LMFDB - Embedded newform 930.2.bn.a.19.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(19,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 15, 4]))

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

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

chi := DirichletCharacter("930.19");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bn (of order $30$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			19.8
Character	$\chi$	$=$	930.19
Dual form			930.2.bn.a.49.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.19398 - 0.431813i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.07600 + 1.86924i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})$	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.19398 - 0.431813i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.07600 + 1.86924i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-1.63893 + 1.52115i) q^{10} +(-1.42683 - 0.303282i) q^{11} +(0.994522 + 0.104528i) q^{12} +(5.26934 - 0.553830i) q^{13} +(2.73249 - 0.580808i) q^{14} +(1.28685 - 1.82866i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.53350 - 7.21455i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.719669 + 6.84719i) q^{19} +(0.267298 + 2.22003i) q^{20} +(-2.55202 + 1.13623i) q^{21} +(-1.08403 + 0.976063i) q^{22} +(4.70936 + 1.53016i) q^{23} +(0.669131 - 0.743145i) q^{24} +(4.62708 + 1.89478i) q^{25} +(2.64918 - 4.58852i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.13623 - 2.55202i) q^{28} +(6.77001 + 4.91870i) q^{29} +(-0.723028 - 2.11595i) q^{30} +(5.12587 + 2.17382i) q^{31} +1.00000i q^{32} +(0.857405 - 1.18012i) q^{33} +(-6.73807 - 2.99998i) q^{34} +(-3.74754 - 4.99751i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.34461 - 0.776311i) q^{37} +(5.11648 + 4.60690i) q^{38} +(-1.63728 + 5.03904i) q^{39} +(1.95316 + 1.08865i) q^{40} +(5.16027 - 2.29750i) q^{41} +(-0.580808 + 2.73249i) q^{42} +(0.119126 + 0.0125206i) q^{43} +(0.152476 + 1.45071i) q^{44} +(1.14716 + 1.91938i) q^{45} +(4.00602 - 2.91054i) q^{46} +(2.21845 + 3.05344i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(0.0840230 + 0.799425i) q^{49} +(4.25263 - 2.62966i) q^{50} +(7.21455 + 1.53350i) q^{51} +(-2.15504 - 4.84030i) q^{52} +(5.66865 - 5.10407i) q^{53} +(0.309017 - 0.951057i) q^{54} +(2.99947 + 1.28152i) q^{55} +(-1.39677 - 2.41927i) q^{56} +(-5.96250 - 3.44245i) q^{57} +(7.95862 - 2.58591i) q^{58} +(-4.74911 - 2.11444i) q^{59} +(-2.13682 - 0.658780i) q^{60} +3.06316 q^{61} +(4.77157 - 2.86917i) q^{62} -2.79353i q^{63} +(0.809017 + 0.587785i) q^{64} +(-11.8000 - 1.06028i) q^{65} +(-0.450764 - 1.38731i) q^{66} +(-7.33560 - 4.23521i) q^{67} +(-6.38757 + 3.68787i) q^{68} +(-3.31334 + 3.67984i) q^{69} +(-6.24582 + 0.0943568i) q^{70} +(0.0611462 + 0.0679097i) q^{71} +(0.406737 + 0.913545i) q^{72} +(2.17919 - 10.2523i) q^{73} +(0.162293 - 1.54412i) q^{74} +(-3.61296 + 3.45637i) q^{75} +(6.73445 - 1.43145i) q^{76} +(-2.39519 - 3.29669i) q^{77} +(3.11430 + 4.28647i) q^{78} +(-10.1149 + 2.14999i) q^{79} +(2.02878 - 0.940244i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.17441 - 5.52519i) q^{82} +(1.79393 + 4.02923i) q^{83} +(1.86924 + 2.07600i) q^{84} +(0.249129 + 16.4908i) q^{85} +(0.0801499 - 0.0890155i) q^{86} +(-7.24707 + 4.18410i) q^{87} +(1.26327 + 0.729352i) q^{88} +(-0.250391 - 0.770623i) q^{89} +(2.22710 + 0.200114i) q^{90} +(11.9744 + 8.69990i) q^{91} -4.95171i q^{92} +(-4.07076 + 3.79854i) q^{93} +3.77426 q^{94} +(4.53564 - 14.7118i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(10.3351 - 3.35809i) q^{97} +(0.696136 + 0.401914i) q^{98} +(0.729352 + 1.26327i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	$ 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) $ 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{15}\right)$

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 $

$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$2$	0.587785	−	0.809017i	0.415627	−	0.572061i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$3$	−0.406737	+	0.913545i	−0.234830	+	0.527436i
$4$	−0.309017	−	0.951057i	−0.154508	−	0.475528i
$5$	−2.19398	−	0.431813i	−0.981177	−	0.193113i
$5$	−2.19398	−	0.431813i	−0.981177	−	0.193113i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	2.07600	+	1.86924i	0.784654	+	0.706506i	0.960612	−	0.277892i	$-0.0896357\pi$
$7$	2.07600	+	1.86924i	0.784654	+	0.706506i	−0.175958	+	0.984398i	$0.556302\pi$
$8$	−0.951057	−	0.309017i	−0.336249	−	0.109254i
$9$	−0.669131	−	0.743145i	−0.223044	−	0.247715i
$10$	−1.63893	+	1.52115i	−0.518276	+	0.481030i
$11$	−1.42683	−	0.303282i	−0.430205	−	0.0914428i	−0.0122802	−	0.999925i	$-0.503909\pi$
$11$	−1.42683	−	0.303282i	−0.430205	−	0.0914428i	−0.417925	+	0.908482i	$0.637242\pi$
$12$	0.994522	+	0.104528i	0.287094	+	0.0301748i
$13$	5.26934	−	0.553830i	1.46145	−	0.153605i	0.659820	−	0.751423i	$-0.270632\pi$
$13$	5.26934	−	0.553830i	1.46145	−	0.153605i	0.801631	+	0.597819i	$0.203966\pi$
$14$	2.73249	−	0.580808i	0.730288	−	0.155228i
$15$	1.28685	−	1.82866i	0.332264	−	0.472159i
$16$	−0.809017	+	0.587785i	−0.202254	+	0.146946i
$17$	−1.53350	−	7.21455i	−0.371929	−	1.74979i	−0.623382	−	0.781917i	$-0.714242\pi$
$17$	−1.53350	−	7.21455i	−0.371929	−	1.74979i	0.251454	−	0.967869i	$-0.419091\pi$
$18$	−0.994522	+	0.104528i	−0.234411	+	0.0246376i
$19$	−0.719669	+	6.84719i	−0.165103	+	1.57085i	0.527513	+	0.849547i	$0.323125\pi$
$19$	−0.719669	+	6.84719i	−0.165103	+	1.57085i	−0.692616	+	0.721306i	$0.743542\pi$
$20$	0.267298	+	2.22003i	0.0597696	+	0.496415i
$21$	−2.55202	+	1.13623i	−0.556896	+	0.247946i
$22$	−1.08403	+	0.976063i	−0.231116	+	0.208097i
$23$	4.70936	+	1.53016i	0.981969	+	0.319061i	0.755638	−	0.654989i	$-0.227327\pi$
$23$	4.70936	+	1.53016i	0.981969	+	0.319061i	0.226331	+	0.974050i	$0.427327\pi$
$24$	0.669131	−	0.743145i	0.136586	−	0.151694i
$25$	4.62708	+	1.89478i	0.925415	+	0.378955i
$26$	2.64918	−	4.58852i	0.519547	−	0.899883i
$27$	0.951057	−	0.309017i	0.183031	−	0.0594703i
$28$	1.13623	−	2.55202i	0.214728	−	0.482286i
$29$	6.77001	+	4.91870i	1.25716	+	0.913379i	0.998615	−	0.0526199i	$-0.0167572\pi$
$29$	6.77001	+	4.91870i	1.25716	+	0.913379i	0.258544	+	0.965999i	$0.416757\pi$
$30$	−0.723028	−	2.11595i	−0.132006	−	0.386317i
$31$	5.12587	+	2.17382i	0.920633	+	0.390430i
$31$	5.12587	+	2.17382i	0.920633	+	0.390430i
$32$			1.00000i			0.176777i
$33$	0.857405	−	1.18012i	0.149255	−	0.205432i
$34$	−6.73807	−	2.99998i	−1.15557	−	0.514492i
$35$	−3.74754	−	4.99751i	−0.633449	−	0.844734i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	1.34461	−	0.776311i	0.221053	−	0.127625i	−0.385385	−	0.922756i	$-0.625931\pi$
$37$	1.34461	−	0.776311i	0.221053	−	0.127625i	0.606438	+	0.795131i	$0.292598\pi$
$38$	5.11648	+	4.60690i	0.830003	+	0.747338i
$39$	−1.63728	+	5.03904i	−0.262175	+	0.806893i
$40$	1.95316	+	1.08865i	0.308822	+	0.172131i
$41$	5.16027	−	2.29750i	0.805899	−	0.358809i	0.0379173	−	0.999281i	$-0.487928\pi$
$41$	5.16027	−	2.29750i	0.805899	−	0.358809i	0.767982	+	0.640471i	$0.221261\pi$
$42$	−0.580808	+	2.73249i	−0.0896207	+	0.421632i
$43$	0.119126	+	0.0125206i	0.0181665	+	0.00190938i	0.113607	−	0.993526i	$-0.463759\pi$
$43$	0.119126	+	0.0125206i	0.0181665	+	0.00190938i	−0.0954408	+	0.995435i	$0.530426\pi$
$44$	0.152476	+	1.45071i	0.0229866	+	0.218703i
$45$	1.14716	+	1.91938i	0.171008	+	0.286125i
$46$	4.00602	−	2.91054i	0.590656	−	0.429136i
$47$	2.21845	+	3.05344i	0.323595	+	0.445390i	0.939561	−	0.342383i	$-0.111234\pi$
$47$	2.21845	+	3.05344i	0.323595	+	0.445390i	−0.615966	+	0.787773i	$0.711234\pi$
$48$	−0.207912	−	0.978148i	−0.0300095	−	0.141183i
$49$	0.0840230	+	0.799425i	0.0120033	+	0.114204i
$50$	4.25263	−	2.62966i	0.601413	−	0.371890i
$51$	7.21455	+	1.53350i	1.01024	+	0.214733i
$52$	−2.15504	−	4.84030i	−0.298850	−	0.671228i
$53$	5.66865	−	5.10407i	0.778649	−	0.701099i	−0.180633	−	0.983551i	$-0.557814\pi$
$53$	5.66865	−	5.10407i	0.778649	−	0.701099i	0.959281	+	0.282452i	$0.0911478\pi$
$54$	0.309017	−	0.951057i	0.0420519	−	0.129422i
$55$	2.99947	+	1.28152i	0.404448	+	0.172800i
$56$	−1.39677	−	2.41927i	−0.186651	−	0.323289i
$57$	−5.96250	−	3.44245i	−0.789753	−	0.455964i
$58$	7.95862	−	2.58591i	1.04502	−	0.339547i
$59$	−4.74911	−	2.11444i	−0.618282	−	0.275277i	0.0735996	−	0.997288i	$-0.476551\pi$
$59$	−4.74911	−	2.11444i	−0.618282	−	0.275277i	−0.691882	+	0.722011i	$0.743218\pi$
$60$	−2.13682	−	0.658780i	−0.275863	−	0.0850482i
$61$	3.06316			0.392198			0.196099	−	0.980584i	$-0.437173\pi$
$61$	3.06316			0.392198			0.196099	+	0.980584i	$0.437173\pi$
$62$	4.77157	−	2.86917i	0.605990	−	0.364385i
$63$		−	2.79353i		−	0.351952i
$64$	0.809017	+	0.587785i	0.101127	+	0.0734732i
$65$	−11.8000	−	1.06028i	−1.46361	−	0.131511i
$66$	−0.450764	−	1.38731i	−0.0554853	−	0.170766i
$67$	−7.33560	−	4.23521i	−0.896186	−	0.517413i	−0.0202254	−	0.999795i	$-0.506438\pi$
$67$	−7.33560	−	4.23521i	−0.896186	−	0.517413i	−0.875961	+	0.482382i	$0.839772\pi$
$68$	−6.38757	+	3.68787i	−0.774607	+	0.447219i
$69$	−3.31334	+	3.67984i	−0.398880	+	0.443001i
$70$	−6.24582	+	0.0943568i	−0.746518	+	0.0112778i
$71$	0.0611462	+	0.0679097i	0.00725671	+	0.00805940i	0.746762	−	0.665091i	$-0.231607\pi$
$71$	0.0611462	+	0.0679097i	0.00725671	+	0.00805940i	−0.739506	+	0.673150i	$0.764941\pi$
$72$	0.406737	+	0.913545i	0.0479344	+	0.107662i
$73$	2.17919	−	10.2523i	0.255055	−	1.19994i	−0.645006	−	0.764177i	$-0.723145\pi$
$73$	2.17919	−	10.2523i	0.255055	−	1.19994i	0.900062	−	0.435763i	$-0.143521\pi$
$74$	0.162293	−	1.54412i	0.0188662	−	0.179500i
$75$	−3.61296	+	3.45637i	−0.417189	+	0.399107i
$76$	6.73445	−	1.43145i	0.772495	−	0.164199i
$77$	−2.39519	−	3.29669i	−0.272957	−	0.375693i
$78$	3.11430	+	4.28647i	0.352625	+	0.485347i
$79$	−10.1149	+	2.14999i	−1.13802	+	0.241893i	−0.738121	−	0.674668i	$-0.764287\pi$
$79$	−10.1149	+	2.14999i	−1.13802	+	0.241893i	−0.399895	+	0.916561i	$0.630954\pi$
$80$	2.02878	−	0.940244i	0.226824	−	0.105122i
$81$	−0.104528	+	0.994522i	−0.0116143	+	0.110502i
$82$	1.17441	−	5.52519i	0.129692	−	0.610155i
$83$	1.79393	+	4.02923i	0.196909	+	0.442265i	0.984832	−	0.173508i	$-0.0555103\pi$
$83$	1.79393	+	4.02923i	0.196909	+	0.442265i	−0.787923	+	0.615773i	$0.788844\pi$
$84$	1.86924	+	2.07600i	0.203951	+	0.226510i
$85$	0.249129	+	16.4908i	0.0270218	+	1.78867i
$86$	0.0801499	−	0.0890155i	0.00864278	−	0.00959878i
$87$	−7.24707	+	4.18410i	−0.776967	+	0.448582i
$88$	1.26327	+	0.729352i	0.134666	+	0.0777492i
$89$	−0.250391	−	0.770623i	−0.0265414	−	0.0816859i	0.936908	−	0.349575i	$-0.113674\pi$
$89$	−0.250391	−	0.770623i	−0.0265414	−	0.0816859i	−0.963450	+	0.267889i	$0.913674\pi$
$90$	2.22710	+	0.200114i	0.234756	+	0.0210939i
$91$	11.9744	+	8.69990i	1.25526	+	0.911998i
$92$		−	4.95171i		−	0.516252i
$93$	−4.07076	+	3.79854i	−0.422118	+	0.393890i
$94$	3.77426			0.389285
$95$	4.53564	−	14.7118i	0.465347	−	1.50940i
$96$	−0.913545	−	0.406737i	−0.0932383	−	0.0415124i
$97$	10.3351	−	3.35809i	1.04937	−	0.340962i	0.266951	−	0.963710i	$-0.413984\pi$
$97$	10.3351	−	3.35809i	1.04937	−	0.340962i	0.782423	+	0.622748i	$0.213984\pi$
$98$	0.696136	+	0.401914i	0.0703204	+	0.0405995i
$99$	0.729352	+	1.26327i	0.0733026	+	0.126964i
$100$	0.372194	−	4.98613i	0.0372194	−	0.498613i
$101$	−5.40079	+	16.6219i	−0.537398	+	1.65394i	0.201011	+	0.979589i	$0.435577\pi$
$101$	−5.40079	+	16.6219i	−0.537398	+	1.65394i	−0.738409	+	0.674353i	$0.764423\pi$
$102$	5.48124	−	4.93533i	0.542723	−	0.488670i
$103$	1.78840	+	4.01681i	0.176216	+	0.395788i	0.979962	−	0.199185i	$-0.0638294\pi$
$103$	1.78840	+	4.01681i	0.176216	+	0.395788i	−0.803746	+	0.594973i	$0.797163\pi$
$104$	−5.18258	−	1.10159i	−0.508194	−	0.108020i
$105$	6.08971	−	1.39087i	0.594295	−	0.135735i
$106$	−0.797335	−	7.58613i	−0.0774440	−	0.736830i
$107$	2.10264	+	9.89216i	0.203270	+	0.956311i	0.954946	+	0.296779i	$0.0959123\pi$
$107$	2.10264	+	9.89216i	0.203270	+	0.956311i	−0.751676	+	0.659532i	$0.770754\pi$
$108$	−0.587785	−	0.809017i	−0.0565597	−	0.0778477i
$109$	1.81650	−	1.31976i	0.173989	−	0.126410i	−0.497383	−	0.867531i	$-0.665706\pi$
$109$	1.81650	−	1.31976i	0.173989	−	0.126410i	0.671371	+	0.741121i	$0.265706\pi$
$110$	2.79981	−	1.67336i	0.266951	−	0.159549i
$111$	0.162293	+	1.54412i	0.0154042	+	0.146561i
$112$	−2.77823	−	0.292004i	−0.262518	−	0.0275918i
$113$	−3.12738	+	14.7132i	−0.294199	+	1.38410i	0.544161	+	0.838981i	$0.316848\pi$
$113$	−3.12738	+	14.7132i	−0.294199	+	1.38410i	−0.838360	+	0.545117i	$0.816485\pi$
$114$	−6.28967	+	2.80034i	−0.589082	+	0.262276i
$115$	−9.67149	−	5.39071i	−0.901871	−	0.502686i
$116$	2.58591	−	7.95862i	0.240096	−	0.738940i
$117$	−3.93745	−	3.54530i	−0.364018	−	0.327763i
$118$	−4.50208	+	2.59928i	−0.414450	+	0.239283i
$119$	10.3022	−	17.8439i	0.944399	−	1.63575i
$120$	−1.78896	+	1.34150i	−0.163309	+	0.122462i
$121$	−8.10514	−	3.60864i	−0.736831	−	0.328058i
$122$	1.80048	−	2.47815i	0.163008	−	0.224361i
$123$			5.64862i			0.509319i
$124$	0.483446	−	5.54674i	0.0434147	−	0.498112i
$125$	−9.33351	−	6.15513i	−0.834815	−	0.550531i
$126$	−2.26002	−	1.64200i	−0.201338	−	0.146281i
$127$	−2.99425	+	6.72519i	−0.265696	+	0.596764i	−0.996291	−	0.0860475i	$-0.972576\pi$
$127$	−2.99425	+	6.72519i	−0.265696	+	0.596764i	0.730595	+	0.682811i	$0.239243\pi$
$128$	0.951057	−	0.309017i	0.0840623	−	0.0273135i
$129$	−0.0598911	+	0.103734i	−0.00527311	+	0.00913330i
$130$	−7.79363	+	8.92316i	−0.683546	+	0.782613i
$131$	4.94017	−	5.48661i	0.431624	−	0.479367i	−0.487619	−	0.873056i	$-0.662135\pi$
$131$	4.94017	−	5.48661i	0.431624	−	0.479367i	0.919244	+	0.393689i	$0.128801\pi$
$132$	−1.38731	−	0.450764i	−0.120750	−	0.0392340i
$133$	−14.2931	+	12.8695i	−1.23937	+	1.11593i
$134$	−7.73812	+	3.44523i	−0.668471	+	0.297623i
$135$	−2.22003	+	0.267298i	−0.191070	+	0.0230053i
$136$	−0.770974	+	7.33533i	−0.0661105	+	0.628999i
$137$	−6.37830	+	0.670387i	−0.544935	+	0.0572750i	−0.372997	−	0.927833i	$-0.621670\pi$
$137$	−6.37830	+	0.670387i	−0.544935	+	0.0572750i	−0.171939	+	0.985108i	$0.555003\pi$
$138$	1.02952	+	4.84351i	0.0876385	+	0.412307i
$139$	−7.09697	+	5.15625i	−0.601957	+	0.437348i	−0.846573	−	0.532273i	$-0.821338\pi$
$139$	−7.09697	+	5.15625i	−0.601957	+	0.437348i	0.244616	+	0.969620i	$0.421338\pi$
$140$	−3.59486	+	5.10843i	−0.303821	+	0.431741i
$141$	−3.69178	+	0.784713i	−0.310904	+	0.0660848i
$142$	0.0908809	−	0.00955197i	0.00762656	−	0.000801583i
$143$	−7.68641	−	0.807874i	−0.642770	−	0.0675578i
$144$	0.978148	+	0.207912i	0.0815123	+	0.0173260i
$145$	−12.7293	−	13.7149i	−1.05711	−	1.13896i
$146$	−7.01338	−	7.78915i	−0.580432	−	0.644635i
$147$	−0.764486	−	0.248397i	−0.0630538	−	0.0204874i
$148$	−1.15382	−	1.03891i	−0.0948437	−	0.0853976i
$149$	−10.4859	−	18.1621i	−0.859037	−	1.48790i	−0.872849	−	0.487991i	$-0.837730\pi$
$149$	−10.4859	−	18.1621i	−0.859037	−	1.48790i	0.0138119	−	0.999905i	$-0.495603\pi$
$150$	0.672614	+	4.95455i	0.0549187	+	0.404538i
$151$	−0.473737	−	1.45801i	−0.0385522	−	0.118651i	0.929928	−	0.367741i	$-0.119869\pi$
$151$	−0.473737	−	1.45801i	−0.0385522	−	0.118651i	−0.968480	+	0.249089i	$0.919869\pi$
$152$	2.80034	−	6.28967i	0.227138	−	0.510160i
$153$	−4.33535	+	5.96709i	−0.350492	+	0.482411i
$154$	−4.07494			−0.328368
$155$	−10.3074	−	6.98273i	−0.827906	−	0.560866i
$156$	5.29836			0.424209
$157$	3.69016	−	5.07907i	0.294507	−	0.405354i	−0.635965	−	0.771718i	$-0.719398\pi$
$157$	3.69016	−	5.07907i	0.294507	−	0.405354i	0.930472	+	0.366364i	$0.119398\pi$
$158$	−4.20602	+	9.44687i	−0.334613	+	0.751553i
$159$	2.35716	+	7.25458i	0.186935	+	0.575326i
$160$	0.431813	−	2.19398i	0.0341378	−	0.173449i
$161$	6.91639	+	11.9795i	0.545088	+	0.944120i
$162$	0.743145	+	0.669131i	0.0583870	+	0.0525719i
$163$	2.13373	+	0.693292i	0.167127	+	0.0543029i	0.391385	−	0.920227i	$-0.371996\pi$
$163$	2.13373	+	0.693292i	0.167127	+	0.0543029i	−0.224258	+	0.974530i	$0.571996\pi$
$164$	−3.77967	−	4.19774i	−0.295142	−	0.327789i
$165$	−2.39072	+	2.21891i	−0.186117	+	0.172742i
$166$	4.31416	+	0.917003i	0.334844	+	0.0711732i
$167$	−11.2634	−	1.18383i	−0.871589	−	0.0916077i	−0.341836	−	0.939760i	$-0.611049\pi$
$167$	−11.2634	−	1.18383i	−0.871589	−	0.0916077i	−0.529753	+	0.848152i	$0.677715\pi$
$168$	2.77823	−	0.292004i	0.214345	−	0.0225286i
$169$	14.7433	−	3.13378i	1.13410	−	0.241060i
$170$	13.4877	+	9.49147i	1.03446	+	0.727963i
$171$	5.57001	−	4.04685i	0.425949	−	0.309470i
$172$	−0.0249041	−	0.117165i	−0.00189892	−	0.00893372i
$173$	8.44349	−	0.887446i	0.641947	−	0.0674713i	0.222038	−	0.975038i	$-0.428729\pi$
$173$	8.44349	−	0.887446i	0.641947	−	0.0674713i	0.419908	+	0.907567i	$0.362062\pi$
$174$	−0.874714	+	8.32235i	−0.0663119	+	0.630916i
$175$	6.06402	+	12.5827i	0.458397	+	0.951160i
$176$	1.33259	−	0.593308i	0.100448	−	0.0447223i
$177$	3.86328	−	3.47851i	0.290382	−	0.261461i
$178$	−0.770623	−	0.250391i	−0.0577606	−	0.0187676i
$179$	−8.09620	+	8.99174i	−0.605138	+	0.672074i	−0.965399	−	0.260778i	$-0.916021\pi$
$179$	−8.09620	+	8.99174i	−0.605138	+	0.672074i	0.360261	+	0.932852i	$0.382688\pi$
$180$	1.47095	−	1.68413i	0.109638	−	0.125528i
$181$	−2.80306	+	4.85503i	−0.208349	+	0.360872i	−0.951195	−	0.308591i	$-0.900142\pi$
$181$	−2.80306	+	4.85503i	−0.208349	+	0.360872i	0.742845	+	0.669463i	$0.233476\pi$
$182$	14.0767	−	4.57381i	1.04344	−	0.339033i
$183$	−1.24590	+	2.79834i	−0.0920996	+	0.206859i
$184$	−4.00602	−	2.91054i	−0.295328	−	0.214568i
$185$	−3.28527	+	1.12259i	−0.241538	+	0.0825344i
$186$	0.680350	+	5.52604i	0.0498857	+	0.405189i
$187$			10.7590i			0.786777i
$188$	2.21845	−	3.05344i	0.161797	−	0.222695i
$189$	2.55202	+	1.13623i	0.185632	+	0.0826487i
$190$	−9.23613	−	12.3168i	−0.670059	−	0.893555i
$191$	10.8334	−	18.7640i	0.783877	−	1.35771i	−0.145791	−	0.989315i	$-0.546573\pi$
$191$	10.8334	−	18.7640i	0.783877	−	1.35771i	0.929668	−	0.368399i	$-0.120094\pi$
$192$	−0.866025	+	0.500000i	−0.0625000	+	0.0360844i
$193$	−7.82304	−	7.04390i	−0.563115	−	0.507031i	0.337689	−	0.941258i	$-0.390355\pi$
$193$	−7.82304	−	7.04390i	−0.563115	−	0.507031i	−0.900804	+	0.434227i	$0.857022\pi$
$194$	3.35809	−	10.3351i	0.241097	−	0.742020i
$195$	5.76809	−	10.3485i	0.413062	−	0.741075i
$196$	0.734334	−	0.326947i	0.0524524	−	0.0233533i
$197$	−3.31684	+	15.6045i	−0.236315	+	1.11178i	0.686679	+	0.726961i	$0.259068\pi$
$197$	−3.31684	+	15.6045i	−0.236315	+	1.11178i	−0.922994	+	0.384815i	$0.874265\pi$
$198$	1.45071	+	0.152476i	0.103098	+	0.0108360i
$199$	−1.55138	−	14.7604i	−0.109974	−	1.04634i	−0.900782	−	0.434272i	$-0.857006\pi$
$199$	−1.55138	−	14.7604i	−0.109974	−	1.04634i	0.790808	−	0.612065i	$-0.209661\pi$
$200$	−3.81509	−	3.23188i	−0.269768	−	0.228529i
$201$	6.85272	−	4.97879i	0.483353	−	0.351177i
$202$	10.2729	+	14.1394i	0.722799	+	0.994848i
$203$	4.86031	+	22.8660i	0.341127	+	1.60488i
$204$	−0.770974	−	7.33533i	−0.0539790	−	0.513576i
$205$	−12.3136	+	2.81239i	−0.860020	+	0.196426i
$206$	4.30086	+	0.914177i	0.299655	+	0.0636937i
$207$	−2.01404	−	4.52362i	−0.139986	−	0.314413i
$208$	−3.93745	+	3.54530i	−0.273013	+	0.245822i
$209$	3.10347	−	9.55150i	0.214672	−	0.660691i
$210$	2.45420	−	5.74422i	0.169356	−	0.396389i
$211$	6.63494	+	11.4920i	0.456768	+	0.791145i	0.998788	−	0.0492204i	$-0.0156737\pi$
$211$	6.63494	+	11.4920i	0.456768	+	0.791145i	−0.542020	+	0.840366i	$0.682340\pi$
$212$	−6.60597	−	3.81396i	−0.453700	−	0.261944i
$213$	−0.0869090	+	0.0282384i	−0.00595491	+	0.00193487i
$214$	9.23883	+	4.11339i	0.631553	+	0.281186i
$215$	−0.255953	−	0.0789101i	−0.0174559	−	0.00538163i
$216$	−1.00000			−0.0680414
$217$	6.57791	+	14.0943i	0.446538	+	0.956785i
$218$		−	2.24531i		−	0.152072i
$219$	8.47958	+	6.16077i	0.572997	+	0.416306i
$220$	0.291907	−	3.24867i	0.0196804	−	0.219025i
$221$	−12.0762	−	37.1666i	−0.812331	−	2.50010i
$222$	1.34461	+	0.776311i	0.0902443	+	0.0521026i
$223$	18.4455	−	10.6495i	1.23520	−	0.713143i	0.267091	−	0.963671i	$-0.413938\pi$
$223$	18.4455	−	10.6495i	1.23520	−	0.713143i	0.968109	+	0.250528i	$0.0806042\pi$
$224$	−1.86924	+	2.07600i	−0.124894	+	0.138709i
$225$	−1.68803	−	4.70644i	−0.112535	−	0.313763i
$226$	10.0650	+	11.1783i	0.669512	+	0.743568i
$227$	−11.2097	−	25.1773i	−0.744012	−	1.67108i	−0.741383	−	0.671083i	$-0.765830\pi$
$227$	−11.2097	−	25.1773i	−0.744012	−	1.67108i	−0.00262970	−	0.999997i	$-0.500837\pi$
$228$	−1.43145	+	6.73445i	−0.0948003	+	0.446000i
$229$	−1.26349	+	12.0213i	−0.0834940	+	0.794392i	0.870014	+	0.493026i	$0.164109\pi$
$229$	−1.26349	+	12.0213i	−0.0834940	+	0.794392i	−0.953508	+	0.301366i	$0.902557\pi$
$230$	−10.0459	+	4.65582i	−0.662409	+	0.306996i
$231$	3.98589	−	0.847227i	0.262252	−	0.0557435i
$232$	−4.91870	−	6.77001i	−0.322928	−	0.444473i
$233$	−15.0599	−	20.7281i	−0.986604	−	1.35794i	−0.933195	−	0.359371i	$-0.882991\pi$
$233$	−15.0599	−	20.7281i	−0.986604	−	1.35794i	−0.0534096	−	0.998573i	$-0.517009\pi$
$234$	−5.18258	+	1.10159i	−0.338796	+	0.0720133i
$235$	−3.54873	−	7.65714i	−0.231493	−	0.499497i
$236$	−0.543397	+	5.17007i	−0.0353721	+	0.336543i
$237$	2.14999	−	10.1149i	0.139657	−	0.657034i
$238$	−8.38055	−	18.8230i	−0.543230	−	1.22011i
$239$	9.13966	+	10.1506i	0.591196	+	0.656589i	0.962296	−	0.272003i	$-0.0876862\pi$
$239$	9.13966	+	10.1506i	0.591196	+	0.656589i	−0.371101	+	0.928593i	$0.621020\pi$
$240$	0.0337769	+	2.23581i	0.00218029	+	0.144321i
$241$	5.82947	−	6.47428i	0.375509	−	0.417045i	−0.525536	−	0.850772i	$-0.676135\pi$
$241$	5.82947	−	6.47428i	0.375509	−	0.417045i	0.901044	+	0.433727i	$0.142802\pi$
$242$	−7.68354	+	4.43609i	−0.493916	+	0.285163i
$243$	−0.866025	−	0.500000i	−0.0555556	−	0.0320750i
$244$	−0.946570	−	2.91324i	−0.0605979	−	0.186501i
$245$	0.160858	−	1.79020i	0.0102768	−	0.114372i
$246$	4.56983	+	3.32018i	0.291362	+	0.211687i
$247$			36.4787i			2.32109i
$248$	−4.20324	−	3.65141i	−0.266906	−	0.231864i
$249$	−4.41054			−0.279507
$250$	−10.4657	+	3.93308i	−0.661909	+	0.248750i
$251$	24.0859	+	10.7237i	1.52029	+	0.676876i	0.985742	−	0.168263i	$-0.0538157\pi$
$251$	24.0859	+	10.7237i	1.52029	+	0.676876i	0.534547	+	0.845139i	$0.320482\pi$
$252$	−2.65681	+	0.863249i	−0.167363	+	0.0543796i
$253$	−6.25538	−	3.61154i	−0.393272	−	0.227056i
$254$	3.68082	+	6.37536i	0.230955	+	0.400026i
$255$	−15.1664	−	6.47980i	−0.949756	−	0.405781i
$256$	0.309017	−	0.951057i	0.0193136	−	0.0594410i
$257$	−13.5115	+	12.1658i	−0.842821	+	0.758880i	−0.972556	−	0.232669i	$-0.925254\pi$
$257$	−13.5115	+	12.1658i	−0.842821	+	0.758880i	0.129735	+	0.991549i	$0.458587\pi$
$258$	0.0487198	+	0.109426i	0.00303316	+	0.00681259i
$259$	4.24252	+	0.901776i	0.263617	+	0.0560336i
$260$	2.63800	+	11.5501i	0.163602	+	0.716305i
$261$	−0.874714	−	8.32235i	−0.0541434	−	0.515140i
$262$	−1.53500	−	7.22163i	−0.0948329	−	0.446154i
$263$	−7.30520	−	10.0547i	−0.450458	−	0.620002i	0.522038	−	0.852922i	$-0.325172\pi$
$263$	−7.30520	−	10.0547i	−0.450458	−	0.620002i	−0.972496	+	0.232920i	$0.925172\pi$
$264$	−1.18012	+	0.857405i	−0.0726311	+	0.0527696i
$265$	−14.6409	+	8.75043i	−0.899383	+	0.537535i
$266$	2.01042	+	19.1279i	0.123267	+	1.17280i
$267$	0.805842	+	0.0846974i	0.0493167	+	0.00518340i
$268$	−1.76110	+	8.28532i	−0.107576	+	0.506107i
$269$	7.68218	−	3.42033i	0.468391	−	0.208541i	−0.158949	−	0.987287i	$-0.550810\pi$
$269$	7.68218	−	3.42033i	0.468391	−	0.208541i	0.627340	+	0.778746i	$0.284144\pi$
$270$	−1.08865	+	1.95316i	−0.0662534	+	0.118865i
$271$	−4.57436	+	14.0784i	−0.277872	+	0.855203i	0.710573	+	0.703624i	$0.248436\pi$
$271$	−4.57436	+	14.0784i	−0.277872	+	0.855203i	−0.988445	+	0.151579i	$0.951564\pi$
$272$	5.48124	+	4.93533i	0.332349	+	0.299248i
$273$	−12.8182	+	7.40058i	−0.775792	+	0.447903i
$274$	−3.20672	+	5.55420i	−0.193725	+	0.335541i
$275$	−6.02739	−	4.10683i	−0.363465	−	0.247651i
$276$	4.52362	+	2.01404i	0.272290	+	0.121231i
$277$	−14.0709	+	19.3670i	−0.845440	+	1.16365i	0.139409	+	0.990235i	$0.455480\pi$
$277$	−14.0709	+	19.3670i	−0.845440	+	1.16365i	−0.984849	+	0.173414i	$0.944520\pi$
$278$			8.77234i			0.526130i
$279$	−1.81441	−	5.26383i	−0.108626	−	0.315137i
$280$	2.01980	+	5.91097i	0.120706	+	0.353248i
$281$	3.92431	+	2.85118i	0.234105	+	0.170087i	0.698653	−	0.715461i	$-0.253783\pi$
$281$	3.92431	+	2.85118i	0.234105	+	0.170087i	−0.464548	+	0.885548i	$0.653783\pi$
$282$	−1.53513	+	3.44796i	−0.0914157	+	0.205323i
$283$	19.7290	−	6.41034i	1.17277	−	0.381055i	0.343092	−	0.939302i	$-0.388526\pi$
$283$	19.7290	−	6.41034i	1.17277	−	0.381055i	0.829675	+	0.558246i	$0.188526\pi$
$284$	0.0456908	−	0.0791387i	0.00271125	−	0.00469602i
$285$	11.5951	+	10.1274i	0.686835	+	0.599892i
$286$	−5.17154	+	5.74358i	−0.305800	+	0.339625i
$287$	15.0073	+	4.87617i	0.885853	+	0.287831i
$288$	0.743145	−	0.669131i	0.0437902	−	0.0394289i
$289$	−34.1679	+	15.2125i	−2.00988	+	0.894855i
$290$	−18.5777	+	2.23680i	−1.09092	+	0.131349i
$291$	−1.13591	+	10.8075i	−0.0665883	+	0.633545i
$292$	−10.4239	+	1.09560i	−0.610013	+	0.0641150i
$293$	0.189014	+	0.889240i	0.0110423	+	0.0519500i	0.983324	−	0.181863i	$-0.0582129\pi$
$293$	0.189014	+	0.889240i	0.0110423	+	0.0519500i	−0.972282	+	0.233813i	$0.924880\pi$
$294$	−0.650311	+	0.472479i	−0.0379269	+	0.0275555i
$295$	9.50641	+	6.68977i	0.553484	+	0.389493i
$296$	−1.51869	+	0.322808i	−0.0882723	+	0.0187629i
$297$	−1.45071	+	0.152476i	−0.0841789	+	0.00884756i
$298$	−20.8569	−	2.19215i	−1.20821	−	0.126988i
$299$	25.6627	+	5.45477i	1.48411	+	0.315457i
$300$	4.40367	+	2.36806i	0.254246	+	0.136720i
$301$	0.223901	+	0.248668i	0.0129055	+	0.0143330i
$302$	−1.45801	−	0.473737i	−0.0838993	−	0.0272605i
$303$	−12.9882	−	11.6946i	−0.746151	−	0.671838i
$304$	−3.44245	−	5.96250i	−0.197438	−	0.341973i
$305$	−6.72051	−	1.32271i	−0.384815	−	0.0757384i
$306$	2.27923	+	7.01474i	0.130295	+	0.401006i
$307$	−0.206635	+	0.464110i	−0.0117933	+	0.0264882i	−0.919346	−	0.393450i	$-0.871282\pi$
$307$	−0.206635	+	0.464110i	−0.0117933	+	0.0264882i	0.907553	+	0.419938i	$0.137948\pi$
$308$	−2.39519	+	3.29669i	−0.136479	+	0.187847i
$309$	−4.39695			−0.250134
$310$	−11.7077	+	4.23448i	−0.664950	+	0.240502i
$311$	4.36406			0.247463			0.123732	−	0.992316i	$-0.460514\pi$
$311$	4.36406			0.247463			0.123732	+	0.992316i	$0.460514\pi$
$312$	3.11430	−	4.28647i	0.176313	−	0.242673i
$313$	8.00719	−	17.9844i	0.452593	−	1.01654i	−0.532799	−	0.846242i	$-0.678860\pi$
$313$	8.00719	−	17.9844i	0.452593	−	1.01654i	0.985392	−	0.170299i	$-0.0544735\pi$
$314$	−1.94003	−	5.97081i	−0.109482	−	0.336952i
$315$	−1.20628	+	6.12895i	−0.0679664	+	0.345327i
$316$	5.17044	+	8.95547i	0.290860	+	0.503785i
$317$	−9.63944	−	8.67939i	−0.541405	−	0.487483i	0.352455	−	0.935829i	$-0.385347\pi$
$317$	−9.63944	−	8.67939i	−0.541405	−	0.487483i	−0.893860	+	0.448345i	$0.852014\pi$
$318$	7.25458	+	2.35716i	0.406817	+	0.132183i
$319$	−8.16789	−	9.07136i	−0.457314	−	0.507898i
$320$	−1.52115	−	1.63893i	−0.0850350	−	0.0916191i
$321$	−9.89216	−	2.10264i	−0.552126	−	0.117358i
$322$	13.7570	+	1.44592i	0.766648	+	0.0805779i
$323$	50.5030	−	5.30808i	2.81006	−	0.295350i
$324$	0.978148	−	0.207912i	0.0543415	−	0.0115506i
$325$	25.4310	+	7.42160i	1.41066	+	0.411676i
$326$	1.81506	−	1.31872i	0.100527	−	0.0730372i
$327$	0.466827	+	2.19625i	0.0258156	+	0.121453i
$328$	−5.61768	+	0.590442i	−0.310184	+	0.0326017i
$329$	−1.10210	+	10.4858i	−0.0607606	+	0.578099i
$330$	0.389909	+	3.23837i	0.0214638	+	0.178267i
$331$	25.8196	−	11.4956i	1.41917	−	0.631856i	0.453414	−	0.891300i	$-0.350206\pi$
$331$	25.8196	−	11.4956i	1.41917	−	0.631856i	0.965758	+	0.259444i	$0.0835392\pi$
$332$	3.27767	−	2.95123i	0.179885	−	0.161970i
$333$	−1.47663	−	0.479787i	−0.0809189	−	0.0262921i
$334$	−7.57821	+	8.41645i	−0.414661	+	0.460528i
$335$	14.2653	+	12.4596i	0.779398	+	0.680739i
$336$	1.39677	−	2.41927i	0.0761999	−	0.131982i
$337$	−28.2643	+	9.18362i	−1.53965	+	0.500264i	−0.951281	−	0.308326i	$-0.900231\pi$
$337$	−28.2643	+	9.18362i	−1.53965	+	0.500264i	−0.588373	+	0.808590i	$0.700231\pi$
$338$	6.13061	−	13.7696i	0.333461	−	0.748966i
$339$	−12.1691	−	8.84139i	−0.660936	−	0.480198i
$340$	15.6067	−	5.33286i	0.846390	−	0.289215i
$341$	−6.65445	−	4.65625i	−0.360359	−	0.252150i
$342$		−	6.88491i		−	0.372293i
$343$	10.1741	−	14.0034i	0.549350	−	0.756115i
$344$	−0.109426	−	0.0487198i	−0.00589988	−	0.00262679i
$345$	8.85840	−	6.64274i	0.476920	−	0.357633i
$346$	4.24500	−	7.35255i	0.228213	−	0.395276i
$347$	0.910139	−	0.525469i	0.0488588	−	0.0282087i	−0.475372	−	0.879785i	$-0.657686\pi$
$347$	0.910139	−	0.525469i	0.0488588	−	0.0282087i	0.524230	+	0.851576i	$0.324353\pi$
$348$	6.21878	+	5.59941i	0.333361	+	0.300160i
$349$	4.36635	−	13.4383i	0.233726	−	0.719333i	−0.763562	−	0.645734i	$-0.776551\pi$
$349$	4.36635	−	13.4383i	0.233726	−	0.719333i	0.997288	−	0.0735993i	$-0.0234486\pi$
$350$	13.7439	+	2.49001i	0.734644	+	0.133097i
$351$	4.84030	−	2.15504i	0.258356	−	0.115027i
$352$	0.303282	−	1.42683i	0.0161650	−	0.0760502i
$353$	−12.8830	−	1.35406i	−0.685694	−	0.0720694i	−0.244726	−	0.969592i	$-0.578698\pi$
$353$	−12.8830	−	1.35406i	−0.685694	−	0.0720694i	−0.440968	+	0.897523i	$0.645365\pi$
$354$	−0.543397	−	5.17007i	−0.0288812	−	0.274786i
$355$	−0.104829	−	0.175396i	−0.00556375	−	0.00930906i
$356$	−0.655531	+	0.476271i	−0.0347431	+	0.0252423i
$357$	12.1109	+	16.6693i	0.640979	+	0.882231i
$358$	2.51564	+	11.8352i	0.132956	+	0.625508i
$359$	−3.09221	−	29.4204i	−0.163200	−	1.55275i	−0.703144	−	0.711047i	$-0.748221\pi$
$359$	−3.09221	−	29.4204i	−0.163200	−	1.55275i	0.539944	−	0.841701i	$-0.318445\pi$
$360$	−0.497890	−	2.17993i	−0.0262411	−	0.114893i
$361$	−27.7813	−	5.90509i	−1.46217	−	0.310794i
$362$	2.28021	+	5.12144i	0.119845	+	0.269177i
$363$	6.59332	−	5.93665i	0.346059	−	0.311593i
$364$	4.57381	−	14.0767i	0.239733	−	0.737822i
$365$	−9.20817	+	21.5523i	−0.481978	+	1.12810i
$366$	1.53158	+	2.65278i	0.0800571	+	0.138663i
$367$	−22.8002	−	13.1637i	−1.19016	−	0.687140i	−0.231819	−	0.972759i	$-0.574468\pi$
$367$	−22.8002	−	13.1637i	−1.19016	−	0.687140i	−0.958343	+	0.285619i	$0.907801\pi$
$368$	−4.70936	+	1.53016i	−0.245492	+	0.0797653i
$369$	−5.16027	−	2.29750i	−0.268633	−	0.119603i
$370$	−1.02284	+	3.31768i	−0.0531748	+	0.172478i
$371$	21.3088			1.10630
$372$	4.87056	+	2.69771i	0.252527	+	0.139870i
$373$			23.2652i			1.20463i	0.798260	+	0.602313i	$0.205754\pi$
$373$			23.2652i			1.20463i	−0.798260	+	0.602313i	$0.794246\pi$
$374$	8.70422	+	6.32399i	0.450085	+	0.327006i
$375$	9.41927	−	6.02307i	0.486409	−	0.311030i
$376$	−1.16631	−	3.58954i	−0.0601479	−	0.185116i
$377$	38.3976	+	22.1689i	1.97758	+	1.14175i
$378$	2.41927	−	1.39677i	0.124434	−	0.0718419i
$379$	−19.1641	+	21.2838i	−0.984391	+	1.09328i	0.0112431	+	0.999937i	$0.496421\pi$
$379$	−19.1641	+	21.2838i	−0.984391	+	1.09328i	−0.995634	+	0.0933403i	$0.970246\pi$
$380$	−15.3934	+	0.232550i	−0.789663	+	0.0119296i
$381$	−4.92590	−	5.47076i	−0.252361	−	0.280276i
$382$	−8.81267	−	19.7936i	−0.450896	−	1.01273i
$383$	−4.27788	+	20.1259i	−0.218590	+	1.02838i	0.722799	+	0.691059i	$0.242855\pi$
$383$	−4.27788	+	20.1259i	−0.218590	+	1.02838i	−0.941388	+	0.337325i	$0.890478\pi$
$384$	−0.104528	+	0.994522i	−0.00533420	+	0.0507515i
$385$	3.83144	+	8.26715i	0.195268	+	0.421333i
$386$	−10.2969	+	2.18867i	−0.524099	+	0.111401i
$387$	−0.0704062	−	0.0969058i	−0.00357895	−	0.00492600i
$388$	−6.38747	−	8.79159i	−0.324274	−	0.446325i
$389$	−3.84475	+	0.817227i	−0.194937	+	0.0414350i	−0.304345	−	0.952562i	$-0.598438\pi$
$389$	−3.84475	+	0.817227i	−0.194937	+	0.0414350i	0.109409	+	0.993997i	$0.465104\pi$
$390$	−4.98175	−	10.7492i	−0.252261	−	0.544307i
$391$	3.81764	−	36.3224i	0.193066	−	1.83690i
$392$	0.167125	−	0.786263i	0.00844111	−	0.0397123i
$393$	3.00292	+	6.74467i	0.151477	+	0.340224i
$394$	10.6747	+	11.8555i	0.537785	+	0.597271i
$395$	23.1203	−	0.349283i	1.16331	−	0.0175743i
$396$	0.976063	−	1.08403i	0.0490490	−	0.0544745i
$397$	27.8355	−	16.0708i	1.39702	−	0.806571i	0.402943	−	0.915225i	$-0.367987\pi$
$397$	27.8355	−	16.0708i	1.39702	−	0.806571i	0.994080	+	0.108654i	$0.0346539\pi$
$398$	−12.8533	−	7.42085i	−0.644277	−	0.371973i
$399$	−5.94339	−	18.2919i	−0.297542	−	0.915739i
$400$	−4.85710	+	1.18682i	−0.242855	+	0.0593410i
$401$	8.89417	+	6.46200i	0.444154	+	0.322697i	0.787283	−	0.616591i	$-0.211487\pi$
$401$	8.89417	+	6.46200i	0.444154	+	0.322697i	−0.343129	+	0.939288i	$0.611487\pi$
$402$		−	8.47042i		−	0.422466i
$403$	28.2139	+	8.61574i	1.40543	+	0.429181i
$404$	17.4773			0.869529
$405$	0.658780	−	2.13682i	0.0327351	−	0.106180i
$406$	21.3558	+	9.50821i	1.05987	+	0.471884i
$407$	−2.15397	+	0.699867i	−0.106768	+	0.0346911i
$408$	−6.38757	−	3.68787i	−0.316232	−	0.182577i
$409$	8.47669	+	14.6821i	0.419145	+	0.725981i	0.995854	−	0.0909693i	$-0.0289965\pi$
$409$	8.47669	+	14.6821i	0.419145	+	0.725981i	−0.576709	+	0.816950i	$0.695663\pi$
$410$	−4.96249	+	11.6150i	−0.245080	+	0.573624i
$411$	1.98186	−	6.09954i	0.0977580	−	0.300868i
$412$	3.26757	−	2.94213i	0.160982	−	0.144948i
$413$	−5.90676	−	13.2668i	−0.290653	−	0.652817i
$414$	−4.84351	−	1.02952i	−0.238045	−	0.0505981i
$415$	−2.19597	−	9.61468i	−0.107796	−	0.471966i
$416$	0.553830	+	5.26934i	0.0271537	+	0.258351i
$417$	−1.82387	−	8.58064i	−0.0893154	−	0.420196i
$418$	−5.90315	−	8.12499i	−0.288733	−	0.397406i
$419$	−23.8695	+	17.3422i	−1.16610	+	0.847221i	−0.990537	−	0.137247i	$-0.956175\pi$
$419$	−23.8695	+	17.3422i	−1.16610	+	0.847221i	−0.175563	+	0.984468i	$0.556175\pi$
$420$	−3.20462	−	5.36186i	−0.156370	−	0.261632i
$421$	−1.58428	−	15.0735i	−0.0772133	−	0.734635i	−0.962810	−	0.270180i	$-0.912917\pi$
$421$	−1.58428	−	15.0735i	−0.0772133	−	0.734635i	0.885597	−	0.464455i	$-0.153750\pi$
$422$	13.1972	+	1.38708i	0.642429	+	0.0675220i
$423$	0.784713	−	3.69178i	0.0381540	−	0.179501i
$424$	−6.96845	+	3.10255i	−0.338418	+	0.150673i
$425$	6.57434	−	36.2879i	0.318902	−	1.76022i
$426$	−0.0282384	+	0.0869090i	−0.00136816	+	0.00421075i
$427$	6.35913	+	5.72578i	0.307740	+	0.277090i
$428$	8.75825	−	5.05658i	0.423346	−	0.244419i
$429$	3.86437	−	6.69329i	0.186574	−	0.323155i
$430$	−0.214285	+	0.160688i	−0.0103337	+	0.00774907i
$431$	−12.1251	−	5.39846i	−0.584048	−	0.260035i	0.0933723	−	0.995631i	$-0.470235\pi$
$431$	−12.1251	−	5.39846i	−0.584048	−	0.260035i	−0.677420	+	0.735596i	$0.736902\pi$
$432$	−0.587785	+	0.809017i	−0.0282798	+	0.0389238i
$433$		−	35.1677i		−	1.69005i	−0.534727	−	0.845025i	$-0.679585\pi$
$433$		−	35.1677i		−	1.69005i	0.534727	−	0.845025i	$-0.320415\pi$
$434$	15.2689	+	2.96279i	0.732933	+	0.142219i
$435$	17.7066	−	6.05043i	0.848969	−	0.290096i
$436$	−1.81650	−	1.31976i	−0.0869943	−	0.0632051i
$437$	−13.8665	+	31.1447i	−0.663325	+	1.48985i
$438$	9.96834	−	3.23891i	0.476306	−	0.154761i
$439$	15.7475	−	27.2754i	0.751585	−	1.30178i	−0.195469	−	0.980710i	$-0.562623\pi$
$439$	15.7475	−	27.2754i	0.751585	−	1.30178i	0.947054	−	0.321074i	$-0.104044\pi$
$440$	−2.45665	−	2.14568i	−0.117116	−	0.102291i
$441$	0.537866	−	0.597361i	0.0256127	−	0.0284458i
$442$	−37.1666	−	12.0762i	−1.76784	−	0.574405i
$443$	−22.8775	+	20.5990i	−1.08694	+	0.978686i	−0.999847	−	0.0175139i	$-0.994425\pi$
$443$	−22.8775	+	20.5990i	−1.08694	+	0.978686i	−0.0870945	+	0.996200i	$0.527758\pi$
$444$	1.41839	−	0.631508i	0.0673139	−	0.0299701i
$445$	0.216586	+	1.79885i	0.0102672	+	0.0852737i
$446$	2.22635	−	21.1823i	0.105421	−	1.00301i
$447$	20.8569	−	2.19215i	0.986496	−	0.103685i
$448$	0.580808	+	2.73249i	0.0274406	+	0.129098i
$449$	−28.9468	+	21.0311i	−1.36608	+	0.992518i	−0.368053	+	0.929805i	$0.619975\pi$
$449$	−28.9468	+	21.0311i	−1.36608	+	0.992518i	−0.998032	+	0.0627137i	$0.980025\pi$
$450$	−4.79979	−	1.40073i	−0.226264	−	0.0660313i
$451$	−8.05961	+	1.71312i	−0.379512	+	0.0806678i
$452$	14.9595	−	1.57230i	0.703634	−	0.0739549i
$453$	1.52465	+	0.160247i	0.0716342	+	0.00752906i
$454$	−26.9578	−	5.73005i	−1.26519	−	0.268925i
$455$	−22.5148	−	24.2581i	−1.05551	−	1.13724i
$456$	4.60690	+	5.11648i	0.215738	+	0.239601i
$457$	34.4117	+	11.1811i	1.60971	+	0.523028i	0.969484	−	0.245156i	$-0.0788392\pi$
$457$	34.4117	+	11.1811i	1.60971	+	0.523028i	0.640230	+	0.768184i	$0.278839\pi$
$458$	8.98280	+	8.08815i	0.419739	+	0.377935i
$459$	−3.68787	−	6.38757i	−0.172135	−	0.298146i
$460$	−2.13821	+	10.8640i	−0.0996947	+	0.506534i
$461$	6.75880	+	20.8014i	0.314789	+	0.968820i	0.975841	+	0.218480i	$0.0701100\pi$
$461$	6.75880	+	20.8014i	0.314789	+	0.968820i	−0.661053	+	0.750340i	$0.729890\pi$
$462$	1.65743	−	3.72264i	0.0771105	−	0.173193i
$463$	10.5552	−	14.5280i	0.490543	−	0.675174i	−0.489945	−	0.871753i	$-0.662983\pi$
$463$	10.5552	−	14.5280i	0.490543	−	0.675174i	0.980488	+	0.196579i	$0.0629833\pi$
$464$	−8.36819			−0.388483
$465$	10.5714	−	6.57610i	0.490238	−	0.304959i
$466$	−25.6214			−1.18689
$467$	11.7599	−	16.1862i	0.544185	−	0.749006i	−0.445024	−	0.895519i	$-0.646805\pi$
$467$	11.7599	−	16.1862i	0.544185	−	0.749006i	0.989209	+	0.146513i	$0.0468049\pi$
$468$	−2.15504	+	4.84030i	−0.0996167	+	0.223743i
$469$	−7.31209	−	22.5043i	−0.337641	−	1.03915i
$470$	−8.28064	−	1.62977i	−0.381958	−	0.0751759i
$471$	3.13904	+	5.43698i	0.144639	+	0.250523i
$472$	3.86328	+	3.47851i	0.177822	+	0.160111i
$473$	−0.166175	−	0.0539935i	−0.00764073	−	0.00248262i
$474$	−6.91940	−	7.68478i	−0.317819	−	0.352974i
$475$	−16.3038	+	30.3189i	−0.748072	+	1.39112i
$476$	−20.1541	−	4.28389i	−0.923762	−	0.196352i
$477$	−7.58613	−	0.797335i	−0.347345	−	0.0365074i
$478$	13.5842	−	1.42776i	0.621326	−	0.0653040i
$479$	34.1685	−	7.26274i	1.56120	−	0.331843i	0.655310	−	0.755360i	$-0.272538\pi$
$479$	34.1685	−	7.26274i	1.56120	−	0.331843i	0.905888	+	0.423517i	$0.139205\pi$
$480$	1.82866	+	1.28685i	0.0834667	+	0.0587365i
$481$	6.65526	−	4.83533i	0.303454	−	0.220472i
$482$	−1.81133	−	8.52162i	−0.0825037	−	0.388149i
$483$	−13.7570	+	1.44592i	−0.625965	+	0.0657916i
$484$	−0.927396	+	8.82358i	−0.0421543	+	0.401072i
$485$	−24.1251	+	2.90473i	−1.09547	+	0.131897i
$486$	−0.913545	+	0.406737i	−0.0414393	+	0.0184499i
$487$	−20.1826	+	18.1725i	−0.914560	+	0.823474i	−0.984735	−	0.174061i	$-0.944311\pi$
$487$	−20.1826	+	18.1725i	−0.914560	+	0.823474i	0.0701746	+	0.997535i	$0.477644\pi$
$488$	−2.91324	−	0.946570i	−0.131876	−	0.0428492i
$489$	−1.50122	+	1.66728i	−0.0678876	+	0.0753968i
$490$	−1.35375	−	1.18239i	−0.0611564	−	0.0534150i
$491$	−3.20890	+	5.55798i	−0.144816	+	0.250828i	−0.929304	−	0.369315i	$-0.879592\pi$
$491$	−3.20890	+	5.55798i	−0.144816	+	0.250828i	0.784488	+	0.620143i	$0.212926\pi$
$492$	5.37216	−	1.74552i	0.242196	−	0.0786941i
$493$	25.1044	−	56.3854i	1.13065	−	2.53947i
$494$	29.5119	+	21.4417i	1.32780	+	0.964706i
$495$	−1.05468	−	3.08654i	−0.0474045	−	0.138730i
$496$	−5.42465	+	1.25425i	−0.243574	+	0.0563175i
$497$			0.255277i			0.0114508i
$498$	−2.59245	+	3.56820i	−0.116170	+	0.159895i
$499$	35.3157	+	15.7236i	1.58095	+	0.703883i	0.994365	−	0.106007i	$-0.0338067\pi$
$499$	35.3157	+	15.7236i	1.58095	+	0.703883i	0.586581	+	0.809890i	$0.300473\pi$
$500$	−2.96966	+	10.7787i	−0.132807	+	0.482040i
$501$	5.66273	−	9.80813i	0.252992	−	0.438195i
$502$	22.8330	−	13.1827i	1.01909	−	0.588371i
$503$	−25.7633	−	23.1973i	−1.14873	−	1.03432i	−0.998960	−	0.0455972i	$-0.985481\pi$
$503$	−25.7633	−	23.1973i	−1.14873	−	1.03432i	−0.149767	−	0.988721i	$-0.547852\pi$
$504$	−0.863249	+	2.65681i	−0.0384522	+	0.118344i
$505$	19.0268	−	34.1360i	0.846680	−	1.51903i
$506$	−6.59862	+	2.93789i	−0.293344	+	0.130605i
$507$	−3.13378	+	14.7433i	−0.139176	+	0.654773i
$508$	7.32131	+	0.769500i	0.324830	+	0.0341411i
$509$	0.385426	+	3.66708i	0.0170837	+	0.162541i	0.999738	−	0.0229086i	$-0.00729267\pi$
$509$	0.385426	+	3.66708i	0.0170837	+	0.162541i	−0.982654	+	0.185449i	$0.940626\pi$
$510$	−14.1568	+	8.46113i	−0.626876	+	0.374665i
$511$	23.6880	−	17.2103i	1.04789	−	0.761340i
$512$	−0.587785	−	0.809017i	−0.0259767	−	0.0357538i
$513$	1.43145	+	6.73445i	0.0632002	+	0.297333i
$514$	1.90048	+	18.0819i	0.0838266	+	0.797557i
$515$	−2.18920	−	9.58505i	−0.0964676	−	0.422368i
$516$	0.117165	+	0.0249041i	0.00515788	+	0.00109634i
$517$	−2.23930	−	5.02955i	−0.0984843	−	0.221199i
$518$	3.22324	−	2.90222i	0.141621	−	0.127516i
$519$	−2.62355	+	8.07447i	−0.115161	+	0.354430i
$520$	10.8948	+	4.65477i	0.477768	+	0.204125i
$521$	10.7034	+	18.5388i	0.468924	+	0.812200i	0.999369	−	0.0355194i	$-0.0113085\pi$
$521$	10.7034	+	18.5388i	0.468924	+	0.812200i	−0.530445	+	0.847719i	$0.677975\pi$
$522$	−7.24707	−	4.18410i	−0.317195	−	0.183133i
$523$	−13.7375	+	4.46359i	−0.600700	+	0.195179i	−0.593552	−	0.804795i	$-0.702275\pi$
$523$	−13.7375	+	4.46359i	−0.600700	+	0.195179i	−0.00714714	+	0.999974i	$0.502275\pi$
$524$	−6.74467	−	3.00292i	−0.294642	−	0.131183i
$525$	−13.9613	+	0.421928i	−0.609321	+	0.0184145i
$526$	−12.4284			−0.541902
$527$	7.82262	−	40.3144i	0.340759	−	1.75612i
$528$			1.45870i			0.0634819i
$529$	1.22928	+	0.893124i	0.0534470	+	0.0388315i
$530$	−1.52646	+	16.9881i	−0.0663050	+	0.737916i
$531$	1.60644	+	4.94412i	0.0697136	+	0.214556i
$532$	16.6565	+	9.61661i	0.722149	+	0.416933i
$533$	25.9188	−	14.9642i	1.12267	−	0.648173i
$534$	0.542184	−	0.602156i	0.0234626	−	0.0260578i
$535$	−0.341591	−	22.6111i	−0.0147682	−	0.977564i
$536$	5.66782	+	6.29475i	0.244812	+	0.271892i
$537$	−4.92134	−	11.0535i	−0.212372	−	0.476994i
$538$	1.74837	−	8.22543i	0.0753776	−	0.354624i
$539$	0.122565	−	1.16612i	0.00527923	−	0.0502285i
$540$	0.940244	+	2.02878i	0.0404616	+	0.0873047i
$541$	12.7913	−	2.71888i	0.549942	−	0.116894i	0.0754436	−	0.997150i	$-0.475963\pi$
$541$	12.7913	−	2.71888i	0.549942	−	0.116894i	0.474499	+	0.880256i	$0.342629\pi$
$542$	8.70094	+	11.9758i	0.373737	+	0.514405i
$543$	−3.29519	−	4.53544i	−0.141410	−	0.194634i
$544$	7.21455	−	1.53350i	0.309321	−	0.0657483i
$545$	−4.55524	+	2.11114i	−0.195125	+	0.0904313i
$546$	−1.54714	+	14.7201i	−0.0662116	+	0.629961i
$547$	0.107520	−	0.505842i	0.00459723	−	0.0216283i	−0.975789	−	0.218713i	$-0.929814\pi$
$547$	0.107520	−	0.505842i	0.00459723	−	0.0216283i	0.980386	+	0.197085i	$0.0631474\pi$
$548$	2.60858	+	5.85897i	0.111433	+	0.250283i
$549$	−2.04966	−	2.27637i	−0.0874772	−	0.0971533i
$550$	−6.86530	+	2.46233i	−0.292737	+	0.104994i
$551$	−38.5514	+	42.8157i	−1.64235	+	1.82401i
$552$	4.28831	−	2.47586i	0.182523	−	0.105379i
$553$	−25.0174	−	14.4438i	−1.06385	−	0.614213i
$554$	7.39753	+	22.7672i	0.314291	+	0.967287i
$555$	0.310702	−	3.45784i	0.0131886	−	0.146777i
$556$	7.09697	+	5.15625i	0.300979	+	0.218674i
$557$		−	19.0119i		−	0.805561i	−0.915297	−	0.402781i	$-0.868044\pi$
$557$		−	19.0119i		−	0.805561i	0.915297	−	0.402781i	$-0.131956\pi$
$558$	−5.32501	−	1.62611i	−0.225426	−	0.0688388i
$559$	0.634649			0.0268428
$560$	5.96928	+	1.84033i	0.252248	+	0.0777679i
$561$	−9.82884	−	4.37608i	−0.414974	−	0.184758i
$562$	4.61331	−	1.49895i	0.194601	−	0.0632296i
$563$	−30.0221	−	17.3333i	−1.26528	−	0.730511i	−0.291190	−	0.956665i	$-0.594051\pi$
$563$	−30.0221	−	17.3333i	−1.26528	−	0.730511i	−0.974091	+	0.226155i	$0.927385\pi$
$564$	1.88713	+	3.26861i	0.0794625	+	0.137633i
$565$	13.2147	−	30.9299i	0.555948	−	1.30123i
$566$	6.41034	−	19.7290i	0.269447	−	0.829272i
$567$	−2.07600	+	1.86924i	−0.0871838	+	0.0785006i
$568$	−0.0371682	−	0.0834812i	−0.00155954	−	0.00350279i
$569$	21.6775	+	4.60769i	0.908768	+	0.193165i	0.638501	−	0.769621i	$-0.279555\pi$
$569$	21.6775	+	4.60769i	0.908768	+	0.193165i	0.270267	+	0.962785i	$0.412888\pi$
$570$	15.0086	−	3.42793i	0.628642	−	0.143580i
$571$	2.45319	+	23.3405i	0.102663	+	0.976770i	0.917677	+	0.397328i	$0.130063\pi$
$571$	2.45319	+	23.3405i	0.102663	+	0.976770i	−0.815014	+	0.579441i	$0.803271\pi$
$572$	1.60690	+	7.55985i	0.0671877	+	0.316093i
$573$	12.7354	+	17.5288i	0.532030	+	0.732276i
$574$	12.7660	−	9.27502i	0.532842	−	0.387132i
$575$	18.8912	+	16.0034i	0.787819	+	0.667386i
$576$	−0.104528	−	0.994522i	−0.00435535	−	0.0414384i
$577$	36.7978	+	3.86760i	1.53191	+	0.161010i	0.832628	−	0.553833i	$-0.186835\pi$
$577$	36.7978	+	3.86760i	1.53191	+	0.161010i	0.699285	+	0.714843i	$0.253502\pi$
$578$	−7.77619	+	36.5841i	−0.323447	+	1.52170i
$579$	9.61684	−	4.28169i	0.399662	−	0.177941i
$580$	−9.11007	+	16.3444i	−0.378275	+	0.678665i
$581$	−3.80740	+	11.7180i	−0.157957	+	0.486143i
$582$	8.07576	+	7.27145i	0.334751	+	0.301411i
$583$	−9.63616	+	5.56344i	−0.399089	+	0.230414i
$584$	−5.24067	+	9.07710i	−0.216860	+	0.375613i
$585$	7.10778	+	9.47855i	0.293870	+	0.391890i
$586$	0.830510	+	0.369767i	0.0343080	+	0.0152749i
$587$	2.62012	−	3.60629i	0.108144	−	0.148847i	−0.751515	−	0.659717i	$-0.770676\pi$
$587$	2.62012	−	3.60629i	0.108144	−	0.148847i	0.859658	+	0.510869i	$0.170676\pi$
$588$			0.803829i			0.0331493i
$589$	−18.5735	+	33.5333i	−0.765307	+	1.38172i
$590$	10.9999	−	3.75870i	0.452857	−	0.154743i
$591$	−12.9064	−	9.37702i	−0.530897	−	0.385719i
$592$	−0.631508	+	1.41839i	−0.0259548	+	0.0582955i
$593$	−26.8644	+	8.72877i	−1.10319	+	0.358448i	−0.803329	−	0.595536i	$-0.796940\pi$
$593$	−26.8644	+	8.72877i	−1.10319	+	0.358448i	−0.299859	+	0.953983i	$0.596940\pi$
$594$	−0.729352	+	1.26327i	−0.0299257	+	0.0518328i
$595$	−30.3080	+	34.7005i	−1.24251	+	1.42258i
$596$	−14.0328	+	15.5851i	−0.574808	+	0.638389i
$597$	14.1153	+	4.58634i	0.577700	+	0.187706i
$598$	19.4971	−	17.5553i	0.797297	−	0.717890i
$599$	−16.9275	+	7.53659i	−0.691637	+	0.307937i	−0.722287	−	0.691594i	$-0.756909\pi$
$599$	−16.9275	+	7.53659i	−0.691637	+	0.307937i	0.0306500	+	0.999530i	$0.490242\pi$
$600$	4.50421	−	2.17073i	0.183884	−	0.0886199i
$601$	1.36688	−	13.0050i	0.0557561	−	0.530484i	−0.930621	−	0.365984i	$-0.880732\pi$
$601$	1.36688	−	13.0050i	0.0557561	−	0.530484i	0.986377	−	0.164500i	$-0.0526009\pi$
$602$	0.332782	−	0.0349768i	0.0135632	−	0.00142555i
$603$	1.76110	+	8.28532i	0.0717175	+	0.337404i
$604$	−1.24026	+	0.901102i	−0.0504655	+	0.0366653i
$605$	16.2242	+	11.4172i	0.659609	+	0.464175i
$606$	−17.0954	+	3.63374i	−0.694453	+	0.147611i
$607$	−15.3178	+	1.60997i	−0.621731	+	0.0653466i	−0.410157	−	0.912015i	$-0.634526\pi$
$607$	−15.3178	+	1.60997i	−0.621731	+	0.0653466i	−0.211575	+	0.977362i	$0.567859\pi$
$608$	−6.84719	−	0.719669i	−0.277690	−	0.0291864i
$609$	−22.8660	−	4.86031i	−0.926576	−	0.196950i
$610$	−5.02032	+	4.65954i	−0.203267	+	0.188659i
$611$	13.3809	+	14.8610i	0.541332	+	0.601211i
$612$	7.01474	+	2.27923i	0.283554	+	0.0921323i
$613$	−9.93396	−	8.94457i	−0.401229	−	0.361268i	0.443674	−	0.896188i	$-0.353675\pi$
$613$	−9.93396	−	8.94457i	−0.401229	−	0.361268i	−0.844902	+	0.534920i	$0.820342\pi$
$614$	0.254016	+	0.439969i	0.0102513	+	0.0177557i
$615$	2.43915	−	12.3930i	0.0983559	−	0.499732i
$616$	1.25923	+	3.87550i	0.0507356	+	0.156148i
$617$	2.52318	−	5.66716i	0.101580	−	0.228151i	−0.855605	−	0.517629i	$-0.826815\pi$
$617$	2.52318	−	5.66716i	0.101580	−	0.228151i	0.957185	+	0.289477i	$0.0934815\pi$
$618$	−2.58446	+	3.55720i	−0.103962	+	0.143092i
$619$	−10.9592			−0.440488			−0.220244	−	0.975445i	$-0.570685\pi$
$619$	−10.9592			−0.440488			−0.220244	+	0.975445i	$0.570685\pi$
$620$	−3.45582	+	11.9607i	−0.138789	+	0.480352i
$621$	4.95171			0.198705
$622$	2.56513	−	3.53060i	0.102852	−	0.141564i
$623$	0.920667	−	2.06785i	0.0368858	−	0.0828468i
$624$	−1.63728	−	5.03904i	−0.0655438	−	0.201723i
$625$	17.8197	+	17.5345i	0.712786	+	0.701382i
$626$	−9.84321	−	17.0489i	−0.393414	−	0.681413i
$627$	7.46343	+	6.72011i	0.298061	+	0.268375i
$628$	−5.97081	−	1.94003i	−0.238261	−	0.0774158i
$629$	−7.66270	−	8.51029i	−0.305532	−	0.339327i
$630$	4.24939	+	4.57841i	0.169300	+	0.182408i
$631$	−30.0867	−	6.39513i	−1.19773	−	0.254586i	−0.434478	−	0.900682i	$-0.643067\pi$
$631$	−30.0867	−	6.39513i	−1.19773	−	0.254586i	−0.763256	+	0.646096i	$0.776400\pi$
$632$	10.2842	+	1.08092i	0.409085	+	0.0429966i
$633$	−13.1972	+	1.38708i	−0.524541	+	0.0551315i
$634$	−12.6877	+	2.69685i	−0.503893	+	0.107106i
$635$	9.47333	−	13.4620i	0.375938	−	0.534222i
$636$	6.17112	−	4.48358i	0.244701	−	0.177785i
$637$	0.885491	+	4.16591i	0.0350844	+	0.165059i
$638$	−12.1398	+	1.27595i	−0.480621	+	0.0505153i
$639$	0.00955197	−	0.0908809i	0.000377870	−	0.00359519i
$640$	−2.22003	+	0.267298i	−0.0877546	+	0.0105659i
$641$	−11.3536	+	5.05495i	−0.448440	+	0.199658i	−0.618515	−	0.785773i	$-0.712266\pi$
$641$	−11.3536	+	5.05495i	−0.448440	+	0.199658i	0.170075	+	0.985431i	$0.445599\pi$
$642$	−7.51554	+	6.76702i	−0.296615	+	0.267073i
$643$	−9.32203	−	3.02891i	−0.367625	−	0.119449i	0.119378	−	0.992849i	$-0.461910\pi$
$643$	−9.32203	−	3.02891i	−0.367625	−	0.119449i	−0.487003	+	0.873400i	$0.661910\pi$
$644$	9.25594	−	10.2798i	0.364735	−	0.405079i
$645$	0.176193	−	0.201729i	0.00693761	−	0.00794308i
$646$	25.3906	−	43.9778i	0.998980	−	1.73028i
$647$	10.6007	−	3.44439i	0.416758	−	0.135413i	−0.0931292	−	0.995654i	$-0.529687\pi$
$647$	10.6007	−	3.44439i	0.416758	−	0.135413i	0.509888	+	0.860241i	$0.329687\pi$
$648$	0.406737	−	0.913545i	0.0159781	−	0.0358875i
$649$	6.13490	+	4.45726i	0.240816	+	0.174963i
$650$	20.9522	−	16.2118i	0.821812	−	0.635880i
$651$	−15.5513	+	0.276543i	−0.609503	+	0.0108386i
$652$		−	2.24354i		−	0.0878639i
$653$	−5.64147	+	7.76481i	−0.220768	+	0.303861i	−0.905007	−	0.425397i	$-0.860134\pi$
$653$	−5.64147	+	7.76481i	−0.220768	+	0.303861i	0.684239	+	0.729258i	$0.260134\pi$
$654$	2.05119	+	0.913251i	0.0802080	+	0.0357109i
$655$	−13.2078	+	9.90427i	−0.516071	+	0.386992i
$656$	−2.82431	+	4.89185i	−0.110271	+	0.190995i
$657$	−9.07710	+	5.24067i	−0.354131	+	0.204458i
$658$	7.83537	+	7.05499i	0.305454	+	0.275032i
$659$	5.25150	−	16.1625i	0.204569	−	0.629600i	−0.795161	−	0.606398i	$-0.792614\pi$
$659$	5.25150	−	16.1625i	0.204569	−	0.629600i	0.999731	−	0.0232021i	$-0.00738612\pi$
$660$	2.84908	+	1.58803i	0.110900	+	0.0618138i
$661$	20.3353	−	9.05387i	0.790952	−	0.352155i	0.0288272	−	0.999584i	$-0.490823\pi$
$661$	20.3353	−	9.05387i	0.790952	−	0.352155i	0.762125	+	0.647430i	$0.224156\pi$
$662$	5.87622	−	27.6454i	0.228386	−	1.07447i
$663$	38.8652	+	4.08490i	1.50940	+	0.158644i
$664$	−0.461027	−	4.38638i	−0.0178913	−	0.170224i
$665$	36.9159	−	22.0635i	1.43154	−	0.855587i
$666$	−1.25610	+	0.912608i	−0.0486728	+	0.0353629i
$667$	24.3560	+	33.5231i	0.943068	+	1.29802i
$668$	2.35469	+	11.0780i	0.0911059	+	0.428619i
$669$	2.22635	+	21.1823i	0.0860757	+	0.818956i
$670$	18.4649	−	4.21734i	0.713363	−	0.162930i
$671$	−4.37061	−	0.929001i	−0.168725	−	0.0358637i
$672$	−1.13623	−	2.55202i	−0.0438311	−	0.0984463i
$673$	29.0282	−	26.1371i	1.11895	−	1.00751i	0.119061	−	0.992887i	$-0.462012\pi$
$673$	29.0282	−	26.1371i	1.11895	−	1.00751i	0.999893	−	0.0146233i	$-0.00465492\pi$
$674$	−9.18362	+	28.2643i	−0.353740	+	1.08870i
$675$	4.98613	+	0.372194i	0.191916	+	0.0143257i
$676$	−7.53634	−	13.0533i	−0.289859	−	0.502051i
$677$	−20.7716	−	11.9925i	−0.798317	−	0.460909i	0.0445652	−	0.999006i	$-0.485810\pi$
$677$	−20.7716	−	11.9925i	−0.798317	−	0.460909i	−0.842882	+	0.538098i	$0.819143\pi$
$678$	−14.3057	+	4.64819i	−0.549406	+	0.178513i
$679$	27.7328	+	12.3474i	1.06429	+	0.473851i
$680$	4.85899	−	15.7606i	0.186334	−	0.604392i
$681$	27.5600			1.05610
$682$	−7.67837	+	2.64669i	−0.294020	+	0.101347i
$683$			29.3481i			1.12297i	0.827485	+	0.561487i	$0.189771\pi$
$683$			29.3481i			1.12297i	−0.827485	+	0.561487i	$0.810229\pi$
$684$	−5.57001	−	4.04685i	−0.212974	−	0.154735i
$685$	14.2833	+	1.28342i	0.545738	+	0.0490370i
$686$	−5.34884	−	16.4620i	−0.204220	−	0.628524i
$687$	−10.4681	−	6.04378i	−0.399384	−	0.230584i
$688$	−0.103734	+	0.0598911i	−0.00395483	+	0.00228333i
$689$	27.0432	−	30.0346i	1.03027	−	1.14423i
$690$	−0.167253	−	11.0711i	−0.00636723	−	0.421470i
$691$	−19.9694	−	22.1783i	−0.759672	−	0.843701i	0.231970	−	0.972723i	$-0.425483\pi$
$691$	−19.9694	−	22.1783i	−0.759672	−	0.843701i	−0.991642	+	0.129022i	$0.958816\pi$
$692$	−3.45319	−	7.75600i	−0.131271	−	0.294839i
$693$	−0.847227	+	3.98589i	−0.0321835	+	0.151411i
$694$	0.109853	−	1.04518i	0.00416996	−	0.0396745i
$695$	17.7971	−	8.24814i	0.675084	−	0.312870i
$696$	8.18533	−	1.73984i	0.310264	−	0.0659486i
$697$	−24.4887	−	33.7059i	−0.927577	−	1.27670i
$698$	−8.30530	−	11.4313i	−0.314360	−	0.432680i
$699$	25.0615	−	5.32698i	0.947912	−	0.201485i
$700$	10.0929	−	9.65548i	0.381477	−	0.364943i
$701$	−2.93450	+	27.9199i	−0.110834	+	1.05452i	0.787833	+	0.615889i	$0.211203\pi$
$701$	−2.93450	+	27.9199i	−0.110834	+	1.05452i	−0.898668	+	0.438630i	$0.855464\pi$
$702$	1.10159	−	5.18258i	0.0415769	−	0.195604i
$703$	4.34788	+	9.76549i	0.163983	+	0.368312i
$704$	−0.976063	−	1.08403i	−0.0367868	−	0.0408559i
$705$	8.43854	−	0.127483i	0.317814	−	0.00480127i
$706$	−8.66791	+	9.62669i	−0.326221	+	0.362305i
$707$	−42.2824	+	24.4117i	−1.59019	+	0.918098i
$708$	−4.50208	−	2.59928i	−0.169198	−	0.0976868i
$709$	−4.16872	−	12.8300i	−0.156559	−	0.481840i	0.841756	−	0.539858i	$-0.181522\pi$
$709$	−4.16872	−	12.8300i	−0.156559	−	0.481840i	−0.998316	+	0.0580175i	$0.981522\pi$
$710$	−0.203515	−	0.0182867i	−0.00763779	−	0.000686289i
$711$	8.36595	+	6.07822i	0.313748	+	0.227951i
$712$			0.810281i			0.0303666i
$713$	20.8132	+	18.0807i	0.779462	+	0.677128i
$714$	20.6044			0.771099
$715$	16.5150	+	5.09155i	0.617624	+	0.190413i
$716$	11.0535	+	4.92134i	0.413089	+	0.183919i
$717$	−12.9905	+	4.22087i	−0.485139	+	0.157631i
$718$	−25.6191	−	14.7912i	−0.956098	−	0.552003i
$719$	−18.4224	−	31.9086i	−0.687041	−	1.18999i	−0.972791	−	0.231686i	$-0.925576\pi$
$719$	−18.4224	−	31.9086i	−0.687041	−	1.18999i	0.285750	−	0.958304i	$-0.407757\pi$
$720$	−2.05625	−	0.878530i	−0.0766321	−	0.0327409i
$721$	−3.79566	+	11.6818i	−0.141358	+	0.435055i
$722$	−21.1067	+	19.0046i	−0.785512	+	0.707278i
$723$	3.54349	+	7.95881i	0.131784	+	0.295991i
$724$	5.48360	+	1.16558i	0.203797	+	0.0433183i
$725$	22.0055	+	35.5868i	0.817264	+	1.32166i
$726$	−0.927396	−	8.82358i	−0.0344189	−	0.327474i
$727$	8.57096	+	40.3232i	0.317879	+	1.49550i	0.789526	+	0.613717i	$0.210326\pi$
$727$	8.57096	+	40.3232i	0.317879	+	1.49550i	−0.471647	+	0.881787i	$0.656340\pi$
$728$	−8.69990	−	11.9744i	−0.322440	−	0.443800i
$729$	0.809017	−	0.587785i	0.0299636	−	0.0217698i
$730$	12.0237	+	20.1177i	0.445019	+	0.744589i
$731$	−0.0923489	−	0.878641i	−0.00341565	−	0.0324977i
$732$	3.04638	+	0.320188i	0.112598	+	0.0118345i
$733$	−1.54761	+	7.28094i	−0.0571624	+	0.268928i	−0.997442	−	0.0714739i	$-0.977230\pi$
$733$	−1.54761	+	7.28094i	−0.0571624	+	0.268928i	0.940280	+	0.340402i	$0.110563\pi$
$734$	−24.0513	+	10.7083i	−0.887750	+	0.395252i
$735$	1.57001	+	0.875092i	0.0579105	+	0.0322782i
$736$	−1.53016	+	4.70936i	−0.0564026	+	0.173589i
$737$	9.18218	+	8.26767i	0.338230	+	0.304544i
$738$	−4.89185	+	2.82431i	−0.180071	+	0.103964i
$739$	4.14758	−	7.18381i	0.152571	−	0.264261i	−0.779601	−	0.626277i	$-0.784578\pi$
$739$	4.14758	−	7.18381i	0.152571	−	0.264261i	0.932172	+	0.362016i	$0.117911\pi$
$740$	2.08285	+	2.77757i	0.0765670	+	0.102106i
$741$	−33.3250	−	14.8372i	−1.22422	−	0.545060i
$742$	12.5250	−	17.2392i	0.459808	−	0.632872i
$743$			12.6443i			0.463873i	0.972731	+	0.231936i	$0.0745061\pi$
$743$			12.6443i			0.463873i	−0.972731	+	0.231936i	$0.925494\pi$
$744$	5.04534	−	2.35469i	0.184971	−	0.0863272i
$745$	15.1632	+	44.3751i	0.555536	+	1.62578i
$746$	18.8219	+	13.6749i	0.689120	+	0.500675i
$747$	1.79393	−	4.02923i	0.0656364	−	0.147422i
$748$	10.2324	−	3.32472i	0.374135	−	0.121564i
$749$	−14.1257	+	24.4665i	−0.516142	+	0.893985i
$750$	0.663740	−	11.1606i	0.0242364	−	0.407528i
$751$	−1.80363	+	2.00314i	−0.0658155	+	0.0730955i	−0.775153	−	0.631773i	$-0.782327\pi$
$751$	−1.80363	+	2.00314i	−0.0658155	+	0.0730955i	0.709338	+	0.704869i	$0.248994\pi$
$752$	−3.58954	−	1.16631i	−0.130897	−	0.0425310i
$753$	−19.5932	+	17.6418i	−0.714017	+	0.642904i
$754$	40.5045	−	18.0338i	1.47509	−	0.656751i
$755$	0.409780	+	3.40342i	0.0149134	+	0.123863i
$756$	0.292004	−	2.77823i	0.0106201	−	0.101043i
$757$	−41.3381	+	4.34481i	−1.50246	+	0.157915i	−0.819727	−	0.572754i	$-0.805875\pi$
$757$	−41.3381	+	4.34481i	−1.50246	+	0.157915i	−0.682732	+	0.730669i	$0.739208\pi$
$758$	5.95464	+	28.0144i	0.216282	+	1.01753i
$759$	5.84360	−	4.24562i	0.212109	−	0.154106i
$760$	−8.85985	+	12.5902i	−0.321381	+	0.456694i
$761$	39.7624	−	8.45175i	1.44139	−	0.306376i	0.580120	−	0.814531i	$-0.303006\pi$
$761$	39.7624	−	8.45175i	1.44139	−	0.306376i	0.861265	+	0.508155i	$0.169672\pi$
$762$	−7.32131	+	0.769500i	−0.265223	+	0.0278761i
$763$	6.23799	+	0.655639i	0.225830	+	0.0237357i
$764$	−21.1933	−	4.50478i	−0.766747	−	0.162977i
$765$	12.0883	−	11.2196i	0.437054	−	0.405646i
$766$	13.7677	+	15.2906i	0.497447	+	0.552470i
$767$	−26.1957	−	8.51151i	−0.945873	−	0.307333i
$768$	0.743145	+	0.669131i	0.0268159	+	0.0241452i
$769$	−9.32253	−	16.1471i	−0.336179	−	0.582279i	0.647532	−	0.762039i	$-0.275801\pi$
$769$	−9.32253	−	16.1471i	−0.336179	−	0.582279i	−0.983711	+	0.179760i	$0.942468\pi$
$770$	8.94032	+	1.75961i	0.322187	+	0.0634120i
$771$	−5.61838	−	17.2916i	−0.202341	−	0.622742i
$772$	−4.28169	+	9.61684i	−0.154102	+	0.346118i
$773$	−20.9132	+	28.7845i	−0.752194	+	1.03531i	0.245630	+	0.969364i	$0.421005\pi$
$773$	−20.9132	+	28.7845i	−0.752194	+	1.03531i	−0.997823	+	0.0659422i	$0.978995\pi$
$774$	−0.119782			−0.00430548
$775$	19.5989	+	19.7708i	0.704012	+	0.710188i
$776$	−10.8670			−0.390103
$777$	−2.54940	+	3.50895i	−0.0914593	+	0.125883i
$778$	−1.59874	+	3.59082i	−0.0573175	+	0.128737i
$779$	12.0177	+	36.9868i	0.430580	+	1.32519i
$780$	−11.6245	−	2.28790i	−0.416224	−	0.0819200i
$781$	−0.0666493	−	0.115440i	−0.00238490	−	0.00413077i
$782$	−27.1415	−	24.4383i	−0.970579	−	0.873913i
$783$	7.95862	+	2.58591i	0.284418	+	0.0924130i
$784$	−0.537866	−	0.597361i	−0.0192095	−	0.0213343i
$785$	−10.2893	+	9.54991i	−0.367242	+	0.340851i
$786$	7.22163	+	1.53500i	0.257587	+	0.0547518i
$787$	−5.75865	−	0.605258i	−0.205274	−	0.0215751i	0.00133356	−	0.999999i	$-0.499576\pi$
$787$	−5.75865	−	0.605258i	−0.205274	−	0.0215751i	−0.206607	+	0.978424i	$0.566242\pi$
$788$	15.8657	−	1.66756i	0.565194	−	0.0594042i
$789$	12.1568	−	2.58400i	0.432792	−	0.0919928i
$790$	13.3072	−	18.9100i	0.473449	−	0.672788i
$791$	−33.9948	+	24.6987i	−1.20872	+	0.878185i
$792$	−0.303282	−	1.42683i	−0.0107766	−	0.0507001i
$793$	16.1408	−	1.69647i	0.573178	−	0.0602435i
$794$	3.35972	−	31.9656i	0.119232	−	1.13442i
$795$	−2.03893	−	16.9342i	−0.0723133	−	0.600596i
$796$	−13.5586	+	6.03666i	−0.480571	+	0.213964i
$797$	−38.8965	+	35.0225i	−1.37778	+	1.24056i	−0.437919	+	0.899014i	$0.644284\pi$
$797$	−38.8965	+	35.0225i	−1.37778	+	1.24056i	−0.939865	+	0.341547i	$0.889049\pi$
$798$	−18.2919	−	5.94339i	−0.647525	−	0.210394i
$799$	18.6272	−	20.6876i	0.658983	−	0.731875i
$800$	−1.89478	+	4.62708i	−0.0669904	+	0.163592i
$801$	−0.405140	+	0.701724i	−0.0143149	+	0.0247942i
$802$	10.4557	−	3.39727i	0.369205	−	0.119962i
$803$	−6.21866	+	13.9673i	−0.219452	+	0.492897i
$804$	−6.85272	−	4.97879i	−0.241677	−	0.175588i
$805$	−10.0015	−	29.2694i	−0.352506	−	1.03161i
$806$	23.5540	−	17.7613i	0.829653	−	0.625615i
$807$			8.40919i			0.296018i
$808$	10.2729	−	14.1394i	0.361400	−	0.497424i
$809$	2.57887	+	1.14819i	0.0906682	+	0.0403681i	0.451570	−	0.892236i	$-0.350864\pi$
$809$	2.57887	+	1.14819i	0.0906682	+	0.0403681i	−0.360901	+	0.932604i	$0.617531\pi$
$810$	−1.34150	−	1.78896i	−0.0471356	−	0.0628575i
$811$	−26.1362	+	45.2692i	−0.917766	+	1.58962i	−0.114966	+	0.993369i	$0.536676\pi$
$811$	−26.1362	+	45.2692i	−0.917766	+	1.58962i	−0.802800	+	0.596248i	$0.796657\pi$
$812$	20.2449	−	11.6884i	0.710457	−	0.410183i
$813$	−11.0007	−	9.90509i	−0.385812	−	0.347387i
$814$	−0.699867	+	2.15397i	−0.0245303	+	0.0754965i
$815$	−4.38199	−	2.44244i	−0.153495	−	0.0855550i
$816$	−6.73807	+	2.99998i	−0.235879	+	0.105020i
$817$	−0.171462	+	0.806667i	−0.00599871	+	0.0282217i
$818$	16.8605	+	1.77211i	0.589514	+	0.0619604i
$819$	−1.54714	−	14.7201i	−0.0540615	−	0.514361i
$820$	6.47986	+	10.8419i	0.226287	+	0.378614i
$821$	−22.1074	+	16.0620i	−0.771555	+	0.560568i	−0.902433	−	0.430831i	$-0.858221\pi$
$821$	−22.1074	+	16.0620i	−0.771555	+	0.560568i	0.130878	+	0.991399i	$0.458221\pi$
$822$	−3.76972	−	5.18858i	−0.131484	−	0.180972i
$823$	−2.57753	−	12.1263i	−0.0898470	−	0.422697i	−0.999965	−	0.00834799i	$-0.997343\pi$
$823$	−2.57753	−	12.1263i	−0.0898470	−	0.422697i	0.910118	−	0.414349i	$-0.135991\pi$
$824$	−0.459606	−	4.37286i	−0.0160111	−	0.152336i
$825$	6.20333	−	3.83590i	0.215972	−	0.133549i
$826$	−14.2050	−	3.01936i	−0.494255	−	0.105057i
$827$	−13.4737	−	30.2623i	−0.468525	−	1.05232i	−0.981068	−	0.193663i	$-0.937963\pi$
$827$	−13.4737	−	30.2623i	−0.468525	−	1.05232i	0.512543	−	0.858661i	$-0.328703\pi$
$828$	−3.67984	+	3.31334i	−0.127883	+	0.115147i
$829$	−14.7469	+	45.3863i	−0.512181	+	1.57633i	0.276172	+	0.961108i	$0.410934\pi$
$829$	−14.7469	+	45.3863i	−0.512181	+	1.57633i	−0.788353	+	0.615223i	$0.789066\pi$
$830$	−9.06919	−	3.87479i	−0.314796	−	0.134496i
$831$	−11.9694	−	20.7317i	−0.415216	−	0.719174i
$832$	4.58852	+	2.64918i	0.159078	+	0.0918439i
$833$	5.63865	−	1.83211i	0.195368	−	0.0634788i
$834$	−8.01393	−	3.56803i	−0.277500	−	0.123551i
$835$	24.2005	+	7.46099i	0.837492	+	0.258198i
$836$	−10.0430			−0.347346
$837$	5.54674	+	0.483446i	0.191723	+	0.0167103i
$838$			29.5043i			1.01921i
$839$	−29.2312	−	21.2377i	−1.00917	−	0.733206i	−0.0451367	−	0.998981i	$-0.514372\pi$
$839$	−29.2312	−	21.2377i	−1.00917	−	0.733206i	−0.964035	+	0.265774i	$0.914372\pi$
$840$	−6.22147	−	0.559026i	−0.214661	−	0.0192882i
$841$	12.6779	+	39.0186i	0.437170	+	1.34547i
$842$	−13.1259	−	7.57824i	−0.452348	−	0.261163i
$843$	−4.20085	+	2.42536i	−0.144685	+	0.0835338i
$844$	8.87928	−	9.86144i	0.305637	−	0.339445i
$845$	−33.6997	+	0.509107i	−1.15930	+	0.0175138i
$846$	−2.52547	−	2.80482i	−0.0868276	−	0.0964318i
$847$	−10.0809	−	22.6420i	−0.346382	−	0.777988i
$848$	−1.58593	+	7.46123i	−0.0544612	+	0.256220i
$849$	−2.16837	+	20.6307i	−0.0744183	+	0.708043i
$850$	−25.4933	−	26.6483i	−0.874411	−	0.914028i
$851$	7.52014	−	1.59845i	0.257787	−	0.0547943i
$852$	0.0537127	+	0.0739292i	0.00184017	+	0.00253277i
$853$	2.86281	+	3.94032i	0.0980208	+	0.134914i	0.855210	−	0.518281i	$-0.173428\pi$
$853$	2.86281	+	3.94032i	0.0980208	+	0.134914i	−0.757189	+	0.653195i	$0.773428\pi$
$854$	8.37006	−	1.77911i	0.286417	−	0.0608799i
$855$	−13.9679	+	6.47349i	−0.477694	+	0.221389i
$856$	1.05711	−	10.0578i	0.0361314	−	0.343767i
$857$	−7.14910	+	33.6339i	−0.244209	+	1.14891i	0.669586	+	0.742735i	$0.266472\pi$
$857$	−7.14910	+	33.6339i	−0.244209	+	1.14891i	−0.913794	+	0.406177i	$0.866862\pi$
$858$	−3.14356	−	7.06056i	−0.107320	−	0.241044i
$859$	−13.7420	−	15.2620i	−0.468870	−	0.520733i	0.461606	−	0.887085i	$-0.347273\pi$
$859$	−13.7420	−	15.2620i	−0.468870	−	0.520733i	−0.930476	+	0.366352i	$0.880607\pi$
$860$	0.00404586	+	0.267810i	0.000137963	+	0.00913226i
$861$	−10.5586	+	11.7265i	−0.359837	+	0.399639i
$862$	−11.4944	+	6.63631i	−0.391502	+	0.226034i
$863$	24.2149	+	13.9805i	0.824284	+	0.475900i	0.851891	−	0.523718i	$-0.175456\pi$
$863$	24.2149	+	13.9805i	0.824284	+	0.475900i	−0.0276077	+	0.999619i	$0.508789\pi$
$864$	0.309017	+	0.951057i	0.0105130	+	0.0323556i
$865$	−18.9080	−	1.69897i	−0.642892	−	0.0577667i
$866$	−28.4512	−	20.6710i	−0.966812	−	0.702430i
$867$		−	37.4014i		−	1.27022i
$868$	11.3718	−	10.6113i	0.385984	−	0.360173i
$869$	15.0843			0.511700
$870$	5.51280	−	17.8813i	0.186901	−	0.606234i
$871$	−40.9994	−	18.2541i	−1.38921	−	0.618516i
$872$	−2.13542	+	0.693839i	−0.0723144	+	0.0234964i
$873$	−9.41110	−	5.43350i	−0.318518	−	0.183896i
$874$	17.0460	+	29.5246i	0.576591	+	0.998685i
$875$	−7.87097	−	30.2246i	−0.266087	−	1.02178i
$876$	3.23891	−	9.96834i	0.109433	−	0.336799i
$877$	20.7251	−	18.6610i	0.699837	−	0.630136i	−0.240393	−	0.970676i	$-0.577276\pi$
$877$	20.7251	−	18.6610i	0.699837	−	0.630136i	0.940230	+	0.340539i	$0.110610\pi$
$878$	−12.8101	−	28.7720i	−0.432321	−	0.971009i
$879$	−0.889240	−	0.189014i	−0.0299933	−	0.00637528i
$880$	−3.17988	+	0.726275i	−0.107194	+	0.0244827i
$881$	−1.14624	−	10.9058i	−0.0386178	−	0.367424i	−0.996716	−	0.0809826i	$-0.974194\pi$
$881$	−1.14624	−	10.9058i	−0.0386178	−	0.367424i	0.958098	−	0.286442i	$-0.0924725\pi$
$882$	−0.167125	−	0.786263i	−0.00562740	−	0.0264749i
$883$	−9.02143	−	12.4169i	−0.303595	−	0.417863i	0.629775	−	0.776777i	$-0.283147\pi$
$883$	−9.02143	−	12.4169i	−0.303595	−	0.417863i	−0.933370	+	0.358914i	$0.883147\pi$
$884$	−31.6158	+	22.9702i	−1.06336	+	0.772573i
$885$	−9.97801	+	5.96356i	−0.335407	+	0.200463i
$886$	3.21787	+	30.6160i	0.108107	+	1.02857i
$887$	27.6972	+	2.91109i	0.929982	+	0.0977450i	0.557390	−	0.830251i	$-0.311803\pi$
$887$	27.6972	+	2.91109i	0.929982	+	0.0977450i	0.372591	+	0.927996i	$0.378469\pi$
$888$	0.322808	−	1.51869i	0.0108327	−	0.0509640i
$889$	−18.7870	+	8.36453i	−0.630097	+	0.280537i
$890$	1.58261	+	0.882116i	0.0530491	+	0.0295686i
$891$	0.450764	−	1.38731i	0.0151012	−	0.0464766i
$892$	−15.8282	−	14.2518i	−0.529969	−	0.477186i
$893$	−22.5040	+	12.9927i	−0.753069	+	0.434785i
$894$	10.4859	−	18.1621i	0.350700	−	0.607431i
$895$	21.6456	−	16.2316i	0.723533	−	0.542563i
$896$	2.55202	+	1.13623i	0.0852570	+	0.0379589i
$897$	−15.4211	+	21.2254i	−0.514896	+	0.708694i
$898$			35.7802i			1.19400i
$899$	24.0098	+	39.9294i	0.800771	+	1.33172i
$900$	−3.95446	+	3.05978i	−0.131815	+	0.101993i
$901$	−45.5165	−	33.0697i	−1.51637	−	1.10171i
$902$	−3.35137	+	7.52731i	−0.111589	+	0.250632i
$903$	−0.318238	+	0.103402i	−0.0105903	+	0.00344100i
$904$	7.52093	−	13.0266i	0.250142	−	0.433259i
$905$	8.24631	−	9.44144i	0.274116	−	0.313844i
$906$	1.02581	−	1.13928i	0.0340802	−	0.0378499i
$907$	−45.6393	−	14.8291i	−1.51543	−	0.492393i	−0.570956	−	0.820981i	$-0.693427\pi$
$907$	−45.6393	−	14.8291i	−1.51543	−	0.492393i	−0.944473	+	0.328588i	$0.893427\pi$
$908$	−20.4811	+	18.4413i	−0.679689	+	0.611995i
$909$	15.9663	−	7.10866i	0.529569	−	0.235779i
$910$	−32.8591	+	3.95632i	−1.08927	+	0.131151i
$911$	−4.19962	+	39.9567i	−0.139140	+	1.32383i	0.672687	+	0.739927i	$0.265140\pi$
$911$	−4.19962	+	39.9567i	−0.139140	+	1.32383i	−0.811827	+	0.583898i	$0.801527\pi$
$912$	6.84719	−	0.719669i	0.226733	−	0.0238306i
$913$	−1.33764	−	6.29308i	−0.0442693	−	0.208271i
$914$	29.2724	−	21.2676i	0.968244	−	0.703470i
$915$	3.94184	−	5.60150i	0.130313	−	0.185180i
$916$	11.8234	−	2.51314i	0.390657	−	0.0830366i
$917$	20.5116	−	2.15585i	0.677352	−	0.0711925i
$918$	−7.33533	−	0.770974i	−0.242102	−	0.0254459i
$919$	−29.8258	−	6.33967i	−0.983862	−	0.209126i	−0.312226	−	0.950008i	$-0.601075\pi$
$919$	−29.8258	−	6.33967i	−0.983862	−	0.209126i	−0.671636	+	0.740881i	$0.734408\pi$
$920$	7.53231	+	8.11552i	0.248333	+	0.267561i
$921$	−0.339940	−	0.377541i	−0.0112014	−	0.0124404i
$922$	20.8014	+	6.75880i	0.685059	+	0.222589i
$923$	0.359810	+	0.323975i	0.0118433	+	0.0106638i
$924$	−2.03747	−	3.52900i	−0.0670278	−	0.116096i
$925$	7.69255	−	1.04432i	0.252929	−	0.0343369i
$926$	−5.54921	−	17.0787i	−0.182358	−	0.561241i
$927$	1.78840	−	4.01681i	0.0587387	−	0.131929i
$928$	−4.91870	+	6.77001i	−0.161464	+	0.222236i
$929$	−31.1654			−1.02250			−0.511251	−	0.859431i	$-0.670818\pi$
$929$	−31.1654			−1.02250			−0.511251	+	0.859431i	$0.670818\pi$
$930$	0.893544	−	12.4178i	0.0293005	−	0.407195i
$931$	−5.53428			−0.181379
$932$	−15.0599	+	20.7281i	−0.493302	+	0.678972i
$933$	−1.77502	+	3.98677i	−0.0581116	+	0.130521i
$934$	−6.18256	−	19.0280i	−0.202300	−	0.622614i
$935$	4.64588	−	23.6050i	0.151936	−	0.771967i
$936$	2.64918	+	4.58852i	0.0865912	+	0.149980i
$937$	−42.5242	−	38.2890i	−1.38921	−	1.25085i	−0.932471	−	0.361244i	$-0.882352\pi$
$937$	−42.5242	−	38.2890i	−1.38921	−	1.25085i	−0.456735	−	0.889603i	$-0.650981\pi$
$938$	−22.5043	−	7.31209i	−0.734791	−	0.238748i
$939$	13.1728	+	14.6299i	0.429878	+	0.477428i
$940$	−6.18576	+	5.74122i	−0.201757	+	0.187258i
$941$	−41.9290	−	8.91228i	−1.36685	−	0.290532i	−0.534678	−	0.845056i	$-0.679567\pi$
$941$	−41.9290	−	8.91228i	−1.36685	−	0.290532i	−0.832168	+	0.554524i	$0.812900\pi$
$942$	6.24369	+	0.656238i	0.203430	+	0.0213814i
$943$	27.8171	−	2.92370i	0.905851	−	0.0952087i
$944$	5.08495	−	1.08084i	0.165501	−	0.0351783i
$945$	−5.10843	−	3.59486i	−0.166177	−	0.116941i
$946$	−0.141357	+	0.102702i	−0.00459591	+	0.00333912i
$947$	2.38110	+	11.2022i	0.0773754	+	0.364023i	0.999752	−	0.0222692i	$-0.00708910\pi$
$947$	2.38110	+	11.2022i	0.0773754	+	0.364023i	−0.922377	+	0.386292i	$0.873756\pi$
$948$	−10.2842	+	1.08092i	−0.334017	+	0.0351066i
$949$	5.80488	−	55.2297i	0.188434	−	1.79283i
$950$	14.9453	+	31.0111i	0.484890	+	1.00613i
$951$	11.8497	−	5.27584i	0.384254	−	0.171081i
$952$	−15.3120	+	13.7870i	−0.496265	+	0.446839i
$953$	−11.2600	−	3.65861i	−0.364748	−	0.118514i	0.120908	−	0.992664i	$-0.461419\pi$
$953$	−11.2600	−	3.65861i	−0.364748	−	0.118514i	−0.485656	+	0.874150i	$0.661419\pi$
$954$	−5.10407	+	5.66865i	−0.165251	+	0.183529i
$955$	−31.8707	+	36.4898i	−1.03131	+	1.18078i
$956$	6.82951	−	11.8290i	0.220882	−	0.382579i
$957$	11.6093	−	3.77208i	0.375275	−	0.121934i
$958$	14.2081	−	31.9118i	0.459041	−	1.03102i
$959$	−14.4945	−	10.5308i	−0.468051	−	0.340059i
$960$	2.11595	−	0.723028i	0.0682919	−	0.0233356i
$961$	21.5490	+	22.2854i	0.695129	+	0.718885i
$962$		−	8.22636i		−	0.265228i
$963$	5.94436	−	8.18171i	0.191554	−	0.263652i
$964$	−7.95881	−	3.54349i	−0.256336	−	0.114128i
$965$	14.1219	+	18.8323i	0.454601	+	0.606232i
$966$	−6.91639	+	11.9795i	−0.222531	+	0.385435i
$967$	33.0577	−	19.0859i	1.06306	−	0.613760i	0.136785	−	0.990601i	$-0.456323\pi$
$967$	33.0577	−	19.0859i	1.06306	−	0.613760i	0.926278	+	0.376841i	$0.122990\pi$
$968$	6.59332	+	5.93665i	0.211917	+	0.190811i
$969$	−15.6923	+	48.2958i	−0.504108	+	1.55148i
$970$	−11.8304	+	21.2250i	−0.379852	+	0.681493i
$971$	33.5747	−	14.9484i	1.07746	−	0.479718i	0.210247	−	0.977648i	$-0.432573\pi$
$971$	33.5747	−	14.9484i	1.07746	−	0.479718i	0.867217	+	0.497931i	$0.165907\pi$
$972$	−0.207912	+	0.978148i	−0.00666877	+	0.0313741i
$973$	−24.3716	−	2.56156i	−0.781317	−	0.0821197i
$974$	2.83882	+	27.0096i	0.0909617	+	0.865443i
$975$	−17.1237	+	20.2138i	−0.548397	+	0.647358i
$976$	−2.47815	+	1.80048i	−0.0793237	+	0.0576320i
$977$	21.1935	+	29.1704i	0.678041	+	0.933243i	0.999908	−	0.0135418i	$-0.00431063\pi$
$977$	21.1935	+	29.1704i	0.678041	+	0.933243i	−0.321868	+	0.946785i	$0.604311\pi$
$978$	0.466458	+	2.19451i	0.0149157	+	0.0701728i
$979$	0.123548	+	1.17549i	0.00394863	+	0.0375687i
$980$	−1.75229	+	0.400219i	−0.0559749	+	0.0127845i
$981$	−2.19625	−	0.466827i	−0.0701207	−	0.0149046i
$982$	2.61036	+	5.86295i	0.0832998	+	0.187094i
$983$	12.0398	−	10.8407i	0.384011	−	0.345765i	−0.454406	−	0.890795i	$-0.650148\pi$
$983$	12.0398	−	10.8407i	0.384011	−	0.345765i	0.838417	+	0.545030i	$0.183482\pi$
$984$	1.74552	−	5.37216i	0.0556452	−	0.171258i
$985$	14.0153	−	32.8037i	0.446565	−	1.04521i
$986$	−30.8608	−	53.4524i	−0.982807	−	1.70227i
$987$	−9.13096	−	5.27176i	−0.290642	−	0.167802i
$988$	34.6933	−	11.2726i	1.10374	−	0.358628i
$989$	0.541848	+	0.241246i	0.0172298	+	0.00767119i
$990$	−3.11699	−	0.960966i	−0.0990645	−	0.0305415i
$991$	−33.7825			−1.07314			−0.536568	−	0.843857i	$-0.680280\pi$
$991$	−33.7825			−1.07314			−0.536568	+	0.843857i	$0.680280\pi$
$992$	−2.17382	+	5.12587i	−0.0690189	+	0.162746i
$993$			28.2630i			0.896901i
$994$	0.206524	+	0.150048i	0.00655053	+	0.00475924i
$995$	−2.97003	+	33.0539i	−0.0941564	+	1.04788i
$996$	1.36293	+	4.19467i	0.0431861	+	0.132913i
$997$	−21.5023	−	12.4143i	−0.680984	−	0.393166i	0.119242	−	0.992865i	$-0.461954\pi$
$997$	−21.5023	−	12.4143i	−0.680984	−	0.393166i	−0.800226	+	0.599699i	$0.795287\pi$
$998$	33.4787	−	19.3289i	1.05975	−	0.611846i
$999$	1.03891	−	1.15382i	0.0328696	−	0.0365054i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bn.a.19.8	yes	112
5.4	even	2	inner	930.2.bn.a.19.6	✓	112
31.18	even	15	inner	930.2.bn.a.49.6	yes	112
155.49	even	30	inner	930.2.bn.a.49.8	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bn.a.19.6	✓	112	5.4	even	2	inner
930.2.bn.a.19.8	yes	112	1.1	even	1	trivial
930.2.bn.a.49.6	yes	112	31.18	even	15	inner
930.2.bn.a.49.8	yes	112	155.49	even	30	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bn (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.19398 - 0.431813i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.07600 + 1.86924i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +O(q^{10})\)	\(q+(0.587785 - 0.809017i) q^{2} +(-0.406737 + 0.913545i) q^{3} +(-0.309017 - 0.951057i) q^{4} +(-2.19398 - 0.431813i) q^{5} +(0.500000 + 0.866025i) q^{6} +(2.07600 + 1.86924i) q^{7} +(-0.951057 - 0.309017i) q^{8} +(-0.669131 - 0.743145i) q^{9} +(-1.63893 + 1.52115i) q^{10} +(-1.42683 - 0.303282i) q^{11} +(0.994522 + 0.104528i) q^{12} +(5.26934 - 0.553830i) q^{13} +(2.73249 - 0.580808i) q^{14} +(1.28685 - 1.82866i) q^{15} +(-0.809017 + 0.587785i) q^{16} +(-1.53350 - 7.21455i) q^{17} +(-0.994522 + 0.104528i) q^{18} +(-0.719669 + 6.84719i) q^{19} +(0.267298 + 2.22003i) q^{20} +(-2.55202 + 1.13623i) q^{21} +(-1.08403 + 0.976063i) q^{22} +(4.70936 + 1.53016i) q^{23} +(0.669131 - 0.743145i) q^{24} +(4.62708 + 1.89478i) q^{25} +(2.64918 - 4.58852i) q^{26} +(0.951057 - 0.309017i) q^{27} +(1.13623 - 2.55202i) q^{28} +(6.77001 + 4.91870i) q^{29} +(-0.723028 - 2.11595i) q^{30} +(5.12587 + 2.17382i) q^{31} +1.00000i q^{32} +(0.857405 - 1.18012i) q^{33} +(-6.73807 - 2.99998i) q^{34} +(-3.74754 - 4.99751i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(1.34461 - 0.776311i) q^{37} +(5.11648 + 4.60690i) q^{38} +(-1.63728 + 5.03904i) q^{39} +(1.95316 + 1.08865i) q^{40} +(5.16027 - 2.29750i) q^{41} +(-0.580808 + 2.73249i) q^{42} +(0.119126 + 0.0125206i) q^{43} +(0.152476 + 1.45071i) q^{44} +(1.14716 + 1.91938i) q^{45} +(4.00602 - 2.91054i) q^{46} +(2.21845 + 3.05344i) q^{47} +(-0.207912 - 0.978148i) q^{48} +(0.0840230 + 0.799425i) q^{49} +(4.25263 - 2.62966i) q^{50} +(7.21455 + 1.53350i) q^{51} +(-2.15504 - 4.84030i) q^{52} +(5.66865 - 5.10407i) q^{53} +(0.309017 - 0.951057i) q^{54} +(2.99947 + 1.28152i) q^{55} +(-1.39677 - 2.41927i) q^{56} +(-5.96250 - 3.44245i) q^{57} +(7.95862 - 2.58591i) q^{58} +(-4.74911 - 2.11444i) q^{59} +(-2.13682 - 0.658780i) q^{60} +3.06316 q^{61} +(4.77157 - 2.86917i) q^{62} -2.79353i q^{63} +(0.809017 + 0.587785i) q^{64} +(-11.8000 - 1.06028i) q^{65} +(-0.450764 - 1.38731i) q^{66} +(-7.33560 - 4.23521i) q^{67} +(-6.38757 + 3.68787i) q^{68} +(-3.31334 + 3.67984i) q^{69} +(-6.24582 + 0.0943568i) q^{70} +(0.0611462 + 0.0679097i) q^{71} +(0.406737 + 0.913545i) q^{72} +(2.17919 - 10.2523i) q^{73} +(0.162293 - 1.54412i) q^{74} +(-3.61296 + 3.45637i) q^{75} +(6.73445 - 1.43145i) q^{76} +(-2.39519 - 3.29669i) q^{77} +(3.11430 + 4.28647i) q^{78} +(-10.1149 + 2.14999i) q^{79} +(2.02878 - 0.940244i) q^{80} +(-0.104528 + 0.994522i) q^{81} +(1.17441 - 5.52519i) q^{82} +(1.79393 + 4.02923i) q^{83} +(1.86924 + 2.07600i) q^{84} +(0.249129 + 16.4908i) q^{85} +(0.0801499 - 0.0890155i) q^{86} +(-7.24707 + 4.18410i) q^{87} +(1.26327 + 0.729352i) q^{88} +(-0.250391 - 0.770623i) q^{89} +(2.22710 + 0.200114i) q^{90} +(11.9744 + 8.69990i) q^{91} -4.95171i q^{92} +(-4.07076 + 3.79854i) q^{93} +3.77426 q^{94} +(4.53564 - 14.7118i) q^{95} +(-0.913545 - 0.406737i) q^{96} +(10.3351 - 3.35809i) q^{97} +(0.696136 + 0.401914i) q^{98} +(0.729352 + 1.26327i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9}+O(q^{10}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9	\( 112 q + 28 q^{4} - 2 q^{5} + 56 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} + 8 q^{14} + 8 q^{15} - 28 q^{16} + 16 q^{19} + 2 q^{20} + 28 q^{21} + 14 q^{24} + 14 q^{25} + 12 q^{26} + 16 q^{29} - 4 q^{30} + 10 q^{34} - 38 q^{35} - 56 q^{36} + 16 q^{39} - 6 q^{40} + 20 q^{41} + 2 q^{44} + 2 q^{45} - 2 q^{46} + 38 q^{49} + 8 q^{50} - 10 q^{51} - 28 q^{54} - 46 q^{55} + 12 q^{56} + 60 q^{59} - 8 q^{60} + 88 q^{61} + 28 q^{64} - 28 q^{65} + 6 q^{66} + 46 q^{69} + 26 q^{70} + 116 q^{71} - 34 q^{74} + 8 q^{75} + 24 q^{76} - 40 q^{79} - 12 q^{80} + 14 q^{81} - 8 q^{84} + 18 q^{85} - 38 q^{86} - 60 q^{89} + 4 q^{90} - 92 q^{91} + 132 q^{94} + 132 q^{95} - 14 q^{96} + 2 q^{99}+O(q^{100}) \) 112 * q + 28 * q^4 - 2 * q^5 + 56 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 + 8 * q^14 + 8 * q^15 - 28 * q^16 + 16 * q^19 + 2 * q^20 + 28 * q^21 + 14 * q^24 + 14 * q^25 + 12 * q^26 + 16 * q^29 - 4 * q^30 + 10 * q^34 - 38 * q^35 - 56 * q^36 + 16 * q^39 - 6 * q^40 + 20 * q^41 + 2 * q^44 + 2 * q^45 - 2 * q^46 + 38 * q^49 + 8 * q^50 - 10 * q^51 - 28 * q^54 - 46 * q^55 + 12 * q^56 + 60 * q^59 - 8 * q^60 + 88 * q^61 + 28 * q^64 - 28 * q^65 + 6 * q^66 + 46 * q^69 + 26 * q^70 + 116 * q^71 - 34 * q^74 + 8 * q^75 + 24 * q^76 - 40 * q^79 - 12 * q^80 + 14 * q^81 - 8 * q^84 + 18 * q^85 - 38 * q^86 - 60 * q^89 + 4 * q^90 - 92 * q^91 + 132 * q^94 + 132 * q^95 - 14 * q^96 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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