LMFDB - Embedded newform 175.2.x.a.122.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

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

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			122.18
Character	$\chi$	$=$	175.122
Dual form			175.2.x.a.33.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.03786 + 1.32340i) q^{2} +(-2.14641 - 0.823930i) q^{3} +(1.58801 + 3.56673i) q^{4} +(-0.304662 + 2.21522i) q^{5} +(-3.28370 - 4.51962i) q^{6} +(2.14884 + 1.54352i) q^{7} +(-0.723845 + 4.57018i) q^{8} +(1.69878 + 1.52959i) q^{9} +O(q^{10})$	\(q+(2.03786 + 1.32340i) q^{2} +(-2.14641 - 0.823930i) q^{3} +(1.58801 + 3.56673i) q^{4} +(-0.304662 + 2.21522i) q^{5} +(-3.28370 - 4.51962i) q^{6} +(2.14884 + 1.54352i) q^{7} +(-0.723845 + 4.57018i) q^{8} +(1.69878 + 1.52959i) q^{9} +(-3.55248 + 4.11111i) q^{10} +(0.0112005 + 0.0124395i) q^{11} +(-0.469788 - 8.96408i) q^{12} +(1.39124 - 2.73047i) q^{13} +(2.33634 + 5.98928i) q^{14} +(2.47911 - 4.50374i) q^{15} +(-2.29834 + 2.55257i) q^{16} +(-5.48928 - 4.44513i) q^{17} +(1.43762 + 5.36527i) q^{18} +(2.90112 + 1.29166i) q^{19} +(-8.38489 + 2.43114i) q^{20} +(-3.34055 - 5.08353i) q^{21} +(0.00636273 + 0.0401727i) q^{22} +(2.98285 - 4.59318i) q^{23} +(5.31918 - 9.21308i) q^{24} +(-4.81436 - 1.34978i) q^{25} +(6.44868 - 3.72315i) q^{26} +(0.745322 + 1.46278i) q^{27} +(-2.09295 + 10.1155i) q^{28} +(-0.0353871 + 0.0487062i) q^{29} +(11.0124 - 5.89714i) q^{30} +(8.96709 - 0.942479i) q^{31} +(0.877177 - 0.235039i) q^{32} +(-0.0137917 - 0.0359286i) q^{33} +(-5.30369 - 16.3231i) q^{34} +(-4.07391 + 4.28990i) q^{35} +(-2.75796 + 8.48811i) q^{36} +(-8.39052 + 0.439728i) q^{37} +(4.20270 + 6.47159i) q^{38} +(-5.23590 + 4.71442i) q^{39} +(-9.90340 - 2.99583i) q^{40} +(-5.83738 + 1.89668i) q^{41} +(-0.0800095 - 14.7804i) q^{42} +(-3.18681 + 3.18681i) q^{43} +(-0.0265816 + 0.0597034i) q^{44} +(-3.90593 + 3.29716i) q^{45} +(12.1573 - 5.41276i) q^{46} +(-2.89679 - 3.57724i) q^{47} +(7.03633 - 3.58519i) q^{48} +(2.23507 + 6.63359i) q^{49} +(-8.02470 - 9.12201i) q^{50} +(8.11977 + 14.0639i) q^{51} +(11.9482 + 0.626178i) q^{52} +(1.55951 - 4.06266i) q^{53} +(-0.416980 + 3.96730i) q^{54} +(-0.0309685 + 0.0210218i) q^{55} +(-8.60961 + 8.70333i) q^{56} +(-5.16276 - 5.16276i) q^{57} +(-0.136572 + 0.0524250i) q^{58} +(2.45075 + 0.520924i) q^{59} +(20.0005 + 1.69033i) q^{60} +(2.77436 + 13.0523i) q^{61} +(19.5210 + 9.94643i) q^{62} +(1.28946 + 5.90896i) q^{63} +(8.63203 + 2.80472i) q^{64} +(5.62472 + 3.91378i) q^{65} +(0.0194425 - 0.0914696i) q^{66} +(0.200158 - 0.247175i) q^{67} +(7.13755 - 26.6377i) q^{68} +(-10.1869 + 7.40119i) q^{69} +(-13.9793 + 3.35080i) q^{70} +(-6.35569 - 4.61768i) q^{71} +(-8.22016 + 6.65655i) q^{72} +(0.174974 - 3.33870i) q^{73} +(-17.6807 - 10.2079i) q^{74} +(9.22147 + 6.86389i) q^{75} +12.3987i q^{76} +(0.00486761 + 0.0440188i) q^{77} +(-16.9091 + 2.67814i) q^{78} +(-5.32825 - 0.560021i) q^{79} +(-4.95427 - 5.86900i) q^{80} +(-1.11138 - 10.5741i) q^{81} +(-14.4058 - 3.86003i) q^{82} +(-8.63403 - 1.36750i) q^{83} +(12.8268 - 19.9876i) q^{84} +(11.5193 - 10.8057i) q^{85} +(-10.7117 + 2.27684i) q^{86} +(0.116086 - 0.0753869i) q^{87} +(-0.0649580 + 0.0421842i) q^{88} +(8.18738 - 1.74028i) q^{89} +(-12.3232 + 1.55004i) q^{90} +(7.20412 - 3.71994i) q^{91} +(21.1194 + 3.34499i) q^{92} +(-20.0236 - 5.36531i) q^{93} +(-1.16913 - 11.1236i) q^{94} +(-3.74518 + 6.03309i) q^{95} +(-2.07644 - 0.218242i) q^{96} +(-6.79613 + 1.07640i) q^{97} +(-4.22415 + 16.4762i) q^{98} +0.0382642i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	2.03786	+	1.32340i	1.44099	+	0.935787i	0.999253	+	0.0386405i	$0.0123027\pi$
$2$	2.03786	+	1.32340i	1.44099	+	0.935787i	0.441733	+	0.897147i	$0.354364\pi$
$3$	−2.14641	−	0.823930i	−1.23923	−	0.475696i	−0.351556	−	0.936167i	$-0.614347\pi$
$3$	−2.14641	−	0.823930i	−1.23923	−	0.475696i	−0.887675	+	0.460471i	$0.847681\pi$
$4$	1.58801	+	3.56673i	0.794006	+	1.78337i
$5$	−0.304662	+	2.21522i	−0.136249	+	0.990675i
$5$	−0.304662	+	2.21522i	−0.136249	+	0.990675i
$6$	−3.28370	−	4.51962i	−1.34056	−	1.84513i
$7$	2.14884	+	1.54352i	0.812187	+	0.583397i
$7$	2.14884	+	1.54352i	0.812187	+	0.583397i
$8$	−0.723845	+	4.57018i	−0.255918	+	1.61580i
$9$	1.69878	+	1.52959i	0.566261	+	0.509864i
$10$	−3.55248	+	4.11111i	−1.12339	+	1.30005i
$11$	0.0112005	+	0.0124395i	0.00337709	+	0.00375064i	0.744831	−	0.667253i	$-0.232530\pi$
$11$	0.0112005	+	0.0124395i	0.00337709	+	0.00375064i	−0.741454	+	0.671004i	$0.765863\pi$
$12$	−0.469788	−	8.96408i	−0.135616	−	2.58771i
$13$	1.39124	−	2.73047i	0.385862	−	0.757297i	−0.613616	−	0.789605i	$-0.710286\pi$
$13$	1.39124	−	2.73047i	0.385862	−	0.757297i	0.999478	+	0.0323079i	$0.0102857\pi$
$14$	2.33634	+	5.98928i	0.624414	+	1.60070i
$15$	2.47911	−	4.50374i	0.640104	−	1.16286i
$16$	−2.29834	+	2.55257i	−0.574586	+	0.638142i
$17$	−5.48928	−	4.44513i	−1.33135	−	1.07810i	−0.990431	−	0.138008i	$-0.955930\pi$
$17$	−5.48928	−	4.44513i	−1.33135	−	1.07810i	−0.340914	−	0.940094i	$-0.610737\pi$
$18$	1.43762	+	5.36527i	0.338850	+	1.26461i
$19$	2.90112	+	1.29166i	0.665563	+	0.296328i	0.711572	−	0.702613i	$-0.247984\pi$
$19$	2.90112	+	1.29166i	0.665563	+	0.296328i	−0.0460087	+	0.998941i	$0.514650\pi$
$20$	−8.38489	+	2.43114i	−1.87492	+	0.543620i
$21$	−3.34055	−	5.08353i	−0.728967	−	1.10932i
$22$	0.00636273	+	0.0401727i	0.00135654	+	0.00856485i
$23$	2.98285	−	4.59318i	0.621966	−	0.957744i	−0.377530	−	0.925997i	$-0.623226\pi$
$23$	2.98285	−	4.59318i	0.621966	−	0.957744i	0.999496	−	0.0317465i	$-0.0101069\pi$
$24$	5.31918	−	9.21308i	1.08577	−	1.88061i
$25$	−4.81436	−	1.34978i	−0.962872	−	0.269957i
$26$	6.44868	−	3.72315i	1.26469	−	0.730169i
$27$	0.745322	+	1.46278i	0.143437	+	0.281512i
$28$	−2.09295	+	10.1155i	−0.395530	+	1.91165i
$29$	−0.0353871	+	0.0487062i	−0.00657122	+	0.00904451i	−0.812290	−	0.583254i	$-0.801779\pi$
$29$	−0.0353871	+	0.0487062i	−0.00657122	+	0.00904451i	0.805719	+	0.592298i	$0.201779\pi$
$30$	11.0124	−	5.89714i	2.01057	−	1.07667i
$31$	8.96709	−	0.942479i	1.61054	−	0.169274i	0.743927	−	0.668260i	$-0.232961\pi$
$31$	8.96709	−	0.942479i	1.61054	−	0.169274i	0.866610	+	0.498986i	$0.166294\pi$
$32$	0.877177	−	0.235039i	0.155065	−	0.0415494i
$33$	−0.0137917	−	0.0359286i	−0.00240083	−	0.00625437i
$34$	−5.30369	−	16.3231i	−0.909576	−	2.79939i
$35$	−4.07391	+	4.28990i	−0.688617	+	0.725126i
$36$	−2.75796	+	8.48811i	−0.459659	+	1.41469i
$37$	−8.39052	+	0.439728i	−1.37939	+	0.0722909i	−0.727546	−	0.686059i	$-0.759339\pi$
$37$	−8.39052	+	0.439728i	−1.37939	+	0.0722909i	−0.651847	+	0.758350i	$0.726006\pi$
$38$	4.20270	+	6.47159i	0.681768	+	1.04983i
$39$	−5.23590	+	4.71442i	−0.838415	+	0.754912i
$40$	−9.90340	−	2.99583i	−1.56587	−	0.473683i
$41$	−5.83738	+	1.89668i	−0.911646	+	0.296212i	−0.727035	−	0.686600i	$-0.759102\pi$
$41$	−5.83738	+	1.89668i	−0.911646	+	0.296212i	−0.184610	+	0.982812i	$0.559102\pi$
$42$	−0.0800095	−	14.7804i	−0.0123457	−	2.28067i
$43$	−3.18681	+	3.18681i	−0.485984	+	0.485984i	−0.907036	−	0.421052i	$-0.861661\pi$
$43$	−3.18681	+	3.18681i	−0.485984	+	0.485984i	0.421052	+	0.907036i	$0.361661\pi$
$44$	−0.0265816	+	0.0597034i	−0.00400733	+	0.00900062i
$45$	−3.90593	+	3.29716i	−0.582261	+	0.491512i
$46$	12.1573	−	5.41276i	1.79249	−	0.798068i
$47$	−2.89679	−	3.57724i	−0.422541	−	0.521794i	0.520774	−	0.853695i	$-0.325644\pi$
$47$	−2.89679	−	3.57724i	−0.422541	−	0.521794i	−0.943314	+	0.331900i	$0.892310\pi$
$48$	7.03633	−	3.58519i	1.01561	−	0.517477i
$49$	2.23507	+	6.63359i	0.319295	+	0.947655i
$50$	−8.02470	−	9.12201i	−1.13486	−	1.29005i
$51$	8.11977	+	14.0639i	1.13700	+	1.96933i
$52$	11.9482	+	0.626178i	1.65691	+	0.0868352i
$53$	1.55951	−	4.06266i	0.214215	−	0.558050i	−0.783801	−	0.621012i	$-0.786722\pi$
$53$	1.55951	−	4.06266i	0.214215	−	0.558050i	0.998016	+	0.0629629i	$0.0200550\pi$
$54$	−0.416980	+	3.96730i	−0.0567438	+	0.539881i
$55$	−0.0309685	+	0.0210218i	−0.00417579	+	0.00283458i
$56$	−8.60961	+	8.70333i	−1.15051	+	1.16303i
$57$	−5.16276	−	5.16276i	−0.683825	−	0.683825i
$58$	−0.136572	+	0.0524250i	−0.0179328	+	0.00688374i
$59$	2.45075	+	0.520924i	0.319061	+	0.0678185i	0.364658	−	0.931141i	$-0.381186\pi$
$59$	2.45075	+	0.520924i	0.319061	+	0.0678185i	−0.0455974	+	0.998960i	$0.514519\pi$
$60$	20.0005	+	1.69033i	2.58205	+	0.218221i
$61$	2.77436	+	13.0523i	0.355221	+	1.67118i	0.686099	+	0.727509i	$0.259322\pi$
$61$	2.77436	+	13.0523i	0.355221	+	1.67118i	−0.330878	+	0.943674i	$0.607345\pi$
$62$	19.5210	+	9.94643i	2.47917	+	1.26320i
$63$	1.28946	+	5.90896i	0.162457	+	0.744460i
$64$	8.63203	+	2.80472i	1.07900	+	0.350590i
$65$	5.62472	+	3.91378i	0.697661	+	0.485444i
$66$	0.0194425	−	0.0914696i	0.00239320	−	0.0112591i
$67$	0.200158	−	0.247175i	0.0244532	−	0.0301972i	−0.764773	−	0.644300i	$-0.777149\pi$
$67$	0.200158	−	0.247175i	0.0244532	−	0.0301972i	0.789226	+	0.614103i	$0.210482\pi$
$68$	7.13755	−	26.6377i	0.865556	−	3.23030i
$69$	−10.1869	+	7.40119i	−1.22635	+	0.890999i
$70$	−13.9793	+	3.35080i	−1.67085	+	0.400497i
$71$	−6.35569	−	4.61768i	−0.754282	−	0.548018i	0.142869	−	0.989742i	$-0.454367\pi$
$71$	−6.35569	−	4.61768i	−0.754282	−	0.548018i	−0.897151	+	0.441724i	$0.854367\pi$
$72$	−8.22016	+	6.65655i	−0.968755	+	0.784482i
$73$	0.174974	−	3.33870i	0.0204791	−	0.390765i	−0.969090	−	0.246707i	$-0.920651\pi$
$73$	0.174974	−	3.33870i	0.0204791	−	0.390765i	0.989569	−	0.144058i	$-0.0460152\pi$
$74$	−17.6807	−	10.2079i	−2.05533	−	1.18665i
$75$	9.22147	+	6.86389i	1.06480	+	0.792573i
$76$			12.3987i			1.42223i
$77$	0.00486761	+	0.0440188i	0.000554716	+	0.00501640i
$78$	−16.9091	+	2.67814i	−1.91458	+	0.303240i
$79$	−5.32825	−	0.560021i	−0.599475	−	0.0630073i	−0.200069	−	0.979782i	$-0.564117\pi$
$79$	−5.32825	−	0.560021i	−0.599475	−	0.0630073i	−0.399405	+	0.916774i	$0.630783\pi$
$80$	−4.95427	−	5.86900i	−0.553905	−	0.656174i
$81$	−1.11138	−	10.5741i	−0.123486	−	1.17490i
$82$	−14.4058	−	3.86003i	−1.59086	−	0.426270i
$83$	−8.63403	−	1.36750i	−0.947708	−	0.150102i	−0.336599	−	0.941648i	$-0.609277\pi$
$83$	−8.63403	−	1.36750i	−0.947708	−	0.150102i	−0.611110	+	0.791546i	$0.709277\pi$
$84$	12.8268	−	19.9876i	1.39952	−	2.18082i
$85$	11.5193	−	10.8057i	1.24944	−	1.17204i
$86$	−10.7117	+	2.27684i	−1.15507	+	0.245518i
$87$	0.116086	−	0.0753869i	0.0124457	−	0.00808233i
$88$	−0.0649580	+	0.0421842i	−0.00692455	+	0.00449685i
$89$	8.18738	−	1.74028i	0.867861	−	0.184470i	0.247597	−	0.968863i	$-0.420359\pi$
$89$	8.18738	−	1.74028i	0.867861	−	0.184470i	0.620264	+	0.784394i	$0.287026\pi$
$90$	−12.3232	+	1.55004i	−1.29898	+	0.163389i
$91$	7.20412	−	3.71994i	0.755197	−	0.389956i
$92$	21.1194	+	3.34499i	2.20185	+	0.348739i
$93$	−20.0236	−	5.36531i	−2.07635	−	0.556356i
$94$	−1.16913	−	11.1236i	−0.120587	−	1.14731i
$95$	−3.74518	+	6.03309i	−0.384247	+	0.618982i
$96$	−2.07644	−	0.218242i	−0.211926	−	0.0222743i
$97$	−6.79613	+	1.07640i	−0.690043	+	0.109292i	−0.491601	−	0.870821i	$-0.663588\pi$
$97$	−6.79613	+	1.07640i	−0.690043	+	0.109292i	−0.198442	+	0.980113i	$0.563588\pi$
$98$	−4.22415	+	16.4762i	−0.426704	+	1.66435i
$99$			0.0382642i			0.00384569i
$100$	−2.83095	−	19.3150i	−0.283095	−	1.93150i
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.0321267	−	0.999484i	$-0.510228\pi$
$101$	−9.18326	−	5.30196i	−0.913768	−	0.527564i	−0.881642	+	0.471919i	$0.843561\pi$
$102$	−2.06518	+	39.4059i	−0.204483	+	3.90177i
$103$	0.170043	−	0.137698i	0.0167548	−	0.0135678i	−0.620906	−	0.783885i	$-0.713235\pi$
$103$	0.170043	−	0.137698i	0.0167548	−	0.0135678i	0.637661	+	0.770317i	$0.279902\pi$
$104$	11.4717	+	8.33468i	1.12489	+	0.817282i
$105$	12.2789	−	5.85127i	1.19829	−	0.571026i
$106$	8.55461	−	6.21528i	0.830897	−	0.603682i
$107$	−1.26699	+	4.72847i	−0.122485	+	0.457119i	−0.999738	−	0.0229097i	$-0.992707\pi$
$107$	−1.26699	+	4.72847i	−0.122485	+	0.457119i	0.877253	+	0.480028i	$0.159374\pi$
$108$	−4.03376	+	4.98127i	−0.388148	+	0.479323i
$109$	−1.60438	+	7.54803i	−0.153672	+	0.722970i	0.832065	+	0.554678i	$0.187158\pi$
$109$	−1.60438	+	7.54803i	−0.153672	+	0.722970i	−0.985737	+	0.168292i	$0.946175\pi$
$110$	−0.0909297	+	0.00185573i	−0.00866981	+	0.000176937i
$111$	18.3718	+	5.96936i	1.74377	+	0.566587i
$112$	−8.87874	+	1.93753i	−0.838962	+	0.183079i
$113$	−3.56746	−	1.81771i	−0.335599	−	0.170996i	0.278068	−	0.960561i	$-0.410306\pi$
$113$	−3.56746	−	1.81771i	−0.335599	−	0.170996i	−0.613666	+	0.789565i	$0.710306\pi$
$114$	−3.68858	−	17.3534i	−0.345467	−	1.62530i
$115$	9.26612	+	8.00701i	0.864070	+	0.746658i
$116$	−0.229917	−	0.0488704i	−0.0213473	−	0.00453750i
$117$	6.53993	−	2.51044i	0.604616	−	0.232091i
$118$	4.30491	+	4.30491i	0.396299	+	0.396299i
$119$	−4.93444	−	18.0247i	−0.452339	−	1.65232i
$120$	18.7884	+	14.5900i	1.71514	+	1.33188i
$121$	1.14978	−	10.9395i	0.104526	−	0.994497i
$122$	−11.6198	+	30.2705i	−1.05200	+	2.74056i
$123$	14.0921	+	0.738538i	1.27065	+	0.0665917i
$124$	17.6014	+	30.4866i	1.58065	+	2.73777i
$125$	4.45681	−	10.2536i	0.398630	−	0.917112i
$126$	−5.19220	+	13.7481i	−0.462558	+	1.22478i
$127$	6.49211	−	3.30790i	0.576082	−	0.293528i	−0.141572	−	0.989928i	$-0.545216\pi$
$127$	6.49211	−	3.30790i	0.576082	−	0.293528i	0.717654	+	0.696399i	$0.245216\pi$
$128$	12.7361	+	15.7278i	1.12572	+	1.39015i
$129$	9.46591	−	4.21449i	0.833427	−	0.371065i
$130$	6.28291	+	15.4195i	0.551047	+	1.35238i
$131$	−4.81183	+	10.8075i	−0.420412	+	0.944260i	0.571880	+	0.820337i	$0.306214\pi$
$131$	−4.81183	+	10.8075i	−0.420412	+	0.944260i	−0.992292	+	0.123923i	$0.960452\pi$
$132$	0.106246	−	0.106246i	0.00924757	−	0.00924757i
$133$	4.24035	+	7.25354i	0.367685	+	0.628962i
$134$	0.735006	−	0.238818i	0.0634949	−	0.0206307i
$135$	−3.46744	+	1.20540i	−0.298430	+	0.103744i
$136$	24.2884	−	21.8694i	2.08272	−	1.87529i
$137$	−1.79416	−	2.76276i	−0.153285	−	0.236039i	0.753682	−	0.657239i	$-0.228276\pi$
$137$	−1.79416	−	2.76276i	−0.153285	−	0.236039i	−0.906968	+	0.421200i	$0.861609\pi$
$138$	−30.5542	+	1.60128i	−2.60094	+	0.136310i
$139$	1.40509	−	4.32443i	0.119179	−	0.366794i	−0.873617	−	0.486614i	$-0.838232\pi$
$139$	1.40509	−	4.32443i	0.119179	−	0.366794i	0.992796	+	0.119820i	$0.0382318\pi$
$140$	−21.7704	−	7.71814i	−1.83993	−	0.652302i
$141$	3.27031	+	10.0650i	0.275410	+	0.847625i
$142$	−6.84097	−	17.8213i	−0.574082	−	1.49553i
$143$	0.0495483	−	0.0132764i	0.00414344	−	0.00111023i
$144$	−7.80877	+	0.820735i	−0.650731	+	0.0683946i
$145$	−0.0971136	−	0.0932290i	−0.00806484	−	0.00774224i
$146$	4.77502	−	6.57225i	0.395183	−	0.543923i
$147$	0.668241	−	16.0799i	0.0551156	−	1.32625i
$148$	−14.8926	−	29.2285i	−1.22417	−	2.40256i
$149$	−15.7486	+	9.09246i	−1.29018	+	0.744884i	−0.978685	−	0.205366i	$-0.934162\pi$
$149$	−15.7486	+	9.09246i	−1.29018	+	0.744884i	−0.311491	+	0.950249i	$0.600828\pi$
$150$	9.70840	+	26.1914i	0.792687	+	2.13852i
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	−0.169072	−	0.985604i	$-0.554077\pi$
$151$	9.44990	−	16.3677i	0.769022	−	1.33198i	0.938094	−	0.346381i	$-0.112590\pi$
$152$	−8.00310	+	12.3237i	−0.649137	+	0.999583i
$153$	−2.52586	−	15.9477i	−0.204204	−	1.28929i
$154$	−0.0483350	+	0.0961460i	−0.00389495	+	0.00774766i
$155$	−0.644136	+	20.1512i	−0.0517382	+	1.61858i
$156$	−25.1298	−	11.1885i	−2.01199	−	0.895796i
$157$	−4.20781	−	15.7038i	−0.335820	−	1.25330i	−0.902978	−	0.429688i	$-0.858624\pi$
$157$	−4.20781	−	15.7038i	−0.335820	−	1.25330i	0.567158	−	0.823609i	$-0.308043\pi$
$158$	−10.1171	−	8.19266i	−0.804873	−	0.651773i
$159$	−6.69470	+	7.43521i	−0.530924	+	0.589651i
$160$	0.253420	+	2.01474i	0.0200346	+	0.159280i
$161$	13.4994	−	5.26593i	1.06390	−	0.415014i
$162$	11.7289	−	23.0193i	0.921510	−	1.80856i
$163$	0.490229	+	9.35413i	0.0383977	+	0.732672i	0.948208	+	0.317649i	$0.102893\pi$
$163$	0.490229	+	9.35413i	0.0383977	+	0.732672i	−0.909811	+	0.415023i	$0.863773\pi$
$164$	−16.0348	−	17.8084i	−1.25211	−	1.39060i
$165$	0.0837915	−	0.0196055i	0.00652316	−	0.00152629i
$166$	−15.7852	−	14.2131i	−1.22517	−	1.10315i
$167$	−1.18224	+	7.46435i	−0.0914842	+	0.577608i	0.898779	+	0.438402i	$0.144455\pi$
$167$	−1.18224	+	7.46435i	−0.0914842	+	0.577608i	−0.990263	+	0.139207i	$0.955545\pi$
$168$	25.6507	−	11.5872i	1.97899	−	0.893972i
$169$	2.12129	+	2.91971i	0.163177	+	0.224593i
$170$	37.7750	−	6.77580i	2.89721	−	0.519680i
$171$	2.95266	+	6.63179i	0.225796	+	0.507145i
$172$	−16.4272	−	6.30581i	−1.25256	−	0.480813i
$173$	19.6275	+	12.7463i	1.49225	+	0.969080i	0.994828	+	0.101572i	$0.0323871\pi$
$173$	19.6275	+	12.7463i	1.49225	+	0.969080i	0.497423	+	0.867508i	$0.334280\pi$
$174$	0.336334			0.0254974
$175$	−8.26189	−	10.3316i	−0.624540	−	0.780993i
$176$	−0.0574953			−0.00433387
$177$	−4.83112	−	3.13737i	−0.363129	−	0.235819i
$178$	18.9878	+	7.28875i	1.42320	+	0.546315i
$179$	5.54190	+	12.4473i	0.414221	+	0.930356i	0.993351	+	0.115121i	$0.0367256\pi$
$179$	5.54190	+	12.4473i	0.414221	+	0.930356i	−0.579130	+	0.815235i	$0.696608\pi$
$180$	−17.9628	−	8.69547i	−1.33887	−	0.648122i
$181$	−3.38018	−	4.65241i	−0.251247	−	0.345811i	0.664701	−	0.747110i	$-0.268559\pi$
$181$	−3.38018	−	4.65241i	−0.251247	−	0.345811i	−0.915947	+	0.401298i	$0.868559\pi$
$182$	19.6040	+	1.95323i	1.45314	+	0.144783i
$183$	4.79930	−	30.3016i	0.354774	−	2.23996i
$184$	18.8325	+	16.9569i	1.38835	+	1.25008i
$185$	1.58218	−	18.7208i	0.116324	−	1.37638i
$186$	−33.7049	−	37.4330i	−2.47136	−	2.74472i
$187$	−0.00618787	−	0.118072i	−0.000452502	−	0.00863424i
$188$	8.15893	−	16.0128i	0.595051	−	1.16785i
$189$	−0.656250	+	4.29370i	−0.0477352	+	0.312321i
$190$	−15.6164	+	7.33824i	−1.13293	+	0.532372i
$191$	−9.91552	+	11.0123i	−0.717462	+	0.796822i	−0.986053	−	0.166432i	$-0.946775\pi$
$191$	−9.91552	+	11.0123i	−0.717462	+	0.796822i	0.268591	+	0.963254i	$0.413442\pi$
$192$	−16.2170	−	13.1323i	−1.17036	−	0.947740i
$193$	4.30663	+	16.0726i	0.309998	+	1.15693i	0.928557	+	0.371191i	$0.121050\pi$
$193$	4.30663	+	16.0726i	0.309998	+	1.15693i	−0.618558	+	0.785739i	$0.712283\pi$
$194$	−15.2741	−	6.80046i	−1.09662	−	0.488245i
$195$	−8.84829	−	13.0350i	−0.633639	−	0.933452i
$196$	−20.1109	+	18.5061i	−1.43649	+	1.32186i
$197$	2.43376	+	15.3662i	0.173398	+	1.09479i	0.908821	+	0.417185i	$0.136983\pi$
$197$	2.43376	+	15.3662i	0.173398	+	1.09479i	−0.735423	+	0.677608i	$0.763017\pi$
$198$	−0.0506389	+	0.0779771i	−0.00359875	+	0.00554159i
$199$	−0.988951	+	1.71291i	−0.0701049	+	0.121425i	−0.898947	−	0.438057i	$-0.855667\pi$
$199$	−0.988951	+	1.71291i	−0.0701049	+	0.121425i	0.828842	+	0.559482i	$0.189000\pi$
$200$	9.65361	−	21.0255i	0.682613	−	1.48672i
$201$	−0.633276	+	0.365622i	−0.0446678	+	0.0257890i
$202$	−11.6976	−	22.9578i	−0.823039	−	1.61531i
$203$	−0.151221	+	0.0500411i	−0.0106136	+	0.00351220i
$204$	−37.2677	+	51.2946i	−2.60926	+	3.59134i
$205$	−2.42313	−	13.5089i	−0.169239	−	0.943503i
$206$	0.528754	−	0.0555743i	0.0368401	−	0.00387205i
$207$	12.0929	−	3.24028i	0.840514	−	0.225215i
$208$	3.77216	+	9.82681i	0.261552	+	0.681367i
$209$	0.0164266	+	0.0505557i	0.00113625	+	0.00349701i
$210$	32.7662	+	4.32579i	2.26108	+	0.298508i
$211$	2.82445	−	8.69276i	0.194443	−	0.598434i	−0.805540	−	0.592542i	$-0.798124\pi$
$211$	2.82445	−	8.69276i	0.194443	−	0.598434i	0.999983	−	0.00589215i	$-0.00187554\pi$
$212$	16.9670	−	0.889200i	1.16530	−	0.0610705i
$213$	9.83728	+	15.1481i	0.674040	+	1.03793i
$214$	−8.83963	+	7.95924i	−0.604264	+	0.544082i
$215$	−6.08857	−	8.03037i	−0.415237	−	0.547667i
$216$	−7.22465	+	2.34743i	−0.491575	+	0.159722i
$217$	20.7236	+	11.8157i	1.40681	+	0.802101i
$218$	−13.2586	+	13.2586i	−0.897985	+	0.897985i
$219$	−3.12642	+	7.02205i	−0.211264	+	0.474506i
$220$	−0.124157	−	0.0770734i	−0.00837069	−	0.00519629i
$221$	−19.7742	+	8.80405i	−1.33016	+	0.592225i
$222$	29.5393	+	36.4780i	1.98255	+	2.44824i
$223$	−6.62726	+	3.37676i	−0.443794	+	0.226124i	−0.661584	−	0.749871i	$-0.730115\pi$
$223$	−6.62726	+	3.37676i	−0.443794	+	0.226124i	0.217789	+	0.975996i	$0.430115\pi$
$224$	2.24771	+	0.848882i	0.150181	+	0.0567183i
$225$	−6.11394	−	9.65699i	−0.407596	−	0.643800i
$226$	−4.86443	−	8.42544i	−0.323577	−	0.560452i
$227$	−11.7014	−	0.613246i	−0.776651	−	0.0407026i	−0.340109	−	0.940386i	$-0.610464\pi$
$227$	−11.7014	−	0.613246i	−0.776651	−	0.0407026i	−0.436543	+	0.899684i	$0.643797\pi$
$228$	10.2157	−	26.6127i	0.676549	−	1.76247i
$229$	2.81607	−	26.7931i	0.186091	−	1.77054i	−0.360134	−	0.932901i	$-0.617269\pi$
$229$	2.81607	−	26.7931i	0.186091	−	1.77054i	0.546225	−	0.837638i	$-0.316064\pi$
$230$	8.28657	+	28.5800i	0.546401	+	1.88451i
$231$	0.0258205	−	0.0984929i	0.00169886	−	0.00648036i
$232$	−0.196981	−	0.196981i	−0.0129324	−	0.0129324i
$233$	20.3954	−	7.82907i	1.33615	−	0.512900i	0.417753	−	0.908561i	$-0.362818\pi$
$233$	20.3954	−	7.82907i	1.33615	−	0.512900i	0.918397	+	0.395661i	$0.129485\pi$
$234$	16.6498	+	3.53902i	1.08843	+	0.231353i
$235$	8.80691	−	5.32717i	0.574499	−	0.347507i
$236$	2.03383	+	9.56842i	0.132391	+	0.622851i
$237$	10.9752	+	5.59214i	0.712915	+	0.363248i
$238$	13.7983	−	43.2622i	0.894409	−	2.80427i
$239$	−4.05851	−	1.31869i	−0.262523	−	0.0852989i	0.174798	−	0.984604i	$-0.444073\pi$
$239$	−4.05851	−	1.31869i	−0.262523	−	0.0852989i	−0.437321	+	0.899305i	$0.644073\pi$
$240$	5.79826	+	16.6792i	0.374276	+	1.07664i
$241$	0.0341430	−	0.160630i	0.00219934	−	0.0103471i	−0.977034	−	0.213082i	$-0.931650\pi$
$241$	0.0341430	−	0.160630i	0.00219934	−	0.0103471i	0.979234	+	0.202735i	$0.0649831\pi$
$242$	16.8204	−	20.7715i	1.08126	−	1.33524i
$243$	−5.05209	+	18.8546i	−0.324092	+	1.20953i
$244$	−42.1485	+	30.6227i	−2.69828	+	1.96042i
$245$	−15.3758	+	2.93015i	−0.982322	+	0.187201i
$246$	27.7405	+	20.1546i	1.76867	+	1.28501i
$247$	7.56302	−	6.12442i	0.481224	−	0.389687i
$248$	−2.18349	+	41.6634i	−0.138652	+	2.64563i
$249$	17.4055	+	10.0490i	1.10303	+	0.636832i
$250$	22.6520	−	14.9973i	1.43264	−	0.948513i
$251$		−	0.132304i		−	0.00835098i	−0.999991	−	0.00417549i	$-0.998671\pi$
$251$		−	0.132304i		−	0.00835098i	0.999991	−	0.00417549i	$-0.00132910\pi$
$252$	−19.0280	+	13.9827i	−1.19865	+	0.880825i
$253$	0.0905461	−	0.0143411i	0.00569259	−	0.000901617i
$254$	17.6077	+	1.85065i	1.10481	+	0.116120i
$255$	−33.6283	+	13.7023i	−2.10588	+	0.858073i
$256$	3.24278	+	30.8530i	0.202674	+	1.92831i
$257$	−8.87663	−	2.37849i	−0.553709	−	0.148366i	−0.0288944	−	0.999582i	$-0.509199\pi$
$257$	−8.87663	−	2.37849i	−0.553709	−	0.148366i	−0.524815	+	0.851217i	$0.675865\pi$
$258$	24.8677	+	3.93865i	1.54819	+	0.245210i
$259$	−18.7087	−	12.0061i	−1.16250	−	0.746020i
$260$	−5.02727	+	26.2770i	−0.311778	+	1.62963i
$261$	−0.134615	+	0.0286134i	−0.00833249	+	0.00177113i
$262$	−24.1086	+	15.6563i	−1.48943	+	0.967249i
$263$	17.5431	−	11.3926i	1.08175	−	0.702499i	0.124637	−	0.992202i	$-0.460223\pi$
$263$	17.5431	−	11.3926i	1.08175	−	0.702499i	0.957117	+	0.289703i	$0.0935566\pi$
$264$	0.174183	−	0.0370238i	0.0107202	−	0.00227866i
$265$	8.52455	+	4.69239i	0.523659	+	0.288251i
$266$	−0.958107	+	20.3934i	−0.0587453	+	1.25040i
$267$	−19.0074	−	3.01047i	−1.16323	−	0.184238i
$268$	1.19946	+	0.321394i	0.0732687	+	0.0196323i
$269$	0.158106	+	1.50428i	0.00963991	+	0.0917176i	0.998284	−	0.0585585i	$-0.0186504\pi$
$269$	0.158106	+	1.50428i	0.00963991	+	0.0917176i	−0.988644	+	0.150276i	$0.951984\pi$
$270$	−8.66139	−	2.13239i	−0.527115	−	0.129773i
$271$	9.03693	+	0.949820i	0.548955	+	0.0576974i	0.374946	−	0.927047i	$-0.377661\pi$
$271$	9.03693	+	0.949820i	0.548955	+	0.0576974i	0.174009	+	0.984744i	$0.444328\pi$
$272$	23.9627	−	3.79533i	1.45295	−	0.230125i
$273$	−18.5280	+	2.04883i	−1.12136	+	0.124001i
$274$		−	8.00453i		−	0.483571i
$275$	−0.0371329	−	0.0750064i	−0.00223920	−	0.00452305i
$276$	−42.5749	−	24.5807i	−2.56271	−	1.47958i
$277$	−0.715125	+	13.6454i	−0.0429677	+	0.819872i	0.889128	+	0.457659i	$0.151312\pi$
$277$	−0.715125	+	13.6454i	−0.0429677	+	0.819872i	−0.932095	+	0.362213i	$0.882021\pi$
$278$	8.58636	−	6.95309i	0.514975	−	0.417019i
$279$	16.6747	+	12.1149i	0.998291	+	0.725301i
$280$	−16.6567	−	21.7237i	−0.995430	−	1.29824i
$281$	−3.22462	+	2.34282i	−0.192365	+	0.139761i	−0.679799	−	0.733399i	$-0.737933\pi$
$281$	−3.22462	+	2.34282i	−0.192365	+	0.139761i	0.487434	+	0.873160i	$0.337933\pi$
$282$	−6.65559	+	24.8390i	−0.396334	+	1.47914i
$283$	11.8922	−	14.6857i	0.706920	−	0.872974i	−0.289529	−	0.957169i	$-0.593499\pi$
$283$	11.8922	−	14.6857i	0.706920	−	0.872974i	0.996449	+	0.0841955i	$0.0268320\pi$
$284$	6.37712	−	30.0020i	0.378413	−	1.78029i
$285$	13.0095	−	9.86374i	0.770618	−	0.584277i
$286$	0.118543	+	0.0385168i	0.00700957	+	0.00227755i
$287$	−15.4712	−	4.93447i	−0.913236	−	0.291272i
$288$	1.84965	+	0.942442i	0.108991	+	0.0555339i
$289$	6.83850	+	32.1726i	0.402265	+	1.89251i
$290$	−0.0745245	−	0.318508i	−0.00437623	−	0.0187034i
$291$	15.4742	+	3.28914i	0.907112	+	0.192813i
$292$	12.1861	−	4.67781i	0.713138	−	0.273748i
$293$	−4.94524	−	4.94524i	−0.288904	−	0.288904i	0.547743	−	0.836647i	$-0.315487\pi$
$293$	−4.94524	−	4.94524i	−0.288904	−	0.288904i	−0.836647	+	0.547743i	$0.815487\pi$
$294$	22.6420	−	31.8843i	1.32051	−	1.85953i
$295$	−1.90061	+	5.27024i	−0.110658	+	0.306845i
$296$	4.06380	−	38.6645i	0.236204	−	2.24733i
$297$	−0.00984815	+	0.0256553i	−0.000571447	+	0.00148867i
$298$	−44.1265	−	2.31257i	−2.55618	−	0.133964i
$299$	−8.39168	−	14.5348i	−0.485303	−	0.840570i
$300$	−9.83785	+	43.7905i	−0.567988	+	2.52824i
$301$	−11.7669	+	1.92904i	−0.678231	+	0.111188i
$302$	40.9187	−	20.8491i	2.35460	−	1.19973i
$303$	15.3426	+	18.9465i	0.881409	+	1.08845i
$304$	−9.96484	+	4.43663i	−0.571523	+	0.254458i
$305$	−29.7590	+	2.16926i	−1.70400	+	0.124211i
$306$	15.9578	−	35.8419i	0.912248	−	2.04894i
$307$	−4.76473	+	4.76473i	−0.271938	+	0.271938i	−0.829880	−	0.557942i	$-0.811591\pi$
$307$	−4.76473	+	4.76473i	−0.271938	+	0.271938i	0.557942	+	0.829880i	$0.311591\pi$
$308$	−0.149273	+	0.0872638i	−0.00850564	+	0.00497232i
$309$	−0.478436	+	0.155453i	−0.0272173	+	0.00884342i
$310$	−27.9808	+	40.2129i	−1.58920	+	2.28394i
$311$	1.95368	−	1.75910i	0.110783	−	0.0997496i	−0.611878	−	0.790952i	$-0.709586\pi$
$311$	1.95368	−	1.75910i	0.110783	−	0.0997496i	0.722661	+	0.691203i	$0.242919\pi$
$312$	−17.7558	−	27.3415i	−1.00522	−	1.54791i
$313$	−4.34316	+	0.227616i	−0.245490	+	0.0128656i	−0.174684	−	0.984625i	$-0.555890\pi$
$313$	−4.34316	+	0.227616i	−0.245490	+	0.0128656i	−0.0708059	+	0.997490i	$0.522557\pi$
$314$	12.2075	−	37.5707i	0.688908	−	2.12024i
$315$	−13.4825	+	1.05619i	−0.759652	+	0.0595098i
$316$	−6.46387	−	19.8938i	−0.363621	−	1.11911i
$317$	7.43621	+	19.3720i	0.417659	+	1.08804i	0.967523	+	0.252784i	$0.0813463\pi$
$317$	7.43621	+	19.3720i	0.417659	+	1.08804i	−0.549864	+	0.835254i	$0.685320\pi$
$318$	−23.4827	+	6.29216i	−1.31684	+	0.352847i
$319$	−0.00100223		0.000105339i	−5.61143e−5		5.89785e-6i
$320$	−8.84291	+	18.2673i	−0.494334	+	1.02117i
$321$	6.61541	−	9.10533i	0.369236	−	0.508210i
$322$	34.4788	+	7.13384i	1.92143	+	0.397553i
$323$	−10.1835	−	19.9862i	−0.566623	−	1.11206i
$324$	35.9500	−	20.7557i	1.99722	−	1.15310i
$325$	−10.3835	+	11.2676i	−0.575973	+	0.625014i
$326$	−11.3803	+	19.7112i	−0.630295	+	1.09170i
$327$	9.66271	−	14.8793i	0.534349	−	0.822825i
$328$	−4.44281	−	28.0508i	−0.245313	−	1.54884i
$329$	−0.703199	−	12.1582i	−0.0387686	−	0.670304i
$330$	0.196702	+	0.0709366i	0.0108281	+	0.00390493i
$331$	14.5178	+	6.46376i	0.797972	+	0.355280i	0.764881	−	0.644172i	$-0.222798\pi$
$331$	14.5178	+	6.46376i	0.797972	+	0.355280i	0.0330919	+	0.999452i	$0.489465\pi$
$332$	−8.83346	−	32.9669i	−0.484799	−	1.80929i
$333$	−14.9263	−	12.0871i	−0.817955	−	0.662367i
$334$	−12.2876	+	13.6467i	−0.672346	+	0.746716i
$335$	0.486565	+	0.518698i	0.0265839	+	0.0283395i
$336$	20.6538	+	3.15673i	1.12676	+	0.172214i
$337$	−11.6113	+	22.7884i	−0.632508	+	1.24137i	0.323000	+	0.946399i	$0.395309\pi$
$337$	−11.6113	+	22.7884i	−0.632508	+	1.24137i	−0.955507	+	0.294967i	$0.904691\pi$
$338$	0.458951	+	8.75730i	0.0249636	+	0.476334i
$339$	6.15957	+	6.84090i	0.334542	+	0.371547i
$340$	56.8337	+	23.9267i	3.08224	+	1.29761i
$341$	0.112160	+	0.100989i	0.00607382	+	0.00546889i
$342$	−2.75941	+	17.4222i	−0.149212	+	0.942086i
$343$	−5.43629	+	17.7044i	−0.293532	+	0.955949i
$344$	−12.2575	−	16.8710i	−0.660882	−	0.909626i
$345$	−13.2917	−	24.8210i	−0.715600	−	1.33632i
$346$	23.1297	+	51.9502i	1.24346	+	2.79286i
$347$	−14.1465	−	5.43034i	−0.759425	−	0.291516i	−0.0523255	−	0.998630i	$-0.516663\pi$
$347$	−14.1465	−	5.43034i	−0.759425	−	0.291516i	−0.707099	+	0.707114i	$0.749997\pi$
$348$	0.453231	+	0.294331i	0.0242957	+	0.0157778i
$349$	−1.48928			−0.0797192			−0.0398596	−	0.999205i	$-0.512691\pi$
$349$	−1.48928			−0.0797192			−0.0398596	+	0.999205i	$0.512691\pi$
$350$	−3.16378	−	31.9881i	−0.169111	−	1.70984i
$351$	5.03100			0.268535
$352$	0.0127486	+	0.00827905i	0.000679504	+	0.000441275i
$353$	−8.77541	−	3.36856i	−0.467068	−	0.179291i	0.113441	−	0.993545i	$-0.463813\pi$
$353$	−8.77541	−	3.36856i	−0.467068	−	0.179291i	−0.580509	+	0.814254i	$0.697146\pi$
$354$	−5.69315	−	12.7870i	−0.302588	−	0.679623i
$355$	12.1655	−	12.6724i	0.645678	−	0.672581i
$356$	19.2088	+	26.4386i	1.01806	+	1.40124i
$357$	−4.25978	+	42.7541i	−0.225451	+	2.26279i
$358$	−5.17918	+	32.7001i	−0.273728	+	1.72825i
$359$	−4.56543	−	4.11073i	−0.240954	−	0.216956i	0.539802	−	0.841792i	$-0.318499\pi$
$359$	−4.56543	−	4.11073i	−0.240954	−	0.216956i	−0.780756	+	0.624836i	$0.785166\pi$
$360$	−12.2413	−	20.2374i	−0.645175	−	1.06661i
$361$	−5.96536	−	6.62520i	−0.313966	−	0.348695i
$362$	−0.731315	−	13.9543i	−0.0384370	−	0.733422i
$363$	−11.4813	+	22.5332i	−0.602610	+	1.18269i
$364$	24.7083	+	19.7879i	1.29506	+	1.03717i
$365$	7.34263	+	1.40478i	0.384331	+	0.0735295i
$366$	49.8815	−	55.3990i	2.60735	−	2.89575i
$367$	28.0420	+	22.7079i	1.46378	+	1.18534i	0.943511	+	0.331341i	$0.107501\pi$
$367$	28.0420	+	22.7079i	1.46378	+	1.18534i	0.520267	+	0.854003i	$0.325832\pi$
$368$	4.86880	+	18.1706i	0.253804	+	0.947209i
$369$	−12.8176	−	5.70676i	−0.667257	−	0.297082i
$370$	27.9994	−	36.0565i	1.45562	−	1.87449i
$371$	9.62196	−	6.32289i	0.499547	−	0.328268i
$372$	−12.6611	−	79.9390i	−0.656447	−	4.14464i
$373$	10.1248	−	15.5909i	0.524244	−	0.807264i	−0.473031	−	0.881046i	$-0.656840\pi$
$373$	10.1248	−	15.5909i	0.524244	−	0.807264i	0.997274	+	0.0737815i	$0.0235067\pi$
$374$	0.143646	−	0.248802i	0.00742777	−	0.0128653i
$375$	−18.0144	+	18.3364i	−0.930261	+	0.946887i
$376$	18.4455	−	10.6495i	0.951252	−	0.549206i
$377$	0.0837587	+	0.164386i	0.00431379	+	0.00846629i
$378$	−7.01965	+	7.88149i	−0.361052	+	0.405380i
$379$	−13.0838	+	18.0083i	−0.672068	+	0.925022i	−0.999805	−	0.0197466i	$-0.993714\pi$
$379$	−13.0838	+	18.0083i	−0.672068	+	0.925022i	0.327737	+	0.944769i	$0.393714\pi$
$380$	−27.4658	−	3.77742i	−1.40897	−	0.193777i
$381$	−16.6602	+	1.75106i	−0.853529	+	0.0897095i
$382$	−34.7802	+	9.31932i	−1.77951	+	0.476818i
$383$	5.51711	+	14.3726i	0.281911	+	0.734403i	0.999288	+	0.0377184i	$0.0120090\pi$
$383$	5.51711	+	14.3726i	0.281911	+	0.734403i	−0.717377	+	0.696685i	$0.754658\pi$
$384$	−14.3783	−	44.2520i	−0.733742	−	2.25822i
$385$	−0.0989940	−	0.00262803i	−0.00504520	−	0.000133937i
$386$	−12.4942	+	38.4531i	−0.635937	+	1.95721i
$387$	−10.2882	+	0.539182i	−0.522979	+	0.0274082i
$388$	−14.6316	−	22.5307i	−0.742806	−	1.14382i
$389$	8.85903	−	7.97670i	0.449171	−	0.404435i	−0.413258	−	0.910614i	$-0.635609\pi$
$389$	8.85903	−	7.97670i	0.449171	−	0.404435i	0.862428	+	0.506179i	$0.168943\pi$
$390$	−0.781097	−	38.2733i	−0.0395524	−	1.93804i
$391$	−36.7909	+	11.9541i	−1.86060	+	0.604545i
$392$	−31.9345	+	5.41296i	−1.61294	+	0.273396i
$393$	19.2328	−	19.2328i	0.970168	−	0.970168i
$394$	−15.3760	+	34.5350i	−0.774629	+	1.73985i
$395$	2.86388	−	11.6326i	0.144098	−	0.585300i
$396$	−0.136478	+	0.0607640i	−0.00685828	+	0.00305350i
$397$	4.26600	+	5.26807i	0.214105	+	0.264397i	0.872872	−	0.487950i	$-0.162255\pi$
$397$	4.26600	+	5.26807i	0.214105	+	0.264397i	−0.658767	+	0.752347i	$0.728922\pi$
$398$	−4.28222	+	2.18190i	−0.214648	+	0.109369i
$399$	−3.12512	−	19.0628i	−0.156452	−	0.954335i
$400$	14.5105	−	9.18673i	0.725524	−	0.459336i
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	0.542220	−	0.840237i	$-0.317584\pi$
$401$	−9.14254	−	15.8353i	−0.456557	−	0.790779i	−0.998776	+	0.0494575i	$0.984251\pi$
$402$	−1.77439	−	0.0929920i	−0.0884987	−	0.00463802i
$403$	9.90201	−	25.7956i	0.493254	−	1.28497i
$404$	4.32754	−	41.1738i	0.215303	−	2.04847i
$405$	23.7624	+	0.759570i	1.18076	+	0.0377433i
$406$	−0.374391	−	0.0981488i	−0.0185807	−	0.00487104i
$407$	−0.0994483	−	0.0994483i	−0.00492947	−	0.00492947i
$408$	−70.1518	+	26.9287i	−3.47303	+	1.33317i
$409$	−15.5613	−	3.30765i	−0.769456	−	0.163553i	−0.193574	−	0.981086i	$-0.562008\pi$
$409$	−15.5613	−	3.30765i	−0.769456	−	0.163553i	−0.575882	+	0.817533i	$0.695341\pi$
$410$	12.9397	−	30.7361i	0.639047	−	1.51795i
$411$	1.57468	+	7.40829i	0.0776732	+	0.365424i
$412$	0.761163	+	0.387832i	0.0374998	+	0.0191071i
$413$	4.46223	+	4.90218i	0.219572	+	0.241221i
$414$	28.9318	+	9.40052i	1.42192	+	0.462010i
$415$	5.65976	−	18.7096i	0.277827	−	0.918419i
$416$	0.578601	−	2.72210i	0.0283683	−	0.133462i
$417$	−6.57894	+	8.12431i	−0.322172	+	0.397849i
$418$	−0.0334306	+	0.124765i	−0.00163514	+	0.00610243i
$419$	28.7560	−	20.8925i	1.40482	−	1.02066i	0.410773	−	0.911738i	$-0.365259\pi$
$419$	28.7560	−	20.8925i	1.40482	−	1.02066i	0.994050	−	0.108926i	$-0.0347411\pi$
$420$	40.3689	+	34.5035i	1.96980	+	1.68360i
$421$	−11.3679	−	8.25925i	−0.554037	−	0.402531i	0.275235	−	0.961377i	$-0.411244\pi$
$421$	−11.3679	−	8.25925i	−0.554037	−	0.402531i	−0.829272	+	0.558846i	$0.811244\pi$
$422$	17.2599	−	13.9768i	0.840197	−	0.680378i
$423$	0.550694	−	10.5079i	0.0267757	−	0.510910i
$424$	17.4383	+	10.0680i	0.846876	+	0.488944i
$425$	20.4274	+	28.8098i	0.990875	+	1.39748i
$426$			43.8884i			2.12640i
$427$	−14.1849	+	32.3298i	−0.686458	+	1.56455i
$428$	−18.8772	+	2.98985i	−0.912464	+	0.144520i
$429$	−0.117290	−	0.0123277i	−0.00566280	−	0.000595185i
$430$	−1.78025	−	24.4224i	−0.0858514	−	1.17775i
$431$	−0.397806	−	3.78487i	−0.0191616	−	0.182311i	0.980755	−	0.195244i	$-0.0625498\pi$
$431$	−0.397806	−	3.78487i	−0.0191616	−	0.182311i	−0.999916	+	0.0129330i	$0.995883\pi$
$432$	−5.44685	−	1.45948i	−0.262061	−	0.0702192i
$433$	1.22529	+	0.194066i	0.0588836	+	0.00932624i	0.185807	−	0.982586i	$-0.440510\pi$
$433$	1.22529	+	0.194066i	0.0588836	+	0.00932624i	−0.126923	+	0.991913i	$0.540510\pi$
$434$	26.5950	+	51.5044i	1.27660	+	2.47229i
$435$	0.131631	+	0.280122i	0.00631124	+	0.0134308i
$436$	−29.4696	+	6.26395i	−1.41134	+	0.299989i
$437$	14.5864	−	9.47255i	0.697764	−	0.453133i
$438$	−15.6642	+	10.1725i	−0.748465	+	0.486059i
$439$	−5.32727	+	1.13235i	−0.254257	+	0.0540439i	−0.333277	−	0.942829i	$-0.608154\pi$
$439$	−5.32727	+	1.13235i	−0.254257	+	0.0540439i	0.0790199	+	0.996873i	$0.474821\pi$
$440$	−0.0736569	−	0.156748i	−0.00351146	−	0.00747266i
$441$	−6.34978	+	14.6878i	−0.302371	+	0.699417i
$442$	−51.9485	−	8.22783i	−2.47094	−	0.391358i
$443$	17.6715	+	4.73507i	0.839599	+	0.224970i	0.652897	−	0.757447i	$-0.273553\pi$
$443$	17.6715	+	4.73507i	0.839599	+	0.224970i	0.186702	+	0.982417i	$0.440220\pi$
$444$	7.88353	+	75.0067i	0.374136	+	3.55966i
$445$	1.36072	+	18.6670i	0.0645042	+	0.884901i
$446$	−17.9743	−	1.88917i	−0.851106	−	0.0894548i
$447$	41.2945	−	6.54041i	1.95316	−	0.309351i
$448$	14.2197	+	19.3507i	0.671820	+	0.914233i
$449$			7.28927i			0.344002i	0.985097	+	0.172001i	$0.0550232\pi$
$449$			7.28927i			0.344002i	−0.985097	+	0.172001i	$0.944977\pi$
$450$	0.320731	−	27.7708i	0.0151194	−	1.30913i
$451$	−0.0889755	−	0.0513700i	−0.00418969	−	0.00241892i
$452$	0.818124	−	15.6107i	0.0384813	−	0.734267i
$453$	−33.7692	+	27.3458i	−1.58662	+	1.28482i
$454$	−23.0343	−	16.7354i	−1.08105	−	0.785432i
$455$	6.04565	+	17.0920i	0.283424	+	0.801285i
$456$	27.3318	−	19.8577i	1.27993	−	0.929922i
$457$	3.05849	−	11.4145i	0.143070	−	0.533946i	−0.856763	−	0.515710i	$-0.827528\pi$
$457$	3.05849	−	11.4145i	0.143070	−	0.533946i	0.999834	−	0.0182361i	$-0.00580504\pi$
$458$	41.1969	−	50.8739i	1.92500	−	2.37718i
$459$	2.41095	−	11.3426i	0.112534	−	0.529429i
$460$	−13.8442	+	45.7650i	−0.645488	+	2.13381i
$461$	−0.809532	−	0.263033i	−0.0377037	−	0.0122507i	0.290104	−	0.956995i	$-0.406310\pi$
$461$	−0.809532	−	0.263033i	−0.0377037	−	0.0122507i	−0.327808	+	0.944744i	$0.606310\pi$
$462$	0.182964	−	0.166544i	0.00851227	−	0.00774833i
$463$	34.4372	+	17.5466i	1.60043	+	0.815460i	0.999874	+	0.0158788i	$0.00505458\pi$
$463$	34.4372	+	17.5466i	1.60043	+	0.815460i	0.600557	+	0.799582i	$0.294945\pi$
$464$	−0.0429941	−	0.202271i	−0.00199595	−	0.00939022i
$465$	17.9857	−	42.7220i	0.834069	−	1.98118i
$466$	51.9241	+	11.0368i	2.40534	+	0.511270i
$467$	−8.34928	+	3.20499i	−0.386358	+	0.148309i	−0.543791	−	0.839221i	$-0.683012\pi$
$467$	−8.34928	+	3.20499i	−0.386358	+	0.148309i	0.157433	+	0.987530i	$0.449678\pi$
$468$	19.3396	+	19.3396i	0.893972	+	0.893972i
$469$	0.811629	−	0.222191i	0.0374775	−	0.0102598i
$470$	24.9973	+	0.799042i	1.15304	+	0.0368570i
$471$	−3.90711	+	37.1737i	−0.180030	+	1.71287i
$472$	−4.15468	+	10.8233i	−0.191235	+	0.498183i
$473$	−0.0753362	−	0.00394820i	−0.00346396	−	0.000181538i
$474$	14.9653	+	25.9206i	0.687377	+	1.19057i
$475$	−12.2236	−	10.1344i	−0.560857	−	0.464999i
$476$	56.4535	−	46.2233i	2.58754	−	2.11864i
$477$	8.86348	−	4.51617i	0.405831	−	0.206781i
$478$	−6.52552	−	8.05835i	−0.298470	−	0.368580i
$479$	0.885419	−	0.394214i	0.0404558	−	0.0180121i	−0.386409	−	0.922328i	$-0.626285\pi$
$479$	0.885419	−	0.394214i	0.0404558	−	0.0180121i	0.426865	+	0.904315i	$0.359618\pi$
$480$	1.11607	−	4.53327i	0.0509412	−	0.206914i
$481$	−10.4726	+	23.5218i	−0.477509	+	1.07250i
$482$	0.282157	−	0.282157i	0.0128519	−	0.0128519i
$483$	−33.3139	+	0.180335i	−1.51584	+	0.00820553i
$484$	40.8440	−	13.2710i	1.85655	−	0.603228i
$485$	−0.313939	−	15.3828i	−0.0142553	−	0.698499i
$486$	−35.2477	+	31.7372i	−1.59887	+	1.43963i
$487$	−18.8835	−	29.0780i	−0.855691	−	1.31765i	−0.946805	−	0.321808i	$-0.895709\pi$
$487$	−18.8835	−	29.0780i	−0.855691	−	1.31765i	0.0911139	−	0.995840i	$-0.470957\pi$
$488$	−61.6598	+	3.23145i	−2.79121	+	0.146281i
$489$	6.65491	−	20.4817i	0.300946	−	0.926215i
$490$	−35.2115	−	14.3771i	−1.59069	−	0.649491i
$491$	1.58176	+	4.86817i	0.0713840	+	0.219697i	0.980383	−	0.197100i	$-0.0631524\pi$
$491$	1.58176	+	4.86817i	0.0713840	+	0.219697i	−0.908999	+	0.416798i	$0.863152\pi$
$492$	19.7443	+	51.4357i	0.890143	+	2.31890i
$493$	0.410755	−	0.110061i	0.0184995	−	0.00495692i
$494$	23.5175	−	2.47179i	1.05810	−	0.111211i
$495$	−0.0847634	−	0.0116576i	−0.00380983	−	0.000523972i
$496$	−18.2037	+	25.0553i	−0.817371	+	1.12501i
$497$	−6.52990	−	19.7329i	−0.292906	−	0.885139i
$498$	22.1710	+	43.5130i	0.993506	+	1.94986i
$499$	31.5502	−	18.2155i	1.41238	−	0.815438i	0.416768	−	0.909013i	$-0.363163\pi$
$499$	31.5502	−	18.2155i	1.41238	−	0.815438i	0.995612	+	0.0935745i	$0.0298293\pi$
$500$	43.6494	−	0.386608i	1.95206	−	0.0172896i
$501$	8.68766	−	15.0475i	0.388136	−	0.672271i
$502$	0.175092	−	0.269618i	0.00781474	−	0.0120336i
$503$	0.209162	+	1.32059i	0.00932605	+	0.0588824i	0.991912	−	0.126924i	$-0.0405104\pi$
$503$	0.209162	+	1.32059i	0.00932605	+	0.0588824i	−0.982586	+	0.185806i	$0.940510\pi$
$504$	−27.9384	+	1.61588i	−1.24448	+	0.0719772i
$505$	14.5428	−	18.7276i	0.647145	−	0.833367i
$506$	0.203500	+	0.0906038i	0.00904666	+	0.00402783i
$507$	−2.14753	−	8.01470i	−0.0953752	−	0.355945i
$508$	22.1079	+	17.9027i	0.980882	+	0.794302i
$509$	−12.8202	+	14.2382i	−0.568244	+	0.631098i	−0.956946	−	0.290265i	$-0.906257\pi$
$509$	−12.8202	+	14.2382i	−0.568244	+	0.631098i	0.388703	+	0.921363i	$0.372923\pi$
$510$	−86.6634	−	16.5803i	−3.83752	−	0.734188i
$511$	5.52935	−	6.90427i	0.244604	−	0.305427i
$512$	−15.8470	+	31.1015i	−0.700346	+	1.37451i
$513$	0.272856	+	5.20640i	0.0120469	+	0.229868i
$514$	−14.9417	−	16.5944i	−0.659048	−	0.731947i
$515$	0.253225	+	0.418633i	0.0111584	+	0.0184472i
$516$	30.0640	+	27.0697i	1.32349	+	1.19168i
$517$	0.0120533	−	0.0761016i	0.000530104	−	0.00334694i
$518$	−22.2368	−	49.2258i	−0.977028	−	2.16286i
$519$	−31.6267	−	43.5304i	−1.38826	−	1.91077i
$520$	−21.9581	+	22.8730i	−0.962926	+	1.00305i
$521$	5.94344	+	13.3492i	0.260387	+	0.584838i	0.995674	−	0.0929175i	$-0.0296193\pi$
$521$	5.94344	+	13.3492i	0.260387	+	0.584838i	−0.735287	+	0.677756i	$0.762953\pi$
$522$	−0.312195	−	0.119840i	−0.0136644	−	0.00524527i
$523$	−29.1893	−	18.9558i	−1.27636	−	0.828877i	−0.284807	−	0.958585i	$-0.591930\pi$
$523$	−29.1893	−	18.9558i	−1.27636	−	0.828877i	−0.991552	+	0.129707i	$0.958596\pi$
$524$	−46.1889			−2.01777
$525$	9.22093	+	28.9830i	0.402434	+	1.26492i
$526$	50.8274			2.21618
$527$	−53.4123	−	34.6864i	−2.32668	−	1.51096i
$528$	0.123408	+	0.0473721i	0.00537066	+	0.00206160i
$529$	−2.84498	−	6.38993i	−0.123695	−	0.277823i
$530$	11.1619	+	20.8439i	0.484843	+	0.905399i
$531$	3.36650	+	4.63359i	0.146094	+	0.201081i
$532$	−19.1377	+	26.6429i	−0.829725	+	1.15512i
$533$	−2.94239	+	18.5775i	−0.127449	+	0.804683i
$534$	−34.7503	−	31.2893i	−1.50379	−	1.35402i
$535$	−10.0886	−	4.24724i	−0.436168	−	0.183624i
$536$	0.984749	+	1.09367i	0.0425347	+	0.0472395i
$537$	−1.63948	−	31.2832i	−0.0707489	−	1.34997i
$538$	−1.66857	+	3.27475i	−0.0719372	+	0.141185i
$539$	−0.0574843	+	0.102103i	−0.00247602	+	0.00439788i
$540$	−9.80566	−	10.4532i	−0.421969	−	0.449836i
$541$	−11.5839	+	12.8652i	−0.498029	+	0.553117i	−0.938782	−	0.344511i	$-0.888045\pi$
$541$	−11.5839	+	12.8652i	−0.498029	+	0.553117i	0.440753	+	0.897628i	$0.354711\pi$
$542$	17.1590	+	13.8951i	0.737043	+	0.596846i
$543$	3.42198	+	12.7710i	0.146851	+	0.548057i
$544$	−5.85985	−	2.60897i	−0.251239	−	0.111859i
$545$	−16.2317	−	5.85365i	−0.695290	−	0.250743i
$546$	−40.4689	−	20.3447i	−1.73191	−	0.870674i
$547$	1.54775	+	9.77211i	0.0661770	+	0.417825i	0.998430	+	0.0560177i	$0.0178403\pi$
$547$	1.54775	+	9.77211i	0.0661770	+	0.417825i	−0.932253	+	0.361808i	$0.882160\pi$
$548$	7.00490	−	10.7866i	0.299234	−	0.460781i
$549$	−15.2517	+	26.4167i	−0.650927	+	1.12744i
$550$	0.0235920	−	0.201994i	0.00100597	−	0.00861307i
$551$	−0.165574	+	0.0955944i	−0.00705370	+	0.00407246i
$552$	−26.4511	−	51.9131i	−1.12583	−	2.20957i
$553$	−10.5852	−	9.42768i	−0.450127	−	0.400906i
$554$	−19.5157	+	26.8610i	−0.829142	+	1.14122i
$555$	−18.8206	+	38.8789i	−0.798890	+	1.65032i
$556$	17.6554	−	1.85566i	0.748756	−	0.0786975i
$557$	15.6719	−	4.19928i	0.664041	−	0.177929i	0.0889717	−	0.996034i	$-0.471642\pi$
$557$	15.6719	−	4.19928i	0.664041	−	0.177929i	0.575069	+	0.818105i	$0.304975\pi$
$558$	17.9479	+	46.7559i	0.759796	+	1.97934i
$559$	4.26786	+	13.1351i	0.180511	+	0.555557i
$560$	−1.58702	−	20.2586i	−0.0670640	−	0.856082i
$561$	−0.0840009	+	0.258528i	−0.00354652	+	0.0109151i
$562$	−9.67182	+	0.506879i	−0.407981	+	0.0213814i
$563$	16.8888	+	26.0064i	0.711776	+	1.09604i	0.990745	+	0.135739i	$0.0433408\pi$
$563$	16.8888	+	26.0064i	0.711776	+	1.09604i	−0.278969	+	0.960300i	$0.589993\pi$
$564$	−30.7058	+	27.6476i	−1.29295	+	1.16418i
$565$	5.11350	−	7.34891i	0.215126	−	0.309171i
$566$	43.6698	−	14.1892i	1.83558	−	0.596416i
$567$	13.9331	−	24.4374i	0.585137	−	1.02628i
$568$	25.7042	−	25.7042i	1.07852	−	1.07852i
$569$	5.42165	−	12.1772i	0.227287	−	0.510496i	−0.763519	−	0.645786i	$-0.776530\pi$
$569$	5.42165	−	12.1772i	0.227287	−	0.510496i	0.990806	+	0.135290i	$0.0431966\pi$
$570$	39.5653	−	2.88408i	1.65721	−	0.120801i
$571$	7.62713	−	3.39582i	0.319185	−	0.142110i	−0.240889	−	0.970553i	$-0.577439\pi$
$571$	7.62713	−	3.39582i	0.319185	−	0.142110i	0.560075	+	0.828442i	$0.310772\pi$
$572$	0.126037	+	0.155642i	0.00526986	+	0.00650774i
$573$	30.3562	−	15.4672i	1.26815	−	0.646153i
$574$	−24.9979	−	30.5304i	−1.04339	−	1.27431i
$575$	−20.5603	+	18.0870i	−0.857424	+	0.754281i
$576$	10.3739	+	17.9681i	0.432245	+	0.748670i
$577$	34.5559	+	1.81100i	1.43858	+	0.0753928i	0.755595	−	0.655039i	$-0.227348\pi$
$577$	34.5559	+	1.81100i	1.43858	+	0.0753928i	0.682986	+	0.730432i	$0.260681\pi$
$578$	−28.6414	+	74.6134i	−1.19133	+	3.10351i
$579$	3.99887	−	38.0467i	0.166187	−	1.58117i
$580$	0.178305	−	0.494427i	0.00740373	−	0.0205300i
$581$	−16.4424	−	16.2654i	−0.682147	−	0.674802i
$582$	27.1814	+	27.1814i	1.12670	+	1.12670i
$583$	0.0680047	−	0.0261045i	0.00281647	−	0.00108114i
$584$	15.1318	+	3.21636i	0.626158	+	0.133094i
$585$	3.56871	+	15.2522i	0.147548	+	0.630600i
$586$	−3.53317	−	16.6222i	−0.145954	−	0.686659i
$587$	17.8813	+	9.11097i	0.738039	+	0.376050i	0.782244	−	0.622973i	$-0.214075\pi$
$587$	17.8813	+	9.11097i	0.738039	+	0.376050i	−0.0442042	+	0.999023i	$0.514075\pi$
$588$	58.4140	−	23.1517i	2.40895	−	0.954760i
$589$	27.2320	+	8.84822i	1.12208	+	0.364584i
$590$	−10.8478	+	8.22475i	−0.446598	+	0.338608i
$591$	7.43679	−	34.9873i	0.305908	−	1.43919i
$592$	18.1619	−	22.4280i	0.746448	−	0.921786i
$593$	4.81121	−	17.9557i	0.197573	−	0.737352i	−0.794013	−	0.607901i	$-0.792012\pi$
$593$	4.81121	−	17.9557i	0.197573	−	0.737352i	0.991586	−	0.129451i	$-0.0413215\pi$
$594$	−0.0540215	+	0.0392489i	−0.00221653	+	0.00161040i
$595$	41.4320	−	5.43940i	1.69855	−	0.222994i
$596$	−57.4394	−	41.7321i	−2.35281	−	1.70942i
$597$	3.53401	−	2.86179i	0.144638	−	0.117125i
$598$	2.13433	−	40.7255i	0.0872794	−	1.66539i
$599$	30.6038	+	17.6691i	1.25044	+	0.721941i	0.971196	−	0.238280i	$-0.0765837\pi$
$599$	30.6038	+	17.6691i	1.25044	+	0.721941i	0.279241	+	0.960221i	$0.409917\pi$
$600$	−38.0441	+	37.1754i	−1.55314	+	1.51768i
$601$		−	0.819532i		−	0.0334294i	−0.999860	−	0.0167147i	$-0.994679\pi$
$601$		−	0.819532i		−	0.0334294i	0.999860	−	0.0167147i	$-0.00532070\pi$
$602$	−26.5322	−	11.6412i	−1.08137	−	0.474460i
$603$	0.718101	−	0.113736i	0.0292433	−	0.00463169i
$604$	73.3858	+	7.71316i	2.98603	+	0.313844i
$605$	23.8830	+	5.87986i	0.970981	+	0.239050i
$606$	6.19220	+	58.9149i	0.251541	+	2.39325i
$607$	13.3713	+	3.58282i	0.542724	+	0.145422i	0.519757	−	0.854314i	$-0.326022\pi$
$607$	13.3713	+	3.58282i	0.542724	+	0.145422i	0.0229662	+	0.999736i	$0.492689\pi$
$608$	2.84839	+	0.451141i	0.115518	+	0.0182962i
$609$	0.365812	+	0.0171863i	0.0148234	+	0.000696423i
$610$	−63.5156	−	34.9625i	−2.57167	−	1.41559i
$611$	−13.7977	+	2.93279i	−0.558196	+	0.118648i
$612$	52.8700	−	34.3341i	2.13714	−	1.38788i
$613$	−32.1471	+	20.8766i	−1.29841	+	0.843197i	−0.994004	−	0.109345i	$-0.965125\pi$
$613$	−32.1471	+	20.8766i	−1.29841	+	0.843197i	−0.304406	+	0.952542i	$0.598458\pi$
$614$	−16.0155	+	3.40421i	−0.646334	+	0.137383i
$615$	−5.92936	+	30.9921i	−0.239095	+	1.24972i
$616$	−0.204697	−	0.00961692i	−0.00824748	−	0.000387477i
$617$	−16.5933	−	2.62812i	−0.668022	−	0.105804i	−0.186793	−	0.982399i	$-0.559809\pi$
$617$	−16.5933	−	2.62812i	−0.668022	−	0.105804i	−0.481229	+	0.876595i	$0.659809\pi$
$618$	−1.18071	−	0.316371i	−0.0474952	−	0.0127263i
$619$	−0.649827	−	6.18269i	−0.0261187	−	0.248503i	−0.999789	−	0.0205421i	$-0.993461\pi$
$619$	−0.649827	−	6.18269i	−0.0261187	−	0.248503i	0.973670	−	0.227961i	$-0.0732059\pi$
$620$	−72.8968	+	29.7029i	−2.92761	+	1.19290i
$621$	8.94198	+	0.939840i	0.358829	+	0.0377145i
$622$	6.30933	−	0.999300i	0.252981	−	0.0400683i
$623$	20.2796	+	8.89783i	0.812484	+	0.356484i
$624$		−	24.2004i		−	0.968790i
$625$	21.3562	+	12.9967i	0.854247	+	0.519868i
$626$	−9.15199	−	5.28391i	−0.365787	−	0.211187i
$627$	0.00639625	−	0.122048i	0.000255442	−	0.00487411i
$628$	49.3291	−	39.9459i	1.96845	−	1.59402i
$629$	48.0125	+	34.8832i	1.91439	+	1.39088i
$630$	−28.8732	−	15.6904i	−1.15034	−	0.625120i
$631$	−16.6120	+	12.0693i	−0.661312	+	0.480471i	−0.867106	−	0.498124i	$-0.834022\pi$
$631$	−16.6120	+	12.0693i	−0.661312	+	0.480471i	0.205794	+	0.978595i	$0.434022\pi$
$632$	6.41622	−	23.9457i	0.255224	−	0.952508i
$633$	−13.2246	+	16.3311i	−0.525632	+	0.649102i
$634$	−10.4830	+	49.3185i	−0.416332	+	1.95869i
$635$	5.34981	+	15.3892i	0.212301	+	0.610703i
$636$	−37.1507	−	12.0710i	−1.47312	−	0.478646i
$637$	21.2223	+	3.12616i	0.840860	+	0.123863i
$638$	−0.00218182	−	0.00111169i	−8.63790e−5	−	4.40123e-5i
$639$	−3.73378	−	17.5661i	−0.147706	−	0.694902i
$640$	−38.7207	+	23.4216i	−1.53057	+	0.925820i
$641$	−9.09717	−	1.93366i	−0.359317	−	0.0763751i	0.0247163	−	0.999695i	$-0.492132\pi$
$641$	−9.09717	−	1.93366i	−0.359317	−	0.0763751i	−0.384033	+	0.923319i	$0.625465\pi$
$642$	25.5313	−	9.80055i	1.00764	−	0.386797i
$643$	−10.6811	−	10.6811i	−0.421223	−	0.421223i	0.464402	−	0.885625i	$-0.346269\pi$
$643$	−10.6811	−	10.6811i	−0.421223	−	0.421223i	−0.885625	+	0.464402i	$0.846269\pi$
$644$	40.2193	+	39.7862i	1.58486	+	1.56780i
$645$	6.45211	+	22.2530i	0.254052	+	0.876212i
$646$	5.69727	−	54.2059i	0.224156	−	2.13270i
$647$	−5.43005	+	14.1458i	−0.213477	+	0.556127i	−0.997947	−	0.0640393i	$-0.979602\pi$
$647$	−5.43005	+	14.1458i	−0.213477	+	0.556127i	0.784470	+	0.620167i	$0.212935\pi$
$648$	49.1298	+	2.57478i	1.93000	+	0.101147i
$649$	0.0209698	+	0.0363207i	0.000823135	+	0.00142571i
$650$	−36.0717	+	9.22025i	−1.41485	+	0.361648i
$651$	−34.7461	−	42.4361i	−1.36181	−	1.66320i
$652$	−32.5852	+	16.6030i	−1.27614	+	0.650223i
$653$	−22.6948	−	28.0257i	−0.888116	−	1.09673i	−0.994740	−	0.102432i	$-0.967337\pi$
$653$	−22.6948	−	28.0257i	−0.888116	−	1.09673i	0.106624	−	0.994299i	$-0.465996\pi$
$654$	39.3825	−	17.5342i	1.53998	−	0.685643i
$655$	−22.4751	−	13.9519i	−0.878174	−	0.545145i
$656$	8.57490	−	19.2595i	0.334794	−	0.751959i
$657$	5.40409	−	5.40409i	0.210833	−	0.210833i
$658$	14.6572	−	25.7074i	0.571397	−	1.00218i
$659$	30.6779	−	9.96786i	1.19504	−	0.388293i	0.357107	−	0.934063i	$-0.383763\pi$
$659$	30.6779	−	9.96786i	1.19504	−	0.388293i	0.837935	+	0.545771i	$0.183763\pi$
$660$	0.202990	+	0.267728i	0.00790136	+	0.0104213i
$661$	−13.5393	+	12.1908i	−0.526618	+	0.474169i	−0.889030	−	0.457849i	$-0.848620\pi$
$661$	−13.5393	+	12.1908i	−0.526618	+	0.474169i	0.362412	+	0.932018i	$0.381953\pi$
$662$	21.0312	+	32.3852i	0.817400	+	1.25869i
$663$	49.6975	−	2.60454i	1.93009	−	0.101152i
$664$	12.4994	−	38.4692i	0.485071	−	1.49290i
$665$	−17.3600	+	7.18341i	−0.673193	+	0.278561i
$666$	−14.4216	−	44.3852i	−0.558827	−	1.71989i
$667$	0.118162	+	0.307822i	0.00457525	+	0.0119189i
$668$	−28.5007	+	7.63675i	−1.10273	+	0.295475i
$669$	17.0070	−	1.78751i	0.657530	−	0.0691092i
$670$	0.305105	+	1.70096i	0.0117872	+	0.0657137i
$671$	−0.131290	+	0.180705i	−0.00506839	+	0.00697604i
$672$	−4.12508	−	3.67400i	−0.159128	−	0.141728i
$673$	−8.71675	−	17.1076i	−0.336006	−	0.659449i	0.659750	−	0.751485i	$-0.270662\pi$
$673$	−8.71675	−	17.1076i	−0.336006	−	0.659449i	−0.995756	+	0.0920367i	$0.970662\pi$
$674$	−53.8205	+	31.0733i	−2.07309	+	1.19690i
$675$	−1.61382	−	8.04836i	−0.0621159	−	0.309782i
$676$	−7.04519	+	12.2026i	−0.270969	+	0.469332i
$677$	19.3296	−	29.7649i	0.742895	−	1.14396i	−0.241911	−	0.970299i	$-0.577774\pi$
$677$	19.3296	−	29.7649i	0.742895	−	1.14396i	0.984806	−	0.173660i	$-0.0555593\pi$
$678$	3.49909	+	22.0924i	0.134382	+	0.848453i
$679$	−16.2653	−	8.17698i	−0.624204	−	0.313804i
$680$	41.0457	+	60.4669i	1.57403	+	2.31880i
$681$	24.6108	+	10.9574i	0.943088	+	0.419890i
$682$	0.0949172	+	0.354236i	0.00363457	+	0.0135644i
$683$	−7.41808	−	6.00704i	−0.283845	−	0.229853i	0.476815	−	0.879004i	$-0.341791\pi$
$683$	−7.41808	−	6.00704i	−0.283845	−	0.229853i	−0.760660	+	0.649151i	$0.775124\pi$
$684$	−18.9650	+	21.0627i	−0.725143	+	0.805353i
$685$	6.66673	−	3.13274i	0.254723	−	0.119696i
$686$	−34.5085	+	28.8848i	−1.31754	+	1.10283i
$687$	−28.1201	+	55.1888i	−1.07285	+	2.10558i
$688$	−0.810168	−	15.4589i	−0.0308874	−	0.589366i
$689$	−8.92332	−	9.91036i	−0.339952	−	0.377554i
$690$	5.76152	−	68.1720i	0.219337	−	2.59526i
$691$	−37.4522	−	33.7221i	−1.42475	−	1.28285i	−0.902926	−	0.429796i	$-0.858585\pi$
$691$	−37.4522	−	33.7221i	−1.42475	−	1.28285i	−0.521823	−	0.853054i	$-0.674748\pi$
$692$	−14.2938	+	90.2473i	−0.543367	+	3.43069i
$693$	−0.0590617	+	0.0822238i	−0.00224357	+	0.00312342i
$694$	−21.6421	−	29.7878i	−0.821524	−	1.13073i
$695$	9.15148	+	4.43008i	0.347135	+	0.168042i
$696$	0.260504	+	0.585101i	0.00987437	+	0.0221782i
$697$	40.4740	+	15.5365i	1.53306	+	0.588487i
$698$	−3.03494	−	1.97091i	−0.114874	−	0.0746002i
$699$	−50.2276			−1.89978
$700$	23.7299	−	45.8746i	0.896907	−	1.73390i
$701$	41.2864			1.55936			0.779682	−	0.626176i	$-0.215381\pi$
$701$	41.2864			1.55936			0.779682	+	0.626176i	$0.215381\pi$
$702$	10.2525	+	6.65804i	0.386955	+	0.251291i
$703$	−24.9099	−	9.56202i	−0.939495	−	0.360638i
$704$	0.0617943	+	0.138792i	0.00232896	+	0.00523093i
$705$	−23.2925	+	4.17803i	−0.877244	+	0.157354i
$706$	−13.4251	−	18.4781i	−0.505261	−	0.695431i
$707$	−11.5497	−	25.5677i	−0.434371	−	0.961571i
$708$	3.51827	−	22.2135i	0.132225	−	0.834834i
$709$	1.43178	+	1.28918i	0.0537715	+	0.0484161i	0.695578	−	0.718450i	$-0.255148\pi$
$709$	1.43178	+	1.28918i	0.0537715	+	0.0484161i	−0.641807	+	0.766866i	$0.721815\pi$
$710$	41.5623	−	9.72475i	1.55981	−	0.364963i
$711$	−8.19493	−	9.10139i	−0.307334	−	0.341329i
$712$	2.02700	+	38.6775i	0.0759651	+	1.44950i
$713$	22.4185	−	43.9987i	0.839578	−	1.64777i
$714$	−65.2617	+	81.4895i	−2.44236	+	3.04967i
$715$	0.0143147	+	0.113805i	0.000535338	+	0.00425606i
$716$	−35.5957	+	39.5330i	−1.33027	+	1.47742i
$717$	7.62472	+	6.17437i	0.284750	+	0.230586i
$718$	−3.86356	−	14.4190i	−0.144187	−	0.538112i
$719$	44.2991	+	19.7232i	1.65208	+	0.735552i	0.999749	−	0.0223865i	$-0.00712643\pi$
$719$	44.2991	+	19.7232i	1.65208	+	0.735552i	0.652327	+	0.757938i	$0.273793\pi$
$720$	0.560930	−	17.5482i	0.0209046	−	0.653981i
$721$	0.577936	−	0.0334263i	0.0215235	−	0.00124486i
$722$	−3.38876	−	21.3958i	−0.126117	−	0.796270i
$723$	−0.205633	+	0.316647i	−0.00764756	+	0.0117762i
$724$	11.2262	−	19.4443i	0.417217	−	0.722641i
$725$	0.236109	−	0.186724i	0.00876887	−	0.00693476i
$726$	−53.2178	+	30.7253i	−1.97510	+	1.14032i
$727$	−3.31875	−	6.51342i	−0.123086	−	0.241569i	0.821239	−	0.570584i	$-0.193283\pi$
$727$	−3.31875	−	6.51342i	−0.123086	−	0.241569i	−0.944325	+	0.329015i	$0.893283\pi$
$728$	11.7861	+	35.6168i	0.436823	+	1.32005i
$729$	7.63022	−	10.5021i	0.282601	−	0.388967i
$730$	13.1042	+	12.5800i	0.485007	+	0.465607i
$731$	31.6591	−	3.32750i	1.17095	−	0.123072i
$732$	115.699	−	31.0015i	4.27636	−	1.14585i
$733$	3.69327	+	9.62129i	0.136414	+	0.355371i	0.984722	−	0.174132i	$-0.0557119\pi$
$733$	3.69327	+	9.62129i	0.136414	+	0.355371i	−0.848308	+	0.529503i	$0.822379\pi$
$734$	27.0939	+	83.3864i	1.00005	+	3.07785i
$735$	35.4169	+	6.37924i	1.30637	+	0.235302i
$736$	1.53691	−	4.73012i	0.0566512	−	0.174354i
$737$	0.00531660		0.000278631i	0.000195839		1.02635e-5i
$738$	−18.5681	−	28.5924i	−0.683502	−	1.05250i
$739$	16.3525	−	14.7239i	0.601537	−	0.541626i	−0.311111	−	0.950374i	$-0.600701\pi$
$739$	16.3525	−	14.7239i	0.601537	−	0.541626i	0.912648	+	0.408747i	$0.134034\pi$
$740$	69.2845	−	24.0856i	2.54695	−	0.885405i
$741$	−21.2794	+	6.91411i	−0.781720	+	0.253996i
$742$	27.9760	−	0.151440i	1.02703	−	0.00555953i
$743$	−32.3075	+	32.3075i	−1.18525	+	1.18525i	−0.206883	+	0.978366i	$0.566332\pi$
$743$	−32.3075	+	32.3075i	−1.18525	+	1.18525i	−0.978366	+	0.206883i	$0.933668\pi$
$744$	39.0144	−	87.6278i	1.43034	−	3.21259i
$745$	−15.3438	−	37.6567i	−0.562152	−	1.37963i
$746$	41.2660	−	18.3728i	1.51086	−	0.672676i
$747$	−12.5756	−	15.5296i	−0.460119	−	0.568199i
$748$	0.411303	−	0.209569i	0.0150387	−	0.00766262i
$749$	−10.0211	+	8.20512i	−0.366162	+	0.299809i
$750$	−60.9773	+	13.5267i	−2.22658	+	0.493924i
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	0.591254	−	0.806485i	$-0.298633\pi$
$751$	−11.0388	−	19.1197i	−0.402810	−	0.697687i	−0.994064	+	0.108798i	$0.965300\pi$
$752$	15.7890	+	0.827466i	0.575765	+	0.0301746i
$753$	−0.109010	+	0.283980i	−0.00397253	+	0.0103488i
$754$	−0.0468599	+	0.445842i	−0.00170654	+	0.0162366i
$755$	33.3790	+	25.9202i	1.21479	+	0.943332i
$756$	−16.3566	+	4.47778i	−0.594885	+	0.162855i
$757$	2.36580	+	2.36580i	0.0859865	+	0.0859865i	0.748792	−	0.662805i	$-0.230634\pi$
$757$	2.36580	+	2.36580i	0.0859865	+	0.0859865i	−0.662805	+	0.748792i	$0.730634\pi$
$758$	−50.4951	+	19.3833i	−1.83406	+	0.704032i
$759$	−0.206165	−	0.0438218i	−0.00748332	−	0.00159063i
$760$	−24.8614	−	21.4831i	−0.901818	−	0.779276i
$761$	−7.78209	−	36.6118i	−0.282101	−	1.32718i	−0.859675	−	0.510841i	$-0.829334\pi$
$761$	−7.78209	−	36.6118i	−0.282101	−	1.32718i	0.577575	−	0.816338i	$-0.303999\pi$
$762$	−36.2686	−	18.4798i	−1.31387	−	0.669451i
$763$	−15.0981	+	13.7431i	−0.546589	+	0.497535i
$764$	−55.0239	−	17.8784i	−1.99070	−	0.646816i
$765$	36.0970	−	0.736683i	1.30509	−	0.0266348i
$766$	−7.77758	+	36.5906i	−0.281015	+	1.32207i
$767$	4.83197	−	5.96698i	0.174472	−	0.215455i
$768$	18.4604	−	68.8951i	0.666132	−	2.48604i
$769$	−31.5396	+	22.9148i	−1.13735	+	0.826330i	−0.986747	−	0.162264i	$-0.948120\pi$
$769$	−31.5396	+	22.9148i	−1.13735	+	0.826330i	−0.150599	+	0.988595i	$0.548120\pi$
$770$	−0.198258	−	0.136365i	−0.00714473	−	0.00491424i
$771$	17.0932	+	12.4189i	0.615596	+	0.447257i
$772$	−50.4876	+	40.8841i	−1.81709	+	1.47145i
$773$	−1.21669	+	23.2158i	−0.0437612	+	0.835014i	0.885285	+	0.465049i	$0.153963\pi$
$773$	−1.21669	+	23.2158i	−0.0437612	+	0.835014i	−0.929046	+	0.369964i	$0.879370\pi$
$774$	−21.6795	−	12.5167i	−0.779254	−	0.449902i
$775$	−44.4430	−	7.56620i	−1.59644	−	0.271786i
$776$		−	31.8387i		−	1.14294i
$777$	30.2643	+	41.1845i	1.08573	+	1.47749i
$778$	28.6099	−	4.53136i	1.02571	−	0.162457i
$779$	−19.3848	−	2.03743i	−0.694534	−	0.0729984i
$780$	32.4410	−	52.2592i	1.16157	−	1.87118i
$781$	−0.0137457	−	0.130782i	−0.000491861	−	0.00467975i
$782$	−90.7949	−	24.3284i	−3.24682	−	0.869983i
$783$	−0.0976210	−	0.0154617i	−0.00348869	−	0.000552554i
$784$	−22.0696	−	9.54110i	−0.788201	−	0.340754i
$785$	36.0692	−	4.53687i	1.28736	−	0.161928i
$786$	64.6466	−	13.7411i	2.30587	−	0.490127i
$787$	−13.8453	+	8.99124i	−0.493531	+	0.320503i	−0.767295	−	0.641294i	$-0.778398\pi$
$787$	−13.8453	+	8.99124i	−0.493531	+	0.320503i	0.273764	+	0.961797i	$0.411731\pi$
$788$	−50.9422	+	33.0822i	−1.81474	+	1.17851i
$789$	−47.0414	+	9.99896i	−1.67472	+	0.355972i
$790$	21.2308	−	19.9156i	0.755358	−	0.708564i
$791$	−4.86024	−	9.41245i	−0.172810	−	0.334668i
$792$	−0.174874	−	0.0276973i	−0.00621388	−	0.000984182i
$793$	39.4989	+	10.5837i	1.40265	+	0.375838i
$794$	1.72174	+	16.3812i	0.0611022	+	0.581349i
$795$	−14.4310	−	17.0954i	−0.511814	−	0.606312i
$796$	−7.67997	−	0.807198i	−0.272209	−	0.0286104i
$797$	−43.0687	+	6.82142i	−1.52557	+	0.241627i	−0.862164	−	0.506630i	$-0.830891\pi$
$797$	−43.0687	+	6.82142i	−1.52557	+	0.241627i	−0.663409	+	0.748257i	$0.730891\pi$
$798$	18.8592	−	42.9832i	0.667609	−	1.52159i
$799$			32.5131i			1.15023i
$800$	−4.54030	−	0.0524369i	−0.160524	−	0.00185393i
$801$	16.5705	+	9.56698i	0.585490	+	0.338033i
$802$	2.32531	−	44.3695i	0.0821095	−	1.56674i
$803$	0.0434914	−	0.0352186i	0.00153478	−	0.00124284i
$804$	−2.30973	−	1.67811i	−0.0814578	−	0.0591825i
$805$	7.55244	+	31.5083i	0.266189	+	1.11052i
$806$	54.3169	−	39.4635i	1.91323	−	1.39004i
$807$	0.900061	−	3.35907i	0.0316836	−	0.118245i
$808$	30.8782	−	38.1313i	1.08629	−	1.34146i
$809$	3.06134	−	14.4025i	0.107631	−	0.506364i	−0.890997	−	0.454008i	$-0.849994\pi$
$809$	3.06134	−	14.4025i	0.107631	−	0.506364i	0.998628	−	0.0523559i	$-0.0166730\pi$
$810$	47.4193	+	32.9951i	1.66614	+	1.15933i
$811$	24.6251	+	8.00118i	0.864704	+	0.280959i	0.707592	−	0.706621i	$-0.249782\pi$
$811$	24.6251	+	8.00118i	0.864704	+	0.280959i	0.157112	+	0.987581i	$0.449782\pi$
$812$	−0.418623	−	0.459897i	−0.0146908	−	0.0161392i
$813$	−18.6144	−	9.48450i	−0.652835	−	0.332636i
$814$	−0.0710517	−	0.334272i	−0.00249036	−	0.0117162i
$815$	−20.8708	−	1.76388i	−0.731071	−	0.0617862i
$816$	−54.5610	−	11.5973i	−1.91002	−	0.405986i
$817$	−13.3616	+	5.12904i	−0.467464	+	0.179442i
$818$	−27.3344	−	27.3344i	−0.955725	−	0.955725i
$819$	17.9282	+	4.69998i	0.626463	+	0.164231i
$820$	44.3347	−	30.0950i	1.54823	−	1.05096i
$821$	−5.12351	+	48.7470i	−0.178812	+	1.70128i	0.425846	+	0.904796i	$0.359977\pi$
$821$	−5.12351	+	48.7470i	−0.178812	+	1.70128i	−0.604657	+	0.796486i	$0.706690\pi$
$822$	−6.59517	+	17.1810i	−0.230033	+	0.599256i
$823$	−52.8866	−	2.77167i	−1.84351	−	0.0966142i	−0.901618	−	0.432533i	$-0.857620\pi$
$823$	−52.8866	−	2.77167i	−1.84351	−	0.0966142i	−0.941891	+	0.335918i	$0.890953\pi$
$824$	0.506220	+	0.876799i	0.0176350	+	0.0305447i
$825$	0.0179024	+	0.191589i	0.000623282	+	0.00667028i
$826$	2.60585	+	15.8953i	0.0906690	+	0.553068i
$827$	4.78458	−	2.43786i	0.166376	−	0.0847728i	−0.368819	−	0.929501i	$-0.620238\pi$
$827$	4.78458	−	2.43786i	0.166376	−	0.0847728i	0.535196	+	0.844728i	$0.320238\pi$
$828$	30.7609	+	37.9865i	1.06901	+	1.32012i
$829$	−32.0214	+	14.2568i	−1.11215	+	0.495161i	−0.878780	−	0.477228i	$-0.841642\pi$
$829$	−32.0214	+	14.2568i	−1.11215	+	0.495161i	−0.233369	+	0.972388i	$0.574975\pi$
$830$	36.2942	−	30.6375i	1.25979	−	1.06344i
$831$	12.7778	−	28.6994i	0.443257	−	0.995571i
$832$	19.6675	−	19.6675i	0.681847	−	0.681847i
$833$	17.2183	−	46.3488i	0.596577	−	1.60589i
$834$	−24.1587	+	7.84964i	−0.836548	+	0.271811i
$835$	−16.1750	−	4.89301i	−0.559757	−	0.169330i
$836$	−0.154233	+	0.138872i	−0.00533427	+	0.00480300i
$837$	8.06201	+	12.4144i	0.278664	+	0.429105i
$838$	86.2499	−	4.52017i	2.97945	−	0.156147i
$839$	−4.17081	+	12.8364i	−0.143992	+	0.443163i	−0.996880	−	0.0789314i	$-0.974849\pi$
$839$	−4.17081	+	12.8364i	−0.143992	+	0.443163i	0.852888	+	0.522095i	$0.174849\pi$
$840$	17.8534	+	60.3520i	0.616000	+	2.08234i
$841$	8.96037	+	27.5772i	0.308978	+	0.950938i
$842$	−12.2359	−	31.8755i	−0.421675	−	1.09850i
$843$	8.85167	−	2.37180i	0.304868	−	0.0816891i
$844$	35.4900	−	3.73015i	1.22162	−	0.128397i
$845$	−7.11407	+	3.80960i	−0.244731	+	0.131054i
$846$	15.0284	−	20.6848i	0.516686	−	0.711158i
$847$	19.3560	−	21.7325i	0.665081	−	0.746737i
$848$	6.78594	+	13.3182i	0.233030	+	0.457347i
$849$	−37.6256	+	21.7232i	−1.29131	+	0.745537i
$850$	3.50126	+	85.7441i	0.120092	+	2.94100i
$851$	−23.0079	+	39.8508i	−0.788699	+	1.36607i
$852$	−38.4075	+	59.1423i	−1.31582	+	2.02618i
$853$	5.33840	+	33.7053i	0.182783	+	1.15405i	0.892997	+	0.450063i	$0.148598\pi$
$853$	5.33840	+	33.7053i	0.182783	+	1.15405i	−0.710214	+	0.703986i	$0.751402\pi$
$854$	−71.6923	+	47.1112i	−2.45326	+	1.61211i
$855$	−15.5904	+	4.52033i	−0.533181	+	0.154592i
$856$	−20.6929	−	9.21306i	−0.707268	−	0.314896i
$857$	1.77688	+	6.63141i	0.0606971	+	0.226525i	0.989611	−	0.143771i	$-0.0459230\pi$
$857$	1.77688	+	6.63141i	0.0606971	+	0.226525i	−0.928914	+	0.370296i	$0.879256\pi$
$858$	−0.222706	−	0.180344i	−0.00760305	−	0.00615683i
$859$	29.6526	−	32.9326i	1.01174	−	1.12365i	0.0194321	−	0.999811i	$-0.493814\pi$
$859$	29.6526	−	32.9326i	1.01174	−	1.12365i	0.992303	−	0.123834i	$-0.0395192\pi$
$860$	18.9735	−	34.4686i	0.646990	−	1.17537i
$861$	29.1419	+	23.3386i	0.993152	+	0.795376i
$862$	4.19824	−	8.23950i	0.142993	−	0.280639i
$863$	0.105676	+	2.01642i	0.00359726	+	0.0686398i	0.999838	−	0.0179852i	$-0.00572516\pi$
$863$	0.105676	+	2.01642i	0.00359726	+	0.0686398i	−0.996241	+	0.0866249i	$0.972392\pi$
$864$	0.997589	+	1.10794i	0.0339387	+	0.0376927i
$865$	−34.2154	+	39.5959i	−1.16336	+	1.34630i
$866$	2.24014	+	2.01703i	0.0761230	+	0.0685415i
$867$	11.8297	−	74.6900i	0.401759	−	2.53661i
$868$	−9.23402	+	92.6791i	−0.313423	+	3.14573i
$869$	−0.0527129	−	0.0725531i	−0.00178816	−	0.00246119i
$870$	−0.102468	+	0.745052i	−0.00347399	+	0.0252596i
$871$	−0.396434	−	0.890406i	−0.0134327	−	0.0301703i
$872$	−33.3345	−	12.7959i	−1.12885	−	0.433324i
$873$	−13.1916	−	8.56673i	−0.446468	−	0.289940i
$874$	42.2612			1.42950
$875$	25.4037	−	15.1542i	0.858802	−	0.512307i
$876$	−30.0106			−1.01396
$877$	−39.3610	−	25.5614i	−1.32913	−	0.863146i	−0.332334	−	0.943162i	$-0.607836\pi$
$877$	−39.3610	−	25.5614i	−1.32913	−	0.863146i	−0.996794	+	0.0800162i	$0.974503\pi$
$878$	−12.3548	−	4.74256i	−0.416954	−	0.160054i
$879$	6.53998	+	14.6890i	0.220588	+	0.495449i
$880$	0.0175166	−	0.127364i	0.000590485	−	0.00429345i
$881$	−12.9945	−	17.8855i	−0.437797	−	0.602576i	0.531924	−	0.846792i	$-0.321469\pi$
$881$	−12.9945	−	17.8855i	−0.437797	−	0.602576i	−0.969721	+	0.244216i	$0.921469\pi$
$882$	−32.3778	+	21.5283i	−1.09022	+	0.724896i
$883$	2.48456	−	15.6869i	0.0836122	−	0.527906i	−0.909959	−	0.414698i	$-0.863887\pi$
$883$	2.48456	−	15.6869i	0.0836122	−	0.527906i	0.993571	−	0.113208i	$-0.0361128\pi$
$884$	−62.8034	−	56.5485i	−2.11231	−	1.90193i
$885$	8.42180	−	9.74614i	0.283096	−	0.327613i
$886$	29.7457	+	33.0360i	0.999327	+	1.10986i
$887$	0.918554	+	17.5270i	0.0308420	+	0.588501i	0.969715	+	0.244238i	$0.0785378\pi$
$887$	0.918554	+	17.5270i	0.0308420	+	0.588501i	−0.938873	+	0.344263i	$0.888129\pi$
$888$	−40.5794	+	79.6415i	−1.36175	+	2.67259i
$889$	19.0564	+	2.91258i	0.639130	+	0.0976848i
$890$	−21.9310	+	39.8416i	−0.735130	+	1.33549i
$891$	0.119088	−	0.132260i	0.00398958	−	0.00443088i
$892$	−22.5682	−	18.2753i	−0.755638	−	0.611904i
$893$	−3.78336	−	14.1197i	−0.126605	−	0.472498i
$894$	92.8081	+	41.3208i	3.10397	+	1.38198i
$895$	−29.2619	+	8.48429i	−0.978117	+	0.283598i
$896$	3.09170	+	53.4551i	0.103287	+	1.78581i
$897$	6.03632	+	38.1118i	0.201547	+	1.27252i
$898$	−9.64664	+	14.8545i	−0.321912	+	0.495702i
$899$	−0.271415	+	0.470104i	−0.00905219	+	0.0156789i
$900$	24.7349	−	37.1422i	0.824497	−	1.23807i
$901$	−26.6196	+	15.3689i	−0.886829	+	0.512011i
$902$	−0.113336	−	0.222435i	−0.00377369	−	0.00740629i
$903$	26.8459	+	5.55457i	0.893377	+	0.184844i
$904$	10.8896	−	14.9882i	0.362182	−	0.498500i
$905$	11.3359	−	6.07041i	0.376818	−	0.201787i
$906$	−105.006	+	11.0366i	−3.48860	+	0.366667i
$907$	−28.7163	+	7.69450i	−0.953508	+	0.255492i	−0.701850	−	0.712325i	$-0.747642\pi$
$907$	−28.7163	+	7.69450i	−0.953508	+	0.255492i	−0.251658	+	0.967816i	$0.580976\pi$
$908$	−16.3947	−	42.7097i	−0.544078	−	1.41737i
$909$	−7.49054	−	23.0535i	−0.248445	−	0.764636i
$910$	−10.2994	+	42.8320i	−0.341422	+	1.41987i
$911$	12.1969	−	37.5382i	0.404101	−	1.24370i	−0.517542	−	0.855658i	$-0.673153\pi$
$911$	12.1969	−	37.5382i	0.404101	−	1.24370i	0.921643	−	0.388038i	$-0.126847\pi$
$912$	25.0441	−	1.31251i	0.829293	−	0.0434614i
$913$	−0.0796949	−	0.122719i	−0.00263752	−	0.00406142i
$914$	21.3387	−	19.2135i	0.705822	−	0.635525i
$915$	65.6624	+	19.8632i	2.17073	+	0.656658i
$916$	100.036	−	32.5036i	3.30528	−	1.07395i
$917$	−27.0216	+	15.7966i	−0.892331	+	0.521648i
$918$	19.9241	−	19.9241i	0.657593	−	0.657593i
$919$	6.01760	−	13.5158i	0.198502	−	0.445844i	−0.786678	−	0.617363i	$-0.788201\pi$
$919$	6.01760	−	13.5158i	0.198502	−	0.445844i	0.985181	+	0.171519i	$0.0548676\pi$
$920$	−43.3007	+	36.5520i	−1.42758	+	1.20508i
$921$	14.1529	−	6.30127i	0.466353	−	0.207634i
$922$	−1.30162	−	1.60736i	−0.0428664	−	0.0529356i
$923$	−21.4508	+	10.9297i	−0.706061	+	0.359756i
$924$	0.392301	−	0.0643132i	0.0129058	−	0.00211575i
$925$	40.9885	+	9.20837i	1.34769	+	0.302769i
$926$	46.9570	+	81.3318i	1.54310	+	2.67273i
$927$	0.499488	+	0.0261771i	0.0164053	+	0.000859767i
$928$	−0.0195929	+	0.0510413i	−0.000643169	+	0.00167551i
$929$	1.81026	−	17.2234i	0.0593925	−	0.565082i	−0.923847	−	0.382763i	$-0.874973\pi$
$929$	1.81026	−	17.2234i	0.0593925	−	0.565082i	0.983239	−	0.182320i	$-0.0583606\pi$
$930$	93.1908	−	63.2591i	3.05585	−	2.07435i
$931$	−2.08416	+	22.1318i	−0.0683056	+	0.725341i
$932$	60.3124	+	60.3124i	1.97560	+	1.97560i
$933$	−5.64278	+	2.16606i	−0.184736	+	0.0709136i
$934$	−21.2562	−	4.51814i	−0.695523	−	0.147838i
$935$	0.263439	+	0.0222644i	0.00861538	+	0.000728125i
$936$	6.73928	+	31.7058i	0.220280	+	1.03634i
$937$	29.8820	+	15.2256i	0.976202	+	0.497400i	0.867911	−	0.496719i	$-0.165462\pi$
$937$	29.8820	+	15.2256i	0.976202	+	0.497400i	0.108291	+	0.994119i	$0.465462\pi$
$938$	1.94804	+	0.621317i	0.0636056	+	0.0202867i
$939$	9.50975	+	3.08990i	0.310339	+	0.100835i
$940$	32.9861	+	22.9523i	1.07589	+	0.748621i
$941$	9.06149	−	42.6310i	0.295396	−	1.38973i	−0.540732	−	0.841195i	$-0.681853\pi$
$941$	9.06149	−	42.6310i	0.295396	−	1.38973i	0.836128	−	0.548534i	$-0.184814\pi$
$942$	−57.1579	+	70.5841i	−1.86230	+	2.29975i
$943$	−8.70021	+	32.4696i	−0.283318	+	1.05736i
$944$	−6.96237	+	5.05846i	−0.226606	+	0.164639i
$945$	−9.31155	−	2.76186i	−0.302905	−	0.0898434i
$946$	−0.148300	−	0.107746i	−0.00482164	−	0.00350312i
$947$	−4.28310	+	3.46839i	−0.139182	+	0.112707i	−0.696383	−	0.717670i	$-0.745209\pi$
$947$	−4.28310	+	3.46839i	−0.139182	+	0.112707i	0.557201	+	0.830378i	$0.311875\pi$
$948$	−2.51693	+	48.0259i	−0.0817462	+	1.55981i
$949$	−8.87279	−	5.12271i	−0.288023	−	0.166290i
$950$	−11.4981	−	36.8293i	−0.373047	−	1.19490i
$951$		−	47.7071i		−	1.54701i
$952$	85.9480	−	9.50416i	2.78559	−	0.308032i
$953$	−6.68823	+	1.05931i	−0.216653	+	0.0343145i	−0.263817	−	0.964573i	$-0.584982\pi$
$953$	−6.68823	+	1.05931i	−0.216653	+	0.0343145i	0.0471642	+	0.998887i	$0.484982\pi$
$954$	24.0393	+	2.52663i	0.778300	+	0.0818026i
$955$	−21.3738	−	25.3201i	−0.691638	−	0.819338i
$956$	−1.74155	−	16.5697i	−0.0563257	−	0.535903i
$957$	0.00223799		0.000599669i	7.23441e−5		1.93845e-5i
$958$	2.32607	+	0.368413i	0.0751518	+	0.0119029i
$959$	0.409023	−	8.70608i	0.0132080	−	0.281134i
$960$	34.0315	−	31.9232i	1.09836	−	1.03032i
$961$	49.1979	−	10.4573i	1.58703	−	0.337333i
$962$	−52.4706	+	34.0748i	−1.69172	+	1.09862i
$963$	−9.38497	+	6.09467i	−0.302426	+	0.196398i
$964$	0.627144	−	0.133304i	0.0201989	−	0.00429342i
$965$	−36.9163	+	4.64342i	−1.18838	+	0.149477i
$966$	−68.1278	−	43.7202i	−2.19198	−	1.40668i
$967$	−57.0421	−	9.03458i	−1.83435	−	0.290533i	−0.859128	−	0.511760i	$-0.828994\pi$
$967$	−57.0421	−	9.03458i	−1.83435	−	0.290533i	−0.975222	+	0.221228i	$0.928994\pi$
$968$	49.1630	+	13.1732i	1.58016	+	0.423403i
$969$	5.39069	+	51.2890i	0.173174	+	1.64764i
$970$	19.7179	−	31.7636i	0.633105	−	1.01987i
$971$	−19.5233	−	2.05199i	−0.626534	−	0.0658514i	−0.214060	−	0.976821i	$-0.568669\pi$
$971$	−19.5233	−	2.05199i	−0.626534	−	0.0658514i	−0.412474	+	0.910969i	$0.635335\pi$
$972$	−75.2723	+	11.9220i	−2.41436	+	0.382397i
$973$	9.69420	−	7.12374i	0.310782	−	0.228377i
$974$		−	84.2473i		−	2.69946i
$975$	31.5710	−	15.6296i	1.01108	−	0.500548i
$976$	−39.6935	−	22.9170i	−1.27056	−	0.733556i
$977$	−1.28796	+	24.5758i	−0.0412056	+	0.786249i	0.897392	+	0.441235i	$0.145459\pi$
$977$	−1.28796	+	24.5758i	−0.0412056	+	0.786249i	−0.938597	+	0.345014i	$0.887874\pi$
$978$	40.6674	−	32.9318i	1.30040	−	1.05304i
$979$	0.113351	+	0.0823545i	0.00362272	+	0.00263206i
$980$	−34.8680	−	50.1882i	−1.11382	−	1.60320i
$981$	−14.2709	+	10.3684i	−0.455634	+	0.331038i
$982$	−3.21913	+	12.0140i	−0.102727	+	0.383381i
$983$	−28.2657	+	34.9053i	−0.901537	+	1.11331i	0.0915351	+	0.995802i	$0.470823\pi$
$983$	−28.2657	+	34.9053i	−0.901537	+	1.11331i	−0.993072	+	0.117504i	$0.962511\pi$
$984$	−13.5758	+	63.8690i	−0.432780	+	2.03607i
$985$	−34.7808	+	0.709822i	−1.10821	+	0.0226168i
$986$	0.982717	+	0.319304i	0.0312961	+	0.0101687i
$987$	−8.50816	+	26.6759i	−0.270818	+	0.849103i
$988$	33.8543	+	17.2496i	1.07705	+	0.548784i
$989$	5.13183	+	24.1433i	0.163183	+	0.767714i
$990$	−0.157308	−	0.135933i	−0.00499959	−	0.00432023i
$991$	45.3163	+	9.63229i	1.43952	+	0.305980i	0.860549	−	0.509368i	$-0.170121\pi$
$991$	45.3163	+	9.63229i	1.43952	+	0.305980i	0.578972	+	0.815347i	$0.303454\pi$
$992$	7.64421	−	2.93434i	0.242704	−	0.0931653i
$993$	−25.8356	−	25.8356i	−0.819867	−	0.819867i
$994$	12.8075	−	48.8545i	0.406229	−	1.54957i
$995$	−3.49318	−	2.71260i	−0.110741	−	0.0859952i
$996$	−8.20219	+	78.0386i	−0.259896	+	2.47275i
$997$	8.86960	−	23.1061i	0.280903	−	0.731778i	−0.718442	−	0.695587i	$-0.755144\pi$
$997$	8.86960	−	23.1061i	0.280903	−	0.731778i	0.999345	−	0.0361906i	$-0.0115223\pi$
$998$	88.4014	+	4.63292i	2.79830	+	0.146653i
$999$	−6.89686	−	11.9457i	−0.218207	−	0.377946i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.122.18	yes	288
5.2	odd	4		875.2.bb.a.493.1		288
5.3	odd	4		875.2.bb.b.493.18		288
5.4	even	2		875.2.bb.c.507.1		288
7.5	odd	6	inner	175.2.x.a.47.18	yes	288
25.6	even	5		875.2.bb.b.857.1		288
25.8	odd	20	inner	175.2.x.a.108.18	yes	288
25.17	odd	20		875.2.bb.c.143.1		288
25.19	even	10		875.2.bb.a.857.18		288
35.12	even	12		875.2.bb.a.243.18		288
35.19	odd	6		875.2.bb.c.257.1		288
35.33	even	12		875.2.bb.b.243.1		288
175.19	odd	30		875.2.bb.a.607.1		288
175.33	even	60	inner	175.2.x.a.33.18	✓	288
175.117	even	60		875.2.bb.c.768.1		288
175.131	odd	30		875.2.bb.b.607.18		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.18	✓	288	175.33	even	60	inner
175.2.x.a.47.18	yes	288	7.5	odd	6	inner
175.2.x.a.108.18	yes	288	25.8	odd	20	inner
175.2.x.a.122.18	yes	288	1.1	even	1	trivial
875.2.bb.a.243.18		288	35.12	even	12
875.2.bb.a.493.1		288	5.2	odd	4
875.2.bb.a.607.1		288	175.19	odd	30
875.2.bb.a.857.18		288	25.19	even	10
875.2.bb.b.243.1		288	35.33	even	12
875.2.bb.b.493.18		288	5.3	odd	4
875.2.bb.b.607.18		288	175.131	odd	30
875.2.bb.b.857.1		288	25.6	even	5
875.2.bb.c.143.1		288	25.17	odd	20
875.2.bb.c.257.1		288	35.19	odd	6
875.2.bb.c.507.1		288	5.4	even	2
875.2.bb.c.768.1		288	175.117	even	60

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.03786 + 1.32340i) q^{2} +(-2.14641 - 0.823930i) q^{3} +(1.58801 + 3.56673i) q^{4} +(-0.304662 + 2.21522i) q^{5} +(-3.28370 - 4.51962i) q^{6} +(2.14884 + 1.54352i) q^{7} +(-0.723845 + 4.57018i) q^{8} +(1.69878 + 1.52959i) q^{9} +O(q^{10})\)	\(q+(2.03786 + 1.32340i) q^{2} +(-2.14641 - 0.823930i) q^{3} +(1.58801 + 3.56673i) q^{4} +(-0.304662 + 2.21522i) q^{5} +(-3.28370 - 4.51962i) q^{6} +(2.14884 + 1.54352i) q^{7} +(-0.723845 + 4.57018i) q^{8} +(1.69878 + 1.52959i) q^{9} +(-3.55248 + 4.11111i) q^{10} +(0.0112005 + 0.0124395i) q^{11} +(-0.469788 - 8.96408i) q^{12} +(1.39124 - 2.73047i) q^{13} +(2.33634 + 5.98928i) q^{14} +(2.47911 - 4.50374i) q^{15} +(-2.29834 + 2.55257i) q^{16} +(-5.48928 - 4.44513i) q^{17} +(1.43762 + 5.36527i) q^{18} +(2.90112 + 1.29166i) q^{19} +(-8.38489 + 2.43114i) q^{20} +(-3.34055 - 5.08353i) q^{21} +(0.00636273 + 0.0401727i) q^{22} +(2.98285 - 4.59318i) q^{23} +(5.31918 - 9.21308i) q^{24} +(-4.81436 - 1.34978i) q^{25} +(6.44868 - 3.72315i) q^{26} +(0.745322 + 1.46278i) q^{27} +(-2.09295 + 10.1155i) q^{28} +(-0.0353871 + 0.0487062i) q^{29} +(11.0124 - 5.89714i) q^{30} +(8.96709 - 0.942479i) q^{31} +(0.877177 - 0.235039i) q^{32} +(-0.0137917 - 0.0359286i) q^{33} +(-5.30369 - 16.3231i) q^{34} +(-4.07391 + 4.28990i) q^{35} +(-2.75796 + 8.48811i) q^{36} +(-8.39052 + 0.439728i) q^{37} +(4.20270 + 6.47159i) q^{38} +(-5.23590 + 4.71442i) q^{39} +(-9.90340 - 2.99583i) q^{40} +(-5.83738 + 1.89668i) q^{41} +(-0.0800095 - 14.7804i) q^{42} +(-3.18681 + 3.18681i) q^{43} +(-0.0265816 + 0.0597034i) q^{44} +(-3.90593 + 3.29716i) q^{45} +(12.1573 - 5.41276i) q^{46} +(-2.89679 - 3.57724i) q^{47} +(7.03633 - 3.58519i) q^{48} +(2.23507 + 6.63359i) q^{49} +(-8.02470 - 9.12201i) q^{50} +(8.11977 + 14.0639i) q^{51} +(11.9482 + 0.626178i) q^{52} +(1.55951 - 4.06266i) q^{53} +(-0.416980 + 3.96730i) q^{54} +(-0.0309685 + 0.0210218i) q^{55} +(-8.60961 + 8.70333i) q^{56} +(-5.16276 - 5.16276i) q^{57} +(-0.136572 + 0.0524250i) q^{58} +(2.45075 + 0.520924i) q^{59} +(20.0005 + 1.69033i) q^{60} +(2.77436 + 13.0523i) q^{61} +(19.5210 + 9.94643i) q^{62} +(1.28946 + 5.90896i) q^{63} +(8.63203 + 2.80472i) q^{64} +(5.62472 + 3.91378i) q^{65} +(0.0194425 - 0.0914696i) q^{66} +(0.200158 - 0.247175i) q^{67} +(7.13755 - 26.6377i) q^{68} +(-10.1869 + 7.40119i) q^{69} +(-13.9793 + 3.35080i) q^{70} +(-6.35569 - 4.61768i) q^{71} +(-8.22016 + 6.65655i) q^{72} +(0.174974 - 3.33870i) q^{73} +(-17.6807 - 10.2079i) q^{74} +(9.22147 + 6.86389i) q^{75} +12.3987i q^{76} +(0.00486761 + 0.0440188i) q^{77} +(-16.9091 + 2.67814i) q^{78} +(-5.32825 - 0.560021i) q^{79} +(-4.95427 - 5.86900i) q^{80} +(-1.11138 - 10.5741i) q^{81} +(-14.4058 - 3.86003i) q^{82} +(-8.63403 - 1.36750i) q^{83} +(12.8268 - 19.9876i) q^{84} +(11.5193 - 10.8057i) q^{85} +(-10.7117 + 2.27684i) q^{86} +(0.116086 - 0.0753869i) q^{87} +(-0.0649580 + 0.0421842i) q^{88} +(8.18738 - 1.74028i) q^{89} +(-12.3232 + 1.55004i) q^{90} +(7.20412 - 3.71994i) q^{91} +(21.1194 + 3.34499i) q^{92} +(-20.0236 - 5.36531i) q^{93} +(-1.16913 - 11.1236i) q^{94} +(-3.74518 + 6.03309i) q^{95} +(-2.07644 - 0.218242i) q^{96} +(-6.79613 + 1.07640i) q^{97} +(-4.22415 + 16.4762i) q^{98} +0.0382642i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9}+O(q^{10}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22} - 40 q^{23} + 2 q^{25} - 48 q^{26} + 22 q^{28} - 58 q^{30} - 18 q^{31} + 8 q^{32} - 30 q^{33} - 2 q^{35} + 40 q^{36} - 10 q^{37} + 72 q^{38} + 30 q^{39} - 48 q^{40} + 6 q^{42} - 108 q^{43} - 10 q^{44} + 186 q^{45} - 6 q^{46} - 54 q^{47} - 248 q^{50} - 16 q^{51} + 216 q^{52} + 50 q^{53} - 30 q^{54} + 4 q^{56} - 216 q^{57} - 4 q^{58} + 90 q^{59} + 96 q^{60} - 18 q^{61} - 66 q^{63} - 100 q^{64} + 14 q^{65} - 90 q^{66} + 4 q^{67} + 342 q^{68} - 60 q^{70} - 24 q^{71} + 58 q^{72} - 6 q^{73} + 216 q^{75} - 80 q^{77} - 132 q^{78} - 10 q^{79} - 6 q^{80} - 10 q^{81} + 216 q^{82} + 20 q^{84} - 48 q^{85} - 6 q^{86} - 48 q^{87} - 122 q^{88} + 120 q^{89} - 12 q^{91} - 4 q^{92} + 106 q^{93} - 30 q^{94} - 98 q^{95} - 90 q^{96} + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more