LMFDB - Embedded newform 570.2.bi.a.473.40

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			473.40
Character	$\chi$	$=$	570.473
Dual form			570.2.bi.a.47.40

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.819152 - 0.573576i) q^{2} +(1.71589 + 0.236090i) q^{3} +(0.342020 - 0.939693i) q^{4} +(0.250579 - 2.22198i) q^{5} +(1.54099 - 0.790798i) q^{6} +(0.373543 + 0.100091i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(2.88852 + 0.810206i) q^{9} +O(q^{10})$	\(q+(0.819152 - 0.573576i) q^{2} +(1.71589 + 0.236090i) q^{3} +(0.342020 - 0.939693i) q^{4} +(0.250579 - 2.22198i) q^{5} +(1.54099 - 0.790798i) q^{6} +(0.373543 + 0.100091i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(2.88852 + 0.810206i) q^{9} +(-1.06922 - 1.96387i) q^{10} +(-3.61556 - 2.08745i) q^{11} +(0.808719 - 1.53166i) q^{12} +(0.240609 + 0.0210505i) q^{13} +(0.363398 - 0.132266i) q^{14} +(0.954552 - 3.75351i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-0.0718475 + 0.0503082i) q^{17} +(2.83085 - 0.993107i) q^{18} +(3.07835 + 3.08606i) q^{19} +(-2.00228 - 0.995430i) q^{20} +(0.617327 + 0.259934i) q^{21} +(-4.15901 + 0.363866i) q^{22} +(1.28298 - 0.598265i) q^{23} +(-0.216059 - 1.71852i) q^{24} +(-4.87442 - 1.11356i) q^{25} +(0.209169 - 0.120764i) q^{26} +(4.76509 + 2.07217i) q^{27} +(0.221814 - 0.316783i) q^{28} +(0.577029 + 3.27249i) q^{29} +(-1.37100 - 3.62220i) q^{30} +(2.14763 + 3.71980i) q^{31} +(-0.996195 - 0.0871557i) q^{32} +(-5.71107 - 4.43542i) q^{33} +(-0.0299985 + 0.0824201i) q^{34} +(0.316002 - 0.804926i) q^{35} +(1.74928 - 2.43722i) q^{36} +(-7.64589 + 7.64589i) q^{37} +(4.29173 + 0.762285i) q^{38} +(0.407887 + 0.0929255i) q^{39} +(-2.21113 + 0.333051i) q^{40} +(3.48276 - 4.15059i) q^{41} +(0.654777 - 0.141159i) q^{42} +(2.61924 + 1.22137i) q^{43} +(-3.19815 + 2.68357i) q^{44} +(2.52407 - 6.21523i) q^{45} +(0.707808 - 1.22596i) q^{46} +(-0.0805908 + 0.115096i) q^{47} +(-1.16269 - 1.28380i) q^{48} +(-5.93266 - 3.42522i) q^{49} +(-4.63161 + 1.88367i) q^{50} +(-0.135159 + 0.0693606i) q^{51} +(0.102074 - 0.218898i) q^{52} +(6.98810 - 3.25860i) q^{53} +(5.09188 - 1.03572i) q^{54} +(-5.54426 + 7.51065i) q^{55} -0.386720i q^{56} +(4.55350 + 6.02209i) q^{57} +(2.34970 + 2.34970i) q^{58} +(-0.127725 + 0.724366i) q^{59} +(-3.20067 - 2.18076i) q^{60} +(6.62009 + 2.40952i) q^{61} +(3.89283 + 1.81525i) q^{62} +(0.997895 + 0.591761i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(0.107065 - 0.529353i) q^{65} +(-7.22228 - 0.357547i) q^{66} +(0.994844 + 0.696598i) q^{67} +(0.0227009 + 0.0847210i) q^{68} +(2.34270 - 0.723655i) q^{69} +(-0.202833 - 0.840608i) q^{70} +(1.77171 + 4.86774i) q^{71} +(0.0349938 - 2.99980i) q^{72} +(0.355016 + 4.05785i) 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} +(0.387421 - 0.157834i) q^{78} +(-9.94584 + 11.8530i) q^{79} +(-1.62022 + 1.54107i) q^{80} +(7.68713 + 4.68060i) q^{81} +(0.472229 - 5.39760i) q^{82} +(-8.49403 - 2.27597i) q^{83} +(0.455396 - 0.491195i) q^{84} +(0.0937805 + 0.172250i) q^{85} +(2.84610 - 0.501844i) q^{86} +(0.217513 + 5.75145i) q^{87} +(-1.08054 + 4.03264i) q^{88} +(1.19787 - 1.00513i) q^{89} +(-1.49732 - 6.53896i) q^{90} +(0.0877708 + 0.0319459i) q^{91} +(-0.123379 - 1.41023i) q^{92} +(2.80688 + 6.88979i) q^{93} +0.140506i q^{94} +(7.62855 - 6.06674i) q^{95} +(-1.68878 - 0.384741i) q^{96} +(-6.33112 - 9.04178i) q^{97} +(-6.82438 + 0.597056i) q^{98} +(-8.75238 - 8.95899i) 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 $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{9}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.819152	−	0.573576i	0.579228	−	0.405580i
$2$	0.819152	−	0.573576i	0.579228	−	0.405580i
$3$	1.71589	+	0.236090i	0.990667	+	0.136306i
$3$	1.71589	+	0.236090i	0.990667	+	0.136306i
$4$	0.342020	−	0.939693i	0.171010	−	0.469846i
$5$	0.250579	−	2.22198i	0.112062	−	0.993701i
$5$	0.250579	−	2.22198i	0.112062	−	0.993701i
$6$	1.54099	−	0.790798i	0.629105	−	0.322842i
$7$	0.373543	+	0.100091i	0.141186	+	0.0378307i	0.328720	−	0.944427i	$-0.393383\pi$
$7$	0.373543	+	0.100091i	0.141186	+	0.0378307i	−0.187534	+	0.982258i	$0.560049\pi$
$8$	−0.258819	−	0.965926i	−0.0915064	−	0.341506i
$9$	2.88852	+	0.810206i	0.962841	+	0.270069i
$10$	−1.06922	−	1.96387i	−0.338116	−	0.621030i
$11$	−3.61556	−	2.08745i	−1.09013	−	0.629389i	−0.156522	−	0.987675i	$-0.550028\pi$
$11$	−3.61556	−	2.08745i	−1.09013	−	0.629389i	−0.933612	+	0.358286i	$0.883361\pi$
$12$	0.808719	−	1.53166i	0.233457	−	0.442151i
$13$	0.240609	+	0.0210505i	0.0667328	+	0.00583836i	0.120473	−	0.992717i	$-0.461559\pi$
$13$	0.240609	+	0.0210505i	0.0667328	+	0.00583836i	−0.0537404	+	0.998555i	$0.517114\pi$
$14$	0.363398	−	0.132266i	0.0971223	−	0.0353496i
$15$	0.954552	−	3.75351i	0.246464	−	0.969152i
$16$	−0.766044	−	0.642788i	−0.191511	−	0.160697i
$17$	−0.0718475	+	0.0503082i	−0.0174256	+	0.0122015i	−0.582257	−	0.813005i	$-0.697830\pi$
$17$	−0.0718475	+	0.0503082i	−0.0174256	+	0.0122015i	0.564831	+	0.825206i	$0.308941\pi$
$18$	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
$21$	0.617327	+	0.259934i	0.134712	+	0.0567222i
$22$	−4.15901	+	0.363866i	−0.886703	+	0.0775765i
$23$	1.28298	−	0.598265i	0.267520	−	0.124747i	−0.284230	−	0.958756i	$-0.591738\pi$
$23$	1.28298	−	0.598265i	0.267520	−	0.124747i	0.551750	+	0.834009i	$0.313960\pi$
$24$	−0.216059	−	1.71852i	−0.0441028	−	0.350792i
$25$	−4.87442	−	1.11356i	−0.974884	−	0.222713i
$26$	0.209169	−	0.120764i	0.0410214	−	0.0236837i
$27$	4.76509	+	2.07217i	0.917043	+	0.398789i
$28$	0.221814	−	0.316783i	0.0419189	−	0.0598663i
$29$	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	$0.844607\pi$
$30$	−1.37100	−	3.62220i	−0.250309	−	0.661321i
$31$	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	$0.707285\pi$
$32$	−0.996195	−	0.0871557i	−0.176104	−	0.0154071i
$33$	−5.71107	−	4.43542i	−0.994169	−	0.772107i
$34$	−0.0299985	+	0.0824201i	−0.00514469	+	0.0141349i
$35$	0.316002	−	0.804926i	0.0534140	−	0.136057i
$36$	1.74928	−	2.43722i	0.291546	−	0.406203i
$37$	−7.64589	+	7.64589i	−1.25698	+	1.25698i	−0.304448	+	0.952529i	$0.598472\pi$
$37$	−7.64589	+	7.64589i	−1.25698	+	1.25698i	−0.952529	+	0.304448i	$0.901528\pi$
$38$	4.29173	+	0.762285i	0.696210	+	0.123659i
$39$	0.407887	+	0.0929255i	0.0653142	+	0.0148800i
$40$	−2.21113	+	0.333051i	−0.349610	+	0.0526600i
$41$	3.48276	−	4.15059i	0.543916	−	0.648214i	−0.422145	−	0.906528i	$-0.638723\pi$
$41$	3.48276	−	4.15059i	0.543916	−	0.648214i	0.966061	+	0.258315i	$0.0831671\pi$
$42$	0.654777	−	0.141159i	0.101034	−	0.0217813i
$43$	2.61924	+	1.22137i	0.399430	+	0.186257i	0.611944	−	0.790901i	$-0.290388\pi$
$43$	2.61924	+	1.22137i	0.399430	+	0.186257i	−0.212515	+	0.977158i	$0.568165\pi$
$44$	−3.19815	+	2.68357i	−0.482140	+	0.404563i
$45$	2.52407	−	6.21523i	0.376266	−	0.926512i
$46$	0.707808	−	1.22596i	0.104361	−	0.180758i
$47$	−0.0805908	+	0.115096i	−0.0117554	+	0.0167884i	−0.824987	−	0.565152i	$-0.808817\pi$
$47$	−0.0805908	+	0.115096i	−0.0117554	+	0.0167884i	0.813231	+	0.581941i	$0.197706\pi$
$48$	−1.16269	−	1.28380i	−0.167820	−	0.185301i
$49$	−5.93266	−	3.42522i	−0.847523	−	0.489318i
$50$	−4.63161	+	1.88367i	−0.655008	+	0.266392i
$51$	−0.135159	+	0.0693606i	−0.0189261	+	0.00971243i
$52$	0.102074	−	0.218898i	0.0141551	−	0.0303557i
$53$	6.98810	−	3.25860i	0.959889	−	0.447603i	0.121449	−	0.992598i	$-0.461246\pi$
$53$	6.98810	−	3.25860i	0.959889	−	0.447603i	0.838440	+	0.544994i	$0.183468\pi$
$54$	5.09188	−	1.03572i	0.692918	−	0.140944i
$55$	−5.54426	+	7.51065i	−0.747587	+	1.01274i
$56$		−	0.386720i		−	0.0516777i
$57$	4.55350	+	6.02209i	0.603126	+	0.797646i
$58$	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	$0.0708019\pi$
$60$	−3.20067	−	2.18076i	−0.413205	−	0.281535i
$61$	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	$0.462176\pi$
$62$	3.89283	+	1.81525i	0.494389	+	0.230538i
$63$	0.997895	+	0.591761i	0.125723	+	0.0745549i
$64$	−0.866025	+	0.500000i	−0.108253	+	0.0625000i
$65$	0.107065	−	0.529353i	0.0132798	−	0.0656582i
$66$	−7.22228	−	0.357547i	−0.889002	−	0.0440110i
$67$	0.994844	+	0.696598i	0.121540	+	0.0851029i	0.632766	−	0.774343i	$-0.281920\pi$
$67$	0.994844	+	0.696598i	0.121540	+	0.0851029i	−0.511226	+	0.859446i	$0.670809\pi$
$68$	0.0227009	+	0.0847210i	0.00275289	+	0.0102739i
$69$	2.34270	−	0.723655i	0.282027	−	0.0871178i
$70$	−0.202833	−	0.840608i	−0.0242432	−	0.100472i
$71$	1.77171	+	4.86774i	0.210264	+	0.577695i	0.999329	−	0.0366141i	$-0.0116572\pi$
$71$	1.77171	+	4.86774i	0.210264	+	0.577695i	−0.789066	+	0.614309i	$0.789435\pi$
$72$	0.0349938	−	2.99980i	0.00412406	−	0.353529i
$73$	0.355016	+	4.05785i	0.0415514	+	0.474935i	0.988253	+	0.152824i	$0.0488368\pi$
$73$	0.355016	+	4.05785i	0.0415514	+	0.474935i	−0.946702	+	0.322111i	$0.895608\pi$
$74$	−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
$78$	0.387421	−	0.157834i	0.0438668	−	0.0178712i
$79$	−9.94584	+	11.8530i	−1.11899	+	1.33357i	−0.182370	+	0.983230i	$0.558377\pi$
$79$	−9.94584	+	11.8530i	−1.11899	+	1.33357i	−0.936624	+	0.350336i	$0.886067\pi$
$80$	−1.62022	+	1.54107i	−0.181146	+	0.172297i
$81$	7.68713	+	4.68060i	0.854126	+	0.520066i
$82$	0.472229	−	5.39760i	0.0521489	−	0.596065i
$83$	−8.49403	−	2.27597i	−0.932340	−	0.249820i	−0.239488	−	0.970899i	$-0.576980\pi$
$83$	−8.49403	−	2.27597i	−0.932340	−	0.249820i	−0.692852	+	0.721079i	$0.743646\pi$
$84$	0.455396	−	0.491195i	0.0496878	−	0.0535938i
$85$	0.0937805	+	0.172250i	0.0101719	+	0.0186832i
$86$	2.84610	−	0.501844i	0.306903	−	0.0541153i
$87$	0.217513	+	5.75145i	0.0233199	+	0.616621i
$88$	−1.08054	+	4.03264i	−0.115186	+	0.429881i
$89$	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	$0.251367\pi$
$90$	−1.49732	−	6.53896i	−0.157831	−	0.689267i
$91$	0.0877708	+	0.0319459i	0.00920088	+	0.00334884i
$92$	−0.123379	−	1.41023i	−0.0128631	−	0.147026i
$93$	2.80688	+	6.88979i	0.291060	+	0.714438i
$94$			0.140506i			0.0144921i
$95$	7.62855	−	6.06674i	0.782672	−	0.622434i
$96$	−1.68878	−	0.384741i	−0.172360	−	0.0392674i
$97$	−6.33112	−	9.04178i	−0.642828	−	0.918054i	0.357043	−	0.934088i	$-0.383785\pi$
$97$	−6.33112	−	9.04178i	−0.642828	−	0.918054i	−0.999871	+	0.0160340i	$0.994896\pi$
$98$	−6.82438	+	0.597056i	−0.689366	+	0.0603117i
$99$	−8.75238	−	8.95899i	−0.879647	−	0.900412i
$100$	−2.71356	+	4.19960i	−0.271356	+	0.419960i
$101$	−3.99064	−	4.75586i	−0.397084	−	0.473226i	0.530045	−	0.847970i	$-0.322175\pi$
$101$	−3.99064	−	4.75586i	−0.397084	−	0.473226i	−0.927128	+	0.374744i	$0.877731\pi$
$102$	−0.0709325	+	0.134341i	−0.00702336	+	0.0133018i
$103$	15.3641	−	4.11679i	1.51387	−	0.405640i	0.596150	−	0.802873i	$-0.296696\pi$
$103$	15.3641	−	4.11679i	1.51387	−	0.405640i	0.917718	+	0.397234i	$0.130030\pi$
$104$	−0.0419408	−	0.237858i	−0.00411264	−	0.0233239i
$105$	0.732258	−	1.30656i	0.0714610	−	0.127507i
$106$	3.85525	−	6.67750i	0.374455	−	0.648576i
$107$	−0.229432	+	0.856251i	−0.0221800	+	0.0827769i	−0.976129	−	0.217193i	$-0.930310\pi$
$107$	−0.229432	+	0.856251i	−0.0221800	+	0.0827769i	0.953949	+	0.299970i	$0.0969766\pi$
$108$	3.57696	−	3.76900i	0.344193	−	0.362672i
$109$	−6.16314	−	16.9331i	−0.590322	−	1.62190i	−0.769909	−	0.638154i	$-0.779698\pi$
$109$	−6.16314	−	16.9331i	−0.590322	−	1.62190i	0.179587	−	0.983742i	$-0.442524\pi$
$110$	−0.233655	+	9.33242i	−0.0222781	+	0.889812i
$111$	−14.9246	+	11.3144i	−1.41658	+	1.07391i
$112$	−0.221814	−	0.316783i	−0.0209594	−	0.0299332i
$113$	−11.3530	+	11.3530i	−1.06800	+	1.06800i	−0.0704836	+	0.997513i	$0.522454\pi$
$113$	−11.3530	+	11.3530i	−1.06800	+	1.06800i	−0.997513	+	0.0704836i	$0.977546\pi$
$114$	7.18414	+	2.32123i	0.672857	+	0.217403i
$115$	−1.00785	−	3.00068i	−0.0939821	−	0.279815i
$116$	3.27249	+	0.577029i	0.303843	+	0.0535758i
$117$	0.677948	+	0.255747i	0.0626763	+	0.0236439i
$118$	0.310853	+	0.666626i	0.0286163	+	0.0613679i
$119$	−0.0318735	+	0.0116010i	−0.00292184	+	0.00106346i
$120$	−3.87267	+	0.0494532i	−0.353525	+	0.00451444i
$121$	3.21487	+	5.56832i	0.292261	+	0.506211i
$122$	6.80490	−	1.82337i	0.616087	−	0.165080i
$123$	6.95593	−	6.29970i	0.627195	−	0.568025i
$124$	4.23000	−	0.745864i	0.379865	−	0.0669805i
$125$	−3.69575	+	10.5518i	−0.330558	+	0.943786i
$126$	1.15685	−	0.0876265i	0.103060	−	0.00780639i
$127$	−1.80890	+	20.6759i	−0.160514	+	1.83469i	0.308184	+	0.951327i	$0.400279\pi$
$127$	−1.80890	+	20.6759i	−0.160514	+	1.83469i	−0.468698	+	0.883358i	$0.655277\pi$
$128$	−0.422618	+	0.906308i	−0.0373545	+	0.0801070i
$129$	4.20595	+	2.71410i	0.370314	+	0.238964i
$130$	−0.215922	−	0.495031i	−0.0189376	−	0.0434171i
$131$	−16.4004	−	2.89183i	−1.43291	−	0.252661i	−0.597315	−	0.802007i	$-0.703766\pi$
$131$	−16.4004	−	2.89183i	−1.43291	−	0.252661i	−0.835595	+	0.549346i	$0.814877\pi$
$132$	−6.12123	+	3.84965i	−0.532785	+	0.335069i
$133$	0.841011	+	1.46089i	0.0729249	+	0.126675i
$134$	1.21448			0.104915
$135$	5.79836	−	10.0687i	0.499043	−	0.866577i
$136$	0.0671895	+	0.0563787i	0.00576145	+	0.00483443i
$137$	−4.56372	−	9.78694i	−0.389905	−	0.836155i	−0.999070	−	0.0431111i	$-0.986273\pi$
$137$	−4.56372	−	9.78694i	−0.389905	−	0.836155i	0.609165	−	0.793044i	$-0.291505\pi$
$138$	1.50395	−	1.93650i	0.128025	−	0.164846i
$139$	3.76351	+	4.48518i	0.319217	+	0.380428i	0.901661	−	0.432443i	$-0.142348\pi$
$139$	3.76351	+	4.48518i	0.319217	+	0.380428i	−0.582445	+	0.812870i	$0.697904\pi$
$140$	−0.648304	−	0.572246i	−0.0547917	−	0.0483636i
$141$	−0.165457	+	0.178464i	−0.0139340	+	0.0150294i
$142$	4.24332	+	2.97121i	0.356092	+	0.249338i
$143$	−0.825994	−	0.578367i	−0.0690731	−	0.0483655i
$144$	−1.69195	−	2.47736i	−0.140996	−	0.206447i
$145$	7.41602	−	0.462131i	0.615867	−	0.0383779i
$146$	2.61830	+	3.12036i	0.216692	+	0.258243i
$147$	−9.37111	−	7.27793i	−0.772916	−	0.600274i
$148$	4.56974	+	9.79984i	0.375630	+	0.805542i
$149$	−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	$0.848118\pi$
$150$	−8.39202	+	2.13869i	−0.685206	+	0.174624i
$151$	6.02542			0.490341			0.245171	−	0.969480i	$-0.421156\pi$
$151$	6.02542			0.490341			0.245171	+	0.969480i	$0.421156\pi$
$152$	2.18417	−	3.77219i	0.177160	−	0.305965i
$153$	−0.248293	+	0.0871051i	−0.0200733	+	0.00704203i
$154$	−1.58999	−	0.280358i	−0.128125	−	0.0225919i
$155$	8.80349	−	3.83989i	0.707113	−	0.308428i
$156$	0.226827	−	0.351506i	0.0181607	−	0.0281430i
$157$	−6.32439	+	13.5627i	−0.504741	+	1.08242i	0.474599	+	0.880202i	$0.342593\pi$
$157$	−6.32439	+	13.5627i	−0.504741	+	1.08242i	−0.979340	+	0.202219i	$0.935185\pi$
$158$	−1.34856	+	15.4141i	−0.107286	+	1.22628i
$159$	12.7601	−	3.94157i	1.01194	−	0.312587i
$160$	−0.443284	+	2.19169i	−0.0350447	+	0.173268i
$161$	0.539130	−	0.0950632i	0.0424894	−	0.00749203i
$162$	8.98161	−	0.575039i	0.705662	−	0.0451793i
$163$	12.3460	−	3.30811i	0.967017	−	0.259111i	0.259449	−	0.965757i	$-0.416459\pi$
$163$	12.3460	−	3.30811i	0.967017	−	0.259111i	0.707568	+	0.706645i	$0.249792\pi$
$164$	−2.70911	−	4.69231i	−0.211546	−	0.366408i
$165$	−11.2865	+	11.5785i	−0.878652	+	0.901383i
$166$	−8.26334	+	3.00761i	−0.641360	+	0.233436i
$167$	8.86975	+	19.0212i	0.686362	+	1.47191i	0.872109	+	0.489311i	$0.162752\pi$
$167$	8.86975	+	19.0212i	0.686362	+	1.47191i	−0.185747	+	0.982598i	$0.559471\pi$
$168$	0.0913007	−	0.663568i	0.00704400	−	0.0511954i
$169$	−12.7451	−	2.24730i	−0.980389	−	0.172869i
$170$	0.175619	+	0.0873088i	0.0134694	+	0.00669628i
$171$	6.39154	+	11.4083i	0.488773	+	0.872411i
$172$	2.04354	−	2.04354i	0.155819	−	0.155819i
$173$	0.0358823	+	0.0512453i	0.00272808	+	0.00389611i	0.820514	−	0.571627i	$-0.193687\pi$
$173$	0.0358823	+	0.0512453i	0.00272808	+	0.00389611i	−0.817786	+	0.575523i	$0.804799\pi$
$174$	3.47707	+	4.58655i	0.263596	+	0.347706i
$175$	−1.70935	−	0.903848i	−0.129215	−	0.0683245i
$176$	1.42790	+	3.92312i	0.107632	+	0.295716i
$177$	−0.390177	+	1.21277i	−0.0293275	+	0.0911577i
$178$	0.404718	−	1.51043i	0.0303349	−	0.113211i
$179$	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	$-0.120331\pi$
$180$	−4.97712	−	4.49758i	−0.370973	−	0.335230i
$181$	−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	$0.958211\pi$
$182$	0.0902210	−	0.0241747i	0.00668763	−	0.00179194i
$183$	10.7905	+	5.69739i	0.797653	+	0.421163i
$184$	−0.909940	−	1.08442i	−0.0670817	−	0.0799448i
$185$	15.0731	+	18.9049i	1.10820	+	1.38992i
$186$	6.25108	+	4.03382i	0.458351	+	0.295774i
$187$	0.364785	−	0.0319146i	0.0266757	−	0.00233382i
$188$	0.0805908	+	0.115096i	0.00587769	+	0.00839421i
$189$	1.57256	+	1.25099i	0.114387	+	0.0909959i
$190$	2.76920	−	9.34513i	0.200899	−	0.677967i
$191$		−	6.91092i		−	0.500056i	−0.968239	−	0.250028i	$-0.919560\pi$
$191$		−	6.91092i		−	0.500056i	0.968239	−	0.250028i	$-0.0804399\pi$
$192$	−1.60404	+	0.653483i	−0.115762	+	0.0471611i
$193$	0.577128	+	6.59660i	0.0415426	+	0.474834i	0.988261	+	0.152772i	$0.0488201\pi$
$193$	0.577128	+	6.59660i	0.0415426	+	0.474834i	−0.946719	+	0.322061i	$0.895624\pi$
$194$	−10.3723	−	3.77521i	−0.744688	−	0.271044i
$195$	0.308687	−	0.883033i	0.0221055	−	0.0632353i
$196$	−5.24775	+	4.40338i	−0.374839	+	0.314527i
$197$	−4.42598	+	16.5180i	−0.315338	+	1.17686i	0.608336	+	0.793680i	$0.291837\pi$
$197$	−4.42598	+	16.5180i	−0.315338	+	1.17686i	−0.923674	+	0.383179i	$0.874829\pi$
$198$	−12.3082	−	2.31862i	−0.874705	−	0.164777i
$199$	−2.82359	+	0.497875i	−0.200159	+	0.0352934i	−0.272829	−	0.962063i	$-0.587959\pi$
$199$	−2.82359	+	0.497875i	−0.200159	+	0.0352934i	0.0726698	+	0.997356i	$0.476848\pi$
$200$	0.185972	+	4.99654i	0.0131502	+	0.353309i
$201$	1.54258	+	1.43015i	0.108805	+	0.100875i
$202$	−5.99679	−	1.60684i	−0.421933	−	0.113057i
$203$	−0.112001	+	1.28017i	−0.00786091	+	0.0898506i
$204$	0.0189504	+	0.150731i	0.00132679	+	0.0105533i
$205$	−8.34984	−	8.77869i	−0.583178	−	0.613130i
$206$	10.2242	−	12.1848i	0.712355	−	0.848952i
$207$	4.19064	−	0.688622i	0.291270	−	0.0478625i
$208$	−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	$-0.233900\pi$
$212$	−0.672015	−	7.68117i	−0.0461542	−	0.527545i
$213$	1.89083	+	8.77077i	0.129558	+	0.600963i
$214$	0.303186	+	0.832996i	0.0207253	+	0.0569424i
$215$	3.37019	−	5.51385i	0.229845	−	0.376041i
$216$	0.768266	−	5.13904i	0.0522739	−	0.349668i
$217$	0.429915	+	1.60446i	0.0291845	+	0.108918i
$218$	−14.7610	−	10.3357i	−0.999739	−	0.700025i
$219$	−0.348850	+	7.04661i	−0.0235731	+	0.476166i
$220$	5.16146	+	7.77869i	0.347985	+	0.524439i
$221$	−0.0183461	+	0.0105922i	−0.00123410	+	0.000712505i
$222$	−5.73586	+	17.8286i	−0.384966	+	1.19658i
$223$	−6.04282	−	2.81781i	−0.404657	−	0.188695i	0.209624	−	0.977782i	$-0.432776\pi$
$223$	−6.04282	−	2.81781i	−0.404657	−	0.188695i	−0.614281	+	0.789087i	$0.710554\pi$
$224$	−0.363398	−	0.132266i	−0.0242806	−	0.00883741i
$225$	−13.1777	−	7.16584i	−0.878511	−	0.477723i
$226$	−2.78801	+	15.8116i	−0.185456	+	1.05177i
$227$	2.98346	+	2.98346i	0.198019	+	0.198019i	0.799150	−	0.601131i	$-0.205283\pi$
$227$	2.98346	+	2.98346i	0.198019	+	0.198019i	−0.601131	+	0.799150i	$0.705283\pi$
$228$	7.21631	−	2.21922i	0.477912	−	0.146971i
$229$		−	21.4179i		−	1.41534i	−0.706545	−	0.707669i	$-0.749747\pi$
$229$		−	21.4179i		−	1.41534i	0.706545	−	0.707669i	$-0.250253\pi$
$230$	−2.54670	−	1.87994i	−0.167924	−	0.123959i
$231$	−1.68939	−	2.22844i	−0.111154	−	0.146621i
$232$	3.01164	−	1.40435i	0.197724	−	0.0922002i
$233$	4.30466	−	9.23136i	0.282007	−	0.604767i	−0.713372	−	0.700785i	$-0.752833\pi$
$233$	4.30466	−	9.23136i	0.282007	−	0.604767i	0.995380	+	0.0960186i	$0.0306108\pi$
$234$	0.702033	−	0.179359i	0.0458934	−	0.0117251i
$235$	0.235546	+	0.207912i	0.0153653	+	0.0135627i
$236$	0.636997	+	0.367770i	0.0414649	+	0.0239398i
$237$	−19.8643	+	17.9903i	−1.29032	+	1.16859i
$238$	−0.0194552	+	0.0277849i	−0.00126109	+	0.00180103i
$239$	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	$-0.0176165\pi$
$240$	−3.14394	+	2.26178i	−0.202940	+	0.145997i
$241$	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	$0.165495\pi$
$242$	5.82732	+	2.71733i	0.374595	+	0.174676i
$243$	12.0852	+	9.84622i	0.775266	+	0.631635i
$244$	4.52841	−	5.39675i	0.289902	−	0.345491i
$245$	−9.09739	+	12.3240i	−0.581211	+	0.787351i
$246$	2.08461	−	9.15017i	0.132910	−	0.583393i
$247$	0.675714	+	0.807334i	0.0429946	+	0.0513694i
$248$	3.03721	−	3.03721i	0.192863	−	0.192863i
$249$	−14.0374	−	5.91065i	−0.889587	−	0.374572i
$250$	3.02491	+	10.7634i	0.191312	+	0.680735i
$251$	10.1608	−	27.9165i	0.641343	−	1.76207i	−0.00612400	−	0.999981i	$-0.501949\pi$
$251$	10.1608	−	27.9165i	0.641343	−	1.76207i	0.647467	−	0.762094i	$-0.275828\pi$
$252$	0.897374	−	0.735320i	0.0565292	−	0.0463208i
$253$	−5.88755	−	0.515094i	−0.370147	−	0.0323837i
$254$	10.3774	+	17.9742i	0.651137	+	1.12780i
$255$	0.120250	+	0.317702i	0.00753035	+	0.0198953i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−11.4442	+	16.3440i	−0.713869	+	1.01951i	0.284283	+	0.958740i	$0.408245\pi$
$257$	−11.4442	+	16.3440i	−0.713869	+	1.01951i	−0.998152	+	0.0607701i	$0.980644\pi$
$258$	5.00206	−	0.189172i	0.311415	−	0.0117773i
$259$	−3.62135	+	2.09079i	−0.225020	+	0.129915i
$260$	−0.460811	−	0.281658i	−0.0285783	−	0.0174677i
$261$	−0.984632	+	9.92019i	−0.0609472	+	0.614044i
$262$	−15.0931	+	7.03803i	−0.932456	+	0.434811i
$263$	14.5696	−	1.27468i	0.898403	−	0.0786001i	0.371409	−	0.928469i	$-0.378875\pi$
$263$	14.5696	−	1.27468i	0.898403	−	0.0786001i	0.526994	+	0.849869i	$0.323319\pi$
$264$	−2.80615	+	6.66444i	−0.172707	+	0.410168i
$265$	−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
$268$	0.994844	−	0.696598i	0.0607698	−	0.0425515i
$269$	−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	$0.957129\pi$
$270$	−1.02544	−	11.5736i	−0.0624062	−	0.704348i
$271$	−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	$0.544753\pi$
$272$	0.0873759	+	0.00764440i	0.00529794	+	0.000463510i
$273$	0.143062	+	0.0755373i	0.00865853	+	0.00457173i
$274$	−9.35194	−	5.39935i	−0.564971	−	0.326186i
$275$	15.2993	+	14.2013i	0.922581	+	0.856368i
$276$	0.121236	−	2.44892i	0.00729756	−	0.147408i
$277$	−6.80449	−	25.3947i	−0.408842	−	1.52582i	−0.796858	−	0.604167i	$-0.793506\pi$
$277$	−6.80449	−	25.3947i	−0.408842	−	1.52582i	0.388016	−	0.921653i	$-0.373161\pi$
$278$	5.65548	+	1.51538i	0.339193	+	0.0908865i
$279$	3.18967	+	12.4848i	0.190961	+	0.747443i
$280$	−0.859287	−	0.0969040i	−0.0513522	−	0.00579112i
$281$	8.94351	−	24.5721i	0.533525	−	1.46585i	−0.321323	−	0.946970i	$-0.604128\pi$
$281$	8.94351	−	24.5721i	0.533525	−	1.46585i	0.854848	−	0.518878i	$-0.173650\pi$
$282$	−0.0331720	+	0.241092i	−0.00197536	+	0.0143568i
$283$	17.2246	−	12.0608i	1.02390	−	0.716939i	0.0641871	−	0.997938i	$-0.479555\pi$
$283$	17.2246	−	12.0608i	1.02390	−	0.716939i	0.959708	+	0.280999i	$0.0906657\pi$
$284$	5.18014			0.307385
$285$	14.5220	−	8.60880i	0.860209	−	0.509941i
$286$	−1.00835			−0.0596251
$287$	1.71640	−	1.20183i	0.101316	−	0.0709421i
$288$	−2.80692	−	1.05887i	−0.165399	−	0.0623947i
$289$	−5.81171	+	15.9675i	−0.341865	+	0.939267i
$290$	5.80978	−	4.63221i	0.341162	−	0.272013i
$291$	−8.72881	−	17.0094i	−0.511692	−	0.997107i
$292$	3.93455	+	1.05426i	0.230252	+	0.0616959i
$293$	−1.47887	−	5.51922i	−0.0863965	−	0.322436i	0.909178	−	0.416407i	$-0.136711\pi$
$293$	−1.47887	−	5.51922i	−0.0863965	−	0.322436i	−0.995575	+	0.0939705i	$0.970044\pi$
$294$	−11.8508	−	0.586687i	−0.691153	−	0.0342163i
$295$	1.57752	+	0.465314i	0.0918470	+	0.0270916i
$296$	9.36427	+	5.40646i	0.544287	+	0.314244i
$297$	−12.9030	−	17.4389i	−0.748705	−	1.01191i
$298$	−9.37016	−	0.819783i	−0.542799	−	0.0474887i
$299$	0.321290	−	0.116940i	0.0185807	−	0.00676283i
$300$	−5.64764	+	6.56538i	−0.326066	+	0.379052i
$301$	0.856150	+	0.718395i	0.0493477	+	0.0414076i
$302$	4.93573	−	3.45604i	0.284019	−	0.198873i
$303$	−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
$306$	−0.153429	+	0.213767i	−0.00877092	+	0.0122203i
$307$	6.48150	−	0.567058i	0.369919	−	0.0323637i	0.0993191	−	0.995056i	$-0.468334\pi$
$307$	6.48150	−	0.567058i	0.369919	−	0.0323637i	0.270600	+	0.962692i	$0.412778\pi$
$308$	−1.46325	+	0.682324i	−0.0833764	+	0.0388790i
$309$	27.3349	−	3.43664i	1.55503	−	0.195504i
$310$	5.00892	−	8.19493i	0.284488	−	0.465441i
$311$	−6.65510	+	3.84232i	−0.377376	+	0.217878i	−0.676676	−	0.736281i	$-0.736580\pi$
$311$	−6.65510	+	3.84232i	−0.377376	+	0.217878i	0.299300	+	0.954159i	$0.403247\pi$
$312$	−0.0158098	−	0.418039i	−0.000895051	−	0.0236668i
$313$	11.0754	−	15.8173i	0.626017	−	0.894045i	−0.373417	−	0.927663i	$-0.621814\pi$
$313$	11.0754	−	15.8173i	0.626017	−	0.894045i	0.999435	+	0.0336180i	$0.0107030\pi$
$314$	2.59861	+	14.7374i	0.146648	+	0.831682i
$315$	1.56493	−	2.06902i	0.0881741	−	0.116576i
$316$	7.73649	+	13.4000i	0.435212	+	0.753809i
$317$	−27.5047	−	2.40635i	−1.54482	−	0.135154i	−0.717367	−	0.696695i	$-0.754653\pi$
$317$	−27.5047	−	2.40635i	−1.54482	−	0.135154i	−0.827449	+	0.561542i	$0.810208\pi$
$318$	8.19166	−	10.5476i	0.459366	−	0.591482i
$319$	4.74487	−	13.0364i	0.265662	−	0.729900i
$320$	0.893984	+	2.04958i	0.0499752	+	0.114575i
$321$	−0.595830	+	1.41506i	−0.0332560	+	0.0789810i
$322$	0.387104	−	0.387104i	0.0215724	−	0.0215724i
$323$	−0.376426	−	0.0668598i	−0.0209449	−	0.00372018i
$324$	7.02748	−	5.62268i	0.390415	−	0.312371i
$325$	−1.14939	−	0.370542i	−0.0637565	−	0.0205540i
$326$	8.21583	−	9.79125i	0.455033	−	0.542287i
$327$	−6.57751	−	30.5103i	−0.363737	−	1.68722i
$328$	−4.91057	−	2.28984i	−0.271141	−	0.126435i
$329$	−0.0416241	+	0.0349268i	−0.00229481	+	0.00192558i
$330$	−2.60421	+	15.9582i	−0.143357	+	0.878470i
$331$	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	$0.00296726\pi$
$332$	−5.04384	+	7.20335i	−0.276817	+	0.395335i
$333$	−28.2801	+	15.8906i	−1.54974	+	0.870799i
$334$	18.1758	+	10.4938i	0.994536	+	0.574196i
$335$	1.79712	−	2.03598i	0.0981869	−	0.111237i
$336$	−0.305818	−	0.595931i	−0.0166837	−	0.0325107i
$337$	3.29350	−	7.06294i	0.179409	−	0.384743i	−0.795952	−	0.605360i	$-0.793029\pi$
$337$	3.29350	−	7.06294i	0.179409	−	0.384743i	0.975361	+	0.220617i	$0.0708070\pi$
$338$	−11.7291	+	5.46938i	−0.637981	+	0.297495i
$339$	−22.1607	+	16.8001i	−1.20360	+	0.912454i
$340$	0.193937	−	0.0292118i	0.0105177	−	0.00158423i
$341$		−	17.9322i		−	0.971086i
$342$	11.7791	+	5.67906i	0.636943	+	0.307088i
$343$	−3.78744	−	3.78744i	−0.204503	−	0.204503i
$344$	0.501844	−	2.84610i	0.0270576	−	0.153451i
$345$	−1.02092	−	5.38676i	−0.0549644	−	0.290014i
$346$	0.0587862	+	0.0213964i	0.00316037	+	0.00115028i
$347$	5.57952	+	2.60177i	0.299525	+	0.139671i	0.566571	−	0.824013i	$-0.308270\pi$
$347$	5.57952	+	2.60177i	0.299525	+	0.139671i	−0.267046	+	0.963684i	$0.586048\pi$
$348$	5.47899	+	1.76272i	0.293705	+	0.0944916i
$349$	7.03299	−	4.06050i	0.376467	−	0.217353i	−0.299813	−	0.953998i	$-0.596924\pi$
$349$	7.03299	−	4.06050i	0.376467	−	0.217353i	0.676280	+	0.736645i	$0.263591\pi$
$350$	−1.91864	+	0.240054i	−0.102556	+	0.0128314i
$351$	1.10290	+	0.598890i	0.0588685	+	0.0319664i
$352$	3.41987	+	2.39462i	0.182280	+	0.127634i
$353$	−1.35752	−	5.06634i	−0.0722535	−	0.269654i	0.920343	−	0.391112i	$-0.127910\pi$
$353$	−1.35752	−	5.06634i	−0.0722535	−	0.269654i	−0.992597	+	0.121458i	$0.961243\pi$
$354$	0.376004	+	1.21724i	0.0199844	+	0.0646957i
$355$	11.2600	−	2.71696i	0.597618	−	0.144201i
$356$	−0.534820	−	1.46941i	−0.0283454	−	0.0778784i
$357$	−0.0574302	+	0.0123810i	−0.00303953	+	0.000655272i
$358$	−1.82918	−	20.9076i	−0.0966752	−	1.10500i
$359$	−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
$363$	4.20172	+	10.3136i	0.220533	+	0.541323i
$364$	0.0600387	−	0.0715514i	0.00314688	−	0.00375031i
$365$	9.10543	+	0.227972i	0.476600	+	0.0119326i
$366$	12.1069	−	1.52212i	0.632838	−	0.0795626i
$367$	−0.483936	+	5.53142i	−0.0252613	+	0.288738i	0.973048	+	0.230604i	$0.0740703\pi$
$367$	−0.483936	+	5.53142i	−0.0252613	+	0.288738i	−0.998309	+	0.0581331i	$0.981485\pi$
$368$	−1.36738	−	0.366388i	−0.0712796	−	0.0190993i
$369$	13.4229	−	9.16733i	0.698767	−	0.477232i
$370$	23.1906	+	6.84042i	1.20562	+	0.355617i
$371$	2.93651	−	0.517786i	0.152456	−	0.0268821i
$372$	7.43429	−	0.281156i	0.385450	−	0.0145773i
$373$	−4.20006	+	15.6748i	−0.217471	+	0.811612i	0.767811	+	0.640676i	$0.221346\pi$
$373$	−4.20006	+	15.6748i	−0.217471	+	0.811612i	−0.985282	+	0.170936i	$0.945321\pi$
$374$	0.280509	−	0.235375i	0.0145048	−	0.0121710i
$375$	−8.83266	+	17.2332i	−0.456117	+	0.889920i
$376$	0.132032	+	0.0480558i	0.00680904	+	0.00247829i
$377$	0.0699504	+	0.799537i	0.00360263	+	0.0411782i
$378$	2.00571	+	0.122763i	0.103162	+	0.00631423i
$379$		−	8.77393i		−	0.450686i	−0.974279	−	0.225343i	$-0.927650\pi$
$379$		−	8.77393i		−	0.450686i	0.974279	−	0.225343i	$-0.0723503\pi$
$380$	−3.09175	−	9.24343i	−0.158604	−	0.474178i
$381$	−7.98523	+	35.0503i	−0.409095	+	1.79568i
$382$	−3.96394	−	5.66109i	−0.202813	−	0.289647i
$383$	−29.5470	+	2.58503i	−1.50978	+	0.132089i	−0.811762	−	0.583989i	$-0.801491\pi$
$383$	−29.5470	+	2.58503i	−1.50978	+	0.132089i	−0.698021	+	0.716078i	$0.745936\pi$
$384$	−0.939134	+	1.45534i	−0.0479250	+	0.0742677i
$385$	−2.82277	+	2.25063i	−0.143861	+	0.114703i
$386$	4.25641	+	5.07259i	0.216646	+	0.258188i
$387$	6.57616	+	5.65007i	0.334285	+	0.287209i
$388$	−10.6619	+	2.85684i	−0.541274	+	0.145034i
$389$	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	$0.852441\pi$
$390$	−0.253625	−	0.900393i	−0.0128428	−	0.0455932i
$391$	−0.0620816	+	0.107528i	−0.00313960	+	0.00543795i
$392$	−1.77303	+	6.61702i	−0.0895513	+	0.334210i
$393$	−27.4585	−	8.83402i	−1.38510	−	0.445617i
$394$	5.84878	+	16.0694i	0.294657	+	0.809564i
$395$	23.8449	+	25.0696i	1.19977	+	1.26139i
$396$	−11.4122	+	5.16039i	−0.573484	+	0.259319i
$397$	19.5944	+	27.9837i	0.983416	+	1.40446i	0.913467	+	0.406913i	$0.133395\pi$
$397$	19.5944	+	27.9837i	0.983416	+	1.40446i	0.0699494	+	0.997551i	$0.477716\pi$
$398$	−2.02738	+	2.02738i	−0.101623	+	0.101623i
$399$	1.09818	+	2.70528i	0.0549776	+	0.135433i
$400$	3.01824	+	3.98626i	0.150912	+	0.199313i
$401$	3.32331	+	0.585988i	0.165958	+	0.0292629i	0.256010	−	0.966674i	$-0.417592\pi$
$401$	3.32331	+	0.585988i	0.165958	+	0.0292629i	−0.0900517	+	0.995937i	$0.528703\pi$
$402$	2.08391	+	0.286726i	0.103936	+	0.0143006i
$403$	0.438434	+	0.940225i	0.0218400	+	0.0468359i
$404$	−5.83393	+	2.12338i	−0.290249	+	0.105642i
$405$	12.3264	−	15.9078i	0.612506	−	0.790466i
$406$	0.642532	+	1.11290i	0.0318883	+	0.0552322i
$407$	43.6046	−	11.6838i	2.16140	−	0.579145i
$408$	0.101979	+	0.112602i	0.00504871	+	0.00557463i
$409$	14.6702	−	2.58675i	0.725395	−	0.127907i	0.201255	−	0.979539i	$-0.435498\pi$
$409$	14.6702	−	2.58675i	0.725395	−	0.127907i	0.524140	+	0.851632i	$0.324387\pi$
$410$	−11.8750	−	2.40181i	−0.586466	−	0.118617i
$411$	−5.52023	−	17.8707i	−0.272293	−	0.881497i
$412$	1.38630	−	15.8455i	0.0682983	−	0.780654i
$413$	−0.120213	+	0.257798i	−0.00591530	+	0.0126854i
$414$	3.03780	−	2.96774i	0.149300	−	0.145856i
$415$	−7.18559	+	18.3033i	−0.352726	+	0.898472i
$416$	−0.237858	−	0.0419408i	−0.0116620	−	0.00205632i
$417$	5.39885	+	8.58457i	0.264383	+	0.420388i
$418$	−13.9258	−	11.7148i	−0.681132	−	0.572992i
$419$	−28.9325			−1.41345			−0.706723	−	0.707491i	$-0.749827\pi$
$419$	−28.9325			−1.41345			−0.706723	+	0.707491i	$0.749827\pi$
$420$	−0.977315	−	1.13497i	−0.0476881	−	0.0553807i
$421$	−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	$0.940825\pi$
$422$	−9.68846	−	20.7770i	−0.471627	−	1.01141i
$423$	−0.326039	+	0.267161i	−0.0158526	+	0.0129898i
$424$	−4.95622	−	5.90659i	−0.240695	−	0.286850i
$425$	0.406237	−	0.165216i	0.0197054	−	0.00801417i
$426$	6.57958	+	6.10005i	0.318782	+	0.295549i
$427$	2.23172	+	1.56267i	0.108001	+	0.0756228i
$428$	0.726142	+	0.508450i	0.0350994	+	0.0245769i
$429$	−1.28076	−	1.18742i	−0.0618359	−	0.0573292i
$430$	−0.401917	−	6.44974i	−0.0193822	−	0.311034i
$431$	2.96319	+	3.53139i	0.142732	+	0.170101i	0.832674	−	0.553763i	$-0.186809\pi$
$431$	2.96319	+	3.53139i	0.142732	+	0.170101i	−0.689942	+	0.723864i	$0.742364\pi$
$432$	−2.31831	−	4.65032i	−0.111540	−	0.223738i
$433$	0.267212	+	0.573039i	0.0128414	+	0.0275385i	0.912624	−	0.408800i	$-0.134053\pi$
$433$	0.267212	+	0.573039i	0.0128414	+	0.0275385i	−0.899782	+	0.436339i	$0.856275\pi$
$434$	1.27245	+	1.06771i	0.0610795	+	0.0512518i
$435$	12.8341	+	0.957882i	0.615350	+	0.0459269i
$436$	−18.0198			−0.862993
$437$	5.79575	+	2.11770i	0.277248	+	0.101303i
$438$	3.75601	+	5.97234i	0.179469	+	0.285369i
$439$	38.5069	+	6.78980i	1.83783	+	0.324060i	0.981367	−	0.192143i	$-0.0615438\pi$
$439$	38.5069	+	6.78980i	1.83783	+	0.324060i	0.856466	+	0.516203i	$0.172655\pi$
$440$	8.68969	+	3.41144i	0.414265	+	0.162634i
$441$	−14.3615	−	14.7005i	−0.683881	−	0.700024i
$442$	−0.00895287	+	0.0191995i	−0.000425845	+	0.000913227i
$443$	−2.83397	+	32.3924i	−0.134646	+	1.53901i	0.565344	+	0.824856i	$0.308744\pi$
$443$	−2.83397	+	32.3924i	−0.134646	+	1.53901i	−0.699989	+	0.714153i	$0.746812\pi$
$444$	5.52751	+	17.8943i	0.262324	+	0.849224i
$445$	−1.93323	−	2.91351i	−0.0916438	−	0.138114i
$446$	−6.56622	+	1.15780i	−0.310919	+	0.0548235i
$447$	−10.9362	−	12.0754i	−0.517264	−	0.571147i
$448$	−0.373543	+	0.100091i	−0.0176483	+	0.00472884i
$449$	−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	$-0.387538\pi$
$450$	−14.9047	+	1.68848i	−0.702613	+	0.0795959i
$451$	−21.2563	+	7.73666i	−1.00092	+	0.364305i
$452$	6.78535	+	14.5512i	0.319156	+	0.684432i
$453$	10.3389	+	1.42254i	0.485765	+	0.0668367i
$454$	4.15514	+	0.732664i	0.195011	+	0.0343856i
$455$	0.0929769	−	0.187020i	0.00435882	−	0.00876764i
$456$	4.63836	−	5.95698i	0.217211	−	0.278961i
$457$	25.1035	−	25.1035i	1.17429	−	1.17429i	0.193118	−	0.981176i	$-0.438140\pi$
$457$	25.1035	−	25.1035i	1.17429	−	1.17429i	0.981176	−	0.193118i	$-0.0618599\pi$
$458$	−12.2848	−	17.5445i	−0.574032	−	0.819803i
$459$	−0.446607	+	0.0908428i	−0.0208458	+	0.00424018i
$460$	−3.16442	−	0.0792273i	−0.147542	−	0.00369399i
$461$	5.33599	+	14.6605i	0.248522	+	0.682808i	0.999741	+	0.0227553i	$0.00724386\pi$
$461$	5.33599	+	14.6605i	0.248522	+	0.682808i	−0.751219	+	0.660053i	$0.770534\pi$
$462$	−2.66205	−	0.856442i	−0.123850	−	0.0398453i
$463$	6.19767	−	23.1300i	0.288030	−	1.07494i	−0.658566	−	0.752523i	$-0.728837\pi$
$463$	6.19767	−	23.1300i	0.288030	−	1.07494i	0.946597	−	0.322421i	$-0.104497\pi$
$464$	1.66149	−	2.87778i	0.0771327	−	0.133598i
$465$	16.0123	−	4.51040i	0.742554	−	0.209165i
$466$	−1.76873	−	10.0309i	−0.0819346	−	0.464674i
$467$	−12.9444	+	3.46845i	−0.598997	+	0.160501i	−0.545562	−	0.838071i	$-0.683684\pi$
$467$	−12.9444	+	3.46845i	−0.598997	+	0.160501i	−0.0534350	+	0.998571i	$0.517017\pi$
$468$	0.472196	−	0.549592i	0.0218273	−	0.0254049i
$469$	0.301895	+	0.359784i	0.0139402	+	0.0166133i
$470$	0.312201	+	0.0352078i	0.0144008	+	0.00162401i
$471$	−14.0539	+	21.7789i	−0.647572	+	1.00352i
$472$	0.732741	−	0.0641066i	0.0337272	−	0.00295074i
$473$	−6.92047	−	9.88345i	−0.318203	−	0.454442i
$474$	−5.95308	+	26.1304i	−0.273434	+	1.20021i
$475$	−11.5686	−	18.4707i	−0.530805	−	0.847494i
$476$			0.0339191i			0.00155468i
$477$	22.8254	−	3.75075i	1.04510	−	0.171735i
$478$	−1.47443	−	16.8528i	−0.0674386	−	0.770827i
$479$	−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	$0.733647\pi$
$480$	−1.27806	+	3.65603i	−0.0583352	+	0.166874i
$481$	−2.00062	+	1.67872i	−0.0912203	+	0.0765429i
$482$	2.77622	−	10.3610i	0.126453	−	0.471931i
$483$	0.947529	−	0.0358344i	0.0431141	−	0.00163052i
$484$	6.33206	−	1.11651i	0.287821	−	0.0507506i
$485$	−21.6771	+	11.8020i	−0.984308	+	0.535900i
$486$	15.5472	+	1.13377i	0.705234	+	0.0514287i
$487$	25.2334	+	6.76127i	1.14343	+	0.306382i	0.780331	−	0.625366i	$-0.215050\pi$
$487$	25.2334	+	6.76127i	1.14343	+	0.306382i	0.363104	+	0.931749i	$0.381717\pi$
$488$	0.614008	−	7.01815i	0.0277948	−	0.317697i
$489$	21.9654	−	2.76157i	0.993310	−	0.124882i
$490$	−0.383397	+	15.3133i	−0.0173201	+	0.691783i
$491$	−11.8707	+	14.1469i	−0.535716	+	0.638442i	−0.964222	−	0.265098i	$-0.914596\pi$
$491$	−11.8707	+	14.1469i	−0.535716	+	0.638442i	0.428506	+	0.903539i	$0.359040\pi$
$492$	−3.54071	−	8.69106i	−0.159628	−	0.391823i
$493$	−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
$497$	0.174596	+	1.99564i	0.00783171	+	0.0895169i
$498$	−14.8890	+	3.20982i	−0.667192	+	0.143836i
$499$	−3.59317	−	9.87215i	−0.160852	−	0.441938i	0.832917	−	0.553399i	$-0.186669\pi$
$499$	−3.59317	−	9.87215i	−0.160852	−	0.441938i	−0.993769	+	0.111461i	$0.964447\pi$
$500$	8.65147	+	7.08181i	0.386906	+	0.316708i
$501$	10.7288	+	34.7323i	0.479326	+	1.55173i
$502$	−7.68903	−	28.6959i	−0.343178	−	1.28076i
$503$	18.6713	+	13.0738i	0.832511	+	0.582931i	0.910257	−	0.414043i	$-0.135884\pi$
$503$	18.6713	+	13.0738i	0.832511	+	0.582931i	−0.0777464	+	0.996973i	$0.524772\pi$
$504$	0.313323	−	1.11705i	0.0139565	−	0.0497574i
$505$	−11.5674	+	7.67542i	−0.514743	+	0.341552i
$506$	−5.11825	+	2.95502i	−0.227534	+	0.131367i
$507$	−21.3385	−	6.86508i	−0.947675	−	0.304889i
$508$	18.8103	+	8.77137i	0.834571	+	0.389167i
$509$	−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	$0.766083\pi$
$510$	0.280730	+	0.191274i	0.0124309	+	0.00846975i
$511$	−0.273539	+	1.55132i	−0.0121006	+	0.0686261i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	8.27377	+	21.0842i	0.365296	+	0.930891i
$514$			19.9523i			0.880060i
$515$	−5.29753	−	35.1703i	−0.233437	−	1.54979i
$516$	3.98894	−	3.02403i	0.175603	−	0.133125i
$517$	0.531637	−	0.247906i	0.0233814	−	0.0109029i
$518$	−1.76721	+	3.78980i	−0.0776468	+	0.166514i
$519$	0.0494715	+	0.0964025i	0.00217156	+	0.00423160i
$520$	−0.539027	+	0.0335896i	−0.0236379	+	0.00147300i
$521$	27.7918	+	16.0456i	1.21758	+	0.702971i	0.964400	−	0.264447i	$-0.0851895\pi$
$521$	27.7918	+	16.0456i	1.21758	+	0.702971i	0.253182	+	0.967419i	$0.418523\pi$
$522$	4.88342	+	8.69090i	0.213742	+	0.380390i
$523$	−11.2039	+	16.0009i	−0.489914	+	0.699669i	−0.985650	−	0.168804i	$-0.946010\pi$
$523$	−11.2039	+	16.0009i	−0.489914	+	0.699669i	0.495736	+	0.868473i	$0.334898\pi$
$524$	−8.32670	+	14.4223i	−0.363754	+	0.630040i
$525$	−2.71966	−	1.95446i	−0.118696	−	0.0852996i
$526$	11.2036	−	9.40096i	0.488502	−	0.409901i
$527$	−0.341438	−	0.159215i	−0.0148733	−	0.00693553i
$528$	1.52390	+	7.06873i	0.0663193	+	0.307627i
$529$	−13.4960	+	16.0839i	−0.586782	+	0.699300i
$530$	−13.8712	−	10.2396i	−0.602528	−	0.444778i
$531$	−0.955823	+	1.98886i	−0.0414792	+	0.0863093i
$532$	1.66043	−	0.290637i	0.0719888	−	0.0126007i
$533$	0.925354	−	0.925354i	0.0400815	−	0.0400815i
$534$	1.05105	−	2.49617i	0.0454832	−	0.108020i
$535$	1.84508	+	0.724352i	0.0797699	+	0.0313164i
$536$	0.415377	−	1.14124i	0.0179415	−	0.0492940i
$537$	22.2972	−	28.7099i	0.962193	−	1.23893i
$538$	−21.9854	−	1.92347i	−0.947858	−	0.0829268i
$539$	14.2999	+	24.7682i	0.615942	+	1.06684i
$540$	−7.47834	−	8.89238i	−0.321817	−	0.382667i
$541$	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	$0.831897\pi$
$542$	−8.88189	+	12.6847i	−0.381510	+	0.544853i
$543$	−0.0761498	−	2.01354i	−0.00326790	−	0.0864093i
$544$	0.0759588	−	0.0438548i	0.00325671	−	0.00188026i
$545$	−39.1694	+	9.45132i	−1.67783	+	0.404850i
$546$	0.160516	−	0.0201807i	0.00686946	−	0.000863653i
$547$	34.2574	−	15.9745i	1.46474	−	0.683019i	0.483417	−	0.875390i	$-0.339396\pi$
$547$	34.2574	−	15.9745i	1.46474	−	0.683019i	0.981322	+	0.192371i	$0.0616178\pi$
$548$	−10.7576	+	0.941168i	−0.459542	+	0.0402047i
$549$	17.1701	+	12.3236i	0.732801	+	0.525958i
$550$	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
$553$	−4.90158	+	3.43212i	−0.208436	+	0.145949i
$554$	−20.1397	−	16.8992i	−0.855654	−	0.717979i
$555$	21.4005	+	35.9973i	0.908401	+	1.52800i
$556$	5.50188	−	2.00252i	0.233332	−	0.0849258i
$557$	9.86765	+	0.863308i	0.418106	+	0.0365795i	0.294268	−	0.955723i	$-0.404924\pi$
$557$	9.86765	+	0.863308i	0.418106	+	0.0365795i	0.123838	+	0.992302i	$0.460480\pi$
$558$	9.77379	+	8.39739i	0.413757	+	0.355490i
$559$	0.604500	+	0.349008i	0.0255676	+	0.0147615i
$560$	−0.759468	+	0.413487i	−0.0320934	+	0.0174730i
$561$	0.633464	+	0.0313603i	0.0267449	+	0.00132403i
$562$	−6.76788	−	25.2581i	−0.285486	−	1.06545i
$563$	−10.8481	−	2.90674i	−0.457194	−	0.122505i	0.0228698	−	0.999738i	$-0.492720\pi$
$563$	−10.8481	−	2.90674i	−0.457194	−	0.122505i	−0.480063	+	0.877234i	$0.659386\pi$
$564$	0.111112	+	0.216517i	0.00467864	+	0.00911703i
$565$	22.3813	+	28.0709i	0.941587	+	1.18095i
$566$	7.19177	−	19.7592i	0.302293	−	0.830542i
$567$	2.40299	+	2.51782i	0.100916	+	0.105738i
$568$	4.24332	−	2.97121i	0.178046	−	0.124669i
$569$	−31.1436			−1.30561			−0.652803	−	0.757528i	$-0.726407\pi$
$569$	−31.1436			−1.30561			−0.652803	+	0.757528i	$0.726407\pi$
$570$	6.95792	−	15.3814i	0.291435	−	0.644256i
$571$	32.3676			1.35454			0.677271	−	0.735733i	$-0.263162\pi$
$571$	32.3676			1.35454			0.677271	+	0.735733i	$0.263162\pi$
$572$	−0.825994	+	0.578367i	−0.0345365	+	0.0241827i
$573$	1.63160	−	11.8583i	0.0681609	−	0.495389i
$574$	0.716647	−	1.96897i	0.0299123	−	0.0821832i
$575$	−6.92001	+	1.48751i	−0.288584	+	0.0620335i
$576$	−2.90664	+	0.742603i	−0.121110	+	0.0309418i
$577$	−27.7460	−	7.43452i	−1.15508	−	0.309503i	−0.370082	−	0.928999i	$-0.620670\pi$
$577$	−27.7460	−	7.43452i	−1.15508	−	0.309503i	−0.785000	+	0.619496i	$0.787337\pi$
$578$	4.39793	+	16.4133i	0.182930	+	0.682704i
$579$	−0.567105	+	11.4553i	−0.0235681	+	0.476064i
$580$	2.10217	−	7.12684i	0.0872877	−	0.295926i
$581$	−2.94508	−	1.70034i	−0.122183	−	0.0705422i
$582$	−16.9064	−	8.92662i	−0.700793	−	0.370020i
$583$	−32.0681	−	2.80559i	−1.32812	−	0.116196i
$584$	3.82769	−	1.39317i	0.158391	−	0.0576497i
$585$	0.738146	−	1.44230i	0.0305186	−	0.0596320i
$586$	−4.37711	−	3.67283i	−0.180817	−	0.151723i
$587$	−6.55433	+	4.58939i	−0.270526	+	0.189424i	−0.700966	−	0.713195i	$-0.747247\pi$
$587$	−6.55433	+	4.58939i	−0.270526	+	0.189424i	0.430440	+	0.902619i	$0.358359\pi$
$588$	−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
$591$	−11.4942	+	27.2981i	−0.472809	+	1.12289i
$592$	10.7718	−	0.942408i	0.442717	−	0.0387327i
$593$	−35.6055	+	16.6031i	−1.46214	+	0.681808i	−0.980852	−	0.194753i	$-0.937609\pi$
$593$	−35.6055	+	16.6031i	−1.46214	+	0.681808i	−0.481290	+	0.876561i	$0.659832\pi$
$594$	−20.5720	−	6.88432i	−0.844081	−	0.282467i
$595$	0.0177904	+	0.0737295i	0.000729337	+	0.00302261i
$596$	−8.14579	+	4.70298i	−0.333665	+	0.192641i
$597$	−4.96250	+	0.187676i	−0.203101	+	0.00768106i
$598$	0.196112	−	0.280076i	0.00801960	−	0.0114532i
$599$	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	$0.722988\pi$
$600$	−0.860524	+	8.61740i	−0.0351308	+	0.351804i
$601$	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	$0.751028\pi$
$602$	1.11337	+	0.0974074i	0.0453776	+	0.00397003i
$603$	2.30924	+	2.81817i	0.0940397	+	0.114765i
$604$	2.06081	−	5.66204i	0.0838533	−	0.230385i
$605$	13.1783	−	5.74808i	0.535774	−	0.233693i
$606$	−9.91045	−	4.17293i	−0.402585	−	0.169514i
$607$	−12.1810	+	12.1810i	−0.494413	+	0.494413i	−0.909693	−	0.415281i	$-0.863683\pi$
$607$	−12.1810	+	12.1810i	−0.494413	+	0.494413i	0.415281	+	0.909693i	$0.363683\pi$
$608$	−2.79767	−	3.34261i	−0.113460	−	0.135561i
$609$	−0.494416	+	2.17019i	−0.0200347	+	0.0879405i
$610$	−2.34633	−	15.5773i	−0.0950001	−	0.630706i
$611$	−0.0218137	+	0.0259965i	−0.000882486	+	0.00105171i
$612$	−0.00306929	+	0.263111i	−0.000124069	+	0.0106356i
$613$	3.77675	+	1.76113i	0.152541	+	0.0711313i	0.497390	−	0.867527i	$-0.334292\pi$
$613$	3.77675	+	1.76113i	0.152541	+	0.0711313i	−0.344848	+	0.938658i	$0.612070\pi$
$614$	4.98408	−	4.18214i	0.201141	−	0.168778i
$615$	−12.2548	−	17.0345i	−0.494162	−	0.686899i
$616$	−0.807259	+	1.39821i	−0.0325254	+	0.0563356i
$617$	−22.8753	+	32.6694i	−0.920927	+	1.31522i	0.0279620	+	0.999609i	$0.491098\pi$
$617$	−22.8753	+	32.6694i	−0.920927	+	1.31522i	−0.948889	+	0.315611i	$0.897791\pi$
$618$	20.4203	−	18.4938i	0.821424	−	0.743930i
$619$	−23.1303	−	13.3543i	−0.929683	−	0.536753i	−0.0429719	−	0.999076i	$-0.513683\pi$
$619$	−23.1303	−	13.3543i	−0.929683	−	0.536753i	−0.886711	+	0.462323i	$0.847016\pi$
$620$	−0.597347	−	9.58589i	−0.0239900	−	0.384979i
$621$	7.35324	−	0.192228i	0.295075	−	0.00771383i
$622$	−3.24767	+	6.96466i	−0.130220	+	0.279257i
$623$	0.548061	−	0.255565i	0.0219576	−	0.0102390i
$624$	−0.252728	−	0.333370i	−0.0101172	−	0.0133455i
$625$	22.5199	+	10.8560i	0.900798	+	0.434238i
$626$		−	19.3093i		−	0.771756i
$627$	−3.89269	−	31.2785i	−0.155459	−	1.24914i
$628$	10.5817	+	10.5817i	0.422256	+	0.422256i
$629$	0.164688	−	0.933989i	0.00656652	−	0.0372406i
$630$	0.0951768	−	2.59245i	0.00379194	−	0.103286i
$631$	−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	$0.828302\pi$
$632$	14.0233	+	6.53916i	0.557816	+	0.260114i
$633$	12.1608	−	37.7990i	0.483348	−	1.50237i
$634$	−23.9107	+	13.8049i	−0.949616	+	0.548261i
$635$	45.4881	+	9.20028i	1.80514	+	0.365102i
$636$	0.660344	−	13.3387i	0.0261844	−	0.528912i
$637$	−1.35535	−	0.949024i	−0.0537008	−	0.0376017i
$638$	−3.59062	−	13.4004i	−0.142154	−	0.530526i
$639$	1.17376	+	15.4960i	0.0464333	+	0.613014i
$640$	1.90790	+	1.16615i	0.0754164	+	0.0460962i
$641$	13.7302	+	37.7234i	0.542310	+	1.48998i	0.843876	+	0.536539i	$0.180269\pi$
$641$	13.7302	+	37.7234i	0.542310	+	1.48998i	−0.301566	+	0.953445i	$0.597509\pi$
$642$	0.323570	+	1.50090i	0.0127703	+	0.0592360i
$643$	0.493763	+	5.64374i	0.0194721	+	0.222567i	0.999696	+	0.0246734i	$0.00785458\pi$
$643$	0.493763	+	5.64374i	0.0194721	+	0.222567i	−0.980223	+	0.197894i	$0.936590\pi$
$644$	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	0.844866	−	0.534978i	$-0.179680\pi$
$647$	7.88238	+	7.88238i	0.309888	+	0.309888i	−0.534978	+	0.844866i	$0.679680\pi$
$648$	2.53153	−	8.63663i	0.0994480	−	0.339279i
$649$	1.97387	−	2.35237i	0.0774813	−	0.0923387i
$650$	−1.15406	+	0.355730i	−0.0452658	+	0.0139529i
$651$	0.358887	+	2.85458i	0.0140659	+	0.111880i
$652$	1.11399	−	12.7329i	0.0436271	−	0.498660i
$653$	29.4972	+	7.90374i	1.15431	+	0.309297i	0.784692	−	0.619885i	$-0.212821\pi$
$653$	29.4972	+	7.90374i	1.15431	+	0.309297i	0.369621	+	0.929183i	$0.379488\pi$
$654$	−22.8880	−	21.2199i	−0.894991	−	0.829762i
$655$	−10.5352	+	35.7168i	−0.411644	+	1.39557i
$656$	−5.33590	+	0.940863i	−0.208332	+	0.0367345i
$657$	−2.26222	+	12.0088i	−0.0882576	+	0.468509i
$658$	−0.0140633	+	0.0524850i	−0.000548245	+	0.00204608i
$659$	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	$-0.0168751\pi$
$660$	7.02000	+	14.5659i	0.273253	+	0.566977i
$661$	−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	$0.968373\pi$
$662$	−1.55999	−	17.8308i	−0.0606307	−	0.693012i
$663$	−0.0339806	+	0.0138436i	−0.00131970	+	0.000537640i
$664$			8.79366i			0.341260i
$665$	3.45682	−	1.50264i	0.134050	−	0.0582700i
$666$	−14.0512	+	29.2376i	−0.544474	+	1.13293i
$667$	2.69814	+	3.85334i	0.104472	+	0.149202i
$668$	20.9078	−	1.82919i	0.808946	−	0.0707736i
$669$	−9.70353	−	6.26169i	−0.375160	−	0.242091i
$670$	0.304323	−	2.69856i	0.0117570	−	0.104254i
$671$	−18.9056	−	22.5309i	−0.729844	−	0.869794i
$672$	−0.592323	−	0.312748i	−0.0228494	−	0.0120645i
$673$	26.4162	−	7.07819i	1.01827	−	0.272844i	0.289188	−	0.957272i	$-0.406615\pi$
$673$	26.4162	−	7.07819i	1.01827	−	0.272844i	0.729080	+	0.684428i	$0.239948\pi$
$674$	−1.35326	−	7.67470i	−0.0521255	−	0.295618i
$675$	−20.9196	−	15.4069i	−0.805195	−	0.593011i
$676$	−6.47083	+	11.2078i	−0.248878	+	0.431070i
$677$	5.91360	−	22.0699i	0.227278	−	0.848214i	−0.754201	−	0.656644i	$-0.771975\pi$
$677$	5.91360	−	22.0699i	0.227278	−	0.848214i	0.981479	−	0.191570i	$-0.0613579\pi$
$678$	−8.51686	+	26.4726i	−0.327088	+	1.01668i
$679$	−1.45995	−	4.01118i	−0.0560278	−	0.153935i
$680$	0.142109	−	0.135167i	0.00544962	−	0.00518340i
$681$	4.41490	+	5.82363i	0.169179	+	0.223162i
$682$	−10.2855	−	14.6892i	−0.393853	−	0.562480i
$683$	−11.2707	+	11.2707i	−0.431262	+	0.431262i	−0.889058	−	0.457795i	$-0.848639\pi$
$683$	−11.2707	+	11.2707i	−0.431262	+	0.431262i	0.457795	+	0.889058i	$0.348639\pi$
$684$	12.9063	−	2.10423i	0.493484	−	0.0804571i
$685$	−22.8900	+	7.68812i	−0.874582	+	0.293748i
$686$	−5.27488	−	0.930103i	−0.201396	−	0.0355115i
$687$	5.05656	−	36.7507i	0.192920	−	1.40213i
$688$	−1.22137	−	2.61924i	−0.0465643	−	0.0998574i
$689$	1.74999	−	0.636945i	0.0666693	−	0.0242657i
$690$	−3.92601	−	3.82700i	−0.149461	−	0.145692i
$691$	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	$0.823494\pi$
$692$	0.0604273	−	0.0161914i	0.00229710	−	0.000615507i
$693$	−2.37268	−	4.22260i	−0.0901307	−	0.160403i
$694$	6.06280	−	1.06903i	0.230141	−	0.0405800i
$695$	10.9090	−	7.23857i	0.413804	−	0.274574i
$696$	5.49918	−	1.69869i	0.208446	−	0.0643886i
$697$	−0.0414190	+	0.473421i	−0.00156886	+	0.0179321i
$698$	3.43208	−	7.36012i	0.129906	−	0.278585i
$699$	9.56572	−	14.8237i	0.361809	−	0.560683i
$700$	−1.43397	+	1.29713i	−0.0541990	+	0.0490269i
$701$	13.6591	+	2.40846i	0.515896	+	0.0909664i	0.425534	−	0.904942i	$-0.360086\pi$
$701$	13.6591	+	2.40846i	0.515896	+	0.0909664i	0.0903625	+	0.995909i	$0.471197\pi$
$702$	1.24695	−	0.142017i	0.0470632	−	0.00536008i
$703$	−47.1324	−	0.0589710i	−1.77763	−	0.00222413i
$704$	4.17489			0.157347
$705$	0.355084	+	0.412363i	0.0133732	+	0.0155305i
$706$	−4.01795	−	3.37146i	−0.151217	−	0.126887i
$707$	−1.01466	−	2.17595i	−0.0381602	−	0.0818349i
$708$	1.00619	+	0.781440i	0.0378148	+	0.0293683i
$709$	21.9263	+	26.1308i	0.823460	+	0.981362i	0.999996	−	0.00293245i	$-0.000933429\pi$
$709$	21.9263	+	26.1308i	0.823460	+	0.981362i	−0.176535	+	0.984294i	$0.556489\pi$
$710$	7.66526	−	8.68407i	0.287672	−	0.325907i
$711$	−38.3322	+	26.1795i	−1.43757	+	0.981807i
$712$	−1.28092	−	0.896907i	−0.0480043	−	0.0336130i
$713$	4.98080	+	3.48759i	0.186532	+	0.130611i
$714$	−0.0399426	+	0.0430825i	−0.00149482	+	0.00161232i
$715$	−1.49210	+	1.69042i	−0.0558013	+	0.0632181i
$716$	−13.4905	−	16.0773i	−0.504164	−	0.600839i
$717$	17.9728	−	23.1419i	0.671207	−	0.864249i
$718$	9.97131	+	21.3835i	0.372126	+	0.798027i
$719$	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	$0.529286\pi$
$720$	−5.92862	+	3.13870i	−0.220947	+	0.116973i
$721$	6.15120			0.229083
$722$	10.8590	+	15.5911i	0.404129	+	0.580241i
$723$	15.7272	−	9.89084i	0.584900	−	0.367844i
$724$	−1.14568	−	0.202014i	−0.0425787	−	0.00750777i
$725$	0.831450	−	16.5941i	0.0308793	−	0.616288i
$726$	9.35748	+	6.03839i	0.347289	+	0.224106i
$727$	−15.0458	+	32.2659i	−0.558019	+	1.19668i	0.401715	+	0.915765i	$0.368414\pi$
$727$	−15.0458	+	32.2659i	−0.558019	+	1.19668i	−0.959734	+	0.280911i	$0.909363\pi$
$728$	0.00814067	−	0.0930483i	0.000301713	−	0.00344860i
$729$	18.4122	+	19.7482i	0.681934	+	0.731414i
$730$	7.58949	−	5.03592i	0.280900	−	0.186388i
$731$	−0.249630	+	0.0440166i	−0.00923292	+	0.00162801i
$732$	9.04435	−	8.19109i	0.334289	−	0.302751i
$733$	−21.3473	+	5.71998i	−0.788479	+	0.211272i	−0.630520	−	0.776173i	$-0.717158\pi$
$733$	−21.3473	+	5.71998i	−0.788479	+	0.211272i	−0.157960	+	0.987446i	$0.550492\pi$
$734$	2.77627	+	4.80865i	0.102474	+	0.177490i
$735$	−18.5196	+	18.9987i	−0.683107	+	0.700779i
$736$	−1.33024	+	0.484169i	−0.0490334	+	0.0178467i
$737$	−2.14281	−	4.59528i	−0.0789315	−	0.169269i
$738$	5.73721	−	15.2085i	0.211190	−	0.559832i
$739$	9.88521	+	1.74303i	0.363633	+	0.0641184i	0.352480	−	0.935819i	$-0.385339\pi$
$739$	9.88521	+	1.74303i	0.363633	+	0.0641184i	0.0111536	+	0.999938i	$0.496450\pi$
$740$	22.9202	−	7.69825i	0.842562	−	0.282993i
$741$	0.968844	+	1.54482i	0.0355914	+	0.0567504i
$742$	2.10846	−	2.10846i	0.0774040	−	0.0774040i
$743$	14.3922	+	20.5542i	0.528000	+	0.754062i	0.991226	−	0.132178i	$-0.0421971\pi$
$743$	14.3922	+	20.5542i	0.528000	+	0.754062i	−0.463226	+	0.886240i	$0.653308\pi$
$744$	5.92855	−	4.49444i	0.217351	−	0.164774i
$745$	−15.2397	+	14.4952i	−0.558339	+	0.531064i
$746$	5.55022	+	15.2491i	0.203208	+	0.558310i
$747$	−22.6912	−	13.4561i	−0.830227	−	0.492333i
$748$	0.0947740	−	0.353701i	0.00346528	−	0.0129326i
$749$	−0.171405	+	0.296883i	−0.00626301	+	0.0108479i
$750$	2.64928	+	19.1828i	0.0967380	+	0.700458i
$751$	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	$0.789517\pi$
$752$	0.135718	−	0.0363656i	0.00494913	−	0.00132612i
$753$	24.0255	−	45.5027i	0.875539	−	1.65821i
$754$	0.515895	+	0.614820i	0.0187878	+	0.0223904i
$755$	1.50984	−	13.3884i	0.0549488	−	0.487253i
$756$	1.71339	−	1.04986i	0.0623154	−	0.0381832i
$757$	4.00393	−	0.350298i	0.145525	−	0.0127318i	−0.0141603	−	0.999900i	$-0.504508\pi$
$757$	4.00393	−	0.350298i	0.145525	−	0.0127318i	0.159686	+	0.987168i	$0.448952\pi$
$758$	−5.03252	−	7.18718i	−0.182789	−	0.261050i
$759$	−9.98076	−	2.27383i	−0.362279	−	0.0825349i
$760$	−7.83443	−	5.79842i	−0.284185	−	0.210331i
$761$			0.572699i			0.0207603i	0.999946	+	0.0103802i	$0.00330417\pi$
$761$			0.572699i			0.0207603i	−0.999946	+	0.0103802i	$0.996696\pi$
$762$	13.5629	+	33.2917i	0.491333	+	1.20603i
$763$	−0.607357	−	6.94212i	−0.0219878	−	0.251321i
$764$	−6.49414	−	2.36367i	−0.234950	−	0.0855147i
$765$	0.131329	+	0.573530i	0.00474821	+	0.0207360i
$766$	−22.7208	+	19.0650i	−0.820936	+	0.688847i
$767$	−0.0459801	+	0.171600i	−0.00166024	+	0.00619611i
$768$	0.0654573	+	1.73081i	0.00236199	+	0.0624554i
$769$	−35.8121	+	6.31464i	−1.29142	+	0.227712i	−0.776822	−	0.629721i	$-0.783169\pi$
$769$	−35.8121	+	6.31464i	−1.29142	+	0.227712i	−0.514597	+	0.857432i	$0.672058\pi$
$770$	−1.02137	+	3.46268i	−0.0368076	+	0.124786i
$771$	−23.4956	+	25.3426i	−0.846172	+	0.912690i
$772$	6.39616	+	1.71385i	0.230203	+	0.0616827i
$773$	1.73190	−	19.7957i	0.0622920	−	0.712001i	−0.899267	−	0.437401i	$-0.855899\pi$
$773$	1.73190	−	19.7957i	0.0622920	−	0.712001i	0.961559	−	0.274600i	$-0.0885454\pi$
$774$	8.62762	+	0.856338i	0.310114	+	0.0307804i
$775$	−6.32621	−	20.5234i	−0.227244	−	0.737222i
$776$	−7.09508	+	8.45558i	−0.254698	+	0.303538i
$777$	−6.70744	+	2.73259i	−0.240628	+	0.0980311i
$778$	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
$782$	0.0108215	+	0.123691i	0.000386977	+	0.00442317i
$783$	−4.03157	+	16.7894i	−0.144077	+	0.600006i
$784$	2.34299	+	6.43731i	0.0836782	+	0.229904i
$785$	28.5513	+	17.4512i	1.01904	+	0.622861i
$786$	−27.5597	+	8.51313i	−0.983020	+	0.303653i
$787$	−6.05780	−	22.6080i	−0.215937	−	0.805889i	−0.985834	−	0.167721i	$-0.946359\pi$
$787$	−6.05780	−	22.6080i	−0.215937	−	0.805889i	0.769897	−	0.638168i	$-0.220308\pi$
$788$	14.0081	+	9.80855i	0.499017	+	0.349415i
$789$	25.3008	+	1.25254i	0.900732	+	0.0445917i
$790$	33.9120	+	6.85892i	1.20653	+	0.244030i
$791$	−5.37715	+	3.10450i	−0.191189	+	0.110383i
$792$	−6.38844	+	10.7729i	−0.227003	+	0.382799i
$793$	1.54213	+	0.719107i	0.0547626	+	0.0255362i
$794$	32.1016	+	11.6840i	1.13924	+	0.414651i
$795$	−5.56069	−	29.3404i	−0.197217	−	1.04060i
$796$	−0.497875	+	2.82359i	−0.0176467	+	0.100079i
$797$	−23.4098	−	23.4098i	−0.829218	−	0.829218i	0.158191	−	0.987409i	$-0.449434\pi$
$797$	−23.4098	−	23.4098i	−0.829218	−	0.829218i	−0.987409	+	0.158191i	$0.949434\pi$
$798$	2.45126	+	1.58614i	0.0867735	+	0.0561489i
$799$		−	0.0123237i		−	0.000435982i
$800$	4.75882	+	1.53416i	0.168250	+	0.0542408i
$801$	4.27444	−	1.93283i	0.151030	−	0.0682931i
$802$	3.05840	−	1.42616i	0.107996	−	0.0503593i
$803$	7.18696	−	15.4125i	0.253622	−	0.543895i
$804$	1.87150	−	0.960409i	0.0660027	−	0.0338710i
$805$	−0.0761343	−	1.22176i	−0.00268338	−	0.0430614i
$806$	0.898435	+	0.518712i	0.0316460	+	0.0182708i
$807$	−25.6598	−	28.3328i	−0.903268	−	0.997361i
$808$	−3.56096	+	5.08557i	−0.125274	+	0.178910i
$809$	−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	$0.294043\pi$
$810$	0.972875	−	20.1011i	0.0341833	−	0.706280i
$811$	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	$0.222466\pi$
$812$	1.16466	+	0.543091i	0.0408717	+	0.0190588i
$813$	−26.2186	+	5.65230i	−0.919528	+	0.198235i
$814$	29.0172	−	34.5814i	1.01705	−	1.21208i
$815$	−4.25691	−	28.2616i	−0.149113	−	0.989962i
$816$	0.148122	+	0.0337455i	0.00518531	+	0.00118133i
$817$	4.29370	+	11.8429i	0.150217	+	0.414331i
$818$	10.5334	−	10.5334i	0.368293	−	0.368293i
$819$	0.227645	+	0.163389i	0.00795456	+	0.00570927i
$820$	−11.1051	+	4.84380i	−0.387806	+	0.169153i
$821$	16.1110	−	44.2647i	0.562279	−	1.54485i	−0.254009	−	0.967202i	$-0.581749\pi$
$821$	16.1110	−	44.2647i	0.562279	−	1.54485i	0.816287	−	0.577646i	$-0.196029\pi$
$822$	−14.7721	−	11.4726i	−0.515237	−	0.400151i
$823$	17.1250	+	1.49824i	0.596940	+	0.0522255i	0.381622	−	0.924318i	$-0.375366\pi$
$823$	17.1250	+	1.49824i	0.596940	+	0.0522255i	0.215318	+	0.976544i	$0.430921\pi$
$824$	−7.95303	−	13.7751i	−0.277057	−	0.479877i
$825$	22.8990	+	27.9797i	0.797242	+	0.974129i
$826$	0.0493940	+	0.280127i	0.00171864	+	0.00974687i
$827$	31.9727	−	45.6617i	1.11180	−	1.58781i	0.354104	−	0.935206i	$-0.384786\pi$
$827$	31.9727	−	45.6617i	1.11180	−	1.58781i	0.757695	−	0.652608i	$-0.226325\pi$
$828$	0.786192	−	4.17344i	0.0273221	−	0.145037i
$829$	14.3311	−	8.27408i	0.497741	−	0.287371i	−0.230039	−	0.973181i	$-0.573886\pi$
$829$	14.3311	−	8.27408i	0.497741	−	0.287371i	0.727780	+	0.685811i	$0.240552\pi$
$830$	4.61224	+	19.1146i	0.160093	+	0.663479i
$831$	−5.68029	−	45.1808i	−0.197047	−	1.56731i
$832$	−0.218898	+	0.102074i	−0.00758894	+	0.00353878i
$833$	0.598564	−	0.0523676i	0.0207390	−	0.00181443i
$834$	9.34638	+	3.93542i	0.323639	+	0.136272i
$835$	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
$838$	−23.7001	+	16.5950i	−0.818707	+	0.573265i
$839$	−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	$0.964417\pi$
$840$	−1.45156	−	0.369145i	−0.0500835	−	0.0127367i
$841$	16.8748	−	6.14194i	0.581891	−	0.211791i
$842$	−25.9196	−	2.26767i	−0.893250	−	0.0781492i
$843$	21.1473	−	40.0514i	0.728350	−	1.37944i
$844$	−19.8535	−	11.4624i	−0.683386	−	0.394553i
$845$	−8.18710	+	27.7562i	−0.281645	+	0.954841i
$846$	−0.113839	+	0.405854i	−0.00391385	+	0.0139536i
$847$	0.643557	+	2.40179i	0.0221129	+	0.0825264i
$848$	−7.44778	−	1.99563i	−0.255758	−	0.0685301i
$849$	32.4028	−	16.6284i	1.11206	−	0.570684i
$850$	0.238005	−	0.368345i	0.00816351	−	0.0126341i
$851$	−5.23528	+	14.3838i	−0.179463	+	0.493071i
$852$	8.88853	+	1.22298i	0.304516	+	0.0418985i
$853$	15.8605	−	11.1056i	0.543052	−	0.380249i	−0.269623	−	0.962966i	$-0.586899\pi$
$853$	15.8605	−	11.1056i	0.543052	−	0.380249i	0.812675	+	0.582717i	$0.198010\pi$
$854$	2.72443			0.0932280
$855$	26.9505	−	11.3432i	0.921689	−	0.387930i
$856$	0.886456			0.0302984
$857$	31.6070	−	22.1315i	1.07967	−	0.755996i	0.108436	−	0.994103i	$-0.465416\pi$
$857$	31.6070	−	22.1315i	1.07967	−	0.755996i	0.971239	+	0.238107i	$0.0765269\pi$
$858$	−1.73022	−	0.238062i	−0.0590686	−	0.00812729i
$859$	−7.57765	+	20.8194i	−0.258546	+	0.710349i	0.740712	+	0.671823i	$0.234489\pi$
$859$	−7.57765	+	20.8194i	−0.258546	+	0.710349i	−0.999258	+	0.0385262i	$0.987734\pi$
$860$	−4.02865	−	5.05279i	−0.137376	−	0.172299i
$861$	3.22888	−	1.65699i	0.110040	−	0.0564699i
$862$	4.45283	+	1.19313i	0.151664	+	0.0406382i
$863$	−1.73881	−	6.48934i	−0.0591899	−	0.220900i	0.929995	−	0.367571i	$-0.119811\pi$
$863$	−1.73881	−	6.48934i	−0.0591899	−	0.220900i	−0.989185	+	0.146672i	$0.953144\pi$
$864$	−4.56636	−	2.47959i	−0.155351	−	0.0843574i
$865$	0.122858	−	0.0668890i	0.00417728	−	0.00227429i
$866$	0.547569	+	0.316139i	0.0186072	+	0.0107428i
$867$	−13.7420	+	26.0264i	−0.466703	+	0.883902i
$868$	1.65474	+	0.144771i	0.0561656	+	0.00491386i
$869$	60.7023	−	22.0938i	2.05919	−	0.749482i
$870$	11.0625	−	6.57671i	0.375055	−	0.222971i
$871$	0.224704	+	0.188549i	0.00761382	+	0.00638875i
$872$	−14.7610	+	10.3357i	−0.499870	+	0.350012i
$873$	−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
$876$	6.50234	+	2.73790i	0.219694	+	0.0925049i
$877$	12.7682	−	1.11708i	0.431153	−	0.0377210i	0.130486	−	0.991450i	$-0.458346\pi$
$877$	12.7682	−	1.11708i	0.431153	−	0.0377210i	0.300667	+	0.953729i	$0.402791\pi$
$878$	35.4375	−	16.5248i	1.19596	−	0.557684i
$879$	−1.23454	−	9.81949i	−0.0416400	−	0.331203i
$880$	9.07490	−	2.18972i	0.305915	−	0.0738153i
$881$	−6.52795	+	3.76891i	−0.219932	+	0.126978i	−0.605919	−	0.795526i	$-0.707194\pi$
$881$	−6.52795	+	3.76891i	−0.219932	+	0.126978i	0.385987	+	0.922504i	$0.373861\pi$
$882$	−20.1961	−	3.80454i	−0.680039	−	0.128106i
$883$	−27.2042	+	38.8516i	−0.915493	+	1.30746i	0.0358594	+	0.999357i	$0.488583\pi$
$883$	−27.2042	+	38.8516i	−0.915493	+	1.30746i	−0.951353	+	0.308103i	$0.900306\pi$
$884$	0.00367862	+	0.0208625i	0.000123725	+	0.000701681i
$885$	2.59699	+	1.17086i	0.0872970	+	0.0393581i
$886$	16.2581	+	28.1598i	0.546200	+	0.946047i
$887$	−18.9921	−	1.66160i	−0.637694	−	0.0557910i	−0.236276	−	0.971686i	$-0.575927\pi$
$887$	−18.9921	−	1.66160i	−0.637694	−	0.0557910i	−0.401418	+	0.915895i	$0.631482\pi$
$888$	14.7916	+	11.4877i	0.496373	+	0.385501i
$889$	−2.74516	+	7.54227i	−0.0920698	+	0.252960i
$890$	−3.25473	−	1.27776i	−0.109099	−	0.0428305i
$891$	−18.0228	−	32.9695i	−0.603787	−	1.10452i
$892$	−4.71464	+	4.71464i	−0.157858	+	0.157858i
$893$	−0.603279	+	0.105596i	−0.0201879	+	0.00353364i
$894$	−15.8846	−	3.61885i	−0.531260	−	0.121032i
$895$	−37.7566	−	27.8714i	−1.26206	−	0.931637i
$896$	−0.248579	+	0.296245i	−0.00830445	+	0.00989685i
$897$	0.578906	−	0.124803i	0.0193291	−	0.00416703i
$898$	−24.5635	−	11.4542i	−0.819696	−	0.382230i
$899$	−10.9338	+	9.17454i	−0.364662	+	0.305988i
$900$	−11.2407	+	9.93209i	−0.374690	+	0.331070i
$901$	−0.338143	+	0.585681i	−0.0112652	+	0.0195119i
$902$	−12.9746	+	18.5296i	−0.432006	+	0.616968i
$903$	1.29945	+	1.43481i	0.0432430	+	0.0477476i
$904$	13.9045	+	8.02775i	0.462456	+	0.266999i
$905$	−2.59629	+	0.161789i	−0.0863037	+	0.00537804i
$906$	9.28508	−	4.76489i	0.308476	−	0.158303i
$907$	11.7681	−	25.2368i	0.390754	−	0.837974i	−0.608267	−	0.793732i	$-0.708135\pi$
$907$	11.7681	−	25.2368i	0.390754	−	0.837974i	0.999021	−	0.0442415i	$-0.0140871\pi$
$908$	3.82393	−	1.78313i	0.126902	−	0.0591752i
$909$	−7.67384	−	16.9707i	−0.254525	−	0.562881i
$910$	−0.0311082	−	0.206527i	−0.00103123	−	0.00684631i
$911$		−	12.2429i		−	0.405624i	−0.979218	−	0.202812i	$-0.934992\pi$
$911$		−	12.2429i		−	0.405624i	0.979218	−	0.202812i	$-0.0650080\pi$
$912$	0.382740	−	7.54013i	0.0126738	−	0.249679i
$913$	25.9597	+	25.9597i	0.859142	+	0.859142i
$914$	6.16481	−	34.9624i	0.203914	−	1.15645i
$915$	15.3634	−	22.5486i	0.507897	−	0.745433i
$916$	−20.1263	−	7.32537i	−0.664991	−	0.242037i
$917$	−5.83682	−	2.72175i	−0.192749	−	0.0898802i
$918$	−0.313734	+	0.330578i	−0.0103548	+	0.0109107i
$919$	−34.4053	+	19.8639i	−1.13493	+	0.655250i	−0.945169	−	0.326581i	$-0.894103\pi$
$919$	−34.4053	+	19.8639i	−1.13493	+	0.655250i	−0.189757	+	0.981831i	$0.560770\pi$
$920$	−2.63758	+	1.75014i	−0.0869586	+	0.0577003i
$921$	11.2554	+	0.557210i	0.370878	+	0.0183607i
$922$	12.7799	+	8.94859i	0.420884	+	0.294706i
$923$	0.323821	+	1.20852i	0.0106587	+	0.0397788i
$924$	−2.67186	+	0.825332i	−0.0878977	+	0.0271514i
$925$	45.7835	−	28.7551i	1.50535	−	0.945462i
$926$	−8.19000	−	22.5018i	−0.269140	−	0.739456i
$927$	47.7149	+	0.556613i	1.56716	+	0.0182816i
$928$	−0.289617	−	3.31033i	−0.00950713	−	0.108667i
$929$	−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
$933$	−12.3265	+	5.02179i	−0.403552	+	0.164406i
$934$	−8.61404	+	10.2658i	−0.281860	+	0.335907i
$935$	0.0204938	−	0.818543i	0.000670219	−	0.0267692i
$936$	0.0715671	−	0.721040i	0.00233924	−	0.0235679i
$937$	−5.10956	+	58.4025i	−0.166922	+	1.90793i	0.203521	+	0.979071i	$0.434762\pi$
$937$	−5.10956	+	58.4025i	−0.166922	+	1.90793i	−0.370443	+	0.928855i	$0.620794\pi$
$938$	0.453661	+	0.121558i	0.0148126	+	0.00396901i
$939$	22.7384	−	24.5258i	0.742039	−	0.800371i
$940$	0.275935	−	0.150231i	0.00900000	−	0.00489999i
$941$	38.7934	−	6.84033i	1.26463	−	0.222988i	0.499188	−	0.866494i	$-0.333632\pi$
$941$	38.7934	−	6.84033i	1.26463	−	0.222988i	0.765441	+	0.643506i	$0.222521\pi$
$942$	0.979555	+	25.9013i	0.0319156	+	0.843908i
$943$	1.98517	−	7.40875i	0.0646460	−	0.241262i
$944$	0.563457	−	0.472796i	0.0183389	−	0.0153882i
$945$	3.17372	−	3.18074i	0.103241	−	0.103469i
$946$	−11.3378	−	4.12663i	−0.368625	−	0.134168i
$947$	−1.13014	−	12.9176i	−0.0367246	−	0.419765i	−0.992197	−	0.124683i	$-0.960209\pi$
$947$	−1.13014	−	12.9176i	−0.0367246	−	0.419765i	0.955472	−	0.295082i	$-0.0953469\pi$
$948$	10.1113	+	24.8194i	0.328401	+	0.806095i
$949$			0.983826i			0.0319363i
$950$	−20.0708	−	8.49481i	−0.651184	−	0.275608i
$951$	−46.6267	−	10.6226i	−1.51198	−	0.344461i
$952$	0.0194552	+	0.0277849i	0.000630547	+	0.000900514i
$953$	11.4656	−	1.00311i	0.371407	−	0.0324939i	0.100075	−	0.994980i	$-0.468092\pi$
$953$	11.4656	−	1.00311i	0.371407	−	0.0324939i	0.271331	+	0.962486i	$0.412536\pi$
$954$	16.5461	−	16.1646i	0.535701	−	0.523347i
$955$	−15.3559	−	1.73173i	−0.496907	−	0.0560375i
$956$	−10.8741	−	12.9593i	−0.351694	−	0.419133i
$957$	11.2194	−	21.2488i	0.362672	−	0.686876i
$958$	−15.8772	+	4.25428i	−0.512969	+	0.137450i
$959$	−0.725168	−	4.11263i	−0.0234169	−	0.132804i
$960$	1.05009	+	3.72791i	0.0338915	+	0.120318i
$961$	6.27538	−	10.8693i	0.202432	−	0.350622i
$962$	−0.675937	+	2.52263i	−0.0217931	+	0.0813329i
$963$	−1.35646	+	2.28741i	−0.0437112	+	0.0737108i
$964$	−3.66868	−	10.0796i	−0.118160	−	0.324642i
$965$	14.8021	+	0.370600i	0.476498	+	0.0119300i
$966$	0.755617	−	0.572834i	0.0243116	−	0.0184306i
$967$	−11.8408	−	16.9105i	−0.380776	−	0.543804i	0.582321	−	0.812959i	$-0.302145\pi$
$967$	−11.8408	−	16.9105i	−0.380776	−	0.543804i	−0.963097	+	0.269155i	$0.913256\pi$
$968$	4.54651	−	4.54651i	0.146130	−	0.146130i
$969$	−0.630119	−	0.203594i	−0.0202423	−	0.00654038i
$970$	−10.9875	+	22.1011i	−0.352789	+	0.709624i
$971$	−47.5183	−	8.37876i	−1.52494	−	0.268887i	−0.652565	−	0.757733i	$-0.726307\pi$
$971$	−47.5183	−	8.37876i	−1.52494	−	0.268887i	−0.872370	+	0.488846i	$0.837418\pi$
$972$	13.3858	−	7.98877i	0.429350	−	0.256240i
$973$	0.956910	+	2.05210i	0.0306771	+	0.0657873i
$974$	24.5481	−	8.93478i	0.786572	−	0.286289i
$975$	−1.88473	−	0.907166i	−0.0603598	−	0.0290526i
$976$	−3.52248	−	6.10111i	−0.112752	−	0.195292i
$977$	−42.2564	+	11.3226i	−1.35190	+	0.362241i	−0.860837	−	0.508881i	$-0.830059\pi$
$977$	−42.2564	+	11.3226i	−1.35190	+	0.362241i	−0.491066	+	0.871122i	$0.663393\pi$
$978$	16.4090	−	14.8610i	0.524703	−	0.475202i
$979$	−6.42914	+	1.13363i	−0.205476	+	0.0362310i
$980$	8.46927	+	12.7638i	0.270541	+	0.407725i
$981$	−4.08309	−	53.9050i	−0.130363	−	1.72106i
$982$	−1.60955	+	18.3972i	−0.0513627	+	0.587079i
$983$	−11.0668	+	23.7329i	−0.352977	+	0.756961i	−0.999985	−	0.00552231i	$-0.998242\pi$
$983$	−11.0668	+	23.7329i	−0.352977	+	0.756961i	0.647008	+	0.762483i	$0.276020\pi$
$984$	−7.88537	−	5.08843i	−0.251376	−	0.162213i
$985$	35.5937	+	13.9735i	1.13411	+	0.445233i
$986$	−0.287029	−	0.0506110i	−0.00914087	−	0.00161178i
$987$	−0.0796681	+	0.0501033i	−0.00253586	+	0.00159481i
$988$	0.989753	−	0.358839i	0.0314882	−	0.0114162i
$989$	4.09114			0.130091
$990$	−8.23610	+	26.7676i	−0.261760	+	0.850730i
$991$	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	$0.659340\pi$
$992$	−1.81525	−	3.89283i	−0.0576344	−	0.123597i
$993$	19.0158	−	24.4848i	0.603448	−	0.777003i
$994$	1.28768	+	1.53459i	0.0408426	+	0.0486743i
$995$	0.398738	+	6.39872i	0.0126408	+	0.202853i
$996$	−10.3553	+	11.1693i	−0.328120	+	0.353913i
$997$	−15.9007	−	11.1338i	−0.503579	−	0.352610i	0.294019	−	0.955800i	$-0.405007\pi$
$997$	−15.9007	−	11.1338i	−0.503579	−	0.352610i	−0.797598	+	0.603190i	$0.793896\pi$
$998$	−8.60578	−	6.02583i	−0.272411	−	0.190744i
$999$	−52.2770	+	20.5898i	−1.65397	+	0.651432i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bi.a.17.12	✓	480	15.2	even	4	inner
570.2.bi.a.17.31	yes	480	5.2	odd	4	inner
570.2.bi.a.47.1	yes	480	95.47	odd	36	inner
570.2.bi.a.47.40	yes	480	285.47	even	36	inner
570.2.bi.a.473.1	yes	480	3.2	odd	2	inner
570.2.bi.a.473.40	yes	480	1.1	even	1	trivial
570.2.bi.a.503.12	yes	480	19.9	even	9	inner
570.2.bi.a.503.31	yes	480	57.47	odd	18	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)

\(f(q)\)	\(=\)	\(q+(0.819152 - 0.573576i) q^{2} +(1.71589 + 0.236090i) q^{3} +(0.342020 - 0.939693i) q^{4} +(0.250579 - 2.22198i) q^{5} +(1.54099 - 0.790798i) q^{6} +(0.373543 + 0.100091i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(2.88852 + 0.810206i) q^{9} +O(q^{10})\)	\(q+(0.819152 - 0.573576i) q^{2} +(1.71589 + 0.236090i) q^{3} +(0.342020 - 0.939693i) q^{4} +(0.250579 - 2.22198i) q^{5} +(1.54099 - 0.790798i) q^{6} +(0.373543 + 0.100091i) q^{7} +(-0.258819 - 0.965926i) q^{8} +(2.88852 + 0.810206i) q^{9} +(-1.06922 - 1.96387i) q^{10} +(-3.61556 - 2.08745i) q^{11} +(0.808719 - 1.53166i) q^{12} +(0.240609 + 0.0210505i) q^{13} +(0.363398 - 0.132266i) q^{14} +(0.954552 - 3.75351i) q^{15} +(-0.766044 - 0.642788i) q^{16} +(-0.0718475 + 0.0503082i) q^{17} +(2.83085 - 0.993107i) q^{18} +(3.07835 + 3.08606i) q^{19} +(-2.00228 - 0.995430i) q^{20} +(0.617327 + 0.259934i) q^{21} +(-4.15901 + 0.363866i) q^{22} +(1.28298 - 0.598265i) q^{23} +(-0.216059 - 1.71852i) q^{24} +(-4.87442 - 1.11356i) q^{25} +(0.209169 - 0.120764i) q^{26} +(4.76509 + 2.07217i) q^{27} +(0.221814 - 0.316783i) q^{28} +(0.577029 + 3.27249i) q^{29} +(-1.37100 - 3.62220i) q^{30} +(2.14763 + 3.71980i) q^{31} +(-0.996195 - 0.0871557i) q^{32} +(-5.71107 - 4.43542i) q^{33} +(-0.0299985 + 0.0824201i) q^{34} +(0.316002 - 0.804926i) q^{35} +(1.74928 - 2.43722i) q^{36} +(-7.64589 + 7.64589i) q^{37} +(4.29173 + 0.762285i) q^{38} +(0.407887 + 0.0929255i) q^{39} +(-2.21113 + 0.333051i) q^{40} +(3.48276 - 4.15059i) q^{41} +(0.654777 - 0.141159i) q^{42} +(2.61924 + 1.22137i) q^{43} +(-3.19815 + 2.68357i) q^{44} +(2.52407 - 6.21523i) q^{45} +(0.707808 - 1.22596i) q^{46} +(-0.0805908 + 0.115096i) q^{47} +(-1.16269 - 1.28380i) q^{48} +(-5.93266 - 3.42522i) q^{49} +(-4.63161 + 1.88367i) q^{50} +(-0.135159 + 0.0693606i) q^{51} +(0.102074 - 0.218898i) q^{52} +(6.98810 - 3.25860i) q^{53} +(5.09188 - 1.03572i) q^{54} +(-5.54426 + 7.51065i) q^{55} -0.386720i q^{56} +(4.55350 + 6.02209i) q^{57} +(2.34970 + 2.34970i) q^{58} +(-0.127725 + 0.724366i) q^{59} +(-3.20067 - 2.18076i) q^{60} +(6.62009 + 2.40952i) q^{61} +(3.89283 + 1.81525i) q^{62} +(0.997895 + 0.591761i) q^{63} +(-0.866025 + 0.500000i) q^{64} +(0.107065 - 0.529353i) q^{65} +(-7.22228 - 0.357547i) q^{66} +(0.994844 + 0.696598i) q^{67} +(0.0227009 + 0.0847210i) q^{68} +(2.34270 - 0.723655i) q^{69} +(-0.202833 - 0.840608i) q^{70} +(1.77171 + 4.86774i) q^{71} +(0.0349938 - 2.99980i) q^{72} +(0.355016 + 4.05785i) 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} +(0.387421 - 0.157834i) q^{78} +(-9.94584 + 11.8530i) q^{79} +(-1.62022 + 1.54107i) q^{80} +(7.68713 + 4.68060i) q^{81} +(0.472229 - 5.39760i) q^{82} +(-8.49403 - 2.27597i) q^{83} +(0.455396 - 0.491195i) q^{84} +(0.0937805 + 0.172250i) q^{85} +(2.84610 - 0.501844i) q^{86} +(0.217513 + 5.75145i) q^{87} +(-1.08054 + 4.03264i) q^{88} +(1.19787 - 1.00513i) q^{89} +(-1.49732 - 6.53896i) q^{90} +(0.0877708 + 0.0319459i) q^{91} +(-0.123379 - 1.41023i) q^{92} +(2.80688 + 6.88979i) q^{93} +0.140506i q^{94} +(7.62855 - 6.06674i) q^{95} +(-1.68878 - 0.384741i) q^{96} +(-6.33112 - 9.04178i) q^{97} +(-6.82438 + 0.597056i) q^{98} +(-8.75238 - 8.95899i) 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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