LMFDB - Embedded newform 930.2.bg.i.541.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(121,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 0, 16]))

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

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

chi := DirichletCharacter("930.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bg (of order $15$, degree $8$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$3$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			541.2
Character	$\chi$	$=$	930.541
Dual form			930.2.bg.i.361.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0785623 - 0.747471i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})$	\(q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0785623 - 0.747471i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-3.05638 + 1.36079i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(0.0198931 + 0.00422841i) q^{13} +(0.686610 + 0.305698i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.17791 + 0.969667i) q^{17} +(0.978148 + 0.207912i) q^{18} +(7.99297 - 1.69896i) q^{19} +(-0.913545 + 0.406737i) q^{20} +(-0.502911 - 0.558539i) q^{21} +(-0.349712 - 3.32729i) q^{22} +(3.30295 - 2.39973i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0101688 + 0.0176128i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.502911 + 0.558539i) q^{28} +(1.89189 - 5.82263i) q^{29} +1.00000 q^{30} +(0.00514584 - 5.56776i) q^{31} -1.00000 q^{32} +(-1.03385 + 3.18187i) q^{33} +(-1.59522 + 1.77167i) q^{34} +(-0.608047 - 0.441772i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.16557 - 5.48292i) q^{37} +(-0.854158 + 8.12677i) q^{38} +(0.0164534 - 0.0119541i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-6.87097 - 7.63099i) q^{41} +(0.686610 - 0.305698i) q^{42} +(-4.19004 + 0.890620i) q^{43} +(3.27251 + 0.695593i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(1.26161 + 3.88285i) q^{46} +(-1.44180 - 4.43742i) q^{47} +(0.913545 + 0.406737i) q^{48} +(6.29449 + 1.33794i) q^{49} +(0.978148 - 0.207912i) q^{50} +(2.17791 - 0.969667i) q^{51} +(-0.0136085 - 0.0151137i) q^{52} +(-0.517839 - 4.92691i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.349712 + 3.32729i) q^{55} +(-0.375794 - 0.650894i) q^{56} +(4.08577 - 7.07676i) q^{57} +(4.95303 + 3.59858i) q^{58} +(-9.39950 + 10.4392i) q^{59} +(-0.309017 + 0.951057i) q^{60} +7.78033 q^{61} +(5.29367 + 1.72543i) q^{62} -0.751588 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.0136085 - 0.0151137i) q^{65} +(-2.70666 - 1.96651i) q^{66} +(6.98870 - 12.1048i) q^{67} +(-1.19201 - 2.06462i) q^{68} +(0.426755 - 4.06030i) q^{69} +(0.608047 - 0.441772i) q^{70} +(1.39609 + 13.2829i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(8.26886 - 3.68153i) q^{73} +(6.19278 - 1.31632i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(-7.46507 - 3.32366i) q^{76} +(0.777032 + 2.39146i) q^{77} +(0.00628464 + 0.0193421i) q^{78} +(-12.8486 - 5.72057i) q^{79} +(0.978148 + 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(9.38075 - 4.17658i) q^{82} +(9.04206 + 10.0422i) q^{83} +(0.0785623 + 0.747471i) q^{84} +(1.92871 - 1.40129i) q^{85} +(0.447763 - 4.26018i) q^{86} +(-3.06114 - 5.30205i) q^{87} +(-1.67281 + 2.89739i) q^{88} +(9.44527 + 6.86239i) q^{89} +(0.669131 - 0.743145i) q^{90} +(0.00472346 - 0.0145373i) q^{91} -4.08267 q^{92} +(-4.13421 - 3.72938i) q^{93} +4.66578 q^{94} +(2.52514 - 7.77159i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(-5.71820 - 4.15452i) q^{97} +(-3.21756 + 5.57297i) q^{98} +(1.67281 + 2.89739i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{11}{15}\right)$

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 $

$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$2$	−0.309017	+	0.951057i	−0.218508	+	0.672499i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$3$	0.669131	−	0.743145i	0.386323	−	0.429055i
$4$	−0.809017	−	0.587785i	−0.404508	−	0.293893i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	0.0785623	−	0.747471i	0.0296938	−	0.282517i	−0.969592	−	0.244727i	$-0.921302\pi$
$7$	0.0785623	−	0.747471i	0.0296938	−	0.282517i	0.999286	−	0.0377900i	$-0.0120318\pi$
$8$	0.809017	−	0.587785i	0.286031	−	0.207813i
$9$	−0.104528	−	0.994522i	−0.0348428	−	0.331507i
$10$	0.669131	+	0.743145i	0.211598	+	0.235003i
$11$	−3.05638	+	1.36079i	−0.921532	+	0.410292i	−0.811978	−	0.583688i	$-0.801609\pi$
$11$	−3.05638	+	1.36079i	−0.921532	+	0.410292i	−0.109554	+	0.993981i	$0.534942\pi$
$12$	−0.978148	+	0.207912i	−0.282367	+	0.0600189i
$13$	0.0198931	+	0.00422841i	0.00551735	+	0.00117275i	0.210670	−	0.977557i	$-0.432436\pi$
$13$	0.0198931	+	0.00422841i	0.00551735	+	0.00117275i	−0.205152	+	0.978730i	$0.565769\pi$
$14$	0.686610	+	0.305698i	0.183504	+	0.0817013i
$15$	−0.309017	−	0.951057i	−0.0797878	−	0.245562i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	2.17791	+	0.969667i	0.528220	+	0.235179i	0.653478	−	0.756945i	$-0.273309\pi$
$17$	2.17791	+	0.969667i	0.528220	+	0.235179i	−0.125258	+	0.992124i	$0.539976\pi$
$18$	0.978148	+	0.207912i	0.230552	+	0.0490053i
$19$	7.99297	−	1.69896i	1.83371	−	0.389768i	0.844416	−	0.535688i	$-0.179948\pi$
$19$	7.99297	−	1.69896i	1.83371	−	0.389768i	0.989296	+	0.145920i	$0.0466143\pi$
$20$	−0.913545	+	0.406737i	−0.204275	+	0.0909491i
$21$	−0.502911	−	0.558539i	−0.109744	−	0.121883i
$22$	−0.349712	−	3.32729i	−0.0745590	−	0.709381i
$23$	3.30295	−	2.39973i	0.688712	−	0.500379i	−0.187524	−	0.982260i	$-0.560046\pi$
$23$	3.30295	−	2.39973i	0.688712	−	0.500379i	0.876237	+	0.481881i	$0.160046\pi$
$24$	0.104528	−	0.994522i	0.0213368	−	0.203006i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−0.0101688	+	0.0176128i	−0.00199426	+	0.00345415i
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.502911	+	0.558539i	−0.0950412	+	0.105554i
$29$	1.89189	−	5.82263i	0.351315	−	1.08124i	−0.606801	−	0.794854i	$-0.707548\pi$
$29$	1.89189	−	5.82263i	0.351315	−	1.08124i	0.958116	−	0.286382i	$-0.0924525\pi$
$30$	1.00000			0.182574
$31$	0.00514584	−	5.56776i	0.000924221	−	1.00000i
$31$	0.00514584	−	5.56776i	0.000924221	−	1.00000i
$32$	−1.00000			−0.176777
$33$	−1.03385	+	3.18187i	−0.179971	+	0.553893i
$34$	−1.59522	+	1.77167i	−0.273578	+	0.303839i
$35$	−0.608047	−	0.441772i	−0.102779	−	0.0746732i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−3.16557	−	5.48292i	−0.520416	−	0.901386i	−0.999718	−	0.0237367i	$-0.992444\pi$
$37$	−3.16557	−	5.48292i	−0.520416	−	0.901386i	0.479303	−	0.877650i	$-0.340890\pi$
$38$	−0.854158	+	8.12677i	−0.138563	+	1.31834i
$39$	0.0164534	−	0.0119541i	0.00263465	−	0.00191419i
$40$	−0.104528	−	0.994522i	−0.0165274	−	0.157248i
$41$	−6.87097	−	7.63099i	−1.07307	−	1.19176i	−0.980595	−	0.196045i	$-0.937190\pi$
$41$	−6.87097	−	7.63099i	−1.07307	−	1.19176i	−0.0924710	−	0.995715i	$-0.529477\pi$
$42$	0.686610	−	0.305698i	0.105946	−	0.0471703i
$43$	−4.19004	+	0.890620i	−0.638975	+	0.135818i	−0.515996	−	0.856591i	$-0.672578\pi$
$43$	−4.19004	+	0.890620i	−0.638975	+	0.135818i	−0.122979	+	0.992409i	$0.539245\pi$
$44$	3.27251	+	0.695593i	0.493349	+	0.104865i
$45$	−0.913545	−	0.406737i	−0.136183	−	0.0606327i
$46$	1.26161	+	3.88285i	0.186015	+	0.572495i
$47$	−1.44180	−	4.43742i	−0.210309	−	0.647264i	−0.999453	−	0.0330566i	$-0.989476\pi$
$47$	−1.44180	−	4.43742i	−0.210309	−	0.647264i	0.789145	−	0.614207i	$-0.210524\pi$
$48$	0.913545	+	0.406737i	0.131859	+	0.0587074i
$49$	6.29449	+	1.33794i	0.899213	+	0.191134i
$50$	0.978148	−	0.207912i	0.138331	−	0.0294032i
$51$	2.17791	−	0.969667i	0.304968	−	0.135781i
$52$	−0.0136085	−	0.0151137i	−0.00188715	−	0.00209590i
$53$	−0.517839	−	4.92691i	−0.0711307	−	0.676763i	−0.970751	−	0.240090i	$-0.922823\pi$
$53$	−0.517839	−	4.92691i	−0.0711307	−	0.676763i	0.899620	−	0.436674i	$-0.143844\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	−0.349712	+	3.32729i	−0.0471552	+	0.448652i
$56$	−0.375794	−	0.650894i	−0.0502176	−	0.0869794i
$57$	4.08577	−	7.07676i	0.541173	−	0.937339i
$58$	4.95303	+	3.59858i	0.650364	+	0.472517i
$59$	−9.39950	+	10.4392i	−1.22371	+	1.35907i	−0.311027	+	0.950401i	$0.600673\pi$
$59$	−9.39950	+	10.4392i	−1.22371	+	1.35907i	−0.912683	+	0.408668i	$0.865994\pi$
$60$	−0.309017	+	0.951057i	−0.0398939	+	0.122781i
$61$	7.78033			0.996169			0.498084	−	0.867128i	$-0.334037\pi$
$61$	7.78033			0.996169			0.498084	+	0.867128i	$0.334037\pi$
$62$	5.29367	+	1.72543i	0.672296	+	0.219129i
$63$	−0.751588			−0.0946912
$64$	0.309017	−	0.951057i	0.0386271	−	0.118882i
$65$	0.0136085	−	0.0151137i	0.00168792	−	0.00187463i
$66$	−2.70666	−	1.96651i	−0.333167	−	0.242060i
$67$	6.98870	−	12.1048i	0.853805	−	1.47883i	−0.0239435	−	0.999713i	$-0.507622\pi$
$67$	6.98870	−	12.1048i	0.853805	−	1.47883i	0.877749	−	0.479121i	$-0.159045\pi$
$68$	−1.19201	−	2.06462i	−0.144552	−	0.250372i
$69$	0.426755	−	4.06030i	0.0513753	−	0.488803i
$70$	0.608047	−	0.441772i	0.0726756	−	0.0528019i
$71$	1.39609	+	13.2829i	0.165685	+	1.57639i	0.689327	+	0.724451i	$0.257906\pi$
$71$	1.39609	+	13.2829i	0.165685	+	1.57639i	−0.523642	+	0.851939i	$0.675427\pi$
$72$	−0.669131	−	0.743145i	−0.0788578	−	0.0875805i
$73$	8.26886	−	3.68153i	0.967797	−	0.430891i	0.138909	−	0.990305i	$-0.455641\pi$
$73$	8.26886	−	3.68153i	0.967797	−	0.430891i	0.828888	+	0.559414i	$0.188974\pi$
$74$	6.19278	−	1.31632i	0.719896	−	0.153019i
$75$	−0.978148	−	0.207912i	−0.112947	−	0.0240076i
$76$	−7.46507	−	3.32366i	−0.856302	−	0.381250i
$77$	0.777032	+	2.39146i	0.0885510	+	0.272532i
$78$	0.00628464	+	0.0193421i	0.000711595	+	0.00219006i
$79$	−12.8486	−	5.72057i	−1.44558	−	0.643614i	−0.474044	−	0.880501i	$-0.657206\pi$
$79$	−12.8486	−	5.72057i	−1.44558	−	0.643614i	−0.971537	+	0.236887i	$0.923873\pi$
$80$	0.978148	+	0.207912i	0.109360	+	0.0232452i
$81$	−0.978148	+	0.207912i	−0.108683	+	0.0231013i
$82$	9.38075	−	4.17658i	1.03593	−	0.461226i
$83$	9.04206	+	10.0422i	0.992495	+	1.10228i	0.994756	+	0.102280i	$0.0326139\pi$
$83$	9.04206	+	10.0422i	0.992495	+	1.10228i	−0.00226017	+	0.999997i	$0.500719\pi$
$84$	0.0785623	+	0.747471i	0.00857185	+	0.0815557i
$85$	1.92871	−	1.40129i	0.209198	−	0.151991i
$86$	0.447763	−	4.26018i	0.0482835	−	0.459387i
$87$	−3.06114	−	5.30205i	−0.328188	−	0.568439i
$88$	−1.67281	+	2.89739i	−0.178322	+	0.308863i
$89$	9.44527	+	6.86239i	1.00120	+	0.727412i	0.962344	−	0.271833i	$-0.0876298\pi$
$89$	9.44527	+	6.86239i	1.00120	+	0.727412i	0.0388523	+	0.999245i	$0.487630\pi$
$90$	0.669131	−	0.743145i	0.0705326	−	0.0783343i
$91$	0.00472346	−	0.0145373i	0.000495153	−	0.00152392i
$92$	−4.08267			−0.425648
$93$	−4.13421	−	3.72938i	−0.428698	−	0.386719i
$94$	4.66578			0.481238
$95$	2.52514	−	7.77159i	0.259074	−	0.797348i
$96$	−0.669131	+	0.743145i	−0.0682929	+	0.0758469i
$97$	−5.71820	−	4.15452i	−0.580595	−	0.421827i	0.258343	−	0.966053i	$-0.416823\pi$
$97$	−5.71820	−	4.15452i	−0.580595	−	0.421827i	−0.838939	+	0.544226i	$0.816823\pi$
$98$	−3.21756	+	5.57297i	−0.325022	+	0.562955i
$99$	1.67281	+	2.89739i	0.168124	+	0.291199i
$100$	−0.104528	+	0.994522i	−0.0104528	+	0.0994522i
$101$	−9.17579	+	6.66660i	−0.913025	+	0.663352i	−0.941778	−	0.336235i	$-0.890846\pi$
$101$	−9.17579	+	6.66660i	−0.913025	+	0.663352i	0.0287529	+	0.999587i	$0.490846\pi$
$102$	0.249198	+	2.37096i	0.0246742	+	0.234760i
$103$	12.5847	+	13.9767i	1.24000	+	1.37716i	0.899499	+	0.436922i	$0.143931\pi$
$103$	12.5847	+	13.9767i	1.24000	+	1.37716i	0.340505	+	0.940243i	$0.389402\pi$
$104$	0.0185792	−	0.00827201i	0.00182184	−	0.000811137i
$105$	−0.735164	+	0.156264i	−0.0717447	+	0.0152498i
$106$	4.84579	+	1.03000i	0.470665	+	0.100043i
$107$	−0.0442981	−	0.0197228i	−0.00428246	−	0.00190667i	0.404594	−	0.914496i	$-0.367413\pi$
$107$	−0.0442981	−	0.0197228i	−0.00428246	−	0.00190667i	−0.408877	+	0.912590i	$0.634079\pi$
$108$	0.309017	+	0.951057i	0.0297352	+	0.0915155i
$109$	3.09180	+	9.51558i	0.296141	+	0.911427i	0.982836	+	0.184482i	$0.0590607\pi$
$109$	3.09180	+	9.51558i	0.296141	+	0.911427i	−0.686695	+	0.726945i	$0.740939\pi$
$110$	−3.05638	−	1.36079i	−0.291414	−	0.129746i
$111$	−6.19278	−	1.31632i	−0.587793	−	0.124939i
$112$	0.735164	−	0.156264i	0.0694665	−	0.0147656i
$113$	−14.9563	+	6.65899i	−1.40697	+	0.626425i	−0.962972	−	0.269601i	$-0.913108\pi$
$113$	−14.9563	+	6.65899i	−1.40697	+	0.626425i	−0.444002	+	0.896026i	$0.646442\pi$
$114$	5.46782	+	6.07263i	0.512109	+	0.568754i
$115$	−0.426755	−	4.06030i	−0.0397951	−	0.378625i
$116$	−4.95303	+	3.59858i	−0.459877	+	0.334120i
$117$	0.00212585	−	0.0202261i	0.000196535	−	0.00186990i
$118$	−7.02367	−	12.1653i	−0.646581	−	1.11991i
$119$	0.895899	−	1.55174i	0.0821270	−	0.142248i
$120$	−0.809017	−	0.587785i	−0.0738528	−	0.0536572i
$121$	0.129257	−	0.143555i	0.0117507	−	0.0130504i
$122$	−2.40425	+	7.39953i	−0.217671	+	0.669922i
$123$	−10.2685			−0.925880
$124$	−3.27681	+	4.50139i	−0.294266	+	0.404237i
$125$	−1.00000			−0.0894427
$126$	0.232253	−	0.714803i	0.0206908	−	0.0636797i
$127$	5.05080	−	5.60948i	0.448186	−	0.497761i	−0.476137	−	0.879371i	$-0.657964\pi$
$127$	5.05080	−	5.60948i	0.448186	−	0.497761i	0.924324	+	0.381610i	$0.124630\pi$
$128$	0.809017	+	0.587785i	0.0715077	+	0.0519534i
$129$	−2.14182	+	3.70974i	−0.188577	+	0.326625i
$130$	0.0101688	+	0.0176128i	0.000891859	+	0.00154474i
$131$	−1.48376	+	14.1171i	−0.129637	+	1.23341i	0.715404	+	0.698711i	$0.246243\pi$
$131$	−1.48376	+	14.1171i	−0.129637	+	1.23341i	−0.845041	+	0.534702i	$0.820424\pi$
$132$	2.70666	−	1.96651i	0.235585	−	0.171162i
$133$	−0.641975	−	6.10798i	−0.0556663	−	0.529629i
$134$	9.35270	+	10.3872i	0.807951	+	0.897320i
$135$	−0.913545	+	0.406737i	−0.0786255	+	0.0350063i
$136$	2.33192	−	0.495665i	0.199961	−	0.0425029i
$137$	11.9986	+	2.55039i	1.02511	+	0.217894i	0.689637	−	0.724155i	$-0.257770\pi$
$137$	11.9986	+	2.55039i	1.02511	+	0.217894i	0.335474	+	0.942049i	$0.391103\pi$
$138$	3.72970	+	1.66057i	0.317493	+	0.141357i
$139$	−1.19750	−	3.68554i	−0.101571	−	0.312603i	0.887339	−	0.461117i	$-0.152551\pi$
$139$	−1.19750	−	3.68554i	−0.101571	−	0.312603i	−0.988910	+	0.148514i	$0.952551\pi$
$140$	0.232253	+	0.714803i	0.0196290	+	0.0604119i
$141$	−4.26240	−	1.89774i	−0.358959	−	0.159819i
$142$	−13.0642	−	2.77688i	−1.09632	−	0.233031i
$143$	−0.0665547	+	0.0141466i	−0.00556558	+	0.00118300i
$144$	0.913545	−	0.406737i	0.0761288	−	0.0338947i
$145$	−4.09660	−	4.54974i	−0.340204	−	0.377835i
$146$	0.946128	+	9.00181i	0.0783021	+	0.744995i
$147$	5.20612	−	3.78247i	0.429393	−	0.311973i
$148$	−0.661783	+	6.29645i	−0.0543983	+	0.517565i
$149$	−1.50959	−	2.61469i	−0.123671	−	0.214204i	0.797542	−	0.603264i	$-0.206133\pi$
$149$	−1.50959	−	2.61469i	−0.123671	−	0.214204i	−0.921212	+	0.389060i	$0.872800\pi$
$150$	0.500000	−	0.866025i	0.0408248	−	0.0707107i
$151$	17.2437	+	12.5283i	1.40327	+	1.01954i	0.994258	+	0.107007i	$0.0341269\pi$
$151$	17.2437	+	12.5283i	1.40327	+	1.01954i	0.409013	+	0.912529i	$0.365873\pi$
$152$	5.46782	−	6.07263i	0.443499	−	0.492556i
$153$	0.736702	−	2.26734i	0.0595588	−	0.183303i
$154$	−2.51453			−0.202626
$155$	−4.81925	−	2.78834i	−0.387092	−	0.223965i
$156$	−0.0203375			−0.00162830
$157$	0.460564	−	1.41747i	0.0367570	−	0.113126i	−0.930995	−	0.365033i	$-0.881058\pi$
$157$	0.460564	−	1.41747i	0.0367570	−	0.113126i	0.967751	+	0.251907i	$0.0810576\pi$
$158$	9.41102	−	10.4520i	0.748701	−	0.831517i
$159$	−4.00791	−	2.91192i	−0.317848	−	0.230930i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−1.53424	−	2.65739i	−0.120915	−	0.209431i
$162$	0.104528	−	0.994522i	0.00821253	−	0.0781370i
$163$	0.890180	−	0.646753i	0.0697243	−	0.0506576i	−0.552377	−	0.833594i	$-0.686279\pi$
$163$	0.890180	−	0.646753i	0.0697243	−	0.0506576i	0.622101	+	0.782937i	$0.286279\pi$
$164$	1.07335	+	10.2123i	0.0838147	+	0.797443i
$165$	2.23866	+	2.48628i	0.174279	+	0.193557i
$166$	−12.3449	+	5.49629i	−0.958148	+	0.426595i
$167$	−5.95803	+	1.26642i	−0.461046	+	0.0979984i	−0.432578	−	0.901596i	$-0.642396\pi$
$167$	−5.95803	+	1.26642i	−0.461046	+	0.0979984i	−0.0284679	+	0.999595i	$0.509063\pi$
$168$	−0.735164	−	0.156264i	−0.0567191	−	0.0120560i
$169$	−11.8757	−	5.28741i	−0.913516	−	0.406724i
$170$	0.736702	+	2.26734i	0.0565025	+	0.173897i
$171$	−2.52514	−	7.77159i	−0.193103	−	0.594308i
$172$	3.91330	+	1.74232i	0.298387	+	0.132850i
$173$	−0.892211	−	0.189645i	−0.0678336	−	0.0144185i	0.173870	−	0.984769i	$-0.444373\pi$
$173$	−0.892211	−	0.189645i	−0.0678336	−	0.0144185i	−0.241703	+	0.970350i	$0.577706\pi$
$174$	5.98849	−	1.27289i	0.453986	−	0.0964978i
$175$	−0.686610	+	0.305698i	−0.0519028	+	0.0231086i
$176$	−2.23866	−	2.48628i	−0.168745	−	0.187410i
$177$	1.46835	+	13.9704i	0.110368	+	1.05008i
$178$	−9.44527	+	6.86239i	−0.707953	+	0.514358i
$179$	−2.14849	+	20.4415i	−0.160586	+	1.52787i	0.556476	+	0.830864i	$0.312153\pi$
$179$	−2.14849	+	20.4415i	−0.160586	+	1.52787i	−0.717062	+	0.697009i	$0.754514\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	0.251840	−	0.436199i	0.0187191	−	0.0324224i	−0.856514	−	0.516124i	$-0.827375\pi$
$181$	0.251840	−	0.436199i	0.0187191	−	0.0324224i	0.875233	+	0.483701i	$0.160708\pi$
$182$	0.0123662	+	0.00898455i	0.000916642	+	0.000665979i
$183$	5.20606	−	5.78191i	0.384843	−	0.427411i
$184$	1.26161	−	3.88285i	0.0930074	−	0.286247i
$185$	−6.33113			−0.465474
$186$	4.82440	−	2.77942i	0.353742	−	0.203797i
$187$	−7.97602			−0.583264
$188$	−1.44180	+	4.43742i	−0.105154	+	0.323632i
$189$	−0.502911	+	0.558539i	−0.0365814	+	0.0406277i
$190$	6.61091	+	4.80311i	0.479606	+	0.348454i
$191$	−0.373423	+	0.646788i	−0.0270200	+	0.0467999i	−0.879219	−	0.476417i	$-0.841935\pi$
$191$	−0.373423	+	0.646788i	−0.0270200	+	0.0467999i	0.852199	+	0.523217i	$0.175268\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	0.814881	−	7.75307i	0.0586564	−	0.558078i	−0.925246	−	0.379369i	$-0.876141\pi$
$193$	0.814881	−	7.75307i	0.0586564	−	0.558078i	0.983902	−	0.178709i	$-0.0571922\pi$
$194$	5.71820	−	4.15452i	0.410543	−	0.298277i
$195$	−0.00212585	−	0.0202261i	−0.000152235	−	0.00144842i
$196$	−4.30593	−	4.78222i	−0.307567	−	0.341587i
$197$	19.3734	−	8.62561i	1.38030	−	0.614549i	0.423660	−	0.905821i	$-0.360745\pi$
$197$	19.3734	−	8.62561i	1.38030	−	0.614549i	0.956640	+	0.291272i	$0.0940786\pi$
$198$	−3.27251	+	0.695593i	−0.232567	+	0.0494337i
$199$	−2.00071	−	0.425265i	−0.141827	−	0.0301462i	0.136451	−	0.990647i	$-0.456430\pi$
$199$	−2.00071	−	0.425265i	−0.141827	−	0.0301462i	−0.278278	+	0.960501i	$0.589764\pi$
$200$	−0.913545	−	0.406737i	−0.0645974	−	0.0287606i
$201$	−4.31925	−	13.2933i	−0.304657	−	0.937637i
$202$	−3.50484	−	10.7868i	−0.246600	−	0.758956i
$203$	−4.20361	−	1.87157i	−0.295036	−	0.131358i
$204$	−2.33192	−	0.495665i	−0.163267	−	0.0347035i
$205$	−10.0441	+	2.13494i	−0.701512	+	0.149111i
$206$	−17.1815	+	7.64970i	−1.19709	+	0.532980i
$207$	−2.73184	−	3.03401i	−0.189876	−	0.210879i
$208$	0.00212585	+	0.0202261i	0.000147401	+	0.00140243i
$209$	−22.1176	+	16.0694i	−1.52991	+	1.11154i
$210$	0.0785623	−	0.747471i	0.00542132	−	0.0515804i
$211$	8.76808	+	15.1868i	0.603619	+	1.04550i	0.992268	+	0.124113i	$0.0396086\pi$
$211$	8.76808	+	15.1868i	0.603619	+	1.04550i	−0.388649	+	0.921386i	$0.627058\pi$
$212$	−2.47702	+	4.29033i	−0.170123	+	0.294661i
$213$	10.8053	+	7.85049i	0.740365	+	0.537907i
$214$	0.0324463	−	0.0360353i	0.00221799	−	0.00246332i
$215$	−1.32372	+	4.07399i	−0.0902769	+	0.277844i
$216$	−1.00000			−0.0680414
$217$	−4.16133	−	0.441263i	−0.282490	−	0.0299549i
$218$	−10.0053			−0.677643
$219$	2.79703	−	8.60839i	0.189006	−	0.581701i
$220$	2.23866	−	2.48628i	0.150930	−	0.167625i
$221$	0.0392252	+	0.0284988i	0.00263857	+	0.00191703i
$222$	3.16557	−	5.48292i	0.212459	−	0.367989i
$223$	10.4900	+	18.1693i	0.702466	+	1.21671i	0.967598	+	0.252494i	$0.0812509\pi$
$223$	10.4900	+	18.1693i	0.702466	+	1.21671i	−0.265133	+	0.964212i	$0.585416\pi$
$224$	−0.0785623	+	0.747471i	−0.00524917	+	0.0499425i
$225$	−0.809017	+	0.587785i	−0.0539345	+	0.0391857i
$226$	−1.71131	−	16.2821i	−0.113835	−	1.08307i
$227$	−14.1610	−	15.7274i	−0.939900	−	1.04386i	−0.998959	−	0.0456099i	$-0.985477\pi$
$227$	−14.1610	−	15.7274i	−0.939900	−	1.04386i	0.0590596	−	0.998254i	$-0.481190\pi$
$228$	−7.46507	+	3.32366i	−0.494386	+	0.220115i
$229$	−10.6072	+	2.25463i	−0.700943	+	0.148990i	−0.544579	−	0.838710i	$-0.683311\pi$
$229$	−10.6072	+	2.25463i	−0.700943	+	0.148990i	−0.156364	+	0.987700i	$0.549977\pi$
$230$	3.99345	+	0.848835i	0.263320	+	0.0559705i
$231$	2.29714	+	1.02275i	0.151140	+	0.0672920i
$232$	−1.89189	−	5.82263i	−0.124208	−	0.382274i
$233$	−0.0506443	−	0.155867i	−0.00331782	−	0.0102112i	0.949384	−	0.314118i	$-0.101709\pi$
$233$	−0.0506443	−	0.155867i	−0.00331782	−	0.0102112i	−0.952702	+	0.303907i	$0.901709\pi$
$234$	0.0185792	+	0.00827201i	0.00121456	+	0.000540758i
$235$	−4.56382	−	0.970070i	−0.297711	−	0.0632804i
$236$	13.7404	−	2.92060i	0.894422	−	0.190115i
$237$	−12.8486	+	5.72057i	−0.834607	+	0.371591i
$238$	1.19895	+	1.33157i	0.0777162	+	0.0863126i
$239$	0.588547	+	5.59965i	0.0380699	+	0.362211i	0.996928	+	0.0783248i	$0.0249571\pi$
$239$	0.588547	+	5.59965i	0.0380699	+	0.362211i	−0.958858	+	0.283886i	$0.908376\pi$
$240$	0.809017	−	0.587785i	0.0522218	−	0.0379414i
$241$	0.108506	−	1.03237i	0.00698951	−	0.0665007i	−0.990471	−	0.137720i	$-0.956022\pi$
$241$	0.108506	−	1.03237i	0.00698951	−	0.0665007i	0.997461	+	0.0712197i	$0.0226891\pi$
$242$	0.0965860	+	0.167292i	0.00620878	+	0.0107539i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−6.29442	−	4.57316i	−0.402959	−	0.292767i
$245$	4.30593	−	4.78222i	0.275096	−	0.305525i
$246$	3.17314	−	9.76593i	0.202312	−	0.622653i
$247$	0.166189			0.0105743
$248$	−3.26849	−	4.50744i	−0.207549	−	0.286223i
$249$	13.5132			0.856361
$250$	0.309017	−	0.951057i	0.0195440	−	0.0601501i
$251$	−13.7929	+	15.3186i	−0.870601	+	0.966900i	−0.999694	−	0.0247323i	$-0.992127\pi$
$251$	−13.7929	+	15.3186i	−0.870601	+	0.966900i	0.129093	+	0.991632i	$0.458793\pi$
$252$	0.608047	+	0.441772i	0.0383034	+	0.0278290i
$253$	−6.82953	+	11.8291i	−0.429369	+	0.743689i
$254$	3.77415	+	6.53702i	0.236811	+	0.410169i
$255$	0.249198	−	2.37096i	0.0156054	−	0.148475i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−0.898065	−	8.54452i	−0.0560198	−	0.532993i	−0.986161	−	0.165791i	$-0.946982\pi$
$257$	−0.898065	−	8.54452i	−0.0560198	−	0.532993i	0.930141	−	0.367202i	$-0.119684\pi$
$258$	−2.86632	−	3.18337i	−0.178449	−	0.198188i
$259$	−4.34702	+	1.93542i	−0.270110	+	0.120261i
$260$	−0.0198931	+	0.00422841i	−0.00123372	+	0.000262235i
$261$	−5.98849	−	1.27289i	−0.370678	−	0.0787901i
$262$	−12.9676	−	5.77355i	−0.801142	−	0.356691i
$263$	−8.99448	−	27.6822i	−0.554624	−	1.70696i	−0.696935	−	0.717134i	$-0.745453\pi$
$263$	−8.99448	−	27.6822i	−0.554624	−	1.70696i	0.142311	−	0.989822i	$-0.454547\pi$
$264$	1.03385	+	3.18187i	0.0636293	+	0.195831i
$265$	−4.52575	−	2.01499i	−0.278015	−	0.123780i
$266$	6.00742	+	1.27692i	0.368338	+	0.0782927i
$267$	11.4199	−	2.42737i	0.698885	−	0.148553i
$268$	−12.7690	+	5.68512i	−0.779990	+	0.347274i
$269$	−5.85087	−	6.49805i	−0.356734	−	0.396193i	0.537889	−	0.843016i	$-0.319222\pi$
$269$	−5.85087	−	6.49805i	−0.356734	−	0.396193i	−0.894622	+	0.446823i	$0.852555\pi$
$270$	−0.104528	−	0.994522i	−0.00636140	−	0.0605247i
$271$	−15.7907	+	11.4726i	−0.959219	+	0.696914i	−0.952969	−	0.303067i	$-0.901989\pi$
$271$	−15.7907	+	11.4726i	−0.959219	+	0.696914i	−0.00625012	+	0.999980i	$0.501989\pi$
$272$	−0.249198	+	2.37096i	−0.0151098	+	0.143760i
$273$	−0.00764272	−	0.0132376i	−0.000462558	−	0.000801174i
$274$	−6.13334	+	10.6233i	−0.370529	+	0.641774i
$275$	2.70666	+	1.96651i	0.163218	+	0.118585i
$276$	−2.73184	+	3.03401i	−0.164437	+	0.182626i
$277$	7.10286	−	21.8603i	0.426769	−	1.31346i	−0.474521	−	0.880244i	$-0.657379\pi$
$277$	7.10286	−	21.8603i	0.426769	−	1.31346i	0.901290	−	0.433216i	$-0.142621\pi$
$278$	3.87521			0.232419
$279$	−5.53780	+	0.576872i	−0.331539	+	0.0345364i
$280$	−0.751588			−0.0449160
$281$	3.99217	−	12.2866i	0.238153	−	0.732959i	−0.758535	−	0.651633i	$-0.774084\pi$
$281$	3.99217	−	12.2866i	0.238153	−	0.732959i	0.996688	−	0.0813263i	$-0.0259156\pi$
$282$	3.12201	−	3.46735i	0.185913	−	0.206478i
$283$	−3.30917	−	2.40426i	−0.196710	−	0.142918i	0.485070	−	0.874475i	$-0.338794\pi$
$283$	−3.30917	−	2.40426i	−0.196710	−	0.142918i	−0.681780	+	0.731557i	$0.738794\pi$
$284$	6.67803	−	11.5667i	0.396268	−	0.686356i
$285$	−4.08577	−	7.07676i	−0.242020	−	0.419191i
$286$	0.00711228	−	0.0676688i	0.000420558	−	0.00400134i
$287$	−6.24374	+	4.53634i	−0.368556	+	0.267772i
$288$	0.104528	+	0.994522i	0.00615940	+	0.0586028i
$289$	−7.57219	−	8.40977i	−0.445423	−	0.494692i
$290$	5.59298	−	2.49015i	0.328431	−	0.146227i
$291$	−6.91363	+	1.46954i	−0.405284	+	0.0861458i
$292$	−8.85360	−	1.88189i	−0.518118	−	0.110129i
$293$	6.23864	+	2.77762i	0.364465	+	0.162270i	0.580795	−	0.814050i	$-0.302742\pi$
$293$	6.23864	+	2.77762i	0.364465	+	0.162270i	−0.216330	+	0.976320i	$0.569409\pi$
$294$	1.98856	+	6.12016i	0.115975	+	0.356935i
$295$	4.34086	+	13.3598i	0.252735	+	0.777838i
$296$	−5.78378	−	2.57510i	−0.336175	−	0.149675i
$297$	3.27251	+	0.695593i	0.189890	+	0.0403624i
$298$	2.95321	−	0.627724i	0.171075	−	0.0363630i
$299$	0.0758529	−	0.0337719i	0.00438669	−	0.00195308i
$300$	0.669131	+	0.743145i	0.0386323	+	0.0429055i
$301$	0.336533	+	3.20190i	0.0193974	+	0.184554i
$302$	−17.2437	+	12.5283i	−0.992262	+	0.720921i
$303$	−1.18555	+	11.2798i	−0.0681081	+	0.648006i
$304$	4.08577	+	7.07676i	0.234335	+	0.405880i
$305$	3.89016	−	6.73796i	0.222750	−	0.385815i
$306$	1.92871	+	1.40129i	0.110257	+	0.0801064i
$307$	−19.1923	+	21.3152i	−1.09536	+	1.21652i	−0.120733	+	0.992685i	$0.538525\pi$
$307$	−19.1923	+	21.3152i	−1.09536	+	1.21652i	−0.974627	+	0.223836i	$0.928142\pi$
$308$	0.777032	−	2.39146i	0.0442755	−	0.136266i
$309$	18.8075			1.06992
$310$	4.14110	−	3.72174i	0.235198	−	0.211380i
$311$	24.5361			1.39132			0.695658	−	0.718373i	$-0.255113\pi$
$311$	24.5361			1.39132			0.695658	+	0.718373i	$0.255113\pi$
$312$	0.00628464	−	0.0193421i	0.000355798	−	0.00109503i
$313$	1.79573	−	1.99436i	0.101501	−	0.112728i	−0.690254	−	0.723567i	$-0.742501\pi$
$313$	1.79573	−	1.99436i	0.101501	−	0.112728i	0.791755	+	0.610839i	$0.209168\pi$
$314$	1.20577	+	0.876044i	0.0680456	+	0.0494380i
$315$	−0.375794	+	0.650894i	−0.0211736	+	0.0366737i
$316$	7.03228	+	12.1803i	0.395597	+	0.685193i
$317$	−2.21844	+	21.1071i	−0.124600	+	1.18549i	0.736277	+	0.676680i	$0.236582\pi$
$317$	−2.21844	+	21.1071i	−0.124600	+	1.18549i	−0.860878	+	0.508812i	$0.830085\pi$
$318$	4.00791	−	2.91192i	0.224752	−	0.163292i
$319$	2.14104	+	20.3706i	0.119875	+	1.14053i
$320$	−0.669131	−	0.743145i	−0.0374055	−	0.0415431i
$321$	−0.0442981	+	0.0197228i	−0.00247248	+	0.00110082i
$322$	3.00143	−	0.637974i	0.167263	−	0.0355529i
$323$	19.0554	+	4.05034i	1.06027	+	0.225367i
$324$	0.913545	+	0.406737i	0.0507525	+	0.0225965i
$325$	−0.00628464	−	0.0193421i	−0.000348609	−	0.00107291i
$326$	0.340018	+	1.04647i	0.0188319	+	0.0579586i
$327$	9.14027	+	4.06951i	0.505458	+	0.225044i
$328$	−10.0441	−	2.13494i	−0.554594	−	0.117883i
$329$	−3.43011	+	0.729093i	−0.189108	+	0.0401962i
$330$	−3.05638	+	1.36079i	−0.168248	+	0.0749088i
$331$	5.35694	+	5.94948i	0.294444	+	0.327013i	0.872156	−	0.489227i	$-0.162721\pi$
$331$	5.35694	+	5.94948i	0.294444	+	0.327013i	−0.577712	+	0.816240i	$0.696054\pi$
$332$	−1.41251	−	13.4391i	−0.0775215	−	0.737568i
$333$	−5.12199	+	3.72135i	−0.280683	+	0.203928i
$334$	0.636697	−	6.05777i	0.0348385	−	0.331466i
$335$	−6.98870	−	12.1048i	−0.381833	−	0.661355i
$336$	0.375794	−	0.650894i	0.0205012	−	0.0355092i
$337$	−3.93173	−	2.85657i	−0.214175	−	0.155607i	0.475526	−	0.879702i	$-0.342258\pi$
$337$	−3.93173	−	2.85657i	−0.214175	−	0.155607i	−0.689701	+	0.724095i	$0.742258\pi$
$338$	8.69842	−	9.66058i	0.473132	−	0.525466i
$339$	−5.05915	+	15.5705i	−0.274775	+	0.845671i
$340$	−2.38402			−0.129292
$341$	7.56081	+	17.0242i	0.409441	+	0.921911i
$342$	8.17153			0.441866
$343$	3.12035	−	9.60346i	0.168483	−	0.518538i
$344$	−2.86632	+	3.18337i	−0.154541	+	0.171636i
$345$	−3.30295	−	2.39973i	−0.177825	−	0.129197i
$346$	0.456072	−	0.789940i	0.0245186	−	0.0424674i
$347$	−9.50587	−	16.4646i	−0.510302	−	0.883869i	−0.999929	−	0.0119366i	$-0.996200\pi$
$347$	−9.50587	−	16.4646i	−0.510302	−	0.883869i	0.489627	−	0.871932i	$-0.337133\pi$
$348$	−0.639952	+	6.08874i	−0.0343050	+	0.326391i
$349$	9.64599	−	7.00822i	0.516338	−	0.375141i	−0.298885	−	0.954289i	$-0.596615\pi$
$349$	9.64599	−	7.00822i	0.516338	−	0.375141i	0.815223	+	0.579148i	$0.196615\pi$
$350$	−0.0785623	−	0.747471i	−0.00419933	−	0.0399540i
$351$	−0.0136085	−	0.0151137i	−0.000726365	−	0.000806711i
$352$	3.05638	−	1.36079i	0.162905	−	0.0725301i
$353$	26.2757	−	5.58508i	1.39852	−	0.297264i	0.553877	−	0.832599i	$-0.313148\pi$
$353$	26.2757	−	5.58508i	1.39852	−	0.297264i	0.844640	+	0.535335i	$0.179814\pi$
$354$	−13.7404	−	2.92060i	−0.730292	−	0.155228i
$355$	12.2014	+	5.43240i	0.647581	+	0.288322i
$356$	−3.60777	−	11.1036i	−0.191212	−	0.588489i
$357$	−0.553696	−	1.70410i	−0.0293047	−	0.0901906i
$358$	−18.7771	−	8.36012i	−0.992403	−	0.441846i
$359$	−12.6339	−	2.68541i	−0.666790	−	0.141731i	−0.137933	−	0.990442i	$-0.544046\pi$
$359$	−12.6339	−	2.68541i	−0.666790	−	0.141731i	−0.528857	+	0.848711i	$0.677379\pi$
$360$	−0.978148	+	0.207912i	−0.0515529	+	0.0109579i
$361$	43.6437	−	19.4314i	2.29704	−	1.02271i
$362$	0.337027	+	0.374307i	0.0177138	+	0.0196731i
$363$	−0.0201920	−	0.192114i	−0.00105980	−	0.0100834i
$364$	−0.0123662	+	0.00898455i	−0.000648164	+	0.000470918i
$365$	0.946128	−	9.00181i	0.0495226	−	0.471176i
$366$	3.89016	+	6.73796i	0.203342	+	0.352199i
$367$	2.27071	−	3.93299i	0.118530	−	0.205301i	−0.800655	−	0.599126i	$-0.795515\pi$
$367$	2.27071	−	3.93299i	0.118530	−	0.205301i	0.919185	+	0.393825i	$0.128848\pi$
$368$	3.30295	+	2.39973i	0.172178	+	0.125095i
$369$	−6.87097	+	7.63099i	−0.357689	+	0.397253i
$370$	1.95643	−	6.02126i	0.101710	−	0.313031i
$371$	−3.72340			−0.193309
$372$	1.15257	+	5.44716i	0.0597579	+	0.282422i
$373$	−6.05274			−0.313399			−0.156700	−	0.987646i	$-0.550085\pi$
$373$	−6.05274			−0.313399			−0.156700	+	0.987646i	$0.550085\pi$
$374$	2.46472	−	7.58564i	0.127448	−	0.392244i
$375$	−0.669131	+	0.743145i	−0.0345538	+	0.0383758i
$376$	−3.77469	−	2.74248i	−0.194665	−	0.141432i
$377$	0.0622559	−	0.107830i	0.00320634	−	0.00555355i
$378$	−0.375794	−	0.650894i	−0.0193288	−	0.0334784i
$379$	−3.70492	+	35.2499i	−0.190309	+	1.81067i	0.316482	+	0.948598i	$0.397498\pi$
$379$	−3.70492	+	35.2499i	−0.190309	+	1.81067i	−0.506791	+	0.862069i	$0.669169\pi$
$380$	−6.61091	+	4.80311i	−0.339133	+	0.246394i
$381$	−0.789013	−	7.50695i	−0.0404223	−	0.384593i
$382$	−0.499738	−	0.555015i	−0.0255688	−	0.0283970i
$383$	−18.7729	+	8.35823i	−0.959249	+	0.427085i	−0.825796	−	0.563970i	$-0.809273\pi$
$383$	−18.7729	+	8.35823i	−0.959249	+	0.427085i	−0.133454	+	0.991055i	$0.542607\pi$
$384$	0.978148	−	0.207912i	0.0499159	−	0.0106099i
$385$	2.45958	+	0.522800i	0.125352	+	0.0266443i
$386$	7.12180	+	3.17083i	0.362490	+	0.161391i
$387$	1.32372	+	4.07399i	0.0672884	+	0.207092i
$388$	2.18416	+	6.72215i	0.110884	+	0.341265i
$389$	0.0143297	+	0.00637999i	0.000726544	+	0.000323478i	0.407100	−	0.913384i	$-0.366540\pi$
$389$	0.0143297	+	0.00637999i	0.000726544	+	0.000323478i	−0.406373	+	0.913707i	$0.633207\pi$
$390$	0.0198931	+	0.00422841i	0.00100733	+	0.000214114i
$391$	9.52046	−	2.02364i	0.481470	−	0.102340i
$392$	5.87877	−	2.61740i	0.296923	−	0.132199i
$393$	9.49819	+	10.5488i	0.479120	+	0.532117i
$394$	2.21672	+	21.0907i	0.111677	+	1.06253i
$395$	−11.3785	+	8.26694i	−0.572513	+	0.415955i
$396$	0.349712	−	3.32729i	0.0175737	−	0.167203i
$397$	−7.67417	−	13.2921i	−0.385156	−	0.667109i	0.606635	−	0.794980i	$-0.292519\pi$
$397$	−7.67417	−	13.2921i	−0.385156	−	0.667109i	−0.991791	+	0.127871i	$0.959186\pi$
$398$	1.02270	−	1.77138i	0.0512636	−	0.0887911i
$399$	−4.96868	−	3.60996i	−0.248745	−	0.180724i
$400$	0.669131	−	0.743145i	0.0334565	−	0.0371572i
$401$	5.96246	−	18.3506i	0.297751	−	0.916384i	−0.684532	−	0.728983i	$-0.739994\pi$
$401$	5.96246	−	18.3506i	0.297751	−	0.916384i	0.982283	−	0.187401i	$-0.0600065\pi$
$402$	13.9774			0.697129
$403$	0.0236451	−	0.110738i	0.00117785	−	0.00551626i
$404$	11.3419			0.564281
$405$	−0.309017	+	0.951057i	−0.0153552	+	0.0472584i
$406$	3.07896	−	3.41953i	0.152806	−	0.169708i
$407$	17.1362	+	12.4502i	0.849412	+	0.617134i
$408$	1.19201	−	2.06462i	0.0590132	−	0.102214i
$409$	2.50171	+	4.33309i	0.123701	+	0.214257i	0.921225	−	0.389031i	$-0.127190\pi$
$409$	2.50171	+	4.33309i	0.123701	+	0.214257i	−0.797523	+	0.603288i	$0.793857\pi$
$410$	1.07335	−	10.2123i	0.0530091	−	0.504347i
$411$	9.92395	−	7.21017i	0.489512	−	0.355652i
$412$	−1.96592	−	18.7045i	−0.0968539	−	0.921503i
$413$	7.06455	+	7.84598i	0.347624	+	0.386075i
$414$	3.72970	−	1.66057i	0.183305	−	0.0816126i
$415$	13.2179	−	2.80954i	0.648839	−	0.137915i
$416$	−0.0198931	−	0.00422841i	−0.000975339	−	0.000207315i
$417$	−3.54018	−	1.57619i	−0.173363	−	0.0771863i
$418$	−8.44817	−	26.0008i	−0.413213	−	1.27174i
$419$	−1.38137	−	4.25142i	−0.0674843	−	0.207695i	0.911628	−	0.411017i	$-0.134826\pi$
$419$	−1.38137	−	4.25142i	−0.0674843	−	0.207695i	−0.979112	+	0.203322i	$0.934826\pi$
$420$	0.686610	+	0.305698i	0.0335031	+	0.0149166i
$421$	−1.75514	−	0.373067i	−0.0855405	−	0.0181822i	0.164943	−	0.986303i	$-0.447256\pi$
$421$	−1.75514	−	0.373067i	−0.0855405	−	0.0181822i	−0.250483	+	0.968121i	$0.580589\pi$
$422$	−17.1529	+	3.64597i	−0.834992	+	0.177483i
$423$	−4.26240	+	1.89774i	−0.207245	+	0.0922714i
$424$	−3.31491	−	3.68158i	−0.160986	−	0.178793i
$425$	−0.249198	−	2.37096i	−0.0120879	−	0.115008i
$426$	−10.8053	+	7.85049i	−0.523517	+	0.380358i
$427$	0.611241	−	5.81557i	0.0295800	−	0.281435i
$428$	0.0242451	+	0.0419938i	0.00117193	+	0.00202985i
$429$	−0.0340208	+	0.0589257i	−0.00164254	+	0.00284496i
$430$	−3.46554	−	2.51786i	−0.167123	−	0.121422i
$431$	−3.91824	+	4.35164i	−0.188735	+	0.209611i	−0.830085	−	0.557637i	$-0.811708\pi$
$431$	−3.91824	+	4.35164i	−0.188735	+	0.209611i	0.641350	+	0.767249i	$0.278375\pi$
$432$	0.309017	−	0.951057i	0.0148676	−	0.0457577i
$433$	26.2680			1.26236			0.631179	−	0.775637i	$-0.282571\pi$
$433$	26.2680			1.26236			0.631179	+	0.775637i	$0.282571\pi$
$434$	1.70559	−	3.82131i	0.0818709	−	0.183429i
$435$	−6.12228			−0.293541
$436$	3.09180	−	9.51558i	0.148070	−	0.455714i
$437$	22.3233	−	24.7926i	1.06787	−	1.18599i
$438$	7.32273	+	5.32027i	0.349894	+	0.254213i
$439$	−16.6835	+	28.8967i	−0.796260	+	1.37916i	0.125777	+	0.992059i	$0.459858\pi$
$439$	−16.6835	+	28.8967i	−0.796260	+	1.37916i	−0.922036	+	0.387103i	$0.873476\pi$
$440$	1.67281	+	2.89739i	0.0797481	+	0.138128i
$441$	0.672653	−	6.39986i	0.0320311	−	0.304755i
$442$	−0.0392252	+	0.0284988i	−0.00186575	+	0.00135555i
$443$	2.86332	+	27.2427i	0.136041	+	1.29434i	0.823166	+	0.567801i	$0.192206\pi$
$443$	2.86332	+	27.2427i	0.136041	+	1.29434i	−0.687125	+	0.726539i	$0.741128\pi$
$444$	4.23635	+	4.70495i	0.201048	+	0.223287i
$445$	10.6656	−	4.74865i	0.505600	−	0.225108i
$446$	−20.5216	+	4.36201i	−0.971727	+	0.206547i
$447$	−2.95321	−	0.627724i	−0.139682	−	0.0296903i
$448$	−0.686610	−	0.305698i	−0.0324393	−	0.0144429i
$449$	−1.57538	−	4.84851i	−0.0743466	−	0.228815i	0.906977	−	0.421181i	$-0.138384\pi$
$449$	−1.57538	−	4.84851i	−0.0743466	−	0.228815i	−0.981323	+	0.192365i	$0.938384\pi$
$450$	−0.309017	−	0.951057i	−0.0145672	−	0.0448332i
$451$	31.3844	+	13.9732i	1.47783	+	0.657974i
$452$	16.0140	+	3.40388i	0.753235	+	0.160105i
$453$	20.8486	−	4.43151i	0.979552	−	0.208210i
$454$	19.3336	−	8.60789i	0.907373	−	0.403988i
$455$	−0.0102279	−	0.0113593i	−0.000479494	−	0.000532532i
$456$	−0.854158	−	8.12677i	−0.0399996	−	0.380571i
$457$	−27.7379	+	20.1528i	−1.29753	+	0.942708i	−0.999928	−	0.0119838i	$-0.996185\pi$
$457$	−27.7379	+	20.1528i	−1.29753	+	0.942708i	−0.297598	+	0.954691i	$0.596185\pi$
$458$	1.13352	−	10.7848i	0.0529661	−	0.503938i
$459$	−1.19201	−	2.06462i	−0.0556382	−	0.0963682i
$460$	−2.04133	+	3.53569i	−0.0951777	+	0.164853i
$461$	0.668071	+	0.485382i	0.0311151	+	0.0226065i	0.603234	−	0.797564i	$-0.293878\pi$
$461$	0.668071	+	0.485382i	0.0311151	+	0.0226065i	−0.572119	+	0.820171i	$0.693878\pi$
$462$	−1.68255	+	1.86866i	−0.0782792	+	0.0869378i
$463$	0.0509567	−	0.156829i	0.00236816	−	0.00728845i	−0.949865	−	0.312659i	$-0.898780\pi$
$463$	0.0509567	−	0.156829i	0.00236816	−	0.00728845i	0.952234	+	0.305371i	$0.0987803\pi$
$464$	6.12228			0.284220
$465$	−5.29685	+	1.71564i	−0.245635	+	0.0795609i
$466$	0.163888			0.00759198
$467$	5.23210	−	16.1027i	0.242113	−	0.745146i	−0.753985	−	0.656891i	$-0.771871\pi$
$467$	5.23210	−	16.1027i	0.242113	−	0.745146i	0.996098	−	0.0882549i	$-0.0281290\pi$
$468$	−0.0136085	+	0.0151137i	−0.000629051	+	0.000698632i
$469$	−8.49892	−	6.17483i	−0.392444	−	0.285127i
$470$	2.33289	−	4.04068i	0.107608	−	0.186383i
$471$	−0.745208	−	1.29074i	−0.0343374	−	0.0594740i
$472$	−1.46835	+	13.9704i	−0.0675861	+	0.643039i
$473$	11.5944	−	8.42381i	0.533110	−	0.387327i
$474$	−1.47015	−	13.9875i	−0.0675261	−	0.642468i
$475$	−5.46782	−	6.07263i	−0.250881	−	0.278632i
$476$	−1.63689	+	0.728790i	−0.0750267	+	0.0334040i
$477$	−4.84579	+	1.03000i	−0.221874	+	0.0471607i
$478$	−5.50745	−	1.17064i	−0.251905	−	0.0535441i
$479$	25.9796	+	11.5669i	1.18704	+	0.528504i	0.902721	−	0.430226i	$-0.141566\pi$
$479$	25.9796	+	11.5669i	1.18704	+	0.528504i	0.284319	+	0.958730i	$0.408233\pi$
$480$	0.309017	+	0.951057i	0.0141046	+	0.0434096i
$481$	−0.0397889	−	0.122458i	−0.00181422	−	0.00558358i
$482$	0.948311	+	0.422215i	0.0431944	+	0.0192314i
$483$	−3.00143	−	0.637974i	−0.136570	−	0.0290288i
$484$	−0.188951	+	0.0401627i	−0.00858867	+	0.00182558i
$485$	−6.45702	+	2.87485i	−0.293198	+	0.130540i
$486$	−0.669131	−	0.743145i	−0.0303524	−	0.0337097i
$487$	−1.03295	−	9.82783i	−0.0468073	−	0.445341i	−0.992677	−	0.120796i	$-0.961455\pi$
$487$	−1.03295	−	9.82783i	−0.0468073	−	0.445341i	0.945870	−	0.324546i	$-0.105211\pi$
$488$	6.29442	−	4.57316i	0.284935	−	0.207017i
$489$	0.115015	−	1.09430i	0.00520116	−	0.0494857i
$490$	3.21756	+	5.57297i	0.145354	+	0.251761i
$491$	4.37800	−	7.58291i	0.197576	−	0.342212i	−0.750166	−	0.661250i	$-0.770026\pi$
$491$	4.37800	−	7.58291i	0.197576	−	0.342212i	0.947742	+	0.319038i	$0.103360\pi$
$492$	8.30740	+	6.03568i	0.374526	+	0.272109i
$493$	9.76637	−	10.8467i	0.439855	−	0.488509i
$494$	−0.0513551	+	0.158055i	−0.00231058	+	0.00711122i
$495$	3.34562			0.150374
$496$	5.29685	−	1.71564i	0.237835	−	0.0770345i
$497$	10.0383			0.450277
$498$	−4.17579	+	12.8518i	−0.187122	+	0.575902i
$499$	28.5923	−	31.7549i	1.27997	−	1.42155i	0.423035	−	0.906113i	$-0.360965\pi$
$499$	28.5923	−	31.7549i	1.27997	−	1.42155i	0.856930	−	0.515432i	$-0.172369\pi$
$500$	0.809017	+	0.587785i	0.0361803	+	0.0262866i
$501$	−3.04557	+	5.27508i	−0.136066	+	0.235673i
$502$	−10.3066	−	17.8515i	−0.460006	−	0.796753i
$503$	4.12989	−	39.2933i	0.184143	−	1.75200i	−0.378774	−	0.925489i	$-0.623654\pi$
$503$	4.12989	−	39.2933i	0.184143	−	1.75200i	0.562917	−	0.826513i	$-0.309679\pi$
$504$	−0.608047	+	0.441772i	−0.0270846	+	0.0196781i
$505$	1.18555	+	11.2798i	0.0527563	+	0.501943i
$506$	−9.13969	−	10.1507i	−0.406309	−	0.451252i
$507$	−11.8757	+	5.28741i	−0.527419	+	0.234822i
$508$	−7.38336	+	1.56938i	−0.327583	+	0.0696300i
$509$	18.0136	+	3.82891i	0.798440	+	0.169714i	0.589027	−	0.808114i	$-0.299511\pi$
$509$	18.0136	+	3.82891i	0.798440	+	0.169714i	0.209413	+	0.977827i	$0.432845\pi$
$510$	2.17791	+	0.969667i	0.0964394	+	0.0429376i
$511$	−2.10222	−	6.46996i	−0.0929966	−	0.286214i
$512$	−0.309017	−	0.951057i	−0.0136568	−	0.0420312i
$513$	−7.46507	−	3.32366i	−0.329591	−	0.146743i
$514$	8.40384	+	1.78629i	0.370677	+	0.0787899i
$515$	18.3965	−	3.91030i	0.810647	−	0.172308i
$516$	3.91330	−	1.74232i	0.172274	−	0.0767011i
$517$	10.4451	+	11.6004i	0.459374	+	0.510186i
$518$	−0.497388	−	4.73233i	−0.0218540	−	0.207927i
$519$	−0.737940	+	0.536145i	−0.0323920	+	0.0235341i
$520$	0.00212585	−	0.0202261i	9.32246e−5	−	0.000886973i
$521$	−3.03009	−	5.24827i	−0.132751	−	0.229931i	0.791985	−	0.610540i	$-0.209048\pi$
$521$	−3.03009	−	5.24827i	−0.132751	−	0.229931i	−0.924736	+	0.380609i	$0.875714\pi$
$522$	3.06114	−	5.30205i	0.133982	−	0.232064i
$523$	26.0698	+	18.9408i	1.13995	+	0.828225i	0.987113	−	0.160026i	$-0.0511578\pi$
$523$	26.0698	+	18.9408i	1.13995	+	0.828225i	0.152841	+	0.988251i	$0.451158\pi$
$524$	9.49819	−	10.5488i	0.414930	−	0.460827i
$525$	−0.232253	+	0.714803i	−0.0101364	+	0.0311965i
$526$	29.1068			1.26912
$527$	5.41008	−	12.1211i	0.235667	−	0.528003i
$528$	−3.34562			−0.145599
$529$	−1.95664	+	6.02191i	−0.0850712	+	0.261822i
$530$	3.31491	−	3.68158i	0.143990	−	0.159917i
$531$	11.3645	+	8.25682i	0.493179	+	0.358315i
$532$	−3.07081	+	5.31881i	−0.133137	+	0.230599i
$533$	−0.104418	−	0.180857i	−0.00452284	−	0.00783380i
$534$	−1.22037	+	11.6110i	−0.0528106	+	0.502459i
$535$	−0.0392295	+	0.0285019i	−0.00169604	+	0.00123224i
$536$	−1.46104	−	13.9008i	−0.0631071	−	0.600424i
$537$	13.7534	+	15.2747i	0.593503	+	0.659152i
$538$	7.98803	−	3.55650i	0.344389	−	0.153332i
$539$	−21.0590	+	4.47622i	−0.907074	+	0.192805i
$540$	0.978148	+	0.207912i	0.0420928	+	0.00894709i
$541$	21.3176	+	9.49122i	0.916517	+	0.408060i	0.810120	−	0.586264i	$-0.199402\pi$
$541$	21.3176	+	9.49122i	0.916517	+	0.408060i	0.106397	+	0.994324i	$0.466069\pi$
$542$	−6.03153	−	18.5631i	−0.259076	−	0.797355i
$543$	−0.155646	−	0.479028i	−0.00667939	−	0.0205570i
$544$	−2.17791	−	0.969667i	−0.0933771	−	0.0415741i
$545$	9.78663	+	2.08021i	0.419213	+	0.0891065i
$546$	0.0149514	−	0.00317802i	0.000639861	−	0.000136007i
$547$	−27.4227	+	12.2094i	−1.17251	+	0.522034i	−0.898191	−	0.439605i	$-0.855119\pi$
$547$	−27.4227	+	12.2094i	−1.17251	+	0.522034i	−0.274317	+	0.961639i	$0.588452\pi$
$548$	−8.20801	−	9.11592i	−0.350629	−	0.389413i
$549$	−0.813266	−	7.73771i	−0.0347093	−	0.330237i
$550$	−2.70666	+	1.96651i	−0.115413	+	0.0838521i
$551$	5.22939	−	49.7543i	0.222780	−	2.11961i
$552$	−2.04133	−	3.53569i	−0.0868850	−	0.150489i
$553$	−5.28538	+	9.15454i	−0.224757	+	0.389291i
$554$	18.5955	+	13.5104i	0.790048	+	0.574003i
$555$	−4.23635	+	4.70495i	−0.179823	+	0.199714i
$556$	−1.19750	+	3.68554i	−0.0507855	+	0.156302i
$557$	27.2509			1.15466			0.577329	−	0.816512i	$-0.304095\pi$
$557$	27.2509			1.15466			0.577329	+	0.816512i	$0.304095\pi$
$558$	1.16264	−	5.44502i	0.0492183	−	0.230506i
$559$	−0.0871187			−0.00368473
$560$	0.232253	−	0.714803i	0.00981450	−	0.0302059i
$561$	−5.33700	+	5.92734i	−0.225328	+	0.250252i
$562$	10.4516	+	7.59355i	0.440875	+	0.320315i
$563$	−13.2034	+	22.8689i	−0.556456	+	0.963810i	0.441333	+	0.897344i	$0.354506\pi$
$563$	−13.2034	+	22.8689i	−0.556456	+	0.963810i	−0.997789	+	0.0664665i	$0.978827\pi$
$564$	2.33289	+	4.04068i	0.0982323	+	0.170143i
$565$	−1.71131	+	16.2821i	−0.0719955	+	0.684992i
$566$	3.30917	−	2.40426i	0.139095	−	0.101058i
$567$	0.0785623	+	0.747471i	0.00329931	+	0.0313908i
$568$	8.93695	+	9.92549i	0.374986	+	0.416464i
$569$	−34.7500	+	15.4717i	−1.45679	+	0.648607i	−0.973880	−	0.227061i	$-0.927088\pi$
$569$	−34.7500	+	15.4717i	−1.45679	+	0.648607i	−0.482914	+	0.875668i	$0.660422\pi$
$570$	7.99297	−	1.69896i	0.334789	−	0.0711615i
$571$	14.3821	+	3.05701i	0.601873	+	0.127932i	0.498764	−	0.866738i	$-0.333788\pi$
$571$	14.3821	+	3.05701i	0.601873	+	0.127932i	0.103109	+	0.994670i	$0.467121\pi$
$572$	0.0621591	+	0.0276750i	0.00259900	+	0.00115715i
$573$	0.230788	+	0.710293i	0.00964132	+	0.0296729i
$574$	−2.38490	−	7.33996i	−0.0995437	−	0.306364i
$575$	−3.72970	−	1.66057i	−0.155539	−	0.0692506i
$576$	−0.978148	−	0.207912i	−0.0407562	−	0.00866299i
$577$	5.53938	−	1.17743i	0.230607	−	0.0490171i	−0.0911585	−	0.995836i	$-0.529057\pi$
$577$	5.53938	−	1.17743i	0.230607	−	0.0490171i	0.321766	+	0.946819i	$0.395724\pi$
$578$	10.3381	−	4.60282i	0.430008	−	0.191452i
$579$	−5.21639	−	5.79339i	−0.216786	−	0.240765i
$580$	0.639952	+	6.08874i	0.0265726	+	0.252821i
$581$	8.21664	−	5.96974i	0.340884	−	0.247666i
$582$	0.738816	−	7.02936i	0.0306249	−	0.291377i
$583$	8.28718	+	14.3538i	0.343220	+	0.594475i
$584$	4.52570	−	7.83874i	0.187275	−	0.324369i
$585$	−0.0164534	−	0.0119541i	−0.000680264	−	0.000494241i
$586$	−4.56952	+	5.07497i	−0.188765	+	0.209645i
$587$	−2.11547	+	6.51074i	−0.0873146	+	0.268727i	−0.985175	−	0.171554i	$-0.945121\pi$
$587$	−2.11547	+	6.51074i	−0.0873146	+	0.268727i	0.897860	+	0.440281i	$0.145121\pi$
$588$	−6.43512			−0.265380
$589$	−9.41826	−	44.5117i	−0.388073	−	1.83407i
$590$	−14.0473			−0.578320
$591$	6.55328	−	20.1689i	0.269566	−	0.829639i
$592$	4.23635	−	4.70495i	0.174113	−	0.193372i
$593$	−4.93984	−	3.58901i	−0.202855	−	0.147383i	0.481720	−	0.876325i	$-0.340012\pi$
$593$	−4.93984	−	3.58901i	−0.202855	−	0.147383i	−0.684575	+	0.728942i	$0.740012\pi$
$594$	−1.67281	+	2.89739i	−0.0686362	+	0.118881i
$595$	−0.895899	−	1.55174i	−0.0367283	−	0.0636153i
$596$	−0.315591	+	3.00264i	−0.0129271	+	0.122993i
$597$	−1.65477	+	1.20226i	−0.0677253	+	0.0492053i
$598$	0.00867914	+	0.0825765i	0.000354916	+	0.00337680i
$599$	0.752283	+	0.835495i	0.0307374	+	0.0341374i	0.758318	−	0.651885i	$-0.226022\pi$
$599$	0.752283	+	0.835495i	0.0307374	+	0.0341374i	−0.727580	+	0.686023i	$0.759355\pi$
$600$	−0.913545	+	0.406737i	−0.0372953	+	0.0166050i
$601$	−20.4060	+	4.33744i	−0.832380	+	0.176928i	−0.604342	−	0.796725i	$-0.706564\pi$
$601$	−20.4060	+	4.33744i	−0.832380	+	0.176928i	−0.228037	+	0.973652i	$0.573231\pi$
$602$	−3.14918	−	0.669379i	−0.128351	−	0.0272819i
$603$	−12.7690	−	5.68512i	−0.519993	−	0.231516i
$604$	−6.58650	−	20.2712i	−0.268001	−	0.824822i
$605$	−0.0596934	−	0.183717i	−0.00242688	−	0.00746918i
$606$	−10.3613	−	4.61317i	−0.420901	−	0.187397i
$607$	9.82518	+	2.08841i	0.398792	+	0.0847658i	0.402942	−	0.915226i	$-0.367988\pi$
$607$	9.82518	+	2.08841i	0.398792	+	0.0847658i	−0.00414999	+	0.999991i	$0.501321\pi$
$608$	−7.99297	+	1.69896i	−0.324158	+	0.0689018i
$609$	−4.20361	+	1.87157i	−0.170339	+	0.0758398i
$610$	5.20606	+	5.78191i	0.210787	+	0.234103i
$611$	−0.00991874	−	0.0943705i	−0.000401269	−	0.00381782i
$612$	−1.92871	+	1.40129i	−0.0779635	+	0.0566438i
$613$	−4.23101	+	40.2554i	−0.170889	+	1.62590i	0.487432	+	0.873161i	$0.337934\pi$
$613$	−4.23101	+	40.2554i	−0.170889	+	1.62590i	−0.658321	+	0.752738i	$0.728733\pi$
$614$	−14.3412	−	24.8397i	−0.578763	−	1.00245i
$615$	−5.13425	+	8.89279i	−0.207033	+	0.358592i
$616$	2.03430	+	1.47800i	0.0819641	+	0.0595504i
$617$	−31.5392	+	35.0278i	−1.26972	+	1.41017i	−0.400081	+	0.916480i	$0.631018\pi$
$617$	−31.5392	+	35.0278i	−1.26972	+	1.41017i	−0.869639	+	0.493688i	$0.835649\pi$
$618$	−5.81184	+	17.8870i	−0.233786	+	0.719520i
$619$	−33.6303			−1.35171			−0.675857	−	0.737033i	$-0.736226\pi$
$619$	−33.6303			−1.35171			−0.675857	+	0.737033i	$0.736226\pi$
$620$	2.25991	+	5.08850i	0.0907602	+	0.204359i
$621$	−4.08267			−0.163832
$622$	−7.58208	+	23.3352i	−0.304014	+	0.935658i
$623$	5.87148	−	6.52094i	0.235236	−	0.261256i
$624$	0.0164534	+	0.0119541i	0.000658663	+	0.000478547i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	1.34184	+	2.32413i	0.0536307	+	0.0928910i
$627$	−2.85769	+	27.1891i	−0.114125	+	1.08583i
$628$	−1.20577	+	0.876044i	−0.0481155	+	0.0349580i
$629$	−1.57770	−	15.0108i	−0.0629071	−	0.598521i
$630$	−0.502911	−	0.558539i	−0.0200364	−	0.0222527i
$631$	9.83277	−	4.37783i	0.391436	−	0.174279i	−0.201574	−	0.979473i	$-0.564606\pi$
$631$	9.83277	−	4.37783i	0.391436	−	0.174279i	0.593011	+	0.805194i	$0.297939\pi$
$632$	−13.7572	+	2.92419i	−0.547232	+	0.116318i
$633$	17.1529	+	3.64597i	0.681768	+	0.144914i
$634$	−19.3885	−	8.63231i	−0.770015	−	0.342833i
$635$	−2.33255	−	7.17886i	−0.0925646	−	0.284885i
$636$	1.53089	+	4.71158i	0.0607036	+	0.186826i
$637$	0.119560	+	0.0532314i	0.00473712	+	0.00210910i
$638$	−20.0352	−	4.25862i	−0.793202	−	0.168600i
$639$	13.0642	−	2.77688i	0.516812	−	0.109852i
$640$	0.913545	−	0.406737i	0.0361111	−	0.0160777i
$641$	−17.2400	−	19.1470i	−0.680941	−	0.756261i	0.299281	−	0.954165i	$-0.403253\pi$
$641$	−17.2400	−	19.1470i	−0.680941	−	0.756261i	−0.980221	+	0.197904i	$0.936587\pi$
$642$	−0.00506862	−	0.0482247i	−0.000200042	−	0.00190328i
$643$	−26.4915	+	19.2472i	−1.04472	+	0.759037i	−0.971202	−	0.238257i	$-0.923424\pi$
$643$	−26.4915	+	19.2472i	−1.04472	+	0.759037i	−0.0735221	+	0.997294i	$0.523424\pi$
$644$	−0.320744	+	3.05168i	−0.0126391	+	0.120253i
$645$	2.14182	+	3.70974i	0.0843342	+	0.146071i
$646$	−9.74054	+	16.8711i	−0.383236	+	0.663785i
$647$	−4.61630	−	3.35394i	−0.181485	−	0.131857i	0.493333	−	0.869840i	$-0.335778\pi$
$647$	−4.61630	−	3.35394i	−0.181485	−	0.131857i	−0.674819	+	0.737983i	$0.735778\pi$
$648$	−0.669131	+	0.743145i	−0.0262859	+	0.0291935i
$649$	14.5229	−	44.6968i	0.570073	−	1.75450i
$650$	0.0203375			0.000797703
$651$	−3.11240	+	2.79721i	−0.121985	+	0.109631i
$652$	−1.10032			−0.0430920
$653$	3.35147	−	10.3148i	0.131153	−	0.403648i	−0.863819	−	0.503803i	$-0.831934\pi$
$653$	3.35147	−	10.3148i	0.131153	−	0.403648i	0.994972	+	0.100155i	$0.0319338\pi$
$654$	−6.69483	+	7.43537i	−0.261789	+	0.290746i
$655$	11.4838	+	8.34350i	0.448711	+	0.326008i
$656$	5.13425	−	8.89279i	0.200459	−	0.347205i
$657$	−4.52570	−	7.83874i	−0.176564	−	0.305818i
$658$	0.366554	−	3.48753i	0.0142898	−	0.135958i
$659$	5.10389	−	3.70819i	0.198819	−	0.144451i	−0.483921	−	0.875111i	$-0.660788\pi$
$659$	5.10389	−	3.70819i	0.198819	−	0.144451i	0.682741	+	0.730661i	$0.260788\pi$
$660$	−0.349712	−	3.32729i	−0.0136125	−	0.129515i
$661$	14.6322	+	16.2507i	0.569127	+	0.632079i	0.957158	−	0.289567i	$-0.0935113\pi$
$661$	14.6322	+	16.2507i	0.569127	+	0.632079i	−0.388031	+	0.921646i	$0.626845\pi$
$662$	−7.31368	+	3.25626i	−0.284254	+	0.126558i
$663$	0.0474255	−	0.0100806i	0.00184185	−	0.000391498i
$664$	13.2179	+	2.80954i	0.512952	+	0.109031i
$665$	−5.61066	−	2.49802i	−0.217572	−	0.0968692i
$666$	−1.95643	−	6.02126i	−0.0758100	−	0.233319i
$667$	−7.72395	−	23.7719i	−0.299073	−	0.920451i
$668$	5.56453	+	2.47749i	0.215298	+	0.0958569i
$669$	20.5216	+	4.36201i	0.793412	+	0.168645i
$670$	13.6720	−	2.90606i	0.528194	−	0.112271i
$671$	−23.7796	+	10.5874i	−0.918002	+	0.408721i
$672$	0.502911	+	0.558539i	0.0194002	+	0.0215461i
$673$	−5.10240	−	48.5461i	−0.196683	−	1.87131i	−0.435418	−	0.900228i	$-0.643399\pi$
$673$	−5.10240	−	48.5461i	−0.196683	−	1.87131i	0.238735	−	0.971085i	$-0.423267\pi$
$674$	3.93173	−	2.85657i	0.151445	−	0.110031i
$675$	−0.104528	+	0.994522i	−0.00402330	+	0.0382792i
$676$	6.49979	+	11.2580i	0.249992	+	0.432999i
$677$	−4.24919	+	7.35982i	−0.163310	+	0.282861i	−0.936054	−	0.351857i	$-0.885550\pi$
$677$	−4.24919	+	7.35982i	−0.163310	+	0.282861i	0.772744	+	0.634718i	$0.218884\pi$
$678$	−13.2450	−	9.62307i	−0.508672	−	0.369572i
$679$	−3.55461	+	3.94780i	−0.136414	+	0.151503i
$680$	0.736702	−	2.26734i	0.0282512	−	0.0869483i
$681$	−21.1633			−0.810980
$682$	−18.5274	+	1.92999i	−0.709450	+	0.0739033i
$683$	27.3780			1.04759			0.523796	−	0.851844i	$-0.324516\pi$
$683$	27.3780			1.04759			0.523796	+	0.851844i	$0.324516\pi$
$684$	−2.52514	+	7.77159i	−0.0965513	+	0.297154i
$685$	8.20801	−	9.11592i	0.313612	−	0.348301i
$686$	8.16919	+	5.93526i	0.311901	+	0.226609i
$687$	−5.42208	+	9.39132i	−0.206865	+	0.358301i
$688$	−2.14182	−	3.70974i	−0.0816562	−	0.141433i
$689$	0.0105316	−	0.100201i	0.000401220	−	0.00381736i
$690$	3.30295	−	2.39973i	0.125741	−	0.0913563i
$691$	1.98713	+	18.9062i	0.0755938	+	0.719227i	0.965025	+	0.262158i	$0.0844342\pi$
$691$	1.98713	+	18.9062i	0.0755938	+	0.719227i	−0.889431	+	0.457069i	$0.848899\pi$
$692$	0.610343	+	0.677855i	0.0232018	+	0.0257682i
$693$	2.29714	−	1.02275i	0.0872610	−	0.0388511i
$694$	18.5963	−	3.95276i	0.705905	−	0.150045i
$695$	−3.79052	−	0.805701i	−0.143783	−	0.0305620i
$696$	−5.59298	−	2.49015i	−0.212001	−	0.0943890i
$697$	−7.56483	−	23.2822i	−0.286538	−	0.881875i
$698$	3.68444	+	11.3395i	0.139458	+	0.429208i
$699$	−0.149719	−	0.0666594i	−0.00566291	−	0.00252129i
$700$	0.735164	+	0.156264i	0.0277866	+	0.00590622i
$701$	−22.2019	+	4.71916i	−0.838553	+	0.178240i	−0.607119	−	0.794611i	$-0.707675\pi$
$701$	−22.2019	+	4.71916i	−0.838553	+	0.178240i	−0.231434	+	0.972851i	$0.574342\pi$
$702$	0.0185792	−	0.00827201i	0.000701228	−	0.000312207i
$703$	−34.6175	−	38.4466i	−1.30562	−	1.45004i
$704$	0.349712	+	3.32729i	0.0131803	+	0.125402i
$705$	−3.77469	+	2.74248i	−0.142163	+	0.103288i
$706$	−2.80792	+	26.7156i	−0.105678	+	1.00546i
$707$	4.26222	+	7.38238i	0.160297	+	0.277643i
$708$	7.02367	−	12.1653i	0.263966	−	0.457202i
$709$	−15.4352	−	11.2143i	−0.579682	−	0.421164i	0.258927	−	0.965897i	$-0.416631\pi$
$709$	−15.4352	−	11.2143i	−0.579682	−	0.421164i	−0.838609	+	0.544733i	$0.816631\pi$
$710$	−8.93695	+	9.92549i	−0.335398	+	0.372497i
$711$	−4.34619	+	13.3762i	−0.162995	+	0.501646i
$712$	11.6750			0.437539
$713$	−13.3441	−	18.4024i	−0.499742	−	0.689175i
$714$	1.79180			0.0670564
$715$	−0.0210260	+	0.0647114i	−0.000786328	+	0.00242007i
$716$	13.7534	−	15.2747i	0.513989	−	0.570843i
$717$	4.55516	+	3.30952i	0.170116	+	0.123596i
$718$	6.45806	−	11.1857i	0.241012	−	0.417446i
$719$	−0.318037	−	0.550857i	−0.0118608	−	0.0205435i	0.860034	−	0.510237i	$-0.170442\pi$
$719$	−0.318037	−	0.550857i	−0.0118608	−	0.0205435i	−0.871895	+	0.489693i	$0.837109\pi$
$720$	0.104528	−	0.994522i	0.00389555	−	0.0370636i
$721$	11.4359	−	8.30863i	0.425893	−	0.309430i
$722$	4.99374	+	47.5123i	0.185848	+	1.76822i
$723$	−0.694595	−	0.771426i	−0.0258323	−	0.0286896i
$724$	−0.460134	+	0.204865i	−0.0171007	+	0.00761374i
$725$	−5.98849	+	1.27289i	−0.222407	+	0.0472740i
$726$	0.188951	+	0.0401627i	0.00701262	+	0.00149058i
$727$	−9.19520	−	4.09397i	−0.341031	−	0.151837i	0.229073	−	0.973409i	$-0.426430\pi$
$727$	−9.19520	−	4.09397i	−0.341031	−	0.151837i	−0.570104	+	0.821572i	$0.693097\pi$
$728$	−0.00472346	−	0.0145373i	−0.000175063	−	0.000538788i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$	8.26886	+	3.68153i	0.306044	+	0.136260i
$731$	−9.98912	−	2.12325i	−0.369461	−	0.0785314i
$732$	−7.61031	+	1.61762i	−0.281285	+	0.0597890i
$733$	−7.05911	+	3.14292i	−0.260734	+	0.116086i	−0.532941	−	0.846152i	$-0.678913\pi$
$733$	−7.05911	+	3.14292i	−0.260734	+	0.116086i	0.272207	+	0.962239i	$0.412247\pi$
$734$	3.03881	+	3.37494i	0.112165	+	0.124571i
$735$	−0.672653	−	6.39986i	−0.0248112	−	0.236063i
$736$	−3.30295	+	2.39973i	−0.121748	+	0.0884553i
$737$	−4.88807	+	46.5069i	−0.180054	+	1.71310i
$738$	−5.13425	−	8.89279i	−0.188995	−	0.327348i
$739$	−8.28745	+	14.3543i	−0.304859	+	0.528031i	−0.977230	−	0.212183i	$-0.931943\pi$
$739$	−8.28745	+	14.3543i	−0.304859	+	0.528031i	0.672371	+	0.740214i	$0.265276\pi$
$740$	5.12199	+	3.72135i	0.188288	+	0.136799i
$741$	0.111202	−	0.123502i	0.00408511	−	0.00453697i
$742$	1.15060	−	3.54117i	0.0422397	−	0.130000i
$743$	16.5217			0.606121			0.303061	−	0.952971i	$-0.401992\pi$
$743$	16.5217			0.606121			0.303061	+	0.952971i	$0.401992\pi$
$744$	−5.53672	−	0.587107i	−0.202986	−	0.0215244i
$745$	−3.01918			−0.110614
$746$	1.87040	−	5.75650i	0.0684802	−	0.210760i
$747$	9.04206	−	10.0422i	0.330832	−	0.367426i
$748$	6.45273	+	4.68818i	0.235935	+	0.171417i
$749$	−0.0182224	+	0.0315621i	−0.000665831	+	0.00115325i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−2.29793	+	21.8633i	−0.0838526	+	0.797805i	0.869090	+	0.494654i	$0.164705\pi$
$751$	−2.29793	+	21.8633i	−0.0838526	+	0.797805i	−0.952943	+	0.303151i	$0.901961\pi$
$752$	3.77469	−	2.74248i	0.137649	−	0.100008i
$753$	2.15466	+	20.5003i	0.0785203	+	0.747071i
$754$	0.0833147	+	0.0925303i	0.00303414	+	0.00336976i
$755$	19.4716	−	8.66933i	0.708646	−	0.315509i
$756$	0.735164	−	0.156264i	0.0267377	−	0.00568326i
$757$	32.3033	+	6.86628i	1.17408	+	0.249559i	0.753347	−	0.657623i	$-0.228438\pi$
$757$	32.3033	+	6.86628i	1.17408	+	0.249559i	0.420737	+	0.907183i	$0.361771\pi$
$758$	−32.3798	−	14.4164i	−1.17609	−	0.523628i
$759$	4.22088	+	12.9905i	0.153208	+	0.471527i
$760$	−2.52514	−	7.77159i	−0.0915966	−	0.281905i
$761$	−32.7001	−	14.5590i	−1.18538	−	0.527763i	−0.283170	−	0.959070i	$-0.591386\pi$
$761$	−32.7001	−	14.5590i	−1.18538	−	0.527763i	−0.902206	+	0.431306i	$0.858053\pi$
$762$	7.38336	+	1.56938i	0.267471	+	0.0568527i
$763$	7.35552	−	1.56346i	0.266288	−	0.0566012i
$764$	0.682278	−	0.303770i	0.0246840	−	0.0109900i
$765$	−1.59522	−	1.77167i	−0.0576753	−	0.0640549i
$766$	−2.14801	−	20.4369i	−0.0776106	−	0.738415i
$767$	−0.231126	+	0.167923i	−0.00834549	+	0.00606335i
$768$	−0.104528	+	0.994522i	−0.00377185	+	0.0358867i
$769$	−4.26531	−	7.38774i	−0.153811	−	0.266409i	0.778814	−	0.627254i	$-0.215821\pi$
$769$	−4.26531	−	7.38774i	−0.153811	−	0.266409i	−0.932626	+	0.360846i	$0.882488\pi$
$770$	−1.25726	+	2.17764i	−0.0453086	+	0.0784769i
$771$	−6.95074	−	5.05001i	−0.250325	−	0.181872i
$772$	−5.21639	+	5.79339i	−0.187742	+	0.208509i
$773$	−2.27602	+	7.00486i	−0.0818627	+	0.251947i	−0.983608	−	0.180320i	$-0.942287\pi$
$773$	−2.27602	+	7.00486i	−0.0818627	+	0.251947i	0.901745	+	0.432268i	$0.142287\pi$
$774$	−4.28364			−0.153972
$775$	−4.82440	+	2.77942i	−0.173297	+	0.0998399i
$776$	−7.06808			−0.253729
$777$	−1.47043	+	4.52551i	−0.0527513	+	0.162352i
$778$	−0.0104958	+	0.0116568i	−0.000376294	+	0.000417917i
$779$	−67.8842	−	49.3208i	−2.43220	−	1.76710i
$780$	−0.0101688	+	0.0176128i	−0.000364100	+	0.000630640i
$781$	−22.3421	−	38.6977i	−0.799465	−	1.38471i
$782$	−1.01739	+	9.67984i	−0.0363819	+	0.346150i
$783$	−4.95303	+	3.59858i	−0.177007	+	0.128603i
$784$	0.672653	+	6.39986i	0.0240233	+	0.228567i
$785$	−0.997282	−	1.10759i	−0.0355945	−	0.0395317i
$786$	−12.9676	+	5.77355i	−0.462539	+	0.205936i
$787$	−12.7529	+	2.71072i	−0.454593	+	0.0966267i	−0.429517	−	0.903059i	$-0.641316\pi$
$787$	−12.7529	+	2.71072i	−0.454593	+	0.0966267i	−0.0250760	+	0.999686i	$0.507983\pi$
$788$	−20.7434	−	4.40915i	−0.738955	−	0.157070i
$789$	−26.5904	−	11.8388i	−0.946642	−	0.421472i
$790$	−4.34619	−	13.3762i	−0.154630	−	0.475903i
$791$	3.80240	+	11.7026i	0.135198	+	0.416095i
$792$	3.05638	+	1.36079i	0.108604	+	0.0483534i
$793$	0.154775	+	0.0328984i	0.00549621	+	0.00116826i
$794$	15.0129	−	3.19110i	0.532789	−	0.113248i
$795$	−4.52575	+	2.01499i	−0.160512	+	0.0714644i
$796$	1.36865	+	1.52004i	0.0485104	+	0.0538762i
$797$	−1.59027	−	15.1305i	−0.0563304	−	0.535948i	−0.985904	−	0.167312i	$-0.946491\pi$
$797$	−1.59027	−	15.1305i	−0.0563304	−	0.535948i	0.929574	−	0.368636i	$-0.120175\pi$
$798$	4.96868	−	3.60996i	0.175889	−	0.127791i
$799$	1.16270	−	11.0624i	0.0411334	−	0.391358i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	5.83750	−	10.1108i	0.206258	−	0.357249i
$802$	15.6099	+	11.3413i	0.551206	+	0.400474i
$803$	−20.2630	+	22.5043i	−0.715064	+	0.794159i
$804$	−4.31925	+	13.2933i	−0.152328	+	0.468818i
$805$	−3.06848			−0.108150
$806$	0.0980116	+	0.0567078i	0.00345231	+	0.00199745i
$807$	−8.74399			−0.307803
$808$	−3.50484	+	10.7868i	−0.123300	+	0.379478i
$809$	−7.82304	+	8.68837i	−0.275044	+	0.305467i	−0.864802	−	0.502113i	$-0.832556\pi$
$809$	−7.82304	+	8.68837i	−0.275044	+	0.305467i	0.589759	+	0.807580i	$0.299223\pi$
$810$	−0.809017	−	0.587785i	−0.0284260	−	0.0206527i
$811$	−23.3583	+	40.4578i	−0.820222	+	1.42067i	0.0852952	+	0.996356i	$0.472817\pi$
$811$	−23.3583	+	40.4578i	−0.820222	+	1.42067i	−0.905517	+	0.424310i	$0.860517\pi$
$812$	2.30071	+	3.98495i	0.0807393	+	0.139844i
$813$	−2.04023	+	19.4115i	−0.0715541	+	0.680791i
$814$	−17.1362	+	12.4502i	−0.600625	+	0.436379i
$815$	−0.115015	−	1.09430i	−0.00402880	−	0.0383315i
$816$	1.59522	+	1.77167i	0.0558438	+	0.0620209i
$817$	−31.9777	+	14.2374i	−1.11876	+	0.498103i
$818$	−4.89408	+	1.04027i	−0.171117	+	0.0363721i
$819$	−0.0149514	−	0.00317802i	−0.000522444	−	0.000111049i
$820$	9.38075	+	4.17658i	0.327590	+	0.145852i
$821$	−5.22778	−	16.0894i	−0.182451	−	0.561525i	0.817444	−	0.576007i	$-0.195390\pi$
$821$	−5.22778	−	16.0894i	−0.182451	−	0.561525i	−0.999895	+	0.0144820i	$0.995390\pi$
$822$	3.79061	+	11.6663i	0.132213	+	0.406909i
$823$	47.7451	+	21.2575i	1.66429	+	0.740990i	0.999979	−	0.00646688i	$-0.00205849\pi$
$823$	47.7451	+	21.2575i	1.66429	+	0.740990i	0.664311	+	0.747456i	$0.268725\pi$
$824$	18.3965	+	3.91030i	0.640873	+	0.136222i
$825$	3.27251	−	0.695593i	0.113934	−	0.0242175i
$826$	−9.64504	+	4.29425i	−0.335594	+	0.149416i
$827$	28.7342	+	31.9126i	0.999186	+	1.10971i	0.993962	+	0.109723i	$0.0349963\pi$
$827$	28.7342	+	31.9126i	0.999186	+	1.10971i	0.00522420	+	0.999986i	$0.498337\pi$
$828$	0.426755	+	4.06030i	0.0148308	+	0.141105i
$829$	14.0736	−	10.2251i	0.488797	−	0.355132i	−0.315925	−	0.948784i	$-0.602315\pi$
$829$	14.0736	−	10.2251i	0.488797	−	0.355132i	0.804721	+	0.593653i	$0.202315\pi$
$830$	−1.41251	+	13.4391i	−0.0490289	+	0.466479i
$831$	−11.4927	−	19.9059i	−0.398676	−	0.690527i
$832$	0.0101688	−	0.0176128i	0.000352538	−	0.000610614i
$833$	12.4115	+	9.01747i	0.430032	+	0.312437i
$834$	2.59302	−	2.87984i	0.0897889	−	0.0997207i
$835$	−1.88227	+	5.79302i	−0.0651385	+	0.200476i
$836$	27.3388			0.945534
$837$	−3.27681	+	4.50139i	−0.113263	+	0.155591i
$838$	4.47020			0.154421
$839$	4.54576	−	13.9904i	0.156937	−	0.483003i	−0.841415	−	0.540390i	$-0.818277\pi$
$839$	4.54576	−	13.9904i	0.156937	−	0.483003i	0.998352	+	0.0573867i	$0.0182768\pi$
$840$	−0.502911	+	0.558539i	−0.0173521	+	0.0192714i
$841$	−6.86229	−	4.98575i	−0.236631	−	0.171922i
$842$	0.897177	−	1.55396i	0.0309188	−	0.0535529i
$843$	−6.45946	−	11.1881i	−0.222476	−	0.385339i
$844$	1.83303	−	17.4401i	0.0630954	−	0.600313i
$845$	−10.5169	+	7.64097i	−0.361792	+	0.262857i
$846$	−0.487707	−	4.64022i	−0.0167677	−	0.159534i
$847$	−0.0971482	−	0.107894i	−0.00333805	−	0.00370728i
$848$	4.52575	−	2.01499i	0.155415	−	0.0691952i
$849$	−4.00098	+	0.850434i	−0.137313	+	0.0291868i
$850$	2.33192	+	0.495665i	0.0799842	+	0.0170012i
$851$	−23.6132	−	10.5133i	−0.809451	−	0.360391i
$852$	−4.12725	−	12.7024i	−0.141397	−	0.435176i
$853$	3.85364	+	11.8603i	0.131946	+	0.406088i	0.995103	−	0.0988484i	$-0.0315159\pi$
$853$	3.85364	+	11.8603i	0.131946	+	0.406088i	−0.863156	+	0.504937i	$0.831516\pi$
$854$	5.34205	+	2.37843i	0.182801	+	0.0813883i
$855$	−7.99297	−	1.69896i	−0.273354	−	0.0581031i
$856$	−0.0474307	+	0.0100817i	−0.00162115	+	0.000344585i
$857$	44.3146	−	19.7301i	1.51376	−	0.673968i	0.529115	−	0.848550i	$-0.322524\pi$
$857$	44.3146	−	19.7301i	1.51376	−	0.673968i	0.984643	+	0.174582i	$0.0558575\pi$
$858$	−0.0455287	−	0.0505648i	−0.00155432	−	0.00172625i
$859$	−1.36090	−	12.9481i	−0.0464333	−	0.441784i	−0.992897	−	0.118974i	$-0.962039\pi$
$859$	−1.36090	−	12.9481i	−0.0464333	−	0.441784i	0.946464	−	0.322809i	$-0.104627\pi$
$860$	3.46554	−	2.51786i	0.118174	−	0.0858584i
$861$	−0.806718	+	7.67541i	−0.0274929	+	0.261577i
$862$	−2.92786	−	5.07120i	−0.0997232	−	0.172726i
$863$	6.77331	−	11.7317i	0.230566	−	0.399353i	−0.727409	−	0.686205i	$-0.759275\pi$
$863$	6.77331	−	11.7317i	0.230566	−	0.399353i	0.957975	+	0.286852i	$0.0926088\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	−0.610343	+	0.677855i	−0.0207523	+	0.0230478i
$866$	−8.11725	+	24.9823i	−0.275835	+	0.848934i
$867$	−11.3165			−0.384327
$868$	3.10722	+	2.80296i	0.105466	+	0.0951387i
$869$	47.0547			1.59622
$870$	1.89189	−	5.82263i	0.0641410	−	0.197406i
$871$	0.190211	−	0.211250i	0.00644504	−	0.00715795i
$872$	8.09444	+	5.88095i	0.274112	+	0.199154i
$873$	−3.53404	+	6.12114i	−0.119609	+	0.207169i
$874$	16.6808	+	28.8921i	0.564238	+	0.977288i
$875$	−0.0785623	+	0.747471i	−0.00265589	+	0.0252691i
$876$	−7.32273	+	5.32027i	−0.247412	+	0.179755i
$877$	2.96522	+	28.2122i	0.100128	+	0.952657i	0.923096	+	0.384569i	$0.125650\pi$
$877$	2.96522	+	28.2122i	0.100128	+	0.952657i	−0.822968	+	0.568088i	$0.807683\pi$
$878$	−22.3269	−	24.7965i	−0.753495	−	0.836841i
$879$	6.23864	−	2.77762i	0.210424	−	0.0936868i
$880$	−3.27251	+	0.695593i	−0.110316	+	0.0234485i
$881$	32.7839	+	6.96844i	1.10452	+	0.234773i	0.723863	−	0.689944i	$-0.242365\pi$
$881$	32.7839	+	6.96844i	1.10452	+	0.234773i	0.380656	+	0.924717i	$0.375698\pi$
$882$	5.87877	+	2.61740i	0.197949	+	0.0881324i
$883$	10.4650	+	32.2080i	0.352175	+	1.08388i	0.957629	+	0.288004i	$0.0929916\pi$
$883$	10.4650	+	32.2080i	0.352175	+	1.08388i	−0.605454	+	0.795880i	$0.707008\pi$
$884$	−0.0149827	−	0.0461120i	−0.000503922	−	0.00155091i
$885$	12.8329	+	5.71357i	0.431372	+	0.192059i
$886$	−26.7942	−	5.69528i	−0.900168	−	0.191337i
$887$	20.3429	−	4.32402i	0.683049	−	0.145186i	0.146697	−	0.989181i	$-0.453136\pi$
$887$	20.3429	−	4.32402i	0.683049	−	0.145186i	0.536351	+	0.843995i	$0.319802\pi$
$888$	−5.78378	+	2.57510i	−0.194091	+	0.0864148i
$889$	−3.79612	−	4.21602i	−0.127318	−	0.141401i
$890$	1.22037	+	11.6110i	0.0409069	+	0.389203i
$891$	2.70666	−	1.96651i	0.0906766	−	0.0658804i
$892$	2.19302	−	20.8652i	0.0734276	−	0.698617i
$893$	−19.0633	−	33.0186i	−0.637928	−	1.10492i
$894$	1.50959	−	2.61469i	0.0504883	−	0.0874483i
$895$	16.6287	+	12.0814i	0.555835	+	0.403837i
$896$	0.502911	−	0.558539i	0.0168011	−	0.0186595i
$897$	0.0256581	−	0.0789675i	0.000856699	−	0.00263665i
$898$	5.09803			0.170123
$899$	−32.4093	−	10.5635i	−1.08091	−	0.352314i
$900$	1.00000			0.0333333
$901$	3.64966	−	11.2325i	0.121588	−	0.374209i
$902$	−22.9877	+	25.5304i	−0.765406	+	0.850069i
$903$	2.60466	+	1.89240i	0.0866776	+	0.0629750i
$904$	−8.18587	+	14.1784i	−0.272258	+	0.471565i
$905$	−0.251840	−	0.436199i	−0.00837144	−	0.0144998i
$906$	−2.22796	+	21.1976i	−0.0740189	+	0.704243i
$907$	−33.0193	+	23.9900i	−1.09639	+	0.796573i	−0.980467	−	0.196685i	$-0.936982\pi$
$907$	−33.0193	+	23.9900i	−1.09639	+	0.796573i	−0.115922	+	0.993258i	$0.536982\pi$
$908$	2.21217	+	21.0474i	0.0734134	+	0.698482i
$909$	7.58921	+	8.42867i	0.251718	+	0.279561i
$910$	0.0139639	−	0.00621714i	0.000462900	−	0.000206096i
$911$	6.23197	−	1.32465i	0.206474	−	0.0438875i	−0.103513	−	0.994628i	$-0.533008\pi$
$911$	6.23197	−	1.32465i	0.206474	−	0.0438875i	0.309988	+	0.950741i	$0.399675\pi$
$912$	7.99297	+	1.69896i	0.264674	+	0.0562581i
$913$	−41.3013	−	18.3885i	−1.36687	−	0.608571i
$914$	−10.5949	−	32.6079i	−0.350450	−	1.07857i
$915$	−2.40425	−	7.39953i	−0.0794822	−	0.244621i
$916$	9.90663	+	4.41072i	0.327324	+	0.145734i
$917$	10.4355	+	2.21814i	0.344611	+	0.0732494i
$918$	2.33192	−	0.495665i	0.0769649	−	0.0163594i
$919$	36.8328	−	16.3990i	1.21500	−	0.540953i	0.303729	−	0.952759i	$-0.401768\pi$
$919$	36.8328	−	16.3990i	1.21500	−	0.540953i	0.911272	+	0.411806i	$0.135102\pi$
$920$	−2.73184	−	3.03401i	−0.0900661	−	0.100028i
$921$	2.99813	+	28.5253i	0.0987916	+	0.939939i
$922$	−0.668071	+	0.485382i	−0.0220017	+	0.0159852i
$923$	−0.0283930	+	0.270141i	−0.000934566	+	0.00889180i
$924$	−1.25726	−	2.17764i	−0.0413609	−	0.0716393i
$925$	−3.16557	+	5.48292i	−0.104083	+	0.180277i
$926$	0.133406	+	0.0969255i	0.00438401	+	0.00318517i
$927$	12.5847	−	13.9767i	0.413335	−	0.459055i
$928$	−1.89189	+	5.82263i	−0.0621042	+	0.191137i
$929$	20.8107			0.682777			0.341388	−	0.939922i	$-0.389103\pi$
$929$	20.8107			0.682777			0.341388	+	0.939922i	$0.389103\pi$
$930$	0.00514584	−	5.56776i	0.000168739	−	0.182574i
$931$	52.5848			1.72340
$932$	−0.0506443	+	0.155867i	−0.00165891	+	0.00510559i
$933$	16.4179	−	18.2339i	0.537497	−	0.596951i
$934$	13.6978	+	9.95204i	0.448206	+	0.325641i
$935$	−3.98801	+	6.90743i	−0.130422	+	0.225897i
$936$	−0.0101688	−	0.0176128i	−0.000332376	−	0.000575692i
$937$	−3.27902	+	31.1978i	−0.107121	+	1.01919i	0.800482	+	0.599357i	$0.204577\pi$
$937$	−3.27902	+	31.1978i	−0.107121	+	1.01919i	−0.907603	+	0.419830i	$0.862090\pi$
$938$	8.49892	−	6.17483i	0.277500	−	0.201615i
$939$	−0.280521	−	2.66898i	−0.00915445	−	0.0870987i
$940$	3.12201	+	3.46735i	0.101829	+	0.113092i
$941$	4.46736	−	1.98900i	0.145632	−	0.0648395i	−0.332627	−	0.943059i	$-0.607935\pi$
$941$	4.46736	−	1.98900i	0.145632	−	0.0648395i	0.478258	+	0.878219i	$0.341268\pi$
$942$	1.45785	−	0.309875i	0.0474992	−	0.0100963i
$943$	−41.0068	−	8.71627i	−1.33537	−	0.283841i
$944$	−12.8329	−	5.71357i	−0.417675	−	0.185961i
$945$	0.232253	+	0.714803i	0.00755521	+	0.0232525i
$946$	4.42866	+	13.6300i	0.143988	+	0.443150i
$947$	−36.4773	−	16.2407i	−1.18535	−	0.527753i	−0.283154	−	0.959074i	$-0.591381\pi$
$947$	−36.4773	−	16.2407i	−1.18535	−	0.527753i	−0.902198	+	0.431322i	$0.858047\pi$
$948$	13.7572	+	2.92419i	0.446813	+	0.0949731i
$949$	0.180060	−	0.0382730i	0.00584500	−	0.00124239i
$950$	7.46507	−	3.32366i	0.242199	−	0.107834i
$951$	14.2012	+	15.7720i	0.460505	+	0.511443i
$952$	−0.187294	−	1.78198i	−0.00607023	−	0.0577544i
$953$	10.1253	−	7.35649i	0.327992	−	0.238300i	−0.411586	−	0.911371i	$-0.635025\pi$
$953$	10.1253	−	7.35649i	0.327992	−	0.238300i	0.739578	+	0.673071i	$0.235025\pi$
$954$	0.517839	−	4.92691i	0.0167657	−	0.159515i
$955$	0.373423	+	0.646788i	0.0120837	+	0.0209296i
$956$	2.81525	−	4.87615i	0.0910515	−	0.157706i
$957$	16.5709	+	12.0395i	0.535662	+	0.389182i
$958$	−19.0289	+	21.1337i	−0.614796	+	0.682800i
$959$	2.84898	−	8.76825i	0.0919983	−	0.283142i
$960$	−1.00000			−0.0322749
$961$	−30.9999	−	0.0573016i	−0.999998	−	0.00184844i
$962$	0.128759			0.00415137
$963$	−0.0149843	+	0.0461170i	−0.000482863	+	0.00148610i
$964$	−0.694595	+	0.771426i	−0.0223714	+	0.0248459i
$965$	−6.30692	−	4.58224i	−0.203027	−	0.147508i
$966$	1.53424	−	2.65739i	0.0493634	−	0.0855000i
$967$	−16.2311	−	28.1131i	−0.521958	−	0.904058i	−0.999674	−	0.0255431i	$-0.991868\pi$
$967$	−16.2311	−	28.1131i	−0.521958	−	0.904058i	0.477716	−	0.878514i	$-0.341465\pi$
$968$	0.0201920	−	0.192114i	0.000648994	−	0.00617477i
$969$	15.7605	−	11.4507i	0.506301	−	0.367849i
$970$	−0.738816	−	7.02936i	−0.0237220	−	0.225699i
$971$	−26.1813	−	29.0772i	−0.840197	−	0.933133i	0.158330	−	0.987386i	$-0.449389\pi$
$971$	−26.1813	−	29.0772i	−0.840197	−	0.933133i	−0.998527	+	0.0542529i	$0.982722\pi$
$972$	0.913545	−	0.406737i	0.0293020	−	0.0130461i
$973$	−2.84891	+	0.605555i	−0.0913319	+	0.0194132i
$974$	9.66602	+	2.05458i	0.309719	+	0.0658329i
$975$	−0.0185792	−	0.00827201i	−0.000595012	−	0.000264916i
$976$	2.40425	+	7.39953i	0.0769583	+	0.236853i
$977$	5.07506	+	15.6194i	0.162365	+	0.499709i	0.998832	−	0.0483078i	$-0.0153828\pi$
$977$	5.07506	+	15.6194i	0.162365	+	0.499709i	−0.836467	+	0.548017i	$0.815383\pi$
$978$	1.00519	+	0.447542i	0.0321426	+	0.0143108i
$979$	−38.2065	−	8.12105i	−1.22109	−	0.259550i
$980$	−6.29449	+	1.33794i	−0.201070	+	0.0427388i
$981$	9.14027	−	4.06951i	0.291826	−	0.129929i
$982$	5.85890	+	6.50697i	0.186965	+	0.207646i
$983$	4.65551	+	44.2942i	0.148488	+	1.41277i	0.774313	+	0.632803i	$0.218096\pi$
$983$	4.65551	+	44.2942i	0.148488	+	1.41277i	−0.625825	+	0.779963i	$0.715238\pi$
$984$	−8.30740	+	6.03568i	−0.264830	+	0.192410i
$985$	2.21672	−	21.0907i	0.0706306	−	0.672005i
$986$	7.29781	+	12.6402i	0.232410	+	0.402545i
$987$	−1.75337	+	3.03693i	−0.0558104	+	0.0966665i
$988$	−0.134449	−	0.0976833i	−0.00427741	−	0.00310772i
$989$	−11.7022	+	12.9966i	−0.372109	+	0.413269i
$990$	−1.03385	+	3.18187i	−0.0328580	+	0.101127i
$991$	49.6716			1.57787			0.788936	−	0.614476i	$-0.210632\pi$
$991$	49.6716			1.57787			0.788936	+	0.614476i	$0.210632\pi$
$992$	−0.00514584	+	5.56776i	−0.000163381	+	0.176777i
$993$	8.00582			0.254057
$994$	−3.10199	+	9.54695i	−0.0983892	+	0.302811i
$995$	−1.36865	+	1.52004i	−0.0433890	+	0.0481884i
$996$	−10.9324	−	7.94283i	−0.346405	−	0.251678i
$997$	−9.05464	+	15.6831i	−0.286763	+	0.496689i	−0.973035	−	0.230656i	$-0.925913\pi$
$997$	−9.05464	+	15.6831i	−0.286763	+	0.496689i	0.686272	+	0.727345i	$0.259246\pi$
$998$	21.3652	+	37.0057i	0.676305	+	1.17139i
$999$	−0.661783	+	6.29645i	−0.0209379	+	0.199211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.i.541.2	yes	24
31.20	even	15	inner	930.2.bg.i.361.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.i.361.2	✓	24	31.20	even	15	inner
930.2.bg.i.541.2	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0785623 - 0.747471i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +O(q^{10})\)	\(q+(-0.309017 + 0.951057i) q^{2} +(0.669131 - 0.743145i) q^{3} +(-0.809017 - 0.587785i) q^{4} +(0.500000 - 0.866025i) q^{5} +(0.500000 + 0.866025i) q^{6} +(0.0785623 - 0.747471i) q^{7} +(0.809017 - 0.587785i) q^{8} +(-0.104528 - 0.994522i) q^{9} +(0.669131 + 0.743145i) q^{10} +(-3.05638 + 1.36079i) q^{11} +(-0.978148 + 0.207912i) q^{12} +(0.0198931 + 0.00422841i) q^{13} +(0.686610 + 0.305698i) q^{14} +(-0.309017 - 0.951057i) q^{15} +(0.309017 + 0.951057i) q^{16} +(2.17791 + 0.969667i) q^{17} +(0.978148 + 0.207912i) q^{18} +(7.99297 - 1.69896i) q^{19} +(-0.913545 + 0.406737i) q^{20} +(-0.502911 - 0.558539i) q^{21} +(-0.349712 - 3.32729i) q^{22} +(3.30295 - 2.39973i) q^{23} +(0.104528 - 0.994522i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-0.0101688 + 0.0176128i) q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.502911 + 0.558539i) q^{28} +(1.89189 - 5.82263i) q^{29} +1.00000 q^{30} +(0.00514584 - 5.56776i) q^{31} -1.00000 q^{32} +(-1.03385 + 3.18187i) q^{33} +(-1.59522 + 1.77167i) q^{34} +(-0.608047 - 0.441772i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-3.16557 - 5.48292i) q^{37} +(-0.854158 + 8.12677i) q^{38} +(0.0164534 - 0.0119541i) q^{39} +(-0.104528 - 0.994522i) q^{40} +(-6.87097 - 7.63099i) q^{41} +(0.686610 - 0.305698i) q^{42} +(-4.19004 + 0.890620i) q^{43} +(3.27251 + 0.695593i) q^{44} +(-0.913545 - 0.406737i) q^{45} +(1.26161 + 3.88285i) q^{46} +(-1.44180 - 4.43742i) q^{47} +(0.913545 + 0.406737i) q^{48} +(6.29449 + 1.33794i) q^{49} +(0.978148 - 0.207912i) q^{50} +(2.17791 - 0.969667i) q^{51} +(-0.0136085 - 0.0151137i) q^{52} +(-0.517839 - 4.92691i) q^{53} +(0.809017 - 0.587785i) q^{54} +(-0.349712 + 3.32729i) q^{55} +(-0.375794 - 0.650894i) q^{56} +(4.08577 - 7.07676i) q^{57} +(4.95303 + 3.59858i) q^{58} +(-9.39950 + 10.4392i) q^{59} +(-0.309017 + 0.951057i) q^{60} +7.78033 q^{61} +(5.29367 + 1.72543i) q^{62} -0.751588 q^{63} +(0.309017 - 0.951057i) q^{64} +(0.0136085 - 0.0151137i) q^{65} +(-2.70666 - 1.96651i) q^{66} +(6.98870 - 12.1048i) q^{67} +(-1.19201 - 2.06462i) q^{68} +(0.426755 - 4.06030i) q^{69} +(0.608047 - 0.441772i) q^{70} +(1.39609 + 13.2829i) q^{71} +(-0.669131 - 0.743145i) q^{72} +(8.26886 - 3.68153i) q^{73} +(6.19278 - 1.31632i) q^{74} +(-0.978148 - 0.207912i) q^{75} +(-7.46507 - 3.32366i) q^{76} +(0.777032 + 2.39146i) q^{77} +(0.00628464 + 0.0193421i) q^{78} +(-12.8486 - 5.72057i) q^{79} +(0.978148 + 0.207912i) q^{80} +(-0.978148 + 0.207912i) q^{81} +(9.38075 - 4.17658i) q^{82} +(9.04206 + 10.0422i) q^{83} +(0.0785623 + 0.747471i) q^{84} +(1.92871 - 1.40129i) q^{85} +(0.447763 - 4.26018i) q^{86} +(-3.06114 - 5.30205i) q^{87} +(-1.67281 + 2.89739i) q^{88} +(9.44527 + 6.86239i) q^{89} +(0.669131 - 0.743145i) q^{90} +(0.00472346 - 0.0145373i) q^{91} -4.08267 q^{92} +(-4.13421 - 3.72938i) q^{93} +4.66578 q^{94} +(2.52514 - 7.77159i) q^{95} +(-0.669131 + 0.743145i) q^{96} +(-5.71820 - 4.15452i) q^{97} +(-3.21756 + 5.57297i) q^{98} +(1.67281 + 2.89739i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9	\( 24 q + 6 q^{2} + 3 q^{3} - 6 q^{4} + 12 q^{5} + 12 q^{6} - 7 q^{7} + 6 q^{8} + 3 q^{9} + 3 q^{10} - 13 q^{11} + 3 q^{12} + 11 q^{13} - 8 q^{14} + 6 q^{15} - 6 q^{16} - 29 q^{17} - 3 q^{18} + 9 q^{19} - 3 q^{20} - 2 q^{21} - 17 q^{22} - 5 q^{23} - 3 q^{24} - 12 q^{25} + 9 q^{26} - 6 q^{27} - 2 q^{28} + 13 q^{29} + 24 q^{30} + 57 q^{31} - 24 q^{32} + 16 q^{33} + 29 q^{34} + q^{35} - 12 q^{36} - 24 q^{37} + 6 q^{38} - 17 q^{39} + 3 q^{40} + 32 q^{41} - 8 q^{42} + 49 q^{43} - 8 q^{44} - 3 q^{45} + 28 q^{47} + 3 q^{48} + 12 q^{49} - 3 q^{50} - 29 q^{51} - 19 q^{52} - 36 q^{53} + 6 q^{54} - 17 q^{55} - 3 q^{56} - 6 q^{57} + 2 q^{58} + 6 q^{60} + 33 q^{62} - 6 q^{63} - 6 q^{64} + 19 q^{65} + 4 q^{66} - 5 q^{67} + 11 q^{68} + 10 q^{69} - q^{70} - 11 q^{71} - 3 q^{72} - 13 q^{73} + 9 q^{74} + 3 q^{75} - 6 q^{76} + 4 q^{77} - 8 q^{78} - 68 q^{79} - 3 q^{80} + 3 q^{81} - 2 q^{82} + 10 q^{83} - 7 q^{84} + 2 q^{85} - 34 q^{86} + 11 q^{87} - 12 q^{88} + 55 q^{89} + 3 q^{90} + 38 q^{91} + 10 q^{92} + 19 q^{93} + 42 q^{94} + 18 q^{95} - 3 q^{96} - q^{97} + 63 q^{98} + 12 q^{99}+O(q^{100}) \) 24 * q + 6 * q^2 + 3 * q^3 - 6 * q^4 + 12 * q^5 + 12 * q^6 - 7 * q^7 + 6 * q^8 + 3 * q^9 + 3 * q^10 - 13 * q^11 + 3 * q^12 + 11 * q^13 - 8 * q^14 + 6 * q^15 - 6 * q^16 - 29 * q^17 - 3 * q^18 + 9 * q^19 - 3 * q^20 - 2 * q^21 - 17 * q^22 - 5 * q^23 - 3 * q^24 - 12 * q^25 + 9 * q^26 - 6 * q^27 - 2 * q^28 + 13 * q^29 + 24 * q^30 + 57 * q^31 - 24 * q^32 + 16 * q^33 + 29 * q^34 + q^35 - 12 * q^36 - 24 * q^37 + 6 * q^38 - 17 * q^39 + 3 * q^40 + 32 * q^41 - 8 * q^42 + 49 * q^43 - 8 * q^44 - 3 * q^45 + 28 * q^47 + 3 * q^48 + 12 * q^49 - 3 * q^50 - 29 * q^51 - 19 * q^52 - 36 * q^53 + 6 * q^54 - 17 * q^55 - 3 * q^56 - 6 * q^57 + 2 * q^58 + 6 * q^60 + 33 * q^62 - 6 * q^63 - 6 * q^64 + 19 * q^65 + 4 * q^66 - 5 * q^67 + 11 * q^68 + 10 * q^69 - q^70 - 11 * q^71 - 3 * q^72 - 13 * q^73 + 9 * q^74 + 3 * q^75 - 6 * q^76 + 4 * q^77 - 8 * q^78 - 68 * q^79 - 3 * q^80 + 3 * q^81 - 2 * q^82 + 10 * q^83 - 7 * q^84 + 2 * q^85 - 34 * q^86 + 11 * q^87 - 12 * q^88 + 55 * q^89 + 3 * q^90 + 38 * q^91 + 10 * q^92 + 19 * q^93 + 42 * q^94 + 18 * q^95 - 3 * q^96 - q^97 + 63 * q^98 + 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more