LMFDB - Embedded newform 570.2.bb.b.41.14

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			41.14
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.b.431.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.766044 - 0.642788i) q^{2} +(1.61856 - 0.616663i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-1.63627 - 0.567997i) q^{6} +(1.59792 + 2.76767i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.23945 - 1.99621i) q^{9} +O(q^{10})$	\(q+(-0.766044 - 0.642788i) q^{2} +(1.61856 - 0.616663i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-1.63627 - 0.567997i) q^{6} +(1.59792 + 2.76767i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.23945 - 1.99621i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(1.69039 + 0.975946i) q^{11} +(0.888354 + 1.48689i) q^{12} +(-1.61284 + 4.43125i) q^{13} +(0.554951 - 3.14728i) q^{14} +(1.70105 - 0.326235i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.460813 + 0.549175i) q^{17} +(-2.99866 + 0.0896911i) q^{18} +(-4.35644 + 0.146517i) q^{19} +1.00000i q^{20} +(4.29304 + 3.49426i) q^{21} +(-0.667586 - 1.83418i) q^{22} +(6.28901 - 1.10892i) q^{23} +(0.275233 - 1.71004i) q^{24} +(0.939693 + 0.342020i) q^{25} +(4.08387 - 2.35782i) q^{26} +(2.39370 - 4.61196i) q^{27} +(-2.44815 + 2.05424i) q^{28} +(-2.60828 + 2.18861i) q^{29} +(-1.51278 - 0.843503i) q^{30} +(-4.36758 + 2.52162i) q^{31} +(0.939693 + 0.342020i) q^{32} +(3.33782 + 0.537225i) q^{33} +(0.706006 - 0.124488i) q^{34} +(1.09304 + 3.00310i) q^{35} +(2.35476 + 1.85879i) q^{36} -2.68401i q^{37} +(3.43140 + 2.68802i) q^{38} +(0.122109 + 8.16682i) q^{39} +(0.642788 - 0.766044i) q^{40} +(7.99149 - 2.90866i) q^{41} +(-1.04259 - 5.43627i) q^{42} +(0.960386 - 5.44662i) q^{43} +(-0.667586 + 1.83418i) q^{44} +(2.55207 - 1.57700i) q^{45} +(-5.53047 - 3.19302i) q^{46} +(-7.46694 - 8.89875i) q^{47} +(-1.31003 + 1.13305i) q^{48} +(-1.60668 + 2.78284i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.407196 + 1.17304i) q^{51} +(-4.64400 - 0.818863i) q^{52} +(-1.45006 - 8.22370i) q^{53} +(-4.79819 + 1.99433i) q^{54} +(1.49524 + 1.25465i) q^{55} +3.19583 q^{56} +(-6.96079 + 2.92360i) q^{57} +3.40487 q^{58} +(-5.27090 - 4.42281i) q^{59} +(0.616663 + 1.61856i) q^{60} +(0.482119 + 2.73423i) q^{61} +(4.96663 + 0.875751i) q^{62} +(9.10331 + 3.00830i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.35782 + 4.08387i) q^{65} +(-2.21160 - 2.55705i) q^{66} +(-2.32344 - 2.76897i) q^{67} +(-0.620852 - 0.358449i) q^{68} +(9.49530 - 5.67306i) q^{69} +(1.09304 - 3.00310i) q^{70} +(-0.518843 + 2.94250i) q^{71} +(-0.609040 - 2.93753i) q^{72} +(14.8952 - 5.42141i) q^{73} +(-1.72525 + 2.05607i) q^{74} +(1.73186 - 0.0258945i) q^{75} +(-0.900779 - 4.26481i) q^{76} +6.23792i q^{77} +(5.15599 - 6.33464i) q^{78} +(3.35294 + 9.21214i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(1.03031 - 8.94083i) q^{81} +(-7.99149 - 2.90866i) q^{82} +(9.58163 - 5.53196i) q^{83} +(-2.69570 + 4.83459i) q^{84} +(-0.549175 + 0.460813i) q^{85} +(-4.23672 + 3.55503i) q^{86} +(-2.87202 + 5.15082i) q^{87} +(1.69039 - 0.975946i) q^{88} +(-14.0605 - 5.11762i) q^{89} +(-2.96868 - 0.432383i) q^{90} +(-14.8415 + 2.61695i) q^{91} +(2.18415 + 6.00091i) q^{92} +(-5.51419 + 6.77472i) q^{93} +11.6165i q^{94} +(-4.31569 - 0.612196i) q^{95} +(1.73186 - 0.0258945i) q^{96} +(5.01490 - 5.97653i) q^{97} +(3.01956 - 1.09903i) q^{98} +(5.73374 - 1.18878i) 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
$3$	1.61856	−	0.616663i	0.934474	−	0.356031i
$3$	1.61856	−	0.616663i	0.934474	−	0.356031i
$4$	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
$6$	−1.63627	−	0.567997i	−0.668004	−	0.231884i
$7$	1.59792	+	2.76767i	0.603956	+	1.04608i	0.992216	+	0.124532i	$0.0397430\pi$
$7$	1.59792	+	2.76767i	0.603956	+	1.04608i	−0.388260	+	0.921550i	$0.626924\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	2.23945	−	1.99621i	0.746485	−	0.665403i
$10$	−0.642788	−	0.766044i	−0.203267	−	0.242245i
$11$	1.69039	+	0.975946i	0.509671	+	0.294259i	0.732698	−	0.680553i	$-0.238261\pi$
$11$	1.69039	+	0.975946i	0.509671	+	0.294259i	−0.223027	+	0.974812i	$0.571594\pi$
$12$	0.888354	+	1.48689i	0.256446	+	0.429227i
$13$	−1.61284	+	4.43125i	−0.447323	+	1.22901i	0.487258	+	0.873258i	$0.337997\pi$
$13$	−1.61284	+	4.43125i	−0.447323	+	1.22901i	−0.934581	+	0.355751i	$0.884225\pi$
$14$	0.554951	−	3.14728i	0.148317	−	0.841146i
$15$	1.70105	−	0.326235i	0.439209	−	0.0842335i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	−0.460813	+	0.549175i	−0.111764	+	0.133195i	−0.819026	−	0.573757i	$-0.805486\pi$
$17$	−0.460813	+	0.549175i	−0.111764	+	0.133195i	0.707262	+	0.706951i	$0.249930\pi$
$18$	−2.99866	+	0.0896911i	−0.706791	+	0.0211404i
$19$	−4.35644	+	0.146517i	−0.999435	+	0.0336134i
$19$	−4.35644	+	0.146517i	−0.999435	+	0.0336134i
$20$			1.00000i			0.223607i
$21$	4.29304	+	3.49426i	0.936818	+	0.762510i
$22$	−0.667586	−	1.83418i	−0.142330	−	0.391048i
$23$	6.28901	−	1.10892i	1.31135	−	0.231226i	0.526109	−	0.850417i	$-0.323650\pi$
$23$	6.28901	−	1.10892i	1.31135	−	0.231226i	0.785241	+	0.619191i	$0.212539\pi$
$24$	0.275233	−	1.71004i	0.0561817	−	0.349061i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	4.08387	−	2.35782i	0.800912	−	0.462407i
$27$	2.39370	−	4.61196i	0.460667	−	0.887573i
$28$	−2.44815	+	2.05424i	−0.462657	+	0.388215i
$29$	−2.60828	+	2.18861i	−0.484346	+	0.406415i	−0.851995	−	0.523550i	$-0.824607\pi$
$29$	−2.60828	+	2.18861i	−0.484346	+	0.406415i	0.367649	+	0.929965i	$0.380163\pi$
$30$	−1.51278	−	0.843503i	−0.276195	−	0.154002i
$31$	−4.36758	+	2.52162i	−0.784441	+	0.452897i	−0.838002	−	0.545667i	$-0.816276\pi$
$31$	−4.36758	+	2.52162i	−0.784441	+	0.452897i	0.0535609	+	0.998565i	$0.482943\pi$
$32$	0.939693	+	0.342020i	0.166116	+	0.0604612i
$33$	3.33782	+	0.537225i	0.581040	+	0.0935188i
$34$	0.706006	−	0.124488i	0.121079	−	0.0213495i
$35$	1.09304	+	3.00310i	0.184757	+	0.507617i
$36$	2.35476	+	1.85879i	0.392460	+	0.309799i
$37$		−	2.68401i		−	0.441248i	−0.975359	−	0.220624i	$-0.929191\pi$
$37$		−	2.68401i		−	0.441248i	0.975359	−	0.220624i	$-0.0708094\pi$
$38$	3.43140	+	2.68802i	0.556647	+	0.436055i
$39$	0.122109	+	8.16682i	0.0195531	+	1.30774i
$40$	0.642788	−	0.766044i	0.101634	−	0.121122i
$41$	7.99149	−	2.90866i	1.24806	−	0.454257i	0.368315	−	0.929701i	$-0.379935\pi$
$41$	7.99149	−	2.90866i	1.24806	−	0.454257i	0.879746	+	0.475444i	$0.157713\pi$
$42$	−1.04259	−	5.43627i	−0.160876	−	0.838835i
$43$	0.960386	−	5.44662i	0.146458	−	0.830602i	−0.819728	−	0.572753i	$-0.805875\pi$
$43$	0.960386	−	5.44662i	0.146458	−	0.830602i	0.966185	−	0.257849i	$-0.0830136\pi$
$44$	−0.667586	+	1.83418i	−0.100642	+	0.276513i
$45$	2.55207	−	1.57700i	0.380440	−	0.235086i
$46$	−5.53047	−	3.19302i	−0.815423	−	0.470785i
$47$	−7.46694	−	8.89875i	−1.08916	−	1.29802i	−0.951538	−	0.307532i	$-0.900497\pi$
$47$	−7.46694	−	8.89875i	−1.08916	−	1.29802i	−0.137627	−	0.990484i	$-0.543947\pi$
$48$	−1.31003	+	1.13305i	−0.189087	+	0.163542i
$49$	−1.60668	+	2.78284i	−0.229525	+	0.397549i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−0.407196	+	1.17304i	−0.0570188	+	0.164258i
$52$	−4.64400	−	0.818863i	−0.644007	−	0.113556i
$53$	−1.45006	−	8.22370i	−0.199181	−	1.12961i	−0.906337	−	0.422555i	$-0.861133\pi$
$53$	−1.45006	−	8.22370i	−0.199181	−	1.12961i	0.707156	−	0.707057i	$-0.249978\pi$
$54$	−4.79819	+	1.99433i	−0.652951	+	0.271394i
$55$	1.49524	+	1.25465i	0.201618	+	0.169177i
$56$	3.19583			0.427061
$57$	−6.96079	+	2.92360i	−0.921979	+	0.387240i
$58$	3.40487			0.447082
$59$	−5.27090	−	4.42281i	−0.686213	−	0.575801i	0.231602	−	0.972811i	$-0.425603\pi$
$59$	−5.27090	−	4.42281i	−0.686213	−	0.575801i	−0.917814	+	0.397010i	$0.870048\pi$
$60$	0.616663	+	1.61856i	0.0796108	+	0.208955i
$61$	0.482119	+	2.73423i	0.0617290	+	0.350083i	0.999991	+	0.00415814i	$0.00132358\pi$
$61$	0.482119	+	2.73423i	0.0617290	+	0.350083i	−0.938262	+	0.345925i	$0.887565\pi$
$62$	4.96663	+	0.875751i	0.630763	+	0.111221i
$63$	9.10331	+	3.00830i	1.14691	+	0.379010i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.35782	+	4.08387i	−0.292452	+	0.506541i
$66$	−2.21160	−	2.55705i	−0.272229	−	0.314751i
$67$	−2.32344	−	2.76897i	−0.283853	−	0.338283i	0.605211	−	0.796065i	$-0.293089\pi$
$67$	−2.32344	−	2.76897i	−0.283853	−	0.338283i	−0.889065	+	0.457782i	$0.848644\pi$
$68$	−0.620852	−	0.358449i	−0.0752893	−	0.0434683i
$69$	9.49530	−	5.67306i	1.14310	−	0.682956i
$70$	1.09304	−	3.00310i	0.130643	−	0.358939i
$71$	−0.518843	+	2.94250i	−0.0615753	+	0.349211i	0.938418	+	0.345503i	$0.112292\pi$
$71$	−0.518843	+	2.94250i	−0.0615753	+	0.349211i	−0.999993	+	0.00370844i	$0.998820\pi$
$72$	−0.609040	−	2.93753i	−0.0717761	−	0.346191i
$73$	14.8952	−	5.42141i	1.74335	−	0.634528i	0.743921	−	0.668267i	$-0.232964\pi$
$73$	14.8952	−	5.42141i	1.74335	−	0.634528i	0.999431	+	0.0337390i	$0.0107415\pi$
$74$	−1.72525	+	2.05607i	−0.200556	+	0.239013i
$75$	1.73186	−	0.0258945i	0.199978	−	0.00299004i
$76$	−0.900779	−	4.26481i	−0.103326	−	0.489207i
$77$			6.23792i			0.710877i
$78$	5.15599	−	6.33464i	0.583801	−	0.717256i
$79$	3.35294	+	9.21214i	0.377236	+	1.03645i	0.972497	+	0.232914i	$0.0748262\pi$
$79$	3.35294	+	9.21214i	0.377236	+	1.03645i	−0.595262	+	0.803532i	$0.702952\pi$
$80$	−0.984808	+	0.173648i	−0.110105	+	0.0194145i
$81$	1.03031	−	8.94083i	0.114478	−	0.993426i
$82$	−7.99149	−	2.90866i	−0.882512	−	0.321208i
$83$	9.58163	−	5.53196i	1.05172	−	0.607211i	0.128590	−	0.991698i	$-0.458955\pi$
$83$	9.58163	−	5.53196i	1.05172	−	0.607211i	0.923131	+	0.384486i	$0.125621\pi$
$84$	−2.69570	+	4.83459i	−0.294125	+	0.527497i
$85$	−0.549175	+	0.460813i	−0.0595664	+	0.0499822i
$86$	−4.23672	+	3.55503i	−0.456857	+	0.383349i
$87$	−2.87202	+	5.15082i	−0.307913	+	0.552226i
$88$	1.69039	−	0.975946i	0.180196	−	0.104036i
$89$	−14.0605	−	5.11762i	−1.49041	−	0.542467i	−0.536856	−	0.843674i	$-0.680388\pi$
$89$	−14.0605	−	5.11762i	−1.49041	−	0.542467i	−0.953559	+	0.301207i	$0.902610\pi$
$90$	−2.96868	−	0.432383i	−0.312926	−	0.0455772i
$91$	−14.8415	+	2.61695i	−1.55581	+	0.274331i
$92$	2.18415	+	6.00091i	0.227714	+	0.625638i
$93$	−5.51419	+	6.77472i	−0.571795	+	0.702506i
$94$			11.6165i			1.19815i
$95$	−4.31569	−	0.612196i	−0.442781	−	0.0628100i
$96$	1.73186	−	0.0258945i	0.176757	−	0.00264285i
$97$	5.01490	−	5.97653i	0.509186	−	0.606824i	−0.448803	−	0.893631i	$-0.648149\pi$
$97$	5.01490	−	5.97653i	0.509186	−	0.606824i	0.957988	+	0.286807i	$0.0925938\pi$
$98$	3.01956	−	1.09903i	0.305022	−	0.111019i
$99$	5.73374	−	1.18878i	0.576262	−	0.119477i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	0.230724	−	0.633908i	0.0229579	−	0.0630762i	−0.927684	−	0.373366i	$-0.878204\pi$
$101$	0.230724	−	0.633908i	0.0229579	−	0.0630762i	0.950642	+	0.310289i	$0.100426\pi$
$102$	1.06594	−	0.636859i	0.105544	−	0.0630584i
$103$	13.1733	+	7.60561i	1.29800	+	0.749403i	0.980059	−	0.198706i	$-0.0636739\pi$
$103$	13.1733	+	7.60561i	1.29800	+	0.749403i	0.317945	+	0.948109i	$0.397007\pi$
$104$	3.03116	+	3.61239i	0.297229	+	0.354224i
$105$	3.62105	+	4.18665i	0.353378	+	0.408576i
$106$	−4.17528	+	7.23180i	−0.405539	+	0.702414i
$107$	0.316054	+	0.547422i	0.0305541	+	0.0529213i	0.880898	−	0.473306i	$-0.156939\pi$
$107$	0.316054	+	0.547422i	0.0305541	+	0.0529213i	−0.850344	+	0.526227i	$0.823606\pi$
$108$	4.95756	+	1.55647i	0.477041	+	0.149771i
$109$	−16.9654	−	2.99146i	−1.62499	−	0.286529i	−0.714368	−	0.699771i	$-0.753286\pi$
$109$	−16.9654	−	2.99146i	−1.62499	−	0.286529i	−0.910622	+	0.413241i	$0.864397\pi$
$110$	−0.338942	−	1.92224i	−0.0323169	−	0.183278i
$111$	−1.65513	−	4.34422i	−0.157098	−	0.412335i
$112$	−2.44815	−	2.05424i	−0.231328	−	0.194108i
$113$	−12.9296			−1.21632			−0.608158	−	0.793816i	$-0.708091\pi$
$113$	−12.9296			−1.21632			−0.608158	+	0.793816i	$0.708091\pi$
$114$	7.21153	+	2.23470i	0.675421	+	0.209299i
$115$	6.38603			0.595501
$116$	−2.60828	−	2.18861i	−0.242173	−	0.203207i
$117$	5.23382	+	13.1432i	0.483866	+	1.21509i
$118$	1.19482	+	6.77614i	0.109992	+	0.623794i
$119$	−2.25628	−	0.397843i	−0.206833	−	0.0364702i
$120$	0.567997	−	1.63627i	0.0518508	−	0.149370i
$121$	−3.59506	−	6.22683i	−0.326824	−	0.566075i
$122$	1.38821	−	2.40444i	0.125682	−	0.217688i
$123$	11.1410	−	9.63589i	1.00455	−	0.868839i
$124$	−3.24174	−	3.86335i	−0.291117	−	0.346939i
$125$	0.866025	+	0.500000i	0.0774597	+	0.0447214i
$126$	−5.03984	−	8.15599i	−0.448985	−	0.726593i
$127$	−7.35093	+	20.1965i	−0.652290	+	1.79215i	−0.0431785	+	0.999067i	$0.513748\pi$
$127$	−7.35093	+	20.1965i	−0.652290	+	1.79215i	−0.609112	+	0.793085i	$0.708474\pi$
$128$	−0.173648	+	0.984808i	−0.0153485	+	0.0870455i
$129$	−1.80429	−	9.40790i	−0.158859	−	0.828319i
$130$	4.43125	−	1.61284i	0.388647	−	0.141456i
$131$	−5.81924	+	6.93510i	−0.508429	+	0.605922i	−0.957804	−	0.287421i	$-0.907202\pi$
$131$	−5.81924	+	6.93510i	−0.508429	+	0.605922i	0.449375	+	0.893343i	$0.351647\pi$
$132$	0.0505432	+	3.38040i	0.00439922	+	0.294226i
$133$	−7.36673	−	11.8231i	−0.638777	−	1.02519i
$134$			3.61463i			0.312256i
$135$	3.15819	−	4.12624i	0.271814	−	0.355130i
$136$	0.245193	+	0.673663i	0.0210252	+	0.0577662i
$137$	−9.04085	+	1.59415i	−0.772412	+	0.136197i	−0.545944	−	0.837822i	$-0.683829\pi$
$137$	−9.04085	+	1.59415i	−0.772412	+	0.136197i	−0.226468	+	0.974019i	$0.572718\pi$
$138$	−10.9204	−	1.75765i	−0.929605	−	0.149621i
$139$	−2.89847	−	1.05496i	−0.245845	−	0.0894802i	0.216159	−	0.976358i	$-0.430647\pi$
$139$	−2.89847	−	1.05496i	−0.245845	−	0.0894802i	−0.462004	+	0.886878i	$0.652869\pi$
$140$	−2.76767	+	1.59792i	−0.233911	+	0.135049i
$141$	−17.5732	−	9.79855i	−1.47993	−	0.825187i
$142$	2.28886	−	1.92058i	0.192077	−	0.161172i
$143$	−7.05100	+	5.91649i	−0.589634	+	0.494762i
$144$	−1.42165	+	2.64176i	−0.118471	+	0.220147i
$145$	−2.94871	+	1.70244i	−0.244877	+	0.141380i
$146$	−14.8952	−	5.42141i	−1.23274	−	0.448679i
$147$	−0.884419	+	5.49497i	−0.0729457	+	0.453217i
$148$	2.64323	−	0.466073i	0.217272	−	0.0383110i
$149$	−1.18324	−	3.25093i	−0.0969350	−	0.266327i	0.881742	−	0.471732i	$-0.156371\pi$
$149$	−1.18324	−	3.25093i	−0.0969350	−	0.266327i	−0.978677	+	0.205405i	$0.934149\pi$
$150$	−1.34332	−	1.09338i	−0.109682	−	0.0892741i
$151$			4.89183i			0.398091i	0.979990	+	0.199046i	$0.0637842\pi$
$151$			4.89183i			0.398091i	−0.979990	+	0.199046i	$0.936216\pi$
$152$	−2.05133	+	3.84604i	−0.166385	+	0.311955i
$153$	0.0642993	+	2.14973i	0.00519829	+	0.173795i
$154$	4.00966	−	4.77852i	0.323107	−	0.385065i
$155$	−4.73910	+	1.72489i	−0.380654	+	0.138547i
$156$	−8.02154	+	1.53841i	−0.642237	+	0.123171i
$157$	0.0994736	−	0.564143i	0.00793886	−	0.0450235i	−0.980581	−	0.196115i	$-0.937168\pi$
$157$	0.0994736	−	0.564143i	0.00793886	−	0.0450235i	0.988520	+	0.151091i	$0.0482787\pi$
$158$	3.35294	−	9.21214i	0.266746	−	0.732878i
$159$	−7.41825	−	12.4163i	−0.588306	−	0.984679i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	13.1185	+	15.6340i	1.03388	+	1.23213i
$162$	−6.53632	+	6.18681i	−0.513541	+	0.486081i
$163$	−9.40051	+	16.2822i	−0.736304	+	1.27532i	0.217844	+	0.975984i	$0.430098\pi$
$163$	−9.40051	+	16.2822i	−0.736304	+	1.27532i	−0.954149	+	0.299333i	$0.903236\pi$
$164$	4.25218	+	7.36499i	0.332040	+	0.575109i
$165$	3.19382	+	1.10867i	0.248639	+	0.0863098i
$166$	−10.8958	−	1.92123i	−0.845681	−	0.149116i
$167$	−2.85785	−	16.2077i	−0.221147	−	1.25419i	−0.869915	−	0.493201i	$-0.835827\pi$
$167$	−2.85785	−	16.2077i	−0.221147	−	1.25419i	0.648768	−	0.760986i	$-0.275284\pi$
$168$	5.17264	−	1.97075i	0.399078	−	0.152047i
$169$	−7.07617	−	5.93761i	−0.544321	−	0.456739i
$170$	0.716898			0.0549835
$171$	−9.46356	+	9.02447i	−0.723696	+	0.690119i
$172$	5.53064			0.421708
$173$	11.4377	+	9.59737i	0.869592	+	0.729675i	0.964012	−	0.265858i	$-0.0856552\pi$
$173$	11.4377	+	9.59737i	0.869592	+	0.729675i	−0.0944199	+	0.995532i	$0.530100\pi$
$174$	5.51098	−	2.09966i	0.417786	−	0.159175i
$175$	0.554951	+	3.14728i	0.0419503	+	0.237912i
$176$	−1.92224	−	0.338942i	−0.144894	−	0.0255487i
$177$	−11.2586	−	3.90820i	−0.846251	−	0.293758i
$178$	7.48146	+	12.9583i	0.560759	+	0.971263i
$179$	−12.2004	+	21.1316i	−0.911898	+	1.57945i	−0.100518	+	0.994935i	$0.532050\pi$
$179$	−12.2004	+	21.1316i	−0.911898	+	1.57945i	−0.811380	+	0.584518i	$0.801283\pi$
$180$	1.99621	+	2.23945i	0.148789	+	0.166919i
$181$	3.85606	+	4.59547i	0.286619	+	0.341579i	0.890072	−	0.455819i	$-0.150654\pi$
$181$	3.85606	+	4.59547i	0.286619	+	0.341579i	−0.603454	+	0.797398i	$0.706209\pi$
$182$	13.0514	+	7.53520i	0.967431	+	0.558546i
$183$	2.46644	+	4.12821i	0.182324	+	0.305166i
$184$	2.18415	−	6.00091i	0.161018	−	0.442393i
$185$	0.466073	−	2.64323i	0.0342664	−	0.194334i
$186$	8.57882	−	1.64528i	0.629030	−	0.120638i
$187$	−1.31492	+	0.478591i	−0.0961563	+	0.0349980i
$188$	7.46694	−	8.89875i	0.544582	−	0.649008i
$189$	16.5893	−	0.744568i	1.20670	−	0.0541594i
$190$	2.91250	+	3.24304i	0.211295	+	0.235275i
$191$			3.10573i			0.224723i	0.993667	+	0.112362i	$0.0358415\pi$
$191$			3.10573i			0.224723i	−0.993667	+	0.112362i	$0.964159\pi$
$192$	−1.34332	−	1.09338i	−0.0969461	−	0.0789079i
$193$	−2.97324	−	8.16892i	−0.214019	−	0.588012i	0.785506	−	0.618855i	$-0.212403\pi$
$193$	−2.97324	−	8.16892i	−0.214019	−	0.588012i	−0.999524	+	0.0308431i	$0.990181\pi$
$194$	−7.68327	+	1.35477i	−0.551627	+	0.0972667i
$195$	−1.29790	+	8.06395i	−0.0929445	+	0.577472i
$196$	−3.01956	−	1.09903i	−0.215683	−	0.0785022i
$197$	1.31650	−	0.760079i	0.0937964	−	0.0541534i	−0.452368	−	0.891831i	$-0.649421\pi$
$197$	1.31650	−	0.760079i	0.0937964	−	0.0541534i	0.546165	+	0.837678i	$0.316087\pi$
$198$	−5.15643	−	2.77492i	−0.366452	−	0.197205i
$199$	5.30466	−	4.45114i	0.376037	−	0.315533i	−0.435107	−	0.900379i	$-0.643289\pi$
$199$	5.30466	−	4.45114i	0.376037	−	0.315533i	0.811144	+	0.584846i	$0.198845\pi$
$200$	0.766044	−	0.642788i	0.0541675	−	0.0454519i
$201$	−5.46814	−	3.04895i	−0.385693	−	0.215056i
$202$	−0.584213	+	0.337296i	−0.0411051	+	0.0237320i
$203$	−10.2252	−	3.72166i	−0.717667	−	0.261209i
$204$	−1.22593	−	0.197314i	−0.0858320	−	0.0138147i
$205$	8.37516	−	1.47677i	0.584947	−	0.103142i
$206$	−5.20254	−	14.2939i	−0.362478	−	0.995901i
$207$	11.8703	−	15.0376i	0.825044	−	1.04518i
$208$		−	4.71564i		−	0.326971i
$209$	−7.50706	−	4.00397i	−0.519274	−	0.276961i
$210$	−0.0827545	−	5.53473i	−0.00571060	−	0.381932i
$211$	−8.26448	+	9.84922i	−0.568950	+	0.678048i	−0.971415	−	0.237387i	$-0.923709\pi$
$211$	−8.26448	+	9.84922i	−0.568950	+	0.678048i	0.402465	+	0.915435i	$0.368153\pi$
$212$	7.84696	−	2.85606i	0.538931	−	0.196155i
$213$	0.974756	+	5.08256i	0.0667892	+	0.348251i
$214$	0.109764	−	0.622505i	0.00750334	−	0.0425536i
$215$	1.89159	−	5.19710i	0.129005	−	0.354440i
$216$	−2.79723	−	4.37898i	−0.190327	−	0.297952i
$217$	−13.9581	−	8.05869i	−0.947535	−	0.547060i
$218$	11.0734	+	13.1967i	0.749983	+	0.893795i
$219$	20.7656	−	17.9602i	1.40321	−	1.21364i
$220$	−0.975946	+	1.69039i	−0.0657983	+	0.113966i
$221$	−1.69032	−	2.92771i	−0.113703	−	0.196939i
$222$	−1.52451	+	4.39176i	−0.102318	+	0.294756i
$223$	−1.32171	−	0.233053i	−0.0885084	−	0.0156064i	0.129219	−	0.991616i	$-0.458753\pi$
$223$	−1.32171	−	0.233053i	−0.0885084	−	0.0156064i	−0.217727	+	0.976010i	$0.569864\pi$
$224$	0.554951	+	3.14728i	0.0370792	+	0.210287i
$225$	2.78714	−	1.10988i	0.185809	−	0.0739923i
$226$	9.90466	+	8.31100i	0.658848	+	0.552839i
$227$	−9.55737			−0.634345			−0.317172	−	0.948368i	$-0.602733\pi$
$227$	−9.55737			−0.634345			−0.317172	+	0.948368i	$0.602733\pi$
$228$	−4.08791	−	6.34736i	−0.270729	−	0.420364i
$229$	11.1872			0.739272			0.369636	−	0.929177i	$-0.379482\pi$
$229$	11.1872			0.739272			0.369636	+	0.929177i	$0.379482\pi$
$230$	−4.89198	−	4.10486i	−0.322568	−	0.270667i
$231$	3.84669	+	10.0964i	0.253094	+	0.664296i
$232$	0.591250	+	3.35314i	0.0388175	+	0.220145i
$233$	−4.44201	−	0.783247i	−0.291006	−	0.0513122i	0.0262394	−	0.999656i	$-0.491647\pi$
$233$	−4.44201	−	0.783247i	−0.291006	−	0.0513122i	−0.317245	+	0.948343i	$0.602758\pi$
$234$	4.43893	−	13.4325i	0.290182	−	0.878109i
$235$	−5.80825	−	10.0602i	−0.378888	−	0.656254i
$236$	3.44033	−	5.95883i	0.223947	−	0.387887i
$237$	11.1077	+	12.8427i	0.721523	+	0.834225i
$238$	1.47268	+	1.75507i	0.0954598	+	0.113765i
$239$	2.66473	+	1.53848i	0.172367	+	0.0995160i	0.583701	−	0.811968i	$-0.301604\pi$
$239$	2.66473	+	1.53848i	0.172367	+	0.0995160i	−0.411335	+	0.911484i	$0.634937\pi$
$240$	−1.48689	+	0.888354i	−0.0959780	+	0.0573430i
$241$	5.18715	−	14.2516i	0.334134	−	0.918025i	−0.652890	−	0.757453i	$-0.726444\pi$
$241$	5.18715	−	14.2516i	0.334134	−	0.918025i	0.987024	−	0.160573i	$-0.0513340\pi$
$242$	−1.24855	+	7.08088i	−0.0802599	+	0.455176i
$243$	−3.84587	−	15.1066i	−0.246713	−	0.969089i
$244$	−2.60898	+	0.949589i	−0.167023	+	0.0607912i
$245$	−2.06550	+	2.46157i	−0.131960	+	0.157264i
$246$	−14.7283	+	0.220216i	−0.939045	+	0.0140405i
$247$	6.37700	−	19.5408i	0.405759	−	1.24335i
$248$			5.04325i			0.320247i
$249$	12.0971	−	14.8624i	0.766620	−	0.941868i
$250$	−0.342020	−	0.939693i	−0.0216313	−	0.0594314i
$251$	14.3906	−	2.53746i	0.908330	−	0.160163i	0.300085	−	0.953913i	$-0.402985\pi$
$251$	14.3906	−	2.53746i	0.908330	−	0.160163i	0.608245	+	0.793749i	$0.291874\pi$
$252$	−1.38182	+	9.48740i	−0.0870468	+	0.597650i
$253$	11.7131	+	4.26323i	0.736398	+	0.268027i
$254$	18.6132	−	10.7463i	1.16790	−	0.674286i
$255$	−0.604706	+	1.08451i	−0.0378681	+	0.0679145i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	23.1276	−	19.4064i	1.44266	−	1.21054i	0.504937	−	0.863156i	$-0.331516\pi$
$257$	23.1276	−	19.4064i	1.44266	−	1.21054i	0.937724	−	0.347380i	$-0.112929\pi$
$258$	−4.66512	+	8.36664i	−0.290437	+	0.520884i
$259$	7.42846	−	4.28882i	0.461582	−	0.266494i
$260$	−4.43125	−	1.61284i	−0.274815	−	0.100024i
$261$	−1.47221	+	10.1080i	−0.0911275	+	0.625667i
$262$	8.91559	−	1.57206i	0.550807	−	0.0971221i
$263$	5.63636	+	15.4858i	0.347553	+	0.954893i	0.983138	+	0.182863i	$0.0585365\pi$
$263$	5.63636	+	15.4858i	0.347553	+	0.954893i	−0.635586	+	0.772030i	$0.719241\pi$
$264$	2.13416	−	2.62202i	0.131348	−	0.161374i
$265$		−	8.35056i		−	0.512971i
$266$	−1.95648	+	13.7922i	−0.119959	+	0.845656i
$267$	−25.9136	+	0.387457i	−1.58589	+	0.0237120i
$268$	2.32344	−	2.76897i	0.141927	−	0.169142i
$269$	6.94321	−	2.52712i	0.423335	−	0.154081i	−0.121563	−	0.992584i	$-0.538791\pi$
$269$	6.94321	−	2.52712i	0.423335	−	0.154081i	0.544898	+	0.838502i	$0.316568\pi$
$270$	−5.07161	+	1.13084i	−0.308648	+	0.0688205i
$271$	2.87527	−	16.3065i	0.174661	−	0.990549i	−0.763874	−	0.645365i	$-0.776705\pi$
$271$	2.87527	−	16.3065i	0.174661	−	0.990549i	0.938535	−	0.345184i	$-0.112184\pi$
$272$	0.245193	−	0.673663i	0.0148670	−	0.0408468i
$273$	−22.4080	+	13.3879i	−1.35619	+	0.810270i
$274$	7.95039	+	4.59016i	0.480301	+	0.277302i
$275$	1.25465	+	1.49524i	0.0756584	+	0.0901661i
$276$	7.23571	+	8.36593i	0.435539	+	0.503570i
$277$	15.8462	−	27.4464i	0.952106	−	1.64910i	0.211249	−	0.977432i	$-0.432247\pi$
$277$	15.8462	−	27.4464i	0.952106	−	1.64910i	0.740857	−	0.671663i	$-0.234420\pi$
$278$	1.54224	+	2.67124i	0.0924976	+	0.160210i
$279$	−4.74731	+	14.3657i	−0.284214	+	0.860050i
$280$	3.14728	+	0.554951i	0.188086	+	0.0331646i
$281$	−1.16816	−	6.62495i	−0.0696864	−	0.395211i	−0.999622	−	0.0274891i	$-0.991249\pi$
$281$	−1.16816	−	6.62495i	−0.0696864	−	0.395211i	0.929936	−	0.367722i	$-0.119862\pi$
$282$	7.16346	+	18.8020i	0.426578	+	1.11964i
$283$	−1.51298	−	1.26954i	−0.0899372	−	0.0754662i	0.596711	−	0.802457i	$-0.296474\pi$
$283$	−1.51298	−	1.26954i	−0.0899372	−	0.0754662i	−0.686648	+	0.726990i	$0.740918\pi$
$284$	−2.98790			−0.177299
$285$	−7.36272	+	1.67045i	−0.436130	+	0.0989492i
$286$	9.20442			0.544269
$287$	20.8200	+	17.4700i	1.22896	+	1.03122i
$288$	2.78714	−	1.10988i	0.164234	−	0.0654005i
$289$	2.86277	+	16.2356i	0.168398	+	0.955035i
$290$	3.35314	+	0.591250i	0.196903	+	0.0347194i
$291$	4.43140	−	12.7658i	0.259773	−	0.748347i
$292$	7.92557	+	13.7275i	0.463809	+	0.803341i
$293$	8.58349	−	14.8670i	0.501453	−	0.868542i	−0.498545	−	0.866864i	$-0.666132\pi$
$293$	8.58349	−	14.8670i	0.501453	−	0.868542i	0.999999	−	0.00167870i	$-0.000534347\pi$
$294$	4.20960	−	3.64090i	0.245509	−	0.212341i
$295$	−4.42281	−	5.27090i	−0.257506	−	0.306884i
$296$	−2.32442	−	1.34200i	−0.135104	−	0.0780024i
$297$	8.54730	−	5.45989i	0.495965	−	0.316815i
$298$	−1.18324	+	3.25093i	−0.0685434	+	0.188321i
$299$	−5.22928	+	29.6567i	−0.302417	+	1.71509i
$300$	0.326235	+	1.70105i	0.0188352	+	0.0982102i
$301$	16.6091	−	6.04521i	0.957331	−	0.348440i
$302$	3.14440	−	3.74736i	0.180940	−	0.215636i
$303$	−0.0174682	−	1.16830i	−0.00100352	−	0.0671168i
$304$	4.04360	−	1.62767i	0.231916	−	0.0933533i
$305$			2.77641i			0.158977i
$306$	1.33256	−	1.68812i	0.0761777	−	0.0965034i
$307$	8.89881	+	24.4493i	0.507882	+	1.39539i	0.883418	+	0.468586i	$0.155236\pi$
$307$	8.89881	+	24.4493i	0.507882	+	1.39539i	−0.375536	+	0.926808i	$0.622541\pi$
$308$	−6.14315	+	1.08320i	−0.350039	+	0.0617213i
$309$	26.0118	+	4.18663i	1.47976	+	0.238169i
$310$	4.73910	+	1.72489i	0.269163	+	0.0979673i
$311$	−7.00115	+	4.04212i	−0.396999	+	0.229207i	−0.685188	−	0.728366i	$-0.740280\pi$
$311$	−7.00115	+	4.04212i	−0.396999	+	0.229207i	0.288189	+	0.957573i	$0.406947\pi$
$312$	7.13373	+	3.97766i	0.403868	+	0.225191i
$313$	−15.4330	+	12.9499i	−0.872327	+	0.731969i	−0.964587	−	0.263766i	$-0.915035\pi$
$313$	−15.4330	+	12.9499i	−0.872327	+	0.731969i	0.0922599	+	0.995735i	$0.470591\pi$
$314$	−0.438825	+	0.368218i	−0.0247643	+	0.0207798i
$315$	8.44263	+	4.54337i	0.475688	+	0.255990i
$316$	−8.48995	+	4.90167i	−0.477597	+	0.275741i
$317$	−7.25183	−	2.63945i	−0.407303	−	0.148246i	0.130240	−	0.991483i	$-0.458425\pi$
$317$	−7.25183	−	2.63945i	−0.407303	−	0.148246i	−0.537543	+	0.843236i	$0.680648\pi$
$318$	−2.29835	+	14.2798i	−0.128885	+	0.800772i
$319$	−6.54498	+	1.15406i	−0.366448	+	0.0646147i
$320$	−0.342020	−	0.939693i	−0.0191195	−	0.0525304i
$321$	0.849126	+	0.691135i	0.0473936	+	0.0385754i
$322$		−	20.4087i		−	1.13733i
$323$	1.92704	−	2.45996i	0.107223	−	0.136876i
$324$	8.98391	−	0.537906i	0.499106	−	0.0298837i
$325$	−3.03116	+	3.61239i	−0.168138	+	0.200379i
$326$	17.6672	−	6.43032i	0.978494	−	0.356143i
$327$	−29.3042	+	5.62008i	−1.62052	+	0.310791i
$328$	1.47677	−	8.37516i	0.0815408	−	0.462441i
$329$	12.6973	−	34.8855i	0.700024	−	1.92330i
$330$	−1.73397	−	2.90224i	−0.0954519	−	0.159763i
$331$	−20.9939	−	12.1208i	−1.15393	−	0.666220i	−0.204085	−	0.978953i	$-0.565422\pi$
$331$	−20.9939	−	12.1208i	−1.15393	−	0.666220i	−0.949841	+	0.312733i	$0.898755\pi$
$332$	7.11175	+	8.47545i	0.390308	+	0.465151i
$333$	−5.35784	−	6.01071i	−0.293608	−	0.329385i
$334$	−8.22885	+	14.2528i	−0.450263	+	0.779878i
$335$	−1.80731	−	3.13036i	−0.0987442	−	0.171030i
$336$	−5.22925	−	1.81522i	−0.285279	−	0.0990286i
$337$	8.25274	+	1.45518i	0.449556	+	0.0792688i	0.393842	−	0.919178i	$-0.371146\pi$
$337$	8.25274	+	1.45518i	0.449556	+	0.0792688i	0.0557133	+	0.998447i	$0.482257\pi$
$338$	1.60404	+	9.09695i	0.0872482	+	0.494809i
$339$	−20.9273	+	7.97321i	−1.13662	+	0.433046i
$340$	−0.549175	−	0.460813i	−0.0297832	−	0.0249911i
$341$	−9.84388			−0.533076
$342$	13.0503	−	0.830089i	0.705681	−	0.0448861i
$343$	12.1015			0.653420
$344$	−4.23672	−	3.55503i	−0.228429	−	0.191674i
$345$	10.3362	−	3.93803i	0.556480	−	0.212016i
$346$	−2.59272	−	14.7040i	−0.139385	−	0.790493i
$347$	−25.1090	−	4.42739i	−1.34792	−	0.237675i	−0.547345	−	0.836907i	$-0.684361\pi$
$347$	−25.1090	−	4.42739i	−1.34792	−	0.237675i	−0.800575	+	0.599233i	$0.795472\pi$
$348$	−5.57129	−	1.93396i	−0.298652	−	0.103671i
$349$	8.11209	+	14.0506i	0.434230	+	0.752109i	0.997232	−	0.0743466i	$-0.0236871\pi$
$349$	8.11209	+	14.0506i	0.434230	+	0.752109i	−0.563002	+	0.826455i	$0.690354\pi$
$350$	1.59792	−	2.76767i	0.0854122	−	0.147938i
$351$	16.5761	+	18.0455i	0.884768	+	0.963195i
$352$	1.25465	+	1.49524i	0.0668732	+	0.0796963i
$353$	18.4954	+	10.6783i	0.984408	+	0.568348i	0.903598	−	0.428381i	$-0.140916\pi$
$353$	18.4954	+	10.6783i	0.984408	+	0.568348i	0.0808102	+	0.996730i	$0.474249\pi$
$354$	6.11247	+	10.2308i	0.324874	+	0.543759i
$355$	−1.02192	+	2.80770i	−0.0542379	+	0.149018i
$356$	2.59828	−	14.7356i	0.137709	−	0.780985i
$357$	−3.89725	+	0.747432i	−0.206264	+	0.0395583i
$358$	22.9292	−	8.34554i	1.21184	−	0.441076i
$359$	−9.49926	+	11.3208i	−0.501352	+	0.597488i	−0.956067	−	0.293149i	$-0.905297\pi$
$359$	−9.49926	+	11.3208i	−0.501352	+	0.597488i	0.454715	+	0.890637i	$0.349741\pi$
$360$	−0.0896911	−	2.99866i	−0.00472714	−	0.158043i
$361$	18.9571	−	1.27659i	0.997740	−	0.0671888i
$362$		−	5.99897i		−	0.315299i
$363$	−9.65866	−	7.86153i	−0.506948	−	0.412623i
$364$	−5.15438	−	14.1616i	−0.270163	−	0.742267i
$365$	15.6103	−	2.75252i	0.817082	−	0.144074i
$366$	0.764160	−	4.74779i	0.0399433	−	0.248171i
$367$	−10.1039	−	3.67752i	−0.527420	−	0.191965i	0.0645661	−	0.997913i	$-0.479434\pi$
$367$	−10.1039	−	3.67752i	−0.527420	−	0.191965i	−0.591986	+	0.805948i	$0.701656\pi$
$368$	−5.53047	+	3.19302i	−0.288295	+	0.166447i
$369$	12.0903	−	22.4665i	0.629394	−	1.16956i
$370$	−2.05607	+	1.72525i	−0.106890	+	0.0896913i
$371$	20.4434	−	17.1541i	1.06137	−	0.890595i
$372$	−7.62933	−	4.25400i	−0.395562	−	0.220560i
$373$	7.82376	−	4.51705i	0.405099	−	0.233884i	−0.283583	−	0.958948i	$-0.591523\pi$
$373$	7.82376	−	4.51705i	0.405099	−	0.233884i	0.688682	+	0.725064i	$0.258190\pi$
$374$	1.31492	+	0.478591i	0.0679928	+	0.0247474i
$375$	1.71004	+	0.275233i	0.0883062	+	0.0142130i
$376$	−11.4400	+	2.01718i	−0.589974	+	0.104028i
$377$	−5.49153	−	15.0879i	−0.282828	−	0.777064i
$378$	−13.1868	−	10.0930i	−0.678254	−	0.519130i
$379$			34.7305i			1.78399i	0.452047	+	0.891994i	$0.350694\pi$
$379$			34.7305i			1.78399i	−0.452047	+	0.891994i	$0.649306\pi$
$380$	−0.146517	−	4.35644i	−0.00751618	−	0.223480i
$381$	0.556542	+	37.2223i	0.0285125	+	1.90696i
$382$	1.99633	−	2.37913i	0.102141	−	0.121727i
$383$	26.6060	−	9.68380i	1.35950	−	0.494819i	0.443604	−	0.896223i	$-0.353700\pi$
$383$	26.6060	−	9.68380i	1.35950	−	0.494819i	0.915901	+	0.401404i	$0.131478\pi$
$384$	0.326235	+	1.70105i	0.0166481	+	0.0868063i
$385$	−1.08320	+	6.14315i	−0.0552052	+	0.313084i
$386$	−2.97324	+	8.16892i	−0.151334	+	0.415787i
$387$	−8.72185	−	14.1146i	−0.443356	−	0.717485i
$388$	6.75656	+	3.90090i	0.343012	+	0.198038i
$389$	−15.2779	−	18.2074i	−0.774618	−	0.923154i	0.224059	−	0.974576i	$-0.428069\pi$
$389$	−15.2779	−	18.2074i	−0.774618	−	0.923154i	−0.998677	+	0.0514219i	$0.983625\pi$
$390$	6.17766	−	5.34307i	0.312818	−	0.270557i
$391$	−2.28907	+	3.96478i	−0.115763	+	0.200507i
$392$	1.60668	+	2.78284i	0.0811494	+	0.140555i
$393$	−5.14215	+	14.8134i	−0.259387	+	0.747235i
$394$	−1.49706	−	0.263973i	−0.0754210	−	0.0132987i
$395$	1.70233	+	9.65441i	0.0856537	+	0.485766i
$396$	2.16637	+	5.44020i	0.108864	+	0.273380i
$397$	−10.2266	−	8.58115i	−0.513259	−	0.430675i	0.349015	−	0.937117i	$-0.386516\pi$
$397$	−10.2266	−	8.58115i	−0.513259	−	0.430675i	−0.862274	+	0.506442i	$0.830961\pi$
$398$	−6.92474			−0.347106
$399$	−19.2143	−	14.5935i	−0.961919	−	0.730590i
$400$	−1.00000			−0.0500000
$401$	−3.74015	−	3.13836i	−0.186774	−	0.156722i	0.544606	−	0.838692i	$-0.316679\pi$
$401$	−3.74015	−	3.13836i	−0.186774	−	0.156722i	−0.731380	+	0.681970i	$0.761124\pi$
$402$	2.22901	+	5.85048i	0.111173	+	0.291796i
$403$	−4.12973	−	23.4209i	−0.205716	−	1.16668i
$404$	0.664343	+	0.117142i	0.0330523	+	0.00582801i
$405$	2.56721	−	8.62609i	0.127566	−	0.428634i
$406$	5.44070	+	9.42357i	0.270017	+	0.467684i
$407$	2.61945	−	4.53701i	0.129841	−	0.224891i
$408$	0.812283	+	0.939161i	0.0402140	+	0.0464954i
$409$	−13.0759	−	15.5832i	−0.646559	−	0.770540i	0.338832	−	0.940847i	$-0.389968\pi$
$409$	−13.0759	−	15.5832i	−0.646559	−	0.770540i	−0.985391	+	0.170308i	$0.945524\pi$
$410$	−7.36499	−	4.25218i	−0.363731	−	0.210000i
$411$	−13.6501	+	8.15537i	−0.673309	+	0.402275i
$412$	−5.20254	+	14.2939i	−0.256311	+	0.704209i
$413$	3.81843	−	21.6554i	0.187893	−	1.06559i
$414$	−18.7591	+	3.88935i	−0.921962	+	0.191151i
$415$	10.3967	−	3.78408i	0.510353	−	0.185753i
$416$	−3.03116	+	3.61239i	−0.148615	+	0.177112i
$417$	−5.34189	+	0.0798712i	−0.261593	+	0.00391131i
$418$	3.17704	+	7.89267i	0.155394	+	0.386043i
$419$			2.20101i			0.107526i	0.998554	+	0.0537631i	$0.0171216\pi$
$419$			2.20101i			0.107526i	−0.998554	+	0.0537631i	$0.982878\pi$
$420$	−3.49426	+	4.29304i	−0.170502	+	0.209479i
$421$	6.25324	+	17.1806i	0.304764	+	0.837332i	0.993655	+	0.112468i	$0.0358755\pi$
$421$	6.25324	+	17.1806i	0.304764	+	0.837332i	−0.688891	+	0.724865i	$0.741902\pi$
$422$	12.6619	−	2.23264i	0.616372	−	0.108683i
$423$	−34.4856	−	5.02278i	−1.67675	−	0.244216i
$424$	−7.84696	−	2.85606i	−0.381082	−	0.138703i
$425$	−0.620852	+	0.358449i	−0.0301157	+	0.0173873i
$426$	2.52030	−	4.52003i	0.122109	−	0.218996i
$427$	−6.79708	+	5.70342i	−0.328934	+	0.276008i
$428$	−0.484223	+	0.406311i	−0.0234058	+	0.0196398i
$429$	−7.76396	+	13.9243i	−0.374848	+	0.672270i
$430$	−4.78968	+	2.76532i	−0.230979	+	0.133356i
$431$	1.16742	+	0.424907i	0.0562327	+	0.0204670i	0.369983	−	0.929038i	$-0.379363\pi$
$431$	1.16742	+	0.424907i	0.0562327	+	0.0204670i	−0.313751	+	0.949505i	$0.601586\pi$
$432$	−0.671954	+	5.15252i	−0.0323294	+	0.247901i
$433$	−37.0764	+	6.53757i	−1.78178	+	0.314175i	−0.964896	−	0.262631i	$-0.915410\pi$
$433$	−37.0764	+	6.53757i	−1.78178	+	0.314175i	−0.816881	+	0.576807i	$0.804299\pi$
$434$	5.51247	+	15.1454i	0.264607	+	0.727002i
$435$	−3.72282	+	4.57385i	−0.178496	+	0.219299i
$436$		−	17.2271i		−	0.825029i
$437$	−27.2352	+	5.75240i	−1.30284	+	0.275175i
$438$	−27.4519	+	0.410457i	−1.31170	+	0.0196124i
$439$	−2.92627	+	3.48739i	−0.139663	+	0.166444i	−0.831342	−	0.555761i	$-0.812427\pi$
$439$	−2.92627	+	3.48739i	−0.139663	+	0.166444i	0.691679	+	0.722205i	$0.256871\pi$
$440$	1.83418	−	0.667586i	0.0874410	−	0.0318259i
$441$	1.95706	+	9.43931i	0.0931933	+	0.449491i
$442$	−0.587041	+	3.32927i	−0.0279227	+	0.158357i
$443$	−2.04397	+	5.61576i	−0.0971119	+	0.266813i	−0.978731	−	0.205149i	$-0.934232\pi$
$443$	−2.04397	+	5.61576i	−0.0971119	+	0.266813i	0.881619	+	0.471962i	$0.156454\pi$
$444$	3.99081	−	2.38435i	0.189396	−	0.113156i
$445$	−12.9583	−	7.48146i	−0.614281	−	0.354655i
$446$	0.862686	+	1.02811i	0.0408494	+	0.0486824i
$447$	−3.91988	−	4.53216i	−0.185404	−	0.214364i
$448$	1.59792	−	2.76767i	0.0754945	−	0.130760i
$449$	4.22124	+	7.31140i	0.199213	+	0.345046i	0.948273	−	0.317455i	$-0.102828\pi$
$449$	4.22124	+	7.31140i	0.199213	+	0.345046i	−0.749061	+	0.662501i	$0.769495\pi$
$450$	−2.84849	−	0.941320i	−0.134279	−	0.0443742i
$451$	16.3474	+	2.88249i	0.769770	+	0.135731i
$452$	−2.24520	−	12.7332i	−0.105606	−	0.598919i
$453$	3.01661	+	7.91770i	0.141733	+	0.372006i
$454$	7.32137	+	6.14336i	0.343609	+	0.288322i
$455$	−15.0704			−0.706512
$456$	−0.948483	+	7.49002i	−0.0444168	+	0.350752i
$457$	17.6853			0.827282			0.413641	−	0.910440i	$-0.364257\pi$
$457$	17.6853			0.827282			0.413641	+	0.910440i	$0.364257\pi$
$458$	−8.56991	−	7.19100i	−0.400445	−	0.336014i
$459$	1.42973	+	3.43981i	0.0667342	+	0.160557i
$460$	1.10892	+	6.28901i	0.0517038	+	0.293227i
$461$	−20.7143	−	3.65249i	−0.964760	−	0.170113i	−0.330990	−	0.943634i	$-0.607382\pi$
$461$	−20.7143	−	3.65249i	−0.964760	−	0.170113i	−0.633770	+	0.773521i	$0.718494\pi$
$462$	3.54312	−	10.2069i	0.164841	−	0.474869i
$463$	−14.1312	−	24.4759i	−0.656731	−	1.13749i	−0.981457	−	0.191683i	$-0.938606\pi$
$463$	−14.1312	−	24.4759i	−0.656731	−	1.13749i	0.324726	−	0.945808i	$-0.394728\pi$
$464$	1.70244	−	2.94871i	0.0790336	−	0.136890i
$465$	−6.60683	+	5.71427i	−0.306385	+	0.264993i
$466$	2.89932	+	3.45527i	0.134308	+	0.160062i
$467$	19.2520	+	11.1152i	0.890878	+	0.514349i	0.874230	−	0.485512i	$-0.161367\pi$
$467$	19.2520	+	11.1152i	0.890878	+	0.514349i	0.0166487	+	0.999861i	$0.494700\pi$
$468$	−12.0346	+	7.43659i	−0.556302	+	0.343756i
$469$	3.95093	−	10.8551i	0.182437	−	0.501242i
$470$	−2.01718	+	11.4400i	−0.0930457	+	0.527688i
$471$	−0.186882	−	0.974439i	−0.00861108	−	0.0448998i
$472$	−6.46571	+	2.35333i	−0.297609	+	0.108321i
$473$	6.93903	−	8.26962i	0.319057	−	0.380237i
$474$	−0.253853	−	16.9780i	−0.0116598	−	0.779825i
$475$	−4.14382	−	1.35231i	−0.190132	−	0.0620481i
$476$		−	2.29109i		−	0.105012i
$477$	−19.6636	−	15.5220i	−0.900332	−	0.710702i
$478$	−1.05238	−	2.89140i	−0.0481349	−	0.132249i
$479$	−25.7421	+	4.53902i	−1.17619	+	0.207393i	−0.727379	−	0.686236i	$-0.759262\pi$
$479$	−25.7421	+	4.53902i	−1.17619	+	0.207393i	−0.448806	+	0.893629i	$0.648151\pi$
$480$	1.71004	+	0.275233i	0.0780524	+	0.0125626i
$481$	11.8935	+	4.32889i	0.542298	+	0.197380i
$482$	−13.1343	+	7.58311i	−0.598252	+	0.345401i
$483$	30.8739	+	17.2148i	1.40481	+	0.783301i
$484$	5.50795	−	4.62172i	0.250361	−	0.210078i
$485$	5.97653	−	5.01490i	0.271380	−	0.227715i
$486$	−6.76423	+	14.0444i	−0.306831	+	0.637067i
$487$	14.2489	−	8.22659i	0.645678	−	0.372783i	−0.141120	−	0.989992i	$-0.545070\pi$
$487$	14.2489	−	8.22659i	0.645678	−	0.372783i	0.786799	+	0.617210i	$0.211737\pi$
$488$	2.60898	+	0.949589i	0.118103	+	0.0429859i
$489$	−5.17465	+	32.1505i	−0.234006	+	1.45390i
$490$	3.16453	−	0.557993i	0.142959	−	0.0252075i
$491$	14.4564	+	39.7185i	0.652406	+	1.79247i	0.608663	+	0.793428i	$0.291706\pi$
$491$	14.4564	+	39.7185i	0.652406	+	1.79247i	0.0437427	+	0.999043i	$0.486072\pi$
$492$	11.4241	+	9.29850i	0.515039	+	0.419209i
$493$		−	2.44094i		−	0.109935i
$494$	−17.4456	+	10.8701i	−0.784916	+	0.489067i
$495$	5.85306	−	0.175067i	0.263075	−	0.00786869i
$496$	3.24174	−	3.86335i	0.145558	−	0.173470i
$497$	−8.97296	+	3.26589i	−0.402492	+	0.146495i
$498$	−18.8203	+	3.60944i	−0.843357	+	0.161743i
$499$	4.07082	−	23.0867i	0.182235	−	1.03350i	−0.747222	−	0.664574i	$-0.768613\pi$
$499$	4.07082	−	23.0867i	0.182235	−	1.03350i	0.929457	−	0.368930i	$-0.120276\pi$
$500$	−0.342020	+	0.939693i	−0.0152956	+	0.0420243i
$501$	−14.6203	−	24.4707i	−0.653185	−	1.09327i
$502$	−12.6549	−	7.30632i	−0.564817	−	0.326097i
$503$	9.70464	+	11.5655i	0.432708	+	0.515682i	0.937702	−	0.347441i	$-0.112949\pi$
$503$	9.70464	+	11.5655i	0.432708	+	0.515682i	−0.504993	+	0.863123i	$0.668505\pi$
$504$	7.15692	−	6.37955i	0.318795	−	0.284168i
$505$	0.337296	−	0.584213i	0.0150095	−	0.0259971i
$506$	−6.23242	−	10.7949i	−0.277065	−	0.479891i
$507$	−15.1147	−	5.24675i	−0.671267	−	0.233016i
$508$	−21.1662	−	3.73217i	−0.939097	−	0.165588i
$509$	−3.31006	−	18.7723i	−0.146716	−	0.832068i	−0.965973	−	0.258642i	$-0.916725\pi$
$509$	−3.31006	−	18.7723i	−0.146716	−	0.832068i	0.819257	−	0.573426i	$-0.194386\pi$
$510$	1.16034	−	0.442084i	0.0513807	−	0.0195758i
$511$	38.8060	+	32.5621i	1.71668	+	1.44046i
$512$	−1.00000			−0.0441942
$513$	−9.75225	+	20.4424i	−0.430572	+	0.902556i
$514$	−30.1910			−1.33167
$515$	11.6525	+	9.77759i	0.513469	+	0.430852i
$516$	8.95166	−	3.41054i	0.394075	−	0.150141i
$517$	−3.93732	−	22.3297i	−0.173163	−	0.982057i
$518$	−8.44733	−	1.48949i	−0.371154	−	0.0654445i
$519$	24.4309	+	8.48069i	1.07240	+	0.372261i
$520$	2.35782	+	4.08387i	0.103397	+	0.179089i
$521$	5.67793	−	9.83447i	0.248755	−	0.430856i	−0.714426	−	0.699711i	$-0.753312\pi$
$521$	5.67793	−	9.83447i	0.248755	−	0.430856i	0.963181	+	0.268855i	$0.0866453\pi$
$522$	7.62505	−	6.79683i	0.333740	−	0.297489i
$523$	−4.41020	−	5.25587i	−0.192844	−	0.229823i	0.660954	−	0.750426i	$-0.270152\pi$
$523$	−4.41020	−	5.25587i	−0.192844	−	0.229823i	−0.853799	+	0.520603i	$0.825707\pi$
$524$	−7.84024	−	4.52656i	−0.342502	−	0.197744i
$525$	2.83903	+	4.75184i	0.123905	+	0.207387i
$526$	5.63636	−	15.4858i	0.245757	−	0.675212i
$527$	0.627824	−	3.56057i	0.0273484	−	0.155101i
$528$	−3.32027	+	0.636775i	−0.144496	+	0.0277121i
$529$	16.7091	−	6.08160i	0.726481	−	0.264417i
$530$	−5.36764	+	6.39690i	−0.233155	+	0.277864i
$531$	−20.6328	+	0.617135i	−0.895386	+	0.0267814i
$532$	10.3642	−	9.30787i	0.449346	−	0.403547i
$533$			40.1035i			1.73708i
$534$	20.1000	+	16.3602i	0.869814	+	0.707973i
$535$	0.216194	+	0.593988i	0.00934687	+	0.0256803i
$536$	−3.55972	+	0.627674i	−0.153756	+	0.0271114i
$537$	−6.71588	+	41.7263i	−0.289812	+	1.80062i
$538$	−6.94321	−	2.52712i	−0.299343	−	0.108952i
$539$	−5.43181	+	3.13606i	−0.233965	+	0.135080i
$540$	4.61196	+	2.39370i	0.198467	+	0.103008i
$541$	−14.6944	+	12.3301i	−0.631761	+	0.530111i	−0.901476	−	0.432830i	$-0.857515\pi$
$541$	−14.6944	+	12.3301i	−0.631761	+	0.530111i	0.269714	+	0.962940i	$0.413071\pi$
$542$	−12.6842	+	10.6433i	−0.544833	+	0.457169i
$543$	9.07511	+	5.06015i	0.389450	+	0.217152i
$544$	−0.620852	+	0.358449i	−0.0266188	+	0.0153684i
$545$	−16.1882	−	5.89202i	−0.693426	−	0.252386i
$546$	25.7710	+	4.14787i	1.10290	+	0.177512i
$547$	42.7919	−	7.54536i	1.82965	−	0.322616i	0.850533	−	0.525922i	$-0.176279\pi$
$547$	42.7919	−	7.54536i	1.82965	−	0.322616i	0.979115	+	0.203305i	$0.0651684\pi$
$548$	−3.13985	−	8.62668i	−0.134128	−	0.368513i
$549$	6.53778	+	5.16078i	0.279026	+	0.220257i
$550$		−	1.95189i		−	0.0832289i
$551$	11.0421	−	9.91670i	0.470411	−	0.422465i
$552$	−0.165363	−	11.0597i	−0.00703832	−	0.470732i
$553$	−20.1385	+	24.0001i	−0.856374	+	1.02059i
$554$	−29.7811	+	10.8394i	−1.26528	+	0.460524i
$555$	−0.875617	−	4.56563i	−0.0371679	−	0.193800i
$556$	0.535615	−	3.03763i	0.0227151	−	0.128824i
$557$	2.11094	−	5.79975i	0.0894432	−	0.245743i	−0.886903	−	0.461955i	$-0.847148\pi$
$557$	2.11094	−	5.79975i	0.0894432	−	0.245743i	0.976346	+	0.216212i	$0.0693703\pi$
$558$	12.8707	−	7.95323i	0.544861	−	0.336687i
$559$	22.5864	+	13.0403i	0.955303	+	0.551545i
$560$	−2.05424	−	2.44815i	−0.0868076	−	0.103453i
$561$	−1.83314	+	1.58549i	−0.0773953	+	0.0669394i
$562$	−3.36357	+	5.82588i	−0.141884	+	0.245750i
$563$	−21.0082	−	36.3873i	−0.885391	−	1.53354i	−0.845264	−	0.534348i	$-0.820557\pi$
$563$	−21.0082	−	36.3873i	−0.885391	−	1.53354i	−0.0401269	−	0.999195i	$-0.512776\pi$
$564$	6.59813	−	19.0077i	0.277832	−	0.800369i
$565$	−12.7332	−	2.24520i	−0.535689	−	0.0944564i
$566$	0.342964	+	1.94505i	0.0144159	+	0.0817564i
$567$	26.3916	−	11.4352i	1.10834	−	0.480231i
$568$	2.28886	+	1.92058i	0.0960385	+	0.0805859i
$569$	−15.1025			−0.633129			−0.316565	−	0.948571i	$-0.602529\pi$
$569$	−15.1025			−0.633129			−0.316565	+	0.948571i	$0.602529\pi$
$570$	6.71392	+	3.45302i	0.281215	+	0.144631i
$571$	12.8800			0.539012			0.269506	−	0.962999i	$-0.413140\pi$
$571$	12.8800			0.539012			0.269506	+	0.962999i	$0.413140\pi$
$572$	−7.05100	−	5.91649i	−0.294817	−	0.247381i
$573$	1.91519	+	5.02681i	0.0800083	+	0.209998i
$574$	−4.71950	−	26.7656i	−0.196988	−	1.11718i
$575$	6.28901	+	1.10892i	0.262270	+	0.0462453i
$576$	−2.84849	−	0.941320i	−0.118687	−	0.0392217i
$577$	22.7440	+	39.3938i	0.946845	+	1.63998i	0.752015	+	0.659146i	$0.229082\pi$
$577$	22.7440	+	39.3938i	0.946845	+	1.63998i	0.194830	+	0.980837i	$0.437584\pi$
$578$	8.24303	−	14.2773i	0.342865	−	0.593859i
$579$	−9.84983	−	11.3884i	−0.409345	−	0.473284i
$580$	−2.18861	−	2.60828i	−0.0908771	−	0.108303i
$581$	30.6213	+	17.6792i	1.27039	+	0.733458i
$582$	−11.6004	+	6.93076i	−0.480851	+	0.287289i
$583$	5.57472	−	15.3164i	0.230881	−	0.634341i
$584$	2.75252	−	15.6103i	0.113900	−	0.645960i
$585$	2.87202	+	13.8523i	0.118743	+	0.572723i
$586$	−16.1317	+	5.87146i	−0.666394	+	0.242548i
$587$	−15.2881	+	18.2197i	−0.631009	+	0.752008i	−0.982921	−	0.184025i	$-0.941087\pi$
$587$	−15.2881	+	18.2197i	−0.631009	+	0.752008i	0.351912	+	0.936033i	$0.385532\pi$
$588$	−5.56507	+	0.0832081i	−0.229499	+	0.00343144i
$589$	18.6576	−	11.6252i	0.768774	−	0.479009i
$590$			6.88067i			0.283273i
$591$	1.66211	−	2.04206i	0.0683701	−	0.0839993i
$592$	0.917985	+	2.52214i	0.0377289	+	0.103659i
$593$	−19.5088	+	3.43992i	−0.801129	+	0.141261i	−0.559199	−	0.829033i	$-0.688891\pi$
$593$	−19.5088	+	3.43992i	−0.801129	+	0.141261i	−0.241929	+	0.970294i	$0.577780\pi$
$594$	−10.0572	−	1.31158i	−0.412650	−	0.0538148i
$595$	−2.15292	−	0.783597i	−0.0882610	−	0.0321244i
$596$	2.99608	−	1.72979i	0.122724	−	0.0708548i
$597$	5.84104	−	10.4756i	0.239058	−	0.428738i
$598$	23.0689	−	19.3571i	0.943355	−	0.791569i
$599$	−13.8537	+	11.6247i	−0.566048	+	0.474971i	−0.880332	−	0.474358i	$-0.842680\pi$
$599$	−13.8537	+	11.6247i	−0.566048	+	0.474971i	0.314284	+	0.949329i	$0.398236\pi$
$600$	0.843503	−	1.51278i	0.0344359	−	0.0617590i
$601$	33.1141	−	19.1185i	1.35075	−	0.779858i	0.362399	−	0.932023i	$-0.381958\pi$
$601$	33.1141	−	19.1185i	1.35075	−	0.779858i	0.988355	+	0.152165i	$0.0486245\pi$
$602$	−16.6091	−	6.04521i	−0.676936	−	0.246384i
$603$	−10.7307	−	1.56290i	−0.436987	−	0.0636464i
$604$	−4.81751	+	0.849457i	−0.196022	+	0.0345639i
$605$	−2.45917	−	6.75650i	−0.0999793	−	0.274691i
$606$	−0.737584	+	0.906195i	−0.0299623	+	0.0368116i
$607$			6.93735i			0.281578i	0.990040	+	0.140789i	$0.0449640\pi$
$607$			6.93735i			0.281578i	−0.990040	+	0.140789i	$0.955036\pi$
$608$	−4.14382	−	1.35231i	−0.168054	−	0.0548433i
$609$	−18.8450	+	0.281768i	−0.763639	+	0.0114178i
$610$	1.78464	−	2.12686i	0.0722581	−	0.0861139i
$611$	51.4756	−	18.7356i	2.08248	−	0.757961i
$612$	−2.10591	+	0.436619i	−0.0851262	+	0.0176493i
$613$	−7.56889	+	42.9253i	−0.305705	+	1.73374i	0.314464	+	0.949269i	$0.398175\pi$
$613$	−7.56889	+	42.9253i	−0.305705	+	1.73374i	−0.620169	+	0.784468i	$0.712936\pi$
$614$	8.89881	−	24.4493i	0.359127	−	0.986692i
$615$	12.6450	−	7.55488i	0.509896	−	0.304642i
$616$	5.40220	+	3.11896i	0.217661	+	0.125667i
$617$	0.675049	+	0.804492i	0.0271764	+	0.0323876i	0.779461	−	0.626450i	$-0.215493\pi$
$617$	0.675049	+	0.804492i	0.0271764	+	0.0323876i	−0.752285	+	0.658838i	$0.771048\pi$
$618$	−17.2351	−	19.9272i	−0.693298	−	0.801591i
$619$	8.51959	−	14.7564i	0.342431	−	0.593109i	−0.642452	−	0.766326i	$-0.722083\pi$
$619$	8.51959	−	14.7564i	0.342431	−	0.593109i	0.984884	+	0.173217i	$0.0554162\pi$
$620$	−2.52162	−	4.36758i	−0.101271	−	0.175406i
$621$	9.93967	−	31.6591i	0.398865	−	1.27044i
$622$	7.96142	+	1.40381i	0.319224	+	0.0562878i
$623$	−8.30368	−	47.0925i	−0.332680	−	1.88672i
$624$	−2.90796	−	7.63254i	−0.116412	−	0.305546i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	20.1464			0.805212
$627$	−14.6197	−	1.85134i	−0.583855	−	0.0739352i
$628$	0.572846			0.0228590
$629$	1.47399	+	1.23683i	0.0587719	+	0.0493155i
$630$	−3.54700	−	8.90724i	−0.141316	−	0.354873i
$631$	1.10296	+	6.25521i	0.0439082	+	0.249016i	0.998859	−	0.0477468i	$-0.0152041\pi$
$631$	1.10296	+	6.25521i	0.0439082	+	0.249016i	−0.954951	+	0.296763i	$0.904093\pi$
$632$	9.65441	+	1.70233i	0.384032	+	0.0677152i
$633$	−7.30288	+	21.0379i	−0.290263	+	0.836182i
$634$	3.85862	+	6.68332i	0.153245	+	0.265429i
$635$	−10.7463	+	18.6132i	−0.426456	+	0.738643i
$636$	10.9395	−	9.46163i	0.433780	−	0.375178i
$637$	−9.74017	−	11.6079i	−0.385920	−	0.459921i
$638$	5.75555	+	3.32297i	0.227865	+	0.131558i
$639$	4.71193	+	7.62532i	0.186401	+	0.301653i
$640$	−0.342020	+	0.939693i	−0.0135195	+	0.0371446i
$641$	0.773044	−	4.38415i	0.0305334	−	0.173163i	−0.965728	−	0.259558i	$-0.916423\pi$
$641$	0.773044	−	4.38415i	0.0305334	−	0.173163i	0.996261	+	0.0863940i	$0.0275344\pi$
$642$	−0.206216	−	1.07525i	−0.00813869	−	0.0424366i
$643$	−42.2535	+	15.3790i	−1.66632	+	0.606490i	−0.991337	−	0.131347i	$-0.958070\pi$
$643$	−42.2535	+	15.3790i	−1.66632	+	0.606490i	−0.674980	+	0.737836i	$0.735848\pi$
$644$	−13.1185	+	15.6340i	−0.516940	+	0.616065i
$645$	−0.143213	−	9.57828i	−0.00563901	−	0.377145i
$646$	−3.05743	+	0.645766i	−0.120293	+	0.0254073i
$647$			21.1076i			0.829824i	0.909862	+	0.414912i	$0.136188\pi$
$647$			21.1076i			0.829824i	−0.909862	+	0.414912i	$0.863812\pi$
$648$	−7.22783	−	5.36269i	−0.283936	−	0.210666i
$649$	−4.59344	−	12.6204i	−0.180308	−	0.495393i
$650$	4.64400	−	0.818863i	0.182153	−	0.0321184i
$651$	−27.5614	−	4.43603i	−1.08022	−	0.173862i
$652$	−17.6672	−	6.43032i	−0.691900	−	0.251831i
$653$	16.1720	−	9.33691i	0.632859	−	0.365382i	−0.148999	−	0.988837i	$-0.547605\pi$
$653$	16.1720	−	9.33691i	0.632859	−	0.365382i	0.781859	+	0.623456i	$0.214272\pi$
$654$	26.0608	+	14.5311i	1.01906	+	0.568212i
$655$	−6.93510	+	5.81924i	−0.270977	+	0.227376i
$656$	−6.51472	+	5.46650i	−0.254357	+	0.213431i
$657$	22.5349	−	41.8749i	0.879169	−	1.63370i
$658$	−32.1506	+	18.5622i	−1.25336	+	0.723629i
$659$	−27.1056	−	9.86562i	−1.05588	−	0.384310i	−0.245003	−	0.969522i	$-0.578789\pi$
$659$	−27.1056	−	9.86562i	−1.05588	−	0.384310i	−0.810880	+	0.585213i	$0.801011\pi$
$660$	−0.537225	+	3.33782i	−0.0209114	+	0.129924i
$661$	41.7137	−	7.35525i	1.62248	−	0.286086i	0.712788	−	0.701380i	$-0.247432\pi$
$661$	41.7137	−	7.35525i	1.62248	−	0.286086i	0.909688	+	0.415293i	$0.136321\pi$
$662$	8.29112	+	22.7797i	0.322244	+	0.885357i
$663$	−4.54129	−	3.69632i	−0.176369	−	0.143553i
$664$		−	11.0639i		−	0.429363i
$665$	−5.20176	−	12.9227i	−0.201716	−	0.501120i
$666$	0.240732	+	8.04842i	0.00932816	+	0.311870i
$667$	−13.9765	+	16.6566i	−0.541173	+	0.644945i
$668$	15.4652	−	5.62886i	0.598366	−	0.217787i
$669$	−2.28298	+	0.437840i	−0.0882652	+	0.0169279i
$670$	−0.627674	+	3.55972i	−0.0242492	+	0.137524i
$671$	−1.85350	+	5.09244i	−0.0715534	+	0.196591i
$672$	2.83903	+	4.75184i	0.109518	+	0.183306i
$673$	−34.8433	−	20.1168i	−1.34311	−	0.775446i	−0.355849	−	0.934543i	$-0.615808\pi$
$673$	−34.8433	−	20.1168i	−1.34311	−	0.775446i	−0.987263	+	0.159097i	$0.949142\pi$
$674$	−5.38660	−	6.41950i	−0.207484	−	0.247270i
$675$	3.82672	−	3.51514i	0.147291	−	0.135298i
$676$	4.61864	−	7.99972i	0.177640	−	0.307682i
$677$	5.39833	+	9.35018i	0.207475	+	0.359357i	0.950918	−	0.309442i	$-0.100142\pi$
$677$	5.39833	+	9.35018i	0.207475	+	0.359357i	−0.743444	+	0.668799i	$0.766809\pi$
$678$	21.1563	+	7.34399i	0.812504	+	0.282044i
$679$	24.5545	+	4.32961i	0.942314	+	0.166155i
$680$	0.124488	+	0.706006i	0.00477390	+	0.0270741i
$681$	−15.4692	+	5.89368i	−0.592779	+	0.225846i
$682$	7.54085	+	6.32752i	0.288754	+	0.242293i
$683$	36.7225			1.40515			0.702574	−	0.711611i	$-0.252034\pi$
$683$	36.7225			1.40515			0.702574	+	0.711611i	$0.252034\pi$
$684$	−10.5307	−	7.75270i	−0.402651	−	0.296432i
$685$	−9.18032			−0.350762
$686$	−9.27029	−	7.77869i	−0.353941	−	0.296992i
$687$	18.1071	−	6.89874i	0.690831	−	0.263203i
$688$	0.960386	+	5.44662i	0.0366144	+	0.207650i
$689$	38.7800	+	6.83796i	1.47740	+	0.260506i
$690$	−10.4493	−	3.62725i	−0.397797	−	0.138087i
$691$	−2.89862	−	5.02056i	−0.110269	−	0.190991i	0.805610	−	0.592446i	$-0.201838\pi$
$691$	−2.89862	−	5.02056i	−0.110269	−	0.190991i	−0.915879	+	0.401455i	$0.868504\pi$
$692$	−7.46543	+	12.9305i	−0.283793	+	0.491544i
$693$	12.4522	+	13.9695i	0.473020	+	0.530659i
$694$	16.3887	+	19.5313i	0.622107	+	0.741398i
$695$	−2.67124	−	1.54224i	−0.101326	−	0.0585006i
$696$	3.02473	+	5.06265i	0.114652	+	0.191899i
$697$	−2.08521	+	5.72908i	−0.0789831	+	0.217004i
$698$	2.81730	−	15.9777i	0.106636	−	0.604765i
$699$	−7.67265	+	1.47150i	−0.290206	+	0.0556571i
$700$	−3.00310	+	1.09304i	−0.113507	+	0.0413130i
$701$	−32.7243	+	38.9993i	−1.23598	+	1.47298i	−0.407267	+	0.913309i	$0.633518\pi$
$701$	−32.7243	+	38.9993i	−1.23598	+	1.47298i	−0.828713	+	0.559674i	$0.810926\pi$
$702$	−1.09865	−	24.4786i	−0.0414661	−	0.923884i
$703$	0.393254	+	11.6927i	0.0148318	+	0.440999i
$704$		−	1.95189i		−	0.0735647i
$705$	−15.6047	−	12.7012i	−0.587708	−	0.478356i
$706$	−7.30439	−	20.0686i	−0.274904	−	0.755293i
$707$	2.12313	−	0.374365i	0.0798484	−	0.0140794i
$708$	1.89379	−	11.7662i	0.0711728	−	0.442202i
$709$	29.7764	+	10.8377i	1.11828	+	0.407020i	0.834023	−	0.551729i	$-0.186032\pi$
$709$	29.7764	+	10.8377i	1.11828	+	0.407020i	0.284254	+	0.958749i	$0.408254\pi$
$710$	2.58759	−	1.49395i	0.0971107	−	0.0560669i
$711$	25.8981	+	13.9370i	0.971255	+	0.522678i
$712$	−11.4623	+	9.61798i	−0.429566	+	0.360449i
$713$	−24.6715	+	20.7018i	−0.923955	+	0.775290i
$714$	3.46591	+	1.93254i	0.129708	+	0.0723234i
$715$	−7.97127	+	4.60221i	−0.298108	+	0.172113i
$716$	−22.9292	−	8.34554i	−0.856904	−	0.311887i
$717$	5.26173	+	0.846880i	0.196503	+	0.0316273i
$718$	14.5537	−	2.56621i	0.543140	−	0.0957702i
$719$	10.8481	+	29.8050i	0.404567	+	1.11154i	0.960005	+	0.279982i	$0.0903284\pi$
$719$	10.8481	+	29.8050i	0.404567	+	1.11154i	−0.555438	+	0.831558i	$0.687449\pi$
$720$	−1.85879	+	2.35476i	−0.0692731	+	0.0877567i
$721$			48.6125i			1.81043i
$722$	−15.3425	−	11.2074i	−0.570990	−	0.417098i
$723$	−0.392721	−	26.2657i	−0.0146055	−	0.976833i
$724$	−3.85606	+	4.59547i	−0.143309	+	0.170789i
$725$	−3.19953	+	1.16453i	−0.118828	+	0.0432497i
$726$	2.34567	+	12.2307i	0.0870559	+	0.453926i
$727$	−8.32687	+	47.2241i	−0.308827	+	1.75144i	0.296095	+	0.955158i	$0.404315\pi$
$727$	−8.32687	+	47.2241i	−0.308827	+	1.75144i	−0.604922	+	0.796285i	$0.706796\pi$
$728$	−5.15438	+	14.1616i	−0.191034	+	0.524862i
$729$	−15.5404	−	22.0793i	−0.575572	−	0.817751i
$730$	−13.7275	−	7.92557i	−0.508077	−	0.293339i
$731$	2.54859	+	3.03729i	0.0942631	+	0.112338i
$732$	−3.63720	+	3.14582i	−0.134435	+	0.116273i
$733$	−8.42009	+	14.5840i	−0.311003	+	0.538673i	−0.978580	−	0.205868i	$-0.933998\pi$
$733$	−8.42009	+	14.5840i	−0.311003	+	0.538673i	0.667577	+	0.744541i	$0.267332\pi$
$734$	5.37618	+	9.31181i	0.198438	+	0.343705i
$735$	−1.82517	+	5.25791i	−0.0673226	+	0.193941i
$736$	6.28901	+	1.10892i	0.231816	+	0.0408754i
$737$	−1.22515	−	6.94818i	−0.0451290	−	0.255939i
$738$	−23.7029	+	9.43886i	−0.872515	+	0.347449i
$739$	−26.2249	−	22.0053i	−0.964699	−	0.809478i	0.0170124	−	0.999855i	$-0.494585\pi$
$739$	−26.2249	−	22.0053i	−0.964699	−	0.809478i	−0.981711	+	0.190377i	$0.939029\pi$
$740$	2.68401			0.0986661
$741$	−1.72854	−	35.5603i	−0.0634996	−	1.30634i
$742$	−26.6870			−0.979711
$743$	33.6915	+	28.2705i	1.23602	+	1.03714i	0.997824	+	0.0659273i	$0.0210005\pi$
$743$	33.6915	+	28.2705i	1.23602	+	1.03714i	0.238196	+	0.971217i	$0.423444\pi$
$744$	3.10999	+	8.16279i	0.114018	+	0.299262i
$745$	−0.600748	−	3.40701i	−0.0220097	−	0.124823i
$746$	−8.89686	−	1.56876i	−0.325737	−	0.0574362i
$747$	10.4147	−	31.5155i	0.381053	−	1.15309i
$748$	−0.699653	−	1.21184i	−0.0255819	−	0.0443091i
$749$	−1.01006	+	1.74947i	−0.0369067	+	0.0639242i
$750$	−1.13305	−	1.31003i	−0.0413732	−	0.0478357i
$751$	−22.3367	−	26.6199i	−0.815078	−	0.971372i	0.184857	−	0.982765i	$-0.440818\pi$
$751$	−22.3367	−	26.6199i	−0.815078	−	0.971372i	−0.999935	+	0.0113931i	$0.996373\pi$
$752$	10.0602	+	5.80825i	0.366857	+	0.211805i
$753$	21.7273	−	12.9812i	0.791788	−	0.473061i
$754$	−5.49153	+	15.0879i	−0.199990	+	0.549467i
$755$	−0.849457	+	4.81751i	−0.0309149	+	0.175327i
$756$	3.61396	+	16.2080i	0.131439	+	0.589480i
$757$	−14.9061	+	5.42538i	−0.541772	+	0.197189i	−0.598387	−	0.801207i	$-0.704191\pi$
$757$	−14.9061	+	5.42538i	−0.541772	+	0.197189i	0.0566151	+	0.998396i	$0.481969\pi$
$758$	22.3244	−	26.6051i	0.810857	−	0.966342i
$759$	21.5873	−	0.322771i	0.783570	−	0.0117158i
$760$	−2.68802	+	3.43140i	−0.0975049	+	0.124470i
$761$		−	22.3879i		−	0.811561i	−0.913971	−	0.405780i	$-0.867000\pi$
$761$		−	22.3879i		−	0.811561i	0.913971	−	0.405780i	$-0.133000\pi$
$762$	23.4997	−	28.8717i	0.851304	−	1.04591i
$763$	−18.8299	−	51.7347i	−0.681688	−	1.87292i
$764$	−3.05855	+	0.539305i	−0.110654	+	0.0195114i
$765$	−0.309974	+	2.12824i	−0.0112072	+	0.0769466i
$766$	−26.6060	−	9.68380i	−0.961315	−	0.349890i
$767$	28.0997	−	16.2234i	1.01462	−	0.585793i
$768$	0.843503	−	1.51278i	0.0304373	−	0.0545877i
$769$	−9.43284	+	7.91509i	−0.340157	+	0.285426i	−0.796823	−	0.604213i	$-0.793488\pi$
$769$	−9.43284	+	7.91509i	−0.340157	+	0.285426i	0.456666	+	0.889638i	$0.349043\pi$
$770$	4.77852	−	4.00966i	0.172206	−	0.144498i
$771$	25.4662	−	45.6723i	0.917142	−	1.64485i
$772$	7.52851	−	4.34659i	0.270957	−	0.156437i
$773$	−37.5324	−	13.6607i	−1.34995	−	0.491341i	−0.437016	−	0.899454i	$-0.643965\pi$
$773$	−37.5324	−	13.6607i	−1.34995	−	0.491341i	−0.912932	+	0.408113i	$0.866187\pi$
$774$	−2.39136	+	16.4187i	−0.0859555	+	0.590158i
$775$	−4.96663	+	0.875751i	−0.178407	+	0.0314579i
$776$	−2.66837	−	7.33129i	−0.0957890	−	0.263178i
$777$	9.37862	−	11.5226i	0.336456	−	0.413369i
$778$			23.7681i			0.852128i
$779$	−34.3882	+	13.8423i	−1.23209	+	0.495952i
$780$	−8.16682	+	0.122109i	−0.292419	+	0.00437221i
$781$	−3.74877	+	4.46761i	−0.134142	+	0.159864i
$782$	4.30204	−	1.56581i	0.153841	−	0.0559934i
$783$	3.85035	+	17.2682i	0.137600	+	0.617114i
$784$	0.557993	−	3.16453i	0.0199283	−	0.113019i
$785$	0.195925	−	0.538299i	0.00699286	−	0.0192127i
$786$	13.4610	−	8.04238i	0.480137	−	0.286862i
$787$	−13.4750	−	7.77980i	−0.480332	−	0.277320i	0.240223	−	0.970718i	$-0.422780\pi$
$787$	−13.4750	−	7.77980i	−0.480332	−	0.277320i	−0.720555	+	0.693398i	$0.756113\pi$
$788$	0.977139	+	1.16451i	0.0348091	+	0.0414839i
$789$	18.6723	+	21.5889i	0.664750	+	0.768584i
$790$	4.90167	−	8.48995i	0.174394	−	0.302059i
$791$	−20.6604	−	35.7849i	−0.734601	−	1.27237i
$792$	1.83735	−	5.55995i	0.0652875	−	0.197564i
$793$	−12.8937	−	2.27350i	−0.457868	−	0.0807344i
$794$	2.31818	+	13.1471i	0.0822693	+	0.466572i
$795$	−5.14948	−	13.5159i	−0.182633	−	0.479358i
$796$	5.30466	+	4.45114i	0.188019	+	0.157766i
$797$	46.5571			1.64914			0.824568	−	0.565762i	$-0.191418\pi$
$797$	46.5571			1.64914			0.824568	+	0.565762i	$0.191418\pi$
$798$	5.33850	+	23.5300i	0.188981	+	0.832953i
$799$	8.32784			0.294618
$800$	0.766044	+	0.642788i	0.0270838	+	0.0227260i
$801$	−41.7038	+	16.6071i	−1.47353	+	0.586783i
$802$	0.847824	+	4.80825i	0.0299377	+	0.169785i
$803$	30.4697	+	5.37263i	1.07525	+	0.189596i
$804$	2.05310	−	5.91451i	0.0724072	−	0.208589i
$805$	10.2043	+	17.6744i	0.359656	+	0.622942i
$806$	−11.8911	+	20.5960i	−0.418845	+	0.725462i
$807$	9.67960	−	8.37191i	0.340738	−	0.294705i
$808$	−0.433619	−	0.516767i	−0.0152547	−	0.0181798i
$809$	21.9238	+	12.6577i	0.770800	+	0.445022i	0.833160	−	0.553032i	$-0.186529\pi$
$809$	21.9238	+	12.6577i	0.770800	+	0.445022i	−0.0623597	+	0.998054i	$0.519863\pi$
$810$	−7.51134	+	4.95780i	−0.263922	+	0.174199i
$811$	−4.44926	+	12.2242i	−0.156234	+	0.429251i	−0.992971	−	0.118354i	$-0.962238\pi$
$811$	−4.44926	+	12.2242i	−0.156234	+	0.429251i	0.836737	+	0.547605i	$0.184460\pi$
$812$	1.88954	−	10.7161i	0.0663097	−	0.376061i
$813$	−5.40181	−	28.1661i	−0.189450	−	0.987827i
$814$	−4.92295	+	1.79181i	−0.172549	+	0.0628028i
$815$	−12.0851	+	14.4024i	−0.423321	+	0.504494i
$816$	−0.0185637	−	1.24156i	−0.000649859	−	0.0434634i
$817$	−3.38584	+	23.8686i	−0.118455	+	0.835055i
$818$			20.3424i			0.711256i
$819$	−28.0128	+	35.4872i	−0.978846	+	1.24002i
$820$	2.90866	+	7.99149i	0.101575	+	0.279075i
$821$	25.0056	−	4.40916i	0.872702	−	0.153881i	0.280679	−	0.959802i	$-0.409440\pi$
$821$	25.0056	−	4.40916i	0.872702	−	0.153881i	0.592023	+	0.805921i	$0.298329\pi$
$822$	15.6987	+	2.52673i	0.547557	+	0.0881297i
$823$	16.4166	+	5.97514i	0.572245	+	0.208280i	0.611903	−	0.790933i	$-0.290404\pi$
$823$	16.4166	+	5.97514i	0.572245	+	0.208280i	−0.0396574	+	0.999213i	$0.512627\pi$
$824$	13.1733	−	7.60561i	0.458914	−	0.264954i
$825$	2.95278	+	1.64643i	0.102803	+	0.0573212i
$826$	−16.8449	+	14.1346i	−0.586110	+	0.491804i
$827$	−11.2788	+	9.46403i	−0.392202	+	0.329097i	−0.817470	−	0.575971i	$-0.804624\pi$
$827$	−11.2788	+	9.46403i	−0.392202	+	0.329097i	0.425268	+	0.905067i	$0.360180\pi$
$828$	16.8704	+	9.07873i	0.586286	+	0.315508i
$829$	−3.99165	+	2.30458i	−0.138636	+	0.0800413i	−0.567714	−	0.823226i	$-0.692172\pi$
$829$	−3.99165	+	2.30458i	−0.138636	+	0.0800413i	0.429078	+	0.903267i	$0.358839\pi$
$830$	−10.3967	−	3.78408i	−0.360874	−	0.131347i
$831$	8.72278	−	54.1954i	0.302590	−	1.88002i
$832$	4.64400	−	0.818863i	0.161002	−	0.0283890i
$833$	−0.787893	−	2.16472i	−0.0272989	−	0.0750030i
$834$	4.14346	+	3.37251i	0.143476	+	0.116781i
$835$		−	16.4577i		−	0.569542i
$836$	2.63956	−	8.08829i	0.0912910	−	0.279739i
$837$	1.17498	+	26.1791i	0.0406133	+	0.904883i
$838$	1.41478	−	1.68607i	0.0488728	−	0.0582443i
$839$	29.8885	−	10.8785i	1.03186	−	0.375568i	0.230074	−	0.973173i	$-0.426103\pi$
$839$	29.8885	−	10.8785i	1.03186	−	0.375568i	0.801790	+	0.597605i	$0.203881\pi$
$840$	5.43627	−	1.04259i	0.187569	−	0.0359729i
$841$	−3.02267	+	17.1424i	−0.104230	+	0.591117i
$842$	6.25324	−	17.1806i	0.215501	−	0.592083i
$843$	−5.97609	−	10.0025i	−0.205827	−	0.344504i
$844$	−11.1347	−	6.42862i	−0.383272	−	0.221282i
$845$	−5.93761	−	7.07617i	−0.204260	−	0.243428i
$846$	23.1889	+	26.0146i	0.797252	+	0.894400i
$847$	11.4892	−	19.8999i	0.394774	−	0.683768i
$848$	4.17528	+	7.23180i	0.143380	+	0.248341i
$849$	−3.23172	−	1.12182i	−0.110912	−	0.0385009i
$850$	0.706006	+	0.124488i	0.0242158	+	0.00426990i
$851$	−2.97636	−	16.8798i	−0.102028	−	0.578631i
$852$	−4.83608	+	1.84253i	−0.165681	+	0.0631239i
$853$	−28.3233	−	23.7661i	−0.969773	−	0.813736i	0.0127425	−	0.999919i	$-0.495944\pi$
$853$	−28.3233	−	23.7661i	−0.969773	−	0.813736i	−0.982515	+	0.186183i	$0.940388\pi$
$854$	8.87295			0.303626
$855$	−10.8869	+	7.24404i	−0.372323	+	0.247741i
$856$	0.632108			0.0216050
$857$	30.8482	+	25.8847i	1.05375	+	0.884205i	0.993483	−	0.113978i	$-0.0363592\pi$
$857$	30.8482	+	25.8847i	1.05375	+	0.884205i	0.0602706	+	0.998182i	$0.480804\pi$
$858$	14.8979	−	5.67603i	0.508605	−	0.193776i
$859$	−7.81289	−	44.3091i	−0.266572	−	1.51181i	−0.764521	−	0.644599i	$-0.777024\pi$
$859$	−7.81289	−	44.3091i	−0.266572	−	1.51181i	0.497948	−	0.867207i	$-0.334087\pi$
$860$	5.44662	+	0.960386i	0.185728	+	0.0327489i
$861$	44.4714	+	15.4373i	1.51558	+	0.526103i
$862$	−0.621172	−	1.07590i	−0.0211572	−	0.0366453i
$863$	16.9262	−	29.3170i	0.576174	−	0.997962i	−0.419740	−	0.907645i	$-0.637879\pi$
$863$	16.9262	−	29.3170i	0.576174	−	0.997962i	0.995913	−	0.0903172i	$-0.0287881\pi$
$864$	3.82672	−	3.51514i	0.130188	−	0.119587i
$865$	9.59737	+	11.4377i	0.326320	+	0.388894i
$866$	32.6044	+	18.8242i	1.10794	+	0.639671i
$867$	14.6455	+	24.5129i	0.497386	+	0.832501i
$868$	5.51247	−	15.1454i	0.187105	−	0.514068i
$869$	−3.32277	+	18.8444i	−0.112717	+	0.639252i
$870$	5.79186	−	1.11079i	0.196362	−	0.0376592i
$871$	16.0173	−	5.82984i	0.542727	−	0.197536i
$872$	−11.0734	+	13.1967i	−0.374992	+	0.446898i
$873$	−0.699752	−	23.3949i	−0.0236830	−	0.791799i
$874$	24.5610	+	13.0999i	0.830787	+	0.443109i
$875$			3.19583i			0.108039i
$876$	21.2932	+	17.3313i	0.719432	+	0.585571i
$877$	−12.6695	−	34.8092i	−0.427819	−	1.17542i	−0.947134	−	0.320839i	$-0.896035\pi$
$877$	−12.6695	−	34.8092i	−0.427819	−	1.17542i	0.519315	−	0.854583i	$-0.326187\pi$
$878$	4.48330	−	0.790527i	0.151304	−	0.0266790i
$879$	4.72492	−	29.3563i	0.159368	−	0.990163i
$880$	−1.83418	−	0.667586i	−0.0618301	−	0.0225043i
$881$	37.6607	−	21.7434i	1.26882	−	0.732554i	0.294056	−	0.955788i	$-0.404995\pi$
$881$	37.6607	−	21.7434i	1.26882	−	0.732554i	0.974765	+	0.223234i	$0.0716615\pi$
$882$	4.56828	−	8.48890i	0.153822	−	0.285836i
$883$	−23.5235	+	19.7386i	−0.791629	+	0.664256i	−0.946148	−	0.323734i	$-0.895062\pi$
$883$	−23.5235	+	19.7386i	−0.791629	+	0.664256i	0.154519	+	0.987990i	$0.450617\pi$
$884$	2.58972	−	2.17303i	0.0871015	−	0.0730869i
$885$	−10.4089	−	5.80387i	−0.349893	−	0.195095i
$886$	5.17551	−	2.98808i	0.173875	−	0.100387i
$887$	46.2154	+	16.8210i	1.55176	+	0.564795i	0.968830	−	0.247726i	$-0.0796832\pi$
$887$	46.2154	+	16.8210i	1.55176	+	0.564795i	0.582932	+	0.812521i	$0.301905\pi$
$888$	−4.58977	−	0.738727i	−0.154023	−	0.0247901i
$889$	−67.6436	+	11.9274i	−2.26869	+	0.400032i
$890$	5.11762	+	14.0605i	0.171543	+	0.471310i
$891$	10.4674	−	14.1080i	0.350671	−	0.472634i
$892$		−	1.34210i		−	0.0449369i
$893$	33.8331	+	37.6728i	1.13218	+	1.26067i
$894$	0.0895838	+	5.99148i	0.00299613	+	0.200385i
$895$	−15.6845	+	18.6920i	−0.524275	+	0.624806i
$896$	−3.00310	+	1.09304i	−0.100327	+	0.0365159i
$897$	9.82432	+	51.2258i	0.328024	+	1.71038i
$898$	1.46602	−	8.31422i	0.0489218	−	0.277449i
$899$	5.87304	−	16.1360i	0.195877	−	0.538167i
$900$	1.57700	+	2.55207i	0.0525668	+	0.0850690i
$901$	5.18446	+	2.99325i	0.172719	+	0.0997196i
$902$	−10.6700	−	12.7160i	−0.355273	−	0.423397i
$903$	23.1549	−	20.0267i	0.770546	−	0.666448i
$904$	−6.46481	+	11.1974i	−0.215016	+	0.372419i
$905$	2.99948	+	5.19526i	0.0997062	+	0.172696i
$906$	2.77854	−	8.00435i	0.0923109	−	0.265927i
$907$	−11.8815	−	2.09502i	−0.394518	−	0.0695641i	−0.0271299	−	0.999632i	$-0.508637\pi$
$907$	−11.8815	−	2.09502i	−0.394518	−	0.0695641i	−0.367388	+	0.930068i	$0.619748\pi$
$908$	−1.65962	−	9.41217i	−0.0550764	−	0.312354i
$909$	−0.748718	−	1.88018i	−0.0248334	−	0.0623617i
$910$	11.5446	+	9.68707i	0.382700	+	0.321123i
$911$	−34.6125			−1.14676			−0.573381	−	0.819289i	$-0.694369\pi$
$911$	−34.6125			−1.14676			−0.573381	+	0.819289i	$0.694369\pi$
$912$	5.54107	−	5.12801i	0.183483	−	0.169806i
$913$	21.5956			0.714709
$914$	−13.5477	−	11.3679i	−0.448118	−	0.376016i
$915$	1.71211	+	4.49378i	0.0566006	+	0.148560i
$916$	1.94264	+	11.0173i	0.0641866	+	0.364020i
$917$	−28.4927	−	5.02404i	−0.940913	−	0.165908i
$918$	1.11583	−	3.55406i	0.0368279	−	0.117302i
$919$	−3.24858	−	5.62670i	−0.107161	−	0.185608i	0.807458	−	0.589925i	$-0.200843\pi$
$919$	−3.24858	−	5.62670i	−0.107161	−	0.185608i	−0.914619	+	0.404317i	$0.867509\pi$
$920$	3.19302	−	5.53047i	0.105271	−	0.182334i
$921$	29.4802	+	34.0850i	0.971405	+	1.12314i
$922$	13.5203	+	16.1128i	0.445267	+	0.530648i
$923$	−12.2022	−	7.04493i	−0.401639	−	0.231887i
$924$	−9.27507	+	5.54148i	−0.305127	+	0.182301i
$925$	0.917985	−	2.52214i	0.0301832	−	0.0829275i
$926$	−4.90770	+	27.8329i	−0.161277	+	0.914647i
$927$	44.6834	−	9.26425i	1.46760	−	0.304278i
$928$	−3.19953	+	1.16453i	−0.105030	+	0.0382277i
$929$	5.19216	−	6.18777i	0.170349	−	0.203014i	−0.674115	−	0.738627i	$-0.735475\pi$
$929$	5.19216	−	6.18777i	0.170349	−	0.203014i	0.844464	+	0.535612i	$0.179919\pi$
$930$	8.73419	−	0.130592i	0.286405	−	0.00428229i
$931$	6.59164	−	12.3587i	0.216032	−	0.405040i
$932$		−	4.51054i		−	0.147748i
$933$	−8.83914	+	10.8597i	−0.289381	+	0.355532i
$934$	−7.60323	−	20.8897i	−0.248785	−	0.683532i
$935$	−1.37805	+	0.242987i	−0.0450670	+	0.00794653i
$936$	13.9992	+	2.03896i	0.457579	+	0.0666456i
$937$	28.0323	+	10.2029i	0.915774	+	0.333314i	0.756556	−	0.653929i	$-0.226881\pi$
$937$	28.0323	+	10.2029i	0.915774	+	0.333314i	0.159218	+	0.987243i	$0.449103\pi$
$938$	−10.0041	+	5.77588i	−0.326646	+	0.188589i
$939$	−16.9936	+	30.4771i	−0.554564	+	0.994581i
$940$	8.89875	−	7.46694i	0.290245	−	0.243545i
$941$	−37.3026	+	31.3006i	−1.21603	+	1.02037i	−0.217009	+	0.976170i	$0.569630\pi$
$941$	−37.3026	+	31.3006i	−1.21603	+	1.02037i	−0.999023	+	0.0442018i	$0.985926\pi$
$942$	−0.483197	+	0.866589i	−0.0157434	+	0.0282350i
$943$	47.0331	−	27.1546i	1.53161	−	0.884274i
$944$	6.46571	+	2.35333i	0.210441	+	0.0765943i
$945$	16.4666	+	2.14745i	0.535659	+	0.0698566i
$946$	−10.6312	+	1.87457i	−0.345651	+	0.0609475i
$947$	−5.12273	−	14.0746i	−0.166466	−	0.457363i	0.828209	−	0.560419i	$-0.189360\pi$
$947$	−5.12273	−	14.0746i	−0.166466	−	0.457363i	−0.994675	+	0.103057i	$0.967138\pi$
$948$	−10.7188	+	13.1691i	−0.348130	+	0.427712i
$949$			74.7483i			2.42643i
$950$	2.30511	+	3.69953i	0.0747875	+	0.120028i
$951$	−13.3652	+	0.199834i	−0.433395	+	0.00648006i
$952$	−1.47268	+	1.75507i	−0.0477299	+	0.0568823i
$953$	−12.4569	+	4.53395i	−0.403519	+	0.146869i	−0.535803	−	0.844343i	$-0.679991\pi$
$953$	−12.4569	+	4.53395i	−0.403519	+	0.146869i	0.132284	+	0.991212i	$0.457769\pi$
$954$	5.08583	+	24.5300i	0.164660	+	0.794188i
$955$	−0.539305	+	3.05855i	−0.0174515	+	0.0989724i
$956$	−1.05238	+	2.89140i	−0.0340365	+	0.0935145i
$957$	−9.88175	+	5.90395i	−0.319432	+	0.190848i
$958$	22.6372	+	13.0696i	0.731375	+	0.422259i
$959$	−18.8586	−	22.4748i	−0.608976	−	0.725749i
$960$	−1.13305	−	1.31003i	−0.0365691	−	0.0422812i
$961$	−2.78282	+	4.81998i	−0.0897683	+	0.155483i
$962$	−6.32841	−	10.9611i	−0.204036	−	0.353401i
$963$	1.80056	+	0.595016i	0.0580221	+	0.0191741i
$964$	14.9358	+	2.63359i	0.481050	+	0.0848221i
$965$	−1.50955	−	8.56111i	−0.0485943	−	0.275592i
$966$	−12.5853	−	33.0326i	−0.404925	−	1.06281i
$967$	39.2134	+	32.9039i	1.26102	+	1.05812i	0.995573	+	0.0939924i	$0.0299630\pi$
$967$	39.2134	+	32.9039i	1.26102	+	1.05812i	0.265444	+	0.964126i	$0.414481\pi$
$968$	−7.19012			−0.231099
$969$	1.60205	−	5.16993i	0.0514653	−	0.166082i
$970$	−7.80180			−0.250501
$971$	−16.0909	−	13.5018i	−0.516381	−	0.433295i	0.346987	−	0.937870i	$-0.387205\pi$
$971$	−16.0909	−	13.5018i	−0.516381	−	0.433295i	−0.863368	+	0.504575i	$0.831649\pi$
$972$	14.2093	−	6.41068i	0.455762	−	0.205623i
$973$	−1.71174	−	9.70774i	−0.0548758	−	0.311216i
$974$	−16.2032	−	2.85707i	−0.519185	−	0.0915463i
$975$	−2.67847	+	7.71606i	−0.0857797	+	0.247112i
$976$	−1.38821	−	2.40444i	−0.0444354	−	0.0769644i
$977$	1.91262	−	3.31275i	0.0611901	−	0.105984i	−0.833808	−	0.552055i	$-0.813844\pi$
$977$	1.91262	−	3.31275i	0.0611901	−	0.105984i	0.894998	+	0.446071i	$0.147177\pi$
$978$	24.6300	−	21.3025i	0.787580	−	0.681180i
$979$	−18.7733	−	22.3731i	−0.599996	−	0.715047i
$980$	−2.78284	−	1.60668i	−0.0888947	−	0.0513234i
$981$	−43.9648	+	27.1672i	−1.40369	+	0.867382i
$982$	14.4564	−	39.7185i	0.461321	−	1.26747i
$983$	−1.52381	+	8.64195i	−0.0486019	+	0.275635i	−0.999418	−	0.0341218i	$-0.989137\pi$
$983$	−1.52381	+	8.64195i	−0.0486019	+	0.275635i	0.950816	+	0.309757i	$0.100248\pi$
$984$	−2.77442	−	14.4663i	−0.0884453	−	0.461170i
$985$	1.42848	−	0.519925i	0.0455152	−	0.0165662i
$986$	−1.56901	+	1.86987i	−0.0499674	+	0.0595489i
$987$	−0.961317	−	64.2941i	−0.0305990	−	2.04650i
$988$	20.3513	+	2.88690i	0.647460	+	0.0918444i
$989$		−	35.3189i		−	1.12307i
$990$	−4.59623	−	3.62816i	−0.146078	−	0.115311i
$991$	−11.6291	−	31.9507i	−0.369411	−	1.01495i	−0.975586	−	0.219617i	$-0.929519\pi$
$991$	−11.6291	−	31.9507i	−0.369411	−	1.01495i	0.606175	−	0.795331i	$-0.292703\pi$
$992$	−4.96663	+	0.875751i	−0.157691	+	0.0278051i
$993$	−41.4542	−	6.67209i	−1.31551	−	0.211732i
$994$	8.97296	+	3.26589i	0.284605	+	0.103588i
$995$	5.99700	−	3.46237i	0.190118	−	0.109765i
$996$	16.7373	+	9.33245i	0.530341	+	0.295710i
$997$	−31.9346	+	26.7963i	−1.01138	+	0.848648i	−0.988520	−	0.151090i	$-0.951722\pi$
$997$	−31.9346	+	26.7963i	−1.01138	+	0.848648i	−0.0228597	+	0.999739i	$0.507277\pi$
$998$	−17.9583	+	15.0688i	−0.568460	+	0.476995i
$999$	−12.3786	−	6.42470i	−0.391640	−	0.203268i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bb.b.41.14	yes	84
3.2	odd	2		570.2.bb.a.41.4	✓	84
19.13	odd	18		570.2.bb.a.431.4	yes	84
57.32	even	18	inner	570.2.bb.b.431.14	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bb.a.41.4	✓	84	3.2	odd	2
570.2.bb.a.431.4	yes	84	19.13	odd	18
570.2.bb.b.41.14	yes	84	1.1	even	1	trivial
570.2.bb.b.431.14	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)

\(f(q)\)	\(=\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.61856 - 0.616663i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-1.63627 - 0.567997i) q^{6} +(1.59792 + 2.76767i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.23945 - 1.99621i) q^{9} +O(q^{10})\)	\(q+(-0.766044 - 0.642788i) q^{2} +(1.61856 - 0.616663i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.984808 + 0.173648i) q^{5} +(-1.63627 - 0.567997i) q^{6} +(1.59792 + 2.76767i) q^{7} +(0.500000 - 0.866025i) q^{8} +(2.23945 - 1.99621i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(1.69039 + 0.975946i) q^{11} +(0.888354 + 1.48689i) q^{12} +(-1.61284 + 4.43125i) q^{13} +(0.554951 - 3.14728i) q^{14} +(1.70105 - 0.326235i) q^{15} +(-0.939693 + 0.342020i) q^{16} +(-0.460813 + 0.549175i) q^{17} +(-2.99866 + 0.0896911i) q^{18} +(-4.35644 + 0.146517i) q^{19} +1.00000i q^{20} +(4.29304 + 3.49426i) q^{21} +(-0.667586 - 1.83418i) q^{22} +(6.28901 - 1.10892i) q^{23} +(0.275233 - 1.71004i) q^{24} +(0.939693 + 0.342020i) q^{25} +(4.08387 - 2.35782i) q^{26} +(2.39370 - 4.61196i) q^{27} +(-2.44815 + 2.05424i) q^{28} +(-2.60828 + 2.18861i) q^{29} +(-1.51278 - 0.843503i) q^{30} +(-4.36758 + 2.52162i) q^{31} +(0.939693 + 0.342020i) q^{32} +(3.33782 + 0.537225i) q^{33} +(0.706006 - 0.124488i) q^{34} +(1.09304 + 3.00310i) q^{35} +(2.35476 + 1.85879i) q^{36} -2.68401i q^{37} +(3.43140 + 2.68802i) q^{38} +(0.122109 + 8.16682i) q^{39} +(0.642788 - 0.766044i) q^{40} +(7.99149 - 2.90866i) q^{41} +(-1.04259 - 5.43627i) q^{42} +(0.960386 - 5.44662i) q^{43} +(-0.667586 + 1.83418i) q^{44} +(2.55207 - 1.57700i) q^{45} +(-5.53047 - 3.19302i) q^{46} +(-7.46694 - 8.89875i) q^{47} +(-1.31003 + 1.13305i) q^{48} +(-1.60668 + 2.78284i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-0.407196 + 1.17304i) q^{51} +(-4.64400 - 0.818863i) q^{52} +(-1.45006 - 8.22370i) q^{53} +(-4.79819 + 1.99433i) q^{54} +(1.49524 + 1.25465i) q^{55} +3.19583 q^{56} +(-6.96079 + 2.92360i) q^{57} +3.40487 q^{58} +(-5.27090 - 4.42281i) q^{59} +(0.616663 + 1.61856i) q^{60} +(0.482119 + 2.73423i) q^{61} +(4.96663 + 0.875751i) q^{62} +(9.10331 + 3.00830i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.35782 + 4.08387i) q^{65} +(-2.21160 - 2.55705i) q^{66} +(-2.32344 - 2.76897i) q^{67} +(-0.620852 - 0.358449i) q^{68} +(9.49530 - 5.67306i) q^{69} +(1.09304 - 3.00310i) q^{70} +(-0.518843 + 2.94250i) q^{71} +(-0.609040 - 2.93753i) q^{72} +(14.8952 - 5.42141i) q^{73} +(-1.72525 + 2.05607i) q^{74} +(1.73186 - 0.0258945i) q^{75} +(-0.900779 - 4.26481i) q^{76} +6.23792i q^{77} +(5.15599 - 6.33464i) q^{78} +(3.35294 + 9.21214i) q^{79} +(-0.984808 + 0.173648i) q^{80} +(1.03031 - 8.94083i) q^{81} +(-7.99149 - 2.90866i) q^{82} +(9.58163 - 5.53196i) q^{83} +(-2.69570 + 4.83459i) q^{84} +(-0.549175 + 0.460813i) q^{85} +(-4.23672 + 3.55503i) q^{86} +(-2.87202 + 5.15082i) q^{87} +(1.69039 - 0.975946i) q^{88} +(-14.0605 - 5.11762i) q^{89} +(-2.96868 - 0.432383i) q^{90} +(-14.8415 + 2.61695i) q^{91} +(2.18415 + 6.00091i) q^{92} +(-5.51419 + 6.77472i) q^{93} +11.6165i q^{94} +(-4.31569 - 0.612196i) q^{95} +(1.73186 - 0.0258945i) q^{96} +(5.01490 - 5.97653i) q^{97} +(3.01956 - 1.09903i) q^{98} +(5.73374 - 1.18878i) 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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