LMFDB - Embedded newform 115.2.l.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [115,2,Mod(7,115)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(115, base_ring=CyclotomicField(44))

chi = DirichletCharacter(H, H._module([11, 38]))

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

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

chi := DirichletCharacter("115.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 115 = 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	115.l (of order $44$, degree $20$, 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:	$0.918279623245$
Analytic rank:	$0$
Dimension:	$200$
Relative dimension:	$10$ over $\Q(\zeta_{44})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{44}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	115.7
Dual form			115.2.l.a.33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.48666 + 0.177849i) q^{2} +(0.639470 - 2.93959i) q^{3} +(4.17220 - 0.599872i) q^{4} +(0.983237 + 2.00829i) q^{5} +(-1.06734 + 7.42350i) q^{6} +(1.40495 - 2.57297i) q^{7} +(-5.39608 + 1.17384i) q^{8} +(-5.50340 - 2.51332i) q^{9} +O(q^{10})$	\(q+(-2.48666 + 0.177849i) q^{2} +(0.639470 - 2.93959i) q^{3} +(4.17220 - 0.599872i) q^{4} +(0.983237 + 2.00829i) q^{5} +(-1.06734 + 7.42350i) q^{6} +(1.40495 - 2.57297i) q^{7} +(-5.39608 + 1.17384i) q^{8} +(-5.50340 - 2.51332i) q^{9} +(-2.80215 - 4.81907i) q^{10} +(1.18463 - 1.02649i) q^{11} +(0.904615 - 12.6482i) q^{12} +(-0.623103 + 0.340240i) q^{13} +(-3.03603 + 6.64798i) q^{14} +(6.53232 - 1.60607i) q^{15} +(5.12071 - 1.50358i) q^{16} +(-1.06504 - 1.42273i) q^{17} +(14.1321 + 5.27099i) q^{18} +(-0.533737 - 3.71222i) q^{19} +(5.30698 + 7.78919i) q^{20} +(-6.66508 - 5.77532i) q^{21} +(-2.76322 + 2.76322i) q^{22} +(-3.47935 + 3.30062i) q^{23} +16.6129i q^{24} +(-3.06649 + 3.94926i) q^{25} +(1.48893 - 0.956879i) q^{26} +(-5.49889 + 7.34565i) q^{27} +(4.31828 - 11.5778i) q^{28} +(3.13134 + 0.450218i) q^{29} +(-15.9580 + 5.15553i) q^{30} +(8.28154 + 5.32222i) q^{31} +(-2.11785 + 0.789919i) q^{32} +(-2.25993 - 4.13875i) q^{33} +(2.90142 + 3.34842i) q^{34} +(6.54869 + 0.291710i) q^{35} +(-24.4689 - 7.18473i) q^{36} +(1.63919 + 4.39484i) q^{37} +(1.98744 + 9.13611i) q^{38} +(0.601712 + 2.04924i) q^{39} +(-7.66305 - 9.68274i) q^{40} +(-1.00131 - 2.19257i) q^{41} +(17.6009 + 13.1759i) q^{42} +(2.90485 + 0.631911i) q^{43} +(4.32676 - 4.99335i) q^{44} +(-0.363663 - 13.5236i) q^{45} +(8.06495 - 8.82632i) q^{46} +(-2.24768 - 2.24768i) q^{47} +(-1.14536 - 16.0143i) q^{48} +(-0.861828 - 1.34103i) q^{49} +(6.92294 - 10.3658i) q^{50} +(-4.86329 + 2.22099i) q^{51} +(-2.39561 + 1.79333i) q^{52} +(6.43181 + 3.51203i) q^{53} +(12.3674 - 19.2441i) q^{54} +(3.22627 + 1.36981i) q^{55} +(-4.56095 + 15.5332i) q^{56} +(-11.2537 - 0.804883i) q^{57} +(-7.86664 - 0.562633i) q^{58} +(-0.982871 + 3.34735i) q^{59} +(26.2907 - 10.6194i) q^{60} +(-2.23932 + 3.48445i) q^{61} +(-21.5399 - 11.7617i) q^{62} +(-14.1987 + 10.6290i) q^{63} +(-4.58332 + 2.09313i) q^{64} +(-1.29596 - 0.916837i) q^{65} +(6.35574 + 9.88973i) q^{66} +(0.180035 + 2.51722i) q^{67} +(-5.29701 - 5.29701i) q^{68} +(7.47755 + 12.3385i) q^{69} +(-16.3362 + 0.439297i) q^{70} +(10.3652 - 11.9621i) q^{71} +(32.6470 + 7.10192i) q^{72} +(4.07004 + 3.04679i) q^{73} +(-4.85773 - 10.6369i) q^{74} +(9.64829 + 11.5397i) q^{75} +(-4.45372 - 15.1680i) q^{76} +(-0.976782 - 4.49020i) q^{77} +(-1.86071 - 4.98875i) q^{78} +(-4.84738 - 1.42332i) q^{79} +(8.05449 + 8.80552i) q^{80} +(6.19088 + 7.14465i) q^{81} +(2.87987 + 5.27409i) q^{82} +(-15.8841 + 5.92447i) q^{83} +(-31.2725 - 20.0976i) q^{84} +(1.81007 - 3.53779i) q^{85} +(-7.33575 - 1.05472i) q^{86} +(3.32585 - 8.91696i) q^{87} +(-5.18743 + 6.92959i) q^{88} +(-7.01782 + 4.51008i) q^{89} +(3.30947 + 33.5640i) q^{90} +2.08125i q^{91} +(-12.5366 + 15.8580i) q^{92} +(20.9410 - 20.9410i) q^{93} +(5.98895 + 5.18946i) q^{94} +(6.93045 - 4.72190i) q^{95} +(0.967737 + 6.73076i) q^{96} +(6.12895 + 2.28598i) q^{97} +(2.38157 + 3.18141i) q^{98} +(-9.09940 + 2.67182i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	$ 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) $ 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/115\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{19}{22}\right)$

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 $

$2$	−2.48666	+	0.177849i	−1.75833	+	0.125758i	−0.912864	−	0.408265i	$-0.866134\pi$
$2$	−2.48666	+	0.177849i	−1.75833	+	0.125758i	−0.845470	+	0.534023i	$0.820680\pi$
$3$	0.639470	−	2.93959i	0.369198	−	1.69718i	−0.299875	−	0.953979i	$-0.596945\pi$
$3$	0.639470	−	2.93959i	0.369198	−	1.69718i	0.669073	−	0.743197i	$-0.266691\pi$
$4$	4.17220	−	0.599872i	2.08610	−	0.299936i
$5$	0.983237	+	2.00829i	0.439717	+	0.898136i
$5$	0.983237	+	2.00829i	0.439717	+	0.898136i
$6$	−1.06734	+	7.42350i	−0.435739	+	3.03063i
$7$	1.40495	−	2.57297i	0.531021	−	0.972493i	−0.465163	−	0.885225i	$-0.654004\pi$
$7$	1.40495	−	2.57297i	0.531021	−	0.972493i	0.996185	−	0.0872683i	$-0.0278137\pi$
$8$	−5.39608	+	1.17384i	−1.90780	+	0.415017i
$9$	−5.50340	−	2.51332i	−1.83447	−	0.837772i
$10$	−2.80215	−	4.81907i	−0.886117	−	1.52393i
$11$	1.18463	−	1.02649i	0.357180	−	0.309498i	−0.457724	−	0.889094i	$-0.651335\pi$
$11$	1.18463	−	1.02649i	0.357180	−	0.309498i	0.814904	+	0.579596i	$0.196790\pi$
$12$	0.904615	−	12.6482i	0.261140	−	3.65121i
$13$	−0.623103	+	0.340240i	−0.172818	+	0.0943655i	−0.563330	−	0.826232i	$-0.690480\pi$
$13$	−0.623103	+	0.340240i	−0.172818	+	0.0943655i	0.390512	+	0.920598i	$0.372298\pi$
$14$	−3.03603	+	6.64798i	−0.811413	+	1.77675i
$15$	6.53232	−	1.60607i	1.68664	−	0.414687i
$16$	5.12071	−	1.50358i	1.28018	−	0.375894i
$17$	−1.06504	−	1.42273i	−0.258310	−	0.345062i	0.652574	−	0.757725i	$-0.273689\pi$
$17$	−1.06504	−	1.42273i	−0.258310	−	0.345062i	−0.910883	+	0.412664i	$0.864598\pi$
$18$	14.1321	+	5.27099i	3.33096	+	1.24238i
$19$	−0.533737	−	3.71222i	−0.122448	−	0.851643i	−0.954769	−	0.297349i	$-0.903898\pi$
$19$	−0.533737	−	3.71222i	−0.122448	−	0.851643i	0.832321	−	0.554294i	$-0.187012\pi$
$20$	5.30698	+	7.78919i	1.18668	+	1.74172i
$21$	−6.66508	−	5.77532i	−1.45444	−	1.26028i
$22$	−2.76322	+	2.76322i	−0.589120	+	0.589120i
$23$	−3.47935	+	3.30062i	−0.725495	+	0.688227i
$23$	−3.47935	+	3.30062i	−0.725495	+	0.688227i
$24$			16.6129i			3.39110i
$25$	−3.06649	+	3.94926i	−0.613298	+	0.789852i
$26$	1.48893	−	0.956879i	0.292004	−	0.187659i
$27$	−5.49889	+	7.34565i	−1.05826	+	1.41367i
$28$	4.31828	−	11.5778i	0.816078	−	2.18799i
$29$	3.13134	+	0.450218i	0.581475	+	0.0836035i	0.426775	−	0.904358i	$-0.359650\pi$
$29$	3.13134	+	0.450218i	0.581475	+	0.0836035i	0.154700	+	0.987961i	$0.450559\pi$
$30$	−15.9580	+	5.15553i	−2.91352	+	0.941266i
$31$	8.28154	+	5.32222i	1.48741	+	0.955900i	0.996403	+	0.0847436i	$0.0270071\pi$
$31$	8.28154	+	5.32222i	1.48741	+	0.955900i	0.491006	+	0.871156i	$0.336629\pi$
$32$	−2.11785	+	0.789919i	−0.374387	+	0.139639i
$33$	−2.25993	−	4.13875i	−0.393403	−	0.720463i
$34$	2.90142	+	3.34842i	0.497589	+	0.574249i
$35$	6.54869	+	0.291710i	1.10693	+	0.0493080i
$36$	−24.4689	−	7.18473i	−4.07816	−	1.19745i
$37$	1.63919	+	4.39484i	0.269481	+	0.722508i	0.999247	+	0.0388099i	$0.0123567\pi$
$37$	1.63919	+	4.39484i	0.269481	+	0.722508i	−0.729765	+	0.683698i	$0.760371\pi$
$38$	1.98744	+	9.13611i	0.322405	+	1.48207i
$39$	0.601712	+	2.04924i	0.0963510	+	0.328141i
$40$	−7.66305	−	9.68274i	−1.21163	−	1.53098i
$41$	−1.00131	−	2.19257i	−0.156379	−	0.342422i	0.815185	−	0.579201i	$-0.196635\pi$
$41$	−1.00131	−	2.19257i	−0.156379	−	0.342422i	−0.971563	+	0.236779i	$0.923908\pi$
$42$	17.6009	+	13.1759i	2.71588	+	2.03308i
$43$	2.90485	+	0.631911i	0.442985	+	0.0963655i	0.428525	−	0.903530i	$-0.359033\pi$
$43$	2.90485	+	0.631911i	0.442985	+	0.0963655i	0.0144601	+	0.999895i	$0.495397\pi$
$44$	4.32676	−	4.99335i	0.652284	−	0.752775i
$45$	−0.363663	−	13.5236i	−0.0542117	−	2.01598i
$46$	8.06495	−	8.82632i	1.18911	−	1.30137i
$47$	−2.24768	−	2.24768i	−0.327857	−	0.327857i	0.523914	−	0.851771i	$-0.324471\pi$
$47$	−2.24768	−	2.24768i	−0.327857	−	0.327857i	−0.851771	+	0.523914i	$0.824471\pi$
$48$	−1.14536	−	16.0143i	−0.165319	−	2.31146i
$49$	−0.861828	−	1.34103i	−0.123118	−	0.191576i
$50$	6.92294	−	10.3658i	0.979052	−	1.46595i
$51$	−4.86329	+	2.22099i	−0.680997	+	0.311001i
$52$	−2.39561	+	1.79333i	−0.332211	+	0.248690i
$53$	6.43181	+	3.51203i	0.883477	+	0.482415i	0.855862	−	0.517204i	$-0.173027\pi$
$53$	6.43181	+	3.51203i	0.883477	+	0.482415i	0.0276146	+	0.999619i	$0.491209\pi$
$54$	12.3674	−	19.2441i	1.68299	−	2.61879i
$55$	3.22627	+	1.36981i	0.435030	+	0.184705i
$56$	−4.56095	+	15.5332i	−0.609482	+	2.07571i
$57$	−11.2537	−	0.804883i	−1.49059	−	0.106609i
$58$	−7.86664	−	0.562633i	−1.03294	−	0.0738774i
$59$	−0.982871	+	3.34735i	−0.127959	+	0.435788i	−0.998404	−	0.0564778i	$-0.982013\pi$
$59$	−0.982871	+	3.34735i	−0.127959	+	0.435788i	0.870445	+	0.492266i	$0.163831\pi$
$60$	26.2907	−	10.6194i	3.39412	−	1.37096i
$61$	−2.23932	+	3.48445i	−0.286716	+	0.446138i	−0.954498	−	0.298219i	$-0.903607\pi$
$61$	−2.23932	+	3.48445i	−0.286716	+	0.446138i	0.667782	+	0.744357i	$0.267244\pi$
$62$	−21.5399	−	11.7617i	−2.73557	−	1.49374i
$63$	−14.1987	+	10.6290i	−1.78887	+	1.33913i
$64$	−4.58332	+	2.09313i	−0.572915	+	0.261641i
$65$	−1.29596	−	0.916837i	−0.160744	−	0.113720i
$66$	6.35574	+	9.88973i	0.782338	+	1.21734i
$67$	0.180035	+	2.51722i	0.0219948	+	0.307527i	0.996526	+	0.0832771i	$0.0265387\pi$
$67$	0.180035	+	2.51722i	0.0219948	+	0.307527i	−0.974532	+	0.224250i	$0.928007\pi$
$68$	−5.29701	−	5.29701i	−0.642356	−	0.642356i
$69$	7.47755	+	12.3385i	0.900191	+	1.48538i
$70$	−16.3362	+	0.439297i	−1.95255	+	0.0525060i
$71$	10.3652	−	11.9621i	1.23013	−	1.41964i	0.355622	−	0.934630i	$-0.384269\pi$
$71$	10.3652	−	11.9621i	1.23013	−	1.41964i	0.874507	−	0.485014i	$-0.161185\pi$
$72$	32.6470	+	7.10192i	3.84748	+	0.836969i
$73$	4.07004	+	3.04679i	0.476362	+	0.356600i	0.810320	−	0.585988i	$-0.199293\pi$
$73$	4.07004	+	3.04679i	0.476362	+	0.356600i	−0.333958	+	0.942588i	$0.608384\pi$
$74$	−4.85773	−	10.6369i	−0.564700	−	1.23652i
$75$	9.64829	+	11.5397i	1.11409	+	1.33249i
$76$	−4.45372	−	15.1680i	−0.510876	−	1.73988i
$77$	−0.976782	−	4.49020i	−0.111315	−	0.511705i
$78$	−1.86071	−	4.98875i	−0.210684	−	0.564865i
$79$	−4.84738	−	1.42332i	−0.545373	−	0.160136i	−0.00257124	−	0.999997i	$-0.500818\pi$
$79$	−4.84738	−	1.42332i	−0.545373	−	0.160136i	−0.542802	+	0.839861i	$0.682637\pi$
$80$	8.05449	+	8.80552i	0.900520	+	0.984487i
$81$	6.19088	+	7.14465i	0.687875	+	0.793851i
$82$	2.87987	+	5.27409i	0.318029	+	0.582426i
$83$	−15.8841	+	5.92447i	−1.74351	+	0.650295i	−0.999834	−	0.0182458i	$-0.994192\pi$
$83$	−15.8841	+	5.92447i	−1.74351	+	0.650295i	−0.743675	+	0.668541i	$0.766919\pi$
$84$	−31.2725	−	20.0976i	−3.41211	−	2.19283i
$85$	1.81007	−	3.53779i	0.196329	−	0.383727i
$86$	−7.33575	−	1.05472i	−0.791034	−	0.113734i
$87$	3.32585	−	8.91696i	0.356569	−	0.955999i
$88$	−5.18743	+	6.92959i	−0.552981	+	0.738697i
$89$	−7.01782	+	4.51008i	−0.743887	+	0.478067i	−0.856872	−	0.515529i	$-0.827595\pi$
$89$	−7.01782	+	4.51008i	−0.743887	+	0.478067i	0.112985	+	0.993597i	$0.463959\pi$
$90$	3.30947	+	33.5640i	0.348849	+	3.53795i
$91$			2.08125i			0.218174i
$92$	−12.5366	+	15.8580i	−1.30703	+	1.65331i
$93$	20.9410	−	20.9410i	2.17148	−	2.17148i
$94$	5.98895	+	5.18946i	0.617713	+	0.535252i
$95$	6.93045	−	4.72190i	0.711049	−	0.484456i
$96$	0.967737	+	6.73076i	0.0987692	+	0.686955i
$97$	6.12895	+	2.28598i	0.622301	+	0.232106i	0.640782	−	0.767723i	$-0.278610\pi$
$97$	6.12895	+	2.28598i	0.622301	+	0.232106i	−0.0184812	+	0.999829i	$0.505883\pi$
$98$	2.38157	+	3.18141i	0.240575	+	0.321371i
$99$	−9.09940	+	2.67182i	−0.914524	+	0.268528i
$100$	−10.4250	+	18.3166i	−1.04250	+	1.83166i
$101$	−3.66168	+	8.01796i	−0.364351	+	0.797817i	0.635322	+	0.772247i	$0.280867\pi$
$101$	−3.66168	+	8.01796i	−0.364351	+	0.797817i	−0.999673	+	0.0255696i	$0.991860\pi$
$102$	11.6984	−	6.38778i	1.15831	−	0.632485i
$103$	−0.835856	+	11.6868i	−0.0823593	+	1.15153i	0.773316	+	0.634021i	$0.218597\pi$
$103$	−0.835856	+	11.6868i	−0.0823593	+	1.15153i	−0.855675	+	0.517513i	$0.826858\pi$
$104$	2.96292	−	2.56739i	0.290538	−	0.251753i
$105$	5.04520	−	19.0639i	0.492361	−	1.86045i
$106$	−16.6183	−	7.58934i	−1.61411	−	0.737142i
$107$	1.39070	−	0.302529i	0.134444	−	0.0292465i	−0.144840	−	0.989455i	$-0.546267\pi$
$107$	1.39070	−	0.302529i	0.134444	−	0.0292465i	0.279284	+	0.960209i	$0.409903\pi$
$108$	−18.5360	+	33.9462i	−1.78363	+	3.26647i
$109$	1.18443	−	8.23788i	0.113448	−	0.789045i	−0.851075	−	0.525044i	$-0.824049\pi$
$109$	1.18443	−	8.23788i	0.113448	−	0.789045i	0.964522	−	0.264001i	$-0.0850422\pi$
$110$	−8.26625	−	2.83245i	−0.788156	−	0.270064i
$111$	13.9673	−	2.00819i	1.32571	−	0.190609i
$112$	3.32568	−	15.2879i	0.314247	−	1.44457i
$113$	11.4736	−	0.820608i	1.07935	−	0.0771963i	0.479677	−	0.877445i	$-0.340754\pi$
$113$	11.4736	−	0.820608i	1.07935	−	0.0771963i	0.599668	+	0.800249i	$0.295299\pi$
$114$	28.1274			2.63437
$115$	−10.0496	−	3.74227i	−0.937134	−	0.348968i
$116$	13.3346			1.23809
$117$	4.28431	−	0.306420i	0.396085	−	0.0283285i
$118$	1.84874	−	8.49852i	0.170190	−	0.782352i
$119$	−5.15696	+	0.741459i	−0.472738	+	0.0679695i
$120$	−33.3636	+	16.3344i	−3.04567	+	1.49112i
$121$	−1.21579	+	8.45601i	−0.110526	+	0.768728i
$122$	4.94872	−	9.06290i	0.448036	−	0.820516i
$123$	−7.08558	+	1.54137i	−0.638885	+	0.138981i
$124$	37.7449	+	17.2375i	3.38959	+	1.54797i
$125$	−10.9464	−	2.27536i	−0.979072	−	0.203514i
$126$	33.4170	−	28.9560i	2.97702	−	2.57960i
$127$	−0.768413	+	10.7438i	−0.0681856	+	0.953359i	0.842085	+	0.539345i	$0.181328\pi$
$127$	−0.768413	+	10.7438i	−0.0681856	+	0.953359i	−0.910270	+	0.414014i	$0.864126\pi$
$128$	14.9926	−	8.18660i	1.32518	−	0.723600i
$129$	3.71512	−	8.13498i	0.327098	−	0.716245i
$130$	3.38567	+	2.04938i	0.296943	+	0.179742i
$131$	9.01533	−	2.64714i	0.787673	−	0.231282i	0.136931	−	0.990581i	$-0.456276\pi$
$131$	9.01533	−	2.64714i	0.787673	−	0.231282i	0.650742	+	0.759299i	$0.274458\pi$
$132$	−11.9116	−	15.9120i	−1.03677	−	1.38496i
$133$	−10.3013	−	3.84220i	−0.893239	−	0.333161i
$134$	−0.895371	−	6.22744i	−0.0773483	−	0.537969i
$135$	−20.1589	−	3.82086i	−1.73501	−	0.328848i
$136$	7.41709	+	6.42694i	0.636010	+	0.551106i
$137$	1.57826	−	1.57826i	0.134840	−	0.134840i	−0.636465	−	0.771305i	$-0.719604\pi$
$137$	1.57826	−	1.57826i	0.134840	−	0.134840i	0.771305	+	0.636465i	$0.219604\pi$
$138$	−20.7885	−	29.3518i	−1.76964	−	2.49859i
$139$		−	5.66770i		−	0.480728i	−0.970683	−	0.240364i	$-0.922733\pi$
$139$		−	5.66770i		−	0.480728i	0.970683	−	0.240364i	$-0.0772668\pi$
$140$	27.4974	−	2.71130i	2.32396	−	0.229147i
$141$	−8.04458	+	5.16994i	−0.677476	+	0.435387i
$142$	−23.6474	+	31.5892i	−1.98444	+	2.65091i
$143$	−0.388895	+	1.04267i	−0.0325210	+	0.0871922i
$144$	−31.9603	−	4.59519i	−2.66335	−	0.382933i
$145$	2.17468	+	6.73132i	0.180597	+	0.559006i
$146$	−10.6627	−	6.85248i	−0.882449	−	0.567116i
$147$	−4.49320	+	1.67588i	−0.370593	+	0.138224i
$148$	9.47538	+	17.3529i	0.778871	+	1.42640i
$149$	−9.52539	−	10.9929i	−0.780350	−	0.900572i	0.216784	−	0.976220i	$-0.430443\pi$
$149$	−9.52539	−	10.9929i	−0.780350	−	0.900572i	−0.997135	+	0.0756472i	$0.975898\pi$
$150$	−26.0443	−	26.9793i	−2.12651	−	2.20285i
$151$	−15.2478	−	4.47717i	−1.24085	−	0.364347i	−0.405516	−	0.914088i	$-0.632908\pi$
$151$	−15.2478	−	4.47717i	−1.24085	−	0.364347i	−0.835335	+	0.549741i	$0.814726\pi$
$152$	7.23766	+	19.4049i	0.587052	+	1.57395i
$153$	2.28557	+	10.5066i	0.184777	+	0.849408i
$154$	3.22750	+	10.9919i	0.260080	+	0.885750i
$155$	−2.54587	+	21.8648i	−0.204489	+	1.75622i
$156$	3.73974	+	8.18890i	0.299419	+	0.655637i
$157$	−14.9782	−	11.2126i	−1.19539	−	0.894860i	−0.199024	−	0.979995i	$-0.563777\pi$
$157$	−14.9782	−	11.2126i	−1.19539	−	0.894860i	−0.996369	+	0.0851346i	$0.972868\pi$
$158$	12.3069	+	2.67721i	0.979087	+	0.212987i
$159$	14.4369	−	16.6611i	1.14492	−	1.32131i
$160$	−3.66874	−	3.47660i	−0.290039	−	0.274849i
$161$	3.60410	+	13.5895i	0.284043	+	1.07100i
$162$	−16.6653	−	16.6653i	−1.30935	−	1.30935i
$163$	−0.421053	−	5.88708i	−0.0329794	−	0.461112i	−0.986930	−	0.161149i	$-0.948480\pi$
$163$	−0.421053	−	5.88708i	−0.0329794	−	0.461112i	0.953951	−	0.299963i	$-0.0969744\pi$
$164$	−5.49294	−	8.54718i	−0.428927	−	0.667423i
$165$	6.08978	−	8.60797i	0.474089	−	0.670129i
$166$	38.4447	−	17.5571i	2.98389	−	1.36270i
$167$	19.9743	−	14.9525i	1.54565	−	1.15706i	0.616510	−	0.787347i	$-0.288546\pi$
$167$	19.9743	−	14.9525i	1.54565	−	1.15706i	0.929145	−	0.369716i	$-0.120545\pi$
$168$	42.7446	+	23.3403i	3.29782	+	1.80074i
$169$	−6.75584	+	10.5123i	−0.519680	+	0.808637i
$170$	−3.87182	+	9.11919i	−0.296955	+	0.699410i
$171$	−6.39263	+	21.7713i	−0.488856	+	1.66489i
$172$	12.4987	+	0.893922i	0.953014	+	0.0681609i
$173$	0.529367	+	0.0378610i	0.0402470	+	0.00287852i	0.0914482	−	0.995810i	$-0.470850\pi$
$173$	0.529367	+	0.0378610i	0.0402470	+	0.00287852i	−0.0512012	+	0.998688i	$0.516305\pi$
$174$	−6.68439	+	22.7649i	−0.506742	+	1.72581i
$175$	5.85307	+	13.4385i	0.442451	+	1.01586i
$176$	4.52275	−	7.03754i	0.340915	−	0.530474i
$177$	9.21134	+	5.02977i	0.692366	+	0.378061i
$178$	16.6488	−	12.4631i	1.24788	−	0.934152i
$179$	−12.6119	+	5.75968i	−0.942661	+	0.430499i	−0.826630	−	0.562746i	$-0.809745\pi$
$179$	−12.6119	+	5.75968i	−0.942661	+	0.430499i	−0.116032	+	0.993245i	$0.537017\pi$
$180$	−9.62972	−	56.2051i	−0.717757	−	4.18928i
$181$	−10.1477	−	15.7901i	−0.754271	−	1.17367i	−0.979907	−	0.199457i	$-0.936082\pi$
$181$	−10.1477	−	15.7901i	−0.754271	−	1.17367i	0.225635	−	0.974212i	$-0.427554\pi$
$182$	−0.370149	−	5.17535i	−0.0274372	−	0.383623i
$183$	8.81089	+	8.81089i	0.651320	+	0.651320i
$184$	14.9004	−	21.8946i	1.09847	−	1.61409i
$185$	−7.21442	+	7.61315i	−0.530415	+	0.559730i
$186$	−48.3487	+	55.7974i	−3.54510	+	4.09126i
$187$	−2.72209	−	0.592155i	−0.199059	−	0.0433026i
$188$	−10.7261	−	8.02944i	−0.782279	−	0.585607i
$189$	11.1745	+	24.4688i	0.812826	+	1.77984i
$190$	−16.3939	+	12.9743i	−1.18934	+	0.941256i
$191$	4.43772	+	15.1135i	0.321102	+	1.09357i	0.949000	+	0.315277i	$0.102098\pi$
$191$	4.43772	+	15.1135i	0.321102	+	1.09357i	−0.627897	+	0.778296i	$0.716084\pi$
$192$	3.22206	+	14.8116i	0.232532	+	1.06893i
$193$	−1.98795	−	5.32991i	−0.143096	−	0.383655i	0.845555	−	0.533889i	$-0.179270\pi$
$193$	−1.98795	−	5.32991i	−0.143096	−	0.383655i	−0.988650	+	0.150234i	$0.951997\pi$
$194$	−15.6472	−	4.59442i	−1.12340	−	0.329860i
$195$	−3.52386	+	3.22330i	−0.252349	+	0.230826i
$196$	−4.40016	−	5.07806i	−0.314297	−	0.362719i
$197$	−5.03777	−	9.22599i	−0.358926	−	0.657325i	0.634356	−	0.773041i	$-0.281265\pi$
$197$	−5.03777	−	9.22599i	−0.358926	−	0.657325i	−0.993282	+	0.115716i	$0.963084\pi$
$198$	22.1519	−	8.26224i	1.57427	−	0.587172i
$199$	−8.01818	−	5.15297i	−0.568394	−	0.365284i	0.224659	−	0.974437i	$-0.427873\pi$
$199$	−8.01818	−	5.15297i	−0.568394	−	0.365284i	−0.793053	+	0.609153i	$0.791510\pi$
$200$	11.9112	−	24.9101i	0.842249	−	1.76141i
$201$	7.51473	+	1.08045i	0.530048	+	0.0762094i
$202$	7.67936	−	20.5892i	0.540318	−	1.44865i
$203$	5.55778	−	7.42432i	0.390079	−	0.521085i
$204$	−18.9583	+	12.1838i	−1.32735	+	0.853035i
$205$	3.41880	−	4.16675i	0.238779	−	0.291018i
$206$		−	29.2097i		−	2.03514i
$207$	27.4438	−	9.41992i	1.90747	−	0.654730i
$208$	−2.67915	+	2.67915i	−0.185766	+	0.185766i
$209$	−4.44284	−	3.84974i	−0.307318	−	0.266292i
$210$	−9.15517	+	48.3028i	−0.631767	+	3.33321i
$211$	−0.0450656	−	0.313438i	−0.00310245	−	0.0215780i	0.988211	−	0.153095i	$-0.0489242\pi$
$211$	−0.0450656	−	0.313438i	−0.00310245	−	0.0215780i	−0.991314	+	0.131517i	$0.958015\pi$
$212$	28.9416	+	10.7946i	1.98771	+	0.741379i
$213$	−28.5355	−	38.1190i	−1.95522	−	2.61187i
$214$	−3.40440	+	0.999621i	−0.232720	+	0.0683327i
$215$	1.58709	+	6.45510i	0.108239	+	0.440234i
$216$	21.0498	−	46.0925i	1.43225	−	3.13620i
$217$	25.3291	−	13.8307i	1.71945	−	0.938892i
$218$	−1.48017	+	20.6954i	−0.100250	+	1.40167i
$219$	11.5590	−	10.0159i	0.781085	−	0.676814i
$220$	14.2823	+	3.77976i	0.962915	+	0.254832i
$221$	1.14770	+	0.524135i	0.0772024	+	0.0352572i
$222$	−34.3747	+	7.47775i	−2.30708	+	0.501874i
$223$	6.33408	−	11.6000i	0.424162	−	0.776794i	−0.574982	−	0.818166i	$-0.694991\pi$
$223$	6.33408	−	11.6000i	0.424162	−	0.776794i	0.999144	+	0.0413719i	$0.0131729\pi$
$224$	−0.943039	+	6.55898i	−0.0630094	+	0.438240i
$225$	26.8019	−	14.0273i	1.78679	−	0.935151i
$226$	−28.3850	+	4.08115i	−1.88814	+	0.271474i
$227$	0.358874	−	1.64972i	0.0238193	−	0.109496i	−0.963702	−	0.266979i	$-0.913975\pi$
$227$	0.358874	−	1.64972i	0.0238193	−	0.109496i	0.987522	+	0.157484i	$0.0503381\pi$
$228$	−47.4357	+	3.39267i	−3.14150	+	0.224685i
$229$	−4.39298			−0.290297			−0.145148	−	0.989410i	$-0.546366\pi$
$229$	−4.39298			−0.290297			−0.145148	+	0.989410i	$0.546366\pi$
$230$	25.6556	+	7.51842i	1.69168	+	0.495750i
$231$	−13.8240			−0.909551
$232$	−17.4254	+	1.24629i	−1.14403	+	0.0818230i
$233$	−0.918219	+	4.22099i	−0.0601545	+	0.276526i	−0.997393	−	0.0721637i	$-0.977010\pi$
$233$	−0.918219	+	4.22099i	−0.0601545	+	0.276526i	0.937238	+	0.348690i	$0.113373\pi$
$234$	−10.5991	+	1.52392i	−0.692887	+	0.0996220i
$235$	2.30400	−	6.72400i	0.150296	−	0.438625i
$236$	−2.09275	+	14.5554i	−0.136227	+	0.947476i
$237$	−7.28374	+	13.3392i	−0.473130	+	0.866472i
$238$	12.6917	−	2.76092i	0.822683	−	0.178964i
$239$	19.7199	+	9.00576i	1.27557	+	0.582534i	0.933984	−	0.357316i	$-0.116308\pi$
$239$	19.7199	+	9.00576i	1.27557	+	0.582534i	0.341588	+	0.939850i	$0.389035\pi$
$240$	31.0352	−	18.0461i	2.00332	−	1.16487i
$241$	3.39135	−	2.93862i	0.218456	−	0.189293i	−0.538757	−	0.842461i	$-0.681106\pi$
$241$	3.39135	−	2.93862i	0.218456	−	0.189293i	0.757213	+	0.653168i	$0.226561\pi$
$242$	1.51936	−	21.2434i	0.0976682	−	1.36558i
$243$	0.800892	−	0.437320i	0.0513772	−	0.0280541i
$244$	−7.25267	+	15.8811i	−0.464304	+	1.01668i
$245$	1.84580	−	3.04935i	0.117924	−	0.194816i
$246$	17.3453	−	5.09303i	1.10589	−	0.324720i
$247$	1.59562	+	2.13150i	0.101527	+	0.135624i
$248$	−50.9353	−	18.9979i	−3.23439	−	1.20637i
$249$	7.25813	+	50.4814i	0.459965	+	3.19913i
$250$	27.6245	+	3.71124i	1.74713	+	0.234719i
$251$	−9.94584	−	8.61812i	−0.627776	−	0.543971i	0.281819	−	0.959468i	$-0.409062\pi$
$251$	−9.94584	−	8.61812i	−0.627776	−	0.543971i	−0.909595	+	0.415497i	$0.863608\pi$
$252$	−52.8638	+	52.8638i	−3.33010	+	3.33010i
$253$	−0.733698	+	7.48154i	−0.0461272	+	0.470361i
$254$		−	26.8529i		−	1.68490i
$255$	−9.24218	−	7.58316i	−0.578767	−	0.474876i
$256$	−27.3481	+	17.5755i	−1.70925	+	1.09847i
$257$	−0.679173	+	0.907268i	−0.0423656	+	0.0565938i	−0.821224	−	0.570606i	$-0.806708\pi$
$257$	−0.679173	+	0.907268i	−0.0423656	+	0.0565938i	0.778858	+	0.627200i	$0.215799\pi$
$258$	−7.79144	+	20.8897i	−0.485074	+	1.30053i
$259$	13.6108	+	1.95694i	0.845734	+	0.121598i
$260$	−5.95699	−	3.04782i	−0.369437	−	0.189018i
$261$	−16.1015	−	10.3478i	−0.996655	−	0.640511i
$262$	−21.9473	+	8.18591i	−1.35591	+	0.505727i
$263$	−4.12825	−	7.56032i	−0.254559	−	0.466189i	0.718881	−	0.695133i	$-0.244655\pi$
$263$	−4.12825	−	7.56032i	−0.254559	−	0.466189i	−0.973440	+	0.228944i	$0.926473\pi$
$264$	17.0530	+	19.6802i	1.04954	+	1.21123i
$265$	−0.729204	+	16.3701i	−0.0447946	+	1.00561i
$266$	26.2992	+	7.72215i	1.61251	+	0.473476i
$267$	8.77012	+	23.5136i	0.536722	+	1.43901i
$268$	2.26115	+	10.3943i	0.138122	+	0.634935i
$269$	4.65407	+	15.8503i	0.283764	+	0.966410i	0.970821	+	0.239806i	$0.0770840\pi$
$269$	4.65407	+	15.8503i	0.283764	+	0.966410i	−0.687057	+	0.726603i	$0.741098\pi$
$270$	50.8079	+	5.91593i	3.09207	+	0.360032i
$271$	7.60121	+	16.6443i	0.461741	+	1.01107i	0.987087	+	0.160183i	$0.0512083\pi$
$271$	7.60121	+	16.6443i	0.461741	+	1.01107i	−0.525347	+	0.850888i	$0.676064\pi$
$272$	−7.59293	−	5.68399i	−0.460389	−	0.344643i
$273$	6.11802	+	1.33089i	0.370280	+	0.0805494i
$274$	−3.64390	+	4.20528i	−0.220136	+	0.254051i
$275$	0.421209	+	7.82614i	0.0253999	+	0.471934i
$276$	38.5994	+	46.9932i	2.32341	+	2.82866i
$277$	−0.460848	−	0.460848i	−0.0276897	−	0.0276897i	0.693126	−	0.720816i	$-0.256233\pi$
$277$	−0.460848	−	0.460848i	−0.0276897	−	0.0276897i	−0.720816	+	0.693126i	$0.756233\pi$
$278$	1.00800	+	14.0936i	0.0604556	+	0.845280i
$279$	−32.2002	−	50.1045i	−1.92777	−	2.99968i
$280$	−35.6796	+	6.11305i	−2.13227	+	0.365325i
$281$	−24.4948	+	11.1864i	−1.46123	+	0.667323i	−0.978083	−	0.208214i	$-0.933235\pi$
$281$	−24.4948	+	11.1864i	−1.46123	+	0.667323i	−0.483151	+	0.875537i	$0.660508\pi$
$282$	19.0847	−	14.2866i	1.13647	−	0.850754i
$283$	−24.7600	−	13.5200i	−1.47183	−	0.803681i	−0.474757	−	0.880117i	$-0.657464\pi$
$283$	−24.7600	−	13.5200i	−1.47183	−	0.803681i	−0.997075	+	0.0764359i	$0.975646\pi$
$284$	36.0701	−	56.1262i	2.14037	−	3.33048i
$285$	−9.44865	−	23.3922i	−0.559690	−	1.38563i
$286$	0.781611	−	2.66192i	0.0462176	−	0.157403i
$287$	−7.04822	−	0.504099i	−0.416043	−	0.0297560i
$288$	13.6407	+	0.975602i	0.803786	+	0.0574879i
$289$	3.89961	−	13.2809i	0.229389	−	0.781227i
$290$	−6.60484	−	16.3517i	−0.387849	−	0.960207i
$291$	10.6391	−	16.5548i	0.623677	−	0.970460i
$292$	18.8087	+	10.2703i	1.10070	+	0.601026i
$293$	−7.26828	+	5.44097i	−0.424618	+	0.317865i	−0.790127	−	0.612943i	$-0.789986\pi$
$293$	−7.26828	+	5.44097i	−0.424618	+	0.317865i	0.365510	+	0.930808i	$0.380895\pi$
$294$	10.8750	−	4.96644i	0.634243	−	0.289649i
$295$	−7.68886	+	1.31734i	−0.447663	+	0.0766988i
$296$	−14.0041	−	21.7908i	−0.813970	−	1.26656i
$297$	1.02608	+	14.3464i	0.0595391	+	0.832465i
$298$	25.6415	+	25.6415i	1.48537	+	1.48537i
$299$	1.04499	−	3.24044i	0.0604334	−	0.187400i
$300$	47.1769	+	42.3581i	2.72376	+	2.44554i
$301$	5.70706	−	6.58629i	0.328949	−	0.379628i
$302$	38.7124	+	8.42137i	2.22765	+	0.484596i
$303$	21.2280	+	15.8911i	1.21952	+	0.912919i
$304$	−8.31472	−	18.2067i	−0.476882	−	1.04423i
$305$	−9.19958	−	1.07117i	−0.526767	−	0.0613352i
$306$	−7.55203	−	25.7198i	−0.431721	−	1.47031i
$307$	−0.956576	−	4.39731i	−0.0545947	−	0.250968i	0.941759	−	0.336289i	$-0.109172\pi$
$307$	−0.956576	−	4.39731i	−0.0545947	−	0.250968i	−0.996353	+	0.0853214i	$0.972808\pi$
$308$	−6.76887	−	18.1481i	−0.385692	−	1.03408i
$309$	33.8199	+	9.93043i	1.92395	+	0.564922i
$310$	2.44208	−	54.8230i	0.138701	−	3.11374i
$311$	−8.58705	−	9.90999i	−0.486927	−	0.561944i	0.458115	−	0.888893i	$-0.348525\pi$
$311$	−8.58705	−	9.90999i	−0.486927	−	0.561944i	−0.945042	+	0.326949i	$0.893979\pi$
$312$	−5.65237	−	10.3515i	−0.320003	−	0.586041i
$313$	0.549823	−	0.205073i	0.0310778	−	0.0115914i	−0.333877	−	0.942617i	$-0.608357\pi$
$313$	0.549823	−	0.205073i	0.0310778	−	0.0115914i	0.364955	+	0.931025i	$0.381084\pi$
$314$	39.2399	+	25.2180i	2.21444	+	1.42313i
$315$	−35.3069	−	18.0643i	−1.98932	−	1.01781i
$316$	−21.0781	−	3.03057i	−1.18573	−	0.170483i
$317$	−5.39394	+	14.4617i	−0.302954	+	0.812251i	0.692879	+	0.721054i	$0.256342\pi$
$317$	−5.39394	+	14.4617i	−0.302954	+	0.812251i	−0.995833	+	0.0911970i	$0.970931\pi$
$318$	−32.9365	+	43.9980i	−1.84699	+	2.46728i
$319$	4.17163	−	2.68094i	0.233566	−	0.150104i
$320$	−8.71011	−	7.14661i	−0.486910	−	0.399507i
$321$		−	4.28156i		−	0.238973i
$322$	−11.3791	−	33.1515i	−0.634130	−	1.84746i
$323$	−4.71302	+	4.71302i	−0.262240	+	0.262240i
$324$	30.1155	+	26.0952i	1.67308	+	1.44973i
$325$	0.567044	−	3.50414i	0.0314539	−	0.194374i
$326$	2.09403	+	14.5643i	0.115978	+	0.806641i
$327$	−23.4586	−	8.74961i	−1.29726	−	0.483854i
$328$	7.97690	+	10.6559i	0.440451	+	0.588373i
$329$	−8.94109	+	2.62534i	−0.492938	+	0.144740i
$330$	−13.6123	+	22.4881i	−0.749331	+	1.23793i
$331$	10.9076	−	23.8843i	0.599535	−	1.31280i	−0.329971	−	0.943991i	$-0.607039\pi$
$331$	10.9076	−	23.8843i	0.599535	−	1.31280i	0.929506	−	0.368808i	$-0.120234\pi$
$332$	−62.7178	+	34.2465i	−3.44209	+	1.87952i
$333$	2.02451	−	28.3064i	0.110943	−	1.55118i
$334$	−47.0099	+	40.7343i	−2.57227	+	2.22888i
$335$	−4.87830	+	2.83658i	−0.266530	+	0.154979i
$336$	−42.8136	−	19.5523i	−2.33567	−	1.06667i
$337$	−23.3979	+	5.08990i	−1.27456	+	0.277265i	−0.798419	−	0.602102i	$-0.794330\pi$
$337$	−23.3979	+	5.08990i	−1.27456	+	0.277265i	−0.476146	+	0.879366i	$0.657966\pi$
$338$	14.9299	−	27.3420i	0.812077	−	1.48721i
$339$	4.92476	−	34.2525i	0.267476	−	1.86034i
$340$	5.42973	−	15.8462i	0.294469	−	0.859379i
$341$	15.2738	−	2.19604i	0.827122	−	0.118922i
$342$	12.0243	−	55.2747i	0.650198	−	2.98891i
$343$	15.8074	−	1.13057i	0.853521	−	0.0610450i
$344$	−16.4165			−0.885120
$345$	−17.4272	+	27.1488i	−0.938249	+	1.46164i
$346$	−1.32309			−0.0711296
$347$	−12.2902	+	0.879009i	−0.659770	+	0.0471877i	−0.397210	−	0.917728i	$-0.630021\pi$
$347$	−12.2902	+	0.879009i	−0.659770	+	0.0471877i	−0.262560	+	0.964916i	$0.584567\pi$
$348$	8.52710	−	39.1984i	0.457100	−	2.10126i
$349$	−5.59225	+	0.804044i	−0.299346	+	0.0430395i	−0.290351	−	0.956920i	$-0.593772\pi$
$349$	−5.59225	+	0.804044i	−0.299346	+	0.0430395i	−0.00899467	+	0.999960i	$0.502863\pi$
$350$	−16.9446	−	32.3760i	−0.905729	−	1.73057i
$351$	0.927088	−	6.44804i	0.0494843	−	0.344171i
$352$	−1.69803	+	3.10972i	−0.0905055	+	0.165749i
$353$	0.672453	−	0.146283i	0.0357911	−	0.00778587i	−0.194634	−	0.980876i	$-0.562352\pi$
$353$	0.672453	−	0.146283i	0.0357911	−	0.00778587i	0.230425	+	0.973090i	$0.425988\pi$
$354$	−23.8000	−	10.8691i	−1.26496	−	0.577686i
$355$	34.2150	+	9.05485i	1.81594	+	0.480582i
$356$	−26.5743	+	23.0267i	−1.40843	+	1.22041i
$357$	−1.11813	+	15.6335i	−0.0591778	+	0.827413i
$358$	30.3373	−	16.5654i	1.60337	−	0.875508i
$359$	−1.48284	+	3.24697i	−0.0782613	+	0.171368i	−0.944718	−	0.327884i	$-0.893665\pi$
$359$	−1.48284	+	3.24697i	−0.0782613	+	0.171368i	0.866457	+	0.499252i	$0.166392\pi$
$360$	17.8370	+	72.5476i	0.940092	+	3.82360i
$361$	4.73464	−	1.39021i	0.249191	−	0.0731692i
$362$	28.0421	+	37.4598i	1.47386	+	1.96885i
$363$	24.0798	+	8.98129i	1.26386	+	0.471396i
$364$	1.24848	+	8.68338i	0.0654382	+	0.455133i
$365$	−2.11704	+	11.1696i	−0.110811	+	0.584641i
$366$	−23.4767	−	20.3427i	−1.22715	−	1.06333i
$367$	26.3183	−	26.3183i	1.37380	−	1.37380i	0.519075	−	0.854729i	$-0.326276\pi$
$367$	26.3183	−	26.3183i	1.37380	−	1.37380i	0.854729	−	0.519075i	$-0.173724\pi$
$368$	−12.8540	+	22.1330i	−0.670062	+	1.15376i
$369$			14.5832i			0.759171i
$370$	16.5858	−	20.2144i	0.862256	−	1.05090i
$371$	18.0727	−	11.6146i	0.938290	−	0.603003i
$372$	74.8080	−	99.9318i	3.87862	−	5.18122i
$373$	−8.84696	+	23.7196i	−0.458078	+	1.22816i	0.478621	+	0.878021i	$0.341137\pi$
$373$	−8.84696	+	23.7196i	−0.458078	+	1.22816i	−0.936700	+	0.350134i	$0.886136\pi$
$374$	6.87423	+	0.988365i	0.355458	+	0.0511071i
$375$	−13.6885	+	30.7228i	−0.706871	+	1.58652i
$376$	14.7671	+	9.49021i	0.761553	+	0.489420i
$377$	−2.10433	+	0.784873i	−0.108378	+	0.0404230i
$378$	−32.1390	−	58.8581i	−1.65305	−	3.02734i
$379$	17.8237	+	20.5697i	0.915543	+	1.05659i	0.998198	+	0.0600143i	$0.0191146\pi$
$379$	17.8237	+	20.5697i	0.915543	+	1.05659i	−0.0826549	+	0.996578i	$0.526340\pi$
$380$	26.0827	−	23.8581i	1.33801	−	1.22389i
$381$	31.0911	+	9.12916i	1.59284	+	0.467701i
$382$	−13.7230	−	36.7928i	−0.702131	−	1.88249i
$383$	−3.69095	−	16.9670i	−0.188599	−	0.866974i	−0.970030	−	0.242984i	$-0.921874\pi$
$383$	−3.69095	−	16.9670i	−0.188599	−	0.866974i	0.781432	−	0.623991i	$-0.214490\pi$
$384$	−14.4780	−	49.3074i	−0.738825	−	2.51621i
$385$	8.05723	−	6.37659i	0.410634	−	0.324981i
$386$	5.89128	+	12.9001i	0.299858	+	0.656598i
$387$	−14.3983	−	10.7785i	−0.731908	−	0.547900i
$388$	26.9425	+	5.86098i	1.36780	+	0.297546i
$389$	−19.0671	+	22.0046i	−0.966742	+	1.11568i	0.0265037	+	0.999649i	$0.491563\pi$
$389$	−19.0671	+	22.0046i	−0.966742	+	1.11568i	−0.993246	+	0.116031i	$0.962983\pi$
$390$	8.18936	−	8.64198i	0.414685	−	0.437603i
$391$	8.40152	+	1.43487i	0.424883	+	0.0725646i
$392$	6.22465	+	6.22465i	0.314392	+	0.314392i
$393$	−2.01649	−	28.1942i	−0.101718	−	1.42221i
$394$	14.1681	+	22.0459i	0.713777	+	1.11066i
$395$	−1.90768	−	11.1344i	−0.0959859	−	0.560234i
$396$	−36.3617	+	16.6059i	−1.82725	+	0.834475i
$397$	11.5208	−	8.62437i	0.578213	−	0.432845i	−0.269727	−	0.962937i	$-0.586934\pi$
$397$	11.5208	−	8.62437i	0.578213	−	0.432845i	0.847940	+	0.530092i	$0.177843\pi$
$398$	20.8549	+	11.3877i	1.04536	+	0.570811i
$399$	−17.8819	+	27.8248i	−0.895214	+	1.39298i
$400$	−9.76459	+	24.8337i	−0.488230	+	1.24168i
$401$	−2.87554	+	9.79318i	−0.143597	+	0.489048i	−0.999611	−	0.0279061i	$-0.991116\pi$
$401$	−2.87554	+	9.79318i	−0.143597	+	0.489048i	0.856013	+	0.516954i	$0.172934\pi$
$402$	−18.8787	−	1.35023i	−0.941585	−	0.0673435i
$403$	−6.97108	−	0.498582i	−0.347254	−	0.0248361i
$404$	−10.4675	+	35.6491i	−0.520778	+	1.77361i
$405$	−8.26147	+	19.4580i	−0.410516	+	0.966875i
$406$	−12.4999	+	19.4502i	−0.620359	+	0.965297i
$407$	6.45310	+	3.52366i	0.319868	+	0.174661i
$408$	23.6356	−	17.6934i	1.17014	−	0.875953i
$409$	35.4366	−	16.1833i	1.75222	−	0.800214i	0.764381	−	0.644765i	$-0.223045\pi$
$409$	35.4366	−	16.1833i	1.75222	−	0.800214i	0.987844	−	0.155449i	$-0.0496826\pi$
$410$	−7.76033	+	10.9693i	−0.383255	+	0.541736i
$411$	−3.63019	−	5.64869i	−0.179064	−	0.278629i
$412$	3.52322	+	49.2610i	0.173577	+	2.42692i
$413$	7.23176	+	7.23176i	0.355852	+	0.355852i
$414$	−66.5680	+	28.3050i	−3.27164	+	1.39111i
$415$	−27.5159	−	26.0748i	−1.35070	−	1.27996i
$416$	1.05088	−	1.21278i	0.0515236	−	0.0594614i
$417$	−16.6607	−	3.62432i	−0.815879	−	0.177484i
$418$	11.7325	+	8.78284i	0.573856	+	0.429583i
$419$	−9.71852	−	21.2806i	−0.474781	−	1.03962i	−0.983866	−	0.178908i	$-0.942743\pi$
$419$	−9.71852	−	21.2806i	−0.474781	−	1.03962i	0.509085	−	0.860716i	$-0.329984\pi$
$420$	9.61364	−	82.5651i	0.469098	−	4.02876i
$421$	−5.84604	−	19.9098i	−0.284919	−	0.970344i	−0.970248	−	0.242111i	$-0.922160\pi$
$421$	−5.84604	−	19.9098i	−0.284919	−	0.970344i	0.685330	−	0.728233i	$-0.259658\pi$
$422$	0.167808	+	0.771399i	0.00816875	+	0.0375511i
$423$	6.72073	+	18.0190i	0.326773	+	0.876113i
$424$	−38.8291	−	11.4013i	−1.88571	−	0.553694i
$425$	8.88464	+	0.156661i	0.430968	+	0.00759915i
$426$	77.7376	+	89.7140i	3.76640	+	4.34666i
$427$	5.81927	+	10.6572i	0.281614	+	0.515738i
$428$	5.62081	−	2.09645i	0.271692	−	0.101336i
$429$	2.81633	+	1.80995i	0.135974	+	0.0873851i
$430$	−5.09459	−	15.7694i	−0.245683	−	0.760467i
$431$	40.8403	+	5.87194i	1.96721	+	0.282842i	0.999530	+	0.0306435i	$0.00975566\pi$
$431$	40.8403	+	5.87194i	1.96721	+	0.282842i	0.967676	+	0.252198i	$0.0811534\pi$
$432$	−17.1135	+	45.8829i	−0.823371	+	2.20754i
$433$	−9.45665	+	12.6326i	−0.454458	+	0.607084i	−0.967991	−	0.250985i	$-0.919245\pi$
$433$	−9.45665	+	12.6326i	−0.454458	+	0.607084i	0.513533	+	0.858070i	$0.328336\pi$
$434$	−60.5251	+	38.8971i	−2.90530	+	1.86712i
$435$	21.1780	−	2.08819i	1.01541	−	0.100121i
$436$		−	35.0806i		−	1.68005i
$437$	14.1097	+	11.1545i	0.674959	+	0.533591i
$438$	−26.9620	+	26.9620i	−1.28829	+	1.28829i
$439$	−26.2311	−	22.7294i	−1.25194	−	1.08481i	−0.992900	−	0.118949i	$-0.962048\pi$
$439$	−26.2311	−	22.7294i	−1.25194	−	1.08481i	−0.259042	−	0.965866i	$-0.583407\pi$
$440$	−19.0171	−	3.60445i	−0.906606	−	0.171835i
$441$	1.37255	+	9.54627i	0.0653593	+	0.454584i
$442$	−2.94715	−	1.09923i	−0.140181	−	0.0522850i
$443$	−2.47538	−	3.30672i	−0.117609	−	0.157107i	0.737874	−	0.674939i	$-0.235830\pi$
$443$	−2.47538	−	3.30672i	−0.117609	−	0.157107i	−0.855482	+	0.517832i	$0.826739\pi$
$444$	57.0696	−	16.7571i	2.70840	−	0.795259i
$445$	−15.9577	−	9.65937i	−0.756469	−	0.457898i
$446$	−13.6877	+	29.9718i	−0.648129	+	1.41920i
$447$	−38.4058	+	20.9712i	−1.81653	+	0.991902i
$448$	−1.05376	+	14.7335i	−0.0497855	+	0.696093i
$449$	21.2939	−	18.4513i	1.00492	−	0.870771i	0.0132967	−	0.999912i	$-0.495767\pi$
$449$	21.2939	−	18.4513i	1.00492	−	0.870771i	0.991626	+	0.129141i	$0.0412220\pi$
$450$	−64.1523	+	39.6477i	−3.02417	+	1.86901i
$451$	−3.43684	−	1.56955i	−0.161834	−	0.0739073i
$452$	47.3779	−	10.3064i	2.22847	−	0.484774i
$453$	−22.9116	+	41.9594i	−1.07648	+	1.97143i
$454$	−0.598996	+	4.16611i	−0.0281123	+	0.195525i
$455$	−4.17976	+	2.04636i	−0.195950	+	0.0959348i
$456$	61.6708	−	8.86693i	2.88800	−	0.415232i
$457$	−7.43945	+	34.1986i	−0.348003	+	1.59974i	0.387267	+	0.921968i	$0.373419\pi$
$457$	−7.43945	+	34.1986i	−0.348003	+	1.59974i	−0.735270	+	0.677775i	$0.762944\pi$
$458$	10.9239	−	0.781289i	0.510438	−	0.0365073i
$459$	16.3074			0.761163
$460$	−44.1740	−	9.58499i	−2.05962	−	0.446903i
$461$	−28.9384			−1.34780			−0.673899	−	0.738824i	$-0.735382\pi$
$461$	−28.9384			−1.34780			−0.673899	+	0.738824i	$0.735382\pi$
$462$	34.3755	−	2.45859i	1.59929	−	0.114384i
$463$	−2.90752	+	13.3657i	−0.135124	+	0.621155i	0.858914	+	0.512120i	$0.171140\pi$
$463$	−2.90752	+	13.3657i	−0.135124	+	0.621155i	−0.994038	+	0.109035i	$0.965224\pi$
$464$	16.7116	−	2.40277i	0.775817	−	0.111546i
$465$	62.6456	+	21.4657i	2.90512	+	0.995448i
$466$	1.53260	−	10.6595i	0.0709962	−	0.493790i
$467$	8.27645	−	15.1572i	0.382988	−	0.701391i	−0.613076	−	0.790024i	$-0.710068\pi$
$467$	8.27645	−	15.1572i	0.382988	−	0.701391i	0.996064	+	0.0886332i	$0.0282499\pi$
$468$	17.6912	−	3.84848i	0.817776	−	0.177896i
$469$	6.72968	+	3.07334i	0.310748	+	0.141914i
$470$	−4.53340	+	17.1300i	−0.209110	+	0.790150i
$471$	−42.5385	+	36.8598i	−1.96007	+	1.69841i
$472$	1.37438	−	19.2163i	0.0632608	−	0.884502i
$473$	4.08982	−	2.23321i	0.188050	−	0.102683i
$474$	15.7398	−	34.4654i	0.722954	−	1.58305i
$475$	16.2972	+	9.27563i	0.747768	+	0.425595i
$476$	−21.0711	+	6.18703i	−0.965792	+	0.283582i
$477$	−26.5699	−	35.4933i	−1.21655	−	1.62513i
$478$	−50.6382	−	18.8871i	−2.31614	−	0.863875i
$479$	2.50569	+	17.4274i	0.114488	+	0.796280i	0.963462	+	0.267845i	$0.0863116\pi$
$479$	2.50569	+	17.4274i	0.114488	+	0.796280i	−0.848974	+	0.528434i	$0.822779\pi$
$480$	−12.5658	+	8.56143i	−0.573549	+	0.390774i
$481$	−2.51669	−	2.18072i	−0.114751	−	0.0994323i
$482$	−7.91049	+	7.91049i	−0.360313	+	0.360313i
$483$	42.2523	−	1.90452i	1.92255	−	0.0866588i
$484$			36.0095i			1.63679i
$485$	1.43529	+	14.5564i	0.0651731	+	0.660972i
$486$	−1.91377	+	1.22990i	−0.0868103	+	0.0557896i
$487$	−5.89394	+	7.87338i	−0.267080	+	0.356777i	−0.913952	−	0.405821i	$-0.866986\pi$
$487$	−5.89394	+	7.87338i	−0.267080	+	0.356777i	0.646873	+	0.762598i	$0.276076\pi$
$488$	7.99334	−	21.4310i	0.361841	−	0.970134i
$489$	−17.5749	−	2.52689i	−0.794764	−	0.114270i
$490$	−4.04755	+	7.91098i	−0.182850	+	0.357382i
$491$	−3.37283	−	2.16759i	−0.152214	−	0.0978218i	0.462317	−	0.886715i	$-0.347018\pi$
$491$	−3.37283	−	2.16759i	−0.152214	−	0.0978218i	−0.614531	+	0.788893i	$0.710655\pi$
$492$	−28.6378	+	10.6814i	−1.29109	+	0.481553i
$493$	−2.69446	−	4.93453i	−0.121352	−	0.222240i
$494$	−4.34685	−	5.01653i	−0.195574	−	0.225704i
$495$	−14.3127	−	15.6472i	−0.643307	−	0.703291i
$496$	50.4097	+	14.8016i	2.26346	+	0.664613i
$497$	−16.2156	−	43.4757i	−0.727369	−	1.95015i
$498$	−27.0266	−	124.239i	−1.21109	−	5.56729i
$499$	6.13443	+	20.8919i	0.274615	+	0.935252i	0.975134	+	0.221618i	$0.0711338\pi$
$499$	6.13443	+	20.8919i	0.274615	+	0.935252i	−0.700519	+	0.713634i	$0.747048\pi$
$500$	−47.0353	−	2.92684i	−2.10348	−	0.130892i
$501$	−31.1815	−	68.2779i	−1.39309	−	3.05043i
$502$	26.2646	+	19.6615i	1.17225	+	0.877534i
$503$	22.9956	+	5.00239i	1.02532	+	0.223046i	0.693622	−	0.720339i	$-0.256014\pi$
$503$	22.9956	+	5.00239i	1.02532	+	0.223046i	0.331702	+	0.943384i	$0.392377\pi$
$504$	64.1405	−	74.0220i	2.85704	−	3.29720i
$505$	−19.7027	+	0.529824i	−0.876759	+	0.0235769i
$506$	0.493870	−	18.7345i	0.0219552	−	0.832852i
$507$	26.5817	+	26.5817i	1.18054	+	1.18054i
$508$	3.23894	+	45.2863i	0.143705	+	2.00925i
$509$	2.29710	+	3.57435i	0.101817	+	0.158430i	0.888424	−	0.459023i	$-0.151801\pi$
$509$	2.29710	+	3.57435i	0.101817	+	0.158430i	−0.786607	+	0.617454i	$0.788164\pi$
$510$	24.3308	+	17.2130i	1.07739	+	0.762206i
$511$	13.5575	−	6.19152i	0.599750	−	0.273897i
$512$	37.5295	−	28.0943i	1.65859	−	1.24160i
$513$	30.2037	+	16.4924i	1.33352	+	0.728159i
$514$	1.52751	−	2.37686i	0.0673757	−	0.104839i
$515$	−24.2924	+	9.81224i	−1.07045	+	0.432379i
$516$	10.6203	−	36.1694i	0.467532	−	1.59227i
$517$	−4.96989	−	0.355453i	−0.218575	−	0.0156328i
$518$	−34.1935	−	2.44557i	−1.50237	−	0.107452i
$519$	0.449810	−	1.53191i	0.0197445	−	0.0672435i
$520$	8.06932	+	3.42607i	0.353863	+	0.150243i
$521$	−10.3905	+	16.1680i	−0.455218	+	0.708333i	−0.990678	−	0.136228i	$-0.956502\pi$
$521$	−10.3905	+	16.1680i	−0.455218	+	0.708333i	0.535460	+	0.844561i	$0.320138\pi$
$522$	41.8792	+	22.8678i	1.83300	+	1.00089i
$523$	−21.8396	+	16.3490i	−0.954981	+	0.714890i	−0.958497	−	0.285104i	$-0.907972\pi$
$523$	−21.8396	+	16.3490i	−0.954981	+	0.714890i	0.00351562	+	0.999994i	$0.498881\pi$
$524$	36.0258	−	16.4524i	1.57380	−	0.718728i
$525$	43.2466	−	8.61214i	1.88744	−	0.375865i
$526$	11.6101	+	18.0657i	0.506226	+	0.787703i
$527$	−1.24810	−	17.4507i	−0.0543681	−	0.760166i
$528$	−17.7953	−	17.7953i	−0.774443	−	0.774443i
$529$	1.21178	−	22.9681i	0.0526863	−	0.998611i
$530$	−1.09813	−	40.8366i	−0.0476999	−	1.77383i
$531$	13.8221	−	15.9515i	0.599827	−	0.692237i
$532$	−45.2840	−	9.85094i	−1.96331	−	0.427092i
$533$	1.36992	+	1.02551i	0.0593379	+	0.0444198i
$534$	−25.9902	−	56.9105i	−1.12470	−	2.46276i
$535$	1.97496	+	2.49548i	0.0853848	+	0.107889i
$536$	−3.92630	−	13.3718i	−0.169590	−	0.577572i
$537$	8.86618	+	40.7572i	0.382604	+	1.75880i
$538$	−14.3920	−	38.5866i	−0.620485	−	1.66358i
$539$	−2.39750	−	0.703970i	−0.103268	−	0.0303221i
$540$	−86.3991	−	3.84863i	−3.71803	−	0.165619i
$541$	1.77187	+	2.04485i	0.0761787	+	0.0879149i	0.792559	−	0.609795i	$-0.208748\pi$
$541$	1.77187	+	2.04485i	0.0761787	+	0.0879149i	−0.716381	+	0.697710i	$0.754203\pi$
$542$	−21.8618	−	40.0369i	−0.939045	−	1.71973i
$543$	−52.9056	+	19.7328i	−2.27040	+	0.846814i
$544$	3.37943	+	2.17183i	0.144892	+	0.0931164i
$545$	17.7087	−	5.72110i	0.758555	−	0.245065i
$546$	−15.4501	−	2.22139i	−0.661205	−	0.0950669i
$547$	−12.2130	+	32.7442i	−0.522189	+	1.40004i	0.361677	+	0.932303i	$0.382204\pi$
$547$	−12.2130	+	32.7442i	−0.522189	+	1.40004i	−0.883866	+	0.467740i	$0.845069\pi$
$548$	5.63806	−	7.53157i	0.240846	−	0.321733i
$549$	21.0814	−	13.5482i	0.899732	−	0.578223i
$550$	−2.43928	−	19.3860i	−0.104011	−	0.826623i
$551$		−	11.8645i		−	0.505446i
$552$	−54.8329	−	57.8022i	−2.33385	−	2.46022i
$553$	−10.4725	+	10.4725i	−0.445336	+	0.445336i
$554$	1.22793	+	1.06401i	0.0521699	+	0.0452055i
$555$	17.7662	+	26.0759i	0.754132	+	1.10686i
$556$	−3.39989	−	23.6468i	−0.144188	−	1.00285i
$557$	25.0889	+	9.35766i	1.06305	+	0.396497i	0.819314	−	0.573345i	$-0.194354\pi$
$557$	25.0889	+	9.35766i	1.06305	+	0.396497i	0.243735	+	0.969842i	$0.421627\pi$
$558$	88.9819	+	118.866i	3.76690	+	5.03200i
$559$	−2.02502	+	0.594599i	−0.0856492	+	0.0251489i
$560$	33.9725	−	8.35269i	1.43560	−	0.352965i
$561$	−3.48139	+	7.62318i	−0.146984	+	0.321851i
$562$	58.9206	−	32.1731i	2.48542	−	1.35714i
$563$	2.73736	−	38.2732i	0.115366	−	1.61302i	−0.529215	−	0.848488i	$-0.677513\pi$
$563$	2.73736	−	38.2732i	0.115366	−	1.61302i	0.644580	−	0.764537i	$-0.277032\pi$
$564$	−30.4623	+	26.3957i	−1.28269	+	1.11146i
$565$	12.9293	+	22.2355i	0.543939	+	0.935455i
$566$	63.9743	+	29.2161i	2.68904	+	1.22804i
$567$	27.0809	−	5.89109i	1.13729	−	0.247402i
$568$	−41.8900	+	76.7157i	−1.75766	+	3.21892i
$569$	−4.63493	+	32.2366i	−0.194306	+	1.35143i	0.626142	+	0.779709i	$0.284633\pi$
$569$	−4.63493	+	32.2366i	−0.194306	+	1.35143i	−0.820448	+	0.571721i	$0.806276\pi$
$570$	27.6559	+	56.4880i	1.15838	+	2.36602i
$571$	−20.8567	+	2.99874i	−0.872826	+	0.125493i	−0.564149	−	0.825673i	$-0.690795\pi$
$571$	−20.8567	+	2.99874i	−0.872826	+	0.125493i	−0.308678	+	0.951167i	$0.599886\pi$
$572$	−0.997080	+	4.58350i	−0.0416900	+	0.191646i
$573$	47.2653	−	3.38048i	1.97454	−	0.141222i
$574$	17.6162			0.735285
$575$	−2.36561	−	23.8622i	−0.0986527	−	0.995122i
$576$	30.4845			1.27019
$577$	2.07257	−	0.148233i	0.0862821	−	0.00617102i	−0.0281314	−	0.999604i	$-0.508956\pi$
$577$	2.07257	−	0.148233i	0.0862821	−	0.00617102i	0.114413	+	0.993433i	$0.463501\pi$
$578$	−7.33502	+	33.7185i	−0.305096	+	1.40251i
$579$	−16.9390	+	2.43546i	−0.703961	+	0.101214i
$580$	13.1111	+	26.7799i	0.544409	+	1.11197i
$581$	−7.07289	+	49.1930i	−0.293433	+	2.04087i
$582$	−23.5116	+	43.0583i	−0.974588	+	1.78483i
$583$	11.2244	−	2.44172i	0.464867	−	0.101126i
$584$	−25.5387	−	11.6631i	−1.05680	−	0.482624i
$585$	4.82788	+	8.30287i	0.199608	+	0.343282i
$586$	17.1061	−	14.8225i	0.706645	−	0.612312i
$587$	1.22121	−	17.0747i	0.0504047	−	0.704750i	−0.907934	−	0.419114i	$-0.862341\pi$
$587$	1.22121	−	17.0747i	0.0504047	−	0.704750i	0.958338	−	0.285636i	$-0.0922048\pi$
$588$	−17.7412	+	9.68743i	−0.731635	+	0.399503i
$589$	15.3371	−	33.5836i	0.631955	−	1.38379i
$590$	18.8853	−	4.64325i	0.777495	−	0.191159i
$591$	−30.3422	+	8.90927i	−1.24811	+	0.366478i
$592$	15.0018	+	20.0401i	0.616570	+	0.823641i
$593$	31.3280	+	11.6848i	1.28649	+	0.479835i	0.897340	−	0.441340i	$-0.145497\pi$
$593$	31.3280	+	11.6848i	1.28649	+	0.479835i	0.389148	+	0.921175i	$0.372769\pi$
$594$	−5.10301	−	35.4922i	−0.209379	−	1.45626i
$595$	−6.55958	−	9.62767i	−0.268917	−	0.394696i
$596$	−46.3362	−	40.1505i	−1.89800	−	1.64463i
$597$	−20.2750	+	20.2750i	−0.829801	+	0.829801i
$598$	−2.02223	+	8.24372i	−0.0826949	+	0.337111i
$599$		−	26.6353i		−	1.08829i	−0.838991	−	0.544145i	$-0.816854\pi$
$599$		−	26.6353i		−	1.08829i	0.838991	−	0.544145i	$-0.183146\pi$
$600$	−65.6087	−	50.9433i	−2.67846	−	2.07975i
$601$	16.8012	−	10.7975i	0.685336	−	0.440438i	−0.151089	−	0.988520i	$-0.548278\pi$
$601$	16.8012	−	10.7975i	0.685336	−	0.440438i	0.836425	+	0.548082i	$0.184642\pi$
$602$	−13.0201	+	17.3929i	−0.530661	+	0.708880i
$603$	5.33576	−	14.3057i	0.217289	−	0.582574i
$604$	−66.3027	−	9.53289i	−2.69782	−	0.387888i
$605$	−18.1776	+	5.87260i	−0.739023	+	0.238755i
$606$	−55.6130	−	35.7403i	−2.25913	−	1.45185i
$607$	−1.96262	+	0.732020i	−0.0796604	+	0.0297118i	−0.388978	−	0.921247i	$-0.627172\pi$
$607$	−1.96262	+	0.732020i	−0.0796604	+	0.0297118i	0.309318	+	0.950959i	$0.399899\pi$
$608$	4.06273	+	7.44034i	0.164766	+	0.301746i
$609$	−18.2705	−	21.0852i	−0.740356	−	0.854417i
$610$	23.0667	+	1.02750i	0.933945	+	0.0416024i
$611$	2.16528	+	0.635784i	0.0875980	+	0.0257211i
$612$	15.8385	+	42.4646i	0.640232	+	1.71653i
$613$	−5.44650	−	25.0372i	−0.219982	−	1.01124i	−0.946151	−	0.323725i	$-0.895065\pi$
$613$	−5.44650	−	25.0372i	−0.219982	−	1.01124i	0.726169	−	0.687516i	$-0.241299\pi$
$614$	3.16074	+	10.7645i	0.127557	+	0.434419i
$615$	−10.0623	−	12.7144i	−0.405752	−	0.512694i
$616$	10.5416	+	23.0828i	0.424733	+	0.930034i
$617$	−28.3312	−	21.2085i	−1.14057	−	0.853822i	−0.149714	−	0.988729i	$-0.547835\pi$
$617$	−28.3312	−	21.2085i	−1.14057	−	0.853822i	−0.990858	+	0.134908i	$0.956926\pi$
$618$	−85.8647	−	18.6787i	−3.45399	−	0.751369i
$619$	9.66168	−	11.1502i	0.388336	−	0.448163i	−0.527597	−	0.849495i	$-0.676907\pi$
$619$	9.66168	−	11.1502i	0.388336	−	0.448163i	0.915933	+	0.401331i	$0.131452\pi$
$620$	2.49417	+	92.7514i	0.100168	+	3.72499i
$621$	−5.11266	−	43.7079i	−0.205164	−	1.75394i
$622$	23.1156	+	23.1156i	0.926849	+	0.926849i
$623$	1.74463	+	24.3931i	0.0698971	+	0.977289i
$624$	6.16238	+	9.58885i	0.246693	+	0.383861i
$625$	−6.19327	−	24.2207i	−0.247731	−	0.968829i
$626$	−1.33075	+	0.607733i	−0.0531875	+	0.0242899i
$627$	−14.1577	+	10.5984i	−0.565406	+	0.423258i
$628$	−69.2183	−	37.7960i	−2.76211	−	1.50823i
$629$	4.50685	−	7.01280i	0.179700	−	0.279619i
$630$	91.0089	+	38.6405i	3.62588	+	1.53948i
$631$	−7.32089	+	24.9327i	−0.291440	+	0.992554i	0.675460	+	0.737397i	$0.263945\pi$
$631$	−7.32089	+	24.9327i	−0.291440	+	0.992554i	−0.966900	+	0.255157i	$0.917873\pi$
$632$	27.8276	+	1.99027i	1.10692	+	0.0791687i
$633$	−0.950200	−	0.0679596i	−0.0377670	−	0.00270115i
$634$	10.8409	−	36.9207i	0.430547	−	1.46631i
$635$	−22.3323	+	9.02052i	−0.886229	+	0.357968i
$636$	50.2391	−	78.1736i	1.99211	−	3.09978i
$637$	0.993279	+	0.542371i	0.0393551	+	0.0214895i
$638$	−9.89661	+	7.40851i	−0.391811	+	0.293306i
$639$	−87.1087	+	39.7812i	−3.44597	+	1.57372i
$640$	31.1824	+	22.0603i	1.23259	+	0.872009i
$641$	16.2815	+	25.3345i	0.643080	+	1.00065i	0.997840	+	0.0656949i	$0.0209264\pi$
$641$	16.2815	+	25.3345i	0.643080	+	1.00065i	−0.354759	+	0.934958i	$0.615437\pi$
$642$	0.761472	+	10.6468i	0.0300529	+	0.420194i
$643$	−22.3307	−	22.3307i	−0.880637	−	0.880637i	0.112963	−	0.993599i	$-0.463966\pi$
$643$	−22.3307	−	22.3307i	−0.880637	−	0.880637i	−0.993599	+	0.112963i	$0.963966\pi$
$644$	23.1890	+	54.5361i	0.913774	+	2.14902i
$645$	19.9903	−	0.537557i	0.787117	−	0.0211663i
$646$	10.8815	−	12.5579i	0.428126	−	0.494084i
$647$	−11.8698	−	2.58211i	−0.466648	−	0.101513i	−0.0269077	−	0.999638i	$-0.508566\pi$
$647$	−11.8698	−	2.58211i	−0.466648	−	0.101513i	−0.439741	+	0.898125i	$0.644930\pi$
$648$	−41.7932	−	31.2860i	−1.64179	−	1.22903i
$649$	2.27168	+	4.97429i	0.0891712	+	0.195258i
$650$	−0.786836	+	8.81444i	−0.0308622	+	0.345731i
$651$	−24.4596	−	83.3016i	−0.958646	−	3.26485i
$652$	−5.28821	−	24.3095i	−0.207102	−	0.952034i
$653$	4.58794	+	12.3007i	0.179540	+	0.481365i	0.995279	−	0.0970551i	$-0.0309423\pi$
$653$	4.58794	+	12.3007i	0.179540	+	0.481365i	−0.815739	+	0.578420i	$0.803670\pi$
$654$	59.8897	+	17.5852i	2.34187	+	0.687636i
$655$	14.1804	+	15.5027i	0.554076	+	0.605739i
$656$	−8.42413	−	9.72196i	−0.328907	−	0.379579i
$657$	−14.7415	−	26.9970i	−0.575120	−	1.05325i
$658$	21.7665	−	8.11850i	0.848548	−	0.316492i
$659$	13.3545	+	8.58244i	0.520219	+	0.334324i	0.774259	−	0.632869i	$-0.218123\pi$
$659$	13.3545	+	8.58244i	0.520219	+	0.334324i	−0.254040	+	0.967194i	$0.581759\pi$
$660$	20.2441	−	39.5672i	0.788000	−	1.54015i
$661$	2.09359	+	0.301012i	0.0814311	+	0.0117080i	0.182910	−	0.983130i	$-0.441448\pi$
$661$	2.09359	+	0.301012i	0.0814311	+	0.0117080i	−0.101479	+	0.994838i	$0.532357\pi$
$662$	−22.8756	+	61.3320i	−0.889087	+	2.38373i
$663$	2.27466	−	3.03859i	0.0883405	−	0.118009i
$664$	78.7575	−	50.6144i	3.05638	−	1.96422i
$665$	−2.41239	−	24.4659i	−0.0935483	−	0.948747i
$666$			70.7484i			2.74144i
$667$	−12.3810	+	8.76889i	−0.479395	+	0.339533i
$668$	74.3670	−	74.3670i	2.87735	−	2.87735i
$669$	−30.0489	−	26.0375i	−1.16176	−	1.00667i
$670$	11.6262	−	7.92122i	0.449158	−	0.306023i
$671$	0.923981	+	6.42643i	0.0356699	+	0.248090i
$672$	18.6777	+	6.96642i	0.720508	+	0.268736i
$673$	−3.08421	−	4.12002i	−0.118887	−	0.158815i	0.737149	−	0.675730i	$-0.236171\pi$
$673$	−3.08421	−	4.12002i	−0.118887	−	0.158815i	−0.856037	+	0.516915i	$0.827080\pi$
$674$	57.2774	−	16.8182i	2.20624	−	0.647811i
$675$	−12.1476	−	44.2419i	−0.467561	−	1.70287i
$676$	−21.8807	+	47.9120i	−0.841564	+	1.84277i
$677$	20.2291	−	11.0459i	0.777467	−	0.424529i	−0.0409449	−	0.999161i	$-0.513037\pi$
$677$	20.2291	−	11.0459i	0.777467	−	0.424529i	0.818412	+	0.574633i	$0.194855\pi$
$678$	−6.15443	+	86.0501i	−0.236359	+	3.30473i
$679$	14.4926	−	12.5579i	0.556176	−	0.481930i
$680$	−5.61444	+	21.2149i	−0.215304	+	0.813554i
$681$	−4.62001	−	2.10989i	−0.177039	−	0.0808511i
$682$	−37.5901	+	8.17724i	−1.43940	+	0.313123i
$683$	12.5580	−	22.9982i	0.480517	−	0.880002i	−0.519162	−	0.854676i	$-0.673756\pi$
$683$	12.5580	−	22.9982i	0.480517	−	0.880002i	0.999679	−	0.0253259i	$-0.00806235\pi$
$684$	−13.6113	+	94.6689i	−0.520442	+	3.61976i
$685$	4.72141	+	1.61781i	0.180396	+	0.0618132i
$686$	−39.1066	+	5.62268i	−1.49310	+	0.214675i
$687$	−2.80918	+	12.9136i	−0.107177	+	0.492684i
$688$	15.8250	−	1.13183i	0.603322	−	0.0431505i
$689$	−5.20261			−0.198204
$690$	38.5071	−	70.6093i	1.46594	−	2.68805i
$691$	27.5581			1.04836			0.524180	−	0.851608i	$-0.324372\pi$
$691$	27.5581			1.04836			0.524180	+	0.851608i	$0.324372\pi$
$692$	2.23133	−	0.159588i	0.0848226	−	0.00606663i
$693$	−5.90967	+	27.1663i	−0.224490	+	1.03196i
$694$	30.4051	−	4.37159i	1.15416	−	0.165943i
$695$	11.3824	−	5.57269i	0.431759	−	0.211384i
$696$	−7.47944	+	52.0206i	−0.283507	+	1.97184i
$697$	−2.05299	+	3.75977i	−0.0777624	+	0.142411i
$698$	13.7630	−	2.99396i	0.520938	−	0.113323i
$699$	11.8208	+	5.39838i	0.447104	+	0.204186i
$700$	32.4816	+	52.5571i	1.22769	+	1.98647i
$701$	6.26138	−	5.42551i	0.236489	−	0.204919i	−0.528551	−	0.848901i	$-0.677265\pi$
$701$	6.26138	−	5.42551i	0.236489	−	0.204919i	0.765040	+	0.643983i	$0.222719\pi$
$702$	−1.15857	+	16.1989i	−0.0437275	+	0.611390i
$703$	15.4397	−	8.43074i	0.582321	−	0.317971i
$704$	−3.28097	+	7.18432i	−0.123656	+	0.270769i
$705$	−18.2925	−	11.0726i	−0.688935	−	0.417019i
$706$	−1.64615	+	0.483352i	−0.0619535	+	0.0181912i
$707$	15.4855	+	20.6862i	0.582393	+	0.777986i
$708$	41.4487	+	15.4596i	1.55774	+	0.581007i
$709$	−6.58975	−	45.8327i	−0.247483	−	1.72128i	−0.612661	−	0.790346i	$-0.709901\pi$
$709$	−6.58975	−	45.8327i	−0.247483	−	1.72128i	0.365177	−	0.930938i	$-0.381008\pi$
$710$	−86.6914	−	16.4312i	−3.25347	−	0.616653i
$711$	23.0998	+	20.0161i	0.866311	+	0.750663i
$712$	32.5745	−	32.5745i	1.22078	−	1.22078i
$713$	−46.3811	+	8.81635i	−1.73698	+	0.330175i
$714$		−	39.0741i		−	1.46231i
$715$	−2.47636	+	0.244174i	−0.0926106	+	0.00913159i
$716$	−49.1645	+	31.5961i	−1.83736	+	1.18080i
$717$	39.0835	−	52.2095i	1.45960	−	1.94980i
$718$	3.10985	−	8.33782i	0.116058	−	0.311165i
$719$	10.1544	+	1.45998i	0.378696	+	0.0544482i	0.329034	−	0.944318i	$-0.393277\pi$
$719$	10.1544	+	1.45998i	0.378696	+	0.0544482i	0.0496612	+	0.998766i	$0.484186\pi$
$720$	−22.1960	−	68.7037i	−0.827196	−	2.56044i
$721$	28.8955	+	18.5700i	1.07612	+	0.691583i
$722$	−11.5262	+	4.29904i	−0.428960	+	0.159994i
$723$	−6.46968	−	11.8483i	−0.240610	−	0.440644i
$724$	−51.8102	−	59.7921i	−1.92551	−	2.22216i
$725$	−11.3802	+	10.9859i	−0.422652	+	0.408005i
$726$	−61.4755	−	18.0508i	−2.28157	−	0.669929i
$727$	12.5641	+	33.6857i	0.465978	+	1.24933i	0.931319	+	0.364203i	$0.118659\pi$
$727$	12.5641	+	33.6857i	0.465978	+	1.24933i	−0.465342	+	0.885131i	$0.654069\pi$
$728$	−2.44306	−	11.2306i	−0.0905459	−	0.416233i
$729$	7.21688	+	24.5784i	0.267292	+	0.910312i
$730$	3.27787	−	28.1514i	0.121319	−	1.04193i
$731$	−2.19474	−	4.80581i	−0.0811753	−	0.177749i
$732$	42.0462	+	31.4754i	1.55407	+	1.16336i
$733$	5.41672	+	1.17834i	0.200071	+	0.0435228i	0.311484	−	0.950251i	$-0.399174\pi$
$733$	5.41672	+	1.17834i	0.200071	+	0.0435228i	−0.111413	+	0.993774i	$0.535538\pi$
$734$	−60.7639	+	70.1253i	−2.24284	+	2.58837i
$735$	−7.78353	−	7.37588i	−0.287100	−	0.272063i
$736$	4.76154	−	9.73864i	0.175513	−	0.358971i
$737$	2.79717	+	2.79717i	0.103035	+	0.103035i
$738$	−2.59361	−	36.2635i	−0.0954722	−	1.33488i
$739$	1.65904	+	2.58151i	0.0610287	+	0.0949626i	0.870427	−	0.492298i	$-0.163843\pi$
$739$	1.65904	+	2.58151i	0.0610287	+	0.0949626i	−0.809398	+	0.587260i	$0.800207\pi$
$740$	−25.5331	+	36.0913i	−0.938616	+	1.32674i
$741$	7.28609	−	3.32745i	0.267661	−	0.122237i
$742$	−42.8751	+	32.0959i	−1.57399	+	1.17828i
$743$	12.9543	+	7.07357i	0.475246	+	0.259504i	0.698973	−	0.715148i	$-0.253641\pi$
$743$	12.9543	+	7.07357i	0.475246	+	0.259504i	−0.223727	+	0.974652i	$0.571822\pi$
$744$	−88.4176	+	137.581i	−3.24155	+	5.04395i
$745$	12.7112	−	29.9384i	0.465704	−	1.09686i
$746$	17.7809	−	60.5560i	0.651003	−	2.21711i
$747$	102.307	+	7.31712i	3.74321	+	0.267719i
$748$	−11.7123	−	0.837682i	−0.428245	−	0.0306287i
$749$	1.17547	−	4.00328i	0.0429507	−	0.146277i
$750$	28.5746	−	78.8317i	1.04340	−	2.87853i
$751$	−15.3958	+	23.9563i	−0.561800	+	0.874177i	−0.999691	−	0.0248505i	$-0.992089\pi$
$751$	−15.3958	+	23.9563i	−0.561800	+	0.874177i	0.437892	+	0.899028i	$0.355725\pi$
$752$	−14.8892	−	8.13015i	−0.542955	−	0.296476i
$753$	−31.6938	+	23.7257i	−1.15499	+	0.864613i
$754$	5.09315	−	2.32597i	0.185482	−	0.0847067i
$755$	−6.00076	−	35.0243i	−0.218390	−	1.27466i
$756$	61.3004	+	95.3853i	2.22948	+	3.46913i
$757$	−1.35660	−	18.9677i	−0.0493064	−	0.689393i	−0.960653	−	0.277752i	$-0.910411\pi$
$757$	−1.35660	−	18.9677i	−0.0493064	−	0.689393i	0.911346	−	0.411640i	$-0.135044\pi$
$758$	−47.9798	−	47.9798i	−1.74270	−	1.74270i
$759$	21.5235	+	6.94099i	0.781254	+	0.251942i
$760$	−31.8544	+	33.6150i	−1.15548	+	1.21934i
$761$	−15.3050	+	17.6629i	−0.554805	+	0.640279i	−0.961996	−	0.273064i	$-0.911963\pi$
$761$	−15.3050	+	17.6629i	−0.554805	+	0.640279i	0.407191	+	0.913343i	$0.366508\pi$
$762$	−78.9365	−	17.1716i	−2.85957	−	0.622061i
$763$	−19.5318	−	14.6213i	−0.707098	−	0.529327i
$764$	27.5812	+	60.3944i	0.997853	+	2.18499i
$765$	−18.8531	+	14.9206i	−0.681635	+	0.539455i
$766$	12.1957	+	41.5348i	0.440649	+	1.50071i
$767$	−0.526472	−	2.42015i	−0.0190098	−	0.0873867i
$768$	34.1767	+	91.6312i	1.23324	+	3.30646i
$769$	−20.5080	−	6.02171i	−0.739539	−	0.217148i	−0.109799	−	0.993954i	$-0.535021\pi$
$769$	−20.5080	−	6.02171i	−0.739539	−	0.217148i	−0.629740	+	0.776806i	$0.716839\pi$
$770$	−18.9015	+	17.2894i	−0.681163	+	0.623066i
$771$	2.23269	+	2.57666i	0.0804084	+	0.0927962i
$772$	−11.4914	−	21.0449i	−0.413584	−	0.757423i
$773$	14.0379	−	5.23588i	0.504910	−	0.188322i	−0.0840848	−	0.996459i	$-0.526797\pi$
$773$	14.0379	−	5.23588i	0.504910	−	0.188322i	0.588995	+	0.808137i	$0.299524\pi$
$774$	37.7207	+	24.2416i	1.35584	+	0.871347i
$775$	−46.4141	+	16.3854i	−1.66724	+	0.588581i
$776$	−35.7557	−	5.14089i	−1.28355	−	0.184547i
$777$	14.4563	−	38.7588i	0.518617	−	1.39047i
$778$	43.4999	−	58.1091i	1.55955	−	2.08331i
$779$	−7.60487	+	4.88736i	−0.272473	+	0.175108i
$780$	−12.7687	+	15.5621i	−0.457191	+	0.557214i
$781$		−	24.8105i		−	0.887791i
$782$	−21.1469	−	2.07383i	−0.756212	−	0.0741600i
$783$	−20.5260	+	20.5260i	−0.733540	+	0.733540i
$784$	−6.42951	−	5.57120i	−0.229625	−	0.198971i
$785$	7.79098	−	41.1053i	0.278072	−	1.46711i
$786$	10.0286	+	69.7507i	0.357710	+	2.48792i
$787$	−30.0212	−	11.1973i	−1.07014	−	0.399142i	−0.248196	−	0.968710i	$-0.579838\pi$
$787$	−30.0212	−	11.1973i	−1.07014	−	0.399142i	−0.821944	+	0.569568i	$0.807110\pi$
$788$	−26.5530	−	35.4707i	−0.945912	−	1.26359i
$789$	−24.8642	+	7.30077i	−0.885187	+	0.259914i
$790$	6.72400	+	27.3483i	0.239229	+	0.973007i
$791$	14.0084	−	30.6742i	0.498083	−	1.09065i
$792$	45.9647	−	25.0986i	1.63329	−	0.891841i
$793$	0.209778	−	2.93308i	0.00744943	−	0.104157i
$794$	−27.1145	+	23.4948i	−0.962257	+	0.833800i
$795$	47.6552	+	12.6118i	1.69016	+	0.447293i
$796$	−36.5446	−	16.6893i	−1.29529	−	0.591538i
$797$	−10.2911	+	2.23870i	−0.364530	+	0.0792987i	−0.391100	−	0.920348i	$-0.627905\pi$
$797$	−10.2911	+	2.23870i	−0.364530	+	0.0792987i	0.0265695	+	0.999647i	$0.491542\pi$
$798$	39.5176	−	72.3710i	1.39891	−	2.56191i
$799$	−0.803964	+	5.59169i	−0.0284422	+	0.197820i
$800$	3.37479	−	10.7862i	0.119317	−	0.381351i
$801$	49.9571	−	7.18275i	1.76515	−	0.253790i
$802$	5.40877	−	24.8637i	0.190990	−	0.877968i
$803$	7.94900	−	0.568524i	0.280514	−	0.0200628i
$804$	32.0011			1.12859
$805$	−23.7480	+	20.5998i	−0.837008	+	0.726047i
$806$	17.4234			0.613712
$807$	49.5696	−	3.54529i	1.74493	−	0.124800i
$808$	10.3469	−	47.5637i	0.364001	−	1.67329i
$809$	12.5572	−	1.80546i	0.441488	−	0.0634764i	0.0820135	−	0.996631i	$-0.473865\pi$
$809$	12.5572	−	1.80546i	0.441488	−	0.0634764i	0.359475	+	0.933155i	$0.382956\pi$
$810$	17.0829	−	49.8547i	0.600231	−	1.75172i
$811$	3.77629	−	26.2647i	0.132603	−	0.922277i	−0.809539	−	0.587066i	$-0.800283\pi$
$811$	3.77629	−	26.2647i	0.132603	−	0.922277i	0.942143	−	0.335212i	$-0.108808\pi$
$812$	18.7345	−	34.3097i	0.657452	−	1.20403i
$813$	53.7883	−	11.7009i	1.88644	−	0.410370i
$814$	−16.6733	−	7.61446i	−0.584400	−	0.266887i
$815$	11.4090	−	6.63400i	0.399640	−	0.232379i
$816$	−21.5641	+	18.6854i	−0.754894	+	0.654119i
$817$	0.795369	−	11.1207i	0.0278264	−	0.389065i
$818$	−85.2404	+	46.5448i	−2.98036	+	1.62740i
$819$	5.23084	−	11.4539i	0.182780	−	0.400233i
$820$	11.7644	−	19.4353i	0.410830	−	0.678712i
$821$	4.27893	−	1.25641i	0.149336	−	0.0438489i	−0.206210	−	0.978508i	$-0.566113\pi$
$821$	4.27893	−	1.25641i	0.149336	−	0.0438489i	0.355546	+	0.934659i	$0.384295\pi$
$822$	10.0317	+	13.4007i	0.349895	+	0.467404i
$823$	16.6277	+	6.20181i	0.579605	+	0.216182i	0.622130	−	0.782914i	$-0.286267\pi$
$823$	16.6277	+	6.20181i	0.579605	+	0.216182i	−0.0425249	+	0.999095i	$0.513540\pi$
$824$	−9.20813	−	64.0440i	−0.320781	−	2.23108i
$825$	23.2750	+	3.76639i	0.810332	+	0.131129i
$826$	−19.2691	−	16.6968i	−0.670457	−	0.580955i
$827$	−21.6985	+	21.6985i	−0.754532	+	0.754532i	−0.975322	−	0.220789i	$-0.929137\pi$
$827$	−21.6985	+	21.6985i	−0.754532	+	0.754532i	0.220789	+	0.975322i	$0.429137\pi$
$828$	108.850	−	55.7645i	3.78280	−	1.93795i
$829$			22.0755i			0.766715i	0.923600	+	0.383358i	$0.125232\pi$
$829$			22.0755i			0.766715i	−0.923600	+	0.383358i	$0.874768\pi$
$830$	73.0601	+	59.9455i	2.53595	+	2.08074i
$831$	−1.64941	+	1.06001i	−0.0572172	+	0.0367713i
$832$	2.14371	−	2.86366i	0.0743198	−	0.0992797i
$833$	−0.990037	+	2.65439i	−0.0343028	+	0.0919693i
$834$	42.0741	+	6.04935i	1.45691	+	0.209472i
$835$	49.6685	+	25.4123i	1.71885	+	0.879429i
$836$	−20.8458	−	13.3968i	−0.720966	−	0.463337i
$837$	−84.6345	+	31.5670i	−2.92540	+	1.09112i
$838$	27.9514	+	51.1891i	0.965564	+	1.76830i
$839$	−2.76549	−	3.19154i	−0.0954752	−	0.110184i	0.706001	−	0.708211i	$-0.250497\pi$
$839$	−2.76549	−	3.19154i	−0.0954752	−	0.110184i	−0.801476	+	0.598026i	$0.795952\pi$
$840$	−4.84615	+	108.793i	−0.167208	+	3.75371i
$841$	−18.2227	−	5.35067i	−0.628370	−	0.184506i
$842$	18.0781	+	48.4692i	0.623011	+	1.67036i
$843$	17.2198	+	79.1580i	0.593080	+	2.72635i
$844$	−0.376046	−	1.28069i	−0.0129440	−	0.0440833i
$845$	−27.7544	−	3.23164i	−0.954779	−	0.111172i
$846$	−19.9168	−	43.6118i	−0.684755	−	1.49940i
$847$	20.0490	+	15.0085i	0.688891	+	0.515697i
$848$	38.2160	+	8.31339i	1.31234	+	0.285483i
$849$	−55.5766	+	64.1388i	−1.90738	+	2.20124i
$850$	−22.1209	+	1.19057i	−0.758742	+	0.0408361i
$851$	−20.2090	−	9.88086i	−0.692757	−	0.338711i
$852$	−141.923	−	141.923i	−4.86219	−	4.86219i
$853$	2.05152	+	28.6840i	0.0702427	+	0.982122i	0.903321	+	0.428966i	$0.141122\pi$
$853$	2.05152	+	28.6840i	0.0702427	+	0.982122i	−0.833078	+	0.553156i	$0.813423\pi$
$854$	−16.3659	−	25.4659i	−0.560030	−	0.871424i
$855$	−50.0086	+	8.56806i	−1.71026	+	0.293021i
$856$	−7.14921	+	3.26493i	−0.244355	+	0.111593i
$857$	10.8005	−	8.08516i	0.368939	−	0.276184i	−0.398681	−	0.917090i	$-0.630532\pi$
$857$	10.8005	−	8.08516i	0.368939	−	0.276184i	0.767620	+	0.640906i	$0.221441\pi$
$858$	−7.32516	−	3.99984i	−0.250077	−	0.136552i
$859$	8.54501	−	13.2963i	0.291552	−	0.453664i	−0.664320	−	0.747449i	$-0.731279\pi$
$859$	8.54501	−	13.2963i	0.291552	−	0.453664i	0.955872	+	0.293785i	$0.0949149\pi$
$860$	10.4939	+	25.9799i	0.357839	+	0.885908i
$861$	−5.98897	+	20.3966i	−0.204104	+	0.695113i
$862$	−102.600	−	7.33811i	−3.49457	−	0.249937i
$863$	51.9151	+	3.71304i	1.76721	+	0.126393i	0.916702	−	0.399571i	$-0.130841\pi$
$863$	51.9151	+	3.71304i	1.76721	+	0.126393i	0.850507	+	0.525964i	$0.176295\pi$
$864$	5.84337	−	19.9007i	0.198795	−	0.677035i
$865$	0.444457	+	1.10035i	0.0151120	+	0.0374130i
$866$	21.2688	−	33.0948i	0.722742	−	1.12461i
$867$	−36.5467	−	19.9560i	−1.24119	−	0.677741i
$868$	97.3814	−	72.8988i	3.30534	−	2.47435i
$869$	−7.20339	+	3.28968i	−0.244358	+	0.111595i
$870$	−52.2910	+	8.95911i	−1.77283	+	0.303742i
$871$	−0.968638	−	1.50723i	−0.0328210	−	0.0510705i
$872$	3.27872	+	45.8425i	0.111032	+	1.55242i
$873$	−27.9846	−	27.9846i	−0.947137	−	0.947137i
$874$	−37.0698	−	25.2280i	−1.25391	−	0.853348i
$875$	−21.2335	+	24.9679i	−0.717824	+	0.844070i
$876$	42.2182	−	48.7224i	1.42642	−	1.64618i
$877$	22.8174	+	4.96362i	0.770488	+	0.167609i	0.580592	−	0.814195i	$-0.302821\pi$
$877$	22.8174	+	4.96362i	0.770488	+	0.167609i	0.189896	+	0.981804i	$0.439185\pi$
$878$	69.2702	+	51.8551i	2.33776	+	1.75002i
$879$	11.3464	+	24.8451i	0.382704	+	0.838006i
$880$	18.5804	+	2.16345i	0.626345	+	0.0729298i
$881$	2.43024	+	8.27665i	0.0818770	+	0.278848i	0.990248	−	0.139319i	$-0.0444912\pi$
$881$	2.43024	+	8.27665i	0.0818770	+	0.278848i	−0.908371	+	0.418166i	$0.862673\pi$
$882$	−5.11085	−	23.4942i	−0.172091	−	0.791091i
$883$	4.39984	+	11.7964i	0.148066	+	0.396981i	0.989717	−	0.143042i	$-0.0456883\pi$
$883$	4.39984	+	11.7964i	0.148066	+	0.396981i	−0.841650	+	0.540023i	$0.818416\pi$
$884$	5.10283	+	1.49833i	0.171627	+	0.0503942i
$885$	−1.04433	+	23.4445i	−0.0351048	+	0.788079i
$886$	6.74351	+	7.78243i	0.226553	+	0.261456i
$887$	−16.7589	−	30.6917i	−0.562710	−	1.03053i	−0.991865	−	0.127296i	$-0.959370\pi$
$887$	−16.7589	−	30.6917i	−0.562710	−	1.03053i	0.429155	−	0.903231i	$-0.358811\pi$
$888$	−73.0111	+	27.2317i	−2.45009	+	0.913838i
$889$	26.5640	+	17.0716i	0.890927	+	0.572564i
$890$	41.3994	+	21.1815i	1.38771	+	0.710005i
$891$	14.6678	+	2.10892i	0.491391	+	0.0706513i
$892$	19.4685	−	52.1972i	0.651855	−	1.74769i
$893$	−7.14421	+	9.54355i	−0.239072	+	0.319363i
$894$	91.7725	−	58.9786i	3.06933	−	1.97254i
$895$	−23.9677	−	19.6654i	−0.801151	−	0.657341i
$896$		−	50.0775i		−	1.67297i
$897$	−8.85734	−	5.14401i	−0.295738	−	0.171754i
$898$	−49.6692	+	49.6692i	−1.65748	+	1.65748i
$899$	23.5361	+	20.3942i	0.784974	+	0.680184i
$900$	103.408	−	74.6022i	3.44694	−	2.48674i
$901$	−1.85347	−	12.8911i	−0.0617479	−	0.429466i
$902$	8.82539	+	3.29170i	0.293853	+	0.109602i
$903$	−15.7115	−	20.9882i	−0.522847	−	0.698442i
$904$	−60.9492	+	17.8963i	−2.02714	+	0.595222i
$905$	21.7336	−	35.9049i	0.722449	−	1.19352i
$906$	49.5108	−	108.414i	1.64489	−	3.60180i
$907$	−24.0314	+	13.1221i	−0.797949	+	0.435713i	−0.825845	−	0.563898i	$-0.809301\pi$
$907$	−24.0314	+	13.1221i	−0.797949	+	0.435713i	0.0278955	+	0.999611i	$0.491119\pi$
$908$	0.507675	−	7.09823i	0.0168478	−	0.235563i
$909$	40.3033	−	34.9230i	1.33678	−	1.15832i
$910$	10.0297	−	5.83197i	0.332481	−	0.193328i
$911$	−8.73337	−	3.98839i	−0.289349	−	0.132141i	0.265452	−	0.964124i	$-0.414479\pi$
$911$	−8.73337	−	3.98839i	−0.289349	−	0.132141i	−0.554802	+	0.831983i	$0.687206\pi$
$912$	−58.8373	+	12.7993i	−1.94830	+	0.423826i
$913$	−12.7354	+	23.3232i	−0.421481	+	0.771885i
$914$	12.4172	−	86.3633i	0.410724	−	2.85664i
$915$	−9.03167	+	26.3581i	−0.298578	+	0.871371i
$916$	−18.3284	+	2.63523i	−0.605588	+	0.0870703i
$917$	5.85507	−	26.9153i	0.193351	−	0.888822i
$918$	−40.5509	+	2.90026i	−1.33838	+	0.0957227i
$919$	2.33453			0.0770090			0.0385045	−	0.999258i	$-0.487741\pi$
$919$	2.33453			0.0770090			0.0385045	+	0.999258i	$0.487741\pi$
$920$	58.6215	+	8.39684i	1.93269	+	0.276836i
$921$	−13.5380			−0.446092
$922$	71.9600	−	5.14668i	2.36988	−	0.169497i
$923$	−2.38862	+	10.9803i	−0.0786224	+	0.361421i
$924$	−57.6764	+	8.29261i	−1.89741	+	0.272807i
$925$	−22.3829	−	7.00315i	−0.735946	−	0.230262i
$926$	4.85294	−	33.7529i	0.159478	−	1.10919i
$927$	33.9727	−	62.2163i	1.11581	−	2.04345i
$928$	−6.98735	+	1.52001i	−0.229371	+	0.0498966i
$929$	37.4190	+	17.0887i	1.22768	+	0.560662i	0.920407	−	0.390961i	$-0.127857\pi$
$929$	37.4190	+	17.0887i	1.22768	+	0.560662i	0.307270	+	0.951622i	$0.400584\pi$
$930$	−159.596	−	42.2364i	−5.23335	−	1.38499i
$931$	−4.51821	+	3.91506i	−0.148078	+	0.128311i
$932$	−1.29894	+	18.1616i	−0.0425483	+	0.594903i
$933$	−34.6225	+	18.9053i	−1.13349	+	0.618932i
$934$	−17.8850	+	39.1627i	−0.585215	+	1.28144i
$935$	−1.48724	−	6.04899i	−0.0486380	−	0.197823i
$936$	−22.7588	+	6.68258i	−0.743894	+	0.218427i
$937$	7.57465	+	10.1185i	0.247453	+	0.330558i	0.907020	−	0.421087i	$-0.138351\pi$
$937$	7.57465	+	10.1185i	0.247453	+	0.330558i	−0.659567	+	0.751646i	$0.729260\pi$
$938$	−17.2810	−	6.44548i	−0.564245	−	0.210452i
$939$	−0.251237	−	1.74739i	−0.00819882	−	0.0570241i
$940$	5.57920	−	29.4360i	0.181974	−	0.960095i
$941$	10.1525	+	8.79722i	0.330963	+	0.286781i	0.804451	−	0.594019i	$-0.202460\pi$
$941$	10.1525	+	8.79722i	0.330963	+	0.286781i	−0.473488	+	0.880800i	$0.657005\pi$
$942$	99.2233	−	99.2233i	3.23287	−	3.23287i
$943$	10.7208	+	4.32377i	0.349116	+	0.140801i
$944$			18.6186i			0.605985i
$945$	−38.1533	+	46.5003i	−1.24113	+	1.51266i
$946$	−9.77282	+	6.28061i	−0.317742	+	0.204200i
$947$	−29.3261	+	39.1751i	−0.952972	+	1.27302i	0.00902483	+	0.999959i	$0.497127\pi$
$947$	−29.3261	+	39.1751i	−0.952972	+	1.27302i	−0.961996	+	0.273062i	$0.911964\pi$
$948$	−22.3874	+	60.0230i	−0.727110	+	1.94946i
$949$	−3.57269	−	0.513676i	−0.115975	−	0.0166746i
$950$	−42.1753	−	20.1669i	−1.36835	−	0.654300i
$951$	39.0623	+	25.1038i	1.26668	+	0.814047i
$952$	26.9570	−	10.0544i	0.873681	−	0.325866i
$953$	−18.8297	−	34.4840i	−0.609953	−	1.11705i	−0.982009	−	0.188836i	$-0.939529\pi$
$953$	−18.8297	−	34.4840i	−0.609953	−	1.11705i	0.372055	−	0.928211i	$-0.378653\pi$
$954$	72.3828	+	83.5343i	2.34348	+	2.70452i
$955$	−25.9890	+	23.7724i	−0.840984	+	0.769256i
$956$	87.6775	+	25.7444i	2.83569	+	0.832634i
$957$	−5.21325	−	13.9773i	−0.168521	−	0.451821i
$958$	−9.33025	−	42.8904i	−0.301447	−	1.38573i
$959$	−1.84345	−	6.27820i	−0.0595279	−	0.202734i
$960$	−26.5780	+	21.0342i	−0.857800	+	0.678874i
$961$	27.3800	+	59.9539i	0.883226	+	1.93400i
$962$	6.64598	+	4.97512i	0.214275	+	0.160404i
$963$	−8.41393	−	1.83034i	−0.271135	−	0.0589818i
$964$	12.3866	−	14.2949i	0.398945	−	0.460407i
$965$	8.74939	−	9.23295i	0.281653	−	0.297219i
$966$	−104.728	+	12.2504i	−3.36958	+	0.394152i
$967$	5.25129	+	5.25129i	0.168870	+	0.168870i	0.786483	−	0.617613i	$-0.211900\pi$
$967$	5.25129	+	5.25129i	0.168870	+	0.168870i	−0.617613	+	0.786483i	$0.711900\pi$
$968$	−3.36554	−	47.0564i	−0.108173	−	1.51245i
$969$	10.8405	+	16.8682i	0.348248	+	0.541885i
$970$	−6.15792	−	35.9415i	−0.197719	−	1.15401i
$971$	−32.5839	+	14.8806i	−1.04567	+	0.477540i	−0.862773	−	0.505592i	$-0.831274\pi$
$971$	−32.5839	+	14.8806i	−1.04567	+	0.477540i	−0.182895	+	0.983132i	$0.558547\pi$
$972$	3.07914	−	2.30502i	0.0987636	−	0.0739335i
$973$	−14.5828	−	7.96283i	−0.467504	−	0.255277i
$974$	13.2559	−	20.6266i	0.424748	−	0.660920i
$975$	−9.93813	−	3.90767i	−0.318275	−	0.125145i
$976$	−6.22777	+	21.2098i	−0.199346	+	0.678910i
$977$	−20.9751	−	1.50017i	−0.671052	−	0.0479946i	−0.268344	−	0.963323i	$-0.586476\pi$
$977$	−20.9751	−	1.50017i	−0.671052	−	0.0479946i	−0.402708	+	0.915329i	$0.631931\pi$
$978$	44.1522	+	3.15782i	1.41183	+	0.100976i
$979$	−3.68399	+	12.5465i	−0.117741	+	0.400988i
$980$	5.87183	−	13.8298i	0.187569	−	0.441775i
$981$	−27.2228	+	42.3595i	−0.869156	+	1.35243i
$982$	8.77258	+	4.79019i	0.279944	+	0.152861i
$983$	31.5866	−	23.6454i	1.00746	−	0.754172i	0.0379596	−	0.999279i	$-0.487914\pi$
$983$	31.5866	−	23.6454i	1.00746	−	0.754172i	0.969496	+	0.245108i	$0.0788233\pi$
$984$	36.4250	−	16.6347i	1.16119	−	0.530296i
$985$	13.5752	−	19.1887i	0.432541	−	0.611402i
$986$	7.57780	+	11.7913i	0.241326	+	0.375511i
$987$	1.99988	+	27.9620i	0.0636569	+	0.890040i
$988$	7.93587	+	7.93587i	0.252474	+	0.252474i
$989$	−12.1927	+	7.38916i	−0.387705	+	0.234962i
$990$	38.3736	+	36.3638i	1.21959	+	1.15572i
$991$	−8.28345	+	9.55962i	−0.263133	+	0.303671i	−0.871906	−	0.489673i	$-0.837116\pi$
$991$	−8.28345	+	9.55962i	−0.263133	+	0.303671i	0.608774	+	0.793344i	$0.291662\pi$
$992$	−21.7432	−	4.72995i	−0.690348	−	0.150176i
$993$	−63.2350	−	47.3371i	−2.00670	−	1.50220i
$994$	48.0548	+	105.225i	1.52421	+	3.33755i
$995$	2.46491	−	21.1695i	0.0781429	−	0.671117i
$996$	60.5647	+	206.264i	1.91907	+	6.53574i
$997$	9.30143	+	42.7580i	0.294579	+	1.35416i	0.851832	+	0.523816i	$0.175492\pi$
$997$	9.30143	+	42.7580i	0.294579	+	1.35416i	−0.557252	+	0.830343i	$0.688144\pi$
$998$	−18.9699	−	50.8601i	−0.600480	−	1.60995i
$999$	−41.2967	−	12.1258i	−1.30657	−	0.383644i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	115.2.l.a.7.1	✓	200
5.2	odd	4		575.2.r.b.168.1		200
5.3	odd	4	inner	115.2.l.a.53.10	yes	200
5.4	even	2		575.2.r.b.7.10		200
23.10	odd	22	inner	115.2.l.a.102.10	yes	200
115.33	even	44	inner	115.2.l.a.33.1	yes	200
115.79	odd	22		575.2.r.b.332.1		200
115.102	even	44		575.2.r.b.493.10		200

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
115.2.l.a.7.1	✓	200	1.1	even	1	trivial
115.2.l.a.33.1	yes	200	115.33	even	44	inner
115.2.l.a.53.10	yes	200	5.3	odd	4	inner
115.2.l.a.102.10	yes	200	23.10	odd	22	inner
575.2.r.b.7.10		200	5.4	even	2
575.2.r.b.168.1		200	5.2	odd	4
575.2.r.b.332.1		200	115.79	odd	22
575.2.r.b.493.10		200	115.102	even	44

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:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.l (of order \(44\), degree \(20\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.48666 + 0.177849i) q^{2} +(0.639470 - 2.93959i) q^{3} +(4.17220 - 0.599872i) q^{4} +(0.983237 + 2.00829i) q^{5} +(-1.06734 + 7.42350i) q^{6} +(1.40495 - 2.57297i) q^{7} +(-5.39608 + 1.17384i) q^{8} +(-5.50340 - 2.51332i) q^{9} +O(q^{10})\)	\(q+(-2.48666 + 0.177849i) q^{2} +(0.639470 - 2.93959i) q^{3} +(4.17220 - 0.599872i) q^{4} +(0.983237 + 2.00829i) q^{5} +(-1.06734 + 7.42350i) q^{6} +(1.40495 - 2.57297i) q^{7} +(-5.39608 + 1.17384i) q^{8} +(-5.50340 - 2.51332i) q^{9} +(-2.80215 - 4.81907i) q^{10} +(1.18463 - 1.02649i) q^{11} +(0.904615 - 12.6482i) q^{12} +(-0.623103 + 0.340240i) q^{13} +(-3.03603 + 6.64798i) q^{14} +(6.53232 - 1.60607i) q^{15} +(5.12071 - 1.50358i) q^{16} +(-1.06504 - 1.42273i) q^{17} +(14.1321 + 5.27099i) q^{18} +(-0.533737 - 3.71222i) q^{19} +(5.30698 + 7.78919i) q^{20} +(-6.66508 - 5.77532i) q^{21} +(-2.76322 + 2.76322i) q^{22} +(-3.47935 + 3.30062i) q^{23} +16.6129i q^{24} +(-3.06649 + 3.94926i) q^{25} +(1.48893 - 0.956879i) q^{26} +(-5.49889 + 7.34565i) q^{27} +(4.31828 - 11.5778i) q^{28} +(3.13134 + 0.450218i) q^{29} +(-15.9580 + 5.15553i) q^{30} +(8.28154 + 5.32222i) q^{31} +(-2.11785 + 0.789919i) q^{32} +(-2.25993 - 4.13875i) q^{33} +(2.90142 + 3.34842i) q^{34} +(6.54869 + 0.291710i) q^{35} +(-24.4689 - 7.18473i) q^{36} +(1.63919 + 4.39484i) q^{37} +(1.98744 + 9.13611i) q^{38} +(0.601712 + 2.04924i) q^{39} +(-7.66305 - 9.68274i) q^{40} +(-1.00131 - 2.19257i) q^{41} +(17.6009 + 13.1759i) q^{42} +(2.90485 + 0.631911i) q^{43} +(4.32676 - 4.99335i) q^{44} +(-0.363663 - 13.5236i) q^{45} +(8.06495 - 8.82632i) q^{46} +(-2.24768 - 2.24768i) q^{47} +(-1.14536 - 16.0143i) q^{48} +(-0.861828 - 1.34103i) q^{49} +(6.92294 - 10.3658i) q^{50} +(-4.86329 + 2.22099i) q^{51} +(-2.39561 + 1.79333i) q^{52} +(6.43181 + 3.51203i) q^{53} +(12.3674 - 19.2441i) q^{54} +(3.22627 + 1.36981i) q^{55} +(-4.56095 + 15.5332i) q^{56} +(-11.2537 - 0.804883i) q^{57} +(-7.86664 - 0.562633i) q^{58} +(-0.982871 + 3.34735i) q^{59} +(26.2907 - 10.6194i) q^{60} +(-2.23932 + 3.48445i) q^{61} +(-21.5399 - 11.7617i) q^{62} +(-14.1987 + 10.6290i) q^{63} +(-4.58332 + 2.09313i) q^{64} +(-1.29596 - 0.916837i) q^{65} +(6.35574 + 9.88973i) q^{66} +(0.180035 + 2.51722i) q^{67} +(-5.29701 - 5.29701i) q^{68} +(7.47755 + 12.3385i) q^{69} +(-16.3362 + 0.439297i) q^{70} +(10.3652 - 11.9621i) q^{71} +(32.6470 + 7.10192i) q^{72} +(4.07004 + 3.04679i) q^{73} +(-4.85773 - 10.6369i) q^{74} +(9.64829 + 11.5397i) q^{75} +(-4.45372 - 15.1680i) q^{76} +(-0.976782 - 4.49020i) q^{77} +(-1.86071 - 4.98875i) q^{78} +(-4.84738 - 1.42332i) q^{79} +(8.05449 + 8.80552i) q^{80} +(6.19088 + 7.14465i) q^{81} +(2.87987 + 5.27409i) q^{82} +(-15.8841 + 5.92447i) q^{83} +(-31.2725 - 20.0976i) q^{84} +(1.81007 - 3.53779i) q^{85} +(-7.33575 - 1.05472i) q^{86} +(3.32585 - 8.91696i) q^{87} +(-5.18743 + 6.92959i) q^{88} +(-7.01782 + 4.51008i) q^{89} +(3.30947 + 33.5640i) q^{90} +2.08125i q^{91} +(-12.5366 + 15.8580i) q^{92} +(20.9410 - 20.9410i) q^{93} +(5.98895 + 5.18946i) q^{94} +(6.93045 - 4.72190i) q^{95} +(0.967737 + 6.73076i) q^{96} +(6.12895 + 2.28598i) q^{97} +(2.38157 + 3.18141i) q^{98} +(-9.09940 + 2.67182i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8}+O(q^{10}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8	\( 200 q - 18 q^{2} - 14 q^{3} - 22 q^{5} - 36 q^{6} - 22 q^{7} - 26 q^{8} - 22 q^{10} - 44 q^{11} - 6 q^{12} - 26 q^{13} - 22 q^{15} - 52 q^{16} - 22 q^{17} + 58 q^{18} - 22 q^{20} - 44 q^{21} + 22 q^{23} - 10 q^{25} - 28 q^{26} - 26 q^{27} + 66 q^{28} - 22 q^{30} - 40 q^{31} - 46 q^{32} - 14 q^{35} - 12 q^{36} + 66 q^{37} - 22 q^{38} - 22 q^{40} - 8 q^{41} + 198 q^{42} - 22 q^{43} - 76 q^{46} + 52 q^{47} + 18 q^{48} - 82 q^{50} - 44 q^{51} + 158 q^{52} - 22 q^{53} - 10 q^{55} + 88 q^{56} + 66 q^{57} - 58 q^{58} - 22 q^{60} + 44 q^{61} + 38 q^{62} - 22 q^{63} - 22 q^{65} + 132 q^{66} - 22 q^{67} + 32 q^{70} + 132 q^{71} - 28 q^{72} + 34 q^{73} + 38 q^{75} + 132 q^{76} - 10 q^{77} + 22 q^{78} + 176 q^{80} - 48 q^{81} - 50 q^{82} - 22 q^{83} + 202 q^{85} - 46 q^{87} - 110 q^{88} + 396 q^{90} + 50 q^{92} - 36 q^{93} + 68 q^{95} + 148 q^{96} - 88 q^{97} - 50 q^{98}+O(q^{100}) \) 200 * q - 18 * q^2 - 14 * q^3 - 22 * q^5 - 36 * q^6 - 22 * q^7 - 26 * q^8 - 22 * q^10 - 44 * q^11 - 6 * q^12 - 26 * q^13 - 22 * q^15 - 52 * q^16 - 22 * q^17 + 58 * q^18 - 22 * q^20 - 44 * q^21 + 22 * q^23 - 10 * q^25 - 28 * q^26 - 26 * q^27 + 66 * q^28 - 22 * q^30 - 40 * q^31 - 46 * q^32 - 14 * q^35 - 12 * q^36 + 66 * q^37 - 22 * q^38 - 22 * q^40 - 8 * q^41 + 198 * q^42 - 22 * q^43 - 76 * q^46 + 52 * q^47 + 18 * q^48 - 82 * q^50 - 44 * q^51 + 158 * q^52 - 22 * q^53 - 10 * q^55 + 88 * q^56 + 66 * q^57 - 58 * q^58 - 22 * q^60 + 44 * q^61 + 38 * q^62 - 22 * q^63 - 22 * q^65 + 132 * q^66 - 22 * q^67 + 32 * q^70 + 132 * q^71 - 28 * q^72 + 34 * q^73 + 38 * q^75 + 132 * q^76 - 10 * q^77 + 22 * q^78 + 176 * q^80 - 48 * q^81 - 50 * q^82 - 22 * q^83 + 202 * q^85 - 46 * q^87 - 110 * q^88 + 396 * q^90 + 50 * q^92 - 36 * q^93 + 68 * q^95 + 148 * q^96 - 88 * q^97 - 50 * q^98

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