LMFDB - Embedded newform 546.2.ch.a.137.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(137,546)]

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([6, 8, 11]))

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

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

chi := DirichletCharacter("546.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.ch (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:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			137.15
Character	$\chi$	$=$	546.137
Dual form			546.2.ch.a.275.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(1.47583 - 0.906598i) q^{3} -1.00000i q^{4} +(3.71236 + 0.994723i) q^{5} +(-0.402510 + 1.68463i) q^{6} +(1.97669 + 1.75860i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.35616 - 2.67597i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(1.47583 - 0.906598i) q^{3} -1.00000i q^{4} +(3.71236 + 0.994723i) q^{5} +(-0.402510 + 1.68463i) q^{6} +(1.97669 + 1.75860i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.35616 - 2.67597i) q^{9} +(-3.32841 + 1.92166i) q^{10} +(0.455992 - 1.70178i) q^{11} +(-0.906598 - 1.47583i) q^{12} +(2.72010 + 2.36665i) q^{13} +(-2.64125 + 0.154214i) q^{14} +(6.38063 - 1.89757i) q^{15} -1.00000 q^{16} -7.25800 q^{17} +(0.933247 + 2.85115i) q^{18} +(-5.64277 + 1.51198i) q^{19} +(0.994723 - 3.71236i) q^{20} +(4.51161 + 0.803336i) q^{21} +(0.880908 + 1.52578i) q^{22} -4.56845 q^{23} +(1.68463 + 0.402510i) q^{24} +(8.46199 + 4.88553i) q^{25} +(-3.59688 + 0.249924i) q^{26} +(-0.424562 - 5.17878i) q^{27} +(1.75860 - 1.97669i) q^{28} +(-7.51370 - 4.33804i) q^{29} +(-3.17000 + 5.85357i) q^{30} +(-1.87746 + 0.503065i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.869866 - 2.92495i) q^{33} +(5.13218 - 5.13218i) q^{34} +(5.58887 + 8.49482i) q^{35} +(-2.67597 - 1.35616i) q^{36} +(2.62365 - 2.62365i) q^{37} +(2.92091 - 5.05917i) q^{38} +(6.16002 + 1.02675i) q^{39} +(1.92166 + 3.32841i) q^{40} +(0.632448 + 2.36033i) q^{41} +(-3.75824 + 2.62215i) q^{42} +(2.02060 - 1.16659i) q^{43} +(-1.70178 - 0.455992i) q^{44} +(7.69641 - 8.58516i) q^{45} +(3.23038 - 3.23038i) q^{46} +(2.75570 - 10.2844i) q^{47} +(-1.47583 + 0.906598i) q^{48} +(0.814638 + 6.95244i) q^{49} +(-9.43812 + 2.52894i) q^{50} +(-10.7116 + 6.58008i) q^{51} +(2.36665 - 2.72010i) q^{52} +(8.03583 + 4.63949i) q^{53} +(3.96216 + 3.36174i) q^{54} +(3.38561 - 5.86404i) q^{55} +(0.154214 + 2.64125i) q^{56} +(-6.95703 + 7.34715i) q^{57} +(8.38044 - 2.24553i) q^{58} +(-4.07981 - 4.07981i) q^{59} +(-1.89757 - 6.38063i) q^{60} +(-0.304174 + 0.526844i) q^{61} +(0.971846 - 1.68329i) q^{62} +(7.38669 - 2.90463i) q^{63} +1.00000i q^{64} +(7.74382 + 11.4916i) q^{65} +(2.68334 + 1.45316i) q^{66} +(-2.29238 + 8.55527i) q^{67} +7.25800i q^{68} +(-6.74227 + 4.14175i) q^{69} +(-9.95867 - 2.05482i) q^{70} +(0.423608 + 0.113506i) q^{71} +(2.85115 - 0.933247i) q^{72} +(0.316181 + 1.18001i) q^{73} +3.71040i q^{74} +(16.9177 - 0.461393i) q^{75} +(1.51198 + 5.64277i) q^{76} +(3.89412 - 2.56200i) q^{77} +(-5.08181 + 3.62977i) q^{78} +(-4.35247 - 7.53869i) q^{79} +(-3.71236 - 0.994723i) q^{80} +(-5.32165 - 7.25810i) q^{81} +(-2.11621 - 1.22180i) q^{82} +(-4.12829 + 4.12829i) q^{83} +(0.803336 - 4.51161i) q^{84} +(-26.9443 - 7.21970i) q^{85} +(-0.603874 + 2.25369i) q^{86} +(-15.0218 + 0.409687i) q^{87} +(1.52578 - 0.880908i) q^{88} +(0.915873 + 0.915873i) q^{89} +(0.628441 + 11.5128i) q^{90} +(1.21480 + 9.46173i) q^{91} +4.56845i q^{92} +(-2.31474 + 2.44454i) q^{93} +(5.32360 + 9.22075i) q^{94} -22.4520 q^{95} +(0.402510 - 1.68463i) q^{96} +(1.14400 - 4.26947i) q^{97} +(-5.49215 - 4.34008i) q^{98} +(-3.93553 - 3.52812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 8 q^{7}+O(q^{10}) $ 152 * q + 8 * q^7	$ 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{11}{12}\right)$

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
$3$	1.47583	−	0.906598i	0.852072	−	0.523424i
$3$	1.47583	−	0.906598i	0.852072	−	0.523424i
$4$		−	1.00000i		−	0.500000i
$5$	3.71236	+	0.994723i	1.66022	+	0.444854i	0.962447	−	0.271469i	$-0.0875095\pi$
$5$	3.71236	+	0.994723i	1.66022	+	0.444854i	0.697769	+	0.716323i	$0.254176\pi$
$6$	−0.402510	+	1.68463i	−0.164324	+	0.687748i
$7$	1.97669	+	1.75860i	0.747120	+	0.664689i
$7$	1.97669	+	1.75860i	0.747120	+	0.664689i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.35616	−	2.67597i	0.452054	−	0.891991i
$10$	−3.32841	+	1.92166i	−1.05253	+	0.607681i
$11$	0.455992	−	1.70178i	0.137487	−	0.513107i	−0.862489	−	0.506076i	$-0.831095\pi$
$11$	0.455992	−	1.70178i	0.137487	−	0.513107i	0.999975	−	0.00703074i	$-0.00223797\pi$
$12$	−0.906598	−	1.47583i	−0.261712	−	0.426036i
$13$	2.72010	+	2.36665i	0.754420	+	0.656392i
$13$	2.72010	+	2.36665i	0.754420	+	0.656392i
$14$	−2.64125	+	0.154214i	−0.705905	+	0.0412155i
$15$	6.38063	−	1.89757i	1.64747	−	0.489950i
$16$	−1.00000			−0.250000
$17$	−7.25800			−1.76032			−0.880162	−	0.474674i	$-0.842566\pi$
$17$	−7.25800			−1.76032			−0.880162	+	0.474674i	$0.842566\pi$
$18$	0.933247	+	2.85115i	0.219968	+	0.672022i
$19$	−5.64277	+	1.51198i	−1.29454	+	0.346871i	−0.839383	−	0.543540i	$-0.817084\pi$
$19$	−5.64277	+	1.51198i	−1.29454	+	0.346871i	−0.455157	+	0.890411i	$0.650417\pi$
$20$	0.994723	−	3.71236i	0.222427	−	0.830108i
$21$	4.51161	+	0.803336i	0.984515	+	0.175302i
$22$	0.880908	+	1.52578i	0.187810	+	0.325297i
$23$	−4.56845			−0.952588			−0.476294	−	0.879286i	$-0.658020\pi$
$23$	−4.56845			−0.952588			−0.476294	+	0.879286i	$0.658020\pi$
$24$	1.68463	+	0.402510i	0.343874	+	0.0821620i
$25$	8.46199	+	4.88553i	1.69240	+	0.977106i
$26$	−3.59688	+	0.249924i	−0.705406	+	0.0490140i
$27$	−0.424562	−	5.17878i	−0.0817070	−	0.996656i
$28$	1.75860	−	1.97669i	0.332345	−	0.373560i
$29$	−7.51370	−	4.33804i	−1.39526	−	0.805553i	−0.401367	−	0.915917i	$-0.631465\pi$
$29$	−7.51370	−	4.33804i	−1.39526	−	0.805553i	−0.993891	+	0.110364i	$0.964798\pi$
$30$	−3.17000	+	5.85357i	−0.578761	+	1.06871i
$31$	−1.87746	+	0.503065i	−0.337202	+	0.0903531i	−0.423447	−	0.905921i	$-0.639180\pi$
$31$	−1.87746	+	0.503065i	−0.337202	+	0.0903531i	0.0862447	+	0.996274i	$0.472513\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−0.869866	−	2.92495i	−0.151424	−	0.509168i
$34$	5.13218	−	5.13218i	0.880162	−	0.880162i
$35$	5.58887	+	8.49482i	0.944692	+	1.43589i
$36$	−2.67597	−	1.35616i	−0.445995	−	0.226027i
$37$	2.62365	−	2.62365i	0.431325	−	0.431325i	−0.457754	−	0.889079i	$-0.651346\pi$
$37$	2.62365	−	2.62365i	0.431325	−	0.431325i	0.889079	+	0.457754i	$0.151346\pi$
$38$	2.92091	−	5.05917i	0.473835	−	0.820706i
$39$	6.16002	+	1.02675i	0.986392	+	0.164411i
$40$	1.92166	+	3.32841i	0.303841	+	0.526267i
$41$	0.632448	+	2.36033i	0.0987717	+	0.368621i	0.997564	−	0.0697531i	$-0.0222211\pi$
$41$	0.632448	+	2.36033i	0.0987717	+	0.368621i	−0.898793	+	0.438374i	$0.855554\pi$
$42$	−3.75824	+	2.62215i	−0.579908	+	0.404606i
$43$	2.02060	−	1.16659i	0.308139	−	0.177904i	−0.337955	−	0.941162i	$-0.609735\pi$
$43$	2.02060	−	1.16659i	0.308139	−	0.177904i	0.646093	+	0.763258i	$0.276402\pi$
$44$	−1.70178	−	0.455992i	−0.256554	−	0.0687433i
$45$	7.69641	−	8.58516i	1.14731	−	1.27980i
$46$	3.23038	−	3.23038i	0.476294	−	0.476294i
$47$	2.75570	−	10.2844i	0.401960	−	1.50013i	−0.407635	−	0.913145i	$-0.633646\pi$
$47$	2.75570	−	10.2844i	0.401960	−	1.50013i	0.809594	−	0.586990i	$-0.199687\pi$
$48$	−1.47583	+	0.906598i	−0.213018	+	0.130856i
$49$	0.814638	+	6.95244i	0.116377	+	0.993205i
$50$	−9.43812	+	2.52894i	−1.33475	+	0.357646i
$51$	−10.7116	+	6.58008i	−1.49992	+	0.921396i
$52$	2.36665	−	2.72010i	0.328196	−	0.377210i
$53$	8.03583	+	4.63949i	1.10381	+	0.637283i	0.937218	−	0.348744i	$-0.113392\pi$
$53$	8.03583	+	4.63949i	1.10381	+	0.637283i	0.166588	+	0.986027i	$0.446725\pi$
$54$	3.96216	+	3.36174i	0.539182	+	0.457475i
$55$	3.38561	−	5.86404i	0.456515	−	0.790707i
$56$	0.154214	+	2.64125i	0.0206078	+	0.352952i
$57$	−6.95703	+	7.34715i	−0.921481	+	0.973153i
$58$	8.38044	−	2.24553i	1.10041	−	0.294853i
$59$	−4.07981	−	4.07981i	−0.531146	−	0.531146i	0.389767	−	0.920913i	$-0.372555\pi$
$59$	−4.07981	−	4.07981i	−0.531146	−	0.531146i	−0.920913	+	0.389767i	$0.872555\pi$
$60$	−1.89757	−	6.38063i	−0.244975	−	0.823736i
$61$	−0.304174	+	0.526844i	−0.0389455	+	0.0674555i	−0.884841	−	0.465893i	$-0.845733\pi$
$61$	−0.304174	+	0.526844i	−0.0389455	+	0.0674555i	0.845896	+	0.533348i	$0.179067\pi$
$62$	0.971846	−	1.68329i	0.123425	−	0.213778i
$63$	7.38669	−	2.90463i	0.930635	−	0.365949i
$64$			1.00000i			0.125000i
$65$	7.74382	+	11.4916i	0.960502	+	1.42536i
$66$	2.68334	+	1.45316i	0.330296	+	0.178872i
$67$	−2.29238	+	8.55527i	−0.280059	+	1.04519i	0.672317	+	0.740264i	$0.265299\pi$
$67$	−2.29238	+	8.55527i	−0.280059	+	1.04519i	−0.952375	+	0.304929i	$0.901367\pi$
$68$			7.25800i			0.880162i
$69$	−6.74227	+	4.14175i	−0.811673	+	0.498608i
$70$	−9.95867	−	2.05482i	−1.19029	−	0.245598i
$71$	0.423608	+	0.113506i	0.0502731	+	0.0134706i	0.283868	−	0.958863i	$-0.408382\pi$
$71$	0.423608	+	0.113506i	0.0502731	+	0.0134706i	−0.233595	+	0.972334i	$0.575049\pi$
$72$	2.85115	−	0.933247i	0.336011	−	0.109984i
$73$	0.316181	+	1.18001i	0.0370062	+	0.138109i	0.981957	−	0.189102i	$-0.0605577\pi$
$73$	0.316181	+	1.18001i	0.0370062	+	0.138109i	−0.944951	+	0.327211i	$0.893891\pi$
$74$			3.71040i			0.431325i
$75$	16.9177	−	0.461393i	1.95349	−	0.0532771i
$76$	1.51198	+	5.64277i	0.173436	+	0.647270i
$77$	3.89412	−	2.56200i	0.443776	−	0.291967i
$78$	−5.08181	+	3.62977i	−0.575402	+	0.410990i
$79$	−4.35247	−	7.53869i	−0.489691	−	0.848169i	0.510239	−	0.860033i	$-0.329557\pi$
$79$	−4.35247	−	7.53869i	−0.489691	−	0.848169i	−0.999930	+	0.0118634i	$0.996224\pi$
$80$	−3.71236	−	0.994723i	−0.415054	−	0.111213i
$81$	−5.32165	−	7.25810i	−0.591295	−	0.806456i
$82$	−2.11621	−	1.22180i	−0.233696	−	0.134925i
$83$	−4.12829	+	4.12829i	−0.453139	+	0.453139i	−0.896395	−	0.443256i	$-0.853823\pi$
$83$	−4.12829	+	4.12829i	−0.453139	+	0.453139i	0.443256	+	0.896395i	$0.353823\pi$
$84$	0.803336	−	4.51161i	0.0876511	−	0.492257i
$85$	−26.9443	−	7.21970i	−2.92252	−	0.783086i
$86$	−0.603874	+	2.25369i	−0.0651174	+	0.243021i
$87$	−15.0218	+	0.409687i	−1.61051	+	0.0439231i
$88$	1.52578	−	0.880908i	0.162648	−	0.0939051i
$89$	0.915873	+	0.915873i	0.0970823	+	0.0970823i	0.753980	−	0.656898i	$-0.228132\pi$
$89$	0.915873	+	0.915873i	0.0970823	+	0.0970823i	−0.656898	+	0.753980i	$0.728132\pi$
$90$	0.628441	+	11.5128i	0.0662435	+	1.21356i
$91$	1.21480	+	9.46173i	0.127346	+	0.991858i
$92$			4.56845i			0.476294i
$93$	−2.31474	+	2.44454i	−0.240028	+	0.253487i
$94$	5.32360	+	9.22075i	0.549087	+	0.951047i
$95$	−22.4520			−2.30352
$96$	0.402510	−	1.68463i	0.0410810	−	0.171937i
$97$	1.14400	−	4.26947i	0.116156	−	0.433499i	−0.883215	−	0.468968i	$-0.844626\pi$
$97$	1.14400	−	4.26947i	0.116156	−	0.433499i	0.999371	+	0.0354692i	$0.0112926\pi$
$98$	−5.49215	−	4.34008i	−0.554791	−	0.438414i
$99$	−3.93553	−	3.52812i	−0.395535	−	0.354589i
$100$	4.88553	−	8.46199i	0.488553	−	0.846199i
$101$	2.52895	+	4.38027i	0.251640	+	0.435854i	0.963978	−	0.265984i	$-0.0856967\pi$
$101$	2.52895	+	4.38027i	0.251640	+	0.435854i	−0.712337	+	0.701837i	$0.752363\pi$
$102$	2.92141	−	12.2271i	0.289263	−	1.21066i
$103$	6.56837	−	3.79225i	0.647200	−	0.373661i	−0.140182	−	0.990126i	$-0.544769\pi$
$103$	6.56837	−	3.79225i	0.647200	−	0.373661i	0.787383	+	0.616464i	$0.211436\pi$
$104$	0.249924	+	3.59688i	0.0245070	+	0.352703i
$105$	15.9496	+	7.47007i	1.55652	+	0.729004i
$106$	−8.96280	+	2.40158i	−0.870544	+	0.233262i
$107$		−	7.68241i		−	0.742686i	−0.928496	−	0.371343i	$-0.878897\pi$
$107$		−	7.68241i		−	0.742686i	0.928496	−	0.371343i	$-0.121103\pi$
$108$	−5.17878	+	0.424562i	−0.498328	+	0.0408535i
$109$	11.5113	−	3.08444i	1.10258	−	0.295435i	0.338765	−	0.940871i	$-0.389991\pi$
$109$	11.5113	−	3.08444i	1.10258	−	0.295435i	0.763815	+	0.645436i	$0.223324\pi$
$110$	1.75252	+	6.54049i	0.167096	+	0.623611i
$111$	1.49347	−	6.25066i	0.141754	−	0.593287i
$112$	−1.97669	−	1.75860i	−0.186780	−	0.166172i
$113$	10.5071	−	6.06628i	0.988425	−	0.570667i	0.0836218	−	0.996498i	$-0.473351\pi$
$113$	10.5071	−	6.06628i	0.988425	−	0.570667i	0.904803	+	0.425830i	$0.140018\pi$
$114$	−0.275853	−	10.1146i	−0.0258360	−	0.947317i
$115$	−16.9597	−	4.54434i	−1.58150	−	0.423762i
$116$	−4.33804	+	7.51370i	−0.402776	+	0.697629i
$117$	10.0220	−	4.06934i	0.926534	−	0.376211i
$118$	5.76972			0.531146
$119$	−14.3468	−	12.7639i	−1.31517	−	1.17007i
$120$	5.85357	+	3.17000i	0.534355	+	0.289380i
$121$	6.83814	+	3.94800i	0.621649	+	0.358909i
$122$	−0.157452	−	0.587619i	−0.0142550	−	0.0532005i
$123$	3.07325	+	2.91007i	0.277106	+	0.262392i
$124$	0.503065	+	1.87746i	0.0451765	+	0.168601i
$125$	12.9660	+	12.9660i	1.15971	+	1.15971i
$126$	−3.16929	+	7.27706i	−0.282343	+	0.648292i
$127$	4.17540	+	2.41067i	0.370507	+	0.213912i	0.673680	−	0.739023i	$-0.264713\pi$
$127$	4.17540	+	2.41067i	0.370507	+	0.213912i	−0.303173	+	0.952936i	$0.598046\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	1.92444	−	3.55357i	0.169437	−	0.312874i
$130$	−13.6015	−	2.65009i	−1.19293	−	0.232428i
$131$	−7.51955	+	4.34141i	−0.656986	+	0.379311i	−0.791128	−	0.611651i	$-0.790506\pi$
$131$	−7.51955	+	4.34141i	−0.656986	+	0.379311i	0.134142	+	0.990962i	$0.457172\pi$
$132$	−2.92495	+	0.869866i	−0.254584	+	0.0757121i
$133$	−13.8130	−	6.93468i	−1.19774	−	0.601313i
$134$	−4.42853	−	7.67045i	−0.382567	−	0.662626i
$135$	3.57532	−	19.6478i	0.307715	−	1.69101i
$136$	−5.13218	−	5.13218i	−0.440081	−	0.440081i
$137$	1.89377	+	1.89377i	0.161796	+	0.161796i	0.783362	−	0.621566i	$-0.213503\pi$
$137$	1.89377	+	1.89377i	0.161796	+	0.161796i	−0.621566	+	0.783362i	$0.713503\pi$
$138$	1.83885	−	7.69616i	0.156533	−	0.655140i
$139$	−2.52718	−	4.37720i	−0.214352	−	0.371269i	0.738720	−	0.674013i	$-0.235431\pi$
$139$	−2.52718	−	4.37720i	−0.214352	−	0.371269i	−0.953072	+	0.302744i	$0.902097\pi$
$140$	8.49482	−	5.58887i	0.717943	−	0.472346i
$141$	−5.25687	−	17.6764i	−0.442708	−	1.48862i
$142$	−0.379797	+	0.219276i	−0.0318719	+	0.0184012i
$143$	5.26788	−	3.54985i	0.440522	−	0.296853i
$144$	−1.35616	+	2.67597i	−0.113013	+	0.222998i
$145$	−23.5784	−	23.5784i	−1.95808	−	1.95808i
$146$	−1.05796	−	0.610816i	−0.0875577	−	0.0505515i
$147$	7.50533	+	9.52208i	0.619029	+	0.785368i
$148$	−2.62365	−	2.62365i	−0.215663	−	0.215663i
$149$	−5.00939	−	18.6953i	−0.410386	−	1.53158i	−0.793902	−	0.608046i	$-0.791954\pi$
$149$	−5.00939	−	18.6953i	−0.410386	−	1.53158i	0.383517	−	0.923534i	$-0.374713\pi$
$150$	−11.6364	+	12.2889i	−0.950105	+	1.00338i
$151$	3.61296	+	13.4837i	0.294018	+	1.09729i	0.941994	+	0.335630i	$0.108949\pi$
$151$	3.61296	+	13.4837i	0.294018	+	1.09729i	−0.647976	+	0.761661i	$0.724384\pi$
$152$	−5.05917	−	2.92091i	−0.410353	−	0.236917i
$153$	−9.84302	+	19.4222i	−0.795761	+	1.57019i
$154$	−0.941950	+	4.56516i	−0.0759045	+	0.367871i
$155$	−7.47022			−0.600023
$156$	1.02675	−	6.16002i	0.0822057	−	0.493196i
$157$	−4.56964	+	7.91484i	−0.364697	+	0.631673i	−0.988727	−	0.149727i	$-0.952161\pi$
$157$	−4.56964	+	7.91484i	−0.364697	+	0.631673i	0.624031	+	0.781400i	$0.285494\pi$
$158$	8.40832	+	2.25300i	0.668930	+	0.179239i
$159$	16.0657	−	0.438157i	1.27409	−	0.0347481i
$160$	3.32841	−	1.92166i	0.263134	−	0.151920i
$161$	−9.03043	−	8.03408i	−0.711697	−	0.633175i
$162$	8.89523	+	1.36928i	0.698875	+	0.107581i
$163$	−2.75263	−	10.2730i	−0.215603	−	0.804641i	−0.985953	−	0.167020i	$-0.946585\pi$
$163$	−2.75263	−	10.2730i	−0.215603	−	0.804641i	0.770350	−	0.637621i	$-0.220081\pi$
$164$	2.36033	−	0.632448i	0.184311	−	0.0493859i
$165$	−0.319739	−	11.7237i	−0.0248917	−	0.912691i
$166$		−	5.83829i		−	0.453139i
$167$	−9.44160	+	2.52987i	−0.730613	+	0.195767i	−0.604902	−	0.796300i	$-0.706788\pi$
$167$	−9.44160	+	2.52987i	−0.730613	+	0.195767i	−0.125711	+	0.992067i	$0.540121\pi$
$168$	2.62215	+	3.75824i	0.202303	+	0.289954i
$169$	1.79789	+	12.8751i	0.138299	+	0.990390i
$170$	24.1576	−	13.9474i	1.85280	−	1.06972i
$171$	−3.60651	+	17.1504i	−0.275796	+	1.31152i
$172$	−1.16659	−	2.02060i	−0.0889520	−	0.154069i
$173$	−9.91427	+	17.1720i	−0.753768	+	1.30556i	0.192216	+	0.981353i	$0.438432\pi$
$173$	−9.91427	+	17.1720i	−0.753768	+	1.30556i	−0.945984	+	0.324212i	$0.894901\pi$
$174$	10.3323	−	10.9117i	0.783292	−	0.827215i
$175$	8.13506	+	24.5385i	0.614953	+	1.85493i
$176$	−0.455992	+	1.70178i	−0.0343717	+	0.128277i
$177$	−9.71986	−	2.32237i	−0.730590	−	0.174560i
$178$	−1.29524			−0.0970823
$179$	−5.43924	−	9.42105i	−0.406548	−	0.704162i	0.587952	−	0.808896i	$-0.299934\pi$
$179$	−5.43924	−	9.42105i	−0.406548	−	0.704162i	−0.994500	+	0.104734i	$0.966601\pi$
$180$	−8.58516	−	7.69641i	−0.639900	−	0.573656i
$181$			6.79556i			0.505110i	0.967583	+	0.252555i	$0.0812708\pi$
$181$			6.79556i			0.505110i	−0.967583	+	0.252555i	$0.918729\pi$
$182$	−7.54945	−	5.83146i	−0.559602	−	0.432256i
$183$	0.0287264	+	1.05330i	0.00212352	+	0.0778620i
$184$	−3.23038	−	3.23038i	−0.238147	−	0.238147i
$185$	12.3497	−	7.13012i	0.907970	−	0.524217i
$186$	−0.0917819	−	3.36532i	−0.00672978	−	0.246757i
$187$	−3.30959	+	12.3515i	−0.242021	+	0.903234i
$188$	−10.2844	−	2.75570i	−0.750067	−	0.200980i
$189$	8.26818	−	10.9835i	0.601422	−	0.798932i
$190$	15.8759	−	15.8759i	1.15176	−	1.15176i
$191$	2.59147	+	1.49619i	0.187512	+	0.108260i	0.590817	−	0.806805i	$-0.298805\pi$
$191$	2.59147	+	1.49619i	0.187512	+	0.108260i	−0.403305	+	0.915066i	$0.632139\pi$
$192$	0.906598	+	1.47583i	0.0654280	+	0.106509i
$193$	−16.8185	−	4.50649i	−1.21062	−	0.324384i	−0.403614	−	0.914929i	$-0.632246\pi$
$193$	−16.8185	−	4.50649i	−1.21062	−	0.324384i	−0.807005	+	0.590545i	$0.798913\pi$
$194$	2.21004	+	3.82790i	0.158672	+	0.274827i
$195$	21.8468	+	9.93917i	1.56448	+	0.711759i
$196$	6.95244	−	0.814638i	0.496603	−	0.0581884i
$197$	5.80798	+	21.6757i	0.413802	+	1.54433i	0.787224	+	0.616667i	$0.211518\pi$
$197$	5.80798	+	21.6757i	0.413802	+	1.54433i	−0.373422	+	0.927661i	$0.621816\pi$
$198$	5.27759	−	0.288084i	0.375062	−	0.0204732i
$199$		−	0.711344i		−	0.0504258i	−0.999682	−	0.0252129i	$-0.991974\pi$
$199$		−	0.711344i		−	0.0504258i	0.999682	−	0.0252129i	$-0.00802637\pi$
$200$	2.52894	+	9.43812i	0.178823	+	0.667376i
$201$	4.37302	+	14.7044i	0.308449	+	1.03717i
$202$	−4.88556	−	1.30908i	−0.343747	−	0.0921067i
$203$	−7.22340	−	21.7886i	−0.506984	−	1.52926i
$204$	6.58008	+	10.7116i	0.460698	+	0.749961i
$205$			9.39149i			0.655930i
$206$	−1.96301	+	7.32606i	−0.136770	+	0.510431i
$207$	−6.19556	+	12.2250i	−0.430621	+	0.849699i
$208$	−2.72010	−	2.36665i	−0.188605	−	0.164098i
$209$			10.2922i			0.711928i
$210$	−16.5602	+	5.99594i	−1.14276	+	0.413759i
$211$	−8.05012	+	13.9432i	−0.554193	+	0.959890i	0.443773	+	0.896139i	$0.353640\pi$
$211$	−8.05012	+	13.9432i	−0.554193	+	0.959890i	−0.997966	+	0.0637511i	$0.979694\pi$
$212$	4.63949	−	8.03583i	0.318641	−	0.551903i
$213$	0.728079	−	0.216527i	0.0498871	−	0.0148362i
$214$	5.43228	+	5.43228i	0.371343	+	0.371343i
$215$	8.66163	−	2.32088i	0.590718	−	0.158282i
$216$	3.36174	−	3.96216i	0.228737	−	0.269591i
$217$	−4.59586	−	2.30731i	−0.311987	−	0.156630i
$218$	−5.95867	+	10.3207i	−0.403572	+	0.699008i
$219$	1.53642	+	1.45484i	0.103822	+	0.0983090i
$220$	−5.86404	−	3.38561i	−0.395354	−	0.228258i
$221$	−19.7425	−	17.1772i	−1.32802	−	1.15546i
$222$	3.36384	+	5.47593i	0.225766	+	0.367520i
$223$	−5.72394	+	1.53372i	−0.383303	+	0.102706i	−0.445325	−	0.895369i	$-0.646912\pi$
$223$	−5.72394	+	1.53372i	−0.383303	+	0.102706i	0.0620218	+	0.998075i	$0.480245\pi$
$224$	2.64125	−	0.154214i	0.176476	−	0.0103039i
$225$	24.5494	−	16.0185i	1.63662	−	1.06790i
$226$	−3.14014	+	11.7191i	−0.208879	+	0.779546i
$227$	5.69515	−	5.69515i	0.378000	−	0.378000i	−0.492380	−	0.870380i	$-0.663873\pi$
$227$	5.69515	−	5.69515i	0.378000	−	0.378000i	0.870380	+	0.492380i	$0.163873\pi$
$228$	7.34715	+	6.95703i	0.486577	+	0.460741i
$229$	19.6579	+	5.26732i	1.29903	+	0.348075i	0.841084	−	0.540905i	$-0.181918\pi$
$229$	19.6579	+	5.26732i	1.29903	+	0.348075i	0.457948	+	0.888979i	$0.348585\pi$
$230$	15.2057	−	8.77899i	1.00263	−	0.578870i
$231$	3.42436	−	7.31148i	0.225306	−	0.481060i
$232$	−2.24553	−	8.38044i	−0.147426	−	0.550203i
$233$	2.41928	+	4.19032i	0.158493	+	0.274517i	0.934325	−	0.356421i	$-0.116003\pi$
$233$	2.41928	+	4.19032i	0.158493	+	0.274517i	−0.775833	+	0.630939i	$0.782670\pi$
$234$	−4.20916	+	9.96408i	−0.275161	+	0.651373i
$235$	20.4603	−	35.4382i	1.33468	−	2.31173i
$236$	−4.07981	+	4.07981i	−0.265573	+	0.265573i
$237$	−13.2581	−	7.17991i	−0.861204	−	0.466385i
$238$	19.1702	−	1.11929i	1.24262	−	0.0725526i
$239$	8.86898	−	8.86898i	0.573687	−	0.573687i	−0.359470	−	0.933157i	$-0.617042\pi$
$239$	8.86898	−	8.86898i	0.573687	−	0.573687i	0.933157	+	0.359470i	$0.117042\pi$
$240$	−6.38063	+	1.89757i	−0.411868	+	0.122488i
$241$	0.697671	−	0.697671i	0.0449409	−	0.0449409i	−0.684279	−	0.729220i	$-0.739883\pi$
$241$	0.697671	−	0.697671i	0.0449409	−	0.0449409i	0.729220	+	0.684279i	$0.239883\pi$
$242$	−7.62695	+	2.04364i	−0.490279	+	0.131370i
$243$	−14.4340	−	5.88714i	−0.925944	−	0.377661i
$244$	0.526844	+	0.304174i	0.0337278	+	0.0194727i
$245$	−3.89152	+	26.6203i	−0.248620	+	1.70071i
$246$	−4.23085	+	0.115387i	−0.269749	+	0.00735682i
$247$	−18.9272	−	9.24177i	−1.20431	−	0.588040i
$248$	−1.68329	−	0.971846i	−0.106889	−	0.0617123i
$249$	−2.34997	+	9.83537i	−0.148923	+	0.623291i
$250$	−18.3367			−1.15971
$251$	5.92230	+	10.2577i	0.373812	+	0.647462i	0.990148	−	0.140021i	$-0.0447172\pi$
$251$	5.92230	+	10.2577i	0.373812	+	0.647462i	−0.616336	+	0.787483i	$0.711384\pi$
$252$	−2.90463	−	7.38669i	−0.182974	−	0.465317i
$253$	−2.08317	+	7.77451i	−0.130968	+	0.488780i
$254$	−4.65706	+	1.24786i	−0.292210	+	0.0782974i
$255$	−46.3106	+	13.7726i	−2.90008	+	0.862471i
$256$	1.00000			0.0625000
$257$	20.8185			1.29862			0.649310	−	0.760524i	$-0.275058\pi$
$257$	20.8185			1.29862			0.649310	+	0.760524i	$0.275058\pi$
$258$	1.15197	+	3.87354i	0.0717186	+	0.241156i
$259$	9.80011	−	0.572197i	0.608949	−	0.0355546i
$260$	11.4916	−	7.74382i	0.712680	−	0.480251i
$261$	−21.7982	+	14.2234i	−1.34928	+	0.880404i
$262$	2.24728	−	8.38696i	0.138837	−	0.518148i
$263$	12.8968	−	7.44596i	0.795249	−	0.459137i	−0.0465580	−	0.998916i	$-0.514825\pi$
$263$	12.8968	−	7.44596i	0.795249	−	0.459137i	0.841807	+	0.539778i	$0.181492\pi$
$264$	1.45316	−	2.68334i	0.0894360	−	0.165148i
$265$	25.2169	+	25.2169i	1.54906	+	1.54906i
$266$	14.6708	−	4.86371i	0.899526	−	0.298213i
$267$	2.18200	+	0.521347i	0.133536	+	0.0319059i
$268$	8.55527	+	2.29238i	0.522596	+	0.140029i
$269$			25.4048i			1.54896i	0.632599	+	0.774480i	$0.281988\pi$
$269$			25.4048i			1.54896i	−0.632599	+	0.774480i	$0.718012\pi$
$270$	11.3650	+	16.4212i	0.691649	+	0.999364i
$271$	12.8874	−	12.8874i	0.782855	−	0.782855i	−0.197457	−	0.980312i	$-0.563268\pi$
$271$	12.8874	−	12.8874i	0.782855	−	0.782855i	0.980312	+	0.197457i	$0.0632683\pi$
$272$	7.25800			0.440081
$273$	10.3708	+	12.8626i	0.627671	+	0.778479i
$274$	−2.67820			−0.161796
$275$	12.1727	−	12.1727i	0.734042	−	0.734042i
$276$	4.14175	+	6.74227i	0.249304	+	0.405837i
$277$		−	23.9060i		−	1.43637i	−0.695850	−	0.718187i	$-0.744972\pi$
$277$		−	23.9060i		−	1.43637i	0.695850	−	0.718187i	$-0.255028\pi$
$278$	4.88213	+	1.30816i	0.292811	+	0.0784584i
$279$	−1.19996	+	5.70627i	−0.0718395	+	0.341626i
$280$	−2.05482	+	9.95867i	−0.122799	+	0.595145i
$281$	10.9328	+	10.9328i	0.652199	+	0.652199i	0.953522	−	0.301323i	$-0.0974284\pi$
$281$	10.9328	+	10.9328i	0.652199	+	0.652199i	−0.301323	+	0.953522i	$0.597428\pi$
$282$	16.2162	+	8.78191i	0.965663	+	0.522955i
$283$	−10.7572	+	6.21069i	−0.639451	+	0.369187i	−0.784403	−	0.620251i	$-0.787031\pi$
$283$	−10.7572	+	6.21069i	−0.639451	+	0.369187i	0.144952	+	0.989439i	$0.453697\pi$
$284$	0.113506	−	0.423608i	0.00673531	−	0.0251365i
$285$	−33.1354	+	20.3549i	−1.96277	+	1.20572i
$286$	−1.21483	+	6.23507i	−0.0718345	+	0.368688i
$287$	−2.90072	+	5.77787i	−0.171224	+	0.341057i
$288$	−0.933247	−	2.85115i	−0.0549921	−	0.168006i
$289$	35.6785			2.09874
$290$	33.3449			1.95808
$291$	−2.18234	−	7.33817i	−0.127931	−	0.430171i
$292$	1.18001	−	0.316181i	0.0690546	−	0.0185031i
$293$	−2.88637	+	10.7721i	−0.168624	+	0.629312i	0.828927	+	0.559357i	$0.188952\pi$
$293$	−2.88637	+	10.7721i	−0.168624	+	0.629312i	−0.997550	+	0.0699544i	$0.977715\pi$
$294$	−12.0402	−	1.42606i	−0.702199	−	0.0831694i
$295$	−11.0874	−	19.2040i	−0.645535	−	1.11810i
$296$	3.71040			0.215663
$297$	−9.00676	−	1.63897i	−0.522625	−	0.0951025i
$298$	16.7618	+	9.67741i	0.970983	+	0.560597i
$299$	−12.4266	−	10.8119i	−0.718651	−	0.625271i
$300$	−0.461393	−	16.9177i	−0.0266386	−	0.976743i
$301$	6.04569	+	1.24743i	0.348468	+	0.0719008i
$302$	−12.0892	−	6.97970i	−0.695655	−	0.401636i
$303$	7.70345	+	4.17181i	0.442552	+	0.239664i
$304$	5.64277	−	1.51198i	0.323635	−	0.0867178i
$305$	−1.65327	+	1.65327i	−0.0946657	+	0.0946657i
$306$	−6.77350	−	20.6936i	−0.387215	−	1.18298i
$307$	23.9228	−	23.9228i	1.36535	−	1.36535i	0.498400	−	0.866947i	$-0.333921\pi$
$307$	23.9228	−	23.9228i	1.36535	−	1.36535i	0.866947	−	0.498400i	$-0.166079\pi$
$308$	−2.56200	−	3.89412i	−0.145983	−	0.221888i
$309$	6.25577	−	11.5516i	0.355878	−	0.657147i
$310$	5.28224	−	5.28224i	0.300011	−	0.300011i
$311$	−14.0629	+	24.3576i	−0.797433	+	1.38119i	0.123850	+	0.992301i	$0.460476\pi$
$311$	−14.0629	+	24.3576i	−0.797433	+	1.38119i	−0.921283	+	0.388894i	$0.872857\pi$
$312$	3.62977	+	5.08181i	0.205495	+	0.287701i
$313$	9.13260	+	15.8181i	0.516205	+	0.894093i	0.999823	+	0.0188142i	$0.00598911\pi$
$313$	9.13260	+	15.8181i	0.516205	+	0.894093i	−0.483618	+	0.875279i	$0.660678\pi$
$314$	−2.36542	−	8.82786i	−0.133488	−	0.498185i
$315$	30.3113	−	3.43531i	1.70785	−	0.193558i
$316$	−7.53869	+	4.35247i	−0.424085	+	0.244845i
$317$	−27.4898	−	7.36586i	−1.54398	−	0.413708i	−0.616430	−	0.787410i	$-0.711422\pi$
$317$	−27.4898	−	7.36586i	−1.54398	−	0.413708i	−0.927549	+	0.373702i	$0.878088\pi$
$318$	−11.0503	+	11.6700i	−0.619672	+	0.654420i
$319$	−10.8086	+	10.8086i	−0.605164	+	0.605164i
$320$	−0.994723	+	3.71236i	−0.0556067	+	0.207527i
$321$	−6.96485	−	11.3379i	−0.388740	−	0.632822i
$322$	12.0664	−	0.704520i	0.672436	−	0.0392614i
$323$	40.9552	−	10.9739i	2.27881	−	0.610605i
$324$	−7.25810	+	5.32165i	−0.403228	+	0.295647i
$325$	11.4551	+	33.3157i	0.635414	+	1.84803i
$326$	9.21049	+	5.31768i	0.510122	+	0.294519i
$327$	14.1924	−	14.9882i	0.784840	−	0.828849i
$328$	−1.22180	+	2.11621i	−0.0674624	+	0.116848i
$329$	23.5333	−	15.4829i	1.29744	−	0.853602i
$330$	8.51602	+	8.06384i	0.468791	+	0.443900i
$331$	−0.285069	+	0.0763839i	−0.0156688	+	0.00419844i	−0.266645	−	0.963795i	$-0.585915\pi$
$331$	−0.285069	+	0.0763839i	−0.0156688	+	0.00419844i	0.250976	+	0.967993i	$0.419248\pi$
$332$	4.12829	+	4.12829i	0.226570	+	0.226570i
$333$	−3.46272	−	10.5789i	−0.189756	−	0.579721i
$334$	4.88733	−	8.46511i	0.267423	−	0.463190i
$335$	−17.0202	+	29.4799i	−0.929916	+	1.61066i
$336$	−4.51161	−	0.803336i	−0.246129	−	0.0438256i
$337$			11.1559i			0.607701i	0.952720	+	0.303850i	$0.0982723\pi$
$337$			11.1559i			0.607701i	−0.952720	+	0.303850i	$0.901728\pi$
$338$	−10.3754	−	7.83275i	−0.564345	−	0.426046i
$339$	10.0070	−	18.4785i	0.543508	−	1.00362i
$340$	−7.21970	+	26.9443i	−0.391543	+	1.46126i
$341$			3.42443i			0.185443i
$342$	−9.57697	−	14.6773i	−0.517863	−	0.793659i
$343$	−10.6163	+	15.1755i	−0.573225	+	0.819398i
$344$	2.25369	+	0.603874i	0.121511	+	0.0325587i
$345$	−29.1496	+	8.66895i	−1.56936	+	0.466721i
$346$	−5.13200	−	19.1529i	−0.275898	−	1.02967i
$347$		−	7.36041i		−	0.395128i	−0.980290	−	0.197564i	$-0.936697\pi$
$347$		−	7.36041i		−	0.395128i	0.980290	−	0.197564i	$-0.0633029\pi$
$348$	0.409687	+	15.0218i	0.0219615	+	0.805254i
$349$	4.27599	+	15.9582i	0.228889	+	0.854224i	0.980809	+	0.194970i	$0.0624611\pi$
$349$	4.27599	+	15.9582i	0.228889	+	0.854224i	−0.751920	+	0.659254i	$0.770872\pi$
$350$	−23.1037	−	11.5990i	−1.23494	−	0.619991i
$351$	11.1015	−	15.0916i	0.592556	−	0.805529i
$352$	−0.880908	−	1.52578i	−0.0469526	−	0.0813242i
$353$	−1.69784	−	0.454934i	−0.0903667	−	0.0242137i	0.213352	−	0.976975i	$-0.431562\pi$
$353$	−1.69784	−	0.454934i	−0.0903667	−	0.0242137i	−0.303719	+	0.952762i	$0.598228\pi$
$354$	8.51514	−	5.23082i	0.452575	−	0.278015i
$355$	1.45968	+	0.842746i	0.0774717	+	0.0447283i
$356$	0.915873	−	0.915873i	0.0485412	−	0.0485412i
$357$	−32.7453	−	5.83061i	−1.73306	−	0.308589i
$358$	10.5078	+	2.81556i	0.555355	+	0.148807i
$359$	−1.87955	+	7.01459i	−0.0991991	+	0.370216i	−0.997623	−	0.0689141i	$-0.978047\pi$
$359$	−1.87955	+	7.01459i	−0.0991991	+	0.370216i	0.898424	+	0.439130i	$0.144713\pi$
$360$	11.5128	−	0.628441i	0.606778	−	0.0331218i
$361$	13.1003	−	7.56347i	0.689491	−	0.398078i
$362$	−4.80518	−	4.80518i	−0.252555	−	0.252555i
$363$	13.6712	−	0.372852i	0.717552	−	0.0195697i
$364$	9.46173	−	1.21480i	0.495929	−	0.0636729i
$365$			4.69511i			0.245753i
$366$	−0.765106	−	0.724481i	−0.0399927	−	0.0378692i
$367$	−15.8830	−	27.5101i	−0.829085	−	1.43602i	−0.898757	−	0.438448i	$-0.855529\pi$
$367$	−15.8830	−	27.5101i	−0.829085	−	1.43602i	0.0696717	−	0.997570i	$-0.477805\pi$
$368$	4.56845			0.238147
$369$	7.17387	+	1.50857i	0.373457	+	0.0785332i
$370$	−3.69082	+	13.7743i	−0.191877	+	0.716093i
$371$	7.72536	+	23.3027i	0.401081	+	1.20981i
$372$	2.44454	+	2.31474i	0.126744	+	0.120014i
$373$	2.36691	−	4.09961i	0.122554	−	0.212270i	−0.798220	−	0.602366i	$-0.794225\pi$
$373$	2.36691	−	4.09961i	0.122554	−	0.212270i	0.920774	+	0.390096i	$0.127558\pi$
$374$	−6.39363	−	11.0741i	−0.330607	−	0.572628i
$375$	30.8906	+	7.38070i	1.59518	+	0.381138i
$376$	9.22075	−	5.32360i	0.475524	−	0.274544i
$377$	−10.1714	−	29.5822i	−0.523853	−	1.52356i
$378$	1.92002	+	13.6130i	0.0987551	+	0.700177i
$379$	−19.7730	+	5.29816i	−1.01567	+	0.272148i	−0.727997	−	0.685580i	$-0.759549\pi$
$379$	−19.7730	+	5.29816i	−1.01567	+	0.272148i	−0.287674	+	0.957728i	$0.592882\pi$
$380$			22.4520i			1.15176i
$381$	8.34771	−	0.227666i	0.427666	−	0.0116637i
$382$	−2.89041	+	0.774484i	−0.147886	+	0.0396260i
$383$	2.99382	+	11.1731i	0.152977	+	0.570919i	0.999270	+	0.0382009i	$0.0121627\pi$
$383$	2.99382	+	11.1731i	0.152977	+	0.570919i	−0.846293	+	0.532718i	$0.821171\pi$
$384$	−1.68463	−	0.402510i	−0.0859685	−	0.0205405i
$385$	17.0048	−	5.63748i	0.866646	−	0.287313i
$386$	15.0790	−	8.70587i	0.767502	−	0.443117i
$387$	−0.381512	−	6.98916i	−0.0193934	−	0.355279i
$388$	−4.26947	−	1.14400i	−0.216749	−	0.0580778i
$389$	−6.63230	+	11.4875i	−0.336271	+	0.582438i	−0.983728	−	0.179664i	$-0.942499\pi$
$389$	−6.63230	+	11.4875i	−0.336271	+	0.582438i	0.647457	+	0.762102i	$0.275832\pi$
$390$	−22.4761	+	8.42000i	−1.13812	+	0.426363i
$391$	33.1578			1.67686
$392$	−4.34008	+	5.49215i	−0.219207	+	0.277395i
$393$	−7.16167	+	13.2244i	−0.361259	+	0.667083i
$394$	−19.4339	−	11.2202i	−0.979065	−	0.565264i
$395$	−8.65900	−	32.3158i	−0.435681	−	1.62599i
$396$	−3.52812	+	3.93553i	−0.177294	+	0.197768i
$397$	−1.50454	−	5.61502i	−0.0755107	−	0.281810i	0.917838	−	0.396955i	$-0.129933\pi$
$397$	−1.50454	−	5.61502i	−0.0755107	−	0.281810i	−0.993349	+	0.115146i	$0.963267\pi$
$398$	0.502996	+	0.502996i	0.0252129	+	0.0252129i
$399$	−26.6726	+	2.28841i	−1.33530	+	0.114564i
$400$	−8.46199	−	4.88553i	−0.423100	−	0.244277i
$401$	6.10571	+	6.10571i	0.304905	+	0.304905i	0.842929	−	0.538025i	$-0.180829\pi$
$401$	6.10571	+	6.10571i	0.304905	+	0.304905i	−0.538025	+	0.842929i	$0.680829\pi$
$402$	−13.4898	−	7.30539i	−0.672809	−	0.364360i
$403$	−6.29747	−	3.07492i	−0.313699	−	0.153173i
$404$	4.38027	−	2.52895i	0.217927	−	0.125820i
$405$	−12.5361	−	32.2382i	−0.622922	−	1.60193i
$406$	20.5146	+	10.2991i	1.01812	+	0.511137i
$407$	−3.26852	−	5.66125i	−0.162015	−	0.280618i
$408$	−12.2271	−	2.92141i	−0.605330	−	0.144632i
$409$	−13.8953	−	13.8953i	−0.687078	−	0.687078i	0.274507	−	0.961585i	$-0.411485\pi$
$409$	−13.8953	−	13.8953i	−0.687078	−	0.687078i	−0.961585	+	0.274507i	$0.911485\pi$
$410$	−6.64078	−	6.64078i	−0.327965	−	0.327965i
$411$	4.51178	+	1.07800i	0.222550	+	0.0531739i
$412$	−3.79225	−	6.56837i	−0.186831	−	0.323600i
$413$	−0.889774	−	15.2393i	−0.0437829	−	0.749877i
$414$	−4.26349	−	13.0253i	−0.209539	−	0.640160i
$415$	−19.4322	+	11.2192i	−0.953889	+	0.550728i
$416$	3.59688	−	0.249924i	0.176351	−	0.0122535i
$417$	−7.69805	−	4.16888i	−0.376975	−	0.204151i
$418$	−7.27770	−	7.27770i	−0.355964	−	0.355964i
$419$	−3.37290	−	1.94734i	−0.164777	−	0.0951340i	0.415344	−	0.909665i	$-0.363661\pi$
$419$	−3.37290	−	1.94734i	−0.164777	−	0.0951340i	−0.580121	+	0.814531i	$0.696995\pi$
$420$	7.47007	−	15.9496i	0.364502	−	0.778262i
$421$	−24.6966	−	24.6966i	−1.20364	−	1.20364i	−0.973052	−	0.230585i	$-0.925936\pi$
$421$	−24.6966	−	24.6966i	−1.20364	−	1.20364i	−0.230585	−	0.973052i	$-0.574064\pi$
$422$	−4.16705	−	15.5516i	−0.202849	−	0.757042i
$423$	−23.7836	−	21.3215i	−1.15640	−	1.03669i
$424$	2.40158	+	8.96280i	0.116631	+	0.435272i
$425$	−61.4171	−	35.4592i	−2.97917	−	1.72002i
$426$	−0.361722	+	0.667937i	−0.0175255	+	0.0323617i
$427$	−1.52777	+	0.506490i	−0.0739339	+	0.0245107i
$428$	−7.68241			−0.371343
$429$	4.55622	−	10.0148i	0.219976	−	0.483520i
$430$	−4.48359	+	7.76581i	−0.216218	+	0.374500i
$431$	12.9392	+	3.46705i	0.623259	+	0.167002i	0.556609	−	0.830775i	$-0.312102\pi$
$431$	12.9392	+	3.46705i	0.623259	+	0.167002i	0.0666504	+	0.997776i	$0.478769\pi$
$432$	0.424562	+	5.17878i	0.0204268	+	0.249164i
$433$	−26.2069	+	15.1305i	−1.25942	+	0.727127i	−0.972962	−	0.230965i	$-0.925812\pi$
$433$	−26.2069	+	15.1305i	−1.25942	+	0.727127i	−0.286459	+	0.958092i	$0.592478\pi$
$434$	4.88127	−	1.61825i	0.234309	−	0.0776786i
$435$	−56.1738	−	13.4216i	−2.69333	−	0.643518i
$436$	−3.08444	−	11.5113i	−0.147718	−	0.551290i
$437$	25.7787	−	6.90739i	1.23316	−	0.330425i
$438$	−2.11514	+	0.0576859i	−0.101065	+	0.00275634i
$439$			9.54346i			0.455485i	0.973721	+	0.227742i	$0.0731344\pi$
$439$			9.54346i			0.455485i	−0.973721	+	0.227742i	$0.926866\pi$
$440$	6.54049	−	1.75252i	0.311806	−	0.0835481i
$441$	19.7093	+	7.24868i	0.938538	+	0.345175i
$442$	26.1061	−	1.81394i	1.24174	−	0.0862806i
$443$	20.6536	−	11.9244i	0.981283	−	0.566544i	0.0786255	−	0.996904i	$-0.474947\pi$
$443$	20.6536	−	11.9244i	0.981283	−	0.566544i	0.902657	+	0.430360i	$0.141614\pi$
$444$	−6.25066	−	1.49347i	−0.296643	−	0.0708771i
$445$	2.48901	+	4.31109i	0.117990	+	0.204365i
$446$	2.96293	−	5.13194i	0.140299	−	0.243004i
$447$	−24.3421	−	23.0496i	−1.15134	−	1.09021i
$448$	−1.75860	+	1.97669i	−0.0830861	+	0.0933900i
$449$	2.28985	−	8.54582i	0.108064	−	0.403302i	−0.890610	−	0.454767i	$-0.849722\pi$
$449$	2.28985	−	8.54582i	0.108064	−	0.403302i	0.998675	+	0.0514651i	$0.0163891\pi$
$450$	−6.03226	+	28.6858i	−0.284363	+	1.35226i
$451$	4.30516			0.202722
$452$	−6.06628	−	10.5071i	−0.285334	−	0.494212i
$453$	17.5564	+	16.6242i	0.824874	+	0.781075i
$454$			8.05415i			0.378000i
$455$	−4.90202	+	36.3337i	−0.229810	+	1.70335i
$456$	−10.1146	+	0.275853i	−0.473659	+	0.0129180i
$457$	6.18168	+	6.18168i	0.289167	+	0.289167i	0.836751	−	0.547584i	$-0.184452\pi$
$457$	6.18168	+	6.18168i	0.289167	+	0.289167i	−0.547584	+	0.836751i	$0.684452\pi$
$458$	−17.6248	+	10.1757i	−0.823553	+	0.475479i
$459$	3.08147	+	37.5876i	0.143831	+	1.75444i
$460$	−4.54434	+	16.9597i	−0.211881	+	0.790751i
$461$	27.4957	+	7.36746i	1.28060	+	0.343137i	0.834084	−	0.551637i	$-0.185997\pi$
$461$	27.4957	+	7.36746i	1.28060	+	0.343137i	0.446519	+	0.894774i	$0.352663\pi$
$462$	2.74861	+	7.59138i	0.127877	+	0.353183i
$463$	14.8280	−	14.8280i	0.689117	−	0.689117i	−0.272920	−	0.962037i	$-0.587989\pi$
$463$	14.8280	−	14.8280i	0.689117	−	0.689117i	0.962037	+	0.272920i	$0.0879894\pi$
$464$	7.51370	+	4.33804i	0.348815	+	0.201388i
$465$	−11.0248	+	6.77248i	−0.511263	+	0.314066i
$466$	−4.67370	−	1.25231i	−0.216505	−	0.0580123i
$467$	−1.13643	−	1.96835i	−0.0525875	−	0.0910842i	0.838533	−	0.544850i	$-0.183414\pi$
$467$	−1.13643	−	1.96835i	−0.0525875	−	0.0910842i	−0.891121	+	0.453766i	$0.850080\pi$
$468$	−4.06934	−	10.0220i	−0.188106	−	0.463267i
$469$	−19.5766	+	12.8798i	−0.903966	+	0.594733i
$470$	10.5910	+	39.5262i	0.488527	+	1.82321i
$471$	0.431560	+	15.8238i	0.0198852	+	0.729122i
$472$		−	5.76972i		−	0.265573i
$473$	−1.06391	−	3.97058i	−0.0489189	−	0.182568i
$474$	14.4518	−	4.29791i	0.663795	−	0.197409i
$475$	−55.1359	−	14.7736i	−2.52981	−	0.677860i
$476$	−12.7639	+	14.3468i	−0.585034	+	0.657586i
$477$	23.3130	−	15.2118i	1.06743	−	0.696498i
$478$			12.5426i			0.573687i
$479$	−4.66706	+	17.4177i	−0.213244	+	0.795836i	0.773534	+	0.633755i	$0.218487\pi$
$479$	−4.66706	+	17.4177i	−0.213244	+	0.795836i	−0.986777	+	0.162081i	$0.948179\pi$
$480$	3.17000	−	5.85357i	0.144690	−	0.267178i
$481$	13.3459	−	0.927317i	0.608519	−	0.0422820i
$482$			0.986655i			0.0449409i
$483$	−20.6111	−	3.67000i	−0.937836	−	0.166991i
$484$	3.94800	−	6.83814i	0.179455	−	0.310824i
$485$	8.49388	−	14.7118i	0.385687	−	0.668030i
$486$	14.3692	−	6.04357i	0.651802	−	0.274142i
$487$	−27.6999	−	27.6999i	−1.25520	−	1.25520i	−0.953356	−	0.301847i	$-0.902397\pi$
$487$	−27.6999	−	27.6999i	−1.25520	−	1.25520i	−0.301847	−	0.953356i	$-0.597603\pi$
$488$	−0.587619	+	0.157452i	−0.0266002	+	0.00712751i
$489$	−13.3759	−	12.6657i	−0.604878	−	0.572761i
$490$	−16.0716	−	21.5751i	−0.726043	−	0.974663i
$491$	1.21285	−	2.10072i	0.0547351	−	0.0948040i	−0.837360	−	0.546652i	$-0.815902\pi$
$491$	1.21285	−	2.10072i	0.0547351	−	0.0948040i	0.892095	+	0.451848i	$0.149235\pi$
$492$	2.91007	−	3.07325i	0.131196	−	0.138553i
$493$	54.5344	+	31.4855i	2.45611	+	1.41803i
$494$	19.9185	−	6.84866i	0.896175	−	0.308136i
$495$	−11.1006	−	17.0124i	−0.498934	−	0.764650i
$496$	1.87746	−	0.503065i	0.0843006	−	0.0225883i
$497$	0.637733	+	0.969324i	0.0286062	+	0.0434801i
$498$	−5.29298	−	8.61633i	−0.237184	−	0.386107i
$499$	−3.61145	+	13.4781i	−0.161671	+	0.603364i	0.836771	+	0.547554i	$0.184441\pi$
$499$	−3.61145	+	13.4781i	−0.161671	+	0.603364i	−0.998441	+	0.0558100i	$0.982226\pi$
$500$	12.9660	−	12.9660i	0.579857	−	0.579857i
$501$	−11.6406	+	12.2934i	−0.520066	+	0.549229i
$502$	−11.4410	−	3.06561i	−0.510637	−	0.136825i
$503$	2.91521	−	1.68310i	0.129983	−	0.0750456i	−0.433599	−	0.901106i	$-0.642756\pi$
$503$	2.91521	−	1.68310i	0.129983	−	0.0750456i	0.563581	+	0.826061i	$0.309423\pi$
$504$	7.27706	+	3.16929i	0.324146	+	0.141172i
$505$	5.03121	+	18.7767i	0.223886	+	0.835554i
$506$	−4.02438	−	6.97044i	−0.178906	−	0.309874i
$507$	14.3259	+	17.3715i	0.636235	+	0.771495i
$508$	2.41067	−	4.17540i	0.106956	−	0.185254i
$509$	22.8988	−	22.8988i	1.01497	−	1.01497i	0.0150853	−	0.999886i	$-0.495198\pi$
$509$	22.8988	−	22.8988i	1.01497	−	1.01497i	0.999886	−	0.0150853i	$-0.00480199\pi$
$510$	23.0079	−	42.4852i	1.01881	−	1.88128i
$511$	−1.45017	+	2.88855i	−0.0641516	+	0.127782i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	10.2259	+	28.5807i	0.451484	+	1.26187i
$514$	−14.7209	+	14.7209i	−0.649310	+	0.649310i
$515$	28.1564	−	7.54447i	1.24072	−	0.332449i
$516$	−3.55357	−	1.92444i	−0.156437	−	0.0847186i
$517$	−16.2453	−	9.37921i	−0.714466	−	0.412497i
$518$	−6.52512	+	7.33433i	−0.286697	+	0.322252i
$519$	0.936311	+	34.3313i	0.0410995	+	1.50698i
$520$	−2.65009	+	13.6015i	−0.116214	+	0.596465i
$521$	1.65096	+	0.953184i	0.0723300	+	0.0417597i	0.535729	−	0.844390i	$-0.320037\pi$
$521$	1.65096	+	0.953184i	0.0723300	+	0.0417597i	−0.463399	+	0.886150i	$0.653370\pi$
$522$	5.35625	−	25.4711i	0.234437	−	1.11484i
$523$	−11.9642			−0.523156			−0.261578	−	0.965182i	$-0.584243\pi$
$523$	−11.9642			−0.523156			−0.261578	+	0.965182i	$0.584243\pi$
$524$	4.34141	+	7.51955i	0.189655	+	0.328493i
$525$	34.2525	+	28.8394i	1.49490	+	1.25866i
$526$	−3.85431	+	14.3845i	−0.168056	+	0.627193i
$527$	13.6266	−	3.65124i	0.593585	−	0.159051i
$528$	0.869866	+	2.92495i	0.0378561	+	0.127292i
$529$	−2.12927			−0.0925769
$530$	−35.6620			−1.54906
$531$	−16.4503	+	5.38457i	−0.713884	+	0.233671i
$532$	−6.93468	+	13.8130i	−0.300656	+	0.598869i
$533$	−3.86576	+	7.91711i	−0.167445	+	0.342928i
$534$	−1.91156	+	1.17426i	−0.0827211	+	0.0508152i
$535$	7.64187	−	28.5198i	0.330387	−	1.23302i
$536$	−7.67045	+	4.42853i	−0.331313	+	0.191284i
$537$	−16.5685	−	8.97268i	−0.714984	−	0.387200i
$538$	−17.9639	−	17.9639i	−0.774480	−	0.774480i
$539$	12.2030	+	1.78391i	0.525621	+	0.0768386i
$540$	−19.6478	−	3.57532i	−0.845506	−	0.153857i
$541$	−12.2159	−	3.27325i	−0.525204	−	0.140728i	−0.0135313	−	0.999908i	$-0.504307\pi$
$541$	−12.2159	−	3.27325i	−0.525204	−	0.140728i	−0.511673	+	0.859180i	$0.670974\pi$
$542$			18.2256i			0.782855i
$543$	6.16084	+	10.0291i	0.264387	+	0.430390i
$544$	−5.13218	+	5.13218i	−0.220040	+	0.220040i
$545$	45.8021			1.96195
$546$	−16.4285	−	1.76194i	−0.703075	−	0.0754042i
$547$	4.78271			0.204494			0.102247	−	0.994759i	$-0.467397\pi$
$547$	4.78271			0.204494			0.102247	+	0.994759i	$0.467397\pi$
$548$	1.89377	−	1.89377i	0.0808980	−	0.0808980i
$549$	0.997312	+	1.52845i	0.0425642	+	0.0652325i
$550$			17.2148i			0.734042i
$551$	48.9571	+	13.1180i	2.08564	+	0.558846i
$552$	−7.69616	−	1.83885i	−0.327570	−	0.0782665i
$553$	4.65407	−	22.5559i	0.197911	−	0.959177i
$554$	16.9041	+	16.9041i	0.718187	+	0.718187i
$555$	11.7620	−	21.7191i	0.499268	−	0.921924i
$556$	−4.37720	+	2.52718i	−0.185635	+	0.107176i
$557$	−1.12619	+	4.20299i	−0.0477181	+	0.178086i	−0.985672	−	0.168674i	$-0.946052\pi$
$557$	−1.12619	+	4.20299i	−0.0477181	+	0.178086i	0.937954	+	0.346760i	$0.112718\pi$
$558$	−3.18645	−	4.88344i	−0.134893	−	0.206733i
$559$	8.25716	+	1.60881i	0.349241	+	0.0680455i
$560$	−5.58887	−	8.49482i	−0.236173	−	0.358972i
$561$	6.31349	+	21.2293i	0.266556	+	0.896301i
$562$	−15.4614			−0.652199
$563$	13.9979			0.589943			0.294971	−	0.955506i	$-0.404690\pi$
$563$	13.9979			0.589943			0.294971	+	0.955506i	$0.404690\pi$
$564$	−17.6764	+	5.25687i	−0.744309	+	0.221354i
$565$	45.0404	−	12.0685i	1.89486	−	0.507727i
$566$	3.21489	−	11.9981i	0.135132	−	0.504319i
$567$	2.24484	−	23.7057i	0.0942743	−	0.995546i
$568$	0.219276	+	0.379797i	0.00920061	+	0.0159359i
$569$	−4.40379			−0.184617			−0.0923083	−	0.995730i	$-0.529425\pi$
$569$	−4.40379			−0.184617			−0.0923083	+	0.995730i	$0.529425\pi$
$570$	9.03714	−	37.8233i	0.378524	−	1.58424i
$571$	−24.6755	−	14.2464i	−1.03264	−	0.596193i	−0.114898	−	0.993377i	$-0.536654\pi$
$571$	−24.6755	−	14.2464i	−1.03264	−	0.596193i	−0.917739	+	0.397184i	$0.869987\pi$
$572$	−3.54985	−	5.26788i	−0.148427	−	0.220261i
$573$	5.18102	−	0.141301i	0.216440	−	0.00590294i
$574$	−2.03445	−	6.13669i	−0.0849163	−	0.256140i
$575$	−38.6582	−	22.3193i	−1.61216	−	0.930779i
$576$	2.67597	+	1.35616i	0.111499	+	0.0565067i
$577$	17.7655	−	4.76026i	0.739589	−	0.198172i	0.130694	−	0.991423i	$-0.458280\pi$
$577$	17.7655	−	4.76026i	0.739589	−	0.198172i	0.608895	+	0.793250i	$0.291613\pi$
$578$	−25.2285	+	25.2285i	−1.04937	+	1.04937i
$579$	−28.9068	+	8.59674i	−1.20133	+	0.357269i
$580$	−23.5784	+	23.5784i	−0.979039	+	0.979039i
$581$	−15.4204	+	0.900348i	−0.639746	+	0.0373527i
$582$	6.73201	+	3.64572i	0.279051	+	0.151120i
$583$	11.5597	−	11.5597i	0.478753	−	0.478753i
$584$	−0.610816	+	1.05796i	−0.0252757	+	0.0437789i
$585$	41.2531	−	5.13775i	1.70561	−	0.212420i
$586$	−5.57604	−	9.65799i	−0.230344	−	0.398968i
$587$	6.76734	+	25.2560i	0.279318	+	1.04243i	0.952892	+	0.303309i	$0.0980915\pi$
$587$	6.76734	+	25.2560i	0.279318	+	1.04243i	−0.673574	+	0.739120i	$0.735242\pi$
$588$	9.52208	−	7.50533i	0.392684	−	0.309515i
$589$	9.83347	−	5.67736i	0.405181	−	0.233931i
$590$	21.4193	+	5.73928i	0.881817	+	0.236282i
$591$	28.2227	+	26.7242i	1.16093	+	1.09929i
$592$	−2.62365	+	2.62365i	−0.107831	+	0.107831i
$593$	6.20809	−	23.1689i	0.254936	−	0.951433i	−0.713190	−	0.700970i	$-0.752751\pi$
$593$	6.20809	−	23.1689i	0.254936	−	0.951433i	0.968126	−	0.250463i	$-0.0805828\pi$
$594$	7.52766	−	5.20982i	0.308864	−	0.213761i
$595$	−40.5640	−	61.6554i	−1.66296	−	2.52762i
$596$	−18.6953	+	5.00939i	−0.765790	+	0.205193i
$597$	−0.644903	−	1.04982i	−0.0263941	−	0.0429664i
$598$	16.4322	−	1.14176i	0.671961	−	0.0466902i
$599$	−32.5877	−	18.8145i	−1.33150	−	0.768741i	−0.345970	−	0.938246i	$-0.612450\pi$
$599$	−32.5877	−	18.8145i	−1.33150	−	0.768741i	−0.985529	+	0.169504i	$0.945783\pi$
$600$	12.2889	+	11.6364i	0.501691	+	0.475052i
$601$	−3.77228	+	6.53379i	−0.153875	+	0.266519i	−0.932649	−	0.360786i	$-0.882509\pi$
$601$	−3.77228	+	6.53379i	−0.153875	+	0.266519i	0.778774	+	0.627305i	$0.215842\pi$
$602$	−5.15701	+	3.39288i	−0.210184	+	0.138283i
$603$	19.7848	+	17.7367i	0.805701	+	0.722293i
$604$	13.4837	−	3.61296i	0.548646	−	0.147009i
$605$	21.4584	+	21.4584i	0.872410	+	0.872410i
$606$	−8.39708	+	2.49725i	−0.341108	+	0.101444i
$607$	−19.6808	+	34.0881i	−0.798817	+	1.38359i	0.121570	+	0.992583i	$0.461207\pi$
$607$	−19.6808	+	34.0881i	−0.798817	+	1.38359i	−0.920387	+	0.391009i	$0.872126\pi$
$608$	−2.92091	+	5.05917i	−0.118459	+	0.205176i
$609$	−30.4140	−	25.6076i	−1.23244	−	1.03767i
$610$		−	2.33807i		−	0.0946657i
$611$	31.8354	−	21.4528i	1.28792	−	0.867888i
$612$	19.4222	+	9.84302i	0.785096	+	0.397880i
$613$	2.44531	−	9.12603i	0.0987652	−	0.368597i	−0.898798	−	0.438363i	$-0.855559\pi$
$613$	2.44531	−	9.12603i	0.0987652	−	0.368597i	0.997563	+	0.0697659i	$0.0222252\pi$
$614$			33.8320i			1.36535i
$615$	8.51430	+	13.8603i	0.343330	+	0.558900i
$616$	4.56516	+	0.941950i	0.183936	+	0.0379522i
$617$	−15.0745	−	4.03921i	−0.606878	−	0.162613i	−0.0577226	−	0.998333i	$-0.518384\pi$
$617$	−15.0745	−	4.03921i	−0.606878	−	0.162613i	−0.549156	+	0.835720i	$0.685051\pi$
$618$	3.74471	+	12.5917i	0.150634	+	0.506513i
$619$	4.83379	+	18.0399i	0.194286	+	0.725086i	0.992450	+	0.122646i	$0.0391380\pi$
$619$	4.83379	+	18.0399i	0.194286	+	0.725086i	−0.798164	+	0.602440i	$0.794195\pi$
$620$			7.47022i			0.300011i
$621$	1.93959	+	23.6590i	0.0778331	+	0.949403i
$622$	−7.27949	−	27.1674i	−0.291881	−	1.08931i
$623$	0.199744	+	3.42106i	0.00800259	+	0.137062i
$624$	−6.16002	−	1.02675i	−0.246598	−	0.0411029i
$625$	10.8092	+	18.7221i	0.432368	+	0.748883i
$626$	−17.6428	−	4.72738i	−0.705149	−	0.188944i
$627$	9.33091	+	15.1896i	0.372641	+	0.606614i
$628$	7.91484	+	4.56964i	0.315837	+	0.182348i
$629$	−19.0424	+	19.0424i	−0.759272	+	0.759272i
$630$	−19.0042	+	23.8625i	−0.757146	+	0.950703i
$631$	43.5005	+	11.6559i	1.73173	+	0.464015i	0.980580	−	0.196118i	$-0.0628337\pi$
$631$	43.5005	+	11.6559i	1.73173	+	0.464015i	0.751148	+	0.660134i	$0.229500\pi$
$632$	2.25300	−	8.40832i	0.0896196	−	0.334465i
$633$	0.760259	+	27.8761i	0.0302176	+	1.10797i
$634$	24.6467	−	14.2298i	0.978844	−	0.565136i
$635$	13.1026	+	13.1026i	0.519962	+	0.519962i
$636$	−0.438157	−	16.0657i	−0.0173740	−	0.637046i
$637$	−14.2381	+	20.8393i	−0.564135	+	0.825683i
$638$		−	15.2856i		−	0.605164i
$639$	0.878219	−	0.979632i	0.0347418	−	0.0387537i
$640$	−1.92166	−	3.32841i	−0.0759602	−	0.131567i
$641$	−36.3795			−1.43690			−0.718451	−	0.695577i	$-0.755149\pi$
$641$	−36.3795			−1.43690			−0.718451	+	0.695577i	$0.755149\pi$
$642$	12.9420	+	3.09224i	0.510781	+	0.122041i
$643$	3.16033	−	11.7945i	0.124631	−	0.465130i	−0.875195	−	0.483770i	$-0.839267\pi$
$643$	3.16033	−	11.7945i	0.124631	−	0.465130i	0.999826	+	0.0186402i	$0.00593369\pi$
$644$	−8.03408	+	9.03043i	−0.316587	+	0.355849i
$645$	10.6790	−	11.2778i	0.420486	−	0.444064i
$646$	−21.2000	+	36.7195i	−0.834102	+	1.44471i
$647$	−18.0134	−	31.2001i	−0.708180	−	1.22660i	−0.965532	−	0.260286i	$-0.916183\pi$
$647$	−18.0134	−	31.2001i	−0.708180	−	1.22660i	0.257352	−	0.966318i	$-0.417150\pi$
$648$	1.36928	−	8.89523i	0.0537903	−	0.349438i
$649$	−8.80332	+	5.08260i	−0.345560	+	0.199509i
$650$	−31.6578	−	15.4578i	−1.24172	−	0.606305i
$651$	−8.87452	+	0.761400i	−0.347820	+	0.0298416i
$652$	−10.2730	+	2.75263i	−0.402321	+	0.107801i
$653$			31.1157i			1.21765i	0.793303	+	0.608827i	$0.208360\pi$
$653$			31.1157i			1.21765i	−0.793303	+	0.608827i	$0.791640\pi$
$654$	0.562742	+	20.6338i	0.0220049	+	0.806844i
$655$	−32.2337	+	8.63700i	−1.25948	+	0.337476i
$656$	−0.632448	−	2.36033i	−0.0246929	−	0.0921553i
$657$	3.58645	+	0.754185i	0.139921	+	0.0294236i
$658$	−5.69249	+	27.5887i	−0.221917	+	1.07552i
$659$	−7.39309	+	4.26840i	−0.287994	+	0.166273i	−0.637037	−	0.770833i	$-0.719840\pi$
$659$	−7.39309	+	4.26840i	−0.287994	+	0.166273i	0.349043	+	0.937107i	$0.386507\pi$
$660$	−11.7237	+	0.319739i	−0.456345	+	0.0124458i
$661$	−3.08402	−	0.826361i	−0.119954	−	0.0321417i	0.198342	−	0.980133i	$-0.436444\pi$
$661$	−3.08402	−	0.826361i	−0.119954	−	0.0321417i	−0.318297	+	0.947991i	$0.603111\pi$
$662$	0.147562	−	0.255586i	0.00573517	−	0.00993361i
$663$	−44.7094	−	7.45214i	−1.73637	−	0.289417i
$664$	−5.83829			−0.226570
$665$	−44.3807	−	39.4841i	−1.72101	−	1.53113i
$666$	9.92893	+	5.03190i	0.384738	+	0.194982i
$667$	34.3259	+	19.8181i	1.32911	+	0.767360i
$668$	2.52987	+	9.44160i	0.0978836	+	0.365307i
$669$	−7.05710	+	7.45282i	−0.272843	+	0.288143i
$670$	−8.81033	−	32.8806i	−0.340373	−	1.27029i
$671$	0.757875	+	0.757875i	0.0292574	+	0.0292574i
$672$	3.75824	−	2.62215i	0.144977	−	0.101152i
$673$	−26.7125	−	15.4225i	−1.02969	−	0.594492i	−0.112794	−	0.993618i	$-0.535980\pi$
$673$	−26.7125	−	15.4225i	−1.02969	−	0.594492i	−0.916896	+	0.399126i	$0.869313\pi$
$674$	−7.88842	−	7.88842i	−0.303850	−	0.303850i
$675$	21.7084	−	45.8970i	0.835559	−	1.76658i
$676$	12.8751	−	1.79789i	0.495195	−	0.0691496i
$677$	−30.7806	+	17.7712i	−1.18300	+	0.683003i	−0.956706	−	0.291057i	$-0.905993\pi$
$677$	−30.7806	+	17.7712i	−1.18300	+	0.683003i	−0.226290	+	0.974060i	$0.572660\pi$
$678$	5.99024	+	20.1423i	0.230054	+	0.773562i
$679$	9.76964	−	6.42759i	0.374924	−	0.246668i
$680$	−13.9474	−	24.1576i	−0.534858	−	0.926401i
$681$	3.24188	−	13.5683i	0.124229	−	0.519938i
$682$	−2.42144	−	2.42144i	−0.0927216	−	0.0927216i
$683$	−0.505821	−	0.505821i	−0.0193547	−	0.0193547i	0.697363	−	0.716718i	$-0.254356\pi$
$683$	−0.505821	−	0.505821i	−0.0193547	−	0.0193547i	−0.716718	+	0.697363i	$0.754356\pi$
$684$	17.1504	+	3.60651i	0.655761	+	0.137898i
$685$	5.14658	+	8.91414i	0.196641	+	0.340592i
$686$	−3.22383	−	18.2375i	−0.123086	−	0.696312i
$687$	33.7871	−	10.0481i	1.28906	−	0.383360i
$688$	−2.02060	+	1.16659i	−0.0770347	+	0.0444760i
$689$	10.8782	+	31.6379i	0.414426	+	1.20531i
$690$	14.4820	−	26.7417i	0.551320	−	1.01804i
$691$	30.9063	+	30.9063i	1.17573	+	1.17573i	0.980821	+	0.194909i	$0.0624411\pi$
$691$	30.9063	+	30.9063i	1.17573	+	1.17573i	0.194909	+	0.980821i	$0.437559\pi$
$692$	17.1720	+	9.91427i	0.652782	+	0.376884i
$693$	−1.57478	−	13.8950i	−0.0598211	−	0.527829i
$694$	5.20460	+	5.20460i	0.197564	+	0.197564i
$695$	−5.02768	−	18.7636i	−0.190711	−	0.711742i
$696$	−10.9117	−	10.3323i	−0.413608	−	0.391646i
$697$	−4.59030	−	17.1312i	−0.173870	−	0.648892i
$698$	−14.3078	−	8.26058i	−0.541556	−	0.312668i
$699$	7.36940	+	3.99090i	0.278736	+	0.150950i
$700$	24.5385	−	8.13506i	0.927467	−	0.307476i
$701$	−12.5650			−0.474573			−0.237286	−	0.971440i	$-0.576258\pi$
$701$	−12.5650			−0.474573			−0.237286	+	0.971440i	$0.576258\pi$
$702$	2.82140	+	18.5213i	0.106487	+	0.699043i
$703$	−10.8378	+	18.7716i	−0.408754	+	0.707983i
$704$	1.70178	+	0.455992i	0.0641384	+	0.0171858i
$705$	−1.93228	−	70.8501i	−0.0727740	−	2.66837i
$706$	1.52224	−	0.878865i	0.0572902	−	0.0330765i
$707$	−2.70419	+	13.1059i	−0.101702	+	0.492897i
$708$	−2.32237	+	9.71986i	−0.0872800	+	0.365295i
$709$	−2.95583	−	11.0313i	−0.111009	−	0.414290i	0.887949	−	0.459942i	$-0.152130\pi$
$709$	−2.95583	−	11.0313i	−0.111009	−	0.414290i	−0.998957	+	0.0456527i	$0.985463\pi$
$710$	−1.62806	+	0.436237i	−0.0611000	+	0.0163717i
$711$	−26.0760	+	1.42339i	−0.977926	+	0.0533813i
$712$			1.29524i			0.0485412i
$713$	8.57709	−	2.29823i	0.321215	−	0.0860692i
$714$	27.2773	−	19.0315i	1.02083	−	0.712238i
$715$	23.0874	−	7.93822i	0.863418	−	0.296873i
$716$	−9.42105	+	5.43924i	−0.352081	+	0.203274i
$717$	5.04853	−	21.1297i	0.188541	−	0.789104i
$718$	−3.63102	−	6.28911i	−0.135508	−	0.234707i
$719$	−6.28707	+	10.8895i	−0.234468	+	0.406111i	−0.959118	−	0.283007i	$-0.908668\pi$
$719$	−6.28707	+	10.8895i	−0.234468	+	0.406111i	0.724650	+	0.689117i	$0.242002\pi$
$720$	−7.69641	+	8.58516i	−0.286828	+	0.319950i
$721$	19.6527	+	4.05503i	0.731905	+	0.151017i
$722$	−3.91514	+	14.6115i	−0.145706	+	0.543784i
$723$	0.397138	−	1.66215i	0.0147697	−	0.0618161i
$724$	6.79556			0.252555
$725$	−42.3872	−	73.4168i	−1.57422	−	2.72663i
$726$	−9.40335	+	9.93064i	−0.348991	+	0.368561i
$727$			8.75483i			0.324699i	0.986733	+	0.162349i	$0.0519072\pi$
$727$			8.75483i			0.324699i	−0.986733	+	0.162349i	$0.948093\pi$
$728$	−5.83146	+	7.54945i	−0.216128	+	0.279801i
$729$	−26.6395	+	4.39743i	−0.986648	+	0.162868i
$730$	−3.31995	−	3.31995i	−0.122877	−	0.122877i
$731$	−14.6655	+	8.46714i	−0.542424	+	0.313169i
$732$	1.05330	−	0.0287264i	0.0389310	−	0.00106176i
$733$	13.0536	−	48.7167i	0.482145	−	1.79939i	−0.110439	−	0.993883i	$-0.535226\pi$
$733$	13.0536	−	48.7167i	0.482145	−	1.79939i	0.592585	−	0.805508i	$-0.298108\pi$
$734$	30.6836	+	8.22164i	1.13255	+	0.303466i
$735$	18.3906	+	42.8151i	0.678349	+	1.57926i
$736$	−3.23038	+	3.23038i	−0.119073	+	0.119073i
$737$	13.5139	+	7.80226i	0.497792	+	0.287400i
$738$	−6.13941	+	4.00597i	−0.225995	+	0.147462i
$739$	25.4683	+	6.82422i	0.936868	+	0.251033i	0.694781	−	0.719222i	$-0.255501\pi$
$739$	25.4683	+	6.82422i	0.936868	+	0.251033i	0.242087	+	0.970255i	$0.422168\pi$
$740$	−7.13012	−	12.3497i	−0.262108	−	0.453985i
$741$	−36.3120	+	3.52008i	−1.33395	+	0.129313i
$742$	−21.9401	−	11.0148i	−0.805448	−	0.404367i
$743$	−1.63351	−	6.09633i	−0.0599275	−	0.223653i	0.929467	−	0.368905i	$-0.120267\pi$
$743$	−1.63351	−	6.09633i	−0.0599275	−	0.223653i	−0.989395	+	0.145252i	$0.953601\pi$
$744$	−3.36532	+	0.0917819i	−0.123379	+	0.00336489i
$745$		−	74.3866i		−	2.72531i
$746$	1.22520	+	4.57252i	0.0448579	+	0.167412i
$747$	5.44856	+	16.6458i	0.199353	+	0.609039i
$748$	12.3515	+	3.30959i	0.451617	+	0.121010i
$749$	13.5103	−	15.1858i	0.493655	−	0.554876i
$750$	−27.0619	+	16.6240i	−0.988161	+	0.607023i
$751$		−	7.47025i		−	0.272593i	−0.990668	−	0.136297i	$-0.956480\pi$
$751$		−	7.47025i		−	0.272593i	0.990668	−	0.136297i	$-0.0435200\pi$
$752$	−2.75570	+	10.2844i	−0.100490	+	0.375034i
$753$	18.0399	+	9.76953i	0.657412	+	0.356022i
$754$	28.1100	+	13.7255i	1.02371	+	0.499855i
$755$			53.6503i			1.95254i
$756$	−10.9835	−	8.26818i	−0.399466	−	0.300711i
$757$	15.1379	−	26.2197i	0.550198	−	0.952971i	−0.448062	−	0.894003i	$-0.647886\pi$
$757$	15.1379	−	26.2197i	0.550198	−	0.952971i	0.998260	−	0.0589682i	$-0.0187811\pi$
$758$	10.2353	−	17.7280i	0.371762	−	0.643910i
$759$	3.97394	+	13.3625i	0.144245	+	0.485027i
$760$	−15.8759	−	15.8759i	−0.575881	−	0.575881i
$761$	27.3537	−	7.32941i	0.991573	−	0.265691i	0.273662	−	0.961826i	$-0.411765\pi$
$761$	27.3537	−	7.32941i	0.991573	−	0.265691i	0.717911	+	0.696135i	$0.245098\pi$
$762$	−5.74174	+	6.06370i	−0.208001	+	0.219665i
$763$	28.1786	+	14.1468i	1.02013	+	0.512147i
$764$	1.49619	−	2.59147i	0.0541302	−	0.0937562i
$765$	−55.8605	+	62.3110i	−2.01964	+	2.25286i
$766$	−10.0175	−	5.78362i	−0.361948	−	0.208971i
$767$	−1.44199	−	20.7530i	−0.0520672	−	0.749347i
$768$	1.47583	−	0.906598i	0.0532545	−	0.0327140i
$769$	1.37880	−	0.369447i	0.0497207	−	0.0133226i	−0.233873	−	0.972267i	$-0.575140\pi$
$769$	1.37880	−	0.369447i	0.0497207	−	0.0133226i	0.283594	+	0.958945i	$0.408473\pi$
$770$	−8.03793	+	16.0105i	−0.289667	+	0.576980i
$771$	30.7246	−	18.8740i	1.10652	−	0.679729i
$772$	−4.50649	+	16.8185i	−0.162192	+	0.605309i
$773$	29.5945	−	29.5945i	1.06444	−	1.06444i	0.0666646	−	0.997775i	$-0.478764\pi$
$773$	29.5945	−	29.5945i	1.06444	−	1.06444i	0.997775	−	0.0666646i	$-0.0212358\pi$
$774$	5.21185	+	4.67231i	0.187336	+	0.167943i
$775$	−18.3448	−	4.91548i	−0.658965	−	0.176569i
$776$	3.82790	−	2.21004i	0.137414	−	0.0793358i
$777$	13.9446	−	9.72922i	0.500258	−	0.349034i
$778$	−3.43313	−	12.8126i	−0.123084	−	0.459354i
$779$	−7.13752	−	12.3625i	−0.255728	−	0.442934i
$780$	9.93917	−	21.8468i	0.355879	−	0.782242i
$781$	0.386324	−	0.669132i	0.0138238	−	0.0239434i
$782$	−23.4461	+	23.4461i	−0.838431	+	0.838431i
$783$	−19.2757	+	40.7535i	−0.688857	+	1.45641i
$784$	−0.814638	−	6.95244i	−0.0290942	−	0.248301i
$785$	−24.8372	+	24.8372i	−0.886478	+	0.886478i
$786$	−4.28699	−	14.4151i	−0.152912	−	0.514171i
$787$	29.8175	−	29.8175i	1.06288	−	1.06288i	0.0649919	−	0.997886i	$-0.479298\pi$
$787$	29.8175	−	29.8175i	1.06288	−	1.06288i	0.997886	−	0.0649919i	$-0.0207021\pi$
$788$	21.6757	−	5.80798i	0.772164	−	0.206901i
$789$	12.2830	−	22.6812i	0.437286	−	0.807471i
$790$	28.9736	+	16.7279i	1.03083	+	0.595152i
$791$	31.4375	+	6.48663i	1.11779	+	0.230638i
$792$	−0.288084	−	5.27759i	−0.0102366	−	0.187531i
$793$	−2.07424	+	0.713195i	−0.0736585	+	0.0253263i
$794$	5.03429	+	2.90655i	0.178660	+	0.103150i
$795$	60.0774	+	14.3543i	2.13073	+	0.509095i
$796$	−0.711344			−0.0252129
$797$	−9.10466	−	15.7697i	−0.322504	−	0.558593i	0.658500	−	0.752580i	$-0.271191\pi$
$797$	−9.10466	−	15.7697i	−0.322504	−	0.558593i	−0.981004	+	0.193988i	$0.937858\pi$
$798$	17.2422	−	20.4785i	0.610369	−	0.724933i
$799$	−20.0009	+	74.6442i	−0.707579	+	2.64072i
$800$	9.43812	−	2.52894i	0.333688	−	0.0894114i
$801$	3.69292	−	1.20878i	0.130483	−	0.0427101i
$802$	−8.63478			−0.304905
$803$	2.15229			0.0759527
$804$	14.7044	−	4.37302i	0.518585	−	0.154225i
$805$	−25.5325	−	38.8082i	−0.899902	−	1.36781i
$806$	6.62728	−	2.27868i	0.233436	−	0.0802633i
$807$	23.0319	+	37.4933i	0.810763	+	1.31982i
$808$	−1.30908	+	4.88556i	−0.0460533	+	0.171873i
$809$	−45.4318	+	26.2301i	−1.59730	+	0.922199i	−0.605291	+	0.796004i	$0.706943\pi$
$809$	−45.4318	+	26.2301i	−1.59730	+	0.922199i	−0.992005	+	0.126195i	$0.959723\pi$
$810$	31.6602	+	13.9315i	1.11243	+	0.489504i
$811$	3.63424	+	3.63424i	0.127615	+	0.127615i	0.768030	−	0.640414i	$-0.221237\pi$
$811$	3.63424	+	3.63424i	0.127615	+	0.127615i	−0.640414	+	0.768030i	$0.721237\pi$
$812$	−21.7886	+	7.22340i	−0.764629	+	0.253492i
$813$	7.33596	−	30.7034i	0.257283	−	1.07681i
$814$	6.31430	+	1.69191i	0.221316	+	0.0593015i
$815$		−	40.8750i		−	1.43179i
$816$	10.7116	−	6.58008i	0.374981	−	0.230349i
$817$	−9.63793	+	9.63793i	−0.337188	+	0.337188i
$818$	19.6509			0.687078
$819$	26.9668	+	9.58086i	0.942296	+	0.334782i
$820$	9.39149			0.327965
$821$	37.6398	−	37.6398i	1.31364	−	1.31364i	0.394925	−	0.918713i	$-0.370770\pi$
$821$	37.6398	−	37.6398i	1.31364	−	1.31364i	0.918713	−	0.394925i	$-0.129230\pi$
$822$	−3.95257	+	2.42805i	−0.137862	+	0.0846879i
$823$			26.1124i			0.910223i	0.890435	+	0.455111i	$0.150401\pi$
$823$			26.1124i			0.910223i	−0.890435	+	0.455111i	$0.849599\pi$
$824$	7.32606	+	1.96301i	0.255215	+	0.0683848i
$825$	6.92913	−	29.0006i	0.241241	−	1.00967i
$826$	11.4050	+	10.1466i	0.396830	+	0.353047i
$827$	13.1068	+	13.1068i	0.455769	+	0.455769i	0.897264	−	0.441495i	$-0.145552\pi$
$827$	13.1068	+	13.1068i	0.455769	+	0.455769i	−0.441495	+	0.897264i	$0.645552\pi$
$828$	12.2250	+	6.19556i	0.424850	+	0.215310i
$829$	43.5501	−	25.1437i	1.51256	−	0.873276i	0.512667	−	0.858588i	$-0.328658\pi$
$829$	43.5501	−	25.1437i	1.51256	−	0.873276i	0.999892	−	0.0146886i	$-0.00467568\pi$
$830$	5.80748	−	21.6738i	0.201581	−	0.752309i
$831$	−21.6732	−	35.2813i	−0.751834	−	1.22389i
$832$	−2.36665	+	2.72010i	−0.0820490	+	0.0943025i
$833$	−5.91264	−	50.4608i	−0.204861	−	1.74836i
$834$	8.39118	−	2.49550i	0.290563	−	0.0864120i
$835$	−37.5671			−1.30006
$836$	10.2922			0.355964
$837$	3.40236	+	9.50938i	0.117603	+	0.328692i
$838$	3.76198	−	1.00802i	0.129955	−	0.0348215i
$839$	−9.62474	+	35.9200i	−0.332283	+	1.24010i	0.574502	+	0.818503i	$0.305196\pi$
$839$	−9.62474	+	35.9200i	−0.332283	+	1.24010i	−0.906785	+	0.421593i	$0.861471\pi$
$840$	5.99594	+	16.5602i	0.206880	+	0.571382i
$841$	23.1371	+	40.0746i	0.797831	+	1.38188i
$842$	34.9262			1.20364
$843$	26.0467	+	6.22335i	0.897097	+	0.214344i
$844$	13.9432	+	8.05012i	0.479945	+	0.277097i
$845$	−6.13273	+	49.5853i	−0.210972	+	1.70579i
$846$	31.8941	−	1.74098i	1.09654	−	0.0598562i
$847$	6.57394	+	19.8296i	0.225883	+	0.681352i
$848$	−8.03583	−	4.63949i	−0.275952	−	0.159321i
$849$	−10.2453	+	18.9184i	−0.351617	+	0.649279i
$850$	68.5019	−	18.3550i	2.34960	−	0.629572i
$851$	−11.9860	+	11.9860i	−0.410875	+	0.410875i
$852$	−0.216527	−	0.728079i	−0.00741810	−	0.0249436i
$853$	1.00151	−	1.00151i	0.0342909	−	0.0342909i	−0.689753	−	0.724044i	$-0.742281\pi$
$853$	1.00151	−	1.00151i	0.0342909	−	0.0342909i	0.724044	+	0.689753i	$0.242281\pi$
$854$	0.722153	−	1.43844i	0.0247116	−	0.0492223i
$855$	−30.4485	+	60.0809i	−1.04132	+	2.05472i
$856$	5.43228	−	5.43228i	0.185672	−	0.185672i
$857$	6.06943	−	10.5126i	0.207328	−	0.359102i	−0.743544	−	0.668687i	$-0.766857\pi$
$857$	6.06943	−	10.5126i	0.207328	−	0.359102i	0.950872	+	0.309585i	$0.100190\pi$
$858$	3.85982	+	10.3033i	0.131772	+	0.351748i
$859$	17.0097	+	29.4617i	0.580365	+	1.00522i	0.995436	+	0.0954327i	$0.0304235\pi$
$859$	17.0097	+	29.4617i	0.580365	+	1.00522i	−0.415071	+	0.909789i	$0.636243\pi$
$860$	−2.32088	−	8.66163i	−0.0791412	−	0.295359i
$861$	0.957225	+	11.1570i	0.0326221	+	0.380228i
$862$	−11.6010	+	6.69782i	−0.395131	+	0.228129i
$863$	−47.3865	−	12.6972i	−1.61305	−	0.432217i	−0.664104	−	0.747640i	$-0.731187\pi$
$863$	−47.3865	−	12.6972i	−1.61305	−	0.432217i	−0.948951	+	0.315424i	$0.897853\pi$
$864$	−3.96216	−	3.36174i	−0.134795	−	0.114369i
$865$	−53.8867	+	53.8867i	−1.83220	+	1.83220i
$866$	7.83214	−	29.2299i	0.266147	−	0.993274i
$867$	52.6555	−	32.3461i	1.78828	−	1.09853i
$868$	−2.30731	+	4.59586i	−0.0783150	+	0.155994i
$869$	−14.8139	+	3.96938i	−0.502528	+	0.134652i
$870$	49.2114	−	30.2304i	1.66842	−	1.02491i
$871$	−26.4829	+	17.8459i	−0.897338	+	0.604686i
$872$	10.3207	+	5.95867i	0.349504	+	0.201786i
$873$	−9.87353	−	8.85140i	−0.334168	−	0.299575i
$874$	−13.3440	+	23.1126i	−0.451369	+	0.781794i
$875$	2.82778	+	48.4319i	0.0955965	+	1.63730i
$876$	1.45484	−	1.53642i	0.0491545	−	0.0519108i
$877$	7.28688	−	1.95251i	0.246060	−	0.0659317i	−0.133681	−	0.991024i	$-0.542680\pi$
$877$	7.28688	−	1.95251i	0.246060	−	0.0659317i	0.379741	+	0.925093i	$0.376013\pi$
$878$	−6.74825	−	6.74825i	−0.227742	−	0.227742i
$879$	5.50615	+	18.5146i	0.185718	+	0.624481i
$880$	−3.38561	+	5.86404i	−0.114129	+	0.197677i
$881$	19.0297	−	32.9603i	0.641126	−	1.11046i	−0.344056	−	0.938949i	$-0.611801\pi$
$881$	19.0297	−	32.9603i	0.641126	−	1.11046i	0.985182	−	0.171513i	$-0.0548656\pi$
$882$	−19.0622	+	8.81099i	−0.641857	+	0.296682i
$883$		−	41.0273i		−	1.38068i	−0.723486	−	0.690339i	$-0.757461\pi$
$883$		−	41.0273i		−	1.38068i	0.723486	−	0.690339i	$-0.242539\pi$
$884$	−17.1772	+	19.7425i	−0.577731	+	0.664011i
$885$	−33.7735	−	18.2900i	−1.13528	−	0.614813i
$886$	−6.17251	+	23.0361i	−0.207369	+	0.773913i
$887$			35.7890i			1.20168i	0.799371	+	0.600838i	$0.205166\pi$
$887$			35.7890i			1.20168i	−0.799371	+	0.600838i	$0.794834\pi$
$888$	5.47593	−	3.36384i	0.183760	−	0.112883i
$889$	4.01409	+	12.1080i	0.134628	+	0.406090i
$890$	−4.80839	−	1.28840i	−0.161178	−	0.0431874i
$891$	−14.7783	+	5.74667i	−0.495093	+	0.192521i
$892$	1.53372	+	5.72394i	0.0513529	+	0.191652i
$893$			62.1991i			2.08141i
$894$	33.5111	−	0.913942i	1.12078	−	0.0305668i
$895$	−10.8211	−	40.3848i	−0.361709	−	1.34992i
$896$	−0.154214	−	2.64125i	−0.00515194	−	0.0882381i
$897$	−28.1417	−	4.69065i	−0.939625	−	0.156616i
$898$	4.42364	+	7.66197i	0.147619	+	0.255683i
$899$	16.2890	+	4.36462i	0.543269	+	0.145568i
$900$	−16.0185	−	24.5494i	−0.533949	−	0.818312i
$901$	−58.3240	−	33.6734i	−1.94306	−	1.12182i
$902$	−3.04421	+	3.04421i	−0.101361	+	0.101361i
$903$	10.0533	−	3.64000i	0.334554	−	0.121132i
$904$	11.7191	+	3.14014i	0.389773	+	0.104439i
$905$	−6.75970	+	25.2275i	−0.224700	+	0.838592i
$906$	−24.1694	+	0.659168i	−0.802974	+	0.0218994i
$907$	30.2055	−	17.4392i	1.00296	−	0.579058i	0.0938359	−	0.995588i	$-0.470087\pi$
$907$	30.2055	−	17.4392i	1.00296	−	0.579058i	0.909122	+	0.416530i	$0.136754\pi$
$908$	−5.69515	−	5.69515i	−0.189000	−	0.189000i
$909$	15.1512	−	0.827045i	0.502532	−	0.0274314i
$910$	−22.2255	−	29.1580i	−0.736770	−	0.966580i
$911$			22.1576i			0.734115i	0.930198	+	0.367057i	$0.119635\pi$
$911$			22.1576i			0.734115i	−0.930198	+	0.367057i	$0.880365\pi$
$912$	6.95703	−	7.34715i	0.230370	−	0.243288i
$913$	5.14300	+	8.90793i	0.170208	+	0.294810i
$914$	−8.74222			−0.289167
$915$	−0.941096	+	3.93879i	−0.0311117	+	0.130212i
$916$	5.26732	−	19.6579i	0.174037	−	0.649516i
$917$	−22.4987	−	4.64225i	−0.742971	−	0.153300i
$918$	−28.7574	−	24.3995i	−0.949134	−	0.805303i
$919$	−1.08915	+	1.88647i	−0.0359279	+	0.0622289i	−0.883430	−	0.468563i	$-0.844772\pi$
$919$	−1.08915	+	1.88647i	−0.0359279	+	0.0622289i	0.847502	+	0.530792i	$0.178105\pi$
$920$	−8.77899	−	15.2057i	−0.289435	−	0.501316i
$921$	13.6177	−	56.9944i	0.448718	−	1.87803i
$922$	−24.6520	+	14.2328i	−0.811870	+	0.468733i
$923$	0.883629	+	1.31128i	0.0290850	+	0.0431614i
$924$	−7.31148	−	3.42436i	−0.240530	−	0.112653i
$925$	35.0192	−	9.38337i	1.15143	−	0.308523i
$926$			20.9700i			0.689117i
$927$	−1.24018	−	22.7197i	−0.0407329	−	0.746212i
$928$	−8.38044	+	2.24553i	−0.275101	+	0.0737132i
$929$	3.28325	+	12.2532i	0.107720	+	0.402016i	0.998640	−	0.0521449i	$-0.0166058\pi$
$929$	3.28325	+	12.2532i	0.107720	+	0.402016i	−0.890920	+	0.454161i	$0.849939\pi$
$930$	3.00684	−	12.5846i	0.0985981	−	0.412665i
$931$	−15.1087	−	37.9993i	−0.495169	−	1.24538i
$932$	4.19032	−	2.41928i	0.137259	−	0.0792463i
$933$	1.32811	+	48.6972i	0.0434804	+	1.59427i
$934$	2.19540	+	0.588257i	0.0718358	+	0.0192484i
$935$	−24.5727	+	42.5612i	−0.803614	+	1.39190i
$936$	9.96408	+	4.20916i	0.325686	+	0.137581i
$937$	3.16819			0.103500			0.0517501	−	0.998660i	$-0.483520\pi$
$937$	3.16819			0.103500			0.0517501	+	0.998660i	$0.483520\pi$
$938$	4.73541	−	22.9502i	0.154616	−	0.749349i
$939$	27.8189	+	15.0653i	0.907834	+	0.491638i
$940$	−35.4382	−	20.4603i	−1.15587	−	0.667340i
$941$	−9.54529	−	35.6235i	−0.311167	−	1.16129i	−0.927505	−	0.373811i	$-0.878051\pi$
$941$	−9.54529	−	35.6235i	−0.311167	−	1.16129i	0.616338	−	0.787482i	$-0.288616\pi$
$942$	−11.4943	−	10.8840i	−0.374504	−	0.354619i
$943$	−2.88931	−	10.7830i	−0.0940887	−	0.351144i
$944$	4.07981	+	4.07981i	0.132787	+	0.132787i
$945$	41.6200	−	32.5501i	1.35390	−	1.05886i
$946$	3.55993	+	2.05533i	0.115743	+	0.0668244i
$947$	−11.6699	−	11.6699i	−0.379220	−	0.379220i	0.491601	−	0.870821i	$-0.336412\pi$
$947$	−11.6699	−	11.6699i	−0.379220	−	0.379220i	−0.870821	+	0.491601i	$0.836412\pi$
$948$	−7.17991	+	13.2581i	−0.233193	+	0.430602i
$949$	−1.93262	+	3.95802i	−0.0627355	+	0.128483i
$950$	49.4335	−	28.5404i	1.60383	−	0.925974i
$951$	−47.2482	+	14.0514i	−1.53213	+	0.455647i
$952$	−1.11929	−	19.1702i	−0.0362763	−	0.621310i
$953$	−5.02706	−	8.70713i	−0.162843	−	0.282052i	0.773044	−	0.634352i	$-0.218733\pi$
$953$	−5.02706	−	8.70713i	−0.162843	−	0.282052i	−0.935887	+	0.352300i	$0.885400\pi$
$954$	−5.72846	+	27.2411i	−0.185466	+	0.881964i
$955$	8.13218	+	8.13218i	0.263151	+	0.263151i
$956$	−8.86898	−	8.86898i	−0.286843	−	0.286843i
$957$	−6.15262	+	25.7507i	−0.198886	+	0.832402i
$958$	−9.01607	−	15.6163i	−0.291296	−	0.504540i
$959$	0.413017	+	7.07380i	0.0133370	+	0.228425i
$960$	1.89757	+	6.38063i	0.0612438	+	0.205934i
$961$	−23.5750	+	13.6110i	−0.760484	+	0.439065i
$962$	−8.78124	+	10.0927i	−0.283119	+	0.325401i
$963$	−20.5579	−	10.4186i	−0.662469	−	0.335734i
$964$	−0.697671	−	0.697671i	−0.0224705	−	0.0224705i
$965$	−57.9534	−	33.4594i	−1.86559	−	1.07710i
$966$	17.1693	−	11.9792i	0.552414	−	0.385423i
$967$	−10.8637	−	10.8637i	−0.349353	−	0.349353i	0.510516	−	0.859868i	$-0.329455\pi$
$967$	−10.8637	−	10.8637i	−0.349353	−	0.349353i	−0.859868	+	0.510516i	$0.829455\pi$
$968$	2.04364	+	7.62695i	0.0656849	+	0.245140i
$969$	50.4941	−	53.3256i	1.62210	−	1.71306i
$970$	4.39675	+	16.4089i	0.141171	+	0.526858i
$971$	44.5578	+	25.7254i	1.42993	+	0.825569i	0.997114	−	0.0759150i	$-0.0241878\pi$
$971$	44.5578	+	25.7254i	1.42993	+	0.825569i	0.432813	+	0.901484i	$0.357521\pi$
$972$	−5.88714	+	14.4340i	−0.188830	+	0.462972i
$973$	2.70229	−	13.0967i	0.0866316	−	0.419860i
$974$	39.1736			1.25520
$975$	47.1098	+	38.7833i	1.50872	+	1.24206i
$976$	0.304174	−	0.526844i	0.00973636	−	0.0168639i
$977$	8.21210	+	2.20043i	0.262728	+	0.0703979i	0.387779	−	0.921753i	$-0.373243\pi$
$977$	8.21210	+	2.20043i	0.262728	+	0.0703979i	−0.125050	+	0.992150i	$0.539909\pi$
$978$	18.4141	−	0.502206i	0.588819	−	0.0160588i
$979$	1.97625	−	1.14099i	0.0631612	−	0.0364661i
$980$	26.6203	+	3.89152i	0.850353	+	0.124310i
$981$	7.35728	−	34.9868i	0.234900	−	1.11704i
$982$	0.627817	+	2.34305i	0.0200345	+	0.0747696i
$983$	−26.7196	+	7.15949i	−0.852223	+	0.228352i	−0.658385	−	0.752681i	$-0.728760\pi$
$983$	−26.7196	+	7.15949i	−0.852223	+	0.228352i	−0.193837	+	0.981034i	$0.562093\pi$
$984$	0.115387	+	4.23085i	0.00367841	+	0.134875i
$985$			86.2452i			2.74800i
$986$	−60.8252	+	16.2981i	−1.93707	+	0.519036i
$987$	20.6945	−	44.1855i	0.658712	−	1.40644i
$988$	−9.24177	+	18.9272i	−0.294020	+	0.602155i
$989$	−9.23101	+	5.32953i	−0.293529	+	0.169469i
$990$	19.8789	+	4.18027i	0.631792	+	0.132858i
$991$	−3.84110	−	6.65297i	−0.122016	−	0.211339i	0.798546	−	0.601933i	$-0.205603\pi$
$991$	−3.84110	−	6.65297i	−0.122016	−	0.211339i	−0.920563	+	0.390595i	$0.872269\pi$
$992$	−0.971846	+	1.68329i	−0.0308562	+	0.0534444i
$993$	−0.351464	+	0.371172i	−0.0111534	+	0.0117788i
$994$	−1.13636	−	0.234470i	−0.0360432	−	0.00743695i
$995$	0.707590	−	2.64076i	0.0224321	−	0.0837178i
$996$	9.83537	+	2.34997i	0.311646	+	0.0744616i
$997$	1.17898			0.0373386			0.0186693	−	0.999826i	$-0.494057\pi$
$997$	1.17898			0.0373386			0.0186693	+	0.999826i	$0.494057\pi$
$998$	−6.97679	−	12.0842i	−0.220846	−	0.382517i
$999$	−14.7012	−	12.4734i	−0.465126	−	0.394641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.ch.a.137.15	yes	152
3.2	odd	2	inner	546.2.ch.a.137.22	yes	152
7.2	even	3		546.2.bw.a.527.30	yes	152
13.2	odd	12		546.2.bw.a.431.11	✓	152
21.2	odd	6		546.2.bw.a.527.11	yes	152
39.2	even	12		546.2.bw.a.431.30	yes	152
91.2	odd	12	inner	546.2.ch.a.275.22	yes	152
273.2	even	12	inner	546.2.ch.a.275.15	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.431.11	✓	152	13.2	odd	12
546.2.bw.a.431.30	yes	152	39.2	even	12
546.2.bw.a.527.11	yes	152	21.2	odd	6
546.2.bw.a.527.30	yes	152	7.2	even	3
546.2.ch.a.137.15	yes	152	1.1	even	1	trivial
546.2.ch.a.137.22	yes	152	3.2	odd	2	inner
546.2.ch.a.275.15	yes	152	273.2	even	12	inner
546.2.ch.a.275.22	yes	152	91.2	odd	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.ch (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.47583 - 0.906598i) q^{3} -1.00000i q^{4} +(3.71236 + 0.994723i) q^{5} +(-0.402510 + 1.68463i) q^{6} +(1.97669 + 1.75860i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.35616 - 2.67597i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(1.47583 - 0.906598i) q^{3} -1.00000i q^{4} +(3.71236 + 0.994723i) q^{5} +(-0.402510 + 1.68463i) q^{6} +(1.97669 + 1.75860i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.35616 - 2.67597i) q^{9} +(-3.32841 + 1.92166i) q^{10} +(0.455992 - 1.70178i) q^{11} +(-0.906598 - 1.47583i) q^{12} +(2.72010 + 2.36665i) q^{13} +(-2.64125 + 0.154214i) q^{14} +(6.38063 - 1.89757i) q^{15} -1.00000 q^{16} -7.25800 q^{17} +(0.933247 + 2.85115i) q^{18} +(-5.64277 + 1.51198i) q^{19} +(0.994723 - 3.71236i) q^{20} +(4.51161 + 0.803336i) q^{21} +(0.880908 + 1.52578i) q^{22} -4.56845 q^{23} +(1.68463 + 0.402510i) q^{24} +(8.46199 + 4.88553i) q^{25} +(-3.59688 + 0.249924i) q^{26} +(-0.424562 - 5.17878i) q^{27} +(1.75860 - 1.97669i) q^{28} +(-7.51370 - 4.33804i) q^{29} +(-3.17000 + 5.85357i) q^{30} +(-1.87746 + 0.503065i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-0.869866 - 2.92495i) q^{33} +(5.13218 - 5.13218i) q^{34} +(5.58887 + 8.49482i) q^{35} +(-2.67597 - 1.35616i) q^{36} +(2.62365 - 2.62365i) q^{37} +(2.92091 - 5.05917i) q^{38} +(6.16002 + 1.02675i) q^{39} +(1.92166 + 3.32841i) q^{40} +(0.632448 + 2.36033i) q^{41} +(-3.75824 + 2.62215i) q^{42} +(2.02060 - 1.16659i) q^{43} +(-1.70178 - 0.455992i) q^{44} +(7.69641 - 8.58516i) q^{45} +(3.23038 - 3.23038i) q^{46} +(2.75570 - 10.2844i) q^{47} +(-1.47583 + 0.906598i) q^{48} +(0.814638 + 6.95244i) q^{49} +(-9.43812 + 2.52894i) q^{50} +(-10.7116 + 6.58008i) q^{51} +(2.36665 - 2.72010i) q^{52} +(8.03583 + 4.63949i) q^{53} +(3.96216 + 3.36174i) q^{54} +(3.38561 - 5.86404i) q^{55} +(0.154214 + 2.64125i) q^{56} +(-6.95703 + 7.34715i) q^{57} +(8.38044 - 2.24553i) q^{58} +(-4.07981 - 4.07981i) q^{59} +(-1.89757 - 6.38063i) q^{60} +(-0.304174 + 0.526844i) q^{61} +(0.971846 - 1.68329i) q^{62} +(7.38669 - 2.90463i) q^{63} +1.00000i q^{64} +(7.74382 + 11.4916i) q^{65} +(2.68334 + 1.45316i) q^{66} +(-2.29238 + 8.55527i) q^{67} +7.25800i q^{68} +(-6.74227 + 4.14175i) q^{69} +(-9.95867 - 2.05482i) q^{70} +(0.423608 + 0.113506i) q^{71} +(2.85115 - 0.933247i) q^{72} +(0.316181 + 1.18001i) q^{73} +3.71040i q^{74} +(16.9177 - 0.461393i) q^{75} +(1.51198 + 5.64277i) q^{76} +(3.89412 - 2.56200i) q^{77} +(-5.08181 + 3.62977i) q^{78} +(-4.35247 - 7.53869i) q^{79} +(-3.71236 - 0.994723i) q^{80} +(-5.32165 - 7.25810i) q^{81} +(-2.11621 - 1.22180i) q^{82} +(-4.12829 + 4.12829i) q^{83} +(0.803336 - 4.51161i) q^{84} +(-26.9443 - 7.21970i) q^{85} +(-0.603874 + 2.25369i) q^{86} +(-15.0218 + 0.409687i) q^{87} +(1.52578 - 0.880908i) q^{88} +(0.915873 + 0.915873i) q^{89} +(0.628441 + 11.5128i) q^{90} +(1.21480 + 9.46173i) q^{91} +4.56845i q^{92} +(-2.31474 + 2.44454i) q^{93} +(5.32360 + 9.22075i) q^{94} -22.4520 q^{95} +(0.402510 - 1.68463i) q^{96} +(1.14400 - 4.26947i) q^{97} +(-5.49215 - 4.34008i) q^{98} +(-3.93553 - 3.52812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 8 q^{7}+O(q^{10}) \) 152 * q + 8 * q^7	\( 152 q + 8 q^{7} - 152 q^{16} - 8 q^{18} + 36 q^{19} + 8 q^{21} + 24 q^{27} - 12 q^{28} - 24 q^{30} - 36 q^{31} + 12 q^{33} + 24 q^{36} - 12 q^{37} - 8 q^{39} - 36 q^{42} + 84 q^{43} - 40 q^{45} + 8 q^{46} + 4 q^{49} - 20 q^{52} - 12 q^{54} + 16 q^{55} - 8 q^{57} + 8 q^{58} + 24 q^{60} - 32 q^{61} - 28 q^{63} + 16 q^{66} + 92 q^{67} + 84 q^{69} - 8 q^{72} + 84 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} - 24 q^{81} - 48 q^{82} - 8 q^{84} - 152 q^{85} - 96 q^{87} - 88 q^{91} - 48 q^{93} + 32 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 8 * q^7 - 152 * q^16 - 8 * q^18 + 36 * q^19 + 8 * q^21 + 24 * q^27 - 12 * q^28 - 24 * q^30 - 36 * q^31 + 12 * q^33 + 24 * q^36 - 12 * q^37 - 8 * q^39 - 36 * q^42 + 84 * q^43 - 40 * q^45 + 8 * q^46 + 4 * q^49 - 20 * q^52 - 12 * q^54 + 16 * q^55 - 8 * q^57 + 8 * q^58 + 24 * q^60 - 32 * q^61 - 28 * q^63 + 16 * q^66 + 92 * q^67 + 84 * q^69 - 8 * q^72 + 84 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 - 24 * q^81 - 48 * q^82 - 8 * q^84 - 152 * q^85 - 96 * q^87 - 88 * q^91 - 48 * q^93 + 32 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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