LMFDB - Embedded newform 75.3.k.a.22.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [75,3,Mod(13,75)]

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([0, 19]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("75.13");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 75 = 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	75.k (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:	$2.04360198270$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			22.5
Character	$\chi$	$=$	75.22
Dual form			75.3.k.a.58.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.186256 + 0.0949024i) q^{2} +(1.71073 - 0.270952i) q^{3} +(-2.32546 + 3.20072i) q^{4} +(-1.31868 + 4.82297i) q^{5} +(-0.292920 + 0.212819i) q^{6} +(5.11319 + 5.11319i) q^{7} +(0.260180 - 1.64271i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})$	\(q+(-0.186256 + 0.0949024i) q^{2} +(1.71073 - 0.270952i) q^{3} +(-2.32546 + 3.20072i) q^{4} +(-1.31868 + 4.82297i) q^{5} +(-0.292920 + 0.212819i) q^{6} +(5.11319 + 5.11319i) q^{7} +(0.260180 - 1.64271i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-0.212098 - 1.02346i) q^{10} +(3.21531 - 9.89570i) q^{11} +(-3.11098 + 6.10564i) q^{12} +(3.78355 + 1.92781i) q^{13} +(-1.43762 - 0.467111i) q^{14} +(-0.949111 + 8.60809i) q^{15} +(-4.78282 - 14.7200i) q^{16} +(-11.4496 - 1.81344i) q^{17} +(-0.443442 + 0.443442i) q^{18} +(18.4753 + 25.4290i) q^{19} +(-12.3704 - 15.4363i) q^{20} +(10.1327 + 7.36184i) q^{21} +(0.340254 + 2.14828i) q^{22} +(-16.0060 - 31.4135i) q^{23} -2.88073i q^{24} +(-21.5221 - 12.7200i) q^{25} -0.887664 q^{26} +(4.62981 - 2.35900i) q^{27} +(-28.2564 + 4.47537i) q^{28} +(21.7754 - 29.9712i) q^{29} +(-0.640150 - 1.69338i) q^{30} +(33.9610 - 24.6741i) q^{31} +(6.99201 + 6.99201i) q^{32} +(2.81925 - 17.8000i) q^{33} +(2.30466 - 0.748830i) q^{34} +(-31.4035 + 17.9181i) q^{35} +(-3.66769 + 11.2880i) q^{36} +(-7.73692 + 15.1846i) q^{37} +(-5.85442 - 2.98297i) q^{38} +(6.99496 + 2.27280i) q^{39} +(7.57966 + 3.42106i) q^{40} +(10.4149 + 32.0538i) q^{41} +(-2.58594 - 0.409573i) q^{42} +(-4.34966 + 4.34966i) q^{43} +(24.1963 + 33.3033i) q^{44} +(0.708713 + 14.9832i) q^{45} +(5.96243 + 4.33196i) q^{46} +(7.65013 + 48.3010i) q^{47} +(-12.1705 - 23.8860i) q^{48} +3.28952i q^{49} +(5.21579 + 0.326671i) q^{50} -20.0785 q^{51} +(-14.9689 + 7.62701i) q^{52} +(20.9647 - 3.32047i) q^{53} +(-0.638456 + 0.878759i) q^{54} +(43.4867 + 28.5566i) q^{55} +(9.72986 - 7.06916i) q^{56} +(38.4962 + 38.4962i) q^{57} +(-1.21146 + 7.64886i) q^{58} +(-31.2170 + 10.1430i) q^{59} +(-25.3449 - 23.0556i) q^{60} +(28.9391 - 89.0654i) q^{61} +(-3.98382 + 7.81868i) q^{62} +(19.3290 + 9.84862i) q^{63} +(56.9142 + 18.4925i) q^{64} +(-14.2871 + 15.7058i) q^{65} +(1.16416 + 3.58292i) q^{66} +(-122.482 - 19.3993i) q^{67} +(32.4299 - 32.4299i) q^{68} +(-35.8934 - 49.4030i) q^{69} +(4.14863 - 6.31763i) q^{70} +(24.0394 + 17.4656i) q^{71} +(-0.780540 - 4.92814i) q^{72} +(17.1663 + 33.6908i) q^{73} -3.56247i q^{74} +(-40.2650 - 15.9289i) q^{75} -124.355 q^{76} +(67.0391 - 34.1581i) q^{77} +(-1.51855 + 0.240515i) q^{78} +(-5.94126 + 8.17745i) q^{79} +(77.3012 - 3.65638i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-4.98182 - 4.98182i) q^{82} +(-10.7439 + 67.8340i) q^{83} +(-47.1263 + 15.3123i) q^{84} +(23.8446 - 52.8298i) q^{85} +(0.397359 - 1.22295i) q^{86} +(29.1309 - 57.1726i) q^{87} +(-15.4192 - 7.85649i) q^{88} +(-86.3664 - 28.0621i) q^{89} +(-1.55395 - 2.72347i) q^{90} +(9.48872 + 29.2033i) q^{91} +(137.767 + 21.8201i) q^{92} +(51.4124 - 51.4124i) q^{93} +(-6.00877 - 8.27036i) q^{94} +(-147.007 + 55.5729i) q^{95} +(13.8559 + 10.0669i) q^{96} +(-13.5037 - 85.2589i) q^{97} +(-0.312183 - 0.612694i) q^{98} -31.2149i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	$ 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) $ 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$26$	$52$
$\chi(n)$	$1$	$e\left(\frac{17}{20}\right)$

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 $

$2$	−0.186256	+	0.0949024i	−0.0931282	+	0.0474512i	−0.499934	−	0.866063i	$-0.666642\pi$
$2$	−0.186256	+	0.0949024i	−0.0931282	+	0.0474512i	0.406806	+	0.913515i	$0.366642\pi$
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$3$	1.71073	−	0.270952i	0.570242	−	0.0903175i
$4$	−2.32546	+	3.20072i	−0.581364	+	0.800179i
$5$	−1.31868	+	4.82297i	−0.263737	+	0.964595i
$5$	−1.31868	+	4.82297i	−0.263737	+	0.964595i
$6$	−0.292920	+	0.212819i	−0.0488200	+	0.0354698i
$7$	5.11319	+	5.11319i	0.730456	+	0.730456i	0.970710	−	0.240254i	$-0.0772306\pi$
$7$	5.11319	+	5.11319i	0.730456	+	0.730456i	−0.240254	+	0.970710i	$0.577231\pi$
$8$	0.260180	−	1.64271i	0.0325225	−	0.205339i
$9$	2.85317	−	0.927051i	0.317019	−	0.103006i
$10$	−0.212098	−	1.02346i	−0.0212098	−	0.102346i
$11$	3.21531	−	9.89570i	0.292301	−	0.899609i	−0.691814	−	0.722076i	$-0.743188\pi$
$11$	3.21531	−	9.89570i	0.292301	−	0.899609i	0.984115	−	0.177533i	$-0.0568118\pi$
$12$	−3.11098	+	6.10564i	−0.259248	+	0.508803i
$13$	3.78355	+	1.92781i	0.291042	+	0.148293i	0.593416	−	0.804896i	$-0.297779\pi$
$13$	3.78355	+	1.92781i	0.291042	+	0.148293i	−0.302374	+	0.953189i	$0.597779\pi$
$14$	−1.43762	−	0.467111i	−0.102687	−	0.0333651i
$15$	−0.949111	+	8.60809i	−0.0632741	+	0.573873i
$16$	−4.78282	−	14.7200i	−0.298926	−	0.920001i
$17$	−11.4496	−	1.81344i	−0.673506	−	0.106673i	−0.189692	−	0.981844i	$-0.560749\pi$
$17$	−11.4496	−	1.81344i	−0.673506	−	0.106673i	−0.483814	+	0.875171i	$0.660749\pi$
$18$	−0.443442	+	0.443442i	−0.0246357	+	0.0246357i
$19$	18.4753	+	25.4290i	0.972383	+	1.33837i	0.940834	+	0.338868i	$0.110044\pi$
$19$	18.4753	+	25.4290i	0.972383	+	1.33837i	0.0315494	+	0.999502i	$0.489956\pi$
$20$	−12.3704	−	15.4363i	−0.618521	−	0.771817i
$21$	10.1327	+	7.36184i	0.482510	+	0.350564i
$22$	0.340254	+	2.14828i	0.0154661	+	0.0976490i
$23$	−16.0060	−	31.4135i	−0.695912	−	1.36580i	−0.920265	−	0.391296i	$-0.872027\pi$
$23$	−16.0060	−	31.4135i	−0.695912	−	1.36580i	0.224353	−	0.974508i	$-0.427973\pi$
$24$		−	2.88073i		−	0.120030i
$25$	−21.5221	−	12.7200i	−0.860886	−	0.508798i
$26$	−0.887664			−0.0341409
$27$	4.62981	−	2.35900i	0.171474	−	0.0873705i
$28$	−28.2564	+	4.47537i	−1.00916	+	0.159835i
$29$	21.7754	−	29.9712i	0.750874	−	1.03349i	−0.247044	−	0.969004i	$-0.579459\pi$
$29$	21.7754	−	29.9712i	0.750874	−	1.03349i	0.997919	−	0.0644856i	$-0.0205407\pi$
$30$	−0.640150	−	1.69338i	−0.0213383	−	0.0564462i
$31$	33.9610	−	24.6741i	1.09551	−	0.795938i	0.115193	−	0.993343i	$-0.463251\pi$
$31$	33.9610	−	24.6741i	1.09551	−	0.795938i	0.980322	+	0.197405i	$0.0632514\pi$
$32$	6.99201	+	6.99201i	0.218500	+	0.218500i
$33$	2.81925	−	17.8000i	0.0854317	−	0.539395i
$34$	2.30466	−	0.748830i	0.0677842	−	0.0220244i
$35$	−31.4035	+	17.9181i	−0.897243	+	0.511946i
$36$	−3.66769	+	11.2880i	−0.101880	+	0.313556i
$37$	−7.73692	+	15.1846i	−0.209106	+	0.410393i	−0.971609	−	0.236591i	$-0.923970\pi$
$37$	−7.73692	+	15.1846i	−0.209106	+	0.410393i	0.762504	+	0.646984i	$0.223970\pi$
$38$	−5.85442	−	2.98297i	−0.154064	−	0.0784993i
$39$	6.99496	+	2.27280i	0.179358	+	0.0582769i
$40$	7.57966	+	3.42106i	0.189492	+	0.0855265i
$41$	10.4149	+	32.0538i	0.254022	+	0.781800i	0.994021	+	0.109191i	$0.0348261\pi$
$41$	10.4149	+	32.0538i	0.254022	+	0.781800i	−0.739999	+	0.672608i	$0.765174\pi$
$42$	−2.58594	−	0.409573i	−0.0615700	−	0.00975173i
$43$	−4.34966	+	4.34966i	−0.101155	+	0.101155i	−0.755873	−	0.654718i	$-0.772787\pi$
$43$	−4.34966	+	4.34966i	−0.101155	+	0.101155i	0.654718	+	0.755873i	$0.272787\pi$
$44$	24.1963	+	33.3033i	0.549915	+	0.756893i
$45$	0.708713	+	14.9832i	0.0157492	+	0.332961i
$46$	5.96243	+	4.33196i	0.129618	+	0.0941731i
$47$	7.65013	+	48.3010i	0.162769	+	1.02768i	0.924887	+	0.380243i	$0.124160\pi$
$47$	7.65013	+	48.3010i	0.162769	+	1.02768i	−0.762118	+	0.647438i	$0.775840\pi$
$48$	−12.1705	−	23.8860i	−0.253553	−	0.497625i
$49$			3.28952i			0.0671331i
$50$	5.21579	+	0.326671i	0.104316	+	0.00653341i
$51$	−20.0785			−0.393696
$52$	−14.9689	+	7.62701i	−0.287863	+	0.146673i
$53$	20.9647	−	3.32047i	0.395559	−	0.0626505i	0.0445137	−	0.999009i	$-0.485826\pi$
$53$	20.9647	−	3.32047i	0.395559	−	0.0626505i	0.351046	+	0.936358i	$0.385826\pi$
$54$	−0.638456	+	0.878759i	−0.0118233	+	0.0162733i
$55$	43.4867	+	28.5566i	0.790668	+	0.519212i
$56$	9.72986	−	7.06916i	0.173748	−	0.126235i
$57$	38.4962	+	38.4962i	0.675372	+	0.675372i
$58$	−1.21146	+	7.64886i	−0.0208873	+	0.131877i
$59$	−31.2170	+	10.1430i	−0.529102	+	0.171916i	−0.561372	−	0.827564i	$-0.689726\pi$
$59$	−31.2170	+	10.1430i	−0.529102	+	0.171916i	0.0322702	+	0.999479i	$0.489726\pi$
$60$	−25.3449	−	23.0556i	−0.422415	−	0.384259i
$61$	28.9391	−	89.0654i	0.474412	−	1.46009i	−0.372338	−	0.928097i	$-0.621444\pi$
$61$	28.9391	−	89.0654i	0.474412	−	1.46009i	0.846749	−	0.531992i	$-0.178556\pi$
$62$	−3.98382	+	7.81868i	−0.0642551	+	0.126108i
$63$	19.3290	+	9.84862i	0.306810	+	0.156327i
$64$	56.9142	+	18.4925i	0.889284	+	0.288946i
$65$	−14.2871	+	15.7058i	−0.219801	+	0.241627i
$66$	1.16416	+	3.58292i	0.0176388	+	0.0542867i
$67$	−122.482	−	19.3993i	−1.82809	−	0.289542i	−0.854776	−	0.518997i	$-0.826305\pi$
$67$	−122.482	−	19.3993i	−1.82809	−	0.289542i	−0.973319	+	0.229456i	$0.926305\pi$
$68$	32.4299	−	32.4299i	0.476910	−	0.476910i
$69$	−35.8934	−	49.4030i	−0.520194	−	0.715986i
$70$	4.14863	−	6.31763i	0.0592662	−	0.0902519i
$71$	24.0394	+	17.4656i	0.338583	+	0.245995i	0.744064	−	0.668109i	$-0.232896\pi$
$71$	24.0394	+	17.4656i	0.338583	+	0.245995i	−0.405481	+	0.914104i	$0.632896\pi$
$72$	−0.780540	−	4.92814i	−0.0108408	−	0.0684464i
$73$	17.1663	+	33.6908i	0.235155	+	0.461518i	0.978184	−	0.207742i	$-0.0666113\pi$
$73$	17.1663	+	33.6908i	0.235155	+	0.461518i	−0.743028	+	0.669260i	$0.766611\pi$
$74$		−	3.56247i		−	0.0481415i
$75$	−40.2650	−	15.9289i	−0.536867	−	0.212385i
$76$	−124.355			−1.63624
$77$	67.0391	−	34.1581i	0.870638	−	0.443612i
$78$	−1.51855	+	0.240515i	−0.0194686	+	0.00308352i
$79$	−5.94126	+	8.17745i	−0.0752059	+	0.103512i	−0.844963	−	0.534825i	$-0.820377\pi$
$79$	−5.94126	+	8.17745i	−0.0752059	+	0.103512i	0.769757	+	0.638337i	$0.220377\pi$
$80$	77.3012	−	3.65638i	0.966266	−	0.0457047i
$81$	7.28115	−	5.29007i	0.0898908	−	0.0653095i
$82$	−4.98182	−	4.98182i	−0.0607540	−	0.0607540i
$83$	−10.7439	+	67.8340i	−0.129444	+	0.817277i	0.834468	+	0.551056i	$0.185775\pi$
$83$	−10.7439	+	67.8340i	−0.129444	+	0.817277i	−0.963912	+	0.266221i	$0.914225\pi$
$84$	−47.1263	+	15.3123i	−0.561028	+	0.182289i
$85$	23.8446	−	52.8298i	0.280525	−	0.621527i
$86$	0.397359	−	1.22295i	0.00462045	−	0.0142203i
$87$	29.1309	−	57.1726i	0.334838	−	0.657156i
$88$	−15.4192	−	7.85649i	−0.175219	−	0.0892783i
$89$	−86.3664	−	28.0621i	−0.970409	−	0.315305i	−0.219428	−	0.975629i	$-0.570419\pi$
$89$	−86.3664	−	28.0621i	−0.970409	−	0.315305i	−0.750981	+	0.660324i	$0.770419\pi$
$90$	−1.55395	−	2.72347i	−0.0172661	−	0.0302608i
$91$	9.48872	+	29.2033i	0.104272	+	0.320915i
$92$	137.767	+	21.8201i	1.49747	+	0.237175i
$93$	51.4124	−	51.4124i	0.552822	−	0.552822i
$94$	−6.00877	−	8.27036i	−0.0639231	−	0.0879826i
$95$	−147.007	+	55.5729i	−1.54744	+	0.584978i
$96$	13.8559	+	10.0669i	0.144332	+	0.104864i
$97$	−13.5037	−	85.2589i	−0.139213	−	0.878958i	−0.954133	−	0.299384i	$-0.903219\pi$
$97$	−13.5037	−	85.2589i	−0.139213	−	0.878958i	0.814920	−	0.579574i	$-0.196781\pi$
$98$	−0.312183	−	0.612694i	−0.00318555	−	0.00625198i
$99$		−	31.2149i		−	0.315302i
$100$	90.7618	−	39.3066i	0.907618	−	0.393066i
$101$	−73.9741			−0.732417			−0.366208	−	0.930533i	$-0.619344\pi$
$101$	−73.9741			−0.732417			−0.366208	+	0.930533i	$0.619344\pi$
$102$	3.73975	−	1.90550i	0.0366642	−	0.0186814i
$103$	−125.188	+	19.8278i	−1.21542	+	0.192503i	−0.731027	−	0.682349i	$-0.760958\pi$
$103$	−125.188	+	19.8278i	−1.21542	+	0.192503i	−0.484390	+	0.874852i	$0.660958\pi$
$104$	4.15125	−	5.71370i	0.0399158	−	0.0549394i
$105$	−48.8678	+	39.1618i	−0.465408	+	0.372970i
$106$	−3.58968	+	2.60806i	−0.0338649	+	0.0246043i
$107$	−120.652	−	120.652i	−1.12759	−	1.12759i	−0.990568	−	0.137020i	$-0.956247\pi$
$107$	−120.652	−	120.652i	−1.12759	−	1.12759i	−0.137020	−	0.990568i	$-0.543753\pi$
$108$	−3.21591	+	20.3045i	−0.0297769	+	0.188004i
$109$	35.1000	−	11.4047i	0.322019	−	0.104630i	−0.143547	−	0.989643i	$-0.545851\pi$
$109$	35.1000	−	11.4047i	0.322019	−	0.104630i	0.465566	+	0.885013i	$0.345851\pi$
$110$	−10.8098	−	1.19186i	−0.0982707	−	0.0108351i
$111$	−9.12145	+	28.0730i	−0.0821753	+	0.252909i
$112$	50.8108	−	99.7218i	0.453668	−	0.890373i
$113$	146.449	+	74.6195i	1.29601	+	0.660350i	0.959600	−	0.281366i	$-0.0907876\pi$
$113$	146.449	+	74.6195i	1.29601	+	0.660350i	0.336409	+	0.941716i	$0.390788\pi$
$114$	−10.8235	−	3.51678i	−0.0949434	−	0.0308490i
$115$	172.613	−	35.7719i	1.50099	−	0.311060i
$116$	45.2917	+	139.393i	0.390445	+	1.20167i
$117$	12.5823	+	1.99284i	0.107541	+	0.0170328i
$118$	4.85177	−	4.85177i	0.0411167	−	0.0411167i
$119$	−49.2716	−	67.8165i	−0.414047	−	0.569887i
$120$	13.8937	+	3.79877i	0.115781	+	0.0316564i
$121$	10.3044	+	7.48658i	0.0851603	+	0.0618726i
$122$	3.06243	+	19.3354i	0.0251019	+	0.158487i
$123$	26.5021	+	52.0133i	0.215464	+	0.422872i
$124$			166.078i			1.33934i
$125$	89.7289	−	87.0271i	0.717831	−	0.696217i
$126$	−4.53481			−0.0359905
$127$	−95.5356	+	48.6778i	−0.752249	+	0.383290i	−0.787682	−	0.616082i	$-0.788719\pi$
$127$	−95.5356	+	48.6778i	−0.752249	+	0.383290i	0.0354329	+	0.999372i	$0.488719\pi$
$128$	−51.4214	+	8.14435i	−0.401730	+	0.0636277i
$129$	−6.26253	+	8.61963i	−0.0485467	+	0.0668188i
$130$	1.17055	−	4.28118i	0.00900422	−	0.0329322i
$131$	−103.178	+	74.9632i	−0.787619	+	0.572238i	−0.907256	−	0.420579i	$-0.861827\pi$
$131$	−103.178	+	74.9632i	−0.787619	+	0.572238i	0.119637	+	0.992818i	$0.461827\pi$
$132$	50.4168	+	50.4168i	0.381945	+	0.381945i
$133$	−35.5559	+	224.491i	−0.267338	+	1.68790i
$134$	24.6542	−	8.01063i	0.183986	−	0.0597808i
$135$	5.27216	+	25.4402i	0.0390531	+	0.188446i
$136$	−5.95792	+	18.3366i	−0.0438082	+	0.134828i
$137$	−7.98004	+	15.6617i	−0.0582485	+	0.114319i	−0.918295	−	0.395896i	$-0.870434\pi$
$137$	−7.98004	+	15.6617i	−0.0582485	+	0.114319i	0.860047	+	0.510215i	$0.170434\pi$
$138$	11.3738	+	5.79526i	0.0824192	+	0.0419947i
$139$	34.3173	+	11.1504i	0.246887	+	0.0802186i	0.429847	−	0.902902i	$-0.358568\pi$
$139$	34.3173	+	11.1504i	0.246887	+	0.0802186i	−0.182959	+	0.983120i	$0.558568\pi$
$140$	15.6766	−	142.181i	0.111976	−	1.01558i
$141$	26.1746	+	80.5570i	0.185635	+	0.571326i
$142$	−6.13502	−	0.971692i	−0.0432044	−	0.00684290i
$143$	31.2423	−	31.2423i	0.218478	−	0.218478i
$144$	−27.2924	−	37.5648i	−0.189531	−	0.260866i
$145$	115.836	+	144.545i	0.798866	+	0.996859i
$146$	−6.39468	−	4.64601i	−0.0437992	−	0.0318220i
$147$	0.891304	+	5.62747i	0.00606329	+	0.0382821i
$148$	−30.6096	−	60.0747i	−0.206821	−	0.405910i
$149$		−	178.885i		−	1.20057i	−0.799787	−	0.600284i	$-0.795054\pi$
$149$		−	178.885i		−	1.20057i	0.799787	−	0.600284i	$-0.204946\pi$
$150$	9.01131	−	0.854388i	0.0600754	−	0.00569592i
$151$	−100.135			−0.663148			−0.331574	−	0.943429i	$-0.607580\pi$
$151$	−100.135			−0.663148			−0.331574	+	0.943429i	$0.607580\pi$
$152$	46.5795	−	23.7334i	0.306444	−	0.156141i
$153$	−34.3488	+	5.44032i	−0.224502	+	0.0355576i
$154$	−9.24478	+	12.7243i	−0.0600310	+	0.0826256i
$155$	74.2187	+	196.330i	0.478830	+	1.26665i
$156$	−23.5411	+	17.1036i	−0.150904	+	0.109638i
$157$	−27.8346	−	27.8346i	−0.177291	−	0.177291i	0.612883	−	0.790174i	$-0.290010\pi$
$157$	−27.8346	−	27.8346i	−0.177291	−	0.177291i	−0.790174	+	0.612883i	$0.790010\pi$
$158$	0.330539	−	2.08694i	0.00209202	−	0.0132085i
$159$	34.9651	−	11.3608i	0.219906	−	0.0714519i
$160$	−42.9425	+	24.5020i	−0.268391	+	0.153138i
$161$	78.7817	−	242.465i	0.489327	−	1.50599i
$162$	−0.854122	+	1.67631i	−0.00527236	+	0.0103476i
$163$	255.286	+	130.075i	1.56617	+	0.798004i	0.999661	−	0.0260500i	$-0.00829290\pi$
$163$	255.286	+	130.075i	1.56617	+	0.798004i	0.566511	+	0.824054i	$0.308293\pi$
$164$	−126.814	−	41.2045i	−0.773259	−	0.251247i
$165$	82.1314	+	37.0698i	0.497766	+	0.224665i
$166$	−4.43650	−	13.6541i	−0.0267259	−	0.0822539i
$167$	−35.3483	−	5.59863i	−0.211667	−	0.0335247i	0.0497005	−	0.998764i	$-0.484173\pi$
$167$	−35.3483	−	5.59863i	−0.211667	−	0.0335247i	−0.261367	+	0.965239i	$0.584173\pi$
$168$	14.7297	−	14.7297i	0.0876769	−	0.0876769i
$169$	−88.7369	−	122.136i	−0.525071	−	0.722698i
$170$	0.572467	+	12.1028i	0.00336745	+	0.0711929i
$171$	76.2871	+	55.4258i	0.446124	+	0.324128i
$172$	−3.80708	−	24.0370i	−0.0221342	−	0.139750i
$173$	−132.206	−	259.470i	−0.764199	−	1.49982i	−0.863269	−	0.504744i	$-0.831587\pi$
$173$	−132.206	−	259.470i	−0.764199	−	1.49982i	0.0990705	−	0.995080i	$-0.468413\pi$
$174$			13.4134i			0.0770883i
$175$	−45.0073	−	175.087i	−0.257185	−	1.00049i
$176$	−161.043			−0.915017
$177$	−50.6555	+	25.8103i	−0.286189	+	0.145821i
$178$	18.7495	−	2.96962i	0.105334	−	0.0166833i
$179$	−167.878	+	231.065i	−0.937868	+	1.29086i	0.0188424	+	0.999822i	$0.494002\pi$
$179$	−167.878	+	231.065i	−0.937868	+	1.29086i	−0.956710	+	0.291042i	$0.905998\pi$
$180$	−49.6052	−	32.5745i	−0.275584	−	0.180969i
$181$	193.147	−	140.329i	1.06711	−	0.775300i	0.0917183	−	0.995785i	$-0.470764\pi$
$181$	193.147	−	140.329i	1.06711	−	0.775300i	0.975390	+	0.220485i	$0.0707641\pi$
$182$	−4.53880	−	4.53880i	−0.0249385	−	0.0249385i
$183$	25.3744	−	160.208i	0.138658	−	0.875452i
$184$	−55.7678	+	18.1201i	−0.303086	+	0.0984785i
$185$	−63.0321	−	57.3386i	−0.340714	−	0.309938i
$186$	−4.69673	+	14.4551i	−0.0252512	+	0.0777153i
$187$	−54.7593	+	107.471i	−0.292830	+	0.574712i
$188$	−172.388	−	87.8360i	−0.916957	−	0.467213i
$189$	35.7351	+	11.6111i	0.189075	+	0.0614341i
$190$	22.1069	−	24.3021i	0.116352	−	0.127906i
$191$	73.6746	+	226.747i	0.385731	+	1.18716i	0.935949	+	0.352136i	$0.114545\pi$
$191$	73.6746	+	226.747i	0.385731	+	1.18716i	−0.550218	+	0.835021i	$0.685455\pi$
$192$	102.375	+	16.2146i	0.533204	+	0.0844512i
$193$	−85.2200	+	85.2200i	−0.441554	+	0.441554i	−0.892534	−	0.450980i	$-0.851075\pi$
$193$	−85.2200	+	85.2200i	−0.441554	+	0.441554i	0.450980	+	0.892534i	$0.351075\pi$
$194$	10.6064	+	14.5985i	0.0546723	+	0.0752500i
$195$	−20.1858	+	30.7394i	−0.103517	+	0.157638i
$196$	−10.5288	−	7.64964i	−0.0537185	−	0.0390288i
$197$	−10.0207	−	63.2683i	−0.0508666	−	0.321159i	−0.999981	−	0.00622639i	$-0.998018\pi$
$197$	−10.0207	−	63.2683i	−0.0508666	−	0.321159i	0.949114	−	0.314933i	$-0.101982\pi$
$198$	2.96237	+	5.81397i	0.0149614	+	0.0293635i
$199$		−	22.6054i		−	0.113595i	−0.998386	−	0.0567976i	$-0.981911\pi$
$199$		−	22.6054i		−	0.113595i	0.998386	−	0.0567976i	$-0.0180890\pi$
$200$	−26.4949	+	32.0452i	−0.132474	+	0.160226i
$201$	−214.790			−1.06861
$202$	13.7782	−	7.02032i	0.0682087	−	0.0347541i
$203$	264.590	−	41.9070i	1.30340	−	0.206438i
$204$	46.6917	−	64.2656i	0.228881	−	0.315027i
$205$	−168.329	+	7.96200i	−0.821115	+	0.0388390i
$206$	21.4353	−	15.5737i	0.104055	−	0.0756005i
$207$	−74.7897	−	74.7897i	−0.361303	−	0.361303i
$208$	10.2814	−	64.9142i	0.0494298	−	0.312088i
$209$	311.042	−	101.064i	1.48824	−	0.483558i
$210$	5.38539	−	11.9318i	0.0256447	−	0.0568182i
$211$	105.780	−	325.558i	0.501327	−	1.54293i	−0.305531	−	0.952182i	$-0.598834\pi$
$211$	105.780	−	325.558i	0.501327	−	1.54293i	0.806858	−	0.590745i	$-0.201166\pi$
$212$	−38.1245	+	74.8235i	−0.179832	+	0.352941i
$213$	45.8572	+	23.3654i	0.215292	+	0.109697i
$214$	33.9224	+	11.0220i	0.158516	+	0.0515049i
$215$	−15.2425	−	26.7141i	−0.0708952	−	0.124252i
$216$	−2.67058	−	8.21921i	−0.0123638	−	0.0380519i
$217$	299.812	+	47.4856i	1.38162	+	0.218828i
$218$	−5.45527	+	5.45527i	−0.0250242	+	0.0250242i
$219$	38.4955	+	52.9845i	0.175779	+	0.241938i
$220$	−192.528	+	72.7814i	−0.875128	+	0.330825i
$221$	−39.8241	−	28.9339i	−0.180200	−	0.130923i
$222$	−0.965261	−	6.09442i	−0.00434802	−	0.0274523i
$223$	−38.2651	−	75.0996i	−0.171593	−	0.336769i	0.789155	−	0.614195i	$-0.210519\pi$
$223$	−38.2651	−	75.0996i	−0.171593	−	0.336769i	−0.960747	+	0.277425i	$0.910519\pi$
$224$			71.5030i			0.319210i
$225$	−73.1984	−	16.3401i	−0.325326	−	0.0726225i
$226$	−34.3586			−0.152029
$227$	−69.0906	+	35.2034i	−0.304364	+	0.155081i	−0.599502	−	0.800374i	$-0.704635\pi$
$227$	−69.0906	+	35.2034i	−0.304364	+	0.155081i	0.295138	+	0.955455i	$0.404635\pi$
$228$	−212.737	+	33.6942i	−0.933056	+	0.147781i
$229$	42.5284	−	58.5354i	0.185714	−	0.255613i	−0.706001	−	0.708211i	$-0.749503\pi$
$229$	42.5284	−	58.5354i	0.185714	−	0.255613i	0.891715	+	0.452598i	$0.149503\pi$
$230$	−28.7555	+	23.0442i	−0.125024	+	0.100192i
$231$	105.430	−	76.5997i	0.456409	−	0.331600i
$232$	−43.5686	−	43.5686i	−0.187796	−	0.187796i
$233$	−59.1335	+	373.354i	−0.253792	+	1.60238i	0.450706	+	0.892673i	$0.351172\pi$
$233$	−59.1335	+	373.354i	−0.253792	+	1.60238i	−0.704498	+	0.709706i	$0.748828\pi$
$234$	−2.53266	+	0.822910i	−0.0108233	+	0.00351671i
$235$	−243.043	−	26.7974i	−1.03422	−	0.114032i
$236$	40.1289	−	123.504i	0.170038	−	0.523322i
$237$	−7.94818	+	15.5992i	−0.0335366	+	0.0658193i
$238$	15.6131	+	7.95527i	0.0656013	+	0.0334255i
$239$	294.798	+	95.7857i	1.23346	+	0.400777i	0.851968	−	0.523593i	$-0.175409\pi$
$239$	294.798	+	95.7857i	1.23346	+	0.400777i	0.381496	+	0.924370i	$0.375409\pi$
$240$	131.251	−	27.2000i	0.546877	−	0.113333i
$241$	77.8489	+	239.594i	0.323025	+	0.994167i	0.972324	+	0.233635i	$0.0750620\pi$
$241$	77.8489	+	239.594i	0.323025	+	0.994167i	−0.649300	+	0.760532i	$0.724938\pi$
$242$	−2.62975	−	0.416512i	−0.0108668	−	0.00172112i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$	217.777	+	299.744i	0.892527	+	1.22846i
$245$	−15.8653	−	4.33784i	−0.0647562	−	0.0177055i
$246$	−9.87238	−	7.17270i	−0.0401316	−	0.0291573i
$247$	20.8796	+	131.829i	0.0845329	+	0.533720i
$248$	−31.6965	−	62.2078i	−0.127808	−	0.250838i
$249$			118.957i			0.477737i
$250$	−8.45351	+	24.7249i	−0.0338140	+	0.0988994i
$251$	173.003			0.689254			0.344627	−	0.938740i	$-0.388005\pi$
$251$	173.003			0.689254			0.344627	+	0.938740i	$0.388005\pi$
$252$	−76.4714	+	38.9641i	−0.303458	+	0.154619i
$253$	−362.323	+	57.3863i	−1.43211	+	0.226823i
$254$	13.1745	−	18.1331i	0.0518681	−	0.0713903i
$255$	26.4772	−	96.8381i	0.103832	−	0.379757i
$256$	−184.852	+	134.303i	−0.722077	+	0.524620i
$257$	235.786	+	235.786i	0.917457	+	0.917457i	0.996844	−	0.0793870i	$-0.0252963\pi$
$257$	235.786	+	235.786i	0.917457	+	0.917457i	−0.0793870	+	0.996844i	$0.525296\pi$
$258$	0.348413	−	2.19979i	0.00135044	−	0.00852632i
$259$	−117.202	+	38.0812i	−0.452517	+	0.147032i
$260$	−17.0457	−	82.2520i	−0.0655603	−	0.316354i
$261$	34.3439	−	105.700i	0.131586	−	0.404980i
$262$	12.1034	−	23.7542i	0.0461961	−	0.0906650i
$263$	−34.4550	−	17.5557i	−0.131008	−	0.0667518i	0.387258	−	0.921971i	$-0.373422\pi$
$263$	−34.4550	−	17.5557i	−0.131008	−	0.0667518i	−0.518266	+	0.855220i	$0.673422\pi$
$264$	−28.5068	−	9.26243i	−0.107980	−	0.0350850i
$265$	−11.6312	+	105.491i	−0.0438913	+	0.398078i
$266$	−14.6822	−	45.1873i	−0.0551964	−	0.169877i
$267$	−155.353	−	24.6055i	−0.581846	−	0.0921553i
$268$	346.919	−	346.919i	1.29447	−	1.29447i
$269$	162.281	+	223.360i	0.603273	+	0.830334i	0.996003	−	0.0893195i	$-0.0284692\pi$
$269$	162.281	+	223.360i	0.603273	+	0.830334i	−0.392730	+	0.919654i	$0.628469\pi$
$270$	−3.39631	−	4.23806i	−0.0125789	−	0.0156965i
$271$	165.243	+	120.056i	0.609754	+	0.443012i	0.849328	−	0.527866i	$-0.177008\pi$
$271$	165.243	+	120.056i	0.609754	+	0.443012i	−0.239574	+	0.970878i	$0.577008\pi$
$272$	28.0676	+	177.212i	0.103190	+	0.651514i
$273$	24.1453	+	47.3878i	0.0884444	+	0.173582i
$274$		−	3.67442i		−	0.0134103i
$275$	−195.073	+	172.078i	−0.709357	+	0.625739i
$276$	241.594			0.875339
$277$	21.0058	−	10.7030i	0.0758331	−	0.0386389i	−0.415663	−	0.909519i	$-0.636450\pi$
$277$	21.0058	−	10.7030i	0.0758331	−	0.0386389i	0.491496	+	0.870880i	$0.336450\pi$
$278$	−7.45002	+	1.17997i	−0.0267986	+	0.00424449i
$279$	74.0222	−	101.883i	0.265313	−	0.365172i
$280$	21.2637	+	56.2488i	0.0759420	+	0.200889i
$281$	182.234	−	132.401i	0.648521	−	0.471178i	−0.214246	−	0.976780i	$-0.568729\pi$
$281$	182.234	−	132.401i	0.648521	−	0.471178i	0.862767	+	0.505602i	$0.168729\pi$
$282$	−12.5202	−	12.5202i	−0.0443980	−	0.0443980i
$283$	78.5434	−	495.903i	0.277538	−	1.75231i	−0.317172	−	0.948368i	$-0.602733\pi$
$283$	78.5434	−	495.903i	0.277538	−	1.75231i	0.594710	−	0.803940i	$-0.297267\pi$
$284$	−111.805	+	36.3277i	−0.393680	+	0.127914i
$285$	−236.431	+	134.902i	−0.829581	+	0.473340i
$286$	−2.85411	+	8.78406i	−0.00997941	+	0.0307135i
$287$	−110.644	+	217.151i	−0.385518	+	0.756623i
$288$	26.4313	+	13.4674i	0.0917754	+	0.0467619i
$289$	−147.050	−	47.7796i	−0.508825	−	0.165327i
$290$	−35.2927	−	15.9293i	−0.121699	−	0.0549285i
$291$	−46.2022	−	142.196i	−0.158771	−	0.488645i
$292$	−147.754	−	23.4020i	−0.506008	−	0.0801438i
$293$	104.707	−	104.707i	0.357362	−	0.357362i	−0.505478	−	0.862840i	$-0.668684\pi$
$293$	104.707	−	104.707i	0.357362	−	0.357362i	0.862840	+	0.505478i	$0.168684\pi$
$294$	−0.700071	−	0.963566i	−0.00238120	−	0.00327743i
$295$	−7.75415	−	163.934i	−0.0262852	−	0.555709i
$296$	22.9309	+	16.6602i	0.0774691	+	0.0562846i
$297$	−8.45774	−	53.4001i	−0.0284772	−	0.179798i
$298$	16.9766	+	33.3184i	0.0569684	+	0.111807i
$299$		−	149.711i		−	0.500706i
$300$	144.618	−	91.8349i	0.482061	−	0.306116i
$301$	−44.4813			−0.147778
$302$	18.6509	−	9.50309i	0.0617578	−	0.0314672i
$303$	−126.549	+	20.0435i	−0.417655	+	0.0661500i
$304$	285.952	−	393.579i	0.940631	−	1.29467i
$305$	391.399	+	257.022i	1.28327	+	0.842694i
$306$	5.88139	−	4.27308i	0.0192202	−	0.0139643i
$307$	280.981	+	280.981i	0.915249	+	0.915249i	0.996679	−	0.0814300i	$-0.0259487\pi$
$307$	280.981	+	280.981i	0.915249	+	0.915249i	−0.0814300	+	0.996679i	$0.525949\pi$
$308$	−46.5660	+	294.006i	−0.151188	+	0.954566i
$309$	−208.790	+	67.8399i	−0.675695	+	0.219547i
$310$	−32.4559	−	29.5242i	−0.104696	−	0.0952394i
$311$	−22.3318	+	68.7303i	−0.0718065	+	0.220998i	−0.980519	−	0.196425i	$-0.937067\pi$
$311$	−22.3318	+	68.7303i	−0.0718065	+	0.220998i	0.908712	+	0.417423i	$0.137067\pi$
$312$	5.55351	−	10.8994i	0.0177997	−	0.0349339i
$313$	−396.882	−	202.221i	−1.26799	−	0.646075i	−0.315007	−	0.949089i	$-0.602007\pi$
$313$	−396.882	−	202.221i	−1.26799	−	0.646075i	−0.952986	+	0.303015i	$0.902007\pi$
$314$	7.82595	+	2.54280i	0.0249234	+	0.00809810i
$315$	−72.9885	+	80.2361i	−0.231709	+	0.254718i
$316$	−12.3575	−	38.0326i	−0.0391061	−	0.120356i
$317$	−268.813	−	42.5757i	−0.847989	−	0.134308i	−0.282708	−	0.959206i	$-0.591233\pi$
$317$	−268.813	−	42.5757i	−0.847989	−	0.134308i	−0.565282	+	0.824898i	$0.691233\pi$
$318$	−5.43430	+	5.43430i	−0.0170890	+	0.0170890i
$319$	−226.572	−	311.849i	−0.710256	−	0.977583i
$320$	−164.241	+	250.110i	−0.513253	+	0.781593i
$321$	−239.093	−	173.712i	−0.744840	−	0.541158i
$322$	8.33692	+	52.6372i	0.0258911	+	0.163470i
$323$	−165.421	−	324.656i	−0.512138	−	1.00513i
$324$			35.6067i			0.109897i
$325$	−56.9083	−	89.6172i	−0.175103	−	0.275745i
$326$	−59.8931			−0.183721
$327$	56.9564	−	29.0207i	0.174179	−	0.0887484i
$328$	55.3649	−	8.76894i	0.168795	−	0.0267346i
$329$	−207.856	+	286.089i	−0.631781	+	0.869572i
$330$	−18.8155	+	0.889980i	−0.0570167	+	0.00269691i
$331$	−134.208	+	97.5079i	−0.405462	+	0.294586i	−0.771762	−	0.635911i	$-0.780624\pi$
$331$	−134.208	+	97.5079i	−0.405462	+	0.294586i	0.366300	+	0.930497i	$0.380624\pi$
$332$	−192.133	−	192.133i	−0.578714	−	0.578714i
$333$	−7.99788	+	50.4966i	−0.0240177	+	0.151641i
$334$	7.11518	−	2.31186i	0.0213029	−	0.00692174i
$335$	255.078	−	565.148i	0.761426	−	1.68701i
$336$	59.9035	−	184.364i	0.178284	−	0.548702i
$337$	−98.7787	+	193.864i	−0.293112	+	0.575264i	−0.989859	−	0.142052i	$-0.954630\pi$
$337$	−98.7787	+	193.864i	−0.293112	+	0.575264i	0.696747	+	0.717317i	$0.254630\pi$
$338$	28.1188	+	14.3273i	0.0831918	+	0.0423883i
$339$	270.753	+	87.9728i	0.798680	+	0.259507i
$340$	113.644	+	199.173i	0.334246	+	0.585803i
$341$	−134.972	−	415.402i	−0.395813	−	1.21819i
$342$	−19.4690	−	3.08359i	−0.0569269	−	0.00901634i
$343$	233.727	−	233.727i	0.681419	−	0.681419i
$344$	6.01355	+	8.27694i	0.0174812	+	0.0240609i
$345$	285.602	−	107.966i	0.827831	−	0.312945i
$346$	49.2486	+	35.7812i	0.142337	+	0.103414i
$347$	−89.1441	−	562.834i	−0.256899	−	1.62200i	−0.692194	−	0.721711i	$-0.743356\pi$
$347$	−89.1441	−	562.834i	−0.256899	−	1.62200i	0.435295	−	0.900288i	$-0.356644\pi$
$348$	115.251	+	226.192i	0.331180	+	0.649977i
$349$		−	173.906i		−	0.498297i	−0.968465	−	0.249149i	$-0.919849\pi$
$349$		−	173.906i		−	0.498297i	0.968465	−	0.249149i	$-0.0801507\pi$
$350$	24.9990	+	28.3397i	0.0714258	+	0.0809706i
$351$	22.0648			0.0628627
$352$	91.6722	−	46.7093i	0.260432	−	0.132697i
$353$	158.792	−	25.1501i	0.449835	−	0.0712469i	0.0725931	−	0.997362i	$-0.476873\pi$
$353$	158.792	−	25.1501i	0.449835	−	0.0712469i	0.377242	+	0.926115i	$0.376873\pi$
$354$	6.98545	−	9.61465i	0.0197329	−	0.0271600i
$355$	−115.937	+	92.9097i	−0.326582	+	0.261717i
$356$	290.660	−	211.177i	0.816461	−	0.593194i
$357$	−102.665	−	102.665i	−0.287578	−	0.287578i
$358$	9.33983	−	58.9694i	0.0260889	−	0.164719i
$359$	115.167	−	37.4199i	0.320798	−	0.104234i	−0.144191	−	0.989550i	$-0.546058\pi$
$359$	115.167	−	37.4199i	0.320798	−	0.104234i	0.464990	+	0.885316i	$0.346058\pi$
$360$	24.7976	+	2.73413i	0.0688821	+	0.00759481i
$361$	−193.745	+	596.286i	−0.536690	+	1.65176i
$362$	−22.6572	+	44.4673i	−0.0625890	+	0.122838i
$363$	19.6565	+	10.0155i	0.0541502	+	0.0275909i
$364$	−115.537	−	37.5403i	−0.317409	−	0.103133i
$365$	−185.127	+	38.3652i	−0.507197	+	0.105110i
$366$	10.4780	+	32.2478i	0.0286283	+	0.0881088i
$367$	−4.81923	−	0.763291i	−0.0131314	−	0.00207981i	0.149865	−	0.988706i	$-0.452116\pi$
$367$	−4.81923	−	0.763291i	−0.0131314	−	0.00207981i	−0.162997	+	0.986627i	$0.552116\pi$
$368$	−385.853	+	385.853i	−1.04851	+	1.04851i
$369$	59.4310	+	81.7997i	0.161060	+	0.221680i
$370$	17.1817	+	4.69778i	0.0464371	+	0.0126967i
$371$	124.175	+	90.2181i	0.334702	+	0.243176i
$372$	44.9992	+	284.114i	0.120966	+	0.763747i
$373$	156.010	+	306.187i	0.418258	+	0.820877i	0.999972	+	0.00748410i	$0.00238228\pi$
$373$	156.010	+	306.187i	0.418258	+	0.820877i	−0.581714	+	0.813393i	$0.697618\pi$
$374$		−	25.2140i		−	0.0674170i
$375$	129.921	−	173.192i	0.346457	−	0.461845i
$376$	81.3351			0.216317
$377$	140.167	−	71.4186i	0.371796	−	0.189439i
$378$	−7.75782	+	1.22872i	−0.0205233	+	0.00325058i
$379$	−30.1261	+	41.4650i	−0.0794884	+	0.109406i	−0.846910	−	0.531737i	$-0.821540\pi$
$379$	−30.1261	+	41.4650i	−0.0794884	+	0.109406i	0.767421	+	0.641143i	$0.221540\pi$
$380$	163.984	−	599.759i	0.431538	−	1.57831i
$381$	−150.246	+	109.160i	−0.394346	+	0.286509i
$382$	−35.2412	−	35.2412i	−0.0922544	−	0.0922544i
$383$	−46.0760	+	290.913i	−0.120303	+	0.759563i	0.851602	+	0.524189i	$0.175631\pi$
$383$	−46.0760	+	290.913i	−0.120303	+	0.759563i	−0.971905	+	0.235374i	$0.924369\pi$
$384$	−85.7612	+	27.8655i	−0.223337	+	0.0725664i
$385$	76.3404	+	368.372i	0.198287	+	0.956810i
$386$	7.78519	−	23.9604i	0.0201689	−	0.0620735i
$387$	−8.37796	+	16.4427i	−0.0216485	+	0.0424875i
$388$	304.292	+	155.044i	0.784257	+	0.399599i
$389$	−387.882	−	126.030i	−0.997125	−	0.323985i	−0.235409	−	0.971896i	$-0.575643\pi$
$389$	−387.882	−	126.030i	−0.997125	−	0.323985i	−0.761716	+	0.647911i	$0.775643\pi$
$390$	0.842492	−	7.64109i	0.00216024	−	0.0195925i
$391$	126.296	+	388.698i	0.323007	+	0.994113i
$392$	5.40374	+	0.855868i	0.0137850	+	0.00218334i
$393$	−156.198	+	156.198i	−0.397450	+	0.397450i
$394$	7.87074	+	10.8331i	0.0199765	+	0.0274953i
$395$	−31.6050	−	39.4380i	−0.0800126	−	0.0998431i
$396$	99.9099	+	72.5888i	0.252298	+	0.183305i
$397$	−5.74463	−	36.2702i	−0.0144701	−	0.0913606i	0.979396	−	0.201947i	$-0.0647270\pi$
$397$	−5.74463	−	36.2702i	−0.0144701	−	0.0913606i	−0.993866	+	0.110587i	$0.964727\pi$
$398$	2.14531	+	4.21041i	0.00539023	+	0.0105789i
$399$			393.677i			0.986660i
$400$	−84.3013	+	377.643i	−0.210753	+	0.944109i
$401$	−646.814			−1.61300			−0.806502	−	0.591232i	$-0.798642\pi$
$401$	−646.814			−1.61300			−0.806502	+	0.591232i	$0.798642\pi$
$402$	40.0060	−	20.3841i	0.0995175	−	0.0507067i
$403$	176.060	−	27.8851i	0.436873	−	0.0691939i
$404$	172.024	−	236.770i	0.425801	−	0.586064i
$405$	15.9123	+	42.0927i	0.0392897	+	0.103933i
$406$	−45.3046	+	32.9157i	−0.111588	+	0.0810731i
$407$	125.385	+	125.385i	0.308072	+	0.308072i
$408$	−5.22403	+	32.9832i	−0.0128040	+	0.0808412i
$409$	−261.970	+	85.1193i	−0.640514	+	0.208116i	−0.611227	−	0.791455i	$-0.709324\pi$
$409$	−261.970	+	85.1193i	−0.640514	+	0.208116i	−0.0292872	+	0.999571i	$0.509324\pi$
$410$	30.5967	−	17.4578i	0.0746260	−	0.0425799i
$411$	−9.40809	+	28.9551i	−0.0228907	+	0.0704504i
$412$	227.656	−	446.800i	0.552563	−	1.08447i
$413$	−211.482	−	107.755i	−0.512063	−	0.260909i
$414$	21.0278	+	6.83234i	0.0507917	+	0.0165032i
$415$	−312.994	−	141.269i	−0.754202	−	0.340407i
$416$	12.9753	+	39.9339i	0.0311906	+	0.0959948i
$417$	61.7288	+	9.77688i	0.148031	+	0.0234458i
$418$	−48.3424	+	48.3424i	−0.115652	+	0.115652i
$419$	355.482	+	489.278i	0.848405	+	1.16773i	0.984212	+	0.176994i	$0.0566372\pi$
$419$	355.482	+	489.278i	0.848405	+	1.16773i	−0.135807	+	0.990735i	$0.543363\pi$
$420$	−11.7059	−	247.481i	−0.0278713	−	0.589241i
$421$	1.11079	+	0.807036i	0.00263846	+	0.00191695i	0.589104	−	0.808057i	$-0.299481\pi$
$421$	1.11079	+	0.807036i	0.00263846	+	0.00191695i	−0.586465	+	0.809974i	$0.699481\pi$
$422$	11.1940	+	70.6760i	0.0265260	+	0.167479i
$423$	66.6046	+	130.719i	0.157458	+	0.309028i
$424$		−	35.3028i		−	0.0832614i
$425$	223.353	+	184.668i	0.525537	+	0.434512i
$426$	−10.7586			−0.0252550
$427$	603.380	−	307.438i	1.41307	−	0.719994i
$428$	666.744	−	105.602i	1.55781	−	0.246733i
$429$	44.9819	−	61.9123i	0.104853	−	0.144318i
$430$	5.37424	+	3.52913i	0.0124982	+	0.00820728i
$431$	−335.462	+	243.727i	−0.778333	+	0.565492i	−0.904478	−	0.426519i	$-0.859740\pi$
$431$	−335.462	+	243.727i	−0.778333	+	0.565492i	0.126145	+	0.992012i	$0.459740\pi$
$432$	−56.8681	−	56.8681i	−0.131639	−	0.131639i
$433$	19.1153	−	120.689i	0.0441462	−	0.278728i	−0.955734	−	0.294233i	$-0.904936\pi$
$433$	19.1153	−	120.689i	0.0441462	−	0.278728i	0.999880	+	0.0155054i	$0.00493571\pi$
$434$	−60.3485	+	19.6084i	−0.139052	+	0.0451807i
$435$	237.328	+	215.890i	0.545581	+	0.496299i
$436$	−45.1204	+	138.866i	−0.103487	+	0.318501i
$437$	503.100	−	987.390i	1.15126	−	2.25947i
$438$	−12.1984	−	6.21539i	−0.0278502	−	0.0141904i
$439$	−184.153	−	59.8348i	−0.419482	−	0.136298i	0.0916676	−	0.995790i	$-0.470780\pi$
$439$	−184.153	−	59.8348i	−0.419482	−	0.136298i	−0.511150	+	0.859492i	$0.670780\pi$
$440$	58.2247	−	64.0063i	0.132329	−	0.145469i
$441$	3.04955	+	9.38556i	0.00691509	+	0.0212825i
$442$	10.1634	+	1.60972i	0.0229941	+	0.00364191i
$443$	−328.869	+	328.869i	−0.742367	+	0.742367i	−0.973033	−	0.230666i	$-0.925910\pi$
$443$	−328.869	+	328.869i	−0.742367	+	0.742367i	0.230666	+	0.973033i	$0.425910\pi$
$444$	−68.6420	−	94.4776i	−0.154599	−	0.212787i
$445$	249.233	−	379.538i	0.560074	−	0.852894i
$446$	14.2543	+	10.3563i	0.0319602	+	0.0232205i
$447$	−48.4692	−	306.022i	−0.108432	−	0.684614i
$448$	196.457	+	385.569i	0.438521	+	0.860646i
$449$		−	436.881i		−	0.973008i	−0.873678	−	0.486504i	$-0.838272\pi$
$449$		−	436.881i		−	0.973008i	0.873678	−	0.486504i	$-0.161728\pi$
$450$	15.1844	−	3.90326i	0.0337431	−	0.00867391i
$451$	350.682			0.777565
$452$	−579.397	+	295.217i	−1.28185	+	0.653136i
$453$	−171.304	+	27.1319i	−0.378155	+	0.0598939i
$454$	9.52768	−	13.1137i	0.0209861	−	0.0288849i
$455$	−153.359	+	7.25395i	−0.337053	+	0.0159428i
$456$	73.2542	−	53.2223i	0.160645	−	0.116715i
$457$	150.072	+	150.072i	0.328385	+	0.328385i	0.851972	−	0.523587i	$-0.175407\pi$
$457$	150.072	+	150.072i	0.328385	+	0.328385i	−0.523587	+	0.851972i	$0.675407\pi$
$458$	−2.36605	+	14.9386i	−0.00516605	+	0.0326171i
$459$	−57.2874	+	18.6138i	−0.124809	+	0.0405529i
$460$	−286.909	+	635.672i	−0.623715	+	1.38190i
$461$	−238.630	+	734.429i	−0.517637	+	1.59312i	0.260797	+	0.965394i	$0.416015\pi$
$461$	−238.630	+	734.429i	−0.517637	+	1.59312i	−0.778433	+	0.627728i	$0.783985\pi$
$462$	−12.3676	+	24.2728i	−0.0267697	+	0.0525385i
$463$	403.382	+	205.533i	0.871235	+	0.443916i	0.831650	−	0.555300i	$-0.187396\pi$
$463$	403.382	+	205.533i	0.871235	+	0.443916i	0.0395848	+	0.999216i	$0.487396\pi$
$464$	−545.324	−	177.187i	−1.17527	−	0.381867i
$465$	180.164	+	315.757i	0.387449	+	0.679048i
$466$	−24.4182	−	75.1515i	−0.0523996	−	0.161269i
$467$	−275.240	−	43.5938i	−0.589380	−	0.0933485i	−0.145381	−	0.989376i	$-0.546441\pi$
$467$	−275.240	−	43.5938i	−0.589380	−	0.0933485i	−0.443999	+	0.896027i	$0.646441\pi$
$468$	−35.6380	+	35.6380i	−0.0761497	+	0.0761497i
$469$	−527.084	−	725.469i	−1.12385	−	1.54684i
$470$	47.8114	−	18.0741i	0.101726	−	0.0384556i
$471$	−55.1593	−	40.0756i	−0.117111	−	0.0850861i
$472$	8.54002	+	53.9196i	0.0180933	+	0.114236i
$473$	29.0574	+	57.0284i	0.0614322	+	0.120567i
$474$		−	3.65975i		−	0.00772099i
$475$	−74.1714	−	782.292i	−0.156150	−	1.64693i
$476$	331.640			0.696724
$477$	56.7375	−	28.9092i	0.118946	−	0.0606062i
$478$	−63.9983	+	10.1363i	−0.133888	+	0.0212057i
$479$	−393.351	+	541.401i	−0.821192	+	1.13027i	0.168308	+	0.985735i	$0.446170\pi$
$479$	−393.351	+	541.401i	−0.821192	+	1.13027i	−0.989499	+	0.144539i	$0.953830\pi$
$480$	−66.8240	+	53.5516i	−0.139217	+	0.111566i
$481$	−58.5460	+	42.5361i	−0.121717	+	0.0884327i
$482$	−37.2379	−	37.2379i	−0.0772571	−	0.0772571i
$483$	69.0774	−	436.137i	0.143017	−	0.902976i
$484$	−47.9248	+	15.5717i	−0.0990182	+	0.0321730i
$485$	429.009	+	47.3017i	0.884554	+	0.0975292i
$486$	−1.00697	+	3.09913i	−0.00207195	+	0.00637681i
$487$	−155.696	+	305.570i	−0.319704	+	0.627454i	−0.993799	−	0.111190i	$-0.964534\pi$
$487$	−155.696	+	305.570i	−0.319704	+	0.627454i	0.674095	+	0.738644i	$0.264534\pi$
$488$	−138.780	−	70.7117i	−0.284384	−	0.144901i
$489$	471.968	+	153.352i	0.965171	+	0.313603i
$490$	3.36668	−	0.697702i	0.00687078	−	0.00142388i
$491$	−240.611	−	740.525i	−0.490043	−	1.50820i	−0.824542	−	0.565801i	$-0.808567\pi$
$491$	−240.611	−	740.525i	−0.490043	−	1.50820i	0.334499	−	0.942396i	$-0.391433\pi$
$492$	−228.109	−	36.1290i	−0.463637	−	0.0734329i
$493$	−303.670	+	303.670i	−0.615964	+	0.615964i
$494$	−16.3998	−	22.5724i	−0.0331981	−	0.0456932i
$495$	150.548	+	41.1625i	0.304138	+	0.0831566i
$496$	−525.632	−	381.894i	−1.05974	−	0.769947i
$497$	33.6129	+	212.223i	0.0676315	+	0.427009i
$498$	−11.2893	−	22.1564i	−0.0226692	−	0.0444908i
$499$			289.465i			0.580090i	0.957013	+	0.290045i	$0.0936703\pi$
$499$			289.465i			0.580090i	−0.957013	+	0.290045i	$0.906330\pi$
$500$	69.8884	+	489.575i	0.139777	+	0.979149i
$501$	−61.9883			−0.123729
$502$	−32.2229	+	16.4184i	−0.0641890	+	0.0327059i
$503$	548.847	−	86.9289i	1.09115	−	0.172821i	0.415171	−	0.909743i	$-0.363722\pi$
$503$	548.847	−	86.9289i	1.09115	−	0.172821i	0.675977	+	0.736923i	$0.263722\pi$
$504$	21.2075	−	29.1896i	0.0420783	−	0.0579158i
$505$	97.5485	−	356.775i	0.193165	−	0.706485i
$506$	62.0388	−	45.0739i	0.122606	−	0.0890788i
$507$	−184.898	−	184.898i	−0.364690	−	0.364690i
$508$	66.3600	−	418.981i	0.130630	−	0.824765i
$509$	828.980	−	269.352i	1.62864	−	0.529178i	0.654685	−	0.755902i	$-0.272801\pi$
$509$	828.980	−	269.352i	1.62864	−	0.529178i	0.973959	+	0.226724i	$0.0728014\pi$
$510$	4.25862	+	20.5495i	0.00835023	+	0.0402931i
$511$	−84.4930	+	260.043i	−0.165348	+	0.508890i
$512$	116.227	−	228.109i	0.227007	−	0.445526i
$513$	145.524	+	74.1483i	0.283673	+	0.144539i
$514$	−66.2934	−	21.5400i	−0.128976	−	0.0419067i
$515$	69.4543	−	629.925i	0.134863	−	1.22315i
$516$	−13.0257	−	40.0891i	−0.0252437	−	0.0776921i
$517$	502.570	+	79.5993i	0.972089	+	0.153964i
$518$	18.2156	−	18.2156i	0.0351653	−	0.0351653i
$519$	−296.473	−	408.060i	−0.571239	−	0.786243i
$520$	22.0828	+	27.5559i	0.0424670	+	0.0529921i
$521$	−243.463	−	176.886i	−0.467300	−	0.339513i	0.329088	−	0.944299i	$-0.393259\pi$
$521$	−243.463	−	176.886i	−0.467300	−	0.339513i	−0.796388	+	0.604786i	$0.793259\pi$
$522$	3.63438	+	22.9466i	0.00696242	+	0.0439590i
$523$	−75.3145	−	147.813i	−0.144005	−	0.282625i	0.807727	−	0.589557i	$-0.200698\pi$
$523$	−75.3145	−	147.813i	−0.144005	−	0.282625i	−0.951732	+	0.306932i	$0.900698\pi$
$524$		−	504.567i		−	0.962915i
$525$	−124.435	−	287.330i	−0.237020	−	0.547296i
$526$	8.08355			0.0153680
$527$	−433.585	+	220.922i	−0.822741	+	0.419208i
$528$	−275.501	+	43.6350i	−0.521781	+	0.0826421i
$529$	−419.678	+	577.637i	−0.793342	+	1.09194i
$530$	−7.84493	−	20.7521i	−0.0148018	−	0.0391550i
$531$	−79.6643	+	57.8795i	−0.150027	+	0.109001i
$532$	−635.849	−	635.849i	−1.19521	−	1.19521i
$533$	−22.3884	+	141.355i	−0.0420046	+	0.265206i
$534$	31.2706	−	10.1604i	0.0585591	−	0.0190270i
$535$	741.003	−	422.799i	1.38505	−	0.790279i
$536$	−63.7350	+	196.156i	−0.118908	+	0.365963i
$537$	−224.586	+	440.776i	−0.418224	+	0.820811i
$538$	−51.4232	−	26.2014i	−0.0955821	−	0.0487015i
$539$	32.5521	+	10.5768i	0.0603935	+	0.0196230i
$540$	−93.6871	−	42.2854i	−0.173495	−	0.0783063i
$541$	−234.751	−	722.489i	−0.433921	−	1.33547i	−0.894189	−	0.447690i	$-0.852247\pi$
$541$	−234.751	−	722.489i	−0.433921	−	1.33547i	0.460268	−	0.887780i	$-0.347753\pi$
$542$	−42.1712	−	6.67927i	−0.0778067	−	0.0123234i
$543$	292.399	−	292.399i	0.538487	−	0.538487i
$544$	−67.3761	−	92.7353i	−0.123853	−	0.170469i
$545$	8.71867	+	184.326i	0.0159976	+	0.338212i
$546$	−8.99444	−	6.53484i	−0.0164733	−	0.0119686i
$547$	44.7745	+	282.695i	0.0818546	+	0.516810i	0.994214	+	0.107419i	$0.0342587\pi$
$547$	44.7745	+	282.695i	0.0818546	+	0.516810i	−0.912359	+	0.409391i	$0.865741\pi$
$548$	−31.5715	−	61.9625i	−0.0576121	−	0.113070i
$549$		−	280.947i		−	0.511743i
$550$	20.0030	−	50.5636i	0.0363691	−	0.0919338i
$551$	1164.44			2.11333
$552$	−90.4938	+	46.1089i	−0.163938	+	0.0835306i
$553$	−72.1917	+	11.4340i	−0.130546	+	0.0206764i
$554$	−2.89672	+	3.98700i	−0.00522874	+	0.00719675i
$555$	−123.367	−	81.0119i	−0.222282	−	0.145967i
$556$	−115.493	+	83.9103i	−0.207721	+	0.150918i
$557$	369.701	+	369.701i	0.663736	+	0.663736i	0.956259	−	0.292523i	$-0.0944948\pi$
$557$	369.701	+	369.701i	0.663736	+	0.663736i	−0.292523	+	0.956259i	$0.594495\pi$
$558$	−4.11819	+	26.0012i	−0.00738027	+	0.0465972i
$559$	−24.8425	+	8.07181i	−0.0444409	+	0.0144397i
$560$	413.952	+	376.561i	0.739200	+	0.672430i
$561$	−64.5586	+	198.691i	−0.115078	+	0.354173i
$562$	−21.3771	+	41.9550i	−0.0380376	+	0.0746531i
$563$	−305.894	−	155.861i	−0.543328	−	0.276840i	0.160710	−	0.987002i	$-0.448622\pi$
$563$	−305.894	−	155.861i	−0.543328	−	0.276840i	−0.704038	+	0.710162i	$0.748622\pi$
$564$	−318.708	−	103.554i	−0.565085	−	0.183607i
$565$	−553.008	+	607.920i	−0.978775	+	1.07597i
$566$	32.4332	+	99.8191i	0.0573025	+	0.176359i
$567$	64.2791	+	10.1808i	0.113367	+	0.0179556i
$568$	34.9456	−	34.9456i	0.0615240	−	0.0615240i
$569$	−105.627	−	145.383i	−0.185636	−	0.255506i	0.706048	−	0.708164i	$-0.250476\pi$
$569$	−105.627	−	145.383i	−0.185636	−	0.255506i	−0.891685	+	0.452657i	$0.850476\pi$
$570$	31.2342	−	47.5642i	0.0547968	−	0.0834459i
$571$	291.972	+	212.130i	0.511335	+	0.371507i	0.813330	−	0.581803i	$-0.197653\pi$
$571$	291.972	+	212.130i	0.511335	+	0.371507i	−0.301995	+	0.953310i	$0.597653\pi$
$572$	27.3451	+	172.650i	0.0478062	+	0.301836i
$573$	187.475	+	367.940i	0.327181	+	0.642129i
$574$		−	50.9461i		−	0.0887562i
$575$	−55.0954	+	879.681i	−0.0958180	+	1.52988i
$576$	179.529			0.311683
$577$	197.873	−	100.821i	0.342934	−	0.174733i	−0.274038	−	0.961719i	$-0.588359\pi$
$577$	197.873	−	100.821i	0.342934	−	0.174733i	0.616971	+	0.786985i	$0.288359\pi$
$578$	31.9235	−	5.05618i	0.0552309	−	0.00874772i
$579$	−122.698	+	168.879i	−0.211913	+	0.291673i
$580$	−732.016	+	34.6246i	−1.26210	+	0.0596976i
$581$	−401.784	+	291.913i	−0.691539	+	0.502432i
$582$	22.1002	+	22.1002i	0.0379728	+	0.0379728i
$583$	34.5494	−	218.136i	0.0592614	−	0.374162i
$584$	59.8107	−	19.4337i	0.102416	−	0.0332768i
$585$	−26.2035	+	58.0561i	−0.0447922	+	0.0992412i
$586$	−9.56541	+	29.4393i	−0.0163232	+	0.0502377i
$587$	−62.5946	+	122.849i	−0.106635	+	0.209282i	−0.938158	−	0.346208i	$-0.887469\pi$
$587$	−62.5946	+	122.849i	−0.106635	+	0.209282i	0.831523	+	0.555490i	$0.187469\pi$
$588$	−20.0846	−	10.2336i	−0.0341575	−	0.0174041i
$589$	1254.88	+	407.734i	2.13052	+	0.692248i
$590$	17.0020	+	29.7979i	0.0288170	+	0.0505049i
$591$	−34.2854	−	105.520i	−0.0580126	−	0.178544i
$592$	260.521	+	41.2625i	0.440069	+	0.0697001i
$593$	−137.601	+	137.601i	−0.232043	+	0.232043i	−0.813545	−	0.581502i	$-0.802465\pi$
$593$	−137.601	+	137.601i	−0.232043	+	0.232043i	0.581502	+	0.813545i	$0.302465\pi$
$594$	6.64311	+	9.14345i	0.0111837	+	0.0153930i
$595$	392.051	−	148.207i	0.658909	−	0.249087i
$596$	572.559	+	415.988i	0.960669	+	0.697967i
$597$	−6.12500	−	38.6717i	−0.0102596	−	0.0647768i
$598$	14.2079	+	27.8846i	0.0237591	+	0.0466298i
$599$			1071.31i			1.78849i	0.447578	+	0.894245i	$0.352287\pi$
$599$			1071.31i			1.78849i	−0.447578	+	0.894245i	$0.647713\pi$
$600$	−36.6427	+	61.9995i	−0.0610712	+	0.103332i
$601$	374.202			0.622631			0.311316	−	0.950307i	$-0.399230\pi$
$601$	374.202			0.622631			0.311316	+	0.950307i	$0.399230\pi$
$602$	8.28493	−	4.22138i	0.0137623	−	0.00701227i
$603$	−367.447	+	58.1979i	−0.609365	+	0.0965139i
$604$	232.860	−	320.505i	0.385530	−	0.530637i
$605$	−49.6958	+	39.8254i	−0.0821419	+	0.0658271i
$606$	21.6685	−	15.7431i	0.0357566	−	0.0259787i
$607$	147.094	+	147.094i	0.242329	+	0.242329i	0.817813	−	0.575484i	$-0.195186\pi$
$607$	147.094	+	147.094i	0.242329	+	0.242329i	−0.575484	+	0.817813i	$0.695186\pi$
$608$	−48.6207	+	306.979i	−0.0799683	+	0.504900i
$609$	441.287	−	143.383i	0.724609	−	0.235440i
$610$	−97.2925	−	10.7273i	−0.159496	−	0.0175857i
$611$	−64.1707	+	197.497i	−0.105026	+	0.323236i
$612$	62.4638	−	122.592i	0.102065	−	0.200314i
$613$	−996.561	−	507.773i	−1.62571	−	0.828341i	−0.998786	−	0.0492612i	$-0.984313\pi$
$613$	−996.561	−	507.773i	−1.62571	−	0.828341i	−0.626925	−	0.779080i	$-0.715687\pi$
$614$	−79.0004	−	25.6688i	−0.128665	−	0.0418059i
$615$	−285.807	+	59.2298i	−0.464726	+	0.0963087i
$616$	−38.6698	−	119.013i	−0.0627756	−	0.193203i
$617$	263.297	+	41.7021i	0.426737	+	0.0675885i	0.366109	−	0.930572i	$-0.380690\pi$
$617$	263.297	+	41.7021i	0.426737	+	0.0675885i	0.0606278	+	0.998160i	$0.480690\pi$
$618$	32.4503	−	32.4503i	0.0525086	−	0.0525086i
$619$	254.710	+	350.578i	0.411486	+	0.566362i	0.963580	−	0.267420i	$-0.0861710\pi$
$619$	254.710	+	350.578i	0.411486	+	0.566362i	−0.552094	+	0.833782i	$0.686171\pi$
$620$	−800.989	−	219.004i	−1.29192	−	0.353233i
$621$	−148.209	−	107.680i	−0.238662	−	0.173398i
$622$	−2.36322	−	14.9208i	−0.00379939	−	0.0239884i
$623$	−298.121	−	585.095i	−0.478525	−	0.939158i
$624$		−	113.836i		−	0.182430i
$625$	301.405	+	547.521i	0.482249	+	0.876034i
$626$	93.1131			0.148743
$627$	504.724	−	257.170i	0.804983	−	0.410159i
$628$	153.819	−	24.3625i	0.244934	−	0.0387938i
$629$	116.121	−	159.827i	0.184612	−	0.254097i
$630$	5.97998	−	21.8713i	0.00949203	−	0.0347163i
$631$	164.634	−	119.614i	0.260910	−	0.189562i	−0.449638	−	0.893211i	$-0.648447\pi$
$631$	164.634	−	119.614i	0.260910	−	0.189562i	0.710548	+	0.703648i	$0.248447\pi$
$632$	11.8874	+	11.8874i	0.0188092	+	0.0188092i
$633$	92.7502	−	585.601i	0.146525	−	0.925121i
$634$	54.1086	−	17.5810i	0.0853448	−	0.0277302i
$635$	−108.791	−	524.957i	−0.171324	−	0.826703i
$636$	−44.9469	+	138.332i	−0.0706713	+	0.217504i
$637$	−6.34158	+	12.4461i	−0.00995539	+	0.0195385i
$638$	71.7956	+	36.5817i	0.112532	+	0.0573381i
$639$	84.7800	+	27.5467i	0.132676	+	0.0431091i
$640$	28.5286	−	258.744i	0.0445759	−	0.404287i
$641$	41.9587	+	129.135i	0.0654581	+	0.201459i	0.978436	−	0.206549i	$-0.0662233\pi$
$641$	41.9587	+	129.135i	0.0654581	+	0.201459i	−0.912978	+	0.408009i	$0.866223\pi$
$642$	61.0183	+	9.66436i	0.0950442	+	0.0150535i
$643$	−624.690	+	624.690i	−0.971524	+	0.971524i	−0.999606	−	0.0280819i	$-0.991060\pi$
$643$	−624.690	+	624.690i	−0.971524	+	0.971524i	0.0280819	+	0.999606i	$0.491060\pi$
$644$	592.858	+	815.999i	0.920587	+	1.26708i
$645$	−33.3139	−	41.5706i	−0.0516495	−	0.0644505i
$646$	61.6213	+	44.7705i	0.0953891	+	0.0693042i
$647$	91.0302	+	574.742i	0.140696	+	0.888318i	0.952533	+	0.304435i	$0.0984675\pi$
$647$	91.0302	+	574.742i	0.140696	+	0.888318i	−0.811837	+	0.583884i	$0.801532\pi$
$648$	−6.79565	−	13.3372i	−0.0104871	−	0.0205821i
$649$			341.527i			0.526236i
$650$	19.1044	+	11.2910i	0.0293914	+	0.0173708i
$651$	525.763			0.807624
$652$	−1009.99	+	514.615i	−1.54906	+	0.789286i
$653$	1046.82	−	165.800i	1.60310	−	0.253906i	0.710145	−	0.704055i	$-0.248629\pi$
$653$	1046.82	−	165.800i	1.60310	−	0.253906i	0.892953	+	0.450150i	$0.148629\pi$
$654$	−7.85436	+	10.8106i	−0.0120097	+	0.0165300i
$655$	−225.486	−	596.478i	−0.344254	−	0.910653i
$656$	422.019	−	306.615i	0.643322	−	0.467401i
$657$	80.2116	+	80.2116i	0.122088	+	0.122088i
$658$	11.5640	−	73.0120i	0.0175744	−	0.110960i
$659$	−257.042	+	83.5179i	−0.390048	+	0.126734i	−0.497474	−	0.867479i	$-0.665739\pi$
$659$	−257.042	+	83.5179i	−0.390048	+	0.126734i	0.107426	+	0.994213i	$0.465739\pi$
$660$	−309.643	+	176.675i	−0.469156	+	0.267689i
$661$	193.786	−	596.411i	0.293170	−	0.902286i	−0.690659	−	0.723180i	$-0.742680\pi$
$661$	193.786	−	596.411i	0.293170	−	0.902286i	0.983830	−	0.179106i	$-0.0573204\pi$
$662$	15.7434	−	30.8981i	0.0237815	−	0.0466739i
$663$	−75.9679	−	38.7076i	−0.114582	−	0.0583825i
$664$	108.636	+	35.2981i	0.163609	+	0.0531598i
$665$	−1035.83	−	467.518i	−1.55764	−	0.703035i
$666$	−3.30259	−	10.1643i	−0.00495885	−	0.0152618i
$667$	−1290.04	−	204.322i	−1.93409	−	0.306329i
$668$	100.121	−	100.121i	0.149881	−	0.149881i
$669$	−85.8096	−	118.107i	−0.128265	−	0.176542i
$670$	6.12397	+	129.470i	0.00914026	+	0.193239i
$671$	−788.317	−	572.746i	−1.17484	−	0.853570i
$672$	19.3739	+	122.322i	0.0288302	+	0.182027i
$673$	436.782	+	857.233i	0.649008	+	1.27375i	0.947628	+	0.319377i	$0.103474\pi$
$673$	436.782	+	857.233i	0.649008	+	1.27375i	−0.298620	+	0.954372i	$0.596526\pi$
$674$		−	45.4828i		−	0.0674819i
$675$	−129.650	−	8.12010i	−0.192074	−	0.0120298i
$676$	597.276			0.883545
$677$	154.586	−	78.7654i	0.228339	−	0.116345i	−0.336078	−	0.941834i	$-0.609101\pi$
$677$	154.586	−	78.7654i	0.228339	−	0.116345i	0.564418	+	0.825489i	$0.309101\pi$
$678$	−58.7782	+	9.30956i	−0.0866936	+	0.0137309i
$679$	366.898	−	504.992i	0.540351	−	0.743730i
$680$	−80.5803	−	52.9151i	−0.118500	−	0.0778163i
$681$	−108.657	+	78.9437i	−0.159555	+	0.115923i
$682$	64.5621	+	64.5621i	0.0946659	+	0.0946659i
$683$	56.7063	−	358.030i	0.0830254	−	0.524202i	−0.910764	−	0.412927i	$-0.864507\pi$
$683$	56.7063	−	358.030i	0.0830254	−	0.524202i	0.993790	−	0.111275i	$-0.0354934\pi$
$684$	−354.805	+	115.283i	−0.518720	+	0.168542i
$685$	−65.0129	−	59.1404i	−0.0949093	−	0.0863363i
$686$	−21.3519	+	65.7143i	−0.0311252	+	0.0957934i
$687$	56.8942	−	111.661i	0.0828155	−	0.162535i
$688$	84.8307	+	43.2234i	0.123300	+	0.0628247i
$689$	85.7220	+	27.8528i	0.124415	+	0.0404249i
$690$	−42.9489	+	47.2136i	−0.0622448	+	0.0684256i
$691$	−174.384	−	536.699i	−0.252365	−	0.776699i	−0.994337	−	0.106269i	$-0.966110\pi$
$691$	−174.384	−	536.699i	−0.252365	−	0.776699i	0.741973	−	0.670430i	$-0.233890\pi$
$692$	1137.93	+	180.230i	1.64441	+	0.260448i
$693$	159.608	−	159.608i	0.230314	−	0.230314i
$694$	70.0179	+	96.3714i	0.100890	+	0.138864i
$695$	−99.0317	+	150.808i	−0.142492	+	0.216990i
$696$	−86.3389	−	62.7289i	−0.124050	−	0.0901277i
$697$	−61.1190	−	385.890i	−0.0876886	−	0.553644i
$698$	16.5041	+	32.3911i	0.0236448	+	0.0464055i
$699$			654.729i			0.936666i
$700$	665.065	+	263.100i	0.950092	+	0.375858i
$701$	6.02418			0.00859370			0.00429685	−	0.999991i	$-0.498632\pi$
$701$	6.02418			0.00859370			0.00429685	+	0.999991i	$0.498632\pi$
$702$	−4.10971	+	2.09400i	−0.00585429	+	0.00298291i
$703$	−529.070	+	83.7965i	−0.752589	+	0.119198i
$704$	365.993	−	503.746i	0.519877	−	0.715549i
$705$	−423.040	+	20.0100i	−0.600057	+	0.0283829i
$706$	−27.1892	+	19.7541i	−0.0385116	+	0.0279803i
$707$	−378.244	−	378.244i	−0.534999	−	0.534999i
$708$	35.1858	−	222.154i	0.0496975	−	0.313777i
$709$	181.555	−	58.9908i	0.256072	−	0.0832029i	−0.178168	−	0.984000i	$-0.557017\pi$
$709$	181.555	−	58.9908i	0.256072	−	0.0832029i	0.434240	+	0.900797i	$0.357017\pi$
$710$	12.7766	−	28.3077i	0.0179952	−	0.0398700i
$711$	−9.37052	+	28.8395i	−0.0131794	+	0.0405619i
$712$	−68.5688	+	134.574i	−0.0963046	+	0.189008i
$713$	−1318.68	−	671.900i	−1.84948	−	0.942356i
$714$	28.8653	+	9.37889i	0.0404275	+	0.0131357i
$715$	109.482	+	191.880i	0.153122	+	0.268363i
$716$	−349.179	−	1074.66i	−0.487680	−	1.50092i
$717$	530.272	+	83.9869i	0.739571	+	0.117136i
$718$	−17.8993	+	17.8993i	−0.0249293	+	0.0249293i
$719$	−356.238	−	490.319i	−0.495463	−	0.681946i	0.485921	−	0.874003i	$-0.338484\pi$
$719$	−356.238	−	490.319i	−0.495463	−	0.681946i	−0.981384	+	0.192057i	$0.938484\pi$
$720$	217.164	−	82.0945i	0.301617	−	0.114020i
$721$	−741.494	−	538.727i	−1.02842	−	0.747194i
$722$	−20.5027	−	129.449i	−0.0283971	−	0.179292i
$723$	198.097	+	388.787i	0.273993	+	0.537741i
$724$			944.537i			1.30461i
$725$	−849.885	+	368.063i	−1.17225	+	0.507673i
$726$	−4.61165			−0.00635213
$727$	−537.892	+	274.069i	−0.739878	+	0.376987i	−0.782950	−	0.622085i	$-0.786286\pi$
$727$	−537.892	+	274.069i	−0.739878	+	0.376987i	0.0430713	+	0.999072i	$0.486286\pi$
$728$	50.4414	−	7.98913i	0.0692876	−	0.0109741i
$729$	15.8702	−	21.8435i	0.0217698	−	0.0299636i
$730$	30.8401	−	24.7148i	0.0422468	−	0.0338558i
$731$	57.6897	−	41.9141i	0.0789189	−	0.0573380i
$732$	453.772	+	453.772i	0.619908	+	0.619908i
$733$	104.036	−	656.855i	0.141931	−	0.896119i	−0.809245	−	0.587471i	$-0.800124\pi$
$733$	104.036	−	656.855i	0.141931	−	0.896119i	0.951176	−	0.308648i	$-0.0998764\pi$
$734$	0.970051	−	0.315189i	0.00132160	−	0.000429412i
$735$	−28.3165	−	3.12212i	−0.0385258	−	0.00424778i
$736$	107.729	−	331.557i	0.146372	−	0.450485i
$737$	−585.788	+	1149.67i	−0.794828	+	1.55994i
$738$	−18.8324	−	9.59559i	−0.0255182	−	0.0130021i
$739$	698.048	+	226.810i	0.944585	+	0.306914i	0.740513	−	0.672042i	$-0.234583\pi$
$739$	698.048	+	226.810i	0.944585	+	0.306914i	0.204071	+	0.978956i	$0.434583\pi$
$740$	330.103	−	68.4097i	0.446085	−	0.0924455i
$741$	71.4387	+	219.866i	0.0964085	+	0.296715i
$742$	−31.6902	−	5.01924i	−0.0427092	−	0.00676447i
$743$	271.717	−	271.717i	0.365702	−	0.365702i	−0.500205	−	0.865907i	$-0.666742\pi$
$743$	271.717	−	271.717i	0.365702	−	0.365702i	0.865907	+	0.500205i	$0.166742\pi$
$744$	−71.0793	−	97.8323i	−0.0955367	−	0.131495i
$745$	862.755	+	235.892i	1.15806	+	0.316634i
$746$	−58.1158	−	42.2236i	−0.0779032	−	0.0566000i
$747$	32.2316	+	203.502i	0.0431480	+	0.272426i
$748$	−216.644	−	425.188i	−0.289631	−	0.568433i
$749$		−	1233.83i		−	1.64731i
$750$	−7.76238	+	44.5880i	−0.0103498	+	0.0594506i
$751$	609.841			0.812039			0.406020	−	0.913864i	$-0.366916\pi$
$751$	609.841			0.812039			0.406020	+	0.913864i	$0.366916\pi$
$752$	674.402	−	343.625i	0.896812	−	0.456948i
$753$	295.960	−	46.8755i	0.393042	−	0.0622517i
$754$	−19.3292	+	26.6044i	−0.0256355	+	0.0352843i
$755$	132.047	−	482.950i	0.174897	−	0.639669i
$756$	−120.264	+	87.3770i	−0.159080	+	0.115578i
$757$	−186.507	−	186.507i	−0.246376	−	0.246376i	0.573105	−	0.819482i	$-0.305739\pi$
$757$	−186.507	−	186.507i	−0.246376	−	0.246376i	−0.819482	+	0.573105i	$0.805739\pi$
$758$	1.67605	−	10.5822i	0.00221115	−	0.0139606i
$759$	−604.286	+	196.344i	−0.796161	+	0.258688i
$760$	53.0421	+	255.949i	0.0697923	+	0.336775i
$761$	187.108	−	575.859i	0.245871	−	0.756713i	−0.749621	−	0.661867i	$-0.769764\pi$
$761$	187.108	−	575.859i	0.245871	−	0.756713i	0.995492	−	0.0948459i	$-0.0302358\pi$
$762$	17.6247	−	34.5905i	0.0231296	−	0.0453943i
$763$	237.788	+	121.159i	0.311648	+	0.158793i
$764$	−897.079	−	291.479i	−1.17419	−	0.381517i
$765$	19.0567	−	172.838i	0.0249108	−	0.225931i
$766$	−19.0264	−	58.5571i	−0.0248386	−	0.0764453i
$767$	−137.665	−	21.8040i	−0.179485	−	0.0284276i
$768$	−279.841	+	279.841i	−0.364376	+	0.364376i
$769$	18.6721	+	25.7000i	0.0242811	+	0.0334200i	0.820985	−	0.570950i	$-0.193425\pi$
$769$	18.6721	+	25.7000i	0.0242811	+	0.0334200i	−0.796704	+	0.604370i	$0.793425\pi$
$770$	−49.1783	−	61.3667i	−0.0638679	−	0.0796970i
$771$	467.253	+	339.479i	0.606035	+	0.440310i
$772$	−74.5896	−	470.940i	−0.0966187	−	0.610026i
$773$	−67.9868	−	133.432i	−0.0879518	−	0.172615i	0.842841	−	0.538163i	$-0.180882\pi$
$773$	−67.9868	−	133.432i	−0.0879518	−	0.172615i	−0.930792	+	0.365548i	$0.880882\pi$
$774$		−	3.85764i		−	0.00498403i
$775$	−1044.77	+	99.0572i	−1.34809	+	0.127816i
$776$	−143.569			−0.185012
$777$	−190.182	+	96.9027i	−0.244765	+	0.124714i
$778$	84.2060	−	13.3369i	0.108234	−	0.0171426i
$779$	−622.679	+	857.044i	−0.799331	+	1.10018i
$780$	−51.4469	−	136.092i	−0.0659575	−	0.174477i
$781$	250.129	−	181.729i	0.320267	−	0.232688i
$782$	−60.4118	−	60.4118i	−0.0772529	−	0.0772529i
$783$	30.1135	−	190.129i	0.0384591	−	0.242821i
$784$	48.4218	−	15.7332i	0.0617625	−	0.0200678i
$785$	170.951	−	97.5405i	0.217772	−	0.124255i
$786$	14.2693	−	43.9164i	0.0181543	−	0.0558733i
$787$	−306.402	+	601.348i	−0.389329	+	0.764102i	−0.999605	−	0.0280869i	$-0.991058\pi$
$787$	−306.402	+	601.348i	−0.389329	+	0.764102i	0.610276	+	0.792189i	$0.291058\pi$
$788$	225.807	+	115.054i	0.286557	+	0.146008i
$789$	−63.6999	−	20.6974i	−0.0807350	−	0.0262324i
$790$	9.62939	+	4.34620i	0.0121891	+	0.00550152i
$791$	367.278	+	1130.37i	0.464322	+	1.42903i
$792$	−51.2771	−	8.12149i	−0.0647438	−	0.0102544i
$793$	281.194	−	281.194i	0.354595	−	0.354595i
$794$	4.51210	+	6.21037i	0.00568274	+	0.00782163i
$795$	8.68515	+	183.617i	0.0109247	+	0.230965i
$796$	72.3536	+	52.5680i	0.0908965	+	0.0660402i
$797$	−187.528	−	1184.00i	−0.235292	−	1.48558i	−0.768641	−	0.639680i	$-0.779067\pi$
$797$	−187.528	−	1184.00i	−0.235292	−	1.48558i	0.533349	−	0.845895i	$-0.320933\pi$
$798$	−37.3609	−	73.3249i	−0.0468182	−	0.0918859i
$799$		−	566.901i		−	0.709513i
$800$	−61.5449	−	239.421i	−0.0769312	−	0.299276i
$801$	−272.433			−0.340116
$802$	120.473	−	61.3842i	0.150216	−	0.0765390i
$803$	388.589	−	61.5465i	0.483922	−	0.0766457i
$804$	499.485	−	687.482i	0.621250	−	0.855077i
$805$	1065.51	+	699.697i	1.32362	+	0.869188i
$806$	−30.1459	+	21.9023i	−0.0374019	+	0.0271741i
$807$	338.137	+	338.137i	0.419006	+	0.419006i
$808$	−19.2466	+	121.518i	−0.0238200	+	0.150394i
$809$	−14.9852	+	4.86898i	−0.0185231	+	0.00601851i	−0.318264	−	0.948002i	$-0.603100\pi$
$809$	−14.9852	+	4.86898i	−0.0185231	+	0.00601851i	0.299741	+	0.954021i	$0.403100\pi$
$810$	−6.95847	−	6.32993i	−0.00859071	−	0.00781472i
$811$	−366.091	+	1126.71i	−0.451407	+	1.38929i	0.423896	+	0.905711i	$0.360662\pi$
$811$	−366.091	+	1126.71i	−0.451407	+	1.38929i	−0.875303	+	0.483576i	$0.839338\pi$
$812$	−481.161	+	944.331i	−0.592562	+	1.16297i
$813$	315.215	+	160.610i	0.387719	+	0.197553i
$814$	−35.2532	−	11.4544i	−0.0433085	−	0.0140718i
$815$	−963.988	+	1059.71i	−1.18281	+	1.30026i
$816$	96.0319	+	295.556i	0.117686	+	0.362201i
$817$	−190.969	−	30.2465i	−0.233744	−	0.0370214i
$818$	40.7156	−	40.7156i	0.0497746	−	0.0497746i
$819$	54.1459	+	74.5254i	0.0661122	+	0.0909956i
$820$	365.957	−	557.287i	0.446288	−	0.679618i
$821$	243.067	+	176.599i	0.296062	+	0.215102i	0.725893	−	0.687808i	$-0.241427\pi$
$821$	243.067	+	176.599i	0.296062	+	0.215102i	−0.429831	+	0.902909i	$0.641427\pi$
$822$	−0.995593	−	6.28593i	−0.00121118	−	0.00764711i
$823$	335.324	+	658.110i	0.407441	+	0.799647i	0.999983	−	0.00589228i	$-0.00187558\pi$
$823$	335.324	+	658.110i	0.407441	+	0.799647i	−0.592542	+	0.805540i	$0.701876\pi$
$824$			210.807i			0.255833i
$825$	−287.092	+	347.234i	−0.347990	+	0.420890i
$826$	49.6161			0.0600679
$827$	397.427	−	202.499i	0.480565	−	0.244860i	−0.196888	−	0.980426i	$-0.563084\pi$
$827$	397.427	−	202.499i	0.480565	−	0.244860i	0.677453	+	0.735566i	$0.263084\pi$
$828$	413.301	−	65.4604i	0.499155	−	0.0790584i
$829$	−125.629	+	172.913i	−0.151543	+	0.208581i	−0.878038	−	0.478591i	$-0.841148\pi$
$829$	−125.629	+	172.913i	−0.151543	+	0.208581i	0.726495	+	0.687171i	$0.241148\pi$
$830$	71.7039	−	3.39162i	0.0863902	−	0.00408629i
$831$	33.0351	−	24.0014i	0.0397535	−	0.0288826i
$832$	179.687	+	179.687i	0.215970	+	0.215970i
$833$	5.96535	−	37.6637i	0.00716128	−	0.0452146i
$834$	−12.4252	+	4.03720i	−0.0148984	+	0.00484077i
$835$	73.6153	−	163.101i	0.0881620	−	0.195331i
$836$	−399.838	+	1230.58i	−0.478275	+	1.47198i
$837$	99.0264	−	194.350i	0.118311	−	0.232199i
$838$	−112.644	−	57.3952i	−0.134421	−	0.0684907i
$839$	35.1917	+	11.4345i	0.0419448	+	0.0136287i	0.329914	−	0.944011i	$-0.392980\pi$
$839$	35.1917	+	11.4345i	0.0419448	+	0.0136287i	−0.287969	+	0.957640i	$0.592980\pi$
$840$	51.6172	+	90.4649i	0.0614491	+	0.107696i
$841$	−164.224	−	505.429i	−0.195272	−	0.600985i
$842$	−0.283482	−	0.0448991i	−0.000336676	−	5.33243e-5i
$843$	275.879	−	275.879i	0.327258	−	0.327258i
$844$	796.030	+	1095.64i	0.943164	+	1.29815i
$845$	706.074	−	266.917i	0.835591	−	0.315878i
$846$	−24.8111	−	18.0263i	−0.0293275	−	0.0213077i
$847$	14.4080	+	90.9687i	0.0170107	+	0.107401i
$848$	−149.148	−	292.719i	−0.175882	−	0.345187i
$849$		−	869.636i		−	1.02431i
$850$	−59.1264	−	13.1988i	−0.0695604	−	0.0155280i
$851$	600.837			0.706036
$852$	−181.425	+	92.4406i	−0.212940	+	0.108498i
$853$	−1336.36	+	211.658i	−1.56665	+	0.248134i	−0.878612	−	0.477536i	$-0.841530\pi$
$853$	−1336.36	+	211.658i	−1.56665	+	0.248134i	−0.688043	+	0.725670i	$0.741530\pi$
$854$	−83.2069	+	114.524i	−0.0974320	+	0.134104i
$855$	−367.916	+	294.842i	−0.430311	+	0.344844i
$856$	−229.588	+	166.805i	−0.268210	+	0.194866i
$857$	604.080	+	604.080i	0.704878	+	0.704878i	0.965453	−	0.260576i	$-0.0839123\pi$
$857$	604.080	+	604.080i	0.704878	+	0.704878i	−0.260576	+	0.965453i	$0.583912\pi$
$858$	−2.50254	+	15.8004i	−0.00291672	+	0.0184154i
$859$	−313.597	+	101.894i	−0.365072	+	0.118619i	−0.485808	−	0.874066i	$-0.661475\pi$
$859$	−313.597	+	101.894i	−0.365072	+	0.118619i	0.120736	+	0.992685i	$0.461475\pi$
$860$	120.950	+	13.3357i	0.140640	+	0.0155066i
$861$	−130.444	+	401.465i	−0.151503	+	0.466277i
$862$	39.3516	−	77.2319i	0.0456515	−	0.0895961i
$863$	630.852	+	321.435i	0.730998	+	0.372462i	0.779535	−	0.626359i	$-0.215456\pi$
$863$	630.852	+	321.435i	0.730998	+	0.372462i	−0.0485362	+	0.998821i	$0.515456\pi$
$864$	48.8658	+	15.8775i	0.0565576	+	0.0183767i
$865$	1425.75	−	295.469i	1.64827	−	0.341583i
$866$	7.89335	+	24.2932i	0.00911472	+	0.0280522i
$867$	−264.509	−	41.8941i	−0.305085	−	0.0483208i
$868$	−849.188	+	849.188i	−0.978328	+	0.978328i
$869$	61.8186	+	85.0860i	0.0711376	+	0.0979125i
$870$	−64.6923	−	17.6880i	−0.0743589	−	0.0203310i
$871$	−426.019	−	309.521i	−0.489115	−	0.355363i
$872$	−9.60230	−	60.6265i	−0.0110118	−	0.0695258i
$873$	−117.568	−	230.740i	−0.134671	−	0.264306i
$874$			231.653i			0.265049i
$875$	903.788	+	13.8148i	1.03290	+	0.0157883i
$876$	−259.108			−0.295785
$877$	485.816	−	247.535i	0.553952	−	0.282253i	−0.154522	−	0.987989i	$-0.549384\pi$
$877$	485.816	−	247.535i	0.553952	−	0.282253i	0.708474	+	0.705737i	$0.249384\pi$
$878$	39.9781	−	6.33191i	0.0455331	−	0.00721174i
$879$	150.754	−	207.496i	0.171507	−	0.236059i
$880$	212.365	−	776.706i	0.241324	−	0.882621i
$881$	−701.744	+	509.847i	−0.796531	+	0.578714i	−0.909894	−	0.414840i	$-0.863838\pi$
$881$	−701.744	+	509.847i	−0.796531	+	0.578714i	0.113364	+	0.993554i	$0.463838\pi$
$882$	−1.45871	−	1.45871i	−0.00165387	−	0.00165387i
$883$	−272.177	+	1718.46i	−0.308241	+	1.94616i	0.0151239	+	0.999886i	$0.495186\pi$
$883$	−272.177	+	1718.46i	−0.308241	+	1.94616i	−0.323365	+	0.946274i	$0.604814\pi$
$884$	185.219	−	60.1812i	0.209523	−	0.0680782i
$885$	−57.6836	−	278.346i	−0.0651792	−	0.314515i
$886$	30.0435	−	92.4643i	0.0339091	−	0.104362i
$887$	637.477	−	1251.12i	0.718689	−	1.41051i	−0.185183	−	0.982704i	$-0.559288\pi$
$887$	637.477	−	1251.12i	0.718689	−	1.41051i	0.903872	−	0.427803i	$-0.140712\pi$
$888$	43.7426	+	22.2880i	0.0492597	+	0.0250990i
$889$	−737.392	−	239.593i	−0.829462	−	0.269509i
$890$	−10.4022	+	94.3441i	−0.0116879	+	0.106005i
$891$	−28.9378	−	89.0613i	−0.0324779	−	0.0999566i
$892$	329.356	+	52.1649i	0.369234	+	0.0584808i
$893$	−1086.91	+	1086.91i	−1.21715	+	1.21715i
$894$	38.0700	+	52.3988i	0.0425839	+	0.0586117i
$895$	−893.041	−	1114.37i	−0.997811	−	1.24511i
$896$	−304.571	−	221.284i	−0.339923	−	0.246969i
$897$	−40.5645	−	256.114i	−0.0452225	−	0.285523i
$898$	41.4610	+	81.3718i	0.0461704	+	0.0906145i
$899$		−	1555.14i		−	1.72985i
$900$	222.520	−	196.289i	0.247244	−	0.218099i
$901$	−246.059			−0.273095
$902$	−65.3167	+	33.2805i	−0.0724132	+	0.0368964i
$903$	−76.0954	+	12.0523i	−0.0842695	+	0.0133470i
$904$	160.682	−	221.159i	0.177745	−	0.244645i
$905$	422.105	+	1116.59i	0.466414	+	1.23380i
$906$	29.3316	−	21.3107i	0.0323749	−	0.0235217i
$907$	−351.677	−	351.677i	−0.387736	−	0.387736i	0.486143	−	0.873879i	$-0.338403\pi$
$907$	−351.677	−	351.677i	−0.387736	−	0.387736i	−0.873879	+	0.486143i	$0.838403\pi$
$908$	47.9910	−	303.003i	0.0528536	−	0.333704i
$909$	−211.061	+	68.5778i	−0.232190	+	0.0754431i
$910$	27.8757	−	15.9053i	0.0306327	−	0.0174783i
$911$	175.955	−	541.533i	0.193145	−	0.594438i	−0.806849	−	0.590758i	$-0.798829\pi$
$911$	175.955	−	541.533i	0.193145	−	0.594438i	0.999993	−	0.00367977i	$-0.00117131\pi$
$912$	382.544	−	750.785i	0.419456	−	0.823229i
$913$	636.720	+	324.425i	0.697394	+	0.355340i
$914$	−42.1940	−	13.7097i	−0.0461641	−	0.0149996i
$915$	739.217	+	333.644i	0.807887	+	0.364638i
$916$	88.4571	+	272.243i	0.0965689	+	0.297208i
$917$	−910.871	−	144.268i	−0.993316	−	0.157326i
$918$	8.90365	−	8.90365i	0.00969896	−	0.00969896i
$919$	−0.851155	−	1.17151i	−0.000926175	−	0.00127477i	0.808554	−	0.588422i	$-0.200251\pi$
$919$	−0.851155	−	1.17151i	−0.000926175	−	0.00127477i	−0.809480	+	0.587148i	$0.800251\pi$
$920$	−13.8524	−	292.861i	−0.0150570	−	0.318327i
$921$	556.815	+	404.550i	0.604577	+	0.439251i
$922$	−25.2526	−	159.439i	−0.0273890	−	0.172927i
$923$	57.2837	+	112.426i	0.0620625	+	0.121804i
$924$			515.582i			0.557989i
$925$	359.662	−	228.391i	0.388824	−	0.246909i
$926$	−94.6381			−0.102201
$927$	−338.801	+	172.628i	−0.365481	+	0.186222i
$928$	361.812	−	57.3054i	0.389884	−	0.0617515i
$929$	250.455	−	344.722i	0.269596	−	0.371067i	−0.652657	−	0.757653i	$-0.726346\pi$
$929$	250.455	−	344.722i	0.269596	−	0.371067i	0.922253	+	0.386586i	$0.126346\pi$
$930$	−63.5228	−	41.7139i	−0.0683041	−	0.0448536i
$931$	−83.6494	+	60.7748i	−0.0898489	+	0.0652791i
$932$	−1057.49	−	1057.49i	−1.13464	−	1.13464i
$933$	−19.5810	+	123.630i	−0.0209871	+	0.132508i
$934$	55.4024	−	18.0013i	0.0593174	−	0.0192734i
$935$	−446.120	−	405.823i	−0.477134	−	0.434035i
$936$	6.54732	−	20.1506i	0.00699500	−	0.0215284i
$937$	452.159	−	887.412i	0.482560	−	0.947078i	−0.513474	−	0.858105i	$-0.671642\pi$
$937$	452.159	−	887.412i	0.482560	−	0.947078i	0.996034	−	0.0889727i	$-0.0283584\pi$
$938$	167.021	+	85.1017i	0.178061	+	0.0907267i
$939$	−733.748	−	238.409i	−0.781415	−	0.253897i
$940$	650.956	−	715.594i	0.692506	−	0.761271i
$941$	316.413	+	973.818i	0.336252	+	1.03488i	0.966102	+	0.258160i	$0.0831161\pi$
$941$	316.413	+	973.818i	0.336252	+	1.03488i	−0.629851	+	0.776716i	$0.716884\pi$
$942$	14.0770	+	2.22958i	0.0149438	+	0.00236686i
$943$	840.221	−	840.221i	0.891008	−	0.891008i
$944$	298.611	+	411.002i	0.316325	+	0.435384i
$945$	−103.123	+	157.038i	−0.109125	+	0.166178i
$946$	−10.8243	−	7.86429i	−0.0114421	−	0.00831320i
$947$	124.659	+	787.068i	0.131636	+	0.831117i	0.961831	+	0.273644i	$0.0882290\pi$
$947$	124.659	+	787.068i	0.131636	+	0.831117i	−0.830195	+	0.557473i	$0.811771\pi$
$948$	−31.4454	−	61.7151i	−0.0331702	−	0.0651003i
$949$			160.564i			0.169193i
$950$	88.0563	+	138.668i	0.0926908	+	0.145966i
$951$	−471.401			−0.495690
$952$	−124.223	+	63.2946i	−0.130486	+	0.0664859i
$953$	981.667	−	155.481i	1.03008	−	0.163149i	0.381559	−	0.924345i	$-0.375387\pi$
$953$	981.667	−	155.481i	1.03008	−	0.163149i	0.648522	+	0.761196i	$0.275387\pi$
$954$	−7.82417	+	10.7690i	−0.00820143	+	0.0112883i
$955$	−1190.75	+	56.3228i	−1.24686	+	0.0589768i
$956$	−992.123	+	720.819i	−1.03779	+	0.753995i
$957$	−472.098	−	472.098i	−0.493311	−	0.493311i
$958$	21.8839	−	138.169i	0.0228433	−	0.144227i
$959$	−120.885	+	39.2779i	−0.126053	+	0.0409571i
$960$	−213.203	+	472.371i	−0.222087	+	0.492053i
$961$	247.571	−	761.946i	0.257618	−	0.792867i
$962$	6.86778	−	13.4788i	0.00713907	−	0.0140112i
$963$	−456.091	−	232.390i	−0.473615	−	0.241319i
$964$	−947.908	−	307.994i	−0.983307	−	0.319496i
$965$	−298.636	−	523.392i	−0.309467	−	0.542375i
$966$	28.5244	+	87.7890i	0.0295283	+	0.0908789i
$967$	7.64878	+	1.21145i	0.00790980	+	0.00125279i	0.160388	−	0.987054i	$-0.448725\pi$
$967$	7.64878	+	1.21145i	0.00790980	+	0.00125279i	−0.152478	+	0.988307i	$0.548725\pi$
$968$	14.9793	−	14.9793i	0.0154745	−	0.0154745i
$969$	−370.956	−	510.577i	−0.382823	−	0.526911i
$970$	−84.3947	+	31.9037i	−0.0870048	+	0.0328904i
$971$	274.997	+	199.797i	0.283210	+	0.205764i	0.720316	−	0.693646i	$-0.243997\pi$
$971$	274.997	+	199.797i	0.283210	+	0.205764i	−0.437106	+	0.899410i	$0.643997\pi$
$972$	9.64773	+	60.9134i	0.00992565	+	0.0626681i
$973$	118.457	+	232.485i	0.121744	+	0.238937i
$974$		−	71.6903i		−	0.0736040i
$975$	−121.637	−	137.891i	−0.124755	−	0.141427i
$976$	−1449.45			−1.48510
$977$	1155.32	−	588.664i	1.18252	−	0.602522i	0.251627	−	0.967824i	$-0.419035\pi$
$977$	1155.32	−	588.664i	1.18252	−	0.602522i	0.930889	+	0.365303i	$0.119035\pi$
$978$	−102.461	+	16.2282i	−0.104765	+	0.0165932i
$979$	−555.389	+	764.427i	−0.567302	+	0.780825i
$980$	50.7782	−	40.6928i	0.0518145	−	0.0415232i
$981$	89.5736	−	65.0790i	0.0913084	−	0.0663395i
$982$	115.093	+	115.093i	0.117203	+	0.117203i
$983$	−116.535	+	735.771i	−0.118550	+	0.748496i	0.854764	+	0.519017i	$0.173702\pi$
$983$	−116.535	+	735.771i	−0.118550	+	0.748496i	−0.973314	+	0.229478i	$0.926298\pi$
$984$	92.3383	−	30.0025i	0.0938397	−	0.0304904i
$985$	318.356	+	35.1013i	0.323204	+	0.0356358i
$986$	27.7415	−	85.3796i	0.0281354	−	0.0865919i
$987$	−278.068	+	545.739i	−0.281731	+	0.552927i
$988$	−470.501	−	239.732i	−0.476216	−	0.242644i
$989$	206.259	+	67.0175i	0.208553	+	0.0677629i
$990$	−31.9470	+	6.62062i	−0.0322697	+	0.00668750i
$991$	−294.521	−	906.441i	−0.297195	−	0.914673i	−0.982475	−	0.186393i	$-0.940320\pi$
$991$	−294.521	−	906.441i	−0.297195	−	0.914673i	0.685280	−	0.728280i	$-0.259680\pi$
$992$	409.977	+	64.9339i	0.413283	+	0.0654576i
$993$	−203.173	+	203.173i	−0.204606	+	0.204606i
$994$	−26.4011	−	36.3380i	−0.0265605	−	0.0365574i
$995$	109.025	+	29.8094i	0.109573	+	0.0299592i
$996$	−380.746	−	276.628i	−0.382275	−	0.277739i
$997$	−198.175	−	1251.23i	−0.198771	−	1.25499i	−0.862129	−	0.506689i	$-0.830869\pi$
$997$	−198.175	−	1251.23i	−0.198771	−	1.25499i	0.663358	−	0.748303i	$-0.269131\pi$
$998$	−27.4709	−	53.9147i	−0.0275260	−	0.0540228i
$999$			88.5529i			0.0886416i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	75.3.k.a.22.5	✓	80
3.2	odd	2		225.3.r.b.172.6		80
5.2	odd	4		375.3.k.b.118.5		80
5.3	odd	4		375.3.k.c.118.6		80
5.4	even	2		375.3.k.a.7.6		80
25.6	even	5		375.3.k.c.232.6		80
25.8	odd	20	inner	75.3.k.a.58.5	yes	80
25.17	odd	20		375.3.k.a.268.6		80
25.19	even	10		375.3.k.b.232.5		80
75.8	even	20		225.3.r.b.208.6		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.3.k.a.22.5	✓	80	1.1	even	1	trivial
75.3.k.a.58.5	yes	80	25.8	odd	20	inner
225.3.r.b.172.6		80	3.2	odd	2
225.3.r.b.208.6		80	75.8	even	20
375.3.k.a.7.6		80	5.4	even	2
375.3.k.a.268.6		80	25.17	odd	20
375.3.k.b.118.5		80	5.2	odd	4
375.3.k.b.232.5		80	25.19	even	10
375.3.k.c.118.6		80	5.3	odd	4
375.3.k.c.232.6		80	25.6	even	5

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:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	75.k (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.186256 + 0.0949024i) q^{2} +(1.71073 - 0.270952i) q^{3} +(-2.32546 + 3.20072i) q^{4} +(-1.31868 + 4.82297i) q^{5} +(-0.292920 + 0.212819i) q^{6} +(5.11319 + 5.11319i) q^{7} +(0.260180 - 1.64271i) q^{8} +(2.85317 - 0.927051i) q^{9} +O(q^{10})\)	\(q+(-0.186256 + 0.0949024i) q^{2} +(1.71073 - 0.270952i) q^{3} +(-2.32546 + 3.20072i) q^{4} +(-1.31868 + 4.82297i) q^{5} +(-0.292920 + 0.212819i) q^{6} +(5.11319 + 5.11319i) q^{7} +(0.260180 - 1.64271i) q^{8} +(2.85317 - 0.927051i) q^{9} +(-0.212098 - 1.02346i) q^{10} +(3.21531 - 9.89570i) q^{11} +(-3.11098 + 6.10564i) q^{12} +(3.78355 + 1.92781i) q^{13} +(-1.43762 - 0.467111i) q^{14} +(-0.949111 + 8.60809i) q^{15} +(-4.78282 - 14.7200i) q^{16} +(-11.4496 - 1.81344i) q^{17} +(-0.443442 + 0.443442i) q^{18} +(18.4753 + 25.4290i) q^{19} +(-12.3704 - 15.4363i) q^{20} +(10.1327 + 7.36184i) q^{21} +(0.340254 + 2.14828i) q^{22} +(-16.0060 - 31.4135i) q^{23} -2.88073i q^{24} +(-21.5221 - 12.7200i) q^{25} -0.887664 q^{26} +(4.62981 - 2.35900i) q^{27} +(-28.2564 + 4.47537i) q^{28} +(21.7754 - 29.9712i) q^{29} +(-0.640150 - 1.69338i) q^{30} +(33.9610 - 24.6741i) q^{31} +(6.99201 + 6.99201i) q^{32} +(2.81925 - 17.8000i) q^{33} +(2.30466 - 0.748830i) q^{34} +(-31.4035 + 17.9181i) q^{35} +(-3.66769 + 11.2880i) q^{36} +(-7.73692 + 15.1846i) q^{37} +(-5.85442 - 2.98297i) q^{38} +(6.99496 + 2.27280i) q^{39} +(7.57966 + 3.42106i) q^{40} +(10.4149 + 32.0538i) q^{41} +(-2.58594 - 0.409573i) q^{42} +(-4.34966 + 4.34966i) q^{43} +(24.1963 + 33.3033i) q^{44} +(0.708713 + 14.9832i) q^{45} +(5.96243 + 4.33196i) q^{46} +(7.65013 + 48.3010i) q^{47} +(-12.1705 - 23.8860i) q^{48} +3.28952i q^{49} +(5.21579 + 0.326671i) q^{50} -20.0785 q^{51} +(-14.9689 + 7.62701i) q^{52} +(20.9647 - 3.32047i) q^{53} +(-0.638456 + 0.878759i) q^{54} +(43.4867 + 28.5566i) q^{55} +(9.72986 - 7.06916i) q^{56} +(38.4962 + 38.4962i) q^{57} +(-1.21146 + 7.64886i) q^{58} +(-31.2170 + 10.1430i) q^{59} +(-25.3449 - 23.0556i) q^{60} +(28.9391 - 89.0654i) q^{61} +(-3.98382 + 7.81868i) q^{62} +(19.3290 + 9.84862i) q^{63} +(56.9142 + 18.4925i) q^{64} +(-14.2871 + 15.7058i) q^{65} +(1.16416 + 3.58292i) q^{66} +(-122.482 - 19.3993i) q^{67} +(32.4299 - 32.4299i) q^{68} +(-35.8934 - 49.4030i) q^{69} +(4.14863 - 6.31763i) q^{70} +(24.0394 + 17.4656i) q^{71} +(-0.780540 - 4.92814i) q^{72} +(17.1663 + 33.6908i) q^{73} -3.56247i q^{74} +(-40.2650 - 15.9289i) q^{75} -124.355 q^{76} +(67.0391 - 34.1581i) q^{77} +(-1.51855 + 0.240515i) q^{78} +(-5.94126 + 8.17745i) q^{79} +(77.3012 - 3.65638i) q^{80} +(7.28115 - 5.29007i) q^{81} +(-4.98182 - 4.98182i) q^{82} +(-10.7439 + 67.8340i) q^{83} +(-47.1263 + 15.3123i) q^{84} +(23.8446 - 52.8298i) q^{85} +(0.397359 - 1.22295i) q^{86} +(29.1309 - 57.1726i) q^{87} +(-15.4192 - 7.85649i) q^{88} +(-86.3664 - 28.0621i) q^{89} +(-1.55395 - 2.72347i) q^{90} +(9.48872 + 29.2033i) q^{91} +(137.767 + 21.8201i) q^{92} +(51.4124 - 51.4124i) q^{93} +(-6.00877 - 8.27036i) q^{94} +(-147.007 + 55.5729i) q^{95} +(13.8559 + 10.0669i) q^{96} +(-13.5037 - 85.2589i) q^{97} +(-0.312183 - 0.612694i) q^{98} -31.2149i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8}+O(q^{10}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8	\( 80 q + 4 q^{2} + 4 q^{5} - 4 q^{7} - 12 q^{8} - 4 q^{10} - 24 q^{12} + 32 q^{13} - 24 q^{15} + 80 q^{16} - 100 q^{17} - 48 q^{18} - 100 q^{19} - 244 q^{20} - 100 q^{22} - 96 q^{23} - 16 q^{25} - 40 q^{26} + 196 q^{28} + 200 q^{29} + 264 q^{30} + 636 q^{32} + 216 q^{33} + 100 q^{34} + 260 q^{35} - 120 q^{36} - 184 q^{37} - 564 q^{38} - 948 q^{40} + 160 q^{41} - 12 q^{42} - 472 q^{43} - 700 q^{44} - 36 q^{45} - 288 q^{47} - 48 q^{48} + 16 q^{50} + 620 q^{52} + 304 q^{53} + 604 q^{55} + 72 q^{57} + 1272 q^{58} + 800 q^{59} + 84 q^{60} - 240 q^{61} + 1212 q^{62} - 12 q^{63} + 100 q^{64} + 272 q^{65} - 80 q^{67} + 104 q^{68} - 260 q^{70} + 36 q^{72} - 116 q^{73} - 24 q^{75} - 88 q^{77} - 120 q^{78} + 200 q^{79} - 164 q^{80} + 180 q^{81} - 168 q^{82} - 1264 q^{83} - 1200 q^{84} - 212 q^{85} - 876 q^{87} - 212 q^{88} - 1500 q^{89} - 444 q^{90} - 1504 q^{92} - 648 q^{93} - 200 q^{94} - 784 q^{95} + 60 q^{96} - 260 q^{97} - 92 q^{98}+O(q^{100}) \) 80 * q + 4 * q^2 + 4 * q^5 - 4 * q^7 - 12 * q^8 - 4 * q^10 - 24 * q^12 + 32 * q^13 - 24 * q^15 + 80 * q^16 - 100 * q^17 - 48 * q^18 - 100 * q^19 - 244 * q^20 - 100 * q^22 - 96 * q^23 - 16 * q^25 - 40 * q^26 + 196 * q^28 + 200 * q^29 + 264 * q^30 + 636 * q^32 + 216 * q^33 + 100 * q^34 + 260 * q^35 - 120 * q^36 - 184 * q^37 - 564 * q^38 - 948 * q^40 + 160 * q^41 - 12 * q^42 - 472 * q^43 - 700 * q^44 - 36 * q^45 - 288 * q^47 - 48 * q^48 + 16 * q^50 + 620 * q^52 + 304 * q^53 + 604 * q^55 + 72 * q^57 + 1272 * q^58 + 800 * q^59 + 84 * q^60 - 240 * q^61 + 1212 * q^62 - 12 * q^63 + 100 * q^64 + 272 * q^65 - 80 * q^67 + 104 * q^68 - 260 * q^70 + 36 * q^72 - 116 * q^73 - 24 * q^75 - 88 * q^77 - 120 * q^78 + 200 * q^79 - 164 * q^80 + 180 * q^81 - 168 * q^82 - 1264 * q^83 - 1200 * q^84 - 212 * q^85 - 876 * q^87 - 212 * q^88 - 1500 * q^89 - 444 * q^90 - 1504 * q^92 - 648 * q^93 - 200 * q^94 - 784 * q^95 + 60 * q^96 - 260 * q^97 - 92 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more