LMFDB - Embedded newform 546.2.bw.a.11.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (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			11.16
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(1.57960 + 0.710547i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.90525 + 0.778459i) q^{5} +(0.277506 - 1.70968i) q^{6} +(-2.63535 - 0.234373i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.99025 + 2.24475i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.57960 + 0.710547i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.90525 + 0.778459i) q^{5} +(0.277506 - 1.70968i) q^{6} +(-2.63535 - 0.234373i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.99025 + 2.24475i) q^{9} -3.00773i q^{10} +(3.91041 + 3.91041i) q^{11} +(-1.72324 + 0.174447i) q^{12} +(-2.00763 + 2.99490i) q^{13} +(0.455692 + 2.60621i) q^{14} +(4.03599 + 3.29396i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.749533 - 1.29823i) q^{17} +(1.65315 - 2.50342i) q^{18} +(-3.56522 - 3.56522i) q^{19} +(-2.90525 + 0.778459i) q^{20} +(-3.99626 - 2.24275i) q^{21} +(2.76508 - 4.78925i) q^{22} +(1.24411 - 2.15485i) q^{23} +(0.614511 + 1.61938i) q^{24} +(3.50434 + 2.02323i) q^{25} +(3.41246 + 1.16408i) q^{26} +(1.54878 + 4.95997i) q^{27} +(2.39947 - 1.11470i) q^{28} +(-0.668381 + 0.385890i) q^{29} +(2.13713 - 4.75100i) q^{30} +(7.27013 - 1.94802i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.39834 + 8.95539i) q^{33} +(-1.06000 + 1.06000i) q^{34} +(-7.47389 - 2.73242i) q^{35} +(-2.84598 - 0.948890i) q^{36} +(0.0896532 + 0.334590i) q^{37} +(-2.52099 + 4.36649i) q^{38} +(-5.29926 + 3.30422i) q^{39} +(1.50387 + 2.60477i) q^{40} +(-2.44411 - 0.654896i) q^{41} +(-1.13203 + 4.44055i) q^{42} +(-8.83229 - 5.09933i) q^{43} +(-5.34172 - 1.43131i) q^{44} +(4.03471 + 8.07089i) q^{45} +(-2.40343 - 0.643996i) q^{46} +(0.879410 - 3.28200i) q^{47} +(1.40515 - 1.01270i) q^{48} +(6.89014 + 1.23531i) q^{49} +(1.04730 - 3.90858i) q^{50} +(-0.261507 - 2.58326i) q^{51} +(0.241209 - 3.59747i) q^{52} +(8.59996 + 4.96519i) q^{53} +(4.39010 - 2.77974i) q^{54} +(8.31661 + 14.4048i) q^{55} +(-1.69775 - 2.02920i) q^{56} +(-3.09835 - 8.16486i) q^{57} +(0.545731 + 0.545731i) q^{58} +(3.53269 - 13.1842i) q^{59} +(-5.14225 - 0.834663i) q^{60} +13.7047 q^{61} +(-3.76329 - 6.51822i) q^{62} +(-4.71889 - 6.38217i) q^{63} +1.00000i q^{64} +(-8.16407 + 7.13807i) q^{65} +(7.77069 - 5.60037i) q^{66} +(-5.85967 - 5.85967i) q^{67} +(1.29823 + 0.749533i) q^{68} +(3.49631 - 2.51980i) q^{69} +(-0.704932 + 7.92643i) q^{70} +(-1.10997 - 4.14248i) q^{71} +(-0.179963 + 2.99460i) q^{72} +(-2.23711 - 8.34901i) q^{73} +(0.299986 - 0.173197i) q^{74} +(4.09784 + 5.68588i) q^{75} +(4.87018 + 1.30496i) q^{76} +(-9.38880 - 11.2218i) q^{77} +(4.56318 + 4.26350i) q^{78} +(-3.29566 - 5.70825i) q^{79} +(2.12679 - 2.12679i) q^{80} +(-1.07783 + 8.93523i) q^{81} +2.53033i q^{82} +(-8.72737 + 8.72737i) q^{83} +(4.58224 - 0.0558458i) q^{84} +(-1.16696 - 4.35516i) q^{85} +(-2.63961 + 9.85114i) q^{86} +(-1.32996 + 0.134634i) q^{87} +5.53015i q^{88} +(-12.4061 + 3.32420i) q^{89} +(6.75162 - 5.98613i) q^{90} +(5.99273 - 7.42207i) q^{91} +2.48821i q^{92} +(12.8680 + 2.08867i) q^{93} -3.39778 q^{94} +(-7.58247 - 13.1332i) q^{95} +(-1.34187 - 1.09516i) q^{96} +(-14.0835 + 3.77366i) q^{97} +(-0.590081 - 6.97508i) q^{98} +(-0.995222 + 16.5606i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	1.57960	+	0.710547i	0.911980	+	0.410234i
$3$	1.57960	+	0.710547i	0.911980	+	0.410234i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	2.90525	+	0.778459i	1.29927	+	0.348137i	0.841173	−	0.540767i	$-0.181866\pi$
$5$	2.90525	+	0.778459i	1.29927	+	0.348137i	0.458094	+	0.888904i	$0.348532\pi$
$6$	0.277506	−	1.70968i	0.113291	−	0.697972i
$7$	−2.63535	−	0.234373i	−0.996069	−	0.0885847i
$7$	−2.63535	−	0.234373i	−0.996069	−	0.0885847i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	1.99025	+	2.24475i	0.663416	+	0.748251i
$10$		−	3.00773i		−	0.951129i
$11$	3.91041	+	3.91041i	1.17903	+	1.17903i	0.979991	+	0.199041i	$0.0637828\pi$
$11$	3.91041	+	3.91041i	1.17903	+	1.17903i	0.199041	+	0.979991i	$0.436217\pi$
$12$	−1.72324	+	0.174447i	−0.497458	+	0.0503584i
$13$	−2.00763	+	2.99490i	−0.556816	+	0.830636i
$13$	−2.00763	+	2.99490i	−0.556816	+	0.830636i
$14$	0.455692	+	2.60621i	0.121789	+	0.696540i
$15$	4.03599	+	3.29396i	1.04209	+	0.850498i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.749533	−	1.29823i	−0.181789	−	0.314867i	0.760701	−	0.649102i	$-0.224855\pi$
$17$	−0.749533	−	1.29823i	−0.181789	−	0.314867i	−0.942490	+	0.334235i	$0.891522\pi$
$18$	1.65315	−	2.50342i	0.389651	−	0.590061i
$19$	−3.56522	−	3.56522i	−0.817918	−	0.817918i	0.167888	−	0.985806i	$-0.446305\pi$
$19$	−3.56522	−	3.56522i	−0.817918	−	0.817918i	−0.985806	+	0.167888i	$0.946305\pi$
$20$	−2.90525	+	0.778459i	−0.649633	+	0.174069i
$21$	−3.99626	−	2.24275i	−0.872054	−	0.489409i
$22$	2.76508	−	4.78925i	0.589516	−	1.02107i
$23$	1.24411	−	2.15485i	0.259414	−	0.449318i	−0.706671	−	0.707542i	$-0.749804\pi$
$23$	1.24411	−	2.15485i	0.259414	−	0.449318i	0.966085	+	0.258224i	$0.0831373\pi$
$24$	0.614511	+	1.61938i	0.125436	+	0.330554i
$25$	3.50434	+	2.02323i	0.700868	+	0.404646i
$26$	3.41246	+	1.16408i	0.669239	+	0.228296i
$27$	1.54878	+	4.95997i	0.298064	+	0.954546i
$28$	2.39947	−	1.11470i	0.453457	−	0.210659i
$29$	−0.668381	+	0.385890i	−0.124115	+	0.0716579i	−0.560772	−	0.827970i	$-0.689496\pi$
$29$	−0.668381	+	0.385890i	−0.124115	+	0.0716579i	0.436657	+	0.899628i	$0.356162\pi$
$30$	2.13713	−	4.75100i	0.390186	−	0.867411i
$31$	7.27013	−	1.94802i	1.30575	−	0.349875i	0.462130	−	0.886812i	$-0.347085\pi$
$31$	7.27013	−	1.94802i	1.30575	−	0.349875i	0.843623	+	0.536936i	$0.180419\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	3.39834	+	8.95539i	0.591575	+	1.55893i
$34$	−1.06000	+	1.06000i	−0.181789	+	0.181789i
$35$	−7.47389	−	2.73242i	−1.26332	−	0.461864i
$36$	−2.84598	−	0.948890i	−0.474330	−	0.158148i
$37$	0.0896532	+	0.334590i	0.0147389	+	0.0550063i	0.972904	−	0.231211i	$-0.0742688\pi$
$37$	0.0896532	+	0.334590i	0.0147389	+	0.0550063i	−0.958165	+	0.286217i	$0.907602\pi$
$38$	−2.52099	+	4.36649i	−0.408959	+	0.708337i
$39$	−5.29926	+	3.30422i	−0.848561	+	0.529098i
$40$	1.50387	+	2.60477i	0.237782	+	0.411851i
$41$	−2.44411	−	0.654896i	−0.381705	−	0.102278i	0.0628640	−	0.998022i	$-0.479977\pi$
$41$	−2.44411	−	0.654896i	−0.381705	−	0.102278i	−0.444569	+	0.895744i	$0.646643\pi$
$42$	−1.13203	+	4.44055i	−0.174676	+	0.685192i
$43$	−8.83229	−	5.09933i	−1.34691	−	0.777640i	−0.359101	−	0.933299i	$-0.616917\pi$
$43$	−8.83229	−	5.09933i	−1.34691	−	0.777640i	−0.987811	+	0.155659i	$0.950250\pi$
$44$	−5.34172	−	1.43131i	−0.805294	−	0.215778i
$45$	4.03471	+	8.07089i	0.601459	+	1.20314i
$46$	−2.40343	−	0.643996i	−0.354366	−	0.0949521i
$47$	0.879410	−	3.28200i	0.128275	−	0.478729i	−0.871660	−	0.490111i	$-0.836956\pi$
$47$	0.879410	−	3.28200i	0.128275	−	0.478729i	0.999935	+	0.0113817i	$0.00362298\pi$
$48$	1.40515	−	1.01270i	0.202816	−	0.146170i
$49$	6.89014	+	1.23531i	0.984305	+	0.176473i
$50$	1.04730	−	3.90858i	0.148111	−	0.552757i
$51$	−0.261507	−	2.58326i	−0.0366183	−	0.361728i
$52$	0.241209	−	3.59747i	0.0334496	−	0.498880i
$53$	8.59996	+	4.96519i	1.18130	+	0.682022i	0.956314	−	0.292341i	$-0.0944343\pi$
$53$	8.59996	+	4.96519i	1.18130	+	0.682022i	0.224982	+	0.974363i	$0.427768\pi$
$54$	4.39010	−	2.77974i	0.597418	−	0.378275i
$55$	8.31661	+	14.4048i	1.12141	+	1.94234i
$56$	−1.69775	−	2.02920i	−0.226871	−	0.271163i
$57$	−3.09835	−	8.16486i	−0.410387	−	1.08146i
$58$	0.545731	+	0.545731i	0.0716579	+	0.0716579i
$59$	3.53269	−	13.1842i	0.459917	−	1.71643i	−0.213298	−	0.976987i	$-0.568420\pi$
$59$	3.53269	−	13.1842i	0.459917	−	1.71643i	0.673215	−	0.739447i	$-0.264913\pi$
$60$	−5.14225	−	0.834663i	−0.663861	−	0.107755i
$61$	13.7047			1.75471			0.877357	−	0.479839i	$-0.159305\pi$
$61$	13.7047			1.75471			0.877357	+	0.479839i	$0.159305\pi$
$62$	−3.76329	−	6.51822i	−0.477939	−	0.827814i
$63$	−4.71889	−	6.38217i	−0.594524	−	0.804078i
$64$			1.00000i			0.125000i
$65$	−8.16407	+	7.13807i	−1.01263	+	0.885368i
$66$	7.77069	−	5.60037i	0.956506	−	0.689358i
$67$	−5.85967	−	5.85967i	−0.715873	−	0.715873i	0.251884	−	0.967757i	$-0.418950\pi$
$67$	−5.85967	−	5.85967i	−0.715873	−	0.715873i	−0.967757	+	0.251884i	$0.918950\pi$
$68$	1.29823	+	0.749533i	0.157434	+	0.0908943i
$69$	3.49631	−	2.51980i	0.420906	−	0.303349i
$70$	−0.704932	+	7.92643i	−0.0842555	+	0.947390i
$71$	−1.10997	−	4.14248i	−0.131730	−	0.491622i	0.868260	−	0.496109i	$-0.165238\pi$
$71$	−1.10997	−	4.14248i	−0.131730	−	0.491622i	−0.999990	+	0.00448706i	$0.998572\pi$
$72$	−0.179963	+	2.99460i	−0.0212088	+	0.352917i
$73$	−2.23711	−	8.34901i	−0.261834	−	0.977178i	−0.964160	−	0.265322i	$-0.914522\pi$
$73$	−2.23711	−	8.34901i	−0.261834	−	0.977178i	0.702326	−	0.711856i	$-0.252145\pi$
$74$	0.299986	−	0.173197i	0.0348726	−	0.0201337i
$75$	4.09784	+	5.68588i	0.473178	+	0.656549i
$76$	4.87018	+	1.30496i	0.558648	+	0.149689i
$77$	−9.38880	−	11.2218i	−1.06995	−	1.27884i
$78$	4.56318	+	4.26350i	0.516678	+	0.482746i
$79$	−3.29566	−	5.70825i	−0.370791	−	0.642228i	0.618897	−	0.785472i	$-0.287580\pi$
$79$	−3.29566	−	5.70825i	−0.370791	−	0.642228i	−0.989687	+	0.143244i	$0.954247\pi$
$80$	2.12679	−	2.12679i	0.237782	−	0.237782i
$81$	−1.07783	+	8.93523i	−0.119759	+	0.992803i
$82$			2.53033i			0.279428i
$83$	−8.72737	+	8.72737i	−0.957953	+	0.957953i	−0.999151	−	0.0411982i	$-0.986882\pi$
$83$	−8.72737	+	8.72737i	−0.957953	+	0.957953i	0.0411982	+	0.999151i	$0.486882\pi$
$84$	4.58224	−	0.0558458i	0.499963	−	0.00609328i
$85$	−1.16696	−	4.35516i	−0.126575	−	0.472383i
$86$	−2.63961	+	9.85114i	−0.284636	+	1.06228i
$87$	−1.32996	+	0.134634i	−0.142587	+	0.0144343i
$88$			5.53015i			0.589516i
$89$	−12.4061	+	3.32420i	−1.31504	+	0.352364i	−0.847118	−	0.531405i	$-0.821664\pi$
$89$	−12.4061	+	3.32420i	−1.31504	+	0.352364i	−0.467924	+	0.883769i	$0.654998\pi$
$90$	6.75162	−	5.98613i	0.711683	−	0.630994i
$91$	5.99273	−	7.42207i	0.628209	−	0.778045i
$92$			2.48821i			0.259414i
$93$	12.8680	+	2.08867i	1.33435	+	0.216585i
$94$	−3.39778			−0.350454
$95$	−7.58247	−	13.1332i	−0.777945	−	1.34744i
$96$	−1.34187	−	1.09516i	−0.136954	−	0.111775i
$97$	−14.0835	+	3.77366i	−1.42996	+	0.383157i	−0.889006	−	0.457895i	$-0.848603\pi$
$97$	−14.0835	+	3.77366i	−1.42996	+	0.383157i	−0.540954	+	0.841052i	$0.681937\pi$
$98$	−0.590081	−	6.97508i	−0.0596071	−	0.704590i
$99$	−0.995222	+	16.5606i	−0.100024	+	1.66440i
$100$	−4.04646			−0.404646
$101$	16.2765			1.61958			0.809788	−	0.586723i	$-0.199582\pi$
$101$	16.2765			1.61958			0.809788	+	0.586723i	$0.199582\pi$
$102$	−2.42755	+	0.921193i	−0.240363	+	0.0912117i
$103$	5.80965	−	3.35420i	0.572441	−	0.330499i	−0.185682	−	0.982610i	$-0.559450\pi$
$103$	5.80965	−	3.35420i	0.572441	−	0.330499i	0.758124	+	0.652111i	$0.226116\pi$
$104$	−3.53732	+	0.698105i	−0.346863	+	0.0684548i
$105$	−9.86422	−	9.62667i	−0.962649	−	0.939467i
$106$	2.57017	−	9.59201i	0.249637	−	0.931659i
$107$	8.49468	+	4.90440i	0.821212	+	0.474127i	0.850834	−	0.525434i	$-0.176097\pi$
$107$	8.49468	+	4.90440i	0.821212	+	0.474127i	−0.0296226	+	0.999561i	$0.509431\pi$
$108$	−3.82127	−	3.52106i	−0.367702	−	0.338815i
$109$	−5.64513	+	1.51261i	−0.540706	+	0.144882i	−0.518827	−	0.854879i	$-0.673631\pi$
$109$	−5.64513	+	1.51261i	−0.540706	+	0.144882i	−0.0218783	+	0.999761i	$0.506965\pi$
$110$	11.7615	−	11.7615i	1.12141	−	1.12141i
$111$	−0.0961262	+	0.592220i	−0.00912389	+	0.0562111i
$112$	−1.52065	+	2.16509i	−0.143688	+	0.204582i
$113$	−6.38620	−	3.68707i	−0.600763	−	0.346851i	0.168579	−	0.985688i	$-0.446082\pi$
$113$	−6.38620	−	3.68707i	−0.600763	−	0.346851i	−0.769342	+	0.638838i	$0.779416\pi$
$114$	−7.08474	+	5.10600i	−0.663547	+	0.478221i
$115$	5.29190	−	5.29190i	0.493472	−	0.493472i
$116$	0.385890	−	0.668381i	0.0358290	−	0.0620576i
$117$	−10.7185	+	1.45396i	−0.990925	+	0.134418i
$118$	−13.6493			−1.25652
$119$	1.67101	+	3.59696i	0.153181	+	0.329733i
$120$	0.524689	+	5.18306i	0.0478973	+	0.473146i
$121$			19.5826i			1.78024i
$122$	−3.54705	−	13.2378i	−0.321135	−	1.19849i
$123$	−3.39537	−	2.77112i	−0.306150	−	0.249864i
$124$	−5.32210	+	5.32210i	−0.477939	+	0.477939i
$125$	−2.02798	−	2.02798i	−0.181388	−	0.181388i
$126$	−4.94337	+	6.20992i	−0.440390	+	0.553224i
$127$	−11.5753	+	6.68302i	−1.02714	+	0.593022i	−0.916165	−	0.400801i	$-0.868732\pi$
$127$	−11.5753	+	6.68302i	−1.02714	+	0.593022i	−0.110979	+	0.993823i	$0.535399\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−10.3281	−	14.3306i	−0.909342	−	1.26174i
$130$	9.00786	+	6.03842i	0.790042	+	0.529604i
$131$	−9.28106	+	5.35842i	−0.810890	+	0.468167i	−0.847265	−	0.531171i	$-0.821752\pi$
$131$	−9.28106	+	5.35842i	−0.810890	+	0.468167i	0.0363751	+	0.999338i	$0.488419\pi$
$132$	−7.42074	−	6.05643i	−0.645893	−	0.527144i
$133$	8.56001	+	10.2312i	0.742247	+	0.887157i
$134$	−4.14341	+	7.17660i	−0.357936	+	0.619964i
$135$	0.638474	+	15.6156i	0.0549511	+	1.34398i
$136$	0.387987	−	1.44799i	0.0332696	−	0.124164i
$137$	−0.570086	+	2.12759i	−0.0487057	+	0.181772i	−0.985993	−	0.166785i	$-0.946662\pi$
$137$	−0.570086	+	2.12759i	−0.0487057	+	0.181772i	0.937288	+	0.348557i	$0.113328\pi$
$138$	−3.33885	−	2.72500i	−0.284222	−	0.231967i
$139$	3.32277	−	5.75521i	0.281834	−	0.488150i	−0.690003	−	0.723807i	$-0.742391\pi$
$139$	3.32277	−	5.75521i	0.281834	−	0.488150i	0.971836	+	0.235656i	$0.0757240\pi$
$140$	7.83879	−	1.37060i	0.662499	−	0.115837i
$141$	3.72113	−	4.55937i	0.313375	−	0.383969i
$142$	−3.71405	+	2.14431i	−0.311676	+	0.179946i
$143$	−19.5619	+	3.86063i	−1.63585	+	0.322842i
$144$	2.93914	−	0.601228i	0.244928	−	0.0501023i
$145$	−2.24221	+	0.600799i	−0.186205	+	0.0498936i
$146$	−7.48552	+	4.32177i	−0.619506	+	0.357672i
$147$	10.0059	+	6.84706i	0.825272	+	0.564736i
$148$	−0.244937	−	0.244937i	−0.0201337	−	0.0201337i
$149$	−1.07401	+	1.07401i	−0.0879861	+	0.0879861i	−0.749730	−	0.661744i	$-0.769817\pi$
$149$	−1.07401	+	1.07401i	−0.0879861	+	0.0879861i	0.661744	+	0.749730i	$0.269817\pi$
$150$	4.43154	−	5.42982i	0.361834	−	0.443343i
$151$	−2.85982	−	10.6730i	−0.232729	−	0.868557i	−0.979159	−	0.203093i	$-0.934900\pi$
$151$	−2.85982	−	10.6730i	−0.232729	−	0.868557i	0.746430	−	0.665464i	$-0.231766\pi$
$152$		−	5.04198i		−	0.408959i
$153$	1.42245	−	4.26632i	0.114998	−	0.344911i
$154$	−8.40942	+	11.9733i	−0.677650	+	0.964836i
$155$	22.6380			1.81833
$156$	2.93719	−	5.51117i	0.235163	−	0.441246i
$157$	−7.39442	+	12.8075i	−0.590139	+	1.02215i	0.404074	+	0.914726i	$0.367594\pi$
$157$	−7.39442	+	12.8075i	−0.590139	+	1.02215i	−0.994213	+	0.107424i	$0.965740\pi$
$158$	−4.66077	+	4.66077i	−0.370791	+	0.370791i
$159$	10.0565	+	13.9537i	0.797530	+	1.10660i
$160$	−2.60477	−	1.50387i	−0.205925	−	0.118891i
$161$	−3.78369	+	5.38721i	−0.298197	+	0.424571i
$162$	8.90973	−	1.27150i	0.700014	−	0.0998985i
$163$	1.38252	−	1.38252i	0.108287	−	0.108287i	−0.650887	−	0.759174i	$-0.725603\pi$
$163$	1.38252	−	1.38252i	0.108287	−	0.108287i	0.759174	+	0.650887i	$0.225603\pi$
$164$	2.44411	−	0.654896i	0.190853	−	0.0511388i
$165$	2.90161	+	28.6631i	0.225890	+	2.23142i
$166$	10.6888	+	6.17118i	0.829611	+	0.478976i
$167$	2.00691	−	7.48989i	0.155299	−	0.579585i	−0.843780	−	0.536689i	$-0.819675\pi$
$167$	2.00691	−	7.48989i	0.155299	−	0.579585i	0.999080	−	0.0428961i	$-0.0136584\pi$
$168$	−1.23991	−	4.41165i	−0.0956613	−	0.340366i
$169$	−4.93884	−	12.0253i	−0.379911	−	0.925023i
$170$	−3.90473	+	2.25440i	−0.299479	+	0.172904i
$171$	0.907370	−	15.0987i	0.0693883	−	1.15463i
$172$	10.1987			0.777640
$173$	6.93218			0.527044			0.263522	−	0.964653i	$-0.415116\pi$
$173$	6.93218			0.527044			0.263522	+	0.964653i	$0.415116\pi$
$174$	0.474267	+	1.24980i	0.0359541	+	0.0947472i
$175$	−8.76097	−	6.15324i	−0.662267	−	0.465141i
$176$	5.34172	−	1.43131i	0.402647	−	0.107889i
$177$	14.9482	−	18.3155i	1.12358	−	1.37668i
$178$	6.42186	+	11.1230i	0.481339	+	0.833703i
$179$	−9.26602			−0.692575			−0.346287	−	0.938128i	$-0.612558\pi$
$179$	−9.26602			−0.692575			−0.346287	+	0.938128i	$0.612558\pi$
$180$	−7.52961	−	4.97224i	−0.561224	−	0.370609i
$181$		−	1.52748i		−	0.113536i	−0.998387	−	0.0567682i	$-0.981920\pi$
$181$		−	1.52748i		−	0.113536i	0.998387	−	0.0567682i	$-0.0180796\pi$
$182$	−8.72021	−	3.86756i	−0.646385	−	0.286683i
$183$	21.6480	+	9.73786i	1.60026	+	0.719844i
$184$	2.40343	−	0.643996i	0.177183	−	0.0474760i
$185$			1.04186i			0.0765990i
$186$	−1.31299	−	12.9701i	−0.0962729	−	0.951017i
$187$	2.14563	−	8.00759i	0.156904	−	0.585573i
$188$	0.879410	+	3.28200i	0.0641375	+	0.239365i
$189$	−2.91911	−	13.4342i	−0.212334	−	0.977197i
$190$	−10.7232	+	10.7232i	−0.777945	+	0.777945i
$191$			9.94052i			0.719271i	0.933093	+	0.359635i	$0.117099\pi$
$191$			9.94052i			0.719271i	−0.933093	+	0.359635i	$0.882901\pi$
$192$	−0.710547	+	1.57960i	−0.0512793	+	0.113998i
$193$	−2.76265	+	2.76265i	−0.198860	+	0.198860i	−0.799511	−	0.600651i	$-0.794908\pi$
$193$	−2.76265	+	2.76265i	−0.198860	+	0.198860i	0.600651	+	0.799511i	$0.294908\pi$
$194$	7.29014	+	12.6269i	0.523402	+	0.906558i
$195$	−17.9679	+	5.47431i	−1.28670	+	0.392024i
$196$	−6.58469	+	2.37526i	−0.470335	+	0.169661i
$197$	−1.91848	−	0.514054i	−0.136686	−	0.0366248i	0.189828	−	0.981817i	$-0.439207\pi$
$197$	−1.91848	−	0.514054i	−0.136686	−	0.0366248i	−0.326513	+	0.945193i	$0.605874\pi$
$198$	16.2539	−	3.32488i	1.15511	−	0.236289i
$199$	−11.9656	+	6.90834i	−0.848218	+	0.489719i	−0.860049	−	0.510211i	$-0.829567\pi$
$199$	−11.9656	+	6.90834i	−0.848218	+	0.489719i	0.0118310	+	0.999930i	$0.496234\pi$
$200$	1.04730	+	3.90858i	0.0740554	+	0.276378i
$201$	−5.09234	−	13.4195i	−0.359186	−	0.946537i
$202$	−4.21268	−	15.7219i	−0.296403	−	1.10619i
$203$	1.85186	−	0.860304i	0.129975	−	0.0603815i
$204$	1.51810	+	2.10641i	0.106288	+	0.147478i
$205$	−6.59092	−	3.80527i	−0.460330	−	0.265772i
$206$	−4.74356	−	4.74356i	−0.330499	−	0.330499i
$207$	7.31319	−	1.49598i	0.508302	−	0.103978i
$208$	1.58984	+	3.23611i	0.110236	+	0.224384i
$209$		−	27.8829i		−	1.92870i
$210$	−6.74561	+	12.0197i	−0.465491	+	0.829436i
$211$	2.16058	+	3.74223i	0.148740	+	0.257626i	0.930762	−	0.365625i	$-0.119145\pi$
$211$	2.16058	+	3.74223i	0.148740	+	0.257626i	−0.782022	+	0.623251i	$0.785811\pi$
$212$	−9.93038			−0.682022
$213$	1.19011	−	7.33213i	0.0815453	−	0.502390i
$214$	2.53871	−	9.47458i	0.173542	−	0.647669i
$215$	−21.6904	−	21.6904i	−1.47927	−	1.47927i
$216$	−2.41207	+	4.60238i	−0.164121	+	0.313152i
$217$	−19.6159	+	3.42980i	−1.33161	+	0.232830i
$218$	2.92214	+	5.06129i	0.197912	+	0.342794i
$219$	2.39863	−	14.7776i	0.162084	−	0.998580i
$220$	−14.4048	−	8.31661i	−0.971171	−	0.560706i
$221$	5.39285	+	0.361588i	0.362763	+	0.0243230i
$222$	0.596920	−	0.0604272i	0.0400627	−	0.00405561i
$223$	2.65646	−	9.91404i	0.177890	−	0.663893i	−0.818152	−	0.575002i	$-0.805001\pi$
$223$	2.65646	−	9.91404i	0.177890	−	0.663893i	0.996041	−	0.0888908i	$-0.0283322\pi$
$224$	2.48489	+	0.908466i	0.166029	+	0.0606994i
$225$	2.43285	+	11.8931i	0.162190	+	0.792873i
$226$	−1.90857	+	7.12288i	−0.126956	+	0.473807i
$227$	15.5188	+	4.15825i	1.03002	+	0.275992i	0.733971	−	0.679181i	$-0.237665\pi$
$227$	15.5188	+	4.15825i	1.03002	+	0.275992i	0.296047	+	0.955173i	$0.404331\pi$
$228$	6.76568	+	5.52180i	0.448068	+	0.365690i
$229$	6.04417	+	1.61953i	0.399410	+	0.107022i	0.452932	−	0.891545i	$-0.350378\pi$
$229$	6.04417	+	1.61953i	0.399410	+	0.107022i	−0.0535221	+	0.998567i	$0.517045\pi$
$230$	−6.48122	−	3.74194i	−0.427359	−	0.246736i
$231$	−6.85691	−	24.3971i	−0.451151	−	1.60521i
$232$	−0.745482	−	0.199751i	−0.0489433	−	0.0131143i
$233$	9.58909	+	16.6088i	0.628202	+	1.08808i	0.987912	+	0.155014i	$0.0495423\pi$
$233$	9.58909	+	16.6088i	0.628202	+	1.08808i	−0.359710	+	0.933064i	$0.617124\pi$
$234$	4.17856	+	9.97695i	0.273161	+	0.652214i
$235$	5.10981	−	8.85044i	0.333327	−	0.577339i
$236$	3.53269	+	13.1842i	0.229959	+	0.858217i
$237$	−1.14983	−	11.3584i	−0.0746897	−	0.737810i
$238$	3.04191	−	2.54504i	0.197178	−	0.164970i
$239$	−10.3165	+	10.3165i	−0.667318	+	0.667318i	−0.957094	−	0.289776i	$-0.906419\pi$
$239$	−10.3165	+	10.3165i	−0.667318	+	0.667318i	0.289776	+	0.957094i	$0.406419\pi$
$240$	4.87065	−	1.84828i	0.314399	−	0.119306i
$241$	10.3139	+	2.76360i	0.664376	+	0.178019i	0.575220	−	0.817999i	$-0.304916\pi$
$241$	10.3139	+	2.76360i	0.664376	+	0.178019i	0.0891559	+	0.996018i	$0.471583\pi$
$242$	18.9153	−	5.06835i	1.21592	−	0.325806i
$243$	−8.05144	+	13.3482i	−0.516500	+	0.856287i
$244$	−11.8687	+	6.85237i	−0.759813	+	0.438678i
$245$	19.0559	+	8.95257i	1.21744	+	0.571959i
$246$	−1.79791	+	3.99689i	−0.114631	+	0.254833i
$247$	17.8351	−	3.51983i	1.13482	−	0.223962i
$248$	6.51822	+	3.76329i	0.413907	+	0.238969i
$249$	−19.9869	+	7.58451i	−1.26662	+	0.480649i
$250$	−1.43400	+	2.48375i	−0.0906939	+	0.157086i
$251$	5.28955	−	9.16177i	0.333873	−	0.578286i	−0.649394	−	0.760452i	$-0.724977\pi$
$251$	5.28955	−	9.16177i	0.333873	−	0.578286i	0.983268	+	0.182166i	$0.0583108\pi$
$252$	7.27776	+	3.16768i	0.458456	+	0.199545i
$253$	13.2913	−	3.56140i	0.835618	−	0.223903i
$254$	9.45121	+	9.45121i	0.593022	+	0.593022i
$255$	1.25122	−	7.70857i	0.0783542	−	0.482730i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−0.996805	+	1.72652i	−0.0621790	+	0.107697i	−0.895439	−	0.445184i	$-0.853138\pi$
$257$	−0.996805	+	1.72652i	−0.0621790	+	0.107697i	0.833260	+	0.552881i	$0.186472\pi$
$258$	−11.1692	+	13.6853i	−0.695364	+	0.852007i
$259$	−0.157849	−	0.902775i	−0.00980824	−	0.0560957i
$260$	3.50126	−	10.2638i	0.217139	−	0.636533i
$261$	−2.19647	−	0.732334i	−0.135958	−	0.0453303i
$262$	7.57795	+	7.57795i	0.468167	+	0.468167i
$263$			15.4280i			0.951331i	0.879626	+	0.475666i	$0.157793\pi$
$263$			15.4280i			0.951331i	−0.879626	+	0.475666i	$0.842207\pi$
$264$	−3.92943	+	8.73541i	−0.241840	+	0.537627i
$265$	21.1198	+	21.1198i	1.29738	+	1.29738i
$266$	7.66708	−	10.9164i	0.470099	−	0.669325i
$267$	−21.9586	−	3.56421i	−1.34384	−	0.218126i
$268$	8.00446	+	2.14479i	0.488950	+	0.131014i
$269$	8.38895	−	4.84336i	0.511484	−	0.295305i	−0.221960	−	0.975056i	$-0.571245\pi$
$269$	8.38895	−	4.84336i	0.511484	−	0.295305i	0.733443	+	0.679751i	$0.237912\pi$
$270$	14.9183	−	4.65833i	0.907896	−	0.283497i
$271$	−7.75488	−	28.9416i	−0.471076	−	1.75808i	−0.635916	−	0.771758i	$-0.719378\pi$
$271$	−7.75488	−	28.9416i	−0.471076	−	1.75808i	0.164841	−	0.986320i	$-0.447289\pi$
$272$	−1.49907			−0.0908943
$273$	14.7398	−	7.46576i	0.892095	−	0.451849i
$274$	2.20264			0.133066
$275$	5.79173	+	21.6150i	0.349255	+	1.30344i
$276$	−1.76799	+	3.93037i	−0.106420	+	0.236580i
$277$	2.42676	−	1.40109i	0.145810	−	0.0841835i	−0.425320	−	0.905043i	$-0.639838\pi$
$277$	2.42676	−	1.40109i	0.145810	−	0.0841835i	0.571130	+	0.820859i	$0.306505\pi$
$278$	−6.41910	−	1.71999i	−0.384992	−	0.103158i
$279$	18.8422	+	12.4426i	1.12805	+	0.744918i
$280$	−3.35273	−	7.21696i	−0.200364	−	0.431296i
$281$	4.78021	+	4.78021i	0.285164	+	0.285164i	0.835164	−	0.550001i	$-0.185373\pi$
$281$	4.78021	+	4.78021i	0.285164	+	0.285164i	−0.550001	+	0.835164i	$0.685373\pi$
$282$	−5.36712	−	2.41428i	−0.319607	−	0.143768i
$283$		−	32.7836i		−	1.94878i	−0.224855	−	0.974392i	$-0.572191\pi$
$283$		−	32.7836i		−	1.94878i	0.224855	−	0.974392i	$-0.427809\pi$
$284$	3.03251	+	3.03251i	0.179946	+	0.179946i
$285$	−2.64547	−	26.1329i	−0.156704	−	1.54798i
$286$	8.79208	+	17.8962i	0.519887	+	1.05822i
$287$	6.28759	+	2.29871i	0.371144	+	0.135689i
$288$	−1.34145	−	2.68338i	−0.0790455	−	0.158120i
$289$	7.37640	−	12.7763i	0.433906	−	0.751547i
$290$	1.16065	+	2.01031i	0.0681559	+	0.118050i
$291$	−24.9276	−	4.04611i	−1.46128	−	0.237187i
$292$	6.11190	+	6.11190i	0.357672	+	0.357672i
$293$	7.01638	−	1.88003i	0.409902	−	0.109833i	−0.0479751	−	0.998849i	$-0.515277\pi$
$293$	7.01638	−	1.88003i	0.409902	−	0.109833i	0.457877	+	0.889016i	$0.348610\pi$
$294$	4.02403	−	11.4371i	0.234686	−	0.667025i
$295$	20.5267	−	35.5533i	1.19511	−	2.06999i
$296$	−0.173197	+	0.299986i	−0.0100669	+	0.0174363i
$297$	−13.3391	+	25.4519i	−0.774014	+	1.47687i
$298$	1.31538	+	0.759438i	0.0761982	+	0.0439930i
$299$	3.95587	+	8.05212i	0.228774	+	0.465666i
$300$	−6.39177	−	2.87520i	−0.369029	−	0.166000i
$301$	22.0810	+	15.5086i	1.27273	+	0.893899i
$302$	−9.56916	+	5.52476i	−0.550643	+	0.317914i
$303$	25.7103	+	11.5652i	1.47702	+	0.664405i
$304$	−4.87018	+	1.30496i	−0.279324	+	0.0748447i
$305$	39.8157	+	10.6686i	2.27984	+	0.610881i
$306$	−4.48910	−	0.269776i	−0.256625	−	0.0154221i
$307$	−0.696352	+	0.696352i	−0.0397429	+	0.0397429i	−0.726699	−	0.686956i	$-0.758946\pi$
$307$	−0.696352	+	0.696352i	−0.0397429	+	0.0397429i	0.686956	+	0.726699i	$0.258946\pi$
$308$	13.7418	+	5.02395i	0.783014	+	0.286266i
$309$	11.5602	−	1.17026i	0.657637	−	0.0665736i
$310$	−5.85914	−	21.8666i	−0.332777	−	1.24194i
$311$	−3.33953	+	5.78424i	−0.189367	+	0.327994i	−0.945040	−	0.326956i	$-0.893977\pi$
$311$	−3.33953	+	5.78424i	−0.189367	+	0.327994i	0.755672	+	0.654950i	$0.227310\pi$
$312$	−6.08358	−	1.41071i	−0.344415	−	0.0798656i
$313$	2.33811	+	4.04972i	0.132158	+	0.228904i	0.924508	−	0.381163i	$-0.124476\pi$
$313$	2.33811	+	4.04972i	0.132158	+	0.228904i	−0.792350	+	0.610066i	$0.791143\pi$
$314$	14.2849	+	3.82763i	0.806145	+	0.216006i
$315$	−8.74128	−	22.2152i	−0.492515	−	1.25169i
$316$	5.70825	+	3.29566i	0.321114	+	0.185395i
$317$	0.0675240	+	0.0180930i	0.00379252	+	0.00101620i	0.260715	−	0.965416i	$-0.416042\pi$
$317$	0.0675240	+	0.0180930i	0.00379252	+	0.00101620i	−0.256922	+	0.966432i	$0.582708\pi$
$318$	10.8754	−	13.3253i	0.609863	−	0.747245i
$319$	−4.12263	−	1.10466i	−0.230823	−	0.0618488i
$320$	−0.778459	+	2.90525i	−0.0435172	+	0.162408i
$321$	9.93335	+	13.7828i	0.554426	+	0.769283i
$322$	6.18293	+	2.26045i	0.344561	+	0.125970i
$323$	−1.95622	+	7.30073i	−0.108847	+	0.406223i
$324$	−3.53418	−	8.27705i	−0.196343	−	0.459836i
$325$	−13.0948	+	6.43324i	−0.726368	+	0.356852i
$326$	−1.69323	−	0.977587i	−0.0937794	−	0.0541436i
$327$	−9.99181	−	1.62182i	−0.552548	−	0.0896868i
$328$	−1.26516	−	2.19133i	−0.0698569	−	0.120996i
$329$	−3.08677	+	8.44311i	−0.170179	+	0.465484i
$330$	26.9354	−	10.2213i	1.48275	−	0.562664i
$331$	7.51304	+	7.51304i	0.412954	+	0.412954i	0.882766	−	0.469812i	$-0.155678\pi$
$331$	7.51304	+	7.51304i	0.412954	+	0.412954i	−0.469812	+	0.882766i	$0.655678\pi$
$332$	3.19444	−	11.9218i	0.175318	−	0.654294i
$333$	−0.572641	+	0.867167i	−0.0313805	+	0.0475205i
$334$	−7.75410			−0.424286
$335$	−12.4623	−	21.5853i	−0.680887	−	1.17933i
$336$	−3.94041	+	2.33948i	−0.214967	+	0.127629i
$337$			34.9059i			1.90145i	0.310039	+	0.950724i	$0.399658\pi$
$337$			34.9059i			1.90145i	−0.310039	+	0.950724i	$0.600342\pi$
$338$	−10.3373	+	7.88293i	−0.562274	+	0.428775i
$339$	−7.46777	−	10.3618i	−0.405594	−	0.562774i
$340$	3.18820	+	3.18820i	0.172904	+	0.172904i
$341$	36.0467	+	20.8116i	1.95204	+	1.12701i
$342$	−14.8191	+	3.03138i	−0.801324	+	0.163918i
$343$	−17.8684	−	4.87034i	−0.964803	−	0.262974i
$344$	−2.63961	−	9.85114i	−0.142318	−	0.531138i
$345$	12.1192	−	4.59892i	0.652476	−	0.247598i
$346$	−1.79418	−	6.69598i	−0.0964558	−	0.359978i
$347$	−26.0127	+	15.0185i	−1.39644	+	0.806234i	−0.994017	−	0.109222i	$-0.965164\pi$
$347$	−26.0127	+	15.0185i	−1.39644	+	0.806234i	−0.402420	+	0.915455i	$0.631831\pi$
$348$	1.08447	−	0.781579i	0.0581335	−	0.0418970i
$349$	28.2569	+	7.57142i	1.51256	+	0.405289i	0.917284	−	0.398233i	$-0.130377\pi$
$349$	28.2569	+	7.57142i	1.51256	+	0.405289i	0.595275	+	0.803522i	$0.297043\pi$
$350$	−3.67607	+	10.0550i	−0.196494	+	0.537463i
$351$	−17.9640	−	5.31932i	−0.958847	−	0.283924i
$352$	−2.76508	−	4.78925i	−0.147379	−	0.255268i
$353$	3.91095	−	3.91095i	0.208159	−	0.208159i	−0.595326	−	0.803484i	$-0.702977\pi$
$353$	3.91095	−	3.91095i	0.208159	−	0.208159i	0.803484	+	0.595326i	$0.202977\pi$
$354$	−21.5603	−	9.69844i	−1.14592	−	0.515466i
$355$		−	12.8990i		−	0.684608i
$356$	9.08188	−	9.08188i	0.481339	−	0.481339i
$357$	0.0837166	+	6.86908i	0.00443075	+	0.363550i
$358$	2.39822	+	8.95029i	0.126750	+	0.473037i
$359$	−0.900380	+	3.36027i	−0.0475203	+	0.177348i	−0.985607	−	0.169052i	$-0.945929\pi$
$359$	−0.900380	+	3.36027i	−0.0475203	+	0.177348i	0.938087	+	0.346400i	$0.112596\pi$
$360$	−2.85401	+	8.55995i	−0.150419	+	0.451149i
$361$			6.42159i			0.337979i
$362$	−1.47543	+	0.395340i	−0.0775468	+	0.0207786i
$363$	−13.9143	+	30.9326i	−0.730314	+	1.62354i
$364$	−1.47882	+	9.42407i	−0.0775113	+	0.493955i
$365$		−	25.9974i		−	1.36077i
$366$	3.80315	−	23.4307i	0.198794	−	1.22474i
$367$	33.5650			1.75208			0.876040	−	0.482239i	$-0.160176\pi$
$367$	33.5650			1.75208			0.876040	+	0.482239i	$0.160176\pi$
$368$	−1.24411	−	2.15485i	−0.0648535	−	0.112329i
$369$	−3.39430	−	6.78982i	−0.176700	−	0.353464i
$370$	1.00636	−	0.269653i	0.0523181	−	0.0140186i
$371$	−21.5002	−	15.1006i	−1.11624	−	0.783985i
$372$	−12.1884	+	4.62517i	−0.631938	+	0.239804i
$373$	8.74564			0.452832			0.226416	−	0.974031i	$-0.427299\pi$
$373$	8.74564			0.452832			0.226416	+	0.974031i	$0.427299\pi$
$374$	−8.29007			−0.428669
$375$	−1.76241	−	4.64436i	−0.0910106	−	0.239833i
$376$	2.94256	−	1.69889i	0.151751	−	0.0876135i
$377$	0.186160	−	2.77646i	0.00958773	−	0.142995i
$378$	−12.2210	+	6.29668i	−0.628578	+	0.323866i
$379$	−4.58304	+	17.1041i	−0.235415	+	0.878580i	0.742547	+	0.669794i	$0.233618\pi$
$379$	−4.58304	+	17.1041i	−0.235415	+	0.878580i	−0.977961	+	0.208785i	$0.933049\pi$
$380$	13.1332	+	7.58247i	0.673720	+	0.388973i
$381$	−23.0329	+	2.33166i	−1.18001	+	0.119455i
$382$	9.60180	−	2.57280i	0.491271	−	0.131636i
$383$	9.71088	−	9.71088i	0.496203	−	0.496203i	−0.414051	−	0.910254i	$-0.635886\pi$
$383$	9.71088	−	9.71088i	0.496203	−	0.496203i	0.910254	+	0.414051i	$0.135886\pi$
$384$	1.70968	+	0.277506i	0.0872465	+	0.0141614i
$385$	−18.5411	−	39.9109i	−0.944941	−	2.03405i
$386$	3.38354	+	1.95349i	0.172218	+	0.0994300i
$387$	−6.13172	−	29.9752i	−0.311693	−	1.52373i
$388$	10.3098	−	10.3098i	0.523402	−	0.523402i
$389$	3.65554	−	6.33159i	0.185343	−	0.321024i	−0.758349	−	0.651849i	$-0.773994\pi$
$389$	3.65554	−	6.33159i	0.185343	−	0.321024i	0.943692	+	0.330825i	$0.107327\pi$
$390$	9.93820	+	15.9388i	0.503240	+	0.807091i
$391$	−3.72999			−0.188634
$392$	3.99857	+	5.74556i	0.201958	+	0.290195i
$393$	−18.4677	+	1.86952i	−0.931574	+	0.0943046i
$394$			1.98615i			0.100061i
$395$	−5.13107	−	19.1494i	−0.258172	−	0.963511i
$396$	−7.41840	−	14.8395i	−0.372789	−	0.745713i
$397$	−11.8942	+	11.8942i	−0.596953	+	0.596953i	−0.939501	−	0.342547i	$-0.888710\pi$
$397$	−11.8942	+	11.8942i	−0.596953	+	0.596953i	0.342547	+	0.939501i	$0.388710\pi$
$398$	9.76987	+	9.76987i	0.489719	+	0.489719i
$399$	6.25162	+	22.2434i	0.312972	+	1.11356i
$400$	3.50434	−	2.02323i	0.175217	−	0.101162i
$401$	−23.7043	+	6.35156i	−1.18374	+	0.317182i	−0.796408	−	0.604759i	$-0.793269\pi$
$401$	−23.7043	+	6.35156i	−1.18374	+	0.317182i	−0.387330	+	0.921941i	$0.626603\pi$
$402$	−11.6442	+	8.39205i	−0.580761	+	0.418557i
$403$	−8.76158	+	25.6842i	−0.436446	+	1.27942i
$404$	−14.0959	+	8.13827i	−0.701297	+	0.404894i
$405$	−10.0871	+	25.1200i	−0.501231	+	1.24822i
$406$	−1.31029	−	1.56610i	−0.0650284	−	0.0777240i
$407$	−0.957804	+	1.65897i	−0.0474766	+	0.0822319i
$408$	1.64173	−	2.01155i	0.0812775	−	0.0995867i
$409$	−3.12815	+	11.6744i	−0.154677	+	0.577263i	0.844456	+	0.535626i	$0.179924\pi$
$409$	−3.12815	+	11.6744i	−0.154677	+	0.577263i	−0.999133	+	0.0416376i	$0.986743\pi$
$410$	−1.96975	+	7.35122i	−0.0972792	+	0.363051i
$411$	−2.41226	+	2.95566i	−0.118988	+	0.145792i
$412$	−3.35420	+	5.80965i	−0.165250	+	0.286221i
$413$	−12.3999	+	33.9170i	−0.610159	+	1.66894i
$414$	−3.33780	−	6.67681i	−0.164044	−	0.328147i
$415$	−32.1490	+	18.5613i	−1.57813	+	0.911137i
$416$	2.71436	−	2.37324i	0.133082	−	0.116358i
$417$	9.33798	−	6.72992i	0.457283	−	0.329566i
$418$	−26.9328	+	7.21664i	−1.31733	+	0.352977i
$419$	12.9325	−	7.46657i	0.631793	−	0.364766i	−0.149653	−	0.988739i	$-0.547816\pi$
$419$	12.9325	−	7.46657i	0.631793	−	0.364766i	0.781446	+	0.623973i	$0.214482\pi$
$420$	13.3560	+	3.40484i	0.651706	+	0.166139i
$421$	−17.8281	−	17.8281i	−0.868889	−	0.868889i	0.123461	−	0.992349i	$-0.460601\pi$
$421$	−17.8281	−	17.8281i	−0.868889	−	0.868889i	−0.992349	+	0.123461i	$0.960601\pi$
$422$	3.05552	−	3.05552i	0.148740	−	0.148740i
$423$	9.11753	−	4.55794i	0.443309	−	0.221614i
$424$	2.57017	+	9.59201i	0.124819	+	0.465829i
$425$		−	6.06591i		−	0.294240i
$426$	−7.39032	+	0.748134i	−0.358062	+	0.0362472i
$427$	−36.1168	−	3.21203i	−1.74781	−	0.155441i
$428$	−9.80881			−0.474127
$429$	−33.6431	−	7.80143i	−1.62430	−	0.376657i
$430$	−15.3374	+	26.5652i	−0.739636	+	1.28109i
$431$	−7.28830	+	7.28830i	−0.351065	+	0.351065i	−0.860506	−	0.509441i	$-0.829852\pi$
$431$	−7.28830	+	7.28830i	−0.351065	+	0.351065i	0.509441	+	0.860506i	$0.329852\pi$
$432$	5.06985	+	1.13870i	0.243923	+	0.0547855i
$433$	−5.49073	−	3.17007i	−0.263867	−	0.152344i	0.362230	−	0.932089i	$-0.382015\pi$
$433$	−5.49073	−	3.17007i	−0.263867	−	0.152344i	−0.626098	+	0.779745i	$0.715349\pi$
$434$	8.38990	+	18.0598i	0.402728	+	0.866898i
$435$	−3.96868	−	0.644176i	−0.190284	−	0.0308859i
$436$	4.13252	−	4.13252i	0.197912	−	0.197912i
$437$	−12.1180	+	3.24702i	−0.579684	+	0.155326i
$438$	−14.8949	+	1.50784i	−0.711706	+	0.0720472i
$439$	−5.05309	−	2.91740i	−0.241171	−	0.139240i	0.374544	−	0.927209i	$-0.377799\pi$
$439$	−5.05309	−	2.91740i	−0.241171	−	0.139240i	−0.615715	+	0.787969i	$0.711133\pi$
$440$	−4.30500	+	16.0665i	−0.205233	+	0.765939i
$441$	10.9401	+	17.9252i	0.520958	+	0.853583i
$442$	−1.04651	−	5.30268i	−0.0497772	−	0.252223i
$443$	18.4965	−	10.6789i	0.878794	−	0.507372i	0.00853318	−	0.999964i	$-0.497284\pi$
$443$	18.4965	−	10.6789i	0.878794	−	0.507372i	0.870260	+	0.492592i	$0.163950\pi$
$444$	−0.212863	−	0.560941i	−0.0101020	−	0.0266211i
$445$	−38.6305			−1.83126
$446$	−10.2638			−0.486004
$447$	−2.45963	+	0.933365i	−0.116336	+	0.0441467i
$448$	0.234373	−	2.63535i	0.0110731	−	0.124509i
$449$	23.7723	−	6.36977i	1.12188	−	0.300608i	0.350239	−	0.936661i	$-0.386101\pi$
$449$	23.7723	−	6.36977i	1.12188	−	0.300608i	0.771646	+	0.636053i	$0.219434\pi$
$450$	10.8582	−	5.42811i	0.511860	−	0.255884i
$451$	−6.99654	−	12.1184i	−0.329454	−	0.570632i
$452$	7.37414			0.346851
$453$	3.06630	−	18.8911i	0.144068	−	0.887580i
$454$		−	16.0662i		−	0.754025i
$455$	23.1881	−	16.8979i	1.08708	−	0.792184i
$456$	3.58256	−	7.96430i	0.167769	−	0.372962i
$457$	10.1755	−	2.72651i	0.475989	−	0.127541i	−0.0128456	−	0.999917i	$-0.504089\pi$
$457$	10.1755	−	2.72651i	0.475989	−	0.127541i	0.488834	+	0.872377i	$0.337422\pi$
$458$		−	6.25738i		−	0.292388i
$459$	5.27831	−	5.72834i	0.246370	−	0.267376i
$460$	−1.93697	+	7.22887i	−0.0903116	+	0.337048i
$461$	0.0584316	+	0.218070i	0.00272143	+	0.0101565i	0.967273	−	0.253737i	$-0.0816598\pi$
$461$	0.0584316	+	0.218070i	0.00272143	+	0.0101565i	−0.964552	+	0.263894i	$0.914993\pi$
$462$	−21.7911	+	12.9377i	−1.01381	+	0.601916i
$463$	0.697155	−	0.697155i	0.0323995	−	0.0323995i	−0.690721	−	0.723121i	$-0.742707\pi$
$463$	0.697155	−	0.697155i	0.0323995	−	0.0323995i	0.723121	+	0.690721i	$0.242707\pi$
$464$			0.771780i			0.0358290i
$465$	35.7588	+	16.0853i	1.65828	+	0.745939i
$466$	13.5610	−	13.5610i	0.628202	−	0.628202i
$467$	0.101856	+	0.176420i	0.00471334	+	0.00816374i	0.868372	−	0.495913i	$-0.165166\pi$
$467$	0.101856	+	0.176420i	0.00471334	+	0.00816374i	−0.863659	+	0.504076i	$0.831833\pi$
$468$	8.55551	−	6.61841i	0.395478	−	0.305936i
$469$	14.0689	+	16.8156i	0.649643	+	0.776474i
$470$	−9.87139	−	2.64503i	−0.455333	−	0.122006i
$471$	−20.7805	+	14.9766i	−0.957516	+	0.690086i
$472$	11.8206	−	6.82463i	0.544088	−	0.314129i
$473$	−14.5974	−	54.4783i	−0.671190	−	2.50492i
$474$	−10.6738	+	4.05044i	−0.490265	+	0.186043i
$475$	−5.28047	−	19.7070i	−0.242285	−	0.904219i
$476$	−3.24562	−	2.27955i	−0.148763	−	0.104483i
$477$	5.97043	+	29.1868i	0.273367	+	1.33637i
$478$	12.6351	+	7.29486i	0.577915	+	0.333659i
$479$	12.0389	+	12.0389i	0.550073	+	0.550073i	0.926462	−	0.376388i	$-0.122834\pi$
$479$	12.0389	+	12.0389i	0.550073	+	0.550073i	−0.376388	+	0.926462i	$0.622834\pi$
$480$	−3.04592	−	4.22631i	−0.139027	−	0.192904i
$481$	−1.18206	−	0.403231i	−0.0538971	−	0.0183858i
$482$		−	10.6777i		−	0.486357i
$483$	−9.80457	+	5.82112i	−0.446123	+	0.264870i
$484$	−9.79129	−	16.9590i	−0.445059	−	0.770865i
$485$	−43.8536			−1.99129
$486$	14.9772	+	4.32232i	0.679381	+	0.196064i
$487$	−4.63330	+	17.2917i	−0.209955	+	0.783563i	0.777927	+	0.628355i	$0.216271\pi$
$487$	−4.63330	+	17.2917i	−0.209955	+	0.783563i	−0.987882	+	0.155208i	$0.950395\pi$
$488$	9.69072	+	9.69072i	0.438678	+	0.438678i
$489$	3.16616	−	1.20148i	0.143179	−	0.0543326i
$490$	3.71549	−	20.7237i	0.167849	−	0.936201i
$491$	17.1833	+	29.7623i	0.775471	+	1.34315i	0.934530	+	0.355885i	$0.115821\pi$
$491$	17.1833	+	29.7623i	0.775471	+	1.34315i	−0.159059	+	0.987269i	$0.550846\pi$
$492$	4.32604	+	0.702180i	0.195033	+	0.0316567i
$493$	1.00195	+	0.578475i	0.0451254	+	0.0260532i
$494$	−8.01597	−	16.3164i	−0.360655	−	0.734110i
$495$	−15.7831	+	47.3378i	−0.709397	+	2.12768i
$496$	1.94802	−	7.27013i	0.0874689	−	0.326438i
$497$	1.95428	+	11.1770i	0.0876616	+	0.501358i
$498$	12.4991	+	17.3429i	0.560097	+	0.777152i
$499$	4.14185	−	15.4576i	0.185415	−	0.691977i	−0.809127	−	0.587634i	$-0.800059\pi$
$499$	4.14185	−	15.4576i	0.185415	−	0.691977i	0.994541	−	0.104343i	$-0.0332740\pi$
$500$	2.77027	+	0.742291i	0.123890	+	0.0331963i
$501$	8.49202	−	10.4050i	0.379396	−	0.464861i
$502$	−10.2186	−	2.73807i	−0.456080	−	0.122206i
$503$	−11.5396	−	6.66237i	−0.514524	−	0.297060i	0.220168	−	0.975462i	$-0.429340\pi$
$503$	−11.5396	−	6.66237i	−0.514524	−	0.297060i	−0.734691	+	0.678402i	$0.762673\pi$
$504$	1.17612	−	7.84963i	0.0523885	−	0.349650i
$505$	47.2873	+	12.6706i	2.10426	+	0.563835i
$506$	−6.88009	−	11.9167i	−0.305857	−	0.529760i
$507$	0.743155	−	22.5044i	0.0330047	−	0.999455i
$508$	6.68302	−	11.5753i	0.296511	−	0.513572i
$509$	−1.49118	−	5.56517i	−0.0660955	−	0.246672i	0.924972	−	0.380036i	$-0.124089\pi$
$509$	−1.49118	−	5.56517i	−0.0660955	−	0.246672i	−0.991067	+	0.133365i	$0.957422\pi$
$510$	−7.76975	+	0.786544i	−0.344050	+	0.0348287i
$511$	3.93879	+	22.5269i	0.174242	+	0.996531i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	12.1616	−	23.2051i	0.536948	−	1.02453i
$514$	1.92568	+	0.515984i	0.0849381	+	0.0227591i
$515$	19.4896	−	5.22221i	0.858813	−	0.230118i
$516$	16.1097	+	7.24662i	0.709192	+	0.319015i
$517$	16.2728	−	9.39512i	0.715678	−	0.413197i
$518$	−0.831160	+	0.386125i	−0.0365191	+	0.0169654i
$519$	10.9501	+	4.92564i	0.480654	+	0.216212i
$520$	−10.8202	−	0.725492i	−0.474499	−	0.0318149i
$521$	−31.0875	−	17.9484i	−1.36197	−	0.786333i	−0.372083	−	0.928199i	$-0.621356\pi$
$521$	−31.0875	−	17.9484i	−1.36197	−	0.786333i	−0.989886	+	0.141866i	$0.954690\pi$
$522$	−0.138892	+	2.31117i	−0.00607912	+	0.101157i
$523$	4.55504	−	7.88956i	0.199178	−	0.344987i	−0.749084	−	0.662475i	$-0.769506\pi$
$523$	4.55504	−	7.88956i	0.199178	−	0.344987i	0.948262	+	0.317488i	$0.102839\pi$
$524$	5.35842	−	9.28106i	0.234084	−	0.405445i
$525$	−9.46662	−	15.9447i	−0.413157	−	0.695884i
$526$	14.9023	−	3.99306i	0.649771	−	0.174106i
$527$	−7.97819	−	7.97819i	−0.347535	−	0.347535i
$528$	9.45477	+	1.53465i	0.411466	+	0.0667870i
$529$	8.40441	+	14.5569i	0.365409	+	0.632907i
$530$	14.9340	−	25.8664i	0.648690	−	1.12356i
$531$	36.6262	−	18.3098i	1.58944	−	0.794576i
$532$	−12.5288	−	4.58047i	−0.543192	−	0.198589i
$533$	6.86821	−	6.00506i	0.297495	−	0.260108i
$534$	2.24054	+	22.1329i	0.0969578	+	0.957782i
$535$	20.8613	+	20.8613i	0.901911	+	0.901911i
$536$		−	8.28683i		−	0.357936i
$537$	−14.6366	−	6.58394i	−0.631614	−	0.284118i
$538$	−6.84955	−	6.84955i	−0.295305	−	0.295305i
$539$	22.1127	+	31.7738i	0.952461	+	1.36860i
$540$	−8.36073	−	13.2043i	−0.359789	−	0.568221i
$541$	1.84531	+	0.494450i	0.0793361	+	0.0212580i	0.298269	−	0.954482i	$-0.403591\pi$
$541$	1.84531	+	0.494450i	0.0793361	+	0.0212580i	−0.218933	+	0.975740i	$0.570257\pi$
$542$	−25.9483	+	14.9813i	−1.11458	+	0.643501i
$543$	1.08534	−	2.41279i	0.0465765	−	0.103543i
$544$	0.387987	+	1.44799i	0.0166348	+	0.0620819i
$545$	−17.5780			−0.752959
$546$	−11.0263	−	12.3053i	−0.471883	−	0.526618i
$547$	−15.2817			−0.653397			−0.326699	−	0.945129i	$-0.605936\pi$
$547$	−15.2817			−0.653397			−0.326699	+	0.945129i	$0.605936\pi$
$548$	−0.570086	−	2.12759i	−0.0243529	−	0.0908861i
$549$	27.2758	+	30.7638i	1.16410	+	1.31297i
$550$	19.3795	−	11.1888i	0.826346	−	0.477091i
$551$	3.75871	+	1.00714i	0.160126	+	0.0429057i
$552$	4.25403	+	0.690493i	0.181064	+	0.0293893i
$553$	7.34735	+	15.8156i	0.312441	+	0.672550i
$554$	−1.98144	−	1.98144i	−0.0841835	−	0.0841835i
$555$	−0.740290	+	1.64572i	−0.0314235	+	0.0698568i
$556$			6.64554i			0.281834i
$557$	−0.944866	−	0.944866i	−0.0400353	−	0.0400353i	0.686806	−	0.726841i	$-0.259012\pi$
$557$	−0.944866	−	0.944866i	−0.0400353	−	0.0400353i	−0.726841	+	0.686806i	$0.759012\pi$
$558$	7.14190	−	21.4205i	0.302341	−	0.906803i
$559$	33.0039	−	16.2143i	1.39592	−	0.685790i
$560$	−6.10329	+	5.10637i	−0.257911	+	0.215784i
$561$	9.07899	−	11.1242i	0.383315	−	0.469664i
$562$	3.38012	−	5.85454i	0.142582	−	0.246959i
$563$	−6.52825	−	11.3073i	−0.275133	−	0.476544i	0.695036	−	0.718975i	$-0.255388\pi$
$563$	−6.52825	−	11.3073i	−0.275133	−	0.476544i	−0.970169	+	0.242431i	$0.922055\pi$
$564$	−0.942903	+	5.80910i	−0.0397034	+	0.244607i
$565$	−15.6832	−	15.6832i	−0.659799	−	0.659799i
$566$	−31.6666	+	8.48503i	−1.33104	+	0.356652i
$567$	4.93464	−	23.2948i	0.207236	−	0.978291i
$568$	2.14431	−	3.71405i	0.0899731	−	0.155838i
$569$	−14.8396	+	25.7030i	−0.622109	+	1.07752i	0.366983	+	0.930228i	$0.380391\pi$
$569$	−14.8396	+	25.7030i	−0.622109	+	1.07752i	−0.989092	+	0.147297i	$0.952943\pi$
$570$	−24.5577	+	9.31902i	−1.02861	+	0.390331i
$571$	13.5048	+	7.79701i	0.565159	+	0.326295i	0.755214	−	0.655479i	$-0.227533\pi$
$571$	13.5048	+	7.79701i	0.565159	+	0.326295i	−0.190054	+	0.981774i	$0.560866\pi$
$572$	15.0108	−	13.1244i	0.627634	−	0.548757i
$573$	−7.06320	+	15.7020i	−0.295069	+	0.655961i
$574$	0.593040	−	6.66829i	0.0247530	−	0.278329i
$575$	8.71953	−	5.03422i	0.363629	−	0.209942i
$576$	−2.24475	+	1.99025i	−0.0935314	+	0.0829270i
$577$	−32.3383	+	8.66502i	−1.34626	+	0.360729i	−0.858753	−	0.512390i	$-0.828760\pi$
$577$	−32.3383	+	8.66502i	−1.34626	+	0.360729i	−0.487507	+	0.873119i	$0.662094\pi$
$578$	−14.2501	−	3.81831i	−0.592726	−	0.158821i
$579$	−6.32687	+	2.40088i	−0.262936	+	0.0997772i
$580$	1.64141	−	1.64141i	0.0681559	−	0.0681559i
$581$	25.0451	−	20.9542i	1.03905	−	0.869327i
$582$	2.54348	+	25.1254i	0.105431	+	1.04148i
$583$	14.2134	+	53.0453i	0.588661	+	2.19691i
$584$	4.32177	−	7.48552i	0.178836	−	0.309753i
$585$	−32.2717	−	4.11980i	−1.33427	−	0.170333i
$586$	−3.63195	−	6.29072i	−0.150034	−	0.259867i
$587$	−33.2460	−	8.90825i	−1.37221	−	0.367683i	−0.503925	−	0.863747i	$-0.668111\pi$
$587$	−33.2460	−	8.90825i	−1.37221	−	0.367683i	−0.868285	+	0.496065i	$0.834778\pi$
$588$	−12.0889	−	0.926780i	−0.498537	−	0.0382198i
$589$	−32.8647	−	18.9745i	−1.35417	−	0.781829i
$590$	−39.6545	−	10.6254i	−1.63255	−	0.437440i
$591$	−2.66516	−	2.17516i	−0.109630	−	0.0894743i
$592$	0.334590	+	0.0896532i	0.0137516	+	0.00368473i
$593$	−1.90121	+	7.09540i	−0.0780732	+	0.291373i	−0.993913	−	0.110172i	$-0.964860\pi$
$593$	−1.90121	+	7.09540i	−0.0780732	+	0.291373i	0.915839	+	0.401545i	$0.131527\pi$
$594$	28.0370	+	6.29716i	1.15037	+	0.258376i
$595$	2.05462	+	11.7509i	0.0842312	+	0.481739i
$596$	0.393114	−	1.46712i	0.0161026	−	0.0600956i
$597$	−23.8095	+	2.41027i	−0.974458	+	0.0986459i
$598$	6.75389	−	5.90511i	0.276187	−	0.241478i
$599$	38.9970	+	22.5149i	1.59337	+	0.919935i	0.992723	+	0.120424i	$0.0384253\pi$
$599$	38.9970	+	22.5149i	1.59337	+	0.919935i	0.600651	+	0.799511i	$0.294908\pi$
$600$	−1.12292	+	6.91813i	−0.0458429	+	0.282432i
$601$	0.733005	+	1.26960i	0.0298999	+	0.0517881i	0.880588	−	0.473882i	$-0.157148\pi$
$601$	0.733005	+	1.26960i	0.0298999	+	0.0517881i	−0.850688	+	0.525671i	$0.823814\pi$
$602$	9.26513	−	25.3426i	0.377618	−	1.03289i
$603$	1.49132	−	24.8157i	0.0607313	−	1.01057i
$604$	7.81319	+	7.81319i	0.317914	+	0.317914i
$605$	−15.2442	+	56.8923i	−0.619766	+	2.31300i
$606$	4.51683	−	27.8276i	0.183484	−	1.13042i
$607$	−40.0365			−1.62503			−0.812515	−	0.582940i	$-0.801902\pi$
$607$	−40.0365			−1.62503			−0.812515	+	0.582940i	$0.801902\pi$
$608$	2.52099	+	4.36649i	0.102240	+	0.177084i
$609$	3.53648	−	0.0431007i	0.143305	−	0.00174653i
$610$		−	41.2202i		−	1.66896i
$611$	8.06374	+	9.22279i	0.326224	+	0.373114i
$612$	0.901281	+	4.40596i	0.0364321	+	0.178100i
$613$	−4.98293	−	4.98293i	−0.201259	−	0.201259i	0.599281	−	0.800539i	$-0.295453\pi$
$613$	−4.98293	−	4.98293i	−0.201259	−	0.201259i	−0.800539	+	0.599281i	$0.795453\pi$
$614$	0.852853	+	0.492395i	0.0344184	+	0.0198715i
$615$	−7.70717	−	10.6940i	−0.310783	−	0.431222i
$616$	1.29612	−	14.5739i	0.0522221	−	0.587199i
$617$	−10.2786	−	38.3603i	−0.413802	−	1.54433i	−0.787224	−	0.616667i	$-0.788483\pi$
$617$	−10.2786	−	38.3603i	−0.413802	−	1.54433i	0.373423	−	0.927661i	$-0.378184\pi$
$618$	−4.12238	−	10.8634i	−0.165827	−	0.436991i
$619$	11.4286	+	42.6520i	0.459353	+	1.71433i	0.674964	+	0.737851i	$0.264159\pi$
$619$	11.4286	+	42.6520i	0.459353	+	1.71433i	−0.215611	+	0.976479i	$0.569174\pi$
$620$	−19.6051	+	11.3190i	−0.787358	+	0.454581i
$621$	12.6149	+	2.83332i	0.506216	+	0.113697i
$622$	6.45148	+	1.72867i	0.258681	+	0.0693133i
$623$	33.4735	−	5.85278i	1.34109	−	0.234486i
$624$	0.211906	+	6.24140i	0.00848302	+	0.249856i
$625$	−14.4292	−	24.9922i	−0.577169	−	0.999686i
$626$	3.30658	−	3.30658i	0.132158	−	0.132158i
$627$	19.8121	−	44.0438i	0.791220	−	1.75894i
$628$		−	14.7888i		−	0.590139i
$629$	0.367177	−	0.367177i	0.0146403	−	0.0146403i
$630$	−19.1959	+	14.1932i	−0.764782	+	0.565469i
$631$	11.3000	+	42.1720i	0.449844	+	1.67884i	0.702819	+	0.711369i	$0.251925\pi$
$631$	11.3000	+	42.1720i	0.449844	+	1.67884i	−0.252974	+	0.967473i	$0.581409\pi$
$632$	1.70596	−	6.36672i	0.0678594	−	0.253255i
$633$	0.753811	+	7.44640i	0.0299613	+	0.295968i
$634$		−	0.0699060i		−	0.00277632i
$635$	−38.8316	+	10.4049i	−1.54099	+	0.412906i
$636$	−15.6860	−	7.05600i	−0.621990	−	0.279789i
$637$	−17.5325	+	18.1552i	−0.694662	+	0.719336i
$638$			4.26806i			0.168974i
$639$	7.08972	−	10.7362i	0.280465	−	0.424717i
$640$	3.00773			0.118891
$641$	14.9771	+	25.9412i	0.591562	+	1.02461i	0.994022	+	0.109178i	$0.0348217\pi$
$641$	14.9771	+	25.9412i	0.591562	+	1.02461i	−0.402461	+	0.915437i	$0.631845\pi$
$642$	10.7423	−	13.1621i	0.423963	−	0.519468i
$643$	−27.2367	+	7.29806i	−1.07411	+	0.287807i	−0.752182	−	0.658956i	$-0.770998\pi$
$643$	−27.2367	+	7.29806i	−1.07411	+	0.287807i	−0.321930	+	0.946763i	$0.604332\pi$
$644$	0.583170	−	6.55730i	0.0229801	−	0.258394i
$645$	−18.8500	−	49.6741i	−0.742218	−	1.95591i
$646$	7.55827			0.297376
$647$	−12.2889			−0.483126			−0.241563	−	0.970385i	$-0.577660\pi$
$647$	−12.2889			−0.483126			−0.241563	+	0.970385i	$0.577660\pi$
$648$	−7.08030	+	5.55602i	−0.278141	+	0.218261i
$649$	65.3698	−	37.7413i	2.56599	−	1.48147i
$650$	9.60321	+	10.9835i	0.376669	+	0.430810i
$651$	−33.4222	−	8.52030i	−1.30992	−	0.333937i
$652$	−0.506036	+	1.88855i	−0.0198179	+	0.0739615i
$653$	−19.6052	−	11.3191i	−0.767210	−	0.442949i	0.0646682	−	0.997907i	$-0.479401\pi$
$653$	−19.6052	−	11.3191i	−0.767210	−	0.442949i	−0.831879	+	0.554958i	$0.812734\pi$
$654$	1.01951	+	10.0711i	0.0398661	+	0.393811i
$655$	−31.1351	+	8.34262i	−1.21655	+	0.325973i
$656$	−1.78921	+	1.78921i	−0.0698569	+	0.0698569i
$657$	14.2891	−	21.6384i	0.557470	−	0.844193i
$658$	8.95433	+	0.796348i	0.349076	+	0.0310449i
$659$	−11.6652	−	6.73493i	−0.454414	−	0.262356i	0.255279	−	0.966867i	$-0.417833\pi$
$659$	−11.6652	−	6.73493i	−0.454414	−	0.262356i	−0.709692	+	0.704512i	$0.751166\pi$
$660$	−16.8444	−	23.3722i	−0.655668	−	0.909760i
$661$	3.56783	−	3.56783i	0.138772	−	0.138772i	−0.634308	−	0.773080i	$-0.718715\pi$
$661$	3.56783	−	3.56783i	0.138772	−	0.138772i	0.773080	+	0.634308i	$0.218715\pi$
$662$	5.31252	−	9.20155i	0.206477	−	0.357628i
$663$	8.26160	+	4.40304i	0.320854	+	0.171000i
$664$	−12.3424			−0.478976
$665$	16.9044	+	36.3878i	0.655524	+	1.41106i
$666$	0.985829	+	0.328689i	0.0382001	+	0.0127364i
$667$			1.92035i			0.0743563i
$668$	2.00691	+	7.48989i	0.0776497	+	0.289792i
$669$	11.2405	−	13.7726i	0.434584	−	0.532481i
$670$	−17.6243	+	17.6243i	−0.680887	+	0.680887i
$671$	53.5912	+	53.5912i	2.06886	+	2.06886i
$672$	3.27962	+	3.20064i	0.126514	+	0.123467i
$673$	−0.948152	+	0.547416i	−0.0365486	+	0.0211013i	−0.518163	−	0.855282i	$-0.673384\pi$
$673$	−0.948152	+	0.547416i	−0.0365486	+	0.0211013i	0.481614	+	0.876383i	$0.340051\pi$
$674$	33.7165	−	9.03432i	1.29871	−	0.347989i
$675$	−4.60769	+	20.5149i	−0.177350	+	0.789621i
$676$	10.2898	+	7.94479i	0.395762	+	0.305569i
$677$	35.5621	−	20.5318i	1.36676	−	0.789100i	0.376249	−	0.926519i	$-0.377214\pi$
$677$	35.5621	−	20.5318i	1.36676	−	0.789100i	0.990513	+	0.137419i	$0.0438806\pi$
$678$	−8.07590	+	9.89514i	−0.310153	+	0.380021i
$679$	37.9993	−	6.64411i	1.45828	−	0.254978i
$680$	2.25440	−	3.90473i	0.0864522	−	0.149740i
$681$	21.5588	+	17.5952i	0.826134	+	0.674248i
$682$	10.7729	−	40.2049i	0.412515	−	1.53953i
$683$	−5.28973	+	19.7415i	−0.202406	+	0.755389i	0.787819	+	0.615907i	$0.211210\pi$
$683$	−5.28973	+	19.7415i	−0.202406	+	0.755389i	−0.990225	+	0.139482i	$0.955456\pi$
$684$	6.76355	+	13.5296i	0.258611	+	0.517315i
$685$	−3.31248	+	5.73738i	−0.126563	+	0.219214i
$686$	−0.0797042	+	18.5201i	−0.00304312	+	0.707100i
$687$	8.39659	+	6.85286i	0.320350	+	0.261453i
$688$	−8.83229	+	5.09933i	−0.336728	+	0.194410i
$689$	−32.1358	+	15.7878i	−1.22428	+	0.601466i
$690$	−7.57890	−	10.5160i	−0.288524	−	0.400336i
$691$	3.44758	−	0.923775i	0.131152	−	0.0351421i	−0.192646	−	0.981268i	$-0.561707\pi$
$691$	3.44758	−	0.923775i	0.131152	−	0.0351421i	0.323798	+	0.946126i	$0.395040\pi$
$692$	−6.00345	+	3.46609i	−0.228217	+	0.131761i
$693$	6.50411	−	43.4097i	0.247071	−	1.64900i
$694$	21.2393	+	21.2393i	0.806234	+	0.806234i
$695$	14.1337	−	14.1337i	0.536120	−	0.536120i
$696$	−1.03563	−	0.845226i	−0.0392554	−	0.0320382i
$697$	0.981733	+	3.66388i	0.0371858	+	0.138779i
$698$		−	29.2537i		−	1.10727i
$699$	3.34557	+	33.0487i	0.126541	+	1.25002i
$700$	10.6638	+	0.948382i	0.403055	+	0.0358455i
$701$	−7.74263			−0.292435			−0.146218	−	0.989252i	$-0.546710\pi$
$701$	−7.74263			−0.292435			−0.146218	+	0.989252i	$0.546710\pi$
$702$	−0.488648	+	18.7286i	−0.0184428	+	0.706866i
$703$	0.873255	−	1.51252i	0.0329354	−	0.0570459i
$704$	−3.91041	+	3.91041i	−0.147379	+	0.147379i
$705$	14.3601	−	10.3494i	0.540832	−	0.389780i
$706$	−4.78991	−	2.76546i	−0.180271	−	0.104079i
$707$	−42.8944	−	3.81478i	−1.61321	−	0.143470i
$708$	−3.78775	+	23.3358i	−0.142352	+	0.877014i
$709$	−34.6936	+	34.6936i	−1.30294	+	1.30294i	−0.376547	+	0.926397i	$0.622889\pi$
$709$	−34.6936	+	34.6936i	−1.30294	+	1.30294i	−0.926397	+	0.376547i	$0.877111\pi$
$710$	−12.4595	+	3.33851i	−0.467596	+	0.125292i
$711$	6.25443	−	18.7588i	0.234560	−	0.703509i
$712$	−11.1230	−	6.42186i	−0.416852	−	0.240669i
$713$	4.84709	−	18.0896i	0.181525	−	0.677461i
$714$	6.61335	−	1.85871i	0.247498	−	0.0695605i
$715$	−59.8376	−	4.01208i	−2.23780	−	0.150043i
$716$	8.02461	−	4.63301i	0.299894	−	0.173144i
$717$	−23.6262	+	8.96554i	−0.882338	+	0.334824i
$718$	3.47880			0.129828
$719$	−13.9158			−0.518970			−0.259485	−	0.965747i	$-0.583553\pi$
$719$	−13.9158			−0.518970			−0.259485	+	0.965747i	$0.583553\pi$
$720$	9.00695	+	0.541280i	0.335669	+	0.0201723i
$721$	−16.0966	+	7.47787i	−0.599468	+	0.278490i
$722$	6.20278	−	1.66203i	0.230844	−	0.0618544i
$723$	14.3281	+	11.6939i	0.532868	+	0.434900i
$724$	0.763738	+	1.32283i	0.0283841	+	0.0491627i
$725$	−3.12298			−0.115984
$726$	33.4799	+	5.43428i	1.24255	+	0.201685i
$727$		−	15.3975i		−	0.571061i	−0.958370	−	0.285531i	$-0.907830\pi$
$727$		−	15.3975i		−	0.571061i	0.958370	−	0.285531i	$-0.0921699\pi$
$728$	9.48570	−	1.01070i	0.351563	−	0.0374589i
$729$	−22.2025	+	15.3638i	−0.822316	+	0.569031i
$730$	−25.1116	+	6.72863i	−0.929422	+	0.249038i
$731$			15.2885i			0.565464i
$732$	−23.6166	+	2.39075i	−0.872895	+	0.0883646i
$733$	−1.99047	+	7.42853i	−0.0735197	+	0.274379i	−0.992894	−	0.119006i	$-0.962029\pi$
$733$	−1.99047	+	7.42853i	−0.0735197	+	0.274379i	0.919374	+	0.393385i	$0.128696\pi$
$734$	−8.68726	−	32.4213i	−0.320653	−	1.19669i
$735$	23.7394	+	27.6816i	0.875642	+	1.02105i
$736$	−1.75943	+	1.75943i	−0.0648535	+	0.0648535i
$737$		−	45.8274i		−	1.68807i
$738$	−5.67996	+	5.03597i	−0.209082	+	0.185377i
$739$	22.9785	−	22.9785i	0.845276	−	0.845276i	−0.144263	−	0.989539i	$-0.546081\pi$
$739$	22.9785	−	22.9785i	0.845276	−	0.845276i	0.989539	+	0.144263i	$0.0460811\pi$
$740$	−0.520930	−	0.902277i	−0.0191498	−	0.0331683i
$741$	30.6733	+	7.11277i	1.12681	+	0.261294i
$742$	−9.02141	+	24.6759i	−0.331187	+	0.905882i
$743$	−5.59667	−	1.49962i	−0.205322	−	0.0550158i	0.154692	−	0.987963i	$-0.450561\pi$
$743$	−5.59667	−	1.49962i	−0.205322	−	0.0550158i	−0.360014	+	0.932947i	$0.617228\pi$
$744$	7.62215	+	10.5760i	0.279442	+	0.387734i
$745$	−3.95633	+	2.28419i	−0.144949	+	0.0836861i
$746$	−2.26354	−	8.44764i	−0.0828740	−	0.309290i
$747$	−36.9604	−	2.22117i	−1.35231	−	0.0812682i
$748$	2.14563	+	8.00759i	0.0784519	+	0.292787i
$749$	−21.2370	−	14.9157i	−0.775983	−	0.545010i
$750$	−4.02996	+	2.90441i	−0.147153	+	0.106054i
$751$	−0.327765	−	0.189235i	−0.0119603	−	0.00690529i	0.494008	−	0.869457i	$-0.335531\pi$
$751$	−0.327765	−	0.189235i	−0.0119603	−	0.00690529i	−0.505968	+	0.862552i	$0.668865\pi$
$752$	−2.40259	−	2.40259i	−0.0876135	−	0.0876135i
$753$	14.8652	−	10.7134i	0.541719	−	0.390419i
$754$	−2.73003	+	0.538783i	−0.0994220	+	0.0196213i
$755$		−	33.2340i		−	1.20951i
$756$	9.24514	+	10.1748i	0.336243	+	0.370055i
$757$	−0.462125	−	0.800425i	−0.0167962	−	0.0290919i	0.857505	−	0.514475i	$-0.172013\pi$
$757$	−0.462125	−	0.800425i	−0.0167962	−	0.0290919i	−0.874301	+	0.485384i	$0.838680\pi$
$758$	17.7075			0.643165
$759$	23.5254	+	3.81853i	0.853920	+	0.138604i
$760$	3.92498	−	14.6482i	0.142374	−	0.531346i
$761$	−15.9451	−	15.9451i	−0.578010	−	0.578010i	0.356344	−	0.934355i	$-0.384023\pi$
$761$	−15.9451	−	15.9451i	−0.578010	−	0.578010i	−0.934355	+	0.356344i	$0.884023\pi$
$762$	8.21357	+	21.6446i	0.297546	+	0.784102i
$763$	15.2314	−	2.66319i	0.551414	−	0.0964138i
$764$	−4.97026	−	8.60874i	−0.179818	−	0.311453i
$765$	7.45372	−	11.2874i	0.269490	−	0.408096i
$766$	−11.8934	−	6.86663i	−0.429724	−	0.248101i
$767$	32.3930	+	37.0490i	1.16964	+	1.33776i
$768$	−0.174447	−	1.72324i	−0.00629480	−	0.0621822i
$769$	−0.822227	+	3.06859i	−0.0296503	+	0.110656i	−0.979165	−	0.203066i	$-0.934909\pi$
$769$	−0.822227	+	3.06859i	−0.0296503	+	0.110656i	0.949515	+	0.313722i	$0.101576\pi$
$770$	−33.7522	+	28.2390i	−1.21634	+	1.01766i
$771$	−2.80132	+	2.01892i	−0.100887	+	0.0727097i
$772$	1.01120	−	3.77385i	0.0363939	−	0.135824i
$773$	14.7698	+	3.95755i	0.531232	+	0.142343i	0.514457	−	0.857516i	$-0.327994\pi$
$773$	14.7698	+	3.95755i	0.531232	+	0.142343i	0.0167747	+	0.999859i	$0.494660\pi$
$774$	−27.3668	+	13.6809i	−0.983681	+	0.491751i
$775$	29.4183	+	7.88260i	1.05674	+	0.283151i
$776$	−12.6269	−	7.29014i	−0.453279	−	0.261701i
$777$	0.392127	−	1.53818i	0.0140675	−	0.0551819i
$778$	−7.06197	−	1.89225i	−0.253184	−	0.0678404i
$779$	6.37893	+	11.0486i	0.228549	+	0.395858i
$780$	12.8235	−	13.7248i	0.459154	−	0.491427i
$781$	11.8583	−	20.5392i	0.424325	−	0.734952i
$782$	0.965393	+	3.60290i	0.0345224	+	0.128839i
$783$	−2.94918	−	2.71749i	−0.105395	−	0.0971150i
$784$	4.51488	−	5.34938i	0.161246	−	0.191049i
$785$	−31.4527	+	31.4527i	−1.12260	+	1.12260i
$786$	6.58561	+	17.3546i	0.234901	+	0.619018i
$787$	37.3326	+	10.0032i	1.33076	+	0.356577i	0.853000	−	0.521911i	$-0.174781\pi$
$787$	37.3326	+	10.0032i	1.33076	+	0.356577i	0.477764	+	0.878488i	$0.341447\pi$
$788$	1.91848	−	0.514054i	0.0683429	−	0.0183124i
$789$	−10.9623	+	24.3700i	−0.390269	+	0.867595i
$790$	−17.1689	+	9.91246i	−0.610842	+	0.352670i
$791$	15.9657	+	11.2135i	0.567675	+	0.398705i
$792$	−12.4138	+	11.0064i	−0.441106	+	0.391094i
$793$	−27.5141	+	41.0443i	−0.977053	+	1.45753i
$794$	14.5674	+	8.41047i	0.516976	+	0.298477i
$795$	18.3542	+	48.3674i	0.650956	+	1.71542i
$796$	6.90834	−	11.9656i	0.244860	−	0.424109i
$797$	−19.8553	+	34.3904i	−0.703311	+	1.21817i	0.263987	+	0.964526i	$0.414963\pi$
$797$	−19.8553	+	34.3904i	−0.703311	+	1.21817i	−0.967298	+	0.253644i	$0.918371\pi$
$798$	19.8675	−	11.7956i	0.703301	−	0.417561i
$799$	−4.91994	+	1.31829i	−0.174055	+	0.0466379i
$800$	−2.86128	−	2.86128i	−0.101162	−	0.101162i
$801$	−32.1532	−	21.2326i	−1.13608	−	0.750217i
$802$	12.2703	+	21.2527i	0.433278	+	0.750460i
$803$	23.9000	−	41.3961i	0.843414	−	1.46084i
$804$	11.1198	+	9.07544i	0.392167	+	0.320066i
$805$	−15.1863	+	12.7057i	−0.535246	+	0.447818i
$806$	27.0767	+	1.81548i	0.953736	+	0.0639475i
$807$	16.6926	−	1.68982i	0.587607	−	0.0594844i
$808$	11.5092	+	11.5092i	0.404894	+	0.404894i
$809$		−	48.8303i		−	1.71678i	−0.512996	−	0.858391i	$-0.671464\pi$
$809$		−	48.8303i		−	1.71678i	0.512996	−	0.858391i	$-0.328536\pi$
$810$	26.8748	+	3.24183i	0.944284	+	0.113906i
$811$	−3.65268	−	3.65268i	−0.128263	−	0.128263i	0.640061	−	0.768324i	$-0.278909\pi$
$811$	−3.65268	−	3.65268i	−0.128263	−	0.128263i	−0.768324	+	0.640061i	$0.778909\pi$
$812$	−1.17361	+	1.67098i	−0.0411855	+	0.0586397i
$813$	8.31479	−	51.2263i	0.291612	−	1.79658i
$814$	1.85034	+	0.495796i	0.0648542	+	0.0173776i
$815$	5.09279	−	2.94032i	0.178393	−	0.102995i
$816$	−2.36792	−	1.06516i	−0.0828938	−	0.0372879i
$817$	13.3088	+	49.6693i	0.465618	+	1.73771i
$818$	12.0863			0.422586
$819$	28.5877	−	1.31956i	0.998936	−	0.0461091i
$820$	7.61054			0.265772
$821$	−0.880384	−	3.28564i	−0.0307256	−	0.114669i	0.948860	−	0.315697i	$-0.102238\pi$
$821$	−0.880384	−	3.28564i	−0.0307256	−	0.114669i	−0.979586	+	0.201028i	$0.935572\pi$
$822$	3.47928	+	1.56508i	0.121354	+	0.0545884i
$823$	−35.9572	+	20.7599i	−1.25339	+	0.723646i	−0.971781	−	0.235884i	$-0.924202\pi$
$823$	−35.9572	+	20.7599i	−1.25339	+	0.723646i	−0.281609	+	0.959529i	$0.590868\pi$
$824$	6.47982	+	1.73626i	0.225735	+	0.0604856i
$825$	−6.20990	+	38.2583i	−0.216201	+	1.33198i
$826$	35.9706	+	3.19902i	1.25158	+	0.111308i
$827$	−37.0354	−	37.0354i	−1.28785	−	1.28785i	−0.936093	−	0.351752i	$-0.885586\pi$
$827$	−37.0354	−	37.0354i	−1.28785	−	1.28785i	−0.351752	−	0.936093i	$-0.614414\pi$
$828$	−5.58542	+	4.95215i	−0.194107	+	0.172099i
$829$		−	40.5008i		−	1.40665i	−0.710867	−	0.703326i	$-0.751697\pi$
$829$		−	40.5008i		−	1.40665i	0.710867	−	0.703326i	$-0.248303\pi$
$830$	26.2496	+	26.2496i	0.911137	+	0.911137i
$831$	4.82885	−	0.488832i	0.167511	−	0.0169574i
$832$	−2.99490	−	2.00763i	−0.103829	−	0.0696020i
$833$	−3.56067	−	9.87089i	−0.123370	−	0.342006i
$834$	−8.91745	−	7.27796i	−0.308786	−	0.252015i
$835$	11.6611	−	20.1977i	0.403550	−	0.698970i
$836$	13.9415	+	24.1473i	0.482176	+	0.835153i
$837$	20.9220	+	33.0425i	0.723170	+	1.14212i
$838$	−10.5593	−	10.5593i	−0.364766	−	0.364766i
$839$	48.3997	−	12.9687i	1.67094	−	0.447728i	0.705578	−	0.708633i	$-0.250688\pi$
$839$	48.3997	−	12.9687i	1.67094	−	0.447728i	0.965364	+	0.260905i	$0.0840209\pi$
$840$	−0.167969	−	13.7821i	−0.00579549	−	0.475529i
$841$	−14.2022	+	24.5989i	−0.489730	+	0.848238i
$842$	−12.6064	+	21.8349i	−0.434444	+	0.752480i
$843$	4.15424	+	10.9474i	0.143080	+	0.377047i
$844$	−3.74223	−	2.16058i	−0.128813	−	0.0743702i
$845$	−4.98737	−	38.7812i	−0.171571	−	1.33411i
$846$	−6.76242	−	7.62717i	−0.232497	−	0.262228i
$847$	4.58963	−	51.6070i	0.157702	−	1.77324i
$848$	8.59996	−	4.96519i	0.295324	−	0.170505i
$849$	23.2943	−	51.7849i	0.799458	−	1.77725i
$850$	−5.85922	+	1.56997i	−0.200970	+	0.0538497i
$851$	0.832531	+	0.223076i	0.0285388	+	0.00764695i
$852$	2.63540	+	6.94487i	0.0902872	+	0.237927i
$853$	11.0392	−	11.0392i	0.377976	−	0.377976i	−0.492395	−	0.870372i	$-0.663879\pi$
$853$	11.0392	−	11.0392i	0.377976	−	0.377976i	0.870372	+	0.492395i	$0.163879\pi$
$854$	6.24514	+	35.7175i	0.213704	+	1.22223i
$855$	14.3899	−	43.1591i	0.492123	−	1.47601i
$856$	2.53871	+	9.47458i	0.0867712	+	0.323835i
$857$	5.74258	−	9.94643i	0.196163	−	0.339764i	−0.751118	−	0.660168i	$-0.770485\pi$
$857$	5.74258	−	9.94643i	0.196163	−	0.339764i	0.947281	+	0.320404i	$0.103819\pi$
$858$	1.17187	+	34.5159i	0.0400070	+	1.17835i
$859$	14.0377	+	24.3139i	0.478959	+	0.829581i	0.999709	−	0.0241283i	$-0.00768103\pi$
$859$	14.0377	+	24.3139i	0.478959	+	0.829581i	−0.520750	+	0.853709i	$0.674348\pi$
$860$	29.6296	+	7.93923i	1.01036	+	0.270725i
$861$	8.29850	+	8.09866i	0.282812	+	0.276002i
$862$	8.92631	+	5.15361i	0.304031	+	0.175533i
$863$	−43.8444	−	11.7481i	−1.49248	−	0.399909i	−0.581906	−	0.813256i	$-0.697693\pi$
$863$	−43.8444	−	11.7481i	−1.49248	−	0.399909i	−0.910574	+	0.413347i	$0.864360\pi$
$864$	−0.212277	−	5.19181i	−0.00722183	−	0.176629i
$865$	20.1397	+	5.39642i	0.684771	+	0.183484i
$866$	−1.64095	+	6.12411i	−0.0557618	+	0.208106i
$867$	20.7299	−	14.9401i	0.704024	−	0.507393i
$868$	15.2730	−	12.7782i	0.518398	−	0.433722i
$869$	9.43421	−	35.2090i	0.320034	−	1.19438i
$870$	0.404944	+	4.00018i	0.0137289	+	0.135619i
$871$	29.3132	−	5.78508i	0.993239	−	0.196020i
$872$	−5.06129	−	2.92214i	−0.171397	−	0.0989560i
$873$	−36.5005	−	24.1034i	−1.23536	−	0.815777i
$874$	6.27276	+	10.8647i	0.212179	+	0.367505i
$875$	4.86912	+	5.81973i	0.164606	+	0.196743i
$876$	5.31154	+	13.9971i	0.179460	+	0.472919i
$877$	−17.7095	−	17.7095i	−0.598006	−	0.598006i	0.341776	−	0.939782i	$-0.388972\pi$
$877$	−17.7095	−	17.7095i	−0.598006	−	0.598006i	−0.939782	+	0.341776i	$0.888972\pi$
$878$	−1.51016	+	5.63599i	−0.0509654	+	0.190206i
$879$	12.4189	+	2.01577i	0.418879	+	0.0679903i
$880$	16.6332			0.560706
$881$	−9.55461	−	16.5491i	−0.321903	−	0.557552i	0.658978	−	0.752163i	$-0.270989\pi$
$881$	−9.55461	−	16.5491i	−0.321903	−	0.557552i	−0.980881	+	0.194610i	$0.937656\pi$
$882$	14.4829	−	15.2067i	0.487666	−	0.512037i
$883$		−	12.4719i		−	0.419712i	−0.977732	−	0.209856i	$-0.932701\pi$
$883$		−	12.4719i		−	0.419712i	0.977732	−	0.209856i	$-0.0672995\pi$
$884$	−4.85114	+	2.38328i	−0.163162	+	0.0801585i
$885$	57.6861	−	41.5746i	1.93910	−	1.39752i
$886$	−15.1023	−	15.1023i	−0.507372	−	0.507372i
$887$	18.1246	+	10.4642i	0.608564	+	0.351355i	0.772403	−	0.635132i	$-0.219054\pi$
$887$	18.1246	+	10.4642i	0.608564	+	0.351355i	−0.163839	+	0.986487i	$0.552388\pi$
$888$	−0.486735	+	0.350792i	−0.0163337	+	0.0117718i
$889$	32.0713	−	14.8991i	1.07564	−	0.499701i
$890$	9.99830	+	37.3142i	0.335144	+	1.25077i
$891$	−39.1552	+	30.7256i	−1.31175	+	1.02935i
$892$	2.65646	+	9.91404i	0.0889448	+	0.331947i
$893$	−14.8363	+	8.56577i	−0.496479	+	0.286643i
$894$	1.53816	+	2.13425i	0.0514438	+	0.0713799i
$895$	−26.9201	−	7.21321i	−0.899839	−	0.241111i
$896$	−2.60621	+	0.455692i	−0.0870675	+	0.0152236i
$897$	0.527266	+	15.5299i	0.0176049	+	0.518529i
$898$	−12.3054	−	21.3137i	−0.410638	−	0.711246i
$899$	−4.10749	+	4.10749i	−0.136992	+	0.136992i
$900$	−8.05346	−	9.08331i	−0.268449	−	0.302777i
$901$		−	14.8863i		−	0.495935i
$902$	−9.89461	+	9.89461i	−0.329454	+	0.329454i
$903$	23.8596	+	40.1869i	0.793996	+	1.33734i
$904$	−1.90857	−	7.12288i	−0.0634781	−	0.236903i
$905$	1.18908	−	4.43770i	0.0395263	−	0.147514i
$906$	−19.0410	+	1.92755i	−0.632595	+	0.0640386i
$907$		−	35.6158i		−	1.18260i	−0.806450	−	0.591302i	$-0.798614\pi$
$907$		−	35.6158i		−	1.18260i	0.806450	−	0.591302i	$-0.201386\pi$
$908$	−15.5188	+	4.15825i	−0.515009	+	0.137996i
$909$	32.3943	+	36.5368i	1.07445	+	1.21185i
$910$	−22.3236	−	18.0245i	−0.740021	−	0.597508i
$911$			29.3542i			0.972549i	0.873806	+	0.486274i	$0.161644\pi$
$911$			29.3542i			0.972549i	−0.873806	+	0.486274i	$0.838356\pi$
$912$	−8.62016	−	1.39918i	−0.285442	−	0.0463315i
$913$	−68.2551			−2.25891
$914$	−5.26721	−	9.12308i	−0.174224	−	0.301765i
$915$	55.3122	+	45.1429i	1.82856	+	1.49238i
$916$	−6.04417	+	1.61953i	−0.199705	+	0.0535108i
$917$	25.7147	−	11.9461i	0.849174	−	0.394494i
$918$	−6.89928	−	3.61585i	−0.227710	−	0.119341i
$919$	9.38818			0.309687			0.154844	−	0.987939i	$-0.450513\pi$
$919$	9.38818			0.309687			0.154844	+	0.987939i	$0.450513\pi$
$920$	7.48387			0.246736
$921$	−1.59475	+	0.605164i	−0.0525486	+	0.0199408i
$922$	0.195516	−	0.112881i	0.00643898	−	0.00371754i
$923$	14.6347	+	4.99231i	0.481708	+	0.164324i
$924$	18.1368	+	17.7000i	0.596657	+	0.582288i
$925$	−0.362778	+	1.35391i	−0.0119281	+	0.0445162i
$926$	−0.853837	−	0.492963i	−0.0280588	−	0.0161998i
$927$	19.0920	+	6.36553i	0.627063	+	0.209072i
$928$	0.745482	−	0.199751i	0.0244716	−	0.00655716i
$929$	−15.1417	+	15.1417i	−0.496784	+	0.496784i	−0.910435	−	0.413652i	$-0.864253\pi$
$929$	−15.1417	+	15.1417i	−0.496784	+	0.496784i	0.413652	+	0.910435i	$0.364253\pi$
$930$	6.28217	−	38.7036i	0.206000	−	1.26914i
$931$	−20.1607	−	28.9690i	−0.660741	−	0.949421i
$932$	−16.6088	−	9.58909i	−0.544039	−	0.314101i
$933$	−9.38508	+	6.76387i	−0.307254	+	0.221439i
$934$	0.144046	−	0.144046i	0.00471334	−	0.00471334i
$935$	12.4672	−	21.5938i	0.407720	−	0.706191i
$936$	−8.60722	−	6.55101i	−0.281336	−	0.214127i
$937$	41.5837			1.35848			0.679240	−	0.733916i	$-0.262310\pi$
$937$	41.5837			1.35848			0.679240	+	0.733916i	$0.262310\pi$
$938$	12.6013	−	17.9418i	0.411449	−	0.585819i
$939$	0.815750	+	8.05826i	0.0266210	+	0.262971i
$940$			10.2196i			0.333327i
$941$	11.1875	+	41.7523i	0.364702	+	1.36109i	0.867825	+	0.496871i	$0.165518\pi$
$941$	11.1875	+	41.7523i	0.364702	+	1.36109i	−0.503123	+	0.864215i	$0.667816\pi$
$942$	19.8447	+	16.1962i	0.646575	+	0.527701i
$943$	−4.45193	+	4.45193i	−0.144975	+	0.144975i
$944$	−9.65149	−	9.65149i	−0.314129	−	0.314129i
$945$	1.97727	−	41.3022i	0.0643207	−	1.34356i
$946$	−48.8439	+	28.2001i	−1.58805	+	0.916863i
$947$	−44.1149	+	11.8205i	−1.43354	+	0.384116i	−0.890267	−	0.455440i	$-0.849482\pi$
$947$	−44.1149	+	11.8205i	−1.43354	+	0.384116i	−0.543274	+	0.839556i	$0.682815\pi$
$948$	6.67501	+	9.26179i	0.216794	+	0.300809i
$949$	29.4957	+	10.0618i	0.957472	+	0.326620i
$950$	−17.6688	+	10.2011i	−0.573252	+	0.330967i
$951$	0.0938047	+	0.0765585i	0.00304183	+	0.00248258i
$952$	−1.36185	+	3.72502i	−0.0441378	+	0.120729i
$953$	−30.2452	+	52.3862i	−0.979737	+	1.69695i	−0.316414	+	0.948621i	$0.602479\pi$
$953$	−30.2452	+	52.3862i	−0.979737	+	1.69695i	−0.663323	+	0.748333i	$0.730855\pi$
$954$	26.6470	−	13.3211i	0.862728	−	0.431286i
$955$	−7.73828	+	28.8797i	−0.250405	+	0.934524i
$956$	3.77610	−	14.0926i	0.122128	−	0.455787i
$957$	−5.72718	−	4.67423i	−0.185133	−	0.151096i
$958$	8.51282	−	14.7446i	0.275037	−	0.476378i
$959$	2.00102	−	5.47333i	0.0646165	−	0.176743i
$960$	−3.29396	+	4.03599i	−0.106312	+	0.130261i
$961$	22.2131	−	12.8248i	0.716553	−	0.413702i
$962$	−0.0835531	+	1.24614i	−0.00269386	+	0.0401772i
$963$	5.89733	+	28.8294i	0.190039	+	0.929015i
$964$	−10.3139	+	2.76360i	−0.332188	+	0.0890095i
$965$	−10.1768	+	5.87558i	−0.327603	+	0.189142i
$966$	8.16038	+	7.96387i	0.262556	+	0.256233i
$967$	27.7443	+	27.7443i	0.892197	+	0.892197i	0.994730	−	0.102533i	$-0.0326947\pi$
$967$	27.7443	+	27.7443i	0.892197	+	0.892197i	−0.102533	+	0.994730i	$0.532695\pi$
$968$	−13.8470	+	13.8470i	−0.445059	+	0.445059i
$969$	−8.27755	+	10.1422i	−0.265913	+	0.325815i
$970$	11.3501	+	42.3593i	0.364431	+	1.36008i
$971$		−	19.6861i		−	0.631756i	−0.948800	−	0.315878i	$-0.897701\pi$
$971$		−	19.6861i		−	0.631756i	0.948800	−	0.315878i	$-0.102299\pi$
$972$	0.298648	−	15.5856i	0.00957915	−	0.499908i
$973$	−10.1055	+	14.3882i	−0.323968	+	0.461265i
$974$	17.9017			0.573608
$975$	−25.2556	+	0.857468i	−0.808826	+	0.0274610i
$976$	6.85237	−	11.8687i	0.219339	−	0.379907i
$977$	39.7785	−	39.7785i	1.27263	−	1.27263i	0.327924	−	0.944704i	$-0.393651\pi$
$977$	39.7785	−	39.7785i	1.27263	−	1.27263i	0.944704	−	0.327924i	$-0.106349\pi$
$978$	−1.98000	−	2.74731i	−0.0633134	−	0.0878494i
$979$	−61.5118	−	35.5139i	−1.96593	−	1.13503i
$980$	−20.9792	+	1.77480i	−0.670156	+	0.0566941i
$981$	−14.6306	−	9.66147i	−0.467121	−	0.308467i
$982$	24.3008	−	24.3008i	0.775471	−	0.775471i
$983$	−38.2739	+	10.2555i	−1.22075	+	0.327098i	−0.810970	−	0.585087i	$-0.801060\pi$
$983$	−38.2739	+	10.2555i	−1.22075	+	0.327098i	−0.409777	+	0.912186i	$0.634394\pi$
$984$	−0.441407	−	4.36037i	−0.0140715	−	0.139003i
$985$	−5.17348	−	2.98691i	−0.164841	−	0.0951708i
$986$	0.299441	−	1.11753i	0.00953613	−	0.0355893i
$987$	−10.8751	+	11.1434i	−0.346157	+	0.354699i
$988$	−13.6857	+	11.9658i	−0.435402	+	0.380684i
$989$	−21.9766	+	12.6882i	−0.698815	+	0.403461i
$990$	49.8098	+	2.99336i	1.58306	+	0.0951353i
$991$	−57.8876			−1.83886			−0.919431	−	0.393252i	$-0.871350\pi$
$991$	−57.8876			−1.83886			−0.919431	+	0.393252i	$0.871350\pi$
$992$	−7.52659			−0.238969
$993$	6.52920	+	17.2059i	0.207198	+	0.546013i
$994$	10.2904	−	4.78052i	0.326391	−	0.151629i
$995$	−40.1409	+	10.7557i	−1.27255	+	0.340979i
$996$	13.5169	−	16.5618i	0.428300	−	0.524782i
$997$	0.985872	+	1.70758i	0.0312229	+	0.0540796i	0.881215	−	0.472716i	$-0.156727\pi$
$997$	0.985872	+	1.70758i	0.0312229	+	0.0540796i	−0.849992	+	0.526796i	$0.823393\pi$
$998$	−16.0029			−0.506563
$999$	−1.52070	+	0.962886i	−0.0481129	+	0.0304644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.16	✓	152
3.2	odd	2	inner	546.2.bw.a.11.35	yes	152
7.2	even	3		546.2.ch.a.401.3	yes	152
13.6	odd	12		546.2.ch.a.305.28	yes	152
21.2	odd	6		546.2.ch.a.401.28	yes	152
39.32	even	12		546.2.ch.a.305.3	yes	152
91.58	odd	12	inner	546.2.bw.a.149.35	yes	152
273.149	even	12	inner	546.2.bw.a.149.16	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.16	✓	152	1.1	even	1	trivial
546.2.bw.a.11.35	yes	152	3.2	odd	2	inner
546.2.bw.a.149.16	yes	152	273.149	even	12	inner
546.2.bw.a.149.35	yes	152	91.58	odd	12	inner
546.2.ch.a.305.3	yes	152	39.32	even	12
546.2.ch.a.305.28	yes	152	13.6	odd	12
546.2.ch.a.401.3	yes	152	7.2	even	3
546.2.ch.a.401.28	yes	152	21.2	odd	6

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

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.57960 + 0.710547i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.90525 + 0.778459i) q^{5} +(0.277506 - 1.70968i) q^{6} +(-2.63535 - 0.234373i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.99025 + 2.24475i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.57960 + 0.710547i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(2.90525 + 0.778459i) q^{5} +(0.277506 - 1.70968i) q^{6} +(-2.63535 - 0.234373i) q^{7} +(0.707107 + 0.707107i) q^{8} +(1.99025 + 2.24475i) q^{9} -3.00773i q^{10} +(3.91041 + 3.91041i) q^{11} +(-1.72324 + 0.174447i) q^{12} +(-2.00763 + 2.99490i) q^{13} +(0.455692 + 2.60621i) q^{14} +(4.03599 + 3.29396i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.749533 - 1.29823i) q^{17} +(1.65315 - 2.50342i) q^{18} +(-3.56522 - 3.56522i) q^{19} +(-2.90525 + 0.778459i) q^{20} +(-3.99626 - 2.24275i) q^{21} +(2.76508 - 4.78925i) q^{22} +(1.24411 - 2.15485i) q^{23} +(0.614511 + 1.61938i) q^{24} +(3.50434 + 2.02323i) q^{25} +(3.41246 + 1.16408i) q^{26} +(1.54878 + 4.95997i) q^{27} +(2.39947 - 1.11470i) q^{28} +(-0.668381 + 0.385890i) q^{29} +(2.13713 - 4.75100i) q^{30} +(7.27013 - 1.94802i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(3.39834 + 8.95539i) q^{33} +(-1.06000 + 1.06000i) q^{34} +(-7.47389 - 2.73242i) q^{35} +(-2.84598 - 0.948890i) q^{36} +(0.0896532 + 0.334590i) q^{37} +(-2.52099 + 4.36649i) q^{38} +(-5.29926 + 3.30422i) q^{39} +(1.50387 + 2.60477i) q^{40} +(-2.44411 - 0.654896i) q^{41} +(-1.13203 + 4.44055i) q^{42} +(-8.83229 - 5.09933i) q^{43} +(-5.34172 - 1.43131i) q^{44} +(4.03471 + 8.07089i) q^{45} +(-2.40343 - 0.643996i) q^{46} +(0.879410 - 3.28200i) q^{47} +(1.40515 - 1.01270i) q^{48} +(6.89014 + 1.23531i) q^{49} +(1.04730 - 3.90858i) q^{50} +(-0.261507 - 2.58326i) q^{51} +(0.241209 - 3.59747i) q^{52} +(8.59996 + 4.96519i) q^{53} +(4.39010 - 2.77974i) q^{54} +(8.31661 + 14.4048i) q^{55} +(-1.69775 - 2.02920i) q^{56} +(-3.09835 - 8.16486i) q^{57} +(0.545731 + 0.545731i) q^{58} +(3.53269 - 13.1842i) q^{59} +(-5.14225 - 0.834663i) q^{60} +13.7047 q^{61} +(-3.76329 - 6.51822i) q^{62} +(-4.71889 - 6.38217i) q^{63} +1.00000i q^{64} +(-8.16407 + 7.13807i) q^{65} +(7.77069 - 5.60037i) q^{66} +(-5.85967 - 5.85967i) q^{67} +(1.29823 + 0.749533i) q^{68} +(3.49631 - 2.51980i) q^{69} +(-0.704932 + 7.92643i) q^{70} +(-1.10997 - 4.14248i) q^{71} +(-0.179963 + 2.99460i) q^{72} +(-2.23711 - 8.34901i) q^{73} +(0.299986 - 0.173197i) q^{74} +(4.09784 + 5.68588i) q^{75} +(4.87018 + 1.30496i) q^{76} +(-9.38880 - 11.2218i) q^{77} +(4.56318 + 4.26350i) q^{78} +(-3.29566 - 5.70825i) q^{79} +(2.12679 - 2.12679i) q^{80} +(-1.07783 + 8.93523i) q^{81} +2.53033i q^{82} +(-8.72737 + 8.72737i) q^{83} +(4.58224 - 0.0558458i) q^{84} +(-1.16696 - 4.35516i) q^{85} +(-2.63961 + 9.85114i) q^{86} +(-1.32996 + 0.134634i) q^{87} +5.53015i q^{88} +(-12.4061 + 3.32420i) q^{89} +(6.75162 - 5.98613i) q^{90} +(5.99273 - 7.42207i) q^{91} +2.48821i q^{92} +(12.8680 + 2.08867i) q^{93} -3.39778 q^{94} +(-7.58247 - 13.1332i) q^{95} +(-1.34187 - 1.09516i) q^{96} +(-14.0835 + 3.77366i) q^{97} +(-0.590081 - 6.97508i) q^{98} +(-0.995222 + 16.5606i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

L-functions

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