LMFDB - Embedded newform 276.2.o.a.35.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [276,2,Mod(35,276)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(276, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([11, 11, 20]))

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

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

chi := DirichletCharacter("276.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 276 = 2^{2} \cdot 3 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	276.o (of order $22$, degree $10$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.20387109579$
Analytic rank:	$0$
Dimension:	$440$
Relative dimension:	$44$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			35.17
Character	$\chi$	$=$	276.35
Dual form			276.2.o.a.71.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.542515 + 1.30602i) q^{2} +(-0.619297 - 1.61755i) q^{3} +(-1.41135 - 1.41707i) q^{4} +(-0.512900 - 1.74678i) q^{5} +(2.44853 + 0.0687346i) q^{6} +(-3.04781 + 2.64094i) q^{7} +(2.61639 - 1.07447i) q^{8} +(-2.23294 + 2.00349i) q^{9} +O(q^{10})$	\(q+(-0.542515 + 1.30602i) q^{2} +(-0.619297 - 1.61755i) q^{3} +(-1.41135 - 1.41707i) q^{4} +(-0.512900 - 1.74678i) q^{5} +(2.44853 + 0.0687346i) q^{6} +(-3.04781 + 2.64094i) q^{7} +(2.61639 - 1.07447i) q^{8} +(-2.23294 + 2.00349i) q^{9} +(2.55957 + 0.277798i) q^{10} +(3.05049 + 1.96043i) q^{11} +(-1.41813 + 3.16052i) q^{12} +(-4.27444 + 4.93297i) q^{13} +(-1.79563 - 5.41324i) q^{14} +(-2.50786 + 1.91142i) q^{15} +(-0.0161603 + 3.99997i) q^{16} +(-3.77945 + 1.72602i) q^{17} +(-1.40518 - 4.00318i) q^{18} +(1.88294 + 0.859910i) q^{19} +(-1.75142 + 3.19213i) q^{20} +(6.15936 + 3.29446i) q^{21} +(-4.21529 + 2.92042i) q^{22} +(-1.84505 - 4.42671i) q^{23} +(-3.35833 - 3.56673i) q^{24} +(1.41811 - 0.911362i) q^{25} +(-4.12359 - 8.25871i) q^{26} +(4.62360 + 2.37114i) q^{27} +(8.04393 + 0.591648i) q^{28} +(-1.91216 + 0.873255i) q^{29} +(-1.13578 - 4.31228i) q^{30} +(-2.21649 + 0.318683i) q^{31} +(-5.21525 - 2.19115i) q^{32} +(1.28194 - 6.14841i) q^{33} +(-0.203795 - 5.87241i) q^{34} +(6.17635 + 3.96930i) q^{35} +(5.99055 + 0.336597i) q^{36} +(-7.66522 - 2.25071i) q^{37} +(-2.14458 + 1.99264i) q^{38} +(10.6265 + 3.85916i) q^{39} +(-3.21881 - 4.01916i) q^{40} +(-0.908324 - 3.09347i) q^{41} +(-7.64416 + 6.25692i) q^{42} +(-6.73787 - 0.968760i) q^{43} +(-1.52726 - 7.08961i) q^{44} +(4.64492 + 2.87286i) q^{45} +(6.78233 - 0.00810976i) q^{46} -2.73062 q^{47} +(6.48016 - 2.45103i) q^{48} +(1.31836 - 9.16942i) q^{49} +(0.420908 + 2.34650i) q^{50} +(5.13252 + 5.04453i) q^{51} +(13.0231 - 0.904993i) q^{52} +(5.77832 - 5.00694i) q^{53} +(-5.60512 + 4.75211i) q^{54} +(1.85984 - 6.33403i) q^{55} +(-5.13666 + 10.1845i) q^{56} +(0.224849 - 3.57829i) q^{57} +(-0.103107 - 2.97107i) q^{58} +(-6.25607 + 7.21989i) q^{59} +(6.24809 + 0.856127i) q^{60} +(0.976622 + 6.79256i) q^{61} +(0.786275 - 3.06766i) q^{62} +(1.51448 - 12.0033i) q^{63} +(5.69103 - 5.62247i) q^{64} +(10.8092 + 4.93638i) q^{65} +(7.33445 + 5.00984i) q^{66} +(6.10076 + 9.49297i) q^{67} +(7.78002 + 2.91971i) q^{68} +(-6.01779 + 5.72592i) q^{69} +(-8.53474 + 5.91301i) q^{70} +(-5.66372 + 3.63985i) q^{71} +(-3.68957 + 7.64114i) q^{72} +(-4.22928 + 9.26083i) q^{73} +(7.09797 - 8.78985i) q^{74} +(-2.35240 - 1.72946i) q^{75} +(-1.43895 - 3.88189i) q^{76} +(-14.4747 + 2.08115i) q^{77} +(-10.8052 + 11.7847i) q^{78} +(-3.73751 - 3.23857i) q^{79} +(6.99534 - 2.02335i) q^{80} +(0.972060 - 8.94735i) q^{81} +(4.53290 + 0.491969i) q^{82} +(4.19720 + 1.23241i) q^{83} +(-4.02456 - 13.3779i) q^{84} +(4.95344 + 5.71658i) q^{85} +(4.92062 - 8.27420i) q^{86} +(2.59673 + 2.55221i) q^{87} +(10.0877 + 1.85160i) q^{88} +(4.93823 + 0.710010i) q^{89} +(-6.27194 + 4.50777i) q^{90} -26.3233i q^{91} +(-3.66892 + 8.86222i) q^{92} +(1.88815 + 3.38793i) q^{93} +(1.48140 - 3.56623i) q^{94} +(0.536311 - 3.73012i) q^{95} +(-0.314505 + 9.79291i) q^{96} +(-0.574550 + 0.168703i) q^{97} +(11.2602 + 6.69636i) q^{98} +(-10.7393 + 1.73410i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	$ 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) $ 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/276\mathbb{Z}\right)^\times$.

$n$	$97$	$139$	$185$
$\chi(n)$	$e\left(\frac{10}{11}\right)$	$-1$	$-1$

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 $

$2$	−0.542515	+	1.30602i	−0.383616	+	0.923493i
$2$	−0.542515	+	1.30602i	−0.383616	+	0.923493i
$3$	−0.619297	−	1.61755i	−0.357551	−	0.933893i
$3$	−0.619297	−	1.61755i	−0.357551	−	0.933893i
$4$	−1.41135	−	1.41707i	−0.705677	−	0.708534i
$5$	−0.512900	−	1.74678i	−0.229376	−	0.781182i	−0.991081	−	0.133259i	$-0.957456\pi$
$5$	−0.512900	−	1.74678i	−0.229376	−	0.781182i	0.761706	−	0.647923i	$-0.224362\pi$
$6$	2.44853	+	0.0687346i	0.999606	+	0.0280608i
$7$	−3.04781	+	2.64094i	−1.15196	+	0.998182i	−0.152012	+	0.988379i	$0.548575\pi$
$7$	−3.04781	+	2.64094i	−1.15196	+	0.998182i	−0.999952	+	0.00980340i	$0.996879\pi$
$8$	2.61639	−	1.07447i	0.925035	−	0.379882i
$9$	−2.23294	+	2.00349i	−0.744314	+	0.667830i
$10$	2.55957	+	0.277798i	0.809408	+	0.0878474i
$11$	3.05049	+	1.96043i	0.919758	+	0.591092i	0.912587	−	0.408882i	$-0.134081\pi$
$11$	3.05049	+	1.96043i	0.919758	+	0.591092i	0.00717026	+	0.999974i	$0.497718\pi$
$12$	−1.41813	+	3.16052i	−0.409379	+	0.912364i
$13$	−4.27444	+	4.93297i	−1.18552	+	1.36816i	−0.271524	+	0.962432i	$0.587528\pi$
$13$	−4.27444	+	4.93297i	−1.18552	+	1.36816i	−0.913994	+	0.405729i	$0.867018\pi$
$14$	−1.79563	−	5.41324i	−0.479902	−	1.44675i
$15$	−2.50786	+	1.91142i	−0.647527	+	0.493525i
$16$	−0.0161603	+	3.99997i	−0.00404007	+	0.999992i
$17$	−3.77945	+	1.72602i	−0.916651	+	0.418620i	−0.817155	−	0.576418i	$-0.804450\pi$
$17$	−3.77945	+	1.72602i	−0.916651	+	0.418620i	−0.0994957	+	0.995038i	$0.531723\pi$
$18$	−1.40518	−	4.00318i	−0.331205	−	0.943559i
$19$	1.88294	+	0.859910i	0.431976	+	0.197277i	0.619523	−	0.784979i	$-0.287326\pi$
$19$	1.88294	+	0.859910i	0.431976	+	0.197277i	−0.187546	+	0.982256i	$0.560053\pi$
$20$	−1.75142	+	3.19213i	−0.391629	+	0.713783i
$21$	6.15936	+	3.29446i	1.34408	+	0.718910i
$22$	−4.21529	+	2.92042i	−0.898703	+	0.622637i
$23$	−1.84505	−	4.42671i	−0.384720	−	0.923033i
$23$	−1.84505	−	4.42671i	−0.384720	−	0.923033i
$24$	−3.35833	−	3.56673i	−0.685517	−	0.728057i
$25$	1.41811	−	0.911362i	0.283621	−	0.182272i
$26$	−4.12359	−	8.25871i	−0.808702	−	1.61967i
$27$	4.62360	+	2.37114i	0.889812	+	0.456327i
$28$	8.04393	+	0.591648i	1.52016	+	0.111811i
$29$	−1.91216	+	0.873255i	−0.355079	+	0.162159i	−0.584965	−	0.811058i	$-0.698892\pi$
$29$	−1.91216	+	0.873255i	−0.355079	+	0.162159i	0.229886	+	0.973218i	$0.426165\pi$
$30$	−1.13578	−	4.31228i	−0.207365	−	0.787311i
$31$	−2.21649	+	0.318683i	−0.398093	+	0.0572372i	−0.338454	−	0.940983i	$-0.609904\pi$
$31$	−2.21649	+	0.318683i	−0.398093	+	0.0572372i	−0.0596391	+	0.998220i	$0.518995\pi$
$32$	−5.21525	−	2.19115i	−0.921935	−	0.387344i
$33$	1.28194	−	6.14841i	0.223157	−	1.07030i
$34$	−0.203795	−	5.87241i	−0.0349506	−	1.00711i
$35$	6.17635	+	3.96930i	1.04399	+	0.670935i
$36$	5.99055	+	0.336597i	0.998425	+	0.0560995i
$37$	−7.66522	−	2.25071i	−1.26015	−	0.370015i	−0.417603	−	0.908630i	$-0.637130\pi$
$37$	−7.66522	−	2.25071i	−1.26015	−	0.370015i	−0.842552	+	0.538615i	$0.818948\pi$
$38$	−2.14458	+	1.99264i	−0.347897	+	0.323248i
$39$	10.6265	+	3.85916i	1.70160	+	0.617960i
$40$	−3.21881	−	4.01916i	−0.508938	−	0.635485i
$41$	−0.908324	−	3.09347i	−0.141856	−	0.483119i	0.857660	−	0.514217i	$-0.171918\pi$
$41$	−0.908324	−	3.09347i	−0.141856	−	0.483119i	−0.999516	+	0.0310987i	$0.990099\pi$
$42$	−7.64416	+	6.25692i	−1.17952	+	0.965464i
$43$	−6.73787	−	0.968760i	−1.02752	−	0.147735i	−0.392115	−	0.919916i	$-0.628256\pi$
$43$	−6.73787	−	0.968760i	−1.02752	−	0.147735i	−0.635402	+	0.772182i	$0.719165\pi$
$44$	−1.52726	−	7.08961i	−0.230243	−	1.06880i
$45$	4.64492	+	2.87286i	0.692424	+	0.428261i
$46$	6.78233	−	0.00810976i	0.999999	−	0.00119572i
$47$	−2.73062			−0.398301			−0.199151	−	0.979969i	$-0.563818\pi$
$47$	−2.73062			−0.398301			−0.199151	+	0.979969i	$0.563818\pi$
$48$	6.48016	−	2.45103i	0.935330	−	0.353775i
$49$	1.31836	−	9.16942i	0.188338	−	1.30992i
$50$	0.420908	+	2.34650i	0.0595254	+	0.331845i
$51$	5.13252	+	5.04453i	0.718697	+	0.706376i
$52$	13.0231	−	0.904993i	1.80598	−	0.125500i
$53$	5.77832	−	5.00694i	0.793713	−	0.687757i	−0.160450	−	0.987044i	$-0.551294\pi$
$53$	5.77832	−	5.00694i	0.793713	−	0.687757i	0.954163	+	0.299287i	$0.0967489\pi$
$54$	−5.60512	+	4.75211i	−0.762761	+	0.646681i
$55$	1.85984	−	6.33403i	0.250781	−	0.854080i
$56$	−5.13666	+	10.1845i	−0.686415	+	1.36096i
$57$	0.224849	−	3.57829i	0.0297819	−	0.473956i
$58$	−0.103107	−	2.97107i	−0.0135387	−	0.390120i
$59$	−6.25607	+	7.21989i	−0.814471	+	0.939950i	−0.999081	−	0.0428622i	$-0.986352\pi$
$59$	−6.25607	+	7.21989i	−0.814471	+	0.939950i	0.184610	+	0.982812i	$0.440898\pi$
$60$	6.24809	+	0.856127i	0.806624	+	0.110525i
$61$	0.976622	+	6.79256i	0.125044	+	0.869698i	0.951708	+	0.307003i	$0.0993262\pi$
$61$	0.976622	+	6.79256i	0.125044	+	0.869698i	−0.826665	+	0.562695i	$0.809765\pi$
$62$	0.786275	−	3.06766i	0.0998570	−	0.389593i
$63$	1.51448	−	12.0033i	0.190807	−	1.51228i
$64$	5.69103	−	5.62247i	0.711379	−	0.702809i
$65$	10.8092	+	4.93638i	1.34071	+	0.612282i
$66$	7.33445	+	5.00984i	0.902809	+	0.616669i
$67$	6.10076	+	9.49297i	0.745326	+	1.15975i	0.982132	+	0.188193i	$0.0602631\pi$
$67$	6.10076	+	9.49297i	0.745326	+	1.15975i	−0.236806	+	0.971557i	$0.576100\pi$
$68$	7.78002	+	2.91971i	0.943466	+	0.354067i
$69$	−6.01779	+	5.72592i	−0.724457	+	0.689320i
$70$	−8.53474	+	5.91301i	−1.02010	+	0.706740i
$71$	−5.66372	+	3.63985i	−0.672160	+	0.431971i	−0.831704	−	0.555220i	$-0.812634\pi$
$71$	−5.66372	+	3.63985i	−0.672160	+	0.431971i	0.159544	+	0.987191i	$0.448998\pi$
$72$	−3.68957	+	7.64114i	−0.434820	+	0.900518i
$73$	−4.22928	+	9.26083i	−0.495000	+	1.08390i	0.483063	+	0.875586i	$0.339524\pi$
$73$	−4.22928	+	9.26083i	−0.495000	+	1.08390i	−0.978062	+	0.208312i	$0.933203\pi$
$74$	7.09797	−	8.78985i	0.825122	−	1.02180i
$75$	−2.35240	−	1.72946i	−0.271632	−	0.199700i
$76$	−1.43895	−	3.88189i	−0.165058	−	0.445284i
$77$	−14.4747	+	2.08115i	−1.64954	+	0.237169i
$78$	−10.8052	+	11.7847i	−1.22344	+	1.33436i
$79$	−3.73751	−	3.23857i	−0.420503	−	0.364368i	0.418757	−	0.908098i	$-0.362466\pi$
$79$	−3.73751	−	3.23857i	−0.420503	−	0.364368i	−0.839260	+	0.543730i	$0.817011\pi$
$80$	6.99534	−	2.02335i	0.782102	−	0.226218i
$81$	0.972060	−	8.94735i	0.108007	−	0.994150i
$82$	4.53290	+	0.491969i	0.500575	+	0.0543289i
$83$	4.19720	+	1.23241i	0.460702	+	0.135274i	0.503844	−	0.863795i	$-0.331919\pi$
$83$	4.19720	+	1.23241i	0.460702	+	0.135274i	−0.0431419	+	0.999069i	$0.513737\pi$
$84$	−4.02456	−	13.3779i	−0.439116	−	1.45965i
$85$	4.95344	+	5.71658i	0.537276	+	0.620050i
$86$	4.92062	−	8.27420i	0.530604	−	0.892230i
$87$	2.59673	+	2.55221i	0.278399	+	0.273626i
$88$	10.0877	+	1.85160i	1.07535	+	0.197381i
$89$	4.93823	+	0.710010i	0.523451	+	0.0752609i	0.398975	−	0.916962i	$-0.369366\pi$
$89$	4.93823	+	0.710010i	0.523451	+	0.0752609i	0.124476	+	0.992223i	$0.460275\pi$
$90$	−6.27194	+	4.50777i	−0.661121	+	0.475161i
$91$		−	26.3233i		−	2.75943i
$92$	−3.66892	+	8.86222i	−0.382512	+	0.923951i
$93$	1.88815	+	3.38793i	0.195792	+	0.351312i
$94$	1.48140	−	3.56623i	0.152795	−	0.367828i
$95$	0.536311	−	3.73012i	0.0550243	−	0.382703i
$96$	−0.314505	+	9.79291i	−0.0320990	+	0.999485i
$97$	−0.574550	+	0.168703i	−0.0583367	+	0.0171292i	−0.310771	−	0.950485i	$-0.600587\pi$
$97$	−0.574550	+	0.168703i	−0.0583367	+	0.0171292i	0.252434	+	0.967614i	$0.418769\pi$
$98$	11.2602	+	6.69636i	1.13745	+	0.676434i
$99$	−10.7393	+	1.73410i	−1.07934	+	0.174283i
$100$	−3.29291	−	0.723299i	−0.329291	−	0.0723299i
$101$	1.92885	−	6.56905i	0.191927	−	0.653645i	−0.806153	−	0.591708i	$-0.798454\pi$
$101$	1.92885	−	6.56905i	0.191927	−	0.653645i	0.998080	−	0.0619371i	$-0.0197278\pi$
$102$	−9.37271	+	3.96642i	−0.928037	+	0.392734i
$103$	5.72121	−	8.90237i	0.563727	−	0.877177i	−0.436014	−	0.899940i	$-0.643610\pi$
$103$	5.72121	−	8.90237i	0.563727	−	0.877177i	0.999741	+	0.0227632i	$0.00724638\pi$
$104$	−5.88330	+	17.4994i	−0.576905	+	1.71595i
$105$	2.59555	−	12.4487i	0.253300	−	1.21487i
$106$	3.40432	+	10.2629i	0.330657	+	0.996823i
$107$	−1.81424	−	12.6183i	−0.175389	−	1.21986i	−0.867266	−	0.497845i	$-0.834125\pi$
$107$	−1.81424	−	12.6183i	−0.175389	−	1.21986i	0.691877	−	0.722016i	$-0.256784\pi$
$108$	−3.16547	−	9.89847i	−0.304597	−	0.952481i
$109$	3.97665	+	8.70764i	0.380894	+	0.834041i	0.998855	+	0.0478327i	$0.0152314\pi$
$109$	3.97665	+	8.70764i	0.380894	+	0.834041i	−0.617962	+	0.786208i	$0.712041\pi$
$110$	7.26335	+	5.86529i	0.692533	+	0.559233i
$111$	1.10641	+	13.7927i	0.105016	+	1.30915i
$112$	−10.5144	−	12.2338i	−0.993520	−	1.15599i
$113$	−0.345825	−	0.538114i	−0.0325325	−	0.0506215i	0.824606	−	0.565707i	$-0.191397\pi$
$113$	−0.345825	−	0.538114i	−0.0325325	−	0.0506215i	−0.857139	+	0.515085i	$0.827760\pi$
$114$	4.55132	+	2.23494i	0.426270	+	0.209321i
$115$	−6.78615	+	5.49336i	−0.632811	+	0.512258i
$116$	3.93620	+	1.47719i	0.365467	+	0.137154i
$117$	−0.338570	−	19.5788i	−0.0313009	−	1.81006i
$118$	−6.03528	−	12.0874i	−0.555592	−	1.11274i
$119$	6.96073	−	15.2419i	0.638089	−	1.39722i
$120$	−4.50780	+	7.69564i	−0.411504	+	0.702512i
$121$	0.892637	+	1.95460i	0.0811488	+	0.177691i
$122$	−9.40102	−	2.40958i	−0.851128	−	0.218153i
$123$	−4.44132	+	3.38504i	−0.400460	+	0.305219i
$124$	3.57985	+	2.69114i	0.321480	+	0.241672i
$125$	−9.19858	−	7.97061i	−0.822746	−	0.712913i
$126$	14.8549	+	8.48993i	1.32338	+	0.756343i
$127$	0.216248	−	0.336488i	0.0191889	−	0.0298585i	−0.831527	−	0.555485i	$-0.812533\pi$
$127$	0.216248	−	0.336488i	0.0191889	−	0.0298585i	0.850716	+	0.525626i	$0.176169\pi$
$128$	4.25556	+	10.4829i	0.376142	+	0.926562i
$129$	2.60573	+	11.4988i	0.229422	+	1.01241i
$130$	−12.3111	+	11.4389i	−1.07976	+	1.00326i
$131$	−2.50373	−	2.88946i	−0.218752	−	0.252454i	0.635758	−	0.771889i	$-0.280688\pi$
$131$	−2.50373	−	2.88946i	−0.218752	−	0.252454i	−0.854510	+	0.519435i	$0.826142\pi$
$132$	−10.5220	+	6.86100i	−0.915821	+	0.597173i
$133$	−8.00982	+	2.35189i	−0.694539	+	0.203935i
$134$	−15.7077	+	2.81761i	−1.35694	+	0.243404i
$135$	1.77041	−	9.29255i	0.152373	−	0.799776i
$136$	−8.03397	+	8.57684i	−0.688908	+	0.735458i
$137$			1.39106i			0.118846i	0.998233	+	0.0594230i	$0.0189261\pi$
$137$			1.39106i			0.118846i	−0.998233	+	0.0594230i	$0.981074\pi$
$138$	−4.21339	−	10.9657i	−0.358668	−	0.933465i
$139$			11.7810i			0.999253i	0.866241	+	0.499626i	$0.166529\pi$
$139$			11.7810i			0.999253i	−0.866241	+	0.499626i	$0.833471\pi$
$140$	−3.09225	−	14.3544i	−0.261343	−	1.21317i
$141$	1.69106	+	4.41691i	0.142413	+	0.371971i
$142$	−1.68105	−	9.37159i	−0.141070	−	0.786446i
$143$	−22.7099	+	6.66823i	−1.89910	+	0.557625i
$144$	−7.97781	−	8.96407i	−0.664817	−	0.747006i
$145$	2.50613	+	2.89223i	0.208123	+	0.240186i
$146$	−9.80034	−	10.5476i	−0.811082	−	0.872930i
$147$	−15.6485	+	3.54608i	−1.29066	+	0.292475i
$148$	7.62893	+	14.0387i	0.627094	+	1.15397i
$149$	7.83753	−	12.1954i	0.642076	−	0.999089i	−0.355839	−	0.934547i	$-0.615805\pi$
$149$	7.83753	−	12.1954i	0.642076	−	0.999089i	0.997915	−	0.0645420i	$-0.0205587\pi$
$150$	3.53491	−	2.13402i	0.288624	−	0.174242i
$151$	0.634864	+	0.550112i	0.0516645	+	0.0447675i	0.680310	−	0.732924i	$-0.261845\pi$
$151$	0.634864	+	0.550112i	0.0516645	+	0.0447675i	−0.628646	+	0.777692i	$0.716390\pi$
$152$	5.85046	+	0.226702i	0.474535	+	0.0183879i
$153$	4.98123	−	11.4262i	0.402709	−	0.923752i
$154$	5.13474	−	20.0332i	0.413769	−	1.61432i
$155$	1.69351	+	3.70826i	0.136026	+	0.297855i
$156$	−9.52905	−	20.5051i	−0.762934	−	1.64172i
$157$	1.41793	−	3.10483i	0.113163	−	0.247792i	−0.844573	−	0.535440i	$-0.820146\pi$
$157$	1.41793	−	3.10483i	0.113163	−	0.247792i	0.957736	+	0.287648i	$0.0928732\pi$
$158$	6.25729	−	3.12427i	0.497803	−	0.248554i
$159$	−11.6775	−	6.24594i	−0.926085	−	0.495335i
$160$	−1.15255	+	10.2337i	−0.0911168	+	0.809047i
$161$	17.3141	+	8.61909i	1.36454	+	0.679280i
$162$	11.1580	+	6.12360i	0.876657	+	0.481116i
$163$	1.85753	+	2.89038i	0.145493	+	0.226392i	0.906350	−	0.422528i	$-0.138857\pi$
$163$	1.85753	+	2.89038i	0.145493	+	0.226392i	−0.760857	+	0.648920i	$0.775221\pi$
$164$	−3.10169	+	5.65314i	−0.242201	+	0.441436i
$165$	−11.3974	+	0.914262i	−0.887287	+	0.0711752i
$166$	−3.88659	+	4.81301i	−0.301658	+	0.373562i
$167$	1.12975	+	2.47382i	0.0874230	+	0.191430i	0.948294	−	0.317394i	$-0.102808\pi$
$167$	1.12975	+	2.47382i	0.0874230	+	0.191430i	−0.860871	+	0.508824i	$0.830081\pi$
$168$	19.6551	+	2.00156i	1.51642	+	0.154424i
$169$	−4.21324	−	29.3038i	−0.324096	−	2.25413i
$170$	−10.1533	+	3.36794i	−0.778720	+	0.258309i
$171$	−5.92732	+	1.85232i	−0.453273	+	0.141651i
$172$	8.13673	+	10.9153i	0.620420	+	0.832283i
$173$	−11.8473	+	18.4348i	−0.900734	+	1.40157i	0.0150454	+	0.999887i	$0.495211\pi$
$173$	−11.8473	+	18.4348i	−0.900734	+	1.40157i	−0.915779	+	0.401682i	$0.868426\pi$
$174$	−4.74200	+	2.00675i	−0.359490	+	0.152132i
$175$	−1.91526	+	6.52279i	−0.144780	+	0.493077i
$176$	−7.89096	+	12.1702i	−0.594803	+	0.917362i
$177$	15.5529	+	5.64826i	1.16903	+	0.424549i
$178$	−3.60635	+	6.06421i	−0.270307	+	0.454532i
$179$	8.21740	−	2.41285i	0.614197	−	0.180345i	0.0401863	−	0.999192i	$-0.487205\pi$
$179$	8.21740	−	2.41285i	0.614197	−	0.180345i	0.574011	+	0.818848i	$0.305387\pi$
$180$	−2.48459	−	10.6368i	−0.185191	−	0.792820i
$181$	−2.05812	+	14.3146i	−0.152979	+	1.06399i	0.758212	+	0.652008i	$0.226073\pi$
$181$	−2.05812	+	14.3146i	−0.152979	+	1.06399i	−0.911191	+	0.411984i	$0.864836\pi$
$182$	34.3787	+	14.2808i	2.54832	+	1.05856i
$183$	10.3825	−	5.78635i	0.767496	−	0.427739i
$184$	−9.58375	−	9.59957i	−0.706524	−	0.707689i
$185$			14.5438i			1.06928i
$186$	−5.44904	+	0.627954i	−0.399543	+	0.0460438i
$187$	−14.9129	−	2.14415i	−1.09054	−	0.156796i
$188$	3.85387	+	3.86947i	0.281072	+	0.282210i
$189$	−20.3539	+	4.98387i	−1.48053	+	0.362523i
$190$	4.58064	+	2.72408i	0.332315	+	0.197626i
$191$	0.426916	+	0.492687i	0.0308906	+	0.0356496i	0.770985	−	0.636854i	$-0.219765\pi$
$191$	0.426916	+	0.492687i	0.0308906	+	0.0356496i	−0.740094	+	0.672503i	$0.765219\pi$
$192$	−12.6191	−	5.72355i	−0.910703	−	0.413062i
$193$	17.3087	+	5.08229i	1.24591	+	0.365832i	0.837232	−	0.546848i	$-0.184172\pi$
$193$	17.3087	+	5.08229i	1.24591	+	0.365832i	0.408676	+	0.912680i	$0.365991\pi$
$194$	0.0913733	−	0.841895i	0.00656022	−	0.0604445i
$195$	1.29076	−	20.5415i	0.0924333	−	1.47100i
$196$	−14.8544	+	11.0731i	−1.06103	+	0.790935i
$197$	12.5108	+	10.8407i	0.891357	+	0.772365i	0.974551	−	0.224168i	$-0.0719664\pi$
$197$	12.5108	+	10.8407i	0.891357	+	0.772365i	−0.0831933	+	0.996533i	$0.526512\pi$
$198$	3.56146	−	14.9664i	0.253102	−	1.06362i
$199$	6.12318	−	0.880380i	0.434061	−	0.0624085i	0.0781786	−	0.996939i	$-0.475090\pi$
$199$	6.12318	−	0.880380i	0.434061	−	0.0624085i	0.355882	+	0.934531i	$0.384180\pi$
$200$	2.73109	−	3.90819i	0.193118	−	0.276351i
$201$	11.5772	−	15.7473i	0.816591	−	1.11073i
$202$	7.53285	+	6.08291i	0.530010	+	0.427992i
$203$	3.52169	−	7.71142i	0.247174	−	0.541236i
$204$	−0.0953596	−	14.3928i	−0.00667651	−	1.00769i
$205$	−4.93772	+	3.17328i	−0.344865	+	0.221631i
$206$	8.52280	+	12.3017i	0.593811	+	0.857097i
$207$	12.9888	+	6.18804i	0.902782	+	0.430099i
$208$	−19.6627	−	17.1774i	−1.36336	−	1.19104i
$209$	4.05810	+	6.31452i	0.280705	+	0.436785i
$210$	14.8501	+	10.1435i	1.02476	+	0.699966i
$211$	12.5719	+	5.74140i	0.865487	+	0.395254i	0.798138	−	0.602475i	$-0.205819\pi$
$211$	12.5719	+	5.74140i	0.865487	+	0.395254i	0.0673488	+	0.997729i	$0.478546\pi$
$212$	−15.2504	−	1.12170i	−1.04740	−	0.0770387i
$213$	9.39517	+	6.90721i	0.643747	+	0.473274i
$214$	17.4640	+	4.47621i	1.19381	+	0.305988i
$215$	1.76365	+	12.2664i	0.120280	+	0.836564i
$216$	14.6449	+	1.23592i	0.996458	+	0.0840940i
$217$	5.91382	−	6.82491i	0.401456	−	0.463305i
$218$	−13.5297	+	0.469533i	−0.916348	+	0.0318008i
$219$	17.5990	+	1.10587i	1.18923	+	0.0747277i
$220$	−11.6006	+	6.30404i	−0.782115	+	0.425018i
$221$	7.64065	−	26.0217i	0.513966	−	1.75041i
$222$	−18.6138	−	6.03779i	−1.24928	−	0.405230i
$223$	−16.4151	+	14.2238i	−1.09924	+	0.952497i	−0.999097	−	0.0424765i	$-0.986475\pi$
$223$	−16.4151	+	14.2238i	−1.09924	+	0.952497i	−0.100142	+	0.994973i	$0.531930\pi$
$224$	21.6818	−	7.09497i	1.44868	−	0.474053i
$225$	−1.34065	+	4.87618i	−0.0893764	+	0.325079i
$226$	0.890401	−	0.159718i	0.0592286	−	0.0106243i
$227$	0.274318	−	1.90792i	0.0182071	−	0.126633i	−0.978691	−	0.205340i	$-0.934170\pi$
$227$	0.274318	−	1.90792i	0.0182071	−	0.126633i	0.996898	+	0.0787067i	$0.0250791\pi$
$228$	−5.38802	+	4.73161i	−0.356831	+	0.313359i
$229$	−14.0913			−0.931183			−0.465591	−	0.885000i	$-0.654158\pi$
$229$	−14.0913			−0.931183			−0.465591	+	0.885000i	$0.654158\pi$
$230$	−3.49282	−	11.8430i	−0.230310	−	0.780907i
$231$	12.3305	+	22.1247i	0.811287	+	1.45570i
$232$	−4.06468	+	4.33934i	−0.266859	+	0.284891i
$233$	−13.7660	−	1.97926i	−0.901842	−	0.129665i	−0.324232	−	0.945978i	$-0.605106\pi$
$233$	−13.7660	−	1.97926i	−0.901842	−	0.129665i	−0.577611	+	0.816312i	$0.696015\pi$
$234$	25.7540	+	10.1796i	1.68359	+	0.665464i
$235$	1.40053	+	4.76977i	0.0913606	+	0.311146i
$236$	19.0606	−	1.32455i	1.24074	−	0.0862206i
$237$	−2.92393	+	8.05126i	−0.189929	+	0.522985i
$238$	16.1298	+	17.3598i	1.04554	+	1.12527i
$239$	20.7329	+	6.08773i	1.34110	+	0.393782i	0.872062	−	0.489396i	$-0.162783\pi$
$239$	20.7329	+	6.08773i	1.34110	+	0.393782i	0.469038	+	0.883178i	$0.344601\pi$
$240$	−7.60507	−	10.0623i	−0.490905	−	0.649516i
$241$	0.164558	+	0.105755i	0.0106001	+	0.00681226i	0.545930	−	0.837831i	$-0.316176\pi$
$241$	0.164558	+	0.105755i	0.0106001	+	0.00681226i	−0.535330	+	0.844643i	$0.679813\pi$
$242$	−3.03701	+	0.105396i	−0.195226	+	0.00677510i
$243$	−15.0748	+	3.96871i	−0.967048	+	0.254593i
$244$	8.24715	−	10.9706i	0.527970	−	0.702323i
$245$	−16.6931	+	2.40011i	−1.06648	+	0.153337i
$246$	−2.01143	−	7.63687i	−0.128244	−	0.486909i
$247$	−12.2904	+	5.61286i	−0.782022	+	0.357137i
$248$	−5.45680	+	3.21535i	−0.346507	+	0.204175i
$249$	−0.605829	−	7.55241i	−0.0383929	−	0.478614i
$250$	15.4001	−	7.68931i	0.973989	−	0.486314i
$251$	0.958869	−	0.616228i	0.0605233	−	0.0388960i	−0.510029	−	0.860157i	$-0.670365\pi$
$251$	0.958869	−	0.616228i	0.0605233	−	0.0388960i	0.570553	+	0.821261i	$0.306729\pi$
$252$	−19.1470	+	14.7948i	−1.20615	+	0.931986i
$253$	3.04994	−	17.1207i	0.191748	−	1.07637i
$254$	0.322141	+	0.464974i	0.0202129	+	0.0291750i
$255$	6.17920	−	11.5527i	0.386957	−	0.723459i
$256$	−15.9995	−	0.129281i	−0.999967	−	0.00808007i
$257$	0.994009	+	0.453949i	0.0620046	+	0.0283166i	0.446176	−	0.894945i	$-0.352786\pi$
$257$	0.994009	+	0.453949i	0.0620046	+	0.0283166i	−0.384171	+	0.923262i	$0.625513\pi$
$258$	−16.4313	−	2.83516i	−1.02297	−	0.176509i
$259$	29.3061	−	13.3837i	1.82099	−	0.831620i
$260$	−8.26037	−	22.2843i	−0.512286	−	1.38201i
$261$	2.52019	−	5.78092i	0.155996	−	0.357830i
$262$	5.13200	−	1.70234i	0.317056	−	0.105171i
$263$	−6.28905	+	7.25795i	−0.387799	+	0.447544i	−0.915761	−	0.401724i	$-0.868411\pi$
$263$	−6.28905	+	7.25795i	−0.387799	+	0.447544i	0.527961	+	0.849268i	$0.322957\pi$
$264$	−3.25223	−	17.4641i	−0.200161	−	1.07484i
$265$	−11.7097	−	7.52537i	−0.719322	−	0.462280i
$266$	1.27384	−	11.7369i	0.0781041	−	0.719635i
$267$	−1.90975	−	8.42754i	−0.116875	−	0.515757i
$268$	4.84184	−	22.0431i	0.295763	−	1.34650i
$269$	−23.7007	+	20.5367i	−1.44506	+	1.25215i	−0.530501	+	0.847684i	$0.677996\pi$
$269$	−23.7007	+	20.5367i	−1.44506	+	1.25215i	−0.914554	+	0.404463i	$0.867458\pi$
$270$	11.1757	+	7.35354i	0.680134	+	0.447522i
$271$	0.0163598	+	0.0557165i	0.000993790	+	0.00338454i	0.959988	−	0.280040i	$-0.0903477\pi$
$271$	0.0163598	+	0.0557165i	0.000993790	+	0.00338454i	−0.958995	+	0.283424i	$0.908530\pi$
$272$	−6.84293	−	15.1456i	−0.414914	−	0.918335i
$273$	−42.5793	+	16.3020i	−2.57702	+	0.986639i
$274$	−1.81674	−	0.754669i	−0.109753	−	0.0455912i
$275$	6.11258			0.368603
$276$	16.6073	+	0.446323i	0.999639	+	0.0268655i
$277$	8.15385			0.489917			0.244959	−	0.969534i	$-0.421226\pi$
$277$	8.15385			0.489917			0.244959	+	0.969534i	$0.421226\pi$
$278$	−15.3862	−	6.39138i	−0.922802	−	0.383330i
$279$	4.31082	−	5.15232i	0.258082	−	0.308461i
$280$	20.4247	+	3.74895i	1.22061	+	0.224043i
$281$	−2.68599	−	9.14764i	−0.160233	−	0.545703i	−0.999996	−	0.00275018i	$-0.999125\pi$
$281$	−2.68599	−	9.14764i	−0.160233	−	0.545703i	0.839763	−	0.542952i	$-0.182694\pi$
$282$	−6.68598	−	0.187688i	−0.398144	−	0.0111766i
$283$	8.34926	−	7.23467i	0.496312	−	0.430057i	−0.370395	−	0.928874i	$-0.620778\pi$
$283$	8.34926	−	7.23467i	0.496312	−	0.430057i	0.866707	+	0.498818i	$0.166232\pi$
$284$	13.1514	+	2.88875i	0.780394	+	0.171416i
$285$	−6.36580	+	1.44255i	−0.377078	+	0.0854490i
$286$	3.61166	−	33.2771i	0.213562	−	1.96772i
$287$	10.9381	+	7.02947i	0.645654	+	0.414937i
$288$	16.0353	−	5.55599i	0.944889	−	0.327390i
$289$	0.172468	−	0.199039i	0.0101452	−	0.0117082i
$290$	−5.13691	+	1.70397i	−0.301649	+	0.100060i
$291$	0.628703	+	0.824886i	0.0368552	+	0.0483557i
$292$	19.0922	−	7.07713i	1.11729	−	0.414158i
$293$	6.05577	−	2.76558i	0.353782	−	0.161567i	−0.230594	−	0.973050i	$-0.574067\pi$
$293$	6.05577	−	2.76558i	0.353782	−	0.161567i	0.584375	+	0.811483i	$0.301340\pi$
$294$	3.85830	−	22.3609i	0.225021	−	1.30412i
$295$	15.8203	+	7.22488i	0.921092	+	0.420649i
$296$	−22.4736	+	2.34730i	−1.30625	+	0.136434i
$297$	9.45579	+	16.2974i	0.548681	+	0.945671i
$298$	11.6755	+	16.8522i	0.676341	+	0.976219i
$299$	29.7234	+	9.82013i	1.71895	+	0.567913i
$300$	0.869318	+	5.77439i	0.0501901	+	0.333384i
$301$	23.0942	−	14.8417i	1.33113	−	0.855464i
$302$	−1.06288	+	0.530697i	−0.0611618	+	0.0305382i
$303$	−11.8203	+	0.948186i	−0.679059	+	0.0544718i
$304$	−3.47004	+	7.51781i	−0.199021	+	0.431176i
$305$	11.3642	−	5.18984i	0.650710	−	0.297170i
$306$	12.2204	+	12.7044i	0.698592	+	0.726265i
$307$	−16.7177	+	2.40364i	−0.954129	+	0.137183i	−0.601759	−	0.798678i	$-0.705533\pi$
$307$	−16.7177	+	2.40364i	−0.954129	+	0.137183i	−0.352370	+	0.935861i	$0.614624\pi$
$308$	23.3780	+	17.5744i	1.33209	+	1.00139i
$309$	−17.9432	−	3.74113i	−1.02075	−	0.212825i
$310$	−5.76180	+	0.199956i	−0.327248	+	0.0113568i
$311$	−15.6318	−	10.0460i	−0.886400	−	0.569655i	0.0163279	−	0.999867i	$-0.494802\pi$
$311$	−15.6318	−	10.0460i	−0.886400	−	0.569655i	−0.902728	+	0.430212i	$0.858439\pi$
$312$	31.9496	−	1.32076i	1.80879	−	0.0747733i
$313$	−22.1469	−	6.50290i	−1.25181	−	0.367566i	−0.412372	−	0.911015i	$-0.635300\pi$
$313$	−22.1469	−	6.50290i	−1.25181	−	0.367566i	−0.839442	+	0.543450i	$0.817118\pi$
$314$	3.28570	+	3.53625i	0.185423	+	0.199562i
$315$	−21.7439	+	3.51104i	−1.22513	+	0.197825i
$316$	0.685677	+	9.86708i	0.0385723	+	0.555067i
$317$	7.75606	+	26.4147i	0.435624	+	1.48360i	0.826385	+	0.563106i	$0.190394\pi$
$317$	7.75606	+	26.4147i	0.435624	+	1.48360i	−0.390761	+	0.920492i	$0.627788\pi$
$318$	14.4925	−	11.8625i	0.812700	−	0.665214i
$319$	−7.54499	−	1.08481i	−0.422438	−	0.0607374i
$320$	−12.7401	−	7.05720i	−0.712195	−	0.394509i
$321$	−19.2872	+	10.7491i	−1.07651	+	0.599958i
$322$	−20.6498	+	17.9364i	−1.15077	+	0.999559i
$323$	−8.60070			−0.478556
$324$	−14.0509	+	11.2504i	−0.780607	+	0.625022i
$325$	−1.56590	+	10.8910i	−0.0868603	+	0.604126i
$326$	−4.78262	+	0.857892i	−0.264885	+	0.0475142i
$327$	11.6223	−	11.8250i	0.642716	−	0.653927i
$328$	−5.70037	−	7.11777i	−0.314750	−	0.393013i
$329$	8.32240	−	7.21140i	0.458829	−	0.397577i
$330$	4.98923	−	15.3812i	0.274648	−	0.846707i
$331$	4.49520	−	15.3092i	0.247078	−	0.841471i	−0.738788	−	0.673938i	$-0.764602\pi$
$331$	4.49520	−	15.3092i	0.247078	−	0.841471i	0.985866	−	0.167534i	$-0.0535803\pi$
$332$	−4.17733	−	7.68708i	−0.229261	−	0.421883i
$333$	21.6253	−	10.3315i	1.18506	−	0.566162i
$334$	−3.84375	+	0.133393i	−0.210321	+	0.00729893i
$335$	13.4530	−	15.5256i	0.735016	−	0.848254i
$336$	−13.2773	+	24.5840i	−0.724334	+	1.34117i
$337$	−2.82983	−	19.6819i	−0.154151	−	1.07214i	−0.909166	−	0.416435i	$-0.863279\pi$
$337$	−2.82983	−	19.6819i	−0.154151	−	1.07214i	0.755015	−	0.655708i	$-0.227630\pi$
$338$	40.5569	+	10.3952i	2.20601	+	0.565423i
$339$	−0.656259	+	0.892642i	−0.0356431	+	0.0484817i
$340$	1.10972	−	15.0875i	0.0601828	−	0.818233i
$341$	−7.38614	−	3.37314i	−0.399982	−	0.182666i
$342$	0.796500	−	8.74608i	0.0430698	−	0.472934i
$343$	4.93560	+	7.67995i	0.266497	+	0.414678i
$344$	−18.6698	+	4.70498i	−1.00661	+	0.253676i
$345$	13.0884	+	7.57492i	0.704657	+	0.407820i
$346$	−17.6487	−	25.4739i	−0.948802	−	1.36949i
$347$	−24.3373	+	15.6407i	−1.30650	+	0.839635i	−0.993904	−	0.110252i	$-0.964834\pi$
$347$	−24.3373	+	15.6407i	−1.30650	+	0.839635i	−0.312594	+	0.949887i	$0.601198\pi$
$348$	−0.0482459	−	7.28182i	−0.00258625	−	0.390347i
$349$	−6.83549	+	14.9676i	−0.365895	+	0.801199i	0.633723	+	0.773560i	$0.281526\pi$
$349$	−6.83549	+	14.9676i	−0.365895	+	0.801199i	−0.999618	+	0.0276387i	$0.991201\pi$
$350$	−7.47981	−	6.04008i	−0.399813	−	0.322856i
$351$	−31.4601	+	12.6728i	−1.67922	+	0.676423i
$352$	−11.6135	−	16.9082i	−0.619001	−	0.901211i
$353$	−12.3732	+	1.77900i	−0.658561	+	0.0946867i	−0.463490	−	0.886102i	$-0.653403\pi$
$353$	−12.3732	+	1.77900i	−0.658561	+	0.0946867i	−0.195071	+	0.980789i	$0.562494\pi$
$354$	−15.8144	+	17.2481i	−0.840526	+	0.916725i
$355$	9.26293	+	8.02637i	0.491625	+	0.425996i
$356$	−5.96345	−	7.99988i	−0.316062	−	0.423993i
$357$	−28.9653	−	1.82009i	−1.53300	−	0.0963292i
$358$	−1.30685	+	12.0411i	−0.0690692	+	0.636390i
$359$	−3.73869	−	1.09778i	−0.197321	−	0.0579386i	0.181579	−	0.983376i	$-0.441879\pi$
$359$	−3.73869	−	1.09778i	−0.197321	−	0.0579386i	−0.378900	+	0.925438i	$0.623697\pi$
$360$	15.2397	+	2.52571i	0.803205	+	0.133116i
$361$	−9.63633	−	11.1209i	−0.507175	−	0.585312i
$362$	−17.5785	−	10.4538i	−0.923904	−	0.549440i
$363$	2.60886	−	2.65436i	0.136930	−	0.139318i
$364$	−37.3019	+	37.1515i	−1.95515	+	1.94727i
$365$	18.3458	+	2.63773i	0.960263	+	0.138065i
$366$	1.92440	+	16.6989i	0.100590	+	0.872864i
$367$			24.3043i			1.26867i	0.773056	+	0.634337i	$0.218727\pi$
$367$			24.3043i			1.26867i	−0.773056	+	0.634337i	$0.781273\pi$
$368$	17.7365	−	7.30862i	0.924580	−	0.380988i
$369$	8.22597	+	5.08772i	0.428227	+	0.264856i
$370$	−18.9945	−	7.89025i	−0.987475	−	0.410194i
$371$	−4.38817	+	30.5204i	−0.227823	+	1.58454i
$372$	2.13607	−	7.45720i	0.110750	−	0.386638i
$373$	23.5823	−	6.92439i	1.22105	−	0.358531i	0.393182	−	0.919461i	$-0.371374\pi$
$373$	23.5823	−	6.92439i	1.22105	−	0.358531i	0.827864	+	0.560929i	$0.189556\pi$
$374$	10.8908	−	18.3133i	0.563149	−	0.946956i
$375$	−7.19622	+	19.8153i	−0.371611	+	1.02326i
$376$	−7.14437	+	2.93396i	−0.368443	+	0.151308i
$377$	3.86569	−	13.1653i	0.199093	−	0.678048i
$378$	4.53329	−	29.2863i	0.233167	−	1.50633i
$379$	−4.70308	+	7.31813i	−0.241581	+	0.375907i	−0.940779	−	0.339021i	$-0.889904\pi$
$379$	−4.70308	+	7.31813i	−0.241581	+	0.375907i	0.699198	+	0.714928i	$0.253541\pi$
$380$	−6.04276	+	4.50454i	−0.309987	+	0.231078i
$381$	−0.678209	−	0.141406i	−0.0347457	−	0.00724444i
$382$	−0.875066	+	0.290268i	−0.0447723	+	0.0148514i
$383$	−1.10471	−	7.68340i	−0.0564478	−	0.392603i	−0.998385	−	0.0568136i	$-0.981906\pi$
$383$	−1.10471	−	7.68340i	−0.0564478	−	0.392603i	0.941937	−	0.335790i	$-0.109003\pi$
$384$	14.3211	−	13.3756i	0.730820	−	0.682570i
$385$	11.0594	+	24.2166i	0.563638	+	1.23419i
$386$	−16.0278	+	19.8482i	−0.815793	+	1.01025i
$387$	16.9862	−	11.3361i	0.863456	−	0.576245i
$388$	1.04996	+	0.576076i	0.0533035	+	0.0292458i
$389$	9.41977	+	14.6574i	0.477601	+	0.743162i	0.993542	−	0.113462i	$-0.0361940\pi$
$389$	9.41977	+	14.6574i	0.477601	+	0.743162i	−0.515941	+	0.856624i	$0.672558\pi$
$390$	26.1272	+	12.8298i	1.32300	+	0.649663i
$391$	14.6139	+	13.5459i	0.739055	+	0.685047i
$392$	−6.40290	−	25.4074i	−0.323395	−	1.28327i
$393$	−3.12330	+	5.83935i	−0.157550	+	0.294556i
$394$	−20.9454	+	10.4581i	−1.05521	+	0.526870i
$395$	−3.74009	+	8.18966i	−0.188185	+	0.412067i
$396$	17.6142	+	12.7708i	0.885149	+	0.641759i
$397$	10.7406	+	23.5187i	0.539058	+	1.18037i	0.961707	+	0.274078i	$0.0883728\pi$
$397$	10.7406	+	23.5187i	0.539058	+	1.18037i	−0.422650	+	0.906293i	$0.638900\pi$
$398$	−2.17213	+	8.47459i	−0.108879	+	0.424793i
$399$	8.76477	+	11.4998i	0.438787	+	0.575708i
$400$	3.62250	+	5.68711i	0.181125	+	0.284355i
$401$	−14.1734	−	12.2813i	−0.707785	−	0.613299i	0.224734	−	0.974420i	$-0.427849\pi$
$401$	−14.1734	−	12.2813i	−0.707785	−	0.613299i	−0.932519	+	0.361121i	$0.882394\pi$
$402$	14.2854	+	23.6631i	0.712489	+	1.18021i
$403$	7.90221	−	12.2961i	0.393637	−	0.612511i
$404$	−12.0311	+	6.53795i	−0.598568	+	0.325275i
$405$	−16.1276	+	2.89112i	−0.801386	+	0.143661i
$406$	8.16067	+	8.78294i	0.405007	+	0.435890i
$407$	−18.9703	−	21.8929i	−0.940324	−	1.08519i
$408$	18.8489	+	7.68375i	0.933159	+	0.380402i
$409$	38.0316	−	11.1671i	1.88054	−	0.552177i	0.884159	−	0.467186i	$-0.154732\pi$
$409$	38.0316	−	11.1671i	1.88054	−	0.552177i	0.996382	−	0.0849902i	$-0.0270859\pi$
$410$	−1.46556	−	8.17029i	−0.0723790	−	0.403502i
$411$	2.25010	−	0.861477i	0.110989	−	0.0424935i
$412$	−20.6899	+	4.45706i	−1.01932	+	0.219584i
$413$		−	38.5268i		−	1.89578i
$414$	−15.1283	+	13.6064i	−0.743515	+	0.668719i
$415$		−	7.96367i		−	0.390921i
$416$	33.1012	−	16.3607i	1.62292	−	0.802152i
$417$	19.0564	−	7.29595i	0.933195	−	0.357284i
$418$	−10.4484	+	1.87421i	−0.511050	+	0.0916707i
$419$	35.5278	−	10.4319i	1.73565	−	0.509632i	0.747647	−	0.664096i	$-0.231183\pi$
$419$	35.5278	−	10.4319i	1.73565	−	0.509632i	0.987998	+	0.154465i	$0.0493653\pi$
$420$	−21.3040	+	13.8915i	−1.03953	+	0.677837i
$421$	−0.415510	−	0.479525i	−0.0202507	−	0.0233706i	0.745534	−	0.666468i	$-0.232195\pi$
$421$	−0.415510	−	0.479525i	−0.0202507	−	0.0233706i	−0.765785	+	0.643097i	$0.777649\pi$
$422$	−14.3188	+	13.3043i	−0.697029	+	0.647644i
$423$	6.09731	−	5.47076i	0.296461	−	0.265997i
$424$	9.73855	−	19.3088i	0.472946	−	0.937716i
$425$	−3.78664	+	5.89212i	−0.183679	+	0.285810i
$426$	−14.1179	+	8.52298i	−0.684017	+	0.412940i
$427$	−20.9153	−	18.1232i	−1.01216	−	0.877044i
$428$	−15.3205	+	20.3798i	−0.740544	+	0.985097i
$429$	24.8504	+	32.6048i	1.19979	+	1.57418i
$430$	−16.9770	−	4.35138i	−0.818702	−	0.209842i
$431$	−10.3078	−	22.5710i	−0.496511	−	1.08721i	−0.977588	−	0.210529i	$-0.932481\pi$
$431$	−10.3078	−	22.5710i	−0.496511	−	1.08721i	0.481077	−	0.876678i	$-0.340246\pi$
$432$	−9.55921	+	18.4559i	−0.459918	+	0.887962i
$433$	4.76902	−	10.4427i	0.229185	−	0.501844i	−0.759747	−	0.650219i	$-0.774677\pi$
$433$	4.76902	−	10.4427i	0.229185	−	0.501844i	0.988931	+	0.148375i	$0.0474043\pi$
$434$	5.70510	+	11.4262i	0.273854	+	0.548473i
$435$	3.12628	−	5.84494i	0.149894	−	0.280243i
$436$	6.72686	−	17.9247i	0.322158	−	0.858439i
$437$	0.332447	−	9.92182i	0.0159031	−	0.474625i
$438$	−10.9920	+	22.3847i	−0.525220	+	1.06958i
$439$	−3.10757	−	4.83548i	−0.148316	−	0.230785i	0.759144	−	0.650923i	$-0.225618\pi$
$439$	−3.10757	−	4.83548i	−0.148316	−	0.230785i	−0.907460	+	0.420138i	$0.861982\pi$
$440$	−1.93965	−	18.5707i	−0.0924692	−	0.885321i
$441$	15.4270	+	23.1161i	0.734620	+	1.10077i
$442$	29.8395	+	24.0960i	1.41932	+	1.14613i
$443$	−1.93314	−	4.23299i	−0.0918464	−	0.201115i	0.858134	−	0.513427i	$-0.171624\pi$
$443$	−1.93314	−	4.23299i	−0.0918464	−	0.201115i	−0.949980	+	0.312311i	$0.898897\pi$
$444$	17.9837	−	21.0343i	0.853469	−	0.998244i
$445$	−1.29259	−	8.99014i	−0.0612745	−	0.426174i
$446$	−9.67104	−	29.1551i	−0.457937	−	1.38053i
$447$	−24.5805	−	5.12501i	−1.16262	−	0.242405i
$448$	−2.49656	+	32.1659i	−0.117952	+	1.51970i
$449$	−0.309849	+	0.482135i	−0.0146227	+	0.0227533i	−0.848488	−	0.529215i	$-0.822487\pi$
$449$	−0.309849	+	0.482135i	−0.0146227	+	0.0227533i	0.833865	+	0.551968i	$0.186123\pi$
$450$	−5.64105	−	4.39631i	−0.265921	−	0.207244i
$451$	3.29370	−	11.2173i	0.155094	−	0.528202i
$452$	−0.274463	+	1.24953i	−0.0129096	+	0.0587728i
$453$	0.496666	−	1.36761i	0.0233354	−	0.0642558i
$454$	2.34296	+	1.39334i	0.109960	+	0.0653927i
$455$	−45.9809	+	13.5012i	−2.15562	+	0.632947i
$456$	−3.25647	−	9.60381i	−0.152498	−	0.449740i
$457$	−3.15264	+	21.9271i	−0.147474	+	1.02571i	0.772861	+	0.634575i	$0.218825\pi$
$457$	−3.15264	+	21.9271i	−0.147474	+	1.02571i	−0.920335	+	0.391131i	$0.872084\pi$
$458$	7.64478	−	18.4035i	0.357217	−	0.859940i
$459$	−21.5673	−	0.981199i	−1.00668	−	0.0457984i
$460$	17.3621	+	1.86336i	0.809513	+	0.0868796i
$461$			21.4765i			1.00026i	0.865950	+	0.500131i	$0.166715\pi$
$461$			21.4765i			1.00026i	−0.865950	+	0.500131i	$0.833285\pi$
$462$	−35.5847	+	4.10083i	−1.65555	+	0.190788i
$463$	40.0075	+	5.75221i	1.85930	+	0.267328i	0.978514	−	0.206179i	$-0.0661029\pi$
$463$	40.0075	+	5.75221i	1.85930	+	0.267328i	0.880790	+	0.473507i	$0.157012\pi$
$464$	−3.46209	−	7.66270i	−0.160723	−	0.355732i
$465$	4.94952	−	5.03585i	0.229528	−	0.233532i
$466$	10.0532	−	16.9049i	0.465707	−	0.783103i
$467$	−1.41547	−	1.63354i	−0.0655002	−	0.0755913i	0.722054	−	0.691837i	$-0.243198\pi$
$467$	−1.41547	−	1.63354i	−0.0655002	−	0.0755913i	−0.787554	+	0.616246i	$0.788653\pi$
$468$	−27.2667	+	28.1125i	−1.26040	+	1.29950i
$469$	−43.6643	−	12.8210i	−2.01623	−	0.592019i
$470$	−6.98921	−	0.758560i	−0.322388	−	0.0349897i
$471$	−5.90033	−	0.370758i	−0.271873	−	0.0170836i
$472$	−8.61079	+	25.6120i	−0.396344	+	1.17889i
$473$	−18.6546	−	16.1643i	−0.857741	−	0.743237i
$474$	−8.92879	−	8.18663i	−0.410113	−	0.376024i
$475$	3.45390	−	0.496596i	0.158476	−	0.0227854i
$476$	−31.4228	+	11.6479i	−1.44026	+	0.533878i
$477$	−2.87130	+	22.7570i	−0.131468	+	1.04197i
$478$	−19.1986	+	23.7748i	−0.878123	+	1.08743i
$479$	−3.63321	+	7.95563i	−0.166006	+	0.363502i	−0.974292	−	0.225287i	$-0.927668\pi$
$479$	−3.63321	+	7.95563i	−0.166006	+	0.363502i	0.808287	+	0.588789i	$0.200395\pi$
$480$	17.2673	−	4.47341i	0.788142	−	0.204182i
$481$	43.8673	−	28.1918i	2.00018	−	1.28543i
$482$	−0.227392	+	0.157541i	−0.0103574	+	0.00717580i
$483$	3.21927	−	33.3442i	0.146482	−	1.51721i
$484$	1.50998	−	4.02356i	0.0686353	−	0.182889i
$485$	0.589373	+	0.917082i	0.0267620	+	0.0416425i
$486$	2.99511	−	21.8410i	0.135861	−	0.990728i
$487$	−23.2726	−	10.6283i	−1.05458	−	0.481613i	−0.188793	−	0.982017i	$-0.560457\pi$
$487$	−23.2726	−	10.6283i	−1.05458	−	0.481613i	−0.865792	+	0.500404i	$0.833185\pi$
$488$	9.85362	+	16.7227i	0.446053	+	0.756999i
$489$	3.52497	−	4.79465i	0.159404	−	0.216822i
$490$	5.92170	−	23.1036i	0.267515	−	1.04371i
$491$	2.88931	+	20.0956i	0.130393	+	0.906901i	0.945043	+	0.326948i	$0.106020\pi$
$491$	2.88931	+	20.0956i	0.130393	+	0.906901i	−0.814650	+	0.579953i	$0.803071\pi$
$492$	11.0651	+	1.51616i	0.498853	+	0.0683540i
$493$	5.71966	−	6.60084i	0.257601	−	0.297287i
$494$	−0.662724	−	19.0966i	−0.0298174	−	0.859195i
$495$	8.53725	+	17.8697i	0.383721	+	0.803183i
$496$	−1.23890	−	8.87104i	−0.0556284	−	0.398321i
$497$	7.64930	−	26.0511i	0.343118	−	1.16855i
$498$	10.1922	+	3.30608i	0.456725	+	0.148149i
$499$	−23.1199	+	20.0335i	−1.03499	+	0.896822i	−0.994747	−	0.102368i	$-0.967358\pi$
$499$	−23.1199	+	20.0335i	−1.03499	+	0.896822i	−0.0402415	+	0.999190i	$0.512813\pi$
$500$	1.68755	+	24.2844i	0.0754696	+	1.08603i
$501$	3.30187	−	3.35946i	0.147517	−	0.150090i
$502$	0.284602	+	1.58661i	0.0127024	+	0.0708139i
$503$	3.37533	−	23.4759i	0.150498	−	1.04674i	−0.764888	−	0.644163i	$-0.777206\pi$
$503$	3.37533	−	23.4759i	0.150498	−	1.04674i	0.915387	−	0.402576i	$-0.131885\pi$
$504$	−8.93472	−	33.0327i	−0.397984	−	1.47139i
$505$	−12.4640			−0.554639
$506$	20.7053	+	13.2715i	0.920464	+	0.589992i
$507$	−44.7911	+	24.9629i	−1.98924	+	1.10864i
$508$	−0.782029	+	0.168466i	−0.0346969	+	0.00747448i
$509$	−25.2559	−	3.63125i	−1.11945	−	0.160953i	−0.442349	−	0.896843i	$-0.645855\pi$
$509$	−25.2559	−	3.63125i	−1.11945	−	0.160953i	−0.677101	+	0.735891i	$0.736764\pi$
$510$	11.7357	+	14.3377i	0.519666	+	0.634882i
$511$	−11.5673	−	39.3945i	−0.511706	−	1.74271i
$512$	8.84881	−	20.8254i	0.391066	−	0.920363i
$513$	6.66700	+	8.44060i	0.294355	+	0.372662i
$514$	−1.13213	+	1.05192i	−0.0499361	+	0.0463981i
$515$	−18.4849	−	5.42764i	−0.814540	−	0.239171i
$516$	12.6170	−	19.9214i	0.555432	−	0.876990i
$517$	−8.32972	−	5.35318i	−0.366341	−	0.235433i
$518$	1.58024	+	45.5351i	0.0694319	+	2.00070i
$519$	37.1562	+	7.74702i	1.63097	+	0.340056i
$520$	33.5850	+	1.30140i	1.47280	+	0.0570700i
$521$	−18.1046	+	2.60304i	−0.793175	+	0.114041i	−0.526980	−	0.849878i	$-0.676676\pi$
$521$	−18.1046	+	2.60304i	−0.793175	+	0.114041i	−0.266195	+	0.963919i	$0.585767\pi$
$522$	6.18273	+	6.42765i	0.270611	+	0.281330i
$523$	−13.2522	+	6.05207i	−0.579478	+	0.264639i	−0.683517	−	0.729934i	$-0.739551\pi$
$523$	−13.2522	+	6.05207i	−0.579478	+	0.264639i	0.104039	+	0.994573i	$0.466823\pi$
$524$	−0.560909	+	7.62602i	−0.0245034	+	0.333144i
$525$	11.7371	−	0.941509i	0.512248	−	0.0410908i
$526$	−6.06709	−	12.1511i	−0.264538	−	0.529815i
$527$	7.82706	−	5.03015i	0.340952	−	0.219117i
$528$	24.5727	+	5.22707i	1.06939	+	0.227479i
$529$	−16.1916	+	16.3350i	−0.703981	+	0.710219i
$530$	16.1810	−	11.2104i	0.702856	−	0.486950i
$531$	−0.495531	−	28.6556i	−0.0215042	−	1.24355i
$532$	14.6375	+	8.03110i	0.634615	+	0.348192i
$533$	19.1426	+	8.74212i	0.829157	+	0.378663i
$534$	12.0426	+	2.07790i	0.521133	+	0.0899197i
$535$	−21.1109	+	9.64102i	−0.912703	+	0.416818i
$536$	26.1619	+	18.2823i	1.13002	+	0.789673i
$537$	−8.99191	−	11.7978i	−0.388030	−	0.509112i
$538$	−13.9633	−	42.0949i	−0.602002	−	1.81484i
$539$	21.9977	−	25.3867i	0.947507	−	1.09348i
$540$	−15.6669	+	10.6063i	−0.674194	+	0.456422i
$541$	−7.42301	−	4.77048i	−0.319140	−	0.205099i	0.371256	−	0.928531i	$-0.378927\pi$
$541$	−7.42301	−	4.77048i	−0.319140	−	0.205099i	−0.690396	+	0.723432i	$0.742564\pi$
$542$	−0.0816421	−	0.00886086i	−0.00350683	−	0.000380607i
$543$	24.4291	−	5.53585i	1.04835	−	0.237566i
$544$	23.4927	−	0.720274i	1.00724	−	0.0308815i
$545$	13.1707	−	11.4125i	0.564170	−	0.488856i
$546$	1.80932	−	64.4533i	0.0774319	−	2.75835i
$547$	8.32500	+	28.3523i	0.355951	+	1.21226i	0.921773	+	0.387731i	$0.126741\pi$
$547$	8.32500	+	28.3523i	0.355951	+	1.21226i	−0.565822	+	0.824528i	$0.691441\pi$
$548$	1.97122	−	1.96327i	0.0842064	−	0.0838668i
$549$	−15.7896	−	13.2107i	−0.673882	−	0.563820i
$550$	−3.31617	+	7.98313i	−0.141402	+	0.340402i
$551$	−4.35141			−0.185376
$552$	−9.59260	+	21.4472i	−0.408288	+	0.912853i
$553$	19.9441			0.848110
$554$	−4.42359	+	10.6491i	−0.187940	+	0.452435i
$555$	23.5254	−	9.00695i	0.998596	−	0.382324i
$556$	16.6945	−	16.6272i	0.708004	−	0.705149i
$557$	−8.80063	−	29.9722i	−0.372895	−	1.26996i	−0.905770	−	0.423769i	$-0.860707\pi$
$557$	−8.80063	−	29.9722i	−0.372895	−	1.26996i	0.532876	−	0.846193i	$-0.321111\pi$
$558$	4.39032	+	8.42520i	0.185857	+	0.356667i
$559$	33.5795	−	29.0968i	1.42026	−	1.23067i
$560$	−15.9769	+	24.6411i	−0.675147	+	1.04128i
$561$	5.76725	+	25.4503i	0.243493	+	1.07451i
$562$	13.4042	+	1.45479i	0.565420	+	0.0613667i
$563$	−9.76083	−	6.27290i	−0.411370	−	0.264371i	0.318547	−	0.947907i	$-0.396805\pi$
$563$	−9.76083	−	6.27290i	−0.411370	−	0.264371i	−0.729917	+	0.683536i	$0.760441\pi$
$564$	3.87237	−	8.63017i	0.163056	−	0.363396i
$565$	−0.762592	+	0.880078i	−0.0320825	+	0.0370252i
$566$	4.91899	+	14.8292i	0.206761	+	0.623317i
$567$	20.6668	+	29.8370i	0.867923	+	1.25304i
$568$	−10.9076	+	15.6088i	−0.457673	+	0.654930i
$569$	17.0131	−	7.76962i	0.713226	−	0.325719i	−0.0255471	−	0.999674i	$-0.508133\pi$
$569$	17.0131	−	7.76962i	0.713226	−	0.325719i	0.738773	+	0.673954i	$0.235406\pi$
$570$	1.56956	−	9.09644i	0.0657416	−	0.381008i
$571$	11.7268	+	5.35546i	0.490753	+	0.224119i	0.645392	−	0.763852i	$-0.276694\pi$
$571$	11.7268	+	5.35546i	0.490753	+	0.224119i	−0.154639	+	0.987971i	$0.549421\pi$
$572$	41.5010	+	22.7702i	1.73525	+	0.952071i
$573$	0.532559	−	0.995678i	0.0222480	−	0.0415951i
$574$	−15.1147	+	10.4717i	−0.630874	+	0.437080i
$575$	−6.65082	−	4.59604i	−0.277358	−	0.191668i
$576$	−1.44318	+	23.9566i	−0.0601327	+	0.998190i
$577$	−12.3058	+	7.90845i	−0.512296	+	0.329233i	−0.771118	−	0.636692i	$-0.780302\pi$
$577$	−12.3058	+	7.90845i	−0.512296	+	0.329233i	0.258822	+	0.965925i	$0.416666\pi$
$578$	0.166381	+	0.333228i	0.00692055	+	0.0138605i
$579$	−2.49836	−	31.1452i	−0.103828	−	1.29435i
$580$	0.561446	−	7.63331i	0.0233128	−	0.316956i
$581$	−16.0470	+	7.32841i	−0.665741	+	0.304034i
$582$	−1.41839	+	0.373582i	−0.0587944	+	0.0154855i
$583$	27.4425	−	3.94563i	1.13655	−	0.163411i
$584$	−1.11498	+	28.7742i	−0.0461383	+	1.19069i
$585$	−34.0262	+	10.6334i	−1.40681	+	0.439637i
$586$	0.326538	+	9.40930i	0.0134892	+	0.388694i
$587$	3.44004	+	2.21078i	0.141986	+	0.0912486i	0.609705	−	0.792628i	$-0.291288\pi$
$587$	3.44004	+	2.21078i	0.141986	+	0.0912486i	−0.467719	+	0.883877i	$0.654924\pi$
$588$	27.1106	+	17.1702i	1.11802	+	0.708086i
$589$	−4.44756	−	1.30592i	−0.183258	−	0.0538095i
$590$	−18.0185	+	16.7419i	−0.741812	+	0.689254i
$591$	9.78743	−	26.9504i	0.402601	−	1.10859i
$592$	9.12665	−	30.6243i	0.375103	−	1.25865i
$593$	−5.30628	−	18.0715i	−0.217903	−	0.742108i	−0.993793	−	0.111241i	$-0.964517\pi$
$593$	−5.30628	−	18.0715i	−0.217903	−	0.742108i	0.775891	−	0.630867i	$-0.217301\pi$
$594$	−26.4146	+	3.50782i	−1.08380	+	0.143928i
$595$	−30.1943	−	4.34128i	−1.23785	−	0.177975i
$596$	−28.3433	+	6.10577i	−1.16099	+	0.250102i
$597$	−5.21613	−	9.35934i	−0.213482	−	0.383052i
$598$	−28.9507	+	33.4917i	−1.18388	+	1.36958i
$599$	10.5916			0.432761			0.216380	−	0.976309i	$-0.430575\pi$
$599$	10.5916			0.432761			0.216380	+	0.976309i	$0.430575\pi$
$600$	−8.01306	−	1.99735i	−0.327132	−	0.0815415i
$601$	1.50312	−	10.4544i	0.0613134	−	0.426444i	−0.935926	−	0.352196i	$-0.885435\pi$
$601$	1.50312	−	10.4544i	0.0613134	−	0.426444i	0.997240	−	0.0742484i	$-0.0236558\pi$
$602$	6.85458	+	38.2133i	0.279372	+	1.55746i
$603$	−32.6417	−	8.97444i	−1.32927	−	0.365467i
$604$	−0.116471	−	1.67605i	−0.00473913	−	0.0681974i
$605$	2.95642	−	2.56175i	0.120196	−	0.104150i
$606$	5.17435	−	15.9519i	0.210194	−	0.648002i
$607$	1.04573	−	3.56144i	0.0424450	−	0.144554i	−0.935544	−	0.353209i	$-0.885090\pi$
$607$	1.04573	−	3.56144i	0.0424450	−	0.144554i	0.977989	+	0.208655i	$0.0669086\pi$
$608$	−7.93582	−	8.61045i	−0.321840	−	0.349200i
$609$	−14.6546	−	0.920848i	−0.593834	−	0.0373147i
$610$	0.612778	+	17.6574i	0.0248106	+	0.714925i
$611$	11.6719	−	13.4701i	0.472193	−	0.544940i
$612$	−23.2220	+	9.06764i	−0.938692	+	0.366538i
$613$	−1.56140	−	10.8597i	−0.0630642	−	0.438621i	−0.996752	−	0.0805327i	$-0.974338\pi$
$613$	−1.56140	−	10.8597i	−0.0630642	−	0.438621i	0.933688	−	0.358088i	$-0.116571\pi$
$614$	5.93041	−	23.1376i	0.239332	−	0.933756i
$615$	8.19086	+	6.02181i	0.330287	+	0.242823i
$616$	−35.6354	+	20.9977i	−1.43579	+	0.846022i
$617$	33.7047	+	15.3924i	1.35690	+	0.619675i	0.955163	−	0.296080i	$-0.0956794\pi$
$617$	33.7047	+	15.3924i	1.35690	+	0.619675i	0.401737	+	0.915755i	$0.368407\pi$
$618$	14.6204	−	21.4044i	0.588120	−	0.861013i
$619$	25.7766	+	40.1091i	1.03605	+	1.61212i	0.758801	+	0.651322i	$0.225785\pi$
$619$	25.7766	+	40.1091i	1.03605	+	1.61212i	0.277246	+	0.960799i	$0.410578\pi$
$620$	2.86472	−	7.63348i	0.115050	−	0.306568i
$621$	1.96557	−	24.8422i	0.0788756	−	0.996884i
$622$	21.6007	−	14.9653i	0.866109	−	0.600055i
$623$	−16.9259	+	10.8776i	−0.678121	+	0.435802i
$624$	−15.6082	+	42.4432i	−0.624829	+	1.69909i
$625$	−5.70359	+	12.4891i	−0.228144	+	0.499565i
$626$	20.5079	−	25.3962i	0.819661	−	1.01504i
$627$	7.70090	−	10.4747i	0.307544	−	0.418321i
$628$	−6.40094	+	2.37271i	−0.255425	+	0.0946815i
$629$	32.8551	−	4.72385i	1.31002	−	0.188352i
$630$	7.21093	−	30.3027i	0.287290	−	1.20729i
$631$	7.25771	+	6.28884i	0.288925	+	0.250355i	0.787248	−	0.616637i	$-0.211505\pi$
$631$	7.25771	+	6.28884i	0.288925	+	0.250355i	−0.498323	+	0.866991i	$0.666051\pi$
$632$	−13.2586	−	4.45754i	−0.527397	−	0.177311i
$633$	1.50126	−	23.8914i	0.0596696	−	0.949596i
$634$	−38.7058	−	4.20086i	−1.53720	−	0.166837i
$635$	−0.698684	−	0.205152i	−0.0277264	−	0.00814121i
$636$	7.63014	+	25.3630i	0.302555	+	1.00571i
$637$	39.5972	+	45.6976i	1.56890	+	1.81061i
$638$	5.51004	−	9.26535i	0.218145	−	0.366819i
$639$	5.35435	−	19.4748i	0.211815	−	0.770411i
$640$	16.1285	−	12.8102i	0.637536	−	0.506366i
$641$	−38.3811	−	5.51837i	−1.51596	−	0.217962i	−0.666457	−	0.745543i	$-0.732190\pi$
$641$	−38.3811	−	5.51837i	−1.51596	−	0.217962i	−0.849505	+	0.527581i	$0.823099\pi$
$642$	−3.57490	−	31.0210i	−0.141090	−	1.22430i
$643$		−	16.0428i		−	0.632667i	−0.948648	−	0.316334i	$-0.897548\pi$
$643$		−	16.0428i		−	0.632667i	0.948648	−	0.316334i	$-0.102452\pi$
$644$	−12.2224	−	36.6998i	−0.481631	−	1.44617i
$645$	18.7494	−	10.4494i	0.738255	−	0.411443i
$646$	4.66601	−	11.2326i	0.183582	−	0.441943i
$647$	−4.72893	+	32.8904i	−0.185913	+	1.29306i	0.656542	+	0.754290i	$0.272019\pi$
$647$	−4.72893	+	32.8904i	−0.185913	+	1.29306i	−0.842455	+	0.538767i	$0.818890\pi$
$648$	−7.07036	−	24.4542i	−0.277750	−	0.960653i
$649$	−33.2382	+	9.75961i	−1.30471	+	0.383098i
$650$	−13.3744	−	7.95365i	−0.524585	−	0.311968i
$651$	−14.7020	−	5.33925i	−0.576219	−	0.209262i
$652$	1.47422	−	6.71159i	0.0577350	−	0.262846i
$653$	−2.93924	+	10.0101i	−0.115021	+	0.391726i	−0.996800	−	0.0799370i	$-0.974528\pi$
$653$	−2.93924	+	10.0101i	−0.115021	+	0.391726i	0.881779	+	0.471663i	$0.156346\pi$
$654$	9.13840	+	21.5942i	0.357340	+	0.844401i
$655$	−3.76308	+	5.85547i	−0.147036	+	0.228792i
$656$	12.3885	−	3.58328i	0.483688	−	0.139903i
$657$	−9.11024	−	29.1522i	−0.355424	−	1.13734i
$658$	4.90317	+	14.7815i	0.191145	+	0.576242i
$659$	3.49902	+	24.3362i	0.136303	+	0.948005i	0.937098	+	0.349067i	$0.113501\pi$
$659$	3.49902	+	24.3362i	0.136303	+	0.948005i	−0.800795	+	0.598938i	$0.795589\pi$
$660$	17.3813	+	14.8605i	0.676568	+	0.578446i
$661$	−15.0331	−	32.9178i	−0.584719	−	1.28036i	−0.938581	−	0.345058i	$-0.887859\pi$
$661$	−15.0331	−	32.9178i	−0.584719	−	1.28036i	0.353863	−	0.935297i	$-0.384868\pi$
$662$	17.5554	+	14.1763i	0.682309	+	0.550977i
$663$	−46.8232	+	3.75600i	−1.81846	+	0.145871i
$664$	12.3057	−	1.28529i	0.477554	−	0.0498791i
$665$	8.21647	+	12.7851i	0.318621	+	0.495784i
$666$	1.76103	+	33.8479i	0.0682386	+	1.31158i
$667$	7.39369	+	6.85338i	0.286285	+	0.265364i
$668$	1.91108	−	5.09237i	0.0739420	−	0.197030i
$669$	33.1736	+	17.7436i	1.28257	+	0.686006i
$670$	12.9782	+	25.9927i	0.501392	+	1.00419i
$671$	−10.3372	+	22.6352i	−0.399062	+	0.873824i
$672$	−24.9040	−	30.6775i	−0.960691	−	1.18341i
$673$	9.73739	+	21.3219i	0.375349	+	0.821899i	0.999186	+	0.0403448i	$0.0128456\pi$
$673$	9.73739	+	21.3219i	0.375349	+	0.821899i	−0.623837	+	0.781554i	$0.714427\pi$
$674$	27.2401	+	6.98194i	1.04925	+	0.268934i
$675$	8.71773	−	0.851241i	0.335545	−	0.0327643i
$676$	−35.5790	+	47.3284i	−1.36842	+	1.82032i
$677$	30.6236	+	26.5355i	1.17696	+	1.01984i	0.999361	+	0.0357378i	$0.0113781\pi$
$677$	30.6236	+	26.5355i	1.17696	+	1.01984i	0.177598	+	0.984103i	$0.443167\pi$
$678$	−0.809774	−	1.34136i	−0.0310992	−	0.0515145i
$679$	1.30558	−	2.03153i	0.0501037	−	0.0779628i
$680$	19.1024	+	9.63450i	0.732545	+	0.369466i
$681$	−3.25605	+	0.737848i	−0.124772	+	0.0282744i
$682$	8.41246	−	7.81643i	0.322130	−	0.299307i
$683$	11.8831	+	13.7138i	0.454695	+	0.524746i	0.936091	−	0.351757i	$-0.114416\pi$
$683$	11.8831	+	13.7138i	0.454695	+	0.524746i	−0.481397	+	0.876503i	$0.659870\pi$
$684$	10.9904	+	5.78513i	0.420229	+	0.221200i
$685$	2.42986	−	0.713472i	0.0928403	−	0.0272604i
$686$	−12.7078	+	2.27948i	−0.485185	+	0.0870311i
$687$	8.72673	+	22.7935i	0.332946	+	0.869625i
$688$	3.98389	−	26.9356i	0.151885	−	1.02691i
$689$			49.9062i			1.90127i
$690$	−16.9936	+	12.9842i	−0.646937	+	0.494299i
$691$		−	21.8978i		−	0.833030i	−0.909129	−	0.416515i	$-0.863251\pi$
$691$		−	21.8978i		−	0.833030i	0.909129	−	0.416515i	$-0.136749\pi$
$692$	42.8440	−	9.22955i	1.62869	−	0.350855i
$693$	28.1516	−	33.6470i	1.06939	−	1.27814i
$694$	−7.22356	−	40.2703i	−0.274203	−	1.52864i
$695$	20.5788	−	6.04248i	0.780598	−	0.229204i
$696$	9.53634	+	3.88749i	0.361474	+	0.147355i
$697$	8.77234	+	10.1238i	0.332276	+	0.383467i
$698$	−15.8396	−	17.0474i	−0.599538	−	0.645255i
$699$	5.32371	+	23.4930i	0.201361	+	0.888587i
$700$	11.9464	−	6.49191i	0.451530	−	0.245371i
$701$	−1.38904	+	2.16139i	−0.0524634	+	0.0816346i	−0.866494	−	0.499187i	$-0.833632\pi$
$701$	−1.38904	+	2.16139i	−0.0524634	+	0.0816346i	0.814031	+	0.580821i	$0.197269\pi$
$702$	0.516746	−	47.9626i	0.0195033	−	1.81023i
$703$	−12.4977	−	10.8294i	−0.471362	−	0.408437i
$704$	28.3829	−	5.99441i	1.06972	−	0.225923i
$705$	6.84801	−	5.21934i	0.257911	−	0.196572i
$706$	4.38926	−	17.1248i	0.165192	−	0.644499i
$707$	11.4697	+	25.1152i	0.431363	+	0.944554i
$708$	−13.9467	−	30.0112i	−0.524149	−	1.12789i
$709$	17.8852	−	39.1631i	0.671692	−	1.47080i	−0.199521	−	0.979894i	$-0.563939\pi$
$709$	17.8852	−	39.1631i	0.671692	−	1.47080i	0.871213	−	0.490906i	$-0.163334\pi$
$710$	−15.5079	+	7.74310i	−0.581999	+	0.290593i
$711$	14.8341	−	0.256521i	0.556322	−	0.00962030i
$712$	13.6832	−	3.44831i	0.512801	−	0.129231i
$713$	5.50026	+	9.22378i	0.205986	+	0.345433i
$714$	18.0912	−	36.8417i	0.677045	−	1.37876i
$715$	23.2958	+	36.2490i	0.871214	+	1.35564i
$716$	−15.0168	−	8.23923i	−0.561205	−	0.307914i
$717$	−2.99262	−	37.3066i	−0.111761	−	1.39324i
$718$	3.46202	−	4.28723i	0.129201	−	0.159998i
$719$	0.384218	+	0.841319i	0.0143289	+	0.0313759i	0.916661	−	0.399665i	$-0.130874\pi$
$719$	0.384218	+	0.841319i	0.0143289	+	0.0313759i	−0.902332	+	0.431041i	$0.858146\pi$
$720$	−11.5664	+	18.5331i	−0.431055	+	0.690688i
$721$	6.07350	+	42.2421i	0.226189	+	1.57318i
$722$	19.7520	−	6.55193i	0.735092	−	0.243838i
$723$	0.0691536	−	0.331674i	0.00257185	−	0.0123351i
$724$	23.1894	−	17.2864i	0.861829	−	0.642444i
$725$	−1.91580	+	2.98104i	−0.0711509	+	0.110713i
$726$	2.05129	+	4.84725i	0.0761307	+	0.179898i
$727$	11.0868	−	37.7582i	0.411187	−	1.40038i	−0.450428	−	0.892813i	$-0.648729\pi$
$727$	11.0868	−	37.7582i	0.411187	−	1.40038i	0.861615	−	0.507562i	$-0.169453\pi$
$728$	−28.2836	−	68.8722i	−1.04826	−	2.55257i
$729$	15.7554	+	21.9264i	0.583532	+	0.812090i
$730$	−13.3978	+	22.5289i	−0.495874	+	0.833831i
$731$	27.1375	−	7.96830i	1.00372	−	0.294718i
$732$	−22.8530	−	6.54610i	−0.844672	−	0.241951i
$733$	−2.11161	+	14.6866i	−0.0779941	+	0.542461i	0.912938	+	0.408098i	$0.133808\pi$
$733$	−2.11161	+	14.6866i	−0.0779941	+	0.542461i	−0.990932	+	0.134363i	$0.957101\pi$
$734$	−31.7418	−	13.1855i	−1.17161	−	0.486684i
$735$	14.2203	+	25.5156i	0.524524	+	0.941157i
$736$	−0.0771654	+	27.1292i	−0.00284435	+	0.999996i
$737$			40.9183i			1.50725i
$738$	−11.1074	+	7.98308i	−0.408867	+	0.293861i
$739$	−40.7502	−	5.85899i	−1.49902	−	0.215527i	−0.656555	−	0.754278i	$-0.727987\pi$
$739$	−40.7502	−	5.85899i	−1.49902	−	0.215527i	−0.842465	+	0.538751i	$0.818896\pi$
$740$	20.6096	−	20.5265i	0.757623	−	0.754568i
$741$	16.6905	+	16.4044i	0.613141	+	0.602630i
$742$	−37.4795	−	22.2888i	−1.37592	−	0.818248i
$743$	−14.5588	−	16.8018i	−0.534111	−	0.616397i	0.422996	−	0.906131i	$-0.360978\pi$
$743$	−14.5588	−	16.8018i	−0.534111	−	0.616397i	−0.957107	+	0.289735i	$0.906433\pi$
$744$	8.58037	+	6.83539i	0.314572	+	0.250597i
$745$	−25.3226	−	7.43538i	−0.927747	−	0.272411i
$746$	−3.75041	+	34.5555i	−0.137312	+	1.26517i
$747$	−11.8412	+	5.65714i	−0.433247	+	0.206984i
$748$	18.0090	+	24.1588i	0.658474	+	0.883332i
$749$	38.8538	+	33.6670i	1.41969	+	1.23016i
$750$	−21.9751	−	20.1485i	−0.802417	−	0.735719i
$751$	−17.5147	+	2.51824i	−0.639122	+	0.0918918i	−0.454255	−	0.890872i	$-0.650094\pi$
$751$	−17.5147	+	2.51824i	−0.639122	+	0.0918918i	−0.184867	+	0.982764i	$0.559185\pi$
$752$	0.0441275	−	10.9224i	0.00160916	−	0.398298i
$753$	−1.59060	−	1.16939i	−0.0579649	−	0.0426150i
$754$	15.0969	+	12.1910i	0.549797	+	0.443971i
$755$	0.635302	−	1.39112i	0.0231210	−	0.0506279i
$756$	35.7890	+	21.8088i	1.30163	+	0.793180i
$757$	−22.0572	+	14.1753i	−0.801682	+	0.515210i	−0.876164	−	0.482012i	$-0.839906\pi$
$757$	−22.0572	+	14.1753i	−0.801682	+	0.515210i	0.0744821	+	0.997222i	$0.476270\pi$
$758$	−7.00610	−	10.1125i	−0.254473	−	0.367302i
$759$	−29.5825	+	5.66939i	−1.07378	+	0.205786i
$760$	−2.60470	−	10.3357i	−0.0944825	−	0.374916i
$761$	−22.0051	−	34.2406i	−0.797684	−	1.24122i	−0.966777	−	0.255621i	$-0.917720\pi$
$761$	−22.0051	−	34.2406i	−0.797684	−	1.24122i	0.169093	−	0.985600i	$-0.445916\pi$
$762$	0.552617	−	0.809037i	0.0200192	−	0.0293083i
$763$	−35.1164	−	16.0371i	−1.27130	−	0.580583i
$764$	0.0956416	−	1.30032i	0.00346019	−	0.0470441i
$765$	−22.5139	−	2.84062i	−0.813990	−	0.102703i
$766$	10.6340	+	2.72560i	0.384221	+	0.0984799i
$767$	−8.87429	−	61.7220i	−0.320432	−	2.22865i
$768$	9.69931	+	25.9600i	0.349994	+	0.936752i
$769$	−19.1303	+	22.0776i	−0.689857	+	0.796138i	−0.987345	−	0.158588i	$-0.949306\pi$
$769$	−19.1303	+	22.0776i	−0.689857	+	0.796138i	0.297488	+	0.954726i	$0.403851\pi$
$770$	−37.6272	+	1.30581i	−1.35599	+	0.0470580i
$771$	0.118698	−	1.88899i	0.00427481	−	0.0680303i
$772$	−17.2268	−	31.7005i	−0.620005	−	1.14093i
$773$	12.4061	−	42.2513i	0.446217	−	1.51967i	−0.362788	−	0.931872i	$-0.618175\pi$
$773$	12.4061	−	42.2513i	0.446217	−	1.51967i	0.809004	−	0.587803i	$-0.200007\pi$
$774$	5.58982	+	28.3342i	0.200922	+	1.01845i
$775$	−2.85278	+	2.47195i	−0.102475	+	0.0887951i
$776$	−1.32198	+	1.05873i	−0.0474564	+	0.0380062i
$777$	−39.7980	−	39.1157i	−1.42774	−	1.40327i
$778$	−24.2532	+	4.35048i	−0.869520	+	0.155972i
$779$	0.949784	−	6.60590i	0.0340296	−	0.236681i
$780$	−30.9303	+	27.1622i	−1.10748	+	0.972562i
$781$	−24.4128			−0.873559
$782$	−25.6195	+	11.7371i	−0.916150	+	0.419716i
$783$	−10.9117	−	0.496424i	−0.389952	−	0.0177408i
$784$	36.6561	+	5.42159i	1.30915	+	0.193628i
$785$	−6.15069	−	0.884336i	−0.219528	−	0.0315633i
$786$	−5.93185	−	7.24702i	−0.211582	−	0.258493i
$787$	9.52298	+	32.4323i	0.339458	+	1.15609i	0.935557	+	0.353176i	$0.114898\pi$
$787$	9.52298	+	32.4323i	0.339458	+	1.15609i	−0.596099	+	0.802911i	$0.703284\pi$
$788$	−2.29521	−	33.0287i	−0.0817633	−	1.17660i
$789$	15.6349	+	5.67803i	0.556617	+	0.202143i
$790$	−8.66677	−	9.32764i	−0.308350	−	0.331863i
$791$	2.47514	+	0.726766i	0.0880058	+	0.0258408i
$792$	−26.2349	+	16.0761i	−0.932218	+	0.571239i
$793$	−37.6820	−	24.2168i	−1.33813	−	0.859962i
$794$	−36.5428	+	1.26818i	−1.29686	+	0.0450058i
$795$	−4.92088	+	23.6015i	−0.174526	+	0.837059i
$796$	−9.88953	−	7.43443i	−0.350525	−	0.263506i
$797$	23.2919	−	3.34887i	0.825042	−	0.118623i	0.283155	−	0.959074i	$-0.408619\pi$
$797$	23.2919	−	3.34887i	0.825042	−	0.118623i	0.541887	+	0.840451i	$0.317710\pi$
$798$	−19.7739	+	5.20812i	−0.699988	+	0.184365i
$799$	10.3202	−	4.71309i	0.365103	−	0.166737i
$800$	−9.39271	+	1.64570i	−0.332083	+	0.0581842i
$801$	−12.4493	+	8.30827i	−0.439873	+	0.293558i
$802$	23.7288	−	11.8479i	0.837895	−	0.418362i
$803$	−31.0566	+	19.9589i	−1.09596	+	0.704333i
$804$	−38.6544	+	5.81931i	−1.36324	+	0.205231i
$805$	6.17525	−	34.6645i	0.217649	−	1.22176i
$806$	11.7718	+	16.9912i	0.414644	+	0.598490i
$807$	47.8970	+	25.6187i	1.68605	+	0.901821i
$808$	−2.01162	−	19.2597i	−0.0707685	−	0.677554i
$809$	−30.4199	−	13.8923i	−1.06951	−	0.488428i	−0.198705	−	0.980059i	$-0.563673\pi$
$809$	−30.4199	−	13.8923i	−1.06951	−	0.488428i	−0.870803	+	0.491631i	$0.836401\pi$
$810$	4.97362	−	22.6314i	0.174755	−	0.795185i
$811$	−33.8347	+	15.4518i	−1.18810	+	0.542585i	−0.908643	−	0.417574i	$-0.862880\pi$
$811$	−33.8347	+	15.4518i	−1.18810	+	0.542585i	−0.279453	+	0.960159i	$0.590153\pi$
$812$	−15.8980	+	5.89307i	−0.557909	+	0.206806i
$813$	0.0799927	−	0.0609680i	0.00280547	−	0.00213824i
$814$	38.8842	−	12.8983i	1.36289	−	0.452085i
$815$	4.09611	−	4.72717i	0.143481	−	0.165585i
$816$	−20.2609	+	20.4484i	−0.709274	+	0.715837i
$817$	−11.8540	−	7.61809i	−0.414718	−	0.266523i
$818$	−6.04834	+	55.7282i	−0.211475	+	1.94849i
$819$	52.7385	+	58.7784i	1.84283	+	2.05388i
$820$	11.4656	+	2.51846i	0.400397	+	0.0879485i
$821$	−42.2696	+	36.6268i	−1.47522	+	1.27829i	−0.594994	+	0.803730i	$0.702846\pi$
$821$	−42.2696	+	36.6268i	−1.47522	+	1.27829i	−0.880226	+	0.474555i	$0.842609\pi$
$822$	−0.0956137	+	3.40604i	−0.00333491	+	0.118799i
$823$	5.16243	+	17.5816i	0.179951	+	0.612857i	0.999222	+	0.0394497i	$0.0125605\pi$
$823$	5.16243	+	17.5816i	0.179951	+	0.612857i	−0.819271	+	0.573407i	$0.805621\pi$
$824$	5.40361	−	29.4394i	0.188244	−	1.02557i
$825$	−3.78551	−	9.88741i	−0.131794	−	0.344236i
$826$	50.3166	+	20.9014i	1.75074	+	0.727252i
$827$	39.7203			1.38121			0.690604	−	0.723233i	$-0.257345\pi$
$827$	39.7203			1.38121			0.690604	+	0.723233i	$0.257345\pi$
$828$	−9.56287	−	27.1395i	−0.332333	−	0.943162i
$829$	40.0150			1.38978			0.694890	−	0.719116i	$-0.255453\pi$
$829$	40.0150			1.38978			0.694890	+	0.719116i	$0.255453\pi$
$830$	10.4007	+	4.32041i	0.361013	+	0.149964i
$831$	−5.04966	−	13.1893i	−0.175171	−	0.457531i
$832$	3.40949	+	52.1066i	0.118203	+	1.80647i
$833$	10.8439	+	36.9309i	0.375718	+	1.27958i
$834$	−0.809763	+	28.8461i	−0.0280398	+	0.998859i
$835$	3.74175	−	3.24225i	0.129489	−	0.112203i
$836$	3.22069	−	14.6626i	0.111390	−	0.507118i
$837$	−11.0038	−	3.78215i	−0.380347	−	0.130730i
$838$	−5.65015	+	52.0593i	−0.195181	+	1.79836i
$839$	1.46064	+	0.938698i	0.0504270	+	0.0324074i	0.565611	−	0.824672i	$-0.308640\pi$
$839$	1.46064	+	0.938698i	0.0504270	+	0.0324074i	−0.515184	+	0.857079i	$0.672277\pi$
$840$	−6.58482	−	35.3597i	−0.227198	−	1.22002i
$841$	−16.0972	+	18.5771i	−0.555075	+	0.640591i
$842$	0.851688	−	0.282514i	0.0293511	−	0.00973606i
$843$	−13.1334	+	10.0098i	−0.452337	+	0.344757i
$844$	−9.60747	−	25.9184i	−0.330703	−	0.892148i
$845$	−49.0261	+	22.3895i	−1.68655	+	0.770222i
$846$	3.83701	+	10.9311i	0.131919	+	0.375821i
$847$	−7.88258	−	3.59985i	−0.270849	−	0.123692i
$848$	19.9342	+	23.1940i	0.684544	+	0.796486i
$849$	−16.8731	−	9.02494i	−0.579084	−	0.309735i
$850$	−5.64089	−	8.14197i	−0.193481	−	0.279267i
$851$	4.17949	+	38.0844i	0.143271	+	1.30552i
$852$	−3.47194	−	23.0621i	−0.118947	−	0.790095i
$853$	18.8976	−	12.1448i	0.647042	−	0.415829i	−0.175542	−	0.984472i	$-0.556168\pi$
$853$	18.8976	−	12.1448i	0.647042	−	0.415829i	0.822584	+	0.568643i	$0.192531\pi$
$854$	35.0161	−	17.4836i	1.19823	−	0.598276i
$855$	6.27571	+	9.40364i	0.214625	+	0.321598i
$856$	−18.3048	−	31.0652i	−0.625645	−	1.06179i
$857$	−25.3751	+	11.5884i	−0.866796	+	0.395852i	−0.798630	−	0.601822i	$-0.794442\pi$
$857$	−25.3751	+	11.5884i	−0.866796	+	0.395852i	−0.0681652	+	0.997674i	$0.521714\pi$
$858$	−56.0641	+	14.7664i	−1.91400	+	0.504116i
$859$	33.5707	−	4.82673i	1.14542	−	0.164686i	0.456634	−	0.889654i	$-0.349055\pi$
$859$	33.5707	−	4.82673i	1.14542	−	0.164686i	0.688782	+	0.724968i	$0.258146\pi$
$860$	14.8932	−	19.8115i	0.507855	−	0.675566i
$861$	4.59661	−	22.0462i	0.156652	−	0.751333i
$862$	35.0702	−	1.21707i	1.19450	−	0.0414536i
$863$	−2.84623	−	1.82916i	−0.0968868	−	0.0622654i	0.491300	−	0.870990i	$-0.336522\pi$
$863$	−2.84623	−	1.82916i	−0.0968868	−	0.0622654i	−0.588187	+	0.808725i	$0.700158\pi$
$864$	−18.9177	−	22.4971i	−0.643594	−	0.765367i
$865$	38.2779	+	11.2394i	1.30149	+	0.382151i
$866$	11.0511	+	11.8937i	0.375530	+	0.404166i
$867$	−0.428765	−	0.155712i	−0.0145616	−	0.00528826i
$868$	−18.0178	+	1.25208i	−0.611565	+	0.0424985i
$869$	−5.05225	−	17.2064i	−0.171386	−	0.583686i
$870$	5.93752	+	7.25395i	0.201301	+	0.245932i
$871$	−72.9059	−	10.4823i	−2.47032	−	0.355179i
$872$	19.7606	+	18.5098i	0.669177	+	0.626822i
$873$	0.944941	−	1.52781i	0.0319814	−	0.0517085i
$874$	12.7777	+	5.81692i	0.432212	+	0.196760i
$875$	49.0854			1.65939
$876$	−23.2714	−	26.4998i	−0.786267	−	0.895345i
$877$	−5.99845	+	41.7201i	−0.202553	+	1.40879i	0.594119	+	0.804377i	$0.297501\pi$
$877$	−5.99845	+	41.7201i	−0.202553	+	1.40879i	−0.796673	+	0.604411i	$0.793408\pi$
$878$	8.00112	−	1.43522i	0.270025	−	0.0484363i
$879$	−8.22378	−	8.08280i	−0.277381	−	0.272626i
$880$	25.3059	+	7.54165i	0.853060	+	0.254229i
$881$	−22.3244	+	19.3442i	−0.752128	+	0.651722i	−0.944093	−	0.329679i	$-0.893059\pi$
$881$	−22.3244	+	19.3442i	−0.752128	+	0.651722i	0.191965	+	0.981402i	$0.438514\pi$
$882$	−38.5594	+	7.60707i	−1.29836	+	0.256143i
$883$	−6.80241	+	23.1669i	−0.228919	+	0.779628i	0.762280	+	0.647248i	$0.224080\pi$
$883$	−6.80241	+	23.1669i	−0.228919	+	0.779628i	−0.991199	+	0.132380i	$0.957738\pi$
$884$	−47.6581	+	25.8985i	−1.60292	+	0.871060i
$885$	1.88916	−	30.0644i	0.0635033	−	1.01061i
$886$	6.57711	−	0.228251i	0.220962	−	0.00766824i
$887$	0.939565	−	1.08432i	0.0315475	−	0.0364078i	−0.739757	−	0.672875i	$-0.765059\pi$
$887$	0.939565	−	1.08432i	0.0315475	−	0.0364078i	0.771304	+	0.636467i	$0.219605\pi$
$888$	17.7147	+	34.8985i	0.594466	+	1.17112i
$889$	0.229564	+	1.59665i	0.00769932	+	0.0535500i
$890$	12.4425	+	3.18915i	0.417074	+	0.106901i
$891$	20.5059	−	25.3882i	0.686974	−	0.850535i
$892$	43.3237	+	3.18655i	1.45058	+	0.106693i
$893$	−5.14159	−	2.34808i	−0.172057	−	0.0785756i
$894$	20.0286	−	29.3221i	0.669858	−	0.980679i
$895$	−8.42940	−	13.1164i	−0.281764	−	0.438433i
$896$	−40.6547	−	20.7110i	−1.35818	−	0.691908i
$897$	−2.52307	−	54.1607i	−0.0842427	−	1.80837i
$898$	−0.461578	−	0.666234i	−0.0154030	−	0.0222325i
$899$	3.96000	−	2.54493i	0.132073	−	0.0848783i
$900$	8.80200	−	4.98223i	0.293400	−	0.166074i
$901$	−13.1968	+	28.8970i	−0.439649	+	0.962697i
$902$	12.8631	+	10.3872i	0.428294	+	0.345855i
$903$	−38.3094	−	28.1646i	−1.27486	−	0.937259i
$904$	−1.48300	−	1.03634i	−0.0493239	−	0.0344682i
$905$	26.0599	−	3.74685i	0.866262	−	0.124550i
$906$	1.51667	+	1.39060i	0.0503879	+	0.0461996i
$907$	−41.8506	−	36.2637i	−1.38962	−	1.20412i	−0.952433	−	0.304749i	$-0.901428\pi$
$907$	−41.8506	−	36.2637i	−1.38962	−	1.20412i	−0.437192	−	0.899368i	$-0.644027\pi$
$908$	−3.09081	+	2.30403i	−0.102572	+	0.0764618i
$909$	8.85402	+	18.5327i	0.293669	+	0.614692i
$910$	7.31256	−	67.3765i	0.242409	−	2.23351i
$911$	−40.4385	−	11.8738i	−1.33979	−	0.393398i	−0.468195	−	0.883625i	$-0.655095\pi$
$911$	−40.4385	−	11.8738i	−1.33979	−	0.393398i	−0.871594	+	0.490228i	$0.836914\pi$
$912$	14.3094	+	0.957214i	0.473832	+	0.0316965i
$913$	10.3875	+	11.9878i	0.343775	+	0.396737i
$914$	−26.9268	−	16.0132i	−0.890658	−	0.529669i
$915$	−15.4326	−	15.1681i	−0.510187	−	0.501441i
$916$	19.8879	+	19.9684i	0.657114	+	0.659774i
$917$	15.2618	+	2.19432i	0.503989	+	0.0724627i
$918$	12.9821	−	27.6349i	0.428472	−	0.912088i
$919$			1.78406i			0.0588506i	0.999567	+	0.0294253i	$0.00936772\pi$
$919$			1.78406i			0.0588506i	−0.999567	+	0.0294253i	$0.990632\pi$
$920$	−11.8528	+	21.6643i	−0.390775	+	0.714250i
$921$	14.2412	+	25.5531i	0.469264	+	0.842004i
$922$	−28.0487	−	11.6513i	−0.923734	−	0.383717i
$923$	6.25397	−	43.4973i	0.205852	−	1.43173i
$924$	13.9495	−	48.6989i	0.458905	−	1.60208i
$925$	−12.9213	+	3.79404i	−0.424850	+	0.124747i
$926$	−29.2171	+	49.1297i	−0.960135	+	1.61450i
$927$	5.06069	+	31.3409i	0.166215	+	1.02937i
$928$	11.8858	−	0.364413i	0.390172	−	0.0119624i
$929$	0.0222026	−	0.0756151i	0.000728444	−	0.00248085i	−0.959128	−	0.282973i	$-0.908679\pi$
$929$	0.0222026	−	0.0756151i	0.000728444	−	0.00248085i	0.959856	+	0.280492i	$0.0904976\pi$
$930$	3.89171	+	9.19617i	0.127614	+	0.301554i
$931$	10.3673	−	16.1318i	0.339774	−	0.528699i
$932$	16.6240	+	22.3008i	0.544537	+	0.730488i
$933$	−6.56912	+	31.5067i	−0.215063	+	1.03148i
$934$	2.90135	−	0.962407i	0.0949350	−	0.0314909i
$935$	3.90347	+	27.1493i	0.127657	+	0.887875i
$936$	−21.9227	−	50.8622i	−0.716566	−	1.66248i
$937$	16.7489	+	36.6749i	0.547161	+	1.19812i	0.958095	+	0.286451i	$0.0924755\pi$
$937$	16.7489	+	36.6749i	0.547161	+	1.19812i	−0.410934	+	0.911665i	$0.634797\pi$
$938$	40.4330	−	50.0707i	1.32018	−	1.63487i
$939$	3.19671	+	39.8509i	0.104321	+	1.30048i
$940$	4.78245	−	8.71649i	0.155986	−	0.284301i
$941$	−7.21722	−	11.2302i	−0.235275	−	0.366094i	0.703460	−	0.710735i	$-0.251637\pi$
$941$	−7.21722	−	11.2302i	−0.235275	−	0.366094i	−0.938735	+	0.344640i	$0.888001\pi$
$942$	3.68524	−	7.50478i	0.120072	−	0.244519i
$943$	−12.0180	+	9.72851i	−0.391360	+	0.316804i
$944$	−28.7782	−	25.1408i	−0.936652	−	0.818262i
$945$	19.1452	+	32.9975i	0.622794	+	1.07341i
$946$	31.2313	−	15.5938i	1.01542	−	0.507000i
$947$	21.7296	−	47.5811i	0.706116	−	1.54618i	−0.126279	−	0.991995i	$-0.540303\pi$
$947$	21.7296	−	47.5811i	0.706116	−	1.54618i	0.832395	−	0.554183i	$-0.186969\pi$
$948$	15.5359	−	7.21977i	0.504582	−	0.234487i
$949$	−27.6056	−	60.4478i	−0.896115	−	1.96222i
$950$	−1.22523	+	4.78026i	−0.0397518	+	0.155092i
$951$	37.9238	−	28.9044i	1.22976	−	0.937289i
$952$	1.83509	−	47.3578i	0.0594755	−	1.53488i
$953$	29.1833	+	25.2874i	0.945338	+	0.819140i	0.983644	−	0.180126i	$-0.0576505\pi$
$953$	29.1833	+	25.2874i	0.945338	+	0.819140i	−0.0383052	+	0.999266i	$0.512196\pi$
$954$	−28.1633	−	16.0960i	−0.911821	−	0.521127i
$955$	0.641649	−	0.998426i	0.0207633	−	0.0323083i
$956$	−20.6347	−	37.9719i	−0.667375	−	1.22810i
$957$	2.91786	+	12.8762i	0.0943211	+	0.416229i
$958$	−8.41910	−	9.06108i	−0.272009	−	0.292750i
$959$	−3.67370	−	4.23967i	−0.118630	−	0.136906i
$960$	−3.52545	+	24.9783i	−0.113783	+	0.806171i
$961$	−24.9330	+	7.32099i	−0.804291	+	0.236161i
$962$	13.0202	+	72.5858i	0.419789	+	2.34026i
$963$	29.3318	+	24.5412i	0.945204	+	0.790829i
$964$	−0.0823874	−	0.382446i	−0.00265352	−	0.0123178i
$965$		−	32.8411i		−	1.05719i
$966$	41.8015	+	22.2941i	1.34494	+	0.717302i
$967$		−	20.2575i		−	0.651438i	−0.945467	−	0.325719i	$-0.894394\pi$
$967$		−	20.2575i		−	0.651438i	0.945467	−	0.325719i	$-0.105606\pi$
$968$	4.43565	+	4.15490i	0.142567	+	0.133543i
$969$	5.32639	+	13.9121i	0.171108	+	0.446920i
$970$	−1.51747	+	0.272199i	−0.0487229	+	0.00873978i
$971$	−32.5130	+	9.54669i	−1.04339	+	0.306368i	−0.758145	−	0.652086i	$-0.773894\pi$
$971$	−32.5130	+	9.54669i	−1.04339	+	0.306368i	−0.285248	+	0.958454i	$0.592076\pi$
$972$	26.8998	+	15.7607i	0.862811	+	0.505526i
$973$	−31.1130	−	35.9063i	−0.997436	−	1.15110i
$974$	26.5064	−	24.6284i	0.849321	−	0.789146i
$975$	18.5866	−	4.21188i	0.595247	−	0.134888i
$976$	−27.1858	+	3.79669i	−0.870196	+	0.121529i
$977$	−8.20424	+	12.7660i	−0.262477	+	0.408422i	−0.947330	−	0.320259i	$-0.896230\pi$
$977$	−8.20424	+	12.7660i	−0.262477	+	0.408422i	0.684853	+	0.728681i	$0.259866\pi$
$978$	4.34955	+	7.20484i	0.139083	+	0.230385i
$979$	13.6721	+	11.8469i	0.436962	+	0.378630i
$980$	26.9610	+	20.2679i	0.861238	+	0.647433i
$981$	−26.3253	−	11.4765i	−0.840502	−	0.366416i
$982$	−27.8126	−	7.12868i	−0.887537	−	0.227485i
$983$	24.5104	+	53.6704i	0.781761	+	1.71182i	0.698857	+	0.715261i	$0.253692\pi$
$983$	24.5104	+	53.6704i	0.781761	+	1.71182i	0.0829044	+	0.996558i	$0.473580\pi$
$984$	−7.98312	+	13.6287i	−0.254493	+	0.434466i
$985$	12.5194	−	27.4137i	0.398902	−	0.873474i
$986$	5.51780	+	11.0510i	0.175723	+	0.351937i
$987$	−16.8188	−	8.99590i	−0.535349	−	0.286343i
$988$	25.3000	+	9.49466i	0.804899	+	0.302065i
$989$	8.14332	+	31.6140i	0.258943	+	1.00527i
$990$	−27.9697	+	1.45520i	−0.888935	+	0.0462492i
$991$	29.3679	+	45.6974i	0.932903	+	1.45163i	0.891779	+	0.452471i	$0.149458\pi$
$991$	29.3679	+	45.6974i	0.932903	+	1.45163i	0.0411241	+	0.999154i	$0.486906\pi$
$992$	12.2578	+	3.19465i	0.389187	+	0.101430i
$993$	−27.5473	+	2.20976i	−0.874188	+	0.0701245i
$994$	29.8733	+	24.1233i	0.947524	+	0.765143i
$995$	−4.67840	−	10.2443i	−0.148315	−	0.324765i
$996$	−9.84723	+	11.5176i	−0.312021	+	0.364950i
$997$	−1.81199	−	12.6027i	−0.0573864	−	0.399131i	−0.998188	−	0.0601732i	$-0.980835\pi$
$997$	−1.81199	−	12.6027i	−0.0573864	−	0.399131i	0.940802	−	0.338958i	$-0.110074\pi$
$998$	−13.6212	−	41.0634i	−0.431170	−	1.29984i
$999$	−30.1042	−	28.5817i	−0.952454	−	0.904286i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	276.2.o.a.35.17	yes	440
3.2	odd	2	inner	276.2.o.a.35.28	yes	440
4.3	odd	2	inner	276.2.o.a.35.43	yes	440
12.11	even	2	inner	276.2.o.a.35.2	✓	440
23.2	even	11	inner	276.2.o.a.71.2	yes	440
69.2	odd	22	inner	276.2.o.a.71.43	yes	440
92.71	odd	22	inner	276.2.o.a.71.28	yes	440
276.71	even	22	inner	276.2.o.a.71.17	yes	440

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
276.2.o.a.35.2	✓	440	12.11	even	2	inner
276.2.o.a.35.17	yes	440	1.1	even	1	trivial
276.2.o.a.35.28	yes	440	3.2	odd	2	inner
276.2.o.a.35.43	yes	440	4.3	odd	2	inner
276.2.o.a.71.2	yes	440	23.2	even	11	inner
276.2.o.a.71.17	yes	440	276.71	even	22	inner
276.2.o.a.71.28	yes	440	92.71	odd	22	inner
276.2.o.a.71.43	yes	440	69.2	odd	22	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:	\( N \)	\(=\)	\( 276 = 2^{2} \cdot 3 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	276.o (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.542515 + 1.30602i) q^{2} +(-0.619297 - 1.61755i) q^{3} +(-1.41135 - 1.41707i) q^{4} +(-0.512900 - 1.74678i) q^{5} +(2.44853 + 0.0687346i) q^{6} +(-3.04781 + 2.64094i) q^{7} +(2.61639 - 1.07447i) q^{8} +(-2.23294 + 2.00349i) q^{9} +O(q^{10})\)	\(q+(-0.542515 + 1.30602i) q^{2} +(-0.619297 - 1.61755i) q^{3} +(-1.41135 - 1.41707i) q^{4} +(-0.512900 - 1.74678i) q^{5} +(2.44853 + 0.0687346i) q^{6} +(-3.04781 + 2.64094i) q^{7} +(2.61639 - 1.07447i) q^{8} +(-2.23294 + 2.00349i) q^{9} +(2.55957 + 0.277798i) q^{10} +(3.05049 + 1.96043i) q^{11} +(-1.41813 + 3.16052i) q^{12} +(-4.27444 + 4.93297i) q^{13} +(-1.79563 - 5.41324i) q^{14} +(-2.50786 + 1.91142i) q^{15} +(-0.0161603 + 3.99997i) q^{16} +(-3.77945 + 1.72602i) q^{17} +(-1.40518 - 4.00318i) q^{18} +(1.88294 + 0.859910i) q^{19} +(-1.75142 + 3.19213i) q^{20} +(6.15936 + 3.29446i) q^{21} +(-4.21529 + 2.92042i) q^{22} +(-1.84505 - 4.42671i) q^{23} +(-3.35833 - 3.56673i) q^{24} +(1.41811 - 0.911362i) q^{25} +(-4.12359 - 8.25871i) q^{26} +(4.62360 + 2.37114i) q^{27} +(8.04393 + 0.591648i) q^{28} +(-1.91216 + 0.873255i) q^{29} +(-1.13578 - 4.31228i) q^{30} +(-2.21649 + 0.318683i) q^{31} +(-5.21525 - 2.19115i) q^{32} +(1.28194 - 6.14841i) q^{33} +(-0.203795 - 5.87241i) q^{34} +(6.17635 + 3.96930i) q^{35} +(5.99055 + 0.336597i) q^{36} +(-7.66522 - 2.25071i) q^{37} +(-2.14458 + 1.99264i) q^{38} +(10.6265 + 3.85916i) q^{39} +(-3.21881 - 4.01916i) q^{40} +(-0.908324 - 3.09347i) q^{41} +(-7.64416 + 6.25692i) q^{42} +(-6.73787 - 0.968760i) q^{43} +(-1.52726 - 7.08961i) q^{44} +(4.64492 + 2.87286i) q^{45} +(6.78233 - 0.00810976i) q^{46} -2.73062 q^{47} +(6.48016 - 2.45103i) q^{48} +(1.31836 - 9.16942i) q^{49} +(0.420908 + 2.34650i) q^{50} +(5.13252 + 5.04453i) q^{51} +(13.0231 - 0.904993i) q^{52} +(5.77832 - 5.00694i) q^{53} +(-5.60512 + 4.75211i) q^{54} +(1.85984 - 6.33403i) q^{55} +(-5.13666 + 10.1845i) q^{56} +(0.224849 - 3.57829i) q^{57} +(-0.103107 - 2.97107i) q^{58} +(-6.25607 + 7.21989i) q^{59} +(6.24809 + 0.856127i) q^{60} +(0.976622 + 6.79256i) q^{61} +(0.786275 - 3.06766i) q^{62} +(1.51448 - 12.0033i) q^{63} +(5.69103 - 5.62247i) q^{64} +(10.8092 + 4.93638i) q^{65} +(7.33445 + 5.00984i) q^{66} +(6.10076 + 9.49297i) q^{67} +(7.78002 + 2.91971i) q^{68} +(-6.01779 + 5.72592i) q^{69} +(-8.53474 + 5.91301i) q^{70} +(-5.66372 + 3.63985i) q^{71} +(-3.68957 + 7.64114i) q^{72} +(-4.22928 + 9.26083i) q^{73} +(7.09797 - 8.78985i) q^{74} +(-2.35240 - 1.72946i) q^{75} +(-1.43895 - 3.88189i) q^{76} +(-14.4747 + 2.08115i) q^{77} +(-10.8052 + 11.7847i) q^{78} +(-3.73751 - 3.23857i) q^{79} +(6.99534 - 2.02335i) q^{80} +(0.972060 - 8.94735i) q^{81} +(4.53290 + 0.491969i) q^{82} +(4.19720 + 1.23241i) q^{83} +(-4.02456 - 13.3779i) q^{84} +(4.95344 + 5.71658i) q^{85} +(4.92062 - 8.27420i) q^{86} +(2.59673 + 2.55221i) q^{87} +(10.0877 + 1.85160i) q^{88} +(4.93823 + 0.710010i) q^{89} +(-6.27194 + 4.50777i) q^{90} -26.3233i q^{91} +(-3.66892 + 8.86222i) q^{92} +(1.88815 + 3.38793i) q^{93} +(1.48140 - 3.56623i) q^{94} +(0.536311 - 3.73012i) q^{95} +(-0.314505 + 9.79291i) q^{96} +(-0.574550 + 0.168703i) q^{97} +(11.2602 + 6.69636i) q^{98} +(-10.7393 + 1.73410i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9}+O(q^{10}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9	\( 440 q - 22 q^{4} - 8 q^{6} - 18 q^{9} - 30 q^{10} - 18 q^{12} - 36 q^{13} - 30 q^{16} - 10 q^{18} - 22 q^{21} - 48 q^{22} - 14 q^{24} - 8 q^{25} - 34 q^{28} - 21 q^{30} - 6 q^{33} - 32 q^{34} + 22 q^{36} - 36 q^{37} - 168 q^{40} + q^{42} - 44 q^{45} - 110 q^{46} - 6 q^{48} - 16 q^{49} - 94 q^{52} + 21 q^{54} - 46 q^{57} - 116 q^{58} - 47 q^{60} - 68 q^{61} - 28 q^{64} - 20 q^{66} - 22 q^{69} - 44 q^{70} - 23 q^{72} - 36 q^{73} - 74 q^{76} + 134 q^{78} - 130 q^{81} + 36 q^{82} + 105 q^{84} - 60 q^{85} + 38 q^{88} + 162 q^{90} - 332 q^{93} - 40 q^{94} + 225 q^{96} - 36 q^{97}+O(q^{100}) \) 440 * q - 22 * q^4 - 8 * q^6 - 18 * q^9 - 30 * q^10 - 18 * q^12 - 36 * q^13 - 30 * q^16 - 10 * q^18 - 22 * q^21 - 48 * q^22 - 14 * q^24 - 8 * q^25 - 34 * q^28 - 21 * q^30 - 6 * q^33 - 32 * q^34 + 22 * q^36 - 36 * q^37 - 168 * q^40 + q^42 - 44 * q^45 - 110 * q^46 - 6 * q^48 - 16 * q^49 - 94 * q^52 + 21 * q^54 - 46 * q^57 - 116 * q^58 - 47 * q^60 - 68 * q^61 - 28 * q^64 - 20 * q^66 - 22 * q^69 - 44 * q^70 - 23 * q^72 - 36 * q^73 - 74 * q^76 + 134 * q^78 - 130 * q^81 + 36 * q^82 + 105 * q^84 - 60 * q^85 + 38 * q^88 + 162 * q^90 - 332 * q^93 - 40 * q^94 + 225 * q^96 - 36 * q^97

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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