$267$	1.65646	+	6.18200i	0.101374	+	0.378332i
$268$	8.88378	+	2.38040i	0.542663	+	0.145406i
$269$	8.69727	−	5.02137i	0.530282	−	0.306158i	−0.210849	−	0.977519i	$-0.567623\pi$
$269$	8.69727	−	5.02137i	0.530282	−	0.306158i	0.741131	+	0.671360i	$0.234290\pi$
$270$			4.04692i			0.246288i
$271$	18.7150	−	5.01468i	1.13686	−	0.304620i	0.359171	−	0.933272i	$-0.383060\pi$
$271$	18.7150	−	5.01468i	1.13686	−	0.304620i	0.777687	+	0.628652i	$0.216393\pi$
$272$	−4.96234			−0.300886
$273$	9.30015	−	2.12304i	0.562870	−	0.128492i
$274$	−17.6652			−1.06719
$275$	−55.7318	+	14.9333i	−3.36075	+	0.900511i
$276$			5.43264i			0.327007i
$277$	19.3451	−	11.1689i	1.16233	−	0.671073i	0.210471	−	0.977600i	$-0.432500\pi$
$277$	19.3451	−	11.1689i	1.16233	−	0.671073i	0.951862	+	0.306527i	$0.0991669\pi$
$278$	12.3455	+	3.30796i	0.740433	+	0.198398i
$279$	−1.06592	−	3.97807i	−0.0638150	−	0.238161i
$280$	1.93263	−	10.5313i	0.115497	−	0.629365i
$281$	−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	$0.945622\pi$
$282$	2.94132			0.175153
$283$	−11.1732			−0.664181			−0.332090	−	0.943248i	$-0.607754\pi$
$283$	−11.1732			−0.664181			−0.332090	+	0.943248i	$0.607754\pi$
$284$	−3.13686	+	3.13686i	−0.186138	+	0.186138i
$285$	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
$289$	−3.81242	+	6.60330i	−0.224260	+	0.388429i
$290$	17.1786	+	29.7542i	1.00876	+	1.74723i
$291$	−9.79094	+	2.62347i	−0.573955	+	0.153791i
$292$	9.39568	−	9.39568i	0.549840	−	0.549840i
$293$	−19.1845	+	5.14048i	−1.12077	+	0.300310i	−0.771196	−	0.636598i	$-0.780341\pi$
$293$	−19.1845	+	5.14048i	−1.12077	+	0.300310i	−0.349577	+	0.936908i	$0.613675\pi$
$294$	−6.38472	+	2.86972i	−0.372365	+	0.167366i
$295$	1.89277	−	3.27837i	0.110201	−	0.190874i
$296$	0.676641	+	0.390659i	0.0393290	+	0.0227066i
$297$	3.58587	+	3.58587i	0.208073	+	0.208073i
$298$	−10.1020	−	5.83237i	−0.585191	−	0.337860i
$299$	−17.9959	+	7.73461i	−1.04073	+	0.447304i
$300$			11.3776i			0.656884i
$301$	−24.3396	+	8.66751i	−1.40291	+	0.499587i
$302$	8.30039	+	14.3767i	0.477634	+	0.827286i
$303$			3.92532i			0.225504i
$304$	−0.375603	−	1.40177i	−0.0215423	−	0.0803971i
$305$	−12.6827	+	47.3326i	−0.726211	+	2.71026i
$306$	−3.50891	−	3.50891i	−0.200591	−	0.200591i
$307$	−2.00335	−	2.00335i	−0.114337	−	0.114337i	0.647623	−	0.761961i	$-0.275763\pi$
$307$	−2.00335	−	2.00335i	−0.114337	−	0.114337i	−0.761961	+	0.647623i	$0.775763\pi$
$308$	−7.61904	−	11.0439i	−0.434135	−	0.629287i
$309$	6.10594	−	3.52526i	0.347355	−	0.200545i
$310$	−4.31370	−	16.0989i	−0.245002	−	0.914358i
$311$	−10.4635	+	18.1233i	−0.593332	+	1.02768i	0.400448	+	0.916319i	$0.368854\pi$
$311$	−10.4635	+	18.1233i	−0.593332	+	1.02768i	−0.993780	+	0.111361i	$0.964479\pi$
$312$	3.56817	−	0.517865i	0.202008	−	0.0293183i
$313$	−22.2663	+	12.8554i	−1.25856	+	0.726632i	−0.972795	−	0.231666i	$-0.925582\pi$
$313$	−22.2663	+	12.8554i	−1.25856	+	0.726632i	−0.285769	+	0.958299i	$0.592249\pi$
$314$	−21.7036	−	5.81547i	−1.22481	−	0.328186i
$315$	8.81332	−	6.08017i	0.496574	−	0.342579i
$316$	2.30231	+	1.32924i	0.129515	+	0.0747755i
$317$	8.42624	−	31.4472i	0.473265	−	1.76625i	−0.154653	−	0.987969i	$-0.549426\pi$
$317$	8.42624	−	31.4472i	0.473265	−	1.76625i	0.627918	−	0.778280i	$-0.283907\pi$
$318$	−4.02691	−	1.07901i	−0.225818	−	0.0605077i
$319$	41.5859	+	11.1429i	2.32836	+	0.623883i
$320$	1.04742	−	3.90903i	0.0585526	−	0.218521i
$321$	6.87275	+	3.96798i	0.383599	+	0.221471i
$322$	11.8311	−	8.16210i	0.659322	−	0.454856i
$323$	−6.95606	−	1.86387i	−0.387046	−	0.103709i
$324$	0.866025	−	0.500000i	0.0481125	−	0.0277778i
$325$	−37.6888	+	16.1986i	−2.09060	+	0.898535i
$326$	0.381795	−	0.661288i	0.0211456	−	0.0366253i
$327$	0.743535	+	2.77491i	0.0411176	+	0.153453i
$328$	3.10255	−	1.79126i	0.171310	−	0.0989058i
$329$	−4.41909	−	6.40555i	−0.243632	−	0.353150i
$330$	14.5117	+	14.5117i	0.798844	+	0.798844i
$331$	12.8665	+	12.8665i	0.707209	+	0.707209i	0.965947	−	0.258738i	$-0.0833067\pi$
$331$	12.8665	+	12.8665i	0.707209	+	0.707209i	−0.258738	+	0.965947i	$0.583307\pi$
$332$	0.374717	−	1.39846i	0.0205653	−	0.0767506i
$333$	0.202220	+	0.754695i	0.0110816	+	0.0413570i
$334$		−	0.0146014i		−	0.000798951i
$335$	18.6101	+	32.2336i	1.01678	+	1.76111i
$336$	−2.49243	+	0.887573i	−0.135973	+	0.0484211i
$337$		−	6.02776i		−	0.328353i	−0.986431	−	0.164177i	$-0.947503\pi$
$337$		−	6.02776i		−	0.328353i	0.986431	−	0.164177i	$-0.0524967\pi$
$338$	6.79556	+	11.0824i	0.369630	+	0.602805i
$339$	−8.22554	−	4.74902i	−0.446750	−	0.257931i
$340$	−14.2003	−	14.2003i	−0.770117	−	0.770117i
$341$	−18.0871	−	10.4426i	−0.979471	−	0.565498i
$342$	0.725610	−	1.25679i	0.0392365	−	0.0679596i
$343$	15.8422	+	9.59301i	0.855396	+	0.517974i
$344$	−9.43266	+	2.52747i	−0.508575	+	0.136272i
$345$	−15.5461	+	15.5461i	−0.836973	+	0.836973i
$346$	−6.98802	+	1.87243i	−0.375678	+	0.100663i
$347$	−15.1018	−	26.1572i	−0.810710	−	1.40419i	−0.912368	−	0.409371i	$-0.865748\pi$
$347$	−15.1018	−	26.1572i	−0.810710	−	1.40419i	0.101658	−	0.994819i	$-0.467585\pi$
$348$	4.24486	−	7.35231i	0.227548	−	0.394125i
$349$	4.66318	−	17.4032i	0.249614	−	0.931573i	−0.721394	−	0.692525i	$-0.756498\pi$
$349$	4.66318	−	17.4032i	0.249614	−	0.931573i	0.971008	−	0.239048i	$-0.0768352\pi$
$350$	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
$353$	−1.18597	+	1.18597i	−0.0631230	+	0.0631230i	−0.737964	−	0.674841i	$-0.764212\pi$
$353$	−1.18597	+	1.18597i	−0.0631230	+	0.0631230i	0.674841	+	0.737964i	$0.264212\pi$
$354$	−0.935412			−0.0497166
$355$	−17.9529			−0.952842
$356$	4.52554	−	4.52554i	0.239853	−	0.239853i
$357$	−2.36979	+	12.9135i	−0.125423	+	0.683454i
$358$	4.17259	+	15.5723i	0.220528	+	0.823022i
$359$	0.214530	+	0.0574832i	0.0113225	+	0.00303385i	0.264476	−	0.964392i	$-0.414801\pi$
$359$	0.214530	+	0.0574832i	0.0113225	+	0.00303385i	−0.253153	+	0.967426i	$0.581468\pi$
$360$	3.50474	−	2.02346i	0.184716	−	0.106646i
$361$			16.8940i			0.889156i
$362$	−6.13974	+	1.64514i	−0.322698	+	0.0864666i
$363$	14.7169			0.772438
$364$	−6.48868	−	6.99264i	−0.340099	−	0.366514i
$365$	53.7734			2.81463
$366$	11.6960	−	3.13392i	0.611357	−	0.163813i
$367$			8.43917i			0.440521i	0.975441	+	0.220261i	$0.0706907\pi$
$367$			8.43917i			0.440521i	−0.975441	+	0.220261i	$0.929309\pi$
$368$	4.70481	−	2.71632i	0.245255	−	0.141598i
$369$	3.46045	+	0.927225i	0.180144	+	0.0482694i
$370$	0.818368	+	3.05419i	0.0425449	+	0.158780i
$371$	3.70026	+	10.3909i	0.192108	+	0.539466i
$372$	−2.91215	+	2.91215i	−0.150988	+	0.150988i
$373$	−10.2853			−0.532551			−0.266275	−	0.963897i	$-0.585793\pi$
$373$	−10.2853			−0.532551			−0.266275	+	0.963897i	$0.585793\pi$
$374$	−25.1649			−1.30125
$375$	−18.2501	+	18.2501i	−0.942431	+	0.942431i
$376$	−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	$-0.120773\pi$
$380$	2.93649	−	5.08614i	0.150639	−	0.260914i
$381$	−7.08657	−	12.2743i	−0.363056	−	0.628831i
$382$	20.1278	−	5.39324i	1.02983	−	0.275942i
$383$	−5.45036	+	5.45036i	−0.278500	+	0.278500i	−0.832510	−	0.554010i	$-0.813097\pi$
$383$	−5.45036	+	5.45036i	−0.278500	+	0.278500i	0.554010	+	0.832510i	$0.313097\pi$
$384$	−0.965926	+	0.258819i	−0.0492922	+	0.0132078i
$385$	9.80071	−	53.4061i	0.499491	−	2.72183i
$386$	5.37141	−	9.30356i	0.273398	−	0.473539i
$387$	−8.45709	−	4.88270i	−0.429898	−	0.248202i
$388$	7.16747	+	7.16747i	0.363873	+	0.363873i
$389$	−22.8006	−	13.1639i	−1.15604	−	0.667438i	−0.205686	−	0.978618i	$-0.565943\pi$
$389$	−22.8006	−	13.1639i	−1.15604	−	0.667438i	−0.950351	+	0.311180i	$0.899276\pi$
$390$	11.6926	+	8.72876i	0.592078	+	0.441998i
$391$		−	26.9586i		−	1.36336i
$392$	5.67762	+	4.09447i	0.286763	+	0.206802i
$393$	4.96946	+	8.60736i	0.250676	+	0.434184i
$394$			11.7713i			0.593028i
$395$	2.78454	+	10.3921i	0.140106	+	0.522881i
$396$	1.31252	−	4.89839i	0.0659566	−	0.246153i
$397$	7.39270	+	7.39270i	0.371029	+	0.371029i	0.867852	−	0.496823i	$-0.165500\pi$
$397$	7.39270	+	7.39270i	0.371029	+	0.371029i	−0.496823	+	0.867852i	$0.665500\pi$
$398$	13.7339	+	13.7339i	0.688417	+	0.688417i
$399$	−3.82719	+	0.308008i	−0.191599	+	0.0154197i
$400$	9.85327	−	5.68879i	0.492663	−	0.284439i
$401$	−2.65406	−	9.90509i	−0.132537	−	0.494636i	0.867458	−	0.497510i	$-0.165752\pi$
$401$	−2.65406	−	9.90509i	−0.132537	−	0.494636i	−0.999996	+	0.00287326i	$0.999085\pi$
$402$	4.59858	−	7.96498i	0.229356	−	0.397257i
$403$	−13.7928	−	5.50053i	−0.687066	−	0.274001i
$404$	3.39942	−	1.96266i	0.169128	−	0.0976459i
$405$	3.90903	+	1.04742i	0.194241	+	0.0520467i
$406$	−22.3893	+	1.80186i	−1.11116	+	0.0894250i
$407$	3.43137	+	1.98110i	0.170087	+	0.0981997i
$408$	−1.28435	+	4.79325i	−0.0635847	+	0.237301i
$409$	15.0571	+	4.03454i	0.744526	+	0.199495i	0.611089	−	0.791562i	$-0.290732\pi$
$409$	15.0571	+	4.03454i	0.744526	+	0.199495i	0.133437	+	0.991057i	$0.457399\pi$
$410$	14.0042	+	3.75240i	0.691616	+	0.185318i
$411$	−4.57208	+	17.0632i	−0.225524	+	0.841668i
$412$	−6.10594	−	3.52526i	−0.300818	−	0.173677i
$413$	1.40538	+	2.03712i	0.0691542	+	0.100240i
$414$	5.24753	+	1.40607i	0.257902	+	0.0691046i
$415$	5.07414	−	2.92955i	0.249080	−	0.143806i
$416$	−2.23257	−	2.83119i	−0.109461	−	0.138811i
$417$	6.39049	−	11.0687i	0.312944	−	0.542035i
$418$	−1.90475	−	7.10864i	−0.0931645	−	0.347695i
$419$	−14.7689	+	8.52681i	−0.721506	+	0.416562i	−0.815307	−	0.579029i	$-0.803432\pi$
$419$	−14.7689	+	8.52681i	−0.721506	+	0.416562i	0.0938005	+	0.995591i	$0.470098\pi$
$420$	−9.67224	−	4.59247i	−0.471957	−	0.224090i
$421$	−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	$-0.532031\pi$
$422$	2.40210	+	2.40210i	0.116932	+	0.116932i
$423$	0.761269	−	2.84109i	0.0370142	−	0.138139i
$424$	1.07901	+	4.02691i	0.0524012	+	0.195564i
$425$		−	56.4594i		−	2.73868i
$426$	2.21809	+	3.84185i	0.107467	+	0.186138i
$427$	−24.3972	−	20.7628i	−1.18066	−	1.00478i
$428$		−	7.93596i		−	0.383599i
$429$	18.0948	−	2.62619i	0.873627	−	0.126794i
$430$	−34.2252	−	19.7599i	−1.65049	−	0.952908i
$431$	19.0284	+	19.0284i	0.916566	+	0.916566i	0.996778	−	0.0802121i	$-0.0255598\pi$
$431$	19.0284	+	19.0284i	0.916566	+	0.916566i	−0.0802121	+	0.996778i	$0.525560\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	10.8841	−	18.8518i	0.523055	−	0.905958i	−0.476585	−	0.879128i	$-0.658126\pi$
$433$	10.8841	−	18.8518i	0.523055	−	0.905958i	0.999640	−	0.0268294i	$-0.00854110\pi$
$434$	10.7173	+	1.96676i	0.514447	+	0.0944077i
$435$	33.1865	−	8.89230i	1.59117	−	0.426353i
$436$	2.03137	−	2.03137i	0.0972852	−	0.0972852i
$437$	7.61532	−	2.04052i	0.364290	−	0.0976112i
$438$	−6.64375	−	11.5073i	−0.317450	−	0.549840i
$439$	−0.827717	+	1.43365i	−0.0395048	+	0.0684243i	−0.885102	−	0.465398i	$-0.845911\pi$
$439$	−0.827717	+	1.43365i	−0.0395048	+	0.0684243i	0.845597	+	0.533822i	$0.179245\pi$
$440$	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	−0.968871	−	0.247567i	$-0.920369\pi$
$443$	−14.7088	−	25.4763i	−0.698835	−	1.21042i	0.270036	−	0.962850i	$-0.412965\pi$
$444$	0.552475	−	0.552475i	0.0262193	−	0.0262193i
$445$	25.9006			1.22781
$446$	−19.3181			−0.914741
$447$	−8.24822	+	8.24822i	−0.390127	+	0.390127i
$448$	2.01488	+	1.71472i	0.0951940	+	0.0810130i
$449$	−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	$-0.385485\pi$
$450$	10.9899	+	2.94473i	0.518068	+	0.138816i
$451$	15.7336	−	9.08381i	0.740867	−	0.427740i
$452$			9.49803i			0.446750i
$453$	16.0351	−	4.29660i	0.753396	−	0.201872i
$454$	0.699115			0.0328111
$455$	1.44216	−	38.5782i	0.0676093	−	1.80857i
$456$	−1.45122			−0.0679596
$457$	−1.01758	+	0.272661i	−0.0476006	+	0.0127545i	−0.282541	−	0.959255i	$-0.591177\pi$
$457$	−1.01758	+	0.272661i	−0.0476006	+	0.0127545i	0.234940	+	0.972010i	$0.424511\pi$
$458$		−	14.3158i		−	0.668932i
$459$	−4.29751	+	2.48117i	−0.200591	+	0.115811i
$460$	21.2363	+	5.69026i	0.990149	+	0.265310i
$461$	5.12435	+	19.1243i	0.238665	+	0.890709i	0.976462	+	0.215687i	$0.0691992\pi$
$461$	5.12435	+	19.1243i	0.238665	+	0.890709i	−0.737798	+	0.675022i	$0.764134\pi$
$462$	−12.6396	+	4.50105i	−0.588046	+	0.209408i
$463$	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	$0.236228\pi$
$464$	−8.48971			−0.394125
$465$	−16.6668			−0.772906
$466$	−11.9978	+	11.9978i	−0.555789	+	0.555789i
$467$	11.3114	+	19.5920i	0.523431	+	0.906609i	0.999628	+	0.0272707i	$0.00868162\pi$
$467$	11.3114	+	19.5920i	0.523431	+	0.906609i	−0.476197	+	0.879339i	$0.657985\pi$
$468$	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
$471$	−11.2346	+	19.4589i	−0.517664	+	0.896620i
$472$	0.467706	+	0.810091i	0.0215279	+	0.0372874i
$473$	−47.8348	+	12.8173i	−2.19944	+	0.589339i
$474$	1.87983	−	1.87983i	0.0863433	−	0.0863433i
$475$	15.9487	−	4.27345i	0.731779	−	0.196080i
$476$	12.3683	−	4.40444i	0.566900	−	0.201877i
$477$	−2.08448	+	3.61043i	−0.0954418	+	0.165310i
$478$	13.3716	+	7.72011i	0.611604	+	0.353110i
$479$	18.4101	+	18.4101i	0.841178	+	0.841178i	0.989012	−	0.147834i	$-0.0472302\pi$
$479$	18.4101	+	18.4101i	0.841178	+	0.841178i	−0.147834	+	0.989012i	$0.547230\pi$
$480$	−3.50474	−	2.02346i	−0.159969	−	0.0923579i
$481$	2.61668	+	1.04353i	0.119310	+	0.0475808i
$482$			0.348325i			0.0158658i
$483$	−4.82187	−	13.5405i	−0.219402	−	0.616114i
$484$	−7.35846	−	12.7452i	−0.334475	−	0.579328i
$485$			41.0209i			1.86266i
$486$	−0.258819	−	0.965926i	−0.0117403	−	0.0438153i
$487$	0.697795	−	2.60421i	0.0316201	−	0.118008i	−0.948312	−	0.317340i	$-0.897210\pi$
$487$	0.697795	−	2.60421i	0.0316201	−	0.118008i	0.979932	+	0.199332i	$0.0638772\pi$
$488$	−8.56203	−	8.56203i	−0.387585	−	0.387585i
$489$	−0.539939	−	0.539939i	−0.0244169	−	0.0244169i
$490$	4.53034	+	27.9639i	0.204660	+	1.26328i
$491$	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	$0.0839970\pi$
$492$	−0.927225	−	3.46045i	−0.0418025	−	0.156009i
$493$	−21.0644	+	36.4846i	−0.948694	+	1.64319i
$494$	−2.06614	−	4.80724i	−0.0929602	−	0.216288i
$495$	17.7732	−	10.2613i	0.798844	−	0.461213i
$496$	3.97807	+	1.06592i	0.178621	+	0.0478613i
$497$	5.03422	−	10.6026i	0.225815	−	0.475592i
$498$	−1.25383	−	0.723897i	−0.0561853	−	0.0324386i
$499$	0.680186	−	2.53849i	0.0304493	−	0.113638i	−0.949029	−	0.315190i	$-0.897932\pi$
$499$	0.680186	−	2.53849i	0.0304493	−	0.113638i	0.979478	+	0.201552i	$0.0645984\pi$
$500$	24.9301	+	6.68000i	1.11491	+	0.298739i
$501$	−0.0141038	−	0.00377911i	−0.000630113	−	0.000168838i
$502$	−0.138602	+	0.517268i	−0.00618609	+	0.0230868i
$503$	28.0460	+	16.1924i	1.25051	+	0.721982i	0.971211	−	0.238222i	$-0.0765646\pi$
$503$	28.0460	+	16.1924i	1.25051	+	0.721982i	0.279299	+	0.960204i	$0.409898\pi$
$504$	0.212241	+	2.63722i	0.00945396	+	0.117471i
$505$	15.3442	+	4.11146i	0.682807	+	0.182957i
$506$	23.8589	−	13.7750i	1.06066	−	0.612372i
$507$	12.4636	−	3.69566i	0.553529	−	0.164130i
$508$	−7.08657	+	12.2743i	−0.314416	+	0.544584i
$509$	6.11884	+	22.8358i	0.271213	+	1.01218i	0.958337	+	0.285640i	$0.0922061\pi$
$509$	6.11884	+	22.8358i	0.271213	+	1.01218i	−0.687124	+	0.726540i	$0.741127\pi$
$510$	−17.3917	+	10.0411i	−0.770117	+	0.444627i
$511$	−15.0787	+	31.7574i	−0.667044	+	1.40487i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−1.02617	−	1.02617i	−0.0453064	−	0.0453064i
$514$	−5.49702	+	20.5152i	−0.242463	+	0.904885i
$515$	−7.38487	−	27.5607i	−0.325416	−	1.21447i
$516$			9.76541i			0.429898i
$517$	−7.45798	−	12.9176i	−0.328002	−	0.568116i
$518$	−2.03322	−	0.373122i	−0.0893345	−	0.0163941i
$519$			7.23453i			0.317561i
$520$	1.71302	−	14.4905i	0.0751210	−	0.635450i
$521$	−5.65413	−	3.26442i	−0.247712	−	0.143017i	0.371004	−	0.928631i	$-0.379014\pi$
$521$	−5.65413	−	3.26442i	−0.247712	−	0.143017i	−0.618716	+	0.785615i	$0.712347\pi$
$522$	−6.00313	−	6.00313i	−0.262750	−	0.262750i
$523$	6.58889	+	3.80410i	0.288112	+	0.166341i	0.637090	−	0.770789i	$-0.280138\pi$
$523$	6.58889	+	3.80410i	0.288112	+	0.166341i	−0.348978	+	0.937131i	$0.613471\pi$
$524$	4.96946	−	8.60736i	0.217092	−	0.376014i
$525$	−10.0984	−	28.3578i	−0.440731	−	1.23764i
$526$	12.0080	−	3.21752i	0.523572	−	0.140291i
$527$	14.4511	−	14.4511i	0.629499	−	0.629499i
$528$	−4.89839	+	1.31252i	−0.213175	+	0.0571201i
$529$	3.25680	+	5.64095i	0.141600	+	0.245259i
$530$	−8.43573	+	14.6111i	−0.366425	+	0.634666i
$531$	−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
$535$	22.7096	−	22.7096i	0.981821	−	0.981821i
$536$	−9.19716			−0.397257
$537$	16.1216			0.695700
$538$	−7.10129	+	7.10129i	−0.306158	+	0.306158i
$539$	28.7922	+	20.7638i	1.24017	+	0.894361i
$540$	−1.04742	−	3.90903i	−0.0450738	−	0.168218i
$541$	8.36067	+	2.24023i	0.359453	+	0.0963152i	0.434026	−	0.900900i	$-0.357093\pi$
$541$	8.36067	+	2.24023i	0.359453	+	0.0963152i	−0.0745728	+	0.997216i	$0.523759\pi$
$542$	−16.7794	+	9.68762i	−0.720739	+	0.416119i
$543$			6.35633i			0.272776i
$544$	4.79325	−	1.28435i	0.205509	−	0.0550660i
$545$	11.6260			0.498003
$546$	−8.43377	+	4.45775i	−0.360932	+	0.190774i
$547$	5.06040			0.216367			0.108184	−	0.994131i	$-0.465497\pi$
$547$	5.06040			0.216367			0.108184	+	0.994131i	$0.465497\pi$
$548$	17.0632	−	4.57208i	0.728906	−	0.195310i
$549$		−	12.1085i		−	0.516780i
$550$	49.9677	−	28.8489i	2.13063	−	1.23012i
$551$	−11.9006	−	3.18876i	−0.506984	−	0.135846i
$552$	−1.40607	−	5.24753i	−0.0598464	−	0.223350i
$553$	−6.91814	−	1.26957i	−0.294189	−	0.0539876i
$554$	−15.7952	+	15.7952i	−0.671073	+	0.671073i
$555$	3.16193			0.134217
$556$	−12.7810			−0.542035
$557$	−3.34236	+	3.34236i	−0.141620	+	0.141620i	−0.774363	−	0.632742i	$-0.781929\pi$
$557$	−3.34236	+	3.34236i	−0.141620	+	0.141620i	0.632742	+	0.774363i	$0.281929\pi$
$558$	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
$562$	13.6958	−	23.7218i	0.577723	−	1.00065i
$563$	0.729952	+	1.26431i	0.0307638	+	0.0532845i	0.880997	−	0.473121i	$-0.156873\pi$
$563$	0.729952	+	1.26431i	0.0307638	+	0.0532845i	−0.850234	+	0.526406i	$0.823539\pi$
$564$	−2.84109	+	0.761269i	−0.119632	+	0.0320552i
$565$	−27.1796	+	27.1796i	−1.14346	+	1.14346i
$566$	10.7925	−	2.89185i	0.453644	−	0.121553i
$567$	−1.71472	+	2.01488i	−0.0720116	+	0.0846169i
$568$	2.21809	−	3.84185i	0.0930692	−	0.161201i
$569$	−3.49714	−	2.01907i	−0.146608	−	0.0846440i	0.424902	−	0.905239i	$-0.360309\pi$
$569$	−3.49714	−	2.01907i	−0.146608	−	0.0846440i	−0.571510	+	0.820595i	$0.693642\pi$
$570$	−4.15282	−	4.15282i	−0.173942	−	0.173942i
$571$	−25.0701	−	14.4742i	−1.04915	−	0.605727i	−0.126739	−	0.991936i	$-0.540451\pi$
$571$	−25.0701	−	14.4742i	−1.04915	−	0.605727i	−0.922411	+	0.386209i	$0.873784\pi$
$572$	−11.3218	−	14.3575i	−0.473387	−	0.600317i
$573$		−	20.8379i		−	0.870515i
$574$	−6.14303	+	7.21834i	−0.256405	+	0.301288i
$575$	30.9051	+	53.5293i	1.28883	+	2.23233i
$576$			1.00000i			0.0416667i
$577$	−1.41837	−	5.29341i	−0.0590474	−	0.220368i	0.930097	−	0.367314i	$-0.119722\pi$
$577$	−1.41837	−	5.29341i	−0.0590474	−	0.220368i	−0.989145	+	0.146946i	$0.953056\pi$
$578$	1.97345	−	7.36502i	0.0820848	−	0.306344i
$579$	−7.59633	−	7.59633i	−0.315693	−	0.315693i
$580$	−24.2942	−	24.2942i	−1.00876	−	1.00876i
$581$	0.307281	+	3.81816i	0.0127482	+	0.158404i
$582$	8.77832	−	5.06816i	0.363873	−	0.210082i
$583$	5.47184	+	20.4212i	0.226621	+	0.845759i
$584$	−6.64375	+	11.5073i	−0.274920	+	0.476176i
$585$	11.4576	−	9.03503i	0.473714	−	0.373552i
$586$	17.2004	−	9.93065i	0.710542	−	0.410231i
$587$	−39.3764	−	10.5509i	−1.62524	−	0.435481i	−0.672703	−	0.739913i	$-0.734867\pi$
$587$	−39.3764	−	10.5509i	−1.62524	−	0.435481i	−0.952534	+	0.304432i	$0.901533\pi$
$588$	5.42443	−	4.42443i	0.223700	−	0.182460i
$589$	5.17598	+	2.98835i	0.213272	+	0.123133i
$590$	−0.979770	+	3.65655i	−0.0403365	+	0.150538i
$591$	11.3702	+	3.04663i	0.467707	+	0.125322i
$592$	−0.754695	−	0.202220i	−0.0310178	−	0.00831119i
$593$	−2.46852	+	9.21264i	−0.101370	+	0.378318i	−0.997908	−	0.0646487i	$-0.979407\pi$
$593$	−2.46852	+	9.21264i	−0.101370	+	0.378318i	0.896538	+	0.442967i	$0.146074\pi$
$594$	−4.39177	−	2.53559i	−0.180197	−	0.104037i
$595$	47.9970	+	22.7894i	1.96768	+	0.934275i
$596$	11.2673	+	3.01906i	0.461526	+	0.123665i
$597$	16.8205	−	9.71131i	0.688417	−	0.397457i
$598$	15.3808	−	12.1287i	0.628970	−	0.495981i
$599$	−17.6775	+	30.6183i	−0.722282	+	1.25103i	0.237800	+	0.971314i	$0.423574\pi$
$599$	−17.6775	+	30.6183i	−0.722282	+	1.25103i	−0.960083	+	0.279716i	$0.909760\pi$
$600$	−2.94473	−	10.9899i	−0.120218	−	0.448660i
$601$	−39.6382	+	22.8851i	−1.61688	+	0.933503i	−0.629154	+	0.777281i	$0.716598\pi$
$601$	−39.6382	+	22.8851i	−1.61688	+	0.933503i	−0.987722	+	0.156222i	$0.950068\pi$
$602$	21.2669	−	14.6717i	0.866776	−	0.597975i
$603$	−6.50338	−	6.50338i	−0.264838	−	0.264838i
$604$	−11.7385	−	11.7385i	−0.477634	−	0.477634i
$605$	15.4148	−	57.5288i	0.626701	−	2.33888i
$606$	−1.01595	−	3.79157i	−0.0412700	−	0.154022i
$607$			34.6434i			1.40613i	0.711124	+	0.703066i	$0.248186\pi$
$607$			34.6434i			1.40613i	−0.711124	+	0.703066i	$0.751814\pi$
$608$	0.725610	+	1.25679i	0.0294274	+	0.0509697i
$609$	−4.05430	+	22.0927i	−0.164289	+	0.895243i
$610$		−	49.0023i		−	1.98405i
$611$	−6.56669	−	8.32743i	−0.265660	−	0.336892i
$612$	4.29751	+	2.48117i	0.173717	+	0.100295i
$613$	−17.1866	−	17.1866i	−0.694161	−	0.694161i	0.268984	−	0.963145i	$-0.413312\pi$
$613$	−17.1866	−	17.1866i	−0.694161	−	0.694161i	−0.963145	+	0.268984i	$0.913312\pi$
$614$	2.45360	+	1.41659i	0.0990192	+	0.0571687i
$615$	7.24909	−	12.5558i	0.292311	−	0.506298i
$616$	10.2178	+	8.69567i	0.411687	+	0.350359i
$617$	−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	$0.456842\pi$
$618$	−4.98548	+	4.98548i	−0.200545	+	0.200545i
$619$	−18.8116	+	5.04055i	−0.756102	+	0.202597i	−0.616223	−	0.787572i	$-0.711338\pi$
$619$	−18.8116	+	5.04055i	−0.756102	+	0.202597i	−0.139879	+	0.990169i	$0.544671\pi$
$620$	8.33342	+	14.4339i	0.334678	+	0.579680i
$621$	2.71632	−	4.70481i	0.109002	−	0.188797i
$622$	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
$626$	18.1803	−	18.1803i	0.726632	−	0.726632i
$627$	−7.35940			−0.293906
$628$	22.4692			0.896620
$629$	−2.74157	+	2.74157i	−0.109314	+	0.109314i
$630$	−6.93935	+	8.15405i	−0.276470	+	0.324865i
$631$	−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	$0.981892\pi$
$632$	−2.56789	−	0.688065i	−0.102145	−	0.0273697i
$633$	2.94196	−	1.69854i	0.116932	−	0.0675109i
$634$			32.5565i			1.29298i
$635$	−55.4031	+	14.8452i	−2.19861	+	0.589115i
$636$	4.16896			0.165310
$637$	22.3791	+	11.6695i	0.886691	+	0.462363i
$638$	−43.0529			−1.70448
$639$	4.28503	−	1.14817i	0.169513	−	0.0454209i
$640$			4.04692i			0.159969i
$641$	11.0356	−	6.37140i	0.435880	−	0.251655i	−0.265969	−	0.963982i	$-0.585692\pi$
$641$	11.0356	−	6.37140i	0.435880	−	0.251655i	0.701848	+	0.712326i	$0.252358\pi$
$642$	−7.66555	−	2.05398i	−0.302535	−	0.0810641i
$643$	−0.166808	−	0.622537i	−0.00657828	−	0.0245505i	0.962559	−	0.271073i	$-0.0873786\pi$
$643$	−0.166808	−	0.622537i	−0.00657828	−	0.0245505i	−0.969137	+	0.246523i	$0.920712\pi$
$644$	−9.31547	+	10.9461i	−0.367081	+	0.431337i
$645$	−27.9447	+	27.9447i	−1.10032	+	1.10032i
$646$	7.20145			0.283337
$647$	−16.8329			−0.661768			−0.330884	−	0.943671i	$-0.607347\pi$
$647$	−16.8329			−0.661768			−0.330884	+	0.943671i	$0.607347\pi$
$648$	−0.707107	+	0.707107i	−0.0277778	+	0.0277778i
$649$	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
$653$	3.60462	−	6.24338i	0.141060	−	0.244322i	−0.786836	−	0.617162i	$-0.788282\pi$
$653$	3.60462	−	6.24338i	0.141060	−	0.244322i	0.927896	+	0.372839i	$0.121616\pi$
$654$	−1.43640	−	2.48792i	−0.0561676	−	0.0972852i
$655$	38.8515	−	10.4102i	1.51805	−	0.406762i
$656$	−2.53322	+	2.53322i	−0.0989058	+	0.0989058i
$657$	−12.8347	+	3.43906i	−0.500731	+	0.134170i
$658$	5.92639	+	5.04354i	0.231035	+	0.196618i
$659$	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	$0.114063\pi$
$660$	−17.7732	−	10.2613i	−0.691820	−	0.399422i
$661$	−1.81867	−	1.81867i	−0.0707382	−	0.0707382i	0.670853	−	0.741591i	$-0.265928\pi$
$661$	−1.81867	−	1.81867i	−0.0707382	−	0.0707382i	−0.741591	+	0.670853i	$0.765928\pi$
$662$	−15.7582	−	9.09802i	−0.612461	−	0.353605i
$663$	−2.10051	+	17.7682i	−0.0815771	+	0.690062i
$664$			1.44779i			0.0561853i
$665$	−2.80467	+	15.2832i	−0.108760	+	0.592657i
$666$	−0.390659	−	0.676641i	−0.0151377	−	0.0262193i
$667$		−	46.1216i		−	1.78583i
$668$	0.00377911	+	0.0141038i	0.000146218	+	0.000545694i
$669$	−4.99990	+	18.6599i	−0.193307	+	0.721433i
$670$	−26.3187	−	26.3187i	−1.01678	−	1.01678i
$671$	−43.4196	−	43.4196i	−1.67620	−	1.67620i
$672$	2.17778	−	1.50242i	0.0840098	−	0.0579570i
$673$	−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	$0.420964\pi$
$674$	1.56010	+	5.82237i	0.0600928	+	0.224269i
$675$	5.68879	−	9.85327i	0.218961	−	0.379252i
$676$	−9.43235	−	8.94599i	−0.362783	−	0.344077i
$677$	6.31593	−	3.64650i	0.242741	−	0.140146i	−0.373695	−	0.927552i	$-0.621909\pi$
$677$	6.31593	−	3.64650i	0.242741	−	0.140146i	0.616436	+	0.787405i	$0.288576\pi$
$678$	9.17439	+	2.45827i	0.352340	+	0.0944094i
$679$	−24.2261	−	11.5028i	−0.929711	−	0.441436i
$680$	17.3917	+	10.0411i	0.666941	+	0.385059i
$681$	0.180944	−	0.675293i	0.00693380	−	0.0258773i
$682$	20.1735	+	5.40548i	0.772484	+	0.206987i
$683$	−45.0392	−	12.0682i	−1.72338	−	0.461777i	−0.744736	−	0.667359i	$-0.767425\pi$
$683$	−45.0392	−	12.0682i	−1.72338	−	0.461777i	−0.978640	+	0.205582i	$0.934091\pi$
$684$	−0.375603	+	1.40177i	−0.0143616	+	0.0535980i
$685$	61.9118	+	35.7448i	2.36553	+	1.36574i
$686$	−17.7852	−	5.16589i	−0.679042	−	0.197234i
$687$	−13.8280	−	3.70519i	−0.527570	−	0.141362i
$688$	8.45709	−	4.88270i	0.322424	−	0.186151i
$689$	5.93547	+	13.8099i	0.226123	+	0.526115i
$690$	10.9927	−	19.0400i	0.418486	−	0.724840i
$691$	−7.53901	−	28.1360i	−0.286798	−	1.07034i	−0.947516	−	0.319709i	$-0.896415\pi$
$691$	−7.53901	−	28.1360i	−0.286798	−	1.07034i	0.660718	−	0.750634i	$-0.270252\pi$
$692$	6.26529	−	3.61727i	0.238170	−	0.137508i
$693$	1.07631	+	13.3739i	0.0408857	+	0.508031i
$694$	21.3572	+	21.3572i	0.810710	+	0.810710i
$695$	−36.5741	−	36.5741i	−1.38734	−	1.38734i
$696$	−2.19730	+	8.20043i	−0.0832884	+	0.310837i
$697$	4.60120	+	17.1719i	0.174283	+	0.650433i
$698$			18.0171i			0.681959i
$699$	8.48375	+	14.6943i	0.320885	+	0.555789i
$700$	−19.5094	+	22.9244i	−0.737385	+	0.866461i
$701$			52.2166i			1.97219i	0.166172	+	0.986097i	$0.446859\pi$
$701$			52.2166i			1.97219i	−0.166172	+	0.986097i	$0.553141\pi$
$702$	−3.34906	−	1.33560i	−0.126402	−	0.0504089i
$703$	−0.981955	−	0.566932i	−0.0370351	−	0.0213822i
$704$	3.58587	+	3.58587i	0.135148	+	0.135148i
$705$	−10.3085	−	5.95164i	−0.388242	−	0.224152i
$706$	0.838610	−	1.45252i	0.0315615	−	0.0546661i
$707$	−6.73083	+	7.90903i	−0.253139	+	0.297450i
$708$	0.903539	−	0.242102i	0.0339571	−	0.00909877i
$709$	−7.29179	+	7.29179i	−0.273849	+	0.273849i	−0.830648	−	0.556799i	$-0.812029\pi$
$709$	−7.29179	+	7.29179i	−0.273849	+	0.273849i	0.556799	+	0.830648i	$0.312029\pi$
$710$	17.3412	−	4.64656i	0.650803	−	0.174382i
$711$	−1.32924	−	2.30231i	−0.0498503	−	0.0863433i
$712$	−3.20004	+	5.54263i	−0.119927	+	0.207719i
$713$	−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
$717$	10.9179	−	10.9179i	0.407736	−	0.407736i
$718$	−0.222098			−0.00828862
$719$	−24.1413			−0.900318			−0.450159	−	0.892948i	$-0.648633\pi$
$719$	−24.1413			−0.900318			−0.450159	+	0.892948i	$0.648633\pi$
$720$	−2.86161	+	2.86161i	−0.106646	+	0.106646i
$721$	18.3476	+	3.36702i	0.683299	+	0.125394i
$722$	−4.37248	−	16.3183i	−0.162727	−	0.607305i
$723$	0.336456	+	0.0901532i	0.0125129	+	0.00335283i
$724$	5.50474	−	3.17816i	0.204582	−	0.118116i
$725$		−	96.5923i		−	3.58735i
$726$	−14.2154	+	3.80902i	−0.527585	+	0.141366i
$727$	50.2420			1.86337			0.931686	−	0.363265i	$-0.118338\pi$
$727$	50.2420			1.86337			0.931686	+	0.363265i	$0.118338\pi$
$728$	8.07741	+	5.07498i	0.299369	+	0.188091i
$729$	−1.00000			−0.0370370
$730$	−51.9411	+	13.9176i	−1.92243	+	0.515113i
$731$		−	48.4593i		−	1.79233i
$732$	−10.4863	+	6.05427i	−0.387585	+	0.223772i
$733$	−23.0344	−	6.17205i	−0.850796	−	0.227970i	−0.193030	−	0.981193i	$-0.561832\pi$
$733$	−23.0344	−	6.17205i	−0.850796	−	0.227970i	−0.657765	+	0.753223i	$0.728498\pi$
$734$	−2.18422	−	8.15161i	−0.0806209	−	0.300881i
$735$	28.1835	+	2.86161i	1.03957	+	0.105552i
$736$	−3.84146	+	3.84146i	−0.141598	+	0.141598i
$737$	−46.6405			−1.71803
$738$	−3.58252			−0.131874
$739$	−28.9229	+	28.9229i	−1.06395	+	1.06395i	−0.0661374	+	0.997811i	$0.521068\pi$
$739$	−28.9229	+	28.9229i	−1.06395	+	1.06395i	−0.997811	+	0.0661374i	$0.978932\pi$
$740$	−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	$0.983443\pi$
$744$	2.05920	−	3.56664i	0.0754940	−	0.130759i
$745$	23.6031	+	40.8818i	0.864752	+	1.49779i
$746$	9.93480	−	2.66202i	0.363739	−	0.0974636i
$747$	−1.02375	+	1.02375i	−0.0374569	+	0.0374569i
$748$	24.3075	−	6.51317i	0.888769	−	0.238145i
$749$	7.04375	+	19.7798i	0.257373	+	0.722740i
$750$	12.9048	−	22.3517i	0.471215	−	0.816169i
$751$	16.1027	+	9.29688i	0.587595	+	0.339248i	0.764146	−	0.645043i	$-0.223161\pi$
$751$	16.1027	+	9.29688i	0.587595	+	0.339248i	−0.176551	+	0.984291i	$0.556494\pi$
$752$	2.07983	+	2.07983i	0.0758434	+	0.0758434i
$753$	0.463770	+	0.267758i	0.0169007	+	0.00975763i
$754$	−30.2927	+	4.39652i	−1.10320	+	0.160112i
$755$		−	67.1821i		−	2.44501i
$756$	2.60230	+	0.477555i	0.0946446	+	0.0173685i
$757$	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	$0.484062\pi$
$758$			23.2904i			0.845944i
$759$	−7.13045	−	26.6112i	−0.258819	−	0.965925i
$760$	−1.52004	+	5.67286i	−0.0551375	+	0.205776i
$761$	31.5422	+	31.5422i	1.14340	+	1.14340i	0.987823	+	0.155581i	$0.0497250\pi$
$761$	31.5422	+	31.5422i	1.14340	+	1.14340i	0.155581	+	0.987823i	$0.450275\pi$
$762$	10.0219	+	10.0219i	0.363056	+	0.363056i
$763$	−3.26007	+	6.86606i	−0.118022	+	0.248568i
$764$	−18.0461	+	10.4189i	−0.652886	+	0.376944i
$765$	5.19766	+	19.3979i	0.187922	+	0.701333i
$766$	3.85399	−	6.67530i	0.139250	−	0.241188i
$767$	2.08837	+	2.64833i	0.0754067	+	0.0956257i
$768$	0.866025	−	0.500000i	0.0312500	−	0.0180422i
$769$	−17.1234	−	4.58821i	−0.617487	−	0.165455i	−0.0635019	−	0.997982i	$-0.520227\pi$
$769$	−17.1234	−	4.58821i	−0.617487	−	0.165455i	−0.553985	+	0.832527i	$0.686894\pi$
$770$	4.35575	+	54.1229i	0.156970	+	1.95046i
$771$	18.3934	+	10.6194i	0.662422	+	0.382449i
$772$	−2.78045	+	10.3768i	−0.100071	+	0.373468i
$773$	7.81454	+	2.09390i	0.281070	+	0.0753124i	0.396600	−	0.917992i	$-0.370190\pi$
$773$	7.81454	+	2.09390i	0.281070	+	0.0753124i	−0.115530	+	0.993304i	$0.536857\pi$
$774$	9.43266	+	2.52747i	0.339050	+	0.0908482i
$775$	−12.1276	+	45.2608i	−0.435636	+	1.62582i
$776$	−8.77832	−	5.06816i	−0.315123	−	0.181936i
$777$	−0.886644	+	1.86737i	−0.0318082	+	0.0669915i
$778$	25.4308	+	6.81416i	0.911738	+	0.244299i
$779$	−4.50249	+	2.59951i	−0.161318	+	0.0931372i
$780$	−13.5534	−	5.40507i	−0.485288	−	0.193532i
$781$	11.2484	−	19.4827i	0.402498	−	0.697147i
$782$	6.97741	+	26.0400i	0.249512	+	0.931190i
$783$	−7.35231	+	4.24486i	−0.262750	+	0.151699i
$784$	−6.54388	−	2.48548i	−0.233710	−	0.0887671i
$785$	64.2981	+	64.2981i	2.29490	+	2.29490i
$786$	−7.02788	−	7.02788i	−0.250676	−	0.250676i
$787$	−7.43270	+	27.7392i	−0.264947	+	0.988796i	0.697336	+	0.716745i	$0.254369\pi$
$787$	−7.43270	+	27.7392i	−0.264947	+	0.988796i	−0.962283	+	0.272051i	$0.912298\pi$
$788$	−3.04663	−	11.3702i	−0.108532	−	0.405046i
$789$		−	12.4316i		−	0.442575i
$790$	−5.37932	−	9.31726i	−0.191388	−	0.331493i
$791$	−8.43020	−	23.6732i	−0.299743	−	0.841722i
$792$			5.07118i			0.180197i
$793$	−34.9847	−	26.1168i	−1.24234	−	0.927434i
$794$	−9.05417	−	5.22743i	−0.321320	−	0.185514i
$795$	11.9299	+	11.9299i	0.423111	+	0.423111i
$796$	−16.8205	−	9.71131i	−0.596186	−	0.344208i
$797$	8.46866	−	14.6682i	0.299975	−	0.519573i	−0.676155	−	0.736760i	$-0.736355\pi$
$797$	8.46866	−	14.6682i	0.299975	−	0.519573i	0.976130	+	0.217187i	$0.0696882\pi$
$798$	3.61707	−	1.28806i	0.128043	−	0.0455969i
$799$	14.0985	−	3.77768i	0.498768	−	0.133645i
$800$	−8.04516	+	8.04516i	−0.284439	+	0.284439i
$801$	−6.18200	+	1.65646i	−0.218430	+	0.0585282i
$802$	5.12725	+	8.88066i	0.181049	+	0.313587i
$803$	−33.6917	+	58.3557i	−1.18895	+	2.05933i
$804$	−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
$808$	−2.77562	+	2.77562i	−0.0976459	+	0.0976459i
$809$	44.4319			1.56214			0.781072	−	0.624441i	$-0.214673\pi$
$809$	44.4319			1.56214			0.781072	+	0.624441i	$0.214673\pi$
$810$	−4.04692			−0.142194
$811$	8.45727	−	8.45727i	0.296975	−	0.296975i	−0.542853	−	0.839828i	$-0.682656\pi$
$811$	8.45727	−	8.45727i	0.296975	−	0.296975i	0.839828	+	0.542853i	$0.182656\pi$
$812$	21.1600	−	7.53524i	0.742571	−	0.264435i
$813$	5.01468	+	18.7150i	0.175873	+	0.656365i
$814$	−3.82720	−	1.02549i	−0.134143	−	0.0359436i
$815$	−2.67618	+	1.54509i	−0.0937425	+	0.0541222i
$816$		−	4.96234i		−	0.173717i
$817$	13.6889	−	3.66792i	0.478913	−	0.128324i
$818$	−15.5883			−0.545031
$819$	2.12304	+	9.30015i	0.0741849	+	0.324973i
$820$	−14.4982			−0.506298
$821$	9.86182	−	2.64247i	0.344180	−	0.0922228i	−0.0825883	−	0.996584i	$-0.526319\pi$
$821$	9.86182	−	2.64247i	0.344180	−	0.0922228i	0.426768	+	0.904361i	$0.359652\pi$
$822$		−	17.6652i		−	0.616143i
$823$	5.29182	−	3.05524i	0.184461	−	0.106499i	−0.404926	−	0.914350i	$-0.632703\pi$
$823$	5.29182	−	3.05524i	0.184461	−	0.106499i	0.589387	+	0.807851i	$0.299369\pi$
$824$	6.81029	+	1.82481i	0.237248	+	0.0635703i
$825$	−14.9333	−	55.7318i	−0.519910	−	1.94033i
$826$	−1.88474	−	1.60397i	−0.0655785	−	0.0558093i
$827$	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	$0.165786\pi$
$828$	−5.43264			−0.188797
$829$	47.0104			1.63274			0.816369	−	0.577531i	$-0.195984\pi$
$829$	47.0104			1.63274			0.816369	+	0.577531i	$0.195984\pi$
$830$	−4.14302	+	4.14302i	−0.143806	+	0.143806i
$831$	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
$835$	−0.0295453	+	0.0511739i	−0.00102246	+	0.00177095i
$836$	3.67970	+	6.37343i	0.127265	+	0.220430i
$837$	3.97807	−	1.06592i	0.137502	−	0.0368436i
$838$	12.0587	−	12.0587i	0.416562	−	0.416562i
$839$	−46.1618	+	12.3690i	−1.59368	+	0.427026i	−0.943127	−	0.332432i	$-0.892131\pi$
$839$	−46.1618	+	12.3690i	−1.59368	+	0.427026i	−0.650556	+	0.759458i	$0.725464\pi$
$840$	10.5313	+	1.93263i	0.363364	+	0.0666820i
$841$	−21.5376	+	37.3042i	−0.742676	+	1.28635i
$842$	27.5270	+	15.8927i	0.948644	+	0.547700i
$843$	−19.3688	−	19.3688i	−0.667097	−	0.667097i
$844$	−2.94196	−	1.69854i	−0.101266	−	0.0584662i
$845$	−1.39176	−	52.5916i	−0.0478779	−	1.80920i
$846$			2.94132i			0.101125i
$847$	29.6528	+	25.2354i	1.01888	+	0.867099i
$848$	−2.08448	−	3.61043i	−0.0715814	−	0.123983i
$849$		−	11.1732i		−	0.383465i
$850$	14.6128	+	54.5356i	0.501214	+	1.87056i
$851$	1.09859	−	4.09999i	0.0376591	−	0.140546i
$852$	−3.13686	−	3.13686i	−0.107467	−	0.107467i
$853$	−27.3996	−	27.3996i	−0.938143	−	0.938143i	0.0600519	−	0.998195i	$-0.480873\pi$
$853$	−27.3996	−	27.3996i	−0.938143	−	0.938143i	−0.998195	+	0.0600519i	$0.980873\pi$
$854$	28.9397	+	13.7409i	0.990296	+	0.470202i
$855$	−5.08614	+	2.93649i	−0.173942	+	0.100426i
$856$	2.05398	+	7.66555i	0.0702035	+	0.262003i
$857$	−24.0598	+	41.6729i	−0.821869	+	1.42352i	0.0824204	+	0.996598i	$0.473735\pi$
$857$	−24.0598	+	41.6729i	−0.821869	+	1.42352i	−0.904289	+	0.426921i	$0.859598\pi$
$858$	−16.7986	+	7.21999i	−0.573493	+	0.246486i
$859$	39.5475	−	22.8327i	1.34934	−	0.779043i	0.361186	−	0.932494i	$-0.382372\pi$
$859$	39.5475	−	22.8327i	1.34934	−	0.779043i	0.988156	+	0.153451i	$0.0490387\pi$
$860$	38.1732	+	10.2285i	1.30170	+	0.348789i
$861$	5.38244	+	7.80195i	0.183433	+	0.265890i
$862$	−23.3049	−	13.4551i	−0.793769	−	0.458283i
$863$	6.69091	−	24.9708i	0.227761	−	0.850016i	−0.753518	−	0.657427i	$-0.771645\pi$
$863$	6.69091	−	24.9708i	0.227761	−	0.850016i	0.981279	−	0.192589i	$-0.0616884\pi$
$864$	0.965926	+	0.258819i	0.0328615	+	0.00880520i
$865$	28.2800	+	7.57759i	0.961548	+	0.257646i
$866$	−5.63401	+	21.0264i	−0.191451	+	0.714506i
$867$	−6.60330	−	3.81242i	−0.224260	−	0.129476i
$868$	−10.8611	+	0.874093i	−0.368651	+	0.0296686i
$869$	−13.0223	−	3.48930i	−0.441750	−	0.118366i
$870$	−29.7542	+	17.1786i	−1.00876	+	0.582409i
$871$	−32.8170	+	4.76289i	−1.11196	+	0.161384i
$872$	−1.43640	+	2.48792i	−0.0486426	+	0.0842515i
$873$	−2.62347	−	9.79094i	−0.0887912	−	0.331373i
$874$	−6.82771	+	3.94198i	−0.230951	+	0.133339i
$875$	−68.0655	+	5.47784i	−2.30104	+	0.185185i
$876$	9.39568	+	9.39568i	0.317450	+	0.317450i
$877$	−0.815934	−	0.815934i	−0.0275521	−	0.0275521i	0.693197	−	0.720749i	$-0.256202\pi$
$877$	−0.815934	−	0.815934i	−0.0275521	−	0.0275521i	−0.720749	+	0.693197i	$0.756202\pi$
$878$	0.428458	−	1.59903i	0.0144598	−	0.0539645i
$879$	−5.14048	−	19.1845i	−0.173384	−	0.647079i
$880$			20.5227i			0.691820i
$881$	15.2953	+	26.4923i	0.515312	+	0.892547i	0.999842	+	0.0177724i	$0.00565742\pi$
$881$	15.2953	+	26.4923i	0.515312	+	0.892547i	−0.484530	+	0.874775i	$0.661009\pi$
$882$	−2.86972	−	6.38472i	−0.0966287	−	0.214985i
$883$		−	7.60820i		−	0.256036i	−0.991772	−	0.128018i	$-0.959138\pi$
$883$		−	7.60820i		−	0.256036i	0.991772	−	0.128018i	$-0.0408616\pi$
$884$	16.4380	−	7.06503i	0.552870	−	0.237623i
$885$	3.27837	+	1.89277i	0.110201	+	0.0636248i
$886$	20.8013	+	20.8013i	0.698835	+	0.698835i
$887$	18.5517	+	10.7109i	0.622907	+	0.359635i	0.778000	−	0.628265i	$-0.216234\pi$
$887$	18.5517	+	10.7109i	0.622907	+	0.359635i	−0.155093	+	0.987900i	$0.549568\pi$
$888$	−0.390659	+	0.676641i	−0.0131097	+	0.0227066i
$889$	6.76845	−	36.8827i	0.227007	−	1.23701i
$890$	−25.0181	+	6.70357i	−0.838608	+	0.224704i
$891$	−3.58587	+	3.58587i	−0.120131	+	0.120131i
$892$	18.6599	−	4.99990i	0.624779	−	0.167409i
$893$	2.13425	+	3.69663i	0.0714199	+	0.123703i
$894$	5.83237	−	10.1020i	0.195064	−	0.337860i
$895$	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
$899$	24.7233	−	24.7233i	0.824569	−	0.824569i
$900$	−11.3776			−0.379252
$901$	−20.6878			−0.689211
$902$	−12.8464	+	12.8464i	−0.427740	+	0.427740i
$903$	−8.66751	−	24.3396i	−0.288437	−	0.809972i
$904$	−2.45827	−	9.17439i	−0.0817609	−	0.305136i
$905$	24.8471	+	6.65775i	0.825944	+	0.221311i
$906$	−14.3767	+	8.30039i	−0.477634	+	0.275762i
$907$		−	28.7807i		−	0.955648i	−0.878456	−	0.477824i	$-0.841426\pi$
$907$		−	28.7807i		−	0.955648i	0.878456	−	0.477824i	$-0.158574\pi$
$908$	−0.675293	+	0.180944i	−0.0224104	+	0.00600485i
$909$	−3.92532			−0.130195
$910$	8.59176	+	37.6370i	0.284814	+	1.24765i
$911$	13.0247			0.431529			0.215764	−	0.976445i	$-0.430776\pi$
$911$	13.0247			0.431529			0.215764	+	0.976445i	$0.430776\pi$
$912$	1.40177	−	0.375603i	0.0464173	−	0.0124375i
$913$			7.34203i			0.242986i
$914$	0.912341	−	0.526740i	0.0301776	−	0.0174230i
$915$	−47.3326	−	12.6827i	−1.56477	−	0.419278i
$916$	3.70519	+	13.8280i	0.122423	+	0.456889i
$917$	−4.74639	+	25.8640i	−0.156739	+	0.854105i
$918$	3.50891	−	3.50891i	0.115811	−	0.115811i
$919$	55.5363			1.83197			0.915986	−	0.401209i	$-0.131410\pi$
$919$	55.5363			1.83197			0.915986	+	0.401209i	$0.131410\pi$
$920$	−21.9855			−0.724840
$921$	2.00335	−	2.00335i	0.0660128	−	0.0660128i
$922$	−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
$926$	−0.930683	+	1.61199i	−0.0305841	+	0.0529733i
$927$	3.52526	+	6.10594i	0.115785	+	0.200545i
$928$	8.20043	−	2.19730i	0.269192	−	0.0721299i
$929$	19.5354	−	19.5354i	0.640936	−	0.640936i	−0.309849	−	0.950786i	$-0.600279\pi$
$929$	19.5354	−	19.5354i	0.640936	−	0.640936i	0.950786	+	0.309849i	$0.100279\pi$
$930$	16.0989	−	4.31370i	0.527905	−	0.141452i
$931$	−8.23947	−	5.94197i	−0.270038	−	0.194740i
$932$	8.48375	−	14.6943i	0.277894	−	0.481327i
$933$	−18.1233	−	10.4635i	−0.593332	−	0.342560i
$934$	−15.9968	−	15.9968i	−0.523431	−	0.523431i
$935$	88.1965	+	50.9203i	2.88433	+	1.66527i
$936$	0.517865	+	3.56817i	0.0169269	+	0.116629i
$937$		−	3.19610i		−	0.104412i	−0.998636	−	0.0522060i	$-0.983375\pi$
$937$		−	3.19610i		−	0.104412i	0.998636	−	0.0522060i	$-0.0166253\pi$
$938$	22.9233	−	8.16315i	0.748472	−	0.266536i
$939$	−12.8554	−	22.2663i	−0.419521	−	0.726632i
$940$			11.9033i			0.388242i
$941$	−4.20141	−	15.6799i	−0.136962	−	0.511149i	−0.999982	−	0.00597943i	$-0.998097\pi$
$941$	−4.20141	−	15.6799i	−0.136962	−	0.511149i	0.863020	−	0.505169i	$-0.168570\pi$
$942$	5.81547	−	21.7036i	0.189478	−	0.707142i
$943$	−13.7621	−	13.7621i	−0.448156	−	0.448156i
$944$	−0.661436	−	0.661436i	−0.0215279	−	0.0215279i
$945$	6.08017	+	8.81332i	0.197788	+	0.286697i
$946$	42.8875	−	24.7611i	1.39439	−	0.805053i
$947$	2.38139	+	8.88747i	0.0773848	+	0.288804i	0.993763	−	0.111508i	$-0.0355682\pi$
$947$	2.38139	+	8.88747i	0.0773848	+	0.288804i	−0.916379	+	0.400313i	$0.868902\pi$
$948$	−1.32924	+	2.30231i	−0.0431717	+	0.0747755i
$949$	−17.7468	+	44.5006i	−0.576084	+	1.44455i
$950$	−14.2993	+	8.25568i	−0.463929	+	0.267850i
$951$	31.4472	+	8.42624i	1.01974	+	0.273240i
$952$	−10.8069	+	7.45551i	−0.350254	+	0.241635i
$953$	−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	$0.745272\pi$
$954$	1.07901	−	4.02691i	0.0349341	−	0.130376i
$955$	−81.4558	−	21.8260i	−2.63585	−	0.706273i
$956$	−14.9141	−	3.99622i	−0.482357	−	0.129247i
$957$	−11.1429	+	41.5859i	−0.360199	+	1.34428i
$958$	−22.5476	−	13.0179i	−0.728481	−	0.420589i
$959$	−38.4709	+	26.5405i	−1.24229	+	0.857036i
$960$	3.90903	+	1.04742i	0.126163	+	0.0338053i
$961$	12.1579	−	7.01939i	0.392191	−	0.226432i
$962$	−2.79760	−	0.330724i	−0.0901983	−	0.0106630i
$963$	−3.96798	+	6.87275i	−0.127866	+	0.221471i
$964$	−0.0901532	−	0.336456i	−0.00290364	−	0.0108365i
$965$	−37.6508	+	21.7377i	−1.21202	+	0.699761i
$966$	8.16210	+	11.8311i	0.262611	+	0.380660i
$967$	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	$0.397413\pi$
$968$	10.4064	+	10.4064i	0.334475	+	0.334475i
$969$	1.86387	−	6.95606i	0.0598762	−	0.223461i
$970$	−10.6170	−	39.6232i	−0.340891	−	1.27222i
$971$		−	39.0924i		−	1.25453i	−0.778804	−	0.627267i	$-0.784173\pi$
$971$		−	39.0924i		−	1.25453i	0.778804	−	0.627267i	$-0.215827\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	31.8557	−	11.3441i	1.02125	−	0.363674i
$974$			2.69607i			0.0863877i
$975$	−16.1986	−	37.6888i	−0.518770	−	1.20701i
$976$	10.4863	+	6.05427i	0.335658	+	0.193792i
$977$	−4.90116	−	4.90116i	−0.156802	−	0.156802i	0.624346	−	0.781148i	$-0.285366\pi$
$977$	−4.90116	−	4.90116i	−0.156802	−	0.156802i	−0.781148	+	0.624346i	$0.785366\pi$
$978$	0.661288	+	0.381795i	0.0211456	+	0.0122084i
$979$	−16.2280	+	28.1077i	−0.518649	+	0.898326i
$980$	−11.6136	−	25.8385i	−0.370981	−	0.825380i
$981$	−2.77491	+	0.743535i	−0.0885960	+	0.0237392i
$982$	−22.1123	+	22.1123i	−0.705631	+	0.705631i
$983$	−1.65319	+	0.442972i	−0.0527287	+	0.0141286i	−0.285087	−	0.958502i	$-0.592022\pi$
$983$	−1.65319	+	0.442972i	−0.0527287	+	0.0141286i	0.232358	+	0.972630i	$0.425356\pi$
$984$	1.79126	+	3.10255i	0.0571033	+	0.0989058i
$985$	23.8187	−	41.2552i	0.758927	−	1.31450i
$986$	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
$990$	−14.5117	+	14.5117i	−0.461213	+	0.461213i
$991$	−28.2764			−0.898230			−0.449115	−	0.893474i	$-0.648261\pi$
$991$	−28.2764			−0.898230			−0.449115	+	0.893474i	$0.648261\pi$
$992$	−4.11840			−0.130759
$993$	−12.8665	+	12.8665i	−0.408307	+	0.408307i
$994$	−2.11852	+	11.5443i	−0.0671955	+	0.366162i
$995$	−20.3436	−	75.9235i	−0.644937	−	2.40694i
$996$	1.39846	+	0.374717i	0.0443120	+	0.0118734i
$997$	0.0369001	−	0.0213043i	0.00116864	−	0.000674713i	−0.499416	−	0.866363i	$-0.666452\pi$
$997$	0.0369001	−	0.0213043i	0.00116864	−	0.000674713i	0.500584	+	0.865688i	$0.333119\pi$
$998$			2.62804i			0.0831890i
$999$	−0.754695	+	0.202220i	−0.0238775	+	0.00639796i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.by.b.19.5	✓	40	91.19	even	12	inner
546.2.by.b.115.5	yes	40	1.1	even	1	trivial
546.2.cg.b.271.10	yes	40	7.5	odd	6
546.2.cg.b.409.10	yes	40	13.6	odd	12

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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.by (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(3.90903 + 1.04742i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.71472 + 2.01488i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +1.00000i q^{3} +(0.866025 - 0.500000i) q^{4} +(3.90903 + 1.04742i) q^{5} +(-0.258819 - 0.965926i) q^{6} +(-1.71472 + 2.01488i) q^{7} +(-0.707107 + 0.707107i) q^{8} -1.00000 q^{9} -4.04692 q^{10} +(-3.58587 + 3.58587i) 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} +(0.500000 - 0.866025i) q^{16} +(-2.48117 - 4.29751i) q^{17} +(0.965926 - 0.258819i) q^{18} +(1.02617 - 1.02617i) q^{19} +(3.90903 - 1.04742i) q^{20} +(-2.01488 - 1.71472i) q^{21} +(2.53559 - 4.39177i) q^{22} +(4.70481 + 2.71632i) q^{23} +(-0.707107 - 0.707107i) q^{24} +(9.85327 + 5.68879i) q^{25} +(1.33560 - 3.34906i) q^{26} -1.00000i q^{27} +(-0.477555 + 2.60230i) q^{28} +(-4.24486 - 7.35231i) q^{29} -4.04692i q^{30} +(1.06592 + 3.97807i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-3.58587 - 3.58587i) q^{33} +(3.50891 + 3.50891i) q^{34} +(-8.81332 + 6.08017i) q^{35} +(-0.866025 + 0.500000i) q^{36} +(-0.202220 - 0.754695i) q^{37} +(-0.725610 + 1.25679i) q^{38} +(-2.88926 - 2.15689i) q^{39} +(-3.50474 + 2.02346i) q^{40} +(-3.46045 - 0.927225i) q^{41} +(2.39002 + 1.13481i) q^{42} +(8.45709 + 4.88270i) q^{43} +(-1.31252 + 4.89839i) q^{44} +(-3.90903 - 1.04742i) q^{45} +(-5.24753 - 1.40607i) q^{46} +(-0.761269 + 2.84109i) q^{47} +(0.866025 + 0.500000i) q^{48} +(-1.11945 - 6.90991i) q^{49} +(-10.9899 - 2.94473i) q^{50} +(4.29751 - 2.48117i) q^{51} +(-0.423290 + 3.58062i) q^{52} +(2.08448 - 3.61043i) q^{53} +(0.258819 + 0.965926i) q^{54} +(-17.7732 + 10.2613i) q^{55} +(-0.212241 - 2.63722i) q^{56} +(1.02617 + 1.02617i) q^{57} +(6.00313 + 6.00313i) q^{58} +(0.242102 - 0.903539i) q^{59} +(1.04742 + 3.90903i) q^{60} +12.1085i q^{61} +(-2.05920 - 3.56664i) q^{62} +(1.71472 - 2.01488i) q^{63} -1.00000i q^{64} +(-11.4576 + 9.03503i) q^{65} +(4.39177 + 2.53559i) q^{66} +(6.50338 + 6.50338i) q^{67} +(-4.29751 - 2.48117i) q^{68} +(-2.71632 + 4.70481i) q^{69} +(6.93935 - 8.15405i) q^{70} +(-4.28503 + 1.14817i) q^{71} +(0.707107 - 0.707107i) q^{72} +(12.8347 - 3.43906i) q^{73} +(0.390659 + 0.676641i) q^{74} +(-5.68879 + 9.85327i) 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} +(2.86161 - 2.86161i) q^{80} +1.00000 q^{81} +3.58252 q^{82} +(1.02375 - 1.02375i) q^{83} +(-2.60230 - 0.477555i) q^{84} +(-5.19766 - 19.3979i) q^{85} +(-9.43266 - 2.52747i) q^{86} +(7.35231 - 4.24486i) q^{87} -5.07118i q^{88} +(6.18200 - 1.65646i) q^{89} +4.04692 q^{90} +(-2.12304 - 9.30015i) q^{91} +5.43264 q^{92} +(-3.97807 + 1.06592i) q^{93} -2.94132i q^{94} +(5.08614 - 2.93649i) q^{95} +(-0.965926 - 0.258819i) q^{96} +(2.62347 + 9.79094i) q^{97} +(2.86972 + 6.38472i) q^{98} +(3.58587 - 3.58587i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{7} - 40 q^{9}+O(q^{10}) \) 40 * q - 4 * q^7 - 40 * q^9	\( 40 q - 4 q^{7} - 40 q^{9} - 4 q^{11} + 20 q^{12} + 4 q^{14} + 20 q^{16} + 8 q^{17} + 8 q^{19} - 8 q^{21} - 4 q^{22} + 24 q^{23} + 24 q^{25} - 8 q^{26} + 4 q^{28} - 12 q^{29} + 24 q^{31} - 4 q^{33} + 8 q^{34} + 28 q^{35} - 8 q^{37} - 8 q^{38} - 16 q^{39} - 20 q^{41} - 12 q^{42} - 24 q^{43} + 8 q^{44} - 4 q^{46} - 16 q^{47} + 4 q^{49} - 16 q^{50} - 24 q^{51} - 4 q^{52} - 4 q^{53} - 24 q^{55} + 12 q^{56} + 8 q^{57} + 24 q^{58} - 12 q^{59} - 32 q^{62} + 4 q^{63} - 4 q^{65} - 24 q^{67} + 24 q^{68} + 8 q^{69} + 52 q^{70} - 28 q^{71} + 108 q^{73} + 20 q^{74} - 36 q^{75} - 4 q^{76} + 12 q^{77} + 4 q^{78} + 40 q^{81} - 48 q^{82} - 60 q^{83} - 8 q^{84} - 4 q^{85} - 20 q^{86} - 36 q^{87} - 60 q^{89} - 40 q^{91} - 16 q^{92} - 48 q^{95} + 48 q^{97} - 8 q^{98} + 4 q^{99}+O(q^{100}) \) 40 * q - 4 * q^7 - 40 * q^9 - 4 * q^11 + 20 * q^12 + 4 * q^14 + 20 * q^16 + 8 * q^17 + 8 * q^19 - 8 * q^21 - 4 * q^22 + 24 * q^23 + 24 * q^25 - 8 * q^26 + 4 * q^28 - 12 * q^29 + 24 * q^31 - 4 * q^33 + 8 * q^34 + 28 * q^35 - 8 * q^37 - 8 * q^38 - 16 * q^39 - 20 * q^41 - 12 * q^42 - 24 * q^43 + 8 * q^44 - 4 * q^46 - 16 * q^47 + 4 * q^49 - 16 * q^50 - 24 * q^51 - 4 * q^52 - 4 * q^53 - 24 * q^55 + 12 * q^56 + 8 * q^57 + 24 * q^58 - 12 * q^59 - 32 * q^62 + 4 * q^63 - 4 * q^65 - 24 * q^67 + 24 * q^68 + 8 * q^69 + 52 * q^70 - 28 * q^71 + 108 * q^73 + 20 * q^74 - 36 * q^75 - 4 * q^76 + 12 * q^77 + 4 * q^78 + 40 * q^81 - 48 * q^82 - 60 * q^83 - 8 * q^84 - 4 * q^85 - 20 * q^86 - 36 * q^87 - 60 * q^89 - 40 * q^91 - 16 * q^92 - 48 * q^95 + 48 * q^97 - 8 * q^98 + 4 * q^99

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