LMFDB - Embedded newform 570.2.bh.a.13.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(13,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(36))

chi = DirichletCharacter(H, H._module([0, 27, 10]))

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

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

chi := DirichletCharacter("570.13");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bh (of order $36$, degree $12$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$10$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			13.5
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.a.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.18820 + 0.460190i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.860238 - 3.21045i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.18820 + 0.460190i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.860238 - 3.21045i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-2.13977 - 0.649154i) q^{10} +(-2.90653 - 5.03426i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-2.53753 + 5.44176i) q^{13} +(0.577155 + 3.27321i) q^{14} +(-2.17767 + 0.507700i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.292005 - 3.33763i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-1.24285 - 4.17796i) q^{19} +(2.07505 + 0.833176i) q^{20} +(2.13644 + 2.54611i) q^{21} +(2.45671 + 5.26842i) q^{22} +(-5.99920 + 4.20069i) q^{23} +(0.984808 - 0.173648i) q^{24} +(4.57645 + 2.01398i) q^{25} +(3.00216 - 5.19989i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(-0.289680 - 3.31106i) q^{28} +(-5.19781 - 4.36148i) q^{29} +(2.21363 - 0.315971i) q^{30} +(3.23015 + 1.86493i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(4.76178 + 3.33424i) q^{33} +(-0.581788 + 3.29948i) q^{34} +(-0.404955 - 7.42099i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.687676 - 0.687676i) q^{37} +(0.873984 + 4.27038i) q^{38} -6.00432i q^{39} +(-1.99453 - 1.01086i) q^{40} +(1.99961 - 5.49387i) q^{41} +(-1.90640 - 2.72262i) q^{42} +(4.59229 - 6.55847i) q^{43} +(-1.98818 - 5.46249i) q^{44} +(1.75907 - 1.38045i) q^{45} +(6.34249 - 3.66184i) q^{46} +(-11.0498 + 0.966737i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(-3.50482 + 2.02351i) q^{49} +(-4.38350 - 2.40518i) q^{50} +(1.14590 + 3.14833i) q^{51} +(-3.44393 + 4.91845i) q^{52} +(-4.98558 - 7.12014i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-4.04336 - 12.3535i) q^{55} +3.32370i q^{56} +(2.89208 + 3.26127i) q^{57} +(4.79790 + 4.79790i) q^{58} +(3.97546 - 3.33580i) q^{59} +(-2.23275 + 0.121838i) q^{60} +(-0.168946 + 0.958139i) q^{61} +(-3.05532 - 2.13936i) q^{62} +(-3.01230 - 1.40466i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-8.05688 + 10.7399i) q^{65} +(-4.45306 - 3.73656i) q^{66} +(-0.153394 - 1.75330i) q^{67} +(0.867143 - 3.23622i) q^{68} +(3.66184 - 6.34249i) q^{69} +(-0.243368 + 7.42804i) q^{70} +(-2.31642 + 0.408448i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(-1.65531 - 3.54982i) q^{73} +(0.625124 + 0.744994i) q^{74} +(-4.99882 + 0.108807i) q^{75} +(-0.498470 - 4.33030i) q^{76} +(-13.6619 + 13.6619i) q^{77} +(-0.523311 + 5.98147i) q^{78} +(5.28161 + 1.92235i) q^{79} +(1.89884 + 1.18085i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-2.47082 + 5.29869i) q^{82} +(13.3173 - 3.56836i) q^{83} +(1.66185 + 2.87841i) q^{84} +(2.17491 - 7.16904i) q^{85} +(-5.14642 + 6.13327i) q^{86} +(6.55406 + 1.75615i) q^{87} +(1.50453 + 5.61499i) q^{88} +(-0.444764 + 0.161881i) q^{89} +(-1.87270 + 1.22189i) q^{90} +(19.6534 + 3.46542i) q^{91} +(-6.63750 + 3.09512i) q^{92} +(-3.71566 - 0.325078i) q^{93} +11.0921 q^{94} +(-0.796941 - 9.71416i) q^{95} +1.00000 q^{96} +(2.46564 + 0.215715i) q^{97} +(3.66784 - 1.71034i) q^{98} +(-5.72475 - 1.00943i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) $ 120 * q - 12 * q^5 + 12 * q^7	$ 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) $ 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$2$	−0.996195	−	0.0871557i	−0.704416	−	0.0616284i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$3$	−0.906308	+	0.422618i	−0.523257	+	0.243999i
$4$	0.984808	+	0.173648i	0.492404	+	0.0868241i
$5$	2.18820	+	0.460190i	0.978593	+	0.205803i
$5$	2.18820	+	0.460190i	0.978593	+	0.205803i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	−0.860238	−	3.21045i	−0.325139	−	1.21344i	−0.914172	−	0.405327i	$-0.867158\pi$
$7$	−0.860238	−	3.21045i	−0.325139	−	1.21344i	0.589032	−	0.808110i	$-0.299509\pi$
$8$	−0.965926	−	0.258819i	−0.341506	−	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	−2.13977	−	0.649154i	−0.676654	−	0.205280i
$11$	−2.90653	−	5.03426i	−0.876352	−	1.51789i	−0.855315	−	0.518108i	$-0.826637\pi$
$11$	−2.90653	−	5.03426i	−0.876352	−	1.51789i	−0.0210368	−	0.999779i	$-0.506697\pi$
$12$	−0.965926	+	0.258819i	−0.278839	+	0.0747146i
$13$	−2.53753	+	5.44176i	−0.703785	+	1.50927i	0.150022	+	0.988683i	$0.452066\pi$
$13$	−2.53753	+	5.44176i	−0.703785	+	1.50927i	−0.853807	+	0.520590i	$0.825712\pi$
$14$	0.577155	+	3.27321i	0.154251	+	0.874802i
$15$	−2.17767	+	0.507700i	−0.562272	+	0.131087i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.292005	−	3.33763i	0.0708216	−	0.809495i	−0.874855	−	0.484385i	$-0.839043\pi$
$17$	0.292005	−	3.33763i	0.0708216	−	0.809495i	0.945676	−	0.325110i	$-0.105401\pi$
$18$	−0.707107	+	0.707107i	−0.166667	+	0.166667i
$19$	−1.24285	−	4.17796i	−0.285128	−	0.958489i
$19$	−1.24285	−	4.17796i	−0.285128	−	0.958489i
$20$	2.07505	+	0.833176i	0.463994	+	0.186304i
$21$	2.13644	+	2.54611i	0.466209	+	0.555606i
$22$	2.45671	+	5.26842i	0.523772	+	1.12323i
$23$	−5.99920	+	4.20069i	−1.25092	+	0.875904i	−0.995849	−	0.0910185i	$-0.970988\pi$
$23$	−5.99920	+	4.20069i	−1.25092	+	0.875904i	−0.255071	+	0.966922i	$0.582099\pi$
$24$	0.984808	−	0.173648i	0.201023	−	0.0354458i
$25$	4.57645	+	2.01398i	0.915290	+	0.402796i
$26$	3.00216	−	5.19989i	0.588772	−	1.01978i
$27$	−0.258819	+	0.965926i	−0.0498097	+	0.185893i
$28$	−0.289680	−	3.31106i	−0.0547444	−	0.625731i
$29$	−5.19781	−	4.36148i	−0.965209	−	0.809907i	0.0165833	−	0.999862i	$-0.494721\pi$
$29$	−5.19781	−	4.36148i	−0.965209	−	0.809907i	−0.981793	+	0.189956i	$0.939166\pi$
$30$	2.21363	−	0.315971i	0.404152	−	0.0576882i
$31$	3.23015	+	1.86493i	0.580152	+	0.334951i	0.761194	−	0.648524i	$-0.224614\pi$
$31$	3.23015	+	1.86493i	0.580152	+	0.334951i	−0.181042	+	0.983475i	$0.557947\pi$
$32$	−0.906308	−	0.422618i	−0.160214	−	0.0747091i
$33$	4.76178	+	3.33424i	0.828920	+	0.580416i
$34$	−0.581788	+	3.29948i	−0.0997758	+	0.565857i
$35$	−0.404955	−	7.42099i	−0.0684498	−	1.25438i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−0.687676	−	0.687676i	−0.113053	−	0.113053i	0.648317	−	0.761370i	$-0.275473\pi$
$37$	−0.687676	−	0.687676i	−0.113053	−	0.113053i	−0.761370	+	0.648317i	$0.775473\pi$
$38$	0.873984	+	4.27038i	0.141779	+	0.692747i
$39$		−	6.00432i		−	0.961460i
$40$	−1.99453	−	1.01086i	−0.315364	−	0.159831i
$41$	1.99961	−	5.49387i	0.312286	−	0.857999i	−0.679908	−	0.733297i	$-0.737980\pi$
$41$	1.99961	−	5.49387i	0.312286	−	0.857999i	0.992194	−	0.124702i	$-0.0397973\pi$
$42$	−1.90640	−	2.72262i	−0.294164	−	0.420109i
$43$	4.59229	−	6.55847i	0.700317	−	1.00016i	−0.298634	−	0.954368i	$-0.596531\pi$
$43$	4.59229	−	6.55847i	0.700317	−	1.00016i	0.998951	−	0.0457890i	$-0.0145802\pi$
$44$	−1.98818	−	5.46249i	−0.299730	−	0.823502i
$45$	1.75907	−	1.38045i	0.262227	−	0.205786i
$46$	6.34249	−	3.66184i	0.935149	−	0.539908i
$47$	−11.0498	+	0.966737i	−1.61179	+	0.141013i	−0.857127	−	0.515104i	$-0.827753\pi$
$47$	−11.0498	+	0.966737i	−1.61179	+	0.141013i	−0.754659	+	0.656117i	$0.772198\pi$
$48$	−0.996195	+	0.0871557i	−0.143788	+	0.0125798i
$49$	−3.50482	+	2.02351i	−0.500688	+	0.289072i
$50$	−4.38350	−	2.40518i	−0.619921	−	0.340144i
$51$	1.14590	+	3.14833i	0.160458	+	0.440854i
$52$	−3.44393	+	4.91845i	−0.477588	+	0.682066i
$53$	−4.98558	−	7.12014i	−0.684822	−	0.978026i	−0.999584	−	0.0288559i	$-0.990814\pi$
$53$	−4.98558	−	7.12014i	−0.684822	−	0.978026i	0.314762	−	0.949171i	$-0.398075\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	−4.04336	−	12.3535i	−0.545206	−	1.66575i
$56$			3.32370i			0.444149i
$57$	2.89208	+	3.26127i	0.383066	+	0.431965i
$58$	4.79790	+	4.79790i	0.629996	+	0.629996i
$59$	3.97546	−	3.33580i	0.517560	−	0.434285i	−0.346220	−	0.938153i	$-0.612535\pi$
$59$	3.97546	−	3.33580i	0.517560	−	0.434285i	0.863780	+	0.503869i	$0.168090\pi$
$60$	−2.23275	+	0.121838i	−0.288246	+	0.0157293i
$61$	−0.168946	+	0.958139i	−0.0216313	+	0.122677i	−0.993711	−	0.111972i	$-0.964283\pi$
$61$	−0.168946	+	0.958139i	−0.0216313	+	0.122677i	0.972080	+	0.234650i	$0.0753943\pi$
$62$	−3.05532	−	2.13936i	−0.388026	−	0.271699i
$63$	−3.01230	−	1.40466i	−0.379514	−	0.176970i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−8.05688	+	10.7399i	−0.999333	+	1.33212i
$66$	−4.45306	−	3.73656i	−0.548134	−	0.459939i
$67$	−0.153394	−	1.75330i	−0.0187401	−	0.214200i	−0.999791	−	0.0204496i	$-0.993490\pi$
$67$	−0.153394	−	1.75330i	−0.0187401	−	0.214200i	0.981051	−	0.193751i	$-0.0620653\pi$
$68$	0.867143	−	3.23622i	0.105157	−	0.392449i
$69$	3.66184	−	6.34249i	0.440833	−	0.763546i
$70$	−0.243368	+	7.42804i	−0.0290881	+	0.887821i
$71$	−2.31642	+	0.408448i	−0.274909	+	0.0484739i	−0.309403	−	0.950931i	$-0.600129\pi$
$71$	−2.31642	+	0.408448i	−0.274909	+	0.0484739i	0.0344940	+	0.999405i	$0.489018\pi$
$72$	−0.819152	+	0.573576i	−0.0965380	+	0.0675966i
$73$	−1.65531	−	3.54982i	−0.193739	−	0.415476i	0.785309	−	0.619104i	$-0.212504\pi$
$73$	−1.65531	−	3.54982i	−0.193739	−	0.415476i	−0.979048	+	0.203629i	$0.934726\pi$
$74$	0.625124	+	0.744994i	0.0726692	+	0.0866038i
$75$	−4.99882	+	0.108807i	−0.577214	+	0.0125639i
$76$	−0.498470	−	4.33030i	−0.0571784	−	0.496720i
$77$	−13.6619	+	13.6619i	−1.55692	+	1.55692i
$78$	−0.523311	+	5.98147i	−0.0592533	+	0.677268i
$79$	5.28161	+	1.92235i	0.594228	+	0.216281i	0.621588	−	0.783344i	$-0.286488\pi$
$79$	5.28161	+	1.92235i	0.594228	+	0.216281i	−0.0273601	+	0.999626i	$0.508710\pi$
$80$	1.89884	+	1.18085i	0.212297	+	0.132023i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	−2.47082	+	5.29869i	−0.272856	+	0.585142i
$83$	13.3173	−	3.56836i	1.46176	−	0.391679i	0.561666	−	0.827364i	$-0.310161\pi$
$83$	13.3173	−	3.56836i	1.46176	−	0.391679i	0.900099	+	0.435686i	$0.143494\pi$
$84$	1.66185	+	2.87841i	0.181323	+	0.314061i
$85$	2.17491	−	7.16904i	0.235902	−	0.777591i
$86$	−5.14642	+	6.13327i	−0.554953	+	0.661367i
$87$	6.55406	+	1.75615i	0.702669	+	0.188280i
$88$	1.50453	+	5.61499i	0.160384	+	0.598560i
$89$	−0.444764	+	0.161881i	−0.0471449	+	0.0171593i	−0.365485	−	0.930817i	$-0.619097\pi$
$89$	−0.444764	+	0.161881i	−0.0471449	+	0.0171593i	0.318340	+	0.947977i	$0.396875\pi$
$90$	−1.87270	+	1.22189i	−0.197399	+	0.128798i
$91$	19.6534	+	3.46542i	2.06024	+	0.363275i
$92$	−6.63750	+	3.09512i	−0.692008	+	0.322688i
$93$	−3.71566	−	0.325078i	−0.385296	−	0.0337091i
$94$	11.0921			1.14406
$95$	−0.796941	−	9.71416i	−0.0817645	−	0.996652i
$96$	1.00000			0.102062
$97$	2.46564	+	0.215715i	0.250348	+	0.0219026i	0.211639	−	0.977348i	$-0.432120\pi$
$97$	2.46564	+	0.215715i	0.250348	+	0.0219026i	0.0387088	+	0.999251i	$0.487676\pi$
$98$	3.66784	−	1.71034i	0.370508	−	0.172771i
$99$	−5.72475	−	1.00943i	−0.575359	−	0.101451i
$100$	4.15720	+	2.77807i	0.415720	+	0.277807i
$101$	10.5728	−	3.84818i	1.05203	−	0.382908i	0.242602	−	0.970126i	$-0.421999\pi$
$101$	10.5728	−	3.84818i	1.05203	−	0.382908i	0.809429	+	0.587218i	$0.199777\pi$
$102$	−0.867143	−	3.23622i	−0.0858599	−	0.320434i
$103$	0.404393	+	0.108357i	0.0398460	+	0.0106767i	0.278687	−	0.960382i	$-0.410101\pi$
$103$	0.404393	+	0.108357i	0.0398460	+	0.0106767i	−0.238841	+	0.971059i	$0.576767\pi$
$104$	3.85950	−	4.59957i	0.378455	−	0.451025i
$105$	3.50326	+	6.55456i	0.341883	+	0.639659i
$106$	4.34604	+	7.52757i	0.422125	+	0.731142i
$107$	16.0315	−	4.29563i	1.54982	−	0.415274i	0.620400	−	0.784286i	$-0.286970\pi$
$107$	16.0315	−	4.29563i	1.54982	−	0.415274i	0.929425	+	0.369011i	$0.120304\pi$
$108$	−0.422618	+	0.906308i	−0.0406665	+	0.0872095i
$109$	2.71947	+	15.4229i	0.260478	+	1.47724i	0.781610	+	0.623767i	$0.214399\pi$
$109$	2.71947	+	15.4229i	0.260478	+	1.47724i	−0.521132	+	0.853476i	$0.674490\pi$
$110$	2.95129	+	12.6589i	0.281394	+	1.20698i
$111$	0.913870	+	0.332622i	0.0867407	+	0.0315710i
$112$	0.289680	−	3.31106i	0.0273722	−	0.312865i
$113$	−6.35203	+	6.35203i	−0.597548	+	0.597548i	−0.939660	−	0.342111i	$-0.888858\pi$
$113$	−6.35203	+	6.35203i	−0.597548	+	0.597548i	0.342111	+	0.939660i	$0.388858\pi$
$114$	−2.59684	−	3.50092i	−0.243216	−	0.327891i
$115$	−15.0606	+	6.43117i	−1.40441	+	0.599710i
$116$	−4.36148	−	5.19781i	−0.404953	−	0.482605i
$117$	2.53753	+	5.44176i	0.234595	+	0.503091i
$118$	−4.25106	+	2.97663i	−0.391342	+	0.274021i
$119$	−10.9665	+	1.93369i	−1.00530	+	0.177261i
$120$	2.23487	+	0.0732220i	0.204015	+	0.00668422i
$121$	−11.3958	+	19.7382i	−1.03599	+	1.79438i
$122$	0.251810	−	0.939769i	0.0227978	−	0.0850826i
$123$	0.509552	+	5.82421i	0.0459448	+	0.525151i
$124$	2.85724	+	2.39751i	0.256587	+	0.215302i
$125$	9.08738	+	6.51303i	0.812800	+	0.582543i
$126$	2.87841	+	1.66185i	0.256429	+	0.148050i
$127$	−11.2409	−	5.24170i	−0.997466	−	0.465126i	−0.145858	−	0.989306i	$-0.546594\pi$
$127$	−11.2409	−	5.24170i	−0.997466	−	0.465126i	−0.851608	+	0.524180i	$0.824372\pi$
$128$	−0.819152	−	0.573576i	−0.0724035	−	0.0506975i
$129$	−1.39030	+	7.88477i	−0.122409	+	0.694216i
$130$	8.96227	−	9.99684i	0.786043	−	0.876781i
$131$	−2.79222	+	2.34295i	−0.243958	+	0.204705i	−0.756565	−	0.653918i	$-0.773124\pi$
$131$	−2.79222	+	2.34295i	−0.243958	+	0.204705i	0.512607	+	0.858623i	$0.328680\pi$
$132$	4.11046	+	4.11046i	0.357769	+	0.357769i
$133$	−12.3440	+	7.58414i	−1.07036	+	0.657628i
$134$			1.76000i			0.152041i
$135$	−1.01086	+	1.99453i	−0.0870008	+	0.171662i
$136$	−1.14590	+	3.14833i	−0.0982600	+	0.269967i
$137$	0.238954	+	0.341261i	0.0204152	+	0.0291559i	0.829230	−	0.558908i	$-0.188779\pi$
$137$	0.238954	+	0.341261i	0.0204152	+	0.0291559i	−0.808815	+	0.588064i	$0.799890\pi$
$138$	−4.20069	+	5.99920i	−0.357586	+	0.510686i
$139$	1.42045	+	3.90266i	0.120481	+	0.331019i	0.985243	−	0.171164i	$-0.0547527\pi$
$139$	1.42045	+	3.90266i	0.120481	+	0.331019i	−0.864761	+	0.502183i	$0.832530\pi$
$140$	0.889839	−	7.37857i	0.0752051	−	0.623603i
$141$	9.60600	−	5.54603i	0.808972	−	0.467060i
$142$	2.34321	−	0.205004i	0.196638	−	0.0172036i
$143$	34.7707	−	3.04204i	2.90767	−	0.254388i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	−9.36675	−	11.9358i	−0.777866	−	0.991213i
$146$	1.33962	+	3.68059i	0.110868	+	0.304607i
$147$	2.32127	−	3.31512i	0.191455	−	0.273426i
$148$	−0.557815	−	0.796642i	−0.0458521	−	0.0654836i
$149$	3.90161	−	10.7196i	0.319633	−	0.878184i	−0.670979	−	0.741476i	$-0.734126\pi$
$149$	3.90161	−	10.7196i	0.319633	−	0.878184i	0.990612	−	0.136707i	$-0.0436519\pi$
$150$	4.98928	+	0.327283i	0.407373	+	0.0267225i
$151$			8.70291i			0.708233i	0.935201	+	0.354116i	$0.115218\pi$
$151$			8.70291i			0.708233i	−0.935201	+	0.354116i	$0.884782\pi$
$152$	0.119162	+	4.35727i	0.00966533	+	0.353421i
$153$	−2.36908	−	2.36908i	−0.191529	−	0.191529i
$154$	14.8007	−	12.4192i	1.19267	−	1.00077i
$155$	6.21000	+	5.56732i	0.498799	+	0.447178i
$156$	1.04264	−	5.91310i	0.0834779	−	0.473427i
$157$	7.66746	+	5.36882i	0.611930	+	0.428478i	0.838029	−	0.545626i	$-0.183708\pi$
$157$	7.66746	+	5.36882i	0.611930	+	0.428478i	−0.226098	+	0.974104i	$0.572597\pi$
$158$	−5.09397	−	2.37536i	−0.405255	−	0.188973i
$159$	7.52757	+	4.34604i	0.596975	+	0.344664i
$160$	−1.78870	−	1.34185i	−0.141409	−	0.106082i
$161$	18.6468	+	15.6466i	1.46958	+	1.23312i
$162$	0.0871557	+	0.996195i	0.00684760	+	0.0782684i
$163$	−0.396446	+	1.47956i	−0.0310520	+	0.115888i	−0.979712	−	0.200409i	$-0.935773\pi$
$163$	−0.396446	+	1.47956i	−0.0310520	+	0.115888i	0.948660	+	0.316297i	$0.102440\pi$
$164$	2.92323	−	5.06318i	0.228266	−	0.395368i
$165$	8.88535	+	9.48731i	0.691724	+	0.738586i
$166$	−13.5776	+	2.39410i	−1.05383	+	0.185818i
$167$	−12.4987	+	8.75170i	−0.967180	+	0.677227i	−0.946549	−	0.322560i	$-0.895456\pi$
$167$	−12.4987	+	8.75170i	−0.967180	+	0.677227i	−0.0206313	+	0.999787i	$0.506568\pi$
$168$	−1.40466	−	3.01230i	−0.108372	−	0.232404i
$169$	−14.8174	−	17.6587i	−1.13980	−	1.35836i
$170$	−2.79146	+	6.95220i	−0.214095	+	0.533209i
$171$	−3.99939	−	1.73346i	−0.305841	−	0.132561i
$172$	5.66139	−	5.66139i	0.431677	−	0.431677i
$173$	1.82534	−	20.8637i	0.138778	−	1.58624i	−0.533411	−	0.845856i	$-0.679090\pi$
$173$	1.82534	−	20.8637i	0.138778	−	1.58624i	0.672189	−	0.740380i	$-0.265354\pi$
$174$	−6.37606	−	2.32070i	−0.483368	−	0.175932i
$175$	2.52895	−	16.4250i	0.191170	−	1.24161i
$176$	−1.00943	−	5.72475i	−0.0760885	−	0.431519i
$177$	−2.19322	+	4.70337i	−0.164852	+	0.353527i
$178$	0.457180	−	0.122501i	0.0342671	−	0.00918184i
$179$	0.727889	+	1.26074i	0.0544050	+	0.0942322i	0.891945	−	0.452143i	$-0.149340\pi$
$179$	0.727889	+	1.26074i	0.0544050	+	0.0942322i	−0.837540	+	0.546376i	$0.816007\pi$
$180$	1.97206	−	1.05402i	0.146989	−	0.0785622i
$181$	−3.45141	+	4.11323i	−0.256541	+	0.305734i	−0.878908	−	0.476992i	$-0.841727\pi$
$181$	−3.45141	+	4.11323i	−0.256541	+	0.305734i	0.622366	+	0.782726i	$0.286171\pi$
$182$	−19.2766	−	5.16514i	−1.42887	−	0.382866i
$183$	−0.251810	−	0.939769i	−0.0186143	−	0.0694697i
$184$	6.88200	−	2.50484i	0.507348	−	0.184660i
$185$	−1.18831	−	1.82123i	−0.0873664	−	0.133900i
$186$	3.67319	+	0.647683i	0.269331	+	0.0474904i
$187$	−17.6512	+	8.23091i	−1.29079	+	0.601904i
$188$	−11.0498	−	0.966737i	−0.805893	−	0.0705065i
$189$	3.32370			0.241764
$190$	−0.0527360	+	9.74665i	−0.00382587	+	0.707096i
$191$	−17.3612			−1.25621			−0.628107	−	0.778127i	$-0.716170\pi$
$191$	−17.3612			−1.25621			−0.628107	+	0.778127i	$0.716170\pi$
$192$	−0.996195	−	0.0871557i	−0.0718942	−	0.00628992i
$193$	8.45518	−	3.94272i	0.608617	−	0.283803i	−0.0937744	−	0.995593i	$-0.529893\pi$
$193$	8.45518	−	3.94272i	0.608617	−	0.283803i	0.702392	+	0.711791i	$0.252115\pi$
$194$	−2.43745	−	0.429789i	−0.174999	−	0.0308570i
$195$	2.76313	−	13.1387i	0.197872	−	0.940879i
$196$	−3.80295	+	1.38416i	−0.271639	+	0.0988686i
$197$	4.63219	+	17.2876i	0.330030	+	1.23169i	0.909158	+	0.416452i	$0.136727\pi$
$197$	4.63219	+	17.2876i	0.330030	+	1.23169i	−0.579128	+	0.815237i	$0.696607\pi$
$198$	5.61499	+	1.50453i	0.399040	+	0.106922i
$199$	−5.19975	+	6.19682i	−0.368600	+	0.439281i	−0.918182	−	0.396159i	$-0.870343\pi$
$199$	−5.19975	+	6.19682i	−0.368600	+	0.439281i	0.549581	+	0.835440i	$0.314787\pi$
$200$	−3.89925	−	3.12983i	−0.275719	−	0.221312i
$201$	0.880001	+	1.52421i	0.0620705	+	0.107509i
$202$	−10.8679	+	2.91206i	−0.764666	+	0.204892i
$203$	−9.53097	+	20.4392i	−0.668943	+	1.43455i
$204$	0.581788	+	3.29948i	0.0407333	+	0.231010i
$205$	6.90377	−	11.1015i	0.482180	−	0.775362i
$206$	−0.393410	−	0.143190i	−0.0274102	−	0.00997649i
$207$	−0.638300	+	7.29581i	−0.0443649	+	0.507094i
$208$	−4.24569	+	4.24569i	−0.294386	+	0.294386i
$209$	−17.4206	+	18.4002i	−1.20500	+	1.27277i
$210$	−2.91866	−	6.83495i	−0.201407	−	0.471656i
$211$	−11.3019	−	13.4690i	−0.778052	−	0.927247i	0.220791	−	0.975321i	$-0.429136\pi$
$211$	−11.3019	−	13.4690i	−0.778052	−	0.927247i	−0.998844	+	0.0480743i	$0.984692\pi$
$212$	−3.67343	−	7.87771i	−0.252293	−	0.541043i
$213$	1.92678	−	1.34914i	0.132020	−	0.0924417i
$214$	−16.3449	+	2.88205i	−1.11731	+	0.197013i
$215$	13.0670	−	12.2379i	0.891162	−	0.834619i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	3.20856	−	11.9745i	0.217812	−	0.812884i
$218$	−1.36493	−	15.6012i	−0.0924446	−	1.05665i
$219$	3.00044	+	2.51767i	0.202751	+	0.170128i
$220$	−1.83676	−	12.8680i	−0.123834	−	0.867559i
$221$	17.4216	+	10.0584i	1.17191	+	0.676600i
$222$	−0.881403	−	0.411005i	−0.0591559	−	0.0275848i
$223$	15.0313	+	10.5250i	1.00657	+	0.704808i	0.955835	−	0.293904i	$-0.0949545\pi$
$223$	15.0313	+	10.5250i	1.00657	+	0.704808i	0.0507358	+	0.998712i	$0.483843\pi$
$224$	−0.577155	+	3.27321i	−0.0385628	+	0.218701i
$225$	4.48448	−	2.21120i	0.298965	−	0.147414i
$226$	6.88147	−	5.77424i	0.457749	−	0.384097i
$227$	10.7347	+	10.7347i	0.712487	+	0.712487i	0.967055	−	0.254568i	$-0.0819333\pi$
$227$	10.7347	+	10.7347i	0.712487	+	0.712487i	−0.254568	+	0.967055i	$0.581933\pi$
$228$	2.28183	+	3.71393i	0.151118	+	0.245961i
$229$		−	28.7355i		−	1.89889i	−0.313928	−	0.949447i	$-0.601645\pi$
$229$		−	28.7355i		−	1.89889i	0.313928	−	0.949447i	$-0.398355\pi$
$230$	15.5638	−	5.09408i	1.02625	−	0.335894i
$231$	6.60814	−	18.1557i	0.434784	−	1.19456i
$232$	3.89187	+	5.55816i	0.255514	+	0.364911i
$233$	−4.72782	+	6.75203i	−0.309730	+	0.442340i	−0.943594	−	0.331104i	$-0.892579\pi$
$233$	−4.72782	+	6.75203i	−0.309730	+	0.442340i	0.633864	+	0.773444i	$0.281468\pi$
$234$	−2.05360	−	5.64221i	−0.134248	−	0.368843i
$235$	−24.6242	−	2.96962i	−1.60630	−	0.193717i
$236$	4.49432	−	2.59480i	0.292555	−	0.168907i
$237$	−5.59919	+	0.489865i	−0.363706	+	0.0318202i
$238$	11.0933	−	0.970539i	0.719072	−	0.0629107i
$239$	−14.0671	+	8.12163i	−0.909923	+	0.525344i	−0.880406	−	0.474220i	$-0.842730\pi$
$239$	−14.0671	+	8.12163i	−0.909923	+	0.525344i	−0.0295168	+	0.999564i	$0.509397\pi$
$240$	−2.21998	−	0.267725i	−0.143299	−	0.0172816i
$241$	−0.528481	−	1.45199i	−0.0340424	−	0.0935308i	0.921507	−	0.388362i	$-0.126959\pi$
$241$	−0.528481	−	1.45199i	−0.0340424	−	0.0935308i	−0.955549	+	0.294831i	$0.904737\pi$
$242$	13.0728	−	18.6699i	0.840350	−	1.20014i
$243$	0.573576	+	0.819152i	0.0367949	+	0.0525486i
$244$	−0.332758	+	0.914246i	−0.0213027	+	0.0585286i
$245$	−8.60044	+	2.81496i	−0.549462	+	0.179841i
$246$		−	5.84646i		−	0.372756i
$247$	25.8892	+	3.83844i	1.64729	+	0.244234i
$248$	−2.63741	−	2.63741i	−0.167475	−	0.167475i
$249$	−10.5615	+	8.86217i	−0.669309	+	0.561617i
$250$	−8.48515	−	7.28026i	−0.536648	−	0.460444i
$251$	−0.943224	+	5.34929i	−0.0595357	+	0.337644i	−0.999997	−	0.00225566i	$-0.999282\pi$
$251$	−0.943224	+	5.34929i	−0.0595357	+	0.337644i	0.940462	+	0.339900i	$0.110393\pi$
$252$	−2.72262	−	1.90640i	−0.171509	−	0.120092i
$253$	38.5842	+	17.9921i	2.42577	+	1.13115i
$254$	10.7412	+	6.20146i	0.673966	+	0.389114i
$255$	1.05862	+	7.41651i	0.0662937	+	0.464440i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.501100	+	5.72760i	0.0312578	+	0.357278i	0.995676	+	0.0928960i	$0.0296124\pi$
$257$	0.501100	+	5.72760i	0.0312578	+	0.357278i	−0.964418	+	0.264382i	$0.914832\pi$
$258$	2.07221	−	7.73360i	0.129010	−	0.481473i
$259$	−1.61619	+	2.79931i	−0.100425	+	0.173941i
$260$	−9.79945	+	9.17769i	−0.607736	+	0.569176i
$261$	−6.68218	+	1.17825i	−0.413616	+	0.0729317i
$262$	2.98580	−	2.09068i	0.184463	−	0.129163i
$263$	−0.136411	−	0.292535i	−0.00841149	−	0.0180385i	0.902057	−	0.431617i	$-0.142057\pi$
$263$	−0.136411	−	0.292535i	−0.00841149	−	0.0180385i	−0.910469	+	0.413578i	$0.864279\pi$
$264$	−3.73656	−	4.45306i	−0.229970	−	0.274067i
$265$	−7.63282	−	17.8746i	−0.468881	−	1.09803i
$266$	12.9580	−	6.47943i	0.794507	−	0.397279i
$267$	0.334679	−	0.334679i	0.0204820	−	0.0204820i
$268$	0.153394	−	1.75330i	0.00937005	−	0.107100i
$269$	−14.5639	−	5.30082i	−0.887975	−	0.323197i	−0.142551	−	0.989787i	$-0.545531\pi$
$269$	−14.5639	−	5.30082i	−0.887975	−	0.323197i	−0.745424	+	0.666591i	$0.767753\pi$
$270$	1.18085	−	1.89884i	0.0718640	−	0.115560i
$271$	−0.480336	−	2.72412i	−0.0291783	−	0.165478i	0.966737	−	0.255773i	$-0.0823301\pi$
$271$	−0.480336	−	2.72412i	−0.0291783	−	0.165478i	−0.995915	+	0.0902950i	$0.971219\pi$
$272$	1.41593	−	3.03648i	0.0858535	−	0.184114i
$273$	−19.2766	+	5.16514i	−1.16667	+	0.312609i
$274$	−0.208301	−	0.360789i	−0.0125840	−	0.0217960i
$275$	−3.16270	−	28.8927i	−0.190718	−	1.74230i
$276$	4.70757	−	5.61026i	0.283362	−	0.337698i
$277$	−5.79873	−	1.55377i	−0.348412	−	0.0933567i	0.0803690	−	0.996765i	$-0.474390\pi$
$277$	−5.79873	−	1.55377i	−0.348412	−	0.0933567i	−0.428781	+	0.903408i	$0.641057\pi$
$278$	−1.07491	−	4.01161i	−0.0644687	−	0.240600i
$279$	3.50492	−	1.27569i	0.209834	−	0.0763733i
$280$	−1.52954	+	7.27293i	−0.0914073	+	0.434641i
$281$	27.7161	+	4.88709i	1.65340	+	0.291539i	0.921066	−	0.389406i	$-0.127320\pi$
$281$	27.7161	+	4.88709i	1.65340	+	0.291539i	0.732335	+	0.680945i	$0.238431\pi$
$282$	−10.0528	+	4.68771i	−0.598637	+	0.279149i
$283$	17.9476	+	1.57021i	1.06688	+	0.0933395i	0.607045	−	0.794667i	$-0.292355\pi$
$283$	17.9476	+	1.57021i	1.06688	+	0.0933395i	0.459830	+	0.888007i	$0.347910\pi$
$284$	−2.35216			−0.139575
$285$	4.82766	+	8.46722i	0.285966	+	0.501555i
$286$	−34.9035			−2.06389
$287$	−19.3579	−	1.69360i	−1.14266	−	0.0999701i
$288$	−0.906308	+	0.422618i	−0.0534047	+	0.0249030i
$289$	5.68720	+	1.00281i	0.334541	+	0.0589886i
$290$	8.29083	+	12.7067i	0.486854	+	0.746165i
$291$	−2.32579	+	0.846519i	−0.136340	+	0.0496238i
$292$	−1.01374	−	3.78334i	−0.0593248	−	0.221403i
$293$	21.1276	+	5.66113i	1.23429	+	0.330727i	0.816248	−	0.577701i	$-0.196050\pi$
$293$	21.1276	+	5.66113i	1.23429	+	0.330727i	0.418041	+	0.908428i	$0.362717\pi$
$294$	−2.60137	+	3.10019i	−0.151715	+	0.180807i
$295$	10.2342	−	5.46994i	0.595858	−	0.318472i
$296$	0.486260	+	0.842227i	0.0282633	+	0.0489535i
$297$	5.61499	−	1.50453i	0.325815	−	0.0873018i
$298$	−4.82104	+	10.3388i	−0.279275	+	0.598908i
$299$	−7.63595	−	43.3056i	−0.441598	−	2.50443i
$300$	−4.94177	−	0.760882i	−0.285313	−	0.0439295i
$301$	−25.0061	−	9.10148i	−1.44133	−	0.524600i
$302$	0.758509	−	8.66979i	0.0436473	−	0.498891i
$303$	−7.95589	+	7.95589i	−0.457054	+	0.457054i
$304$	0.261052	−	4.35107i	0.0149724	−	0.249551i
$305$	−0.810614	+	2.01885i	−0.0464156	+	0.115599i
$306$	2.15358	+	2.56654i	0.123112	+	0.146719i
$307$	−7.37652	−	15.8190i	−0.421000	−	0.902838i	−0.996385	−	0.0849549i	$-0.972925\pi$
$307$	−7.37652	−	15.8190i	−0.421000	−	0.902838i	0.575385	−	0.817883i	$-0.304852\pi$
$308$	−15.8268	+	11.0820i	−0.901813	+	0.631456i
$309$	−0.412298	+	0.0726992i	−0.0234548	+	0.00413571i
$310$	−5.70114	−	6.08737i	−0.323803	−	0.345740i
$311$	8.84425	−	15.3187i	0.501512	−	0.868643i	−0.498487	−	0.866897i	$-0.666111\pi$
$311$	8.84425	−	15.3187i	0.501512	−	0.868643i	0.999998	−	0.00174623i	$-0.000555842\pi$
$312$	−1.55403	+	5.79972i	−0.0879797	+	0.328345i
$313$	−2.24085	−	25.6130i	−0.126660	−	1.44773i	−0.747744	−	0.663987i	$-0.768863\pi$
$313$	−2.24085	−	25.6130i	−0.126660	−	1.44773i	0.621084	−	0.783744i	$-0.286693\pi$
$314$	−7.17036	−	6.01665i	−0.404647	−	0.339539i
$315$	−5.94511	−	4.45991i	−0.334969	−	0.251287i
$316$	4.86756	+	2.81029i	0.273822	+	0.158091i
$317$	−15.9411	−	7.43343i	−0.895339	−	0.417503i	−0.0802065	−	0.996778i	$-0.525558\pi$
$317$	−15.9411	−	7.43343i	−0.895339	−	0.417503i	−0.815132	+	0.579275i	$0.803336\pi$
$318$	−7.12014	−	4.98558i	−0.399278	−	0.279577i
$319$	−6.84923	+	38.8439i	−0.383483	+	2.17484i
$320$	1.66494	+	1.49264i	0.0930731	+	0.0834410i
$321$	−12.7141	+	10.6684i	−0.709630	+	0.595450i
$322$	−17.2122	−	17.2122i	−0.959199	−	0.959199i
$323$	−14.3074	+	2.92818i	−0.796086	+	0.162928i
$324$		−	1.00000i		−	0.0555556i
$325$	−22.5725	+	19.7934i	−1.25210	+	1.09794i
$326$	0.523889	−	1.43937i	0.0290155	−	0.0797195i
$327$	−8.98266	−	12.8286i	−0.496742	−	0.709422i
$328$	−3.35339	+	4.78914i	−0.185160	+	0.264436i
$329$	12.6092	+	34.6434i	0.695166	+	1.90995i
$330$	−8.02467	−	10.2256i	−0.441744	−	0.562901i
$331$	−1.61993	+	0.935265i	−0.0890392	+	0.0514068i	−0.543858	−	0.839177i	$-0.683037\pi$
$331$	−1.61993	+	0.935265i	−0.0890392	+	0.0514068i	0.454819	+	0.890584i	$0.349704\pi$
$332$	13.7346	−	1.20162i	0.753786	−	0.0659477i
$333$	−0.968820	+	0.0847607i	−0.0530910	+	0.00464486i
$334$	13.2139	−	7.62906i	0.723034	−	0.417444i
$335$	0.471197	−	3.90717i	0.0257442	−	0.213472i
$336$	1.13677	+	3.12326i	0.0620161	+	0.170388i
$337$	−3.42044	+	4.88489i	−0.186323	+	0.266097i	−0.901436	−	0.432912i	$-0.857486\pi$
$337$	−3.42044	+	4.88489i	−0.186323	+	0.266097i	0.715113	+	0.699009i	$0.246375\pi$
$338$	13.2220	+	18.8829i	0.719181	+	1.02710i
$339$	3.07241	−	8.44137i	0.166870	−	0.458472i
$340$	3.38676	−	6.68245i	0.183673	−	0.362407i
$341$		−	21.6819i		−	1.17414i
$342$	3.83309	+	2.07544i	0.207270	+	0.112227i
$343$	−6.94015	−	6.94015i	−0.374733	−	0.374733i
$344$	−6.13327	+	5.14642i	−0.330684	+	0.277476i
$345$	10.9316	−	12.1935i	0.588537	−	0.656476i
$346$	−3.63678	+	20.6252i	−0.195514	+	1.10882i
$347$	−8.71737	−	6.10397i	−0.467973	−	0.327678i	0.315692	−	0.948862i	$-0.397763\pi$
$347$	−8.71737	−	6.10397i	−0.467973	−	0.327678i	−0.783665	+	0.621184i	$0.786652\pi$
$348$	6.14953	+	2.86758i	0.329650	+	0.153718i
$349$	21.4837	+	12.4036i	1.15000	+	0.663952i	0.948887	−	0.315617i	$-0.102211\pi$
$349$	21.4837	+	12.4036i	1.15000	+	0.663952i	0.201111	+	0.979568i	$0.435545\pi$
$350$	−3.95085	+	16.1421i	−0.211182	+	0.862829i
$351$	−4.59957	−	3.85950i	−0.245507	−	0.206005i
$352$	0.506642	+	5.79094i	0.0270041	+	0.308658i
$353$	2.37025	−	8.84587i	0.126155	−	0.470818i	−0.873723	−	0.486424i	$-0.838301\pi$
$353$	2.37025	−	8.84587i	0.126155	−	0.470818i	0.999878	+	0.0156057i	$0.00496766\pi$
$354$	2.59480	−	4.49432i	0.137912	−	0.238870i
$355$	−5.25677	−	0.172230i	−0.279000	−	0.00914100i
$356$	−0.466117	+	0.0821890i	−0.0247042	+	0.00435601i
$357$	9.12182	−	6.38717i	0.482778	−	0.338045i
$358$	−0.615238	−	1.31938i	−0.0325164	−	0.0697315i
$359$	16.0745	+	19.1568i	0.848379	+	1.01106i	0.999745	+	0.0225809i	$0.00718833\pi$
$359$	16.0745	+	19.1568i	0.848379	+	1.01106i	−0.151366	+	0.988478i	$0.548367\pi$
$360$	−2.05642	+	0.878135i	−0.108383	+	0.0462818i
$361$	−15.9107	+	10.3851i	−0.837403	+	0.546585i
$362$	3.79677	−	3.79677i	0.199554	−	0.199554i
$363$	1.98643	−	22.7050i	0.104260	−	1.19170i
$364$	18.7530	+	6.82555i	0.982927	+	0.357756i
$365$	−1.98856	−	8.52949i	−0.104086	−	0.446454i
$366$	0.168946	+	0.958139i	0.00883094	+	0.0500827i
$367$	14.6431	−	31.4023i	0.764365	−	1.63919i	−0.00467915	−	0.999989i	$-0.501489\pi$
$367$	14.6431	−	31.4023i	0.764365	−	1.63919i	0.769044	−	0.639196i	$-0.220733\pi$
$368$	−7.07413	+	1.89551i	−0.368764	+	0.0988101i
$369$	−2.92323	−	5.06318i	−0.152177	−	0.263579i
$370$	1.02506	+	1.91787i	0.0532902	+	0.0997054i
$371$	−18.5701	+	22.1310i	−0.964111	+	1.14898i
$372$	−3.60276	−	0.965358i	−0.186795	−	0.0500515i
$373$	−6.39620	−	23.8709i	−0.331183	−	1.23599i	−0.907949	−	0.419081i	$-0.862352\pi$
$373$	−6.39620	−	23.8709i	−0.331183	−	1.23599i	0.576766	−	0.816909i	$-0.304314\pi$
$374$	18.3014	−	6.66118i	0.946345	−	0.344441i
$375$	−10.9885	−	2.06232i	−0.567443	−	0.106498i
$376$	10.9235	+	1.92612i	0.563339	+	0.0993318i
$377$	36.9238	−	17.2178i	1.90167	−	0.886763i
$378$	−3.31106	−	0.289680i	−0.170302	−	0.0148995i
$379$	11.6215			0.596957			0.298479	−	0.954416i	$-0.403521\pi$
$379$	11.6215			0.596957			0.298479	+	0.954416i	$0.403521\pi$
$380$	0.902012	−	9.70497i	0.0462722	−	0.497854i
$381$	12.4029			0.635421
$382$	17.2952	+	1.51313i	0.884897	+	0.0774185i
$383$	−20.1357	+	9.38945i	−1.02889	+	0.479778i	−0.862380	−	0.506262i	$-0.831027\pi$
$383$	−20.1357	+	9.38945i	−1.02889	+	0.479778i	−0.166508	+	0.986040i	$0.553249\pi$
$384$	0.984808	+	0.173648i	0.0502558	+	0.00886145i
$385$	−36.1822	+	23.6080i	−1.84401	+	1.20317i
$386$	−8.76664	+	3.19080i	−0.446210	+	0.162407i
$387$	−2.07221	−	7.73360i	−0.105336	−	0.393121i
$388$	2.39072	+	0.640592i	0.121370	+	0.0325211i
$389$	9.78508	−	11.6614i	0.496123	−	0.591257i	−0.458641	−	0.888622i	$-0.651663\pi$
$389$	9.78508	−	11.6614i	0.496123	−	0.591257i	0.954764	+	0.297365i	$0.0961079\pi$
$390$	−3.89772	+	12.8478i	−0.197369	+	0.650575i
$391$	12.2686	+	21.2498i	0.620448	+	1.07465i
$392$	3.90911	−	1.04744i	0.197440	−	0.0529039i
$393$	1.54044	−	3.30348i	0.0777049	−	0.166639i
$394$	−3.10785	−	17.6255i	−0.156571	−	0.887961i
$395$	10.6726	+	6.63704i	0.536996	+	0.333946i
$396$	−5.46249	−	1.98818i	−0.274501	−	0.0999100i
$397$	−0.317209	+	3.62572i	−0.0159203	+	0.181970i	0.984071	+	0.177776i	$0.0568903\pi$
$397$	−0.317209	+	3.62572i	−0.0159203	+	0.181970i	−0.999991	+	0.00419329i	$0.998665\pi$
$398$	5.72005	−	5.72005i	0.286720	−	0.286720i
$399$	7.98226	−	12.0904i	0.399613	−	0.605275i
$400$	3.61163	+	3.45776i	0.180582	+	0.172888i
$401$	10.4920	+	12.5038i	0.523944	+	0.624412i	0.961509	−	0.274775i	$-0.0886033\pi$
$401$	10.4920	+	12.5038i	0.523944	+	0.624412i	−0.437565	+	0.899187i	$0.644159\pi$
$402$	−0.743809	−	1.59510i	−0.0370978	−	0.0795565i
$403$	−18.3451	+	12.8454i	−0.913835	+	0.639874i
$404$	11.0804	−	1.95377i	0.551270	−	0.0972038i
$405$	0.0732220	−	2.23487i	0.00363843	−	0.111052i
$406$	11.2761	−	19.5308i	0.559624	−	0.969296i
$407$	−1.46319	+	5.46069i	−0.0725275	+	0.270676i
$408$	−0.292005	−	3.33763i	−0.0144564	−	0.165237i
$409$	16.1012	+	13.5105i	0.796153	+	0.668052i	0.947260	−	0.320466i	$-0.103839\pi$
$409$	16.1012	+	13.5105i	0.796153	+	0.668052i	−0.151107	+	0.988517i	$0.548284\pi$
$410$	−7.84506	+	10.4576i	−0.387440	+	0.516462i
$411$	−0.360789	−	0.208301i	−0.0177964	−	0.0102748i
$412$	0.379433	+	0.176933i	0.0186933	+	0.00871684i
$413$	−14.1293	−	9.89343i	−0.695256	−	0.486824i
$414$	1.27174	−	7.21241i	0.0625027	−	0.354471i
$415$	30.7831	−	1.67980i	1.51108	−	0.0824579i
$416$	4.59957	−	3.85950i	0.225513	−	0.189228i
$417$	−2.93670	−	2.93670i	−0.143811	−	0.143811i
$418$	18.9579	−	16.8119i	0.927263	−	0.822295i
$419$		−	13.0627i		−	0.638157i	−0.947728	−	0.319079i	$-0.896627\pi$
$419$		−	13.0627i		−	0.638157i	0.947728	−	0.319079i	$-0.103373\pi$
$420$	2.31185	+	7.06331i	0.112807	+	0.344654i
$421$	2.00687	−	5.51384i	0.0978090	−	0.268728i	−0.881132	−	0.472870i	$-0.843218\pi$
$421$	2.00687	−	5.51384i	0.0978090	−	0.268728i	0.978941	+	0.204142i	$0.0654404\pi$
$422$	10.0850	+	14.4028i	0.490928	+	0.701118i
$423$	−6.36214	+	9.08608i	−0.309338	+	0.441780i
$424$	2.97287	+	8.16789i	0.144375	+	0.396668i
$425$	8.05827	−	14.6864i	0.390883	−	0.712396i
$426$	−2.03703	+	1.17608i	−0.0986944	+	0.0569812i
$427$	3.22139	−	0.281835i	0.155894	−	0.0136390i
$428$	16.5339	−	1.44653i	0.799195	−	0.0699205i
$429$	−30.2273	+	17.4517i	−1.45939	+	0.842578i
$430$	−14.0839	+	11.0525i	−0.679185	+	0.532998i
$431$	1.69668	+	4.66158i	0.0817261	+	0.224540i	0.973825	−	0.227300i	$-0.0729898\pi$
$431$	1.69668	+	4.66158i	0.0817261	+	0.224540i	−0.892099	+	0.451841i	$0.850768\pi$
$432$	−0.573576	+	0.819152i	−0.0275962	+	0.0394115i
$433$	−6.32309	−	9.03031i	−0.303868	−	0.433969i	0.637957	−	0.770072i	$-0.279780\pi$
$433$	−6.32309	−	9.03031i	−0.303868	−	0.433969i	−0.941825	+	0.336103i	$0.890891\pi$
$434$	−4.24000	+	11.6493i	−0.203527	+	0.559185i
$435$	13.5334	+	6.85894i	0.648879	+	0.328861i
$436$			15.6608i			0.750016i
$437$	25.0064	+	19.8436i	1.19622	+	0.949249i
$438$	−2.76959	−	2.76959i	−0.132336	−	0.132336i
$439$	−22.5878	+	18.9534i	−1.07806	+	0.904597i	−0.995758	−	0.0920111i	$-0.970670\pi$
$439$	−22.5878	+	18.9534i	−1.07806	+	0.904597i	−0.0822983	+	0.996608i	$0.526226\pi$
$440$	0.708254	+	12.9791i	0.0337647	+	0.618754i
$441$	−0.702756	+	3.98553i	−0.0334646	+	0.189787i
$442$	−16.4787	−	11.5385i	−0.783811	−	0.548830i
$443$	19.3233	+	9.01062i	0.918079	+	0.428107i	0.823439	−	0.567404i	$-0.192052\pi$
$443$	19.3233	+	9.01062i	0.918079	+	0.428107i	0.0946398	+	0.995512i	$0.469830\pi$
$444$	0.842227	+	0.486260i	0.0399703	+	0.0230769i
$445$	−1.04773	+	0.149552i	−0.0496671	+	0.00708943i
$446$	−14.0568	−	11.7950i	−0.665608	−	0.558512i
$447$	0.994234	+	11.3641i	0.0470257	+	0.537506i
$448$	0.860238	−	3.21045i	0.0406424	−	0.151680i
$449$	−7.28507	+	12.6181i	−0.343804	+	0.595486i	−0.985136	−	0.171778i	$-0.945049\pi$
$449$	−7.28507	+	12.6181i	−0.343804	+	0.595486i	0.641332	+	0.767264i	$0.278382\pi$
$450$	−4.66014	+	1.81194i	−0.219681	+	0.0854157i
$451$	−33.4695	+	5.90157i	−1.57602	+	0.277894i
$452$	−7.35854	+	5.15251i	−0.346117	+	0.242354i
$453$	−3.67801	−	7.88752i	−0.172808	−	0.370588i
$454$	−9.75825	−	11.6294i	−0.457978	−	0.545796i
$455$	41.4108	+	16.6273i	1.94137	+	0.779502i
$456$	−1.94946	−	3.89867i	−0.0912918	−	0.182572i
$457$	21.7286	−	21.7286i	1.01642	−	1.01642i	0.0165585	−	0.999863i	$-0.494729\pi$
$457$	21.7286	−	21.7286i	1.01642	−	1.01642i	0.999863	−	0.0165585i	$-0.00527098\pi$
$458$	−2.50446	+	28.6261i	−0.117026	+	1.33761i
$459$	3.14833	+	1.14590i	0.146951	+	0.0534860i
$460$	−15.9485	+	3.71823i	−0.743604	+	0.173363i
$461$	3.55767	+	20.1766i	0.165697	+	0.939716i	0.948343	+	0.317248i	$0.102759\pi$
$461$	3.55767	+	20.1766i	0.165697	+	0.939716i	−0.782645	+	0.622468i	$0.786130\pi$
$462$	−8.16537	+	17.5107i	−0.379887	+	0.814671i
$463$	35.8559	−	9.60757i	1.66637	−	0.446502i	0.702240	−	0.711941i	$-0.252184\pi$
$463$	35.8559	−	9.60757i	1.66637	−	0.446502i	0.964128	+	0.265439i	$0.0855169\pi$
$464$	−3.39263	−	5.87621i	−0.157499	−	0.272796i
$465$	−7.98102	−	2.42125i	−0.370111	−	0.112283i
$466$	5.29831	−	6.31428i	0.245439	−	0.292503i
$467$	14.2514	+	3.81866i	0.659478	+	0.176706i	0.573010	−	0.819548i	$-0.305776\pi$
$467$	14.2514	+	3.81866i	0.659478	+	0.176706i	0.0864673	+	0.996255i	$0.472442\pi$
$468$	1.55403	+	5.79972i	0.0718351	+	0.268092i
$469$	−5.49695	+	2.00072i	−0.253825	+	0.0923849i
$470$	24.2717	+	5.10446i	1.11957	+	0.235451i
$471$	−9.21804	−	1.62539i	−0.424745	−	0.0748940i
$472$	−4.70337	+	2.19322i	−0.216490	+	0.100951i
$473$	−46.3647	−	4.05638i	−2.13185	−	0.186513i
$474$	5.62057			0.258162
$475$	2.72650	−	21.6233i	0.125100	−	0.992144i
$476$	−11.1357			−0.510403
$477$	−8.65901	−	0.757565i	−0.396469	−	0.0346865i
$478$	14.7214	−	6.86470i	0.673341	−	0.313984i
$479$	−17.1564	−	3.02513i	−0.783895	−	0.138222i	−0.232645	−	0.972562i	$-0.574738\pi$
$479$	−17.1564	−	3.02513i	−0.783895	−	0.138222i	−0.551250	+	0.834340i	$0.685849\pi$
$480$	2.18820	+	0.460190i	0.0998773	+	0.0210047i
$481$	5.48717	−	1.99717i	0.250193	−	0.0910629i
$482$	0.399921	+	1.49252i	0.0182159	+	0.0679826i
$483$	−23.5123	−	6.30010i	−1.06985	−	0.286665i
$484$	−14.6502	+	17.4595i	−0.665919	+	0.793611i
$485$	5.29604	+	1.60669i	0.240481	+	0.0729561i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−24.8659	+	6.66280i	−1.12678	+	0.301920i	−0.773625	−	0.633644i	$-0.781558\pi$
$487$	−24.8659	+	6.66280i	−1.12678	+	0.301920i	−0.353157	+	0.935564i	$0.614892\pi$
$488$	0.411174	−	0.881765i	0.0186130	−	0.0399156i
$489$	−0.265986	−	1.50848i	−0.0120283	−	0.0682158i
$490$	8.81305	−	2.05467i	0.398133	−	0.0928204i
$491$	7.47595	+	2.72102i	0.337385	+	0.122798i	0.505156	−	0.863028i	$-0.331435\pi$
$491$	7.47595	+	2.72102i	0.337385	+	0.122798i	−0.167771	+	0.985826i	$0.553657\pi$
$492$	−0.509552	+	5.82421i	−0.0229724	+	0.262576i
$493$	−16.0748	+	16.0748i	−0.723973	+	0.723973i
$494$	−25.4561	−	6.08023i	−1.14533	−	0.273562i
$495$	−12.0624	−	4.84331i	−0.542163	−	0.217690i
$496$	2.39751	+	2.85724i	0.107651	+	0.128294i
$497$	3.30398	+	7.08541i	0.148204	+	0.317824i
$498$	11.2937	−	7.90795i	0.506084	−	0.354364i
$499$	30.5754	−	5.39126i	1.36874	−	0.241346i	0.559504	−	0.828828i	$-0.310992\pi$
$499$	30.5754	−	5.39126i	1.36874	−	0.241346i	0.809237	+	0.587482i	$0.199881\pi$
$500$	7.81835	+	7.99209i	0.349647	+	0.357417i
$501$	7.62906	−	13.2139i	0.340841	−	0.590355i
$502$	1.40586	−	5.24672i	0.0627464	−	0.234173i
$503$	−3.48288	−	39.8095i	−0.155294	−	1.77502i	−0.530122	−	0.847921i	$-0.677854\pi$
$503$	−3.48288	−	39.8095i	−0.155294	−	1.77502i	0.374828	−	0.927094i	$-0.377702\pi$
$504$	2.54611	+	2.13644i	0.113413	+	0.0951644i
$505$	24.9063	−	3.55510i	1.10831	−	0.158200i
$506$	−36.8693	−	21.2865i	−1.63904	−	0.946300i
$507$	20.8920	+	9.74212i	0.927848	+	0.432663i
$508$	−10.1599	−	7.11402i	−0.450772	−	0.315634i
$509$	0.456928	−	2.59137i	0.0202530	−	0.114860i	−0.973005	−	0.230783i	$-0.925871\pi$
$509$	0.456928	−	2.59137i	0.0202530	−	0.114860i	0.993258	+	0.115922i	$0.0369824\pi$
$510$	−0.408205	−	7.48055i	−0.0180756	−	0.331245i
$511$	−9.97258	+	8.36799i	−0.441161	+	0.370178i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	4.35727	−	0.119162i	0.192378	−	0.00526114i
$514$		−	5.74948i		−	0.253599i
$515$	0.835028	+	0.423204i	0.0367957	+	0.0186486i
$516$	−2.73835	+	7.52356i	−0.120549	+	0.331206i
$517$	36.9835	+	52.8180i	1.62653	+	2.32293i
$518$	1.85401	−	2.64780i	0.0814606	−	0.116338i
$519$	7.16306	+	19.6803i	0.314423	+	0.863871i
$520$	10.5620	−	8.28869i	0.463176	−	0.363483i
$521$	1.26284	−	0.729102i	0.0553261	−	0.0319426i	−0.472082	−	0.881555i	$-0.656497\pi$
$521$	1.26284	−	0.729102i	0.0553261	−	0.0319426i	0.527408	+	0.849612i	$0.323164\pi$
$522$	6.75944	−	0.591374i	0.295853	−	0.0258838i
$523$	−18.8096	+	1.64563i	−0.822486	+	0.0719582i	−0.490626	−	0.871370i	$-0.663232\pi$
$523$	−18.8096	+	1.64563i	−0.822486	+	0.0719582i	−0.331860	+	0.943329i	$0.607676\pi$
$524$	−3.15665	+	1.82250i	−0.137899	+	0.0796161i
$525$	4.64949	+	15.9549i	0.202920	+	0.696327i
$526$	0.110396	+	0.303311i	0.00481350	+	0.0132250i
$527$	7.16767	−	10.2365i	0.312228	−	0.445908i
$528$	3.33424	+	4.76178i	0.145104	+	0.207230i
$529$	10.4782	−	28.7886i	0.455574	−	1.25168i
$530$	6.04590	+	18.4718i	0.262617	+	0.802365i
$531$		−	5.18959i		−	0.225209i
$532$	−13.4734	+	5.32541i	−0.584147	+	0.230886i
$533$	24.8223	+	24.8223i	1.07517	+	1.07517i
$534$	−0.362575	+	0.304236i	−0.0156901	+	0.0131656i
$535$	37.0570	−	2.02216i	1.60211	−	0.0874254i
$536$	−0.305621	+	1.73326i	−0.0132008	+	0.0748656i
$537$	−1.19250	−	0.835000i	−0.0514603	−	0.0360329i
$538$	14.0465	+	6.54997i	0.605586	+	0.282389i
$539$	20.3737	+	11.7628i	0.877558	+	0.506658i
$540$	−1.34185	+	1.78870i	−0.0577439	+	0.0769733i
$541$	−19.7042	−	16.5338i	−0.847151	−	0.710844i	0.112009	−	0.993707i	$-0.464271\pi$
$541$	−19.7042	−	16.5338i	−0.847151	−	0.710844i	−0.959160	+	0.282863i	$0.908716\pi$
$542$	0.241085	+	2.75562i	0.0103555	+	0.118364i
$543$	1.38971	−	5.18648i	0.0596383	−	0.222573i
$544$	−1.67519	+	2.90152i	−0.0718232	+	0.124401i
$545$	−1.14671	+	34.9998i	−0.0491198	+	1.49923i
$546$	19.6534	−	3.46542i	0.841087	−	0.148306i
$547$	−3.72785	+	2.61027i	−0.159391	+	0.111607i	−0.650551	−	0.759463i	$-0.725462\pi$
$547$	−3.72785	+	2.61027i	−0.159391	+	0.111607i	0.491160	+	0.871069i	$0.336573\pi$
$548$	0.176064	+	0.377570i	0.00752108	+	0.0161290i
$549$	0.625381	+	0.745300i	0.0266906	+	0.0318086i
$550$	0.632499	+	29.0584i	0.0269699	+	1.23906i
$551$	−11.7620	+	27.1369i	−0.501078	+	1.15607i
$552$	−5.17862	+	5.17862i	−0.220417	+	0.220417i
$553$	1.62817	−	18.6100i	0.0692367	−	0.791380i
$554$	5.64125	+	2.05325i	0.239674	+	0.0872340i
$555$	1.84666	+	1.14840i	0.0783865	+	0.0487467i
$556$	0.721182	+	4.09003i	0.0305849	+	0.173456i
$557$	1.38999	−	2.98085i	0.0588959	−	0.126303i	−0.874657	−	0.484742i	$-0.838913\pi$
$557$	1.38999	−	2.98085i	0.0588959	−	0.126303i	0.933553	+	0.358440i	$0.116691\pi$
$558$	−3.60276	+	0.965358i	−0.152517	+	0.0408669i
$559$	24.0365	+	41.6325i	1.01664	+	1.76087i
$560$	2.15759	−	7.11195i	0.0911750	−	0.300535i
$561$	12.5189	−	14.9195i	0.528549	−	0.629900i
$562$	−27.1846	−	7.28410i	−1.14672	−	0.307261i
$563$	2.49767	+	9.32145i	0.105264	+	0.392852i	0.998375	−	0.0569849i	$-0.0181487\pi$
$563$	2.49767	+	9.32145i	0.105264	+	0.392852i	−0.893111	+	0.449837i	$0.851482\pi$
$564$	10.4231	−	3.79371i	0.438893	−	0.159744i
$565$	−16.8227	+	10.9764i	−0.707734	+	0.461779i
$566$	−17.7425	−	3.12848i	−0.745772	−	0.131500i
$567$	−3.01230	+	1.40466i	−0.126505	+	0.0589901i
$568$	2.34321	+	0.205004i	0.0983188	+	0.00860178i
$569$	5.42172			0.227290			0.113645	−	0.993521i	$-0.463747\pi$
$569$	5.42172			0.227290			0.113645	+	0.993521i	$0.463747\pi$
$570$	−4.07132	−	8.85575i	−0.170529	−	0.370927i
$571$	8.11442			0.339578			0.169789	−	0.985480i	$-0.445691\pi$
$571$	8.11442			0.339578			0.169789	+	0.985480i	$0.445691\pi$
$572$	34.7707	+	3.04204i	1.45383	+	0.127194i
$573$	15.7346	−	7.33717i	0.657323	−	0.306515i
$574$	19.1367	+	3.37431i	0.798750	+	0.140841i
$575$	−35.9151	+	7.14197i	−1.49777	+	0.297841i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	4.34835	+	16.2282i	0.181024	+	0.675591i	0.995447	+	0.0953188i	$0.0303871\pi$
$577$	4.34835	+	16.2282i	0.181024	+	0.675591i	−0.814423	+	0.580272i	$0.802946\pi$
$578$	−5.57816	−	1.49466i	−0.232021	−	0.0621698i
$579$	−5.99673	+	7.14663i	−0.249216	+	0.297004i
$580$	−7.15182	−	13.3810i	−0.296963	−	0.555615i
$581$	−22.9121	−	39.6849i	−0.950554	−	1.64641i
$582$	2.39072	−	0.640592i	0.0990985	−	0.0265534i
$583$	−21.3539	+	45.7936i	−0.884388	+	1.89658i
$584$	0.680145	+	3.85729i	0.0281446	+	0.159616i
$585$	3.04839	+	13.0754i	0.126035	+	0.540602i
$586$	−20.5538	−	7.48099i	−0.849071	−	0.309037i
$587$	1.39720	−	15.9701i	0.0576686	−	0.659155i	−0.911263	−	0.411825i	$-0.864891\pi$
$587$	1.39720	−	15.9701i	0.0576686	−	0.659155i	0.968931	−	0.247330i	$-0.0795530\pi$
$588$	2.86167	−	2.86167i	0.118013	−	0.118013i
$589$	3.77701	−	15.8133i	0.155629	−	0.651574i
$590$	−10.6720	+	4.55716i	−0.439359	+	0.187615i
$591$	−11.5042	−	13.7102i	−0.473221	−	0.563963i
$592$	−0.411005	−	0.881403i	−0.0168922	−	0.0362254i
$593$	−8.08217	+	5.65919i	−0.331895	+	0.232395i	−0.727631	−	0.685969i	$-0.759378\pi$
$593$	−8.08217	+	5.65919i	−0.331895	+	0.232395i	0.395736	+	0.918364i	$0.370490\pi$
$594$	−5.72475	+	1.00943i	−0.234889	+	0.0414173i
$595$	−24.8868	−	0.815377i	−1.02026	−	0.0334272i
$596$	5.70378	−	9.87923i	0.233636	−	0.404669i
$597$	2.09368	−	7.81374i	0.0856888	−	0.319795i
$598$	3.83256	+	43.8063i	0.156725	+	1.79137i
$599$	−32.9600	−	27.6568i	−1.34671	−	1.13002i	−0.979847	−	0.199749i	$-0.935987\pi$
$599$	−32.9600	−	27.6568i	−1.34671	−	1.13002i	−0.366863	−	0.930275i	$-0.619568\pi$
$600$	4.85665	+	1.18869i	0.198272	+	0.0485281i
$601$	−6.11282	−	3.52924i	−0.249347	−	0.143961i	0.370118	−	0.928985i	$-0.379317\pi$
$601$	−6.11282	−	3.52924i	−0.249347	−	0.143961i	−0.619465	+	0.785024i	$0.712651\pi$
$602$	24.1177	+	11.2463i	0.982964	+	0.458364i
$603$	−1.44171	−	1.00950i	−0.0587109	−	0.0411098i
$604$	−1.51124	+	8.57069i	−0.0614917	+	0.348737i
$605$	−34.0197	+	37.9469i	−1.38310	+	1.54276i
$606$	8.61901	−	7.23221i	0.350123	−	0.293788i
$607$	−34.3717	−	34.3717i	−1.39510	−	1.39510i	−0.813401	−	0.581703i	$-0.802387\pi$
$607$	−34.3717	−	34.3717i	−1.39510	−	1.39510i	−0.581703	−	0.813401i	$-0.697613\pi$
$608$	−0.639280	+	4.31177i	−0.0259262	+	0.174865i
$609$		−	22.5522i		−	0.913861i
$610$	0.983484	−	1.94052i	0.0398201	−	0.0785694i
$611$	22.7786	−	62.5837i	0.921524	−	2.53187i
$612$	−1.92170	−	2.74447i	−0.0776801	−	0.110939i
$613$	7.05776	−	10.0795i	0.285060	−	0.407108i	−0.650928	−	0.759139i	$-0.725620\pi$
$613$	7.05776	−	10.0795i	0.285060	−	0.407108i	0.935988	+	0.352031i	$0.114509\pi$
$614$	5.96973	+	16.4017i	0.240919	+	0.661919i
$615$	−1.56524	+	12.9790i	−0.0631167	+	0.523365i
$616$	16.7324	−	9.66045i	0.674167	−	0.389231i
$617$	24.8594	−	2.17491i	1.00080	−	0.0875586i	0.425038	−	0.905176i	$-0.360261\pi$
$617$	24.8594	−	2.17491i	1.00080	−	0.0875586i	0.575762	+	0.817617i	$0.304705\pi$
$618$	0.417065	−	0.0364885i	0.0167768	−	0.00146778i
$619$	−9.63914	+	5.56516i	−0.387430	+	0.223683i	−0.681046	−	0.732241i	$-0.738475\pi$
$619$	−9.63914	+	5.56516i	−0.387430	+	0.223683i	0.293616	+	0.955923i	$0.405141\pi$
$620$	5.14890	+	6.56110i	0.206785	+	0.263500i
$621$	−2.50484	−	6.88200i	−0.100516	−	0.276165i
$622$	−10.1457	+	14.4896i	−0.406806	+	0.580979i
$623$	0.902313	+	1.28864i	0.0361504	+	0.0516281i
$624$	2.05360	−	5.64221i	0.0822097	−	0.225869i
$625$	16.8878	+	18.4337i	0.675511	+	0.737350i
$626$			25.7108i			1.02761i
$627$	8.01213	−	24.0385i	0.319974	−	0.960004i
$628$	6.61869	+	6.61869i	0.264115	+	0.264115i
$629$	−2.49601	+	2.09440i	−0.0995226	+	0.0835094i
$630$	5.53378	+	4.96109i	0.220471	+	0.197654i
$631$	−1.98440	+	11.2541i	−0.0789978	+	0.448019i	0.919493	+	0.393106i	$0.128599\pi$
$631$	−1.98440	+	11.2541i	−0.0789978	+	0.448019i	−0.998491	+	0.0549132i	$0.982512\pi$
$632$	−4.60411	−	3.22383i	−0.183141	−	0.128237i
$633$	15.9352	+	7.43072i	0.633368	+	0.295345i
$634$	15.2325	+	8.79450i	0.604961	+	0.349274i
$635$	−22.1851	−	16.6428i	−0.880389	−	0.660451i
$636$	6.65852	+	5.58717i	0.264028	+	0.221546i
$637$	−2.11784	−	24.2071i	−0.0839121	−	0.959119i
$638$	10.2086	−	38.0992i	0.404164	−	1.50836i
$639$	−1.17608	+	2.03703i	−0.0465250	+	0.0805836i
$640$	−1.52852	−	1.63207i	−0.0604199	−	0.0645131i
$641$	18.5429	−	3.26961i	0.732401	−	0.129142i	0.205004	−	0.978761i	$-0.434279\pi$
$641$	18.5429	−	3.26961i	0.732401	−	0.129142i	0.527397	+	0.849619i	$0.323168\pi$
$642$	13.5955	−	9.51967i	0.536572	−	0.375711i
$643$	−13.9706	−	29.9601i	−0.550948	−	1.18151i	−0.962789	−	0.270256i	$-0.912892\pi$
$643$	−13.9706	−	29.9601i	−0.550948	−	1.18151i	0.411841	−	0.911256i	$-0.364886\pi$
$644$	15.6466	+	18.6468i	0.616561	+	0.734789i
$645$	−6.67075	+	16.6137i	−0.262661	+	0.654163i
$646$	14.5082	−	1.67006i	0.570816	−	0.0657078i
$647$	−12.2648	+	12.2648i	−0.482178	+	0.482178i	−0.905827	−	0.423649i	$-0.860749\pi$
$647$	−12.2648	+	12.2648i	−0.482178	+	0.482178i	0.423649	+	0.905827i	$0.360749\pi$
$648$	−0.0871557	+	0.996195i	−0.00342380	+	0.0391342i
$649$	−28.3481	−	10.3179i	−1.11276	−	0.405012i
$650$	24.2117	−	17.7508i	0.949661	−	0.696242i
$651$	2.15271	+	12.2086i	0.0843712	+	0.478493i
$652$	−0.647345	+	1.38824i	−0.0253520	+	0.0543675i
$653$	−13.3452	+	3.57583i	−0.522238	+	0.139933i	−0.510302	−	0.859996i	$-0.670466\pi$
$653$	−13.3452	+	3.57583i	−0.522238	+	0.139933i	−0.0119363	+	0.999929i	$0.503800\pi$
$654$	7.83040	+	13.5626i	0.306193	+	0.530341i
$655$	−7.18816	+	3.84190i	−0.280864	+	0.150116i
$656$	3.75803	−	4.47865i	0.146726	−	0.174862i
$657$	−3.78334	−	1.01374i	−0.147602	−	0.0395498i
$658$	−9.54181	−	35.6105i	−0.371979	−	1.38824i
$659$	−5.99828	+	2.18320i	−0.233660	+	0.0850452i	−0.456196	−	0.889879i	$-0.650789\pi$
$659$	−5.99828	+	2.18320i	−0.233660	+	0.0850452i	0.222537	+	0.974924i	$0.428566\pi$
$660$	7.10291	+	10.8861i	0.276480	+	0.423741i
$661$	14.2406	+	2.51101i	0.553896	+	0.0976668i	0.443588	−	0.896231i	$-0.353705\pi$
$661$	14.2406	+	2.51101i	0.553896	+	0.0976668i	0.110308	+	0.993897i	$0.464816\pi$
$662$	1.69528	−	0.790520i	0.0658888	−	0.0307244i
$663$	−20.0402	−	1.75329i	−0.778297	−	0.0680922i
$664$	−13.7871			−0.535043
$665$	−30.5013	+	10.9150i	−1.18279	+	0.423267i
$666$	0.972520			0.0376844
$667$	49.5039	+	4.33103i	1.91680	+	0.167698i
$668$	−13.8286	+	6.44836i	−0.535043	+	0.249495i
$669$	−18.0711	−	3.18642i	−0.698668	−	0.123194i
$670$	−0.809936	+	3.85124i	−0.0312906	+	0.148786i
$671$	5.31457	−	1.93434i	0.205167	−	0.0746745i
$672$	−0.860238	−	3.21045i	−0.0331844	−	0.123846i
$673$	4.95733	+	1.32831i	0.191091	+	0.0512027i	0.353095	−	0.935587i	$-0.385129\pi$
$673$	4.95733	+	1.32831i	0.191091	+	0.0512027i	−0.162004	+	0.986790i	$0.551796\pi$
$674$	3.83317	−	4.56819i	0.147648	−	0.175960i
$675$	−3.12983	+	3.89925i	−0.120467	+	0.150082i
$676$	−11.5259	−	19.9635i	−0.443304	−	0.767825i
$677$	−35.8719	+	9.61184i	−1.37867	+	0.369413i	−0.870637	−	0.491925i	$-0.836293\pi$
$677$	−35.8719	+	9.61184i	−1.37867	+	0.369413i	−0.508031	+	0.861339i	$0.669627\pi$
$678$	−3.79643	+	8.14147i	−0.145801	+	0.312671i
$679$	−1.42849	−	8.10138i	−0.0548205	−	0.310902i
$680$	−3.95629	+	6.36185i	−0.151717	+	0.243966i
$681$	−14.2656	−	5.19226i	−0.546660	−	0.198968i
$682$	−1.88970	+	21.5994i	−0.0723604	+	0.827083i
$683$	31.6489	−	31.6489i	1.21101	−	1.21101i	0.240319	−	0.970694i	$-0.422748\pi$
$683$	31.6489	−	31.6489i	1.21101	−	1.21101i	0.970694	−	0.240319i	$-0.0772520\pi$
$684$	−3.63762	−	2.40162i	−0.139088	−	0.0918281i
$685$	0.365833	+	0.856712i	0.0139778	+	0.0327333i
$686$	6.30887	+	7.51862i	0.240874	+	0.287062i
$687$	12.1441	+	26.0432i	0.463328	+	0.993609i
$688$	6.55847	−	4.59229i	0.250039	−	0.175079i
$689$	51.3972	−	9.06271i	1.95808	−	0.345262i
$690$	−11.9527	+	11.1943i	−0.455032	+	0.426162i
$691$	−16.0067	+	27.7243i	−0.608922	+	1.05468i	0.382497	+	0.923957i	$0.375064\pi$
$691$	−16.0067	+	27.7243i	−0.608922	+	1.05468i	−0.991418	+	0.130727i	$0.958269\pi$
$692$	5.42054	−	20.2297i	0.206058	−	0.769020i
$693$	1.68393	+	19.2474i	0.0639671	+	0.731148i
$694$	8.15220	+	6.84051i	0.309453	+	0.259662i
$695$	1.31227	+	9.19348i	0.0497772	+	0.348729i
$696$	−5.87621	−	3.39263i	−0.222737	−	0.128597i
$697$	−17.7526	−	8.27819i	−0.672429	−	0.313559i
$698$	−20.3209	−	14.2289i	−0.769159	−	0.538571i
$699$	1.43133	−	8.11748i	0.0541379	−	0.307031i
$700$	5.34269	−	15.7363i	0.201935	−	0.594776i
$701$	2.02252	−	1.69710i	0.0763896	−	0.0640985i	−0.603793	−	0.797141i	$-0.706345\pi$
$701$	2.02252	−	1.69710i	0.0763896	−	0.0640985i	0.680183	+	0.733042i	$0.261900\pi$
$702$	4.24569	+	4.24569i	0.160243	+	0.160243i
$703$	−2.01841	+	3.72776i	−0.0761256	+	0.140595i
$704$		−	5.81306i		−	0.219088i
$705$	23.5721	−	7.71524i	0.887777	−	0.290573i
$706$	−3.13219	+	8.60563i	−0.117882	+	0.323877i
$707$	−21.4495	−	30.6331i	−0.806692	−	1.15208i
$708$	−2.97663	+	4.25106i	−0.111868	+	0.159765i
$709$	−17.1595	−	47.1453i	−0.644438	−	1.77058i	−0.637315	−	0.770603i	$-0.719955\pi$
$709$	−17.1595	−	47.1453i	−0.644438	−	1.77058i	−0.00712235	−	0.999975i	$-0.502267\pi$
$710$	5.22175	+	0.629732i	0.195969	+	0.0236334i
$711$	4.86756	−	2.81029i	0.182548	−	0.105394i
$712$	0.471507	−	0.0412515i	0.0176705	−	0.00154596i
$713$	−27.2123	+	2.38077i	−1.01911	+	0.0891605i
$714$	−9.64378	+	5.56784i	−0.360910	+	0.208371i
$715$	77.4851	+	9.34453i	2.89778	+	0.349466i
$716$	0.497905	+	1.36798i	0.0186076	+	0.0511240i
$717$	9.31675	−	13.3057i	0.347940	−	0.496910i
$718$	−14.3437	−	20.4849i	−0.535302	−	0.764490i
$719$	−4.12651	+	11.3375i	−0.153893	+	0.422817i	−0.992549	−	0.121844i	$-0.961119\pi$
$719$	−4.12651	+	11.3375i	−0.153893	+	0.422817i	0.838657	+	0.544661i	$0.183342\pi$
$720$	2.12513	−	0.695564i	0.0791990	−	0.0259221i
$721$		−	1.39150i		−	0.0518220i
$722$	16.7552	−	8.95889i	0.623566	−	0.333416i
$723$	1.09260	+	1.09260i	0.0406344	+	0.0406344i
$724$	−4.11323	+	3.45141i	−0.152867	+	0.128271i
$725$	−15.0036	−	30.4284i	−0.557219	−	1.13008i
$726$	−3.95774	+	22.4454i	−0.146885	+	0.833028i
$727$	23.4891	+	16.4473i	0.871163	+	0.609995i	0.921345	−	0.388745i	$-0.127091\pi$
$727$	23.4891	+	16.4473i	0.871163	+	0.609995i	−0.0501824	+	0.998740i	$0.515980\pi$
$728$	−18.0868	−	8.43401i	−0.670341	−	0.312585i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	1.23760	+	8.67034i	0.0458055	+	0.320904i
$731$	−20.5488	−	17.2425i	−0.760024	−	0.637736i
$732$	−0.0847956	−	0.969218i	−0.00313413	−	0.0358233i
$733$	9.38772	−	35.0355i	0.346743	−	1.29406i	−0.543819	−	0.839203i	$-0.683022\pi$
$733$	9.38772	−	35.0355i	0.346743	−	1.29406i	0.890562	−	0.454861i	$-0.150311\pi$
$734$	−17.3243	+	30.0065i	−0.639451	+	1.10756i
$735$	6.60499	−	6.18592i	0.243629	−	0.228171i
$736$	7.21241	−	1.27174i	0.265853	−	0.0468771i
$737$	−8.38075	+	5.86826i	−0.308709	+	0.216160i
$738$	2.47082	+	5.29869i	0.0909521	+	0.195047i
$739$	7.41306	+	8.83454i	0.272694	+	0.324984i	0.884959	−	0.465668i	$-0.154186\pi$
$739$	7.41306	+	8.83454i	0.272694	+	0.324984i	−0.612265	+	0.790652i	$0.709742\pi$
$740$	−0.854004	−	1.99991i	−0.0313938	−	0.0735183i
$741$	−25.0858	+	7.46244i	−0.921549	+	0.274140i
$742$	20.4283	−	20.4283i	0.749945	−	0.749945i
$743$	3.19869	−	36.5612i	0.117349	−	1.34130i	−0.677961	−	0.735098i	$-0.737136\pi$
$743$	3.19869	−	36.5612i	0.117349	−	1.34130i	0.795309	−	0.606204i	$-0.207308\pi$
$744$	3.50492	+	1.27569i	0.128497	+	0.0467689i
$745$	13.4706	−	21.6611i	0.493524	−	0.793603i
$746$	4.29137	+	24.3376i	0.157118	+	0.891062i
$747$	5.82668	−	12.4953i	0.213187	−	0.457181i
$748$	−18.8124	+	5.04076i	−0.687848	+	0.184308i
$749$	−27.5818	−	47.7731i	−1.00782	−	1.74559i
$750$	10.7669	+	3.01218i	0.393153	+	0.109989i
$751$	−12.8999	+	15.3735i	−0.470725	+	0.560988i	−0.948207	−	0.317653i	$-0.897105\pi$
$751$	−12.8999	+	15.3735i	−0.470725	+	0.560988i	0.477482	+	0.878642i	$0.341550\pi$
$752$	−10.7141	−	2.87084i	−0.390703	−	0.104689i
$753$	−1.40586	−	5.24672i	−0.0512322	−	0.191201i
$754$	−38.2839	+	13.9342i	−1.39422	+	0.507453i
$755$	−4.00500	+	19.0437i	−0.145757	+	0.693072i
$756$	3.27321	+	0.577155i	0.119046	+	0.0209909i
$757$	−8.15202	+	3.80135i	−0.296290	+	0.138162i	−0.565079	−	0.825037i	$-0.691154\pi$
$757$	−8.15202	+	3.80135i	−0.296290	+	0.138162i	0.268789	+	0.963199i	$0.413377\pi$
$758$	−11.5773	−	1.01288i	−0.420506	−	0.0367895i
$759$	−42.5730			−1.54530
$760$	−1.74442	+	9.58942i	−0.0632769	+	0.347845i
$761$	−5.39421			−0.195540			−0.0977701	−	0.995209i	$-0.531171\pi$
$761$	−5.39421			−0.195540			−0.0977701	+	0.995209i	$0.531171\pi$
$762$	−12.3557	−	1.08099i	−0.447601	−	0.0391600i
$763$	47.1750	−	21.9981i	1.70785	−	0.796383i
$764$	−17.0975	−	3.01475i	−0.618565	−	0.109070i
$765$	−4.09379	−	6.27425i	−0.148011	−	0.226846i
$766$	20.8775	−	7.59877i	0.754333	−	0.274555i
$767$	8.06479	+	30.0982i	0.291203	+	1.08678i
$768$	−0.965926	−	0.258819i	−0.0348548	−	0.00933933i
$769$	−17.8294	+	21.2482i	−0.642943	+	0.766230i	−0.984832	−	0.173510i	$-0.944489\pi$
$769$	−17.8294	+	21.2482i	−0.642943	+	0.766230i	0.341889	+	0.939740i	$0.388933\pi$
$770$	38.1021	−	20.3647i	1.37310	−	0.733891i
$771$	−2.87474	−	4.97920i	−0.103531	−	0.179321i
$772$	9.01137	−	2.41459i	0.324326	−	0.0869030i
$773$	−3.02406	+	6.48511i	−0.108768	+	0.233253i	−0.953156	−	0.302478i	$-0.902186\pi$
$773$	−3.02406	+	6.48511i	−0.108768	+	0.233253i	0.844389	+	0.535731i	$0.179964\pi$
$774$	1.39030	+	7.88477i	0.0499732	+	0.283412i
$775$	11.0267	+	15.0402i	0.396091	+	0.540260i
$776$	−2.32579	−	0.846519i	−0.0834911	−	0.0303883i
$777$	0.281720	−	3.22007i	0.0101066	−	0.115519i
$778$	−10.7642	+	10.7642i	−0.385915	+	0.385915i
$779$	−25.4384	−	1.52623i	−0.911424	−	0.0546829i
$780$	5.00265	−	12.4592i	0.179124	−	0.446112i
$781$	8.78899	+	10.4743i	0.314495	+	0.374800i
$782$	−10.3698	−	22.2382i	−0.370824	−	0.795236i
$783$	5.55816	−	3.89187i	0.198632	−	0.139084i
$784$	−3.98553	+	0.702756i	−0.142340	+	0.0250984i
$785$	14.3073	+	15.2765i	0.510649	+	0.545243i
$786$	−1.82250	+	3.15665i	−0.0650063	+	0.112594i
$787$	9.60446	−	35.8443i	0.342362	−	1.27771i	−0.553302	−	0.832981i	$-0.686632\pi$
$787$	9.60446	−	35.8443i	0.342362	−	1.27771i	0.895664	−	0.444732i	$-0.146701\pi$
$788$	1.55986	+	17.8293i	0.0555678	+	0.635143i
$789$	0.247261	+	0.207477i	0.00880274	+	0.00738638i
$790$	−10.0535	−	7.54196i	−0.357688	−	0.268331i
$791$	25.8571	+	14.9286i	0.919374	+	0.530801i
$792$	5.26842	+	2.45671i	0.187205	+	0.0872953i
$793$	−4.78526	−	3.35067i	−0.169929	−	0.118986i
$794$	0.632004	−	3.58427i	0.0224290	−	0.127201i
$795$	14.4718	+	12.9741i	0.513263	+	0.460145i
$796$	−6.19682	+	5.19975i	−0.219640	+	0.184300i
$797$	−27.3325	−	27.3325i	−0.968166	−	0.968166i	0.0313429	−	0.999509i	$-0.490022\pi$
$797$	−27.3325	−	27.3325i	−0.968166	−	0.968166i	−0.999509	+	0.0313429i	$0.990022\pi$
$798$	−9.00563	+	11.3487i	−0.318796	+	0.401738i
$799$			37.1626i			1.31472i
$800$	−3.29653	−	3.75938i	−0.116550	−	0.132914i
$801$	−0.161881	+	0.444764i	−0.00571977	+	0.0157150i
$802$	−9.36227	−	13.3707i	−0.330593	−	0.472136i
$803$	−13.0595	+	18.6509i	−0.460861	+	0.658177i
$804$	0.601956	+	1.65386i	0.0212294	+	0.0583272i
$805$	33.6027	+	42.8189i	1.18434	+	1.50917i
$806$	19.3948	−	11.1976i	0.683154	−	0.394419i
$807$	15.4396	−	1.35079i	0.543499	−	0.0475500i
$808$	−11.2085	+	0.980617i	−0.394314	+	0.0344980i
$809$	41.8447	−	24.1591i	1.47118	−	0.849387i	0.471706	−	0.881756i	$-0.343639\pi$
$809$	41.8447	−	24.1591i	1.47118	−	0.849387i	0.999476	+	0.0323691i	$0.0103052\pi$
$810$	−0.267725	+	2.21998i	−0.00940690	+	0.0780022i
$811$	−8.87539	−	24.3849i	−0.311657	−	0.856271i	−0.992323	−	0.123676i	$-0.960532\pi$
$811$	−8.87539	−	24.3849i	−0.311657	−	0.856271i	0.680666	−	0.732594i	$-0.261691\pi$
$812$	−12.9354	+	18.4737i	−0.453944	+	0.648299i
$813$	1.58659	+	2.26589i	0.0556443	+	0.0794683i
$814$	1.93355	−	5.31238i	0.0677709	−	0.186199i
$815$	−1.54838	+	3.05513i	−0.0542374	+	0.107016i
$816$			3.35038i			0.117287i
$817$	−33.1085	−	11.0352i	−1.15832	−	0.386073i
$818$	−14.8624	−	14.8624i	−0.519652	−	0.519652i
$819$	15.2876	−	12.8278i	0.534193	−	0.448241i
$820$	8.72664	−	9.73401i	0.304747	−	0.339927i
$821$	4.06008	−	23.0259i	0.141698	−	0.803609i	−0.828261	−	0.560342i	$-0.810670\pi$
$821$	4.06008	−	23.0259i	0.141698	−	0.803609i	0.969959	−	0.243267i	$-0.0782191\pi$
$822$	0.341261	+	0.238954i	0.0119028	+	0.00833446i
$823$	3.89304	+	1.81536i	0.135703	+	0.0632793i	0.489284	−	0.872125i	$-0.337258\pi$
$823$	3.89304	+	1.81536i	0.135703	+	0.0632793i	−0.353581	+	0.935404i	$0.615036\pi$
$824$	−0.362569	−	0.209329i	−0.0126307	−	0.00729232i
$825$	15.0770	+	24.8491i	0.524913	+	0.865134i
$826$	13.2132	+	11.0872i	0.459748	+	0.385774i
$827$	−0.904986	−	10.3440i	−0.0314694	−	0.359697i	−0.995560	−	0.0941250i	$-0.969995\pi$
$827$	−0.904986	−	10.3440i	−0.0314694	−	0.359697i	0.964091	−	0.265572i	$-0.0855609\pi$
$828$	−1.89551	+	7.07413i	−0.0658734	+	0.245843i
$829$	4.23276	−	7.33136i	0.147010	−	0.254629i	−0.783111	−	0.621882i	$-0.786368\pi$
$829$	4.23276	−	7.33136i	0.147010	−	0.254629i	0.930121	+	0.367253i	$0.119702\pi$
$830$	−30.8123	−	1.00952i	−1.06951	−	0.0350409i
$831$	5.91208	−	1.04246i	0.205088	−	0.0361625i
$832$	−4.91845	+	3.44393i	−0.170517	+	0.119397i
$833$	5.73030	+	12.2887i	0.198543	+	0.425777i
$834$	2.66958	+	3.18148i	0.0924399	+	0.110166i
$835$	−31.3772	+	13.3987i	−1.08585	+	0.463681i
$836$	−20.3511	+	15.0956i	−0.703856	+	0.522092i
$837$	−2.63741	+	2.63741i	−0.0911621	+	0.0911621i
$838$	−1.13849	+	13.0130i	−0.0393286	+	0.449528i
$839$	22.3701	+	8.14205i	0.772301	+	0.281095i	0.697959	−	0.716138i	$-0.254092\pi$
$839$	22.3701	+	8.14205i	0.772301	+	0.281095i	0.0743426	+	0.997233i	$0.476314\pi$
$840$	−1.68744	−	7.23793i	−0.0582223	−	0.249732i
$841$	2.95892	+	16.7809i	0.102032	+	0.578652i
$842$	−2.47980	+	5.31794i	−0.0854595	+	0.183268i
$843$	−27.1846	+	7.28410i	−0.936289	+	0.250878i
$844$	−8.79129	−	15.2270i	−0.302609	−	0.524134i
$845$	−24.2971	−	45.4597i	−0.835847	−	1.56386i
$846$	7.12984	−	8.49701i	0.245129	−	0.292133i
$847$	73.1716	+	19.6063i	2.51421	+	0.673680i
$848$	−2.24968	−	8.39591i	−0.0772542	−	0.288317i
$849$	−16.9297	+	6.16190i	−0.581025	+	0.211476i
$850$	−9.30761	+	13.9282i	−0.319248	+	0.477734i
$851$	7.01422	+	1.23680i	0.240444	+	0.0423968i
$852$	2.13178	−	0.994065i	0.0730336	−	0.0340561i
$853$	−40.7451	−	3.56474i	−1.39509	−	0.122054i	−0.635319	−	0.772250i	$-0.719131\pi$
$853$	−40.7451	−	3.56474i	−1.39509	−	0.122054i	−0.759767	+	0.650195i	$0.774687\pi$
$854$	−3.23370			−0.110655
$855$	−7.95374	−	5.63365i	−0.272012	−	0.192667i
$856$	−16.5970			−0.567275
$857$	−30.6593	−	2.68234i	−1.04730	−	0.0916271i	−0.449508	−	0.893276i	$-0.648401\pi$
$857$	−30.6593	−	2.68234i	−1.04730	−	0.0916271i	−0.597795	+	0.801649i	$0.703956\pi$
$858$	31.6333	−	14.7508i	1.07994	−	0.503585i
$859$	17.9794	+	3.17025i	0.613448	+	0.108167i	0.471735	−	0.881740i	$-0.343628\pi$
$859$	17.9794	+	3.17025i	0.613448	+	0.108167i	0.141713	+	0.989908i	$0.454739\pi$
$860$	14.9936	−	9.78294i	0.511276	−	0.333595i
$861$	18.2600	−	6.64610i	0.622299	−	0.226498i
$862$	−1.28394	−	4.79172i	−0.0437311	−	0.163207i
$863$	6.42184	+	1.72073i	0.218602	+	0.0585742i	0.366458	−	0.930435i	$-0.380570\pi$
$863$	6.42184	+	1.72073i	0.218602	+	0.0585742i	−0.147856	+	0.989009i	$0.547237\pi$
$864$	0.642788	−	0.766044i	0.0218681	−	0.0260614i
$865$	13.5955	−	44.8139i	0.462260	−	1.52372i
$866$	5.51199	+	9.54704i	0.187305	+	0.324422i
$867$	−5.57816	+	1.49466i	−0.189444	+	0.0507614i
$868$	5.23917	−	11.2354i	0.177829	−	0.381356i
$869$	−5.67356	−	32.1764i	−0.192462	−	1.09151i
$870$	−12.8841	−	8.01235i	−0.436813	−	0.271644i
$871$	9.93031	+	3.61434i	0.336476	+	0.122467i
$872$	1.36493	−	15.6012i	0.0462223	−	0.528323i
$873$	1.75013	−	1.75013i	0.0592329	−	0.0592329i
$874$	−23.1817	−	21.9475i	−0.784134	−	0.742387i
$875$	13.0925	−	34.7774i	0.442606	−	1.17569i
$876$	2.51767	+	3.00044i	0.0850642	+	0.101376i
$877$	−10.4320	−	22.3715i	−0.352263	−	0.755431i	0.647716	−	0.761882i	$-0.275724\pi$
$877$	−10.4320	−	22.3715i	−0.352263	−	0.755431i	−0.999979	+	0.00645084i	$0.997947\pi$
$878$	24.1537	−	16.9126i	0.815149	−	0.570773i
$879$	−21.5406	+	3.79820i	−0.726548	+	0.128110i
$880$	0.425644	−	12.9914i	0.0143485	−	0.437941i
$881$	13.6482	−	23.6394i	0.459820	−	0.796432i	−0.539131	−	0.842222i	$-0.681247\pi$
$881$	13.6482	−	23.6394i	0.459820	−	0.796432i	0.998951	+	0.0457900i	$0.0145805\pi$
$882$	1.04744	−	3.90911i	0.0352693	−	0.131627i
$883$	2.01789	+	23.0646i	0.0679074	+	0.776185i	0.951444	+	0.307823i	$0.0996003\pi$
$883$	2.01789	+	23.0646i	0.0679074	+	0.776185i	−0.883536	+	0.468363i	$0.844844\pi$
$884$	15.4103	+	12.9308i	0.518306	+	0.434910i
$885$	−6.96364	+	9.28261i	−0.234080	+	0.312032i
$886$	−18.4645	−	10.6605i	−0.620326	−	0.358145i
$887$	39.8982	+	18.6048i	1.33965	+	0.624689i	0.954513	−	0.298170i	$-0.0963761\pi$
$887$	39.8982	+	18.6048i	1.33965	+	0.624689i	0.385138	+	0.922859i	$0.374154\pi$
$888$	−0.796642	−	0.557815i	−0.0267336	−	0.0187190i
$889$	−7.15841	+	40.5974i	−0.240085	+	1.36159i
$890$	1.05678	−	0.0576670i	0.0354232	−	0.00193300i
$891$	−4.45306	+	3.73656i	−0.149183	+	0.125180i
$892$	12.9753	+	12.9753i	0.434445	+	0.434445i
$893$	17.7722	+	44.9643i	0.594726	+	1.50467i
$894$		−	11.4076i		−	0.381526i
$895$	1.01259	+	3.09372i	0.0338470	+	0.103412i
$896$	−1.13677	+	3.12326i	−0.0379770	+	0.104341i
$897$	25.2223	+	36.0211i	0.842147	+	1.20271i
$898$	8.35709	−	11.9352i	0.278880	−	0.398282i
$899$	−8.65586	−	23.7818i	−0.288689	−	0.793167i
$900$	4.80032	−	1.39889i	0.160011	−	0.0466296i
$901$	−25.2202	+	14.5609i	−0.840208	+	0.485094i
$902$	33.8565	−	2.96206i	1.12730	−	0.0986258i
$903$	26.5097	−	2.31930i	0.882187	−	0.0771813i
$904$	7.77961	−	4.49156i	0.258746	−	0.149387i
$905$	−9.44525	+	7.41227i	−0.313971	+	0.246392i
$906$	2.97657	+	8.17806i	0.0988899	+	0.271698i
$907$	9.23306	−	13.1862i	0.306579	−	0.437840i	−0.636067	−	0.771634i	$-0.719440\pi$
$907$	9.23306	−	13.1862i	0.306579	−	0.437840i	0.942646	+	0.333794i	$0.108329\pi$
$908$	8.70755	+	12.4357i	0.288970	+	0.412692i
$909$	3.84818	−	10.5728i	0.127636	−	0.350677i
$910$	−39.8041	−	20.1733i	−1.31949	−	0.668737i
$911$			44.1109i			1.46146i	0.682667	+	0.730730i	$0.260820\pi$
$911$			44.1109i			1.46146i	−0.682667	+	0.730730i	$0.739180\pi$
$912$	1.60225	+	4.05374i	0.0530558	+	0.134233i
$913$	−56.6712	−	56.6712i	−1.87554	−	1.87554i
$914$	−23.5397	+	19.7522i	−0.778624	+	0.653343i
$915$	−0.118539	−	2.17228i	−0.00391878	−	0.0718135i
$916$	4.98986	−	28.2989i	0.164870	−	0.935023i
$917$	9.92392	+	6.94881i	0.327717	+	0.229470i
$918$	−3.03648	−	1.41593i	−0.100219	−	0.0467328i
$919$	−50.1986	−	28.9822i	−1.65590	−	0.956034i	−0.974578	−	0.224050i	$-0.928072\pi$
$919$	−50.1986	−	28.9822i	−1.65590	−	0.956034i	−0.681322	−	0.731984i	$-0.738594\pi$
$920$	16.2119	−	2.31407i	0.534491	−	0.0762927i
$921$	13.3708	+	11.2194i	0.440583	+	0.369693i
$922$	−1.78563	−	20.4099i	−0.0588066	−	0.672163i
$923$	3.65533	−	13.6419i	0.120317	−	0.449028i
$924$	9.66045	−	16.7324i	0.317806	−	0.550455i
$925$	−1.76215	−	4.53208i	−0.0579391	−	0.149014i
$926$	−36.5569	+	6.44596i	−1.20133	+	0.211827i
$927$	0.342945	−	0.240132i	0.0112638	−	0.00788698i
$928$	2.86758	+	6.14953i	0.0941328	+	0.201868i
$929$	17.3530	+	20.6805i	0.569335	+	0.678507i	0.971494	−	0.237063i	$-0.0761847\pi$
$929$	17.3530	+	20.6805i	0.569335	+	0.678507i	−0.402160	+	0.915570i	$0.631740\pi$
$930$	7.73962	+	3.10763i	0.253792	+	0.101903i
$931$	12.8101	+	12.1281i	0.419833	+	0.397481i
$932$	−5.82847	+	5.82847i	−0.190918	+	0.190918i
$933$	−1.54165	+	17.6212i	−0.0504715	+	0.576892i
$934$	−13.8644	−	5.04622i	−0.453656	−	0.165117i
$935$	−42.4122	+	9.88795i	−1.38703	+	0.323371i
$936$	−1.04264	−	5.91310i	−0.0340797	−	0.193276i
$937$	−4.35847	+	9.34677i	−0.142385	+	0.305346i	−0.964548	−	0.263906i	$-0.914989\pi$
$937$	−4.35847	+	9.34677i	−0.142385	+	0.305346i	0.822163	+	0.569252i	$0.192767\pi$
$938$	5.65040	−	1.51402i	0.184492	−	0.0494345i
$939$	12.8554	+	22.2662i	0.419520	+	0.726631i
$940$	−23.7344	−	7.20045i	−0.774131	−	0.234853i
$941$	2.14078	−	2.55129i	0.0697876	−	0.0831696i	−0.730021	−	0.683425i	$-0.760490\pi$
$941$	2.14078	−	2.55129i	0.0697876	−	0.0831696i	0.799809	+	0.600255i	$0.204934\pi$
$942$	9.04130	+	2.42261i	0.294582	+	0.0789329i
$943$	11.0820	+	41.3586i	0.360879	+	1.34682i
$944$	4.87662	−	1.77494i	0.158720	−	0.0577695i
$945$	7.27293	+	1.52954i	0.236589	+	0.0497558i
$946$	45.8347	+	8.08189i	1.49021	+	0.262765i
$947$	−49.5609	+	23.1106i	−1.61051	+	0.750994i	−0.999184	−	0.0403827i	$-0.987142\pi$
$947$	−49.5609	+	23.1106i	−1.61051	+	0.750994i	−0.611328	+	0.791377i	$0.709365\pi$
$948$	−5.59919	−	0.489865i	−0.181853	−	0.0159101i
$949$	23.5177			0.763417
$950$	−4.60071	+	21.3034i	−0.149267	+	0.691172i
$951$	17.5890			0.570363
$952$	11.0933	+	0.970539i	0.359536	+	0.0314553i
$953$	−4.98648	+	2.32523i	−0.161528	+	0.0753217i	−0.501701	−	0.865041i	$-0.667292\pi$
$953$	−4.98648	+	2.32523i	−0.161528	+	0.0753217i	0.340173	+	0.940363i	$0.389514\pi$
$954$	8.56003	+	1.50936i	0.277141	+	0.0488675i
$955$	−37.9899	−	7.98947i	−1.22932	−	0.258533i
$956$	−15.2637	+	5.55552i	−0.493662	+	0.179678i
$957$	−10.2086	−	38.0992i	−0.329998	−	1.23157i
$958$	16.8274	+	4.50890i	0.543670	+	0.145676i
$959$	0.890045	−	1.06071i	0.0287411	−	0.0342523i
$960$	−2.13977	−	0.649154i	−0.0690607	−	0.0209513i
$961$	−8.54409	−	14.7988i	−0.275616	−	0.477380i
$962$	−5.64035	+	1.51133i	−0.181852	+	0.0487271i
$963$	7.01421	−	15.0420i	0.226030	−	0.484723i
$964$	−0.268317	−	1.52170i	−0.00864190	−	0.0490106i
$965$	20.3160	−	4.73646i	0.653997	−	0.152472i
$966$	22.8737	+	8.32536i	0.735951	+	0.267864i
$967$	−2.44928	+	27.9954i	−0.0787635	+	0.900271i	0.849315	+	0.527886i	$0.177015\pi$
$967$	−2.44928	+	27.9954i	−0.0787635	+	0.900271i	−0.928079	+	0.372385i	$0.878540\pi$
$968$	16.1162	−	16.1162i	0.517993	−	0.517993i
$969$	11.7294	−	8.70041i	0.376803	−	0.279497i
$970$	−5.13586	−	2.06216i	−0.164902	−	0.0662119i
$971$	−27.2316	−	32.4534i	−0.873904	−	1.04148i	−0.998784	−	0.0493059i	$-0.984299\pi$
$971$	−27.2316	−	32.4534i	−0.873904	−	1.04148i	0.124880	−	0.992172i	$-0.460145\pi$
$972$	0.422618	+	0.906308i	0.0135555	+	0.0290698i
$973$	11.3074	−	7.91751i	0.362498	−	0.253824i
$974$	25.3520	−	4.47024i	0.812330	−	0.143236i
$975$	12.0926	−	27.4785i	0.387272	−	0.880015i
$976$	−0.486460	+	0.842573i	−0.0155712	+	0.0269701i
$977$	−6.58565	+	24.5780i	−0.210694	+	0.786320i	0.776945	+	0.629569i	$0.216769\pi$
$977$	−6.58565	+	24.5780i	−0.210694	+	0.786320i	−0.987638	+	0.156751i	$0.949898\pi$
$978$	0.133501	+	1.52592i	0.00426888	+	0.0487936i
$979$	2.10767	+	1.76854i	0.0673614	+	0.0565229i
$980$	−8.95859	+	1.27874i	−0.286172	+	0.0408478i
$981$	13.5626	+	7.83040i	0.433022	+	0.250005i
$982$	−7.21035	−	3.36224i	−0.230091	−	0.107293i
$983$	41.1098	+	28.7854i	1.31120	+	0.918112i	0.999486	−	0.0320647i	$-0.0102083\pi$
$983$	41.1098	+	28.7854i	1.31120	+	0.918112i	0.311713	+	0.950176i	$0.399097\pi$
$984$	1.01523	−	5.75764i	0.0323642	−	0.183547i
$985$	2.18059	+	39.9604i	0.0694794	+	1.27324i
$986$	17.4147	−	14.6126i	0.554596	−	0.465361i
$987$	−26.0687	−	26.0687i	−0.829776	−	0.829776i
$988$	24.8294	+	8.27574i	0.789927	+	0.263286i
$989$			58.6363i			1.86453i
$990$	11.5944	+	5.87618i	0.368493	+	0.186757i
$991$	−13.7938	+	37.8982i	−0.438176	+	1.20388i	0.502502	+	0.864576i	$0.332413\pi$
$991$	−13.7938	+	37.8982i	−0.438176	+	1.20388i	−0.940678	+	0.339302i	$0.889809\pi$
$992$	−2.13936	−	3.05532i	−0.0679247	−	0.0970065i
$993$	1.07289	−	1.53225i	0.0340472	−	0.0486244i
$994$	−2.67387	−	7.34640i	−0.0848101	−	0.233014i
$995$	−14.2298	+	11.1670i	−0.451115	+	0.354018i
$996$	−11.9400	+	6.89355i	−0.378332	+	0.218430i
$997$	−23.6090	+	2.06552i	−0.747703	+	0.0654156i	−0.454637	−	0.890677i	$-0.650231\pi$
$997$	−23.6090	+	2.06552i	−0.747703	+	0.0654156i	−0.293066	+	0.956092i	$0.594676\pi$
$998$	−30.9289	+	2.70593i	−0.979037	+	0.0856546i
$999$	0.842227	−	0.486260i	0.0266469	−	0.0153846i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.13.5	✓	120
5.2	odd	4	inner	570.2.bh.a.127.7	yes	120
19.3	odd	18	inner	570.2.bh.a.193.7	yes	120
95.22	even	36	inner	570.2.bh.a.307.5	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.13.5	✓	120	1.1	even	1	trivial
570.2.bh.a.127.7	yes	120	5.2	odd	4	inner
570.2.bh.a.193.7	yes	120	19.3	odd	18	inner
570.2.bh.a.307.5	yes	120	95.22	even	36	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bh (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.18820 + 0.460190i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.860238 - 3.21045i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(-0.996195 - 0.0871557i) q^{2} +(-0.906308 + 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(2.18820 + 0.460190i) q^{5} +(0.939693 - 0.342020i) q^{6} +(-0.860238 - 3.21045i) q^{7} +(-0.965926 - 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-2.13977 - 0.649154i) q^{10} +(-2.90653 - 5.03426i) q^{11} +(-0.965926 + 0.258819i) q^{12} +(-2.53753 + 5.44176i) q^{13} +(0.577155 + 3.27321i) q^{14} +(-2.17767 + 0.507700i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.292005 - 3.33763i) q^{17} +(-0.707107 + 0.707107i) q^{18} +(-1.24285 - 4.17796i) q^{19} +(2.07505 + 0.833176i) q^{20} +(2.13644 + 2.54611i) q^{21} +(2.45671 + 5.26842i) q^{22} +(-5.99920 + 4.20069i) q^{23} +(0.984808 - 0.173648i) q^{24} +(4.57645 + 2.01398i) q^{25} +(3.00216 - 5.19989i) q^{26} +(-0.258819 + 0.965926i) q^{27} +(-0.289680 - 3.31106i) q^{28} +(-5.19781 - 4.36148i) q^{29} +(2.21363 - 0.315971i) q^{30} +(3.23015 + 1.86493i) q^{31} +(-0.906308 - 0.422618i) q^{32} +(4.76178 + 3.33424i) q^{33} +(-0.581788 + 3.29948i) q^{34} +(-0.404955 - 7.42099i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.687676 - 0.687676i) q^{37} +(0.873984 + 4.27038i) q^{38} -6.00432i q^{39} +(-1.99453 - 1.01086i) q^{40} +(1.99961 - 5.49387i) q^{41} +(-1.90640 - 2.72262i) q^{42} +(4.59229 - 6.55847i) q^{43} +(-1.98818 - 5.46249i) q^{44} +(1.75907 - 1.38045i) q^{45} +(6.34249 - 3.66184i) q^{46} +(-11.0498 + 0.966737i) q^{47} +(-0.996195 + 0.0871557i) q^{48} +(-3.50482 + 2.02351i) q^{49} +(-4.38350 - 2.40518i) q^{50} +(1.14590 + 3.14833i) q^{51} +(-3.44393 + 4.91845i) q^{52} +(-4.98558 - 7.12014i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-4.04336 - 12.3535i) q^{55} +3.32370i q^{56} +(2.89208 + 3.26127i) q^{57} +(4.79790 + 4.79790i) q^{58} +(3.97546 - 3.33580i) q^{59} +(-2.23275 + 0.121838i) q^{60} +(-0.168946 + 0.958139i) q^{61} +(-3.05532 - 2.13936i) q^{62} +(-3.01230 - 1.40466i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-8.05688 + 10.7399i) q^{65} +(-4.45306 - 3.73656i) q^{66} +(-0.153394 - 1.75330i) q^{67} +(0.867143 - 3.23622i) q^{68} +(3.66184 - 6.34249i) q^{69} +(-0.243368 + 7.42804i) q^{70} +(-2.31642 + 0.408448i) q^{71} +(-0.819152 + 0.573576i) q^{72} +(-1.65531 - 3.54982i) q^{73} +(0.625124 + 0.744994i) q^{74} +(-4.99882 + 0.108807i) q^{75} +(-0.498470 - 4.33030i) q^{76} +(-13.6619 + 13.6619i) q^{77} +(-0.523311 + 5.98147i) q^{78} +(5.28161 + 1.92235i) q^{79} +(1.89884 + 1.18085i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(-2.47082 + 5.29869i) q^{82} +(13.3173 - 3.56836i) q^{83} +(1.66185 + 2.87841i) q^{84} +(2.17491 - 7.16904i) q^{85} +(-5.14642 + 6.13327i) q^{86} +(6.55406 + 1.75615i) q^{87} +(1.50453 + 5.61499i) q^{88} +(-0.444764 + 0.161881i) q^{89} +(-1.87270 + 1.22189i) q^{90} +(19.6534 + 3.46542i) q^{91} +(-6.63750 + 3.09512i) q^{92} +(-3.71566 - 0.325078i) q^{93} +11.0921 q^{94} +(-0.796941 - 9.71416i) q^{95} +1.00000 q^{96} +(2.46564 + 0.215715i) q^{97} +(3.66784 - 1.71034i) q^{98} +(-5.72475 - 1.00943i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 12 q^{5} + 12 q^{7}+O(q^{10}) \) 120 * q - 12 * q^5 + 12 * q^7	\( 120 q - 12 q^{5} + 12 q^{7} - 12 q^{10} + 48 q^{13} + 12 q^{17} + 36 q^{21} - 36 q^{22} - 96 q^{23} + 12 q^{25} + 12 q^{26} + 12 q^{30} + 24 q^{38} + 60 q^{41} + 96 q^{43} - 48 q^{47} - 24 q^{52} - 72 q^{53} + 108 q^{55} + 12 q^{57} + 24 q^{58} - 12 q^{60} - 24 q^{61} + 24 q^{62} + 24 q^{66} + 72 q^{67} + 12 q^{68} - 48 q^{70} + 36 q^{73} - 12 q^{76} - 24 q^{78} + 12 q^{80} - 72 q^{82} + 12 q^{83} - 108 q^{85} - 24 q^{86} + 12 q^{87} - 48 q^{91} - 84 q^{92} - 48 q^{93} - 204 q^{95} + 120 q^{96} + 24 q^{97} - 96 q^{98}+O(q^{100}) \) 120 * q - 12 * q^5 + 12 * q^7 - 12 * q^10 + 48 * q^13 + 12 * q^17 + 36 * q^21 - 36 * q^22 - 96 * q^23 + 12 * q^25 + 12 * q^26 + 12 * q^30 + 24 * q^38 + 60 * q^41 + 96 * q^43 - 48 * q^47 - 24 * q^52 - 72 * q^53 + 108 * q^55 + 12 * q^57 + 24 * q^58 - 12 * q^60 - 24 * q^61 + 24 * q^62 + 24 * q^66 + 72 * q^67 + 12 * q^68 - 48 * q^70 + 36 * q^73 - 12 * q^76 - 24 * q^78 + 12 * q^80 - 72 * q^82 + 12 * q^83 - 108 * q^85 - 24 * q^86 + 12 * q^87 - 48 * q^91 - 84 * q^92 - 48 * q^93 - 204 * q^95 + 120 * q^96 + 24 * q^97 - 96 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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