LMFDB - Embedded newform 570.2.bb.b.431.6

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			431.6
Character	$\chi$	$=$	570.431
Dual form			570.2.bb.b.41.6

$q$-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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$1$

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	−0.483173	−	0.875525i	$-0.660516\pi$
$7$	1.36690	−	2.36755i	0.516641	−	0.894848i	0.999813	−	0.0193228i	$-0.00615103\pi$
$8$	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	−0.394492	−	0.918900i	$-0.629079\pi$
$11$	0.676767	−	0.390732i	0.204053	−	0.117810i	0.598545	+	0.801090i	$0.295746\pi$
$12$	1.66818	+	0.466031i	0.481561	+	0.134531i
$13$	−1.83374	−	5.03816i	−0.508588	−	1.39734i	−0.882694	−	0.469949i	$-0.844272\pi$
$13$	−1.83374	−	5.03816i	−0.508588	−	1.39734i	0.374105	−	0.927386i	$-0.377950\pi$
$14$	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	0.437880	−	0.899033i	$-0.355730\pi$
$17$	−2.15858	−	2.57249i	−0.523532	−	0.623922i	−0.961412	+	0.275112i	$0.911285\pi$
$18$	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	−0.168747	−	0.985659i	$-0.553972\pi$
$23$	−3.18651	−	0.561867i	−0.664433	−	0.117157i	−0.495686	+	0.868502i	$0.665083\pi$
$24$	−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	0.460225	−	0.887802i	$-0.347769\pi$
$29$	−1.79957	−	1.51002i	−0.334172	−	0.280404i	−0.794397	+	0.607399i	$0.792213\pi$
$30$	1.21167	+	1.23768i	0.221219	+	0.225969i
$31$	1.09008	+	0.629356i	0.195784	+	0.113036i	0.594687	−	0.803957i	$-0.297276\pi$
$31$	1.09008	+	0.629356i	0.195784	+	0.113036i	−0.398904	+	0.916993i	$0.630609\pi$
$32$	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	$-0.771428\pi$
$37$		−	8.00419i		−	1.31588i	0.753070	−	0.657940i	$-0.228572\pi$
$38$	−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	0.863257	−	0.504764i	$-0.168421\pi$
$41$	7.68435	+	2.79688i	1.20009	+	0.436799i	0.336837	+	0.941563i	$0.390643\pi$
$42$	−4.72119	+	0.362570i	−0.728495	+	0.0559457i
$43$	0.817700	+	4.63741i	0.124698	+	0.707198i	0.981487	+	0.191530i	$0.0613450\pi$
$43$	0.817700	+	4.63741i	0.124698	+	0.707198i	−0.856789	+	0.515668i	$0.827544\pi$
$44$	−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	−0.819941	−	0.572448i	$-0.805994\pi$
$47$	−0.780232	+	0.929844i	−0.113809	+	0.135632i	0.706132	+	0.708080i	$0.250438\pi$
$48$	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	0.859481	+	0.511167i	$0.170787\pi$
$53$	−0.895427	+	5.07822i	−0.122996	+	0.697547i	−0.982478	+	0.186380i	$0.940324\pi$
$54$	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	−0.455076	−	0.890453i	$-0.650388\pi$
$59$	2.63329	−	2.20959i	0.342825	−	0.287665i	0.797901	+	0.602788i	$0.205944\pi$
$60$	−1.72376	−	0.169275i	−0.222536	−	0.0218533i
$61$	−1.18539	+	6.72266i	−0.151773	+	0.860749i	0.809903	+	0.586563i	$0.199519\pi$
$61$	−1.18539	+	6.72266i	−0.151773	+	0.860749i	−0.961677	+	0.274186i	$0.911592\pi$
$62$	−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	−0.330797	−	0.943702i	$-0.607317\pi$
$67$	5.36968	−	6.39933i	0.656011	−	0.781803i	0.986807	+	0.161899i	$0.0517618\pi$
$68$	−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	−0.623960	−	0.781457i	$-0.714477\pi$
$71$	−2.56916	−	14.5704i	−0.304903	−	1.72919i	0.319056	−	0.947736i	$-0.396634\pi$
$72$	−0.965953	−	2.84024i	−0.113839	−	0.334725i
$73$	−5.90744	−	2.15013i	−0.691414	−	0.251654i	−0.0276735	−	0.999617i	$-0.508810\pi$
$73$	−5.90744	−	2.15013i	−0.691414	−	0.251654i	−0.663741	+	0.747963i	$0.731032\pi$
$74$	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	−0.948580	−	0.316536i	$-0.897480\pi$
$79$	−0.164078	+	0.450801i	−0.0184602	+	0.0507190i	0.930120	+	0.367255i	$0.119702\pi$
$80$	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	−0.472474	−	0.881345i	$-0.656639\pi$
$83$	−13.4104	−	7.74247i	−1.47198	−	0.849847i	−0.999504	+	0.0314977i	$0.989972\pi$
$84$	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	0.641115	−	0.767445i	$-0.278472\pi$
$89$	15.3353	−	5.58160i	1.62554	−	0.591649i	0.984427	+	0.175796i	$0.0562498\pi$
$90$	−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	0.915207	−	0.402984i	$-0.132027\pi$
$97$	3.53989	+	4.21868i	0.359421	+	0.428342i	−0.555786	+	0.831326i	$0.687582\pi$
$98$	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	−0.983601	−	0.180361i	$-0.942274\pi$
$101$	−3.47778	−	9.55513i	−0.346052	−	0.950771i	0.637548	−	0.770410i	$-0.279949\pi$
$102$	−1.56500	+	5.60199i	−0.154958	+	0.554680i
$103$	−10.1752	+	5.87466i	−1.00259	+	0.578847i	−0.909014	−	0.416765i	$-0.863164\pi$
$103$	−10.1752	+	5.87466i	−1.00259	+	0.578847i	−0.0935782	+	0.995612i	$0.529831\pi$
$104$	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	−0.896695	−	0.442649i	$-0.854039\pi$
$107$	−0.672386	+	1.16461i	−0.0650020	+	0.112587i	0.831693	+	0.555236i	$0.187372\pi$
$108$	−4.63697	−	2.34490i	−0.446192	−	0.225638i
$109$	−5.09821	+	0.898952i	−0.488320	+	0.0861040i	−0.412387	−	0.911009i	$-0.635305\pi$
$109$	−5.09821	+	0.898952i	−0.488320	+	0.0861040i	−0.0759334	+	0.997113i	$0.524194\pi$
$110$	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	−0.623237	−	0.782033i	$-0.714183\pi$
$127$	−7.30812	−	20.0789i	−0.648491	−	1.78171i	−0.0252542	−	0.999681i	$-0.508040\pi$
$128$	−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	0.271809	−	0.962351i	$-0.412378\pi$
$131$	−8.27650	−	9.86355i	−0.723122	−	0.861783i	−0.994930	+	0.100569i	$0.967934\pi$
$132$	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	0.874012	−	0.485904i	$-0.161510\pi$
$137$	17.8980	+	3.15589i	1.52913	+	0.269626i	0.655114	+	0.755530i	$0.272621\pi$
$138$	2.31442	+	5.10412i	0.197016	+	0.434492i
$139$	−4.26956	+	1.55399i	−0.362140	+	0.131808i	−0.516680	−	0.856178i	$-0.672832\pi$
$139$	−4.26956	+	1.55399i	−0.362140	+	0.131808i	0.154541	+	0.987986i	$0.450610\pi$
$140$	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	0.0948614	+	0.995490i	$0.469759\pi$
$149$	−7.53994	+	20.7158i	−0.617696	+	1.69710i	−0.712557	+	0.701614i	$0.752463\pi$
$150$	−1.40818	−	1.00848i	−0.114978	−	0.0823417i
$151$			0.916825i			0.0746101i	0.999304	+	0.0373051i	$0.0118773\pi$
$151$			0.916825i			0.0746101i	−0.999304	+	0.0373051i	$0.988123\pi$
$152$	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	0.999181	−	0.0404720i	$-0.0128862\pi$
$157$	0.581587	+	3.29835i	0.0464157	+	0.263237i	−0.952765	+	0.303709i	$0.901775\pi$
$158$	−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	0.902640	−	0.430397i	$-0.141626\pi$
$163$	1.00331	+	1.73778i	0.0785852	+	0.136114i	−0.824055	+	0.566510i	$0.808293\pi$
$164$	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	−0.750534	−	0.660832i	$-0.770203\pi$
$167$	2.33587	−	13.2474i	0.180755	−	1.02511i	0.931289	−	0.364282i	$-0.118685\pi$
$168$	−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	−0.378292	+	0.925686i	$0.623489\pi$
$173$	−17.8302	+	14.9613i	−1.35560	+	1.13749i	−0.977313	+	0.211801i	$0.932067\pi$
$174$	−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	0.832254	−	0.554394i	$-0.187050\pi$
$179$	−0.856163	−	1.48292i	−0.0639926	−	0.110838i	−0.896247	+	0.443556i	$0.853717\pi$
$180$	0.583578	−	2.94269i	0.0434973	−	0.219335i
$181$	4.80217	−	5.72301i	0.356943	−	0.425388i	−0.557454	−	0.830208i	$-0.688222\pi$
$181$	4.80217	−	5.72301i	0.356943	−	0.425388i	0.914396	+	0.404820i	$0.132666\pi$
$182$	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	$-0.943587\pi$
$191$		−	4.87308i		−	0.352604i	0.984336	−	0.176302i	$-0.0564135\pi$
$192$	−1.40818	−	1.00848i	−0.101627	−	0.0727805i
$193$	1.34677	−	3.70022i	0.0969425	−	0.266347i	−0.881737	−	0.471742i	$-0.843625\pi$
$193$	1.34677	−	3.70022i	0.0969425	−	0.266347i	0.978679	+	0.205394i	$0.0658477\pi$
$194$	−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	−0.995699	−	0.0926482i	$-0.970467\pi$
$197$	−22.0891	−	12.7532i	−1.57378	−	0.908625i	−0.578085	−	0.815976i	$-0.696200\pi$
$198$	1.21505	−	2.00495i	0.0863501	−	0.142485i
$199$	15.2010	+	12.7551i	1.07757	+	0.904188i	0.995717	−	0.0924567i	$-0.0294720\pi$
$199$	15.2010	+	12.7551i	1.07757	+	0.904188i	0.0818523	+	0.996644i	$0.473916\pi$
$200$	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	0.997306	+	0.0733527i	$0.0233699\pi$
$211$	13.0204	+	15.5172i	0.896364	+	1.06825i	−0.100942	+	0.994892i	$0.532186\pi$
$212$	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	0.710955	−	0.703237i	$-0.248263\pi$
$223$	24.1851	−	4.26449i	1.61956	−	0.285571i	0.908601	+	0.417666i	$0.137152\pi$
$224$	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	0.914118	−	0.405448i	$-0.132884\pi$
$233$	29.1821	−	5.14558i	1.91178	−	0.337098i	0.997661	+	0.0683492i	$0.0217732\pi$
$234$	−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	−0.442862	−	0.896590i	$-0.646037\pi$
$239$	1.73420	−	1.00124i	0.112176	−	0.0647649i	0.555038	+	0.831825i	$0.312704\pi$
$240$	−0.466031	+	1.66818i	−0.0300822	+	0.107680i
$241$	2.13395	+	5.86298i	0.137460	+	0.377668i	0.989254	−	0.146209i	$-0.0467073\pi$
$241$	2.13395	+	5.86298i	0.137460	+	0.377668i	−0.851794	+	0.523877i	$0.824485\pi$
$242$	−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	−0.0583300	−	0.998297i	$-0.518578\pi$
$251$	−7.20190	−	1.26989i	−0.454580	−	0.0801547i	−0.396250	+	0.918143i	$0.629689\pi$
$252$	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	0.990391	−	0.138294i	$-0.0441620\pi$
$257$	16.4509	+	13.8039i	1.02618	+	0.861065i	0.0357863	+	0.999359i	$0.488606\pi$
$258$	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	−0.998613	−	0.0526506i	$-0.983233\pi$
$263$	−3.24002	+	8.90187i	−0.199788	+	0.548913i	0.798825	+	0.601563i	$0.205455\pi$
$264$	−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	0.738133	−	0.674655i	$-0.235708\pi$
$269$	14.2677	+	5.19301i	0.869916	+	0.316624i	0.131783	+	0.991279i	$0.457930\pi$
$270$	−2.84328	−	4.34922i	−0.173037	−	0.264685i
$271$	−1.85456	−	10.5177i	−0.112656	−	0.638907i	−0.987884	−	0.155195i	$-0.950399\pi$
$271$	−1.85456	−	10.5177i	−0.112656	−	0.638907i	0.875227	−	0.483712i	$-0.160712\pi$
$272$	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	0.821581	−	0.570092i	$-0.193092\pi$
$277$	−1.38012	−	2.39044i	−0.0829236	−	0.143628i	−0.904505	+	0.426464i	$0.859759\pi$
$278$	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	−0.717837	−	0.696212i	$-0.754867\pi$
$281$	3.26591	−	18.5219i	0.194828	−	1.10492i	0.912664	−	0.408710i	$-0.134021\pi$
$282$	2.09234	+	0.205470i	0.124597	+	0.0122356i
$283$	−4.18546	+	3.51201i	−0.248800	+	0.208768i	−0.758655	−	0.651492i	$-0.774143\pi$
$283$	−4.18546	+	3.51201i	−0.248800	+	0.208768i	0.509856	+	0.860260i	$0.329699\pi$
$284$	−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	−0.997348	−	0.0727750i	$-0.976814\pi$
$293$	−9.61474	−	16.6532i	−0.561699	−	0.972892i	0.435649	−	0.900117i	$-0.356519\pi$
$294$	−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	0.632171	+	0.774829i	$0.282164\pi$
$307$	−6.13513	+	16.8561i	−0.350150	+	0.962030i	−0.982322	+	0.187201i	$0.940058\pi$
$308$	−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	0.423577	−	0.905860i	$-0.360774\pi$
$311$	−2.62998	−	1.51842i	−0.149133	−	0.0861018i	−0.572710	+	0.819758i	$0.694108\pi$
$312$	6.49636	+	6.63584i	0.367784	+	0.375680i
$313$	22.5115	+	18.8894i	1.27243	+	1.06769i	0.994241	+	0.107164i	$0.0341769\pi$
$313$	22.5115	+	18.8894i	1.27243	+	1.06769i	0.278184	+	0.960528i	$0.410268\pi$
$314$	−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	−0.419910	−	0.907566i	$-0.637938\pi$
$317$	−2.81681	+	1.02523i	−0.158208	+	0.0575829i	0.261702	+	0.965149i	$0.415716\pi$
$318$	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	−0.308007	−	0.951384i	$-0.599662\pi$
$331$	6.58443	−	3.80152i	0.361913	−	0.208950i	0.669919	+	0.742434i	$0.266329\pi$
$332$	−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	−0.00824465	−	0.999966i	$-0.502624\pi$
$337$	5.98487	−	1.05529i	0.326016	−	0.0574855i	0.334261	+	0.942481i	$0.391513\pi$
$338$	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	−0.975750	−	0.218888i	$-0.929757\pi$
$347$	−33.8617	+	5.97073i	−1.81779	+	0.320526i	−0.842041	+	0.539413i	$0.818646\pi$
$348$	−2.29829	−	3.35764i	−0.123201	−	0.179988i
$349$	−6.95446	+	12.0455i	−0.372264	+	0.644780i	−0.989913	−	0.141674i	$-0.954752\pi$
$349$	−6.95446	+	12.0455i	−0.372264	+	0.644780i	0.617650	+	0.786453i	$0.288085\pi$
$350$	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	−0.853664	−	0.520824i	$-0.825625\pi$
$353$	−15.5839	+	8.99739i	−0.829450	+	0.478883i	0.0242146	+	0.999707i	$0.492291\pi$
$354$	−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	0.900766	+	0.434305i	$0.143006\pi$
$359$	22.2073	+	26.4656i	1.17206	+	1.39680i	0.271291	+	0.962497i	$0.412550\pi$
$360$	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	−0.653385	−	0.757026i	$-0.726652\pi$
$367$	−12.7836	+	4.65286i	−0.667300	+	0.242877i	−0.0139152	+	0.999903i	$0.504429\pi$
$368$	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	0.710774	−	0.703421i	$-0.248345\pi$
$373$	8.82576	+	5.09556i	0.456981	+	0.263838i	−0.253793	+	0.967258i	$0.581678\pi$
$374$	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	$-0.830159\pi$
$379$		−	19.8032i		−	1.01722i	0.860997	−	0.508610i	$-0.169841\pi$
$380$	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	0.233453	−	0.972368i	$-0.424998\pi$
$383$	−4.16337	−	1.51534i	−0.212739	−	0.0774305i	−0.446191	+	0.894938i	$0.647220\pi$
$384$	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	0.148609	−	0.988896i	$-0.452520\pi$
$389$	21.6298	−	25.7774i	1.09668	−	1.30697i	0.948067	−	0.318071i	$-0.103035\pi$
$390$	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	0.386572	−	0.922259i	$-0.373659\pi$
$397$	27.1366	−	22.7703i	1.36195	−	1.14281i	0.975376	−	0.220551i	$-0.0707854\pi$
$398$	−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	−0.943128	−	0.332428i	$-0.892132\pi$
$401$	−15.6099	+	13.0983i	−0.779523	+	0.654097i	0.163606	+	0.986526i	$0.447688\pi$
$402$	−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	0.0121238	+	0.999927i	$0.496141\pi$
$409$	−19.7124	+	23.4924i	−0.974717	+	1.16162i	−0.986841	+	0.161696i	$0.948304\pi$
$410$	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	$0.128406\pi$
$419$			16.0705i			0.785096i	−0.919732	+	0.392548i	$0.871594\pi$
$420$	−2.75698	+	3.84970i	−0.134527	+	0.187846i
$421$	−11.7063	+	32.1628i	−0.570530	+	1.56752i	0.233140	+	0.972443i	$0.425100\pi$
$421$	−11.7063	+	32.1628i	−0.570530	+	1.56752i	−0.803670	+	0.595076i	$0.797122\pi$
$422$	−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	0.271415	−	0.962463i	$-0.412509\pi$
$431$	22.7948	−	8.29665i	1.09799	−	0.399635i	0.826575	+	0.562827i	$0.190286\pi$
$432$	−3.11447	+	4.15933i	−0.149845	+	0.200116i
$433$	14.7958	+	2.60889i	0.711038	+	0.125375i	0.517457	−	0.855709i	$-0.326879\pi$
$433$	14.7958	+	2.60889i	0.711038	+	0.125375i	0.193581	+	0.981084i	$0.437990\pi$
$434$	−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	0.977646	+	0.210260i	$0.0674310\pi$
$439$	21.2655	+	25.3432i	1.01494	+	1.20956i	0.0372990	+	0.999304i	$0.488125\pi$
$440$	−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	0.925747	−	0.378142i	$-0.123437\pi$
$443$	−0.557369	−	1.53136i	−0.0264814	−	0.0727571i	−0.952229	+	0.305385i	$0.901215\pi$
$444$	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	0.219450	+	0.975624i	$0.429574\pi$
$449$	−15.5784	+	26.9826i	−0.735190	+	1.27339i	−0.954640	+	0.297762i	$0.903760\pi$
$450$	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	0.274171	−	0.961681i	$-0.411596\pi$
$461$	18.4805	−	3.25861i	0.860722	−	0.151769i	0.586551	+	0.809912i	$0.300485\pi$
$462$	−3.05348	+	2.09009i	−0.142061	+	0.0972399i
$463$	−11.8899	+	20.5938i	−0.552568	+	0.957076i	0.445520	+	0.895272i	$0.353019\pi$
$463$	−11.8899	+	20.5938i	−0.552568	+	0.957076i	−0.998088	+	0.0618044i	$0.980315\pi$
$464$	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	−0.172089	−	0.985081i	$-0.555052\pi$
$467$	12.8575	−	7.42326i	0.594972	−	0.343507i	0.767061	+	0.641574i	$0.221718\pi$
$468$	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	0.203585	−	0.979057i	$-0.434741\pi$
$479$	1.31392	+	0.231680i	0.0600347	+	0.0105857i	−0.143550	+	0.989643i	$0.545852\pi$
$480$	−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	0.290571	−	0.956853i	$-0.406155\pi$
$487$	−8.66841	−	5.00471i	−0.392803	−	0.226785i	−0.683374	+	0.730068i	$0.739488\pi$
$488$	−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	−0.991159	−	0.132680i	$-0.957642\pi$
$491$	−3.24848	+	8.92512i	−0.146602	+	0.402785i	0.844557	+	0.535466i	$0.179864\pi$
$492$	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	−0.640407	−	0.768036i	$-0.721234\pi$
$499$	−6.73065	−	38.1714i	−0.301305	−	1.70879i	0.339102	−	0.940750i	$-0.389877\pi$
$500$	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	−0.295297	−	0.955405i	$-0.595419\pi$
$503$	15.6292	−	18.6262i	0.696871	−	0.830499i	0.992169	+	0.124906i	$0.0398631\pi$
$504$	−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	0.890620	+	0.454747i	$0.150270\pi$
$509$	−2.29720	+	13.0281i	−0.101822	+	0.577460i	−0.992442	+	0.122713i	$0.960841\pi$
$510$	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	0.971859	−	0.235563i	$-0.0756935\pi$
$521$	6.43508	+	11.1459i	0.281926	+	0.488310i	−0.689933	+	0.723873i	$0.742360\pi$
$522$	−6.91290	−	1.37093i	−0.302569	−	0.0600038i
$523$	−14.6215	+	17.4252i	−0.639352	+	0.761950i	−0.984268	−	0.176684i	$-0.943463\pi$
$523$	−14.6215	+	17.4252i	−0.639352	+	0.761950i	0.344916	+	0.938634i	$0.387908\pi$
$524$	−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	0.490111	−	0.871660i	$-0.336956\pi$
$541$	−6.58706	−	5.52720i	−0.283200	−	0.237633i	−0.773311	+	0.634027i	$0.781401\pi$
$542$	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	−0.595813	−	0.803124i	$-0.703170\pi$
$547$	−33.4537	−	5.89879i	−1.43038	−	0.252214i	−0.834565	+	0.550909i	$0.814281\pi$
$548$	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	0.882337	+	0.470619i	$0.155969\pi$
$557$	12.0113	+	33.0008i	0.508936	+	1.39829i	−0.373401	+	0.927670i	$0.621808\pi$
$558$	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	−0.456486	−	0.889731i	$-0.650892\pi$
$563$	12.8672	−	22.2866i	0.542286	−	0.939267i	0.998772	−	0.0495367i	$-0.0157745\pi$
$564$	−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	−0.861901	−	0.507076i	$-0.830726\pi$
$577$	0.196726	−	0.340739i	0.00818980	−	0.0141852i	0.870091	+	0.492891i	$0.164060\pi$
$578$	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	0.913384	−	0.407098i	$-0.133459\pi$
$587$	8.57342	+	10.2174i	0.353863	+	0.421718i	−0.559521	+	0.828816i	$0.689015\pi$
$588$	−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	0.700936	−	0.713225i	$-0.252766\pi$
$593$	27.1682	+	4.79048i	1.11566	+	0.196721i	0.414727	+	0.909946i	$0.363877\pi$
$594$	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	−0.00676271	−	0.999977i	$-0.502153\pi$
$599$	−24.2964	−	20.3871i	−0.992722	−	0.832993i	−0.985960	+	0.166984i	$0.946597\pi$
$600$	−1.23768	+	1.21167i	−0.0505282	+	0.0494662i
$601$	14.9017	+	8.60351i	0.607854	+	0.350944i	0.772125	−	0.635471i	$-0.219194\pi$
$601$	14.9017	+	8.60351i	0.607854	+	0.350944i	−0.164271	+	0.986415i	$0.552527\pi$
$602$	−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	$0.228864\pi$
$607$			32.4539i			1.31726i	−0.752466	+	0.658631i	$0.771136\pi$
$608$	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	−0.984332	−	0.176327i	$-0.943578\pi$
$613$	−2.96289	−	16.8034i	−0.119670	−	0.678682i	0.864662	−	0.502355i	$-0.167533\pi$
$614$	−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	−0.856183	−	0.516672i	$-0.827171\pi$
$617$	−4.93525	+	5.88161i	−0.198686	+	0.236785i	0.657497	+	0.753457i	$0.271615\pi$
$618$	18.3514	+	8.79585i	0.738200	+	0.353821i
$619$	8.77468	+	15.1982i	0.352684	+	0.610867i	0.986719	−	0.162438i	$-0.0519357\pi$
$619$	8.77468	+	15.1982i	0.352684	+	0.610867i	−0.634035	+	0.773305i	$0.718602\pi$
$620$	−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	−0.630232	−	0.776407i	$-0.717040\pi$
$631$	5.71572	−	32.4155i	0.227539	−	1.29044i	0.857771	−	0.514032i	$-0.171849\pi$
$632$	−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	−0.985287	−	0.170905i	$-0.945331\pi$
$641$	−2.98431	−	16.9249i	−0.117873	−	0.668492i	0.867414	−	0.497587i	$-0.165780\pi$
$642$	2.32237	−	0.178350i	0.0916568	−	0.00703890i
$643$	9.88767	+	3.59882i	0.389932	+	0.141923i	0.529543	−	0.848283i	$-0.322363\pi$
$643$	9.88767	+	3.59882i	0.389932	+	0.141923i	−0.139612	+	0.990206i	$0.544585\pi$
$644$	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	$0.111291\pi$
$647$			17.4264i			0.685101i	−0.939499	+	0.342551i	$0.888709\pi$
$648$	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	0.674152	−	0.738592i	$-0.264509\pi$
$653$	9.49553	+	5.48225i	0.371589	+	0.214537i	−0.302564	+	0.953129i	$0.597842\pi$
$654$	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	0.240576	−	0.970630i	$-0.422664\pi$
$659$	26.9232	−	9.79923i	1.04878	−	0.381724i	0.808201	+	0.588906i	$0.200441\pi$
$660$	−1.23272	+	0.558968i	−0.0479837	+	0.0217578i
$661$	−25.5439	−	4.50408i	−0.993543	−	0.175188i	−0.346835	−	0.937926i	$-0.612744\pi$
$661$	−25.5439	−	4.50408i	−0.993543	−	0.175188i	−0.646708	+	0.762738i	$0.723855\pi$
$662$	−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	0.567957	−	0.823059i	$-0.307734\pi$
$673$	40.5925	−	23.4361i	1.56472	−	0.903394i	0.996768	−	0.0803356i	$-0.0255992\pi$
$674$	−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	−0.814167	−	0.580631i	$-0.802806\pi$
$677$	2.49156	−	4.31550i	0.0957583	−	0.165858i	0.909925	+	0.414773i	$0.136139\pi$
$678$	−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	−0.990044	−	0.140757i	$-0.955046\pi$
$691$	−9.80824	+	16.9884i	−0.373123	+	0.646268i	0.616921	+	0.787025i	$0.288380\pi$
$692$	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	−0.995003	−	0.0998499i	$-0.968164\pi$
$701$	−24.3730	−	29.0466i	−0.920555	−	1.09707i	0.0744474	−	0.997225i	$-0.476281\pi$
$702$	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	−0.184595	−	0.982815i	$-0.559097\pi$
$709$	8.14093	−	2.96305i	0.305739	−	0.111280i	0.490333	+	0.871535i	$0.336875\pi$
$710$	−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	−0.644303	−	0.764770i	$-0.722852\pi$
$719$	9.13952	−	25.1106i	0.340847	−	0.936468i	0.985150	−	0.171698i	$-0.0549254\pi$
$720$	−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	0.998954	−	0.0457304i	$-0.0145615\pi$
$727$	1.20264	+	6.82053i	0.0446036	+	0.252959i	−0.954350	+	0.298690i	$0.903450\pi$
$728$	−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	0.997690	+	0.0679288i	$0.0216391\pi$
$733$	15.0984	+	26.1512i	0.557673	+	0.965918i	−0.440017	+	0.897989i	$0.645028\pi$
$734$	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	0.301323	−	0.953522i	$-0.402572\pi$
$739$	35.1410	−	29.4868i	1.29268	−	1.08469i	0.991360	−	0.131168i	$-0.0418728\pi$
$740$	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	0.573296	−	0.819348i	$-0.305665\pi$
$743$	40.3350	−	33.8451i	1.47975	−	1.24166i	0.906453	−	0.422308i	$-0.138780\pi$
$744$	−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	−0.0141816	−	0.999899i	$-0.504514\pi$
$751$	26.6642	−	31.7771i	0.972990	−	1.15956i	0.987171	−	0.159665i	$-0.0510413\pi$
$752$	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	−0.583822	−	0.811882i	$-0.698443\pi$
$757$	−42.7265	−	15.5512i	−1.55292	−	0.565218i	−0.969101	+	0.246664i	$0.920665\pi$
$758$	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	$0.269241\pi$
$761$			41.2983i			1.49706i	−0.663099	+	0.748532i	$0.730759\pi$
$762$	−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	0.873259	−	0.487256i	$-0.162002\pi$
$769$	15.1146	+	12.6826i	0.545046	+	0.457348i	−0.328214	+	0.944604i	$0.606447\pi$
$770$	−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	−0.694143	−	0.719837i	$-0.744217\pi$
$773$	−21.2188	+	7.72300i	−0.763186	+	0.277777i	−0.0690426	+	0.997614i	$0.521994\pi$
$774$	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	−0.217114	−	0.976146i	$-0.569664\pi$
$787$	14.5793	−	8.41738i	0.519697	−	0.300047i	0.736811	+	0.676099i	$0.236331\pi$
$788$	−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	−0.925777	−	0.378071i	$-0.876588\pi$
$809$	−30.1850	+	17.4273i	−1.06125	+	0.612711i	−0.135470	+	0.990781i	$0.543254\pi$
$810$	7.97831	−	4.16492i	0.280329	−	0.146340i
$811$	−11.0768	−	30.4333i	−0.388959	−	1.06866i	−0.967471	−	0.252982i	$-0.918589\pi$
$811$	−11.0768	−	30.4333i	−0.388959	−	1.06866i	0.578512	−	0.815674i	$-0.303634\pi$
$812$	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	0.198181	−	0.980165i	$-0.436497\pi$
$821$	1.40900	+	0.248444i	0.0491743	+	0.00867075i	−0.149007	+	0.988836i	$0.547608\pi$
$822$	−12.9996	−	28.6688i	−0.453413	−	0.999939i
$823$	−8.60472	+	3.13186i	−0.299942	+	0.109170i	−0.487607	−	0.873063i	$-0.662130\pi$
$823$	−8.60472	+	3.13186i	−0.299942	+	0.109170i	0.187666	+	0.982233i	$0.439908\pi$
$824$	−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	0.865454	−	0.500988i	$-0.167030\pi$
$827$	15.0219	+	12.6049i	0.522362	+	0.438314i	−0.343092	+	0.939302i	$0.611474\pi$
$828$	5.03095	−	8.30152i	0.174838	−	0.288498i
$829$	−27.0740	−	15.6312i	−0.940318	−	0.542893i	−0.0502577	−	0.998736i	$-0.516004\pi$
$829$	−27.0740	−	15.6312i	−0.940318	−	0.542893i	−0.890060	+	0.455844i	$0.849338\pi$
$830$	−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	0.644536	−	0.764574i	$-0.277051\pi$
$839$	18.7355	+	6.81915i	0.646820	+	0.235423i	0.00228403	+	0.999997i	$0.499273\pi$
$840$	−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	−0.227478	−	0.973783i	$-0.573048\pi$
$853$	20.2110	−	16.9590i	0.692011	−	0.580666i	0.919488	+	0.393117i	$0.128603\pi$
$854$	−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	−0.465526	−	0.885034i	$-0.654135\pi$
$857$	9.52082	−	7.98892i	0.325225	−	0.272896i	0.790751	+	0.612138i	$0.209690\pi$
$858$	−0.709230	+	7.22224i	−0.0242127	+	0.246563i
$859$	8.19991	−	46.5040i	0.279777	−	1.58670i	−0.443588	−	0.896231i	$-0.646295\pi$
$859$	8.19991	−	46.5040i	0.279777	−	1.58670i	0.723365	−	0.690466i	$-0.242594\pi$
$860$	−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	−0.995578	−	0.0939336i	$-0.970056\pi$
$863$	−17.0133	−	29.4678i	−0.579138	−	1.00310i	0.416440	−	0.909163i	$-0.363277\pi$
$864$	−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	−0.943885	−	0.330273i	$-0.892859\pi$
$877$	−0.252654	+	0.694160i	−0.00853151	+	0.0234401i	0.935354	+	0.353714i	$0.115081\pi$
$878$	−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	−0.141530	−	0.989934i	$-0.545202\pi$
$881$	−31.7476	−	18.3295i	−1.06960	−	0.617536i	−0.928073	+	0.372398i	$0.878536\pi$
$882$	−1.21532	−	0.736520i	−0.0409221	−	0.0247999i
$883$	−13.9478	−	11.7036i	−0.469382	−	0.393859i	0.377187	−	0.926137i	$-0.376891\pi$
$883$	−13.9478	−	11.7036i	−0.469382	−	0.393859i	−0.846569	+	0.532279i	$0.821336\pi$
$884$	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	0.486720	−	0.873558i	$-0.338193\pi$
$887$	42.3234	−	15.4045i	1.42108	−	0.517232i	0.934362	+	0.356326i	$0.115971\pi$
$888$	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	−0.343996	−	0.938971i	$-0.611781\pi$
$907$	−10.4233	+	1.83790i	−0.346099	+	0.0610265i	−0.00210298	+	0.999998i	$0.500669\pi$
$908$	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	0.221855	+	0.975080i	$0.428789\pi$
$919$	−22.2366	+	38.5149i	−0.733517	+	1.27049i	−0.955371	+	0.295408i	$0.904544\pi$
$920$	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	0.974753	−	0.223286i	$-0.0716783\pi$
$929$	17.8487	+	21.2712i	0.585595	+	0.697886i	−0.389158	+	0.921171i	$0.627234\pi$
$930$	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	−0.240794	−	0.970576i	$-0.577408\pi$
$937$	6.07991	−	2.21291i	0.198622	−	0.0722925i	0.439416	+	0.898284i	$0.355186\pi$
$938$	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	0.919216	−	0.393753i	$-0.128823\pi$
$941$	21.1990	+	17.7880i	0.691066	+	0.579873i	−0.228150	+	0.973626i	$0.573268\pi$
$942$	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	−0.960856	−	0.277050i	$-0.910643\pi$
$947$	−1.43753	+	3.94957i	−0.0467133	+	0.128344i	0.914142	+	0.405394i	$0.132866\pi$
$948$	−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	−0.0583207	−	0.998298i	$-0.518575\pi$
$953$	−22.9891	−	8.36735i	−0.744691	−	0.271045i	−0.686370	+	0.727253i	$0.740797\pi$
$954$	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	−0.491133	−	0.871085i	$-0.663417\pi$
$967$	8.75165	−	7.34350i	0.281434	−	0.236151i	0.772567	+	0.634934i	$0.218973\pi$
$968$	−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	−0.455941	−	0.890010i	$-0.650697\pi$
$971$	10.6375	−	8.92595i	0.341375	−	0.286447i	0.797315	+	0.603563i	$0.206253\pi$
$972$	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	0.989382	+	0.145341i	$0.0464281\pi$
$977$	19.3968	+	33.5963i	0.620560	+	1.07484i	−0.368821	+	0.929500i	$0.620239\pi$
$978$	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	0.973054	+	0.230577i	$0.0740613\pi$
$983$	4.31240	+	24.4568i	0.137544	+	0.780052i	−0.835510	+	0.549475i	$0.814828\pi$
$984$	−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	−0.288080	−	0.957606i	$-0.593017\pi$
$991$	17.2555	−	47.4092i	0.548140	−	1.50600i	0.836219	−	0.548395i	$-0.184761\pi$
$992$	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	0.801017	−	0.598642i	$-0.204293\pi$
$997$	11.0692	+	9.28817i	0.350565	+	0.294159i	−0.450452	+	0.892801i	$0.648737\pi$
$998$	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.431.6	yes	84
3.2	odd	2		570.2.bb.a.431.5	yes	84
19.3	odd	18		570.2.bb.a.41.5	✓	84
57.41	even	18	inner	570.2.bb.b.41.6	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.5	✓	84	19.3	odd	18
570.2.bb.a.431.5	yes	84	3.2	odd	2
570.2.bb.b.41.6	yes	84	57.41	even	18	inner
570.2.bb.b.431.6	yes	84	1.1	even	1	trivial

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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