LMFDB - Embedded newform 978.2.m.a.61.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [978,2,Mod(25,978)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("978.25"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(978, base_ring=CyclotomicField(54)) chi = DirichletCharacter(H, H._module([0, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 978 = 2 \cdot 3 \cdot 163 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	978.m (of order $27$, degree $18$, minimal)

Newform invariants

comment:select newform

sage:traces = [108,0,0,0,0,0,-18] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.80936931768$
Analytic rank:	$0$
Dimension:	$108$
Relative dimension:	$6$ over $\Q(\zeta_{27})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{27}]$

Embedding invariants

Embedding label			61.4
Character	$\chi$	$=$	978.61
Dual form			978.2.m.a.481.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0581448 - 0.998308i) q^{2} +(0.396080 - 0.918216i) q^{3} +(-0.993238 + 0.116093i) q^{4} +(0.577692 + 0.484741i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(-0.741048 - 0.372168i) q^{7} +(0.173648 + 0.984808i) q^{8} +(-0.686242 - 0.727374i) q^{9} +(0.450331 - 0.604899i) q^{10} +(0.886297 - 2.05467i) q^{11} +(-0.286803 + 0.957990i) q^{12} +(-0.00821219 + 0.0465737i) q^{13} +(-0.328450 + 0.761434i) q^{14} +(0.673909 - 0.338450i) q^{15} +(0.973045 - 0.230616i) q^{16} +(-0.601596 - 3.41182i) q^{17} +(-0.686242 + 0.727374i) q^{18} +(-3.64090 - 2.39466i) q^{19} +(-0.630060 - 0.414397i) q^{20} +(-0.635245 + 0.533034i) q^{21} +(-2.10273 - 0.765330i) q^{22} +(0.383881 + 0.664901i) q^{23} +(0.973045 + 0.230616i) q^{24} +(-0.769487 - 4.36398i) q^{25} +(0.0469724 + 0.00549028i) q^{26} +(-0.939693 + 0.342020i) q^{27} +(0.779243 + 0.283621i) q^{28} +(0.256728 - 4.40784i) q^{29} +(-0.377061 - 0.653090i) q^{30} +(2.81618 + 2.36306i) q^{31} +(-0.286803 - 0.957990i) q^{32} +(-1.53559 - 1.62763i) q^{33} +(-3.37107 + 0.798958i) q^{34} +(-0.247692 - 0.574215i) q^{35} +(0.766044 + 0.642788i) q^{36} +(4.15569 - 1.51255i) q^{37} +(-2.17891 + 3.77398i) q^{38} +(0.0395120 + 0.0259874i) q^{39} +(-0.377061 + 0.653090i) q^{40} +(-11.5659 - 1.35186i) q^{41} +(0.569068 + 0.603177i) q^{42} +(-5.88050 - 7.89888i) q^{43} +(-0.641772 + 2.14367i) q^{44} +(-0.0438483 - 0.752847i) q^{45} +(0.641456 - 0.421892i) q^{46} +(0.201239 + 3.45514i) q^{47} +(0.173648 - 0.984808i) q^{48} +(-3.76947 - 5.06327i) q^{49} +(-4.31185 + 1.02193i) q^{50} +(-3.37107 - 0.798958i) q^{51} +(0.00274979 - 0.0472121i) q^{52} +(1.14744 + 1.98742i) q^{53} +(0.396080 + 0.918216i) q^{54} +(1.50799 - 0.757340i) q^{55} +(0.237833 - 0.794416i) q^{56} +(-3.64090 + 2.39466i) q^{57} -4.41531 q^{58} +8.34071 q^{59} +(-0.630060 + 0.414397i) q^{60} +(0.0540789 - 0.306697i) q^{61} +(2.19531 - 2.94882i) q^{62} +(0.237833 + 0.794416i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(-0.0273203 + 0.0229244i) q^{65} +(-1.53559 + 1.62763i) q^{66} +(6.44753 + 0.753608i) q^{67} +(0.993617 + 3.31891i) q^{68} +(0.762570 - 0.0891317i) q^{69} +(-0.558841 + 0.280661i) q^{70} +(7.09115 + 9.52507i) q^{71} +(0.597159 - 0.802123i) q^{72} +(-9.14822 + 1.06927i) q^{73} +(-1.75162 - 4.06071i) q^{74} +(-4.31185 - 1.02193i) q^{75} +(3.89429 + 1.95579i) q^{76} +(-1.42147 + 1.19276i) q^{77} +(0.0236461 - 0.0409562i) q^{78} +(2.99357 - 3.17300i) q^{79} +(0.673909 + 0.338450i) q^{80} +(-0.0581448 + 0.998308i) q^{81} +(-0.677076 + 11.6249i) q^{82} +(-2.13123 - 1.07035i) q^{83} +(0.569068 - 0.603177i) q^{84} +(1.30631 - 2.26260i) q^{85} +(-7.54360 + 6.32983i) q^{86} +(-3.94567 - 1.98159i) q^{87} +(2.17736 + 0.516043i) q^{88} +(1.49746 + 3.47149i) q^{89} +(-0.749024 + 0.0875483i) q^{90} +(0.0234189 - 0.0314570i) q^{91} +(-0.458476 - 0.615840i) q^{92} +(3.28523 - 1.64990i) q^{93} +(3.43759 - 0.401797i) q^{94} +(-0.942530 - 3.14827i) q^{95} +(-0.993238 - 0.116093i) q^{96} +(9.01158 - 9.55172i) q^{97} +(-4.83553 + 4.05749i) q^{98} +(-2.10273 + 0.765330i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 108 q - 18 q^{7} + 18 q^{11} + 9 q^{13} + 18 q^{14} + 27 q^{17} - 9 q^{19} - 18 q^{22} + 9 q^{23} - 36 q^{25} - 18 q^{29} + 9 q^{30} + 45 q^{31} + 36 q^{34} - 27 q^{37} + 27 q^{39} + 9 q^{40} + 36 q^{41}+ \cdots - 18 q^{99}+O(q^{100}) $ 108 * q - 18 * q^7 + 18 * q^11 + 9 * q^13 + 18 * q^14 + 27 * q^17 - 9 * q^19 - 18 * q^22 + 9 * q^23 - 36 * q^25 - 18 * q^29 + 9 * q^30 + 45 * q^31 + 36 * q^34 - 27 * q^37 + 27 * q^39 + 9 * q^40 + 36 * q^41 + 9 * q^42 + 81 * q^43 + 9 * q^46 - 9 * q^47 + 36 * q^49 + 18 * q^50 + 36 * q^51 + 27 * q^52 + 27 * q^53 + 63 * q^55 - 18 * q^56 - 9 * q^57 - 54 * q^58 - 36 * q^59 + 18 * q^61 - 9 * q^62 - 18 * q^63 + 63 * q^65 + 45 * q^67 + 9 * q^68 - 36 * q^69 - 45 * q^70 + 9 * q^71 - 18 * q^74 + 18 * q^75 - 9 * q^76 - 54 * q^77 + 18 * q^78 + 27 * q^79 + 18 * q^82 + 9 * q^83 + 9 * q^84 - 27 * q^86 + 9 * q^87 - 27 * q^89 - 117 * q^91 + 18 * q^92 + 9 * q^93 + 27 * q^94 - 54 * q^95 - 90 * q^97 - 18 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/978\mathbb{Z}\right)^\times$.

$n$	$653$	$817$
$\chi(n)$	$1$	$e\left(\frac{13}{27}\right)$

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 $

$2$	−0.0581448	−	0.998308i	−0.0411146	−	0.705910i
$2$	−0.0581448	−	0.998308i	−0.0411146	−	0.705910i
$3$	0.396080	−	0.918216i	0.228677	−	0.530132i
$3$	0.396080	−	0.918216i	0.228677	−	0.530132i
$4$	−0.993238	+	0.116093i	−0.496619	+	0.0580465i
$5$	0.577692	+	0.484741i	0.258352	+	0.216783i	0.762759	−	0.646683i	$-0.223844\pi$
$5$	0.577692	+	0.484741i	0.258352	+	0.216783i	−0.504407	+	0.863466i	$0.668289\pi$
$6$	−0.939693	−	0.342020i	−0.383628	−	0.139629i
$7$	−0.741048	−	0.372168i	−0.280090	−	0.140666i	0.303209	−	0.952924i	$-0.401942\pi$
$7$	−0.741048	−	0.372168i	−0.280090	−	0.140666i	−0.583299	+	0.812258i	$0.698238\pi$
$8$	0.173648	+	0.984808i	0.0613939	+	0.348182i
$9$	−0.686242	−	0.727374i	−0.228747	−	0.242458i
$10$	0.450331	−	0.604899i	0.142407	−	0.191286i
$11$	0.886297	−	2.05467i	0.267229	−	0.619506i	−0.730778	−	0.682615i	$-0.760842\pi$
$11$	0.886297	−	2.05467i	0.267229	−	0.619506i	0.998007	+	0.0631095i	$0.0201017\pi$
$12$	−0.286803	+	0.957990i	−0.0827930	+	0.276548i
$13$	−0.00821219	+	0.0465737i	−0.00227765	+	0.0129172i	−0.985925	−	0.167186i	$-0.946532\pi$
$13$	−0.00821219	+	0.0465737i	−0.00227765	+	0.0129172i	0.983648	+	0.180103i	$0.0576431\pi$
$14$	−0.328450	+	0.761434i	−0.0877821	+	0.203502i
$15$	0.673909	−	0.338450i	0.174002	−	0.0873873i
$16$	0.973045	−	0.230616i	0.243261	−	0.0576540i
$17$	−0.601596	−	3.41182i	−0.145908	−	0.827488i	−0.966633	−	0.256164i	$-0.917541\pi$
$17$	−0.601596	−	3.41182i	−0.145908	−	0.827488i	0.820725	−	0.571324i	$-0.193570\pi$
$18$	−0.686242	+	0.727374i	−0.161749	+	0.171444i
$19$	−3.64090	−	2.39466i	−0.835281	−	0.549373i	0.0582876	−	0.998300i	$-0.481436\pi$
$19$	−3.64090	−	2.39466i	−0.835281	−	0.549373i	−0.893568	+	0.448927i	$0.851806\pi$
$20$	−0.630060	−	0.414397i	−0.140886	−	0.0926620i
$21$	−0.635245	+	0.533034i	−0.138622	+	0.116318i
$22$	−2.10273	−	0.765330i	−0.448303	−	0.163169i
$23$	0.383881	+	0.664901i	0.0800447	+	0.138641i	0.903269	−	0.429075i	$-0.141160\pi$
$23$	0.383881	+	0.664901i	0.0800447	+	0.138641i	−0.823224	+	0.567716i	$0.807827\pi$
$24$	0.973045	+	0.230616i	0.198622	+	0.0470743i
$25$	−0.769487	−	4.36398i	−0.153897	−	0.872795i
$26$	0.0469724	+	0.00549028i	0.00921204	+	0.00107673i
$27$	−0.939693	+	0.342020i	−0.180844	+	0.0658218i
$28$	0.779243	+	0.283621i	0.147263	+	0.0535994i
$29$	0.256728	−	4.40784i	0.0476731	−	0.818516i	−0.886728	−	0.462292i	$-0.847027\pi$
$29$	0.256728	−	4.40784i	0.0476731	−	0.818516i	0.934401	−	0.356224i	$-0.115936\pi$
$30$	−0.377061	−	0.653090i	−0.0688417	−	0.119237i
$31$	2.81618	+	2.36306i	0.505801	+	0.424418i	0.859649	−	0.510886i	$-0.170682\pi$
$31$	2.81618	+	2.36306i	0.505801	+	0.424418i	−0.353848	+	0.935303i	$0.615127\pi$
$32$	−0.286803	−	0.957990i	−0.0507001	−	0.169350i
$33$	−1.53559	−	1.62763i	−0.267311	−	0.283333i
$34$	−3.37107	+	0.798958i	−0.578134	+	0.137020i
$35$	−0.247692	−	0.574215i	−0.0418676	−	0.0970600i
$36$	0.766044	+	0.642788i	0.127674	+	0.107131i
$37$	4.15569	−	1.51255i	0.683192	−	0.248661i	0.0229743	−	0.999736i	$-0.492686\pi$
$37$	4.15569	−	1.51255i	0.683192	−	0.248661i	0.660217	+	0.751075i	$0.270464\pi$
$38$	−2.17891	+	3.77398i	−0.353466	+	0.612221i
$39$	0.0395120	+	0.0259874i	0.00632698	+	0.00416132i
$40$	−0.377061	+	0.653090i	−0.0596186	+	0.103263i
$41$	−11.5659	−	1.35186i	−1.80629	−	0.211125i	−0.854833	−	0.518904i	$-0.826340\pi$
$41$	−11.5659	−	1.35186i	−1.80629	−	0.211125i	−0.951458	+	0.307779i	$0.900414\pi$
$42$	0.569068	+	0.603177i	0.0878091	+	0.0930722i
$43$	−5.88050	−	7.89888i	−0.896768	−	1.20457i	−0.978153	−	0.207886i	$-0.933342\pi$
$43$	−5.88050	−	7.89888i	−0.896768	−	1.20457i	0.0813851	−	0.996683i	$-0.474066\pi$
$44$	−0.641772	+	2.14367i	−0.0967508	+	0.323170i
$45$	−0.0438483	−	0.752847i	−0.00653653	−	0.112228i
$46$	0.641456	−	0.421892i	0.0945775	−	0.0622046i
$47$	0.201239	+	3.45514i	0.0293537	+	0.503983i	0.980658	+	0.195730i	$0.0627075\pi$
$47$	0.201239	+	3.45514i	0.0293537	+	0.503983i	−0.951304	+	0.308254i	$0.900255\pi$
$48$	0.173648	−	0.984808i	0.0250640	−	0.142145i
$49$	−3.76947	−	5.06327i	−0.538495	−	0.723325i
$50$	−4.31185	+	1.02193i	−0.609788	+	0.144522i
$51$	−3.37107	−	0.798958i	−0.472044	−	0.111876i
$52$	0.00274979	−	0.0472121i	0.000381328	−	0.00654714i
$53$	1.14744	+	1.98742i	0.157613	+	0.272993i	0.934007	−	0.357254i	$-0.116287\pi$
$53$	1.14744	+	1.98742i	0.157613	+	0.272993i	−0.776395	+	0.630247i	$0.782954\pi$
$54$	0.396080	+	0.918216i	0.0538996	+	0.124953i
$55$	1.50799	−	0.757340i	0.203337	−	0.102120i
$56$	0.237833	−	0.794416i	0.0317817	−	0.106158i
$57$	−3.64090	+	2.39466i	−0.482250	+	0.317181i
$58$	−4.41531			−0.579759
$59$	8.34071			1.08587			0.542934	−	0.839776i	$-0.317313\pi$
$59$	8.34071			1.08587			0.542934	+	0.839776i	$0.317313\pi$
$60$	−0.630060	+	0.414397i	−0.0813405	+	0.0534985i
$61$	0.0540789	−	0.306697i	0.00692410	−	0.0392685i	−0.981150	−	0.193248i	$-0.938098\pi$
$61$	0.0540789	−	0.306697i	0.00692410	−	0.0392685i	0.988074	+	0.153979i	$0.0492089\pi$
$62$	2.19531	−	2.94882i	0.278805	−	0.374500i
$63$	0.237833	+	0.794416i	0.0299641	+	0.100087i
$64$	−0.939693	+	0.342020i	−0.117462	+	0.0427525i
$65$	−0.0273203	+	0.0229244i	−0.00338866	+	0.00284342i
$66$	−1.53559	+	1.62763i	−0.189017	+	0.200347i
$67$	6.44753	+	0.753608i	0.787691	+	0.0920679i	0.500421	−	0.865782i	$-0.333178\pi$
$67$	6.44753	+	0.753608i	0.787691	+	0.0920679i	0.287269	+	0.957850i	$0.407252\pi$
$68$	0.993617	+	3.31891i	0.120494	+	0.402477i
$69$	0.762570	−	0.0891317i	0.0918027	−	0.0107302i
$70$	−0.558841	+	0.280661i	−0.0667943	+	0.0335454i
$71$	7.09115	+	9.52507i	0.841565	+	1.13042i	0.989940	+	0.141486i	$0.0451882\pi$
$71$	7.09115	+	9.52507i	0.841565	+	1.13042i	−0.148376	+	0.988931i	$0.547404\pi$
$72$	0.597159	−	0.802123i	0.0703758	−	0.0945311i
$73$	−9.14822	+	1.06927i	−1.07072	+	0.125149i	−0.633145	−	0.774034i	$-0.718236\pi$
$73$	−9.14822	+	1.06927i	−1.07072	+	0.125149i	−0.437574	+	0.899183i	$0.644162\pi$
$74$	−1.75162	−	4.06071i	−0.203622	−	0.472049i
$75$	−4.31185	−	1.02193i	−0.497890	−	0.118002i
$76$	3.89429	+	1.95579i	0.446706	+	0.224344i
$77$	−1.42147	+	1.19276i	−0.161992	+	0.135927i
$78$	0.0236461	−	0.0409562i	0.00267739	−	0.00463737i
$79$	2.99357	−	3.17300i	0.336803	−	0.356991i	−0.536731	−	0.843754i	$-0.680341\pi$
$79$	2.99357	−	3.17300i	0.336803	−	0.356991i	0.873534	+	0.486763i	$0.161822\pi$
$80$	0.673909	+	0.338450i	0.0753453	+	0.0378398i
$81$	−0.0581448	+	0.998308i	−0.00646054	+	0.110923i
$82$	−0.677076	+	11.6249i	−0.0747705	+	1.28376i
$83$	−2.13123	−	1.07035i	−0.233933	−	0.117486i	0.327972	−	0.944688i	$-0.393635\pi$
$83$	−2.13123	−	1.07035i	−0.233933	−	0.117486i	−0.561905	+	0.827202i	$0.689931\pi$
$84$	0.569068	−	0.603177i	0.0620904	−	0.0658120i
$85$	1.30631	−	2.26260i	0.141689	−	0.245413i
$86$	−7.54360	+	6.32983i	−0.813447	+	0.682563i
$87$	−3.94567	−	1.98159i	−0.423020	−	0.212449i
$88$	2.17736	+	0.516043i	0.232107	+	0.0550104i
$89$	1.49746	+	3.47149i	0.158730	+	0.367978i	0.978959	−	0.204058i	$-0.0654131\pi$
$89$	1.49746	+	3.47149i	0.158730	+	0.367978i	−0.820229	+	0.572036i	$0.806154\pi$
$90$	−0.749024	+	0.0875483i	−0.0789540	+	0.00922840i
$91$	0.0234189	−	0.0314570i	0.00245496	−	0.00329759i
$92$	−0.458476	−	0.615840i	−0.0477994	−	0.0642057i
$93$	3.28523	−	1.64990i	0.340662	−	0.171087i
$94$	3.43759	−	0.401797i	0.354560	−	0.0414422i
$95$	−0.942530	−	3.14827i	−0.0967016	−	0.323006i
$96$	−0.993238	−	0.116093i	−0.101372	−	0.0118487i
$97$	9.01158	−	9.55172i	0.914988	−	0.969830i	−0.0846590	−	0.996410i	$-0.526980\pi$
$97$	9.01158	−	9.55172i	0.914988	−	0.969830i	0.999647	+	0.0265797i	$0.00846158\pi$
$98$	−4.83553	+	4.05749i	−0.488463	+	0.409869i
$99$	−2.10273	+	0.765330i	−0.211332	+	0.0769185i
$100$	1.27091	+	4.24514i	0.127091	+	0.424514i
$101$	−9.40963	+	12.6393i	−0.936293	+	1.25766i	0.0298240	+	0.999555i	$0.490505\pi$
$101$	−9.40963	+	12.6393i	−0.936293	+	1.25766i	−0.966117	+	0.258105i	$0.916902\pi$
$102$	−0.601596	+	3.41182i	−0.0595669	+	0.337821i
$103$	−0.269701	+	0.177385i	−0.0265744	+	0.0174782i	−0.562727	−	0.826643i	$-0.690248\pi$
$103$	−0.269701	+	0.177385i	−0.0265744	+	0.0174782i	0.536152	+	0.844121i	$0.319877\pi$
$104$	−0.0472921			−0.00463737
$105$	−0.625359			−0.0610288
$106$	1.91734	−	1.26105i	0.186228	−	0.122484i
$107$	−4.74541	+	15.8508i	−0.458756	+	1.53235i	0.345703	+	0.938344i	$0.387641\pi$
$107$	−4.74541	+	15.8508i	−0.458756	+	1.53235i	−0.804459	+	0.594008i	$0.797545\pi$
$108$	0.893633	−	0.448799i	0.0859898	−	0.0431857i
$109$	−7.34123	−	17.0189i	−0.703162	−	1.63011i	−0.774433	−	0.632656i	$-0.781965\pi$
$109$	−7.34123	−	17.0189i	−0.703162	−	1.63011i	0.0712712	−	0.997457i	$-0.477294\pi$
$110$	−0.843741	−	1.46140i	−0.0804475	−	0.139339i
$111$	0.257139	−	4.41491i	0.0244066	−	0.419045i
$112$	−0.806901	−	0.191239i	−0.0762450	−	0.0180704i
$113$	12.7970	−	3.03296i	1.20385	−	0.285317i	0.420726	−	0.907188i	$-0.361775\pi$
$113$	12.7970	−	3.03296i	1.20385	−	0.285317i	0.783119	+	0.621871i	$0.213627\pi$
$114$	2.60231	+	3.49551i	0.243729	+	0.327384i
$115$	−0.100540	+	0.570191i	−0.00937540	+	0.0531705i
$116$	0.256728	+	4.40784i	0.0238366	+	0.409258i
$117$	0.0395120	−	0.0259874i	0.00365289	−	0.00240254i
$118$	−0.484969	−	8.32659i	−0.0446450	−	0.766525i
$119$	−0.823960	+	2.75222i	−0.0755323	+	0.252295i
$120$	0.450331	+	0.604899i	0.0411094	+	0.0552195i
$121$	4.11252	+	4.35902i	0.373865	+	0.396274i
$122$	−0.309322	−	0.0361546i	−0.0280047	−	0.00327328i
$123$	−5.82232	+	10.0846i	−0.524981	+	0.909294i
$124$	−3.07147	−	2.02014i	−0.275826	−	0.181414i
$125$	3.55618	−	6.15948i	0.318074	−	0.550921i
$126$	0.779243	−	0.283621i	0.0694205	−	0.0252670i
$127$	2.33732	+	1.96125i	0.207404	+	0.174033i	0.740573	−	0.671976i	$-0.234554\pi$
$127$	2.33732	+	1.96125i	0.207404	+	0.174033i	−0.533169	+	0.846009i	$0.678999\pi$
$128$	0.396080	+	0.918216i	0.0350088	+	0.0811596i
$129$	−9.58203	+	2.27098i	−0.843651	+	0.199949i
$130$	0.0244742	+	0.0259411i	0.00214653	+	0.00227519i
$131$	3.99062	+	13.3296i	0.348662	+	1.16461i	0.935030	+	0.354567i	$0.115372\pi$
$131$	3.99062	+	13.3296i	0.348662	+	1.16461i	−0.586369	+	0.810044i	$0.699443\pi$
$132$	1.71416	+	1.43835i	0.149198	+	0.125192i
$133$	1.80687	+	3.12959i	0.156675	+	0.271370i
$134$	0.377443	−	6.48044i	0.0326061	−	0.559825i
$135$	−0.708644	−	0.257925i	−0.0609903	−	0.0221987i
$136$	3.25552	−	1.18491i	0.279159	−	0.101605i
$137$	−1.70452	−	0.199230i	−0.145627	−	0.0170214i	0.0429669	−	0.999076i	$-0.486319\pi$
$137$	−1.70452	−	0.199230i	−0.145627	−	0.0170214i	−0.188594	+	0.982055i	$0.560393\pi$
$138$	−0.133320	−	0.756098i	−0.0113490	−	0.0643633i
$139$	6.00657	+	1.42358i	0.509471	+	0.120747i	0.477308	−	0.878736i	$-0.341612\pi$
$139$	6.00657	+	1.42358i	0.509471	+	0.120747i	0.0321625	+	0.999483i	$0.489761\pi$
$140$	0.312679	+	0.541577i	0.0264262	+	0.0457716i
$141$	3.25227	+	1.18373i	0.273890	+	0.0996880i
$142$	9.09664	−	7.63299i	0.763373	−	0.640546i
$143$	0.0884150	+	0.0581514i	0.00739363	+	0.00486287i
$144$	−0.835488	−	0.549509i	−0.0696240	−	0.0457924i
$145$	2.28497	−	2.42193i	0.189756	−	0.201130i
$146$	1.59939	+	9.07057i	0.132366	+	0.750686i
$147$	−6.14219	+	1.45573i	−0.506599	+	0.120066i
$148$	−3.95200	+	1.98477i	−0.324852	+	0.163147i
$149$	1.70727	−	3.95789i	0.139865	−	0.324243i	−0.833858	−	0.551979i	$-0.813873\pi$
$149$	1.70727	−	3.95789i	0.139865	−	0.324243i	0.973723	+	0.227736i	$0.0731322\pi$
$150$	−0.769487	+	4.36398i	−0.0628283	+	0.356317i
$151$	6.10700	−	20.3988i	0.496981	−	1.66003i	−0.229860	−	0.973224i	$-0.573827\pi$
$151$	6.10700	−	20.3988i	0.496981	−	1.66003i	0.726840	−	0.686807i	$-0.240988\pi$
$152$	1.72604	−	4.00142i	0.140001	−	0.324558i
$153$	−2.06883	+	2.77892i	−0.167255	+	0.224662i
$154$	1.27339	+	1.34971i	0.102613	+	0.108763i
$155$	0.481414	+	2.73024i	0.0386681	+	0.219298i
$156$	−0.0422618	−	0.0212247i	−0.00338365	−	0.00169933i
$157$	−2.63128	−	0.957707i	−0.209999	−	0.0764334i	0.234879	−	0.972025i	$-0.424531\pi$
$157$	−2.63128	−	0.957707i	−0.209999	−	0.0764334i	−0.444878	+	0.895591i	$0.646753\pi$
$158$	−3.34170	−	2.80402i	−0.265851	−	0.223076i
$159$	2.27936	−	0.266419i	0.180765	−	0.0211284i
$160$	0.298693	−	0.692448i	0.0236137	−	0.0547428i
$161$	−0.0370190	−	0.635592i	−0.00291751	−	0.0500917i
$162$	1.00000			0.0785674
$163$	3.95337	−	12.1396i	0.309652	−	0.950850i
$163$	3.95337	−	12.1396i	0.309652	−	0.950850i
$164$	11.6446			0.909294
$165$	−0.0981183	−	1.68463i	−0.00763850	−	0.131148i
$166$	−0.944615	+	2.18986i	−0.0733163	+	0.169966i
$167$	3.00995	−	0.351812i	0.232917	−	0.0272241i	0.00116622	−	0.999999i	$-0.499629\pi$
$167$	3.00995	−	0.351812i	0.232917	−	0.0272241i	0.231750	+	0.972775i	$0.425555\pi$
$168$	−0.635245	−	0.533034i	−0.0490102	−	0.0411244i
$169$	12.2139	+	4.44550i	0.939531	+	0.341961i
$170$	−2.33473	−	1.17254i	−0.179065	−	0.0899300i
$171$	0.756727	+	4.29161i	0.0578684	+	0.328188i
$172$	6.75774	+	7.16279i	0.515273	+	0.546158i
$173$	3.80580	−	5.11208i	0.289350	−	0.388664i	−0.633552	−	0.773700i	$-0.718404\pi$
$173$	3.80580	−	5.11208i	0.289350	−	0.388664i	0.922901	+	0.385036i	$0.125811\pi$
$174$	−1.74882	+	4.05421i	−0.132577	+	0.307349i
$175$	−1.05391	+	3.52029i	−0.0796679	+	0.266109i
$176$	0.388568	−	2.20368i	0.0292894	−	0.166109i
$177$	3.30358	−	7.65857i	0.248313	−	0.575653i
$178$	3.37855	−	1.69677i	0.253233	−	0.127178i
$179$	1.88772	−	0.447398i	0.141095	−	0.0334401i	−0.159461	−	0.987204i	$-0.550976\pi$
$179$	1.88772	−	0.447398i	0.141095	−	0.0334401i	0.300556	+	0.953764i	$0.402828\pi$
$180$	0.130952	+	0.742666i	0.00976059	+	0.0553551i
$181$	4.15506	−	4.40411i	0.308843	−	0.327355i	−0.554297	−	0.832319i	$-0.687013\pi$
$181$	4.15506	−	4.40411i	0.308843	−	0.327355i	0.863140	+	0.504964i	$0.168494\pi$
$182$	−0.0327655	−	0.0215502i	−0.00242874	−	0.00159741i
$183$	−0.260194	−	0.171133i	−0.0192341	−	0.0126505i
$184$	−0.588140	+	0.493508i	−0.0433582	+	0.0363819i
$185$	3.13390	+	1.14065i	0.230409	+	0.0838621i
$186$	−1.83813	−	3.18374i	−0.134778	−	0.233443i
$187$	−7.54335	−	1.78781i	−0.551625	−	0.130737i
$188$	−0.600995	−	3.40841i	−0.0438321	−	0.248584i
$189$	0.823646	+	0.0962704i	0.0599114	+	0.00700264i
$190$	−3.08814	+	1.12399i	−0.224037	+	0.0815429i
$191$	−14.9020	−	5.42389i	−1.07827	−	0.392459i	−0.259008	−	0.965875i	$-0.583396\pi$
$191$	−14.9020	−	5.42389i	−1.07827	−	0.392459i	−0.819264	+	0.573416i	$0.805618\pi$
$192$	−0.0581448	+	0.998308i	−0.00419624	+	0.0720467i
$193$	3.06055	+	5.30104i	0.220304	+	0.381577i	0.954900	−	0.296927i	$-0.0959619\pi$
$193$	3.06055	+	5.30104i	0.220304	+	0.381577i	−0.734597	+	0.678504i	$0.762629\pi$
$194$	−10.0595	−	8.44095i	−0.722233	−	0.606025i
$195$	0.0102286	+	0.0341658i	0.000732483	+	0.00244666i
$196$	4.33179	+	4.59143i	0.309414	+	0.327959i
$197$	1.16562	−	0.276256i	0.0830468	−	0.0196824i	−0.188882	−	0.982000i	$-0.560487\pi$
$197$	1.16562	−	0.276256i	0.0830468	−	0.0196824i	0.271929	+	0.962317i	$0.412338\pi$
$198$	0.886297	+	2.05467i	0.0629864	+	0.146019i
$199$	13.6447	+	11.4492i	0.967245	+	0.811615i	0.982116	−	0.188275i	$-0.0602895\pi$
$199$	13.6447	+	11.4492i	0.967245	+	0.811615i	−0.0148715	+	0.999889i	$0.504734\pi$
$200$	4.16406	−	1.51559i	0.294443	−	0.107169i
$201$	3.24571	−	5.62174i	0.228935	−	0.396527i
$202$	13.1651	+	8.65880i	0.926291	+	0.609231i
$203$	−1.83071	+	3.17088i	−0.128490	+	0.222552i
$204$	3.44103	+	0.402199i	0.240920	+	0.0281595i
$205$	−6.02622	−	6.38742i	−0.420890	−	0.446117i
$206$	0.192766	+	0.258930i	0.0134307	+	0.0180405i
$207$	0.220197	−	0.735508i	0.0153047	−	0.0511213i
$208$	0.00274979	+	0.0472121i	0.000190664	+	0.00327357i
$209$	−8.14716	+	5.35847i	−0.563551	+	0.370653i
$210$	0.0363614	+	0.624301i	0.00250917	+	0.0430809i
$211$	−2.39170	+	13.5640i	−0.164651	+	0.933784i	0.784772	+	0.619785i	$0.212780\pi$
$211$	−2.39170	+	13.5640i	−0.164651	+	0.933784i	−0.949423	+	0.313999i	$0.898331\pi$
$212$	−1.37040	−	1.84077i	−0.0941197	−	0.126425i
$213$	11.5547	−	2.73852i	0.791717	−	0.187640i
$214$	16.0999	+	3.81574i	1.10057	+	0.260839i
$215$	0.431795	−	7.41364i	0.0294482	−	0.505606i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	−1.20747	−	2.79923i	−0.0819684	−	0.190024i
$218$	−16.5632	+	8.31837i	−1.12180	+	0.563391i
$219$	−2.64160	+	8.82356i	−0.178503	+	0.596241i
$220$	−1.40987	+	0.927286i	−0.0950534	+	0.0625176i
$221$	0.163841			0.0110212
$222$	−4.42240			−0.296812
$223$	0.776125	−	0.510465i	0.0519732	−	0.0341833i	−0.523257	−	0.852175i	$-0.675283\pi$
$223$	0.776125	−	0.510465i	0.0519732	−	0.0341833i	0.575230	+	0.817992i	$0.304913\pi$
$224$	−0.143998	+	0.816655i	−0.00962129	+	0.0545651i
$225$	−2.64619	+	3.55445i	−0.176413	+	0.236963i
$226$	−3.77191	−	12.5990i	−0.250904	−	0.838076i
$227$	15.3822	−	5.59867i	1.02095	−	0.371597i	0.223324	−	0.974744i	$-0.428309\pi$
$227$	15.3822	−	5.59867i	1.02095	−	0.371597i	0.797630	+	0.603148i	$0.206087\pi$
$228$	3.33828	−	2.80115i	0.221083	−	0.185511i
$229$	13.1120	−	13.8980i	0.866468	−	0.918403i	−0.130864	−	0.991400i	$-0.541775\pi$
$229$	13.1120	−	13.8980i	0.866468	−	0.918403i	0.997332	+	0.0729976i	$0.0232565\pi$
$230$	0.575072	+	0.0672163i	0.0379191	+	0.00443211i
$231$	0.532192	+	1.77764i	0.0350156	+	0.116960i
$232$	4.38546	−	0.512586i	0.287919	−	0.0336530i
$233$	10.3427	−	5.19432i	0.677575	−	0.340291i	−0.0765091	−	0.997069i	$-0.524377\pi$
$233$	10.3427	−	5.19432i	0.677575	−	0.340291i	0.754084	+	0.656778i	$0.228081\pi$
$234$	−0.0282409	−	0.0379341i	−0.00184617	−	0.00247983i
$235$	−1.55859	+	2.09355i	−0.101671	+	0.136568i
$236$	−8.28431	+	0.968297i	−0.539263	+	0.0630308i
$237$	−1.72781	−	4.00551i	−0.112233	−	0.260186i
$238$	2.79547	+	0.662539i	0.181203	+	0.0429460i
$239$	11.2693	+	5.65963i	0.728948	+	0.366091i	0.774248	−	0.632882i	$-0.218128\pi$
$239$	11.2693	+	5.65963i	0.728948	+	0.366091i	−0.0453006	+	0.998973i	$0.514425\pi$
$240$	0.577692	−	0.484741i	0.0372898	−	0.0312899i
$241$	−1.18676	+	2.05553i	−0.0764460	+	0.132408i	−0.901714	−	0.432333i	$-0.857691\pi$
$241$	−1.18676	+	2.05553i	−0.0764460	+	0.132408i	0.825268	+	0.564741i	$0.191024\pi$
$242$	4.11252	−	4.35902i	0.264363	−	0.280208i
$243$	0.893633	+	0.448799i	0.0573266	+	0.0287905i
$244$	−0.0181079	+	0.310901i	−0.00115924	+	0.0199034i
$245$	0.276786	−	4.75223i	0.0176832	−	0.303609i
$246$	10.4060	+	5.22610i	0.663464	+	0.333204i
$247$	0.141428	−	0.149905i	0.00899884	−	0.00953822i
$248$	−1.83813	+	3.18374i	−0.116721	+	0.202168i
$249$	−1.82695	+	1.53299i	−0.115778	+	0.0971493i
$250$	−6.35584	−	3.19202i	−0.401978	−	0.201881i
$251$	30.5832	+	7.24835i	1.93040	+	0.457512i	0.994427	+	0.105428i	$0.0336213\pi$
$251$	30.5832	+	7.24835i	1.93040	+	0.457512i	0.935968	+	0.352084i	$0.114527\pi$
$252$	−0.328450	−	0.761434i	−0.0206904	−	0.0479658i
$253$	1.70638	−	0.199448i	0.107279	−	0.0125392i
$254$	1.82203	−	2.44741i	0.114324	−	0.153564i
$255$	−1.56015	−	2.09565i	−0.0977004	−	0.131234i
$256$	0.893633	−	0.448799i	0.0558520	−	0.0280499i
$257$	−26.5772	+	3.10642i	−1.65784	+	0.193773i	−0.892876	−	0.450302i	$-0.851316\pi$
$257$	−26.5772	+	3.10642i	−1.65784	+	0.193773i	−0.764962	+	0.644076i	$0.777242\pi$
$258$	2.82429	+	9.43377i	0.175832	+	0.587321i
$259$	−3.64249	−	0.425746i	−0.226333	−	0.0264546i
$260$	0.0244742	−	0.0259411i	0.00151782	−	0.00160880i
$261$	−3.38233	+	2.83811i	−0.209361	+	0.175674i
$262$	13.0750	−	4.75891i	0.807776	−	0.294007i
$263$	3.10761	+	10.3801i	0.191623	+	0.640067i	0.998764	+	0.0497073i	$0.0158288\pi$
$263$	3.10761	+	10.3801i	0.191623	+	0.640067i	−0.807140	+	0.590360i	$0.798986\pi$
$264$	1.33625	−	1.79489i	0.0822403	−	0.110468i
$265$	−0.300518	+	1.70432i	−0.0184607	+	0.104696i
$266$	3.01923	−	1.98578i	0.185121	−	0.121756i
$267$	3.78069			0.231375
$268$	−6.49142			−0.396527
$269$	18.1737	−	11.9530i	1.10807	−	0.728789i	0.142724	−	0.989763i	$-0.454414\pi$
$269$	18.1737	−	11.9530i	1.10807	−	0.728789i	0.965346	+	0.260973i	$0.0840435\pi$
$270$	−0.216285	+	0.722442i	−0.0131627	+	0.0439664i
$271$	−5.24134	+	2.63230i	−0.318388	+	0.159901i	−0.600815	−	0.799388i	$-0.705157\pi$
$271$	−5.24134	+	2.63230i	−0.318388	+	0.159901i	0.282426	+	0.959289i	$0.408861\pi$
$272$	−1.37220	−	3.18112i	−0.0832018	−	0.192884i
$273$	−0.0196086	−	0.0339631i	−0.00118677	−	0.00205554i
$274$	−0.0997839	+	1.71322i	−0.00602816	+	0.103500i
$275$	−9.64852	−	2.28674i	−0.581828	−	0.137896i
$276$	−0.747067	+	0.177058i	−0.0449681	+	0.0106576i
$277$	−5.62462	−	7.55518i	−0.337951	−	0.453947i	0.600365	−	0.799726i	$-0.295022\pi$
$277$	−5.62462	−	7.55518i	−0.337951	−	0.453947i	−0.938316	+	0.345779i	$0.887615\pi$
$278$	1.07192	−	6.07919i	0.0642898	−	0.364605i
$279$	−0.213756	−	3.67004i	−0.0127972	−	0.219720i
$280$	0.522480	−	0.343640i	0.0312241	−	0.0205364i
$281$	−0.744525	−	12.7830i	−0.0444146	−	0.762570i	−0.944835	−	0.327548i	$-0.893778\pi$
$281$	−0.744525	−	12.7830i	−0.0444146	−	0.762570i	0.900420	−	0.435022i	$-0.143259\pi$
$282$	0.992624	−	3.31559i	0.0591099	−	0.197441i
$283$	−7.00116	−	9.40419i	−0.416176	−	0.559021i	0.543760	−	0.839241i	$-0.317000\pi$
$283$	−7.00116	−	9.40419i	−0.416176	−	0.559021i	−0.959936	+	0.280220i	$0.909593\pi$
$284$	−8.14899	−	8.63743i	−0.483554	−	0.512537i
$285$	−3.26411	−	0.381520i	−0.193349	−	0.0225993i
$286$	0.0529122	−	0.0916466i	0.00312876	−	0.00541918i
$287$	8.06777	+	5.30625i	0.476225	+	0.313218i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	4.69617	−	1.70927i	0.276245	−	0.100545i
$290$	−2.55069	−	2.14028i	−0.149782	−	0.125682i
$291$	−5.20124	−	12.0578i	−0.304902	−	0.706842i
$292$	8.96223	−	2.12409i	0.524475	−	0.124303i
$293$	−0.922785	−	0.978095i	−0.0539097	−	0.0571409i	0.699857	−	0.714283i	$-0.253247\pi$
$293$	−0.922785	−	0.978095i	−0.0539097	−	0.0571409i	−0.753767	+	0.657142i	$0.771765\pi$
$294$	1.81040	+	6.04715i	0.105585	+	0.352677i
$295$	4.81836	+	4.04308i	0.280535	+	0.235397i
$296$	2.21120	+	3.82991i	0.128523	+	0.222609i
$297$	−0.130109	+	2.23389i	−0.00754970	+	0.129623i
$298$	−4.05047	−	1.47425i	−0.234637	−	0.0854009i
$299$	−0.0341194	+	0.0124184i	−0.00197317	+	0.000718177i
$300$	4.40134	+	0.514442i	0.254111	+	0.0297013i
$301$	1.41802	+	8.04199i	0.0817333	+	0.463532i
$302$	−20.7194	−	4.91058i	−1.19227	−	0.282572i
$303$	7.87867	+	13.6463i	0.452618	+	0.783957i
$304$	−4.09501	−	1.49046i	−0.234865	−	0.0854839i
$305$	0.179909	−	0.150962i	0.0103016	−	0.00864405i
$306$	2.89451	+	1.90375i	0.165468	+	0.108830i
$307$	7.47222	+	4.91455i	0.426462	+	0.280488i	0.744542	−	0.667575i	$-0.232668\pi$
$307$	7.47222	+	4.91455i	0.426462	+	0.280488i	−0.318080	+	0.948064i	$0.603038\pi$
$308$	1.27339	−	1.34971i	0.0725581	−	0.0769071i
$309$	0.0560547	+	0.317902i	0.00318884	+	0.0180848i
$310$	2.69763	−	0.639349i	0.153215	−	0.0363126i
$311$	−4.27914	+	2.14907i	−0.242648	+	0.121862i	−0.565968	−	0.824427i	$-0.691497\pi$
$311$	−4.27914	+	2.14907i	−0.242648	+	0.121862i	0.323320	+	0.946290i	$0.395201\pi$
$312$	−0.0187315	+	0.0434244i	−0.00106046	+	0.00245842i
$313$	−1.13046	+	6.41117i	−0.0638975	+	0.362381i	0.936047	+	0.351874i	$0.114455\pi$
$313$	−1.13046	+	6.41117i	−0.0638975	+	0.362381i	−0.999945	+	0.0105065i	$0.996656\pi$
$314$	−0.803092	+	2.68251i	−0.0453211	+	0.151383i
$315$	−0.247692	+	0.574215i	−0.0139559	+	0.0323533i
$316$	−2.60497	+	3.49908i	−0.146541	+	0.196839i
$317$	8.67719	+	9.19729i	0.487360	+	0.516571i	0.923651	−	0.383234i	$-0.125190\pi$
$317$	8.67719	+	9.19729i	0.487360	+	0.516571i	−0.436291	+	0.899805i	$0.643708\pi$
$318$	−0.398501	−	2.26001i	−0.0223468	−	0.126735i
$319$	−8.82912	−	4.43415i	−0.494336	−	0.248265i
$320$	−0.708644	−	0.257925i	−0.0396144	−	0.0144185i
$321$	12.6749	+	10.6355i	0.707443	+	0.593615i
$322$	−0.632364	+	0.0739128i	−0.0352403	+	0.00411900i
$323$	−5.97980	+	13.8627i	−0.332725	+	0.771343i
$324$	−0.0581448	−	0.998308i	−0.00323027	−	0.0554616i
$325$	0.209566			0.0116246
$326$	−12.3490	−	3.24083i	−0.683946	−	0.179493i
$327$	−18.5347			−1.02497
$328$	−0.677076	−	11.6249i	−0.0373852	−	0.641880i
$329$	1.13676	−	2.63532i	0.0626719	−	0.145290i
$330$	−1.67607	+	0.195905i	−0.0922647	+	0.0107842i
$331$	7.11842	+	5.97307i	0.391264	+	0.328309i	0.817105	−	0.576488i	$-0.195577\pi$
$331$	7.11842	+	5.97307i	0.391264	+	0.328309i	−0.425841	+	0.904798i	$0.640022\pi$
$332$	2.24108	+	0.815687i	0.122995	+	0.0447667i
$333$	−3.95200	−	1.98477i	−0.216568	−	0.108765i
$334$	−0.526230	−	2.98440i	−0.0287940	−	0.163299i
$335$	3.35938	+	3.56073i	0.183542	+	0.194544i
$336$	−0.495196	+	0.665163i	−0.0270151	+	0.0362876i
$337$	−9.05823	+	20.9993i	−0.493433	+	1.14391i	0.471608	+	0.881808i	$0.343674\pi$
$337$	−9.05823	+	20.9993i	−0.493433	+	1.14391i	−0.965041	+	0.262098i	$0.915586\pi$
$338$	3.72780	−	12.4517i	0.202766	−	0.677284i
$339$	2.28374	−	12.9517i	0.124036	−	0.703442i
$340$	−1.03481	+	2.39895i	−0.0561203	+	0.130101i
$341$	7.35127	−	3.69195i	0.398094	−	0.199930i
$342$	4.24035	−	1.00498i	0.229292	−	0.0543432i
$343$	1.91695	+	10.8716i	0.103506	+	0.587011i
$344$	6.75774	−	7.16279i	0.364353	−	0.386192i
$345$	0.483736	+	0.318158i	0.0260435	+	0.0171291i
$346$	−5.32472	−	3.50212i	−0.286259	−	0.188275i
$347$	−10.2503	+	8.60100i	−0.550263	+	0.461726i	−0.875030	−	0.484068i	$-0.839159\pi$
$347$	−10.2503	+	8.60100i	−0.550263	+	0.461726i	0.324767	+	0.945794i	$0.394714\pi$
$348$	4.14904	+	1.51013i	0.222412	+	0.0809512i
$349$	12.1686	+	21.0766i	0.651370	+	1.12821i	0.982791	+	0.184723i	$0.0591388\pi$
$349$	12.1686	+	21.0766i	0.651370	+	1.12821i	−0.331420	+	0.943483i	$0.607528\pi$
$350$	3.57562	+	0.847437i	0.191125	+	0.0452974i
$351$	−0.00821219	−	0.0465737i	−0.000438334	−	0.00248592i
$352$	−2.22254	−	0.259778i	−0.118462	−	0.0138462i
$353$	−7.66045	+	2.78818i	−0.407725	+	0.148400i	−0.537737	−	0.843113i	$-0.680721\pi$
$353$	−7.66045	+	2.78818i	−0.407725	+	0.148400i	0.130012	+	0.991512i	$0.458498\pi$
$354$	−7.83770	−	2.85269i	−0.416569	−	0.151619i
$355$	−0.520691	+	8.93992i	−0.0276354	+	0.474482i
$356$	−1.89035	−	3.27418i	−0.100188	−	0.173531i
$357$	2.20078	+	1.84667i	0.116477	+	0.0977362i
$358$	−0.556403	−	1.85851i	−0.0294068	−	0.0982256i
$359$	6.48478	+	6.87346i	0.342253	+	0.362767i	0.875522	−	0.483179i	$-0.160518\pi$
$359$	6.48478	+	6.87346i	0.342253	+	0.362767i	−0.533268	+	0.845946i	$0.679036\pi$
$360$	0.733795	−	0.173913i	0.0386744	−	0.00916600i
$361$	−0.00372732	−	0.00864089i	−0.000196175	−	0.000454784i
$362$	−4.63825	−	3.89196i	−0.243781	−	0.204557i
$363$	5.63140	−	2.04966i	0.295572	−	0.107579i
$364$	−0.0196086	+	0.0339631i	−0.00102777	+	0.00178015i
$365$	−5.80317	−	3.81681i	−0.303752	−	0.199781i
$366$	−0.155714	+	0.269705i	−0.00813930	+	0.0140977i
$367$	−4.59760	−	0.537382i	−0.239993	−	0.0280511i	−0.00475382	−	0.999989i	$-0.501513\pi$
$367$	−4.59760	−	0.537382i	−0.239993	−	0.0280511i	−0.235239	+	0.971938i	$0.575587\pi$
$368$	0.526870	+	0.558450i	0.0274650	+	0.0291112i
$369$	6.95370	+	9.34044i	0.361995	+	0.486244i
$370$	0.956497	−	3.19492i	0.0497259	−	0.166096i
$371$	−0.110651	−	1.89981i	−0.00574474	−	0.0986333i
$372$	−3.07147	+	2.02014i	−0.159248	+	0.104739i
$373$	1.04756	+	17.9858i	0.0542404	+	0.931272i	0.910184	+	0.414203i	$0.135940\pi$
$373$	1.04756	+	17.9858i	0.0542404	+	0.931272i	−0.855944	+	0.517068i	$0.827023\pi$
$374$	−1.34618	+	7.63454i	−0.0696091	+	0.394773i
$375$	−4.24721	−	5.70499i	−0.219325	−	0.294604i
$376$	−3.36770	+	0.798160i	−0.173676	+	0.0411619i
$377$	0.203181	+	0.0481548i	0.0104644	+	0.00248010i
$378$	0.0482168	−	0.827850i	0.00248000	−	0.0425800i
$379$	−1.32973	−	2.30316i	−0.0683036	−	0.118305i	0.829851	−	0.557985i	$-0.188425\pi$
$379$	−1.32973	−	2.30316i	−0.0683036	−	0.118305i	−0.898155	+	0.439680i	$0.855092\pi$
$380$	1.30165	+	3.01756i	0.0667732	+	0.154798i
$381$	2.72662	−	1.36936i	0.139689	−	0.0701543i
$382$	−4.54824	+	15.1922i	−0.232708	+	0.777300i
$383$	−26.2045	+	17.2349i	−1.33899	+	0.880664i	−0.998229	−	0.0594873i	$-0.981053\pi$
$383$	−26.2045	+	17.2349i	−1.33899	+	0.880664i	−0.340756	+	0.940152i	$0.610683\pi$
$384$	1.00000			0.0510310
$385$	−1.39935			−0.0713175
$386$	5.11411	−	3.36360i	0.260301	−	0.171203i
$387$	−1.71000	+	9.69786i	−0.0869239	+	0.492970i
$388$	−7.84176	+	10.5333i	−0.398105	+	0.534748i
$389$	−1.66849	−	5.57314i	−0.0845957	−	0.282569i	0.905216	−	0.424952i	$-0.139709\pi$
$389$	−1.66849	−	5.57314i	−0.0845957	−	0.282569i	−0.989812	+	0.142382i	$0.954524\pi$
$390$	0.0335133	−	0.0121978i	0.00169701	−	0.000617661i
$391$	2.03758	−	1.70973i	0.103045	−	0.0864650i
$392$	4.33179	−	4.59143i	0.218788	−	0.231902i
$393$	13.8200	+	1.61533i	0.697129	+	0.0814827i
$394$	−0.343563	−	1.14758i	−0.0173085	−	0.0578143i
$395$	3.26745	−	0.381910i	0.164403	−	0.0192160i
$396$	1.99966	−	1.00427i	0.100487	−	0.0504663i
$397$	−21.9488	−	29.4824i	−1.10158	−	1.47968i	−0.860692	−	0.509126i	$-0.829969\pi$
$397$	−21.9488	−	29.4824i	−1.10158	−	1.47968i	−0.240888	−	0.970553i	$-0.577439\pi$
$398$	10.6365	−	14.2873i	0.533160	−	0.716158i
$399$	3.58930	−	0.419529i	0.179690	−	0.0210027i
$400$	−1.75515	−	4.06889i	−0.0877574	−	0.203444i
$401$	4.76521	+	1.12937i	0.237963	+	0.0563983i	0.347867	−	0.937544i	$-0.386906\pi$
$401$	4.76521	+	1.12937i	0.237963	+	0.0563983i	−0.109904	+	0.993942i	$0.535054\pi$
$402$	−5.80095	−	2.91334i	−0.289325	−	0.145304i
$403$	−0.133183	+	0.111754i	−0.00663433	+	0.00556686i
$404$	7.87867	−	13.6463i	0.391978	−	0.678926i
$405$	−0.517510	+	0.548529i	−0.0257153	+	0.0272566i
$406$	3.27196	+	1.64324i	0.162385	+	0.0815526i
$407$	0.575394	−	9.87914i	0.0285212	−	0.489691i
$408$	0.201440	−	3.45859i	0.00997277	−	0.171226i
$409$	−1.05098	−	0.527821i	−0.0519676	−	0.0260991i	0.422626	−	0.906304i	$-0.361109\pi$
$409$	−1.05098	−	0.527821i	−0.0519676	−	0.0260991i	−0.474593	+	0.880205i	$0.657405\pi$
$410$	−6.02622	+	6.38742i	−0.297614	+	0.315452i
$411$	−0.858063	+	1.48621i	−0.0423251	+	0.0733093i
$412$	0.247284	−	0.207496i	0.0121828	−	0.0102226i
$413$	−6.18086	−	3.10415i	−0.304140	−	0.152745i
$414$	−0.747067	−	0.177058i	−0.0367163	−	0.00870193i
$415$	−0.712355	−	1.65143i	−0.0349682	−	0.0810653i
$416$	0.0469724	−	0.00549028i	0.00230301	−	0.000269183i
$417$	3.68624	−	4.95148i	0.180516	−	0.242475i
$418$	5.82312	+	7.82181i	0.284818	+	0.382577i
$419$	−2.27034	+	1.14021i	−0.110914	+	0.0557029i	−0.503391	−	0.864059i	$-0.667914\pi$
$419$	−2.27034	+	1.14021i	−0.110914	+	0.0557029i	0.392477	+	0.919762i	$0.371618\pi$
$420$	0.621130	−	0.0725997i	0.0303081	−	0.00354250i
$421$	4.74895	+	15.8626i	0.231450	+	0.773096i	0.992266	+	0.124129i	$0.0396136\pi$
$421$	4.74895	+	15.8626i	0.231450	+	0.773096i	−0.760816	+	0.648967i	$0.775201\pi$
$422$	13.6801	+	1.59898i	0.665938	+	0.0778369i
$423$	2.37508	−	2.51743i	0.115480	−	0.122402i
$424$	−1.75798	+	1.47512i	−0.0853748	+	0.0716380i
$425$	−14.4262	+	5.25070i	−0.699773	+	0.254697i
$426$	−3.40574	−	11.3760i	−0.165008	−	0.551167i
$427$	−0.154218	+	0.207151i	−0.00746313	+	0.0100247i
$428$	2.87316	−	16.2945i	0.138880	−	0.787625i
$429$	0.0884150	−	0.0581514i	0.00426871	−	0.00280758i
$430$	−7.42620			−0.358123
$431$	16.2386			0.782183			0.391092	−	0.920352i	$-0.372098\pi$
$431$	16.2386			0.782183			0.391092	+	0.920352i	$0.372098\pi$
$432$	−0.835488	+	0.549509i	−0.0401974	+	0.0264383i
$433$	5.38757	−	17.9958i	0.258910	−	0.864821i	−0.725393	−	0.688335i	$-0.758342\pi$
$433$	5.38757	−	17.9958i	0.258910	−	0.864821i	0.984303	−	0.176486i	$-0.0564729\pi$
$434$	−2.72429	+	1.36819i	−0.130770	+	0.0656752i
$435$	−1.31882	−	3.05737i	−0.0632327	−	0.146590i
$436$	9.26736	+	16.0515i	0.443826	+	0.768729i
$437$	0.194539	−	3.34011i	0.00930607	−	0.159779i
$438$	8.96223	+	2.12409i	0.428232	+	0.101493i
$439$	−27.1896	+	6.44406i	−1.29769	+	0.307558i	−0.820705	−	0.571353i	$-0.806419\pi$
$439$	−27.1896	+	6.44406i	−1.29769	+	0.307558i	−0.476986	+	0.878911i	$0.658271\pi$
$440$	1.00769	+	1.35357i	0.0480399	+	0.0645288i
$441$	−1.09613	+	6.21644i	−0.0521965	+	0.296021i
$442$	−0.00952653	−	0.163564i	−0.000453131	−	0.00777995i
$443$	−1.18674	+	0.780531i	−0.0563837	+	0.0370841i	−0.577388	−	0.816470i	$-0.695928\pi$
$443$	−1.18674	+	0.780531i	−0.0563837	+	0.0370841i	0.521004	+	0.853554i	$0.325558\pi$
$444$	0.257139	+	4.41491i	0.0122033	+	0.209523i
$445$	−0.817707	+	2.73133i	−0.0387630	+	0.129478i
$446$	−0.554729	−	0.745131i	−0.0262672	−	0.0352830i
$447$	−2.95799	−	3.13528i	−0.139908	−	0.148294i
$448$	0.823646	+	0.0962704i	0.0389136	+	0.00454835i
$449$	7.10730	−	12.3102i	0.335414	−	0.580955i	−0.648150	−	0.761513i	$-0.724457\pi$
$449$	7.10730	−	12.3102i	0.335414	−	0.580955i	0.983564	+	0.180558i	$0.0577904\pi$
$450$	3.70230	+	2.43504i	0.174528	+	0.114789i
$451$	−13.0285	+	22.5659i	−0.613486	+	1.06259i
$452$	−12.3584	+	4.49810i	−0.581291	+	0.211573i
$453$	−16.3116	−	13.6871i	−0.766388	−	0.643076i
$454$	−6.48359	−	15.0307i	−0.304290	−	0.705424i
$455$	0.0287774	−	0.00682036i	0.00134910	−	0.000319743i
$456$	−2.99052	−	3.16976i	−0.140044	−	0.148438i
$457$	−5.72284	−	19.1156i	−0.267703	−	0.894190i	−0.981112	−	0.193442i	$-0.938035\pi$
$457$	−5.72284	−	19.1156i	−0.267703	−	0.894190i	0.713409	−	0.700748i	$-0.247150\pi$
$458$	−14.6368	−	12.2818i	−0.683935	−	0.573889i
$459$	1.73223	+	3.00030i	0.0808534	+	0.140042i
$460$	0.0336651	−	0.578007i	0.00156964	−	0.0269497i
$461$	7.24696	+	2.63768i	0.337525	+	0.122849i	0.505222	−	0.862990i	$-0.331411\pi$
$461$	7.24696	+	2.63768i	0.337525	+	0.122849i	−0.167697	+	0.985839i	$0.553633\pi$
$462$	1.74369	−	0.634652i	0.0811239	−	0.0295267i
$463$	−39.6608	−	4.63568i	−1.84319	−	0.215438i	−0.878304	−	0.478102i	$-0.841325\pi$
$463$	−39.6608	−	4.63568i	−1.84319	−	0.215438i	−0.964887	+	0.262664i	$0.915399\pi$
$464$	−0.766711	−	4.34823i	−0.0355937	−	0.201862i
$465$	2.69763	+	0.639349i	0.125099	+	0.0296491i
$466$	−5.78690	−	10.0232i	−0.268073	−	0.464316i
$467$	−21.3559	−	7.77291i	−0.988233	−	0.359687i	−0.203197	−	0.979138i	$-0.565133\pi$
$467$	−21.3559	−	7.77291i	−0.988233	−	0.359687i	−0.785036	+	0.619450i	$0.787356\pi$
$468$	−0.0362279	+	0.0303988i	−0.00167463	+	0.00140518i
$469$	−4.49746	−	2.95802i	−0.207673	−	0.136589i
$470$	2.18063	+	1.43423i	0.100585	+	0.0661559i
$471$	−1.92158	+	2.03675i	−0.0885417	+	0.0938487i
$472$	1.44835	+	8.21399i	0.0666656	+	0.378080i
$473$	−21.4415	+	5.08172i	−0.985879	+	0.233658i
$474$	−3.89827	+	1.95779i	−0.179054	+	0.0899241i
$475$	−7.64862	+	17.7315i	−0.350943	+	0.813576i
$476$	0.498876	−	2.82926i	0.0228659	−	0.129679i
$477$	0.658177	−	2.19847i	0.0301359	−	0.100661i
$478$	4.99481	−	11.5793i	0.228457	−	0.529623i
$479$	9.00700	−	12.0985i	0.411541	−	0.552795i	−0.547228	−	0.836984i	$-0.684317\pi$
$479$	9.00700	−	12.0985i	0.411541	−	0.552795i	0.958768	+	0.284189i	$0.0917243\pi$
$480$	−0.517510	−	0.548529i	−0.0236210	−	0.0250368i
$481$	0.0363176	+	0.205967i	0.00165594	+	0.00939129i
$482$	2.12106	+	1.06523i	0.0966115	+	0.0485201i
$483$	−0.598273	−	0.217754i	−0.0272224	−	0.00990813i
$484$	−4.59076	−	3.85211i	−0.208671	−	0.175096i
$485$	9.83602	−	1.14967i	0.446631	−	0.0522037i
$486$	0.396080	−	0.918216i	0.0179665	−	0.0416511i
$487$	−0.166028	−	2.85059i	−0.00752345	−	0.129173i	−0.999978	−	0.00656332i	$-0.997911\pi$
$487$	−0.166028	−	2.85059i	−0.00752345	−	0.129173i	0.992455	−	0.122609i	$-0.0391262\pi$
$488$	0.311428			0.0140977
$489$	−9.58096	−	8.43832i	−0.433266	−	0.381594i
$490$	−4.76028			−0.215047
$491$	1.92893	+	33.1185i	0.0870516	+	1.49462i	0.705453	+	0.708756i	$0.250743\pi$
$491$	1.92893	+	33.1185i	0.0870516	+	1.49462i	−0.618402	+	0.785862i	$0.712220\pi$
$492$	4.61221	−	10.6923i	0.207934	−	0.482046i
$493$	−15.1932	+	1.77583i	−0.684268	+	0.0799795i
$494$	−0.157875	−	0.132472i	−0.00710311	−	0.00596022i
$495$	−1.58571	−	0.577153i	−0.0712725	−	0.0259411i
$496$	3.28523	+	1.64990i	0.147511	+	0.0740829i
$497$	−1.70995	−	9.69763i	−0.0767019	−	0.434998i
$498$	1.63662	+	1.73472i	0.0733389	+	0.0777347i
$499$	−13.5616	+	18.2164i	−0.607101	+	0.815479i	−0.994311	−	0.106513i	$-0.966031\pi$
$499$	−13.5616	+	18.2164i	−0.607101	+	0.815479i	0.387210	+	0.921992i	$0.373439\pi$
$500$	−2.81706	+	6.53068i	−0.125983	+	0.292061i
$501$	0.869139	−	2.90313i	0.0388303	−	0.129702i
$502$	5.45784	−	30.9529i	0.243595	−	1.38150i
$503$	2.42724	−	5.62698i	0.108225	−	0.250895i	−0.855494	−	0.517813i	$-0.826746\pi$
$503$	2.42724	−	5.62698i	0.108225	−	0.250895i	0.963719	+	0.266919i	$0.0860055\pi$
$504$	−0.741048	+	0.372168i	−0.0330089	+	0.0165777i
$505$	−11.5627	+	2.74040i	−0.514532	+	0.121946i
$506$	−0.298328	−	1.69190i	−0.0132623	−	0.0752141i
$507$	8.91961	−	9.45423i	0.396134	−	0.419877i
$508$	−2.54921	−	1.67664i	−0.113103	−	0.0743889i
$509$	2.74768	+	1.80718i	0.121789	+	0.0801017i	0.608942	−	0.793215i	$-0.291594\pi$
$509$	2.74768	+	1.80718i	0.121789	+	0.0801017i	−0.487153	+	0.873317i	$0.661965\pi$
$510$	−2.00139	+	1.67936i	−0.0886229	+	0.0743634i
$511$	7.17722	+	2.61229i	0.317502	+	0.115561i
$512$	−0.500000	−	0.866025i	−0.0220971	−	0.0382733i
$513$	4.24035	+	1.00498i	0.187216	+	0.0443711i
$514$	4.64649	+	26.3516i	0.204948	+	1.16232i
$515$	−0.241789	−	0.0282611i	−0.0106545	−	0.00124533i
$516$	9.25359	−	3.36803i	0.407367	−	0.148269i
$517$	7.27752	+	2.64880i	0.320065	+	0.116494i
$518$	−0.213234	+	3.66108i	−0.00936895	+	0.160859i
$519$	−3.18659	−	5.51934i	−0.139876	−	0.242272i
$520$	−0.0273203	−	0.0229244i	−0.00119807	−	0.00100530i
$521$	7.82762	+	26.1461i	0.342934	+	1.14548i	0.939395	+	0.342838i	$0.111388\pi$
$521$	7.82762	+	26.1461i	0.342934	+	1.14548i	−0.596460	+	0.802643i	$0.703427\pi$
$522$	3.02997	+	3.21158i	0.132618	+	0.140567i
$523$	10.5149	−	2.49208i	0.459786	−	0.108971i	0.00580572	−	0.999983i	$-0.498152\pi$
$523$	10.5149	−	2.49208i	0.459786	−	0.108971i	0.453980	+	0.891012i	$0.350004\pi$
$524$	−5.51110	−	12.7762i	−0.240754	−	0.558130i
$525$	2.81496	+	2.36203i	0.122855	+	0.103088i
$526$	10.1819	−	3.70590i	0.443951	−	0.161585i
$527$	6.36812	−	11.0299i	0.277400	−	0.480470i
$528$	−1.86955	−	1.22962i	−0.0813617	−	0.0535124i
$529$	11.2053	−	19.4081i	0.487186	−	0.843830i
$530$	1.71892	+	0.200912i	0.0746649	+	0.00872708i
$531$	−5.72374	−	6.06681i	−0.248389	−	0.263277i
$532$	−2.15797	−	2.89866i	−0.0935600	−	0.125673i
$533$	0.157942	−	0.527565i	0.00684125	−	0.0228514i
$534$	−0.219828	−	3.77430i	−0.00951288	−	0.163330i
$535$	−10.4249	+	6.85657i	−0.450708	+	0.296435i
$536$	0.377443	+	6.48044i	0.0163030	+	0.279912i
$537$	0.336880	−	1.91054i	0.0145375	−	0.0824460i
$538$	−12.9895	−	17.4479i	−0.560018	−	0.752234i
$539$	−13.7442	+	3.25744i	−0.592005	+	0.140308i
$540$	0.733795	+	0.173913i	0.0315775	+	0.00748401i
$541$	−1.02278	+	17.5604i	−0.0439727	+	0.754981i	0.902200	+	0.431318i	$0.141951\pi$
$541$	−1.02278	+	17.5604i	−0.0439727	+	0.754981i	−0.946172	+	0.323663i	$0.895086\pi$
$542$	2.93260	+	5.07941i	0.125966	+	0.218179i
$543$	−2.39819	−	5.55962i	−0.102916	−	0.238586i
$544$	−3.09595	+	1.55484i	−0.132738	+	0.0666634i
$545$	4.00878	−	13.3903i	0.171717	−	0.573575i
$546$	−0.0327655	+	0.0215502i	−0.00140223	+	0.000922262i
$547$	−3.94674			−0.168750			−0.0843752	−	0.996434i	$-0.526889\pi$
$547$	−3.94674			−0.168750			−0.0843752	+	0.996434i	$0.526889\pi$
$548$	1.71613			0.0733093
$549$	−0.260194	+	0.171133i	−0.0111048	+	0.00730376i
$550$	−1.72186	+	9.76516i	−0.0734204	+	0.416388i
$551$	−11.4900	+	15.4338i	−0.489491	+	0.657500i
$552$	0.220197	+	0.735508i	0.00937219	+	0.0313053i
$553$	−3.39927	+	1.23723i	−0.144552	+	0.0526126i
$554$	−7.21535	+	6.05440i	−0.306551	+	0.257227i
$555$	2.28864	−	2.42581i	0.0971472	−	0.102970i
$556$	−6.13123	−	0.716638i	−0.260022	−	0.0303922i
$557$	−4.85802	−	16.2269i	−0.205841	−	0.687557i	−0.997102	−	0.0760779i	$-0.975760\pi$
$557$	−4.85802	−	16.2269i	−0.205841	−	0.687557i	0.791261	−	0.611479i	$-0.209425\pi$
$558$	−3.65141	+	0.426788i	−0.154576	+	0.0180674i
$559$	0.416172	−	0.209009i	0.0176022	−	0.00884015i
$560$	−0.373438	−	0.501615i	−0.0157807	−	0.0211971i
$561$	−4.62936	+	6.21831i	−0.195452	+	0.262537i
$562$	−12.7181	+	1.48653i	−0.536480	+	0.0627055i
$563$	2.96924	+	6.88346i	0.125138	+	0.290103i	0.969256	−	0.246055i	$-0.0791343\pi$
$563$	2.96924	+	6.88346i	0.125138	+	0.290103i	−0.844118	+	0.536158i	$0.819875\pi$
$564$	−3.36770	−	0.798160i	−0.141806	−	0.0336086i
$565$	8.86295	+	4.45114i	0.372867	+	0.187261i
$566$	−8.98120	+	7.53612i	−0.377508	+	0.316767i
$567$	0.414627	−	0.718154i	0.0174127	−	0.0301597i
$568$	−8.14899	+	8.63743i	−0.341924	+	0.362419i
$569$	−18.6179	−	9.35024i	−0.780501	−	0.391982i	0.0134923	−	0.999909i	$-0.495705\pi$
$569$	−18.6179	−	9.35024i	−0.780501	−	0.391982i	−0.793993	+	0.607927i	$0.792001\pi$
$570$	−0.191083	+	3.28077i	−0.00800359	+	0.137416i
$571$	−0.761020	+	13.0662i	−0.0318477	+	0.546804i	0.944217	+	0.329324i	$0.106821\pi$
$571$	−0.761020	+	13.0662i	−0.0318477	+	0.546804i	−0.976065	+	0.217480i	$0.930216\pi$
$572$	−0.0945681	−	0.0474939i	−0.00395409	−	0.00198582i
$573$	−10.8827	+	11.5350i	−0.454631	+	0.481881i
$574$	4.82818	−	8.36265i	0.201524	−	0.349050i
$575$	2.60622	−	2.18688i	0.108687	−	0.0911992i
$576$	0.893633	+	0.448799i	0.0372347	+	0.0187000i
$577$	−33.3316	−	7.89974i	−1.38761	−	0.328871i	−0.532114	−	0.846673i	$-0.678602\pi$
$577$	−33.3316	−	7.89974i	−1.38761	−	0.328871i	−0.855500	+	0.517802i	$0.826750\pi$
$578$	−1.97943	−	4.58884i	−0.0823335	−	0.190871i
$579$	6.07972	−	0.710617i	0.252665	−	0.0295323i
$580$	−1.98835	+	2.67082i	−0.0825618	+	0.110900i
$581$	1.18100	+	1.58635i	0.0489960	+	0.0658131i
$582$	−11.7350	+	5.89354i	−0.486431	+	0.244295i
$583$	5.10046	−	0.596158i	0.211239	−	0.0246903i
$584$	−2.64160	−	8.82356i	−0.109310	−	0.365122i
$585$	0.0354229	+	0.00414035i	0.00146456	+	0.000171182i
$586$	−0.922785	+	0.978095i	−0.0381199	+	0.0404047i
$587$	−22.4056	+	18.8005i	−0.924776	+	0.775979i	−0.974872	−	0.222765i	$-0.928492\pi$
$587$	−22.4056	+	18.8005i	−0.924776	+	0.775979i	0.0500959	+	0.998744i	$0.484047\pi$
$588$	5.93166	−	2.15895i	0.244617	−	0.0890335i
$589$	−4.59473	−	15.3475i	−0.189323	−	0.632381i
$590$	3.75608	−	5.04529i	0.154635	−	0.207711i
$591$	0.208014	−	1.17971i	0.00855656	−	0.0485267i
$592$	3.69486	−	2.43015i	0.151858	−	0.0998784i
$593$	−12.9182			−0.530486			−0.265243	−	0.964182i	$-0.585452\pi$
$593$	−12.9182			−0.530486			−0.265243	+	0.964182i	$0.585452\pi$
$594$	2.23767			0.0918129
$595$	−1.81011	+	1.19053i	−0.0742071	+	0.0488068i
$596$	−1.23624	+	4.12933i	−0.0506384	+	0.169144i
$597$	15.9173	−	7.99394i	0.651450	−	0.327170i
$598$	0.0143813	+	0.0333396i	0.000588095	+	0.00136336i
$599$	−20.4864	−	35.4835i	−0.837052	−	1.44982i	−0.892349	−	0.451347i	$-0.850944\pi$
$599$	−20.4864	−	35.4835i	−0.837052	−	1.44982i	0.0552963	−	0.998470i	$-0.482390\pi$
$600$	0.257657	−	4.42380i	0.0105188	−	0.180601i
$601$	17.3581	+	4.11394i	0.708051	+	0.167811i	0.568836	−	0.822451i	$-0.307394\pi$
$601$	17.3581	+	4.11394i	0.708051	+	0.167811i	0.139215	+	0.990262i	$0.455542\pi$
$602$	7.94593	−	1.88322i	0.323852	−	0.0767543i
$603$	−3.87641	−	5.20692i	−0.157860	−	0.212042i
$604$	−3.69755	+	20.9698i	−0.150451	+	0.853251i
$605$	0.262775	+	4.51167i	0.0106833	+	0.183426i
$606$	13.1651	−	8.65880i	0.534794	−	0.351740i
$607$	0.362480	+	6.22354i	0.0147126	+	0.252606i	0.997643	+	0.0686253i	$0.0218613\pi$
$607$	0.362480	+	6.22354i	0.0147126	+	0.252606i	−0.982930	+	0.183981i	$0.941102\pi$
$608$	−1.24984	+	4.17475i	−0.0506876	+	0.169308i
$609$	2.18644	+	2.93690i	0.0885992	+	0.119009i
$610$	−0.161167	−	0.170827i	−0.00652547	−	0.00691660i
$611$	−0.162571	−	0.0190018i	−0.00657692	−	0.000768731i
$612$	1.73223	−	3.00030i	0.0700211	−	0.121280i
$613$	−7.99984	−	5.26158i	−0.323111	−	0.212513i	0.377583	−	0.925976i	$-0.376755\pi$
$613$	−7.99984	−	5.26158i	−0.323111	−	0.212513i	−0.700693	+	0.713463i	$0.747126\pi$
$614$	4.47177	−	7.74533i	0.180466	−	0.312576i
$615$	−8.25190	+	3.00345i	−0.332749	+	0.121111i
$616$	−1.42147	−	1.19276i	−0.0572727	−	0.0480575i
$617$	−7.47972	−	17.3399i	−0.301122	−	0.698080i	0.698728	−	0.715387i	$-0.253750\pi$
$617$	−7.47972	−	17.3399i	−0.301122	−	0.698080i	−0.999850	+	0.0173078i	$0.994490\pi$
$618$	0.314105	−	0.0744442i	0.0126351	−	0.00299458i
$619$	7.01191	+	7.43219i	0.281833	+	0.298725i	0.852789	−	0.522255i	$-0.174909\pi$
$619$	7.01191	+	7.43219i	0.281833	+	0.298725i	−0.570957	+	0.820980i	$0.693428\pi$
$620$	−0.795120	−	2.65589i	−0.0319328	−	0.106663i
$621$	−0.588140	−	0.493508i	−0.0236012	−	0.0198038i
$622$	2.39424	+	4.14694i	0.0960003	+	0.166277i
$623$	0.182293	−	3.12985i	0.00730341	−	0.125395i
$624$	0.0444401	+	0.0161749i	0.00177903	+	0.000647513i
$625$	−15.7802	+	5.74351i	−0.631207	+	0.229740i
$626$	6.46605	+	0.755773i	0.258435	+	0.0302068i
$627$	1.69331	+	9.60323i	0.0676243	+	0.383516i
$628$	2.72467	+	0.645759i	0.108726	+	0.0257686i
$629$	−7.66059	−	13.2685i	−0.305448	−	0.529051i
$630$	0.587645	+	0.213885i	0.0234123	+	0.00852140i
$631$	−23.6420	+	19.8380i	−0.941172	+	0.789737i	−0.977789	−	0.209593i	$-0.932786\pi$
$631$	−23.6420	+	19.8380i	−0.941172	+	0.789737i	0.0366172	+	0.999329i	$0.488342\pi$
$632$	3.64463	+	2.39711i	0.144975	+	0.0953519i
$633$	11.5074	+	7.56852i	0.457377	+	0.300822i
$634$	8.67719	−	9.19729i	0.344615	−	0.365271i
$635$	0.399556	+	2.26599i	0.0158559	+	0.0899232i
$636$	−2.23302	+	0.529234i	−0.0885448	+	0.0209855i
$637$	0.266771	−	0.133977i	0.0105698	−	0.00530837i
$638$	−3.91328	+	9.07200i	−0.154928	+	0.359164i
$639$	2.06204	−	11.6944i	0.0815731	−	0.462624i
$640$	−0.216285	+	0.722442i	−0.00854941	+	0.0285570i
$641$	2.07047	−	4.79990i	0.0817788	−	0.189584i	−0.872421	−	0.488756i	$-0.837451\pi$
$641$	2.07047	−	4.79990i	0.0817788	−	0.189584i	0.954199	+	0.299171i	$0.0967102\pi$
$642$	9.88051	−	13.2718i	0.389953	−	0.523797i
$643$	−16.6598	−	17.6584i	−0.656999	−	0.696379i	0.310121	−	0.950697i	$-0.399630\pi$
$643$	−16.6598	−	17.6584i	−0.656999	−	0.696379i	−0.967121	+	0.254318i	$0.918149\pi$
$644$	0.110556	+	0.626997i	0.00435653	+	0.0247071i
$645$	−6.63630	−	3.33287i	−0.261304	−	0.131232i
$646$	14.1870	+	5.16364i	0.558179	+	0.203161i
$647$	29.4223	+	24.6882i	1.15671	+	0.970595i	0.999855	−	0.0170263i	$-0.00541991\pi$
$647$	29.4223	+	24.6882i	1.15671	+	0.970595i	0.156855	+	0.987622i	$0.449864\pi$
$648$	−0.993238	+	0.116093i	−0.0390181	+	0.00456056i
$649$	7.39235	−	17.1374i	0.290175	−	0.672701i
$650$	−0.0121852	−	0.209211i	−0.000477941	−	0.00820593i
$651$	−3.04855			−0.119482
$652$	−2.51731	+	12.5165i	−0.0985856	+	0.490185i
$653$	7.71835			0.302043			0.151021	−	0.988531i	$-0.451744\pi$
$653$	7.71835			0.302043			0.151021	+	0.988531i	$0.451744\pi$
$654$	1.07770	+	18.5034i	0.0421413	+	0.723539i
$655$	−4.15605	+	9.63481i	−0.162390	+	0.376463i
$656$	−11.5659	+	1.35186i	−0.451573	+	0.0527813i
$657$	7.05565	+	5.92040i	0.275267	+	0.230977i
$658$	−2.69695	−	0.981611i	−0.105138	−	0.0382672i
$659$	27.0555	+	13.5878i	1.05393	+	0.529305i	0.889430	−	0.457072i	$-0.151102\pi$
$659$	27.0555	+	13.5878i	1.05393	+	0.529305i	0.164503	+	0.986377i	$0.447398\pi$
$660$	0.293028	+	1.66184i	0.0114061	+	0.0646872i
$661$	1.16995	+	1.24007i	0.0455057	+	0.0482332i	0.749727	−	0.661748i	$-0.230185\pi$
$661$	1.16995	+	1.24007i	0.0455057	+	0.0482332i	−0.704221	+	0.709981i	$0.748704\pi$
$662$	5.54906	−	7.45368i	0.215670	−	0.289696i
$663$	0.0648943	−	0.150442i	0.00252028	−	0.00584267i
$664$	0.684000	−	2.28472i	0.0265443	−	0.0886643i
$665$	−0.473226	+	2.68380i	−0.0183509	+	0.104073i
$666$	−1.75162	+	4.06071i	−0.0678740	+	0.157350i
$667$	3.02933	−	1.52139i	0.117296	−	0.0589084i
$668$	−2.94875	+	0.698867i	−0.114091	+	0.0270400i
$669$	−0.161310	−	0.914835i	−0.00623661	−	0.0353696i
$670$	3.35938	−	3.56073i	0.129784	−	0.137563i
$671$	−0.582230	−	0.382939i	−0.0224767	−	0.0147832i
$672$	0.692831	+	0.455682i	0.0267265	+	0.0175783i
$673$	19.8977	−	16.6962i	0.767001	−	0.643590i	−0.172938	−	0.984933i	$-0.555326\pi$
$673$	19.8977	−	16.6962i	0.767001	−	0.643590i	0.939939	+	0.341343i	$0.110882\pi$
$674$	21.4905	+	7.82190i	0.827783	+	0.301288i
$675$	2.21565	+	3.83762i	0.0852804	+	0.147710i
$676$	−12.6474	−	2.99749i	−0.486439	−	0.115288i
$677$	−4.69050	−	26.6011i	−0.180270	−	1.02236i	−0.931883	−	0.362759i	$-0.881835\pi$
$677$	−4.69050	−	26.6011i	−0.180270	−	1.02236i	0.751612	−	0.659605i	$-0.229276\pi$
$678$	−13.0626	−	1.52680i	−0.501667	−	0.0586365i
$679$	−10.2329	+	3.72446i	−0.392701	+	0.142932i
$680$	2.45506	+	0.893570i	0.0941474	+	0.0342668i
$681$	0.951796	−	16.3417i	0.0364729	−	0.626216i
$682$	−4.11314	−	7.12417i	−0.157500	−	0.272798i
$683$	7.38313	+	6.19518i	0.282508	+	0.237052i	0.773019	−	0.634383i	$-0.218746\pi$
$683$	7.38313	+	6.19518i	0.282508	+	0.237052i	−0.490512	+	0.871435i	$0.663190\pi$
$684$	−1.24984	−	4.17475i	−0.0477887	−	0.159625i
$685$	−0.888113	−	0.941345i	−0.0339331	−	0.0359669i
$686$	10.7417	−	2.54584i	0.410121	−	0.0972006i
$687$	−7.56791	−	17.5444i	−0.288734	−	0.669360i
$688$	−7.54360	−	6.32983i	−0.287597	−	0.241323i
$689$	−0.101984	+	0.0371193i	−0.00388529	+	0.00141413i
$690$	0.289493	−	0.501417i	0.0110208	−	0.0190886i
$691$	6.94829	+	4.56996i	0.264325	+	0.173850i	0.674753	−	0.738044i	$-0.264250\pi$
$691$	6.94829	+	4.56996i	0.264325	+	0.173850i	−0.410428	+	0.911893i	$0.634621\pi$
$692$	−3.18659	+	5.51934i	−0.121136	+	0.209814i
$693$	1.84305	+	0.215422i	0.0700118	+	0.00818320i
$694$	9.18245	+	9.73283i	0.348561	+	0.369453i
$695$	2.77988	+	3.73402i	0.105447	+	0.141640i
$696$	1.26633	−	4.22982i	0.0480000	−	0.160331i
$697$	2.34570	+	40.2741i	0.0888496	+	1.52549i
$698$	20.3334	−	13.3735i	0.769632	−	0.506195i
$699$	−0.672957	−	11.5542i	−0.0254536	−	0.437021i
$700$	0.638100	−	3.61884i	0.0241179	−	0.136779i
$701$	−4.08098	−	5.48170i	−0.154136	−	0.207041i	0.718347	−	0.695685i	$-0.244899\pi$
$701$	−4.08098	−	5.48170i	−0.154136	−	0.207041i	−0.872483	+	0.488644i	$0.837492\pi$
$702$	−0.0460174	+	0.0109063i	−0.00173681	+	0.000411632i
$703$	−18.7525	−	4.44443i	−0.707265	−	0.167625i
$704$	−0.130109	+	2.23389i	−0.00490367	+	0.0841928i
$705$	1.30501	+	2.26034i	0.0491494	+	0.0851292i
$706$	3.22888	+	7.48537i	0.121520	+	0.281716i
$707$	11.6769	−	5.86438i	0.439157	−	0.220553i
$708$	−2.39214	+	7.99031i	−0.0899022	+	0.300294i
$709$	−22.9357	+	15.0851i	−0.861369	+	0.566531i	−0.901557	−	0.432661i	$-0.857575\pi$
$709$	−22.9357	+	15.0851i	−0.861369	+	0.566531i	0.0401879	+	0.999192i	$0.487204\pi$
$710$	8.95507			0.336078
$711$	−4.36227			−0.163598
$712$	−3.15872	+	2.07753i	−0.118378	+	0.0778586i
$713$	−0.490121	+	2.77961i	−0.0183552	+	0.104097i
$714$	1.71558	−	2.30443i	0.0642041	−	0.0862410i
$715$	0.0228882	+	0.0764519i	0.000855970	+	0.00285914i
$716$	−1.82302	+	0.663524i	−0.0681294	+	0.0247971i
$717$	9.66029	−	8.10595i	0.360770	−	0.302722i
$718$	6.48478	−	6.87346i	0.242010	−	0.256515i
$719$	49.0085	+	5.72827i	1.82771	+	0.213628i	0.959333	−	0.282278i	$-0.0910902\pi$
$719$	49.0085	+	5.72827i	1.82771	+	0.213628i	0.868376	+	0.495907i	$0.165164\pi$
$720$	−0.216285	−	0.722442i	−0.00806046	−	0.0269238i
$721$	0.265878	−	0.0310767i	0.00990181	−	0.00115736i
$722$	−0.00840955	+	0.00422343i	−0.000312971	+	0.000157180i
$723$	1.41737	+	1.90386i	0.0527125	+	0.0708052i
$724$	−3.61568	+	4.85670i	−0.134376	+	0.180498i
$725$	−19.4333	+	2.27142i	−0.721734	+	0.0843586i
$726$	−2.37363	−	5.50270i	−0.0880938	−	0.204224i
$727$	−27.4674	−	6.50989i	−1.01871	−	0.241439i	−0.312859	−	0.949800i	$-0.601287\pi$
$727$	−27.4674	−	6.50989i	−1.01871	−	0.241439i	−0.705850	+	0.708361i	$0.749435\pi$
$728$	0.0350457	+	0.0176006i	0.00129888	+	0.000652323i
$729$	0.766044	−	0.642788i	0.0283720	−	0.0238069i
$730$	−3.47292	+	6.01528i	−0.128539	+	0.222636i
$731$	−23.4119	+	24.8152i	−0.865920	+	0.917822i
$732$	0.278302	+	0.139769i	0.0102863	+	0.00516600i
$733$	−0.0543197	+	0.932633i	−0.00200634	+	0.0344476i	−0.999163	−	0.0409124i	$-0.986974\pi$
$733$	−0.0543197	+	0.932633i	−0.00200634	+	0.0344476i	0.997156	+	0.0753600i	$0.0240106\pi$
$734$	−0.269147	+	4.62107i	−0.00993438	+	0.170567i
$735$	−4.25394	−	2.13641i	−0.156909	−	0.0788026i
$736$	0.526870	−	0.558450i	0.0194207	−	0.0205847i
$737$	7.26284	−	12.5796i	0.267530	−	0.463376i
$738$	8.92031	−	7.48503i	0.328361	−	0.275528i
$739$	−31.9171	−	16.0294i	−1.17409	−	0.589650i	−0.248668	−	0.968589i	$-0.579993\pi$
$739$	−31.9171	−	16.0294i	−1.17409	−	0.589650i	−0.925422	+	0.378939i	$0.876289\pi$
$740$	−3.24513	−	0.769111i	−0.119293	−	0.0282731i
$741$	−0.0816283	−	0.189236i	−0.00299869	−	0.00695175i
$742$	−1.89016	+	0.220929i	−0.0693901	+	0.00811054i
$743$	15.9758	−	21.4592i	0.586095	−	0.787262i	−0.405849	−	0.913940i	$-0.633024\pi$
$743$	15.9758	−	21.4592i	0.586095	−	0.787262i	0.991944	+	0.126678i	$0.0404316\pi$
$744$	2.19531	+	2.94882i	0.0804841	+	0.108109i
$745$	2.90483	−	1.45886i	0.106425	−	0.0534485i
$746$	17.8945	−	2.09157i	0.655164	−	0.0765777i
$747$	0.684000	+	2.28472i	0.0250262	+	0.0835935i
$748$	7.69990	+	0.899989i	0.281536	+	0.0329069i
$749$	9.41573	−	9.98009i	0.344043	−	0.364665i
$750$	−5.44838	+	4.57174i	−0.198947	+	0.166936i
$751$	36.0452	−	13.1194i	1.31531	−	0.478733i	0.413356	−	0.910570i	$-0.364357\pi$
$751$	36.0452	−	13.1194i	1.31531	−	0.478733i	0.901952	+	0.431837i	$0.142134\pi$
$752$	0.992624	+	3.31559i	0.0361973	+	0.120907i
$753$	18.7689	−	25.2111i	0.683979	−	0.918743i
$754$	0.0362594	−	0.205637i	0.00132049	−	0.00748887i
$755$	13.4161	−	8.82390i	0.488262	−	0.321135i
$756$	−0.829253			−0.0301597
$757$	46.0729			1.67455			0.837273	−	0.546785i	$-0.184148\pi$
$757$	46.0729			1.67455			0.837273	+	0.546785i	$0.184148\pi$
$758$	−2.22195	+	1.46140i	−0.0807047	+	0.0530803i
$759$	0.492728	−	1.64583i	0.0178849	−	0.0597397i
$760$	2.93677	−	1.47490i	0.106528	−	0.0535003i
$761$	−1.94217	−	4.50246i	−0.0704036	−	0.163214i	0.879381	−	0.476119i	$-0.157957\pi$
$761$	−1.94217	−	4.50246i	−0.0704036	−	0.163214i	−0.949784	+	0.312905i	$0.898698\pi$
$762$	−1.52558	−	2.64238i	−0.0552659	−	0.0957234i
$763$	−0.893685	+	15.3440i	−0.0323536	+	0.555489i
$764$	15.4309	+	3.65720i	0.558272	+	0.132313i
$765$	−2.54220	+	0.602512i	−0.0919134	+	0.0217839i
$766$	18.7294	+	25.1580i	0.676722	+	0.908995i
$767$	−0.0684955	+	0.388457i	−0.00247323	+	0.0140264i
$768$	−0.0581448	−	0.998308i	−0.00209812	−	0.0360233i
$769$	39.4237	−	25.9294i	1.42165	−	0.935037i	0.422060	−	0.906568i	$-0.361307\pi$
$769$	39.4237	−	25.9294i	1.42165	−	0.935037i	0.999595	−	0.0284693i	$-0.00906328\pi$
$770$	0.0813649	+	1.39698i	0.00293219	+	0.0503437i
$771$	−7.67431	+	25.6340i	−0.276383	+	0.923185i
$772$	−3.65527	−	4.90988i	−0.131556	−	0.176711i
$773$	27.1463	+	28.7734i	0.976386	+	1.03491i	0.999381	+	0.0351734i	$0.0111984\pi$
$773$	27.1463	+	28.7734i	0.976386	+	1.03491i	−0.0229949	+	0.999736i	$0.507320\pi$
$774$	9.78088	+	1.14322i	0.351567	+	0.0410922i
$775$	8.14531	−	14.1081i	0.292588	−	0.506778i
$776$	10.9715	+	7.21604i	0.393852	+	0.259041i
$777$	−1.83364	+	3.17596i	−0.0657816	+	0.113937i
$778$	−5.46670	+	1.98971i	−0.195991	+	0.0713347i
$779$	38.8731	+	32.6184i	1.39277	+	1.16868i
$780$	−0.0141258	−	0.0327473i	−0.000505785	−	0.00117254i
$781$	25.8557	−	6.12792i	0.925191	−	0.219274i
$782$	−1.82532	−	1.93472i	−0.0652732	−	0.0691856i
$783$	1.26633	+	4.22982i	0.0452548	+	0.151162i
$784$	−4.83553	−	4.05749i	−0.172698	−	0.144910i
$785$	−1.05583	−	1.82875i	−0.0376841	−	0.0652708i
$786$	0.809035	−	13.8906i	0.0288573	−	0.495461i
$787$	7.19536	+	2.61890i	0.256487	+	0.0933536i	0.467063	−	0.884224i	$-0.345312\pi$
$787$	7.19536	+	2.61890i	0.256487	+	0.0933536i	−0.210577	+	0.977577i	$0.567534\pi$
$788$	−1.12566	+	0.409708i	−0.0401001	+	0.0145952i
$789$	10.7621	+	1.25791i	0.383140	+	0.0447826i
$790$	−0.571249	−	3.23971i	−0.0203241	−	0.115264i
$791$	−10.6120	−	2.51509i	−0.377319	−	0.0894263i
$792$	−1.11884	−	1.93788i	−0.0397561	−	0.0688597i
$793$	0.0138399	+	0.00503731i	0.000491469	+	0.000178880i
$794$	−28.1563	+	23.6259i	−0.999230	+	0.838453i
$795$	1.44591	+	0.950990i	0.0512811	+	0.0337281i
$796$	−14.8816	−	9.78777i	−0.527464	−	0.346918i
$797$	−3.31968	+	3.51866i	−0.117589	+	0.124637i	−0.783494	−	0.621400i	$-0.786564\pi$
$797$	−3.31968	+	3.51866i	−0.117589	+	0.124637i	0.665905	+	0.746037i	$0.268046\pi$
$798$	−0.627519	−	3.55884i	−0.0222139	−	0.125981i
$799$	11.6672	−	2.76519i	0.412757	−	0.0978253i
$800$	−3.95995	+	1.98876i	−0.140005	+	0.0703134i
$801$	1.49746	−	3.47149i	0.0529100	−	0.122659i
$802$	0.850392	−	4.82281i	0.0300284	−	0.170299i
$803$	−5.91104	+	19.7443i	−0.208596	+	0.696760i
$804$	−2.57112	+	5.96053i	−0.0906764	+	0.210212i
$805$	0.286712	−	0.385121i	0.0101053	−	0.0135737i
$806$	0.119309	+	0.126460i	0.00420247	+	0.00445436i
$807$	−3.77723	−	21.4217i	−0.132965	−	0.754081i
$808$	−14.0813	−	7.07188i	−0.495377	−	0.248788i
$809$	28.8613	+	10.5047i	1.01471	+	0.369324i	0.795240	−	0.606295i	$-0.207345\pi$
$809$	28.8613	+	10.5047i	1.01471	+	0.369324i	0.219470	+	0.975619i	$0.429567\pi$
$810$	0.577692	+	0.484741i	0.0202980	+	0.0170321i
$811$	−4.23239	+	0.494695i	−0.148619	+	0.0173711i	−0.190077	−	0.981769i	$-0.560874\pi$
$811$	−4.23239	+	0.494695i	−0.148619	+	0.0173711i	0.0414580	+	0.999140i	$0.486800\pi$
$812$	1.45021	−	3.36197i	0.0508924	−	0.117982i
$813$	0.341031	+	5.85528i	0.0119605	+	0.205354i
$814$	−9.89588			−0.346850
$815$	8.16841	−	5.09661i	0.286127	−	0.178526i
$816$	−3.46445			−0.121280
$817$	2.49520	+	42.8409i	0.0872959	+	1.49881i
$818$	−0.465819	+	1.07989i	−0.0162870	+	0.0377575i
$819$	−0.0389520	+	0.00455283i	−0.00136109	+	0.000159089i
$820$	6.72701	+	5.64463i	0.234917	+	0.197119i
$821$	17.6987	+	6.44180i	0.617689	+	0.224820i	0.631864	−	0.775079i	$-0.282290\pi$
$821$	17.6987	+	6.44180i	0.617689	+	0.224820i	−0.0141753	+	0.999900i	$0.504512\pi$
$822$	1.53359	+	0.770196i	0.0534900	+	0.0268637i
$823$	−6.20532	−	35.1921i	−0.216304	−	1.22672i	−0.878630	−	0.477504i	$-0.841542\pi$
$823$	−6.20532	−	35.1921i	−0.216304	−	1.22672i	0.662326	−	0.749216i	$-0.269569\pi$
$824$	−0.221523	−	0.234801i	−0.00771712	−	0.00817967i
$825$	−5.92131	+	7.95370i	−0.206153	+	0.276912i
$826$	−2.73951	+	6.35089i	−0.0953197	+	0.220976i
$827$	0.264782	−	0.884434i	0.00920738	−	0.0307548i	−0.953262	−	0.302144i	$-0.902298\pi$
$827$	0.264782	−	0.884434i	0.00920738	−	0.0307548i	0.962470	+	0.271389i	$0.0874829\pi$
$828$	−0.133320	+	0.756098i	−0.00463321	+	0.0262762i
$829$	2.90179	−	6.72709i	0.100783	−	0.233642i	−0.860363	−	0.509682i	$-0.829763\pi$
$829$	2.90179	−	6.72709i	0.100783	−	0.233642i	0.961146	+	0.276040i	$0.0890223\pi$
$830$	−1.60721	+	0.807172i	−0.0557871	+	0.0280174i
$831$	−9.16509	+	2.17217i	−0.317933	+	0.0753516i
$832$	−0.00821219	−	0.0465737i	−0.000284707	−	0.00161465i
$833$	−15.0073	+	15.9068i	−0.519972	+	0.551138i
$834$	−5.15744	−	3.39210i	−0.178588	−	0.117459i
$835$	1.90936	+	1.25581i	0.0660761	+	0.0434589i
$836$	7.46999	−	6.26807i	0.258355	−	0.216786i
$837$	−3.45456	−	1.25736i	−0.119407	−	0.0434606i
$838$	1.27029	+	2.20021i	0.0438814	+	0.0760049i
$839$	11.3703	+	2.69482i	0.392548	+	0.0930356i	0.422150	−	0.906526i	$-0.361276\pi$
$839$	11.3703	+	2.69482i	0.392548	+	0.0930356i	−0.0296016	+	0.999562i	$0.509424\pi$
$840$	−0.108592	−	0.615858i	−0.00374679	−	0.0212491i
$841$	9.44075	+	1.10347i	0.325543	+	0.0380505i
$842$	15.5596	−	5.66325i	0.536221	−	0.195168i
$843$	−12.0324	−	4.37945i	−0.414420	−	0.150836i
$844$	0.800843	−	13.7499i	0.0275661	−	0.473293i
$845$	4.90096	+	8.48870i	0.168598	+	0.292020i
$846$	−2.65127	−	2.22468i	−0.0911527	−	0.0764862i
$847$	−1.42529	−	4.76079i	−0.0489734	−	0.163583i
$848$	1.57484	+	1.66923i	0.0540802	+	0.0573216i
$849$	−11.4081	+	2.70377i	−0.391525	+	0.0927931i
$850$	6.08063	+	14.0965i	0.208564	+	0.483505i
$851$	2.60099	+	2.18249i	0.0891607	+	0.0748147i
$852$	−11.1587	+	4.06143i	−0.382290	+	0.139142i
$853$	−28.8489	+	49.9678i	−0.987769	+	1.71087i	−0.358850	+	0.933395i	$0.616831\pi$
$853$	−28.8489	+	49.9678i	−0.987769	+	1.71087i	−0.628919	+	0.777471i	$0.716502\pi$
$854$	0.215767	+	0.141912i	0.00738340	+	0.00485614i
$855$	−1.64317	+	2.84605i	−0.0561951	+	0.0973327i
$856$	−16.4340	−	1.92086i	−0.561703	−	0.0656536i
$857$	−17.5656	−	18.6184i	−0.600028	−	0.635993i	0.354165	−	0.935183i	$-0.384765\pi$
$857$	−17.5656	−	18.6184i	−0.600028	−	0.635993i	−0.954194	+	0.299190i	$0.903284\pi$
$858$	−0.0631939	−	0.0848842i	−0.00215741	−	0.00289790i
$859$	−1.64435	+	5.49250i	−0.0561044	+	0.187402i	−0.981448	−	0.191727i	$-0.938591\pi$
$859$	−1.64435	+	5.49250i	−0.0561044	+	0.187402i	0.925344	+	0.379129i	$0.123776\pi$
$860$	0.431795	+	7.41364i	0.0147241	+	0.252803i
$861$	8.06777	−	5.30625i	0.274949	−	0.180837i
$862$	−0.944188	−	16.2111i	−0.0321592	−	0.552151i
$863$	9.34017	−	52.9707i	0.317943	−	1.80314i	−0.237278	−	0.971442i	$-0.576255\pi$
$863$	9.34017	−	52.9707i	0.317943	−	1.80314i	0.555221	−	0.831703i	$-0.312634\pi$
$864$	0.597159	+	0.802123i	0.0203157	+	0.0272888i
$865$	4.67661	−	1.10838i	0.159010	−	0.0376860i
$866$	−18.2786	−	4.33210i	−0.621131	−	0.147211i
$867$	0.290582	−	4.98911i	0.00986869	−	0.169439i
$868$	1.52428	+	2.64013i	0.0517373	+	0.0896117i
$869$	−3.86627	−	8.96303i	−0.131154	−	0.304050i
$870$	−2.97552	+	1.49436i	−0.100880	+	0.0506636i
$871$	−0.0880466	+	0.294096i	−0.00298335	+	0.00996507i
$872$	15.4855	−	10.1850i	0.524406	−	0.344907i
$873$	−13.1318			−0.444444
$874$	−3.34577			−0.113172
$875$	−4.92766	+	3.24097i	−0.166585	+	0.109565i
$876$	1.59939	−	9.07057i	0.0540383	−	0.306466i
$877$	17.4488	−	23.4378i	0.589203	−	0.791437i	−0.403115	−	0.915149i	$-0.632073\pi$
$877$	17.4488	−	23.4378i	0.589203	−	0.791437i	0.992318	+	0.123713i	$0.0394801\pi$
$878$	8.01410	+	26.7689i	0.270463	+	0.903408i
$879$	−1.26360	+	0.459912i	−0.0426201	+	0.0155125i
$880$	1.29269	−	1.08469i	0.0435764	−	0.0365650i
$881$	7.01723	−	7.43783i	0.236416	−	0.250587i	−0.598293	−	0.801277i	$-0.704154\pi$
$881$	7.01723	−	7.43783i	0.236416	−	0.250587i	0.834709	+	0.550691i	$0.185636\pi$
$882$	6.26966	+	0.732818i	0.211110	+	0.0246753i
$883$	13.6342	+	45.5413i	0.458827	+	1.53259i	0.804337	+	0.594173i	$0.202521\pi$
$883$	13.6342	+	45.5413i	0.458827	+	1.53259i	−0.345510	+	0.938415i	$0.612294\pi$
$884$	−0.162734	+	0.0190208i	−0.00547332	+	0.000639739i
$885$	5.62087	−	2.82291i	0.188944	−	0.0948911i
$886$	0.848213	+	1.13935i	0.0284963	+	0.0382771i
$887$	24.5286	−	32.9476i	0.823590	−	1.10627i	−0.169103	−	0.985598i	$-0.554087\pi$
$887$	24.5286	−	32.9476i	0.823590	−	1.10627i	0.992692	−	0.120674i	$-0.0385057\pi$
$888$	4.39249	−	0.513409i	0.147402	−	0.0172289i
$889$	−1.00215	−	2.32326i	−0.0336112	−	0.0779195i
$890$	2.77426	+	0.657511i	0.0929933	+	0.0220398i
$891$	1.99966	+	1.00427i	0.0669911	+	0.0336442i
$892$	−0.711616	+	0.597116i	−0.0238267	+	0.0199929i
$893$	7.54119	−	13.0617i	0.252356	−	0.437094i
$894$	−2.95799	+	3.13528i	−0.0989299	+	0.104860i
$895$	1.30739	+	0.656598i	0.0437013	+	0.0219476i
$896$	0.0482168	−	0.827850i	0.00161081	−	0.0276565i
$897$	−0.00211119	+	0.0362477i	−7.04904e−5	+	0.00121027i
$898$	−12.7026	−	6.37950i	−0.423892	−	0.212887i
$899$	11.1390	−	11.8066i	0.371506	−	0.393773i
$900$	2.21565	−	3.83762i	0.0738550	−	0.127921i
$901$	6.09042	−	5.11047i	0.202901	−	0.170255i
$902$	23.2853	+	11.6943i	0.775316	+	0.389378i
$903$	7.94593	+	1.88322i	0.264424	+	0.0626696i
$904$	5.20906	+	12.0760i	0.173251	+	0.401641i
$905$	4.53520	−	0.530088i	0.150755	−	0.0176207i
$906$	−12.7155	+	17.0799i	−0.422444	+	0.567441i
$907$	−14.9285	−	20.0525i	−0.495693	−	0.665831i	0.481927	−	0.876212i	$-0.339937\pi$
$907$	−14.9285	−	20.0525i	−0.495693	−	0.665831i	−0.977620	+	0.210380i	$0.932530\pi$
$908$	−14.6282	+	7.34658i	−0.485455	+	0.243805i
$909$	15.6508	−	1.82932i	0.519104	−	0.0606745i
$910$	−0.00848208	−	0.0283321i	−0.000281178	−	0.000939200i
$911$	34.6459	+	4.04953i	1.14787	+	0.134167i	0.668684	−	0.743547i	$-0.266858\pi$
$911$	34.6459	+	4.04953i	1.14787	+	0.134167i	0.479186	+	0.877713i	$0.340932\pi$
$912$	−2.99052	+	3.16976i	−0.0990259	+	0.104961i
$913$	−4.08811	+	3.43033i	−0.135297	+	0.113527i
$914$	−18.7505	+	6.82463i	−0.620212	+	0.225739i
$915$	−0.0673572	−	0.224989i	−0.00222676	−	0.00743790i
$916$	−11.4099	+	15.3262i	−0.376995	+	0.506392i
$917$	2.00361	−	11.3630i	0.0661651	−	0.375241i
$918$	2.89451	−	1.90375i	0.0955330	−	0.0628331i
$919$	5.66531			0.186881			0.0934407	−	0.995625i	$-0.470213\pi$
$919$	5.66531			0.186881			0.0934407	+	0.995625i	$0.470213\pi$
$920$	−0.578987			−0.0190886
$921$	7.47222	−	4.91455i	0.246218	−	0.161940i
$922$	2.21184	−	7.38807i	0.0728432	−	0.243313i
$923$	−0.501851	+	0.252039i	−0.0165186	+	0.00829597i
$924$	−0.734965	−	1.70384i	−0.0241786	−	0.0560522i
$925$	−9.79848	−	16.9715i	−0.322172	−	0.558018i
$926$	−2.32177	+	39.8632i	−0.0762980	+	1.30999i
$927$	0.314105	+	0.0744442i	0.0103166	+	0.00244507i
$928$	−4.29630	+	1.01824i	−0.141033	+	0.0334254i
$929$	−25.3689	−	34.0763i	−0.832325	−	1.11801i	−0.991416	−	0.130743i	$-0.958264\pi$
$929$	−25.3689	−	34.0763i	−0.832325	−	1.11801i	0.159091	−	0.987264i	$-0.449144\pi$
$930$	0.481414	−	2.73024i	0.0157862	−	0.0895280i
$931$	1.59945	+	27.4615i	0.0524199	+	0.900014i
$932$	−9.66978	+	6.35991i	−0.316744	+	0.208326i
$933$	0.278425	+	4.78038i	0.00911524	+	0.156503i
$934$	−6.51803	+	21.7717i	−0.213276	+	0.712393i
$935$	−3.49111	−	4.68937i	−0.114171	−	0.153359i
$936$	0.0324538	+	0.0343990i	0.00106079	+	0.00112437i
$937$	41.3248	+	4.83017i	1.35002	+	0.157795i	0.760174	−	0.649720i	$-0.225114\pi$
$937$	41.3248	+	4.83017i	1.35002	+	0.157795i	0.589848	+	0.807515i	$0.299188\pi$
$938$	−2.69152	+	4.66184i	−0.0878811	+	0.152215i
$939$	5.43908	+	3.57734i	0.177498	+	0.116742i
$940$	1.30501	−	2.26034i	0.0425646	−	0.0737241i
$941$	−38.4408	+	13.9913i	−1.25313	+	0.456103i	−0.881459	−	0.472260i	$-0.843438\pi$
$941$	−38.4408	+	13.9913i	−1.25313	+	0.456103i	−0.371674	+	0.928363i	$0.621216\pi$
$942$	2.14504	+	1.79990i	0.0698891	+	0.0586439i
$943$	−3.54108	−	8.20914i	−0.115313	−	0.267326i
$944$	8.11588	−	1.92350i	0.264149	−	0.0626046i
$945$	0.429147	+	0.454870i	0.0139602	+	0.0147969i
$946$	6.31983	+	21.1097i	0.205475	+	0.686336i
$947$	−1.92517	−	1.61541i	−0.0625596	−	0.0524937i	0.610972	−	0.791652i	$-0.290779\pi$
$947$	−1.92517	−	1.61541i	−0.0625596	−	0.0524937i	−0.673531	+	0.739159i	$0.735223\pi$
$948$	2.18114	+	3.77784i	0.0708400	+	0.122699i
$949$	0.0253270	−	0.434847i	0.000822148	−	0.0141157i
$950$	18.1462	+	6.60468i	0.588741	+	0.214284i
$951$	11.8820	−	4.32468i	0.385299	−	0.140237i
$952$	−2.85348	−	0.333524i	−0.0924820	−	0.0108096i
$953$	−1.90474	−	10.8023i	−0.0617005	−	0.349921i	−0.999992	−	0.00407473i	$-0.998703\pi$
$953$	−1.90474	−	10.8023i	−0.0617005	−	0.349921i	0.938291	−	0.345846i	$-0.112408\pi$
$954$	−2.23302	−	0.529234i	−0.0722965	−	0.0171346i
$955$	−5.97959	−	10.3570i	−0.193495	−	0.335143i
$956$	−11.8501	−	4.31308i	−0.383260	−	0.139495i
$957$	−7.56854	+	6.35076i	−0.244656	+	0.205291i
$958$	−12.6017	−	8.28830i	−0.407144	−	0.267783i
$959$	1.18899	+	0.782008i	0.0383943	+	0.0252524i
$960$	−0.517510	+	0.548529i	−0.0167026	+	0.0177037i
$961$	−3.03625	−	17.2194i	−0.0979437	−	0.555466i
$962$	0.203507	−	0.0482320i	0.00656133	−	0.00155506i
$963$	14.7859	−	7.42578i	0.476470	−	0.239292i
$964$	0.940104	−	2.17941i	0.0302787	−	0.0701939i
$965$	−0.801572	+	4.54594i	−0.0258035	+	0.146339i
$966$	−0.182599	+	0.609922i	−0.00587502	+	0.0196239i
$967$	2.57966	−	5.98032i	0.0829562	−	0.192314i	−0.871689	−	0.490059i	$-0.836975\pi$
$967$	2.57966	−	5.98032i	0.0829562	−	0.192314i	0.954645	+	0.297745i	$0.0962345\pi$
$968$	−3.57866	+	4.80698i	−0.115023	+	0.154502i
$969$	10.3605	+	10.9815i	0.332827	+	0.352777i
$970$	−1.71964	−	9.75254i	−0.0552142	−	0.313135i
$971$	−27.8473	−	13.9855i	−0.893663	−	0.448815i	−0.0581645	−	0.998307i	$-0.518525\pi$
$971$	−27.8473	−	13.9855i	−0.893663	−	0.448815i	−0.835499	+	0.549492i	$0.814821\pi$
$972$	−0.939693	−	0.342020i	−0.0301407	−	0.0109703i
$973$	−3.92135	−	3.29040i	−0.125713	−	0.105485i
$974$	−2.83612	+	0.331494i	−0.0908750	+	0.0106218i
$975$	0.0830047	−	0.192426i	0.00265828	−	0.00616258i
$976$	−0.0181079	−	0.310901i	−0.000579621	−	0.00995170i
$977$	−58.0435			−1.85698			−0.928488	−	0.371361i	$-0.878891\pi$
$977$	−58.0435			−1.85698			−0.928488	+	0.371361i	$0.878891\pi$
$978$	−7.86696	+	10.0554i	−0.251557	+	0.321536i
$979$	8.45996			0.270382
$980$	0.276786	+	4.75223i	0.00884159	+	0.151804i
$981$	−7.34123	+	17.0189i	−0.234387	+	0.543371i
$982$	32.9503	−	3.85134i	1.05149	−	0.122901i
$983$	30.7365	+	25.7910i	0.980343	+	0.822605i	0.984141	−	0.177387i	$-0.0567645\pi$
$983$	30.7365	+	25.7910i	0.980343	+	0.822605i	−0.00379809	+	0.999993i	$0.501209\pi$
$984$	−10.9424	−	3.98270i	−0.348830	−	0.126964i
$985$	0.807280	+	0.405431i	0.0257221	+	0.0129181i
$986$	2.65623	+	15.0643i	0.0845917	+	0.479744i
$987$	−1.96954	−	2.08759i	−0.0626912	−	0.0664488i
$988$	−0.123069	+	0.165310i	−0.00391534	+	0.00525921i
$989$	2.99457	−	6.94218i	0.0952216	−	0.220749i
$990$	−0.483975	+	1.61659i	−0.0153817	+	0.0513786i
$991$	−2.23687	+	12.6859i	−0.0710565	+	0.402982i	0.928447	+	0.371466i	$0.121145\pi$
$991$	−2.23687	+	12.6859i	−0.0710565	+	0.402982i	−0.999503	+	0.0315160i	$0.989966\pi$
$992$	1.45609	−	3.37560i	0.0462310	−	0.107176i
$993$	8.30403	−	4.17044i	0.263520	−	0.132345i
$994$	−9.58180	+	2.27093i	−0.303916	+	0.0720295i
$995$	2.33250	+	13.2283i	0.0739452	+	0.419364i
$996$	1.63662	−	1.73472i	0.0518584	−	0.0549667i
$997$	−45.5213	−	29.9399i	−1.44168	−	0.948205i	−0.998663	−	0.0516890i	$-0.983540\pi$
$997$	−45.5213	−	29.9399i	−1.44168	−	0.948205i	−0.443012	−	0.896516i	$-0.646090\pi$
$998$	18.9741	+	12.4795i	0.600616	+	0.395031i
$999$	−3.38775	+	2.84266i	−0.107184	+	0.0899378i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	978.2.m.a.61.4	✓	108
163.155	even	27	inner	978.2.m.a.481.4	yes	108

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
978.2.m.a.61.4	✓	108	1.1	even	1	trivial
978.2.m.a.481.4	yes	108	163.155	even	27	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:	\( N \)	\(=\)	\( 978 = 2 \cdot 3 \cdot 163 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	978.m (of order \(27\), degree \(18\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0581448 - 0.998308i) q^{2} +(0.396080 - 0.918216i) q^{3} +(-0.993238 + 0.116093i) q^{4} +(0.577692 + 0.484741i) q^{5} +(-0.939693 - 0.342020i) q^{6} +(-0.741048 - 0.372168i) q^{7} +(0.173648 + 0.984808i) q^{8} +(-0.686242 - 0.727374i) q^{9} +(0.450331 - 0.604899i) q^{10} +(0.886297 - 2.05467i) q^{11} +(-0.286803 + 0.957990i) q^{12} +(-0.00821219 + 0.0465737i) q^{13} +(-0.328450 + 0.761434i) q^{14} +(0.673909 - 0.338450i) q^{15} +(0.973045 - 0.230616i) q^{16} +(-0.601596 - 3.41182i) q^{17} +(-0.686242 + 0.727374i) q^{18} +(-3.64090 - 2.39466i) q^{19} +(-0.630060 - 0.414397i) q^{20} +(-0.635245 + 0.533034i) q^{21} +(-2.10273 - 0.765330i) q^{22} +(0.383881 + 0.664901i) q^{23} +(0.973045 + 0.230616i) q^{24} +(-0.769487 - 4.36398i) q^{25} +(0.0469724 + 0.00549028i) q^{26} +(-0.939693 + 0.342020i) q^{27} +(0.779243 + 0.283621i) q^{28} +(0.256728 - 4.40784i) q^{29} +(-0.377061 - 0.653090i) q^{30} +(2.81618 + 2.36306i) q^{31} +(-0.286803 - 0.957990i) q^{32} +(-1.53559 - 1.62763i) q^{33} +(-3.37107 + 0.798958i) q^{34} +(-0.247692 - 0.574215i) q^{35} +(0.766044 + 0.642788i) q^{36} +(4.15569 - 1.51255i) q^{37} +(-2.17891 + 3.77398i) q^{38} +(0.0395120 + 0.0259874i) q^{39} +(-0.377061 + 0.653090i) q^{40} +(-11.5659 - 1.35186i) q^{41} +(0.569068 + 0.603177i) q^{42} +(-5.88050 - 7.89888i) q^{43} +(-0.641772 + 2.14367i) q^{44} +(-0.0438483 - 0.752847i) q^{45} +(0.641456 - 0.421892i) q^{46} +(0.201239 + 3.45514i) q^{47} +(0.173648 - 0.984808i) q^{48} +(-3.76947 - 5.06327i) q^{49} +(-4.31185 + 1.02193i) q^{50} +(-3.37107 - 0.798958i) q^{51} +(0.00274979 - 0.0472121i) q^{52} +(1.14744 + 1.98742i) q^{53} +(0.396080 + 0.918216i) q^{54} +(1.50799 - 0.757340i) q^{55} +(0.237833 - 0.794416i) q^{56} +(-3.64090 + 2.39466i) q^{57} -4.41531 q^{58} +8.34071 q^{59} +(-0.630060 + 0.414397i) q^{60} +(0.0540789 - 0.306697i) q^{61} +(2.19531 - 2.94882i) q^{62} +(0.237833 + 0.794416i) q^{63} +(-0.939693 + 0.342020i) q^{64} +(-0.0273203 + 0.0229244i) q^{65} +(-1.53559 + 1.62763i) q^{66} +(6.44753 + 0.753608i) q^{67} +(0.993617 + 3.31891i) q^{68} +(0.762570 - 0.0891317i) q^{69} +(-0.558841 + 0.280661i) q^{70} +(7.09115 + 9.52507i) q^{71} +(0.597159 - 0.802123i) q^{72} +(-9.14822 + 1.06927i) q^{73} +(-1.75162 - 4.06071i) q^{74} +(-4.31185 - 1.02193i) q^{75} +(3.89429 + 1.95579i) q^{76} +(-1.42147 + 1.19276i) q^{77} +(0.0236461 - 0.0409562i) q^{78} +(2.99357 - 3.17300i) q^{79} +(0.673909 + 0.338450i) q^{80} +(-0.0581448 + 0.998308i) q^{81} +(-0.677076 + 11.6249i) q^{82} +(-2.13123 - 1.07035i) q^{83} +(0.569068 - 0.603177i) q^{84} +(1.30631 - 2.26260i) q^{85} +(-7.54360 + 6.32983i) q^{86} +(-3.94567 - 1.98159i) q^{87} +(2.17736 + 0.516043i) q^{88} +(1.49746 + 3.47149i) q^{89} +(-0.749024 + 0.0875483i) q^{90} +(0.0234189 - 0.0314570i) q^{91} +(-0.458476 - 0.615840i) q^{92} +(3.28523 - 1.64990i) q^{93} +(3.43759 - 0.401797i) q^{94} +(-0.942530 - 3.14827i) q^{95} +(-0.993238 - 0.116093i) q^{96} +(9.01158 - 9.55172i) q^{97} +(-4.83553 + 4.05749i) q^{98} +(-2.10273 + 0.765330i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 108 q - 18 q^{7} + 18 q^{11} + 9 q^{13} + 18 q^{14} + 27 q^{17} - 9 q^{19} - 18 q^{22} + 9 q^{23} - 36 q^{25} - 18 q^{29} + 9 q^{30} + 45 q^{31} + 36 q^{34} - 27 q^{37} + 27 q^{39} + 9 q^{40} + 36 q^{41}+ \cdots - 18 q^{99}+O(q^{100}) \) 108 * q - 18 * q^7 + 18 * q^11 + 9 * q^13 + 18 * q^14 + 27 * q^17 - 9 * q^19 - 18 * q^22 + 9 * q^23 - 36 * q^25 - 18 * q^29 + 9 * q^30 + 45 * q^31 + 36 * q^34 - 27 * q^37 + 27 * q^39 + 9 * q^40 + 36 * q^41 + 9 * q^42 + 81 * q^43 + 9 * q^46 - 9 * q^47 + 36 * q^49 + 18 * q^50 + 36 * q^51 + 27 * q^52 + 27 * q^53 + 63 * q^55 - 18 * q^56 - 9 * q^57 - 54 * q^58 - 36 * q^59 + 18 * q^61 - 9 * q^62 - 18 * q^63 + 63 * q^65 + 45 * q^67 + 9 * q^68 - 36 * q^69 - 45 * q^70 + 9 * q^71 - 18 * q^74 + 18 * q^75 - 9 * q^76 - 54 * q^77 + 18 * q^78 + 27 * q^79 + 18 * q^82 + 9 * q^83 + 9 * q^84 - 27 * q^86 + 9 * q^87 - 27 * q^89 - 117 * q^91 + 18 * q^92 + 9 * q^93 + 27 * q^94 - 54 * q^95 - 90 * q^97 - 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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