LMFDB - Embedded newform 273.2.bj.d.142.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(25,273)]

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([0, 4, 3]))

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

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

chi := DirichletCharacter("273.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.bj (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:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 11x^{14} + 85x^{12} - 310x^{10} + 807x^{8} - 1196x^{6} + 1273x^{4} - 688x^{2} + 256 $ x^16 - 11x^14 + 85x^12 - 310x^10 + 807x^8 - 1196x^6 + 1273x^4 - 688*x^2 + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			142.4
Root			$-2.17587 + 1.25624i$ of defining polynomial
Character	$\chi$	$=$	273.142
Dual form			273.2.bj.d.25.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.504542 - 0.291297i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.830292 - 1.43811i) q^{4} +(-1.26176 - 0.728479i) q^{5} -0.582595i q^{6} +(-2.46845 - 0.952230i) q^{7} +2.13264i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.504542 - 0.291297i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.830292 - 1.43811i) q^{4} +(-1.26176 - 0.728479i) q^{5} -0.582595i q^{6} +(-2.46845 - 0.952230i) q^{7} +2.13264i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.424408 + 0.735096i) q^{10} +(-2.68042 + 1.54754i) q^{11} +(0.830292 - 1.43811i) q^{12} +(-3.54446 - 0.660933i) q^{13} +(0.968055 + 1.19949i) q^{14} -1.45696i q^{15} +(-1.03935 + 1.80021i) q^{16} +(1.75040 + 3.03179i) q^{17} +(0.504542 - 0.291297i) q^{18} +(-3.96420 - 2.28873i) q^{19} +2.41940i q^{20} +(-0.409571 - 2.61386i) q^{21} +1.80318 q^{22} +(3.01852 - 5.22824i) q^{23} +(-1.84692 + 1.06632i) q^{24} +(-1.43864 - 2.49179i) q^{25} +(1.59580 + 1.36596i) q^{26} -1.00000 q^{27} +(0.680126 + 4.34053i) q^{28} -5.81338 q^{29} +(-0.424408 + 0.735096i) q^{30} +(7.82929 - 4.52024i) q^{31} +(4.74263 - 2.73816i) q^{32} +(-2.68042 - 1.54754i) q^{33} -2.03955i q^{34} +(2.42092 + 2.99970i) q^{35} +1.66058 q^{36} +(-4.72494 - 2.72795i) q^{37} +(1.33340 + 2.30952i) q^{38} +(-1.19984 - 3.40006i) q^{39} +(1.55358 - 2.69088i) q^{40} +8.30215i q^{41} +(-0.554764 + 1.43811i) q^{42} -8.12434 q^{43} +(4.45106 + 2.56982i) q^{44} +(1.26176 - 0.728479i) q^{45} +(-3.04594 + 1.75858i) q^{46} +(9.47860 + 5.47247i) q^{47} -2.07870 q^{48} +(5.18651 + 4.70107i) q^{49} +1.67628i q^{50} +(-1.75040 + 3.03179i) q^{51} +(1.99244 + 5.64608i) q^{52} +(-3.62864 - 6.28499i) q^{53} +(0.504542 + 0.291297i) q^{54} +4.50940 q^{55} +(2.03076 - 5.26431i) q^{56} -4.57747i q^{57} +(2.93310 + 1.69342i) q^{58} +(-3.86508 + 2.23151i) q^{59} +(-2.09526 + 1.20970i) q^{60} +(3.83770 - 6.64709i) q^{61} -5.26694 q^{62} +(2.05888 - 1.66163i) q^{63} +0.966935 q^{64} +(3.99079 + 3.41600i) q^{65} +(0.901588 + 1.56160i) q^{66} +(10.9344 - 6.31301i) q^{67} +(2.90669 - 5.03454i) q^{68} +6.03705 q^{69} +(-0.347650 - 2.21868i) q^{70} +1.67628i q^{71} +(-1.84692 - 1.06632i) q^{72} +(-1.45937 + 0.842567i) q^{73} +(1.58929 + 2.75273i) q^{74} +(1.43864 - 2.49179i) q^{75} +7.60126i q^{76} +(8.09010 - 1.26765i) q^{77} +(-0.385056 + 2.06498i) q^{78} +(-6.05987 + 10.4960i) q^{79} +(2.62283 - 1.51429i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.41839 - 4.18878i) q^{82} -6.48599i q^{83} +(-3.41894 + 2.75927i) q^{84} -5.10053i q^{85} +(4.09907 + 2.36660i) q^{86} +(-2.90669 - 5.03454i) q^{87} +(-3.30034 - 5.71635i) q^{88} +(-13.1681 - 7.60260i) q^{89} -0.848816 q^{90} +(8.11996 + 5.00662i) q^{91} -10.0250 q^{92} +(7.82929 + 4.52024i) q^{93} +(-3.18823 - 5.52218i) q^{94} +(3.33459 + 5.77567i) q^{95} +(4.74263 + 2.73816i) q^{96} -1.56662i q^{97} +(-1.24740 - 3.88270i) q^{98} -3.09508i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	$ 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) $ 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

Display 100 coefficients 10 coefficients

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$1$	$-1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.504542	−	0.291297i	−0.356765	−	0.205978i	0.310896	−	0.950444i	$-0.399371\pi$
$2$	−0.504542	−	0.291297i	−0.356765	−	0.205978i	−0.667661	+	0.744466i	$0.732704\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.830292	−	1.43811i	−0.415146	−	0.719054i
$5$	−1.26176	−	0.728479i	−0.564277	−	0.325786i	0.190583	−	0.981671i	$-0.438962\pi$
$5$	−1.26176	−	0.728479i	−0.564277	−	0.325786i	−0.754861	+	0.655885i	$0.772295\pi$
$6$		−	0.582595i		−	0.237843i
$7$	−2.46845	−	0.952230i	−0.932987	−	0.359909i
$7$	−2.46845	−	0.952230i	−0.932987	−	0.359909i
$8$			2.13264i			0.754001i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.424408	+	0.735096i	0.134210	+	0.232458i
$11$	−2.68042	+	1.54754i	−0.808176	+	0.466601i	−0.846322	−	0.532671i	$-0.821188\pi$
$11$	−2.68042	+	1.54754i	−0.808176	+	0.466601i	0.0381460	+	0.999272i	$0.487855\pi$
$12$	0.830292	−	1.43811i	0.239685	−	0.415146i
$13$	−3.54446	−	0.660933i	−0.983055	−	0.183310i
$13$	−3.54446	−	0.660933i	−0.983055	−	0.183310i
$14$	0.968055	+	1.19949i	0.258724	+	0.320578i
$15$		−	1.45696i		−	0.376185i
$16$	−1.03935	+	1.80021i	−0.259838	+	0.450053i
$17$	1.75040	+	3.03179i	0.424535	+	0.735317i	0.996377	−	0.0850472i	$-0.0271041\pi$
$17$	1.75040	+	3.03179i	0.424535	+	0.735317i	−0.571842	+	0.820364i	$0.693771\pi$
$18$	0.504542	−	0.291297i	0.118922	−	0.0686594i
$19$	−3.96420	−	2.28873i	−0.909450	−	0.525071i	−0.0291959	−	0.999574i	$-0.509295\pi$
$19$	−3.96420	−	2.28873i	−0.909450	−	0.525071i	−0.880254	+	0.474502i	$0.842628\pi$
$20$			2.41940i			0.540994i
$21$	−0.409571	−	2.61386i	−0.0893756	−	0.570391i
$22$	1.80318			0.384439
$23$	3.01852	−	5.22824i	0.629406	−	1.09016i	−0.358265	−	0.933620i	$-0.616632\pi$
$23$	3.01852	−	5.22824i	0.629406	−	1.09016i	0.987671	−	0.156543i	$-0.0500350\pi$
$24$	−1.84692	+	1.06632i	−0.377000	+	0.217661i
$25$	−1.43864	−	2.49179i	−0.287727	−	0.498358i
$26$	1.59580	+	1.36596i	0.312962	+	0.267887i
$27$	−1.00000			−0.192450
$28$	0.680126	+	4.34053i	0.128532	+	0.820283i
$29$	−5.81338			−1.07952			−0.539759	−	0.841819i	$-0.681485\pi$
$29$	−5.81338			−1.07952			−0.539759	+	0.841819i	$0.681485\pi$
$30$	−0.424408	+	0.735096i	−0.0774859	+	0.134210i
$31$	7.82929	−	4.52024i	1.40618	−	0.811859i	0.411164	−	0.911561i	$-0.365122\pi$
$31$	7.82929	−	4.52024i	1.40618	−	0.811859i	0.995017	+	0.0997023i	$0.0317890\pi$
$32$	4.74263	−	2.73816i	0.838386	−	0.484042i
$33$	−2.68042	−	1.54754i	−0.466601	−	0.269392i
$34$		−	2.03955i		−	0.349780i
$35$	2.42092	+	2.99970i	0.409210	+	0.507043i
$36$	1.66058			0.276764
$37$	−4.72494	−	2.72795i	−0.776775	−	0.448472i	0.0585108	−	0.998287i	$-0.481365\pi$
$37$	−4.72494	−	2.72795i	−0.776775	−	0.448472i	−0.835286	+	0.549815i	$0.814698\pi$
$38$	1.33340	+	2.30952i	0.216307	+	0.374654i
$39$	−1.19984	−	3.40006i	−0.192129	−	0.544445i
$40$	1.55358	−	2.69088i	0.245643	−	0.425466i
$41$			8.30215i			1.29658i	0.761394	+	0.648289i	$0.224515\pi$
$41$			8.30215i			1.29658i	−0.761394	+	0.648289i	$0.775485\pi$
$42$	−0.554764	+	1.43811i	−0.0856020	+	0.221905i
$43$	−8.12434			−1.23895			−0.619475	−	0.785016i	$-0.712655\pi$
$43$	−8.12434			−1.23895			−0.619475	+	0.785016i	$0.712655\pi$
$44$	4.45106	+	2.56982i	0.671022	+	0.387415i
$45$	1.26176	−	0.728479i	0.188092	−	0.108595i
$46$	−3.04594	+	1.75858i	−0.449100	+	0.259288i
$47$	9.47860	+	5.47247i	1.38260	+	0.798242i	0.992466	−	0.122518i	$-0.0390970\pi$
$47$	9.47860	+	5.47247i	1.38260	+	0.798242i	0.390129	+	0.920760i	$0.372430\pi$
$48$	−2.07870			−0.300035
$49$	5.18651	+	4.70107i	0.740931	+	0.671581i
$50$			1.67628i			0.237062i
$51$	−1.75040	+	3.03179i	−0.245106	+	0.424535i
$52$	1.99244	+	5.64608i	0.276302	+	0.782970i
$53$	−3.62864	−	6.28499i	−0.498432	−	0.863309i	0.501566	−	0.865119i	$-0.332757\pi$
$53$	−3.62864	−	6.28499i	−0.498432	−	0.863309i	−0.999998	+	0.00180978i	$0.999424\pi$
$54$	0.504542	+	0.291297i	0.0686594	+	0.0396406i
$55$	4.50940			0.608047
$56$	2.03076	−	5.26431i	0.271372	−	0.703473i
$57$		−	4.57747i		−	0.606300i
$58$	2.93310	+	1.69342i	0.385134	+	0.222357i
$59$	−3.86508	+	2.23151i	−0.503191	+	0.290518i	−0.730030	−	0.683415i	$-0.760494\pi$
$59$	−3.86508	+	2.23151i	−0.503191	+	0.290518i	0.226839	+	0.973932i	$0.427161\pi$
$60$	−2.09526	+	1.20970i	−0.270497	+	0.156172i
$61$	3.83770	−	6.64709i	0.491367	−	0.851073i	−0.508584	−	0.861013i	$-0.669831\pi$
$61$	3.83770	−	6.64709i	0.491367	−	0.851073i	0.999951	+	0.00994000i	$0.00316405\pi$
$62$	−5.26694			−0.668902
$63$	2.05888	−	1.66163i	0.259395	−	0.209345i
$64$	0.966935			0.120867
$65$	3.99079	+	3.41600i	0.494996	+	0.423703i
$66$	0.901588	+	1.56160i	0.110978	+	0.192219i
$67$	10.9344	−	6.31301i	1.33586	−	0.771256i	0.349665	−	0.936875i	$-0.386295\pi$
$67$	10.9344	−	6.31301i	1.33586	−	0.771256i	0.986190	+	0.165618i	$0.0529619\pi$
$68$	2.90669	−	5.03454i	0.352488	−	0.610527i
$69$	6.03705			0.726775
$70$	−0.347650	−	2.21868i	−0.0415521	−	0.265183i
$71$			1.67628i			0.198938i	0.995041	+	0.0994692i	$0.0317145\pi$
$71$			1.67628i			0.198938i	−0.995041	+	0.0994692i	$0.968286\pi$
$72$	−1.84692	−	1.06632i	−0.217661	−	0.125667i
$73$	−1.45937	+	0.842567i	−0.170806	+	0.0986150i	−0.582966	−	0.812497i	$-0.698108\pi$
$73$	−1.45937	+	0.842567i	−0.170806	+	0.0986150i	0.412160	+	0.911112i	$0.364775\pi$
$74$	1.58929	+	2.75273i	0.184751	+	0.319998i
$75$	1.43864	−	2.49179i	0.166119	−	0.287727i
$76$			7.60126i			0.871925i
$77$	8.09010	−	1.26765i	0.921952	−	0.144463i
$78$	−0.385056	+	2.06498i	−0.0435990	+	0.233813i
$79$	−6.05987	+	10.4960i	−0.681788	+	1.18089i	0.292646	+	0.956221i	$0.405464\pi$
$79$	−6.05987	+	10.4960i	−0.681788	+	1.18089i	−0.974435	+	0.224671i	$0.927869\pi$
$80$	2.62283	−	1.51429i	0.293241	−	0.169303i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	2.41839	−	4.18878i	0.267067	−	0.462574i
$83$		−	6.48599i		−	0.711930i	−0.934499	−	0.355965i	$-0.884152\pi$
$83$		−	6.48599i		−	0.711930i	0.934499	−	0.355965i	$-0.115848\pi$
$84$	−3.41894	+	2.75927i	−0.373037	+	0.301061i
$85$		−	5.10053i		−	0.553230i
$86$	4.09907	+	2.36660i	0.442014	+	0.255197i
$87$	−2.90669	−	5.03454i	−0.311630	−	0.539759i
$88$	−3.30034	−	5.71635i	−0.351817	−	0.609365i
$89$	−13.1681	−	7.60260i	−1.39582	−	0.805874i	−0.401865	−	0.915699i	$-0.631638\pi$
$89$	−13.1681	−	7.60260i	−1.39582	−	0.805874i	−0.993951	+	0.109825i	$0.964971\pi$
$90$	−0.848816			−0.0894731
$91$	8.11996	+	5.00662i	0.851203	+	0.524836i
$92$	−10.0250			−1.04518
$93$	7.82929	+	4.52024i	0.811859	+	0.468727i
$94$	−3.18823	−	5.52218i	−0.328841	−	0.569569i
$95$	3.33459	+	5.77567i	0.342121	+	0.592572i
$96$	4.74263	+	2.73816i	0.484042	+	0.279462i
$97$		−	1.56662i		−	0.159066i	−0.996832	−	0.0795331i	$-0.974657\pi$
$97$		−	1.56662i		−	0.159066i	0.996832	−	0.0795331i	$-0.0253430\pi$
$98$	−1.24740	−	3.88270i	−0.126007	−	0.392212i
$99$		−	3.09508i		−	0.311067i
$100$	−2.38898	+	4.13783i	−0.238898	+	0.413783i
$101$	5.72587	+	9.91749i	0.569745	+	0.986827i	0.996591	+	0.0825029i	$0.0262914\pi$
$101$	5.72587	+	9.91749i	0.569745	+	0.986827i	−0.426846	+	0.904324i	$0.640375\pi$
$102$	1.76630	−	1.01978i	0.174890	−	0.100973i
$103$	1.53705	−	2.66225i	0.151450	−	0.262319i	−0.780311	−	0.625392i	$-0.784939\pi$
$103$	1.53705	−	2.66225i	0.151450	−	0.262319i	0.931761	+	0.363073i	$0.118272\pi$
$104$	1.40953	−	7.55904i	0.138216	−	0.741224i
$105$	−1.38736	+	3.59643i	−0.135392	+	0.350976i
$106$			4.22805i			0.410665i
$107$	4.10582	−	7.11149i	0.396925	−	0.687493i	−0.596420	−	0.802672i	$-0.703411\pi$
$107$	4.10582	−	7.11149i	0.396925	−	0.687493i	0.993345	+	0.115179i	$0.0367441\pi$
$108$	0.830292	+	1.43811i	0.0798949	+	0.138382i
$109$	−4.41034	+	2.54631i	−0.422434	+	0.243892i	−0.696118	−	0.717927i	$-0.745091\pi$
$109$	−4.41034	+	2.54631i	−0.422434	+	0.243892i	0.273684	+	0.961820i	$0.411758\pi$
$110$	−2.27518	−	1.31358i	−0.216930	−	0.125245i
$111$		−	5.45589i		−	0.517850i
$112$	4.27981	−	3.45403i	0.404404	−	0.326375i
$113$	−16.6085			−1.56240			−0.781199	−	0.624282i	$-0.785392\pi$
$113$	−16.6085			−1.56240			−0.781199	+	0.624282i	$0.785392\pi$
$114$	−1.33340	+	2.30952i	−0.124885	+	0.216307i
$115$	−7.61732	+	4.39786i	−0.710319	+	0.410103i
$116$	4.82680	+	8.36027i	0.448158	+	0.776232i
$117$	2.34461	−	2.73912i	0.216760	−	0.253232i
$118$	2.60013			0.239361
$119$	−1.43383	−	9.15062i	−0.131439	−	0.838836i
$120$	3.10716			0.283644
$121$	−0.710244	+	1.23018i	−0.0645676	+	0.111834i
$122$	−3.87256	+	2.23582i	−0.350605	+	0.202422i
$123$	−7.18987	+	4.15108i	−0.648289	+	0.374290i
$124$	−13.0012	−	7.50624i	−1.16754	−	0.674080i
$125$			11.4769i			1.02652i
$126$	−1.52282	+	0.238614i	−0.135664	+	0.0212574i
$127$	−0.904114			−0.0802272			−0.0401136	−	0.999195i	$-0.512772\pi$
$127$	−0.904114			−0.0802272			−0.0401136	+	0.999195i	$0.512772\pi$
$128$	−9.97312	−	5.75798i	−0.881507	−	0.508938i
$129$	−4.06217	−	7.03589i	−0.357654	−	0.619475i
$130$	−1.01845	−	2.88602i	−0.0893236	−	0.253121i
$131$	−1.93864	+	3.35782i	−0.169379	+	0.293374i	−0.938202	−	0.346089i	$-0.887510\pi$
$131$	−1.93864	+	3.35782i	−0.169379	+	0.293374i	0.768822	+	0.639462i	$0.220843\pi$
$132$			5.13964i			0.447348i
$133$	7.60604	+	9.42446i	0.659527	+	0.817204i
$134$	−7.35585			−0.635449
$135$	1.26176	+	0.728479i	0.108595	+	0.0626975i
$136$	−6.46570	+	3.73298i	−0.554430	+	0.320100i
$137$	−16.1496	+	9.32396i	−1.37975	+	0.796600i	−0.992129	−	0.125219i	$-0.960037\pi$
$137$	−16.1496	+	9.32396i	−1.37975	+	0.796600i	−0.387622	+	0.921818i	$0.626703\pi$
$138$	−3.04594	−	1.75858i	−0.259288	−	0.149700i
$139$	1.90068			0.161214			0.0806068	−	0.996746i	$-0.474314\pi$
$139$	1.90068			0.161214			0.0806068	+	0.996746i	$0.474314\pi$
$140$	2.30383	−	5.97217i	0.194709	−	0.504741i
$141$			10.9449i			0.921730i
$142$	0.488297	−	0.845756i	0.0409770	−	0.0709742i
$143$	10.5234	−	3.71361i	0.880014	−	0.310548i
$144$	−1.03935	−	1.80021i	−0.0866127	−	0.150018i
$145$	7.33511	+	4.23493i	0.609148	+	0.351692i
$146$	0.981750			0.0812502
$147$	−1.47799	+	6.84219i	−0.121902	+	0.564334i
$148$			9.05996i			0.744724i
$149$	−18.9572	−	10.9449i	−1.55303	−	0.896645i	−0.997893	−	0.0648885i	$-0.979331\pi$
$149$	−18.9572	−	10.9449i	−1.55303	−	0.896645i	−0.555141	−	0.831756i	$-0.687336\pi$
$150$	−1.45170	+	0.838142i	−0.118531	+	0.0684340i
$151$	−1.93837	+	1.11912i	−0.157742	+	0.0910726i	−0.576793	−	0.816890i	$-0.695696\pi$
$151$	−1.93837	+	1.11912i	−0.157742	+	0.0910726i	0.419051	+	0.907963i	$0.362363\pi$
$152$	4.88104	−	8.45420i	0.395904	−	0.685726i
$153$	−3.50081			−0.283024
$154$	−4.45106	−	1.71704i	−0.358676	−	0.138363i
$155$	−13.1716			−1.05797
$156$	−3.89342	+	4.54854i	−0.311723	+	0.364175i
$157$	−0.522820	−	0.905550i	−0.0417256	−	0.0722708i	0.844408	−	0.535700i	$-0.179952\pi$
$157$	−0.522820	−	0.905550i	−0.0417256	−	0.0722708i	−0.886134	+	0.463429i	$0.846619\pi$
$158$	6.11491	−	3.53045i	0.486476	−	0.280867i
$159$	3.62864	−	6.28499i	0.287770	−	0.498432i
$160$	−7.97876			−0.630776
$161$	−12.4296	+	10.0313i	−0.979587	+	0.790579i
$162$			0.582595i			0.0457730i
$163$	−6.08149	−	3.51115i	−0.476339	−	0.275014i	0.242551	−	0.970139i	$-0.422016\pi$
$163$	−6.08149	−	3.51115i	−0.476339	−	0.275014i	−0.718889	+	0.695124i	$0.755349\pi$
$164$	11.9394	−	6.89321i	0.932309	−	0.538269i
$165$	2.25470	+	3.90525i	0.175528	+	0.304024i
$166$	−1.88935	+	3.27245i	−0.146642	+	0.253992i
$167$		−	11.9623i		−	0.925671i	−0.886444	−	0.462835i	$-0.846832\pi$
$167$		−	11.9623i		−	0.925671i	0.886444	−	0.462835i	$-0.153168\pi$
$168$	5.57441	−	0.873465i	0.430075	−	0.0673893i
$169$	12.1263	+	4.68530i	0.932795	+	0.360407i
$170$	−1.48577	+	2.57343i	−0.113953	+	0.197373i
$171$	3.96420	−	2.28873i	0.303150	−	0.175024i
$172$	6.74557	+	11.6837i	0.514345	+	0.890872i
$173$	−0.667991	+	1.15699i	−0.0507864	+	0.0879646i	−0.890301	−	0.455372i	$-0.849506\pi$
$173$	−0.667991	+	1.15699i	−0.0507864	+	0.0879646i	0.839515	+	0.543337i	$0.182839\pi$
$174$			3.38685i			0.256756i
$175$	1.17845	+	7.52078i	0.0890822	+	0.568518i
$176$		−	6.43375i		−	0.484962i
$177$	−3.86508	−	2.23151i	−0.290518	−	0.167730i
$178$	4.42924	+	7.67166i	0.331985	+	0.575016i
$179$	−1.16370	−	2.01558i	−0.0869787	−	0.150651i	0.819254	−	0.573431i	$-0.194388\pi$
$179$	−1.16370	−	2.01558i	−0.0869787	−	0.150651i	−0.906233	+	0.422779i	$0.861055\pi$
$180$	−2.09526	−	1.20970i	−0.156172	−	0.0901657i
$181$	−2.31096			−0.171772			−0.0858861	−	0.996305i	$-0.527372\pi$
$181$	−2.31096			−0.171772			−0.0858861	+	0.996305i	$0.527372\pi$
$182$	−2.63844	−	4.89137i	−0.195575	−	0.362573i
$183$	7.67540			0.567382
$184$	11.1499	+	6.43742i	0.821984	+	0.474573i
$185$	3.97450	+	6.88404i	0.292211	+	0.506125i
$186$	−2.63347	−	4.56130i	−0.193095	−	0.334451i
$187$	−9.38363	−	5.41764i	−0.686199	−	0.396177i
$188$		−	18.1750i		−	1.32555i
$189$	2.46845	+	0.952230i	0.179553	+	0.0692646i
$190$		−	3.88543i		−	0.281878i
$191$	4.63857	−	8.03424i	0.335635	−	0.581337i	−0.647971	−	0.761665i	$-0.724382\pi$
$191$	4.63857	−	8.03424i	0.335635	−	0.581337i	0.983607	+	0.180327i	$0.0577157\pi$
$192$	0.483468	+	0.837391i	0.0348913	+	0.0604335i
$193$	5.85868	−	3.38251i	0.421717	−	0.243478i	−0.274095	−	0.961703i	$-0.588378\pi$
$193$	5.85868	−	3.38251i	0.421717	−	0.243478i	0.695812	+	0.718224i	$0.255045\pi$
$194$	−0.456353	+	0.790426i	−0.0327642	+	0.0567493i
$195$	−0.962951	+	5.16412i	−0.0689584	+	0.369811i
$196$	2.45432	−	11.3620i	0.175309	−	0.811573i
$197$		−	10.5817i		−	0.753913i	−0.926231	−	0.376957i	$-0.876971\pi$
$197$		−	10.5817i		−	0.753913i	0.926231	−	0.376957i	$-0.123029\pi$
$198$	−0.901588	+	1.56160i	−0.0640731	+	0.110978i
$199$	−4.73698	−	8.20470i	−0.335796	−	0.581616i	0.647842	−	0.761775i	$-0.275672\pi$
$199$	−4.73698	−	8.20470i	−0.335796	−	0.581616i	−0.983637	+	0.180160i	$0.942339\pi$
$200$	5.31409	−	3.06809i	0.375763	−	0.216947i
$201$	10.9344	+	6.31301i	0.771256	+	0.445285i
$202$		−	6.67172i		−	0.469421i
$203$	14.3501	+	5.53568i	1.00718	+	0.388529i
$204$	5.81338			0.407018
$205$	6.04794	−	10.4753i	0.422407	−	0.731630i
$206$	−1.55101	+	0.895476i	−0.108064	+	0.0623908i
$207$	3.01852	+	5.22824i	0.209802	+	0.363388i
$208$	4.87376	−	5.69382i	0.337934	−	0.394796i
$209$	14.1676			0.979994
$210$	1.74761	−	1.41042i	0.120597	−	0.0973279i
$211$	−1.26188			−0.0868717			−0.0434358	−	0.999056i	$-0.513830\pi$
$211$	−1.26188			−0.0868717			−0.0434358	+	0.999056i	$0.513830\pi$
$212$	−6.02566	+	10.4367i	−0.413844	+	0.716799i
$213$	−1.45170	+	0.838142i	−0.0994692	+	0.0574286i
$214$	−4.14311	+	2.39203i	−0.283218	+	0.163516i
$215$	10.2510	+	5.91841i	0.699112	+	0.403632i
$216$		−	2.13264i		−	0.145108i
$217$	−23.6305	+	3.70272i	−1.60414	+	0.251357i
$218$	2.96694			0.200946
$219$	−1.45937	−	0.842567i	−0.0986150	−	0.0569354i
$220$	−3.74412	−	6.48500i	−0.252428	−	0.437219i
$221$	−4.20042	−	11.9029i	−0.282551	−	0.800679i
$222$	−1.58929	+	2.75273i	−0.106666	+	0.184751i
$223$		−	3.46335i		−	0.231923i	−0.993254	−	0.115962i	$-0.963005\pi$
$223$		−	3.46335i		−	0.231923i	0.993254	−	0.115962i	$-0.0369950\pi$
$224$	−14.3143	+	2.24294i	−0.956415	+	0.149863i
$225$	2.87727			0.191818
$226$	8.37969	+	4.83802i	0.557409	+	0.321820i
$227$	1.24307	−	0.717687i	0.0825055	−	0.0476345i	−0.458180	−	0.888860i	$-0.651498\pi$
$227$	1.24307	−	0.717687i	0.0825055	−	0.0476345i	0.540685	+	0.841225i	$0.318165\pi$
$228$	−6.58289	+	3.80063i	−0.435962	+	0.251703i
$229$	20.6692	+	11.9334i	1.36586	+	0.788581i	0.990397	−	0.138256i	$-0.0441496\pi$
$229$	20.6692	+	11.9334i	1.36586	+	0.788581i	0.375465	+	0.926836i	$0.377483\pi$
$230$	5.12434			0.337889
$231$	5.14287	+	6.37240i	0.338376	+	0.419273i
$232$		−	12.3978i		−	0.813958i
$233$	6.80227	−	11.7819i	0.445631	−	0.771856i	−0.552465	−	0.833536i	$-0.686313\pi$
$233$	6.80227	−	11.7819i	0.445631	−	0.771856i	0.998096	+	0.0616802i	$0.0196459\pi$
$234$	−1.98085	+	0.699022i	−0.129492	+	0.0456965i
$235$	−7.97316	−	13.8099i	−0.520112	−	0.900860i
$236$	6.41830	+	3.70560i	0.417795	+	0.241214i
$237$	−12.1197			−0.787261
$238$	−1.94212	+	5.03454i	−0.125889	+	0.326341i
$239$			11.9280i			0.771560i	0.922591	+	0.385780i	$0.126068\pi$
$239$			11.9280i			0.771560i	−0.922591	+	0.385780i	$0.873932\pi$
$240$	2.62283	+	1.51429i	0.169303	+	0.0977471i
$241$	−8.59672	+	4.96332i	−0.553763	+	0.319715i	−0.750639	−	0.660713i	$-0.770254\pi$
$241$	−8.59672	+	4.96332i	−0.553763	+	0.319715i	0.196875	+	0.980429i	$0.436921\pi$
$242$	0.716695	−	0.413784i	0.0460709	−	0.0265991i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−12.7456			−0.815956
$245$	−3.11952	−	9.70990i	−0.199299	−	0.620343i
$246$	4.83679			0.308382
$247$	12.5382	+	10.7324i	0.797789	+	0.682885i
$248$	9.64003	+	16.6970i	0.612143	+	1.06026i
$249$	5.61703	−	3.24299i	0.355965	−	0.205516i
$250$	3.34318	−	5.79055i	0.211441	−	0.366227i
$251$	18.9920			1.19876			0.599381	−	0.800464i	$-0.295414\pi$
$251$	18.9920			1.19876			0.599381	+	0.800464i	$0.295414\pi$
$252$	−4.09907	−	1.58126i	−0.258217	−	0.0996099i
$253$			18.6851i			1.17472i
$254$	0.456164	+	0.263366i	0.0286222	+	0.0165251i
$255$	4.41719	−	2.55027i	0.276615	−	0.159704i
$256$	2.38763	+	4.13550i	0.149227	+	0.258469i
$257$	−9.98567	+	17.2957i	−0.622889	+	1.07888i	0.366056	+	0.930593i	$0.380708\pi$
$257$	−9.98567	+	17.2957i	−0.622889	+	1.07888i	−0.988945	+	0.148283i	$0.952625\pi$
$258$			4.73320i			0.294676i
$259$	9.06566	+	11.2330i	0.563313	+	0.697987i
$260$	1.59906	−	8.57546i	0.0991696	−	0.531827i
$261$	2.90669	−	5.03454i	0.179920	−	0.311630i
$262$	1.95625	−	1.12944i	0.120857	−	0.0697770i
$263$	−1.65452	−	2.86571i	−0.102022	−	0.176707i	0.810496	−	0.585745i	$-0.199198\pi$
$263$	−1.65452	−	2.86571i	−0.102022	−	0.176707i	−0.912518	+	0.409037i	$0.865865\pi$
$264$	3.30034	−	5.71635i	0.203122	−	0.351817i
$265$			10.5735i			0.649528i
$266$	−1.09225	−	6.97065i	−0.0669699	−	0.427398i
$267$		−	15.2052i		−	0.930544i
$268$	−18.1576	−	10.4833i	−1.10915	−	0.640368i
$269$	11.9326	+	20.6679i	0.727545	+	1.26014i	0.957918	+	0.287042i	$0.0926720\pi$
$269$	11.9326	+	20.6679i	0.727545	+	1.26014i	−0.230373	+	0.973102i	$0.573995\pi$
$270$	−0.424408	−	0.735096i	−0.0258286	−	0.0447365i
$271$	1.44819	+	0.836111i	0.0879711	+	0.0507901i	0.543340	−	0.839513i	$-0.317159\pi$
$271$	1.44819	+	0.836111i	0.0879711	+	0.0507901i	−0.455369	+	0.890303i	$0.650493\pi$
$272$	−7.27714			−0.441242
$273$	−0.275880	+	9.53540i	−0.0166970	+	0.577109i
$274$	10.8642			0.656329
$275$	7.71229	+	4.45269i	0.465069	+	0.268508i
$276$	−5.01251	−	8.68192i	−0.301718	−	0.522590i
$277$	−2.74960	−	4.76244i	−0.165207	−	0.286147i	0.771522	−	0.636203i	$-0.219496\pi$
$277$	−2.74960	−	4.76244i	−0.165207	−	0.286147i	−0.936729	+	0.350056i	$0.886163\pi$
$278$	−0.958972	−	0.553663i	−0.0575153	−	0.0332065i
$279$			9.04048i			0.541239i
$280$	−6.39728	+	5.16294i	−0.382311	+	0.308545i
$281$			32.5989i			1.94469i	0.233552	+	0.972344i	$0.424965\pi$
$281$			32.5989i			1.94469i	−0.233552	+	0.972344i	$0.575035\pi$
$282$	3.18823	−	5.52218i	0.189856	−	0.328841i
$283$	−8.82509	−	15.2855i	−0.524597	−	0.908629i	−0.999590	−	0.0286390i	$-0.990883\pi$
$283$	−8.82509	−	15.2855i	−0.524597	−	0.908629i	0.474993	−	0.879990i	$-0.342451\pi$
$284$	2.41068	−	1.39181i	0.143047	−	0.0825884i
$285$	−3.33459	+	5.77567i	−0.197524	+	0.342121i
$286$	−6.39128	−	1.19178i	−0.377924	−	0.0704714i
$287$	7.90556	−	20.4935i	0.466650	−	1.20969i
$288$			5.47632i			0.322695i
$289$	2.37217	−	4.10872i	0.139539	−	0.241689i
$290$	−2.46725	−	4.27340i	−0.144882	−	0.250943i
$291$	1.35673	−	0.783311i	0.0795331	−	0.0459185i
$292$	2.42340	+	1.39915i	0.141819	+	0.0818792i
$293$			6.86489i			0.401051i	0.979688	+	0.200526i	$0.0642650\pi$
$293$			6.86489i			0.401051i	−0.979688	+	0.200526i	$0.935735\pi$
$294$	2.73882	−	3.02164i	0.159731	−	0.176225i
$295$	6.50243			0.378586
$296$	5.81772	−	10.0766i	0.338148	−	0.585689i
$297$	2.68042	−	1.54754i	0.155534	−	0.0897973i
$298$	6.37647	+	11.0444i	0.369379	+	0.639783i
$299$	−14.1545	+	16.5362i	−0.818578	+	0.956314i
$300$	−4.77795			−0.275855
$301$	20.0546	+	7.73625i	1.15593	+	0.445910i
$302$	1.30399			0.0750359
$303$	−5.72587	+	9.91749i	−0.328942	+	0.569745i
$304$	8.24040	−	4.75760i	0.472619	−	0.272867i
$305$	−9.68453	+	5.59137i	−0.554535	+	0.320161i
$306$	1.76630	+	1.01978i	0.100973	+	0.0582967i
$307$		−	28.3680i		−	1.61905i	−0.587089	−	0.809523i	$-0.699726\pi$
$307$		−	28.3680i		−	1.61905i	0.587089	−	0.809523i	$-0.300274\pi$
$308$	−8.54016	−	10.5819i	−0.486621	−	0.602960i
$309$	3.07410			0.174879
$310$	6.64562	+	3.83685i	0.377446	+	0.217919i
$311$	−9.08499	−	15.7357i	−0.515163	−	0.892288i	−0.999845	−	0.0175977i	$-0.994398\pi$
$311$	−9.08499	−	15.7357i	−0.515163	−	0.892288i	0.484683	−	0.874690i	$-0.338935\pi$
$312$	7.25108	−	2.55883i	0.410512	−	0.144865i
$313$	−6.49909	+	11.2568i	−0.367350	+	0.636269i	−0.989150	−	0.146907i	$-0.953068\pi$
$313$	−6.49909	+	11.2568i	−0.367350	+	0.636269i	0.621800	+	0.783176i	$0.286402\pi$
$314$			0.609184i			0.0343782i
$315$	−3.80828	+	0.596727i	−0.214572	+	0.0336218i
$316$	20.1258			1.13217
$317$	−6.87879	−	3.97147i	−0.386352	−	0.223060i	0.294227	−	0.955736i	$-0.404938\pi$
$317$	−6.87879	−	3.97147i	−0.386352	−	0.223060i	−0.680578	+	0.732676i	$0.738271\pi$
$318$	−3.66160	+	2.11403i	−0.205332	+	0.118549i
$319$	15.5823	−	8.99644i	0.872441	−	0.503704i
$320$	−1.22004	−	0.704392i	−0.0682025	−	0.0393767i
$321$	8.21164			0.458329
$322$	9.19334	−	1.44052i	0.512325	−	0.0802772i
$323$		−	16.0248i		−	0.891645i
$324$	−0.830292	+	1.43811i	−0.0461273	+	0.0798949i
$325$	3.45228	+	9.78289i	0.191498	+	0.542657i
$326$	2.04558	+	3.54304i	0.113294	+	0.196231i
$327$	−4.41034	−	2.54631i	−0.243892	−	0.140811i
$328$	−17.7055			−0.977621
$329$	−18.1864	−	22.5343i	−1.00265	−	1.24236i
$330$		−	2.62715i		−	0.144620i
$331$	−4.21336	−	2.43259i	−0.231587	−	0.133707i	0.379717	−	0.925103i	$-0.376021\pi$
$331$	−4.21336	−	2.43259i	−0.231587	−	0.133707i	−0.611304	+	0.791396i	$0.709355\pi$
$332$	−9.32755	+	5.38526i	−0.511916	+	0.295555i
$333$	4.72494	−	2.72795i	0.258925	−	0.149491i
$334$	−3.48459	+	6.03548i	−0.190668	+	0.330247i
$335$	−18.3956			−1.00506
$336$	5.13118	+	1.97940i	0.279929	+	0.107985i
$337$	7.89831			0.430248			0.215124	−	0.976587i	$-0.430984\pi$
$337$	7.89831			0.430248			0.215124	+	0.976587i	$0.430984\pi$
$338$	−4.75343	−	5.89630i	−0.258552	−	0.320716i
$339$	−8.30426	−	14.3834i	−0.451025	−	0.781199i
$340$	−7.33511	+	4.23493i	−0.397802	+	0.229671i
$341$	−13.9905	+	24.2323i	−0.757628	+	1.31225i
$342$	−2.66681			−0.144204
$343$	−8.32616	−	16.5431i	−0.449571	−	0.893245i
$344$		−	17.3263i		−	0.934170i
$345$	−7.61732	−	4.39786i	−0.410103	−	0.236773i
$346$	0.674059	−	0.389168i	0.0362376	−	0.0209218i
$347$	2.00510	+	3.47294i	0.107640	+	0.186437i	0.914814	−	0.403876i	$-0.132337\pi$
$347$	2.00510	+	3.47294i	0.107640	+	0.186437i	−0.807174	+	0.590314i	$0.799004\pi$
$348$	−4.82680	+	8.36027i	−0.258744	+	0.448158i
$349$			14.1849i			0.759300i	0.925130	+	0.379650i	$0.123956\pi$
$349$			14.1849i			0.759300i	−0.925130	+	0.379650i	$0.876044\pi$
$350$	1.59621	−	4.13783i	0.0853210	−	0.221176i
$351$	3.54446	+	0.660933i	0.189189	+	0.0352780i
$352$	−8.47481	+	14.6788i	−0.451709	+	0.782383i
$353$	−0.540295	+	0.311940i	−0.0287570	+	0.0166029i	−0.514310	−	0.857605i	$-0.671952\pi$
$353$	−0.540295	+	0.311940i	−0.0287570	+	0.0166029i	0.485553	+	0.874207i	$0.338618\pi$
$354$	1.30006	+	2.25178i	0.0690977	+	0.119681i
$355$	1.22114	−	2.11507i	0.0648113	−	0.112256i
$356$			25.2495i			1.33822i
$357$	7.20775	−	5.81704i	0.381475	−	0.307870i
$358$			1.35593i			0.0716629i
$359$	18.1864	+	10.4999i	0.959843	+	0.554166i	0.896125	−	0.443802i	$-0.146371\pi$
$359$	18.1864	+	10.4999i	0.959843	+	0.554166i	0.0637184	+	0.997968i	$0.479704\pi$
$360$	1.55358	+	2.69088i	0.0818809	+	0.141822i
$361$	0.976595	+	1.69151i	0.0513997	+	0.0890269i
$362$	1.16598	+	0.673176i	0.0612823	+	0.0353814i
$363$	−1.42049			−0.0745563
$364$	0.458121	−	15.8343i	0.0240121	−	0.829944i
$365$	2.45517			0.128509
$366$	−3.87256	−	2.23582i	−0.202422	−	0.116868i
$367$	−1.78938	−	3.09930i	−0.0934049	−	0.161782i	0.815537	−	0.578705i	$-0.196442\pi$
$367$	−1.78938	−	3.09930i	−0.0934049	−	0.161782i	−0.908942	+	0.416923i	$0.863108\pi$
$368$	6.27462	+	10.8680i	0.327087	+	0.566531i
$369$	−7.18987	−	4.15108i	−0.374290	−	0.216096i
$370$		−	4.63105i		−	0.240757i
$371$	2.97237	+	18.9695i	0.154318	+	0.984847i
$372$		−	15.0125i		−	0.778360i
$373$	11.8376	−	20.5033i	0.612928	−	1.06162i	−0.377817	−	0.925880i	$-0.623325\pi$
$373$	11.8376	−	20.5033i	0.612928	−	1.06162i	0.990744	−	0.135741i	$-0.0433416\pi$
$374$	3.15629	+	5.46685i	0.163208	+	0.282684i
$375$	−9.93925	+	5.73843i	−0.513261	+	0.296331i
$376$	−11.6708	+	20.2144i	−0.601875	+	1.04248i
$377$	20.6053	+	3.84226i	1.06123	+	0.197886i
$378$	−0.968055	−	1.19949i	−0.0497914	−	0.0616953i
$379$		−	20.5212i		−	1.05410i	−0.849833	−	0.527052i	$-0.823297\pi$
$379$		−	20.5212i		−	1.05410i	0.849833	−	0.527052i	$-0.176703\pi$
$380$	5.53736	−	9.59099i	0.284061	−	0.492007i
$381$	−0.452057	−	0.782986i	−0.0231596	−	0.0401136i
$382$	−4.68071	+	2.70241i	−0.239486	+	0.138267i
$383$	2.53122	+	1.46140i	0.129340	+	0.0746742i	0.563274	−	0.826270i	$-0.309542\pi$
$383$	2.53122	+	1.46140i	0.129340	+	0.0746742i	−0.433934	+	0.900945i	$0.642875\pi$
$384$		−	11.5160i		−	0.587671i
$385$	−11.1312	−	4.29399i	−0.567300	−	0.218842i
$386$	−3.94127			−0.200605
$387$	4.06217	−	7.03589i	0.206492	−	0.357654i
$388$	−2.25297	+	1.30075i	−0.114377	+	0.0660357i
$389$	−6.44084	−	11.1559i	−0.326564	−	0.565625i	0.655264	−	0.755400i	$-0.272557\pi$
$389$	−6.44084	−	11.1559i	−0.326564	−	0.565625i	−0.981828	+	0.189775i	$0.939224\pi$
$390$	1.99014	−	2.32501i	0.100775	−	0.117732i
$391$	21.1346			1.06882
$392$	−10.0257	+	11.0610i	−0.506373	+	0.558662i
$393$	−3.87727			−0.195583
$394$	−3.08241	+	5.33890i	−0.155290	+	0.268970i
$395$	15.2922	−	8.82897i	0.769436	−	0.444234i
$396$	−4.45106	+	2.56982i	−0.223674	+	0.129138i
$397$	−28.6326	−	16.5310i	−1.43703	−	0.829669i	−0.439386	−	0.898298i	$-0.644804\pi$
$397$	−28.6326	−	16.5310i	−1.43703	−	0.829669i	−0.997642	+	0.0686298i	$0.978137\pi$
$398$			5.51948i			0.276667i
$399$	−4.35880	+	11.2993i	−0.218213	+	0.565670i
$400$	5.98100			0.299050
$401$	−0.355349	−	0.205161i	−0.0177453	−	0.0102453i	0.491101	−	0.871103i	$-0.336595\pi$
$401$	−0.355349	−	0.205161i	−0.0177453	−	0.0102453i	−0.508846	+	0.860857i	$0.669928\pi$
$402$	−3.67792	−	6.37035i	−0.183438	−	0.317724i
$403$	−30.7381	+	10.8472i	−1.53118	+	0.540336i
$404$	9.50828	−	16.4688i	0.473055	−	0.819355i
$405$			1.45696i			0.0723968i
$406$	−5.62768	−	6.97312i	−0.279297	−	0.346070i
$407$	16.8864			0.837028
$408$	−6.46570	−	3.73298i	−0.320100	−	0.184810i
$409$	−0.741857	+	0.428312i	−0.0366825	+	0.0211786i	−0.518229	−	0.855242i	$-0.673409\pi$
$409$	−0.741857	+	0.428312i	−0.0366825	+	0.0211786i	0.481547	+	0.876420i	$0.340075\pi$
$410$	−6.10288	+	3.52350i	−0.301400	+	0.174013i
$411$	−16.1496	−	9.32396i	−0.796600	−	0.459917i
$412$	−5.10479			−0.251495
$413$	11.6657	−	1.82792i	0.574031	−	0.0899461i
$414$		−	3.51715i		−	0.172859i
$415$	−4.72491	+	8.18378i	−0.231937	+	0.401726i
$416$	−18.6198	+	6.57072i	−0.912910	+	0.322156i
$417$	0.950340	+	1.64604i	0.0465383	+	0.0806068i
$418$	−7.14815	−	4.12699i	−0.349628	−	0.201858i
$419$	27.0368			1.32084			0.660418	−	0.750898i	$-0.270379\pi$
$419$	27.0368			1.32084			0.660418	+	0.750898i	$0.270379\pi$
$420$	6.32397	−	0.990915i	0.308578	−	0.0483517i
$421$		−	17.1867i		−	0.837628i	−0.908072	−	0.418814i	$-0.862446\pi$
$421$		−	17.1867i		−	0.837628i	0.908072	−	0.418814i	$-0.137554\pi$
$422$	0.636673	+	0.367584i	0.0309928	+	0.0178937i
$423$	−9.47860	+	5.47247i	−0.460865	+	0.266081i
$424$	13.4036	−	7.73857i	0.650936	−	0.375818i
$425$	5.03639	−	8.72329i	0.244301	−	0.423142i
$426$	0.976595			0.0473162
$427$	−15.8027	+	12.7537i	−0.764748	+	0.617192i
$428$	−13.6361			−0.659126
$429$	8.47780	+	7.25676i	0.409312	+	0.350360i
$430$	−3.44804	−	5.97217i	−0.166279	−	0.288004i
$431$	−2.12084	+	1.22447i	−0.102157	+	0.0589805i	−0.550208	−	0.835028i	$-0.685452\pi$
$431$	−2.12084	+	1.22447i	−0.102157	+	0.0589805i	0.448051	+	0.894008i	$0.352118\pi$
$432$	1.03935	−	1.80021i	0.0500058	−	0.0866127i
$433$	40.8612			1.96366			0.981832	−	0.189754i	$-0.0607689\pi$
$433$	40.8612			1.96366			0.981832	+	0.189754i	$0.0607689\pi$
$434$	13.0012	+	5.01534i	0.624077	+	0.240744i
$435$			8.46986i			0.406099i
$436$	7.32374	+	4.22836i	0.350743	+	0.202502i
$437$	−23.9321	+	13.8172i	−1.14483	+	0.660966i
$438$	0.490875	+	0.850221i	0.0234549	+	0.0406251i
$439$	−15.7826	+	27.3363i	−0.753264	+	1.30469i	0.192969	+	0.981205i	$0.438188\pi$
$439$	−15.7826	+	27.3363i	−0.753264	+	1.30469i	−0.946233	+	0.323486i	$0.895145\pi$
$440$			9.61691i			0.458468i
$441$	−6.66450	+	2.14112i	−0.317357	+	0.101958i
$442$	−1.34801	+	7.22910i	−0.0641182	+	0.343853i
$443$	−19.2093	+	33.2715i	−0.912663	+	1.58078i	−0.102376	+	0.994746i	$0.532644\pi$
$443$	−19.2093	+	33.2715i	−0.912663	+	1.58078i	−0.810287	+	0.586033i	$0.800689\pi$
$444$	−7.84616	+	4.52998i	−0.372362	+	0.214983i
$445$	11.0767	+	19.1854i	0.525085	+	0.909473i
$446$	−1.00887	+	1.74741i	−0.0477712	+	0.0827421i
$447$		−	21.8899i		−	1.03536i
$448$	−2.38683	−	0.920745i	−0.112767	−	0.0435011i
$449$			24.0362i			1.13434i	0.823602	+	0.567168i	$0.191961\pi$
$449$			24.0362i			1.13434i	−0.823602	+	0.567168i	$0.808039\pi$
$450$	−1.45170	−	0.838142i	−0.0684340	−	0.0395104i
$451$	−12.8479	−	22.2532i	−0.604984	−	1.04786i
$452$	13.7899	+	23.8848i	0.648623	+	1.12345i
$453$	−1.93837	−	1.11912i	−0.0910726	−	0.0525808i
$454$	−0.836241			−0.0392467
$455$	−6.59824	−	12.2324i	−0.309330	−	0.573463i
$456$	9.76207			0.457151
$457$	−31.0833	−	17.9460i	−1.45402	−	0.839477i	−0.455312	−	0.890332i	$-0.650472\pi$
$457$	−31.0833	−	17.9460i	−1.45402	−	0.839477i	−0.998706	+	0.0508547i	$0.983805\pi$
$458$	−6.95233	−	12.0418i	−0.324861	−	0.562676i
$459$	−1.75040	−	3.03179i	−0.0817019	−	0.141512i
$460$	12.6492	+	7.30302i	0.589772	+	0.340505i
$461$		−	19.9043i		−	0.927036i	−0.886087	−	0.463518i	$-0.846587\pi$
$461$		−	19.9043i		−	0.927036i	0.886087	−	0.463518i	$-0.153413\pi$
$462$	−0.738528	−	4.71325i	−0.0343594	−	0.219280i
$463$			2.71044i			0.125965i	0.998015	+	0.0629825i	$0.0200612\pi$
$463$			2.71044i			0.125965i	−0.998015	+	0.0629825i	$0.979939\pi$
$464$	6.04215	−	10.4653i	0.280500	−	0.485840i
$465$	−6.58580	−	11.4069i	−0.305409	−	0.528984i
$466$	−6.86406	+	3.96297i	−0.317971	+	0.183581i
$467$	−16.3733	+	28.3593i	−0.757664	+	1.31231i	0.186375	+	0.982479i	$0.440326\pi$
$467$	−16.3733	+	28.3593i	−0.757664	+	1.31231i	−0.944039	+	0.329834i	$0.893007\pi$
$468$	−5.88586	−	1.09753i	−0.272074	−	0.0507335i
$469$	−33.0026	+	5.17124i	−1.52392	+	0.238786i
$470$			9.29024i			0.428527i
$471$	0.522820	−	0.905550i	0.0240903	−	0.0417256i
$472$	−4.75900	−	8.24282i	−0.219051	−	0.379407i
$473$	21.7766	−	12.5727i	1.00129	−	0.578095i
$474$	6.11491	+	3.53045i	0.280867	+	0.162159i
$475$			13.1706i			0.604310i
$476$	−11.9691	+	9.65968i	−0.548602	+	0.442751i
$477$	7.25728			0.332288
$478$	3.47460	−	6.01819i	0.158925	−	0.275266i
$479$	11.5460	−	6.66606i	0.527548	−	0.304580i	−0.212469	−	0.977168i	$-0.568151\pi$
$479$	11.5460	−	6.66606i	0.527548	−	0.304580i	0.740018	+	0.672588i	$0.234817\pi$
$480$	−3.98938	−	6.90981i	−0.182089	−	0.315388i
$481$	14.9444	+	12.7920i	0.681404	+	0.583263i
$482$	5.78321			0.263418
$483$	−14.9022	−	5.74866i	−0.678072	−	0.261573i
$484$	2.35884			0.107220
$485$	−1.14125	+	1.97670i	−0.0518215	+	0.0897575i
$486$	−0.504542	+	0.291297i	−0.0228865	+	0.0132135i
$487$	32.3489	−	18.6767i	1.46587	−	0.846320i	0.466597	−	0.884470i	$-0.345480\pi$
$487$	32.3489	−	18.6767i	1.46587	−	0.846320i	0.999272	+	0.0381500i	$0.0121465\pi$
$488$	14.1758	+	8.18442i	0.641710	+	0.370491i
$489$		−	7.02229i		−	0.317559i
$490$	−1.25454	+	5.80776i	−0.0566744	+	0.262368i
$491$	4.41544			0.199266			0.0996329	−	0.995024i	$-0.468233\pi$
$491$	4.41544			0.199266			0.0996329	+	0.995024i	$0.468233\pi$
$492$	11.9394	+	6.89321i	0.538269	+	0.310770i
$493$	−10.1758	−	17.6250i	−0.458294	−	0.793788i
$494$	−3.19975	−	9.06729i	−0.143964	−	0.407957i
$495$	−2.25470	+	3.90525i	−0.101341	+	0.175528i
$496$			18.7925i			0.843807i
$497$	1.59621	−	4.13783i	0.0715998	−	0.185607i
$498$	−3.77870			−0.169328
$499$	−24.6507	−	14.2321i	−1.10352	−	0.637116i	−0.166374	−	0.986063i	$-0.553206\pi$
$499$	−24.6507	−	14.2321i	−1.10352	−	0.637116i	−0.937142	+	0.348947i	$0.886539\pi$
$500$	16.5050	−	9.52914i	0.738124	−	0.426156i
$501$	10.3597	−	5.98115i	0.462835	−	0.267218i
$502$	−9.58224	−	5.53231i	−0.427676	−	0.246919i
$503$	−22.6474			−1.00980			−0.504899	−	0.863179i	$-0.668470\pi$
$503$	−22.6474			−1.00980			−0.504899	+	0.863179i	$0.668470\pi$
$504$	3.54365	+	4.39085i	0.157847	+	0.195584i
$505$		−	16.6847i		−	0.742459i
$506$	5.44293	−	9.42744i	0.241968	−	0.419101i
$507$	2.00558	+	12.8444i	0.0890711	+	0.570438i
$508$	0.750679	+	1.30021i	0.0333060	+	0.0576877i
$509$	−15.5392	−	8.97157i	−0.688764	−	0.397658i	0.114385	−	0.993436i	$-0.463510\pi$
$509$	−15.5392	−	8.97157i	−0.688764	−	0.397658i	−0.803149	+	0.595779i	$0.796844\pi$
$510$	−2.97154			−0.131582
$511$	4.40470	−	0.690181i	0.194852	−	0.0305318i
$512$			20.2499i			0.894927i
$513$	3.96420	+	2.28873i	0.175024	+	0.101050i
$514$	10.0764	−	5.81760i	0.444450	−	0.256603i
$515$	−3.87878	+	2.23942i	−0.170919	+	0.0986804i
$516$	−6.74557	+	11.6837i	−0.296957	+	0.514345i
$517$	−33.8755			−1.48984
$518$	−1.30185	−	8.30834i	−0.0572000	−	0.365047i
$519$	−1.33598			−0.0586431
$520$	−7.28509	+	8.51090i	−0.319472	+	0.373227i
$521$	3.28321	+	5.68668i	0.143840	+	0.249138i	0.928940	−	0.370231i	$-0.120722\pi$
$521$	3.28321	+	5.68668i	0.143840	+	0.249138i	−0.785100	+	0.619370i	$0.787388\pi$
$522$	−2.93310	+	1.69342i	−0.128378	+	0.0741191i
$523$	8.80679	−	15.2538i	0.385094	−	0.667002i	−0.606688	−	0.794940i	$-0.707502\pi$
$523$	8.80679	−	15.2538i	0.385094	−	0.667002i	0.991782	+	0.127938i	$0.0408357\pi$
$524$	6.43854			0.281269
$525$	−5.92397	+	4.78096i	−0.258543	+	0.208658i
$526$			1.92783i			0.0840573i
$527$	27.4088	+	15.8245i	1.19395	+	0.689326i
$528$	5.57179	−	3.21688i	0.242481	−	0.139997i
$529$	−6.72298	−	11.6445i	−0.292303	−	0.506284i
$530$	3.08005	−	5.33480i	0.133789	−	0.231729i
$531$		−	4.46302i		−	0.193678i
$532$	7.23815	−	18.7634i	0.313814	−	0.813495i
$533$	5.48717	−	29.4266i	0.237676	−	1.27461i
$534$	−4.42924	+	7.67166i	−0.191672	+	0.331985i
$535$	−10.3611	+	5.98201i	−0.447951	+	0.258625i
$536$	13.4633	+	23.3192i	0.581528	+	1.00724i
$537$	1.16370	−	2.01558i	0.0502172	−	0.0869787i
$538$		−	13.9038i		−	0.599434i
$539$	−21.1771	−	4.57449i	−0.912163	−	0.197037i
$540$		−	2.41940i		−	0.104114i
$541$	13.0409	+	7.52918i	0.560673	+	0.323705i	0.753416	−	0.657545i	$-0.228405\pi$
$541$	13.0409	+	7.52918i	0.560673	+	0.323705i	−0.192742	+	0.981249i	$0.561738\pi$
$542$	−0.487114	−	0.843706i	−0.0209233	−	0.0362403i
$543$	−1.15548	−	2.00135i	−0.0495864	−	0.0858861i
$544$	16.6030	+	9.58577i	0.711849	+	0.410986i
$545$	7.41974			0.317827
$546$	2.91683	−	4.73065i	0.124829	−	0.202453i
$547$	32.9549			1.40905			0.704525	−	0.709679i	$-0.251160\pi$
$547$	32.9549			1.40905			0.704525	+	0.709679i	$0.251160\pi$
$548$	26.8177	+	15.4832i	1.14560	+	0.661410i
$549$	3.83770	+	6.64709i	0.163789	+	0.283691i
$550$	−2.59412	−	4.49314i	−0.110613	−	0.191588i
$551$	23.0454	+	13.3053i	0.981768	+	0.566824i
$552$			12.8748i			0.547989i
$553$	24.9531	−	20.1385i	1.06111	−	0.856376i
$554$			3.20380i			0.136116i
$555$	−3.97450	+	6.88404i	−0.168708	+	0.292211i
$556$	−1.57812	−	2.73338i	−0.0669271	−	0.115921i
$557$	10.1984	−	5.88807i	0.432121	−	0.249485i	−0.268129	−	0.963383i	$-0.586405\pi$
$557$	10.1984	−	5.88807i	0.432121	−	0.249485i	0.700250	+	0.713898i	$0.253072\pi$
$558$	2.63347	−	4.56130i	0.111484	−	0.193095i
$559$	28.7964	+	5.36965i	1.21796	+	0.227112i
$560$	−7.91629	+	1.24042i	−0.334524	+	0.0524173i
$561$		−	10.8353i		−	0.457466i
$562$	9.49598	−	16.4475i	0.400564	−	0.693797i
$563$	−2.39918	−	4.15551i	−0.101114	−	0.175134i	0.811030	−	0.585004i	$-0.198907\pi$
$563$	−2.39918	−	4.15551i	−0.101114	−	0.175134i	−0.912144	+	0.409871i	$0.865574\pi$
$564$	15.7400	−	9.08749i	0.662774	−	0.382653i
$565$	20.9560	+	12.0990i	0.881626	+	0.509007i
$566$			10.2829i			0.432222i
$567$	0.409571	+	2.61386i	0.0172003	+	0.109772i
$568$	−3.57491			−0.150000
$569$	15.8171	−	27.3961i	0.663089	−	1.14850i	−0.316710	−	0.948522i	$-0.602578\pi$
$569$	15.8171	−	27.3961i	0.663089	−	1.14850i	0.979800	−	0.199982i	$-0.0640884\pi$
$570$	3.36488	−	1.94271i	0.140939	−	0.0813713i
$571$	18.6468	+	32.2972i	0.780344	+	1.35160i	0.931742	+	0.363122i	$0.118289\pi$
$571$	18.6468	+	32.2972i	0.780344	+	1.35160i	−0.151398	+	0.988473i	$0.548377\pi$
$572$	−14.0781	−	12.0505i	−0.588635	−	0.503855i
$573$	9.27714			0.387558
$574$	−9.95838	+	8.03694i	−0.415655	+	0.335456i
$575$	−17.3702			−0.724389
$576$	−0.483468	+	0.837391i	−0.0201445	+	0.0348913i
$577$	4.77775	−	2.75844i	0.198901	−	0.114835i	−0.397242	−	0.917714i	$-0.630033\pi$
$577$	4.77775	−	2.75844i	0.198901	−	0.114835i	0.596143	+	0.802879i	$0.296699\pi$
$578$	−2.39372	+	1.38201i	−0.0995655	+	0.0574842i
$579$	5.85868	+	3.38251i	0.243478	+	0.140572i
$580$		−	14.0649i		−	0.584013i
$581$	−6.17615	+	16.0104i	−0.256230	+	0.664221i
$582$	−0.912705			−0.0378329
$583$	19.4525	+	11.2309i	0.805641	+	0.465137i
$584$	−1.79689	−	3.11230i	−0.0743558	−	0.128788i
$585$	−4.95374	+	1.74812i	−0.204812	+	0.0722759i
$586$	1.99973	−	3.46363i	0.0826079	−	0.143081i
$587$		−	4.46413i		−	0.184255i	−0.995747	−	0.0921273i	$-0.970633\pi$
$587$		−	4.46413i		−	0.184255i	0.995747	−	0.0921273i	$-0.0293667\pi$
$588$	11.0670	−	3.55551i	0.456394	−	0.146627i
$589$	−41.3825			−1.70514
$590$	−3.28075	−	1.89414i	−0.135066	−	0.0779805i
$591$	9.16400	−	5.29084i	0.376957	−	0.217636i
$592$	9.82175	−	5.67059i	0.403672	−	0.233060i
$593$	2.71683	+	1.56856i	0.111567	+	0.0644132i	0.554745	−	0.832020i	$-0.312816\pi$
$593$	2.71683	+	1.56856i	0.111567	+	0.0644132i	−0.443178	+	0.896434i	$0.646149\pi$
$594$	−1.80318			−0.0739852
$595$	−4.85688	+	12.5904i	−0.199113	+	0.516157i
$596$			36.3500i			1.48895i
$597$	4.73698	−	8.20470i	0.193872	−	0.335796i
$598$	11.9585	−	4.22003i	0.489020	−	0.172570i
$599$	−23.6009	−	40.8779i	−0.964306	−	1.67023i	−0.711468	−	0.702719i	$-0.751969\pi$
$599$	−23.6009	−	40.8779i	−0.964306	−	1.67023i	−0.252838	−	0.967509i	$-0.581364\pi$
$600$	5.31409	+	3.06809i	0.216947	+	0.125254i
$601$	−25.2066			−1.02820			−0.514099	−	0.857731i	$-0.671874\pi$
$601$	−25.2066			−1.02820			−0.514099	+	0.857731i	$0.671874\pi$
$602$	−7.86481	−	9.74510i	−0.320546	−	0.397181i
$603$			12.6260i			0.514171i
$604$	3.21883	+	1.85839i	0.130972	+	0.0756168i
$605$	1.79232	−	1.03480i	0.0728681	−	0.0420704i
$606$	5.77788	−	3.33586i	0.234710	−	0.135510i
$607$	2.01193	−	3.48476i	0.0816615	−	0.141442i	−0.822302	−	0.569051i	$-0.807311\pi$
$607$	2.01193	−	3.48476i	0.0816615	−	0.141442i	0.903964	+	0.427609i	$0.140644\pi$
$608$	−25.0676			−1.01663
$609$	2.38099	+	15.1954i	0.0964826	+	0.615747i
$610$	6.51500			0.263785
$611$	−29.9795	−	25.6616i	−1.21284	−	1.03816i
$612$	2.90669	+	5.03454i	0.117496	+	0.203509i
$613$	−22.8690	+	13.2034i	−0.923671	+	0.533282i	−0.884804	−	0.465963i	$-0.845708\pi$
$613$	−22.8690	+	13.2034i	−0.923671	+	0.533282i	−0.0388668	+	0.999244i	$0.512375\pi$
$614$	−8.26351	+	14.3128i	−0.333488	+	0.577619i
$615$	12.0959			0.487753
$616$	2.70344	+	17.2532i	0.108925	+	0.695153i
$617$		−	20.2789i		−	0.816396i	−0.912893	−	0.408198i	$-0.866157\pi$
$617$		−	20.2789i		−	0.816396i	0.912893	−	0.408198i	$-0.133843\pi$
$618$	−1.55101	−	0.895476i	−0.0623908	−	0.0360213i
$619$	−12.2471	+	7.07089i	−0.492254	+	0.284203i	−0.725509	−	0.688213i	$-0.758396\pi$
$619$	−12.2471	+	7.07089i	−0.492254	+	0.284203i	0.233255	+	0.972416i	$0.425062\pi$
$620$	10.9363	+	18.9422i	0.439211	+	0.760736i
$621$	−3.01852	+	5.22824i	−0.121129	+	0.209802i
$622$			10.5857i			0.424449i
$623$	25.2654	+	31.3057i	1.01224	+	1.25424i
$624$	7.36787	+	1.37388i	0.294951	+	0.0549994i
$625$	1.16746	−	2.02211i	0.0466985	−	0.0808842i
$626$	6.55813	−	3.78634i	0.262115	−	0.151332i
$627$	7.08381	+	12.2695i	0.282900	+	0.489997i
$628$	−0.868186	+	1.50374i	−0.0346444	+	0.0600058i
$629$		−	19.1000i		−	0.761568i
$630$	2.09526	+	0.808268i	0.0834772	+	0.0322022i
$631$		−	10.6582i		−	0.424295i	−0.977238	−	0.212148i	$-0.931954\pi$
$631$		−	10.6582i		−	0.424295i	0.977238	−	0.212148i	$-0.0680458\pi$
$632$	−22.3842	−	12.9235i	−0.890394	−	0.514069i
$633$	−0.630942	−	1.09282i	−0.0250777	−	0.0434358i
$634$	2.31376	+	4.00755i	0.0918911	+	0.159160i
$635$	1.14078	+	0.658628i	0.0452704	+	0.0261369i
$636$	−12.0513			−0.477866
$637$	−15.2763	−	20.0907i	−0.605268	−	0.796022i
$638$	−10.4826			−0.415008
$639$	−1.45170	−	0.838142i	−0.0574286	−	0.0331564i
$640$	8.38914	+	14.5304i	0.331610	+	0.574365i
$641$	3.86852	+	6.70048i	0.152798	+	0.264653i	0.932255	−	0.361802i	$-0.117838\pi$
$641$	3.86852	+	6.70048i	0.152798	+	0.264653i	−0.779457	+	0.626455i	$0.784505\pi$
$642$	−4.14311	−	2.39203i	−0.163516	−	0.0944058i
$643$			45.0898i			1.77817i	0.457744	+	0.889084i	$0.348658\pi$
$643$			45.0898i			1.77817i	−0.457744	+	0.889084i	$0.651342\pi$
$644$	24.7463	+	9.54613i	0.975140	+	0.376170i
$645$			11.8368i			0.466075i
$646$	−4.66799	+	8.08520i	−0.183660	+	0.318108i
$647$	−10.3836	−	17.9850i	−0.408223	−	0.707064i	0.586467	−	0.809973i	$-0.300518\pi$
$647$	−10.3836	−	17.9850i	−0.408223	−	0.707064i	−0.994691	+	0.102909i	$0.967185\pi$
$648$	1.84692	−	1.06632i	0.0725538	−	0.0418889i
$649$	6.90669	−	11.9627i	0.271111	−	0.469579i
$650$	1.10791	−	5.94152i	0.0434559	−	0.233045i
$651$	−15.0219	−	18.6133i	−0.588755	−	0.729512i
$652$			11.6611i			0.456684i
$653$	10.8366	−	18.7695i	0.424068	−	0.734508i	−0.572265	−	0.820069i	$-0.693935\pi$
$653$	10.8366	−	18.7695i	0.424068	−	0.734508i	0.996333	+	0.0855614i	$0.0272684\pi$
$654$	1.48347	+	2.56944i	0.0580082	+	0.100473i
$655$	4.89220	−	2.82451i	0.191154	−	0.110363i
$656$	−14.9456	−	8.62886i	−0.583528	−	0.336900i
$657$		−	1.68513i		−	0.0657433i
$658$	2.61161	+	16.6672i	0.101811	+	0.649754i
$659$	23.6665			0.921916			0.460958	−	0.887422i	$-0.347506\pi$
$659$	23.6665			0.921916			0.460958	+	0.887422i	$0.347506\pi$
$660$	3.74412	−	6.48500i	0.145740	−	0.252428i
$661$	30.0061	−	17.3240i	1.16710	−	0.673827i	0.214107	−	0.976810i	$-0.431316\pi$
$661$	30.0061	−	17.3240i	1.16710	−	0.673827i	0.952996	+	0.302983i	$0.0979826\pi$
$662$	1.41721	+	2.45468i	0.0550815	+	0.0954039i
$663$	8.20804	−	9.58914i	0.318774	−	0.372411i
$664$	13.8323			0.536796
$665$	−2.73150	−	17.4323i	−0.105923	−	0.675995i
$666$	−3.17857			−0.123167
$667$	−17.5478	+	30.3938i	−0.679455	+	1.17685i
$668$	−17.2031	+	9.93220i	−0.665607	+	0.384288i
$669$	2.99935	−	1.73168i	0.115962	−	0.0669505i
$670$	9.28133	+	5.35858i	0.358569	+	0.207020i
$671$			23.7560i			0.917089i
$672$	−9.09960	−	11.2751i	−0.351025	−	0.434946i
$673$	4.43176			0.170832			0.0854160	−	0.996345i	$-0.472778\pi$
$673$	4.43176			0.170832			0.0854160	+	0.996345i	$0.472778\pi$
$674$	−3.98503	−	2.30076i	−0.153498	−	0.0886219i
$675$	1.43864	+	2.49179i	0.0553732	+	0.0959091i
$676$	−3.33044	−	21.3291i	−0.128094	−	0.820351i
$677$	13.3513	−	23.1251i	0.513132	−	0.888770i	−0.486752	−	0.873540i	$-0.661819\pi$
$677$	13.3513	−	23.1251i	0.513132	−	0.888770i	0.999884	−	0.0152304i	$-0.00484816\pi$
$678$			9.67604i			0.371606i
$679$	−1.49178	+	3.86713i	−0.0572494	+	0.148407i
$680$	10.8776			0.417136
$681$	1.24307	+	0.717687i	0.0476345	+	0.0275018i
$682$	14.1176	−	8.15079i	0.540590	−	0.312110i
$683$	34.2170	−	19.7552i	1.30928	−	0.755912i	0.327303	−	0.944920i	$-0.393860\pi$
$683$	34.2170	−	19.7552i	1.30928	−	0.755912i	0.981976	+	0.189007i	$0.0605270\pi$
$684$	−6.58289	−	3.80063i	−0.251703	−	0.145321i
$685$	27.1692			1.03808
$686$	−0.618071	+	10.7721i	−0.0235980	+	0.411280i
$687$			23.8668i			0.910575i
$688$	8.44405	−	14.6255i	0.321926	−	0.557593i
$689$	8.70760	+	24.6751i	0.331733	+	0.940048i
$690$	2.56217	+	4.43781i	0.0975402	+	0.168945i
$691$	−27.1777	−	15.6911i	−1.03389	−	0.596917i	−0.115793	−	0.993273i	$-0.536941\pi$
$691$	−27.1777	−	15.6911i	−1.03389	−	0.596917i	−0.918097	+	0.396357i	$0.870274\pi$
$692$	2.21851			0.0843350
$693$	−2.94723	+	7.64005i	−0.111956	+	0.290222i
$694$		−	2.33633i		−	0.0886857i
$695$	−2.39821	−	1.38460i	−0.0909691	−	0.0525211i
$696$	10.7368	−	6.19892i	0.406979	−	0.234969i
$697$	−25.1704	+	14.5321i	−0.953396	+	0.550443i
$698$	4.13203	−	7.15688i	0.156399	−	0.270892i
$699$	13.6045			0.514571
$700$	9.83724	−	7.93918i	0.371813	−	0.300073i
$701$	−6.25790			−0.236358			−0.118179	−	0.992992i	$-0.537706\pi$
$701$	−6.25790			−0.236358			−0.118179	+	0.992992i	$0.537706\pi$
$702$	−1.59580	−	1.36596i	−0.0602295	−	0.0515548i
$703$	12.4871	+	21.6283i	0.470959	+	0.815725i
$704$	−2.59179	+	1.49637i	−0.0976818	+	0.0563966i
$705$	7.97316	−	13.8099i	0.300287	−	0.520112i
$706$	0.363469			0.0136793
$707$	−4.69029	−	29.9332i	−0.176397	−	1.12575i
$708$			7.41121i			0.278530i
$709$	26.5406	+	15.3233i	0.996755	+	0.575477i	0.907287	−	0.420513i	$-0.138150\pi$
$709$	26.5406	+	15.3233i	0.996755	+	0.575477i	0.0894685	+	0.995990i	$0.471483\pi$
$710$	−1.23223	+	0.711429i	−0.0462448	+	0.0266994i
$711$	−6.05987	−	10.4960i	−0.227263	−	0.393631i
$712$	16.2136	−	28.0828i	0.607630	−	1.05245i
$713$		−	54.5778i		−	2.04396i
$714$	−5.33110	+	0.835341i	−0.199511	+	0.0312618i
$715$	−15.9834	−	2.98041i	−0.597744	−	0.111461i
$716$	−1.93241	+	3.34704i	−0.0722177	+	0.125085i
$717$	−10.3300	+	5.96401i	−0.385780	+	0.222730i
$718$	−6.11721	−	10.5953i	−0.228292	−	0.395414i
$719$	−10.8125	+	18.7278i	−0.403237	+	0.698427i	−0.994115	−	0.108334i	$-0.965448\pi$
$719$	−10.8125	+	18.7278i	−0.403237	+	0.698427i	0.590877	+	0.806761i	$0.298782\pi$
$720$			3.02858i			0.112869i
$721$	−6.32920	+	5.10800i	−0.235712	+	0.190232i
$722$		−	1.13792i		−	0.0423489i
$723$	−8.59672	−	4.96332i	−0.319715	−	0.184588i
$724$	1.91877	+	3.32341i	0.0713105	+	0.123513i
$725$	8.36335	+	14.4857i	0.310607	+	0.537987i
$726$	0.716695	+	0.413784i	0.0265991	+	0.0153570i
$727$	−23.1806			−0.859722			−0.429861	−	0.902895i	$-0.641437\pi$
$727$	−23.1806			−0.859722			−0.429861	+	0.902895i	$0.641437\pi$
$728$	−10.6773	+	17.3169i	−0.395727	+	0.641808i
$729$	1.00000			0.0370370
$730$	−1.23874	−	0.715184i	−0.0458477	−	0.0264702i
$731$	−14.2209	−	24.6313i	−0.525978	−	0.911021i
$732$	−6.37282	−	11.0380i	−0.235546	−	0.407978i
$733$	−6.25915	−	3.61372i	−0.231187	−	0.133476i	0.379933	−	0.925014i	$-0.375947\pi$
$733$	−6.25915	−	3.61372i	−0.231187	−	0.133476i	−0.611119	+	0.791538i	$0.709281\pi$
$734$			2.08497i			0.0769576i
$735$	6.84926	−	7.55653i	0.252639	−	0.278727i
$736$		−	33.0608i		−	1.21864i
$737$	−19.5393	+	33.8430i	−0.719738	+	1.24662i
$738$	2.41839	+	4.18878i	0.0890223	+	0.154191i
$739$	−40.2868	+	23.2596i	−1.48197	+	0.855618i	−0.999791	−	0.0204525i	$-0.993489\pi$
$739$	−40.2868	+	23.2596i	−1.48197	+	0.855618i	−0.482183	+	0.876070i	$0.660156\pi$
$740$	6.59999	−	11.4315i	0.242621	−	0.420231i
$741$	−3.02540	+	16.2246i	−0.111141	+	0.596026i
$742$	4.02608	−	10.4367i	0.147802	−	0.383145i
$743$		−	27.0715i		−	0.993157i	−0.867992	−	0.496578i	$-0.834590\pi$
$743$		−	27.0715i		−	0.993157i	0.867992	−	0.496578i	$-0.165410\pi$
$744$	−9.64003	+	16.6970i	−0.353421	+	0.612143i
$745$	15.9463	+	27.6198i	0.584228	+	1.01191i
$746$	−11.9451	+	6.89652i	−0.437342	+	0.252500i
$747$	5.61703	+	3.24299i	0.205516	+	0.118655i
$748$			17.9929i			0.657885i
$749$	−16.9068	+	13.6447i	−0.617761	+	0.498566i
$750$	6.68636			0.244151
$751$	24.0464	−	41.6497i	0.877467	−	1.51982i	0.0233564	−	0.999727i	$-0.492565\pi$
$751$	24.0464	−	41.6497i	0.877467	−	1.51982i	0.854111	−	0.520091i	$-0.174102\pi$
$752$	−19.7032	+	11.3756i	−0.718502	+	0.414827i
$753$	9.49598	+	16.4475i	0.346053	+	0.599381i
$754$	−9.27699	−	7.94084i	−0.337848	−	0.289189i
$755$	3.26102			0.118681
$756$	−0.680126	−	4.34053i	−0.0247359	−	0.157863i
$757$	−5.24707			−0.190708			−0.0953540	−	0.995443i	$-0.530398\pi$
$757$	−5.24707			−0.190708			−0.0953540	+	0.995443i	$0.530398\pi$
$758$	−5.97778	+	10.3538i	−0.217123	+	0.376068i
$759$	−16.1818	+	9.34257i	−0.587362	+	0.339114i
$760$	−12.3174	+	7.11146i	−0.446800	+	0.257960i
$761$	−2.29268	−	1.32368i	−0.0831095	−	0.0479833i	0.457869	−	0.889020i	$-0.348613\pi$
$761$	−2.29268	−	1.32368i	−0.0831095	−	0.0479833i	−0.540979	+	0.841036i	$0.681946\pi$
$762$			0.526732i			0.0190815i
$763$	13.3114	−	2.08579i	0.481905	−	0.0755106i
$764$	−15.4055			−0.557350
$765$	4.41719	+	2.55027i	0.159704	+	0.0922050i
$766$	−0.851406	−	1.47468i	−0.0307625	−	0.0532823i
$767$	15.1745	−	5.35492i	0.547919	−	0.193355i
$768$	−2.38763	+	4.13550i	−0.0861563	+	0.149227i
$769$		−	39.4880i		−	1.42397i	−0.702193	−	0.711987i	$-0.747796\pi$
$769$		−	39.4880i		−	1.42397i	0.702193	−	0.711987i	$-0.252204\pi$
$770$	4.36535	+	5.40900i	0.157316	+	0.194927i
$771$	−19.9713			−0.719250
$772$	−9.72883	−	5.61694i	−0.350148	−	0.202158i
$773$	22.6299	−	13.0654i	0.813939	−	0.469928i	−0.0343826	−	0.999409i	$-0.510946\pi$
$773$	22.6299	−	13.0654i	0.813939	−	0.469928i	0.848322	+	0.529481i	$0.177613\pi$
$774$	−4.09907	+	2.36660i	−0.147338	+	0.0850657i
$775$	−22.5270	−	13.0060i	−0.809194	−	0.467188i
$776$	3.34103			0.119936
$777$	−5.19526	+	13.4676i	−0.186379	+	0.483148i
$778$			7.50480i			0.269060i
$779$	19.0014	−	32.9114i	0.680796	−	1.17917i
$780$	8.22609	−	2.90290i	0.294541	−	0.103941i
$781$	−2.59412	−	4.49314i	−0.0928248	−	0.160777i
$782$	−10.6633	−	6.15644i	−0.381318	−	0.220154i
$783$	5.81338			0.207753
$784$	−13.8535	+	4.45075i	−0.494769	+	0.158955i
$785$			1.52345i			0.0543744i
$786$	1.95625	+	1.12944i	0.0697770	+	0.0402858i
$787$	3.17249	−	1.83164i	0.113087	−	0.0652908i	−0.442390	−	0.896823i	$-0.645869\pi$
$787$	3.17249	−	1.83164i	0.113087	−	0.0652908i	0.555477	+	0.831532i	$0.312536\pi$
$788$	−15.2176	+	8.78588i	−0.542104	+	0.312984i
$789$	1.65452	−	2.86571i	0.0589024	−	0.102022i
$790$	−10.2874			−0.366010
$791$	40.9973	+	15.8151i	1.45770	+	0.562321i
$792$	6.60068			0.234545
$793$	−17.9958	+	21.0239i	−0.639051	+	0.746579i
$794$	9.63089	+	16.6812i	0.341788	+	0.591993i
$795$	−9.15696	+	5.28677i	−0.324764	+	0.187503i
$796$	−7.86616	+	13.6246i	−0.278809	+	0.482911i
$797$	−53.7046			−1.90232			−0.951158	−	0.308704i	$-0.900105\pi$
$797$	−53.7046			−1.90232			−0.951158	+	0.308704i	$0.900105\pi$
$798$	5.49064	−	4.43124i	0.194367	−	0.156864i
$799$			38.3161i			1.35553i
$800$	−13.6458	−	7.87843i	−0.482453	−	0.278545i
$801$	13.1681	−	7.60260i	0.465272	−	0.268625i
$802$	0.119526	+	0.207025i	0.00422060	+	0.00731030i
$803$	2.60781	−	4.51686i	0.0920277	−	0.159397i
$804$		−	20.9665i		−	0.739433i
$805$	22.9908	−	3.60247i	0.810318	−	0.126970i
$806$	18.6684	+	3.48109i	0.657567	+	0.122616i
$807$	−11.9326	+	20.6679i	−0.420048	+	0.727545i
$808$	−21.1504	+	12.2112i	−0.744069	+	0.429588i
$809$	−18.6379	−	32.2819i	−0.655275	−	1.13497i	−0.981825	−	0.189790i	$-0.939219\pi$
$809$	−18.6379	−	32.2819i	−0.655275	−	1.13497i	0.326550	−	0.945180i	$-0.394114\pi$
$810$	0.424408	−	0.735096i	0.0149122	−	0.0258286i
$811$			2.11417i			0.0742387i	0.999311	+	0.0371193i	$0.0118182\pi$
$811$			2.11417i			0.0742387i	−0.999311	+	0.0371193i	$0.988182\pi$
$812$	−3.95383	−	25.2332i	−0.138752	−	0.885510i
$813$			1.67222i			0.0586474i
$814$	−8.51990	−	4.91897i	−0.298622	−	0.172410i
$815$	5.11559	+	8.86047i	0.179191	+	0.310369i
$816$	−3.63857	−	6.30219i	−0.127376	−	0.220621i
$817$	32.2065	+	18.5945i	1.12676	+	0.650537i
$818$	0.499064			0.0174494
$819$	−8.39584	+	4.52878i	−0.293374	+	0.158248i
$820$	−20.0862			−0.701441
$821$	−28.9900	−	16.7374i	−1.01176	−	0.584138i	−0.100051	−	0.994982i	$-0.531901\pi$
$821$	−28.9900	−	16.7374i	−1.01176	−	0.584138i	−0.911706	+	0.410844i	$0.865234\pi$
$822$	5.43209	+	9.40866i	0.189466	+	0.328165i
$823$	−16.9290	−	29.3218i	−0.590107	−	1.02210i	−0.994217	−	0.107385i	$-0.965752\pi$
$823$	−16.9290	−	29.3218i	−0.590107	−	1.02210i	0.404110	−	0.914710i	$-0.367581\pi$
$824$	5.67760	+	3.27797i	0.197789	+	0.114193i
$825$			8.90539i			0.310046i
$826$	−6.41830	−	2.47592i	−0.223321	−	0.0861483i
$827$			2.13815i			0.0743506i	0.999309	+	0.0371753i	$0.0118360\pi$
$827$			2.13815i			0.0743506i	−0.999309	+	0.0371753i	$0.988164\pi$
$828$	5.01251	−	8.68192i	0.174197	−	0.301718i
$829$	13.1393	+	22.7579i	0.456346	+	0.790415i	0.998764	−	0.0496939i	$-0.0158246\pi$
$829$	13.1393	+	22.7579i	0.456346	+	0.790415i	−0.542418	+	0.840108i	$0.682491\pi$
$830$	4.76783	−	2.75271i	0.165494	−	0.0955478i
$831$	2.74960	−	4.76244i	0.0953824	−	0.165207i
$832$	−3.42726	−	0.639079i	−0.118819	−	0.0221561i
$833$	−5.17416	+	23.9532i	−0.179274	+	0.829929i
$834$		−	1.10733i		−	0.0383436i
$835$	−8.71429	+	15.0936i	−0.301570	+	0.522335i
$836$	−11.7633	−	20.3746i	−0.406841	−	0.704669i
$837$	−7.82929	+	4.52024i	−0.270620	+	0.156242i
$838$	−13.6412	−	7.87576i	−0.471228	−	0.272064i
$839$			9.33965i			0.322441i	0.986918	+	0.161220i	$0.0515430\pi$
$839$			9.33965i			0.322441i	−0.986918	+	0.161220i	$0.948457\pi$
$840$	−7.66988	−	2.95873i	−0.264636	−	0.102086i
$841$	4.79544			0.165360
$842$	−5.00643	+	8.67140i	−0.172533	+	0.298836i
$843$	−28.2315	+	16.2995i	−0.972344	+	0.561383i
$844$	1.04773	+	1.81473i	0.0360644	+	0.0624654i
$845$	−11.8874	−	14.7455i	−0.408940	−	0.507261i
$846$	6.37647			0.219227
$847$	2.92462	−	2.36032i	0.100491	−	0.0811016i
$848$	15.0857			0.518046
$849$	8.82509	−	15.2855i	0.302876	−	0.524597i
$850$	−5.08214	+	2.93418i	−0.174316	+	0.100641i
$851$	−28.5247	+	16.4687i	−0.977814	+	0.564541i
$852$	2.41068	+	1.39181i	0.0825884	+	0.0476825i
$853$			5.14425i			0.176136i	0.996114	+	0.0880678i	$0.0280692\pi$
$853$			5.14425i			0.176136i	−0.996114	+	0.0880678i	$0.971931\pi$
$854$	11.6882	−	1.83145i	0.399964	−	0.0626711i
$855$	−6.66917			−0.228081
$856$	15.1662	+	8.75622i	0.518371	+	0.299281i
$857$	7.81827	+	13.5416i	0.267067	+	0.462573i	0.968103	−	0.250552i	$-0.0806122\pi$
$857$	7.81827	+	13.5416i	0.267067	+	0.462573i	−0.701036	+	0.713126i	$0.747279\pi$
$858$	−2.16353	−	6.13090i	−0.0738617	−	0.209305i
$859$	7.15629	−	12.3951i	0.244169	−	0.422914i	−0.717728	−	0.696323i	$-0.754818\pi$
$859$	7.15629	−	12.3951i	0.244169	−	0.422914i	0.961898	+	0.273409i	$0.0881514\pi$
$860$		−	19.6560i		−	0.670265i
$861$	21.7006	−	3.40032i	0.739556	−	0.115883i
$862$	1.42674			0.0485948
$863$	8.02067	+	4.63074i	0.273027	+	0.157632i	0.630262	−	0.776382i	$-0.282947\pi$
$863$	8.02067	+	4.63074i	0.273027	+	0.157632i	−0.357236	+	0.934014i	$0.616281\pi$
$864$	−4.74263	+	2.73816i	−0.161347	+	0.0931540i
$865$	1.68569	−	0.973234i	0.0573152	−	0.0330910i
$866$	−20.6162	−	11.9028i	−0.700566	−	0.404472i
$867$	4.74434			0.161126
$868$	24.9451	+	30.9089i	0.846693	+	1.04912i
$869$		−	37.5115i		−	1.27249i
$870$	2.46725	−	4.27340i	0.0836475	−	0.144882i
$871$	−42.9291	+	15.1492i	−1.45460	+	0.513312i
$872$	−5.43036	−	9.40565i	−0.183895	−	0.318516i
$873$	1.35673	+	0.783311i	0.0459185	+	0.0265110i
$874$	16.0996			0.544579
$875$	10.9286	−	28.3301i	0.369454	−	0.957731i
$876$			2.79831i			0.0945460i
$877$	22.3441	+	12.9003i	0.754505	+	0.435614i	0.827319	−	0.561732i	$-0.189865\pi$
$877$	22.3441	+	12.9003i	0.754505	+	0.435614i	−0.0728142	+	0.997346i	$0.523198\pi$
$878$	15.9260	−	9.19487i	0.537476	−	0.310312i
$879$	−5.94517	+	3.43245i	−0.200526	+	0.115774i
$880$	−4.68685	+	8.11787i	−0.157994	+	0.273653i
$881$	−50.1659			−1.69013			−0.845066	−	0.534661i	$-0.820439\pi$
$881$	−50.1659			−1.69013			−0.845066	+	0.534661i	$0.820439\pi$
$882$	3.98622	+	0.861069i	0.134223	+	0.0289937i
$883$	−42.9847			−1.44655			−0.723275	−	0.690560i	$-0.757364\pi$
$883$	−42.9847			−1.44655			−0.723275	+	0.690560i	$0.757364\pi$
$884$	−13.6301	+	15.9236i	−0.458431	+	0.535568i
$885$	3.25121	+	5.63127i	0.109288	+	0.189293i
$886$	19.3838	−	11.1913i	0.651212	−	0.375978i
$887$	−5.40363	+	9.35937i	−0.181436	+	0.314257i	−0.942370	−	0.334573i	$-0.891408\pi$
$887$	−5.40363	+	9.35937i	−0.181436	+	0.314257i	0.760934	+	0.648830i	$0.224741\pi$
$888$	11.6354			0.390460
$889$	2.23176	+	0.860925i	0.0748509	+	0.0288745i
$890$		−	12.9064i		−	0.432624i
$891$	2.68042	+	1.54754i	0.0897973	+	0.0518445i
$892$	−4.98067	+	2.87559i	−0.166765	+	0.0962819i
$893$	−25.0500	−	43.3880i	−0.838268	−	1.45192i
$894$	−6.37647	+	11.0444i	−0.213261	+	0.369379i
$895$			3.39091i			0.113346i
$896$	19.1352	+	23.7100i	0.639263	+	0.792096i
$897$	−21.3981	−	3.99008i	−0.714460	−	0.133225i
$898$	7.00167	−	12.1272i	0.233649	−	0.404691i
$899$	−45.5147	+	26.2779i	−1.51800	+	0.876417i
$900$	−2.38898	−	4.13783i	−0.0796325	−	0.137928i
$901$	12.7032	−	22.0025i	0.423204	−	0.733011i
$902$			14.9702i			0.498455i
$903$	3.32749	+	21.2359i	0.110732	+	0.706686i
$904$		−	35.4199i		−	1.17805i
$905$	2.91588	+	1.68348i	0.0969272	+	0.0559609i
$906$	0.651993	+	1.12928i	0.0216610	+	0.0375180i
$907$	16.4957	+	28.5713i	0.547729	+	0.948695i	0.998430	+	0.0560196i	$0.0178409\pi$
$907$	16.4957	+	28.5713i	0.547729	+	0.948695i	−0.450700	+	0.892675i	$0.648826\pi$
$908$	−2.06422	−	1.19178i	−0.0685036	−	0.0395506i
$909$	−11.4517			−0.379830
$910$	−0.234171	+	8.09380i	−0.00776269	+	0.268307i
$911$	−17.6639			−0.585232			−0.292616	−	0.956230i	$-0.594526\pi$
$911$	−17.6639			−0.585232			−0.292616	+	0.956230i	$0.594526\pi$
$912$	8.24040	+	4.75760i	0.272867	+	0.157540i
$913$	10.0373	+	17.3852i	0.332187	+	0.575365i
$914$	10.4552	+	18.1090i	0.345828	+	0.598992i
$915$	−9.68453	−	5.59137i	−0.320161	−	0.184845i
$916$		−	39.6328i		−	1.30950i
$917$	7.98285	−	6.44258i	0.263617	−	0.212753i
$918$			2.03955i			0.0673153i
$919$	−16.9325	+	29.3280i	−0.558552	+	0.967441i	0.439065	+	0.898455i	$0.355310\pi$
$919$	−16.9325	+	29.3280i	−0.558552	+	0.967441i	−0.997618	+	0.0689860i	$0.978024\pi$
$920$	−9.37904	−	16.2450i	−0.309218	−	0.535581i
$921$	24.5674	−	14.1840i	0.809523	−	0.467378i
$922$	−5.79807	+	10.0426i	−0.190949	+	0.330734i
$923$	1.10791	−	5.94152i	0.0364674	−	0.195567i
$924$	4.89412	−	12.6869i	0.161005	−	0.417370i
$925$			15.6981i			0.516150i
$926$	0.789545	−	1.36753i	0.0259461	−	0.0449399i
$927$	1.53705	+	2.66225i	0.0504833	+	0.0874396i
$928$	−27.5707	+	15.9180i	−0.905053	+	0.522533i
$929$	1.59169	+	0.918962i	0.0522216	+	0.0301502i	0.525884	−	0.850557i	$-0.323735\pi$
$929$	1.59169	+	0.918962i	0.0522216	+	0.0301502i	−0.473662	+	0.880707i	$0.657068\pi$
$930$			7.67370i			0.251631i
$931$	−9.80090	−	30.5065i	−0.321211	−	0.999811i
$932$	−22.5915			−0.740008
$933$	9.08499	−	15.7357i	0.297429	−	0.515163i
$934$	16.5220	−	9.53897i	0.540616	−	0.312125i
$935$	7.89327	+	13.6715i	0.258138	+	0.447107i
$936$	5.84155	+	5.00021i	0.190937	+	0.163437i
$937$	−6.63406			−0.216725			−0.108363	−	0.994111i	$-0.534561\pi$
$937$	−6.63406			−0.216725			−0.108363	+	0.994111i	$0.534561\pi$
$938$	18.1576	+	7.00446i	0.592865	+	0.228704i
$939$	−12.9982			−0.424180
$940$	−13.2401	+	22.9325i	−0.431844	+	0.747976i
$941$	−1.92634	+	1.11217i	−0.0627968	+	0.0362557i	−0.531070	−	0.847328i	$-0.678210\pi$
$941$	−1.92634	+	1.11217i	−0.0627968	+	0.0362557i	0.468273	+	0.883584i	$0.344876\pi$
$942$	−0.527569	+	0.304592i	−0.0171891	+	0.00992414i
$943$	43.4056	+	25.0602i	1.41348	+	0.816074i
$944$		−	9.27729i		−	0.301950i
$945$	−2.42092	−	2.99970i	−0.0787526	−	0.0975804i
$946$	−14.6496			−0.476300
$947$	24.5852	+	14.1943i	0.798912	+	0.461252i	0.843091	−	0.537771i	$-0.180734\pi$
$947$	24.5852	+	14.1943i	0.798912	+	0.461252i	−0.0441784	+	0.999024i	$0.514067\pi$
$948$	10.0629	+	17.4295i	0.326828	+	0.566083i
$949$	5.72955	−	2.02190i	0.185989	−	0.0656335i
$950$	3.83657	−	6.64513i	0.124475	−	0.215596i
$951$		−	7.94295i		−	0.257568i
$952$	19.5149	−	3.05783i	0.632483	−	0.0991050i
$953$	54.5711			1.76773			0.883865	−	0.467742i	$-0.154932\pi$
$953$	54.5711			1.76773			0.883865	+	0.467742i	$0.154932\pi$
$954$	−3.66160	−	2.11403i	−0.118549	−	0.0684441i
$955$	−11.7056	+	6.75820i	−0.378783	+	0.218690i
$956$	17.1538	−	9.90374i	0.554793	−	0.320310i
$957$	15.5823	+	8.99644i	0.503704	+	0.290814i
$958$	−7.76723			−0.250948
$959$	48.7430	−	7.63764i	1.57399	−	0.246632i
$960$		−	1.40878i		−	0.0454683i
$961$	25.3651	−	43.9337i	0.818231	−	1.41722i
$962$	−3.81379	−	10.8073i	−0.122962	−	0.348442i
$963$	4.10582	+	7.11149i	0.132308	+	0.229164i
$964$	14.2756	+	8.24200i	0.459785	+	0.265457i
$965$	−9.85635			−0.317287
$966$	5.84420	+	7.24140i	0.188034	+	0.232988i
$967$			36.7255i			1.18101i	0.807033	+	0.590507i	$0.201072\pi$
$967$			36.7255i			1.18101i	−0.807033	+	0.590507i	$0.798928\pi$
$968$	−2.62352	−	1.51469i	−0.0843232	−	0.0486840i
$969$	13.8779	−	8.01241i	0.445823	−	0.257396i
$970$	1.15162	−	0.664887i	0.0369762	−	0.0213482i
$971$	22.4374	−	38.8626i	0.720049	−	1.24716i	−0.240931	−	0.970542i	$-0.577453\pi$
$971$	22.4374	−	38.8626i	0.720049	−	1.24716i	0.960980	−	0.276619i	$-0.0892140\pi$
$972$	−1.66058			−0.0532632
$973$	−4.69174	−	1.80988i	−0.150410	−	0.0580222i
$974$	−21.7618			−0.697294
$975$	−6.74609	+	7.88120i	−0.216048	+	0.252401i
$976$	7.97744	+	13.8173i	0.255352	+	0.442282i
$977$	−22.1420	+	12.7837i	−0.708385	+	0.408986i	−0.810463	−	0.585790i	$-0.800784\pi$
$977$	−22.1420	+	12.7837i	−0.708385	+	0.408986i	0.102078	+	0.994776i	$0.467451\pi$
$978$	−2.04558	+	3.54304i	−0.0654103	+	0.113294i
$979$	47.0613			1.50409
$980$	−11.3738	+	12.5483i	−0.363322	+	0.400839i
$981$		−	5.09262i		−	0.162595i
$982$	−2.22777	−	1.28620i	−0.0710911	−	0.0410444i
$983$	41.0816	−	23.7185i	1.31030	−	0.756502i	0.328155	−	0.944624i	$-0.393573\pi$
$983$	41.0816	−	23.7185i	1.31030	−	0.756502i	0.982146	+	0.188122i	$0.0602400\pi$
$984$	−8.85274	−	15.3334i	−0.282215	−	0.488811i
$985$	−7.70853	+	13.3516i	−0.245614	+	0.425416i
$986$			11.8567i			0.377594i
$987$	10.4221	−	27.0171i	0.331739	−	0.859963i
$988$	5.02392	−	26.9423i	0.159832	−	0.857150i
$989$	−24.5235	+	42.4760i	−0.779803	+	1.35066i
$990$	2.27518	−	1.31358i	0.0723100	−	0.0417482i
$991$	−7.21288	−	12.4931i	−0.229125	−	0.396856i	0.728424	−	0.685126i	$-0.240253\pi$
$991$	−7.21288	−	12.4931i	−0.229125	−	0.396856i	−0.957549	+	0.288271i	$0.906920\pi$
$992$	24.7543	−	42.8756i	0.785949	−	1.36130i
$993$		−	4.86517i		−	0.154392i
$994$	−2.01069	+	1.62274i	−0.0637753	+	0.0514701i
$995$			13.8032i			0.437590i
$996$	−9.32755	−	5.38526i	−0.295555	−	0.170639i
$997$	12.1208	+	20.9938i	0.383868	+	0.664879i	0.991611	−	0.129254i	$-0.0412584\pi$
$997$	12.1208	+	20.9938i	0.383868	+	0.664879i	−0.607743	+	0.794134i	$0.707925\pi$
$998$	8.29154	+	14.3614i	0.262464	+	0.454601i
$999$	4.72494	+	2.72795i	0.149491	+	0.0863084i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.bj.d.142.4	yes	16
3.2	odd	2		819.2.dl.g.415.5		16
7.2	even	3		1911.2.c.j.883.5		8
7.4	even	3	inner	273.2.bj.d.25.5	yes	16
7.5	odd	6		1911.2.c.m.883.5		8
13.12	even	2	inner	273.2.bj.d.142.5	yes	16
21.11	odd	6		819.2.dl.g.298.4		16
39.38	odd	2		819.2.dl.g.415.4		16
91.12	odd	6		1911.2.c.m.883.4		8
91.25	even	6	inner	273.2.bj.d.25.4	✓	16
91.51	even	6		1911.2.c.j.883.4		8
273.116	odd	6		819.2.dl.g.298.5		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.bj.d.25.4	✓	16	91.25	even	6	inner
273.2.bj.d.25.5	yes	16	7.4	even	3	inner
273.2.bj.d.142.4	yes	16	1.1	even	1	trivial
273.2.bj.d.142.5	yes	16	13.12	even	2	inner
819.2.dl.g.298.4		16	21.11	odd	6
819.2.dl.g.298.5		16	273.116	odd	6
819.2.dl.g.415.4		16	39.38	odd	2
819.2.dl.g.415.5		16	3.2	odd	2
1911.2.c.j.883.4		8	91.51	even	6
1911.2.c.j.883.5		8	7.2	even	3
1911.2.c.m.883.4		8	91.12	odd	6
1911.2.c.m.883.5		8	7.5	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.bj (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.504542 - 0.291297i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.830292 - 1.43811i) q^{4} +(-1.26176 - 0.728479i) q^{5} -0.582595i q^{6} +(-2.46845 - 0.952230i) q^{7} +2.13264i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.504542 - 0.291297i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.830292 - 1.43811i) q^{4} +(-1.26176 - 0.728479i) q^{5} -0.582595i q^{6} +(-2.46845 - 0.952230i) q^{7} +2.13264i q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.424408 + 0.735096i) q^{10} +(-2.68042 + 1.54754i) q^{11} +(0.830292 - 1.43811i) q^{12} +(-3.54446 - 0.660933i) q^{13} +(0.968055 + 1.19949i) q^{14} -1.45696i q^{15} +(-1.03935 + 1.80021i) q^{16} +(1.75040 + 3.03179i) q^{17} +(0.504542 - 0.291297i) q^{18} +(-3.96420 - 2.28873i) q^{19} +2.41940i q^{20} +(-0.409571 - 2.61386i) q^{21} +1.80318 q^{22} +(3.01852 - 5.22824i) q^{23} +(-1.84692 + 1.06632i) q^{24} +(-1.43864 - 2.49179i) q^{25} +(1.59580 + 1.36596i) q^{26} -1.00000 q^{27} +(0.680126 + 4.34053i) q^{28} -5.81338 q^{29} +(-0.424408 + 0.735096i) q^{30} +(7.82929 - 4.52024i) q^{31} +(4.74263 - 2.73816i) q^{32} +(-2.68042 - 1.54754i) q^{33} -2.03955i q^{34} +(2.42092 + 2.99970i) q^{35} +1.66058 q^{36} +(-4.72494 - 2.72795i) q^{37} +(1.33340 + 2.30952i) q^{38} +(-1.19984 - 3.40006i) q^{39} +(1.55358 - 2.69088i) q^{40} +8.30215i q^{41} +(-0.554764 + 1.43811i) q^{42} -8.12434 q^{43} +(4.45106 + 2.56982i) q^{44} +(1.26176 - 0.728479i) q^{45} +(-3.04594 + 1.75858i) q^{46} +(9.47860 + 5.47247i) q^{47} -2.07870 q^{48} +(5.18651 + 4.70107i) q^{49} +1.67628i q^{50} +(-1.75040 + 3.03179i) q^{51} +(1.99244 + 5.64608i) q^{52} +(-3.62864 - 6.28499i) q^{53} +(0.504542 + 0.291297i) q^{54} +4.50940 q^{55} +(2.03076 - 5.26431i) q^{56} -4.57747i q^{57} +(2.93310 + 1.69342i) q^{58} +(-3.86508 + 2.23151i) q^{59} +(-2.09526 + 1.20970i) q^{60} +(3.83770 - 6.64709i) q^{61} -5.26694 q^{62} +(2.05888 - 1.66163i) q^{63} +0.966935 q^{64} +(3.99079 + 3.41600i) q^{65} +(0.901588 + 1.56160i) q^{66} +(10.9344 - 6.31301i) q^{67} +(2.90669 - 5.03454i) q^{68} +6.03705 q^{69} +(-0.347650 - 2.21868i) q^{70} +1.67628i q^{71} +(-1.84692 - 1.06632i) q^{72} +(-1.45937 + 0.842567i) q^{73} +(1.58929 + 2.75273i) q^{74} +(1.43864 - 2.49179i) q^{75} +7.60126i q^{76} +(8.09010 - 1.26765i) q^{77} +(-0.385056 + 2.06498i) q^{78} +(-6.05987 + 10.4960i) q^{79} +(2.62283 - 1.51429i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(2.41839 - 4.18878i) q^{82} -6.48599i q^{83} +(-3.41894 + 2.75927i) q^{84} -5.10053i q^{85} +(4.09907 + 2.36660i) q^{86} +(-2.90669 - 5.03454i) q^{87} +(-3.30034 - 5.71635i) q^{88} +(-13.1681 - 7.60260i) q^{89} -0.848816 q^{90} +(8.11996 + 5.00662i) q^{91} -10.0250 q^{92} +(7.82929 + 4.52024i) q^{93} +(-3.18823 - 5.52218i) q^{94} +(3.33459 + 5.77567i) q^{95} +(4.74263 + 2.73816i) q^{96} -1.56662i q^{97} +(-1.24740 - 3.88270i) q^{98} -3.09508i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9}+O(q^{10}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9	\( 16 q + 8 q^{3} + 8 q^{4} - 8 q^{9} - 16 q^{10} - 8 q^{12} + 6 q^{13} - 10 q^{14} - 28 q^{16} - 2 q^{17} + 60 q^{22} + 24 q^{23} + 10 q^{25} + 14 q^{26} - 16 q^{27} + 24 q^{29} + 16 q^{30} - 30 q^{35} - 16 q^{36} + 3 q^{39} + 26 q^{40} + 4 q^{42} - 76 q^{43} - 56 q^{48} + 2 q^{49} + 2 q^{51} + 10 q^{53} - 16 q^{55} + 72 q^{56} + 26 q^{61} - 104 q^{62} - 84 q^{64} - 32 q^{65} + 30 q^{66} - 12 q^{68} + 48 q^{69} - 54 q^{74} - 10 q^{75} - 10 q^{77} + 28 q^{78} - 10 q^{79} - 8 q^{81} - 48 q^{82} + 12 q^{87} + 68 q^{88} + 32 q^{90} - 57 q^{91} + 16 q^{92} - 48 q^{94} + 18 q^{95}+O(q^{100}) \) 16 * q + 8 * q^3 + 8 * q^4 - 8 * q^9 - 16 * q^10 - 8 * q^12 + 6 * q^13 - 10 * q^14 - 28 * q^16 - 2 * q^17 + 60 * q^22 + 24 * q^23 + 10 * q^25 + 14 * q^26 - 16 * q^27 + 24 * q^29 + 16 * q^30 - 30 * q^35 - 16 * q^36 + 3 * q^39 + 26 * q^40 + 4 * q^42 - 76 * q^43 - 56 * q^48 + 2 * q^49 + 2 * q^51 + 10 * q^53 - 16 * q^55 + 72 * q^56 + 26 * q^61 - 104 * q^62 - 84 * q^64 - 32 * q^65 + 30 * q^66 - 12 * q^68 + 48 * q^69 - 54 * q^74 - 10 * q^75 - 10 * q^77 + 28 * q^78 - 10 * q^79 - 8 * q^81 - 48 * q^82 + 12 * q^87 + 68 * q^88 + 32 * q^90 - 57 * q^91 + 16 * q^92 - 48 * q^94 + 18 * q^95

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