LMFDB - Embedded newform 930.2.bg.g.121.2

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			121.2
Character	$\chi$	$=$	930.121
Dual form			930.2.bg.g.661.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.809017 + 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.813060 + 0.172821i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})$	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.813060 + 0.172821i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.104528 - 0.994522i) q^{10} +(2.87236 + 3.19008i) q^{11} +(0.913545 + 0.406737i) q^{12} +(5.10256 - 2.27180i) q^{13} +(0.556197 - 0.617720i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.58470 - 1.75999i) q^{17} +(0.913545 - 0.406737i) q^{18} +(1.60962 + 0.716647i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.0868866 - 0.826670i) q^{21} +(-4.19887 - 0.892498i) q^{22} +(0.945547 + 2.91009i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.79272 + 4.83714i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.0868866 + 0.826670i) q^{28} +(-4.43401 + 3.22150i) q^{29} +1.00000 q^{30} +(-2.94938 + 4.72241i) q^{31} +1.00000 q^{32} +(-3.47285 + 2.52317i) q^{33} +(-0.247554 + 2.35532i) q^{34} +(0.256862 - 0.790541i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.33468 - 4.04378i) q^{37} +(-1.72344 + 0.366329i) q^{38} +(1.72600 + 5.31207i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(0.770057 + 7.32660i) q^{41} +(0.556197 + 0.617720i) q^{42} +(2.26879 + 1.01013i) q^{43} +(3.92156 - 1.74599i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-2.47547 - 1.79854i) q^{46} +(2.33397 + 1.69573i) q^{47} +(0.669131 - 0.743145i) q^{48} +(-5.76362 + 2.56613i) q^{49} +(0.913545 + 0.406737i) q^{50} +(1.58470 + 1.75999i) q^{51} +(-0.583838 - 5.55485i) q^{52} +(6.65906 + 1.41543i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-4.19887 + 0.892498i) q^{55} +(-0.415612 - 0.719861i) q^{56} +(-0.880972 + 1.52589i) q^{57} +(1.69364 - 5.21249i) q^{58} +(-0.391292 + 3.72289i) q^{59} +(-0.809017 + 0.587785i) q^{60} -1.28112 q^{61} +(-0.389660 - 5.55411i) q^{62} +0.831224 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.583838 + 5.55485i) q^{65} +(1.32651 - 4.08258i) q^{66} +(-3.45186 + 5.97879i) q^{67} +(-1.18415 - 2.05100i) q^{68} +(-2.99299 + 0.636179i) q^{69} +(0.256862 + 0.790541i) q^{70} +(1.60889 + 0.341980i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-4.17731 - 4.63937i) q^{73} +(4.26566 + 1.89920i) q^{74} +(0.913545 - 0.406737i) q^{75} +(1.17897 - 1.30938i) q^{76} +(-2.88672 - 2.09732i) q^{77} +(-4.51872 - 3.28304i) q^{78} +(1.13450 - 1.25999i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-4.92946 - 5.47472i) q^{82} +(-0.538577 - 5.12422i) q^{83} +(-0.813060 - 0.172821i) q^{84} +(0.731844 + 2.25238i) q^{85} +(-2.42923 + 0.516349i) q^{86} +(-2.74037 - 4.74646i) q^{87} +(-2.14634 + 3.71757i) q^{88} +(-4.92988 + 15.1726i) q^{89} +(-0.104528 + 0.994522i) q^{90} +(-3.75607 + 2.72894i) q^{91} +3.05985 q^{92} +(-4.38824 - 3.42685i) q^{93} -2.88494 q^{94} +(-1.42544 + 1.03564i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(2.72642 - 8.39106i) q^{97} +(3.15453 - 5.46381i) q^{98} +(-2.14634 - 3.71757i) 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} + 9 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 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{15}\right)$

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 $

$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$2$	−0.809017	+	0.587785i	−0.572061	+	0.415627i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$3$	−0.104528	+	0.994522i	−0.0603495	+	0.574187i
$4$	0.309017	−	0.951057i	0.154508	−	0.475528i
$5$	−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
$7$	−0.813060	+	0.172821i	−0.307308	+	0.0653203i	−0.358984	−	0.933344i	$-0.616877\pi$
$7$	−0.813060	+	0.172821i	−0.307308	+	0.0653203i	0.0516766	+	0.998664i	$0.483543\pi$
$8$	0.309017	+	0.951057i	0.109254	+	0.336249i
$9$	−0.978148	−	0.207912i	−0.326049	−	0.0693039i
$10$	−0.104528	−	0.994522i	−0.0330548	−	0.314495i
$11$	2.87236	+	3.19008i	0.866050	+	0.961846i	0.999574	−	0.0291997i	$-0.00929589\pi$
$11$	2.87236	+	3.19008i	0.866050	+	0.961846i	−0.133524	+	0.991046i	$0.542629\pi$
$12$	0.913545	+	0.406737i	0.263718	+	0.117415i
$13$	5.10256	−	2.27180i	1.41519	−	0.630085i	0.450337	−	0.892859i	$-0.351304\pi$
$13$	5.10256	−	2.27180i	1.41519	−	0.630085i	0.964858	+	0.262773i	$0.0846371\pi$
$14$	0.556197	−	0.617720i	0.148650	−	0.165093i
$15$	−0.809017	−	0.587785i	−0.208887	−	0.151765i
$16$	−0.809017	−	0.587785i	−0.202254	−	0.146946i
$17$	1.58470	−	1.75999i	0.384346	−	0.426859i	−0.519664	−	0.854371i	$-0.673943\pi$
$17$	1.58470	−	1.75999i	0.384346	−	0.426859i	0.904010	+	0.427511i	$0.140610\pi$
$18$	0.913545	−	0.406737i	0.215325	−	0.0958687i
$19$	1.60962	+	0.716647i	0.369271	+	0.164410i	0.582978	−	0.812488i	$-0.301887\pi$
$19$	1.60962	+	0.716647i	0.369271	+	0.164410i	−0.213707	+	0.976898i	$0.568554\pi$
$20$	0.669131	+	0.743145i	0.149622	+	0.166172i
$21$	−0.0868866	−	0.826670i	−0.0189602	−	0.180394i
$22$	−4.19887	−	0.892498i	−0.895203	−	0.190281i
$23$	0.945547	+	2.91009i	0.197160	+	0.606796i	0.999945	+	0.0105271i	$0.00335095\pi$
$23$	0.945547	+	2.91009i	0.197160	+	0.606796i	−0.802784	+	0.596269i	$0.796649\pi$
$24$	−0.978148	+	0.207912i	−0.199664	+	0.0424398i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$	−2.79272	+	4.83714i	−0.547698	+	0.948641i
$27$	0.309017	−	0.951057i	0.0594703	−	0.183031i
$28$	−0.0868866	+	0.826670i	−0.0164200	+	0.156226i
$29$	−4.43401	+	3.22150i	−0.823375	+	0.598217i	−0.917677	−	0.397327i	$-0.869938\pi$
$29$	−4.43401	+	3.22150i	−0.823375	+	0.598217i	0.0943021	+	0.995544i	$0.469938\pi$
$30$	1.00000			0.182574
$31$	−2.94938	+	4.72241i	−0.529725	+	0.848169i
$31$	−2.94938	+	4.72241i	−0.529725	+	0.848169i
$32$	1.00000			0.176777
$33$	−3.47285	+	2.52317i	−0.604546	+	0.439228i
$34$	−0.247554	+	2.35532i	−0.0424552	+	0.403934i
$35$	0.256862	−	0.790541i	0.0434177	−	0.133626i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−2.33468	−	4.04378i	−0.383818	−	0.664793i	0.607786	−	0.794101i	$-0.292058\pi$
$37$	−2.33468	−	4.04378i	−0.383818	−	0.664793i	−0.991604	+	0.129308i	$0.958724\pi$
$38$	−1.72344	+	0.366329i	−0.279579	+	0.0594264i
$39$	1.72600	+	5.31207i	0.276381	+	0.850612i
$40$	−0.978148	−	0.207912i	−0.154659	−	0.0328737i
$41$	0.770057	+	7.32660i	0.120263	+	1.14422i	0.873619	+	0.486611i	$0.161767\pi$
$41$	0.770057	+	7.32660i	0.120263	+	1.14422i	−0.753356	+	0.657613i	$0.771566\pi$
$42$	0.556197	+	0.617720i	0.0858231	+	0.0953162i
$43$	2.26879	+	1.01013i	0.345987	+	0.154044i	0.572371	−	0.819995i	$-0.306024\pi$
$43$	2.26879	+	1.01013i	0.345987	+	0.154044i	−0.226384	+	0.974038i	$0.572690\pi$
$44$	3.92156	−	1.74599i	0.591197	−	0.263218i
$45$	0.669131	−	0.743145i	0.0997481	−	0.110781i
$46$	−2.47547	−	1.79854i	−0.364989	−	0.265180i
$47$	2.33397	+	1.69573i	0.340444	+	0.247347i	0.744849	−	0.667233i	$-0.232521\pi$
$47$	2.33397	+	1.69573i	0.340444	+	0.247347i	−0.404405	+	0.914580i	$0.632521\pi$
$48$	0.669131	−	0.743145i	0.0965807	−	0.107264i
$49$	−5.76362	+	2.56613i	−0.823374	+	0.366590i
$50$	0.913545	+	0.406737i	0.129195	+	0.0575212i
$51$	1.58470	+	1.75999i	0.221902	+	0.246447i
$52$	−0.583838	−	5.55485i	−0.0809638	−	0.770319i
$53$	6.65906	+	1.41543i	0.914693	+	0.194424i	0.641132	−	0.767431i	$-0.278465\pi$
$53$	6.65906	+	1.41543i	0.914693	+	0.194424i	0.273561	+	0.961855i	$0.411799\pi$
$54$	0.309017	+	0.951057i	0.0420519	+	0.129422i
$55$	−4.19887	+	0.892498i	−0.566176	+	0.120344i
$56$	−0.415612	−	0.719861i	−0.0555385	−	0.0961955i
$57$	−0.880972	+	1.52589i	−0.116688	+	0.202109i
$58$	1.69364	−	5.21249i	0.222386	−	0.684434i
$59$	−0.391292	+	3.72289i	−0.0509418	+	0.484679i	0.939073	+	0.343717i	$0.111686\pi$
$59$	−0.391292	+	3.72289i	−0.0509418	+	0.484679i	−0.990015	+	0.140962i	$0.954980\pi$
$60$	−0.809017	+	0.587785i	−0.104444	+	0.0758827i
$61$	−1.28112			−0.164030			−0.0820150	−	0.996631i	$-0.526136\pi$
$61$	−1.28112			−0.164030			−0.0820150	+	0.996631i	$0.526136\pi$
$62$	−0.389660	−	5.55411i	−0.0494868	−	0.705373i
$63$	0.831224			0.104724
$64$	−0.809017	+	0.587785i	−0.101127	+	0.0734732i
$65$	−0.583838	+	5.55485i	−0.0724162	+	0.688994i
$66$	1.32651	−	4.08258i	0.163282	−	0.502531i
$67$	−3.45186	+	5.97879i	−0.421712	+	0.730426i	−0.996107	−	0.0881520i	$-0.971904\pi$
$67$	−3.45186	+	5.97879i	−0.421712	+	0.730426i	0.574395	+	0.818578i	$0.305237\pi$
$68$	−1.18415	−	2.05100i	−0.143599	−	0.248721i
$69$	−2.99299	+	0.636179i	−0.360313	+	0.0765870i
$70$	0.256862	+	0.790541i	0.0307009	+	0.0944877i
$71$	1.60889	+	0.341980i	0.190940	+	0.0405855i	0.302389	−	0.953185i	$-0.402216\pi$
$71$	1.60889	+	0.341980i	0.190940	+	0.0405855i	−0.111449	+	0.993770i	$0.535549\pi$
$72$	−0.104528	−	0.994522i	−0.0123188	−	0.117206i
$73$	−4.17731	−	4.63937i	−0.488917	−	0.542997i	0.447317	−	0.894376i	$-0.352380\pi$
$73$	−4.17731	−	4.63937i	−0.488917	−	0.542997i	−0.936233	+	0.351379i	$0.885713\pi$
$74$	4.26566	+	1.89920i	0.495873	+	0.220777i
$75$	0.913545	−	0.406737i	0.105487	−	0.0469659i
$76$	1.17897	−	1.30938i	0.135237	−	0.150196i
$77$	−2.88672	−	2.09732i	−0.328972	−	0.239012i
$78$	−4.51872	−	3.28304i	−0.511644	−	0.371731i
$79$	1.13450	−	1.25999i	0.127641	−	0.141760i	−0.675936	−	0.736960i	$-0.736261\pi$
$79$	1.13450	−	1.25999i	0.127641	−	0.141760i	0.803578	+	0.595200i	$0.202927\pi$
$80$	0.913545	−	0.406737i	0.102137	−	0.0454745i
$81$	0.913545	+	0.406737i	0.101505	+	0.0451930i
$82$	−4.92946	−	5.47472i	−0.544368	−	0.604582i
$83$	−0.538577	−	5.12422i	−0.0591165	−	0.562456i	−0.983489	−	0.180966i	$-0.942078\pi$
$83$	−0.538577	−	5.12422i	−0.0591165	−	0.562456i	0.924373	−	0.381490i	$-0.124589\pi$
$84$	−0.813060	−	0.172821i	−0.0887121	−	0.0188563i
$85$	0.731844	+	2.25238i	0.0793796	+	0.244305i
$86$	−2.42923	+	0.516349i	−0.261951	+	0.0556793i
$87$	−2.74037	−	4.74646i	−0.293798	−	0.508874i
$88$	−2.14634	+	3.71757i	−0.228801	+	0.396294i
$89$	−4.92988	+	15.1726i	−0.522566	+	1.60829i	0.246513	+	0.969140i	$0.420715\pi$
$89$	−4.92988	+	15.1726i	−0.522566	+	1.60829i	−0.769079	+	0.639154i	$0.779285\pi$
$90$	−0.104528	+	0.994522i	−0.0110183	+	0.104832i
$91$	−3.75607	+	2.72894i	−0.393743	+	0.286071i
$92$	3.05985			0.319012
$93$	−4.38824	−	3.42685i	−0.455040	−	0.355348i
$94$	−2.88494			−0.297559
$95$	−1.42544	+	1.03564i	−0.146247	+	0.106255i
$96$	−0.104528	+	0.994522i	−0.0106684	+	0.101503i
$97$	2.72642	−	8.39106i	0.276826	−	0.851984i	−0.711904	−	0.702277i	$-0.752167\pi$
$97$	2.72642	−	8.39106i	0.276826	−	0.851984i	0.988730	−	0.149707i	$-0.0478330\pi$
$98$	3.15453	−	5.46381i	0.318656	−	0.551928i
$99$	−2.14634	−	3.71757i	−0.215715	−	0.373630i
$100$	−0.978148	+	0.207912i	−0.0978148	+	0.0207912i
$101$	1.46401	+	4.50575i	0.145674	+	0.448338i	0.997097	−	0.0761411i	$-0.0242599\pi$
$101$	1.46401	+	4.50575i	0.145674	+	0.448338i	−0.851423	+	0.524480i	$0.824260\pi$
$102$	−2.31654	−	0.492396i	−0.229372	−	0.0487545i
$103$	1.31049	+	12.4685i	0.129126	+	1.22856i	0.846699	+	0.532072i	$0.178586\pi$
$103$	1.31049	+	12.4685i	0.129126	+	1.22856i	−0.717573	+	0.696483i	$0.754747\pi$
$104$	3.73739	+	4.15079i	0.366481	+	0.407019i
$105$	0.759361	+	0.338089i	0.0741060	+	0.0329941i
$106$	−6.21926	+	2.76899i	−0.604068	+	0.268948i
$107$	−0.391888	+	0.435236i	−0.0378852	+	0.0420758i	−0.761790	−	0.647825i	$-0.775679\pi$
$107$	−0.391888	+	0.435236i	−0.0378852	+	0.0420758i	0.723904	+	0.689900i	$0.242346\pi$
$108$	−0.809017	−	0.587785i	−0.0778477	−	0.0565597i
$109$	−5.09732	−	3.70342i	−0.488235	−	0.354723i	0.316270	−	0.948669i	$-0.397569\pi$
$109$	−5.09732	−	3.70342i	−0.488235	−	0.354723i	−0.804505	+	0.593946i	$0.797569\pi$
$110$	2.87236	−	3.19008i	0.273869	−	0.304162i
$111$	4.26566	−	1.89920i	0.404879	−	0.180264i
$112$	0.759361	+	0.338089i	0.0717528	+	0.0319464i
$113$	7.56353	+	8.40015i	0.711517	+	0.790220i	0.985165	−	0.171610i	$-0.0548970\pi$
$113$	7.56353	+	8.40015i	0.711517	+	0.790220i	−0.273648	+	0.961830i	$0.588230\pi$
$114$	−0.184173	−	1.75229i	−0.0172494	−	0.164117i
$115$	−2.99299	−	0.636179i	−0.279098	−	0.0593240i
$116$	1.69364	+	5.21249i	0.157251	+	0.483968i
$117$	−5.46339	+	1.16128i	−0.505090	+	0.107360i
$118$	−1.87170	−	3.24188i	−0.172304	−	0.298439i
$119$	−0.984292	+	1.70484i	−0.0902299	+	0.156283i
$120$	0.309017	−	0.951057i	0.0282093	−	0.0868192i
$121$	−0.776342	+	7.38640i	−0.0705766	+	0.671491i
$122$	1.03644	−	0.753021i	0.0938353	−	0.0681753i
$123$	−7.36696			−0.664257
$124$	3.57987	+	4.26434i	0.321482	+	0.382949i
$125$	1.00000			0.0894427
$126$	−0.672474	+	0.488581i	−0.0599088	+	0.0435263i
$127$	1.23749	−	11.7739i	0.109809	−	1.04477i	−0.791375	−	0.611331i	$-0.790634\pi$
$127$	1.23749	−	11.7739i	0.109809	−	1.04477i	0.901184	−	0.433436i	$-0.142699\pi$
$128$	0.309017	−	0.951057i	0.0273135	−	0.0840623i
$129$	−1.24175	+	2.15078i	−0.109330	+	0.189365i
$130$	−2.79272	−	4.83714i	−0.244938	−	0.424245i
$131$	−1.45183	+	0.308595i	−0.126847	+	0.0269621i	−0.270897	−	0.962608i	$-0.587320\pi$
$131$	−1.45183	+	0.308595i	−0.126847	+	0.0269621i	0.144051	+	0.989570i	$0.453987\pi$
$132$	1.32651	+	4.08258i	0.115458	+	0.355343i
$133$	−1.43257	−	0.304501i	−0.124219	−	0.0264036i
$134$	−0.721635	−	6.86590i	−0.0623398	−	0.593123i
$135$	0.669131	+	0.743145i	0.0575896	+	0.0639597i
$136$	2.16355	+	0.963273i	0.185522	+	0.0825999i
$137$	0.770129	−	0.342884i	0.0657966	−	0.0292945i	−0.373575	−	0.927600i	$-0.621868\pi$
$137$	0.770129	−	0.342884i	0.0657966	−	0.0292945i	0.439371	+	0.898306i	$0.355201\pi$
$138$	2.04744	−	2.27391i	0.174290	−	0.193568i
$139$	5.99119	+	4.35285i	0.508166	+	0.369204i	0.812127	−	0.583480i	$-0.198309\pi$
$139$	5.99119	+	4.35285i	0.508166	+	0.369204i	−0.303962	+	0.952684i	$0.598309\pi$
$140$	−0.672474	−	0.488581i	−0.0568344	−	0.0412926i
$141$	−1.93040	+	2.14393i	−0.162569	+	0.180551i
$142$	−1.50263	+	0.669014i	−0.126098	+	0.0561424i
$143$	21.9036	+	9.75213i	1.83167	+	0.815514i
$144$	0.669131	+	0.743145i	0.0557609	+	0.0619287i
$145$	−0.572893	−	5.45072i	−0.0475762	−	0.452657i
$146$	6.10646	+	1.29797i	0.505375	+	0.107421i
$147$	−1.94961	−	6.00028i	−0.160801	−	0.494895i
$148$	−4.56731	+	0.970813i	−0.375431	+	0.0798003i
$149$	−4.02478	−	6.97112i	−0.329723	−	0.571096i	0.652734	−	0.757587i	$-0.273622\pi$
$149$	−4.02478	−	6.97112i	−0.329723	−	0.571096i	−0.982457	+	0.186491i	$0.940289\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	3.02752	−	9.31776i	0.246376	−	0.758268i	−0.749031	−	0.662535i	$-0.769480\pi$
$151$	3.02752	−	9.31776i	0.246376	−	0.758268i	0.995407	−	0.0957331i	$-0.0305195\pi$
$152$	−0.184173	+	1.75229i	−0.0149384	+	0.142130i
$153$	−1.91599	+	1.39205i	−0.154899	+	0.112540i
$154$	3.56818			0.287532
$155$	−2.61503	−	4.91545i	−0.210044	−	0.394818i
$156$	5.58544			0.447193
$157$	11.3858	−	8.27230i	0.908689	−	0.660202i	−0.0319936	−	0.999488i	$-0.510186\pi$
$157$	11.3858	−	8.27230i	0.908689	−	0.660202i	0.940683	+	0.339287i	$0.110186\pi$
$158$	−0.177226	+	1.68620i	−0.0140994	+	0.134147i
$159$	−2.10374	+	6.47463i	−0.166837	+	0.513472i
$160$	−0.500000	+	0.866025i	−0.0395285	+	0.0684653i
$161$	−1.27171	−	2.20267i	−0.100225	−	0.173595i
$162$	−0.978148	+	0.207912i	−0.0768505	+	0.0163351i
$163$	1.18723	+	3.65390i	0.0929907	+	0.286196i	0.986725	−	0.162401i	$-0.0519239\pi$
$163$	1.18723	+	3.65390i	0.0929907	+	0.286196i	−0.893734	+	0.448597i	$0.851924\pi$
$164$	7.20598	+	1.53168i	0.562692	+	0.119604i
$165$	−0.448707	−	4.26916i	−0.0349318	−	0.332354i
$166$	3.44766	+	3.82901i	0.267590	+	0.297189i
$167$	−16.3943	−	7.29921i	−1.26863	−	0.564830i	−0.341608	−	0.939842i	$-0.610972\pi$
$167$	−16.3943	−	7.29921i	−1.26863	−	0.564830i	−0.927020	+	0.375013i	$0.877638\pi$
$168$	0.759361	−	0.338089i	0.0585860	−	0.0260841i
$169$	12.1763	−	13.5231i	0.936638	−	1.04024i
$170$	−1.91599	−	1.39205i	−0.146950	−	0.106765i
$171$	−1.42544	−	1.03564i	−0.109006	−	0.0791977i
$172$	1.66179	−	1.84560i	0.126710	−	0.140726i
$173$	−7.49912	+	3.33882i	−0.570147	+	0.253846i	−0.671500	−	0.741005i	$-0.734350\pi$
$173$	−7.49912	+	3.33882i	−0.570147	+	0.253846i	0.101353	+	0.994851i	$0.467683\pi$
$174$	5.00690	+	2.22922i	0.379572	+	0.168997i
$175$	0.556197	+	0.617720i	0.0420446	+	0.0466952i
$176$	−0.448707	−	4.26916i	−0.0338226	−	0.321800i
$177$	−3.66160	−	0.778296i	−0.275222	−	0.0585003i
$178$	−4.92988	−	15.1726i	−0.369510	−	1.13724i
$179$	22.3354	−	4.74753i	1.66942	−	0.354847i	0.726323	−	0.687354i	$-0.241228\pi$
$179$	22.3354	−	4.74753i	1.66942	−	0.354847i	0.943101	+	0.332507i	$0.107895\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−2.87165	+	4.97385i	−0.213448	+	0.369703i	−0.952791	−	0.303625i	$-0.901803\pi$
$181$	−2.87165	+	4.97385i	−0.213448	+	0.369703i	0.739343	+	0.673329i	$0.235136\pi$
$182$	1.43469	−	4.41552i	0.106346	−	0.327300i
$183$	0.133913	−	1.27410i	0.00989914	−	0.0941840i
$184$	−2.47547	+	1.79854i	−0.182494	+	0.132590i
$185$	4.66935			0.343298
$186$	5.56442	+	0.193038i	0.408003	+	0.0141542i
$187$	10.1663			0.743436
$188$	2.33397	−	1.69573i	0.170222	−	0.123673i
$189$	−0.0868866	+	0.826670i	−0.00632007	+	0.0601314i
$190$	0.544471	−	1.67571i	0.0395001	−	0.121569i
$191$	5.82151	−	10.0832i	0.421230	−	0.729591i	−0.574830	−	0.818273i	$-0.694932\pi$
$191$	5.82151	−	10.0832i	0.421230	−	0.729591i	0.996060	+	0.0886813i	$0.0282653\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	3.89409	−	0.827715i	0.280303	−	0.0595803i	−0.0656149	−	0.997845i	$-0.520901\pi$
$193$	3.89409	−	0.827715i	0.280303	−	0.0595803i	0.345918	+	0.938265i	$0.387568\pi$
$194$	2.72642	+	8.39106i	0.195746	+	0.602443i
$195$	−5.46339	−	1.16128i	−0.391241	−	0.0831609i
$196$	0.659477	+	6.27451i	0.0471055	+	0.448179i
$197$	−16.4406	−	18.2592i	−1.17135	−	1.30091i	−0.945077	−	0.326847i	$-0.894014\pi$
$197$	−16.4406	−	18.2592i	−1.17135	−	1.30091i	−0.226269	−	0.974065i	$-0.572653\pi$
$198$	3.92156	+	1.74599i	0.278693	+	0.124082i
$199$	17.1218	−	7.62312i	1.21373	−	0.540389i	0.302844	−	0.953040i	$-0.402064\pi$
$199$	17.1218	−	7.62312i	1.21373	−	0.540389i	0.910889	+	0.412651i	$0.135397\pi$
$200$	0.669131	−	0.743145i	0.0473147	−	0.0525483i
$201$	−5.58522	−	4.05790i	−0.393951	−	0.286222i
$202$	−3.83282	−	2.78470i	−0.269676	−	0.195931i
$203$	3.04837	−	3.38556i	0.213954	−	0.237620i
$204$	2.16355	−	0.963273i	0.151478	−	0.0674426i
$205$	−6.73005	−	2.99641i	−0.470047	−	0.209279i
$206$	−8.38899	−	9.31692i	−0.584489	−	0.649141i
$207$	−0.319842	−	3.04309i	−0.0222305	−	0.211509i
$208$	−5.46339	−	1.16128i	−0.378818	−	0.0805202i
$209$	2.33724	+	7.19328i	0.161670	+	0.497569i
$210$	−0.813060	+	0.172821i	−0.0561064	+	0.0119258i
$211$	7.61917	+	13.1968i	0.524525	+	0.908504i	0.999592	+	0.0285548i	$0.00909051\pi$
$211$	7.61917	+	13.1968i	0.524525	+	0.908504i	−0.475067	+	0.879950i	$0.657576\pi$
$212$	3.40392	−	5.89575i	0.233782	−	0.404922i
$213$	−0.508281	+	1.56433i	−0.0348269	+	0.107186i
$214$	0.0612189	−	0.582459i	0.00418484	−	0.0398161i
$215$	−2.00919	+	1.45977i	−0.137026	+	0.0995552i
$216$	1.00000			0.0680414
$217$	1.58189	−	4.34931i	0.107386	−	0.295251i
$218$	6.30064			0.426733
$219$	5.05060	−	3.66948i	0.341288	−	0.247960i
$220$	−0.448707	+	4.26916i	−0.0302518	+	0.287827i
$221$	4.08767	−	12.5806i	0.274967	−	0.846260i
$222$	−2.33468	+	4.04378i	−0.156693	+	0.271401i
$223$	14.1584	+	24.5231i	0.948118	+	1.64219i	0.749384	+	0.662136i	$0.230350\pi$
$223$	14.1584	+	24.5231i	0.948118	+	1.64219i	0.198735	+	0.980053i	$0.436317\pi$
$224$	−0.813060	+	0.172821i	−0.0543248	+	0.0115471i
$225$	0.309017	+	0.951057i	0.0206011	+	0.0634038i
$226$	−11.0565	−	2.35013i	−0.735468	−	0.156329i
$227$	0.926715	+	8.81710i	0.0615082	+	0.585212i	0.981257	+	0.192704i	$0.0617257\pi$
$227$	0.926715	+	8.81710i	0.0615082	+	0.585212i	−0.919749	+	0.392508i	$0.871608\pi$
$228$	1.17897	+	1.30938i	0.0780792	+	0.0867158i
$229$	−15.5322	−	6.91538i	−1.02640	−	0.456981i	−0.176706	−	0.984264i	$-0.556544\pi$
$229$	−15.5322	−	6.91538i	−1.02640	−	0.456981i	−0.849690	+	0.527282i	$0.823211\pi$
$230$	2.79532	−	1.24455i	0.184318	−	0.0820635i
$231$	2.38758	−	2.65167i	0.157091	−	0.174467i
$232$	−4.43401	−	3.22150i	−0.291107	−	0.211502i
$233$	17.3837	+	12.6300i	1.13884	+	0.827418i	0.986958	−	0.160981i	$-0.0514656\pi$
$233$	17.3837	+	12.6300i	1.13884	+	0.827418i	0.151885	+	0.988398i	$0.451466\pi$
$234$	3.73739	−	4.15079i	0.244321	−	0.271346i
$235$	−2.63552	+	1.17341i	−0.171923	+	0.0765449i
$236$	3.41976	+	1.52258i	0.222608	+	0.0991113i
$237$	1.13450	+	1.25999i	0.0736937	+	0.0818451i
$238$	−0.205773	−	1.95780i	−0.0133383	−	0.126905i
$239$	17.9205	+	3.80913i	1.15918	+	0.246392i	0.747073	−	0.664742i	$-0.231459\pi$
$239$	17.9205	+	3.80913i	1.15918	+	0.246392i	0.412110	+	0.911134i	$0.364792\pi$
$240$	0.309017	+	0.951057i	0.0199470	+	0.0613904i
$241$	5.03335	−	1.06987i	0.324226	−	0.0689164i	−0.0429232	−	0.999078i	$-0.513667\pi$
$241$	5.03335	−	1.06987i	0.324226	−	0.0689164i	0.367149	+	0.930162i	$0.380334\pi$
$242$	−3.71354	−	6.43205i	−0.238716	−	0.413468i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−0.395887	+	1.21841i	−0.0253440	+	0.0780009i
$245$	0.659477	−	6.27451i	0.0421324	−	0.400863i
$246$	5.96000	−	4.33019i	0.379996	−	0.276083i
$247$	9.84124			0.626183
$248$	−5.40269	−	1.34573i	−0.343071	−	0.0854537i
$249$	5.15245			0.326523
$250$	−0.809017	+	0.587785i	−0.0511667	+	0.0371748i
$251$	1.28178	−	12.1953i	0.0809052	−	0.769762i	−0.876575	−	0.481264i	$-0.840178\pi$
$251$	1.28178	−	12.1953i	0.0809052	−	0.769762i	0.957481	−	0.288497i	$-0.0931557\pi$
$252$	0.256862	−	0.790541i	0.0161808	−	0.0497994i
$253$	−6.56748	+	11.3752i	−0.412894	+	0.715154i
$254$	5.91939	+	10.2527i	0.371415	+	0.643310i
$255$	−2.31654	+	0.492396i	−0.145068	+	0.0308351i
$256$	0.309017	+	0.951057i	0.0193136	+	0.0594410i
$257$	−18.7125	−	3.97747i	−1.16725	−	0.248108i	−0.416780	−	0.909007i	$-0.636842\pi$
$257$	−18.7125	−	3.97747i	−1.16725	−	0.248108i	−0.750474	+	0.660900i	$0.770175\pi$
$258$	−0.259597	−	2.46990i	−0.0161618	−	0.153769i
$259$	2.59708	+	2.88435i	0.161375	+	0.179225i
$260$	5.10256	+	2.27180i	0.316447	+	0.140891i
$261$	5.00690	−	2.22922i	0.309920	−	0.137985i
$262$	0.993164	−	1.10302i	0.0613579	−	0.0681448i
$263$	3.35398	+	2.43681i	0.206815	+	0.150260i	0.686372	−	0.727251i	$-0.259202\pi$
$263$	3.35398	+	2.43681i	0.206815	+	0.150260i	−0.479556	+	0.877511i	$0.659202\pi$
$264$	−3.47285	−	2.52317i	−0.213739	−	0.155291i
$265$	−4.55533	+	5.05920i	−0.279832	+	0.310784i
$266$	1.33795	−	0.595694i	0.0820351	−	0.0365244i
$267$	−14.5742	−	6.48884i	−0.891925	−	0.397111i
$268$	4.61949	+	5.13046i	0.282180	+	0.313393i
$269$	−2.77875	−	26.4380i	−0.169423	−	1.61195i	−0.667356	−	0.744739i	$-0.732574\pi$
$269$	−2.77875	−	26.4380i	−0.169423	−	1.61195i	0.497933	−	0.867216i	$-0.334093\pi$
$270$	−0.978148	−	0.207912i	−0.0595282	−	0.0126531i
$271$	−1.98149	−	6.09839i	−0.120367	−	0.370451i	0.872662	−	0.488325i	$-0.162392\pi$
$271$	−1.98149	−	6.09839i	−0.120367	−	0.370451i	−0.993029	+	0.117874i	$0.962392\pi$
$272$	−2.31654	+	0.492396i	−0.140461	+	0.0298559i
$273$	−2.32138	−	4.02074i	−0.140496	−	0.243346i
$274$	−0.421506	+	0.730069i	−0.0254641	+	0.0441051i
$275$	1.32651	−	4.08258i	0.0799916	−	0.246189i
$276$	−0.319842	+	3.04309i	−0.0192522	+	0.183173i
$277$	17.2759	−	12.5516i	1.03801	−	0.754155i	0.0681105	−	0.997678i	$-0.478303\pi$
$277$	17.2759	−	12.5516i	1.03801	−	0.754155i	0.969895	+	0.243522i	$0.0783029\pi$
$278$	−7.40551			−0.444153
$279$	3.86678	−	4.00600i	0.231498	−	0.239833i
$280$	0.831224			0.0496751
$281$	4.97233	−	3.61261i	0.296624	−	0.215510i	−0.429512	−	0.903061i	$-0.641314\pi$
$281$	4.97233	−	3.61261i	0.296624	−	0.215510i	0.726136	+	0.687551i	$0.241314\pi$
$282$	0.301558	−	2.86914i	0.0179575	−	0.170855i
$283$	4.53520	−	13.9579i	0.269590	−	0.829711i	−0.721011	−	0.692924i	$-0.756322\pi$
$283$	4.53520	−	13.9579i	0.269590	−	0.829711i	0.990600	−	0.136788i	$-0.0436778\pi$
$284$	0.822416	−	1.42447i	0.0488014	−	0.0845265i
$285$	−0.880972	−	1.52589i	−0.0521843	−	0.0903858i
$286$	−23.4526	+	4.98500i	−1.38678	+	0.294769i
$287$	−1.89229	−	5.82388i	−0.111699	−	0.343773i
$288$	−0.978148	−	0.207912i	−0.0576379	−	0.0122513i
$289$	1.19070	+	11.3288i	0.0700413	+	0.666399i
$290$	3.66733	+	4.07298i	0.215353	+	0.239174i
$291$	8.06011	+	3.58859i	0.472492	+	0.210367i
$292$	−5.70316	+	2.53921i	−0.333752	+	0.148596i
$293$	6.04344	−	6.71192i	0.353062	−	0.392115i	−0.540286	−	0.841482i	$-0.681684\pi$
$293$	6.04344	−	6.71192i	0.353062	−	0.392115i	0.893347	+	0.449367i	$0.148350\pi$
$294$	5.10414	+	3.70838i	0.297680	+	0.216277i
$295$	−3.02847	−	2.20031i	−0.176325	−	0.128107i
$296$	3.12441	−	3.47000i	0.181602	−	0.201690i
$297$	3.92156	−	1.74599i	0.227552	−	0.101313i
$298$	7.35363	+	3.27405i	0.425984	+	0.189660i
$299$	11.4359	+	12.7008i	0.661353	+	0.734507i
$300$	−0.104528	−	0.994522i	−0.00603495	−	0.0574187i
$301$	−2.01923	−	0.429202i	−0.116387	−	0.0247388i
$302$	3.02752	+	9.31776i	0.174214	+	0.536177i
$303$	−4.63409	+	0.985007i	−0.266222	+	0.0565872i
$304$	−0.880972	−	1.52589i	−0.0505272	−	0.0875157i
$305$	0.640558	−	1.10948i	0.0366782	−	0.0635286i
$306$	0.731844	−	2.25238i	0.0418367	−	0.128760i
$307$	3.05891	−	29.1036i	0.174581	−	1.66103i	−0.459811	−	0.888017i	$-0.652083\pi$
$307$	3.05891	−	29.1036i	0.174581	−	1.66103i	0.634392	−	0.773012i	$-0.281251\pi$
$308$	−2.88672	+	2.09732i	−0.164486	+	0.119506i
$309$	−12.5372			−0.713214
$310$	5.00483	+	2.43960i	0.284255	+	0.138560i
$311$	14.4736			0.820724			0.410362	−	0.911923i	$-0.365402\pi$
$311$	14.4736			0.820724			0.410362	+	0.911923i	$0.365402\pi$
$312$	−4.51872	+	3.28304i	−0.255822	+	0.185866i
$313$	1.66758	−	15.8660i	0.0942572	−	0.896798i	−0.840572	−	0.541700i	$-0.817781\pi$
$313$	1.66758	−	15.8660i	0.0942572	−	0.896798i	0.934829	−	0.355098i	$-0.115552\pi$
$314$	−4.34901	+	13.3849i	−0.245429	+	0.755352i
$315$	−0.415612	+	0.719861i	−0.0234171	+	0.0405596i
$316$	−0.847742	−	1.46833i	−0.0476892	−	0.0826001i
$317$	−19.8029	+	4.20923i	−1.11224	+	0.236414i	−0.727160	−	0.686468i	$-0.759160\pi$
$317$	−19.8029	+	4.20923i	−1.11224	+	0.236414i	−0.385081	+	0.922883i	$0.625827\pi$
$318$	−2.10374	−	6.47463i	−0.117972	−	0.363079i
$319$	−23.0129	−	4.89155i	−1.28848	−	0.273874i
$320$	−0.104528	−	0.994522i	−0.00584332	−	0.0555955i
$321$	−0.391888	−	0.435236i	−0.0218730	−	0.0242925i
$322$	2.32353	+	1.03450i	0.129485	+	0.0576506i
$323$	3.81205	−	1.69723i	0.212108	−	0.0944365i
$324$	0.669131	−	0.743145i	0.0371739	−	0.0412858i
$325$	−4.51872	−	3.28304i	−0.250653	−	0.182110i
$326$	−3.10820	−	2.25824i	−0.172147	−	0.125072i
$327$	4.21595	−	4.68229i	0.233143	−	0.258931i
$328$	−6.73005	+	2.99641i	−0.371605	+	0.165449i
$329$	−2.19071	−	0.975367i	−0.120778	−	0.0537737i
$330$	2.87236	+	3.19008i	0.158118	+	0.175608i
$331$	3.00698	+	28.6095i	0.165279	+	1.57252i	0.691629	+	0.722253i	$0.256893\pi$
$331$	3.00698	+	28.6095i	0.165279	+	1.57252i	−0.526350	+	0.850268i	$0.676440\pi$
$332$	−5.03985	−	1.07125i	−0.276598	−	0.0587927i
$333$	1.44291	+	4.44082i	0.0790709	+	0.243355i
$334$	17.5536	−	3.73114i	0.960492	−	0.204159i
$335$	−3.45186	−	5.97879i	−0.188595	−	0.326656i
$336$	−0.415612	+	0.719861i	−0.0226735	+	0.0392716i
$337$	9.39607	−	28.9181i	0.511837	−	1.57527i	−0.277128	−	0.960833i	$-0.589383\pi$
$337$	9.39607	−	28.9181i	0.511837	−	1.57527i	0.788965	−	0.614438i	$-0.210617\pi$
$338$	−1.90212	+	18.0975i	−0.103462	+	0.984374i
$339$	−9.14474	+	6.64404i	−0.496674	+	0.360855i
$340$	2.36830			0.128439
$341$	−23.5366	+	4.15569i	−1.27458	+	0.225043i
$342$	1.76194			0.0952750
$343$	8.95000	−	6.50256i	0.483255	−	0.351105i
$344$	−0.259597	+	2.46990i	−0.0139965	+	0.133168i
$345$	0.945547	−	2.91009i	0.0509065	−	0.156674i
$346$	4.10440	−	7.10903i	0.220654	−	0.382184i
$347$	15.2503	+	26.4143i	0.818679	+	1.41799i	0.906656	+	0.421871i	$0.138627\pi$
$347$	15.2503	+	26.4143i	0.818679	+	1.41799i	−0.0879769	+	0.996123i	$0.528040\pi$
$348$	−5.36097	+	1.13951i	−0.287378	+	0.0610841i
$349$	6.05475	+	18.6346i	0.324104	+	0.997488i	0.971844	+	0.235627i	$0.0757143\pi$
$349$	6.05475	+	18.6346i	0.324104	+	0.997488i	−0.647740	+	0.761861i	$0.724286\pi$
$350$	−0.813060	−	0.172821i	−0.0434599	−	0.00923768i
$351$	−0.583838	−	5.55485i	−0.0311630	−	0.296496i
$352$	2.87236	+	3.19008i	0.153097	+	0.170032i
$353$	−32.7697	−	14.5900i	−1.74415	−	0.776547i	−0.993231	−	0.116156i	$-0.962943\pi$
$353$	−32.7697	−	14.5900i	−1.74415	−	0.776547i	−0.750922	−	0.660391i	$-0.770391\pi$
$354$	3.41976	−	1.52258i	0.181758	−	0.0809241i
$355$	−1.10061	+	1.22235i	−0.0584142	+	0.0648755i
$356$	12.9066	+	9.37719i	0.684048	+	0.496990i
$357$	−1.59262	−	1.15710i	−0.0842903	−	0.0612405i
$358$	−15.2792	+	16.9692i	−0.807529	+	0.896851i
$359$	−25.3518	+	11.2873i	−1.33802	+	0.595723i	−0.945979	−	0.324226i	$-0.894896\pi$
$359$	−25.3518	+	11.2873i	−1.33802	+	0.595723i	−0.392037	+	0.919950i	$0.628229\pi$
$360$	0.913545	+	0.406737i	0.0481481	+	0.0214369i
$361$	−10.6362	−	11.8127i	−0.559800	−	0.621721i
$362$	−0.600339	−	5.71185i	−0.0315531	−	0.300208i
$363$	−7.26479	−	1.54418i	−0.381303	−	0.0810484i
$364$	1.43469	+	4.41552i	0.0751982	+	0.231436i
$365$	6.10646	−	1.29797i	0.319627	−	0.0679388i
$366$	0.640558	+	1.10948i	0.0334825	+	0.0579934i
$367$	−5.15105	+	8.92188i	−0.268883	+	0.465718i	−0.968574	−	0.248727i	$-0.919988\pi$
$367$	−5.15105	+	8.92188i	−0.268883	+	0.465718i	0.699691	+	0.714446i	$0.253321\pi$
$368$	0.945547	−	2.91009i	0.0492900	−	0.151699i
$369$	0.770057	−	7.32660i	0.0400876	−	0.381408i
$370$	−3.77758	+	2.74458i	−0.196387	+	0.142684i
$371$	−5.65883			−0.293792
$372$	−4.61517	+	3.11451i	−0.239286	+	0.161480i
$373$	−8.42213			−0.436081			−0.218041	−	0.975940i	$-0.569967\pi$
$373$	−8.42213			−0.436081			−0.218041	+	0.975940i	$0.569967\pi$
$374$	−8.22473	+	5.97562i	−0.425291	+	0.308992i
$375$	−0.104528	+	0.994522i	−0.00539783	+	0.0513569i
$376$	−0.891495	+	2.74374i	−0.0459754	+	0.141498i
$377$	−15.3062	+	26.5111i	−0.788309	+	1.36539i
$378$	−0.415612	−	0.719861i	−0.0213768	−	0.0370257i
$379$	−11.3373	+	2.40983i	−0.582360	+	0.123785i	−0.489666	−	0.871910i	$-0.662881\pi$
$379$	−11.3373	+	2.40983i	−0.582360	+	0.123785i	−0.0926944	+	0.995695i	$0.529548\pi$
$380$	0.544471	+	1.67571i	0.0279308	+	0.0859620i
$381$	11.5801	+	2.46142i	0.593265	+	0.126102i
$382$	1.21703	+	11.5792i	0.0622685	+	0.592446i
$383$	1.45030	+	1.61072i	0.0741068	+	0.0823040i	0.779058	−	0.626952i	$-0.215698\pi$
$383$	1.45030	+	1.61072i	0.0741068	+	0.0823040i	−0.704951	+	0.709256i	$0.749031\pi$
$384$	0.913545	+	0.406737i	0.0466192	+	0.0207562i
$385$	3.25969	−	1.45131i	0.166129	−	0.0739655i
$386$	−2.66387	+	2.95853i	−0.135587	+	0.150585i
$387$	−2.00919	−	1.45977i	−0.102133	−	0.0742040i
$388$	−7.13787	−	5.18596i	−0.362370	−	0.263277i
$389$	−15.3176	+	17.0119i	−0.776631	+	0.862537i	−0.993520	−	0.113660i	$-0.963743\pi$
$389$	−15.3176	+	17.0119i	−0.776631	+	0.862537i	0.216888	+	0.976196i	$0.430409\pi$
$390$	5.10256	−	2.27180i	0.258378	−	0.115037i
$391$	6.62013	+	2.94747i	0.334794	+	0.149060i
$392$	−4.22159	−	4.68855i	−0.213222	−	0.236808i
$393$	−0.155147	−	1.47613i	−0.00782615	−	0.0744609i
$394$	24.0332	+	5.10842i	1.21078	+	0.257358i
$395$	0.523933	+	1.61250i	0.0263619	+	0.0811337i
$396$	−4.19887	+	0.892498i	−0.211001	+	0.0448497i
$397$	12.5490	+	21.7356i	0.629818	+	1.09088i	0.987588	+	0.157068i	$0.0502041\pi$
$397$	12.5490	+	21.7356i	0.629818	+	1.09088i	−0.357769	+	0.933810i	$0.616463\pi$
$398$	−9.37108	+	16.2312i	−0.469730	+	0.813596i
$399$	0.452577	−	1.39289i	0.0226572	−	0.0697317i
$400$	−0.104528	+	0.994522i	−0.00522642	+	0.0497261i
$401$	1.50767	−	1.09539i	0.0752894	−	0.0547009i	−0.549504	−	0.835491i	$-0.685183\pi$
$401$	1.50767	−	1.09539i	0.0752894	−	0.0547009i	0.624793	+	0.780790i	$0.285183\pi$
$402$	6.90372			0.344326
$403$	−4.32101	+	30.7968i	−0.215245	+	1.53410i
$404$	4.73762			0.235705
$405$	−0.809017	+	0.587785i	−0.0402004	+	0.0292073i
$406$	−0.476203	+	4.53076i	−0.0236335	+	0.224858i
$407$	6.19394	−	19.0630i	0.307022	−	0.944918i
$408$	−1.18415	+	2.05100i	−0.0586240	+	0.101540i
$409$	6.80193	+	11.7813i	0.336334	+	0.582547i	0.983740	−	0.179598i	$-0.0574797\pi$
$409$	6.80193	+	11.7813i	0.336334	+	0.582547i	−0.647406	+	0.762145i	$0.724146\pi$
$410$	7.20598	−	1.53168i	0.355878	−	0.0756442i
$411$	0.260505	+	0.801752i	0.0128498	+	0.0395475i
$412$	12.2632	+	2.60662i	0.604164	+	0.128419i
$413$	−0.325251	−	3.09456i	−0.0160046	−	0.152273i
$414$	2.04744	+	2.27391i	0.100626	+	0.111757i
$415$	4.70699	+	2.09569i	0.231057	+	0.102873i
$416$	5.10256	−	2.27180i	0.250173	−	0.111384i
$417$	−4.95526	+	5.50337i	−0.242660	+	0.269501i
$418$	−6.11897	−	4.44569i	−0.299288	−	0.217446i
$419$	−18.7084	−	13.5925i	−0.913967	−	0.664036i	0.0280477	−	0.999607i	$-0.491071\pi$
$419$	−18.7084	−	13.5925i	−0.913967	−	0.664036i	−0.942015	+	0.335570i	$0.891071\pi$
$420$	0.556197	−	0.617720i	0.0271397	−	0.0301416i
$421$	16.4159	−	7.30882i	0.800060	−	0.356210i	0.0343619	−	0.999409i	$-0.489060\pi$
$421$	16.4159	−	7.30882i	0.800060	−	0.356210i	0.765699	+	0.643200i	$0.222393\pi$
$422$	−13.9209	−	6.19799i	−0.677660	−	0.301713i
$423$	−1.93040	−	2.14393i	−0.0938593	−	0.104241i
$424$	0.711612	+	6.77054i	0.0345589	+	0.328806i
$425$	−2.31654	−	0.492396i	−0.112369	−	0.0238847i
$426$	−0.508281	−	1.56433i	−0.0246263	−	0.0757920i
$427$	1.04162	−	0.221404i	0.0504077	−	0.0107145i
$428$	0.292834	+	0.507203i	0.0141546	+	0.0245166i
$429$	−11.9883	+	20.7643i	−0.578799	+	1.00251i
$430$	0.767444	−	2.36195i	0.0370094	−	0.113903i
$431$	2.57861	−	24.5338i	0.124207	−	1.18175i	−0.737859	−	0.674955i	$-0.764163\pi$
$431$	2.57861	−	24.5338i	0.124207	−	1.18175i	0.862066	−	0.506796i	$-0.169170\pi$
$432$	−0.809017	+	0.587785i	−0.0389238	+	0.0282798i
$433$	−13.9718			−0.671443			−0.335722	−	0.941961i	$-0.608980\pi$
$433$	−13.9718			−0.671443			−0.335722	+	0.941961i	$0.608980\pi$
$434$	1.27668	+	4.44848i	0.0612828	+	0.213534i
$435$	5.48074			0.262781
$436$	−5.09732	+	3.70342i	−0.244117	+	0.177362i
$437$	−0.563543	+	5.36176i	−0.0269579	+	0.256488i
$438$	−1.92916	+	5.93734i	−0.0921787	+	0.283697i
$439$	10.8631	−	18.8155i	0.518469	−	0.898015i	−0.481300	−	0.876556i	$-0.659835\pi$
$439$	10.8631	−	18.8155i	0.518469	−	0.898015i	0.999770	−	0.0214596i	$-0.00683132\pi$
$440$	−2.14634	−	3.71757i	−0.102323	−	0.177228i
$441$	6.17120	−	1.31173i	0.293867	−	0.0624633i
$442$	4.08767	+	12.5806i	0.194431	+	0.598396i
$443$	4.86384	+	1.03384i	0.231088	+	0.0491193i	0.322000	−	0.946740i	$-0.395645\pi$
$443$	4.86384	+	1.03384i	0.231088	+	0.0491193i	−0.0909120	+	0.995859i	$0.528978\pi$
$444$	−0.488080	−	4.64377i	−0.0231633	−	0.220384i
$445$	−10.6749	−	11.8557i	−0.506040	−	0.562014i
$446$	−25.8687	−	11.5175i	−1.22492	−	0.545370i
$447$	7.35363	−	3.27405i	0.347815	−	0.154857i
$448$	0.556197	−	0.617720i	0.0262779	−	0.0291845i
$449$	−19.8732	−	14.4387i	−0.937873	−	0.681404i	0.0100350	−	0.999950i	$-0.496806\pi$
$449$	−19.8732	−	14.4387i	−0.937873	−	0.681404i	−0.947908	+	0.318545i	$0.896806\pi$
$450$	−0.809017	−	0.587785i	−0.0381374	−	0.0277085i
$451$	−21.1606	+	23.5012i	−0.996413	+	1.10663i
$452$	10.3263	−	4.59755i	0.485707	−	0.216251i
$453$	8.95025	+	3.98491i	0.420520	+	0.187227i
$454$	−5.93229	−	6.58848i	−0.278416	−	0.309212i
$455$	−0.485300	−	4.61732i	−0.0227512	−	0.216463i
$456$	−1.72344	−	0.366329i	−0.0807075	−	0.0171549i
$457$	11.7049	+	36.0238i	0.547530	+	1.68512i	0.714897	+	0.699230i	$0.246474\pi$
$457$	11.7049	+	36.0238i	0.547530	+	1.68512i	−0.167367	+	0.985895i	$0.553526\pi$
$458$	16.6306	−	3.53494i	0.777095	−	0.165177i
$459$	−1.18415	−	2.05100i	−0.0552713	−	0.0957327i
$460$	−1.52993	+	2.64991i	−0.0713332	+	0.123553i
$461$	2.71274	−	8.34894i	0.126345	−	0.388849i	−0.867799	−	0.496915i	$-0.834466\pi$
$461$	2.71274	−	8.34894i	0.126345	−	0.388849i	0.994144	+	0.108066i	$0.0344659\pi$
$462$	−0.372976	+	3.54863i	−0.0173524	+	0.165097i
$463$	26.3887	−	19.1725i	1.22639	−	0.891023i	0.229774	−	0.973244i	$-0.426201\pi$
$463$	26.3887	−	19.1725i	1.22639	−	0.891023i	0.996614	+	0.0822210i	$0.0262013\pi$
$464$	5.48074			0.254437
$465$	5.16186	−	2.08690i	0.239376	−	0.0967778i
$466$	−21.4874			−0.995385
$467$	−4.73168	+	3.43777i	−0.218956	+	0.159081i	−0.691857	−	0.722035i	$-0.743207\pi$
$467$	−4.73168	+	3.43777i	−0.218956	+	0.159081i	0.472901	+	0.881116i	$0.343207\pi$
$468$	−0.583838	+	5.55485i	−0.0269879	+	0.256773i
$469$	1.77330	−	5.45767i	0.0818836	−	0.252012i
$470$	1.44247	−	2.49843i	0.0665362	−	0.115244i
$471$	7.03684	+	12.1882i	0.324240	+	0.561601i
$472$	−3.66160	+	0.778296i	−0.168539	+	0.0358240i
$473$	3.29439	+	10.1391i	0.151476	+	0.466196i
$474$	−1.65843	−	0.352511i	−0.0761744	−	0.0161914i
$475$	−0.184173	−	1.75229i	−0.00845045	−	0.0804007i
$476$	1.31724	+	1.46294i	0.0603756	+	0.0670539i
$477$	−6.21926	−	2.76899i	−0.284760	−	0.126784i
$478$	−16.7370	+	7.45177i	−0.765531	+	0.340836i
$479$	9.08005	−	10.0844i	0.414878	−	0.460769i	−0.499093	−	0.866549i	$-0.666333\pi$
$479$	9.08005	−	10.0844i	0.414878	−	0.460769i	0.913971	+	0.405780i	$0.133000\pi$
$480$	−0.809017	−	0.587785i	−0.0369264	−	0.0268286i
$481$	−21.0995	−	15.3297i	−0.962054	−	0.698973i
$482$	−3.44321	+	3.82407i	−0.156834	+	0.174182i
$483$	2.32353	−	1.03450i	0.105724	−	0.0470715i
$484$	6.78498	+	3.02087i	0.308408	+	0.137312i
$485$	5.90366	+	6.55668i	0.268072	+	0.297724i
$486$	−0.104528	−	0.994522i	−0.00474151	−	0.0451124i
$487$	−12.0130	−	2.55343i	−0.544359	−	0.115707i	−0.0724792	−	0.997370i	$-0.523091\pi$
$487$	−12.0130	−	2.55343i	−0.544359	−	0.115707i	−0.471880	+	0.881663i	$0.656424\pi$
$488$	−0.395887	−	1.21841i	−0.0179209	−	0.0551550i
$489$	−3.75799	+	0.798785i	−0.169942	+	0.0361223i
$490$	3.15453	+	5.46381i	0.142507	+	0.246830i
$491$	−17.8360	+	30.8929i	−0.804927	+	1.39418i	0.111413	+	0.993774i	$0.464462\pi$
$491$	−17.8360	+	30.8929i	−0.804927	+	1.39418i	−0.916340	+	0.400401i	$0.868871\pi$
$492$	−2.27652	+	7.00640i	−0.102633	+	0.315873i
$493$	−1.35678	+	12.9089i	−0.0611063	+	0.581388i
$494$	−7.96173	+	5.78454i	−0.358215	+	0.260259i
$495$	4.29268			0.192942
$496$	5.16186	−	2.08690i	0.231775	−	0.0937047i
$497$	−1.36722			−0.0613284
$498$	−4.16842	+	3.02853i	−0.186791	+	0.135712i
$499$	−3.62132	+	34.4546i	−0.162113	+	1.54240i	0.546897	+	0.837200i	$0.315809\pi$
$499$	−3.62132	+	34.4546i	−0.162113	+	1.54240i	−0.709009	+	0.705199i	$0.750858\pi$
$500$	0.309017	−	0.951057i	0.0138197	−	0.0425325i
$501$	8.97289	−	15.5415i	0.400879	−	0.694343i
$502$	6.13125	+	10.6196i	0.273651	+	0.473977i
$503$	−25.4741	+	5.41469i	−1.13583	+	0.241429i	−0.737196	−	0.675679i	$-0.763850\pi$
$503$	−25.4741	+	5.41469i	−1.13583	+	0.241429i	−0.398638	+	0.917108i	$0.630517\pi$
$504$	0.256862	+	0.790541i	0.0114416	+	0.0352135i
$505$	−4.63409	−	0.985007i	−0.206214	−	0.0438322i
$506$	−1.37298	−	13.0630i	−0.0610363	−	0.580722i
$507$	12.1763	+	13.5231i	0.540768	+	0.600584i
$508$	−10.8153	−	4.81526i	−0.479850	−	0.213643i
$509$	8.91863	−	3.97083i	0.395311	−	0.176004i	−0.199447	−	0.979909i	$-0.563914\pi$
$509$	8.91863	−	3.97083i	0.395311	−	0.176004i	0.594758	+	0.803905i	$0.297248\pi$
$510$	1.58470	−	1.75999i	0.0701716	−	0.0779335i
$511$	4.19818	+	3.05016i	0.185717	+	0.134931i
$512$	−0.809017	−	0.587785i	−0.0357538	−	0.0259767i
$513$	1.17897	−	1.30938i	0.0520528	−	0.0578105i
$514$	17.4766	−	7.78110i	0.770861	−	0.343210i
$515$	−11.4533	−	5.09932i	−0.504691	−	0.224703i
$516$	1.66179	+	1.84560i	0.0731561	+	0.0812481i
$517$	1.29449	+	12.3163i	0.0569317	+	0.541669i
$518$	−3.79646	−	0.806963i	−0.166807	−	0.0354559i
$519$	−2.53666	−	7.80704i	−0.111347	−	0.342691i
$520$	−5.46339	+	1.16128i	−0.239585	+	0.0509255i
$521$	3.77608	+	6.54036i	0.165433	+	0.286538i	0.936809	−	0.349841i	$-0.113765\pi$
$521$	3.77608	+	6.54036i	0.165433	+	0.286538i	−0.771376	+	0.636380i	$0.780431\pi$
$522$	−2.74037	+	4.74646i	−0.119943	+	0.207747i
$523$	8.45802	−	26.0311i	0.369844	−	1.13826i	−0.577049	−	0.816710i	$-0.695796\pi$
$523$	8.45802	−	26.0311i	0.369844	−	1.13826i	0.946892	−	0.321551i	$-0.104204\pi$
$524$	−0.155147	+	1.47613i	−0.00677765	+	0.0644850i
$525$	−0.672474	+	0.488581i	−0.0293492	+	0.0213234i
$526$	−4.14575			−0.180763
$527$	3.63749	+	12.6745i	0.158451	+	0.552109i
$528$	4.29268			0.186815
$529$	11.0328	−	8.01580i	0.479687	−	0.348513i
$530$	0.711612	−	6.77054i	0.0309105	−	0.294093i
$531$	1.15677	−	3.56018i	0.0501997	−	0.154499i
$532$	−0.732285	+	1.26835i	−0.0317486	+	0.0549902i
$533$	20.5739	+	35.6350i	0.891153	+	1.54352i
$534$	15.6048	−	3.31690i	0.675286	−	0.143536i
$535$	−0.180981	−	0.557003i	−0.00782450	−	0.0240813i
$536$	−6.75285	−	1.43536i	−0.291679	−	0.0619983i
$537$	2.38684	+	22.7093i	0.103000	+	0.979977i
$538$	17.7879	+	19.7555i	0.766892	+	0.851720i
$539$	−24.7414	−	11.0156i	−1.06569	−	0.474474i
$540$	0.913545	−	0.406737i	0.0393127	−	0.0175032i
$541$	5.74681	−	6.38248i	0.247075	−	0.274404i	−0.606832	−	0.794830i	$-0.707560\pi$
$541$	5.74681	−	6.38248i	0.247075	−	0.274404i	0.853907	+	0.520426i	$0.174227\pi$
$542$	5.18760	+	3.76901i	0.222827	+	0.161893i
$543$	−4.64643	−	3.37583i	−0.199398	−	0.144871i
$544$	1.58470	−	1.75999i	0.0679434	−	0.0754588i
$545$	5.75592	−	2.56270i	0.246556	−	0.109774i
$546$	4.24137	+	1.88838i	0.181514	+	0.0808151i
$547$	−4.40090	−	4.88769i	−0.188169	−	0.208983i	0.641678	−	0.766974i	$-0.278239\pi$
$547$	−4.40090	−	4.88769i	−0.188169	−	0.208983i	−0.829846	+	0.557992i	$0.811572\pi$
$548$	−0.0881187	−	0.838393i	−0.00376424	−	0.0358144i
$549$	1.25312	+	0.266359i	0.0534819	+	0.0113679i
$550$	1.32651	+	4.08258i	0.0565626	+	0.174082i
$551$	−9.44573	+	2.00775i	−0.402402	+	0.0855331i
$552$	−1.52993	−	2.64991i	−0.0651180	−	0.112788i
$553$	−0.704663	+	1.22051i	−0.0299653	+	0.0519015i
$554$	−6.59879	+	20.3090i	−0.280356	+	0.862846i
$555$	−0.488080	+	4.64377i	−0.0207178	+	0.197117i
$556$	5.99119	−	4.35285i	0.254083	−	0.184602i
$557$	−18.4543			−0.781932			−0.390966	−	0.920405i	$-0.627859\pi$
$557$	−18.4543			−0.781932			−0.390966	+	0.920405i	$0.627859\pi$
$558$	−0.773620	+	5.51376i	−0.0327500	+	0.233416i
$559$	13.8715			0.586700
$560$	−0.672474	+	0.488581i	−0.0284172	+	0.0206463i
$561$	−1.06267	+	10.1106i	−0.0448660	+	0.426872i
$562$	−1.89926	+	5.84532i	−0.0801155	+	0.246570i
$563$	3.97543	−	6.88564i	0.167544	−	0.290195i	−0.770012	−	0.638030i	$-0.779750\pi$
$563$	3.97543	−	6.88564i	0.167544	−	0.290195i	0.937556	+	0.347835i	$0.113083\pi$
$564$	1.44247	+	2.49843i	0.0607389	+	0.105203i
$565$	−11.0565	+	2.35013i	−0.465151	+	0.0988708i
$566$	4.53520	+	13.9579i	0.190629	+	0.586695i
$567$	−0.813060	−	0.172821i	−0.0341453	−	0.00725781i
$568$	0.171932	+	1.63582i	0.00721410	+	0.0686376i
$569$	−27.6839	−	30.7461i	−1.16057	−	1.28895i	−0.950312	−	0.311300i	$-0.899236\pi$
$569$	−27.6839	−	30.7461i	−1.16057	−	1.28895i	−0.210260	−	0.977646i	$-0.567431\pi$
$570$	1.60962	+	0.716647i	0.0674194	+	0.0300170i
$571$	−30.7318	+	13.6827i	−1.28608	+	0.572601i	−0.931948	−	0.362592i	$-0.881892\pi$
$571$	−30.7318	+	13.6827i	−1.28608	+	0.572601i	−0.354136	+	0.935194i	$0.615225\pi$
$572$	16.0434	−	17.8180i	0.670809	−	0.745009i
$573$	9.41940	+	6.84360i	0.393501	+	0.285895i
$574$	4.95409	+	3.59936i	0.206780	+	0.150234i
$575$	2.04744	−	2.27391i	0.0853842	−	0.0948288i
$576$	0.913545	−	0.406737i	0.0380644	−	0.0169474i
$577$	−36.6334	−	16.3103i	−1.52507	−	0.679005i	−0.538542	−	0.842599i	$-0.681025\pi$
$577$	−36.6334	−	16.3103i	−1.52507	−	0.679005i	−0.986528	+	0.163594i	$0.947691\pi$
$578$	−7.62219	−	8.46529i	−0.317041	−	0.352110i
$579$	0.416137	+	3.95928i	0.0172941	+	0.164542i
$580$	−5.36097	−	1.13951i	−0.222602	−	0.0473156i
$581$	1.32347	+	4.07322i	0.0549067	+	0.168986i
$582$	−8.63009	+	1.83438i	−0.357729	+	0.0760376i
$583$	14.6119	+	25.3086i	0.605164	+	1.04817i
$584$	3.12144	−	5.40650i	0.129166	−	0.223722i
$585$	1.72600	−	5.31207i	0.0713612	−	0.219627i
$586$	−0.944078	+	8.98230i	−0.0389995	+	0.371056i
$587$	−9.40607	+	6.83391i	−0.388230	+	0.282066i	−0.764730	−	0.644351i	$-0.777128\pi$
$587$	−9.40607	+	6.83391i	−0.388230	+	0.282066i	0.376500	+	0.926417i	$0.377128\pi$
$588$	−6.30907			−0.260182
$589$	−8.13168	+	5.48759i	−0.335060	+	0.226112i
$590$	3.74340			0.154113
$591$	19.8777	−	14.4420i	0.817657	−	0.594063i
$592$	−0.488080	+	4.64377i	−0.0200600	+	0.190858i
$593$	12.7817	−	39.3379i	0.524880	−	1.61541i	−0.239673	−	0.970854i	$-0.577040\pi$
$593$	12.7817	−	39.3379i	0.524880	−	1.61541i	0.764553	−	0.644561i	$-0.222960\pi$
$594$	−2.14634	+	3.71757i	−0.0880654	+	0.152534i
$595$	−0.984292	−	1.70484i	−0.0403520	−	0.0698918i
$596$	−7.87365	+	1.67360i	−0.322517	+	0.0685532i
$597$	5.79165	+	17.8249i	0.237036	+	0.729523i
$598$	−16.7172	−	3.55334i	−0.683616	−	0.145307i
$599$	−0.865734	−	8.23691i	−0.0353729	−	0.336551i	−0.997869	−	0.0652542i	$-0.979214\pi$
$599$	−0.865734	−	8.23691i	−0.0353729	−	0.336551i	0.962496	−	0.271297i	$-0.0874525\pi$
$600$	0.669131	+	0.743145i	0.0273171	+	0.0303388i
$601$	37.4626	+	16.6794i	1.52813	+	0.680368i	0.987022	−	0.160585i	$-0.0513380\pi$
$601$	37.4626	+	16.6794i	1.52813	+	0.680368i	0.541109	+	0.840953i	$0.318005\pi$
$602$	1.88587	−	0.839645i	0.0768625	−	0.0342214i
$603$	4.61949	−	5.13046i	0.188120	−	0.208929i
$604$	−7.92616	−	5.75869i	−0.322511	−	0.234318i
$605$	−6.00864	−	4.36553i	−0.244286	−	0.177484i
$606$	3.17009	−	3.52074i	0.128776	−	0.143020i
$607$	39.4322	−	17.5563i	1.60050	−	0.712590i	0.604066	−	0.796935i	$-0.293546\pi$
$607$	39.4322	−	17.5563i	1.60050	−	0.712590i	0.996437	+	0.0843450i	$0.0268798\pi$
$608$	1.60962	+	0.716647i	0.0652786	+	0.0290639i
$609$	3.04837	+	3.38556i	0.123526	+	0.137190i
$610$	0.133913	+	1.27410i	0.00542198	+	0.0515867i
$611$	15.7615	+	3.35022i	0.637644	+	0.135535i
$612$	0.731844	+	2.25238i	0.0295830	+	0.0910472i
$613$	5.52520	−	1.17442i	0.223161	−	0.0474343i	−0.0949741	−	0.995480i	$-0.530277\pi$
$613$	5.52520	−	1.17442i	0.223161	−	0.0474343i	0.318135	+	0.948045i	$0.396943\pi$
$614$	14.6319	+	25.3433i	0.590497	+	1.02277i
$615$	3.68348	−	6.37998i	0.148532	−	0.257265i
$616$	1.10263	−	3.39354i	0.0444261	−	0.136730i
$617$	−2.91893	+	27.7718i	−0.117512	+	1.11805i	0.763780	+	0.645477i	$0.223341\pi$
$617$	−2.91893	+	27.7718i	−0.117512	+	1.11805i	−0.881292	+	0.472573i	$0.843325\pi$
$618$	10.1428	−	7.36915i	0.408002	−	0.296431i
$619$	38.8507			1.56154			0.780770	−	0.624818i	$-0.214827\pi$
$619$	38.8507			1.56154			0.780770	+	0.624818i	$0.214827\pi$
$620$	−5.48296	+	0.968088i	−0.220201	+	0.0388793i
$621$	3.05985			0.122788
$622$	−11.7094	+	8.50739i	−0.469505	+	0.341115i
$623$	1.38614	−	13.1882i	0.0555344	−	0.528375i
$624$	1.72600	−	5.31207i	0.0690952	−	0.212653i
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	7.97668	+	13.8160i	0.318812	+	0.552199i
$627$	−7.39818	+	1.57253i	−0.295455	+	0.0628009i
$628$	−4.34901	−	13.3849i	−0.173544	−	0.534114i
$629$	−10.8168	−	2.29917i	−0.431292	−	0.0916740i
$630$	−0.0868866	−	0.826670i	−0.00346164	−	0.0329353i
$631$	6.09610	+	6.77040i	0.242682	+	0.269526i	0.852165	−	0.523274i	$-0.175289\pi$
$631$	6.09610	+	6.77040i	0.242682	+	0.269526i	−0.609483	+	0.792799i	$0.708623\pi$
$632$	1.54890	+	0.689615i	0.0616120	+	0.0274314i
$633$	−13.9209	+	6.19799i	−0.553307	+	0.246348i
$634$	13.5467	−	15.0452i	0.538010	−	0.597521i
$635$	9.57777	+	6.95866i	0.380082	+	0.276146i
$636$	5.50765	+	4.00154i	0.218393	+	0.158671i
$637$	−23.5795	+	26.1876i	−0.934252	+	1.03759i
$638$	21.4930	−	9.56931i	0.850917	−	0.378853i
$639$	−1.50263	−	0.669014i	−0.0594431	−	0.0264658i
$640$	0.669131	+	0.743145i	0.0264497	+	0.0293754i
$641$	−2.18172	−	20.7577i	−0.0861727	−	0.819878i	−0.949190	−	0.314704i	$-0.898095\pi$
$641$	−2.18172	−	20.7577i	−0.0861727	−	0.819878i	0.863017	−	0.505174i	$-0.168572\pi$
$642$	0.572869	+	0.121767i	0.0226093	+	0.00480576i
$643$	−1.42297	−	4.37946i	−0.0561166	−	0.172709i	0.919070	−	0.394095i	$-0.128942\pi$
$643$	−1.42297	−	4.37946i	−0.0561166	−	0.172709i	−0.975186	+	0.221386i	$0.928942\pi$
$644$	−2.48784	+	0.528807i	−0.0980348	+	0.0208379i
$645$	−1.24175	−	2.15078i	−0.0488939	−	0.0846867i
$646$	−2.08640	+	3.61375i	−0.0820884	+	0.142181i
$647$	15.0803	−	46.4125i	0.592870	−	1.82466i	0.0278123	−	0.999613i	$-0.491146\pi$
$647$	15.0803	−	46.4125i	0.592870	−	1.82466i	0.565057	−	0.825052i	$-0.308854\pi$
$648$	−0.104528	+	0.994522i	−0.00410627	+	0.0390685i
$649$	−13.0003	+	9.44524i	−0.510305	+	0.370758i
$650$	5.58544			0.219079
$651$	4.16014	+	2.02785i	0.163049	+	0.0794779i
$652$	3.84194			0.150462
$653$	0.454579	−	0.330271i	0.0177890	−	0.0129245i	−0.578855	−	0.815430i	$-0.696500\pi$
$653$	0.454579	−	0.330271i	0.0177890	−	0.0129245i	0.596644	+	0.802506i	$0.296500\pi$
$654$	−0.658596	+	6.26612i	−0.0257531	+	0.245025i
$655$	0.458662	−	1.41162i	0.0179214	−	0.0551564i
$656$	3.68348	−	6.37998i	0.143816	−	0.249096i
$657$	3.12144	+	5.40650i	0.121779	+	0.210928i
$658$	2.34563	−	0.498579i	0.0914421	−	0.0194366i
$659$	−5.03722	−	15.5030i	−0.196222	−	0.603910i	−0.999960	−	0.00892672i	$-0.997159\pi$
$659$	−5.03722	−	15.5030i	−0.196222	−	0.603910i	0.803738	−	0.594984i	$-0.202841\pi$
$660$	−4.19887	−	0.892498i	−0.163441	−	0.0347404i
$661$	−3.82341	−	36.3773i	−0.148713	−	1.41491i	−0.773341	−	0.633990i	$-0.781416\pi$
$661$	−3.82341	−	36.3773i	−0.148713	−	1.41491i	0.624628	−	0.780923i	$-0.285251\pi$
$662$	−19.2489	−	21.3781i	−0.748132	−	0.830884i
$663$	12.0844	+	5.38031i	0.469318	+	0.208954i
$664$	4.70699	−	2.09569i	0.182667	−	0.0813285i
$665$	0.979989	−	1.08839i	0.0380023	−	0.0422059i
$666$	−3.77758	−	2.74458i	−0.146378	−	0.106350i
$667$	−13.5674	−	9.85731i	−0.525333	−	0.381677i
$668$	−12.0081	+	13.3363i	−0.464606	+	0.515998i
$669$	−25.8687	+	11.5175i	−1.00014	+	0.445292i
$670$	6.30686	+	2.80799i	0.243655	+	0.108482i
$671$	−3.67983	−	4.08686i	−0.142058	−	0.157772i
$672$	−0.0868866	−	0.826670i	−0.00335172	−	0.0318895i
$673$	16.0756	+	3.41697i	0.619668	+	0.131714i	0.507040	−	0.861923i	$-0.330740\pi$
$673$	16.0756	+	3.41697i	0.619668	+	0.131714i	0.112628	+	0.993637i	$0.464073\pi$
$674$	9.39607	+	28.9181i	0.361923	+	1.11389i
$675$	−0.978148	+	0.207912i	−0.0376489	+	0.00800252i
$676$	−9.09859	−	15.7592i	−0.349946	−	0.606124i
$677$	−15.7591	+	27.2956i	−0.605672	+	1.04905i	0.386273	+	0.922385i	$0.373762\pi$
$677$	−15.7591	+	27.2956i	−0.605672	+	1.04905i	−0.991945	+	0.126670i	$0.959571\pi$
$678$	3.49298	−	10.7503i	0.134147	−	0.412862i
$679$	−0.766590	+	7.29362i	−0.0294190	+	0.279903i
$680$	−1.91599	+	1.39205i	−0.0734749	+	0.0533826i
$681$	−8.86567			−0.339733
$682$	16.5988	−	17.1965i	0.635602	−	0.658487i
$683$	−6.18892			−0.236812			−0.118406	−	0.992965i	$-0.537778\pi$
$683$	−6.18892			−0.236812			−0.118406	+	0.992965i	$0.537778\pi$
$684$	−1.42544	+	1.03564i	−0.0545032	+	0.0395989i
$685$	−0.0881187	+	0.838393i	−0.00336684	+	0.0320334i
$686$	−3.41860	+	10.5214i	−0.130523	+	0.401707i
$687$	8.50105	−	14.7243i	0.324335	−	0.561765i
$688$	−1.24175	−	2.15078i	−0.0473413	−	0.0819975i
$689$	37.1938	−	7.90579i	1.41697	−	0.301187i
$690$	0.945547	+	2.91009i	0.0359963	+	0.110785i
$691$	−32.3445	−	6.87503i	−1.23044	−	0.261538i	−0.453583	−	0.891214i	$-0.649855\pi$
$691$	−32.3445	−	6.87503i	−1.23044	−	0.261538i	−0.776858	+	0.629675i	$0.783188\pi$
$692$	0.858054	+	8.16384i	0.0326183	+	0.310342i
$693$	2.38758	+	2.65167i	0.0906965	+	0.100729i
$694$	−27.8637	−	12.4057i	−1.05769	−	0.470914i
$695$	−6.76527	+	3.01209i	−0.256621	+	0.114255i
$696$	3.66733	−	4.07298i	0.139010	−	0.154386i
$697$	14.1150	+	10.2552i	0.534645	+	0.388442i
$698$	−15.8516	−	11.5168i	−0.599990	−	0.435918i
$699$	−14.3779	+	15.9683i	−0.543821	+	0.603975i
$700$	0.759361	−	0.338089i	0.0287011	−	0.0127786i
$701$	−35.9018	−	15.9845i	−1.35599	−	0.603727i	−0.405392	−	0.914143i	$-0.632865\pi$
$701$	−35.9018	−	15.9845i	−1.35599	−	0.603727i	−0.950601	+	0.310417i	$0.899531\pi$
$702$	3.73739	+	4.15079i	0.141059	+	0.156662i
$703$	−0.859970	−	8.18207i	−0.0324344	−	0.308592i
$704$	−4.19887	−	0.892498i	−0.158251	−	0.0336373i
$705$	−0.891495	−	2.74374i	−0.0335757	−	0.103335i
$706$	35.0870	−	7.45797i	1.32052	−	0.280684i
$707$	−1.96901	−	3.41043i	−0.0740523	−	0.128262i
$708$	−1.87170	+	3.24188i	−0.0703428	+	0.121837i
$709$	0.543140	−	1.67161i	0.0203980	−	0.0627787i	−0.940339	−	0.340238i	$-0.889492\pi$
$709$	0.543140	−	1.67161i	0.0203980	−	0.0627787i	0.960737	+	0.277459i	$0.0894924\pi$
$710$	0.171932	−	1.63582i	0.00645249	−	0.0613913i
$711$	−1.37168	+	0.996580i	−0.0514418	+	0.0373747i
$712$	−15.9534			−0.597880
$713$	−16.5314	−	4.11773i	−0.619107	−	0.154210i
$714$	1.96858			0.0736724
$715$	−19.3974	+	14.0930i	−0.725422	+	0.527050i
$716$	2.38684	−	22.7093i	0.0892004	−	0.848685i
$717$	−5.66146	+	17.4242i	−0.211431	+	0.650718i
$718$	13.8755	−	24.0331i	0.517829	−	0.896906i
$719$	−9.90430	−	17.1548i	−0.369368	−	0.639764i	0.620099	−	0.784524i	$-0.287093\pi$
$719$	−9.90430	−	17.1548i	−0.369368	−	0.639764i	−0.989467	+	0.144759i	$0.953759\pi$
$720$	−0.978148	+	0.207912i	−0.0364534	+	0.00774841i
$721$	−3.22032	−	9.91113i	−0.119931	−	0.369110i
$722$	15.5482	+	3.30487i	0.578644	+	0.122995i
$723$	0.537882	+	5.11760i	0.0200040	+	0.190326i
$724$	3.84302	+	4.26811i	0.142825	+	0.158623i
$725$	5.00690	+	2.22922i	0.185952	+	0.0827911i
$726$	6.78498	−	3.02087i	0.251814	−	0.112115i
$727$	32.1230	−	35.6762i	1.19138	−	1.32316i	0.257193	−	0.966360i	$-0.417202\pi$
$727$	32.1230	−	35.6762i	1.19138	−	1.32316i	0.934182	−	0.356796i	$-0.116131\pi$
$728$	−3.75607	−	2.72894i	−0.139209	−	0.101141i
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$	−4.17731	+	4.63937i	−0.154609	+	0.171711i
$731$	5.37317	−	2.39229i	0.198734	−	0.0884820i
$732$	−1.17036	−	0.521077i	−0.0432577	−	0.0192595i
$733$	−24.3047	−	26.9932i	−0.897716	−	0.997015i	−0.999997	−	0.00225951i	$-0.999281\pi$
$733$	−24.3047	−	26.9932i	−0.897716	−	0.997015i	0.102281	−	0.994756i	$-0.467386\pi$
$734$	−1.07686	−	10.2457i	−0.0397477	−	0.378174i
$735$	6.17120	+	1.31173i	0.227628	+	0.0483838i
$736$	0.945547	+	2.91009i	0.0348533	+	0.107267i
$737$	−28.9878	+	6.16155i	−1.06778	+	0.226964i
$738$	3.68348	+	6.37998i	0.135591	+	0.234850i
$739$	−11.1523	+	19.3163i	−0.410243	+	0.710562i	−0.994916	−	0.100707i	$-0.967890\pi$
$739$	−11.1523	+	19.3163i	−0.410243	+	0.710562i	0.584673	+	0.811269i	$0.301223\pi$
$740$	1.44291	−	4.44082i	0.0530424	−	0.163248i
$741$	−1.02869	+	9.78733i	−0.0377899	+	0.359547i
$742$	4.57809	−	3.32618i	0.168067	−	0.122108i
$743$	7.83123			0.287300			0.143650	−	0.989629i	$-0.454116\pi$
$743$	7.83123			0.287300			0.143650	+	0.989629i	$0.454116\pi$
$744$	1.90309	−	5.23242i	0.0697706	−	0.191830i
$745$	8.04955			0.294913
$746$	6.81365	−	4.95041i	0.249465	−	0.181247i
$747$	−0.538577	+	5.12422i	−0.0197055	+	0.187485i
$748$	3.14157	−	9.66876i	0.114867	−	0.353525i
$749$	0.243410	−	0.421599i	0.00889402	−	0.0154049i
$750$	−0.500000	−	0.866025i	−0.0182574	−	0.0316228i
$751$	−45.7675	+	9.72818i	−1.67008	+	0.354986i	−0.943315	−	0.331900i	$-0.892310\pi$
$751$	−45.7675	+	9.72818i	−1.67008	+	0.354986i	−0.726765	+	0.686886i	$0.758977\pi$
$752$	−0.891495	−	2.74374i	−0.0325095	−	0.100054i
$753$	11.9945	+	2.54952i	0.437105	+	0.0929095i
$754$	−3.19986	−	30.4447i	−0.116532	−	1.10873i
$755$	6.55565	+	7.28079i	0.238585	+	0.264975i
$756$	0.759361	+	0.338089i	0.0276177	+	0.0122962i
$757$	14.1059	−	6.28033i	0.512686	−	0.228263i	−0.134053	−	0.990974i	$-0.542799\pi$
$757$	14.1059	−	6.28033i	0.512686	−	0.228263i	0.646739	+	0.762712i	$0.276132\pi$
$758$	7.75565	−	8.61352i	0.281698	−	0.312857i
$759$	−10.6264	−	7.72054i	−0.385714	−	0.280238i
$760$	−1.42544	−	1.03564i	−0.0517062	−	0.0375668i
$761$	5.78333	−	6.42304i	0.209646	−	0.232835i	−0.629147	−	0.777287i	$-0.716595\pi$
$761$	5.78333	−	6.42304i	0.209646	−	0.232835i	0.838792	+	0.544452i	$0.183262\pi$
$762$	−10.8153	+	4.81526i	−0.391796	+	0.174439i
$763$	4.78446	+	2.13018i	0.173209	+	0.0771176i
$764$	−7.79070	−	8.65245i	−0.281858	−	0.313035i
$765$	−0.247554	−	2.35532i	−0.00895034	−	0.0851568i
$766$	−2.12007	−	0.450636i	−0.0766014	−	0.0162821i
$767$	6.46110	+	19.8852i	0.233297	+	0.718013i
$768$	−0.978148	+	0.207912i	−0.0352959	+	0.00750237i
$769$	−7.00958	−	12.1410i	−0.252772	−	0.437814i	0.711516	−	0.702670i	$-0.248009\pi$
$769$	−7.00958	−	12.1410i	−0.252772	−	0.437814i	−0.964288	+	0.264856i	$0.914676\pi$
$770$	−1.78409	+	3.09013i	−0.0642941	+	0.111361i
$771$	5.91167	−	18.1942i	0.212904	−	0.655250i
$772$	0.416137	−	3.95928i	0.0149771	−	0.142498i
$773$	34.9399	−	25.3853i	1.25670	−	0.913047i	0.258110	−	0.966116i	$-0.416900\pi$
$773$	34.9399	−	25.3853i	1.25670	−	0.913047i	0.998591	+	0.0530690i	$0.0169003\pi$
$774$	2.48350			0.0892676
$775$	5.56442	+	0.193038i	0.199880	+	0.00693413i
$776$	8.82289			0.316723
$777$	−3.14002	+	2.28136i	−0.112648	+	0.0818432i
$778$	2.39284	−	22.7663i	0.0857874	−	0.816213i
$779$	−4.01109	+	12.3449i	−0.143712	+	0.442301i
$780$	−2.79272	+	4.83714i	−0.0999955	+	0.173197i
$781$	3.53037	+	6.11478i	0.126327	+	0.218804i
$782$	−7.08828	+	1.50666i	−0.253476	+	0.0538781i
$783$	1.69364	+	5.21249i	0.0605258	+	0.186279i
$784$	6.17120	+	1.31173i	0.220400	+	0.0468475i
$785$	1.47110	+	13.9966i	0.0525058	+	0.499559i
$786$	0.993164	+	1.10302i	0.0354250	+	0.0393434i
$787$	34.8206	+	15.5031i	1.24122	+	0.552626i	0.919082	−	0.394067i	$-0.128932\pi$
$787$	34.8206	+	15.5031i	1.24122	+	0.552626i	0.322137	+	0.946693i	$0.395599\pi$
$788$	−22.4459	+	9.99357i	−0.799603	+	0.356006i
$789$	−2.77405	+	3.08089i	−0.0987587	+	0.109683i
$790$	−1.37168	−	0.996580i	−0.0488020	−	0.0354567i
$791$	−7.60132	−	5.52268i	−0.270272	−	0.196364i
$792$	2.87236	−	3.19008i	0.102065	−	0.113355i
$793$	−6.53697	+	2.91044i	−0.232134	+	0.103353i
$794$	−22.9282	−	10.2083i	−0.813693	−	0.362279i
$795$	−4.55533	−	5.05920i	−0.161561	−	0.179431i
$796$	−1.95909	−	18.6395i	−0.0694381	−	0.660659i
$797$	3.09044	+	0.656894i	0.109469	+	0.0232684i	0.262320	−	0.964981i	$-0.415512\pi$
$797$	3.09044	+	0.656894i	0.109469	+	0.0232684i	−0.152851	+	0.988249i	$0.548846\pi$
$798$	0.452577	+	1.39289i	0.0160211	+	0.0493077i
$799$	6.68309	−	1.42053i	0.236431	−	0.0502549i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	7.97671	−	13.8161i	0.281843	−	0.488167i
$802$	−0.575878	+	1.77237i	−0.0203350	+	0.0625846i
$803$	2.80123	−	26.6519i	0.0988532	−	0.940525i
$804$	−5.58522	+	4.05790i	−0.196976	+	0.143111i
$805$	2.54342			0.0896439
$806$	−14.6061	−	27.4549i	−0.514479	−	0.967059i
$807$	26.5836			0.935789
$808$	−3.83282	+	2.78470i	−0.134838	+	0.0979655i
$809$	−0.420191	+	3.99785i	−0.0147731	+	0.140557i	−0.999422	−	0.0339887i	$-0.989179\pi$
$809$	−0.420191	+	3.99785i	−0.0147731	+	0.140557i	0.984649	+	0.174546i	$0.0558456\pi$
$810$	0.309017	−	0.951057i	0.0108578	−	0.0334167i
$811$	6.54173	−	11.3306i	0.229711	−	0.397871i	−0.728011	−	0.685565i	$-0.759555\pi$
$811$	6.54173	−	11.3306i	0.229711	−	0.397871i	0.957722	+	0.287694i	$0.0928885\pi$
$812$	−2.27786	−	3.94537i	−0.0799372	−	0.138455i
$813$	6.27211	−	1.33318i	0.219972	−	0.0467566i
$814$	6.19394	+	19.0630i	0.217098	+	0.668158i
$815$	−3.75799	−	0.798785i	−0.131637	−	0.0279802i
$816$	−0.247554	−	2.35532i	−0.00866613	−	0.0824527i
$817$	2.92798	+	3.25185i	0.102437	+	0.113768i
$818$	−12.4277	−	5.53319i	−0.434526	−	0.193463i
$819$	4.24137	−	1.88838i	0.148205	−	0.0659853i
$820$	−4.92946	+	5.47472i	−0.172144	+	0.191185i
$821$	14.4495	+	10.4982i	0.504290	+	0.366388i	0.810653	−	0.585526i	$-0.199112\pi$
$821$	14.4495	+	10.4982i	0.504290	+	0.366388i	−0.306363	+	0.951915i	$0.599112\pi$
$822$	−0.682011	−	0.495510i	−0.0237879	−	0.0172829i
$823$	11.6914	−	12.9847i	0.407538	−	0.452617i	−0.504079	−	0.863658i	$-0.668168\pi$
$823$	11.6914	−	12.9847i	0.407538	−	0.452617i	0.911617	+	0.411041i	$0.134835\pi$
$824$	−11.4533	+	5.09932i	−0.398993	+	0.177643i
$825$	3.92156	+	1.74599i	0.136531	+	0.0607876i
$826$	2.08207	+	2.31237i	0.0724444	+	0.0804577i
$827$	1.18243	+	11.2501i	0.0411171	+	0.391204i	0.995655	+	0.0931149i	$0.0296824\pi$
$827$	1.18243	+	11.2501i	0.0411171	+	0.391204i	−0.954538	+	0.298089i	$0.903651\pi$
$828$	−2.99299	−	0.636179i	−0.104014	−	0.0221088i
$829$	−9.22325	−	28.3862i	−0.320337	−	0.985895i	−0.973502	−	0.228679i	$-0.926559\pi$
$829$	−9.22325	−	28.3862i	−0.320337	−	0.985895i	0.653165	−	0.757215i	$-0.273441\pi$
$830$	−5.03985	+	1.07125i	−0.174936	+	0.0371838i
$831$	10.6771	+	18.4932i	0.370383	+	0.641523i
$832$	−2.79272	+	4.83714i	−0.0968202	+	0.167698i
$833$	−4.61725	+	14.2104i	−0.159978	+	0.492362i
$834$	0.774087	−	7.36495i	0.0268044	−	0.255027i
$835$	14.5184	−	10.5483i	0.502431	−	0.365038i
$836$	7.56346			0.261588
$837$	3.57987	+	4.26434i	0.123738	+	0.147397i
$838$	23.1249			0.798837
$839$	29.3133	−	21.2973i	1.01201	−	0.735266i	0.0473777	−	0.998877i	$-0.484914\pi$
$839$	29.3133	−	21.2973i	1.01201	−	0.735266i	0.964629	+	0.263611i	$0.0849136\pi$
$840$	−0.0868866	+	0.826670i	−0.00299787	+	0.0285228i
$841$	0.320915	−	0.987675i	0.0110660	−	0.0340578i
$842$	−8.98470	+	15.5620i	−0.309633	+	0.536301i
$843$	3.07307	+	5.32271i	0.105842	+	0.183324i
$844$	14.9053	−	3.16823i	0.513063	−	0.109055i
$845$	5.62324	+	17.3066i	0.193445	+	0.595364i
$846$	2.82190	+	0.599813i	0.0970188	+	0.0206220i
$847$	−0.645314	−	6.13975i	−0.0221733	−	0.210964i
$848$	−4.55533	−	5.05920i	−0.156431	−	0.173734i
$849$	13.4074	+	5.96935i	0.460140	+	0.204868i
$850$	2.16355	−	0.963273i	0.0742090	−	0.0330400i
$851$	9.56022	−	10.6177i	0.327720	−	0.363970i
$852$	1.33070	+	0.966808i	0.0455889	+	0.0331223i
$853$	−15.6352	−	11.3596i	−0.535338	−	0.388946i	0.287012	−	0.957927i	$-0.407338\pi$
$853$	−15.6352	−	11.3596i	−0.535338	−	0.388946i	−0.822351	+	0.568981i	$0.807338\pi$
$854$	−0.712553	+	0.791370i	−0.0243831	+	0.0270801i
$855$	1.60962	−	0.716647i	0.0550477	−	0.0245088i
$856$	−0.535034	−	0.238212i	−0.0182871	−	0.00814193i
$857$	29.5330	+	32.7997i	1.00883	+	1.12042i	0.992708	+	0.120548i	$0.0384651\pi$
$857$	29.5330	+	32.7997i	1.00883	+	1.12042i	0.0161212	+	0.999870i	$0.494868\pi$
$858$	−2.50623	−	23.8452i	−0.0855612	−	0.814061i
$859$	27.1260	+	5.76580i	0.925526	+	0.196727i	0.645935	−	0.763393i	$-0.276468\pi$
$859$	27.1260	+	5.76580i	0.925526	+	0.196727i	0.279591	+	0.960119i	$0.409801\pi$
$860$	0.767444	+	2.36195i	0.0261696	+	0.0805418i
$861$	5.98978	−	1.27317i	0.204131	−	0.0433894i
$862$	12.3345	+	21.3639i	0.420114	+	0.727658i
$863$	7.87557	−	13.6409i	0.268087	−	0.464341i	−0.700280	−	0.713868i	$-0.746942\pi$
$863$	7.87557	−	13.6409i	0.268087	−	0.464341i	0.968368	+	0.249527i	$0.0802750\pi$
$864$	0.309017	−	0.951057i	0.0105130	−	0.0323556i
$865$	0.858054	−	8.16384i	0.0291747	−	0.277579i
$866$	11.3034	−	8.21244i	0.384107	−	0.279070i
$867$	−11.3912			−0.386865
$868$	−3.64761	−	2.84848i	−0.123808	−	0.0966838i
$869$	7.27817			0.246895
$870$	−4.43401	+	3.22150i	−0.150327	+	0.109219i
$871$	−4.03065	+	38.3491i	−0.136573	+	1.29941i
$872$	1.94700	−	5.99226i	0.0659339	−	0.202924i
$873$	−4.41144	+	7.64084i	−0.149305	+	0.258603i
$874$	−2.69565	−	4.66899i	−0.0911816	−	0.157931i
$875$	−0.813060	+	0.172821i	−0.0274864	+	0.00584242i
$876$	−1.92916	−	5.93734i	−0.0651802	−	0.200604i
$877$	30.3624	+	6.45372i	1.02526	+	0.217927i	0.689704	−	0.724092i	$-0.257741\pi$
$877$	30.3624	+	6.45372i	1.02526	+	0.217927i	0.335561	+	0.942019i	$0.391074\pi$
$878$	2.27101	+	21.6073i	0.0766430	+	0.729210i
$879$	6.04344	+	6.71192i	0.203840	+	0.226387i
$880$	3.92156	+	1.74599i	0.132196	+	0.0588573i
$881$	31.7650	−	14.1427i	1.07019	−	0.476480i	0.205435	−	0.978671i	$-0.434139\pi$
$881$	31.7650	−	14.1427i	1.07019	−	0.476480i	0.864757	+	0.502191i	$0.167472\pi$
$882$	−4.22159	+	4.68855i	−0.142148	+	0.157872i
$883$	3.84232	+	2.79161i	0.129304	+	0.0939451i	0.650558	−	0.759457i	$-0.274535\pi$
$883$	3.84232	+	2.79161i	0.129304	+	0.0939451i	−0.521253	+	0.853402i	$0.674535\pi$
$884$	−10.7017	−	7.77521i	−0.359936	−	0.261509i
$885$	2.50482	−	2.78189i	0.0841987	−	0.0935121i
$886$	−4.54261	+	2.02250i	−0.152612	+	0.0679472i
$887$	−4.74819	−	2.11403i	−0.159429	−	0.0709823i	0.325471	−	0.945552i	$-0.394477\pi$
$887$	−4.74819	−	2.11403i	−0.159429	−	0.0709823i	−0.484900	+	0.874570i	$0.661144\pi$
$888$	3.12441	+	3.47000i	0.104848	+	0.116446i
$889$	1.02863	+	9.78676i	0.0344992	+	0.328238i
$890$	15.6048	+	3.31690i	0.523074	+	0.111183i
$891$	1.32651	+	4.08258i	0.0444398	+	0.136772i
$892$	27.6981	−	5.88741i	0.927400	−	0.197125i
$893$	2.54155	+	4.40210i	0.0850498	+	0.147311i
$894$	−4.02478	+	6.97112i	−0.134609	+	0.233149i
$895$	−7.05620	+	21.7168i	−0.235863	+	0.725911i
$896$	−0.0868866	+	0.826670i	−0.00290268	+	0.0276171i
$897$	−13.8266	+	10.0456i	−0.461657	+	0.335414i
$898$	24.5646			0.819731
$899$	−2.13562	−	30.4406i	−0.0712270	−	1.01525i
$900$	1.00000			0.0333333
$901$	13.0437	−	9.47683i	0.434550	−	0.315719i
$902$	3.30561	−	31.4508i	0.110065	−	1.04720i
$903$	0.637918	−	1.96331i	0.0212286	−	0.0653348i
$904$	−5.65176	+	9.78913i	−0.187975	+	0.325582i
$905$	−2.87165	−	4.97385i	−0.0954570	−	0.165336i
$906$	−9.58318	+	2.03697i	−0.318380	+	0.0676737i
$907$	1.41529	+	4.35580i	0.0469938	+	0.144632i	0.971800	−	0.235806i	$-0.0757731\pi$
$907$	1.41529	+	4.35580i	0.0469938	+	0.144632i	−0.924806	+	0.380438i	$0.875773\pi$
$908$	8.67193	+	1.84328i	0.287788	+	0.0611713i
$909$	−0.495216	−	4.71167i	−0.0164253	−	0.156276i
$910$	3.10661	+	3.45024i	0.102983	+	0.114374i
$911$	29.6819	+	13.2152i	0.983404	+	0.437840i	0.834498	−	0.551012i	$-0.185758\pi$
$911$	29.6819	+	13.2152i	0.983404	+	0.437840i	0.148906	+	0.988851i	$0.452425\pi$
$912$	1.60962	−	0.716647i	0.0532997	−	0.0237306i
$913$	14.7997	−	16.4367i	0.489798	−	0.543976i
$914$	−30.6437	−	22.2640i	−1.01360	−	0.736426i
$915$	1.03644	+	0.753021i	0.0342638	+	0.0248941i
$916$	−11.3766	+	12.6350i	−0.375894	+	0.417473i
$917$	1.12709	−	0.501812i	0.0372198	−	0.0165713i
$918$	2.16355	+	0.963273i	0.0714076	+	0.0317927i
$919$	−23.4981	−	26.0973i	−0.775131	−	0.860871i	0.218231	−	0.975897i	$-0.429971\pi$
$919$	−23.4981	−	26.0973i	−0.775131	−	0.860871i	−0.993362	+	0.115027i	$0.963305\pi$
$920$	−0.319842	−	3.04309i	−0.0105449	−	0.100328i
$921$	28.6244	+	6.08430i	0.943206	+	0.200485i
$922$	2.71274	+	8.34894i	0.0893392	+	0.274958i
$923$	8.98636	−	1.91011i	0.295790	−	0.0628720i
$924$	−1.78409	−	3.09013i	−0.0586922	−	0.101658i
$925$	−2.33468	+	4.04378i	−0.0767637	+	0.132959i
$926$	−10.0796	+	31.0218i	−0.331236	+	1.01944i
$927$	1.31049	−	12.4685i	0.0430421	−	0.409518i
$928$	−4.43401	+	3.22150i	−0.145554	+	0.105751i
$929$	−51.7039			−1.69635			−0.848175	−	0.529717i	$-0.822298\pi$
$929$	−51.7039			−1.69635			−0.848175	+	0.529717i	$0.822298\pi$
$930$	−2.94938	+	4.72241i	−0.0967141	+	0.154854i
$931$	−11.1162			−0.364320
$932$	17.3837	−	12.6300i	0.569421	−	0.413709i
$933$	−1.51291	+	14.3943i	−0.0495303	+	0.471250i
$934$	1.80734	−	5.56242i	0.0591380	−	0.182008i
$935$	−5.08317	+	8.80430i	−0.166237	+	0.287931i
$936$	−2.79272	−	4.83714i	−0.0912830	−	0.158107i
$937$	49.1889	−	10.4554i	1.60693	−	0.341564i	0.684888	−	0.728649i	$-0.259851\pi$
$937$	49.1889	−	10.4554i	1.60693	−	0.341564i	0.922044	+	0.387085i	$0.126518\pi$
$938$	1.77330	+	5.45767i	0.0579005	+	0.178199i
$939$	15.6047	+	3.31689i	0.509242	+	0.108243i
$940$	0.301558	+	2.86914i	0.00983575	+	0.0935809i
$941$	24.5968	+	27.3175i	0.801832	+	0.890525i	0.995900	−	0.0904633i	$-0.0288348\pi$
$941$	24.5968	+	27.3175i	0.801832	+	0.890525i	−0.194068	+	0.980988i	$0.562168\pi$
$942$	−12.8569	−	5.72428i	−0.418902	−	0.186507i
$943$	−20.5930	+	9.16858i	−0.670600	+	0.298570i
$944$	2.50482	−	2.78189i	0.0815250	−	0.0905427i
$945$	−0.672474	−	0.488581i	−0.0218756	−	0.0158935i
$946$	−8.62483	−	6.26630i	−0.280417	−	0.203735i
$947$	−31.5375	+	35.0259i	−1.02483	+	1.13819i	−0.0345089	+	0.999404i	$0.510987\pi$
$947$	−31.5375	+	35.0259i	−1.02483	+	1.13819i	−0.990322	+	0.138786i	$0.955680\pi$
$948$	1.54890	−	0.689615i	0.0503060	−	0.0223977i
$949$	−31.8547	−	14.1826i	−1.03405	−	0.460387i
$950$	1.17897	+	1.30938i	0.0382509	+	0.0424819i
$951$	−2.11621	−	20.1344i	−0.0686228	−	0.652902i
$952$	−1.92557	−	0.409292i	−0.0624079	−	0.0132652i
$953$	1.55990	+	4.80089i	0.0505302	+	0.155516i	0.973138	−	0.230224i	$-0.0739460\pi$
$953$	1.55990	+	4.80089i	0.0505302	+	0.155516i	−0.922607	+	0.385740i	$0.873946\pi$
$954$	6.65906	−	1.41543i	0.215595	−	0.0458262i
$955$	5.82151	+	10.0832i	0.188380	+	0.326283i
$956$	9.16044	−	15.8663i	0.296270	−	0.513154i
$957$	7.27026	−	22.3756i	0.235014	−	0.723299i
$958$	−1.41844	+	13.4956i	−0.0458278	+	0.436023i
$959$	−0.566903	+	0.411879i	−0.0183063	+	0.0133003i
$960$	1.00000			0.0322749
$961$	−13.6023	−	27.8564i	−0.438783	−	0.898593i
$962$	26.0804			0.840866
$963$	0.473815	−	0.344247i	0.0152685	−	0.0110932i
$964$	0.537882	−	5.11760i	0.0173240	−	0.164827i
$965$	−1.23022	+	3.78624i	−0.0396023	+	0.121883i
$966$	−1.27171	+	2.20267i	−0.0409166	+	0.0708697i
$967$	2.93079	+	5.07627i	0.0942478	+	0.163242i	0.909294	−	0.416153i	$-0.136622\pi$
$967$	2.93079	+	5.07627i	0.0942478	+	0.163242i	−0.815047	+	0.579395i	$0.803289\pi$
$968$	−7.26479	+	1.54418i	−0.233499	+	0.0496318i
$969$	1.28947	+	3.96857i	0.0414237	+	0.127489i
$970$	−8.63009	−	1.83438i	−0.277095	−	0.0588984i
$971$	0.377246	+	3.58926i	0.0121064	+	0.115185i	0.998906	−	0.0467607i	$-0.0148898\pi$
$971$	0.377246	+	3.58926i	0.0121064	+	0.115185i	−0.986800	+	0.161945i	$0.948223\pi$
$972$	0.669131	+	0.743145i	0.0214624	+	0.0238364i
$973$	−5.62346	−	2.50372i	−0.180280	−	0.0802657i
$974$	11.2196	−	4.99527i	0.359498	−	0.160059i
$975$	3.73739	−	4.15079i	0.119692	−	0.132932i
$976$	1.03644	+	0.753021i	0.0331758	+	0.0241036i
$977$	10.1816	+	7.39735i	0.325737	+	0.236662i	0.738620	−	0.674122i	$-0.235478\pi$
$977$	10.1816	+	7.39735i	0.325737	+	0.236662i	−0.412882	+	0.910784i	$0.635478\pi$
$978$	2.57076	−	2.85512i	0.0822039	−	0.0912967i
$979$	−62.5623	+	27.8545i	−1.99950	+	0.890234i
$980$	−5.76362	−	2.56613i	−0.184112	−	0.0819720i
$981$	4.21595	+	4.68229i	0.134605	+	0.149494i
$982$	−3.72874	−	35.4766i	−0.118989	−	1.13210i
$983$	1.59853	+	0.339778i	0.0509852	+	0.0108372i	0.233334	−	0.972397i	$-0.425037\pi$
$983$	1.59853	+	0.339778i	0.0509852	+	0.0108372i	−0.182348	+	0.983234i	$0.558370\pi$
$984$	−2.27652	−	7.00640i	−0.0725727	−	0.223356i
$985$	24.0332	−	5.10842i	0.765762	−	0.162768i
$986$	−6.49000	−	11.2410i	−0.206684	−	0.357987i
$987$	1.19902	−	2.07676i	0.0381651	−	0.0661039i
$988$	3.04111	−	9.35958i	0.0967506	−	0.297768i
$989$	−0.794327	+	7.55752i	−0.0252581	+	0.240315i
$990$	−3.47285	+	2.52317i	−0.110374	+	0.0801917i
$991$	−53.8616			−1.71097			−0.855485	−	0.517828i	$-0.826741\pi$
$991$	−53.8616			−1.71097			−0.855485	+	0.517828i	$0.826741\pi$
$992$	−2.94938	+	4.72241i	−0.0936430	+	0.149937i
$993$	−28.7671			−0.912896
$994$	1.10611	−	0.803634i	0.0350836	−	0.0254897i
$995$	−1.95909	+	18.6395i	−0.0621073	+	0.590911i
$996$	1.59219	−	4.90027i	0.0504506	−	0.155271i
$997$	10.4189	−	18.0460i	0.329969	−	0.571523i	−0.652536	−	0.757758i	$-0.726295\pi$
$997$	10.4189	−	18.0460i	0.329969	−	0.571523i	0.982505	+	0.186234i	$0.0596283\pi$
$998$	−17.3222	−	30.0029i	−0.548324	−	0.949725i
$999$	−4.56731	+	0.970813i	−0.144503	+	0.0307152i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bg.g.121.2	✓	24
31.10	even	15	inner	930.2.bg.g.661.2	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bg.g.121.2	✓	24	1.1	even	1	trivial
930.2.bg.g.661.2	yes	24	31.10	even	15	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.bg (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.813060 + 0.172821i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +O(q^{10})\)	\(q+(-0.809017 + 0.587785i) q^{2} +(-0.104528 + 0.994522i) q^{3} +(0.309017 - 0.951057i) q^{4} +(-0.500000 + 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.813060 + 0.172821i) q^{7} +(0.309017 + 0.951057i) q^{8} +(-0.978148 - 0.207912i) q^{9} +(-0.104528 - 0.994522i) q^{10} +(2.87236 + 3.19008i) q^{11} +(0.913545 + 0.406737i) q^{12} +(5.10256 - 2.27180i) q^{13} +(0.556197 - 0.617720i) q^{14} +(-0.809017 - 0.587785i) q^{15} +(-0.809017 - 0.587785i) q^{16} +(1.58470 - 1.75999i) q^{17} +(0.913545 - 0.406737i) q^{18} +(1.60962 + 0.716647i) q^{19} +(0.669131 + 0.743145i) q^{20} +(-0.0868866 - 0.826670i) q^{21} +(-4.19887 - 0.892498i) q^{22} +(0.945547 + 2.91009i) q^{23} +(-0.978148 + 0.207912i) q^{24} +(-0.500000 - 0.866025i) q^{25} +(-2.79272 + 4.83714i) q^{26} +(0.309017 - 0.951057i) q^{27} +(-0.0868866 + 0.826670i) q^{28} +(-4.43401 + 3.22150i) q^{29} +1.00000 q^{30} +(-2.94938 + 4.72241i) q^{31} +1.00000 q^{32} +(-3.47285 + 2.52317i) q^{33} +(-0.247554 + 2.35532i) q^{34} +(0.256862 - 0.790541i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-2.33468 - 4.04378i) q^{37} +(-1.72344 + 0.366329i) q^{38} +(1.72600 + 5.31207i) q^{39} +(-0.978148 - 0.207912i) q^{40} +(0.770057 + 7.32660i) q^{41} +(0.556197 + 0.617720i) q^{42} +(2.26879 + 1.01013i) q^{43} +(3.92156 - 1.74599i) q^{44} +(0.669131 - 0.743145i) q^{45} +(-2.47547 - 1.79854i) q^{46} +(2.33397 + 1.69573i) q^{47} +(0.669131 - 0.743145i) q^{48} +(-5.76362 + 2.56613i) q^{49} +(0.913545 + 0.406737i) q^{50} +(1.58470 + 1.75999i) q^{51} +(-0.583838 - 5.55485i) q^{52} +(6.65906 + 1.41543i) q^{53} +(0.309017 + 0.951057i) q^{54} +(-4.19887 + 0.892498i) q^{55} +(-0.415612 - 0.719861i) q^{56} +(-0.880972 + 1.52589i) q^{57} +(1.69364 - 5.21249i) q^{58} +(-0.391292 + 3.72289i) q^{59} +(-0.809017 + 0.587785i) q^{60} -1.28112 q^{61} +(-0.389660 - 5.55411i) q^{62} +0.831224 q^{63} +(-0.809017 + 0.587785i) q^{64} +(-0.583838 + 5.55485i) q^{65} +(1.32651 - 4.08258i) q^{66} +(-3.45186 + 5.97879i) q^{67} +(-1.18415 - 2.05100i) q^{68} +(-2.99299 + 0.636179i) q^{69} +(0.256862 + 0.790541i) q^{70} +(1.60889 + 0.341980i) q^{71} +(-0.104528 - 0.994522i) q^{72} +(-4.17731 - 4.63937i) q^{73} +(4.26566 + 1.89920i) q^{74} +(0.913545 - 0.406737i) q^{75} +(1.17897 - 1.30938i) q^{76} +(-2.88672 - 2.09732i) q^{77} +(-4.51872 - 3.28304i) q^{78} +(1.13450 - 1.25999i) q^{79} +(0.913545 - 0.406737i) q^{80} +(0.913545 + 0.406737i) q^{81} +(-4.92946 - 5.47472i) q^{82} +(-0.538577 - 5.12422i) q^{83} +(-0.813060 - 0.172821i) q^{84} +(0.731844 + 2.25238i) q^{85} +(-2.42923 + 0.516349i) q^{86} +(-2.74037 - 4.74646i) q^{87} +(-2.14634 + 3.71757i) q^{88} +(-4.92988 + 15.1726i) q^{89} +(-0.104528 + 0.994522i) q^{90} +(-3.75607 + 2.72894i) q^{91} +3.05985 q^{92} +(-4.38824 - 3.42685i) q^{93} -2.88494 q^{94} +(-1.42544 + 1.03564i) q^{95} +(-0.104528 + 0.994522i) q^{96} +(2.72642 - 8.39106i) q^{97} +(3.15453 - 5.46381i) q^{98} +(-2.14634 - 3.71757i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9}+O(q^{10}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9	\( 24 q - 6 q^{2} + 3 q^{3} - 6 q^{4} - 12 q^{5} - 12 q^{6} + 9 q^{7} - 6 q^{8} + 3 q^{9} + 3 q^{10} + 3 q^{11} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 6 q^{15} - 6 q^{16} - 9 q^{17} + 3 q^{18} + q^{19} + 3 q^{20} + 4 q^{21} + 3 q^{22} + 5 q^{23} + 3 q^{24} - 12 q^{25} - 3 q^{26} - 6 q^{27} + 4 q^{28} - 15 q^{29} + 24 q^{30} + 15 q^{31} + 24 q^{32} + 4 q^{33} - 9 q^{34} - 3 q^{35} - 12 q^{36} + 6 q^{38} - 9 q^{39} + 3 q^{40} - 20 q^{41} - 6 q^{42} - 13 q^{43} - 2 q^{44} + 3 q^{45} - 10 q^{46} + 4 q^{47} + 3 q^{48} + 3 q^{50} - 9 q^{51} - 3 q^{52} - 6 q^{54} + 3 q^{55} - 11 q^{56} - 14 q^{57} + 22 q^{59} - 6 q^{60} + 16 q^{61} - 5 q^{62} + 22 q^{63} - 6 q^{64} - 3 q^{65} - 6 q^{66} - 19 q^{67} - 9 q^{68} - 10 q^{69} - 3 q^{70} - 45 q^{71} + 3 q^{72} + 11 q^{73} - 35 q^{74} + 3 q^{75} + 6 q^{76} - 50 q^{77} + 6 q^{78} + 36 q^{79} + 3 q^{80} + 3 q^{81} - 20 q^{82} - 4 q^{83} + 9 q^{84} - 12 q^{85} + 22 q^{86} - 15 q^{87} - 2 q^{88} - 7 q^{89} + 3 q^{90} - 32 q^{91} + 10 q^{92} + 7 q^{93} + 54 q^{94} - 2 q^{95} + 3 q^{96} + 11 q^{97} - 15 q^{98} - 2 q^{99}+O(q^{100}) \) 24 * q - 6 * q^2 + 3 * q^3 - 6 * q^4 - 12 * q^5 - 12 * q^6 + 9 * q^7 - 6 * q^8 + 3 * q^9 + 3 * q^10 + 3 * q^11 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 6 * q^15 - 6 * q^16 - 9 * q^17 + 3 * q^18 + q^19 + 3 * q^20 + 4 * q^21 + 3 * q^22 + 5 * q^23 + 3 * q^24 - 12 * q^25 - 3 * q^26 - 6 * q^27 + 4 * q^28 - 15 * q^29 + 24 * q^30 + 15 * q^31 + 24 * q^32 + 4 * q^33 - 9 * q^34 - 3 * q^35 - 12 * q^36 + 6 * q^38 - 9 * q^39 + 3 * q^40 - 20 * q^41 - 6 * q^42 - 13 * q^43 - 2 * q^44 + 3 * q^45 - 10 * q^46 + 4 * q^47 + 3 * q^48 + 3 * q^50 - 9 * q^51 - 3 * q^52 - 6 * q^54 + 3 * q^55 - 11 * q^56 - 14 * q^57 + 22 * q^59 - 6 * q^60 + 16 * q^61 - 5 * q^62 + 22 * q^63 - 6 * q^64 - 3 * q^65 - 6 * q^66 - 19 * q^67 - 9 * q^68 - 10 * q^69 - 3 * q^70 - 45 * q^71 + 3 * q^72 + 11 * q^73 - 35 * q^74 + 3 * q^75 + 6 * q^76 - 50 * q^77 + 6 * q^78 + 36 * q^79 + 3 * q^80 + 3 * q^81 - 20 * q^82 - 4 * q^83 + 9 * q^84 - 12 * q^85 + 22 * q^86 - 15 * q^87 - 2 * q^88 - 7 * q^89 + 3 * q^90 - 32 * q^91 + 10 * q^92 + 7 * q^93 + 54 * q^94 - 2 * q^95 + 3 * q^96 + 11 * q^97 - 15 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

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Database

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