LMFDB - Embedded newform 570.2.bi.a.17.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(17,570)]

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([18, 9, 20]))

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

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

chi := DirichletCharacter("570.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bi (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:	$480$
Relative dimension:	$40$ over $\Q(\zeta_{36})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{36}]$

Embedding invariants

Embedding label			17.14
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(0.986006 - 1.42401i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.55782 + 1.60412i) q^{5} +(-1.73203 + 0.00908702i) q^{6} +(-0.120110 + 0.448257i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.05558 - 2.80816i) q^{9} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(0.986006 - 1.42401i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.55782 + 1.60412i) q^{5} +(-1.73203 + 0.00908702i) q^{6} +(-0.120110 + 0.448257i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.05558 - 2.80816i) q^{9} +(2.20755 + 0.356004i) q^{10} +(-1.57240 - 0.907823i) q^{11} +(1.00089 + 1.41358i) q^{12} +(0.311947 - 3.56558i) q^{13} +(0.436083 - 0.158721i) q^{14} +(0.748259 + 3.80001i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-4.13121 - 5.89998i) q^{17} +(-1.69485 + 2.47538i) q^{18} +(-3.89390 + 1.95896i) q^{19} +(-0.974576 - 2.01251i) q^{20} +(0.519891 + 0.613022i) q^{21} +(0.158244 + 1.80874i) q^{22} +(-1.11563 - 2.39248i) q^{23} +(0.583849 - 1.63068i) q^{24} +(-0.146408 - 4.99786i) q^{25} +(-3.09967 + 1.78960i) q^{26} +(-5.03964 - 1.26570i) q^{27} +(-0.380144 - 0.266179i) q^{28} +(0.307517 + 1.74401i) q^{29} +(2.68361 - 2.79254i) q^{30} +(-2.70760 - 4.68969i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-2.84314 + 1.34398i) q^{33} +(-2.46341 + 6.76818i) q^{34} +(-0.531949 - 0.890974i) q^{35} +(2.99983 - 0.0314779i) q^{36} +(0.279417 + 0.279417i) q^{37} +(3.83814 + 2.06608i) q^{38} +(-4.76982 - 3.95989i) q^{39} +(-1.08956 + 1.95265i) q^{40} +(-3.76030 + 4.48135i) q^{41} +(0.203961 - 0.777485i) q^{42} +(3.02987 - 6.49758i) q^{43} +(1.39087 - 1.16708i) q^{44} +(6.14903 + 2.68131i) q^{45} +(-1.31990 + 2.28614i) q^{46} +(11.0436 + 7.73283i) q^{47} +(-1.67066 + 0.457059i) q^{48} +(5.87567 + 3.39232i) q^{49} +(-4.01003 + 2.98658i) q^{50} +(-12.4750 + 0.0654496i) q^{51} +(3.24385 + 1.51263i) q^{52} +(4.54103 + 9.73828i) q^{53} +(1.85382 + 4.85421i) q^{54} +(3.90577 - 1.10809i) q^{55} +0.464070i q^{56} +(-1.04984 + 7.47649i) q^{57} +(1.25223 - 1.25223i) q^{58} +(2.46327 - 13.9699i) q^{59} +(-3.82677 - 0.596548i) q^{60} +(-8.37266 - 3.04740i) q^{61} +(-2.28856 + 4.90783i) q^{62} +(1.38556 - 0.135885i) q^{63} +(0.866025 - 0.500000i) q^{64} +(5.23366 + 6.05492i) q^{65} +(2.73168 + 1.55809i) q^{66} +(-4.30882 + 6.15364i) q^{67} +(6.95712 - 1.86416i) q^{68} +(-4.50692 - 0.770334i) q^{69} +(-0.424730 + 0.946789i) q^{70} +(-0.814145 - 2.23684i) q^{71} +(-1.74642 - 2.43927i) q^{72} +(-1.60452 + 0.140378i) q^{73} +(0.0686180 - 0.389152i) q^{74} +(-7.26133 - 4.71943i) q^{75} +(-0.509027 - 4.32908i) q^{76} +(0.595799 - 0.595799i) q^{77} +(-0.507901 + 6.17851i) q^{78} +(4.77508 - 5.69072i) q^{79} +(2.22447 - 0.227482i) q^{80} +(-6.77149 + 5.92849i) q^{81} +(5.82773 + 0.509860i) q^{82} +(-0.560820 + 2.09301i) q^{83} +(-0.753865 + 0.278872i) q^{84} +(15.8999 + 2.56413i) q^{85} +(-7.06037 + 1.24493i) q^{86} +(2.78670 + 1.28170i) q^{87} +(-1.75378 - 0.469924i) q^{88} +(-10.9641 + 9.20001i) q^{89} +(-1.33054 - 6.57493i) q^{90} +(1.56083 + 0.568094i) q^{91} +(2.62976 - 0.230074i) q^{92} +(-9.34786 - 0.768435i) q^{93} -13.4818i q^{94} +(2.92358 - 9.29799i) q^{95} +(1.33265 + 1.10636i) q^{96} +(10.5824 - 7.40989i) q^{97} +(-0.591320 - 6.75882i) q^{98} +(-0.889515 + 5.37382i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 480 q+O(q^{10}) $ 480 * q	$ 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) $ 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$2$	−0.573576	−	0.819152i	−0.405580	−	0.579228i
$3$	0.986006	−	1.42401i	0.569271	−	0.822150i
$3$	0.986006	−	1.42401i	0.569271	−	0.822150i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	−1.55782	+	1.60412i	−0.696677	+	0.717385i
$5$	−1.55782	+	1.60412i	−0.696677	+	0.717385i
$6$	−1.73203	+	0.00908702i	−0.707097	+	0.00370976i
$7$	−0.120110	+	0.448257i	−0.0453974	+	0.169425i	−0.984903	−	0.173109i	$-0.944619\pi$
$7$	−0.120110	+	0.448257i	−0.0453974	+	0.169425i	0.939505	+	0.342534i	$0.111285\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	−1.05558	−	2.80816i	−0.351861	−	0.936052i
$10$	2.20755	+	0.356004i	0.698087	+	0.112578i
$11$	−1.57240	−	0.907823i	−0.474095	−	0.273719i	0.243857	−	0.969811i	$-0.421587\pi$
$11$	−1.57240	−	0.907823i	−0.474095	−	0.273719i	−0.717953	+	0.696092i	$0.754921\pi$
$12$	1.00089	+	1.41358i	0.288933	+	0.408066i
$13$	0.311947	−	3.56558i	0.0865186	−	0.988913i	−0.821563	−	0.570118i	$-0.806897\pi$
$13$	0.311947	−	3.56558i	0.0865186	−	0.988913i	0.908081	−	0.418794i	$-0.137547\pi$
$14$	0.436083	−	0.158721i	0.116548	−	0.0424200i
$15$	0.748259	+	3.80001i	0.193200	+	0.981159i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−4.13121	−	5.89998i	−1.00197	−	1.43095i	−0.899859	−	0.436181i	$-0.856331\pi$
$17$	−4.13121	−	5.89998i	−1.00197	−	1.43095i	−0.102107	−	0.994773i	$-0.532558\pi$
$18$	−1.69485	+	2.47538i	−0.399480	+	0.583452i
$19$	−3.89390	+	1.95896i	−0.893322	+	0.449416i
$19$	−3.89390	+	1.95896i	−0.893322	+	0.449416i
$20$	−0.974576	−	2.01251i	−0.217922	−	0.450011i
$21$	0.519891	+	0.613022i	0.113450	+	0.133772i
$22$	0.158244	+	1.80874i	0.0337377	+	0.385624i
$23$	−1.11563	−	2.39248i	−0.232625	−	0.498866i	0.754995	−	0.655730i	$-0.227639\pi$
$23$	−1.11563	−	2.39248i	−0.232625	−	0.498866i	−0.987620	+	0.156864i	$0.949861\pi$
$24$	0.583849	−	1.63068i	0.119178	−	0.332861i
$25$	−0.146408	−	4.99786i	−0.0292816	−	0.999571i
$26$	−3.09967	+	1.78960i	−0.607896	+	0.350969i
$27$	−5.03964	−	1.26570i	−0.969880	−	0.243585i
$28$	−0.380144	−	0.266179i	−0.0718404	−	0.0503032i
$29$	0.307517	+	1.74401i	0.0571044	+	0.323855i	0.999956	−	0.00935707i	$-0.00297849\pi$
$29$	0.307517	+	1.74401i	0.0571044	+	0.323855i	−0.942852	+	0.333212i	$0.891867\pi$
$30$	2.68361	−	2.79254i	0.489957	−	0.509845i
$31$	−2.70760	−	4.68969i	−0.486299	−	0.842294i	0.513577	−	0.858043i	$-0.328320\pi$
$31$	−2.70760	−	4.68969i	−0.486299	−	0.842294i	−0.999876	+	0.0157495i	$0.994987\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$	−2.84314	+	1.34398i	−0.494927	+	0.233957i
$34$	−2.46341	+	6.76818i	−0.422472	+	1.16073i
$35$	−0.531949	−	0.890974i	−0.0899158	−	0.150602i
$36$	2.99983	−	0.0314779i	0.499972	−	0.00524632i
$37$	0.279417	+	0.279417i	0.0459358	+	0.0459358i	0.729702	−	0.683766i	$-0.239659\pi$
$37$	0.279417	+	0.279417i	0.0459358	+	0.0459358i	−0.683766	+	0.729702i	$0.739659\pi$
$38$	3.83814	+	2.06608i	0.622628	+	0.335163i
$39$	−4.76982	−	3.95989i	−0.763782	−	0.634091i
$40$	−1.08956	+	1.95265i	−0.172274	+	0.308742i
$41$	−3.76030	+	4.48135i	−0.587260	+	0.699870i	−0.975077	−	0.221867i	$-0.928785\pi$
$41$	−3.76030	+	4.48135i	−0.587260	+	0.699870i	0.387817	+	0.921737i	$0.373229\pi$
$42$	0.203961	−	0.777485i	0.0314718	−	0.119968i
$43$	3.02987	−	6.49758i	0.462051	−	0.990871i	−0.527880	−	0.849319i	$-0.677013\pi$
$43$	3.02987	−	6.49758i	0.462051	−	0.990871i	0.989931	−	0.141552i	$-0.0452093\pi$
$44$	1.39087	−	1.16708i	0.209681	−	0.175943i
$45$	6.14903	+	2.68131i	0.916643	+	0.399706i
$46$	−1.31990	+	2.28614i	−0.194609	+	0.337073i
$47$	11.0436	+	7.73283i	1.61088	+	1.12795i	0.909950	+	0.414717i	$0.136120\pi$
$47$	11.0436	+	7.73283i	1.61088	+	1.12795i	0.700928	+	0.713232i	$0.252769\pi$
$48$	−1.67066	+	0.457059i	−0.241139	+	0.0659708i
$49$	5.87567	+	3.39232i	0.839381	+	0.484617i
$50$	−4.01003	+	2.98658i	−0.567104	+	0.422367i
$51$	−12.4750	+	0.0654496i	−1.74685	+	0.00916478i
$52$	3.24385	+	1.51263i	0.449841	+	0.209764i
$53$	4.54103	+	9.73828i	0.623759	+	1.33766i	0.923487	+	0.383631i	$0.125326\pi$
$53$	4.54103	+	9.73828i	0.623759	+	1.33766i	−0.299727	+	0.954025i	$0.596896\pi$
$54$	1.85382	+	4.85421i	0.252273	+	0.660574i
$55$	3.90577	−	1.10809i	0.526653	−	0.149415i
$56$			0.464070i			0.0620139i
$57$	−1.04984	+	7.47649i	−0.139055	+	0.990285i
$58$	1.25223	−	1.25223i	0.164426	−	0.164426i
$59$	2.46327	−	13.9699i	0.320691	−	1.81873i	−0.217682	−	0.976020i	$-0.569850\pi$
$59$	2.46327	−	13.9699i	0.320691	−	1.81873i	0.538373	−	0.842707i	$-0.319039\pi$
$60$	−3.82677	−	0.596548i	−0.494033	−	0.0770140i
$61$	−8.37266	−	3.04740i	−1.07201	−	0.390179i	−0.255081	−	0.966920i	$-0.582102\pi$
$61$	−8.37266	−	3.04740i	−1.07201	−	0.390179i	−0.816928	+	0.576740i	$0.804324\pi$
$62$	−2.28856	+	4.90783i	−0.290647	+	0.623295i
$63$	1.38556	−	0.135885i	0.174564	−	0.0171199i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	5.23366	+	6.05492i	0.649155	+	0.751020i
$66$	2.73168	+	1.55809i	0.336247	+	0.191787i
$67$	−4.30882	+	6.15364i	−0.526407	+	0.751787i	−0.991018	−	0.133728i	$-0.957305\pi$
$67$	−4.30882	+	6.15364i	−0.526407	+	0.751787i	0.464611	+	0.885515i	$0.346194\pi$
$68$	6.95712	−	1.86416i	0.843675	−	0.226062i
$69$	−4.50692	−	0.770334i	−0.542570	−	0.0927373i
$70$	−0.424730	+	0.946789i	−0.0507649	+	0.113163i
$71$	−0.814145	−	2.23684i	−0.0966212	−	0.265465i	0.881961	−	0.471323i	$-0.156223\pi$
$71$	−0.814145	−	2.23684i	−0.0966212	−	0.265465i	−0.978582	+	0.205859i	$0.934001\pi$
$72$	−1.74642	−	2.43927i	−0.205818	−	0.287470i
$73$	−1.60452	+	0.140378i	−0.187795	+	0.0164300i	−0.180665	−	0.983545i	$-0.557825\pi$
$73$	−1.60452	+	0.140378i	−0.187795	+	0.0164300i	−0.00712989	+	0.999975i	$0.502270\pi$
$74$	0.0686180	−	0.389152i	0.00797668	−	0.0452380i
$75$	−7.26133	−	4.71943i	−0.838467	−	0.544953i
$76$	−0.509027	−	4.32908i	−0.0583894	−	0.496579i
$77$	0.595799	−	0.595799i	0.0678976	−	0.0678976i
$78$	−0.507901	+	6.17851i	−0.0575084	+	0.699578i
$79$	4.77508	−	5.69072i	0.537238	−	0.640256i	−0.427328	−	0.904097i	$-0.640545\pi$
$79$	4.77508	−	5.69072i	0.537238	−	0.640256i	0.964566	+	0.263841i	$0.0849894\pi$
$80$	2.22447	−	0.227482i	0.248703	−	0.0254333i
$81$	−6.77149	+	5.92849i	−0.752387	+	0.658721i
$82$	5.82773	+	0.509860i	0.643565	+	0.0563046i
$83$	−0.560820	+	2.09301i	−0.0615579	+	0.229737i	−0.989850	−	0.142114i	$-0.954610\pi$
$83$	−0.560820	+	2.09301i	−0.0615579	+	0.229737i	0.928292	+	0.371851i	$0.121277\pi$
$84$	−0.753865	+	0.278872i	−0.0822534	+	0.0304274i
$85$	15.8999	+	2.56413i	1.72459	+	0.278119i
$86$	−7.06037	+	1.24493i	−0.761339	+	0.134245i
$87$	2.78670	+	1.28170i	0.298766	+	0.137413i
$88$	−1.75378	−	0.469924i	−0.186954	−	0.0500941i
$89$	−10.9641	+	9.20001i	−1.16220	+	0.975199i	−0.999933	−	0.0115488i	$-0.996324\pi$
$89$	−10.9641	+	9.20001i	−1.16220	+	0.975199i	−0.162263	+	0.986748i	$0.551879\pi$
$90$	−1.33054	−	6.57493i	−0.140251	−	0.693058i
$91$	1.56083	+	0.568094i	0.163619	+	0.0595525i
$92$	2.62976	−	0.230074i	0.274172	−	0.0239869i
$93$	−9.34786	−	0.768435i	−0.969327	−	0.0796830i
$94$		−	13.4818i		−	1.39054i
$95$	2.92358	−	9.29799i	0.299953	−	0.953954i
$96$	1.33265	+	1.10636i	0.136013	+	0.112918i
$97$	10.5824	−	7.40989i	1.07448	−	0.752360i	0.104253	−	0.994551i	$-0.466755\pi$
$97$	10.5824	−	7.40989i	1.07448	−	0.752360i	0.970229	+	0.242191i	$0.0778660\pi$
$98$	−0.591320	−	6.75882i	−0.0597324	−	0.682744i
$99$	−0.889515	+	5.37382i	−0.0893996	+	0.540089i
$100$	4.74652	+	1.57179i	0.474652	+	0.157179i
$101$	−6.26365	−	7.46473i	−0.623257	−	0.742768i	0.358370	−	0.933580i	$-0.383333\pi$
$101$	−6.26365	−	7.46473i	−0.623257	−	0.742768i	−0.981627	+	0.190811i	$0.938888\pi$
$102$	7.20898	+	10.1814i	0.713795	+	1.00811i
$103$	−2.86579	−	10.6953i	−0.282375	−	1.05384i	−0.950737	−	0.310000i	$-0.899671\pi$
$103$	−2.86579	−	10.6953i	−0.282375	−	1.05384i	0.668362	−	0.743836i	$-0.266996\pi$
$104$	−0.621521	−	3.52482i	−0.0609451	−	0.345637i
$105$	−1.79326	−	0.121008i	−0.175004	−	0.0118091i
$106$	5.37250	−	9.30545i	0.521824	−	0.903825i
$107$	9.91944	+	2.65791i	0.958949	+	0.256950i	0.704155	−	0.710046i	$-0.251326\pi$
$107$	9.91944	+	2.65791i	0.958949	+	0.256950i	0.254793	+	0.966996i	$0.417993\pi$
$108$	2.91303	−	4.30282i	0.280307	−	0.414039i
$109$	0.289884	+	0.796451i	0.0277659	+	0.0762862i	0.952801	−	0.303595i	$-0.0981870\pi$
$109$	0.289884	+	0.796451i	0.0277659	+	0.0762862i	−0.925035	+	0.379881i	$0.875965\pi$
$110$	−3.14795	−	2.56384i	−0.300145	−	0.244453i
$111$	0.673398	−	0.122384i	0.0639161	−	0.0116162i
$112$	0.380144	−	0.266179i	0.0359202	−	0.0251516i
$113$	−2.14515	−	2.14515i	−0.201799	−	0.201799i	0.598972	−	0.800770i	$-0.295576\pi$
$113$	−2.14515	−	2.14515i	−0.201799	−	0.201799i	−0.800770	+	0.598972i	$0.795576\pi$
$114$	6.72654	−	3.42836i	0.629998	−	0.321095i
$115$	5.57577	+	1.93744i	0.519944	+	0.180667i
$116$	−1.74401	−	0.307517i	−0.161928	−	0.0285522i
$117$	−10.3420	+	2.88777i	−0.956116	+	0.266974i
$118$	−12.8563	+	5.99501i	−1.18352	+	0.551886i
$119$	3.14091	−	1.14320i	0.287926	−	0.104797i
$120$	1.70628	+	3.47687i	0.155761	+	0.317393i
$121$	−3.85171	−	6.67136i	−0.350156	−	0.606488i
$122$	2.30608	+	8.60639i	0.208782	+	0.779186i
$123$	2.67379	+	9.77333i	0.241088	+	0.881231i
$124$	5.33292	−	0.940338i	0.478911	−	0.0844449i
$125$	8.24524	+	7.55089i	0.737477	+	0.675372i
$126$	−0.906036	−	1.05705i	−0.0807161	−	0.0941691i
$127$	−7.38205	−	0.645845i	−0.655051	−	0.0573095i	−0.245215	−	0.969469i	$-0.578858\pi$
$127$	−7.38205	−	0.645845i	−0.655051	−	0.0573095i	−0.409836	+	0.912159i	$0.634414\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$	−6.26512	−	10.7212i	−0.551613	−	0.943949i
$130$	1.95800	−	7.76012i	0.171728	−	0.680607i
$131$	−8.61883	−	1.51973i	−0.753031	−	0.132780i	−0.216060	−	0.976380i	$-0.569321\pi$
$131$	−8.61883	−	1.51973i	−0.753031	−	0.132780i	−0.536971	+	0.843601i	$0.680432\pi$
$132$	−0.290519	−	3.13134i	−0.0252864	−	0.272549i
$133$	−0.410420	−	1.98076i	−0.0355880	−	0.171754i
$134$	7.51221			0.648956
$135$	9.88119	−	6.11246i	0.850437	−	0.526077i
$136$	−5.51747	−	4.62971i	−0.473119	−	0.396994i
$137$	9.71289	−	4.52920i	0.829828	−	0.386955i	0.0391848	−	0.999232i	$-0.487524\pi$
$137$	9.71289	−	4.52920i	0.829828	−	0.386955i	0.790644	+	0.612277i	$0.209746\pi$
$138$	1.95404	+	4.13370i	0.166339	+	0.351884i
$139$	7.84568	+	9.35012i	0.665462	+	0.793067i	0.988159	−	0.153435i	$-0.0490337\pi$
$139$	7.84568	+	9.35012i	0.665462	+	0.793067i	−0.322696	+	0.946503i	$0.604589\pi$
$140$	1.01918	−	0.195137i	0.0861363	−	0.0164921i
$141$	21.9007	−	8.10157i	1.84437	−	0.682275i
$142$	−1.36534	+	1.94991i	−0.114577	+	0.163633i
$143$	−3.72742	+	5.32330i	−0.311702	+	0.445157i
$144$	−0.996424	+	2.82969i	−0.0830354	+	0.235807i
$145$	−3.27666	−	2.22356i	−0.272112	−	0.184657i
$146$	1.03531	+	1.23383i	0.0856826	+	0.102113i
$147$	10.6241	−	5.02214i	0.876263	−	0.414219i
$148$	−0.358132	+	0.167000i	−0.0294383	+	0.0137273i
$149$	5.40483	+	4.53519i	0.442781	+	0.371537i	0.836749	−	0.547587i	$-0.184453\pi$
$149$	5.40483	+	4.53519i	0.442781	+	0.371537i	−0.393968	+	0.919124i	$0.628898\pi$
$150$	0.298998	+	8.65509i	0.0244131	+	0.706685i
$151$	13.0789			1.06434			0.532172	−	0.846636i	$-0.321376\pi$
$151$	13.0789			1.06434			0.532172	+	0.846636i	$0.321376\pi$
$152$	−3.25420	+	2.90003i	−0.263951	+	0.235223i
$153$	−12.2072	+	17.8290i	−0.986896	+	1.44139i
$154$	−0.829786	−	0.146314i	−0.0668661	−	0.0117903i
$155$	11.7408	+	2.96238i	0.943042	+	0.237944i
$156$	5.35246	−	3.12780i	0.428539	−	0.250424i
$157$	6.42637	+	2.99667i	0.512880	+	0.239160i	0.661788	−	0.749691i	$-0.269798\pi$
$157$	6.42637	+	2.99667i	0.512880	+	0.239160i	−0.148908	+	0.988851i	$0.547576\pi$
$158$	−7.40044	−	0.647454i	−0.588747	−	0.0515087i
$159$	18.3449	+	3.13555i	1.45484	+	0.248665i
$160$	−1.46224	−	1.69170i	−0.115601	−	0.133740i
$161$	1.20644	−	0.212729i	0.0950811	−	0.0167654i
$162$	8.74030	+	2.14644i	0.686703	+	0.168640i
$163$	0.587408	+	2.19224i	0.0460093	+	0.171709i	0.985107	−	0.171940i	$-0.0550035\pi$
$163$	0.587408	+	2.19224i	0.0460093	+	0.171709i	−0.939098	+	0.343649i	$0.888337\pi$
$164$	−2.92499	−	5.06624i	−0.228404	−	0.395607i
$165$	2.27318	−	6.65442i	0.176967	−	0.518046i
$166$	2.03616	−	0.741103i	0.158037	−	0.0575208i
$167$	4.50744	−	2.10186i	0.348796	−	0.162646i	−0.240322	−	0.970693i	$-0.577253\pi$
$167$	4.50744	−	2.10186i	0.348796	−	0.162646i	0.589118	+	0.808047i	$0.299475\pi$
$168$	0.660838	+	0.457576i	0.0509848	+	0.0353027i
$169$	0.186486	+	0.0328825i	0.0143451	+	0.00252942i
$170$	−7.01942	−	14.4952i	−0.538365	−	1.11173i
$171$	9.61141	+	8.86684i	0.735003	+	0.678064i
$172$	5.06945	+	5.06945i	0.386542	+	0.386542i
$173$	6.44204	−	4.51076i	0.489779	−	0.342947i	−0.302456	−	0.953163i	$-0.597806\pi$
$173$	6.44204	−	4.51076i	0.489779	−	0.342947i	0.792235	+	0.610217i	$0.208918\pi$
$174$	−0.548475	−	3.01789i	−0.0415798	−	0.228785i
$175$	2.25791	+	0.534665i	0.170682	+	0.0404168i
$176$	0.620988	+	1.70615i	0.0468087	+	0.128606i
$177$	−17.4644	−	17.2821i	−1.31271	−	1.29900i
$178$	13.8250	+	3.70439i	1.03623	+	0.277656i
$179$	−3.87478	+	6.71132i	−0.289615	+	0.501628i	−0.973718	−	0.227758i	$-0.926861\pi$
$179$	−3.87478	+	6.71132i	−0.289615	+	0.501628i	0.684103	+	0.729385i	$0.260194\pi$
$180$	−4.62270	+	4.86113i	−0.344556	+	0.362328i
$181$	0.874347	+	4.95867i	0.0649897	+	0.368575i	0.999906	+	0.0137067i	$0.00436312\pi$
$181$	0.874347	+	4.95867i	0.0649897	+	0.368575i	−0.934916	+	0.354868i	$0.884526\pi$
$182$	−0.429897	−	1.60440i	−0.0318661	−	0.118926i
$183$	−12.5950	+	8.91796i	−0.931049	+	0.659234i
$184$	−1.69684	−	2.02221i	−0.125092	−	0.149079i
$185$	−0.883499	+	0.0129379i	−0.0649561	+	0.000951213i
$186$	4.73224	+	8.09807i	0.346985	+	0.593779i
$187$	1.13976	+	13.0275i	0.0833475	+	0.952666i
$188$	−11.0436	+	7.73283i	−0.805439	+	0.563975i
$189$	1.17267	−	2.10703i	0.0852994	−	0.153264i
$190$	−9.29337	+	2.93825i	−0.674212	+	0.213163i
$191$		−	17.1496i		−	1.24090i	−0.784247	−	0.620449i	$-0.786950\pi$
$191$		−	17.1496i		−	1.24090i	0.784247	−	0.620449i	$-0.213050\pi$
$192$	0.141904	−	1.72623i	0.0102410	−	0.124580i
$193$	−16.4826	+	1.44204i	−1.18645	+	0.103801i	−0.663241	−	0.748406i	$-0.730820\pi$
$193$	−16.4826	+	1.44204i	−1.18645	+	0.103801i	−0.523206	+	0.852206i	$0.675264\pi$
$194$	−12.1396	−	4.41847i	−0.871576	−	0.317228i
$195$	13.7827	−	1.48257i	0.986996	−	0.106169i
$196$	−5.19734	+	4.36108i	−0.371238	+	0.311506i
$197$	12.2234	+	3.27524i	0.870878	+	0.233351i	0.666468	−	0.745534i	$-0.267805\pi$
$197$	12.2234	+	3.27524i	0.870878	+	0.233351i	0.204411	+	0.978885i	$0.434472\pi$
$198$	4.91218	−	2.35365i	0.349093	−	0.167266i
$199$	5.84798	−	1.03116i	0.414552	−	0.0730968i	0.0375178	−	0.999296i	$-0.488055\pi$
$199$	5.84798	−	1.03116i	0.414552	−	0.0730968i	0.377035	+	0.926199i	$0.376944\pi$
$200$	−1.43496	−	4.78967i	−0.101467	−	0.338680i
$201$	4.51429	+	12.2033i	0.318413	+	0.860756i
$202$	−2.52207	+	9.41248i	−0.177452	+	0.662260i
$203$	−0.818702	−	0.0716272i	−0.0574617	−	0.00502724i
$204$	4.20520	−	11.7450i	0.294423	−	0.822318i
$205$	−1.33077	−	13.0131i	−0.0929448	−	0.908875i
$206$	−7.11730	+	8.48207i	−0.495886	+	0.590974i
$207$	−5.54081	+	5.65833i	−0.385113	+	0.393281i
$208$	−2.53087	+	2.53087i	−0.175484	+	0.175484i
$209$	7.90115	+	0.454715i	0.546534	+	0.0314533i
$210$	0.929446	+	1.53836i	0.0641379	+	0.106157i
$211$	−0.0770378	+	0.436903i	−0.00530350	+	0.0300777i	−0.987345	−	0.158589i	$-0.949305\pi$
$211$	−0.0770378	+	0.436903i	−0.00530350	+	0.0300777i	0.982041	+	0.188667i	$0.0604166\pi$
$212$	−10.7041	+	0.936489i	−0.735162	+	0.0643183i
$213$	−3.98803	−	1.04620i	−0.273255	−	0.0716841i
$214$	−3.51233	−	9.65004i	−0.240098	−	0.659663i
$215$	5.70291	+	14.9823i	0.388936	+	1.02179i
$216$	−5.19551	+	0.0817802i	−0.353510	+	0.00556443i
$217$	2.42740	−	0.650419i	0.164782	−	0.0441533i
$218$	0.486144	−	0.694285i	0.0329258	−	0.0470229i
$219$	−1.38217	+	2.42326i	−0.0933985	+	0.163749i
$220$	−0.294586	+	4.04921i	−0.0198610	+	0.272998i
$221$	−22.3255	+	12.8897i	−1.50178	+	0.867052i
$222$	−0.486497	−	0.481418i	−0.0326515	−	0.0323107i
$223$	8.66774	−	18.5880i	0.580435	−	1.24475i	−0.368603	−	0.929587i	$-0.620164\pi$
$223$	8.66774	−	18.5880i	0.580435	−	1.24475i	0.949038	−	0.315160i	$-0.102058\pi$
$224$	−0.436083	−	0.158721i	−0.0291370	−	0.0106050i
$225$	−13.8802	+	5.68679i	−0.925348	+	0.379119i
$226$	−0.526796	+	2.98761i	−0.0350419	+	0.198733i
$227$	−0.390613	+	0.390613i	−0.0259259	+	0.0259259i	−0.719951	−	0.694025i	$-0.755836\pi$
$227$	−0.390613	+	0.390613i	−0.0259259	+	0.0259259i	0.694025	+	0.719951i	$0.255836\pi$
$228$	−6.66653	−	3.54364i	−0.441502	−	0.234683i
$229$		−	6.58608i		−	0.435220i	−0.976036	−	0.217610i	$-0.930174\pi$
$229$		−	6.58608i		−	0.435220i	0.976036	−	0.217610i	$-0.0698261\pi$
$230$	−1.61108	−	5.67868i	−0.106231	−	0.374441i
$231$	−0.260960	−	1.43588i	−0.0171699	−	0.0944741i
$232$	0.748423	+	1.60500i	0.0491363	+	0.105373i
$233$	5.74943	+	2.68100i	0.376658	+	0.175638i	0.601722	−	0.798705i	$-0.294481\pi$
$233$	5.74943	+	2.68100i	0.376658	+	0.175638i	−0.225064	+	0.974344i	$0.572259\pi$
$234$	8.29743	+	6.81530i	0.542420	+	0.445530i
$235$	−29.6084	+	5.66897i	−1.93144	+	0.369803i
$236$	12.2849	+	7.09270i	0.799681	+	0.461696i
$237$	−3.39536	−	12.4108i	−0.220552	−	0.806169i
$238$	−2.73800	−	1.91717i	−0.177478	−	0.124272i
$239$	10.7724	−	18.6584i	0.696811	−	1.20691i	−0.272755	−	0.962083i	$-0.587935\pi$
$239$	10.7724	−	18.6584i	0.696811	−	1.20691i	0.969566	−	0.244829i	$-0.0787317\pi$
$240$	1.86940	−	3.39195i	0.120669	−	0.218950i
$241$	−12.2688	+	10.2948i	−0.790304	+	0.663143i	−0.945821	−	0.324690i	$-0.894740\pi$
$241$	−12.2688	+	10.2948i	−0.790304	+	0.663143i	0.155517	+	0.987833i	$0.450296\pi$
$242$	−3.25561	+	6.98168i	−0.209278	+	0.448799i
$243$	1.76547	+	15.4882i	0.113255	+	0.993566i
$244$	5.72723	−	6.82545i	0.366649	−	0.436955i
$245$	−14.5949	+	4.14067i	−0.932435	+	0.264538i
$246$	6.47222	−	7.79599i	0.412654	−	0.497054i
$247$	5.77013	+	14.4951i	0.367144	+	0.922301i
$248$	−3.82912	−	3.82912i	−0.243149	−	0.243149i
$249$	2.42748	+	2.86233i	0.153835	+	0.181393i
$250$	1.45605	−	11.0851i	0.0920889	−	0.701085i
$251$	7.83333	−	21.5219i	0.494436	−	1.35845i	−0.402147	−	0.915575i	$-0.631736\pi$
$251$	7.83333	−	21.5219i	0.494436	−	1.35845i	0.896583	−	0.442876i	$-0.146042\pi$
$252$	−0.346200	+	1.34848i	−0.0218086	+	0.0849461i
$253$	−0.417734	+	4.77472i	−0.0262627	+	0.300184i
$254$	3.70512	+	6.41746i	0.232480	+	0.402667i
$255$	19.3288	−	20.1134i	1.21042	−	1.25955i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−11.3191	−	7.92570i	−0.706065	−	0.494392i	0.164543	−	0.986370i	$-0.447385\pi$
$257$	−11.3191	−	7.92570i	−0.706065	−	0.494392i	−0.870608	+	0.491978i	$0.836274\pi$
$258$	−5.18877	+	11.2815i	−0.323039	+	0.702356i
$259$	−0.158811	+	0.0916898i	−0.00986806	+	0.00569732i
$260$	−7.47978	+	2.84712i	−0.463876	+	0.176571i
$261$	4.57286	−	2.70451i	0.283053	−	0.167405i
$262$	3.69867	+	7.93182i	0.228504	+	0.490029i
$263$	−2.27063	−	25.9534i	−0.140013	−	1.60036i	−0.663402	−	0.748263i	$-0.730888\pi$
$263$	−2.27063	−	25.9534i	−0.140013	−	1.60036i	0.523389	−	0.852094i	$-0.324667\pi$
$264$	−2.39841	+	2.03404i	−0.147612	+	0.125187i
$265$	−22.6955	−	7.88610i	−1.39417	−	0.484439i
$266$	−1.38714	+	1.47231i	−0.0850508	+	0.0902734i
$267$	2.29015	+	24.6843i	0.140155	+	1.51065i
$268$	−4.30882	−	6.15364i	−0.263203	−	0.375893i
$269$	−23.1551	−	19.4294i	−1.41179	−	1.18463i	−0.955569	−	0.294768i	$-0.904757\pi$
$269$	−23.1551	−	19.4294i	−1.41179	−	1.18463i	−0.456223	−	0.889865i	$-0.650798\pi$
$270$	−10.6746	−	4.58823i	−0.649639	−	0.279231i
$271$	−15.8256	+	5.76006i	−0.961338	+	0.349899i	−0.774558	−	0.632503i	$-0.782028\pi$
$271$	−15.8256	+	5.76006i	−0.961338	+	0.349899i	−0.186781	+	0.982402i	$0.559805\pi$
$272$	−0.627743	+	7.17514i	−0.0380625	+	0.435056i
$273$	2.34795	−	1.66248i	0.142105	−	0.100618i
$274$	−9.28119	−	5.35850i	−0.560697	−	0.323719i
$275$	−4.30696	+	7.99152i	−0.259719	+	0.481907i
$276$	2.26533	−	3.97165i	0.136357	−	0.239065i
$277$	−22.9191	+	6.14116i	−1.37708	+	0.368987i	−0.870059	−	0.492948i	$-0.835919\pi$
$277$	−22.9191	+	6.14116i	−1.37708	+	0.368987i	−0.507019	+	0.861935i	$0.669252\pi$
$278$	3.15907	−	11.7898i	0.189469	−	0.707106i
$279$	−10.3113	+	12.5537i	−0.617321	+	0.751571i
$280$	−0.744424	−	0.722936i	−0.0444878	−	0.0432037i
$281$	−11.1465	+	30.6248i	−0.664946	+	1.82692i	−0.111997	+	0.993709i	$0.535725\pi$
$281$	−11.1465	+	30.6248i	−0.664946	+	1.82692i	−0.552949	+	0.833215i	$0.686498\pi$
$282$	−19.1981	−	13.2931i	−1.14323	−	0.791594i
$283$	9.76365	+	13.9439i	0.580389	+	0.828881i	0.996770	−	0.0803090i	$-0.0255907\pi$
$283$	9.76365	+	13.9439i	0.580389	+	0.828881i	−0.416381	+	0.909190i	$0.636702\pi$
$284$	2.38040			0.141251
$285$	−10.3577	−	13.3311i	−0.613539	−	0.789665i
$286$	6.49855			0.384268
$287$	−1.55715	−	2.22384i	−0.0919155	−	0.131269i
$288$	2.88947	−	0.806820i	0.170264	−	0.0475423i
$289$	−11.9285	+	32.7733i	−0.701677	+	1.92784i
$290$	0.0579822	+	3.95947i	0.00340483	+	0.232508i
$291$	−0.117393	−	22.3756i	−0.00688169	−	1.31168i
$292$	0.416867	−	1.55577i	0.0243953	−	0.0910446i
$293$	28.3244	−	7.58950i	1.65473	−	0.443383i	0.693797	−	0.720170i	$-0.255936\pi$
$293$	28.3244	−	7.58950i	1.65473	−	0.443383i	0.960931	+	0.276787i	$0.0892697\pi$
$294$	−10.2076	−	5.82220i	−0.595322	−	0.339557i
$295$	18.5721	+	25.7139i	1.08131	+	1.49712i
$296$	0.342214	+	0.197578i	0.0198908	+	0.0114840i
$297$	6.77528	+	6.56529i	0.393142	+	0.380957i
$298$	0.614928	−	7.02866i	0.0356218	−	0.407159i
$299$	−8.87858	+	3.23154i	−0.513461	+	0.186885i
$300$	6.91834	−	5.20928i	0.399430	−	0.300758i
$301$	2.54867	+	2.13859i	0.146903	+	0.123266i
$302$	−7.50174	−	10.7136i	−0.431677	−	0.616498i
$303$	−16.8058	+	1.55921i	−0.965469	+	0.0895740i
$304$	4.24210	+	1.00230i	0.243301	+	0.0574860i
$305$	17.9315	−	8.68346i	1.02675	−	0.497214i
$306$	21.6064	−	0.226721i	1.23516	−	0.0129608i
$307$	−0.536481	−	6.13201i	−0.0306186	−	0.349972i	−0.996015	−	0.0891855i	$-0.971574\pi$
$307$	−0.536481	−	6.13201i	−0.0306186	−	0.349972i	0.965396	−	0.260787i	$-0.0839819\pi$
$308$	0.356093	+	0.763643i	0.0202903	+	0.0435126i
$309$	−18.0558	−	6.46470i	−1.02716	−	0.367764i
$310$	−4.30760	−	11.3166i	−0.244655	−	0.642741i
$311$	−1.30731	+	0.754777i	−0.0741309	+	0.0427995i	−0.536607	−	0.843832i	$-0.680294\pi$
$311$	−1.30731	+	0.754777i	−0.0741309	+	0.0427995i	0.462476	+	0.886632i	$0.346961\pi$
$312$	−5.63219	−	2.59044i	−0.318860	−	0.146655i
$313$	10.2200	+	7.15610i	0.577667	+	0.404487i	0.825571	−	0.564298i	$-0.190853\pi$
$313$	10.2200	+	7.15610i	0.577667	+	0.404487i	−0.247904	+	0.968784i	$0.579742\pi$
$314$	−1.23129	−	6.98299i	−0.0694857	−	0.394073i
$315$	−1.94048	+	2.43429i	−0.109334	+	0.137157i
$316$	3.71435	+	6.43345i	0.208949	+	0.361910i
$317$	0.903897	−	10.3316i	0.0507679	−	0.580280i	−0.927623	−	0.373517i	$-0.878152\pi$
$317$	0.903897	−	10.3316i	0.0507679	−	0.580280i	0.978391	−	0.206763i	$-0.0662928\pi$
$318$	−7.95369	−	16.8257i	−0.446021	−	0.943538i
$319$	1.09972	−	3.02145i	0.0615724	−	0.169169i
$320$	−0.547049	+	2.16812i	−0.0305810	+	0.121201i
$321$	13.5655	−	11.5046i	0.757153	−	0.642126i
$322$	−0.866245	−	0.866245i	−0.0482739	−	0.0482739i
$323$	27.6443	+	14.8811i	1.53817	+	0.828005i
$324$	−3.25497	−	8.39078i	−0.180832	−	0.466154i
$325$	−17.8659	−	1.03704i	−0.991022	−	0.0575246i
$326$	1.45885	−	1.73859i	0.0807983	−	0.0962917i
$327$	1.41998	+	0.372509i	0.0785250	+	0.0205998i
$328$	−2.47231	+	5.30189i	−0.136511	+	0.292748i
$329$	−4.79275	+	4.02159i	−0.264233	+	0.221718i
$330$	−6.75482	+	1.95473i	−0.371841	+	0.107605i
$331$	2.39000	−	4.13959i	0.131366	−	0.227533i	−0.792837	−	0.609433i	$-0.791397\pi$
$331$	2.39000	−	4.13959i	0.131366	−	0.227533i	0.924203	+	0.381901i	$0.124730\pi$
$332$	−1.77497	−	1.24285i	−0.0974142	−	0.0682102i
$333$	0.489698	−	1.07959i	0.0268353	−	0.0591614i
$334$	−4.30710	−	2.48671i	−0.235674	−	0.136067i
$335$	−3.15882	−	16.4981i	−0.172585	−	0.901389i
$336$	−0.00421701	−	0.803781i	−0.000230057	−	0.0438499i
$337$	−22.1440	−	10.3259i	−1.20626	−	0.562488i	−0.287681	−	0.957726i	$-0.592884\pi$
$337$	−22.1440	−	10.3259i	−1.20626	−	0.562488i	−0.918579	+	0.395238i	$0.870662\pi$
$338$	−0.0800281	−	0.171621i	−0.00435296	−	0.00933495i
$339$	−5.16983	+	0.939573i	−0.280787	+	0.0510306i
$340$	−7.84760	+	14.0641i	−0.425596	+	0.762732i
$341$			9.83208i			0.532437i
$342$	1.75042	−	12.9590i	0.0946517	−	0.700743i
$343$	−4.52339	+	4.52339i	−0.244240	+	0.244240i
$344$	1.24493	−	7.06037i	0.0671223	−	0.380669i
$345$	8.25667	−	6.02961i	0.444524	−	0.324623i
$346$	−7.39000	−	2.68974i	−0.397289	−	0.144601i
$347$	0.665578	−	1.42734i	0.0357301	−	0.0766234i	−0.887633	−	0.460552i	$-0.847651\pi$
$347$	0.665578	−	1.42734i	0.0357301	−	0.0766234i	0.923363	+	0.383929i	$0.125429\pi$
$348$	−2.15751	+	2.18027i	−0.115655	+	0.116875i
$349$	−11.8602	+	6.84749i	−0.634862	+	0.366538i	−0.782633	−	0.622484i	$-0.786124\pi$
$349$	−11.8602	+	6.84749i	−0.634862	+	0.366538i	0.147770	+	0.989022i	$0.452790\pi$
$350$	−0.857112	−	2.15624i	−0.0458145	−	0.115256i
$351$	−6.08506	+	17.5744i	−0.324797	+	0.938052i
$352$	1.04141	−	1.48729i	0.0555075	−	0.0792729i
$353$	−15.2275	+	4.08019i	−0.810476	+	0.217166i	−0.640178	−	0.768226i	$-0.721140\pi$
$353$	−15.2275	+	4.08019i	−0.810476	+	0.217166i	−0.170298	+	0.985393i	$0.554473\pi$
$354$	−4.13951	+	24.2186i	−0.220012	+	1.28721i
$355$	4.85646	+	2.17861i	0.257754	+	0.115629i
$356$	−4.89522	−	13.4495i	−0.259446	−	0.712823i
$357$	1.46904	−	5.59987i	0.0777496	−	0.296376i
$358$	7.72008	−	0.675419i	0.408019	−	0.0356970i
$359$	−0.00411454	+	0.0233347i	−0.000217157	+	0.00123156i	−0.984916	−	0.173032i	$-0.944643\pi$
$359$	−0.00411454	+	0.0233347i	−0.000217157	+	0.00123156i	0.984699	+	0.174264i	$0.0557546\pi$
$360$	6.63348	+	0.998463i	0.349615	+	0.0526236i
$361$	11.3250	−	15.2560i	0.596050	−	0.802947i
$362$	3.56040	−	3.56040i	0.187130	−	0.187130i
$363$	−13.2979	−	1.09314i	−0.697957	−	0.0573752i
$364$	−1.06767	+	1.27240i	−0.0559610	+	0.0666917i
$365$	2.27437	−	2.79253i	0.119046	−	0.146168i
$366$	14.5294	+	5.20209i	0.759462	+	0.271918i
$367$	6.78508	+	0.593617i	0.354178	+	0.0309866i	0.262857	−	0.964835i	$-0.415335\pi$
$367$	6.78508	+	0.593617i	0.354178	+	0.0309866i	0.0913215	+	0.995821i	$0.470891\pi$
$368$	−0.683232	+	2.54986i	−0.0356160	+	0.132921i
$369$	16.5536	+	5.82907i	0.861748	+	0.303449i
$370$	0.517352	+	0.716299i	0.0268959	+	0.0372386i
$371$	−4.91068	+	0.865885i	−0.254950	+	0.0449545i
$372$	3.91925	−	8.52129i	0.203204	−	0.441808i
$373$	23.2821	+	6.23841i	1.20550	+	0.323013i	0.804995	−	0.593282i	$-0.202168\pi$
$373$	23.2821	+	6.23841i	1.20550	+	0.323013i	0.400505	+	0.916295i	$0.368835\pi$
$374$	10.0178	−	8.40591i	0.518007	−	0.434659i
$375$	18.8824	−	4.29604i	0.975082	−	0.221847i
$376$	12.6687	+	4.61104i	0.653340	+	0.237796i
$377$	6.31434	−	0.552433i	0.325205	−	0.0284518i
$378$	−2.39860	+	0.247947i	−0.123370	+	0.0127530i
$379$			36.8540i			1.89306i	0.322610	+	0.946532i	$0.395440\pi$
$379$			36.8540i			1.89306i	−0.322610	+	0.946532i	$0.604560\pi$
$380$	7.73733	+	5.92737i	0.396917	+	0.304068i
$381$	−8.19843	+	9.87527i	−0.420018	+	0.505925i
$382$	−14.0481	+	9.83658i	−0.718763	+	0.503283i
$383$	−0.787226	−	8.99804i	−0.0402254	−	0.459778i	−0.989419	−	0.145086i	$-0.953654\pi$
$383$	−0.787226	−	8.99804i	−0.0402254	−	0.459778i	0.949194	−	0.314692i	$-0.101901\pi$
$384$	−1.49544	+	0.873883i	−0.0763136	+	0.0445952i
$385$	0.0275874	+	1.88388i	0.00140598	+	0.0960114i
$386$	10.6353	+	12.6747i	0.541323	+	0.645124i
$387$	−21.4445	−	1.64961i	−1.09008	−	0.0838546i
$388$	3.34362	+	12.4785i	0.169746	+	0.633502i
$389$	5.34581	+	30.3176i	0.271044	+	1.53716i	0.751255	+	0.660012i	$0.229449\pi$
$389$	5.34581	+	30.3176i	0.271044	+	1.53716i	−0.480212	+	0.877153i	$0.659440\pi$
$390$	−9.11986	−	10.4397i	−0.461802	−	0.528636i
$391$	−9.50666	+	16.4660i	−0.480773	+	0.832723i
$392$	6.55346	+	1.75599i	0.331000	+	0.0886911i
$393$	−10.6623	+	10.7748i	−0.537843	+	0.543517i
$394$	−4.32811	−	11.8914i	−0.218047	−	0.599080i
$395$	1.68990	+	16.5249i	0.0850279	+	0.831458i
$396$	−4.74551	−	2.67382i	−0.238471	−	0.134365i
$397$	−8.11195	+	5.68005i	−0.407127	+	0.285074i	−0.759147	−	0.650919i	$-0.774384\pi$
$397$	−8.11195	+	5.68005i	−0.407127	+	0.285074i	0.352020	+	0.935992i	$0.385495\pi$
$398$	−4.19894	−	4.19894i	−0.210474	−	0.210474i
$399$	−3.22529	−	1.36860i	−0.161466	−	0.0685157i
$400$	−3.10041	+	3.92269i	−0.155020	+	0.196134i
$401$	13.7028	+	2.41617i	0.684284	+	0.120658i	0.504973	−	0.863135i	$-0.331502\pi$
$401$	13.7028	+	2.41617i	0.684284	+	0.120658i	0.179310	+	0.983793i	$0.442613\pi$
$402$	7.40708	−	10.6974i	0.369432	−	0.533539i
$403$	−17.5661	+	8.19120i	−0.875029	+	0.408033i
$404$	9.15685	−	3.33282i	0.455570	−	0.165814i
$405$	1.03873	−	20.0978i	0.0516150	−	0.998667i
$406$	0.410915	+	0.711725i	0.0203934	+	0.0353223i
$407$	−0.185693	−	0.693015i	−0.00920445	−	0.0343515i
$408$	−12.0330	+	3.29199i	−0.595721	+	0.162978i
$409$	−6.55571	+	1.15595i	−0.324159	+	0.0571580i	−0.333360	−	0.942800i	$-0.608182\pi$
$409$	−6.55571	+	1.15595i	−0.324159	+	0.0571580i	0.00920080	+	0.999958i	$0.497071\pi$
$410$	−9.89642	+	8.55411i	−0.488749	+	0.422457i
$411$	3.12737	−	18.2970i	0.154262	−	0.902526i
$412$	11.0304	+	0.965037i	0.543430	+	0.0475440i
$413$	5.96624	+	2.78210i	0.293580	+	0.136898i
$414$	7.81311	+	1.29328i	0.383993	+	0.0635615i
$415$	−2.48378	−	4.16015i	−0.121924	−	0.204214i
$416$	3.52482	+	0.621521i	0.172818	+	0.0304726i
$417$	21.0505	−	1.95302i	1.03085	−	0.0956398i
$418$	−4.15943	−	6.73305i	−0.203444	−	0.329324i
$419$	13.5343			0.661193			0.330597	−	0.943772i	$-0.392750\pi$
$419$	13.5343			0.661193			0.330597	+	0.943772i	$0.392750\pi$
$420$	0.727040	−	1.64372i	0.0354759	−	0.0802055i
$421$	−2.28552	−	1.91778i	−0.111389	−	0.0934668i	0.585392	−	0.810751i	$-0.300941\pi$
$421$	−2.28552	−	1.91778i	−0.111389	−	0.0934668i	−0.696781	+	0.717284i	$0.745385\pi$
$422$	0.402077	−	0.187492i	0.0195728	−	0.00912695i
$423$	10.0575	−	39.1749i	0.489014	−	1.90475i
$424$	6.90676	+	8.23115i	0.335422	+	0.399740i
$425$	−28.8824	+	21.5110i	−1.40100	+	1.04344i
$426$	1.43045	+	3.86688i	0.0693054	+	0.187351i
$427$	2.37166	−	3.38708i	0.114773	−	0.163912i
$428$	−5.89026	+	8.41217i	−0.284717	+	0.406618i
$429$	3.90516	+	10.5567i	0.188543	+	0.509681i
$430$	9.00174	−	13.2651i	0.434102	−	0.639698i
$431$	−16.7667	−	19.9818i	−0.807623	−	0.962488i	0.192199	−	0.981356i	$-0.438438\pi$
$431$	−16.7667	−	19.9818i	−0.807623	−	0.962488i	−0.999822	+	0.0188682i	$0.993994\pi$
$432$	3.04701	+	4.20900i	0.146599	+	0.202506i
$433$	12.8164	−	5.97641i	0.615919	−	0.287208i	−0.0895127	−	0.995986i	$-0.528531\pi$
$433$	12.8164	−	5.97641i	0.615919	−	0.287208i	0.705432	+	0.708778i	$0.250753\pi$
$434$	−1.92509	−	1.61534i	−0.0924073	−	0.0775389i
$435$	−6.39718	+	2.47354i	−0.306721	+	0.118597i
$436$	−0.847565			−0.0405910
$437$	9.03093	+	7.13060i	0.432008	+	0.341103i
$438$	2.77780	−	0.257718i	0.132728	−	0.0123142i
$439$	19.5346	+	3.44449i	0.932338	+	0.164396i	0.619130	−	0.785288i	$-0.287485\pi$
$439$	19.5346	+	3.44449i	0.932338	+	0.164396i	0.313208	+	0.949685i	$0.398596\pi$
$440$	3.48588	−	2.08122i	0.166183	−	0.0992183i
$441$	3.32390	−	20.0807i	0.158281	−	0.956223i
$442$	23.3640	+	10.8948i	1.11131	+	0.518213i
$443$	−10.8247	−	0.947035i	−0.514295	−	0.0449950i	−0.172945	−	0.984931i	$-0.555328\pi$
$443$	−10.8247	−	0.947035i	−0.514295	−	0.0449950i	−0.341350	+	0.939936i	$0.610884\pi$
$444$	−0.115312	+	0.674645i	−0.00547246	+	0.0320172i
$445$	2.32221	−	31.9197i	0.110083	−	1.51314i
$446$	−20.1980	+	3.56146i	−0.956405	+	0.168640i
$447$	11.7873	−	3.22478i	0.557522	−	0.152527i
$448$	0.120110	+	0.448257i	0.00567467	+	0.0211782i
$449$	−3.02438	−	5.23838i	−0.142729	−	0.247214i	0.785794	−	0.618488i	$-0.212254\pi$
$449$	−3.02438	−	5.23838i	−0.142729	−	0.247214i	−0.928523	+	0.371274i	$0.878921\pi$
$450$	12.6197	+	8.10820i	0.594899	+	0.382224i
$451$	9.98096	−	3.63277i	0.469985	−	0.171061i
$452$	2.74946	−	1.28210i	0.129324	−	0.0603047i
$453$	12.8959	−	18.6244i	0.605900	−	0.875051i
$454$	0.544018	+	0.0959251i	0.0255320	+	0.00450199i
$455$	−3.34277	+	1.61877i	−0.156712	+	0.0758889i
$456$	0.920987	+	7.49345i	0.0431292	+	0.350913i
$457$	−27.1756	−	27.1756i	−1.27122	−	1.27122i	−0.945447	−	0.325775i	$-0.894375\pi$
$457$	−27.1756	−	27.1756i	−1.27122	−	1.27122i	−0.325775	−	0.945447i	$-0.605625\pi$
$458$	−5.39500	+	3.77762i	−0.252092	+	0.176517i
$459$	13.3522	+	34.9627i	0.623227	+	1.63192i
$460$	−3.72762	+	4.57687i	−0.173801	+	0.213398i
$461$	1.29614	+	3.56111i	0.0603671	+	0.165857i	0.966210	−	0.257757i	$-0.0829834\pi$
$461$	1.29614	+	3.56111i	0.0603671	+	0.165857i	−0.905843	+	0.423614i	$0.860761\pi$
$462$	−1.02653	+	1.03735i	−0.0477583	+	0.0482621i
$463$	31.0807	+	8.32804i	1.44444	+	0.387037i	0.894086	−	0.447895i	$-0.147826\pi$
$463$	31.0807	+	8.32804i	1.44444	+	0.387037i	0.550354	+	0.834931i	$0.314493\pi$
$464$	0.885459	−	1.53366i	0.0411064	−	0.0711984i
$465$	15.7949	−	13.7980i	0.732472	−	0.639867i
$466$	−1.10159	−	6.24742i	−0.0510301	−	0.289406i
$467$	1.82831	+	6.82336i	0.0846043	+	0.315747i	0.995239	−	0.0974650i	$-0.0310734\pi$
$467$	1.82831	+	6.82336i	0.0846043	+	0.315747i	−0.910635	+	0.413212i	$0.864407\pi$
$468$	0.823554	−	10.7060i	0.0380688	−	0.494883i
$469$	−2.24088	−	2.67057i	−0.103474	−	0.123316i
$470$	21.6264	+	21.0022i	0.997552	+	0.968757i
$471$	10.6037	−	6.19646i	0.488593	−	0.285518i
$472$	−1.23634	−	14.1314i	−0.0569072	−	0.650452i
$473$	−10.6628	+	7.46618i	−0.490277	+	0.343295i
$474$	−8.21885	+	9.89987i	−0.377504	+	0.454716i
$475$	10.3607	+	19.1744i	0.475381	+	0.879780i
$476$			3.34248i			0.153202i
$477$	22.5532	−	23.0315i	1.03264	−	1.05454i
$478$	−21.4629	+	1.87776i	−0.981690	+	0.0858867i
$479$	−7.91079	−	2.87929i	−0.361453	−	0.131558i	0.154908	−	0.987929i	$-0.450492\pi$
$479$	−7.91079	−	2.87929i	−0.361453	−	0.131558i	−0.516362	+	0.856371i	$0.672714\pi$
$480$	−3.85077	+	0.414219i	−0.175763	+	0.0189064i
$481$	1.08345	−	0.909118i	0.0494008	−	0.0414522i
$482$	15.4701	+	4.14519i	0.704642	+	0.188808i
$483$	0.886634	−	1.92773i	0.0403433	−	0.0877149i
$484$	7.58639	−	1.33769i	0.344836	−	0.0608039i
$485$	−4.59912	+	28.5187i	−0.208835	+	1.29497i
$486$	11.6745	−	10.3298i	0.529567	−	0.468571i
$487$	8.27902	−	30.8977i	0.375158	−	1.40011i	−0.477955	−	0.878384i	$-0.658622\pi$
$487$	8.27902	−	30.8977i	0.375158	−	1.40011i	0.853113	−	0.521725i	$-0.174711\pi$
$488$	−8.87609	−	0.776557i	−0.401802	−	0.0351531i
$489$	3.70094	+	1.32509i	0.167363	+	0.0599225i
$490$	11.7631	+	9.58046i	0.531404	+	0.432801i
$491$	11.7250	−	13.9733i	0.529141	−	0.630606i	−0.433576	−	0.901117i	$-0.642748\pi$
$491$	11.7250	−	13.9733i	0.529141	−	0.630606i	0.962717	+	0.270511i	$0.0871928\pi$
$492$	−10.0984	−	0.830135i	−0.455272	−	0.0374254i
$493$	9.01923	−	9.01923i	0.406206	−	0.406206i
$494$	8.56408	−	13.0407i	0.385316	−	0.586727i
$495$	−7.23455	−	9.79832i	−0.325169	−	0.440402i
$496$	−0.940338	+	5.33292i	−0.0422224	+	0.239455i
$497$	1.10047	−	0.0962785i	0.0493627	−	0.00431868i
$498$	0.952335	−	3.63024i	0.0426752	−	0.162675i
$499$	−7.11763	−	19.5555i	−0.318629	−	0.875425i	−0.990837	−	0.135063i	$-0.956876\pi$
$499$	−7.11763	−	19.5555i	−0.318629	−	0.875425i	0.672208	−	0.740362i	$-0.265346\pi$
$500$	−9.91556	+	5.16544i	−0.443437	+	0.231005i
$501$	1.45131	−	8.49107i	0.0648399	−	0.379353i
$502$	−22.1227	+	5.92777i	−0.987386	+	0.264569i
$503$	10.6025	−	15.1419i	0.472741	−	0.675144i	−0.509991	−	0.860180i	$-0.670351\pi$
$503$	10.6025	−	15.1419i	0.472741	−	0.675144i	0.982732	+	0.185036i	$0.0592402\pi$
$504$	1.30318	−	0.489864i	0.0580483	−	0.0218203i
$505$	21.7320	+	1.58103i	0.967059	+	0.0703551i
$506$	4.15082	−	2.39648i	0.184527	−	0.106536i
$507$	0.230701	−	0.233135i	0.0102458	−	0.0103539i
$508$	3.13170	−	6.71596i	0.138947	−	0.297973i
$509$	−0.931773	−	0.339138i	−0.0413001	−	0.0150320i	0.321288	−	0.946982i	$-0.395884\pi$
$509$	−0.931773	−	0.339138i	−0.0413001	−	0.0150320i	−0.362588	+	0.931950i	$0.618107\pi$
$510$	−27.5624	−	4.29666i	−1.22049	−	0.190259i
$511$	0.129794	−	0.736099i	0.00574176	−	0.0325631i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	22.1033	−	4.94393i	0.975886	−	0.218280i
$514$			13.8180i			0.609488i
$515$	21.6209	+	12.0642i	0.952730	+	0.531612i
$516$	12.2174	−	2.22042i	0.537842	−	0.0977483i
$517$	−10.3449	−	22.1847i	−0.454969	−	0.975684i
$518$	0.166198	+	0.0774995i	0.00730233	+	0.00340513i
$519$	−0.0714628	−	13.6211i	−0.00313687	−	0.597901i
$520$	6.62245	+	4.49403i	0.290414	+	0.197076i
$521$	−19.9525	−	11.5196i	−0.874135	−	0.504682i	−0.00541513	−	0.999985i	$-0.501724\pi$
$521$	−19.9525	−	11.5196i	−0.874135	−	0.504682i	−0.868720	+	0.495303i	$0.835057\pi$
$522$	−4.83829	−	2.19462i	−0.211766	−	0.0960560i
$523$	−11.5769	−	8.10624i	−0.506223	−	0.354461i	0.292397	−	0.956297i	$-0.405547\pi$
$523$	−11.5769	−	8.10624i	−0.506223	−	0.354461i	−0.798620	+	0.601836i	$0.794436\pi$
$524$	4.37590	−	7.57927i	0.191162	−	0.331102i
$525$	2.98768	−	2.68809i	0.130393	−	0.117318i
$526$	−19.9574	+	16.7463i	−0.870185	+	0.730172i
$527$	−16.4834	+	35.3489i	−0.718030	+	1.53982i
$528$	3.04186	+	0.797984i	0.132380	+	0.0347278i
$529$	10.3048	−	12.2808i	0.448035	−	0.533947i
$530$	6.55768	+	23.1143i	0.284848	+	1.00402i
$531$	−41.8299	+	7.82915i	−1.81526	+	0.339756i
$532$	2.00168	+	0.291791i	0.0867837	+	0.0126507i
$533$	14.8056	+	14.8056i	0.641301	+	0.641301i
$534$	18.9066	−	16.0343i	0.818168	−	0.693872i
$535$	−19.7163	+	11.7715i	−0.852409	+	0.508924i
$536$	−2.56933	+	7.05916i	−0.110978	+	0.304909i
$537$	5.73640	+	12.1351i	0.247544	+	0.523669i
$538$	−2.63444	+	30.1118i	−0.113579	+	1.29821i
$539$	−6.15925	−	10.6681i	−0.265298	−	0.459509i
$540$	2.36427	+	11.3759i	0.101742	+	0.489539i
$541$	7.34296	+	41.6440i	0.315699	+	1.79042i	0.568274	+	0.822839i	$0.307611\pi$
$541$	7.34296	+	41.6440i	0.315699	+	1.79042i	−0.252576	+	0.967577i	$0.581278\pi$
$542$	13.7956	+	9.65976i	0.592570	+	0.414922i
$543$	7.92328	+	3.64420i	0.340021	+	0.156388i
$544$	6.23759	−	3.60127i	0.267434	−	0.154403i
$545$	−1.72919	−	0.775716i	−0.0740704	−	0.0332280i
$546$	−2.70855	−	0.969771i	−0.115915	−	0.0415024i
$547$	−15.8822	−	34.0594i	−0.679073	−	1.45628i	−0.879174	−	0.476502i	$-0.841905\pi$
$547$	−15.8822	−	34.0594i	−0.679073	−	1.45628i	0.200101	−	0.979775i	$-0.435873\pi$
$548$	0.934047	+	10.6762i	0.0399005	+	0.456065i
$549$	0.280468	+	26.7285i	0.0119701	+	1.14075i
$550$	9.01664	−	1.05569i	0.384471	−	0.0450150i
$551$	−4.61389	−	6.18861i	−0.196559	−	0.263644i
$552$	−4.55273	+	0.422392i	−0.193777	+	0.0179782i
$553$	1.97737	+	2.82398i	0.0840863	+	0.120088i
$554$	18.1764	+	15.2518i	0.772242	+	0.647988i
$555$	−0.852712	+	1.27086i	−0.0361956	+	0.0539452i
$556$	−11.4696	+	4.17460i	−0.486420	+	0.177043i
$557$	−0.571141	+	6.52817i	−0.0242000	+	0.276608i	0.974447	+	0.224615i	$0.0721126\pi$
$557$	−0.571141	+	6.52817i	−0.0242000	+	0.276608i	−0.998647	+	0.0519920i	$0.983443\pi$
$558$	16.1977	+	1.24601i	0.685704	+	0.0527477i
$559$	−22.2224	−	12.8301i	−0.939909	−	0.542657i
$560$	−0.165211	+	1.02446i	−0.00698142	+	0.0432912i
$561$	19.6751	+	11.2222i	0.830682	+	0.473801i
$562$	31.4798	−	8.43498i	1.32789	−	0.355808i
$563$	5.20085	−	19.4098i	0.219190	−	0.818027i	−0.765460	−	0.643484i	$-0.777488\pi$
$563$	5.20085	−	19.4098i	0.219190	−	0.818027i	0.984649	−	0.174543i	$-0.0558449\pi$
$564$	0.122509	+	23.3508i	0.00515857	+	0.983246i
$565$	6.78283	−	0.0993272i	0.285356	−	0.00417873i
$566$	5.82201	−	15.9958i	0.244717	−	0.672355i
$567$	−1.84416	−	3.74744i	−0.0774475	−	0.157378i
$568$	−1.36534	−	1.94991i	−0.0572884	−	0.0818164i
$569$	−39.6238			−1.66112			−0.830558	−	0.556933i	$-0.811978\pi$
$569$	−39.6238			−1.66112			−0.830558	+	0.556933i	$0.811978\pi$
$570$	−4.97923	+	16.1309i	−0.208557	+	0.675651i
$571$	21.2667			0.889982			0.444991	−	0.895535i	$-0.353207\pi$
$571$	21.2667			0.889982			0.444991	+	0.895535i	$0.353207\pi$
$572$	−3.72742	−	5.32330i	−0.155851	−	0.222579i
$573$	−24.4211	−	16.9096i	−1.02020	−	0.706408i
$574$	−0.928517	+	2.55108i	−0.0387556	+	0.106480i
$575$	−11.7939	+	5.92604i	−0.491841	+	0.247133i
$576$	−2.31824	−	1.90414i	−0.0965934	−	0.0793393i
$577$	0.0129132	−	0.0481928i	0.000537585	−	0.00200629i	−0.965657	−	0.259822i	$-0.916336\pi$
$577$	0.0129132	−	0.0481928i	0.000537585	−	0.00200629i	0.966194	+	0.257816i	$0.0830028\pi$
$578$	33.6882	−	9.02674i	1.40125	−	0.375463i
$579$	−14.1985	+	24.8932i	−0.590070	+	1.03453i
$580$	3.21015	−	2.31855i	0.133294	−	0.0962727i
$581$	−0.870845	−	0.502783i	−0.0361287	−	0.0208589i
$582$	−18.2617	+	12.9303i	−0.756972	+	0.535978i
$583$	1.70033	−	19.4349i	0.0704206	−	0.804911i
$584$	−1.51352	+	0.550875i	−0.0626298	+	0.0227954i
$585$	11.4786	−	21.0884i	0.474581	−	0.871898i
$586$	−22.4632	−	18.8488i	−0.927944	−	0.778638i
$587$	2.38808	+	3.41053i	0.0985667	+	0.140768i	0.865406	−	0.501071i	$-0.167061\pi$
$587$	2.38808	+	3.41053i	0.0985667	+	0.140768i	−0.766839	+	0.641839i	$0.778172\pi$
$588$	1.08560	+	11.7011i	0.0447694	+	0.482545i
$589$	19.7300	+	12.9571i	0.812962	+	0.533890i
$590$	10.4111	−	29.9623i	0.428619	−	1.23353i
$591$	16.7163	−	14.1767i	0.687615	−	0.583153i
$592$	−0.0344400	−	0.393651i	−0.00141548	−	0.0161790i
$593$	−13.1307	−	28.1590i	−0.539215	−	1.15635i	−0.967538	−	0.252725i	$-0.918673\pi$
$593$	−13.1307	−	28.1590i	−0.539215	−	1.15635i	0.428323	−	0.903626i	$-0.359105\pi$
$594$	1.49183	−	9.31568i	0.0612106	−	0.382227i
$595$	−3.05913	+	6.81929i	−0.125412	+	0.279563i
$596$	−6.11025	+	3.52775i	−0.250286	+	0.144502i
$597$	4.29777	−	9.34428i	0.175896	−	0.382436i
$598$	7.73966	+	5.41937i	0.316498	+	0.221615i
$599$	−0.465346	−	2.63911i	−0.0190135	−	0.107831i	0.973824	−	0.227303i	$-0.0729909\pi$
$599$	−0.465346	−	2.63911i	−0.0190135	−	0.107831i	−0.992838	+	0.119472i	$0.961880\pi$
$600$	−8.23539	−	2.67925i	−0.336208	−	0.109380i
$601$	7.34857	+	12.7281i	0.299754	+	0.519190i	0.976080	−	0.217413i	$-0.0697620\pi$
$601$	7.34857	+	12.7281i	0.299754	+	0.519190i	−0.676325	+	0.736603i	$0.736429\pi$
$602$	0.289971	−	3.31439i	0.0118183	−	0.135084i
$603$	21.8287	+	5.60417i	0.888934	+	0.228220i
$604$	−4.47324	+	12.2901i	−0.182014	+	0.500078i
$605$	16.7019	+	4.21415i	0.679030	+	0.171330i
$606$	10.9166	+	12.8722i	0.443458	+	0.522897i
$607$	−20.2965	−	20.2965i	−0.823810	−	0.823810i	0.162843	−	0.986652i	$-0.447934\pi$
$607$	−20.2965	−	20.2965i	−0.823810	−	0.823810i	−0.986652	+	0.162843i	$0.947934\pi$
$608$	−1.61213	−	4.04982i	−0.0653805	−	0.164242i
$609$	−0.909243	+	1.09521i	−0.0368444	+	0.0443802i
$610$	−17.3981	−	9.70797i	−0.704430	−	0.393064i
$611$	31.0170	−	36.9646i	1.25481	−	1.49543i
$612$	−12.5787	−	17.5689i	−0.508462	−	0.710181i
$613$	−14.3056	+	30.6786i	−0.577799	+	1.23909i	0.372579	+	0.928000i	$0.378473\pi$
$613$	−14.3056	+	30.6786i	−0.577799	+	1.23909i	−0.950379	+	0.311095i	$0.899304\pi$
$614$	−4.71533	+	3.95664i	−0.190295	+	0.159677i
$615$	−19.8429	−	10.9360i	−0.800142	−	0.440981i
$616$	0.421293	−	0.729702i	0.0169744	−	0.0294005i
$617$	−21.4068	−	14.9892i	−0.861804	−	0.603442i	0.0569036	−	0.998380i	$-0.481877\pi$
$617$	−21.4068	−	14.9892i	−0.861804	−	0.603442i	−0.918708	+	0.394938i	$0.870766\pi$
$618$	5.06081	+	18.4985i	0.203576	+	0.744117i
$619$	−33.0123	−	19.0596i	−1.32688	−	0.766072i	−0.342060	−	0.939678i	$-0.611125\pi$
$619$	−33.0123	−	19.0596i	−1.32688	−	0.766072i	−0.984815	+	0.173606i	$0.944458\pi$
$620$	−6.79931	+	10.0195i	−0.273067	+	0.402394i
$621$	2.59421	+	13.4693i	0.104102	+	0.540504i
$622$	1.36812	+	0.637965i	0.0548566	+	0.0255801i
$623$	−2.80706	−	6.01977i	−0.112463	−	0.241177i
$624$	1.10852	+	6.09943i	0.0443763	+	0.244173i
$625$	−24.9571	+	1.46345i	−0.998285	+	0.0585380i
$626$		−	12.4763i		−	0.498652i
$627$	8.43810	−	10.8029i	0.336985	−	0.431427i
$628$	−5.01390	+	5.01390i	−0.200076	+	0.200076i
$629$	0.494224	−	2.80288i	0.0197060	−	0.111758i
$630$	3.10707	+	0.193293i	0.123789	+	0.00770099i
$631$	−5.96664	−	2.17168i	−0.237528	−	0.0864532i	0.220513	−	0.975384i	$-0.429227\pi$
$631$	−5.96664	−	2.17168i	−0.237528	−	0.0864532i	−0.458042	+	0.888931i	$0.651449\pi$
$632$	3.13951	−	6.73269i	0.124883	−	0.267812i
$633$	0.546193	+	0.540491i	0.0217092	+	0.0214826i
$634$	−8.98160	+	5.18553i	−0.356705	+	0.205944i
$635$	12.5359	−	10.8356i	0.497472	−	0.429997i
$636$	−9.22076	+	16.1661i	−0.365627	+	0.641028i
$637$	13.9285	−	19.8919i	0.551866	−	0.788146i
$638$	−3.10580	+	0.832197i	−0.122960	+	0.0329470i
$639$	−5.42201	+	4.64742i	−0.214491	+	0.183849i
$640$	2.08979	−	0.795465i	0.0826063	−	0.0314435i
$641$	11.2564	+	30.9267i	0.444601	+	1.22153i	0.936435	+	0.350842i	$0.114105\pi$
$641$	11.2564	+	30.9267i	0.444601	+	1.22153i	−0.491833	+	0.870689i	$0.663673\pi$
$642$	−17.2049	−	4.51343i	−0.679023	−	0.178131i
$643$	42.0137	−	3.67572i	1.65686	−	0.144956i	0.780025	−	0.625749i	$-0.215207\pi$
$643$	42.0137	−	3.67572i	1.65686	−	0.144956i	0.876834	+	0.480793i	$0.159651\pi$
$644$	−0.212729	+	1.20644i	−0.00838268	+	0.0475405i
$645$	26.9580	+	6.65168i	1.06147	+	0.261910i
$646$	−3.66629	−	31.1803i	−0.144248	−	1.22677i
$647$	−27.6976	+	27.6976i	−1.08891	+	1.08891i	−0.0932655	+	0.995641i	$0.529731\pi$
$647$	−27.6976	+	27.6976i	−1.08891	+	1.08891i	−0.995641	+	0.0932655i	$0.970269\pi$
$648$	−5.00635	+	7.47907i	−0.196668	+	0.293806i
$649$	−16.5554	+	19.7300i	−0.649858	+	0.774471i
$650$	9.39797	+	15.2297i	0.368619	+	0.597358i
$651$	1.46723	−	4.09794i	0.0575052	−	0.160611i
$652$	−2.26093	−	0.197806i	−0.0885450	−	0.00774668i
$653$	−1.20198	+	4.48584i	−0.0470370	+	0.175545i	−0.985448	−	0.169976i	$-0.945631\pi$
$653$	−1.20198	+	4.48584i	−0.0470370	+	0.175545i	0.938411	+	0.345521i	$0.112298\pi$
$654$	−0.509325	−	1.37684i	−0.0199162	−	0.0538387i
$655$	15.8644	−	11.4582i	0.619874	−	0.447708i
$656$	5.76111	−	1.01584i	0.224934	−	0.0396619i
$657$	2.08791	+	4.35757i	0.0814571	+	0.170005i
$658$	6.04330	+	1.61930i	0.235592	+	0.0631268i
$659$	−3.77881	+	3.17080i	−0.147201	+	0.123517i	−0.713415	−	0.700742i	$-0.752852\pi$
$659$	−3.77881	+	3.17080i	−0.147201	+	0.123517i	0.566213	+	0.824259i	$0.308408\pi$
$660$	5.47563	+	4.41204i	0.213139	+	0.171738i
$661$	44.0543	+	16.0345i	1.71351	+	0.623668i	0.997246	−	0.0741585i	$-0.0236271\pi$
$661$	44.0543	+	16.0345i	1.71351	+	0.623668i	0.716267	+	0.697826i	$0.245849\pi$
$662$	−4.76180	+	0.416604i	−0.185073	+	0.0161918i
$663$	−3.65818	+	44.5010i	−0.142072	+	1.72827i
$664$			2.16684i			0.0840897i
$665$	3.81674	+	2.42730i	0.148007	+	0.0941266i
$666$	−1.16523	+	0.218092i	−0.0451518	+	0.00845090i
$667$	3.82944	−	2.68140i	0.148277	−	0.103824i
$668$	0.433462	+	4.95449i	0.0167711	+	0.191695i
$669$	−17.9230	−	30.6708i	−0.692944	−	1.18580i
$670$	−11.7026	+	12.0505i	−0.452113	+	0.465551i
$671$	10.3986	+	12.3926i	0.401435	+	0.478411i
$672$	−0.656000	+	0.464484i	−0.0253058	+	0.0179179i
$673$	−10.1654	−	37.9378i	−0.391848	−	1.46240i	−0.827083	−	0.562080i	$-0.810001\pi$
$673$	−10.1654	−	37.9378i	−0.391848	−	1.46240i	0.435235	−	0.900317i	$-0.356665\pi$
$674$	4.24278	+	24.0620i	0.163426	+	0.926834i
$675$	−5.58796	+	25.3727i	−0.215081	+	0.976596i
$676$	−0.0946814	+	0.163993i	−0.00364159	+	0.00630742i
$677$	−19.2491	−	5.15778i	−0.739803	−	0.198230i	−0.130813	−	0.991407i	$-0.541759\pi$
$677$	−19.2491	−	5.15778i	−0.739803	−	0.198230i	−0.608991	+	0.793177i	$0.708425\pi$
$678$	3.73495	+	3.69596i	0.143440	+	0.141943i
$679$	2.05048	+	5.63364i	0.0786902	+	0.216199i
$680$	16.0218	−	1.63845i	0.614409	−	0.0628316i
$681$	0.171088	+	0.941383i	0.00655612	+	0.0360739i
$682$	8.05397	−	5.63945i	0.308402	−	0.215946i
$683$	7.52428	+	7.52428i	0.287909	+	0.287909i	0.836253	−	0.548344i	$-0.184742\pi$
$683$	7.52428	+	7.52428i	0.287909	+	0.287909i	−0.548344	+	0.836253i	$0.684742\pi$
$684$	−11.6194	+	5.99913i	−0.444279	+	0.229382i
$685$	−7.86554	+	22.6363i	−0.300527	+	0.864889i
$686$	6.29985	+	1.11083i	0.240529	+	0.0424118i
$687$	−9.37861	−	6.49391i	−0.357816	−	0.247758i
$688$	−6.49758	+	3.02987i	−0.247718	+	0.115513i
$689$	36.1391	−	13.1536i	1.37679	−	0.501111i
$690$	−9.67500	−	3.30503i	−0.368321	−	0.125820i
$691$	−13.3705	−	23.1585i	−0.508640	−	0.880990i	−0.999950	−	0.0100051i	$-0.996815\pi$
$691$	−13.3705	−	23.1585i	−0.508640	−	0.880990i	0.491310	−	0.870985i	$-0.336518\pi$
$692$	2.03542	+	7.59631i	0.0773752	+	0.288768i
$693$	−2.30201	−	1.04418i	−0.0874462	−	0.0396652i
$694$	−1.55097	+	0.273477i	−0.0588739	+	0.0103810i
$695$	−27.2209	−	1.98036i	−1.03255	−	0.0751193i
$696$	3.02347	+	0.516779i	0.114604	+	0.0195885i
$697$	41.9745	+	3.67229i	1.58990	+	0.139098i
$698$	12.4119	+	5.78775i	0.469796	+	0.219070i
$699$	9.48674	−	5.54374i	0.358822	−	0.209683i
$700$	−1.27467	+	1.93887i	−0.0481780	+	0.0732826i
$701$	−19.2721	−	3.39820i	−0.727899	−	0.128348i	−0.202595	−	0.979263i	$-0.564937\pi$
$701$	−19.2721	−	3.39820i	−0.727899	−	0.128348i	−0.525304	+	0.850915i	$0.676048\pi$
$702$	17.8863	−	5.09566i	0.675077	−	0.192323i
$703$	−1.63539	−	0.540655i	−0.0616798	−	0.0203912i
$704$	−1.81565			−0.0684298
$705$	−21.1214	+	47.7521i	−0.795477	+	1.79845i
$706$	12.0764	+	10.1333i	0.454501	+	0.381372i
$707$	4.09845	−	1.91114i	0.154138	−	0.0718757i
$708$	22.2131	−	10.5004i	0.834818	−	0.394627i
$709$	7.73144	+	9.21397i	0.290360	+	0.346038i	0.891430	−	0.453159i	$-0.149703\pi$
$709$	7.73144	+	9.21397i	0.290360	+	0.346038i	−0.601070	+	0.799197i	$0.705259\pi$
$710$	−1.00094	−	5.22778i	−0.0375645	−	0.196195i
$711$	−21.0209	−	7.40214i	−0.788346	−	0.277602i
$712$	−8.20941	+	11.7243i	−0.307661	+	0.439385i
$713$	−8.19931	+	11.7098i	−0.307067	+	0.438537i
$714$	−5.42975	+	2.00859i	−0.203203	+	0.0751695i
$715$	−2.73259	−	14.2720i	−0.102193	−	0.533741i
$716$	−4.98132	−	5.93651i	−0.186161	−	0.221858i
$717$	−15.9480	−	33.7373i	−0.595588	−	1.25994i
$718$	0.0214747	−	0.0100138i	0.000801429	−	0.000373712i
$719$	23.5917	+	19.7958i	0.879823	+	0.738259i	0.966143	−	0.258009i	$-0.0830663\pi$
$719$	23.5917	+	19.7958i	0.879823	+	0.738259i	−0.0863200	+	0.996267i	$0.527511\pi$
$720$	−2.98692	−	6.00652i	−0.111316	−	0.223850i
$721$	5.13844			0.191365
$722$	−18.9927	−	0.526377i	−0.706835	−	0.0195897i
$723$	2.56266	+	27.6215i	0.0953065	+	1.02726i
$724$	−4.95867	−	0.874347i	−0.184287	−	0.0324948i
$725$	8.67131	−	1.79226i	0.322044	−	0.0665629i
$726$	6.73189	+	11.5200i	0.249844	+	0.427547i
$727$	17.5813	+	8.19829i	0.652054	+	0.304058i	0.720354	−	0.693607i	$-0.243980\pi$
$727$	17.5813	+	8.19829i	0.652054	+	0.304058i	−0.0682995	+	0.997665i	$0.521757\pi$
$728$	1.65468	+	0.144765i	0.0613264	+	0.00536536i
$729$	23.7960	+	12.7574i	0.881333	+	0.472496i
$730$	−3.59203	−	0.261326i	−0.132947	−	0.00967211i
$731$	−50.8526	+	8.96668i	−1.88085	+	0.331645i
$732$	−4.07239	−	14.8856i	−0.150520	−	0.550186i
$733$	−10.8534	−	40.5053i	−0.400878	−	1.49610i	−0.811534	−	0.584306i	$-0.801367\pi$
$733$	−10.8534	−	40.5053i	−0.400878	−	1.49610i	0.410656	−	0.911790i	$-0.365300\pi$
$734$	−3.40550	−	5.89850i	−0.125699	−	0.217717i
$735$	−8.49434	+	24.8660i	−0.313318	+	0.917195i
$736$	2.48061	−	0.902867i	0.0914364	−	0.0332801i
$737$	12.3616	−	5.76431i	0.455345	−	0.212331i
$738$	−4.71989	−	16.9034i	−0.173741	−	0.622222i
$739$	18.0542	+	3.18345i	0.664136	+	0.117105i	0.495546	−	0.868581i	$-0.334968\pi$
$739$	18.0542	+	3.18345i	0.664136	+	0.117105i	0.168589	+	0.985686i	$0.446079\pi$
$740$	0.290017	−	0.834642i	0.0106612	−	0.0306821i
$741$	26.3305	+	6.07556i	0.967274	+	0.223191i
$742$	3.52594	+	3.52594i	0.129441	+	0.129441i
$743$	7.54022	−	5.27972i	0.276624	−	0.193694i	−0.427029	−	0.904238i	$-0.640440\pi$
$743$	7.54022	−	5.27972i	0.276624	−	0.193694i	0.703653	+	0.710544i	$0.251551\pi$
$744$	−9.22822	+	1.67715i	−0.338323	+	0.0614874i
$745$	−15.6947	+	1.60500i	−0.575011	+	0.0588027i
$746$	−8.24384	−	22.6498i	−0.301828	−	0.829266i
$747$	6.46948	−	0.634475i	0.236706	−	0.0232142i
$748$	−12.6317	−	3.38465i	−0.461860	−	0.123755i
$749$	−2.38285	+	4.12722i	−0.0870675	+	0.150805i
$750$	−14.3496	−	13.0034i	−0.523973	−	0.474818i
$751$	0.441945	+	2.50640i	0.0161268	+	0.0914597i	0.991809	−	0.127731i	$-0.0407694\pi$
$751$	0.441945	+	2.50640i	0.0161268	+	0.0914597i	−0.975682	+	0.219191i	$0.929658\pi$
$752$	−3.48934	−	13.0224i	−0.127243	−	0.474878i
$753$	−22.9236	−	32.3754i	−0.835382	−	1.17983i
$754$	−4.07429	−	4.85554i	−0.148377	−	0.176828i
$755$	−20.3745	+	20.9801i	−0.741504	+	0.763544i
$756$	1.57888	+	1.82260i	0.0574235	+	0.0662873i
$757$	4.12189	+	47.1134i	0.149813	+	1.71237i	0.584175	+	0.811628i	$0.301418\pi$
$757$	4.12189	+	47.1134i	0.149813	+	1.71237i	−0.434362	+	0.900738i	$0.643026\pi$
$758$	30.1891	−	21.1386i	1.09652	−	0.767789i
$759$	6.38734	+	5.30276i	0.231846	+	0.192478i
$760$	0.417465	−	9.73785i	0.0151431	−	0.353229i
$761$			7.21156i			0.261419i	0.991421	+	0.130709i	$0.0417255\pi$
$761$			7.21156i			0.261419i	−0.991421	+	0.130709i	$0.958275\pi$
$762$	12.7918	+	1.05154i	0.463397	+	0.0380933i
$763$	−0.391833	+	0.0342809i	−0.0141853	+	0.00124105i
$764$	16.1153	+	5.86550i	0.583032	+	0.212206i
$765$	−9.58324	−	47.3562i	−0.346483	−	1.71217i
$766$	−6.91923	+	5.80592i	−0.250002	+	0.209776i
$767$	−49.0423	−	13.1409i	−1.77082	−	0.474489i
$768$	1.57359	+	0.723751i	0.0567820	+	0.0261161i
$769$	10.2205	−	1.80215i	0.368562	−	0.0649874i	0.0136999	−	0.999906i	$-0.495639\pi$
$769$	10.2205	−	1.80215i	0.368562	−	0.0649874i	0.354862	+	0.934919i	$0.384528\pi$
$770$	1.52736	−	1.10315i	0.0550422	−	0.0397547i
$771$	−22.4469	+	8.30363i	−0.808406	+	0.299048i
$772$	4.28232	−	15.9818i	0.154124	−	0.575199i
$773$	27.9099	+	2.44180i	1.00385	+	0.0878256i	0.577210	−	0.816596i	$-0.304141\pi$
$773$	27.9099	+	2.44180i	1.00385	+	0.0878256i	0.426641	+	0.904421i	$0.359697\pi$
$774$	10.9488	+	18.5125i	0.393546	+	0.665417i
$775$	−23.0420	+	14.2188i	−0.827693	+	0.510754i
$776$	8.30401	−	9.89633i	0.298097	−	0.355258i
$777$	−0.0260222	+	0.316555i	−0.000933542	+	0.0113563i
$778$	21.7685	−	21.7685i	0.780439	−	0.780439i
$779$	5.86345	−	24.8162i	0.210080	−	0.889133i
$780$	−3.32079	+	13.4585i	−0.118903	+	0.481893i
$781$	−0.750501	+	4.25631i	−0.0268551	+	0.152303i
$782$	18.9410	−	1.65712i	0.677328	−	0.0592585i
$783$	0.657630	−	9.17843i	0.0235018	−	0.328010i
$784$	−2.32048	−	6.37548i	−0.0828744	−	0.227696i
$785$	−14.8181	+	5.64042i	−0.528882	+	0.201315i
$786$	14.9419	+	2.55390i	0.532958	+	0.0910945i
$787$	−2.34498	+	0.628335i	−0.0835894	+	0.0223977i	−0.300371	−	0.953822i	$-0.597111\pi$
$787$	−2.34498	+	0.628335i	−0.0835894	+	0.0223977i	0.216782	+	0.976220i	$0.430444\pi$
$788$	−7.25835	+	10.3660i	−0.258568	+	0.369274i
$789$	−39.1967	−	22.3569i	−1.39544	−	0.795925i
$790$	12.5671	−	10.8626i	0.447118	−	0.386473i
$791$	1.21923	−	0.703924i	0.0433509	−	0.0250286i
$792$	0.531641	+	5.42093i	0.0188911	+	0.192624i
$793$	−13.4776	+	28.9027i	−0.478602	+	1.02637i
$794$	9.30565	+	3.38698i	0.330245	+	0.120199i
$795$	−33.6077	+	24.5428i	−1.19194	+	0.870442i
$796$	−1.03116	+	5.84798i	−0.0365484	+	0.207276i
$797$	−9.22327	+	9.22327i	−0.326705	+	0.326705i	−0.851332	−	0.524627i	$-0.824205\pi$
$797$	−9.22327	+	9.22327i	−0.326705	+	0.326705i	0.524627	+	0.851332i	$0.324205\pi$
$798$	0.728859	+	3.42700i	0.0258013	+	0.121314i
$799$		−	97.1031i		−	3.43526i
$800$	4.99160	+	0.289741i	0.176480	+	0.0102439i
$801$	37.4086	+	21.0776i	1.32177	+	0.744742i
$802$	−5.88038	−	12.6105i	−0.207643	−	0.445293i
$803$	2.65038	+	1.23589i	0.0935300	+	0.0436138i
$804$	−13.0113	+	0.0682635i	−0.458875	+	0.00240747i
$805$	−1.53818	+	2.26667i	−0.0542136	+	0.0798898i
$806$	16.7853	+	9.69101i	0.591238	+	0.341351i
$807$	−50.4987	+	13.8154i	−1.77764	+	0.486327i
$808$	−7.98224	−	5.58922i	−0.280814	−	0.196628i
$809$	8.62912	−	14.9461i	0.303384	−	0.525476i	−0.673517	−	0.739172i	$-0.735217\pi$
$809$	8.62912	−	14.9461i	0.303384	−	0.525476i	0.976900	+	0.213696i	$0.0685503\pi$
$810$	−17.0589	+	10.6767i	−0.599390	+	0.375142i
$811$	−38.6259	+	32.4110i	−1.35634	+	1.13810i	−0.379244	+	0.925297i	$0.623816\pi$
$811$	−38.6259	+	32.4110i	−1.35634	+	1.13810i	−0.977094	+	0.212807i	$0.931739\pi$
$812$	0.347320	−	0.744831i	0.0121886	−	0.0261384i
$813$	−7.40181	+	28.2152i	−0.259593	+	0.989551i
$814$	−0.461176	+	0.549608i	−0.0161642	+	0.0192637i
$815$	−4.43169	−	2.47283i	−0.155235	−	0.0866195i
$816$	9.59847	+	7.96864i	0.336014	+	0.278958i
$817$	0.930475	+	31.2363i	0.0325532	+	1.09282i
$818$	4.70710	+	4.70710i	0.164580	+	0.164580i
$819$	−0.0522847	−	4.98271i	−0.00182698	−	0.174110i
$820$	12.6835	+	3.20023i	0.442926	+	0.111757i
$821$	13.9308	−	38.2744i	0.486187	−	1.33579i	−0.417922	−	0.908483i	$-0.637241\pi$
$821$	13.9308	−	38.2744i	0.486187	−	1.33579i	0.904108	−	0.427304i	$-0.140536\pi$
$822$	−16.7818	+	7.93295i	−0.585334	+	0.276693i
$823$	0.751185	−	8.58608i	0.0261847	−	0.299292i	−0.971799	−	0.235813i	$-0.924225\pi$
$823$	0.751185	−	8.58608i	0.0261847	−	0.299292i	0.997983	−	0.0634792i	$-0.0202197\pi$
$824$	−5.53628	−	9.58911i	−0.192865	−	0.334053i
$825$	7.13328	+	14.0128i	0.248349	+	0.487864i
$826$	−1.14313	−	6.48301i	−0.0397746	−	0.225573i
$827$	23.1867	+	16.2355i	0.806282	+	0.564565i	0.902447	−	0.430801i	$-0.141769\pi$
$827$	23.1867	+	16.2355i	0.806282	+	0.564565i	−0.0961652	+	0.995365i	$0.530658\pi$
$828$	−3.42202	−	7.14192i	−0.118923	−	0.248199i
$829$	−4.60115	+	2.65647i	−0.159804	+	0.0922631i	−0.577770	−	0.816200i	$-0.696077\pi$
$829$	−4.60115	+	2.65647i	−0.159804	+	0.0922631i	0.417965	+	0.908463i	$0.362743\pi$
$830$	−1.98315	+	4.42076i	−0.0688363	+	0.153447i
$831$	−13.8534	+	38.6922i	−0.480568	+	1.34222i
$832$	−1.51263	−	3.24385i	−0.0524411	−	0.112460i
$833$	−4.25901	−	48.6807i	−0.147566	−	1.68669i
$834$	−13.6739	−	16.1234i	−0.473488	−	0.558307i
$835$	−3.65015	+	10.5048i	−0.126318	+	0.363533i
$836$	−3.12964	+	7.26913i	−0.108241	+	0.251408i
$837$	7.70956	+	27.0614i	0.266481	+	0.935378i
$838$	−7.76295	−	11.0866i	−0.268167	−	0.382982i
$839$	−29.7982	−	25.0037i	−1.02875	−	0.863222i	−0.0380466	−	0.999276i	$-0.512114\pi$
$839$	−29.7982	−	25.0037i	−1.02875	−	0.863222i	−0.990701	+	0.136054i	$0.956558\pi$
$840$	−1.76347	+	0.347244i	−0.0608456	+	0.0119811i
$841$	24.3041	−	8.84596i	0.838071	−	0.305033i
$842$	−0.260032	+	2.97218i	−0.00896130	+	0.102428i
$843$	32.6194	+	46.0690i	1.12347	+	1.58670i
$844$	−0.384206	−	0.221822i	−0.0132249	−	0.00763541i
$845$	−0.343258	+	0.247921i	−0.0118085	+	0.00852874i
$846$	−37.8589	+	14.2311i	−1.30162	+	0.489277i
$847$	3.45311	−	0.925259i	0.118650	−	0.0317923i
$848$	2.78101	−	10.3789i	0.0955003	−	0.356412i
$849$	29.4833	−	0.154683i	1.01186	−	0.00530870i
$850$	34.1870	+	11.3209i	1.17261	+	0.388303i
$851$	0.356773	−	0.980225i	0.0122300	−	0.0336017i
$852$	2.34709	−	3.38970i	0.0804099	−	0.116129i
$853$	10.2234	+	14.6006i	0.350044	+	0.499915i	0.955106	−	0.296263i	$-0.0957406\pi$
$853$	10.2234	+	14.6006i	0.350044	+	0.499915i	−0.605062	+	0.796178i	$0.706852\pi$
$854$	−4.13486			−0.141492
$855$	−29.1963	+	1.60493i	−0.998493	+	0.0548875i
$856$	10.2694			0.351000
$857$	−16.9092	−	24.1489i	−0.577608	−	0.824910i	0.418932	−	0.908017i	$-0.362404\pi$
$857$	−16.9092	−	24.1489i	−0.577608	−	0.824910i	−0.996541	+	0.0831074i	$0.973516\pi$
$858$	6.40762	−	9.25398i	0.218752	−	0.315926i
$859$	−9.64038	+	26.4867i	−0.328926	+	0.903715i	0.659459	+	0.751741i	$0.270785\pi$
$859$	−9.64038	+	26.4867i	−0.328926	+	0.903715i	−0.988384	+	0.151975i	$0.951437\pi$
$860$	−16.0293	+	0.234732i	−0.546594	+	0.00800428i
$861$	−4.70211	+	0.0246695i	−0.160248	+	0.000840733i
$862$	−6.75112	+	25.1955i	−0.229944	+	0.858164i
$863$	8.19211	−	2.19507i	0.278863	−	0.0747210i	−0.116677	−	0.993170i	$-0.537224\pi$
$863$	8.19211	−	2.19507i	0.278863	−	0.0747210i	0.395540	+	0.918449i	$0.370558\pi$
$864$	1.70012	−	4.91015i	0.0578393	−	0.167047i
$865$	−2.79971	+	17.3608i	−0.0951930	+	0.590283i
$866$	−12.2468	−	7.07069i	−0.416163	−	0.240272i
$867$	34.9078	+	49.3009i	1.18553	+	1.67435i
$868$	−0.219025	+	2.50346i	−0.00743418	+	0.0849731i
$869$	−12.6745	+	4.61313i	−0.429952	+	0.156490i
$870$	5.69548	+	3.82149i	0.193095	+	0.129561i
$871$	20.5971	+	17.2830i	0.697907	+	0.585614i
$872$	0.486144	+	0.694285i	0.0164629	+	0.0235115i
$873$	−31.9787	−	21.8953i	−1.08232	−	0.741044i
$874$	0.661119	−	11.4876i	0.0223627	−	0.388575i
$875$	−4.37508	+	2.78905i	−0.147905	+	0.0942871i
$876$	−1.80439	−	2.12762i	−0.0609647	−	0.0718856i
$877$	−3.41424	−	39.0249i	−0.115291	−	1.31778i	−0.804819	−	0.593520i	$-0.797738\pi$
$877$	−3.41424	−	39.0249i	−0.115291	−	1.31778i	0.689528	−	0.724259i	$-0.257818\pi$
$878$	−8.38306	−	17.9775i	−0.282914	−	0.606712i
$879$	17.1205	−	47.8174i	0.577461	−	1.61284i
$880$	−3.70426	−	1.66173i	−0.124870	−	0.0560169i
$881$	0.827444	−	0.477725i	0.0278773	−	0.0160950i	−0.485997	−	0.873961i	$-0.661543\pi$
$881$	0.827444	−	0.477725i	0.0278773	−	0.0160950i	0.513874	+	0.857866i	$0.328210\pi$
$882$	−18.3556	+	8.79502i	−0.618067	+	0.296144i
$883$	−5.75055	−	4.02658i	−0.193522	−	0.135505i	0.472800	−	0.881170i	$-0.343243\pi$
$883$	−5.75055	−	4.02658i	−0.193522	−	0.135505i	−0.666322	+	0.745665i	$0.732132\pi$
$884$	−4.47653	−	25.3877i	−0.150562	−	0.853879i
$885$	54.9290	−	1.09264i	1.84642	−	0.0367288i
$886$	5.43300	+	9.41024i	0.182525	+	0.316143i
$887$	2.64632	−	30.2476i	0.0888548	−	1.01562i	−0.812623	−	0.582790i	$-0.801961\pi$
$887$	2.64632	−	30.2476i	0.0888548	−	1.01562i	0.901478	−	0.432825i	$-0.142483\pi$
$888$	0.618777	−	0.292502i	0.0207648	−	0.00981574i
$889$	1.17616	−	3.23148i	0.0394472	−	0.108380i
$890$	−27.4791	+	16.4062i	−0.921101	+	0.549936i
$891$	16.0295	−	3.17462i	0.537008	−	0.106354i
$892$	14.5025	+	14.5025i	0.485580	+	0.485580i
$893$	−58.1511	−	8.47687i	−1.94595	−	0.283667i
$894$	−9.40253	−	7.80596i	−0.314467	−	0.261070i
$895$	−4.72956	−	16.6706i	−0.158092	−	0.557238i
$896$	0.298298	−	0.355498i	0.00996545	−	0.0118764i
$897$	−4.15261	+	15.8295i	−0.138651	+	0.528530i
$898$	−2.55631	+	5.48203i	−0.0853053	+	0.182938i
$899$	7.34626	−	6.16425i	0.245012	−	0.205589i
$900$	−0.596521	−	14.9881i	−0.0198840	−	0.499604i
$901$	38.6957	−	67.0229i	1.28914	−	2.23286i
$902$	−8.70064	−	6.09225i	−0.289699	−	0.202850i
$903$	5.55836	−	1.52066i	0.184971	−	0.0506043i
$904$	−2.62726	−	1.51685i	−0.0873813	−	0.0504496i
$905$	−9.31637	−	6.32214i	−0.309687	−	0.210155i
$906$	−22.6530	+	0.118848i	−0.752595	+	0.00394846i
$907$	−12.9187	−	6.02409i	−0.428959	−	0.200027i	0.196134	−	0.980577i	$-0.437161\pi$
$907$	−12.9187	−	6.02409i	−0.428959	−	0.200027i	−0.625093	+	0.780550i	$0.714939\pi$
$908$	−0.233459	−	0.500654i	−0.00774760	−	0.0166148i
$909$	−14.3503	+	25.4690i	−0.475970	+	0.844752i
$910$	3.24335	+	1.80975i	0.107516	+	0.0599928i
$911$			2.37347i			0.0786367i	0.999227	+	0.0393184i	$0.0125187\pi$
$911$			2.37347i			0.0786367i	−0.999227	+	0.0393184i	$0.987481\pi$
$912$	5.61002	−	5.05249i	0.185766	−	0.167305i
$913$	2.78191	−	2.78191i	0.0920678	−	0.0920678i
$914$	−6.67367	+	37.8483i	−0.220745	+	1.25191i
$915$	5.31524	−	34.0965i	0.175716	−	1.12719i
$916$	6.18889	+	2.25257i	0.204487	+	0.0744270i
$917$	1.71644	−	3.68092i	0.0566818	−	0.121555i
$918$	20.9812	−	30.9912i	0.692484	−	1.02286i
$919$	−11.4152	+	6.59055i	−0.376552	+	0.217402i	−0.676317	−	0.736611i	$-0.736425\pi$
$919$	−11.4152	+	6.59055i	−0.376552	+	0.217402i	0.299765	+	0.954013i	$0.403092\pi$
$920$	5.88723	+	0.428305i	0.194096	+	0.0141208i
$921$	−9.26099	−	5.28225i	−0.305160	−	0.174056i
$922$	2.17365	−	3.10430i	0.0715855	−	0.102235i
$923$	−8.22961	+	2.20512i	−0.270881	+	0.0725823i
$924$	1.43854	+	0.245879i	0.0473245	+	0.00808882i
$925$	1.35558	−	1.43739i	0.0445711	−	0.0472612i
$926$	−11.0052	−	30.2365i	−0.361653	−	0.993635i
$927$	−27.0089	+	19.3373i	−0.887089	+	0.635121i
$928$	−1.76418	+	0.154346i	−0.0579120	+	0.00506665i
$929$	10.3852	−	58.8972i	0.340726	−	1.93236i	−0.0202848	−	0.999794i	$-0.506457\pi$
$929$	10.3852	−	58.8972i	0.340726	−	1.93236i	0.361011	−	0.932561i	$-0.382432\pi$
$930$	−20.3623	−	5.02423i	−0.667705	−	0.164751i
$931$	−29.5247	−	1.69916i	−0.967633	−	0.0556877i
$932$	−4.48574	+	4.48574i	−0.146935	+	0.146935i
$933$	−0.214211	+	2.60583i	−0.00701296	+	0.0853112i
$934$	4.54069	−	5.41138i	0.148576	−	0.177066i
$935$	−22.6732	−	18.4662i	−0.741494	−	0.603909i
$936$	−9.24218	+	5.46607i	−0.302090	+	0.178664i
$937$	28.3467	+	2.48001i	0.926046	+	0.0810186i	0.540193	−	0.841541i	$-0.318351\pi$
$937$	28.3467	+	2.48001i	0.926046	+	0.0810186i	0.385854	+	0.922560i	$0.373907\pi$
$938$	−0.902292	+	3.36740i	−0.0294609	+	0.109949i
$939$	20.2673	−	7.49733i	0.661398	−	0.244666i
$940$	4.79956	−	29.7617i	0.156544	−	0.970718i
$941$	16.0631	−	2.83236i	0.523642	−	0.0923322i	0.0944221	−	0.995532i	$-0.469900\pi$
$941$	16.0631	−	2.83236i	0.523642	−	0.0923322i	0.429220	+	0.903200i	$0.358789\pi$
$942$	−11.1579	−	5.13191i	−0.363543	−	0.167207i
$943$	14.9166	+	3.99690i	0.485753	+	0.130157i
$944$	−10.8667	+	9.11821i	−0.353679	+	0.296772i
$945$	1.55312	+	5.16348i	0.0505231	+	0.167968i
$946$	12.2319	+	4.45204i	0.397693	+	0.144748i
$947$	19.2581	−	1.68487i	0.625804	−	0.0547508i	0.230157	−	0.973153i	$-0.426076\pi$
$947$	19.2581	−	1.68487i	0.625804	−	0.0547508i	0.395647	+	0.918403i	$0.370520\pi$
$948$	12.8236	+	1.05416i	0.416492	+	0.0342375i
$949$			5.76484i			0.187135i
$950$	9.76406	−	19.4849i	0.316788	−	0.632175i
$951$	−13.8210	−	11.4742i	−0.448176	−	0.372075i
$952$	2.73800	−	1.91717i	0.0887391	−	0.0621358i
$953$	−0.0852104	−	0.973959i	−0.00276024	−	0.0315496i	0.994690	−	0.102920i	$-0.0328184\pi$
$953$	−0.0852104	−	0.973959i	−0.00276024	−	0.0315496i	−0.997450	+	0.0713700i	$0.977263\pi$
$954$	−31.8023	−	5.26415i	−1.02964	−	0.170433i
$955$	27.5100	+	26.7159i	0.890202	+	0.864506i
$956$	13.8488	+	16.5043i	0.447901	+	0.533788i
$957$	−3.21824	−	4.54518i	−0.104031	−	0.146925i
$958$	2.17886	+	8.13163i	0.0703959	+	0.262721i
$959$	0.863627	+	4.89787i	0.0278880	+	0.158161i
$960$	2.54802	+	2.91678i	0.0822369	+	0.0941386i
$961$	0.837850	−	1.45120i	0.0270274	−	0.0468129i
$962$	−1.36614	−	0.366057i	−0.0440463	−	0.0118022i
$963$	−3.00698	−	30.6610i	−0.0968986	−	0.988037i
$964$	−5.47772	−	15.0499i	−0.176426	−	0.484725i
$965$	23.3637	−	28.6866i	0.752105	−	0.923454i
$966$	−2.08766	+	0.379415i	−0.0671694	+	0.0122075i
$967$	44.5989	−	31.2285i	1.43420	−	1.00424i	0.439857	−	0.898068i	$-0.355029\pi$
$967$	44.5989	−	31.2285i	1.43420	−	1.00424i	0.994348	−	0.106173i	$-0.0338596\pi$
$968$	−5.44714	−	5.44714i	−0.175078	−	0.175078i
$969$	48.4482	−	24.6929i	1.55638	−	0.793250i
$970$	25.9991	−	12.5903i	0.834781	−	0.404250i
$971$	−8.64032	−	1.52352i	−0.277281	−	0.0488921i	0.0332783	−	0.999446i	$-0.489405\pi$
$971$	−8.64032	−	1.52352i	−0.277281	−	0.0488921i	−0.310559	+	0.950554i	$0.600516\pi$
$972$	−15.1579	−	3.63826i	−0.486191	−	0.116697i
$973$	−5.13360	+	2.39384i	−0.164576	+	0.0767429i
$974$	−30.0586	+	10.9404i	−0.963139	+	0.350554i
$975$	−19.0926	+	24.4186i	−0.611454	+	0.782022i
$976$	4.45500	+	7.71628i	0.142601	+	0.246992i
$977$	1.16878	+	4.36195i	0.0373927	+	0.139551i	0.982099	−	0.188367i	$-0.0603195\pi$
$977$	1.16878	+	4.36195i	0.0373927	+	0.139551i	−0.944706	+	0.327919i	$0.893653\pi$
$978$	−1.03733	−	3.79168i	−0.0331701	−	0.121244i
$979$	25.5920	−	4.51255i	0.817922	−	0.144222i
$980$	1.10080	−	15.1309i	0.0351637	−	0.483340i
$981$	1.93056	−	1.65476i	0.0616381	−	0.0528325i
$982$	−18.1714	−	1.58979i	−0.579873	−	0.0507323i
$983$	42.8932	+	20.0014i	1.36808	+	0.637947i	0.961281	−	0.275570i	$-0.0888665\pi$
$983$	42.8932	+	20.0014i	1.36808	+	0.637947i	0.406801	+	0.913517i	$0.366644\pi$
$984$	5.11221	+	8.74828i	0.162971	+	0.278885i
$985$	−24.2956	+	14.5055i	−0.774124	+	0.462184i
$986$	−12.5613	−	2.21490i	−0.400035	−	0.0705369i
$987$	1.00109	+	10.7902i	0.0318651	+	0.343456i
$988$	−15.5944	+	0.464531i	−0.496125	+	0.0147787i
$989$	−18.9255			−0.601797
$990$	−3.87674	+	11.5463i	−0.123211	+	0.366965i
$991$	29.0749	+	24.3967i	0.923593	+	0.774987i	0.974656	−	0.223709i	$-0.0718164\pi$
$991$	29.0749	+	24.3967i	0.923593	+	0.774987i	−0.0510628	+	0.998695i	$0.516261\pi$
$992$	4.90783	−	2.28856i	0.155824	−	0.0726618i
$993$	−3.53825	−	7.48503i	−0.112283	−	0.237530i
$994$	−0.710069	−	0.846228i	−0.0225220	−	0.0268407i
$995$	−7.45599	+	10.9872i	−0.236371	+	0.348318i
$996$	−3.51996	+	1.30211i	−0.111534	+	0.0412590i
$997$	−5.76601	+	8.23472i	−0.182611	+	0.260796i	−0.900012	−	0.435864i	$-0.856443\pi$
$997$	−5.76601	+	8.23472i	−0.182611	+	0.260796i	0.717401	+	0.696661i	$0.245332\pi$
$998$	−11.9364	+	17.0470i	−0.377841	+	0.539613i
$999$	−1.05450	−	1.76182i	−0.0333630	−	0.0557415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.14	✓	480
3.2	odd	2	inner	570.2.bi.a.17.34	yes	480
5.3	odd	4	inner	570.2.bi.a.473.17	yes	480
15.8	even	4	inner	570.2.bi.a.473.25	yes	480
19.9	even	9	inner	570.2.bi.a.47.25	yes	480
57.47	odd	18	inner	570.2.bi.a.47.17	yes	480
95.28	odd	36	inner	570.2.bi.a.503.34	yes	480
285.218	even	36	inner	570.2.bi.a.503.14	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.14	✓	480	1.1	even	1	trivial
570.2.bi.a.17.34	yes	480	3.2	odd	2	inner
570.2.bi.a.47.17	yes	480	57.47	odd	18	inner
570.2.bi.a.47.25	yes	480	19.9	even	9	inner
570.2.bi.a.473.17	yes	480	5.3	odd	4	inner
570.2.bi.a.473.25	yes	480	15.8	even	4	inner
570.2.bi.a.503.14	yes	480	285.218	even	36	inner
570.2.bi.a.503.34	yes	480	95.28	odd	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.bi (of order \(36\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(0.986006 - 1.42401i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.55782 + 1.60412i) q^{5} +(-1.73203 + 0.00908702i) q^{6} +(-0.120110 + 0.448257i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.05558 - 2.80816i) q^{9} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(0.986006 - 1.42401i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(-1.55782 + 1.60412i) q^{5} +(-1.73203 + 0.00908702i) q^{6} +(-0.120110 + 0.448257i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-1.05558 - 2.80816i) q^{9} +(2.20755 + 0.356004i) q^{10} +(-1.57240 - 0.907823i) q^{11} +(1.00089 + 1.41358i) q^{12} +(0.311947 - 3.56558i) q^{13} +(0.436083 - 0.158721i) q^{14} +(0.748259 + 3.80001i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-4.13121 - 5.89998i) q^{17} +(-1.69485 + 2.47538i) q^{18} +(-3.89390 + 1.95896i) q^{19} +(-0.974576 - 2.01251i) q^{20} +(0.519891 + 0.613022i) q^{21} +(0.158244 + 1.80874i) q^{22} +(-1.11563 - 2.39248i) q^{23} +(0.583849 - 1.63068i) q^{24} +(-0.146408 - 4.99786i) q^{25} +(-3.09967 + 1.78960i) q^{26} +(-5.03964 - 1.26570i) q^{27} +(-0.380144 - 0.266179i) q^{28} +(0.307517 + 1.74401i) q^{29} +(2.68361 - 2.79254i) q^{30} +(-2.70760 - 4.68969i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-2.84314 + 1.34398i) q^{33} +(-2.46341 + 6.76818i) q^{34} +(-0.531949 - 0.890974i) q^{35} +(2.99983 - 0.0314779i) q^{36} +(0.279417 + 0.279417i) q^{37} +(3.83814 + 2.06608i) q^{38} +(-4.76982 - 3.95989i) q^{39} +(-1.08956 + 1.95265i) q^{40} +(-3.76030 + 4.48135i) q^{41} +(0.203961 - 0.777485i) q^{42} +(3.02987 - 6.49758i) q^{43} +(1.39087 - 1.16708i) q^{44} +(6.14903 + 2.68131i) q^{45} +(-1.31990 + 2.28614i) q^{46} +(11.0436 + 7.73283i) q^{47} +(-1.67066 + 0.457059i) q^{48} +(5.87567 + 3.39232i) q^{49} +(-4.01003 + 2.98658i) q^{50} +(-12.4750 + 0.0654496i) q^{51} +(3.24385 + 1.51263i) q^{52} +(4.54103 + 9.73828i) q^{53} +(1.85382 + 4.85421i) q^{54} +(3.90577 - 1.10809i) q^{55} +0.464070i q^{56} +(-1.04984 + 7.47649i) q^{57} +(1.25223 - 1.25223i) q^{58} +(2.46327 - 13.9699i) q^{59} +(-3.82677 - 0.596548i) q^{60} +(-8.37266 - 3.04740i) q^{61} +(-2.28856 + 4.90783i) q^{62} +(1.38556 - 0.135885i) q^{63} +(0.866025 - 0.500000i) q^{64} +(5.23366 + 6.05492i) q^{65} +(2.73168 + 1.55809i) q^{66} +(-4.30882 + 6.15364i) q^{67} +(6.95712 - 1.86416i) q^{68} +(-4.50692 - 0.770334i) q^{69} +(-0.424730 + 0.946789i) q^{70} +(-0.814145 - 2.23684i) q^{71} +(-1.74642 - 2.43927i) q^{72} +(-1.60452 + 0.140378i) q^{73} +(0.0686180 - 0.389152i) q^{74} +(-7.26133 - 4.71943i) q^{75} +(-0.509027 - 4.32908i) q^{76} +(0.595799 - 0.595799i) q^{77} +(-0.507901 + 6.17851i) q^{78} +(4.77508 - 5.69072i) q^{79} +(2.22447 - 0.227482i) q^{80} +(-6.77149 + 5.92849i) q^{81} +(5.82773 + 0.509860i) q^{82} +(-0.560820 + 2.09301i) q^{83} +(-0.753865 + 0.278872i) q^{84} +(15.8999 + 2.56413i) q^{85} +(-7.06037 + 1.24493i) q^{86} +(2.78670 + 1.28170i) q^{87} +(-1.75378 - 0.469924i) q^{88} +(-10.9641 + 9.20001i) q^{89} +(-1.33054 - 6.57493i) q^{90} +(1.56083 + 0.568094i) q^{91} +(2.62976 - 0.230074i) q^{92} +(-9.34786 - 0.768435i) q^{93} -13.4818i q^{94} +(2.92358 - 9.29799i) q^{95} +(1.33265 + 1.10636i) q^{96} +(10.5824 - 7.40989i) q^{97} +(-0.591320 - 6.75882i) q^{98} +(-0.889515 + 5.37382i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 480 q+O(q^{10}) \) 480 * q	\( 480 q - 36 q^{15} - 48 q^{18} + 24 q^{22} - 24 q^{25} + 72 q^{33} + 24 q^{43} - 36 q^{45} + 24 q^{51} - 120 q^{55} + 108 q^{57} - 48 q^{60} - 48 q^{61} - 36 q^{63} - 24 q^{66} + 48 q^{67} - 48 q^{70} - 48 q^{78} - 144 q^{81} - 48 q^{85} - 96 q^{87} - 168 q^{90} - 144 q^{91} - 228 q^{93} + 48 q^{97}+O(q^{100}) \) 480 * q - 36 * q^15 - 48 * q^18 + 24 * q^22 - 24 * q^25 + 72 * q^33 + 24 * q^43 - 36 * q^45 + 24 * q^51 - 120 * q^55 + 108 * q^57 - 48 * q^60 - 48 * q^61 - 36 * q^63 - 24 * q^66 + 48 * q^67 - 48 * q^70 - 48 * q^78 - 144 * q^81 - 48 * q^85 - 96 * q^87 - 168 * q^90 - 144 * q^91 - 228 * q^93 + 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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