LMFDB - Embedded newform 75.2.l.a.8.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,2,Mod(2,75)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(75, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 1]))

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

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

chi := DirichletCharacter("75.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	75.l (of order $20$, 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:	$0.598878015160$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			8.8
Character	$\chi$	$=$	75.8
Dual form			75.2.l.a.47.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.12503 - 2.20799i) q^{2} +(-1.73197 + 0.0162612i) q^{3} +(-2.43396 - 3.35006i) q^{4} +(2.18396 + 0.479921i) q^{5} +(-1.91261 + 3.84248i) q^{6} +(-1.56473 + 1.56473i) q^{7} +(-5.24001 + 0.829937i) q^{8} +(2.99947 - 0.0563281i) q^{9} +O(q^{10})$	\(q+(1.12503 - 2.20799i) q^{2} +(-1.73197 + 0.0162612i) q^{3} +(-2.43396 - 3.35006i) q^{4} +(2.18396 + 0.479921i) q^{5} +(-1.91261 + 3.84248i) q^{6} +(-1.56473 + 1.56473i) q^{7} +(-5.24001 + 0.829937i) q^{8} +(2.99947 - 0.0563281i) q^{9} +(3.51667 - 4.28223i) q^{10} +(2.96536 - 0.963502i) q^{11} +(4.27003 + 5.76264i) q^{12} +(-1.61265 + 0.821689i) q^{13} +(1.69454 + 5.21527i) q^{14} +(-3.79036 - 0.795697i) q^{15} +(-1.50345 + 4.62713i) q^{16} +(0.290369 + 1.83332i) q^{17} +(3.25011 - 6.68617i) q^{18} +(-3.62080 + 4.98360i) q^{19} +(-3.70790 - 8.48450i) q^{20} +(2.68463 - 2.73552i) q^{21} +(1.20870 - 7.63144i) q^{22} +(-3.38221 - 1.72332i) q^{23} +(9.06207 - 1.52264i) q^{24} +(4.53935 + 2.09626i) q^{25} +4.48515i q^{26} +(-5.19409 + 0.146334i) q^{27} +(9.05042 + 1.43345i) q^{28} +(-1.02316 + 0.743368i) q^{29} +(-6.02115 + 7.47390i) q^{30} +(-2.59659 - 1.88653i) q^{31} +(1.02237 + 1.02237i) q^{32} +(-5.12025 + 1.71698i) q^{33} +(4.37461 + 1.42140i) q^{34} +(-4.16825 + 2.66636i) q^{35} +(-7.48930 - 9.91130i) q^{36} +(-2.20458 - 4.32674i) q^{37} +(6.93024 + 13.6014i) q^{38} +(2.77972 - 1.44937i) q^{39} +(-11.8423 - 0.702246i) q^{40} +(-3.49297 - 1.13493i) q^{41} +(-3.01971 - 9.00515i) q^{42} +(0.478175 + 0.478175i) q^{43} +(-10.4453 - 7.58899i) q^{44} +(6.57775 + 1.31649i) q^{45} +(-7.61015 + 5.52910i) q^{46} +(11.8168 + 1.87160i) q^{47} +(2.52869 - 8.03853i) q^{48} +2.10324i q^{49} +(9.73540 - 7.66450i) q^{50} +(-0.532723 - 3.17053i) q^{51} +(6.67784 + 3.40253i) q^{52} +(0.590684 - 3.72943i) q^{53} +(-5.52039 + 11.6331i) q^{54} +(6.93862 - 0.681113i) q^{55} +(6.90058 - 9.49783i) q^{56} +(6.19009 - 8.69035i) q^{57} +(0.490268 + 3.09543i) q^{58} +(3.54168 - 10.9002i) q^{59} +(6.55997 + 14.6346i) q^{60} +(-1.39483 - 4.29285i) q^{61} +(-7.08667 + 3.61084i) q^{62} +(-4.60522 + 4.78150i) q^{63} +(-5.84669 + 1.89970i) q^{64} +(-3.91632 + 1.02059i) q^{65} +(-1.96934 + 13.2371i) q^{66} +(-2.12196 + 0.336085i) q^{67} +(5.43497 - 5.43497i) q^{68} +(5.88592 + 2.92975i) q^{69} +(1.19790 + 12.2032i) q^{70} +(2.82511 + 3.88843i) q^{71} +(-15.6705 + 2.78453i) q^{72} +(2.61273 - 5.12778i) q^{73} -12.0336 q^{74} +(-7.89613 - 3.55685i) q^{75} +25.5082 q^{76} +(-3.13236 + 6.14760i) q^{77} +(-0.0729340 - 7.76816i) q^{78} +(-0.567733 - 0.781418i) q^{79} +(-5.50412 + 9.38393i) q^{80} +(8.99365 - 0.337909i) q^{81} +(-6.43561 + 6.43561i) q^{82} +(0.118177 - 0.0187175i) q^{83} +(-15.6984 - 2.33552i) q^{84} +(-0.245694 + 4.14324i) q^{85} +(1.59377 - 0.517846i) q^{86} +(1.76000 - 1.30413i) q^{87} +(-14.7389 + 7.50982i) q^{88} +(3.39784 + 10.4575i) q^{89} +(10.3069 - 13.0425i) q^{90} +(1.23765 - 3.80909i) q^{91} +(2.45893 + 15.5251i) q^{92} +(4.52790 + 3.22520i) q^{93} +(17.4267 - 23.9859i) q^{94} +(-10.2994 + 9.14628i) q^{95} +(-1.78735 - 1.75410i) q^{96} +(-2.60317 + 16.4357i) q^{97} +(4.64394 + 2.36621i) q^{98} +(8.84023 - 3.05703i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	$ 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) $ 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/75\mathbb{Z}\right)^\times$.

$n$	$26$	$52$
$\chi(n)$	$-1$	$e\left(\frac{3}{20}\right)$

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 $

$2$	1.12503	−	2.20799i	0.795514	−	1.56128i	−0.0317668	−	0.999495i	$-0.510113\pi$
$2$	1.12503	−	2.20799i	0.795514	−	1.56128i	0.827281	−	0.561789i	$-0.189887\pi$
$3$	−1.73197	+	0.0162612i	−0.999956	+	0.00938843i
$3$	−1.73197	+	0.0162612i	−0.999956	+	0.00938843i
$4$	−2.43396	−	3.35006i	−1.21698	−	1.67503i
$5$	2.18396	+	0.479921i	0.976696	+	0.214627i
$5$	2.18396	+	0.479921i	0.976696	+	0.214627i
$6$	−1.91261	+	3.84248i	−0.780821	+	1.56868i
$7$	−1.56473	+	1.56473i	−0.591412	+	0.591412i	−0.938013	−	0.346601i	$-0.887336\pi$
$7$	−1.56473	+	1.56473i	−0.591412	+	0.591412i	0.346601	+	0.938013i	$0.387336\pi$
$8$	−5.24001	+	0.829937i	−1.85262	+	0.293427i
$9$	2.99947	−	0.0563281i	0.999824	−	0.0187760i
$10$	3.51667	−	4.28223i	1.11207	−	1.35416i
$11$	2.96536	−	0.963502i	0.894088	−	0.290507i	0.174293	−	0.984694i	$-0.444236\pi$
$11$	2.96536	−	0.963502i	0.894088	−	0.290507i	0.719795	+	0.694187i	$0.244236\pi$
$12$	4.27003	+	5.76264i	1.23265	+	1.66353i
$13$	−1.61265	+	0.821689i	−0.447270	+	0.227895i	−0.663093	−	0.748537i	$-0.730757\pi$
$13$	−1.61265	+	0.821689i	−0.447270	+	0.227895i	0.215823	+	0.976433i	$0.430757\pi$
$14$	1.69454	+	5.21527i	0.452886	+	1.39384i
$15$	−3.79036	−	0.795697i	−0.978668	−	0.205448i
$16$	−1.50345	+	4.62713i	−0.375862	+	1.15678i
$17$	0.290369	+	1.83332i	0.0704247	+	0.444644i	0.997554	+	0.0699022i	$0.0222687\pi$
$17$	0.290369	+	1.83332i	0.0704247	+	0.444644i	−0.927129	+	0.374742i	$0.877731\pi$
$18$	3.25011	−	6.68617i	0.766059	−	1.57595i
$19$	−3.62080	+	4.98360i	−0.830668	+	1.14332i	0.157130	+	0.987578i	$0.449776\pi$
$19$	−3.62080	+	4.98360i	−0.830668	+	1.14332i	−0.987798	+	0.155738i	$0.950224\pi$
$20$	−3.70790	−	8.48450i	−0.829113	−	1.89719i
$21$	2.68463	−	2.73552i	0.585834	−	0.596938i
$22$	1.20870	−	7.63144i	0.257696	−	1.62703i
$23$	−3.38221	−	1.72332i	−0.705239	−	0.359337i	0.0643055	−	0.997930i	$-0.479517\pi$
$23$	−3.38221	−	1.72332i	−0.705239	−	0.359337i	−0.769545	+	0.638593i	$0.779517\pi$
$24$	9.06207	−	1.52264i	1.84979	−	0.310807i
$25$	4.53935	+	2.09626i	0.907870	+	0.419251i
$26$			4.48515i			0.879610i
$27$	−5.19409	+	0.146334i	−0.999603	+	0.0281620i
$28$	9.05042	+	1.43345i	1.71037	+	0.270896i
$29$	−1.02316	+	0.743368i	−0.189996	+	0.138040i	−0.678717	−	0.734400i	$-0.737464\pi$
$29$	−1.02316	+	0.743368i	−0.189996	+	0.138040i	0.488721	+	0.872440i	$0.337464\pi$
$30$	−6.02115	+	7.47390i	−1.09931	+	1.36454i
$31$	−2.59659	−	1.88653i	−0.466361	−	0.338831i	0.329661	−	0.944100i	$-0.393066\pi$
$31$	−2.59659	−	1.88653i	−0.466361	−	0.338831i	−0.796021	+	0.605269i	$0.793066\pi$
$32$	1.02237	+	1.02237i	0.180731	+	0.180731i
$33$	−5.12025	+	1.71698i	−0.891322	+	0.298888i
$34$	4.37461	+	1.42140i	0.750240	+	0.243768i
$35$	−4.16825	+	2.66636i	−0.704563	+	0.450697i
$36$	−7.48930	−	9.91130i	−1.24822	−	1.65188i
$37$	−2.20458	−	4.32674i	−0.362431	−	0.711311i	0.635731	−	0.771911i	$-0.280699\pi$
$37$	−2.20458	−	4.32674i	−0.362431	−	0.711311i	−0.998162	+	0.0605993i	$0.980699\pi$
$38$	6.93024	+	13.6014i	1.12423	+	2.20643i
$39$	2.77972	−	1.44937i	0.445111	−	0.232085i
$40$	−11.8423	−	0.702246i	−1.87243	−	0.111035i
$41$	−3.49297	−	1.13493i	−0.545510	−	0.177247i	0.0232809	−	0.999729i	$-0.492589\pi$
$41$	−3.49297	−	1.13493i	−0.545510	−	0.177247i	−0.568791	+	0.822482i	$0.692589\pi$
$42$	−3.01971	−	9.00515i	−0.465952	−	1.38953i
$43$	0.478175	+	0.478175i	0.0729211	+	0.0729211i	0.742627	−	0.669706i	$-0.233580\pi$
$43$	0.478175	+	0.478175i	0.0729211	+	0.0729211i	−0.669706	+	0.742627i	$0.733580\pi$
$44$	−10.4453	−	7.58899i	−1.57470	−	1.14408i
$45$	6.57775	+	1.31649i	0.980554	+	0.196251i
$46$	−7.61015	+	5.52910i	−1.12206	+	0.815221i
$47$	11.8168	+	1.87160i	1.72366	+	0.273002i	0.938247	−	0.345966i	$-0.112449\pi$
$47$	11.8168	+	1.87160i	1.72366	+	0.273002i	0.785417	+	0.618967i	$0.212449\pi$
$48$	2.52869	−	8.03853i	0.364985	−	1.16026i
$49$			2.10324i			0.300464i
$50$	9.73540	−	7.66450i	1.37679	−	1.08392i
$51$	−0.532723	−	3.17053i	−0.0745961	−	0.443963i
$52$	6.67784	+	3.40253i	0.926050	+	0.471846i
$53$	0.590684	−	3.72943i	0.0811366	−	0.512277i	−0.913330	−	0.407221i	$-0.866498\pi$
$53$	0.590684	−	3.72943i	0.0811366	−	0.512277i	0.994466	−	0.105056i	$-0.0335021\pi$
$54$	−5.52039	+	11.6331i	−0.751230	+	1.58307i
$55$	6.93862	−	0.681113i	0.935603	−	0.0918413i
$56$	6.90058	−	9.49783i	0.922128	−	1.26920i
$57$	6.19009	−	8.69035i	0.819897	−	1.15106i
$58$	0.490268	+	3.09543i	0.0643754	+	0.406450i
$59$	3.54168	−	10.9002i	0.461087	−	1.41908i	−0.402750	−	0.915310i	$-0.631946\pi$
$59$	3.54168	−	10.9002i	0.461087	−	1.41908i	0.863837	−	0.503771i	$-0.168054\pi$
$60$	6.55997	+	14.6346i	0.846888	+	1.88932i
$61$	−1.39483	−	4.29285i	−0.178590	−	0.549644i	0.821189	−	0.570656i	$-0.193311\pi$
$61$	−1.39483	−	4.29285i	−0.178590	−	0.549644i	−0.999779	+	0.0210125i	$0.993311\pi$
$62$	−7.08667	+	3.61084i	−0.900008	+	0.458577i
$63$	−4.60522	+	4.78150i	−0.580203	+	0.602412i
$64$	−5.84669	+	1.89970i	−0.730836	+	0.237463i
$65$	−3.91632	+	1.02059i	−0.485759	+	0.126588i
$66$	−1.96934	+	13.2371i	−0.242409	+	1.62938i
$67$	−2.12196	+	0.336085i	−0.259238	+	0.0410593i	−0.284701	−	0.958616i	$-0.591894\pi$
$67$	−2.12196	+	0.336085i	−0.259238	+	0.0410593i	0.0254624	+	0.999676i	$0.491894\pi$
$68$	5.43497	−	5.43497i	0.659087	−	0.659087i
$69$	5.88592	+	2.92975i	0.708582	+	0.352700i
$70$	1.19790	+	12.2032i	0.143176	+	1.45856i
$71$	2.82511	+	3.88843i	0.335279	+	0.461472i	0.943055	−	0.332637i	$-0.107938\pi$
$71$	2.82511	+	3.88843i	0.335279	+	0.461472i	−0.607776	+	0.794108i	$0.707938\pi$
$72$	−15.6705	+	2.78453i	−1.84679	+	0.328160i
$73$	2.61273	−	5.12778i	0.305797	−	0.600161i	−0.686055	−	0.727549i	$-0.740659\pi$
$73$	2.61273	−	5.12778i	0.305797	−	0.600161i	0.991853	+	0.127388i	$0.0406593\pi$
$74$	−12.0336			−1.39888
$75$	−7.89613	−	3.55685i	−0.911766	−	0.410709i
$76$	25.5082			2.92599
$77$	−3.13236	+	6.14760i	−0.356965	+	0.700584i
$78$	−0.0729340	−	7.76816i	−0.00825815	−	0.879571i
$79$	−0.567733	−	0.781418i	−0.0638750	−	0.0879164i	0.775884	−	0.630875i	$-0.217304\pi$
$79$	−0.567733	−	0.781418i	−0.0638750	−	0.0879164i	−0.839759	+	0.542959i	$0.817304\pi$
$80$	−5.50412	+	9.38393i	−0.615380	+	1.04916i
$81$	8.99365	−	0.337909i	0.999295	−	0.0375454i
$82$	−6.43561	+	6.43561i	−0.710694	+	0.710694i
$83$	0.118177	−	0.0187175i	0.0129716	−	0.00205451i	−0.149945	−	0.988694i	$-0.547910\pi$
$83$	0.118177	−	0.0187175i	0.0129716	−	0.00205451i	0.162917	+	0.986640i	$0.447910\pi$
$84$	−15.6984	−	2.33552i	−1.71284	−	0.254826i
$85$	−0.245694	+	4.14324i	−0.0266492	+	0.449397i
$86$	1.59377	−	0.517846i	0.171860	−	0.0558408i
$87$	1.76000	−	1.30413i	0.188691	−	0.139818i
$88$	−14.7389	+	7.50982i	−1.57117	+	0.800550i
$89$	3.39784	+	10.4575i	0.360170	+	1.10849i	0.952950	+	0.303126i	$0.0980303\pi$
$89$	3.39784	+	10.4575i	0.360170	+	1.10849i	−0.592780	+	0.805364i	$0.701970\pi$
$90$	10.3069	−	13.0425i	1.08645	−	1.37480i
$91$	1.23765	−	3.80909i	0.129741	−	0.399301i
$92$	2.45893	+	15.5251i	0.256361	+	1.61860i
$93$	4.52790	+	3.22520i	0.469521	+	0.334438i
$94$	17.4267	−	23.9859i	1.79743	−	2.47395i
$95$	−10.2994	+	9.14628i	−1.05670	+	0.938389i
$96$	−1.78735	−	1.75410i	−0.182420	−	0.179027i
$97$	−2.60317	+	16.4357i	−0.264311	+	1.66880i	0.396340	+	0.918104i	$0.370280\pi$
$97$	−2.60317	+	16.4357i	−0.264311	+	1.66880i	−0.660652	+	0.750693i	$0.729720\pi$
$98$	4.64394	+	2.36621i	0.469109	+	0.239023i
$99$	8.84023	−	3.05703i	0.888476	−	0.307243i
$100$	−4.02602	−	20.3093i	−0.402602	−	2.03093i
$101$		−	14.5454i		−	1.44732i	−0.690157	−	0.723660i	$-0.742458\pi$
$101$		−	14.5454i		−	1.44732i	0.690157	−	0.723660i	$-0.257542\pi$
$102$	−7.59983	−	2.39069i	−0.752495	−	0.236713i
$103$	1.36967	+	0.216934i	0.134957	+	0.0213752i	0.223548	−	0.974693i	$-0.428236\pi$
$103$	1.36967	+	0.216934i	0.134957	+	0.0213752i	−0.0885902	+	0.996068i	$0.528236\pi$
$104$	7.76839	−	5.64406i	0.761753	−	0.553446i
$105$	7.17595	−	4.68584i	0.700301	−	0.457292i
$106$	−7.57001	−	5.49993i	−0.735264	−	0.534201i
$107$	−7.71945	−	7.71945i	−0.746268	−	0.746268i	0.227508	−	0.973776i	$-0.426942\pi$
$107$	−7.71945	−	7.71945i	−0.746268	−	0.746268i	−0.973776	+	0.227508i	$0.926942\pi$
$108$	13.1324	+	17.0443i	1.26367	+	1.64009i
$109$	−6.89530	−	2.24042i	−0.660450	−	0.214593i	−0.0404336	−	0.999182i	$-0.512874\pi$
$109$	−6.89530	−	2.24042i	−0.660450	−	0.214593i	−0.620016	+	0.784589i	$0.712874\pi$
$110$	6.30224	−	16.0867i	0.600895	−	1.53380i
$111$	3.88864	+	7.45795i	0.369093	+	0.707877i
$112$	−4.88772	−	9.59270i	−0.461847	−	0.906425i
$113$	−4.19874	−	8.24049i	−0.394984	−	0.775200i	0.604791	−	0.796384i	$-0.293256\pi$
$113$	−4.19874	−	8.24049i	−0.394984	−	0.775200i	−0.999776	+	0.0211838i	$0.993256\pi$
$114$	−12.2242	−	23.4445i	−1.14490	−	2.19578i
$115$	−6.55954	−	5.38686i	−0.611681	−	0.502327i
$116$	4.98066	+	1.61831i	0.462442	+	0.150257i
$117$	−4.79083	+	2.55547i	−0.442912	+	0.236253i
$118$	−20.0830	−	20.0830i	−1.84879	−	1.84879i
$119$	−3.32299	−	2.41429i	−0.304618	−	0.221318i
$120$	20.5219	+	1.02370i	1.87339	+	0.0934507i
$121$	−1.03419	+	0.751383i	−0.0940173	+	0.0683076i
$122$	−11.0478	−	1.74980i	−1.00022	−	0.158419i
$123$	6.06819	+	1.90888i	0.547150	+	0.172118i
$124$			13.2905i			1.19352i
$125$	8.90772	+	6.75667i	0.796731	+	0.604335i
$126$	5.37650	+	15.5476i	0.478977	+	1.38509i
$127$	14.2672	+	7.26953i	1.26601	+	0.645066i	0.952506	−	0.304520i	$-0.0984959\pi$
$127$	14.2672	+	7.26953i	1.26601	+	0.645066i	0.313507	+	0.949586i	$0.398496\pi$
$128$	−2.83552	+	17.9027i	−0.250627	+	1.58239i
$129$	−0.835963	−	0.820412i	−0.0736025	−	0.0722332i
$130$	−2.15252	+	9.79537i	−0.188788	+	0.859111i
$131$	−12.1388	+	16.7076i	−1.06057	+	1.45975i	−0.181303	+	0.983427i	$0.558031\pi$
$131$	−12.1388	+	16.7076i	−1.06057	+	1.45975i	−0.879269	+	0.476325i	$0.841969\pi$
$132$	18.2145	+	12.9741i	1.58537	+	1.12925i
$133$	−2.13242	−	13.4636i	−0.184904	−	1.16744i
$134$	−1.64519	+	5.06336i	−0.142122	+	0.437408i
$135$	−11.4139	−	2.17317i	−0.982353	−	0.187036i
$136$	−3.04307	−	9.36561i	−0.260941	−	0.803094i
$137$	3.53930	−	1.80336i	0.302383	−	0.154072i	−0.296215	−	0.955121i	$-0.595725\pi$
$137$	3.53930	−	1.80336i	0.302383	−	0.154072i	0.598598	+	0.801049i	$0.295725\pi$
$138$	13.0907	−	9.70000i	1.11435	−	0.825719i
$139$	7.67326	−	2.49319i	0.650838	−	0.211470i	0.0350543	−	0.999385i	$-0.488840\pi$
$139$	7.67326	−	2.49319i	0.650838	−	0.211470i	0.615783	+	0.787915i	$0.288840\pi$
$140$	19.0778	+	7.47408i	1.61237	+	0.631675i
$141$	−20.4969	−	3.04941i	−1.72615	−	0.256807i
$142$	11.7639	−	1.86322i	0.987207	−	0.156358i
$143$	−3.99040	+	3.99040i	−0.333694	+	0.333694i
$144$	−4.24891	+	13.9636i	−0.354076	+	1.16364i
$145$	−2.59129	+	1.13245i	−0.215195	+	0.0940449i
$146$	−8.38269	−	11.5378i	−0.693756	−	0.954873i
$147$	−0.0342014	−	3.64277i	−0.00282088	−	0.300450i
$148$	−9.12896	+	17.9166i	−0.750396	+	1.47274i
$149$	−12.2135			−1.00057			−0.500286	−	0.865860i	$-0.666772\pi$
$149$	−12.2135			−1.00057			−0.500286	+	0.865860i	$0.666772\pi$
$150$	−16.7368	+	13.4330i	−1.36656	+	1.09680i
$151$	−2.06910			−0.168381			−0.0841903	−	0.996450i	$-0.526830\pi$
$151$	−2.06910			−0.168381			−0.0841903	+	0.996450i	$0.526830\pi$
$152$	14.8370	−	29.1192i	1.20344	−	2.36188i
$153$	0.974219	+	5.48262i	0.0787610	+	0.443244i
$154$	10.0498	+	13.8324i	0.809840	+	1.11465i
$155$	−4.76545	−	5.36626i	−0.382770	−	0.431029i
$156$	−11.6212	−	5.78451i	−0.930439	−	0.463131i
$157$	0.228812	−	0.228812i	0.0182612	−	0.0182612i	−0.697917	−	0.716178i	$-0.745890\pi$
$157$	0.228812	−	0.228812i	0.0182612	−	0.0182612i	0.716178	+	0.697917i	$0.245890\pi$
$158$	−2.36408	+	0.374433i	−0.188076	+	0.0297883i
$159$	−0.962404	+	6.46888i	−0.0763236	+	0.513016i
$160$	1.74216	+	2.72347i	0.137730	+	0.215310i
$161$	7.98877	−	2.59571i	0.629603	−	0.204571i
$162$	9.37200	−	20.2380i	0.736334	−	1.59005i
$163$	11.2508	−	5.73256i	0.881230	−	0.449009i	0.0460200	−	0.998941i	$-0.485346\pi$
$163$	11.2508	−	5.73256i	0.881230	−	0.449009i	0.835210	+	0.549932i	$0.185346\pi$
$164$	4.69965	+	14.4640i	0.366981	+	1.12945i
$165$	−12.0064	+	1.29250i	−0.934700	+	0.100621i
$166$	0.0916247	−	0.281992i	0.00711146	−	0.0218868i
$167$	−1.61691	−	10.2088i	−0.125120	−	0.789978i	−0.967829	−	0.251608i	$-0.919041\pi$
$167$	−1.61691	−	10.2088i	−0.125120	−	0.789978i	0.842709	−	0.538369i	$-0.180959\pi$
$168$	−11.7972	+	16.5622i	−0.910172	+	1.27780i
$169$	−5.71572	+	7.86702i	−0.439671	+	0.605155i
$170$	8.87181	+	5.20374i	0.680437	+	0.399109i
$171$	−10.5798	+	15.1521i	−0.809055	+	1.15871i
$172$	0.438056	−	2.76578i	0.0334014	−	0.210888i
$173$	1.53474	+	0.781987i	0.116684	+	0.0594534i	0.511358	−	0.859368i	$-0.329143\pi$
$173$	1.53474	+	0.781987i	0.116684	+	0.0594534i	−0.394674	+	0.918821i	$0.629143\pi$
$174$	−0.899468	−	5.35324i	−0.0681885	−	0.405828i
$175$	−10.3829	+	3.82278i	−0.784876	+	0.288975i
$176$			15.1697i			1.14346i
$177$	−5.95685	+	18.9364i	−0.447744	+	1.42335i
$178$	26.9127	+	4.26255i	2.01719	+	0.319491i
$179$	14.7883	−	10.7444i	1.10533	−	0.803070i	0.123410	−	0.992356i	$-0.460617\pi$
$179$	14.7883	−	10.7444i	1.10533	−	0.803070i	0.981922	+	0.189285i	$0.0606171\pi$
$180$	−11.5997	−	25.2402i	−0.864588	−	1.88129i
$181$	−6.12804	−	4.45228i	−0.455494	−	0.330936i	0.336267	−	0.941767i	$-0.390835\pi$
$181$	−6.12804	−	4.45228i	−0.455494	−	0.330936i	−0.791761	+	0.610831i	$0.790835\pi$
$182$	−7.01804	−	7.01804i	−0.520212	−	0.520212i
$183$	2.48562	+	7.41243i	0.183742	+	0.547943i
$184$	19.1531	+	6.22321i	1.41198	+	0.458781i
$185$	−2.73823	−	10.5074i	−0.201318	−	0.772523i
$186$	12.2152	−	6.36912i	0.895663	−	0.467006i
$187$	2.62745	+	5.15666i	0.192138	+	0.377092i
$188$	−22.4917	−	44.1425i	−1.64038	−	3.21943i
$189$	7.89837	−	8.35632i	0.574522	−	0.607833i
$190$	8.60778	+	33.0308i	0.624474	+	2.39631i
$191$	17.6862	+	5.74660i	1.27973	+	0.415809i	0.868485	−	0.495716i	$-0.165094\pi$
$191$	17.6862	+	5.74660i	1.27973	+	0.415809i	0.411244	+	0.911525i	$0.365094\pi$
$192$	10.0954	−	3.38531i	0.728574	−	0.244314i
$193$	12.0270	+	12.0270i	0.865722	+	0.865722i	0.991995	−	0.126274i	$-0.0403017\pi$
$193$	12.0270	+	12.0270i	0.865722	+	0.865722i	−0.126274	+	0.991995i	$0.540302\pi$
$194$	33.3613	+	24.2384i	2.39520	+	1.74022i
$195$	6.76637	−	1.83132i	0.484550	−	0.131143i
$196$	7.04599	−	5.11921i	0.503285	−	0.365658i
$197$	20.6601	+	3.27224i	1.47197	+	0.233138i	0.840310	−	0.542106i	$-0.182373\pi$
$197$	20.6601	+	3.27224i	1.47197	+	0.233138i	0.631663	+	0.775243i	$0.282373\pi$
$198$	3.19560	−	22.9584i	0.227101	−	1.63158i
$199$		−	9.90370i		−	0.702054i	−0.936365	−	0.351027i	$-0.885832\pi$
$199$		−	9.90370i		−	0.702054i	0.936365	−	0.351027i	$-0.114168\pi$
$200$	−25.5260	−	7.21703i	−1.80496	−	0.510321i
$201$	3.66971	−	0.616596i	0.258841	−	0.0434913i
$202$	−32.1161	−	16.3639i	−2.25968	−	1.15136i
$203$	0.437796	−	2.76414i	0.0307273	−	0.194004i
$204$	−9.32485	+	9.50161i	−0.652870	+	0.665245i
$205$	−7.08382	−	4.15500i	−0.494756	−	0.290198i
$206$	2.01990	−	2.78016i	0.140733	−	0.193703i
$207$	−10.2419	−	4.97854i	−0.711862	−	0.346032i
$208$	−1.37752	−	8.69734i	−0.0955140	−	0.603052i
$209$	−5.93524	+	18.2668i	−0.410549	+	1.26354i
$210$	−2.27316	−	21.1161i	−0.156863	−	1.45715i
$211$	1.66755	+	5.13218i	0.114799	+	0.353314i	0.991905	−	0.126982i	$-0.0405292\pi$
$211$	1.66755	+	5.13218i	0.114799	+	0.353314i	−0.877106	+	0.480296i	$0.840529\pi$
$212$	−13.9315	+	7.09846i	−0.956820	+	0.487524i
$213$	−4.95625	−	6.68872i	−0.339596	−	0.458304i
$214$	−25.7291	+	8.35988i	−1.75880	+	0.571470i
$215$	0.814829	+	1.27380i	0.0555709	+	0.0868726i
$216$	27.0957	−	5.07756i	1.84363	−	0.345484i
$217$	7.01487	−	1.11105i	0.476200	−	0.0754227i
$218$	−12.7042	+	12.7042i	−0.860438	+	0.860438i
$219$	−4.44181	+	8.92367i	−0.300149	+	0.603006i
$220$	−19.1701	−	21.5870i	−1.29245	−	1.45539i
$221$	−1.97468	−	2.71791i	−0.132831	−	0.182827i
$222$	20.8419	−	0.195681i	1.39882	−	0.0131333i
$223$	3.82306	−	7.50318i	0.256011	−	0.502450i	−0.726850	−	0.686796i	$-0.759017\pi$
$223$	3.82306	−	7.50318i	0.256011	−	0.502450i	0.982861	+	0.184346i	$0.0590167\pi$
$224$	−3.19947			−0.213773
$225$	13.7337	+	6.03197i	0.915582	+	0.402131i
$226$	−22.9186			−1.52452
$227$	−5.32153	+	10.4441i	−0.353203	+	0.693199i	−0.997431	−	0.0716340i	$-0.977179\pi$
$227$	−5.32153	+	10.4441i	−0.353203	+	0.693199i	0.644228	+	0.764833i	$0.277179\pi$
$228$	−44.1796	+	0.414795i	−2.92587	+	0.0274705i
$229$	−17.1419	−	23.5938i	−1.13277	−	1.55912i	−0.782699	−	0.622401i	$-0.786157\pi$
$229$	−17.1419	−	23.5938i	−1.13277	−	1.55912i	−0.350071	−	0.936723i	$-0.613843\pi$
$230$	−19.2738	+	8.42305i	−1.27088	+	0.555399i
$231$	5.32520	−	10.6984i	0.350372	−	0.703904i
$232$	4.74442	−	4.74442i	0.311486	−	0.311486i
$233$	24.1451	−	3.82420i	1.58180	−	0.250532i	0.697195	−	0.716881i	$-0.254431\pi$
$233$	24.1451	−	3.82420i	1.58180	−	0.250532i	0.884601	+	0.466349i	$0.154431\pi$
$234$	0.252640	+	13.4531i	0.0165156	+	0.879454i
$235$	24.9093	+	9.75866i	1.62490	+	0.636585i
$236$	−45.1365	+	14.6657i	−2.93814	+	0.954658i
$237$	0.996007	+	1.34416i	0.0646976	+	0.0873128i
$238$	−9.06919	+	4.62098i	−0.587868	+	0.299534i
$239$	−5.39643	−	16.6085i	−0.349066	−	1.07432i	−0.959371	−	0.282149i	$-0.908953\pi$
$239$	−5.39643	−	16.6085i	−0.349066	−	1.07432i	0.610304	−	0.792167i	$-0.291047\pi$
$240$	9.38041	−	16.3422i	0.605503	−	1.05489i
$241$	−5.07543	+	15.6206i	−0.326937	+	1.00621i	0.643621	+	0.765344i	$0.277431\pi$
$241$	−5.07543	+	15.6206i	−0.326937	+	1.00621i	−0.970559	+	0.240865i	$0.922569\pi$
$242$	0.495554	+	3.12881i	0.0318554	+	0.201127i
$243$	−15.5713	+	0.731498i	−0.998898	+	0.0469256i
$244$	−10.9863	+	15.1214i	−0.703329	+	0.968049i
$245$	−1.00939	+	4.59340i	−0.0644877	+	0.293462i
$246$	11.0417	−	11.2510i	0.703990	−	0.717335i
$247$	1.74413	−	11.0120i	0.110976	−	0.700677i
$248$	15.1719	+	7.73045i	0.963414	+	0.490884i
$249$	−0.204376	+	0.0343399i	−0.0129518	+	0.00217620i
$250$	24.9401	−	12.0667i	1.57735	−	0.763166i
$251$			14.3155i			0.903586i	0.892123	+	0.451793i	$0.149216\pi$
$251$			14.3155i			0.903586i	−0.892123	+	0.451793i	$0.850784\pi$
$252$	27.2272	+	3.78979i	1.71515	+	0.238734i
$253$	−11.6899	−	1.85149i	−0.734936	−	0.116402i
$254$	32.1021	−	23.3235i	2.01426	−	1.46345i
$255$	0.358161	−	7.17998i	0.0224289	−	0.449628i
$256$	26.3920	+	19.1749i	1.64950	+	1.19843i
$257$	2.74685	+	2.74685i	0.171344	+	0.171344i	0.787570	−	0.616226i	$-0.211339\pi$
$257$	2.74685	+	2.74685i	0.171344	+	0.171344i	−0.616226	+	0.787570i	$0.711339\pi$
$258$	−2.75194	+	0.922813i	−0.171328	+	0.0574518i
$259$	10.2198	+	3.32060i	0.635024	+	0.206332i
$260$	12.9512	+	10.6358i	0.803199	+	0.659606i
$261$	−3.02706	+	2.28734i	−0.187370	+	0.141583i
$262$	23.2338	+	45.5989i	1.43539	+	2.81711i
$263$	6.08584	+	11.9441i	0.375269	+	0.736507i	0.998980	−	0.0451478i	$-0.0143759\pi$
$263$	6.08584	+	11.9441i	0.375269	+	0.736507i	−0.623711	+	0.781655i	$0.714376\pi$
$264$	25.4052	−	13.2465i	1.56358	−	0.815265i
$265$	3.07986	−	7.86144i	0.189194	−	0.482924i
$266$	−32.1264	−	10.4385i	−1.96980	−	0.640026i
$267$	−6.05502	−	18.0568i	−0.370561	−	1.10506i
$268$	6.29066	+	6.29066i	0.384263	+	0.384263i
$269$	−18.5658	−	13.4888i	−1.13197	−	0.822428i	−0.145994	−	0.989285i	$-0.546638\pi$
$269$	−18.5658	−	13.4888i	−1.13197	−	0.822428i	−0.985981	+	0.166858i	$0.946638\pi$
$270$	−17.6393	+	22.7569i	−1.07349	+	1.38494i
$271$	3.77616	−	2.74354i	0.229385	−	0.166658i	−0.467156	−	0.884175i	$-0.654721\pi$
$271$	3.77616	−	2.74354i	0.229385	−	0.166658i	0.696541	+	0.717517i	$0.254721\pi$
$272$	−8.91955	−	1.41272i	−0.540827	−	0.0856586i
$273$	−2.08163	+	6.61737i	−0.125986	+	0.400501i
$274$		−	9.84358i		−	0.594672i
$275$	15.4805	+	1.84247i	0.933512	+	0.111105i
$276$	−4.51127	−	26.8491i	−0.271546	−	1.61612i
$277$	−17.3485	−	8.83951i	−1.04237	−	0.531115i	−0.152965	−	0.988232i	$-0.548882\pi$
$277$	−17.3485	−	8.83951i	−1.04237	−	0.531115i	−0.889407	+	0.457117i	$0.848882\pi$
$278$	3.12768	−	19.7474i	0.187586	−	1.18437i
$279$	−7.89465	−	5.51233i	−0.472640	−	0.330015i
$280$	19.6288	−	17.4311i	1.17304	−	1.04171i
$281$	−11.4764	+	15.7960i	−0.684626	+	0.942308i	−0.999978	−	0.00666749i	$-0.997878\pi$
$281$	−11.4764	+	15.7960i	−0.684626	+	0.942308i	0.315351	+	0.948975i	$0.397878\pi$
$282$	−29.7926	+	41.8263i	−1.77413	+	2.49072i
$283$	2.05624	+	12.9826i	0.122231	+	0.771734i	0.970310	+	0.241865i	$0.0777591\pi$
$283$	2.05624	+	12.9826i	0.122231	+	0.771734i	−0.848079	+	0.529869i	$0.822241\pi$
$284$	6.15026	−	18.9286i	0.364951	−	1.12320i
$285$	17.6896	−	16.0086i	1.04784	−	0.948268i
$286$	4.32145	+	13.3001i	0.255533	+	0.786449i
$287$	7.24142	−	3.68969i	0.427447	−	0.217795i
$288$	3.12416	+	3.00898i	0.184093	+	0.177306i
$289$	12.8912	−	4.18861i	0.758308	−	0.246389i
$290$	−0.414837	+	6.99559i	−0.0243601	+	0.410795i
$291$	4.24135	−	28.5086i	0.248632	−	1.67120i
$292$	−23.5377	+	3.72800i	−1.37744	+	0.218165i
$293$	−1.80765	+	1.80765i	−0.105604	+	0.105604i	−0.757935	−	0.652331i	$-0.773791\pi$
$293$	−1.80765	+	1.80765i	−0.105604	+	0.105604i	0.652331	+	0.757935i	$0.273791\pi$
$294$	−8.08167	−	4.02269i	−0.471332	−	0.234608i
$295$	12.9661	−	22.1058i	0.754916	−	1.28705i
$296$	15.1430	+	20.8425i	0.880167	+	1.21145i
$297$	−15.2613	+	5.43845i	−0.885552	+	0.315571i
$298$	−13.7405	+	26.9673i	−0.795969	+	1.56218i
$299$	6.87037			0.397324
$300$	7.30322	+	35.1097i	0.421652	+	2.02706i
$301$	−1.49643			−0.0862528
$302$	−2.32779	+	4.56854i	−0.133949	+	0.262890i
$303$	0.236526	+	25.1922i	0.0135881	+	1.44726i
$304$	−17.6161	−	24.2465i	−1.01035	−	1.39063i
$305$	−0.986026	−	10.0448i	−0.0564597	−	0.575165i
$306$	13.2016	+	4.01703i	0.754685	+	0.229638i
$307$	13.3679	−	13.3679i	0.762944	−	0.762944i	−0.213910	−	0.976853i	$-0.568620\pi$
$307$	13.3679	−	13.3679i	0.762944	−	0.762944i	0.976853	+	0.213910i	$0.0686199\pi$
$308$	28.2189	−	4.46943i	1.60792	−	0.254669i
$309$	−2.37576	−	0.353452i	−0.135152	−	0.0201072i
$310$	−17.2099	+	4.48488i	−0.977457	+	0.254724i
$311$	16.6965	−	5.42503i	0.946773	−	0.307625i	0.205370	−	0.978684i	$-0.434160\pi$
$311$	16.6965	−	5.42503i	0.946773	−	0.307625i	0.741404	+	0.671059i	$0.234160\pi$
$312$	−13.3629	+	9.90170i	−0.756523	+	0.560573i
$313$	−7.76371	+	3.95581i	−0.438831	+	0.223595i	−0.659425	−	0.751770i	$-0.729200\pi$
$313$	−7.76371	+	3.95581i	−0.438831	+	0.223595i	0.220594	+	0.975366i	$0.429200\pi$
$314$	−0.247795	−	0.762634i	−0.0139839	−	0.0430379i
$315$	−12.3524	+	8.23245i	−0.695976	+	0.463846i
$316$	−1.23596	+	3.80388i	−0.0695279	+	0.213985i
$317$	−0.141432	−	0.892964i	−0.00794359	−	0.0501539i	0.983398	−	0.181461i	$-0.0580826\pi$
$317$	−0.141432	−	0.892964i	−0.00794359	−	0.0501539i	−0.991342	+	0.131307i	$0.958083\pi$
$318$	13.2005	+	9.40264i	0.740247	+	0.527274i
$319$	−2.31779	+	3.19017i	−0.129771	+	0.178615i
$320$	−13.6806	+	1.34293i	−0.764771	+	0.0750719i
$321$	13.4954	+	13.2444i	0.753241	+	0.739229i
$322$	3.25628	−	20.5594i	0.181466	−	1.14573i
$323$	−10.1879	−	5.19098i	−0.566869	−	0.288834i
$324$	−23.0222	−	29.3068i	−1.27901	−	1.62816i
$325$	−9.04288	+	0.349397i	−0.501609	+	0.0193811i
$326$		−	31.2909i		−	1.73304i
$327$	11.9789	+	3.76822i	0.662435	+	0.208383i
$328$	19.2451	+	3.04813i	1.06263	+	0.168305i
$329$	−21.4187	+	15.5616i	−1.18085	+	0.857939i
$330$	−10.6537	+	27.9642i	−0.586469	+	1.53938i
$331$	15.6465	+	11.3679i	0.860012	+	0.624835i	0.927888	−	0.372859i	$-0.121622\pi$
$331$	15.6465	+	11.3679i	0.860012	+	0.624835i	−0.0678765	+	0.997694i	$0.521622\pi$
$332$	−0.350344	−	0.350344i	−0.0192276	−	0.0192276i
$333$	−6.85630	−	12.8537i	−0.375723	−	0.704381i
$334$	−24.3599	−	7.91501i	−1.33291	−	0.433090i
$335$	−4.79556	−	0.284376i	−0.262009	−	0.0155371i
$336$	8.62140	+	16.5348i	0.470336	+	0.902049i
$337$	−10.1065	−	19.8351i	−0.550536	−	1.08049i	−0.983808	−	0.179224i	$-0.942641\pi$
$337$	−10.1065	−	19.8351i	−0.550536	−	1.08049i	0.433273	−	0.901263i	$-0.357359\pi$
$338$	10.9400	+	21.4709i	0.595055	+	1.16786i
$339$	7.40611	+	14.2040i	0.402245	+	0.771458i
$340$	14.4781	−	9.26139i	0.785185	−	0.502269i
$341$	−9.51748	−	3.09242i	−0.515400	−	0.167464i
$342$	21.5532	+	40.4065i	1.16546	+	2.18494i
$343$	−14.2441	−	14.2441i	−0.769110	−	0.769110i
$344$	−2.90250	−	2.10879i	−0.156492	−	0.113698i
$345$	11.4486	+	9.22323i	0.616370	+	0.496562i
$346$	3.45324	−	2.50892i	0.185647	−	0.134881i
$347$	−24.7725	−	3.92358i	−1.32986	−	0.210629i	−0.549255	−	0.835655i	$-0.685088\pi$
$347$	−24.7725	−	3.92358i	−1.32986	−	0.210629i	−0.780604	+	0.625026i	$0.785088\pi$
$348$	−8.65268	−	2.72189i	−0.463833	−	0.145908i
$349$			30.7060i			1.64366i	0.569736	+	0.821828i	$0.307045\pi$
$349$			30.7060i			1.64366i	−0.569736	+	0.821828i	$0.692955\pi$
$350$	−3.24041	+	27.2261i	−0.173207	+	1.45530i
$351$	8.25604	−	4.50391i	0.440675	−	0.240401i
$352$	4.01675	+	2.04664i	0.214094	+	0.109086i
$353$	5.26697	−	33.2543i	0.280333	−	1.76995i	−0.298408	−	0.954438i	$-0.596456\pi$
$353$	5.26697	−	33.2543i	0.280333	−	1.76995i	0.578741	−	0.815512i	$-0.303544\pi$
$354$	35.1098	+	34.4566i	1.86606	+	1.83135i
$355$	4.30378	+	9.84800i	0.228421	+	0.522677i
$356$	26.7630	−	36.8361i	1.41843	−	1.95231i
$357$	5.79459	+	4.12746i	0.306682	+	0.218448i
$358$	−7.08614	−	44.7402i	−0.374514	−	2.36459i
$359$	−4.75066	+	14.6210i	−0.250730	+	0.771669i	0.743910	+	0.668279i	$0.232969\pi$
$359$	−4.75066	+	14.6210i	−0.250730	+	0.771669i	−0.994641	+	0.103390i	$0.967031\pi$
$360$	−35.5601	−	1.43931i	−1.87418	−	0.0758584i
$361$	−5.85477	−	18.0191i	−0.308146	−	0.948376i
$362$	−16.7248	+	8.52171i	−0.879036	+	0.447891i
$363$	1.77897	−	1.31819i	0.0933719	−	0.0691872i
$364$	−15.7731	+	5.12498i	−0.826733	+	0.268622i
$365$	8.16704	−	9.94496i	0.427482	−	0.520543i
$366$	19.1630	+	2.85096i	1.00166	+	0.149022i
$367$	−25.0446	+	3.96667i	−1.30732	+	0.207058i	−0.770933	−	0.636917i	$-0.780210\pi$
$367$	−25.0446	+	3.96667i	−1.30732	+	0.207058i	−0.536382	+	0.843975i	$0.680210\pi$
$368$	13.0590	−	13.0590i	0.680748	−	0.680748i
$369$	−10.5410	−	3.20745i	−0.548742	−	0.166973i
$370$	−26.2809	−	5.77518i	−1.36628	−	0.300237i
$371$	4.91129	+	6.75981i	0.254981	+	0.350952i
$372$	−0.216119	−	23.0187i	−0.0112053	−	1.19347i
$373$	−9.96569	+	19.5588i	−0.516004	+	1.01271i	0.475139	+	0.879911i	$0.342398\pi$
$373$	−9.96569	+	19.5588i	−0.516004	+	1.01271i	−0.991142	+	0.132804i	$0.957602\pi$
$374$	14.3418			0.741597
$375$	−15.5378	−	11.5575i	−0.802369	−	0.596828i
$376$	−63.4738			−3.27341
$377$	1.03918	−	2.03951i	0.0535207	−	0.105040i
$378$	−9.56478	−	26.8406i	−0.491959	−	1.38053i
$379$	9.06150	+	12.4721i	0.465458	+	0.640648i	0.975629	−	0.219425i	$-0.0704181\pi$
$379$	9.06150	+	12.4721i	0.465458	+	0.640648i	−0.510172	+	0.860073i	$0.670418\pi$
$380$	55.7089	+	12.2419i	2.85781	+	0.627998i
$381$	−24.8287	−	12.3586i	−1.27201	−	0.633152i
$382$	32.5859	−	32.5859i	1.66724	−	1.66724i
$383$	−14.5296	+	2.30126i	−0.742427	+	0.117589i	−0.516179	−	0.856481i	$-0.672646\pi$
$383$	−14.5296	+	2.30126i	−0.742427	+	0.117589i	−0.226248	+	0.974070i	$0.572646\pi$
$384$	4.61992	−	31.0532i	0.235759	−	1.58468i
$385$	−9.79130	+	11.9228i	−0.499011	+	0.607643i
$386$	40.0862	−	13.0248i	2.04033	−	0.662944i
$387$	1.46121	+	1.40734i	0.0742774	+	0.0715390i
$388$	61.3967	−	31.2832i	3.11694	−	1.58816i
$389$	−0.890618	−	2.74104i	−0.0451561	−	0.138976i	0.925937	−	0.377679i	$-0.123278\pi$
$389$	−0.890618	−	2.74104i	−0.0451561	−	0.138976i	−0.971093	+	0.238703i	$0.923278\pi$
$390$	3.56882	−	17.0003i	0.180714	−	0.860846i
$391$	2.17730	−	6.70105i	0.110111	−	0.338887i
$392$	−1.74556	−	11.0210i	−0.0881641	−	0.556646i
$393$	20.7524	−	29.1346i	1.04682	−	1.46965i
$394$	30.4683	−	41.9360i	1.53497	−	2.11270i
$395$	−0.864887	−	1.97905i	−0.0435172	−	0.0995769i
$396$	−31.7580	−	22.1746i	−1.59590	−	1.11431i
$397$	−2.07287	+	13.0876i	−0.104034	+	0.656846i	0.879469	+	0.475956i	$0.157898\pi$
$397$	−2.07287	+	13.0876i	−0.104034	+	0.656846i	−0.983503	+	0.180890i	$0.942102\pi$
$398$	−21.8673	−	11.1419i	−1.09611	−	0.558494i
$399$	3.91223	+	23.2839i	0.195856	+	1.16565i
$400$	−16.5243	+	17.8526i	−0.826216	+	0.892629i
$401$			1.97899i			0.0988261i	0.998778	+	0.0494130i	$0.0157351\pi$
$401$			1.97899i			0.0988261i	−0.998778	+	0.0494130i	$0.984265\pi$
$402$	2.76708	−	8.79637i	0.138010	−	0.438723i
$403$	5.73754	+	0.908737i	0.285807	+	0.0452674i
$404$	−48.7279	+	35.4029i	−2.42430	+	1.76136i
$405$	19.8039	+	3.57826i	0.984066	+	0.177805i
$406$	−5.61065	−	4.07638i	−0.278452	−	0.202307i
$407$	−10.7062	−	10.7062i	−0.530686	−	0.530686i
$408$	5.42282	+	16.1715i	0.268469	+	0.800609i
$409$	14.6485	+	4.75959i	0.724323	+	0.235347i	0.647896	−	0.761728i	$-0.275649\pi$
$409$	14.6485	+	4.75959i	0.724323	+	0.235347i	0.0764264	+	0.997075i	$0.475649\pi$
$410$	−17.1437	+	10.9665i	−0.846666	+	0.541598i
$411$	−6.10066	+	3.18094i	−0.300923	+	0.156904i
$412$	−2.60698	−	5.11648i	−0.128436	−	0.252071i
$413$	11.5140	+	22.5976i	0.566569	+	1.11195i
$414$	−22.5150	+	17.0130i	−1.10655	+	0.836145i
$415$	0.267077	+	0.0158377i	0.0131103	+	0.000777440i
$416$	−2.48880	−	0.808661i	−0.122024	−	0.0396479i
$417$	−13.2494	+	4.44293i	−0.648824	+	0.217571i
$418$	33.6556	+	33.6556i	1.64615	+	1.64615i
$419$	6.99133	+	5.07950i	0.341549	+	0.248150i	0.745315	−	0.666712i	$-0.232299\pi$
$419$	6.99133	+	5.07950i	0.341549	+	0.248150i	−0.403766	+	0.914862i	$0.632299\pi$
$420$	−33.1638	−	12.6347i	−1.61823	−	0.616509i
$421$	21.5780	−	15.6774i	1.05165	−	0.764068i	0.0791238	−	0.996865i	$-0.474788\pi$
$421$	21.5780	−	15.6774i	1.05165	−	0.764068i	0.972525	+	0.232797i	$0.0747878\pi$
$422$	13.2078	+	2.09192i	0.642947	+	0.101833i
$423$	35.5497	+	4.94820i	1.72849	+	0.240590i
$424$			20.0325i			0.972864i
$425$	−2.52501	+	8.93075i	−0.122481	+	0.433205i
$426$	−20.3445	+	3.41835i	−0.985696	+	0.165620i
$427$	8.89969	+	4.53462i	0.430686	+	0.219446i
$428$	−7.07178	+	44.6495i	−0.341827	+	2.15821i
$429$	6.84638	−	6.97615i	0.330546	−	0.336812i
$430$	3.72924	−	0.366072i	0.179840	−	0.0176536i
$431$	−1.45875	+	2.00780i	−0.0702655	+	0.0967122i	−0.842703	−	0.538378i	$-0.819037\pi$
$431$	−1.45875	+	2.00780i	−0.0702655	+	0.0967122i	0.772438	+	0.635090i	$0.219037\pi$
$432$	7.13193	−	24.2538i	0.343135	−	1.16691i
$433$	3.38157	+	21.3504i	0.162508	+	1.02603i	0.925257	+	0.379340i	$0.123849\pi$
$433$	3.38157	+	21.3504i	0.162508	+	1.02603i	−0.762749	+	0.646694i	$0.776151\pi$
$434$	5.43873	−	16.7387i	0.261068	−	0.803483i
$435$	4.46964	−	2.00351i	0.214303	−	0.0960611i
$436$	9.27735	+	28.5527i	0.444304	+	1.36743i
$437$	20.8346	−	10.6158i	0.996656	−	0.507821i
$438$	14.7062	+	19.8468i	0.702690	+	0.948318i
$439$	−3.91868	+	1.27326i	−0.187028	+	0.0607692i	−0.401034	−	0.916063i	$-0.631349\pi$
$439$	−3.91868	+	1.27326i	−0.187028	+	0.0607692i	0.214005	+	0.976832i	$0.431349\pi$
$440$	−35.7932	+	9.32766i	−1.70637	+	0.444679i
$441$	0.118472	+	6.30862i	0.00564151	+	0.300411i
$442$	−8.22269	+	1.30235i	−0.391113	+	0.0619463i
$443$	5.90521	−	5.90521i	0.280565	−	0.280565i	−0.552769	−	0.833334i	$-0.686429\pi$
$443$	5.90521	−	5.90521i	0.280565	−	0.280565i	0.833334	+	0.552769i	$0.186429\pi$
$444$	15.5198	−	31.1795i	0.736536	−	1.47972i
$445$	2.40198	+	24.4694i	0.113865	+	1.15996i
$446$	−12.2659	−	16.8825i	−0.580807	−	0.799412i
$447$	21.1535	−	0.198607i	1.00053	−	0.00939379i
$448$	6.17596	−	12.1210i	0.291787	−	0.572664i
$449$	−10.5523			−0.497992			−0.248996	−	0.968504i	$-0.580101\pi$
$449$	−10.5523			−0.497992			−0.248996	+	0.968504i	$0.580101\pi$
$450$	28.7693	−	23.5378i	1.35620	−	1.10958i
$451$	−11.4514			−0.539226
$452$	−17.3866	+	34.1231i	−0.817795	+	1.60501i
$453$	3.58362	−	0.0336460i	0.168373	−	0.00158083i
$454$	17.0736	+	23.4998i	0.801303	+	1.10290i
$455$	4.53103	−	7.72492i	0.212418	−	0.362150i
$456$	−25.2237	+	50.6749i	−1.18121	+	2.37307i
$457$	−2.95505	+	2.95505i	−0.138232	+	0.138232i	−0.772837	−	0.634605i	$-0.781163\pi$
$457$	−2.95505	+	2.95505i	−0.138232	+	0.138232i	0.634605	+	0.772837i	$0.281163\pi$
$458$	−71.3800	+	11.3055i	−3.33537	+	0.528271i
$459$	−1.77648	−	9.47992i	−0.0829189	−	0.442485i
$460$	−2.08061	+	35.0863i	−0.0970090	+	1.63590i
$461$	−21.0601	+	6.84283i	−0.980865	+	0.318702i	−0.755194	−	0.655501i	$-0.772457\pi$
$461$	−21.0601	+	6.84283i	−0.980865	+	0.318702i	−0.225671	+	0.974204i	$0.572457\pi$
$462$	−17.6310	−	23.7940i	−0.820269	−	1.10700i
$463$	−33.0664	+	16.8481i	−1.53672	+	0.783000i	−0.998221	−	0.0596238i	$-0.981010\pi$
$463$	−33.0664	+	16.8481i	−1.53672	+	0.783000i	−0.538503	+	0.842624i	$0.681010\pi$
$464$	−1.90140	−	5.85191i	−0.0882703	−	0.271668i
$465$	8.34090	+	9.21674i	0.386800	+	0.427416i
$466$	18.7200	−	57.6144i	0.867189	−	2.66893i
$467$	−2.83781	−	17.9172i	−0.131318	−	0.829110i	−0.962137	−	0.272567i	$-0.912127\pi$
$467$	−2.83781	−	17.9172i	−0.131318	−	0.829110i	0.830819	−	0.556543i	$-0.187873\pi$
$468$	20.2217	+	9.82964i	0.934746	+	0.454375i
$469$	2.79441	−	3.84617i	0.129034	−	0.177600i
$470$	49.5706	−	44.0207i	2.28652	−	2.03052i
$471$	−0.392576	+	0.400017i	−0.0180889	+	0.0184318i
$472$	−9.51200	+	60.0564i	−0.437825	+	2.76432i
$473$	1.87868	+	0.957237i	0.0863820	+	0.0440138i
$474$	4.08843	−	0.686951i	0.187788	−	0.0315527i
$475$	−26.8830	+	15.0322i	−1.23348	+	0.689724i
$476$			17.0085i			0.779584i
$477$	1.56167	−	11.2196i	0.0715038	−	0.513710i
$478$	−42.7426	−	6.76976i	−1.95500	−	0.309641i
$479$	−0.835878	+	0.607301i	−0.0381923	+	0.0277483i	−0.606718	−	0.794917i	$-0.707514\pi$
$479$	−0.835878	+	0.607301i	−0.0381923	+	0.0277483i	0.568525	+	0.822666i	$0.307514\pi$
$480$	−3.06166	−	4.68866i	−0.139745	−	0.214007i
$481$	7.11047	+	5.16606i	0.324209	+	0.235552i
$482$	28.7801	+	28.7801i	1.31090	+	1.31090i
$483$	−13.7941	+	4.62561i	−0.627655	+	0.210472i
$484$	5.03436	+	1.63576i	0.228834	+	0.0743528i
$485$	−13.5731	+	34.6457i	−0.616321	+	1.57318i
$486$	−15.9030	+	35.2042i	−0.721373	+	1.59689i
$487$	−15.3730	−	30.1712i	−0.696616	−	1.36719i	−0.919791	−	0.392408i	$-0.871642\pi$
$487$	−15.3730	−	30.1712i	−0.696616	−	1.36719i	0.223175	−	0.974778i	$-0.428358\pi$
$488$	10.8717	+	21.3370i	0.492140	+	0.965880i
$489$	−19.3929	+	10.1116i	−0.876975	+	0.457263i
$490$	9.00658	+	7.39642i	0.406876	+	0.334136i
$491$	25.1739	+	8.17951i	1.13608	+	0.369136i	0.815885	−	0.578214i	$-0.196250\pi$
$491$	25.1739	+	8.17951i	1.13608	+	0.369136i	0.320199	+	0.947350i	$0.396250\pi$
$492$	−8.37488	−	24.9749i	−0.377569	−	1.12596i
$493$	−1.65992	−	1.65992i	−0.0747591	−	0.0747591i
$494$	−22.3522	−	16.2398i	−1.00567	−	0.730663i
$495$	20.7738	−	2.43382i	0.933714	−	0.109392i
$496$	12.6331	−	9.17846i	0.567241	−	0.412125i
$497$	−10.5049	−	1.66381i	−0.471208	−	0.0746320i
$498$	−0.154106	+	0.489893i	−0.00690566	+	0.0219526i
$499$		−	4.05591i		−	0.181567i	−0.995871	−	0.0907837i	$-0.971063\pi$
$499$		−	4.05591i		−	0.181567i	0.995871	−	0.0907837i	$-0.0289372\pi$
$500$	0.954195	−	46.2868i	0.0426729	−	2.07001i
$501$	2.96645	+	17.6550i	0.132531	+	0.788768i
$502$	31.6085	+	16.1053i	1.41076	+	0.718816i
$503$	−1.48123	+	9.35210i	−0.0660446	+	0.416989i	0.932409	+	0.361404i	$0.117702\pi$
$503$	−1.48123	+	9.35210i	−0.0660446	+	0.416989i	−0.998454	+	0.0555853i	$0.982298\pi$
$504$	20.1631	−	28.8772i	0.898135	−	1.28629i
$505$	6.98064	−	31.7665i	0.310634	−	1.41359i
$506$	−17.2395	+	23.7281i	−0.766389	+	1.05484i
$507$	9.77156	−	13.7184i	0.433970	−	0.609257i
$508$	−10.3726	−	65.4899i	−0.460209	−	2.90564i
$509$	6.07003	−	18.6816i	0.269049	−	0.828049i	−0.721683	−	0.692223i	$-0.756631\pi$
$509$	6.07003	−	18.6816i	0.269049	−	0.828049i	0.990733	−	0.135825i	$-0.0433686\pi$
$510$	−15.4504	−	8.86848i	−0.684154	−	0.392703i
$511$	3.93537	+	12.1118i	0.174090	+	0.535795i
$512$	39.7292	−	20.2431i	1.75580	−	0.894625i
$513$	18.0775	−	26.4151i	0.798140	−	1.16626i
$514$	9.15530	−	2.97474i	0.403823	−	0.131210i
$515$	2.88719	+	1.13111i	0.127225	+	0.0498426i
$516$	−0.713727	+	4.79738i	−0.0314201	+	0.211193i
$517$	36.8444	−	5.83559i	1.62042	−	0.256649i
$518$	18.8293	−	18.8293i	0.827314	−	0.827314i
$519$	−2.67084	−	1.32942i	−0.117237	−	0.0583553i
$520$	19.6745	−	8.59819i	0.862786	−	0.377055i
$521$	−21.6574	−	29.8089i	−0.948830	−	1.30595i	−0.952045	−	0.305957i	$-0.901024\pi$
$521$	−21.6574	−	29.8089i	−0.948830	−	1.30595i	0.00321572	−	0.999995i	$-0.498976\pi$
$522$	1.64491	+	9.25704i	0.0719956	+	0.405170i
$523$	−12.9262	+	25.3690i	−0.565222	+	1.10931i	0.414706	+	0.909956i	$0.363884\pi$
$523$	−12.9262	+	25.3690i	−0.565222	+	1.10931i	−0.979927	+	0.199354i	$0.936116\pi$
$524$	85.5169			3.73582
$525$	17.9208	−	6.78980i	0.782128	−	0.296331i
$526$	33.2193			1.44843
$527$	2.70464	−	5.30815i	0.117816	−	0.231227i
$528$	−0.246678	−	26.2735i	−0.0107353	−	1.14341i
$529$	−5.04956	−	6.95013i	−0.219546	−	0.302180i
$530$	−13.8930	−	15.6446i	−0.603475	−	0.679559i
$531$	10.0092	−	32.8942i	0.434361	−	1.42749i
$532$	−39.9135	+	39.9135i	−1.73047	+	1.73047i
$533$	6.56552	−	1.03988i	0.284384	−	0.0450420i
$534$	−46.6813	−	6.94499i	−2.02010	−	0.300539i
$535$	−13.1542	−	20.5637i	−0.568707	−	0.889046i
$536$	10.8402	−	3.52218i	0.468223	−	0.152135i
$537$	−25.4383	+	18.8494i	−1.09774	+	0.813412i
$538$	−50.6702	+	25.8177i	−2.18455	+	1.11308i
$539$	2.02648	+	6.23687i	0.0872867	+	0.268641i
$540$	20.5008	+	43.5267i	0.882213	+	1.87309i
$541$	−9.28899	+	28.5886i	−0.399365	+	1.22912i	0.526145	+	0.850395i	$0.323637\pi$
$541$	−9.28899	+	28.5886i	−0.399365	+	1.22912i	−0.925510	+	0.378724i	$0.876363\pi$
$542$	−1.80943	−	11.4243i	−0.0777215	−	0.490714i
$543$	10.6860	+	7.61159i	0.458581	+	0.326645i
$544$	−1.57746	+	2.17119i	−0.0676332	+	0.0930891i
$545$	−13.9838	−	8.20218i	−0.599001	−	0.351343i
$546$	12.2692	+	12.0409i	0.525073	+	0.515305i
$547$	−1.03492	+	6.53424i	−0.0442500	+	0.279384i	−0.999885	−	0.0151701i	$-0.995171\pi$
$547$	−1.03492	+	6.53424i	−0.0442500	+	0.279384i	0.955635	+	0.294554i	$0.0951710\pi$
$548$	−14.6559	−	7.46755i	−0.626069	−	0.318998i
$549$	−4.42557	−	12.7977i	−0.188879	−	0.546193i
$550$	21.4842	−	32.1080i	0.916088	−	1.36909i
$551$		−	7.79060i		−	0.331891i
$552$	−33.2738	−	10.4670i	−1.41623	−	0.445504i
$553$	2.11106	+	0.334359i	0.0897713	+	0.0142184i
$554$	−39.0351	+	28.3607i	−1.65844	+	1.20493i
$555$	4.91340	+	18.1541i	0.208562	+	0.770599i
$556$	−27.0288	−	19.6375i	−1.14628	−	0.832818i
$557$	18.6108	+	18.6108i	0.788564	+	0.788564i	0.981259	−	0.192695i	$-0.0617227\pi$
$557$	18.6108	+	18.6108i	0.788564	+	0.788564i	−0.192695	+	0.981259i	$0.561723\pi$
$558$	−21.0529	+	11.2298i	−0.891239	+	0.475395i
$559$	−1.16404	−	0.378221i	−0.0492338	−	0.0159970i
$560$	−6.07085	−	23.2958i	−0.256540	−	0.984426i
$561$	−4.63453	−	8.88848i	−0.195670	−	0.375272i
$562$	21.9660	+	43.1107i	0.926580	+	1.81852i
$563$	−0.423451	−	0.831069i	−0.0178463	−	0.0350254i	0.881911	−	0.471415i	$-0.156257\pi$
$563$	−0.423451	−	0.831069i	−0.0178463	−	0.0350254i	−0.899758	+	0.436390i	$0.856257\pi$
$564$	39.6729	+	76.0880i	1.67053	+	3.20388i
$565$	−5.21509	−	20.0120i	−0.219400	−	0.841909i
$566$	30.9787	+	10.0656i	1.30213	+	0.423089i
$567$	−13.5439	+	14.6014i	−0.568790	+	0.613200i
$568$	−18.0308	−	18.0308i	−0.756554	−	0.756554i
$569$	19.6855	+	14.3024i	0.825259	+	0.599586i	0.918214	−	0.396085i	$-0.129631\pi$
$569$	19.6855	+	14.3024i	0.825259	+	0.599586i	−0.0929550	+	0.995670i	$0.529631\pi$
$570$	−15.4456	−	57.0685i	−0.646944	−	2.39034i
$571$	−21.5571	+	15.6622i	−0.902138	+	0.655441i	−0.939014	−	0.343878i	$-0.888259\pi$
$571$	−21.5571	+	15.6622i	−0.902138	+	0.655441i	0.0368765	+	0.999320i	$0.488259\pi$
$572$	23.0805	+	3.65560i	0.965045	+	0.152848i
$573$	−30.7255	−	9.66536i	−1.28358	−	0.403776i
$574$		−	20.1400i		−	0.840626i
$575$	−11.7405	−	14.9127i	−0.489613	−	0.621904i
$576$	−17.4300	+	6.02744i	−0.726249	+	0.251143i
$577$	12.8174	+	6.53081i	0.533597	+	0.271881i	0.699958	−	0.714184i	$-0.253202\pi$
$577$	12.8174	+	6.53081i	0.533597	+	0.271881i	−0.166361	+	0.986065i	$0.553202\pi$
$578$	5.25456	−	33.1760i	0.218561	−	1.37994i
$579$	−21.0260	−	20.6349i	−0.873812	−	0.857556i
$580$	10.1009	+	5.92465i	0.419416	+	0.246008i
$581$	−0.155628	+	0.214203i	−0.00645653	+	0.00888665i
$582$	−58.1751	−	41.4378i	−2.41143	−	1.71765i
$583$	−1.84173	−	11.6282i	−0.0762766	−	0.481591i
$584$	−9.43503	+	29.0380i	−0.390424	+	1.20160i
$585$	−11.6894	+	3.28182i	−0.483297	+	0.135687i
$586$	1.95762	+	6.02492i	0.0808684	+	0.248887i
$587$	−24.8545	+	12.6640i	−1.02585	+	0.522698i	−0.884146	−	0.467210i	$-0.845259\pi$
$587$	−24.8545	+	12.6640i	−1.02585	+	0.522698i	−0.141707	+	0.989909i	$0.545259\pi$
$588$	−12.1202	+	8.98093i	−0.499830	+	0.370367i
$589$	18.8034	−	6.10961i	0.774782	−	0.251742i
$590$	−34.2221	−	53.4986i	−1.40890	−	2.20250i
$591$	−35.8360	−	5.33148i	−1.47410	−	0.219308i
$592$	23.3349	−	3.69588i	0.959057	−	0.151900i
$593$	3.80445	−	3.80445i	0.156230	−	0.156230i	−0.624664	−	0.780894i	$-0.714764\pi$
$593$	3.80445	−	3.80445i	0.156230	−	0.156230i	0.780894	+	0.624664i	$0.214764\pi$
$594$	−5.16137	+	39.8153i	−0.211773	+	1.63364i
$595$	−6.09860	−	6.86749i	−0.250018	−	0.281540i
$596$	29.7272	+	40.9160i	1.21768	+	1.67599i
$597$	0.161046	+	17.1529i	0.00659119	+	0.702023i
$598$	7.72935	−	15.1697i	0.316077	−	0.620335i
$599$	5.36984			0.219406			0.109703	−	0.993964i	$-0.465010\pi$
$599$	5.36984			0.219406			0.109703	+	0.993964i	$0.465010\pi$
$600$	44.3278	+	12.0846i	1.80967	+	0.493353i
$601$	21.5855			0.880489			0.440245	−	0.897878i	$-0.354892\pi$
$601$	21.5855			0.880489			0.440245	+	0.897878i	$0.354892\pi$
$602$	−1.68352	+	3.30410i	−0.0686153	+	0.134665i
$603$	−6.34582	+	1.12760i	−0.258422	+	0.0459195i
$604$	5.03610	+	6.93159i	0.204916	+	0.282042i
$605$	−2.61923	+	1.14466i	−0.106487	+	0.0465371i
$606$	55.8903	+	27.8197i	2.27039	+	1.13010i
$607$	−12.6373	+	12.6373i	−0.512932	+	0.512932i	−0.915424	−	0.402492i	$-0.868144\pi$
$607$	−12.6373	+	12.6373i	−0.512932	+	0.512932i	0.402492	+	0.915424i	$0.368144\pi$
$608$	−8.79689	+	1.39329i	−0.356761	+	0.0565054i
$609$	−0.713304	+	4.79453i	−0.0289045	+	0.194284i
$610$	−23.2882	−	9.12356i	−0.942910	−	0.369402i
$611$	−20.5944	+	6.69152i	−0.833159	+	0.270710i
$612$	15.9959	−	16.6082i	0.646596	−	0.671346i
$613$	38.2195	−	19.4738i	1.54367	−	0.786539i	0.545017	−	0.838425i	$-0.316523\pi$
$613$	38.2195	−	19.4738i	1.54367	−	0.786539i	0.998653	+	0.0518855i	$0.0165231\pi$
$614$	−14.4769	−	44.5553i	−0.584239	−	1.79810i
$615$	12.3366	+	7.08116i	0.497458	+	0.285540i
$616$	11.3115	−	34.8132i	0.455753	−	1.40266i
$617$	6.76379	+	42.7049i	0.272300	+	1.71923i	0.622552	+	0.782578i	$0.286096\pi$
$617$	6.76379	+	42.7049i	0.272300	+	1.71923i	−0.350252	+	0.936655i	$0.613904\pi$
$618$	−3.45321	+	4.84801i	−0.138908	+	0.195015i
$619$	−4.97024	+	6.84094i	−0.199771	+	0.274961i	−0.897135	−	0.441756i	$-0.854356\pi$
$619$	−4.97024	+	6.84094i	−0.199771	+	0.274961i	0.697365	+	0.716716i	$0.254356\pi$
$620$	−6.37837	+	29.0258i	−0.256162	+	1.16570i
$621$	17.8197	+	8.45616i	0.715079	+	0.339334i
$622$	6.80563	−	42.9691i	0.272881	−	1.72290i
$623$	−21.6798	−	11.0464i	−0.868584	−	0.442566i
$624$	2.52726	+	15.0412i	0.101172	+	0.602128i
$625$	16.2114	+	19.0313i	0.648457	+	0.761251i
$626$			21.5926i			0.863013i
$627$	9.98265	−	31.7341i	0.398668	−	1.26734i
$628$	−1.32345	−	0.209614i	−0.0528115	−	0.00836452i
$629$	7.29213	−	5.29805i	0.290756	−	0.211247i
$630$	4.28043	+	36.5356i	0.170537	+	1.45561i
$631$	16.2185	+	11.7834i	0.645649	+	0.469092i	0.861786	−	0.507271i	$-0.169346\pi$
$631$	16.2185	+	11.7834i	0.645649	+	0.469092i	−0.216137	+	0.976363i	$0.569346\pi$
$632$	3.62346	+	3.62346i	0.144133	+	0.144133i
$633$	−2.97160	−	8.86169i	−0.118111	−	0.352221i
$634$	−2.13077	−	0.692329i	−0.0846237	−	0.0274959i
$635$	27.6703	+	22.7235i	1.09806	+	0.901754i
$636$	24.0136	−	12.5209i	0.952201	−	0.496486i
$637$	−1.72821	−	3.39181i	−0.0684743	−	0.134388i
$638$	4.43628	+	8.70668i	0.175634	+	0.344701i
$639$	8.69286	+	11.5041i	0.343884	+	0.455095i
$640$	−14.7846	+	37.7380i	−0.584411	+	1.49173i
$641$	29.4270	+	9.56142i	1.16230	+	0.377653i	0.825763	−	0.564018i	$-0.190745\pi$
$641$	29.4270	+	9.56142i	1.16230	+	0.377653i	0.336535	+	0.941671i	$0.390745\pi$
$642$	44.4261	−	14.8975i	1.75336	−	0.587957i
$643$	−18.5682	−	18.5682i	−0.732259	−	0.732259i	0.238808	−	0.971067i	$-0.423243\pi$
$643$	−18.5682	−	18.5682i	−0.732259	−	0.732259i	−0.971067	+	0.238808i	$0.923243\pi$
$644$	−28.1401	−	20.4450i	−1.10888	−	0.805646i
$645$	−1.43198	−	2.19294i	−0.0563840	−	0.0863470i
$646$	−22.9233	+	16.6547i	−0.901904	+	0.655271i
$647$	−18.6386	−	2.95206i	−0.732758	−	0.116057i	−0.221105	−	0.975250i	$-0.570966\pi$
$647$	−18.6386	−	2.95206i	−0.732758	−	0.116057i	−0.511653	+	0.859192i	$0.670966\pi$
$648$	−46.8464	+	9.23481i	−1.84030	+	0.362778i
$649$		−	35.7353i		−	1.40273i
$650$	−9.40201	+	20.3597i	−0.368777	+	0.798571i
$651$	−12.1315	+	2.03837i	−0.475471	+	0.0798901i
$652$	−46.5884	−	23.7380i	−1.82454	−	0.929651i
$653$	−4.01444	+	25.3462i	−0.157097	+	0.991872i	0.775604	+	0.631220i	$0.217446\pi$
$653$	−4.01444	+	25.3462i	−0.157097	+	0.991872i	−0.932701	+	0.360651i	$0.882554\pi$
$654$	21.7968	−	22.2100i	0.852322	−	0.868478i
$655$	−34.5290	+	30.6631i	−1.34916	+	1.19811i
$656$	10.5030	−	14.4561i	0.410073	−	0.564417i
$657$	7.54798	−	15.5278i	0.294475	−	0.605797i
$658$	10.2632	+	64.7995i	0.400103	+	2.52615i
$659$	11.8237	−	36.3895i	0.460585	−	1.41753i	−0.403866	−	0.914818i	$-0.632334\pi$
$659$	11.8237	−	36.3895i	0.460585	−	1.41753i	0.864451	−	0.502717i	$-0.167666\pi$
$660$	33.5531	+	37.0764i	1.30605	+	1.44320i
$661$	−1.59416	−	4.90633i	−0.0620058	−	0.190834i	0.915255	−	0.402875i	$-0.131989\pi$
$661$	−1.59416	−	4.90633i	−0.0620058	−	0.190834i	−0.977261	+	0.212041i	$0.931989\pi$
$662$	42.7029	−	21.7582i	1.65970	−	0.845657i
$663$	3.46429	+	4.67524i	0.134542	+	0.181571i
$664$	−0.603717	+	0.196159i	−0.0234287	+	0.00761246i
$665$	1.80433	−	30.4272i	0.0699690	−	1.17992i
$666$	−36.0945	+	0.677830i	−1.39863	+	0.0262654i
$667$	4.74160	−	0.750995i	0.183595	−	0.0290787i
$668$	−30.2645	+	30.2645i	−1.17097	+	1.17097i
$669$	−6.49943	+	13.0575i	−0.251282	+	0.504831i
$670$	−6.02303	+	10.2686i	−0.232690	+	0.396711i
$671$	−8.27235	−	11.3859i	−0.319350	−	0.439548i
$672$	5.54140	−	0.0520273i	0.213764	−	0.00200700i
$673$	11.4111	−	22.3956i	0.439867	−	0.863287i	−0.559538	−	0.828804i	$-0.689022\pi$
$673$	11.4111	−	22.3956i	0.439867	−	0.863287i	0.999405	−	0.0344829i	$-0.0109784\pi$
$674$	−55.1658			−2.12491
$675$	−23.8846	−	10.2239i	−0.919317	−	0.393517i
$676$	40.2668			1.54872
$677$	19.8551	−	38.9679i	0.763094	−	1.49766i	−0.101307	−	0.994855i	$-0.532303\pi$
$677$	19.8551	−	38.9679i	0.763094	−	1.49766i	0.864402	−	0.502802i	$-0.167697\pi$
$678$	39.6944	−	0.372685i	1.52446	−	0.0143129i
$679$	−21.6442	−	29.7907i	−0.830629	−	1.14326i
$680$	−2.15119	−	21.9145i	−0.0824943	−	0.840384i
$681$	9.04693	−	18.1754i	0.346679	−	0.696485i
$682$	−17.5354	+	17.5354i	−0.671467	+	0.671467i
$683$	0.223698	−	0.0354302i	0.00855955	−	0.00135570i	−0.152153	−	0.988357i	$-0.548621\pi$
$683$	0.223698	−	0.0354302i	0.00855955	−	0.00135570i	0.160713	+	0.987001i	$0.448621\pi$
$684$	76.5112	−	1.43683i	2.92548	−	0.0549386i
$685$	8.59516	−	2.23989i	0.328404	−	0.0855817i
$686$	−47.4759	+	15.4258i	−1.81264	+	0.588961i
$687$	30.0730	+	40.5852i	1.14736	+	1.54842i
$688$	−2.93149	+	1.49367i	−0.111762	+	0.0569456i
$689$	2.11186	+	6.49964i	0.0804555	+	0.247617i
$690$	33.2447	−	14.9019i	1.26561	−	0.567306i
$691$	9.07781	−	27.9386i	0.345336	−	1.06284i	−0.616067	−	0.787693i	$-0.711275\pi$
$691$	9.07781	−	27.9386i	0.345336	−	1.06284i	0.961404	−	0.275142i	$-0.0887249\pi$
$692$	−1.11578	−	7.04478i	−0.0424157	−	0.267802i
$693$	−9.04914	+	18.6160i	−0.343748	+	0.707163i
$694$	−36.5330	+	50.2833i	−1.38677	+	1.90873i
$695$	17.9546	−	1.76247i	0.681058	−	0.0668544i
$696$	−8.14006	+	8.29436i	−0.308548	+	0.314397i
$697$	1.06644	−	6.73327i	0.0403945	−	0.255041i
$698$	67.7985	+	34.5451i	2.56621	+	1.30755i
$699$	−41.7565	+	7.01605i	−1.57937	+	0.265371i
$700$	38.0782	+	25.4789i	1.43922	+	0.963013i
$701$		−	22.1771i		−	0.837619i	−0.908074	−	0.418809i	$-0.862448\pi$
$701$		−	22.1771i		−	0.837619i	0.908074	−	0.418809i	$-0.137552\pi$
$702$	−0.656329	−	23.2963i	−0.0247715	−	0.879261i
$703$	29.5451	+	4.67948i	1.11431	+	0.176490i
$704$	−15.5071	+	11.2666i	−0.584447	+	0.424626i
$705$	−43.3009	−	16.4967i	−1.63081	−	0.621301i
$706$	−67.4997	−	49.0414i	−2.54039	−	1.84570i
$707$	22.7596	+	22.7596i	0.855962	+	0.855962i
$708$	77.9368	−	26.1347i	2.92904	−	0.982201i
$709$	39.9401	+	12.9773i	1.49998	+	0.487373i	0.940012	−	0.341141i	$-0.110813\pi$
$709$	39.9401	+	12.9773i	1.49998	+	0.487373i	0.559968	+	0.828514i	$0.310813\pi$
$710$	26.5861	+	1.57655i	0.997760	+	0.0591671i
$711$	−1.74692	−	2.31186i	−0.0655145	−	0.0867016i
$712$	−26.4838	−	51.9773i	−0.992521	−	1.94793i
$713$	5.53110	+	10.8554i	0.207141	+	0.406538i
$714$	15.6325	−	8.15090i	0.585030	−	0.305040i
$715$	−10.6299	+	6.79979i	−0.397537	+	0.254298i
$716$	−71.9884	−	23.3905i	−2.69033	−	0.874142i
$717$	9.61656	+	28.6778i	0.359137	+	1.07099i
$718$	26.9385	+	26.9385i	1.00533	+	1.00533i
$719$	15.7102	+	11.4141i	0.585892	+	0.425675i	0.840843	−	0.541278i	$-0.182059\pi$
$719$	15.7102	+	11.4141i	0.585892	+	0.425675i	−0.254951	+	0.966954i	$0.582059\pi$
$720$	−15.9809	+	28.4569i	−0.595572	+	1.06053i
$721$	−2.48260	+	1.80372i	−0.0924570	+	0.0671739i
$722$	−46.3728	−	7.34474i	−1.72582	−	0.273343i
$723$	8.53651	−	27.1370i	0.317476	−	1.00923i
$724$			31.3660i			1.16571i
$725$	−6.20277	+	1.22961i	−0.230365	+	0.0456665i
$726$	−0.909166	−	5.41096i	−0.0337423	−	0.200819i
$727$	20.4226	+	10.4058i	0.757433	+	0.385931i	0.789656	−	0.613549i	$-0.210259\pi$
$727$	20.4226	+	10.4058i	0.757433	+	0.385931i	−0.0322234	+	0.999481i	$0.510259\pi$
$728$	−3.32399	+	20.9868i	−0.123195	+	0.777824i
$729$	26.9572	−	1.52014i	0.998414	−	0.0563016i
$730$	−12.7702	−	29.2211i	−0.472647	−	1.08152i
$731$	−0.737799	+	1.01549i	−0.0272885	+	0.0375594i
$732$	18.7822	−	26.3685i	0.694209	−	0.974609i
$733$	−1.18984	−	7.51236i	−0.0439478	−	0.277475i	0.955922	−	0.293621i	$-0.0948604\pi$
$733$	−1.18984	−	7.51236i	−0.0439478	−	0.277475i	−0.999870	+	0.0161457i	$0.994860\pi$
$734$	−19.4174	+	59.7607i	−0.716710	+	2.20581i
$735$	1.67355	−	7.97207i	0.0617297	−	0.294054i
$736$	−1.69600	−	5.21975i	−0.0625153	−	0.192402i
$737$	−5.96854	+	3.04112i	−0.219854	+	0.112021i
$738$	−18.9409	+	19.6659i	−0.697225	+	0.723913i
$739$	10.6892	−	3.47313i	0.393208	−	0.127761i	−0.105738	−	0.994394i	$-0.533721\pi$
$739$	10.6892	−	3.47313i	0.393208	−	0.127761i	0.498946	+	0.866633i	$0.333721\pi$
$740$	−28.5358	+	34.7479i	−1.04900	+	1.27736i
$741$	−2.84172	+	19.1009i	−0.104393	+	0.701688i
$742$	20.4509	−	3.23911i	0.750777	−	0.118911i
$743$	−16.0909	+	16.0909i	−0.590317	+	0.590317i	−0.937717	−	0.347400i	$-0.887065\pi$
$743$	−16.0909	+	16.0909i	−0.590317	+	0.590317i	0.347400	+	0.937717i	$0.387065\pi$
$744$	−26.4030	−	13.1422i	−0.967980	−	0.481817i
$745$	−26.6738	−	5.86153i	−0.977254	−	0.214750i
$746$	31.9739	+	44.0083i	1.17065	+	1.61126i
$747$	0.353415	−	0.0627992i	0.0129308	−	0.00229770i
$748$	10.8800	−	21.3532i	0.397813	−	0.780751i
$749$	24.1577			0.882704
$750$	−42.9993	+	21.3048i	−1.57011	+	0.777941i
$751$	−47.2674			−1.72481			−0.862406	−	0.506217i	$-0.831043\pi$
$751$	−47.2674			−1.72481			−0.862406	+	0.506217i	$0.831043\pi$
$752$	−26.4262	+	51.8643i	−0.963663	+	1.89130i
$753$	−0.232788	−	24.7941i	−0.00848326	−	0.903547i
$754$	−3.33412	−	4.58902i	−0.121421	−	0.167122i
$755$	−4.51882	−	0.993002i	−0.164457	−	0.0361391i
$756$	−47.2185	−	6.12107i	−1.71732	−	0.222621i
$757$	−10.5135	+	10.5135i	−0.382121	+	0.382121i	−0.871866	−	0.489745i	$-0.837090\pi$
$757$	−10.5135	+	10.5135i	−0.382121	+	0.382121i	0.489745	+	0.871866i	$0.337090\pi$
$758$	37.7326	−	5.97626i	1.37051	−	0.217068i
$759$	20.2767	+	3.01665i	0.735996	+	0.109497i
$760$	46.3782	−	56.4745i	1.68231	−	2.04855i
$761$	43.2653	−	14.0577i	1.56837	−	0.509593i	0.609339	−	0.792909i	$-0.291435\pi$
$761$	43.2653	−	14.0577i	1.56837	−	0.509593i	0.959026	+	0.283316i	$0.0914347\pi$
$762$	−55.2207	+	40.9178i	−2.00043	+	1.48229i
$763$	14.2949	−	7.28362i	0.517511	−	0.263685i
$764$	−23.7961	−	73.2368i	−0.860912	−	2.64961i
$765$	−0.503570	+	12.4414i	−0.0182066	+	0.449818i
$766$	−11.2650	+	34.6701i	−0.407021	+	1.25268i
$767$	3.24504	+	20.4884i	0.117172	+	0.739792i
$768$	−46.0222	−	32.7813i	−1.66068	−	1.18290i
$769$	2.64937	−	3.64654i	0.0955386	−	0.131498i	−0.758572	−	0.651590i	$-0.774102\pi$
$769$	2.64937	−	3.64654i	0.0955386	−	0.131498i	0.854110	+	0.520092i	$0.174102\pi$
$770$	15.3100	+	35.0326i	0.551733	+	1.26249i
$771$	−4.80214	−	4.71281i	−0.172945	−	0.169728i
$772$	11.0179	−	69.5644i	0.396543	−	2.50368i
$773$	1.38385	+	0.705109i	0.0497738	+	0.0253610i	0.478700	−	0.877978i	$-0.341108\pi$
$773$	1.38385	+	0.705109i	0.0497738	+	0.0253610i	−0.428926	+	0.903339i	$0.641108\pi$
$774$	4.75129	−	1.64304i	0.170781	−	0.0590578i
$775$	−7.83217	−	14.0067i	−0.281340	−	0.503137i
$776$		−	88.2840i		−	3.16921i
$777$	−17.7543	−	5.58501i	−0.636934	−	0.200361i
$778$	−7.05416	−	1.11727i	−0.252904	−	0.0400560i
$779$	18.3034	−	13.2982i	0.655787	−	0.476457i
$780$	−22.6041	−	18.2104i	−0.809356	−	0.652036i
$781$	12.1240	+	8.80858i	0.433830	+	0.315196i
$782$	−12.3463	−	12.3463i	−0.441504	−	0.441504i
$783$	5.20560	−	4.01085i	0.186033	−	0.143336i
$784$	−9.73200	−	3.16212i	−0.347571	−	0.112933i
$785$	0.609528	−	0.389904i	0.0217550	−	0.0139163i
$786$	−40.9818	−	78.5983i	−1.46177	−	2.80351i
$787$	−6.12843	−	12.0277i	−0.218455	−	0.428742i	0.755606	−	0.655026i	$-0.227342\pi$
$787$	−6.12843	−	12.0277i	−0.218455	−	0.428742i	−0.974061	+	0.226284i	$0.927342\pi$
$788$	−39.3237	−	77.1771i	−1.40085	−	2.74932i
$789$	−10.7348	−	20.5880i	−0.382167	−	0.732951i
$790$	−5.34275	−	0.316824i	−0.190086	−	0.0112721i
$791$	19.4640	+	6.32425i	0.692061	+	0.224864i
$792$	−43.7858	+	23.3557i	−1.55586	+	0.829909i
$793$	5.77677	+	5.77677i	0.205139	+	0.205139i
$794$	26.5652	+	19.3007i	0.942762	+	0.684957i
$795$	−5.20640	+	13.6659i	−0.184652	+	0.484679i
$796$	−33.1780	+	24.1052i	−1.17596	+	0.854386i
$797$	−7.79652	−	1.23485i	−0.276167	−	0.0437406i	0.0168146	−	0.999859i	$-0.494647\pi$
$797$	−7.79652	−	1.23485i	−0.276167	−	0.0437406i	−0.292982	+	0.956118i	$0.594647\pi$
$798$	55.8119	+	17.5568i	1.97572	+	0.621504i
$799$			22.2075i			0.785643i
$800$	2.49775	+	6.78405i	0.0883088	+	0.239853i
$801$	10.7808	+	31.1755i	0.380920	+	1.10153i
$802$	4.36959	+	2.22642i	0.154296	+	0.0786175i
$803$	2.80706	−	17.7231i	0.0990589	−	0.625434i
$804$	−10.9976	−	10.7930i	−0.387854	−	0.380639i
$805$	18.6929	−	1.83494i	0.658837	−	0.0646732i
$806$	8.46137	−	11.6461i	0.298039	−	0.410215i
$807$	32.3748	+	23.0604i	1.13965	+	0.811764i
$808$	12.0717	+	76.2180i	0.424683	+	2.68134i
$809$	−10.0045	+	30.7907i	−0.351739	+	1.08254i	0.606137	+	0.795360i	$0.292718\pi$
$809$	−10.0045	+	30.7907i	−0.351739	+	1.08254i	−0.957876	+	0.287181i	$0.907282\pi$
$810$	30.1807	−	39.7012i	1.06044	−	1.39496i
$811$	7.15200	+	22.0116i	0.251141	+	0.772931i	0.994566	+	0.104112i	$0.0332001\pi$
$811$	7.15200	+	22.0116i	0.251141	+	0.772931i	−0.743425	+	0.668819i	$0.766800\pi$
$812$	−10.3256	+	5.26116i	−0.362357	+	0.184630i
$813$	−6.49559	+	4.81314i	−0.227810	+	0.168804i
$814$	−35.6839	+	11.5944i	−1.25072	+	0.406384i
$815$	27.3224	−	7.12019i	0.957063	−	0.249409i
$816$	15.4714	+	2.30175i	0.541607	+	0.0805773i
$817$	−4.11441	+	0.651659i	−0.143945	+	0.0227987i
$818$	26.9891	−	26.9891i	0.943652	−	0.943652i
$819$	3.49773	−	11.4950i	0.122221	−	0.401667i
$820$	3.32225	+	33.8443i	0.116018	+	1.18190i
$821$	−32.0977	−	44.1787i	−1.12022	−	1.54185i	−0.805438	−	0.592680i	$-0.798070\pi$
$821$	−32.0977	−	44.1787i	−1.12022	−	1.54185i	−0.314779	−	0.949165i	$-0.601930\pi$
$822$	0.160069	+	17.0488i	0.00558304	+	0.594646i
$823$	4.91864	−	9.65338i	0.171453	−	0.336496i	−0.789251	−	0.614071i	$-0.789531\pi$
$823$	4.91864	−	9.65338i	0.171453	−	0.336496i	0.960704	+	0.277575i	$0.0895308\pi$
$824$	−7.35712			−0.256298
$825$	−26.8419	−	2.93937i	−0.934514	−	0.102336i
$826$	62.8488			2.18679
$827$	−8.69790	+	17.0706i	−0.302456	+	0.593603i	−0.991348	−	0.131261i	$-0.958097\pi$
$827$	−8.69790	+	17.0706i	−0.302456	+	0.593603i	0.688892	+	0.724864i	$0.258097\pi$
$828$	8.25000	+	46.4286i	0.286707	+	1.61350i
$829$	3.00953	+	4.14227i	0.104525	+	0.143867i	0.858075	−	0.513524i	$-0.171660\pi$
$829$	3.00953	+	4.14227i	0.104525	+	0.143867i	−0.753550	+	0.657391i	$0.771660\pi$
$830$	0.335438	−	0.571886i	0.0116432	−	0.0198505i
$831$	30.1909	+	15.0277i	1.04731	+	0.521305i
$832$	7.86773	−	7.86773i	0.272764	−	0.272764i
$833$	−3.85591	+	0.610716i	−0.133599	+	0.0211601i
$834$	−5.09594	+	34.2528i	−0.176458	+	1.18608i
$835$	1.36814	−	23.0715i	0.0473463	−	0.798422i
$836$	75.6410	−	24.5772i	2.61610	−	0.850022i
$837$	13.7630	+	9.41885i	0.475718	+	0.325563i
$838$	19.0809	−	9.72221i	0.659139	−	0.335848i
$839$	−3.23355	−	9.95184i	−0.111634	−	0.343576i	0.879596	−	0.475722i	$-0.157813\pi$
$839$	−3.23355	−	9.95184i	−0.111634	−	0.343576i	−0.991230	+	0.132146i	$0.957813\pi$
$840$	−33.7131	+	30.5095i	−1.16321	+	1.05268i
$841$	−8.46724	+	26.0595i	−0.291974	+	0.898602i
$842$	−10.3396	−	65.2815i	−0.356325	−	2.24975i
$843$	19.6200	−	27.5448i	0.675750	−	0.948694i
$844$	13.1344	−	18.0779i	0.452104	−	0.622267i
$845$	−16.2585	+	14.4382i	−0.559308	+	0.496687i
$846$	50.9200	−	72.9265i	1.75066	−	2.50727i
$847$	0.442517	−	2.79394i	0.0152050	−	0.0960009i
$848$	16.3685	+	8.34017i	0.562097	+	0.286403i
$849$	−3.77247	−	22.4521i	−0.129471	−	0.770553i
$850$	16.8783	+	15.6225i	0.578921	+	0.535848i
$851$			18.4331i			0.631880i
$852$	−10.3443	+	32.8838i	−0.354390	+	1.12658i
$853$	−23.7081	−	3.75499i	−0.811749	−	0.128568i	−0.263259	−	0.964725i	$-0.584797\pi$
$853$	−23.7081	−	3.75499i	−0.811749	−	0.128568i	−0.548490	+	0.836157i	$0.684797\pi$
$854$	20.0248	−	14.5488i	0.685234	−	0.497851i
$855$	−30.3776	+	28.0142i	−1.03889	+	0.958064i
$856$	46.8567	+	34.0434i	1.60153	+	1.16358i
$857$	1.42221	+	1.42221i	0.0485816	+	0.0485816i	0.730980	−	0.682399i	$-0.239063\pi$
$857$	1.42221	+	1.42221i	0.0485816	+	0.0485816i	−0.682399	+	0.730980i	$0.739063\pi$
$858$	−7.70092	−	22.9651i	−0.262905	−	0.784015i
$859$	−40.0982	−	13.0287i	−1.36813	−	0.444534i	−0.469384	−	0.882994i	$-0.655524\pi$
$859$	−40.0982	−	13.0287i	−1.36813	−	0.444534i	−0.898750	+	0.438461i	$0.855524\pi$
$860$	2.28405	−	5.83011i	0.0778855	−	0.198805i
$861$	−12.4820	+	6.50820i	−0.425384	+	0.221799i
$862$	2.79206	+	5.47973i	0.0950980	+	0.186640i
$863$	−21.1953	−	41.5982i	−0.721498	−	1.41602i	−0.901688	−	0.432387i	$-0.857671\pi$
$863$	−21.1953	−	41.5982i	−0.721498	−	1.41602i	0.180191	−	0.983632i	$-0.442329\pi$
$864$	−5.45990	−	5.16068i	−0.185749	−	0.175570i
$865$	2.97651	+	2.44438i	0.101204	+	0.0831114i
$866$	50.9458	+	16.5533i	1.73121	+	0.562504i
$867$	−22.2592	+	7.46420i	−0.755961	+	0.253498i
$868$	−20.7960	−	20.7960i	−0.705861	−	0.705861i
$869$	−2.43643	−	1.77017i	−0.0826502	−	0.0600489i
$870$	0.604731	−	12.1229i	0.0205023	−	0.411006i
$871$	3.14583	−	2.28558i	0.106592	−	0.0774438i
$872$	37.9909	+	6.01716i	1.28653	+	0.203767i
$873$	−6.88233	+	49.4452i	−0.232931	+	1.67346i
$874$		−	57.9457i		−	1.96004i
$875$	−24.5105	+	3.36582i	−0.828607	+	0.113785i
$876$	40.7060	−	6.83955i	1.37533	−	0.231087i
$877$	16.4317	+	8.37237i	0.554859	+	0.282715i	0.708852	−	0.705357i	$-0.249213\pi$
$877$	16.4317	+	8.37237i	0.554859	+	0.282715i	−0.153993	+	0.988072i	$0.549213\pi$
$878$	−1.59728	+	10.0848i	−0.0539057	+	0.340347i
$879$	3.10141	−	3.16020i	0.104608	−	0.106591i
$880$	−7.28024	+	33.1299i	−0.245417	+	1.11681i
$881$	12.3826	−	17.0432i	0.417180	−	0.574199i	−0.547771	−	0.836628i	$-0.684524\pi$
$881$	12.3826	−	17.0432i	0.417180	−	0.574199i	0.964951	+	0.262429i	$0.0845235\pi$
$882$	14.0627	+	6.83578i	0.473514	+	0.230173i
$883$	3.59865	+	22.7210i	0.121104	+	0.764623i	0.971248	+	0.238071i	$0.0765153\pi$
$883$	3.59865	+	22.7210i	0.121104	+	0.764623i	−0.850143	+	0.526551i	$0.823485\pi$
$884$	−4.29888	+	13.2306i	−0.144587	+	0.444993i
$885$	−22.0975	+	38.4975i	−0.742799	+	1.29408i
$886$	−6.39512	−	19.6822i	−0.214848	−	0.661235i
$887$	−37.0369	+	18.8713i	−1.24358	+	0.633635i	−0.946957	−	0.321360i	$-0.895860\pi$
$887$	−37.0369	+	18.8713i	−1.24358	+	0.633635i	−0.296622	+	0.954995i	$0.595860\pi$
$888$	−26.5662	−	35.8524i	−0.891502	−	1.20313i
$889$	−33.6992	+	10.9495i	−1.13024	+	0.367236i
$890$	56.7304	+	22.2252i	1.90161	+	0.744990i
$891$	26.3438	−	9.66743i	0.882551	−	0.323871i
$892$	−34.4413	+	5.45496i	−1.15318	+	0.182646i
$893$	−52.1137	+	52.1137i	−1.74392	+	1.74392i
$894$	23.3598	−	46.9302i	0.781267	−	1.56958i
$895$	37.4535	−	16.3680i	1.25193	−	0.547121i
$896$	−23.5761	−	32.4498i	−0.787623	−	1.08407i
$897$	−11.8993	+	0.111721i	−0.397306	+	0.00373024i
$898$	−11.8716	+	23.2993i	−0.396160	+	0.777507i
$899$	4.05911			0.135379
$900$	−13.2199	−	60.6904i	−0.440664	−	2.02301i
$901$	7.00874			0.233495
$902$	−12.8831	+	25.2846i	−0.428962	+	0.841885i
$903$	2.59178	−	0.0243338i	0.0862490	−	0.000809778i
$904$	28.8405	+	39.6956i	0.959222	+	1.32026i
$905$	−11.2466	−	12.6646i	−0.373851	−	0.420985i
$906$	3.95738	−	7.95045i	0.131475	−	0.264136i
$907$	−28.8944	+	28.8944i	−0.959422	+	0.959422i	−0.999208	−	0.0397860i	$-0.987332\pi$
$907$	−28.8944	+	28.8944i	−0.959422	+	0.959422i	0.0397860	+	0.999208i	$0.487332\pi$
$908$	47.9408	−	7.59307i	1.59097	−	0.251985i
$909$	−0.819314	−	43.6285i	−0.0271749	−	1.44706i
$910$	−11.9590	−	18.6952i	−0.396437	−	0.619740i
$911$	−35.2299	+	11.4469i	−1.16722	+	0.379252i	−0.827604	−	0.561312i	$-0.810297\pi$
$911$	−35.2299	+	11.4469i	−1.16722	+	0.379252i	−0.339615	+	0.940565i	$0.610297\pi$
$912$	30.9049	+	41.7078i	1.02336	+	1.38108i
$913$	0.332404	−	0.169368i	0.0110010	−	0.00560526i
$914$	3.20021	+	9.84924i	0.105854	+	0.325784i
$915$	1.87111	+	17.3813i	0.0618571	+	0.574610i
$916$	−37.3180	+	114.853i	−1.23302	+	3.79485i
$917$	−7.14898	−	45.1369i	−0.236080	−	1.49055i
$918$	−22.9301	−	6.74272i	−0.756807	−	0.222543i
$919$	9.97931	−	13.7353i	0.329187	−	0.453087i	−0.612057	−	0.790813i	$-0.709658\pi$
$919$	9.97931	−	13.7353i	0.329187	−	0.453087i	0.941244	+	0.337726i	$0.109658\pi$
$920$	38.8429	+	22.7832i	1.28061	+	0.751140i
$921$	−22.9354	+	23.3702i	−0.755747	+	0.770073i
$922$	−8.58424	+	54.1987i	−0.282707	+	1.78494i
$923$	−7.75100	−	3.94933i	−0.255127	−	0.129994i
$924$	−48.8017	+	8.19981i	−1.60546	+	0.269754i
$925$	−0.937429	−	24.2620i	−0.0308225	−	0.797728i
$926$			91.9648i			3.02215i
$927$	4.12050	+	0.573537i	0.135335	+	0.0188374i
$928$	−1.80605	−	0.286050i	−0.0592864	−	0.00939004i
$929$	−24.0791	+	17.4945i	−0.790011	+	0.573976i	−0.907967	−	0.419043i	$-0.862366\pi$
$929$	−24.0791	+	17.4945i	−0.790011	+	0.573976i	0.117956	+	0.993019i	$0.462366\pi$
$930$	29.7342	−	8.04755i	0.975023	−	0.263890i
$931$	−10.4817	−	7.61542i	−0.343525	−	0.249585i
$932$	−71.5794	−	71.5794i	−2.34466	−	2.34466i
$933$	−28.8297	+	9.66752i	−0.943844	+	0.316500i
$934$	−42.7536	−	13.8915i	−1.39894	−	0.454544i
$935$	3.26345	+	12.5229i	0.106726	+	0.409543i
$936$	22.9831	−	17.3668i	0.751227	−	0.567651i
$937$	−7.08811	−	13.9112i	−0.231558	−	0.454459i	0.745766	−	0.666209i	$-0.232084\pi$
$937$	−7.08811	−	13.9112i	−0.231558	−	0.454459i	−0.977324	+	0.211749i	$0.932084\pi$
$938$	−5.34852	−	10.4971i	−0.174635	−	0.342741i
$939$	13.3822	−	6.97761i	0.436712	−	0.227706i
$940$	−27.9361	−	107.200i	−0.911176	−	3.49647i
$941$	−26.4479	−	8.59345i	−0.862177	−	0.280138i	−0.155640	−	0.987814i	$-0.549744\pi$
$941$	−26.4479	−	8.59345i	−0.862177	−	0.280138i	−0.706538	+	0.707676i	$0.749744\pi$
$942$	0.441576	+	1.31683i	0.0143873	+	0.0429047i
$943$	9.85810	+	9.85810i	0.321024	+	0.321024i
$944$	45.1118	+	32.7756i	1.46826	+	1.06676i
$945$	21.2601	−	14.4593i	0.691591	−	0.470360i
$946$	4.22714	−	3.07120i	0.137436	−	0.0998532i
$947$	6.78655	+	1.07488i	0.220533	+	0.0349290i	0.265723	−	0.964049i	$-0.414389\pi$
$947$	6.78655	+	1.07488i	0.220533	+	0.0349290i	−0.0451899	+	0.998978i	$0.514389\pi$
$948$	2.07879	−	6.60832i	0.0675159	−	0.214628i
$949$			10.4162i			0.338124i
$950$	2.94687	+	76.2689i	0.0956089	+	2.47449i
$951$	0.259477	+	1.54429i	0.00841411	+	0.0500771i
$952$	19.4162	+	9.89306i	0.629284	+	0.320636i
$953$	−3.60008	+	22.7300i	−0.116618	+	0.736296i	0.858204	+	0.513310i	$0.171581\pi$
$953$	−3.60008	+	22.7300i	−0.116618	+	0.736296i	−0.974821	+	0.222987i	$0.928419\pi$
$954$	−23.0158	−	16.0705i	−0.745165	−	0.520301i
$955$	35.8680	+	21.0383i	1.16066	+	0.680784i
$956$	−42.5048	+	58.5028i	−1.37470	+	1.89212i
$957$	3.96248	−	5.56298i	0.128089	−	0.179826i
$958$	0.400529	+	2.52884i	0.0129405	+	0.0817031i
$959$	−2.71627	+	8.35983i	−0.0877130	+	0.269953i
$960$	23.6727	−	2.54838i	0.764032	−	0.0822486i
$961$	−6.39626	−	19.6857i	−0.206331	−	0.635022i
$962$	19.4061	−	9.88788i	0.625676	−	0.318798i
$963$	−23.5891	−	22.7195i	−0.760148	−	0.732124i
$964$	64.6832	−	21.0169i	2.08331	−	0.676907i
$965$	20.4944	+	32.0385i	0.659740	+	1.03135i
$966$	−5.30548	+	35.6612i	−0.170701	+	1.14738i
$967$	15.7486	−	2.49433i	0.506440	−	0.0802122i	0.102014	−	0.994783i	$-0.467471\pi$
$967$	15.7486	−	2.49433i	0.506440	−	0.0802122i	0.404426	+	0.914571i	$0.367471\pi$
$968$	4.79557	−	4.79557i	0.154136	−	0.154136i
$969$	17.7296	+	8.82498i	0.569555	+	0.283499i
$970$	61.2272	+	68.9465i	1.96589	+	2.21374i
$971$	−21.3596	−	29.3990i	−0.685462	−	0.943458i	0.314521	−	0.949250i	$-0.398156\pi$
$971$	−21.3596	−	29.3990i	−0.685462	−	0.943458i	−0.999983	+	0.00579289i	$0.998156\pi$
$972$	40.3504	+	50.3843i	1.29424	+	1.61608i
$973$	−8.10541	+	15.9078i	−0.259847	+	0.509979i
$974$	−83.9126			−2.68873
$975$	15.6564	−	0.752195i	0.501405	−	0.0240895i
$976$	21.9607			0.702944
$977$	7.49385	−	14.7075i	0.239750	−	0.470535i	−0.739510	−	0.673146i	$-0.764943\pi$
$977$	7.49385	−	14.7075i	0.239750	−	0.470535i	0.979259	+	0.202611i	$0.0649426\pi$
$978$	0.508829	+	54.1950i	0.0162705	+	1.73297i
$979$	20.1516	+	27.7363i	0.644048	+	0.886456i
$980$	17.8450	−	7.79863i	0.570037	−	0.249118i
$981$	−20.8084	−	6.33167i	−0.664362	−	0.202155i
$982$	46.3816	−	46.3816i	1.48010	−	1.48010i
$983$	34.7531	−	5.50435i	1.10845	−	0.175561i	0.424741	−	0.905315i	$-0.360365\pi$
$983$	34.7531	−	5.50435i	1.10845	−	0.175561i	0.683710	+	0.729754i	$0.260365\pi$
$984$	−33.3817	−	4.96633i	−1.06417	−	0.158321i
$985$	43.5504	+	17.0617i	1.38763	+	0.543630i
$986$	−5.53254	+	1.79763i	−0.176192	+	0.0572483i
$987$	36.8436	−	27.3006i	1.17275	−	0.868988i
$988$	−41.1360	+	20.9598i	−1.30871	+	0.666821i
$989$	−0.793239	−	2.44134i	−0.0252235	−	0.0776301i
$990$	17.9973	−	48.6065i	0.571990	−	1.54482i
$991$	14.8124	−	45.5879i	0.470531	−	1.44815i	−0.381359	−	0.924427i	$-0.624544\pi$
$991$	14.8124	−	45.5879i	0.470531	−	1.44815i	0.851891	−	0.523720i	$-0.175456\pi$
$992$	−0.725941	−	4.58341i	−0.0230486	−	0.145523i
$993$	−27.2843	−	19.4344i	−0.865840	−	0.616733i
$994$	−15.4919	+	21.3228i	−0.491374	+	0.676318i
$995$	4.75299	−	21.6293i	0.150680	−	0.685694i
$996$	0.612483	+	0.601089i	0.0194073	+	0.0190462i
$997$	1.52520	−	9.62975i	0.0483036	−	0.304977i	−0.951694	−	0.307047i	$-0.900659\pi$
$997$	1.52520	−	9.62975i	0.0483036	−	0.304977i	0.999998	+	0.00207027i	$0.000658989\pi$
$998$	−8.95540	−	4.56300i	−0.283478	−	0.144439i
$999$	12.0840	+	22.1509i	0.382319	+	0.700823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.2.l.a.8.8	yes	64
3.2	odd	2	inner	75.2.l.a.8.1	✓	64
5.2	odd	4		375.2.l.a.107.8		64
5.3	odd	4		375.2.l.b.107.1		64
5.4	even	2		375.2.l.c.143.1		64
15.2	even	4		375.2.l.a.107.1		64
15.8	even	4		375.2.l.b.107.8		64
15.14	odd	2		375.2.l.c.143.8		64
25.3	odd	20		375.2.l.c.257.8		64
25.4	even	10		375.2.l.b.368.8		64
25.21	even	5		375.2.l.a.368.1		64
25.22	odd	20	inner	75.2.l.a.47.1	yes	64
75.29	odd	10		375.2.l.b.368.1		64
75.47	even	20	inner	75.2.l.a.47.8	yes	64
75.53	even	20		375.2.l.c.257.1		64
75.71	odd	10		375.2.l.a.368.8		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.l.a.8.1	✓	64	3.2	odd	2	inner
75.2.l.a.8.8	yes	64	1.1	even	1	trivial
75.2.l.a.47.1	yes	64	25.22	odd	20	inner
75.2.l.a.47.8	yes	64	75.47	even	20	inner
375.2.l.a.107.1		64	15.2	even	4
375.2.l.a.107.8		64	5.2	odd	4
375.2.l.a.368.1		64	25.21	even	5
375.2.l.a.368.8		64	75.71	odd	10
375.2.l.b.107.1		64	5.3	odd	4
375.2.l.b.107.8		64	15.8	even	4
375.2.l.b.368.1		64	75.29	odd	10
375.2.l.b.368.8		64	25.4	even	10
375.2.l.c.143.1		64	5.4	even	2
375.2.l.c.143.8		64	15.14	odd	2
375.2.l.c.257.1		64	75.53	even	20
375.2.l.c.257.8		64	25.3	odd	20

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:	\( N \)	\(=\)	\( 75 = 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	75.l (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.12503 - 2.20799i) q^{2} +(-1.73197 + 0.0162612i) q^{3} +(-2.43396 - 3.35006i) q^{4} +(2.18396 + 0.479921i) q^{5} +(-1.91261 + 3.84248i) q^{6} +(-1.56473 + 1.56473i) q^{7} +(-5.24001 + 0.829937i) q^{8} +(2.99947 - 0.0563281i) q^{9} +O(q^{10})\)	\(q+(1.12503 - 2.20799i) q^{2} +(-1.73197 + 0.0162612i) q^{3} +(-2.43396 - 3.35006i) q^{4} +(2.18396 + 0.479921i) q^{5} +(-1.91261 + 3.84248i) q^{6} +(-1.56473 + 1.56473i) q^{7} +(-5.24001 + 0.829937i) q^{8} +(2.99947 - 0.0563281i) q^{9} +(3.51667 - 4.28223i) q^{10} +(2.96536 - 0.963502i) q^{11} +(4.27003 + 5.76264i) q^{12} +(-1.61265 + 0.821689i) q^{13} +(1.69454 + 5.21527i) q^{14} +(-3.79036 - 0.795697i) q^{15} +(-1.50345 + 4.62713i) q^{16} +(0.290369 + 1.83332i) q^{17} +(3.25011 - 6.68617i) q^{18} +(-3.62080 + 4.98360i) q^{19} +(-3.70790 - 8.48450i) q^{20} +(2.68463 - 2.73552i) q^{21} +(1.20870 - 7.63144i) q^{22} +(-3.38221 - 1.72332i) q^{23} +(9.06207 - 1.52264i) q^{24} +(4.53935 + 2.09626i) q^{25} +4.48515i q^{26} +(-5.19409 + 0.146334i) q^{27} +(9.05042 + 1.43345i) q^{28} +(-1.02316 + 0.743368i) q^{29} +(-6.02115 + 7.47390i) q^{30} +(-2.59659 - 1.88653i) q^{31} +(1.02237 + 1.02237i) q^{32} +(-5.12025 + 1.71698i) q^{33} +(4.37461 + 1.42140i) q^{34} +(-4.16825 + 2.66636i) q^{35} +(-7.48930 - 9.91130i) q^{36} +(-2.20458 - 4.32674i) q^{37} +(6.93024 + 13.6014i) q^{38} +(2.77972 - 1.44937i) q^{39} +(-11.8423 - 0.702246i) q^{40} +(-3.49297 - 1.13493i) q^{41} +(-3.01971 - 9.00515i) q^{42} +(0.478175 + 0.478175i) q^{43} +(-10.4453 - 7.58899i) q^{44} +(6.57775 + 1.31649i) q^{45} +(-7.61015 + 5.52910i) q^{46} +(11.8168 + 1.87160i) q^{47} +(2.52869 - 8.03853i) q^{48} +2.10324i q^{49} +(9.73540 - 7.66450i) q^{50} +(-0.532723 - 3.17053i) q^{51} +(6.67784 + 3.40253i) q^{52} +(0.590684 - 3.72943i) q^{53} +(-5.52039 + 11.6331i) q^{54} +(6.93862 - 0.681113i) q^{55} +(6.90058 - 9.49783i) q^{56} +(6.19009 - 8.69035i) q^{57} +(0.490268 + 3.09543i) q^{58} +(3.54168 - 10.9002i) q^{59} +(6.55997 + 14.6346i) q^{60} +(-1.39483 - 4.29285i) q^{61} +(-7.08667 + 3.61084i) q^{62} +(-4.60522 + 4.78150i) q^{63} +(-5.84669 + 1.89970i) q^{64} +(-3.91632 + 1.02059i) q^{65} +(-1.96934 + 13.2371i) q^{66} +(-2.12196 + 0.336085i) q^{67} +(5.43497 - 5.43497i) q^{68} +(5.88592 + 2.92975i) q^{69} +(1.19790 + 12.2032i) q^{70} +(2.82511 + 3.88843i) q^{71} +(-15.6705 + 2.78453i) q^{72} +(2.61273 - 5.12778i) q^{73} -12.0336 q^{74} +(-7.89613 - 3.55685i) q^{75} +25.5082 q^{76} +(-3.13236 + 6.14760i) q^{77} +(-0.0729340 - 7.76816i) q^{78} +(-0.567733 - 0.781418i) q^{79} +(-5.50412 + 9.38393i) q^{80} +(8.99365 - 0.337909i) q^{81} +(-6.43561 + 6.43561i) q^{82} +(0.118177 - 0.0187175i) q^{83} +(-15.6984 - 2.33552i) q^{84} +(-0.245694 + 4.14324i) q^{85} +(1.59377 - 0.517846i) q^{86} +(1.76000 - 1.30413i) q^{87} +(-14.7389 + 7.50982i) q^{88} +(3.39784 + 10.4575i) q^{89} +(10.3069 - 13.0425i) q^{90} +(1.23765 - 3.80909i) q^{91} +(2.45893 + 15.5251i) q^{92} +(4.52790 + 3.22520i) q^{93} +(17.4267 - 23.9859i) q^{94} +(-10.2994 + 9.14628i) q^{95} +(-1.78735 - 1.75410i) q^{96} +(-2.60317 + 16.4357i) q^{97} +(4.64394 + 2.36621i) q^{98} +(8.84023 - 3.05703i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9}+O(q^{10}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9	\( 64 q - 10 q^{3} - 20 q^{4} - 6 q^{6} - 20 q^{7} - 10 q^{9} - 20 q^{10} - 10 q^{12} - 20 q^{13} - 10 q^{15} - 8 q^{16} - 10 q^{18} - 6 q^{21} + 20 q^{22} + 40 q^{25} - 10 q^{27} + 40 q^{28} - 10 q^{30} - 12 q^{31} - 10 q^{33} + 20 q^{34} - 22 q^{36} - 20 q^{37} + 30 q^{39} - 20 q^{40} + 90 q^{42} - 20 q^{43} + 70 q^{45} - 12 q^{46} + 100 q^{48} - 16 q^{51} + 20 q^{52} + 120 q^{54} - 20 q^{55} + 70 q^{57} - 20 q^{58} + 50 q^{60} - 12 q^{61} - 20 q^{63} - 100 q^{64} - 30 q^{66} - 60 q^{67} - 80 q^{69} - 100 q^{70} - 150 q^{72} - 60 q^{73} - 90 q^{75} - 64 q^{76} - 80 q^{78} - 60 q^{79} + 14 q^{81} - 60 q^{82} - 130 q^{84} + 60 q^{85} - 60 q^{87} + 20 q^{88} - 70 q^{90} - 12 q^{91} - 20 q^{93} + 260 q^{94} + 42 q^{96} + 120 q^{97}+O(q^{100}) \) 64 * q - 10 * q^3 - 20 * q^4 - 6 * q^6 - 20 * q^7 - 10 * q^9 - 20 * q^10 - 10 * q^12 - 20 * q^13 - 10 * q^15 - 8 * q^16 - 10 * q^18 - 6 * q^21 + 20 * q^22 + 40 * q^25 - 10 * q^27 + 40 * q^28 - 10 * q^30 - 12 * q^31 - 10 * q^33 + 20 * q^34 - 22 * q^36 - 20 * q^37 + 30 * q^39 - 20 * q^40 + 90 * q^42 - 20 * q^43 + 70 * q^45 - 12 * q^46 + 100 * q^48 - 16 * q^51 + 20 * q^52 + 120 * q^54 - 20 * q^55 + 70 * q^57 - 20 * q^58 + 50 * q^60 - 12 * q^61 - 20 * q^63 - 100 * q^64 - 30 * q^66 - 60 * q^67 - 80 * q^69 - 100 * q^70 - 150 * q^72 - 60 * q^73 - 90 * q^75 - 64 * q^76 - 80 * q^78 - 60 * q^79 + 14 * q^81 - 60 * q^82 - 130 * q^84 + 60 * q^85 - 60 * q^87 + 20 * q^88 - 70 * q^90 - 12 * q^91 - 20 * q^93 + 260 * q^94 + 42 * q^96 + 120 * q^97

Introduction

L-functions

Modular forms

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