LMFDB - Embedded newform 273.2.bh.a.131.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(131,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("273.131");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bh (of order $6$, degree $2$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			131.9
Character	$\chi$	$=$	273.131
Dual form			273.2.bh.a.248.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.15260 - 0.665454i) q^{2} +(-0.732991 + 1.56931i) q^{3} +(-0.114341 - 0.198044i) q^{4} +(-0.0955042 + 0.165418i) q^{5} +(1.88915 - 1.32101i) q^{6} +(2.46727 - 0.955290i) q^{7} +2.96617i q^{8} +(-1.92545 - 2.30058i) q^{9} +O(q^{10})$	\(q+(-1.15260 - 0.665454i) q^{2} +(-0.732991 + 1.56931i) q^{3} +(-0.114341 - 0.198044i) q^{4} +(-0.0955042 + 0.165418i) q^{5} +(1.88915 - 1.32101i) q^{6} +(2.46727 - 0.955290i) q^{7} +2.96617i q^{8} +(-1.92545 - 2.30058i) q^{9} +(0.220156 - 0.127107i) q^{10} +(-2.17942 + 1.25829i) q^{11} +(0.394602 - 0.0342713i) q^{12} +1.00000i q^{13} +(-3.47948 - 0.540787i) q^{14} +(-0.189588 - 0.271125i) q^{15} +(1.74517 - 3.02272i) q^{16} +(3.30158 + 5.71850i) q^{17} +(0.688346 + 3.93294i) q^{18} +(5.52593 + 3.19039i) q^{19} +0.0436801 q^{20} +(-0.309342 + 4.57212i) q^{21} +3.34934 q^{22} +(0.428618 + 0.247463i) q^{23} +(-4.65483 - 2.17418i) q^{24} +(2.48176 + 4.29853i) q^{25} +(0.665454 - 1.15260i) q^{26} +(5.02165 - 1.33532i) q^{27} +(-0.471299 - 0.379399i) q^{28} +3.66565i q^{29} +(0.0380979 + 0.438662i) q^{30} +(-7.59527 + 4.38513i) q^{31} +(1.11459 - 0.643508i) q^{32} +(-0.377147 - 4.34250i) q^{33} -8.78820i q^{34} +(-0.0776123 + 0.499365i) q^{35} +(-0.235458 + 0.644373i) q^{36} +(0.433184 - 0.750296i) q^{37} +(-4.24612 - 7.35450i) q^{38} +(-1.56931 - 0.732991i) q^{39} +(-0.490659 - 0.283282i) q^{40} +3.55741 q^{41} +(3.39909 - 5.06398i) q^{42} -2.13560 q^{43} +(0.498394 + 0.287748i) q^{44} +(0.564445 - 0.0987896i) q^{45} +(-0.329351 - 0.570452i) q^{46} +(4.61080 - 7.98614i) q^{47} +(3.46439 + 4.95434i) q^{48} +(5.17484 - 4.71392i) q^{49} -6.60599i q^{50} +(-11.3941 + 0.989581i) q^{51} +(0.198044 - 0.114341i) q^{52} +(-5.02935 + 2.90370i) q^{53} +(-6.67655 - 1.80258i) q^{54} -0.480688i q^{55} +(2.83356 + 7.31835i) q^{56} +(-9.05716 + 6.33334i) q^{57} +(2.43932 - 4.22503i) q^{58} +(-5.58681 - 9.67665i) q^{59} +(-0.0320171 + 0.0685475i) q^{60} +(1.06610 + 0.615513i) q^{61} +11.6724 q^{62} +(-6.94832 - 3.83678i) q^{63} -8.69359 q^{64} +(-0.165418 - 0.0955042i) q^{65} +(-2.45504 + 5.25614i) q^{66} +(2.38054 + 4.12321i) q^{67} +(0.755009 - 1.30771i) q^{68} +(-0.702519 + 0.491246i) q^{69} +(0.421761 - 0.523922i) q^{70} -5.29316i q^{71} +(6.82390 - 5.71121i) q^{72} +(6.07426 - 3.50698i) q^{73} +(-0.998576 + 0.576528i) q^{74} +(-8.56482 + 0.743857i) q^{75} -1.45917i q^{76} +(-4.17519 + 5.18653i) q^{77} +(1.32101 + 1.88915i) q^{78} +(-5.62114 + 9.73610i) q^{79} +(0.333342 + 0.577366i) q^{80} +(-1.58529 + 8.85928i) q^{81} +(-4.10028 - 2.36730i) q^{82} -10.2566 q^{83} +(0.940852 - 0.461517i) q^{84} -1.26126 q^{85} +(2.46150 + 1.42115i) q^{86} +(-5.75253 - 2.68689i) q^{87} +(-3.73231 - 6.46455i) q^{88} +(3.24190 - 5.61513i) q^{89} +(-0.716320 - 0.261748i) q^{90} +(0.955290 + 2.46727i) q^{91} -0.113180i q^{92} +(-1.31435 - 15.1336i) q^{93} +(-10.6288 + 6.13656i) q^{94} +(-1.05550 + 0.609392i) q^{95} +(0.192879 + 2.22082i) q^{96} -16.0239i q^{97} +(-9.10142 + 1.98965i) q^{98} +(7.09116 + 2.59115i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	$ 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) $ 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.15260	−	0.665454i	−0.815012	−	0.470547i	0.0336814	−	0.999433i	$-0.489277\pi$
$2$	−1.15260	−	0.665454i	−0.815012	−	0.470547i	−0.848693	+	0.528885i	$0.822610\pi$
$3$	−0.732991	+	1.56931i	−0.423192	+	0.906040i
$3$	−0.732991	+	1.56931i	−0.423192	+	0.906040i
$4$	−0.114341	−	0.198044i	−0.0571704	−	0.0990220i
$5$	−0.0955042	+	0.165418i	−0.0427108	+	0.0739772i	−0.886591	−	0.462555i	$-0.846933\pi$
$5$	−0.0955042	+	0.165418i	−0.0427108	+	0.0739772i	0.843880	+	0.536532i	$0.180266\pi$
$6$	1.88915	−	1.32101i	0.771242	−	0.539301i
$7$	2.46727	−	0.955290i	0.932540	−	0.361066i
$7$	2.46727	−	0.955290i	0.932540	−	0.361066i
$8$			2.96617i			1.04870i
$9$	−1.92545	−	2.30058i	−0.641816	−	0.766858i
$10$	0.220156	−	0.127107i	0.0696196	−	0.0401949i
$11$	−2.17942	+	1.25829i	−0.657121	+	0.379389i	−0.791179	−	0.611584i	$-0.790532\pi$
$11$	−2.17942	+	1.25829i	−0.657121	+	0.379389i	0.134058	+	0.990973i	$0.457199\pi$
$12$	0.394602	−	0.0342713i	0.113912	−	0.00989328i
$13$			1.00000i			0.277350i
$13$			1.00000i			0.277350i
$14$	−3.47948	−	0.540787i	−0.929930	−	0.144531i
$15$	−0.189588	−	0.271125i	−0.0489515	−	0.0700043i
$16$	1.74517	−	3.02272i	0.436293	−	0.755681i
$17$	3.30158	+	5.71850i	0.800750	+	1.38694i	0.919123	+	0.393971i	$0.128899\pi$
$17$	3.30158	+	5.71850i	0.800750	+	1.38694i	−0.118373	+	0.992969i	$0.537768\pi$
$18$	0.688346	+	3.93294i	0.162245	+	0.927004i
$19$	5.52593	+	3.19039i	1.26773	+	0.731927i	0.974559	−	0.224132i	$-0.0719547\pi$
$19$	5.52593	+	3.19039i	1.26773	+	0.731927i	0.293175	+	0.956059i	$0.405288\pi$
$20$	0.0436801			0.00976716
$21$	−0.309342	+	4.57212i	−0.0675040	+	0.997719i
$22$	3.34934			0.714082
$23$	0.428618	+	0.247463i	0.0893731	+	0.0515996i	0.544020	−	0.839072i	$-0.316901\pi$
$23$	0.428618	+	0.247463i	0.0893731	+	0.0515996i	−0.454647	+	0.890672i	$0.650235\pi$
$24$	−4.65483	−	2.17418i	−0.950164	−	0.443802i
$25$	2.48176	+	4.29853i	0.496352	+	0.859706i
$26$	0.665454	−	1.15260i	0.130506	−	0.226044i
$27$	5.02165	−	1.33532i	0.966416	−	0.256983i
$28$	−0.471299	−	0.379399i	−0.0890671	−	0.0716997i
$29$			3.66565i			0.680694i	0.940300	+	0.340347i	$0.110545\pi$
$29$			3.66565i			0.680694i	−0.940300	+	0.340347i	$0.889455\pi$
$30$	0.0380979	+	0.438662i	0.00695569	+	0.0800883i
$31$	−7.59527	+	4.38513i	−1.36415	+	0.787593i	−0.990173	−	0.139845i	$-0.955340\pi$
$31$	−7.59527	+	4.38513i	−1.36415	+	0.787593i	−0.373978	+	0.927438i	$0.622006\pi$
$32$	1.11459	−	0.643508i	0.197033	−	0.113757i
$33$	−0.377147	−	4.34250i	−0.0656529	−	0.755932i
$34$		−	8.78820i		−	1.50716i
$35$	−0.0776123	+	0.499365i	−0.0131189	+	0.0844082i
$36$	−0.235458	+	0.644373i	−0.0392430	+	0.107395i
$37$	0.433184	−	0.750296i	0.0712150	−	0.123348i	−0.828219	−	0.560404i	$-0.810646\pi$
$37$	0.433184	−	0.750296i	0.0712150	−	0.123348i	0.899434	+	0.437057i	$0.143979\pi$
$38$	−4.24612	−	7.35450i	−0.688812	−	1.19306i
$39$	−1.56931	−	0.732991i	−0.251290	−	0.117372i
$40$	−0.490659	−	0.283282i	−0.0775800	−	0.0447908i
$41$	3.55741			0.555575			0.277787	−	0.960643i	$-0.410399\pi$
$41$	3.55741			0.555575			0.277787	+	0.960643i	$0.410399\pi$
$42$	3.39909	−	5.06398i	0.524491	−	0.781389i
$43$	−2.13560			−0.325676			−0.162838	−	0.986653i	$-0.552065\pi$
$43$	−2.13560			−0.325676			−0.162838	+	0.986653i	$0.552065\pi$
$44$	0.498394	+	0.287748i	0.0751357	+	0.0433796i
$45$	0.564445	−	0.0987896i	0.0841426	−	0.0147267i
$46$	−0.329351	−	0.570452i	−0.0485601	−	0.0841086i
$47$	4.61080	−	7.98614i	0.672554	−	1.16490i	−0.304623	−	0.952473i	$-0.598530\pi$
$47$	4.61080	−	7.98614i	0.672554	−	1.16490i	0.977177	−	0.212425i	$-0.0681362\pi$
$48$	3.46439	+	4.95434i	0.500041	+	0.715097i
$49$	5.17484	−	4.71392i	0.739263	−	0.673417i
$50$		−	6.60599i		−	0.934228i
$51$	−11.3941	+	0.989581i	−1.59549	+	0.138569i
$52$	0.198044	−	0.114341i	0.0274638	−	0.0158562i
$53$	−5.02935	+	2.90370i	−0.690835	+	0.398854i	−0.803925	−	0.594731i	$-0.797258\pi$
$53$	−5.02935	+	2.90370i	−0.690835	+	0.398854i	0.113090	+	0.993585i	$0.463925\pi$
$54$	−6.67655	−	1.80258i	−0.908563	−	0.245301i
$55$		−	0.480688i		−	0.0648160i
$56$	2.83356	+	7.31835i	0.378650	+	0.977955i
$57$	−9.05716	+	6.33334i	−1.19965	+	0.838872i
$58$	2.43932	−	4.22503i	0.320299	−	0.554774i
$59$	−5.58681	−	9.67665i	−0.727341	−	1.25979i	−0.958003	−	0.286758i	$-0.907422\pi$
$59$	−5.58681	−	9.67665i	−0.727341	−	1.25979i	0.230662	−	0.973034i	$-0.425911\pi$
$60$	−0.0320171	+	0.0685475i	−0.00413339	+	0.00884944i
$61$	1.06610	+	0.615513i	0.136500	+	0.0788084i	0.566695	−	0.823928i	$-0.308222\pi$
$61$	1.06610	+	0.615513i	0.136500	+	0.0788084i	−0.430195	+	0.902736i	$0.641555\pi$
$62$	11.6724			1.48240
$63$	−6.94832	−	3.83678i	−0.875406	−	0.483388i
$64$	−8.69359			−1.08670
$65$	−0.165418	−	0.0955042i	−0.0205176	−	0.0118458i
$66$	−2.45504	+	5.25614i	−0.302194	+	0.646987i
$67$	2.38054	+	4.12321i	0.290829	+	0.503730i	0.974006	−	0.226522i	$-0.0727356\pi$
$67$	2.38054	+	4.12321i	0.290829	+	0.503730i	−0.683177	+	0.730253i	$0.739402\pi$
$68$	0.755009	−	1.30771i	0.0915583	−	0.158584i
$69$	−0.702519	+	0.491246i	−0.0845733	+	0.0591390i
$70$	0.421761	−	0.523922i	0.0504101	−	0.0626206i
$71$		−	5.29316i		−	0.628182i	−0.949393	−	0.314091i	$-0.898300\pi$
$71$		−	5.29316i		−	0.628182i	0.949393	−	0.314091i	$-0.101700\pi$
$72$	6.82390	−	5.71121i	0.804205	−	0.673073i
$73$	6.07426	−	3.50698i	0.710938	−	0.410460i	−0.100470	−	0.994940i	$-0.532035\pi$
$73$	6.07426	−	3.50698i	0.710938	−	0.410460i	0.811408	+	0.584480i	$0.198701\pi$
$74$	−0.998576	+	0.576528i	−0.116082	+	0.0670201i
$75$	−8.56482	+	0.743857i	−0.988980	+	0.0858932i
$76$		−	1.45917i		−	0.167378i
$77$	−4.17519	+	5.18653i	−0.475807	+	0.591059i
$78$	1.32101	+	1.88915i	0.149575	+	0.213904i
$79$	−5.62114	+	9.73610i	−0.632428	+	1.09540i	0.354626	+	0.935008i	$0.384608\pi$
$79$	−5.62114	+	9.73610i	−0.632428	+	1.09540i	−0.987054	+	0.160389i	$0.948725\pi$
$80$	0.333342	+	0.577366i	0.0372688	+	0.0645515i
$81$	−1.58529	+	8.85928i	−0.176144	+	0.984364i
$82$	−4.10028	−	2.36730i	−0.452800	−	0.261424i
$83$	−10.2566			−1.12581			−0.562904	−	0.826522i	$-0.690316\pi$
$83$	−10.2566			−1.12581			−0.562904	+	0.826522i	$0.690316\pi$
$84$	0.940852	−	0.461517i	0.102655	−	0.0503556i
$85$	−1.26126			−0.136803
$86$	2.46150	+	1.42115i	0.265430	+	0.153246i
$87$	−5.75253	−	2.68689i	−0.616736	−	0.288065i
$88$	−3.73231	−	6.46455i	−0.397865	−	0.689123i
$89$	3.24190	−	5.61513i	0.343640	−	0.595203i	−0.641465	−	0.767152i	$-0.721673\pi$
$89$	3.24190	−	5.61513i	0.343640	−	0.595203i	0.985106	+	0.171949i	$0.0550065\pi$
$90$	−0.716320	−	0.261748i	−0.0755068	−	0.0275906i
$91$	0.955290	+	2.46727i	0.100142	+	0.258640i
$92$		−	0.113180i		−	0.0117999i
$93$	−1.31435	−	15.1336i	−0.136292	−	1.56928i
$94$	−10.6288	+	6.13656i	−1.09628	+	0.632937i
$95$	−1.05550	+	0.609392i	−0.108292	+	0.0625223i
$96$	0.192879	+	2.22082i	0.0196856	+	0.226661i
$97$		−	16.0239i		−	1.62698i	−0.581576	−	0.813492i	$-0.697564\pi$
$97$		−	16.0239i		−	1.62698i	0.581576	−	0.813492i	$-0.302436\pi$
$98$	−9.10142	+	1.98965i	−0.919383	+	0.200985i
$99$	7.09116	+	2.59115i	0.712689	+	0.260421i
$100$	0.567532	−	0.982994i	0.0567532	−	0.0982994i
$101$	8.89291	+	15.4030i	0.884878	+	1.53265i	0.845853	+	0.533415i	$0.179092\pi$
$101$	8.89291	+	15.4030i	0.884878	+	1.53265i	0.0390245	+	0.999238i	$0.487575\pi$
$102$	13.7914	+	6.44167i	1.36555	+	0.637820i
$103$	4.33872	+	2.50496i	0.427507	+	0.246821i	0.698284	−	0.715821i	$-0.253947\pi$
$103$	4.33872	+	2.50496i	0.427507	+	0.246821i	−0.270777	+	0.962642i	$0.587281\pi$
$104$	−2.96617			−0.290857
$105$	−0.726769	−	0.487828i	−0.0709254	−	0.0476071i
$106$	7.72911			0.750718
$107$	5.04072	+	2.91026i	0.487305	+	0.281346i	0.723456	−	0.690371i	$-0.242553\pi$
$107$	5.04072	+	2.91026i	0.487305	+	0.281346i	−0.236151	+	0.971716i	$0.575886\pi$
$108$	−0.838631	−	0.841825i	−0.0806973	−	0.0810046i
$109$	7.73973	+	13.4056i	0.741331	+	1.28402i	0.951889	+	0.306442i	$0.0991387\pi$
$109$	7.73973	+	13.4056i	0.741331	+	1.28402i	−0.210558	+	0.977581i	$0.567528\pi$
$110$	−0.319876	+	0.554042i	−0.0304990	+	0.0528258i
$111$	0.859926	+	1.22976i	0.0816205	+	0.116724i
$112$	1.41823	−	9.12502i	0.134010	−	0.862234i
$113$		−	18.6070i		−	1.75040i	−0.483760	−	0.875201i	$-0.660729\pi$
$113$		−	18.6070i		−	1.75040i	0.483760	−	0.875201i	$-0.339271\pi$
$114$	14.6538	−	1.27269i	1.37246	−	0.119198i
$115$	−0.0818697	+	0.0472675i	−0.00763439	+	0.00440772i
$116$	0.725960	−	0.419133i	0.0674037	−	0.0389155i
$117$	2.30058	−	1.92545i	0.212688	−	0.178008i
$118$			14.8711i			1.36899i
$119$	13.6087	+	10.9551i	1.24751	+	1.00425i
$120$	0.804205	−	0.562351i	0.0734135	−	0.0513354i
$121$	−2.33341	+	4.04158i	−0.212128	+	0.367417i
$122$	−0.819192	−	1.41888i	−0.0741662	−	0.128460i
$123$	−2.60755	+	5.58267i	−0.235115	+	0.503373i
$124$	1.73690	+	1.00280i	0.155978	+	0.0900540i
$125$	−1.90312			−0.170220
$126$	5.45544	+	9.04606i	0.486009	+	0.805887i
$127$	−12.0626			−1.07038			−0.535191	−	0.844731i	$-0.679760\pi$
$127$	−12.0626			−1.07038			−0.535191	+	0.844731i	$0.679760\pi$
$128$	7.79106	+	4.49817i	0.688639	+	0.397586i
$129$	1.56538	−	3.35142i	0.137824	−	0.295076i
$130$	0.127107	+	0.220156i	0.0111481	+	0.0193090i
$131$	3.07185	−	5.32061i	0.268389	−	0.464864i	−0.700057	−	0.714087i	$-0.746842\pi$
$131$	3.07185	−	5.32061i	0.268389	−	0.464864i	0.968446	+	0.249223i	$0.0801754\pi$
$132$	−0.816883	+	0.571216i	−0.0711005	+	0.0497180i
$133$	16.6817	+	2.59270i	1.44649	+	0.224816i
$134$		−	6.33655i		−	0.547395i
$135$	−0.258702	+	0.958200i	−0.0222655	+	0.0824687i
$136$	−16.9621	+	9.79305i	−1.45448	+	0.839747i
$137$	11.6042	−	6.69968i	0.991413	−	0.572392i	0.0857165	−	0.996320i	$-0.472682\pi$
$137$	11.6042	−	6.69968i	0.991413	−	0.572392i	0.905696	+	0.423927i	$0.139349\pi$
$138$	1.13663	−	0.0987162i	0.0967560	−	0.00840328i
$139$		−	2.97193i		−	0.252076i	−0.992025	−	0.126038i	$-0.959774\pi$
$139$		−	2.97193i		−	0.252076i	0.992025	−	0.126038i	$-0.0402261\pi$
$140$	0.107771	−	0.0417272i	0.00910827	−	0.00352659i
$141$	9.15303	+	13.0895i	0.770824	+	1.10234i
$142$	−3.52235	+	6.10090i	−0.295589	+	0.511976i
$143$	−1.25829	−	2.17942i	−0.105224	−	0.182253i
$144$	−10.3142	+	1.80521i	−0.859520	+	0.150434i
$145$	−0.606365	−	0.350085i	−0.0503559	−	0.0290730i
$146$	−9.33493			−0.772564
$147$	3.60447	+	11.5762i	0.297292	+	0.954787i
$148$	−0.198122			−0.0162855
$149$	0.996078	+	0.575086i	0.0816019	+	0.0471129i	0.540246	−	0.841507i	$-0.318331\pi$
$149$	0.996078	+	0.575086i	0.0816019	+	0.0471129i	−0.458644	+	0.888620i	$0.651665\pi$
$150$	10.3668	+	4.84213i	0.846448	+	0.395358i
$151$	−7.56130	−	13.0966i	−0.615330	−	1.06578i	−0.990326	−	0.138757i	$-0.955689\pi$
$151$	−7.56130	−	13.0966i	−0.615330	−	1.06578i	0.374996	−	0.927026i	$-0.377644\pi$
$152$	−9.46326	+	16.3908i	−0.767572	+	1.32947i
$153$	6.79882	−	18.6062i	0.549652	−	1.50422i
$154$	8.26373	−	3.19959i	0.665910	−	0.257831i
$155$		−	1.67519i		−	0.134555i
$156$	0.0342713	+	0.394602i	0.00274390	+	0.0315935i
$157$	8.08391	−	4.66725i	0.645166	−	0.372487i	−0.141436	−	0.989947i	$-0.545172\pi$
$157$	8.08391	−	4.66725i	0.645166	−	0.372487i	0.786602	+	0.617461i	$0.211839\pi$
$158$	12.9579	−	7.48123i	1.03087	−	0.595175i
$159$	−0.870325	−	10.0210i	−0.0690212	−	0.794716i
$160$			0.245831i			0.0194347i
$161$	1.29392	+	0.201103i	0.101975	+	0.0158491i
$162$	7.72266	−	9.15628i	0.606749	−	0.719385i
$163$	−0.357336	+	0.618924i	−0.0279887	+	0.0484779i	−0.879680	−	0.475565i	$-0.842244\pi$
$163$	−0.357336	+	0.618924i	−0.0279887	+	0.0484779i	0.851692	+	0.524043i	$0.175577\pi$
$164$	−0.406757	−	0.704524i	−0.0317624	−	0.0550141i
$165$	0.754348	+	0.352340i	0.0587259	+	0.0274296i
$166$	11.8218	+	6.82530i	0.917547	+	0.529746i
$167$	−12.7431			−0.986090			−0.493045	−	0.870004i	$-0.664116\pi$
$167$	−12.7431			−0.986090			−0.493045	+	0.870004i	$0.664116\pi$
$168$	−13.5617	−	0.917562i	−1.04631	−	0.0707914i
$169$	−1.00000			−0.0769231
$170$	1.45373	+	0.839310i	0.111496	+	0.0643721i
$171$	−3.30015	−	18.8557i	−0.252368	−	1.44194i
$172$	0.244186	+	0.422943i	0.0186190	+	0.0322491i
$173$	−2.31696	+	4.01309i	−0.176155	+	0.305109i	−0.940560	−	0.339626i	$-0.889699\pi$
$173$	−2.31696	+	4.01309i	−0.176155	+	0.305109i	0.764405	+	0.644736i	$0.223033\pi$
$174$	4.84237	+	6.92496i	0.367099	+	0.524980i
$175$	10.2295	+	8.23484i	0.773278	+	0.622495i
$176$			8.78373i			0.662099i
$177$	19.2807	−	1.67453i	1.44923	−	0.125866i
$178$	−7.47323	+	4.31467i	−0.560142	+	0.323398i
$179$	−12.9064	+	7.45154i	−0.964673	+	0.556954i	−0.897608	−	0.440794i	$-0.854697\pi$
$179$	−12.9064	+	7.45154i	−0.964673	+	0.556954i	−0.0670648	+	0.997749i	$0.521363\pi$
$180$	−0.0841038	−	0.100489i	−0.00626873	−	0.00749003i
$181$			14.2820i			1.06157i	0.847507	+	0.530785i	$0.178103\pi$
$181$			14.2820i			1.06157i	−0.847507	+	0.530785i	$0.821897\pi$
$182$	0.540787	−	3.47948i	0.0400858	−	0.257916i
$183$	−1.74737	+	1.22187i	−0.129169	+	0.0903235i
$184$	−0.734018	+	1.27136i	−0.0541125	+	0.0937256i
$185$	0.0827418	+	0.143313i	0.00608330	+	0.0105366i
$186$	−8.55578	+	18.3176i	−0.627340	+	1.34311i
$187$	−14.3911	−	8.30869i	−1.05238	−	0.607591i
$188$	−2.10881			−0.153801
$189$	11.1141	−	8.09173i	0.808434	−	0.588586i
$190$	1.62209			0.117679
$191$	−7.69788	−	4.44437i	−0.556999	−	0.321583i	0.194941	−	0.980815i	$-0.437548\pi$
$191$	−7.69788	−	4.44437i	−0.556999	−	0.321583i	−0.751940	+	0.659232i	$0.770882\pi$
$192$	6.37232	−	13.6429i	0.459882	−	0.984592i
$193$	−10.0910	−	17.4781i	−0.726364	−	1.25810i	−0.958410	−	0.285395i	$-0.907875\pi$
$193$	−10.0910	−	17.4781i	−0.726364	−	1.25810i	0.232046	−	0.972705i	$-0.425458\pi$
$194$	−10.6632	+	18.4692i	−0.765573	+	1.32601i
$195$	0.271125	−	0.189588i	0.0194157	−	0.0135767i
$196$	−1.52526	−	0.485853i	−0.108947	−	0.0347038i
$197$			15.8563i			1.12972i	0.825188	+	0.564858i	$0.191069\pi$
$197$			15.8563i			1.12972i	−0.825188	+	0.564858i	$0.808931\pi$
$198$	−6.44899	−	7.70541i	−0.458309	−	0.547600i
$199$	2.51039	−	1.44937i	0.177957	−	0.102743i	−0.408376	−	0.912814i	$-0.633905\pi$
$199$	2.51039	−	1.44937i	0.177957	−	0.102743i	0.586332	+	0.810071i	$0.300571\pi$
$200$	−12.7502	+	7.36132i	−0.901574	+	0.520524i
$201$	−8.21549	+	0.713518i	−0.579476	+	0.0503277i
$202$		−	23.6713i		−	1.66551i
$203$	3.50176	+	9.04415i	0.245775	+	0.634775i
$204$	1.49879	+	2.14338i	0.104936	+	0.150067i
$205$	−0.339748	+	0.588461i	−0.0237290	+	0.0410999i
$206$	−3.33388	−	5.77444i	−0.232282	−	0.402324i
$207$	−0.255976	−	1.46255i	−0.0177915	−	0.101654i
$208$	3.02272	+	1.74517i	0.209588	+	0.121006i
$209$	−16.0578			−1.11074
$210$	0.513047	+	1.04590i	0.0354036	+	0.0721741i
$211$	−4.15357			−0.285943			−0.142972	−	0.989727i	$-0.545666\pi$
$211$	−4.15357			−0.285943			−0.142972	+	0.989727i	$0.545666\pi$
$212$	1.15012	+	0.664022i	0.0789905	+	0.0456052i
$213$	8.30659	+	3.87983i	0.569158	+	0.265842i
$214$	−3.87329	−	6.70874i	−0.264773	−	0.458600i
$215$	0.203959	−	0.353268i	0.0139099	−	0.0240926i
$216$	3.96079	+	14.8951i	0.269498	+	1.01348i
$217$	−14.5505	+	18.0750i	−0.987753	+	1.22701i
$218$		−	20.6017i		−	1.39533i
$219$	1.05115	+	12.1030i	0.0710298	+	0.817842i
$220$	−0.0951974	+	0.0549623i	−0.00641821	+	0.00370555i
$221$	−5.71850	+	3.30158i	−0.384668	+	0.222088i
$222$	−0.172803	−	1.98966i	−0.0115978	−	0.133537i
$223$			1.82370i			0.122124i	0.998134	+	0.0610620i	$0.0194487\pi$
$223$			1.82370i			0.122124i	−0.998134	+	0.0610620i	$0.980551\pi$
$224$	2.13526	−	2.65247i	0.142668	−	0.177225i
$225$	5.11059	−	13.9861i	0.340706	−	0.932405i
$226$	−12.3821	+	21.4465i	−0.823647	+	1.42660i
$227$	4.75273	+	8.23196i	0.315450	+	0.546375i	0.979533	−	0.201284i	$-0.0645114\pi$
$227$	4.75273	+	8.23196i	0.315450	+	0.546375i	−0.664083	+	0.747658i	$0.731178\pi$
$228$	2.28988	+	1.06956i	0.151651	+	0.0708331i
$229$	−7.16847	−	4.13872i	−0.473706	−	0.273494i	0.244084	−	0.969754i	$-0.421513\pi$
$229$	−7.16847	−	4.13872i	−0.473706	−	0.273494i	−0.717790	+	0.696260i	$0.754846\pi$
$230$	0.125817			0.00829616
$231$	−5.07887	−	10.3538i	−0.334165	−	0.681232i
$232$	−10.8729			−0.713844
$233$	22.7537	+	13.1368i	1.49064	+	0.860623i	0.999943	−	0.0107054i	$-0.00340771\pi$
$233$	22.7537	+	13.1368i	1.49064	+	0.860623i	0.490700	+	0.871328i	$0.336741\pi$
$234$	−3.93294	+	0.688346i	−0.257105	+	0.0449986i
$235$	0.880702	+	1.52542i	0.0574507	+	0.0995074i
$236$	−1.27760	+	2.21287i	−0.0831647	+	0.144046i
$237$	−11.1587	−	15.9578i	−0.724835	−	1.03657i
$238$	−8.39528	−	21.6829i	−0.544185	−	1.40549i
$239$		−	19.4680i		−	1.25928i	−0.776887	−	0.629640i	$-0.783203\pi$
$239$		−	19.4680i		−	1.25928i	0.776887	−	0.629640i	$-0.216797\pi$
$240$	−1.15040	+	0.0999126i	−0.0742581	+	0.00644933i
$241$	3.58162	−	2.06785i	0.230712	−	0.133202i	−0.380188	−	0.924909i	$-0.624141\pi$
$241$	3.58162	−	2.06785i	0.230712	−	0.133202i	0.610901	+	0.791707i	$0.290807\pi$
$242$	5.37898	−	3.10555i	0.345774	−	0.199633i
$243$	−12.7409	−	8.98158i	−0.817331	−	0.576169i
$244$		−	0.281513i		−	0.0180220i
$245$	0.285549	+	1.30621i	0.0182430	+	0.0834508i
$246$	6.72048	−	4.69939i	0.428482	−	0.299622i
$247$	−3.19039	+	5.52593i	−0.203000	+	0.351606i
$248$	−13.0071	−	22.5289i	−0.825949	−	1.43059i
$249$	7.51799	−	16.0957i	0.476433	−	1.02003i
$250$	2.19353	+	1.26644i	0.138731	+	0.0800965i
$251$	−0.856009			−0.0540308			−0.0270154	−	0.999635i	$-0.508600\pi$
$251$	−0.856009			−0.0540308			−0.0270154	+	0.999635i	$0.508600\pi$
$252$	0.0346256	+	1.81477i	0.00218121	+	0.114320i
$253$	−1.24552			−0.0783053
$254$	13.9033	+	8.02710i	0.872373	+	0.503665i
$255$	0.924491	−	1.97930i	0.0578938	−	0.123949i
$256$	2.70693	+	4.68855i	0.169183	+	0.293034i
$257$	6.57009	−	11.3797i	0.409831	−	0.709848i	−0.585040	−	0.811005i	$-0.698921\pi$
$257$	6.57009	−	11.3797i	0.409831	−	0.709848i	0.994870	+	0.101157i	$0.0322544\pi$
$258$	−4.03447	+	2.82116i	−0.251175	+	0.175638i
$259$	0.352030	−	2.26500i	0.0218741	−	0.140740i
$260$			0.0436801i			0.00270892i
$261$	8.43310	−	7.05802i	0.521996	−	0.436881i
$262$	−7.08124	+	4.08836i	−0.437481	+	0.252580i
$263$	12.3378	−	7.12324i	0.760782	−	0.439238i	−0.0687945	−	0.997631i	$-0.521915\pi$
$263$	12.3378	−	7.12324i	0.760782	−	0.439238i	0.829576	+	0.558393i	$0.188582\pi$
$264$	12.8806	−	1.11868i	0.792746	−	0.0688502i
$265$		−	1.10926i		−	0.0681414i
$266$	−17.5020	−	14.0893i	−1.07312	−	0.863868i
$267$	6.43558	+	9.20337i	0.393851	+	0.563237i
$268$	0.544385	−	0.942902i	0.0332536	−	0.0575969i
$269$	−4.21180	−	7.29505i	−0.256798	−	0.444787i	0.708584	−	0.705626i	$-0.249334\pi$
$269$	−4.21180	−	7.29505i	−0.256798	−	0.444787i	−0.965382	+	0.260839i	$0.916001\pi$
$270$	0.935819	−	0.932268i	0.0569521	−	0.0567360i
$271$	2.77942	+	1.60470i	0.168838	+	0.0974785i	0.582038	−	0.813162i	$-0.302256\pi$
$271$	2.77942	+	1.60470i	0.168838	+	0.0974785i	−0.413200	+	0.910640i	$0.635589\pi$
$272$	23.0473			1.39745
$273$	−4.57212	−	0.309342i	−0.276717	−	0.0187222i
$274$	−17.8333			−1.07735
$275$	−10.8176	−	6.24555i	−0.652326	−	0.376621i
$276$	0.177615	+	0.0829602i	0.0106912	+	0.00499362i
$277$	−10.2491	−	17.7520i	−0.615811	−	1.06662i	−0.990242	−	0.139361i	$-0.955495\pi$
$277$	−10.2491	−	17.7520i	−0.615811	−	1.06662i	0.374431	−	0.927255i	$-0.377838\pi$
$278$	−1.97768	+	3.42545i	−0.118614	+	0.205445i
$279$	24.7126	+	9.03014i	1.47951	+	0.540621i
$280$	−1.48120	−	0.230211i	−0.0885189	−	0.0137578i
$281$		−	1.09912i		−	0.0655680i	−0.999462	−	0.0327840i	$-0.989563\pi$
$281$		−	1.09912i		−	0.0655680i	0.999462	−	0.0327840i	$-0.0104373\pi$
$282$	−1.83931	−	21.1779i	−0.109529	−	1.26113i
$283$	17.5809	−	10.1504i	1.04508	−	0.603376i	0.123810	−	0.992306i	$-0.460489\pi$
$283$	17.5809	−	10.1504i	1.04508	−	0.603376i	0.921267	+	0.388930i	$0.127155\pi$
$284$	−1.04828	+	0.605223i	−0.0622038	+	0.0359134i
$285$	−0.182653	−	2.10308i	−0.0108194	−	0.124576i
$286$			3.34934i			0.198051i
$287$	8.77710	−	3.39836i	0.518096	−	0.200599i
$288$	−3.62652	−	1.32515i	−0.213695	−	0.0780854i
$289$	−13.3008	+	23.0377i	−0.782401	+	1.35516i
$290$	0.465931	+	0.807017i	0.0273604	+	0.0473897i
$291$	25.1465	+	11.7454i	1.47411	+	0.688527i
$292$	−1.38907	−	0.801980i	−0.0812892	−	0.0469323i
$293$	28.1912			1.64695			0.823474	−	0.567354i	$-0.192033\pi$
$293$	28.1912			1.64695			0.823474	+	0.567354i	$0.192033\pi$
$294$	3.54889	−	15.7413i	0.206976	−	0.918052i
$295$	2.13426			0.124261
$296$	2.22551	+	1.28490i	0.129355	+	0.0746832i
$297$	−9.26407	+	9.22892i	−0.537556	+	0.535516i
$298$	−0.765387	−	1.32569i	−0.0443377	−	0.0767951i
$299$	−0.247463	+	0.428618i	−0.0143112	+	0.0247876i
$300$	1.12662	+	1.61116i	0.0650457	+	0.0930202i
$301$	−5.26911	+	2.04012i	−0.303706	+	0.117591i
$302$			20.1268i			1.15817i
$303$	−30.6904	+	2.66547i	−1.76312	+	0.153127i
$304$	19.2874	−	11.1356i	1.10621	−	0.638669i
$305$	−0.203634	+	0.117568i	−0.0116601	+	0.00673194i
$306$	−20.2179	+	16.9212i	−1.15578	+	0.967322i
$307$			3.41432i			0.194865i	0.995242	+	0.0974327i	$0.0310631\pi$
$307$			3.41432i			0.194865i	−0.995242	+	0.0974327i	$0.968937\pi$
$308$	1.50455	+	0.233841i	0.0857300	+	0.0133243i
$309$	−7.11130	+	4.97267i	−0.404548	+	0.282885i
$310$	−1.11477	+	1.93083i	−0.0633144	+	0.109664i
$311$	3.39631	+	5.88258i	0.192587	+	0.333570i	0.946107	−	0.323855i	$-0.104979\pi$
$311$	3.39631	+	5.88258i	0.192587	+	0.333570i	−0.753520	+	0.657425i	$0.771646\pi$
$312$	2.17418	−	4.65483i	0.123089	−	0.263528i
$313$	23.9070	+	13.8027i	1.35130	+	0.780176i	0.988432	−	0.151663i	$-0.0484630\pi$
$313$	23.9070	+	13.8027i	1.35130	+	0.780176i	0.362872	+	0.931839i	$0.381796\pi$
$314$	−12.4234			−0.701091
$315$	1.29827	−	0.782950i	0.0731490	−	0.0441142i
$316$	2.57090			0.144625
$317$	−28.5140	−	16.4625i	−1.60150	−	0.924629i	−0.991187	−	0.132471i	$-0.957709\pi$
$317$	−28.5140	−	16.4625i	−1.60150	−	0.924629i	−0.610317	−	0.792157i	$-0.708958\pi$
$318$	−5.66537	+	12.1294i	−0.317698	+	0.680180i
$319$	−4.61245	−	7.98900i	−0.258248	−	0.447298i
$320$	0.830274	−	1.43808i	0.0464137	−	0.0803909i
$321$	−8.26189	+	5.77724i	−0.461134	+	0.322454i
$322$	−1.35754	−	1.09283i	−0.0756530	−	0.0609012i
$323$			42.1333i			2.34436i
$324$	1.93579	−	0.699019i	0.107544	−	0.0388344i
$325$	−4.29853	+	2.48176i	−0.238440	+	0.137663i
$326$	0.823732	−	0.475582i	0.0456223	−	0.0263400i
$327$	−26.7107	+	2.31983i	−1.47710	+	0.128287i
$328$			10.5519i			0.582631i
$329$	3.74701	−	24.1086i	0.206579	−	1.32915i
$330$	−0.634995	−	0.908091i	−0.0349553	−	0.0499888i
$331$	3.43459	−	5.94888i	0.188782	−	0.326980i	−0.756062	−	0.654499i	$-0.772879\pi$
$331$	3.43459	−	5.94888i	0.188782	−	0.326980i	0.944844	+	0.327520i	$0.106213\pi$
$332$	1.17275	+	2.03126i	0.0643628	+	0.111480i
$333$	−2.56019	+	0.448086i	−0.140297	+	0.0245549i
$334$	14.6877	+	8.47995i	0.803675	+	0.464002i
$335$	−0.909405			−0.0496861
$336$	13.2804	+	8.91419i	0.724506	+	0.486309i
$337$	−1.58731			−0.0864664			−0.0432332	−	0.999065i	$-0.513766\pi$
$337$	−1.58731			−0.0864664			−0.0432332	+	0.999065i	$0.513766\pi$
$338$	1.15260	+	0.665454i	0.0626932	+	0.0361960i
$339$	29.2001	+	13.6388i	1.58593	+	0.740757i
$340$	0.144213	+	0.249785i	0.00782106	+	0.0135465i
$341$	11.0355	−	19.1141i	0.597608	−	1.03509i
$342$	−8.74389	+	23.9292i	−0.472815	+	1.29395i
$343$	8.26457	−	16.5740i	0.446245	−	0.894911i
$344$		−	6.33457i		−	0.341537i
$345$	−0.0141675	−	0.163125i	−0.000762751	−	0.00878238i
$346$	5.34106	−	3.08366i	0.287137	−	0.165779i
$347$	24.7165	−	14.2701i	1.32685	−	0.766059i	0.342041	−	0.939685i	$-0.388882\pi$
$347$	24.7165	−	14.2701i	1.32685	−	0.766059i	0.984812	+	0.173627i	$0.0555486\pi$
$348$	0.125627	+	1.44647i	0.00673430	+	0.0775392i
$349$		−	15.9772i		−	0.855240i	−0.903959	−	0.427620i	$-0.859352\pi$
$349$		−	15.9772i		−	0.855240i	0.903959	−	0.427620i	$-0.140648\pi$
$350$	−6.31064	−	16.2988i	−0.337318	−	0.871205i
$351$	1.33532	+	5.02165i	0.0712741	+	0.268036i
$352$	−1.61944	+	2.80496i	−0.0863165	+	0.149505i
$353$	7.67267	+	13.2894i	0.408375	+	0.707326i	0.994708	−	0.102744i	$-0.0327623\pi$
$353$	7.67267	+	13.2894i	0.408375	+	0.707326i	−0.586333	+	0.810070i	$0.699429\pi$
$354$	−23.3373	−	10.9004i	−1.24036	−	0.579348i
$355$	0.875584	+	0.505519i	0.0464712	+	0.0268301i
$356$	−1.48272			−0.0785842
$357$	−27.1670	+	13.3262i	−1.43783	+	0.705300i
$358$	19.8346			1.04829
$359$	−18.3741	−	10.6083i	−0.969750	−	0.559885i	−0.0705898	−	0.997505i	$-0.522488\pi$
$359$	−18.3741	−	10.6083i	−0.969750	−	0.559885i	−0.899160	+	0.437620i	$0.855821\pi$
$360$	0.293027	+	1.67424i	0.0154439	+	0.0882403i
$361$	10.8572	+	18.8053i	0.571433	+	0.989752i
$362$	9.50399	−	16.4614i	0.499519	−	0.865192i
$363$	−4.63212	−	6.62428i	−0.243123	−	0.347684i
$364$	0.379399	−	0.471299i	0.0198859	−	0.0247028i
$365$			1.33972i			0.0701243i
$366$	2.82712	−	0.245536i	0.147776	−	0.0128344i
$367$	3.92926	−	2.26856i	0.205105	−	0.118418i	−0.393929	−	0.919141i	$-0.628884\pi$
$367$	3.92926	−	2.26856i	0.205105	−	0.118418i	0.599035	+	0.800723i	$0.295551\pi$
$368$	1.49602	−	0.863730i	0.0779857	−	0.0450251i
$369$	−6.84962	−	8.18410i	−0.356577	−	0.426047i
$370$		−	0.220244i		−	0.0114499i
$371$	−9.63489	+	11.9687i	−0.500219	+	0.621384i
$372$	−2.84683	+	1.99068i	−0.147601	+	0.103212i
$373$	−3.90407	+	6.76204i	−0.202145	+	0.350125i	−0.949219	−	0.314615i	$-0.898125\pi$
$373$	−3.90407	+	6.76204i	−0.202145	+	0.350125i	0.747074	+	0.664740i	$0.231458\pi$
$374$	11.0581	+	19.1532i	0.571801	+	0.990389i
$375$	1.39497	−	2.98657i	0.0720357	−	0.154226i
$376$	23.6883	+	13.6764i	1.22163	+	0.705308i
$377$	−3.66565			−0.188791
$378$	−18.1948	+	1.93058i	−0.935841	+	0.0992983i
$379$	8.74327			0.449112			0.224556	−	0.974461i	$-0.427907\pi$
$379$	8.74327			0.449112			0.224556	+	0.974461i	$0.427907\pi$
$380$	0.241373	+	0.139357i	0.0123822	+	0.00714885i
$381$	8.84176	−	18.9299i	0.452977	−	0.969808i
$382$	5.91505	+	10.2452i	0.302640	+	0.524189i
$383$	−10.9192	+	18.9126i	−0.557944	+	0.966388i	0.439724	+	0.898133i	$0.355076\pi$
$383$	−10.9192	+	18.9126i	−0.557944	+	0.966388i	−0.997668	+	0.0682545i	$0.978257\pi$
$384$	−12.7698	+	8.92944i	−0.651655	+	0.455679i
$385$	−0.459197	−	1.18599i	−0.0234028	−	0.0604435i
$386$			26.8603i			1.36715i
$387$	4.11199	+	4.91312i	0.209024	+	0.249748i
$388$	−3.17344	+	1.83219i	−0.161107	+	0.0930153i
$389$	−27.0401	+	15.6116i	−1.37099	+	0.791539i	−0.991052	−	0.133474i	$-0.957387\pi$
$389$	−27.0401	+	15.6116i	−1.37099	+	0.791539i	−0.379934	+	0.925014i	$0.624053\pi$
$390$	−0.438662	+	0.0380979i	−0.0222125	+	0.00192916i
$391$			3.26807i			0.165273i
$392$	13.9823	+	15.3495i	0.706212	+	0.775265i
$393$	6.09803	+	8.72064i	0.307605	+	0.439898i
$394$	10.5517	−	18.2760i	0.531585	−	0.920732i
$395$	−1.07369	−	1.85968i	−0.0540230	−	0.0935705i
$396$	−0.297646	−	1.70064i	−0.0149573	−	0.0854602i
$397$	−7.40812	−	4.27708i	−0.371803	−	0.214661i	0.302443	−	0.953168i	$-0.402198\pi$
$397$	−7.40812	−	4.27708i	−0.371803	−	0.214661i	−0.674246	+	0.738507i	$0.735531\pi$
$398$	−3.85796			−0.193382
$399$	−16.2963	+	24.2783i	−0.815834	+	1.21543i
$400$	17.3244			0.866218
$401$	3.50384	+	2.02294i	0.174973	+	0.101021i	0.584929	−	0.811085i	$-0.301122\pi$
$401$	3.50384	+	2.02294i	0.174973	+	0.101021i	−0.409955	+	0.912106i	$0.634456\pi$
$402$	9.94400	+	4.64464i	0.495962	+	0.231653i
$403$	−4.38513	−	7.59527i	−0.218439	−	0.378347i
$404$	2.03364	−	3.52238i	0.101178	−	0.175245i
$405$	−1.31408	−	1.10833i	−0.0652973	−	0.0550736i
$406$	1.98234	−	12.7546i	0.0983817	−	0.632998i
$407$			2.18029i			0.108073i
$408$	−2.93527	−	33.7969i	−0.145317	−	1.67319i
$409$	20.4845	−	11.8267i	1.01289	−	0.584794i	0.100855	−	0.994901i	$-0.467842\pi$
$409$	20.4845	−	11.8267i	1.01289	−	0.584794i	0.912037	+	0.410107i	$0.134509\pi$
$410$	0.783188	−	0.452174i	0.0386789	−	0.0223313i
$411$	2.00809	+	23.1213i	0.0990520	+	1.14049i
$412$		−	1.14568i		−	0.0564434i
$413$	−23.0282	−	18.5379i	−1.13314	−	0.912189i
$414$	−0.678220	+	1.85607i	−0.0333327	+	0.0912210i
$415$	0.979548	−	1.69663i	0.0480841	−	0.0832841i
$416$	0.643508	+	1.11459i	0.0315506	+	0.0546472i
$417$	4.66387	+	2.17840i	0.228391	+	0.106677i
$418$	18.5082	+	10.6857i	0.905266	+	0.522656i
$419$	−18.1178			−0.885113			−0.442556	−	0.896741i	$-0.645928\pi$
$419$	−18.1178			−0.885113			−0.442556	+	0.896741i	$0.645928\pi$
$420$	−0.0135121	+	0.199711i	−0.000659322	+	0.00974489i
$421$	3.25502			0.158640			0.0793199	−	0.996849i	$-0.474725\pi$
$421$	3.25502			0.158640			0.0793199	+	0.996849i	$0.474725\pi$
$422$	4.78740	+	2.76401i	0.233047	+	0.134550i
$423$	−27.2506	+	4.76941i	−1.32497	+	0.231897i
$424$	−8.61287	−	14.9179i	−0.418278	−	0.724478i
$425$	−16.3874	+	28.3839i	−0.794907	+	1.37682i
$426$	−6.99233	−	9.99956i	−0.338779	−	0.484480i
$427$	3.21835	+	0.500202i	0.155747	+	0.0242065i
$428$		−	1.33105i		−	0.0643385i
$429$	4.34250	−	0.377147i	0.209658	−	0.0182088i
$430$	−0.470167	+	0.271451i	−0.0226735	+	0.0130905i
$431$	5.59093	−	3.22793i	0.269306	−	0.155484i	−0.359266	−	0.933235i	$-0.616973\pi$
$431$	5.59093	−	3.22793i	0.269306	−	0.155484i	0.628572	+	0.777751i	$0.283640\pi$
$432$	4.72732	−	17.5094i	0.227443	−	0.842422i
$433$		−	7.21337i		−	0.346652i	−0.984864	−	0.173326i	$-0.944549\pi$
$433$		−	7.21337i		−	0.346652i	0.984864	−	0.173326i	$-0.0554515\pi$
$434$	28.7990	−	11.1506i	1.38240	−	0.535244i
$435$	0.993851	−	0.694964i	0.0476515	−	0.0333210i
$436$	1.76993	−	3.06561i	0.0847644	−	0.146816i
$437$	1.57901	+	2.73492i	0.0755342	+	0.130829i
$438$	6.84242	−	14.6494i	0.326943	−	0.699974i
$439$	−1.86794	−	1.07846i	−0.0891521	−	0.0514720i	0.454761	−	0.890613i	$-0.349725\pi$
$439$	−1.86794	−	1.07846i	−0.0891521	−	0.0514720i	−0.543913	+	0.839141i	$0.683058\pi$
$440$	1.42580			0.0679726
$441$	−20.8086	−	2.82870i	−0.990886	−	0.134700i
$442$	8.78820			0.418012
$443$	−7.56329	−	4.36667i	−0.359343	−	0.207467i	0.309450	−	0.950916i	$-0.399855\pi$
$443$	−7.56329	−	4.36667i	−0.359343	−	0.207467i	−0.668793	+	0.743449i	$0.733189\pi$
$444$	0.145222	−	0.310915i	0.00689192	−	0.0147554i
$445$	0.619230	+	1.07254i	0.0293543	+	0.0508431i
$446$	1.21359	−	2.10200i	0.0574651	−	0.0995325i
$447$	−1.63260	+	1.14162i	−0.0772194	+	0.0539967i
$448$	−21.4494	+	8.30490i	−1.01339	+	0.392370i
$449$		−	12.1932i		−	0.575434i	−0.957715	−	0.287717i	$-0.907104\pi$
$449$		−	12.1932i		−	0.575434i	0.957715	−	0.287717i	$-0.0928962\pi$
$450$	−15.1976	+	12.7195i	−0.716420	+	0.599603i
$451$	−7.75311	+	4.47626i	−0.365080	+	0.210779i
$452$	−3.68501	+	2.12754i	−0.173328	+	0.100071i
$453$	26.0949	−	2.26635i	1.22605	−	0.106482i
$454$		−	12.6509i		−	0.593736i
$455$	−0.499365	−	0.0776123i	−0.0234106	−	0.00363852i
$456$	−18.7858	−	26.8651i	−0.879725	−	1.25807i
$457$	5.23946	−	9.07502i	0.245092	−	0.424511i	−0.717066	−	0.697006i	$-0.754515\pi$
$457$	5.23946	−	9.07502i	0.245092	−	0.424511i	0.962157	+	0.272494i	$0.0878486\pi$
$458$	5.50825	+	9.54058i	0.257384	+	0.445802i
$459$	24.2154	+	24.3076i	1.13028	+	1.13458i
$460$	0.0187221	+	0.0108092i	0.000872922	+	0.000503982i
$461$	22.7828			1.06110			0.530550	−	0.847654i	$-0.321986\pi$
$461$	22.7828			1.06110			0.530550	+	0.847654i	$0.321986\pi$
$462$	−1.03609	+	15.3136i	−0.0482034	+	0.712453i
$463$	7.71541			0.358565			0.179283	−	0.983798i	$-0.442622\pi$
$463$	7.71541			0.358565			0.179283	+	0.983798i	$0.442622\pi$
$464$	11.0803	+	6.39719i	0.514388	+	0.296982i
$465$	2.62889	+	1.22790i	0.121912	+	0.0569426i
$466$	−17.4839	−	30.2831i	−0.809928	−	1.40284i
$467$	15.1559	−	26.2509i	0.701334	−	1.21475i	−0.266665	−	0.963789i	$-0.585922\pi$
$467$	15.1559	−	26.2509i	0.701334	−	1.21475i	0.967998	−	0.250956i	$-0.0807450\pi$
$468$	−0.644373	−	0.235458i	−0.0297862	−	0.0108840i
$469$	9.81229	+	7.89897i	0.453089	+	0.364740i
$470$		−	2.34427i		−	0.108133i
$471$	1.39891	+	16.1072i	0.0644585	+	0.742180i
$472$	28.7026	−	16.5715i	1.32114	−	0.762763i
$473$	4.65438	−	2.68721i	0.214009	−	0.123558i
$474$	2.24235	+	25.8185i	0.102994	+	1.18588i
$475$			31.6711i			1.45317i
$476$	0.613565	−	3.94774i	0.0281227	−	0.180944i
$477$	16.3639	+	5.97948i	0.749253	+	0.273782i
$478$	−12.9551	+	22.4388i	−0.592551	+	1.02633i
$479$	1.17005	+	2.02658i	0.0534609	+	0.0925970i	0.891517	−	0.452986i	$-0.149641\pi$
$479$	1.17005	+	2.02658i	0.0534609	+	0.0925970i	−0.838056	+	0.545583i	$0.816308\pi$
$480$	−0.385784	−	0.180192i	−0.0176086	−	0.00822460i
$481$	0.750296	+	0.433184i	0.0342106	+	0.0197515i
$482$	−5.50424			−0.250711
$483$	−1.26402	+	1.88315i	−0.0575149	+	0.0856861i
$484$	1.06721			0.0485097
$485$	2.65065	+	1.53035i	0.120360	+	0.0694898i
$486$	8.70837	+	18.8307i	0.395020	+	0.854177i
$487$	−13.7176	−	23.7595i	−0.621602	−	1.07665i	−0.989187	−	0.146657i	$-0.953149\pi$
$487$	−13.7176	−	23.7595i	−0.621602	−	1.07665i	0.367585	−	0.929990i	$-0.380185\pi$
$488$	−1.82572	+	3.16224i	−0.0826464	+	0.143148i
$489$	−0.709358	−	1.01444i	−0.0320783	−	0.0458744i
$490$	0.540101	−	1.69556i	0.0243993	−	0.0765976i
$491$		−	17.1609i		−	0.774461i	−0.921983	−	0.387230i	$-0.873432\pi$
$491$		−	17.1609i		−	0.774461i	0.921983	−	0.387230i	$-0.126568\pi$
$492$	1.40376	−	0.121917i	0.0632866	−	0.00549645i
$493$	−20.9620	+	12.1024i	−0.944082	+	0.545066i
$494$	7.35450	−	4.24612i	0.330895	−	0.191042i
$495$	−1.10586	+	0.925541i	−0.0497047	+	0.0416000i
$496$			30.6112i			1.37448i
$497$	−5.05650	−	13.0596i	−0.226815	−	0.585805i
$498$	−19.3762	+	13.5491i	−0.868270	+	0.607149i
$499$	8.79195	−	15.2281i	0.393582	−	0.681704i	−0.599337	−	0.800497i	$-0.704569\pi$
$499$	8.79195	−	15.2281i	0.393582	−	0.681704i	0.992919	+	0.118793i	$0.0379025\pi$
$500$	0.217604	+	0.376901i	0.00973153	+	0.0168555i
$501$	9.34057	−	19.9978i	0.417306	−	0.893437i
$502$	0.986636	+	0.569635i	0.0440357	+	0.0254240i
$503$	28.8300			1.28547			0.642734	−	0.766090i	$-0.277800\pi$
$503$	28.8300			1.28547			0.642734	+	0.766090i	$0.277800\pi$
$504$	11.3805	−	20.6099i	0.506929	−	0.918038i
$505$	−3.39724			−0.151175
$506$	1.43559	+	0.828838i	0.0638197	+	0.0368463i
$507$	0.732991	−	1.56931i	0.0325533	−	0.0696954i
$508$	1.37924	+	2.38892i	0.0611941	+	0.105991i
$509$	6.42549	−	11.1293i	0.284805	−	0.493296i	−0.687757	−	0.725941i	$-0.741405\pi$
$509$	6.42549	−	11.1293i	0.284805	−	0.493296i	0.972562	+	0.232645i	$0.0747379\pi$
$510$	−2.38270	+	1.66614i	−0.105508	+	0.0737778i
$511$	11.6367	−	14.4553i	0.514775	−	0.639466i
$512$		−	25.1980i		−	1.11361i
$513$	32.0094	+	8.64215i	1.41325	+	0.381560i
$514$	−15.1454	+	8.74419i	−0.668034	+	0.385690i
$515$	−0.828732	+	0.478469i	−0.0365183	+	0.0210839i
$516$	−0.842714	+	0.0731899i	−0.0370984	+	0.00322201i
$517$			23.2069i			1.02064i
$518$	−1.91301	+	2.37638i	−0.0840526	+	0.104412i
$519$	−4.59946	−	6.57757i	−0.201894	−	0.288723i
$520$	0.283282	−	0.490659i	0.0124227	−	0.0215168i
$521$	8.47267	+	14.6751i	0.371195	+	0.642928i	0.989750	−	0.142814i	$-0.0456150\pi$
$521$	8.47267	+	14.6751i	0.371195	+	0.642928i	−0.618555	+	0.785741i	$0.712282\pi$
$522$	−14.4168	+	2.52324i	−0.631006	+	0.110439i
$523$	31.2120	+	18.0203i	1.36481	+	0.787972i	0.990259	−	0.139235i	$-0.0444645\pi$
$523$	31.2120	+	18.0203i	1.36481	+	0.787972i	0.374548	+	0.927207i	$0.377798\pi$
$524$	−1.40495			−0.0613756
$525$	−20.4211	+	10.0172i	−0.891251	+	0.437186i
$526$	−18.9608			−0.826728
$527$	−50.1527	−	28.9557i	−2.18469	−	1.26133i
$528$	−13.7844	−	6.43839i	−0.599888	−	0.280195i
$529$	−11.3775	−	19.7064i	−0.494675	−	0.856802i
$530$	−0.738163	+	1.27854i	−0.0320638	+	0.0555360i
$531$	−11.5047	+	31.4848i	−0.499262	+	1.36632i
$532$	−1.39393	−	3.60016i	−0.0604345	−	0.156087i
$533$			3.55741i			0.154089i
$534$	−1.29324	−	14.8904i	−0.0559638	−	0.644371i
$535$	−0.962820	+	0.555884i	−0.0416263	+	0.0240330i
$536$	−12.2302	+	7.06108i	−0.528262	+	0.304992i
$537$	−2.23345	−	25.7161i	−0.0963804	−	1.10973i
$538$			11.2110i			0.483342i
$539$	−5.34669	+	16.7851i	−0.230298	+	0.722985i
$540$	0.219346	−	0.0583269i	0.00943914	−	0.00250999i
$541$	0.408827	−	0.708110i	0.0175769	−	0.0304440i	−0.857103	−	0.515145i	$-0.827738\pi$
$541$	0.408827	−	0.708110i	0.0175769	−	0.0304440i	0.874680	+	0.484701i	$0.161071\pi$
$542$	−2.13571	−	3.69915i	−0.0917365	−	0.158892i
$543$	−22.4128	−	10.4685i	−0.961824	−	0.449248i
$544$	7.35981	+	4.24919i	0.315549	+	0.182182i
$545$	−2.95671			−0.126651
$546$	5.06398	+	3.39909i	0.216718	+	0.145468i
$547$	30.8867			1.32062			0.660310	−	0.750993i	$-0.270425\pi$
$547$	30.8867			1.32062			0.660310	+	0.750993i	$0.270425\pi$
$548$	−2.65366	−	1.53209i	−0.113359	−	0.0654478i
$549$	−0.636687	−	3.63778i	−0.0271732	−	0.155257i
$550$	8.31225	+	14.3972i	0.354436	+	0.613901i
$551$	−11.6949	+	20.2561i	−0.498218	+	0.862939i
$552$	−1.45712	−	2.08379i	−0.0620191	−	0.0886920i
$553$	−4.56807	+	29.3914i	−0.194254	+	1.24985i
$554$			27.2813i			1.15907i
$555$	−0.285551	+	0.0248002i	−0.0121210	+	0.00105271i
$556$	−0.588573	+	0.339813i	−0.0249610	+	0.0144113i
$557$	−3.22545	+	1.86222i	−0.136667	+	0.0789047i	−0.566775	−	0.823873i	$-0.691809\pi$
$557$	−3.22545	+	1.86222i	−0.136667	+	0.0789047i	0.430108	+	0.902778i	$0.358476\pi$
$558$	−22.4747	−	26.8533i	−0.951428	−	1.13679i
$559$		−	2.13560i		−	0.0903264i
$560$	1.37400	+	1.10608i	0.0580620	+	0.0467404i
$561$	23.5874	−	16.4938i	0.995861	−	0.696369i
$562$	−0.731414	+	1.26685i	−0.0308528	+	0.0534387i
$563$	12.8328	+	22.2271i	0.540839	+	0.936760i	0.998856	+	0.0478168i	$0.0152264\pi$
$563$	12.8328	+	22.2271i	0.540839	+	0.936760i	−0.458017	+	0.888943i	$0.651440\pi$
$564$	1.54574	−	3.30937i	0.0650873	−	0.139350i
$565$	3.07794	+	1.77705i	0.129490	+	0.0747610i
$566$	−27.0184			−1.13567
$567$	4.55184	+	23.3726i	0.191159	+	0.981559i
$568$	15.7004			0.658775
$569$	−9.95423	−	5.74708i	−0.417303	−	0.240930i	0.276620	−	0.960979i	$-0.410786\pi$
$569$	−9.95423	−	5.74708i	−0.417303	−	0.240930i	−0.693923	+	0.720049i	$0.744119\pi$
$570$	−1.18898	+	2.54556i	−0.0498008	+	0.106622i
$571$	−19.7883	−	34.2743i	−0.828113	−	1.43433i	−0.899517	−	0.436886i	$-0.856081\pi$
$571$	−19.7883	−	34.2743i	−0.828113	−	1.43433i	0.0714042	−	0.997447i	$-0.477252\pi$
$572$	−0.287748	+	0.498394i	−0.0120313	+	0.0208389i
$573$	12.6171	−	8.82265i	0.527085	−	0.368571i
$574$	−12.3779	−	1.92380i	−0.516646	−	0.0802980i
$575$			2.45657i			0.102446i
$576$	16.7391	+	20.0002i	0.697461	+	0.833344i
$577$	39.3970	−	22.7459i	1.64012	−	0.946923i	0.659329	−	0.751854i	$-0.270840\pi$
$577$	39.3970	−	22.7459i	1.64012	−	0.946923i	0.980790	−	0.195069i	$-0.0624930\pi$
$578$	30.6611	−	17.7022i	1.27533	−	0.736314i
$579$	34.8251	−	3.02456i	1.44728	−	0.125697i
$580$			0.160116i			0.00664845i
$581$	−25.3058	+	9.79803i	−1.04986	+	0.406491i
$582$	−21.1678	−	30.2716i	−0.877434	−	1.25480i
$583$	7.30739	−	12.6568i	0.302641	−	0.524190i
$584$	10.4023	+	18.0173i	0.430450	+	0.745561i
$585$	0.0987896	+	0.564445i	0.00408445	+	0.0233369i
$586$	−32.4932	−	18.7600i	−1.34228	−	0.774967i
$587$	−13.0663			−0.539305			−0.269652	−	0.962958i	$-0.586909\pi$
$587$	−13.0663			−0.539305			−0.269652	+	0.962958i	$0.586909\pi$
$588$	1.88045	−	2.03747i	0.0775486	−	0.0840239i
$589$	−55.9612			−2.30584
$590$	−2.45995	−	1.42025i	−0.101274	−	0.0584708i
$591$	−24.8834	−	11.6225i	−1.02357	−	0.478087i
$592$	−1.51196	−	2.61879i	−0.0621412	−	0.107632i
$593$	12.1219	−	20.9958i	0.497787	−	0.862193i	−0.502209	−	0.864746i	$-0.667479\pi$
$593$	12.1219	−	20.9958i	0.497787	−	0.862193i	0.999997	+	0.00255311i	$0.000812680\pi$
$594$	16.8192	−	4.47244i	0.690100	−	0.183507i
$595$	−3.11186	+	1.20487i	−0.127574	+	0.0493948i
$596$		−	0.263023i		−	0.0107738i
$597$	0.434420	+	5.00194i	0.0177796	+	0.204716i
$598$	0.570452	−	0.329351i	0.0233275	−	0.0134681i
$599$	22.2708	−	12.8580i	0.909959	−	0.525365i	0.0295412	−	0.999564i	$-0.490595\pi$
$599$	22.2708	−	12.8580i	0.909959	−	0.525365i	0.880418	+	0.474198i	$0.157262\pi$
$600$	−2.20641	−	25.4047i	−0.0900762	−	1.03714i
$601$			7.67311i			0.312993i	0.987679	+	0.156496i	$0.0500199\pi$
$601$			7.67311i			0.312993i	−0.987679	+	0.156496i	$0.949980\pi$
$602$	7.43079	+	1.15491i	0.302856	+	0.0470705i
$603$	4.90215	−	13.4156i	0.199631	−	0.546327i
$604$	−1.72913	+	2.99494i	−0.0703573	+	0.121862i
$605$	−0.445701	−	0.771976i	−0.0181203	−	0.0313853i
$606$	37.1476	+	17.3509i	1.50902	+	0.704830i
$607$	−35.1786	−	20.3104i	−1.42786	−	0.824372i	−0.430904	−	0.902398i	$-0.641805\pi$
$607$	−35.1786	−	20.3104i	−1.42786	−	0.824372i	−0.996951	+	0.0780255i	$0.975138\pi$
$608$	8.21218			0.333048
$609$	−16.7598	−	1.13394i	−0.679141	−	0.0459496i
$610$	0.312945			0.0126708
$611$	7.98614	+	4.61080i	0.323085	+	0.186533i
$612$	−4.46223	+	0.780982i	−0.180375	+	0.0315693i
$613$	13.0128	+	22.5389i	0.525584	+	0.910338i	0.999556	+	0.0297981i	$0.00948642\pi$
$613$	13.0128	+	22.5389i	0.525584	+	0.910338i	−0.473972	+	0.880540i	$0.657180\pi$
$614$	2.27207	−	3.93535i	0.0916934	−	0.158818i
$615$	−0.674443	−	0.964505i	−0.0271962	−	0.0388926i
$616$	−15.3841	−	12.3843i	−0.619844	−	0.498979i
$617$			45.8721i			1.84674i	0.383912	+	0.923370i	$0.374577\pi$
$617$			45.8721i			1.84674i	−0.383912	+	0.923370i	$0.625423\pi$
$618$	11.5056	−	0.999262i	0.462822	−	0.0401962i
$619$	−12.2518	+	7.07361i	−0.492443	+	0.284312i	−0.725587	−	0.688130i	$-0.758432\pi$
$619$	−12.2518	+	7.07361i	−0.492443	+	0.284312i	0.233144	+	0.972442i	$0.425099\pi$
$620$	−0.331762	+	0.191543i	−0.0133239	+	0.00769255i
$621$	2.48281	+	0.670328i	0.0996318	+	0.0268993i
$622$		−	9.04035i		−	0.362485i
$623$	2.63455	−	16.9510i	0.105551	−	0.679127i
$624$	−4.95434	+	3.46439i	−0.198332	+	0.138687i
$625$	−12.2270	+	21.1778i	−0.489081	+	0.847114i
$626$	−18.3702	−	31.8180i	−0.734219	−	1.27170i
$627$	11.7702	−	25.1996i	0.470057	−	1.00637i
$628$	−1.84864	−	1.06731i	−0.0737688	−	0.0425904i
$629$	5.72076			0.228102
$630$	−2.01740	+	0.0384917i	−0.0803752	+	0.00153355i
$631$	−17.4425			−0.694376			−0.347188	−	0.937796i	$-0.612863\pi$
$631$	−17.4425			−0.694376			−0.347188	+	0.937796i	$0.612863\pi$
$632$	−28.8790	−	16.6733i	−1.14874	−	0.663227i
$633$	3.04453	−	6.51822i	0.121009	−	0.259076i
$634$	21.9101	+	37.9495i	0.870163	+	1.50717i
$635$	1.15203	−	1.99537i	0.0457168	−	0.0791839i
$636$	−1.88508	+	1.31817i	−0.0747483	+	0.0522688i
$637$	4.71392	+	5.17484i	0.186772	+	0.205035i
$638$			12.2775i			0.486071i
$639$	−12.1773	+	10.1917i	−0.481727	+	0.403178i
$640$	−1.48816	+	0.859188i	−0.0588246	+	0.0339624i
$641$	−25.1041	+	14.4939i	−0.991552	+	0.572473i	−0.905738	−	0.423838i	$-0.860682\pi$
$641$	−25.1041	+	14.4939i	−0.991552	+	0.572473i	−0.0858140	+	0.996311i	$0.527349\pi$
$642$	13.3672	−	1.16094i	0.527560	−	0.0458187i
$643$		−	10.2617i		−	0.404682i	−0.979315	−	0.202341i	$-0.935145\pi$
$643$		−	10.2617i		−	0.404682i	0.979315	−	0.202341i	$-0.0648549\pi$
$644$	−0.108120	−	0.279247i	−0.00426053	−	0.0110039i
$645$	0.404885	+	0.579016i	0.0159423	+	0.0227987i
$646$	28.0378	−	48.5629i	1.10313	−	1.91068i
$647$	0.260149	+	0.450591i	0.0102275	+	0.0177146i	0.871094	−	0.491117i	$-0.163411\pi$
$647$	0.260149	+	0.450591i	0.0102275	+	0.0177146i	−0.860866	+	0.508831i	$0.830078\pi$
$648$	−26.2781	−	4.70225i	−1.03230	−	0.184722i
$649$	24.3521	+	14.0597i	0.955902	+	0.551890i
$650$	6.60599			0.259108
$651$	−17.6998	−	36.0830i	−0.693711	−	1.41421i
$652$	0.163432			0.00640050
$653$	34.4007	+	19.8613i	1.34620	+	0.777231i	0.987710	−	0.156300i	$-0.0499568\pi$
$653$	34.4007	+	19.8613i	1.34620	+	0.777231i	0.358495	+	0.933532i	$0.383290\pi$
$654$	32.3305	+	15.1009i	1.26422	+	0.590491i
$655$	0.586750	+	1.01628i	0.0229262	+	0.0397094i
$656$	6.20829	−	10.7531i	0.242393	−	0.419837i
$657$	−19.7637	−	7.22179i	−0.771057	−	0.281749i
$658$	−20.3620	+	25.2942i	−0.793793	+	0.986069i
$659$		−	39.4682i		−	1.53746i	−0.639572	−	0.768731i	$-0.720888\pi$
$659$		−	39.4682i		−	1.53746i	0.639572	−	0.768731i	$-0.279112\pi$
$660$	−0.0164738	−	0.189681i	−0.000641243	−	0.00738332i
$661$	−18.7374	+	10.8181i	−0.728802	+	0.420774i	−0.817984	−	0.575241i	$-0.804908\pi$
$661$	−18.7374	+	10.8181i	−0.728802	+	0.420774i	0.0891818	+	0.996015i	$0.471575\pi$
$662$	−7.91741	+	4.57112i	−0.307719	+	0.177662i
$663$	−0.989581	−	11.3941i	−0.0384321	−	0.442510i
$664$		−	30.4228i		−	1.18063i
$665$	−2.02205	+	2.51184i	−0.0784118	+	0.0974051i
$666$	3.24905	+	1.18722i	0.125898	+	0.0460040i
$667$	−0.907113	+	1.57116i	−0.0351235	+	0.0608358i
$668$	1.45705	+	2.52369i	0.0563751	+	0.0976446i
$669$	−2.86194	−	1.33675i	−0.110649	−	0.0516819i
$670$	1.04818	+	0.605168i	0.0404948	+	0.0233797i
$671$	−3.09798			−0.119596
$672$	2.59741	+	5.29510i	0.100197	+	0.204263i
$673$	−46.0377			−1.77462			−0.887312	−	0.461170i	$-0.847430\pi$
$673$	−46.0377			−1.77462			−0.887312	+	0.461170i	$0.847430\pi$
$674$	1.82954	+	1.05628i	0.0704712	+	0.0406866i
$675$	18.2024	+	18.2718i	0.700612	+	0.703280i
$676$	0.114341	+	0.198044i	0.00439772	+	0.00761708i
$677$	−10.4937	+	18.1756i	−0.403306	+	0.698546i	−0.994123	−	0.108260i	$-0.965472\pi$
$677$	−10.4937	+	18.1756i	−0.403306	+	0.698546i	0.590817	+	0.806806i	$0.298806\pi$
$678$	−24.5801	−	35.1514i	−0.943994	−	1.34998i
$679$	−15.3075	−	39.5354i	−0.587448	−	1.51723i
$680$		−	3.74111i		−	0.143465i
$681$	−16.4022	+	1.42453i	−0.628533	+	0.0545882i
$682$	−25.4392	+	14.6873i	−0.974116	+	0.562406i
$683$	−13.6338	+	7.87149i	−0.521684	+	0.301194i	−0.737623	−	0.675212i	$-0.764052\pi$
$683$	−13.6338	+	7.87149i	−0.521684	+	0.301194i	0.215939	+	0.976407i	$0.430719\pi$
$684$	−3.35693	+	2.80955i	−0.128355	+	0.107426i
$685$			2.55939i			0.0977893i
$686$	−20.5550	+	13.6035i	−0.784793	+	0.519384i
$687$	11.7493	−	8.21588i	0.448265	−	0.313456i
$688$	−3.72699	+	6.45534i	−0.142090	+	0.246108i
$689$	−2.90370	−	5.02935i	−0.110622	−	0.191603i
$690$	−0.0922231	+	0.197446i	−0.00351087	+	0.00751665i
$691$	−7.04135	−	4.06532i	−0.267865	−	0.154652i	0.360052	−	0.932932i	$-0.382759\pi$
$691$	−7.04135	−	4.06532i	−0.267865	−	0.154652i	−0.627917	+	0.778280i	$0.716092\pi$
$692$	1.05969			0.0402834
$693$	19.9711	−	0.381046i	0.758640	−	0.0144747i
$694$	−37.9844			−1.44187
$695$	0.491611	+	0.283832i	0.0186479	+	0.0107664i
$696$	7.96977	−	17.0630i	0.302093	−	0.646771i
$697$	11.7451	+	20.3431i	0.444876	+	0.770549i
$698$	−10.6321	+	18.4153i	−0.402431	+	0.697031i
$699$	−37.2940	+	26.0783i	−1.41059	+	0.986373i
$700$	0.461210	−	2.96747i	0.0174321	−	0.112160i
$701$		−	25.4148i		−	0.959904i	−0.877295	−	0.479952i	$-0.840654\pi$
$701$		−	25.4148i		−	0.959904i	0.877295	−	0.479952i	$-0.159346\pi$
$702$	1.80258	−	6.67655i	0.0680342	−	0.251990i
$703$	4.78748	−	2.76405i	0.180563	−	0.104248i
$704$	18.9470	−	10.9391i	0.714092	−	0.412281i
$705$	−3.03940	+	0.263973i	−0.114470	+	0.00994178i
$706$		−	20.4232i		−	0.768639i
$707$	36.6555	+	29.5080i	1.37857	+	1.10976i
$708$	−2.53620	−	3.62696i	−0.0953163	−	0.136310i
$709$	3.63519	−	6.29633i	0.136522	−	0.236464i	−0.789656	−	0.613550i	$-0.789741\pi$
$709$	3.63519	−	6.29633i	0.136522	−	0.236464i	0.926178	+	0.377087i	$0.123074\pi$
$710$	−0.672799	−	1.16532i	−0.0252497	−	0.0437338i
$711$	33.2219	−	5.81451i	1.24592	−	0.218061i
$712$	16.6554	+	9.61602i	0.624189	+	0.360376i
$713$	−4.34063			−0.162558
$714$	40.1807	+	2.71856i	1.50373	+	0.101739i
$715$	0.480688			0.0179767
$716$	2.95146	+	1.70403i	0.110301	+	0.0636825i
$717$	30.5512	+	14.2699i	1.14096	+	0.532917i
$718$	14.1187	+	24.4543i	0.526905	+	0.912626i
$719$	1.38474	−	2.39844i	0.0516420	−	0.0894466i	−0.839049	−	0.544056i	$-0.816888\pi$
$719$	1.38474	−	2.39844i	0.0516420	−	0.0894466i	0.890691	+	0.454610i	$0.150221\pi$
$720$	0.686440	−	1.87857i	0.0255821	−	0.0700101i
$721$	13.0978	+	2.03568i	0.487786	+	0.0758126i
$722$		−	28.9000i		−	1.07555i
$723$	0.619796	+	7.13638i	0.0230505	+	0.265405i
$724$	2.82846	−	1.63301i	0.105119	−	0.0606903i
$725$	−15.7569	+	9.09726i	−0.585197	+	0.337864i
$726$	0.930827	+	10.7176i	0.0345462	+	0.397768i
$727$		−	31.4996i		−	1.16826i	−0.811661	−	0.584128i	$-0.801436\pi$
$727$		−	31.4996i		−	1.16826i	0.811661	−	0.584128i	$-0.198564\pi$
$728$	−7.31835	+	2.83356i	−0.271236	+	0.105019i
$729$	23.4338	−	13.4110i	0.867920	−	0.496704i
$730$	0.891525	−	1.54417i	0.0329968	−	0.0571522i
$731$	−7.05086	−	12.2124i	−0.260785	−	0.451694i
$732$	0.441780	+	0.206346i	0.0163287	+	0.00762678i
$733$	−25.3224	−	14.6199i	−0.935305	−	0.539999i	−0.0468197	−	0.998903i	$-0.514909\pi$
$733$	−25.3224	−	14.6199i	−0.935305	−	0.539999i	−0.888486	+	0.458905i	$0.848242\pi$
$734$	−6.03849			−0.222885
$735$	−2.25915	−	0.509328i	−0.0833301	−	0.0187868i
$736$	0.636978			0.0234793
$737$	−10.3764	−	5.99082i	−0.382219	−	0.220675i
$738$	2.44873	+	13.9911i	0.0901391	+	0.515020i
$739$	−7.27050	−	12.5929i	−0.267450	−	0.463237i	0.700753	−	0.713404i	$-0.252848\pi$
$739$	−7.27050	−	12.5929i	−0.267450	−	0.463237i	−0.968203	+	0.250168i	$0.919514\pi$
$740$	0.0189215	−	0.0327730i	0.000695569	−	0.00120476i
$741$	−6.33334	−	9.05716i	−0.232661	−	0.332723i
$742$	19.0698	−	7.38355i	0.700075	−	0.271059i
$743$			49.4264i			1.81328i	0.421908	+	0.906639i	$0.361361\pi$
$743$			49.4264i			1.81328i	−0.421908	+	0.906639i	$0.638639\pi$
$744$	44.8888	−	3.89860i	1.64570	−	0.142930i
$745$	−0.190259	+	0.109846i	−0.00697056	+	0.00402445i
$746$	8.99966	−	5.19596i	0.329501	−	0.190237i
$747$	19.7486	+	23.5961i	0.722562	+	0.863335i
$748$			3.80009i			0.138945i
$749$	15.2170	+	2.36505i	0.556016	+	0.0864170i
$750$	−3.59527	+	2.51404i	−0.131281	+	0.0917998i
$751$	−23.8423	+	41.2960i	−0.870016	+	1.50691i	−0.00803813	+	0.999968i	$0.502559\pi$
$751$	−23.8423	+	41.2960i	−0.870016	+	1.50691i	−0.861978	+	0.506945i	$0.830775\pi$
$752$	−16.0933	−	27.8744i	−0.586861	−	1.01647i
$753$	0.627446	−	1.34334i	0.0228654	−	0.0489540i
$754$	4.22503	+	2.43932i	0.153867	+	0.0888349i
$755$	2.88855			0.105125
$756$	−2.87332	−	1.27587i	−0.104501	−	0.0464031i
$757$	−10.2924			−0.374085			−0.187043	−	0.982352i	$-0.559890\pi$
$757$	−10.2924			−0.374085			−0.187043	+	0.982352i	$0.559890\pi$
$758$	−10.0775	−	5.81825i	−0.366031	−	0.211328i
$759$	0.912956	−	1.95461i	0.0331382	−	0.0709477i
$760$	−1.80756	−	3.13079i	−0.0655672	−	0.113566i
$761$	−23.4579	+	40.6302i	−0.850346	+	1.47284i	0.0305495	+	0.999533i	$0.490274\pi$
$761$	−23.4579	+	40.6302i	−0.850346	+	1.47284i	−0.880896	+	0.473310i	$0.843059\pi$
$762$	−22.7880	+	15.9348i	−0.825522	+	0.577258i
$763$	31.9022	+	25.6815i	1.15494	+	0.929734i
$764$			2.03269i			0.0735402i
$765$	2.42849	+	2.90162i	0.0878022	+	0.104908i
$766$	25.1709	−	14.5324i	0.909462	−	0.525078i
$767$	9.67665	−	5.58681i	0.349403	−	0.201728i
$768$	−9.34193	+	0.811349i	−0.337098	+	0.0292770i
$769$			44.9218i			1.61992i	0.586485	+	0.809960i	$0.300511\pi$
$769$			44.9218i			1.61992i	−0.586485	+	0.809960i	$0.699489\pi$
$770$	−0.259950	+	1.67255i	−0.00936795	+	0.0602743i
$771$	13.0425	+	18.6517i	0.469713	+	0.671725i
$772$	−2.30762	+	3.99691i	−0.0830530	+	0.143852i
$773$	−25.9463	−	44.9404i	−0.933225	−	1.61639i	−0.777769	−	0.628550i	$-0.783649\pi$
$773$	−25.9463	−	44.9404i	−0.933225	−	1.61639i	−0.155456	−	0.987843i	$-0.549685\pi$
$774$	−1.47003	−	8.39921i	−0.0528393	−	0.301903i
$775$	−37.6992	−	21.7657i	−1.35420	−	0.781846i
$776$	47.5297			1.70622
$777$	3.29645	+	2.21267i	0.118259	+	0.0793790i
$778$	41.5552			1.48983
$779$	19.6580	+	11.3496i	0.704321	+	0.406640i
$780$	−0.0685475	−	0.0320171i	−0.00245439	−	0.00114640i
$781$	6.66033	+	11.5360i	0.238325	+	0.412792i
$782$	2.17475	−	3.76678i	0.0777690	−	0.134700i
$783$	4.89482	+	18.4076i	0.174927	+	0.657834i
$784$	−5.21790	−	23.8687i	−0.186353	−	0.852454i
$785$			1.78297i			0.0636368i
$786$	−1.22540	−	14.1094i	−0.0437087	−	0.503265i
$787$	−21.6127	+	12.4781i	−0.770409	+	0.444796i	−0.833020	−	0.553242i	$-0.813390\pi$
$787$	−21.6127	+	12.4781i	−0.770409	+	0.444796i	0.0626117	+	0.998038i	$0.480057\pi$
$788$	3.14025	−	1.81302i	0.111867	−	0.0645863i
$789$	2.13505	+	24.5831i	0.0760097	+	0.875181i
$790$			2.85796i			0.101681i
$791$	−17.7751	−	45.9085i	−0.632010	−	1.63232i
$792$	−7.68581	+	21.0336i	−0.273103	+	0.747397i
$793$	−0.615513	+	1.06610i	−0.0218575	+	0.0378583i
$794$	5.69241	+	9.85954i	0.202016	+	0.349902i
$795$	1.74077	+	0.813078i	0.0617388	+	0.0288369i
$796$	−0.574079	−	0.331445i	−0.0203477	−	0.0117477i
$797$	25.6822			0.909709			0.454855	−	0.890566i	$-0.349691\pi$
$797$	25.6822			0.909709			0.454855	+	0.890566i	$0.349691\pi$
$798$	34.9392	−	17.1387i	1.23683	−	0.606705i
$799$	60.8917			2.15419
$800$	5.53228	+	3.19406i	0.195596	+	0.112927i
$801$	−19.1601	+	3.35342i	−0.676990	+	0.118487i
$802$	−2.69235	−	4.66329i	−0.0950703	−	0.164667i
$803$	−8.82559	+	15.2864i	−0.311448	+	0.539444i
$804$	1.08067	+	1.54544i	0.0381124	+	0.0545036i
$805$	−0.156841	+	0.194831i	−0.00552790	+	0.00686689i
$806$			11.6724i			0.411144i
$807$	14.5354	−	1.26240i	0.511669	−	0.0444386i
$808$	−45.6879	+	26.3779i	−1.60729	+	0.927972i
$809$	−41.0967	+	23.7272i	−1.44488	+	0.834204i	−0.998170	−	0.0604734i	$-0.980739\pi$
$809$	−41.0967	+	23.7272i	−1.44488	+	0.834204i	−0.446713	+	0.894677i	$0.647406\pi$
$810$	0.777068	+	2.15193i	0.0273034	+	0.0756111i
$811$		−	3.82566i		−	0.134337i	−0.997742	−	0.0671685i	$-0.978603\pi$
$811$		−	3.82566i		−	0.134337i	0.997742	−	0.0671685i	$-0.0213965\pi$
$812$	1.39074	−	1.72762i	0.0488056	−	0.0606275i
$813$	−4.55555	+	3.18553i	−0.159770	+	0.111722i
$814$	1.45088	−	2.51300i	0.0508533	−	0.0880806i
$815$	−0.0682542	−	0.118220i	−0.00239084	−	0.00414106i
$816$	−16.8934	+	36.1682i	−0.591388	+	1.26614i
$817$	−11.8012	−	6.81342i	−0.412871	−	0.238371i
$818$	−31.4806			−1.10069
$819$	3.83678	−	6.94832i	0.134068	−	0.242794i
$820$	0.155388			0.00542639
$821$	−12.8904	−	7.44226i	−0.449877	−	0.259737i	0.257901	−	0.966171i	$-0.416969\pi$
$821$	−12.8904	−	7.44226i	−0.449877	−	0.259737i	−0.707778	+	0.706435i	$0.750302\pi$
$822$	13.0717	−	27.9860i	0.455927	−	0.976123i
$823$	17.2073	+	29.8040i	0.599810	+	1.03890i	0.992849	+	0.119380i	$0.0380906\pi$
$823$	17.2073	+	29.8040i	0.599810	+	1.03890i	−0.393038	+	0.919522i	$0.628576\pi$
$824$	−7.43015	+	12.8694i	−0.258841	+	0.448327i
$825$	17.7304	−	12.3982i	0.617293	−	0.431650i
$826$	14.2062	+	36.6910i	0.494297	+	1.27664i
$827$			19.1094i			0.664501i	0.943191	+	0.332250i	$0.107808\pi$
$827$			19.1094i			0.664501i	−0.943191	+	0.332250i	$0.892192\pi$
$828$	−0.260380	+	0.217923i	−0.00904883	+	0.00757335i
$829$	−8.10581	+	4.67989i	−0.281526	+	0.162539i	−0.634114	−	0.773239i	$-0.718635\pi$
$829$	−8.10581	+	4.67989i	−0.281526	+	0.162539i	0.352588	+	0.935779i	$0.385302\pi$
$830$	−2.25806	+	1.30369i	−0.0783783	+	0.0452517i
$831$	35.3709	−	3.07197i	1.22700	−	0.106566i
$832$		−	8.69359i		−	0.301396i
$833$	44.0417	+	14.0290i	1.52595	+	0.486075i
$834$	−3.92596	−	5.61442i	−0.135945	−	0.194411i
$835$	1.21702	−	2.10794i	0.0421167	−	0.0729482i
$836$	1.83606	+	3.18015i	0.0635014	+	0.109988i
$837$	−32.2852	+	32.1627i	−1.11594	+	1.11171i
$838$	20.8826	+	12.0566i	0.721377	+	0.416487i
$839$	40.0145			1.38145			0.690727	−	0.723115i	$-0.257291\pi$
$839$	40.0145			1.38145			0.690727	+	0.723115i	$0.257291\pi$
$840$	1.44698	−	2.15572i	0.0499256	−	0.0743794i
$841$	15.5630			0.536655
$842$	−3.75174	−	2.16607i	−0.129293	−	0.0746476i
$843$	1.72486	+	0.805644i	0.0594072	+	0.0277479i
$844$	0.474922	+	0.822589i	0.0163475	+	0.0283147i
$845$	0.0955042	−	0.165418i	0.00328544	−	0.00569056i
$846$	34.5829	+	12.6368i	1.18898	+	0.434462i
$847$	−1.89626	+	12.2008i	−0.0651564	+	0.419223i
$848$			20.2698i			0.696068i
$849$	3.04236	+	35.0300i	0.104414	+	1.20223i
$850$	37.7763	−	21.8102i	1.29572	−	0.748083i
$851$	0.371341	−	0.214394i	0.0127294	−	0.00734933i
$852$	−0.181403	−	2.08869i	−0.00621478	−	0.0715574i
$853$		−	5.23561i		−	0.179264i	−0.995975	−	0.0896320i	$-0.971431\pi$
$853$		−	5.23561i		−	0.179264i	0.995975	−	0.0896320i	$-0.0285691\pi$
$854$	−3.37661	−	2.71820i	−0.115545	−	0.0930149i
$855$	3.43426	+	1.25490i	0.117449	+	0.0429167i
$856$	−8.63233	+	14.9516i	−0.295047	+	0.511037i
$857$	−10.4175	−	18.0436i	−0.355854	−	0.616357i	0.631410	−	0.775449i	$-0.282477\pi$
$857$	−10.4175	−	18.0436i	−0.355854	−	0.616357i	−0.987264	+	0.159092i	$0.949143\pi$
$858$	−5.25614	−	2.45504i	−0.179442	−	0.0838135i
$859$	−24.7747	−	14.3037i	−0.845301	−	0.488035i	0.0137615	−	0.999905i	$-0.495619\pi$
$859$	−24.7747	−	14.3037i	−0.845301	−	0.488035i	−0.859063	+	0.511870i	$0.828953\pi$
$860$	−0.0932833			−0.00318093
$861$	−1.10046	+	16.2649i	−0.0375035	+	0.554307i
$862$	−8.59216			−0.292650
$863$	44.3675	+	25.6156i	1.51029	+	0.871964i	0.999928	+	0.0120017i	$0.00382034\pi$
$863$	44.3675	+	25.6156i	1.51029	+	0.871964i	0.510358	+	0.859962i	$0.329513\pi$
$864$	4.73778	−	4.71981i	0.161183	−	0.160571i
$865$	−0.442558	−	0.766534i	−0.0150474	−	0.0260629i
$866$	−4.80017	+	8.31414i	−0.163116	+	0.282526i
$867$	−26.4038	−	37.7595i	−0.896722	−	1.28238i
$868$	5.24336	+	0.814932i	0.177971	+	0.0276606i
$869$		−	28.2921i		−	0.959745i
$870$	−1.60798	+	0.139653i	−0.0545156	+	0.00473470i
$871$	−4.12321	+	2.38054i	−0.139710	+	0.0806614i
$872$	−39.7633	+	22.9574i	−1.34656	+	0.777434i
$873$	−36.8643	+	30.8533i	−1.24767	+	1.04422i
$874$		−	4.20303i		−	0.142170i
$875$	−4.69550	+	1.81803i	−0.158737	+	0.0614606i
$876$	2.27673	−	1.59203i	0.0769236	−	0.0537898i
$877$	−4.65379	+	8.06059i	−0.157147	+	0.272187i	−0.933839	−	0.357694i	$-0.883563\pi$
$877$	−4.65379	+	8.06059i	−0.157147	+	0.272187i	0.776692	+	0.629881i	$0.216896\pi$
$878$	1.43533	+	2.48606i	0.0484400	+	0.0839006i
$879$	−20.6639	+	44.2407i	−0.696976	+	1.49220i
$880$	−1.45299	−	0.838883i	−0.0489802	−	0.0282788i
$881$	41.4793			1.39747			0.698737	−	0.715379i	$-0.253746\pi$
$881$	41.4793			1.39747			0.698737	+	0.715379i	$0.253746\pi$
$882$	22.1017	+	17.1075i	0.744202	+	0.576041i
$883$	11.0204			0.370867			0.185433	−	0.982657i	$-0.440631\pi$
$883$	11.0204			0.370867			0.185433	+	0.982657i	$0.440631\pi$
$884$	1.30771	+	0.755009i	0.0439832	+	0.0253937i
$885$	−1.56439	+	3.34930i	−0.0525864	+	0.112586i
$886$	5.81164	+	10.0661i	0.195246	+	0.338176i
$887$	12.6612	−	21.9299i	0.425122	−	0.736334i	−0.571310	−	0.820735i	$-0.693564\pi$
$887$	12.6612	−	21.9299i	0.425122	−	0.736334i	0.996432	+	0.0844012i	$0.0268977\pi$
$888$	−3.64768	+	2.55069i	−0.122408	+	0.0855955i
$889$	−29.7616	+	11.5233i	−0.998174	+	0.386478i
$890$		−	1.64828i		−	0.0552504i
$891$	−7.69253	−	21.3029i	−0.257709	−	0.713673i
$892$	0.361173	−	0.208523i	0.0120930	−	0.00698187i
$893$	50.9579	−	29.4205i	1.70524	−	0.984521i
$894$	2.64143	−	0.229409i	0.0883428	−	0.00767259i
$895$		−	2.84661i		−	0.0951518i
$896$	23.5197	+	3.65547i	0.785738	+	0.122121i
$897$	−0.491246	−	0.702519i	−0.0164022	−	0.0234564i
$898$	−8.11404	+	14.0539i	−0.270769	+	0.468985i
$899$	−16.0744	−	27.8416i	−0.536110	−	0.928570i
$900$	−3.35421	+	0.587055i	−0.111807	+	0.0195685i
$901$	−33.2096	−	19.1736i	−1.10637	−	0.638764i
$902$	11.9150			0.396726
$903$	0.660632	−	9.76424i	0.0219844	−	0.324934i
$904$	55.1916			1.83565
$905$	−2.36250	−	1.36399i	−0.0785320	−	0.0453405i
$906$	−31.5852	−	14.7528i	−1.04935	−	0.490128i
$907$	3.90748	+	6.76795i	0.129746	+	0.224726i	0.923578	−	0.383411i	$-0.125251\pi$
$907$	3.90748	+	6.76795i	0.129746	+	0.224726i	−0.793832	+	0.608137i	$0.791917\pi$
$908$	1.08686	−	1.88250i	0.0360687	−	0.0624729i
$909$	18.3129	−	50.1165i	0.607399	−	1.66226i
$910$	0.523922	+	0.421761i	0.0173678	+	0.0139812i
$911$			5.10544i			0.169151i	0.996417	+	0.0845754i	$0.0269534\pi$
$911$			5.10544i			0.169151i	−0.996417	+	0.0845754i	$0.973047\pi$
$912$	3.33766	+	38.4301i	0.110521	+	1.27255i
$913$	22.3535	−	12.9058i	0.739792	−	0.427119i
$914$	−12.0780	+	6.97325i	−0.399505	+	0.230655i
$915$	−0.0352387	−	0.405741i	−0.00116496	−	0.0134134i
$916$			1.89290i			0.0625430i
$917$	2.49637	−	16.0619i	0.0824373	−	0.530410i
$918$	−11.7351	−	44.1312i	−0.387315	−	1.45655i
$919$	19.8444	−	34.3715i	0.654606	−	1.13381i	−0.327387	−	0.944890i	$-0.606168\pi$
$919$	19.8444	−	34.3715i	0.654606	−	1.13381i	0.981992	−	0.188920i	$-0.0604987\pi$
$920$	−0.140204	−	0.242840i	−0.00462237	−	0.00800619i
$921$	−5.35811	−	2.50266i	−0.176556	−	0.0824656i
$922$	−26.2594	−	15.1609i	−0.864809	−	0.499298i
$923$	5.29316			0.174226
$924$	−1.46979	+	2.18971i	−0.0483526	+	0.0720360i
$925$	4.30023			0.141391
$926$	−8.89278	−	5.13425i	−0.292235	−	0.168722i
$927$	−2.59113	−	14.8047i	−0.0851040	−	0.486251i
$928$	2.35888	+	4.08569i	0.0774339	+	0.134119i
$929$	7.75225	−	13.4273i	0.254343	−	0.440535i	−0.710374	−	0.703825i	$-0.751474\pi$
$929$	7.75225	−	13.4273i	0.254343	−	0.440535i	0.964717	+	0.263289i	$0.0848074\pi$
$930$	−2.21295	−	3.16469i	−0.0725656	−	0.103774i
$931$	43.6350	−	9.53898i	1.43008	−	0.312627i
$932$		−	6.00830i		−	0.196809i
$933$	−11.7210	+	1.01797i	−0.383729	+	0.0333270i
$934$	−34.9375	+	20.1712i	−1.14319	+	0.660021i
$935$	2.74882	−	1.58703i	0.0898959	−	0.0519014i
$936$	5.71121	+	6.82390i	0.186677	+	0.223046i
$937$		−	20.9796i		−	0.685374i	−0.939450	−	0.342687i	$-0.888663\pi$
$937$		−	20.9796i		−	0.685374i	0.939450	−	0.342687i	$-0.111337\pi$
$938$	−6.05325	−	15.6340i	−0.197646	−	0.510468i
$939$	−39.1843	+	27.4002i	−1.27873	+	0.894171i
$940$	0.201400	−	0.348835i	0.00656895	−	0.0113778i
$941$	19.7896	+	34.2765i	0.645121	+	1.11738i	0.984274	+	0.176651i	$0.0565264\pi$
$941$	19.7896	+	34.2765i	0.645121	+	1.11738i	−0.339152	+	0.940731i	$0.610140\pi$
$942$	9.10621	−	19.4961i	0.296696	−	0.635216i
$943$	1.52477	+	0.880328i	0.0496534	+	0.0286674i
$944$	−38.9998			−1.26933
$945$	0.277072	+	2.61127i	0.00901314	+	0.0849447i
$946$	−7.15286			−0.232560
$947$	36.6389	+	21.1535i	1.19060	+	0.687395i	0.958443	−	0.285283i	$-0.0920875\pi$
$947$	36.6389	+	21.1535i	1.19060	+	0.687395i	0.232160	+	0.972678i	$0.425421\pi$
$948$	−1.88445	+	4.03453i	−0.0612040	+	0.131036i
$949$	3.50698	+	6.07426i	0.113841	+	0.197179i
$950$	21.0757	−	36.5042i	0.683786	−	1.18435i
$951$	46.7353	−	32.6803i	1.51549	−	1.05973i
$952$	−32.4948	+	40.3658i	−1.05316	+	1.30826i
$953$		−	32.6315i		−	1.05704i	−0.848921	−	0.528519i	$-0.822747\pi$
$953$		−	32.6315i		−	1.05704i	0.848921	−	0.528519i	$-0.177253\pi$
$954$	−14.8820	−	17.7814i	−0.481823	−	0.575694i
$955$	1.47036	−	0.848912i	0.0475797	−	0.0274702i
$956$	−3.85552	+	2.22598i	−0.124696	+	0.0719935i
$957$	15.9181	−	1.38249i	0.514559	−	0.0446896i
$958$		−	3.11446i		−	0.100624i
$959$	22.2305	−	27.6153i	0.717861	−	0.891744i
$960$	1.64820	+	2.35705i	0.0531955	+	0.0760735i
$961$	22.9588	−	39.7657i	0.740605	−	1.28277i
$962$	−0.576528	−	0.998576i	−0.0185880	−	0.0321954i
$963$	−3.01038	−	17.2001i	−0.0970080	−	0.554266i
$964$	−0.819050	−	0.472879i	−0.0263798	−	0.0152304i
$965$	3.85492			0.124094
$966$	2.71006	−	1.32937i	0.0871947	−	0.0427717i
$967$	−26.0337			−0.837186			−0.418593	−	0.908174i	$-0.637477\pi$
$967$	−26.0337			−0.837186			−0.418593	+	0.908174i	$0.637477\pi$
$968$	−11.9880	−	6.92129i	−0.385310	−	0.222459i
$969$	−66.1201	−	30.8833i	−2.12408	−	0.992116i
$970$	−2.03676	−	3.52777i	−0.0653964	−	0.113270i
$971$	−5.29039	+	9.16323i	−0.169777	+	0.294062i	−0.938341	−	0.345710i	$-0.887638\pi$
$971$	−5.29039	+	9.16323i	−0.169777	+	0.294062i	0.768565	+	0.639772i	$0.220971\pi$
$972$	−0.321941	+	3.55022i	−0.0103263	+	0.113873i
$973$	−2.83906	−	7.33255i	−0.0910160	−	0.235071i
$974$			36.5136i			1.16997i
$975$	−0.743857	−	8.56482i	−0.0238225	−	0.274294i
$976$	3.72105	−	2.14835i	0.119108	−	0.0687671i
$977$	−27.2185	+	15.7146i	−0.870797	+	0.502755i	−0.867613	−	0.497240i	$-0.834347\pi$
$977$	−27.2185	+	15.7146i	−0.870797	+	0.502755i	−0.00318407	+	0.999995i	$0.501014\pi$
$978$	0.142546	+	1.64129i	0.00455812	+	0.0524825i
$979$			16.3170i			0.521494i
$980$	0.226037	−	0.205904i	0.00722050	−	0.00657737i
$981$	15.9381	−	43.6176i	0.508866	−	1.39260i
$982$	−11.4198	+	19.7797i	−0.364420	+	0.631195i
$983$	−18.2311	−	31.5772i	−0.581483	−	1.00716i	−0.995304	−	0.0967994i	$-0.969139\pi$
$983$	−18.2311	−	31.5772i	−0.581483	−	1.00716i	0.413821	−	0.910358i	$-0.364194\pi$
$984$	−16.5592	−	7.73445i	−0.527887	−	0.246565i
$985$	−2.62292	−	1.51435i	−0.0835733	−	0.0482510i
$986$	32.2145			1.02592
$987$	35.0873	+	23.5516i	1.11684	+	0.749656i
$988$	1.45917			0.0464223
$989$	−0.915359	−	0.528483i	−0.0291067	−	0.0168048i
$990$	1.89052	−	0.330880i	0.0600847	−	0.0105161i
$991$	−27.7032	−	47.9833i	−0.880020	−	1.52424i	−0.851317	−	0.524652i	$-0.824195\pi$
$991$	−27.7032	−	47.9833i	−0.880020	−	1.52424i	−0.0287038	−	0.999588i	$-0.509138\pi$
$992$	−5.64374	+	9.77524i	−0.179189	+	0.310364i
$993$	6.81809	+	9.75039i	0.216366	+	0.309419i
$994$	−2.86247	+	18.4174i	−0.0907921	+	0.584165i
$995$			0.553685i			0.0175530i
$996$	−4.04728	+	0.351507i	−0.128243	+	0.0111379i
$997$	−25.2822	+	14.5967i	−0.800695	+	0.462282i	−0.843714	−	0.536793i	$-0.819636\pi$
$997$	−25.2822	+	14.5967i	−0.800695	+	0.462282i	0.0430189	+	0.999074i	$0.486302\pi$
$998$	−20.2672	+	11.7013i	−0.641548	+	0.370398i
$999$	1.17341	−	4.34616i	0.0371250	−	0.137506i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bh.a.131.9	✓	64
3.2	odd	2	inner	273.2.bh.a.131.24	yes	64
7.3	odd	6	inner	273.2.bh.a.248.24	yes	64
21.17	even	6	inner	273.2.bh.a.248.9	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bh.a.131.9	✓	64	1.1	even	1	trivial
273.2.bh.a.131.24	yes	64	3.2	odd	2	inner
273.2.bh.a.248.9	yes	64	21.17	even	6	inner
273.2.bh.a.248.24	yes	64	7.3	odd	6	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.15260 - 0.665454i) q^{2} +(-0.732991 + 1.56931i) q^{3} +(-0.114341 - 0.198044i) q^{4} +(-0.0955042 + 0.165418i) q^{5} +(1.88915 - 1.32101i) q^{6} +(2.46727 - 0.955290i) q^{7} +2.96617i q^{8} +(-1.92545 - 2.30058i) q^{9} +O(q^{10})\)	\(q+(-1.15260 - 0.665454i) q^{2} +(-0.732991 + 1.56931i) q^{3} +(-0.114341 - 0.198044i) q^{4} +(-0.0955042 + 0.165418i) q^{5} +(1.88915 - 1.32101i) q^{6} +(2.46727 - 0.955290i) q^{7} +2.96617i q^{8} +(-1.92545 - 2.30058i) q^{9} +(0.220156 - 0.127107i) q^{10} +(-2.17942 + 1.25829i) q^{11} +(0.394602 - 0.0342713i) q^{12} +1.00000i q^{13} +(-3.47948 - 0.540787i) q^{14} +(-0.189588 - 0.271125i) q^{15} +(1.74517 - 3.02272i) q^{16} +(3.30158 + 5.71850i) q^{17} +(0.688346 + 3.93294i) q^{18} +(5.52593 + 3.19039i) q^{19} +0.0436801 q^{20} +(-0.309342 + 4.57212i) q^{21} +3.34934 q^{22} +(0.428618 + 0.247463i) q^{23} +(-4.65483 - 2.17418i) q^{24} +(2.48176 + 4.29853i) q^{25} +(0.665454 - 1.15260i) q^{26} +(5.02165 - 1.33532i) q^{27} +(-0.471299 - 0.379399i) q^{28} +3.66565i q^{29} +(0.0380979 + 0.438662i) q^{30} +(-7.59527 + 4.38513i) q^{31} +(1.11459 - 0.643508i) q^{32} +(-0.377147 - 4.34250i) q^{33} -8.78820i q^{34} +(-0.0776123 + 0.499365i) q^{35} +(-0.235458 + 0.644373i) q^{36} +(0.433184 - 0.750296i) q^{37} +(-4.24612 - 7.35450i) q^{38} +(-1.56931 - 0.732991i) q^{39} +(-0.490659 - 0.283282i) q^{40} +3.55741 q^{41} +(3.39909 - 5.06398i) q^{42} -2.13560 q^{43} +(0.498394 + 0.287748i) q^{44} +(0.564445 - 0.0987896i) q^{45} +(-0.329351 - 0.570452i) q^{46} +(4.61080 - 7.98614i) q^{47} +(3.46439 + 4.95434i) q^{48} +(5.17484 - 4.71392i) q^{49} -6.60599i q^{50} +(-11.3941 + 0.989581i) q^{51} +(0.198044 - 0.114341i) q^{52} +(-5.02935 + 2.90370i) q^{53} +(-6.67655 - 1.80258i) q^{54} -0.480688i q^{55} +(2.83356 + 7.31835i) q^{56} +(-9.05716 + 6.33334i) q^{57} +(2.43932 - 4.22503i) q^{58} +(-5.58681 - 9.67665i) q^{59} +(-0.0320171 + 0.0685475i) q^{60} +(1.06610 + 0.615513i) q^{61} +11.6724 q^{62} +(-6.94832 - 3.83678i) q^{63} -8.69359 q^{64} +(-0.165418 - 0.0955042i) q^{65} +(-2.45504 + 5.25614i) q^{66} +(2.38054 + 4.12321i) q^{67} +(0.755009 - 1.30771i) q^{68} +(-0.702519 + 0.491246i) q^{69} +(0.421761 - 0.523922i) q^{70} -5.29316i q^{71} +(6.82390 - 5.71121i) q^{72} +(6.07426 - 3.50698i) q^{73} +(-0.998576 + 0.576528i) q^{74} +(-8.56482 + 0.743857i) q^{75} -1.45917i q^{76} +(-4.17519 + 5.18653i) q^{77} +(1.32101 + 1.88915i) q^{78} +(-5.62114 + 9.73610i) q^{79} +(0.333342 + 0.577366i) q^{80} +(-1.58529 + 8.85928i) q^{81} +(-4.10028 - 2.36730i) q^{82} -10.2566 q^{83} +(0.940852 - 0.461517i) q^{84} -1.26126 q^{85} +(2.46150 + 1.42115i) q^{86} +(-5.75253 - 2.68689i) q^{87} +(-3.73231 - 6.46455i) q^{88} +(3.24190 - 5.61513i) q^{89} +(-0.716320 - 0.261748i) q^{90} +(0.955290 + 2.46727i) q^{91} -0.113180i q^{92} +(-1.31435 - 15.1336i) q^{93} +(-10.6288 + 6.13656i) q^{94} +(-1.05550 + 0.609392i) q^{95} +(0.192879 + 2.22082i) q^{96} -16.0239i q^{97} +(-9.10142 + 1.98965i) q^{98} +(7.09116 + 2.59115i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9}+O(q^{10}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9	\( 64 q + 32 q^{4} - 4 q^{7} - 4 q^{9} - 12 q^{10} - 30 q^{12} + 12 q^{15} - 16 q^{16} - 10 q^{18} + 10 q^{21} - 8 q^{22} + 36 q^{24} - 36 q^{25} - 20 q^{28} - 22 q^{30} + 12 q^{31} + 36 q^{36} - 36 q^{40} + 48 q^{42} - 32 q^{43} - 6 q^{45} - 48 q^{46} + 36 q^{49} - 16 q^{51} - 54 q^{54} - 8 q^{57} - 12 q^{58} + 16 q^{60} - 72 q^{61} - 86 q^{63} - 48 q^{64} - 78 q^{66} + 32 q^{67} - 4 q^{70} + 62 q^{72} + 48 q^{73} + 48 q^{75} - 20 q^{78} - 64 q^{79} + 28 q^{81} + 72 q^{82} - 18 q^{84} + 64 q^{85} + 60 q^{87} + 44 q^{88} + 8 q^{91} - 38 q^{93} + 72 q^{94} + 66 q^{96} - 68 q^{99}+O(q^{100}) \) 64 * q + 32 * q^4 - 4 * q^7 - 4 * q^9 - 12 * q^10 - 30 * q^12 + 12 * q^15 - 16 * q^16 - 10 * q^18 + 10 * q^21 - 8 * q^22 + 36 * q^24 - 36 * q^25 - 20 * q^28 - 22 * q^30 + 12 * q^31 + 36 * q^36 - 36 * q^40 + 48 * q^42 - 32 * q^43 - 6 * q^45 - 48 * q^46 + 36 * q^49 - 16 * q^51 - 54 * q^54 - 8 * q^57 - 12 * q^58 + 16 * q^60 - 72 * q^61 - 86 * q^63 - 48 * q^64 - 78 * q^66 + 32 * q^67 - 4 * q^70 + 62 * q^72 + 48 * q^73 + 48 * q^75 - 20 * q^78 - 64 * q^79 + 28 * q^81 + 72 * q^82 - 18 * q^84 + 64 * q^85 + 60 * q^87 + 44 * q^88 + 8 * q^91 - 38 * q^93 + 72 * q^94 + 66 * q^96 - 68 * q^99

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