LMFDB - Embedded newform 216.2.v.b.11.4

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			11.4
Character	$\chi$	$=$	216.11
Dual form			216.2.v.b.59.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.30304 + 0.549629i) q^{2} +(-1.04101 + 1.38431i) q^{3} +(1.39582 - 1.43237i) q^{4} +(0.437371 + 0.159190i) q^{5} +(0.595617 - 2.37597i) q^{6} +(3.46177 + 0.610403i) q^{7} +(-1.03153 + 2.63362i) q^{8} +(-0.832609 - 2.88215i) q^{9} +(-0.657406 + 0.0329610i) q^{10} +(0.485871 + 1.33492i) q^{11} +(0.529790 + 3.42335i) q^{12} +(1.62110 + 1.93196i) q^{13} +(-4.84631 + 1.10731i) q^{14} +(-0.675674 + 0.439738i) q^{15} +(-0.103392 - 3.99866i) q^{16} +(-0.667069 + 0.385133i) q^{17} +(2.66903 + 3.29792i) q^{18} +(-3.66125 + 6.34147i) q^{19} +(0.838509 - 0.404279i) q^{20} +(-4.44871 + 4.15671i) q^{21} +(-1.36682 - 1.47240i) q^{22} +(1.25561 + 7.12090i) q^{23} +(-2.57191 - 4.16957i) 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} +(0.638737 - 0.944365i) q^{30} +(7.80121 - 1.37556i) q^{31} +(2.33250 + 5.15358i) q^{32} +(-2.35373 - 0.717067i) q^{33} +(0.657537 - 0.868483i) q^{34} +(1.41691 + 0.818051i) q^{35} +(-5.29048 - 2.83034i) q^{36} +(2.79436 - 1.61333i) q^{37} +(1.28529 - 10.2755i) q^{38} +(-4.36200 + 0.232925i) q^{39} +(-0.870406 + 0.987659i) q^{40} +(1.74280 + 2.07699i) q^{41} +(3.51219 - 7.86149i) q^{42} +(-1.99564 + 0.726352i) q^{43} +(2.59029 + 1.16735i) q^{44} +(0.0946497 - 1.39311i) q^{45} +(-5.54996 - 8.58869i) q^{46} +(1.82437 - 10.3465i) q^{47} +(5.64301 + 4.01951i) q^{48} +(5.03339 + 1.83200i) q^{49} +(6.46462 + 1.99245i) q^{50} +(0.161282 - 1.32435i) q^{51} +(5.03005 + 0.374630i) q^{52} +8.73592 q^{53} +(-7.34381 + 0.261600i) q^{54} +0.661201i q^{55} +(-5.17848 + 8.48733i) q^{56} +(-4.96715 - 11.6698i) q^{57} +(5.57026 + 1.71680i) q^{58} +(0.818263 - 2.24816i) q^{59} +(-0.313248 + 1.58161i) q^{60} +(-3.02492 - 0.533375i) q^{61} +(-9.40923 + 6.08018i) q^{62} +(-1.12303 - 10.4855i) q^{63} +(-5.87190 - 5.43331i) q^{64} +(0.401476 + 1.10305i) q^{65} +(3.46113 - 0.359315i) q^{66} +(-4.04105 + 3.39085i) q^{67} +(-0.379452 + 1.49307i) q^{68} +(-11.1646 - 5.67476i) q^{69} +(-2.29591 - 0.287180i) q^{70} +(-5.70758 - 9.88583i) q^{71} +(8.44933 + 0.780240i) q^{72} +(2.96144 - 5.12936i) q^{73} +(-2.75443 + 3.63809i) q^{74} +(8.07084 - 1.87170i) q^{75} +(3.97293 + 14.0958i) q^{76} +(0.867134 + 4.91776i) q^{77} +(5.55583 - 2.70099i) 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} +(-0.255613 + 12.1742i) q^{84} +(-0.353066 + 0.0622550i) q^{85} +(2.20117 - 2.04332i) q^{86} +(6.95426 - 1.61276i) q^{87} +(-4.01686 - 0.0974085i) q^{88} +(8.59338 + 4.96139i) q^{89} +(0.642361 + 1.86730i) q^{90} +(4.43261 + 7.67751i) q^{91} +(11.9524 + 8.14098i) q^{92} +(-6.21691 + 12.2312i) q^{93} +(3.30951 + 14.4846i) q^{94} +(-2.61082 + 2.19074i) q^{95} +(-9.56229 - 2.13602i) q^{96} +(-1.95198 + 0.710462i) q^{97} +(-7.56562 + 0.379324i) 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 $

$2$	−1.30304	+	0.549629i	−0.921387	+	0.388646i
$2$	−1.30304	+	0.549629i	−0.921387	+	0.388646i
$3$	−1.04101	+	1.38431i	−0.601026	+	0.799230i
$3$	−1.04101	+	1.38431i	−0.601026	+	0.799230i
$4$	1.39582	−	1.43237i	0.697908	−	0.716187i
$5$	0.437371	+	0.159190i	0.195598	+	0.0711919i	0.437962	−	0.898994i	$-0.355700\pi$
$5$	0.437371	+	0.159190i	0.195598	+	0.0711919i	−0.242364	+	0.970185i	$0.577923\pi$
$6$	0.595617	−	2.37597i	0.243160	−	0.969986i
$7$	3.46177	+	0.610403i	1.30842	+	0.230711i	0.784008	−	0.620751i	$-0.213172\pi$
$7$	3.46177	+	0.610403i	1.30842	+	0.230711i	0.524417	+	0.851462i	$0.324283\pi$
$8$	−1.03153	+	2.63362i	−0.364700	+	0.931125i
$9$	−0.832609	−	2.88215i	−0.277536	−	0.960715i
$10$	−0.657406	+	0.0329610i	−0.207890	+	0.0104232i
$11$	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	$0.820187\pi$
$12$	0.529790	+	3.42335i	0.152937	+	0.988236i
$13$	1.62110	+	1.93196i	0.449614	+	0.535829i	0.942474	−	0.334280i	$-0.108493\pi$
$13$	1.62110	+	1.93196i	0.449614	+	0.535829i	−0.492860	+	0.870108i	$0.664049\pi$
$14$	−4.84631	+	1.10731i	−1.29523	+	0.295940i
$15$	−0.675674	+	0.439738i	−0.174458	+	0.113540i
$16$	−0.103392	−	3.99866i	−0.0258479	−	0.999666i
$17$	−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	$0.363110\pi$
$18$	2.66903	+	3.29792i	0.629097	+	0.777327i
$19$	−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	$0.849252\pi$
$20$	0.838509	−	0.404279i	0.187496	−	0.0903995i
$21$	−4.44871	+	4.15671i	−0.970788	+	0.907069i
$22$	−1.36682	−	1.47240i	−0.291407	−	0.313917i
$23$	1.25561	+	7.12090i	0.261812	+	1.48481i	0.777961	+	0.628312i	$0.216254\pi$
$23$	1.25561	+	7.12090i	0.261812	+	1.48481i	−0.516149	+	0.856499i	$0.672635\pi$
$24$	−2.57191	−	4.16957i	−0.524988	−	0.851109i
$25$	−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	0.300709	−	0.953716i	$-0.402777\pi$
$29$	−3.15733	−	2.64931i	−0.586301	−	0.491965i	−0.887010	+	0.461751i	$0.847221\pi$
$30$	0.638737	−	0.944365i	0.116617	−	0.172417i
$31$	7.80121	−	1.37556i	1.40114	−	0.247059i	0.578528	−	0.815663i	$-0.303627\pi$
$31$	7.80121	−	1.37556i	1.40114	−	0.247059i	0.822611	+	0.568604i	$0.192516\pi$
$32$	2.33250	+	5.15358i	0.412332	+	0.911034i
$33$	−2.35373	−	0.717067i	−0.409733	−	0.124825i
$34$	0.657537	−	0.868483i	0.112767	−	0.148944i
$35$	1.41691	+	0.818051i	0.239501	+	0.138276i
$36$	−5.29048	−	2.83034i	−0.881747	−	0.471723i
$37$	2.79436	−	1.61333i	0.459390	−	0.265229i	−0.252397	−	0.967624i	$-0.581219\pi$
$37$	2.79436	−	1.61333i	0.459390	−	0.265229i	0.711788	+	0.702394i	$0.247886\pi$
$38$	1.28529	−	10.2755i	0.208502	−	1.66691i
$39$	−4.36200	+	0.232925i	−0.698479	+	0.0372978i
$40$	−0.870406	+	0.987659i	−0.137623	+	0.156163i
$41$	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	$0.709872\pi$
$42$	3.51219	−	7.86149i	0.541942	−	1.21305i
$43$	−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	$0.440661\pi$
$44$	2.59029	+	1.16735i	0.390501	+	0.175985i
$45$	0.0946497	−	1.39311i	0.0141095	−	0.207673i
$46$	−5.54996	−	8.58869i	−0.818296	−	1.26633i
$47$	1.82437	−	10.3465i	0.266111	−	1.50919i	−0.499741	−	0.866175i	$-0.666572\pi$
$47$	1.82437	−	10.3465i	0.266111	−	1.50919i	0.765852	−	0.643017i	$-0.222317\pi$
$48$	5.64301	+	4.01951i	0.814498	+	0.580166i
$49$	5.03339	+	1.83200i	0.719055	+	0.261715i
$50$	6.46462	+	1.99245i	0.914235	+	0.281775i
$51$	0.161282	−	1.32435i	0.0225840	−	0.185447i
$52$	5.03005	+	0.374630i	0.697543	+	0.0519518i
$53$	8.73592			1.19997			0.599986	−	0.800011i	$-0.295173\pi$
$53$	8.73592			1.19997			0.599986	+	0.800011i	$0.295173\pi$
$54$	−7.34381	+	0.261600i	−0.999366	+	0.0355993i
$55$			0.661201i			0.0891564i
$56$	−5.17848	+	8.48733i	−0.692003	+	1.13417i
$57$	−4.96715	−	11.6698i	−0.657916	−	1.54570i
$58$	5.57026	+	1.71680i	0.731410	+	0.225427i
$59$	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	$0.0613367\pi$
$60$	−0.313248	+	1.58161i	−0.0404402	+	0.204185i
$61$	−3.02492	−	0.533375i	−0.387301	−	0.0682916i	−0.0233926	−	0.999726i	$-0.507447\pi$
$61$	−3.02492	−	0.533375i	−0.387301	−	0.0682916i	−0.363908	+	0.931435i	$0.618558\pi$
$62$	−9.40923	+	6.08018i	−1.19497	+	0.772184i
$63$	−1.12303	−	10.4855i	−0.141488	−	1.32105i
$64$	−5.87190	−	5.43331i	−0.733987	−	0.679163i
$65$	0.401476	+	1.10305i	0.0497969	+	0.136816i
$66$	3.46113	−	0.359315i	0.426035	−	0.0442286i
$67$	−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	$0.382212\pi$
$68$	−0.379452	+	1.49307i	−0.0460154	+	0.181061i
$69$	−11.1646	−	5.67476i	−1.34406	−	0.683161i
$70$	−2.29591	−	0.287180i	−0.274413	−	0.0343245i
$71$	−5.70758	−	9.88583i	−0.677366	−	1.17323i	−0.975771	−	0.218793i	$-0.929788\pi$
$71$	−5.70758	−	9.88583i	−0.677366	−	1.17323i	0.298406	−	0.954439i	$-0.403545\pi$
$72$	8.44933	+	0.780240i	0.995763	+	0.0919521i
$73$	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	$0.0539994\pi$
$74$	−2.75443	+	3.63809i	−0.320196	+	0.422919i
$75$	8.07084	−	1.87170i	0.931940	−	0.216126i
$76$	3.97293	+	14.0958i	0.455726	+	1.61690i
$77$	0.867134	+	4.91776i	0.0988191	+	0.560431i
$78$	5.55583	−	2.70099i	0.629074	−	0.305827i
$79$	−8.94667	+	10.6622i	−1.00658	+	1.19959i	−0.0267740	+	0.999642i	$0.508523\pi$
$79$	−8.94667	+	10.6622i	−1.00658	+	1.19959i	−0.979805	+	0.199953i	$0.935921\pi$
$80$	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	$0.00410530\pi$
$84$	−0.255613	+	12.1742i	−0.0278896	+	1.32832i
$85$	−0.353066	+	0.0622550i	−0.0382954	+	0.00675251i
$86$	2.20117	−	2.04332i	0.237358	−	0.220337i
$87$	6.95426	−	1.61276i	0.745575	−	0.172906i
$88$	−4.01686	−	0.0974085i	−0.428199	−	0.0103838i
$89$	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	$0.490393\pi$
$90$	0.642361	+	1.86730i	0.0677108	+	0.196830i
$91$	4.43261	+	7.67751i	0.464664	+	0.804822i
$92$	11.9524	+	8.14098i	1.24612	+	0.848755i
$93$	−6.21691	+	12.2312i	−0.644664	+	1.26832i
$94$	3.30951	+	14.4846i	0.341350	+	1.49397i
$95$	−2.61082	+	2.19074i	−0.267865	+	0.224765i
$96$	−9.56229	−	2.13602i	−0.975947	−	0.218006i
$97$	−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	$0.422519\pi$
$98$	−7.56562	+	0.379324i	−0.764243	+	0.0383175i
$99$	3.44289	−	2.51182i	0.346024	−	0.252447i
$100$	−9.51875	+	0.956906i	−0.951875	+	0.0956906i
$101$	1.48081	−	8.39808i	0.147346	−	0.835641i	−0.818108	−	0.575065i	$-0.804977\pi$
$101$	1.48081	−	8.39808i	0.147346	−	0.835641i	0.965454	−	0.260575i	$-0.0839123\pi$
$102$	0.517746	+	1.81433i	0.0512645	+	0.179645i
$103$	−2.93036	+	8.05109i	−0.288737	+	0.793298i	0.707507	+	0.706706i	$0.249820\pi$
$103$	−2.93036	+	8.05109i	−0.288737	+	0.793298i	−0.996244	+	0.0865915i	$0.972403\pi$
$104$	−6.76025	+	2.27650i	−0.662898	+	0.223229i
$105$	−2.60744	+	1.10984i	−0.254460	+	0.108309i
$106$	−11.3832	+	4.80151i	−1.10564	+	0.466364i
$107$		−	10.8657i		−	1.05042i	−0.850972	−	0.525211i	$-0.823986\pi$
$107$		−	10.8657i		−	1.05042i	0.850972	−	0.525211i	$-0.176014\pi$
$108$	9.42548	−	4.37724i	0.906968	−	0.421201i
$109$		−	8.94866i		−	0.857126i	−0.903512	−	0.428563i	$-0.859020\pi$
$109$		−	8.94866i		−	0.857126i	0.903512	−	0.428563i	$-0.140980\pi$
$110$	−0.363415	−	0.861570i	−0.0346503	−	0.0821475i
$111$	−0.675613	+	5.54774i	−0.0641264	+	0.526568i
$112$	2.08288	−	13.9055i	0.196813	−	1.31395i
$113$	−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	$0.169159\pi$
$114$	12.8865	+	12.4761i	1.20693	+	1.16850i
$115$	−0.584410	+	3.31436i	−0.0544966	+	0.309065i
$116$	−8.20186	+	0.824520i	−0.761523	+	0.0765548i
$117$	4.21844	−	6.28082i	0.389994	−	0.580662i
$118$	0.169425	+	3.37918i	0.0155968	+	0.311078i
$119$	−2.54432	+	0.926058i	−0.233238	+	0.0848916i
$120$	−0.461124	−	2.23307i	−0.0420947	−	0.203850i
$121$	6.88055	−	5.77346i	0.625504	−	0.524860i
$122$	4.23474	−	0.967574i	0.383395	−	0.0876000i
$123$	−4.68946	+	0.250410i	−0.422834	+	0.0225787i
$124$	8.91874	−	13.0943i	0.800926	−	1.17590i
$125$	−2.27679	−	3.94351i	−0.203642	−	0.352718i
$126$	7.22650	+	13.0458i	0.643788	+	1.16221i
$127$	9.84084	+	5.68161i	0.873233	+	0.504162i	0.868421	−	0.495827i	$-0.165135\pi$
$127$	9.84084	+	5.68161i	0.873233	+	0.504162i	0.00481202	+	0.999988i	$0.498468\pi$
$128$	10.6376	+	3.85244i	0.940241	+	0.340511i
$129$	1.07198	−	3.51871i	0.0943823	−	0.309805i
$130$	−1.12940	−	1.21665i	−0.0990553	−	0.106707i
$131$	−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	$0.776171\pi$
$132$	−4.31249	+	2.37053i	−0.375354	+	0.206329i
$133$	−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	$0.129201\pi$
$138$	17.6669	+	1.25805i	1.50391	+	0.107092i
$139$	−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	$-0.269253\pi$
$140$	3.14950	−	0.887690i	0.266181	−	0.0750235i
$141$	12.4235	+	13.2963i	1.04625	+	1.11975i
$142$	12.8707	+	9.74456i	1.08009	+	0.817745i
$143$	−1.79136	+	3.10273i	−0.149801	+	0.259463i
$144$	−11.4386	+	3.62731i	−0.953220	+	0.302276i
$145$	−0.959179	−	1.66135i	−0.0796555	−	0.137967i
$146$	−1.03962	+	8.31144i	−0.0860398	+	0.687860i
$147$	−7.77584	+	5.06062i	−0.641341	+	0.417393i
$148$	1.58953	−	6.25448i	0.130659	−	0.514115i
$149$	6.53906	−	5.48692i	0.535700	−	0.449506i	−0.334364	−	0.942444i	$-0.608521\pi$
$149$	6.53906	−	5.48692i	0.535700	−	0.449506i	0.870064	+	0.492938i	$0.164077\pi$
$150$	−9.48787	+	6.87486i	−0.774682	+	0.561330i
$151$	−1.70566	−	4.68627i	−0.138805	−	0.381364i	0.850740	−	0.525586i	$-0.176154\pi$
$151$	−1.70566	−	4.68627i	−0.138805	−	0.381364i	−0.989545	+	0.144223i	$0.953932\pi$
$152$	−12.9243	−	16.1837i	−1.04830	−	1.31268i
$153$	1.66542	+	1.60193i	0.134641	+	0.129508i
$154$	−3.83285	−	5.93143i	−0.308860	−	0.477968i
$155$	3.63100	+	0.640243i	0.291649	+	0.0514256i
$156$	−5.75492	+	6.57314i	−0.460762	+	0.526272i
$157$	7.74744	−	21.2859i	0.618313	−	1.69880i	−0.0927644	−	0.995688i	$-0.529570\pi$
$157$	7.74744	−	21.2859i	0.618313	−	1.69880i	0.711078	−	0.703113i	$-0.248207\pi$
$158$	5.79759	−	18.8106i	0.461231	−	1.49649i
$159$	−9.09416	+	12.0932i	−0.721214	+	0.959053i
$160$	0.199770	+	2.62534i	0.0157932	+	0.207551i
$161$			25.4173i			2.00317i
$162$	7.28282	−	10.4384i	0.572193	−	0.820119i
$163$	−24.9254			−1.95231			−0.976156	−	0.217071i	$-0.930350\pi$
$163$	−24.9254			−1.95231			−0.976156	+	0.217071i	$0.930350\pi$
$164$	5.40765	+	0.402753i	0.422267	+	0.0314497i
$165$	−0.915305	−	0.688315i	−0.0712564	−	0.0535853i
$166$	−4.80315	+	15.5841i	−0.372797	+	1.20956i
$167$	−0.989406	−	0.360114i	−0.0765625	−	0.0278665i	0.303455	−	0.952846i	$-0.401860\pi$
$167$	−0.989406	−	0.360114i	−0.0765625	−	0.0278665i	−0.380017	+	0.924979i	$0.624082\pi$
$168$	−6.35823	−	16.0040i	−0.490548	−	1.23473i
$169$	1.15295	−	6.53869i	0.0886883	−	0.502976i
$170$	0.425841	−	0.275176i	0.0326605	−	0.0211050i
$171$	21.3254	+	5.27229i	1.63080	+	0.403182i
$172$	−1.74513	+	3.87235i	−0.133065	+	0.295264i
$173$	−3.27836	+	1.19323i	−0.249249	+	0.0907192i	−0.463623	−	0.886032i	$-0.653451\pi$
$173$	−3.27836	+	1.19323i	−0.249249	+	0.0907192i	0.214374	+	0.976752i	$0.431229\pi$
$174$	−8.17525	+	5.92374i	−0.619764	+	0.449078i
$175$	−10.8080	−	12.8805i	−0.817012	−	0.973677i
$176$	5.28766	−	2.08086i	0.398573	−	0.156850i
$177$	2.26032	+	3.47308i	0.169896	+	0.261052i
$178$	−13.9244	−	1.74171i	−1.04368	−	0.130547i
$179$	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	$0.161132\pi$
$180$	−1.86334	−	2.08010i	−0.138885	−	0.155041i
$181$	2.04781	+	1.18231i	0.152213	+	0.0878801i	0.574172	−	0.818735i	$-0.305324\pi$
$181$	2.04781	+	1.18231i	0.152213	+	0.0878801i	−0.421959	+	0.906615i	$0.638657\pi$
$182$	−9.99564	−	7.56780i	−0.740926	−	0.560963i
$183$	3.88731	−	3.63217i	0.287359	−	0.268497i
$184$	−20.0489	−	4.03862i	−1.47803	−	0.297731i
$185$	1.47900	−	0.260787i	0.108738	−	0.0191735i
$186$	1.37823	−	19.3548i	0.101057	−	1.41916i
$187$	−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	0.292512	−	0.956262i	$-0.405509\pi$
$191$	−8.27044	−	6.93973i	−0.598428	−	0.502141i	−0.890940	+	0.454121i	$0.849953\pi$
$192$	13.6340	−	2.47240i	0.983953	−	0.178430i
$193$	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	$0.678994\pi$
$194$	2.15301	−	1.99862i	0.154577	−	0.143493i
$195$	−1.94489	−	0.592513i	−0.139277	−	0.0424307i
$196$	9.64980	−	4.65255i	0.689271	−	0.332325i
$197$	1.27921	−	2.21565i	0.0911396	−	0.157858i	−0.816851	−	0.576848i	$-0.804282\pi$
$197$	1.27921	−	2.21565i	0.0911396	−	0.157858i	0.907991	+	0.418990i	$0.137616\pi$
$198$	−3.10565	+	5.16531i	−0.220709	+	0.367082i
$199$	18.0736	−	10.4348i	1.28121	−	0.739704i	0.304136	−	0.952628i	$-0.401632\pi$
$199$	18.0736	−	10.4348i	1.28121	−	0.739704i	0.977069	+	0.212924i	$0.0682988\pi$
$200$	11.8774	−	6.47866i	0.839856	−	0.458111i
$201$	−0.487206	−	9.12395i	−0.0343649	−	0.643554i
$202$	2.68628	+	11.7569i	0.189006	+	0.827214i
$203$	−9.31278	−	11.0985i	−0.653629	−	0.778965i
$204$	−1.67185	−	2.07957i	−0.117053	−	0.145599i
$205$	0.431614	+	1.18585i	0.0301453	+	0.0828234i
$206$	−0.606743	−	12.1015i	−0.0422738	−	0.843151i
$207$	19.4780	−	9.54777i	1.35382	−	0.663616i
$208$	7.55764	−	6.68200i	0.524028	−	0.463313i
$209$	−10.2443	−	1.80634i	−0.708610	−	0.124947i
$210$	2.78760	−	2.87928i	0.192363	−	0.198689i
$211$	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	$0.610946\pi$
$212$	12.1937	−	12.5131i	0.837470	−	0.859404i
$213$	19.6266	+	2.39017i	1.34480	+	0.163772i
$214$	5.97208	+	14.1584i	0.408243	+	0.967846i
$215$	−0.988461			−0.0674125
$216$	−9.87590	+	10.8842i	−0.671970	+	0.740578i
$217$	27.8456			1.89028
$218$	4.91844	+	11.6604i	0.333119	+	0.789745i
$219$	4.01773	+	9.43924i	0.271493	+	0.637845i
$220$	0.947088	+	0.922916i	0.0638526	+	0.0622230i
$221$	−1.82545	−	0.664409i	−0.122793	−	0.0446930i
$222$	−2.16885	−	7.60025i	−0.145563	−	0.510095i
$223$	−2.68574	−	0.473569i	−0.179851	−	0.0317125i	0.0829974	−	0.996550i	$-0.473551\pi$
$223$	−2.68574	−	0.473569i	−0.179851	−	0.0317125i	−0.262848	+	0.964837i	$0.584662\pi$
$224$	4.92882	+	19.2643i	0.329321	+	1.28715i
$225$	−5.81079	+	13.1210i	−0.387386	+	0.874732i
$226$	−0.273042	−	5.44582i	−0.0181625	−	0.362251i
$227$	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	$0.867444\pi$
$228$	−23.6488	−	9.17409i	−1.56618	−	0.607569i
$229$	−4.00131	−	4.76857i	−0.264414	−	0.315116i	0.617459	−	0.786603i	$-0.288162\pi$
$229$	−4.00131	−	4.76857i	−0.264414	−	0.315116i	−0.881873	+	0.471487i	$0.843718\pi$
$230$	−1.06016	−	4.63994i	−0.0699046	−	0.305949i
$231$	−7.71038	−	3.91904i	−0.507306	−	0.257854i
$232$	10.2342	−	5.58236i	0.671905	−	0.366500i
$233$	−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	$0.635382\pi$
$234$	−2.04466	+	10.5027i	−0.133664	+	0.686585i
$235$	2.44498	−	4.23484i	0.159493	−	0.276250i
$236$	−2.07806	−	4.31008i	−0.135270	−	0.280562i
$237$	−5.44625	−	23.4844i	−0.353772	−	1.52548i
$238$	2.80636	−	2.60512i	0.181909	−	0.168865i
$239$	4.43265	+	25.1388i	0.286725	+	1.62610i	0.699059	+	0.715064i	$0.253602\pi$
$239$	4.43265	+	25.1388i	0.286725	+	1.62610i	−0.412335	+	0.911032i	$0.635287\pi$
$240$	1.82822	+	2.65633i	0.118011	+	0.171465i
$241$	−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
$246$	5.97291	−	2.90375i	0.380819	−	0.185137i
$247$	−18.1867	+	3.20681i	−1.15719	+	0.204044i
$248$	−4.42446	+	21.9644i	−0.280953	+	1.39474i
$249$	4.51207	+	19.4562i	0.285941	+	1.23299i
$250$	5.13421	+	3.88716i	0.324716	+	0.245845i
$251$	−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	$0.711177\pi$
$252$	−16.5868	−	13.0273i	−1.04487	−	0.820642i
$253$	−8.89578	+	5.13598i	−0.559273	+	0.322896i
$254$	−15.9458	−	1.99455i	−1.00053	−	0.125149i
$255$	0.281364	−	0.553559i	0.0176197	−	0.0346652i
$256$	−15.9786	+	0.826857i	−0.998664	+	0.0516785i
$257$	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	$0.577747\pi$
$258$	0.537157	+	5.17420i	0.0334419	+	0.322132i
$259$	10.6582	−	3.87927i	0.662269	−	0.241046i
$260$	2.14036	+	0.964586i	0.132740	+	0.0598211i
$261$	−5.00688	+	11.3057i	−0.309918	+	0.699806i
$262$	23.4783	−	15.1715i	1.45049	−	0.937299i
$263$	−3.00966	+	17.0686i	−0.185583	+	1.05250i	0.739620	+	0.673024i	$0.235005\pi$
$263$	−3.00966	+	17.0686i	−0.185583	+	1.05250i	−0.925204	+	0.379471i	$0.876106\pi$
$264$	4.31642	−	5.45917i	0.265658	−	0.335988i
$265$	3.82084	+	1.39067i	0.234712	+	0.0854283i
$266$	10.7216	−	34.7869i	0.657383	−	2.13292i
$267$	−15.8138	+	6.73103i	−0.967792	+	0.411932i
$268$	−0.783609	+	10.5213i	−0.0478665	+	0.642691i
$269$	10.9959			0.670431			0.335215	−	0.942142i	$-0.391191\pi$
$269$	10.9959			0.670431			0.335215	+	0.942142i	$0.391191\pi$
$270$	−3.25361	−	1.05464i	−0.198009	−	0.0641837i
$271$			19.7167i			1.19770i	0.800861	+	0.598851i	$0.204376\pi$
$271$			19.7167i			1.19770i	−0.800861	+	0.598851i	$0.795624\pi$
$272$	1.60898	+	2.62757i	0.0975590	+	0.159320i
$273$	−15.2424	−	1.85625i	−0.922513	−	0.112345i
$274$	−2.80916	+	9.11451i	−0.169708	+	0.550627i
$275$	2.32410	−	6.38541i	0.140148	−	0.385055i
$276$	−23.7121	+	8.07097i	−1.42730	+	0.485815i
$277$	18.3745	+	3.23992i	1.10402	+	0.194668i	0.695813	−	0.718223i	$-0.255044\pi$
$277$	18.3745	+	3.23992i	1.10402	+	0.194668i	0.408203	+	0.912891i	$0.366155\pi$
$278$	11.2581	+	17.4222i	0.675216	+	1.04491i
$279$	−10.4599	−	21.3389i	−0.626220	−	1.27753i
$280$	−3.61601	+	2.88775i	−0.216098	+	0.172576i
$281$	−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	$-0.371815\pi$
$282$	−23.4964	−	10.4972i	−1.39919	−	0.625099i
$283$	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	$0.103064\pi$
$284$	−22.1269	−	5.62340i	−1.31299	−	0.333688i
$285$	−0.314772	−	5.89476i	−0.0186455	−	0.349175i
$286$	0.628863	−	5.02756i	0.0371855	−	0.297286i
$287$	4.76537	+	8.25386i	0.281291	+	0.487210i
$288$	12.9113	−	11.0135i	0.760807	−	0.648979i
$289$	−8.20335	+	14.2086i	−0.482550	+	0.835801i
$290$	2.16297	+	1.63761i	0.127014	+	0.0961636i
$291$	1.04853	−	3.44173i	0.0614657	−	0.201758i
$292$	−3.21354	−	11.4015i	−0.188058	−	0.667224i
$293$	4.42079	+	25.0715i	0.258265	+	1.46470i	0.787550	+	0.616251i	$0.211349\pi$
$293$	4.42079	+	25.0715i	0.258265	+	1.46470i	−0.529285	+	0.848444i	$0.677540\pi$
$294$	7.35076	−	10.8680i	0.428705	−	0.633835i
$295$	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
$300$	8.58444	−	14.1730i	0.495623	−	0.818280i
$301$	−7.35179	+	1.29632i	−0.423750	+	0.0747186i
$302$	4.79826	+	5.16891i	0.276109	+	0.297437i
$303$	10.0840	+	10.7924i	0.579310	+	0.620005i
$304$	25.7360	+	13.9845i	1.47606	+	0.802063i
$305$	−1.23810	−	0.714819i	−0.0708936	−	0.0409304i
$306$	−3.05056	−	1.17201i	−0.174389	−	0.0669993i
$307$	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	$0.547473\pi$
$308$	8.25443	+	5.62223i	0.470340	+	0.320356i
$309$	−8.09466	−	12.4378i	−0.460489	−	0.707559i
$310$	−5.08323	+	1.16144i	−0.288708	+	0.0659654i
$311$	11.9153	−	9.99813i	0.675655	−	0.566942i	−0.239078	−	0.971000i	$-0.576845\pi$
$311$	11.9153	−	9.99813i	0.675655	−	0.566942i	0.914733	+	0.404058i	$0.132401\pi$
$312$	3.88609	−	11.7281i	0.220007	−	0.663974i
$313$	−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	$0.481888\pi$
$314$	1.60414	+	31.9946i	0.0905269	+	1.80556i
$315$	1.17801	−	4.76485i	0.0663735	−	0.268469i
$316$	2.78439	+	27.6975i	0.156634	+	1.55811i
$317$	−5.74143	+	32.5613i	−0.322471	+	1.82882i	0.204410	+	0.978885i	$0.434472\pi$
$317$	−5.74143	+	32.5613i	−0.322471	+	1.82882i	−0.526881	+	0.849939i	$0.676639\pi$
$318$	5.20327	−	20.7563i	0.291785	−	1.16396i
$319$	2.00257	−	5.50201i	0.112122	−	0.308053i
$320$	−1.70327	−	3.31112i	−0.0952157	−	0.185097i
$321$	15.0414	+	11.3112i	0.839529	+	0.631331i
$322$	−13.9701	−	33.1197i	−0.778523	−	1.84569i
$323$		−	5.64027i		−	0.313833i
$324$	−3.75255	+	17.6045i	−0.208475	+	0.978028i
$325$		−	12.0636i		−	0.669168i
$326$	32.4788	−	13.6997i	1.79883	−	0.758758i
$327$	12.3877	+	9.31561i	0.685040	+	0.515155i
$328$	−7.26774	+	2.44740i	−0.401294	+	0.135135i
$329$	12.6311	−	34.7035i	0.696373	−	1.91327i
$330$	1.57100	+	0.393823i	0.0864804	+	0.0216792i
$331$	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	$-0.0432437\pi$
$332$	−2.30679	−	22.9467i	−0.126602	−	1.25936i
$333$	−6.97645	−	6.71049i	−0.382307	−	0.367733i
$334$	1.48716	−	0.0745632i	0.0813739	−	0.00407991i
$335$	−2.30723	+	0.839763i	−0.126057	+	0.0458811i
$336$	17.0813	+	17.3591i	0.931859	+	0.947017i
$337$	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	$0.221914\pi$
$338$	2.09152	+	9.15386i	0.113764	+	0.497904i
$339$	−3.64270	−	5.59715i	−0.197844	−	0.303995i
$340$	−0.403643	+	0.592619i	−0.0218906	+	0.0321393i
$341$	5.62665	+	9.74565i	0.304700	+	0.527756i
$342$	−30.6857	+	4.85108i	−1.65929	+	0.262316i
$343$	−5.00343	−	2.88873i	−0.270160	−	0.155977i
$344$	0.145621	−	6.00500i	0.00785134	−	0.323768i
$345$	−3.97971	−	4.25927i	−0.214260	−	0.229311i
$346$	3.61600	−	3.35670i	0.194397	−	0.180457i
$347$	−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	$0.778308\pi$
$348$	7.39680	−	12.2122i	0.396510	−	0.654643i
$349$	0.166560	−	0.198498i	0.00891573	−	0.0106254i	−0.761568	−	0.648085i	$-0.775570\pi$
$349$	0.166560	−	0.198498i	0.00891573	−	0.0106254i	0.770484	+	0.637459i	$0.220015\pi$
$350$	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	$0.292437\pi$
$354$	−4.85419	−	3.28321i	−0.257997	−	0.174501i
$355$	−0.922607	−	5.23236i	−0.0489669	−	0.277705i
$356$	19.1013	−	5.38374i	1.01237	−	0.285338i
$357$	1.36671	−	4.48616i	0.0723340	−	0.237433i
$358$	−11.7633	+	15.5371i	−0.621709	+	0.821161i
$359$	−0.180226	+	0.312161i	−0.00951198	+	0.0164752i	−0.870742	−	0.491740i	$-0.836361\pi$
$359$	−0.180226	+	0.312161i	−0.00951198	+	0.0164752i	0.861230	+	0.508215i	$0.169694\pi$
$360$	3.57129	+	1.68630i	0.188223	+	0.0888760i
$361$	−17.3095	−	29.9810i	−0.911027	−	1.57794i
$362$	−3.31821	−	0.415052i	−0.174401	−	0.0218147i
$363$	0.829547	+	15.5350i	0.0435399	+	0.815376i
$364$	17.1842	+	4.36724i	0.900696	+	0.228905i
$365$	2.11179	−	1.77200i	0.110536	−	0.0927508i
$366$	−3.06898	+	6.86943i	−0.160418	+	0.359071i
$367$	−10.6705	−	29.3168i	−0.556993	−	1.53033i	−0.823975	−	0.566626i	$-0.808249\pi$
$367$	−10.6705	−	29.3168i	−0.556993	−	1.53033i	0.266982	−	0.963702i	$-0.413974\pi$
$368$	28.3443	−	5.75699i	1.47755	−	0.300104i
$369$	4.53511	−	6.75232i	0.236088	−	0.351512i
$370$	−1.78386	+	1.15272i	−0.0927382	+	0.0599268i
$371$	30.2417	+	5.33243i	1.57007	+	0.276846i
$372$	8.84204	+	25.9775i	0.458438	+	1.34687i
$373$	2.92591	−	8.03888i	0.151498	−	0.416237i	−0.840607	−	0.541645i	$-0.817802\pi$
$373$	2.92591	−	8.03888i	0.151498	−	0.416237i	0.992105	+	0.125408i	$0.0400239\pi$
$374$	1.47883	+	0.455788i	0.0764687	+	0.0235683i
$375$	7.82918	+	0.953451i	0.404297	+	0.0492360i
$376$	25.3668	+	15.4774i	1.30819	+	0.798185i
$377$		−	10.3946i		−	0.535351i
$378$	−25.5822	−	3.57708i	−1.31581	−	0.183985i
$379$	−11.8737			−0.609912			−0.304956	−	0.952366i	$-0.598642\pi$
$379$	−11.8737			−0.609912			−0.304956	+	0.952366i	$0.598642\pi$
$380$	−0.506270	+	6.79755i	−0.0259711	+	0.348707i
$381$	−18.1095	+	7.70814i	−0.927777	+	0.394900i
$382$	14.5910	+	4.49706i	0.746539	+	0.230089i
$383$	−21.6357	−	7.87475i	−1.10553	−	0.402381i	−0.276179	−	0.961106i	$-0.589068\pi$
$383$	−21.6357	−	7.87475i	−1.10553	−	0.402381i	−0.829353	+	0.558725i	$0.811291\pi$
$384$	−16.4068	+	10.7153i	−0.837255	+	0.546812i
$385$	−0.403599	+	2.28892i	−0.0205693	+	0.116654i
$386$	−15.7938	−	24.4413i	−0.803885	−	1.24403i
$387$	3.75504	+	5.14695i	0.190879	+	0.261634i
$388$	−1.70696	+	3.78764i	−0.0866576	+	0.192288i
$389$	−17.2027	+	6.26126i	−0.872210	+	0.317458i	−0.739062	−	0.673638i	$-0.764731\pi$
$389$	−17.2027	+	6.26126i	−0.872210	+	0.317458i	−0.133148	+	0.991096i	$0.542509\pi$
$390$	2.85993	−	0.296902i	0.144818	−	0.0150342i
$391$	−3.58007	−	4.26656i	−0.181052	−	0.215769i
$392$	−10.0169	+	11.3663i	−0.505929	+	0.574083i
$393$	15.5127	−	30.5199i	0.782512	−	1.53952i
$394$	−0.449069	+	3.59016i	−0.0226238	+	0.180870i
$395$	−5.61034	+	3.23913i	−0.282287	+	0.162978i
$396$	1.20778	−	8.43755i	0.0606935	−	0.424003i
$397$	5.79128	+	3.34360i	0.290656	+	0.167810i	0.638238	−	0.769839i	$-0.279664\pi$
$397$	5.79128	+	3.34360i	0.290656	+	0.167810i	−0.347582	+	0.937650i	$0.612997\pi$
$398$	−17.8153	+	23.5307i	−0.893003	+	1.17949i
$399$	−10.0718	−	43.4301i	−0.504223	−	2.17423i
$400$	−11.9158	+	14.9701i	−0.595789	+	0.748504i
$401$	−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	$0.508317\pi$
$402$	5.64963	+	11.6211i	0.281778	+	0.579607i
$403$	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
$408$	3.32148	+	1.79086i	0.164438	+	0.0886610i
$409$	−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	$0.991992\pi$
$410$	−1.21419	−	1.30798i	−0.0599644	−	0.0645966i
$411$	2.63892	+	11.3791i	0.130168	+	0.561291i
$412$	7.44193	+	15.4352i	0.366638	+	0.760439i
$413$	4.20492	−	7.28313i	0.206910	−	0.358379i
$414$	−20.1329	+	23.1468i	−0.989479	+	1.13760i
$415$	4.64802	−	2.68353i	0.228162	−	0.131729i
$416$	−6.17527	+	12.8608i	−0.302768	+	0.630552i
$417$	22.6474	+	11.5113i	1.10905	+	0.563709i
$418$	14.3415	−	3.27681i	0.701464	−	0.160274i
$419$	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	$0.549730\pi$
$420$	−2.04981	+	5.28396i	−0.100021	+	0.257831i
$421$	−6.51235	−	17.8925i	−0.317392	−	0.872029i	−0.991111	−	0.133040i	$-0.957526\pi$
$421$	−6.51235	−	17.8925i	−0.317392	−	0.872029i	0.673718	−	0.738988i	$-0.264696\pi$
$422$	−0.0213417	+	0.00107003i	−0.00103890	+	5.20882e-5i
$423$	−31.3391	+	3.35650i	−1.52376	+	0.163198i
$424$	−9.01135	+	23.0071i	−0.437630	+	1.11732i
$425$	3.62848	+	0.639800i	0.176007	+	0.0310348i
$426$	−26.8880	+	7.67289i	−1.30273	+	0.371753i
$427$	−10.1460	−	3.69284i	−0.490999	−	0.178709i
$428$	−15.5637	−	15.1665i	−0.752299	−	0.733099i
$429$	−2.43031	−	5.70975i	−0.117336	−	0.275670i
$430$	1.28800	−	0.543287i	0.0621130	−	0.0261996i
$431$	19.2221			0.925894			0.462947	−	0.886386i	$-0.346792\pi$
$431$	19.2221			0.925894			0.462947	+	0.886386i	$0.346792\pi$
$432$	6.88639	−	19.6106i	0.331322	−	0.943518i
$433$	13.6658			0.656735			0.328367	−	0.944550i	$-0.393502\pi$
$433$	13.6658			0.656735			0.328367	+	0.944550i	$0.393502\pi$
$434$	−36.2839	+	15.3048i	−1.74168	+	0.734652i
$435$	3.29833	+	0.401676i	0.158143	+	0.0192589i
$436$	−12.8178	−	12.4907i	−0.613862	−	0.598195i
$437$	−49.7541	−	18.1090i	−2.38006	−	0.866271i
$438$	−10.4233	−	10.0914i	−0.498046	−	0.482187i
$439$	24.1314	+	4.25502i	1.15173	+	0.203081i	0.716731	−	0.697350i	$-0.245638\pi$
$439$	24.1314	+	4.25502i	1.15173	+	0.203081i	0.434999	+	0.900431i	$0.356749\pi$
$440$	−1.74135	−	0.682048i	−0.0830157	−	0.0325154i
$441$	1.08926	−	16.0323i	0.0518693	−	0.763443i
$442$	2.74381	−	0.137569i	0.130510	−	0.00654347i
$443$	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	$0.782732\pi$
$444$	7.00341	+	8.71136i	0.332367	+	0.413423i
$445$	2.96869	+	3.53795i	0.140729	+	0.167715i
$446$	3.75991	−	0.859083i	0.178037	−	0.0406787i
$447$	0.788376	+	14.7640i	0.0372889	+	0.698312i
$448$	−17.0106	−	22.3931i	−0.803677	−	1.05797i
$449$	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	$0.192910\pi$
$450$	0.360021	−	20.2909i	0.0169716	−	0.956522i
$451$	−1.92584	+	3.33565i	−0.0906842	+	0.157070i
$452$	3.34896	+	6.94604i	0.157522	+	0.326714i
$453$	8.26285	+	2.51728i	0.388222	+	0.118272i
$454$	−1.95182	−	2.10259i	−0.0916033	−	0.0986795i
$455$	0.716513	+	4.06355i	0.0335907	+	0.190502i
$456$	35.8576	−	1.04385i	1.67919	−	0.0488828i
$457$	−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	0.144141	−	0.989557i	$-0.453958\pi$
$461$	−17.2916	−	14.5094i	−0.805352	−	0.675771i	−0.949494	+	0.313786i	$0.898402\pi$
$462$	12.2009	+	0.868817i	0.567639	+	0.0404210i
$463$	−9.30336	+	1.64043i	−0.432364	+	0.0762374i	−0.385594	−	0.922668i	$-0.626004\pi$
$463$	−9.30336	+	1.64043i	−0.432364	+	0.0762374i	−0.0467691	+	0.998906i	$0.514893\pi$
$464$	−10.2673	+	12.8990i	−0.476646	+	0.598821i
$465$	−4.66619	+	4.35992i	−0.216389	+	0.202186i
$466$	21.1818	−	27.9771i	0.981226	−	1.29602i
$467$	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	$0.608848\pi$
$468$	−3.10833	−	14.8093i	−0.143683	−	0.684558i
$469$	−16.0590	+	9.27165i	−0.741534	+	0.428125i
$470$	−0.858320	+	6.86198i	−0.0395913	+	0.316520i
$471$	21.4011	+	32.8836i	0.986111	+	1.51520i
$472$	5.07673	+	4.47403i	0.233676	+	0.205934i
$473$	−1.93924	−	2.31110i	−0.0891666	−	0.106265i
$474$	20.0044	+	27.6076i	0.918831	+	1.26806i
$475$	32.9139	−	11.9797i	1.51019	−	0.549665i
$476$	−2.22495	+	4.93703i	−0.101980	+	0.226288i
$477$	−7.27361	−	25.1782i	−0.333036	−	1.15283i
$478$	−19.5929	−	30.3205i	−0.896160	−	1.38683i
$479$	4.13778	−	23.4665i	0.189060	−	1.07221i	−0.731567	−	0.681770i	$-0.761211\pi$
$479$	4.13778	−	23.4665i	0.189060	−	1.07221i	0.920627	−	0.390444i	$-0.127678\pi$
$480$	−3.84224	−	2.45645i	−0.175373	−	0.112121i
$481$	7.64683	+	2.78322i	0.348666	+	0.126904i
$482$	22.2977	+	6.87232i	1.01563	+	0.313025i
$483$	−35.1854	−	26.4596i	−1.60099	−	1.20395i
$484$	1.33422	−	17.9142i	0.0606464	−	0.814283i
$485$	−0.966837			−0.0439018
$486$	6.86849	+	20.9481i	0.311561	+	0.950226i
$487$			5.00210i			0.226667i	0.993557	+	0.113333i	$0.0361528\pi$
$487$			5.00210i			0.226667i	−0.993557	+	0.113333i	$0.963847\pi$
$488$	4.52499	−	7.41629i	0.204837	−	0.335720i
$489$	25.9476	−	34.5045i	1.17339	−	1.56035i
$490$	−3.36937	−	1.03847i	−0.152212	−	0.0469131i
$491$	−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	$0.860037\pi$
$492$	−6.18694	+	7.06658i	−0.278929	+	0.318586i
$493$	3.12649	+	0.551285i	0.140810	+	0.0248286i
$494$	21.9354	−	14.1745i	0.986922	−	0.637743i
$495$	1.90568	−	0.550522i	0.0856539	−	0.0247441i
$496$	−6.30700	−	31.0522i	−0.283193	−	1.39428i
$497$	−13.7240	−	37.7063i	−0.615605	−	1.69136i
$498$	−16.5731	−	22.8722i	−0.742658	−	1.02493i
$499$	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	$0.188472\pi$
$500$	−8.82656	−	2.24321i	−0.394736	−	0.100319i
$501$	1.52849	−	0.994759i	0.0682877	−	0.0444426i
$502$	6.19729	+	0.775178i	0.276599	+	0.0345979i
$503$	0.0403972	+	0.0699700i	0.00180122	+	0.00311981i	0.866925	−	0.498439i	$-0.166093\pi$
$503$	0.0403972	+	0.0699700i	0.00180122	+	0.00311981i	−0.865123	+	0.501559i	$0.832760\pi$
$504$	28.7734	+	7.85850i	1.28167	+	0.350046i
$505$	1.98455	−	3.43735i	0.0883115	−	0.152960i
$506$	8.76865	−	11.5817i	0.389814	−	0.514872i
$507$	7.85133	+	8.40286i	0.348690	+	0.373184i
$508$	21.8742	−	6.16528i	0.970511	−	0.273540i
$509$	−7.45238	−	42.2646i	−0.330321	−	1.87334i	−0.469286	−	0.883046i	$-0.655489\pi$
$509$	−7.45238	−	42.2646i	−0.330321	−	1.87334i	0.138964	−	0.990297i	$-0.455623\pi$
$510$	−0.0623759	+	0.875955i	−0.00276205	+	0.0387879i
$511$	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
$516$	−3.54383	−	6.44695i	−0.156008	−	0.283811i
$517$	14.6982	−	2.59168i	0.646424	−	0.113982i
$518$	−11.7559	+	10.9129i	−0.516524	+	0.479485i
$519$	1.76101	−	5.78041i	0.0772995	−	0.253732i
$520$	−3.31914	−	0.0804887i	−0.145554	−	0.00352966i
$521$	−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	$0.732134\pi$
$522$	0.310213	−	17.4837i	0.0135777	−	0.765241i
$523$	−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	$0.869176\pi$
$524$	−22.2544	+	32.6734i	−0.972188	+	1.42734i
$525$	29.0819	−	1.55293i	1.26924	−	0.0677754i
$526$	−5.45970	−	23.8952i	−0.238054	−	1.04188i
$527$	−4.67417	+	3.92210i	−0.203610	+	0.170849i
$528$	−2.62395	+	9.48593i	−0.114193	+	0.412822i
$529$	−27.5178	+	10.0157i	−1.19643	+	0.435463i
$530$	−5.74305	+	0.287944i	−0.249462	+	0.0125075i
$531$	−7.16081	−	0.486515i	−0.310753	−	0.0211130i
$532$	5.14922	+	51.2215i	0.223247	+	2.22073i
$533$	−1.18739	+	6.73403i	−0.0514316	+	0.291683i
$534$	16.9065	−	17.4625i	0.731615	−	0.755677i
$535$	1.72970	−	4.75232i	0.0747816	−	0.205461i
$536$	−4.76174	−	14.1404i	−0.205676	−	0.610770i
$537$	−2.88533	+	23.6926i	−0.124511	+	1.02241i
$538$	−14.3281	+	6.04365i	−0.617726	+	0.260560i
$539$			7.60929i			0.327755i
$540$	4.81925	−	0.414037i	0.207387	−	0.0178173i
$541$			23.3927i			1.00573i	0.864365	+	0.502865i	$0.167721\pi$
$541$			23.3927i			1.00573i	−0.864365	+	0.502865i	$0.832279\pi$
$542$	−10.8368	−	25.6915i	−0.465482	−	1.10355i
$543$	−3.76846	+	1.60401i	−0.161720	+	0.0688348i
$544$	−3.54075	−	2.53947i	−0.151809	−	0.108879i
$545$	1.42454	−	3.91388i	0.0610204	−	0.167652i
$546$	20.8817	−	5.95891i	0.893654	−	0.255018i
$547$	−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	$0.897409\pi$
$548$	−1.34915	−	13.4205i	−0.0576327	−	0.573297i
$549$	0.981311	+	9.16234i	0.0418813	+	0.391039i
$550$	0.481215	+	9.59783i	0.0205191	+	0.409253i
$551$	28.3603	−	10.3223i	1.20819	−	0.439745i
$552$	26.4618	−	23.5496i	1.12629	−	1.00234i
$553$	−37.4796	+	31.4491i	−1.59379	+	1.33735i
$554$	−25.7234	+	5.87741i	−1.09288	+	0.249707i
$555$	−1.17864	+	2.31887i	−0.0500304	+	0.0984305i
$556$	−24.2455	−	16.5140i	−1.02824	−	0.700349i
$557$	13.3979	+	23.2059i	0.567688	+	0.983265i	0.996794	+	0.0800105i	$0.0254954\pi$
$557$	13.3979	+	23.2059i	0.567688	+	0.983265i	−0.429106	+	0.903254i	$0.641171\pi$
$558$	25.3582	+	22.0563i	1.07350	+	0.933719i
$559$	−4.63842	−	2.67799i	−0.196184	−	0.113267i
$560$	3.12461	−	5.75031i	0.132039	−	0.242995i
$561$	1.84627	−	0.428167i	0.0779496	−	0.0180772i
$562$	23.5631	+	25.3834i	0.993951	+	1.07073i
$563$	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	$0.255477\pi$
$564$	36.3862	+	0.763973i	1.53214	+	0.0321691i
$565$	−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	$0.175296\pi$
$570$	3.65009	+	7.50808i	0.152885	+	0.314479i
$571$	−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	$-0.125190\pi$
$572$	1.94386	+	6.89674i	0.0812767	+	0.288367i
$573$	18.2163	−	4.22453i	0.760997	−	0.176482i
$574$	−10.7460	−	8.13591i	−0.448530	−	0.339586i
$575$	17.2937	−	29.9535i	0.721196	−	1.24915i
$576$	−10.7706	+	21.4475i	−0.448774	+	0.893645i
$577$	−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	$0.903879\pi$
$578$	2.87981	−	23.0232i	0.119784	−	0.957637i
$579$	−31.7718	−	16.1490i	−1.32039	−	0.671130i
$580$	−3.71851	−	0.945032i	−0.154403	−	0.0392403i
$581$	31.0508	−	26.0547i	1.28821	−	1.08093i
$582$	0.525406	+	5.06101i	0.0217788	+	0.209785i
$583$	4.24453	+	11.6618i	0.175791	+	0.482981i
$584$	10.4540	+	13.0904i	0.432589	+	0.541684i
$585$	2.84487	−	2.07552i	0.117621	−	0.0858121i
$586$	−19.5405	−	30.2394i	−0.807210	−	1.24918i
$587$	−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	$0.722906\pi$
$588$	−3.60495	+	18.2016i	−0.148666	+	0.750622i
$589$	−19.8391	+	54.5074i	−0.817455	+	2.24594i
$590$	−0.463830	+	1.50492i	−0.0190956	+	0.0619568i
$591$	1.73548	+	4.07732i	0.0713879	+	0.167718i
$592$	−6.74006	−	11.0069i	−0.277015	−	0.452381i
$593$			3.37367i			0.138540i	0.997598	+	0.0692700i	$0.0220670\pi$
$593$			3.37367i			0.138540i	−0.997598	+	0.0692700i	$0.977933\pi$
$594$	−3.91736	−	9.67630i	−0.160731	−	0.397023i
$595$	−1.26023			−0.0516645
$596$	1.26800	−	17.0251i	0.0519394	−	0.697376i
$597$	−4.36979	+	35.8821i	−0.178844	+	1.46856i
$598$	7.59592	−	24.6454i	0.310620	−	1.00783i
$599$	5.23313	+	1.90470i	0.213820	+	0.0778241i	0.446709	−	0.894679i	$-0.352596\pi$
$599$	5.23313	+	1.90470i	0.213820	+	0.0778241i	−0.232889	+	0.972503i	$0.574818\pi$
$600$	−3.39595	+	23.1862i	−0.138639	+	0.946574i
$601$	−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	$0.859261\pi$
$602$	8.86717	−	5.72991i	0.361399	−	0.233534i
$603$	13.1375	+	8.82366i	0.535002	+	0.359327i
$604$	−9.09329	−	4.09803i	−0.370001	−	0.166746i
$605$	3.92843	−	1.42983i	0.159713	−	0.0581309i
$606$	−19.0716	−	8.52040i	−0.774731	−	0.346118i
$607$	12.4758	+	14.8681i	0.506379	+	0.603479i	0.957304	−	0.289083i	$-0.0933504\pi$
$607$	12.4758	+	14.8681i	0.506379	+	0.603479i	−0.450925	+	0.892562i	$0.648906\pi$
$608$	−41.2212	−	4.07706i	−1.67174	−	0.165347i
$609$	25.0585	−	1.33809i	1.01542	−	0.0542220i
$610$	2.00618	+	0.250940i	0.0812279	+	0.0101602i
$611$	22.9465	−	13.2482i	0.928315	−	0.535963i
$612$	4.61917	−	0.149505i	0.186719	−	0.00604336i
$613$	4.17880	+	2.41263i	0.168780	+	0.0974452i	0.582010	−	0.813181i	$-0.302266\pi$
$613$	4.17880	+	2.41263i	0.168780	+	0.0974452i	−0.413230	+	0.910626i	$0.635600\pi$
$614$	−30.9024	−	23.3965i	−1.24712	−	0.944206i
$615$	−2.09089	−	0.636992i	−0.0843130	−	0.0256860i
$616$	−13.8460	−	2.78911i	−0.557870	−	0.112376i
$617$	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	$0.296359\pi$
$618$	17.3838	+	11.7578i	0.699279	+	0.472969i
$619$	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
$624$	1.38238	+	17.4181i	0.0553396	+	0.697282i
$625$	3.78508	+	21.4663i	0.151403	+	0.858650i
$626$	10.5632	−	9.80568i	0.422188	−	0.391914i
$627$	13.1649	−	12.3008i	0.525754	−	0.491246i
$628$	−19.6754	−	40.8085i	−0.785134	−	1.62844i
$629$	−1.24269	+	2.15240i	−0.0495493	+	0.0858218i
$630$	1.08390	+	6.85625i	0.0431836	+	0.273159i
$631$	−27.6553	+	15.9668i	−1.10094	+	0.635628i	−0.936468	−	0.350754i	$-0.885925\pi$
$631$	−27.6553	+	15.9668i	−1.10094	+	0.635628i	−0.164472	+	0.986382i	$0.552592\pi$
$632$	−18.8515	−	34.5605i	−0.749873	−	1.37474i
$633$	−0.0219348	+	0.0142754i	−0.000871829	+	0.000567398i
$634$	−10.4153	−	45.5843i	−0.413645	−	1.81038i
$635$	3.39964	+	4.05154i	0.134911	+	0.160780i
$636$	4.62821	+	29.9061i	0.183520	+	1.18585i
$637$	4.62030	+	12.6942i	0.183063	+	0.502961i
$638$	0.414640	+	8.26999i	0.0164157	+	0.327412i
$639$	−23.7402	+	24.6811i	−0.939148	+	0.976370i
$640$	4.03931	+	3.37835i	0.159668	+	0.133541i
$641$	−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	$0.698522\pi$
$642$	−25.8165	−	6.47177i	−1.01890	−	0.255420i
$643$	−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	$0.758467\pi$
$644$	36.4071	+	35.4779i	1.43464	+	1.39803i
$645$	1.02900	−	1.36833i	0.0405166	−	0.0538781i
$646$	3.10005	+	7.34948i	0.121970	+	0.289162i
$647$	−46.7102			−1.83637			−0.918183	−	0.396157i	$-0.870344\pi$
$647$	−46.7102			−1.83637			−0.918183	+	0.396157i	$0.870344\pi$
$648$	−4.78623	−	25.0018i	−0.188021	−	0.982165i
$649$	3.39868			0.133410
$650$	6.63050	+	15.7193i	0.260070	+	0.616563i
$651$	−28.9875	+	38.5469i	−1.13611	+	1.51077i
$652$	−34.7914	+	35.7026i	−1.36253	+	1.39822i
$653$	10.0893	+	3.67221i	0.394825	+	0.143705i	0.531800	−	0.846870i	$-0.321516\pi$
$653$	10.0893	+	3.67221i	0.394825	+	0.143705i	−0.136975	+	0.990575i	$0.543738\pi$
$654$	−21.2618	−	5.32997i	−0.831400	−	0.208418i
$655$	−9.06022	−	1.59756i	−0.354012	−	0.0624219i
$656$	8.12499	−	7.18361i	0.317227	−	0.280473i
$657$	−17.2493	−	4.26454i	−0.672959	−	0.166376i
$658$	2.61531	+	52.1624i	0.101956	+	2.03350i
$659$	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	$0.608251\pi$
$660$	−2.26352	+	0.350298i	−0.0881075	+	0.0136353i
$661$	8.48287	+	10.1095i	0.329945	+	0.393213i	0.905358	−	0.424650i	$-0.139603\pi$
$661$	8.48287	+	10.1095i	0.329945	+	0.393213i	−0.575412	+	0.817863i	$0.695158\pi$
$662$	3.50085	+	15.3220i	0.136065	+	0.595508i
$663$	2.82005	−	1.83533i	0.109522	−	0.0712782i
$664$	15.6180	+	28.6325i	0.606095	+	1.11116i
$665$	−10.3753	+	5.99018i	−0.402337	+	0.232289i
$666$	12.7789	+	4.90957i	0.495171	+	0.190242i
$667$	14.9011	−	25.8095i	0.576974	−	0.999349i
$668$	−1.89685	+	0.914546i	−0.0733912	+	0.0353848i
$669$	3.45144	−	3.22490i	0.133440	−	0.124682i
$670$	2.54485	−	2.36236i	0.0983161	−	0.0912660i
$671$	−0.757708	−	4.29718i	−0.0292510	−	0.165891i
$672$	−31.7986	−	13.2312i	−1.22666	−	0.510406i
$673$	−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	0.634243	−	0.773133i	$-0.281312\pi$
$677$	−0.442568	−	0.371358i	−0.0170093	−	0.0142725i	−0.651253	+	0.758861i	$0.725756\pi$
$678$	7.82293	+	5.29116i	0.300438	+	0.203206i
$679$	−7.19096	+	1.26796i	−0.275964	+	0.0486598i
$680$	0.200241	−	0.994059i	0.00767891	−	0.0381204i
$681$	−3.36113	−	1.02397i	−0.128799	−	0.0392386i
$682$	−12.6882	−	9.60638i	−0.485857	−	0.367847i
$683$	−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	$0.668032\pi$
$684$	37.3183	−	23.1869i	1.42690	−	0.886571i
$685$	2.71843	−	1.56949i	0.103866	−	0.0599670i
$686$	8.10740	+	1.01410i	0.309542	+	0.0387185i
$687$	10.7666	−	0.574919i	0.410770	−	0.0219345i
$688$	3.11077	+	7.90478i	0.118597	+	0.301367i
$689$	14.1618	+	16.8774i	0.539523	+	0.642979i
$690$	7.52673	+	3.36263i	0.286538	+	0.128013i
$691$	−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	$0.475834\pi$
$692$	−2.86684	+	6.36136i	−0.108981	+	0.241823i
$693$	13.4517	−	6.59378i	0.510988	−	0.250477i
$694$	38.3606	−	24.7884i	1.45615	−	0.940955i
$695$	1.18548	−	6.72318i	0.0449677	−	0.255025i
$696$	−2.92613	+	19.9785i	−0.110915	+	0.757282i
$697$	−1.96248	−	0.714286i	−0.0743344	−	0.0270555i
$698$	−0.107933	+	0.350196i	−0.00408534	+	0.0132551i
$699$	5.19551	−	42.6625i	0.196512	−	1.61364i
$700$	−33.5358	−	2.49769i	−1.26753	−	0.0944038i
$701$	−5.36891			−0.202781			−0.101391	−	0.994847i	$-0.532329\pi$
$701$	−5.36891			−0.202781			−0.101391	+	0.994847i	$0.532329\pi$
$702$	−12.4105	−	13.7638i	−0.468404	−	0.519483i
$703$			23.6272i			0.891115i
$704$	4.40004	−	10.4784i	0.165833	−	0.394920i
$705$	3.31707	+	7.79310i	0.124928	+	0.293505i
$706$	3.42471	−	11.1117i	0.128891	−	0.418194i
$707$	10.2524	−	28.1683i	0.385582	−	1.05938i
$708$	8.12974	+	1.61015i	0.305534	+	0.0605130i
$709$	16.2741	+	2.86956i	0.611187	+	0.107769i	0.470670	−	0.882310i	$-0.344012\pi$
$709$	16.2741	+	2.86956i	0.611187	+	0.107769i	0.140517	+	0.990078i	$0.455124\pi$
$710$	4.07805	+	6.31088i	0.153046	+	0.236843i
$711$	38.1792	+	16.9081i	1.43183	+	0.634105i
$712$	−21.9307	+	17.5139i	−0.821888	+	0.656360i
$713$	19.5905	+	53.8245i	0.733671	+	2.01574i
$714$	0.684845	+	6.59682i	0.0256297	+	0.246880i
$715$	−1.27741	+	1.07188i	−0.0477725	+	0.0400859i
$716$	6.78838	−	26.7109i	0.253694	−	0.998233i
$717$	−39.4143	−	20.0335i	−1.47195	−	0.748167i
$718$	0.0632691	−	0.505815i	0.00236118	−	0.0188769i
$719$	−1.17170	−	2.02945i	−0.0436971	−	0.0756857i	0.843350	−	0.537365i	$-0.180580\pi$
$719$	−1.17170	−	2.02945i	−0.0436971	−	0.0756857i	−0.887047	+	0.461680i	$0.847247\pi$
$720$	−5.58036	−	0.234436i	−0.207968	−	0.00873693i
$721$	−15.0586	+	26.0823i	−0.560812	+	0.971356i
$722$	39.0333	+	29.5525i	1.45267	+	1.09983i
$723$	27.8378	−	6.45584i	1.03530	−	0.240095i
$724$	4.55188	−	1.28295i	0.169169	−	0.0476806i
$725$	3.42349	+	19.4156i	0.127145	+	0.721077i
$726$	−9.61941	−	19.7868i	−0.357010	−	0.734355i
$727$	10.6227	−	12.6596i	0.393974	−	0.469520i	−0.532198	−	0.846620i	$-0.678634\pi$
$727$	10.6227	−	12.6596i	0.393974	−	0.469520i	0.926173	+	0.377099i	$0.123078\pi$
$728$	−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
$732$	0.223356	−	10.6379i	0.00825548	−	0.393189i
$733$	35.2664	−	6.21842i	1.30260	−	0.229683i	0.521047	−	0.853528i	$-0.325542\pi$
$733$	35.2664	−	6.21842i	1.30260	−	0.229683i	0.781548	+	0.623845i	$0.214430\pi$
$734$	30.0174	+	32.3362i	1.10796	+	1.19355i
$735$	−4.20653	+	0.975532i	−0.155160	+	0.0359831i
$736$	−33.7695	+	23.0804i	−1.24476	+	0.850755i
$737$	−6.48994	−	3.74697i	−0.239060	−	0.138021i
$738$	−2.19815	+	11.2912i	−0.0809151	+	0.415633i
$739$	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	$0.645243\pi$
$740$	1.69087	−	2.48249i	0.0621575	−	0.0912582i
$741$	14.4933	−	28.5143i	0.532425	−	1.04750i
$742$	−42.3370	+	9.67336i	−1.55424	+	0.355120i
$743$	37.2460	−	31.2531i	1.36642	−	1.14657i	0.392485	−	0.919758i	$-0.371616\pi$
$743$	37.2460	−	31.2531i	1.36642	−	1.14657i	0.973940	−	0.226808i	$-0.0728289\pi$
$744$	−25.7995	−	28.9899i	−0.945856	−	1.06282i
$745$	3.73346	−	1.35887i	0.136783	−	0.0497850i
$746$	0.605823	+	12.0831i	0.0221807	+	0.442395i
$747$	−31.6305	−	14.0080i	−1.15730	−	0.512524i
$748$	−2.17749	+	0.218900i	−0.0796169	+	0.00800377i
$749$	6.63243	−	37.6144i	0.242344	−	1.37440i
$750$	−10.7258	+	3.06076i	−0.391649	+	0.111763i
$751$	−1.78479	+	4.90367i	−0.0651279	+	0.178937i	−0.967988	−	0.250998i	$-0.919241\pi$
$751$	−1.78479	+	4.90367i	−0.0651279	+	0.178937i	0.902860	+	0.429935i	$0.141464\pi$
$752$	−41.5608	−	6.22529i	−1.51557	−	0.227013i
$753$	7.03822	−	2.99576i	0.256487	−	0.109171i
$754$	5.71319	+	13.5446i	0.208062	+	0.493265i
$755$		−	2.32116i		−	0.0844758i
$756$	35.3007	−	9.39966i	1.28387	−	0.341862i
$757$		−	23.5414i		−	0.855626i	−0.903867	−	0.427813i	$-0.859284\pi$
$757$		−	23.5414i		−	0.855626i	0.903867	−	0.427813i	$-0.140716\pi$
$758$	15.4719	−	6.52613i	0.561965	−	0.237040i
$759$	2.15080	−	17.6611i	0.0780689	−	0.641056i
$760$	−3.07644	−	9.13573i	−0.111594	−	0.331388i
$761$	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	$-0.0877873\pi$
$762$	19.3607	−	19.9975i	0.701365	−	0.724433i
$763$	5.46228	−	30.9782i	0.197748	−	1.12148i
$764$	−21.4843	+	2.15978i	−0.777275	+	0.0781383i
$765$	0.473394	+	0.965753i	0.0171156	+	0.0349169i
$766$	32.5203	−	1.63050i	1.17501	−	0.0589123i
$767$	5.66984	−	2.06365i	0.204726	−	0.0745141i
$768$	15.4892	−	22.9801i	0.558919	−	0.829222i
$769$	−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	$0.358840\pi$
$770$	−0.732153	−	3.20439i	−0.0263850	−	0.115478i
$771$	−32.5998	+	1.74078i	−1.17405	+	0.0626927i
$772$	34.0136	+	23.1672i	1.22418	+	0.833808i
$773$	−7.86483	−	13.6223i	−0.282878	−	0.489959i	0.689214	−	0.724558i	$-0.257956\pi$
$773$	−7.86483	−	13.6223i	−0.282878	−	0.489959i	−0.972092	+	0.234598i	$0.924623\pi$
$774$	−7.72187	−	4.64279i	−0.277557	−	0.166882i
$775$	−32.8152	−	18.9459i	−1.17876	−	0.680555i
$776$	0.142435	−	5.87363i	0.00511311	−	0.210851i
$777$	−5.72517	+	18.7926i	−0.205389	+	0.674180i
$778$	18.9744	−	17.6137i	0.680264	−	0.631483i
$779$	−19.5520	+	3.44754i	−0.700523	+	0.123521i
$780$	−3.56341	+	1.95877i	−0.127591	+	0.0701354i
$781$	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
$786$	−3.43903	+	48.2948i	−0.122666	+	1.72262i
$787$	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	$0.915070\pi$
$788$	−1.38810	−	4.92494i	−0.0494491	−	0.175444i
$789$	−20.4951	−	21.9348i	−0.729645	−	0.780900i
$790$	5.53016	−	7.30431i	0.196754	−	0.259876i
$791$	−6.77657	+	11.7374i	−0.240947	+	0.417333i
$792$	3.06373	+	11.6583i	0.108865	+	0.414259i
$793$	−3.87325	−	6.70867i	−0.137543	−	0.238232i
$794$	−9.38400	−	1.17378i	−0.333026	−	0.0416559i
$795$	−5.90264	+	3.84151i	−0.209345	+	0.136244i
$796$	10.2809	−	40.4533i	0.364397	−	1.43383i
$797$	−1.73089	+	1.45239i	−0.0613111	+	0.0514461i	−0.672928	−	0.739708i	$-0.734964\pi$
$797$	−1.73089	+	1.45239i	−0.0613111	+	0.0514461i	0.611617	+	0.791154i	$0.290519\pi$
$798$	36.9944	+	51.0553i	1.30959	+	1.80734i
$799$	2.76779	+	7.60445i	0.0979175	+	0.269026i
$800$	7.29874	−	26.0558i	0.258049	−	0.921213i
$801$	7.14452	−	28.8983i	0.252439	−	1.02107i
$802$	9.48186	−	6.12711i	0.334816	−	0.216356i
$803$	8.28617	+	1.46107i	0.292412	+	0.0515602i
$804$	−13.7490	−	12.0375i	−0.484889	−	0.424530i
$805$	−4.04618	+	11.1168i	−0.142609	+	0.391816i
$806$	−27.0000	−	8.32161i	−0.951034	−	0.293116i
$807$	−11.4468	+	15.2217i	−0.402946	+	0.535828i
$808$	20.5899	+	12.5627i	0.724349	+	0.441956i
$809$		−	3.55121i		−	0.124854i	−0.998050	−	0.0624270i	$-0.980116\pi$
$809$		−	3.55121i		−	0.124854i	0.998050	−	0.0624270i	$-0.0198841\pi$
$810$	4.84699	−	3.40611i	0.170306	−	0.119678i
$811$	−24.8246			−0.871710			−0.435855	−	0.900017i	$-0.643554\pi$
$811$	−24.8246			−0.871710			−0.435855	+	0.900017i	$0.643554\pi$
$812$	−28.8962	−	2.15214i	−1.01406	−	0.0755253i
$813$	−27.2939	−	20.5252i	−0.957239	−	0.719849i
$814$	−6.19486	−	1.90930i	−0.217130	−	0.0669211i
$815$	−10.9017	−	3.96788i	−0.381869	−	0.138989i
$816$	−5.31232	−	0.507986i	−0.185968	−	0.0177831i
$817$	2.70038	−	15.3146i	0.0944744	−	0.535791i
$818$	4.62023	+	7.14991i	0.161543	+	0.249991i
$819$	18.4371	−	19.1678i	0.644243	−	0.669777i
$820$	2.30104	+	1.03700i	0.0803557	+	0.0362135i
$821$	7.98474	−	2.90621i	0.278669	−	0.101427i	−0.198905	−	0.980019i	$-0.563738\pi$
$821$	7.98474	−	2.90621i	0.278669	−	0.101427i	0.477574	+	0.878591i	$0.341516\pi$
$822$	−9.69291	−	13.3770i	−0.338079	−	0.466577i
$823$	21.2355	+	25.3075i	0.740223	+	0.882163i	0.996427	−	0.0844593i	$-0.0269163\pi$
$823$	21.2355	+	25.3075i	0.740223	+	0.882163i	−0.256204	+	0.966623i	$0.582472\pi$
$824$	−18.1808	−	16.0224i	−0.633357	−	0.558166i
$825$	6.41996	+	9.86452i	0.223514	+	0.343439i
$826$	−1.47615	+	11.8013i	−0.0513618	+	0.410621i
$827$	−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	$0.520245\pi$
$828$	13.5118	−	41.2268i	0.469568	−	1.43273i
$829$	3.48406	+	2.01153i	0.121007	+	0.0698632i	0.559282	−	0.828978i	$-0.311077\pi$
$829$	3.48406	+	2.01153i	0.121007	+	0.0698632i	−0.438275	+	0.898841i	$0.644410\pi$
$830$	−4.58160	+	6.05143i	−0.159030	+	0.210048i
$831$	−23.6130	+	22.0631i	−0.819126	+	0.765362i
$832$	0.977953	−	20.1522i	0.0339044	−	0.698652i
$833$	−4.06318	+	0.716448i	−0.140781	+	0.0248235i
$834$	−35.8374	−	2.55195i	−1.24095	−	0.0883667i
$835$	−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	0.387990	−	0.921664i	$-0.373170\pi$
$839$	−13.1010	−	10.9931i	−0.452298	−	0.379523i	−0.840288	+	0.542140i	$0.817614\pi$
$840$	−0.233233	−	8.01184i	−0.00804729	−	0.276435i
$841$	−2.08594	−	11.8299i	−0.0719288	−	0.407929i
$842$	18.3201	+	19.7353i	0.631352	+	0.680123i
$843$	40.5770	+	12.3618i	1.39755	+	0.425763i
$844$	0.0272210	−	0.0131243i	0.000936985	−	0.000451758i
$845$	1.54516	−	2.67630i	0.0531551	−	0.0920674i
$846$	38.9912	−	21.5985i	1.34054	−	0.742572i
$847$	27.3430	−	15.7865i	0.939516	−	0.542430i
$848$	−0.903221	−	34.9320i	−0.0310167	−	1.19957i
$849$	1.62122	+	30.3607i	0.0556401	+	1.04198i
$850$	−5.07971	+	1.16064i	−0.174232	+	0.0398095i
$851$	14.9970	+	17.8727i	0.514089	+	0.612668i
$852$	30.8188	−	24.7765i	1.05584	−	0.848828i
$853$	4.54120	+	12.4769i	0.155488	+	0.427199i	0.992838	−	0.119467i	$-0.0381187\pi$
$853$	4.54120	+	12.4769i	0.155488	+	0.427199i	−0.837350	+	0.546667i	$0.815896\pi$
$854$	15.2503	−	0.764617i	0.521854	−	0.0261647i
$855$	8.48783	+	5.70074i	0.290278	+	0.194961i
$856$	28.6160	+	11.2082i	0.978075	+	0.383090i
$857$	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	$0.547851\pi$
$858$	6.30503	+	6.10426i	0.215250	+	0.208396i
$859$	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	$0.534665\pi$
$860$	−1.37971	+	1.41585i	−0.0470477	+	0.0482800i
$861$	−16.3867	−	1.99559i	−0.558456	−	0.0680097i
$862$	−25.0471	+	10.5650i	−0.853107	+	0.359845i
$863$	−32.7283			−1.11408			−0.557041	−	0.830485i	$-0.688064\pi$
$863$	−32.7283			−1.11408			−0.557041	+	0.830485i	$0.688064\pi$
$864$	1.80534	+	29.3384i	0.0614189	+	0.998112i
$865$	−1.62381			−0.0552111
$866$	−17.8070	+	7.51110i	−0.605107	+	0.255237i
$867$	−11.1293	−	26.1472i	−0.377972	−	0.888006i
$868$	38.8674	−	39.8853i	1.31924	−	1.35380i
$869$	−18.5802	−	6.76263i	−0.630289	−	0.229406i
$870$	−4.51862	+	1.28946i	−0.153195	+	0.0437166i
$871$	−13.1019	−	2.31023i	−0.443942	−	0.0782790i
$872$	23.5674	+	9.23079i	0.798091	+	0.312594i
$873$	3.67289	+	5.03435i	0.124308	+	0.170387i
$874$	74.7847	−	3.74955i	2.52963	−	0.126830i
$875$	−5.47457	−	15.0413i	−0.185074	−	0.508488i
$876$	19.1285	+	7.42055i	0.646293	+	0.250717i
$877$	−16.7454	−	19.9563i	−0.565450	−	0.673878i	0.405240	−	0.914210i	$-0.367188\pi$
$877$	−16.7454	−	19.9563i	−0.565450	−	0.673878i	−0.970691	+	0.240333i	$0.922743\pi$
$878$	−33.7828	+	7.71886i	−1.14012	+	0.260499i
$879$	−39.3088	−	19.9799i	−1.32585	−	0.673906i
$880$	2.64392	−	0.0683627i	0.0891266	−	0.00230451i
$881$	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	$0.118930\pi$
$882$	7.39247	+	21.4894i	0.248917	+	0.723585i
$883$	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	$-0.00900081\pi$
$884$	−3.49967	+	1.68733i	−0.117707	+	0.0567511i
$885$	0.435721	+	1.87884i	0.0146466	+	0.0631566i
$886$	−13.2583	−	14.2825i	−0.445423	−	0.479831i
$887$	1.60872	+	9.12349i	0.0540154	+	0.306337i	0.999831	−	0.0183666i	$-0.00584661\pi$
$887$	1.60872	+	9.12349i	0.0540154	+	0.306337i	−0.945816	+	0.324703i	$0.894735\pi$
$888$	−13.9137	−	7.50196i	−0.466914	−	0.251749i
$889$	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
$894$	−9.14199	−	18.8047i	−0.305754	−	0.628924i
$895$	6.31633	−	1.11374i	0.211132	−	0.0372282i
$896$	34.4734	+	19.8295i	1.15167	+	0.662456i
$897$	−7.13560	−	30.7689i	−0.238251	−	1.02734i
$898$	−15.4469	+	20.4025i	−0.515471	+	0.680841i
$899$	−28.2753	−	16.3247i	−0.943033	−	0.544461i
$900$	10.6833	+	26.6377i	0.356111	+	0.887923i
$901$	−5.82747	+	3.36449i	−0.194141	+	0.112087i
$902$	0.676072	−	5.40497i	0.0225107	−	0.179966i
$903$	5.85877	−	11.5266i	0.194967	−	0.383582i
$904$	−8.18157	−	7.21027i	−0.272115	−	0.239810i
$905$	0.707443	+	0.843097i	0.0235162	+	0.0280255i
$906$	−12.1504	+	1.26138i	−0.403669	+	0.0419067i
$907$	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	$0.308344\pi$
$908$	3.69894	+	1.66698i	0.122754	+	0.0553207i
$909$	−25.4374	+	2.72442i	−0.843706	+	0.0903632i
$910$	−3.16709	−	4.90114i	−0.104988	−	0.162471i
$911$	−2.78022	+	15.7674i	−0.0921129	+	0.522398i	0.903481	+	0.428628i	$0.141003\pi$
$911$	−2.78022	+	15.7674i	−0.0921129	+	0.522398i	−0.995594	+	0.0937702i	$0.970108\pi$
$912$	−46.1501	+	21.0685i	−1.52818	+	0.697649i
$913$	15.3932	+	5.60266i	0.509440	+	0.185421i
$914$	8.98645	+	2.76969i	0.297245	+	0.0916134i
$915$	2.27840	−	0.969782i	0.0753217	−	0.0320600i
$916$	−12.4155	−	0.924684i	−0.410219	−	0.0305524i
$917$	−69.4815			−2.29448
$918$	4.79808	−	3.00285i	0.158360	−	0.0991087i
$919$		−	35.6444i		−	1.17580i	−0.808934	−	0.587900i	$-0.799955\pi$
$919$		−	35.6444i		−	1.17580i	0.808934	−	0.587900i	$-0.200045\pi$
$920$	−8.12592	−	4.95797i	−0.267903	−	0.163459i
$921$	−47.1232	−	5.73875i	−1.55276	−	0.189098i
$922$	30.5065	+	9.40233i	1.00468	+	0.309649i
$923$	9.84640	−	27.0528i	0.324098	−	0.890453i
$924$	−16.3758	+	5.57388i	−0.538725	+	0.183367i
$925$	−15.1998	−	2.68013i	−0.499766	−	0.0881222i
$926$	11.2210	−	7.25094i	0.368745	−	0.238281i
$927$	25.6443	+	1.74230i	0.842268	+	0.0572248i
$928$	6.28898	−	22.4511i	0.206446	−	0.736993i
$929$	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	$0.805054\pi$
$930$	3.68388	−	8.24581i	0.120799	−	0.270391i
$931$	−30.0461	+	25.2117i	−0.984721	+	0.826279i
$932$	−12.2236	+	48.0974i	−0.400398	+	1.57548i
$933$	1.43656	+	26.9026i	0.0470308	+	0.880750i
$934$	−10.9562	−	1.37044i	−0.358499	−	0.0448422i
$935$	−0.254650	−	0.441067i	−0.00832795	−	0.0144244i
$936$	12.1899	+	17.5886i	0.398438	+	0.574901i
$937$	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	$0.133461\pi$
$938$	15.8295	−	20.9078i	0.516851	−	0.682663i
$939$	5.14430	−	16.8859i	0.167878	−	0.551050i
$940$	−2.65312	−	9.41318i	−0.0865352	−	0.307024i
$941$	3.12587	+	17.7277i	0.101900	+	0.577906i	0.992413	+	0.122948i	$0.0392348\pi$
$941$	3.12587	+	17.7277i	0.101900	+	0.577906i	−0.890513	+	0.454959i	$0.849654\pi$
$942$	−45.9602	−	31.0860i	−1.49747	−	1.01284i
$943$	−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	$0.250566\pi$
$948$	−41.2404	−	24.9788i	−1.33943	−	0.811275i
$949$	14.7105	−	2.59386i	0.477523	−	0.0842002i
$950$	−36.3036	+	33.7004i	−1.17785	+	1.09338i
$951$	−39.0979	−	41.8444i	−1.26784	−	1.35690i
$952$	0.185658	−	7.65603i	0.00601721	−	0.248133i
$953$	−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	$0.719841\pi$
$954$	23.3165	+	28.8104i	0.754898	+	0.932770i
$955$	−2.51252	−	4.35181i	−0.0813031	−	0.140821i
$956$	42.1954	+	28.7400i	1.36470	+	0.929517i
$957$	5.53178	+	8.49979i	0.178817	+	0.274759i
$958$	7.50619	+	32.8520i	0.242514	+	1.06140i
$959$	18.1603	−	15.2383i	0.586428	−	0.492071i
$960$	6.35672	+	1.08905i	0.205162	+	0.0351489i
$961$	29.8362	−	10.8595i	0.962460	−	0.350307i
$962$	−11.4939	+	0.576277i	−0.370577	+	0.0185799i
$963$	−31.3164	+	9.04685i	−1.00916	+	0.291531i
$964$	−32.8319	+	3.30054i	−1.05745	+	0.106303i
$965$	−1.66309	+	9.43186i	−0.0535368	+	0.303622i
$966$	60.3908	+	15.1390i	1.94304	+	0.487089i
$967$	−1.87573	+	5.15353i	−0.0603195	+	0.165726i	−0.966192	−	0.257825i	$-0.916994\pi$
$967$	−1.87573	+	5.15353i	−0.0603195	+	0.165726i	0.905872	+	0.423551i	$0.139217\pi$
$968$	8.10763	+	24.0762i	0.260589	+	0.773839i
$969$	7.80786	+	5.87156i	0.250825	+	0.188622i
$970$	1.25983	−	0.531401i	0.0404505	−	0.0170623i
$971$		−	22.2762i		−	0.714877i	−0.933937	−	0.357439i	$-0.883650\pi$
$971$		−	22.2762i		−	0.714877i	0.933937	−	0.357439i	$-0.116350\pi$
$972$	−20.4636	−	23.5211i	−0.656370	−	0.754439i
$973$		−	51.5591i		−	1.65291i
$974$	−2.74930	−	6.51792i	−0.0880931	−	0.208848i
$975$	16.6997	+	12.5583i	0.534819	+	0.402187i
$976$	−1.82003	+	12.1508i	−0.0582579	+	0.388937i
$977$	−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	$0.982199\pi$
$978$	−14.8460	+	59.2221i	−0.474723	+	1.89372i
$979$	−2.44778	+	13.8821i	−0.0782315	+	0.443673i
$980$	4.96118	−	0.498740i	0.158479	−	0.0159317i
$981$	−25.7913	+	7.45073i	−0.823454	+	0.237884i
$982$	−2.22665	−	44.4106i	−0.0710553	−	1.41720i
$983$	−19.2748	+	7.01545i	−0.614771	+	0.223758i	−0.630589	−	0.776117i	$-0.717187\pi$
$983$	−19.2748	+	7.01545i	−0.614771	+	0.223758i	0.0158187	+	0.999875i	$0.494965\pi$
$984$	4.17782	−	12.6085i	0.133184	−	0.401946i
$985$	0.912196	−	0.765424i	0.0290650	−	0.0243884i
$986$	−4.37694	+	1.00006i	−0.139390	+	0.0318485i
$987$	34.8913	+	53.6119i	1.11060	+	1.70649i
$988$	−20.7920	+	30.5263i	−0.661481	+	0.971171i
$989$	−7.67802	−	13.2987i	−0.244147	−	0.422875i
$990$	−2.18059	+	1.76477i	−0.0693036	+	0.0560880i
$991$	−19.3983	−	11.1996i	−0.616207	−	0.355767i	0.159184	−	0.987249i	$-0.449114\pi$
$991$	−19.3983	−	11.1996i	−0.616207	−	0.355767i	−0.775391	+	0.631482i	$0.782447\pi$
$992$	25.2854	+	36.9957i	0.802813	+	1.17461i
$993$	13.1418	+	14.0650i	0.417043	+	0.446339i
$994$	38.6074	+	41.5897i	1.22455	+	1.31915i
$995$	9.56599	−	1.68674i	0.303262	−	0.0534733i
$996$	34.1666	+	20.6943i	1.08261	+	0.655725i
$997$	27.6176	−	32.9134i	0.874659	−	1.04238i	−0.124085	−	0.992272i	$-0.539600\pi$
$997$	27.6176	−	32.9134i	0.874659	−	1.04238i	0.998744	−	0.0501062i	$-0.0159560\pi$
$998$	−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.11.4	✓	192
3.2	odd	2		648.2.v.b.35.29		192
4.3	odd	2		864.2.bh.b.335.22		192
8.3	odd	2	inner	216.2.v.b.11.15	yes	192
8.5	even	2		864.2.bh.b.335.21		192
24.11	even	2		648.2.v.b.35.18		192
27.5	odd	18	inner	216.2.v.b.59.15	yes	192
27.22	even	9		648.2.v.b.611.18		192
108.59	even	18		864.2.bh.b.815.21		192
216.5	odd	18		864.2.bh.b.815.22		192
216.59	even	18	inner	216.2.v.b.59.4	yes	192
216.211	odd	18		648.2.v.b.611.29		192

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
216.2.v.b.11.4	✓	192	1.1	even	1	trivial
216.2.v.b.11.15	yes	192	8.3	odd	2	inner
216.2.v.b.59.4	yes	192	216.59	even	18	inner
216.2.v.b.59.15	yes	192	27.5	odd	18	inner
648.2.v.b.35.18		192	24.11	even	2
648.2.v.b.35.29		192	3.2	odd	2
648.2.v.b.611.18		192	27.22	even	9
648.2.v.b.611.29		192	216.211	odd	18
864.2.bh.b.335.21		192	8.5	even	2
864.2.bh.b.335.22		192	4.3	odd	2
864.2.bh.b.815.21		192	108.59	even	18
864.2.bh.b.815.22		192	216.5	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 $\F_{q}$
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+(-1.30304 + 0.549629i) q^{2} +(-1.04101 + 1.38431i) q^{3} +(1.39582 - 1.43237i) q^{4} +(0.437371 + 0.159190i) q^{5} +(0.595617 - 2.37597i) q^{6} +(3.46177 + 0.610403i) q^{7} +(-1.03153 + 2.63362i) q^{8} +(-0.832609 - 2.88215i) q^{9} +(-0.657406 + 0.0329610i) q^{10} +(0.485871 + 1.33492i) q^{11} +(0.529790 + 3.42335i) q^{12} +(1.62110 + 1.93196i) q^{13} +(-4.84631 + 1.10731i) q^{14} +(-0.675674 + 0.439738i) q^{15} +(-0.103392 - 3.99866i) q^{16} +(-0.667069 + 0.385133i) q^{17} +(2.66903 + 3.29792i) q^{18} +(-3.66125 + 6.34147i) q^{19} +(0.838509 - 0.404279i) q^{20} +(-4.44871 + 4.15671i) q^{21} +(-1.36682 - 1.47240i) q^{22} +(1.25561 + 7.12090i) q^{23} +(-2.57191 - 4.16957i) 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} +(0.638737 - 0.944365i) q^{30} +(7.80121 - 1.37556i) q^{31} +(2.33250 + 5.15358i) q^{32} +(-2.35373 - 0.717067i) q^{33} +(0.657537 - 0.868483i) q^{34} +(1.41691 + 0.818051i) q^{35} +(-5.29048 - 2.83034i) q^{36} +(2.79436 - 1.61333i) q^{37} +(1.28529 - 10.2755i) q^{38} +(-4.36200 + 0.232925i) q^{39} +(-0.870406 + 0.987659i) q^{40} +(1.74280 + 2.07699i) q^{41} +(3.51219 - 7.86149i) q^{42} +(-1.99564 + 0.726352i) q^{43} +(2.59029 + 1.16735i) q^{44} +(0.0946497 - 1.39311i) q^{45} +(-5.54996 - 8.58869i) q^{46} +(1.82437 - 10.3465i) q^{47} +(5.64301 + 4.01951i) q^{48} +(5.03339 + 1.83200i) q^{49} +(6.46462 + 1.99245i) q^{50} +(0.161282 - 1.32435i) q^{51} +(5.03005 + 0.374630i) q^{52} +8.73592 q^{53} +(-7.34381 + 0.261600i) q^{54} +0.661201i q^{55} +(-5.17848 + 8.48733i) q^{56} +(-4.96715 - 11.6698i) q^{57} +(5.57026 + 1.71680i) q^{58} +(0.818263 - 2.24816i) q^{59} +(-0.313248 + 1.58161i) q^{60} +(-3.02492 - 0.533375i) q^{61} +(-9.40923 + 6.08018i) q^{62} +(-1.12303 - 10.4855i) q^{63} +(-5.87190 - 5.43331i) q^{64} +(0.401476 + 1.10305i) q^{65} +(3.46113 - 0.359315i) q^{66} +(-4.04105 + 3.39085i) q^{67} +(-0.379452 + 1.49307i) q^{68} +(-11.1646 - 5.67476i) q^{69} +(-2.29591 - 0.287180i) q^{70} +(-5.70758 - 9.88583i) q^{71} +(8.44933 + 0.780240i) q^{72} +(2.96144 - 5.12936i) q^{73} +(-2.75443 + 3.63809i) q^{74} +(8.07084 - 1.87170i) q^{75} +(3.97293 + 14.0958i) q^{76} +(0.867134 + 4.91776i) q^{77} +(5.55583 - 2.70099i) 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} +(-0.255613 + 12.1742i) q^{84} +(-0.353066 + 0.0622550i) q^{85} +(2.20117 - 2.04332i) q^{86} +(6.95426 - 1.61276i) q^{87} +(-4.01686 - 0.0974085i) q^{88} +(8.59338 + 4.96139i) q^{89} +(0.642361 + 1.86730i) q^{90} +(4.43261 + 7.67751i) q^{91} +(11.9524 + 8.14098i) q^{92} +(-6.21691 + 12.2312i) q^{93} +(3.30951 + 14.4846i) q^{94} +(-2.61082 + 2.19074i) q^{95} +(-9.56229 - 2.13602i) q^{96} +(-1.95198 + 0.710462i) q^{97} +(-7.56562 + 0.379324i) 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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