LMFDB - Embedded newform 175.2.t.a.44.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(4,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([3, 20]))

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

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

chi := DirichletCharacter("175.4");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.t (of order $30$, 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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$18$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			44.18
Character	$\chi$	$=$	175.44
Dual form			175.2.t.a.4.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.537983 - 2.53101i) q^{2} +(-0.0303653 + 0.0682015i) q^{3} +(-4.28951 - 1.90981i) q^{4} +(-2.22433 - 0.228782i) q^{5} +(0.156283 + 0.113546i) q^{6} +(-0.537537 - 2.59057i) q^{7} +(-4.09959 + 5.64260i) q^{8} +(2.00366 + 2.22529i) q^{9} +O(q^{10})$	\(q+(0.537983 - 2.53101i) q^{2} +(-0.0303653 + 0.0682015i) q^{3} +(-4.28951 - 1.90981i) q^{4} +(-2.22433 - 0.228782i) q^{5} +(0.156283 + 0.113546i) q^{6} +(-0.537537 - 2.59057i) q^{7} +(-4.09959 + 5.64260i) q^{8} +(2.00366 + 2.22529i) q^{9} +(-1.77571 + 5.50673i) q^{10} +(2.52729 - 2.80684i) q^{11} +(0.260504 - 0.234559i) q^{12} +(-2.66684 - 0.866509i) q^{13} +(-6.84595 - 0.0331700i) q^{14} +(0.0831458 - 0.144756i) q^{15} +(5.79224 + 6.43293i) q^{16} +(-0.299235 - 0.0314508i) q^{17} +(6.71018 - 3.87412i) q^{18} +(3.68296 - 1.63976i) q^{19} +(9.10437 + 5.22942i) q^{20} +(0.193003 + 0.0420025i) q^{21} +(-5.74450 - 7.90663i) q^{22} +(1.46161 - 6.87632i) q^{23} +(-0.260349 - 0.450937i) q^{24} +(4.89532 + 1.01778i) q^{25} +(-3.62786 + 6.28364i) q^{26} +(-0.425616 + 0.138291i) q^{27} +(-2.64173 + 12.1389i) q^{28} +(2.21189 - 1.60703i) q^{29} +(-0.321648 - 0.288319i) q^{30} +(-0.929782 + 8.84628i) q^{31} +(7.31754 - 4.22478i) q^{32} +(0.114689 + 0.257595i) q^{33} +(-0.240586 + 0.740447i) q^{34} +(0.602985 + 5.88527i) q^{35} +(-4.34484 - 13.3720i) q^{36} +(2.42430 - 2.18285i) q^{37} +(-2.16888 - 10.2038i) q^{38} +(0.140077 - 0.155571i) q^{39} +(10.4098 - 11.6131i) q^{40} +(0.700664 - 2.15642i) q^{41} +(0.210141 - 0.465897i) q^{42} +9.05803i q^{43} +(-16.2014 + 7.21331i) q^{44} +(-3.94771 - 5.40820i) q^{45} +(-16.6177 - 7.39869i) q^{46} +(5.52047 - 0.580225i) q^{47} +(-0.614619 + 0.199702i) q^{48} +(-6.42211 + 2.78506i) q^{49} +(5.20960 - 11.8426i) q^{50} +(0.0112313 - 0.0194532i) q^{51} +(9.78456 + 8.81006i) q^{52} +(1.49269 - 3.35264i) q^{53} +(0.121042 + 1.15164i) q^{54} +(-6.26369 + 5.66514i) q^{55} +(16.8212 + 7.58716i) q^{56} +0.300975i q^{57} +(-2.87746 - 6.46288i) q^{58} +(8.63331 - 1.83507i) q^{59} +(-0.633111 + 0.462139i) q^{60} +(-13.3724 - 2.84238i) q^{61} +(21.8898 + 7.11244i) q^{62} +(4.68773 - 6.38681i) q^{63} +(-1.40634 - 4.32826i) q^{64} +(5.73370 + 2.53753i) q^{65} +(0.713678 - 0.151697i) q^{66} +(-3.42017 - 0.359475i) q^{67} +(1.22350 + 0.706390i) q^{68} +(0.424593 + 0.308485i) q^{69} +(15.2201 + 1.64001i) q^{70} +(-2.69801 + 1.96022i) q^{71} +(-20.7706 + 2.18308i) q^{72} +(9.72229 + 8.75399i) q^{73} +(-4.22058 - 7.31027i) q^{74} +(-0.218062 + 0.302963i) q^{75} -18.9297 q^{76} +(-8.62982 - 5.03834i) q^{77} +(-0.318393 - 0.438230i) q^{78} +(0.885368 + 8.42371i) q^{79} +(-11.4121 - 15.6341i) q^{80} +(-0.935516 + 8.90084i) q^{81} +(-5.08098 - 2.93351i) q^{82} +(-2.74589 + 3.77939i) q^{83} +(-0.747672 - 0.548770i) q^{84} +(0.658402 + 0.138417i) q^{85} +(22.9260 + 4.87307i) q^{86} +(0.0424374 + 0.199652i) q^{87} +(5.47702 + 25.7673i) q^{88} +(7.53425 + 1.60146i) q^{89} +(-15.8120 + 7.08217i) q^{90} +(-0.811226 + 7.37442i) q^{91} +(-19.4021 + 26.7046i) q^{92} +(-0.575097 - 0.332032i) q^{93} +(1.50137 - 14.2845i) q^{94} +(-8.56728 + 2.80478i) q^{95} +(0.0659376 + 0.627354i) q^{96} +(-5.87358 - 8.08430i) q^{97} +(3.59403 + 17.7527i) q^{98} +11.3099 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) $ 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{9}{10}\right)$

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 $

$2$	0.537983	−	2.53101i	0.380412	−	1.78970i	−0.204787	−	0.978807i	$-0.565650\pi$
$2$	0.537983	−	2.53101i	0.380412	−	1.78970i	0.585199	−	0.810890i	$-0.301016\pi$
$3$	−0.0303653	+	0.0682015i	−0.0175314	+	0.0393762i	−0.922099	−	0.386954i	$-0.873527\pi$
$3$	−0.0303653	+	0.0682015i	−0.0175314	+	0.0393762i	0.904568	+	0.426330i	$0.140194\pi$
$4$	−4.28951	−	1.90981i	−2.14475	−	0.954906i
$5$	−2.22433	−	0.228782i	−0.994752	−	0.102315i
$5$	−2.22433	−	0.228782i	−0.994752	−	0.102315i
$6$	0.156283	+	0.113546i	0.0638022	+	0.0463550i
$7$	−0.537537	−	2.59057i	−0.203170	−	0.979143i
$7$	−0.537537	−	2.59057i	−0.203170	−	0.979143i
$8$	−4.09959	+	5.64260i	−1.44942	+	1.99496i
$9$	2.00366	+	2.22529i	0.667887	+	0.741764i
$10$	−1.77571	+	5.50673i	−0.561527	+	1.74138i
$11$	2.52729	−	2.80684i	0.762006	−	0.846293i	−0.229907	−	0.973213i	$-0.573842\pi$
$11$	2.52729	−	2.80684i	0.762006	−	0.846293i	0.991913	+	0.126919i	$0.0405089\pi$
$12$	0.260504	−	0.234559i	0.0752011	−	0.0677114i
$13$	−2.66684	−	0.866509i	−0.739648	−	0.240326i	−0.0851272	−	0.996370i	$-0.527130\pi$
$13$	−2.66684	−	0.866509i	−0.739648	−	0.240326i	−0.654521	+	0.756044i	$0.727130\pi$
$14$	−6.84595	−	0.0331700i	−1.82966	−	0.00886506i
$15$	0.0831458	−	0.144756i	0.0214682	−	0.0373758i
$16$	5.79224	+	6.43293i	1.44806	+	1.60823i
$17$	−0.299235	−	0.0314508i	−0.0725751	−	0.00762795i	0.0681713	−	0.997674i	$-0.478284\pi$
$17$	−0.299235	−	0.0314508i	−0.0725751	−	0.00762795i	−0.140746	+	0.990046i	$0.544950\pi$
$18$	6.71018	−	3.87412i	1.58160	−	0.913140i
$19$	3.68296	−	1.63976i	0.844929	−	0.376187i	0.0618323	−	0.998087i	$-0.480306\pi$
$19$	3.68296	−	1.63976i	0.844929	−	0.376187i	0.783097	+	0.621900i	$0.213639\pi$
$20$	9.10437	+	5.22942i	2.03580	+	1.16933i
$21$	0.193003	+	0.0420025i	0.0421168	+	0.00916570i
$22$	−5.74450	−	7.90663i	−1.22473	−	1.68570i
$23$	1.46161	−	6.87632i	0.304766	−	1.43381i	−0.513063	−	0.858351i	$-0.671489\pi$
$23$	1.46161	−	6.87632i	0.304766	−	1.43381i	0.817829	−	0.575461i	$-0.195177\pi$
$24$	−0.260349	−	0.450937i	−0.0531435	−	0.0920472i
$25$	4.89532	+	1.01778i	0.979063	+	0.203555i
$26$	−3.62786	+	6.28364i	−0.711482	+	1.23232i
$27$	−0.425616	+	0.138291i	−0.0819098	+	0.0266141i
$28$	−2.64173	+	12.1389i	−0.499240	+	2.29403i
$29$	2.21189	−	1.60703i	0.410738	−	0.298418i	−0.363163	−	0.931726i	$-0.618303\pi$
$29$	2.21189	−	1.60703i	0.410738	−	0.298418i	0.773900	+	0.633307i	$0.218303\pi$
$30$	−0.321648	−	0.288319i	−0.0587246	−	0.0526397i
$31$	−0.929782	+	8.84628i	−0.166994	+	1.58884i	0.514810	+	0.857304i	$0.327862\pi$
$31$	−0.929782	+	8.84628i	−0.166994	+	1.58884i	−0.681804	+	0.731535i	$0.738804\pi$
$32$	7.31754	−	4.22478i	1.29357	−	0.746843i
$33$	0.114689	+	0.257595i	0.0199648	+	0.0448416i
$34$	−0.240586	+	0.740447i	−0.0412601	+	0.126986i
$35$	0.602985	+	5.88527i	0.101923	+	0.994792i
$36$	−4.34484	−	13.3720i	−0.724139	−	2.22867i
$37$	2.42430	−	2.18285i	0.398552	−	0.358858i	−0.445349	−	0.895357i	$-0.646920\pi$
$37$	2.42430	−	2.18285i	0.398552	−	0.358858i	0.843901	+	0.536499i	$0.180254\pi$
$38$	−2.16888	−	10.2038i	−0.351839	−	1.65527i
$39$	0.140077	−	0.155571i	0.0224302	−	0.0249113i
$40$	10.4098	−	11.6131i	1.64593	−	1.83619i
$41$	0.700664	−	2.15642i	0.109425	−	0.336776i	−0.881318	−	0.472523i	$-0.843343\pi$
$41$	0.700664	−	2.15642i	0.109425	−	0.336776i	0.990744	+	0.135747i	$0.0433433\pi$
$42$	0.210141	−	0.465897i	0.0324255	−	0.0718895i
$43$			9.05803i			1.38134i	0.723172	+	0.690668i	$0.242683\pi$
$43$			9.05803i			1.38134i	−0.723172	+	0.690668i	$0.757317\pi$
$44$	−16.2014	+	7.21331i	−2.44245	+	1.08745i
$45$	−3.94771	−	5.40820i	−0.588489	−	0.806206i
$46$	−16.6177	−	7.39869i	−2.45015	−	1.09088i
$47$	5.52047	−	0.580225i	0.805244	−	0.0846345i	0.307042	−	0.951696i	$-0.400661\pi$
$47$	5.52047	−	0.580225i	0.805244	−	0.0846345i	0.498201	+	0.867061i	$0.333994\pi$
$48$	−0.614619	+	0.199702i	−0.0887126	+	0.0288245i
$49$	−6.42211	+	2.78506i	−0.917444	+	0.397865i
$50$	5.20960	−	11.8426i	0.736749	−	1.67479i
$51$	0.0112313	−	0.0194532i	0.00157270	−	0.00272400i
$52$	9.78456	+	8.81006i	1.35687	+	1.22174i
$53$	1.49269	−	3.35264i	0.205037	−	0.460521i	−0.781532	−	0.623865i	$-0.785561\pi$
$53$	1.49269	−	3.35264i	0.205037	−	0.460521i	0.986569	+	0.163344i	$0.0522281\pi$
$54$	0.121042	+	1.15164i	0.0164717	+	0.156718i
$55$	−6.26369	+	5.66514i	−0.844595	+	0.763888i
$56$	16.8212	+	7.58716i	2.24783	+	1.01388i
$57$			0.300975i			0.0398652i
$58$	−2.87746	−	6.46288i	−0.377829	−	0.848618i
$59$	8.63331	−	1.83507i	1.12396	−	0.238905i	0.391809	−	0.920047i	$-0.371849\pi$
$59$	8.63331	−	1.83507i	1.12396	−	0.238905i	0.732152	+	0.681141i	$0.238516\pi$
$60$	−0.633111	+	0.462139i	−0.0817343	+	0.0596619i
$61$	−13.3724	−	2.84238i	−1.71215	−	0.363930i	−0.755499	−	0.655150i	$-0.772605\pi$
$61$	−13.3724	−	2.84238i	−1.71215	−	0.363930i	−0.956656	+	0.291220i	$0.905939\pi$
$62$	21.8898	+	7.11244i	2.78001	+	0.903281i
$63$	4.68773	−	6.38681i	0.590599	−	0.804662i
$64$	−1.40634	−	4.32826i	−0.175792	−	0.541033i
$65$	5.73370	+	2.53753i	0.711178	+	0.314742i
$66$	0.713678	−	0.151697i	0.0878477	−	0.0186726i
$67$	−3.42017	−	0.359475i	−0.417841	−	0.0439168i	−0.106724	−	0.994289i	$-0.534036\pi$
$67$	−3.42017	−	0.359475i	−0.417841	−	0.0439168i	−0.311116	+	0.950372i	$0.600703\pi$
$68$	1.22350	+	0.706390i	0.148372	+	0.0856624i
$69$	0.424593	+	0.308485i	0.0511150	+	0.0371372i
$70$	15.2201	+	1.64001i	1.81915	+	0.196019i
$71$	−2.69801	+	1.96022i	−0.320195	+	0.232635i	−0.736258	−	0.676700i	$-0.763409\pi$
$71$	−2.69801	+	1.96022i	−0.320195	+	0.232635i	0.416064	+	0.909335i	$0.363409\pi$
$72$	−20.7706	+	2.18308i	−2.44784	+	0.257278i
$73$	9.72229	+	8.75399i	1.13791	+	1.02458i	0.999415	+	0.0342137i	$0.0108927\pi$
$73$	9.72229	+	8.75399i	1.13791	+	1.02458i	0.138494	+	0.990363i	$0.455774\pi$
$74$	−4.22058	−	7.31027i	−0.490633	−	0.849801i
$75$	−0.218062	+	0.302963i	−0.0251796	+	0.0349832i
$76$	−18.9297			−2.17139
$77$	−8.62982	−	5.03834i	−0.983459	−	0.574172i
$78$	−0.318393	−	0.438230i	−0.0360509	−	0.0496198i
$79$	0.885368	+	8.42371i	0.0996116	+	0.947741i	0.924174	+	0.381971i	$0.124755\pi$
$79$	0.885368	+	8.42371i	0.0996116	+	0.947741i	−0.824563	+	0.565771i	$0.808579\pi$
$80$	−11.4121	−	15.6341i	−1.27591	−	1.74795i
$81$	−0.935516	+	8.90084i	−0.103946	+	0.988982i
$82$	−5.08098	−	2.93351i	−0.561101	−	0.323952i
$83$	−2.74589	+	3.77939i	−0.301401	+	0.414842i	−0.932675	−	0.360717i	$-0.882532\pi$
$83$	−2.74589	+	3.77939i	−0.301401	+	0.414842i	0.631275	+	0.775559i	$0.282532\pi$
$84$	−0.747672	−	0.548770i	−0.0815778	−	0.0598757i
$85$	0.658402	+	0.138417i	0.0714137	+	0.0150134i
$86$	22.9260	+	4.87307i	2.47217	+	0.525476i
$87$	0.0424374	+	0.199652i	0.00454977	+	0.0214050i
$88$	5.47702	+	25.7673i	0.583852	+	2.74681i
$89$	7.53425	+	1.60146i	0.798629	+	0.169754i	0.589112	−	0.808051i	$-0.299478\pi$
$89$	7.53425	+	1.60146i	0.798629	+	0.169754i	0.209517	+	0.977805i	$0.432811\pi$
$90$	−15.8120	+	7.08217i	−1.66673	+	0.746527i
$91$	−0.811226	+	7.37442i	−0.0850396	+	0.773049i
$92$	−19.4021	+	26.7046i	−2.02280	+	2.78415i
$93$	−0.575097	−	0.332032i	−0.0596348	−	0.0344302i
$94$	1.50137	−	14.2845i	0.154854	−	1.47334i
$95$	−8.56728	+	2.80478i	−0.878984	+	0.287764i
$96$	0.0659376	+	0.627354i	0.00672972	+	0.0640290i
$97$	−5.87358	−	8.08430i	−0.596372	−	0.820836i	0.398998	−	0.916952i	$-0.369358\pi$
$97$	−5.87358	−	8.08430i	−0.596372	−	0.820836i	−0.995370	+	0.0961159i	$0.969358\pi$
$98$	3.59403	+	17.7527i	0.363051	+	1.79330i
$99$	11.3099			1.13668
$100$	−19.0547	−	13.7149i	−1.90547	−	1.37149i
$101$	−1.10483	−	1.91362i	−0.109934	−	0.190412i	0.805809	−	0.592175i	$-0.201731\pi$
$101$	−1.10483	−	1.91362i	−0.109934	−	0.190412i	−0.915744	+	0.401763i	$0.868397\pi$
$102$	−0.0431941	−	0.0388922i	−0.00427686	−	0.00385090i
$103$	4.07612	−	0.428418i	0.401632	−	0.0422133i	0.0984408	−	0.995143i	$-0.468614\pi$
$103$	4.07612	−	0.428418i	0.401632	−	0.0422133i	0.303192	+	0.952930i	$0.401948\pi$
$104$	15.8223	−	11.4956i	1.55150	−	1.12723i
$105$	−0.419694	−	0.137583i	−0.0409580	−	0.0134268i
$106$	−7.68254	−	5.58169i	−0.746194	−	0.542142i
$107$	−8.31490	−	4.80061i	−0.803831	−	0.464092i	0.0409777	−	0.999160i	$-0.486953\pi$
$107$	−8.31490	−	4.80061i	−0.803831	−	0.464092i	−0.844809	+	0.535068i	$0.820286\pi$
$108$	2.08979	+	0.219646i	0.201090	+	0.0211355i
$109$	5.62465	−	1.19556i	0.538744	−	0.114514i	0.0694996	−	0.997582i	$-0.477860\pi$
$109$	5.62465	−	1.19556i	0.538744	−	0.114514i	0.469244	+	0.883068i	$0.344526\pi$
$110$	10.9688	+	18.9012i	1.04583	+	1.80216i
$111$	0.0752591	+	0.231624i	0.00714328	+	0.0219847i
$112$	13.5514	−	18.4631i	1.28049	−	1.74460i
$113$	−2.42087	−	0.786587i	−0.227736	−	0.0739959i	0.192926	−	0.981213i	$-0.438202\pi$
$113$	−2.42087	−	0.786587i	−0.227736	−	0.0739959i	−0.420662	+	0.907217i	$0.638202\pi$
$114$	0.761772	+	0.161920i	0.0713465	+	0.0151652i
$115$	−4.82428	+	14.9608i	−0.449866	+	1.39510i
$116$	−12.5571	+	2.66908i	−1.16589	+	0.247818i
$117$	−3.41521	−	7.67069i	−0.315736	−	0.709155i
$118$		−	22.8383i		−	2.10243i
$119$	0.0793742	+	0.792094i	0.00727622	+	0.0726112i
$120$	0.475936	+	1.06260i	0.0434468	+	0.0970015i
$121$	−0.341340	−	3.24763i	−0.0310309	−	0.295239i
$122$	−14.3882	+	32.3165i	−1.30265	+	2.92579i
$123$	0.125795	+	0.113267i	0.0113426	+	0.0102129i
$124$	20.8830	−	36.1705i	1.87535	−	3.24821i
$125$	−10.6560	−	3.38384i	−0.953099	−	0.302660i
$126$	−13.6432	−	15.3007i	−1.21543	−	1.36310i
$127$	12.7417	−	4.14002i	1.13064	−	0.367368i	0.316822	−	0.948485i	$-0.397384\pi$
$127$	12.7417	−	4.14002i	1.13064	−	0.367368i	0.813820	+	0.581118i	$0.197384\pi$
$128$	5.09508	−	0.535515i	0.450346	−	0.0473333i
$129$	−0.617771	−	0.275050i	−0.0543917	−	0.0242168i
$130$	9.50716	−	13.1469i	0.833833	−	1.15306i
$131$	15.2146	−	6.77396i	1.32930	−	0.591844i	0.385609	−	0.922662i	$-0.373992\pi$
$131$	15.2146	−	6.77396i	1.32930	−	0.591844i	0.943694	+	0.330819i	$0.107325\pi$
$132$		−	1.32399i		−	0.115239i
$133$	−6.22764	−	8.65954i	−0.540005	−	0.750877i
$134$	−2.74983	+	8.46311i	−0.237549	+	0.731101i
$135$	0.978350	−	0.210232i	0.0842030	−	0.0180939i
$136$	1.40420	−	1.55953i	0.120409	−	0.133728i
$137$	−1.82498	−	8.58584i	−0.155918	−	0.733538i	−0.984741	−	0.174026i	$-0.944322\pi$
$137$	−1.82498	−	8.58584i	−0.155918	−	0.733538i	0.828823	−	0.559511i	$-0.189011\pi$
$138$	1.00920	−	0.908691i	0.0859091	−	0.0773529i
$139$	−3.27911	−	10.0921i	−0.278131	−	0.855998i	−0.988374	−	0.152042i	$-0.951415\pi$
$139$	−3.27911	−	10.0921i	−0.278131	−	0.855998i	0.710243	−	0.703956i	$-0.248585\pi$
$140$	8.65325	−	26.3965i	0.731333	−	2.23091i
$141$	−0.128058	+	0.394123i	−0.0107845	+	0.0331912i
$142$	3.50985	+	7.88325i	0.294540	+	0.661548i
$143$	−9.17202	+	5.29547i	−0.767003	+	0.442829i
$144$	−2.70947	+	25.7788i	−0.225789	+	2.14824i
$145$	−5.28764	+	3.06853i	−0.439115	+	0.254828i
$146$	27.3869	−	19.8977i	2.26656	−	1.64675i
$147$	0.00506400	−	0.522567i	0.000417671	−	0.0431006i
$148$	−14.5679	+	4.73339i	−1.19747	+	0.389082i
$149$	−0.695327	+	1.20434i	−0.0569634	+	0.0986635i	−0.893101	−	0.449856i	$-0.851475\pi$
$149$	−0.695327	+	1.20434i	−0.0569634	+	0.0986635i	0.836138	+	0.548520i	$0.184809\pi$
$150$	0.649490	+	0.714906i	0.0530306	+	0.0583718i
$151$	7.74195	+	13.4095i	0.630031	+	1.09125i	0.987545	+	0.157338i	$0.0502912\pi$
$151$	7.74195	+	13.4095i	0.630031	+	1.09125i	−0.357514	+	0.933908i	$0.616375\pi$
$152$	−5.84611	+	27.5038i	−0.474182	+	2.23085i
$153$	−0.529578	−	0.728901i	−0.0428138	−	0.0589282i
$154$	−17.3948	+	19.1316i	−1.40171	+	1.54167i
$155$	4.09202	−	19.4644i	0.328679	−	1.56342i
$156$	−0.897971	+	0.399802i	−0.0718952	+	0.0320098i
$157$	−1.34793	+	0.778227i	−0.107576	+	0.0621093i	−0.552823	−	0.833299i	$-0.686449\pi$
$157$	−1.34793	+	0.778227i	−0.107576	+	0.0621093i	0.445246	+	0.895408i	$0.353116\pi$
$158$	21.7968	+	2.29094i	1.73406	+	0.182257i
$159$	0.183329	+	0.203608i	0.0145390	+	0.0161472i
$160$	−17.2432	+	7.72320i	−1.36319	+	0.610573i
$161$	−18.5993	−	0.0901171i	−1.46583	−	0.00710222i
$162$	22.0249	+	7.15631i	1.73044	+	0.562253i
$163$	7.43098	−	6.69088i	0.582039	−	0.524071i	−0.324670	−	0.945827i	$-0.605253\pi$
$163$	7.43098	−	6.69088i	0.582039	−	0.524071i	0.906709	+	0.421757i	$0.138586\pi$
$164$	−7.12386	+	7.91185i	−0.556280	+	0.617812i
$165$	−0.196173	−	0.599217i	−0.0152720	−	0.0466490i
$166$	8.08845	+	8.98314i	0.627786	+	0.697227i
$167$	−8.72392	+	12.0074i	−0.675077	+	0.929164i	−0.999862	−	0.0166240i	$-0.994708\pi$
$167$	−8.72392	+	12.0074i	−0.675077	+	0.929164i	0.324785	+	0.945788i	$0.394708\pi$
$168$	−1.02824	+	0.916847i	−0.0793302	+	0.0707363i
$169$	−4.15602	−	3.01953i	−0.319694	−	0.232271i
$170$	0.704544	−	1.59196i	0.0540360	−	0.122098i
$171$	11.0284	+	4.91014i	0.843359	+	0.375488i
$172$	17.2991	−	38.8545i	1.31905	−	2.96263i
$173$	−1.09980	+	5.17415i	−0.0836163	+	0.393384i	−0.999976	−	0.00697303i	$-0.997780\pi$
$173$	−1.09980	+	5.17415i	−0.0836163	+	0.393384i	0.916359	+	0.400357i	$0.131114\pi$
$174$	0.528153			0.0400392
$175$	0.00520637	−	13.2288i	0.000393564	−	1.00000i
$176$	32.6948			2.46447
$177$	−0.136999	+	0.644527i	−0.0102974	+	0.0484456i
$178$	8.10661	−	18.2077i	0.607616	−	1.36473i
$179$	−2.11260	−	0.940590i	−0.157903	−	0.0703030i	0.326263	−	0.945279i	$-0.394210\pi$
$179$	−2.11260	−	0.940590i	−0.157903	−	0.0703030i	−0.484166	+	0.874976i	$0.660877\pi$
$180$	6.60508	+	30.7379i	0.492313	+	2.29107i
$181$	−14.4034	−	10.4647i	−1.07060	−	0.777834i	−0.0945769	−	0.995518i	$-0.530150\pi$
$181$	−14.4034	−	10.4647i	−1.07060	−	0.777834i	−0.976019	+	0.217684i	$0.930150\pi$
$182$	18.2283	+	6.02054i	1.35117	+	0.446272i
$183$	0.599910	−	0.825706i	0.0443466	−	0.0610379i
$184$	32.8083	+	36.4373i	2.41866	+	2.68620i
$185$	−5.89185	+	4.30075i	−0.433177	+	0.316197i
$186$	−1.14977	+	1.27695i	−0.0843053	+	0.0936305i
$187$	−0.844529	+	0.760418i	−0.0617581	+	0.0556072i
$188$	−24.7882	−	8.05419i	−1.80787	−	0.587412i
$189$	0.587037	+	1.02825i	0.0427007	+	0.0747943i
$190$	2.48987	+	23.1928i	0.180634	+	1.68258i
$191$	−8.60554	−	9.55742i	−0.622675	−	0.691551i	0.346465	−	0.938063i	$-0.387382\pi$
$191$	−8.60554	−	9.55742i	−0.622675	−	0.691551i	−0.969140	+	0.246512i	$0.920715\pi$
$192$	0.337898	+	0.0355145i	0.0243857	+	0.00256304i
$193$	−23.0217	+	13.2916i	−1.65714	+	0.956751i	−0.683116	+	0.730310i	$0.739376\pi$
$193$	−23.0217	+	13.2916i	−1.65714	+	0.956751i	−0.974025	+	0.226441i	$0.927291\pi$
$194$	−23.6213	+	10.5169i	−1.69591	+	0.755069i
$195$	−0.347169	+	0.313994i	−0.0248613	+	0.0224856i
$196$	32.8666	+	0.318498i	2.34762	+	0.0227499i
$197$	−1.94609	−	2.67856i	−0.138653	−	0.190840i	0.734044	−	0.679102i	$-0.237631\pi$
$197$	−1.94609	−	2.67856i	−0.138653	−	0.190840i	−0.872697	+	0.488263i	$0.837631\pi$
$198$	6.08452	−	28.6254i	0.432408	−	2.03432i
$199$	7.70711	+	13.3491i	0.546342	+	0.946293i	0.998521	+	0.0543655i	$0.0173136\pi$
$199$	7.70711	+	13.3491i	0.546342	+	0.946293i	−0.452179	+	0.891927i	$0.649353\pi$
$200$	−25.8117	+	23.4498i	−1.82516	+	1.65815i
$201$	0.128371	−	0.222345i	0.00905461	−	0.0156830i
$202$	−5.43777	+	1.76684i	−0.382600	+	0.124314i
$203$	−5.35210	−	4.86622i	−0.375644	−	0.341541i
$204$	−0.0853290	+	0.0619951i	−0.00597422	+	0.00434053i
$205$	−2.05186	+	4.63630i	−0.143308	+	0.323813i
$206$	1.10856	−	10.5472i	0.0772367	−	0.734858i
$207$	18.2304	−	10.5253i	1.26710	−	0.731560i
$208$	−9.87278	−	22.1746i	−0.684554	−	1.53753i
$209$	4.70536	−	14.4816i	0.325477	−	1.00171i
$210$	−0.574014	+	0.988234i	−0.0396107	+	0.0681946i
$211$	3.86469	+	11.8943i	0.266056	+	0.818836i	0.991448	+	0.130500i	$0.0416584\pi$
$211$	3.86469	+	11.8943i	0.266056	+	0.818836i	−0.725392	+	0.688336i	$0.758342\pi$
$212$	−12.8058	+	11.5304i	−0.879508	+	0.791913i
$213$	−0.0517641	−	0.243531i	−0.00354681	−	0.0166865i
$214$	−16.6237	+	18.4625i	−1.13637	+	1.26207i
$215$	2.07232	−	20.1481i	0.141331	−	1.37409i
$216$	0.964529	−	2.96852i	0.0656279	−	0.201982i
$217$	23.4167	−	2.34654i	1.58963	−	0.159294i
$218$		−	14.8792i		−	1.00775i
$219$	−0.892256	+	0.397258i	−0.0602930	+	0.0268442i
$220$	37.6875	−	12.3382i	2.54089	−	0.831842i
$221$	0.770758	+	0.343164i	0.0518468	+	0.0230837i
$222$	0.626731	−	0.0658720i	0.0420634	−	0.00442104i
$223$	7.39692	−	2.40341i	0.495334	−	0.160944i	−0.0506879	−	0.998715i	$-0.516141\pi$
$223$	7.39692	−	2.40341i	0.495334	−	0.160944i	0.546022	+	0.837771i	$0.316141\pi$
$224$	−14.8780	−	16.6856i	−0.994081	−	1.11485i
$225$	7.54371	+	12.9328i	0.502914	+	0.862186i
$226$	−3.29325	+	5.70407i	−0.219064	+	0.379429i
$227$	−5.12621	−	4.61566i	−0.340238	−	0.306352i	0.481243	−	0.876587i	$-0.340185\pi$
$227$	−5.12621	−	4.61566i	−0.340238	−	0.306352i	−0.821482	+	0.570235i	$0.806852\pi$
$228$	0.574806	−	1.29104i	0.0380675	−	0.0855010i
$229$	−1.91955	−	18.2633i	−0.126848	−	1.20688i	−0.853953	−	0.520349i	$-0.825802\pi$
$229$	−1.91955	−	18.2633i	−0.126848	−	1.20688i	0.727106	−	0.686526i	$-0.240865\pi$
$230$	35.2707	+	20.2590i	2.32568	+	1.33584i
$231$	0.605669	−	0.435577i	0.0398501	−	0.0286588i
$232$			19.0690i			1.25194i
$233$	3.64307	+	8.18247i	0.238666	+	0.536052i	0.992675	−	0.120811i	$-0.0385496\pi$
$233$	3.64307	+	8.18247i	0.238666	+	0.536052i	−0.754010	+	0.656863i	$0.771883\pi$
$234$	−21.2519	+	4.51724i	−1.38928	+	0.295301i
$235$	−12.4121	+	0.0276269i	−0.809677	+	0.00180218i
$236$	−40.5373	−	8.61647i	−2.63875	−	0.560884i
$237$	−0.601394	−	0.195405i	−0.0390648	−	0.0126929i
$238$	2.04750	+	0.225236i	0.132720	+	0.0145999i
$239$	5.12153	+	15.7624i	0.331284	+	1.01959i	0.968524	+	0.248922i	$0.0800761\pi$
$239$	5.12153	+	15.7624i	0.331284	+	1.01959i	−0.637240	+	0.770666i	$0.719924\pi$
$240$	1.41281	−	0.303589i	0.0911962	−	0.0195966i
$241$	5.74126	−	1.22034i	0.369827	−	0.0786091i	−0.0192493	−	0.999815i	$-0.506128\pi$
$241$	5.74126	−	1.22034i	0.369827	−	0.0786091i	0.389076	+	0.921206i	$0.372794\pi$
$242$	−8.40343	−	0.883236i	−0.540193	−	0.0567766i
$243$	−1.74133	−	1.00536i	−0.111707	−	0.0644938i
$244$	51.9324	+	37.7311i	3.32463	+	2.41549i
$245$	14.9221	−	4.72563i	0.953337	−	0.301909i
$246$	0.354355	−	0.257454i	0.0225929	−	0.0164147i
$247$	−11.2427	+	1.18166i	−0.715358	+	0.0751871i
$248$	−46.1043	−	41.5125i	−2.92763	−	2.63605i
$249$	−0.174381	−	0.302036i	−0.0110509	−	0.0191408i
$250$	−14.2973	+	25.1499i	−0.904239	+	1.59062i
$251$	−3.59519			−0.226927			−0.113463	−	0.993542i	$-0.536194\pi$
$251$	−3.59519			−0.226927			−0.113463	+	0.993542i	$0.536194\pi$
$252$	−32.3057	+	18.4436i	−2.03507	+	1.16184i
$253$	−15.6068	−	21.4809i	−0.981192	−	1.35049i
$254$	−3.62364	−	34.4766i	−0.227367	−	2.16326i
$255$	−0.0294328	+	0.0407010i	−0.00184315	+	0.00254879i
$256$	2.33709	−	22.2360i	0.146068	−	1.38975i
$257$	3.78375	+	2.18455i	0.236024	+	0.136268i	0.613348	−	0.789813i	$-0.289822\pi$
$257$	3.78375	+	2.18455i	0.236024	+	0.136268i	−0.377324	+	0.926081i	$0.623156\pi$
$258$	−1.02850	+	1.41562i	−0.0640319	+	0.0881324i
$259$	−6.95797	−	5.10695i	−0.432347	−	0.317331i
$260$	−19.7485	−	21.8350i	−1.22475	−	1.35415i
$261$	8.00800	+	1.70215i	0.495683	+	0.105361i
$262$	−8.95980	−	42.1525i	−0.553538	−	2.60419i
$263$	1.63997	+	7.71547i	0.101125	+	0.475756i	0.999344	+	0.0362085i	$0.0115280\pi$
$263$	1.63997	+	7.71547i	0.101125	+	0.475756i	−0.898219	+	0.439548i	$0.855139\pi$
$264$	−1.92368	−	0.408892i	−0.118395	−	0.0251655i
$265$	−4.08727	+	7.11589i	−0.251079	+	0.437126i
$266$	−25.2678	+	11.1036i	−1.54927	+	0.680802i
$267$	−0.338001	+	0.465219i	−0.0206854	+	0.0284709i
$268$	13.9843	+	8.07386i	0.854229	+	0.493189i
$269$	1.86154	−	17.7114i	0.113500	−	1.07988i	−0.778436	−	0.627724i	$-0.783987\pi$
$269$	1.86154	−	17.7114i	0.113500	−	1.07988i	0.891937	−	0.452160i	$-0.149347\pi$
$270$	−0.00576331	−	2.58932i	−0.000350744	−	0.157581i
$271$	1.11434	+	10.6022i	0.0676912	+	0.644039i	0.974791	+	0.223122i	$0.0716249\pi$
$271$	1.11434	+	10.6022i	0.0676912	+	0.644039i	−0.907099	+	0.420917i	$0.861708\pi$
$272$	−1.53092	−	2.10713i	−0.0928255	−	0.127763i
$273$	−0.478313	−	0.279253i	−0.0289488	−	0.0169012i
$274$	−22.7127			−1.37212
$275$	15.2286	−	11.1681i	0.918320	−	0.673465i
$276$	−1.23215	−	2.13414i	−0.0741666	−	0.128460i
$277$	2.03436	+	1.83175i	0.122233	+	0.110059i	0.727980	−	0.685598i	$-0.240459\pi$
$277$	2.03436	+	1.83175i	0.122233	+	0.110059i	−0.605748	+	0.795657i	$0.707126\pi$
$278$	−27.3073	+	2.87011i	−1.63778	+	0.172138i
$279$	−21.5485	+	15.6559i	−1.29008	+	0.937296i
$280$	−35.6802	−	20.7248i	−2.13230	−	1.23854i
$281$	11.9857	+	8.70811i	0.715006	+	0.519483i	0.884785	−	0.466000i	$-0.154305\pi$
$281$	11.9857	+	8.70811i	0.715006	+	0.519483i	−0.169779	+	0.985482i	$0.554305\pi$
$282$	0.928638	+	0.536150i	0.0552996	+	0.0319272i
$283$	6.51967	+	0.685244i	0.387554	+	0.0407336i	0.296302	−	0.955094i	$-0.404246\pi$
$283$	6.51967	+	0.685244i	0.387554	+	0.0407336i	0.0912519	+	0.995828i	$0.470913\pi$
$284$	15.3168	−	3.25568i	0.908883	−	0.193189i
$285$	0.0688579	−	0.669469i	0.00407879	−	0.0396559i
$286$	8.46850	+	26.0634i	0.500753	+	1.54116i
$287$	−5.96299	−	0.655962i	−0.351984	−	0.0387202i
$288$	24.0633	+	7.81862i	1.41794	+	0.460717i
$289$	−16.5400	−	3.51568i	−0.972939	−	0.206804i
$290$	4.92183	+	15.0339i	0.289020	+	0.882821i
$291$	0.729714	−	0.155106i	0.0427766	−	0.00909245i
$292$	−24.9854	−	56.1181i	−1.46216	−	3.28406i
$293$			31.4682i			1.83839i	0.393798	+	0.919197i	$0.371161\pi$
$293$			31.4682i			1.83839i	−0.393798	+	0.919197i	$0.628839\pi$
$294$	−1.31990	−	0.293949i	−0.0769780	−	0.0171435i
$295$	−19.6232	+	2.10665i	−1.14251	+	0.122654i
$296$	2.37831	+	22.6281i	0.138237	+	1.31523i
$297$	−0.687494	+	1.54414i	−0.0398924	+	0.0895999i
$298$	2.67413	+	2.40780i	0.154908	+	0.139480i
$299$	−9.85626	+	17.0715i	−0.570002	+	0.987273i
$300$	1.51398	−	0.883106i	0.0874097	−	0.0509861i
$301$	23.4655	−	4.86903i	1.35253	−	0.280646i
$302$	38.1045	−	12.3809i	2.19267	−	0.712442i
$303$	0.164060	−	0.0172434i	0.00942501	−	0.000990608i
$304$	31.8810	+	14.1944i	1.82850	+	0.814102i
$305$	29.0943	+	9.38177i	1.66593	+	0.537198i
$306$	−2.12976	+	0.948231i	−0.121750	+	0.0542068i
$307$			19.5635i			1.11655i	0.829657	+	0.558274i	$0.188536\pi$
$307$			19.5635i			1.11655i	−0.829657	+	0.558274i	$0.811464\pi$
$308$	27.3954	+	38.0933i	1.56100	+	2.17057i
$309$	−0.0945539	+	0.291007i	−0.00537898	+	0.0165548i
$310$	−47.0631	−	20.8285i	−2.67301	−	1.18298i
$311$	22.1198	−	24.5666i	1.25430	−	1.39304i	0.368069	−	0.929798i	$-0.380019\pi$
$311$	22.1198	−	24.5666i	1.25430	−	1.39304i	0.886231	−	0.463243i	$-0.153314\pi$
$312$	0.303567	+	1.42817i	0.0171861	+	0.0808543i
$313$	−5.65656	+	5.09319i	−0.319728	+	0.287884i	−0.813329	−	0.581804i	$-0.802347\pi$
$313$	−5.65656	+	5.09319i	−0.319728	+	0.287884i	0.493601	+	0.869688i	$0.335680\pi$
$314$	1.24454	+	3.83030i	0.0702334	+	0.216156i
$315$	−11.8883	+	13.1339i	−0.669828	+	0.740012i
$316$	12.2899	−	37.8245i	0.691362	−	2.12779i
$317$	9.11123	+	20.4642i	0.511738	+	1.14938i	0.966007	+	0.258517i	$0.0832337\pi$
$317$	9.11123	+	20.4642i	0.511738	+	1.14938i	−0.454269	+	0.890864i	$0.650100\pi$
$318$	0.613962	−	0.354471i	0.0344293	−	0.0198778i
$319$	1.07940	−	10.2698i	0.0604351	−	0.575001i
$320$	2.13793	+	9.94924i	0.119514	+	0.556179i
$321$	0.579893	−	0.421317i	0.0323665	−	0.0235156i
$322$	−10.2342	+	47.0265i	−0.570328	+	2.62068i
$323$	−1.15364	+	0.374841i	−0.0641903	+	0.0208567i
$324$	21.0118	−	36.3936i	1.16732	−	2.02187i
$325$	−12.1731	−	6.95608i	−0.675243	−	0.385854i
$326$	−12.9370	−	22.4075i	−0.716513	−	1.24104i
$327$	−0.0892553	+	0.419913i	−0.00493583	+	0.0232212i
$328$	9.29539	+	12.7940i	0.513252	+	0.706431i
$329$	−4.47057	−	13.9893i	−0.246471	−	0.771254i
$330$	−1.62216	+	0.174148i	−0.0892971	+	0.00958651i
$331$	8.50853	−	3.78824i	0.467671	−	0.208221i	−0.159351	−	0.987222i	$-0.550940\pi$
$331$	8.50853	−	3.78824i	0.467671	−	0.208221i	0.627022	+	0.779001i	$0.284274\pi$
$332$	18.9965	−	10.9676i	1.04257	−	0.601926i
$333$	9.71495	+	1.02108i	0.532376	+	0.0559550i
$334$	25.6977	+	28.5402i	1.40611	+	1.56165i
$335$	7.52536	+	1.58207i	0.411154	+	0.0864375i
$336$	0.847722	+	1.48487i	0.0462470	+	0.0810061i
$337$	13.7643	+	4.47228i	0.749788	+	0.243621i	0.658890	−	0.752239i	$-0.271026\pi$
$337$	13.7643	+	4.47228i	0.749788	+	0.243621i	0.0908979	+	0.995860i	$0.471026\pi$
$338$	−9.87834	+	8.89449i	−0.537311	+	0.483797i
$339$	0.127157	−	0.141222i	0.00690620	−	0.00767012i
$340$	−2.55987	−	1.85116i	−0.138829	−	0.100393i
$341$	22.4803	+	24.9668i	1.21737	+	1.35203i
$342$	18.3607	−	25.2713i	0.992833	−	1.36652i
$343$	10.6670	+	15.1398i	0.575964	+	0.817475i
$344$	−51.1108	−	37.1342i	−2.75571	−	2.00214i
$345$	−0.873861	−	0.783313i	−0.0470471	−	0.0421722i
$346$	12.5042	+	5.56722i	0.672228	+	0.299295i
$347$	−1.32960	+	2.98632i	−0.0713765	+	0.160314i	−0.945710	−	0.325011i	$-0.894632\pi$
$347$	−1.32960	+	2.98632i	−0.0713765	+	0.160314i	0.874334	+	0.485325i	$0.161299\pi$
$348$	0.199263	−	0.937458i	0.0106816	−	0.0502530i
$349$	20.1244			1.07724			0.538618	−	0.842550i	$-0.318947\pi$
$349$	20.1244			1.07724			0.538618	+	0.842550i	$0.318947\pi$
$350$	−33.4793	−	7.13003i	−1.78955	−	0.381116i
$351$	1.25488			0.0669805
$352$	6.63525	−	31.2164i	0.353660	−	1.66384i
$353$	−12.8577	+	28.8788i	−0.684345	+	1.53707i	0.151713	+	0.988425i	$0.451521\pi$
$353$	−12.8577	+	28.8788i	−0.684345	+	1.53707i	−0.836058	+	0.548641i	$0.815146\pi$
$354$	1.55760	+	0.693490i	0.0827857	+	0.0368586i
$355$	6.44973	−	3.74292i	0.342316	−	0.198654i
$356$	−29.2598	−	21.2585i	−1.55076	−	1.12670i
$357$	−0.0564323	−	0.0186387i	−0.00298671	−	0.000986466i
$358$	−3.51719	+	4.84100i	−0.185889	+	0.255855i
$359$	6.91359	+	7.67832i	0.364885	+	0.405246i	0.897431	−	0.441155i	$-0.145431\pi$
$359$	6.91359	+	7.67832i	0.364885	+	0.405246i	−0.532546	+	0.846401i	$0.678765\pi$
$360$	46.7002	−	0.103945i	2.46132	−	0.00547841i
$361$	−1.83810	+	2.04141i	−0.0967419	+	0.107443i
$362$	−34.2350	+	30.8254i	−1.79935	+	1.62015i
$363$	0.231858	+	0.0753353i	0.0121694	+	0.00395408i
$364$	17.5635	−	30.0833i	0.920578	−	1.57680i
$365$	−19.6229	−	21.6961i	−1.02711	−	1.13562i
$366$	−1.76713	−	1.96260i	−0.0923693	−	0.102587i
$367$	−16.9994	−	1.78671i	−0.887363	−	0.0932656i	−0.350132	−	0.936701i	$-0.613863\pi$
$367$	−16.9994	−	1.78671i	−0.887363	−	0.0932656i	−0.537231	+	0.843435i	$0.680530\pi$
$368$	52.7009	−	30.4269i	2.74722	−	1.58611i
$369$	6.20256	−	2.76156i	0.322892	−	0.143761i
$370$	7.71553	+	17.2261i	0.401111	+	0.895541i
$371$	−9.48763	−	2.06475i	−0.492573	−	0.107197i
$372$	1.83276	+	2.52258i	0.0950244	+	0.130790i
$373$	−5.39135	+	25.3643i	−0.279154	+	1.31331i	0.585388	+	0.810753i	$0.300942\pi$
$373$	−5.39135	+	25.3643i	−0.279154	+	1.31331i	−0.864542	+	0.502561i	$0.832391\pi$
$374$	1.47028	+	2.54661i	0.0760266	+	0.131682i
$375$	0.554354	−	0.624002i	0.0286267	−	0.0322233i
$376$	−19.3577	+	33.5285i	−0.998297	+	1.72910i
$377$	−7.29126	+	2.36908i	−0.375519	+	0.122014i
$378$	2.91833	−	0.932616i	0.150103	−	0.0479686i
$379$	6.09850	−	4.43082i	0.313259	−	0.227596i	−0.420035	−	0.907508i	$-0.637982\pi$
$379$	6.09850	−	4.43082i	0.313259	−	0.227596i	0.733293	+	0.679912i	$0.237982\pi$
$380$	42.1060	+	4.33079i	2.15999	+	0.222165i
$381$	−0.104549	+	0.994715i	−0.00535620	+	0.0509608i
$382$	−28.8196	+	16.6390i	−1.47454	+	0.851325i
$383$	−6.86409	−	15.4170i	−0.350739	−	0.787772i	−0.999638	−	0.0268979i	$-0.991437\pi$
$383$	−6.86409	−	15.4170i	−0.350739	−	0.787772i	0.648900	−	0.760874i	$-0.275230\pi$
$384$	−0.118191	+	0.363754i	−0.00603139	+	0.0185627i
$385$	18.0429	+	13.1813i	0.919552	+	0.671781i
$386$	21.2559	+	65.4190i	1.08190	+	3.32974i
$387$	−20.1568	+	18.1492i	−1.02463	+	0.922577i
$388$	9.75530	+	45.8951i	0.495251	+	2.32997i
$389$	−7.08687	+	7.87077i	−0.359319	+	0.399064i	−0.895516	−	0.445029i	$-0.853193\pi$
$389$	−7.08687	+	7.87077i	−0.359319	+	0.399064i	0.536198	+	0.844092i	$0.319860\pi$
$390$	0.607952	+	1.04761i	0.0307849	+	0.0530479i
$391$	−0.653629	+	2.01166i	−0.0330554	+	0.101734i
$392$	10.6130	−	47.6550i	0.536039	−	2.40694i
$393$			1.24335i			0.0627187i
$394$	−7.82644	+	3.48456i	−0.394290	+	0.175549i
$395$	−0.0421560	−	18.9397i	−0.00212110	−	0.952960i
$396$	−48.5138	−	21.5997i	−2.43791	−	1.08543i
$397$	35.4347	−	3.72434i	1.77842	−	0.186919i	0.842394	−	0.538862i	$-0.181145\pi$
$397$	35.4347	−	3.72434i	1.77842	−	0.186919i	0.936022	+	0.351943i	$0.114479\pi$
$398$	37.9330	−	12.3252i	1.90141	−	0.617806i
$399$	0.779698	−	0.161785i	0.0390337	−	0.00809940i
$400$	21.8076	+	37.3864i	1.09038	+	1.86932i
$401$	2.81098	−	4.86877i	0.140374	−	0.243135i	−0.787264	−	0.616617i	$-0.788503\pi$
$401$	2.81098	−	4.86877i	0.140374	−	0.243135i	0.927637	+	0.373482i	$0.121836\pi$
$402$	−0.493698	−	0.444527i	−0.0246234	−	0.0221710i
$403$	10.1450	−	22.7860i	0.505356	−	1.13505i
$404$	1.08452	+	10.3185i	0.0539568	+	0.513364i
$405$	4.11726	−	19.5844i	0.204588	−	0.973157i
$406$	−15.1958	+	10.9283i	−0.754155	+	0.542362i
$407$		−	12.3213i		−	0.610744i
$408$	0.0637230	+	0.143124i	0.00315476	+	0.00708570i
$409$	−10.7297	+	2.28066i	−0.530548	+	0.112772i	−0.465394	−	0.885104i	$-0.654087\pi$
$409$	−10.7297	+	2.28066i	−0.530548	+	0.112772i	−0.0651544	+	0.997875i	$0.520754\pi$
$410$	10.6307	+	7.68754i	0.525011	+	0.379660i
$411$	0.640983	+	0.136245i	0.0316174	+	0.00672048i
$412$	−18.3028	−	5.94693i	−0.901712	−	0.292984i
$413$	−9.39460	−	21.3788i	−0.462278	−	1.05198i
$414$	−16.8321	−	51.8038i	−0.827251	−	2.54602i
$415$	6.97244	−	7.77842i	0.342263	−	0.381828i
$416$	−23.1755	+	4.92611i	−1.13627	+	0.241522i
$417$	0.787866	+	0.0828080i	0.0385820	+	0.00405513i
$418$	−34.1217	−	19.7002i	−1.66895	−	0.963568i
$419$	−10.3403	−	7.51266i	−0.505156	−	0.367018i	0.305827	−	0.952087i	$-0.401067\pi$
$419$	−10.3403	−	7.51266i	−0.505156	−	0.367018i	−0.810983	+	0.585070i	$0.801067\pi$
$420$	1.53752	+	1.39170i	0.0750235	+	0.0679081i
$421$	−31.8380	+	23.1317i	−1.55169	+	1.12737i	−0.609260	+	0.792971i	$0.708533\pi$
$421$	−31.8380	+	23.1317i	−1.55169	+	1.12737i	−0.942432	+	0.334399i	$0.891467\pi$
$422$	32.1837	−	3.38265i	1.56668	−	0.164665i
$423$	12.3523	+	11.1221i	0.600591	+	0.540775i
$424$	12.7982	+	22.1671i	0.621535	+	1.07653i
$425$	−1.43284	−	0.458516i	−0.0695029	−	0.0222413i
$426$	−0.644228			−0.0312129
$427$	−0.175250	+	36.1699i	−0.00848096	+	1.75038i
$428$	26.4986	+	36.4721i	1.28086	+	1.76295i
$429$	−0.0826481	−	0.786344i	−0.00399029	−	0.0379651i
$430$	−49.8802	−	16.0844i	−2.40543	−	0.775658i
$431$	1.35516	−	12.8935i	0.0652760	−	0.621059i	−0.912161	−	0.409832i	$-0.865587\pi$
$431$	1.35516	−	12.8935i	0.0652760	−	0.621059i	0.977437	−	0.211227i	$-0.0677460\pi$
$432$	−3.35489	−	1.93694i	−0.161412	−	0.0931913i
$433$	18.1008	−	24.9136i	0.869868	−	1.19727i	−0.109258	−	0.994013i	$-0.534847\pi$
$433$	18.1008	−	24.9136i	0.869868	−	1.19727i	0.979126	−	0.203257i	$-0.0651525\pi$
$434$	6.65867	−	60.5304i	0.319627	−	2.90555i
$435$	−0.0487180	−	0.453802i	−0.00233585	−	0.0217581i
$436$	−26.4103	−	5.61368i	−1.26482	−	0.268846i
$437$	−5.89247	−	27.7219i	−0.281875	−	1.32612i
$438$	0.525446	+	2.47203i	0.0251068	+	0.118118i
$439$	−9.57539	−	2.03531i	−0.457008	−	0.0971401i	−0.0263453	−	0.999653i	$-0.508387\pi$
$439$	−9.57539	−	2.03531i	−0.457008	−	0.0971401i	−0.430663	+	0.902513i	$0.641720\pi$
$440$	−6.28760	−	58.5682i	−0.299750	−	2.79213i
$441$	−19.0653	−	8.71076i	−0.907871	−	0.414798i
$442$	1.28321	−	1.76618i	0.0610359	−	0.0840087i
$443$	−23.8217	−	13.7534i	−1.13180	−	0.653446i	−0.187414	−	0.982281i	$-0.560011\pi$
$443$	−23.8217	−	13.7534i	−1.13180	−	0.653446i	−0.944387	+	0.328835i	$0.893344\pi$
$444$	0.119533	−	1.13728i	0.00567280	−	0.0539730i
$445$	−16.3923	−	5.28587i	−0.777070	−	0.250574i
$446$	−2.10363	−	20.0147i	−0.0996097	−	0.947723i
$447$	−0.0610241	−	0.0839925i	−0.00288634	−	0.00397271i
$448$	−10.4567	+	5.96982i	−0.494033	+	0.282047i
$449$	21.4940			1.01436			0.507182	−	0.861839i	$-0.330687\pi$
$449$	21.4940			1.01436			0.507182	+	0.861839i	$0.330687\pi$
$450$	36.7915	−	12.1356i	1.73437	−	0.572078i
$451$	−4.28195	−	7.41655i	−0.201629	−	0.349232i
$452$	8.88209	+	7.99747i	0.417778	+	0.376169i
$453$	−1.14963	+	0.120831i	−0.0540144	+	0.00567714i
$454$	−14.4401	+	10.4913i	−0.677708	+	0.492383i
$455$	3.49157	−	16.2176i	0.163687	−	0.760291i
$456$	−1.69828	−	1.23387i	−0.0795294	−	0.0577815i
$457$	17.1453	+	9.89884i	0.802023	+	0.463048i	0.844178	−	0.536063i	$-0.180089\pi$
$457$	17.1453	+	9.89884i	0.802023	+	0.463048i	−0.0421551	+	0.999111i	$0.513422\pi$
$458$	−47.2574	−	4.96695i	−2.20819	−	0.232091i
$459$	0.131708	−	0.0279955i	0.00614762	−	0.00130672i
$460$	49.2662	−	54.9612i	2.29705	−	2.56258i
$461$	−1.92363	−	5.92031i	−0.0895922	−	0.275736i	0.896214	−	0.443621i	$-0.146306\pi$
$461$	−1.92363	−	5.92031i	−0.0895922	−	0.275736i	−0.985807	+	0.167885i	$0.946306\pi$
$462$	−0.776610	−	1.76729i	−0.0361312	−	0.0822217i
$463$	−10.4735	−	3.40304i	−0.486744	−	0.158153i	0.0553559	−	0.998467i	$-0.482371\pi$
$463$	−10.4735	−	3.40304i	−0.486744	−	0.158153i	−0.542100	+	0.840314i	$0.682371\pi$
$464$	23.1497	+	4.92063i	1.07470	+	0.228434i
$465$	1.20324	+	0.870123i	0.0557991	+	0.0403510i
$466$	22.6699	−	4.81863i	1.05016	−	0.223219i
$467$	−4.57435	−	10.2742i	−0.211676	−	0.475431i	0.776237	−	0.630441i	$-0.217126\pi$
$467$	−4.57435	−	10.2742i	−0.211676	−	0.475431i	−0.987913	+	0.155010i	$0.950459\pi$
$468$			39.4259i			1.82246i
$469$	0.907226	+	9.05343i	0.0418918	+	0.418048i
$470$	−6.60759	+	31.4301i	−0.304785	+	1.44976i
$471$	−0.0121460	−	0.115562i	−0.000559660	−	0.00532481i
$472$	−25.0385	+	56.2373i	−1.15249	+	2.58853i
$473$	25.4244	+	22.8922i	1.16902	+	1.05259i
$474$	−0.818112	+	1.41701i	−0.0375772	+	0.0650855i
$475$	19.6982	−	4.27871i	0.903814	−	0.196321i
$476$	1.17228	−	3.54928i	0.0537311	−	0.162681i
$477$	10.4515	−	3.39589i	0.478540	−	0.155487i
$478$	42.6502	−	4.48272i	1.95078	−	0.205035i
$479$	27.1792	+	12.1010i	1.24185	+	0.552908i	0.919268	−	0.393633i	$-0.128782\pi$
$479$	27.1792	+	12.1010i	1.24185	+	0.552908i	0.322584	+	0.946541i	$0.395449\pi$
$480$	−0.00313956	−	1.41053i	−0.000143301	−	0.0643816i
$481$	−8.35667	+	3.72063i	−0.381032	+	0.169646i
$482$		−	15.1877i		−	0.691782i
$483$	0.570918	−	1.26576i	0.0259777	−	0.0575941i
$484$	−4.73819	+	14.5826i	−0.215372	+	0.662847i
$485$	11.2153	+	19.3259i	0.509259	+	0.877546i
$486$	−3.48138	+	3.86647i	−0.157919	+	0.175387i
$487$	7.29192	+	34.3058i	0.330428	+	1.55454i	0.759034	+	0.651051i	$0.225672\pi$
$487$	7.29192	+	34.3058i	0.330428	+	1.55454i	−0.428606	+	0.903492i	$0.640995\pi$
$488$	70.8596	−	63.8023i	3.20766	−	2.88819i
$489$	0.230685	+	0.709975i	0.0104319	+	0.0321062i
$490$	−3.93279	−	40.3103i	−0.177665	−	1.82103i
$491$	0.608859	−	1.87387i	0.0274774	−	0.0845667i	−0.936377	−	0.350995i	$-0.885843\pi$
$491$	0.608859	−	1.87387i	0.0274774	−	0.0845667i	0.963855	+	0.266428i	$0.0858435\pi$
$492$	−0.323282	−	0.726104i	−0.0145747	−	0.0327353i
$493$	−0.712417	+	0.411314i	−0.0320856	+	0.0185246i
$494$	−3.05761	+	29.0912i	−0.137568	+	1.30888i
$495$	−25.1569	−	2.58750i	−1.13072	−	0.116299i
$496$	−62.2930	+	45.2585i	−2.79704	+	2.03217i
$497$	6.52836	+	5.93569i	0.292837	+	0.266252i
$498$	−0.858272	+	0.278869i	−0.0384601	+	0.0124964i
$499$	−8.83166	+	15.2969i	−0.395359	+	0.684783i	−0.993147	−	0.116872i	$-0.962713\pi$
$499$	−8.83166	+	15.2969i	−0.395359	+	0.684783i	0.597788	+	0.801655i	$0.296047\pi$
$500$	39.2464	+	34.8659i	1.75515	+	1.55925i
$501$	−0.554022	−	0.959594i	−0.0247519	−	0.0428715i
$502$	−1.93415	+	9.09948i	−0.0863255	+	0.406130i
$503$	−2.37581	−	3.27003i	−0.105932	−	0.145803i	0.752760	−	0.658296i	$-0.228722\pi$
$503$	−2.37581	−	3.27003i	−0.105932	−	0.145803i	−0.858692	+	0.512492i	$0.828722\pi$
$504$	16.8204	+	52.6343i	0.749240	+	2.34452i
$505$	2.01970	+	4.50929i	0.0898756	+	0.200661i
$506$	−62.7647	+	27.9446i	−2.79023	+	1.24229i
$507$	0.332135	−	0.191758i	0.0147506	−	0.00851629i
$508$	−62.5622	−	6.57555i	−2.77575	−	0.291743i
$509$	−9.19444	−	10.2115i	−0.407536	−	0.452615i	0.504080	−	0.863657i	$-0.331832\pi$
$509$	−9.19444	−	10.2115i	−0.407536	−	0.452615i	−0.911616	+	0.411042i	$0.865165\pi$
$510$	0.0871803	+	0.0963912i	0.00386041	+	0.00426828i
$511$	17.4517	−	29.8919i	0.772019	−	1.32234i
$512$	−45.2774	−	14.7115i	−2.00100	−	0.650163i
$513$	−1.34076	+	1.20723i	−0.0591961	+	0.0533004i
$514$	7.56472	−	8.40147i	0.333665	−	0.370573i
$515$	−9.16467	+	0.0203987i	−0.403844	+	0.000898876i
$516$	2.12464	+	2.35965i	0.0935322	+	0.103878i
$517$	12.3232	−	16.9615i	0.541975	−	0.745965i
$518$	−16.6690	+	14.8633i	−0.732396	+	0.653054i
$519$	−0.319489	−	0.232123i	−0.0140240	−	0.0101891i
$520$	−37.8241	+	21.9501i	−1.65869	+	0.962577i
$521$	−13.7884	−	6.13900i	−0.604082	−	0.268955i	0.0818217	−	0.996647i	$-0.473926\pi$
$521$	−13.7884	−	6.13900i	−0.604082	−	0.268955i	−0.685904	+	0.727692i	$0.740593\pi$
$522$	8.61634	−	19.3526i	0.377127	−	0.847041i
$523$	−4.47583	+	21.0571i	−0.195714	+	0.920763i	0.765173	+	0.643824i	$0.222653\pi$
$523$	−4.47583	+	21.0571i	−0.195714	+	0.920763i	−0.960888	+	0.276939i	$0.910680\pi$
$524$	−78.2000			−3.41618
$525$	0.902063	+	0.402050i	0.0393693	+	0.0175469i
$526$	20.4102			0.889929
$527$	0.556446	−	2.61787i	0.0242392	−	0.114036i
$528$	−0.992788	+	2.22984i	−0.0432056	+	0.0970413i
$529$	−24.1359	−	10.7460i	−1.04939	−	0.467217i
$530$	15.8115	+	14.1732i	0.686809	+	0.615643i
$531$	21.3818	+	15.5348i	0.927891	+	0.674152i
$532$	10.1754	+	49.0388i	0.441161	+	2.12610i
$533$	−3.73712	+	5.14370i	−0.161872	+	0.222798i
$534$	0.995636	+	1.10577i	0.0430854	+	0.0478512i
$535$	17.3968	+	12.5805i	0.752130	+	0.543900i
$536$	16.0497	−	17.8250i	0.693240	−	0.769921i
$537$	0.128299	−	0.115521i	0.00553653	−	0.00498511i
$538$	−43.8263	−	14.2400i	−1.88949	−	0.613932i
$539$	−8.41331	+	25.0645i	−0.362387	+	1.07960i
$540$	−4.59815	−	0.966674i	−0.197873	−	0.0415990i
$541$	−25.2587	−	28.0526i	−1.08595	−	1.20607i	−0.977270	−	0.211998i	$-0.932003\pi$
$541$	−25.2587	−	28.0526i	−1.08595	−	1.20607i	−0.108684	−	0.994076i	$-0.534664\pi$
$542$	27.4338	+	2.88341i	1.17838	+	0.123853i
$543$	1.15107	−	0.664571i	0.0493972	−	0.0285195i
$544$	−2.32253	+	1.03406i	−0.0995778	+	0.0443349i
$545$	−12.7846	+	1.37249i	−0.547633	+	0.0587912i
$546$	−0.964118	+	1.06038i	−0.0412604	+	0.0453802i
$547$	−2.11101	−	2.90556i	−0.0902603	−	0.124233i	0.761499	−	0.648166i	$-0.224464\pi$
$547$	−2.11101	−	2.90556i	−0.0902603	−	0.124233i	−0.851759	+	0.523934i	$0.824464\pi$
$548$	−8.56909	+	40.3144i	−0.366053	+	1.72215i
$549$	−20.4686	−	35.4526i	−0.873577	−	1.51308i
$550$	−20.0740	−	44.5521i	−0.855957	−	1.89971i
$551$	5.51116	−	9.54560i	0.234783	−	0.406656i
$552$	−3.48132	+	1.13115i	−0.148175	+	0.0481449i
$553$	21.3463	−	6.82167i	0.907737	−	0.290087i
$554$	5.73063	−	4.16354i	0.243471	−	0.176892i
$555$	−0.114410	−	0.532426i	−0.00485643	−	0.0226002i
$556$	−5.20818	+	49.5525i	−0.220876	+	2.10149i
$557$	−12.2763	+	7.08773i	−0.520164	+	0.300317i	−0.737002	−	0.675891i	$-0.763759\pi$
$557$	−12.2763	+	7.08773i	−0.520164	+	0.300317i	0.216838	+	0.976208i	$0.430426\pi$
$558$	28.0326	+	62.9622i	1.18671	+	2.66540i
$559$	7.84886	−	24.1563i	0.331971	−	1.02170i
$560$	−34.3669	+	37.9678i	−1.45227	+	1.60443i
$561$	−0.0262173	−	0.0806885i	−0.00110689	−	0.00340667i
$562$	28.4885	−	25.6511i	1.20171	−	1.08203i
$563$	−3.31546	−	15.5980i	−0.139730	−	0.657378i	−0.991134	−	0.132867i	$-0.957582\pi$
$563$	−3.31546	−	15.5980i	−0.139730	−	0.657378i	0.851404	−	0.524511i	$-0.175752\pi$
$564$	1.30201	−	1.44603i	0.0548245	−	0.0608888i
$565$	5.20486	+	2.30348i	0.218970	+	0.0969083i
$566$	5.24183	−	16.1327i	0.220331	−	0.678108i
$567$	23.5611	−	2.36101i	0.989474	−	0.0991533i
$568$		−	23.2599i		−	0.975962i
$569$	−32.3178	+	14.3888i	−1.35483	+	0.603210i	−0.950306	−	0.311317i	$-0.899230\pi$
$569$	−32.3178	+	14.3888i	−1.35483	+	0.603210i	−0.404526	+	0.914527i	$0.632563\pi$
$570$	−1.65739	−	0.534444i	−0.0694205	−	0.0223854i
$571$	18.1029	+	8.05995i	0.757585	+	0.337298i	0.748917	−	0.662664i	$-0.230574\pi$
$571$	18.1029	+	8.05995i	0.757585	+	0.337298i	0.00866787	+	0.999962i	$0.497241\pi$
$572$	49.4568	−	5.19812i	2.06789	−	0.217344i
$573$	0.913140	−	0.296697i	0.0381470	−	0.0123947i
$574$	−4.86824	+	14.7395i	−0.203196	+	0.615216i
$575$	14.1536	−	32.1742i	0.590245	−	1.34176i
$576$	6.81382	−	11.8019i	0.283909	−	0.491745i
$577$	−14.8704	−	13.3894i	−0.619063	−	0.557407i	0.298794	−	0.954318i	$-0.403416\pi$
$577$	−14.8704	−	13.3894i	−0.619063	−	0.557407i	−0.917857	+	0.396911i	$0.870082\pi$
$578$	−17.7964	+	39.9715i	−0.740234	+	1.66259i
$579$	−0.207446	−	1.97372i	−0.00862118	−	0.0820250i
$580$	28.5417	−	3.06410i	1.18513	−	0.127230i
$581$	11.2668	+	5.08186i	0.467426	+	0.210831i
$582$		−	1.93036i		−	0.0800160i
$583$	−5.63786	−	12.6628i	−0.233496	−	0.524441i
$584$	−89.2526	+	18.9712i	−3.69330	+	0.785035i
$585$	5.84165	+	17.8435i	0.241522	+	0.737738i
$586$	79.6465	+	16.9294i	3.29017	+	0.699347i
$587$	−14.6973	−	4.77544i	−0.606623	−	0.197104i	−0.0104308	−	0.999946i	$-0.503320\pi$
$587$	−14.6973	−	4.77544i	−0.606623	−	0.197104i	−0.596192	+	0.802842i	$0.703320\pi$
$588$	−1.01973	+	2.23188i	−0.0420528	+	0.0920413i
$589$	11.0814	+	34.1051i	0.456602	+	1.40528i
$590$	−5.22499	+	50.7999i	−0.215109	+	2.09140i
$591$	0.241776	−	0.0513910i	0.00994532	−	0.00211394i
$592$	28.0842	+	2.95177i	1.15425	+	0.121317i
$593$	−3.16592	−	1.82785i	−0.130009	−	0.0750607i	0.433585	−	0.901113i	$-0.357248\pi$
$593$	−3.16592	−	1.82785i	−0.130009	−	0.0750607i	−0.563594	+	0.826052i	$0.690582\pi$
$594$	3.53837	+	2.57077i	0.145181	+	0.105480i
$595$	0.00466258	−	1.78004i	0.000191147	−	0.0729746i
$596$	5.28268	−	3.83809i	0.216387	−	0.157214i
$597$	−1.14446	+	0.120287i	−0.0468395	+	0.00492303i
$598$	37.9058	+	34.1305i	1.55008	+	1.39570i
$599$	3.07128	+	5.31962i	0.125489	+	0.217354i	0.921924	−	0.387371i	$-0.126617\pi$
$599$	3.07128	+	5.31962i	0.125489	+	0.217354i	−0.796435	+	0.604724i	$0.793283\pi$
$600$	−0.815536	−	2.47246i	−0.0332941	−	0.100938i
$601$	33.2947			1.35812			0.679060	−	0.734083i	$-0.262388\pi$
$601$	33.2947			1.35812			0.679060	+	0.734083i	$0.262388\pi$
$602$	0.300455	−	62.0108i	0.0122456	−	2.52737i
$603$	−6.05293	−	8.33115i	−0.246495	−	0.339271i
$604$	−7.59963	−	72.3056i	−0.309225	−	2.94208i
$605$	0.0162526	+	7.30191i	0.000660762	+	0.296865i
$606$	0.0446183	−	0.424515i	0.00181250	−	0.0172447i
$607$	−35.6231	−	20.5670i	−1.44590	−	0.834788i	−0.447662	−	0.894203i	$-0.647743\pi$
$607$	−35.6231	−	20.5670i	−1.44590	−	0.834788i	−0.998233	+	0.0594149i	$0.981077\pi$
$608$	20.0226	−	27.5587i	0.812023	−	1.11765i
$609$	0.494402	−	0.217258i	0.0200342	−	0.00880372i
$610$	39.3976	−	68.5908i	1.59516	−	2.77716i
$611$	−15.2250	−	3.23617i	−0.615937	−	0.130921i
$612$	0.879564	+	4.13802i	0.0355543	+	0.167270i
$613$	−4.82936	−	22.7203i	−0.195056	−	0.917666i	−0.961383	−	0.275215i	$-0.911251\pi$
$613$	−4.82936	−	22.7203i	−0.195056	−	0.917666i	0.766327	−	0.642451i	$-0.222082\pi$
$614$	49.5155	+	10.5248i	1.99828	+	0.424748i
$615$	−0.253897	−	0.280723i	−0.0102381	−	0.0113198i
$616$	63.8080	−	28.0395i	2.57090	−	1.12974i
$617$	1.58759	−	2.18514i	0.0639141	−	0.0879702i	−0.775863	−	0.630901i	$-0.782685\pi$
$617$	1.58759	−	2.18514i	0.0639141	−	0.0879702i	0.839777	+	0.542931i	$0.182685\pi$
$618$	0.685674	+	0.395874i	0.0275818	+	0.0159244i
$619$	5.01708	−	47.7343i	0.201654	−	1.91861i	−0.161495	−	0.986874i	$-0.551631\pi$
$619$	5.01708	−	47.7343i	0.201654	−	1.91861i	0.363148	−	0.931731i	$-0.381702\pi$
$620$	−54.7260	+	75.6776i	−2.19785	+	3.03928i
$621$	0.328850	+	3.12880i	0.0131963	+	0.125554i
$622$	−50.2782	−	69.2020i	−2.01597	−	2.77475i
$623$	0.0987396	−	20.3789i	0.00395592	−	0.816462i
$624$	1.81213			0.0725434
$625$	22.9283	+	9.96468i	0.917130	+	0.398587i
$626$	9.84779	+	17.0569i	0.393597	+	0.681730i
$627$	0.844789	+	0.760651i	0.0337376	+	0.0303775i
$628$	7.26822	−	0.763920i	0.290033	−	0.0304837i
$629$	−0.794086	+	0.576938i	−0.0316623	+	0.0230040i
$630$	26.8464	+	37.1552i	1.06959	+	1.48030i
$631$	−18.3629	−	13.3414i	−0.731016	−	0.531114i	0.158869	−	0.987300i	$-0.449215\pi$
$631$	−18.3629	−	13.3414i	−0.731016	−	0.531114i	−0.889885	+	0.456186i	$0.849215\pi$
$632$	−51.1613	−	29.5380i	−2.03509	−	1.17496i
$633$	−0.928561	−	0.0975956i	−0.0369070	−	0.00387908i
$634$	56.6967	−	12.0513i	2.25171	−	0.478617i
$635$	−29.2889	+	6.29372i	−1.16229	+	0.249759i
$636$	−0.397540	−	1.22350i	−0.0157635	−	0.0485150i
$637$	19.5400	−	1.86249i	0.774203	−	0.0737944i
$638$	−25.4124	−	8.25699i	−1.00609	−	0.326898i
$639$	−9.76795	−	2.07624i	−0.386414	−	0.0821349i
$640$	−11.4557	+	0.0254981i	−0.452825	+	0.00100790i
$641$	32.8748	−	6.98776i	1.29848	−	0.276000i	0.493729	−	0.869616i	$-0.335633\pi$
$641$	32.8748	−	6.98776i	1.29848	−	0.276000i	0.804749	+	0.593615i	$0.202300\pi$
$642$	−0.754386	−	1.69438i	−0.0297732	−	0.0668718i
$643$		−	2.04600i		−	0.0806863i	−0.999186	−	0.0403432i	$-0.987155\pi$
$643$		−	2.04600i		−	0.0806863i	0.999186	−	0.0403432i	$-0.0128451\pi$
$644$	79.6095	+	35.9076i	3.13706	+	1.41496i
$645$	1.31120	+	0.753137i	0.0516286	+	0.0296547i
$646$	0.328087	+	3.12154i	0.0129084	+	0.122815i
$647$	−6.34621	+	14.2538i	−0.249495	+	0.560376i	−0.994265	−	0.106946i	$-0.965893\pi$
$647$	−6.34621	+	14.2538i	−0.249495	+	0.560376i	0.744769	+	0.667322i	$0.232559\pi$
$648$	−46.3886	−	41.7685i	−1.82232	−	1.64082i
$649$	16.6681	−	28.8700i	0.654281	−	1.13325i
$650$	−24.1549	+	27.0680i	−0.947432	+	1.06170i
$651$	−0.551017	+	1.66831i	−0.0215961	+	0.0653862i
$652$	−44.6536	+	14.5088i	−1.74877	+	0.568210i
$653$	−35.4456	+	3.72548i	−1.38709	+	0.145789i	−0.768464	−	0.639893i	$-0.778979\pi$
$653$	−35.4456	+	3.72548i	−1.38709	+	0.145789i	−0.618630	+	0.785683i	$0.712312\pi$
$654$	1.01479	+	0.451813i	0.0396813	+	0.0176673i
$655$	−35.3920	+	11.5867i	−1.38288	+	0.452731i
$656$	17.9305	−	7.98318i	0.700069	−	0.311691i
$657$			39.1750i			1.52836i
$658$	−37.8121	+	3.78908i	−1.47407	+	0.147714i
$659$	−4.30237	+	13.2413i	−0.167596	+	0.515809i	−0.999218	−	0.0395337i	$-0.987413\pi$
$659$	−4.30237	+	13.2413i	−0.167596	+	0.515809i	0.831622	+	0.555342i	$0.187413\pi$
$660$	−0.302906	+	2.94500i	−0.0117906	+	0.114634i
$661$	5.10093	−	5.66516i	0.198403	−	0.220349i	−0.635731	−	0.771911i	$-0.719301\pi$
$661$	5.10093	−	5.66516i	0.198403	−	0.220349i	0.834134	+	0.551562i	$0.185968\pi$
$662$	−5.01064	−	23.5732i	−0.194744	−	0.916199i
$663$	−0.0468086	+	0.0421466i	−0.00181789	+	0.00163684i
$664$	−10.0686	−	30.9879i	−0.390737	−	1.20256i
$665$	11.8712	+	20.6865i	0.460345	+	0.802187i
$666$	7.81086	−	24.0393i	0.302665	−	0.931506i
$667$	−7.81755	−	17.5585i	−0.302697	−	0.679868i
$668$	60.3533	−	34.8450i	2.33514	−	1.34819i
$669$	−0.0606936	+	0.577461i	−0.00234655	+	0.0223259i
$670$	8.05275	−	18.1957i	0.311105	−	0.702960i
$671$	−41.7739	+	30.3505i	−1.61266	+	1.17167i
$672$	1.58976	−	0.508042i	0.0613263	−	0.0195981i
$673$	−15.9860	+	5.19416i	−0.616214	+	0.200220i	−0.600459	−	0.799656i	$-0.705015\pi$
$673$	−15.9860	+	5.19416i	−0.616214	+	0.200220i	−0.0157555	+	0.999876i	$0.505015\pi$
$674$	18.7244	−	32.4315i	0.721235	−	1.24922i
$675$	−2.22427	+	0.243796i	−0.0856124	+	0.00938373i
$676$	12.0606	+	20.8895i	0.463868	+	0.803443i
$677$	−2.44298	+	11.4933i	−0.0938915	+	0.441725i	0.905941	+	0.423405i	$0.139165\pi$
$677$	−2.44298	+	11.4933i	−0.0938915	+	0.441725i	−0.999832	+	0.0183202i	$0.994168\pi$
$678$	−0.289026	−	0.397810i	−0.0111000	−	0.0152778i
$679$	−17.7857	+	19.5615i	−0.682551	+	0.750703i
$680$	−3.48021	+	3.14765i	−0.133460	+	0.120707i
$681$	0.470454	−	0.209459i	0.0180278	−	0.00802650i
$682$	75.2854	−	43.4661i	2.88283	−	1.66440i
$683$	−3.98400	−	0.418735i	−0.152443	−	0.0160224i	0.0279993	−	0.999608i	$-0.491086\pi$
$683$	−3.98400	−	0.418735i	−0.152443	−	0.0160224i	−0.180443	+	0.983585i	$0.557753\pi$
$684$	−37.9288	−	42.1242i	−1.45024	−	1.61066i
$685$	2.09507	+	19.5153i	0.0800484	+	0.745641i
$686$	44.0578	−	18.8533i	1.68214	−	0.719824i
$687$	1.30388	+	0.423655i	0.0497459	+	0.0161634i
$688$	−58.2697	+	52.4663i	−2.22151	+	2.00026i
$689$	−6.88587	+	7.64753i	−0.262331	+	0.291348i
$690$	−2.45270	+	1.79034i	−0.0933726	+	0.0681572i
$691$	11.3903	+	12.6502i	0.433309	+	0.481238i	0.919766	−	0.392466i	$-0.128378\pi$
$691$	11.3903	+	12.6502i	0.433309	+	0.481238i	−0.486458	+	0.873704i	$0.661711\pi$
$692$	14.5993	−	20.0942i	0.554981	−	0.763865i
$693$	−6.07947	−	29.2990i	−0.230940	−	1.11298i
$694$	6.84312	+	4.97182i	0.259761	+	0.188728i
$695$	4.98495	+	23.1983i	0.189090	+	0.879963i
$696$	−1.30053	−	0.579035i	−0.0492966	−	0.0219483i
$697$	−0.277484	+	0.623239i	−0.0105105	+	0.0236069i
$698$	10.8266	−	50.9351i	0.409793	−	1.92792i
$699$	−0.668680			−0.0252918
$700$	−25.2868	+	56.7349i	−0.955750	+	2.14438i
$701$	−42.3252			−1.59860			−0.799300	−	0.600932i	$-0.794796\pi$
$701$	−42.3252			−1.59860			−0.799300	+	0.600932i	$0.794796\pi$
$702$	0.675105	−	3.17612i	0.0254802	−	0.119875i
$703$	5.34925	−	12.0146i	0.201751	−	0.453140i
$704$	−15.7029	−	6.99140i	−0.591827	−	0.263498i
$705$	0.375013	−	0.847364i	0.0141238	−	0.0319136i
$706$	66.1755	+	48.0793i	2.49055	+	1.80949i
$707$	−4.36348	+	3.89078i	−0.164105	+	0.146328i
$708$	1.81858	−	2.50306i	0.0683465	−	0.0940709i
$709$	7.25637	+	8.05902i	0.272519	+	0.302663i	0.863833	−	0.503779i	$-0.168057\pi$
$709$	7.25637	+	8.05902i	0.272519	+	0.302663i	−0.591314	+	0.806441i	$0.701391\pi$
$710$	−6.00353	−	18.3380i	−0.225308	−	0.688212i
$711$	−16.9712	+	18.8485i	−0.636471	+	0.706873i
$712$	−39.9237	+	35.9475i	−1.49620	+	1.34719i
$713$	59.4709	+	19.3233i	2.22720	+	0.723662i
$714$	−0.0775345	+	0.132803i	−0.00290165	+	0.00497004i
$715$	21.6131	−	9.68049i	0.808286	−	0.362030i
$716$	7.26567	+	8.06934i	0.271531	+	0.301565i
$717$	−1.23054	−	0.129335i	−0.0459553	−	0.00483010i
$718$	23.1533	−	13.3676i	0.864074	−	0.498873i
$719$	7.69245	−	3.42490i	0.286880	−	0.127727i	−0.258252	−	0.966078i	$-0.583146\pi$
$719$	7.69245	−	3.42490i	0.286880	−	0.127727i	0.545132	+	0.838350i	$0.316480\pi$
$720$	11.9245	−	56.7209i	0.444400	−	2.11386i
$721$	−3.30091	−	10.3292i	−0.122932	−	0.384679i
$722$	4.17797	+	5.75049i	0.155488	+	0.214011i
$723$	−0.0911057	+	0.428619i	−0.00338826	+	0.0159405i
$724$	41.7979	+	72.3961i	1.55341	+	2.69058i
$725$	12.4635	−	5.61572i	0.462883	−	0.208563i
$726$	0.315411	−	0.546307i	0.0117060	−	0.0202754i
$727$	−10.6486	+	3.45993i	−0.394934	+	0.128322i	−0.499750	−	0.866170i	$-0.666575\pi$
$727$	−10.6486	+	3.45993i	−0.394934	+	0.128322i	0.104816	+	0.994492i	$0.466575\pi$
$728$	−38.2852	−	34.8095i	−1.41894	−	1.29013i
$729$	−21.6003	+	15.6936i	−0.800013	+	0.581243i
$730$	−65.4698	+	37.9936i	−2.42315	+	1.40621i
$731$	0.284882	−	2.71048i	0.0105368	−	0.100251i
$732$	−4.15026	+	2.39616i	−0.153398	+	0.0885644i
$733$	8.68312	+	19.5026i	0.320718	+	0.720345i	0.999907	−	0.0136185i	$-0.00433503\pi$
$733$	8.68312	+	19.5026i	0.320718	+	0.720345i	−0.679189	+	0.733963i	$0.737668\pi$
$734$	−13.6676	+	42.0646i	−0.504480	+	1.55263i
$735$	−0.130818	+	1.16120i	−0.00482530	+	0.0428316i
$736$	−18.3556	−	56.4927i	−0.676596	−	2.08235i
$737$	−9.65275	+	8.69137i	−0.355563	+	0.320151i
$738$	−3.65266	−	17.1844i	−0.134456	−	0.632568i
$739$	−3.96668	+	4.40544i	−0.145917	+	0.162057i	−0.811672	−	0.584113i	$-0.801443\pi$
$739$	−3.96668	+	4.40544i	−0.145917	+	0.162057i	0.665756	+	0.746170i	$0.268109\pi$
$740$	33.4867	−	7.19577i	1.23100	−	0.264522i
$741$	0.260798	−	0.802653i	0.00958064	−	0.0294862i
$742$	−10.3301	+	22.9025i	−0.379230	+	0.840778i
$743$			31.5615i			1.15788i	0.815371	+	0.578939i	$0.196533\pi$
$743$			31.5615i			1.15788i	−0.815371	+	0.578939i	$0.803467\pi$
$744$	4.23119	−	1.88385i	0.155123	−	0.0690651i
$745$	1.82217	−	2.51978i	0.0667592	−	0.0923175i
$746$	61.2969	+	27.2912i	2.24424	+	0.999200i
$747$	−13.9121	+	1.46222i	−0.509017	+	0.0534998i
$748$	5.07487	−	1.64893i	0.185556	−	0.0602907i
$749$	−7.96674	+	24.1208i	−0.291099	+	0.881356i
$750$	−1.28112	−	1.73878i	−0.0467800	−	0.0634913i
$751$	17.6528	−	30.5755i	0.644160	−	1.11572i	−0.340335	−	0.940304i	$-0.610540\pi$
$751$	17.6528	−	30.5755i	0.644160	−	1.11572i	0.984495	−	0.175413i	$-0.0561262\pi$
$752$	35.7084	+	32.1520i	1.30215	+	1.17246i
$753$	0.109169	−	0.245198i	0.00397834	−	0.00893550i
$754$	2.07358	+	19.7288i	0.0755154	+	0.718481i
$755$	−14.1528	−	31.5983i	−0.515074	−	1.14998i
$756$	−0.554333	−	5.53182i	−0.0201609	−	0.201191i
$757$		−	9.26089i		−	0.336593i	−0.985736	−	0.168296i	$-0.946173\pi$
$757$		−	9.26089i		−	0.336593i	0.985736	−	0.168296i	$-0.0538266\pi$
$758$	−7.93356	−	17.8191i	−0.288160	−	0.647218i
$759$	1.93894	−	0.412134i	0.0703790	−	0.0149595i
$760$	19.2961	−	59.8401i	0.699943	−	2.17063i
$761$	−49.4584	−	10.5127i	−1.79287	−	0.381086i	−0.813243	−	0.581925i	$-0.802300\pi$
$761$	−49.4584	−	10.5127i	−1.79287	−	0.381086i	−0.979624	+	0.200839i	$0.935633\pi$
$762$	2.46139	+	0.799754i	0.0891668	+	0.0289720i
$763$	−6.12063	−	13.9284i	−0.221582	−	0.504242i
$764$	18.6607	+	57.4316i	0.675119	+	2.07780i
$765$	1.01120	+	1.74248i	0.0365599	+	0.0629994i
$766$	−42.7134	+	9.07901i	−1.54330	+	0.328038i
$767$	−24.6138	−	2.58701i	−0.888751	−	0.0934115i
$768$	1.44556	+	0.834595i	0.0521622	+	0.0301158i
$769$	14.4845	+	10.5236i	0.522325	+	0.379492i	0.817479	−	0.575958i	$-0.195371\pi$
$769$	14.4845	+	10.5236i	0.522325	+	0.379492i	−0.295154	+	0.955450i	$0.595371\pi$
$770$	43.0688	−	38.5755i	1.55209	−	1.39017i
$771$	−0.263884	+	0.191723i	−0.00950356	+	0.00690474i
$772$	124.136	−	13.0473i	4.46777	−	0.469581i
$773$	7.13915	+	6.42812i	0.256778	+	0.231204i	0.787458	−	0.616369i	$-0.211397\pi$
$773$	7.13915	+	6.42812i	0.256778	+	0.231204i	−0.530680	+	0.847572i	$0.678063\pi$
$774$	35.0919	+	60.7810i	1.26135	+	2.18473i
$775$	−13.5551	+	42.3590i	−0.486914	+	1.52158i
$776$	69.6957			2.50193
$777$	0.559583	−	0.319470i	0.0200749	−	0.0114609i
$778$	16.1084	+	22.1713i	0.577514	+	0.794880i
$779$	−0.955496	−	9.09094i	−0.0342342	−	0.325717i
$780$	2.08885	−	0.683854i	0.0747930	−	0.0244859i
$781$	−1.31663	+	12.5269i	−0.0471127	+	0.448248i
$782$	4.73990	+	2.73659i	0.169499	+	0.0978601i
$783$	−0.719178	+	0.989863i	−0.0257013	+	0.0353748i
$784$	−55.1144	−	25.1813i	−1.96837	−	0.899331i
$785$	3.17629	−	1.42265i	0.113367	−	0.0507767i
$786$	3.14693	+	0.668902i	0.112247	+	0.0238589i
$787$	0.158251	+	0.744513i	0.00564104	+	0.0265390i	0.980878	−	0.194623i	$-0.0623484\pi$
$787$	0.158251	+	0.744513i	0.00564104	+	0.0265390i	−0.975237	+	0.221162i	$0.929015\pi$
$788$	3.23222	+	15.2064i	0.115143	+	0.541705i
$789$	−0.576005	−	0.122434i	−0.0205063	−	0.00435876i
$790$	−47.9593	−	10.0825i	−1.70632	−	0.358721i
$791$	−0.736403	+	6.69424i	−0.0261835	+	0.238020i
$792$	−46.3658	+	63.8170i	−1.64754	+	2.26764i
$793$	33.1990	+	19.1674i	1.17893	+	0.680656i
$794$	9.63693	−	91.6893i	0.342002	−	3.25393i
$795$	−0.361204	−	0.494834i	−0.0128106	−	0.0175500i
$796$	−7.56543	−	71.9802i	−0.268149	−	2.55127i
$797$	10.7176	+	14.7515i	0.379636	+	0.522524i	0.955488	−	0.295030i	$-0.0953296\pi$
$797$	10.7176	+	14.7515i	0.379636	+	0.522524i	−0.575852	+	0.817554i	$0.695330\pi$
$798$	0.00998335	−	2.06046i	0.000353407	−	0.0729396i
$799$	−1.67017			−0.0590862
$800$	40.1216	−	13.2340i	1.41851	−	0.467894i
$801$	11.5324	+	19.9747i	0.407477	+	0.705771i
$802$	−10.8107	−	9.73396i	−0.381737	−	0.343718i
$803$	49.1421	−	5.16504i	1.73419	−	0.182270i
$804$	−0.975287	+	0.708588i	−0.0343957	+	0.0249900i
$805$	41.3503	+	4.45563i	1.45741	+	0.157040i
$806$	−52.2137	−	37.9355i	−1.83915	−	1.33622i
$807$	1.15142	+	0.664772i	0.0405319	+	0.0234011i
$808$	15.3271	+	1.61095i	0.539206	+	0.0566729i
$809$	26.8468	−	5.70647i	0.943885	−	0.200629i	0.289832	−	0.957078i	$-0.406401\pi$
$809$	26.8468	−	5.70647i	0.943885	−	0.200629i	0.654053	+	0.756449i	$0.273067\pi$
$810$	−47.3534	−	20.9569i	−1.66383	−	0.736351i
$811$	−8.93291	−	27.4927i	−0.313677	−	0.965399i	−0.976296	−	0.216442i	$-0.930555\pi$
$811$	−8.93291	−	27.4927i	−0.313677	−	0.965399i	0.662619	−	0.748957i	$-0.269445\pi$
$812$	13.6643	+	31.0952i	0.479524	+	1.09123i
$813$	−0.756925	−	0.245940i	−0.0265465	−	0.00862548i
$814$	−31.1854	−	6.62865i	−1.09305	−	0.232334i
$815$	−18.0597	+	13.1827i	−0.632605	+	0.461769i
$816$	0.190196	−	0.0404274i	0.00665819	−	0.00141524i
$817$	14.8530	+	33.3604i	0.519640	+	1.16713i
$818$			28.3839i			0.992420i
$819$	−18.0357	+	12.9706i	−0.630217	+	0.453230i
$820$	17.6559	−	15.9688i	0.616572	−	0.557654i
$821$	−2.40366	−	22.8693i	−0.0838884	−	0.798145i	−0.952886	−	0.303329i	$-0.901902\pi$
$821$	−2.40366	−	22.8693i	−0.0838884	−	0.798145i	0.868998	−	0.494816i	$-0.164765\pi$
$822$	0.689677	−	1.54904i	0.0240552	−	0.0540289i
$823$	−31.9252	−	28.7456i	−1.11284	−	1.00201i	−0.999965	−	0.00840016i	$-0.997326\pi$
$823$	−31.9252	−	28.7456i	−1.11284	−	1.00201i	−0.112879	−	0.993609i	$-0.536007\pi$
$824$	−14.2930	+	24.7563i	−0.497921	+	0.862425i
$825$	0.299264	+	1.37774i	0.0104190	+	0.0479667i
$826$	−59.1641	+	12.2764i	−2.05858	+	0.427151i
$827$	32.8898	−	10.6865i	1.14369	−	0.371608i	0.324927	−	0.945739i	$-0.394660\pi$
$827$	32.8898	−	10.6865i	1.14369	−	0.371608i	0.818763	+	0.574131i	$0.194660\pi$
$828$	−98.3008	+	10.3318i	−3.41619	+	0.359056i
$829$	−31.5148	−	14.0313i	−1.09456	−	0.487328i	−0.221605	−	0.975136i	$-0.571130\pi$
$829$	−31.5148	−	14.0313i	−1.09456	−	0.487328i	−0.872950	+	0.487809i	$0.837796\pi$
$830$	−15.9362	−	21.8320i	−0.553155	−	0.757799i
$831$	−0.186702	+	0.0831250i	−0.00647662	+	0.00288357i
$832$			12.7614i			0.442421i
$833$	2.00931	−	0.631405i	0.0696184	−	0.0218769i
$834$	0.633447	−	1.94955i	0.0219345	−	0.0675074i
$835$	22.1520	−	24.7127i	0.766601	−	0.855218i
$836$	−47.8409	+	53.1327i	−1.65461	+	1.83763i
$837$	−0.827631	−	3.89370i	−0.0286071	−	0.134586i
$838$	−24.5776	+	22.1297i	−0.849017	+	0.764459i
$839$	0.970542	+	2.98702i	0.0335068	+	0.103123i	0.966411	−	0.257001i	$-0.0827343\pi$
$839$	0.970542	+	2.98702i	0.0335068	+	0.103123i	−0.932904	+	0.360124i	$0.882734\pi$
$840$	2.49690	−	1.80413i	0.0861513	−	0.0622484i
$841$	−6.65159	+	20.4715i	−0.229365	+	0.705913i
$842$	41.4183	+	93.0270i	1.42737	+	3.20592i
$843$	−0.957856	+	0.553018i	−0.0329903	+	0.0190470i
$844$	6.13824	−	58.4015i	0.211287	−	2.01026i
$845$	8.55357	+	7.66726i	0.294252	+	0.263762i
$846$	34.7955	−	25.2804i	1.19629	−	0.869159i
$847$	−8.22974	+	2.62999i	−0.282777	+	0.0903675i
$848$	30.2133	−	9.81691i	1.03753	−	0.337114i
$849$	−0.244706	+	0.423844i	−0.00839830	+	0.0145463i
$850$	−1.93135	+	3.37986i	−0.0662448	+	0.115928i
$851$	−11.4666	−	19.8607i	−0.393070	−	0.680817i
$852$	−0.243056	+	1.14349i	−0.00832695	+	0.0391752i
$853$	−3.81712	−	5.25381i	−0.130696	−	0.179887i	0.738654	−	0.674085i	$-0.235462\pi$
$853$	−3.81712	−	5.25381i	−0.130696	−	0.179887i	−0.869349	+	0.494198i	$0.835462\pi$
$854$	91.4522	+	19.9024i	3.12943	+	0.681045i
$855$	−23.4074	−	13.4449i	−0.800516	−	0.459805i
$856$	61.1756	−	27.2371i	2.09094	−	0.930945i
$857$	−29.0894	+	16.7947i	−0.993674	+	0.573698i	−0.906370	−	0.422484i	$-0.861158\pi$
$857$	−29.0894	+	16.7947i	−0.993674	+	0.573698i	−0.0873032	+	0.996182i	$0.527825\pi$
$858$	−2.03471	−	0.213857i	−0.0694639	−	0.00730095i
$859$	35.5783	+	39.5137i	1.21392	+	1.34819i	0.919784	+	0.392426i	$0.128364\pi$
$859$	35.5783	+	39.5137i	1.21392	+	1.34819i	0.294133	+	0.955765i	$0.404969\pi$
$860$	−47.3683	+	82.4676i	−1.61524	+	2.81212i
$861$	0.225806	−	0.386767i	0.00769543	−	0.0131810i
$862$	−31.9046	−	10.3664i	−1.08668	−	0.353082i
$863$	15.1367	−	13.6291i	0.515258	−	0.463941i	−0.370006	−	0.929029i	$-0.620644\pi$
$863$	15.1367	−	13.6291i	0.515258	−	0.463941i	0.885264	+	0.465089i	$0.153978\pi$
$864$	−2.53021	+	2.81008i	−0.0860795	+	0.0956010i
$865$	3.63008	−	11.2574i	0.123426	−	0.382764i
$866$	−53.3187	−	59.2164i	−1.81184	−	2.01225i
$867$	0.742015	−	1.02130i	0.0252001	−	0.0346850i
$868$	−104.928	−	34.6560i	−3.56148	−	1.17630i
$869$	25.8816	+	18.8041i	0.877972	+	0.637884i
$870$	−1.17479	−	0.120832i	−0.0398291	−	0.00409659i
$871$	8.80956	+	3.92227i	0.298501	+	0.132901i
$872$	−16.3127	+	36.6389i	−0.552418	+	1.24075i
$873$	6.22124	−	29.2686i	0.210557	−	0.990594i
$874$	−73.3345			−2.48058
$875$	−3.03809	+	29.4240i	−0.102706	+	0.994712i
$876$	4.58603			0.154947
$877$	10.1063	−	47.5462i	0.341264	−	1.60552i	−0.388249	−	0.921555i	$-0.626920\pi$
$877$	10.1063	−	47.5462i	0.341264	−	1.60552i	0.729513	−	0.683967i	$-0.239747\pi$
$878$	−10.3028	+	23.1405i	−0.347703	+	0.780953i
$879$	−2.14618	−	0.955542i	−0.0723889	−	0.0322296i
$880$	−72.7242	−	7.48001i	−2.45153	−	0.252151i
$881$	−21.5813	−	15.6797i	−0.727092	−	0.528263i	0.161550	−	0.986864i	$-0.448351\pi$
$881$	−21.5813	−	15.6797i	−0.727092	−	0.528263i	−0.888642	+	0.458602i	$0.848351\pi$
$882$	−32.3038	+	43.5683i	−1.08773	+	1.46702i
$883$	12.0556	−	16.5931i	0.405702	−	0.558401i	−0.556461	−	0.830873i	$-0.687841\pi$
$883$	12.0556	−	16.5931i	0.405702	−	0.558401i	0.962164	+	0.272472i	$0.0878413\pi$
$884$	−2.65080	−	2.94401i	−0.0891559	−	0.0990177i
$885$	0.452187	−	1.40230i	0.0152001	−	0.0471378i
$886$	−47.6258	+	52.8938i	−1.60002	+	1.77700i
$887$	8.54556	−	7.69446i	0.286932	−	0.258355i	−0.513077	−	0.858342i	$-0.671495\pi$
$887$	8.54556	−	7.69446i	0.286932	−	0.258355i	0.800009	+	0.599988i	$0.204828\pi$
$888$	−1.61549	−	0.524905i	−0.0542123	−	0.0176147i
$889$	−17.5741	−	30.7828i	−0.589418	−	1.03242i
$890$	−22.1974	+	38.6454i	−0.744059	+	1.29540i
$891$	22.6189	+	25.1208i	0.757762	+	0.841579i
$892$	−36.3192	−	3.81730i	−1.21606	−	0.127813i
$893$	19.3803	−	11.1892i	0.648536	−	0.374432i
$894$	−0.245416	+	0.109266i	−0.00820794	+	0.00365441i
$895$	4.48394	+	2.57551i	0.149881	+	0.0860899i
$896$	−4.12609	−	12.9113i	−0.137843	−	0.431337i
$897$	−0.865017	−	1.19059i	−0.0288821	−	0.0397528i
$898$	11.5634	−	54.4015i	0.385876	−	1.81540i
$899$	12.1597	+	21.0612i	0.405548	+	0.702430i
$900$	−7.65961	−	69.8824i	−0.255320	−	2.32941i
$901$	−0.552109	+	0.956280i	−0.0183934	+	0.0318583i
$902$	−21.0750	+	6.84768i	−0.701720	+	0.228003i
$903$	−0.380460	+	1.74823i	−0.0126609	+	0.0581774i
$904$	14.3629	−	10.4353i	0.477705	−	0.347073i
$905$	29.6438	+	26.5722i	0.985394	+	0.883289i
$906$	−0.312658	+	2.97474i	−0.0103874	+	0.0988291i
$907$	21.9203	−	12.6557i	0.727851	−	0.420225i	−0.0897847	−	0.995961i	$-0.528618\pi$
$907$	21.9203	−	12.6557i	0.727851	−	0.420225i	0.817635	+	0.575736i	$0.195285\pi$
$908$	13.1739	+	29.5890i	0.437190	+	0.981945i
$909$	2.04466	−	6.29281i	0.0678170	−	0.208719i
$910$	−39.1685	−	17.5620i	−1.29842	−	0.582175i
$911$	−1.82038	−	5.60255i	−0.0603118	−	0.185621i	0.916361	−	0.400352i	$-0.131112\pi$
$911$	−1.82038	−	5.60255i	−0.0603118	−	0.185621i	−0.976673	+	0.214732i	$0.931112\pi$
$912$	−1.93615	+	1.74332i	−0.0641125	+	0.0577271i
$913$	3.66849	+	17.2589i	0.121409	+	0.571186i
$914$	34.2780	−	38.0695i	1.13381	−	1.25923i
$915$	−1.52331	+	1.69940i	−0.0503590	+	0.0561803i
$916$	−26.6456	+	82.0067i	−0.880395	+	2.70958i
$917$	−25.7268	−	35.7731i	−0.849574	−	1.18133i
$918$		−	0.348417i		−	0.0114995i
$919$	−13.1046	+	5.83456i	−0.432282	+	0.192464i	−0.611330	−	0.791376i	$-0.709365\pi$
$919$	−13.1046	+	5.83456i	−0.432282	+	0.192464i	0.179048	+	0.983840i	$0.442698\pi$
$920$	−64.6404	−	88.5547i	−2.13113	−	2.91956i
$921$	−1.33426	−	0.594051i	−0.0439654	−	0.0195746i
$922$	−16.0193	+	1.68369i	−0.527566	+	0.0554495i
$923$	8.89370	−	2.88974i	0.292740	−	0.0951169i
$924$	−3.42989	+	0.711695i	−0.112835	+	0.0234130i
$925$	14.0894	−	8.21834i	0.463255	−	0.270217i
$926$	−14.2477	+	24.6777i	−0.468209	+	0.810961i
$927$	9.12053	+	8.21216i	0.299558	+	0.269723i
$928$	9.39623	−	21.1043i	0.308446	−	0.692782i
$929$	1.90614	+	18.1357i	0.0625384	+	0.595013i	0.980250	+	0.197765i	$0.0633682\pi$
$929$	1.90614	+	18.1357i	0.0625384	+	0.595013i	−0.917711	+	0.397248i	$0.869965\pi$
$930$	2.84962	−	2.57731i	0.0934426	−	0.0845135i
$931$	−19.0855	+	20.7880i	−0.625503	+	0.681298i
$932$		−	42.0564i		−	1.37760i
$933$	1.00380	+	2.25458i	0.0328630	+	0.0738115i
$934$	−28.4649	+	6.05041i	−0.931401	+	0.197975i
$935$	2.05248	−	1.49821i	0.0671234	−	0.0489967i
$936$	57.2836	+	12.1760i	1.87237	+	0.397985i
$937$	34.5518	+	11.2266i	1.12876	+	0.366756i	0.813104	−	0.582118i	$-0.197776\pi$
$937$	34.5518	+	11.2266i	1.12876	+	0.366756i	0.315655	+	0.948874i	$0.397776\pi$
$938$	23.4024	+	2.57439i	0.764116	+	0.0840569i
$939$	−0.175600	−	0.540442i	−0.00573050	−	0.0176367i
$940$	53.2947	+	23.5863i	1.73828	+	0.769301i
$941$	−42.4175	+	9.01612i	−1.38277	+	0.293917i	−0.838458	−	0.544966i	$-0.816543\pi$
$941$	−42.4175	+	9.01612i	−1.38277	+	0.293917i	−0.544312	+	0.838883i	$0.683209\pi$
$942$	−0.299023	−	0.0314286i	−0.00974269	−	0.00102400i
$943$	−13.8041	−	7.96983i	−0.449525	−	0.259533i
$944$	61.8110	+	44.9084i	2.01178	+	1.46164i
$945$	−1.07052	−	2.42148i	−0.0348240	−	0.0787707i
$946$	71.6185	−	52.0339i	2.32852	−	1.69177i
$947$	−27.3732	+	2.87704i	−0.889509	+	0.0934911i	−0.538248	−	0.842787i	$-0.680914\pi$
$947$	−27.3732	+	2.87704i	−0.889509	+	0.0934911i	−0.351261	+	0.936278i	$0.614247\pi$
$948$	2.20650	+	1.98674i	0.0716638	+	0.0645264i
$949$	−18.3424	−	31.7699i	−0.595419	−	1.03130i
$950$	−0.232189	−	52.1582i	−0.00753320	−	1.69224i
$951$	−1.67235			−0.0542297
$952$	−4.79487	−	2.79938i	−0.155403	−	0.0907285i
$953$	−19.5661	−	26.9305i	−0.633809	−	0.872363i	0.364457	−	0.931220i	$-0.381254\pi$
$953$	−19.5661	−	26.9305i	−0.633809	−	0.872363i	−0.998266	+	0.0588568i	$0.981254\pi$
$954$	−2.97232	−	28.2797i	−0.0962323	−	0.915590i
$955$	16.9550	+	23.2277i	0.548652	+	0.751630i
$956$	8.13446	−	77.3943i	0.263087	−	2.50311i
$957$	0.667643	+	0.385464i	0.0215818	+	0.0124603i
$958$	45.2497	−	62.2809i	1.46195	−	2.01220i
$959$	−21.2612	+	9.34294i	−0.686561	+	0.301699i
$960$	−0.743472	−	0.156301i	−0.0239955	−	0.00504460i
$961$	−47.0696	−	10.0050i	−1.51838	−	0.322741i
$962$	4.92121	+	23.1525i	0.158666	+	0.746466i
$963$	−5.97749	−	28.1219i	−0.192622	−	0.906215i
$964$	−26.9578	−	5.73006i	−0.868252	−	0.184553i
$965$	54.2489	−	24.2980i	1.74633	−	0.782180i
$966$	−2.89651	−	2.12596i	−0.0931938	−	0.0684016i
$967$	−10.1761	+	14.0062i	−0.327242	+	0.450410i	−0.940661	−	0.339348i	$-0.889794\pi$
$967$	−10.1761	+	14.0062i	−0.327242	+	0.450410i	0.613419	+	0.789758i	$0.289794\pi$
$968$	19.7244	+	11.3879i	0.633967	+	0.366021i
$969$	0.00946592	−	0.0900622i	0.000304089	−	0.00289322i
$970$	54.9478	−	17.9889i	1.76427	−	0.577590i
$971$	2.30411	+	21.9221i	0.0739424	+	0.703515i	0.967208	+	0.253986i	$0.0817416\pi$
$971$	2.30411	+	21.9221i	0.0739424	+	0.703515i	−0.893266	+	0.449529i	$0.851592\pi$
$972$	5.54941	+	7.63811i	0.177998	+	0.244993i
$973$	−24.3816	+	13.9196i	−0.781637	+	0.446243i
$974$	90.7513			2.90786
$975$	0.844055	−	0.619002i	0.0270314	−	0.0198239i
$976$	−59.1710	−	102.487i	−1.89402	−	3.28054i
$977$	−15.0209	−	13.5249i	−0.480560	−	0.432698i	0.392909	−	0.919577i	$-0.371469\pi$
$977$	−15.0209	−	13.5249i	−0.480560	−	0.432698i	−0.873469	+	0.486879i	$0.838135\pi$
$978$	1.92106	−	0.201912i	0.0614287	−	0.00645642i
$979$	23.5363	−	17.1001i	0.752222	−	0.546521i
$980$	−73.0334	−	8.22775i	−2.33297	−	0.262826i
$981$	13.9304	+	10.1210i	0.444762	+	0.323139i
$982$	−4.41524	−	2.54914i	−0.140896	−	0.0813464i
$983$	58.2178	+	6.11894i	1.85686	+	0.195164i	0.965900	−	0.258916i	$-0.0833653\pi$
$983$	58.2178	+	6.11894i	1.85686	+	0.195164i	0.890961	+	0.454080i	$0.150032\pi$
$984$	−1.15483	+	0.245466i	−0.0368146	+	0.00782518i
$985$	3.71594	+	6.40325i	0.118400	+	0.204024i
$986$	0.657772	+	2.02442i	0.0209477	+	0.0644705i
$987$	1.08984	+	0.119888i	0.0346900	+	0.00381609i
$988$	50.4825	+	16.4028i	1.60606	+	0.521842i
$989$	62.2859	+	13.2393i	1.98058	+	0.420984i
$990$	−20.0830	+	62.2804i	−0.638279	+	1.97940i
$991$	−12.4042	+	2.63659i	−0.394032	+	0.0837541i	−0.400667	−	0.916224i	$-0.631221\pi$
$991$	−12.4042	+	2.63659i	−0.394032	+	0.0837541i	0.00663458	+	0.999978i	$0.497888\pi$
$992$	30.5699	+	68.6611i	0.970595	+	2.17999i
$993$			0.695326i			0.0220655i
$994$	18.5354	−	13.3301i	0.587909	−	0.422804i
$995$	−14.0891	−	31.4561i	−0.446656	−	0.997226i
$996$	0.171175	+	1.62862i	0.00542389	+	0.0516049i
$997$	−0.300615	+	0.675192i	−0.00952056	+	0.0213835i	−0.918243	−	0.396017i	$-0.870392\pi$
$997$	−0.300615	+	0.675192i	−0.00952056	+	0.0213835i	0.908723	+	0.417401i	$0.137059\pi$
$998$	33.9653	+	30.5825i	1.07515	+	0.968073i
$999$	−0.729952	+	1.26431i	−0.0230947	+	0.0400011i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.t.a.44.18	yes	144
5.2	odd	4		875.2.q.b.401.35		288
5.3	odd	4		875.2.q.b.401.2		288
5.4	even	2		875.2.u.a.849.1		144
7.4	even	3	inner	175.2.t.a.144.18	yes	144
25.3	odd	20		875.2.q.b.226.35		288
25.4	even	10	inner	175.2.t.a.79.18	yes	144
25.21	even	5		875.2.u.a.149.1		144
25.22	odd	20		875.2.q.b.226.2		288
35.4	even	6		875.2.u.a.599.1		144
35.18	odd	12		875.2.q.b.151.35		288
35.32	odd	12		875.2.q.b.151.2		288
175.4	even	30	inner	175.2.t.a.4.18	✓	144
175.46	even	15		875.2.u.a.774.1		144
175.53	odd	60		875.2.q.b.851.2		288
175.172	odd	60		875.2.q.b.851.35		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.t.a.4.18	✓	144	175.4	even	30	inner
175.2.t.a.44.18	yes	144	1.1	even	1	trivial
175.2.t.a.79.18	yes	144	25.4	even	10	inner
175.2.t.a.144.18	yes	144	7.4	even	3	inner
875.2.q.b.151.2		288	35.32	odd	12
875.2.q.b.151.35		288	35.18	odd	12
875.2.q.b.226.2		288	25.22	odd	20
875.2.q.b.226.35		288	25.3	odd	20
875.2.q.b.401.2		288	5.3	odd	4
875.2.q.b.401.35		288	5.2	odd	4
875.2.q.b.851.2		288	175.53	odd	60
875.2.q.b.851.35		288	175.172	odd	60
875.2.u.a.149.1		144	25.21	even	5
875.2.u.a.599.1		144	35.4	even	6
875.2.u.a.774.1		144	175.46	even	15
875.2.u.a.849.1		144	5.4	even	2

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.t (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.537983 - 2.53101i) q^{2} +(-0.0303653 + 0.0682015i) q^{3} +(-4.28951 - 1.90981i) q^{4} +(-2.22433 - 0.228782i) q^{5} +(0.156283 + 0.113546i) q^{6} +(-0.537537 - 2.59057i) q^{7} +(-4.09959 + 5.64260i) q^{8} +(2.00366 + 2.22529i) q^{9} +O(q^{10})\)	\(q+(0.537983 - 2.53101i) q^{2} +(-0.0303653 + 0.0682015i) q^{3} +(-4.28951 - 1.90981i) q^{4} +(-2.22433 - 0.228782i) q^{5} +(0.156283 + 0.113546i) q^{6} +(-0.537537 - 2.59057i) q^{7} +(-4.09959 + 5.64260i) q^{8} +(2.00366 + 2.22529i) q^{9} +(-1.77571 + 5.50673i) q^{10} +(2.52729 - 2.80684i) q^{11} +(0.260504 - 0.234559i) q^{12} +(-2.66684 - 0.866509i) q^{13} +(-6.84595 - 0.0331700i) q^{14} +(0.0831458 - 0.144756i) q^{15} +(5.79224 + 6.43293i) q^{16} +(-0.299235 - 0.0314508i) q^{17} +(6.71018 - 3.87412i) q^{18} +(3.68296 - 1.63976i) q^{19} +(9.10437 + 5.22942i) q^{20} +(0.193003 + 0.0420025i) q^{21} +(-5.74450 - 7.90663i) q^{22} +(1.46161 - 6.87632i) q^{23} +(-0.260349 - 0.450937i) q^{24} +(4.89532 + 1.01778i) q^{25} +(-3.62786 + 6.28364i) q^{26} +(-0.425616 + 0.138291i) q^{27} +(-2.64173 + 12.1389i) q^{28} +(2.21189 - 1.60703i) q^{29} +(-0.321648 - 0.288319i) q^{30} +(-0.929782 + 8.84628i) q^{31} +(7.31754 - 4.22478i) q^{32} +(0.114689 + 0.257595i) q^{33} +(-0.240586 + 0.740447i) q^{34} +(0.602985 + 5.88527i) q^{35} +(-4.34484 - 13.3720i) q^{36} +(2.42430 - 2.18285i) q^{37} +(-2.16888 - 10.2038i) q^{38} +(0.140077 - 0.155571i) q^{39} +(10.4098 - 11.6131i) q^{40} +(0.700664 - 2.15642i) q^{41} +(0.210141 - 0.465897i) q^{42} +9.05803i q^{43} +(-16.2014 + 7.21331i) q^{44} +(-3.94771 - 5.40820i) q^{45} +(-16.6177 - 7.39869i) q^{46} +(5.52047 - 0.580225i) q^{47} +(-0.614619 + 0.199702i) q^{48} +(-6.42211 + 2.78506i) q^{49} +(5.20960 - 11.8426i) q^{50} +(0.0112313 - 0.0194532i) q^{51} +(9.78456 + 8.81006i) q^{52} +(1.49269 - 3.35264i) q^{53} +(0.121042 + 1.15164i) q^{54} +(-6.26369 + 5.66514i) q^{55} +(16.8212 + 7.58716i) q^{56} +0.300975i q^{57} +(-2.87746 - 6.46288i) q^{58} +(8.63331 - 1.83507i) q^{59} +(-0.633111 + 0.462139i) q^{60} +(-13.3724 - 2.84238i) q^{61} +(21.8898 + 7.11244i) q^{62} +(4.68773 - 6.38681i) q^{63} +(-1.40634 - 4.32826i) q^{64} +(5.73370 + 2.53753i) q^{65} +(0.713678 - 0.151697i) q^{66} +(-3.42017 - 0.359475i) q^{67} +(1.22350 + 0.706390i) q^{68} +(0.424593 + 0.308485i) q^{69} +(15.2201 + 1.64001i) q^{70} +(-2.69801 + 1.96022i) q^{71} +(-20.7706 + 2.18308i) q^{72} +(9.72229 + 8.75399i) q^{73} +(-4.22058 - 7.31027i) q^{74} +(-0.218062 + 0.302963i) q^{75} -18.9297 q^{76} +(-8.62982 - 5.03834i) q^{77} +(-0.318393 - 0.438230i) q^{78} +(0.885368 + 8.42371i) q^{79} +(-11.4121 - 15.6341i) q^{80} +(-0.935516 + 8.90084i) q^{81} +(-5.08098 - 2.93351i) q^{82} +(-2.74589 + 3.77939i) q^{83} +(-0.747672 - 0.548770i) q^{84} +(0.658402 + 0.138417i) q^{85} +(22.9260 + 4.87307i) q^{86} +(0.0424374 + 0.199652i) q^{87} +(5.47702 + 25.7673i) q^{88} +(7.53425 + 1.60146i) q^{89} +(-15.8120 + 7.08217i) q^{90} +(-0.811226 + 7.37442i) q^{91} +(-19.4021 + 26.7046i) q^{92} +(-0.575097 - 0.332032i) q^{93} +(1.50137 - 14.2845i) q^{94} +(-8.56728 + 2.80478i) q^{95} +(0.0659376 + 0.627354i) q^{96} +(-5.87358 - 8.08430i) q^{97} +(3.59403 + 17.7527i) q^{98} +11.3099 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9}+O(q^{10}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9	\( 144 q - 5 q^{2} - 5 q^{3} - 19 q^{4} - 3 q^{5} - 12 q^{6} - 50 q^{8} - 17 q^{9} - q^{10} - 5 q^{12} - 20 q^{13} - 18 q^{14} + 12 q^{15} + 5 q^{16} + 5 q^{17} - 11 q^{19} - 24 q^{20} - 9 q^{21} - 60 q^{22} + 25 q^{23} + 50 q^{24} - 11 q^{25} - 60 q^{26} + 40 q^{27} - 24 q^{29} + 53 q^{30} + 15 q^{31} + 20 q^{33} - 20 q^{34} - 14 q^{35} + 16 q^{36} - 5 q^{37} - 20 q^{38} + 13 q^{39} + 7 q^{40} - 62 q^{41} + 40 q^{42} - 15 q^{44} - 41 q^{45} - 27 q^{46} - 5 q^{47} - 38 q^{49} + 54 q^{50} - 8 q^{51} - 130 q^{52} + 25 q^{53} - 29 q^{54} - 20 q^{55} + 32 q^{56} - 65 q^{58} - 39 q^{59} + 79 q^{60} + 7 q^{61} - 20 q^{62} - 45 q^{63} + 34 q^{64} - 13 q^{65} + 11 q^{66} + 25 q^{67} + 74 q^{69} + 85 q^{70} - 46 q^{71} + 60 q^{72} + 35 q^{73} + 6 q^{74} - 107 q^{75} + 180 q^{76} - 5 q^{77} + 10 q^{78} + 9 q^{79} + 88 q^{80} - 59 q^{81} + 90 q^{83} - 51 q^{84} - 6 q^{85} + 11 q^{86} - 5 q^{87} + 140 q^{88} - 42 q^{89} + 4 q^{90} + 22 q^{91} + 10 q^{92} + 5 q^{94} + 13 q^{95} + 53 q^{96} + 120 q^{97} - 180 q^{98} - 44 q^{99}+O(q^{100}) \) 144 * q - 5 * q^2 - 5 * q^3 - 19 * q^4 - 3 * q^5 - 12 * q^6 - 50 * q^8 - 17 * q^9 - q^10 - 5 * q^12 - 20 * q^13 - 18 * q^14 + 12 * q^15 + 5 * q^16 + 5 * q^17 - 11 * q^19 - 24 * q^20 - 9 * q^21 - 60 * q^22 + 25 * q^23 + 50 * q^24 - 11 * q^25 - 60 * q^26 + 40 * q^27 - 24 * q^29 + 53 * q^30 + 15 * q^31 + 20 * q^33 - 20 * q^34 - 14 * q^35 + 16 * q^36 - 5 * q^37 - 20 * q^38 + 13 * q^39 + 7 * q^40 - 62 * q^41 + 40 * q^42 - 15 * q^44 - 41 * q^45 - 27 * q^46 - 5 * q^47 - 38 * q^49 + 54 * q^50 - 8 * q^51 - 130 * q^52 + 25 * q^53 - 29 * q^54 - 20 * q^55 + 32 * q^56 - 65 * q^58 - 39 * q^59 + 79 * q^60 + 7 * q^61 - 20 * q^62 - 45 * q^63 + 34 * q^64 - 13 * q^65 + 11 * q^66 + 25 * q^67 + 74 * q^69 + 85 * q^70 - 46 * q^71 + 60 * q^72 + 35 * q^73 + 6 * q^74 - 107 * q^75 + 180 * q^76 - 5 * q^77 + 10 * q^78 + 9 * q^79 + 88 * q^80 - 59 * q^81 + 90 * q^83 - 51 * q^84 - 6 * q^85 + 11 * q^86 - 5 * q^87 + 140 * q^88 - 42 * q^89 + 4 * q^90 + 22 * q^91 + 10 * q^92 + 5 * q^94 + 13 * q^95 + 53 * q^96 + 120 * q^97 - 180 * q^98 - 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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