LMFDB - Embedded newform 690.2.w.b.103.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [690,2,Mod(7,690)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(690, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([0, 11, 38]))

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

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

chi := DirichletCharacter("690.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 690 = 2 \cdot 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	690.w (of order $44$, degree $20$, 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:	$5.50967773947$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$12$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			103.1
Character	$\chi$	$=$	690.103
Dual form			690.2.w.b.67.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212565 + 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.06444 + 0.859123i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.0521646 + 0.729356i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +O(q^{10})$	\(q+(-0.212565 + 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.06444 + 0.859123i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.0521646 + 0.729356i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +(-0.400661 - 2.19988i) q^{10} +(-2.88238 + 4.48507i) q^{11} +(0.977147 - 0.212565i) q^{12} +(-1.14707 + 0.0820403i) q^{13} +(-0.701600 - 0.206008i) q^{14} +(1.13782 - 1.92494i) q^{15} +(0.654861 + 0.755750i) q^{16} +(1.44296 - 3.86871i) q^{17} +(0.877679 + 0.479249i) q^{18} +(1.39010 - 3.04389i) q^{19} +(2.23477 + 0.0761134i) q^{20} +(-0.395327 - 0.615141i) q^{21} +(-3.76988 - 3.76988i) q^{22} +(-4.73949 - 0.732943i) q^{23} +1.00000i q^{24} +(3.52382 - 3.54721i) q^{25} +(0.163663 - 1.13830i) q^{26} +(0.349464 + 0.936950i) q^{27} +(0.350436 - 0.641776i) q^{28} +(0.942972 - 0.430641i) q^{29} +(1.63908 + 1.52099i) q^{30} +(-0.548623 - 3.81576i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(-0.380338 - 5.31782i) q^{33} +(3.47358 + 2.23233i) q^{34} +(-0.518916 - 1.55053i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-4.89858 - 8.97108i) q^{37} +(2.67884 + 2.00535i) q^{38} +(0.869115 - 0.753092i) q^{39} +(-0.549409 + 2.16752i) q^{40} +(-2.29133 + 0.672794i) q^{41} +(0.685116 - 0.255535i) q^{42} +(1.27152 + 1.69856i) q^{43} +(4.48507 - 2.88238i) q^{44} +(0.242703 + 2.22286i) q^{45} +(1.72365 - 4.47538i) q^{46} +(5.98423 - 5.98423i) q^{47} +(-0.977147 - 0.212565i) q^{48} +(6.39951 + 0.920111i) q^{49} +(2.71711 + 4.19730i) q^{50} +(1.16329 + 3.96179i) q^{51} +(1.07750 + 0.401885i) q^{52} +(-7.56893 - 0.541340i) q^{53} +(-0.989821 + 0.142315i) q^{54} +(2.09727 - 11.7355i) q^{55} +(0.552619 + 0.478847i) q^{56} +(0.711304 + 3.26981i) q^{57} +(0.220356 + 1.01296i) q^{58} +(3.23773 + 2.80551i) q^{59} +(-1.83464 + 1.27832i) q^{60} +(6.71188 - 0.965023i) q^{61} +(3.84518 + 0.275012i) q^{62} +(0.685116 + 0.255535i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(2.29758 - 1.15484i) q^{65} +(5.27714 + 0.758739i) q^{66} +(-9.98575 - 2.17227i) q^{67} +(-2.91968 + 2.91968i) q^{68} +(4.23340 - 2.25352i) q^{69} +(1.62540 - 0.177469i) q^{70} +(-1.93075 + 1.24082i) q^{71} +(-0.599278 - 0.800541i) q^{72} +(-8.25109 + 3.07750i) q^{73} +(9.80733 - 2.87969i) q^{74} +(-0.695195 + 4.95143i) q^{75} +(-2.52895 + 2.19135i) q^{76} +(-3.12085 - 2.33624i) q^{77} +(0.551138 + 1.00933i) q^{78} +(0.664656 - 0.767054i) q^{79} +(-2.00120 - 0.997593i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(-0.170362 - 2.38198i) q^{82} +(-13.4405 + 7.33909i) q^{83} +(0.104063 + 0.723777i) q^{84} +(0.344806 + 9.22640i) q^{85} +(-1.93002 + 0.881410i) q^{86} +(-0.496814 + 0.909848i) q^{87} +(1.86314 + 4.99526i) q^{88} +(-1.07681 + 7.48936i) q^{89} +(-2.22365 - 0.235346i) q^{90} -0.840905i q^{91} +(4.00672 + 2.63557i) q^{92} +(2.72590 + 2.72590i) q^{93} +(4.57543 + 7.11951i) q^{94} +(-0.254697 + 7.47818i) q^{95} +(0.415415 - 0.909632i) q^{96} +(-9.70436 - 5.29898i) q^{97} +(-2.25940 + 6.05768i) q^{98} +(3.49133 + 4.02921i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 24 q^{6}+O(q^{10}) $ 240 * q + 24 * q^6	$ 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) $ 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/690\mathbb{Z}\right)^\times$.

$n$	$277$	$461$	$511$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{9}{22}\right)$

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 $

$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$2$	−0.212565	+	0.977147i	−0.150306	+	0.690947i
$3$	−0.800541	+	0.599278i	−0.462193	+	0.345993i
$3$	−0.800541	+	0.599278i	−0.462193	+	0.345993i
$4$	−0.909632	−	0.415415i	−0.454816	−	0.207708i
$5$	−2.06444	+	0.859123i	−0.923245	+	0.384211i
$5$	−2.06444	+	0.859123i	−0.923245	+	0.384211i
$6$	−0.415415	−	0.909632i	−0.169592	−	0.371356i
$7$	−0.0521646	+	0.729356i	−0.0197164	+	0.275671i	0.978024	+	0.208490i	$0.0668549\pi$
$7$	−0.0521646	+	0.729356i	−0.0197164	+	0.275671i	−0.997741	+	0.0671806i	$0.978600\pi$
$8$	0.599278	−	0.800541i	0.211877	−	0.283034i
$9$	0.281733	−	0.959493i	0.0939109	−	0.319831i
$10$	−0.400661	−	2.19988i	−0.126700	−	0.695663i
$11$	−2.88238	+	4.48507i	−0.869069	+	1.35230i	0.0659948	+	0.997820i	$0.478978\pi$
$11$	−2.88238	+	4.48507i	−0.869069	+	1.35230i	−0.935064	+	0.354478i	$0.884658\pi$
$12$	0.977147	−	0.212565i	0.282078	−	0.0613623i
$13$	−1.14707	+	0.0820403i	−0.318141	+	0.0227539i	−0.229497	−	0.973309i	$-0.573708\pi$
$13$	−1.14707	+	0.0820403i	−0.318141	+	0.0227539i	−0.0886444	+	0.996063i	$0.528253\pi$
$14$	−0.701600	−	0.206008i	−0.187510	−	0.0550580i
$15$	1.13782	−	1.92494i	0.293783	−	0.497016i
$16$	0.654861	+	0.755750i	0.163715	+	0.188937i
$17$	1.44296	−	3.86871i	0.349968	−	0.938301i	−0.636048	−	0.771650i	$-0.719432\pi$
$17$	1.44296	−	3.86871i	0.349968	−	0.938301i	0.986016	−	0.166651i	$-0.0532953\pi$
$18$	0.877679	+	0.479249i	0.206871	+	0.112960i
$19$	1.39010	−	3.04389i	0.318910	−	0.698315i	−0.680497	−	0.732751i	$-0.738236\pi$
$19$	1.39010	−	3.04389i	0.318910	−	0.698315i	0.999407	+	0.0344355i	$0.0109633\pi$
$20$	2.23477	+	0.0761134i	0.499710	+	0.0170195i
$21$	−0.395327	−	0.615141i	−0.0862674	−	0.134235i
$22$	−3.76988	−	3.76988i	−0.803740	−	0.803740i
$23$	−4.73949	−	0.732943i	−0.988253	−	0.152829i
$23$	−4.73949	−	0.732943i	−0.988253	−	0.152829i
$24$			1.00000i			0.204124i
$25$	3.52382	−	3.54721i	0.704763	−	0.709443i
$26$	0.163663	−	1.13830i	0.0320969	−	0.223239i
$27$	0.349464	+	0.936950i	0.0672544	+	0.180316i
$28$	0.350436	−	0.641776i	0.0662262	−	0.121284i
$29$	0.942972	−	0.430641i	0.175105	−	0.0799680i	−0.325934	−	0.945393i	$-0.605679\pi$
$29$	0.942972	−	0.430641i	0.175105	−	0.0799680i	0.501039	+	0.865425i	$0.332951\pi$
$30$	1.63908	+	1.52099i	0.299255	+	0.277693i
$31$	−0.548623	−	3.81576i	−0.0985357	−	0.685331i	−0.977883	−	0.209151i	$-0.932930\pi$
$31$	−0.548623	−	3.81576i	−0.0985357	−	0.685331i	0.879348	−	0.476180i	$-0.157979\pi$
$32$	−0.877679	+	0.479249i	−0.155153	+	0.0847201i
$33$	−0.380338	−	5.31782i	−0.0662084	−	0.925714i
$34$	3.47358	+	2.23233i	0.595714	+	0.382842i
$35$	−0.518916	−	1.55053i	−0.0877128	−	0.262087i
$36$	−0.654861	+	0.755750i	−0.109143	+	0.125958i
$37$	−4.89858	−	8.97108i	−0.805321	−	1.47484i	−0.878618	−	0.477526i	$-0.841534\pi$
$37$	−4.89858	−	8.97108i	−0.805321	−	1.47484i	0.0732966	−	0.997310i	$-0.476648\pi$
$38$	2.67884	+	2.00535i	0.434565	+	0.325311i
$39$	0.869115	−	0.753092i	0.139170	−	0.120591i
$40$	−0.549409	+	2.16752i	−0.0868692	+	0.342715i
$41$	−2.29133	+	0.672794i	−0.357845	+	0.105073i	−0.455713	−	0.890127i	$-0.650616\pi$
$41$	−2.29133	+	0.672794i	−0.357845	+	0.105073i	0.0978683	+	0.995199i	$0.468798\pi$
$42$	0.685116	−	0.255535i	0.105716	−	0.0394299i
$43$	1.27152	+	1.69856i	0.193905	+	0.259027i	0.886948	−	0.461869i	$-0.152821\pi$
$43$	1.27152	+	1.69856i	0.193905	+	0.259027i	−0.693043	+	0.720897i	$0.743730\pi$
$44$	4.48507	−	2.88238i	0.676149	−	0.434535i
$45$	0.242703	+	2.22286i	0.0361800	+	0.331364i
$46$	1.72365	−	4.47538i	0.254138	−	0.659859i
$47$	5.98423	−	5.98423i	0.872890	−	0.872890i	−0.119897	−	0.992786i	$-0.538256\pi$
$47$	5.98423	−	5.98423i	0.872890	−	0.872890i	0.992786	+	0.119897i	$0.0382563\pi$
$48$	−0.977147	−	0.212565i	−0.141039	−	0.0306812i
$49$	6.39951	+	0.920111i	0.914216	+	0.131444i
$50$	2.71711	+	4.19730i	0.384257	+	0.593588i
$51$	1.16329	+	3.96179i	0.162893	+	0.554762i
$52$	1.07750	+	0.401885i	0.149422	+	0.0557314i
$53$	−7.56893	−	0.541340i	−1.03967	−	0.0743588i	−0.458951	−	0.888462i	$-0.651775\pi$
$53$	−7.56893	−	0.541340i	−1.03967	−	0.0743588i	−0.580721	+	0.814103i	$0.697229\pi$
$54$	−0.989821	+	0.142315i	−0.134698	+	0.0193666i
$55$	2.09727	−	11.7355i	0.282796	−	1.58241i
$56$	0.552619	+	0.478847i	0.0738468	+	0.0639886i
$57$	0.711304	+	3.26981i	0.0942145	+	0.433097i
$58$	0.220356	+	1.01296i	0.0289342	+	0.133008i
$59$	3.23773	+	2.80551i	0.421517	+	0.365246i	0.839639	−	0.543144i	$-0.182766\pi$
$59$	3.23773	+	2.80551i	0.421517	+	0.365246i	−0.418123	+	0.908391i	$0.637312\pi$
$60$	−1.83464	+	1.27832i	−0.236851	+	0.165030i
$61$	6.71188	−	0.965023i	0.859369	−	0.123559i	0.301478	−	0.953473i	$-0.402520\pi$
$61$	6.71188	−	0.965023i	0.859369	−	0.123559i	0.557891	+	0.829915i	$0.311611\pi$
$62$	3.84518	+	0.275012i	0.488338	+	0.0349266i
$63$	0.685116	+	0.255535i	0.0863165	+	0.0321944i
$64$	−0.281733	−	0.959493i	−0.0352166	−	0.119937i
$65$	2.29758	−	1.15484i	0.284980	−	0.143241i
$66$	5.27714	+	0.758739i	0.649571	+	0.0933943i
$67$	−9.98575	−	2.17227i	−1.21995	−	0.265385i	−0.443914	−	0.896069i	$-0.646410\pi$
$67$	−9.98575	−	2.17227i	−1.21995	−	0.265385i	−0.776039	+	0.630685i	$0.782774\pi$
$68$	−2.91968	+	2.91968i	−0.354063	+	0.354063i
$69$	4.23340	−	2.25352i	0.509641	−	0.271292i
$70$	1.62540	−	0.177469i	0.194272	−	0.0212116i
$71$	−1.93075	+	1.24082i	−0.229137	+	0.147258i	−0.650172	−	0.759787i	$-0.725303\pi$
$71$	−1.93075	+	1.24082i	−0.229137	+	0.147258i	0.421035	+	0.907044i	$0.361667\pi$
$72$	−0.599278	−	0.800541i	−0.0706256	−	0.0943447i
$73$	−8.25109	+	3.07750i	−0.965717	+	0.360194i	−0.782342	−	0.622849i	$-0.785975\pi$
$73$	−8.25109	+	3.07750i	−0.965717	+	0.360194i	−0.183375	+	0.983043i	$0.558702\pi$
$74$	9.80733	−	2.87969i	1.14008	−	0.334757i
$75$	−0.695195	+	4.95143i	−0.0802742	+	0.571742i
$76$	−2.52895	+	2.19135i	−0.290091	+	0.251365i
$77$	−3.12085	−	2.33624i	−0.355654	−	0.266239i
$78$	0.551138	+	1.00933i	0.0624041	+	0.114285i
$79$	0.664656	−	0.767054i	0.0747797	−	0.0863004i	−0.717127	−	0.696943i	$-0.754543\pi$
$79$	0.664656	−	0.767054i	0.0747797	−	0.0863004i	0.791907	+	0.610642i	$0.209089\pi$
$80$	−2.00120	−	0.997593i	−0.223741	−	0.111534i
$81$	−0.841254	−	0.540641i	−0.0934726	−	0.0600712i
$82$	−0.170362	−	2.38198i	−0.0188134	−	0.263045i
$83$	−13.4405	+	7.33909i	−1.47529	+	0.805570i	−0.997345	−	0.0728195i	$-0.976800\pi$
$83$	−13.4405	+	7.33909i	−1.47529	+	0.805570i	−0.477946	+	0.878389i	$0.658618\pi$
$84$	0.104063	+	0.723777i	0.0113542	+	0.0789705i
$85$	0.344806	+	9.22640i	0.0373995	+	1.00074i
$86$	−1.93002	+	0.881410i	−0.208119	+	0.0950449i
$87$	−0.496814	+	0.909848i	−0.0532641	+	0.0975459i
$88$	1.86314	+	4.99526i	0.198611	+	0.532497i
$89$	−1.07681	+	7.48936i	−0.114141	+	0.793870i	0.849676	+	0.527306i	$0.176798\pi$
$89$	−1.07681	+	7.48936i	−0.114141	+	0.793870i	−0.963817	+	0.266565i	$0.914111\pi$
$90$	−2.22365	−	0.235346i	−0.234393	−	0.0248077i
$91$		−	0.840905i		−	0.0881508i
$92$	4.00672	+	2.63557i	0.417729	+	0.274777i
$93$	2.72590	+	2.72590i	0.282662	+	0.282662i
$94$	4.57543	+	7.11951i	0.471920	+	0.734322i
$95$	−0.254697	+	7.47818i	−0.0261314	+	0.767245i
$96$	0.415415	−	0.909632i	0.0423981	−	0.0928389i
$97$	−9.70436	−	5.29898i	−0.985328	−	0.538030i	−0.0960402	−	0.995377i	$-0.530618\pi$
$97$	−9.70436	−	5.29898i	−0.985328	−	0.538030i	−0.889288	+	0.457348i	$0.848800\pi$
$98$	−2.25940	+	6.05768i	−0.228234	+	0.611918i
$99$	3.49133	+	4.02921i	0.350892	+	0.404951i
$100$	−4.67894	+	1.76281i	−0.467894	+	0.176281i
$101$	−6.67351	−	1.95952i	−0.664039	−	0.194979i	−0.0676921	−	0.997706i	$-0.521564\pi$
$101$	−6.67351	−	1.95952i	−0.664039	−	0.194979i	−0.596347	+	0.802727i	$0.703382\pi$
$102$	−4.11853	+	0.294563i	−0.407795	+	0.0291661i
$103$	11.6825	−	2.54136i	1.15111	−	0.250408i	0.403775	−	0.914858i	$-0.367698\pi$
$103$	11.6825	−	2.54136i	1.15111	−	0.250408i	0.747332	+	0.664451i	$0.231334\pi$
$104$	−0.621739	+	0.967445i	−0.0609665	+	0.0948658i
$105$	1.34461	+	0.930286i	0.131221	+	0.0907867i
$106$	2.13786	−	7.28088i	0.207647	−	0.707182i
$107$	−4.71208	+	6.29461i	−0.455534	+	0.608523i	−0.968234	−	0.250045i	$-0.919554\pi$
$107$	−4.71208	+	6.29461i	−0.455534	+	0.608523i	0.512700	+	0.858568i	$0.328645\pi$
$108$	0.0713392	−	0.997452i	0.00686462	−	0.0959799i
$109$	−5.46199	−	11.9601i	−0.523164	−	1.14557i	−0.968228	−	0.250070i	$-0.919546\pi$
$109$	−5.46199	−	11.9601i	−0.523164	−	1.14557i	0.445064	−	0.895499i	$-0.353181\pi$
$110$	11.0215	+	4.54389i	1.05086	+	0.433243i
$111$	9.29768	+	4.24611i	0.882497	+	0.403023i
$112$	−0.585371	+	0.438203i	−0.0553124	+	0.0414063i
$113$	3.15532	−	14.5048i	0.296828	−	1.36449i	−0.551125	−	0.834423i	$-0.685801\pi$
$113$	3.15532	−	14.5048i	0.296828	−	1.36449i	0.847953	−	0.530072i	$-0.177835\pi$
$114$	−3.34628			−0.313408
$115$	10.4141	−	2.55869i	0.971118	−	0.238599i
$116$	−1.03665			−0.0962507
$117$	−0.244451	+	1.12372i	−0.0225995	+	0.103888i
$118$	−3.42962	+	2.56738i	−0.315723	+	0.236347i
$119$	2.74640	+	1.25424i	0.251762	+	0.114976i
$120$	−0.859123	−	2.06444i	−0.0784268	−	0.188457i
$121$	−7.23816	−	15.8494i	−0.658014	−	1.44085i
$122$	−0.483744	+	6.76363i	−0.0437961	+	0.612350i
$123$	1.43111	−	1.91174i	0.129039	−	0.172376i
$124$	−1.08608	+	3.69884i	−0.0975327	+	0.332166i
$125$	−4.22721	+	10.3504i	−0.378093	+	0.925767i
$126$	−0.395327	+	0.615141i	−0.0352185	+	0.0548011i
$127$	−1.00437	+	0.218488i	−0.0891238	+	0.0193877i	−0.256906	−	0.966436i	$-0.582703\pi$
$127$	−1.00437	+	0.218488i	−0.0891238	+	0.0193877i	0.167782	+	0.985824i	$0.446339\pi$
$128$	0.997452	−	0.0713392i	0.0881631	−	0.00630555i
$129$	−2.03581	−	0.597769i	−0.179243	−	0.0526306i
$130$	0.640067	+	2.49055i	0.0561376	+	0.218436i
$131$	2.23551	+	2.57991i	0.195317	+	0.225408i	0.844957	−	0.534834i	$-0.179626\pi$
$131$	2.23551	+	2.57991i	0.195317	+	0.225408i	−0.649640	+	0.760242i	$0.725080\pi$
$132$	−1.86314	+	4.99526i	−0.162165	+	0.434782i
$133$	2.14756	+	1.17266i	0.186217	+	0.101682i
$134$	4.24525	−	9.29579i	0.366733	−	0.803034i
$135$	−1.52640	−	1.63404i	−0.131372	−	0.140636i
$136$	−2.23233	−	3.47358i	−0.191421	−	0.297857i
$137$	0.325816	+	0.325816i	0.0278363	+	0.0278363i	0.720888	−	0.693052i	$-0.243734\pi$
$137$	0.325816	+	0.325816i	0.0278363	+	0.0278363i	−0.693052	+	0.720888i	$0.743734\pi$
$138$	1.30215	+	4.61567i	0.110846	+	0.392912i
$139$			4.04375i			0.342986i	0.985185	+	0.171493i	$0.0548591\pi$
$139$			4.04375i			0.342986i	−0.985185	+	0.171493i	$0.945141\pi$
$140$	−0.172090	+	1.62597i	−0.0145442	+	0.137420i
$141$	−1.20441	+	8.37684i	−0.101429	+	0.705457i
$142$	−0.802049	−	2.15038i	−0.0673065	−	0.180456i
$143$	2.93834	−	5.38117i	0.245717	−	0.449996i
$144$	0.909632	−	0.415415i	0.0758027	−	0.0346179i
$145$	−1.57673	+	1.69916i	−0.130941	+	0.141108i
$146$	−1.25327	−	8.71670i	−0.103722	−	0.721399i
$147$	−5.67447	+	3.09850i	−0.468023	+	0.255560i
$148$	0.729184	+	10.1953i	0.0599385	+	0.838050i
$149$	3.21266	+	2.06465i	0.263191	+	0.169143i	0.665581	−	0.746326i	$-0.268184\pi$
$149$	3.21266	+	2.06465i	0.263191	+	0.169143i	−0.402390	+	0.915469i	$0.631820\pi$
$150$	−4.69050	−	1.73181i	−0.382978	−	0.141402i
$151$	−13.7527	+	15.8715i	−1.11918	+	1.29161i	−0.167040	+	0.985950i	$0.553421\pi$
$151$	−13.7527	+	15.8715i	−1.11918	+	1.29161i	−0.952142	+	0.305655i	$0.901124\pi$
$152$	−1.60370	−	2.93696i	−0.130077	−	0.238219i
$153$	−3.30547	−	2.47445i	−0.267232	−	0.200047i
$154$	2.94624	−	2.55293i	0.237414	−	0.205721i
$155$	4.41081	+	7.40607i	0.354284	+	0.594870i
$156$	−1.10342	+	0.323994i	−0.0883444	+	0.0259402i
$157$	−14.0894	+	5.25507i	−1.12445	+	0.419400i	−0.841783	−	0.539817i	$-0.818494\pi$
$157$	−14.0894	+	5.25507i	−1.12445	+	0.419400i	−0.282672	+	0.959217i	$0.591221\pi$
$158$	0.608242	+	0.812516i	0.0483891	+	0.0646403i
$159$	6.38365	−	4.10252i	0.506256	−	0.325351i
$160$	1.40018	−	1.74341i	0.110694	−	0.137829i
$161$	0.781811	−	3.41855i	0.0616153	−	0.269419i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	13.2615	+	2.88486i	1.03872	+	0.225960i	0.699415	−	0.714716i	$-0.253444\pi$
$163$	13.2615	+	2.88486i	1.03872	+	0.225960i	0.339306	+	0.940676i	$0.389808\pi$
$164$	2.36375	+	0.339856i	0.184578	+	0.0265383i
$165$	5.35385	+	10.6516i	0.416797	+	0.829223i
$166$	−4.31438	−	14.6934i	−0.334861	−	1.14043i
$167$	−21.2835	−	7.93835i	−1.64697	−	0.614288i	−0.656789	−	0.754075i	$-0.728086\pi$
$167$	−21.2835	−	7.93835i	−1.64697	−	0.614288i	−0.990182	+	0.139787i	$0.955358\pi$
$168$	−0.729356	−	0.0521646i	−0.0562711	−	0.00402459i
$169$	−11.5586	+	1.66188i	−0.889125	+	0.127837i
$170$	−9.08884	−	1.62429i	−0.697082	−	0.124577i
$171$	−2.52895	−	2.19135i	−0.193394	−	0.167577i
$172$	−0.451012	−	2.07327i	−0.0343894	−	0.158085i
$173$	3.72384	+	17.1182i	0.283118	+	1.30147i	0.870502	+	0.492165i	$0.163794\pi$
$173$	3.72384	+	17.1182i	0.283118	+	1.30147i	−0.587384	+	0.809308i	$0.699842\pi$
$174$	−0.783449	−	0.678863i	−0.0593931	−	0.0514644i
$175$	2.40336	+	2.75516i	0.181677	+	0.208270i
$176$	−5.27714	+	0.758739i	−0.397780	+	0.0571921i
$177$	−4.27322	−	0.305626i	−0.321195	−	0.0229723i
$178$	−7.08931	−	2.64418i	−0.531366	−	0.198189i
$179$	1.02598	+	3.49417i	0.0766854	+	0.261166i	0.988908	−	0.148528i	$-0.0474535\pi$
$179$	1.02598	+	3.49417i	0.0766854	+	0.261166i	−0.912223	+	0.409694i	$0.865635\pi$
$180$	0.702638	−	2.12280i	0.0523716	−	0.158225i
$181$	−24.2033	−	3.47991i	−1.79902	−	0.258660i	−0.840118	−	0.542404i	$-0.817514\pi$
$181$	−24.2033	−	3.47991i	−1.79902	−	0.258660i	−0.958900	+	0.283744i	$0.908423\pi$
$182$	0.821688	+	0.178747i	0.0609076	+	0.0132496i
$183$	−4.79482	+	4.79482i	−0.354444	+	0.354444i
$184$	−3.42702	+	3.35492i	−0.252644	+	0.247328i
$185$	17.8201	+	14.3118i	1.31016	+	1.05222i
$186$	−3.24303	+	2.08417i	−0.237791	+	0.152819i
$187$	13.1923	+	17.6228i	0.964716	+	1.28871i
$188$	−7.92939	+	2.95751i	−0.578310	+	0.215698i
$189$	−0.701600	+	0.206008i	−0.0510339	+	0.0149849i
$190$	−7.25314	−	1.83848i	−0.526198	−	0.133377i
$191$	11.5142	−	9.97710i	0.833138	−	0.721918i	−0.129830	−	0.991536i	$-0.541443\pi$
$191$	11.5142	−	9.97710i	0.833138	−	0.721918i	0.962967	+	0.269618i	$0.0868976\pi$
$192$	0.800541	+	0.599278i	0.0577741	+	0.0432491i
$193$	−6.81226	−	12.4757i	−0.490357	−	0.898022i	−0.999307	−	0.0372259i	$-0.988148\pi$
$193$	−6.81226	−	12.4757i	−0.490357	−	0.898022i	0.508950	−	0.860796i	$-0.330034\pi$
$194$	7.24069	−	8.35620i	0.519851	−	0.599940i
$195$	−1.14724	+	2.30139i	−0.0821553	+	0.164806i
$196$	−5.43897	−	3.49541i	−0.388498	−	0.249672i
$197$	−1.53410	−	21.4495i	−0.109300	−	1.52821i	−0.695784	−	0.718251i	$-0.744943\pi$
$197$	−1.53410	−	21.4495i	−0.109300	−	1.52821i	0.586485	−	0.809960i	$-0.300511\pi$
$198$	−4.67927	+	2.55507i	−0.332541	+	0.181581i
$199$	1.87852	+	13.0654i	0.133165	+	0.926183i	0.941393	+	0.337313i	$0.109518\pi$
$199$	1.87852	+	13.0654i	0.133165	+	0.926183i	−0.808228	+	0.588870i	$0.799573\pi$
$200$	−0.727946	−	4.94673i	−0.0514735	−	0.349786i
$201$	9.29579	−	4.24525i	0.655675	−	0.299437i
$202$	3.33329	−	6.10447i	0.234530	−	0.429509i
$203$	0.264901	+	0.710227i	0.0185924	+	0.0498481i
$204$	0.587625	−	4.08702i	0.0411420	−	0.286149i
$205$	4.15229	−	3.35747i	0.290009	−	0.234496i
$206$			11.9557i			0.832992i
$207$	−2.03852	+	4.34102i	−0.141687	+	0.301721i
$208$	−0.813176	−	0.813176i	−0.0563836	−	0.0563836i
$209$	9.64525	+	15.0083i	0.667176	+	1.03815i
$210$	−1.19484	+	1.11614i	−0.0824521	+	0.0770206i
$211$	−0.865610	+	1.89542i	−0.0595910	+	0.130486i	−0.937085	−	0.349102i	$-0.886487\pi$
$211$	−0.865610	+	1.89542i	−0.0595910	+	0.130486i	0.877494	+	0.479588i	$0.159214\pi$
$212$	6.66006	+	3.63667i	0.457415	+	0.249767i
$213$	0.802049	−	2.15038i	0.0549555	−	0.147341i
$214$	−5.14913	−	5.94241i	−0.351987	−	0.406215i
$215$	−4.08425	−	2.41417i	−0.278543	−	0.164645i
$216$	0.959493	+	0.281733i	0.0652852	+	0.0191695i
$217$	2.81167	−	0.201094i	0.190868	−	0.0136512i
$218$	12.8478	−	2.79487i	0.870163	−	0.189292i
$219$	4.76106	−	7.40836i	0.321723	−	0.500611i
$220$	−6.78283	+	9.80371i	−0.457298	+	0.660966i
$221$	−1.33779	+	4.55608i	−0.0899892	+	0.306475i
$222$	−6.12543	+	8.18262i	−0.411112	+	0.549182i
$223$	−1.02055	+	14.2691i	−0.0683409	+	0.955531i	0.841416	+	0.540388i	$0.181723\pi$
$223$	−1.02055	+	14.2691i	−0.0683409	+	0.955531i	−0.909757	+	0.415142i	$0.863732\pi$
$224$	−0.303760	−	0.665141i	−0.0202958	−	0.0444416i
$225$	−2.41075	−	4.38044i	−0.160717	−	0.292029i
$226$	13.5026	+	6.16643i	0.898179	+	0.410185i
$227$	−13.5844	+	10.1692i	−0.901630	+	0.674951i	−0.946036	−	0.324062i	$-0.894951\pi$
$227$	−13.5844	+	10.1692i	−0.901630	+	0.674951i	0.0444062	+	0.999014i	$0.485860\pi$
$228$	0.711304	−	3.26981i	0.0471072	−	0.216548i
$229$	8.23639			0.544276			0.272138	−	0.962258i	$-0.412269\pi$
$229$	8.23639			0.544276			0.272138	+	0.962258i	$0.412269\pi$
$230$	0.286543	+	10.7200i	0.0188941	+	0.706854i
$231$	3.89843			0.256498
$232$	0.220356	−	1.01296i	0.0144671	−	0.0665042i
$233$	−0.704713	+	0.527542i	−0.0461673	+	0.0345604i	−0.622112	−	0.782928i	$-0.713725\pi$
$233$	−0.704713	+	0.527542i	−0.0461673	+	0.0345604i	0.575945	+	0.817489i	$0.304634\pi$
$234$	−1.04608	−	0.477729i	−0.0683844	−	0.0312301i
$235$	−7.21289	+	17.4953i	−0.470517	+	1.14127i
$236$	−1.77969	−	3.89698i	−0.115848	−	0.253672i
$237$	−0.0724063	+	1.01237i	−0.00470329	+	0.0657606i
$238$	−1.80936	+	2.41703i	−0.117284	+	0.156673i
$239$	4.77159	−	16.2506i	0.308649	−	1.05116i	−0.648416	−	0.761286i	$-0.724568\pi$
$239$	4.77159	−	16.2506i	0.308649	−	1.05116i	0.957065	−	0.289875i	$-0.0936136\pi$
$240$	2.19988	−	0.400661i	0.142002	−	0.0258626i
$241$	7.42687	−	11.5564i	0.478407	−	0.744415i	−0.515230	−	0.857052i	$-0.672293\pi$
$241$	7.42687	−	11.5564i	0.478407	−	0.744415i	0.993636	+	0.112637i	$0.0359297\pi$
$242$	17.0257	−	3.70372i	1.09446	−	0.238084i
$243$	0.997452	−	0.0713392i	0.0639866	−	0.00457641i
$244$	−6.50623	−	1.91040i	−0.416519	−	0.122301i
$245$	−14.0019	+	3.59845i	−0.894548	+	0.229897i
$246$	1.56385	+	1.80477i	0.0997072	+	0.115068i
$247$	−1.34482	+	3.60561i	−0.0855689	+	0.229419i
$248$	−3.38345	−	1.84750i	−0.214849	−	0.117317i
$249$	6.36155	−	13.9299i	0.403147	−	0.882769i
$250$	−9.21530	−	6.33074i	−0.582827	−	0.400391i
$251$	6.55796	+	10.2044i	0.413935	+	0.644095i	0.984137	−	0.177409i	$-0.0567716\pi$
$251$	6.55796	+	10.2044i	0.413935	+	0.644095i	−0.570203	+	0.821504i	$0.693135\pi$
$252$	−0.517050	−	0.517050i	−0.0325711	−	0.0325711i
$253$	16.9483	−	19.1443i	1.06553	−	1.20359i
$254$		−	1.02786i		−	0.0644939i
$255$	−5.80520	−	7.17948i	−0.363536	−	0.449596i
$256$	−0.142315	+	0.989821i	−0.00889468	+	0.0618638i
$257$	−4.02658	−	10.7957i	−0.251171	−	0.673416i	−0.999944	−	0.0105891i	$-0.996629\pi$
$257$	−4.02658	−	10.7957i	−0.251171	−	0.673416i	0.748773	−	0.662827i	$-0.230643\pi$
$258$	1.01685	−	1.86222i	0.0633064	−	0.115937i
$259$	6.79864	−	3.10484i	0.422447	−	0.192925i
$260$	−2.56969	+	0.0960337i	−0.159366	+	0.00595576i
$261$	−0.147531	−	1.02610i	−0.00913194	−	0.0635140i
$262$	−2.99615	+	1.63602i	−0.185102	+	0.101074i
$263$	−0.0552028	−	0.771836i	−0.00340395	−	0.0475935i	0.995466	−	0.0951156i	$-0.0303221\pi$
$263$	−0.0552028	−	0.771836i	−0.00340395	−	0.0475935i	−0.998870	+	0.0475221i	$0.984868\pi$
$264$	−4.48507	−	2.88238i	−0.276037	−	0.177398i
$265$	16.0907	−	5.38507i	0.988442	−	0.330802i
$266$	−1.60236	+	1.84922i	−0.0982468	+	0.113383i
$267$	−3.62618	−	6.64084i	−0.221918	−	0.406413i
$268$	8.18096	+	6.12419i	0.499732	+	0.374095i
$269$	−9.21202	+	7.98226i	−0.561667	+	0.486687i	−0.888803	−	0.458290i	$-0.848462\pi$
$269$	−9.21202	+	7.98226i	−0.561667	+	0.486687i	0.327136	+	0.944977i	$0.393917\pi$
$270$	1.92116	−	1.14418i	0.116918	−	0.0696325i
$271$	25.8655	−	7.59479i	1.57122	−	0.461350i	0.623860	−	0.781536i	$-0.285563\pi$
$271$	25.8655	−	7.59479i	1.57122	−	0.461350i	0.947355	+	0.320185i	$0.103745\pi$
$272$	3.86871	−	1.44296i	0.234575	−	0.0874920i
$273$	0.503936	+	0.673179i	0.0304996	+	0.0407427i
$274$	−0.387627	+	0.249113i	−0.0234174	+	0.0150495i
$275$	5.75252	+	26.0290i	0.346890	+	1.56960i
$276$	−4.78698	+	0.291258i	−0.288142	+	0.0175317i
$277$	13.1094	−	13.1094i	0.787670	−	0.787670i	−0.193442	−	0.981112i	$-0.561965\pi$
$277$	13.1094	−	13.1094i	0.787670	−	0.787670i	0.981112	+	0.193442i	$0.0619651\pi$
$278$	−3.95134	−	0.859561i	−0.236985	−	0.0515530i
$279$	−3.81576	−	0.548623i	−0.228444	−	0.0328452i
$280$	−1.55224	−	0.513783i	−0.0927638	−	0.0307044i
$281$	−7.82466	−	26.6483i	−0.466780	−	1.58971i	−0.770823	−	0.637049i	$-0.780155\pi$
$281$	−7.82466	−	26.6483i	−0.466780	−	1.58971i	0.304043	−	0.952658i	$-0.401663\pi$
$282$	−7.92939	−	2.95751i	−0.472188	−	0.176117i
$283$	0.0101123		0.000723245i	0.000601113		4.29925e-5i	0.0716397	−	0.997431i	$-0.477177\pi$
$283$	0.0101123		0.000723245i	0.000601113		4.29925e-5i	−0.0710386	+	0.997474i	$0.522631\pi$
$284$	2.27172	−	0.326624i	0.134802	−	0.0193816i
$285$	−4.27761	−	6.13923i	−0.253384	−	0.363656i
$286$	4.63361	+	4.01504i	0.273991	+	0.237414i
$287$	−0.371181	−	1.70629i	−0.0219101	−	0.100719i
$288$	0.212565	+	0.977147i	0.0125255	+	0.0575789i
$289$	−0.0370715	−	0.0321227i	−0.00218068	−	0.00188957i
$290$	−1.32517	−	1.90188i	−0.0778166	−	0.111682i
$291$	10.9443	−	1.57355i	0.641566	−	0.0922433i
$292$	8.78390	+	0.628237i	0.514039	+	0.0367648i
$293$	10.2022	+	3.80522i	0.596019	+	0.222304i	0.629326	−	0.777142i	$-0.283331\pi$
$293$	10.2022	+	3.80522i	0.596019	+	0.222304i	−0.0333069	+	0.999445i	$0.510604\pi$
$294$	−1.82149	−	6.20343i	−0.106231	−	0.361791i
$295$	−9.09438	−	3.01020i	−0.529495	−	0.175260i
$296$	−10.1173	−	1.45465i	−0.588058	−	0.0845499i
$297$	−5.20957	−	1.13327i	−0.302290	−	0.0657591i
$298$	−2.70037	+	2.70037i	−0.156428	+	0.156428i
$299$	5.49668	+	0.451911i	0.317881	+	0.0261347i
$300$	2.68927	−	4.21519i	0.155265	−	0.243364i
$301$	−1.30518	+	0.838789i	−0.0752294	+	0.0483470i
$302$	−12.5854	−	16.8122i	−0.724211	−	0.967433i
$303$	6.51672	−	2.43061i	0.374376	−	0.139635i
$304$	3.21074	−	0.942757i	0.184148	−	0.0540708i
$305$	−13.0272	+	7.75856i	−0.745935	+	0.444254i
$306$	3.12053	−	2.70395i	0.178389	−	0.154575i
$307$	20.6641	+	15.4689i	1.17936	+	0.882858i	0.994988	−	0.0999989i	$-0.0318839\pi$
$307$	20.6641	+	15.4689i	1.17936	+	0.882858i	0.184372	+	0.982856i	$0.440975\pi$
$308$	1.86832	+	3.42157i	0.106457	+	0.194962i
$309$	−7.82931	+	9.03550i	−0.445394	+	0.514012i
$310$	−8.17440	+	2.73573i	−0.464275	+	0.155379i
$311$	−15.2611	−	9.80771i	−0.865377	−	0.556144i	0.0309584	−	0.999521i	$-0.490144\pi$
$311$	−15.2611	−	9.80771i	−0.865377	−	0.556144i	−0.896335	+	0.443377i	$0.853780\pi$
$312$	−0.0820403	−	1.14707i	−0.00464462	−	0.0649403i
$313$	−10.6095	+	5.79325i	−0.599687	+	0.327454i	−0.750258	−	0.661145i	$-0.770071\pi$
$313$	−10.6095	+	5.79325i	−0.599687	+	0.327454i	0.150571	+	0.988599i	$0.451889\pi$
$314$	−2.14006	−	14.8844i	−0.120771	−	0.839977i
$315$	−1.63392	+	0.0610622i	−0.0920607	+	0.00344046i
$316$	−0.923239	+	0.421629i	−0.0519362	+	0.0237185i
$317$	12.7135	−	23.2831i	0.714064	−	1.30771i	−0.228454	−	0.973555i	$-0.573367\pi$
$317$	12.7135	−	23.2831i	0.714064	−	1.30771i	0.942518	−	0.334156i	$-0.108451\pi$
$318$	2.65183	+	7.10982i	0.148707	+	0.398699i
$319$	−0.786548	+	5.47056i	−0.0440382	+	0.306293i
$320$	1.40594	+	1.73877i	0.0785945	+	0.0972003i
$321$		−	7.86294i		−	0.438866i
$322$	3.17424	+	1.49061i	0.176893	+	0.0830683i
$323$	−9.77007	−	9.77007i	−0.543621	−	0.543621i
$324$	0.540641	+	0.841254i	0.0300356	+	0.0467363i
$325$	−3.75106	+	4.35801i	−0.208072	+	0.241739i
$326$	−5.63787	+	12.3452i	−0.312253	+	0.683738i
$327$	11.5400	+	6.30130i	0.638162	+	0.348463i
$328$	−0.834541	+	2.23749i	−0.0460798	+	0.123545i
$329$	4.05247	+	4.67680i	0.223420	+	0.257840i
$330$	−11.5462	+	2.96734i	−0.635597	+	0.163347i
$331$	22.0841	+	6.48447i	1.21385	+	0.356419i	0.825133	−	0.564938i	$-0.191100\pi$
$331$	22.0841	+	6.48447i	1.21385	+	0.356419i	0.388718	+	0.921357i	$0.372918\pi$
$332$	15.2747	−	1.09247i	0.838309	−	0.0599570i
$333$	−9.98777	+	2.17271i	−0.547327	+	0.119064i
$334$	12.2811	−	19.1097i	0.671991	−	1.04564i
$335$	22.4812	−	4.09447i	1.22828	−	0.223705i
$336$	0.206008	−	0.701600i	0.0112387	−	0.0382754i
$337$	−6.07439	+	8.11444i	−0.330893	+	0.442022i	−0.934875	−	0.354976i	$-0.884489\pi$
$337$	−6.07439	+	8.11444i	−0.330893	+	0.442022i	0.603982	+	0.796998i	$0.293580\pi$
$338$	0.833063	−	11.6477i	0.0453126	−	0.633553i
$339$	6.16643	+	13.5026i	0.334914	+	0.733360i
$340$	3.51914	−	8.53586i	0.190852	−	0.462922i
$341$	18.6953	+	8.53785i	1.01241	+	0.462350i
$342$	2.67884	−	2.00535i	0.144855	−	0.108437i
$343$	−2.09294	+	9.62109i	−0.113008	+	0.519490i
$344$	2.12176			0.114398
$345$	−6.80354	+	8.28926i	−0.366290	+	0.446279i
$346$	−17.5186			−0.941803
$347$	0.623890	−	2.86797i	0.0334922	−	0.153961i	−0.957364	−	0.288885i	$-0.906715\pi$
$347$	0.623890	−	2.86797i	0.0334922	−	0.153961i	0.990856	+	0.134924i	$0.0430791\pi$
$348$	0.829883	−	0.621242i	0.0444864	−	0.0333021i
$349$	−2.04340	−	0.933191i	−0.109381	−	0.0499526i	0.359973	−	0.932963i	$-0.382786\pi$
$349$	−2.04340	−	0.933191i	−0.109381	−	0.0499526i	−0.469354	+	0.883010i	$0.655513\pi$
$350$	−3.20306	+	1.76279i	−0.171211	+	0.0942250i
$351$	−0.477729	−	1.04608i	−0.0254993	−	0.0558356i
$352$	0.380338	−	5.31782i	0.0202721	−	0.283441i
$353$	9.72782	−	12.9948i	0.517760	−	0.691646i	−0.463113	−	0.886299i	$-0.653267\pi$
$353$	9.72782	−	12.9948i	0.517760	−	0.691646i	0.980872	+	0.194654i	$0.0623583\pi$
$354$	1.20698	−	4.11059i	0.0641502	−	0.218476i
$355$	2.91990	−	4.22034i	0.154972	−	0.223992i
$356$	4.09069	−	6.36524i	0.216806	−	0.337357i
$357$	−2.95024	+	0.641786i	−0.156143	+	0.0339669i
$358$	−3.63240	+	0.259795i	−0.191978	+	0.0137306i
$359$	−14.1744	−	4.16198i	−0.748096	−	0.219661i	−0.114605	−	0.993411i	$-0.536560\pi$
$359$	−14.1744	−	4.16198i	−0.748096	−	0.219661i	−0.633491	+	0.773750i	$0.718379\pi$
$360$	1.92494	+	1.13782i	0.101453	+	0.0599681i
$361$	5.10948	+	5.89665i	0.268920	+	0.310350i
$362$	8.54517	−	22.9105i	0.449124	−	1.20415i
$363$	15.2926	+	8.35039i	0.802654	+	0.438282i
$364$	−0.349325	+	0.764914i	−0.0183096	+	0.0400924i
$365$	14.3899	−	13.4420i	0.753203	−	0.703587i
$366$	−3.66603	−	5.70446i	−0.191627	−	0.298177i
$367$	11.8008	+	11.8008i	0.615995	+	0.615995i	0.944502	−	0.328507i	$-0.106545\pi$
$367$	11.8008	+	11.8008i	0.615995	+	0.615995i	−0.328507	+	0.944502i	$0.606545\pi$
$368$	−2.54979	−	4.06185i	−0.132917	−	0.211738i
$369$			2.38806i			0.124317i
$370$	−17.7726	+	14.3706i	−0.923954	+	0.747094i
$371$	0.789660	−	5.49221i	0.0409971	−	0.285141i
$372$	−1.34718	−	3.61194i	−0.0698482	−	0.187270i
$373$	8.19515	−	15.0083i	0.424329	−	0.777100i	−0.574823	−	0.818278i	$-0.694929\pi$
$373$	8.19515	−	15.0083i	0.424329	−	0.777100i	0.999152	+	0.0411775i	$0.0131109\pi$
$374$	−20.0243	+	9.14480i	−1.03543	+	0.472866i
$375$	−2.81870	−	10.8192i	−0.145557	−	0.558701i
$376$	−1.20441	−	8.37684i	−0.0621126	−	0.432003i
$377$	−1.04633	+	0.571338i	−0.0538886	+	0.0294254i
$378$	−0.0521646	−	0.729356i	−0.00268306	−	0.0375140i
$379$	−14.2896	−	9.18335i	−0.734006	−	0.471717i	0.119478	−	0.992837i	$-0.461878\pi$
$379$	−14.2896	−	9.18335i	−0.734006	−	0.471717i	−0.853483	+	0.521120i	$0.825514\pi$
$380$	3.33823	−	6.69659i	0.171248	−	0.343528i
$381$	0.673108	−	0.776808i	0.0344844	−	0.0397971i
$382$	7.30158	+	13.3718i	0.373581	+	0.684163i
$383$	−25.3705	−	18.9922i	−1.29637	−	0.970454i	−0.999881	−	0.0154187i	$-0.995092\pi$
$383$	−25.3705	−	18.9922i	−1.29637	−	0.970454i	−0.296493	−	0.955035i	$-0.595817\pi$
$384$	−0.755750	+	0.654861i	−0.0385667	+	0.0334182i
$385$	8.44993	+	2.14183i	0.430648	+	0.109158i
$386$	13.6387	−	4.00467i	0.694190	−	0.203832i
$387$	1.98798	−	0.741479i	0.101055	−	0.0376915i
$388$	6.62612	+	8.85146i	0.336390	+	0.449365i
$389$	26.3866	−	16.9576i	1.33785	−	0.859785i	0.341077	−	0.940035i	$-0.389208\pi$
$389$	26.3866	−	16.9576i	1.33785	−	0.859785i	0.996775	+	0.0802501i	$0.0255719\pi$
$390$	−2.00493	−	1.61021i	−0.101524	−	0.0815363i
$391$	−9.67442	+	17.2781i	−0.489257	+	0.873793i
$392$	4.57167	−	4.57167i	0.230904	−	0.230904i
$393$	−3.33570	−	0.725637i	−0.168264	−	0.0366035i
$394$	21.2854	+	3.06037i	1.07234	+	0.154179i
$395$	−0.713149	+	2.15456i	−0.0358824	+	0.108408i
$396$	−1.50203	−	5.11545i	−0.0754799	−	0.257061i
$397$	−11.6960	−	4.36238i	−0.587005	−	0.218942i	0.0383729	−	0.999263i	$-0.487783\pi$
$397$	−11.6960	−	4.36238i	−0.587005	−	0.218942i	−0.625378	+	0.780322i	$0.715055\pi$
$398$	−13.1661	−	0.941661i	−0.659959	−	0.0472012i
$399$	−2.42196	+	0.348226i	−0.121250	+	0.0174331i
$400$	4.98841	+	0.340192i	0.249421	+	0.0170096i
$401$	4.68309	+	4.05792i	0.233862	+	0.202643i	0.763906	−	0.645327i	$-0.223279\pi$
$401$	4.68309	+	4.05792i	0.233862	+	0.202643i	−0.530044	+	0.847970i	$0.677825\pi$
$402$	2.17227	+	9.98575i	0.108343	+	0.498044i
$403$	0.942358	+	4.33195i	0.0469422	+	0.215790i
$404$	5.25642	+	4.55472i	0.261517	+	0.226606i
$405$	2.20119	+	0.393380i	0.109378	+	0.0195472i
$406$	−0.750304	+	0.107877i	−0.0372370	+	0.00535387i
$407$	54.3554	+	3.88758i	2.69430	+	0.192700i
$408$	3.86871	+	1.44296i	0.191530	+	0.0714369i
$409$	−1.14624	−	3.90373i	−0.0566779	−	0.193027i	0.926288	−	0.376817i	$-0.122982\pi$
$409$	−1.14624	−	3.90373i	−0.0566779	−	0.193027i	−0.982966	+	0.183790i	$0.941163\pi$
$410$	2.39811	+	4.77108i	0.118434	+	0.235627i
$411$	−0.456083	−	0.0655749i	−0.0224969	−	0.00323457i
$412$	−11.6825	−	2.54136i	−0.575553	−	0.125204i
$413$	−2.21511	+	2.21511i	−0.108999	+	0.108999i
$414$	−3.80849	−	2.91469i	−0.187177	−	0.143249i
$415$	21.4420	−	26.6982i	1.05255	−	1.31056i
$416$	0.967445	−	0.621739i	0.0474329	−	0.0304833i
$417$	−2.42333	−	3.23719i	−0.118671	−	0.158526i
$418$	−16.7156	+	6.23458i	−0.817585	+	0.304943i
$419$	−38.5066	+	11.3066i	−1.88117	+	0.552361i	−0.884930	+	0.465725i	$0.845794\pi$
$419$	−38.5066	+	11.3066i	−1.88117	+	0.552361i	−0.996240	+	0.0866363i	$0.972388\pi$
$420$	−0.836645	−	1.40479i	−0.0408241	−	0.0685467i
$421$	−23.0461	+	19.9695i	−1.12320	+	0.973256i	−0.999818	−	0.0191035i	$-0.993919\pi$
$421$	−23.0461	+	19.9695i	−1.12320	+	0.973256i	−0.123380	+	0.992360i	$0.539373\pi$
$422$	−1.66811	−	1.24873i	−0.0812021	−	0.0607872i
$423$	−4.05588	−	7.42778i	−0.197203	−	0.361151i
$424$	−4.96925	+	5.73482i	−0.241328	+	0.278508i
$425$	−8.63844	−	18.7511i	−0.419026	−	0.909562i
$426$	1.93075	+	1.24082i	0.0935450	+	0.0601177i
$427$	0.353723	+	4.94570i	0.0171179	+	0.239339i
$428$	6.90114	−	3.76831i	0.333579	−	0.182148i
$429$	0.872552	+	6.06873i	0.0421272	+	0.293001i
$430$	3.22717	−	3.47774i	0.155628	−	0.167712i
$431$	−17.4812	+	7.98341i	−0.842041	+	0.384547i	−0.789260	−	0.614059i	$-0.789536\pi$
$431$	−17.4812	+	7.98341i	−0.842041	+	0.384547i	−0.0527810	+	0.998606i	$0.516809\pi$
$432$	−0.479249	+	0.877679i	−0.0230579	+	0.0422274i
$433$	12.9575	+	34.7405i	0.622699	+	1.66952i	0.736849	+	0.676057i	$0.236313\pi$
$433$	12.9575	+	34.7405i	0.622699	+	1.66952i	−0.114150	+	0.993463i	$0.536415\pi$
$434$	−0.401164	+	2.79016i	−0.0192565	+	0.133932i
$435$	0.243972	−	2.30515i	0.0116976	−	0.110523i
$436$			13.1483i			0.629688i
$437$	−8.81935	+	13.4076i	−0.421887	+	0.641373i
$438$	6.22702	+	6.22702i	0.297538	+	0.297538i
$439$	−9.33852	−	14.5310i	−0.445703	−	0.693528i	0.543609	−	0.839338i	$-0.317057\pi$
$439$	−9.33852	−	14.5310i	−0.445703	−	0.693528i	−0.989313	+	0.145811i	$0.953421\pi$
$440$	−8.13787	−	8.71175i	−0.387958	−	0.415316i
$441$	2.68579	−	5.88106i	0.127895	−	0.280050i
$442$	−4.16759	−	2.27568i	−0.198232	−	0.108243i
$443$	11.9886	−	32.1427i	0.569596	−	1.52715i	−0.258186	−	0.966095i	$-0.583125\pi$
$443$	11.9886	−	32.1427i	0.569596	−	1.52715i	0.827782	−	0.561050i	$-0.189603\pi$
$444$	−6.69357	−	7.72479i	−0.317663	−	0.366602i
$445$	−4.21127	−	16.3864i	−0.199634	−	0.776791i
$446$	−13.7261	−	4.03034i	−0.649949	−	0.190842i
$447$	−3.80916	+	0.272437i	−0.180167	+	0.0128858i
$448$	0.714509	−	0.155432i	0.0337574	−	0.00734347i
$449$	−4.23591	+	6.59121i	−0.199905	+	0.311058i	−0.926704	−	0.375792i	$-0.877371\pi$
$449$	−4.23591	+	6.59121i	−0.199905	+	0.311058i	0.726799	+	0.686850i	$0.241007\pi$
$450$	4.79278	−	1.42453i	0.225934	−	0.0671529i
$451$	3.58694	−	12.2160i	0.168902	−	0.575229i
$452$	−8.89569	+	11.8832i	−0.418418	+	0.558941i
$453$	1.49820	−	20.9475i	0.0703914	−	0.984200i
$454$	−7.04920	−	15.4356i	−0.330835	−	0.724428i
$455$	0.722441	+	1.73600i	0.0338685	+	0.0813848i
$456$	3.04389	+	1.39010i	0.142543	+	0.0650972i
$457$	−28.5658	+	21.3841i	−1.33625	+	1.00030i	−0.338002	+	0.941145i	$0.609751\pi$
$457$	−28.5658	+	21.3841i	−1.33625	+	1.00030i	−0.998249	+	0.0591593i	$0.981158\pi$
$458$	−1.75077	+	8.04816i	−0.0818082	+	0.376066i
$459$	4.12905			0.192728
$460$	−10.5359	−	1.99870i	−0.491239	−	0.0931899i
$461$	0.770936			0.0359061			0.0179530	−	0.999839i	$-0.494285\pi$
$461$	0.770936			0.0359061			0.0179530	+	0.999839i	$0.494285\pi$
$462$	−0.828671	+	3.80934i	−0.0385533	+	0.177226i
$463$	2.58244	−	1.93319i	0.120016	−	0.0898431i	−0.537584	−	0.843211i	$-0.680663\pi$
$463$	2.58244	−	1.93319i	0.120016	−	0.0898431i	0.657600	+	0.753367i	$0.271572\pi$
$464$	0.942972	+	0.430641i	0.0437764	+	0.0199920i
$465$	−7.96932	−	3.28557i	−0.369568	−	0.152364i
$466$	−0.365688	−	0.800745i	−0.0169402	−	0.0370938i
$467$	0.0983634	−	1.37530i	0.00455172	−	0.0636413i	−0.994669	−	0.103124i	$-0.967116\pi$
$467$	0.0983634	−	1.37530i	0.00455172	−	0.0636413i	0.999220	+	0.0394822i	$0.0125709\pi$
$468$	0.689172	−	0.920626i	0.0318570	−	0.0425559i
$469$	2.10526	−	7.16985i	0.0972118	−	0.331073i
$470$	−15.5622	−	10.7669i	−0.717832	−	0.496642i
$471$	8.12988	−	12.6503i	0.374605	−	0.582897i
$472$	4.18623	−	0.910658i	0.192687	−	0.0419164i
$473$	−11.2831	+	0.806986i	−0.518799	+	0.0371053i
$474$	−0.973845	−	0.285947i	−0.0447302	−	0.0131340i
$475$	−5.89887	−	15.6571i	−0.270659	−	0.718395i
$476$	−1.97718	−	2.28179i	−0.0906240	−	0.104586i
$477$	−2.65183	+	7.10982i	−0.121419	+	0.325536i
$478$	14.8649	+	8.11685i	0.679905	+	0.371256i
$479$	1.33873	−	2.93141i	0.0611681	−	0.133940i	−0.876579	−	0.481257i	$-0.840180\pi$
$479$	1.33873	−	2.93141i	0.0611681	−	0.133940i	0.937747	+	0.347318i	$0.112908\pi$
$480$	−0.0761134	+	2.23477i	−0.00347409	+	0.102003i
$481$	6.35502	+	9.88860i	0.289764	+	0.450882i
$482$	9.71364	+	9.71364i	0.442444	+	0.442444i
$483$	1.42279	+	3.20521i	0.0647390	+	0.145842i
$484$			17.4239i			0.791996i
$485$	24.5865	+	2.60219i	1.11642	+	0.118159i
$486$	−0.142315	+	0.989821i	−0.00645553	+	0.0448992i
$487$	9.66064	+	25.9012i	0.437765	+	1.17369i	0.949283	+	0.314422i	$0.101811\pi$
$487$	9.66064	+	25.9012i	0.437765	+	1.17369i	−0.511518	+	0.859272i	$0.670917\pi$
$488$	3.24974	−	5.95146i	0.147109	−	0.269410i
$489$	−12.3452	+	5.63787i	−0.558270	+	0.254953i
$490$	−0.539901	−	14.4468i	−0.0243903	−	0.652640i
$491$	−1.77368	−	12.3362i	−0.0800451	−	0.556726i	−0.989897	−	0.141792i	$-0.954714\pi$
$491$	−1.77368	−	12.3362i	−0.0800451	−	0.556726i	0.909851	−	0.414934i	$-0.136195\pi$
$492$	−2.09595	+	1.14448i	−0.0944927	+	0.0515969i
$493$	−0.305359	−	4.26948i	−0.0137527	−	0.192288i
$494$	−3.23734	−	2.08051i	−0.145655	−	0.0936068i
$495$	−10.6692	−	5.31858i	−0.479546	−	0.239052i
$496$	2.52449	−	2.91341i	0.113353	−	0.130816i
$497$	−0.804280	−	1.47293i	−0.0360769	−	0.0660699i
$498$	12.2593	+	9.17718i	0.549351	+	0.411239i
$499$	−4.18631	+	3.62746i	−0.187405	+	0.162387i	−0.743510	−	0.668724i	$-0.766841\pi$
$499$	−4.18631	+	3.62746i	−0.187405	+	0.162387i	0.556105	+	0.831112i	$0.312295\pi$
$500$	8.14492	−	7.65900i	0.364252	−	0.342521i
$501$	21.7956	−	6.39978i	0.973757	−	0.285921i
$502$	−11.3652	+	4.23899i	−0.507253	+	0.189195i
$503$	−15.4433	−	20.6299i	−0.688585	−	0.919841i	0.310948	−	0.950427i	$-0.399354\pi$
$503$	−15.4433	−	20.6299i	−0.688585	−	0.919841i	−0.999532	+	0.0305858i	$0.990263\pi$
$504$	0.615141	−	0.395327i	0.0274006	−	0.0176093i
$505$	15.4605	−	1.68806i	0.687984	−	0.0751175i
$506$	15.1042	+	20.6304i	0.671463	+	0.917133i
$507$	8.25723	−	8.25723i	0.366717	−	0.366717i
$508$	1.00437	+	0.218488i	0.0445619	+	0.00969385i
$509$	−16.7782	−	2.41234i	−0.743679	−	0.106925i	−0.239949	−	0.970786i	$-0.577131\pi$
$509$	−16.7782	−	2.41234i	−0.743679	−	0.106925i	−0.503731	+	0.863861i	$0.668040\pi$
$510$	8.24939	−	4.14643i	0.365289	−	0.183607i
$511$	−1.81418	−	6.17852i	−0.0802545	−	0.273322i
$512$	−0.936950	−	0.349464i	−0.0414077	−	0.0154443i
$513$	3.33776	+	0.238721i	0.147366	+	0.0105398i
$514$	11.4049	−	1.63977i	0.503047	−	0.0723273i
$515$	−21.9344	+	15.2832i	−0.966544	+	0.673456i
$516$	1.60352	+	1.38946i	0.0705910	+	0.0611674i
$517$	9.59086	+	44.0885i	0.421806	+	1.93901i
$518$	1.58873	+	7.30325i	0.0698046	+	0.320887i
$519$	−13.2396	−	11.4722i	−0.581156	−	0.503574i
$520$	0.452388	−	2.53138i	0.0198385	−	0.111008i
$521$	−33.6976	+	4.84498i	−1.47632	+	0.212262i	−0.832972	−	0.553315i	$-0.813363\pi$
$521$	−33.6976	+	4.84498i	−1.47632	+	0.212262i	−0.643344	+	0.765577i	$0.722454\pi$
$522$	1.03401	+	0.0739539i	0.0452574	+	0.00323687i
$523$	3.86576	+	1.44185i	0.169038	+	0.0630478i	0.432558	−	0.901606i	$-0.357611\pi$
$523$	3.86576	+	1.44185i	0.169038	+	0.0630478i	−0.263521	+	0.964654i	$0.584884\pi$
$524$	−0.961754	−	3.27543i	−0.0420144	−	0.143088i
$525$	−3.57510	−	0.765334i	−0.156030	−	0.0334019i
$526$	0.765932	+	0.110124i	0.0333962	+	0.00480165i
$527$	−15.5537	−	3.38350i	−0.677530	−	0.147388i
$528$	3.76988	−	3.76988i	0.164063	−	0.164063i
$529$	21.9256	+	6.94756i	0.953286	+	0.302068i
$530$	1.84169	+	16.8676i	0.0799979	+	0.732683i
$531$	3.60404	−	2.31618i	0.156402	−	0.100514i
$532$	−1.46635	−	1.95882i	−0.0635745	−	0.0849255i
$533$	2.57312	−	0.959726i	0.111454	−	0.0415703i
$534$	7.25988	−	2.13169i	0.314166	−	0.0922474i
$535$	4.31997	−	17.0431i	0.186769	−	0.736837i
$536$	−7.72323	+	6.69221i	−0.333593	+	0.289060i
$537$	−2.91532	−	2.18238i	−0.125805	−	0.0941766i
$538$	−5.84169	−	10.6982i	−0.251853	−	0.461234i
$539$	−22.5726	+	26.0501i	−0.972269	+	1.12206i
$540$	0.709658	+	2.12047i	0.0305388	+	0.0912504i
$541$	−6.06421	−	3.89723i	−0.260721	−	0.167555i	0.403750	−	0.914869i	$-0.367707\pi$
$541$	−6.06421	−	3.89723i	−0.260721	−	0.167555i	−0.664471	+	0.747314i	$0.731343\pi$
$542$	1.92312	+	26.8888i	0.0826051	+	1.15497i
$543$	21.4612	−	11.7187i	0.920987	−	0.502897i
$544$	0.587625	+	4.08702i	0.0251942	+	0.175230i
$545$	21.5511	+	19.9984i	0.923149	+	0.856636i
$546$	−0.764914	+	0.349325i	−0.0327353	+	0.0149497i
$547$	7.36841	−	13.4942i	0.315051	−	0.576972i	−0.671387	−	0.741107i	$-0.734301\pi$
$547$	7.36841	−	13.4942i	0.315051	−	0.576972i	0.986438	+	0.164135i	$0.0524831\pi$
$548$	−0.161024	−	0.431722i	−0.00687860	−	0.0184422i
$549$	0.965023	−	6.71188i	0.0411862	−	0.286456i
$550$	−26.6569	+	0.0882016i	−1.13665	+	0.00376093i
$551$		−	3.46893i		−	0.147781i
$552$	0.732943	−	4.73949i	0.0311961	−	0.201726i
$553$	0.524784	+	0.524784i	0.0223161	+	0.0223161i
$554$	10.0232	+	15.5965i	0.425847	+	0.662630i
$555$	−22.8424	−	0.777983i	−0.969607	−	0.0330235i
$556$	1.67983	−	3.67832i	0.0712408	−	0.155996i
$557$	−23.3572	−	12.7540i	−0.989675	−	0.540404i	−0.0990213	−	0.995085i	$-0.531571\pi$
$557$	−23.3572	−	12.7540i	−0.989675	−	0.540404i	−0.890654	+	0.454682i	$0.849753\pi$
$558$	1.34718	−	3.61194i	0.0570308	−	0.152906i
$559$	−1.59788	−	1.84405i	−0.0675831	−	0.0779951i
$560$	0.831993	−	1.40755i	0.0351581	−	0.0594798i
$561$	−21.1219	−	6.20196i	−0.891769	−	0.261847i
$562$	27.7026	−	1.98133i	1.16856	−	0.0835773i
$563$	22.3139	−	4.85409i	0.940419	−	0.204576i	0.283873	−	0.958862i	$-0.408380\pi$
$563$	22.3139	−	4.85409i	0.940419	−	0.204576i	0.656546	+	0.754286i	$0.272017\pi$
$564$	4.57543	−	7.11951i	0.192660	−	0.299786i
$565$	5.94742	+	32.6550i	0.250210	+	1.37381i
$566$	−0.00285624	+	0.00972746i	−0.000120057	+	0.000408876i
$567$	0.438203	−	0.585371i	0.0184028	−	0.0245833i
$568$	−0.163729	+	2.28923i	−0.00686993	+	0.0960542i
$569$	19.2133	+	42.0712i	0.805461	+	1.76371i	0.625796	+	0.779987i	$0.284774\pi$
$569$	19.2133	+	42.0712i	0.805461	+	1.76371i	0.179665	+	0.983728i	$0.442499\pi$
$570$	6.90820	−	2.87487i	0.289353	−	0.120415i
$571$	37.3985	+	17.0793i	1.56508	+	0.714748i	0.994326	−	0.106373i	$-0.0339239\pi$
$571$	37.3985	+	17.0793i	1.56508	+	0.714748i	0.570754	+	0.821121i	$0.306651\pi$
$572$	−4.90823	+	3.67426i	−0.205223	+	0.153628i
$573$	−3.23853	+	14.8873i	−0.135292	+	0.621925i
$574$	1.74620			0.0728848
$575$	−19.3010	+	14.2292i	−0.804908	+	0.593400i
$576$	−1.00000			−0.0416667
$577$	5.09829	−	23.4365i	0.212245	−	0.975673i	−0.740537	−	0.672016i	$-0.765429\pi$
$577$	5.09829	−	23.4365i	0.212245	−	0.975673i	0.952781	−	0.303657i	$-0.0982077\pi$
$578$	0.0392687	−	0.0293962i	0.00163336	−	0.00122272i
$579$	12.9299	+	5.90490i	0.537349	+	0.245399i
$580$	2.14010	−	0.890611i	0.0888630	−	0.0369806i
$581$	−4.65169	−	10.1858i	−0.192985	−	0.422578i
$582$	−0.788786	+	11.0287i	−0.0326962	+	0.457153i
$583$	24.2444	−	32.3868i	1.00410	−	1.34132i
$584$	−2.48103	+	8.44962i	−0.102666	+	0.349648i
$585$	−0.460762	−	2.52987i	−0.0190502	−	0.104597i
$586$	−5.88690	+	9.16019i	−0.243185	+	0.378404i
$587$	7.93895	−	1.72701i	0.327676	−	0.0712815i	−0.0457182	−	0.998954i	$-0.514558\pi$
$587$	7.93895	−	1.72701i	0.327676	−	0.0712815i	0.373394	+	0.927673i	$0.378194\pi$
$588$	6.44885	−	0.461231i	0.265946	−	0.0190208i
$589$	−12.3774	−	3.63433i	−0.510001	−	0.149750i
$590$	4.87455	−	8.24668i	0.200682	−	0.339510i
$591$	14.0823	+	16.2518i	0.579268	+	0.668511i
$592$	3.57200	−	9.57690i	0.146808	−	0.393608i
$593$	−27.5200	−	15.0271i	−1.13011	−	0.617088i	−0.198340	−	0.980133i	$-0.563555\pi$
$593$	−27.5200	−	15.0271i	−1.13011	−	0.617088i	−0.931771	+	0.363045i	$0.881737\pi$
$594$	2.21475	−	4.84962i	0.0908722	−	0.198982i
$595$	−6.74732	−	0.229805i	−0.276613	−	0.00942108i
$596$	−2.06465	−	3.21266i	−0.0845714	−	0.131596i
$597$	−9.33365	−	9.33365i	−0.382001	−	0.382001i
$598$	−1.60999	+	5.27500i	−0.0658372	+	0.215711i
$599$		−	35.7889i		−	1.46230i	−0.682219	−	0.731148i	$-0.738985\pi$
$599$		−	35.7889i		−	1.46230i	0.682219	−	0.731148i	$-0.261015\pi$
$600$	3.54721	+	3.52382i	0.144814	+	0.143859i
$601$	−6.24159	+	43.4112i	−0.254600	+	1.77078i	0.315229	+	0.949016i	$0.397919\pi$
$601$	−6.24159	+	43.4112i	−0.254600	+	1.77078i	−0.569829	+	0.821763i	$0.692990\pi$
$602$	−0.542184	−	1.45365i	−0.0220978	−	0.0592464i
$603$	−4.89758	+	8.96926i	−0.199445	+	0.365256i
$604$	19.1032	−	8.72414i	0.777298	−	0.354980i
$605$	28.5593	+	26.5016i	1.16110	+	1.07744i
$606$	0.989835	+	6.88445i	0.0402093	+	0.279662i
$607$	−27.8632	+	15.2145i	−1.13093	+	0.617537i	−0.931993	−	0.362475i	$-0.881932\pi$
$607$	−27.8632	+	15.2145i	−1.13093	+	0.617537i	−0.198940	+	0.980012i	$0.563750\pi$
$608$	0.238721	+	3.33776i	0.00968142	+	0.135364i
$609$	−0.637687	−	0.409817i	−0.0258404	−	0.0166066i
$610$	−4.81213	−	14.3787i	−0.194837	−	0.582176i
$611$	−6.37341	+	7.35530i	−0.257840	+	0.297564i
$612$	1.97884	+	3.62398i	0.0799900	+	0.146491i
$613$	−16.8305	−	12.5992i	−0.679778	−	0.508875i	0.202693	−	0.979242i	$-0.435031\pi$
$613$	−16.8305	−	12.5992i	−0.679778	−	0.508875i	−0.882471	+	0.470367i	$0.844121\pi$
$614$	−19.5079	+	16.9037i	−0.787273	+	0.682176i
$615$	−1.31202	+	5.17617i	−0.0529058	+	0.208723i
$616$	−3.74052	+	1.09831i	−0.150710	+	0.0442524i
$617$	15.2381	−	5.68351i	0.613462	−	0.228810i	−0.0234760	−	0.999724i	$-0.507473\pi$
$617$	15.2381	−	5.68351i	0.613462	−	0.228810i	0.636938	+	0.770915i	$0.280201\pi$
$618$	−7.16477	−	9.57102i	−0.288209	−	0.385003i
$619$	−36.2848	+	23.3188i	−1.45841	+	0.937262i	−0.459617	+	0.888117i	$0.652013\pi$
$619$	−36.2848	+	23.3188i	−1.45841	+	0.937262i	−0.998792	+	0.0491454i	$0.984350\pi$
$620$	−0.935618	−	8.56911i	−0.0375753	−	0.344144i
$621$	−0.969552	−	4.69680i	−0.0389068	−	0.188476i
$622$	12.8275	−	12.8275i	0.514338	−	0.514338i
$623$	−5.40624	−	1.17606i	−0.216596	−	0.0471177i
$624$	1.13830	+	0.163663i	0.0455684	+	0.00655175i
$625$	−0.165437	−	24.9995i	−0.00661747	−	0.999978i
$626$	−3.40564	−	11.5985i	−0.136117	−	0.463571i
$627$	−16.7156	−	6.23458i	−0.667555	−	0.248985i
$628$	14.9992	+	1.07276i	0.598533	+	0.0428079i
$629$	−41.7749	+	6.00633i	−1.66568	+	0.239488i
$630$	0.287647	−	1.60956i	0.0114601	−	0.0641262i
$631$	−17.7450	−	15.3761i	−0.706417	−	0.612113i	0.225732	−	0.974189i	$-0.427523\pi$
$631$	−17.7450	−	15.3761i	−0.706417	−	0.612113i	−0.932149	+	0.362076i	$0.882068\pi$
$632$	−0.215745	−	0.991763i	−0.00858187	−	0.0394502i
$633$	−0.442927	−	2.03610i	−0.0176048	−	0.0809278i
$634$	20.0486	+	17.3722i	0.796231	+	0.689938i
$635$	1.88576	−	1.31394i	0.0748342	−	0.0521420i
$636$	−7.51102	+	1.07992i	−0.297831	+	0.0428217i
$637$	−7.41620	−	0.530417i	−0.293840	−	0.0210159i
$638$	−5.17835	−	1.93142i	−0.205013	−	0.0764658i
$639$	0.646599	+	2.20212i	0.0255791	+	0.0871143i
$640$	−1.99789	+	1.00421i	−0.0789735	+	0.0396949i
$641$	14.5971	+	2.09874i	0.576549	+	0.0828953i	0.424420	−	0.905465i	$-0.360478\pi$
$641$	14.5971	+	2.09874i	0.576549	+	0.0828953i	0.152129	+	0.988361i	$0.451387\pi$
$642$	7.68325	+	1.67139i	0.303234	+	0.0659644i
$643$	−1.60689	+	1.60689i	−0.0633697	+	0.0633697i	−0.738081	−	0.674712i	$-0.764268\pi$
$643$	−1.60689	+	1.60689i	−0.0633697	+	0.0633697i	0.674712	+	0.738081i	$0.264268\pi$
$644$	−2.13128	+	2.78484i	−0.0839840	+	0.109738i
$645$	4.71637	−	0.514956i	0.185707	−	0.0202764i
$646$	11.6236	−	7.47002i	0.457323	−	0.293904i
$647$	12.7299	+	17.0052i	0.500465	+	0.668543i	0.977645	−	0.210262i	$-0.0674318\pi$
$647$	12.7299	+	17.0052i	0.500465	+	0.668543i	−0.477180	+	0.878806i	$0.658341\pi$
$648$	−0.936950	+	0.349464i	−0.0368069	+	0.0137282i
$649$	−21.9153	+	6.43490i	−0.860249	+	0.252592i
$650$	−3.46107	−	4.59170i	−0.135754	−	0.180101i
$651$	−2.13034	+	1.84595i	−0.0834948	+	0.0723486i
$652$	−10.8647	−	8.13319i	−0.425493	−	0.318520i
$653$	4.71193	+	8.62925i	0.184392	+	0.337689i	0.953481	−	0.301453i	$-0.0974716\pi$
$653$	4.71193	+	8.62925i	0.184392	+	0.337689i	−0.769089	+	0.639142i	$0.779290\pi$
$654$	−8.61029	+	9.93681i	−0.336689	+	0.388560i
$655$	−6.83153	−	3.40550i	−0.266930	−	0.133064i
$656$	−2.00896	−	1.29108i	−0.0784368	−	0.0504083i
$657$	0.628237	+	8.78390i	0.0245098	+	0.342692i
$658$	−5.43134	+	2.96573i	−0.211736	+	0.115616i
$659$	5.21156	+	36.2472i	0.203013	+	1.41199i	0.795278	+	0.606245i	$0.207325\pi$
$659$	5.21156	+	36.2472i	0.203013	+	1.41199i	−0.592264	+	0.805744i	$0.701766\pi$
$660$	−0.445212	−	11.9131i	−0.0173298	−	0.463716i
$661$	23.2683	−	10.6263i	0.905033	−	0.413315i	0.0921521	−	0.995745i	$-0.470625\pi$
$661$	23.2683	−	10.6263i	0.905033	−	0.413315i	0.812881	+	0.582430i	$0.197898\pi$
$662$	−11.0306	+	20.2010i	−0.428716	+	0.785135i
$663$	−1.65940	−	4.44903i	−0.0644459	−	0.172786i
$664$	−2.17937	+	15.1579i	−0.0845760	+	0.588239i
$665$	−5.44097	−	0.575861i	−0.210992	−	0.0223309i
$666$		−	10.2214i		−	0.396070i
$667$	−4.78484	+	1.34987i	−0.185270	+	0.0522673i
$668$	16.0625	+	16.0625i	0.621476	+	0.621476i
$669$	−7.73417	−	12.0346i	−0.299020	−	0.465285i
$670$	−0.777825	+	22.8378i	−0.0300500	+	0.882301i
$671$	−15.0180	+	32.8848i	−0.579763	+	1.26950i
$672$	0.641776	+	0.350436i	0.0247570	+	0.0135184i
$673$	−7.98917	+	21.4198i	−0.307960	+	0.825672i	0.687115	+	0.726549i	$0.258877\pi$
$673$	−7.98917	+	21.4198i	−0.307960	+	0.825672i	−0.995075	+	0.0991240i	$0.968396\pi$
$674$	−6.63780	−	7.66042i	−0.255678	−	0.295069i
$675$	4.55501	+	2.06201i	0.175322	+	0.0793670i
$676$	11.2045	+	3.28993i	0.430941	+	0.126536i
$677$	−21.3685	+	1.52831i	−0.821259	+	0.0587376i	−0.475643	−	0.879638i	$-0.657785\pi$
$677$	−21.3685	+	1.52831i	−0.821259	+	0.0587376i	−0.345616	+	0.938376i	$0.612330\pi$
$678$	−14.5048	+	3.15532i	−0.557053	+	0.121179i
$679$	4.37107	−	6.80152i	0.167746	−	0.261018i
$680$	7.59274	+	5.25314i	0.291168	+	0.201449i
$681$	4.78073	−	16.2817i	0.183198	−	0.623915i
$682$	−12.3167	+	16.4532i	−0.471631	+	0.630025i
$683$	−1.75202	+	24.4965i	−0.0670392	+	0.937331i	0.846971	+	0.531639i	$0.178424\pi$
$683$	−1.75202	+	24.4965i	−0.0670392	+	0.937331i	−0.914010	+	0.405691i	$0.867031\pi$
$684$	1.39010	+	3.04389i	0.0531517	+	0.116386i
$685$	−0.952543	−	0.392711i	−0.0363948	−	0.0150047i
$686$	−8.95633	−	4.09022i	−0.341954	−	0.156165i
$687$	−6.59357	+	4.93589i	−0.251560	+	0.188316i
$688$	−0.451012	+	2.07327i	−0.0171947	+	0.0790427i
$689$	8.72653			0.332454
$690$	−6.65363	−	8.41006i	−0.253299	−	0.320166i
$691$	−8.38961			−0.319156			−0.159578	−	0.987185i	$-0.551013\pi$
$691$	−8.38961			−0.319156			−0.159578	+	0.987185i	$0.551013\pi$
$692$	3.72384	−	17.1182i	0.141559	−	0.650736i
$693$	−3.12085	+	2.33624i	−0.118551	+	0.0887465i
$694$	2.66982	+	1.21926i	0.101345	+	0.0462826i
$695$	−3.47408	−	8.34807i	−0.131779	−	0.316660i
$696$	0.430641	+	0.942972i	0.0163234	+	0.0357432i
$697$	−0.703434	+	9.83529i	−0.0266445	+	0.372538i
$698$	1.34622	−	1.79834i	0.0509552	−	0.0680682i
$699$	0.248008	−	0.844638i	0.00938052	−	0.0319471i
$700$	−1.04164	−	3.50457i	−0.0393704	−	0.132460i
$701$	−19.1231	+	29.7562i	−0.722271	+	1.12388i	0.264910	+	0.964273i	$0.414658\pi$
$701$	−19.1231	+	29.7562i	−0.722271	+	1.12388i	−0.987181	+	0.159603i	$0.948979\pi$
$702$	1.12372	−	0.244451i	0.0424122	−	0.00922620i
$703$	−34.1164	+	2.44006i	−1.28673	+	0.0920284i
$704$	5.11545	+	1.50203i	0.192796	+	0.0566099i
$705$	−4.71031	−	18.3282i	−0.177400	−	0.690280i
$706$	10.6301	+	12.2678i	0.400068	+	0.461703i
$707$	1.77731	−	4.76515i	0.0668426	−	0.179212i
$708$	3.76009	+	2.05317i	0.141313	+	0.0771627i
$709$	−3.05990	+	6.70024i	−0.114917	+	0.251633i	−0.958347	−	0.285606i	$-0.907805\pi$
$709$	−3.05990	+	6.70024i	−0.114917	+	0.251633i	0.843430	+	0.537239i	$0.180533\pi$
$710$	3.50322	+	3.75026i	0.131473	+	0.140745i
$711$	−0.548728	−	0.853837i	−0.0205789	−	0.0320214i
$712$	5.35023	+	5.35023i	0.200508	+	0.200508i
$713$	−0.196539	+	18.4869i	−0.00736045	+	0.692339i
$714$		−	3.01924i		−	0.112992i
$715$	−1.44294	+	13.6335i	−0.0539629	+	0.509864i
$716$	0.518265	−	3.60462i	0.0193685	−	0.134711i
$717$	5.91874	+	15.8687i	0.221039	+	0.592629i
$718$	7.07985	−	12.9658i	0.264218	−	0.483879i
$719$	37.9605	−	17.3360i	1.41569	−	0.646523i	0.446938	−	0.894565i	$-0.352514\pi$
$719$	37.9605	−	17.3360i	1.41569	−	0.646523i	0.968749	+	0.248042i	$0.0797872\pi$
$720$	−1.52099	+	1.63908i	−0.0566838	+	0.0610851i
$721$	1.24415	+	8.65325i	0.0463345	+	0.322264i
$722$	−6.84799	+	3.73929i	−0.254856	+	0.139162i
$723$	0.979998	+	13.7022i	0.0364465	+	0.509589i
$724$	20.5705	+	13.2199i	0.764497	+	0.491312i
$725$	1.79528	−	4.86242i	0.0666752	−	0.180586i
$726$	−11.4102	+	13.1681i	−0.423474	+	0.488715i
$727$	5.37606	+	9.84552i	0.199387	+	0.365150i	0.958173	−	0.286190i	$-0.0923889\pi$
$727$	5.37606	+	9.84552i	0.199387	+	0.365150i	−0.758786	+	0.651340i	$0.774207\pi$
$728$	−0.673179	−	0.503936i	−0.0249497	−	0.0186771i
$729$	−0.755750	+	0.654861i	−0.0279907	+	0.0242541i
$730$	10.0760	+	16.9184i	0.372930	+	0.626177i
$731$	8.40597	−	2.46822i	0.310906	−	0.0912903i
$732$	6.35337	−	2.36968i	0.234827	−	0.0875860i
$733$	11.7595	+	15.7089i	0.434348	+	0.580221i	0.963299	−	0.268432i	$-0.0865054\pi$
$733$	11.7595	+	15.7089i	0.434348	+	0.580221i	−0.528951	+	0.848652i	$0.677414\pi$
$734$	−14.0395	+	9.02264i	−0.518208	+	0.333032i
$735$	9.05262	−	11.2717i	0.333911	−	0.415764i
$736$	4.51102	−	1.62811i	0.166278	−	0.0600129i
$737$	38.5255	−	38.5255i	1.41910	−	1.41910i
$738$	−2.33348	−	0.507619i	−0.0858968	−	0.0186857i
$739$	−29.1991	−	4.19819i	−1.07410	−	0.154433i	−0.417507	−	0.908674i	$-0.637096\pi$
$739$	−29.1991	−	4.19819i	−1.07410	−	0.154433i	−0.656598	+	0.754241i	$0.728005\pi$
$740$	−10.2644	−	20.4212i	−0.377326	−	0.750697i
$741$	−1.08417	−	3.69236i	−0.0398281	−	0.135642i
$742$	5.19884	+	1.93907i	0.190855	+	0.0711854i
$743$	−40.5621	−	2.90106i	−1.48808	−	0.106430i	−0.696528	−	0.717530i	$-0.745273\pi$
$743$	−40.5621	−	2.90106i	−1.48808	−	0.106430i	−0.791553	+	0.611100i	$0.790727\pi$
$744$	3.81576	−	0.548623i	0.139893	−	0.0201135i
$745$	−8.40612	−	1.50228i	−0.307977	−	0.0550391i
$746$	12.9233	+	11.1981i	0.473156	+	0.409992i
$747$	3.25517	+	14.9638i	0.119100	+	0.547496i
$748$	−4.67934	−	21.5106i	−0.171094	−	0.786504i
$749$	−4.34521	−	3.76514i	−0.158770	−	0.137575i
$750$	11.1711	−	0.454501i	0.407911	−	0.0165960i
$751$	5.65139	−	0.812548i	0.206222	−	0.0296503i	−0.0384294	−	0.999261i	$-0.512235\pi$
$751$	5.65139	−	0.812548i	0.206222	−	0.0296503i	0.244652	+	0.969611i	$0.421326\pi$
$752$	8.44142	+	0.603742i	0.307827	+	0.0220162i
$753$	−11.3652	−	4.23899i	−0.414170	−	0.154477i
$754$	−0.335868	−	1.14386i	−0.0122316	−	0.0416570i
$755$	14.7561	−	44.5811i	0.537030	−	1.62247i
$756$	0.723777	+	0.104063i	0.0263235	+	0.00378475i
$757$	29.5047	+	6.41834i	1.07236	+	0.233279i	0.713888	−	0.700260i	$-0.246933\pi$
$757$	29.5047	+	6.41834i	1.07236	+	0.233279i	0.358477	+	0.933539i	$0.383296\pi$
$758$	12.0109	−	12.0109i	0.436257	−	0.436257i
$759$	−2.09505	+	25.4826i	−0.0760456	+	0.924958i
$760$	5.83396	+	4.68540i	0.211620	+	0.169957i
$761$	24.0716	−	15.4699i	0.872595	−	0.560783i	−0.0259501	−	0.999663i	$-0.508261\pi$
$761$	24.0716	−	15.4699i	0.872595	−	0.560783i	0.898546	+	0.438880i	$0.144625\pi$
$762$	0.615976	+	0.822848i	0.0223145	+	0.0298086i
$763$	9.00809	−	3.35985i	0.326115	−	0.121635i
$764$	−14.6183	+	4.29233i	−0.528872	+	0.155291i
$765$	8.94980	+	2.26854i	0.323581	+	0.0820191i
$766$	23.9510	−	20.7537i	0.865385	−	0.749861i
$767$	−3.94408	−	2.95250i	−0.142413	−	0.106609i
$768$	−0.479249	−	0.877679i	−0.0172934	−	0.0316705i
$769$	4.61815	−	5.32962i	0.166535	−	0.192191i	−0.666348	−	0.745641i	$-0.732143\pi$
$769$	4.61815	−	5.32962i	0.166535	−	0.192191i	0.832883	+	0.553450i	$0.186689\pi$
$770$	−3.88905	+	7.80154i	−0.140152	+	0.281148i
$771$	9.69305	+	6.22935i	0.349087	+	0.224344i
$772$	1.01405	+	14.1782i	0.0364964	+	0.510286i
$773$	−12.2339	+	6.68020i	−0.440022	+	0.240270i	−0.683958	−	0.729521i	$-0.739743\pi$
$773$	−12.2339	+	6.68020i	−0.440022	+	0.240270i	0.243937	+	0.969791i	$0.421561\pi$
$774$	0.301958	+	2.10016i	0.0108536	+	0.0754888i
$775$	−15.4686	−	11.5000i	−0.555647	−	0.413090i
$776$	−10.0577	+	4.59318i	−0.361049	+	0.164885i
$777$	−3.58194	+	6.55982i	−0.128501	+	0.235332i
$778$	10.9612	+	29.3881i	0.392979	+	1.05362i
$779$	−1.13726	+	7.90979i	−0.0407464	+	0.283397i
$780$	1.99959	−	1.61684i	0.0715970	−	0.0578921i
$781$		−	12.2360i		−	0.437839i
$782$	−14.8268	−	13.1261i	−0.530206	−	0.469387i
$783$	0.733024	+	0.733024i	0.0261961	+	0.0261961i
$784$	3.49541	+	5.43897i	0.124836	+	0.194249i
$785$	24.5719	−	22.9533i	0.877009	−	0.819237i
$786$	1.41811	−	3.10522i	0.0505822	−	0.110760i
$787$	−22.6158	−	12.3492i	−0.806166	−	0.440200i	0.0226350	−	0.999744i	$-0.492794\pi$
$787$	−22.6158	−	12.3492i	−0.806166	−	0.440200i	−0.828801	+	0.559544i	$0.810976\pi$
$788$	−7.51497	+	20.1484i	−0.267710	+	0.717757i
$789$	0.506736	+	0.584805i	0.0180403	+	0.0208196i
$790$	−1.95373	−	1.15484i	−0.0695106	−	0.0410872i
$791$	10.4146	+	3.05799i	0.370299	+	0.108730i
$792$	5.31782	−	0.380338i	0.188961	−	0.0135147i
$793$	−7.61986	+	1.65760i	−0.270589	+	0.0588630i
$794$	6.74885	−	10.5014i	0.239508	−	0.372681i
$795$	−9.65409	+	13.9537i	−0.342395	+	0.494888i
$796$	3.71881	−	12.6651i	0.131810	−	0.448902i
$797$	29.2959	−	39.1347i	1.03771	−	1.38622i	0.118279	−	0.992980i	$-0.462262\pi$
$797$	29.2959	−	39.1347i	1.03771	−	1.38622i	0.919435	−	0.393243i	$-0.128647\pi$
$798$	0.174558	−	2.44063i	0.00617927	−	0.0863975i
$799$	−14.5163	−	31.7862i	−0.513549	−	1.12452i
$800$	−1.39278	+	4.80210i	−0.0492423	+	0.169780i
$801$	6.88261	+	3.14318i	0.243185	+	0.111059i
$802$	−4.96064	+	3.71349i	−0.175166	+	0.131128i
$803$	9.97997	−	45.8772i	0.352186	−	1.61897i
$804$	−10.2193			−0.360407
$805$	1.32295	+	7.72905i	0.0466279	+	0.272413i
$806$	−4.43326			−0.156155
$807$	2.59101	−	11.9107i	0.0912079	−	0.419276i
$808$	−5.56796	+	4.16812i	−0.195880	+	0.146634i
$809$	10.2008	+	4.65856i	0.358642	+	0.163786i	0.586584	−	0.809888i	$-0.300472\pi$
$809$	10.2008	+	4.65856i	0.358642	+	0.163786i	−0.227942	+	0.973675i	$0.573200\pi$
$810$	−0.852287	+	2.06727i	−0.0299463	+	0.0726365i
$811$	−9.13314	−	19.9988i	−0.320708	−	0.702252i	0.678777	−	0.734344i	$-0.262510\pi$
$811$	−9.13314	−	19.9988i	−0.320708	−	0.702252i	−0.999485	+	0.0320921i	$0.989783\pi$
$812$	0.0540765	−	0.756089i	0.00189771	−	0.0265335i
$813$	−16.1550	+	21.5805i	−0.566580	+	0.756863i
$814$	−15.3528	+	52.2869i	−0.538116	+	1.83265i
$815$	−29.8560	+	5.43763i	−1.04581	+	0.190472i
$816$	−2.23233	+	3.47358i	−0.0781473	+	0.121600i
$817$	6.93775	−	1.50921i	0.242721	−	0.0528007i
$818$	4.05817	−	0.290246i	0.141891	−	0.0101482i
$819$	−0.806843	−	0.236910i	−0.0281934	−	0.00827832i
$820$	−5.17180	+	1.32914i	−0.180607	+	0.0464156i
$821$	29.5133	+	34.0602i	1.03002	+	1.18871i	0.981809	+	0.189871i	$0.0608069\pi$
$821$	29.5133	+	34.0602i	1.03002	+	1.18871i	0.0482122	+	0.998837i	$0.484648\pi$
$822$	0.161024	−	0.431722i	0.00561635	−	0.0150580i
$823$	13.5460	+	7.39669i	0.472185	+	0.257832i	0.697677	−	0.716413i	$-0.254217\pi$
$823$	13.5460	+	7.39669i	0.472185	+	0.257832i	−0.225492	+	0.974245i	$0.572399\pi$
$824$	4.96657	−	10.8753i	0.173019	−	0.378858i
$825$	−20.2037	−	17.3899i	−0.703402	−	0.605438i
$826$	−1.69363	−	2.63535i	−0.0589290	−	0.0916954i
$827$	6.21093	+	6.21093i	0.215975	+	0.215975i	0.806800	−	0.590825i	$-0.201198\pi$
$827$	6.21093	+	6.21093i	0.215975	+	0.215975i	−0.590825	+	0.806800i	$0.701198\pi$
$828$	3.65763	−	3.10189i	0.127111	−	0.107798i
$829$		−	10.9717i		−	0.381064i	−0.981681	−	0.190532i	$-0.938979\pi$
$829$		−	10.9717i		−	0.381064i	0.981681	−	0.190532i	$-0.0610212\pi$
$830$	21.5302	+	26.6271i	0.747325	+	0.924240i
$831$	−2.63845	+	18.3508i	−0.0915269	+	0.636584i
$832$	0.401885	+	1.07750i	0.0139329	+	0.0373554i
$833$	12.7938	−	23.4302i	0.443281	−	0.811808i
$834$	3.67832	−	1.67983i	0.127370	−	0.0581679i
$835$	50.7586	−	1.89693i	1.75657	−	0.0656461i
$836$	−2.53895	−	17.6588i	−0.0878116	−	0.610743i
$837$	3.38345	−	1.84750i	0.116949	−	0.0638591i
$838$	−2.86300	−	40.0300i	−0.0989007	−	1.38281i
$839$	12.0716	+	7.75792i	0.416757	+	0.267833i	0.732171	−	0.681121i	$-0.238507\pi$
$839$	12.0716	+	7.75792i	0.416757	+	0.267833i	−0.315414	+	0.948954i	$0.602144\pi$
$840$	1.55053	−	0.518916i	0.0534983	−	0.0179043i
$841$	−18.2872	+	21.1046i	−0.630594	+	0.727744i
$842$	−14.6144	−	26.7642i	−0.503645	−	0.922357i
$843$	22.2337	+	16.6440i	0.765770	+	0.573248i
$844$	1.57477	−	1.36455i	0.0542059	−	0.0469697i
$845$	22.4343	−	13.3611i	0.771764	−	0.459637i
$846$	8.12017	−	2.38430i	0.279177	−	0.0819738i
$847$	11.9374	−	4.45242i	0.410174	−	0.152987i
$848$	−4.54747	−	6.07472i	−0.156161	−	0.208607i
$849$	−0.00852873	+	0.00548108i	−0.000292705	+	0.000188110i
$850$	20.1588	−	4.45519i	0.691441	−	0.152812i
$851$	16.6415	+	46.1087i	0.570463	+	1.58059i
$852$	−1.62287	+	1.62287i	−0.0555986	+	0.0555986i
$853$	−44.1016	−	9.59372i	−1.51001	−	0.328483i	−0.620066	−	0.784550i	$-0.712894\pi$
$853$	−44.1016	−	9.59372i	−1.51001	−	0.328483i	−0.889946	+	0.456067i	$0.849258\pi$
$854$	−4.90786	−	0.705644i	−0.167944	−	0.0241466i
$855$	7.10351	+	2.35123i	0.242935	+	0.0804103i
$856$	2.21525	+	7.54443i	0.0757155	+	0.257863i
$857$	35.2751	+	13.1569i	1.20498	+	0.449433i	0.870122	−	0.492837i	$-0.164040\pi$
$857$	35.2751	+	13.1569i	1.20498	+	0.449433i	0.334854	+	0.942270i	$0.391313\pi$
$858$	−6.11552	−	0.437391i	−0.208780	−	0.0149323i
$859$	−1.04274	+	0.149924i	−0.0355779	+	0.00511533i	−0.160081	−	0.987104i	$-0.551175\pi$
$859$	−1.04274	+	0.149924i	−0.0355779	+	0.00511533i	0.124503	+	0.992219i	$0.460266\pi$
$860$	2.71228	+	3.89266i	0.0924880	+	0.132739i
$861$	1.31969	+	1.14351i	0.0449748	+	0.0389709i
$862$	−4.08506	−	18.7787i	−0.139138	−	0.639606i
$863$	5.93625	+	27.2885i	0.202072	+	0.928912i	0.960744	+	0.277438i	$0.0894853\pi$
$863$	5.93625	+	27.2885i	0.202072	+	0.928912i	−0.758671	+	0.651474i	$0.774151\pi$
$864$	−0.755750	−	0.654861i	−0.0257111	−	0.0222788i
$865$	−22.3943	−	32.1402i	−0.761428	−	1.09280i
$866$	−36.7009	+	5.27679i	−1.24715	+	0.179313i
$867$	0.0489277	+	0.00349938i	0.00166167	+	0.000118845i
$868$	−2.64112	−	0.985087i	−0.0896455	−	0.0334360i
$869$	1.52450	+	5.19197i	0.0517151	+	0.176125i
$870$	2.20061	+	0.728391i	0.0746076	+	0.0246948i
$871$	11.6326	+	1.67252i	0.394156	+	0.0566710i
$872$	−12.8478	−	2.79487i	−0.435081	−	0.0946462i
$873$	−7.81837	+	7.81837i	−0.264612	+	0.264612i
$874$	−11.2265	−	11.4678i	−0.379743	−	0.387904i
$875$	−7.32862	−	3.62307i	−0.247752	−	0.122482i
$876$	−7.40836	+	4.76106i	−0.250305	+	0.160861i
$877$	7.66894	+	10.2445i	0.258962	+	0.345932i	0.911113	−	0.412156i	$-0.135224\pi$
$877$	7.66894	+	10.2445i	0.258962	+	0.345932i	−0.652151	+	0.758089i	$0.726133\pi$
$878$	16.1840	−	6.03632i	0.546183	−	0.203716i
$879$	−10.4477	+	3.06771i	−0.352391	+	0.103471i
$880$	10.2425	−	6.10008i	0.345274	−	0.205634i
$881$	−36.5586	+	31.6782i	−1.23169	+	1.06726i	−0.236267	+	0.971688i	$0.575924\pi$
$881$	−36.5586	+	31.6782i	−1.23169	+	1.06726i	−0.995422	+	0.0955767i	$0.969530\pi$
$882$	5.17575	+	3.87452i	0.174277	+	0.130462i
$883$	9.82720	+	17.9972i	0.330712	+	0.605653i	0.989138	−	0.146992i	$-0.0469593\pi$
$883$	9.82720	+	17.9972i	0.330712	+	0.605653i	−0.658426	+	0.752645i	$0.728777\pi$
$884$	3.10956	−	3.58862i	0.104586	−	0.120698i
$885$	9.08437	−	3.04027i	0.305368	−	0.102198i
$886$	28.8598	+	18.5470i	0.969563	+	0.623100i
$887$	1.53311	+	21.4357i	0.0514768	+	0.719740i	0.956009	+	0.293336i	$0.0947654\pi$
$887$	1.53311	+	21.4357i	0.0514768	+	0.719740i	−0.904533	+	0.426404i	$0.859780\pi$
$888$	8.97108	−	4.89858i	0.301050	−	0.164386i
$889$	−0.106963	−	0.743944i	−0.00358742	−	0.0249511i
$890$	16.9071	−	0.631847i	0.566728	−	0.0211796i
$891$	4.84962	−	2.21475i	0.162468	−	0.0741968i
$892$	6.85593	−	12.5557i	0.229553	−	0.420396i
$893$	−9.89666	−	26.5340i	−0.331179	−	0.887926i
$894$	0.543485	−	3.78002i	0.0181769	−	0.126423i
$895$	−5.11999	−	6.33205i	−0.171143	−	0.211657i
$896$			0.731219i			0.0244283i
$897$	−4.67114	+	2.93226i	−0.155965	+	0.0979054i
$898$	−5.54017	−	5.54017i	−0.184878	−	0.184878i
$899$	−2.16056	−	3.36189i	−0.0720586	−	0.112125i
$900$	0.373196	+	4.98605i	0.0124399	+	0.166202i
$901$	−13.0159	+	28.5009i	−0.433623	+	0.949502i
$902$	11.1744	+	6.10166i	0.372066	+	0.203163i
$903$	0.542184	−	1.45365i	0.0180427	−	0.0483745i
$904$	−9.72076	−	11.2184i	−0.323308	−	0.373117i
$905$	52.9559	−	13.6096i	1.76031	−	0.452397i
$906$	20.1503	+	5.91667i	0.669450	+	0.196568i
$907$	−56.0918	+	4.01176i	−1.86250	+	0.133208i	−0.956805	−	0.290729i	$-0.906102\pi$
$907$	−56.0918	+	4.01176i	−1.86250	+	0.133208i	−0.905691	+	0.423938i	$0.860648\pi$
$908$	16.5812	−	3.60703i	0.550268	−	0.119703i
$909$	−3.76029	+	5.85112i	−0.124721	+	0.194070i
$910$	−1.84989	+	0.336918i	−0.0613233	+	0.0111687i
$911$	15.7642	−	53.6881i	0.522292	−	1.77876i	−0.0988895	−	0.995098i	$-0.531529\pi$
$911$	15.7642	−	53.6881i	0.522292	−	1.77876i	0.621182	−	0.783666i	$-0.286653\pi$
$912$	−2.00535	+	2.67884i	−0.0664039	+	0.0887052i
$913$	5.82440	−	81.4357i	0.192759	−	2.69513i
$914$	−14.8233	−	32.4585i	−0.490311	−	1.07363i
$915$	5.77928	−	14.0180i	0.191057	−	0.463420i
$916$	−7.49209	−	3.42152i	−0.247545	−	0.113050i
$917$	−1.99829	+	1.49590i	−0.0659894	+	0.0493990i
$918$	−0.877693	+	4.03469i	−0.0289682	+	0.133165i
$919$	−17.2725			−0.569766			−0.284883	−	0.958562i	$-0.591955\pi$
$919$	−17.2725			−0.569766			−0.284883	+	0.958562i	$0.591955\pi$
$920$	4.19259	−	9.87027i	0.138226	−	0.325413i
$921$	−25.8126			−0.850554
$922$	−0.163874	+	0.753317i	−0.00539691	+	0.0248092i
$923$	2.11291	−	1.58171i	0.0695473	−	0.0520625i
$924$	−3.54614	−	1.61947i	−0.116659	−	0.0532765i
$925$	−49.0840	−	14.2361i	−1.61387	−	0.468081i
$926$	1.34008	+	2.93436i	0.0440376	+	0.0964289i
$927$	0.852909	−	11.9252i	0.0280132	−	0.391676i
$928$	−0.621242	+	0.829883i	−0.0203933	+	0.0272422i
$929$	−3.47946	+	11.8499i	−0.114157	+	0.388784i	−0.996674	−	0.0814980i	$-0.974030\pi$
$929$	−3.47946	+	11.8499i	−0.114157	+	0.388784i	0.882516	+	0.470282i	$0.155848\pi$
$930$	4.90448	−	7.08880i	0.160824	−	0.232451i
$931$	11.6966	−	18.2003i	0.383342	−	0.596492i
$932$	0.860178	−	0.187120i	0.0281761	−	0.00612933i
$933$	18.0947	−	1.29416i	0.592393	−	0.0423688i
$934$	1.32296	+	0.388457i	0.0432886	+	0.0127107i
$935$	−42.3749	−	25.0475i	−1.38581	−	0.819140i
$936$	0.753092	+	0.869115i	0.0246156	+	0.0284079i
$937$	9.40305	−	25.2105i	0.307184	−	0.823592i	−0.688013	−	0.725699i	$-0.741517\pi$
$937$	9.40305	−	25.2105i	0.307184	−	0.823592i	0.995197	−	0.0978938i	$-0.0312106\pi$
$938$	6.55850	+	3.58121i	0.214142	+	0.116931i
$939$	5.02162	−	10.9958i	0.163874	−	0.358834i
$940$	13.8289	−	12.9179i	0.451048	−	0.421336i
$941$	3.33939	+	5.19619i	0.108861	+	0.169391i	0.891410	−	0.453198i	$-0.149717\pi$
$941$	3.33939	+	5.19619i	0.108861	+	0.169391i	−0.782549	+	0.622589i	$0.786081\pi$
$942$	10.6331	+	10.6331i	0.346446	+	0.346446i
$943$	11.3528	−	1.50929i	0.369700	−	0.0491493i
$944$			4.28413i			0.139437i
$945$	1.27142	−	1.02805i	0.0413594	−	0.0334425i
$946$	1.60986	−	11.1968i	0.0523411	−	0.364040i
$947$	9.77214	+	26.2001i	0.317552	+	0.851389i	0.993437	+	0.114382i	$0.0364888\pi$
$947$	9.77214	+	26.2001i	0.317552	+	0.851389i	−0.675885	+	0.737007i	$0.736238\pi$
$948$	0.486418	−	0.890808i	0.0157981	−	0.0289321i
$949$	9.21213	−	4.20704i	0.299038	−	0.136566i
$950$	16.5531	−	2.43591i	0.537055	−	0.0790314i
$951$	3.77534	+	26.2580i	0.122424	+	0.851476i
$952$	2.64992	−	1.44697i	0.0858846	−	0.0468965i
$953$	0.553792	+	7.74303i	0.0179391	+	0.250821i	0.998506	+	0.0546375i	$0.0174003\pi$
$953$	0.553792	+	7.74303i	0.0179391	+	0.250821i	−0.980567	+	0.196184i	$0.937145\pi$
$954$	−6.38365	−	4.10252i	−0.206678	−	0.132824i
$955$	−15.1988	+	30.4892i	−0.491821	+	0.986608i
$956$	−11.0911	+	12.7998i	−0.358712	+	0.413976i
$957$	−2.64872	−	4.85077i	−0.0856210	−	0.156803i
$958$	2.57985	+	1.93125i	0.0833512	+	0.0623959i
$959$	−0.254632	+	0.220640i	−0.00822250	+	0.00712484i
$960$	−2.16752	−	0.549409i	−0.0699565	−	0.0177321i
$961$	15.4852	−	4.54688i	0.499524	−	0.146674i
$962$	−11.0135	+	4.10781i	−0.355089	+	0.132441i
$963$	4.71208	+	6.29461i	0.151845	+	0.202841i
$964$	−11.5564	+	7.42687i	−0.372208	+	0.239203i
$965$	24.7817	+	19.9028i	0.797750	+	0.640694i
$966$	−3.43439	+	0.708955i	−0.110500	+	0.0228103i
$967$	35.4668	−	35.4668i	1.14054	−	1.14054i	0.152183	−	0.988352i	$-0.451370\pi$
$967$	35.4668	−	35.4668i	1.14054	−	1.14054i	0.988352	−	0.152183i	$-0.0486303\pi$
$968$	−17.0257	−	3.70372i	−0.547228	−	0.119042i
$969$	13.6763	+	1.96636i	0.439347	+	0.0631686i
$970$	−7.76896	+	23.4715i	−0.249446	+	0.753625i
$971$	−9.83105	−	33.4815i	−0.315494	−	1.07447i	−0.952734	−	0.303807i	$-0.901742\pi$
$971$	−9.83105	−	33.4815i	−0.315494	−	1.07447i	0.637240	−	0.770665i	$-0.280076\pi$
$972$	−0.936950	−	0.349464i	−0.0300527	−	0.0112091i
$973$	−2.94933	−	0.210941i	−0.0945513	−	0.00676244i
$974$	−27.3628	+	3.93417i	−0.876759	+	0.126059i
$975$	0.391223	−	5.73669i	0.0125291	−	0.183721i
$976$	5.12467	+	4.44055i	0.164037	+	0.142138i
$977$	−2.05411	−	9.44258i	−0.0657167	−	0.302095i	0.932543	−	0.361058i	$-0.117584\pi$
$977$	−2.05411	−	9.44258i	−0.0657167	−	0.302095i	−0.998260	+	0.0589628i	$0.981221\pi$
$978$	−2.88486	−	13.2615i	−0.0922477	−	0.424056i
$979$	−30.4865	−	26.4167i	−0.974353	−	0.844281i
$980$	14.2314	+	2.54333i	0.454606	+	0.0812436i
$981$	−13.0144	+	1.87120i	−0.415519	+	0.0597427i
$982$	12.4313	+	0.889106i	0.396700	+	0.0283725i
$983$	20.7613	+	7.74358i	0.662184	+	0.246982i	0.658010	−	0.753010i	$-0.271399\pi$
$983$	20.7613	+	7.74358i	0.662184	+	0.246982i	0.00417409	+	0.999991i	$0.498671\pi$
$984$	−0.672794	−	2.29133i	−0.0214479	−	0.0730448i
$985$	21.5948	+	42.9631i	0.688067	+	1.36892i
$986$	4.23682	+	0.609163i	0.134928	+	0.0193997i
$987$	−6.04687	−	1.31542i	−0.192474	−	0.0418702i
$988$	2.72112	−	2.72112i	0.0865702	−	0.0865702i
$989$	−4.78143	−	8.98225i	−0.152041	−	0.285619i
$990$	7.46494	−	9.29485i	0.237251	−	0.295410i
$991$	−27.7599	+	17.8402i	−0.881821	+	0.566712i	−0.901347	−	0.433097i	$-0.857421\pi$
$991$	−27.7599	+	17.8402i	−0.881821	+	0.566712i	0.0195258	+	0.999809i	$0.493784\pi$
$992$	2.31021	+	3.08608i	0.0733494	+	0.0979833i
$993$	−21.5652	+	8.04341i	−0.684351	+	0.255250i
$994$	1.61023	−	0.472806i	0.0510734	−	0.0149965i
$995$	−15.1029	−	25.3589i	−0.478794	−	0.803930i
$996$	−11.5733	+	10.0284i	−0.366716	+	0.317761i
$997$	32.0467	+	23.9899i	1.01493	+	0.759766i	0.970954	−	0.239266i	$-0.0769069\pi$
$997$	32.0467	+	23.9899i	1.01493	+	0.759766i	0.0439751	+	0.999033i	$0.485998\pi$
$998$	−2.65470	−	4.86171i	−0.0840330	−	0.153895i
$999$	6.69357	−	7.72479i	0.211775	−	0.244402i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	690.2.w.b.103.1	yes	240
5.2	odd	4	inner	690.2.w.b.517.6	yes	240
23.21	odd	22	inner	690.2.w.b.343.6	yes	240
115.67	even	44	inner	690.2.w.b.67.1	✓	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
690.2.w.b.67.1	✓	240	115.67	even	44	inner
690.2.w.b.103.1	yes	240	1.1	even	1	trivial
690.2.w.b.343.6	yes	240	23.21	odd	22	inner
690.2.w.b.517.6	yes	240	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	690.w (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212565 + 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.06444 + 0.859123i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.0521646 + 0.729356i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +O(q^{10})\)	\(q+(-0.212565 + 0.977147i) q^{2} +(-0.800541 + 0.599278i) q^{3} +(-0.909632 - 0.415415i) q^{4} +(-2.06444 + 0.859123i) q^{5} +(-0.415415 - 0.909632i) q^{6} +(-0.0521646 + 0.729356i) q^{7} +(0.599278 - 0.800541i) q^{8} +(0.281733 - 0.959493i) q^{9} +(-0.400661 - 2.19988i) q^{10} +(-2.88238 + 4.48507i) q^{11} +(0.977147 - 0.212565i) q^{12} +(-1.14707 + 0.0820403i) q^{13} +(-0.701600 - 0.206008i) q^{14} +(1.13782 - 1.92494i) q^{15} +(0.654861 + 0.755750i) q^{16} +(1.44296 - 3.86871i) q^{17} +(0.877679 + 0.479249i) q^{18} +(1.39010 - 3.04389i) q^{19} +(2.23477 + 0.0761134i) q^{20} +(-0.395327 - 0.615141i) q^{21} +(-3.76988 - 3.76988i) q^{22} +(-4.73949 - 0.732943i) q^{23} +1.00000i q^{24} +(3.52382 - 3.54721i) q^{25} +(0.163663 - 1.13830i) q^{26} +(0.349464 + 0.936950i) q^{27} +(0.350436 - 0.641776i) q^{28} +(0.942972 - 0.430641i) q^{29} +(1.63908 + 1.52099i) q^{30} +(-0.548623 - 3.81576i) q^{31} +(-0.877679 + 0.479249i) q^{32} +(-0.380338 - 5.31782i) q^{33} +(3.47358 + 2.23233i) q^{34} +(-0.518916 - 1.55053i) q^{35} +(-0.654861 + 0.755750i) q^{36} +(-4.89858 - 8.97108i) q^{37} +(2.67884 + 2.00535i) q^{38} +(0.869115 - 0.753092i) q^{39} +(-0.549409 + 2.16752i) q^{40} +(-2.29133 + 0.672794i) q^{41} +(0.685116 - 0.255535i) q^{42} +(1.27152 + 1.69856i) q^{43} +(4.48507 - 2.88238i) q^{44} +(0.242703 + 2.22286i) q^{45} +(1.72365 - 4.47538i) q^{46} +(5.98423 - 5.98423i) q^{47} +(-0.977147 - 0.212565i) q^{48} +(6.39951 + 0.920111i) q^{49} +(2.71711 + 4.19730i) q^{50} +(1.16329 + 3.96179i) q^{51} +(1.07750 + 0.401885i) q^{52} +(-7.56893 - 0.541340i) q^{53} +(-0.989821 + 0.142315i) q^{54} +(2.09727 - 11.7355i) q^{55} +(0.552619 + 0.478847i) q^{56} +(0.711304 + 3.26981i) q^{57} +(0.220356 + 1.01296i) q^{58} +(3.23773 + 2.80551i) q^{59} +(-1.83464 + 1.27832i) q^{60} +(6.71188 - 0.965023i) q^{61} +(3.84518 + 0.275012i) q^{62} +(0.685116 + 0.255535i) q^{63} +(-0.281733 - 0.959493i) q^{64} +(2.29758 - 1.15484i) q^{65} +(5.27714 + 0.758739i) q^{66} +(-9.98575 - 2.17227i) q^{67} +(-2.91968 + 2.91968i) q^{68} +(4.23340 - 2.25352i) q^{69} +(1.62540 - 0.177469i) q^{70} +(-1.93075 + 1.24082i) q^{71} +(-0.599278 - 0.800541i) q^{72} +(-8.25109 + 3.07750i) q^{73} +(9.80733 - 2.87969i) q^{74} +(-0.695195 + 4.95143i) q^{75} +(-2.52895 + 2.19135i) q^{76} +(-3.12085 - 2.33624i) q^{77} +(0.551138 + 1.00933i) q^{78} +(0.664656 - 0.767054i) q^{79} +(-2.00120 - 0.997593i) q^{80} +(-0.841254 - 0.540641i) q^{81} +(-0.170362 - 2.38198i) q^{82} +(-13.4405 + 7.33909i) q^{83} +(0.104063 + 0.723777i) q^{84} +(0.344806 + 9.22640i) q^{85} +(-1.93002 + 0.881410i) q^{86} +(-0.496814 + 0.909848i) q^{87} +(1.86314 + 4.99526i) q^{88} +(-1.07681 + 7.48936i) q^{89} +(-2.22365 - 0.235346i) q^{90} -0.840905i q^{91} +(4.00672 + 2.63557i) q^{92} +(2.72590 + 2.72590i) q^{93} +(4.57543 + 7.11951i) q^{94} +(-0.254697 + 7.47818i) q^{95} +(0.415415 - 0.909632i) q^{96} +(-9.70436 - 5.29898i) q^{97} +(-2.25940 + 6.05768i) q^{98} +(3.49133 + 4.02921i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 24 q^{6}+O(q^{10}) \) 240 * q + 24 * q^6	\( 240 q + 24 q^{6} - 44 q^{10} + 24 q^{16} - 44 q^{21} + 96 q^{23} + 16 q^{25} + 16 q^{26} + 44 q^{28} - 16 q^{31} + 44 q^{33} + 16 q^{35} - 24 q^{36} + 44 q^{37} - 88 q^{43} + 8 q^{46} + 96 q^{47} - 24 q^{50} - 24 q^{55} + 44 q^{57} - 16 q^{58} + 88 q^{61} + 56 q^{62} - 88 q^{65} + 132 q^{67} - 56 q^{70} + 16 q^{71} + 48 q^{73} + 24 q^{81} - 24 q^{82} + 44 q^{85} - 16 q^{87} + 44 q^{88} - 124 q^{92} + 32 q^{93} + 20 q^{95} - 24 q^{96} - 56 q^{98}+O(q^{100}) \) 240 * q + 24 * q^6 - 44 * q^10 + 24 * q^16 - 44 * q^21 + 96 * q^23 + 16 * q^25 + 16 * q^26 + 44 * q^28 - 16 * q^31 + 44 * q^33 + 16 * q^35 - 24 * q^36 + 44 * q^37 - 88 * q^43 + 8 * q^46 + 96 * q^47 - 24 * q^50 - 24 * q^55 + 44 * q^57 - 16 * q^58 + 88 * q^61 + 56 * q^62 - 88 * q^65 + 132 * q^67 - 56 * q^70 + 16 * q^71 + 48 * q^73 + 24 * q^81 - 24 * q^82 + 44 * q^85 - 16 * q^87 + 44 * q^88 - 124 * q^92 + 32 * q^93 + 20 * q^95 - 24 * q^96 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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