LMFDB - Embedded newform 216.2.v.b.11.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,2,Mod(11,216)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(216, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("216.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	216.v (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:	$1.72476868366$
Analytic rank:	$0$
Dimension:	$192$
Relative dimension:	$32$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.15
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.315008 + 1.37868i) q^{2} +(-1.04101 + 1.38431i) q^{3} +(-1.80154 - 0.868594i) q^{4} +(-0.437371 - 0.159190i) q^{5} +(-1.58060 - 1.87129i) q^{6} +(-3.46177 - 0.610403i) q^{7} +(1.76502 - 2.21014i) q^{8} +(-0.832609 - 2.88215i) q^{9} +(0.357248 - 0.552850i) q^{10} +(0.485871 + 1.33492i) q^{11} +(3.07782 - 1.58967i) q^{12} +(-1.62110 - 1.93196i) q^{13} +(1.93204 - 4.58040i) q^{14} +(0.675674 - 0.439738i) q^{15} +(2.49109 + 3.12961i) q^{16} +(-0.667069 + 0.385133i) q^{17} +(4.23585 - 0.240005i) q^{18} +(-3.66125 + 6.34147i) q^{19} +(0.649669 + 0.666685i) q^{20} +(4.44871 - 4.15671i) q^{21} +(-1.99349 + 0.249352i) q^{22} +(-1.25561 - 7.12090i) q^{23} +(1.22212 + 4.74409i) q^{24} +(-3.66427 - 3.07469i) q^{25} +(3.17422 - 1.62641i) q^{26} +(4.85652 + 1.84775i) q^{27} +(5.70632 + 4.10653i) q^{28} +(3.15733 + 2.64931i) q^{29} +(0.393416 + 1.07006i) q^{30} +(-7.80121 + 1.37556i) q^{31} +(-5.09946 + 2.44857i) q^{32} +(-2.35373 - 0.717067i) q^{33} +(-0.320844 - 1.04100i) q^{34} +(1.41691 + 0.818051i) q^{35} +(-1.00344 + 5.91550i) q^{36} +(-2.79436 + 1.61333i) q^{37} +(-7.58956 - 7.04532i) q^{38} +(4.36200 - 0.232925i) q^{39} +(-1.12380 + 0.685678i) q^{40} +(1.74280 + 2.07699i) q^{41} +(4.32941 + 7.44276i) q^{42} +(-1.99564 + 0.726352i) q^{43} +(0.284188 - 2.82694i) q^{44} +(-0.0946497 + 1.39311i) q^{45} +(10.2130 + 0.512058i) q^{46} +(-1.82437 + 10.3465i) q^{47} +(-6.92558 + 0.190482i) q^{48} +(5.03339 + 1.83200i) q^{49} +(5.39330 - 4.08332i) q^{50} +(0.161282 - 1.32435i) q^{51} +(1.24240 + 4.88858i) q^{52} -8.73592 q^{53} +(-4.07731 + 6.11356i) q^{54} -0.661201i q^{55} +(-7.45915 + 6.57361i) q^{56} +(-4.96715 - 11.6698i) q^{57} +(-4.64715 + 3.51840i) q^{58} +(0.818263 - 2.24816i) q^{59} +(-1.59921 + 0.205318i) q^{60} +(3.02492 + 0.533375i) q^{61} +(0.560979 - 11.1887i) q^{62} +(1.12303 + 10.4855i) q^{63} +(-1.76943 - 7.80187i) q^{64} +(0.401476 + 1.10305i) q^{65} +(1.73005 - 3.01917i) q^{66} +(-4.04105 + 3.39085i) q^{67} +(1.53628 - 0.114419i) q^{68} +(11.1646 + 5.67476i) q^{69} +(-1.57417 + 1.69577i) q^{70} +(5.70758 + 9.88583i) q^{71} +(-7.83951 - 3.24685i) q^{72} +(2.96144 - 5.12936i) q^{73} +(-1.34402 - 4.36075i) q^{74} +(8.07084 - 1.87170i) q^{75} +(12.1041 - 8.24427i) q^{76} +(-0.867134 - 4.91776i) q^{77} +(-1.05294 + 6.08720i) q^{78} +(8.94667 - 10.6622i) q^{79} +(-0.591327 - 1.76536i) q^{80} +(-7.61352 + 4.79940i) q^{81} +(-3.41251 + 1.74850i) q^{82} +(7.41209 - 8.83338i) q^{83} +(-11.6250 + 3.62436i) q^{84} +(0.353066 - 0.0622550i) q^{85} +(-0.372768 - 2.98016i) q^{86} +(-6.95426 + 1.61276i) q^{87} +(3.80793 + 1.28231i) q^{88} +(8.59338 + 4.96139i) q^{89} +(-1.89084 - 0.569333i) q^{90} +(4.43261 + 7.67751i) q^{91} +(-3.92315 + 13.9192i) q^{92} +(6.21691 - 12.2312i) q^{93} +(-13.6899 - 5.77446i) q^{94} +(2.61082 - 2.19074i) q^{95} +(1.91900 - 9.60820i) q^{96} +(-1.95198 + 0.710462i) q^{97} +(-4.11131 + 6.36235i) q^{98} +(3.44289 - 2.51182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) $ 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/216\mathbb{Z}\right)^\times$.

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{13}{18}\right)$

Coefficient data

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

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

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

$2$	−0.315008	+	1.37868i	−0.222745	+	0.974877i
$2$	−0.315008	+	1.37868i	−0.222745	+	0.974877i
$3$	−1.04101	+	1.38431i	−0.601026	+	0.799230i
$3$	−1.04101	+	1.38431i	−0.601026	+	0.799230i
$4$	−1.80154	−	0.868594i	−0.900770	−	0.434297i
$5$	−0.437371	−	0.159190i	−0.195598	−	0.0711919i	0.242364	−	0.970185i	$-0.422077\pi$
$5$	−0.437371	−	0.159190i	−0.195598	−	0.0711919i	−0.437962	+	0.898994i	$0.644300\pi$
$6$	−1.58060	−	1.87129i	−0.645275	−	0.763950i
$7$	−3.46177	−	0.610403i	−1.30842	−	0.230711i	−0.524417	−	0.851462i	$-0.675717\pi$
$7$	−3.46177	−	0.610403i	−1.30842	−	0.230711i	−0.784008	+	0.620751i	$0.786828\pi$
$8$	1.76502	−	2.21014i	0.624028	−	0.781402i
$9$	−0.832609	−	2.88215i	−0.277536	−	0.960715i
$10$	0.357248	−	0.552850i	0.112972	−	0.174827i
$11$	0.485871	+	1.33492i	0.146496	+	0.402494i	0.991138	−	0.132838i	$-0.0424089\pi$
$11$	0.485871	+	1.33492i	0.146496	+	0.402494i	−0.844642	+	0.535331i	$0.820187\pi$
$12$	3.07782	−	1.58967i	0.888489	−	0.458898i
$13$	−1.62110	−	1.93196i	−0.449614	−	0.535829i	0.492860	−	0.870108i	$-0.335951\pi$
$13$	−1.62110	−	1.93196i	−0.449614	−	0.535829i	−0.942474	+	0.334280i	$0.891507\pi$
$14$	1.93204	−	4.58040i	0.516359	−	1.22416i
$15$	0.675674	−	0.439738i	0.174458	−	0.113540i
$16$	2.49109	+	3.12961i	0.622772	+	0.782403i
$17$	−0.667069	+	0.385133i	−0.161788	+	0.0934084i	−0.578708	−	0.815535i	$-0.696443\pi$
$17$	−0.667069	+	0.385133i	−0.161788	+	0.0934084i	0.416920	+	0.908943i	$0.363110\pi$
$18$	4.23585	−	0.240005i	0.998399	−	0.0565697i
$19$	−3.66125	+	6.34147i	−0.839948	+	1.45483i	0.0499885	+	0.998750i	$0.484082\pi$
$19$	−3.66125	+	6.34147i	−0.839948	+	1.45483i	−0.889937	+	0.456084i	$0.849252\pi$
$20$	0.649669	+	0.666685i	0.145271	+	0.149075i
$21$	4.44871	−	4.15671i	0.970788	−	0.907069i
$22$	−1.99349	+	0.249352i	−0.425013	+	0.0531620i
$23$	−1.25561	−	7.12090i	−0.261812	−	1.48481i	−0.777961	−	0.628312i	$-0.783746\pi$
$23$	−1.25561	−	7.12090i	−0.261812	−	1.48481i	0.516149	−	0.856499i	$-0.327365\pi$
$24$	1.22212	+	4.74409i	0.249463	+	0.968384i
$25$	−3.66427	−	3.07469i	−0.732854	−	0.614938i
$26$	3.17422	−	1.62641i	0.622516	−	0.318965i
$27$	4.85652	+	1.84775i	0.934639	+	0.355599i
$28$	5.70632	+	4.10653i	1.07839	+	0.776062i
$29$	3.15733	+	2.64931i	0.586301	+	0.491965i	0.887010	−	0.461751i	$-0.152779\pi$
$29$	3.15733	+	2.64931i	0.586301	+	0.491965i	−0.300709	+	0.953716i	$0.597223\pi$
$30$	0.393416	+	1.07006i	0.0718276	+	0.195366i
$31$	−7.80121	+	1.37556i	−1.40114	+	0.247059i	−0.822611	−	0.568604i	$-0.807484\pi$
$31$	−7.80121	+	1.37556i	−1.40114	+	0.247059i	−0.578528	+	0.815663i	$0.696373\pi$
$32$	−5.09946	+	2.44857i	−0.901466	+	0.432850i
$33$	−2.35373	−	0.717067i	−0.409733	−	0.124825i
$34$	−0.320844	−	1.04100i	−0.0550242	−	0.178530i
$35$	1.41691	+	0.818051i	0.239501	+	0.138276i
$36$	−1.00344	+	5.91550i	−0.167239	+	0.985916i
$37$	−2.79436	+	1.61333i	−0.459390	+	0.265229i	−0.711788	−	0.702394i	$-0.752114\pi$
$37$	−2.79436	+	1.61333i	−0.459390	+	0.265229i	0.252397	+	0.967624i	$0.418781\pi$
$38$	−7.58956	−	7.04532i	−1.23119	−	1.14290i
$39$	4.36200	−	0.232925i	0.698479	−	0.0372978i
$40$	−1.12380	+	0.685678i	−0.177688	+	0.108415i
$41$	1.74280	+	2.07699i	0.272180	+	0.324371i	0.884769	−	0.466031i	$-0.154316\pi$
$41$	1.74280	+	2.07699i	0.272180	+	0.324371i	−0.612589	+	0.790402i	$0.709872\pi$
$42$	4.32941	+	7.44276i	0.668043	+	1.14844i
$43$	−1.99564	+	0.726352i	−0.304332	+	0.110768i	−0.489672	−	0.871907i	$-0.662883\pi$
$43$	−1.99564	+	0.726352i	−0.304332	+	0.110768i	0.185340	+	0.982674i	$0.440661\pi$
$44$	0.284188	−	2.82694i	0.0428429	−	0.426177i
$45$	−0.0946497	+	1.39311i	−0.0141095	+	0.207673i
$46$	10.2130	+	0.512058i	1.50583	+	0.0754989i
$47$	−1.82437	+	10.3465i	−0.266111	+	1.50919i	0.499741	+	0.866175i	$0.333428\pi$
$47$	−1.82437	+	10.3465i	−0.266111	+	1.50919i	−0.765852	+	0.643017i	$0.777683\pi$
$48$	−6.92558	+	0.190482i	−0.999622	+	0.0274937i
$49$	5.03339	+	1.83200i	0.719055	+	0.261715i
$50$	5.39330	−	4.08332i	0.762728	−	0.577468i
$51$	0.161282	−	1.32435i	0.0225840	−	0.185447i
$52$	1.24240	+	4.88858i	0.172290	+	0.677924i
$53$	−8.73592			−1.19997			−0.599986	−	0.800011i	$-0.704827\pi$
$53$	−8.73592			−1.19997			−0.599986	+	0.800011i	$0.704827\pi$
$54$	−4.07731	+	6.11356i	−0.554851	+	0.831950i
$55$		−	0.661201i		−	0.0891564i
$56$	−7.45915	+	6.57361i	−0.996771	+	0.878436i
$57$	−4.96715	−	11.6698i	−0.657916	−	1.54570i
$58$	−4.64715	+	3.51840i	−0.610201	+	0.461989i
$59$	0.818263	−	2.24816i	0.106529	−	0.292685i	−0.874963	−	0.484190i	$-0.839114\pi$
$59$	0.818263	−	2.24816i	0.106529	−	0.292685i	0.981492	+	0.191504i	$0.0613367\pi$
$60$	−1.59921	+	0.205318i	−0.206457	+	0.0265065i
$61$	3.02492	+	0.533375i	0.387301	+	0.0682916i	0.363908	−	0.931435i	$-0.381442\pi$
$61$	3.02492	+	0.533375i	0.387301	+	0.0682916i	0.0233926	+	0.999726i	$0.492553\pi$
$62$	0.560979	−	11.1887i	0.0712444	−	1.42097i
$63$	1.12303	+	10.4855i	0.141488	+	1.32105i
$64$	−1.76943	−	7.80187i	−0.221179	−	0.975233i
$65$	0.401476	+	1.10305i	0.0497969	+	0.136816i
$66$	1.73005	−	3.01917i	0.212955	−	0.371635i
$67$	−4.04105	+	3.39085i	−0.493693	+	0.414258i	−0.855348	−	0.518054i	$-0.826657\pi$
$67$	−4.04105	+	3.39085i	−0.493693	+	0.414258i	0.361654	+	0.932312i	$0.382212\pi$
$68$	1.53628	−	0.114419i	0.186301	−	0.0138754i
$69$	11.1646	+	5.67476i	1.34406	+	0.683161i
$70$	−1.57417	+	1.69577i	−0.188149	+	0.202684i
$71$	5.70758	+	9.88583i	0.677366	+	1.17323i	0.975771	+	0.218793i	$0.0702118\pi$
$71$	5.70758	+	9.88583i	0.677366	+	1.17323i	−0.298406	+	0.954439i	$0.596455\pi$
$72$	−7.83951	−	3.24685i	−0.923895	−	0.382645i
$73$	2.96144	−	5.12936i	0.346610	−	0.600346i	−0.639035	−	0.769178i	$-0.720666\pi$
$73$	2.96144	−	5.12936i	0.346610	−	0.600346i	0.985645	+	0.168832i	$0.0539994\pi$
$74$	−1.34402	−	4.36075i	−0.156239	−	0.506927i
$75$	8.07084	−	1.87170i	0.931940	−	0.216126i
$76$	12.1041	−	8.24427i	1.38843	−	0.945683i
$77$	−0.867134	−	4.91776i	−0.0988191	−	0.560431i
$78$	−1.05294	+	6.08720i	−0.119222	+	0.689239i
$79$	8.94667	−	10.6622i	1.00658	−	1.19959i	0.0267740	−	0.999642i	$-0.491477\pi$
$79$	8.94667	−	10.6622i	1.00658	−	1.19959i	0.979805	−	0.199953i	$-0.0640790\pi$
$80$	−0.591327	−	1.76536i	−0.0661123	−	0.197373i
$81$	−7.61352	+	4.79940i	−0.845947	+	0.533267i
$82$	−3.41251	+	1.74850i	−0.376848	+	0.193090i
$83$	7.41209	−	8.83338i	0.813582	−	0.969590i	−0.186335	−	0.982486i	$-0.559661\pi$
$83$	7.41209	−	8.83338i	0.813582	−	0.969590i	0.999917	+	0.0128968i	$0.00410530\pi$
$84$	−11.6250	+	3.62436i	−1.26839	+	0.395450i
$85$	0.353066	−	0.0622550i	0.0382954	−	0.00675251i
$86$	−0.372768	−	2.98016i	−0.0401966	−	0.321359i
$87$	−6.95426	+	1.61276i	−0.745575	+	0.172906i
$88$	3.80793	+	1.28231i	0.405927	+	0.136695i
$89$	8.59338	+	4.96139i	0.910896	+	0.525906i	0.880719	−	0.473639i	$-0.157060\pi$
$89$	8.59338	+	4.96139i	0.910896	+	0.525906i	0.0301767	+	0.999545i	$0.490393\pi$
$90$	−1.89084	−	0.569333i	−0.199312	−	0.0600130i
$91$	4.43261	+	7.67751i	0.464664	+	0.804822i
$92$	−3.92315	+	13.9192i	−0.409016	+	1.45118i
$93$	6.21691	−	12.2312i	0.644664	−	1.26832i
$94$	−13.6899	−	5.77446i	−1.41200	−	0.595590i
$95$	2.61082	−	2.19074i	0.267865	−	0.224765i
$96$	1.91900	−	9.60820i	0.195857	−	0.980632i
$97$	−1.95198	+	0.710462i	−0.198193	+	0.0721365i	−0.439210	−	0.898385i	$-0.644741\pi$
$97$	−1.95198	+	0.710462i	−0.198193	+	0.0721365i	0.241016	+	0.970521i	$0.422519\pi$
$98$	−4.11131	+	6.36235i	−0.415305	+	0.642695i
$99$	3.44289	−	2.51182i	0.346024	−	0.252447i
$100$	3.93067	+	8.72193i	0.393067	+	0.872193i
$101$	−1.48081	+	8.39808i	−0.147346	+	0.835641i	0.818108	+	0.575065i	$0.195023\pi$
$101$	−1.48081	+	8.39808i	−0.147346	+	0.835641i	−0.965454	+	0.260575i	$0.916088\pi$
$102$	1.77506	+	0.639540i	0.175757	+	0.0633239i
$103$	2.93036	−	8.05109i	0.288737	−	0.793298i	−0.707507	−	0.706706i	$-0.750180\pi$
$103$	2.93036	−	8.05109i	0.288737	−	0.793298i	0.996244	−	0.0865915i	$-0.0275975\pi$
$104$	−7.13117	+	0.172930i	−0.699269	+	0.0169572i
$105$	−2.60744	+	1.10984i	−0.254460	+	0.108309i
$106$	2.75189	−	12.0441i	0.267287	−	1.16982i
$107$		−	10.8657i		−	1.05042i	−0.850972	−	0.525211i	$-0.823986\pi$
$107$		−	10.8657i		−	1.05042i	0.850972	−	0.525211i	$-0.176014\pi$
$108$	−7.14428	−	7.54714i	−0.687459	−	0.726224i
$109$			8.94866i			0.857126i	0.903512	+	0.428563i	$0.140980\pi$
$109$			8.94866i			0.857126i	−0.903512	+	0.428563i	$0.859020\pi$
$110$	0.911588	+	0.208284i	0.0869165	+	0.0198591i
$111$	0.675613	−	5.54774i	0.0641264	−	0.526568i
$112$	−6.71324	−	12.3546i	−0.634342	−	1.16740i
$113$	−1.31870	+	3.62309i	−0.124053	+	0.340832i	−0.986137	−	0.165933i	$-0.946936\pi$
$113$	−1.31870	+	3.62309i	−0.124053	+	0.340832i	0.862084	+	0.506765i	$0.169159\pi$
$114$	17.6537	−	3.17205i	1.65342	−	0.297090i
$115$	−0.584410	+	3.31436i	−0.0544966	+	0.309065i
$116$	−3.38687	−	7.51528i	−0.314463	−	0.697776i
$117$	−4.21844	+	6.28082i	−0.389994	+	0.580662i
$118$	2.84174	+	1.83631i	0.261603	+	0.169046i
$119$	2.54432	−	0.926058i	0.233238	−	0.0848916i
$120$	0.220695	−	2.26948i	0.0201466	−	0.207174i
$121$	6.88055	−	5.77346i	0.625504	−	0.524860i
$122$	−1.68823	+	4.00239i	−0.152845	+	0.362359i
$123$	−4.68946	+	0.250410i	−0.422834	+	0.0225787i
$124$	15.2490	+	4.29795i	1.36940	+	0.385968i
$125$	2.27679	+	3.94351i	0.203642	+	0.352718i
$126$	−14.8100	−	1.75473i	−1.31938	−	0.156324i
$127$	−9.84084	−	5.68161i	−0.873233	−	0.504162i	−0.00481202	−	0.999988i	$-0.501532\pi$
$127$	−9.84084	−	5.68161i	−0.873233	−	0.504162i	−0.868421	+	0.495827i	$0.834865\pi$
$128$	11.3137	+	0.0181658i	0.999999	+	0.00160564i
$129$	1.07198	−	3.51871i	0.0943823	−	0.309805i
$130$	−1.64722	+	0.206040i	−0.144471	+	0.0180709i
$131$	−19.4659	+	3.43236i	−1.70074	+	0.299887i	−0.937954	−	0.346760i	$-0.887282\pi$
$131$	−19.4659	+	3.43236i	−1.70074	+	0.299887i	−0.762790	+	0.646647i	$0.776171\pi$
$132$	3.61751	+	3.33626i	0.314863	+	0.290384i
$133$	16.5452	−	19.7179i	1.43465	−	1.70975i
$134$	−3.40194	−	6.63948i	−0.293883	−	0.573564i
$135$	−1.82996	−	1.58126i	−0.157498	−	0.136093i
$136$	−0.326192	+	2.15408i	−0.0279707	+	0.184711i
$137$	4.33502	−	5.16628i	0.370366	−	0.441385i	−0.548383	−	0.836227i	$-0.684756\pi$
$137$	4.33502	−	5.16628i	0.370366	−	0.441385i	0.918749	+	0.394843i	$0.129201\pi$
$138$	−11.3407	+	13.6049i	−0.965380	+	1.15812i
$139$	−2.54700	−	14.4448i	−0.216034	−	1.22519i	−0.879103	−	0.476631i	$-0.841858\pi$
$139$	−2.54700	−	14.4448i	−0.216034	−	1.22519i	0.663069	−	0.748558i	$-0.269253\pi$
$140$	−1.84206	−	2.70447i	−0.155682	−	0.228569i
$141$	−12.4235	−	13.2963i	−1.04625	−	1.11975i
$142$	−15.4274	+	4.75484i	−1.29464	+	0.399017i
$143$	1.79136	−	3.10273i	0.149801	−	0.259463i
$144$	6.94590	−	9.78542i	0.578825	−	0.815452i
$145$	−0.959179	−	1.66135i	−0.0796555	−	0.137967i
$146$	6.13889	+	5.69868i	0.508058	+	0.471626i
$147$	−7.77584	+	5.06062i	−0.641341	+	0.417393i
$148$	6.43548	−	0.479304i	0.528993	−	0.0393985i
$149$	−6.53906	+	5.48692i	−0.535700	+	0.449506i	−0.870064	−	0.492938i	$-0.835923\pi$
$149$	−6.53906	+	5.48692i	−0.535700	+	0.449506i	0.334364	+	0.942444i	$0.391479\pi$
$150$	0.0381031	+	11.7167i	0.00311110	+	0.956668i
$151$	1.70566	+	4.68627i	0.138805	+	0.381364i	0.989545	−	0.144223i	$-0.0460682\pi$
$151$	1.70566	+	4.68627i	0.138805	+	0.381364i	−0.850740	+	0.525586i	$0.823846\pi$
$152$	7.55337	+	19.2847i	0.612659	+	1.56419i
$153$	1.66542	+	1.60193i	0.134641	+	0.129508i
$154$	7.05319	+	0.353632i	0.568362	+	0.0284965i
$155$	3.63100	+	0.640243i	0.291649	+	0.0514256i
$156$	−8.06064	−	3.36919i	−0.645367	−	0.269751i
$157$	−7.74744	+	21.2859i	−0.618313	+	1.69880i	0.0927644	+	0.995688i	$0.470430\pi$
$157$	−7.74744	+	21.2859i	−0.618313	+	1.69880i	−0.711078	+	0.703113i	$0.751793\pi$
$158$	11.8816	+	15.6933i	0.945247	+	1.24849i
$159$	9.09416	−	12.0932i	0.721214	−	0.959053i
$160$	2.62014	−	0.259150i	0.207141	−	0.0204876i
$161$			25.4173i			2.00317i
$162$	−4.21853	−	12.0085i	−0.331439	−	0.943477i
$163$	−24.9254			−1.95231			−0.976156	−	0.217071i	$-0.930350\pi$
$163$	−24.9254			−1.95231			−0.976156	+	0.217071i	$0.930350\pi$
$164$	−1.33566	−	5.25556i	−0.104298	−	0.410390i
$165$	0.915305	+	0.688315i	0.0712564	+	0.0535853i
$166$	9.84357	+	13.0015i	0.764009	+	1.00911i
$167$	0.989406	+	0.360114i	0.0765625	+	0.0278665i	0.380017	−	0.924979i	$-0.375918\pi$
$167$	0.989406	+	0.360114i	0.0765625	+	0.0278665i	−0.303455	+	0.952846i	$0.598140\pi$
$168$	−1.33487	−	17.1689i	−0.102987	−	1.32461i
$169$	1.15295	−	6.53869i	0.0886883	−	0.502976i
$170$	−0.0253887	+	0.506377i	−0.00194722	+	0.0388374i
$171$	21.3254	+	5.27229i	1.63080	+	0.403182i
$172$	4.22612	+	0.424846i	0.322239	+	0.0323942i
$173$	3.27836	−	1.19323i	0.249249	−	0.0907192i	−0.214374	−	0.976752i	$-0.568771\pi$
$173$	3.27836	−	1.19323i	0.249249	−	0.0907192i	0.463623	+	0.886032i	$0.346549\pi$
$174$	−0.0328316	−	10.0958i	−0.00248896	−	0.765358i
$175$	10.8080	+	12.8805i	0.817012	+	0.973677i
$176$	−2.96744	+	4.84599i	−0.223679	+	0.365281i
$177$	2.26032	+	3.47308i	0.169896	+	0.261052i
$178$	−9.54717	+	10.2847i	−0.715591	+	0.770869i
$179$	11.9338	−	6.89000i	0.891976	−	0.514983i	0.0173878	−	0.999849i	$-0.494465\pi$
$179$	11.9338	−	6.89000i	0.891976	−	0.514983i	0.874588	+	0.484866i	$0.161132\pi$
$180$	1.38056	−	2.42753i	0.102901	−	0.180937i
$181$	−2.04781	−	1.18231i	−0.152213	−	0.0878801i	0.421959	−	0.906615i	$-0.361343\pi$
$181$	−2.04781	−	1.18231i	−0.152213	−	0.0878801i	−0.574172	+	0.818735i	$0.694676\pi$
$182$	−11.9812	+	3.69269i	−0.888104	+	0.273721i
$183$	−3.88731	+	3.63217i	−0.287359	+	0.268497i
$184$	−17.9544	−	9.79345i	−1.32361	−	0.721982i
$185$	1.47900	−	0.260787i	0.108738	−	0.0191735i
$186$	14.9046	+	12.4241i	1.09286	+	0.910979i
$187$	−0.838231	−	0.703359i	−0.0612975	−	0.0514347i
$188$	12.2736	−	17.0550i	0.895142	−	1.24386i
$189$	−15.6843	−	9.36091i	−1.14086	−	0.680906i
$190$	2.19791	+	4.28960i	0.159453	+	0.311200i
$191$	8.27044	+	6.93973i	0.598428	+	0.502141i	0.890940	−	0.454121i	$-0.150047\pi$
$191$	8.27044	+	6.93973i	0.598428	+	0.502141i	−0.292512	+	0.956262i	$0.594491\pi$
$192$	12.6422	+	5.67236i	0.912370	+	0.409367i
$193$	3.57316	+	20.2644i	0.257201	+	1.45866i	0.790358	+	0.612645i	$0.209894\pi$
$193$	3.57316	+	20.2644i	0.257201	+	1.45866i	−0.533157	+	0.846016i	$0.678994\pi$
$194$	−0.364613	−	2.91496i	−0.0261777	−	0.209282i
$195$	−1.94489	−	0.592513i	−0.139277	−	0.0424307i
$196$	−7.47658	−	7.67240i	−0.534041	−	0.548028i
$197$	−1.27921	+	2.21565i	−0.0911396	+	0.157858i	−0.907991	−	0.418990i	$-0.862384\pi$
$197$	−1.27921	+	2.21565i	−0.0911396	+	0.157858i	0.816851	+	0.576848i	$0.195718\pi$
$198$	2.37846	+	5.53791i	0.169030	+	0.393562i
$199$	−18.0736	+	10.4348i	−1.28121	+	0.739704i	−0.977069	−	0.212924i	$-0.931701\pi$
$199$	−18.0736	+	10.4348i	−1.28121	+	0.739704i	−0.304136	+	0.952628i	$0.598368\pi$
$200$	−13.2630	+	2.67167i	−0.937835	+	0.188916i
$201$	−0.487206	−	9.12395i	−0.0343649	−	0.643554i
$202$	−11.1118	−	4.68703i	−0.781826	−	0.329779i
$203$	−9.31278	−	11.0985i	−0.653629	−	0.778965i
$204$	−1.44088	+	2.24579i	−0.100882	+	0.157237i
$205$	−0.431614	−	1.18585i	−0.0301453	−	0.0828234i
$206$	10.1768	+	6.57620i	0.709053	+	0.458185i
$207$	−19.4780	+	9.54777i	−1.35382	+	0.663616i
$208$	2.00796	−	9.88611i	0.139227	−	0.685478i
$209$	−10.2443	−	1.80634i	−0.708610	−	0.124947i
$210$	−0.708746	−	3.94445i	−0.0489081	−	0.272193i
$211$	0.0141986	+	0.00516787i	0.000977473	+	0.000355771i	0.342509	−	0.939515i	$-0.388723\pi$
$211$	0.0141986	+	0.00516787i	0.000977473	+	0.000355771i	−0.341531	+	0.939870i	$0.610946\pi$
$212$	15.7381	+	7.58797i	1.08090	+	0.521144i
$213$	−19.6266	−	2.39017i	−1.34480	−	0.163772i
$214$	14.9803	+	3.42277i	1.02403	+	0.233976i
$215$	0.988461			0.0674125
$216$	12.6556	−	7.47229i	0.861106	−	0.508425i
$217$	27.8456			1.89028
$218$	−12.3374	−	2.81890i	−0.835592	−	0.190920i
$219$	4.01773	+	9.43924i	0.271493	+	0.637845i
$220$	−0.574315	+	1.19118i	−0.0387203	+	0.0803093i
$221$	1.82545	+	0.664409i	0.122793	+	0.0446930i
$222$	7.43576	+	2.67904i	0.499055	+	0.179805i
$223$	2.68574	+	0.473569i	0.179851	+	0.0317125i	0.262848	−	0.964837i	$-0.415338\pi$
$223$	2.68574	+	0.473569i	0.179851	+	0.0317125i	−0.0829974	+	0.996550i	$0.526449\pi$
$224$	19.1478	−	5.36365i	1.27936	−	0.358374i
$225$	−5.81079	+	13.1210i	−0.387386	+	0.874732i
$226$	−4.57970	−	2.95937i	−0.304637	−	0.196855i
$227$	0.693824	+	1.90627i	0.0460507	+	0.126523i	0.960586	−	0.277983i	$-0.0896657\pi$
$227$	0.693824	+	1.90627i	0.0460507	+	0.126523i	−0.914535	+	0.404506i	$0.867444\pi$
$228$	−1.18780	+	25.3381i	−0.0786642	+	1.67805i
$229$	4.00131	+	4.76857i	0.264414	+	0.315116i	0.881873	−	0.471487i	$-0.156282\pi$
$229$	4.00131	+	4.76857i	0.264414	+	0.315116i	−0.617459	+	0.786603i	$0.711838\pi$
$230$	−4.38536	−	1.84977i	−0.289162	−	0.121970i
$231$	7.71038	+	3.91904i	0.507306	+	0.257854i
$232$	11.4281	−	2.30205i	0.750291	−	0.151137i
$233$	−21.4888	+	12.4066i	−1.40778	+	0.812783i	−0.995174	−	0.0981264i	$-0.968715\pi$
$233$	−21.4888	+	12.4066i	−1.40778	+	0.812783i	−0.412607	+	0.910909i	$0.635382\pi$
$234$	−7.33043	−	7.79440i	−0.479205	−	0.509536i
$235$	2.44498	−	4.23484i	0.159493	−	0.276250i
$236$	−3.42687	+	3.33941i	−0.223070	+	0.217377i
$237$	5.44625	+	23.4844i	0.353772	+	1.52548i
$238$	0.475258	+	3.79953i	0.0308064	+	0.246287i
$239$	−4.43265	−	25.1388i	−0.286725	−	1.62610i	−0.699059	−	0.715064i	$-0.746398\pi$
$239$	−4.43265	−	25.1388i	−0.286725	−	1.62610i	0.412335	−	0.911032i	$-0.364713\pi$
$240$	3.05937	+	1.01917i	0.197482	+	0.0657873i
$241$	−12.6387	−	10.6052i	−0.814133	−	0.683139i	0.137458	−	0.990508i	$-0.456107\pi$
$241$	−12.6387	−	10.6052i	−0.814133	−	0.683139i	−0.951590	+	0.307369i	$0.900551\pi$
$242$	5.79235	+	11.3048i	0.372347	+	0.726699i
$243$	1.28189	−	15.5357i	0.0822332	−	0.996613i
$244$	−4.98622	−	3.58832i	−0.319210	−	0.229719i
$245$	−1.90982	−	1.60253i	−0.122014	−	0.102382i
$246$	1.13198	−	6.54416i	0.0721725	−	0.417240i
$247$	18.1867	−	3.20681i	1.15719	−	0.204044i
$248$	−10.7291	+	19.6697i	−0.681297	+	1.24902i
$249$	4.51207	+	19.4562i	0.285941	+	1.23299i
$250$	−6.15406	+	1.89673i	−0.389217	+	0.119960i
$251$	−3.82463	−	2.20815i	−0.241408	−	0.139377i	0.374416	−	0.927261i	$-0.377843\pi$
$251$	−3.82463	−	2.20815i	−0.241408	−	0.139377i	−0.615824	+	0.787884i	$0.711177\pi$
$252$	7.08450	−	19.8656i	0.446281	−	1.25141i
$253$	8.89578	−	5.13598i	0.559273	−	0.322896i
$254$	10.9331	−	11.7777i	0.686003	−	0.738996i
$255$	−0.281364	+	0.553559i	−0.0176197	+	0.0346652i
$256$	−3.58895	+	15.5923i	−0.224310	+	0.974518i
$257$	12.1155	+	14.4386i	0.755741	+	0.900657i	0.997571	−	0.0696615i	$-0.0221919\pi$
$257$	12.1155	+	14.4386i	0.755741	+	0.900657i	−0.241830	+	0.970319i	$0.577747\pi$
$258$	4.51351	+	2.58634i	0.280999	+	0.161019i
$259$	10.6582	−	3.87927i	0.662269	−	0.241046i
$260$	0.234824	−	2.33590i	0.0145632	−	0.144866i
$261$	5.00688	−	11.3057i	0.309918	−	0.699806i
$262$	1.39978	−	27.9185i	0.0864785	−	1.72481i
$263$	3.00966	−	17.0686i	0.185583	−	1.05250i	−0.739620	−	0.673024i	$-0.764995\pi$
$263$	3.00966	−	17.0686i	0.185583	−	1.05250i	0.925204	−	0.379471i	$-0.123894\pi$
$264$	−5.73920	+	3.93645i	−0.353223	+	0.242272i
$265$	3.82084	+	1.39067i	0.234712	+	0.0854283i
$266$	21.9728	+	29.0220i	1.34724	+	1.77945i
$267$	−15.8138	+	6.73103i	−0.967792	+	0.411932i
$268$	10.2254	−	2.59871i	0.624615	−	0.158741i
$269$	−10.9959			−0.670431			−0.335215	−	0.942142i	$-0.608809\pi$
$269$	−10.9959			−0.670431			−0.335215	+	0.942142i	$0.608809\pi$
$270$	2.75651	−	2.02483i	0.167756	−	0.123227i
$271$		−	19.7167i		−	1.19770i	−0.800861	−	0.598851i	$-0.795624\pi$
$271$		−	19.7167i		−	1.19770i	0.800861	−	0.598851i	$-0.204376\pi$
$272$	−2.86704	−	1.12827i	−0.173840	−	0.0684113i
$273$	−15.2424	−	1.85625i	−0.922513	−	0.112345i
$274$	5.75709	+	7.60404i	0.347799	+	0.459377i
$275$	2.32410	−	6.38541i	0.140148	−	0.385055i
$276$	−15.1844	−	19.9208i	−0.913994	−	1.19909i
$277$	−18.3745	−	3.23992i	−1.10402	−	0.194668i	−0.408203	−	0.912891i	$-0.633845\pi$
$277$	−18.3745	−	3.23992i	−1.10402	−	0.194668i	−0.695813	+	0.718223i	$0.744956\pi$
$278$	20.7171	+	1.03871i	1.24253	+	0.0622978i
$279$	10.4599	+	21.3389i	0.626220	+	1.27753i
$280$	4.30887	−	1.68769i	0.257504	−	0.100859i
$281$	−8.37613	−	23.0132i	−0.499678	−	1.37285i	−0.891587	−	0.452850i	$-0.850407\pi$
$281$	−8.37613	−	23.0132i	−0.499678	−	1.37285i	0.391909	−	0.920004i	$-0.371815\pi$
$282$	22.2449	−	12.9397i	1.32466	−	0.770548i
$283$	13.4469	−	11.2833i	0.799338	−	0.670724i	−0.148700	−	0.988882i	$-0.547509\pi$
$283$	13.4469	−	11.2833i	0.799338	−	0.670724i	0.948038	+	0.318159i	$0.103064\pi$
$284$	−1.69567	−	22.7673i	−0.100619	−	1.35099i
$285$	0.314772	+	5.89476i	0.0186455	+	0.349175i
$286$	3.71339	+	3.44711i	0.219577	+	0.203832i
$287$	−4.76537	−	8.25386i	−0.281291	−	0.487210i
$288$	11.3030	+	12.6587i	0.666035	+	0.745920i
$289$	−8.20335	+	14.2086i	−0.482550	+	0.835801i
$290$	2.59262	−	0.799067i	0.152244	−	0.0469228i
$291$	1.04853	−	3.44173i	0.0614657	−	0.201758i
$292$	−9.79048	+	6.66846i	−0.572944	+	0.390242i
$293$	−4.42079	−	25.0715i	−0.258265	−	1.46470i	−0.787550	−	0.616251i	$-0.788651\pi$
$293$	−4.42079	−	25.0715i	−0.258265	−	1.46470i	0.529285	−	0.848444i	$-0.322460\pi$
$294$	−4.52754	−	12.3146i	−0.264052	−	0.718200i
$295$	−0.715769	+	0.853020i	−0.0416737	+	0.0496647i
$296$	−1.36642	+	9.02348i	−0.0794217	+	0.524479i
$297$	−0.106949	+	7.38084i	−0.00620583	+	0.428280i
$298$	−5.50487	−	10.7437i	−0.318889	−	0.622367i
$299$	−11.7218	+	13.9695i	−0.677890	+	0.807878i
$300$	−16.1657	−	3.63834i	−0.933326	−	0.210060i
$301$	7.35179	−	1.29632i	0.423750	−	0.0747186i
$302$	−6.99819	+	0.875357i	−0.402701	+	0.0503711i
$303$	−10.0840	−	10.7924i	−0.579310	−	0.620005i
$304$	−28.9669	+	4.33887i	−1.66136	+	0.248851i
$305$	−1.23810	−	0.714819i	−0.0708936	−	0.0409304i
$306$	−2.73317	+	1.79146i	−0.156245	+	0.102411i
$307$	13.7038	+	23.7357i	0.782117	+	1.35467i	0.930706	+	0.365768i	$0.119194\pi$
$307$	13.7038	+	23.7357i	0.782117	+	1.35467i	−0.148589	+	0.988899i	$0.547473\pi$
$308$	−2.70936	+	9.61273i	−0.154380	+	0.547736i
$309$	8.09466	+	12.4378i	0.460489	+	0.707559i
$310$	−2.02649	+	4.80432i	−0.115097	+	0.272867i
$311$	−11.9153	+	9.99813i	−0.675655	+	0.566942i	−0.914733	−	0.404058i	$-0.867599\pi$
$311$	−11.9153	+	9.99813i	−0.675655	+	0.566942i	0.239078	+	0.971000i	$0.423155\pi$
$312$	7.18421	−	10.0517i	0.406726	−	0.569068i
$313$	−9.57684	+	3.48568i	−0.541315	+	0.197022i	−0.598183	−	0.801359i	$-0.704111\pi$
$313$	−9.57684	+	3.48568i	−0.541315	+	0.197022i	0.0568687	+	0.998382i	$0.481888\pi$
$314$	−26.9061	−	17.3865i	−1.51840	−	0.981178i
$315$	1.17801	−	4.76485i	0.0663735	−	0.268469i
$316$	−25.3789	+	11.4374i	−1.42768	+	0.643404i
$317$	5.74143	−	32.5613i	0.322471	−	1.82882i	−0.204410	−	0.978885i	$-0.565528\pi$
$317$	5.74143	−	32.5613i	0.322471	−	1.82882i	0.526881	−	0.849939i	$-0.323361\pi$
$318$	13.8080	+	16.3474i	0.774312	+	0.916718i
$319$	−2.00257	+	5.50201i	−0.112122	+	0.308053i
$320$	−0.468081	+	3.69399i	−0.0261665	+	0.206500i
$321$	15.0414	+	11.3112i	0.839529	+	0.631331i
$322$	−35.0425	−	8.00667i	−1.95284	−	0.446194i
$323$		−	5.64027i		−	0.313833i
$324$	17.8848	−	2.03325i	0.993600	−	0.112958i
$325$			12.0636i			0.669168i
$326$	7.85172	−	34.3643i	0.434867	−	1.90326i
$327$	−12.3877	−	9.31561i	−0.685040	−	0.515155i
$328$	7.66651	−	0.185912i	0.423312	−	0.0102653i
$329$	12.6311	−	34.7035i	0.696373	−	1.91327i
$330$	−1.23730	+	1.04509i	−0.0681110	+	0.0575304i
$331$	1.92984	−	10.9447i	0.106074	−	0.601574i	−0.884712	−	0.466138i	$-0.845645\pi$
$331$	1.92984	−	10.9447i	0.106074	−	0.601574i	0.990786	−	0.135437i	$-0.0432437\pi$
$332$	−21.0258	+	9.47559i	−1.15394	+	0.520041i
$333$	6.97645	+	6.71049i	0.382307	+	0.367733i
$334$	−0.808155	+	1.25064i	−0.0442203	+	0.0684319i
$335$	2.30723	−	0.839763i	0.126057	−	0.0458811i
$336$	24.0910	+	3.56799i	1.31427	+	0.194650i
$337$	4.91071	−	4.12058i	0.267504	−	0.224462i	−0.499162	−	0.866509i	$-0.666359\pi$
$337$	4.91071	−	4.12058i	0.267504	−	0.224462i	0.766666	+	0.642046i	$0.221914\pi$
$338$	8.65160	+	3.64929i	0.470585	+	0.198495i
$339$	−3.64270	−	5.59715i	−0.197844	−	0.303995i
$340$	−0.690137	−	0.194516i	−0.0374279	−	0.0105491i
$341$	−5.62665	−	9.74565i	−0.304700	−	0.527756i
$342$	−13.9865	+	27.7402i	−0.756304	+	1.50002i
$343$	5.00343	+	2.88873i	0.270160	+	0.155977i
$344$	−1.91699	+	5.69266i	−0.103357	+	0.306928i
$345$	−3.97971	−	4.25927i	−0.214260	−	0.229311i
$346$	0.612370	+	4.89570i	0.0329212	+	0.263194i
$347$	−31.8049	+	5.60806i	−1.70738	+	0.301056i	−0.940261	−	0.340453i	$-0.889419\pi$
$347$	−31.8049	+	5.60806i	−1.70738	+	0.301056i	−0.767115	+	0.641510i	$0.778308\pi$
$348$	13.9292	+	3.13498i	0.746684	+	0.168053i
$349$	−0.166560	+	0.198498i	−0.00891573	+	0.0106254i	−0.770484	−	0.637459i	$-0.779985\pi$
$349$	−0.166560	+	0.198498i	−0.00891573	+	0.0106254i	0.761568	+	0.648085i	$0.224430\pi$
$350$	−21.1628	+	10.8434i	−1.13120	+	0.579605i
$351$	−4.30317	−	12.3780i	−0.229686	−	0.660688i
$352$	−5.74633	−	5.61768i	−0.306280	−	0.299424i
$353$	−5.28492	+	6.29832i	−0.281288	+	0.335226i	−0.888126	−	0.459599i	$-0.847993\pi$
$353$	−5.28492	+	6.29832i	−0.281288	+	0.335226i	0.606839	+	0.794825i	$0.292437\pi$
$354$	−5.50029	+	2.02222i	−0.292337	+	0.107480i
$355$	−0.922607	−	5.23236i	−0.0489669	−	0.277705i
$356$	−11.1719	−	16.4023i	−0.592108	−	0.869320i
$357$	−1.36671	+	4.48616i	−0.0723340	+	0.237433i
$358$	5.73988	+	18.6234i	0.303362	+	0.984276i
$359$	0.180226	−	0.312161i	0.00951198	−	0.0164752i	−0.861230	−	0.508215i	$-0.830306\pi$
$359$	0.180226	−	0.312161i	0.00951198	−	0.0164752i	0.870742	+	0.491740i	$0.163639\pi$
$360$	2.91191	+	2.66805i	0.153471	+	0.140619i
$361$	−17.3095	−	29.9810i	−0.911027	−	1.57794i
$362$	2.27510	−	2.45085i	0.119577	−	0.128814i
$363$	0.829547	+	15.5350i	0.0435399	+	0.815376i
$364$	−1.31689	−	17.6815i	−0.0690236	−	0.926761i
$365$	−2.11179	+	1.77200i	−0.110536	+	0.0927508i
$366$	−3.78307	−	6.50354i	−0.197744	−	0.339946i
$367$	10.6705	+	29.3168i	0.556993	+	1.53033i	0.823975	+	0.566626i	$0.191751\pi$
$367$	10.6705	+	29.3168i	0.556993	+	1.53033i	−0.266982	+	0.963702i	$0.586026\pi$
$368$	19.1578	−	21.6684i	0.998671	−	1.12954i
$369$	4.53511	−	6.75232i	0.236088	−	0.351512i
$370$	−0.106354	+	2.12122i	−0.00552906	+	0.110277i
$371$	30.2417	+	5.33243i	1.57007	+	0.276846i
$372$	−21.8240	+	16.6351i	−1.13152	+	0.862489i
$373$	−2.92591	+	8.03888i	−0.151498	+	0.416237i	−0.992105	−	0.125408i	$-0.959976\pi$
$373$	−2.92591	+	8.03888i	−0.151498	+	0.416237i	0.840607	+	0.541645i	$0.182198\pi$
$374$	1.23376	−	0.934092i	0.0637962	−	0.0483007i
$375$	−7.82918	−	0.953451i	−0.404297	−	0.0492360i
$376$	19.6472	+	22.2938i	1.01322	+	1.14972i
$377$		−	10.3946i		−	0.535351i
$378$	17.8464	−	18.6749i	0.917920	−	0.960534i
$379$	−11.8737			−0.609912			−0.304956	−	0.952366i	$-0.598642\pi$
$379$	−11.8737			−0.609912			−0.304956	+	0.952366i	$0.598642\pi$
$380$	−6.60637	+	1.67896i	−0.338899	+	0.0861289i
$381$	18.1095	−	7.70814i	0.927777	−	0.394900i
$382$	−12.1729	+	9.21626i	−0.622822	+	0.471545i
$383$	21.6357	+	7.87475i	1.10553	+	0.402381i	0.829353	−	0.558725i	$-0.188709\pi$
$383$	21.6357	+	7.87475i	1.10553	+	0.402381i	0.276179	+	0.961106i	$0.410932\pi$
$384$	−11.8028	+	15.6427i	−0.602308	+	0.798264i
$385$	−0.403599	+	2.28892i	−0.0205693	+	0.116654i
$386$	−29.0637	−	1.45719i	−1.47931	−	0.0741692i
$387$	3.75504	+	5.14695i	0.190879	+	0.261634i
$388$	4.13367	+	0.415551i	0.209855	+	0.0210964i
$389$	17.2027	−	6.26126i	0.872210	−	0.317458i	0.133148	−	0.991096i	$-0.457491\pi$
$389$	17.2027	−	6.26126i	0.872210	−	0.317458i	0.739062	+	0.673638i	$0.235269\pi$
$390$	1.42955	−	2.49475i	0.0723878	−	0.126326i
$391$	3.58007	+	4.26656i	0.181052	+	0.215769i
$392$	12.9330	−	7.89097i	0.653215	−	0.398554i
$393$	15.5127	−	30.5199i	0.782512	−	1.53952i
$394$	−2.65172	−	2.46157i	−0.133592	−	0.124012i
$395$	−5.61034	+	3.23913i	−0.282287	+	0.162978i
$396$	−8.38426	+	1.53466i	−0.421325	+	0.0771197i
$397$	−5.79128	−	3.34360i	−0.290656	−	0.167810i	0.347582	−	0.937650i	$-0.387003\pi$
$397$	−5.79128	−	3.34360i	−0.290656	−	0.167810i	−0.638238	+	0.769839i	$0.720336\pi$
$398$	−8.69296	−	28.2049i	−0.435739	−	1.41378i
$399$	10.0718	+	43.4301i	0.504223	+	2.17423i
$400$	0.494560	−	19.1271i	0.0247280	−	0.956353i
$401$	−7.86143	+	1.38618i	−0.392581	+	0.0692226i	−0.366454	−	0.930436i	$-0.619428\pi$
$401$	−7.86143	+	1.38618i	−0.392581	+	0.0692226i	−0.0261266	+	0.999659i	$0.508317\pi$
$402$	12.7325	+	2.20242i	0.635041	+	0.109847i
$403$	15.3041	+	12.8417i	0.762352	+	0.639689i
$404$	9.96226	−	13.8433i	0.495641	−	0.688728i
$405$	4.09395	−	0.887122i	0.203430	−	0.0440814i
$406$	18.2350	−	9.34325i	0.904987	−	0.463698i
$407$	−3.51136	−	2.94638i	−0.174052	−	0.146047i
$408$	−2.64234	−	2.69396i	−0.130815	−	0.133371i
$409$	−1.04527	−	5.92801i	−0.0516852	−	0.293121i	0.947998	−	0.318275i	$-0.103104\pi$
$409$	−1.04527	−	5.92801i	−0.0516852	−	0.293121i	−0.999684	+	0.0251538i	$0.991992\pi$
$410$	1.77088	−	0.221507i	0.0874573	−	0.0109394i
$411$	2.63892	+	11.3791i	0.130168	+	0.561291i
$412$	−12.2723	+	11.9591i	−0.604612	+	0.589181i
$413$	−4.20492	+	7.28313i	−0.206910	+	0.358379i
$414$	−7.02761	−	29.8617i	−0.345388	−	1.46762i
$415$	−4.64802	+	2.68353i	−0.228162	+	0.131729i
$416$	12.9973	+	5.88255i	0.637245	+	0.288416i
$417$	22.6474	+	11.5113i	1.10905	+	0.563709i
$418$	5.71740	−	13.5546i	0.279647	−	0.662976i
$419$	17.2811	+	20.5948i	0.844237	+	1.00612i	0.999833	+	0.0183011i	$0.00582575\pi$
$419$	17.2811	+	20.5948i	0.844237	+	1.00612i	−0.155596	+	0.987821i	$0.549730\pi$
$420$	5.66141	+	0.265397i	0.276248	+	0.0129500i
$421$	6.51235	+	17.8925i	0.317392	+	0.872029i	0.991111	+	0.133040i	$0.0424739\pi$
$421$	6.51235	+	17.8925i	0.317392	+	0.872029i	−0.673718	+	0.738988i	$0.735304\pi$
$422$	−0.0115975	+	0.0179475i	−0.000564560	+	0.000873670i
$423$	31.3391	−	3.35650i	1.52376	−	0.163198i
$424$	−15.4191	+	19.3076i	−0.748815	+	0.937660i
$425$	3.62848	+	0.639800i	0.176007	+	0.0310348i
$426$	9.47784	−	26.3060i	0.459203	−	1.27453i
$427$	−10.1460	−	3.69284i	−0.490999	−	0.178709i
$428$	−9.43785	+	19.5749i	−0.456195	+	0.946189i
$429$	2.43031	+	5.70975i	0.117336	+	0.275670i
$430$	−0.311374	+	1.36278i	−0.0150158	+	0.0657189i
$431$	−19.2221			−0.925894			−0.462947	−	0.886386i	$-0.653208\pi$
$431$	−19.2221			−0.925894			−0.462947	+	0.886386i	$0.653208\pi$
$432$	6.31530	+	19.8019i	0.303845	+	0.952721i
$433$	13.6658			0.656735			0.328367	−	0.944550i	$-0.393502\pi$
$433$	13.6658			0.656735			0.328367	+	0.944550i	$0.393502\pi$
$434$	−8.77160	+	38.3903i	−0.421050	+	1.84279i
$435$	3.29833	+	0.401676i	0.158143	+	0.0192589i
$436$	7.77275	−	16.1214i	0.372247	−	0.772073i
$437$	49.7541	+	18.1090i	2.38006	+	0.866271i
$438$	−14.2793	+	2.56574i	−0.682293	+	0.122596i
$439$	−24.1314	−	4.25502i	−1.15173	−	0.203081i	−0.434999	−	0.900431i	$-0.643251\pi$
$439$	−24.1314	−	4.25502i	−1.15173	−	0.203081i	−0.716731	+	0.697350i	$0.754362\pi$
$440$	−1.46135	−	1.16703i	−0.0696670	−	0.0556360i
$441$	1.08926	−	16.0323i	0.0518693	−	0.763443i
$442$	−1.49104	+	2.30742i	−0.0709216	+	0.109753i
$443$	4.71302	+	12.9489i	0.223922	+	0.615222i	0.999879	−	0.0155648i	$-0.00495462\pi$
$443$	4.71302	+	12.9489i	0.223922	+	0.615222i	−0.775956	+	0.630786i	$0.782732\pi$
$444$	−6.03588	+	9.40764i	−0.286450	+	0.446467i
$445$	−2.96869	−	3.53795i	−0.140729	−	0.167715i
$446$	−1.49893	+	3.55361i	−0.0709765	+	0.168268i
$447$	−0.788376	−	14.7640i	−0.0372889	−	0.698312i
$448$	1.36308	+	28.0883i	0.0643994	+	1.32705i
$449$	15.6709	−	9.04759i	0.739555	−	0.426982i	−0.0823526	−	0.996603i	$-0.526243\pi$
$449$	15.6709	−	9.04759i	0.739555	−	0.426982i	0.821907	+	0.569621i	$0.192910\pi$
$450$	−16.2592	−	12.1445i	−0.766467	−	0.572495i
$451$	−1.92584	+	3.33565i	−0.0906842	+	0.157070i
$452$	5.52268	−	5.38173i	0.259765	−	0.253135i
$453$	−8.26285	−	2.51728i	−0.388222	−	0.118272i
$454$	−2.84670	+	0.356074i	−0.133602	+	0.0167114i
$455$	−0.716513	−	4.06355i	−0.0335907	−	0.190502i
$456$	−34.5590	−	9.61931i	−1.61837	−	0.450465i
$457$	−5.09369	−	4.27411i	−0.238273	−	0.199935i	0.515830	−	0.856691i	$-0.327484\pi$
$457$	−5.09369	−	4.27411i	−0.238273	−	0.199935i	−0.754103	+	0.656756i	$0.771928\pi$
$458$	−7.83480	+	4.01440i	−0.366096	+	0.187581i
$459$	−3.95127	+	0.637831i	−0.184429	+	0.0297714i
$460$	3.93167	−	5.46333i	0.183315	−	0.254729i
$461$	17.2916	+	14.5094i	0.805352	+	0.675771i	0.949494	−	0.313786i	$-0.101598\pi$
$461$	17.2916	+	14.5094i	0.805352	+	0.675771i	−0.144141	+	0.989557i	$0.546042\pi$
$462$	−7.83196	+	9.39565i	−0.364376	+	0.437125i
$463$	9.30336	−	1.64043i	0.432364	−	0.0762374i	0.0467691	−	0.998906i	$-0.485107\pi$
$463$	9.30336	−	1.64043i	0.432364	−	0.0762374i	0.385594	+	0.922668i	$0.373996\pi$
$464$	−0.426139	+	16.4809i	−0.0197830	+	0.765106i
$465$	−4.66619	+	4.35992i	−0.216389	+	0.202186i
$466$	−10.3356	−	33.5345i	−0.478788	−	1.55346i
$467$	6.76157	+	3.90380i	0.312888	+	0.180646i	0.648218	−	0.761455i	$-0.275514\pi$
$467$	6.76157	+	3.90380i	0.312888	+	0.180646i	−0.335330	+	0.942101i	$0.608848\pi$
$468$	13.0552	−	7.65105i	0.603475	−	0.353670i
$469$	16.0590	−	9.27165i	0.741534	−	0.428125i
$470$	5.06831	+	4.70487i	0.233784	+	0.217019i
$471$	−21.4011	−	32.8836i	−0.986111	−	1.51520i
$472$	−3.52450	−	5.77651i	−0.162228	−	0.265886i
$473$	−1.93924	−	2.31110i	−0.0891666	−	0.106265i
$474$	−34.0932	+	0.110872i	−1.56595	+	0.00509250i
$475$	32.9139	−	11.9797i	1.51019	−	0.549665i
$476$	−5.38807	−	0.541654i	−0.246962	−	0.0248267i
$477$	7.27361	+	25.1782i	0.333036	+	1.15283i
$478$	36.0548	+	1.80771i	1.64911	+	0.0826829i
$479$	−4.13778	+	23.4665i	−0.189060	+	1.07221i	0.731567	+	0.681770i	$0.238789\pi$
$479$	−4.13778	+	23.4665i	−0.189060	+	1.07221i	−0.920627	+	0.390444i	$0.872322\pi$
$480$	−2.36884	+	3.89686i	−0.108122	+	0.177866i
$481$	7.64683	+	2.78322i	0.348666	+	0.126904i
$482$	18.6025	−	14.0841i	0.847320	−	0.641514i
$483$	−35.1854	−	26.4596i	−1.60099	−	1.20395i
$484$	−17.4104	+	4.42472i	−0.791381	+	0.201124i
$485$	0.966837			0.0439018
$486$	21.0150	+	6.66118i	0.953258	+	0.302157i
$487$		−	5.00210i		−	0.226667i	−0.993557	−	0.113333i	$-0.963847\pi$
$487$		−	5.00210i		−	0.226667i	0.993557	−	0.113333i	$-0.0361528\pi$
$488$	6.51786	−	5.74407i	0.295050	−	0.260022i
$489$	25.9476	−	34.5045i	1.17339	−	1.56035i
$490$	2.81099	−	2.12823i	0.126988	−	0.0961436i
$491$	−10.7540	+	29.5462i	−0.485319	+	1.33340i	0.419557	+	0.907729i	$0.362185\pi$
$491$	−10.7540	+	29.5462i	−0.485319	+	1.33340i	−0.904876	+	0.425674i	$0.860037\pi$
$492$	8.66574	+	3.62211i	0.390682	+	0.163297i
$493$	−3.12649	−	0.551285i	−0.140810	−	0.0248286i
$494$	−1.30779	+	26.0839i	−0.0588404	+	1.17357i
$495$	−1.90568	+	0.550522i	−0.0856539	+	0.0247441i
$496$	−23.7385	−	20.9881i	−1.06589	−	0.942394i
$497$	−13.7240	−	37.7063i	−0.615605	−	1.69136i
$498$	−28.2453	+	0.0918542i	−1.26570	+	0.00411609i
$499$	9.47652	−	7.95175i	0.424227	−	0.355969i	−0.405541	−	0.914077i	$-0.632917\pi$
$499$	9.47652	−	7.95175i	0.424227	−	0.355969i	0.829769	+	0.558108i	$0.188472\pi$
$500$	−0.676412	−	9.08199i	−0.0302500	−	0.406159i
$501$	−1.52849	+	0.994759i	−0.0682877	+	0.0444426i
$502$	4.24913	−	4.57737i	0.189648	−	0.204298i
$503$	−0.0403972	−	0.0699700i	−0.00180122	−	0.00311981i	0.865123	−	0.501559i	$-0.167240\pi$
$503$	−0.0403972	−	0.0699700i	−0.00180122	−	0.00311981i	−0.866925	+	0.498439i	$0.833907\pi$
$504$	25.1567	+	16.0251i	1.12057	+	0.713815i
$505$	1.98455	−	3.43735i	0.0883115	−	0.152960i
$506$	4.27865	+	13.8823i	0.190209	+	0.617145i
$507$	7.85133	+	8.40286i	0.348690	+	0.373184i
$508$	12.7936	+	18.7833i	0.567626	+	0.833376i
$509$	7.45238	+	42.2646i	0.330321	+	1.87334i	0.469286	+	0.883046i	$0.344511\pi$
$509$	7.45238	+	42.2646i	0.330321	+	1.87334i	−0.138964	+	0.990297i	$0.544377\pi$
$510$	−0.674551	−	0.562288i	−0.0298696	−	0.0248985i
$511$	−13.3828	+	15.9490i	−0.592019	+	0.705541i
$512$	−20.3663	−	9.85973i	−0.900071	−	0.435743i
$513$	−29.4984	+	24.0324i	−1.30239	+	1.06106i
$514$	−23.7228	+	12.1551i	−1.04637	+	0.536138i
$515$	−2.56331	+	3.05483i	−0.112953	+	0.134612i
$516$	−4.98754	+	5.40798i	−0.219564	+	0.238073i
$517$	−14.6982	+	2.59168i	−0.646424	+	0.113982i
$518$	1.99086	+	15.9163i	0.0874735	+	0.699322i
$519$	−1.76101	+	5.78041i	−0.0772995	+	0.253732i
$520$	3.14650	+	1.05958i	0.137983	+	0.0464655i
$521$	−8.07399	−	4.66152i	−0.353728	−	0.204225i	0.312598	−	0.949886i	$-0.398801\pi$
$521$	−8.07399	−	4.66152i	−0.353728	−	0.204225i	−0.666326	+	0.745661i	$0.732134\pi$
$522$	14.0098	+	10.4643i	0.613192	+	0.458010i
$523$	−2.56968	−	4.45082i	−0.112364	−	0.194621i	0.804359	−	0.594144i	$-0.202509\pi$
$523$	−2.56968	−	4.45082i	−0.112364	−	0.194621i	−0.916723	+	0.399523i	$0.869176\pi$
$524$	38.0499	+	10.7244i	1.66222	+	0.468499i
$525$	−29.0819	+	1.55293i	−1.26924	+	0.0677754i
$526$	22.5841	+	9.52612i	0.984716	+	0.415359i
$527$	4.67417	−	3.92210i	0.203610	−	0.170849i
$528$	−3.61922	−	9.15255i	−0.157506	−	0.398314i
$529$	−27.5178	+	10.0157i	−1.19643	+	0.435463i
$530$	−3.12089	+	4.82966i	−0.135563	+	0.209787i
$531$	−7.16081	−	0.486515i	−0.310753	−	0.0211130i
$532$	−46.9337	+	21.1514i	−2.03484	+	0.917029i
$533$	1.18739	−	6.73403i	0.0514316	−	0.291683i
$534$	−4.29847	−	23.9226i	−0.186013	−	1.03523i
$535$	−1.72970	+	4.75232i	−0.0747816	+	0.205461i
$536$	0.361716	+	14.9162i	0.0156238	+	0.644282i
$537$	−2.88533	+	23.6926i	−0.124511	+	1.02241i
$538$	3.46379	−	15.1598i	0.149335	−	0.653587i
$539$			7.60929i			0.327755i
$540$	1.92327	+	4.43820i	0.0827644	+	0.190990i
$541$		−	23.3927i		−	1.00573i	−0.864365	−	0.502865i	$-0.832279\pi$
$541$		−	23.3927i		−	1.00573i	0.864365	−	0.502865i	$-0.167721\pi$
$542$	27.1830	+	6.21091i	1.16761	+	0.266781i
$543$	3.76846	−	1.60401i	0.161720	−	0.0688348i
$544$	2.45867	−	3.59733i	0.105415	−	0.154234i
$545$	1.42454	−	3.91388i	0.0610204	−	0.167652i
$546$	7.36067	−	20.4297i	0.315007	−	0.874312i
$547$	−3.87158	+	21.9568i	−0.165537	+	0.938806i	0.782972	+	0.622056i	$0.213703\pi$
$547$	−3.87158	+	21.9568i	−0.165537	+	0.938806i	−0.948509	+	0.316749i	$0.897409\pi$
$548$	−12.2971	+	5.54188i	−0.525306	+	0.236737i
$549$	−0.981311	−	9.16234i	−0.0418813	−	0.391039i
$550$	8.07135	+	5.21566i	0.344164	+	0.222396i
$551$	−28.3603	+	10.3223i	−1.20819	+	0.439745i
$552$	32.2477	−	14.6593i	1.37255	−	0.623941i
$553$	−37.4796	+	31.4491i	−1.59379	+	1.33735i
$554$	10.2549	−	24.3120i	0.435691	−	1.03292i
$555$	−1.17864	+	2.31887i	−0.0500304	+	0.0984305i
$556$	−7.95811	+	28.2351i	−0.337499	+	1.19744i
$557$	−13.3979	−	23.2059i	−0.567688	−	0.983265i	−0.996794	−	0.0800105i	$-0.974505\pi$
$557$	−13.3979	−	23.2059i	−0.567688	−	0.983265i	0.429106	−	0.903254i	$-0.358829\pi$
$558$	−32.7146	+	7.69901i	−1.38492	+	0.325925i
$559$	4.63842	+	2.67799i	0.196184	+	0.113267i
$560$	0.969456	+	6.47220i	0.0409670	+	0.273501i
$561$	1.84627	−	0.428167i	0.0779496	−	0.0180772i
$562$	34.3665	−	4.29868i	1.44966	−	0.181329i
$563$	26.1430	−	4.60972i	1.10180	−	0.194276i	0.406961	−	0.913446i	$-0.366589\pi$
$563$	26.1430	−	4.60972i	1.10180	−	0.194276i	0.694835	+	0.719169i	$0.255477\pi$
$564$	10.8325	+	34.7447i	0.456129	+	1.46302i
$565$	1.15352	−	1.37471i	0.0485290	−	0.0578346i
$566$	11.3202	+	22.0934i	0.475825	+	0.928656i
$567$	29.2858	−	11.9671i	1.22989	−	0.502571i
$568$	31.9230	+	4.83409i	1.33946	+	0.202834i
$569$	4.50444	−	5.36818i	0.188836	−	0.225046i	−0.663317	−	0.748338i	$-0.730852\pi$
$569$	4.50444	−	5.36818i	0.188836	−	0.225046i	0.852153	+	0.523292i	$0.175296\pi$
$570$	−8.22616	−	1.42293i	−0.344556	−	0.0595998i
$571$	−1.80104	−	10.2142i	−0.0753710	−	0.427450i	−0.999022	−	0.0442155i	$-0.985921\pi$
$571$	−1.80104	−	10.2142i	−0.0753710	−	0.427450i	0.923651	−	0.383235i	$-0.125190\pi$
$572$	−5.92222	+	4.03372i	−0.247620	+	0.168658i
$573$	−18.2163	+	4.22453i	−0.760997	+	0.176482i
$574$	12.8806	−	3.96990i	0.537626	−	0.165700i
$575$	−17.2937	+	29.9535i	−0.721196	+	1.24915i
$576$	−21.0129	+	11.5957i	−0.875536	+	0.483153i
$577$	−5.28015	−	9.14548i	−0.219815	−	0.380731i	0.734936	−	0.678136i	$-0.237212\pi$
$577$	−5.28015	−	9.14548i	−0.219815	−	0.380731i	−0.954751	+	0.297405i	$0.903879\pi$
$578$	−17.0051	−	15.7857i	−0.707317	−	0.656597i
$579$	−31.7718	−	16.1490i	−1.32039	−	0.671130i
$580$	0.284963	+	3.82612i	0.0118324	+	0.158871i
$581$	−31.0508	+	26.0547i	−1.28821	+	1.08093i
$582$	4.41477	+	2.52976i	0.182998	+	0.104862i
$583$	−4.24453	−	11.6618i	−0.175791	−	0.482981i
$584$	−6.10961	−	15.5986i	−0.252818	−	0.645475i
$585$	2.84487	−	2.07552i	0.117621	−	0.0858121i
$586$	35.9583	+	1.80287i	1.48542	+	0.0744760i
$587$	−23.9487	−	4.22280i	−0.988467	−	0.174293i	−0.344037	−	0.938956i	$-0.611794\pi$
$587$	−23.9487	−	4.22280i	−0.988467	−	0.174293i	−0.644431	+	0.764663i	$0.722906\pi$
$588$	18.4041	−	2.36286i	0.758973	−	0.0974427i
$589$	19.8391	−	54.5074i	0.817455	−	2.24594i
$590$	−0.950572	−	1.25553i	−0.0391344	−	0.0516892i
$591$	−1.73548	−	4.07732i	−0.0713879	−	0.167718i
$592$	−12.0101	−	4.72634i	−0.493612	−	0.194251i
$593$			3.37367i			0.138540i	0.997598	+	0.0692700i	$0.0220670\pi$
$593$			3.37367i			0.138540i	−0.997598	+	0.0692700i	$0.977933\pi$
$594$	−10.1422	−	2.47248i	−0.416138	−	0.101447i
$595$	−1.26023			−0.0516645
$596$	16.5463	−	4.20512i	0.677762	−	0.172248i
$597$	4.36979	−	35.8821i	0.178844	−	1.46856i
$598$	−15.5671	−	20.5612i	−0.636585	−	0.840809i
$599$	−5.23313	−	1.90470i	−0.213820	−	0.0778241i	0.232889	−	0.972503i	$-0.425182\pi$
$599$	−5.23313	−	1.90470i	−0.213820	−	0.0778241i	−0.446709	+	0.894679i	$0.647404\pi$
$600$	10.1084	−	21.1413i	0.412676	−	0.863089i
$601$	−4.92392	+	27.9250i	−0.200851	+	1.13908i	0.702985	+	0.711205i	$0.251850\pi$
$601$	−4.92392	+	27.9250i	−0.200851	+	1.13908i	−0.903836	+	0.427879i	$0.859261\pi$
$602$	−0.528661	+	10.5442i	−0.0215466	+	0.429748i
$603$	13.1375	+	8.82366i	0.535002	+	0.359327i
$604$	0.997648	−	9.92404i	0.0405937	−	0.403803i
$605$	−3.92843	+	1.42983i	−0.159713	+	0.0581309i
$606$	18.0558	−	10.5030i	0.733466	−	0.426653i
$607$	−12.4758	−	14.8681i	−0.506379	−	0.603479i	0.450925	−	0.892562i	$-0.351094\pi$
$607$	−12.4758	−	14.8681i	−0.506379	−	0.603479i	−0.957304	+	0.289083i	$0.906650\pi$
$608$	3.14287	−	41.3029i	0.127460	−	1.67505i
$609$	25.0585	−	1.33809i	1.01542	−	0.0542220i
$610$	1.37552	−	1.48178i	0.0556933	−	0.0599955i
$611$	22.9465	−	13.2482i	0.928315	−	0.535963i
$612$	−1.60889	−	4.33250i	−0.0650355	−	0.175131i
$613$	−4.17880	−	2.41263i	−0.168780	−	0.0974452i	0.413230	−	0.910626i	$-0.364400\pi$
$613$	−4.17880	−	2.41263i	−0.168780	−	0.0974452i	−0.582010	+	0.813181i	$0.697734\pi$
$614$	−37.0408	+	11.4163i	−1.49485	+	0.460723i
$615$	2.09089	+	0.636992i	0.0843130	+	0.0256860i
$616$	−12.3994	−	6.76344i	−0.499588	−	0.272507i
$617$	21.9486	−	3.87013i	0.883617	−	0.155806i	0.286616	−	0.958046i	$-0.407470\pi$
$617$	21.9486	−	3.87013i	0.883617	−	0.155806i	0.597002	+	0.802240i	$0.296359\pi$
$618$	−19.6976	+	7.24198i	−0.792354	+	0.291315i
$619$	7.17245	+	6.01840i	0.288285	+	0.241900i	0.775448	−	0.631411i	$-0.217524\pi$
$619$	7.17245	+	6.01840i	0.288285	+	0.241900i	−0.487163	+	0.873311i	$0.661968\pi$
$620$	−5.98528	−	4.30729i	−0.240374	−	0.172985i
$621$	7.05974	−	36.9029i	0.283298	−	1.48086i
$622$	−10.0308	−	19.5769i	−0.402200	−	0.784964i
$623$	−26.7198	−	22.4206i	−1.07051	−	0.898262i
$624$	11.5951	+	13.0711i	0.464175	+	0.523264i
$625$	3.78508	+	21.4663i	0.151403	+	0.858650i
$626$	−1.78887	−	14.3014i	−0.0714977	−	0.571601i
$627$	13.1649	−	12.3008i	0.525754	−	0.491246i
$628$	32.4461	−	31.6180i	1.29474	−	1.26170i
$629$	1.24269	−	2.15240i	0.0495493	−	0.0858218i
$630$	6.19813	+	3.12507i	0.246940	+	0.124506i
$631$	27.6553	−	15.9668i	1.10094	−	0.635628i	0.164472	−	0.986382i	$-0.447408\pi$
$631$	27.6553	−	15.9668i	1.10094	−	0.635628i	0.936468	+	0.350754i	$0.114075\pi$
$632$	−7.77399	−	38.5924i	−0.309233	−	1.53512i
$633$	−0.0219348	+	0.0142754i	−0.000871829	+	0.000567398i
$634$	43.0831	+	18.1727i	1.71105	+	0.721730i
$635$	3.39964	+	4.05154i	0.134911	+	0.160780i
$636$	−26.8876	+	13.8872i	−1.06616	+	0.550665i
$637$	−4.62030	−	12.6942i	−0.183063	−	0.502961i
$638$	−6.95470	−	4.49408i	−0.275339	−	0.177922i
$639$	23.7402	−	24.6811i	0.939148	−	0.976370i
$640$	−4.94539	−	1.80897i	−0.195484	−	0.0715059i
$641$	−21.6518	−	3.81780i	−0.855195	−	0.150794i	−0.271172	−	0.962531i	$-0.587411\pi$
$641$	−21.6518	−	3.81780i	−0.855195	−	0.150794i	−0.584023	+	0.811737i	$0.698522\pi$
$642$	−20.3328	+	17.1742i	−0.802471	+	0.677812i
$643$	−21.2821	−	7.74607i	−0.839286	−	0.305475i	−0.113622	−	0.993524i	$-0.536245\pi$
$643$	−21.2821	−	7.74607i	−0.839286	−	0.305475i	−0.725664	+	0.688049i	$0.758467\pi$
$644$	22.0773	−	45.7903i	0.869969	−	1.80439i
$645$	−1.02900	+	1.36833i	−0.0405166	+	0.0538781i
$646$	7.77615	+	1.77673i	0.305948	+	0.0699046i
$647$	46.7102			1.83637			0.918183	−	0.396157i	$-0.129656\pi$
$647$	46.7102			1.83637			0.918183	+	0.396157i	$0.129656\pi$
$648$	−2.83065	+	25.2980i	−0.111199	+	0.993798i
$649$	3.39868			0.133410
$650$	−16.6319	−	3.80014i	−0.652357	−	0.149054i
$651$	−28.9875	+	38.5469i	−1.13611	+	1.51077i
$652$	44.9042	+	21.6501i	1.75858	+	0.847883i
$653$	−10.0893	−	3.67221i	−0.394825	−	0.143705i	0.136975	−	0.990575i	$-0.456262\pi$
$653$	−10.0893	−	3.67221i	−0.394825	−	0.143705i	−0.531800	+	0.846870i	$0.678484\pi$
$654$	16.7455	−	14.1442i	0.654801	−	0.553082i
$655$	9.06022	+	1.59756i	0.354012	+	0.0624219i
$656$	−2.15870	+	10.6283i	−0.0842831	+	0.414964i
$657$	−17.2493	−	4.26454i	−0.672959	−	0.166376i
$658$	43.8663	+	28.3461i	1.71009	+	1.10505i
$659$	13.5526	+	37.2355i	0.527935	+	1.45049i	0.861497	+	0.507762i	$0.169527\pi$
$659$	13.5526	+	37.2355i	0.527935	+	1.45049i	−0.333562	+	0.942728i	$0.608251\pi$
$660$	−1.05109	−	2.03506i	−0.0409137	−	0.0792144i
$661$	−8.48287	−	10.1095i	−0.329945	−	0.393213i	0.575412	−	0.817863i	$-0.304842\pi$
$661$	−8.48287	−	10.1095i	−0.329945	−	0.393213i	−0.905358	+	0.424650i	$0.860397\pi$
$662$	14.4813	+	6.10831i	0.562833	+	0.237406i
$663$	−2.82005	+	1.83533i	−0.109522	+	0.0712782i
$664$	−6.44055	−	31.9728i	−0.249942	−	1.24079i
$665$	−10.3753	+	5.99018i	−0.402337	+	0.232289i
$666$	−11.4493	+	7.50446i	−0.443651	+	0.290792i
$667$	14.9011	−	25.8095i	0.576974	−	0.999349i
$668$	−1.46966	−	1.50815i	−0.0568629	−	0.0583521i
$669$	−3.45144	+	3.22490i	−0.133440	+	0.124682i
$670$	0.430971	+	3.44547i	0.0166499	+	0.133110i
$671$	0.757708	+	4.29718i	0.0292510	+	0.165891i
$672$	−12.5080	+	32.0900i	−0.482507	+	1.23790i
$673$	−4.00717	−	3.36241i	−0.154465	−	0.129612i	0.562280	−	0.826947i	$-0.309924\pi$
$673$	−4.00717	−	3.36241i	−0.154465	−	0.129612i	−0.716745	+	0.697335i	$0.754369\pi$
$674$	4.13406	+	8.06834i	0.159238	+	0.310781i
$675$	−12.1144	−	21.7029i	−0.466282	−	0.835347i
$676$	−7.75655	+	10.7783i	−0.298329	+	0.414549i
$677$	0.442568	+	0.371358i	0.0170093	+	0.0142725i	0.651253	−	0.758861i	$-0.274244\pi$
$677$	0.442568	+	0.371358i	0.0170093	+	0.0142725i	−0.634243	+	0.773133i	$0.718688\pi$
$678$	8.86418	−	3.25898i	0.340427	−	0.125160i
$679$	7.19096	−	1.26796i	0.275964	−	0.0486598i
$680$	0.485575	−	0.890206i	0.0186209	−	0.0341378i
$681$	−3.36113	−	1.02397i	−0.128799	−	0.0392386i
$682$	15.2086	−	4.68742i	0.582368	−	0.179490i
$683$	−0.194169	−	0.112104i	−0.00742968	−	0.00428953i	0.496281	−	0.868162i	$-0.334699\pi$
$683$	−0.194169	−	0.112104i	−0.00742968	−	0.00428953i	−0.503710	+	0.863873i	$0.668032\pi$
$684$	−33.8391	−	28.0214i	−1.29387	−	1.07142i
$685$	−2.71843	+	1.56949i	−0.103866	+	0.0599670i
$686$	−5.55878	+	5.98818i	−0.212235	+	0.228630i
$687$	−10.7666	+	0.574919i	−0.410770	+	0.0219345i
$688$	−7.24451	−	4.43616i	−0.276194	−	0.169127i
$689$	14.1618	+	16.8774i	0.539523	+	0.642979i
$690$	7.12583	−	4.14506i	0.271276	−	0.157800i
$691$	−13.3272	+	4.85069i	−0.506989	+	0.184529i	−0.582835	−	0.812591i	$-0.698057\pi$
$691$	−13.3272	+	4.85069i	−0.506989	+	0.184529i	0.0758457	+	0.997120i	$0.475834\pi$
$692$	−6.94252	−	0.697921i	−0.263915	−	0.0265310i
$693$	−13.4517	+	6.59378i	−0.510988	+	0.250477i
$694$	2.28706	−	45.6155i	0.0868157	−	1.73154i
$695$	−1.18548	+	6.72318i	−0.0449677	+	0.255025i
$696$	−8.70997	+	18.2164i	−0.330151	+	0.690492i
$697$	−1.96248	−	0.714286i	−0.0743344	−	0.0270555i
$698$	−0.221198	−	0.292162i	−0.00837248	−	0.0110585i
$699$	5.19551	−	42.6625i	0.196512	−	1.61364i
$700$	−8.28317	−	32.5926i	−0.313075	−	1.23188i
$701$	5.36891			0.202781			0.101391	−	0.994847i	$-0.467671\pi$
$701$	5.36891			0.202781			0.101391	+	0.994847i	$0.467671\pi$
$702$	18.4209	−	2.03354i	0.695251	−	0.0767509i
$703$		−	23.6272i		−	0.891115i
$704$	9.55515	−	6.15275i	0.360123	−	0.231891i
$705$	3.31707	+	7.79310i	0.124928	+	0.293505i
$706$	−7.01860	−	9.27026i	−0.264149	−	0.348891i
$707$	10.2524	−	28.1683i	0.385582	−	1.05938i
$708$	−1.05537	−	8.22018i	−0.0396632	−	0.308933i
$709$	−16.2741	−	2.86956i	−0.611187	−	0.107769i	−0.140517	−	0.990078i	$-0.544876\pi$
$709$	−16.2741	−	2.86956i	−0.611187	−	0.107769i	−0.470670	+	0.882310i	$0.655988\pi$
$710$	7.50441	+	0.376255i	0.281635	+	0.0141206i
$711$	−38.1792	−	16.9081i	−1.43183	−	0.634105i
$712$	26.1328	−	10.2356i	0.979368	−	0.383596i
$713$	19.5905	+	53.8245i	0.733671	+	2.01574i
$714$	−5.75447	−	3.29744i	−0.215356	−	0.123404i
$715$	−1.27741	+	1.07188i	−0.0477725	+	0.0400859i
$716$	−27.4839	+	2.04695i	−1.02712	+	0.0764982i
$717$	39.4143	+	20.0335i	1.47195	+	0.748167i
$718$	0.373599	+	0.346809i	0.0139426	+	0.0129428i
$719$	1.17170	+	2.02945i	0.0436971	+	0.0756857i	0.887047	−	0.461680i	$-0.152753\pi$
$719$	1.17170	+	2.02945i	0.0436971	+	0.0756857i	−0.843350	+	0.537365i	$0.819420\pi$
$720$	−4.59567	+	3.17414i	−0.171271	+	0.118293i
$721$	−15.0586	+	26.0823i	−0.560812	+	0.971356i
$722$	46.7869	−	14.4201i	1.74123	−	0.536660i
$723$	27.8378	−	6.45584i	1.03530	−	0.240095i
$724$	2.66227	+	3.90869i	0.0989426	+	0.145265i
$725$	−3.42349	−	19.4156i	−0.127145	−	0.721077i
$726$	−21.6792	−	3.74997i	−0.804590	−	0.139175i
$727$	−10.6227	+	12.6596i	−0.393974	+	0.469520i	−0.926173	−	0.377099i	$-0.876922\pi$
$727$	−10.6227	+	12.6596i	−0.393974	+	0.469520i	0.532198	+	0.846620i	$0.321366\pi$
$728$	24.7920	+	3.75424i	0.918853	+	0.139142i
$729$	20.1717	+	17.9473i	0.747099	+	0.664713i
$730$	−1.77780	−	3.46969i	−0.0657993	−	0.128419i
$731$	1.05149	−	1.25311i	0.0388906	−	0.0463480i
$732$	10.1580	−	3.16699i	0.375451	−	0.117055i
$733$	−35.2664	+	6.21842i	−1.30260	+	0.229683i	−0.781548	−	0.623845i	$-0.785570\pi$
$733$	−35.2664	+	6.21842i	−1.30260	+	0.229683i	−0.521047	+	0.853528i	$0.674458\pi$
$734$	−43.7800	+	5.47614i	−1.61595	+	0.202128i
$735$	4.20653	−	0.975532i	0.155160	−	0.0359831i
$736$	23.8390	+	33.2383i	0.878715	+	1.22518i
$737$	−6.48994	−	3.74697i	−0.239060	−	0.138021i
$738$	7.88072	+	8.37952i	0.290093	+	0.308455i
$739$	15.1448	+	26.2316i	0.557112	+	0.964946i	0.997736	+	0.0672539i	$0.0214238\pi$
$739$	15.1448	+	26.2316i	0.557112	+	0.964946i	−0.440624	+	0.897692i	$0.645243\pi$
$740$	−2.89099	−	0.814831i	−0.106275	−	0.0299538i
$741$	−14.4933	+	28.5143i	−0.532425	+	1.04750i
$742$	−16.8781	+	40.0140i	−0.619616	+	1.46896i
$743$	−37.2460	+	31.2531i	−1.36642	+	1.14657i	−0.392485	+	0.919758i	$0.628384\pi$
$743$	−37.2460	+	31.2531i	−1.36642	+	1.14657i	−0.973940	+	0.226808i	$0.927171\pi$
$744$	−16.0598	−	35.3286i	−0.588780	−	1.29521i
$745$	3.73346	−	1.35887i	0.136783	−	0.0497850i
$746$	−10.1614	−	6.56622i	−0.372035	−	0.240407i
$747$	−31.6305	−	14.0080i	−1.15730	−	0.512524i
$748$	0.899173	+	1.99521i	0.0328770	+	0.0729522i
$749$	−6.63243	+	37.6144i	−0.242344	+	1.37440i
$750$	3.78076	−	10.4936i	0.138054	−	0.383173i
$751$	1.78479	−	4.90367i	0.0651279	−	0.178937i	−0.902860	−	0.429935i	$-0.858536\pi$
$751$	1.78479	−	4.90367i	0.0651279	−	0.178937i	0.967988	+	0.250998i	$0.0807586\pi$
$752$	−36.9252	+	20.0645i	−1.34652	+	0.731676i
$753$	7.03822	−	2.99576i	0.256487	−	0.109171i
$754$	14.3309	+	3.27440i	0.521901	+	0.119246i
$755$		−	2.32116i		−	0.0844758i
$756$	20.1250	+	30.4873i	0.731940	+	1.10881i
$757$			23.5414i			0.855626i	0.903867	+	0.427813i	$0.140716\pi$
$757$			23.5414i			0.855626i	−0.903867	+	0.427813i	$0.859284\pi$
$758$	3.74032	−	16.3701i	0.135855	−	0.594589i
$759$	−2.15080	+	17.6611i	−0.0780689	+	0.641056i
$760$	−0.233696	−	9.63698i	−0.00847703	−	0.349570i
$761$	11.0387	−	30.3285i	0.400151	−	1.09941i	−0.562059	−	0.827097i	$-0.689990\pi$
$761$	11.0387	−	30.3285i	0.400151	−	1.09941i	0.962210	−	0.272309i	$-0.0877873\pi$
$762$	4.92246	+	27.3954i	0.178322	+	0.992430i
$763$	5.46228	−	30.9782i	0.197748	−	1.12148i
$764$	−8.87173	−	19.6858i	−0.320968	−	0.712209i
$765$	−0.473394	−	0.965753i	−0.0171156	−	0.0349169i
$766$	−17.6722	+	27.3482i	−0.638523	+	0.988129i
$767$	−5.66984	+	2.06365i	−0.204726	+	0.0745141i
$768$	−17.8484	−	21.1999i	−0.644048	−	0.764985i
$769$	−10.7031	+	8.98096i	−0.385964	+	0.323862i	−0.815038	−	0.579407i	$-0.803284\pi$
$769$	−10.7031	+	8.98096i	−0.385964	+	0.323862i	0.429075	+	0.903269i	$0.358840\pi$
$770$	−3.02857	−	1.27747i	−0.109142	−	0.0460367i
$771$	−32.5998	+	1.74078i	−1.17405	+	0.0626927i
$772$	11.1643	−	39.6107i	0.401813	−	1.42562i
$773$	7.86483	+	13.6223i	0.282878	+	0.489959i	0.972092	−	0.234598i	$-0.0753774\pi$
$773$	7.86483	+	13.6223i	0.282878	+	0.489959i	−0.689214	+	0.724558i	$0.742044\pi$
$774$	−8.27888	+	3.55568i	−0.297578	+	0.127806i
$775$	32.8152	+	18.9459i	1.17876	+	0.680555i
$776$	−1.87505	+	5.56812i	−0.0673105	+	0.199884i
$777$	−5.72517	+	18.7926i	−0.205389	+	0.674180i
$778$	3.21331	+	25.6894i	0.115203	+	0.921009i
$779$	−19.5520	+	3.44754i	−0.700523	+	0.123521i
$780$	2.98915	+	2.75676i	0.107029	+	0.0987077i
$781$	−10.4236	+	12.4224i	−0.372987	+	0.444509i
$782$	−7.00999	+	3.59178i	−0.250677	+	0.128442i
$783$	10.4384	+	18.7004i	0.373037	+	0.668298i
$784$	6.80515	+	20.3162i	0.243041	+	0.725580i
$785$	6.77701	−	8.07653i	0.241882	−	0.288264i
$786$	37.1907	+	31.0011i	1.32655	+	1.10577i
$787$	0.897820	+	5.09179i	0.0320038	+	0.181503i	0.996619	−	0.0821580i	$-0.0261812\pi$
$787$	0.897820	+	5.09179i	0.0320038	+	0.181503i	−0.964616	+	0.263661i	$0.915070\pi$
$788$	4.22904	−	2.88047i	0.150653	−	0.102612i
$789$	20.4951	+	21.9348i	0.729645	+	0.780900i
$790$	−2.69843	−	8.75523i	−0.0960059	−	0.311497i
$791$	6.77657	−	11.7374i	0.240947	−	0.417333i
$792$	0.525296	−	12.0427i	0.0186656	−	0.427918i
$793$	−3.87325	−	6.70867i	−0.137543	−	0.238232i
$794$	6.43407	−	6.93108i	0.228336	−	0.245975i
$795$	−5.90264	+	3.84151i	−0.209345	+	0.136244i
$796$	41.6240	−	3.10008i	1.47532	−	0.109880i
$797$	1.73089	−	1.45239i	0.0613111	−	0.0514461i	−0.611617	−	0.791154i	$-0.709481\pi$
$797$	1.73089	−	1.45239i	0.0613111	−	0.0514461i	0.672928	+	0.739708i	$0.265036\pi$
$798$	−63.0491	+	0.205037i	−2.23191	+	0.00725823i
$799$	−2.76779	−	7.60445i	−0.0979175	−	0.269026i
$800$	26.2144	+	6.70703i	0.926819	+	0.237129i
$801$	7.14452	−	28.8983i	0.252439	−	1.02107i
$802$	0.565309	−	11.2751i	0.0199617	−	0.398137i
$803$	8.28617	+	1.46107i	0.292412	+	0.0515602i
$804$	−7.04729	+	16.8603i	−0.248539	+	0.594619i
$805$	4.04618	−	11.1168i	0.142609	−	0.391816i
$806$	−22.5255	+	17.0543i	−0.793428	+	0.600712i
$807$	11.4468	−	15.2217i	0.402946	−	0.535828i
$808$	15.9473	+	18.0956i	0.561024	+	0.636599i
$809$		−	3.55121i		−	0.124854i	−0.998050	−	0.0624270i	$-0.980116\pi$
$809$		−	3.55121i		−	0.124854i	0.998050	−	0.0624270i	$-0.0198841\pi$
$810$	−0.0665683	+	5.92372i	−0.00233897	+	0.208138i
$811$	−24.8246			−0.871710			−0.435855	−	0.900017i	$-0.643554\pi$
$811$	−24.8246			−0.871710			−0.435855	+	0.900017i	$0.643554\pi$
$812$	7.13722	+	28.0835i	0.250467	+	0.985537i
$813$	27.2939	+	20.5252i	0.957239	+	0.719849i
$814$	5.16824	−	3.91292i	0.181147	−	0.137148i
$815$	10.9017	+	3.96788i	0.381869	+	0.138989i
$816$	4.54648	−	2.79433i	0.159159	−	0.0978212i
$817$	2.70038	−	15.3146i	0.0944744	−	0.535791i
$818$	8.50212	+	0.426278i	0.297270	+	0.0149045i
$819$	18.4371	−	19.1678i	0.644243	−	0.669777i
$820$	−0.252453	+	2.51125i	−0.00881603	+	0.0876968i
$821$	−7.98474	+	2.90621i	−0.278669	+	0.101427i	−0.477574	−	0.878591i	$-0.658484\pi$
$821$	−7.98474	+	2.90621i	−0.278669	+	0.101427i	0.198905	+	0.980019i	$0.436262\pi$
$822$	−16.5195	+	0.0537217i	−0.576184	+	0.00187376i
$823$	−21.2355	−	25.3075i	−0.740223	−	0.882163i	0.256204	−	0.966623i	$-0.417528\pi$
$823$	−21.2355	−	25.3075i	−0.740223	−	0.882163i	−0.996427	+	0.0844593i	$0.973084\pi$
$824$	−12.6219	−	20.6868i	−0.439705	−	0.720659i
$825$	6.41996	+	9.86452i	0.223514	+	0.343439i
$826$	−8.71655	−	8.09150i	−0.303288	−	0.281539i
$827$	−27.5962	+	15.9327i	−0.959613	+	0.554033i	−0.896054	−	0.443945i	$-0.853578\pi$
$827$	−27.5962	+	15.9327i	−0.959613	+	0.554033i	−0.0635591	+	0.997978i	$0.520245\pi$
$828$	43.3836	−	0.282172i	1.50768	−	0.00980614i
$829$	−3.48406	−	2.01153i	−0.121007	−	0.0698632i	0.438275	−	0.898841i	$-0.355590\pi$
$829$	−3.48406	−	2.01153i	−0.121007	−	0.0698632i	−0.559282	+	0.828978i	$0.688923\pi$
$830$	−2.23558	−	7.25348i	−0.0775982	−	0.251772i
$831$	23.6130	−	22.0631i	0.819126	−	0.765362i
$832$	−12.2044	+	16.0661i	−0.423113	+	0.556992i
$833$	−4.06318	+	0.716448i	−0.140781	+	0.0248235i
$834$	−23.0045	+	27.5975i	−0.796582	+	0.955624i
$835$	−0.375411	−	0.315007i	−0.0129916	−	0.0109013i
$836$	16.8865	+	12.1523i	0.584030	+	0.420296i
$837$	−40.4285	−	7.73420i	−1.39741	−	0.267333i
$838$	−33.8374	+	17.3376i	−1.16889	+	0.598918i
$839$	13.1010	+	10.9931i	0.452298	+	0.379523i	0.840288	−	0.542140i	$-0.182386\pi$
$839$	13.1010	+	10.9931i	0.452298	+	0.379523i	−0.387990	+	0.921664i	$0.626830\pi$
$840$	−2.14929	+	7.72169i	−0.0741575	+	0.266424i
$841$	−2.08594	−	11.8299i	−0.0719288	−	0.407929i
$842$	−26.7196	+	3.34217i	−0.920818	+	0.115179i
$843$	40.5770	+	12.3618i	1.39755	+	0.425763i
$844$	−0.0210906	−	0.0216430i	−0.000725968	−	0.000744981i
$845$	−1.54516	+	2.67630i	−0.0531551	+	0.0920674i
$846$	−5.24452	+	44.2640i	−0.180310	+	1.52183i
$847$	−27.3430	+	15.7865i	−0.939516	+	0.542430i
$848$	−21.7620	−	27.3401i	−0.747309	−	0.938861i
$849$	1.62122	+	30.3607i	0.0556401	+	1.04198i
$850$	−2.02508	+	4.80099i	−0.0694598	+	0.164673i
$851$	14.9970	+	17.8727i	0.514089	+	0.612668i
$852$	33.2821	+	21.3536i	1.14023	+	0.731561i
$853$	−4.54120	−	12.4769i	−0.155488	−	0.427199i	0.837350	−	0.546667i	$-0.184104\pi$
$853$	−4.54120	−	12.4769i	−0.155488	−	0.427199i	−0.992838	+	0.119467i	$0.961881\pi$
$854$	8.28732	−	12.8248i	0.283586	−	0.438857i
$855$	−8.48783	−	5.70074i	−0.290278	−	0.194961i
$856$	−24.0146	−	19.1781i	−0.820803	−	0.655493i
$857$	1.39542	+	0.246051i	0.0476668	+	0.00840494i	0.197431	−	0.980317i	$-0.436740\pi$
$857$	1.39542	+	0.246051i	0.0476668	+	0.00840494i	−0.149764	+	0.988722i	$0.547851\pi$
$858$	−8.63751	+	1.55201i	−0.294880	+	0.0529846i
$859$	13.1020	+	4.76873i	0.447034	+	0.162707i	0.555721	−	0.831369i	$-0.312442\pi$
$859$	13.1020	+	4.76873i	0.447034	+	0.162707i	−0.108687	+	0.994076i	$0.534665\pi$
$860$	−1.78075	−	0.858572i	−0.0607231	−	0.0292770i
$861$	16.3867	+	1.99559i	0.558456	+	0.0680097i
$862$	6.05511	−	26.5011i	0.206238	−	0.902633i
$863$	32.7283			1.11408			0.557041	−	0.830485i	$-0.311936\pi$
$863$	32.7283			1.11408			0.557041	+	0.830485i	$0.311936\pi$
$864$	−29.2900	+	2.46903i	−0.996466	+	0.0839980i
$865$	−1.62381			−0.0552111
$866$	−4.30483	+	18.8408i	−0.146284	+	0.640236i
$867$	−11.1293	−	26.1472i	−0.377972	−	0.888006i
$868$	−50.1650	−	24.1865i	−1.70271	−	0.820945i
$869$	18.5802	+	6.76263i	0.630289	+	0.229406i
$870$	−1.59278	+	4.42082i	−0.0540004	+	0.149880i
$871$	13.1019	+	2.31023i	0.443942	+	0.0782790i
$872$	19.7778	+	15.7945i	0.669760	+	0.534870i
$873$	3.67289	+	5.03435i	0.124308	+	0.170387i
$874$	−40.6396	+	62.8907i	−1.37465	+	2.12731i
$875$	−5.47457	−	15.0413i	−0.185074	−	0.508488i
$876$	0.960766	−	20.4949i	0.0324613	−	0.692460i
$877$	16.7454	+	19.9563i	0.565450	+	0.673878i	0.970691	−	0.240333i	$-0.0772565\pi$
$877$	16.7454	+	19.9563i	0.565450	+	0.673878i	−0.405240	+	0.914210i	$0.632812\pi$
$878$	13.4679	−	31.9292i	0.454520	−	1.07756i
$879$	39.3088	+	19.9799i	1.32585	+	0.673906i
$880$	2.06930	−	1.64711i	0.0697562	−	0.0555241i
$881$	32.0686	−	18.5148i	1.08042	−	0.623779i	0.149408	−	0.988776i	$-0.452263\pi$
$881$	32.0686	−	18.5148i	1.08042	−	0.623779i	0.931009	+	0.364996i	$0.118930\pi$
$882$	21.7603	+	6.55205i	0.732709	+	0.220619i
$883$	15.5793	−	26.9841i	0.524285	−	0.908089i	−0.475315	−	0.879816i	$-0.657666\pi$
$883$	15.5793	−	26.9841i	0.524285	−	0.908089i	0.999600	−	0.0282731i	$-0.00900081\pi$
$884$	−2.71152	−	2.78253i	−0.0911981	−	0.0935867i
$885$	−0.435721	−	1.87884i	−0.0146466	−	0.0631566i
$886$	−19.3371	+	2.41875i	−0.649643	+	0.0812595i
$887$	−1.60872	−	9.12349i	−0.0540154	−	0.306337i	0.945816	−	0.324703i	$-0.105265\pi$
$887$	−1.60872	−	9.12349i	−0.0540154	−	0.306337i	−0.999831	+	0.0183666i	$0.994153\pi$
$888$	−11.0688	−	11.2851i	−0.371445	−	0.378702i
$889$	30.5986	+	25.6753i	1.02624	+	0.861122i
$890$	5.81287	−	2.97840i	0.194848	−	0.0998363i
$891$	−10.1060	−	7.83156i	−0.338564	−	0.262367i
$892$	−4.42713	−	3.18597i	−0.148231	−	0.106674i
$893$	−58.9325	−	49.4503i	−1.97210	−	1.65479i
$894$	20.6032	+	3.56386i	0.689075	+	0.119193i
$895$	−6.31633	+	1.11374i	−0.211132	+	0.0372282i
$896$	−39.1543	−	6.96880i	−1.30805	−	0.232811i
$897$	−7.13560	−	30.7689i	−0.238251	−	1.02734i
$898$	7.53731	+	24.4553i	0.251523	+	0.816083i
$899$	−28.2753	−	16.3247i	−0.943033	−	0.544461i
$900$	21.8652	−	18.5907i	0.728839	−	0.619691i
$901$	5.82747	−	3.36449i	0.194141	−	0.112087i
$902$	−3.99215	−	3.70588i	−0.132924	−	0.123392i
$903$	−5.85877	+	11.5266i	−0.194967	+	0.383582i
$904$	5.68002	+	9.30932i	0.188915	+	0.309624i
$905$	0.707443	+	0.843097i	0.0235162	+	0.0280255i
$906$	6.07340	−	10.5989i	0.201775	−	0.352125i
$907$	14.1698	−	5.15740i	0.470502	−	0.171249i	−0.0958780	−	0.995393i	$-0.530566\pi$
$907$	14.1698	−	5.15740i	0.470502	−	0.171249i	0.566380	+	0.824145i	$0.308344\pi$
$908$	0.405820	−	4.03686i	0.0134676	−	0.133968i
$909$	25.4374	−	2.72442i	0.843706	−	0.0903632i
$910$	5.82806	+	0.292206i	0.193198	+	0.00968655i
$911$	2.78022	−	15.7674i	0.0921129	−	0.522398i	−0.903481	−	0.428628i	$-0.858997\pi$
$911$	2.78022	−	15.7674i	0.0921129	−	0.522398i	0.995594	−	0.0937702i	$-0.0298919\pi$
$912$	24.1484	−	44.6158i	0.799632	−	1.47738i
$913$	15.3932	+	5.60266i	0.509440	+	0.185421i
$914$	7.49721	−	5.67621i	0.247986	−	0.187752i
$915$	2.27840	−	0.969782i	0.0753217	−	0.0320600i
$916$	−3.06656	−	12.0663i	−0.101322	−	0.398681i
$917$	69.4815			2.29448
$918$	0.365315	−	5.64847i	0.0120572	−	0.186427i
$919$			35.6444i			1.17580i	0.808934	+	0.587900i	$0.200045\pi$
$919$			35.6444i			1.17580i	−0.808934	+	0.587900i	$0.799955\pi$
$920$	6.29369	+	7.14152i	0.207497	+	0.235449i
$921$	−47.1232	−	5.73875i	−1.55276	−	0.189098i
$922$	−25.4509	+	19.2691i	−0.838181	+	0.634595i
$923$	9.84640	−	27.0528i	0.324098	−	0.890453i
$924$	−10.4865	−	13.7575i	−0.344980	−	0.452589i
$925$	15.1998	+	2.68013i	0.499766	+	0.0881222i
$926$	−0.668997	+	13.3431i	−0.0219846	+	0.438483i
$927$	−25.6443	−	1.74230i	−0.842268	−	0.0572248i
$928$	−22.5877	−	5.77913i	−0.741477	−	0.189709i
$929$	5.42788	+	14.9130i	0.178083	+	0.489279i	0.996331	−	0.0855870i	$-0.0272766\pi$
$929$	5.42788	+	14.9130i	0.178083	+	0.489279i	−0.818248	+	0.574866i	$0.805054\pi$
$930$	−4.54106	−	7.80661i	−0.148907	−	0.255989i
$931$	−30.0461	+	25.2117i	−0.984721	+	0.826279i
$932$	49.4893	−	3.68588i	1.62108	−	0.120735i
$933$	−1.43656	−	26.9026i	−0.0470308	−	0.880750i
$934$	−7.51205	+	8.09234i	−0.245802	+	0.264790i
$935$	0.254650	+	0.441067i	0.00832795	+	0.0144244i
$936$	6.43589	+	20.4091i	0.210364	+	0.667092i
$937$	3.18741	−	5.52076i	0.104128	−	0.180355i	−0.809253	−	0.587460i	$-0.800128\pi$
$937$	3.18741	−	5.52076i	0.104128	−	0.180355i	0.913382	+	0.407104i	$0.133461\pi$
$938$	7.72397	+	25.0609i	0.252196	+	0.818267i
$939$	5.14430	−	16.8859i	0.167878	−	0.551050i
$940$	−8.08309	+	5.50552i	−0.263641	+	0.179570i
$941$	−3.12587	−	17.7277i	−0.101900	−	0.577906i	−0.992413	−	0.122948i	$-0.960765\pi$
$941$	−3.12587	−	17.7277i	−0.101900	−	0.577906i	0.890513	−	0.454959i	$-0.150346\pi$
$942$	52.0777	−	19.1467i	1.69678	−	0.623834i
$943$	12.6018	−	15.0182i	0.410370	−	0.489060i
$944$	9.07423	−	3.03952i	0.295341	−	0.0989278i
$945$	5.36969	+	6.59097i	0.174676	+	0.214404i
$946$	3.79716	−	1.94559i	0.123456	−	0.0632566i
$947$	−3.51808	+	4.19268i	−0.114322	+	0.136244i	−0.820171	−	0.572119i	$-0.806122\pi$
$947$	−3.51808	+	4.19268i	−0.114322	+	0.136244i	0.705848	+	0.708363i	$0.250566\pi$
$948$	10.5868	−	47.0386i	0.343843	−	1.52774i
$949$	−14.7105	+	2.59386i	−0.477523	+	0.0842002i
$950$	6.14803	+	49.1515i	0.199468	+	1.59469i
$951$	39.0979	+	41.8444i	1.26784	+	1.35690i
$952$	2.44406	−	7.25782i	0.0792123	−	0.235227i
$953$	−8.89078	−	5.13310i	−0.288001	−	0.166277i	0.349039	−	0.937108i	$-0.386508\pi$
$953$	−8.89078	−	5.13310i	−0.288001	−	0.166277i	−0.637040	+	0.770831i	$0.719841\pi$
$954$	−37.0040	+	2.09667i	−1.19805	+	0.0678821i
$955$	−2.51252	−	4.35181i	−0.0813031	−	0.140821i
$956$	−13.8498	+	49.1388i	−0.447936	+	1.58926i
$957$	−5.53178	−	8.49979i	−0.178817	−	0.274759i
$958$	−31.0495	−	13.0969i	−1.00316	−	0.423140i
$959$	−18.1603	+	15.2383i	−0.586428	+	0.492071i
$960$	−4.62633	−	4.49343i	−0.149314	−	0.145025i
$961$	29.8362	−	10.8595i	0.962460	−	0.350307i
$962$	−6.24600	+	9.66583i	−0.201379	+	0.311639i
$963$	−31.3164	+	9.04685i	−1.00916	+	0.291531i
$964$	13.5576	+	30.0836i	0.436661	+	0.968926i
$965$	1.66309	−	9.43186i	0.0535368	−	0.303622i
$966$	47.5631	−	40.1745i	1.53032	−	1.29259i
$967$	1.87573	−	5.15353i	0.0603195	−	0.165726i	−0.905872	−	0.423551i	$-0.860783\pi$
$967$	1.87573	−	5.15353i	0.0603195	−	0.165726i	0.966192	+	0.257825i	$0.0830057\pi$
$968$	−0.615880	−	25.3972i	−0.0197951	−	0.816298i
$969$	7.80786	+	5.87156i	0.250825	+	0.188622i
$970$	−0.304562	+	1.33296i	−0.00977889	+	0.0427988i
$971$		−	22.2762i		−	0.714877i	−0.933937	−	0.357439i	$-0.883650\pi$
$971$		−	22.2762i		−	0.714877i	0.933937	−	0.357439i	$-0.116350\pi$
$972$	−15.8036	+	26.8747i	−0.506899	+	0.862005i
$973$			51.5591i			1.65291i
$974$	6.89631	+	1.57570i	0.220972	+	0.0504887i
$975$	−16.6997	−	12.5583i	−0.534819	−	0.402187i
$976$	5.86608	+	10.7955i	0.187769	+	0.345556i
$977$	−8.42429	+	23.1456i	−0.269517	+	0.740492i	0.728920	+	0.684599i	$0.240023\pi$
$977$	−8.42429	+	23.1456i	−0.269517	+	0.740492i	−0.998437	+	0.0558929i	$0.982199\pi$
$978$	39.3970	+	46.6427i	1.25978	+	1.49147i
$979$	−2.44778	+	13.8821i	−0.0782315	+	0.443673i
$980$	2.04867	+	4.54588i	0.0654423	+	0.145213i
$981$	25.7913	−	7.45073i	0.823454	−	0.237884i
$982$	−37.3473	−	24.1336i	−1.19180	−	0.770135i
$983$	19.2748	−	7.01545i	0.614771	−	0.223758i	−0.0158187	−	0.999875i	$-0.505035\pi$
$983$	19.2748	−	7.01545i	0.614771	−	0.223758i	0.630589	+	0.776117i	$0.282813\pi$
$984$	−7.72353	+	10.8063i	−0.246217	+	0.344493i
$985$	0.912196	−	0.765424i	0.0290650	−	0.0243884i
$986$	1.74492	−	4.13679i	0.0555695	−	0.131742i
$987$	34.8913	+	53.6119i	1.11060	+	1.70649i
$988$	−35.5495	−	10.0197i	−1.13098	−	0.318769i
$989$	7.67802	+	13.2987i	0.244147	+	0.422875i
$990$	−0.158692	−	2.80075i	−0.00504355	−	0.0890136i
$991$	19.3983	+	11.1996i	0.616207	+	0.355767i	0.775391	−	0.631482i	$-0.217553\pi$
$991$	19.3983	+	11.1996i	0.616207	+	0.355767i	−0.159184	+	0.987249i	$0.550886\pi$
$992$	36.4138	−	26.1164i	1.15614	−	0.829198i
$993$	13.1418	+	14.0650i	0.417043	+	0.446339i
$994$	56.3083	−	7.04323i	1.78599	−	0.223398i
$995$	9.56599	−	1.68674i	0.303262	−	0.0534733i
$996$	8.77087	−	38.9703i	0.277916	−	1.23482i
$997$	−27.6176	+	32.9134i	−0.874659	+	1.04238i	0.124085	+	0.992272i	$0.460400\pi$
$997$	−27.6176	+	32.9134i	−0.874659	+	1.04238i	−0.998744	+	0.0501062i	$0.984044\pi$
$998$	7.97776	+	15.5700i	0.252532	+	0.492860i
$999$	−16.5519	+	2.67188i	−0.523679	+	0.0845346i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.2.v.b.11.15	yes	192
3.2	odd	2		648.2.v.b.35.18		192
4.3	odd	2		864.2.bh.b.335.21		192
8.3	odd	2	inner	216.2.v.b.11.4	✓	192
8.5	even	2		864.2.bh.b.335.22		192
24.11	even	2		648.2.v.b.35.29		192
27.5	odd	18	inner	216.2.v.b.59.4	yes	192
27.22	even	9		648.2.v.b.611.29		192
108.59	even	18		864.2.bh.b.815.22		192
216.5	odd	18		864.2.bh.b.815.21		192
216.59	even	18	inner	216.2.v.b.59.15	yes	192
216.211	odd	18		648.2.v.b.611.18		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.4	✓	192	8.3	odd	2	inner
216.2.v.b.11.15	yes	192	1.1	even	1	trivial
216.2.v.b.59.4	yes	192	27.5	odd	18	inner
216.2.v.b.59.15	yes	192	216.59	even	18	inner
648.2.v.b.35.18		192	3.2	odd	2
648.2.v.b.35.29		192	24.11	even	2
648.2.v.b.611.18		192	216.211	odd	18
648.2.v.b.611.29		192	27.22	even	9
864.2.bh.b.335.21		192	4.3	odd	2
864.2.bh.b.335.22		192	8.5	even	2
864.2.bh.b.815.21		192	216.5	odd	18
864.2.bh.b.815.22		192	108.59	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	216.v (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.315008 + 1.37868i) q^{2} +(-1.04101 + 1.38431i) q^{3} +(-1.80154 - 0.868594i) q^{4} +(-0.437371 - 0.159190i) q^{5} +(-1.58060 - 1.87129i) q^{6} +(-3.46177 - 0.610403i) q^{7} +(1.76502 - 2.21014i) q^{8} +(-0.832609 - 2.88215i) q^{9} +(0.357248 - 0.552850i) q^{10} +(0.485871 + 1.33492i) q^{11} +(3.07782 - 1.58967i) q^{12} +(-1.62110 - 1.93196i) q^{13} +(1.93204 - 4.58040i) q^{14} +(0.675674 - 0.439738i) q^{15} +(2.49109 + 3.12961i) q^{16} +(-0.667069 + 0.385133i) q^{17} +(4.23585 - 0.240005i) q^{18} +(-3.66125 + 6.34147i) q^{19} +(0.649669 + 0.666685i) q^{20} +(4.44871 - 4.15671i) q^{21} +(-1.99349 + 0.249352i) q^{22} +(-1.25561 - 7.12090i) q^{23} +(1.22212 + 4.74409i) q^{24} +(-3.66427 - 3.07469i) q^{25} +(3.17422 - 1.62641i) q^{26} +(4.85652 + 1.84775i) q^{27} +(5.70632 + 4.10653i) q^{28} +(3.15733 + 2.64931i) q^{29} +(0.393416 + 1.07006i) q^{30} +(-7.80121 + 1.37556i) q^{31} +(-5.09946 + 2.44857i) q^{32} +(-2.35373 - 0.717067i) q^{33} +(-0.320844 - 1.04100i) q^{34} +(1.41691 + 0.818051i) q^{35} +(-1.00344 + 5.91550i) q^{36} +(-2.79436 + 1.61333i) q^{37} +(-7.58956 - 7.04532i) q^{38} +(4.36200 - 0.232925i) q^{39} +(-1.12380 + 0.685678i) q^{40} +(1.74280 + 2.07699i) q^{41} +(4.32941 + 7.44276i) q^{42} +(-1.99564 + 0.726352i) q^{43} +(0.284188 - 2.82694i) q^{44} +(-0.0946497 + 1.39311i) q^{45} +(10.2130 + 0.512058i) q^{46} +(-1.82437 + 10.3465i) q^{47} +(-6.92558 + 0.190482i) q^{48} +(5.03339 + 1.83200i) q^{49} +(5.39330 - 4.08332i) q^{50} +(0.161282 - 1.32435i) q^{51} +(1.24240 + 4.88858i) q^{52} -8.73592 q^{53} +(-4.07731 + 6.11356i) q^{54} -0.661201i q^{55} +(-7.45915 + 6.57361i) q^{56} +(-4.96715 - 11.6698i) q^{57} +(-4.64715 + 3.51840i) q^{58} +(0.818263 - 2.24816i) q^{59} +(-1.59921 + 0.205318i) q^{60} +(3.02492 + 0.533375i) q^{61} +(0.560979 - 11.1887i) q^{62} +(1.12303 + 10.4855i) q^{63} +(-1.76943 - 7.80187i) q^{64} +(0.401476 + 1.10305i) q^{65} +(1.73005 - 3.01917i) q^{66} +(-4.04105 + 3.39085i) q^{67} +(1.53628 - 0.114419i) q^{68} +(11.1646 + 5.67476i) q^{69} +(-1.57417 + 1.69577i) q^{70} +(5.70758 + 9.88583i) q^{71} +(-7.83951 - 3.24685i) q^{72} +(2.96144 - 5.12936i) q^{73} +(-1.34402 - 4.36075i) q^{74} +(8.07084 - 1.87170i) q^{75} +(12.1041 - 8.24427i) q^{76} +(-0.867134 - 4.91776i) q^{77} +(-1.05294 + 6.08720i) q^{78} +(8.94667 - 10.6622i) q^{79} +(-0.591327 - 1.76536i) q^{80} +(-7.61352 + 4.79940i) q^{81} +(-3.41251 + 1.74850i) q^{82} +(7.41209 - 8.83338i) q^{83} +(-11.6250 + 3.62436i) q^{84} +(0.353066 - 0.0622550i) q^{85} +(-0.372768 - 2.98016i) q^{86} +(-6.95426 + 1.61276i) q^{87} +(3.80793 + 1.28231i) q^{88} +(8.59338 + 4.96139i) q^{89} +(-1.89084 - 0.569333i) q^{90} +(4.43261 + 7.67751i) q^{91} +(-3.92315 + 13.9192i) q^{92} +(6.21691 - 12.2312i) q^{93} +(-13.6899 - 5.77446i) q^{94} +(2.61082 - 2.19074i) q^{95} +(1.91900 - 9.60820i) q^{96} +(-1.95198 + 0.710462i) q^{97} +(-4.11131 + 6.36235i) q^{98} +(3.44289 - 2.51182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 192 q - 6 q^{2} - 12 q^{3} - 6 q^{4} - 6 q^{6} - 9 q^{8} - 12 q^{9} - 3 q^{10} - 30 q^{11} - 3 q^{12} + 9 q^{14} - 6 q^{16} - 18 q^{17} + 63 q^{18} - 6 q^{19} - 27 q^{20} - 18 q^{22} - 30 q^{24} - 12 q^{25}+ \cdots - 12 q^{99}+O(q^{100}) \) 192 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 6 * q^6 - 9 * q^8 - 12 * q^9 - 3 * q^10 - 30 * q^11 - 3 * q^12 + 9 * q^14 - 6 * q^16 - 18 * q^17 + 63 * q^18 - 6 * q^19 - 27 * q^20 - 18 * q^22 - 30 * q^24 - 12 * q^25 + 18 * q^27 - 12 * q^28 - 21 * q^30 - 36 * q^32 - 30 * q^33 + 12 * q^34 - 18 * q^35 - 36 * q^36 - 102 * q^38 + 9 * q^40 + 18 * q^41 - 6 * q^42 - 42 * q^43 - 81 * q^44 - 3 * q^46 - 81 * q^48 - 12 * q^49 + 57 * q^50 - 18 * q^51 + 21 * q^52 + 78 * q^54 - 69 * q^56 - 36 * q^57 - 33 * q^58 - 84 * q^59 - 54 * q^60 + 90 * q^62 - 51 * q^64 - 12 * q^65 + 87 * q^66 + 30 * q^67 + 63 * q^68 - 33 * q^70 + 12 * q^72 - 6 * q^73 + 51 * q^74 - 96 * q^75 + 30 * q^76 + 90 * q^78 - 12 * q^81 - 12 * q^82 - 72 * q^83 - 48 * q^84 + 42 * q^86 - 78 * q^88 + 144 * q^89 + 120 * q^90 - 6 * q^91 - 3 * q^92 - 33 * q^94 - 78 * q^96 - 42 * q^97 + 162 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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