LMFDB - Embedded newform 570.2.bb.b.41.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(41,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 0, 13]))

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

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

chi := DirichletCharacter("570.41");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bb (of order $18$, degree $6$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$14$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			41.6
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.b.431.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(-0.169275 - 1.72376i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-0.978339 + 1.42928i) q^{6} +(1.36690 + 2.36755i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.94269 + 0.583578i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.169275 - 1.72376i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-0.978339 + 1.42928i) q^{6} +(1.36690 + 2.36755i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.94269 + 0.583578i) q^{9} +(0.642788 + 0.766044i) q^{10} +(0.676767 + 0.390732i) q^{11} +(1.66818 - 0.466031i) q^{12} +(-1.83374 + 5.03816i) q^{13} +(0.474720 - 2.69227i) q^{14} +(-0.132625 + 1.72697i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.15858 + 2.57249i) q^{17} +(2.62935 + 1.44448i) q^{18} +(3.57411 + 2.49514i) q^{19} -1.00000i q^{20} +(3.84970 - 2.75698i) q^{21} +(-0.267276 - 0.734335i) q^{22} +(-3.18651 + 0.561867i) q^{23} +(-1.57746 - 0.715283i) q^{24} +(0.939693 + 0.342020i) q^{25} +(4.64320 - 2.68075i) q^{26} +(1.50407 + 4.97371i) q^{27} +(-2.09422 + 1.75726i) q^{28} +(-1.79957 + 1.51002i) q^{29} +(1.21167 - 1.23768i) q^{30} +(1.09008 - 0.629356i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.558968 - 1.23272i) q^{33} +(3.30713 - 0.583137i) q^{34} +(-0.935017 - 2.56894i) q^{35} +(-1.08571 - 2.79665i) q^{36} +8.00419i q^{37} +(-1.13409 - 4.20878i) q^{38} +(8.99499 + 2.30810i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(7.68435 - 2.79688i) q^{41} +(-4.72119 - 0.362570i) q^{42} +(0.817700 - 4.63741i) q^{43} +(-0.267276 + 0.734335i) q^{44} +(2.99932 - 0.0637190i) q^{45} +(2.80217 + 1.61783i) q^{46} +(-0.780232 - 0.929844i) q^{47} +(0.748627 + 1.56191i) q^{48} +(-0.236847 + 0.410231i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.79975 + 3.28541i) q^{51} +(-5.28005 - 0.931015i) q^{52} +(-0.895427 - 5.07822i) q^{53} +(2.04485 - 4.77688i) q^{54} +(-0.598636 - 0.502315i) q^{55} +2.73381 q^{56} +(3.69601 - 6.58328i) q^{57} +2.34917 q^{58} +(2.63329 + 2.20959i) q^{59} +(-1.72376 + 0.169275i) q^{60} +(-1.18539 - 6.72266i) q^{61} +(-1.23959 - 0.218573i) q^{62} +(-5.40402 - 6.16926i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.68075 - 4.64320i) q^{65} +(-1.22057 + 0.585024i) q^{66} +(5.36968 + 6.39933i) q^{67} +(-2.90825 - 1.67908i) q^{68} +(1.50792 + 5.39766i) q^{69} +(-0.935017 + 2.56894i) q^{70} +(-2.56916 + 14.5704i) q^{71} +(-0.965953 + 2.84024i) q^{72} +(-5.90744 + 2.15013i) q^{73} +(5.14499 - 6.13156i) q^{74} +(0.430494 - 1.67770i) q^{75} +(-1.83659 + 3.95309i) q^{76} +2.13637i q^{77} +(-5.40695 - 7.54997i) q^{78} +(-0.164078 - 0.450801i) q^{79} +(0.984808 - 0.173648i) q^{80} +(8.31887 - 3.43458i) q^{81} +(-7.68435 - 2.79688i) q^{82} +(-13.4104 + 7.74247i) q^{83} +(3.38359 + 3.31247i) q^{84} +(2.57249 - 2.15858i) q^{85} +(-3.60726 + 3.02685i) q^{86} +(2.90753 + 2.84642i) q^{87} +(0.676767 - 0.390732i) q^{88} +(15.3353 + 5.58160i) q^{89} +(-2.33857 - 1.87912i) q^{90} +(-14.4346 + 2.54521i) q^{91} +(-1.10666 - 3.04053i) q^{92} +(-1.26938 - 1.77250i) q^{93} +1.21383i q^{94} +(-3.08654 - 3.07787i) q^{95} +(0.430494 - 1.67770i) q^{96} +(3.53989 - 4.21868i) q^{97} +(0.445127 - 0.162013i) q^{98} +(-2.21954 - 0.754857i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) $ 84 * q - 6 * q^6 + 42 * q^8	$ 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) $ 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{13}{18}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$2$	−0.766044	−	0.642788i	−0.541675	−	0.454519i
$3$	−0.169275	−	1.72376i	−0.0977308	−	0.995213i
$3$	−0.169275	−	1.72376i	−0.0977308	−	0.995213i
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$	−0.984808	−	0.173648i	−0.440419	−	0.0776578i
$5$	−0.984808	−	0.173648i	−0.440419	−	0.0776578i
$6$	−0.978339	+	1.42928i	−0.399405	+	0.583503i
$7$	1.36690	+	2.36755i	0.516641	+	0.894848i	0.999813	+	0.0193228i	$0.00615103\pi$
$7$	1.36690	+	2.36755i	0.516641	+	0.894848i	−0.483173	+	0.875525i	$0.660516\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	−2.94269	+	0.583578i	−0.980897	+	0.194526i
$10$	0.642788	+	0.766044i	0.203267	+	0.242245i
$11$	0.676767	+	0.390732i	0.204053	+	0.117810i	0.598545	−	0.801090i	$-0.295746\pi$
$11$	0.676767	+	0.390732i	0.204053	+	0.117810i	−0.394492	+	0.918900i	$0.629079\pi$
$12$	1.66818	−	0.466031i	0.481561	−	0.134531i
$13$	−1.83374	+	5.03816i	−0.508588	+	1.39734i	0.374105	+	0.927386i	$0.377950\pi$
$13$	−1.83374	+	5.03816i	−0.508588	+	1.39734i	−0.882694	+	0.469949i	$0.844272\pi$
$14$	0.474720	−	2.69227i	0.126874	−	0.719540i
$15$	−0.132625	+	1.72697i	−0.0342435	+	0.445901i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−2.15858	+	2.57249i	−0.523532	+	0.623922i	−0.961412	−	0.275112i	$-0.911285\pi$
$17$	−2.15858	+	2.57249i	−0.523532	+	0.623922i	0.437880	+	0.899033i	$0.355730\pi$
$18$	2.62935	+	1.44448i	0.619744	+	0.340467i
$19$	3.57411	+	2.49514i	0.819958	+	0.572423i
$19$	3.57411	+	2.49514i	0.819958	+	0.572423i
$20$		−	1.00000i		−	0.223607i
$21$	3.84970	−	2.75698i	0.840073	−	0.601622i
$22$	−0.267276	−	0.734335i	−0.0569835	−	0.156561i
$23$	−3.18651	+	0.561867i	−0.664433	+	0.117157i	−0.495686	−	0.868502i	$-0.665083\pi$
$23$	−3.18651	+	0.561867i	−0.664433	+	0.117157i	−0.168747	+	0.985659i	$0.553972\pi$
$24$	−1.57746	−	0.715283i	−0.321997	−	0.146007i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	4.64320	−	2.68075i	0.910606	−	0.525739i
$27$	1.50407	+	4.97371i	0.289459	+	0.957191i
$28$	−2.09422	+	1.75726i	−0.395770	+	0.332090i
$29$	−1.79957	+	1.51002i	−0.334172	+	0.280404i	−0.794397	−	0.607399i	$-0.792213\pi$
$29$	−1.79957	+	1.51002i	−0.334172	+	0.280404i	0.460225	+	0.887802i	$0.347769\pi$
$30$	1.21167	−	1.23768i	0.221219	−	0.225969i
$31$	1.09008	−	0.629356i	0.195784	−	0.113036i	−0.398904	−	0.916993i	$-0.630609\pi$
$31$	1.09008	−	0.629356i	0.195784	−	0.113036i	0.594687	+	0.803957i	$0.297276\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	0.558968	−	1.23272i	0.0973038	−	0.214590i
$34$	3.30713	−	0.583137i	0.567169	−	0.100007i
$35$	−0.935017	−	2.56894i	−0.158047	−	0.434230i
$36$	−1.08571	−	2.79665i	−0.180951	−	0.466108i
$37$			8.00419i			1.31588i	0.753070	+	0.657940i	$0.228572\pi$
$37$			8.00419i			1.31588i	−0.753070	+	0.657940i	$0.771428\pi$
$38$	−1.13409	−	4.20878i	−0.183973	−	0.682755i
$39$	8.99499	+	2.30810i	1.44035	+	0.369591i
$40$	−0.642788	+	0.766044i	−0.101634	+	0.121122i
$41$	7.68435	−	2.79688i	1.20009	−	0.436799i	0.336837	−	0.941563i	$-0.390643\pi$
$41$	7.68435	−	2.79688i	1.20009	−	0.436799i	0.863257	+	0.504764i	$0.168421\pi$
$42$	−4.72119	−	0.362570i	−0.728495	−	0.0559457i
$43$	0.817700	−	4.63741i	0.124698	−	0.707198i	−0.856789	−	0.515668i	$-0.827544\pi$
$43$	0.817700	−	4.63741i	0.124698	−	0.707198i	0.981487	−	0.191530i	$-0.0613450\pi$
$44$	−0.267276	+	0.734335i	−0.0402934	+	0.110705i
$45$	2.99932	−	0.0637190i	0.447113	−	0.00949866i
$46$	2.80217	+	1.61783i	0.413157	+	0.238536i
$47$	−0.780232	−	0.929844i	−0.113809	−	0.135632i	0.706132	−	0.708080i	$-0.250438\pi$
$47$	−0.780232	−	0.929844i	−0.113809	−	0.135632i	−0.819941	+	0.572448i	$0.805994\pi$
$48$	0.748627	+	1.56191i	0.108055	+	0.225442i
$49$	−0.236847	+	0.410231i	−0.0338353	+	0.0586044i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	4.79975	+	3.28541i	0.672100	+	0.460050i
$52$	−5.28005	−	0.931015i	−0.732211	−	0.129109i
$53$	−0.895427	−	5.07822i	−0.122996	−	0.697547i	−0.982478	−	0.186380i	$-0.940324\pi$
$53$	−0.895427	−	5.07822i	−0.122996	−	0.697547i	0.859481	−	0.511167i	$-0.170787\pi$
$54$	2.04485	−	4.77688i	0.278269	−	0.650051i
$55$	−0.598636	−	0.502315i	−0.0807200	−	0.0677321i
$56$	2.73381			0.365320
$57$	3.69601	−	6.58328i	0.489548	−	0.871976i
$58$	2.34917			0.308462
$59$	2.63329	+	2.20959i	0.342825	+	0.287665i	0.797901	−	0.602788i	$-0.205944\pi$
$59$	2.63329	+	2.20959i	0.342825	+	0.287665i	−0.455076	+	0.890453i	$0.650388\pi$
$60$	−1.72376	+	0.169275i	−0.222536	+	0.0218533i
$61$	−1.18539	−	6.72266i	−0.151773	−	0.860749i	−0.961677	−	0.274186i	$-0.911592\pi$
$61$	−1.18539	−	6.72266i	−0.151773	−	0.860749i	0.809903	−	0.586563i	$-0.199519\pi$
$62$	−1.23959	−	0.218573i	−0.157428	−	0.0277588i
$63$	−5.40402	−	6.16926i	−0.680843	−	0.777254i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.68075	−	4.64320i	0.332506	−	0.575918i
$66$	−1.22057	+	0.585024i	−0.150242	+	0.0720115i
$67$	5.36968	+	6.39933i	0.656011	+	0.781803i	0.986807	−	0.161899i	$-0.0517618\pi$
$67$	5.36968	+	6.39933i	0.656011	+	0.781803i	−0.330797	+	0.943702i	$0.607317\pi$
$68$	−2.90825	−	1.67908i	−0.352677	−	0.203618i
$69$	1.50792	+	5.39766i	0.181532	+	0.649802i
$70$	−0.935017	+	2.56894i	−0.111756	+	0.307047i
$71$	−2.56916	+	14.5704i	−0.304903	+	1.72919i	0.319056	+	0.947736i	$0.396634\pi$
$71$	−2.56916	+	14.5704i	−0.304903	+	1.72919i	−0.623960	+	0.781457i	$0.714477\pi$
$72$	−0.965953	+	2.84024i	−0.113839	+	0.334725i
$73$	−5.90744	+	2.15013i	−0.691414	+	0.251654i	−0.663741	−	0.747963i	$-0.731032\pi$
$73$	−5.90744	+	2.15013i	−0.691414	+	0.251654i	−0.0276735	+	0.999617i	$0.508810\pi$
$74$	5.14499	−	6.13156i	0.598093	−	0.712780i
$75$	0.430494	−	1.67770i	0.0497092	−	0.193724i
$76$	−1.83659	+	3.95309i	−0.210671	+	0.453451i
$77$			2.13637i			0.243462i
$78$	−5.40695	−	7.54997i	−0.612216	−	0.854866i
$79$	−0.164078	−	0.450801i	−0.0184602	−	0.0507190i	0.930120	−	0.367255i	$-0.119702\pi$
$79$	−0.164078	−	0.450801i	−0.0184602	−	0.0507190i	−0.948580	+	0.316536i	$0.897480\pi$
$80$	0.984808	−	0.173648i	0.110105	−	0.0194145i
$81$	8.31887	−	3.43458i	0.924319	−	0.381620i
$82$	−7.68435	−	2.79688i	−0.848595	−	0.308863i
$83$	−13.4104	+	7.74247i	−1.47198	+	0.849847i	−0.999504	−	0.0314977i	$-0.989972\pi$
$83$	−13.4104	+	7.74247i	−1.47198	+	0.849847i	−0.472474	+	0.881345i	$0.656639\pi$
$84$	3.38359	+	3.31247i	0.369179	+	0.361420i
$85$	2.57249	−	2.15858i	0.279026	−	0.234131i
$86$	−3.60726	+	3.02685i	−0.388981	+	0.326394i
$87$	2.90753	+	2.84642i	0.311720	+	0.305168i
$88$	0.676767	−	0.390732i	0.0721436	−	0.0416521i
$89$	15.3353	+	5.58160i	1.62554	+	0.591649i	0.984427	−	0.175796i	$-0.0562498\pi$
$89$	15.3353	+	5.58160i	1.62554	+	0.591649i	0.641115	+	0.767445i	$0.278472\pi$
$90$	−2.33857	−	1.87912i	−0.246507	−	0.198076i
$91$	−14.4346	+	2.54521i	−1.51316	+	0.266811i
$92$	−1.10666	−	3.04053i	−0.115378	−	0.316997i
$93$	−1.26938	−	1.77250i	−0.131629	−	0.183799i
$94$			1.21383i			0.125197i
$95$	−3.08654	−	3.07787i	−0.316672	−	0.315783i
$96$	0.430494	−	1.67770i	0.0439371	−	0.171229i
$97$	3.53989	−	4.21868i	0.359421	−	0.428342i	−0.555786	−	0.831326i	$-0.687582\pi$
$97$	3.53989	−	4.21868i	0.359421	−	0.428342i	0.915207	+	0.402984i	$0.132027\pi$
$98$	0.445127	−	0.162013i	0.0449646	−	0.0163658i
$99$	−2.21954	−	0.754857i	−0.223072	−	0.0758660i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−3.47778	+	9.55513i	−0.346052	+	0.950771i	0.637548	+	0.770410i	$0.279949\pi$
$101$	−3.47778	+	9.55513i	−0.346052	+	0.950771i	−0.983601	+	0.180361i	$0.942274\pi$
$102$	−1.56500	−	5.60199i	−0.154958	−	0.554680i
$103$	−10.1752	−	5.87466i	−1.00259	−	0.578847i	−0.0935782	−	0.995612i	$-0.529831\pi$
$103$	−10.1752	−	5.87466i	−1.00259	−	0.578847i	−0.909014	+	0.416765i	$0.863164\pi$
$104$	3.44631	+	4.10715i	0.337938	+	0.402739i
$105$	−4.26995	+	2.04660i	−0.416705	+	0.199728i
$106$	−2.57828	+	4.46571i	−0.250425	+	0.433748i
$107$	−0.672386	−	1.16461i	−0.0650020	−	0.112587i	0.831693	−	0.555236i	$-0.187372\pi$
$107$	−0.672386	−	1.16461i	−0.0650020	−	0.112587i	−0.896695	+	0.442649i	$0.854039\pi$
$108$	−4.63697	+	2.34490i	−0.446192	+	0.225638i
$109$	−5.09821	−	0.898952i	−0.488320	−	0.0861040i	−0.0759334	−	0.997113i	$-0.524194\pi$
$109$	−5.09821	−	0.898952i	−0.488320	−	0.0861040i	−0.412387	+	0.911009i	$0.635305\pi$
$110$	0.135700	+	0.769591i	0.0129385	+	0.0733776i
$111$	13.7973	−	1.35491i	1.30958	−	0.128602i
$112$	−2.09422	−	1.75726i	−0.197885	−	0.166045i
$113$	1.25063			0.117649			0.0588246	−	0.998268i	$-0.481265\pi$
$113$	1.25063			0.117649			0.0588246	+	0.998268i	$0.481265\pi$
$114$	−7.06295	+	2.66734i	−0.661506	+	0.249819i
$115$	3.23566			0.301727
$116$	−1.79957	−	1.51002i	−0.167086	−	0.140202i
$117$	2.45598	−	15.8959i	0.227055	−	1.46958i
$118$	−0.596919	−	3.38529i	−0.0549508	−	0.311642i
$119$	−9.04106	−	1.59418i	−0.828793	−	0.146139i
$120$	1.42928	+	0.978339i	0.130475	+	0.0893097i
$121$	−5.19466	−	8.99741i	−0.472242	−	0.817946i
$122$	−3.41319	+	5.91181i	−0.309015	+	0.535230i
$123$	−6.12191	−	12.7725i	−0.551994	−	1.15166i
$124$	0.809085	+	0.964230i	0.0726580	+	0.0865904i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	0.174195	+	8.19957i	0.0155186	+	0.730475i
$127$	−7.30812	+	20.0789i	−0.648491	+	1.78171i	−0.0252542	+	0.999681i	$0.508040\pi$
$127$	−7.30812	+	20.0789i	−0.648491	+	1.78171i	−0.623237	+	0.782033i	$0.714183\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−8.13219	−	0.624522i	−0.716000	−	0.0549861i
$130$	−5.03816	+	1.83374i	−0.441876	+	0.160830i
$131$	−8.27650	+	9.86355i	−0.723122	+	0.861783i	−0.994930	−	0.100569i	$-0.967934\pi$
$131$	−8.27650	+	9.86355i	−0.723122	+	0.861783i	0.271809	+	0.962351i	$0.412378\pi$
$132$	1.31106	+	0.336415i	0.114113	+	0.0292812i
$133$	−1.02188	+	11.8725i	−0.0886081	+	1.02948i
$134$		−	8.35374i		−	0.721653i
$135$	−0.617546	−	5.15933i	−0.0531499	−	0.444044i
$136$	1.14856	+	3.15563i	0.0984879	+	0.270593i
$137$	17.8980	−	3.15589i	1.52913	−	0.269626i	0.655114	−	0.755530i	$-0.272621\pi$
$137$	17.8980	−	3.15589i	1.52913	−	0.269626i	0.874012	+	0.485904i	$0.161510\pi$
$138$	2.31442	−	5.10412i	0.197016	−	0.434492i
$139$	−4.26956	−	1.55399i	−0.362140	−	0.131808i	0.154541	−	0.987986i	$-0.450610\pi$
$139$	−4.26956	−	1.55399i	−0.362140	−	0.131808i	−0.516680	+	0.856178i	$0.672832\pi$
$140$	2.36755	−	1.36690i	0.200094	−	0.115524i
$141$	−1.47075	+	1.50233i	−0.123860	+	0.126519i
$142$	11.3338	−	9.51018i	0.951110	−	0.798076i
$143$	−3.20959	+	2.69316i	−0.268399	+	0.225214i
$144$	2.56563	−	1.55484i	0.213803	−	0.129570i
$145$	2.03444	−	1.17459i	0.168951	−	0.0975442i
$146$	5.90744	+	2.15013i	0.488904	+	0.177946i
$147$	0.747231	+	0.338825i	0.0616306	+	0.0279458i
$148$	−7.88259	+	1.38991i	−0.647945	+	0.114250i
$149$	−7.53994	−	20.7158i	−0.617696	−	1.69710i	−0.712557	−	0.701614i	$-0.752463\pi$
$149$	−7.53994	−	20.7158i	−0.617696	−	1.69710i	0.0948614	−	0.995490i	$-0.469759\pi$
$150$	−1.40818	+	1.00848i	−0.114978	+	0.0823417i
$151$		−	0.916825i		−	0.0746101i	−0.999304	−	0.0373051i	$-0.988123\pi$
$151$		−	0.916825i		−	0.0746101i	0.999304	−	0.0373051i	$-0.0118773\pi$
$152$	3.94791	−	1.84771i	0.320218	−	0.149869i
$153$	4.85078	−	8.82976i	0.392163	−	0.713844i
$154$	1.37323	−	1.63655i	0.110658	−	0.131877i
$155$	−1.18280	+	0.430505i	−0.0950050	+	0.0345790i
$156$	−0.711067	+	9.25913i	−0.0569309	+	0.741324i
$157$	0.581587	−	3.29835i	0.0464157	−	0.263237i	−0.952765	−	0.303709i	$-0.901775\pi$
$157$	0.581587	−	3.29835i	0.0464157	−	0.263237i	0.999181	+	0.0404720i	$0.0128862\pi$
$158$	−0.164078	+	0.450801i	−0.0130533	+	0.0358638i
$159$	−8.60205	+	2.40311i	−0.682187	+	0.190579i
$160$	−0.866025	−	0.500000i	−0.0684653	−	0.0395285i
$161$	−5.68589	−	6.77618i	−0.448111	−	0.534038i
$162$	−8.58033	−	2.71623i	−0.674135	−	0.213407i
$163$	1.00331	−	1.73778i	0.0785852	−	0.136114i	−0.824055	−	0.566510i	$-0.808293\pi$
$163$	1.00331	−	1.73778i	0.0785852	−	0.136114i	0.902640	+	0.430397i	$0.141626\pi$
$164$	4.08876	+	7.08194i	0.319278	+	0.553007i
$165$	−0.764536	+	1.11693i	−0.0595191	+	0.0869531i
$166$	15.2497	+	2.68893i	1.18361	+	0.208702i
$167$	2.33587	+	13.2474i	0.180755	+	1.02511i	0.931289	+	0.364282i	$0.118685\pi$
$167$	2.33587	+	13.2474i	0.180755	+	1.02511i	−0.750534	+	0.660832i	$0.770203\pi$
$168$	−0.462764	−	4.71242i	−0.0357030	−	0.363571i
$169$	−12.0619	−	10.1211i	−0.927839	−	0.778549i
$170$	−3.35815			−0.257559
$171$	−11.9736	−	5.25664i	−0.915646	−	0.401985i
$172$	4.70895			0.359054
$173$	−17.8302	−	14.9613i	−1.35560	−	1.13749i	−0.977313	−	0.211801i	$-0.932067\pi$
$173$	−17.8302	−	14.9613i	−1.35560	−	1.13749i	−0.378292	−	0.925686i	$-0.623489\pi$
$174$	−0.397656	−	4.04941i	−0.0301462	−	0.306985i
$175$	0.474720	+	2.69227i	0.0358855	+	0.203517i
$176$	−0.769591	−	0.135700i	−0.0580101	−	0.0102287i
$177$	3.36306	−	4.91319i	0.252783	−	0.369298i
$178$	−8.15976	−	14.1331i	−0.611600	−	1.05932i
$179$	−0.856163	+	1.48292i	−0.0639926	+	0.110838i	−0.896247	−	0.443556i	$-0.853717\pi$
$179$	−0.856163	+	1.48292i	−0.0639926	+	0.110838i	0.832254	+	0.554394i	$0.187050\pi$
$180$	0.583578	+	2.94269i	0.0434973	+	0.219335i
$181$	4.80217	+	5.72301i	0.356943	+	0.425388i	0.914396	−	0.404820i	$-0.132666\pi$
$181$	4.80217	+	5.72301i	0.356943	+	0.425388i	−0.557454	+	0.830208i	$0.688222\pi$
$182$	12.6936	+	7.32865i	0.940912	+	0.543236i
$183$	−11.3876	+	3.18130i	−0.841796	+	0.235168i
$184$	−1.10666	+	3.04053i	−0.0815842	+	0.224151i
$185$	1.38991	−	7.88259i	0.102188	−	0.579539i
$186$	−0.166936	+	2.17375i	−0.0122404	+	0.159387i
$187$	−2.46601	+	0.897554i	−0.180333	+	0.0656357i
$188$	0.780232	−	0.929844i	0.0569043	−	0.0678159i
$189$	−9.71956	+	10.3595i	−0.706994	+	0.753545i
$190$	0.386012	+	4.34177i	0.0280042	+	0.314985i
$191$			4.87308i			0.352604i	0.984336	+	0.176302i	$0.0564135\pi$
$191$			4.87308i			0.352604i	−0.984336	+	0.176302i	$0.943587\pi$
$192$	−1.40818	+	1.00848i	−0.101627	+	0.0727805i
$193$	1.34677	+	3.70022i	0.0969425	+	0.266347i	0.978679	−	0.205394i	$-0.0658477\pi$
$193$	1.34677	+	3.70022i	0.0969425	+	0.266347i	−0.881737	+	0.471742i	$0.843625\pi$
$194$	−5.42343	+	0.956297i	−0.389379	+	0.0686581i
$195$	−8.45754	−	3.83499i	−0.605657	−	0.274630i
$196$	−0.445127	−	0.162013i	−0.0317948	−	0.0115723i
$197$	−22.0891	+	12.7532i	−1.57378	+	0.908625i	−0.578085	+	0.815976i	$0.696200\pi$
$197$	−22.0891	+	12.7532i	−1.57378	+	0.908625i	−0.995699	+	0.0926482i	$0.970467\pi$
$198$	1.21505	+	2.00495i	0.0863501	+	0.142485i
$199$	15.2010	−	12.7551i	1.07757	−	0.904188i	0.0818523	−	0.996644i	$-0.473916\pi$
$199$	15.2010	−	12.7551i	1.07757	−	0.904188i	0.995717	+	0.0924567i	$0.0294720\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	10.1220	−	10.3393i	0.713948	−	0.729277i
$202$	8.80606	−	5.08418i	0.619592	−	0.357722i
$203$	−6.03488	−	2.19652i	−0.423566	−	0.154165i
$204$	−2.40203	+	5.29734i	−0.168176	+	0.370888i
$205$	−8.05328	+	1.42001i	−0.562466	+	0.0991779i
$206$	4.01850	+	11.0407i	0.279982	+	0.769245i
$207$	9.04902	−	3.51298i	0.628950	−	0.244169i
$208$		−	5.36150i		−	0.371753i
$209$	1.44391	+	3.08515i	0.0998777	+	0.213404i
$210$	4.58650	+	1.17689i	0.316499	+	0.0812129i
$211$	13.0204	−	15.5172i	0.896364	−	1.06825i	−0.100942	−	0.994892i	$-0.532186\pi$
$211$	13.0204	−	15.5172i	0.896364	−	1.06825i	0.997306	−	0.0733527i	$-0.0233699\pi$
$212$	4.84558	−	1.76365i	0.332796	−	0.121128i
$213$	25.5508	+	1.96221i	1.75071	+	0.134448i
$214$	−0.233517	+	1.32434i	−0.0159629	+	0.0905301i
$215$	−1.61056	+	4.42496i	−0.109839	+	0.301780i
$216$	5.05939	+	1.18429i	0.344248	+	0.0805807i
$217$	2.98006	+	1.72054i	0.202300	+	0.116798i
$218$	3.32762	+	3.96571i	0.225375	+	0.268591i
$219$	4.70629	+	9.81905i	0.318022	+	0.663510i
$220$	0.390732	−	0.676767i	0.0263431	−	0.0456276i
$221$	−9.00237	−	15.5926i	−0.605565	−	1.04887i
$222$	−11.4403	−	7.83081i	−0.767820	−	0.525570i
$223$	24.1851	+	4.26449i	1.61956	+	0.285571i	0.908601	−	0.417666i	$-0.137152\pi$
$223$	24.1851	+	4.26449i	1.61956	+	0.285571i	0.710955	+	0.703237i	$0.248263\pi$
$224$	0.474720	+	2.69227i	0.0317186	+	0.179885i
$225$	−2.96482	−	0.458076i	−0.197655	−	0.0305384i
$226$	−0.958036	−	0.803888i	−0.0637276	−	0.0534738i
$227$	12.9486			0.859427			0.429714	−	0.902965i	$-0.358615\pi$
$227$	12.9486			0.859427			0.429714	+	0.902965i	$0.358615\pi$
$228$	7.12507	+	2.49668i	0.471869	+	0.165347i
$229$	17.5070			1.15690			0.578449	−	0.815719i	$-0.303658\pi$
$229$	17.5070			1.15690			0.578449	+	0.815719i	$0.303658\pi$
$230$	−2.47866	−	2.07985i	−0.163438	−	0.137141i
$231$	3.68259	−	0.361633i	0.242296	−	0.0237937i
$232$	0.407930	+	2.31349i	0.0267819	+	0.151888i
$233$	29.1821	+	5.14558i	1.91178	+	0.337098i	0.997661	−	0.0683492i	$-0.0217732\pi$
$233$	29.1821	+	5.14558i	1.91178	+	0.337098i	0.914118	+	0.405448i	$0.132884\pi$
$234$	−12.0991	+	10.5983i	−0.790941	+	0.692832i
$235$	0.606913	+	1.05120i	0.0395906	+	0.0685730i
$236$	−1.71876	+	2.97698i	−0.111882	+	0.193785i
$237$	−0.749297	+	0.359140i	−0.0486721	+	0.0233287i
$238$	5.90114	+	7.03270i	0.382514	+	0.455862i
$239$	1.73420	+	1.00124i	0.112176	+	0.0647649i	0.555038	−	0.831825i	$-0.312704\pi$
$239$	1.73420	+	1.00124i	0.112176	+	0.0647649i	−0.442862	+	0.896590i	$0.646037\pi$
$240$	−0.466031	−	1.66818i	−0.0300822	−	0.107680i
$241$	2.13395	−	5.86298i	0.137460	−	0.377668i	−0.851794	−	0.523877i	$-0.824485\pi$
$241$	2.13395	−	5.86298i	0.137460	−	0.377668i	0.989254	+	0.146209i	$0.0467073\pi$
$242$	−1.80409	+	10.2315i	−0.115971	+	0.657704i
$243$	−7.32857	−	13.7583i	−0.470128	−	0.882598i
$244$	6.41469	−	2.33476i	0.410659	−	0.149467i
$245$	0.304484	−	0.362870i	0.0194528	−	0.0231829i
$246$	−3.52037	+	13.7194i	−0.224451	+	0.874718i
$247$	−19.1249	+	13.4315i	−1.21689	+	0.854629i
$248$		−	1.25871i		−	0.0799283i
$249$	15.6162	+	21.8056i	0.989636	+	1.38188i
$250$	0.342020	+	0.939693i	0.0216313	+	0.0594314i
$251$	−7.20190	+	1.26989i	−0.454580	+	0.0801547i	−0.396250	−	0.918143i	$-0.629689\pi$
$251$	−7.20190	+	1.26989i	−0.454580	+	0.0801547i	−0.0583300	+	0.998297i	$0.518578\pi$
$252$	5.13714	−	6.39320i	0.323609	−	0.402734i
$253$	−2.37606	−	0.864816i	−0.149382	−	0.0543705i
$254$	18.5048	−	10.6838i	1.16110	−	0.670359i
$255$	−4.15633	−	4.06897i	−0.260279	−	0.254809i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	16.4509	−	13.8039i	1.02618	−	0.861065i	0.0357863	−	0.999359i	$-0.488606\pi$
$257$	16.4509	−	13.8039i	1.02618	−	0.861065i	0.990391	+	0.138294i	$0.0441620\pi$
$258$	5.82819	+	5.70568i	0.362847	+	0.355220i
$259$	−18.9503	+	10.9409i	−1.17751	+	0.679837i
$260$	5.03816	+	1.83374i	0.312454	+	0.113724i
$261$	4.41437	−	5.49371i	0.273243	−	0.340052i
$262$	12.6803	−	2.23589i	0.783394	−	0.138134i
$263$	−3.24002	−	8.90187i	−0.199788	−	0.548913i	0.798825	−	0.601563i	$-0.205455\pi$
$263$	−3.24002	−	8.90187i	−0.199788	−	0.548913i	−0.998613	+	0.0526506i	$0.983233\pi$
$264$	−0.788087	−	1.10044i	−0.0485034	−	0.0677276i
$265$			5.15656i			0.316765i
$266$	8.41429	−	8.43800i	0.515913	−	0.517367i
$267$	7.02546	−	27.3792i	0.429951	−	1.67558i
$268$	−5.36968	+	6.39933i	−0.328005	+	0.390902i
$269$	14.2677	−	5.19301i	0.869916	−	0.316624i	0.131783	−	0.991279i	$-0.457930\pi$
$269$	14.2677	−	5.19301i	0.869916	−	0.316624i	0.738133	+	0.674655i	$0.235708\pi$
$270$	−2.84328	+	4.34922i	−0.173037	+	0.264685i
$271$	−1.85456	+	10.5177i	−0.112656	+	0.638907i	0.875227	+	0.483712i	$0.160712\pi$
$271$	−1.85456	+	10.5177i	−0.112656	+	0.638907i	−0.987884	+	0.155195i	$0.950399\pi$
$272$	1.14856	−	3.15563i	0.0696414	−	0.191338i
$273$	6.83075	+	24.4510i	0.413416	+	1.47984i
$274$	−15.7392	−	9.08703i	−0.950840	−	0.548968i
$275$	0.502315	+	0.598636i	0.0302907	+	0.0360991i
$276$	−5.05381	+	2.42231i	−0.304204	+	0.145806i
$277$	−1.38012	+	2.39044i	−0.0829236	+	0.143628i	−0.904505	−	0.426464i	$-0.859759\pi$
$277$	−1.38012	+	2.39044i	−0.0829236	+	0.143628i	0.821581	+	0.570092i	$0.193092\pi$
$278$	2.27179	+	3.93485i	0.136253	+	0.235997i
$279$	−2.84048	+	2.48815i	−0.170055	+	0.148961i
$280$	−2.69227	−	0.474720i	−0.160894	−	0.0283700i
$281$	3.26591	+	18.5219i	0.194828	+	1.10492i	0.912664	+	0.408710i	$0.134021\pi$
$281$	3.26591	+	18.5219i	0.194828	+	1.10492i	−0.717837	+	0.696212i	$0.754867\pi$
$282$	2.09234	−	0.205470i	0.124597	−	0.0122356i
$283$	−4.18546	−	3.51201i	−0.248800	−	0.208768i	0.509856	−	0.860260i	$-0.329699\pi$
$283$	−4.18546	−	3.51201i	−0.248800	−	0.208768i	−0.758655	+	0.651492i	$0.774143\pi$
$284$	−14.7952			−0.877934
$285$	−4.78303	+	5.84146i	−0.283322	+	0.346018i
$286$	4.18982			0.247749
$287$	17.1255	+	14.3700i	1.01089	+	0.848234i
$288$	−2.96482	−	0.458076i	−0.174704	−	0.0269924i
$289$	0.993755	+	5.63587i	0.0584562	+	0.331522i
$290$	−2.31349	−	0.407930i	−0.135853	−	0.0239545i
$291$	−7.87120	−	5.38780i	−0.461418	−	0.315839i
$292$	−3.14329	−	5.44433i	−0.183947	−	0.318605i
$293$	−9.61474	+	16.6532i	−0.561699	+	0.972892i	0.435649	+	0.900117i	$0.356519\pi$
$293$	−9.61474	+	16.6532i	−0.561699	+	0.972892i	−0.997348	+	0.0727750i	$0.976814\pi$
$294$	−0.354620	−	0.739866i	−0.0206818	−	0.0431499i
$295$	−2.20959	−	2.63329i	−0.128648	−	0.153316i
$296$	6.93183	+	4.00209i	0.402904	+	0.232617i
$297$	−0.925479	+	3.95373i	−0.0537017	+	0.229419i
$298$	−7.53994	+	20.7158i	−0.436777	+	1.20003i
$299$	3.01245	−	17.0845i	0.174215	−	0.988020i
$300$	1.72697	+	0.132625i	0.0997064	+	0.00765708i
$301$	12.0970	−	4.40295i	0.697259	−	0.253782i
$302$	−0.589324	+	0.702329i	−0.0339118	+	0.0404145i
$303$	17.0594	+	4.37742i	0.980040	+	0.251476i
$304$	−4.21196	−	1.12224i	−0.241572	−	0.0643650i
$305$			6.82637i			0.390877i
$306$	−9.39157	+	3.64596i	−0.536881	+	0.208426i
$307$	−6.13513	−	16.8561i	−0.350150	−	0.962030i	−0.982322	−	0.187201i	$-0.940058\pi$
$307$	−6.13513	−	16.8561i	−0.350150	−	0.962030i	0.632171	−	0.774829i	$-0.282164\pi$
$308$	−2.10391	+	0.370977i	−0.119882	+	0.0211384i
$309$	−8.40409	+	18.5340i	−0.478092	+	1.05436i
$310$	1.18280	+	0.430505i	0.0671787	+	0.0244510i
$311$	−2.62998	+	1.51842i	−0.149133	+	0.0861018i	−0.572710	−	0.819758i	$-0.694108\pi$
$311$	−2.62998	+	1.51842i	−0.149133	+	0.0861018i	0.423577	+	0.905860i	$0.360774\pi$
$312$	6.49636	−	6.63584i	0.367784	−	0.375680i
$313$	22.5115	−	18.8894i	1.27243	−	1.06769i	0.278184	−	0.960528i	$-0.410268\pi$
$313$	22.5115	−	18.8894i	1.27243	−	1.06769i	0.994241	−	0.107164i	$-0.0341769\pi$
$314$	−2.56566	+	2.15284i	−0.144788	+	0.121492i
$315$	4.25064	+	7.01394i	0.239496	+	0.395191i
$316$	0.415460	−	0.239866i	0.0233715	−	0.0134935i
$317$	−2.81681	−	1.02523i	−0.158208	−	0.0575829i	0.261702	−	0.965149i	$-0.415716\pi$
$317$	−2.81681	−	1.02523i	−0.158208	−	0.0575829i	−0.419910	+	0.907566i	$0.637938\pi$
$318$	8.13425	+	3.68840i	0.456146	+	0.206835i
$319$	−1.80790	+	0.318782i	−0.101223	+	0.0178484i
$320$	0.342020	+	0.939693i	0.0191195	+	0.0525304i
$321$	−1.89368	+	1.35617i	−0.105695	+	0.0756940i
$322$			8.84568i			0.492950i
$323$	−14.1337	+	3.80844i	−0.786422	+	0.211907i
$324$	4.82696	+	7.59608i	0.268164	+	0.422005i
$325$	−3.44631	+	4.10715i	−0.191167	+	0.227824i
$326$	−1.88560	+	0.686304i	−0.104434	+	0.0380108i
$327$	−0.686579	+	8.94026i	−0.0379679	+	0.494398i
$328$	1.42001	−	8.05328i	0.0784070	−	0.444668i
$329$	1.13495	−	3.11824i	0.0625717	−	0.171914i
$330$	1.30362	−	0.364186i	0.0717619	−	0.0200478i
$331$	6.58443	+	3.80152i	0.361913	+	0.208950i	0.669919	−	0.742434i	$-0.266329\pi$
$331$	6.58443	+	3.80152i	0.361913	+	0.208950i	−0.308007	+	0.951384i	$0.599662\pi$
$332$	−9.95353	−	11.8622i	−0.546271	−	0.651020i
$333$	−4.67107	−	23.5539i	−0.255973	−	1.29074i
$334$	6.72588	−	11.6496i	0.368024	−	0.637436i
$335$	−4.17687	−	7.23455i	−0.228207	−	0.395266i
$336$	−2.67459	+	3.90738i	−0.145911	+	0.213165i
$337$	5.98487	+	1.05529i	0.326016	+	0.0574855i	0.334261	−	0.942481i	$-0.391513\pi$
$337$	5.98487	+	1.05529i	0.326016	+	0.0574855i	−0.00824465	+	0.999966i	$0.502624\pi$
$338$	2.73421	+	15.5065i	0.148722	+	0.843442i
$339$	−0.211700	−	2.15578i	−0.0114979	−	0.117086i
$340$	2.57249	+	2.15858i	0.139513	+	0.117065i
$341$	0.983638			0.0532670
$342$	5.79343	+	11.7233i	0.313273	+	0.633925i
$343$	17.8417			0.963359
$344$	−3.60726	−	3.02685i	−0.194491	−	0.163197i
$345$	−0.547716	−	5.57751i	−0.0294881	−	0.300283i
$346$	4.04178	+	22.9221i	0.217287	+	1.23230i
$347$	−33.8617	−	5.97073i	−1.81779	−	0.320526i	−0.842041	−	0.539413i	$-0.818646\pi$
$347$	−33.8617	−	5.97073i	−1.81779	−	0.320526i	−0.975750	+	0.218888i	$0.929757\pi$
$348$	−2.29829	+	3.35764i	−0.123201	+	0.179988i
$349$	−6.95446	−	12.0455i	−0.372264	−	0.644780i	0.617650	−	0.786453i	$-0.288085\pi$
$349$	−6.95446	−	12.0455i	−0.372264	−	0.644780i	−0.989913	+	0.141674i	$0.954752\pi$
$350$	1.36690	−	2.36755i	0.0730640	−	0.126551i
$351$	−27.8164	−	1.54274i	−1.48473	−	0.0823452i
$352$	0.502315	+	0.598636i	0.0267735	+	0.0319074i
$353$	−15.5839	−	8.99739i	−0.829450	−	0.478883i	0.0242146	−	0.999707i	$-0.492291\pi$
$353$	−15.5839	−	8.99739i	−0.829450	−	0.478883i	−0.853664	+	0.520824i	$0.825625\pi$
$354$	−5.73439	+	1.60199i	−0.304779	+	0.0851448i
$355$	5.06026	−	13.9029i	0.268571	−	0.737892i
$356$	−2.83385	+	16.0716i	−0.150194	+	0.851792i
$357$	−1.21756	+	15.8545i	−0.0644404	+	0.839108i
$358$	1.60906	−	0.585650i	0.0850415	−	0.0309526i
$359$	22.2073	−	26.4656i	1.17206	−	1.39680i	0.271291	−	0.962497i	$-0.412550\pi$
$359$	22.2073	−	26.4656i	1.17206	−	1.39680i	0.900766	−	0.434305i	$-0.143006\pi$
$360$	1.44448	−	2.62935i	0.0761307	−	0.138579i
$361$	6.54859	+	17.8358i	0.344663	+	0.938727i
$362$		−	7.47085i		−	0.392659i
$363$	−14.6300	+	10.4774i	−0.767878	+	0.549920i
$364$	−5.01309	−	13.7734i	−0.262757	−	0.721920i
$365$	6.19106	−	1.09165i	0.324055	−	0.0571397i
$366$	10.7683	+	4.88279i	0.562868	+	0.255228i
$367$	−12.7836	−	4.65286i	−0.667300	−	0.242877i	−0.0139152	−	0.999903i	$-0.504429\pi$
$367$	−12.7836	−	4.65286i	−0.667300	−	0.242877i	−0.653385	+	0.757026i	$0.726652\pi$
$368$	2.80217	−	1.61783i	0.146073	−	0.0843353i
$369$	−20.9805	+	12.7148i	−1.09220	+	0.661904i
$370$	−6.13156	+	5.14499i	−0.318765	+	0.267475i
$371$	10.7989	−	9.06139i	0.560654	−	0.470444i
$372$	1.52514	−	1.55789i	0.0790749	−	0.0807727i
$373$	8.82576	−	5.09556i	0.456981	−	0.263838i	−0.253793	−	0.967258i	$-0.581678\pi$
$373$	8.82576	−	5.09556i	0.456981	−	0.263838i	0.710774	+	0.703421i	$0.248345\pi$
$374$	2.46601	+	0.897554i	0.127514	+	0.0464114i
$375$	−0.715283	+	1.57746i	−0.0369371	+	0.0814595i
$376$	−1.19539	+	0.210779i	−0.0616473	+	0.0108701i
$377$	−4.30778	−	11.8355i	−0.221862	−	0.609561i
$378$	14.1046	−	1.68825i	0.725462	−	0.0868342i
$379$			19.8032i			1.01722i	0.860997	+	0.508610i	$0.169841\pi$
$379$			19.8032i			1.01722i	−0.860997	+	0.508610i	$0.830159\pi$
$380$	2.49514	−	3.57411i	0.127998	−	0.183348i
$381$	35.8483	+	9.19859i	1.83656	+	0.471258i
$382$	3.13235	−	3.73300i	0.160265	−	0.190997i
$383$	−4.16337	+	1.51534i	−0.212739	+	0.0774305i	−0.446191	−	0.894938i	$-0.647220\pi$
$383$	−4.16337	+	1.51534i	−0.212739	+	0.0774305i	0.233453	+	0.972368i	$0.424998\pi$
$384$	1.72697	+	0.132625i	0.0881289	+	0.00676797i
$385$	0.370977	−	2.10391i	0.0189067	−	0.107225i
$386$	1.34677	−	3.70022i	0.0685487	−	0.188336i
$387$	0.300049	+	14.1237i	0.0152524	+	0.717946i
$388$	4.76928	+	2.75355i	0.242124	+	0.139790i
$389$	21.6298	+	25.7774i	1.09668	+	1.30697i	0.948067	+	0.318071i	$0.103035\pi$
$389$	21.6298	+	25.7774i	1.09668	+	1.30697i	0.148609	+	0.988896i	$0.452520\pi$
$390$	4.01376	+	8.37418i	0.203245	+	0.424043i
$391$	5.43293	−	9.41011i	0.274755	−	0.475890i
$392$	0.236847	+	0.410231i	0.0119626	+	0.0207198i
$393$	18.4034	+	12.5971i	0.928329	+	0.635437i
$394$	25.1188	+	4.42912i	1.26547	+	0.223136i
$395$	0.0833046	+	0.472444i	0.00419151	+	0.0237712i
$396$	0.357970	−	2.31690i	0.0179887	−	0.116429i
$397$	27.1366	+	22.7703i	1.36195	+	1.14281i	0.975376	+	0.220551i	$0.0707854\pi$
$397$	27.1366	+	22.7703i	1.36195	+	1.14281i	0.386572	+	0.922259i	$0.373659\pi$
$398$	−19.8435			−0.994663
$399$	20.6383	−	0.248240i	1.03321	−	0.0124275i
$400$	−1.00000			−0.0500000
$401$	−15.6099	−	13.0983i	−0.779523	−	0.654097i	0.163606	−	0.986526i	$-0.447688\pi$
$401$	−15.6099	−	13.0983i	−0.779523	−	0.654097i	−0.943128	+	0.332428i	$0.892132\pi$
$402$	−14.3998	+	1.41408i	−0.718198	+	0.0705278i
$403$	1.17188	+	6.64606i	0.0583755	+	0.331064i
$404$	−10.0139	−	1.76572i	−0.498209	−	0.0878477i
$405$	−8.78890	+	1.93784i	−0.436724	+	0.0962923i
$406$	3.21109	+	5.56178i	0.159364	+	0.276026i
$407$	−3.12749	+	5.41697i	−0.155024	+	0.268509i
$408$	5.24513	−	2.51400i	0.259673	−	0.124462i
$409$	−19.7124	−	23.4924i	−0.974717	−	1.16162i	−0.986841	−	0.161696i	$-0.948304\pi$
$409$	−19.7124	−	23.4924i	−0.974717	−	1.16162i	0.0121238	−	0.999927i	$-0.496141\pi$
$410$	7.08194	+	4.08876i	0.349752	+	0.201929i
$411$	−8.46967	−	30.3176i	−0.417778	−	1.49546i
$412$	4.01850	−	11.0407i	0.197977	−	0.543938i
$413$	−1.63186	+	9.25474i	−0.0802986	+	0.455396i
$414$	−9.19005	−	3.12550i	−0.451666	−	0.153610i
$415$	14.5511	−	5.29616i	0.714285	−	0.259978i
$416$	−3.44631	+	4.10715i	−0.168969	+	0.201370i
$417$	−1.95598	+	7.62275i	−0.0957848	+	0.373288i
$418$	0.876991	−	3.29149i	0.0428950	−	0.160992i
$419$		−	16.0705i		−	0.785096i	−0.919732	−	0.392548i	$-0.871594\pi$
$419$		−	16.0705i		−	0.785096i	0.919732	−	0.392548i	$-0.128406\pi$
$420$	−2.75698	−	3.84970i	−0.134527	−	0.187846i
$421$	−11.7063	−	32.1628i	−0.570530	−	1.56752i	−0.803670	−	0.595076i	$-0.797122\pi$
$421$	−11.7063	−	32.1628i	−0.570530	−	1.56752i	0.233140	−	0.972443i	$-0.425100\pi$
$422$	−19.9485	+	3.51745i	−0.971076	+	0.171227i
$423$	2.83862	+	2.28092i	0.138018	+	0.110902i
$424$	−4.84558	−	1.76365i	−0.235322	−	0.0856503i
$425$	−2.90825	+	1.67908i	−0.141071	+	0.0814472i
$426$	−18.3118	−	17.9269i	−0.887208	−	0.868560i
$427$	14.2959	−	11.9957i	0.691827	−	0.580512i
$428$	1.03015	−	0.864402i	0.0497944	−	0.0417825i
$429$	5.18567	+	5.07667i	0.250366	+	0.245104i
$430$	4.07807	−	2.35447i	0.196662	−	0.113543i
$431$	22.7948	+	8.29665i	1.09799	+	0.399635i	0.826575	−	0.562827i	$-0.190286\pi$
$431$	22.7948	+	8.29665i	1.09799	+	0.399635i	0.271415	+	0.962463i	$0.412509\pi$
$432$	−3.11447	−	4.15933i	−0.149845	−	0.200116i
$433$	14.7958	−	2.60889i	0.711038	−	0.125375i	0.193581	−	0.981084i	$-0.437990\pi$
$433$	14.7958	−	2.60889i	0.711038	−	0.125375i	0.517457	+	0.855709i	$0.326879\pi$
$434$	−1.17692	−	3.23355i	−0.0564938	−	0.155216i
$435$	−2.36909	−	3.30806i	−0.113589	−	0.158610i
$436$		−	5.17686i		−	0.247927i
$437$	−12.7909	−	5.94259i	−0.611871	−	0.284273i
$438$	2.70633	−	10.5470i	0.129314	−	0.503954i
$439$	21.2655	−	25.3432i	1.01494	−	1.20956i	0.0372990	−	0.999304i	$-0.488125\pi$
$439$	21.2655	−	25.3432i	1.01494	−	1.20956i	0.977646	−	0.210260i	$-0.0674310\pi$
$440$	−0.734335	+	0.267276i	−0.0350081	+	0.0127419i
$441$	0.457566	−	1.34540i	0.0217888	−	0.0640667i
$442$	−3.12649	+	17.7312i	−0.148712	+	0.843388i
$443$	−0.557369	+	1.53136i	−0.0264814	+	0.0727571i	−0.952229	−	0.305385i	$-0.901215\pi$
$443$	−0.557369	+	1.53136i	−0.0264814	+	0.0727571i	0.925747	+	0.378142i	$0.123437\pi$
$444$	3.73020	+	13.3524i	0.177027	+	0.633677i
$445$	−14.1331	−	8.15976i	−0.669974	−	0.386810i
$446$	−15.7857	−	18.8127i	−0.747475	−	0.890807i
$447$	−34.4327	+	16.5037i	−1.62861	+	0.780598i
$448$	1.36690	−	2.36755i	0.0645801	−	0.111856i
$449$	−15.5784	−	26.9826i	−0.735190	−	1.27339i	−0.954640	−	0.297762i	$-0.903760\pi$
$449$	−15.5784	−	26.9826i	−0.735190	−	1.27339i	0.219450	−	0.975624i	$-0.429574\pi$
$450$	1.97674	+	2.25666i	0.0931844	+	0.106380i
$451$	6.29335	+	1.10969i	0.296342	+	0.0522531i
$452$	0.217169	+	1.23163i	0.0102148	+	0.0579309i
$453$	−1.58039	+	0.155195i	−0.0742530	+	0.00729171i
$454$	−9.91918	−	8.32318i	−0.465530	−	0.390626i
$455$	14.6573			0.687145
$456$	−3.85328	−	6.49247i	−0.180446	−	0.304038i
$457$	−3.97596			−0.185987			−0.0929937	−	0.995667i	$-0.529644\pi$
$457$	−3.97596			−0.185987			−0.0929937	+	0.995667i	$0.529644\pi$
$458$	−13.4112	−	11.2533i	−0.626662	−	0.525832i
$459$	−16.0415	−	6.86693i	−0.748753	−	0.320521i
$460$	0.561867	+	3.18651i	0.0261972	+	0.148572i
$461$	18.4805	+	3.25861i	0.860722	+	0.151769i	0.586551	−	0.809912i	$-0.300485\pi$
$461$	18.4805	+	3.25861i	0.860722	+	0.151769i	0.274171	+	0.961681i	$0.411596\pi$
$462$	−3.05348	−	2.09009i	−0.142061	−	0.0972399i
$463$	−11.8899	−	20.5938i	−0.552568	−	0.957076i	−0.998088	−	0.0618044i	$-0.980315\pi$
$463$	−11.8899	−	20.5938i	−0.552568	−	0.957076i	0.445520	−	0.895272i	$-0.353019\pi$
$464$	1.17459	−	2.03444i	0.0545288	−	0.0944467i
$465$	0.942306	+	1.96599i	0.0436984	+	0.0911708i
$466$	−19.0472	−	22.6996i	−0.882346	−	1.05154i
$467$	12.8575	+	7.42326i	0.594972	+	0.343507i	0.767061	−	0.641574i	$-0.221718\pi$
$467$	12.8575	+	7.42326i	0.594972	+	0.343507i	−0.172089	+	0.985081i	$0.555052\pi$
$468$	16.0809	−	0.341629i	0.743339	−	0.0157918i
$469$	−7.81088	+	21.4602i	−0.360673	+	0.990941i
$470$	0.210779	−	1.19539i	0.00972249	−	0.0551390i
$471$	−5.78400	−	0.444190i	−0.266513	−	0.0204672i
$472$	3.23021	−	1.17570i	0.148682	−	0.0541160i
$473$	2.36538	−	2.81894i	0.108760	−	0.129615i
$474$	0.804846	+	0.206522i	0.0369678	+	0.00948586i
$475$	2.50518	+	3.56708i	0.114946	+	0.163669i
$476$		−	9.18054i		−	0.420789i
$477$	5.59850	+	14.4211i	0.256338	+	0.660296i
$478$	−0.684889	−	1.88172i	−0.0313261	−	0.0860677i
$479$	1.31392	−	0.231680i	0.0600347	−	0.0105857i	−0.143550	−	0.989643i	$-0.545852\pi$
$479$	1.31392	−	0.231680i	0.0600347	−	0.0105857i	0.203585	+	0.979057i	$0.434741\pi$
$480$	−0.715283	+	1.57746i	−0.0326481	+	0.0720007i
$481$	−40.3264	−	14.6776i	−1.83873	−	0.669242i
$482$	−5.40335	+	3.11963i	−0.246116	+	0.142095i
$483$	−10.7180	+	10.9481i	−0.487687	+	0.498158i
$484$	7.95868	−	6.67812i	0.361758	−	0.303551i
$485$	−4.21868	+	3.53989i	−0.191560	+	0.160738i
$486$	−3.22969	+	15.2502i	−0.146502	+	0.691764i
$487$	−8.66841	+	5.00471i	−0.392803	+	0.226785i	−0.683374	−	0.730068i	$-0.739488\pi$
$487$	−8.66841	+	5.00471i	−0.392803	+	0.226785i	0.290571	+	0.956853i	$0.406155\pi$
$488$	−6.41469	−	2.33476i	−0.290379	−	0.105689i
$489$	−3.16535	−	1.43530i	−0.143142	−	0.0649065i
$490$	−0.466497	+	0.0822561i	−0.0210742	+	0.00371595i
$491$	−3.24848	−	8.92512i	−0.146602	−	0.402785i	0.844557	−	0.535466i	$-0.179864\pi$
$491$	−3.24848	−	8.92512i	−0.146602	−	0.402785i	−0.991159	+	0.132680i	$0.957642\pi$
$492$	11.5154	−	8.24683i	0.519156	−	0.371796i
$493$		−	7.88889i		−	0.355298i
$494$	23.2842	+	2.00409i	1.04760	+	0.0901685i
$495$	2.05474	+	1.12881i	0.0923537	+	0.0507361i
$496$	−0.809085	+	0.964230i	−0.0363290	+	0.0432952i
$497$	−38.0080	+	13.8338i	−1.70489	+	0.620529i
$498$	2.05368	−	26.7420i	0.0920278	−	1.19834i
$499$	−6.73065	+	38.1714i	−0.301305	+	1.70879i	0.339102	+	0.940750i	$0.389877\pi$
$499$	−6.73065	+	38.1714i	−0.301305	+	1.70879i	−0.640407	+	0.768036i	$0.721234\pi$
$500$	0.342020	−	0.939693i	0.0152956	−	0.0420243i
$501$	22.4399	−	6.26893i	1.00254	−	0.280075i
$502$	6.33325	+	3.65650i	0.282667	+	0.163198i
$503$	15.6292	+	18.6262i	0.696871	+	0.830499i	0.992169	−	0.124906i	$-0.0398631\pi$
$503$	15.6292	+	18.6262i	0.696871	+	0.830499i	−0.295297	+	0.955405i	$0.595419\pi$
$504$	−8.04475	+	1.59539i	−0.358342	+	0.0710643i
$505$	5.08418	−	8.80606i	0.226243	−	0.391864i
$506$	1.26428	+	2.18979i	0.0562040	+	0.0973481i
$507$	−15.4046	+	22.5051i	−0.684144	+	0.999486i
$508$	−21.0429	−	3.71043i	−0.933628	−	0.164624i
$509$	−2.29720	−	13.0281i	−0.101822	−	0.577460i	−0.992442	−	0.122713i	$-0.960841\pi$
$509$	−2.29720	−	13.0281i	−0.101822	−	0.577460i	0.890620	−	0.454747i	$-0.150270\pi$
$510$	0.568451	+	5.78865i	0.0251714	+	0.256326i
$511$	−13.1654	−	11.0471i	−0.582405	−	0.488696i
$512$	−1.00000			−0.0441942
$513$	−7.03435	+	21.5295i	−0.310574	+	0.950549i
$514$	−21.4751			−0.947226
$515$	9.00050	+	7.55231i	0.396609	+	0.332795i
$516$	−0.797106	−	8.11709i	−0.0350906	−	0.357335i
$517$	−0.164716	−	0.934150i	−0.00724419	−	0.0410839i
$518$	21.5495	+	3.79975i	0.946829	+	0.166951i
$519$	−22.7715	+	33.2675i	−0.999558	+	1.46028i
$520$	−2.68075	−	4.64320i	−0.117559	−	0.203618i
$521$	6.43508	−	11.1459i	0.281926	−	0.488310i	−0.689933	−	0.723873i	$-0.742360\pi$
$521$	6.43508	−	11.1459i	0.281926	−	0.488310i	0.971859	+	0.235563i	$0.0756935\pi$
$522$	−6.91290	+	1.37093i	−0.302569	+	0.0600038i
$523$	−14.6215	−	17.4252i	−0.639352	−	0.761950i	0.344916	−	0.938634i	$-0.387908\pi$
$523$	−14.6215	−	17.4252i	−0.639352	−	0.761950i	−0.984268	+	0.176684i	$0.943463\pi$
$524$	−11.1509	−	6.43798i	−0.487130	−	0.281244i
$525$	4.56047	−	1.27404i	0.199035	−	0.0556036i
$526$	−3.24002	+	8.90187i	−0.141271	+	0.388140i
$527$	−0.734002	+	4.16273i	−0.0319736	+	0.181331i
$528$	−0.103641	+	1.34956i	−0.00451041	+	0.0587321i
$529$	−11.7748	+	4.28567i	−0.511947	+	0.186334i
$530$	3.31457	−	3.95015i	0.143976	−	0.171584i
$531$	−9.03844	−	4.96542i	−0.392235	−	0.215481i
$532$	−11.8696	+	1.05528i	−0.514611	+	0.0457523i
$533$			43.8438i			1.89909i
$534$	−22.9809	+	16.4578i	−0.994479	+	0.712200i
$535$	0.459939	+	1.26367i	0.0198849	+	0.0546333i
$536$	8.22683	−	1.45061i	0.355345	−	0.0626569i
$537$	2.70112	+	1.22480i	0.116562	+	0.0528540i
$538$	−14.2677	−	5.19301i	−0.615124	−	0.223887i
$539$	−0.320580	+	0.185087i	−0.0138084	+	0.00797227i
$540$	4.97371	−	1.50407i	0.214034	−	0.0647249i
$541$	−6.58706	+	5.52720i	−0.283200	+	0.237633i	−0.773311	−	0.634027i	$-0.781401\pi$
$541$	−6.58706	+	5.52720i	−0.283200	+	0.237633i	0.490111	+	0.871660i	$0.336956\pi$
$542$	8.18134	−	6.86496i	0.351419	−	0.294875i
$543$	9.05220	−	9.24655i	0.388467	−	0.396807i
$544$	−2.90825	+	1.67908i	−0.124690	+	0.0719898i
$545$	4.86466	+	1.77059i	0.208379	+	0.0758438i
$546$	10.4841	−	23.1213i	0.448679	−	0.989499i
$547$	−33.4537	+	5.89879i	−1.43038	+	0.252214i	−0.834565	−	0.550909i	$-0.814281\pi$
$547$	−33.4537	+	5.89879i	−1.43038	+	0.252214i	−0.595813	+	0.803124i	$0.703170\pi$
$548$	6.21590	+	17.0780i	0.265530	+	0.729538i
$549$	7.41143	+	19.0910i	0.316312	+	0.814783i
$550$		−	0.781463i		−	0.0333217i
$551$	−10.1996	+	0.906809i	−0.434517	+	0.0386314i
$552$	5.42847	+	1.39293i	0.231051	+	0.0592872i
$553$	0.843012	−	1.00466i	0.0358485	−	0.0427226i
$554$	2.59378	−	0.944060i	0.110199	−	0.0401093i
$555$	−13.8230	−	1.06155i	−0.586752	−	0.0450604i
$556$	0.788983	−	4.47455i	0.0334603	−	0.189763i
$557$	12.0113	−	33.0008i	0.508936	−	1.39829i	−0.373401	−	0.927670i	$-0.621808\pi$
$557$	12.0113	−	33.0008i	0.508936	−	1.39829i	0.882337	−	0.470619i	$-0.155969\pi$
$558$	3.77529	−	0.0802039i	0.159821	−	0.00339530i
$559$	21.8646	+	12.6235i	0.924773	+	0.533918i
$560$	1.75726	+	2.09422i	0.0742576	+	0.0884968i
$561$	1.96460	+	4.09888i	0.0829455	+	0.173055i
$562$	9.40380	−	16.2879i	0.396675	−	0.687062i
$563$	12.8672	+	22.2866i	0.542286	+	0.939267i	0.998772	+	0.0495367i	$0.0157745\pi$
$563$	12.8672	+	22.2866i	0.542286	+	0.939267i	−0.456486	+	0.889731i	$0.650892\pi$
$564$	−1.73490	−	1.18753i	−0.0730525	−	0.0500042i
$565$	−1.23163	−	0.217169i	−0.0518150	−	0.00913638i
$566$	0.948766	+	5.38072i	0.0398796	+	0.226168i
$567$	19.5026	+	15.0006i	0.819033	+	0.629965i
$568$	11.3338	+	9.51018i	0.475555	+	0.399038i
$569$	−22.7561			−0.953986			−0.476993	−	0.878907i	$-0.658273\pi$
$569$	−22.7561			−0.953986			−0.476993	+	0.878907i	$0.658273\pi$
$570$	7.41883	−	1.40034i	0.310741	−	0.0586540i
$571$	−31.7792			−1.32992			−0.664960	−	0.746879i	$-0.731551\pi$
$571$	−31.7792			−1.32992			−0.664960	+	0.746879i	$0.731551\pi$
$572$	−3.20959	−	2.69316i	−0.134200	−	0.112607i
$573$	8.40002	−	0.824889i	0.350916	−	0.0344602i
$574$	−3.88204	−	22.0161i	−0.162033	−	0.918935i
$575$	−3.18651	−	0.561867i	−0.132887	−	0.0234315i
$576$	1.97674	+	2.25666i	0.0823641	+	0.0940274i
$577$	0.196726	+	0.340739i	0.00818980	+	0.0141852i	0.870091	−	0.492891i	$-0.164060\pi$
$577$	0.196726	+	0.340739i	0.00818980	+	0.0141852i	−0.861901	+	0.507076i	$0.830726\pi$
$578$	2.86140	−	4.95610i	0.119019	−	0.206147i
$579$	6.15031	−	2.94786i	0.255598	−	0.122509i
$580$	1.51002	+	1.79957i	0.0627002	+	0.0747232i
$581$	−36.6613	−	21.1664i	−1.52097	−	0.878131i
$582$	2.56647	+	9.18681i	0.106384	+	0.380805i
$583$	1.37823	−	3.78664i	0.0570803	−	0.156827i
$584$	−1.09165	+	6.19106i	−0.0451729	+	0.256188i
$585$	−5.17896	+	15.2279i	−0.214124	+	0.629597i
$586$	18.0698	−	6.57687i	0.746457	−	0.271688i
$587$	8.57342	−	10.2174i	0.353863	−	0.421718i	−0.559521	−	0.828816i	$-0.689015\pi$
$587$	8.57342	−	10.2174i	0.353863	−	0.421718i	0.913384	+	0.407098i	$0.133459\pi$
$588$	−0.203922	+	0.794716i	−0.00840962	+	0.0327735i
$589$	5.46639	+	0.470499i	0.225239	+	0.0193866i
$590$			3.43752i			0.141520i
$591$	25.7225	+	35.9175i	1.05808	+	1.47745i
$592$	−2.73759	−	7.52148i	−0.112514	−	0.309131i
$593$	27.1682	−	4.79048i	1.11566	−	0.196721i	0.414727	−	0.909946i	$-0.363877\pi$
$593$	27.1682	−	4.79048i	1.11566	−	0.196721i	0.700936	+	0.713225i	$0.252766\pi$
$594$	3.25037	−	2.43385i	0.133364	−	0.0998619i
$595$	8.62688	+	3.13993i	0.353668	+	0.128725i
$596$	19.0918	−	11.0226i	0.782030	−	0.451505i
$597$	−24.5599	−	24.0437i	−1.00517	−	0.984043i
$598$	−13.2894	+	11.1511i	−0.543442	+	0.456002i
$599$	−24.2964	+	20.3871i	−0.992722	+	0.832993i	−0.985960	−	0.166984i	$-0.946597\pi$
$599$	−24.2964	+	20.3871i	−0.992722	+	0.832993i	−0.00676271	+	0.999977i	$0.502153\pi$
$600$	−1.23768	−	1.21167i	−0.0505282	−	0.0494662i
$601$	14.9017	−	8.60351i	0.607854	−	0.350944i	−0.164271	−	0.986415i	$-0.552527\pi$
$601$	14.9017	−	8.60351i	0.607854	−	0.350944i	0.772125	+	0.635471i	$0.219194\pi$
$602$	−12.0970	−	4.40295i	−0.493037	−	0.179451i
$603$	−19.5358	−	15.6976i	−0.795560	−	0.639258i
$604$	0.902896	−	0.159205i	0.0367383	−	0.00647796i
$605$	3.55335	+	9.76276i	0.144464	+	0.396913i
$606$	−10.2545	−	14.3189i	−0.416562	−	0.581665i
$607$		−	32.4539i		−	1.31726i	−0.752466	−	0.658631i	$-0.771136\pi$
$607$		−	32.4539i		−	1.31726i	0.752466	−	0.658631i	$-0.228864\pi$
$608$	2.50518	+	3.56708i	0.101599	+	0.144664i
$609$	−2.76471	+	10.7745i	−0.112032	+	0.436605i
$610$	4.38791	−	5.22930i	0.177661	−	0.211728i
$611$	6.11545	−	2.22584i	0.247405	−	0.0900480i
$612$	9.53794	+	3.24382i	0.385549	+	0.131124i
$613$	−2.96289	+	16.8034i	−0.119670	+	0.678682i	0.864662	+	0.502355i	$0.167533\pi$
$613$	−2.96289	+	16.8034i	−0.119670	+	0.678682i	−0.984332	+	0.176327i	$0.943578\pi$
$614$	−6.13513	+	16.8561i	−0.247594	+	0.680258i
$615$	3.81098	+	13.6416i	0.153673	+	0.550080i
$616$	1.85015	+	1.06818i	0.0745447	+	0.0430384i
$617$	−4.93525	−	5.88161i	−0.198686	−	0.236785i	0.657497	−	0.753457i	$-0.271615\pi$
$617$	−4.93525	−	5.88161i	−0.198686	−	0.236785i	−0.856183	+	0.516672i	$0.827171\pi$
$618$	18.3514	−	8.79585i	0.738200	−	0.353821i
$619$	8.77468	−	15.1982i	0.352684	−	0.610867i	−0.634035	−	0.773305i	$-0.718602\pi$
$619$	8.77468	−	15.1982i	0.352684	−	0.610867i	0.986719	+	0.162438i	$0.0519357\pi$
$620$	−0.629356	−	1.09008i	−0.0252756	−	0.0437785i
$621$	−7.58730	−	15.0037i	−0.304468	−	0.602077i
$622$	2.99071	+	0.527343i	0.119916	+	0.0211445i
$623$	7.74721	+	43.9366i	0.310385	+	1.76028i
$624$	−9.24194	+	0.907567i	−0.369974	+	0.0363318i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−29.3867			−1.17453
$627$	5.07363	−	3.01120i	0.202621	−	0.120256i
$628$	3.34923			0.133649
$629$	−20.5907	−	17.2777i	−0.821006	−	0.688906i
$630$	1.25229	−	8.10525i	0.0498925	−	0.322921i
$631$	5.71572	+	32.4155i	0.227539	+	1.29044i	0.857771	+	0.514032i	$0.171849\pi$
$631$	5.71572	+	32.4155i	0.227539	+	1.29044i	−0.630232	+	0.776407i	$0.717040\pi$
$632$	−0.472444	−	0.0833046i	−0.0187928	−	0.00331368i
$633$	−28.9519	−	19.8174i	−1.15073	−	0.787673i
$634$	1.49879	+	2.59598i	0.0595246	+	0.103100i
$635$	10.6838	−	18.5048i	0.423972	−	0.734341i
$636$	−3.86034	−	8.05407i	−0.153072	−	0.319365i
$637$	−1.63249	−	1.94553i	−0.0646818	−	0.0770847i
$638$	1.58984	+	0.917897i	0.0629425	+	0.0363399i
$639$	−0.942735	−	44.3756i	−0.0372940	−	1.75547i
$640$	0.342020	−	0.939693i	0.0135195	−	0.0371446i
$641$	−2.98431	+	16.9249i	−0.117873	+	0.668492i	0.867414	+	0.497587i	$0.165780\pi$
$641$	−2.98431	+	16.9249i	−0.117873	+	0.668492i	−0.985287	+	0.170905i	$0.945331\pi$
$642$	2.32237	+	0.178350i	0.0916568	+	0.00703890i
$643$	9.88767	−	3.59882i	0.389932	−	0.141923i	−0.139612	−	0.990206i	$-0.544585\pi$
$643$	9.88767	−	3.59882i	0.389932	−	0.141923i	0.529543	+	0.848283i	$0.322363\pi$
$644$	5.68589	−	6.77618i	0.224056	−	0.267019i
$645$	7.90020	+	2.02717i	0.311070	+	0.0798199i
$646$	13.2751	+	6.16755i	0.522301	+	0.242659i
$647$		−	17.4264i		−	0.685101i	−0.939499	−	0.342551i	$-0.888709\pi$
$647$		−	17.4264i		−	0.685101i	0.939499	−	0.342551i	$-0.111291\pi$
$648$	1.18500	−	8.92165i	0.0465513	−	0.350475i
$649$	0.918767	+	2.52429i	0.0360648	+	0.0990871i
$650$	5.28005	−	0.931015i	0.207101	−	0.0365174i
$651$	2.46134	−	5.42815i	0.0964677	−	0.212746i
$652$	1.88560	+	0.686304i	0.0738459	+	0.0268777i
$653$	9.49553	−	5.48225i	0.371589	−	0.214537i	−0.302564	−	0.953129i	$-0.597842\pi$
$653$	9.49553	−	5.48225i	0.371589	−	0.214537i	0.674152	+	0.738592i	$0.264509\pi$
$654$	6.27264	−	6.40731i	0.245280	−	0.250546i
$655$	9.86355	−	8.27650i	0.385401	−	0.323390i
$656$	−6.26434	+	5.25641i	−0.244582	+	0.205228i
$657$	16.1290	−	9.77464i	0.629253	−	0.381345i
$658$	−2.87379	+	1.65918i	−0.112032	+	0.0646816i
$659$	26.9232	+	9.79923i	1.04878	+	0.381724i	0.808201	−	0.588906i	$-0.200441\pi$
$659$	26.9232	+	9.79923i	1.04878	+	0.381724i	0.240576	+	0.970630i	$0.422664\pi$
$660$	−1.23272	−	0.558968i	−0.0479837	−	0.0217578i
$661$	−25.5439	+	4.50408i	−0.993543	+	0.175188i	−0.646708	−	0.762738i	$-0.723855\pi$
$661$	−25.5439	+	4.50408i	−0.993543	+	0.175188i	−0.346835	+	0.937926i	$0.612744\pi$
$662$	−2.60039	−	7.14452i	−0.101067	−	0.277680i
$663$	−25.3540	+	18.1573i	−0.984666	+	0.705173i
$664$			15.4849i			0.600932i
$665$	3.06799	−	11.5147i	0.118972	−	0.446520i
$666$	−11.5619	+	21.0458i	−0.448014	+	0.815508i
$667$	4.88592	−	5.82281i	0.189184	−	0.225460i
$668$	−12.6405	+	4.60077i	−0.489076	+	0.178009i
$669$	3.25702	−	42.4112i	0.125924	−	1.63971i
$670$	−1.45061	+	8.22683i	−0.0560420	+	0.317830i
$671$	1.82453	−	5.01285i	0.0704351	−	0.193519i
$672$	4.56047	−	1.27404i	0.175924	−	0.0491471i
$673$	40.5925	+	23.4361i	1.56472	+	0.903394i	0.996768	+	0.0803356i	$0.0255992\pi$
$673$	40.5925	+	23.4361i	1.56472	+	0.903394i	0.567957	+	0.823059i	$0.307734\pi$
$674$	−3.90634	−	4.65540i	−0.150467	−	0.179319i
$675$	−0.287743	+	5.18818i	−0.0110752	+	0.199693i
$676$	7.87285	−	13.6362i	0.302802	−	0.524468i
$677$	2.49156	+	4.31550i	0.0957583	+	0.165858i	0.909925	−	0.414773i	$-0.136139\pi$
$677$	2.49156	+	4.31550i	0.0957583	+	0.165858i	−0.814167	+	0.580631i	$0.802806\pi$
$678$	−1.22354	+	1.78750i	−0.0469897	+	0.0686486i
$679$	14.8266	+	2.61433i	0.568993	+	0.100329i
$680$	−0.583137	−	3.30713i	−0.0223623	−	0.126823i
$681$	−2.19187	−	22.3202i	−0.0839925	−	0.855313i
$682$	−0.753510	−	0.632270i	−0.0288534	−	0.0242109i
$683$	38.2737			1.46450			0.732251	−	0.681035i	$-0.238470\pi$
$683$	38.2737			1.46450			0.732251	+	0.681035i	$0.238470\pi$
$684$	3.09758	−	12.7045i	0.118439	−	0.485770i
$685$	−18.1741			−0.694395
$686$	−13.6675	−	11.4684i	−0.521828	−	0.437865i
$687$	−2.96350	−	30.1779i	−0.113065	−	1.15136i
$688$	0.817700	+	4.63741i	0.0311745	+	0.176800i
$689$	27.2269	+	4.80083i	1.03726	+	0.182897i
$690$	−3.16558	+	4.62468i	−0.120511	+	0.176059i
$691$	−9.80824	−	16.9884i	−0.373123	−	0.646268i	0.616921	−	0.787025i	$-0.288380\pi$
$691$	−9.80824	−	16.9884i	−0.373123	−	0.646268i	−0.990044	+	0.140757i	$0.955046\pi$
$692$	11.6378	−	20.1573i	0.442404	−	0.766266i
$693$	−1.24674	−	6.28668i	−0.0473597	−	0.238811i
$694$	22.1017	+	26.3397i	0.838967	+	0.999842i
$695$	3.93485	+	2.27179i	0.149257	+	0.0861738i
$696$	3.91884	−	1.09479i	0.148543	−	0.0414978i
$697$	−9.39234	+	25.8052i	−0.355760	+	0.977443i
$698$	−2.41526	+	13.6976i	−0.0914189	+	0.518462i
$699$	3.92996	−	51.1739i	0.148645	−	1.93557i
$700$	−2.56894	+	0.935017i	−0.0970967	+	0.0353403i
$701$	−24.3730	+	29.0466i	−0.920555	+	1.09707i	0.0744474	+	0.997225i	$0.476281\pi$
$701$	−24.3730	+	29.0466i	−0.920555	+	1.09707i	−0.995003	+	0.0998499i	$0.968164\pi$
$702$	20.3170	+	19.0619i	0.766815	+	0.719444i
$703$	−19.9715	+	28.6079i	−0.753241	+	1.07897i
$704$		−	0.781463i		−	0.0294525i
$705$	1.70929	−	1.22411i	0.0643755	−	0.0461028i
$706$	6.15458	+	16.9096i	0.231631	+	0.636400i
$707$	−27.3760	+	4.82713i	−1.02958	+	0.181543i
$708$	5.42254	+	2.45880i	0.203791	+	0.0924073i
$709$	8.14093	+	2.96305i	0.305739	+	0.111280i	0.490333	−	0.871535i	$-0.336875\pi$
$709$	8.14093	+	2.96305i	0.305739	+	0.111280i	−0.184595	+	0.982815i	$0.559097\pi$
$710$	−12.8130	+	7.39760i	−0.480864	+	0.277627i
$711$	0.745908	+	1.23081i	0.0279737	+	0.0461592i
$712$	12.5015	−	10.4900i	0.468513	−	0.393129i
$713$	−3.11992	+	2.61793i	−0.116842	+	0.0980421i
$714$	11.1238	−	11.3626i	0.416297	−	0.425234i
$715$	3.62849	−	2.09491i	0.135698	−	0.0783451i
$716$	−1.60906	−	0.585650i	−0.0601334	−	0.0218868i
$717$	1.43234	−	3.15883i	0.0534918	−	0.117969i
$718$	−34.0236	+	5.99927i	−1.26975	+	0.223891i
$719$	9.13952	+	25.1106i	0.340847	+	0.936468i	0.985150	+	0.171698i	$0.0549254\pi$
$719$	9.13952	+	25.1106i	0.340847	+	0.936468i	−0.644303	+	0.764770i	$0.722852\pi$
$720$	−2.79665	+	1.08571i	−0.104225	+	0.0404618i
$721$		−	32.1203i		−	1.19622i
$722$	6.44812	−	17.8724i	0.239974	−	0.665141i
$723$	−10.4676	−	2.68596i	−0.389294	−	0.0998920i
$724$	−4.80217	+	5.72301i	−0.178471	+	0.212694i
$725$	−2.20750	+	0.803465i	−0.0819846	+	0.0298399i
$726$	17.9420	+	1.37788i	0.665890	+	0.0511379i
$727$	1.20264	−	6.82053i	0.0446036	−	0.252959i	−0.954350	−	0.298690i	$-0.903450\pi$
$727$	1.20264	−	6.82053i	0.0446036	−	0.252959i	0.998954	+	0.0457304i	$0.0145615\pi$
$728$	−5.01309	+	13.7734i	−0.185798	+	0.510475i
$729$	−22.4755	+	14.9616i	−0.832427	+	0.554134i
$730$	−5.44433	−	3.14329i	−0.201504	−	0.116338i
$731$	10.1646	+	12.1137i	0.375953	+	0.448043i
$732$	−5.11040	−	10.6622i	−0.188886	−	0.394085i
$733$	15.0984	−	26.1512i	0.557673	−	0.965918i	−0.440017	−	0.897989i	$-0.645028\pi$
$733$	15.0984	−	26.1512i	0.557673	−	0.965918i	0.997690	−	0.0679288i	$-0.0216391\pi$
$734$	6.80203	+	11.7815i	0.251067	+	0.434862i
$735$	−0.677043	−	0.463433i	−0.0249731	−	0.0170940i
$736$	−3.18651	−	0.561867i	−0.117456	−	0.0207107i
$737$	1.13360	+	6.42896i	0.0417567	+	0.236814i
$738$	24.2449	+	3.74593i	0.892467	+	0.137889i
$739$	35.1410	+	29.4868i	1.29268	+	1.08469i	0.991360	+	0.131168i	$0.0418728\pi$
$739$	35.1410	+	29.4868i	1.29268	+	1.08469i	0.301323	+	0.953522i	$0.402572\pi$
$740$	8.00419			0.294240
$741$	26.3901	+	30.6931i	0.969465	+	1.12754i
$742$	−14.0970			−0.517518
$743$	40.3350	+	33.8451i	1.47975	+	1.24166i	0.906453	+	0.422308i	$0.138780\pi$
$743$	40.3350	+	33.8451i	1.47975	+	1.24166i	0.573296	+	0.819348i	$0.305665\pi$
$744$	−2.16972	+	0.213068i	−0.0795457	+	0.00781146i
$745$	3.82813	+	21.7104i	0.140252	+	0.795407i
$746$	−10.0363	−	1.76967i	−0.367455	−	0.0647921i
$747$	34.9442	−	30.6097i	1.27854	−	1.11995i
$748$	−1.31214	−	2.27269i	−0.0479765	−	0.0830977i
$749$	1.83817	−	3.18381i	0.0671653	−	0.116334i
$750$	1.56191	−	0.748627i	0.0570328	−	0.0273360i
$751$	26.6642	+	31.7771i	0.972990	+	1.15956i	0.987171	+	0.159665i	$0.0510413\pi$
$751$	26.6642	+	31.7771i	0.972990	+	1.15956i	−0.0141816	+	0.999899i	$0.504514\pi$
$752$	1.05120	+	0.606913i	0.0383335	+	0.0221318i
$753$	3.40809	+	12.1994i	0.124198	+	0.444570i
$754$	−4.30778	+	11.8355i	−0.156880	+	0.431024i
$755$	−0.159205	+	0.902896i	−0.00579406	+	0.0328598i
$756$	−11.8899	−	7.77298i	−0.432433	−	0.282701i
$757$	−42.7265	+	15.5512i	−1.55292	+	0.565218i	−0.969101	−	0.246664i	$-0.920665\pi$
$757$	−42.7265	+	15.5512i	−1.55292	+	0.565218i	−0.583822	+	0.811882i	$0.698443\pi$
$758$	12.7292	−	15.1701i	0.462346	−	0.551003i
$759$	−1.08853	+	4.24215i	−0.0395110	+	0.153980i
$760$	−4.20878	+	1.13409i	−0.152669	+	0.0411377i
$761$		−	41.2983i		−	1.49706i	−0.663099	−	0.748532i	$-0.730759\pi$
$761$		−	41.2983i		−	1.49706i	0.663099	−	0.748532i	$-0.269241\pi$
$762$	−21.5486	−	30.0894i	−0.780624	−	1.09002i
$763$	−4.84045	−	13.2990i	−0.175236	−	0.481457i
$764$	−4.79905	+	0.846201i	−0.173623	+	0.0306145i
$765$	−6.31036	+	7.85328i	−0.228152	+	0.283936i
$766$	4.16337	+	1.51534i	0.150429	+	0.0547516i
$767$	−15.9611	+	9.21513i	−0.576321	+	0.332739i
$768$	−1.23768	−	1.21167i	−0.0446610	−	0.0437223i
$769$	15.1146	−	12.6826i	0.545046	−	0.457348i	−0.328214	−	0.944604i	$-0.606447\pi$
$769$	15.1146	−	12.6826i	0.545046	−	0.457348i	0.873259	+	0.487256i	$0.162002\pi$
$770$	−1.63655	+	1.37323i	−0.0589773	+	0.0494878i
$771$	−26.5794	−	26.0207i	−0.957232	−	0.937112i
$772$	−3.41014	+	1.96884i	−0.122734	+	0.0708602i
$773$	−21.2188	−	7.72300i	−0.763186	−	0.277777i	−0.0690426	−	0.997614i	$-0.521994\pi$
$773$	−21.2188	−	7.72300i	−0.763186	−	0.277777i	−0.694143	+	0.719837i	$0.744217\pi$
$774$	8.84866	−	11.0122i	0.318059	−	0.395826i
$775$	1.23959	−	0.218573i	0.0445274	−	0.00785138i
$776$	−1.88354	−	5.17497i	−0.0676150	−	0.185771i
$777$	22.0674	+	30.8137i	0.791662	+	1.10543i
$778$		−	33.6500i		−	1.20641i
$779$	34.4434	+	9.17715i	1.23406	+	0.328806i
$780$	2.30810	−	8.99499i	0.0826431	−	0.322072i
$781$	−7.43185	+	8.85694i	−0.265933	+	0.316926i
$782$	−10.2106	+	3.71634i	−0.365129	+	0.132896i
$783$	−10.2171	−	6.67937i	−0.365129	−	0.238701i
$784$	0.0822561	−	0.466497i	0.00293772	−	0.0166606i
$785$	−1.14550	+	3.14724i	−0.0408848	+	0.112330i
$786$	−6.00059	−	21.4794i	−0.214034	−	0.766144i
$787$	14.5793	+	8.41738i	0.519697	+	0.300047i	0.736811	−	0.676099i	$-0.236331\pi$
$787$	14.5793	+	8.41738i	0.519697	+	0.300047i	−0.217114	+	0.976146i	$0.569664\pi$
$788$	−16.3951	−	19.5390i	−0.584053	−	0.696047i
$789$	−14.7962	+	7.09187i	−0.526760	+	0.252477i
$790$	0.239866	−	0.415460i	0.00853405	−	0.0147814i
$791$	1.70949	+	2.96092i	0.0607823	+	0.105278i
$792$	−1.76349	+	1.54475i	−0.0626631	+	0.0548903i
$793$	36.0436	+	6.35546i	1.27995	+	0.225689i
$794$	−6.15137	−	34.8862i	−0.218304	−	1.23806i
$795$	8.88866	−	0.872875i	0.315248	−	0.0309577i
$796$	15.2010	+	12.7551i	0.538784	+	0.452094i
$797$	43.1773			1.52942			0.764709	−	0.644376i	$-0.222883\pi$
$797$	43.1773			1.52942			0.764709	+	0.644376i	$0.222883\pi$
$798$	−15.9694	−	13.0759i	−0.565311	−	0.462881i
$799$	4.07621			0.144206
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−48.3845	−	7.47558i	−1.70958	−	0.264137i
$802$	3.53849	+	20.0677i	0.124948	+	0.708617i
$803$	−4.83809	−	0.853086i	−0.170732	−	0.0301047i
$804$	11.9399	+	8.17279i	0.421087	+	0.288232i
$805$	4.42284	+	7.66058i	0.155885	+	0.270000i
$806$	3.37429	−	5.84445i	0.118854	−	0.205862i
$807$	−11.3667	−	23.7150i	−0.400126	−	0.834808i
$808$	6.53609	+	7.78941i	0.229939	+	0.274031i
$809$	−30.1850	−	17.4273i	−1.06125	−	0.612711i	−0.135470	−	0.990781i	$-0.543254\pi$
$809$	−30.1850	−	17.4273i	−1.06125	−	0.612711i	−0.925777	+	0.378071i	$0.876588\pi$
$810$	7.97831	+	4.16492i	0.280329	+	0.146340i
$811$	−11.0768	+	30.4333i	−0.388959	+	1.06866i	0.578512	+	0.815674i	$0.303634\pi$
$811$	−11.0768	+	30.4333i	−0.388959	+	1.06866i	−0.967471	+	0.252982i	$0.918589\pi$
$812$	1.11520	−	6.32462i	0.0391359	−	0.221951i
$813$	18.4440	+	1.41643i	0.646858	+	0.0496763i
$814$	5.87776	−	2.13933i	0.206015	−	0.0749834i
$815$	−1.28983	+	1.53716i	−0.0451807	+	0.0538443i
$816$	−5.63397	−	1.44567i	−0.197228	−	0.0506084i
$817$	14.4935	−	14.5344i	0.507064	−	0.508493i
$818$			30.6671i			1.07225i
$819$	40.9913	−	15.9135i	1.43235	−	0.556063i
$820$	−2.79688	−	7.68435i	−0.0976712	−	0.268349i
$821$	1.40900	−	0.248444i	0.0491743	−	0.00867075i	−0.149007	−	0.988836i	$-0.547608\pi$
$821$	1.40900	−	0.248444i	0.0491743	−	0.00867075i	0.198181	+	0.980165i	$0.436497\pi$
$822$	−12.9996	+	28.6688i	−0.453413	+	0.999939i
$823$	−8.60472	−	3.13186i	−0.299942	−	0.109170i	0.187666	−	0.982233i	$-0.439908\pi$
$823$	−8.60472	−	3.13186i	−0.299942	−	0.109170i	−0.487607	+	0.873063i	$0.662130\pi$
$824$	−10.1752	+	5.87466i	−0.354470	+	0.204653i
$825$	0.946875	−	0.967204i	0.0329659	−	0.0336737i
$826$	7.19891	−	6.04060i	0.250482	−	0.210179i
$827$	15.0219	−	12.6049i	0.522362	−	0.438314i	−0.343092	−	0.939302i	$-0.611474\pi$
$827$	15.0219	−	12.6049i	0.522362	−	0.438314i	0.865454	+	0.500988i	$0.167030\pi$
$828$	5.03095	+	8.30152i	0.174838	+	0.288498i
$829$	−27.0740	+	15.6312i	−0.940318	+	0.542893i	−0.890060	−	0.455844i	$-0.849338\pi$
$829$	−27.0740	+	15.6312i	−0.940318	+	0.542893i	−0.0502577	+	0.998736i	$0.516004\pi$
$830$	−14.5511	−	5.29616i	−0.505076	−	0.183833i
$831$	4.35417	+	1.97436i	0.151044	+	0.0684897i
$832$	5.28005	−	0.931015i	0.183053	−	0.0322771i
$833$	−0.544064	−	1.49480i	−0.0188507	−	0.0517919i
$834$	6.39818	−	4.58208i	0.221551	−	0.158665i
$835$		−	13.4518i		−	0.465517i
$836$	−2.78754	+	1.95771i	−0.0964092	+	0.0677088i
$837$	4.76979	+	4.47513i	0.164868	+	0.154683i
$838$	−10.3299	+	12.3107i	−0.356841	+	0.425267i
$839$	18.7355	−	6.81915i	0.646820	−	0.235423i	0.00228403	−	0.999997i	$-0.499273\pi$
$839$	18.7355	−	6.81915i	0.646820	−	0.235423i	0.644536	+	0.764574i	$0.277051\pi$
$840$	−0.362570	+	4.72119i	−0.0125098	+	0.162896i
$841$	−4.07750	+	23.1246i	−0.140603	+	0.797402i
$842$	−11.7063	+	32.1628i	−0.403426	+	1.10840i
$843$	31.3744	−	8.76492i	1.08059	−	0.301880i
$844$	17.5424	+	10.1281i	0.603834	+	0.348624i
$845$	10.1211	+	12.0619i	0.348178	+	0.414942i
$846$	−0.708362	−	3.57192i	−0.0243540	−	0.122805i
$847$	14.2012	−	24.5972i	0.487958	−	0.845169i
$848$	2.57828	+	4.46571i	0.0885385	+	0.153353i
$849$	−5.34538	+	7.80921i	−0.183453	+	0.268012i
$850$	3.30713	+	0.583137i	0.113434	+	0.0200014i
$851$	−4.49729	−	25.5054i	−0.154165	−	0.874314i
$852$	2.50446	+	25.5034i	0.0858012	+	0.873731i
$853$	20.2110	+	16.9590i	0.692011	+	0.580666i	0.919488	−	0.393117i	$-0.128603\pi$
$853$	20.2110	+	16.9590i	0.692011	+	0.580666i	−0.227478	+	0.973783i	$0.573048\pi$
$854$	−18.6620			−0.638600
$855$	10.8789	+	7.25598i	0.372051	+	0.248149i
$856$	−1.34477			−0.0459633
$857$	9.52082	+	7.98892i	0.325225	+	0.272896i	0.790751	−	0.612138i	$-0.209690\pi$
$857$	9.52082	+	7.98892i	0.325225	+	0.272896i	−0.465526	+	0.885034i	$0.654135\pi$
$858$	−0.709230	−	7.22224i	−0.0242127	−	0.246563i
$859$	8.19991	+	46.5040i	0.279777	+	1.58670i	0.723365	+	0.690466i	$0.242594\pi$
$859$	8.19991	+	46.5040i	0.279777	+	1.58670i	−0.443588	+	0.896231i	$0.646295\pi$
$860$	−4.63741	−	0.817700i	−0.158134	−	0.0278834i
$861$	21.8715	−	31.9527i	0.745379	−	1.08895i
$862$	−12.1289	−	21.0078i	−0.413112	−	0.715530i
$863$	−17.0133	+	29.4678i	−0.579138	+	1.00310i	0.416440	+	0.909163i	$0.363277\pi$
$863$	−17.0133	+	29.4678i	−0.579138	+	1.00310i	−0.995578	+	0.0939336i	$0.970056\pi$
$864$	−0.287743	+	5.18818i	−0.00978923	+	0.176505i
$865$	14.9613	+	17.8302i	0.508700	+	0.606245i
$866$	−13.0112	−	7.51200i	−0.442137	−	0.255268i
$867$	9.54666	−	2.66701i	0.324222	−	0.0905762i
$868$	−1.17692	+	3.23355i	−0.0399472	+	0.109754i
$869$	0.0650995	−	0.369197i	0.00220835	−	0.0125242i
$870$	−0.311558	+	4.05694i	−0.0105628	+	0.137543i
$871$	−42.0875	+	15.3186i	−1.42608	+	0.519051i
$872$	−3.32762	+	3.96571i	−0.112687	+	0.134296i
$873$	−7.95488	+	14.4801i	−0.269232	+	0.490076i
$874$	5.97856	+	12.7741i	0.202228	+	0.432091i
$875$		−	2.73381i		−	0.0924195i
$876$	−8.85263	+	6.33985i	−0.299103	+	0.214204i
$877$	−0.252654	−	0.694160i	−0.00853151	−	0.0234401i	0.935354	−	0.353714i	$-0.115081\pi$
$877$	−0.252654	−	0.694160i	−0.00853151	−	0.0234401i	−0.943885	+	0.330273i	$0.892859\pi$
$878$	−32.5806	+	5.74483i	−1.09954	+	0.193879i
$879$	30.3337	+	13.7545i	1.02313	+	0.463929i
$880$	0.734335	+	0.267276i	0.0247544	+	0.00900988i
$881$	−31.7476	+	18.3295i	−1.06960	+	0.617536i	−0.928073	−	0.372398i	$-0.878536\pi$
$881$	−31.7476	+	18.3295i	−1.06960	+	0.617536i	−0.141530	+	0.989934i	$0.545202\pi$
$882$	−1.21532	+	0.736520i	−0.0409221	+	0.0247999i
$883$	−13.9478	+	11.7036i	−0.469382	+	0.393859i	−0.846569	−	0.532279i	$-0.821336\pi$
$883$	−13.9478	+	11.7036i	−0.469382	+	0.393859i	0.377187	+	0.926137i	$0.376891\pi$
$884$	13.7924	−	11.5732i	0.463890	−	0.389250i
$885$	−4.16513	+	4.25456i	−0.140009	+	0.143015i
$886$	1.41131	−	0.814820i	0.0474139	−	0.0273744i
$887$	42.3234	+	15.4045i	1.42108	+	0.517232i	0.934362	−	0.356326i	$-0.115971\pi$
$887$	42.3234	+	15.4045i	1.42108	+	0.517232i	0.486720	+	0.873558i	$0.338193\pi$
$888$	5.72526	−	12.6263i	0.192127	−	0.423710i
$889$	−57.5272	+	10.1436i	−1.92940	+	0.340205i
$890$	5.58160	+	15.3353i	0.187096	+	0.514041i
$891$	6.97194	+	0.926036i	0.233569	+	0.0310234i
$892$			24.5582i			0.822270i
$893$	−0.468551	−	5.27016i	−0.0156795	−	0.176359i
$894$	36.9854	+	9.49037i	1.23698	+	0.317405i
$895$	1.10066	−	1.31172i	0.0367911	−	0.0438459i
$896$	−2.56894	+	0.935017i	−0.0858222	+	0.0312367i
$897$	−29.9594	−	2.30077i	−1.00032	−	0.0768206i
$898$	−5.41032	+	30.6834i	−0.180545	+	1.02392i
$899$	−1.01133	+	2.77861i	−0.0337298	+	0.0926718i
$900$	−0.0637190	−	2.99932i	−0.00212397	−	0.0999774i
$901$	14.9965	+	8.65825i	0.499607	+	0.288448i
$902$	−4.10769	−	4.89535i	−0.136771	−	0.162997i
$903$	−9.63733	−	20.1070i	−0.320710	−	0.669119i
$904$	0.625314	−	1.08308i	0.0207976	−	0.0360225i
$905$	−3.73543	−	6.46995i	−0.124170	−	0.215068i
$906$	1.31040	+	0.896966i	0.0435352	+	0.0297997i
$907$	−10.4233	−	1.83790i	−0.346099	−	0.0610265i	−0.00210298	−	0.999998i	$-0.500669\pi$
$907$	−10.4233	−	1.83790i	−0.346099	−	0.0610265i	−0.343996	+	0.938971i	$0.611781\pi$
$908$	2.24850	+	12.7519i	0.0746190	+	0.423185i
$909$	4.65788	−	30.1474i	0.154492	−	0.999925i
$910$	−11.2281	−	9.42153i	−0.372209	−	0.312321i
$911$	6.25956			0.207388			0.103694	−	0.994609i	$-0.466934\pi$
$911$	6.25956			0.207388			0.103694	+	0.994609i	$0.466934\pi$
$912$	−1.22150	+	7.45037i	−0.0404478	+	0.246706i
$913$	−12.1009			−0.400482
$914$	3.04576	+	2.55570i	0.100745	+	0.0845349i
$915$	11.7670	−	1.15553i	0.389006	−	0.0382007i
$916$	3.04006	+	17.2411i	0.100447	+	0.569661i
$917$	−34.6656	−	6.11248i	−1.14476	−	0.201852i
$918$	7.87452	+	15.5716i	0.259898	+	0.513941i
$919$	−22.2366	−	38.5149i	−0.733517	−	1.27049i	−0.955371	−	0.295408i	$-0.904544\pi$
$919$	−22.2366	−	38.5149i	−0.733517	−	1.27049i	0.221855	−	0.975080i	$-0.428789\pi$
$920$	1.61783	−	2.80217i	0.0533384	−	0.0923847i
$921$	−28.0174	+	13.4288i	−0.923204	+	0.442494i
$922$	−12.0623	−	14.3753i	−0.397250	−	0.473424i
$923$	−68.6971	−	39.6623i	−2.26119	−	1.30550i
$924$	0.995614	+	3.56384i	0.0327533	+	0.117242i
$925$	−2.73759	+	7.52148i	−0.0900115	+	0.247305i
$926$	−4.12930	+	23.4184i	−0.135697	+	0.769578i
$927$	33.3708	+	11.3493i	1.09604	+	0.372759i
$928$	−2.20750	+	0.803465i	−0.0724648	+	0.0263750i
$929$	17.8487	−	21.2712i	0.585595	−	0.697886i	−0.389158	−	0.921171i	$-0.627234\pi$
$929$	17.8487	−	21.2712i	0.585595	−	0.697886i	0.974753	+	0.223286i	$0.0716783\pi$
$930$	0.541868	−	2.11174i	0.0177686	−	0.0692467i
$931$	−1.87010	+	0.875247i	−0.0612900	+	0.0286851i
$932$			29.6322i			0.970636i
$933$	3.06258	+	4.27643i	0.100265	+	0.140004i
$934$	−5.07781	−	13.9512i	−0.166151	−	0.456496i
$935$	2.58440	−	0.455700i	0.0845191	−	0.0149030i
$936$	−12.5383	−	10.0749i	−0.409826	−	0.329308i
$937$	6.07991	+	2.21291i	0.198622	+	0.0722925i	0.439416	−	0.898284i	$-0.355186\pi$
$937$	6.07991	+	2.21291i	0.198622	+	0.0722925i	−0.240794	+	0.970576i	$0.577408\pi$
$938$	19.7779	−	11.4187i	0.645770	−	0.372835i
$939$	−36.3714	−	35.6069i	−1.18694	−	1.16199i
$940$	−0.929844	+	0.780232i	−0.0303282	+	0.0254484i
$941$	21.1990	−	17.7880i	0.691066	−	0.579873i	−0.228150	−	0.973626i	$-0.573268\pi$
$941$	21.1990	−	17.7880i	0.691066	−	0.579873i	0.919216	+	0.393753i	$0.128823\pi$
$942$	4.14528	+	4.05815i	0.135061	+	0.132222i
$943$	−22.9148	+	13.2299i	−0.746208	+	0.430823i
$944$	−3.23021	−	1.17570i	−0.105134	−	0.0382658i
$945$	11.3708	−	8.51436i	0.369892	−	0.276972i
$946$	−3.62397	+	0.639003i	−0.117825	+	0.0207758i
$947$	−1.43753	−	3.94957i	−0.0467133	−	0.128344i	0.914142	−	0.405394i	$-0.132866\pi$
$947$	−1.43753	−	3.94957i	−0.0467133	−	0.128344i	−0.960856	+	0.277050i	$0.910643\pi$
$948$	−0.483798	−	0.675550i	−0.0157130	−	0.0219408i
$949$		−	33.7055i		−	1.09413i
$950$	0.373794	−	4.34284i	0.0121275	−	0.140900i
$951$	−1.29044	+	5.02905i	−0.0418455	+	0.163078i
$952$	−5.90114	+	7.03270i	−0.191257	+	0.227931i
$953$	−22.9891	+	8.36735i	−0.744691	+	0.271045i	−0.686370	−	0.727253i	$-0.740797\pi$
$953$	−22.9891	+	8.36735i	−0.744691	+	0.271045i	−0.0583207	+	0.998298i	$0.518575\pi$
$954$	4.98099	−	14.6458i	0.161266	−	0.474176i
$955$	0.846201	−	4.79905i	0.0273824	−	0.155293i
$956$	−0.684889	+	1.88172i	−0.0221509	+	0.0608591i
$957$	0.855536	+	3.06243i	0.0276556	+	0.0989943i
$958$	−1.15544	−	0.667096i	−0.0373307	−	0.0215529i
$959$	31.9365	+	38.0604i	1.03128	+	1.22904i
$960$	1.56191	−	0.748627i	0.0504104	−	0.0241618i
$961$	−14.7078	+	25.4747i	−0.474446	+	0.821764i
$962$	21.4572	+	37.1650i	0.691809	+	1.19825i
$963$	2.65826	+	3.03469i	0.0856613	+	0.0977914i
$964$	6.14446	+	1.08343i	0.197900	+	0.0348951i
$965$	−0.683772	−	3.87786i	−0.0220114	−	0.124833i
$966$	15.2478	−	1.49735i	0.490591	−	0.0481765i
$967$	8.75165	+	7.34350i	0.281434	+	0.236151i	0.772567	−	0.634934i	$-0.218973\pi$
$967$	8.75165	+	7.34350i	0.281434	+	0.236151i	−0.491133	+	0.871085i	$0.663417\pi$
$968$	−10.3893			−0.333925
$969$	8.95732	+	23.7185i	0.287751	+	0.761947i
$970$	5.50709			0.176822
$971$	10.6375	+	8.92595i	0.341375	+	0.286447i	0.797315	−	0.603563i	$-0.206253\pi$
$971$	10.6375	+	8.92595i	0.341375	+	0.286447i	−0.455941	+	0.890010i	$0.650697\pi$
$972$	12.2767	−	9.60634i	0.393776	−	0.308124i
$973$	−2.15693	−	12.2325i	−0.0691479	−	0.392157i
$974$	9.85735	+	1.73812i	0.315850	+	0.0556929i
$975$	7.66311	+	5.24537i	0.245416	+	0.167986i
$976$	3.41319	+	5.91181i	0.109253	+	0.189232i
$977$	19.3968	−	33.5963i	0.620560	−	1.07484i	−0.368821	−	0.929500i	$-0.620239\pi$
$977$	19.3968	−	33.5963i	0.620560	−	1.07484i	0.989382	−	0.145341i	$-0.0464281\pi$
$978$	1.50221	+	3.13415i	0.0480353	+	0.100219i
$979$	8.19754	+	9.76945i	0.261994	+	0.312233i
$980$	0.410231	+	0.236847i	0.0131043	+	0.00756580i
$981$	15.5271	−	0.329864i	0.495741	−	0.0105318i
$982$	−3.24848	+	8.92512i	−0.103663	+	0.284812i
$983$	4.31240	−	24.4568i	0.137544	−	0.780052i	−0.835510	−	0.549475i	$-0.814828\pi$
$983$	4.31240	−	24.4568i	0.137544	−	0.780052i	0.973054	−	0.230577i	$-0.0740613\pi$
$984$	−14.1223	−	1.08454i	−0.450202	−	0.0345739i
$985$	23.9681	−	8.72367i	0.763687	−	0.277959i
$986$	−5.07088	+	6.04324i	−0.161490	+	0.192456i
$987$	−5.56722	−	1.42854i	−0.177206	−	0.0454708i
$988$	−16.5485	−	16.5020i	−0.526478	−	0.524998i
$989$			15.2366i			0.484495i
$990$	−0.848439	−	2.18548i	−0.0269652	−	0.0694591i
$991$	17.2555	+	47.4092i	0.548140	+	1.50600i	0.836219	+	0.548395i	$0.184761\pi$
$991$	17.2555	+	47.4092i	0.548140	+	1.50600i	−0.288080	+	0.957606i	$0.593017\pi$
$992$	1.23959	−	0.218573i	0.0393570	−	0.00693970i
$993$	5.43833	−	11.9935i	0.172580	−	0.380601i
$994$	38.0080	+	13.8338i	1.20554	+	0.438780i
$995$	−17.1850	+	9.92174i	−0.544800	+	0.314540i
$996$	−18.7626	+	19.1655i	−0.594516	+	0.607281i
$997$	11.0692	−	9.28817i	0.350565	−	0.294159i	−0.450452	−	0.892801i	$-0.648737\pi$
$997$	11.0692	−	9.28817i	0.350565	−	0.294159i	0.801017	+	0.598642i	$0.204293\pi$
$998$	29.6921	−	24.9146i	0.939886	−	0.788658i
$999$	−39.8105	+	12.0389i	−1.25955	+	0.380893i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.41.6	yes	84
3.2	odd	2		570.2.bb.a.41.5	✓	84
19.13	odd	18		570.2.bb.a.431.5	yes	84
57.32	even	18	inner	570.2.bb.b.431.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.5	✓	84	3.2	odd	2
570.2.bb.a.431.5	yes	84	19.13	odd	18
570.2.bb.b.41.6	yes	84	1.1	even	1	trivial
570.2.bb.b.431.6	yes	84	57.32	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bb (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.169275 - 1.72376i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-0.978339 + 1.42928i) q^{6} +(1.36690 + 2.36755i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.94269 + 0.583578i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(-0.169275 - 1.72376i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-0.978339 + 1.42928i) q^{6} +(1.36690 + 2.36755i) q^{7} +(0.500000 - 0.866025i) q^{8} +(-2.94269 + 0.583578i) q^{9} +(0.642788 + 0.766044i) q^{10} +(0.676767 + 0.390732i) q^{11} +(1.66818 - 0.466031i) q^{12} +(-1.83374 + 5.03816i) q^{13} +(0.474720 - 2.69227i) q^{14} +(-0.132625 + 1.72697i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-2.15858 + 2.57249i) q^{17} +(2.62935 + 1.44448i) q^{18} +(3.57411 + 2.49514i) q^{19} -1.00000i q^{20} +(3.84970 - 2.75698i) q^{21} +(-0.267276 - 0.734335i) q^{22} +(-3.18651 + 0.561867i) q^{23} +(-1.57746 - 0.715283i) q^{24} +(0.939693 + 0.342020i) q^{25} +(4.64320 - 2.68075i) q^{26} +(1.50407 + 4.97371i) q^{27} +(-2.09422 + 1.75726i) q^{28} +(-1.79957 + 1.51002i) q^{29} +(1.21167 - 1.23768i) q^{30} +(1.09008 - 0.629356i) q^{31} +(0.939693 + 0.342020i) q^{32} +(0.558968 - 1.23272i) q^{33} +(3.30713 - 0.583137i) q^{34} +(-0.935017 - 2.56894i) q^{35} +(-1.08571 - 2.79665i) q^{36} +8.00419i q^{37} +(-1.13409 - 4.20878i) q^{38} +(8.99499 + 2.30810i) q^{39} +(-0.642788 + 0.766044i) q^{40} +(7.68435 - 2.79688i) q^{41} +(-4.72119 - 0.362570i) q^{42} +(0.817700 - 4.63741i) q^{43} +(-0.267276 + 0.734335i) q^{44} +(2.99932 - 0.0637190i) q^{45} +(2.80217 + 1.61783i) q^{46} +(-0.780232 - 0.929844i) q^{47} +(0.748627 + 1.56191i) q^{48} +(-0.236847 + 0.410231i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(4.79975 + 3.28541i) q^{51} +(-5.28005 - 0.931015i) q^{52} +(-0.895427 - 5.07822i) q^{53} +(2.04485 - 4.77688i) q^{54} +(-0.598636 - 0.502315i) q^{55} +2.73381 q^{56} +(3.69601 - 6.58328i) q^{57} +2.34917 q^{58} +(2.63329 + 2.20959i) q^{59} +(-1.72376 + 0.169275i) q^{60} +(-1.18539 - 6.72266i) q^{61} +(-1.23959 - 0.218573i) q^{62} +(-5.40402 - 6.16926i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.68075 - 4.64320i) q^{65} +(-1.22057 + 0.585024i) q^{66} +(5.36968 + 6.39933i) q^{67} +(-2.90825 - 1.67908i) q^{68} +(1.50792 + 5.39766i) q^{69} +(-0.935017 + 2.56894i) q^{70} +(-2.56916 + 14.5704i) q^{71} +(-0.965953 + 2.84024i) q^{72} +(-5.90744 + 2.15013i) q^{73} +(5.14499 - 6.13156i) q^{74} +(0.430494 - 1.67770i) q^{75} +(-1.83659 + 3.95309i) q^{76} +2.13637i q^{77} +(-5.40695 - 7.54997i) q^{78} +(-0.164078 - 0.450801i) q^{79} +(0.984808 - 0.173648i) q^{80} +(8.31887 - 3.43458i) q^{81} +(-7.68435 - 2.79688i) q^{82} +(-13.4104 + 7.74247i) q^{83} +(3.38359 + 3.31247i) q^{84} +(2.57249 - 2.15858i) q^{85} +(-3.60726 + 3.02685i) q^{86} +(2.90753 + 2.84642i) q^{87} +(0.676767 - 0.390732i) q^{88} +(15.3353 + 5.58160i) q^{89} +(-2.33857 - 1.87912i) q^{90} +(-14.4346 + 2.54521i) q^{91} +(-1.10666 - 3.04053i) q^{92} +(-1.26938 - 1.77250i) q^{93} +1.21383i q^{94} +(-3.08654 - 3.07787i) q^{95} +(0.430494 - 1.67770i) q^{96} +(3.53989 - 4.21868i) q^{97} +(0.445127 - 0.162013i) q^{98} +(-2.21954 - 0.754857i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{6} + 42 q^{8}+O(q^{10}) \) 84 * q - 6 * q^6 + 42 * q^8	\( 84 q - 6 q^{6} + 42 q^{8} + 24 q^{13} - 24 q^{14} + 12 q^{17} - 12 q^{19} + 36 q^{22} + 24 q^{27} - 12 q^{28} - 12 q^{29} + 36 q^{33} + 12 q^{34} + 6 q^{36} + 18 q^{38} + 12 q^{39} + 6 q^{41} + 24 q^{43} + 36 q^{44} + 12 q^{47} - 12 q^{48} - 54 q^{49} - 42 q^{50} + 96 q^{51} + 12 q^{52} - 60 q^{53} - 18 q^{54} - 96 q^{57} - 24 q^{58} - 18 q^{59} - 48 q^{61} - 12 q^{62} - 114 q^{63} - 42 q^{64} - 24 q^{66} + 6 q^{67} - 54 q^{68} - 48 q^{69} + 48 q^{71} + 84 q^{73} + 24 q^{74} - 12 q^{79} - 36 q^{81} - 6 q^{82} + 36 q^{83} + 18 q^{84} + 12 q^{86} + 6 q^{87} - 12 q^{89} - 24 q^{90} + 24 q^{91} - 6 q^{93} - 12 q^{95} - 42 q^{97} + 36 q^{98} - 6 q^{99}+O(q^{100}) \) 84 * q - 6 * q^6 + 42 * q^8 + 24 * q^13 - 24 * q^14 + 12 * q^17 - 12 * q^19 + 36 * q^22 + 24 * q^27 - 12 * q^28 - 12 * q^29 + 36 * q^33 + 12 * q^34 + 6 * q^36 + 18 * q^38 + 12 * q^39 + 6 * q^41 + 24 * q^43 + 36 * q^44 + 12 * q^47 - 12 * q^48 - 54 * q^49 - 42 * q^50 + 96 * q^51 + 12 * q^52 - 60 * q^53 - 18 * q^54 - 96 * q^57 - 24 * q^58 - 18 * q^59 - 48 * q^61 - 12 * q^62 - 114 * q^63 - 42 * q^64 - 24 * q^66 + 6 * q^67 - 54 * q^68 - 48 * q^69 + 48 * q^71 + 84 * q^73 + 24 * q^74 - 12 * q^79 - 36 * q^81 - 6 * q^82 + 36 * q^83 + 18 * q^84 + 12 * q^86 + 6 * q^87 - 12 * q^89 - 24 * q^90 + 24 * q^91 - 6 * q^93 - 12 * q^95 - 42 * q^97 + 36 * q^98 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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