LMFDB - Embedded newform 570.2.bi.a.17.12

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			17.12
Character	$\chi$	$=$	570.17
Dual form			570.2.bi.a.503.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.573576 - 0.819152i) q^{2} +(0.530463 + 1.64882i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.62022 + 1.54107i) q^{5} +(1.04637 - 1.38025i) q^{6} +(-0.100091 + 0.373543i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.43722 + 1.74928i) q^{9} +O(q^{10})$	\(q+(-0.573576 - 0.819152i) q^{2} +(0.530463 + 1.64882i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.62022 + 1.54107i) q^{5} +(1.04637 - 1.38025i) q^{6} +(-0.100091 + 0.373543i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.43722 + 1.74928i) q^{9} +(0.333051 - 2.21113i) q^{10} +(3.61556 + 2.08745i) q^{11} +(-1.73081 - 0.0654573i) q^{12} +(0.0210505 - 0.240609i) q^{13} +(0.363398 - 0.132266i) q^{14} +(-1.68148 + 3.48893i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(0.0503082 + 0.0718475i) q^{17} +(2.83085 + 0.993107i) q^{18} +(-3.07835 - 3.08606i) q^{19} +(-2.00228 + 0.995430i) q^{20} +(-0.669000 + 0.0331196i) q^{21} +(-0.363866 - 4.15901i) q^{22} +(0.598265 + 1.28298i) q^{23} +(0.939134 + 1.45534i) q^{24} +(0.250212 + 4.99374i) q^{25} +(-0.209169 + 0.120764i) q^{26} +(-4.17710 - 3.09061i) q^{27} +(-0.316783 - 0.221814i) q^{28} +(0.577029 + 3.27249i) q^{29} +(3.82242 - 0.623780i) q^{30} +(2.14763 + 3.71980i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-1.52390 + 7.06873i) q^{33} +(0.0299985 - 0.0824201i) q^{34} +(-0.737825 + 0.450975i) q^{35} +(-0.810206 - 2.88852i) q^{36} +(-7.64589 - 7.64589i) q^{37} +(-0.762285 + 4.29173i) q^{38} +(0.407887 - 0.0929255i) q^{39} +(1.96387 + 1.06922i) q^{40} +(-3.48276 + 4.15059i) q^{41} +(0.410853 + 0.529016i) q^{42} +(1.22137 - 2.61924i) q^{43} +(-3.19815 + 2.68357i) q^{44} +(-6.64458 - 0.921709i) q^{45} +(0.707808 - 1.22596i) q^{46} +(0.115096 + 0.0805908i) q^{47} +(0.653483 - 1.60404i) q^{48} +(5.93266 + 3.42522i) q^{49} +(3.94711 - 3.06925i) q^{50} +(-0.0917770 + 0.121062i) q^{51} +(0.218898 + 0.102074i) q^{52} +(3.25860 + 6.98810i) q^{53} +(-0.135791 + 5.19438i) q^{54} +(2.64110 + 8.95395i) q^{55} +0.386720i q^{56} +(3.45541 - 6.71269i) q^{57} +(2.34970 - 2.34970i) q^{58} +(-0.127725 + 0.724366i) q^{59} +(-2.70342 - 2.77336i) q^{60} +(6.62009 + 2.40952i) q^{61} +(1.81525 - 3.89283i) q^{62} +(-0.409488 - 1.08549i) q^{63} +(0.866025 - 0.500000i) q^{64} +(0.404901 - 0.357398i) q^{65} +(6.66444 - 2.80615i) q^{66} +(-0.696598 + 0.994844i) q^{67} +(-0.0847210 + 0.0227009i) q^{68} +(-1.79805 + 1.66701i) q^{69} +(0.792616 + 0.345722i) q^{70} +(-1.77171 - 4.86774i) q^{71} +(-1.90142 + 2.32047i) q^{72} +(4.05785 - 0.355016i) q^{73} +(-1.87764 + 10.6486i) q^{74} +(-8.10104 + 3.06155i) q^{75} +(3.95281 - 1.83721i) q^{76} +(-1.14164 + 1.14164i) q^{77} +(-0.310074 - 0.280821i) q^{78} +(9.94584 - 11.8530i) q^{79} +(-0.250579 - 2.22198i) q^{80} +(2.88006 - 8.52674i) q^{81} +(5.39760 + 0.472229i) q^{82} +(2.27597 - 8.49403i) q^{83} +(0.197689 - 0.639982i) q^{84} +(-0.0292118 + 0.193937i) q^{85} +(-2.84610 + 0.501844i) q^{86} +(-5.08966 + 2.68736i) q^{87} +(4.03264 + 1.08054i) q^{88} +(1.19787 - 1.00513i) q^{89} +(3.05615 + 5.97159i) q^{90} +(0.0877708 + 0.0319459i) q^{91} +(-1.41023 + 0.123379i) q^{92} +(-4.99405 + 5.51427i) q^{93} -0.140506i q^{94} +(-0.231762 - 9.74404i) q^{95} +(-1.68878 + 0.384741i) q^{96} +(9.04178 - 6.33112i) q^{97} +(-0.597056 - 6.82438i) q^{98} +(-12.4634 + 1.23706i) 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
$3$	0.530463	+	1.64882i	0.306263	+	0.951947i
$3$	0.530463	+	1.64882i	0.306263	+	0.951947i
$4$	−0.342020	+	0.939693i	−0.171010	+	0.469846i
$5$	1.62022	+	1.54107i	0.724583	+	0.689187i
$5$	1.62022	+	1.54107i	0.724583	+	0.689187i
$6$	1.04637	−	1.38025i	0.427180	−	0.563487i
$7$	−0.100091	+	0.373543i	−0.0378307	+	0.141186i	−0.982258	−	0.187534i	$-0.939951\pi$
$7$	−0.100091	+	0.373543i	−0.0378307	+	0.141186i	0.944427	+	0.328720i	$0.106617\pi$
$8$	0.965926	−	0.258819i	0.341506	−	0.0915064i
$9$	−2.43722	+	1.74928i	−0.812406	+	0.583092i
$10$	0.333051	−	2.21113i	0.105320	−	0.699219i
$11$	3.61556	+	2.08745i	1.09013	+	0.629389i	0.933612	−	0.358286i	$-0.116639\pi$
$11$	3.61556	+	2.08745i	1.09013	+	0.629389i	0.156522	+	0.987675i	$0.449972\pi$
$12$	−1.73081	−	0.0654573i	−0.499643	−	0.0188959i
$13$	0.0210505	−	0.240609i	0.00583836	−	0.0667328i	−0.992717	−	0.120473i	$-0.961559\pi$
$13$	0.0210505	−	0.240609i	0.00583836	−	0.0667328i	0.998555	+	0.0537404i	$0.0171144\pi$
$14$	0.363398	−	0.132266i	0.0971223	−	0.0353496i
$15$	−1.68148	+	3.48893i	−0.434156	+	0.900838i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	0.0503082	+	0.0718475i	0.0122015	+	0.0174256i	0.825206	−	0.564831i	$-0.191059\pi$
$17$	0.0503082	+	0.0718475i	0.0122015	+	0.0174256i	−0.813005	+	0.582257i	$0.802170\pi$
$18$	2.83085	+	0.993107i	0.667239	+	0.234078i
$19$	−3.07835	−	3.08606i	−0.706222	−	0.707991i
$19$	−3.07835	−	3.08606i	−0.706222	−	0.707991i
$20$	−2.00228	+	0.995430i	−0.447723	+	0.222585i
$21$	−0.669000	+	0.0331196i	−0.145988	+	0.00722728i
$22$	−0.363866	−	4.15901i	−0.0775765	−	0.886703i
$23$	0.598265	+	1.28298i	0.124747	+	0.267520i	0.958756	−	0.284230i	$-0.0917379\pi$
$23$	0.598265	+	1.28298i	0.124747	+	0.267520i	−0.834009	+	0.551750i	$0.813960\pi$
$24$	0.939134	+	1.45534i	0.191700	+	0.297071i
$25$	0.250212	+	4.99374i	0.0500425	+	0.998747i
$26$	−0.209169	+	0.120764i	−0.0410214	+	0.0236837i
$27$	−4.17710	−	3.09061i	−0.803883	−	0.594787i
$28$	−0.316783	−	0.221814i	−0.0598663	−	0.0419189i
$29$	0.577029	+	3.27249i	0.107152	+	0.607687i	0.990339	+	0.138667i	$0.0442817\pi$
$29$	0.577029	+	3.27249i	0.107152	+	0.607687i	−0.883188	+	0.469020i	$0.844607\pi$
$30$	3.82242	−	0.623780i	0.697875	−	0.113886i
$31$	2.14763	+	3.71980i	0.385726	+	0.668096i	0.991870	−	0.127259i	$-0.0406178\pi$
$31$	2.14763	+	3.71980i	0.385726	+	0.668096i	−0.606144	+	0.795355i	$0.707285\pi$
$32$	−0.0871557	+	0.996195i	−0.0154071	+	0.176104i
$33$	−1.52390	+	7.06873i	−0.265277	+	1.23051i
$34$	0.0299985	−	0.0824201i	0.00514469	−	0.0141349i
$35$	−0.737825	+	0.450975i	−0.124715	+	0.0762287i
$36$	−0.810206	−	2.88852i	−0.135034	−	0.481421i
$37$	−7.64589	−	7.64589i	−1.25698	−	1.25698i	−0.952529	−	0.304448i	$-0.901528\pi$
$37$	−7.64589	−	7.64589i	−1.25698	−	1.25698i	−0.304448	−	0.952529i	$-0.598472\pi$
$38$	−0.762285	+	4.29173i	−0.123659	+	0.696210i
$39$	0.407887	−	0.0929255i	0.0653142	−	0.0148800i
$40$	1.96387	+	1.06922i	0.310515	+	0.169058i
$41$	−3.48276	+	4.15059i	−0.543916	+	0.648214i	−0.966061	−	0.258315i	$-0.916833\pi$
$41$	−3.48276	+	4.15059i	−0.543916	+	0.648214i	0.422145	+	0.906528i	$0.361277\pi$
$42$	0.410853	+	0.529016i	0.0633960	+	0.0816290i
$43$	1.22137	−	2.61924i	0.186257	−	0.399430i	−0.790901	−	0.611944i	$-0.790388\pi$
$43$	1.22137	−	2.61924i	0.186257	−	0.399430i	0.977158	+	0.212515i	$0.0681654\pi$
$44$	−3.19815	+	2.68357i	−0.482140	+	0.404563i
$45$	−6.64458	−	0.921709i	−0.990516	−	0.137400i
$46$	0.707808	−	1.22596i	0.104361	−	0.180758i
$47$	0.115096	+	0.0805908i	0.0167884	+	0.0117554i	0.581941	−	0.813231i	$-0.302294\pi$
$47$	0.115096	+	0.0805908i	0.0167884	+	0.0117554i	−0.565152	+	0.824987i	$0.691183\pi$
$48$	0.653483	−	1.60404i	0.0943221	−	0.231524i
$49$	5.93266	+	3.42522i	0.847523	+	0.489318i
$50$	3.94711	−	3.06925i	0.558206	−	0.434058i
$51$	−0.0917770	+	0.121062i	−0.0128514	+	0.0169520i
$52$	0.218898	+	0.102074i	0.0303557	+	0.0141551i
$53$	3.25860	+	6.98810i	0.447603	+	0.959889i	0.992598	+	0.121449i	$0.0387541\pi$
$53$	3.25860	+	6.98810i	0.447603	+	0.959889i	−0.544994	+	0.838440i	$0.683468\pi$
$54$	−0.135791	+	5.19438i	−0.0184788	+	0.706865i
$55$	2.64110	+	8.95395i	0.356126	+	1.20735i
$56$			0.386720i			0.0516777i
$57$	3.45541	−	6.71269i	0.457680	−	0.889117i
$58$	2.34970	−	2.34970i	0.308531	−	0.308531i
$59$	−0.127725	+	0.724366i	−0.0166284	+	0.0943044i	−0.991992	−	0.126297i	$-0.959691\pi$
$59$	−0.127725	+	0.724366i	−0.0166284	+	0.0943044i	0.975364	+	0.220601i	$0.0708019\pi$
$60$	−2.70342	−	2.77336i	−0.349010	−	0.358039i
$61$	6.62009	+	2.40952i	0.847616	+	0.308507i	0.729068	−	0.684441i	$-0.239954\pi$
$61$	6.62009	+	2.40952i	0.847616	+	0.308507i	0.118548	+	0.992948i	$0.462176\pi$
$62$	1.81525	−	3.89283i	0.230538	−	0.494389i
$63$	−0.409488	−	1.08549i	−0.0515907	−	0.136759i
$64$	0.866025	−	0.500000i	0.108253	−	0.0625000i
$65$	0.404901	−	0.357398i	0.0502218	−	0.0443298i
$66$	6.66444	−	2.80615i	0.820336	−	0.345413i
$67$	−0.696598	+	0.994844i	−0.0851029	+	0.121540i	−0.859446	−	0.511226i	$-0.829191\pi$
$67$	−0.696598	+	0.994844i	−0.0851029	+	0.121540i	0.774343	+	0.632766i	$0.218080\pi$
$68$	−0.0847210	+	0.0227009i	−0.0102739	+	0.00275289i
$69$	−1.79805	+	1.66701i	−0.216460	+	0.200684i
$70$	0.792616	+	0.345722i	0.0947357	+	0.0413217i
$71$	−1.77171	−	4.86774i	−0.210264	−	0.577695i	0.789066	−	0.614309i	$-0.210565\pi$
$71$	−1.77171	−	4.86774i	−0.210264	−	0.577695i	−0.999329	+	0.0366141i	$0.988343\pi$
$72$	−1.90142	+	2.32047i	−0.224085	+	0.273470i
$73$	4.05785	−	0.355016i	0.474935	−	0.0415514i	0.152824	−	0.988253i	$-0.451163\pi$
$73$	4.05785	−	0.355016i	0.474935	−	0.0415514i	0.322111	+	0.946702i	$0.395608\pi$
$74$	−1.87764	+	10.6486i	−0.218272	+	1.23788i
$75$	−8.10104	+	3.06155i	−0.935428	+	0.353517i
$76$	3.95281	−	1.83721i	0.453418	−	0.210742i
$77$	−1.14164	+	1.14164i	−0.130101	+	0.130101i
$78$	−0.310074	−	0.280821i	−0.0351090	−	0.0317968i
$79$	9.94584	−	11.8530i	1.11899	−	1.33357i	0.182370	−	0.983230i	$-0.441623\pi$
$79$	9.94584	−	11.8530i	1.11899	−	1.33357i	0.936624	−	0.350336i	$-0.113933\pi$
$80$	−0.250579	−	2.22198i	−0.0280156	−	0.248425i
$81$	2.88006	−	8.52674i	0.320006	−	0.947415i
$82$	5.39760	+	0.472229i	0.596065	+	0.0521489i
$83$	2.27597	−	8.49403i	0.249820	−	0.932340i	−0.721079	−	0.692852i	$-0.756354\pi$
$83$	2.27597	−	8.49403i	0.249820	−	0.932340i	0.970899	−	0.239488i	$-0.0769796\pi$
$84$	0.197689	−	0.639982i	0.0215697	−	0.0698278i
$85$	−0.0292118	+	0.193937i	−0.00316846	+	0.0210354i
$86$	−2.84610	+	0.501844i	−0.306903	+	0.0541153i
$87$	−5.08966	+	2.68736i	−0.545669	+	0.288115i
$88$	4.03264	+	1.08054i	0.429881	+	0.115186i
$89$	1.19787	−	1.00513i	0.126974	−	0.106544i	−0.577089	−	0.816681i	$-0.695812\pi$
$89$	1.19787	−	1.00513i	0.126974	−	0.106544i	0.704063	+	0.710137i	$0.251367\pi$
$90$	3.05615	+	5.97159i	0.322147	+	0.629461i
$91$	0.0877708	+	0.0319459i	0.00920088	+	0.00334884i
$92$	−1.41023	+	0.123379i	−0.147026	+	0.0128631i
$93$	−4.99405	+	5.51427i	−0.517859	+	0.571803i
$94$		−	0.140506i		−	0.0144921i
$95$	−0.231762	−	9.74404i	−0.0237783	−	0.999717i
$96$	−1.68878	+	0.384741i	−0.172360	+	0.0392674i
$97$	9.04178	−	6.33112i	0.918054	−	0.642828i	−0.0160340	−	0.999871i	$-0.505104\pi$
$97$	9.04178	−	6.33112i	0.918054	−	0.642828i	0.934088	+	0.357043i	$0.116215\pi$
$98$	−0.597056	−	6.82438i	−0.0603117	−	0.689366i
$99$	−12.4634	+	1.23706i	−1.25262	+	0.124330i
$100$	−4.77815	−	1.47284i	−0.477815	−	0.147284i
$101$	3.99064	+	4.75586i	0.397084	+	0.473226i	0.927128	−	0.374744i	$-0.122269\pi$
$101$	3.99064	+	4.75586i	0.397084	+	0.473226i	−0.530045	+	0.847970i	$0.677825\pi$
$102$	0.151809	+	0.00574124i	0.0150313	+	0.000568467i
$103$	−4.11679	−	15.3641i	−0.405640	−	1.51387i	−0.802873	−	0.596150i	$-0.796696\pi$
$103$	−4.11679	−	15.3641i	−0.405640	−	1.51387i	0.397234	−	0.917718i	$-0.369970\pi$
$104$	−0.0419408	−	0.237858i	−0.00411264	−	0.0233239i
$105$	−1.13497	−	0.977315i	−0.110761	−	0.0953761i
$106$	3.85525	−	6.67750i	0.374455	−	0.648576i
$107$	0.856251	+	0.229432i	0.0827769	+	0.0221800i	0.299970	−	0.953949i	$-0.403023\pi$
$107$	0.856251	+	0.229432i	0.0827769	+	0.0221800i	−0.217193	+	0.976129i	$0.569690\pi$
$108$	4.33287	−	2.86814i	0.416931	−	0.275987i
$109$	6.16314	+	16.9331i	0.590322	+	1.62190i	0.769909	+	0.638154i	$0.220302\pi$
$109$	6.16314	+	16.9331i	0.590322	+	1.62190i	−0.179587	+	0.983742i	$0.557476\pi$
$110$	5.81978	−	7.29924i	0.554894	−	0.695955i
$111$	8.55084	−	16.6626i	0.811609	−	1.58154i
$112$	0.316783	−	0.221814i	0.0299332	−	0.0209594i
$113$	−11.3530	−	11.3530i	−1.06800	−	1.06800i	−0.997513	−	0.0704836i	$-0.977546\pi$
$113$	−11.3530	−	11.3530i	−1.06800	−	1.06800i	−0.0704836	−	0.997513i	$-0.522454\pi$
$114$	−7.48065	+	1.01973i	−0.700627	+	0.0955067i
$115$	−1.00785	+	3.00068i	−0.0939821	+	0.279815i
$116$	−3.27249	−	0.577029i	−0.303843	−	0.0535758i
$117$	0.369586	+	0.623239i	0.0341683	+	0.0576184i
$118$	0.666626	−	0.310853i	0.0613679	−	0.0286163i
$119$	−0.0318735	+	0.0116010i	−0.00292184	+	0.00106346i
$120$	−0.721184	+	3.80525i	−0.0658348	+	0.347370i
$121$	3.21487	+	5.56832i	0.292261	+	0.506211i
$122$	−1.82337	−	6.80490i	−0.165080	−	0.616087i
$123$	−8.69106	−	3.54071i	−0.783647	−	0.319255i
$124$	−4.23000	+	0.745864i	−0.379865	+	0.0669805i
$125$	−7.29029	+	8.47653i	−0.652064	+	0.758164i
$126$	−0.654311	+	0.958046i	−0.0582906	+	0.0853495i
$127$	−20.6759	−	1.80890i	−1.83469	−	0.160514i	−0.883358	−	0.468698i	$-0.844723\pi$
$127$	−20.6759	−	1.80890i	−1.83469	−	0.160514i	−0.951327	+	0.308184i	$0.900279\pi$
$128$	−0.906308	−	0.422618i	−0.0801070	−	0.0373545i
$129$	4.96654	+	0.624411i	0.437279	+	0.0549763i
$130$	−0.525005	−	0.126680i	−0.0460460	−	0.0111106i
$131$	16.4004	+	2.89183i	1.43291	+	0.252661i	0.835595	−	0.549346i	$-0.185123\pi$
$131$	16.4004	+	2.89183i	1.43291	+	0.252661i	0.597315	+	0.802007i	$0.296234\pi$
$132$	−6.12123	−	3.84965i	−0.532785	−	0.335069i
$133$	1.46089	−	0.841011i	0.126675	−	0.0729249i
$134$	1.21448			0.104915
$135$	−2.00497	−	11.4447i	−0.172561	−	0.984999i
$136$	0.0671895	+	0.0563787i	0.00576145	+	0.00483443i
$137$	−9.78694	+	4.56372i	−0.836155	+	0.389905i	−0.793044	−	0.609165i	$-0.791505\pi$
$137$	−9.78694	+	4.56372i	−0.836155	+	0.389905i	−0.0431111	+	0.999070i	$0.513727\pi$
$138$	2.39685	+	0.516721i	0.204034	+	0.0439863i
$139$	−3.76351	−	4.48518i	−0.319217	−	0.380428i	0.582445	−	0.812870i	$-0.302096\pi$
$139$	−3.76351	−	4.48518i	−0.319217	−	0.380428i	−0.901661	+	0.432443i	$0.857652\pi$
$140$	−0.171427	−	0.847571i	−0.0144882	−	0.0716328i
$141$	−0.0718258	+	0.232522i	−0.00604882	+	0.0195819i
$142$	−2.97121	+	4.24332i	−0.249338	+	0.356092i
$143$	0.578367	−	0.825994i	0.0483655	−	0.0690731i
$144$	2.99143	+	0.226589i	0.249286	+	0.0188824i
$145$	−4.10823	+	6.19139i	−0.341170	+	0.514167i
$146$	−2.61830	−	3.12036i	−0.216692	−	0.258243i
$147$	−2.50052	+	11.5988i	−0.206239	+	0.956657i
$148$	9.79984	−	4.56974i	0.805542	−	0.375630i
$149$	−7.20538	−	6.04603i	−0.590287	−	0.495310i	0.298020	−	0.954560i	$-0.403674\pi$
$149$	−7.20538	−	6.04603i	−0.590287	−	0.495310i	−0.888307	+	0.459250i	$0.848118\pi$
$150$	7.15444	+	4.87995i	0.584158	+	0.398447i
$151$	6.02542			0.490341			0.245171	−	0.969480i	$-0.421156\pi$
$151$	6.02542			0.490341			0.245171	+	0.969480i	$0.421156\pi$
$152$	−3.77219	−	2.18417i	−0.305965	−	0.177160i
$153$	−0.248293	−	0.0871051i	−0.0200733	−	0.00704203i
$154$	1.58999	+	0.280358i	0.128125	+	0.0225919i
$155$	−2.25285	+	9.33653i	−0.180953	+	0.749929i
$156$	−0.0521841	+	0.415071i	−0.00417807	+	0.0332322i
$157$	−13.5627	−	6.32439i	−1.08242	−	0.504741i	−0.202219	−	0.979340i	$-0.564815\pi$
$157$	−13.5627	−	6.32439i	−1.08242	−	0.504741i	−0.880202	+	0.474599i	$0.842593\pi$
$158$	−15.4141	−	1.34856i	−1.22628	−	0.107286i
$159$	−9.79354	+	9.07978i	−0.776679	+	0.720073i
$160$	−1.67642	+	1.47974i	−0.132532	+	0.116984i
$161$	−0.539130	+	0.0950632i	−0.0424894	+	0.00749203i
$162$	−8.63663	+	2.53153i	−0.678558	+	0.198896i
$163$	−3.30811	−	12.3460i	−0.259111	−	0.967017i	−0.965757	−	0.259449i	$-0.916459\pi$
$163$	−3.30811	−	12.3460i	−0.259111	−	0.967017i	0.706645	−	0.707568i	$-0.250208\pi$
$164$	−2.70911	−	4.69231i	−0.211546	−	0.366408i
$165$	−13.3625	+	9.10445i	−1.04027	+	0.708780i
$166$	−8.26334	+	3.00761i	−0.641360	+	0.233436i
$167$	19.0212	−	8.86975i	1.47191	−	0.686362i	0.489311	−	0.872109i	$-0.337248\pi$
$167$	19.0212	−	8.86975i	1.47191	−	0.686362i	0.982598	+	0.185747i	$0.0594706\pi$
$168$	−0.637633	+	0.205141i	−0.0491944	+	0.0158270i
$169$	12.7451	+	2.24730i	0.980389	+	0.172869i
$170$	0.175619	−	0.0873088i	0.0134694	−	0.00669628i
$171$	12.9010	+	2.13652i	0.986563	+	0.163383i
$172$	2.04354	+	2.04354i	0.155819	+	0.155819i
$173$	−0.0512453	+	0.0358823i	−0.00389611	+	0.00272808i	−0.575523	−	0.817786i	$-0.695201\pi$
$173$	−0.0512453	+	0.0358823i	−0.00389611	+	0.00272808i	0.571627	+	0.820514i	$0.306313\pi$
$174$	5.12066	+	2.62780i	0.388196	+	0.199213i
$175$	−1.89042	−	0.406361i	−0.142902	−	0.0307180i
$176$	−1.42790	−	3.92312i	−0.107632	−	0.295716i
$177$	−1.26210	+	0.173654i	−0.0948654	+	0.0130526i
$178$	−1.51043	−	0.404718i	−0.113211	−	0.0303349i
$179$	10.4937	−	18.1757i	0.784339	−	1.35852i	−0.145054	−	0.989424i	$-0.546336\pi$
$179$	10.4937	−	18.1757i	0.784339	−	1.35852i	0.929393	−	0.369092i	$-0.120331\pi$
$180$	3.13870	−	5.92862i	0.233945	−	0.441893i
$181$	−0.202014	−	1.14568i	−0.0150155	−	0.0851574i	0.976379	−	0.216065i	$-0.0693221\pi$
$181$	−0.202014	−	1.14568i	−0.0150155	−	0.0851574i	−0.991395	+	0.130907i	$0.958211\pi$
$182$	−0.0241747	−	0.0902210i	−0.00179194	−	0.00668763i
$183$	−0.461144	+	12.1935i	−0.0340887	+	0.901370i
$184$	0.909940	+	1.08442i	0.0670817	+	0.0799448i
$185$	−0.605164	−	24.1709i	−0.0444925	−	1.77708i
$186$	7.38150	+	0.928027i	0.541238	+	0.0680463i
$187$	0.0319146	+	0.364785i	0.00233382	+	0.0266757i
$188$	−0.115096	+	0.0805908i	−0.00839421	+	0.00587769i
$189$	1.57256	−	1.25099i	0.114387	−	0.0909959i
$190$	−7.84892	+	5.77880i	−0.569420	+	0.419238i
$191$			6.91092i			0.500056i	0.968239	+	0.250028i	$0.0804399\pi$
$191$			6.91092i			0.500056i	−0.968239	+	0.250028i	$0.919560\pi$
$192$	1.28380	+	1.16269i	0.0926506	+	0.0839098i
$193$	6.59660	−	0.577128i	0.474834	−	0.0415426i	0.152772	−	0.988261i	$-0.451180\pi$
$193$	6.59660	−	0.577128i	0.474834	−	0.0415426i	0.322061	+	0.946719i	$0.395624\pi$
$194$	−10.3723	−	3.77521i	−0.744688	−	0.271044i
$195$	0.804070	+	0.478022i	0.0575807	+	0.0342319i
$196$	−5.24775	+	4.40338i	−0.374839	+	0.314527i
$197$	16.5180	+	4.42598i	1.17686	+	0.315338i	0.793680	−	0.608336i	$-0.208163\pi$
$197$	16.5180	+	4.42598i	1.17686	+	0.315338i	0.383179	+	0.923674i	$0.374829\pi$
$198$	8.16208	+	9.49990i	0.580054	+	0.675129i
$199$	2.82359	−	0.497875i	0.200159	−	0.0352934i	−0.0726698	−	0.997356i	$-0.523152\pi$
$199$	2.82359	−	0.497875i	0.200159	−	0.0352934i	0.272829	+	0.962063i	$0.412041\pi$
$200$	1.53416	+	4.75882i	0.108482	+	0.336499i
$201$	−2.00984	−	0.620836i	−0.141763	−	0.0437904i
$202$	1.60684	−	5.99679i	0.113057	−	0.421933i
$203$	−1.28017	−	0.112001i	−0.0898506	−	0.00786091i
$204$	−0.0823711	−	0.127648i	−0.00576713	−	0.00893713i
$205$	−12.0392	+	1.35769i	−0.840853	+	0.0948252i
$206$	−10.2242	+	12.1848i	−0.712355	+	0.848952i
$207$	−3.70239	−	2.08038i	−0.257334	−	0.144596i
$208$	−0.170786	+	0.170786i	−0.0118419	+	0.0118419i
$209$	−4.68798	−	17.5837i	−0.324274	−	1.21629i
$210$	−0.149580	+	1.49027i	−0.0103220	+	0.102839i
$211$	3.98086	−	22.5766i	0.274054	−	1.55423i	−0.467899	−	0.883782i	$-0.654989\pi$
$211$	3.98086	−	22.5766i	0.274054	−	1.55423i	0.741952	−	0.670453i	$-0.233900\pi$
$212$	−7.68117	+	0.672015i	−0.527545	+	0.0461542i
$213$	7.08620	−	5.50339i	0.485539	−	0.377086i
$214$	−0.303186	−	0.832996i	−0.0207253	−	0.0569424i
$215$	6.01531	−	2.36152i	0.410241	−	0.161054i
$216$	−4.83468	−	1.90418i	−0.328958	−	0.129563i
$217$	−1.60446	+	0.429915i	−0.108918	+	0.0291845i
$218$	10.3357	−	14.7610i	0.700025	−	0.999739i
$219$	2.73790	+	6.50234i	0.185010	+	0.439387i
$220$	−9.31727	−	0.580608i	−0.628170	−	0.0391446i
$221$	0.0183461	−	0.0105922i	0.00123410	−	0.000712505i
$222$	−18.5537	+	2.55282i	−1.24524	+	0.171334i
$223$	−2.81781	+	6.04282i	−0.188695	+	0.404657i	−0.977782	−	0.209624i	$-0.932776\pi$
$223$	−2.81781	+	6.04282i	−0.188695	+	0.404657i	0.789087	+	0.614281i	$0.210554\pi$
$224$	−0.363398	−	0.132266i	−0.0242806	−	0.00883741i
$225$	−9.34525	−	11.7331i	−0.623017	−	0.782209i
$226$	−2.78801	+	15.8116i	−0.185456	+	1.05177i
$227$	2.98346	−	2.98346i	0.198019	−	0.198019i	−0.601131	−	0.799150i	$-0.705283\pi$
$227$	2.98346	−	2.98346i	0.198019	−	0.198019i	0.799150	+	0.601131i	$0.205283\pi$
$228$	5.12604	+	5.54290i	0.339480	+	0.367087i
$229$			21.4179i			1.41534i	0.706545	+	0.707669i	$0.250253\pi$
$229$			21.4179i			1.41534i	−0.706545	+	0.707669i	$0.749747\pi$
$230$	3.03609	−	0.895540i	0.200194	−	0.0590502i
$231$	−2.48795	−	1.27676i	−0.163695	−	0.0840044i
$232$	1.40435	+	3.01164i	0.0922002	+	0.197724i
$233$	9.23136	+	4.30466i	0.604767	+	0.282007i	0.700785	−	0.713372i	$-0.252833\pi$
$233$	9.23136	+	4.30466i	0.604767	+	0.282007i	−0.0960186	+	0.995380i	$0.530611\pi$
$234$	0.298541	−	0.660222i	0.0195162	−	0.0431601i
$235$	0.0622840	+	0.307945i	0.00406296	+	0.0200881i
$236$	−0.636997	−	0.367770i	−0.0414649	−	0.0239398i
$237$	24.8194	+	10.1113i	1.61219	+	0.656801i
$238$	0.0277849	+	0.0194552i	0.00180103	+	0.00126109i
$239$	8.45857	−	14.6507i	0.547139	−	0.947673i	−0.451330	−	0.892357i	$-0.649050\pi$
$239$	8.45857	−	14.6507i	0.547139	−	0.947673i	0.998469	−	0.0553157i	$-0.0176165\pi$
$240$	3.53073	−	1.59184i	0.227908	−	0.102753i
$241$	8.21697	−	6.89486i	0.529302	−	0.444137i	−0.338558	−	0.940945i	$-0.609939\pi$
$241$	8.21697	−	6.89486i	0.529302	−	0.444137i	0.867860	+	0.496808i	$0.165495\pi$
$242$	2.71733	−	5.82732i	0.174676	−	0.374595i
$243$	15.5868	+	0.225574i	0.999895	+	0.0144706i
$244$	−4.52841	+	5.39675i	−0.289902	+	0.345491i
$245$	4.33370	+	14.6922i	0.276870	+	0.938653i
$246$	2.08461	+	9.15017i	0.132910	+	0.583393i
$247$	−0.807334	+	0.675714i	−0.0513694	+	0.0429946i
$248$	3.03721	+	3.03721i	0.192863	+	0.192863i
$249$	15.2124	−	0.753108i	0.964049	−	0.0477263i
$250$	11.1251	+	1.10992i	0.703614	+	0.0701974i
$251$	−10.1608	+	27.9165i	−0.641343	+	1.76207i	0.00612400	+	0.999981i	$0.498051\pi$
$251$	−10.1608	+	27.9165i	−0.641343	+	1.76207i	−0.647467	+	0.762094i	$0.724172\pi$
$252$	1.16008	−	0.0135328i	0.0730783	−	0.000852487i
$253$	−0.515094	+	5.88755i	−0.0323837	+	0.370147i
$254$	10.3774	+	17.9742i	0.651137	+	1.12780i
$255$	−0.335263	+	0.0547115i	−0.0209950	+	0.00342617i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	16.3440	+	11.4442i	1.01951	+	0.713869i	0.958740	−	0.284283i	$-0.0917555\pi$
$257$	16.3440	+	11.4442i	1.01951	+	0.713869i	0.0607701	+	0.998152i	$0.480644\pi$
$258$	−2.33720	−	4.42650i	−0.145508	−	0.275582i
$259$	3.62135	−	2.09079i	0.225020	−	0.129915i
$260$	0.197360	+	0.502720i	0.0122397	+	0.0311773i
$261$	−7.13084	−	6.96639i	−0.441388	−	0.431209i
$262$	−7.03803	−	15.0931i	−0.434811	−	0.932456i
$263$	1.27468	+	14.5696i	0.0786001	+	0.898403i	0.928469	+	0.371409i	$0.121125\pi$
$263$	1.27468	+	14.5696i	0.0786001	+	0.898403i	−0.849869	+	0.526994i	$0.823319\pi$
$264$	0.357547	+	7.22228i	0.0220055	+	0.444501i
$265$	−5.48949	+	16.3440i	−0.337217	+	1.00400i
$266$	−1.52685	−	0.714308i	−0.0936171	−	0.0437970i
$267$	2.29271	+	1.44189i	0.140312	+	0.0882421i
$268$	−0.696598	−	0.994844i	−0.0425515	−	0.0607698i
$269$	−16.9061	−	14.1859i	−1.03078	−	0.864931i	−0.0398406	−	0.999206i	$-0.512685\pi$
$269$	−16.9061	−	14.1859i	−1.03078	−	0.864931i	−0.990944	+	0.134275i	$0.957129\pi$
$270$	−8.22491	+	8.20676i	−0.500552	+	0.499448i
$271$	−14.5512	+	5.29622i	−0.883925	+	0.321722i	−0.743793	−	0.668410i	$-0.766975\pi$
$271$	−14.5512	+	5.29622i	−0.883925	+	0.321722i	−0.140132	+	0.990133i	$0.544753\pi$
$272$	0.00764440	−	0.0873759i	0.000463510	−	0.00529794i
$273$	−0.00611396	+	0.161664i	−0.000370033	+	0.00978437i
$274$	9.35194	+	5.39935i	0.564971	+	0.326186i
$275$	−9.51950	+	18.5775i	−0.574047	+	1.12026i
$276$	−0.951504	−	2.25977i	−0.0572738	−	0.136022i
$277$	25.3947	−	6.80449i	1.52582	−	0.408842i	0.604167	−	0.796858i	$-0.293506\pi$
$277$	25.3947	−	6.80449i	1.52582	−	0.408842i	0.921653	+	0.388016i	$0.126839\pi$
$278$	−1.51538	+	5.65548i	−0.0908865	+	0.339193i
$279$	−11.7412	−	5.30917i	−0.702928	−	0.317852i
$280$	−0.595963	+	0.626571i	−0.0356156	+	0.0374448i
$281$	−8.94351	+	24.5721i	−0.533525	+	1.46585i	0.321323	+	0.946970i	$0.395872\pi$
$281$	−8.94351	+	24.5721i	−0.533525	+	1.46585i	−0.854848	+	0.518878i	$0.826350\pi$
$282$	0.231669	−	0.0745332i	0.0137957	−	0.00443838i
$283$	−12.0608	−	17.2246i	−0.716939	−	1.02390i	−0.997938	−	0.0641871i	$-0.979555\pi$
$283$	−12.0608	−	17.2246i	−0.716939	−	1.02390i	0.280999	−	0.959708i	$-0.409334\pi$
$284$	5.18014			0.307385
$285$	15.9432	−	5.55099i	0.944395	−	0.328812i
$286$	−1.00835			−0.0596251
$287$	−1.20183	−	1.71640i	−0.0709421	−	0.101316i
$288$	−1.53020	−	2.58040i	−0.0901681	−	0.152052i
$289$	5.81171	−	15.9675i	0.341865	−	0.939267i
$290$	7.42808	−	0.185976i	0.436192	−	0.0109209i
$291$	15.2352	+	11.5498i	0.893104	+	0.677064i
$292$	−1.05426	+	3.93455i	−0.0616959	+	0.230252i
$293$	5.51922	−	1.47887i	0.322436	−	0.0863965i	−0.0939705	−	0.995575i	$-0.529956\pi$
$293$	5.51922	−	1.47887i	0.322436	−	0.0863965i	0.416407	+	0.909178i	$0.363289\pi$
$294$	10.9355	−	4.60452i	0.637769	−	0.268541i
$295$	−1.32324	+	0.976797i	−0.0770420	+	0.0568713i
$296$	−9.36427	−	5.40646i	−0.544287	−	0.314244i
$297$	−8.65109	−	19.8938i	−0.501987	−	1.15435i
$298$	−0.819783	+	9.37016i	−0.0474887	+	0.542799i
$299$	0.321290	−	0.116940i	0.0185807	−	0.00676283i
$300$	−0.106194	−	8.65960i	−0.00613114	−	0.499962i
$301$	0.856150	+	0.718395i	0.0493477	+	0.0414076i
$302$	−3.45604	−	4.93573i	−0.198873	−	0.284019i
$303$	−5.72467	+	9.10266i	−0.328874	+	0.522934i
$304$	0.374470	+	4.34278i	0.0214773	+	0.249076i
$305$	7.01276	+	14.1060i	0.401549	+	0.807705i
$306$	0.0710629	+	0.253351i	0.00406239	+	0.0144831i
$307$	0.567058	+	6.48150i	0.0323637	+	0.369919i	0.995056	+	0.0993191i	$0.0316664\pi$
$307$	0.567058	+	6.48150i	0.0323637	+	0.369919i	−0.962692	+	0.270600i	$0.912778\pi$
$308$	−0.682324	−	1.46325i	−0.0388790	−	0.0833764i
$309$	23.1488	−	14.9379i	1.31689	−	0.849789i
$310$	8.94022	−	3.50979i	0.507770	−	0.199343i
$311$	6.65510	−	3.84232i	0.377376	−	0.217878i	−0.299300	−	0.954159i	$-0.596753\pi$
$311$	6.65510	−	3.84232i	0.377376	−	0.217878i	0.676676	+	0.736281i	$0.263420\pi$
$312$	0.369938	−	0.195328i	0.0209436	−	0.0110583i
$313$	−15.8173	−	11.0754i	−0.894045	−	0.626017i	0.0336180	−	0.999435i	$-0.489297\pi$
$313$	−15.8173	−	11.0754i	−0.894045	−	0.626017i	−0.927663	+	0.373417i	$0.878186\pi$
$314$	2.59861	+	14.7374i	0.146648	+	0.831682i
$315$	1.00936	−	2.38978i	0.0568709	−	0.134649i
$316$	7.73649	+	13.4000i	0.435212	+	0.753809i
$317$	−2.40635	+	27.5047i	−0.135154	+	1.54482i	0.561542	+	0.827449i	$0.310208\pi$
$317$	−2.40635	+	27.5047i	−0.135154	+	1.54482i	−0.696695	+	0.717367i	$0.745347\pi$
$318$	13.0551	+	2.81446i	0.732092	+	0.157827i
$319$	−4.74487	+	13.0364i	−0.265662	+	0.729900i
$320$	2.17368	+	0.524496i	0.121513	+	0.0293202i
$321$	0.0759179	+	1.53351i	0.00423733	+	0.0855921i
$322$	0.387104	+	0.387104i	0.0215724	+	0.0215724i
$323$	0.0668598	−	0.376426i	0.00372018	−	0.0209449i
$324$	7.02748	+	5.62268i	0.390415	+	0.312371i
$325$	1.20680	+	0.0449175i	0.0669414	+	0.00249157i
$326$	−8.21583	+	9.79125i	−0.455033	+	0.542287i
$327$	−24.6503	+	19.1443i	−1.36317	+	1.05868i
$328$	−2.28984	+	4.91057i	−0.126435	+	0.271141i
$329$	−0.0416241	+	0.0349268i	−0.00229481	+	0.00192558i
$330$	15.1223	+	5.72378i	0.832456	+	0.315084i
$331$	8.94943	−	15.5009i	0.491905	−	0.852005i	−0.508051	−	0.861327i	$-0.669634\pi$
$331$	8.94943	−	15.5009i	0.491905	−	0.852005i	0.999957	+	0.00932178i	$0.00296726\pi$
$332$	7.20335	+	5.04384i	0.395335	+	0.276817i
$333$	32.0095	+	5.25991i	1.75411	+	0.288241i
$334$	−18.1758	−	10.4938i	−0.994536	−	0.574196i
$335$	−2.66176	+	0.538360i	−0.145428	+	0.0294137i
$336$	0.533773	+	0.404654i	0.0291197	+	0.0220757i
$337$	7.06294	+	3.29350i	0.384743	+	0.179409i	0.605360	−	0.795952i	$-0.293029\pi$
$337$	7.06294	+	3.29350i	0.384743	+	0.179409i	−0.220617	+	0.975361i	$0.570807\pi$
$338$	−5.46938	−	11.7291i	−0.297495	−	0.637981i
$339$	12.6967	−	24.7413i	0.689588	−	1.34376i
$340$	−0.172250	−	0.0937805i	−0.00934158	−	0.00508596i
$341$			17.9322i			0.971086i
$342$	−5.64957	−	11.7933i	−0.305494	−	0.637710i
$343$	−3.78744	+	3.78744i	−0.204503	+	0.204503i
$344$	0.501844	−	2.84610i	0.0270576	−	0.153451i
$345$	−5.48221	−	0.0700067i	−0.295152	−	0.00376903i
$346$	0.0587862	+	0.0213964i	0.00316037	+	0.00115028i
$347$	2.60177	−	5.57952i	0.139671	−	0.299525i	−0.824013	−	0.566571i	$-0.808270\pi$
$347$	2.60177	−	5.57952i	0.139671	−	0.299525i	0.963684	+	0.267046i	$0.0860476\pi$
$348$	−0.784521	−	5.70185i	−0.0420547	−	0.305651i
$349$	−7.03299	+	4.06050i	−0.376467	+	0.217353i	−0.676280	−	0.736645i	$-0.736409\pi$
$349$	−7.03299	+	4.06050i	−0.376467	+	0.217353i	0.299813	+	0.953998i	$0.403076\pi$
$350$	0.751429	+	1.78162i	0.0401656	+	0.0952316i
$351$	−0.831556	+	0.939987i	−0.0443852	+	0.0501728i
$352$	−2.39462	+	3.41987i	−0.127634	+	0.182280i
$353$	5.06634	−	1.35752i	0.269654	−	0.0722535i	−0.121458	−	0.992597i	$-0.538757\pi$
$353$	5.06634	−	1.35752i	0.269654	−	0.0722535i	0.391112	+	0.920343i	$0.372090\pi$
$354$	0.866161	+	0.934250i	0.0460359	+	0.0496548i
$355$	4.63096	−	10.6171i	0.245786	−	0.563499i
$356$	0.534820	+	1.46941i	0.0283454	+	0.0778784i
$357$	−0.0360357	−	0.0463998i	−0.00190721	−	0.00245574i
$358$	−20.9076	+	1.82918i	−1.10500	+	0.0966752i
$359$	−4.09708	+	23.2357i	−0.216236	+	1.22633i	0.662514	+	0.749049i	$0.269489\pi$
$359$	−4.09708	+	23.2357i	−0.216236	+	1.22633i	−0.878750	+	0.477283i	$0.841622\pi$
$360$	−6.65673	+	0.829441i	−0.350840	+	0.0437154i
$361$	−0.0475447	+	18.9999i	−0.00250235	+	0.999997i
$362$	−0.822612	+	0.822612i	−0.0432355	+	0.0432355i
$363$	−7.47579	+	8.25453i	−0.392377	+	0.433251i
$364$	−0.0600387	+	0.0715514i	−0.00314688	+	0.00375031i
$365$	7.12170	+	5.67822i	0.372767	+	0.297212i
$366$	10.2528	−	6.61616i	0.535924	−	0.345832i
$367$	−5.53142	−	0.483936i	−0.288738	−	0.0252613i	−0.0581331	−	0.998309i	$-0.518515\pi$
$367$	−5.53142	−	0.483936i	−0.288738	−	0.0252613i	−0.230604	+	0.973048i	$0.574070\pi$
$368$	0.366388	−	1.36738i	0.0190993	−	0.0712796i
$369$	1.22771	−	16.2082i	0.0639119	−	0.843766i
$370$	−19.4525	+	14.3596i	−1.01129	+	0.746518i
$371$	−2.93651	+	0.517786i	−0.152456	+	0.0268821i
$372$	−3.47366	−	6.57886i	−0.180101	−	0.341098i
$373$	15.6748	+	4.20006i	0.811612	+	0.217471i	0.640676	−	0.767811i	$-0.278654\pi$
$373$	15.6748	+	4.20006i	0.811612	+	0.217471i	0.170936	+	0.985282i	$0.445321\pi$
$374$	0.280509	−	0.235375i	0.0145048	−	0.0121710i
$375$	−17.8435	−	7.52389i	−0.921435	−	0.388532i
$376$	0.132032	+	0.0480558i	0.00680904	+	0.00247829i
$377$	0.799537	−	0.0699504i	0.0411782	−	0.00360263i
$378$	−1.92673	−	0.570632i	−0.0991005	−	0.0293502i
$379$			8.77393i			0.450686i	0.974279	+	0.225343i	$0.0723503\pi$
$379$			8.77393i			0.450686i	−0.974279	+	0.225343i	$0.927650\pi$
$380$	9.23567	+	3.11487i	0.473780	+	0.159790i
$381$	−7.98523	−	35.0503i	−0.409095	−	1.79568i
$382$	5.66109	−	3.96394i	0.289647	−	0.202813i
$383$	−2.58503	−	29.5470i	−0.132089	−	1.50978i	−0.716078	−	0.698021i	$-0.754064\pi$
$383$	−2.58503	−	29.5470i	−0.132089	−	1.50978i	0.583989	−	0.811762i	$-0.301491\pi$
$384$	0.216059	−	1.71852i	0.0110257	−	0.0876980i
$385$	−3.60904	+	0.0903592i	−0.183934	+	0.00460513i
$386$	−4.25641	−	5.07259i	−0.216646	−	0.258188i
$387$	1.60503	+	8.52016i	0.0815881	+	0.433104i
$388$	2.85684	+	10.6619i	0.145034	+	0.541274i
$389$	1.95238	+	11.0725i	0.0989894	+	0.561397i	0.993452	+	0.114253i	$0.0364476\pi$
$389$	1.95238	+	11.0725i	0.0989894	+	0.561397i	−0.894462	+	0.447144i	$0.852441\pi$
$390$	−0.0696228	−	0.932838i	−0.00352549	−	0.0472361i
$391$	−0.0620816	+	0.107528i	−0.00313960	+	0.00543795i
$392$	6.61702	+	1.77303i	0.334210	+	0.0895513i
$393$	3.93170	+	28.5753i	0.198328	+	1.44143i
$394$	−5.84878	−	16.0694i	−0.294657	−	0.809564i
$395$	34.3807	−	3.87720i	1.72988	−	0.195083i
$396$	3.10029	−	12.1349i	0.155795	−	0.609802i
$397$	−27.9837	+	19.5944i	−1.40446	+	0.983416i	−0.406913	+	0.913467i	$0.633395\pi$
$397$	−27.9837	+	19.5944i	−1.40446	+	0.983416i	−0.997551	+	0.0699494i	$0.977716\pi$
$398$	−2.02738	−	2.02738i	−0.101623	−	0.101623i
$399$	2.16162	+	1.96262i	0.108217	+	0.0982540i
$400$	3.01824	−	3.98626i	0.150912	−	0.199313i
$401$	−3.32331	−	0.585988i	−0.165958	−	0.0292629i	0.0900517	−	0.995937i	$-0.471297\pi$
$401$	−3.32331	−	0.585988i	−0.165958	−	0.0292629i	−0.256010	+	0.966674i	$0.582408\pi$
$402$	0.644237	+	2.00246i	0.0321316	+	0.0998737i
$403$	0.940225	−	0.438434i	0.0468359	−	0.0218400i
$404$	−5.83393	+	2.12338i	−0.290249	+	0.105642i
$405$	17.8066	−	9.37681i	0.884818	−	0.465937i
$406$	0.642532	+	1.11290i	0.0318883	+	0.0552322i
$407$	−11.6838	−	43.6046i	−0.579145	−	2.16140i
$408$	−0.0573168	+	0.140690i	−0.00283760	+	0.00696520i
$409$	−14.6702	+	2.58675i	−0.725395	+	0.127907i	−0.524140	−	0.851632i	$-0.675613\pi$
$409$	−14.6702	+	2.58675i	−0.725395	+	0.127907i	−0.201255	+	0.979539i	$0.564502\pi$
$410$	8.01755	+	9.08318i	0.395958	+	0.448586i
$411$	−12.7164	−	13.7160i	−0.627252	−	0.676561i
$412$	15.8455	+	1.38630i	0.780654	+	0.0682983i
$413$	−0.257798	−	0.120213i	−0.0126854	−	0.00591530i
$414$	0.419461	+	4.22608i	0.0206154	+	0.207700i
$415$	16.7774	−	10.2548i	0.823572	−	0.503386i
$416$	0.237858	+	0.0419408i	0.0116620	+	0.00205632i
$417$	5.39885	−	8.58457i	0.264383	−	0.420388i
$418$	−11.7148	+	13.9258i	−0.572992	+	0.681132i
$419$	−28.9325			−1.41345			−0.706723	−	0.707491i	$-0.749827\pi$
$419$	−28.9325			−1.41345			−0.706723	+	0.707491i	$0.749827\pi$
$420$	1.30656	−	0.732258i	0.0637534	−	0.0357305i
$421$	−19.9314	−	16.7245i	−0.971399	−	0.815101i	0.0113705	−	0.999935i	$-0.496381\pi$
$421$	−19.9314	−	16.7245i	−0.971399	−	0.815101i	−0.982770	+	0.184835i	$0.940825\pi$
$422$	−20.7770	+	9.68846i	−1.01141	+	0.471627i
$423$	−0.421489	+	0.00491683i	−0.0204935	+	0.000239064i
$424$	4.95622	+	5.90659i	0.240695	+	0.286850i
$425$	−0.346200	+	0.269203i	−0.0167932	+	0.0130583i
$426$	−8.57259	−	2.64806i	−0.415344	−	0.128299i
$427$	−1.56267	+	2.23172i	−0.0756228	+	0.108001i
$428$	−0.508450	+	0.726142i	−0.0245769	+	0.0350994i
$429$	1.66872	+	0.515464i	0.0805665	+	0.0248868i
$430$	−5.38468	−	3.57294i	−0.259672	−	0.172302i
$431$	−2.96319	−	3.53139i	−0.142732	−	0.170101i	0.689942	−	0.723864i	$-0.257636\pi$
$431$	−2.96319	−	3.53139i	−0.142732	−	0.170101i	−0.832674	+	0.553763i	$0.813191\pi$
$432$	1.21324	+	5.05253i	0.0583720	+	0.243090i
$433$	0.573039	−	0.267212i	0.0275385	−	0.0128414i	−0.408800	−	0.912624i	$-0.634053\pi$
$433$	0.573039	−	0.267212i	0.0275385	−	0.0128414i	0.436339	+	0.899782i	$0.356275\pi$
$434$	1.27245	+	1.06771i	0.0610795	+	0.0512518i
$435$	−12.3878	−	3.48942i	−0.593948	−	0.167305i
$436$	−18.0198			−0.862993
$437$	2.11770	−	5.79575i	0.101303	−	0.277248i
$438$	3.75601	−	5.97234i	0.179469	−	0.285369i
$439$	−38.5069	−	6.78980i	−1.83783	−	0.324060i	−0.856466	−	0.516203i	$-0.827345\pi$
$439$	−38.5069	−	6.78980i	−1.83783	−	0.324060i	−0.981367	+	0.192143i	$0.938456\pi$
$440$	4.86856	+	7.96529i	0.232100	+	0.379730i
$441$	−20.4509	+	2.02986i	−0.973850	+	0.0966598i
$442$	−0.0191995	−	0.00895287i	−0.000913227	−	0.000425845i
$443$	−32.3924	−	2.83397i	−1.53901	−	0.134646i	−0.714153	−	0.699989i	$-0.753188\pi$
$443$	−32.3924	−	2.83397i	−1.53901	−	0.134646i	−0.824856	+	0.565344i	$0.808744\pi$
$444$	12.7331	+	13.7341i	0.604288	+	0.651791i
$445$	3.48979	+	0.217467i	0.165432	+	0.0103089i
$446$	6.56622	−	1.15780i	0.310919	−	0.0548235i
$447$	6.14663	−	15.0876i	0.290725	−	0.713617i
$448$	0.100091	+	0.373543i	0.00472884	+	0.0176483i
$449$	−13.5514	−	23.4718i	−0.639531	−	1.10770i	−0.985536	−	0.169468i	$-0.945795\pi$
$449$	−13.5514	−	23.4718i	−0.639531	−	1.10770i	0.346004	−	0.938233i	$-0.387538\pi$
$450$	−4.25100	+	14.3850i	−0.200394	+	0.678117i
$451$	−21.2563	+	7.73666i	−1.00092	+	0.364305i
$452$	14.5512	−	6.78535i	0.684432	−	0.319156i
$453$	3.19626	+	9.93483i	0.150173	+	0.466779i
$454$	−4.15514	−	0.732664i	−0.195011	−	0.0343856i
$455$	0.0929769	+	0.187020i	0.00435882	+	0.00876764i
$456$	1.60030	−	7.37828i	0.0749408	−	0.345520i
$457$	25.1035	+	25.1035i	1.17429	+	1.17429i	0.981176	+	0.193118i	$0.0618599\pi$
$457$	25.1035	+	25.1035i	1.17429	+	1.17429i	0.193118	+	0.981176i	$0.438140\pi$
$458$	17.5445	−	12.2848i	0.819803	−	0.574032i
$459$	0.0119102	−	0.455597i	0.000555919	−	0.0212655i
$460$	−2.47501	−	1.97336i	−0.115398	−	0.0920083i
$461$	−5.33599	−	14.6605i	−0.248522	−	0.682808i	−0.999741	−	0.0227553i	$-0.992756\pi$
$461$	−5.33599	−	14.6605i	−0.248522	−	0.682808i	0.751219	−	0.660053i	$-0.229466\pi$
$462$	0.381171	+	2.77033i	0.0177337	+	0.128887i
$463$	−23.1300	−	6.19767i	−1.07494	−	0.288030i	−0.322421	−	0.946597i	$-0.604497\pi$
$463$	−23.1300	−	6.19767i	−1.07494	−	0.288030i	−0.752523	+	0.658566i	$0.771163\pi$
$464$	1.66149	−	2.87778i	0.0771327	−	0.133598i
$465$	−16.5893	+	1.23815i	−0.769311	+	0.0574179i
$466$	−1.76873	−	10.0309i	−0.0819346	−	0.464674i
$467$	3.46845	+	12.9444i	0.160501	+	0.598997i	0.998571	+	0.0534350i	$0.0170170\pi$
$467$	3.46845	+	12.9444i	0.160501	+	0.598997i	−0.838071	+	0.545562i	$0.816316\pi$
$468$	−0.712059	+	0.134138i	−0.0329149	+	0.00620051i
$469$	−0.301895	−	0.359784i	−0.0139402	−	0.0166133i
$470$	0.216529	−	0.227650i	0.00998774	−	0.0105007i
$471$	3.23327	−	25.7173i	0.148981	−	1.18499i
$472$	0.0641066	+	0.732741i	0.00295074	+	0.0337272i
$473$	9.88345	−	6.92047i	0.454442	−	0.318203i
$474$	−5.95308	−	26.1304i	−0.273434	−	1.20021i
$475$	14.6407	−	16.1446i	0.671763	−	0.740766i
$476$		−	0.0339191i		−	0.00155468i
$477$	−20.1660	−	11.3313i	−0.923340	−	0.518825i
$478$	−16.8528	+	1.47443i	−0.770827	+	0.0674386i
$479$	−15.4460	−	5.62188i	−0.705746	−	0.256870i	−0.0358837	−	0.999356i	$-0.511425\pi$
$479$	−15.4460	−	5.62188i	−0.705746	−	0.256870i	−0.669862	+	0.742486i	$0.733647\pi$
$480$	−3.32910	−	1.97916i	−0.151952	−	0.0903360i
$481$	−2.00062	+	1.67872i	−0.0912203	+	0.0765429i
$482$	−10.3610	−	2.77622i	−0.471931	−	0.126453i
$483$	−0.442731	−	0.838502i	−0.0201450	−	0.0381531i
$484$	−6.33206	+	1.11651i	−0.287821	+	0.0507506i
$485$	24.4064	+	3.67621i	1.10824	+	0.166928i
$486$	−8.75546	−	12.8974i	−0.397156	−	0.585036i
$487$	−6.76127	+	25.2334i	−0.306382	+	1.14343i	0.625366	+	0.780331i	$0.284950\pi$
$487$	−6.76127	+	25.2334i	−0.306382	+	1.14343i	−0.931749	+	0.363104i	$0.881717\pi$
$488$	7.01815	+	0.614008i	0.317697	+	0.0277948i
$489$	18.6016	−	12.0036i	0.841192	−	0.542822i
$490$	9.54948	−	11.9771i	0.431401	−	0.541070i
$491$	11.8707	−	14.1469i	0.535716	−	0.638442i	−0.428506	−	0.903539i	$-0.640960\pi$
$491$	11.8707	−	14.1469i	0.535716	−	0.638442i	0.964222	+	0.265098i	$0.0854042\pi$
$492$	6.29970	−	6.95593i	0.284012	−	0.313598i
$493$	−0.206091	+	0.206091i	−0.00928189	+	0.00928189i
$494$	1.01658	+	0.273755i	0.0457381	+	0.0123168i
$495$	−22.0999	−	17.2027i	−0.993316	−	0.773204i
$496$	0.745864	−	4.23000i	0.0334903	−	0.189933i
$497$	1.99564	−	0.174596i	0.0895169	−	0.00783171i
$498$	−9.34241	−	12.0293i	−0.418643	−	0.539047i
$499$	3.59317	+	9.87215i	0.160852	+	0.441938i	0.993769	−	0.111461i	$-0.0355529\pi$
$499$	3.59317	+	9.87215i	0.160852	+	0.441938i	−0.832917	+	0.553399i	$0.813331\pi$
$500$	−5.47191	−	9.74978i	−0.244711	−	0.436023i
$501$	24.7147	+	26.6575i	1.10417	+	1.19097i
$502$	28.6959	−	7.68903i	1.28076	−	0.343178i
$503$	−13.0738	+	18.6713i	−0.582931	+	0.832511i	−0.996973	−	0.0777464i	$-0.975228\pi$
$503$	−13.0738	+	18.6713i	−0.582931	+	0.832511i	0.414043	+	0.910257i	$0.364116\pi$
$504$	−0.676481	−	0.942522i	−0.0301329	−	0.0419833i
$505$	−0.863402	+	13.8554i	−0.0384209	+	0.616557i
$506$	5.11825	−	2.95502i	0.227534	−	0.131367i
$507$	3.05539	+	22.2064i	0.135695	+	0.986221i
$508$	8.77137	−	18.8103i	0.389167	−	0.834571i
$509$	−19.8373	−	7.22018i	−0.879272	−	0.320029i	−0.137356	−	0.990522i	$-0.543861\pi$
$509$	−19.8373	−	7.22018i	−0.879272	−	0.320029i	−0.741916	+	0.670493i	$0.766083\pi$
$510$	0.237116	+	0.243250i	0.0104997	+	0.0107713i
$511$	−0.273539	+	1.55132i	−0.0121006	+	0.0686261i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	3.32077	+	22.4047i	0.146615	+	0.989194i
$514$		−	19.9523i		−	0.880060i
$515$	17.0070	−	31.2374i	0.749418	−	1.37648i
$516$	−2.28541	+	4.45346i	−0.100610	+	0.196053i
$517$	0.247906	+	0.531637i	0.0109029	+	0.0233814i
$518$	−3.78980	−	1.76721i	−0.166514	−	0.0776468i
$519$	−0.0863473	−	0.0654600i	−0.00379023	−	0.00287338i
$520$	0.298603	−	0.450016i	0.0130946	−	0.0197345i
$521$	−27.7918	−	16.0456i	−1.21758	−	0.702971i	−0.253182	−	0.967419i	$-0.581477\pi$
$521$	−27.7918	−	16.0456i	−1.21758	−	0.702971i	−0.964400	+	0.264447i	$0.914810\pi$
$522$	−1.61645	+	9.83701i	−0.0707502	+	0.430554i
$523$	16.0009	+	11.2039i	0.699669	+	0.489914i	0.868473	−	0.495736i	$-0.165102\pi$
$523$	16.0009	+	11.2039i	0.699669	+	0.489914i	−0.168804	+	0.985650i	$0.553990\pi$
$524$	−8.32670	+	14.4223i	−0.363754	+	0.630040i
$525$	−0.332782	−	3.33252i	−0.0145238	−	0.145443i
$526$	11.2036	−	9.40096i	0.488502	−	0.409901i
$527$	−0.159215	+	0.341438i	−0.00693553	+	0.0148733i
$528$	5.71107	−	4.43542i	0.248542	−	0.193027i
$529$	13.4960	−	16.0839i	0.586782	−	0.699300i
$530$	16.5368	−	4.87779i	0.718314	−	0.211878i
$531$	−0.955823	−	1.98886i	−0.0414792	−	0.0863093i
$532$	0.290637	+	1.66043i	0.0126007	+	0.0719888i
$533$	0.925354	+	0.925354i	0.0400815	+	0.0400815i
$534$	−0.133919	−	2.70511i	−0.00579526	−	0.117062i
$535$	1.03374	+	1.69127i	0.0446926	+	0.0731200i
$536$	−0.415377	+	1.14124i	−0.0179415	+	0.0492940i
$537$	35.5350	+	7.66076i	1.53345	+	0.330586i
$538$	−1.92347	+	21.9854i	−0.0829268	+	0.947858i
$539$	14.2999	+	24.7682i	0.615942	+	1.06684i
$540$	11.4402	+	2.03024i	0.492308	+	0.0873678i
$541$	2.79703	+	15.8628i	0.120254	+	0.681993i	0.984014	+	0.178090i	$0.0569920\pi$
$541$	2.79703	+	15.8628i	0.120254	+	0.681993i	−0.863760	+	0.503903i	$0.831897\pi$
$542$	12.6847	+	8.88189i	0.544853	+	0.381510i
$543$	1.78185	−	0.940823i	0.0764666	−	0.0403746i
$544$	−0.0759588	+	0.0438548i	−0.00325671	+	0.00188026i
$545$	−16.1094	+	36.9331i	−0.690052	+	1.58204i
$546$	0.135935	−	0.0877186i	0.00581746	−	0.00375401i
$547$	15.9745	+	34.2574i	0.683019	+	1.46474i	0.875390	+	0.483417i	$0.160604\pi$
$547$	15.9745	+	34.2574i	0.683019	+	1.46474i	−0.192371	+	0.981322i	$0.561618\pi$
$548$	−0.941168	−	10.7576i	−0.0402047	−	0.459542i
$549$	−20.3495	+	5.70786i	−0.868496	+	0.243606i
$550$	20.6779	−	2.85769i	0.881710	−	0.121852i
$551$	8.32282	−	11.8546i	0.354564	−	0.505024i
$552$	−1.30533	+	2.07557i	−0.0555586	+	0.0883423i
$553$	3.43212	+	4.90158i	0.145949	+	0.208436i
$554$	−20.1397	−	16.8992i	−0.855654	−	0.717979i
$555$	39.5324	−	13.8196i	1.67806	−	0.586608i
$556$	5.50188	−	2.00252i	0.233332	−	0.0849258i
$557$	0.863308	−	9.86765i	0.0365795	−	0.418106i	−0.955723	−	0.294268i	$-0.904924\pi$
$557$	0.863308	−	9.86765i	0.0365795	−	0.418106i	0.992302	−	0.123838i	$-0.0395203\pi$
$558$	2.38546	+	12.6630i	0.100985	+	0.536069i
$559$	−0.604500	−	0.349008i	−0.0255676	−	0.0147615i
$560$	0.855088	+	0.128798i	0.0361340	+	0.00544269i
$561$	−0.584536	+	0.246126i	−0.0246791	+	0.0103915i
$562$	25.2581	−	6.76788i	1.06545	−	0.285486i
$563$	2.90674	−	10.8481i	0.122505	−	0.457194i	−0.877234	−	0.480063i	$-0.840614\pi$
$563$	2.90674	−	10.8481i	0.122505	−	0.457194i	0.999738	+	0.0228698i	$0.00728031\pi$
$564$	−0.193934	−	0.147021i	−0.00816608	−	0.00619072i
$565$	−0.898574	−	35.8900i	−0.0378033	−	1.50990i
$566$	−7.19177	+	19.7592i	−0.302293	+	0.830542i
$567$	2.89684	+	1.92927i	0.121656	+	0.0810218i
$568$	−2.97121	−	4.24332i	−0.124669	−	0.178046i
$569$	−31.1436			−1.30561			−0.652803	−	0.757528i	$-0.726407\pi$
$569$	−31.1436			−1.30561			−0.652803	+	0.757528i	$0.726407\pi$
$570$	−13.6918	−	9.87601i	−0.573485	−	0.413661i
$571$	32.3676			1.35454			0.677271	−	0.735733i	$-0.263162\pi$
$571$	32.3676			1.35454			0.677271	+	0.735733i	$0.263162\pi$
$572$	0.578367	+	0.825994i	0.0241827	+	0.0345365i
$573$	−11.3949	+	3.66599i	−0.476027	+	0.153149i
$574$	−0.716647	+	1.96897i	−0.0299123	+	0.0821832i
$575$	−6.25718	+	3.30859i	−0.260943	+	0.137978i
$576$	−1.23605	+	2.73353i	−0.0515022	+	0.113897i
$577$	7.43452	−	27.7460i	0.309503	−	1.15508i	−0.619496	−	0.785000i	$-0.712663\pi$
$577$	7.43452	−	27.7460i	0.309503	−	1.15508i	0.928999	−	0.370082i	$-0.120670\pi$
$578$	−16.4133	+	4.39793i	−0.682704	+	0.182930i
$579$	4.45083	+	10.5705i	0.184970	+	0.439293i
$580$	−4.41291	−	5.97805i	−0.183236	−	0.248225i
$581$	2.94508	+	1.70034i	0.122183	+	0.0705422i
$582$	0.722516	−	19.1047i	0.0299493	−	0.791914i
$583$	−2.80559	+	32.0681i	−0.116196	+	1.32812i
$584$	3.82769	−	1.39317i	0.158391	−	0.0576497i
$585$	−0.361643	+	1.57934i	−0.0149521	+	0.0652977i
$586$	−4.37711	−	3.67283i	−0.180817	−	0.151723i
$587$	4.58939	+	6.55433i	0.189424	+	0.270526i	0.902619	−	0.430440i	$-0.141641\pi$
$587$	4.58939	+	6.55433i	0.189424	+	0.270526i	−0.713195	+	0.700966i	$0.752753\pi$
$588$	−10.0441	−	6.31676i	−0.414213	−	0.260499i
$589$	4.86839	−	18.0786i	0.200598	−	0.744914i
$590$	1.55912	+	0.523667i	0.0641882	+	0.0215590i
$591$	1.46454	+	29.5830i	0.0602431	+	1.21688i
$592$	0.942408	+	10.7718i	0.0387327	+	0.442717i
$593$	−16.6031	−	35.6055i	−0.681808	−	1.46214i	−0.876561	−	0.481290i	$-0.840168\pi$
$593$	−16.6031	−	35.6055i	−0.681808	−	1.46214i	0.194753	−	0.980852i	$-0.437609\pi$
$594$	−11.3339	+	18.4972i	−0.465038	+	0.758947i
$595$	−0.0695201	−	0.0303232i	−0.00285004	−	0.00124313i
$596$	8.14579	−	4.70298i	0.333665	−	0.192641i
$597$	2.31872	+	4.39148i	0.0948987	+	0.179732i
$598$	−0.280076	−	0.196112i	−0.0114532	−	0.00801960i
$599$	5.44794	+	30.8968i	0.222597	+	1.26241i	0.867226	+	0.497915i	$0.165901\pi$
$599$	5.44794	+	30.8968i	0.222597	+	1.26241i	−0.644629	+	0.764496i	$0.722988\pi$
$600$	−7.03262	+	5.05393i	−0.287106	+	0.206326i
$601$	6.26850	+	10.8574i	0.255698	+	0.442881i	0.965085	−	0.261938i	$-0.0843615\pi$
$601$	6.26850	+	10.8574i	0.255698	+	0.442881i	−0.709387	+	0.704819i	$0.751028\pi$
$602$	0.0974074	−	1.11337i	0.00397003	−	0.0453776i
$603$	−0.0424993	−	3.64319i	−0.00173070	−	0.148362i
$604$	−2.06081	+	5.66204i	−0.0838533	+	0.230385i
$605$	−3.37237	+	13.9762i	−0.137106	+	0.568214i
$606$	10.7400	−	0.531695i	0.436283	−	0.0215986i
$607$	−12.1810	−	12.1810i	−0.494413	−	0.494413i	0.415281	−	0.909693i	$-0.363683\pi$
$607$	−12.1810	−	12.1810i	−0.494413	−	0.494413i	−0.909693	+	0.415281i	$0.863683\pi$
$608$	3.34261	−	2.79767i	0.135561	−	0.113460i
$609$	−0.494416	−	2.17019i	−0.0200347	−	0.0879405i
$610$	7.53257	−	13.8354i	0.304985	−	0.560177i
$611$	0.0218137	−	0.0259965i	0.000882486	−	0.00105171i
$612$	0.166773	−	0.203528i	0.00674141	−	0.00822712i
$613$	1.76113	−	3.77675i	0.0711313	−	0.152541i	−0.867527	−	0.497390i	$-0.834292\pi$
$613$	1.76113	−	3.77675i	0.0711313	−	0.152541i	0.938658	+	0.344848i	$0.112070\pi$
$614$	4.98408	−	4.18214i	0.201141	−	0.168778i
$615$	−8.62493	−	19.1302i	−0.347791	−	0.771406i
$616$	−0.807259	+	1.39821i	−0.0325254	+	0.0563356i
$617$	32.6694	+	22.8753i	1.31522	+	0.920927i	0.999609	−	0.0279620i	$-0.00890175\pi$
$617$	32.6694	+	22.8753i	1.31522	+	0.920927i	0.315611	+	0.948889i	$0.397791\pi$
$618$	−25.5140	−	10.3943i	−1.02633	−	0.418122i
$619$	23.1303	+	13.3543i	0.929683	+	0.536753i	0.886711	−	0.462323i	$-0.152984\pi$
$619$	23.1303	+	13.3543i	0.929683	+	0.536753i	0.0429719	+	0.999076i	$0.486317\pi$
$620$	−8.00295	−	5.31027i	−0.321406	−	0.213265i
$621$	1.46618	−	7.20815i	0.0588359	−	0.289253i
$622$	−6.96466	−	3.24767i	−0.279257	−	0.130220i
$623$	0.255565	+	0.548061i	0.0102390	+	0.0219576i
$624$	−0.372191	−	0.191000i	−0.0148996	−	0.00764610i
$625$	−24.8748	+	2.49899i	−0.994992	+	0.0999596i
$626$			19.3093i			0.771756i
$627$	26.5056	−	17.0572i	1.05853	−	0.681197i
$628$	10.5817	−	10.5817i	0.422256	−	0.422256i
$629$	0.164688	−	0.933989i	0.00656652	−	0.0372406i
$630$	−2.53654	+	0.543906i	−0.101058	+	0.0216697i
$631$	−29.7704	−	10.8355i	−1.18514	−	0.431356i	−0.327125	−	0.944981i	$-0.606080\pi$
$631$	−29.7704	−	10.8355i	−1.18514	−	0.431356i	−0.858015	+	0.513625i	$0.828302\pi$
$632$	6.53916	−	14.0233i	0.260114	−	0.557816i
$633$	39.3364	−	5.41232i	1.56348	−	0.215120i
$634$	23.9107	−	13.8049i	0.949616	−	0.548261i
$635$	−30.7117	−	34.7937i	−1.21876	−	1.38075i
$636$	−5.18261	−	12.3084i	−0.205504	−	0.488059i
$637$	0.949024	−	1.35535i	0.0376017	−	0.0537008i
$638$	13.4004	−	3.59062i	0.530526	−	0.142154i
$639$	12.8331	+	8.76452i	0.507669	+	0.346719i
$640$	−0.817132	−	2.08142i	−0.0323000	−	0.0822752i
$641$	−13.7302	−	37.7234i	−0.542310	−	1.48998i	−0.843876	−	0.536539i	$-0.819731\pi$
$641$	−13.7302	−	37.7234i	−0.542310	−	1.48998i	0.301566	−	0.953445i	$-0.402491\pi$
$642$	1.21263	−	0.941773i	0.0478588	−	0.0371688i
$643$	5.64374	−	0.493763i	0.222567	−	0.0194721i	0.0246734	−	0.999696i	$-0.492145\pi$
$643$	5.64374	−	0.493763i	0.222567	−	0.0194721i	0.197894	+	0.980223i	$0.436590\pi$
$644$	0.0950632	−	0.539130i	0.00374602	−	0.0212447i
$645$	7.08462	+	8.66546i	0.278957	+	0.341202i
$646$	−0.346699	+	0.161141i	−0.0136407	+	0.00634000i
$647$	7.88238	−	7.88238i	0.309888	−	0.309888i	−0.534978	−	0.844866i	$-0.679680\pi$
$647$	7.88238	−	7.88238i	0.309888	−	0.309888i	0.844866	+	0.534978i	$0.179680\pi$
$648$	0.575039	−	8.98161i	0.0225897	−	0.352831i
$649$	−1.97387	+	2.35237i	−0.0774813	+	0.0923387i
$650$	−0.655399	−	1.01432i	−0.0257069	−	0.0397848i
$651$	−1.55996	−	2.41742i	−0.0611397	−	0.0947462i
$652$	12.7329	+	1.11399i	0.498660	+	0.0436271i
$653$	−7.90374	+	29.4972i	−0.309297	+	1.15431i	0.619885	+	0.784692i	$0.287179\pi$
$653$	−7.90374	+	29.4972i	−0.309297	+	1.15431i	−0.929183	+	0.369621i	$0.879488\pi$
$654$	29.8209	+	9.21163i	1.16609	+	0.360203i
$655$	22.1157	+	29.9596i	0.864132	+	1.17062i
$656$	5.33590	−	0.940863i	0.208332	−	0.0367345i
$657$	−9.26883	+	7.96355i	−0.361612	+	0.310688i
$658$	0.0524850	+	0.0140633i	0.00204608	+	0.000548245i
$659$	31.4260	−	26.3696i	1.22418	−	1.02721i	0.225589	−	0.974223i	$-0.427569\pi$
$659$	31.4260	−	26.3696i	1.22418	−	1.02721i	0.998595	−	0.0529897i	$-0.0168751\pi$
$660$	−3.98515	−	15.6705i	−0.155122	−	0.609973i
$661$	−43.5416	−	15.8479i	−1.69357	−	0.616410i	−0.698505	−	0.715605i	$-0.746151\pi$
$661$	−43.5416	−	15.8479i	−1.69357	−	0.616410i	−0.995068	+	0.0991949i	$0.968373\pi$
$662$	−17.8308	+	1.55999i	−0.693012	+	0.0606307i
$663$	0.0271965	+	0.0246308i	0.00105623	+	0.000956579i
$664$		−	8.79366i		−	0.341260i
$665$	3.66302	+	0.888714i	0.142046	+	0.0344628i
$666$	−14.0512	−	29.2376i	−0.544474	−	1.13293i
$667$	−3.85334	+	2.69814i	−0.149202	+	0.104472i
$668$	1.82919	+	20.9078i	0.0707736	+	0.808946i
$669$	−11.4583	−	1.44057i	−0.443002	−	0.0556958i
$670$	1.96772	+	1.87160i	0.0760198	+	0.0723062i
$671$	18.9056	+	22.5309i	0.729844	+	0.869794i
$672$	0.0253137	−	0.669341i	0.000976497	−	0.0258204i
$673$	−7.07819	−	26.4162i	−0.272844	−	1.01827i	−0.957272	−	0.289188i	$-0.906615\pi$
$673$	−7.07819	−	26.4162i	−0.272844	−	1.01827i	0.684428	−	0.729080i	$-0.260052\pi$
$674$	−1.35326	−	7.67470i	−0.0521255	−	0.295618i
$675$	14.3885	−	21.6326i	0.553814	−	0.832640i
$676$	−6.47083	+	11.2078i	−0.248878	+	0.431070i
$677$	−22.0699	−	5.91360i	−0.848214	−	0.227278i	−0.191570	−	0.981479i	$-0.561358\pi$
$677$	−22.0699	−	5.91360i	−0.848214	−	0.227278i	−0.656644	+	0.754201i	$0.728025\pi$
$678$	−27.5494	+	3.79054i	−1.05803	+	0.145575i
$679$	1.45995	+	4.01118i	0.0560278	+	0.153935i
$680$	0.0219782	+	0.194889i	0.000842825	+	0.00747367i
$681$	6.50180	+	3.33657i	0.249149	+	0.127858i
$682$	14.6892	−	10.2855i	0.562480	−	0.393853i
$683$	−11.2707	−	11.2707i	−0.431262	−	0.431262i	0.457795	−	0.889058i	$-0.348639\pi$
$683$	−11.2707	−	11.2707i	−0.431262	−	0.431262i	−0.889058	+	0.457795i	$0.848639\pi$
$684$	−6.42006	+	11.3922i	−0.245477	+	0.435593i
$685$	−22.8900	−	7.68812i	−0.874582	−	0.293748i
$686$	5.27488	+	0.930103i	0.201396	+	0.0355115i
$687$	−35.3143	+	11.3614i	−1.34733	+	0.433466i
$688$	−2.61924	+	1.22137i	−0.0998574	+	0.0465643i
$689$	1.74999	−	0.636945i	0.0666693	−	0.0242657i
$690$	3.08712	+	4.53092i	0.117525	+	0.172489i
$691$	0.812393	+	1.40711i	0.0309049	+	0.0535288i	0.881064	−	0.472997i	$-0.156828\pi$
$691$	0.812393	+	1.40711i	0.0309049	+	0.0535288i	−0.850159	+	0.526526i	$0.823494\pi$
$692$	−0.0161914	−	0.0604273i	−0.000615507	−	0.00229710i
$693$	0.785377	−	4.77945i	0.0298340	−	0.181556i
$694$	−6.06280	+	1.06903i	−0.230141	+	0.0405800i
$695$	0.814260	−	13.0668i	0.0308867	−	0.495652i
$696$	−4.22070	+	3.91309i	−0.159985	+	0.148325i
$697$	−0.473421	−	0.0414190i	−0.0179321	−	0.00156886i
$698$	7.36012	+	3.43208i	0.278585	+	0.129906i
$699$	−2.20070	+	17.5043i	−0.0832383	+	0.662074i
$700$	1.02842	−	1.63743i	0.0388705	−	0.0618891i
$701$	−13.6591	−	2.40846i	−0.515896	−	0.0909664i	−0.0903625	−	0.995909i	$-0.528803\pi$
$701$	−13.6591	−	2.40846i	−0.515896	−	0.0909664i	−0.425534	+	0.904942i	$0.639914\pi$
$702$	1.24695	+	0.142017i	0.0470632	+	0.00536008i
$703$	−0.0589710	+	47.1324i	−0.00222413	+	1.77763i
$704$	4.17489			0.157347
$705$	−0.474706	+	0.266049i	−0.0178785	+	0.0100200i
$706$	−4.01795	−	3.37146i	−0.151217	−	0.126887i
$707$	−2.17595	+	1.01466i	−0.0818349	+	0.0381602i
$708$	0.268484	−	1.24538i	0.0100902	−	0.0468043i
$709$	−21.9263	−	26.1308i	−0.823460	−	0.981362i	0.176535	−	0.984294i	$-0.443511\pi$
$709$	−21.9263	−	26.1308i	−0.823460	−	0.981362i	−0.999996	+	0.00293245i	$0.999067\pi$
$710$	−11.3533	+	2.29627i	−0.426080	+	0.0861776i
$711$	−3.50600	+	46.2864i	−0.131485	+	1.73587i
$712$	0.896907	−	1.28092i	0.0336130	−	0.0480043i
$713$	−3.48759	+	4.98080i	−0.130611	+	0.186532i
$714$	−0.0173393	+	0.0561326i	−0.000648906	+	0.00210071i
$715$	2.20999	−	0.446986i	0.0826491	−	0.0167163i
$716$	13.4905	+	16.0773i	0.504164	+	0.600839i
$717$	28.6433	+	6.17502i	1.06970	+	0.230610i
$718$	21.3835	−	9.97131i	0.798027	−	0.372126i
$719$	23.4038	+	19.6381i	0.872815	+	0.732379i	0.964689	−	0.263392i	$-0.0848413\pi$
$719$	23.4038	+	19.6381i	0.872815	+	0.732379i	−0.0918741	+	0.995771i	$0.529286\pi$
$720$	4.49758	+	4.97712i	0.167615	+	0.185486i
$721$	6.15120			0.229083
$722$	15.5911	−	10.8590i	0.580241	−	0.404129i
$723$	15.7272	+	9.89084i	0.584900	+	0.367844i
$724$	1.14568	+	0.202014i	0.0425787	+	0.00750777i
$725$	−16.1976	+	3.70035i	−0.601563	+	0.137427i
$726$	11.0497	+	1.38920i	0.410091	+	0.0515581i
$727$	−32.2659	−	15.0458i	−1.19668	−	0.558019i	−0.280911	−	0.959734i	$-0.590637\pi$
$727$	−32.2659	−	15.0458i	−1.19668	−	0.558019i	−0.915765	+	0.401715i	$0.868414\pi$
$728$	0.0930483	+	0.00814067i	0.00344860	+	0.000301713i
$729$	7.89631	+	25.8195i	0.292456	+	0.956279i
$730$	0.566486	−	9.09065i	0.0209666	−	0.336460i
$731$	0.249630	−	0.0440166i	0.00923292	−	0.00162801i
$732$	−11.3004	−	4.60376i	−0.417676	−	0.170160i
$733$	5.71998	+	21.3473i	0.211272	+	0.788479i	0.987446	+	0.157960i	$0.0504916\pi$
$733$	5.71998	+	21.3473i	0.211272	+	0.788479i	−0.776173	+	0.630520i	$0.782842\pi$
$734$	2.77627	+	4.80865i	0.102474	+	0.177490i
$735$	−21.9260	+	14.9392i	−0.808753	+	0.551040i
$736$	−1.33024	+	0.484169i	−0.0490334	+	0.0178467i
$737$	−4.59528	+	2.14281i	−0.169269	+	0.0789315i
$738$	−13.9812	+	8.29097i	−0.514654	+	0.305195i
$739$	−9.88521	−	1.74303i	−0.363633	−	0.0641184i	−0.0111536	−	0.999938i	$-0.503550\pi$
$739$	−9.88521	−	1.74303i	−0.363633	−	0.0641184i	−0.352480	+	0.935819i	$0.614661\pi$
$740$	22.9202	+	7.69825i	0.842562	+	0.282993i
$741$	−1.54239	−	0.972707i	−0.0566612	−	0.0357333i
$742$	2.10846	+	2.10846i	0.0774040	+	0.0774040i
$743$	−20.5542	+	14.3922i	−0.754062	+	0.528000i	−0.886240	−	0.463226i	$-0.846692\pi$
$743$	−20.5542	+	14.3922i	−0.754062	+	0.528000i	0.132178	+	0.991226i	$0.457803\pi$
$744$	−3.39668	+	6.61893i	−0.124528	+	0.242662i
$745$	−2.35693	−	20.8999i	−0.0863513	−	0.765712i
$746$	−5.55022	−	15.2491i	−0.203208	−	0.558310i
$747$	9.31138	+	24.6831i	0.340686	+	0.903107i
$748$	−0.353701	−	0.0947740i	−0.0129326	−	0.00346528i
$749$	−0.171405	+	0.296883i	−0.00626301	+	0.0108479i
$750$	4.07141	+	18.9321i	0.148667	+	0.691302i
$751$	4.45158	+	25.2461i	0.162440	+	0.921245i	0.951664	+	0.307140i	$0.0993719\pi$
$751$	4.45158	+	25.2461i	0.162440	+	0.921245i	−0.789224	+	0.614105i	$0.789517\pi$
$752$	−0.0363656	−	0.135718i	−0.00132612	−	0.00494913i
$753$	−51.4192	−	1.94462i	−1.87382	−	0.0708657i
$754$	−0.515895	−	0.614820i	−0.0187878	−	0.0223904i
$755$	9.76249	+	9.28558i	0.355293	+	0.337937i
$756$	0.637694	+	1.90559i	0.0231927	+	0.0693056i
$757$	0.350298	+	4.00393i	0.0127318	+	0.145525i	0.999900	−	0.0141603i	$-0.00450752\pi$
$757$	0.350298	+	4.00393i	0.0127318	+	0.145525i	−0.987168	+	0.159686i	$0.948952\pi$
$758$	7.18718	−	5.03252i	0.261050	−	0.182789i
$759$	−9.98076	+	2.27383i	−0.362279	+	0.0825349i
$760$	−2.74581	−	9.35203i	−0.0996009	−	0.339234i
$761$		−	0.572699i		−	0.0207603i	−0.999946	−	0.0103802i	$-0.996696\pi$
$761$		−	0.572699i		−	0.0207603i	0.999946	−	0.0103802i	$-0.00330417\pi$
$762$	−24.1314	+	26.6452i	−0.874189	+	0.965252i
$763$	−6.94212	+	0.607357i	−0.251321	+	0.0219878i
$764$	−6.49414	−	2.36367i	−0.234950	−	0.0855147i
$765$	−0.268054	−	0.523766i	−0.00969152	−	0.0189368i
$766$	−22.7208	+	19.0650i	−0.820936	+	0.688847i
$767$	0.171600	+	0.0459801i	0.00619611	+	0.00166024i
$768$	−1.53166	+	0.808719i	−0.0552689	+	0.0291821i
$769$	35.8121	−	6.31464i	1.29142	−	0.227712i	0.514597	−	0.857432i	$-0.327942\pi$
$769$	35.8121	−	6.31464i	1.29142	−	0.227712i	0.776822	+	0.629721i	$0.216831\pi$
$770$	2.14408	+	2.90452i	0.0772672	+	0.104672i
$771$	−10.1995	+	33.0190i	−0.367327	+	1.18915i
$772$	−1.71385	+	6.39616i	−0.0616827	+	0.230203i
$773$	19.7957	+	1.73190i	0.712001	+	0.0622920i	0.437401	−	0.899267i	$-0.355899\pi$
$773$	19.7957	+	1.73190i	0.712001	+	0.0622920i	0.274600	+	0.961559i	$0.411455\pi$
$774$	6.05870	−	6.20172i	0.217775	−	0.222916i
$775$	−18.0383	+	11.6554i	−0.647956	+	0.418675i
$776$	7.09508	−	8.45558i	0.254698	−	0.303538i
$777$	5.36833	+	4.86187i	0.192588	+	0.174419i
$778$	7.95021	−	7.95021i	0.285029	−	0.285029i
$779$	23.5301	−	2.02896i	0.843055	−	0.0726950i
$780$	−0.724202	+	0.592086i	−0.0259306	+	0.0212001i
$781$	3.75541	−	21.2980i	0.134379	−	0.762102i
$782$	0.123691	−	0.0108215i	0.00442317	−	0.000386977i
$783$	7.70368	−	15.4529i	0.275307	−	0.552242i
$784$	−2.34299	−	6.43731i	−0.0836782	−	0.229904i
$785$	−12.2282	−	31.1480i	−0.436443	−	1.11172i
$786$	21.1524	−	19.6108i	0.754482	−	0.699494i
$787$	22.6080	−	6.05780i	0.805889	−	0.215937i	0.167721	−	0.985834i	$-0.446359\pi$
$787$	22.6080	−	6.05780i	0.805889	−	0.215937i	0.638168	+	0.769897i	$0.279692\pi$
$788$	−9.80855	+	14.0081i	−0.349415	+	0.499017i
$789$	−23.3466	+	9.83038i	−0.831160	+	0.349971i
$790$	−22.8960	−	25.9392i	−0.814602	−	0.922874i
$791$	5.37715	−	3.10450i	0.191189	−	0.110383i
$792$	−11.7186	+	4.42069i	−0.416402	+	0.157082i
$793$	0.719107	−	1.54213i	0.0255362	−	0.0547626i
$794$	32.1016	+	11.6840i	1.13924	+	0.414651i
$795$	−29.8602	−	0.381309i	−1.05903	−	0.0135237i
$796$	−0.497875	+	2.82359i	−0.0176467	+	0.100079i
$797$	−23.4098	+	23.4098i	−0.829218	+	0.829218i	−0.987409	−	0.158191i	$-0.949434\pi$
$797$	−23.4098	+	23.4098i	−0.829218	+	0.829218i	0.158191	+	0.987409i	$0.449434\pi$
$798$	0.367829	−	2.89641i	0.0130210	−	0.102532i
$799$			0.0123237i			0.000435982i
$800$	−4.99654	−	0.185972i	−0.176654	−	0.00657512i
$801$	−1.16122	+	4.54514i	−0.0410295	+	0.160595i
$802$	1.42616	+	3.05840i	0.0503593	+	0.107996i
$803$	15.4125	+	7.18696i	0.543895	+	0.253622i
$804$	1.27080	−	1.67629i	0.0448177	−	0.0591183i
$805$	−1.02001	−	0.676814i	−0.0359506	−	0.0238546i
$806$	−0.898435	−	0.518712i	−0.0316460	−	0.0182708i
$807$	14.4220	−	35.4003i	0.507677	−	1.24615i
$808$	5.08557	+	3.56096i	0.178910	+	0.125274i
$809$	−11.0805	+	19.1920i	−0.389570	+	0.674755i	−0.992392	−	0.123121i	$-0.960710\pi$
$809$	−11.0805	+	19.1920i	−0.389570	+	0.674755i	0.602822	+	0.797876i	$0.294043\pi$
$810$	−17.8945	−	9.20801i	−0.628748	−	0.323536i
$811$	7.54351	−	6.32975i	0.264888	−	0.222268i	−0.500663	−	0.865642i	$-0.666911\pi$
$811$	7.54351	−	6.32975i	0.264888	−	0.222268i	0.765552	+	0.643374i	$0.222466\pi$
$812$	0.543091	−	1.16466i	0.0190588	−	0.0408717i
$813$	−16.4514	−	21.1829i	−0.576976	−	0.742918i
$814$	−29.0172	+	34.5814i	−1.01705	+	1.21208i
$815$	13.6662	−	25.1013i	0.478708	−	0.879261i
$816$	0.148122	−	0.0337455i	0.00518531	−	0.00118133i
$817$	−11.8429	+	4.29370i	−0.414331	+	0.150217i
$818$	10.5334	+	10.5334i	0.368293	+	0.368293i
$819$	−0.269799	+	0.0756762i	−0.00942753	+	0.00264434i
$820$	2.84183	−	11.7775i	0.0992411	−	0.411288i
$821$	−16.1110	+	44.2647i	−0.562279	+	1.54485i	0.254009	+	0.967202i	$0.418251\pi$
$821$	−16.1110	+	44.2647i	−0.562279	+	1.54485i	−0.816287	+	0.577646i	$0.803971\pi$
$822$	−3.94169	+	18.2838i	−0.137482	+	0.637722i
$823$	1.49824	−	17.1250i	0.0522255	−	0.596940i	−0.924318	−	0.381622i	$-0.875366\pi$
$823$	1.49824	−	17.1250i	0.0522255	−	0.596940i	0.976544	−	0.215318i	$-0.0690789\pi$
$824$	−7.95303	−	13.7751i	−0.277057	−	0.479877i
$825$	−35.6807	−	5.84127i	−1.24224	−	0.203367i
$826$	0.0493940	+	0.280127i	0.00171864	+	0.00974687i
$827$	−45.6617	−	31.9727i	−1.58781	−	1.11180i	−0.935206	−	0.354104i	$-0.884786\pi$
$827$	−45.6617	−	31.9727i	−1.58781	−	1.11180i	−0.652608	−	0.757695i	$-0.726325\pi$
$828$	3.22121	−	2.76758i	0.111945	−	0.0961801i
$829$	−14.3311	+	8.27408i	−0.497741	+	0.287371i	−0.727780	−	0.685811i	$-0.759448\pi$
$829$	−14.3311	+	8.27408i	−0.497741	+	0.287371i	0.230039	+	0.973181i	$0.426114\pi$
$830$	−18.0233	−	7.86139i	−0.625599	−	0.272873i
$831$	24.6903	+	38.2618i	0.856498	+	1.32729i
$832$	−0.102074	−	0.218898i	−0.00353878	−	0.00758894i
$833$	0.0523676	+	0.598564i	0.00181443	+	0.0207390i
$834$	−10.1287	+	0.501433i	−0.350729	+	0.0173632i
$835$	44.4875	+	14.9421i	1.53955	+	0.517093i
$836$	18.1267	+	1.60874i	0.626925	+	0.0556393i
$837$	2.52559	−	22.1755i	0.0872970	−	0.766496i
$838$	16.5950	+	23.7001i	0.573265	+	0.818707i
$839$	−30.6010	−	25.6773i	−1.05646	−	0.886478i	−0.0627052	−	0.998032i	$-0.519973\pi$
$839$	−30.6010	−	25.6773i	−1.05646	−	0.886478i	−0.993758	+	0.111554i	$0.964417\pi$
$840$	−1.34924	−	0.650263i	−0.0465532	−	0.0224362i
$841$	16.8748	−	6.14194i	0.581891	−	0.211791i
$842$	−2.26767	+	25.9196i	−0.0781492	+	0.893250i
$843$	−45.2592	−	1.71165i	−1.55881	−	0.0589523i
$844$	19.8535	+	11.4624i	0.683386	+	0.394553i
$845$	17.1865	+	23.2821i	0.591234	+	0.800929i
$846$	0.245784	+	0.342443i	0.00845021	+	0.0117734i
$847$	−2.40179	+	0.643557i	−0.0825264	+	0.0221129i
$848$	1.99563	−	7.44778i	0.0685301	−	0.255758i
$849$	22.0024	−	29.0231i	0.755122	−	0.996069i
$850$	0.419090	+	0.129182i	0.0143747	+	0.00443090i
$851$	5.23528	−	14.3838i	0.179463	−	0.493071i
$852$	2.74787	+	8.54112i	0.0941406	+	0.292614i
$853$	−11.1056	−	15.8605i	−0.380249	−	0.543052i	0.582717	−	0.812675i	$-0.301990\pi$
$853$	−11.1056	−	15.8605i	−0.380249	−	0.543052i	−0.962966	+	0.269623i	$0.913101\pi$
$854$	2.72443			0.0932280
$855$	17.6099	+	23.3429i	0.602245	+	0.798311i
$856$	0.886456			0.0302984
$857$	−22.1315	−	31.6070i	−0.755996	−	1.07967i	−0.994103	−	0.108436i	$-0.965416\pi$
$857$	−22.1315	−	31.6070i	−0.755996	−	1.07967i	0.238107	−	0.971239i	$-0.423473\pi$
$858$	−0.534894	−	1.66259i	−0.0182610	−	0.0567600i
$859$	7.57765	−	20.8194i	0.258546	−	0.710349i	−0.740712	−	0.671823i	$-0.765511\pi$
$859$	7.57765	−	20.8194i	0.258546	−	0.710349i	0.999258	−	0.0385262i	$-0.0122663\pi$
$860$	0.161744	+	6.46023i	0.00551543	+	0.220292i
$861$	2.19250	−	2.89210i	0.0747203	−	0.0985624i
$862$	−1.19313	+	4.45283i	−0.0406382	+	0.151664i
$863$	6.48934	−	1.73881i	0.220900	−	0.0591899i	−0.146672	−	0.989185i	$-0.546856\pi$
$863$	6.48934	−	1.73881i	0.220900	−	0.0591899i	0.367571	+	0.929995i	$0.380189\pi$
$864$	3.44290	−	3.89184i	0.117130	−	0.132403i
$865$	−0.138326	−	0.0208353i	−0.00470322	−	0.000708422i
$866$	−0.547569	−	0.316139i	−0.0186072	−	0.0107428i
$867$	29.4105	+	1.11227i	0.998833	+	0.0377747i
$868$	0.144771	−	1.65474i	0.00491386	−	0.0561656i
$869$	60.7023	−	22.0938i	2.05919	−	0.749482i
$870$	4.24696	+	12.1489i	0.143986	+	0.411887i
$871$	0.224704	+	0.188549i	0.00761382	+	0.00638875i
$872$	10.3357	+	14.7610i	0.350012	+	0.499870i
$873$	−10.9619	+	31.2469i	−0.371004	+	1.05755i
$874$	−5.96226	+	1.58959i	−0.201677	+	0.0537687i
$875$	−2.43666	−	3.57166i	−0.0823742	−	0.120744i
$876$	−7.04661	+	0.348850i	−0.238083	+	0.0117865i
$877$	1.11708	+	12.7682i	0.0377210	+	0.431153i	0.991450	+	0.130486i	$0.0416537\pi$
$877$	1.11708	+	12.7682i	0.0377210	+	0.431153i	−0.953729	+	0.300667i	$0.902791\pi$
$878$	16.5248	+	35.4375i	0.557684	+	1.19596i
$879$	5.36613	+	8.31571i	0.180995	+	0.280482i
$880$	3.73229	−	8.55679i	0.125815	−	0.288449i
$881$	6.52795	−	3.76891i	0.219932	−	0.126978i	−0.385987	−	0.922504i	$-0.626139\pi$
$881$	6.52795	−	3.76891i	0.219932	−	0.126978i	0.605919	+	0.795526i	$0.292806\pi$
$882$	13.3929	+	15.5881i	0.450962	+	0.524878i
$883$	38.8516	+	27.2042i	1.30746	+	0.915493i	0.999357	−	0.0358594i	$-0.0114169\pi$
$883$	38.8516	+	27.2042i	1.30746	+	0.915493i	0.308103	+	0.951353i	$0.400306\pi$
$884$	0.00367862	+	0.0208625i	0.000123725	+	0.000701681i
$885$	−2.31249	−	1.66363i	−0.0777336	−	0.0559223i
$886$	16.2581	+	28.1598i	0.546200	+	0.946047i
$887$	−1.66160	+	18.9921i	−0.0557910	+	0.637694i	0.915895	+	0.401418i	$0.131482\pi$
$887$	−1.66160	+	18.9921i	−0.0557910	+	0.637694i	−0.971686	+	0.236276i	$0.924073\pi$
$888$	3.94688	−	18.3079i	0.132449	−	0.614374i
$889$	2.74516	−	7.54227i	0.0920698	−	0.252960i
$890$	−1.82352	−	2.98340i	−0.0611246	−	0.100004i
$891$	28.2121	−	24.8170i	0.945142	−	0.831401i
$892$	−4.71464	−	4.71464i	−0.157858	−	0.157858i
$893$	−0.105596	−	0.603279i	−0.00353364	−	0.0201879i
$894$	−15.8846	+	3.61885i	−0.531260	+	0.121032i
$895$	45.0122	−	13.2770i	1.50459	−	0.443801i
$896$	0.248579	−	0.296245i	0.00830445	−	0.00989685i
$897$	0.363246	+	0.467718i	0.0121284	+	0.0156166i
$898$	−11.4542	+	24.5635i	−0.382230	+	0.819696i
$899$	−10.9338	+	9.17454i	−0.364662	+	0.305988i
$900$	14.2218	−	4.76870i	0.474060	−	0.158957i
$901$	−0.338143	+	0.585681i	−0.0112652	+	0.0195119i
$902$	18.5296	+	12.9746i	0.616968	+	0.432006i
$903$	−0.730348	+	1.79272i	−0.0243045	+	0.0596580i
$904$	−13.9045	−	8.02775i	−0.462456	−	0.266999i
$905$	1.43826	−	2.16756i	0.0478094	−	0.0720522i
$906$	6.30483	−	8.31661i	0.209464	−	0.276301i
$907$	25.2368	+	11.7681i	0.837974	+	0.390754i	0.793732	−	0.608267i	$-0.208135\pi$
$907$	25.2368	+	11.7681i	0.837974	+	0.390754i	0.0442415	+	0.999021i	$0.485913\pi$
$908$	1.78313	+	3.82393i	0.0591752	+	0.126902i
$909$	−18.0454	−	4.61033i	−0.598528	−	0.152915i
$910$	0.0998686	−	0.183433i	0.00331061	−	0.00608073i
$911$			12.2429i			0.405624i	0.979218	+	0.202812i	$0.0650080\pi$
$911$			12.2429i			0.405624i	−0.979218	+	0.202812i	$0.934992\pi$
$912$	−6.96183	+	2.92112i	−0.230529	+	0.0967280i
$913$	25.9597	−	25.9597i	0.859142	−	0.859142i
$914$	6.16481	−	34.9624i	0.203914	−	1.15645i
$915$	−19.5382	+	19.0455i	−0.645912	+	0.629624i
$916$	−20.1263	−	7.32537i	−0.664991	−	0.242037i
$917$	−2.72175	+	5.83682i	−0.0898802	+	0.192749i
$918$	−0.380035	+	0.251564i	−0.0125430	+	0.00830283i
$919$	34.4053	−	19.8639i	1.13493	−	0.655250i	0.189757	−	0.981831i	$-0.439230\pi$
$919$	34.4053	−	19.8639i	1.13493	−	0.655250i	0.945169	+	0.326581i	$0.105897\pi$
$920$	−0.196872	+	3.15928i	−0.00649066	+	0.104158i
$921$	−10.3860	+	4.37318i	−0.342231	+	0.144101i
$922$	−8.94859	+	12.7799i	−0.294706	+	0.420884i
$923$	−1.20852	+	0.323821i	−0.0397788	+	0.0106587i
$924$	2.05069	−	1.90123i	0.0674627	−	0.0625459i
$925$	36.2685	−	40.0947i	1.19250	−	1.31830i
$926$	8.19000	+	22.5018i	0.269140	+	0.739456i
$927$	36.9096	+	30.2442i	1.21227	+	0.993349i
$928$	−3.31033	+	0.289617i	−0.108667	+	0.00950713i
$929$	−4.73144	+	26.8333i	−0.155234	+	0.880373i	0.803338	+	0.595523i	$0.203055\pi$
$929$	−4.73144	+	26.8333i	−0.155234	+	0.880373i	−0.958572	+	0.284850i	$0.908056\pi$
$930$	10.5295	+	12.8790i	0.345275	+	0.422319i
$931$	−7.69235	−	28.8526i	−0.252107	−	0.945605i
$932$	−7.20237	+	7.20237i	−0.235921	+	0.235921i
$933$	9.86559	+	8.93485i	0.322985	+	0.292514i
$934$	8.61404	−	10.2658i	0.281860	−	0.335907i
$935$	−0.510450	+	0.640214i	−0.0166935	+	0.0209372i
$936$	0.518299	+	0.506346i	0.0169411	+	0.0165504i
$937$	−58.4025	−	5.10956i	−1.90793	−	0.166922i	−0.928855	−	0.370443i	$-0.879206\pi$
$937$	−58.4025	−	5.10956i	−1.90793	−	0.166922i	−0.979071	+	0.203521i	$0.934762\pi$
$938$	−0.121558	+	0.453661i	−0.00396901	+	0.0148126i
$939$	9.87082	−	31.9549i	0.322122	−	1.04281i
$940$	−0.310676	−	0.0467956i	−0.0101331	−	0.00152630i
$941$	−38.7934	+	6.84033i	−1.26463	+	0.222988i	−0.765441	−	0.643506i	$-0.777479\pi$
$941$	−38.7934	+	6.84033i	−1.26463	+	0.222988i	−0.499188	+	0.866494i	$0.666368\pi$
$942$	−22.9209	+	12.1023i	−0.746804	+	0.394314i
$943$	−7.40875	−	1.98517i	−0.241262	−	0.0646460i
$944$	0.563457	−	0.472796i	0.0183389	−	0.0153882i
$945$	4.47575	+	0.396558i	0.145596	+	0.0129000i
$946$	−11.3378	−	4.12663i	−0.368625	−	0.134168i
$947$	−12.9176	+	1.13014i	−0.419765	+	0.0367246i	−0.295082	−	0.955472i	$-0.595347\pi$
$947$	−12.9176	+	1.13014i	−0.419765	+	0.0367246i	−0.124683	+	0.992197i	$0.539791\pi$
$948$	−17.9903	+	19.8643i	−0.584296	+	0.645162i
$949$		−	0.983826i		−	0.0319363i
$950$	−21.6225	−	2.73281i	−0.701526	−	0.0886640i
$951$	−46.6267	+	10.6226i	−1.51198	+	0.344461i
$952$	−0.0277849	+	0.0194552i	−0.000900514	+	0.000630547i
$953$	1.00311	+	11.4656i	0.0324939	+	0.371407i	0.994980	+	0.100075i	$0.0319084\pi$
$953$	1.00311	+	11.4656i	0.0324939	+	0.371407i	−0.962486	+	0.271331i	$0.912536\pi$
$954$	2.28470	+	23.0184i	0.0739699	+	0.745249i
$955$	−10.6502	+	11.1972i	−0.344632	+	0.362333i
$956$	10.8741	+	12.9593i	0.351694	+	0.419133i
$957$	−24.0117	−	0.908095i	−0.776188	−	0.0293545i
$958$	4.25428	+	15.8772i	0.137450	+	0.512969i
$959$	−0.725168	−	4.11263i	−0.0234169	−	0.132804i
$960$	0.288260	+	3.86224i	0.00930356	+	0.124653i
$961$	6.27538	−	10.8693i	0.202432	−	0.350622i
$962$	2.52263	+	0.675937i	0.0813329	+	0.0217931i
$963$	−2.48821	+	0.938645i	−0.0801814	+	0.0302474i
$964$	3.66868	+	10.0796i	0.118160	+	0.324642i
$965$	11.5773	+	9.23074i	0.372687	+	0.297148i
$966$	−0.432920	+	0.843609i	−0.0139290	+	0.0271427i
$967$	16.9105	−	11.8408i	0.543804	−	0.380776i	−0.269155	−	0.963097i	$-0.586744\pi$
$967$	16.9105	−	11.8408i	0.543804	−	0.380776i	0.812959	+	0.582321i	$0.197855\pi$
$968$	4.54651	+	4.54651i	0.146130	+	0.146130i
$969$	0.656125	−	0.0894404i	0.0210778	−	0.00287324i
$970$	−10.9875	−	22.1011i	−0.352789	−	0.709624i
$971$	47.5183	+	8.37876i	1.52494	+	0.268887i	0.872370	−	0.488846i	$-0.162582\pi$
$971$	47.5183	+	8.37876i	1.52494	+	0.268887i	0.652565	+	0.757733i	$0.273693\pi$
$972$	−5.54298	+	14.5697i	−0.177791	+	0.467322i
$973$	2.05210	−	0.956910i	0.0657873	−	0.0306771i
$974$	24.5481	−	8.93478i	0.786572	−	0.286289i
$975$	0.566104	+	2.01363i	0.0181298	+	0.0644877i
$976$	−3.52248	−	6.10111i	−0.112752	−	0.195292i
$977$	11.3226	+	42.2564i	0.362241	+	1.35190i	0.871122	+	0.491066i	$0.163393\pi$
$977$	11.3226	+	42.2564i	0.362241	+	1.35190i	−0.508881	+	0.860837i	$0.669941\pi$
$978$	−20.5022	−	8.35253i	−0.655588	−	0.267085i
$979$	6.42914	−	1.13363i	0.205476	−	0.0362310i
$980$	−15.2884	−	0.952701i	−0.488370	−	0.0304329i
$981$	−44.6416	−	30.4886i	−1.42530	−	0.973426i
$982$	−18.3972	−	1.60955i	−0.587079	−	0.0513627i
$983$	−23.7329	−	11.0668i	−0.756961	−	0.352977i	0.00552231	−	0.999985i	$-0.498242\pi$
$983$	−23.7329	−	11.0668i	−0.756961	−	0.352977i	−0.762483	+	0.647008i	$0.776020\pi$
$984$	−9.31132	−	1.17065i	−0.296834	−	0.0373190i
$985$	19.9420	+	32.6264i	0.635405	+	1.03956i
$986$	0.287029	+	0.0506110i	0.00914087	+	0.00161178i
$987$	−0.0796681	−	0.0501033i	−0.00253586	−	0.00159481i
$988$	−0.358839	−	0.989753i	−0.0114162	−	0.0314882i
$989$	4.09114			0.130091
$990$	−1.41566	+	27.9702i	−0.0449926	+	0.888953i
$991$	9.46615	+	7.94304i	0.300702	+	0.252319i	0.780636	−	0.624985i	$-0.214895\pi$
$991$	9.46615	+	7.94304i	0.300702	+	0.252319i	−0.479934	+	0.877304i	$0.659340\pi$
$992$	−3.89283	+	1.81525i	−0.123597	+	0.0576344i
$993$	30.3055	+	6.53336i	0.961716	+	0.207330i
$994$	−1.28768	−	1.53459i	−0.0408426	−	0.0486743i
$995$	5.34209	+	3.54468i	0.169356	+	0.112374i
$996$	−4.49527	+	14.5526i	−0.142438	+	0.461117i
$997$	11.1338	−	15.9007i	0.352610	−	0.503579i	−0.603190	−	0.797598i	$-0.706104\pi$
$997$	11.1338	−	15.9007i	0.352610	−	0.503579i	0.955800	+	0.294019i	$0.0949927\pi$
$998$	6.02583	−	8.60578i	0.190744	−	0.272411i
$999$	8.30720	+	55.5681i	0.262828	+	1.75810i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bi.a.17.12	✓	480
3.2	odd	2	inner	570.2.bi.a.17.31	yes	480
5.3	odd	4	inner	570.2.bi.a.473.1	yes	480
15.8	even	4	inner	570.2.bi.a.473.40	yes	480
19.9	even	9	inner	570.2.bi.a.47.40	yes	480
57.47	odd	18	inner	570.2.bi.a.47.1	yes	480
95.28	odd	36	inner	570.2.bi.a.503.31	yes	480
285.218	even	36	inner	570.2.bi.a.503.12	yes	480

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.12	✓	480	1.1	even	1	trivial
570.2.bi.a.17.31	yes	480	3.2	odd	2	inner
570.2.bi.a.47.1	yes	480	57.47	odd	18	inner
570.2.bi.a.47.40	yes	480	19.9	even	9	inner
570.2.bi.a.473.1	yes	480	5.3	odd	4	inner
570.2.bi.a.473.40	yes	480	15.8	even	4	inner
570.2.bi.a.503.12	yes	480	285.218	even	36	inner
570.2.bi.a.503.31	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)

\(f(q)\)	\(=\)	\(q+(-0.573576 - 0.819152i) q^{2} +(0.530463 + 1.64882i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.62022 + 1.54107i) q^{5} +(1.04637 - 1.38025i) q^{6} +(-0.100091 + 0.373543i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.43722 + 1.74928i) q^{9} +O(q^{10})\)	\(q+(-0.573576 - 0.819152i) q^{2} +(0.530463 + 1.64882i) q^{3} +(-0.342020 + 0.939693i) q^{4} +(1.62022 + 1.54107i) q^{5} +(1.04637 - 1.38025i) q^{6} +(-0.100091 + 0.373543i) q^{7} +(0.965926 - 0.258819i) q^{8} +(-2.43722 + 1.74928i) q^{9} +(0.333051 - 2.21113i) q^{10} +(3.61556 + 2.08745i) q^{11} +(-1.73081 - 0.0654573i) q^{12} +(0.0210505 - 0.240609i) q^{13} +(0.363398 - 0.132266i) q^{14} +(-1.68148 + 3.48893i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(0.0503082 + 0.0718475i) q^{17} +(2.83085 + 0.993107i) q^{18} +(-3.07835 - 3.08606i) q^{19} +(-2.00228 + 0.995430i) q^{20} +(-0.669000 + 0.0331196i) q^{21} +(-0.363866 - 4.15901i) q^{22} +(0.598265 + 1.28298i) q^{23} +(0.939134 + 1.45534i) q^{24} +(0.250212 + 4.99374i) q^{25} +(-0.209169 + 0.120764i) q^{26} +(-4.17710 - 3.09061i) q^{27} +(-0.316783 - 0.221814i) q^{28} +(0.577029 + 3.27249i) q^{29} +(3.82242 - 0.623780i) q^{30} +(2.14763 + 3.71980i) q^{31} +(-0.0871557 + 0.996195i) q^{32} +(-1.52390 + 7.06873i) q^{33} +(0.0299985 - 0.0824201i) q^{34} +(-0.737825 + 0.450975i) q^{35} +(-0.810206 - 2.88852i) q^{36} +(-7.64589 - 7.64589i) q^{37} +(-0.762285 + 4.29173i) q^{38} +(0.407887 - 0.0929255i) q^{39} +(1.96387 + 1.06922i) q^{40} +(-3.48276 + 4.15059i) q^{41} +(0.410853 + 0.529016i) q^{42} +(1.22137 - 2.61924i) q^{43} +(-3.19815 + 2.68357i) q^{44} +(-6.64458 - 0.921709i) q^{45} +(0.707808 - 1.22596i) q^{46} +(0.115096 + 0.0805908i) q^{47} +(0.653483 - 1.60404i) q^{48} +(5.93266 + 3.42522i) q^{49} +(3.94711 - 3.06925i) q^{50} +(-0.0917770 + 0.121062i) q^{51} +(0.218898 + 0.102074i) q^{52} +(3.25860 + 6.98810i) q^{53} +(-0.135791 + 5.19438i) q^{54} +(2.64110 + 8.95395i) q^{55} +0.386720i q^{56} +(3.45541 - 6.71269i) q^{57} +(2.34970 - 2.34970i) q^{58} +(-0.127725 + 0.724366i) q^{59} +(-2.70342 - 2.77336i) q^{60} +(6.62009 + 2.40952i) q^{61} +(1.81525 - 3.89283i) q^{62} +(-0.409488 - 1.08549i) q^{63} +(0.866025 - 0.500000i) q^{64} +(0.404901 - 0.357398i) q^{65} +(6.66444 - 2.80615i) q^{66} +(-0.696598 + 0.994844i) q^{67} +(-0.0847210 + 0.0227009i) q^{68} +(-1.79805 + 1.66701i) q^{69} +(0.792616 + 0.345722i) q^{70} +(-1.77171 - 4.86774i) q^{71} +(-1.90142 + 2.32047i) q^{72} +(4.05785 - 0.355016i) q^{73} +(-1.87764 + 10.6486i) q^{74} +(-8.10104 + 3.06155i) q^{75} +(3.95281 - 1.83721i) q^{76} +(-1.14164 + 1.14164i) q^{77} +(-0.310074 - 0.280821i) q^{78} +(9.94584 - 11.8530i) q^{79} +(-0.250579 - 2.22198i) q^{80} +(2.88006 - 8.52674i) q^{81} +(5.39760 + 0.472229i) q^{82} +(2.27597 - 8.49403i) q^{83} +(0.197689 - 0.639982i) q^{84} +(-0.0292118 + 0.193937i) q^{85} +(-2.84610 + 0.501844i) q^{86} +(-5.08966 + 2.68736i) q^{87} +(4.03264 + 1.08054i) q^{88} +(1.19787 - 1.00513i) q^{89} +(3.05615 + 5.97159i) q^{90} +(0.0877708 + 0.0319459i) q^{91} +(-1.41023 + 0.123379i) q^{92} +(-4.99405 + 5.51427i) q^{93} -0.140506i q^{94} +(-0.231762 - 9.74404i) q^{95} +(-1.68878 + 0.384741i) q^{96} +(9.04178 - 6.33112i) q^{97} +(-0.597056 - 6.82438i) q^{98} +(-12.4634 + 1.23706i) 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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