LMFDB - Embedded newform 990.2.bg.a.31.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [990,2,Mod(31,990)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(990, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([10, 0, 18])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("990.31"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	990.bg (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [88,11,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$7.90518980011$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$11$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			31.9
Character	$\chi$	$=$	990.31
Dual form			990.2.bg.a.511.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.978148 + 0.207912i) q^{2} +(1.22140 + 1.22809i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(-1.45004 - 0.947306i) q^{6} +(0.0524430 - 0.498962i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.0163876 + 2.99996i) q^{9} +1.00000 q^{10} +(3.13579 - 1.08020i) q^{11} +(1.61531 + 0.625126i) q^{12} +(2.95426 + 3.28104i) q^{13} +(0.0524430 + 0.498962i) q^{14} +(-0.939371 - 1.45519i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-0.791452 - 2.43584i) q^{17} +(-0.607696 - 2.93781i) q^{18} +(-0.146517 + 0.106451i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(0.676821 - 0.545025i) q^{21} +(-2.84268 + 1.70856i) q^{22} +(-0.385331 + 0.667413i) q^{23} +(-1.70998 - 0.275624i) q^{24} +(0.913545 + 0.406737i) q^{25} +(-3.57187 - 2.59512i) q^{26} +(-3.70422 + 3.64401i) q^{27} +(-0.155037 - 0.477155i) q^{28} +(0.300739 - 2.86134i) q^{29} +(1.22140 + 1.22809i) q^{30} +(6.44466 + 7.15752i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.15661 + 2.53167i) q^{33} +(1.28060 + 2.21806i) q^{34} +(-0.155037 + 0.477155i) q^{35} +(1.20522 + 2.74726i) q^{36} +(-0.841887 - 0.611667i) q^{37} +(0.121183 - 0.134587i) q^{38} +(-0.421077 + 7.63554i) q^{39} +(0.913545 - 0.406737i) q^{40} +(0.0614830 + 0.584972i) q^{41} +(-0.548714 + 0.673834i) q^{42} +(3.57269 + 6.18808i) q^{43} +(2.42533 - 2.26225i) q^{44} +(0.639755 - 2.93099i) q^{45} +(0.238148 - 0.732943i) q^{46} +(1.01514 + 0.451972i) q^{47} +(1.72992 - 0.0859240i) q^{48} +(6.60082 + 1.40305i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(2.02474 - 3.94709i) q^{51} +(4.03338 + 1.79577i) q^{52} +(-2.91276 + 8.96457i) q^{53} +(2.86564 - 4.33453i) q^{54} +(-3.29185 + 0.404623i) q^{55} +(0.250855 + 0.434494i) q^{56} +(-0.309685 - 0.0499167i) q^{57} +(0.300739 + 2.86134i) q^{58} +(-2.41143 + 1.07364i) q^{59} +(-1.45004 - 0.947306i) q^{60} +(2.69730 - 2.99566i) q^{61} +(-7.79196 - 5.66119i) q^{62} +(1.49600 + 0.165503i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-2.20754 - 3.82357i) q^{65} +(-5.57029 - 1.40423i) q^{66} +(-2.85511 + 4.94520i) q^{67} +(-1.71377 - 1.90334i) q^{68} +(-1.29028 + 0.341956i) q^{69} +(0.0524430 - 0.498962i) q^{70} +(-1.08364 - 3.33511i) q^{71} +(-1.75007 - 2.43665i) q^{72} +(-2.39794 - 1.74220i) q^{73} +(0.950662 + 0.423262i) q^{74} +(0.616293 + 1.61870i) q^{75} +(-0.0905523 + 0.156841i) q^{76} +(-0.374526 - 1.62129i) q^{77} +(-1.17564 - 7.55623i) q^{78} +(1.16554 - 0.247744i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-8.99946 - 0.0983241i) q^{81} +(-0.181762 - 0.559405i) q^{82} +(-2.25862 + 2.50845i) q^{83} +(0.396625 - 0.773193i) q^{84} +(0.267718 + 2.54716i) q^{85} +(-4.78119 - 5.31005i) q^{86} +(3.88129 - 3.12550i) q^{87} +(-1.90198 + 2.71707i) q^{88} -2.22432 q^{89} +(-0.0163876 + 2.99996i) q^{90} +(1.79205 - 1.30200i) q^{91} +(-0.0805561 + 0.766441i) q^{92} +(-0.918569 + 16.6567i) q^{93} +(-1.08693 - 0.231034i) q^{94} +(0.165447 - 0.0736618i) q^{95} +(-1.67425 + 0.443717i) q^{96} +(5.80640 - 1.23419i) q^{97} -6.74829 q^{98} +(3.18915 + 9.42493i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) $ 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/990\mathbb{Z}\right)^\times$.

$n$	$397$	$541$	$551$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$2$	−0.978148	+	0.207912i	−0.691655	+	0.147016i
$3$	1.22140	+	1.22809i	0.705173	+	0.709035i
$3$	1.22140	+	1.22809i	0.705173	+	0.709035i
$4$	0.913545	−	0.406737i	0.456773	−	0.203368i
$5$	−0.978148	−	0.207912i	−0.437441	−	0.0929809i
$5$	−0.978148	−	0.207912i	−0.437441	−	0.0929809i
$6$	−1.45004	−	0.947306i	−0.591976	−	0.386736i
$7$	0.0524430	−	0.498962i	0.0198216	−	0.188590i	−0.980131	−	0.198352i	$-0.936441\pi$
$7$	0.0524430	−	0.498962i	0.0198216	−	0.188590i	0.999952	+	0.00976262i	$0.00310759\pi$
$8$	−0.809017	+	0.587785i	−0.286031	+	0.207813i
$9$	−0.0163876	+	2.99996i	−0.00546253	+	0.999985i
$10$	1.00000			0.316228
$11$	3.13579	−	1.08020i	0.945476	−	0.325691i
$11$	3.13579	−	1.08020i	0.945476	−	0.325691i
$12$	1.61531	+	0.625126i	0.466299	+	0.180458i
$13$	2.95426	+	3.28104i	0.819365	+	0.909998i	0.997254	−	0.0740530i	$-0.0235934\pi$
$13$	2.95426	+	3.28104i	0.819365	+	0.909998i	−0.177889	+	0.984051i	$0.556927\pi$
$14$	0.0524430	+	0.498962i	0.0140160	+	0.133353i
$15$	−0.939371	−	1.45519i	−0.242545	−	0.375729i
$16$	0.669131	−	0.743145i	0.167283	−	0.185786i
$17$	−0.791452	−	2.43584i	−0.191955	−	0.590778i	−0.999999	−	0.00165479i	$-0.999473\pi$
$17$	−0.791452	−	2.43584i	−0.191955	−	0.590778i	0.808043	−	0.589123i	$-0.200527\pi$
$18$	−0.607696	−	2.93781i	−0.143235	−	0.692448i
$19$	−0.146517	+	0.106451i	−0.0336132	+	0.0244214i	−0.604465	−	0.796632i	$-0.706613\pi$
$19$	−0.146517	+	0.106451i	−0.0336132	+	0.0244214i	0.570852	+	0.821053i	$0.306613\pi$
$20$	−0.978148	+	0.207912i	−0.218720	+	0.0464905i
$21$	0.676821	−	0.545025i	0.147695	−	0.118934i
$22$	−2.84268	+	1.70856i	−0.606061	+	0.364266i
$23$	−0.385331	+	0.667413i	−0.0803471	+	0.139165i	−0.903399	−	0.428801i	$-0.858936\pi$
$23$	−0.385331	+	0.667413i	−0.0803471	+	0.139165i	0.823052	+	0.567966i	$0.192270\pi$
$24$	−1.70998	−	0.275624i	−0.349048	−	0.0562615i
$25$	0.913545	+	0.406737i	0.182709	+	0.0813473i
$26$	−3.57187	−	2.59512i	−0.700502	−	0.508945i
$27$	−3.70422	+	3.64401i	−0.712877	+	0.701289i
$28$	−0.155037	−	0.477155i	−0.0292992	−	0.0901738i
$29$	0.300739	−	2.86134i	0.0558459	−	0.531338i	−0.930458	−	0.366399i	$-0.880591\pi$
$29$	0.300739	−	2.86134i	0.0558459	−	0.531338i	0.986304	−	0.164939i	$-0.0527427\pi$
$30$	1.22140	+	1.22809i	0.222995	+	0.224217i
$31$	6.44466	+	7.15752i	1.15749	+	1.28553i	0.951733	+	0.306926i	$0.0993004\pi$
$31$	6.44466	+	7.15752i	1.15749	+	1.28553i	0.205761	+	0.978602i	$0.434033\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	5.15661	+	2.53167i	0.897651	+	0.440708i
$34$	1.28060	+	2.21806i	0.219621	+	0.380394i
$35$	−0.155037	+	0.477155i	−0.0262060	+	0.0806539i
$36$	1.20522	+	2.74726i	0.200870	+	0.457877i
$37$	−0.841887	−	0.611667i	−0.138405	−	0.100557i	0.516428	−	0.856330i	$-0.327261\pi$
$37$	−0.841887	−	0.611667i	−0.138405	−	0.100557i	−0.654834	+	0.755773i	$0.727261\pi$
$38$	0.121183	−	0.134587i	0.0196584	−	0.0218329i
$39$	−0.421077	+	7.63554i	−0.0674262	+	1.22266i
$40$	0.913545	−	0.406737i	0.144444	−	0.0643107i
$41$	0.0614830	+	0.584972i	0.00960203	+	0.0913572i	0.998273	−	0.0587395i	$-0.0187081\pi$
$41$	0.0614830	+	0.584972i	0.00960203	+	0.0913572i	−0.988671	+	0.150097i	$0.952041\pi$
$42$	−0.548714	+	0.673834i	−0.0846684	+	0.103975i
$43$	3.57269	+	6.18808i	0.544830	+	0.943674i	0.998618	+	0.0525635i	$0.0167392\pi$
$43$	3.57269	+	6.18808i	0.544830	+	0.943674i	−0.453787	+	0.891110i	$0.649927\pi$
$44$	2.42533	−	2.26225i	0.365632	−	0.341047i
$45$	0.639755	−	2.93099i	0.0953691	−	0.436926i
$46$	0.238148	−	0.732943i	0.0351130	−	0.108067i
$47$	1.01514	+	0.451972i	0.148074	+	0.0659268i	0.479436	−	0.877577i	$-0.340841\pi$
$47$	1.01514	+	0.451972i	0.148074	+	0.0659268i	−0.331362	+	0.943504i	$0.607508\pi$
$48$	1.72992	−	0.0859240i	0.249692	−	0.0124021i
$49$	6.60082	+	1.40305i	0.942974	+	0.200435i
$50$	−0.978148	−	0.207912i	−0.138331	−	0.0294032i
$51$	2.02474	−	3.94709i	0.283521	−	0.552704i
$52$	4.03338	+	1.79577i	0.559328	+	0.249029i
$53$	−2.91276	+	8.96457i	−0.400099	+	1.23138i	0.524820	+	0.851213i	$0.324133\pi$
$53$	−2.91276	+	8.96457i	−0.400099	+	1.23138i	−0.924919	+	0.380165i	$0.875867\pi$
$54$	2.86564	−	4.33453i	0.389964	−	0.589854i
$55$	−3.29185	+	0.404623i	−0.443873	+	0.0545594i
$56$	0.250855	+	0.434494i	0.0335219	+	0.0580617i
$57$	−0.309685	−	0.0499167i	−0.0410188	−	0.00661163i
$58$	0.300739	+	2.86134i	0.0394890	+	0.375713i
$59$	−2.41143	+	1.07364i	−0.313942	+	0.139776i	−0.557658	−	0.830071i	$-0.688300\pi$
$59$	−2.41143	+	1.07364i	−0.313942	+	0.139776i	0.243716	+	0.969847i	$0.421633\pi$
$60$	−1.45004	−	0.947306i	−0.187199	−	0.122297i
$61$	2.69730	−	2.99566i	0.345354	−	0.383555i	−0.545296	−	0.838243i	$-0.683583\pi$
$61$	2.69730	−	2.99566i	0.345354	−	0.383555i	0.890650	+	0.454689i	$0.150250\pi$
$62$	−7.79196	−	5.66119i	−0.989580	−	0.718972i
$63$	1.49600	+	0.165503i	0.188479	+	0.0208515i
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	−2.20754	−	3.82357i	−0.273812	−	0.474256i
$66$	−5.57029	−	1.40423i	−0.685655	−	0.172849i
$67$	−2.85511	+	4.94520i	−0.348808	+	0.604153i	−0.986038	−	0.166521i	$-0.946747\pi$
$67$	−2.85511	+	4.94520i	−0.348808	+	0.604153i	0.637230	+	0.770674i	$0.280080\pi$
$68$	−1.71377	−	1.90334i	−0.207826	−	0.230814i
$69$	−1.29028	+	0.341956i	−0.155332	+	0.0411666i
$70$	0.0524430	−	0.498962i	0.00626814	−	0.0596374i
$71$	−1.08364	−	3.33511i	−0.128605	−	0.395805i	0.865936	−	0.500155i	$-0.166724\pi$
$71$	−1.08364	−	3.33511i	−0.128605	−	0.395805i	−0.994541	+	0.104350i	$0.966724\pi$
$72$	−1.75007	−	2.43665i	−0.206248	−	0.287162i
$73$	−2.39794	−	1.74220i	−0.280657	−	0.203909i	0.438547	−	0.898708i	$-0.355493\pi$
$73$	−2.39794	−	1.74220i	−0.280657	−	0.203909i	−0.719204	+	0.694799i	$0.755493\pi$
$74$	0.950662	+	0.423262i	0.110512	+	0.0492032i
$75$	0.616293	+	1.61870i	0.0711633	+	0.186911i
$76$	−0.0905523	+	0.156841i	−0.0103871	+	0.0179909i
$77$	−0.374526	−	1.62129i	−0.0426812	−	0.184763i
$78$	−1.17564	−	7.55623i	−0.133115	−	0.855575i
$79$	1.16554	−	0.247744i	0.131134	−	0.0278734i	−0.141877	−	0.989884i	$-0.545314\pi$
$79$	1.16554	−	0.247744i	0.131134	−	0.0278734i	0.273011	+	0.962011i	$0.411980\pi$
$80$	−0.809017	+	0.587785i	−0.0904508	+	0.0657164i
$81$	−8.99946	−	0.0983241i	−0.999940	−	0.0109249i
$82$	−0.181762	−	0.559405i	−0.0200722	−	0.0617760i
$83$	−2.25862	+	2.50845i	−0.247916	+	0.275338i	−0.854240	−	0.519879i	$-0.825977\pi$
$83$	−2.25862	+	2.50845i	−0.247916	+	0.275338i	0.606324	+	0.795218i	$0.292644\pi$
$84$	0.396625	−	0.773193i	0.0432754	−	0.0843623i
$85$	0.267718	+	2.54716i	0.0290381	+	0.276279i
$86$	−4.78119	−	5.31005i	−0.515569	−	0.572598i
$87$	3.88129	−	3.12550i	0.416118	−	0.335088i
$88$	−1.90198	+	2.71707i	−0.202752	+	0.289640i
$89$	−2.22432			−0.235778			−0.117889	−	0.993027i	$-0.537613\pi$
$89$	−2.22432			−0.235778			−0.117889	+	0.993027i	$0.537613\pi$
$90$	−0.0163876	+	2.99996i	−0.00172740	+	0.316223i
$91$	1.79205	−	1.30200i	0.187857	−	0.136486i
$92$	−0.0805561	+	0.766441i	−0.00839856	+	0.0799069i
$93$	−0.918569	+	16.6567i	−0.0952512	+	1.72722i
$94$	−1.08693	−	0.231034i	−0.112108	−	0.0238294i
$95$	0.165447	−	0.0736618i	0.0169745	−	0.00755755i
$96$	−1.67425	+	0.443717i	−0.170878	+	0.0452866i
$97$	5.80640	−	1.23419i	0.589551	−	0.125313i	0.0965296	−	0.995330i	$-0.469226\pi$
$97$	5.80640	−	1.23419i	0.589551	−	0.125313i	0.493021	+	0.870017i	$0.335892\pi$
$98$	−6.74829			−0.681680
$99$	3.18915	+	9.42493i	0.320522	+	0.947241i
$100$	1.00000			0.100000
$101$	−4.37656	+	0.930266i	−0.435484	+	0.0925650i	−0.420437	−	0.907322i	$-0.638123\pi$
$101$	−4.37656	+	0.930266i	−0.435484	+	0.0925650i	−0.0150471	+	0.999887i	$0.504790\pi$
$102$	−1.15985	+	4.28181i	−0.114842	+	0.423962i
$103$	−12.1945	+	5.42934i	−1.20156	+	0.534968i	−0.907189	−	0.420723i	$-0.861776\pi$
$103$	−12.1945	+	5.42934i	−1.20156	+	0.534968i	−0.294370	+	0.955692i	$0.595110\pi$
$104$	−4.31860	−	0.917946i	−0.423473	−	0.0900121i
$105$	−0.775348	+	0.392396i	−0.0756663	+	0.0382939i
$106$	0.985275	−	9.37427i	0.0956984	−	0.910509i
$107$	13.0943	−	9.51357i	1.26587	−	0.919711i	0.266844	−	0.963740i	$-0.414019\pi$
$107$	13.0943	−	9.51357i	1.26587	−	0.919711i	0.999030	+	0.0440283i	$0.0140192\pi$
$108$	−1.90182	+	4.83561i	−0.183003	+	0.465306i
$109$	3.70074			0.354466			0.177233	−	0.984169i	$-0.443285\pi$
$109$	3.70074			0.354466			0.177233	+	0.984169i	$0.443285\pi$
$110$	3.13579	−	1.08020i	0.298986	−	0.102993i
$111$	−0.277098	−	1.78100i	−0.0263010	−	0.169045i
$112$	−0.335710	−	0.372843i	−0.0317216	−	0.0352304i
$113$	0.778772	+	7.40952i	0.0732607	+	0.697029i	0.968087	+	0.250615i	$0.0806327\pi$
$113$	0.778772	+	7.40952i	0.0732607	+	0.697029i	−0.894826	+	0.446415i	$0.852701\pi$
$114$	0.313296	−	0.0155612i	0.0293429	−	0.00145744i
$115$	0.515674	−	0.572714i	0.0480868	−	0.0534058i
$116$	−0.889074	−	2.73629i	−0.0825484	−	0.254058i
$117$	−9.89140	+	8.80889i	−0.914460	+	0.814382i
$118$	2.13551	−	1.55154i	0.196590	−	0.142831i
$119$	−1.25690	+	0.267162i	−0.115220	+	0.0244907i
$120$	1.61531	+	0.625126i	0.147457	+	0.0570659i
$121$	8.66636	−	6.77453i	0.787851	−	0.615866i
$122$	−2.01553	+	3.49099i	−0.182477	+	0.316060i
$123$	−0.643300	+	0.789988i	−0.0580044	+	0.0712308i
$124$	8.79871	+	3.91744i	0.790148	+	0.351796i
$125$	−0.809017	−	0.587785i	−0.0723607	−	0.0525731i
$126$	−1.49772	+	0.149150i	−0.133428	+	0.0132873i
$127$	−1.98451	−	6.10771i	−0.176097	−	0.541971i	0.823585	−	0.567193i	$-0.191971\pi$
$127$	−1.98451	−	6.10771i	−0.176097	−	0.541971i	−0.999682	+	0.0252219i	$0.991971\pi$
$128$	−0.104528	+	0.994522i	−0.00923910	+	0.0879041i
$129$	−3.23583	+	11.9457i	−0.284899	+	1.05176i
$130$	2.95426	+	3.28104i	0.259106	+	0.287766i
$131$	5.96537	−	10.3323i	0.521196	−	0.902739i	−0.478500	−	0.878088i	$-0.658819\pi$
$131$	5.96537	−	10.3323i	0.521196	−	0.902739i	0.999696	−	0.0246510i	$-0.00784746\pi$
$132$	5.74052	+	0.215415i	0.499648	+	0.0187495i
$133$	0.0454310	+	0.0786888i	0.00393937	+	0.00682318i
$134$	1.76456	−	5.43075i	0.152435	−	0.469145i
$135$	4.38090	−	2.79423i	0.377048	−	0.240489i
$136$	2.07205	+	1.50543i	0.177677	+	0.129090i
$137$	−13.9106	+	15.4493i	−1.18846	+	1.31992i	−0.252595	+	0.967572i	$0.581284\pi$
$137$	−13.9106	+	15.4493i	−1.18846	+	1.31992i	−0.935868	+	0.352350i	$0.885383\pi$
$138$	1.19099	−	0.602748i	0.101384	−	0.0513093i
$139$	15.3226	−	6.82206i	1.29965	−	0.578640i	0.363940	−	0.931422i	$-0.381431\pi$
$139$	15.3226	−	6.82206i	1.29965	−	0.578640i	0.935705	+	0.352783i	$0.114764\pi$
$140$	0.0524430	+	0.498962i	0.00443224	+	0.0421700i
$141$	0.684833	+	1.79872i	0.0576734	+	0.151480i
$142$	1.75337	+	3.03693i	0.147140	+	0.254854i
$143$	12.8081	+	7.09748i	1.07107	+	0.593521i
$144$	2.21844	+	2.01954i	0.184870	+	0.168295i
$145$	−0.889074	+	2.73629i	−0.0738336	+	0.227236i
$146$	2.70776	+	1.20557i	0.224096	+	0.0997738i
$147$	6.33915	+	9.82005i	0.522844	+	0.809944i
$148$	−1.01789	−	0.216359i	−0.0836700	−	0.0177846i
$149$	5.91064	+	1.25635i	0.484219	+	0.102924i	0.443551	−	0.896249i	$-0.353718\pi$
$149$	5.91064	+	1.25635i	0.484219	+	0.102924i	0.0406672	+	0.999173i	$0.487052\pi$
$150$	−0.939371	−	1.45519i	−0.0766994	−	0.118816i
$151$	−8.43212	−	3.75422i	−0.686196	−	0.305514i	0.0338633	−	0.999426i	$-0.489219\pi$
$151$	−8.43212	−	3.75422i	−0.686196	−	0.305514i	−0.720060	+	0.693912i	$0.755886\pi$
$152$	0.0559644	−	0.172241i	0.00453931	−	0.0139706i
$153$	7.32038	−	2.33440i	0.591818	−	0.188725i
$154$	0.703427	+	1.50799i	0.0566837	+	0.121517i
$155$	−4.81570	−	8.34103i	−0.386806	−	0.669968i
$156$	2.72098	+	7.14668i	0.217853	+	0.572192i
$157$	1.01435	+	9.65088i	0.0809538	+	0.770224i	0.957408	+	0.288739i	$0.0932359\pi$
$157$	1.01435	+	9.65088i	0.0809538	+	0.770224i	−0.876454	+	0.481485i	$0.840097\pi$
$158$	−1.08856	+	0.484660i	−0.0866016	+	0.0385575i
$159$	−14.5669	+	7.37216i	−1.15523	+	0.584650i
$160$	0.669131	−	0.743145i	0.0528994	−	0.0587508i
$161$	0.312806	+	0.227267i	0.0246526	+	0.0179111i
$162$	8.82325	−	1.77492i	0.693220	−	0.139451i
$163$	2.00556	−	6.17249i	0.157088	−	0.483467i	−0.841279	−	0.540602i	$-0.818197\pi$
$163$	2.00556	−	6.17249i	0.157088	−	0.483467i	0.998366	+	0.0571350i	$0.0181966\pi$
$164$	0.294097	+	0.509391i	0.0229651	+	0.0397767i
$165$	−4.51756	−	3.54847i	−0.351692	−	0.276248i
$166$	1.68773	−	2.92323i	0.130993	−	0.226887i
$167$	−13.2573	−	14.7237i	−1.02588	−	1.13935i	−0.990153	−	0.139991i	$-0.955293\pi$
$167$	−13.2573	−	14.7237i	−1.02588	−	1.13935i	−0.0357252	−	0.999362i	$-0.511374\pi$
$168$	−0.227202	+	0.838760i	−0.0175290	+	0.0647118i
$169$	−0.678695	+	6.45735i	−0.0522073	+	0.496719i
$170$	−0.791452	−	2.43584i	−0.0607016	−	0.186820i
$171$	−0.316946	−	0.441288i	−0.0242375	−	0.0337461i
$172$	5.78073	+	4.19995i	0.440777	+	0.320243i
$173$	−11.4492	−	5.09753i	−0.870469	−	0.387558i	−0.0776252	−	0.996983i	$-0.524734\pi$
$173$	−11.4492	−	5.09753i	−0.870469	−	0.387558i	−0.792844	+	0.609425i	$0.791400\pi$
$174$	−3.14665	+	3.86416i	−0.238547	+	0.292941i
$175$	0.250855	−	0.434494i	0.0189629	−	0.0328447i
$176$	1.29551	−	3.05314i	0.0976528	−	0.230139i
$177$	−4.26383	−	1.65011i	−0.320489	−	0.124030i
$178$	2.17571	−	0.462462i	0.163077	−	0.0346630i
$179$	14.6007	−	10.6080i	1.09131	−	0.792882i	0.111689	−	0.993743i	$-0.464374\pi$
$179$	14.6007	−	10.6080i	1.09131	−	0.792882i	0.979620	+	0.200861i	$0.0643739\pi$
$180$	−0.607696	−	2.93781i	−0.0452950	−	0.218971i
$181$	−6.56043	−	20.1909i	−0.487633	−	1.50078i	−0.828131	−	0.560535i	$-0.810596\pi$
$181$	−6.56043	−	20.1909i	−0.487633	−	1.50078i	0.340498	−	0.940245i	$-0.389404\pi$
$182$	−1.48218	+	1.64613i	−0.109867	+	0.122020i
$183$	6.97339	−	0.346364i	0.515488	−	0.0256040i
$184$	−0.0805561	−	0.766441i	−0.00593868	−	0.0565027i
$185$	0.696317	+	0.773338i	0.0511942	+	0.0568570i
$186$	−2.56464	−	16.4837i	−0.188048	−	1.20865i
$187$	−5.11301	−	6.78336i	−0.373900	−	0.496048i
$188$	1.11121			0.0810436
$189$	1.62396	+	2.03937i	0.118126	+	0.148342i
$190$	−0.146517	+	0.106451i	−0.0106294	+	0.00772274i
$191$	0.385918	−	3.67177i	0.0279241	−	0.265680i	−0.971648	−	0.236432i	$-0.924022\pi$
$191$	0.385918	−	3.67177i	0.0279241	−	0.265680i	0.999572	−	0.0292481i	$-0.00931128\pi$
$192$	1.54541	−	0.782117i	0.111530	−	0.0564444i
$193$	9.12284	+	1.93912i	0.656677	+	0.139581i	0.524187	−	0.851603i	$-0.324369\pi$
$193$	9.12284	+	1.93912i	0.656677	+	0.139581i	0.132490	+	0.991184i	$0.457703\pi$
$194$	−5.42292	+	2.41444i	−0.389343	+	0.173347i
$195$	1.99939	−	7.38114i	0.143180	−	0.528574i
$196$	6.60082	−	1.40305i	0.471487	−	0.100218i
$197$	21.2493			1.51395			0.756977	−	0.653442i	$-0.226676\pi$
$197$	21.2493			1.51395			0.756977	+	0.653442i	$0.226676\pi$
$198$	−5.07901	−	8.55591i	−0.360950	−	0.608042i
$199$	−21.6690			−1.53608			−0.768038	−	0.640405i	$-0.778767\pi$
$199$	−21.6690			−1.53608			−0.768038	+	0.640405i	$0.778767\pi$
$200$	−0.978148	+	0.207912i	−0.0691655	+	0.0147016i
$201$	−9.56035	+	2.53372i	−0.674335	+	0.178715i
$202$	4.08751	−	1.81988i	0.287596	−	0.128046i
$203$	−1.41193	−	0.300115i	−0.0990980	−	0.0210639i
$204$	0.244267	−	4.42939i	0.0171021	−	0.310119i
$205$	0.0614830	−	0.584972i	0.00429416	−	0.0408562i
$206$	10.7992	−	7.84607i	0.752415	−	0.546661i
$207$	−1.99589	−	1.16691i	−0.138724	−	0.0811061i
$208$	4.41508			0.306131
$209$	−0.344458	+	0.492073i	−0.0238267	+	0.0340374i
$210$	0.676821	−	0.545025i	0.0467051	−	0.0376103i
$211$	−18.5126	−	20.5604i	−1.27446	−	1.41543i	−0.863950	−	0.503578i	$-0.832017\pi$
$211$	−18.5126	−	20.5604i	−1.27446	−	1.41543i	−0.410512	−	0.911855i	$-0.634650\pi$
$212$	0.985275	+	9.37427i	0.0676690	+	0.643827i
$213$	2.77225	−	5.40430i	0.189951	−	0.370297i
$214$	−10.8302	+	12.0281i	−0.740336	+	0.822226i
$215$	−2.20804	−	6.79566i	−0.150587	−	0.463460i
$216$	0.854882	−	5.12535i	0.0581673	−	0.348736i
$217$	3.90931	−	2.84028i	0.265381	−	0.192811i
$218$	−3.61987	+	0.769427i	−0.245168	+	0.0521121i
$219$	−0.789254	−	5.07279i	−0.0533328	−	0.342787i
$220$	−2.84268	+	1.70856i	−0.191653	+	0.115191i
$221$	5.65394	−	9.79290i	0.380325	−	0.658742i
$222$	0.641332	+	1.68446i	0.0430434	+	0.113054i
$223$	14.7007	+	6.54515i	0.984428	+	0.438296i	0.834864	−	0.550456i	$-0.185546\pi$
$223$	14.7007	+	6.54515i	0.984428	+	0.438296i	0.149564	+	0.988752i	$0.452213\pi$
$224$	0.405892	+	0.294898i	0.0271198	+	0.0197037i
$225$	−1.23516	+	2.73393i	−0.0823442	+	0.182262i
$226$	−2.30228	−	7.08569i	−0.153145	−	0.471333i
$227$	−0.614669	+	5.84818i	−0.0407970	+	0.388158i	0.955003	+	0.296598i	$0.0958520\pi$
$227$	−0.614669	+	5.84818i	−0.0407970	+	0.388158i	−0.995800	+	0.0915601i	$0.970815\pi$
$228$	−0.303214	+	0.0803591i	−0.0200809	+	0.00532191i
$229$	14.1003	+	15.6600i	0.931773	+	1.03484i	0.999311	+	0.0371224i	$0.0118191\pi$
$229$	14.1003	+	15.6600i	0.931773	+	1.03484i	−0.0675374	+	0.997717i	$0.521514\pi$
$230$	−0.385331	+	0.667413i	−0.0254080	+	0.0440079i
$231$	1.53364	−	2.44018i	0.100906	−	0.160552i
$232$	1.43855	+	2.49164i	0.0944455	+	0.163584i
$233$	3.78870	−	11.6604i	0.248206	−	0.763899i	−0.746887	−	0.664951i	$-0.768452\pi$
$233$	3.78870	−	11.6604i	0.248206	−	0.763899i	0.995093	−	0.0989479i	$-0.0315477\pi$
$234$	7.84377	−	10.6729i	0.512763	−	0.697711i
$235$	−0.898991	−	0.653155i	−0.0586437	−	0.0426072i
$236$	−1.76626	+	1.96164i	−0.114974	+	0.127692i
$237$	1.72784	+	1.12879i	0.112235	+	0.0733230i
$238$	1.17389	−	0.522647i	0.0760917	−	0.0338782i
$239$	0.671734	+	6.39112i	0.0434509	+	0.413407i	0.994529	+	0.104458i	$0.0333108\pi$
$239$	0.671734	+	6.39112i	0.0434509	+	0.413407i	−0.951078	+	0.308950i	$0.900023\pi$
$240$	−1.70998	−	0.275624i	−0.110379	−	0.0177914i
$241$	−2.88972	−	5.00515i	−0.186143	−	0.322410i	0.757818	−	0.652466i	$-0.226266\pi$
$241$	−2.88972	−	5.00515i	−0.186143	−	0.322410i	−0.943961	+	0.330056i	$0.892932\pi$
$242$	−7.06847	+	8.42833i	−0.454379	+	0.541793i
$243$	−10.8712	−	11.1722i	−0.697385	−	0.716697i
$244$	1.24566	−	3.83376i	0.0797455	−	0.245431i
$245$	−6.16487	−	2.74478i	−0.393859	−	0.175357i
$246$	0.464995	−	0.906474i	0.0296470	−	0.0577947i
$247$	−0.782118	−	0.166244i	−0.0497650	−	0.0105779i
$248$	−9.42092	−	2.00248i	−0.598229	−	0.127158i
$249$	−5.83926	+	0.290032i	−0.370048	+	0.0183801i
$250$	0.913545	+	0.406737i	0.0577777	+	0.0257243i
$251$	2.13062	−	6.55739i	0.134484	−	0.413899i	−0.861026	−	0.508562i	$-0.830177\pi$
$251$	2.13062	−	6.55739i	0.134484	−	0.413899i	0.995509	+	0.0946631i	$0.0301774\pi$
$252$	1.43398	−	0.457285i	0.0903325	−	0.0288062i
$253$	−0.487381	+	2.50910i	−0.0306414	+	0.157746i
$254$	3.21101	+	5.56164i	0.201477	+	0.348968i
$255$	−2.80115	+	3.43987i	−0.175415	+	0.215413i
$256$	−0.104528	−	0.994522i	−0.00653303	−	0.0621576i
$257$	0.513267	−	0.228521i	0.0320167	−	0.0142548i	−0.390666	−	0.920533i	$-0.627755\pi$
$257$	0.513267	−	0.228521i	0.0320167	−	0.0142548i	0.422683	+	0.906278i	$0.361089\pi$
$258$	0.681472	−	12.3574i	0.0424266	−	0.769337i
$259$	−0.349349	+	0.387992i	−0.0217075	+	0.0241086i
$260$	−3.57187	−	2.59512i	−0.221518	−	0.160942i
$261$	8.57897	+	0.949094i	0.531025	+	0.0587475i
$262$	−3.68680	+	11.3468i	−0.227771	+	0.701008i
$263$	−11.1773	−	19.3597i	−0.689223	−	1.19377i	−0.972090	−	0.234610i	$-0.924619\pi$
$263$	−11.1773	−	19.3597i	−0.689223	−	1.19377i	0.282867	−	0.959159i	$-0.408715\pi$
$264$	−5.65987	+	0.982814i	−0.348341	+	0.0604880i
$265$	4.71295	−	8.16307i	0.289514	−	0.501454i
$266$	−0.0607985	−	0.0675236i	−0.00372780	−	0.00414014i
$267$	−2.71678	−	2.73166i	−0.166264	−	0.167175i
$268$	−0.596881	+	5.67895i	−0.0364603	+	0.346897i
$269$	−6.83206	−	21.0269i	−0.416558	−	1.28203i	−0.910850	−	0.412738i	$-0.864572\pi$
$269$	−6.83206	−	21.0269i	−0.416558	−	1.28203i	0.494292	−	0.869296i	$-0.335428\pi$
$270$	−3.70422	+	3.64401i	−0.225431	+	0.221767i
$271$	−23.0218	−	16.7264i	−1.39848	−	1.01605i	−0.994874	−	0.101120i	$-0.967758\pi$
$271$	−23.0218	−	16.7264i	−1.39848	−	1.01605i	−0.403604	−	0.914934i	$-0.632242\pi$
$272$	−2.33977	−	1.04173i	−0.141869	−	0.0631642i
$273$	3.78776	+	0.610532i	0.229246	+	0.0369511i
$274$	10.3945	−	18.0039i	0.627957	−	1.08765i
$275$	3.30404	+	0.288633i	0.199241	+	0.0174052i
$276$	−1.03965	+	0.837197i	−0.0625793	+	0.0503933i
$277$	−20.5114	+	4.35984i	−1.23241	+	0.261957i	−0.777674	−	0.628668i	$-0.783600\pi$
$277$	−20.5114	+	4.35984i	−1.23241	+	0.261957i	−0.454738	+	0.890625i	$0.650267\pi$
$278$	−13.5694	+	9.85873i	−0.813837	+	0.591287i
$279$	−21.5778	+	19.2164i	−1.29183	+	1.15046i
$280$	−0.155037	−	0.477155i	−0.00926523	−	0.0285155i
$281$	14.6724	−	16.2954i	0.875284	−	0.972101i	−0.124514	−	0.992218i	$-0.539737\pi$
$281$	14.6724	−	16.2954i	0.875284	−	0.972101i	0.999798	+	0.0201166i	$0.00640374\pi$
$282$	−1.04384	−	1.61703i	−0.0621599	−	0.0962927i
$283$	−0.164895	−	1.56887i	−0.00980199	−	0.0932597i	0.988527	−	0.151043i	$-0.0482633\pi$
$283$	−0.164895	−	1.56887i	−0.00980199	−	0.0932597i	−0.998329	+	0.0577837i	$0.981597\pi$
$284$	−2.34647	−	2.60602i	−0.139237	−	0.154639i
$285$	0.292539	+	0.113213i	0.0173285	+	0.00670616i
$286$	−14.0039	−	4.27942i	−0.828067	−	0.253048i
$287$	0.295103			0.0174194
$288$	−2.58984	−	1.51417i	−0.152608	−	0.0892233i
$289$	8.44637	−	6.13665i	0.496845	−	0.360979i
$290$	0.300739	−	2.86134i	0.0176600	−	0.168024i
$291$	8.60760	+	5.62333i	0.504587	+	0.329645i
$292$	−2.89924	−	0.616253i	−0.169665	−	0.0360635i
$293$	−14.6829	+	6.53725i	−0.857784	+	0.381910i	−0.788017	−	0.615653i	$-0.788892\pi$
$293$	−14.6829	+	6.53725i	−0.857784	+	0.381910i	−0.0697670	+	0.997563i	$0.522226\pi$
$294$	−8.24232	−	8.28747i	−0.480702	−	0.483335i
$295$	2.58196	−	0.548812i	0.150327	−	0.0319531i
$296$	1.04063			0.0604854
$297$	−7.67941	+	15.4281i	−0.445604	+	0.895230i
$298$	−6.04269			−0.350044
$299$	−3.32818	+	0.707427i	−0.192474	+	0.0409115i
$300$	1.22140	+	1.22809i	0.0705173	+	0.0709035i
$301$	3.27498	−	1.45811i	0.188767	−	0.0840443i
$302$	9.02841	+	1.91905i	0.519526	+	0.110429i
$303$	−6.48795	−	4.23857i	−0.372723	−	0.243499i
$304$	−0.0189306	+	0.180112i	−0.00108574	+	0.0103302i
$305$	−3.26119	+	2.36939i	−0.186735	+	0.135671i
$306$	−6.67506	+	3.80538i	−0.381588	+	0.217539i
$307$	23.9731			1.36822			0.684108	−	0.729381i	$-0.260192\pi$
$307$	23.9731			1.36822			0.684108	+	0.729381i	$0.260192\pi$
$308$	−1.00158	−	1.32879i	−0.0570705	−	0.0757147i
$309$	−21.5620	−	8.34451i	−1.22662	−	0.474702i
$310$	6.44466	+	7.15752i	0.366032	+	0.406520i
$311$	0.546139	+	5.19617i	0.0309687	+	0.294648i	0.999034	+	0.0439487i	$0.0139938\pi$
$311$	0.546139	+	5.19617i	0.0309687	+	0.294648i	−0.968065	+	0.250699i	$0.919340\pi$
$312$	−4.14740	−	6.42478i	−0.234800	−	0.363732i
$313$	13.1354	−	14.5883i	0.742455	−	0.824580i	−0.247061	−	0.969000i	$-0.579465\pi$
$313$	13.1354	−	14.5883i	0.742455	−	0.824580i	0.989517	+	0.144420i	$0.0461316\pi$
$314$	−2.99871	−	9.22909i	−0.169227	−	0.520828i
$315$	−1.42890	−	0.472924i	−0.0805095	−	0.0266462i
$316$	0.964011	−	0.700395i	0.0542298	−	0.0394003i
$317$	−8.24054	+	1.75158i	−0.462835	+	0.0983786i	−0.433427	−	0.901189i	$-0.642696\pi$
$317$	−8.24054	+	1.75158i	−0.462835	+	0.0983786i	−0.0294083	+	0.999567i	$0.509362\pi$
$318$	12.7158	−	10.2397i	0.713067	−	0.574213i
$319$	−2.14775	−	9.29742i	−0.120251	−	0.520556i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	27.6768	+	4.46110i	1.54477	+	0.248994i
$322$	−0.353222	−	0.157264i	−0.0196843	−	0.00876400i
$323$	0.375257	+	0.272641i	0.0208799	+	0.0151701i
$324$	−8.26141	+	3.57059i	−0.458967	+	0.198366i
$325$	1.36433	+	4.19899i	0.0756797	+	0.232918i
$326$	−0.678404	+	6.45459i	−0.0375733	+	0.357487i
$327$	4.52006	+	4.54482i	0.249960	+	0.251329i
$328$	−0.393578	−	0.437113i	−0.0217317	−	0.0241355i
$329$	0.278754	−	0.482816i	0.0153682	−	0.0266185i
$330$	5.15661	+	2.53167i	0.283862	+	0.139364i
$331$	−16.0079	−	27.7266i	−0.879876	−	1.52399i	−0.851476	−	0.524393i	$-0.824292\pi$
$331$	−16.0079	−	27.7266i	−0.879876	−	1.52399i	−0.0283994	−	0.999597i	$-0.509041\pi$
$332$	−1.04307	+	3.21025i	−0.0572461	+	0.176185i
$333$	1.84877	−	2.51560i	0.101312	−	0.137854i
$334$	16.0288	+	11.6456i	0.877056	+	0.637219i
$335$	3.82089	−	4.24353i	0.208757	−	0.231849i
$336$	0.0478493	−	0.867669i	0.00261039	−	0.0473352i
$337$	22.3949	−	9.97087i	1.21993	−	0.543148i	0.307175	−	0.951653i	$-0.400616\pi$
$337$	22.3949	−	9.97087i	1.21993	−	0.543148i	0.912756	+	0.408505i	$0.133950\pi$
$338$	−0.678695	−	6.45735i	−0.0369161	−	0.351234i
$339$	−8.14834	+	10.0064i	−0.442557	+	0.543471i
$340$	1.28060	+	2.21806i	0.0694501	+	0.120291i
$341$	27.9406	+	15.4830i	1.51307	+	0.838451i
$342$	0.401769	+	0.365748i	0.0217252	+	0.0197774i
$343$	2.13149	−	6.56006i	0.115090	−	0.354210i
$344$	−6.52763	−	2.90629i	−0.351946	−	0.156697i
$345$	1.33318	−	0.0662184i	0.0717761	−	0.00356508i
$346$	12.2589	+	2.60570i	0.659041	+	0.140084i
$347$	15.3349	+	3.25954i	0.823221	+	0.174981i	0.600218	−	0.799837i	$-0.295081\pi$
$347$	15.3349	+	3.25954i	0.823221	+	0.174981i	0.223004	+	0.974818i	$0.428414\pi$
$348$	2.27448	−	4.43395i	0.121925	−	0.237684i
$349$	−13.6205	−	6.06425i	−0.729090	−	0.324612i	0.00840447	−	0.999965i	$-0.497325\pi$
$349$	−13.6205	−	6.06425i	−0.729090	−	0.324612i	−0.737495	+	0.675353i	$0.763991\pi$
$350$	−0.155037	+	0.477155i	−0.00828708	+	0.0255050i
$351$	−22.8994	−	1.38834i	−1.22228	−	0.0741041i
$352$	−0.632418	+	3.25577i	−0.0337080	+	0.173533i
$353$	−2.84834	−	4.93347i	−0.151602	−	0.262582i	0.780215	−	0.625512i	$-0.215110\pi$
$353$	−2.84834	−	4.93347i	−0.151602	−	0.262582i	−0.931816	+	0.362930i	$0.881776\pi$
$354$	4.51373	+	0.727548i	0.239902	+	0.0386688i
$355$	0.366555	+	3.48754i	0.0194547	+	0.185099i
$356$	−2.03202	+	0.904713i	−0.107697	+	0.0479497i
$357$	−1.86327	−	1.21727i	−0.0986145	−	0.0644246i
$358$	−12.0761	+	13.4119i	−0.638243	+	0.708840i
$359$	−4.37876	−	3.18136i	−0.231102	−	0.167906i	0.466208	−	0.884675i	$-0.345620\pi$
$359$	−4.37876	−	3.18136i	−0.231102	−	0.167906i	−0.697310	+	0.716770i	$0.745620\pi$
$360$	1.20522	+	2.74726i	0.0635207	+	0.144793i
$361$	−5.86119	+	18.0389i	−0.308484	+	0.949415i
$362$	10.6150	+	18.3857i	0.557912	+	0.966332i
$363$	18.9047	+	2.36865i	0.992242	+	0.124322i
$364$	1.10755	−	1.91832i	0.0580511	−	0.100548i
$365$	1.98331	+	2.20269i	0.103811	+	0.115294i
$366$	−6.74899	+	1.78865i	−0.352776	+	0.0934940i
$367$	0.629353	−	5.98789i	0.0328520	−	0.312565i	−0.965740	−	0.259513i	$-0.916438\pi$
$367$	0.629353	−	5.98789i	0.0328520	−	0.312565i	0.998592	−	0.0530529i	$-0.0168952\pi$
$368$	0.238148	+	0.732943i	0.0124143	+	0.0382073i
$369$	−1.75590	+	0.174860i	−0.0914083	+	0.00910284i
$370$	−0.841887	−	0.611667i	−0.0437676	−	0.0317990i
$371$	4.32022	+	1.92349i	0.224295	+	0.0998625i
$372$	5.93576	+	15.5903i	0.307755	+	0.808320i
$373$	−1.48929	+	2.57953i	−0.0771125	+	0.133563i	−0.902003	−	0.431730i	$-0.857903\pi$
$373$	−1.48929	+	2.57953i	−0.0771125	+	0.133563i	0.824890	+	0.565293i	$0.191237\pi$
$374$	6.41162	+	5.57207i	0.331537	+	0.288125i
$375$	−0.266279	−	1.71146i	−0.0137506	−	0.0883794i
$376$	−1.08693	+	0.231034i	−0.0560542	+	0.0119147i
$377$	10.2766	−	7.46642i	0.529274	−	0.384540i
$378$	−2.01248	−	1.65716i	−0.103511	−	0.0852351i
$379$	−11.5833	−	35.6497i	−0.594994	−	1.83120i	−0.554756	−	0.832013i	$-0.687188\pi$
$379$	−11.5833	−	35.6497i	−0.594994	−	1.83120i	−0.0402384	−	0.999190i	$-0.512812\pi$
$380$	0.121183	−	0.134587i	0.00621653	−	0.00690416i
$381$	5.07691	−	9.89708i	0.260098	−	0.507043i
$382$	0.385918	+	3.67177i	0.0197453	+	0.187864i
$383$	−1.25144	−	1.38987i	−0.0639458	−	0.0710190i	0.710323	−	0.703876i	$-0.248549\pi$
$383$	−1.25144	−	1.38987i	−0.0639458	−	0.0710190i	−0.774269	+	0.632857i	$0.781882\pi$
$384$	−1.34903	+	1.08633i	−0.0688423	+	0.0554368i
$385$	0.0292570	+	1.66373i	0.00149107	+	0.0847914i
$386$	−9.32665			−0.474714
$387$	−18.6225	+	10.6165i	−0.946636	+	0.539667i
$388$	4.80242	−	3.48917i	0.243806	−	0.177136i
$389$	−1.62587	+	15.4691i	−0.0824350	+	0.784316i	0.872722	+	0.488217i	$0.162353\pi$
$389$	−1.62587	+	15.4691i	−0.0824350	+	0.784316i	−0.955157	+	0.296099i	$0.904314\pi$
$390$	−0.421077	+	7.63554i	−0.0213220	+	0.386641i
$391$	1.93068	+	0.410379i	0.0976388	+	0.0207538i
$392$	−6.16487	+	2.74478i	−0.311373	+	0.138632i
$393$	19.9750	−	5.29386i	1.00761	−	0.267040i
$394$	−20.7850	+	4.41799i	−1.04713	+	0.222575i
$395$	−1.19158			−0.0599550
$396$	6.74690	+	7.31296i	0.339044	+	0.367490i
$397$	−16.0139			−0.803716			−0.401858	−	0.915702i	$-0.631635\pi$
$397$	−16.0139			−0.803716			−0.401858	+	0.915702i	$0.631635\pi$
$398$	21.1955	−	4.50524i	1.06243	−	0.225827i
$399$	−0.0411474	+	0.151903i	−0.00205994	+	0.00760468i
$400$	0.913545	−	0.406737i	0.0456773	−	0.0203368i
$401$	25.0191	+	5.31798i	1.24939	+	0.265567i	0.784684	−	0.619896i	$-0.212825\pi$
$401$	25.0191	+	5.31798i	1.24939	+	0.265567i	0.464711	+	0.885463i	$0.346158\pi$
$402$	8.82465	−	4.46606i	0.440133	−	0.222747i
$403$	−4.44490	+	42.2904i	−0.221416	+	2.10663i
$404$	−3.61981	+	2.62995i	−0.180092	+	0.130845i
$405$	8.78236	+	1.96727i	0.436399	+	0.0977544i
$406$	1.44347			0.0716383
$407$	−3.30070	−	1.00866i	−0.163610	−	0.0499972i
$408$	0.681992	+	4.38338i	0.0337636	+	0.217010i
$409$	16.9577	+	18.8334i	0.838505	+	0.931254i	0.998438	−	0.0558739i	$-0.0177945\pi$
$409$	16.9577	+	18.8334i	0.838505	+	0.931254i	−0.159933	+	0.987128i	$0.551128\pi$
$410$	0.0614830	+	0.584972i	0.00303643	+	0.0288897i
$411$	−35.9634	+	1.78628i	−1.77394	+	0.0881107i
$412$	−8.93191	+	9.91989i	−0.440044	+	0.488718i
$413$	0.409242	+	1.25952i	0.0201375	+	0.0619768i
$414$	2.19489	+	0.726444i	0.107873	+	0.0357028i
$415$	2.73080	−	1.98404i	0.134050	−	0.0973928i
$416$	−4.31860	+	0.917946i	−0.211737	+	0.0450060i
$417$	27.0930	+	10.4850i	1.32675	+	0.513454i
$418$	0.234623	−	0.552937i	0.0114758	−	0.0270450i
$419$	−11.3454	+	19.6507i	−0.554257	+	0.960001i	0.443704	+	0.896173i	$0.353664\pi$
$419$	−11.3454	+	19.6507i	−0.554257	+	0.960001i	−0.997961	+	0.0638276i	$0.979669\pi$
$420$	−0.548714	+	0.673834i	−0.0267745	+	0.0328797i
$421$	−14.6072	−	6.50356i	−0.711913	−	0.316964i	0.0186340	−	0.999826i	$-0.494068\pi$
$421$	−14.6072	−	6.50356i	−0.711913	−	0.316964i	−0.730547	+	0.682862i	$0.760735\pi$
$422$	22.3828	+	16.2621i	1.08958	+	0.791625i
$423$	−1.37253	+	3.03798i	−0.0667347	+	0.147712i
$424$	−2.91276	−	8.96457i	−0.141456	−	0.435358i
$425$	0.267718	−	2.54716i	0.0129862	−	0.123556i
$426$	−1.58805	+	5.86259i	−0.0769413	+	0.284043i
$427$	−1.35326	−	1.50295i	−0.0654890	−	0.0727329i
$428$	8.09273	−	14.0170i	0.391177	−	0.677538i
$429$	6.92747	+	24.3983i	0.334461	+	1.17796i
$430$	3.57269	+	6.18808i	0.172290	+	0.298416i
$431$	−8.77404	+	27.0037i	−0.422631	+	1.30072i	0.482614	+	0.875833i	$0.339687\pi$
$431$	−8.77404	+	27.0037i	−0.422631	+	1.30072i	−0.905245	+	0.424891i	$0.860313\pi$
$432$	0.229419	+	5.19109i	0.0110379	+	0.249756i
$433$	−17.7655	−	12.9074i	−0.853753	−	0.620288i	0.0724250	−	0.997374i	$-0.476926\pi$
$433$	−17.7655	−	12.9074i	−0.853753	−	0.620288i	−0.926178	+	0.377086i	$0.876926\pi$
$434$	−3.23335	+	3.59100i	−0.155206	+	0.172374i
$435$	−4.44631	+	2.25023i	−0.213184	+	0.107890i
$436$	3.38079	−	1.50523i	0.161911	−	0.0720872i
$437$	−0.0145891	−	0.138806i	−0.000697890	−	0.00663998i
$438$	1.82670	+	4.79784i	0.0872830	+	0.229250i
$439$	9.77054	+	16.9231i	0.466323	+	0.807694i	0.999260	−	0.0384602i	$-0.0122453\pi$
$439$	9.77054	+	16.9231i	0.466323	+	0.807694i	−0.532938	+	0.846155i	$0.678912\pi$
$440$	2.42533	−	2.26225i	0.115623	−	0.107848i
$441$	−4.31725	+	19.7792i	−0.205583	+	0.941865i
$442$	−3.49432	+	10.7544i	−0.166208	+	0.511536i
$443$	13.0495	+	5.81003i	0.620002	+	0.276043i	0.692604	−	0.721318i	$-0.256464\pi$
$443$	13.0495	+	5.81003i	0.620002	+	0.276043i	−0.0726017	+	0.997361i	$0.523130\pi$
$444$	−0.977538	−	1.51431i	−0.0463919	−	0.0718662i
$445$	2.17571	+	0.462462i	0.103139	+	0.0219228i
$446$	−15.7402	−	3.34569i	−0.745321	−	0.158423i
$447$	5.67633	+	8.79327i	0.268481	+	0.415907i
$448$	−0.458335	−	0.204064i	−0.0216543	−	0.00964112i
$449$	3.10427	−	9.55395i	0.146499	−	0.450879i	−0.850701	−	0.525649i	$-0.823822\pi$
$449$	3.10427	−	9.55395i	0.146499	−	0.450879i	0.997201	+	0.0747704i	$0.0238224\pi$
$450$	0.639755	−	2.93099i	0.0301584	−	0.138168i
$451$	0.824681	+	1.76793i	0.0388327	+	0.0832488i
$452$	3.72517	+	6.45218i	0.175217	+	0.303485i
$453$	−5.68845	−	14.9408i	−0.267267	−	0.701978i
$454$	−0.614669	−	5.84818i	−0.0288478	−	0.274469i
$455$	−2.02359	+	0.900959i	−0.0948672	+	0.0422376i
$456$	0.279881	−	0.141645i	0.0131066	−	0.00663313i
$457$	3.32065	−	3.68795i	0.155333	−	0.172515i	−0.660455	−	0.750865i	$-0.729637\pi$
$457$	3.32065	−	3.68795i	0.155333	−	0.172515i	0.815789	+	0.578350i	$0.196303\pi$
$458$	−17.0481	−	12.3861i	−0.796603	−	0.578766i
$459$	11.8079	+	6.13882i	0.551147	+	0.286536i
$460$	0.238148	−	0.732943i	0.0111037	−	0.0341737i
$461$	20.6778	+	35.8151i	0.963063	+	1.66807i	0.714731	+	0.699399i	$0.246549\pi$
$461$	20.6778	+	35.8151i	0.963063	+	1.66807i	0.248332	+	0.968675i	$0.420118\pi$
$462$	−0.992780	+	2.70572i	−0.0461883	+	0.125882i
$463$	−14.1429	+	24.4962i	−0.657276	+	1.13844i	0.324042	+	0.946043i	$0.394958\pi$
$463$	−14.1429	+	24.4962i	−0.657276	+	1.13844i	−0.981318	+	0.192393i	$0.938375\pi$
$464$	−1.92516	−	2.13810i	−0.0893732	−	0.0992590i
$465$	4.36163	−	16.1018i	0.202266	−	0.746702i
$466$	−1.28157	+	12.1933i	−0.0593676	+	0.564845i
$467$	2.59374	+	7.98272i	0.120024	+	0.369396i	0.992962	−	0.118436i	$-0.0377879\pi$
$467$	2.59374	+	7.98272i	0.120024	+	0.369396i	−0.872938	+	0.487832i	$0.837788\pi$
$468$	−5.45334	+	12.0705i	−0.252081	+	0.557960i
$469$	2.31774	+	1.68393i	0.107023	+	0.0777569i
$470$	1.01514	+	0.451972i	0.0468251	+	0.0208479i
$471$	−10.6132	+	13.0332i	−0.489030	+	0.600540i
$472$	1.31982	−	2.28600i	0.0607497	−	0.105222i
$473$	17.8875	+	15.5453i	0.822470	+	0.714775i
$474$	−1.92477	−	0.744889i	−0.0884077	−	0.0342139i
$475$	−0.177147	+	0.0376537i	−0.00812806	+	0.00172767i
$476$	−1.03957	+	0.755291i	−0.0476485	+	0.0346187i
$477$	−26.8456	−	8.88507i	−1.22917	−	0.406819i
$478$	−1.98584	−	6.11180i	−0.0908304	−	0.279547i
$479$	17.1235	−	19.0175i	0.782391	−	0.868933i	−0.211717	−	0.977331i	$-0.567905\pi$
$479$	17.1235	−	19.0175i	0.782391	−	0.868933i	0.994108	+	0.108398i	$0.0345720\pi$
$480$	1.72992	−	0.0859240i	0.0789596	−	0.00392187i
$481$	−0.480252	−	4.56929i	−0.0218976	−	0.208342i
$482$	3.86721	+	4.29497i	0.176146	+	0.195630i
$483$	0.102957	+	0.661735i	0.00468469	+	0.0301100i
$484$	5.16166	−	9.71377i	0.234621	−	0.441535i
$485$	−5.93612			−0.269545
$486$	12.9564	+	8.66782i	0.587715	+	0.393180i
$487$	7.39497	−	5.37276i	0.335098	−	0.243463i	−0.407493	−	0.913208i	$-0.633597\pi$
$487$	7.39497	−	5.37276i	0.335098	−	0.243463i	0.742591	+	0.669746i	$0.233597\pi$
$488$	−0.421360	+	4.00897i	−0.0190741	+	0.181478i
$489$	10.0299	−	5.07605i	0.453569	−	0.229547i
$490$	6.60082	+	1.40305i	0.298195	+	0.0633832i
$491$	−26.9664	+	12.0062i	−1.21698	+	0.541833i	−0.911867	−	0.410485i	$-0.865359\pi$
$491$	−26.9664	+	12.0062i	−1.21698	+	0.541833i	−0.305109	+	0.952318i	$0.598693\pi$
$492$	−0.266367	+	0.983343i	−0.0120087	+	0.0443325i
$493$	−7.20779	+	1.53206i	−0.324623	+	0.0690007i
$494$	0.799591			0.0359753
$495$	−1.15991	−	9.88204i	−0.0521339	−	0.444164i
$496$	9.63139			0.432462
$497$	−1.72092	+	0.365794i	−0.0771940	+	0.0164081i
$498$	5.65136	−	1.49775i	0.253243	−	0.0671156i
$499$	5.01881	−	2.23452i	0.224673	−	0.100031i	−0.291313	−	0.956628i	$-0.594092\pi$
$499$	5.01881	−	2.23452i	0.224673	−	0.100031i	0.515986	+	0.856597i	$0.327426\pi$
$500$	−0.978148	−	0.207912i	−0.0437441	−	0.00929809i
$501$	1.88958	−	34.2645i	0.0844203	−	1.53082i
$502$	−0.720707	+	6.85707i	−0.0321667	+	0.306046i
$503$	−21.2513	+	15.4400i	−0.947551	+	0.688436i	−0.950226	−	0.311561i	$-0.899148\pi$
$503$	−21.2513	+	15.4400i	−0.947551	+	0.688436i	0.00267571	+	0.999996i	$0.499148\pi$
$504$	−1.30757	+	0.745434i	−0.0582439	+	0.0332043i
$505$	4.47433			0.199105
$506$	−0.0449407	−	2.55560i	−0.00199786	−	0.113610i
$507$	−8.75913	+	7.05348i	−0.389007	+	0.313256i
$508$	−4.29717	−	4.77249i	−0.190656	−	0.211745i
$509$	1.84274	+	17.5325i	0.0816779	+	0.777114i	0.956316	+	0.292336i	$0.0944327\pi$
$509$	1.84274	+	17.5325i	0.0816779	+	0.777114i	−0.874638	+	0.484777i	$0.838901\pi$
$510$	2.02474	−	3.94709i	0.0896571	−	0.174780i
$511$	−0.995047	+	1.10511i	−0.0440183	+	0.0488873i
$512$	0.309017	+	0.951057i	0.0136568	+	0.0420312i
$513$	0.154823	−	0.928223i	0.00683560	−	0.0409821i
$514$	−0.454539	+	0.330242i	−0.0200488	+	0.0145663i
$515$	13.0568	−	2.77531i	0.575353	−	0.122295i
$516$	1.90266	+	12.2290i	0.0837601	+	0.538353i
$517$	3.67150	+	0.320733i	0.161472	+	0.0141058i
$518$	0.261047	−	0.452147i	0.0114698	−	0.0198662i
$519$	−7.72384	−	20.2867i	−0.339039	−	0.890489i
$520$	4.03338	+	1.79577i	0.176875	+	0.0787499i
$521$	34.0437	+	24.7342i	1.49148	+	1.08362i	0.973625	+	0.228156i	$0.0732695\pi$
$521$	34.0437	+	24.7342i	1.49148	+	1.08362i	0.517855	+	0.855468i	$0.326731\pi$
$522$	−8.58883	+	0.855313i	−0.375923	+	0.0374361i
$523$	−8.44042	−	25.9769i	−0.369074	−	1.13589i	−0.947391	−	0.320080i	$-0.896290\pi$
$523$	−8.44042	−	25.9769i	−0.369074	−	1.13589i	0.578317	−	0.815812i	$-0.303710\pi$
$524$	1.24710	−	11.8654i	0.0544799	−	0.518341i
$525$	0.839989	−	0.222617i	0.0366601	−	0.00971581i
$526$	14.9582	+	16.6127i	0.652207	+	0.724350i
$527$	12.3339	−	21.3630i	0.537274	−	0.930587i
$528$	5.33185	−	2.13809i	0.232039	−	0.0930484i
$529$	11.2030	+	19.4042i	0.487089	+	0.843662i
$530$	−2.91276	+	8.96457i	−0.126522	+	0.389396i
$531$	−3.18135	−	7.25178i	−0.138059	−	0.314701i
$532$	0.0735089	+	0.0534073i	0.00318702	+	0.00231550i
$533$	−1.73768	+	1.92989i	−0.0752673	+	0.0835928i
$534$	3.22535	+	2.10711i	0.139575	+	0.0911838i
$535$	−14.7861	+	6.58322i	−0.639261	+	0.284617i
$536$	−0.596881	−	5.67895i	−0.0257814	−	0.245293i
$537$	30.8608	+	4.97432i	1.33174	+	0.214658i
$538$	11.0545	+	19.1470i	0.476594	+	0.825485i
$539$	22.2144	−	2.73051i	0.956840	−	0.117612i
$540$	2.86564	−	4.33453i	0.123317	−	0.186528i
$541$	−10.1612	+	31.2730i	−0.436865	+	1.34453i	0.454299	+	0.890849i	$0.349890\pi$
$541$	−10.1612	+	31.2730i	−0.436865	+	1.34453i	−0.891163	+	0.453682i	$0.850110\pi$
$542$	25.9964	+	11.5743i	1.11664	+	0.497160i
$543$	16.7833	−	32.7179i	0.720241	−	1.40406i
$544$	2.50523	+	0.532502i	0.107411	+	0.0228308i
$545$	−3.61987	−	0.769427i	−0.155058	−	0.0329586i
$546$	−3.83193	+	0.190329i	−0.163991	+	0.00814535i
$547$	−29.8865	−	13.3063i	−1.27786	−	0.568938i	−0.348218	−	0.937414i	$-0.613213\pi$
$547$	−29.8865	−	13.3063i	−1.27786	−	0.568938i	−0.929637	+	0.368476i	$0.879880\pi$
$548$	−6.42418	+	19.7716i	−0.274427	+	0.844600i
$549$	8.94263	+	8.14088i	0.381662	+	0.347444i
$550$	−3.29185	+	0.404623i	−0.140365	+	0.0172532i
$551$	0.260528	+	0.451248i	0.0110989	+	0.0192238i
$552$	0.842864	−	1.03506i	0.0358747	−	0.0440549i
$553$	−0.0624902	−	0.594554i	−0.00265735	−	0.0252830i
$554$	19.1567	−	8.52913i	0.813892	−	0.362368i
$555$	−0.0992473	+	1.79969i	−0.00421282	+	0.0763925i
$556$	11.2231	−	12.4645i	0.475966	−	0.528614i
$557$	−14.4020	−	10.4636i	−0.610230	−	0.443358i	0.239265	−	0.970954i	$-0.423094\pi$
$557$	−14.4020	−	10.4636i	−0.610230	−	0.443358i	−0.849495	+	0.527596i	$0.823094\pi$
$558$	17.1110	−	23.2828i	0.724367	−	0.985638i
$559$	−9.74869	+	30.0034i	−0.412326	+	1.26901i
$560$	0.250855	+	0.434494i	0.0106006	+	0.0183607i
$561$	2.08554	−	14.5644i	0.0880514	−	0.614908i
$562$	−10.9638	+	18.9899i	−0.462480	+	0.801039i
$563$	−0.943075	−	1.04739i	−0.0397459	−	0.0441423i	0.722944	−	0.690907i	$-0.242788\pi$
$563$	−0.943075	−	1.04739i	−0.0397459	−	0.0441423i	−0.762690	+	0.646764i	$0.776122\pi$
$564$	1.35723	+	1.36467i	0.0571498	+	0.0574628i
$565$	0.778772	−	7.40952i	0.0327632	−	0.311721i
$566$	0.487478	+	1.50030i	0.0204902	+	0.0630625i
$567$	−0.521019	+	4.48523i	−0.0218807	+	0.188362i
$568$	2.83702	+	2.06121i	0.119039	+	0.0864866i
$569$	−5.96127	−	2.65413i	−0.249909	−	0.111267i	0.277959	−	0.960593i	$-0.410342\pi$
$569$	−5.96127	−	2.65413i	−0.249909	−	0.111267i	−0.527869	+	0.849326i	$0.677009\pi$
$570$	−0.309685	−	0.0499167i	−0.0129713	−	0.00209078i
$571$	9.07930	−	15.7258i	0.379957	−	0.658104i	−0.611099	−	0.791554i	$-0.709272\pi$
$571$	9.07930	−	15.7258i	0.379957	−	0.658104i	0.991056	+	0.133450i	$0.0426055\pi$
$572$	14.5876	+	1.27434i	0.609938	+	0.0532827i
$573$	4.98060	−	4.01074i	0.208068	−	0.167551i
$574$	−0.288654	+	0.0613553i	−0.0120482	+	0.00256092i
$575$	−0.623479	+	0.452984i	−0.0260009	+	0.0188907i
$576$	2.84806	+	0.942623i	0.118669	+	0.0392759i
$577$	−5.53051	−	17.0212i	−0.230238	−	0.708601i	−0.997717	−	0.0675268i	$-0.978489\pi$
$577$	−5.53051	−	17.0212i	−0.230238	−	0.708601i	0.767479	−	0.641074i	$-0.221511\pi$
$578$	−6.98592	+	7.75864i	−0.290576	+	0.322717i
$579$	8.76119	+	13.5721i	0.364103	+	0.564036i
$580$	0.300739	+	2.86134i	0.0124875	+	0.118811i
$581$	1.13317	+	1.25852i	0.0470119	+	0.0522120i
$582$	−9.58866	−	3.71082i	−0.397463	−	0.153819i
$583$	0.549666	+	31.2574i	0.0227649	+	1.29455i
$584$	2.96401			0.122652
$585$	11.5067	−	6.55986i	0.475744	−	0.271217i
$586$	13.0029	−	9.44714i	0.537144	−	0.390258i
$587$	3.21084	−	30.5491i	0.132526	−	1.26090i	−0.702898	−	0.711290i	$-0.748111\pi$
$587$	3.21084	−	30.5491i	0.132526	−	1.26090i	0.835424	−	0.549606i	$-0.185222\pi$
$588$	9.78527	+	6.39270i	0.403538	+	0.263630i
$589$	−1.70617	−	0.362658i	−0.0703016	−	0.0149431i
$590$	−2.41143	+	1.07364i	−0.0992771	+	0.0442010i
$591$	25.9538	+	26.0960i	1.06760	+	1.07345i
$592$	−1.01789	+	0.216359i	−0.0418350	+	0.00889230i
$593$	−28.5544			−1.17259			−0.586295	−	0.810098i	$-0.699414\pi$
$593$	−28.5544			−1.17259			−0.586295	+	0.810098i	$0.699414\pi$
$594$	4.30391	−	16.6876i	0.176592	−	0.684701i
$595$	1.28498			0.0526789
$596$	5.91064	−	1.25635i	0.242109	−	0.0514619i
$597$	−26.4664	−	26.6114i	−1.08320	−	1.08913i
$598$	3.10837	−	1.38394i	0.127111	−	0.0565933i
$599$	42.4067	+	9.01383i	1.73269	+	0.368295i	0.962870	−	0.269964i	$-0.0870118\pi$
$599$	42.4067	+	9.01383i	1.73269	+	0.368295i	0.769822	+	0.638259i	$0.220345\pi$
$600$	−1.45004	−	0.947306i	−0.0591976	−	0.0386736i
$601$	−3.76073	+	35.7810i	−0.153403	+	1.45954i	0.598956	+	0.800782i	$0.295583\pi$
$601$	−3.76073	+	35.7810i	−0.153403	+	1.45954i	−0.752359	+	0.658753i	$0.771084\pi$
$602$	−2.90025	+	2.10716i	−0.118206	+	0.0858813i
$603$	−14.7886	−	8.64626i	−0.602238	−	0.352103i
$604$	−9.23011			−0.375568
$605$	−9.88548	+	4.82465i	−0.401902	+	0.196150i
$606$	7.22742	+	2.79702i	0.293594	+	0.113621i
$607$	−23.1362	−	25.6954i	−0.939071	−	1.04294i	−0.998999	−	0.0447413i	$-0.985754\pi$
$607$	−23.1362	−	25.6954i	−0.939071	−	1.04294i	0.0599276	−	0.998203i	$-0.480913\pi$
$608$	−0.0189306	−	0.180112i	−0.000767736	−	0.00730452i
$609$	−1.35596	−	2.10053i	−0.0549461	−	0.0851177i
$610$	2.69730	−	2.99566i	0.109211	−	0.121291i
$611$	1.51607	+	4.66598i	0.0613335	+	0.188765i
$612$	5.73801	−	5.11005i	0.231945	−	0.206562i
$613$	−29.0612	+	21.1142i	−1.17377	+	0.852793i	−0.991455	−	0.130447i	$-0.958359\pi$
$613$	−29.0612	+	21.1142i	−1.17377	+	0.852793i	−0.182314	+	0.983240i	$0.558359\pi$
$614$	−23.4492	+	4.98428i	−0.946333	+	0.201149i
$615$	0.793490	−	0.638975i	0.0319966	−	0.0257660i
$616$	1.25597	+	1.09151i	0.0506044	+	0.0439781i
$617$	−11.9753	+	20.7418i	−0.482107	+	0.835034i	−0.999789	−	0.0205389i	$-0.993462\pi$
$617$	−11.9753	+	20.7418i	−0.482107	+	0.835034i	0.517682	+	0.855573i	$0.326795\pi$
$618$	22.8257	+	3.67917i	0.918185	+	0.147998i
$619$	−3.62722	−	1.61494i	−0.145790	−	0.0649100i	0.332545	−	0.943088i	$-0.392093\pi$
$619$	−3.62722	−	1.61494i	−0.145790	−	0.0649100i	−0.478335	+	0.878178i	$0.658759\pi$
$620$	−7.79196	−	5.66119i	−0.312933	−	0.227359i
$621$	−1.00471	−	3.87639i	−0.0403175	−	0.155554i
$622$	−1.61455	−	4.96907i	−0.0647375	−	0.199242i
$623$	−0.116650	+	1.10985i	−0.00467349	+	0.0444653i
$624$	5.39256	+	5.42209i	0.215875	+	0.217057i
$625$	0.669131	+	0.743145i	0.0267652	+	0.0297258i
$626$	−9.81525	+	17.0005i	−0.392296	+	0.679477i
$627$	−1.02503	+	0.177992i	−0.0409356	+	0.00710832i
$628$	4.85202	+	8.40394i	0.193617	+	0.335354i
$629$	−0.823609	+	2.53481i	−0.0328394	+	0.101069i
$630$	1.49600	+	0.165503i	0.0596022	+	0.00659382i
$631$	−36.9811	−	26.8684i	−1.47220	−	1.06961i	−0.979970	−	0.199146i	$-0.936183\pi$
$631$	−36.9811	−	26.8684i	−1.47220	−	1.06961i	−0.492226	−	0.870467i	$-0.663817\pi$
$632$	−0.797324	+	0.885518i	−0.0317159	+	0.0352240i
$633$	2.63864	−	47.8474i	0.104876	−	1.90176i
$634$	7.69629	−	3.42661i	0.305659	−	0.136088i
$635$	0.671284	+	6.38684i	0.0266391	+	0.253454i
$636$	−10.3090	+	12.6597i	−0.408778	+	0.501989i
$637$	14.8971	+	25.8025i	0.590245	+	1.02233i
$638$	4.03386	+	8.64771i	0.159702	+	0.342366i
$639$	10.0230	−	3.19623i	0.396502	−	0.126441i
$640$	0.309017	−	0.951057i	0.0122150	−	0.0375938i
$641$	7.88590	+	3.51103i	0.311474	+	0.138677i	0.556520	−	0.830834i	$-0.312136\pi$
$641$	7.88590	+	3.51103i	0.311474	+	0.138677i	−0.245046	+	0.969512i	$0.578803\pi$
$642$	−27.9995	+	1.39072i	−1.10505	+	0.0548873i
$643$	−26.7855	−	5.69344i	−1.05632	−	0.224527i	−0.353161	−	0.935563i	$-0.614893\pi$
$643$	−26.7855	−	5.69344i	−1.05632	−	0.224527i	−0.703156	+	0.711035i	$0.748227\pi$
$644$	0.378200	+	0.0803889i	0.0149032	+	0.00316777i
$645$	5.64876	−	11.0119i	0.222420	−	0.433591i
$646$	−0.423742	−	0.188662i	−0.0166719	−	0.00742282i
$647$	−3.23866	+	9.96756i	−0.127325	+	0.391865i	−0.994317	−	0.106456i	$-0.966050\pi$
$647$	−3.23866	+	9.96756i	−0.127325	+	0.391865i	0.866993	+	0.498321i	$0.166050\pi$
$648$	7.33851	−	5.21021i	0.288284	−	0.204676i
$649$	−6.40201	+	5.97152i	−0.251301	+	0.234403i
$650$	−2.20754	−	3.82357i	−0.0865868	−	0.149973i
$651$	8.26291	+	1.33186i	0.323849	+	0.0521998i
$652$	−0.678404	−	6.45459i	−0.0265684	−	0.252781i
$653$	14.1114	−	6.28280i	0.552222	−	0.245865i	−0.111603	−	0.993753i	$-0.535599\pi$
$653$	14.1114	−	6.28280i	0.552222	−	0.245865i	0.663825	+	0.747888i	$0.268932\pi$
$654$	−5.36621	−	3.50573i	−0.209835	−	0.137085i
$655$	−7.98322	+	8.86626i	−0.311930	+	0.346434i
$656$	0.475859	+	0.345732i	0.0185792	+	0.0134986i
$657$	5.26582	−	7.16515i	0.205439	−	0.279539i
$658$	−0.172279	+	0.530221i	−0.00671615	+	0.0206702i
$659$	−24.6956	−	42.7740i	−0.962003	−	1.66624i	−0.717460	−	0.696599i	$-0.754696\pi$
$659$	−24.6956	−	42.7740i	−0.962003	−	1.66624i	−0.244543	−	0.969639i	$-0.578638\pi$
$660$	−5.57029	−	1.40423i	−0.216823	−	0.0546596i
$661$	15.0634	−	26.0906i	0.585900	−	1.01481i	−0.408863	−	0.912596i	$-0.634075\pi$
$661$	15.0634	−	26.0906i	0.585900	−	1.01481i	0.994763	−	0.102212i	$-0.0325920\pi$
$662$	21.4228	+	23.7924i	0.832621	+	0.924719i
$663$	18.9322	−	5.01749i	0.735266	−	0.194863i
$664$	0.352831	−	3.35696i	0.0136925	−	0.130275i
$665$	−0.0280779	−	0.0864149i	−0.00108881	−	0.00335103i
$666$	−1.28535	+	2.84501i	−0.0498062	+	0.110242i
$667$	1.79381	+	1.30328i	0.0694567	+	0.0504633i
$668$	−18.0998	−	8.05854i	−0.700301	−	0.311794i
$669$	9.91730	+	26.0479i	0.383425	+	1.00707i
$670$	−2.85511	+	4.94520i	−0.110303	+	0.191050i
$671$	5.22228	−	12.3074i	0.201604	−	0.475120i
$672$	0.133595	+	0.858657i	0.00515354	+	0.0331234i
$673$	17.0719	−	3.62874i	0.658073	−	0.139878i	0.133241	−	0.991084i	$-0.457462\pi$
$673$	17.0719	−	3.62874i	0.658073	−	0.139878i	0.524832	+	0.851206i	$0.324128\pi$
$674$	−19.8325	+	14.4092i	−0.763920	+	0.555020i
$675$	−4.86612	+	1.82232i	−0.187297	+	0.0701413i
$676$	2.00642	+	6.17513i	0.0771701	+	0.237505i
$677$	15.3438	−	17.0410i	0.589709	−	0.654938i	−0.372250	−	0.928133i	$-0.621414\pi$
$677$	15.3438	−	17.0410i	0.589709	−	0.654938i	0.961959	+	0.273194i	$0.0880802\pi$
$678$	5.88984	−	11.4818i	0.226198	−	0.440957i
$679$	−0.311308	−	2.96190i	−0.0119469	−	0.113667i
$680$	−1.71377	−	1.90334i	−0.0657202	−	0.0729897i
$681$	−7.93282	+	6.38808i	−0.303986	+	0.244792i
$682$	−30.5491	−	9.33546i	−1.16979	−	0.357473i
$683$	−31.3640			−1.20011			−0.600054	−	0.799959i	$-0.704854\pi$
$683$	−31.3640			−1.20011			−0.600054	+	0.799959i	$0.704854\pi$
$684$	−0.469032	−	0.274223i	−0.0179339	−	0.0104852i
$685$	16.8187	−	12.2195i	0.642610	−	0.466883i
$686$	−0.721002	+	6.85987i	−0.0275280	+	0.261911i
$687$	−2.00974	+	36.4434i	−0.0766764	+	1.39040i
$688$	6.98924	+	1.48561i	0.266462	+	0.0566383i
$689$	−38.0182	+	16.9268i	−1.44838	+	0.644860i
$690$	−1.29028	+	0.341956i	−0.0491202	+	0.0130180i
$691$	−40.8767	+	8.68861i	−1.55502	+	0.330530i	−0.903665	−	0.428240i	$-0.859134\pi$
$691$	−40.8767	+	8.68861i	−1.55502	+	0.330530i	−0.651358	+	0.758770i	$0.725801\pi$
$692$	−12.5327			−0.476423
$693$	4.86993	−	1.09699i	0.184993	−	0.0416713i
$694$	−15.6775			−0.595110
$695$	−16.4061	+	3.48723i	−0.622321	+	0.132278i
$696$	−1.30291	+	4.80995i	−0.0493868	+	0.182321i
$697$	1.37624	−	0.612740i	0.0521287	−	0.0232092i
$698$	14.5837	+	3.09987i	0.552002	+	0.117332i
$699$	18.9475	−	9.58913i	0.716660	−	0.362694i
$700$	0.0524430	−	0.498962i	0.00198216	−	0.0188590i
$701$	−10.3804	+	7.54181i	−0.392063	+	0.284850i	−0.766300	−	0.642483i	$-0.777905\pi$
$701$	−10.3804	+	7.54181i	−0.392063	+	0.284850i	0.374237	+	0.927333i	$0.377905\pi$
$702$	22.6876	−	3.40305i	0.856289	−	0.128440i
$703$	0.188463			0.00710800
$704$	−0.0583144	−	3.31611i	−0.00219781	−	0.124981i
$705$	−0.295893	−	1.90180i	−0.0111440	−	0.0716259i
$706$	3.81182	+	4.23346i	0.143460	+	0.159328i
$707$	0.234648	+	2.23252i	0.00882483	+	0.0839626i
$708$	−4.56636	+	0.226808i	−0.171614	+	0.00852398i
$709$	6.67744	−	7.41604i	0.250776	−	0.278515i	−0.604592	−	0.796535i	$-0.706664\pi$
$709$	6.67744	−	7.41604i	0.250776	−	0.278515i	0.855369	+	0.518020i	$0.173331\pi$
$710$	−1.08364	−	3.33511i	−0.0406684	−	0.125165i
$711$	0.724120	+	3.50064i	0.0271566	+	0.131284i
$712$	1.79951	−	1.30742i	0.0674396	−	0.0489978i
$713$	−7.26035	+	1.54323i	−0.271902	+	0.0577946i
$714$	2.07563	+	0.803272i	0.0776786	+	0.0300617i
$715$	−11.0526	−	9.60534i	−0.413343	−	0.359219i
$716$	9.02374	−	15.6296i	0.337233	−	0.584105i
$717$	−7.02839	+	8.63103i	−0.262480	+	0.322332i
$718$	4.94452	+	2.20144i	0.184528	+	0.0821571i
$719$	36.6112	+	26.5996i	1.36537	+	0.991997i	0.998083	+	0.0618874i	$0.0197120\pi$
$719$	36.6112	+	26.5996i	1.36537	+	0.991997i	0.367283	+	0.930109i	$0.380288\pi$
$720$	−1.75007	−	2.43665i	−0.0652213	−	0.0908085i
$721$	2.06952	+	6.36932i	0.0770728	+	0.237206i
$722$	1.98261	−	18.8633i	0.0737852	−	0.702019i
$723$	2.61725	−	9.66209i	0.0973368	−	0.359337i
$724$	−14.2056	−	15.7770i	−0.527949	−	0.586346i
$725$	1.43855	−	2.49164i	0.0534265	−	0.0925373i
$726$	−18.9841	+	1.61363i	−0.704566	+	0.0598875i
$727$	−9.41599	−	16.3090i	−0.349220	−	0.604866i	0.636891	−	0.770954i	$-0.280220\pi$
$727$	−9.41599	−	16.3090i	−0.349220	−	0.604866i	−0.986111	+	0.166087i	$0.946887\pi$
$728$	−0.684501	+	2.10668i	−0.0253693	+	0.0780786i
$729$	0.442447	−	26.9964i	0.0163869	−	0.999866i
$730$	−2.39794	−	1.74220i	−0.0887516	−	0.0644818i
$731$	12.2456	−	13.6001i	0.452918	−	0.503017i
$732$	6.22963	−	3.15275i	0.230254	−	0.116529i
$733$	−21.4592	+	9.55424i	−0.792612	+	0.352894i	−0.762777	−	0.646661i	$-0.776165\pi$
$733$	−21.4592	+	9.55424i	−0.792612	+	0.352894i	−0.0298349	+	0.999555i	$0.509498\pi$
$734$	0.629353	+	5.98789i	0.0232298	+	0.221017i
$735$	−4.15892	−	10.9234i	−0.153404	−	0.402917i
$736$	−0.385331	−	0.667413i	−0.0142035	−	0.0246012i
$737$	−3.61125	+	18.5912i	−0.133022	+	0.684816i
$738$	1.68117	−	0.536110i	0.0618847	−	0.0197345i
$739$	−7.12086	+	21.9158i	−0.261945	+	0.806185i	0.730436	+	0.682981i	$0.239317\pi$
$739$	−7.12086	+	21.9158i	−0.261945	+	0.806185i	−0.992381	+	0.123204i	$0.960683\pi$
$740$	0.950662	+	0.423262i	0.0349470	+	0.0155594i
$741$	−0.751113	−	1.16356i	−0.0275928	−	0.0427443i
$742$	−4.62573	−	0.983230i	−0.169816	−	0.0360955i
$743$	−13.2192	−	2.80983i	−0.484966	−	0.103083i	−0.0410614	−	0.999157i	$-0.513074\pi$
$743$	−13.2192	−	2.80983i	−0.484966	−	0.103083i	−0.443905	+	0.896074i	$0.646407\pi$
$744$	−9.04745	−	14.0155i	−0.331696	−	0.513834i
$745$	−5.52027	−	2.45778i	−0.202247	−	0.0900462i
$746$	0.920432	−	2.83280i	0.0336994	−	0.103716i
$747$	−7.48823	−	6.81687i	−0.273980	−	0.249416i
$748$	−7.43001	−	4.11726i	−0.271668	−	0.150542i
$749$	−4.06020	−	7.03248i	−0.148357	−	0.256961i
$750$	0.616293	+	1.61870i	0.0225038	+	0.0591065i
$751$	−3.80136	−	36.1676i	−0.138714	−	1.31977i	−0.813416	−	0.581683i	$-0.802394\pi$
$751$	−3.80136	−	36.1676i	−0.138714	−	1.31977i	0.674702	−	0.738090i	$-0.264272\pi$
$752$	1.01514	−	0.451972i	0.0370185	−	0.0164817i
$753$	10.6554	−	5.39257i	0.388303	−	0.196516i
$754$	−8.49972	+	9.43990i	−0.309542	+	0.343781i
$755$	7.46731	+	5.42532i	0.271763	+	0.197448i
$756$	2.31305	+	1.20253i	0.0841247	+	0.0437356i
$757$	9.79431	−	30.1438i	0.355980	−	1.09559i	−0.599458	−	0.800406i	$-0.704617\pi$
$757$	9.79431	−	30.1438i	0.355980	−	1.09559i	0.955439	−	0.295189i	$-0.0953827\pi$
$758$	18.7422	+	32.4624i	0.680746	+	1.17909i
$759$	−3.67667	+	2.46606i	−0.133455	+	0.0895122i
$760$	−0.0905523	+	0.156841i	−0.00328468	+	0.00568922i
$761$	19.9915	+	22.2028i	0.724691	+	0.804851i	0.987100	−	0.160106i	$-0.0511836\pi$
$761$	19.9915	+	22.2028i	0.724691	+	0.804851i	−0.262409	+	0.964957i	$0.584517\pi$
$762$	−2.90825	+	10.7364i	−0.105355	+	0.388937i
$763$	0.194078	−	1.84653i	0.00702609	−	0.0668488i
$764$	−1.14089	−	3.51129i	−0.0412759	−	0.127034i
$765$	−7.64576	+	0.761399i	−0.276433	+	0.0275284i
$766$	1.51307	+	1.09931i	0.0546693	+	0.0397196i
$767$	−10.6467	−	4.74020i	−0.384429	−	0.171159i
$768$	1.09369	−	1.34307i	0.0394650	−	0.0484640i
$769$	−0.930722	+	1.61206i	−0.0335627	+	0.0581323i	−0.882319	−	0.470652i	$-0.844019\pi$
$769$	−0.930722	+	1.61206i	−0.0335627	+	0.0581323i	0.848756	+	0.528784i	$0.177352\pi$
$770$	−0.374526	−	1.62129i	−0.0134970	−	0.0584272i
$771$	0.907545	+	0.351221i	0.0326844	+	0.0126489i
$772$	9.12284	−	1.93912i	0.328338	−	0.0697905i
$773$	−41.6558	+	30.2647i	−1.49825	+	1.08855i	−0.527184	+	0.849751i	$0.676752\pi$
$773$	−41.6558	+	30.2647i	−1.49825	+	1.08855i	−0.971070	+	0.238794i	$0.923248\pi$
$774$	16.0083	−	14.2563i	0.575405	−	0.512434i
$775$	2.97626	+	9.16000i	0.106911	+	0.329037i
$776$	−3.97204	+	4.41140i	−0.142588	+	0.158360i
$777$	−0.903181	+	0.0448604i	−0.0324014	+	0.00160936i
$778$	−1.62587	−	15.4691i	−0.0582903	−	0.554595i
$779$	−0.0712788	−	0.0791632i	−0.00255383	−	0.00283631i
$780$	−1.17564	−	7.55623i	−0.0420948	−	0.270556i
$781$	−7.00066	−	9.28767i	−0.250503	−	0.332339i
$782$	−1.97382			−0.0705835
$783$	9.31274	+	11.6949i	0.332810	+	0.417943i
$784$	5.45948	−	3.96654i	0.194981	−	0.141662i
$785$	1.01435	−	9.65088i	0.0362036	−	0.344455i
$786$	−18.4379	+	9.33122i	−0.657657	+	0.332834i
$787$	16.7698	+	3.56453i	0.597779	+	0.127062i	0.496857	−	0.867833i	$-0.334487\pi$
$787$	16.7698	+	3.56453i	0.597779	+	0.127062i	0.100922	+	0.994894i	$0.467821\pi$
$788$	19.4122	−	8.64289i	0.691533	−	0.307890i
$789$	10.1234	−	37.3725i	0.360403	−	1.33050i
$790$	1.16554	−	0.247744i	0.0414682	−	0.00881433i
$791$	3.73791			0.132905
$792$	−8.11991	−	5.75039i	−0.288528	−	0.204331i
$793$	17.7974			0.632005
$794$	15.6640	−	3.32948i	0.555894	−	0.118159i
$795$	15.7813	−	4.18243i	0.559706	−	0.148335i
$796$	−19.7956	+	8.81358i	−0.701637	+	0.312389i
$797$	2.95269	+	0.627614i	0.104590	+	0.0222312i	0.259909	−	0.965633i	$-0.416307\pi$
$797$	2.95269	+	0.627614i	0.104590	+	0.0222312i	−0.155319	+	0.987864i	$0.549641\pi$
$798$	0.00866573	−	0.157139i	0.000306763	−	0.00556265i
$799$	0.297492	−	2.83044i	0.0105245	−	0.100134i
$800$	−0.809017	+	0.587785i	−0.0286031	+	0.0207813i
$801$	0.0364513	−	6.67287i	0.00128794	−	0.235774i
$802$	−25.5781			−0.903193
$803$	−9.40134	−	2.87294i	−0.331766	−	0.101384i
$804$	−7.70326	+	6.20322i	−0.271673	+	0.218771i
$805$	−0.258719	−	0.287336i	−0.00911864	−	0.0101273i
$806$	−4.44490	−	42.2904i	−0.156565	−	1.48962i
$807$	17.4782	−	34.0725i	0.615262	−	1.19941i
$808$	2.99391	−	3.32508i	0.105326	−	0.116976i
$809$	−2.12054	−	6.52635i	−0.0745542	−	0.229454i	0.906834	−	0.421488i	$-0.138492\pi$
$809$	−2.12054	−	6.52635i	−0.0745542	−	0.229454i	−0.981388	+	0.192033i	$0.938492\pi$
$810$	−8.99946	−	0.0983241i	−0.316209	−	0.00345476i
$811$	−5.53723	+	4.02303i	−0.194438	+	0.141268i	−0.680745	−	0.732520i	$-0.738344\pi$
$811$	−5.53723	+	4.02303i	−0.194438	+	0.141268i	0.486307	+	0.873788i	$0.338344\pi$
$812$	−1.41193	+	0.300115i	−0.0495490	+	0.0105320i
$813$	−7.57739	−	48.7023i	−0.265751	−	1.70806i
$814$	3.43828	+	0.300360i	0.120512	+	0.0105276i
$815$	−3.24507	+	5.62063i	−0.113670	+	0.196882i
$816$	−1.57845	−	4.14580i	−0.0552566	−	0.145132i
$817$	−1.18218	−	0.526342i	−0.0413594	−	0.0184144i
$818$	−20.5028	−	14.8962i	−0.716865	−	0.520833i
$819$	3.87657	+	5.39739i	0.135458	+	0.188600i
$820$	−0.181762	−	0.559405i	−0.00634740	−	0.0195353i
$821$	−2.40599	+	22.8915i	−0.0839697	+	0.798918i	0.868787	+	0.495185i	$0.164900\pi$
$821$	−2.40599	+	22.8915i	−0.0839697	+	0.798918i	−0.952757	+	0.303733i	$0.901767\pi$
$822$	34.8061	−	9.22445i	1.21400	−	0.321740i
$823$	32.8418	+	36.4745i	1.14479	+	1.27142i	0.957281	+	0.289159i	$0.0933756\pi$
$823$	32.8418	+	36.4745i	1.14479	+	1.27142i	0.187512	+	0.982262i	$0.439958\pi$
$824$	6.67426	−	11.5602i	0.232509	−	0.402717i
$825$	3.68107	+	4.41018i	0.128159	+	0.153543i
$826$	−0.662168	−	1.14691i	−0.0230398	−	0.0399060i
$827$	15.3444	−	47.2253i	0.533578	−	1.64218i	−0.213124	−	0.977025i	$-0.568364\pi$
$827$	15.3444	−	47.2253i	0.533578	−	1.64218i	0.746702	−	0.665158i	$-0.231636\pi$
$828$	−2.29797	−	0.254225i	−0.0798599	−	0.00883493i
$829$	28.7456	+	20.8849i	0.998376	+	0.725362i	0.961739	−	0.273966i	$-0.0883357\pi$
$829$	28.7456	+	20.8849i	0.998376	+	0.725362i	0.0366363	+	0.999329i	$0.488336\pi$
$830$	−2.25862	+	2.50845i	−0.0783978	+	0.0870696i
$831$	−30.4068	−	19.8647i	−1.05480	−	0.689099i
$832$	4.03338	−	1.79577i	0.139832	−	0.0622573i
$833$	−1.80664	−	17.1890i	−0.0625962	−	0.595563i
$834$	−28.6809	−	4.62295i	−0.993139	−	0.160080i
$835$	9.90634	+	17.1583i	0.342823	+	0.593787i
$836$	−0.114534	+	0.589635i	−0.00396123	+	0.0203929i
$837$	−49.9545	−	3.02863i	−1.72668	−	0.104685i
$838$	7.01181	−	21.5801i	0.242219	−	0.745474i
$839$	−6.94779	−	3.09336i	−0.239864	−	0.106795i	0.283284	−	0.959036i	$-0.408576\pi$
$839$	−6.94779	−	3.09336i	−0.239864	−	0.106795i	−0.523149	+	0.852242i	$0.675243\pi$
$840$	0.396625	−	0.773193i	0.0136849	−	0.0266777i
$841$	20.2694	+	4.30840i	0.698946	+	0.148566i
$842$	15.6402	+	3.32443i	0.538997	+	0.114567i
$843$	37.9330	−	1.88411i	1.30648	−	0.0648921i
$844$	−25.2748	−	11.2531i	−0.869994	−	0.387346i
$845$	2.00642	−	6.17513i	0.0690230	−	0.212431i
$846$	0.710905	−	3.25696i	0.0244414	−	0.111977i
$847$	−2.92574	−	4.67946i	−0.100530	−	0.160788i
$848$	4.71295	+	8.16307i	0.161843	+	0.280321i
$849$	1.72531	−	2.11872i	0.0592123	−	0.0727142i
$850$	0.267718	+	2.54716i	0.00918264	+	0.0873670i
$851$	0.732640	−	0.326192i	0.0251146	−	0.0111817i
$852$	0.334447	−	6.06465i	0.0114580	−	0.207771i
$853$	−6.60781	+	7.33872i	−0.226247	+	0.251273i	−0.845571	−	0.533862i	$-0.820740\pi$
$853$	−6.60781	+	7.33872i	−0.226247	+	0.251273i	0.619324	+	0.785135i	$0.287407\pi$
$854$	1.63617	+	1.18875i	0.0559887	+	0.0406782i
$855$	0.218271	+	0.497541i	0.00746471	+	0.0170156i
$856$	−5.00158	+	15.3933i	−0.170950	+	0.526131i
$857$	19.2745	+	33.3845i	0.658406	+	1.14039i	0.981028	+	0.193864i	$0.0621022\pi$
$857$	19.2745	+	33.3845i	0.658406	+	1.14039i	−0.322623	+	0.946528i	$0.604564\pi$
$858$	−11.8488	−	22.4248i	−0.404510	−	0.765571i
$859$	−9.89391	+	17.1367i	−0.337576	+	0.584698i	−0.983976	−	0.178300i	$-0.942940\pi$
$859$	−9.89391	+	17.1367i	−0.337576	+	0.584698i	0.646400	+	0.762998i	$0.276274\pi$
$860$	−4.78119	−	5.31005i	−0.163037	−	0.181071i
$861$	0.360437	+	0.362412i	0.0122837	+	0.0123510i
$862$	2.96792	−	28.2379i	0.101088	−	0.961785i
$863$	7.67217	+	23.6125i	0.261164	+	0.803779i	0.992552	+	0.121819i	$0.0388726\pi$
$863$	7.67217	+	23.6125i	0.261164	+	0.803779i	−0.731389	+	0.681961i	$0.761127\pi$
$864$	−1.30369	−	5.02995i	−0.0443525	−	0.171122i
$865$	10.1392	+	7.36656i	0.344743	+	0.250471i
$866$	20.0608	+	8.93166i	0.681695	+	0.303510i
$867$	17.8527	+	2.87759i	0.606309	+	0.0977282i
$868$	2.41608	−	4.18478i	0.0820072	−	0.142041i
$869$	3.38729	−	2.03589i	0.114906	−	0.0690628i
$870$	3.88129	−	3.12550i	0.131588	−	0.105964i
$871$	−24.6602	+	5.24168i	−0.835579	+	0.177608i
$872$	−2.99396	+	2.17524i	−0.101388	+	0.0736629i
$873$	3.60736	+	17.4392i	0.122091	+	0.590227i
$874$	0.0431296	+	0.132739i	0.00145888	+	0.00448998i
$875$	−0.335710	+	0.372843i	−0.0113491	+	0.0126044i
$876$	−2.78431	−	4.31320i	−0.0940730	−	0.145730i
$877$	−1.24455	−	11.8411i	−0.0420254	−	0.399845i	−0.995233	−	0.0975276i	$-0.968907\pi$
$877$	−1.24455	−	11.8411i	−0.0420254	−	0.399845i	0.953207	−	0.302317i	$-0.0977601\pi$
$878$	−13.0755	−	14.5219i	−0.441278	−	0.490089i
$879$	−25.9619	−	10.0473i	−0.875674	−	0.338887i
$880$	−1.90198	+	2.71707i	−0.0641159	+	0.0915923i
$881$	27.5072			0.926742			0.463371	−	0.886164i	$-0.346640\pi$
$881$	27.5072			0.926742			0.463371	+	0.886164i	$0.346640\pi$
$882$	0.110588	−	20.2446i	0.00372370	−	0.681670i
$883$	34.7423	−	25.2418i	1.16917	−	0.849453i	0.178263	−	0.983983i	$-0.442952\pi$
$883$	34.7423	−	25.2418i	1.16917	−	0.849453i	0.990910	+	0.134530i	$0.0429523\pi$
$884$	1.18199	−	11.2459i	0.0397548	−	0.378241i
$885$	3.82758	+	2.50055i	0.128663	+	0.0840550i
$886$	−13.9723	−	2.96991i	−0.469410	−	0.0997762i
$887$	−42.8248	+	19.0668i	−1.43792	+	0.640201i	−0.969897	−	0.243517i	$-0.921699\pi$
$887$	−42.8248	+	19.0668i	−1.43792	+	0.640201i	−0.468019	+	0.883718i	$0.655032\pi$
$888$	1.27102	+	1.27798i	0.0426526	+	0.0428863i
$889$	−3.15159	+	0.669891i	−0.105701	+	0.0224674i
$890$	−2.22432			−0.0745594
$891$	−28.3266	+	9.41285i	−0.948978	+	0.315342i
$892$	16.0919			0.538796
$893$	−0.196848	+	0.0418414i	−0.00658727	+	0.00140017i
$894$	−7.38051	−	7.42094i	−0.246841	−	0.248193i
$895$	−16.4872	+	7.34057i	−0.551106	+	0.245368i
$896$	0.490747	+	0.104311i	0.0163947	+	0.00348480i
$897$	−4.93380	−	3.22324i	−0.164735	−	0.107621i
$898$	−1.05005	+	9.99059i	−0.0350407	+	0.333390i
$899$	22.4183	−	16.2878i	0.747691	−	0.543229i
$900$	−0.0163876	+	2.99996i	−0.000546253	+	0.0999985i
$901$	24.1416			0.804272
$902$	−1.17423	−	1.55784i	−0.0390977	−	0.0518704i
$903$	5.79073	+	2.24102i	0.192704	+	0.0745765i
$904$	−4.98525	−	5.53668i	−0.165807	−	0.184147i
$905$	2.21914	+	21.1137i	0.0737667	+	0.701843i
$906$	8.67050	+	13.4316i	0.288058	+	0.446234i
$907$	11.0265	−	12.2462i	0.366129	−	0.406627i	−0.531728	−	0.846915i	$-0.678457\pi$
$907$	11.0265	−	12.2462i	0.366129	−	0.406627i	0.897856	+	0.440288i	$0.145124\pi$
$908$	1.81714	+	5.59259i	0.0603040	+	0.185597i
$909$	−2.71904	−	13.1447i	−0.0901847	−	0.435983i
$910$	1.79205	−	1.30200i	0.0594057	−	0.0431608i
$911$	12.9235	−	2.74698i	0.428175	−	0.0910114i	0.0112169	−	0.999937i	$-0.496429\pi$
$911$	12.9235	−	2.74698i	0.428175	−	0.0910114i	0.416958	+	0.908926i	$0.363096\pi$
$912$	−0.244315	+	0.196740i	−0.00809008	+	0.00651471i
$913$	−4.37294	+	10.3057i	−0.144723	+	0.341070i
$914$	−2.48132	+	4.29776i	−0.0820746	+	0.142157i
$915$	−6.89302	−	1.11105i	−0.227876	−	0.0367303i
$916$	19.2507	+	8.57098i	0.636062	+	0.283193i
$917$	−4.84259	−	3.51835i	−0.159916	−	0.116186i
$918$	−12.8262	−	3.54967i	−0.423329	−	0.117157i
$919$	−7.16028	−	22.0371i	−0.236196	−	0.726936i	−0.996961	−	0.0779085i	$-0.975176\pi$
$919$	−7.16028	−	22.0371i	−0.236196	−	0.726936i	0.760765	−	0.649028i	$-0.224824\pi$
$920$	−0.0805561	+	0.766441i	−0.00265586	+	0.0252688i
$921$	29.2806	+	29.4410i	0.964828	+	0.970113i
$922$	−27.6724	−	30.7333i	−0.911340	−	1.01215i
$923$	7.74128	−	13.4083i	0.254807	−	0.441339i
$924$	0.408534	−	2.85300i	0.0134398	−	0.0938570i
$925$	−0.520315	−	0.901211i	−0.0171078	−	0.0296317i
$926$	8.74079	−	26.9014i	0.287240	−	0.884034i
$927$	−16.0879	−	36.6719i	−0.528397	−	1.20446i
$928$	2.32763	+	1.69112i	0.0764080	+	0.0555137i
$929$	−19.8382	+	22.0326i	−0.650870	+	0.722865i	−0.974766	−	0.223228i	$-0.928341\pi$
$929$	−19.8382	+	22.0326i	−0.650870	+	0.722865i	0.323896	+	0.946093i	$0.395007\pi$
$930$	−0.918569	+	16.6567i	−0.0301211	+	0.546196i
$931$	−1.11649	+	0.497091i	−0.0365913	+	0.0162915i
$932$	−1.28157	−	12.1933i	−0.0419792	−	0.399406i
$933$	−5.71429	+	7.01728i	−0.187077	+	0.229736i
$934$	−4.19677	−	7.26901i	−0.137322	−	0.237849i
$935$	3.59094	+	7.69818i	0.117436	+	0.251757i
$936$	2.82457	−	12.9406i	0.0923240	−	0.422975i
$937$	−10.4218	+	32.0750i	−0.340465	+	1.04784i	0.623501	+	0.781822i	$0.285710\pi$
$937$	−10.4218	+	32.0750i	−0.340465	+	1.04784i	−0.963967	+	0.266023i	$0.914290\pi$
$938$	−2.61720	−	1.16525i	−0.0854546	−	0.0380468i
$939$	33.9592	−	1.68673i	1.10822	−	0.0550444i
$940$	−1.08693	−	0.231034i	−0.0354518	−	0.00753551i
$941$	−34.2369	−	7.27727i	−1.11609	−	0.237232i	−0.387289	−	0.921958i	$-0.626589\pi$
$941$	−34.2369	−	7.27727i	−1.11609	−	0.237232i	−0.728801	+	0.684726i	$0.759922\pi$
$942$	7.67150	−	14.9550i	0.249951	−	0.487262i
$943$	−0.414109	−	0.184373i	−0.0134852	−	0.00600402i
$944$	−0.815694	+	2.51045i	−0.0265486	+	0.0817081i
$945$	−1.16446	−	2.33244i	−0.0378800	−	0.0758743i
$946$	−20.7287	−	11.4866i	−0.673948	−	0.373461i
$947$	3.68684	+	6.38580i	0.119806	+	0.207511i	0.919691	−	0.392643i	$-0.128439\pi$
$947$	3.68684	+	6.38580i	0.119806	+	0.207511i	−0.799885	+	0.600154i	$0.795106\pi$
$948$	2.03758	+	0.328429i	0.0661776	+	0.0106669i
$949$	−1.36790	−	13.0147i	−0.0444038	−	0.422474i
$950$	0.165447	−	0.0736618i	0.00536782	−	0.00238991i
$951$	−12.2160	−	7.98071i	−0.396132	−	0.258792i
$952$	0.859818	−	0.954924i	0.0278669	−	0.0309493i
$953$	−25.6323	−	18.6230i	−0.830312	−	0.603257i	0.0893354	−	0.996002i	$-0.471526\pi$
$953$	−25.6323	−	18.6230i	−0.830312	−	0.603257i	−0.919648	+	0.392744i	$0.871526\pi$
$954$	28.1062	+	3.10940i	0.909973	+	0.100671i
$955$	−1.14089	+	3.51129i	−0.0369183	+	0.113623i
$956$	3.21316	+	5.56536i	0.103921	+	0.179997i
$957$	8.79478	−	13.9935i	0.284295	−	0.452344i
$958$	−12.7953	+	22.1621i	−0.413398	+	0.716026i
$959$	6.97909	+	7.75107i	0.225367	+	0.250295i
$960$	−1.67425	+	0.443717i	−0.0540362	+	0.0143209i
$961$	−6.45606	+	61.4253i	−0.208260	+	1.98146i
$962$	1.41977	+	4.36959i	0.0457751	+	0.140881i
$963$	28.3257	+	39.4382i	0.912783	+	1.27088i
$964$	−4.67567	−	3.39707i	−0.150593	−	0.109412i
$965$	−8.52032	−	3.79349i	−0.274279	−	0.122117i
$966$	−0.238289	−	0.625868i	−0.00766683	−	0.0201370i
$967$	−9.61728	+	16.6576i	−0.309271	+	0.535673i	−0.978203	−	0.207650i	$-0.933418\pi$
$967$	−9.61728	+	16.6576i	−0.309271	+	0.535673i	0.668932	+	0.743324i	$0.266752\pi$
$968$	−3.02926	+	10.5747i	−0.0973641	+	0.339883i
$969$	0.123512	+	0.793850i	0.00396777	+	0.0255021i
$970$	5.80640	−	1.23419i	0.186432	−	0.0396274i
$971$	−25.3262	+	18.4006i	−0.812757	+	0.590503i	−0.914629	−	0.404295i	$-0.867517\pi$
$971$	−25.3262	+	18.4006i	−0.812757	+	0.590503i	0.101871	+	0.994798i	$0.467517\pi$
$972$	−14.4754	−	5.78462i	−0.464300	−	0.185542i
$973$	−2.60038	−	8.00316i	−0.0833645	−	0.256570i
$974$	−6.11631	+	6.79285i	−0.195979	+	0.217657i
$975$	−3.49033	+	6.80414i	−0.111780	+	0.217907i
$976$	−0.421360	−	4.00897i	−0.0134874	−	0.128324i
$977$	−36.7054	−	40.7655i	−1.17431	−	1.30420i	−0.943564	−	0.331191i	$-0.892549\pi$
$977$	−36.7054	−	40.7655i	−1.17431	−	1.30420i	−0.230748	−	0.973014i	$-0.574117\pi$
$978$	−8.75538	+	7.05046i	−0.279966	+	0.225449i
$979$	−6.97501	+	2.40270i	−0.222922	+	0.0767907i
$980$	−6.74829			−0.215566
$981$	−0.0606462	+	11.1020i	−0.00193628	+	0.354461i
$982$	23.8809	−	17.3505i	0.762069	−	0.553676i
$983$	5.56442	−	52.9419i	0.177477	−	1.68859i	−0.436850	−	0.899534i	$-0.643906\pi$
$983$	5.56442	−	52.9419i	0.177477	−	1.68859i	0.614327	−	0.789051i	$-0.289427\pi$
$984$	0.0560975	−	1.01724i	0.00178832	−	0.0324283i
$985$	−20.7850	−	4.41799i	−0.662265	−	0.140769i
$986$	6.73175	−	2.99717i	0.214383	−	0.0954493i
$987$	0.933408	−	0.247375i	0.0297107	−	0.00787404i
$988$	−0.782118	+	0.166244i	−0.0248825	+	0.00528893i
$989$	−5.50668			−0.175102
$990$	3.18915	+	9.42493i	0.101358	+	0.299544i
$991$	47.8721			1.52071			0.760354	−	0.649509i	$-0.225025\pi$
$991$	47.8721			1.52071			0.760354	+	0.649509i	$0.225025\pi$
$992$	−9.42092	+	2.00248i	−0.299115	+	0.0635788i
$993$	14.4986	−	53.5242i	0.460098	−	1.69854i
$994$	1.60727	−	0.715601i	0.0509794	−	0.0226975i
$995$	21.1955	+	4.50524i	0.671942	+	0.142826i
$996$	−5.21646	+	2.64000i	−0.165290	+	0.0836516i
$997$	4.80472	−	45.7139i	0.152167	−	1.44777i	−0.605871	−	0.795563i	$-0.707175\pi$
$997$	4.80472	−	45.7139i	0.152167	−	1.44777i	0.758038	−	0.652211i	$-0.226158\pi$
$998$	−4.44455	+	3.22916i	−0.140690	+	0.102217i
$999$	5.34745	−	0.802095i	0.169186	−	0.0253771i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	990.2.bg.a.31.9	✓	88
9.7	even	3	inner	990.2.bg.a.691.4	yes	88
11.5	even	5	inner	990.2.bg.a.841.4	yes	88
99.16	even	15	inner	990.2.bg.a.511.9	yes	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.bg.a.31.9	✓	88	1.1	even	1	trivial
990.2.bg.a.511.9	yes	88	99.16	even	15	inner
990.2.bg.a.691.4	yes	88	9.7	even	3	inner
990.2.bg.a.841.4	yes	88	11.5	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 990 = 2 \cdot 3^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	990.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.978148 + 0.207912i) q^{2} +(1.22140 + 1.22809i) q^{3} +(0.913545 - 0.406737i) q^{4} +(-0.978148 - 0.207912i) q^{5} +(-1.45004 - 0.947306i) q^{6} +(0.0524430 - 0.498962i) q^{7} +(-0.809017 + 0.587785i) q^{8} +(-0.0163876 + 2.99996i) q^{9} +1.00000 q^{10} +(3.13579 - 1.08020i) q^{11} +(1.61531 + 0.625126i) q^{12} +(2.95426 + 3.28104i) q^{13} +(0.0524430 + 0.498962i) q^{14} +(-0.939371 - 1.45519i) q^{15} +(0.669131 - 0.743145i) q^{16} +(-0.791452 - 2.43584i) q^{17} +(-0.607696 - 2.93781i) q^{18} +(-0.146517 + 0.106451i) q^{19} +(-0.978148 + 0.207912i) q^{20} +(0.676821 - 0.545025i) q^{21} +(-2.84268 + 1.70856i) q^{22} +(-0.385331 + 0.667413i) q^{23} +(-1.70998 - 0.275624i) q^{24} +(0.913545 + 0.406737i) q^{25} +(-3.57187 - 2.59512i) q^{26} +(-3.70422 + 3.64401i) q^{27} +(-0.155037 - 0.477155i) q^{28} +(0.300739 - 2.86134i) q^{29} +(1.22140 + 1.22809i) q^{30} +(6.44466 + 7.15752i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(5.15661 + 2.53167i) q^{33} +(1.28060 + 2.21806i) q^{34} +(-0.155037 + 0.477155i) q^{35} +(1.20522 + 2.74726i) q^{36} +(-0.841887 - 0.611667i) q^{37} +(0.121183 - 0.134587i) q^{38} +(-0.421077 + 7.63554i) q^{39} +(0.913545 - 0.406737i) q^{40} +(0.0614830 + 0.584972i) q^{41} +(-0.548714 + 0.673834i) q^{42} +(3.57269 + 6.18808i) q^{43} +(2.42533 - 2.26225i) q^{44} +(0.639755 - 2.93099i) q^{45} +(0.238148 - 0.732943i) q^{46} +(1.01514 + 0.451972i) q^{47} +(1.72992 - 0.0859240i) q^{48} +(6.60082 + 1.40305i) q^{49} +(-0.978148 - 0.207912i) q^{50} +(2.02474 - 3.94709i) q^{51} +(4.03338 + 1.79577i) q^{52} +(-2.91276 + 8.96457i) q^{53} +(2.86564 - 4.33453i) q^{54} +(-3.29185 + 0.404623i) q^{55} +(0.250855 + 0.434494i) q^{56} +(-0.309685 - 0.0499167i) q^{57} +(0.300739 + 2.86134i) q^{58} +(-2.41143 + 1.07364i) q^{59} +(-1.45004 - 0.947306i) q^{60} +(2.69730 - 2.99566i) q^{61} +(-7.79196 - 5.66119i) q^{62} +(1.49600 + 0.165503i) q^{63} +(0.309017 - 0.951057i) q^{64} +(-2.20754 - 3.82357i) q^{65} +(-5.57029 - 1.40423i) q^{66} +(-2.85511 + 4.94520i) q^{67} +(-1.71377 - 1.90334i) q^{68} +(-1.29028 + 0.341956i) q^{69} +(0.0524430 - 0.498962i) q^{70} +(-1.08364 - 3.33511i) q^{71} +(-1.75007 - 2.43665i) q^{72} +(-2.39794 - 1.74220i) q^{73} +(0.950662 + 0.423262i) q^{74} +(0.616293 + 1.61870i) q^{75} +(-0.0905523 + 0.156841i) q^{76} +(-0.374526 - 1.62129i) q^{77} +(-1.17564 - 7.55623i) q^{78} +(1.16554 - 0.247744i) q^{79} +(-0.809017 + 0.587785i) q^{80} +(-8.99946 - 0.0983241i) q^{81} +(-0.181762 - 0.559405i) q^{82} +(-2.25862 + 2.50845i) q^{83} +(0.396625 - 0.773193i) q^{84} +(0.267718 + 2.54716i) q^{85} +(-4.78119 - 5.31005i) q^{86} +(3.88129 - 3.12550i) q^{87} +(-1.90198 + 2.71707i) q^{88} -2.22432 q^{89} +(-0.0163876 + 2.99996i) q^{90} +(1.79205 - 1.30200i) q^{91} +(-0.0805561 + 0.766441i) q^{92} +(-0.918569 + 16.6567i) q^{93} +(-1.08693 - 0.231034i) q^{94} +(0.165447 - 0.0736618i) q^{95} +(-1.67425 + 0.443717i) q^{96} +(5.80640 - 1.23419i) q^{97} -6.74829 q^{98} +(3.18915 + 9.42493i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 11 q^{2} - 8 q^{3} + 11 q^{4} + 11 q^{5} + q^{6} - 2 q^{7} - 22 q^{8} + 6 q^{9} + 88 q^{10} + 3 q^{11} + 2 q^{12} + 2 q^{13} - 2 q^{14} + 7 q^{15} + 11 q^{16} + 18 q^{17} - 6 q^{18} + 12 q^{19}+ \cdots - 128 q^{99}+O(q^{100}) \) 88 * q + 11 * q^2 - 8 * q^3 + 11 * q^4 + 11 * q^5 + q^6 - 2 * q^7 - 22 * q^8 + 6 * q^9 + 88 * q^10 + 3 * q^11 + 2 * q^12 + 2 * q^13 - 2 * q^14 + 7 * q^15 + 11 * q^16 + 18 * q^17 - 6 * q^18 + 12 * q^19 + 11 * q^20 + 36 * q^21 + 3 * q^22 + 46 * q^23 + 7 * q^24 + 11 * q^25 + 26 * q^26 + 16 * q^27 + 4 * q^28 - 9 * q^29 - 8 * q^30 - 20 * q^31 - 44 * q^32 + 35 * q^33 + 26 * q^34 + 4 * q^35 + 15 * q^36 + 4 * q^37 + 4 * q^38 - 33 * q^39 + 11 * q^40 + 22 * q^41 - 29 * q^42 - 2 * q^43 + 14 * q^44 + 8 * q^46 - 16 * q^47 + q^48 - 5 * q^49 + 11 * q^50 - 13 * q^51 - 13 * q^52 + 64 * q^53 - 4 * q^54 + 4 * q^55 + 8 * q^56 - 25 * q^57 - 9 * q^58 - 27 * q^59 + q^60 + 4 * q^61 + q^63 - 22 * q^64 + 22 * q^65 + 40 * q^66 - 6 * q^67 - 9 * q^68 - 54 * q^69 - 2 * q^70 + 52 * q^71 + 6 * q^72 - 22 * q^73 - 2 * q^74 + q^75 + 4 * q^76 + 12 * q^77 - 32 * q^78 + 2 * q^79 - 22 * q^80 - 30 * q^81 + 36 * q^82 + 33 * q^83 + 8 * q^84 - 4 * q^85 - 17 * q^86 - 192 * q^87 + 3 * q^88 - 76 * q^89 + 6 * q^90 - 24 * q^91 - 19 * q^92 - 28 * q^93 - q^94 - 6 * q^95 + 7 * q^96 - 38 * q^97 - 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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