LMFDB - Embedded newform 570.2.bh.a.13.7

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			13.7
Character	$\chi$	$=$	570.13
Dual form			570.2.bh.a.307.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.02193 + 0.954879i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.864180 + 3.22516i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})$	\(q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.02193 + 0.954879i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.864180 + 3.22516i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-2.09746 + 0.775022i) q^{10} +(1.60700 + 2.78340i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-1.33220 + 2.85690i) q^{13} +(0.579800 + 3.28821i) q^{14} +(-1.42894 + 1.71992i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.0681268 - 0.778693i) q^{17} +(0.707107 - 0.707107i) q^{18} +(2.36134 - 3.66389i) q^{19} +(-2.15703 + 0.589267i) q^{20} +(2.14623 + 2.55777i) q^{21} +(1.35829 + 2.91287i) q^{22} +(0.454196 - 0.318031i) q^{23} +(0.984808 - 0.173648i) q^{24} +(3.17641 - 3.86140i) q^{25} +(-1.57612 + 2.72992i) q^{26} +(0.258819 - 0.965926i) q^{27} +(0.291007 + 3.32623i) q^{28} +(-5.20114 - 4.36428i) q^{29} +(-1.57341 + 1.58883i) q^{30} +(7.41186 + 4.27924i) q^{31} +(0.906308 + 0.422618i) q^{32} +(2.63275 + 1.84347i) q^{33} +(0.135735 - 0.769792i) q^{34} +(-4.82695 - 5.69587i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.330990 - 0.330990i) q^{37} +(2.67168 - 3.44414i) q^{38} +3.15224i q^{39} +(-2.20018 + 0.399028i) q^{40} +(0.0366776 - 0.100771i) q^{41} +(1.91513 + 2.73509i) q^{42} +(0.308956 - 0.441235i) q^{43} +(1.09925 + 3.02017i) q^{44} +(-0.568193 + 2.16267i) q^{45} +(0.480185 - 0.277235i) q^{46} +(-2.86676 + 0.250809i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(-3.59269 + 2.07424i) q^{49} +(3.50087 - 3.56986i) q^{50} +(-0.267346 - 0.734527i) q^{51} +(-1.80805 + 2.58217i) q^{52} +(-5.69419 - 8.13215i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-5.90705 - 4.09336i) q^{55} +3.33893i q^{56} +(0.591671 - 4.31856i) q^{57} +(-4.80098 - 4.80098i) q^{58} +(7.73966 - 6.49435i) q^{59} +(-1.70589 + 1.44566i) q^{60} +(0.957173 - 5.42840i) q^{61} +(7.01070 + 4.90894i) q^{62} +(3.02610 + 1.41109i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.0343877 - 7.04854i) q^{65} +(2.46206 + 2.06592i) q^{66} +(-0.0165210 - 0.188836i) q^{67} +(0.202310 - 0.755032i) q^{68} +(0.277235 - 0.480185i) q^{69} +(-4.31216 - 6.09489i) q^{70} +(-13.4904 + 2.37872i) q^{71} +(0.819152 - 0.573576i) q^{72} +(3.62506 + 7.77396i) q^{73} +(-0.300883 - 0.358578i) q^{74} +(1.24691 - 4.84203i) q^{75} +(2.96169 - 3.19819i) q^{76} +(-7.58819 + 7.58819i) q^{77} +(-0.274736 + 3.14025i) q^{78} +(-11.3178 - 4.11935i) q^{79} +(-2.22658 + 0.205751i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(0.0453208 - 0.0971907i) q^{82} +(9.04398 - 2.42333i) q^{83} +(1.66947 + 2.89160i) q^{84} +(0.605809 + 1.63952i) q^{85} +(0.346237 - 0.412629i) q^{86} +(-6.55826 - 1.75728i) q^{87} +(0.831843 + 3.10448i) q^{88} +(-2.03388 + 0.740273i) q^{89} +(-0.754520 + 2.10492i) q^{90} +(-10.3652 - 1.82767i) q^{91} +(0.502521 - 0.234329i) q^{92} +(8.52592 + 0.745921i) q^{93} -2.87771 q^{94} +(-1.27589 + 9.66292i) q^{95} +1.00000 q^{96} +(1.53486 + 0.134283i) q^{97} +(-3.75980 + 1.75322i) q^{98} +(3.16517 + 0.558104i) 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
$5$	−2.02193	+	0.954879i	−0.904235	+	0.427035i
$5$	−2.02193	+	0.954879i	−0.904235	+	0.427035i
$6$	0.939693	−	0.342020i	0.383628	−	0.139629i
$7$	0.864180	+	3.22516i	0.326629	+	1.21900i	0.912664	+	0.408711i	$0.134022\pi$
$7$	0.864180	+	3.22516i	0.326629	+	1.21900i	−0.586035	+	0.810286i	$0.699312\pi$
$8$	0.965926	+	0.258819i	0.341506	+	0.0915064i
$9$	0.642788	−	0.766044i	0.214263	−	0.255348i
$10$	−2.09746	+	0.775022i	−0.663275	+	0.245084i
$11$	1.60700	+	2.78340i	0.484528	+	0.839227i	0.999842	−	0.0177744i	$-0.00565806\pi$
$11$	1.60700	+	2.78340i	0.484528	+	0.839227i	−0.515314	+	0.857001i	$0.672325\pi$
$12$	0.965926	−	0.258819i	0.278839	−	0.0747146i
$13$	−1.33220	+	2.85690i	−0.369484	+	0.792362i	0.630386	+	0.776282i	$0.282897\pi$
$13$	−1.33220	+	2.85690i	−0.369484	+	0.792362i	−0.999871	+	0.0160803i	$0.994881\pi$
$14$	0.579800	+	3.28821i	0.154958	+	0.878811i
$15$	−1.42894	+	1.71992i	−0.368951	+	0.444081i
$16$	0.939693	+	0.342020i	0.234923	+	0.0855050i
$17$	0.0681268	−	0.778693i	0.0165232	−	0.188861i	−0.983447	−	0.181194i	$-0.942004\pi$
$17$	0.0681268	−	0.778693i	0.0165232	−	0.188861i	0.999971	−	0.00766705i	$-0.00244052\pi$
$18$	0.707107	−	0.707107i	0.166667	−	0.166667i
$19$	2.36134	−	3.66389i	0.541728	−	0.840554i
$19$	2.36134	−	3.66389i	0.541728	−	0.840554i
$20$	−2.15703	+	0.589267i	−0.482326	+	0.131764i
$21$	2.14623	+	2.55777i	0.468345	+	0.558152i
$22$	1.35829	+	2.91287i	0.289589	+	0.621026i
$23$	0.454196	−	0.318031i	0.0947063	−	0.0663141i	−0.525264	−	0.850939i	$-0.676033\pi$
$23$	0.454196	−	0.318031i	0.0947063	−	0.0663141i	0.619970	+	0.784625i	$0.287145\pi$
$24$	0.984808	−	0.173648i	0.201023	−	0.0354458i
$25$	3.17641	−	3.86140i	0.635283	−	0.772280i
$26$	−1.57612	+	2.72992i	−0.309103	+	0.535382i
$27$	0.258819	−	0.965926i	0.0498097	−	0.185893i
$28$	0.291007	+	3.32623i	0.0549952	+	0.628598i
$29$	−5.20114	−	4.36428i	−0.965828	−	0.810426i	0.0160630	−	0.999871i	$-0.494887\pi$
$29$	−5.20114	−	4.36428i	−0.965828	−	0.810426i	−0.981891	+	0.189445i	$0.939331\pi$
$30$	−1.57341	+	1.58883i	−0.287263	+	0.290080i
$31$	7.41186	+	4.27924i	1.33121	+	0.768575i	0.985485	−	0.169761i	$-0.0542997\pi$
$31$	7.41186	+	4.27924i	1.33121	+	0.768575i	0.345725	+	0.938336i	$0.387633\pi$
$32$	0.906308	+	0.422618i	0.160214	+	0.0747091i
$33$	2.63275	+	1.84347i	0.458303	+	0.320907i
$34$	0.135735	−	0.769792i	0.0232784	−	0.132018i
$35$	−4.82695	−	5.69587i	−0.815904	−	0.962778i
$36$	0.766044	−	0.642788i	0.127674	−	0.107131i
$37$	−0.330990	−	0.330990i	−0.0544144	−	0.0544144i	0.679376	−	0.733790i	$-0.262251\pi$
$37$	−0.330990	−	0.330990i	−0.0544144	−	0.0544144i	−0.733790	+	0.679376i	$0.762251\pi$
$38$	2.67168	−	3.44414i	0.433404	−	0.558714i
$39$			3.15224i			0.504763i
$40$	−2.20018	+	0.399028i	−0.347878	+	0.0630918i
$41$	0.0366776	−	0.100771i	0.00572807	−	0.0157378i	−0.936796	−	0.349877i	$-0.886223\pi$
$41$	0.0366776	−	0.100771i	0.00572807	−	0.0157378i	0.942524	+	0.334139i	$0.108446\pi$
$42$	1.91513	+	2.73509i	0.295512	+	0.422034i
$43$	0.308956	−	0.441235i	0.0471154	−	0.0672877i	−0.794903	−	0.606736i	$-0.792478\pi$
$43$	0.308956	−	0.441235i	0.0471154	−	0.0672877i	0.842019	+	0.539449i	$0.181367\pi$
$44$	1.09925	+	3.02017i	0.165718	+	0.455307i
$45$	−0.568193	+	2.16267i	−0.0847012	+	0.322392i
$46$	0.480185	−	0.277235i	0.0707995	−	0.0408761i
$47$	−2.86676	+	0.250809i	−0.418160	+	0.0365842i	−0.294294	−	0.955715i	$-0.595085\pi$
$47$	−2.86676	+	0.250809i	−0.418160	+	0.0365842i	−0.123865	+	0.992299i	$0.539529\pi$
$48$	0.996195	−	0.0871557i	0.143788	−	0.0125798i
$49$	−3.59269	+	2.07424i	−0.513242	+	0.296320i
$50$	3.50087	−	3.56986i	0.495098	−	0.504855i
$51$	−0.267346	−	0.734527i	−0.0374359	−	0.102854i
$52$	−1.80805	+	2.58217i	−0.250732	+	0.358082i
$53$	−5.69419	−	8.13215i	−0.782157	−	1.11704i	−0.990301	−	0.138938i	$-0.955631\pi$
$53$	−5.69419	−	8.13215i	−0.782157	−	1.11704i	0.208144	−	0.978098i	$-0.433258\pi$
$54$	0.342020	−	0.939693i	0.0465430	−	0.127876i
$55$	−5.90705	−	4.09336i	−0.796506	−	0.551948i
$56$			3.33893i			0.446184i
$57$	0.591671	−	4.31856i	0.0783687	−	0.572007i
$58$	−4.80098	−	4.80098i	−0.630400	−	0.630400i
$59$	7.73966	−	6.49435i	1.00762	−	0.845492i	0.0195968	−	0.999808i	$-0.493762\pi$
$59$	7.73966	−	6.49435i	1.00762	−	0.845492i	0.988022	+	0.154316i	$0.0493173\pi$
$60$	−1.70589	+	1.44566i	−0.220230	+	0.186633i
$61$	0.957173	−	5.42840i	0.122553	−	0.695035i	−0.860177	−	0.509995i	$-0.829647\pi$
$61$	0.957173	−	5.42840i	0.122553	−	0.695035i	0.982731	−	0.185040i	$-0.0592416\pi$
$62$	7.01070	+	4.90894i	0.890360	+	0.623437i
$63$	3.02610	+	1.41109i	0.381253	+	0.177781i
$64$	0.866025	+	0.500000i	0.108253	+	0.0625000i
$65$	−0.0343877	−	7.04854i	−0.00426527	−	0.874264i
$66$	2.46206	+	2.06592i	0.303059	+	0.254297i
$67$	−0.0165210	−	0.188836i	−0.00201836	−	0.0230700i	0.995119	−	0.0986849i	$-0.0314636\pi$
$67$	−0.0165210	−	0.188836i	−0.00201836	−	0.0230700i	−0.997137	+	0.0756149i	$0.975908\pi$
$68$	0.202310	−	0.755032i	0.0245337	−	0.0915611i
$69$	0.277235	−	0.480185i	0.0333752	−	0.0578075i
$70$	−4.31216	−	6.09489i	−0.515401	−	0.728479i
$71$	−13.4904	+	2.37872i	−1.60101	+	0.282302i	−0.901651	−	0.432464i	$-0.857644\pi$
$71$	−13.4904	+	2.37872i	−1.60101	+	0.282302i	−0.699363	+	0.714766i	$0.746533\pi$
$72$	0.819152	−	0.573576i	0.0965380	−	0.0675966i
$73$	3.62506	+	7.77396i	0.424281	+	0.909873i	0.995994	+	0.0894196i	$0.0285012\pi$
$73$	3.62506	+	7.77396i	0.424281	+	0.909873i	−0.571713	+	0.820454i	$0.693721\pi$
$74$	−0.300883	−	0.358578i	−0.0349769	−	0.0416838i
$75$	1.24691	−	4.84203i	0.143981	−	0.559109i
$76$	2.96169	−	3.19819i	0.339729	−	0.366857i
$77$	−7.58819	+	7.58819i	−0.864754	+	0.864754i
$78$	−0.274736	+	3.14025i	−0.0311077	+	0.355563i
$79$	−11.3178	−	4.11935i	−1.27335	−	0.463463i	−0.385125	−	0.922864i	$-0.625842\pi$
$79$	−11.3178	−	4.11935i	−1.27335	−	0.463463i	−0.888229	+	0.459401i	$0.848064\pi$
$80$	−2.22658	+	0.205751i	−0.248939	+	0.0230037i
$81$	−0.173648	−	0.984808i	−0.0192942	−	0.109423i
$82$	0.0453208	−	0.0971907i	0.00500484	−	0.0107329i
$83$	9.04398	−	2.42333i	0.992706	−	0.265995i	0.274319	−	0.961639i	$-0.411548\pi$
$83$	9.04398	−	2.42333i	0.992706	−	0.265995i	0.718387	+	0.695644i	$0.244881\pi$
$84$	1.66947	+	2.89160i	0.182154	+	0.315500i
$85$	0.605809	+	1.63952i	0.0657093	+	0.177830i
$86$	0.346237	−	0.412629i	0.0373356	−	0.0444949i
$87$	−6.55826	−	1.75728i	−0.703119	−	0.188400i
$88$	0.831843	+	3.10448i	0.0886748	+	0.330939i
$89$	−2.03388	+	0.740273i	−0.215591	+	0.0784688i	−0.447558	−	0.894255i	$-0.647706\pi$
$89$	−2.03388	+	0.740273i	−0.215591	+	0.0784688i	0.231967	+	0.972724i	$0.425484\pi$
$90$	−0.754520	+	2.10492i	−0.0795334	+	0.221878i
$91$	−10.3652	−	1.82767i	−1.08657	−	0.191592i
$92$	0.502521	−	0.234329i	0.0523914	−	0.0244305i
$93$	8.52592	+	0.745921i	0.884096	+	0.0773484i
$94$	−2.87771			−0.296813
$95$	−1.27589	+	9.66292i	−0.130903	+	0.991395i
$96$	1.00000			0.102062
$97$	1.53486	+	0.134283i	0.155842	+	0.0136344i	0.164810	−	0.986325i	$-0.447299\pi$
$97$	1.53486	+	0.134283i	0.155842	+	0.0136344i	−0.00896789	+	0.999960i	$0.502855\pi$
$98$	−3.75980	+	1.75322i	−0.379797	+	0.177102i
$99$	3.16517	+	0.558104i	0.318111	+	0.0560916i
$100$	3.79868	−	3.25116i	0.379868	−	0.325116i
$101$	4.99336	−	1.81744i	0.496858	−	0.180842i	−0.0814221	−	0.996680i	$-0.525946\pi$
$101$	4.99336	−	1.81744i	0.496858	−	0.180842i	0.578280	+	0.815838i	$0.303724\pi$
$102$	−0.202310	−	0.755032i	−0.0200317	−	0.0747593i
$103$	6.25556	+	1.67617i	0.616379	+	0.165158i	0.553481	−	0.832862i	$-0.313299\pi$
$103$	6.25556	+	1.67617i	0.616379	+	0.165158i	0.0628978	+	0.998020i	$0.479966\pi$
$104$	−2.02622	+	2.41476i	−0.198687	+	0.236786i
$105$	−6.78188	−	3.12225i	−0.661844	−	0.304701i
$106$	−4.96376	−	8.59748i	−0.482123	−	0.835061i
$107$	−16.1171	+	4.31858i	−1.55810	+	0.417492i	−0.932062	−	0.362298i	$-0.881992\pi$
$107$	−16.1171	+	4.31858i	−1.55810	+	0.417492i	−0.626041	+	0.779790i	$0.715326\pi$
$108$	0.422618	−	0.906308i	0.0406665	−	0.0872095i
$109$	2.18285	+	12.3796i	0.209079	+	1.18575i	0.890890	+	0.454219i	$0.150082\pi$
$109$	2.18285	+	12.3796i	0.209079	+	1.18575i	−0.681811	+	0.731529i	$0.738807\pi$
$110$	−5.52781	−	4.59262i	−0.527056	−	0.437889i
$111$	−0.439861	−	0.160096i	−0.0417498	−	0.0151957i
$112$	−0.291007	+	3.32623i	−0.0274976	+	0.314299i
$113$	7.11542	−	7.11542i	0.669363	−	0.669363i	−0.288206	−	0.957569i	$-0.593059\pi$
$113$	7.11542	−	7.11542i	0.669363	−	0.669363i	0.957569	+	0.288206i	$0.0930587\pi$
$114$	0.965806	−	4.25056i	0.0904560	−	0.398101i
$115$	−0.614671	+	1.07674i	−0.0573184	+	0.100406i
$116$	−4.36428	−	5.20114i	−0.405213	−	0.482914i
$117$	1.33220	+	2.85690i	0.123161	+	0.264121i
$118$	8.27623	−	5.79508i	0.761889	−	0.533480i
$119$	2.57028	−	0.453210i	0.235618	−	0.0415457i
$120$	−1.82540	+	1.29148i	−0.166636	+	0.117895i
$121$	0.335118	−	0.580442i	0.0304653	−	0.0527675i
$122$	1.42665	−	5.32432i	0.129163	−	0.482041i
$123$	−0.00934641	−	0.106830i	−0.000842737	−	0.00963253i
$124$	6.55618	+	5.50129i	0.588762	+	0.494030i
$125$	−2.73532	+	10.8406i	−0.244655	+	0.969610i
$126$	2.89160	+	1.66947i	0.257604	+	0.148728i
$127$	7.07901	+	3.30100i	0.628161	+	0.292916i	0.710510	−	0.703687i	$-0.248464\pi$
$127$	7.07901	+	3.30100i	0.628161	+	0.292916i	−0.0823490	+	0.996604i	$0.526242\pi$
$128$	0.819152	+	0.573576i	0.0724035	+	0.0506975i
$129$	0.0935353	−	0.530465i	0.00823532	−	0.0467048i
$130$	0.580064	−	7.02472i	0.0508750	−	0.616109i
$131$	13.6696	−	11.4702i	1.19432	−	1.00215i	0.194544	−	0.980894i	$-0.437677\pi$
$131$	13.6696	−	11.4702i	1.19432	−	1.00215i	0.999774	−	0.0212582i	$-0.00676719\pi$
$132$	2.27264	+	2.27264i	0.197808	+	0.197808i
$133$	13.8573	+	4.44944i	1.20158	+	0.385815i
$134$		−	0.189557i		−	0.0163752i
$135$	0.399028	+	2.20018i	0.0343428	+	0.189361i
$136$	0.267346	−	0.734527i	0.0229247	−	0.0629852i
$137$	−6.81498	−	9.73280i	−0.582243	−	0.831529i	0.414676	−	0.909969i	$-0.363895\pi$
$137$	−6.81498	−	9.73280i	−0.582243	−	0.831529i	−0.996919	+	0.0784402i	$0.975006\pi$
$138$	0.318031	−	0.454196i	0.0270726	−	0.0386637i
$139$	−7.07092	−	19.4272i	−0.599748	−	1.64779i	−0.751777	−	0.659418i	$-0.770803\pi$
$139$	−7.07092	−	19.4272i	−0.599748	−	1.64779i	0.152029	−	0.988376i	$-0.451419\pi$
$140$	−3.76454	−	6.44753i	−0.318162	−	0.544916i
$141$	−2.49217	+	1.43885i	−0.209878	+	0.121173i
$142$	−13.6464	+	1.19390i	−1.14518	+	0.100190i
$143$	−10.0927	+	0.883000i	−0.843997	+	0.0738402i
$144$	0.866025	−	0.500000i	0.0721688	−	0.0416667i
$145$	14.6837	+	3.85781i	1.21942	+	0.320374i
$146$	2.93372	+	8.06032i	0.242796	+	0.667077i
$147$	−2.37947	+	3.39824i	−0.196256	+	0.280282i
$148$	−0.268486	−	0.383437i	−0.0220694	−	0.0315183i
$149$	−1.84640	+	5.07294i	−0.151263	+	0.415591i	−0.992061	−	0.125758i	$-0.959864\pi$
$149$	−1.84640	+	5.07294i	−0.151263	+	0.415591i	0.840798	+	0.541349i	$0.182086\pi$
$150$	1.66418	−	4.71493i	0.135879	−	0.384972i
$151$		−	18.1238i		−	1.47490i	−0.675404	−	0.737448i	$-0.736031\pi$
$151$		−	18.1238i		−	1.47490i	0.675404	−	0.737448i	$-0.263969\pi$
$152$	3.22916	−	2.92789i	0.261919	−	0.237483i
$153$	−0.552722	−	0.552722i	−0.0446849	−	0.0446849i
$154$	−8.22067	+	6.89796i	−0.662440	+	0.555853i
$155$	−19.0724	−	1.57490i	−1.53194	−	0.126499i
$156$	−0.547381	+	3.10435i	−0.0438256	+	0.248547i
$157$	12.2008	+	8.54310i	0.973731	+	0.681814i	0.948138	−	0.317859i	$-0.102964\pi$
$157$	12.2008	+	8.54310i	0.973731	+	0.681814i	0.0255928	+	0.999672i	$0.491853\pi$
$158$	−10.9157	−	5.09009i	−0.868409	−	0.404946i
$159$	−8.59748	−	4.96376i	−0.681825	−	0.393652i
$160$	−2.23604	+	0.0109090i	−0.176775	+	0.000862430i
$161$	1.41821	+	1.19002i	0.111771	+	0.0937866i
$162$	−0.0871557	−	0.996195i	−0.00684760	−	0.0782684i
$163$	−2.10267	+	7.84729i	−0.164694	+	0.614647i	0.833385	+	0.552693i	$0.186400\pi$
$163$	−2.10267	+	7.84729i	−0.164694	+	0.614647i	−0.998079	+	0.0619538i	$0.980267\pi$
$164$	0.0536190	−	0.0928709i	0.00418694	−	0.00725200i
$165$	−7.08353	−	1.21342i	−0.551452	−	0.0944643i
$166$	9.22077	−	1.62587i	0.715671	−	0.126192i
$167$	−18.6036	+	13.0264i	−1.43959	+	1.00801i	−0.445992	+	0.895037i	$0.647149\pi$
$167$	−18.6036	+	13.0264i	−1.43959	+	1.00801i	−0.993598	+	0.112975i	$0.963962\pi$
$168$	1.41109	+	3.02610i	0.108868	+	0.233469i
$169$	1.96910	+	2.34668i	0.151469	+	0.180514i
$170$	0.460611	+	1.68608i	0.0353272	+	0.129316i
$171$	−1.28886	−	4.16399i	−0.0985619	−	0.318428i
$172$	0.380882	−	0.380882i	0.0290420	−	0.0290420i
$173$	1.47815	−	16.8953i	0.112382	−	1.28453i	−0.705322	−	0.708887i	$-0.749197\pi$
$173$	1.47815	−	16.8953i	0.112382	−	1.28453i	0.817703	−	0.575640i	$-0.195247\pi$
$174$	−6.38015	−	2.32218i	−0.483678	−	0.176044i
$175$	15.1986	+	6.90751i	1.14891	+	0.522158i
$176$	0.558104	+	3.16517i	0.0420687	+	0.238583i
$177$	4.26989	−	9.15680i	0.320944	−	0.688267i
$178$	−2.09066	+	0.560192i	−0.156702	+	0.0419881i
$179$	−7.71239	−	13.3583i	−0.576451	−	0.998443i	−0.995882	−	0.0906557i	$-0.971104\pi$
$179$	−7.71239	−	13.3583i	−0.576451	−	0.998443i	0.419431	−	0.907787i	$-0.362230\pi$
$180$	−0.935105	+	2.03115i	−0.0696986	+	0.151393i
$181$	−1.30614	+	1.55660i	−0.0970847	+	0.115701i	−0.812399	−	0.583102i	$-0.801839\pi$
$181$	−1.30614	+	1.55660i	−0.0970847	+	0.115701i	0.715315	+	0.698803i	$0.246283\pi$
$182$	−10.1665	−	2.72410i	−0.753591	−	0.201924i
$183$	−1.42665	−	5.32432i	−0.105461	−	0.393585i
$184$	0.521032	−	0.189640i	0.0384110	−	0.0139804i
$185$	0.985294	+	0.353184i	0.0724402	+	0.0259666i
$186$	8.42846	+	1.48617i	0.618005	+	0.108971i
$187$	2.27689	−	1.06173i	0.166503	−	0.0776416i
$188$	−2.86676	−	0.250809i	−0.209080	−	0.0182921i
$189$	3.33893			0.242872
$190$	−2.11321	+	9.51495i	−0.153309	+	0.690287i
$191$	15.7421			1.13906			0.569529	−	0.821971i	$-0.307126\pi$
$191$	15.7421			1.13906			0.569529	+	0.821971i	$0.307126\pi$
$192$	0.996195	+	0.0871557i	0.0718942	+	0.00628992i
$193$	−11.1449	+	5.19695i	−0.802227	+	0.374085i	−0.780088	−	0.625670i	$-0.784826\pi$
$193$	−11.1449	+	5.19695i	−0.802227	+	0.374085i	−0.0221395	+	0.999755i	$0.507048\pi$
$194$	1.51732	+	0.267544i	0.108937	+	0.0192085i
$195$	−3.01001	−	6.37362i	−0.215551	−	0.456424i
$196$	−3.89830	+	1.41886i	−0.278450	+	0.101347i
$197$	2.70886	+	10.1096i	0.192999	+	0.720281i	0.992776	+	0.119984i	$0.0382842\pi$
$197$	2.70886	+	10.1096i	0.192999	+	0.720281i	−0.799777	+	0.600297i	$0.795049\pi$
$198$	3.10448	+	0.831843i	0.220626	+	0.0591165i
$199$	13.2025	−	15.7342i	0.935903	−	1.11537i	−0.0572284	−	0.998361i	$-0.518226\pi$
$199$	13.2025	−	15.7342i	0.935903	−	1.11537i	0.993131	−	0.117005i	$-0.0373292\pi$
$200$	4.06758	−	2.90771i	0.287622	−	0.205606i
$201$	−0.0947785	−	0.164161i	−0.00668516	−	0.0115790i
$202$	5.13276	−	1.37532i	0.361140	−	0.0967672i
$203$	9.58079	−	20.5461i	0.672439	−	1.44205i
$204$	−0.135735	−	0.769792i	−0.00950336	−	0.0538962i
$205$	0.0220644	+	0.238774i	0.00154104	+	0.0166767i
$206$	6.08567	+	2.21500i	0.424009	+	0.154327i
$207$	0.0483253	−	0.552360i	0.00335884	−	0.0383917i
$208$	−2.22897	+	2.22897i	−0.154551	+	0.154551i
$209$	13.9927	+	0.684685i	0.967898	+	0.0473607i
$210$	−6.48395	−	3.70145i	−0.447435	−	0.255425i
$211$	−7.48190	−	8.91658i	−0.515075	−	0.613843i	0.444334	−	0.895861i	$-0.353440\pi$
$211$	−7.48190	−	8.91658i	−0.515075	−	0.613843i	−0.959409	+	0.282019i	$0.908996\pi$
$212$	−4.19555	−	8.99739i	−0.288152	−	0.617943i
$213$	−11.2212	+	7.85714i	−0.768861	+	0.538362i
$214$	−16.4322	+	2.89744i	−1.12328	+	0.198065i
$215$	−0.203362	+	1.18716i	−0.0138692	+	0.0809638i
$216$	0.500000	−	0.866025i	0.0340207	−	0.0589256i
$217$	−7.39607	+	27.6025i	−0.502078	+	1.87378i
$218$	1.09559	+	12.5227i	0.0742031	+	0.848145i
$219$	6.57083	+	5.51358i	0.444016	+	0.372574i
$220$	−5.10650	−	5.05692i	−0.344280	−	0.340937i
$221$	2.13389	+	1.23200i	0.143541	+	0.0828734i
$222$	−0.424234	−	0.197824i	−0.0284727	−	0.0132770i
$223$	12.2019	+	8.54384i	0.817097	+	0.572138i	0.905695	−	0.423930i	$-0.139350\pi$
$223$	12.2019	+	8.54384i	0.817097	+	0.572138i	−0.0885979	+	0.996067i	$0.528239\pi$
$224$	−0.579800	+	3.28821i	−0.0387395	+	0.219703i
$225$	−0.916244	−	4.91533i	−0.0610829	−	0.327689i
$226$	7.70850	−	6.46820i	0.512762	−	0.430258i
$227$	11.9201	+	11.9201i	0.791165	+	0.791165i	0.981684	−	0.190518i	$-0.0610168\pi$
$227$	11.9201	+	11.9201i	0.791165	+	0.791165i	−0.190518	+	0.981684i	$0.561017\pi$
$228$	1.33259	−	4.15020i	0.0882530	−	0.274854i
$229$			3.66688i			0.242314i	0.992633	+	0.121157i	$0.0386605\pi$
$229$			3.66688i			0.242314i	−0.992633	+	0.121157i	$0.961340\pi$
$230$	−0.706176	+	1.01907i	−0.0465639	+	0.0671954i
$231$	−3.67033	+	10.0841i	−0.241490	+	0.663488i
$232$	−3.89436	−	5.56172i	−0.255677	−	0.365145i
$233$	−3.42922	+	4.89744i	−0.224656	+	0.320842i	−0.915618	−	0.402049i	$-0.868298\pi$
$233$	−3.42922	+	4.89744i	−0.224656	+	0.320842i	0.690962	+	0.722891i	$0.257187\pi$
$234$	1.07813	+	2.96214i	0.0704796	+	0.193641i
$235$	5.55689	−	3.24452i	0.362492	−	0.211649i
$236$	8.74981	−	5.05171i	0.569564	−	0.328838i
$237$	−11.9983	+	1.04972i	−0.779376	+	0.0681866i
$238$	2.60000	−	0.227471i	0.168533	−	0.0147447i
$239$	1.27662	−	0.737059i	0.0825779	−	0.0476764i	−0.458142	−	0.888879i	$-0.651485\pi$
$239$	1.27662	−	0.737059i	0.0825779	−	0.0476764i	0.540720	+	0.841202i	$0.318152\pi$
$240$	−1.93101	+	1.12747i	−0.124646	+	0.0727778i
$241$	8.45409	+	23.2274i	0.544576	+	1.49621i	0.840937	+	0.541133i	$0.182005\pi$
$241$	8.45409	+	23.2274i	0.544576	+	1.49621i	−0.296361	+	0.955076i	$0.595773\pi$
$242$	0.384432	−	0.549026i	0.0247122	−	0.0352927i
$243$	−0.573576	−	0.819152i	−0.0367949	−	0.0525486i
$244$	1.88526	−	5.17972i	0.120692	−	0.331598i
$245$	5.28353	−	7.62456i	0.337552	−	0.487115i
$246$		−	0.107238i		−	0.00683725i
$247$	7.32161	+	11.6271i	0.465863	+	0.739816i
$248$	6.05176	+	6.05176i	0.384287	+	0.384287i
$249$	7.17249	−	6.01843i	0.454538	−	0.381403i
$250$	−3.66973	+	10.5609i	−0.232094	+	0.667931i
$251$	0.117279	−	0.665123i	0.00740259	−	0.0419822i	−0.980883	−	0.194600i	$-0.937659\pi$
$251$	0.117279	−	0.665123i	0.00740259	−	0.0419822i	0.988285	+	0.152618i	$0.0487703\pi$
$252$	2.73509	+	1.91513i	0.172295	+	0.120642i
$253$	1.61510	+	0.753133i	0.101540	+	0.0473491i
$254$	6.76437	+	3.90541i	0.424434	+	0.245047i
$255$	1.24194	+	1.22988i	0.0777732	+	0.0770181i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	2.36875	+	27.0749i	0.147759	+	1.68889i	0.602384	+	0.798206i	$0.294217\pi$
$257$	2.36875	+	27.0749i	0.147759	+	1.68889i	−0.454626	+	0.890683i	$0.650227\pi$
$258$	0.139412	−	0.520294i	0.00867944	−	0.0323921i
$259$	0.781461	−	1.35353i	0.0485576	−	0.0841043i
$260$	1.19010	−	6.94743i	0.0738070	−	0.430861i
$261$	−6.68646	+	1.17900i	−0.413882	+	0.0729785i
$262$	14.6173	−	10.2351i	0.903058	−	0.632328i
$263$	7.52459	+	16.1365i	0.463986	+	0.995021i	0.989540	+	0.144261i	$0.0460803\pi$
$263$	7.52459	+	16.1365i	0.463986	+	0.995021i	−0.525554	+	0.850760i	$0.676142\pi$
$264$	2.06592	+	2.46206i	0.127148	+	0.151529i
$265$	19.2785	+	11.0054i	1.18427	+	0.676055i
$266$	13.4167	+	5.64024i	0.822633	+	0.345826i
$267$	−1.53047	+	1.53047i	−0.0936634	+	0.0936634i
$268$	0.0165210	−	0.188836i	0.00100918	−	0.0115350i
$269$	−25.3126	−	9.21303i	−1.54334	−	0.561728i	−0.576493	−	0.817102i	$-0.695579\pi$
$269$	−25.3126	−	9.21303i	−1.54334	−	0.561728i	−0.966842	+	0.255374i	$0.917801\pi$
$270$	0.205751	+	2.22658i	0.0125216	+	0.135505i
$271$	−5.32858	−	30.2199i	−0.323688	−	1.83573i	−0.518738	−	0.854933i	$-0.673598\pi$
$271$	−5.32858	−	30.2199i	−0.323688	−	1.83573i	0.195049	−	0.980793i	$-0.437513\pi$
$272$	0.330347	−	0.708431i	0.0200302	−	0.0429549i
$273$	−10.1665	+	2.72410i	−0.615304	+	0.164870i
$274$	−5.94078	−	10.2897i	−0.358895	−	0.621625i
$275$	15.8523	+	2.63597i	0.955930	+	0.158955i
$276$	0.356407	−	0.424749i	0.0214532	−	0.0255669i
$277$	−18.4970	−	4.95626i	−1.11138	−	0.297793i	−0.343989	−	0.938974i	$-0.611778\pi$
$277$	−18.4970	−	4.95626i	−1.11138	−	0.297793i	−0.767390	+	0.641181i	$0.778445\pi$
$278$	−5.35082	−	19.9695i	−0.320921	−	1.19769i
$279$	8.04234	−	2.92717i	0.481483	−	0.175245i
$280$	−3.18828	−	6.75110i	−0.190536	−	0.403455i
$281$	−9.02399	−	1.59117i	−0.538326	−	0.0949214i	−0.102126	−	0.994771i	$-0.532565\pi$
$281$	−9.02399	−	1.59117i	−0.538326	−	0.0949214i	−0.436199	+	0.899850i	$0.643676\pi$
$282$	−2.60809	+	1.21617i	−0.155309	+	0.0724220i
$283$	−22.2877	−	1.94992i	−1.32487	−	0.115911i	−0.597338	−	0.801989i	$-0.703775\pi$
$283$	−22.2877	−	1.94992i	−1.32487	−	0.115911i	−0.727527	+	0.686079i	$0.759331\pi$
$284$	−13.6985			−0.812856
$285$	2.92738	+	9.29680i	0.173403	+	0.550695i
$286$	−10.1313			−0.599076
$287$	0.356698	+	0.0312071i	0.0210552	+	0.00184209i
$288$	0.906308	−	0.422618i	0.0534047	−	0.0249030i
$289$	16.1400	+	2.84592i	0.949412	+	0.167407i
$290$	14.2916	+	5.12290i	0.839232	+	0.300827i
$291$	1.44781	−	0.526959i	0.0848720	−	0.0308909i
$292$	2.22005	+	8.28534i	0.129919	+	0.484863i
$293$	14.1829	+	3.80029i	0.828572	+	0.222015i	0.648091	−	0.761563i	$-0.275568\pi$
$293$	14.1829	+	3.80029i	0.828572	+	0.222015i	0.180482	+	0.983578i	$0.442234\pi$
$294$	−2.66659	+	3.17792i	−0.155519	+	0.185340i
$295$	−9.44775	+	20.5216i	−0.550069	+	1.19481i
$296$	−0.234045	−	0.405378i	−0.0136036	−	0.0235621i
$297$	3.10448	−	0.831843i	0.180140	−	0.0482684i
$298$	−2.28151	+	4.89271i	−0.132164	+	0.283427i
$299$	0.303507	+	1.72127i	0.0175522	+	0.0995437i
$300$	2.06878	−	4.55194i	0.119441	−	0.262806i
$301$	1.69005	+	0.615127i	0.0974128	+	0.0354553i
$302$	1.57960	−	18.0549i	0.0908955	−	1.03894i
$303$	3.75744	−	3.75744i	0.215859	−	0.215859i
$304$	3.47205	−	2.63531i	0.199136	−	0.151145i
$305$	3.24812	+	11.8898i	0.185987	+	0.680810i
$306$	−0.502446	−	0.598792i	−0.0287229	−	0.0342306i
$307$	−9.17780	−	19.6819i	−0.523805	−	1.12330i	−0.973198	−	0.229969i	$-0.926137\pi$
$307$	−9.17780	−	19.6819i	−0.523805	−	1.12330i	0.449393	−	0.893334i	$-0.351640\pi$
$308$	−8.79058	+	6.15523i	−0.500890	+	0.350727i
$309$	6.37785	−	1.12459i	0.362823	−	0.0639755i
$310$	−18.8626	−	3.23118i	−1.07132	−	0.183519i
$311$	−5.58882	+	9.68012i	−0.316913	+	0.548909i	−0.979842	−	0.199773i	$-0.935980\pi$
$311$	−5.58882	+	9.68012i	−0.316913	+	0.548909i	0.662929	+	0.748682i	$0.269313\pi$
$312$	−0.815860	+	3.04483i	−0.0461890	+	0.172380i
$313$	1.89668	+	21.6791i	0.107206	+	1.22538i	0.839108	+	0.543965i	$0.183078\pi$
$313$	1.89668	+	21.6791i	0.107206	+	1.22538i	−0.731901	+	0.681410i	$0.761367\pi$
$314$	11.4098	+	9.57396i	0.643892	+	0.540290i
$315$	−7.46600	+	0.0364243i	−0.420661	+	0.00205228i
$316$	−10.4306	−	6.02209i	−0.586765	−	0.338769i
$317$	20.3803	+	9.50351i	1.14467	+	0.533770i	0.900024	−	0.435841i	$-0.143549\pi$
$317$	20.3803	+	9.50351i	1.14467	+	0.533770i	0.244650	+	0.969611i	$0.421327\pi$
$318$	−8.13215	−	5.69419i	−0.456028	−	0.319314i
$319$	3.78931	−	21.4903i	0.212161	−	1.20322i
$320$	−2.22848	−	0.184016i	−0.124576	−	0.0102868i
$321$	−12.7820	+	10.7254i	−0.713421	+	0.598631i
$322$	1.30910	+	1.30910i	0.0729530	+	0.0729530i
$323$	−2.69217	−	2.08836i	−0.149797	−	0.116200i
$324$		−	1.00000i		−	0.0555556i
$325$	6.80003	+	14.2188i	0.377198	+	0.788719i
$326$	−2.77861	+	7.63417i	−0.153893	+	0.422817i
$327$	7.21017	+	10.2972i	0.398723	+	0.569436i
$328$	0.0615092	−	0.0878443i	0.00339628	−	0.00485039i
$329$	−3.28629	−	9.02902i	−0.181179	−	0.497786i
$330$	−6.95082	−	1.82617i	−0.382630	−	0.100527i
$331$	−17.6099	+	10.1671i	−0.967930	+	0.558835i	−0.898605	−	0.438759i	$-0.855418\pi$
$331$	−17.6099	+	10.1671i	−0.967930	+	0.558835i	−0.0693255	+	0.997594i	$0.522085\pi$
$332$	9.32739	−	0.816041i	0.511907	−	0.0447861i
$333$	−0.466309	+	0.0407968i	−0.0255536	+	0.00223565i
$334$	−19.6681	+	11.3554i	−1.07619	+	0.621340i
$335$	0.213720	+	0.366037i	0.0116767	+	0.0199988i
$336$	1.14198	+	3.13757i	0.0623003	+	0.171169i
$337$	18.1517	−	25.9233i	0.988787	−	1.41213i	0.0790876	−	0.996868i	$-0.474799\pi$
$337$	18.1517	−	25.9233i	0.988787	−	1.41213i	0.909700	−	0.415267i	$-0.136312\pi$
$338$	1.75708	+	2.50937i	0.0955724	+	0.136491i
$339$	3.44166	−	9.45587i	0.186925	−	0.513573i
$340$	0.311907	+	1.71981i	0.0169155	+	0.0932696i
$341$			27.5069i			1.48958i
$342$	−0.921044	−	4.26048i	−0.0498044	−	0.230380i
$343$	6.73238	+	6.73238i	0.363515	+	0.363515i
$344$	0.412629	−	0.346237i	0.0222474	−	0.0186678i
$345$	−0.102032	+	1.23563i	−0.00549320	+	0.0665240i
$346$	2.94505	−	16.7022i	0.158327	−	0.897916i
$347$	−5.45178	−	3.81738i	−0.292667	−	0.204928i	0.418017	−	0.908439i	$-0.362725\pi$
$347$	−5.45178	−	3.81738i	−0.292667	−	0.204928i	−0.710684	+	0.703512i	$0.751614\pi$
$348$	−6.15348	−	2.86941i	−0.329861	−	0.153817i
$349$	−13.2060	−	7.62452i	−0.706904	−	0.408131i	0.103010	−	0.994680i	$-0.467153\pi$
$349$	−13.2060	−	7.62452i	−0.706904	−	0.408131i	−0.809913	+	0.586549i	$0.800486\pi$
$350$	14.5388	+	8.20587i	0.777130	+	0.438622i
$351$	2.41476	+	2.02622i	0.128890	+	0.108152i
$352$	0.280118	+	3.20176i	0.0149303	+	0.170655i
$353$	−7.64063	+	28.5152i	−0.406670	+	1.51771i	0.394285	+	0.918988i	$0.370992\pi$
$353$	−7.64063	+	28.5152i	−0.406670	+	1.51771i	−0.800955	+	0.598725i	$0.795674\pi$
$354$	5.05171	−	8.74981i	0.268495	−	0.465047i
$355$	25.0052	−	17.6913i	1.32714	−	0.938956i
$356$	−2.13153	+	0.375847i	−0.112971	+	0.0199198i
$357$	2.13793	−	1.49700i	0.113151	−	0.0792295i
$358$	−6.51880	−	13.9796i	−0.344529	−	0.738845i
$359$	18.8229	+	22.4323i	0.993437	+	1.18393i	0.982929	+	0.183987i	$0.0589006\pi$
$359$	18.8229	+	22.4323i	0.993437	+	1.18393i	0.0105085	+	0.999945i	$0.496655\pi$
$360$	−1.10857	+	1.94192i	−0.0584269	+	0.102348i
$361$	−7.84818	−	17.3034i	−0.413062	−	0.910703i
$362$	−1.43684	+	1.43684i	−0.0755185	+	0.0755185i
$363$	0.0584150	−	0.667687i	0.00306599	−	0.0350445i
$364$	−9.89039	−	3.59981i	−0.518397	−	0.188681i
$365$	−14.7528	−	12.2569i	−0.772197	−	0.641557i
$366$	−0.957173	−	5.42840i	−0.0500322	−	0.283747i
$367$	−1.53588	+	3.29370i	−0.0801721	+	0.171930i	−0.942308	−	0.334748i	$-0.891349\pi$
$367$	−1.53588	+	3.29370i	−0.0801721	+	0.171930i	0.862136	+	0.506678i	$0.169127\pi$
$368$	0.535577	−	0.143507i	0.0279189	−	0.00748085i
$369$	−0.0536190	−	0.0928709i	−0.00279129	−	0.00483466i
$370$	0.950763	+	0.437714i	0.0494278	+	0.0227556i
$371$	21.3067	−	25.3923i	1.10619	−	1.31830i
$372$	8.26686	+	2.21510i	0.428617	+	0.114848i
$373$	5.66638	+	21.1472i	0.293394	+	1.09496i	0.942484	+	0.334250i	$0.108483\pi$
$373$	5.66638	+	21.1472i	0.293394	+	1.09496i	−0.649090	+	0.760711i	$0.724850\pi$
$374$	2.36077	−	0.859248i	0.122072	−	0.0444307i
$375$	2.10238	+	10.9809i	0.108566	+	0.567051i
$376$	−2.83399	−	0.499709i	−0.146152	−	0.0257705i
$377$	19.3973	−	9.04509i	0.999009	−	0.465846i
$378$	3.32623	+	0.291007i	0.171083	+	0.0149678i
$379$	−29.7730			−1.52934			−0.764669	−	0.644423i	$-0.777098\pi$
$379$	−29.7730			−1.52934			−0.764669	+	0.644423i	$0.777098\pi$
$380$	−2.93446	+	9.29457i	−0.150534	+	0.476801i
$381$	7.81082			0.400161
$382$	15.6822	+	1.37201i	0.802371	+	0.0701983i
$383$	0.167807	−	0.0782495i	0.00857452	−	0.00399836i	−0.418326	−	0.908297i	$-0.637383\pi$
$383$	0.167807	−	0.0782495i	0.00857452	−	0.00399836i	0.426901	+	0.904298i	$0.359605\pi$
$384$	0.984808	+	0.173648i	0.0502558	+	0.00886145i
$385$	8.09700	−	22.5886i	0.412661	−	1.15122i
$386$	−11.5554	+	4.20583i	−0.588156	+	0.214071i
$387$	−0.139412	−	0.520294i	−0.00708673	−	0.0264481i
$388$	1.48823	+	0.398769i	0.0755532	+	0.0202444i
$389$	1.36607	−	1.62802i	0.0692625	−	0.0825438i	−0.730301	−	0.683126i	$-0.760620\pi$
$389$	1.36607	−	1.62802i	0.0692625	−	0.0825438i	0.799563	+	0.600582i	$0.205064\pi$
$390$	−2.44306	−	6.61170i	−0.123709	−	0.334797i
$391$	−0.216706	−	0.375345i	−0.0109593	−	0.0189820i
$392$	−4.00713	+	1.07371i	−0.202390	+	0.0542304i
$393$	7.54137	−	16.1725i	0.380412	−	0.815795i
$394$	1.81744	+	10.3072i	0.0915616	+	0.519271i
$395$	26.8173	−	2.47810i	1.34933	−	0.124687i
$396$	3.02017	+	1.09925i	0.151769	+	0.0552394i
$397$	−0.449465	+	5.13741i	−0.0225580	+	0.257839i	0.976539	+	0.215343i	$0.0690868\pi$
$397$	−0.449465	+	5.13741i	−0.0225580	+	0.257839i	−0.999097	+	0.0424968i	$0.986469\pi$
$398$	14.5236	−	14.5236i	0.728003	−	0.728003i
$399$	14.4394	−	1.82377i	0.722872	−	0.0913029i
$400$	4.30553	−	2.54213i	0.215276	−	0.127107i
$401$	10.4259	+	12.4251i	0.520643	+	0.620478i	0.960733	−	0.277476i	$-0.0894978\pi$
$401$	10.4259	+	12.4251i	0.520643	+	0.620478i	−0.440090	+	0.897954i	$0.645053\pi$
$402$	−0.0801103	−	0.171797i	−0.00399554	−	0.00856846i
$403$	−22.0994	+	15.4742i	−1.10085	+	0.770824i
$404$	5.23310	−	0.922736i	0.260356	−	0.0459079i
$405$	1.29148	+	1.82540i	0.0641740	+	0.0907049i
$406$	11.3350	−	19.6329i	0.562548	−	0.974362i
$407$	0.389378	−	1.45318i	0.0193007	−	0.0720313i
$408$	−0.0681268	−	0.778693i	−0.00337278	−	0.0385510i
$409$	10.1728	+	8.53598i	0.503012	+	0.422077i	0.858662	−	0.512542i	$-0.171296\pi$
$409$	10.1728	+	8.53598i	0.503012	+	0.422077i	−0.355650	+	0.934619i	$0.615741\pi$
$410$	0.00116986	+	0.239789i	5.77751e−5	+	0.0118423i
$411$	−10.2897	−	5.94078i	−0.507555	−	0.293037i
$412$	5.86946	+	2.73698i	0.289168	+	0.134841i
$413$	27.6338	+	19.3494i	1.35977	+	0.952121i
$414$	0.0962828	−	0.546047i	0.00473204	−	0.0268367i
$415$	−15.9723	+	13.5357i	−0.784050	+	0.664442i
$416$	−2.41476	+	2.02622i	−0.118393	+	0.0993437i
$417$	−14.6187	−	14.6187i	−0.715882	−	0.715882i
$418$	13.8798	+	1.90163i	0.678884	+	0.0930116i
$419$			28.7483i			1.40444i	0.711958	+	0.702222i	$0.247809\pi$
$419$			28.7483i			1.40444i	−0.711958	+	0.702222i	$0.752191\pi$
$420$	−6.13668	−	4.25248i	−0.299439	−	0.207500i
$421$	3.49121	−	9.59203i	0.170151	−	0.467487i	−0.825082	−	0.565014i	$-0.808871\pi$
$421$	3.49121	−	9.59203i	0.170151	−	0.467487i	0.995233	+	0.0975268i	$0.0310932\pi$
$422$	−6.67630	−	9.53474i	−0.324997	−	0.464144i
$423$	−1.65059	+	2.35728i	−0.0802542	+	0.114615i
$424$	−3.39541	−	9.32882i	−0.164896	−	0.453047i
$425$	−2.79044	−	2.73651i	−0.135356	−	0.132740i
$426$	−11.8632	+	6.84925i	−0.574776	+	0.331847i
$427$	18.3346	−	1.60407i	0.887276	−	0.0776266i
$428$	−16.6222	+	1.45425i	−0.803464	+	0.0702940i
$429$	−8.77395	+	5.06565i	−0.423611	+	0.244572i
$430$	−0.306056	+	1.16492i	−0.0147593	+	0.0561775i
$431$	−12.3271	−	33.8685i	−0.593777	−	1.63139i	−0.763433	−	0.645887i	$-0.776488\pi$
$431$	−12.3271	−	33.8685i	−0.593777	−	1.63139i	0.169656	−	0.985503i	$-0.445734\pi$
$432$	0.573576	−	0.819152i	0.0275962	−	0.0394115i
$433$	−22.4625	−	32.0798i	−1.07948	−	1.54166i	−0.816930	−	0.576737i	$-0.804326\pi$
$433$	−22.4625	−	32.0798i	−1.07948	−	1.54166i	−0.262549	−	0.964919i	$-0.584563\pi$
$434$	−9.77364	+	26.8529i	−0.469150	+	1.28898i
$435$	14.9383	−	2.70924i	0.716239	−	0.129898i
$436$			12.5705i			0.602020i
$437$	−0.0927226	−	2.41510i	−0.00443552	−	0.115530i
$438$	6.06529	+	6.06529i	0.289811	+	0.289811i
$439$	−20.8363	+	17.4837i	−0.994461	+	0.834452i	−0.986207	−	0.165514i	$-0.947072\pi$
$439$	−20.8363	+	17.4837i	−0.994461	+	0.834452i	−0.00825400	+	0.999966i	$0.502627\pi$
$440$	−4.64633	−	5.48274i	−0.221505	−	0.261379i
$441$	−0.720377	+	4.08546i	−0.0343036	+	0.194546i
$442$	2.01839	+	1.41329i	0.0960052	+	0.0672236i
$443$	1.51999	+	0.708784i	0.0722170	+	0.0336753i	0.458391	−	0.888751i	$-0.348426\pi$
$443$	1.51999	+	0.708784i	0.0722170	+	0.0336753i	−0.386174	+	0.922426i	$0.626204\pi$
$444$	−0.405378	−	0.234045i	−0.0192384	−	0.0111073i
$445$	3.40550	−	3.43889i	0.161436	−	0.163019i
$446$	11.4108	+	9.57479i	0.540316	+	0.453379i
$447$	0.470511	+	5.37796i	0.0222544	+	0.254369i
$448$	−0.864180	+	3.22516i	−0.0408287	+	0.152375i
$449$	−6.13660	+	10.6289i	−0.289604	+	0.501609i	−0.973715	−	0.227769i	$-0.926857\pi$
$449$	−6.13660	+	10.6289i	−0.289604	+	0.501609i	0.684111	+	0.729378i	$0.260190\pi$
$450$	−0.484358	−	4.97648i	−0.0228329	−	0.234594i
$451$	0.339426	−	0.0598500i	0.0159830	−	0.00281823i
$452$	8.24291	−	5.77174i	0.387714	−	0.271480i
$453$	−7.65946	−	16.4258i	−0.359873	−	0.771750i
$454$	10.8358	+	12.9137i	0.508551	+	0.606068i
$455$	22.7030	−	6.20212i	1.06433	−	0.290760i
$456$	1.68923	−	4.01827i	0.0791057	−	0.188173i
$457$	4.26449	−	4.26449i	0.199484	−	0.199484i	−0.600295	−	0.799779i	$-0.704950\pi$
$457$	4.26449	−	4.26449i	0.199484	−	0.199484i	0.799779	+	0.600295i	$0.204950\pi$
$458$	−0.319590	+	3.65293i	−0.0149334	+	0.170690i
$459$	−0.734527	−	0.267346i	−0.0342848	−	0.0124786i
$460$	−0.792307	+	0.953644i	−0.0369415	+	0.0444639i
$461$	−3.30943	−	18.7687i	−0.154135	−	0.874145i	−0.959572	−	0.281463i	$-0.909180\pi$
$461$	−3.30943	−	18.7687i	−0.154135	−	0.874145i	0.805437	−	0.592682i	$-0.201931\pi$
$462$	−4.53525	+	9.72588i	−0.210999	+	0.452489i
$463$	−38.5050	+	10.3174i	−1.78948	+	0.479490i	−0.992258	−	0.124197i	$-0.960365\pi$
$463$	−38.5050	+	10.3174i	−1.78948	+	0.479490i	−0.797222	+	0.603686i	$0.793698\pi$
$464$	−3.39481	−	5.87998i	−0.157600	−	0.272971i
$465$	−17.9511	+	6.63302i	−0.832461	+	0.307599i
$466$	−3.84302	+	4.57993i	−0.178024	+	0.212161i
$467$	−2.65383	−	0.711092i	−0.122805	−	0.0329054i	0.196893	−	0.980425i	$-0.436915\pi$
$467$	−2.65383	−	0.711092i	−0.122805	−	0.0329054i	−0.319698	+	0.947520i	$0.603581\pi$
$468$	0.815860	+	3.04483i	0.0377132	+	0.140747i
$469$	0.594749	−	0.216471i	0.0274630	−	0.00999570i
$470$	5.81853	−	2.74786i	0.268389	−	0.126749i
$471$	14.6682	+	2.58639i	0.675873	+	0.119175i
$472$	9.15680	−	4.26989i	0.421476	−	0.196537i
$473$	1.72463	+	0.150885i	0.0792984	+	0.00693771i
$474$	−12.0442			−0.553207
$475$	−6.64716	−	20.7561i	−0.304993	−	0.952355i
$476$	2.60994			0.119626
$477$	−9.88974	−	0.865240i	−0.452820	−	0.0396166i
$478$	1.33601	−	0.622989i	0.0611074	−	0.0284949i
$479$	22.8896	+	4.03605i	1.04585	+	0.184412i	0.670071	−	0.742297i	$-0.266264\pi$
$479$	22.8896	+	4.03605i	1.04585	+	0.184412i	0.375780	+	0.926709i	$0.377375\pi$
$480$	−2.02193	+	0.954879i	−0.0922881	+	0.0435841i
$481$	1.38655	−	0.504662i	0.0632212	−	0.0230106i
$482$	6.39751	+	23.8758i	0.291399	+	1.08752i
$483$	1.78826	+	0.479162i	0.0813685	+	0.0218026i
$484$	0.430820	−	0.513431i	0.0195827	−	0.0233378i
$485$	−3.23161	+	1.19410i	−0.146740	+	0.0542211i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−12.4320	+	3.33114i	−0.563347	+	0.150948i	−0.529244	−	0.848470i	$-0.677524\pi$
$487$	−12.4320	+	3.33114i	−0.563347	+	0.150948i	−0.0341036	+	0.999418i	$0.510858\pi$
$488$	2.32953	−	4.99570i	0.105453	−	0.226145i
$489$	1.41074	+	8.00069i	0.0637957	+	0.361803i
$490$	5.92795	−	7.13506i	0.267797	−	0.322329i
$491$	11.0765	+	4.03153i	0.499877	+	0.181940i	0.579639	−	0.814874i	$-0.303194\pi$
$491$	11.0765	+	4.03153i	0.499877	+	0.181940i	−0.0797616	+	0.996814i	$0.525416\pi$
$492$	0.00934641	−	0.106830i	0.000421369	−	0.00481627i
$493$	−3.75277	+	3.75277i	−0.169016	+	0.169016i
$494$	6.28038	+	12.2210i	0.282568	+	0.549849i
$495$	−6.93267	+	1.89390i	−0.311600	+	0.0851246i
$496$	5.50129	+	6.55618i	0.247015	+	0.294381i
$497$	−19.3299	−	41.4531i	−0.867064	−	1.85942i
$498$	7.66973	−	5.37041i	0.343689	−	0.240654i
$499$	−8.08510	+	1.42562i	−0.361939	+	0.0638195i	−0.351660	−	0.936128i	$-0.614383\pi$
$499$	−8.08510	+	1.42562i	−0.361939	+	0.0638195i	−0.0102782	+	0.999947i	$0.503272\pi$
$500$	−4.57621	+	10.2009i	−0.204654	+	0.456198i
$501$	−11.3554	+	19.6681i	−0.507322	+	0.878707i
$502$	0.174802	−	0.652371i	0.00780180	−	0.0291167i
$503$	−1.27978	−	14.6279i	−0.0570625	−	0.652227i	−0.969836	−	0.243760i	$-0.921619\pi$
$503$	−1.27978	−	14.6279i	−0.0570625	−	0.652227i	0.912773	−	0.408467i	$-0.133937\pi$
$504$	2.55777	+	2.14623i	0.113932	+	0.0956005i
$505$	−8.36081	+	8.44279i	−0.372051	+	0.375699i
$506$	1.54331	+	0.891032i	0.0686087	+	0.0396112i
$507$	2.77636	+	1.29464i	0.123302	+	0.0574968i
$508$	6.39825	+	4.48010i	0.283877	+	0.198773i
$509$	4.37116	−	24.7901i	0.193748	−	1.09880i	−0.720442	−	0.693516i	$-0.756061\pi$
$509$	4.37116	−	24.7901i	0.193748	−	1.09880i	0.914190	−	0.405286i	$-0.132828\pi$
$510$	1.13002	+	1.33344i	0.0500382	+	0.0590458i
$511$	−21.9396	+	18.4095i	−0.970550	+	0.814388i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−2.92789	−	3.22916i	−0.129269	−	0.142571i
$514$			27.1784i			1.19879i
$515$	−14.2489	+	2.58420i	−0.627880	+	0.113873i
$516$	0.184229	−	0.506164i	0.00811021	−	0.0222826i
$517$	−5.30497	−	7.57629i	−0.233312	−	0.333205i
$518$	0.896456	−	1.28027i	0.0393880	−	0.0562519i
$519$	−5.80061	−	15.9371i	−0.254619	−	0.699559i
$520$	1.79108	−	6.81727i	0.0785441	−	0.298957i
$521$	−24.5582	+	14.1787i	−1.07591	+	0.621180i	−0.929791	−	0.368087i	$-0.880013\pi$
$521$	−24.5582	+	14.1787i	−1.07591	+	0.621180i	−0.146123	+	0.989266i	$0.546680\pi$
$522$	−6.76378	+	0.591754i	−0.296042	+	0.0259004i
$523$	−39.4089	+	3.44783i	−1.72323	+	0.150763i	−0.905362	−	0.424641i	$-0.860400\pi$
$523$	−39.4089	+	3.44783i	−1.72323	+	0.150763i	−0.817869	+	0.575404i	$0.804845\pi$
$524$	15.4537	−	8.92220i	0.675098	−	0.389768i
$525$	16.6939	−	0.162893i	0.728581	−	0.00710922i
$526$	6.08956	+	16.7309i	0.265518	+	0.729503i
$527$	3.83716	−	5.48003i	0.167149	−	0.238714i
$528$	1.84347	+	2.63275i	0.0802268	+	0.114576i
$529$	−7.76131	+	21.3240i	−0.337448	+	0.927132i
$530$	18.2459	+	12.6437i	0.792553	+	0.549209i
$531$		−	10.1034i		−	0.438451i
$532$	12.8741	+	6.78813i	0.558163	+	0.294303i
$533$	0.239031	+	0.239031i	0.0103536	+	0.0103536i
$534$	−1.65804	+	1.39126i	−0.0717503	+	0.0602057i
$535$	28.4640	−	24.1218i	1.23061	−	1.04288i
$536$	0.0329162	−	0.186677i	0.00142176	−	0.00806323i
$537$	−12.6352	−	8.84729i	−0.545251	−	0.381789i
$538$	−24.4133	−	11.3841i	−1.05253	−	0.490804i
$539$	−11.5469	−	6.66660i	−0.497360	−	0.287151i
$540$	0.0109090	+	2.23604i	0.000469447	+	0.0962239i
$541$	−23.6592	−	19.8524i	−1.01719	−	0.853523i	−0.0279173	−	0.999610i	$-0.508888\pi$
$541$	−23.6592	−	19.8524i	−1.01719	−	0.853523i	−0.989272	+	0.146087i	$0.953332\pi$
$542$	−2.67447	−	30.5693i	−0.114878	−	1.31306i
$543$	−0.525919	+	1.96276i	−0.0225693	+	0.0842299i
$544$	0.390834	−	0.676944i	0.0167568	−	0.0290237i
$545$	−16.2346	−	22.9463i	−0.695412	−	0.982911i
$546$	−10.3652	+	1.82767i	−0.443591	+	0.0782170i
$547$	−0.315300	+	0.220775i	−0.0134813	+	0.00943968i	−0.580298	−	0.814404i	$-0.697064\pi$
$547$	−0.315300	+	0.220775i	−0.0134813	+	0.00943968i	0.566816	+	0.823844i	$0.308175\pi$
$548$	−5.02136	−	10.7683i	−0.214502	−	0.460001i
$549$	−3.54314	−	4.22255i	−0.151217	−	0.180214i
$550$	15.5622	+	4.00756i	0.663576	+	0.170883i
$551$	−28.2719	+	8.75089i	−1.20442	+	0.372801i
$552$	0.392070	−	0.392070i	0.0166876	−	0.0166876i
$553$	3.50494	−	40.0617i	0.149045	−	1.70360i
$554$	−17.9947	−	6.54953i	−0.764521	−	0.278263i
$555$	1.04224	−	0.0963102i	0.0442407	−	0.00408814i
$556$	−3.59000	−	20.3599i	−0.152250	−	0.863453i
$557$	10.9380	−	23.4566i	0.463459	−	0.993890i	−0.526189	−	0.850368i	$-0.676379\pi$
$557$	10.9380	−	23.4566i	0.463459	−	0.993890i	0.989647	−	0.143522i	$-0.0458428\pi$
$558$	8.26686	−	2.21510i	0.349964	−	0.0937726i
$559$	0.848975	+	1.47047i	0.0359078	+	0.0621942i
$560$	−2.58775	−	7.00328i	−0.109352	−	0.295943i
$561$	1.61486	−	1.92451i	0.0681794	−	0.0812530i
$562$	−8.85097	−	2.37161i	−0.373356	−	0.100040i
$563$	−1.56953	−	5.85756i	−0.0661477	−	0.246867i	0.924933	−	0.380130i	$-0.124121\pi$
$563$	−1.56953	−	5.85756i	−0.0661477	−	0.246867i	−0.991081	+	0.133264i	$0.957454\pi$
$564$	−2.70416	+	0.984234i	−0.113866	+	0.0414437i
$565$	−7.59253	+	21.1813i	−0.319420	+	0.891103i
$566$	−22.0329	−	3.88500i	−0.926113	−	0.163299i
$567$	3.02610	−	1.41109i	0.127084	−	0.0592604i
$568$	−13.6464	−	1.19390i	−0.572589	−	0.0500950i
$569$	41.9165			1.75723			0.878616	−	0.477528i	$-0.158467\pi$
$569$	41.9165			1.75723			0.878616	+	0.477528i	$0.158467\pi$
$570$	2.10597	+	9.51656i	0.0882094	+	0.398605i
$571$	28.7206			1.20192			0.600959	−	0.799280i	$-0.294785\pi$
$571$	28.7206			1.20192			0.600959	+	0.799280i	$0.294785\pi$
$572$	−10.0927	−	0.883000i	−0.421999	−	0.0369201i
$573$	14.2672	−	6.65290i	0.596020	−	0.277929i
$574$	0.352621	+	0.0621766i	0.0147181	+	0.00259520i
$575$	0.214668	−	2.76403i	0.00895225	−	0.115268i
$576$	0.939693	−	0.342020i	0.0391539	−	0.0142508i
$577$	−8.92255	−	33.2994i	−0.371451	−	1.38627i	−0.858462	−	0.512877i	$-0.828580\pi$
$577$	−8.92255	−	33.2994i	−0.371451	−	1.38627i	0.487011	−	0.873396i	$-0.338087\pi$
$578$	15.8306	+	4.24178i	0.658464	+	0.176435i
$579$	−7.90438	+	9.42007i	−0.328495	+	0.391485i
$580$	13.7907	+	6.34900i	0.572629	+	0.263628i
$581$	15.6312	+	27.0741i	0.648494	+	1.12322i
$582$	1.48823	−	0.398769i	0.0616890	−	0.0165295i
$583$	13.4845	−	28.9176i	0.558470	−	1.19764i
$584$	1.48949	+	8.44730i	0.0616354	+	0.349552i
$585$	−5.42160	−	4.50437i	−0.224156	−	0.186233i
$586$	13.7977	+	5.02195i	0.569977	+	0.207455i
$587$	1.72492	−	19.7159i	0.0711949	−	0.813761i	−0.873717	−	0.486435i	$-0.838297\pi$
$587$	1.72492	−	19.7159i	0.0711949	−	0.813761i	0.944912	−	0.327326i	$-0.106147\pi$
$588$	−2.93342	+	2.93342i	−0.120972	+	0.120972i
$589$	33.1806	−	17.0515i	1.36718	−	0.702596i
$590$	−11.2004	+	19.6201i	−0.461112	+	0.807745i
$591$	6.72757	+	8.01761i	0.276735	+	0.329800i
$592$	−0.197824	−	0.424234i	−0.00813050	−	0.0174359i
$593$	−0.565004	+	0.395620i	−0.0232019	+	0.0162462i	−0.585120	−	0.810947i	$-0.698953\pi$
$593$	−0.565004	+	0.395620i	−0.0232019	+	0.0162462i	0.561918	+	0.827193i	$0.310064\pi$
$594$	3.16517	−	0.558104i	0.129868	−	0.0228993i
$595$	−4.76418	+	3.37067i	−0.195312	+	0.138184i
$596$	−2.69925	+	4.67524i	−0.110566	+	0.191505i
$597$	5.31601	−	19.8396i	0.217570	−	0.811982i
$598$	0.152333	+	1.74117i	0.00622936	+	0.0712019i
$599$	−23.5658	−	19.7741i	−0.962873	−	0.807946i	0.0185454	−	0.999828i	$-0.494096\pi$
$599$	−23.5658	−	19.7741i	−0.962873	−	0.807946i	−0.981418	+	0.191882i	$0.938541\pi$
$600$	2.45763	−	4.35431i	0.100332	−	0.177764i
$601$	−10.0830	−	5.82141i	−0.411294	−	0.237460i	0.280052	−	0.959985i	$-0.409648\pi$
$601$	−10.0830	−	5.82141i	−0.411294	−	0.237460i	−0.691345	+	0.722524i	$0.742982\pi$
$602$	1.63001	+	0.760084i	0.0664340	+	0.0309787i
$603$	−0.155276	−	0.108725i	−0.00632333	−	0.00442764i
$604$	3.14717	−	17.8485i	0.128056	−	0.726244i
$605$	−0.123335	+	1.49361i	−0.00501426	+	0.0607240i
$606$	4.07063	−	3.41566i	0.165358	−	0.138752i
$607$	−18.2410	−	18.2410i	−0.740379	−	0.740379i	0.232272	−	0.972651i	$-0.425384\pi$
$607$	−18.2410	−	18.2410i	−0.740379	−	0.740379i	−0.972651	+	0.232272i	$0.925384\pi$
$608$	3.68852	−	2.32267i	0.149589	−	0.0941966i
$609$		−	22.6701i		−	0.918638i
$610$	2.19950	+	12.1277i	0.0890550	+	0.491036i
$611$	3.10254	−	8.52417i	0.125516	−	0.344851i
$612$	−0.448346	−	0.640304i	−0.0181233	−	0.0258828i
$613$	4.14333	−	5.91729i	0.167348	−	0.238997i	−0.726715	−	0.686939i	$-0.758954\pi$
$613$	4.14333	−	5.91729i	0.167348	−	0.238997i	0.894063	+	0.447942i	$0.147843\pi$
$614$	−7.42749	−	20.4069i	−0.299749	−	0.823554i
$615$	0.120907	+	0.207078i	0.00487546	+	0.00835020i
$616$	−9.29359	+	5.36566i	−0.374450	+	0.216189i
$617$	−30.1408	+	2.63698i	−1.21342	+	0.106161i	−0.675838	−	0.737050i	$-0.736218\pi$
$617$	−30.1408	+	2.63698i	−1.21342	+	0.106161i	−0.537583	+	0.843211i	$0.680663\pi$
$618$	6.45159	−	0.564441i	0.259521	−	0.0227051i
$619$	−25.7350	+	14.8581i	−1.03438	+	0.597197i	−0.918235	−	0.396036i	$-0.870386\pi$
$619$	−25.7350	+	14.8581i	−1.03438	+	0.597197i	−0.116140	+	0.993233i	$0.537052\pi$
$620$	−18.5092	−	4.86287i	−0.743348	−	0.195298i
$621$	−0.189640	−	0.521032i	−0.00760999	−	0.0209083i
$622$	−6.41123	+	9.15618i	−0.257067	+	0.367130i
$623$	−4.14514	−	5.91988i	−0.166072	−	0.237175i
$624$	−1.07813	+	2.96214i	−0.0431598	+	0.118580i
$625$	−4.82080	−	24.5308i	−0.192832	−	0.981232i
$626$			21.7619i			0.869781i
$627$	12.9711	−	5.29305i	0.518015	−	0.211384i
$628$	10.5320	+	10.5320i	0.420271	+	0.420271i
$629$	−0.280289	+	0.235190i	−0.0111758	+	0.00937764i
$630$	−7.44076	−	0.614419i	−0.296447	−	0.0244790i
$631$	1.52511	−	8.64933i	0.0607137	−	0.344324i	−0.939286	−	0.343136i	$-0.888511\pi$
$631$	1.52511	−	8.64933i	0.0607137	−	0.344324i	0.999999	−	0.00118807i	$-0.000378176\pi$
$632$	−9.86601	−	6.90825i	−0.392449	−	0.274796i
$633$	−10.5492	−	4.91918i	−0.419294	−	0.195520i
$634$	19.4745	+	11.2436i	0.773431	+	0.446541i
$635$	−17.4653	+	0.0852081i	−0.693090	+	0.00338138i
$636$	−7.60492	−	6.38129i	−0.301555	−	0.253034i
$637$	−1.13974	−	13.0273i	−0.0451581	−	0.516159i
$638$	5.64789	−	21.0782i	0.223602	−	0.834495i
$639$	−6.84925	+	11.8632i	−0.270952	+	0.469303i
$640$	−2.20397	−	0.377541i	−0.0871194	−	0.0149236i
$641$	9.56537	−	1.68663i	0.377809	−	0.0666180i	0.0184811	−	0.999829i	$-0.494117\pi$
$641$	9.56537	−	1.68663i	0.377809	−	0.0666180i	0.359328	+	0.933211i	$0.383006\pi$
$642$	−13.6681	+	9.57052i	−0.539438	+	0.377718i
$643$	0.993115	+	2.12974i	0.0391646	+	0.0839888i	0.924917	−	0.380170i	$-0.124134\pi$
$643$	0.993115	+	2.12974i	0.0391646	+	0.0839888i	−0.885752	+	0.464159i	$0.846357\pi$
$644$	1.19002	+	1.41821i	0.0468933	+	0.0558853i
$645$	0.317408	+	1.16188i	0.0124979	+	0.0457489i
$646$	−2.49992	−	2.31506i	−0.0983579	−	0.0910847i
$647$	−18.8812	+	18.8812i	−0.742296	+	0.742296i	−0.973019	−	0.230724i	$-0.925891\pi$
$647$	−18.8812	+	18.8812i	−0.742296	+	0.742296i	0.230724	+	0.973019i	$0.425891\pi$
$648$	0.0871557	−	0.996195i	0.00342380	−	0.0391342i
$649$	30.5140	+	11.1062i	1.19778	+	0.435956i
$650$	5.53491	+	14.7574i	0.217097	+	0.578832i
$651$	4.96221	+	28.1421i	0.194484	+	1.10298i
$652$	−3.43340	+	7.36294i	−0.134462	+	0.288355i
$653$	−2.98527	+	0.799902i	−0.116823	+	0.0313026i	−0.316757	−	0.948507i	$-0.602594\pi$
$653$	−2.98527	+	0.799902i	−0.116823	+	0.0313026i	0.199934	+	0.979809i	$0.435927\pi$
$654$	6.28527	+	10.8864i	0.245774	+	0.425692i
$655$	−16.6864	+	36.2447i	−0.651991	+	1.41620i
$656$	0.0689313	−	0.0821491i	0.00269131	−	0.00320738i
$657$	8.28534	+	2.22005i	0.323242	+	0.0866124i
$658$	−2.48686	−	9.28108i	−0.0969478	−	0.361814i
$659$	−22.4866	+	8.18446i	−0.875954	+	0.318821i	−0.740576	−	0.671973i	$-0.765447\pi$
$659$	−22.4866	+	8.18446i	−0.875954	+	0.318821i	−0.135378	+	0.990794i	$0.543225\pi$
$660$	−6.76521	−	2.42502i	−0.263335	−	0.0943939i
$661$	−14.5181	−	2.55994i	−0.564689	−	0.0995700i	−0.115986	−	0.993251i	$-0.537003\pi$
$661$	−14.5181	−	2.55994i	−0.564689	−	0.0995700i	−0.448703	+	0.893681i	$0.648114\pi$
$662$	−18.4291	+	8.59361i	−0.716266	+	0.334000i
$663$	2.45463	+	0.214752i	0.0953298	+	0.00834028i
$664$	9.36302			0.363356
$665$	−32.2671	+	4.23555i	−1.25126	+	0.164248i
$666$	−0.468090			−0.0181381
$667$	−3.75031	−	0.328110i	−0.145213	−	0.0127045i
$668$	−20.5830	+	9.59800i	−0.796379	+	0.371358i
$669$	14.6694	+	2.58662i	0.567153	+	0.100004i
$670$	0.181004	+	0.383271i	0.00699279	+	0.0148071i
$671$	16.6476	−	6.05923i	0.642673	−	0.233914i
$672$	0.864180	+	3.22516i	0.0333365	+	0.124413i
$673$	−3.67534	−	0.984804i	−0.141674	−	0.0379614i	0.187285	−	0.982306i	$-0.440031\pi$
$673$	−3.67534	−	0.984804i	−0.141674	−	0.0379614i	−0.328959	+	0.944344i	$0.606698\pi$
$674$	20.3420	−	24.2427i	0.783545	−	0.933793i
$675$	−2.90771	−	4.06758i	−0.111918	−	0.156561i
$676$	1.53168	+	2.65296i	0.0589109	+	0.102037i
$677$	5.25852	−	1.40902i	0.202101	−	0.0541529i	−0.156348	−	0.987702i	$-0.549972\pi$
$677$	5.25852	−	1.40902i	0.202101	−	0.0541529i	0.358450	+	0.933549i	$0.383306\pi$
$678$	4.25269	−	9.11993i	0.163324	−	0.350249i
$679$	0.893312	+	5.06623i	0.0342822	+	0.194424i
$680$	0.160829	+	1.74045i	0.00616751	+	0.0667430i
$681$	15.8409	+	5.76563i	0.607026	+	0.220939i
$682$	−2.39739	+	27.4023i	−0.0918007	+	1.04929i
$683$	9.12761	−	9.12761i	0.349258	−	0.349258i	−0.510575	−	0.859833i	$-0.670567\pi$
$683$	9.12761	−	9.12761i	0.349258	−	0.349258i	0.859833	+	0.510575i	$0.170567\pi$
$684$	−0.546214	−	4.32454i	−0.0208850	−	0.165353i
$685$	23.0731	+	13.1716i	0.881576	+	0.503260i
$686$	6.12000	+	7.29353i	0.233663	+	0.278468i
$687$	1.54969	+	3.32332i	0.0591244	+	0.126793i
$688$	0.441235	−	0.308956i	0.0168219	−	0.0117788i
$689$	30.8185	−	5.43414i	1.17409	−	0.207024i
$690$	−0.209335	+	1.22203i	−0.00796926	+	0.0465220i
$691$	17.8078	−	30.8440i	0.677440	−	1.17336i	−0.298309	−	0.954469i	$-0.596423\pi$
$691$	17.8078	−	30.8440i	0.677440	−	1.17336i	0.975749	−	0.218892i	$-0.0702441\pi$
$692$	4.38953	−	16.3820i	0.166865	−	0.622749i
$693$	0.935296	+	10.6905i	0.0355290	+	0.406098i
$694$	−5.09833	−	4.27801i	−0.193530	−	0.162391i
$695$	32.8475	+	32.5286i	1.24598	+	1.23388i
$696$	−5.87998	−	3.39481i	−0.222880	−	0.128680i
$697$	−0.0759707	−	0.0354257i	−0.00287760	−	0.00134185i
$698$	−12.4913	−	8.74649i	−0.472802	−	0.331059i
$699$	−1.03819	+	5.88784i	−0.0392678	+	0.222699i
$700$	13.7683	+	9.44178i	0.520391	+	0.356866i
$701$	−34.7504	+	29.1591i	−1.31251	+	1.10132i	−0.324669	+	0.945828i	$0.605253\pi$
$701$	−34.7504	+	29.1591i	−1.31251	+	1.10132i	−0.987837	+	0.155495i	$0.950303\pi$
$702$	2.22897	+	2.22897i	0.0841271	+	0.0841271i
$703$	−1.99429	+	0.431132i	−0.0752160	+	0.0162604i
$704$			3.21399i			0.121132i
$705$	3.66506	−	5.28898i	0.138034	−	0.199195i
$706$	−10.0968	+	27.7408i	−0.379999	+	1.04404i
$707$	10.1767	+	14.5338i	0.382734	+	0.546601i
$708$	5.79508	−	8.27623i	0.217792	−	0.311040i
$709$	16.4362	+	45.1580i	0.617273	+	1.69594i	0.713565	+	0.700589i	$0.247079\pi$
$709$	16.4362	+	45.1580i	0.617273	+	1.69594i	−0.0962921	+	0.995353i	$0.530698\pi$
$710$	26.4520	−	15.4446i	0.992726	−	0.579626i
$711$	−10.4306	+	6.02209i	−0.391177	+	0.225846i
$712$	−2.15618	+	0.188641i	−0.0808062	+	0.00706963i
$713$	4.72737	−	0.413591i	0.177041	−	0.0154891i
$714$	2.26027	−	1.30497i	0.0845885	−	0.0488372i
$715$	19.5637	−	11.4227i	0.731640	−	0.427185i
$716$	−5.27559	−	14.4946i	−0.197158	−	0.541687i
$717$	0.845520	−	1.20753i	0.0315765	−	0.0450959i
$718$	16.7962	+	23.9875i	0.626829	+	0.895205i
$719$	−9.45123	+	25.9670i	−0.352471	+	0.968407i	0.629102	+	0.777323i	$0.283423\pi$
$719$	−9.45123	+	25.9670i	−0.352471	+	0.968407i	−0.981574	+	0.191085i	$0.938799\pi$
$720$	−1.27360	+	1.83791i	−0.0474644	+	0.0684950i
$721$			21.6237i			0.805310i
$722$	−6.31023	−	17.9215i	−0.234842	−	0.666970i
$723$	17.4783	+	17.4783i	0.650026	+	0.650026i
$724$	−1.55660	+	1.30614i	−0.0578505	+	0.0485423i
$725$	−33.3732	+	6.22094i	−1.23945	+	0.231040i
$726$	0.116385	−	0.660055i	0.00431947	−	0.0244969i
$727$	26.2272	+	18.3645i	0.972714	+	0.681102i	0.947893	−	0.318590i	$-0.103209\pi$
$727$	26.2272	+	18.3645i	0.972714	+	0.681102i	0.0248214	+	0.999692i	$0.492098\pi$
$728$	−9.53901	−	4.44811i	−0.353539	−	0.164858i
$729$	−0.866025	−	0.500000i	−0.0320750	−	0.0185185i
$730$	−13.6284	−	13.4961i	−0.504410	−	0.499512i
$731$	−0.322538	−	0.270642i	−0.0119295	−	0.0100100i
$732$	−0.480415	−	5.49117i	−0.0177566	−	0.202959i
$733$	8.84506	−	33.0102i	0.326700	−	1.21926i	−0.585892	−	0.810389i	$-0.699256\pi$
$733$	8.84506	−	33.0102i	0.326700	−	1.21926i	0.912592	−	0.408871i	$-0.134077\pi$
$734$	−1.81710	+	3.14731i	−0.0670703	+	0.116169i
$735$	1.56622	−	9.14311i	0.0577710	−	0.337249i
$736$	0.546047	−	0.0962828i	0.0201275	−	0.00354903i
$737$	0.499056	−	0.349443i	0.0183830	−	0.0128719i
$738$	−0.0453208	−	0.0971907i	−0.00166828	−	0.00357764i
$739$	−28.3399	−	33.7742i	−1.04250	−	1.24240i	−0.969505	−	0.245070i	$-0.921189\pi$
$739$	−28.3399	−	33.7742i	−1.04250	−	1.24240i	−0.0729944	−	0.997332i	$-0.523256\pi$
$740$	0.908995	+	0.518912i	0.0334153	+	0.0190756i
$741$	11.5495	+	7.44350i	0.424280	+	0.273444i
$742$	23.4387	−	23.4387i	0.860462	−	0.860462i
$743$	−1.08645	+	12.4182i	−0.0398582	+	0.455581i	0.949873	+	0.312637i	$0.101212\pi$
$743$	−1.08645	+	12.4182i	−0.0398582	+	0.455581i	−0.989731	+	0.142944i	$0.954343\pi$
$744$	8.04234	+	2.92717i	0.294847	+	0.107315i
$745$	−1.11075	−	12.0202i	−0.0406947	−	0.440387i
$746$	3.80172	+	21.5606i	0.139191	+	0.789390i
$747$	3.95698	−	8.48577i	0.144778	−	0.310478i
$748$	2.42667	−	0.650224i	0.0887279	−	0.0237746i
$749$	−27.8562	−	48.2484i	−1.01784	−	1.76296i
$750$	1.13733	+	11.1223i	0.0415295	+	0.406130i
$751$	−0.783832	+	0.934134i	−0.0286024	+	0.0340870i	−0.780156	−	0.625585i	$-0.784860\pi$
$751$	−0.783832	+	0.934134i	−0.0286024	+	0.0340870i	0.751554	+	0.659672i	$0.229305\pi$
$752$	−2.77965	−	0.744806i	−0.101363	−	0.0271603i
$753$	−0.174802	−	0.652371i	−0.00637014	−	0.0237737i
$754$	20.1118	−	7.32009i	0.732428	−	0.266582i
$755$	17.3061	+	36.6451i	0.629832	+	1.33365i
$756$	3.28821	+	0.579800i	0.119591	+	0.0210871i
$757$	8.16326	−	3.80659i	0.296699	−	0.138353i	−0.268569	−	0.963260i	$-0.586551\pi$
$757$	8.16326	−	3.80659i	0.296699	−	0.138353i	0.565268	+	0.824908i	$0.308773\pi$
$758$	−29.6597	−	2.59489i	−1.07729	−	0.0942507i
$759$	1.78206			0.0646849
$760$	−3.73336	+	9.00344i	−0.135423	+	0.326589i
$761$	−34.3348			−1.24463			−0.622317	−	0.782765i	$-0.713809\pi$
$761$	−34.3348			−1.24463			−0.622317	+	0.782765i	$0.713809\pi$
$762$	7.78110	+	0.680758i	0.281880	+	0.0246613i
$763$	−38.0397	+	17.7382i	−1.37713	+	0.642167i
$764$	15.5029	+	2.73359i	0.560876	+	0.0988977i
$765$	1.64535	+	0.589784i	0.0594877	+	0.0213237i
$766$	0.173988	−	0.0633265i	0.00628644	−	0.00228808i
$767$	8.24297	+	30.7632i	0.297637	+	1.11079i
$768$	0.965926	+	0.258819i	0.0348548	+	0.00933933i
$769$	−13.0227	+	15.5199i	−0.469612	+	0.559662i	−0.947911	−	0.318535i	$-0.896809\pi$
$769$	−13.0227	+	15.5199i	−0.469612	+	0.559662i	0.478299	+	0.878197i	$0.341254\pi$
$770$	10.0349	−	21.7969i	0.361633	−	0.785507i
$771$	13.5892	+	23.5372i	0.489402	+	0.847670i
$772$	−11.8780	+	3.18271i	−0.427499	+	0.114548i
$773$	11.5690	−	24.8098i	0.416108	−	0.892346i	−0.580821	−	0.814031i	$-0.697268\pi$
$773$	11.5690	−	24.8098i	0.416108	−	0.892346i	0.996929	−	0.0783146i	$-0.0249539\pi$
$774$	−0.0935353	−	0.530465i	−0.00336206	−	0.0190672i
$775$	40.0670	−	15.0275i	1.43925	−	0.539805i
$776$	1.44781	+	0.526959i	0.0519733	+	0.0189167i
$777$	0.136218	−	1.55698i	0.00488678	−	0.0558562i
$778$	1.50276	−	1.50276i	0.0538766	−	0.0538766i
$779$	−0.282605	−	0.372336i	−0.0101254	−	0.0133403i
$780$	−1.85751	−	6.79947i	−0.0665096	−	0.243460i
$781$	−28.2999	−	33.7266i	−1.01265	−	1.20683i
$782$	−0.183167	−	0.392804i	−0.00655006	−	0.0140466i
$783$	−5.56172	+	3.89436i	−0.198760	+	0.139173i
$784$	−4.08546	+	0.720377i	−0.145909	+	0.0257277i
$785$	−32.8268	−	5.62327i	−1.17164	−	0.200703i
$786$	8.92220	−	15.4537i	0.318244	−	0.551215i
$787$	4.92430	−	18.3777i	0.175532	−	0.655095i	−0.820928	−	0.571031i	$-0.806543\pi$
$787$	4.92430	−	18.3777i	0.175532	−	0.655095i	0.996460	−	0.0840636i	$-0.0267899\pi$
$788$	0.912194	+	10.4264i	0.0324956	+	0.371426i
$789$	13.6392	+	11.4446i	0.485568	+	0.407440i
$790$	26.9313	−	0.131390i	0.958172	−	0.00467463i
$791$	29.0974	+	16.7994i	1.03458	+	0.597318i
$792$	2.91287	+	1.35829i	0.103504	+	0.0482648i
$793$	14.2333	+	9.96624i	0.505438	+	0.353911i
$794$	−0.895510	+	5.07869i	−0.0317805	+	0.180236i
$795$	22.1233	+	1.82683i	0.784633	+	0.0647908i
$796$	15.7342	−	13.2025i	0.557683	−	0.467952i
$797$	10.7327	+	10.7327i	0.380171	+	0.380171i	0.871164	−	0.490993i	$-0.163366\pi$
$797$	10.7327	+	10.7327i	0.380171	+	0.380171i	−0.490993	+	0.871164i	$0.663366\pi$
$798$	14.5434	−	0.558361i	0.514829	−	0.0197658i
$799$			2.24941i			0.0795784i
$800$	4.51071	−	2.15721i	0.159478	−	0.0762687i
$801$	−0.740273	+	2.03388i	−0.0261563	+	0.0718638i
$802$	9.30328	+	13.2865i	0.328510	+	0.469161i
$803$	−15.8126	+	22.5827i	−0.558014	+	0.796927i
$804$	−0.0648323	−	0.178125i	−0.00228646	−	0.00628200i
$805$	−4.00384	−	1.05192i	−0.141117	−	0.0370752i
$806$	−23.3640	+	13.4892i	−0.822961	+	0.475137i
$807$	−26.8346	+	2.34772i	−0.944622	+	0.0826437i
$808$	5.29361	−	0.463131i	0.186228	−	0.0162929i
$809$	−22.0310	+	12.7196i	−0.774570	+	0.447198i	−0.834502	−	0.551004i	$-0.814245\pi$
$809$	−22.0310	+	12.7196i	−0.774570	+	0.447198i	0.0599325	+	0.998202i	$0.480911\pi$
$810$	1.12747	+	1.93101i	0.0396152	+	0.0678489i
$811$	2.22733	+	6.11953i	0.0782121	+	0.214886i	0.972636	−	0.232334i	$-0.0746363\pi$
$811$	2.22733	+	6.11953i	0.0782121	+	0.214886i	−0.894424	+	0.447220i	$0.852414\pi$
$812$	13.0030	−	18.5702i	0.456316	−	0.651687i
$813$	−17.6008	−	25.1366i	−0.617287	−	0.881578i
$814$	0.514549	−	1.41371i	0.0180349	−	0.0495505i
$815$	−3.24174	−	17.8745i	−0.113553	−	0.626116i
$816$		−	0.781667i		−	0.0273638i
$817$	−0.887087	−	2.17389i	−0.0310352	−	0.0760546i
$818$	9.39012	+	9.39012i	0.328318	+	0.328318i
$819$	−8.06272	+	6.76542i	−0.281734	+	0.236403i
$820$	−0.0197336	+	0.238978i	−0.000689126	+	0.00834548i
$821$	−0.205098	+	1.16317i	−0.00715796	+	0.0405948i	−0.988178	−	0.153314i	$-0.951005\pi$
$821$	−0.205098	+	1.16317i	−0.00715796	+	0.0405948i	0.981020	+	0.193909i	$0.0621166\pi$
$822$	−9.73280	−	6.81498i	−0.339470	−	0.237700i
$823$	−2.16281	−	1.00853i	−0.0753908	−	0.0351553i	0.384557	−	0.923101i	$-0.374354\pi$
$823$	−2.16281	−	1.00853i	−0.0753908	−	0.0351553i	−0.459948	+	0.887946i	$0.652132\pi$
$824$	5.60858	+	3.23812i	0.195384	+	0.112805i
$825$	15.4811	−	4.31047i	0.538982	−	0.150071i
$826$	25.8422	+	21.6842i	0.899166	+	0.754490i
$827$	−3.06371	−	35.0184i	−0.106536	−	1.21771i	−0.841748	−	0.539871i	$-0.818473\pi$
$827$	−3.06371	−	35.0184i	−0.106536	−	1.21771i	0.735212	−	0.677837i	$-0.237083\pi$
$828$	0.143507	−	0.535577i	0.00498723	−	0.0186126i
$829$	−13.7440	+	23.8053i	−0.477349	+	0.826792i	−0.999663	−	0.0259607i	$-0.991736\pi$
$829$	−13.7440	+	23.8053i	−0.477349	+	0.826792i	0.522314	+	0.852753i	$0.325069\pi$
$830$	−17.0913	+	12.0921i	−0.593246	+	0.419724i
$831$	−18.8586	+	3.32528i	−0.654198	+	0.115353i
$832$	−2.58217	+	1.80805i	−0.0895205	+	0.0626829i
$833$	1.37044	+	2.93891i	0.0474829	+	0.101827i
$834$	−13.2890	−	15.8372i	−0.460160	−	0.548397i
$835$	25.1766	−	44.1026i	0.871272	−	1.52623i
$836$	13.6613	+	3.10410i	0.472485	+	0.107357i
$837$	6.05176	−	6.05176i	0.209179	−	0.209179i
$838$	−2.50558	+	28.6389i	−0.0865537	+	0.989313i
$839$	37.8508	+	13.7766i	1.30675	+	0.475620i	0.899191	−	0.437557i	$-0.144156\pi$
$839$	37.8508	+	13.7766i	1.30675	+	0.475620i	0.407564	+	0.913177i	$0.366378\pi$
$840$	−5.74270	−	4.77115i	−0.198142	−	0.164620i
$841$	2.96918	+	16.8391i	0.102386	+	0.580657i
$842$	4.31393	−	9.25125i	0.148668	−	0.318819i
$843$	−8.85097	+	2.37161i	−0.304843	+	0.0816826i
$844$	−5.81988	−	10.0803i	−0.200329	−	0.346979i
$845$	−6.22217	−	2.86457i	−0.214049	−	0.0985443i
$846$	−1.84976	+	2.20445i	−0.0635959	+	0.0757906i
$847$	2.16162	+	0.579205i	0.0742743	+	0.0199017i
$848$	−2.56943	−	9.58925i	−0.0882346	−	0.329296i
$849$	−21.0236	+	7.65196i	−0.721527	+	0.262614i
$850$	−2.54132	−	2.96930i	−0.0871666	−	0.101846i
$851$	−0.255599	−	0.0450690i	−0.00876183	−	0.00154495i
$852$	−12.4151	+	5.78924i	−0.425333	+	0.198336i
$853$	45.2056	+	3.95498i	1.54781	+	0.135416i	0.828785	−	0.559567i	$-0.189033\pi$
$853$	45.2056	+	3.95498i	1.54781	+	0.135416i	0.719026	+	0.694983i	$0.244588\pi$
$854$	18.4047			0.629795
$855$	6.58210	+	7.18860i	0.225103	+	0.245845i
$856$	−16.6857			−0.570305
$857$	34.4588	+	3.01475i	1.17709	+	0.102982i	0.658864	−	0.752262i	$-0.271037\pi$
$857$	34.4588	+	3.01475i	1.17709	+	0.102982i	0.518225	+	0.855244i	$0.326593\pi$
$858$	−9.18207	+	4.28167i	−0.313471	+	0.146174i
$859$	43.8463	+	7.73129i	1.49602	+	0.263788i	0.860958	−	0.508675i	$-0.169865\pi$
$859$	43.8463	+	7.73129i	1.49602	+	0.263788i	0.635059	+	0.772464i	$0.280976\pi$
$860$	−0.406421	+	1.13381i	−0.0138588	+	0.0386627i
$861$	0.336467	−	0.122464i	0.0114668	−	0.00417356i
$862$	−9.32839	−	34.8140i	−0.317726	−	1.18577i
$863$	10.8692	+	2.91239i	0.369992	+	0.0991390i	0.439024	−	0.898475i	$-0.355324\pi$
$863$	10.8692	+	2.91239i	0.369992	+	0.0991390i	−0.0690320	+	0.997614i	$0.521991\pi$
$864$	0.642788	−	0.766044i	0.0218681	−	0.0260614i
$865$	13.1443	+	35.5726i	0.446918	+	1.20951i
$866$	−19.5811	−	33.9154i	−0.665392	−	1.15249i
$867$	15.8306	−	4.24178i	0.537634	−	0.144059i
$868$	−12.0768	+	25.8988i	−0.409914	+	0.879064i
$869$	−6.72191	−	38.1218i	−0.228025	−	1.29319i
$870$	15.1176	−	1.39697i	0.512536	−	0.0473618i
$871$	0.561494	+	0.204367i	0.0190255	+	0.00692472i
$872$	−1.09559	+	12.5227i	−0.0371015	+	0.424072i
$873$	1.08946	−	1.08946i	0.0368725	−	0.0368725i
$874$	0.118120	−	2.41399i	0.00399547	−	0.0816545i
$875$	−37.3264	+	0.546348i	−1.26186	+	0.0184699i
$876$	5.51358	+	6.57083i	0.186287	+	0.222008i
$877$	0.392625	+	0.841988i	0.0132580	+	0.0284319i	0.912825	−	0.408350i	$-0.133896\pi$
$877$	0.392625	+	0.841988i	0.0132580	+	0.0284319i	−0.899567	+	0.436782i	$0.856118\pi$
$878$	−22.2808	+	15.6012i	−0.751941	+	0.526514i
$879$	14.4601	−	2.54971i	0.487728	−	0.0859996i
$880$	−4.15080	−	5.86683i	−0.139923	−	0.197771i
$881$	−5.86706	+	10.1620i	−0.197666	+	0.342368i	−0.947771	−	0.318951i	$-0.896670\pi$
$881$	−5.86706	+	10.1620i	−0.197666	+	0.342368i	0.750105	+	0.661319i	$0.230003\pi$
$882$	−1.07371	+	4.00713i	−0.0361536	+	0.134927i
$883$	2.38579	+	27.2697i	0.0802882	+	0.917698i	0.924373	+	0.381489i	$0.124589\pi$
$883$	2.38579	+	27.2697i	0.0802882	+	0.917698i	−0.844085	+	0.536209i	$0.819856\pi$
$884$	1.88754	+	1.58383i	0.0634847	+	0.0532700i
$885$	0.110218	+	22.5916i	0.00370493	+	0.759410i
$886$	1.45243	+	0.838562i	0.0487954	+	0.0281721i
$887$	29.1880	+	13.6106i	0.980036	+	0.456998i	0.845538	−	0.533916i	$-0.179280\pi$
$887$	29.1880	+	13.6106i	0.980036	+	0.456998i	0.134498	+	0.990914i	$0.457058\pi$
$888$	−0.383437	−	0.268486i	−0.0128673	−	0.00900979i
$889$	−4.52872	+	25.6836i	−0.151888	+	0.861401i
$890$	3.69226	−	3.12900i	0.123765	−	0.104884i
$891$	2.46206	−	2.06592i	0.0824822	−	0.0692108i
$892$	10.5329	+	10.5329i	0.352666	+	0.352666i
$893$	−5.85044	+	11.0957i	−0.195778	+	0.371304i
$894$			5.39851i			0.180553i
$895$	28.3494	+	19.6451i	0.947617	+	0.656662i
$896$	−1.14198	+	3.13757i	−0.0381510	+	0.104819i
$897$	1.00251	+	1.43173i	0.0334729	+	0.0478042i
$898$	−7.03961	+	10.0536i	−0.234915	+	0.335493i
$899$	−19.8744	−	54.6044i	−0.662848	−	1.82116i
$900$	−0.0487858	−	4.99976i	−0.00162619	−	0.166659i
$901$	−6.72037	+	3.88001i	−0.223888	+	0.129262i
$902$	0.343351	−	0.0300393i	0.0114323	−	0.00100020i
$903$	1.79167	−	0.156751i	0.0596230	−	0.00521633i
$904$	8.71458	−	5.03137i	0.289843	−	0.167341i
$905$	1.15456	−	4.39454i	0.0383790	−	0.146079i
$906$	−6.19871	−	17.0308i	−0.205938	−	0.565811i
$907$	3.37960	−	4.82657i	0.112218	−	0.160264i	−0.759114	−	0.650957i	$-0.774368\pi$
$907$	3.37960	−	4.82657i	0.112218	−	0.160264i	0.871332	+	0.490694i	$0.163257\pi$
$908$	9.66911	+	13.8089i	0.320881	+	0.458265i
$909$	1.81744	−	4.99336i	0.0602805	−	0.165619i
$910$	23.1571	−	4.19982i	0.767652	−	0.139223i
$911$			0.459804i			0.0152340i	0.999971	+	0.00761699i	$0.00242459\pi$
$911$			0.459804i			0.0152340i	−0.999971	+	0.00761699i	$0.997575\pi$
$912$	2.03302	−	3.85575i	0.0673201	−	0.127677i
$913$	21.2787	+	21.2787i	0.704224	+	0.704224i
$914$	4.61993	−	3.87659i	0.152814	−	0.128226i
$915$	7.96866	+	9.40313i	0.263436	+	0.310858i
$916$	−0.636747	+	3.61117i	−0.0210387	+	0.119316i
$917$	48.8061	+	34.1744i	1.61172	+	1.12854i
$918$	−0.708431	−	0.330347i	−0.0233817	−	0.0109031i
$919$	−6.61154	−	3.81717i	−0.218094	−	0.125917i	0.386973	−	0.922091i	$-0.373521\pi$
$919$	−6.61154	−	3.81717i	−0.218094	−	0.125917i	−0.605068	+	0.796174i	$0.706854\pi$
$920$	−0.872407	+	0.880961i	−0.0287624	+	0.0290444i
$921$	−16.6358	−	13.9591i	−0.548169	−	0.459969i
$922$	−1.66103	−	18.9857i	−0.0547033	−	0.625261i
$923$	11.1761	−	41.7096i	0.367865	−	1.37289i
$924$	−5.36566	+	9.29359i	−0.176517	+	0.305737i
$925$	−2.32944	+	0.226723i	−0.0765916	+	0.00745462i
$926$	−39.2577	+	6.92219i	−1.29009	+	0.227477i
$927$	5.30502	−	3.71462i	0.174240	−	0.122004i
$928$	−2.86941	−	6.15348i	−0.0941931	−	0.201998i
$929$	20.4338	+	24.3520i	0.670410	+	0.798963i	0.988840	−	0.148983i	$-0.0476001\pi$
$929$	20.4338	+	24.3520i	0.670410	+	0.798963i	−0.318430	+	0.947946i	$0.603156\pi$
$930$	−18.4609	+	5.04324i	−0.605356	+	0.165374i
$931$	−0.883761	+	18.0612i	−0.0289641	+	0.591932i
$932$	−4.22756	+	4.22756i	−0.138478	+	0.138478i
$933$	−0.974195	+	11.1351i	−0.0318937	+	0.364547i
$934$	−2.58176	−	0.939683i	−0.0844777	−	0.0307474i
$935$	−3.58990	+	4.32091i	−0.117402	+	0.141309i
$936$	0.547381	+	3.10435i	0.0178917	+	0.101469i
$937$	−21.3342	+	45.7513i	−0.696957	+	1.49463i	0.164274	+	0.986415i	$0.447472\pi$
$937$	−21.3342	+	45.7513i	−0.696957	+	1.49463i	−0.861231	+	0.508214i	$0.830306\pi$
$938$	0.611352	−	0.163811i	0.0199614	−	0.00534863i
$939$	10.8810	+	18.8464i	0.355087	+	0.615028i
$940$	6.03588	−	2.23029i	0.196869	−	0.0727440i
$941$	−5.04822	+	6.01624i	−0.164567	+	0.196124i	−0.842026	−	0.539437i	$-0.818637\pi$
$941$	−5.04822	+	6.01624i	−0.164567	+	0.196124i	0.677458	+	0.735561i	$0.263081\pi$
$942$	14.3869	+	3.85497i	0.468751	+	0.125602i
$943$	−0.0153895	−	0.0574343i	−0.000501150	−	0.00187032i
$944$	9.49410	−	3.45557i	0.309007	−	0.112469i
$945$	−6.75110	+	3.18828i	−0.219613	+	0.103715i
$946$	1.70491	+	0.300622i	0.0554315	+	0.00977406i
$947$	−1.53240	+	0.714569i	−0.0497962	+	0.0232204i	−0.447357	−	0.894356i	$-0.647635\pi$
$947$	−1.53240	+	0.714569i	−0.0497962	+	0.0232204i	0.397561	+	0.917576i	$0.369857\pi$
$948$	−11.9983	−	1.04972i	−0.389688	−	0.0340933i
$949$	−27.0387			−0.877714
$950$	−4.81285	−	21.2564i	−0.156150	−	0.689650i
$951$	22.4872			0.729198
$952$	2.60000	+	0.227471i	0.0842666	+	0.00737237i
$953$	2.43878	−	1.13722i	0.0789998	−	0.0368382i	−0.382717	−	0.923866i	$-0.625012\pi$
$953$	2.43878	−	1.13722i	0.0789998	−	0.0368382i	0.461717	+	0.887028i	$0.347234\pi$
$954$	−9.77670	−	1.72390i	−0.316532	−	0.0558132i
$955$	−31.8294	+	15.0318i	−1.02998	+	0.486417i
$956$	1.38522	−	0.504178i	0.0448012	−	0.0163063i
$957$	−5.64789	−	21.0782i	−0.182570	−	0.681362i
$958$	22.4507	+	6.01565i	0.725350	+	0.194357i
$959$	25.5005	−	30.3903i	0.823454	−	0.981354i
$960$	−2.09746	+	0.775022i	−0.0676952	+	0.0250137i
$961$	21.1238	+	36.5875i	0.681414	+	1.18024i
$962$	1.42526	−	0.381896i	0.0459521	−	0.0123128i
$963$	−7.05168	+	15.1224i	−0.227237	+	0.487312i
$964$	4.29225	+	24.3426i	0.138244	+	0.784022i
$965$	17.5718	−	21.1499i	0.565655	−	0.680839i
$966$	1.73969	+	0.633196i	0.0559736	+	0.0203727i
$967$	−3.84830	+	43.9863i	−0.123753	+	1.41450i	0.639693	+	0.768631i	$0.279062\pi$
$967$	−3.84830	+	43.9863i	−0.123753	+	1.41450i	−0.763445	+	0.645872i	$0.776494\pi$
$968$	0.473929	−	0.473929i	0.0152327	−	0.0152327i
$969$	−3.32252	−	0.754939i	−0.106735	−	0.0242521i
$970$	−3.32339	+	0.907899i	−0.106707	+	0.0291509i
$971$	26.7466	+	31.8754i	0.858339	+	1.02293i	0.999457	+	0.0329361i	$0.0104858\pi$
$971$	26.7466	+	31.8754i	0.858339	+	1.02293i	−0.141118	+	0.989993i	$0.545070\pi$
$972$	−0.422618	−	0.906308i	−0.0135555	−	0.0290698i
$973$	56.5453	−	39.5935i	1.81276	−	1.26931i
$974$	−12.6750	+	2.23495i	−0.406134	+	0.0716123i
$975$	12.1721	+	10.0128i	0.389818	+	0.320667i
$976$	2.75607	−	4.77365i	0.0882197	−	0.152801i
$977$	7.54314	−	28.1514i	0.241327	−	0.900643i	−0.733868	−	0.679292i	$-0.762287\pi$
$977$	7.54314	−	28.1514i	0.241327	−	0.900643i	0.975194	−	0.221351i	$-0.0710465\pi$
$978$	0.708063	+	8.09319i	0.0226413	+	0.258792i
$979$	−5.32892	−	4.47150i	−0.170313	−	0.142910i
$980$	6.52725	−	6.59125i	0.208505	−	0.210550i
$981$	10.8864	+	6.28527i	0.347576	+	0.200673i
$982$	10.6830	+	4.98157i	0.340909	+	0.158968i
$983$	−32.8591	−	23.0082i	−1.04804	−	0.733848i	−0.0831628	−	0.996536i	$-0.526502\pi$
$983$	−32.8591	−	23.0082i	−1.04804	−	0.733848i	−0.964881	+	0.262688i	$0.915391\pi$
$984$	0.0186217	−	0.105609i	0.000593638	−	0.00336669i
$985$	−15.1306	−	17.8543i	−0.482101	−	0.568886i
$986$	−4.06556	+	3.41141i	−0.129474	+	0.108642i
$987$	−6.79422	−	6.79422i	−0.216262	−	0.216262i
$988$	5.19135	+	12.7219i	0.165159	+	0.404736i
$989$		−	0.298665i		−	0.00949698i
$990$	−7.07136	+	1.28247i	−0.224742	+	0.0407597i
$991$	−11.0074	+	30.2425i	−0.349661	+	0.960685i	0.632816	+	0.774302i	$0.281899\pi$
$991$	−11.0074	+	30.2425i	−0.349661	+	0.960685i	−0.982477	+	0.186383i	$0.940323\pi$
$992$	4.90894	+	7.01070i	0.155859	+	0.222590i
$993$	−11.6632	+	16.6568i	−0.370121	+	0.528588i
$994$	−15.6435	−	42.9800i	−0.496180	−	1.36324i
$995$	−11.6704	+	44.4202i	−0.369976	+	1.40822i
$996$	8.10861	−	4.68151i	0.256931	−	0.148339i
$997$	−61.3266	+	5.36538i	−1.94223	+	0.169923i	−0.990550	−	0.137155i	$-0.956204\pi$
$997$	−61.3266	+	5.36538i	−1.94223	+	0.169923i	−0.951684	+	0.307079i	$0.900648\pi$
$998$	−8.17858	+	0.715533i	−0.258888	+	0.0226498i
$999$	−0.405378	+	0.234045i	−0.0128256	+	0.00740486i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bh.a.13.7	✓	120
5.2	odd	4	inner	570.2.bh.a.127.5	yes	120
19.3	odd	18	inner	570.2.bh.a.193.5	yes	120
95.22	even	36	inner	570.2.bh.a.307.7	yes	120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bh.a.13.7	✓	120	1.1	even	1	trivial
570.2.bh.a.127.5	yes	120	5.2	odd	4	inner
570.2.bh.a.193.5	yes	120	19.3	odd	18	inner
570.2.bh.a.307.7	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)

\(f(q)\)	\(=\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.02193 + 0.954879i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.864180 + 3.22516i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +O(q^{10})\)	\(q+(0.996195 + 0.0871557i) q^{2} +(0.906308 - 0.422618i) q^{3} +(0.984808 + 0.173648i) q^{4} +(-2.02193 + 0.954879i) q^{5} +(0.939693 - 0.342020i) q^{6} +(0.864180 + 3.22516i) q^{7} +(0.965926 + 0.258819i) q^{8} +(0.642788 - 0.766044i) q^{9} +(-2.09746 + 0.775022i) q^{10} +(1.60700 + 2.78340i) q^{11} +(0.965926 - 0.258819i) q^{12} +(-1.33220 + 2.85690i) q^{13} +(0.579800 + 3.28821i) q^{14} +(-1.42894 + 1.71992i) q^{15} +(0.939693 + 0.342020i) q^{16} +(0.0681268 - 0.778693i) q^{17} +(0.707107 - 0.707107i) q^{18} +(2.36134 - 3.66389i) q^{19} +(-2.15703 + 0.589267i) q^{20} +(2.14623 + 2.55777i) q^{21} +(1.35829 + 2.91287i) q^{22} +(0.454196 - 0.318031i) q^{23} +(0.984808 - 0.173648i) q^{24} +(3.17641 - 3.86140i) q^{25} +(-1.57612 + 2.72992i) q^{26} +(0.258819 - 0.965926i) q^{27} +(0.291007 + 3.32623i) q^{28} +(-5.20114 - 4.36428i) q^{29} +(-1.57341 + 1.58883i) q^{30} +(7.41186 + 4.27924i) q^{31} +(0.906308 + 0.422618i) q^{32} +(2.63275 + 1.84347i) q^{33} +(0.135735 - 0.769792i) q^{34} +(-4.82695 - 5.69587i) q^{35} +(0.766044 - 0.642788i) q^{36} +(-0.330990 - 0.330990i) q^{37} +(2.67168 - 3.44414i) q^{38} +3.15224i q^{39} +(-2.20018 + 0.399028i) q^{40} +(0.0366776 - 0.100771i) q^{41} +(1.91513 + 2.73509i) q^{42} +(0.308956 - 0.441235i) q^{43} +(1.09925 + 3.02017i) q^{44} +(-0.568193 + 2.16267i) q^{45} +(0.480185 - 0.277235i) q^{46} +(-2.86676 + 0.250809i) q^{47} +(0.996195 - 0.0871557i) q^{48} +(-3.59269 + 2.07424i) q^{49} +(3.50087 - 3.56986i) q^{50} +(-0.267346 - 0.734527i) q^{51} +(-1.80805 + 2.58217i) q^{52} +(-5.69419 - 8.13215i) q^{53} +(0.342020 - 0.939693i) q^{54} +(-5.90705 - 4.09336i) q^{55} +3.33893i q^{56} +(0.591671 - 4.31856i) q^{57} +(-4.80098 - 4.80098i) q^{58} +(7.73966 - 6.49435i) q^{59} +(-1.70589 + 1.44566i) q^{60} +(0.957173 - 5.42840i) q^{61} +(7.01070 + 4.90894i) q^{62} +(3.02610 + 1.41109i) q^{63} +(0.866025 + 0.500000i) q^{64} +(-0.0343877 - 7.04854i) q^{65} +(2.46206 + 2.06592i) q^{66} +(-0.0165210 - 0.188836i) q^{67} +(0.202310 - 0.755032i) q^{68} +(0.277235 - 0.480185i) q^{69} +(-4.31216 - 6.09489i) q^{70} +(-13.4904 + 2.37872i) q^{71} +(0.819152 - 0.573576i) q^{72} +(3.62506 + 7.77396i) q^{73} +(-0.300883 - 0.358578i) q^{74} +(1.24691 - 4.84203i) q^{75} +(2.96169 - 3.19819i) q^{76} +(-7.58819 + 7.58819i) q^{77} +(-0.274736 + 3.14025i) q^{78} +(-11.3178 - 4.11935i) q^{79} +(-2.22658 + 0.205751i) q^{80} +(-0.173648 - 0.984808i) q^{81} +(0.0453208 - 0.0971907i) q^{82} +(9.04398 - 2.42333i) q^{83} +(1.66947 + 2.89160i) q^{84} +(0.605809 + 1.63952i) q^{85} +(0.346237 - 0.412629i) q^{86} +(-6.55826 - 1.75728i) q^{87} +(0.831843 + 3.10448i) q^{88} +(-2.03388 + 0.740273i) q^{89} +(-0.754520 + 2.10492i) q^{90} +(-10.3652 - 1.82767i) q^{91} +(0.502521 - 0.234329i) q^{92} +(8.52592 + 0.745921i) q^{93} -2.87771 q^{94} +(-1.27589 + 9.66292i) q^{95} +1.00000 q^{96} +(1.53486 + 0.134283i) q^{97} +(-3.75980 + 1.75322i) q^{98} +(3.16517 + 0.558104i) 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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