LMFDB - Embedded newform 261.2.x.a.14.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [261,2,Mod(2,261)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(261, base_ring=CyclotomicField(84)) chi = DirichletCharacter(H, H._module([14, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("261.2"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 261 = 3^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	261.x (of order $84$, degree $24$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.08409549276$
Analytic rank:	$0$
Dimension:	$672$
Relative dimension:	$28$ over $\Q(\zeta_{84})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{84}]$

Embedding invariants

Embedding label			14.22
Character	$\chi$	$=$	261.14
Dual form			261.2.x.a.56.22

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03117 + 1.39718i) q^{2} +(-1.73182 - 0.0285716i) q^{3} +(-0.299298 + 0.970301i) q^{4} +(-1.46016 - 3.72043i) q^{5} +(-1.74587 - 2.44912i) q^{6} +(0.524586 - 0.161813i) q^{7} +(1.61379 - 0.564688i) q^{8} +(2.99837 + 0.0989614i) q^{9} +(3.69245 - 5.87649i) q^{10} +(-0.576982 - 3.04942i) q^{11} +(0.546052 - 1.67183i) q^{12} +(-0.400833 - 0.0300383i) q^{13} +(0.767018 + 0.566085i) q^{14} +(2.42243 + 6.48482i) q^{15} +(4.13100 + 2.81647i) q^{16} +(2.69557 + 2.69557i) q^{17} +(2.95355 + 4.29130i) q^{18} +(-5.36550 - 3.37137i) q^{19} +(4.04697 - 0.303278i) q^{20} +(-0.913110 + 0.265243i) q^{21} +(3.66563 - 3.95061i) q^{22} +(-1.02148 - 6.77709i) q^{23} +(-2.81091 + 0.931827i) q^{24} +(-8.04430 + 7.46402i) q^{25} +(-0.371356 - 0.591010i) q^{26} +(-5.18979 - 0.257051i) q^{27} +0.557437i q^{28} +(5.11766 - 1.67616i) q^{29} +(-6.56253 + 10.0715i) q^{30} +(1.59052 + 0.693937i) q^{31} +(0.196775 + 5.25892i) q^{32} +(0.912100 + 5.29752i) q^{33} +(-0.986616 + 6.54577i) q^{34} +(-1.36800 - 1.71542i) q^{35} +(-0.993428 + 2.87970i) q^{36} +(2.74830 + 7.85418i) q^{37} +(-0.822313 - 10.9730i) q^{38} +(0.693311 + 0.0634732i) q^{39} +(-4.45727 - 5.17945i) q^{40} +(0.912701 + 3.40625i) q^{41} +(-1.31216 - 1.00227i) q^{42} +(0.611906 + 1.40250i) q^{43} +(3.13155 + 0.352841i) q^{44} +(-4.00993 - 11.2997i) q^{45} +(8.41550 - 8.41550i) q^{46} +(9.57858 - 1.81237i) q^{47} +(-7.07365 - 4.99563i) q^{48} +(-5.53466 + 3.77347i) q^{49} +(-18.7236 - 3.54269i) q^{50} +(-4.59121 - 4.74524i) q^{51} +(0.149115 - 0.379938i) q^{52} +(2.20154 + 1.75567i) q^{53} +(-4.99239 - 7.51613i) q^{54} +(-10.5027 + 6.59928i) q^{55} +(0.755196 - 0.557360i) q^{56} +(9.19573 + 5.99189i) q^{57} +(7.61906 + 5.42189i) q^{58} +(-1.88972 - 1.09103i) q^{59} +(-7.01726 + 0.409594i) q^{60} +(3.44312 - 6.51471i) q^{61} +(0.670535 + 2.93781i) q^{62} +(1.58892 - 0.433262i) q^{63} +(0.673195 - 0.536855i) q^{64} +(0.473526 + 1.53513i) q^{65} +(-6.46107 + 6.73699i) q^{66} +(4.54628 + 6.66818i) q^{67} +(-3.42229 + 1.80873i) q^{68} +(1.57539 + 11.7659i) q^{69} +(0.986111 - 3.68022i) q^{70} +(-12.9810 + 6.25130i) q^{71} +(4.89460 - 1.53344i) q^{72} +(-0.0593993 + 0.527184i) q^{73} +(-8.13976 + 11.9388i) q^{74} +(14.1445 - 12.6965i) q^{75} +(4.87713 - 4.19711i) q^{76} +(-0.796115 - 1.50632i) q^{77} +(0.626235 + 1.03413i) q^{78} +(9.06925 + 7.80472i) q^{79} +(4.44655 - 19.4816i) q^{80} +(8.98041 + 0.593445i) q^{81} +(-3.81799 + 4.78761i) q^{82} +(-4.78588 - 5.15796i) q^{83} +(0.0159269 - 0.965378i) q^{84} +(6.09271 - 13.9647i) q^{85} +(-1.32857 + 2.30115i) q^{86} +(-8.91074 + 2.75659i) q^{87} +(-2.65310 - 4.59530i) q^{88} +(-0.918803 + 0.103524i) q^{89} +(11.6529 - 17.2545i) q^{90} +(-0.215132 + 0.0491025i) q^{91} +(6.88155 + 1.03723i) q^{92} +(-2.73466 - 1.24721i) q^{93} +(12.4093 + 11.5141i) q^{94} +(-4.70845 + 24.8847i) q^{95} +(-0.190522 - 9.11310i) q^{96} +(9.19060 + 0.343888i) q^{97} +(-10.9794 - 3.84185i) q^{98} +(-1.42823 - 9.20039i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) $ 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/261\mathbb{Z}\right)^\times$.

$n$	$118$	$146$
$\chi(n)$	$e\left(\frac{13}{28}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.03117	+	1.39718i	0.729144	+	0.987955i	0.999681	+	0.0252456i	$0.00803679\pi$
$2$	1.03117	+	1.39718i	0.729144	+	0.987955i	−0.270537	+	0.962710i	$0.587201\pi$
$3$	−1.73182	−	0.0285716i	−0.999864	−	0.0164958i
$3$	−1.73182	−	0.0285716i	−0.999864	−	0.0164958i
$4$	−0.299298	+	0.970301i	−0.149649	+	0.485151i
$5$	−1.46016	−	3.72043i	−0.653005	−	1.66383i	−0.744168	−	0.667993i	$-0.767154\pi$
$5$	−1.46016	−	3.72043i	−0.653005	−	1.66383i	0.0911628	−	0.995836i	$-0.470942\pi$
$6$	−1.74587	−	2.44912i	−0.712748	−	0.999849i
$7$	0.524586	−	0.161813i	0.198275	−	0.0611598i	−0.194027	−	0.980996i	$-0.562155\pi$
$7$	0.524586	−	0.161813i	0.198275	−	0.0611598i	0.392302	+	0.919836i	$0.371679\pi$
$8$	1.61379	−	0.564688i	0.570559	−	0.199647i
$9$	2.99837	+	0.0989614i	0.999456	+	0.0329871i
$10$	3.69245	−	5.87649i	1.16765	−	1.85831i
$11$	−0.576982	−	3.04942i	−0.173967	−	0.919436i	−0.955370	−	0.295410i	$-0.904544\pi$
$11$	−0.576982	−	3.04942i	−0.173967	−	0.919436i	0.781404	−	0.624026i	$-0.214504\pi$
$12$	0.546052	−	1.67183i	0.157632	−	0.482616i
$13$	−0.400833	−	0.0300383i	−0.111171	−	0.00833112i	0.0190283	−	0.999819i	$-0.493943\pi$
$13$	−0.400833	−	0.0300383i	−0.111171	−	0.00833112i	−0.130199	+	0.991488i	$0.541562\pi$
$14$	0.767018	+	0.566085i	0.204994	+	0.151293i
$15$	2.42243	+	6.48482i	0.625470	+	1.67437i
$16$	4.13100	+	2.81647i	1.03275	+	0.704117i
$17$	2.69557	+	2.69557i	0.653771	+	0.653771i	0.953899	−	0.300128i	$-0.0970293\pi$
$17$	2.69557	+	2.69557i	0.653771	+	0.653771i	−0.300128	+	0.953899i	$0.597029\pi$
$18$	2.95355	+	4.29130i	0.696157	+	1.01147i
$19$	−5.36550	−	3.37137i	−1.23093	−	0.773445i	−0.250083	−	0.968224i	$-0.580458\pi$
$19$	−5.36550	−	3.37137i	−1.23093	−	0.773445i	−0.980847	+	0.194780i	$0.937601\pi$
$20$	4.04697	−	0.303278i	0.904929	−	0.0678151i
$21$	−0.913110	+	0.265243i	−0.199257	+	0.0578807i
$22$	3.66563	−	3.95061i	0.781515	−	0.842273i
$23$	−1.02148	−	6.77709i	−0.212994	−	1.41312i	−0.798276	−	0.602292i	$-0.794254\pi$
$23$	−1.02148	−	6.77709i	−0.212994	−	1.41312i	0.585282	−	0.810829i	$-0.300984\pi$
$24$	−2.81091	+	0.931827i	−0.573775	+	0.190208i
$25$	−8.04430	+	7.46402i	−1.60886	+	1.49280i
$26$	−0.371356	−	0.591010i	−0.0728290	−	0.115907i
$27$	−5.18979	−	0.257051i	−0.998776	−	0.0494695i
$28$			0.557437i			0.105346i
$29$	5.11766	−	1.67616i	0.950326	−	0.311256i
$29$	5.11766	−	1.67616i	0.950326	−	0.311256i
$30$	−6.56253	+	10.0715i	−1.19815	+	1.83880i
$31$	1.59052	+	0.693937i	0.285666	+	0.124635i	0.537839	−	0.843047i	$-0.319241\pi$
$31$	1.59052	+	0.693937i	0.285666	+	0.124635i	−0.252174	+	0.967682i	$0.581145\pi$
$32$	0.196775	+	5.25892i	0.0347852	+	0.929655i
$33$	0.912100	+	5.29752i	0.158776	+	0.922181i
$34$	−0.986616	+	6.54577i	−0.169203	+	1.12259i
$35$	−1.36800	−	1.71542i	−0.231234	−	0.289958i
$36$	−0.993428	+	2.87970i	−0.165571	+	0.479950i
$37$	2.74830	+	7.85418i	0.451817	+	1.29122i	0.914460	+	0.404675i	$0.132615\pi$
$37$	2.74830	+	7.85418i	0.451817	+	1.29122i	−0.462643	+	0.886545i	$0.653099\pi$
$38$	−0.822313	−	10.9730i	−0.133397	−	1.78006i
$39$	0.693311	+	0.0634732i	0.111019	+	0.0101638i
$40$	−4.45727	−	5.17945i	−0.704757	−	0.818942i
$41$	0.912701	+	3.40625i	0.142540	+	0.531966i	0.999853	+	0.0171701i	$0.00546570\pi$
$41$	0.912701	+	3.40625i	0.142540	+	0.531966i	−0.857313	+	0.514796i	$0.827868\pi$
$42$	−1.31216	−	1.00227i	−0.202471	−	0.154654i
$43$	0.611906	+	1.40250i	0.0933147	+	0.213880i	0.956960	−	0.290221i	$-0.0937288\pi$
$43$	0.611906	+	1.40250i	0.0933147	+	0.213880i	−0.863645	+	0.504101i	$0.831824\pi$
$44$	3.13155	+	0.352841i	0.472099	+	0.0531928i
$45$	−4.00993	−	11.2997i	−0.597764	−	1.68446i
$46$	8.41550	−	8.41550i	1.24080	−	1.24080i
$47$	9.57858	−	1.81237i	1.39718	−	0.264361i	0.567855	−	0.823128i	$-0.307773\pi$
$47$	9.57858	−	1.81237i	1.39718	−	0.264361i	0.829324	+	0.558768i	$0.188726\pi$
$48$	−7.07365	−	4.99563i	−1.02099	−	0.721057i
$49$	−5.53466	+	3.77347i	−0.790666	+	0.539067i
$50$	−18.7236	−	3.54269i	−2.64791	−	0.501012i
$51$	−4.59121	−	4.74524i	−0.642898	−	0.664467i
$52$	0.149115	−	0.379938i	0.0206785	−	0.0526880i
$53$	2.20154	+	1.75567i	0.302405	+	0.241160i	0.762921	−	0.646491i	$-0.223764\pi$
$53$	2.20154	+	1.75567i	0.302405	+	0.241160i	−0.460517	+	0.887651i	$0.652336\pi$
$54$	−4.99239	−	7.51613i	−0.679378	−	1.02282i
$55$	−10.5027	+	6.59928i	−1.41618	+	0.889847i
$56$	0.755196	−	0.557360i	0.100917	−	0.0744804i
$57$	9.19573	+	5.99189i	1.21800	+	0.793645i
$58$	7.61906	+	5.42189i	1.00043	+	0.711929i
$59$	−1.88972	−	1.09103i	−0.246021	−	0.142040i	0.371920	−	0.928265i	$-0.378700\pi$
$59$	−1.88972	−	1.09103i	−0.246021	−	0.142040i	−0.617941	+	0.786224i	$0.712033\pi$
$60$	−7.01726	+	0.409594i	−0.905925	+	0.0528783i
$61$	3.44312	−	6.51471i	0.440847	−	0.834123i	−0.559140	−	0.829073i	$-0.688869\pi$
$61$	3.44312	−	6.51471i	0.440847	−	0.834123i	0.999987	−	0.00504999i	$-0.00160747\pi$
$62$	0.670535	+	2.93781i	0.0851580	+	0.373102i
$63$	1.58892	−	0.433262i	0.200185	−	0.0545859i
$64$	0.673195	−	0.536855i	0.0841494	−	0.0671069i
$65$	0.473526	+	1.53513i	0.0587337	+	0.190410i
$66$	−6.46107	+	6.73699i	−0.795302	+	0.829266i
$67$	4.54628	+	6.66818i	0.555417	+	0.814647i	0.996567	−	0.0827860i	$-0.0263818\pi$
$67$	4.54628	+	6.66818i	0.555417	+	0.814647i	−0.441150	+	0.897433i	$0.645429\pi$
$68$	−3.42229	+	1.80873i	−0.415014	+	0.219341i
$69$	1.57539	+	11.7659i	0.189654	+	1.41644i
$70$	0.986111	−	3.68022i	0.117863	−	0.439870i
$71$	−12.9810	+	6.25130i	−1.54056	+	0.741892i	−0.995342	−	0.0964048i	$-0.969266\pi$
$71$	−12.9810	+	6.25130i	−1.54056	+	0.741892i	−0.545213	+	0.838297i	$0.683551\pi$
$72$	4.89460	−	1.53344i	0.576835	−	0.180718i
$73$	−0.0593993	+	0.527184i	−0.00695217	+	0.0617022i	−0.996709	−	0.0810594i	$-0.974170\pi$
$73$	−0.0593993	+	0.527184i	−0.00695217	+	0.0617022i	0.989757	+	0.142762i	$0.0455982\pi$
$74$	−8.13976	+	11.9388i	−0.946227	+	1.38786i
$75$	14.1445	−	12.6965i	1.63327	−	1.46606i
$76$	4.87713	−	4.19711i	0.559445	−	0.481441i
$77$	−0.796115	−	1.50632i	−0.0907257	−	0.171661i
$78$	0.626235	+	1.03413i	0.0709071	+	0.117092i
$79$	9.06925	+	7.80472i	1.02037	+	0.878099i	0.992590	−	0.121515i	$-0.0387751\pi$
$79$	9.06925	+	7.80472i	1.02037	+	0.878099i	0.0277804	+	0.999614i	$0.491156\pi$
$80$	4.44655	−	19.4816i	0.497139	−	2.17811i
$81$	8.98041	+	0.593445i	0.997824	+	0.0659384i
$82$	−3.81799	+	4.78761i	−0.421627	+	0.528703i
$83$	−4.78588	−	5.15796i	−0.525319	−	0.566159i	0.413529	−	0.910491i	$-0.364296\pi$
$83$	−4.78588	−	5.15796i	−0.525319	−	0.566159i	−0.938848	+	0.344332i	$0.888106\pi$
$84$	0.0159269	−	0.965378i	0.00173776	−	0.105331i
$85$	6.09271	−	13.9647i	0.660848	−	1.51468i
$86$	−1.32857	+	2.30115i	−0.143264	+	0.248140i
$87$	−8.91074	+	2.75659i	−0.955331	+	0.295537i
$88$	−2.65310	−	4.59530i	−0.282821	−	0.489861i
$89$	−0.918803	+	0.103524i	−0.0973929	+	0.0109735i	−0.160526	−	0.987032i	$-0.551319\pi$
$89$	−0.918803	+	0.103524i	−0.0973929	+	0.0109735i	0.0631335	+	0.998005i	$0.479891\pi$
$90$	11.6529	−	17.2545i	1.22832	−	1.81878i
$91$	−0.215132	+	0.0491025i	−0.0225520	+	0.00514734i
$92$	6.88155	+	1.03723i	0.717451	+	0.108138i
$93$	−2.73466	−	1.24721i	−0.283571	−	0.129330i
$94$	12.4093	+	11.5141i	1.27992	+	1.18759i
$95$	−4.70845	+	24.8847i	−0.483077	+	2.55312i
$96$	−0.190522	−	9.11310i	−0.0194451	−	0.930102i
$97$	9.19060	+	0.343888i	0.933164	+	0.0349165i	0.499647	−	0.866229i	$-0.333463\pi$
$97$	9.19060	+	0.343888i	0.933164	+	0.0349165i	0.433517	+	0.901146i	$0.357273\pi$
$98$	−10.9794	−	3.84185i	−1.10908	−	0.388085i
$99$	−1.42823	−	9.20039i	−0.143542	−	0.924674i
$100$	−4.83470	−	10.0394i	−0.483470	−	1.00394i
$101$	−12.8283	+	5.59693i	−1.27646	+	0.556915i	−0.925242	−	0.379378i	$-0.876138\pi$
$101$	−12.8283	+	5.59693i	−1.27646	+	0.556915i	−0.351221	+	0.936293i	$0.614233\pi$
$102$	1.89566	−	11.3079i	0.187698	−	1.11965i
$103$	−0.380474	+	5.07708i	−0.0374893	+	0.500259i	0.946579	+	0.322471i	$0.104513\pi$
$103$	−0.380474	+	5.07708i	−0.0374893	+	0.500259i	−0.984069	+	0.177789i	$0.943106\pi$
$104$	−0.663821	+	0.177870i	−0.0650930	+	0.0174416i
$105$	2.32011	+	3.00987i	0.226419	+	0.293733i
$106$	−0.182834	+	4.88633i	−0.0177584	+	0.474603i
$107$	1.02857	−	2.13585i	0.0994356	−	0.206480i	−0.845316	−	0.534266i	$-0.820588\pi$
$107$	1.02857	−	2.13585i	0.0994356	−	0.206480i	0.944752	+	0.327786i	$0.106302\pi$
$108$	1.80271	−	4.95872i	0.173466	−	0.477153i
$109$	0.343427	+	0.0783850i	0.0328943	+	0.00750792i	0.238936	−	0.971035i	$-0.423201\pi$
$109$	0.343427	+	0.0783850i	0.0328943	+	0.00750792i	−0.206042	+	0.978543i	$0.566058\pi$
$110$	−20.0504	−	7.86920i	−1.91173	−	0.750299i
$111$	−4.53514	−	13.6805i	−0.430456	−	1.29850i
$112$	2.62281	+	0.809029i	0.247832	+	0.0764461i
$113$	19.5885	−	0.732949i	1.84273	−	0.0689500i	0.906887	−	0.421373i	$-0.138452\pi$
$113$	19.5885	−	0.732949i	1.84273	−	0.0689500i	0.935841	+	0.352423i	$0.114642\pi$
$114$	1.11058	+	19.0267i	0.104015	+	1.78202i
$115$	−23.7222	+	13.6960i	−2.21211	+	1.27716i
$116$	0.0946761	+	5.46735i	0.00879045	+	0.507630i
$117$	−1.19887	−	0.129733i	−0.110836	−	0.0119938i
$118$	−0.424250	−	3.76532i	−0.0390553	−	0.346626i
$119$	1.85024	+	0.977879i	0.169611	+	0.0896420i
$120$	7.57119	+	9.09720i	0.691152	+	0.830457i
$121$	1.27353	−	0.499824i	0.115776	−	0.0454386i
$122$	12.6526	−	1.90708i	1.14552	−	0.172659i
$123$	−1.48331	−	5.92507i	−0.133745	−	0.534245i
$124$	−1.14937	+	1.33559i	−0.103216	+	0.119939i
$125$	21.5108	+	10.3591i	1.92399	+	0.926543i
$126$	2.24378	+	1.77324i	0.199892	+	0.157972i
$127$	1.48514	−	4.24429i	0.131785	−	0.376620i	−0.859016	−	0.511949i	$-0.828924\pi$
$127$	1.48514	−	4.24429i	0.131785	−	0.376620i	0.990801	+	0.135329i	$0.0432093\pi$
$128$	11.6108	+	3.11111i	1.02626	+	0.274986i
$129$	−1.01964	−	2.44636i	−0.0897739	−	0.215390i
$130$	−1.65657	+	2.24458i	−0.145291	+	0.196863i
$131$	10.2878	−	13.9395i	0.898848	−	1.21790i	−0.0764654	−	0.997072i	$-0.524363\pi$
$131$	10.2878	−	13.9395i	0.898848	−	1.21790i	0.975314	−	0.220824i	$-0.0708746\pi$
$132$	−5.41318	−	0.700529i	−0.471157	−	0.0609732i
$133$	−3.36020	−	0.900363i	−0.291366	−	0.0780714i
$134$	−4.62867	+	13.2280i	−0.399856	+	1.14272i
$135$	6.62160	+	19.6836i	0.569896	+	1.69410i
$136$	5.87222	+	2.82791i	0.503539	+	0.242492i
$137$	−1.72920	+	2.00937i	−0.147736	+	0.171672i	−0.826964	−	0.562255i	$-0.809934\pi$
$137$	−1.72920	+	2.00937i	−0.147736	+	0.171672i	0.679228	+	0.733927i	$0.262315\pi$
$138$	−14.8145	+	14.3336i	−1.26110	+	1.22016i
$139$	2.11112	−	0.318200i	0.179063	−	0.0269894i	−0.0588987	−	0.998264i	$-0.518759\pi$
$139$	2.11112	−	0.318200i	0.179063	−	0.0269894i	0.237961	+	0.971275i	$0.423521\pi$
$140$	2.07391	−	0.813949i	0.175277	−	0.0687913i
$141$	−16.6401	+	2.86501i	−1.40135	+	0.241277i
$142$	−22.1197	−	11.6906i	−1.85624	−	0.981053i
$143$	0.139674	+	1.23964i	0.0116801	+	0.103664i
$144$	12.1075	+	8.85361i	1.00896	+	0.737801i
$145$	−13.7087	−	16.5925i	−1.13844	−	1.37793i
$146$	−0.797821	+	0.460622i	−0.0660281	+	0.0381214i
$147$	9.69283	−	6.37682i	0.799451	−	0.525951i
$148$	−8.44348	+	0.315933i	−0.694050	+	0.0259695i
$149$	2.07495	+	0.640038i	0.169987	+	0.0524340i	0.378580	−	0.925568i	$-0.376412\pi$
$149$	2.07495	+	0.640038i	0.169987	+	0.0524340i	−0.208594	+	0.978002i	$0.566889\pi$
$150$	32.3246	+	6.67025i	2.63929	+	0.544624i
$151$	0.908066	+	0.356390i	0.0738974	+	0.0290026i	0.402002	−	0.915639i	$-0.368315\pi$
$151$	0.908066	+	0.356390i	0.0738974	+	0.0290026i	−0.328104	+	0.944641i	$0.606410\pi$
$152$	−10.5625	−	2.41083i	−0.856735	−	0.195544i
$153$	7.81554	+	8.34906i	0.631849	+	0.674981i
$154$	1.28368	−	2.66558i	0.103442	−	0.214799i
$155$	0.259328	−	6.93069i	0.0208297	−	0.556686i
$156$	−0.269095	+	0.653723i	−0.0215448	+	0.0523397i
$157$	3.66546	−	0.982158i	0.292536	−	0.0783848i	−0.109566	−	0.993979i	$-0.534946\pi$
$157$	3.66546	−	0.982158i	0.292536	−	0.0783848i	0.402102	+	0.915595i	$0.368280\pi$
$158$	−1.55270	+	20.7193i	−0.123526	+	1.64834i
$159$	−3.76250	−	3.10340i	−0.298386	−	0.246115i
$160$	19.2781	−	8.41097i	1.52407	−	0.664945i
$161$	−1.63248	−	3.38988i	−0.128657	−	0.267160i
$162$	8.43114	+	13.1592i	0.662413	+	1.03388i
$163$	−0.141584	−	0.0495424i	−0.0110897	−	0.00388046i	0.324729	−	0.945807i	$-0.394727\pi$
$163$	−0.141584	−	0.0495424i	−0.0110897	−	0.00388046i	−0.335818	+	0.941927i	$0.609013\pi$
$164$	−3.57825	−	0.133889i	−0.279415	−	0.0104550i
$165$	18.3773	−	11.1287i	1.43067	−	0.866365i
$166$	2.27155	−	12.0054i	0.176307	−	0.931803i
$167$	−10.5592	−	9.79747i	−0.817092	−	0.758151i	0.156199	−	0.987726i	$-0.450076\pi$
$167$	−10.5592	−	9.79747i	−0.817092	−	0.758151i	−0.973291	+	0.229575i	$0.926266\pi$
$168$	−1.32378	+	0.943667i	−0.102132	+	0.0728055i
$169$	−12.6950	−	1.91347i	−0.976541	−	0.147190i
$170$	25.7937	−	5.88725i	1.97829	−	0.451531i
$171$	−15.7541	−	10.6396i	−1.20475	−	0.813629i
$172$	−1.54399	+	0.173966i	−0.117728	+	0.0132648i
$173$	4.19462	+	7.26529i	0.318911	+	0.552370i	0.980261	−	0.197707i	$-0.0633496\pi$
$173$	4.19462	+	7.26529i	0.318911	+	0.552370i	−0.661350	+	0.750077i	$0.730016\pi$
$174$	−13.0399	−	9.60740i	−0.988552	−	0.728335i
$175$	−3.01215	+	5.21720i	−0.227697	+	0.394383i
$176$	6.20509	−	14.2222i	0.467726	−	1.07204i
$177$	3.24148	+	1.94346i	0.243645	+	0.146079i
$178$	−1.09208	−	1.17698i	−0.0818548	−	0.0882185i
$179$	−11.0513	+	13.8580i	−0.826017	+	1.03579i	0.172692	+	0.984976i	$0.444754\pi$
$179$	−11.0513	+	13.8580i	−0.826017	+	1.03579i	−0.998708	+	0.0508160i	$0.983818\pi$
$180$	12.1643	−	0.508846i	0.906674	−	0.0379271i
$181$	4.32644	−	18.9554i	0.321582	−	1.40894i	−0.513156	−	0.858295i	$-0.671524\pi$
$181$	4.32644	−	18.9554i	0.321582	−	1.40894i	0.834738	−	0.550647i	$-0.185619\pi$
$182$	−0.290442	−	0.249946i	−0.0215290	−	0.0185272i
$183$	−6.14899	+	11.1839i	−0.454546	+	0.826737i
$184$	−5.47539	−	10.3600i	−0.403651	−	0.763746i
$185$	25.2080	−	21.6933i	1.85333	−	1.59492i
$186$	−1.07730	−	5.10689i	−0.0789918	−	0.374456i
$187$	6.66463	−	9.77522i	0.487366	−	0.714835i
$188$	−1.10831	+	9.83655i	−0.0808320	+	0.717404i
$189$	−2.76409	+	0.704933i	−0.201058	+	0.0512763i
$190$	−39.6236	+	19.0817i	−2.87460	+	1.38434i
$191$	4.46461	−	16.6622i	0.323048	−	1.20563i	−0.593212	−	0.805046i	$-0.702140\pi$
$191$	4.46461	−	16.6622i	0.323048	−	1.20563i	0.916260	−	0.400585i	$-0.131193\pi$
$192$	−1.18119	+	0.910500i	−0.0852449	+	0.0657096i
$193$	1.84801	−	0.976701i	0.133023	−	0.0703045i	−0.399433	−	0.916762i	$-0.630793\pi$
$193$	1.84801	−	0.976701i	0.133023	−	0.0703045i	0.532456	+	0.846458i	$0.321269\pi$
$194$	8.99655	+	13.1955i	0.645915	+	0.947383i
$195$	−0.776199	−	2.67210i	−0.0555847	−	0.191353i
$196$	−2.00489	−	6.49968i	−0.143206	−	0.464263i
$197$	11.5562	−	9.21574i	0.823343	−	0.656595i	−0.118385	−	0.992968i	$-0.537772\pi$
$197$	11.5562	−	9.21574i	0.823343	−	0.656595i	0.941729	+	0.336373i	$0.109200\pi$
$198$	11.3819	−	11.4826i	0.808874	−	0.816034i
$199$	3.86265	+	16.9234i	0.273816	+	1.19967i	0.905468	+	0.424415i	$0.139520\pi$
$199$	3.86265	+	16.9234i	0.273816	+	1.19967i	−0.631652	+	0.775252i	$0.717623\pi$
$200$	−8.76693	+	16.5878i	−0.619916	+	1.17294i
$201$	−7.68280	−	11.6779i	−0.541903	−	0.823698i
$202$	−21.0480	−	12.1521i	−1.48093	−	0.855017i
$203$	2.41343	−	1.70740i	0.169390	−	0.119836i
$204$	5.97845	−	3.03461i	0.418575	−	0.212465i
$205$	11.3400	−	8.36932i	0.792022	−	0.584539i
$206$	−7.48592	+	4.70372i	−0.521569	+	0.327723i
$207$	−2.39211	−	20.4213i	−0.166263	−	1.41938i
$208$	−1.57124	−	1.25302i	−0.108946	−	0.0868814i
$209$	−7.18493	+	18.3069i	−0.496992	+	1.26632i
$210$	−1.81291	+	6.34528i	−0.125103	+	0.437866i
$211$	0.996034	+	0.188460i	0.0685698	+	0.0129741i	0.220083	−	0.975481i	$-0.429367\pi$
$211$	0.996034	+	0.188460i	0.0685698	+	0.0129741i	−0.151513	+	0.988455i	$0.548415\pi$
$212$	−2.36245	+	1.61069i	−0.162253	+	0.110622i
$213$	22.6592	−	10.4552i	1.55258	−	0.716379i
$214$	4.04479	−	0.765316i	0.276496	−	0.0523159i
$215$	4.32444	−	4.32444i	0.294924	−	0.294924i
$216$	−8.52036	+	2.51579i	−0.579737	+	0.171178i
$217$	0.946654	+	0.106662i	0.0642630	+	0.00724071i
$218$	0.244612	+	0.560657i	0.0165672	+	0.0379725i
$219$	0.117931	−	0.911288i	0.00796905	−	0.0615791i
$220$	−3.25985	−	12.1659i	−0.219779	−	0.820227i
$221$	−0.999503	−	1.16144i	−0.0672338	−	0.0781271i
$222$	14.4377	−	20.4433i	0.968992	−	1.37206i
$223$	1.17013	+	15.6143i	0.0783575	+	1.04561i	0.888350	+	0.459168i	$0.151852\pi$
$223$	1.17013	+	15.6143i	0.0783575	+	1.04561i	−0.809992	+	0.586441i	$0.800529\pi$
$224$	0.954190	+	2.72692i	0.0637545	+	0.182200i
$225$	−24.8584	+	21.5838i	−1.65723	+	1.43892i
$226$	21.2230	+	26.6128i	1.41173	+	1.77026i
$227$	−1.88279	+	12.4915i	−0.124965	+	0.829088i	0.835259	+	0.549857i	$0.185318\pi$
$227$	−1.88279	+	12.4915i	−0.124965	+	0.829088i	−0.960224	+	0.279231i	$0.909920\pi$
$228$	−8.56620	+	7.12927i	−0.567310	+	0.472147i
$229$	0.286783	+	7.66445i	0.0189512	+	0.506481i	0.976156	+	0.217070i	$0.0696500\pi$
$229$	0.286783	+	7.66445i	0.0189512	+	0.506481i	−0.957205	+	0.289411i	$0.906541\pi$
$230$	−43.5973	−	19.0213i	−2.87472	−	1.25423i
$231$	1.33569	+	2.63142i	0.0878817	+	0.173135i
$232$	7.31230	−	5.59485i	0.480076	−	0.367320i
$233$		−	25.2517i		−	1.65429i	−0.561985	−	0.827147i	$-0.689962\pi$
$233$		−	25.2517i		−	1.65429i	0.561985	−	0.827147i	$-0.310038\pi$
$234$	−1.05498	−	1.80882i	−0.0689659	−	0.118246i
$235$	−20.7291	−	32.9901i	−1.35222	−	2.15204i
$236$	1.62422	−	1.50706i	0.105728	−	0.0981011i
$237$	−15.4833	−	13.7755i	−1.00575	−	0.894812i
$238$	0.541628	+	3.59347i	0.0351085	+	0.232930i
$239$	−14.3600	+	15.4764i	−0.928869	+	1.00108i	0.0711245	+	0.997467i	$0.477341\pi$
$239$	−14.3600	+	15.4764i	−0.928869	+	1.00108i	−0.999993	+	0.00361518i	$0.998849\pi$
$240$	−8.25722	+	33.6115i	−0.533001	+	2.16961i
$241$	−23.6484	+	1.77220i	−1.52333	+	0.114158i	−0.809899	−	0.586569i	$-0.800478\pi$
$241$	−23.6484	+	1.77220i	−1.52333	+	0.114158i	−0.713430	+	0.700727i	$0.752859\pi$
$242$	2.01157	+	1.26395i	0.129308	+	0.0812498i
$243$	−15.5355	−	1.28432i	−0.996600	−	0.0823893i
$244$	5.29071	+	5.29071i	0.338703	+	0.338703i
$245$	22.1205	+	15.0815i	1.41322	+	0.963520i
$246$	6.74885	−	8.18217i	0.430291	−	0.521676i
$247$	2.04940	+	1.51253i	0.130400	+	0.0962398i
$248$	2.95862	+	0.221718i	0.187872	+	0.0140791i
$249$	8.14089	+	9.06937i	0.515908	+	0.574748i
$250$	7.70774	+	40.7364i	0.487480	+	2.57639i
$251$	−10.9893	+	17.4894i	−0.693642	+	1.10392i	0.295269	+	0.955414i	$0.404591\pi$
$251$	−10.9893	+	17.4894i	−0.693642	+	1.10392i	−0.988911	+	0.148510i	$0.952552\pi$
$252$	−0.0551648	+	1.67140i	−0.00347505	+	0.105288i
$253$	−20.0768	+	7.02519i	−1.26222	+	0.441670i
$254$	7.46146	−	2.30156i	0.468174	−	0.144412i
$255$	−10.9504	+	24.0101i	−0.685744	+	1.50357i
$256$	6.99675	+	17.8274i	0.437297	+	1.11421i
$257$	0.608529	−	1.97280i	0.0379590	−	0.123060i	−0.934610	−	0.355674i	$-0.884252\pi$
$257$	0.608529	−	1.97280i	0.0379590	−	0.123060i	0.972569	+	0.232613i	$0.0747277\pi$
$258$	2.36659	−	3.94721i	0.147337	−	0.245743i
$259$	2.71263	+	3.67549i	0.168555	+	0.228384i
$260$	−1.63127			−0.101167
$261$	15.5105	−	4.51930i	0.960076	−	0.279738i
$262$	30.0843			1.85862
$263$	−5.55074	−	7.52099i	−0.342273	−	0.463764i	0.599323	−	0.800507i	$-0.295436\pi$
$263$	−5.55074	−	7.52099i	−0.342273	−	0.463764i	−0.941596	+	0.336743i	$0.890675\pi$
$264$	4.46338	+	8.03402i	0.274702	+	0.494460i
$265$	3.31725	−	10.7543i	0.203777	−	0.660628i
$266$	−2.20695	−	5.62323i	−0.135317	−	0.344782i
$267$	1.59415	−	0.153033i	0.0975607	−	0.00936548i
$268$	−7.83083	+	2.41549i	−0.478344	+	0.147550i
$269$	−16.5693	+	5.79784i	−1.01025	+	0.353501i	−0.784128	−	0.620599i	$-0.786889\pi$
$269$	−16.5693	+	5.79784i	−1.01025	+	0.353501i	−0.226119	+	0.974100i	$0.572604\pi$
$270$	−20.6736	+	29.5486i	−1.25815	+	1.79827i
$271$	4.13972	−	6.58833i	0.251470	−	0.400213i	−0.697004	−	0.717067i	$-0.745484\pi$
$271$	4.13972	−	6.58833i	0.251470	−	0.400213i	0.948474	+	0.316855i	$0.102627\pi$
$272$	3.54341	+	18.7274i	0.214851	+	1.13551i
$273$	0.373972	−	0.0788898i	0.0226338	−	0.00477463i
$274$	−4.59054	−	0.344013i	−0.277325	−	0.0207826i
$275$	27.4024	+	20.2239i	1.65243	+	1.21955i
$276$	−11.8879	−	1.99290i	−0.715569	−	0.119959i
$277$	−6.49120	−	4.42562i	−0.390018	−	0.265910i	0.352396	−	0.935851i	$-0.385367\pi$
$277$	−6.49120	−	4.42562i	−0.390018	−	0.265910i	−0.742414	+	0.669941i	$0.766319\pi$
$278$	2.62150	+	2.62150i	0.157227	+	0.157227i
$279$	4.70029	+	2.23808i	0.281399	+	0.133990i
$280$	−3.17633	−	1.99582i	−0.189822	−	0.119273i
$281$	−26.2974	+	1.97072i	−1.56877	+	0.117563i	−0.830531	−	0.556972i	$-0.811963\pi$
$281$	−26.2974	+	1.97072i	−1.56877	+	0.117563i	−0.738243	+	0.674535i	$0.764344\pi$
$282$	−21.1616	−	20.2949i	−1.26016	−	1.20855i
$283$	−2.95583	+	3.18562i	−0.175706	+	0.189366i	−0.814764	−	0.579792i	$-0.803134\pi$
$283$	−2.95583	+	3.18562i	−0.175706	+	0.189366i	0.639059	+	0.769158i	$0.279324\pi$
$284$	−2.18046	−	14.4664i	−0.129387	−	0.858425i
$285$	8.86516	−	42.9612i	0.525127	−	2.54480i
$286$	−1.58798	+	1.47343i	−0.0938989	+	0.0871255i
$287$	1.02997	+	1.63918i	0.0607970	+	0.0967579i
$288$	0.0695734	+	15.7876i	0.00409965	+	0.930296i
$289$		−	2.46783i		−	0.145167i
$290$	9.04673	−	36.2631i	0.531242	−	2.12944i
$291$	−15.9066	−	0.858140i	−0.932461	−	0.0503051i
$292$	−0.493749	−	0.215420i	−0.0288945	−	0.0126065i
$293$	0.792751	+	21.1867i	0.0463130	+	1.23774i	0.807759	+	0.589512i	$0.200680\pi$
$293$	0.792751	+	21.1867i	0.0463130	+	1.23774i	−0.761446	+	0.648228i	$0.775510\pi$
$294$	18.9045	+	6.96707i	1.10253	+	0.406328i
$295$	−1.29981	+	8.62368i	−0.0756779	+	0.502090i
$296$	8.87033	+	11.1230i	0.515577	+	0.646513i
$297$	2.21056	+	15.9742i	0.128270	+	0.926916i
$298$	1.24537	+	3.55907i	0.0721424	+	0.206171i
$299$	0.205872	+	2.74717i	0.0119059	+	0.158873i
$300$	8.08597	+	17.5245i	0.466844	+	1.01177i
$301$	0.547941	+	0.636719i	0.0315828	+	0.0366999i
$302$	0.438426	+	1.63623i	0.0252286	+	0.0941544i
$303$	22.3761	−	9.32632i	1.28548	−	0.535783i
$304$	−12.6695	−	29.0389i	−0.726647	−	1.66549i
$305$	−29.2651	−	3.29738i	−1.67571	−	0.188808i
$306$	−3.60601	+	19.5290i	−0.206142	+	1.11640i
$307$	1.42348	−	1.42348i	0.0812425	−	0.0812425i	−0.665318	−	0.746560i	$-0.731704\pi$
$307$	1.42348	−	1.42348i	0.0812425	−	0.0812425i	0.746560	+	0.665318i	$0.231704\pi$
$308$	1.69986	−	0.321631i	0.0968587	−	0.0183267i
$309$	0.803971	−	8.78169i	0.0457363	−	0.499573i
$310$	9.95082	−	6.78436i	0.565169	−	0.385326i
$311$	5.56844	+	1.05361i	0.315757	+	0.0597445i	0.341375	−	0.939927i	$-0.389108\pi$
$311$	5.56844	+	1.05361i	0.315757	+	0.0597445i	−0.0256174	+	0.999672i	$0.508155\pi$
$312$	1.15470	−	0.289072i	0.0653719	−	0.0163655i
$313$	11.1255	−	28.3474i	0.628851	−	1.60229i	−0.159594	−	0.987183i	$-0.551019\pi$
$313$	11.1255	−	28.3474i	0.628851	−	1.60229i	0.788446	−	0.615105i	$-0.210886\pi$
$314$	5.15195	+	4.10854i	0.290741	+	0.231859i
$315$	−3.93200	−	5.27883i	−0.221543	−	0.297428i
$316$	−10.2873	+	6.46396i	−0.578708	+	0.363626i
$317$	−27.8967	+	20.5887i	−1.56683	+	1.15638i	−0.648062	+	0.761588i	$0.724420\pi$
$317$	−27.8967	+	20.5887i	−1.56683	+	1.15638i	−0.918772	+	0.394789i	$0.870818\pi$
$318$	0.456244	−	8.45700i	0.0255849	−	0.474245i
$319$	−8.06414	−	14.6388i	−0.451505	−	0.819616i
$320$	−2.98031	−	1.72068i	−0.166604	−	0.0961890i
$321$	−1.84232	+	3.66951i	−0.102828	+	0.204812i
$322$	3.05291	−	5.77640i	0.170132	−	0.321906i
$323$	−5.37532	−	23.5508i	−0.299091	−	1.31040i
$324$	−3.26364	+	8.53609i	−0.181313	+	0.474227i
$325$	3.44863	−	2.75019i	0.191295	−	0.152553i
$326$	−0.0767769	−	0.248905i	−0.00425228	−	0.0137856i
$327$	−0.592513	−	0.145561i	−0.0327660	−	0.00804952i
$328$	3.39637	+	4.98156i	0.187533	+	0.275061i
$329$	4.73153	−	2.50069i	0.260858	−	0.137867i
$330$	34.4987	+	14.2009i	1.89909	+	0.781732i
$331$	0.362543	−	1.35303i	0.0199272	−	0.0743692i	−0.955246	−	0.295812i	$-0.904410\pi$
$331$	0.362543	−	1.35303i	0.0199272	−	0.0743692i	0.975173	+	0.221443i	$0.0710765\pi$
$332$	6.43718	−	3.09998i	0.353286	−	0.170134i
$333$	7.46314	+	23.8217i	0.408978	+	1.30542i
$334$	2.80058	−	24.8559i	0.153241	−	1.36005i
$335$	18.1702	−	26.6508i	0.992744	−	1.45609i
$336$	−4.51910	−	1.47603i	−0.246537	−	0.0805238i
$337$	−10.4407	+	8.98496i	−0.568742	+	0.489442i	−0.889012	−	0.457884i	$-0.848607\pi$
$337$	−10.4407	+	8.98496i	−0.568742	+	0.489442i	0.320270	+	0.947326i	$0.396226\pi$
$338$	−10.4172	−	19.7103i	−0.566622	−	1.07210i
$339$	−33.9445	+	0.709658i	−1.84361	+	0.0385433i
$340$	11.7264	+	10.0914i	0.635952	+	0.547281i
$341$	1.19841	−	5.25056i	0.0648973	−	0.284334i
$342$	−1.37969	−	32.9825i	−0.0746052	−	1.78349i
$343$	−4.68878	+	5.87954i	−0.253170	+	0.317465i
$344$	1.77946	+	1.91780i	0.0959421	+	0.103401i
$345$	41.4738	−	23.0412i	2.23287	−	1.24050i
$346$	−5.82557	+	13.3524i	−0.313185	+	0.717827i
$347$	3.36991	−	5.83686i	0.180907	−	0.313339i	−0.761283	−	0.648420i	$-0.775430\pi$
$347$	3.36991	−	5.83686i	0.180907	−	0.313339i	0.942189	+	0.335081i	$0.108764\pi$
$348$	−0.00775071	−	9.47114i	−0.000415482	−	0.507706i
$349$	8.53408	+	14.7815i	0.456819	+	0.791233i	0.998791	−	0.0491632i	$-0.0156554\pi$
$349$	8.53408	+	14.7815i	0.456819	+	0.791233i	−0.541972	+	0.840397i	$0.682322\pi$
$350$	−10.3954	+	1.17128i	−0.555657	+	0.0626075i
$351$	2.07252	+	0.258927i	0.110623	+	0.0138205i
$352$	15.9231	−	3.63435i	0.848706	−	0.193712i
$353$	15.9672	+	2.40667i	0.849848	+	0.128094i	0.559503	−	0.828828i	$-0.310992\pi$
$353$	15.9672	+	2.40667i	0.849848	+	0.128094i	0.290345	+	0.956922i	$0.406230\pi$
$354$	0.627141	+	6.53296i	0.0333322	+	0.347223i
$355$	42.2119	+	39.1669i	2.24037	+	2.07876i
$356$	0.174546	−	0.922500i	0.00925094	−	0.0488924i
$357$	−3.17633	−	1.74637i	−0.168109	−	0.0924277i
$358$	−30.7578	−	1.15088i	−1.62560	−	0.0608257i
$359$	−26.6079	−	9.31051i	−1.40431	−	0.491390i	−0.481434	−	0.876482i	$-0.659884\pi$
$359$	−26.6079	−	9.31051i	−1.40431	−	0.491390i	−0.922878	+	0.385092i	$0.874170\pi$
$360$	−12.8520	−	15.9710i	−0.677359	−	0.841745i
$361$	9.17869	+	19.0597i	0.483089	+	1.00314i
$362$	30.9453	−	13.5013i	1.62645	−	0.709613i
$363$	−2.21980	+	0.829216i	−0.116509	+	0.0435226i
$364$	0.0167445	−	0.223439i	0.000877648	−	0.0117114i
$365$	2.04809	−	0.548783i	0.107202	−	0.0287246i
$366$	−21.9665	+	2.94120i	−1.14821	+	0.153739i
$367$	−0.281578	+	7.52533i	−0.0146983	+	0.392819i	0.972460	+	0.233071i	$0.0748776\pi$
$367$	−0.281578	+	7.52533i	−0.0146983	+	0.392819i	−0.987158	+	0.159748i	$0.948932\pi$
$368$	14.8677	−	30.8731i	0.775033	−	1.60937i
$369$	2.39953	+	10.3035i	0.124914	+	0.536379i
$370$	56.3030	+	12.8508i	2.92705	+	0.668081i
$371$	1.43899	+	0.564762i	0.0747086	+	0.0293210i
$372$	2.02865	−	2.28015i	0.105181	−	0.118221i
$373$	32.2472	+	9.94695i	1.66970	+	0.515034i	0.978256	−	0.207399i	$-0.0664999\pi$
$373$	32.2472	+	9.94695i	1.66970	+	0.515034i	0.691441	+	0.722433i	$0.256976\pi$
$374$	20.5301	−	0.768182i	1.06159	−	0.0397217i
$375$	−36.9568	−	18.5546i	−1.90844	−	0.958154i
$376$	14.4344	−	8.33368i	0.744395	−	0.429777i
$377$	−2.10168	+	0.518136i	−0.108242	+	0.0266854i
$378$	−3.83515	−	3.13503i	−0.197259	−	0.161248i
$379$	−0.332817	−	2.95383i	−0.0170957	−	0.151728i	0.982264	−	0.187502i	$-0.0600391\pi$
$379$	−0.332817	−	2.95383i	−0.0170957	−	0.151728i	−0.999360	+	0.0357736i	$0.988610\pi$
$380$	−22.7365	−	12.0166i	−1.16636	−	0.616437i
$381$	−2.69326	+	7.30789i	−0.137980	+	0.374395i
$382$	27.8838	−	10.9436i	1.42666	−	0.559922i
$383$	14.0475	−	2.11733i	0.717796	−	0.108190i	0.220019	−	0.975496i	$-0.429388\pi$
$383$	14.0475	−	2.11733i	0.717796	−	0.108190i	0.497777	+	0.867305i	$0.334150\pi$
$384$	−20.0189	−	5.71961i	−1.02159	−	0.291877i
$385$	−4.44172	+	5.16137i	−0.226371	+	0.263048i
$386$	3.27023	+	1.57486i	0.166450	+	0.0801583i
$387$	1.69592	+	4.26577i	0.0862087	+	0.216841i
$388$	−3.08440	+	8.81472i	−0.156587	+	0.447500i
$389$	12.0039	+	3.21643i	0.608621	+	0.163080i	0.549950	−	0.835198i	$-0.314647\pi$
$389$	12.0039	+	3.21643i	0.608621	+	0.163080i	0.0586716	+	0.998277i	$0.481314\pi$
$390$	2.93301	−	3.83986i	0.148519	−	0.194439i
$391$	15.5146	−	21.0216i	0.784609	−	1.06311i
$392$	−6.80093	+	9.21493i	−0.343499	+	0.465424i
$393$	−18.2148	+	23.8466i	−0.918816	+	1.20290i
$394$	24.7924	+	6.64310i	1.24902	+	0.334674i
$395$	15.7944	−	45.1377i	0.794701	−	2.27112i
$396$	9.35462	+	1.36785i	0.470087	+	0.0687370i
$397$	−8.19230	−	3.94521i	−0.411160	−	0.198004i	0.216858	−	0.976203i	$-0.430419\pi$
$397$	−8.19230	−	3.94521i	−0.411160	−	0.198004i	−0.628018	+	0.778199i	$0.716133\pi$
$398$	−19.6620	+	22.8476i	−0.985566	+	1.14525i
$399$	5.79352	+	1.65527i	0.290039	+	0.0828671i
$400$	−54.2531	+	8.17734i	−2.71266	+	0.408867i
$401$	−19.5913	+	7.68902i	−0.978343	+	0.383971i	−0.800002	−	0.599998i	$-0.795168\pi$
$401$	−19.5913	+	7.68902i	−0.978343	+	0.383971i	−0.178341	+	0.983969i	$0.557073\pi$
$402$	8.39394	−	22.7761i	0.418652	−	1.13597i
$403$	−0.616689	−	0.325929i	−0.0307194	−	0.0162357i
$404$	−1.59122	−	14.1225i	−0.0791661	−	0.702618i
$405$	−10.9050	−	34.2776i	−0.541873	−	1.70327i
$406$	4.87419	+	1.61138i	0.241902	+	0.0799717i
$407$	22.3650	−	12.9124i	1.10859	−	0.640046i
$408$	−10.0888	−	5.06520i	−0.499470	−	0.250765i
$409$	−23.5962	+	0.882909i	−1.16676	+	0.0436570i	−0.613738	−	0.789510i	$-0.710335\pi$
$409$	−23.5962	+	0.882909i	−1.16676	+	0.0436570i	−0.553021	+	0.833167i	$0.686525\pi$
$410$	23.3869	+	7.21390i	1.15500	+	0.356269i
$411$	3.05207	−	3.43045i	0.150547	−	0.169211i
$412$	−4.81242	−	1.88874i	−0.237091	−	0.0930513i
$413$	−1.16787	−	0.266558i	−0.0574670	−	0.0131165i
$414$	26.0656	−	24.3999i	1.28105	−	1.19919i
$415$	−12.2017	+	25.3370i	−0.598956	+	1.24375i
$416$	0.0790951	−	2.11386i	0.00387796	−	0.103641i
$417$	−3.66516	+	0.490746i	−0.179484	+	0.0240319i
$418$	−32.9869	+	8.83881i	−1.61344	+	0.432320i
$419$	1.54522	−	20.6195i	0.0754889	−	1.00733i	−0.822916	−	0.568163i	$-0.807654\pi$
$419$	1.54522	−	20.6195i	0.0754889	−	1.00733i	0.898405	−	0.439167i	$-0.144726\pi$
$420$	−3.61488	+	1.35035i	−0.176388	+	0.0658906i
$421$	10.6450	−	4.64437i	0.518806	−	0.226353i	−0.124139	−	0.992265i	$-0.539617\pi$
$421$	10.6450	−	4.64437i	0.518806	−	0.226353i	0.642946	+	0.765912i	$0.277712\pi$
$422$	0.763764	+	1.58597i	0.0371794	+	0.0772039i
$423$	28.8995	−	4.48623i	1.40514	−	0.218128i
$424$	4.54422	+	1.59009i	0.220687	+	0.0772216i
$425$	−41.8037	−	1.56418i	−2.02778	−	0.0758741i
$426$	37.9732	+	20.8780i	1.83981	+	1.01154i
$427$	0.752049	−	3.97467i	0.0363942	−	0.192348i
$428$	1.76457	+	1.63728i	0.0852935	+	0.0791408i
$429$	−0.206471	−	2.15082i	−0.00996852	−	0.103843i
$430$	10.5012	+	1.58281i	0.506414	+	0.0763296i
$431$	25.2984	−	5.77421i	1.21858	−	0.278134i	0.435579	−	0.900150i	$-0.356544\pi$
$431$	25.2984	−	5.77421i	1.21858	−	0.278134i	0.783004	+	0.622017i	$0.213686\pi$
$432$	−20.7150	−	15.6787i	−0.996653	−	0.754344i
$433$	16.3402	−	1.84110i	0.785261	−	0.0884777i	0.289777	−	0.957094i	$-0.406419\pi$
$433$	16.3402	−	1.84110i	0.785261	−	0.0884777i	0.495485	+	0.868617i	$0.334990\pi$
$434$	0.827130	+	1.43263i	0.0397035	+	0.0687685i
$435$	23.2668	+	29.1267i	1.11556	+	1.39652i
$436$	−0.178844	+	0.309767i	−0.00856508	+	0.0148352i
$437$	−17.3673	+	39.8063i	−0.830791	+	1.90419i
$438$	1.39484	−	0.774917i	0.0666480	−	0.0370270i
$439$	11.1166	+	11.9809i	0.530568	+	0.571817i	0.940282	−	0.340398i	$-0.110562\pi$
$439$	11.1166	+	11.9809i	0.530568	+	0.571817i	−0.409713	+	0.912214i	$0.634371\pi$
$440$	−13.2226	+	16.5806i	−0.630361	+	0.790448i
$441$	−16.9684	+	10.7665i	−0.808018	+	0.512692i
$442$	0.592092	−	2.59412i	0.0281629	−	0.123390i
$443$	−7.28700	−	6.27097i	−0.346216	−	0.297943i	0.461940	−	0.886911i	$-0.347153\pi$
$443$	−7.28700	−	6.27097i	−0.346216	−	0.297943i	−0.808156	+	0.588968i	$0.799534\pi$
$444$	14.6316	−	0.305894i	0.694384	−	0.0145171i
$445$	1.72676	+	3.26718i	0.0818561	+	0.154879i
$446$	−20.6093	+	17.7358i	−0.975880	+	0.839813i
$447$	−3.57515	−	1.16771i	−0.169099	−	0.0552309i
$448$	0.266279	−	0.390559i	0.0125805	−	0.0184522i
$449$	−0.173703	+	1.54165i	−0.00819753	+	0.0727551i	−0.997145	−	0.0755119i	$-0.975941\pi$
$449$	−0.173703	+	1.54165i	−0.00819753	+	0.0727551i	0.988947	+	0.148267i	$0.0473695\pi$
$450$	−55.7896	−	12.4752i	−2.62995	−	0.588087i
$451$	9.86048	−	4.74856i	0.464312	−	0.223601i
$452$	−5.15161	+	19.2261i	−0.242312	+	0.904319i
$453$	−1.56242	−	0.643146i	−0.0734089	−	0.0302176i
$454$	−19.3943	+	10.2502i	−0.910220	+	0.481065i
$455$	0.496811	+	0.728688i	0.0232909	+	0.0341614i
$456$	18.2235	+	4.47690i	0.853393	+	0.209650i
$457$	4.23695	+	13.7359i	0.198196	+	0.642536i	0.999046	+	0.0436710i	$0.0139053\pi$
$457$	4.23695	+	13.7359i	0.198196	+	0.642536i	−0.800850	+	0.598865i	$0.795618\pi$
$458$	−10.4129	+	8.30400i	−0.486563	+	0.388021i
$459$	−13.2965	−	14.6823i	−0.620629	−	0.685312i
$460$	−6.18925	−	27.1169i	−0.288575	−	1.26433i
$461$	−16.1712	+	30.5973i	−0.753166	+	1.42506i	0.146830	+	0.989162i	$0.453093\pi$
$461$	−16.1712	+	30.5973i	−0.753166	+	1.42506i	−0.899996	+	0.435898i	$0.856431\pi$
$462$	−2.29925	+	4.57962i	−0.106971	+	0.213063i
$463$	−13.6253	−	7.86655i	−0.633220	−	0.365589i	0.148778	−	0.988871i	$-0.452466\pi$
$463$	−13.6253	−	7.86655i	−0.633220	−	0.365589i	−0.781998	+	0.623281i	$0.785799\pi$
$464$	25.8619	+	7.48950i	1.20061	+	0.347691i
$465$	−0.647129	+	11.9953i	−0.0300099	+	0.556267i
$466$	35.2812	−	26.0387i	1.63437	−	1.20622i
$467$	−0.946636	+	0.594811i	−0.0438051	+	0.0275246i	−0.553757	−	0.832679i	$-0.686806\pi$
$467$	−0.946636	+	0.594811i	−0.0438051	+	0.0275246i	0.509952	+	0.860203i	$0.329663\pi$
$468$	0.484700	−	1.12444i	0.0224053	−	0.0519772i
$469$	3.46392	+	2.76238i	0.159949	+	0.127555i
$470$	24.7180	−	62.9805i	1.14016	−	2.90508i
$471$	−6.37597	+	1.59619i	−0.293789	+	0.0735485i
$472$	−3.66570	−	0.693588i	−0.168728	−	0.0319250i
$473$	3.92377	−	2.67518i	0.180415	−	0.123005i
$474$	3.28097	−	35.8377i	0.150700	−	1.64608i
$475$	68.3256	−	12.9279i	3.13500	−	0.593173i
$476$	−1.50261	+	1.50261i	−0.0688720	+	0.0688720i
$477$	6.42728	+	5.48201i	0.294285	+	0.251004i
$478$	−36.4308	−	4.10476i	−1.66630	−	0.187747i
$479$	15.6382	+	35.8432i	0.714528	+	1.63772i	0.769039	+	0.639202i	$0.220735\pi$
$479$	15.6382	+	35.8432i	0.714528	+	1.63772i	−0.0545108	+	0.998513i	$0.517360\pi$
$480$	−33.6265	+	14.0154i	−1.53483	+	0.639714i
$481$	−0.865683	−	3.23077i	−0.0394717	−	0.147310i
$482$	−26.8615	−	31.2137i	−1.22351	−	1.42174i
$483$	2.73030	+	5.91729i	0.124233	+	0.269246i
$484$	0.103814	+	1.38530i	0.00471883	+	0.0629684i
$485$	−12.1404	−	34.6952i	−0.551265	−	1.57543i
$486$	−14.2252	−	23.0302i	−0.645268	−	1.04467i
$487$	3.07673	+	3.85810i	0.139420	+	0.174827i	0.846639	−	0.532167i	$-0.178622\pi$
$487$	3.07673	+	3.85810i	0.139420	+	0.174827i	−0.707219	+	0.706994i	$0.750051\pi$
$488$	1.87769	−	12.4576i	0.0849989	−	0.563931i
$489$	0.243782	+	0.0898435i	0.0110242	+	0.00406286i
$490$	1.73833	+	46.4578i	0.0785296	+	2.09875i
$491$	−9.12109	−	3.97949i	−0.411629	−	0.179592i	0.183865	−	0.982951i	$-0.441139\pi$
$491$	−9.12109	−	3.97949i	−0.411629	−	0.179592i	−0.595494	+	0.803360i	$0.703044\pi$
$492$	6.19305	+	0.334107i	0.279204	+	0.0150627i
$493$	18.3132	+	9.27679i	0.824786	+	0.417806i
$494$			4.42305i			0.199002i
$495$	−32.1440	+	18.7477i	−1.44477	+	0.842647i
$496$	4.61598	+	7.34630i	0.207264	+	0.329859i
$497$	−5.79809	+	5.37984i	−0.260080	+	0.241319i
$498$	−4.27692	+	20.7263i	−0.191654	+	0.928768i
$499$	−6.19589	−	41.1070i	−0.277366	−	1.84020i	−0.500898	−	0.865507i	$-0.666997\pi$
$499$	−6.19589	−	41.1070i	−0.277366	−	1.84020i	0.223532	−	0.974697i	$-0.428241\pi$
$500$	−16.4896	+	17.7715i	−0.737436	+	0.794766i
$501$	18.0066	+	17.2691i	0.804475	+	0.771526i
$502$	−35.7677	+	2.68042i	−1.59639	+	0.119633i
$503$	23.6134	+	14.8373i	1.05287	+	0.661563i	0.943139	−	0.332398i	$-0.107858\pi$
$503$	23.6134	+	14.8373i	1.05287	+	0.661563i	0.109732	+	0.993961i	$0.465001\pi$
$504$	2.31951	−	1.59643i	0.103319	−	0.0711108i
$505$	39.5544	+	39.5544i	1.76015	+	1.76015i
$506$	−30.5180	−	20.8068i	−1.35669	−	0.924976i
$507$	21.9308	+	3.67649i	0.973980	+	0.163279i
$508$	3.67374	+	2.71134i	0.162996	+	0.120296i
$509$	−24.2619	−	1.81818i	−1.07539	−	0.0805893i	−0.474759	−	0.880116i	$-0.657465\pi$
$509$	−24.2619	−	1.81818i	−1.07539	−	0.0805893i	−0.600630	+	0.799527i	$0.705084\pi$
$510$	−44.8382	+	9.45866i	−1.98547	+	0.418836i
$511$	0.0541454	+	0.286165i	0.00239525	+	0.0126592i
$512$	−4.90282	+	7.80279i	−0.216676	+	0.344838i
$513$	26.9792	+	18.8759i	1.19116	+	0.833391i
$514$	3.38386	−	1.18406i	0.149255	−	0.0522267i
$515$	19.4445	−	5.99783i	0.856827	−	0.264296i
$516$	2.67888	−	0.257163i	0.117931	−	0.0113210i
$517$	−11.0533	−	28.1635i	−0.486125	−	1.23863i
$518$	−2.33814	+	7.58007i	−0.102732	+	0.333049i
$519$	−7.05672	−	12.7020i	−0.309756	−	0.557555i
$520$	1.63104	+	2.20998i	0.0715259	+	0.0969142i
$521$	−2.60813			−0.114264			−0.0571322	−	0.998367i	$-0.518196\pi$
$521$	−2.60813			−0.114264			−0.0571322	+	0.998367i	$0.518196\pi$
$522$	22.3082	+	17.0108i	0.976403	+	0.744543i
$523$	21.7770			0.952240			0.476120	−	0.879380i	$-0.342043\pi$
$523$	21.7770			0.952240			0.476120	+	0.879380i	$0.342043\pi$
$524$	10.4464	+	14.1543i	0.456351	+	0.618334i
$525$	5.36555	−	8.94916i	0.234172	−	0.390573i
$526$	4.78444	−	15.5108i	0.208611	−	0.676301i
$527$	2.41680	+	6.15791i	0.105277	+	0.268243i
$528$	−11.1524	+	24.4530i	−0.485347	+	1.06418i
$529$	−22.9074	+	7.06598i	−0.995972	+	0.307217i
$530$	18.4462	−	6.45462i	0.801254	−	0.280371i
$531$	−5.55812	−	3.45833i	−0.241202	−	0.150079i
$532$	1.87933	−	2.99093i	0.0814791	−	0.129673i
$533$	−0.263523	−	1.39275i	−0.0114144	−	0.0603268i
$534$	1.85765	+	2.06952i	0.0803885	+	0.0895568i
$535$	−9.44816	−	0.708042i	−0.408480	−	0.0306113i
$536$	11.1022	+	8.19377i	0.479541	+	0.353917i
$537$	19.5348	−	23.6837i	0.842990	−	1.02203i
$538$	−25.1863	−	17.1717i	−1.08586	−	0.740325i
$539$	14.7003	+	14.7003i	0.633187	+	0.633187i
$540$	−21.0809	+	0.533674i	−0.907176	+	0.0229657i
$541$	−13.9221	−	8.74785i	−0.598559	−	0.376099i	0.198411	−	0.980119i	$-0.436422\pi$
$541$	−13.9221	−	8.74785i	−0.598559	−	0.376099i	−0.796969	+	0.604020i	$0.793565\pi$
$542$	13.4738	−	1.00972i	0.578750	−	0.0433713i
$543$	−8.03418	+	32.7036i	−0.344780	+	1.40345i
$544$	−13.6454	+	14.7062i	−0.585040	+	0.630523i
$545$	−0.209833	−	1.39215i	−0.00898827	−	0.0596333i
$546$	0.495851	+	0.441158i	0.0212204	+	0.0188798i
$547$	−14.0672	+	13.0524i	−0.601469	+	0.558082i	−0.921034	−	0.389483i	$-0.872654\pi$
$547$	−14.0672	+	13.0524i	−0.601469	+	0.558082i	0.319565	+	0.947564i	$0.396463\pi$
$548$	−1.43214	−	2.27925i	−0.0611782	−	0.0973645i
$549$	10.9685	−	19.1928i	0.468122	−	0.819127i
$550$			59.1402i			2.52175i
$551$	−33.1098	−	8.26007i	−1.41052	−	0.351891i
$552$	9.18637	+	18.0980i	0.390998	+	0.770300i
$553$	6.02051	+	2.62672i	0.256018	+	0.111700i
$554$	−0.510108	−	13.6329i	−0.0216724	−	0.579207i
$555$	−44.2754	+	36.8485i	−1.87939	+	1.56413i
$556$	−0.323104	+	2.14366i	−0.0137027	+	0.0909114i
$557$	8.87207	+	11.1252i	0.375922	+	0.471391i	0.933419	−	0.358788i	$-0.116810\pi$
$557$	8.87207	+	11.1252i	0.375922	+	0.471391i	−0.557498	+	0.830179i	$0.688238\pi$
$558$	1.71978	+	8.87498i	0.0728041	+	0.375708i
$559$	−0.203143	−	0.580550i	−0.00859204	−	0.0245547i
$560$	−0.819787	−	10.9393i	−0.0346423	−	0.462270i
$561$	−11.8212	+	16.7385i	−0.499092	+	0.706698i
$562$	−29.8705	−	34.7101i	−1.26001	−	1.46416i
$563$	4.18320	+	15.6119i	0.176301	+	0.657963i	0.996326	+	0.0856366i	$0.0272924\pi$
$563$	4.18320	+	15.6119i	0.176301	+	0.657963i	−0.820026	+	0.572327i	$0.806041\pi$
$564$	2.20044	−	17.0034i	0.0926552	−	0.715973i
$565$	−31.3292	−	71.8074i	−1.31803	−	3.02096i
$566$	−7.49884	−	0.844916i	−0.315200	−	0.0355145i
$567$	4.80703	−	1.14184i	0.201876	−	0.0479527i
$568$	−17.4184	+	17.4184i	−0.730862	+	0.730862i
$569$	41.4095	−	7.83511i	1.73598	−	0.328465i	0.780863	−	0.624702i	$-0.214779\pi$
$569$	41.4095	−	7.83511i	1.73598	−	0.328465i	0.955114	+	0.296237i	$0.0957319\pi$
$570$	69.1660	−	31.9139i	2.89705	−	1.33673i
$571$	−6.15035	+	4.19324i	−0.257384	+	0.175482i	−0.685137	−	0.728414i	$-0.740258\pi$
$571$	−6.15035	+	4.19324i	−0.257384	+	0.175482i	0.427753	+	0.903896i	$0.359305\pi$
$572$	−1.24463	−	0.235497i	−0.0520406	−	0.00984661i
$573$	−8.20794	+	28.7282i	−0.342892	+	1.20014i
$574$	−1.22817	+	3.12932i	−0.0512627	+	0.130615i
$575$	58.8014	+	46.8926i	2.45219	+	1.95556i
$576$	2.07161	−	1.54307i	0.0863172	−	0.0642945i
$577$	26.0769	−	16.3852i	1.08560	−	0.682125i	0.134467	−	0.990918i	$-0.457068\pi$
$577$	26.0769	−	16.3852i	1.08560	−	0.682125i	0.951129	+	0.308793i	$0.0999249\pi$
$578$	3.44801	−	2.54474i	0.143418	−	0.105847i
$579$	−3.22832	+	1.63867i	−0.134164	+	0.0681006i
$580$	20.2027	−	8.33545i	0.838870	−	0.346111i
$581$	−3.34524	−	1.93137i	−0.138784	−	0.0801269i
$582$	−15.2034	−	23.1093i	−0.630199	−	0.957909i
$583$	4.08353	−	7.72642i	0.169123	−	0.319996i
$584$	0.201837	+	0.884304i	0.00835205	+	0.0365927i
$585$	1.26789	+	4.64976i	0.0524207	+	0.192244i
$586$	−28.7842	+	22.9546i	−1.18906	+	0.948246i
$587$	5.07641	+	16.4573i	0.209526	+	0.679266i	0.997942	+	0.0641239i	$0.0204253\pi$
$587$	5.07641	+	16.4573i	0.209526	+	0.679266i	−0.788416	+	0.615142i	$0.789099\pi$
$588$	3.28639	+	11.3135i	0.135528	+	0.466562i
$589$	−6.19442	−	9.08555i	−0.255237	−	0.374363i
$590$	−13.3892	+	7.07637i	−0.551223	+	0.291330i
$591$	−20.2765	+	15.6298i	−0.834063	+	0.642923i
$592$	−10.7678	+	40.1861i	−0.442555	+	1.65164i
$593$	−6.27585	+	3.02229i	−0.257718	+	0.124111i	−0.558282	−	0.829651i	$-0.688539\pi$
$593$	−6.27585	+	3.02229i	−0.257718	+	0.124111i	0.300564	+	0.953762i	$0.402825\pi$
$594$	−20.0394	+	19.5606i	−0.822225	+	0.802580i
$595$	0.936487	−	8.31155i	0.0383922	−	0.340740i
$596$	−1.24206	+	1.82177i	−0.0508767	+	0.0746225i
$597$	−6.20587	−	29.4185i	−0.253989	−	1.20402i
$598$	−3.62600	+	3.12042i	−0.148278	+	0.127604i
$599$	−21.7703	−	41.1914i	−0.889510	−	1.68303i	−0.715880	−	0.698223i	$-0.753974\pi$
$599$	−21.7703	−	41.1914i	−0.889510	−	1.68303i	−0.173629	−	0.984811i	$-0.555549\pi$
$600$	15.6566	−	28.4766i	0.639180	−	1.16255i
$601$	32.4819	+	27.9529i	1.32496	+	1.14022i	0.979423	+	0.201820i	$0.0646855\pi$
$601$	32.4819	+	27.9529i	1.32496	+	1.14022i	0.345541	+	0.938404i	$0.387695\pi$
$602$	−0.324593	+	1.42214i	−0.0132294	+	0.0579619i
$603$	12.9715	+	20.4435i	0.528242	+	0.832526i
$604$	−0.617588	+	0.774431i	−0.0251293	+	0.0315111i
$605$	−3.71913	−	4.00826i	−0.151204	−	0.162959i
$606$	36.1040	+	21.6465i	1.46663	+	0.879329i
$607$	−14.3541	+	32.8999i	−0.582613	+	1.33536i	0.336616	+	0.941642i	$0.390717\pi$
$607$	−14.3541	+	32.8999i	−0.582613	+	1.33536i	−0.919230	+	0.393722i	$0.871187\pi$
$608$	16.6740	−	28.8801i	0.676218	−	1.17124i
$609$	−4.22840	+	2.88795i	−0.171343	+	0.117025i
$610$	−25.5701	−	44.2887i	−1.03530	−	1.79320i
$611$	−3.89385	+	0.438732i	−0.157528	+	0.0177492i
$612$	−10.4403	+	5.08457i	−0.422023	+	0.205532i
$613$	−36.7355	+	8.38463i	−1.48373	+	0.338652i	−0.886241	−	0.463224i	$-0.846693\pi$
$613$	−36.7355	+	8.38463i	−1.48373	+	0.338652i	−0.597491	+	0.801876i	$0.703835\pi$
$614$	3.45671	+	0.521015i	0.139501	+	0.0210265i
$615$	−19.8779	+	14.1701i	−0.801556	+	0.571394i
$616$	−2.13536	−	1.98133i	−0.0860362	−	0.0798299i
$617$	6.44348	−	34.0546i	0.259405	−	1.37099i	−0.574241	−	0.818686i	$-0.694703\pi$
$617$	6.44348	−	34.0546i	0.259405	−	1.37099i	0.833645	−	0.552300i	$-0.186250\pi$
$618$	13.0986	−	7.93208i	0.526904	−	0.319075i
$619$	−14.3066	−	0.535315i	−0.575030	−	0.0215161i	−0.251705	−	0.967804i	$-0.580991\pi$
$619$	−14.3066	−	0.535315i	−0.575030	−	0.0215161i	−0.323325	+	0.946288i	$0.604801\pi$
$620$	6.64724	+	2.32597i	0.266959	+	0.0934132i
$621$	3.55922	+	35.4343i	0.142827	+	1.42193i
$622$	4.26991	+	8.86655i	0.171208	+	0.355516i
$623$	−0.465240	+	0.202982i	−0.0186394	+	0.00813231i
$624$	2.68529	+	2.21489i	0.107498	+	0.0886667i
$625$	3.03059	−	40.4404i	0.121223	−	1.61761i
$626$	51.0786	−	13.6865i	2.04151	−	0.547021i
$627$	12.9660	−	31.4989i	0.517813	−	1.25794i
$628$	−0.144078	+	3.85056i	−0.00574933	+	0.153654i
$629$	−13.7633	+	28.5797i	−0.548777	+	1.13955i
$630$	3.32092	−	10.9371i	0.132309	−	0.435743i
$631$	−14.4465	−	3.29732i	−0.575106	−	0.131264i	−0.0749315	−	0.997189i	$-0.523874\pi$
$631$	−14.4465	−	3.29732i	−0.575106	−	0.131264i	−0.500175	+	0.865924i	$0.666731\pi$
$632$	19.0430	+	7.47385i	0.757492	+	0.297294i
$633$	−1.71956	−	0.354836i	−0.0683465	−	0.0141035i
$634$	−57.5322	−	17.7463i	−2.28490	−	0.704797i
$635$	−17.9592	+	0.671984i	−0.712687	+	0.0266669i
$636$	4.13734	−	2.72191i	0.164056	−	0.107931i
$637$	2.33183	−	1.34628i	0.0923903	−	0.0533416i
$638$	12.1376	−	26.3621i	0.480532	−	1.04368i
$639$	−39.5403	+	17.4591i	−1.56419	+	0.690670i
$640$	−5.37901	−	47.7400i	−0.212624	−	1.88709i
$641$	−23.3152	−	12.3225i	−0.920896	−	0.486708i	−0.0615509	−	0.998104i	$-0.519605\pi$
$641$	−23.3152	−	12.3225i	−0.920896	−	0.486708i	−0.859345	+	0.511396i	$0.829128\pi$
$642$	−7.02669	+	1.20982i	−0.277322	+	0.0477477i
$643$	−28.7532	+	11.2848i	−1.13391	+	0.445029i	−0.856718	−	0.515785i	$-0.827500\pi$
$643$	−28.7532	+	11.2848i	−1.13391	+	0.445029i	−0.277196	+	0.960813i	$0.589405\pi$
$644$	3.77780	−	0.569412i	0.148866	−	0.0224380i
$645$	−7.61268	+	7.36557i	−0.299749	+	0.290019i
$646$	27.3619	−	31.7951i	1.07654	−	1.25096i
$647$	−21.5212	−	10.3641i	−0.846087	−	0.407454i	−0.0399631	−	0.999201i	$-0.512724\pi$
$647$	−21.5212	−	10.3641i	−0.846087	−	0.407454i	−0.806124	+	0.591747i	$0.798438\pi$
$648$	14.8276	−	4.11344i	0.582482	−	0.161591i
$649$	−2.23668	+	6.39208i	−0.0877976	+	0.250911i
$650$	7.39861	+	1.98245i	0.290198	+	0.0777582i
$651$	−1.63638	−	0.211767i	−0.0641349	−	0.00829979i
$652$	0.0904469	−	0.122551i	0.00354217	−	0.00479947i
$653$	−2.23017	+	3.02177i	−0.0872732	+	0.118251i	−0.846059	−	0.533089i	$-0.821031\pi$
$653$	−2.23017	+	3.02177i	−0.0872732	+	0.118251i	0.758786	+	0.651340i	$0.225793\pi$
$654$	−0.407604	−	0.977944i	−0.0159386	−	0.0382406i
$655$	−66.8827	−	17.9212i	−2.61332	−	0.700238i
$656$	−5.82321	+	16.6418i	−0.227358	+	0.649753i
$657$	−0.230272	+	1.57481i	−0.00898376	+	0.0614393i
$658$	8.37290	+	4.03217i	0.326409	+	0.157191i
$659$	24.3595	−	28.3063i	0.948912	−	1.10266i	−0.0456967	−	0.998955i	$-0.514551\pi$
$659$	24.3595	−	28.3063i	0.948912	−	1.10266i	0.994609	−	0.103700i	$-0.0330683\pi$
$660$	5.29786	+	21.1623i	0.206219	+	0.823741i
$661$	29.3605	−	4.42538i	1.14199	−	0.172127i	0.449312	−	0.893375i	$-0.351669\pi$
$661$	29.3605	−	4.42538i	1.14199	−	0.172127i	0.692678	+	0.721247i	$0.256431\pi$
$662$	2.26427	−	0.888659i	0.0880032	−	0.0345387i
$663$	1.69777	+	2.03996i	0.0659359	+	0.0792256i
$664$	−10.6360	−	5.62130i	−0.412758	−	0.218149i
$665$	1.55670	+	13.8161i	0.0603662	+	0.535765i
$666$	−25.5875	+	34.9915i	−0.991494	+	1.35589i
$667$	−16.5871	−	32.9707i	−0.642256	−	1.27663i
$668$	12.6668	−	7.31320i	0.490094	−	0.282956i
$669$	−1.58032	−	27.0744i	−0.0610987	−	1.04676i
$670$	55.9724	−	2.09434i	2.16240	−	0.0809114i
$671$	−21.8527	−	6.74068i	−0.843615	−	0.260221i
$672$	−1.57457	−	4.74978i	−0.0607403	−	0.183227i
$673$	−33.4731	−	13.1372i	−1.29029	−	0.506403i	−0.381777	−	0.924254i	$-0.624688\pi$
$673$	−33.4731	−	13.1372i	−1.29029	−	0.506403i	−0.908515	+	0.417852i	$0.862783\pi$
$674$	−23.3197	−	5.32257i	−0.898242	−	0.205018i
$675$	43.6669	−	36.6689i	1.68074	−	1.41139i
$676$	5.65624	−	11.7453i	0.217548	−	0.451743i
$677$	−0.118113	+	3.15663i	−0.00453944	+	0.121319i	0.995188	+	0.0979818i	$0.0312387\pi$
$677$	−0.118113	+	3.15663i	−0.00453944	+	0.121319i	−0.999728	+	0.0233373i	$0.992571\pi$
$678$	−35.9940	−	46.6949i	−1.38234	−	1.79331i
$679$	4.87691	−	1.30676i	0.187159	−	0.0501490i
$680$	1.94666	−	25.9764i	0.0746512	−	0.996151i
$681$	3.61754	−	21.5791i	0.138624	−	0.826914i
$682$	8.57173	−	3.73981i	0.328229	−	0.143205i
$683$	10.4087	+	21.6139i	0.398279	+	0.827035i	0.999607	+	0.0280324i	$0.00892416\pi$
$683$	10.4087	+	21.6139i	0.398279	+	0.827035i	−0.601328	+	0.799002i	$0.705362\pi$
$684$	15.0388	−	12.1018i	0.575022	−	0.462725i
$685$	10.0006	+	3.49937i	0.382105	+	0.133704i
$686$	−13.0497	−	0.488285i	−0.498239	−	0.0186428i
$687$	−0.277671	−	13.2816i	−0.0105938	−	0.506725i
$688$	−1.42232	+	7.51715i	−0.0542255	+	0.286588i
$689$	−0.829713	−	0.769861i	−0.0316095	−	0.0293294i
$690$	74.9590	+	34.1870i	2.85364	+	1.30148i
$691$	47.5965	+	7.17402i	1.81066	+	0.272913i	0.965272	−	0.261246i	$-0.0841334\pi$
$691$	47.5965	+	7.17402i	1.81066	+	0.272913i	0.845384	+	0.534159i	$0.179372\pi$
$692$	−8.30496	+	1.89555i	−0.315707	+	0.0720581i
$693$	−2.23798	−	4.59529i	−0.0850137	−	0.174561i
$694$	11.6301	−	1.31040i	0.441472	−	0.0497420i
$695$	−4.26642	−	7.38966i	−0.161835	−	0.280306i
$696$	−12.8234	+	9.48032i	−0.486070	+	0.359351i
$697$	−6.72152	+	11.6420i	−0.254596	+	0.440973i
$698$	−11.8523	+	27.1658i	−0.448616	+	1.02824i
$699$	−0.721481	+	43.7313i	−0.0272889	+	1.65407i
$700$	−4.16072	−	4.48419i	−0.157261	−	0.169487i
$701$	16.4837	−	20.6699i	0.622580	−	0.780691i	−0.366125	−	0.930566i	$-0.619316\pi$
$701$	16.4837	−	20.6699i	0.622580	−	0.780691i	0.988705	+	0.149875i	$0.0478872\pi$
$702$	1.77534	+	3.16268i	0.0670060	+	0.119368i
$703$	11.7333	−	51.4072i	0.442532	−	1.93886i
$704$	−2.02552	−	1.74310i	−0.0763397	−	0.0656956i
$705$	34.9563	+	57.7251i	1.31653	+	2.17405i
$706$	13.1023	+	24.7907i	0.493110	+	0.933010i
$707$	−5.82389	+	5.01186i	−0.219030	+	0.188490i
$708$	−2.85591	+	2.56354i	−0.107332	+	0.0963437i
$709$	−7.30713	+	10.7176i	−0.274425	+	0.402508i	−0.938566	−	0.345100i	$-0.887845\pi$
$709$	−7.30713	+	10.7176i	−0.274425	+	0.402508i	0.664141	+	0.747607i	$0.268798\pi$
$710$	−11.1958	+	99.3651i	−0.420169	+	3.72910i
$711$	26.4206	+	24.2989i	0.990849	+	0.911281i
$712$	−1.42429	+	0.685903i	−0.0533776	+	0.0257053i
$713$	3.07818	−	11.4879i	0.115279	−	0.430227i
$714$	−0.835329	−	6.23870i	−0.0312614	−	0.233477i
$715$	4.40806	−	2.32973i	0.164852	−	0.0871269i
$716$	−10.1387	−	14.8708i	−0.378902	−	0.555748i
$717$	25.3110	−	26.3919i	0.945256	−	0.985624i
$718$	−14.4287	−	46.7767i	−0.538475	−	1.74569i
$719$	−27.3782	+	21.8334i	−1.02104	+	0.814248i	−0.982735	−	0.185018i	$-0.940766\pi$
$719$	−27.3782	+	21.8334i	−1.02104	+	0.814248i	−0.0383000	+	0.999266i	$0.512194\pi$
$720$	15.2603	−	57.9730i	0.568718	−	2.16053i
$721$	0.621948	+	2.72493i	0.0231626	+	0.101482i
$722$	−17.1651	+	32.4780i	−0.638820	+	1.20871i
$723$	41.0053	−	2.39346i	1.52501	−	0.0890137i
$724$	17.0975	+	9.87126i	0.635425	+	0.366863i
$725$	−28.6571	+	51.6819i	−1.06430	+	1.91942i
$726$	−3.44755	−	2.24640i	−0.127950	−	0.0833718i
$727$	−24.5048	+	18.0854i	−0.908833	+	0.670749i	−0.944464	−	0.328616i	$-0.893418\pi$
$727$	−24.5048	+	18.0854i	−0.908833	+	0.670749i	0.0356307	+	0.999365i	$0.488656\pi$
$728$	−0.319450	+	0.200724i	−0.0118396	+	0.00743931i
$729$	26.8678	+	2.66808i	0.995106	+	0.0988178i
$730$	2.87866	+	2.29566i	0.106544	+	0.0849661i
$731$	−2.13111	+	5.42997i	−0.0788218	+	0.200835i
$732$	−9.01136	−	9.31369i	−0.333070	−	0.344244i
$733$	−12.7738	−	2.41693i	−0.471809	−	0.0892712i	−0.0554309	−	0.998463i	$-0.517653\pi$
$733$	−12.7738	−	2.41693i	−0.471809	−	0.0892712i	−0.416379	+	0.909191i	$0.636701\pi$
$734$	−10.8046	+	7.36645i	−0.398805	+	0.271901i
$735$	−37.8776	−	26.7503i	−1.39714	−	0.986701i
$736$	35.4392	−	6.70545i	1.30631	−	0.247166i
$737$	17.7110	−	17.7110i	0.652392	−	0.652392i
$738$	−11.9215	+	13.9772i	−0.438838	+	0.514507i
$739$	4.48512	+	0.505351i	0.164988	+	0.0185896i	0.194072	−	0.980987i	$-0.437831\pi$
$739$	4.48512	+	0.505351i	0.164988	+	0.0185896i	−0.0290842	+	0.999577i	$0.509259\pi$
$740$	13.5043	+	30.9521i	0.496427	+	1.13782i
$741$	−3.50597	−	2.67797i	−0.128795	−	0.0983777i
$742$	0.694763	+	2.59289i	0.0255055	+	0.0951879i
$743$	3.18401	+	3.69989i	0.116810	+	0.135736i	0.813332	−	0.581800i	$-0.197651\pi$
$743$	3.18401	+	3.69989i	0.116810	+	0.135736i	−0.696522	+	0.717535i	$0.745270\pi$
$744$	−5.11744	−	0.468506i	−0.187614	−	0.0171763i
$745$	−0.648549	−	8.65429i	−0.0237610	−	0.317068i
$746$	19.3545	+	55.3121i	0.708620	+	2.02512i
$747$	−13.8394	−	15.9391i	−0.506357	−	0.583180i
$748$	7.49020	+	9.39241i	0.273869	+	0.343420i
$749$	0.193965	−	1.28687i	0.00708733	−	0.0470213i
$750$	−12.1845	−	70.7681i	−0.444914	−	2.58409i
$751$	0.361792	+	9.66910i	0.0132020	+	0.352830i	0.990206	+	0.139611i	$0.0445853\pi$
$751$	0.361792	+	9.66910i	0.0132020	+	0.352830i	−0.977004	+	0.213219i	$0.931605\pi$
$752$	44.6736	+	19.4909i	1.62908	+	0.710759i
$753$	19.5312	−	29.9745i	0.711757	−	1.09233i
$754$	−2.89111	−	2.40214i	−0.105288	−	0.0874807i
$755$		−	3.89879i		−	0.141891i
$756$	0.143290	−	2.89298i	0.00521140	−	0.105217i
$757$	11.6705	+	18.5734i	0.424170	+	0.675063i	0.988625	−	0.150401i	$-0.0480564\pi$
$757$	11.6705	+	18.5734i	0.424170	+	0.675063i	−0.564455	+	0.825464i	$0.690914\pi$
$758$	3.78385	−	3.51090i	0.137436	−	0.127522i
$759$	34.9701	−	11.5927i	1.26933	−	0.420789i
$760$	6.45369	+	42.8174i	0.234100	+	1.55315i
$761$	−11.0195	+	11.8762i	−0.399455	+	0.430510i	−0.900463	−	0.434932i	$-0.856772\pi$
$761$	−11.0195	+	11.8762i	−0.399455	+	0.430510i	0.501008	+	0.865443i	$0.332963\pi$
$762$	−12.9876	+	3.77268i	−0.470492	+	0.136670i
$763$	0.192841	−	0.0144514i	0.00698131	−	0.000523177i
$764$	14.8311	+	9.31897i	0.536569	+	0.337149i
$765$	19.6502	−	41.2682i	0.710453	−	1.49206i
$766$	17.4436	+	17.4436i	0.630264	+	0.630264i
$767$	0.724691	+	0.494086i	0.0261671	+	0.0178404i
$768$	−11.6077	−	31.0737i	−0.418857	−	1.12128i
$769$	13.2235	+	9.75941i	0.476853	+	0.351933i	0.805576	−	0.592493i	$-0.201856\pi$
$769$	13.2235	+	9.75941i	0.476853	+	0.351933i	−0.328723	+	0.944426i	$0.606618\pi$
$770$	−11.7915	−	0.883652i	−0.424937	−	0.0318446i
$771$	−1.11023	+	3.39914i	−0.0399838	+	0.122417i
$772$	0.394588	+	2.08545i	0.0142015	+	0.0750570i
$773$	2.74554	−	4.36951i	0.0987504	−	0.157160i	−0.793695	−	0.608316i	$-0.791845\pi$
$773$	2.74554	−	4.36951i	0.0987504	−	0.157160i	0.892445	+	0.451156i	$0.148988\pi$
$774$	−4.21127	+	6.76823i	−0.151371	+	0.243279i
$775$	−17.9742	+	6.28944i	−0.645651	+	0.225923i
$776$	15.0258	−	4.63486i	0.539396	−	0.166382i
$777$	−4.59276	−	6.44277i	−0.164764	−	0.231133i
$778$	7.88406	+	20.0883i	0.282657	+	0.720199i
$779$	6.58661	−	21.3533i	0.235990	−	0.765060i
$780$	2.82505	+	0.0466079i	0.101153	+	0.00166883i
$781$	26.5526	+	35.9775i	0.950128	+	1.28738i
$782$	45.3691			1.62239
$783$	−26.9905	+	7.38344i	−0.964560	+	0.263863i
$784$	−33.4915			−1.19613
$785$	−9.00623	−	12.2030i	−0.321446	−	0.435544i
$786$	−52.1005	−	0.859557i	−1.85836	−	0.0306594i
$787$	−3.92570	+	12.7268i	−0.139936	+	0.453661i	−0.998228	−	0.0594998i	$-0.981049\pi$
$787$	−3.92570	+	12.7268i	−0.139936	+	0.453661i	0.858292	+	0.513161i	$0.171526\pi$
$788$	5.48330	+	13.9712i	0.195335	+	0.497704i
$789$	9.39797	+	13.1836i	0.334577	+	0.469347i
$790$	79.3521	−	24.4769i	2.82322	−	0.870848i
$791$	10.1572	−	3.55417i	0.361150	−	0.126372i
$792$	−7.50021	−	14.0410i	−0.266508	−	0.498924i
$793$	−1.57581	+	2.50789i	−0.0559586	+	0.0890576i
$794$	−2.93546	−	15.5143i	−0.104176	−	0.550581i
$795$	−6.05212	+	18.5296i	−0.214647	+	0.657177i
$796$	−17.5769	−	1.31720i	−0.622995	−	0.0466870i
$797$	−14.4981	−	10.7001i	−0.513551	−	0.379018i	0.305994	−	0.952034i	$-0.401011\pi$
$797$	−14.4981	−	10.7001i	−0.513551	−	0.379018i	−0.819544	+	0.573016i	$0.805773\pi$
$798$	3.66137	+	9.80145i	0.129611	+	0.346968i
$799$	30.7051	+	20.9344i	1.08627	+	0.740604i
$800$	−40.8356	−	40.8356i	−1.44376	−	1.44376i
$801$	−2.76515	+	0.219478i	−0.0977019	+	0.00775486i
$802$	−30.9448	−	19.4439i	−1.09270	−	0.686588i
$803$	1.64188	−	0.123042i	0.0579407	−	0.00434205i
$804$	13.6306	−	3.95945i	0.480713	−	0.139639i
$805$	−10.2281	+	11.0233i	−0.360495	+	0.388521i
$806$	−0.180526	−	1.19771i	−0.00635876	−	0.0421876i
$807$	28.8606	−	9.56738i	1.01594	−	0.336788i
$808$	−17.5416	+	16.2762i	−0.617111	+	0.572595i
$809$	9.46657	+	15.0660i	0.332827	+	0.529691i	0.970651	−	0.240491i	$-0.0773084\pi$
$809$	9.46657	+	15.0660i	0.332827	+	0.529691i	−0.637825	+	0.770182i	$0.720166\pi$
$810$	36.6471	−	50.5821i	1.28765	−	1.77727i
$811$			20.1055i			0.705999i	0.935623	+	0.353000i	$0.114838\pi$
$811$			20.1055i			0.705999i	−0.935623	+	0.353000i	$0.885162\pi$
$812$	0.934356	+	2.85278i	0.0327895	+	0.100113i
$813$	−7.35748	+	11.2915i	−0.258038	+	0.396010i
$814$	41.1030	+	17.9331i	1.44066	+	0.628554i
$815$	0.0224165	+	0.599094i	0.000785216	+	0.0209853i
$816$	−5.60146	−	32.5336i	−0.196090	−	1.13890i
$817$	1.44517	−	9.58809i	0.0505602	−	0.335445i
$818$	−25.5652	−	32.0578i	−0.893866	−	1.12087i
$819$	−0.649905	+	0.125938i	−0.0227095	+	0.00440062i
$820$	4.72671	+	13.5082i	0.165064	+	0.471725i
$821$	1.06487	+	14.2097i	0.0371643	+	0.495923i	0.984465	+	0.175579i	$0.0561796\pi$
$821$	1.06487	+	14.2097i	0.0371643	+	0.495923i	−0.947301	+	0.320344i	$0.896201\pi$
$822$	7.94014	+	0.726927i	0.276944	+	0.0253545i
$823$	−14.4511	−	16.7925i	−0.503734	−	0.585349i	0.447320	−	0.894374i	$-0.352378\pi$
$823$	−14.4511	−	16.7925i	−0.503734	−	0.585349i	−0.951054	+	0.309024i	$0.899997\pi$
$824$	2.25296	+	8.40816i	0.0784856	+	0.292912i
$825$	−46.8780	−	35.8069i	−1.63208	−	1.24664i
$826$	−0.831835	−	1.90659i	−0.0289432	−	0.0663386i
$827$	−44.4380	−	5.00696i	−1.54526	−	0.174109i	−0.702221	−	0.711959i	$-0.747808\pi$
$827$	−44.4380	−	5.00696i	−1.54526	−	0.174109i	−0.843040	+	0.537850i	$0.819237\pi$
$828$	20.5308	+	3.79099i	0.713493	+	0.131746i
$829$	−11.9822	+	11.9822i	−0.416158	+	0.416158i	−0.883877	−	0.467719i	$-0.845076\pi$
$829$	−11.9822	+	11.9822i	−0.416158	+	0.416158i	0.467719	+	0.883877i	$0.345076\pi$
$830$	−47.9823	+	9.07874i	−1.66549	+	0.315128i
$831$	11.1151	+	7.84982i	0.385579	+	0.272307i
$832$	−0.285965	+	0.194968i	−0.00991406	+	0.00675929i
$833$	−25.0907	−	4.74742i	−0.869341	−	0.164488i
$834$	−4.46505	−	4.61485i	−0.154612	−	0.159799i
$835$	−21.0327	+	53.5906i	−0.727868	+	1.85458i
$836$	−15.6128	−	12.4508i	−0.539979	−	0.430619i
$837$	−8.07609	−	4.01023i	−0.279150	−	0.138614i
$838$	30.4026	−	19.1032i	1.05024	−	0.659909i
$839$	7.71941	−	5.69718i	0.266504	−	0.196689i	−0.452368	−	0.891831i	$-0.649421\pi$
$839$	7.71941	−	5.69718i	0.266504	−	0.196689i	0.718872	+	0.695143i	$0.244659\pi$
$840$	5.44379	+	3.54715i	0.187829	+	0.122388i
$841$	23.3809	−	17.1561i	0.806240	−	0.591589i
$842$	17.4658	+	10.0839i	0.601911	+	0.347514i
$843$	45.5986	−	2.66156i	1.57050	−	0.0916692i
$844$	−0.480974	+	0.910047i	−0.0165558	+	0.0313251i
$845$	11.4179	+	50.0250i	0.392787	+	1.72091i
$846$	36.0682	+	35.7517i	1.24005	+	1.22917i
$847$	0.587199	−	0.468275i	0.0201764	−	0.0160901i
$848$	4.14977	+	13.4532i	0.142504	+	0.461986i
$849$	5.20997	−	5.43246i	0.178806	−	0.186442i
$850$	−40.9211	−	60.0202i	−1.40358	−	2.05868i
$851$	50.4212	−	26.6484i	1.72842	−	0.913494i
$852$	3.36283	+	25.1155i	0.115209	+	0.860443i
$853$	1.46139	−	5.45398i	0.0500370	−	0.186741i	−0.936384	−	0.350977i	$-0.885849\pi$
$853$	1.46139	−	5.45398i	0.0500370	−	0.186741i	0.986421	+	0.164237i	$0.0525161\pi$
$854$	6.32882	−	3.04780i	0.216568	−	0.104293i
$855$	−16.5803	+	74.1476i	−0.567034	+	2.53580i
$856$	0.453804	−	4.02762i	0.0155107	−	0.137661i
$857$	30.7559	−	45.1106i	1.05060	−	1.54095i	0.226907	−	0.973916i	$-0.427139\pi$
$857$	30.7559	−	45.1106i	1.05060	−	1.54095i	0.823695	−	0.567033i	$-0.191909\pi$
$858$	2.79218	−	2.50633i	0.0953234	−	0.0855647i
$859$	35.5018	−	30.5518i	1.21131	−	1.04241i	0.213452	−	0.976954i	$-0.431529\pi$
$859$	35.5018	−	30.5518i	1.21131	−	1.04241i	0.997855	−	0.0654604i	$-0.0208516\pi$
$860$	2.90171	+	5.49030i	0.0989475	+	0.187218i
$861$	−1.73688	−	2.86819i	−0.0591927	−	0.0977477i
$862$	34.1545	+	29.3923i	1.16331	+	1.00111i
$863$	−0.932385	+	4.08505i	−0.0317388	+	0.139057i	−0.988315	−	0.152426i	$-0.951291\pi$
$863$	−0.932385	+	4.08505i	−0.0317388	+	0.139057i	0.956576	+	0.291483i	$0.0941486\pi$
$864$	0.330590	−	27.3433i	0.0112469	−	0.930237i
$865$	20.9052	−	26.2143i	0.710799	−	0.891313i
$866$	19.4218	+	20.9318i	0.659981	+	0.711290i
$867$	−0.0705099	+	4.27383i	−0.00239464	+	0.145147i
$868$	−0.386826	+	0.886615i	−0.0131297	+	0.0300937i
$869$	18.5671	−	32.1592i	0.629846	−	1.09092i
$870$	−16.7034	+	62.5424i	−0.566297	+	2.12039i
$871$	−1.62200	−	2.80939i	−0.0549594	−	0.0951925i
$872$	0.598481	−	0.0674326i	0.0202671	−	0.00228356i
$873$	27.5228	+	1.94062i	0.931504	+	0.0656799i
$874$	−73.5251	+	16.7816i	−2.48702	+	0.567647i
$875$	12.9605	+	1.95348i	0.438145	+	0.0660398i
$876$	0.848927	+	0.387176i	0.0286826	+	0.0130814i
$877$	−15.7253	−	14.5910i	−0.531006	−	0.492702i	0.368489	−	0.929632i	$-0.379875\pi$
$877$	−15.7253	−	14.5910i	−0.531006	−	0.492702i	−0.899495	+	0.436930i	$0.856066\pi$
$878$	−5.27636	+	27.8862i	−0.178068	+	0.941115i
$879$	−0.767560	−	36.7141i	−0.0258891	−	1.23834i
$880$	−61.9733	−	2.31888i	−2.08912	−	0.0781693i
$881$	−5.61368	−	1.96431i	−0.189130	−	0.0661794i	0.234052	−	0.972224i	$-0.424801\pi$
$881$	−5.61368	−	1.96431i	−0.189130	−	0.0661794i	−0.423182	+	0.906045i	$0.639087\pi$
$882$	−32.5400	−	12.6058i	−1.09568	−	0.424460i
$883$	−3.41041	−	7.08180i	−0.114770	−	0.238321i	0.835669	−	0.549233i	$-0.185080\pi$
$883$	−3.41041	−	7.08180i	−0.114770	−	0.238321i	−0.950439	+	0.310911i	$0.899366\pi$
$884$	1.42610	−	0.622201i	0.0479649	−	0.0209269i
$885$	2.49742	−	14.8975i	0.0839500	−	0.500773i
$886$	1.24757	−	16.6477i	0.0419129	−	0.559289i
$887$	−17.1389	+	4.59235i	−0.575467	+	0.154196i	−0.534803	−	0.844977i	$-0.679614\pi$
$887$	−17.1389	+	4.59235i	−0.575467	+	0.154196i	−0.0406644	+	0.999173i	$0.512947\pi$
$888$	−15.0440	−	19.5165i	−0.504842	−	0.654930i
$889$	0.0923016	−	2.46681i	0.00309570	−	0.0827343i
$890$	−2.78427	+	5.78160i	−0.0933289	+	0.193800i
$891$	−3.37187	−	27.7275i	−0.112962	−	0.928906i
$892$	−15.5008	−	3.53795i	−0.519004	−	0.118459i
$893$	−57.5040	−	22.5687i	−1.92430	−	0.755232i
$894$	−2.05506	−	6.19923i	−0.0687316	−	0.207333i
$895$	67.6944	+	20.8809i	2.26277	+	0.697973i
$896$	6.59430	−	0.246741i	0.220300	−	0.00824305i
$897$	−0.278041	−	4.76347i	−0.00928351	−	0.159047i
$898$	−2.33308	+	1.34701i	−0.0778560	+	0.0449502i
$899$	9.30290	+	0.885362i	0.310269	+	0.0295285i
$900$	−13.5027	−	30.5801i	−0.450090	−	1.01934i
$901$	1.20187	+	10.6669i	0.0400402	+	0.355367i
$902$	16.8024	+	8.88031i	0.559458	+	0.295682i
$903$	−0.930741	−	1.11834i	−0.0309731	−	0.0372159i
$904$	31.1977	−	12.2442i	1.03762	−	0.407236i
$905$	−76.8395	+	11.5817i	−2.55423	+	0.384989i
$906$	−0.712523	−	2.84617i	−0.0236720	−	0.0945577i
$907$	4.87330	−	5.66288i	0.161815	−	0.188033i	−0.671211	−	0.741267i	$-0.734225\pi$
$907$	4.87330	−	5.66288i	0.161815	−	0.188033i	0.833026	+	0.553234i	$0.186606\pi$
$908$	−11.5570	−	5.56555i	−0.383532	−	0.184699i
$909$	−39.0178	+	15.5121i	−1.29414	+	0.514505i
$910$	−0.505813	+	1.44553i	−0.0167676	+	0.0479189i
$911$	−24.1576	−	6.47302i	−0.800378	−	0.214461i	−0.164628	−	0.986356i	$-0.552642\pi$
$911$	−24.1576	−	6.47302i	−0.800378	−	0.214461i	−0.635750	+	0.771895i	$0.719309\pi$
$912$	21.1116	+	50.6519i	0.699075	+	1.67725i
$913$	−12.9674	+	17.5702i	−0.429159	+	0.581490i
$914$	−14.8225	+	20.0837i	−0.490283	+	0.664310i
$915$	50.5875	+	6.54660i	1.67237	+	0.216424i
$916$	−7.52266	−	2.01569i	−0.248556	−	0.0666003i
$917$	3.14124	−	8.97715i	0.103733	−	0.296452i
$918$	6.80292	−	33.7176i	0.224530	−	1.11285i
$919$	31.6896	+	15.2609i	1.04534	+	0.503410i	0.876082	−	0.482161i	$-0.160148\pi$
$919$	31.6896	+	15.2609i	1.04534	+	0.503410i	0.169260	+	0.985572i	$0.445862\pi$
$920$	−30.5486	+	35.4981i	−1.00716	+	1.17034i
$921$	−2.50588	+	2.42454i	−0.0825716	+	0.0798913i
$922$	−59.4251	+	8.95689i	−1.95706	+	0.294980i
$923$	5.39097	−	2.11580i	0.177446	−	0.0696425i
$924$	−2.95304	+	0.508438i	−0.0971478	+	0.0167264i
$925$	−80.7319	−	42.6681i	−2.65445	−	1.40292i
$926$	−3.05892	−	27.1486i	−0.100522	−	0.892160i
$927$	−1.64324	+	15.1853i	−0.0539710	+	0.498750i
$928$	9.82184	+	26.5836i	0.322418	+	0.872648i
$929$	−4.85046	+	2.80041i	−0.159138	+	0.0918786i	−0.577454	−	0.816423i	$-0.695954\pi$
$929$	−4.85046	+	2.80041i	−0.159138	+	0.0918786i	0.418316	+	0.908302i	$0.362621\pi$
$930$	−17.4268	+	11.4649i	−0.571448	+	0.375950i
$931$	42.4180	−	1.58717i	1.39019	−	0.0520174i
$932$	24.5018	+	7.55779i	0.802582	+	0.247564i
$933$	−9.61340	−	1.98375i	−0.314729	−	0.0649450i
$934$	−1.80720	−	0.709272i	−0.0591333	−	0.0232081i
$935$	−46.0995	−	10.5219i	−1.50762	−	0.344103i
$936$	−2.00798	+	0.467628i	−0.0656329	+	0.0152849i
$937$	−10.7173	+	22.2548i	−0.350120	+	0.727033i	−0.999439	−	0.0334837i	$-0.989340\pi$
$937$	−10.7173	+	22.2548i	−0.350120	+	0.727033i	0.649319	+	0.760516i	$0.275054\pi$
$938$	−0.287672	+	7.68819i	−0.00939282	+	0.251028i
$939$	−20.0773	+	48.7745i	−0.655197	+	1.59170i
$940$	38.2145	−	10.2396i	1.24642	−	0.333977i
$941$	0.708850	−	9.45895i	0.0231079	−	0.308353i	−0.973659	−	0.228008i	$-0.926779\pi$
$941$	0.708850	−	9.45895i	0.0231079	−	0.308353i	0.996767	−	0.0803450i	$-0.0256022\pi$
$942$	−8.80484	−	7.26244i	−0.286877	−	0.236623i
$943$	22.1521	−	9.66487i	0.721373	−	0.314732i
$944$	−4.73359	−	9.82940i	−0.154065	−	0.319920i
$945$	6.65868	+	9.25429i	0.216607	+	0.301042i
$946$	7.78376	+	2.72365i	0.253072	+	0.0885536i
$947$	−59.3770	−	2.22173i	−1.92949	−	0.0721966i	−0.954999	−	0.296609i	$-0.904144\pi$
$947$	−59.3770	−	2.22173i	−1.92949	−	0.0721966i	−0.974494	+	0.224412i	$0.927954\pi$
$948$	18.0005	−	10.9005i	0.584627	−	0.354031i
$949$	0.0396449	−	0.209528i	0.00128693	−	0.00680158i
$950$	88.5177	+	82.1324i	2.87189	+	2.66473i
$951$	48.9002	−	34.8588i	1.58570	−	1.13037i
$952$	3.53808	+	0.533280i	0.114670	+	0.0172837i
$953$	−15.1319	+	3.45376i	−0.490170	+	0.111878i	−0.460460	−	0.887680i	$-0.652316\pi$
$953$	−15.1319	+	3.45376i	−0.490170	+	0.111878i	−0.0297101	+	0.999559i	$0.509458\pi$
$954$	−1.03176	+	14.6329i	−0.0334045	+	0.473759i
$955$	−68.5095	+	7.71917i	−2.21692	+	0.249786i
$956$	−10.7188	−	18.5655i	−0.346671	−	0.600452i
$957$	13.5473	+	25.5821i	0.437923	+	0.826952i
$958$	−33.9537	+	58.8096i	−1.09700	+	1.90005i
$959$	−0.581972	+	1.33390i	−0.0187929	+	0.0430737i
$960$	5.11218	+	3.06506i	0.164995	+	0.0989242i
$961$	−19.0371	−	20.5172i	−0.614102	−	0.661844i
$962$	3.62131	−	4.54097i	0.116756	−	0.146407i
$963$	3.29540	−	6.30227i	0.106193	−	0.203088i
$964$	5.35836	−	23.4765i	0.172581	−	0.756128i
$965$	−6.33215	−	5.44925i	−0.203839	−	0.175418i
$966$	−5.45212	+	9.91642i	−0.175419	+	0.319056i
$967$	20.6198	+	39.0147i	0.663090	+	1.25463i	0.954552	+	0.298044i	$0.0963344\pi$
$967$	20.6198	+	39.0147i	0.663090	+	1.25463i	−0.291462	+	0.956582i	$0.594142\pi$
$968$	1.77296	−	1.52576i	0.0569851	−	0.0490397i
$969$	8.63618	+	40.9392i	0.277434	+	1.31516i
$970$	35.9566	−	52.7387i	1.15450	−	1.69334i
$971$	5.19866	−	46.1394i	0.166833	−	1.48068i	−0.579424	−	0.815027i	$-0.696722\pi$
$971$	5.19866	−	46.1394i	0.166833	−	1.48068i	0.746257	−	0.665658i	$-0.231849\pi$
$972$	5.89592	−	14.6897i	0.189112	−	0.471172i
$973$	1.05598	−	0.508531i	0.0338530	−	0.0163028i
$974$	−2.21784	+	8.27708i	−0.0710641	+	0.265215i
$975$	−6.05096	+	4.66429i	−0.193786	+	0.149377i
$976$	32.5720	−	17.2148i	1.04260	−	0.551032i
$977$	−1.40916	−	2.06686i	−0.0450830	−	0.0661247i	0.803035	−	0.595931i	$-0.203217\pi$
$977$	−1.40916	−	2.06686i	−0.0450830	−	0.0661247i	−0.848119	+	0.529807i	$0.822265\pi$
$978$	0.125852	+	0.433250i	0.00402430	+	0.0138538i
$979$	0.845822	+	2.74209i	0.0270326	+	0.0876375i
$980$	−21.2542	+	16.9496i	−0.678940	+	0.541437i
$981$	1.02196	+	0.269013i	0.0326288	+	0.00858892i
$982$	−3.84529	−	16.8473i	−0.122708	−	0.537619i
$983$	28.3854	−	53.7078i	0.905353	−	1.71301i	0.233455	−	0.972368i	$-0.424997\pi$
$983$	28.3854	−	53.7078i	0.905353	−	1.71301i	0.671898	−	0.740643i	$-0.265479\pi$
$984$	−5.73955	−	8.72418i	−0.182970	−	0.278117i
$985$	−51.1605	−	29.5375i	−1.63011	−	0.941143i
$986$	5.92261	+	35.1528i	0.188614	+	1.11949i
$987$	−8.26558	+	4.19554i	−0.263096	+	0.133545i
$988$	−2.08099	+	1.53584i	−0.0662051	+	0.0488616i
$989$	8.87984	−	5.57957i	0.282362	−	0.177420i
$990$	−59.3397	−	25.5790i	−1.88594	−	0.812953i
$991$	0.911519	+	0.726912i	0.0289554	+	0.0230911i	0.637861	−	0.770152i	$-0.279820\pi$
$991$	0.911519	+	0.726912i	0.0289554	+	0.0230911i	−0.608905	+	0.793243i	$0.708391\pi$
$992$	−3.33638	+	8.50097i	−0.105930	+	0.269906i
$993$	−0.666516	+	2.33284i	−0.0211512	+	0.0740304i
$994$	−13.4954	−	2.55347i	−0.428048	−	0.0809910i
$995$	57.3222	−	39.0816i	1.81724	−	1.23897i
$996$	−11.2366	+	5.18467i	−0.356044	+	0.164283i
$997$	−22.2279	+	4.20575i	−0.703965	+	0.133197i	−0.525556	−	0.850759i	$-0.676143\pi$
$997$	−22.2279	+	4.20575i	−0.703965	+	0.133197i	−0.178409	+	0.983956i	$0.557095\pi$
$998$	51.0449	−	51.0449i	1.61580	−	1.61580i
$999$	−12.2442	−	41.4680i	−0.387388	−	1.31199i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	261.2.x.a.14.22	✓	672
3.2	odd	2		783.2.be.a.449.7		672
9.2	odd	6	inner	261.2.x.a.101.7	yes	672
9.7	even	3		783.2.be.a.710.22		672
29.27	odd	28	inner	261.2.x.a.230.7	yes	672
87.56	even	28		783.2.be.a.665.22		672
261.56	even	84	inner	261.2.x.a.56.22	yes	672
261.259	odd	84		783.2.be.a.143.7		672

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
261.2.x.a.14.22	✓	672	1.1	even	1	trivial
261.2.x.a.56.22	yes	672	261.56	even	84	inner
261.2.x.a.101.7	yes	672	9.2	odd	6	inner
261.2.x.a.230.7	yes	672	29.27	odd	28	inner
783.2.be.a.143.7		672	261.259	odd	84
783.2.be.a.449.7		672	3.2	odd	2
783.2.be.a.665.22		672	87.56	even	28
783.2.be.a.710.22		672	9.7	even	3

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 261 = 3^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	261.x (of order \(84\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03117 + 1.39718i) q^{2} +(-1.73182 - 0.0285716i) q^{3} +(-0.299298 + 0.970301i) q^{4} +(-1.46016 - 3.72043i) q^{5} +(-1.74587 - 2.44912i) q^{6} +(0.524586 - 0.161813i) q^{7} +(1.61379 - 0.564688i) q^{8} +(2.99837 + 0.0989614i) q^{9} +(3.69245 - 5.87649i) q^{10} +(-0.576982 - 3.04942i) q^{11} +(0.546052 - 1.67183i) q^{12} +(-0.400833 - 0.0300383i) q^{13} +(0.767018 + 0.566085i) q^{14} +(2.42243 + 6.48482i) q^{15} +(4.13100 + 2.81647i) q^{16} +(2.69557 + 2.69557i) q^{17} +(2.95355 + 4.29130i) q^{18} +(-5.36550 - 3.37137i) q^{19} +(4.04697 - 0.303278i) q^{20} +(-0.913110 + 0.265243i) q^{21} +(3.66563 - 3.95061i) q^{22} +(-1.02148 - 6.77709i) q^{23} +(-2.81091 + 0.931827i) q^{24} +(-8.04430 + 7.46402i) q^{25} +(-0.371356 - 0.591010i) q^{26} +(-5.18979 - 0.257051i) q^{27} +0.557437i q^{28} +(5.11766 - 1.67616i) q^{29} +(-6.56253 + 10.0715i) q^{30} +(1.59052 + 0.693937i) q^{31} +(0.196775 + 5.25892i) q^{32} +(0.912100 + 5.29752i) q^{33} +(-0.986616 + 6.54577i) q^{34} +(-1.36800 - 1.71542i) q^{35} +(-0.993428 + 2.87970i) q^{36} +(2.74830 + 7.85418i) q^{37} +(-0.822313 - 10.9730i) q^{38} +(0.693311 + 0.0634732i) q^{39} +(-4.45727 - 5.17945i) q^{40} +(0.912701 + 3.40625i) q^{41} +(-1.31216 - 1.00227i) q^{42} +(0.611906 + 1.40250i) q^{43} +(3.13155 + 0.352841i) q^{44} +(-4.00993 - 11.2997i) q^{45} +(8.41550 - 8.41550i) q^{46} +(9.57858 - 1.81237i) q^{47} +(-7.07365 - 4.99563i) q^{48} +(-5.53466 + 3.77347i) q^{49} +(-18.7236 - 3.54269i) q^{50} +(-4.59121 - 4.74524i) q^{51} +(0.149115 - 0.379938i) q^{52} +(2.20154 + 1.75567i) q^{53} +(-4.99239 - 7.51613i) q^{54} +(-10.5027 + 6.59928i) q^{55} +(0.755196 - 0.557360i) q^{56} +(9.19573 + 5.99189i) q^{57} +(7.61906 + 5.42189i) q^{58} +(-1.88972 - 1.09103i) q^{59} +(-7.01726 + 0.409594i) q^{60} +(3.44312 - 6.51471i) q^{61} +(0.670535 + 2.93781i) q^{62} +(1.58892 - 0.433262i) q^{63} +(0.673195 - 0.536855i) q^{64} +(0.473526 + 1.53513i) q^{65} +(-6.46107 + 6.73699i) q^{66} +(4.54628 + 6.66818i) q^{67} +(-3.42229 + 1.80873i) q^{68} +(1.57539 + 11.7659i) q^{69} +(0.986111 - 3.68022i) q^{70} +(-12.9810 + 6.25130i) q^{71} +(4.89460 - 1.53344i) q^{72} +(-0.0593993 + 0.527184i) q^{73} +(-8.13976 + 11.9388i) q^{74} +(14.1445 - 12.6965i) q^{75} +(4.87713 - 4.19711i) q^{76} +(-0.796115 - 1.50632i) q^{77} +(0.626235 + 1.03413i) q^{78} +(9.06925 + 7.80472i) q^{79} +(4.44655 - 19.4816i) q^{80} +(8.98041 + 0.593445i) q^{81} +(-3.81799 + 4.78761i) q^{82} +(-4.78588 - 5.15796i) q^{83} +(0.0159269 - 0.965378i) q^{84} +(6.09271 - 13.9647i) q^{85} +(-1.32857 + 2.30115i) q^{86} +(-8.91074 + 2.75659i) q^{87} +(-2.65310 - 4.59530i) q^{88} +(-0.918803 + 0.103524i) q^{89} +(11.6529 - 17.2545i) q^{90} +(-0.215132 + 0.0491025i) q^{91} +(6.88155 + 1.03723i) q^{92} +(-2.73466 - 1.24721i) q^{93} +(12.4093 + 11.5141i) q^{94} +(-4.70845 + 24.8847i) q^{95} +(-0.190522 - 9.11310i) q^{96} +(9.19060 + 0.343888i) q^{97} +(-10.9794 - 3.84185i) q^{98} +(-1.42823 - 9.20039i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 672 q - 36 q^{2} - 24 q^{3} - 14 q^{4} - 42 q^{5} - 28 q^{6} - 10 q^{7} - 28 q^{9} - 56 q^{10} - 48 q^{11} - 10 q^{12} - 14 q^{13} - 24 q^{14} - 20 q^{15} - 54 q^{16} - 50 q^{18} - 48 q^{19} - 30 q^{20}+ \cdots - 16 q^{99}+O(q^{100}) \) 672 * q - 36 * q^2 - 24 * q^3 - 14 * q^4 - 42 * q^5 - 28 * q^6 - 10 * q^7 - 28 * q^9 - 56 * q^10 - 48 * q^11 - 10 * q^12 - 14 * q^13 - 24 * q^14 - 20 * q^15 - 54 * q^16 - 50 * q^18 - 48 * q^19 - 30 * q^20 - 80 * q^21 - 14 * q^22 - 30 * q^23 - 16 * q^24 + 30 * q^25 + 36 * q^27 - 168 * q^30 - 12 * q^31 + 24 * q^32 - 70 * q^33 - 14 * q^34 + 128 * q^36 - 48 * q^37 - 42 * q^38 - 44 * q^39 - 2 * q^40 - 24 * q^41 - 28 * q^42 - 12 * q^43 + 24 * q^45 - 64 * q^46 - 42 * q^47 - 28 * q^48 + 22 * q^49 - 66 * q^50 - 28 * q^51 + 22 * q^52 - 36 * q^54 + 76 * q^55 - 42 * q^56 - 42 * q^58 - 132 * q^59 - 20 * q^60 - 28 * q^63 - 308 * q^64 - 66 * q^65 - 46 * q^66 - 14 * q^67 + 60 * q^68 - 64 * q^69 - 14 * q^70 + 56 * q^72 - 48 * q^73 + 66 * q^74 + 24 * q^75 - 28 * q^76 + 30 * q^77 + 72 * q^78 - 12 * q^79 + 140 * q^81 - 136 * q^82 + 246 * q^83 + 238 * q^84 + 34 * q^85 + 118 * q^87 + 8 * q^88 - 48 * q^90 - 56 * q^91 + 462 * q^92 + 28 * q^93 + 26 * q^94 - 246 * q^95 + 126 * q^96 - 36 * q^97 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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