LMFDB - Embedded newform 152.2.t.a.101.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [152,2,Mod(5,152)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(152, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 9, 16]))

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

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

chi := DirichletCharacter("152.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, 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:	$1.21372611072$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$18$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.7
Character	$\chi$	$=$	152.101
Dual form			152.2.t.a.149.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.678879 - 1.24061i) q^{2} +(-0.339733 + 0.933408i) q^{3} +(-1.07825 + 1.68445i) q^{4} +(0.0653175 - 0.0115172i) q^{5} +(1.38864 - 0.212194i) q^{6} +(1.72211 - 2.98278i) q^{7} +(2.82176 + 0.194145i) q^{8} +(1.54230 + 1.29414i) q^{9} +O(q^{10})$	\(q+(-0.678879 - 1.24061i) q^{2} +(-0.339733 + 0.933408i) q^{3} +(-1.07825 + 1.68445i) q^{4} +(0.0653175 - 0.0115172i) q^{5} +(1.38864 - 0.212194i) q^{6} +(1.72211 - 2.98278i) q^{7} +(2.82176 + 0.194145i) q^{8} +(1.54230 + 1.29414i) q^{9} +(-0.0586312 - 0.0732150i) q^{10} +(5.02419 - 2.90072i) q^{11} +(-1.20597 - 1.57871i) q^{12} +(0.741143 + 2.03627i) q^{13} +(-4.86958 - 0.111524i) q^{14} +(-0.0114402 + 0.0648807i) q^{15} +(-1.67477 - 3.63251i) q^{16} +(-2.63821 + 2.21372i) q^{17} +(0.558497 - 2.79197i) q^{18} +(-1.75292 + 3.99090i) q^{19} +(-0.0510281 + 0.122443i) q^{20} +(2.19909 + 2.62078i) q^{21} +(-7.00949 - 4.26384i) q^{22} +(1.43964 - 8.16462i) q^{23} +(-1.13986 + 2.56789i) q^{24} +(-4.69433 + 1.70860i) q^{25} +(2.02308 - 2.30186i) q^{26} +(-4.31263 + 2.48990i) q^{27} +(3.16750 + 6.11698i) q^{28} +(2.84323 - 3.38843i) q^{29} +(0.0882584 - 0.0298533i) q^{30} +(-2.29739 + 3.97920i) q^{31} +(-3.36957 + 4.54378i) q^{32} +(1.00067 + 5.67508i) q^{33} +(4.53740 + 1.77015i) q^{34} +(0.0781304 - 0.214662i) q^{35} +(-3.84291 + 1.20253i) q^{36} +0.627345i q^{37} +(6.14119 - 0.534645i) q^{38} -2.15246 q^{39} +(0.186546 - 0.0198178i) q^{40} +(7.06806 + 2.57256i) q^{41} +(1.75845 - 4.50741i) q^{42} +(-0.788746 + 0.139077i) q^{43} +(-0.531184 + 11.5907i) q^{44} +(0.115644 + 0.0667673i) q^{45} +(-11.1065 + 3.75675i) q^{46} +(-4.03976 - 3.38976i) q^{47} +(3.95959 - 0.329164i) q^{48} +(-2.43131 - 4.21115i) q^{49} +(5.30659 + 4.66392i) q^{50} +(-1.17002 - 3.21460i) q^{51} +(-4.22915 - 0.947182i) q^{52} +(-5.64643 - 0.995618i) q^{53} +(6.01676 + 3.65997i) q^{54} +(0.294759 - 0.247332i) q^{55} +(5.43846 - 8.08233i) q^{56} +(-3.12961 - 2.99203i) q^{57} +(-6.13394 - 1.22701i) q^{58} +(-4.20266 - 5.00853i) q^{59} +(-0.0969532 - 0.0892278i) q^{60} +(-6.93517 - 1.22286i) q^{61} +(6.49631 + 0.148780i) q^{62} +(6.51616 - 2.37169i) q^{63} +(7.92462 + 1.09566i) q^{64} +(0.0718619 + 0.124468i) q^{65} +(6.36125 - 5.09414i) q^{66} +(-0.861477 + 1.02667i) q^{67} +(-0.884273 - 6.83087i) q^{68} +(7.13183 + 4.11756i) q^{69} +(-0.319353 + 0.0487996i) q^{70} +(1.65826 + 9.40446i) q^{71} +(4.10075 + 3.95119i) q^{72} +(1.81006 + 0.658809i) q^{73} +(0.778293 - 0.425892i) q^{74} -4.96219i q^{75} +(-4.83241 - 7.25588i) q^{76} -19.9814i q^{77} +(1.46126 + 2.67038i) q^{78} +(-1.51401 - 0.551054i) q^{79} +(-0.151229 - 0.217978i) q^{80} +(0.189884 + 1.07689i) q^{81} +(-1.60680 - 10.5152i) q^{82} +(-8.56814 - 4.94682i) q^{83} +(-6.78574 + 0.878431i) q^{84} +(-0.146825 + 0.174980i) q^{85} +(0.708004 + 0.884112i) q^{86} +(2.19685 + 3.80505i) q^{87} +(14.7402 - 7.20969i) q^{88} +(-12.0507 + 4.38609i) q^{89} +(0.00432386 - 0.188797i) q^{90} +(7.35008 + 1.29602i) q^{91} +(12.2006 + 11.2285i) q^{92} +(-2.93372 - 3.49627i) q^{93} +(-1.46288 + 7.31303i) q^{94} +(-0.0685321 + 0.280864i) q^{95} +(-3.09645 - 4.68886i) q^{96} +(9.04283 - 7.58783i) q^{97} +(-3.57385 + 5.87518i) q^{98} +(11.5028 + 2.02825i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9	$ 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) $ 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−0.678879	−	1.24061i	−0.480040	−	0.877246i
$2$	−0.678879	−	1.24061i	−0.480040	−	0.877246i
$3$	−0.339733	+	0.933408i	−0.196145	+	0.538903i	−0.998305	−	0.0582061i	$-0.981462\pi$
$3$	−0.339733	+	0.933408i	−0.196145	+	0.538903i	0.802160	+	0.597109i	$0.203684\pi$
$4$	−1.07825	+	1.68445i	−0.539123	+	0.842227i
$5$	0.0653175	−	0.0115172i	0.0292109	−	0.00515067i	−0.159024	−	0.987275i	$-0.550835\pi$
$5$	0.0653175	−	0.0115172i	0.0292109	−	0.00515067i	0.188235	+	0.982124i	$0.439723\pi$
$6$	1.38864	−	0.212194i	0.566908	−	0.0866280i
$7$	1.72211	−	2.98278i	0.650896	−	1.12738i	−0.332010	−	0.943276i	$-0.607727\pi$
$7$	1.72211	−	2.98278i	0.650896	−	1.12738i	0.982906	−	0.184108i	$-0.0589397\pi$
$8$	2.82176	+	0.194145i	0.997641	+	0.0686406i
$9$	1.54230	+	1.29414i	0.514101	+	0.431382i
$10$	−0.0586312	−	0.0732150i	−0.0185408	−	0.0231526i
$11$	5.02419	−	2.90072i	1.51485	−	0.874599i	0.515001	−	0.857190i	$-0.327792\pi$
$11$	5.02419	−	2.90072i	1.51485	−	0.874599i	0.999848	−	0.0174093i	$-0.00554183\pi$
$12$	−1.20597	−	1.57871i	−0.348133	−	0.455733i
$13$	0.741143	+	2.03627i	0.205556	+	0.564761i	0.999039	−	0.0438318i	$-0.0139566\pi$
$13$	0.741143	+	2.03627i	0.205556	+	0.564761i	−0.793483	+	0.608593i	$0.791734\pi$
$14$	−4.86958	−	0.111524i	−1.30145	−	0.0298061i
$15$	−0.0114402	+	0.0648807i	−0.00295385	+	0.0167521i
$16$	−1.67477	−	3.63251i	−0.418693	−	0.908128i
$17$	−2.63821	+	2.21372i	−0.639859	+	0.536906i	−0.903975	−	0.427585i	$-0.859364\pi$
$17$	−2.63821	+	2.21372i	−0.639859	+	0.536906i	0.264116	+	0.964491i	$0.414920\pi$
$18$	0.558497	−	2.79197i	0.131639	−	0.658073i
$19$	−1.75292	+	3.99090i	−0.402147	+	0.915575i
$19$	−1.75292	+	3.99090i	−0.402147	+	0.915575i
$20$	−0.0510281	+	0.122443i	−0.0114102	+	0.0273790i
$21$	2.19909	+	2.62078i	0.479881	+	0.571900i
$22$	−7.00949	−	4.26384i	−1.49443	−	0.909054i
$23$	1.43964	−	8.16462i	0.300186	−	1.70244i	−0.345154	−	0.938546i	$-0.612173\pi$
$23$	1.43964	−	8.16462i	0.300186	−	1.70244i	0.645341	−	0.763895i	$-0.276715\pi$
$24$	−1.13986	+	2.56789i	−0.232673	+	0.524169i
$25$	−4.69433	+	1.70860i	−0.938866	+	0.341719i
$26$	2.02308	−	2.30186i	0.396759	−	0.451431i
$27$	−4.31263	+	2.48990i	−0.829967	+	0.479182i
$28$	3.16750	+	6.11698i	0.598601	+	1.15600i
$29$	2.84323	−	3.38843i	0.527974	−	0.629215i	−0.434473	−	0.900685i	$-0.643065\pi$
$29$	2.84323	−	3.38843i	0.527974	−	0.629215i	0.962447	+	0.271470i	$0.0875097\pi$
$30$	0.0882584	−	0.0298533i	0.0161137	−	0.00545044i
$31$	−2.29739	+	3.97920i	−0.412624	+	0.714686i	−0.995176	−	0.0981075i	$-0.968721\pi$
$31$	−2.29739	+	3.97920i	−0.412624	+	0.714686i	0.582552	+	0.812794i	$0.302054\pi$
$32$	−3.36957	+	4.54378i	−0.595662	+	0.803235i
$33$	1.00067	+	5.67508i	0.174194	+	0.987905i
$34$	4.53740	+	1.77015i	0.778157	+	0.303578i
$35$	0.0781304	−	0.214662i	0.0132065	−	0.0362844i
$36$	−3.84291	+	1.20253i	−0.640485	+	0.200422i
$37$			0.627345i			0.103135i	0.998670	+	0.0515674i	$0.0164217\pi$
$37$			0.627345i			0.103135i	−0.998670	+	0.0515674i	$0.983578\pi$
$38$	6.14119	−	0.534645i	0.996232	−	0.0867309i
$39$	−2.15246			−0.344670
$40$	0.186546	−	0.0198178i	0.0294955	−	0.00313347i
$41$	7.06806	+	2.57256i	1.10385	+	0.401767i	0.828732	−	0.559645i	$-0.189063\pi$
$41$	7.06806	+	2.57256i	1.10385	+	0.401767i	0.275113	+	0.961412i	$0.411285\pi$
$42$	1.75845	−	4.50741i	0.271335	−	0.695509i
$43$	−0.788746	+	0.139077i	−0.120283	+	0.0212091i	−0.233465	−	0.972365i	$-0.575007\pi$
$43$	−0.788746	+	0.139077i	−0.120283	+	0.0212091i	0.113183	+	0.993574i	$0.463895\pi$
$44$	−0.531184	+	11.5907i	−0.0800790	+	1.74736i
$45$	0.115644	+	0.0667673i	0.0172392	+	0.00995308i
$46$	−11.1065	+	3.75675i	−1.63756	+	0.553903i
$47$	−4.03976	−	3.38976i	−0.589260	−	0.494448i	0.298713	−	0.954343i	$-0.403443\pi$
$47$	−4.03976	−	3.38976i	−0.589260	−	0.494448i	−0.887973	+	0.459895i	$0.847887\pi$
$48$	3.95959	−	0.329164i	0.571517	−	0.0475107i
$49$	−2.43131	−	4.21115i	−0.347330	−	0.601593i
$50$	5.30659	+	4.66392i	0.750465	+	0.659578i
$51$	−1.17002	−	3.21460i	−0.163835	−	0.450134i
$52$	−4.22915	−	0.947182i	−0.586477	−	0.131350i
$53$	−5.64643	−	0.995618i	−0.775597	−	0.136759i	−0.228180	−	0.973619i	$-0.573278\pi$
$53$	−5.64643	−	0.995618i	−0.775597	−	0.136759i	−0.547417	+	0.836860i	$0.684389\pi$
$54$	6.01676	+	3.65997i	0.818778	+	0.498059i
$55$	0.294759	−	0.247332i	0.0397453	−	0.0333503i
$56$	5.43846	−	8.08233i	0.726745	−	1.08005i
$57$	−3.12961	−	2.99203i	−0.414527	−	0.396304i
$58$	−6.13394	−	1.22701i	−0.805425	−	0.161115i
$59$	−4.20266	−	5.00853i	−0.547139	−	0.652055i	0.419633	−	0.907694i	$-0.362159\pi$
$59$	−4.20266	−	5.00853i	−0.547139	−	0.652055i	−0.966772	+	0.255639i	$0.917714\pi$
$60$	−0.0969532	−	0.0892278i	−0.0125166	−	0.0115193i
$61$	−6.93517	−	1.22286i	−0.887958	−	0.156571i	−0.288979	−	0.957336i	$-0.593316\pi$
$61$	−6.93517	−	1.22286i	−0.887958	−	0.156571i	−0.598979	+	0.800765i	$0.704427\pi$
$62$	6.49631	+	0.148780i	0.825032	+	0.0188951i
$63$	6.51616	−	2.37169i	0.820958	−	0.298804i
$64$	7.92462	+	1.09566i	0.990577	+	0.136957i
$65$	0.0718619	+	0.124468i	0.00891337	+	0.0154384i
$66$	6.36125	−	5.09414i	0.783016	−	0.627046i
$67$	−0.861477	+	1.02667i	−0.105246	+	0.125427i	−0.816096	−	0.577916i	$-0.803866\pi$
$67$	−0.861477	+	1.02667i	−0.105246	+	0.125427i	0.710850	+	0.703344i	$0.248310\pi$
$68$	−0.884273	−	6.83087i	−0.107234	−	0.828365i
$69$	7.13183	+	4.11756i	0.858571	+	0.495696i
$70$	−0.319353	+	0.0487996i	−0.0381700	+	0.00583267i
$71$	1.65826	+	9.40446i	0.196799	+	1.11610i	0.909833	+	0.414975i	$0.136210\pi$
$71$	1.65826	+	9.40446i	0.196799	+	1.11610i	−0.713034	+	0.701130i	$0.752679\pi$
$72$	4.10075	+	3.95119i	0.483278	+	0.465652i
$73$	1.81006	+	0.658809i	0.211852	+	0.0771078i	0.445766	−	0.895149i	$-0.352931\pi$
$73$	1.81006	+	0.658809i	0.211852	+	0.0771078i	−0.233914	+	0.972257i	$0.575154\pi$
$74$	0.778293	−	0.425892i	0.0904747	−	0.0495089i
$75$		−	4.96219i		−	0.572984i
$76$	−4.83241	−	7.25588i	−0.554316	−	0.832306i
$77$		−	19.9814i		−	2.27709i
$78$	1.46126	+	2.67038i	0.165456	+	0.302361i
$79$	−1.51401	−	0.551054i	−0.170339	−	0.0619985i	0.255443	−	0.966824i	$-0.417779\pi$
$79$	−1.51401	−	0.551054i	−0.170339	−	0.0619985i	−0.425782	+	0.904826i	$0.640001\pi$
$80$	−0.151229	−	0.217978i	−0.0169079	−	0.0243707i
$81$	0.189884	+	1.07689i	0.0210982	+	0.119654i
$82$	−1.60680	−	10.5152i	−0.177442	−	1.16121i
$83$	−8.56814	−	4.94682i	−0.940476	−	0.542984i	−0.0503663	−	0.998731i	$-0.516039\pi$
$83$	−8.56814	−	4.94682i	−0.940476	−	0.542984i	−0.890109	+	0.455747i	$0.849372\pi$
$84$	−6.78574	+	0.878431i	−0.740385	+	0.0958446i
$85$	−0.146825	+	0.174980i	−0.0159254	+	0.0189792i
$86$	0.708004	+	0.884112i	0.0763460	+	0.0953363i
$87$	2.19685	+	3.80505i	0.235527	+	0.407944i
$88$	14.7402	−	7.20969i	1.57131	−	0.768556i
$89$	−12.0507	+	4.38609i	−1.27737	+	0.464925i	−0.889562	−	0.456815i	$-0.848990\pi$
$89$	−12.0507	+	4.38609i	−1.27737	+	0.464925i	−0.387809	+	0.921740i	$0.626768\pi$
$90$	0.00432386	−	0.188797i	0.000455775	−	0.0199009i
$91$	7.35008	+	1.29602i	0.770498	+	0.135860i
$92$	12.2006	+	11.2285i	1.27200	+	1.17065i
$93$	−2.93372	−	3.49627i	−0.304213	−	0.362546i
$94$	−1.46288	+	7.31303i	−0.150884	+	0.754281i
$95$	−0.0685321	+	0.280864i	−0.00703125	+	0.0288161i
$96$	−3.09645	−	4.68886i	−0.316030	−	0.478555i
$97$	9.04283	−	7.58783i	0.918160	−	0.770428i	−0.0554937	−	0.998459i	$-0.517673\pi$
$97$	9.04283	−	7.58783i	0.918160	−	0.770428i	0.973654	+	0.228031i	$0.0732288\pi$
$98$	−3.57385	+	5.87518i	−0.361013	+	0.593483i
$99$	11.5028	+	2.02825i	1.15607	+	0.203846i
$100$	2.18359	−	9.74967i	0.218359	−	0.974967i
$101$	4.64376	+	12.7586i	0.462071	+	1.26953i	0.923925	+	0.382574i	$0.124962\pi$
$101$	4.64376	+	12.7586i	0.462071	+	1.26953i	−0.461853	+	0.886956i	$0.652815\pi$
$102$	−3.19377	+	3.63386i	−0.316231	+	0.359806i
$103$	0.407374	+	0.705593i	0.0401398	+	0.0695242i	0.885397	−	0.464835i	$-0.153886\pi$
$103$	0.407374	+	0.705593i	0.0401398	+	0.0695242i	−0.845258	+	0.534359i	$0.820553\pi$
$104$	1.69599	+	5.88976i	0.166306	+	0.577538i
$105$	0.173823	+	0.145855i	0.0169634	+	0.0142340i
$106$	2.59807	+	7.68094i	0.252347	+	0.746039i
$107$	4.05878	+	2.34334i	0.392377	+	0.226539i	0.683190	−	0.730241i	$-0.260592\pi$
$107$	4.05878	+	2.34334i	0.392377	+	0.226539i	−0.290812	+	0.956780i	$0.593926\pi$
$108$	0.455955	−	9.94916i	0.0438742	−	0.957358i
$109$	−18.8613	+	3.32575i	−1.80658	+	0.318549i	−0.972467	−	0.233042i	$-0.925132\pi$
$109$	−18.8613	+	3.32575i	−1.80658	+	0.318549i	−0.834115	+	0.551591i	$0.814021\pi$
$110$	−0.506950	−	0.197774i	−0.0483358	−	0.0188570i
$111$	−0.585569	−	0.213130i	−0.0555797	−	0.0202294i
$112$	−13.7191	−	1.26010i	−1.29633	−	0.119068i
$113$	2.78221			0.261728			0.130864	−	0.991400i	$-0.458225\pi$
$113$	2.78221			0.261728			0.130864	+	0.991400i	$0.458225\pi$
$114$	−1.58732	+	5.91387i	−0.148666	+	0.553884i
$115$		−	0.549874i		−	0.0512760i
$116$	2.64195	+	8.44284i	0.245299	+	0.783898i
$117$	−1.49217	+	4.09970i	−0.137951	+	0.379017i
$118$	−3.36056	+	8.61406i	−0.309364	+	0.792989i
$119$	2.05976	+	11.6815i	0.188817	+	1.07084i
$120$	−0.0448777	+	0.180856i	−0.00409676	+	0.0165099i
$121$	11.3283	−	19.6212i	1.02985	−	1.78375i
$122$	3.19105	+	9.43404i	0.288904	+	0.854118i
$123$	−4.80250	+	5.72340i	−0.433027	+	0.516061i
$124$	−4.22563	−	8.16042i	−0.379473	−	0.732827i
$125$	−0.574140	+	0.331480i	−0.0513526	+	0.0296485i
$126$	−7.36603	−	6.47394i	−0.656218	−	0.576745i
$127$	−18.9363	+	6.89226i	−1.68033	+	0.611590i	−0.993355	−	0.115093i	$-0.963283\pi$
$127$	−18.9363	+	6.89226i	−1.68033	+	0.611590i	−0.686974	+	0.726682i	$0.741061\pi$
$128$	−4.02057	−	10.5752i	−0.355371	−	0.934725i
$129$	0.138147	−	0.783470i	0.0121632	−	0.0689807i
$130$	0.105632	−	0.173652i	0.00926452	−	0.0152303i
$131$	1.95683	+	2.33206i	0.170969	+	0.203753i	0.844725	−	0.535201i	$-0.179764\pi$
$131$	1.95683	+	2.33206i	0.170969	+	0.203753i	−0.673755	+	0.738955i	$0.735320\pi$
$132$	−10.6384	−	4.43355i	−0.925953	−	0.385891i
$133$	8.88525	+	12.1013i	0.770449	+	1.04932i
$134$	1.85854	+	0.371776i	0.160553	+	0.0321166i
$135$	−0.253014	+	0.212304i	−0.0217760	+	0.0182722i
$136$	−7.87416	+	5.73438i	−0.675204	+	0.491719i
$137$	0.323758	−	1.83612i	0.0276605	−	0.156871i	−0.967849	−	0.251532i	$-0.919066\pi$
$137$	0.323758	−	1.83612i	0.0276605	−	0.156871i	0.995510	+	0.0946613i	$0.0301768\pi$
$138$	0.266654	−	11.6432i	0.0226991	−	0.991132i
$139$	3.70164	+	10.1702i	0.313969	+	0.862623i	0.991845	+	0.127447i	$0.0406783\pi$
$139$	3.70164	+	10.1702i	0.313969	+	0.862623i	−0.677876	+	0.735176i	$0.737099\pi$
$140$	0.277344	+	0.363065i	0.0234398	+	0.0306846i
$141$	4.53647	−	2.61913i	0.382040	−	0.220571i
$142$	10.5415	−	8.44176i	0.884627	−	0.708416i
$143$	9.63030	+	8.08078i	0.805326	+	0.675749i
$144$	2.11799	−	7.76983i	0.176499	−	0.647485i
$145$	0.146687	−	0.254070i	0.0121817	−	0.0210993i
$146$	−0.411487	−	2.69284i	−0.0340549	−	0.222861i
$147$	4.75672	−	0.838738i	0.392327	−	0.0691779i
$148$	−1.05673	−	0.676432i	−0.0868630	−	0.0556024i
$149$	−1.12160	+	3.08157i	−0.0918851	+	0.252452i	−0.977119	−	0.212694i	$-0.931776\pi$
$149$	−1.12160	+	3.08157i	−0.0918851	+	0.252452i	0.885234	+	0.465147i	$0.153998\pi$
$150$	−6.15616	+	3.36873i	−0.502648	+	0.275056i
$151$	−5.35276			−0.435601			−0.217801	−	0.975993i	$-0.569888\pi$
$151$	−5.35276			−0.435601			−0.217801	+	0.975993i	$0.569888\pi$
$152$	−5.72112	+	10.9210i	−0.464044	+	0.885812i
$153$	−6.93379			−0.560563
$154$	−24.7892	+	13.5649i	−1.99757	+	1.09309i
$155$	−0.104231	+	0.286371i	−0.00837201	+	0.0230019i
$156$	2.32089	−	3.62573i	0.185820	−	0.290291i
$157$	16.4266	−	2.89645i	1.31098	−	0.231162i	0.525898	−	0.850548i	$-0.323729\pi$
$157$	16.4266	−	2.89645i	1.31098	−	0.231162i	0.785087	+	0.619386i	$0.212618\pi$
$158$	0.344184	+	2.25240i	0.0273818	+	0.179191i
$159$	2.84759	−	4.93218i	0.225829	−	0.391147i
$160$	−0.167760	+	0.335597i	−0.0132626	+	0.0265313i
$161$	−21.8740	−	18.3545i	−1.72391	−	1.44654i
$162$	1.20709	−	0.966649i	0.0948381	−	0.0759471i
$163$	11.1838	−	6.45696i	0.875982	−	0.505748i	0.00665046	−	0.999978i	$-0.497883\pi$
$163$	11.1838	−	6.45696i	0.875982	−	0.505748i	0.869331	+	0.494229i	$0.164550\pi$
$164$	−11.9545	+	9.13197i	−0.933487	+	0.713087i
$165$	0.130723	+	0.359158i	0.0101767	+	0.0279604i
$166$	−0.320357	+	13.9880i	−0.0248645	+	1.08568i
$167$	2.31203	−	13.1122i	0.178911	−	1.01465i	−0.754622	−	0.656160i	$-0.772180\pi$
$167$	2.31203	−	13.1122i	0.178911	−	1.01465i	0.933533	−	0.358493i	$-0.116709\pi$
$168$	5.69649	+	7.82213i	0.439494	+	0.603491i
$169$	6.36146	−	5.33790i	0.489343	−	0.410607i
$170$	0.316759	+	0.0633635i	0.0242943	+	0.00485976i
$171$	−7.86833	+	3.88664i	−0.601706	+	0.297219i
$172$	0.616192	−	1.47857i	0.0469842	−	0.112740i
$173$	−11.5628	−	13.7800i	−0.879100	−	1.04767i	−0.998496	−	0.0548236i	$-0.982540\pi$
$173$	−11.5628	−	13.7800i	−0.879100	−	1.04767i	0.119396	−	0.992847i	$-0.461904\pi$
$174$	3.22920	−	5.30861i	0.244805	−	0.402445i
$175$	−2.98778	+	16.9445i	−0.225855	+	1.28089i
$176$	−18.9513	−	13.3924i	−1.42850	−	1.00949i
$177$	6.10278	−	2.22123i	0.458713	−	0.166958i
$178$	13.6224	+	11.9726i	1.02104	+	0.897386i
$179$	2.00133	−	1.15547i	0.149587	−	0.0863639i	−0.423338	−	0.905972i	$-0.639142\pi$
$179$	2.00133	−	1.15547i	0.149587	−	0.0863639i	0.572925	+	0.819608i	$0.305809\pi$
$180$	−0.237159	+	0.122806i	−0.0176768	+	0.00915342i
$181$	8.54617	−	10.1849i	0.635232	−	0.757040i	−0.348377	−	0.937355i	$-0.613267\pi$
$181$	8.54617	−	10.1849i	0.635232	−	0.757040i	0.983609	+	0.180314i	$0.0577115\pi$
$182$	−3.38196	−	9.99845i	−0.250688	−	0.741135i
$183$	3.49753	−	6.05790i	0.258545	−	0.447813i
$184$	5.64744	−	22.7591i	0.416335	−	1.67782i
$185$	0.00722529	+	0.0409766i	0.000531214	+	0.00301266i
$186$	−2.34588	+	6.01316i	−0.172008	+	0.440906i
$187$	−6.83348	+	18.7748i	−0.499714	+	1.37295i
$188$	10.0658	−	3.14980i	0.734121	−	0.229723i
$189$			17.1515i			1.24759i
$190$	0.394969	−	0.105651i	0.0286541	−	0.00766475i
$191$	1.92403			0.139218			0.0696088	−	0.997574i	$-0.477825\pi$
$191$	1.92403			0.139218			0.0696088	+	0.997574i	$0.477825\pi$
$192$	−3.71495	+	7.02467i	−0.268103	+	0.506962i
$193$	6.60800	+	2.40512i	0.475654	+	0.173124i	0.568712	−	0.822537i	$-0.307442\pi$
$193$	6.60800	+	2.40512i	0.475654	+	0.173124i	−0.0930578	+	0.995661i	$0.529664\pi$
$194$	−15.5526	−	6.06743i	−1.11661	−	0.435616i
$195$	−0.140594	+	0.0247905i	−0.0100681	+	0.00177528i
$196$	9.71504	+	0.445225i	0.693932	+	0.0318018i
$197$	13.8740	+	8.01018i	0.988484	+	0.570701i	0.904821	−	0.425793i	$-0.140005\pi$
$197$	13.8740	+	8.01018i	0.988484	+	0.570701i	0.0836632	+	0.996494i	$0.473338\pi$
$198$	−5.29271	−	15.6474i	−0.376137	−	1.11201i
$199$	−2.42025	−	2.03083i	−0.171567	−	0.143962i	0.552961	−	0.833207i	$-0.313498\pi$
$199$	−2.42025	−	2.03083i	−0.171567	−	0.143962i	−0.724528	+	0.689245i	$0.757942\pi$
$200$	−13.5780	+	3.90986i	−0.960107	+	0.276469i
$201$	−0.665628	−	1.15290i	−0.0469498	−	0.0813194i
$202$	12.6760	−	14.4227i	0.891878	−	1.01478i
$203$	−5.21058	−	14.3160i	−0.365711	−	1.00478i
$204$	6.67641	+	1.49528i	0.467442	+	0.104691i
$205$	0.491297	+	0.0866289i	0.0343137	+	0.00605043i
$206$	0.598810	−	0.984407i	0.0417211	−	0.0685869i
$207$	12.7866	−	10.7292i	0.888727	−	0.745731i
$208$	6.15554	−	6.10251i	0.426810	−	0.423133i
$209$	2.76948	+	25.1357i	0.191569	+	1.73868i
$210$	0.0629448	−	0.314666i	0.00434360	−	0.0217140i
$211$	2.93872	+	3.50223i	0.202310	+	0.241103i	0.857654	−	0.514227i	$-0.171921\pi$
$211$	2.93872	+	3.50223i	0.202310	+	0.241103i	−0.655344	+	0.755330i	$0.727477\pi$
$212$	7.76531	−	8.43763i	0.533324	−	0.579499i
$213$	−9.34156	−	1.64717i	−0.640073	−	0.112862i
$214$	0.151755	−	6.62622i	0.0103738	−	0.452959i
$215$	−0.0499171	+	0.0181683i	−0.00340432	+	0.00123907i
$216$	−12.6526	+	6.18862i	−0.860901	+	0.421082i
$217$	7.91272	+	13.7052i	0.537151	+	0.930372i
$218$	16.9305	+	21.1418i	1.14668	+	1.43190i
$219$	−1.22988	+	1.46571i	−0.0831073	+	0.0990434i
$220$	0.0987973	+	0.763194i	0.00666091	+	0.0514545i
$221$	−6.46303	−	3.73143i	−0.434750	−	0.251003i
$222$	0.133119	+	0.871154i	0.00893437	+	0.0584680i
$223$	3.18786	+	18.0792i	0.213475	+	1.21067i	0.883534	+	0.468367i	$0.155158\pi$
$223$	3.18786	+	18.0792i	0.213475	+	1.21067i	−0.670059	+	0.742308i	$0.733731\pi$
$224$	7.75033	+	17.8756i	0.517841	+	1.19436i
$225$	−9.45124	−	3.43997i	−0.630083	−	0.229331i
$226$	−1.88878	−	3.45164i	−0.125640	−	0.229600i
$227$		−	18.7793i		−	1.24642i	−0.782053	−	0.623212i	$-0.785827\pi$
$227$		−	18.7793i		−	1.24642i	0.782053	−	0.623212i	$-0.214173\pi$
$228$	8.41442	−	2.04555i	0.557259	−	0.135470i
$229$			23.4954i			1.55262i	0.630351	+	0.776310i	$0.282911\pi$
$229$			23.4954i			1.55262i	−0.630351	+	0.776310i	$0.717089\pi$
$230$	−0.682181	+	0.373298i	−0.0449817	+	0.0246145i
$231$	18.6508	+	6.78833i	1.22713	+	0.446639i
$232$	8.68074	−	9.00932i	0.569919	−	0.591491i
$233$	1.15950	+	6.57587i	0.0759615	+	0.430799i	0.998943	+	0.0459560i	$0.0146334\pi$
$233$	1.15950	+	6.57587i	0.0759615	+	0.430799i	−0.922982	+	0.384843i	$0.874255\pi$
$234$	6.09914	−	0.931996i	0.398713	−	0.0609265i
$235$	−0.302908	−	0.174884i	−0.0197595	−	0.0114082i
$236$	12.9681	−	1.67876i	0.844154	−	0.109278i
$237$	1.02872	−	1.22598i	0.0668223	−	0.0796358i
$238$	13.0938	−	10.4857i	0.848748	−	0.679684i
$239$	−9.71666	−	16.8297i	−0.628518	−	1.08863i	−0.987849	−	0.155416i	$-0.950328\pi$
$239$	−9.71666	−	16.8297i	−0.628518	−	1.08863i	0.359331	−	0.933210i	$-0.383005\pi$
$240$	0.254840	−	0.0671037i	0.0164498	−	0.00433153i
$241$	12.4918	−	4.54663i	0.804666	−	0.292874i	0.0932472	−	0.995643i	$-0.470275\pi$
$241$	12.4918	−	4.54663i	0.804666	−	0.292874i	0.711418	+	0.702769i	$0.248053\pi$
$242$	−32.0329	−	0.733624i	−2.05915	−	0.0471591i
$243$	−15.7821	−	2.78281i	−1.01242	−	0.178518i
$244$	9.53767	−	10.3634i	0.610587	−	0.663451i
$245$	−0.207308	−	0.247060i	−0.0132444	−	0.0157841i
$246$	10.3608	+	2.07255i	0.660583	+	0.132141i
$247$	−9.42573	−	0.611593i	−0.599745	−	0.0389147i
$248$	−7.25523	+	10.7823i	−0.460708	+	0.684678i
$249$	7.52828	−	6.31697i	0.477085	−	0.400322i
$250$	0.801010	+	0.487251i	0.0506603	+	0.0308165i
$251$	15.8441	+	2.79375i	1.00007	+	0.176340i	0.649635	−	0.760246i	$-0.274922\pi$
$251$	15.8441	+	2.79375i	1.00007	+	0.176340i	0.350438	+	0.936586i	$0.386033\pi$
$252$	−3.03102	+	13.5334i	−0.190936	+	0.852526i
$253$	−16.4502	−	45.1966i	−1.03422	−	2.84148i
$254$	21.4061	+	18.8137i	1.34314	+	1.18047i
$255$	−0.113446	−	0.196494i	−0.00710426	−	0.0123049i
$256$	−10.3903	+	12.1673i	−0.649392	+	0.760454i
$257$	−7.95730	−	6.67697i	−0.496363	−	0.416498i	0.359937	−	0.932976i	$-0.382798\pi$
$257$	−7.95730	−	6.67697i	−0.496363	−	0.416498i	−0.856300	+	0.516479i	$0.827243\pi$
$258$	−1.06577	+	0.360495i	−0.0663519	+	0.0224434i
$259$	1.87123	+	1.08036i	0.116273	+	0.0671300i
$260$	−0.287146	−	0.0131595i	−0.0178081	−	0.000816116i
$261$	8.77023	−	1.54643i	0.542863	−	0.0957215i
$262$	1.56474	−	4.01087i	0.0966697	−	0.247792i
$263$	−22.5707	−	8.21507i	−1.39177	−	0.506563i	−0.466045	−	0.884761i	$-0.654322\pi$
$263$	−22.5707	−	8.21507i	−1.39177	−	0.506563i	−0.925725	+	0.378198i	$0.876544\pi$
$264$	1.72186	+	16.2080i	0.105973	+	0.997532i
$265$	−0.380278			−0.0233603
$266$	8.98105	−	19.2385i	0.550664	−	1.17959i
$267$		−	12.7383i		−	0.779572i
$268$	−0.800492	−	2.55812i	−0.0488978	−	0.156262i
$269$	6.97012	−	19.1502i	0.424976	−	1.16761i	−0.523850	−	0.851810i	$-0.675505\pi$
$269$	6.97012	−	19.1502i	0.424976	−	1.16761i	0.948826	−	0.315800i	$-0.102273\pi$
$270$	0.435153	+	0.169764i	0.0264826	+	0.0103315i
$271$	0.664328	+	3.76759i	0.0403550	+	0.228865i	0.998314	−	0.0580395i	$-0.0184849\pi$
$271$	0.664328	+	3.76759i	0.0403550	+	0.228865i	−0.957959	+	0.286904i	$0.907374\pi$
$272$	12.4598	+	5.87584i	0.755484	+	0.356275i
$273$	−3.70678	+	6.42032i	−0.224344	+	0.388576i
$274$	−2.49771	+	0.844847i	−0.150892	+	0.0510391i
$275$	−18.6290	+	22.2012i	−1.12337	+	1.33878i
$276$	−14.6257	+	7.57349i	−0.880364	+	0.455871i
$277$	−3.07452	+	1.77507i	−0.184730	+	0.106654i	−0.589513	−	0.807759i	$-0.700680\pi$
$277$	−3.07452	+	1.77507i	−0.184730	+	0.106654i	0.404783	+	0.914413i	$0.367347\pi$
$278$	10.1043	−	11.4966i	0.606015	−	0.689522i
$279$	−8.69294	+	3.16397i	−0.520433	+	0.189422i
$280$	0.262141	−	0.590554i	0.0156659	−	0.0352924i
$281$	−1.38638	+	7.86254i	−0.0827044	+	0.469040i	0.915124	+	0.403173i	$0.132093\pi$
$281$	−1.38638	+	7.86254i	−0.0827044	+	0.469040i	−0.997828	+	0.0658674i	$0.979019\pi$
$282$	−6.32905	−	3.84993i	−0.376889	−	0.229260i
$283$	−21.0046	−	25.0323i	−1.24859	−	1.48801i	−0.806717	−	0.590937i	$-0.798758\pi$
$283$	−21.0046	−	25.0323i	−1.24859	−	1.48801i	−0.441875	−	0.897077i	$-0.645686\pi$
$284$	−17.6294	−	7.34705i	−1.04611	−	0.435967i
$285$	−0.238879	−	0.159387i	−0.0141499	−	0.00944129i
$286$	3.48732	−	17.4334i	0.206209	−	1.03086i
$287$	19.8453	−	16.6522i	1.17143	−	0.982950i
$288$	−11.0772	+	2.64717i	−0.652731	+	0.155986i
$289$	−0.892431	+	5.06123i	−0.0524959	+	0.297719i
$290$	−0.414785	−	0.00949950i	−0.0243570	−	0.000557830i
$291$	4.01040	+	11.0185i	0.235094	+	0.645915i
$292$	−3.06143	+	2.33861i	−0.179156	+	0.136857i
$293$	−18.8681	+	10.8935i	−1.10229	+	0.636406i	−0.936821	−	0.349810i	$-0.886246\pi$
$293$	−18.8681	+	10.8935i	−1.10229	+	0.636406i	−0.165466	+	0.986215i	$0.552913\pi$
$294$	−4.26979	−	5.33185i	−0.249019	−	0.310960i
$295$	−0.332192	−	0.278742i	−0.0193409	−	0.0162290i
$296$	−0.121796	+	1.77021i	−0.00707924	+	0.102892i
$297$	−14.4450	+	25.0195i	−0.838183	+	1.45178i
$298$	4.58447	−	0.700543i	0.265571	−	0.0405813i
$299$	17.6924	−	3.11965i	1.02318	−	0.180414i
$300$	8.35858	+	5.35046i	0.482583	+	0.308909i
$301$	−0.943469	+	2.59216i	−0.0543806	+	0.149410i
$302$	3.63388	+	6.64070i	0.209106	+	0.382130i
$303$	−13.4866			−0.774787
$304$	17.4327	−	0.316359i	0.999835	−	0.0181444i
$305$	−0.467072			−0.0267445
$306$	4.70720	+	8.60215i	0.269093	+	0.491752i
$307$	−0.341876	+	0.939297i	−0.0195119	+	0.0536085i	−0.949066	−	0.315077i	$-0.897970\pi$
$307$	−0.341876	+	0.939297i	−0.0195119	+	0.0536085i	0.929554	+	0.368685i	$0.120192\pi$
$308$	33.6577	+	21.5448i	1.91783	+	1.22763i
$309$	−0.797004	+	0.140533i	−0.0453400	+	0.00799467i
$310$	0.426036	−	0.0651017i	0.0241972	−	0.00369753i
$311$	3.18482	−	5.51627i	0.180595	−	0.312799i	−0.761489	−	0.648178i	$-0.775531\pi$
$311$	3.18482	−	5.51627i	0.180595	−	0.312799i	0.942083	+	0.335379i	$0.108864\pi$
$312$	−6.07373	−	0.417890i	−0.343857	−	0.0236584i
$313$	−4.57485	−	3.83875i	−0.258586	−	0.216979i	0.504273	−	0.863544i	$-0.331760\pi$
$313$	−4.57485	−	3.83875i	−0.258586	−	0.216979i	−0.762859	+	0.646565i	$0.776205\pi$
$314$	−14.7451	−	18.4127i	−0.832111	−	1.03909i
$315$	0.398304	−	0.229961i	0.0224419	−	0.0129568i
$316$	2.56070	−	1.95611i	0.144051	−	0.110040i
$317$	6.10859	+	16.7832i	0.343093	+	0.942640i	0.984492	+	0.175432i	$0.0561322\pi$
$317$	6.10859	+	16.7832i	0.343093	+	0.942640i	−0.641399	+	0.767208i	$0.721646\pi$
$318$	−8.05210	−	0.184411i	−0.451539	−	0.0103412i
$319$	4.45604	−	25.2715i	0.249491	−	1.41493i
$320$	0.530235	−	0.0197040i	0.0296411	−	0.00110149i
$321$	−3.56619	+	2.99239i	−0.199045	+	0.167019i
$322$	−7.92101	+	39.5977i	−0.441420	+	2.20669i
$323$	−4.21017	−	14.4093i	−0.234260	−	0.801754i
$324$	−2.01871	−	0.841297i	−0.112150	−	0.0467387i
$325$	−6.95834	−	8.29263i	−0.385979	−	0.459992i
$326$	−15.6030	−	9.49126i	−0.864173	−	0.525672i
$327$	3.30351	−	18.7351i	0.182684	−	1.03605i
$328$	19.4449	+	8.63137i	1.07366	+	0.476588i
$329$	−17.0678	+	6.21218i	−0.940979	+	0.342488i
$330$	0.356831	−	0.406001i	0.0196429	−	0.0223496i
$331$	8.10842	−	4.68140i	0.445679	−	0.257313i	−0.260325	−	0.965521i	$-0.583830\pi$
$331$	8.10842	−	4.68140i	0.445679	−	0.257313i	0.706004	+	0.708208i	$0.250496\pi$
$332$	17.5712	−	9.09876i	0.964348	−	0.499359i
$333$	−0.811875	+	0.967555i	−0.0444905	+	0.0530217i
$334$	−17.8368	+	6.03326i	−0.975985	+	0.330125i
$335$	−0.0444452	+	0.0769813i	−0.00242830	+	0.00420594i
$336$	5.83702	−	12.3774i	0.318435	−	0.675244i
$337$	3.56493	+	20.2177i	0.194194	+	1.10133i	0.913562	+	0.406701i	$0.133321\pi$
$337$	3.56493	+	20.2177i	0.194194	+	1.10133i	−0.719367	+	0.694630i	$0.755568\pi$
$338$	−10.9409	−	4.26832i	−0.595108	−	0.232166i
$339$	−0.945206	+	2.59693i	−0.0513366	+	0.141046i
$340$	−0.136431	−	0.435991i	−0.00739903	−	0.0236450i
$341$			26.6564i			1.44352i
$342$	10.1635	+	7.12300i	0.549577	+	0.385168i
$343$	7.36160			0.397489
$344$	−2.25265	+	0.239311i	−0.121455	+	0.0129028i
$345$	0.513256	+	0.186810i	0.0276328	+	0.0100575i
$346$	−9.24588	+	23.6998i	−0.497062	+	1.27411i
$347$	−6.07927	+	1.07194i	−0.326352	+	0.0575447i	−0.334424	−	0.942423i	$-0.608542\pi$
$347$	−6.07927	+	1.07194i	−0.326352	+	0.0575447i	0.00807166	+	0.999967i	$0.497431\pi$
$348$	−8.77817	−	0.402290i	−0.470559	−	0.0215650i
$349$	1.29750	+	0.749109i	0.0694533	+	0.0400989i	0.534325	−	0.845279i	$-0.320566\pi$
$349$	1.29750	+	0.749109i	0.0694533	+	0.0400989i	−0.464871	+	0.885378i	$0.653899\pi$
$350$	23.0500	−	7.79661i	1.23207	−	0.416747i
$351$	−8.26640	−	6.93633i	−0.441228	−	0.370234i
$352$	−3.74915	+	32.6030i	−0.199830	+	1.73775i
$353$	5.88413	+	10.1916i	0.313181	+	0.542445i	0.979049	−	0.203624i	$-0.0652721\pi$
$353$	5.88413	+	10.1916i	0.313181	+	0.542445i	−0.665868	+	0.746069i	$0.731939\pi$
$354$	−6.89874	−	6.06325i	−0.366664	−	0.322258i
$355$	0.216627	+	0.595178i	0.0114974	+	0.0315888i
$356$	5.60543	−	25.0281i	0.297087	−	1.32649i
$357$	−11.6033	−	2.04598i	−0.614113	−	0.108285i
$358$	−2.79216	−	1.69846i	−0.147570	−	0.0897663i
$359$	−14.9043	+	12.5062i	−0.786620	+	0.660053i	−0.944906	−	0.327341i	$-0.893848\pi$
$359$	−14.9043	+	12.5062i	−0.786620	+	0.660053i	0.158286	+	0.987393i	$0.449403\pi$
$360$	0.313358	+	0.210853i	0.0165154	+	0.0111129i
$361$	−12.8546	−	13.9914i	−0.676556	−	0.736391i
$362$	−18.4374	−	3.68816i	−0.969048	−	0.193845i
$363$	14.4660	+	17.2399i	0.759267	+	0.904860i
$364$	−10.1083	+	10.9835i	−0.529818	+	0.575689i
$365$	0.125817	+	0.0221848i	0.00658554	+	0.00116121i
$366$	−9.88991	−	0.226501i	−0.516954	−	0.0118394i
$367$	7.83779	−	2.85272i	0.409129	−	0.148911i	−0.129253	−	0.991612i	$-0.541258\pi$
$367$	7.83779	−	2.85272i	0.409129	−	0.148911i	0.538382	+	0.842701i	$0.319036\pi$
$368$	−32.0691	+	8.44437i	−1.67172	+	0.440193i
$369$	7.57181	+	13.1148i	0.394173	+	0.682727i
$370$	0.0459311	−	0.0367820i	0.00238784	−	0.00191220i
$371$	−12.6935	+	15.1275i	−0.659012	+	0.785380i
$372$	9.05258	−	1.17188i	0.469354	−	0.0607591i
$373$	16.6867	+	9.63405i	0.864003	+	0.498832i	0.865351	−	0.501167i	$-0.167096\pi$
$373$	16.6867	+	9.63405i	0.864003	+	0.498832i	−0.00134766	+	0.999999i	$0.500429\pi$
$374$	27.9314	−	4.26814i	1.44430	−	0.220700i
$375$	−0.114352	−	0.648521i	−0.00590510	−	0.0334895i
$376$	−10.7411	−	10.3494i	−0.553931	−	0.533729i
$377$	9.00700	+	3.27828i	0.463884	+	0.168840i
$378$	21.2784	−	11.6438i	1.09444	−	0.598893i
$379$		−	21.5137i		−	1.10508i	−0.833485	−	0.552542i	$-0.813658\pi$
$379$		−	21.5137i		−	1.10508i	0.833485	−	0.552542i	$-0.186342\pi$
$380$	−0.399209	−	0.418280i	−0.0204790	−	0.0214573i
$381$		−	20.0169i		−	1.02549i
$382$	−1.30618	−	2.38697i	−0.0668300	−	0.122128i
$383$	0.180501	+	0.0656971i	0.00922319	+	0.00335697i	0.346628	−	0.938003i	$-0.387327\pi$
$383$	0.180501	+	0.0656971i	0.00922319	+	0.00335697i	−0.337404	+	0.941360i	$0.609549\pi$
$384$	11.2369	−	0.160086i	0.573431	−	0.00816937i
$385$	−0.230130	−	1.30513i	−0.0117285	−	0.0665158i
$386$	−1.50222	−	9.83076i	−0.0764608	−	0.500372i
$387$	−1.39647	−	0.806252i	−0.0709865	−	0.0409841i
$388$	3.03097	+	23.4138i	0.153874	+	1.18865i
$389$	20.1622	−	24.0284i	1.02226	−	1.21829i	0.0466223	−	0.998913i	$-0.485154\pi$
$389$	20.1622	−	24.0284i	1.02226	−	1.21829i	0.975641	−	0.219373i	$-0.0704013\pi$
$390$	0.126202	+	0.157593i	0.00639046	+	0.00798002i
$391$	14.2761	+	24.7269i	0.721973	+	1.25049i
$392$	−6.04299	−	12.3549i	−0.305217	−	0.624015i
$393$	−2.84157	+	1.03425i	−0.143338	+	0.0521708i
$394$	0.518741	−	22.6503i	0.0261338	−	1.14110i
$395$	−0.105238	−	0.0185563i	−0.00529510	−	0.000933669i
$396$	−15.8193	+	17.1889i	−0.794949	+	0.863776i
$397$	14.8800	+	17.7333i	0.746808	+	0.890011i	0.996938	−	0.0782012i	$-0.0249177\pi$
$397$	14.8800	+	17.7333i	0.746808	+	0.890011i	−0.250130	+	0.968212i	$0.580473\pi$
$398$	−0.876418	+	4.38128i	−0.0439309	+	0.219614i
$399$	−14.3141	+	4.18235i	−0.716600	+	0.209379i
$400$	14.0684	+	14.1907i	0.703422	+	0.709535i
$401$	1.34027	−	1.12462i	0.0669299	−	0.0561609i	−0.608709	−	0.793394i	$-0.708312\pi$
$401$	1.34027	−	1.12462i	0.0669299	−	0.0561609i	0.675639	+	0.737233i	$0.263868\pi$
$402$	−0.978425	+	1.60847i	−0.0487994	+	0.0802232i
$403$	−9.80545	−	1.72897i	−0.488444	−	0.0861259i
$404$	−26.4984	−	5.93473i	−1.31835	−	0.295264i
$405$	0.0248055	+	0.0681526i	0.00123260	+	0.00338653i
$406$	−14.2232	+	16.1831i	−0.705886	+	0.803155i
$407$	1.81975	+	3.15190i	0.0902017	+	0.156234i
$408$	−2.67741	−	9.29796i	−0.132551	−	0.460318i
$409$	10.2938	+	8.63753i	0.508996	+	0.427098i	0.860776	−	0.508985i	$-0.169979\pi$
$409$	10.2938	+	8.63753i	0.508996	+	0.427098i	−0.351780	+	0.936083i	$0.614423\pi$
$410$	−0.226058	−	0.668321i	−0.0111642	−	0.0330060i
$411$	1.60386	+	0.925989i	0.0791126	+	0.0456757i
$412$	−1.62779	−	0.0745990i	−0.0801954	−	0.00367523i
$413$	−22.1768	+	3.91036i	−1.09125	+	0.192416i
$414$	−21.9913	−	8.57935i	−1.08081	−	0.421652i
$415$	−0.616624	−	0.224433i	−0.0302689	−	0.0110170i
$416$	−11.7497	−	3.49378i	−0.576078	−	0.171297i
$417$	−10.7505			−0.526454
$418$	29.3036	−	20.5000i	1.43329	−	1.00269i
$419$			19.8153i			0.968040i	0.875057	+	0.484020i	$0.160824\pi$
$419$			19.8153i			0.968040i	−0.875057	+	0.484020i	$0.839176\pi$
$420$	−0.433111	+	0.135530i	−0.0211336	+	0.00661318i
$421$	6.66692	−	18.3172i	0.324926	−	0.892726i	−0.664449	−	0.747334i	$-0.731334\pi$
$421$	6.66692	−	18.3172i	0.324926	−	0.892726i	0.989374	−	0.145392i	$-0.0464442\pi$
$422$	2.34988	−	6.02341i	0.114390	−	0.293215i
$423$	−1.84369	−	10.4561i	−0.0896432	−	0.508392i
$424$	−15.7396	−	3.90562i	−0.764380	−	0.189674i
$425$	8.60226	−	14.8996i	0.417271	−	0.722735i
$426$	4.29829	+	12.7075i	0.208253	+	0.615681i
$427$	−15.5906	+	18.5802i	−0.754483	+	0.899158i
$428$	−8.32361	+	4.31014i	−0.402337	+	0.208338i
$429$	−10.8144	+	6.24369i	−0.522124	+	0.301448i
$430$	0.0564276	+	0.0495938i	0.00272118	+	0.00239162i
$431$	36.2781	−	13.2042i	1.74745	−	0.636022i	0.747843	−	0.663876i	$-0.231090\pi$
$431$	36.2781	−	13.2042i	1.74745	−	0.636022i	0.999612	+	0.0278541i	$0.00886738\pi$
$432$	16.2673	+	11.4957i	0.782660	+	0.553086i
$433$	6.30643	−	35.7655i	0.303068	−	1.71878i	−0.329396	−	0.944192i	$-0.606845\pi$
$433$	6.30643	−	35.7655i	0.303068	−	1.71878i	0.632463	−	0.774590i	$-0.282044\pi$
$434$	11.6311	−	19.1208i	0.558312	−	0.917830i
$435$	0.187316	+	0.223235i	0.00898113	+	0.0107033i
$436$	14.7350	−	35.3569i	0.705679	−	1.69329i
$437$	30.0606	+	20.0574i	1.43799	+	0.959474i
$438$	2.65331	+	0.530761i	0.126780	+	0.0253607i
$439$	−2.80086	+	2.35020i	−0.133678	+	0.112169i	−0.707175	−	0.707038i	$-0.750031\pi$
$439$	−2.80086	+	2.35020i	−0.133678	+	0.112169i	0.573497	+	0.819207i	$0.305586\pi$
$440$	0.879757	−	0.640686i	0.0419408	−	0.0305435i
$441$	1.70003	−	9.64133i	0.0809537	−	0.459111i
$442$	−0.241648	+	10.5513i	−0.0114940	+	0.501875i
$443$	8.86001	+	24.3427i	0.420952	+	1.15656i	0.951163	+	0.308690i	$0.0998906\pi$
$443$	8.86001	+	24.3427i	0.420952	+	1.15656i	−0.530211	+	0.847866i	$0.677887\pi$
$444$	0.990394	−	0.756558i	0.0470020	−	0.0359046i
$445$	−0.736606	+	0.425280i	−0.0349185	+	0.0201602i
$446$	20.2652	−	16.2285i	0.959584	−	0.768443i
$447$	−2.49532	−	2.09382i	−0.118025	−	0.0990343i
$448$	16.9151	−	21.7505i	0.799166	−	1.02762i
$449$	7.43343	−	12.8751i	0.350805	−	0.607612i	−0.635586	−	0.772030i	$-0.719241\pi$
$449$	7.43343	−	12.8751i	0.350805	−	0.607612i	0.986391	+	0.164418i	$0.0525746\pi$
$450$	2.14858	+	14.0607i	0.101285	+	0.662826i
$451$	42.9735	−	7.57739i	2.02354	−	0.356806i
$452$	−2.99990	+	4.68650i	−0.141104	+	0.220434i
$453$	1.81851	−	4.99630i	0.0854409	−	0.234747i
$454$	−23.2978	+	12.7489i	−1.09342	+	0.598334i
$455$	0.495016			0.0232067
$456$	−8.25012	−	9.05037i	−0.386347	−	0.423822i
$457$	26.0434			1.21826			0.609129	−	0.793071i	$-0.291519\pi$
$457$	26.0434			1.21826			0.609129	+	0.793071i	$0.291519\pi$
$458$	29.1487	−	15.9506i	1.36203	−	0.745320i
$459$	5.86569	−	16.1158i	0.273787	−	0.752223i
$460$	0.926237	+	0.592899i	0.0431860	+	0.0276440i
$461$	15.3357	−	2.70410i	0.714254	−	0.125942i	0.195299	−	0.980744i	$-0.437432\pi$
$461$	15.3357	−	2.70410i	0.714254	−	0.125942i	0.518955	+	0.854801i	$0.326321\pi$
$462$	−4.23994	−	27.7469i	−0.197260	−	1.29090i
$463$	−4.53155	+	7.84888i	−0.210599	+	0.364768i	−0.951902	−	0.306402i	$-0.900875\pi$
$463$	−4.53155	+	7.84888i	−0.210599	+	0.364768i	0.741303	+	0.671170i	$0.234208\pi$
$464$	−17.0703	−	4.65321i	−0.792467	−	0.216020i
$465$	−0.231891	−	0.194579i	−0.0107537	−	0.00902341i
$466$	7.37095	−	5.90272i	0.341453	−	0.273438i
$467$	−14.6396	+	8.45219i	−0.677441	+	0.391121i	−0.798890	−	0.601477i	$-0.794579\pi$
$467$	−14.6396	+	8.45219i	−0.677441	+	0.391121i	0.121449	+	0.992598i	$0.461246\pi$
$468$	−5.29683	−	6.93397i	−0.244846	−	0.320523i
$469$	1.57877	+	4.33763i	0.0729007	+	0.200293i
$470$	−0.0113255	+	0.494517i	−0.000522408	+	0.0228104i
$471$	−2.87708	+	16.3167i	−0.132569	+	0.751835i
$472$	−10.8865	−	14.9488i	−0.501091	−	0.688073i
$473$	−3.55938	+	2.98668i	−0.163661	+	0.137328i
$474$	−2.21934	−	0.443950i	−0.101938	−	0.0203913i
$475$	1.40994	−	21.7296i	0.0646924	−	0.997024i
$476$	−21.8978	−	9.12591i	−1.00368	−	0.418285i
$477$	−7.42002	−	8.84284i	−0.339740	−	0.404886i
$478$	−14.2828	+	23.4800i	−0.653279	+	1.07395i
$479$	2.25090	−	12.7655i	0.102846	−	0.583270i	−0.889213	−	0.457494i	$-0.848747\pi$
$479$	2.25090	−	12.7655i	0.102846	−	0.583270i	0.992059	−	0.125775i	$-0.0401419\pi$
$480$	−0.256255	−	0.270602i	−0.0116964	−	0.0123512i
$481$	−1.27745	+	0.464953i	−0.0582466	+	0.0212000i
$482$	−14.1210	−	12.4108i	−0.643195	−	0.565299i
$483$	24.5635	−	14.1818i	1.11768	−	0.645293i
$484$	20.8363	+	40.2385i	0.947106	+	1.82902i
$485$	0.503264	−	0.599767i	0.0228521	−	0.0272340i
$486$	7.26176	+	21.4687i	0.329400	+	0.973841i
$487$	−13.9196	+	24.1094i	−0.630757	+	1.09250i	0.356640	+	0.934242i	$0.383922\pi$
$487$	−13.9196	+	24.1094i	−0.630757	+	1.09250i	−0.987397	+	0.158261i	$0.949411\pi$
$488$	−19.3320	−	4.79704i	−0.875116	−	0.217152i
$489$	2.22748	+	12.6327i	0.100730	+	0.571269i
$490$	−0.165769	+	0.424913i	−0.00748868	+	0.0191956i
$491$	3.97464	−	10.9202i	0.179373	−	0.492823i	−0.817123	−	0.576463i	$-0.804432\pi$
$491$	3.97464	−	10.9202i	0.179373	−	0.492823i	0.996496	+	0.0836400i	$0.0266546\pi$
$492$	−4.46253	−	14.2608i	−0.201186	−	0.642928i
$493$			15.2335i			0.686081i
$494$	5.64018	+	12.1089i	0.253764	+	0.544805i
$495$	0.774692			0.0348198
$496$	18.3021	+	1.68105i	0.821789	+	0.0754812i
$497$	30.9071	+	11.2493i	1.38637	+	0.504599i
$498$	−12.9477	−	5.05122i	−0.580201	−	0.226351i
$499$	−21.8031	+	3.84447i	−0.976039	+	0.172102i	−0.638847	−	0.769334i	$-0.720588\pi$
$499$	−21.8031	+	3.84447i	−0.976039	+	0.172102i	−0.337192	+	0.941436i	$0.609477\pi$
$500$	0.0607011	−	1.32453i	0.00271464	−	0.0592348i
$501$	11.4536	+	6.61271i	0.511707	+	0.295434i
$502$	−7.29029	−	21.5531i	−0.325382	−	0.961960i
$503$	−1.90284	−	1.59667i	−0.0848433	−	0.0711920i	0.599380	−	0.800465i	$-0.295414\pi$
$503$	−1.90284	−	1.59667i	−0.0848433	−	0.0711920i	−0.684223	+	0.729273i	$0.739858\pi$
$504$	18.8475	−	5.42724i	0.839532	−	0.241749i
$505$	0.450263	+	0.779879i	0.0200364	+	0.0347041i
$506$	−44.9038	+	51.0914i	−1.99622	+	2.27129i
$507$	2.82124	+	7.75129i	0.125296	+	0.344247i
$508$	8.80832	−	39.3290i	0.390806	−	1.74494i
$509$	19.2945	+	3.40215i	0.855215	+	0.150798i	0.584033	−	0.811730i	$-0.301474\pi$
$509$	19.2945	+	3.40215i	0.855215	+	0.150798i	0.271183	+	0.962528i	$0.412585\pi$
$510$	−0.166757	+	0.274138i	−0.00738413	+	0.0121391i
$511$	5.08220	−	4.26448i	0.224824	−	0.188649i
$512$	22.1486	+	4.63021i	0.978840	+	0.204628i
$513$	−2.37725	−	21.5759i	−0.104958	−	0.952599i
$514$	−2.88149	+	14.4048i	−0.127097	+	0.635368i
$515$	0.0347352	+	0.0413958i	0.00153061	+	0.00182412i
$516$	1.17076	+	1.07748i	0.0515400	+	0.0474332i
$517$	−30.1293	−	5.31260i	−1.32508	−	0.233648i
$518$	0.0699641	−	3.05491i	0.00307405	−	0.134225i
$519$	16.7906	−	6.11126i	0.737024	−	0.268255i
$520$	0.178612	+	0.365171i	0.00783265	+	0.0160138i
$521$	−21.5097	−	37.2558i	−0.942355	−	1.63221i	−0.760963	−	0.648796i	$-0.775273\pi$
$521$	−21.5097	−	37.2558i	−0.942355	−	1.63221i	−0.181392	−	0.983411i	$-0.558060\pi$
$522$	−7.87245	−	9.83063i	−0.344568	−	0.430275i
$523$	−15.9179	+	18.9702i	−0.696040	+	0.829509i	−0.992072	−	0.125670i	$-0.959892\pi$
$523$	−15.9179	+	18.9702i	−0.696040	+	0.829509i	0.296032	+	0.955178i	$0.404337\pi$
$524$	−6.03820	+	0.781660i	−0.263780	+	0.0341470i
$525$	−14.8011	−	8.54542i	−0.645973	−	0.372953i
$526$	5.13107	+	33.5786i	0.223725	+	1.46410i
$527$	−2.74784	−	15.5838i	−0.119698	−	0.678839i
$528$	18.9389	−	13.1394i	0.824210	−	0.571820i
$529$	−42.9755	−	15.6418i	−1.86850	−	0.680079i
$530$	0.258163	+	0.471778i	0.0112139	+	0.0204927i
$531$		−	13.1635i		−	0.571248i
$532$	−29.9646	+	1.91861i	−1.29913	+	0.0831822i
$533$			16.2991i			0.705994i
$534$	−15.8033	+	8.64778i	−0.683877	+	0.374226i
$535$	0.292098	+	0.106315i	0.0126285	+	0.00459640i
$536$	−2.63020	+	2.72976i	−0.113607	+	0.117908i
$537$	0.398607	+	2.26061i	0.0172012	+	0.0975526i
$538$	−28.4899	+	4.35348i	−1.22829	+	0.187692i
$539$	−24.4307	−	14.1051i	−1.05231	−	0.607549i
$540$	−0.0848051	−	0.655106i	−0.00364943	−	0.0281913i
$541$	−1.86864	+	2.22696i	−0.0803390	+	0.0957443i	−0.804717	−	0.593659i	$-0.797683\pi$
$541$	−1.86864	+	2.22696i	−0.0803390	+	0.0957443i	0.724378	+	0.689403i	$0.242127\pi$
$542$	4.22313	−	3.38191i	0.181399	−	0.145266i
$543$	6.60328	+	11.4372i	0.283374	+	0.490818i
$544$	−1.16902	−	19.4467i	−0.0501215	−	0.833772i
$545$	−1.19367	+	0.434460i	−0.0511311	+	0.0186102i
$546$	10.4816	+	0.240052i	0.448571	+	0.0102733i
$547$	36.3250	+	6.40508i	1.55315	+	0.273861i	0.883361	−	0.468694i	$-0.155275\pi$
$547$	36.3250	+	6.40508i	1.55315	+	0.273861i	0.669785	+	0.742555i	$0.266386\pi$
$548$	2.74377	+	2.52515i	0.117208	+	0.107869i
$549$	−9.11357	−	10.8611i	−0.388958	−	0.463542i
$550$	40.1900	+	8.03949i	1.71371	+	0.342805i
$551$	8.53893	+	17.2867i	0.363770	+	0.736437i
$552$	19.3249	+	13.0034i	0.822521	+	0.553460i
$553$	−4.25096	+	3.56698i	−0.180769	+	0.151683i
$554$	4.28941	+	2.60923i	0.182240	+	0.110856i
$555$	−0.0407026	−	0.00717696i	−0.00172773	−	0.000304645i
$556$	−21.1225	−	4.73070i	−0.895793	−	0.200626i
$557$	−4.40046	−	12.0902i	−0.186453	−	0.512276i	0.810884	−	0.585207i	$-0.198987\pi$
$557$	−4.40046	−	12.0902i	−0.186453	−	0.512276i	−0.997337	+	0.0729310i	$0.976765\pi$
$558$	9.82673	+	8.63663i	0.415999	+	0.365618i
$559$	−0.867773	−	1.50303i	−0.0367029	−	0.0635712i
$560$	−0.910611	+	0.0756999i	−0.0384804	+	0.00319890i
$561$	−15.2030	−	12.7568i	−0.641872	−	0.538595i
$562$	10.6956	−	3.61776i	0.451165	−	0.152606i
$563$	−11.5218	−	6.65214i	−0.485588	−	0.280354i	0.237154	−	0.971472i	$-0.423785\pi$
$563$	−11.5218	−	6.65214i	−0.485588	−	0.280354i	−0.722742	+	0.691118i	$0.757119\pi$
$564$	−0.479620	+	10.4655i	−0.0201956	+	0.440679i
$565$	0.181727	−	0.0320434i	0.00764531	−	0.00134807i
$566$	−16.7958	+	43.0525i	−0.705981	+	1.80963i
$567$	3.53911	+	1.28813i	0.148629	+	0.0540965i
$568$	2.85338	+	26.8590i	0.119725	+	1.12698i
$569$	24.8586			1.04213			0.521064	−	0.853518i	$-0.325535\pi$
$569$	24.8586			1.04213			0.521064	+	0.853518i	$0.325535\pi$
$570$	−0.0355683	+	0.404561i	−0.00148979	+	0.0169452i
$571$			26.2382i			1.09804i	0.835810	+	0.549018i	$0.184998\pi$
$571$			26.2382i			1.09804i	−0.835810	+	0.549018i	$0.815002\pi$
$572$	−23.9955	+	7.50873i	−1.00330	+	0.313956i
$573$	−0.653654	+	1.79590i	−0.0273068	+	0.0750248i
$574$	−34.1316	−	13.3156i	−1.42462	−	0.555781i
$575$	7.19188	+	40.7872i	0.299922	+	1.70094i
$576$	10.8042	+	11.9454i	0.450175	+	0.497726i
$577$	−11.7884	+	20.4182i	−0.490759	+	0.850020i	−0.999943	−	0.0106376i	$-0.996614\pi$
$577$	−11.7884	+	20.4182i	−0.490759	+	0.850020i	0.509184	+	0.860658i	$0.329947\pi$
$578$	6.88488	−	2.32880i	0.286373	−	0.0968654i
$579$	−4.48991	+	5.35086i	−0.186594	+	0.222374i
$580$	0.269804	+	0.521038i	0.0112030	+	0.0216349i
$581$	−29.5105	+	17.0379i	−1.22430	+	0.706852i
$582$	10.9471	−	12.4556i	0.453772	−	0.516300i
$583$	−31.2567	+	11.3765i	−1.29452	+	0.471167i
$584$	4.97965	+	2.21041i	0.206059	+	0.0914675i
$585$	−0.0502475	+	0.284968i	−0.00207748	+	0.0117820i
$586$	26.3238	+	16.0127i	1.08743	+	0.661477i
$587$	29.6107	+	35.2887i	1.22217	+	1.45652i	0.848698	+	0.528878i	$0.177387\pi$
$587$	29.6107	+	35.2887i	1.22217	+	1.45652i	0.373468	+	0.927643i	$0.378169\pi$
$588$	−3.71609	+	8.91684i	−0.153249	+	0.367724i
$589$	−11.8535	−	16.1439i	−0.488413	−	0.665197i
$590$	−0.120293	+	0.601354i	−0.00495238	+	0.0247573i
$591$	−12.1902	+	10.2288i	−0.501439	+	0.420757i
$592$	2.27884	−	1.05066i	0.0936597	−	0.0431819i
$593$	−4.75919	+	26.9907i	−0.195436	+	1.10837i	0.716360	+	0.697731i	$0.245807\pi$
$593$	−4.75919	+	26.9907i	−0.195436	+	1.10837i	−0.911796	+	0.410643i	$0.865304\pi$
$594$	40.8459	+	0.935461i	1.67593	+	0.0383824i
$595$	0.269076	+	0.739281i	0.0110311	+	0.0303076i
$596$	−3.98141	−	5.21197i	−0.163085	−	0.213491i
$597$	2.71783	−	1.56914i	0.111233	−	0.0642206i
$598$	−15.8813	−	19.8316i	−0.649434	−	0.810973i
$599$	−7.17544	−	6.02091i	−0.293180	−	0.246008i	0.484319	−	0.874892i	$-0.339068\pi$
$599$	−7.17544	−	6.02091i	−0.293180	−	0.246008i	−0.777499	+	0.628884i	$0.783512\pi$
$600$	0.963384	−	14.0021i	0.0393300	−	0.571633i
$601$	11.3846	−	19.7186i	0.464386	−	0.804340i	−0.534788	−	0.844986i	$-0.679608\pi$
$601$	11.3846	−	19.7186i	0.464386	−	0.804340i	0.999174	+	0.0406466i	$0.0129418\pi$
$602$	3.85637	−	0.589283i	0.157174	−	0.0240174i
$603$	−2.65731	+	0.468556i	−0.108214	+	0.0190811i
$604$	5.77159	−	9.01647i	0.234842	−	0.366875i
$605$	0.513955	−	1.41208i	0.0208952	−	0.0574092i
$606$	9.15580	+	16.7317i	0.371929	+	0.679679i
$607$	−7.13126			−0.289449			−0.144725	−	0.989472i	$-0.546230\pi$
$607$	−7.13126			−0.289449			−0.144725	+	0.989472i	$0.546230\pi$
$608$	−12.2272	−	21.4125i	−0.495878	−	0.868392i
$609$	15.1328			0.613213
$610$	0.317086	+	0.579456i	0.0128384	+	0.0234615i
$611$	3.90845	−	10.7384i	0.158119	−	0.434428i
$612$	7.47632	−	11.6796i	0.302212	−	0.472122i
$613$	18.6048	−	3.28053i	0.751442	−	0.132499i	0.215207	−	0.976568i	$-0.430957\pi$
$613$	18.6048	−	3.28053i	0.751442	−	0.132499i	0.536235	+	0.844069i	$0.319846\pi$
$614$	1.39740	−	0.213533i	0.0563944	−	0.00861749i
$615$	−0.247770	+	0.429150i	−0.00999104	+	0.0173050i
$616$	3.87928	−	56.3826i	0.156301	−	2.27172i
$617$	−7.65606	−	6.42419i	−0.308221	−	0.258628i	0.475535	−	0.879697i	$-0.342254\pi$
$617$	−7.65606	−	6.42419i	−0.308221	−	0.258628i	−0.783756	+	0.621068i	$0.786699\pi$
$618$	0.715418	+	0.893370i	0.0287783	+	0.0359366i
$619$	29.5752	−	17.0753i	1.18873	−	0.686313i	0.230711	−	0.973022i	$-0.425895\pi$
$619$	29.5752	−	17.0753i	1.18873	−	0.686313i	0.958017	+	0.286710i	$0.0925615\pi$
$620$	−0.369993	−	0.484351i	−0.0148593	−	0.0194520i
$621$	14.1204	+	38.7956i	0.566634	+	1.55681i
$622$	−9.00568	−	0.206250i	−0.361095	−	0.00826987i
$623$	−7.66985	+	43.4979i	−0.307286	+	1.74271i
$624$	3.60489	+	7.81885i	0.144311	+	0.313005i
$625$	19.1006	−	16.0273i	0.764023	−	0.641092i
$626$	−1.65664	+	8.28167i	−0.0662126	+	0.331002i
$627$	−24.4028	−	5.95438i	−0.974553	−	0.237795i
$628$	−12.8330	+	30.7929i	−0.512091	+	1.22877i
$629$	−1.38877	−	1.65507i	−0.0553737	−	0.0659918i
$630$	−0.555693	−	0.338026i	−0.0221393	−	0.0134673i
$631$	0.394807	−	2.23906i	0.0157170	−	0.0891355i	−0.975940	−	0.218038i	$-0.930034\pi$
$631$	0.394807	−	2.23906i	0.0157170	−	0.0891355i	0.991657	+	0.128902i	$0.0411454\pi$
$632$	−4.16518	−	1.84888i	−0.165682	−	0.0735444i
$633$	−4.26739	+	1.55320i	−0.169613	+	0.0617343i
$634$	16.6745	−	18.9722i	0.662229	−	0.753482i
$635$	−1.15750	+	0.668280i	−0.0459338	+	0.0265199i
$636$	5.23762	+	10.1147i	0.207685	+	0.401076i
$637$	6.77311	−	8.07188i	0.268360	−	0.319820i
$638$	−34.3773	+	11.6281i	−1.36101	+	0.460359i
$639$	−9.61320	+	16.6505i	−0.380292	+	0.658685i
$640$	−0.384411	−	0.644441i	−0.0151952	−	0.0254738i
$641$	−4.61846	−	26.1926i	−0.182418	−	1.03455i	−0.929228	−	0.369507i	$-0.879526\pi$
$641$	−4.61846	−	26.1926i	−0.182418	−	1.03455i	0.746810	−	0.665038i	$-0.231585\pi$
$642$	6.13341	+	2.39279i	0.242066	+	0.0944360i
$643$	3.12884	−	8.59641i	0.123389	−	0.339009i	−0.862584	−	0.505914i	$-0.831155\pi$
$643$	3.12884	−	8.59641i	0.123389	−	0.339009i	0.985973	+	0.166905i	$0.0533774\pi$
$644$	54.5029	−	17.0552i	2.14771	−	0.672067i
$645$		−	0.0527654i		−	0.00207764i
$646$	−15.0182	+	15.0054i	−0.590882	+	0.590378i
$647$	6.52267			0.256433			0.128216	−	0.991746i	$-0.459075\pi$
$647$	6.52267			0.256433			0.128216	+	0.991746i	$0.459075\pi$
$648$	0.326735	+	3.07558i	0.0128354	+	0.120820i
$649$	−35.6433	−	12.9731i	−1.39912	−	0.509238i
$650$	−5.56407	+	14.2623i	−0.218241	+	0.559414i
$651$	−15.4808	+	2.72968i	−0.606740	+	0.106985i
$652$	−1.18241	+	25.8008i	−0.0463067	+	1.01044i
$653$	−13.9261	−	8.04025i	−0.544971	−	0.314639i	0.202120	−	0.979361i	$-0.435217\pi$
$653$	−13.9261	−	8.04025i	−0.544971	−	0.314639i	−0.747091	+	0.664721i	$0.768550\pi$
$654$	−25.4857	+	8.62051i	−0.996571	+	0.337089i
$655$	0.154675	+	0.129787i	0.00604363	+	0.00507121i
$656$	−2.49253	−	29.9833i	−0.0973171	−	1.17065i
$657$	1.93907	+	3.35857i	0.0756503	+	0.131030i
$658$	19.2939	+	16.9573i	0.752155	+	0.661063i
$659$	−2.61235	−	7.17736i	−0.101763	−	0.279590i	0.878355	−	0.478009i	$-0.158642\pi$
$659$	−2.61235	−	7.17736i	−0.101763	−	0.279590i	−0.980117	+	0.198419i	$0.936419\pi$
$660$	−0.745936	−	0.167064i	−0.0290355	−	0.00650294i
$661$	−39.3240	−	6.93388i	−1.52953	−	0.269697i	−0.655357	−	0.755319i	$-0.727482\pi$
$661$	−39.3240	−	6.93388i	−1.52953	−	0.269697i	−0.874169	+	0.485622i	$0.838593\pi$
$662$	−11.3124	−	6.88131i	−0.439671	−	0.267450i
$663$	5.67865	−	4.76495i	0.220540	−	0.185055i
$664$	−23.2168	−	15.6222i	−0.900987	−	0.606258i
$665$	0.719737	+	0.688095i	0.0279102	+	0.0266832i
$666$	1.75153	+	0.350370i	0.0678703	+	0.0135766i
$667$	−23.5720	−	28.0920i	−0.912711	−	1.08773i
$668$	19.5940	+	18.0327i	0.758113	+	0.697706i
$669$	−17.9583	−	3.16654i	−0.694309	−	0.122425i
$670$	0.125677	+	0.00287828i	0.00485532	+	0.000111198i
$671$	−38.3908	+	13.9731i	−1.48206	+	0.539425i
$672$	−19.3182	+	1.16130i	−0.745217	+	0.0447981i
$673$	6.05201	+	10.4824i	0.233288	+	0.404066i	0.958774	−	0.284171i	$-0.0917183\pi$
$673$	6.05201	+	10.4824i	0.233288	+	0.404066i	−0.725486	+	0.688237i	$0.758385\pi$
$674$	22.6622	−	18.1481i	0.872917	−	0.699039i
$675$	15.9907	−	19.0570i	0.615482	−	0.733503i
$676$	2.13223	+	16.4711i	0.0820089	+	0.633506i
$677$	−22.4267	−	12.9480i	−0.861926	−	0.497633i	0.00273047	−	0.999996i	$-0.499131\pi$
$677$	−22.4267	−	12.9480i	−0.861926	−	0.497633i	−0.864657	+	0.502363i	$0.832464\pi$
$678$	3.86347	−	0.590368i	0.148376	−	0.0226730i
$679$	−7.06010	−	40.0398i	−0.270942	−	1.53659i
$680$	−0.448277	+	0.465244i	−0.0171906	+	0.0178413i
$681$	17.5287	+	6.37993i	0.671702	+	0.244480i
$682$	33.0702	−	18.0965i	1.26633	−	0.692949i
$683$		−	11.5939i		−	0.443630i	−0.975089	−	0.221815i	$-0.928802\pi$
$683$		−	11.5939i		−	0.443630i	0.975089	−	0.221815i	$-0.0711980\pi$
$684$	1.93712	−	17.4446i	0.0740676	−	0.667011i
$685$		−	0.123660i		−	0.00472480i
$686$	−4.99764	−	9.13290i	−0.190811	−	0.348696i
$687$	−21.9308	−	7.98216i	−0.836712	−	0.304538i
$688$	1.82617	+	2.63220i	0.0696220	+	0.100352i
$689$	−2.15746	−	12.2356i	−0.0821928	−	0.466138i
$690$	−0.116680	−	0.763574i	−0.00444193	−	0.0290688i
$691$	−29.3550	−	16.9481i	−1.11672	−	0.644737i	−0.176156	−	0.984362i	$-0.556366\pi$
$691$	−29.3550	−	16.9481i	−1.11672	−	0.644737i	−0.940561	+	0.339625i	$0.889700\pi$
$692$	35.6792	−	4.61876i	1.35632	−	0.175579i
$693$	25.8588	−	30.8173i	0.982295	−	1.17065i
$694$	5.45696	+	6.81431i	0.207143	+	0.258668i
$695$	0.358915	+	0.621658i	0.0136144	+	0.0235808i
$696$	5.46023	+	11.1634i	0.206970	+	0.423149i
$697$	−24.3419	+	8.85974i	−0.922017	+	0.335587i
$698$	0.0485125	−	2.11825i	0.00183622	−	0.0801768i
$699$	−6.53189	−	1.15175i	−0.247059	−	0.0435631i
$700$	−25.3207	−	23.3031i	−0.957034	−	0.880776i
$701$	7.33690	+	8.74378i	0.277111	+	0.330248i	0.886592	−	0.462553i	$-0.153066\pi$
$701$	7.33690	+	8.74378i	0.277111	+	0.330248i	−0.609481	+	0.792801i	$0.708622\pi$
$702$	−2.99342	+	14.9643i	−0.112979	+	0.564793i
$703$	−2.50367	−	1.09968i	−0.0944277	−	0.0414754i
$704$	42.9930	−	17.4823i	1.62036	−	0.658888i
$705$	0.266146	−	0.223323i	0.0100236	−	0.00841083i
$706$	8.64924	−	14.2188i	0.325519	−	0.535132i
$707$	46.0532	+	8.12042i	1.73201	+	0.305400i
$708$	−2.83874	+	12.6749i	−0.106686	+	0.476352i
$709$	−11.0909	−	30.4720i	−0.416528	−	1.14440i	−0.953656	−	0.300901i	$-0.902713\pi$
$709$	−11.0909	−	30.4720i	−0.416528	−	1.14440i	0.537127	−	0.843501i	$-0.319509\pi$
$710$	0.591322	−	0.672804i	0.0221919	−	0.0252499i
$711$	−1.62191	−	2.80924i	−0.0608266	−	0.105355i
$712$	−34.8557	+	10.0369i	−1.30627	+	0.376149i
$713$	29.1813	+	24.4860i	1.09285	+	0.917007i
$714$	5.33899	+	15.7842i	0.199807	+	0.590710i
$715$	0.722095	+	0.416902i	0.0270048	+	0.0155913i
$716$	−0.211592	+	4.61704i	−0.00790755	+	0.172547i
$717$	19.0101	−	3.35199i	0.709945	−	0.125182i
$718$	25.6336	+	10.0003i	0.956638	+	0.373208i
$719$	39.1650	+	14.2549i	1.46061	+	0.531617i	0.945532	−	0.325529i	$-0.105542\pi$
$719$	39.1650	+	14.2549i	1.46061	+	0.531617i	0.515074	+	0.857146i	$0.327764\pi$
$720$	0.0488548	−	0.531899i	0.00182071	−	0.0198227i
$721$	2.80617			0.104507
$722$	−8.63128	+	25.4460i	−0.321223	+	0.947004i
$723$			13.2046i			0.491083i
$724$	7.94118	+	25.3775i	0.295132	+	0.943147i
$725$	−7.55759	+	20.7643i	−0.280682	+	0.771167i
$726$	11.5674	−	29.6505i	0.429306	−	1.10043i
$727$	−4.65171	−	26.3811i	−0.172522	−	0.978422i	−0.940965	−	0.338504i	$-0.890079\pi$
$727$	−4.65171	−	26.3811i	−0.172522	−	0.978422i	0.768443	−	0.639918i	$-0.221032\pi$
$728$	20.4885	+	5.08403i	0.759355	+	0.188427i
$729$	6.31896	−	10.9448i	0.234035	−	0.405361i
$730$	−0.0578914	−	0.171151i	−0.00214266	−	0.00633457i
$731$	1.77300	−	2.11298i	0.0655767	−	0.0781512i
$732$	6.43306	+	12.4233i	0.237773	+	0.459180i
$733$	−18.2927	+	10.5613i	−0.675658	+	0.390091i	−0.798217	−	0.602370i	$-0.794223\pi$
$733$	−18.2927	+	10.5613i	−0.675658	+	0.390091i	0.122559	+	0.992461i	$0.460890\pi$
$734$	−8.86004	−	7.78702i	−0.327030	−	0.287424i
$735$	0.301037	−	0.109569i	0.0111039	−	0.00404150i
$736$	32.2473	+	34.0527i	1.18865	+	1.25520i
$737$	−1.35015	+	7.65707i	−0.0497334	+	0.282052i
$738$	11.1300	−	18.2970i	0.409701	−	0.673523i
$739$	−13.2819	−	15.8287i	−0.488582	−	0.582269i	0.464274	−	0.885691i	$-0.346315\pi$
$739$	−13.2819	−	15.8287i	−0.488582	−	0.582269i	−0.952856	+	0.303422i	$0.901871\pi$
$740$	−0.0768139	−	0.0320122i	−0.00282374	−	0.00117679i
$741$	3.77309	−	8.59027i	0.138608	−	0.315571i
$742$	27.3847	+	5.47795i	1.00532	+	0.201102i
$743$	22.6446	−	19.0010i	0.830748	−	0.697081i	−0.124714	−	0.992193i	$-0.539801\pi$
$743$	22.6446	−	19.0010i	0.830748	−	0.697081i	0.955463	+	0.295112i	$0.0953569\pi$
$744$	−7.59946	−	10.4352i	−0.278610	−	0.382573i
$745$	−0.0377690	+	0.214198i	−0.00138375	+	0.00784762i
$746$	0.623904	−	27.2421i	0.0228427	−	0.997403i
$747$	−6.81276	−	18.7179i	−0.249266	−	0.684852i
$748$	−24.2572	−	31.7546i	−0.886930	−	1.16106i
$749$	13.9793	−	8.07096i	0.510793	−	0.294906i
$750$	−0.726933	+	0.582134i	−0.0265439	+	0.0212565i
$751$	18.9976	+	15.9409i	0.693233	+	0.581692i	0.919840	−	0.392295i	$-0.128319\pi$
$751$	18.9976	+	15.9409i	0.693233	+	0.581692i	−0.226607	+	0.973986i	$0.572763\pi$
$752$	−5.54767	+	20.3516i	−0.202303	+	0.742145i
$753$	−7.99047	+	13.8399i	−0.291189	+	0.504354i
$754$	−2.04759	−	13.3998i	−0.0745688	−	0.487991i
$755$	−0.349629	+	0.0616490i	−0.0127243	+	0.00224364i
$756$	−28.8909	−	18.4935i	−1.05075	−	0.672603i
$757$	15.5822	−	42.8116i	0.566343	−	1.55601i	−0.243827	−	0.969819i	$-0.578403\pi$
$757$	15.5822	−	42.8116i	0.566343	−	1.55601i	0.810170	−	0.586196i	$-0.199375\pi$
$758$	−26.6902	+	14.6052i	−0.969431	+	0.530485i
$759$	47.7755			1.73414
$760$	−0.247909	+	0.779226i	−0.00899262	+	0.0282655i
$761$	−16.6714			−0.604339			−0.302170	−	0.953254i	$-0.597711\pi$
$761$	−16.6714			−0.604339			−0.302170	+	0.953254i	$0.597711\pi$
$762$	−24.8332	+	13.5890i	−0.899611	+	0.492279i
$763$	−22.5612	+	61.9863i	−0.816769	+	2.24405i
$764$	−2.07457	+	3.24093i	−0.0750554	+	0.117253i
$765$	−0.452898	+	0.0798581i	−0.0163746	+	0.00288728i
$766$	−0.0410339	−	0.268533i	−0.00148261	−	0.00970249i
$767$	7.08397	−	12.2698i	0.255787	−	0.443037i
$768$	−7.82711	−	13.8320i	−0.282436	−	0.499118i
$769$	29.1997	+	24.5014i	1.05297	+	0.883544i	0.993402	−	0.114680i	$-0.0365844\pi$
$769$	29.1997	+	24.5014i	1.05297	+	0.883544i	0.0595643	+	0.998224i	$0.481029\pi$
$770$	−1.46294	+	1.17153i	−0.0527206	+	0.0422191i
$771$	8.93569	−	5.15902i	0.321811	−	0.185798i
$772$	−11.1764	+	8.53757i	−0.402246	+	0.307274i
$773$	6.66218	+	18.3042i	0.239622	+	0.658356i	0.999961	+	0.00882974i	$0.00281063\pi$
$773$	6.66218	+	18.3042i	0.239622	+	0.658356i	−0.760339	+	0.649527i	$0.774967\pi$
$774$	−0.0522131	+	2.27983i	−0.00187676	+	0.0819467i
$775$	3.98587	−	22.6050i	0.143177	−	0.811996i
$776$	26.9898	−	19.6554i	0.968877	−	0.705588i
$777$	−1.64413	+	1.37959i	−0.0589829	+	0.0494925i
$778$	−43.4976	−	8.70113i	−1.55946	−	0.311951i
$779$	−22.6566	+	23.6984i	−0.811756	+	0.849084i
$780$	0.109836	−	0.263554i	0.00393276	−	0.00943674i
$781$	35.6111	+	42.4396i	1.27426	+	1.51861i
$782$	20.9848	−	34.4977i	0.750416	−	1.23364i
$783$	−3.82496	+	21.6924i	−0.136693	+	0.775223i
$784$	−11.2252	+	15.8845i	−0.400899	+	0.567303i
$785$	1.03959	−	0.378378i	0.0371044	−	0.0135049i
$786$	3.21218	+	2.82316i	0.114575	+	0.100699i
$787$	−36.1724	+	20.8841i	−1.28941	+	0.744439i	−0.978548	−	0.206018i	$-0.933949\pi$
$787$	−36.1724	+	20.8841i	−1.28941	+	0.744439i	−0.310857	+	0.950457i	$0.600616\pi$
$788$	−28.4524	+	14.7332i	−1.01357	+	0.524850i
$789$	15.3360	−	18.2768i	0.545977	−	0.650670i
$790$	0.0484227	+	0.143157i	0.00172280	+	0.00509330i
$791$	4.79126	−	8.29870i	0.170358	−	0.295068i
$792$	32.0642	+	7.95642i	1.13935	+	0.282719i
$793$	−2.64988	−	15.0282i	−0.0941001	−	0.533668i
$794$	11.8985	−	30.4992i	0.422261	−	1.08238i
$795$	0.129193	−	0.354954i	0.00458199	−	0.0125889i
$796$	6.03046	−	1.88707i	0.213744	−	0.0668853i
$797$			26.6022i			0.942298i	0.882054	+	0.471149i	$0.156161\pi$
$797$			26.6022i			0.942298i	−0.882054	+	0.471149i	$0.843839\pi$
$798$	14.9062	+	14.9189i	0.527674	+	0.528125i
$799$	18.1617			0.642515
$800$	8.05440	−	27.0873i	0.284766	−	0.957679i
$801$	−24.2620	−	8.83066i	−0.857257	−	0.312016i
$802$	−2.30510	−	0.899277i	−0.0813960	−	0.0317546i
$803$	11.0051	−	1.94050i	0.388362	−	0.0684787i
$804$	2.65972	+	0.121891i	0.0938012	+	0.00429876i
$805$	−1.64015	−	0.946941i	−0.0578077	−	0.0333753i
$806$	4.51174	+	13.3385i	0.158919	+	0.469830i
$807$	15.5070	+	13.0119i	0.545872	+	0.458041i
$808$	10.6265	+	36.9033i	0.373840	+	1.29825i
$809$	13.9569	+	24.1740i	0.490697	+	0.849912i	0.999943	−	0.0107090i	$-0.00340885\pi$
$809$	13.9569	+	24.1740i	0.490697	+	0.849912i	−0.509246	+	0.860621i	$0.670076\pi$
$810$	0.0677111	−	0.0770415i	0.00237913	−	0.00270696i
$811$	−9.28262	−	25.5038i	−0.325957	−	0.895559i	−0.989124	−	0.147087i	$-0.953010\pi$
$811$	−9.28262	−	25.5038i	−0.325957	−	0.895559i	0.663167	−	0.748472i	$-0.269212\pi$
$812$	29.7329	+	6.65913i	1.04342	+	0.233689i
$813$	−3.74239	−	0.659885i	−0.131251	−	0.0231432i
$814$	2.67490	−	4.39737i	0.0937552	−	0.154128i
$815$	0.656131	−	0.550559i	0.0229833	−	0.0192853i
$816$	−9.71754	+	9.63382i	−0.340182	+	0.337251i
$817$	0.827563	−	3.39160i	0.0289528	−	0.118657i
$818$	3.72758	−	18.6345i	0.130332	−	0.651539i
$819$	9.65881	+	11.5109i	0.337506	+	0.402224i
$820$	−0.675661	+	0.734160i	−0.0235951	+	0.0256380i
$821$	−43.5693	−	7.68244i	−1.52058	−	0.268119i	−0.649918	−	0.760004i	$-0.725197\pi$
$821$	−43.5693	−	7.68244i	−1.52058	−	0.268119i	−0.870660	+	0.491885i	$0.836308\pi$
$822$	0.0599673	−	2.61841i	0.00209160	−	0.0913274i
$823$	−19.6903	+	7.16669i	−0.686361	+	0.249815i	−0.661576	−	0.749878i	$-0.730112\pi$
$823$	−19.6903	+	7.16669i	−0.686361	+	0.249815i	−0.0247847	+	0.999693i	$0.507890\pi$
$824$	1.01252	+	2.07010i	0.0352729	+	0.0721154i
$825$	−14.3939	−	24.9310i	−0.501131	−	0.867985i
$826$	19.9066	+	24.8581i	0.692639	+	0.864925i
$827$	6.26880	−	7.47087i	0.217988	−	0.259787i	−0.645958	−	0.763373i	$-0.723542\pi$
$827$	6.26880	−	7.47087i	0.217988	−	0.259787i	0.863945	+	0.503586i	$0.167986\pi$
$828$	4.28579	+	33.1071i	0.148942	+	1.15055i
$829$	44.1649	+	25.4986i	1.53391	+	0.885604i	0.999176	+	0.0405847i	$0.0129221\pi$
$829$	44.1649	+	25.4986i	1.53391	+	0.885604i	0.534735	+	0.845020i	$0.320411\pi$
$830$	0.140179	+	0.917354i	0.00486568	+	0.0318418i
$831$	−0.612354	−	3.47283i	−0.0212423	−	0.120471i
$832$	3.64221	+	16.9487i	0.126271	+	0.587592i
$833$	15.7366	+	5.72766i	0.545241	+	0.198452i
$834$	7.29829	+	13.3372i	0.252719	+	0.461830i
$835$		−	0.883085i		−	0.0305604i
$836$	−45.3262	−	22.4374i	−1.56764	−	0.776015i
$837$		−	22.8811i		−	0.790888i
$838$	24.5831	−	13.4522i	0.849209	−	0.464698i
$839$	3.34084	+	1.21596i	0.115338	+	0.0419798i	0.399045	−	0.916931i	$-0.369342\pi$
$839$	3.34084	+	1.21596i	0.115338	+	0.0419798i	−0.283706	+	0.958911i	$0.591564\pi$
$840$	0.462170	+	0.445315i	0.0159464	+	0.0153648i
$841$	1.63831	+	9.29129i	0.0564933	+	0.320389i
$842$	−27.2506	+	4.16410i	−0.939118	+	0.143504i
$843$	−6.86796	−	3.96522i	−0.236545	−	0.136569i
$844$	−9.06801	+	1.17388i	−0.312134	+	0.0404065i
$845$	0.354037	−	0.421925i	0.0121792	−	0.0145147i
$846$	−11.7203	+	9.38572i	−0.402953	+	0.322688i
$847$	−39.0171	−	67.5797i	−1.34064	−	2.32206i
$848$	5.83990	+	22.1782i	0.200543	+	0.761601i
$849$	30.5013	−	11.1015i	1.04680	−	0.381004i
$850$	−24.3245	−	0.557085i	−0.834323	−	0.0191078i
$851$	5.12203	+	0.903153i	0.175581	+	0.0309597i
$852$	12.8471	−	13.9594i	0.440134	−	0.478241i
$853$	−1.51056	−	1.80022i	−0.0517207	−	0.0616383i	0.739564	−	0.673086i	$-0.235032\pi$
$853$	−1.51056	−	1.80022i	−0.0517207	−	0.0616383i	−0.791285	+	0.611448i	$0.790587\pi$
$854$	33.6350	+	6.72824i	1.15097	+	0.230236i
$855$	−0.469176	+	0.344487i	−0.0160455	+	0.0117812i
$856$	10.9979	+	7.40032i	0.375902	+	0.252938i
$857$	−22.6700	+	19.0224i	−0.774391	+	0.649791i	−0.941829	−	0.336091i	$-0.890895\pi$
$857$	−22.6700	+	19.0224i	−0.774391	+	0.649791i	0.167438	+	0.985883i	$0.446451\pi$
$858$	15.0877	+	9.17777i	0.515085	+	0.313324i
$859$	33.5273	+	5.91176i	1.14394	+	0.201707i	0.713326	−	0.700832i	$-0.247188\pi$
$859$	33.5273	+	5.91176i	1.14394	+	0.201707i	0.430609	+	0.902539i	$0.358299\pi$
$860$	0.0232192	−	0.103673i	0.000791767	−	0.00353522i
$861$	8.80120	+	24.1811i	0.299944	+	0.824090i
$862$	−41.0097	−	36.0431i	−1.39680	−	1.22763i
$863$	−8.20482	−	14.2112i	−0.279295	−	0.483754i	0.691914	−	0.721980i	$-0.256768\pi$
$863$	−8.20482	−	14.2112i	−0.279295	−	0.483754i	−0.971210	+	0.238226i	$0.923434\pi$
$864$	3.21817	−	27.9856i	0.109484	−	0.952089i
$865$	−0.913957	−	0.766901i	−0.0310755	−	0.0260754i
$866$	−48.6525	+	16.4566i	−1.65328	+	0.559220i
$867$	−4.42100	−	2.55247i	−0.150145	−	0.0866863i
$868$	−31.6177	−	1.44899i	−1.07317	−	0.0491819i
$869$	−9.20512	+	1.62311i	−0.312262	+	0.0550603i
$870$	0.149783	−	0.383937i	0.00507812	−	0.0130167i
$871$	−2.72906	−	0.993295i	−0.0924705	−	0.0336565i
$872$	−53.8676	+	5.72264i	−1.82419	+	0.193793i
$873$	23.7665			0.804375
$874$	4.47594	−	50.9101i	0.151401	−	1.72206i
$875$			2.28338i			0.0771922i
$876$	−1.14281	−	3.65206i	−0.0386120	−	0.123392i
$877$	−12.4099	+	34.0959i	−0.419053	+	1.15134i	0.533190	+	0.845996i	$0.320993\pi$
$877$	−12.4099	+	34.0959i	−0.419053	+	1.15134i	−0.952243	+	0.305342i	$0.901229\pi$
$878$	4.81714	+	1.87928i	0.162570	+	0.0634227i
$879$	−3.75797	−	21.3125i	−0.126753	−	0.718854i
$880$	−1.39209	−	0.656491i	−0.0469274	−	0.0221303i
$881$	−3.99053	+	6.91180i	−0.134444	+	0.232864i	−0.925385	−	0.379028i	$-0.876258\pi$
$881$	−3.99053	+	6.91180i	−0.134444	+	0.232864i	0.790941	+	0.611893i	$0.209592\pi$
$882$	−13.1153	+	4.43623i	−0.441615	+	0.149375i
$883$	15.5992	−	18.5904i	0.524955	−	0.625616i	−0.436790	−	0.899563i	$-0.643885\pi$
$883$	15.5992	−	18.5904i	0.524955	−	0.625616i	0.961745	+	0.273947i	$0.0883293\pi$
$884$	13.2542	−	6.86328i	0.445786	−	0.230837i
$885$	0.373036	−	0.215373i	0.0125395	−	0.00723967i
$886$	24.1850	−	27.5176i	0.812511	−	0.924472i
$887$	7.03701	−	2.56126i	0.236280	−	0.0859988i	−0.221166	−	0.975236i	$-0.570986\pi$
$887$	7.03701	−	2.56126i	0.236280	−	0.0859988i	0.457446	+	0.889237i	$0.348764\pi$
$888$	−1.61095	−	0.715085i	−0.0540601	−	0.0239967i
$889$	−12.0523	+	68.3521i	−0.404222	+	2.29246i
$890$	1.02767	+	0.625130i	0.0344477	+	0.0209544i
$891$	4.07776	+	4.85968i	0.136610	+	0.162805i
$892$	−33.8909	−	14.1241i	−1.13475	−	0.472908i
$893$	20.6096	−	10.1803i	0.689673	−	0.340671i
$894$	−0.903603	+	4.51718i	−0.0302210	+	0.151077i
$895$	0.117414	−	0.0985223i	0.00392473	−	0.00329324i
$896$	−38.4674	−	6.21918i	−1.28510	−	0.207768i
$897$	−3.09878	+	17.5741i	−0.103465	+	0.586781i
$898$	−21.0194	−	0.481391i	−0.701426	−	0.0160642i
$899$	6.95123	+	19.0983i	0.231836	+	0.636965i
$900$	15.9852	−	12.2111i	0.532841	−	0.407035i
$901$	17.1005	−	9.87296i	0.569699	−	0.328916i
$902$	−38.5745	−	48.1694i	−1.28439	−	1.60387i
$903$	−2.09901	−	1.76128i	−0.0698508	−	0.0586118i
$904$	7.85071	+	0.540151i	0.261111	+	0.0179652i
$905$	0.440913	−	0.763683i	0.0146564	−	0.0253857i
$906$	−7.43303	+	1.13582i	−0.246946	+	0.0377352i
$907$	40.2222	−	7.09225i	1.33555	−	0.235494i	0.540148	−	0.841570i	$-0.318368\pi$
$907$	40.2222	−	7.09225i	1.33555	−	0.235494i	0.795407	+	0.606076i	$0.207257\pi$
$908$	31.6328	+	20.2487i	1.04977	+	0.671976i
$909$	−9.34943	+	25.6873i	−0.310101	+	0.851995i
$910$	−0.336056	−	0.614123i	−0.0111401	−	0.0203580i
$911$	−53.4489			−1.77084			−0.885420	−	0.464791i	$-0.846129\pi$
$911$	−53.4489			−1.77084			−0.885420	+	0.464791i	$0.846129\pi$
$912$	−5.62717	+	16.3793i	−0.186334	+	0.542373i
$913$	−57.3973			−1.89957
$914$	−17.6803	−	32.3098i	−0.584813	−	1.06871i
$915$	0.158680	−	0.435969i	0.00524579	−	0.0144127i
$916$	−39.5770	−	25.3338i	−1.30766	−	0.837053i
$917$	10.3259	−	1.82074i	0.340992	−	0.0601260i
$918$	−23.9756	+	3.66366i	−0.791314	+	0.120919i
$919$	−18.0957	+	31.3426i	−0.596921	+	1.03390i	0.396351	+	0.918099i	$0.370276\pi$
$919$	−18.0957	+	31.3426i	−0.596921	+	1.03390i	−0.993273	+	0.115799i	$0.963057\pi$
$920$	0.106755	−	1.55161i	0.00351961	−	0.0511550i
$921$	−0.760600	−	0.638220i	−0.0250626	−	0.0210300i
$922$	−13.7658	−	17.1899i	−0.453353	−	0.566120i
$923$	−17.9211	+	10.3467i	−0.589879	+	0.340567i
$924$	−31.5447	+	24.0969i	−1.03775	+	0.792730i
$925$	−1.07188	−	2.94496i	−0.0352432	−	0.0968298i
$926$	12.8138	+	0.293464i	0.421088	+	0.00964384i
$927$	−0.284845	+	1.61544i	−0.00935555	+	0.0530580i
$928$	5.81581	+	24.3366i	0.190913	+	0.798887i
$929$	17.5459	−	14.7228i	0.575664	−	0.483039i	−0.307856	−	0.951433i	$-0.599612\pi$
$929$	17.5459	−	14.7228i	0.575664	−	0.483039i	0.883520	+	0.468394i	$0.155167\pi$
$930$	−0.0839721	+	0.419783i	−0.00275355	+	0.0137652i
$931$	21.0682	−	2.32131i	0.690481	−	0.0760779i
$932$	−12.3270	−	5.13727i	−0.403784	−	0.168277i
$933$	4.06695	+	4.84680i	0.133146	+	0.158677i
$934$	20.4244	+	12.4241i	0.668308	+	0.406529i
$935$	−0.230112	+	1.30503i	−0.00752546	+	0.0426790i
$936$	−5.00647	+	11.2786i	−0.163641	+	0.368654i
$937$	18.2090	−	6.62752i	0.594861	−	0.216512i	−0.0270053	−	0.999635i	$-0.508597\pi$
$937$	18.2090	−	6.62752i	0.594861	−	0.216512i	0.621866	+	0.783124i	$0.286375\pi$
$938$	4.30953	−	4.90337i	0.140711	−	0.160101i
$939$	5.13735	−	2.96605i	0.167651	−	0.0967933i
$940$	0.621193	−	0.321667i	0.0202611	−	0.0104916i
$941$	16.0220	−	19.0943i	0.522302	−	0.622455i	−0.438822	−	0.898574i	$-0.644604\pi$
$941$	16.0220	−	19.0943i	0.522302	−	0.622455i	0.961123	+	0.276119i	$0.0890484\pi$
$942$	22.1959	−	7.50775i	0.723183	−	0.244616i
$943$	31.1795	−	54.0044i	1.01534	−	1.75863i
$944$	−11.1550	+	23.6544i	−0.363066	+	0.769884i
$945$	0.197538	+	1.12029i	0.00642591	+	0.0364432i
$946$	6.12170	+	2.38823i	0.199034	+	0.0776479i
$947$	−5.61938	+	15.4391i	−0.182605	+	0.501704i	−0.996894	−	0.0787562i	$-0.974905\pi$
$947$	−5.61938	+	15.4391i	−0.182605	+	0.501704i	0.814289	+	0.580460i	$0.197127\pi$
$948$	0.955893	+	3.05473i	0.0310460	+	0.0992130i
$949$			4.17406i			0.135496i
$950$	−27.9153	+	13.0026i	−0.905690	+	0.421860i
$951$	−17.7409			−0.575287
$952$	3.54423	+	33.3621i	0.114869	+	1.08127i
$953$	−26.3225	−	9.58061i	−0.852669	−	0.310346i	−0.121541	−	0.992586i	$-0.538784\pi$
$953$	−26.3225	−	9.58061i	−0.852669	−	0.310346i	−0.731128	+	0.682240i	$0.761006\pi$
$954$	−5.93325	+	15.2086i	−0.192096	+	0.492397i
$955$	0.125673	−	0.0221595i	0.00406667	−	0.000717064i
$956$	38.8259	+	1.77933i	1.25572	+	0.0575476i
$957$	22.0747	+	12.7449i	0.713575	+	0.411983i
$958$	−17.3651	+	5.87373i	−0.561042	+	0.189772i
$959$	−4.91920	−	4.12770i	−0.158849	−	0.133290i
$960$	−0.161746	+	0.501620i	−0.00522034	+	0.0161897i
$961$	4.94395	+	8.56318i	0.159482	+	0.276232i
$962$	1.44406	+	1.26917i	0.0465583	+	0.0409197i
$963$	3.22724	+	8.86678i	0.103997	+	0.285728i
$964$	−5.81060	+	25.9442i	−0.187147	+	0.835606i
$965$	0.459319	+	0.0809902i	0.0147860	+	0.00260717i
$966$	−34.2698	−	20.8462i	−1.10261	−	0.670714i
$967$	−8.73852	+	7.33249i	−0.281012	+	0.235797i	−0.772389	−	0.635150i	$-0.780938\pi$
$967$	−8.73852	+	7.33249i	−0.281012	+	0.235797i	0.491377	+	0.870947i	$0.336494\pi$
$968$	35.7751	−	53.1669i	1.14985	−	1.70885i
$969$	14.8801	+	0.965501i	0.478017	+	0.0310164i
$970$	−1.08574	−	0.217187i	−0.0348609	−	0.00697346i
$971$	23.2659	+	27.7272i	0.746638	+	0.889808i	0.996925	−	0.0783636i	$-0.0249695\pi$
$971$	23.2659	+	27.7272i	0.746638	+	0.889808i	−0.250287	+	0.968172i	$0.580525\pi$
$972$	21.7045	−	23.5837i	0.696173	−	0.756448i
$973$	36.7100	+	6.47297i	1.17687	+	0.207514i
$974$	39.3602	+	0.901436i	1.26118	+	0.0288839i
$975$	10.1044	−	3.67769i	0.323599	−	0.117780i
$976$	7.17280	+	27.2401i	0.229596	+	0.871934i
$977$	9.19420	+	15.9248i	0.294148	+	0.509480i	0.974786	−	0.223140i	$-0.0716307\pi$
$977$	9.19420	+	15.9248i	0.294148	+	0.509480i	−0.680638	+	0.732620i	$0.738297\pi$
$978$	14.1601	−	11.3395i	0.452790	−	0.362598i
$979$	−47.8221	+	56.9922i	−1.52840	+	1.82148i
$980$	0.639690	−	0.0828095i	0.0204342	−	0.00264525i
$981$	−33.3938	−	19.2799i	−1.06618	−	0.615560i
$982$	−16.2461	+	2.48253i	−0.518434	+	0.0792207i
$983$	−4.81472	−	27.3056i	−0.153566	−	0.870914i	−0.960085	−	0.279707i	$-0.909763\pi$
$983$	−4.81472	−	27.3056i	−0.153566	−	0.870914i	0.806520	−	0.591207i	$-0.201348\pi$
$984$	−14.6627	+	15.2177i	−0.467428	+	0.485121i
$985$	0.998473	+	0.363414i	0.0318140	+	0.0115793i
$986$	18.8989	−	10.3417i	0.601863	−	0.329347i
$987$		−	18.0417i		−	0.574274i
$988$	11.1935	−	15.2178i	0.356111	−	0.484142i
$989$			6.64003i			0.211141i
$990$	−0.525922	−	0.961093i	−0.0167149	−	0.0305455i
$991$	41.6021	+	15.1419i	1.32154	+	0.481000i	0.903950	−	0.427638i	$-0.140654\pi$
$991$	41.6021	+	15.1419i	1.32154	+	0.481000i	0.417586	+	0.908638i	$0.362876\pi$
$992$	−10.3394	−	23.8471i	−0.328276	−	0.757146i
$993$	1.61496	+	9.15888i	0.0512492	+	0.290648i
$994$	−7.02621	−	45.9807i	−0.222858	−	1.45842i
$995$	−0.181474	−	0.104774i	−0.00575312	−	0.00332157i
$996$	2.52332	+	19.4923i	0.0799546	+	0.617637i
$997$	−14.9229	+	17.7845i	−0.472614	+	0.563240i	−0.948708	−	0.316155i	$-0.897608\pi$
$997$	−14.9229	+	17.7845i	−0.472614	+	0.563240i	0.476093	+	0.879395i	$0.342052\pi$
$998$	19.5712	+	24.4393i	0.619514	+	0.773611i
$999$	−1.56203	−	2.70551i	−0.0494203	−	0.0855986i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.2.t.a.101.7	✓	108
4.3	odd	2		608.2.bf.a.177.12		108
8.3	odd	2		608.2.bf.a.177.7		108
8.5	even	2	inner	152.2.t.a.101.15	yes	108
19.16	even	9	inner	152.2.t.a.149.15	yes	108
76.35	odd	18		608.2.bf.a.529.7		108
152.35	odd	18		608.2.bf.a.529.12		108
152.149	even	18	inner	152.2.t.a.149.7	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.2.t.a.101.7	✓	108	1.1	even	1	trivial
152.2.t.a.101.15	yes	108	8.5	even	2	inner
152.2.t.a.149.7	yes	108	152.149	even	18	inner
152.2.t.a.149.15	yes	108	19.16	even	9	inner
608.2.bf.a.177.7		108	8.3	odd	2
608.2.bf.a.177.12		108	4.3	odd	2
608.2.bf.a.529.7		108	76.35	odd	18
608.2.bf.a.529.12		108	152.35	odd	18

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:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.678879 - 1.24061i) q^{2} +(-0.339733 + 0.933408i) q^{3} +(-1.07825 + 1.68445i) q^{4} +(0.0653175 - 0.0115172i) q^{5} +(1.38864 - 0.212194i) q^{6} +(1.72211 - 2.98278i) q^{7} +(2.82176 + 0.194145i) q^{8} +(1.54230 + 1.29414i) q^{9} +O(q^{10})\)	\(q+(-0.678879 - 1.24061i) q^{2} +(-0.339733 + 0.933408i) q^{3} +(-1.07825 + 1.68445i) q^{4} +(0.0653175 - 0.0115172i) q^{5} +(1.38864 - 0.212194i) q^{6} +(1.72211 - 2.98278i) q^{7} +(2.82176 + 0.194145i) q^{8} +(1.54230 + 1.29414i) q^{9} +(-0.0586312 - 0.0732150i) q^{10} +(5.02419 - 2.90072i) q^{11} +(-1.20597 - 1.57871i) q^{12} +(0.741143 + 2.03627i) q^{13} +(-4.86958 - 0.111524i) q^{14} +(-0.0114402 + 0.0648807i) q^{15} +(-1.67477 - 3.63251i) q^{16} +(-2.63821 + 2.21372i) q^{17} +(0.558497 - 2.79197i) q^{18} +(-1.75292 + 3.99090i) q^{19} +(-0.0510281 + 0.122443i) q^{20} +(2.19909 + 2.62078i) q^{21} +(-7.00949 - 4.26384i) q^{22} +(1.43964 - 8.16462i) q^{23} +(-1.13986 + 2.56789i) q^{24} +(-4.69433 + 1.70860i) q^{25} +(2.02308 - 2.30186i) q^{26} +(-4.31263 + 2.48990i) q^{27} +(3.16750 + 6.11698i) q^{28} +(2.84323 - 3.38843i) q^{29} +(0.0882584 - 0.0298533i) q^{30} +(-2.29739 + 3.97920i) q^{31} +(-3.36957 + 4.54378i) q^{32} +(1.00067 + 5.67508i) q^{33} +(4.53740 + 1.77015i) q^{34} +(0.0781304 - 0.214662i) q^{35} +(-3.84291 + 1.20253i) q^{36} +0.627345i q^{37} +(6.14119 - 0.534645i) q^{38} -2.15246 q^{39} +(0.186546 - 0.0198178i) q^{40} +(7.06806 + 2.57256i) q^{41} +(1.75845 - 4.50741i) q^{42} +(-0.788746 + 0.139077i) q^{43} +(-0.531184 + 11.5907i) q^{44} +(0.115644 + 0.0667673i) q^{45} +(-11.1065 + 3.75675i) q^{46} +(-4.03976 - 3.38976i) q^{47} +(3.95959 - 0.329164i) q^{48} +(-2.43131 - 4.21115i) q^{49} +(5.30659 + 4.66392i) q^{50} +(-1.17002 - 3.21460i) q^{51} +(-4.22915 - 0.947182i) q^{52} +(-5.64643 - 0.995618i) q^{53} +(6.01676 + 3.65997i) q^{54} +(0.294759 - 0.247332i) q^{55} +(5.43846 - 8.08233i) q^{56} +(-3.12961 - 2.99203i) q^{57} +(-6.13394 - 1.22701i) q^{58} +(-4.20266 - 5.00853i) q^{59} +(-0.0969532 - 0.0892278i) q^{60} +(-6.93517 - 1.22286i) q^{61} +(6.49631 + 0.148780i) q^{62} +(6.51616 - 2.37169i) q^{63} +(7.92462 + 1.09566i) q^{64} +(0.0718619 + 0.124468i) q^{65} +(6.36125 - 5.09414i) q^{66} +(-0.861477 + 1.02667i) q^{67} +(-0.884273 - 6.83087i) q^{68} +(7.13183 + 4.11756i) q^{69} +(-0.319353 + 0.0487996i) q^{70} +(1.65826 + 9.40446i) q^{71} +(4.10075 + 3.95119i) q^{72} +(1.81006 + 0.658809i) q^{73} +(0.778293 - 0.425892i) q^{74} -4.96219i q^{75} +(-4.83241 - 7.25588i) q^{76} -19.9814i q^{77} +(1.46126 + 2.67038i) q^{78} +(-1.51401 - 0.551054i) q^{79} +(-0.151229 - 0.217978i) q^{80} +(0.189884 + 1.07689i) q^{81} +(-1.60680 - 10.5152i) q^{82} +(-8.56814 - 4.94682i) q^{83} +(-6.78574 + 0.878431i) q^{84} +(-0.146825 + 0.174980i) q^{85} +(0.708004 + 0.884112i) q^{86} +(2.19685 + 3.80505i) q^{87} +(14.7402 - 7.20969i) q^{88} +(-12.0507 + 4.38609i) q^{89} +(0.00432386 - 0.188797i) q^{90} +(7.35008 + 1.29602i) q^{91} +(12.2006 + 11.2285i) q^{92} +(-2.93372 - 3.49627i) q^{93} +(-1.46288 + 7.31303i) q^{94} +(-0.0685321 + 0.280864i) q^{95} +(-3.09645 - 4.68886i) q^{96} +(9.04283 - 7.58783i) q^{97} +(-3.57385 + 5.87518i) q^{98} +(11.5028 + 2.02825i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9}+O(q^{10}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9	\( 108 q - 6 q^{2} - 12 q^{4} - 12 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 9 q^{10} - 3 q^{12} - 9 q^{14} - 12 q^{15} - 12 q^{17} - 12 q^{18} - 42 q^{20} - 12 q^{22} - 12 q^{23} - 36 q^{24} - 12 q^{25} + 21 q^{26} + 24 q^{28} - 48 q^{30} + 30 q^{31} + 39 q^{32} - 30 q^{33} - 60 q^{34} + 69 q^{36} - 42 q^{38} - 24 q^{39} + 36 q^{40} - 24 q^{41} - 81 q^{42} + 45 q^{44} - 18 q^{46} - 48 q^{47} - 21 q^{48} - 24 q^{49} - 12 q^{50} + 3 q^{52} + 63 q^{54} - 42 q^{55} + 30 q^{56} - 12 q^{57} - 84 q^{58} + 30 q^{60} - 6 q^{62} + 30 q^{63} + 3 q^{64} - 6 q^{65} + 54 q^{66} + 36 q^{68} + 123 q^{70} - 12 q^{71} + 150 q^{72} + 12 q^{73} + 75 q^{74} + 42 q^{76} + 39 q^{78} - 12 q^{79} + 51 q^{80} - 18 q^{81} + 99 q^{82} + 75 q^{84} - 48 q^{86} - 6 q^{87} - 27 q^{88} - 12 q^{89} + 66 q^{90} - 48 q^{92} + 54 q^{94} - 72 q^{95} + 42 q^{96} - 12 q^{97} + 93 q^{98}+O(q^{100}) \) 108 * q - 6 * q^2 - 12 * q^4 - 12 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 9 * q^10 - 3 * q^12 - 9 * q^14 - 12 * q^15 - 12 * q^17 - 12 * q^18 - 42 * q^20 - 12 * q^22 - 12 * q^23 - 36 * q^24 - 12 * q^25 + 21 * q^26 + 24 * q^28 - 48 * q^30 + 30 * q^31 + 39 * q^32 - 30 * q^33 - 60 * q^34 + 69 * q^36 - 42 * q^38 - 24 * q^39 + 36 * q^40 - 24 * q^41 - 81 * q^42 + 45 * q^44 - 18 * q^46 - 48 * q^47 - 21 * q^48 - 24 * q^49 - 12 * q^50 + 3 * q^52 + 63 * q^54 - 42 * q^55 + 30 * q^56 - 12 * q^57 - 84 * q^58 + 30 * q^60 - 6 * q^62 + 30 * q^63 + 3 * q^64 - 6 * q^65 + 54 * q^66 + 36 * q^68 + 123 * q^70 - 12 * q^71 + 150 * q^72 + 12 * q^73 + 75 * q^74 + 42 * q^76 + 39 * q^78 - 12 * q^79 + 51 * q^80 - 18 * q^81 + 99 * q^82 + 75 * q^84 - 48 * q^86 - 6 * q^87 - 27 * q^88 - 12 * q^89 + 66 * q^90 - 48 * q^92 + 54 * q^94 - 72 * q^95 + 42 * q^96 - 12 * q^97 + 93 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more