LMFDB - Embedded newform 570.2.bb.a.41.4

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			41.4
Character	$\chi$	$=$	570.41
Dual form			570.2.bb.a.431.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(-1.63627 + 0.567997i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.61856 - 0.616663i) q^{6} +(1.59792 + 2.76767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.35476 - 1.85879i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(-1.63627 + 0.567997i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.61856 - 0.616663i) q^{6} +(1.59792 + 2.76767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.35476 - 1.85879i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(-1.69039 - 0.975946i) q^{11} +(-0.843503 - 1.51278i) q^{12} +(-1.61284 + 4.43125i) q^{13} +(-0.554951 + 3.14728i) q^{14} +(1.71004 - 0.275233i) 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} +(-4.18665 - 3.62105i) q^{21} +(-0.667586 - 1.83418i) q^{22} +(-6.28901 + 1.10892i) q^{23} +(0.326235 - 1.70105i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-4.08387 + 2.35782i) q^{26} +(-2.79723 + 4.37898i) q^{27} +(-2.44815 + 2.05424i) q^{28} +(2.60828 - 2.18861i) q^{29} +(1.48689 + 0.888354i) q^{30} +(-4.36758 + 2.52162i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(3.32027 + 0.636775i) q^{33} +(0.706006 - 0.124488i) q^{34} +(-1.09304 - 3.00310i) q^{35} +(2.23945 + 1.99621i) 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} +(-0.879598 - 5.46501i) q^{42} +(0.960386 - 5.44662i) q^{43} +(0.667586 - 1.83418i) q^{44} +(-2.64176 + 1.42165i) q^{45} +(-5.53047 - 3.19302i) q^{46} +(7.46694 + 8.89875i) q^{47} +(1.34332 - 1.09338i) q^{48} +(-1.60668 + 2.78284i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.442084 + 1.16034i) q^{51} +(-4.64400 - 0.818863i) q^{52} +(1.45006 + 8.22370i) q^{53} +(-4.95756 + 1.55647i) q^{54} +(1.49524 + 1.25465i) q^{55} -3.19583 q^{56} +(7.04508 - 2.71419i) q^{57} +3.40487 q^{58} +(5.27090 + 4.42281i) q^{59} +(0.567997 + 1.63627i) q^{60} +(0.482119 + 2.73423i) q^{61} +(-4.96663 - 0.875751i) q^{62} +(8.90724 + 3.54700i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.35782 - 4.08387i) q^{65} +(2.13416 + 2.62202i) q^{66} +(-2.32344 - 2.76897i) q^{67} +(0.620852 + 0.358449i) q^{68} +(9.66066 - 5.38664i) q^{69} +(1.09304 - 3.00310i) q^{70} +(0.518843 - 2.94250i) q^{71} +(0.432383 + 2.96868i) 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} +(5.34307 - 6.17766i) q^{78} +(3.35294 + 9.21214i) q^{79} +(0.984808 - 0.173648i) q^{80} +(2.08977 - 8.75402i) q^{81} +(-7.99149 - 2.90866i) q^{82} +(-9.58163 + 5.53196i) q^{83} +(2.83903 - 4.75184i) q^{84} +(-0.549175 + 0.460813i) q^{85} +(4.23672 - 3.55503i) q^{86} +(-3.02473 + 5.06265i) q^{87} +(1.69039 - 0.975946i) q^{88} +(14.0605 + 5.11762i) q^{89} +(-2.93753 - 0.609040i) q^{90} +(-14.8415 + 2.61695i) q^{91} +(-2.18415 - 6.00091i) q^{92} +(5.71427 - 6.60683i) 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} +(-5.79454 + 0.843965i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	$ 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) $ 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * 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
$3$	−1.63627	+	0.567997i	−0.944701	+	0.327933i
$3$	−1.63627	+	0.567997i	−0.944701	+	0.327933i
$4$	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
$6$	−1.61856	−	0.616663i	−0.660773	−	0.251752i
$7$	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
$9$	2.35476	−	1.85879i	0.784919	−	0.619598i
$10$	−0.642788	−	0.766044i	−0.203267	−	0.242245i
$11$	−1.69039	−	0.975946i	−0.509671	−	0.294259i	0.223027	−	0.974812i	$-0.428406\pi$
$11$	−1.69039	−	0.975946i	−0.509671	−	0.294259i	−0.732698	+	0.680553i	$0.761739\pi$
$12$	−0.843503	−	1.51278i	−0.243498	−	0.436702i
$13$	−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
$15$	1.71004	−	0.275233i	0.441531	−	0.0710648i
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	0.460813	−	0.549175i	0.111764	−	0.133195i	−0.707262	−	0.706951i	$-0.750070\pi$
$17$	0.460813	−	0.549175i	0.111764	−	0.133195i	0.819026	+	0.573757i	$0.194514\pi$
$18$	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
$21$	−4.18665	−	3.62105i	−0.913603	−	0.790177i
$22$	−0.667586	−	1.83418i	−0.142330	−	0.391048i
$23$	−6.28901	+	1.10892i	−1.31135	+	0.231226i	−0.785241	−	0.619191i	$-0.787461\pi$
$23$	−6.28901	+	1.10892i	−1.31135	+	0.231226i	−0.526109	+	0.850417i	$0.676350\pi$
$24$	0.326235	−	1.70105i	0.0665924	−	0.347225i
$25$	0.939693	+	0.342020i	0.187939	+	0.0684040i
$26$	−4.08387	+	2.35782i	−0.800912	+	0.462407i
$27$	−2.79723	+	4.37898i	−0.538327	+	0.842736i
$28$	−2.44815	+	2.05424i	−0.462657	+	0.388215i
$29$	2.60828	−	2.18861i	0.484346	−	0.406415i	−0.367649	−	0.929965i	$-0.619837\pi$
$29$	2.60828	−	2.18861i	0.484346	−	0.406415i	0.851995	+	0.523550i	$0.175393\pi$
$30$	1.48689	+	0.888354i	0.271467	+	0.162190i
$31$	−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
$33$	3.32027	+	0.636775i	0.577984	+	0.110848i
$34$	0.706006	−	0.124488i	0.121079	−	0.0213495i
$35$	−1.09304	−	3.00310i	−0.184757	−	0.507617i
$36$	2.23945	+	1.99621i	0.373242	+	0.332701i
$37$		−	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	−0.879746	−	0.475444i	$-0.842287\pi$
$41$	−7.99149	+	2.90866i	−1.24806	+	0.454257i	−0.368315	+	0.929701i	$0.620065\pi$
$42$	−0.879598	−	5.46501i	−0.135725	−	0.843270i
$43$	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
$45$	−2.64176	+	1.42165i	−0.393810	+	0.211928i
$46$	−5.53047	−	3.19302i	−0.815423	−	0.470785i
$47$	7.46694	+	8.89875i	1.08916	+	1.29802i	0.951538	+	0.307532i	$0.0995030\pi$
$47$	7.46694	+	8.89875i	1.08916	+	1.29802i	0.137627	+	0.990484i	$0.456053\pi$
$48$	1.34332	−	1.09338i	0.193892	−	0.157816i
$49$	−1.60668	+	2.78284i	−0.229525	+	0.397549i
$50$	0.500000	+	0.866025i	0.0707107	+	0.122474i
$51$	−0.442084	+	1.16034i	−0.0619042	+	0.162480i
$52$	−4.64400	−	0.818863i	−0.644007	−	0.113556i
$53$	1.45006	+	8.22370i	0.199181	+	1.12961i	0.906337	+	0.422555i	$0.138867\pi$
$53$	1.45006	+	8.22370i	0.199181	+	1.12961i	−0.707156	+	0.707057i	$0.750022\pi$
$54$	−4.95756	+	1.55647i	−0.674638	+	0.211809i
$55$	1.49524	+	1.25465i	0.201618	+	0.169177i
$56$	−3.19583			−0.427061
$57$	7.04508	−	2.71419i	0.933144	−	0.359503i
$58$	3.40487			0.447082
$59$	5.27090	+	4.42281i	0.686213	+	0.575801i	0.917814	−	0.397010i	$-0.129952\pi$
$59$	5.27090	+	4.42281i	0.686213	+	0.575801i	−0.231602	+	0.972811i	$0.574397\pi$
$60$	0.567997	+	1.63627i	0.0733281	+	0.211242i
$61$	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
$63$	8.90724	+	3.54700i	1.12221	+	0.446880i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	2.35782	−	4.08387i	0.292452	−	0.506541i
$66$	2.13416	+	2.62202i	0.262697	+	0.322749i
$67$	−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
$69$	9.66066	−	5.38664i	1.16301	−	0.648475i
$70$	1.09304	−	3.00310i	0.130643	−	0.358939i
$71$	0.518843	−	2.94250i	0.0615753	−	0.349211i	−0.938418	−	0.345503i	$-0.887708\pi$
$71$	0.518843	−	2.94250i	0.0615753	−	0.349211i	0.999993	−	0.00370844i	$-0.00118043\pi$
$72$	0.432383	+	2.96868i	0.0509568	+	0.349862i
$73$	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
$78$	5.34307	−	6.17766i	0.604984	−	0.699482i
$79$	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
$81$	2.08977	−	8.75402i	0.232197	−	0.972669i
$82$	−7.99149	−	2.90866i	−0.882512	−	0.321208i
$83$	−9.58163	+	5.53196i	−1.05172	+	0.607211i	−0.923131	−	0.384486i	$-0.874379\pi$
$83$	−9.58163	+	5.53196i	−1.05172	+	0.607211i	−0.128590	+	0.991698i	$0.541045\pi$
$84$	2.83903	−	4.75184i	0.309764	−	0.518468i
$85$	−0.549175	+	0.460813i	−0.0595664	+	0.0499822i
$86$	4.23672	−	3.55503i	0.456857	−	0.383349i
$87$	−3.02473	+	5.06265i	−0.324285	+	0.542773i
$88$	1.69039	−	0.975946i	0.180196	−	0.104036i
$89$	14.0605	+	5.11762i	1.49041	+	0.542467i	0.953559	−	0.301207i	$-0.0973897\pi$
$89$	14.0605	+	5.11762i	1.49041	+	0.542467i	0.536856	+	0.843674i	$0.319612\pi$
$90$	−2.93753	−	0.609040i	−0.309643	−	0.0641985i
$91$	−14.8415	+	2.61695i	−1.55581	+	0.274331i
$92$	−2.18415	−	6.00091i	−0.227714	−	0.625638i
$93$	5.71427	−	6.60683i	0.592542	−	0.685097i
$94$			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
$99$	−5.79454	+	0.843965i	−0.582373	+	0.0848217i
$100$	−0.173648	+	0.984808i	−0.0173648	+	0.0984808i
$101$	−0.230724	+	0.633908i	−0.0229579	+	0.0630762i	−0.950642	−	0.310289i	$-0.899574\pi$
$101$	−0.230724	+	0.633908i	−0.0229579	+	0.0630762i	0.927684	+	0.373366i	$0.121796\pi$
$102$	−1.08451	+	0.604706i	−0.107382	+	0.0598748i
$103$	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
$105$	3.49426	+	4.29304i	0.341005	+	0.418958i
$106$	−4.17528	+	7.23180i	−0.405539	+	0.702414i
$107$	−0.316054	−	0.547422i	−0.0305541	−	0.0529213i	0.850344	−	0.526227i	$-0.176394\pi$
$107$	−0.316054	−	0.547422i	−0.0305541	−	0.0529213i	−0.880898	+	0.473306i	$0.843061\pi$
$108$	−4.79819	−	1.99433i	−0.461706	−	0.191905i
$109$	−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
$111$	1.52451	+	4.39176i	0.144700	+	0.416848i
$112$	−2.44815	−	2.05424i	−0.231328	−	0.194108i
$113$	12.9296			1.21632			0.608158	−	0.793816i	$-0.291909\pi$
$113$	12.9296			1.21632			0.608158	+	0.793816i	$0.291909\pi$
$114$	7.14149	+	2.44931i	0.668862	+	0.229398i
$115$	6.38603			0.595501
$116$	2.60828	+	2.18861i	0.242173	+	0.203207i
$117$	4.43893	+	13.4325i	0.410379	+	1.24183i
$118$	1.19482	+	6.77614i	0.109992	+	0.623794i
$119$	2.25628	+	0.397843i	0.206833	+	0.0364702i
$120$	−0.616663	+	1.61856i	−0.0562934	+	0.147753i
$121$	−3.59506	−	6.22683i	−0.326824	−	0.566075i
$122$	−1.38821	+	2.40444i	−0.125682	+	0.217688i
$123$	11.4241	−	9.29850i	1.03008	−	0.838418i
$124$	−3.24174	−	3.86335i	−0.291117	−	0.346939i
$125$	−0.866025	−	0.500000i	−0.0774597	−	0.0447214i
$126$	4.54337	+	8.44263i	0.404756	+	0.752129i
$127$	−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
$129$	1.52221	+	9.45764i	0.134023	+	0.832698i
$130$	4.43125	−	1.61284i	0.388647	−	0.141456i
$131$	5.81924	−	6.93510i	0.508429	−	0.605922i	−0.449375	−	0.893343i	$-0.648353\pi$
$131$	5.81924	−	6.93510i	0.508429	−	0.605922i	0.957804	+	0.287421i	$0.0927978\pi$
$132$	−0.0505432	+	3.38040i	−0.00439922	+	0.294226i
$133$	−7.36673	−	11.8231i	−0.638777	−	1.02519i
$134$		−	3.61463i		−	0.312256i
$135$	3.51514	−	3.82672i	0.302535	−	0.329352i
$136$	0.245193	+	0.673663i	0.0210252	+	0.0577662i
$137$	9.04085	−	1.59415i	0.772412	−	0.136197i	0.226468	−	0.974019i	$-0.427282\pi$
$137$	9.04085	−	1.59415i	0.772412	−	0.136197i	0.545944	+	0.837822i	$0.316171\pi$
$138$	10.8630	+	2.08335i	0.924717	+	0.177346i
$139$	−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
$141$	−17.2724	−	10.3196i	−1.45460	−	0.869063i
$142$	2.28886	−	1.92058i	0.192077	−	0.161172i
$143$	7.05100	−	5.91649i	0.589634	−	0.494762i
$144$	−1.57700	+	2.55207i	−0.131417	+	0.212672i
$145$	−2.94871	+	1.70244i	−0.244877	+	0.141380i
$146$	14.8952	+	5.42141i	1.23274	+	0.448679i
$147$	1.04831	−	5.46607i	0.0864629	−	0.450834i
$148$	2.64323	−	0.466073i	0.217272	−	0.0383110i
$149$	1.18324	+	3.25093i	0.0969350	+	0.266327i	0.978677	−	0.205405i	$-0.0658512\pi$
$149$	1.18324	+	3.25093i	0.0969350	+	0.266327i	−0.881742	+	0.471732i	$0.843629\pi$
$150$	−1.31003	−	1.13305i	−0.106964	−	0.0925134i
$151$			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
$156$	8.06395	−	1.29790i	0.645633	−	0.103915i
$157$	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
$159$	−7.04373	−	12.6326i	−0.558604	−	1.00183i
$160$	0.866025	+	0.500000i	0.0684653	+	0.0395285i
$161$	−13.1185	−	15.6340i	−1.03388	−	1.23213i
$162$	7.22783	−	5.36269i	0.567872	−	0.421332i
$163$	−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
$165$	−3.15925	−	1.20366i	−0.245947	−	0.0937048i
$166$	−10.8958	−	1.92123i	−0.845681	−	0.149116i
$167$	2.85785	+	16.2077i	0.221147	+	1.25419i	0.869915	+	0.493201i	$0.164173\pi$
$167$	2.85785	+	16.2077i	0.221147	+	1.25419i	−0.648768	+	0.760986i	$0.724716\pi$
$168$	5.22925	−	1.81522i	0.403445	−	0.140048i
$169$	−7.07617	−	5.93761i	−0.544321	−	0.456739i
$170$	−0.716898			−0.0549835
$171$	−9.98601	+	8.44273i	−0.763649	+	0.645631i
$172$	5.53064			0.421708
$173$	−11.4377	−	9.59737i	−0.869592	−	0.729675i	0.0944199	−	0.995532i	$-0.469900\pi$
$173$	−11.4377	−	9.59737i	−0.869592	−	0.729675i	−0.964012	+	0.265858i	$0.914345\pi$
$174$	−5.57129	+	1.93396i	−0.422358	+	0.146613i
$175$	0.554951	+	3.14728i	0.0419503	+	0.237912i
$176$	1.92224	+	0.338942i	0.144894	+	0.0255487i
$177$	−11.1368	−	4.24305i	−0.837090	−	0.318927i
$178$	7.48146	+	12.9583i	0.560759	+	0.971263i
$179$	12.2004	−	21.1316i	0.911898	−	1.57945i	0.100518	−	0.994935i	$-0.467950\pi$
$179$	12.2004	−	21.1316i	0.911898	−	1.57945i	0.811380	−	0.584518i	$-0.198717\pi$
$180$	−1.85879	−	2.35476i	−0.138546	−	0.175513i
$181$	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
$183$	−2.34191	−	4.20010i	−0.173119	−	0.310480i
$184$	2.18415	−	6.00091i	0.161018	−	0.442393i
$185$	−0.466073	+	2.64323i	−0.0342664	+	0.194334i
$186$	8.62417	−	1.38807i	0.632355	−	0.101778i
$187$	−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	$-0.964159\pi$
$191$		−	3.10573i		−	0.224723i	0.993667	−	0.112362i	$-0.0358415\pi$
$192$	1.31003	+	1.13305i	0.0945436	+	0.0817710i
$193$	−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
$195$	−1.53841	+	8.02154i	−0.110168	+	0.574435i
$196$	−3.01956	−	1.09903i	−0.215683	−	0.0785022i
$197$	−1.31650	+	0.760079i	−0.0937964	+	0.0541534i	−0.546165	−	0.837678i	$-0.683913\pi$
$197$	−1.31650	+	0.760079i	−0.0937964	+	0.0541534i	0.452368	+	0.891831i	$0.350579\pi$
$198$	−4.98136	−	3.07814i	−0.354010	−	0.218754i
$199$	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
$201$	5.37454	+	3.21107i	0.379091	+	0.226491i
$202$	−0.584213	+	0.337296i	−0.0411051	+	0.0237320i
$203$	10.2252	+	3.72166i	0.717667	+	0.261209i
$204$	−1.21948	−	0.233877i	−0.0853806	−	0.0163747i
$205$	8.37516	−	1.47677i	0.584947	−	0.103142i
$206$	5.20254	+	14.2939i	0.362478	+	0.995901i
$207$	−12.7479	+	14.3012i	−0.886037	+	0.994004i
$208$		−	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
$213$	0.822367	+	5.10943i	0.0563477	+	0.350093i
$214$	0.109764	−	0.622505i	0.00750334	−	0.0425536i
$215$	−1.89159	+	5.19710i	−0.129005	+	0.354440i
$216$	−2.39370	−	4.61196i	−0.162870	−	0.313804i
$217$	−13.9581	−	8.05869i	−0.947535	−	0.547060i
$218$	−11.0734	−	13.1967i	−0.749983	−	0.893795i
$219$	−21.2932	+	17.3313i	−1.43886	+	1.17114i
$220$	−0.975946	+	1.69039i	−0.0657983	+	0.113966i
$221$	1.69032	+	2.92771i	0.113703	+	0.196939i
$222$	−1.65513	+	4.34422i	−0.111085	+	0.291565i
$223$	−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
$225$	2.84849	−	0.941320i	0.189900	−	0.0627546i
$226$	9.90466	+	8.31100i	0.658848	+	0.552839i
$227$	9.55737			0.634345			0.317172	−	0.948368i	$-0.397267\pi$
$227$	9.55737			0.634345			0.317172	+	0.948368i	$0.397267\pi$
$228$	3.89632	+	6.46674i	0.258040	+	0.428270i
$229$	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
$231$	3.54312	+	10.2069i	0.233120	+	0.671566i
$232$	0.591250	+	3.35314i	0.0388175	+	0.220145i
$233$	4.44201	+	0.783247i	0.291006	+	0.0513122i	0.317245	−	0.948343i	$-0.397242\pi$
$233$	4.44201	+	0.783247i	0.291006	+	0.0513122i	−0.0262394	+	0.999656i	$0.508353\pi$
$234$	−5.23382	+	13.1432i	−0.342145	+	0.859195i
$235$	−5.80825	−	10.0602i	−0.378888	−	0.656254i
$236$	−3.44033	+	5.95883i	−0.223947	+	0.387887i
$237$	−10.7188	−	13.1691i	−0.696260	−	0.855424i
$238$	1.47268	+	1.75507i	0.0954598	+	0.113765i
$239$	−2.66473	−	1.53848i	−0.172367	−	0.0995160i	0.411335	−	0.911484i	$-0.365063\pi$
$239$	−2.66473	−	1.53848i	−0.172367	−	0.0995160i	−0.583701	+	0.811968i	$0.698396\pi$
$240$	−1.51278	+	0.843503i	−0.0976495	+	0.0544479i
$241$	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
$243$	1.55282	+	15.5109i	0.0996137	+	0.995026i
$244$	−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
$249$	12.5360	−	14.4941i	0.794437	−	0.918527i
$250$	−0.342020	−	0.939693i	−0.0216313	−	0.0594314i
$251$	−14.3906	+	2.53746i	−0.908330	+	0.160163i	−0.608245	−	0.793749i	$-0.708126\pi$
$251$	−14.3906	+	2.53746i	−0.908330	+	0.160163i	−0.300085	+	0.953913i	$0.597015\pi$
$252$	−1.94639	+	9.38785i	−0.122611	+	0.591379i
$253$	11.7131	+	4.26323i	0.736398	+	0.268027i
$254$	−18.6132	+	10.7463i	−1.16790	+	0.674286i
$255$	0.636859	−	1.06594i	0.0398816	−	0.0667520i
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−23.1276	+	19.4064i	−1.44266	+	1.21054i	−0.504937	+	0.863156i	$0.668484\pi$
$257$	−23.1276	+	19.4064i	−1.44266	+	1.21054i	−0.937724	+	0.347380i	$0.887071\pi$
$258$	−4.91317	+	8.22343i	−0.305880	+	0.511968i
$259$	7.42846	−	4.28882i	0.461582	−	0.266494i
$260$	4.43125	+	1.61284i	0.274815	+	0.100024i
$261$	2.07370	−	10.0019i	0.128359	−	0.619102i
$262$	8.91559	−	1.57206i	0.550807	−	0.0971221i
$263$	−5.63636	−	15.4858i	−0.347553	−	0.954893i	−0.983138	−	0.182863i	$-0.941464\pi$
$263$	−5.63636	−	15.4858i	−0.347553	−	0.954893i	0.635586	−	0.772030i	$-0.280759\pi$
$264$	−2.21160	+	2.55705i	−0.136114	+	0.157375i
$265$		−	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	−0.544898	−	0.838502i	$-0.683432\pi$
$269$	−6.94321	+	2.52712i	−0.423335	+	0.154081i	0.121563	+	0.992584i	$0.461209\pi$
$270$	5.15252	−	0.671954i	0.313572	−	0.0408938i
$271$	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
$273$	22.7982	−	12.7119i	1.37981	−	0.769362i
$274$	7.95039	+	4.59016i	0.480301	+	0.277302i
$275$	−1.25465	−	1.49524i	−0.0756584	−	0.0901661i
$276$	6.98236	+	8.57851i	0.420289	+	0.516366i
$277$	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
$279$	−5.59742	+	14.0563i	−0.335109	+	0.841526i
$280$	3.14728	+	0.554951i	0.188086	+	0.0331646i
$281$	1.16816	+	6.62495i	0.0696864	+	0.395211i	0.999622	+	0.0274891i	$0.00875116\pi$
$281$	1.16816	+	6.62495i	0.0696864	+	0.395211i	−0.929936	+	0.367722i	$0.880138\pi$
$282$	−6.59813	−	19.0077i	−0.392913	−	1.13189i
$283$	−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
$285$	−7.40937	+	1.44958i	−0.438893	+	0.0858660i
$286$	9.20442			0.544269
$287$	−20.8200	−	17.4700i	−1.22896	−	1.03122i
$288$	−2.84849	+	0.941320i	−0.167849	+	0.0554678i
$289$	2.86277	+	16.2356i	0.168398	+	0.955035i
$290$	−3.35314	−	0.591250i	−0.196903	−	0.0347194i
$291$	−4.81108	+	12.6277i	−0.282031	+	0.740246i
$292$	7.92557	+	13.7275i	0.463809	+	0.803341i
$293$	−8.58349	+	14.8670i	−0.501453	+	0.868542i	0.498545	+	0.866864i	$0.333868\pi$
$293$	−8.58349	+	14.8670i	−0.501453	+	0.868542i	−0.999999	+	0.00167870i	$0.999466\pi$
$294$	4.31657	−	3.51341i	0.251748	−	0.204906i
$295$	−4.42281	−	5.27090i	−0.257506	−	0.306884i
$296$	2.32442	+	1.34200i	0.135104	+	0.0780024i
$297$	9.00206	−	4.67224i	0.522352	−	0.271111i
$298$	−1.18324	+	3.25093i	−0.0685434	+	0.188321i
$299$	5.22928	−	29.6567i	0.302417	−	1.71509i
$300$	−0.275233	−	1.71004i	−0.0158906	−	0.0987294i
$301$	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
$306$	1.43108	−	1.60546i	0.0818092	−	0.0917780i
$307$	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
$309$	−25.8750	−	4.96243i	−1.47198	−	0.282303i
$310$	4.73910	+	1.72489i	0.269163	+	0.0979673i
$311$	7.00115	−	4.04212i	0.396999	−	0.229207i	−0.288189	−	0.957573i	$-0.593053\pi$
$311$	7.00115	−	4.04212i	0.396999	−	0.229207i	0.685188	+	0.728366i	$0.259720\pi$
$312$	7.01162	+	4.18916i	0.396955	+	0.237164i
$313$	−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
$315$	−8.15599	−	5.03984i	−0.459538	−	0.283963i
$316$	−8.48995	+	4.90167i	−0.477597	+	0.275741i
$317$	7.25183	+	2.63945i	0.407303	+	0.148246i	0.537543	−	0.843236i	$-0.319352\pi$
$317$	7.25183	+	2.63945i	0.407303	+	0.148246i	−0.130240	+	0.991483i	$0.541575\pi$
$318$	2.72424	−	14.2047i	0.152768	−	0.796561i
$319$	−6.54498	+	1.15406i	−0.366448	+	0.0646147i
$320$	0.342020	+	0.939693i	0.0191195	+	0.0525304i
$321$	0.828084	+	0.716212i	0.0462191	+	0.0399751i
$322$		−	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
$327$	29.4591	−	4.74146i	1.62909	−	0.262204i
$328$	1.47677	−	8.37516i	0.0815408	−	0.462441i
$329$	−12.6973	+	34.8855i	−0.700024	+	1.92330i
$330$	−1.64643	−	2.95278i	−0.0906328	−	0.162545i
$331$	−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
$333$	−4.98902	−	6.32019i	−0.273396	−	0.346344i
$334$	−8.22885	+	14.2528i	−0.450263	+	0.779878i
$335$	1.80731	+	3.13036i	0.0987442	+	0.171030i
$336$	5.17264	+	1.97075i	0.282191	+	0.107513i
$337$	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
$339$	−21.1563	+	7.34399i	−1.14905	+	0.398871i
$340$	−0.549175	−	0.460813i	−0.0297832	−	0.0249911i
$341$	9.84388			0.533076
$342$	−13.0766	+	0.0486220i	−0.707102	+	0.00262918i
$343$	12.1015			0.653420
$344$	4.23672	+	3.55503i	0.228429	+	0.191674i
$345$	−10.4493	+	3.62725i	−0.562570	+	0.195284i
$346$	−2.59272	−	14.7040i	−0.139385	−	0.790493i
$347$	25.1090	+	4.42739i	1.34792	+	0.237675i	0.800575	−	0.599233i	$-0.204528\pi$
$347$	25.1090	+	4.42739i	1.34792	+	0.237675i	0.547345	+	0.836907i	$0.315639\pi$
$348$	−5.51098	−	2.09966i	−0.295420	−	0.112553i
$349$	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
$351$	−14.8929	−	19.4579i	−0.794924	−	1.03858i
$352$	1.25465	+	1.49524i	0.0668732	+	0.0796963i
$353$	−18.4954	−	10.6783i	−0.984408	−	0.568348i	−0.0808102	−	0.996730i	$-0.525751\pi$
$353$	−18.4954	−	10.6783i	−0.984408	−	0.568348i	−0.903598	+	0.428381i	$0.859084\pi$
$354$	−5.80387	−	10.4089i	−0.308472	−	0.553229i
$355$	−1.02192	+	2.80770i	−0.0542379	+	0.149018i
$356$	−2.59828	+	14.7356i	−0.137709	+	0.780985i
$357$	−3.91785	+	0.630582i	−0.207355	+	0.0333739i
$358$	22.9292	−	8.34554i	1.21184	−	0.441076i
$359$	9.49926	−	11.3208i	0.501352	−	0.597488i	−0.454715	−	0.890637i	$-0.650259\pi$
$359$	9.49926	−	11.3208i	0.501352	−	0.597488i	0.956067	+	0.293149i	$0.0947033\pi$
$360$	0.0896911	−	2.99866i	0.00472714	−	0.158043i
$361$	18.9571	−	1.27659i	0.997740	−	0.0671888i
$362$			5.99897i			0.315299i
$363$	9.41931	+	8.14678i	0.494385	+	0.427595i
$364$	−5.15438	−	14.1616i	−0.270163	−	0.742267i
$365$	−15.6103	+	2.75252i	−0.817082	+	0.144074i
$366$	0.905763	−	4.72282i	0.0473450	−	0.246866i
$367$	−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
$369$	−13.4114	+	21.7037i	−0.698171	+	1.12985i
$370$	−2.05607	+	1.72525i	−0.106890	+	0.0896913i
$371$	−20.4434	+	17.1541i	−1.06137	+	0.890595i
$372$	7.49873	+	4.48019i	0.388791	+	0.232287i
$373$	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
$375$	1.70105	+	0.326235i	0.0878418	+	0.0168467i
$376$	−11.4400	+	2.01718i	−0.589974	+	0.104028i
$377$	5.49153	+	15.0879i	0.282828	+	0.777064i
$378$	−12.2296	−	11.2338i	−0.629021	−	0.577804i
$379$			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	−0.915901	−	0.401404i	$-0.868522\pi$
$383$	−26.6060	+	9.68380i	−1.35950	+	0.494819i	−0.443604	+	0.896223i	$0.646300\pi$
$384$	0.275233	+	1.71004i	0.0140454	+	0.0872653i
$385$	−1.08320	+	6.14315i	−0.0552052	+	0.313084i
$386$	2.97324	−	8.16892i	0.151334	−	0.415787i
$387$	−7.86266	−	14.6106i	−0.399682	−	0.742700i
$388$	6.75656	+	3.90090i	0.343012	+	0.198038i
$389$	15.2779	+	18.2074i	0.774618	+	0.923154i	0.998677	−	0.0514219i	$-0.0163753\pi$
$389$	15.2779	+	18.2074i	0.774618	+	0.923154i	−0.224059	+	0.974576i	$0.571931\pi$
$390$	−6.33464	+	5.15599i	−0.320767	+	0.261084i
$391$	−2.28907	+	3.96478i	−0.115763	+	0.200507i
$392$	−1.60668	−	2.78284i	−0.0811494	−	0.140555i
$393$	−5.58273	+	14.6530i	−0.281611	+	0.739146i
$394$	−1.49706	−	0.263973i	−0.0754210	−	0.0132987i
$395$	−1.70233	−	9.65441i	−0.0856537	−	0.485766i
$396$	−1.83735	−	5.55995i	−0.0923305	−	0.279398i
$397$	−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
$399$	18.7694	+	15.1614i	0.939647	+	0.759022i
$400$	−1.00000			−0.0500000
$401$	3.74015	+	3.13836i	0.186774	+	0.156722i	0.731380	−	0.681970i	$-0.238876\pi$
$401$	3.74015	+	3.13836i	0.186774	+	0.156722i	−0.544606	+	0.838692i	$0.683321\pi$
$402$	2.05310	+	5.91451i	0.102399	+	0.294989i
$403$	−4.12973	−	23.4209i	−0.205716	−	1.16668i
$404$	−0.664343	−	0.117142i	−0.0330523	−	0.00582801i
$405$	−3.57814	+	8.25814i	−0.177799	+	0.410350i
$406$	5.44070	+	9.42357i	0.270017	+	0.467684i
$407$	−2.61945	+	4.53701i	−0.129841	+	0.224891i
$408$	−0.783842	−	0.963026i	−0.0388059	−	0.0476769i
$409$	−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
$411$	−13.8878	+	7.74363i	−0.685035	+	0.381965i
$412$	−5.20254	+	14.2939i	−0.256311	+	0.704209i
$413$	−3.81843	+	21.6554i	−0.187893	+	1.06559i
$414$	−18.9581	+	2.76121i	−0.931738	+	0.135706i
$415$	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	$-0.982878\pi$
$419$		−	2.20101i		−	0.107526i	0.998554	−	0.0537631i	$-0.0171216\pi$
$420$	−3.62105	+	4.18665i	−0.176689	+	0.204288i
$421$	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
$423$	34.1238	+	7.07491i	1.65915	+	0.343994i
$424$	−7.84696	−	2.85606i	−0.381082	−	0.138703i
$425$	0.620852	−	0.358449i	0.0301157	−	0.0173873i
$426$	−2.65431	+	4.44266i	−0.128602	+	0.215248i
$427$	−6.79708	+	5.70342i	−0.328934	+	0.276008i
$428$	0.484223	−	0.406311i	0.0234058	−	0.0196398i
$429$	−8.17679	+	13.6859i	−0.394779	+	0.660763i
$430$	−4.78968	+	2.76532i	−0.230979	+	0.133356i
$431$	−1.16742	−	0.424907i	−0.0562327	−	0.0204670i	0.313751	−	0.949505i	$-0.398414\pi$
$431$	−1.16742	−	0.424907i	−0.0562327	−	0.0204670i	−0.369983	+	0.929038i	$0.620637\pi$
$432$	1.13084	−	5.07161i	0.0544074	−	0.244008i
$433$	−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
$435$	3.85790	−	4.46050i	0.184972	−	0.213865i
$436$		−	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
$441$	1.38940	+	9.53940i	0.0661619	+	0.454257i
$442$	−0.587041	+	3.32927i	−0.0279227	+	0.158357i
$443$	2.04397	−	5.61576i	0.0971119	−	0.266813i	−0.881619	−	0.471962i	$-0.843546\pi$
$443$	2.04397	−	5.61576i	0.0971119	−	0.266813i	0.978731	+	0.205149i	$0.0657681\pi$
$444$	−4.06031	+	2.26397i	−0.192694	+	0.107443i
$445$	−12.9583	−	7.48146i	−0.614281	−	0.354655i
$446$	−0.862686	−	1.02811i	−0.0408494	−	0.0486824i
$447$	−3.78263	−	4.64733i	−0.178912	−	0.219811i
$448$	1.59792	−	2.76767i	0.0754945	−	0.130760i
$449$	−4.22124	−	7.31140i	−0.199213	−	0.345046i	0.749061	−	0.662501i	$-0.230505\pi$
$449$	−4.22124	−	7.31140i	−0.199213	−	0.345046i	−0.948273	+	0.317455i	$0.897172\pi$
$450$	2.78714	+	1.10988i	0.131387	+	0.0523204i
$451$	16.3474	+	2.88249i	0.769770	+	0.135731i
$452$	2.24520	+	12.7332i	0.105606	+	0.598919i
$453$	−2.77854	−	8.00435i	−0.130547	−	0.376077i
$454$	7.32137	+	6.14336i	0.343609	+	0.288322i
$455$	15.0704			0.706512
$456$	−1.17199	+	7.45831i	−0.0548834	+	0.349268i
$457$	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
$459$	1.11583	+	3.55406i	0.0520825	+	0.165889i
$460$	1.10892	+	6.28901i	0.0517038	+	0.293227i
$461$	20.7143	+	3.65249i	0.964760	+	0.170113i	0.633770	−	0.773521i	$-0.281506\pi$
$461$	20.7143	+	3.65249i	0.964760	+	0.170113i	0.330990	+	0.943634i	$0.392618\pi$
$462$	−3.84669	+	10.0964i	−0.178964	+	0.469728i
$463$	−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
$465$	−6.77472	+	5.51419i	−0.314170	+	0.255714i
$466$	2.89932	+	3.45527i	0.134308	+	0.160062i
$467$	−19.2520	−	11.1152i	−0.890878	−	0.514349i	−0.0166487	−	0.999861i	$-0.505300\pi$
$467$	−19.2520	−	11.1152i	−0.890878	−	0.514349i	−0.874230	+	0.485512i	$0.838633\pi$
$468$	−12.4576	+	6.70402i	−0.575853	+	0.309893i
$469$	3.95093	−	10.8551i	0.182437	−	0.501242i
$470$	2.01718	−	11.4400i	0.0930457	−	0.527688i
$471$	0.157666	+	0.979591i	0.00726486	+	0.0451372i
$472$	−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
$477$	18.7007	+	16.6695i	0.856246	+	0.763242i
$478$	−1.05238	−	2.89140i	−0.0481349	−	0.132249i
$479$	25.7421	−	4.53902i	1.17619	−	0.207393i	0.448806	−	0.893629i	$-0.351849\pi$
$479$	25.7421	−	4.53902i	1.17619	−	0.207393i	0.727379	+	0.686236i	$0.240738\pi$
$480$	−1.70105	−	0.326235i	−0.0776420	−	0.0148905i
$481$	11.8935	+	4.32889i	0.542298	+	0.197380i
$482$	13.1343	−	7.58311i	0.598252	−	0.345401i
$483$	30.3454	+	18.1301i	1.38076	+	0.824950i
$484$	5.50795	−	4.62172i	0.250361	−	0.210078i
$485$	−5.97653	+	5.01490i	−0.271380	+	0.227715i
$486$	−8.78070	+	12.8802i	−0.398301	+	0.584257i
$487$	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
$489$	6.13355	−	31.9815i	0.277369	−	1.44625i
$490$	3.16453	−	0.557993i	0.142959	−	0.0252075i
$491$	−14.4564	−	39.7185i	−0.652406	−	1.79247i	−0.608663	−	0.793428i	$-0.708294\pi$
$491$	−14.4564	−	39.7185i	−0.652406	−	1.79247i	−0.0437427	−	0.999043i	$-0.513928\pi$
$492$	11.1410	+	9.63589i	0.502276	+	0.434420i
$493$		−	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
$498$	18.9198	−	3.04515i	0.847815	−	0.136457i
$499$	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
$501$	−13.8821	−	24.8969i	−0.620207	−	1.11231i
$502$	−12.6549	−	7.30632i	−0.564817	−	0.326097i
$503$	−9.70464	−	11.5655i	−0.432708	−	0.515682i	0.504993	−	0.863123i	$-0.331495\pi$
$503$	−9.70464	−	11.5655i	−0.432708	−	0.515682i	−0.937702	+	0.347441i	$0.887051\pi$
$504$	−7.52542	+	5.94039i	−0.335209	+	0.264606i
$505$	0.337296	−	0.584213i	0.0150095	−	0.0259971i
$506$	6.23242	+	10.7949i	0.277065	+	0.479891i
$507$	14.9511	+	5.69629i	0.664000	+	0.252981i
$508$	−21.1662	−	3.73217i	−0.939097	−	0.165588i
$509$	3.31006	+	18.7723i	0.146716	+	0.832068i	0.965973	+	0.258642i	$0.0832749\pi$
$509$	3.31006	+	18.7723i	0.146716	+	0.832068i	−0.819257	+	0.573426i	$0.805614\pi$
$510$	1.17304	−	0.407196i	0.0519430	−	0.0180309i
$511$	38.8060	+	32.5621i	1.71668	+	1.44046i
$512$	1.00000			0.0441942
$513$	11.5444	−	19.4866i	0.509696	−	0.860355i
$514$	−30.1910			−1.33167
$515$	−11.6525	−	9.77759i	−0.513469	−	0.430852i
$516$	−9.04962	+	3.14139i	−0.398388	+	0.138292i
$517$	−3.93732	−	22.3297i	−0.173163	−	0.982057i
$518$	8.44733	+	1.48949i	0.371154	+	0.0654445i
$519$	24.1664	+	9.20731i	1.06079	+	0.404156i
$520$	2.35782	+	4.08387i	0.103397	+	0.179089i
$521$	−5.67793	+	9.83447i	−0.248755	+	0.430856i	−0.963181	−	0.268855i	$-0.913355\pi$
$521$	−5.67793	+	9.83447i	−0.248755	+	0.430856i	0.714426	+	0.699711i	$0.246688\pi$
$522$	8.01765	−	6.32895i	0.350923	−	0.277011i
$523$	−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
$525$	−2.69570	−	4.83459i	−0.117650	−	0.210999i
$526$	5.63636	−	15.4858i	0.245757	−	0.675212i
$527$	−0.627824	+	3.56057i	−0.0273484	+	0.155101i
$528$	−3.33782	+	0.537225i	−0.145260	+	0.0233797i
$529$	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
$534$	−19.6019	−	16.9538i	−0.848259	−	0.733662i
$535$	0.216194	+	0.593988i	0.00934687	+	0.0256803i
$536$	3.55972	−	0.627674i	0.153756	−	0.0271114i
$537$	−7.96037	+	41.5069i	−0.343515	+	1.79115i
$538$	−6.94321	−	2.52712i	−0.299343	−	0.108952i
$539$	5.43181	−	3.13606i	0.233965	−	0.135080i
$540$	4.37898	+	2.79723i	0.188441	+	0.120374i
$541$	−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
$543$	−8.91977	−	5.32921i	−0.382784	−	0.228698i
$544$	−0.620852	+	0.358449i	−0.0266188	+	0.0153684i
$545$	16.1882	+	5.89202i	0.693426	+	0.252386i
$546$	25.6355	+	4.91649i	1.09710	+	0.210407i
$547$	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
$549$	6.21765	+	5.54230i	0.265363	+	0.236540i
$550$		−	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
$555$	−0.738727	−	4.58977i	−0.0313572	−	0.194825i
$556$	0.535615	−	3.03763i	0.0227151	−	0.128824i
$557$	−2.11094	+	5.79975i	−0.0894432	+	0.245743i	−0.976346	−	0.216212i	$-0.930630\pi$
$557$	−2.11094	+	5.79975i	−0.0894432	+	0.245743i	0.886903	+	0.461955i	$0.152852\pi$
$558$	−13.3231	+	7.16976i	−0.564010	+	0.303520i
$559$	22.5864	+	13.0403i	0.955303	+	0.551545i
$560$	2.05424	+	2.44815i	0.0868076	+	0.103453i
$561$	1.87972	−	1.52997i	0.0793620	−	0.0645956i
$562$	−3.36357	+	5.82588i	−0.141884	+	0.245750i
$563$	21.0082	+	36.3873i	0.885391	+	1.53354i	0.845264	+	0.534348i	$0.179443\pi$
$563$	21.0082	+	36.3873i	0.885391	+	1.53354i	0.0401269	+	0.999195i	$0.487224\pi$
$564$	7.16346	−	18.8020i	0.301636	−	0.791705i
$565$	−12.7332	−	2.24520i	−0.535689	−	0.0944564i
$566$	−0.342964	−	1.94505i	−0.0144159	−	0.0817564i
$567$	27.5675	−	8.20438i	1.15773	−	0.344552i
$568$	2.28886	+	1.92058i	0.0960385	+	0.0805859i
$569$	15.1025			0.633129			0.316565	−	0.948571i	$-0.397471\pi$
$569$	15.1025			0.633129			0.316565	+	0.948571i	$0.397471\pi$
$570$	−6.60768	−	3.65220i	−0.276765	−	0.152974i
$571$	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
$573$	1.76405	+	5.08182i	0.0736942	+	0.212296i
$574$	−4.71950	−	26.7656i	−0.196988	−	1.11718i
$575$	−6.28901	−	1.10892i	−0.262270	−	0.0462453i
$576$	−2.78714	−	1.10988i	−0.116131	−	0.0462452i
$577$	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
$579$	9.50495	+	11.6778i	0.395012	+	0.485311i
$580$	−2.18861	−	2.60828i	−0.0908771	−	0.108303i
$581$	−30.6213	−	17.6792i	−1.27039	−	0.733458i
$582$	−11.8024	+	6.58084i	−0.489225	+	0.272785i
$583$	5.57472	−	15.3164i	0.230881	−	0.634341i
$584$	−2.75252	+	15.6103i	−0.113900	+	0.645960i
$585$	−2.03896	−	13.9992i	−0.0843008	−	0.578797i
$586$	−16.1317	+	5.87146i	−0.666394	+	0.242548i
$587$	15.2881	−	18.2197i	0.631009	−	0.752008i	−0.351912	−	0.936033i	$-0.614468\pi$
$587$	15.2881	−	18.2197i	0.631009	−	0.752008i	0.982921	+	0.184025i	$0.0589129\pi$
$588$	5.56507	+	0.0832081i	0.229499	+	0.00343144i
$589$	18.6576	−	11.6252i	0.768774	−	0.479009i
$590$		−	6.88067i		−	0.283273i
$591$	1.72242	−	1.99146i	0.0708508	−	0.0819177i
$592$	0.917985	+	2.52214i	0.0377289	+	0.103659i
$593$	19.5088	−	3.43992i	0.801129	−	0.141261i	0.241929	−	0.970294i	$-0.422220\pi$
$593$	19.5088	−	3.43992i	0.801129	−	0.141261i	0.559199	+	0.829033i	$0.311109\pi$
$594$	9.89923	+	2.20727i	0.406170	+	0.0905654i
$595$	−2.15292	−	0.783597i	−0.0882610	−	0.0321244i
$596$	−2.99608	+	1.72979i	−0.122724	+	0.0708548i
$597$	−6.15162	+	10.2963i	−0.251769	+	0.421399i
$598$	23.0689	−	19.3571i	0.943355	−	0.791569i
$599$	13.8537	−	11.6247i	0.566048	−	0.474971i	−0.314284	−	0.949329i	$-0.601764\pi$
$599$	13.8537	−	11.6247i	0.566048	−	0.474971i	0.880332	+	0.474358i	$0.157320\pi$
$600$	0.888354	−	1.48689i	0.0362669	−	0.0607018i
$601$	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
$603$	−10.6181	−	2.20145i	−0.432401	−	0.0896502i
$604$	−4.81751	+	0.849457i	−0.196022	+	0.0345639i
$605$	2.45917	+	6.75650i	0.0999793	+	0.274691i
$606$	0.764347	−	0.883738i	0.0310495	−	0.0358994i
$607$			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
$612$	2.12824	−	0.309974i	0.0860289	−	0.0125300i
$613$	−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
$615$	−12.8652	+	7.17346i	−0.518776	+	0.289262i
$616$	5.40220	+	3.11896i	0.217661	+	0.125667i
$617$	−0.675049	−	0.804492i	−0.0271764	−	0.0323876i	0.752285	−	0.658838i	$-0.228952\pi$
$617$	−0.675049	−	0.804492i	−0.0271764	−	0.0323876i	−0.779461	+	0.626450i	$0.784507\pi$
$618$	−16.6316	−	20.4336i	−0.669023	−	0.821960i
$619$	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
$621$	12.7359	−	30.6414i	0.511073	−	1.22960i
$622$	7.96142	+	1.40381i	0.319224	+	0.0562878i
$623$	8.30368	+	47.0925i	0.332680	+	1.88672i
$624$	2.67847	+	7.71606i	0.107225	+	0.308890i
$625$	0.766044	+	0.642788i	0.0306418	+	0.0257115i
$626$	−20.1464			−0.805212
$627$	−14.5578	−	2.28759i	−0.581383	−	0.0913577i
$628$	0.572846			0.0228590
$629$	−1.47399	−	1.23683i	−0.0587719	−	0.0493155i
$630$	−3.00830	−	9.10331i	−0.119854	−	0.362685i
$631$	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
$633$	7.92858	−	20.8102i	0.315133	−	0.827130i
$634$	3.85862	+	6.68332i	0.153245	+	0.265429i
$635$	10.7463	−	18.6132i	0.426456	−	0.738643i
$636$	11.2175	−	9.13034i	0.444803	−	0.362041i
$637$	−9.74017	−	11.6079i	−0.385920	−	0.459921i
$638$	−5.75555	−	3.32297i	−0.227865	−	0.131558i
$639$	−4.24776	−	7.89331i	−0.168039	−	0.312254i
$640$	−0.342020	+	0.939693i	−0.0135195	+	0.0371446i
$641$	−0.773044	+	4.38415i	−0.0305334	+	0.173163i	−0.996261	−	0.0863940i	$-0.972466\pi$
$641$	−0.773044	+	4.38415i	−0.0305334	+	0.173163i	0.965728	+	0.259558i	$0.0835767\pi$
$642$	0.173977	+	1.08093i	0.00686632	+	0.0426610i
$643$	−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	$-0.863812\pi$
$647$		−	21.1076i		−	0.829824i	0.909862	−	0.414912i	$-0.136188\pi$
$648$	6.53632	+	6.18681i	0.256771	+	0.243041i
$649$	−4.59344	−	12.6204i	−0.180308	−	0.495393i
$650$	−4.64400	+	0.818863i	−0.182153	+	0.0321184i
$651$	27.4165	+	5.25805i	1.07454	+	0.206079i
$652$	−17.6672	−	6.43032i	−0.691900	−	0.251831i
$653$	−16.1720	+	9.33691i	−0.632859	+	0.365382i	−0.781859	−	0.623456i	$-0.785728\pi$
$653$	−16.1720	+	9.33691i	−0.632859	+	0.365382i	0.148999	+	0.988837i	$0.452395\pi$
$654$	25.6147	+	15.3038i	1.00161	+	0.598425i
$655$	−6.93510	+	5.81924i	−0.270977	+	0.227376i
$656$	6.51472	−	5.46650i	0.254357	−	0.213431i
$657$	24.9973	−	40.4532i	0.975239	−	1.57823i
$658$	−32.1506	+	18.5622i	−1.25336	+	0.723629i
$659$	27.1056	+	9.86562i	1.05588	+	0.384310i	0.810880	−	0.585213i	$-0.198989\pi$
$659$	27.1056	+	9.86562i	1.05588	+	0.384310i	0.245003	+	0.969522i	$0.421211\pi$
$660$	0.636775	−	3.32027i	0.0247864	−	0.129241i
$661$	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
$663$	−4.42875	−	3.83044i	−0.171998	−	0.148762i
$664$		−	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
$669$	2.29505	−	0.369390i	0.0887318	−	0.0142815i
$670$	−0.627674	+	3.55972i	−0.0242492	+	0.137524i
$671$	1.85350	−	5.09244i	0.0715534	−	0.196591i
$672$	2.69570	+	4.83459i	0.103989	+	0.186498i
$673$	−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
$675$	−4.12624	+	3.15819i	−0.158819	+	0.121559i
$676$	4.61864	−	7.99972i	0.177640	−	0.307682i
$677$	−5.39833	−	9.35018i	−0.207475	−	0.359357i	0.743444	−	0.668799i	$-0.233191\pi$
$677$	−5.39833	−	9.35018i	−0.207475	−	0.359357i	−0.950918	+	0.309442i	$0.899858\pi$
$678$	−20.9273	−	7.97321i	−0.803709	−	0.306209i
$679$	24.5545	+	4.32961i	0.942314	+	0.166155i
$680$	−0.124488	−	0.706006i	−0.00477390	−	0.0270741i
$681$	−15.6384	+	5.42856i	−0.599266	+	0.208023i
$682$	7.54085	+	6.32752i	0.288754	+	0.242293i
$683$	−36.7225			−1.40515			−0.702574	−	0.711611i	$-0.747966\pi$
$683$	−36.7225			−1.40515			−0.702574	+	0.711611i	$0.747966\pi$
$684$	−10.0485	−	8.36823i	−0.384215	−	0.319967i
$685$	−9.18032			−0.350762
$686$	9.27029	+	7.77869i	0.353941	+	0.296992i
$687$	−18.3053	+	6.35431i	−0.698391	+	0.242432i
$688$	0.960386	+	5.44662i	0.0366144	+	0.207650i
$689$	−38.7800	−	6.83796i	−1.47740	−	0.260506i
$690$	−10.3362	−	3.93803i	−0.393491	−	0.149918i
$691$	−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
$693$	−11.5950	−	14.6888i	−0.440458	−	0.557981i
$694$	16.3887	+	19.5313i	0.622107	+	0.741398i
$695$	2.67124	+	1.54224i	0.101326	+	0.0585006i
$696$	−2.87202	−	5.15082i	−0.108864	−	0.195241i
$697$	−2.08521	+	5.72908i	−0.0789831	+	0.217004i
$698$	−2.81730	+	15.9777i	−0.106636	+	0.604765i
$699$	−7.71322	+	1.24145i	−0.291741	+	0.0469559i
$700$	−3.00310	+	1.09304i	−0.113507	+	0.0413130i
$701$	32.7243	−	38.9993i	1.23598	−	1.47298i	0.407267	−	0.913309i	$-0.366482\pi$
$701$	32.7243	−	38.9993i	1.23598	−	1.47298i	0.828713	−	0.559674i	$-0.189074\pi$
$702$	1.09865	−	24.4786i	0.0414661	−	0.923884i
$703$	0.393254	+	11.6927i	0.0148318	+	0.440999i
$704$			1.95189i			0.0735647i
$705$	15.2180	+	13.1621i	0.573143	+	0.495713i
$706$	−7.30439	−	20.0686i	−0.274904	−	0.755293i
$707$	−2.12313	+	0.374365i	−0.0798484	+	0.0140794i
$708$	2.24471	−	11.7044i	0.0843616	−	0.439877i
$709$	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
$711$	25.0188	+	15.4599i	0.938279	+	0.579792i
$712$	−11.4623	+	9.61798i	−0.429566	+	0.360449i
$713$	24.6715	−	20.7018i	0.923955	−	0.775290i
$714$	−3.40658	−	2.03529i	−0.127488	−	0.0761690i
$715$	−7.97127	+	4.60221i	−0.298108	+	0.172113i
$716$	22.9292	+	8.34554i	0.856904	+	0.311887i
$717$	5.23406	+	1.00381i	0.195470	+	0.0374880i
$718$	14.5537	−	2.56621i	0.543140	−	0.0957702i
$719$	−10.8481	−	29.8050i	−0.404567	−	1.11154i	−0.960005	−	0.279982i	$-0.909672\pi$
$719$	−10.8481	−	29.8050i	−0.404567	−	1.11154i	0.555438	−	0.831558i	$-0.312551\pi$
$720$	1.99621	−	2.23945i	0.0743943	−	0.0834595i
$721$			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
$726$	1.97896	+	12.2954i	0.0734459	+	0.456326i
$727$	−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
$729$	−11.3510	−	24.4981i	−0.420407	−	0.907335i
$730$	−13.7275	−	7.92557i	−0.508077	−	0.293339i
$731$	−2.54859	−	3.03729i	−0.0942631	−	0.112338i
$732$	3.72962	−	3.03567i	0.137851	−	0.112202i
$733$	−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
$735$	−1.98155	+	5.20099i	−0.0730907	+	0.191841i
$736$	6.28901	+	1.10892i	0.231816	+	0.0408754i
$737$	1.22515	+	6.94818i	0.0451290	+	0.255939i
$738$	−24.2246	+	8.00532i	−0.891721	+	0.294680i
$739$	−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
$741$	0.664620	+	35.5961i	0.0244154	+	1.30766i
$742$	−26.6870			−0.979711
$743$	−33.6915	−	28.2705i	−1.23602	−	1.03714i	−0.997824	−	0.0659273i	$-0.978999\pi$
$743$	−33.6915	−	28.2705i	−1.23602	−	1.03714i	−0.238196	−	0.971217i	$-0.576556\pi$
$744$	2.86455	+	8.25212i	0.105020	+	0.302537i
$745$	−0.600748	−	3.40701i	−0.0220097	−	0.124823i
$746$	8.89686	+	1.56876i	0.325737	+	0.0574362i
$747$	−12.2797	+	30.8367i	−0.449289	+	1.12826i
$748$	−0.699653	−	1.21184i	−0.0255819	−	0.0443091i
$749$	1.01006	−	1.74947i	0.0369067	−	0.0639242i
$750$	1.09338	+	1.34332i	0.0399246	+	0.0490513i
$751$	−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
$753$	22.1057	−	12.3258i	0.805577	−	0.449178i
$754$	−5.49153	+	15.0879i	−0.199990	+	0.549467i
$755$	0.849457	−	4.81751i	0.0309149	−	0.175327i
$756$	−2.14745	−	16.4666i	−0.0781021	−	0.598884i
$757$	−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	$0.133000\pi$
$761$			22.3879i			0.811561i	−0.913971	+	0.405780i	$0.867000\pi$
$762$	24.3524	−	28.1562i	0.882193	−	1.01999i
$763$	−18.8299	−	51.7347i	−0.681688	−	1.87292i
$764$	3.05855	−	0.539305i	0.110654	−	0.0195114i
$765$	−0.436619	+	2.10591i	−0.0157860	+	0.0761392i
$766$	−26.6060	−	9.68380i	−0.961315	−	0.349890i
$767$	−28.0997	+	16.2234i	−1.01462	+	0.585793i
$768$	−0.888354	+	1.48689i	−0.0320557	+	0.0536533i
$769$	−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
$771$	26.8203	−	44.8905i	0.965908	−	1.61669i
$772$	7.52851	−	4.34659i	0.270957	−	0.156437i
$773$	37.5324	+	13.6607i	1.34995	+	0.491341i	0.912932	−	0.408113i	$-0.133813\pi$
$773$	37.5324	+	13.6607i	1.34995	+	0.491341i	0.437016	+	0.899454i	$0.356035\pi$
$774$	3.36838	−	16.2464i	0.121074	−	0.583965i
$775$	−4.96663	+	0.875751i	−0.178407	+	0.0314579i
$776$	2.66837	+	7.33129i	0.0957890	+	0.263178i
$777$	−9.71892	+	11.2370i	−0.348664	+	0.403126i
$778$			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
$783$	2.28792	+	17.5437i	0.0817634	+	0.626960i
$784$	0.557993	−	3.16453i	0.0199283	−	0.113019i
$785$	−0.195925	+	0.538299i	−0.00699286	+	0.0192127i
$786$	−13.6954	+	7.63634i	−0.488498	+	0.272379i
$787$	−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
$789$	18.0185	+	22.1375i	0.641475	+	0.788114i
$790$	4.90167	−	8.48995i	0.174394	−	0.302059i
$791$	20.6604	+	35.7849i	0.734601	+	1.27237i
$792$	2.16637	−	5.44020i	0.0769787	−	0.193309i
$793$	−12.8937	−	2.27350i	−0.457868	−	0.0807344i
$794$	−2.31818	−	13.1471i	−0.0822693	−	0.466572i
$795$	4.74310	+	13.6638i	0.168220	+	0.484604i
$796$	5.30466	+	4.45114i	0.188019	+	0.157766i
$797$	−46.5571			−1.64914			−0.824568	−	0.565762i	$-0.808582\pi$
$797$	−46.5571			−1.64914			−0.824568	+	0.565762i	$0.808582\pi$
$798$	4.63263	+	23.6791i	0.163993	+	0.838231i
$799$	8.32784			0.294618
$800$	−0.766044	−	0.642788i	−0.0270838	−	0.0227260i
$801$	42.6218	−	14.0849i	1.50597	−	0.497665i
$802$	0.847824	+	4.80825i	0.0299377	+	0.169785i
$803$	−30.4697	−	5.37263i	−1.07525	−	0.189596i
$804$	−2.22901	+	5.85048i	−0.0786111	+	0.206331i
$805$	10.2043	+	17.6744i	0.359656	+	0.622942i
$806$	11.8911	−	20.5960i	0.418845	−	0.725462i
$807$	9.92557	−	8.07878i	0.349397	−	0.284386i
$808$	−0.433619	−	0.516767i	−0.0152547	−	0.0181798i
$809$	−21.9238	−	12.6577i	−0.770800	−	0.445022i	0.0623597	−	0.998054i	$-0.480137\pi$
$809$	−21.9238	−	12.6577i	−0.770800	−	0.445022i	−0.833160	+	0.553032i	$0.813471\pi$
$810$	−8.04925	+	4.02612i	−0.282822	+	0.141463i
$811$	−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
$813$	4.55732	+	28.3150i	0.159832	+	0.993050i
$814$	−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
$819$	−30.0837	+	33.7495i	−1.05121	+	1.17930i
$820$	2.90866	+	7.99149i	0.101575	+	0.279075i
$821$	−25.0056	+	4.40916i	−0.872702	+	0.153881i	−0.592023	−	0.805921i	$-0.701671\pi$
$821$	−25.0056	+	4.40916i	−0.872702	+	0.153881i	−0.280679	+	0.959802i	$0.590560\pi$
$822$	−15.6162	−	2.99494i	−0.544677	−	0.104461i
$823$	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
$825$	2.90224	+	1.73397i	0.101043	+	0.0603691i
$826$	−16.8449	+	14.1346i	−0.586110	+	0.491804i
$827$	11.2788	−	9.46403i	0.392202	−	0.329097i	−0.425268	−	0.905067i	$-0.639820\pi$
$827$	11.2788	−	9.46403i	0.392202	−	0.329097i	0.817470	+	0.575971i	$0.195376\pi$
$828$	−16.2976	−	10.0708i	−0.566381	−	0.349985i
$829$	−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
$831$	−10.3392	+	53.9103i	−0.358662	+	1.87013i
$832$	4.64400	−	0.818863i	0.161002	−	0.0283890i
$833$	0.787893	+	2.16472i	0.0272989	+	0.0750030i
$834$	4.04078	+	3.49488i	0.139921	+	0.121018i
$835$		−	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	−0.801790	−	0.597605i	$-0.796119\pi$
$839$	−29.8885	+	10.8785i	−1.03186	+	0.375568i	−0.230074	+	0.973173i	$0.573897\pi$
$840$	−5.46501	+	0.879598i	−0.188561	+	0.0303490i
$841$	−3.02267	+	17.1424i	−0.104230	+	0.591117i
$842$	−6.25324	+	17.1806i	−0.215501	+	0.592083i
$843$	−5.67437	−	10.1767i	−0.195436	−	0.350504i
$844$	−11.1347	−	6.42862i	−0.383272	−	0.221282i
$845$	5.93761	+	7.07617i	0.204260	+	0.243428i
$846$	21.5927	+	27.3540i	0.742371	+	0.940451i
$847$	11.4892	−	19.8999i	0.394774	−	0.683768i
$848$	−4.17528	−	7.23180i	−0.143380	−	0.248341i
$849$	3.19673	+	1.21794i	0.109712	+	0.0417996i
$850$	0.706006	+	0.124488i	0.0242158	+	0.00426990i
$851$	2.97636	+	16.8798i	0.102028	+	0.578631i
$852$	−4.88901	+	1.69712i	−0.167495	+	0.0581423i
$853$	−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
$855$	11.3004	−	6.58041i	0.386464	−	0.225045i
$856$	0.632108			0.0216050
$857$	−30.8482	−	25.8847i	−1.05375	−	0.884205i	−0.0602706	−	0.998182i	$-0.519196\pi$
$857$	−30.8482	−	25.8847i	−1.05375	−	0.884205i	−0.993483	+	0.113978i	$0.963641\pi$
$858$	−15.0609	+	5.22809i	−0.514171	+	0.178484i
$859$	−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
$861$	43.9900	+	16.7600i	1.49918	+	0.571179i
$862$	−0.621172	−	1.07590i	−0.0211572	−	0.0366453i
$863$	−16.9262	+	29.3170i	−0.576174	+	0.997962i	0.419740	+	0.907645i	$0.362121\pi$
$863$	−16.9262	+	29.3170i	−0.576174	+	0.997962i	−0.995913	+	0.0903172i	$0.971212\pi$
$864$	4.12624	−	3.15819i	0.140377	−	0.107444i
$865$	9.59737	+	11.4377i	0.326320	+	0.388894i
$866$	−32.6044	−	18.8242i	−1.10794	−	0.639671i
$867$	−13.9060	−	24.9398i	−0.472274	−	0.846999i
$868$	5.51247	−	15.1454i	0.187105	−	0.514068i
$869$	3.32277	−	18.8444i	0.112717	−	0.639252i
$870$	5.82248	−	0.937132i	0.197400	−	0.0317718i
$871$	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
$876$	−20.7656	−	17.9602i	−0.701603	−	0.606818i
$877$	−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
$879$	5.60047	−	29.2019i	0.188899	−	0.984956i
$880$	−1.83418	−	0.667586i	−0.0618301	−	0.0225043i
$881$	−37.6607	+	21.7434i	−1.26882	+	0.732554i	−0.974765	−	0.223234i	$-0.928338\pi$
$881$	−37.6607	+	21.7434i	−1.26882	+	0.732554i	−0.294056	+	0.955788i	$0.595005\pi$
$882$	−5.06747	+	8.20069i	−0.170631	+	0.276132i
$883$	−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
$885$	10.2308	+	6.11247i	0.343903	+	0.205468i
$886$	5.17551	−	2.98808i	0.173875	−	0.100387i
$887$	−46.2154	−	16.8210i	−1.55176	−	0.564795i	−0.582932	−	0.812521i	$-0.698095\pi$
$887$	−46.2154	−	16.8210i	−1.55176	−	0.564795i	−0.968830	+	0.247726i	$0.920317\pi$
$888$	−4.56563	−	0.875617i	−0.153213	−	0.0293838i
$889$	−67.6436	+	11.9274i	−2.26869	+	0.400032i
$890$	−5.11762	−	14.0605i	−0.171543	−	0.471310i
$891$	−12.0760	+	12.7582i	−0.404560	+	0.427415i
$892$		−	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
$897$	8.28843	+	51.4967i	0.276743	+	1.71942i
$898$	1.46602	−	8.31422i	0.0489218	−	0.277449i
$899$	−5.87304	+	16.1360i	−0.195877	+	0.538167i
$900$	1.42165	+	2.64176i	0.0473885	+	0.0880587i
$901$	5.18446	+	2.99325i	0.172719	+	0.0997196i
$902$	10.6700	+	12.7160i	0.355273	+	0.423397i
$903$	−23.7433	+	19.3255i	−0.790127	+	0.643113i
$904$	−6.46481	+	11.1974i	−0.215016	+	0.372419i
$905$	−2.99948	−	5.19526i	−0.0997062	−	0.172696i
$906$	3.01661	−	7.91770i	0.100220	−	0.263048i
$907$	−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
$909$	0.635006	+	1.92157i	0.0210618	+	0.0637344i
$910$	11.5446	+	9.68707i	0.382700	+	0.321123i
$911$	34.6125			1.14676			0.573381	−	0.819289i	$-0.305631\pi$
$911$	34.6125			1.14676			0.573381	+	0.819289i	$0.305631\pi$
$912$	−5.69191	+	4.96006i	−0.188478	+	0.164244i
$913$	21.5956			0.714709
$914$	13.5477	+	11.3679i	0.448118	+	0.376016i
$915$	1.57699	+	4.54296i	0.0521338	+	0.150186i
$916$	1.94264	+	11.0173i	0.0641866	+	0.364020i
$917$	28.4927	+	5.02404i	0.940913	+	0.165908i
$918$	−1.42973	+	3.43981i	−0.0471882	+	0.113531i
$919$	−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
$921$	−28.4480	−	34.9511i	−0.937392	−	1.15168i
$922$	13.5203	+	16.1128i	0.445267	+	0.530648i
$923$	12.2022	+	7.04493i	0.401639	+	0.231887i
$924$	−9.43660	+	5.26171i	−0.310441	+	0.173097i
$925$	0.917985	−	2.52214i	0.0301832	−	0.0829275i
$926$	4.90770	−	27.8329i	0.161277	−	0.914647i
$927$	45.1572	−	6.57708i	1.48316	−	0.216020i
$928$	−3.19953	+	1.16453i	−0.105030	+	0.0382277i
$929$	−5.19216	+	6.18777i	−0.170349	+	0.203014i	−0.844464	−	0.535612i	$-0.820081\pi$
$929$	−5.19216	+	6.18777i	−0.170349	+	0.203014i	0.674115	+	0.738627i	$0.264525\pi$
$930$	−8.73419	−	0.130592i	−0.286405	−	0.00428229i
$931$	6.59164	−	12.3587i	0.216032	−	0.405040i
$932$			4.51054i			0.147748i
$933$	−9.15986	+	10.5906i	−0.299881	+	0.346722i
$934$	−7.60323	−	20.8897i	−0.248785	−	0.683532i
$935$	1.37805	−	0.242987i	0.0450670	−	0.00794653i
$936$	−13.8523	−	2.87202i	−0.452778	−	0.0938748i
$937$	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
$939$	17.8971	−	29.9554i	0.584051	−	0.977557i
$940$	8.89875	−	7.46694i	0.290245	−	0.243545i
$941$	37.3026	−	31.3006i	1.21603	−	1.02037i	0.217009	−	0.976170i	$-0.430370\pi$
$941$	37.3026	−	31.3006i	1.21603	−	1.02037i	0.999023	−	0.0442018i	$-0.0140745\pi$
$942$	−0.508890	+	0.851756i	−0.0165805	+	0.0277517i
$943$	47.0331	−	27.1546i	1.53161	−	0.884274i
$944$	−6.46571	−	2.35333i	−0.210441	−	0.0765943i
$945$	16.2080	+	3.61396i	0.527247	+	0.117562i
$946$	−10.6312	+	1.87457i	−0.345651	+	0.0609475i
$947$	5.12273	+	14.0746i	0.166466	+	0.457363i	0.994675	−	0.103057i	$-0.0328623\pi$
$947$	5.12273	+	14.0746i	0.166466	+	0.457363i	−0.828209	+	0.560419i	$0.810640\pi$
$948$	11.1077	−	12.8427i	0.360762	−	0.417113i
$949$			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	−0.132284	−	0.991212i	$-0.542231\pi$
$953$	12.4569	−	4.53395i	0.403519	−	0.146869i	0.535803	+	0.844343i	$0.320009\pi$
$954$	3.61064	+	24.7901i	0.116899	+	0.802610i
$955$	−0.539305	+	3.05855i	−0.0174515	+	0.0989724i
$956$	1.05238	−	2.89140i	0.0340365	−	0.0935145i
$957$	10.0538	−	5.60587i	0.324995	−	0.181212i
$958$	22.6372	+	13.0696i	0.731375	+	0.422259i
$959$	18.8586	+	22.4748i	0.608976	+	0.725749i
$960$	−1.09338	−	1.34332i	−0.0352887	−	0.0433556i
$961$	−2.78282	+	4.81998i	−0.0897683	+	0.155483i
$962$	6.32841	+	10.9611i	0.204036	+	0.353401i
$963$	−1.76178	−	0.701567i	−0.0567724	−	0.0226077i
$964$	14.9358	+	2.63359i	0.481050	+	0.0848221i
$965$	1.50955	+	8.56111i	0.0485943	+	0.275592i
$966$	11.5921	+	33.3941i	0.372969	+	1.07444i
$967$	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
$969$	1.75590	−	5.11972i	0.0564077	−	0.164469i
$970$	−7.80180			−0.250501
$971$	16.0909	+	13.5018i	0.516381	+	0.433295i	0.863368	−	0.504575i	$-0.168351\pi$
$971$	16.0909	+	13.5018i	0.516381	+	0.433295i	−0.346987	+	0.937870i	$0.612795\pi$
$972$	−15.0056	+	4.22268i	−0.481306	+	0.135442i
$973$	−1.71174	−	9.70774i	−0.0548758	−	0.311216i
$974$	16.2032	+	2.85707i	0.519185	+	0.0915463i
$975$	2.90796	−	7.63254i	0.0931293	−	0.244437i
$976$	−1.38821	−	2.40444i	−0.0444354	−	0.0769644i
$977$	−1.91262	+	3.31275i	−0.0611901	+	0.105984i	−0.894998	−	0.446071i	$-0.852823\pi$
$977$	−1.91262	+	3.31275i	−0.0611901	+	0.105984i	0.833808	+	0.552055i	$0.186156\pi$
$978$	25.2559	−	20.5566i	0.807593	−	0.657329i
$979$	−18.7733	−	22.3731i	−0.599996	−	0.715047i
$980$	2.78284	+	1.60668i	0.0888947	+	0.0513234i
$981$	−45.5099	+	24.4910i	−1.45302	+	0.781937i
$982$	14.4564	−	39.7185i	0.461321	−	1.26747i
$983$	1.52381	−	8.64195i	0.0486019	−	0.275635i	−0.950816	−	0.309757i	$-0.899752\pi$
$983$	1.52381	−	8.64195i	0.0486019	−	0.275635i	0.999418	+	0.0341218i	$0.0108634\pi$
$984$	2.34068	+	14.5428i	0.0746181	+	0.463608i
$985$	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
$990$	4.37117	+	3.89638i	0.138925	+	0.123835i
$991$	−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
$993$	41.2362	+	7.90846i	1.30859	+	0.250967i
$994$	8.97296	+	3.26589i	0.284605	+	0.103588i
$995$	−5.99700	+	3.46237i	−0.190118	+	0.109765i
$996$	16.4508	+	9.82867i	0.521263	+	0.311433i
$997$	−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
$999$	11.7532	+	7.50779i	0.371856	+	0.237536i

Twists

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

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

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)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.63627 + 0.567997i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.61856 - 0.616663i) q^{6} +(1.59792 + 2.76767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.35476 - 1.85879i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(-1.63627 + 0.567997i) q^{3} +(0.173648 + 0.984808i) q^{4} +(-0.984808 - 0.173648i) q^{5} +(-1.61856 - 0.616663i) q^{6} +(1.59792 + 2.76767i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(2.35476 - 1.85879i) q^{9} +(-0.642788 - 0.766044i) q^{10} +(-1.69039 - 0.975946i) q^{11} +(-0.843503 - 1.51278i) q^{12} +(-1.61284 + 4.43125i) q^{13} +(-0.554951 + 3.14728i) q^{14} +(1.71004 - 0.275233i) 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} +(-4.18665 - 3.62105i) q^{21} +(-0.667586 - 1.83418i) q^{22} +(-6.28901 + 1.10892i) q^{23} +(0.326235 - 1.70105i) q^{24} +(0.939693 + 0.342020i) q^{25} +(-4.08387 + 2.35782i) q^{26} +(-2.79723 + 4.37898i) q^{27} +(-2.44815 + 2.05424i) q^{28} +(2.60828 - 2.18861i) q^{29} +(1.48689 + 0.888354i) q^{30} +(-4.36758 + 2.52162i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(3.32027 + 0.636775i) q^{33} +(0.706006 - 0.124488i) q^{34} +(-1.09304 - 3.00310i) q^{35} +(2.23945 + 1.99621i) 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} +(-0.879598 - 5.46501i) q^{42} +(0.960386 - 5.44662i) q^{43} +(0.667586 - 1.83418i) q^{44} +(-2.64176 + 1.42165i) q^{45} +(-5.53047 - 3.19302i) q^{46} +(7.46694 + 8.89875i) q^{47} +(1.34332 - 1.09338i) q^{48} +(-1.60668 + 2.78284i) q^{49} +(0.500000 + 0.866025i) q^{50} +(-0.442084 + 1.16034i) q^{51} +(-4.64400 - 0.818863i) q^{52} +(1.45006 + 8.22370i) q^{53} +(-4.95756 + 1.55647i) q^{54} +(1.49524 + 1.25465i) q^{55} -3.19583 q^{56} +(7.04508 - 2.71419i) q^{57} +3.40487 q^{58} +(5.27090 + 4.42281i) q^{59} +(0.567997 + 1.63627i) q^{60} +(0.482119 + 2.73423i) q^{61} +(-4.96663 - 0.875751i) q^{62} +(8.90724 + 3.54700i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(2.35782 - 4.08387i) q^{65} +(2.13416 + 2.62202i) q^{66} +(-2.32344 - 2.76897i) q^{67} +(0.620852 + 0.358449i) q^{68} +(9.66066 - 5.38664i) q^{69} +(1.09304 - 3.00310i) q^{70} +(0.518843 - 2.94250i) q^{71} +(0.432383 + 2.96868i) 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} +(5.34307 - 6.17766i) q^{78} +(3.35294 + 9.21214i) q^{79} +(0.984808 - 0.173648i) q^{80} +(2.08977 - 8.75402i) q^{81} +(-7.99149 - 2.90866i) q^{82} +(-9.58163 + 5.53196i) q^{83} +(2.83903 - 4.75184i) q^{84} +(-0.549175 + 0.460813i) q^{85} +(4.23672 - 3.55503i) q^{86} +(-3.02473 + 5.06265i) q^{87} +(1.69039 - 0.975946i) q^{88} +(14.0605 + 5.11762i) q^{89} +(-2.93753 - 0.609040i) q^{90} +(-14.8415 + 2.61695i) q^{91} +(-2.18415 - 6.00091i) q^{92} +(5.71427 - 6.60683i) 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} +(-5.79454 + 0.843965i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9}+O(q^{10}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9	\( 84 q - 6 q^{3} - 42 q^{8} + 6 q^{9} + 24 q^{13} + 24 q^{14} - 12 q^{17} - 12 q^{19} + 36 q^{22} - 6 q^{24} - 6 q^{27} - 12 q^{28} + 12 q^{29} - 6 q^{33} + 12 q^{34} - 18 q^{38} + 12 q^{39} - 6 q^{41} + 24 q^{43} - 36 q^{44} - 12 q^{47} - 54 q^{49} + 42 q^{50} - 54 q^{51} + 12 q^{52} + 60 q^{53} - 54 q^{54} - 60 q^{57} - 24 q^{58} + 18 q^{59} - 48 q^{61} + 12 q^{62} + 18 q^{63} - 42 q^{64} + 54 q^{66} + 6 q^{67} + 54 q^{68} - 60 q^{69} - 48 q^{71} - 12 q^{72} + 84 q^{73} - 24 q^{74} + 36 q^{78} - 12 q^{79} + 114 q^{81} - 6 q^{82} - 36 q^{83} - 18 q^{84} - 12 q^{86} + 6 q^{87} + 12 q^{89} + 24 q^{91} + 6 q^{93} + 12 q^{95} - 42 q^{97} - 36 q^{98} + 102 q^{99}+O(q^{100}) \) 84 * q - 6 * q^3 - 42 * q^8 + 6 * q^9 + 24 * q^13 + 24 * q^14 - 12 * q^17 - 12 * q^19 + 36 * q^22 - 6 * q^24 - 6 * q^27 - 12 * q^28 + 12 * q^29 - 6 * q^33 + 12 * q^34 - 18 * q^38 + 12 * q^39 - 6 * q^41 + 24 * q^43 - 36 * q^44 - 12 * q^47 - 54 * q^49 + 42 * q^50 - 54 * q^51 + 12 * q^52 + 60 * q^53 - 54 * q^54 - 60 * q^57 - 24 * q^58 + 18 * q^59 - 48 * q^61 + 12 * q^62 + 18 * q^63 - 42 * q^64 + 54 * q^66 + 6 * q^67 + 54 * q^68 - 60 * q^69 - 48 * q^71 - 12 * q^72 + 84 * q^73 - 24 * q^74 + 36 * q^78 - 12 * q^79 + 114 * q^81 - 6 * q^82 - 36 * q^83 - 18 * q^84 - 12 * q^86 + 6 * q^87 + 12 * q^89 + 24 * q^91 + 6 * q^93 + 12 * q^95 - 42 * q^97 - 36 * q^98 + 102 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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