LMFDB - Embedded newform 175.2.t.a.9.15

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			9.15
Character	$\chi$	$=$	175.9
Dual form			175.2.t.a.39.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.792476 + 1.77993i) q^{2} +(-1.79059 - 1.61225i) q^{3} +(-1.20187 + 1.33481i) q^{4} +(2.07142 - 0.842152i) q^{5} +(1.45070 - 4.46479i) q^{6} +(2.52107 + 0.802620i) q^{7} +(0.377701 + 0.122722i) q^{8} +(0.293262 + 2.79020i) q^{9} +O(q^{10})$	\(q+(0.792476 + 1.77993i) q^{2} +(-1.79059 - 1.61225i) q^{3} +(-1.20187 + 1.33481i) q^{4} +(2.07142 - 0.842152i) q^{5} +(1.45070 - 4.46479i) q^{6} +(2.52107 + 0.802620i) q^{7} +(0.377701 + 0.122722i) q^{8} +(0.293262 + 2.79020i) q^{9} +(3.14052 + 3.01960i) q^{10} +(-0.259436 + 2.46837i) q^{11} +(4.30412 - 0.452381i) q^{12} +(-2.29720 - 3.16183i) q^{13} +(0.569281 + 5.12339i) q^{14} +(-5.06682 - 1.83170i) q^{15} +(0.456383 + 4.34220i) q^{16} +(-0.643690 - 3.02832i) q^{17} +(-4.73395 + 2.73315i) q^{18} +(3.42697 + 3.80604i) q^{19} +(-1.36546 + 3.77712i) q^{20} +(-3.22017 - 5.50177i) q^{21} +(-4.59912 + 1.49435i) q^{22} +(-1.85446 - 4.16518i) q^{23} +(-0.478447 - 0.828694i) q^{24} +(3.58156 - 3.48890i) q^{25} +(3.80736 - 6.59454i) q^{26} +(-0.275367 + 0.379010i) q^{27} +(-4.10135 + 2.40052i) q^{28} +(-0.797815 - 2.45542i) q^{29} +(-0.755029 - 10.4702i) q^{30} +(-6.17093 + 1.31167i) q^{31} +(-6.67927 + 3.85628i) q^{32} +(4.44418 - 4.00156i) q^{33} +(4.88009 - 3.54559i) q^{34} +(5.89813 - 0.460563i) q^{35} +(-4.07686 - 2.96201i) q^{36} +(-8.11444 + 0.852862i) q^{37} +(-4.05869 + 9.11597i) q^{38} +(-0.984323 + 9.36521i) q^{39} +(0.885727 - 0.0638719i) q^{40} +(-4.21399 + 3.06164i) q^{41} +(7.24085 - 10.0917i) q^{42} +5.80714i q^{43} +(-2.98301 - 3.31296i) q^{44} +(2.95724 + 5.53270i) q^{45} +(5.94411 - 6.60161i) q^{46} +(-0.453202 + 2.13215i) q^{47} +(6.18352 - 8.51089i) q^{48} +(5.71160 + 4.04692i) q^{49} +(9.04830 + 3.61005i) q^{50} +(-3.72984 + 6.46027i) q^{51} +(6.98140 + 0.733775i) q^{52} +(-5.71138 - 5.14255i) q^{53} +(-0.892832 - 0.189777i) q^{54} +(1.54134 + 5.33152i) q^{55} +(0.853711 + 0.612542i) q^{56} -12.3402i q^{57} +(3.73823 - 3.36592i) q^{58} +(-10.0978 - 4.49584i) q^{59} +(8.53466 - 4.56179i) q^{60} +(7.90679 - 3.52033i) q^{61} +(-7.22500 - 9.94436i) q^{62} +(-1.50013 + 7.26967i) q^{63} +(-5.09255 - 3.69995i) q^{64} +(-7.42122 - 4.61488i) q^{65} +(10.6444 + 4.73919i) q^{66} +(-1.78260 - 8.38650i) q^{67} +(4.81588 + 2.78045i) q^{68} +(-3.39475 + 10.4480i) q^{69} +(5.49389 + 10.1333i) q^{70} +(4.36571 + 13.4363i) q^{71} +(-0.231655 + 1.08985i) q^{72} +(12.2347 + 1.28592i) q^{73} +(-7.94853 - 13.7673i) q^{74} +(-12.0381 + 0.472808i) q^{75} -9.19914 q^{76} +(-2.63522 + 6.01471i) q^{77} +(-17.4495 + 5.66968i) q^{78} +(6.11718 + 1.30025i) q^{79} +(4.60215 + 8.61017i) q^{80} +(9.33690 - 1.98462i) q^{81} +(-8.78899 - 5.07433i) q^{82} +(-4.78601 - 1.55507i) q^{83} +(11.2141 + 2.31409i) q^{84} +(-3.88366 - 5.73084i) q^{85} +(-10.3363 + 4.60202i) q^{86} +(-2.53020 + 5.68293i) q^{87} +(-0.400913 + 0.900466i) q^{88} +(-12.6922 + 5.65094i) q^{89} +(-7.50428 + 9.64821i) q^{90} +(-3.25367 - 9.81498i) q^{91} +(7.78856 + 2.53066i) q^{92} +(13.1644 + 7.60044i) q^{93} +(-4.15423 + 0.883008i) q^{94} +(10.3040 + 4.99787i) q^{95} +(18.1771 + 3.86367i) q^{96} +(4.30851 - 1.39992i) q^{97} +(-2.67694 + 13.3733i) q^{98} -6.96332 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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{10}\right)$

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 $

$2$	0.792476	+	1.77993i	0.560365	+	1.25860i	0.942411	+	0.334457i	$0.108553\pi$
$2$	0.792476	+	1.77993i	0.560365	+	1.25860i	−0.382046	+	0.924143i	$0.624780\pi$
$3$	−1.79059	−	1.61225i	−1.03380	−	0.930835i	−0.0361464	−	0.999347i	$-0.511508\pi$
$3$	−1.79059	−	1.61225i	−1.03380	−	0.930835i	−0.997650	+	0.0685118i	$0.978175\pi$
$4$	−1.20187	+	1.33481i	−0.600936	+	0.667407i
$5$	2.07142	−	0.842152i	0.926367	−	0.376622i
$5$	2.07142	−	0.842152i	0.926367	−	0.376622i
$6$	1.45070	−	4.46479i	0.592246	−	1.82274i
$7$	2.52107	+	0.802620i	0.952875	+	0.303362i
$7$	2.52107	+	0.802620i	0.952875	+	0.303362i
$8$	0.377701	+	0.122722i	0.133537	+	0.0433889i
$9$	0.293262	+	2.79020i	0.0977539	+	0.930066i
$10$	3.14052	+	3.01960i	0.993121	+	0.954880i
$11$	−0.259436	+	2.46837i	−0.0782230	+	0.744242i	0.883168	+	0.469056i	$0.155406\pi$
$11$	−0.259436	+	2.46837i	−0.0782230	+	0.744242i	−0.961391	+	0.275185i	$0.911261\pi$
$12$	4.30412	−	0.452381i	1.24249	−	0.130591i
$13$	−2.29720	−	3.16183i	−0.637130	−	0.876934i	0.361329	−	0.932439i	$-0.382323\pi$
$13$	−2.29720	−	3.16183i	−0.637130	−	0.876934i	−0.998458	+	0.0555046i	$0.982323\pi$
$14$	0.569281	+	5.12339i	0.152147	+	1.36928i
$15$	−5.06682	−	1.83170i	−1.30825	−	0.472944i
$16$	0.456383	+	4.34220i	0.114096	+	1.08555i
$17$	−0.643690	−	3.02832i	−0.156118	−	0.734476i	−0.984651	−	0.174536i	$-0.944158\pi$
$17$	−0.643690	−	3.02832i	−0.156118	−	0.734476i	0.828533	−	0.559940i	$-0.189176\pi$
$18$	−4.73395	+	2.73315i	−1.11580	+	0.644210i
$19$	3.42697	+	3.80604i	0.786202	+	0.873166i	0.994482	−	0.104904i	$-0.0334534\pi$
$19$	3.42697	+	3.80604i	0.786202	+	0.873166i	−0.208281	+	0.978069i	$0.566787\pi$
$20$	−1.36546	+	3.77712i	−0.305327	+	0.844590i
$21$	−3.22017	−	5.50177i	−0.702700	−	1.20058i
$22$	−4.59912	+	1.49435i	−0.980537	+	0.318596i
$23$	−1.85446	−	4.16518i	−0.386681	−	0.868500i	−0.997077	−	0.0764033i	$-0.975656\pi$
$23$	−1.85446	−	4.16518i	−0.386681	−	0.868500i	0.610396	−	0.792096i	$-0.291010\pi$
$24$	−0.478447	−	0.828694i	−0.0976625	−	0.169156i
$25$	3.58156	−	3.48890i	0.716312	−	0.697780i
$26$	3.80736	−	6.59454i	0.746684	−	1.29330i
$27$	−0.275367	+	0.379010i	−0.0529943	+	0.0729405i
$28$	−4.10135	+	2.40052i	−0.775083	+	0.453655i
$29$	−0.797815	−	2.45542i	−0.148151	−	0.455960i	0.849252	−	0.527987i	$-0.177053\pi$
$29$	−0.797815	−	2.45542i	−0.148151	−	0.455960i	−0.997403	+	0.0720270i	$0.977053\pi$
$30$	−0.755029	−	10.4702i	−0.137849	−	1.91158i
$31$	−6.17093	+	1.31167i	−1.10833	+	0.235583i	−0.725492	−	0.688231i	$-0.758388\pi$
$31$	−6.17093	+	1.31167i	−1.10833	+	0.235583i	−0.382841	+	0.923814i	$0.625054\pi$
$32$	−6.67927	+	3.85628i	−1.18074	+	0.681700i
$33$	4.44418	−	4.00156i	0.773633	−	0.696582i
$34$	4.88009	−	3.54559i	0.836929	−	0.608064i
$35$	5.89813	−	0.460563i	0.996965	−	0.0778494i
$36$	−4.07686	−	2.96201i	−0.679476	−	0.493669i
$37$	−8.11444	+	0.852862i	−1.33401	+	0.140210i	−0.744537	−	0.667581i	$-0.767330\pi$
$37$	−8.11444	+	0.852862i	−1.33401	+	0.140210i	−0.589469	+	0.807791i	$0.700663\pi$
$38$	−4.05869	+	9.11597i	−0.658407	+	1.47881i
$39$	−0.984323	+	9.36521i	−0.157618	+	1.49963i
$40$	0.885727	−	0.0638719i	0.140046	−	0.0100990i
$41$	−4.21399	+	3.06164i	−0.658114	+	0.478148i	−0.866026	−	0.500000i	$-0.833333\pi$
$41$	−4.21399	+	3.06164i	−0.658114	+	0.478148i	0.207911	+	0.978148i	$0.433333\pi$
$42$	7.24085	−	10.0917i	1.11729	−	1.55718i
$43$			5.80714i			0.885580i	0.896625	+	0.442790i	$0.146011\pi$
$43$			5.80714i			0.885580i	−0.896625	+	0.442790i	$0.853989\pi$
$44$	−2.98301	−	3.31296i	−0.449705	−	0.499448i
$45$	2.95724	+	5.53270i	0.440839	+	0.824766i
$46$	5.94411	−	6.60161i	0.876412	−	0.973354i
$47$	−0.453202	+	2.13215i	−0.0661063	+	0.311006i	−0.998761	−	0.0497646i	$-0.984153\pi$
$47$	−0.453202	+	2.13215i	−0.0661063	+	0.311006i	0.932655	+	0.360770i	$0.117486\pi$
$48$	6.18352	−	8.51089i	0.892515	−	1.22844i
$49$	5.71160	+	4.04692i	0.815943	+	0.578132i
$50$	9.04830	+	3.61005i	1.27962	+	0.510539i
$51$	−3.72984	+	6.46027i	−0.522282	+	0.904618i
$52$	6.98140	+	0.733775i	0.968146	+	0.101756i
$53$	−5.71138	−	5.14255i	−0.784518	−	0.706384i	0.176064	−	0.984379i	$-0.443663\pi$
$53$	−5.71138	−	5.14255i	−0.784518	−	0.706384i	−0.960582	+	0.277995i	$0.910330\pi$
$54$	−0.892832	−	0.189777i	−0.121499	−	0.0258254i
$55$	1.54134	+	5.33152i	0.207835	+	0.718901i
$56$	0.853711	+	0.612542i	0.114082	+	0.0818543i
$57$		−	12.3402i		−	1.63450i
$58$	3.73823	−	3.36592i	0.490854	−	0.441967i
$59$	−10.0978	−	4.49584i	−1.31462	−	0.585308i	−0.374843	−	0.927088i	$-0.622304\pi$
$59$	−10.0978	−	4.49584i	−1.31462	−	0.585308i	−0.939780	+	0.341780i	$0.888970\pi$
$60$	8.53466	−	4.56179i	1.10182	−	0.588925i
$61$	7.90679	−	3.52033i	1.01236	−	0.450732i	0.167588	−	0.985857i	$-0.446402\pi$
$61$	7.90679	−	3.52033i	1.01236	−	0.450732i	0.844773	+	0.535125i	$0.179736\pi$
$62$	−7.22500	−	9.94436i	−0.917576	−	1.26294i
$63$	−1.50013	+	7.26967i	−0.188999	+	0.915892i
$64$	−5.09255	−	3.69995i	−0.636568	−	0.462494i
$65$	−7.42122	−	4.61488i	−0.920489	−	0.572406i
$66$	10.6444	+	4.73919i	1.31024	+	0.583354i
$67$	−1.78260	−	8.38650i	−0.217780	−	1.02457i	−0.942158	−	0.335170i	$-0.891206\pi$
$67$	−1.78260	−	8.38650i	−0.217780	−	1.02457i	0.724378	−	0.689403i	$-0.242127\pi$
$68$	4.81588	+	2.78045i	0.584011	+	0.337179i
$69$	−3.39475	+	10.4480i	−0.408680	+	1.25779i
$70$	5.49389	+	10.1333i	0.656646	+	1.21116i
$71$	4.36571	+	13.4363i	0.518114	+	1.59459i	0.777543	+	0.628830i	$0.216466\pi$
$71$	4.36571	+	13.4363i	0.518114	+	1.59459i	−0.259428	+	0.965762i	$0.583534\pi$
$72$	−0.231655	+	1.08985i	−0.0273008	+	0.128440i
$73$	12.2347	+	1.28592i	1.43197	+	0.150506i	0.788532	−	0.614993i	$-0.210841\pi$
$73$	12.2347	+	1.28592i	1.43197	+	0.150506i	0.643437	+	0.765499i	$0.277508\pi$
$74$	−7.94853	−	13.7673i	−0.923998	−	1.60041i
$75$	−12.0381	+	0.472808i	−1.39004	+	0.0545952i
$76$	−9.19914			−1.05521
$77$	−2.63522	+	6.01471i	−0.300311	+	0.685440i
$78$	−17.4495	+	5.66968i	−1.97576	+	0.641965i
$79$	6.11718	+	1.30025i	0.688237	+	0.146289i	0.538739	−	0.842473i	$-0.318901\pi$
$79$	6.11718	+	1.30025i	0.688237	+	0.146289i	0.149498	+	0.988762i	$0.452234\pi$
$80$	4.60215	+	8.61017i	0.514536	+	0.962646i
$81$	9.33690	−	1.98462i	1.03743	−	0.220513i
$82$	−8.78899	−	5.07433i	−0.970582	−	0.560366i
$83$	−4.78601	−	1.55507i	−0.525332	−	0.170691i	0.0343315	−	0.999410i	$-0.489070\pi$
$83$	−4.78601	−	1.55507i	−0.525332	−	0.170691i	−0.559664	+	0.828720i	$0.689070\pi$
$84$	11.2141	+	2.31409i	1.22356	+	0.252487i
$85$	−3.88366	−	5.73084i	−0.421242	−	0.621597i
$86$	−10.3363	+	4.60202i	−1.11459	+	0.496248i
$87$	−2.53020	+	5.68293i	−0.271266	+	0.609274i
$88$	−0.400913	+	0.900466i	−0.0427375	+	0.0959900i
$89$	−12.6922	+	5.65094i	−1.34537	+	0.598998i	−0.947886	−	0.318610i	$-0.896784\pi$
$89$	−12.6922	+	5.65094i	−1.34537	+	0.598998i	−0.397486	+	0.917608i	$0.630117\pi$
$90$	−7.50428	+	9.64821i	−0.791020	+	1.01701i
$91$	−3.25367	−	9.81498i	−0.341077	−	1.02889i
$92$	7.78856	+	2.53066i	0.812014	+	0.263839i
$93$	13.1644	+	7.60044i	1.36508	+	0.788129i
$94$	−4.15423	+	0.883008i	−0.428476	+	0.0910753i
$95$	10.3040	+	4.99787i	1.05716	+	0.512771i
$96$	18.1771	+	3.86367i	1.85519	+	0.394334i
$97$	4.30851	−	1.39992i	0.437463	−	0.142140i	−0.0820021	−	0.996632i	$-0.526131\pi$
$97$	4.30851	−	1.39992i	0.437463	−	0.142140i	0.519465	+	0.854492i	$0.326131\pi$
$98$	−2.67694	+	13.3733i	−0.270411	+	1.35091i
$99$	−6.96332			−0.699840
$100$	0.352460	+	8.97393i	0.0352460	+	0.897393i
$101$	−5.70073	−	9.87396i	−0.567244	−	0.982495i	−0.996837	−	0.0794728i	$-0.974676\pi$
$101$	−5.70073	−	9.87396i	−0.567244	−	0.982495i	0.429593	−	0.903023i	$-0.358657\pi$
$102$	−14.4546	−	1.51924i	−1.43122	−	0.150427i
$103$	0.317764	−	1.49496i	0.0313103	−	0.147303i	−0.959716	−	0.280973i	$-0.909343\pi$
$103$	0.317764	−	1.49496i	0.0313103	−	0.147303i	0.991026	+	0.133670i	$0.0426762\pi$
$104$	−0.479628	−	1.47614i	−0.0470314	−	0.144748i
$105$	−11.3037	−	8.68459i	−1.10312	−	0.847529i
$106$	4.62725	−	14.2412i	0.449438	−	1.38323i
$107$	7.85780	+	4.53670i	0.759642	+	0.438580i	0.829167	−	0.559000i	$-0.188815\pi$
$107$	7.85780	+	4.53670i	0.759642	+	0.438580i	−0.0695249	+	0.997580i	$0.522148\pi$
$108$	−0.174952	−	0.823085i	−0.0168348	−	0.0792014i
$109$	3.47290	+	1.54623i	0.332643	+	0.148102i	0.566260	−	0.824226i	$-0.308390\pi$
$109$	3.47290	+	1.54623i	0.332643	+	0.148102i	−0.233617	+	0.972329i	$0.575056\pi$
$110$	−8.26825	+	6.96858i	−0.788347	+	0.664428i
$111$	15.9046	+	11.5554i	1.50960	+	1.09679i
$112$	−2.33456	+	11.3133i	−0.220595	+	1.06901i
$113$	7.52234	+	10.3536i	0.707643	+	0.973986i	0.999845	+	0.0176298i	$0.00561202\pi$
$113$	7.52234	+	10.3536i	0.707643	+	0.973986i	−0.292202	+	0.956357i	$0.594388\pi$
$114$	21.9647	−	9.77931i	2.05718	−	0.915917i
$115$	−7.34907	−	7.06610i	−0.685305	−	0.658917i
$116$	4.23640	+	1.88617i	0.393340	+	0.175126i
$117$	8.14845	−	7.33690i	0.753324	−	0.678296i
$118$		−	21.5362i		−	1.98257i
$119$	0.807804	−	8.15125i	0.0740512	−	0.747224i
$120$	−1.68895	−	1.31365i	−0.154179	−	0.119919i
$121$	4.73408	+	1.00626i	0.430371	+	0.0914781i
$122$	12.5319	+	11.2838i	1.13458	+	1.02158i
$123$	12.4817	+	1.31188i	1.12543	+	0.118288i
$124$	5.66584	−	9.81351i	0.508807	−	0.881280i
$125$	4.48072	−	10.2432i	0.400768	−	0.916179i
$126$	−14.1283	+	3.09090i	−1.25865	+	0.275359i
$127$	5.72589	−	7.88102i	0.508091	−	0.699327i	−0.475505	−	0.879713i	$-0.657735\pi$
$127$	5.72589	−	7.88102i	0.508091	−	0.699327i	0.983596	+	0.180386i	$0.0577346\pi$
$128$	−0.657126	+	3.09154i	−0.0580823	+	0.273256i
$129$	9.36258	−	10.3982i	0.824329	−	0.915510i
$130$	2.33303	−	16.8664i	0.204620	−	1.47928i
$131$	−11.9460	−	13.2674i	−1.04373	−	1.15918i	−0.986989	−	0.160786i	$-0.948597\pi$
$131$	−11.9460	−	13.2674i	−1.04373	−	1.15918i	−0.0567371	−	0.998389i	$-0.518070\pi$
$132$			10.7415i			0.934929i
$133$	5.58484	+	12.3459i	0.484267	+	1.07052i
$134$	13.5147	−	9.81901i	1.16749	−	0.848233i
$135$	−0.251216	+	1.01699i	−0.0216212	+	0.0875285i
$136$	0.128521	−	1.22279i	0.0110206	−	0.104854i
$137$	1.31728	−	2.95866i	0.112543	−	0.252775i	−0.848489	−	0.529213i	$-0.822487\pi$
$137$	1.31728	−	2.95866i	0.112543	−	0.252775i	0.961032	+	0.276438i	$0.0891539\pi$
$138$	−21.2869	+	2.23735i	−1.81206	+	0.190456i
$139$	6.18949	+	4.49693i	0.524986	+	0.381424i	0.818479	−	0.574537i	$-0.194818\pi$
$139$	6.18949	+	4.49693i	0.524986	+	0.381424i	−0.293493	+	0.955961i	$0.594818\pi$
$140$	−6.47403	+	8.42644i	−0.547155	+	0.712164i
$141$	4.24906	−	3.08712i	0.357836	−	0.259983i
$142$	−20.4559	+	18.4186i	−1.71662	+	1.54565i
$143$	8.40055	−	4.85006i	0.702489	−	0.405582i
$144$	−11.9817	+	2.54680i	−0.998479	+	0.212233i
$145$	−3.72045	−	4.41433i	−0.308966	−	0.366590i
$146$	7.40689	+	22.7961i	0.612999	+	1.88662i
$147$	−3.70246	−	16.4549i	−0.305374	−	1.35718i
$148$	8.61411	−	11.8563i	0.708075	−	0.974582i
$149$	1.84866	−	3.20197i	0.151448	−	0.262315i	−0.780312	−	0.625390i	$-0.784940\pi$
$149$	1.84866	−	3.20197i	0.151448	−	0.262315i	0.931760	+	0.363075i	$0.118273\pi$
$150$	−10.3815	−	21.0523i	−0.847643	−	1.71891i
$151$	1.10361	+	1.91151i	0.0898105	+	0.155556i	0.907431	−	0.420201i	$-0.138041\pi$
$151$	1.10361	+	1.91151i	0.0898105	+	0.155556i	−0.817620	+	0.575758i	$0.804707\pi$
$152$	0.827284	+	1.85811i	0.0671016	+	0.150713i
$153$	8.26085	−	2.68411i	0.667850	−	0.216998i
$154$	−12.7941	+	0.0760043i	−1.03098	+	0.00612460i
$155$	−11.6780	+	7.91389i	−0.937997	+	0.635659i
$156$	−11.3178	−	12.5697i	−0.906148	−	1.00638i
$157$	−20.8287	+	12.0255i	−1.66231	+	0.959738i	−0.690709	+	0.723133i	$0.742701\pi$
$157$	−20.8287	+	12.0255i	−1.66231	+	0.959738i	−0.971606	+	0.236605i	$0.923965\pi$
$158$	2.53337	+	11.9186i	0.201544	+	0.948191i
$159$	1.93564	+	18.4164i	0.153506	+	1.46051i
$160$	−10.5880	+	13.6129i	−0.837055	+	1.07620i
$161$	−1.33216	−	11.9891i	−0.104989	−	0.944876i
$162$	10.9318	+	15.0463i	0.858880	+	1.18215i
$163$	−0.964031	+	0.101324i	−0.0755087	+	0.00793629i	−0.142207	−	0.989837i	$-0.545420\pi$
$163$	−0.964031	+	0.101324i	−0.0755087	+	0.00793629i	0.0666988	+	0.997773i	$0.478753\pi$
$164$	0.977952	−	9.30459i	0.0763652	−	0.726567i
$165$	5.83584	−	12.0316i	0.454320	−	0.936658i
$166$	−1.02488	−	9.75111i	−0.0795463	−	0.756833i
$167$	1.74340	+	0.566466i	0.134908	+	0.0438344i	0.375693	−	0.926744i	$-0.377405\pi$
$167$	1.74340	+	0.566466i	0.134908	+	0.0438344i	−0.240785	+	0.970579i	$0.577405\pi$
$168$	−0.541072	−	2.47321i	−0.0417446	−	0.190812i
$169$	−0.702803	+	2.16301i	−0.0540618	+	0.166385i
$170$	7.12279	−	11.4542i	0.546293	−	0.878497i
$171$	−9.61460	+	10.6781i	−0.735247	+	0.816575i
$172$	−7.75145	−	6.97944i	−0.591043	−	0.532177i
$173$	−3.18744	−	7.15910i	−0.242336	−	0.544297i	0.750899	−	0.660417i	$-0.229621\pi$
$173$	−3.18744	−	7.15910i	−0.242336	−	0.544297i	−0.993235	+	0.116121i	$0.962954\pi$
$174$	−12.1203			−0.918841
$175$	11.8296	−	5.92114i	0.894236	−	0.447596i
$176$	−10.8365			−0.816836
$177$	10.8326	+	24.3304i	0.814228	+	1.82879i
$178$	−20.1165	−	18.1130i	−1.50780	−	1.35763i
$179$	7.15162	−	7.94267i	0.534537	−	0.593663i	−0.414021	−	0.910267i	$-0.635876\pi$
$179$	7.15162	−	7.94267i	0.534537	−	0.593663i	0.948558	+	0.316604i	$0.102543\pi$
$180$	−10.9393	−	2.70223i	−0.815371	−	0.201412i
$181$	−1.89456	+	5.83087i	−0.140822	+	0.433405i	−0.996450	−	0.0841859i	$-0.973171\pi$
$181$	−1.89456	+	5.83087i	−0.140822	+	0.433405i	0.855628	+	0.517591i	$0.173171\pi$
$182$	14.8915	−	13.5694i	1.10383	−	1.00583i
$183$	−19.8335	−	6.44429i	−1.46613	−	0.476375i
$184$	−0.189269	−	1.80077i	−0.0139531	−	0.132755i
$185$	−16.0902	+	8.60023i	−1.18297	+	0.632301i
$186$	−3.09582	+	29.4548i	−0.226997	+	2.15973i
$187$	7.64202	−	0.803208i	0.558840	−	0.0587364i
$188$	−2.30133	−	3.16751i	−0.167842	−	0.231014i
$189$	−0.998420	+	0.734496i	−0.0726244	+	0.0534267i
$190$	−0.730218	+	22.3010i	−0.0529755	+	1.61789i
$191$	−2.24060	−	21.3179i	−0.162124	−	1.54251i	−0.708949	−	0.705260i	$-0.750830\pi$
$191$	−2.24060	−	21.3179i	−0.162124	−	1.54251i	0.546825	−	0.837247i	$-0.315836\pi$
$192$	3.15340	+	14.8356i	0.227577	+	1.07066i
$193$	1.64900	−	0.952048i	0.118697	−	0.0685299i	−0.439476	−	0.898254i	$-0.644836\pi$
$193$	1.64900	−	0.952048i	0.118697	−	0.0685299i	0.558173	+	0.829724i	$0.311502\pi$
$194$	5.90615	+	6.55944i	0.424037	+	0.470940i
$195$	5.84799	+	20.2282i	0.418783	+	1.44857i
$196$	−12.2665	+	2.76004i	−0.876179	+	0.197146i
$197$	3.23369	−	1.05069i	0.230391	−	0.0748586i	−0.191546	−	0.981484i	$-0.561350\pi$
$197$	3.23369	−	1.05069i	0.230391	−	0.0748586i	0.421937	+	0.906625i	$0.361350\pi$
$198$	−5.51827	−	12.3942i	−0.392166	−	0.880820i
$199$	4.13160	+	7.15614i	0.292881	+	0.507286i	0.974490	−	0.224432i	$-0.0720525\pi$
$199$	4.13160	+	7.15614i	0.292881	+	0.507286i	−0.681608	+	0.731717i	$0.738719\pi$
$200$	1.78092	−	0.878223i	0.125930	−	0.0620997i
$201$	−10.3292	+	17.8908i	−0.728569	+	1.26192i
$202$	13.0573	−	17.9718i	0.918706	−	1.26449i
$203$	−0.0405779	−	6.83064i	−0.00284801	−	0.479417i
$204$	−4.14047	−	12.7431i	−0.289891	−	0.892192i
$205$	−6.15057	+	9.89076i	−0.429574	+	0.690801i
$206$	2.91275	−	0.619125i	0.202941	−	0.0431365i
$207$	11.0778	−	6.39579i	0.769962	−	0.444538i
$208$	12.6809	−	11.4179i	0.879261	−	0.791690i
$209$	−10.2838	+	7.47162i	−0.711345	+	0.516823i
$210$	6.50009	−	27.0021i	0.448549	−	1.86332i
$211$	−18.1583	−	13.1928i	−1.25007	−	0.908228i	−0.251842	−	0.967768i	$-0.581036\pi$
$211$	−18.1583	−	13.1928i	−1.25007	−	0.908228i	−0.998226	+	0.0595406i	$0.981036\pi$
$212$	13.7287	−	1.44294i	0.942891	−	0.0991018i
$213$	13.8455	−	31.0975i	0.948677	−	2.13076i
$214$	−1.84790	+	17.5816i	−0.126320	+	1.20185i
$215$	4.89050	+	12.0290i	0.333529	+	0.820373i
$216$	−0.150519	+	0.109359i	−0.0102415	+	0.00744091i
$217$	−16.6101	−	1.64609i	−1.12757	−	0.111744i
$218$			7.40687i			0.501656i
$219$	−19.8342	−	22.0281i	−1.34027	−	1.48852i
$220$	−8.96908	−	4.35039i	−0.604695	−	0.293304i
$221$	−8.09635	+	8.99191i	−0.544620	+	0.604861i
$222$	−7.96376	+	37.4665i	−0.534493	+	2.51459i
$223$	5.23518	−	7.20560i	0.350573	−	0.482523i	−0.596919	−	0.802302i	$-0.703609\pi$
$223$	5.23518	−	7.20560i	0.350573	−	0.482523i	0.947492	+	0.319779i	$0.103609\pi$
$224$	−19.9340	+	4.36104i	−1.33190	+	0.291384i
$225$	10.7851	+	8.97010i	0.719004	+	0.598006i
$226$	−12.4674	+	21.5942i	−0.829322	+	1.43643i
$227$	12.5009	+	1.31390i	0.829717	+	0.0872067i	0.509858	−	0.860259i	$-0.329698\pi$
$227$	12.5009	+	1.31390i	0.829717	+	0.0872067i	0.319859	+	0.947465i	$0.396365\pi$
$228$	16.4719	+	14.8313i	1.09088	+	0.982230i
$229$	16.1762	+	3.43837i	1.06896	+	0.227214i	0.708607	−	0.705604i	$-0.249324\pi$
$229$	16.1762	+	3.43837i	1.06896	+	0.227214i	0.360350	+	0.932817i	$0.382657\pi$
$230$	6.75320	−	18.6806i	0.445293	−	1.23176i
$231$	14.4158	−	6.52123i	0.948492	−	0.429065i
$232$		−	1.02532i		−	0.0673158i
$233$	4.33261	−	3.90110i	0.283839	−	0.255570i	−0.514896	−	0.857253i	$-0.672170\pi$
$233$	4.33261	−	3.90110i	0.283839	−	0.255570i	0.798735	+	0.601683i	$0.205503\pi$
$234$	19.5166	+	8.68936i	1.27584	+	0.568041i
$235$	0.856822	+	4.79824i	0.0558929	+	0.313003i
$236$	18.1374	−	8.07529i	1.18064	−	0.525656i
$237$	−8.85703	−	12.1907i	−0.575326	−	0.791868i
$238$	15.1488	−	5.02184i	0.981953	−	0.325517i
$239$	−3.29768	−	2.39590i	−0.213309	−	0.154978i	0.476001	−	0.879445i	$-0.342086\pi$
$239$	−3.29768	−	2.39590i	−0.213309	−	0.154978i	−0.689310	+	0.724467i	$0.742086\pi$
$240$	5.64121	−	22.8371i	0.364138	−	1.47413i
$241$	20.7888	+	9.25578i	1.33913	+	0.596217i	0.946268	−	0.323382i	$-0.104820\pi$
$241$	20.7888	+	9.25578i	1.33913	+	0.596217i	0.392857	+	0.919599i	$0.371487\pi$
$242$	1.96057	+	9.22377i	0.126030	+	0.592926i
$243$	−18.7011	−	10.7971i	−1.19968	−	0.692634i
$244$	−4.80397	+	14.7851i	−0.307542	+	0.946518i
$245$	15.2393	+	3.57284i	0.973600	+	0.228260i
$246$	7.55637	+	23.2561i	0.481776	+	1.48276i
$247$	4.16159	−	19.5788i	0.264796	−	1.24577i
$248$	−2.49174	−	0.261892i	−0.158225	−	0.0166302i
$249$	6.06260	+	10.5007i	0.384202	+	0.665457i
$250$	21.7830	−	0.142112i	1.37768	−	0.00898793i
$251$	2.64599			0.167014			0.0835068	−	0.996507i	$-0.473388\pi$
$251$	2.64599			0.167014			0.0835068	+	0.996507i	$0.473388\pi$
$252$	−7.90068	−	10.7396i	−0.497696	−	0.676532i
$253$	10.7623	−	3.49689i	0.676621	−	0.219848i
$254$	18.5653	+	3.94617i	1.16489	+	0.247605i
$255$	−2.28553	+	16.5230i	−0.143125	+	1.03471i
$256$	−18.3378	+	3.89783i	−1.14611	+	0.243614i
$257$	−1.72089	−	0.993558i	−0.107346	−	0.0619765i	0.445366	−	0.895349i	$-0.353074\pi$
$257$	−1.72089	−	0.993558i	−0.107346	−	0.0619765i	−0.552712	+	0.833372i	$0.686407\pi$
$258$	25.9277	+	8.42441i	1.61419	+	0.524481i
$259$	−21.1416	−	4.36268i	−1.31368	−	0.271084i
$260$	15.0794	−	4.35945i	0.935182	−	0.270362i
$261$	6.61714	−	2.94614i	0.409591	−	0.182362i
$262$	14.1481	−	31.7771i	0.874071	−	1.96320i
$263$	−11.9709	+	26.8870i	−0.738156	+	1.65793i	0.0148314	+	0.999890i	$0.495279\pi$
$263$	−11.9709	+	26.8870i	−0.738156	+	1.65793i	−0.752987	+	0.658035i	$0.771388\pi$
$264$	2.16965	−	0.965991i	0.133533	−	0.0594526i
$265$	−16.1615	−	5.84253i	−0.992792	−	0.358904i
$266$	−17.5489	+	19.7244i	−1.07599	+	1.20938i
$267$	31.8373	+	10.3446i	1.94841	+	0.633077i
$268$	13.3369	+	7.70005i	0.814679	+	0.470355i
$269$	23.3934	−	4.97242i	1.42632	−	0.303174i	0.570862	−	0.821046i	$-0.306609\pi$
$269$	23.3934	−	4.97242i	1.42632	−	0.303174i	0.855458	+	0.517872i	$0.173276\pi$
$270$	−2.00925	+	0.358792i	−0.122279	+	0.0218354i
$271$	−11.8053	−	2.50929i	−0.717118	−	0.152428i	−0.165120	−	0.986273i	$-0.552801\pi$
$271$	−11.8053	−	2.50929i	−0.717118	−	0.152428i	−0.551998	+	0.833845i	$0.686135\pi$
$272$	12.8558	−	4.17710i	0.779497	−	0.253274i
$273$	−9.99826	+	22.8203i	−0.605122	+	1.38115i
$274$	6.31012			0.381208
$275$	7.68272	+	9.74576i	0.463285	+	0.587692i
$276$	−9.86605	−	17.0885i	−0.593866	−	1.02861i
$277$	−18.5617	−	1.95092i	−1.11527	−	0.117219i	−0.471082	−	0.882090i	$-0.656136\pi$
$277$	−18.5617	−	1.95092i	−1.11527	−	0.117219i	−0.644184	+	0.764871i	$0.722803\pi$
$278$	−3.09919	+	14.5806i	−0.185877	+	0.874484i
$279$	−5.46952	−	16.8335i	−0.327452	−	1.00779i
$280$	2.28425	+	0.549877i	0.136510	+	0.0328614i
$281$	2.07291	−	6.37978i	0.123660	−	0.380585i	−0.869995	−	0.493061i	$-0.835878\pi$
$281$	2.07291	−	6.37978i	0.123660	−	0.380585i	0.993655	+	0.112475i	$0.0358780\pi$
$282$	8.86214	+	5.11656i	0.527733	+	0.304687i
$283$	1.85380	+	8.72143i	0.110197	+	0.518435i	0.998273	+	0.0587397i	$0.0187082\pi$
$283$	1.85380	+	8.72143i	0.110197	+	0.518435i	−0.888077	+	0.459696i	$0.847958\pi$
$284$	−23.1820	−	10.3213i	−1.37560	−	0.612455i
$285$	−10.3923	−	25.5617i	−0.615588	−	1.51415i
$286$	15.2900	+	11.1088i	0.904116	+	0.656879i
$287$	−13.0811	+	4.33639i	−0.772153	+	0.255969i
$288$	−12.7186	−	17.5056i	−0.749448	−	1.03153i
$289$	6.77388	−	3.01592i	0.398463	−	0.177407i
$290$	4.90883	−	10.1204i	0.288256	−	0.594290i
$291$	−9.97178	−	4.43972i	−0.584556	−	0.260261i
$292$	−16.4211	+	14.7856i	−0.960971	+	0.865262i
$293$			21.1628i			1.23634i	0.786043	+	0.618171i	$0.212126\pi$
$293$			21.1628i			1.23634i	−0.786043	+	0.618171i	$0.787874\pi$
$294$	26.3545	−	19.6303i	1.53703	−	1.14486i
$295$	−24.7030	−	0.808866i	−1.43826	−	0.0470940i
$296$	−3.16949	−	0.673697i	−0.184223	−	0.0391578i
$297$	−0.864096	−	0.778036i	−0.0501400	−	0.0451462i
$298$	7.16430	+	0.752998i	0.415017	+	0.0436200i
$299$	−8.90952	+	15.4317i	−0.515251	+	0.892441i
$300$	13.8371	−	16.6369i	0.798887	−	0.960530i
$301$	−4.66093	+	14.6402i	−0.268651	+	0.843848i
$302$	−2.52777	+	3.47917i	−0.145457	+	0.200204i
$303$	−5.71165	+	26.8712i	−0.328126	+	1.54371i
$304$	−14.9626	+	16.6176i	−0.858162	+	0.953085i
$305$	13.4136	−	13.9508i	0.768062	−	0.798821i
$306$	11.3241	+	12.5766i	0.647353	+	0.718958i
$307$			20.4087i			1.16479i	0.812907	+	0.582393i	$0.197884\pi$
$307$			20.4087i			1.16479i	−0.812907	+	0.582393i	$0.802116\pi$
$308$	−4.86132	−	10.7464i	−0.277000	−	0.612335i
$309$	−2.97925	+	2.16455i	−0.169483	+	0.123137i
$310$	−23.3407	−	14.5144i	−1.32566	−	0.824362i
$311$	0.300451	−	2.85860i	0.0170370	−	0.162096i	−0.982695	−	0.185229i	$-0.940697\pi$
$311$	0.300451	−	2.85860i	0.0170370	−	0.162096i	0.999732	+	0.0231326i	$0.00736399\pi$
$312$	−1.52110	+	3.41645i	−0.0861153	+	0.193418i
$313$	4.06737	−	0.427498i	0.229901	−	0.0241636i	0.0111228	−	0.999938i	$-0.496459\pi$
$313$	4.06737	−	0.427498i	0.229901	−	0.0241636i	0.218779	+	0.975775i	$0.429793\pi$
$314$	−37.9108	−	27.5438i	−2.13943	−	1.55439i
$315$	3.01476	+	16.3219i	0.169862	+	0.919633i
$316$	−9.08766	+	6.60257i	−0.511221	+	0.371424i
$317$	−2.54564	+	2.29211i	−0.142978	+	0.128738i	−0.737516	−	0.675329i	$-0.764001\pi$
$317$	−2.54564	+	2.29211i	−0.142978	+	0.128738i	0.594539	+	0.804067i	$0.297335\pi$
$318$	−31.2459	+	18.0398i	−1.75218	+	1.01162i
$319$	6.26787	−	1.33228i	0.350934	−	0.0745932i
$320$	−13.6647	−	3.37545i	−0.763881	−	0.188694i
$321$	−6.75577	−	20.7921i	−0.377071	−	1.16050i
$322$	20.2841	−	11.8723i	1.13039	−	0.661615i
$323$	9.32001	−	12.8279i	0.518579	−	0.713763i
$324$	−8.57267	+	14.8483i	−0.476259	+	0.824905i
$325$	−19.2589	−	3.30956i	−1.06829	−	0.183581i
$326$	−0.944320	−	1.63561i	−0.0523011	−	0.0905881i
$327$	−3.72561	−	8.36785i	−0.206027	−	0.462743i
$328$	−1.96736	+	0.639233i	−0.108629	+	0.0352957i
$329$	−2.85386	+	5.01155i	−0.157338	+	0.276296i
$330$	26.0401	+	0.852650i	1.43346	+	0.0469368i
$331$	18.0195	+	20.0127i	0.990440	+	1.10000i	0.994987	+	0.100006i	$0.0318861\pi$
$331$	18.0195	+	20.0127i	0.990440	+	1.10000i	−0.00454674	+	0.999990i	$0.501447\pi$
$332$	7.82789	−	4.51944i	0.429612	−	0.248036i
$333$	−4.75931	−	22.3908i	−0.260808	−	1.22701i
$334$	0.373335	+	3.55204i	0.0204280	+	0.194359i
$335$	−10.7552	−	15.8707i	−0.587621	−	0.867111i
$336$	22.4201	−	16.4935i	1.22312	−	0.899797i
$337$	15.3283	+	21.0976i	0.834986	+	1.14926i	0.986974	+	0.160877i	$0.0514323\pi$
$337$	15.3283	+	21.0976i	0.834986	+	1.14926i	−0.151988	+	0.988382i	$0.548568\pi$
$338$	−4.40695	+	0.463190i	−0.239707	+	0.0251942i
$339$	3.22323	−	30.6670i	0.175062	−	1.66560i
$340$	12.3173	+	1.70377i	0.667998	+	0.0924001i
$341$	−1.63673	−	15.5724i	−0.0886339	−	0.843295i
$342$	−26.6256	−	8.65119i	−1.43975	−	0.467803i
$343$	11.1512	+	14.7868i	0.602109	+	0.798414i
$344$	−0.712666	+	2.19336i	−0.0384244	+	0.118258i
$345$	1.76683	+	24.5010i	0.0951229	+	1.31909i
$346$	10.2167	−	11.3468i	0.549255	−	0.610010i
$347$	−18.0885	−	16.2870i	−0.971042	−	0.874330i	0.0210580	−	0.999778i	$-0.493297\pi$
$347$	−18.0885	−	16.2870i	−0.971042	−	0.874330i	−0.992100	+	0.125448i	$0.959963\pi$
$348$	−4.54468	−	10.2075i	−0.243620	−	0.547180i
$349$	28.5904			1.53041			0.765206	−	0.643786i	$-0.222637\pi$
$349$	28.5904			1.53041			0.765206	+	0.643786i	$0.222637\pi$
$350$	19.9139	+	16.3636i	1.06444	+	0.874669i
$351$	1.83094			0.0977282
$352$	−7.78588	−	17.4874i	−0.414989	−	0.932080i
$353$	−1.29650	−	1.16737i	−0.0690056	−	0.0621329i	0.633906	−	0.773410i	$-0.281451\pi$
$353$	−1.29650	−	1.16737i	−0.0690056	−	0.0621329i	−0.702912	+	0.711277i	$0.748117\pi$
$354$	−34.7219	+	38.5626i	−1.84545	+	2.04958i
$355$	20.3586	+	24.1556i	1.08052	+	1.28204i
$356$	7.71147	−	23.7335i	0.408707	−	1.25787i
$357$	−14.5883	+	13.2932i	−0.772096	+	0.703548i
$358$	19.8049	+	6.43500i	1.04672	+	0.340100i
$359$	−1.13764	−	10.8239i	−0.0600424	−	0.571266i	−0.982643	−	0.185508i	$-0.940607\pi$
$359$	−1.13764	−	10.8239i	−0.0600424	−	0.571266i	0.922600	−	0.385757i	$-0.126060\pi$
$360$	0.437965	+	2.45262i	0.0230828	+	0.129265i
$361$	−0.755751	+	7.19049i	−0.0397763	+	0.378447i
$362$	−11.8799	+	1.24863i	−0.624395	+	0.0656266i
$363$	−6.85444	−	9.43433i	−0.359765	−	0.495174i
$364$	17.0117	+	7.45331i	0.891654	+	0.390660i
$365$	26.4262	−	7.63983i	1.38321	−	0.399887i
$366$	−4.24717	−	40.4091i	−0.222003	−	2.11222i
$367$	2.59091	+	12.1893i	0.135244	+	0.636275i	0.992588	+	0.121530i	$0.0387800\pi$
$367$	2.59091	+	12.1893i	0.135244	+	0.636275i	−0.857343	+	0.514745i	$0.827887\pi$
$368$	17.2397	−	9.95333i	0.898680	−	0.518853i
$369$	−9.77838	−	10.8600i	−0.509042	−	0.565349i
$370$	−28.0589	−	21.8239i	−1.45871	−	1.13457i
$371$	−10.2713	−	17.5488i	−0.533259	−	0.911089i
$372$	−25.9670	+	8.43721i	−1.34633	+	0.437449i
$373$	−5.29572	−	11.8944i	−0.274202	−	0.615868i	0.722981	−	0.690868i	$-0.242771\pi$
$373$	−5.29572	−	11.8944i	−0.274202	−	0.615868i	−0.997184	+	0.0749993i	$0.976105\pi$
$374$	7.48577	+	12.9657i	0.387080	+	0.670442i
$375$	−24.5378	+	11.1173i	−1.26712	+	0.574094i
$376$	−0.432837	+	0.749696i	−0.0223219	+	0.0386626i
$377$	−5.93088	+	8.16316i	−0.305456	+	0.420424i
$378$	−2.09858	−	1.19505i	−0.107939	−	0.0614666i
$379$	2.26229	+	6.96260i	0.116206	+	0.357645i	0.992197	−	0.124683i	$-0.0397914\pi$
$379$	2.26229	+	6.96260i	0.116206	+	0.357645i	−0.875991	+	0.482328i	$0.839791\pi$
$380$	−19.0553	+	7.74708i	−0.977515	+	0.397417i
$381$	−22.9589	+	4.88007i	−1.17622	+	0.250013i
$382$	36.1687	−	20.8820i	1.85055	−	1.06842i
$383$	5.12036	−	4.61039i	0.261638	−	0.235580i	−0.527862	−	0.849330i	$-0.677006\pi$
$383$	5.12036	−	4.61039i	0.261638	−	0.235580i	0.789501	+	0.613750i	$0.210340\pi$
$384$	6.16098	−	4.47622i	0.314401	−	0.228426i
$385$	−0.393346	+	14.6782i	−0.0200468	+	0.748073i
$386$	3.00137	+	2.18062i	0.152766	+	0.110991i
$387$	−16.2031	+	1.70301i	−0.823648	+	0.0865689i
$388$	−3.30964	+	7.43358i	−0.168022	+	0.377383i
$389$	−1.04796	+	9.97067i	−0.0531337	+	0.505533i	0.935297	+	0.353863i	$0.115132\pi$
$389$	−1.04796	+	9.97067i	−0.0531337	+	0.505533i	−0.988431	+	0.151671i	$0.951535\pi$
$390$	−31.3705	+	26.4394i	−1.58850	+	1.33881i
$391$	−11.4198	+	8.29697i	−0.577524	+	0.419596i
$392$	1.66063	+	2.22947i	0.0838743	+	0.112605i
$393$			43.0164i			2.16989i
$394$	4.43278	+	4.92310i	0.223320	+	0.248022i
$395$	13.7663	−	2.45824i	0.692656	−	0.123688i
$396$	8.36903	−	9.29474i	0.420559	−	0.467078i
$397$	−2.30820	+	10.8592i	−0.115845	+	0.545010i	0.881499	+	0.472185i	$0.156535\pi$
$397$	−2.30820	+	10.8592i	−0.115845	+	0.545010i	−0.997345	+	0.0728247i	$0.976799\pi$
$398$	−9.46324	+	13.0250i	−0.474349	+	0.652886i
$399$	9.90449	−	31.1105i	0.495845	−	1.55747i
$400$	16.7841	+	13.9596i	0.839203	+	0.697978i
$401$	3.57303	−	6.18867i	0.178429	−	0.309048i	−0.762914	−	0.646500i	$-0.776232\pi$
$401$	3.57303	−	6.18867i	0.178429	−	0.309048i	0.941343	+	0.337453i	$0.109565\pi$
$402$	−40.0300	−	4.20732i	−1.99652	−	0.209842i
$403$	18.3232	+	16.4983i	0.912743	+	0.821837i
$404$	20.0314	+	4.25782i	0.996602	+	0.211834i
$405$	17.6693	−	11.9741i	0.877994	−	0.594997i
$406$	12.1259	−	5.48534i	0.601798	−	0.272233i
$407$		−	20.2507i		−	1.00379i
$408$	−2.20158	+	1.98231i	−0.108994	+	0.0981391i
$409$	−3.58156	−	1.59461i	−0.177097	−	0.0788486i	0.316273	−	0.948668i	$-0.397568\pi$
$409$	−3.58156	−	1.59461i	−0.177097	−	0.0788486i	−0.493370	+	0.869820i	$0.664235\pi$
$410$	−22.4790	−	3.10939i	−1.11016	−	0.153562i
$411$	−7.12881	+	3.17395i	−0.351638	+	0.156560i
$412$	1.61359	+	2.22091i	0.0794957	+	0.109416i
$413$	−21.8489	−	19.4390i	−1.07511	−	0.956532i
$414$	20.1630	+	14.6493i	0.990956	+	0.719972i
$415$	−11.2234	+	0.809349i	−0.550937	+	0.0397294i
$416$	27.5365	+	12.2601i	1.35009	+	0.601099i
$417$	−3.83264	−	18.0312i	−0.187685	−	0.882990i
$418$	−21.4486	−	12.3834i	−1.04909	−	0.605690i
$419$	−7.25128	+	22.3171i	−0.354248	+	1.09026i	0.602196	+	0.798348i	$0.294293\pi$
$419$	−7.25128	+	22.3171i	−0.354248	+	1.09026i	−0.956444	+	0.291915i	$0.905707\pi$
$420$	25.1779	−	4.65052i	1.22855	−	0.226922i
$421$	−10.2298	−	31.4841i	−0.498571	−	1.53444i	−0.811317	−	0.584606i	$-0.801249\pi$
$421$	−10.2298	−	31.4841i	−0.498571	−	1.53444i	0.312746	−	0.949837i	$-0.398751\pi$
$422$	9.09220	−	42.7754i	0.442601	−	2.08228i
$423$	−6.08202	−	0.639246i	−0.295718	−	0.0310812i
$424$	−1.52609	−	2.64326i	−0.0741133	−	0.128368i
$425$	−12.8709	−	8.60034i	−0.624332	−	0.417178i
$426$	66.3235			3.21339
$427$	22.7591	−	2.52886i	1.10139	−	0.122380i
$428$	−15.4997	+	5.03617i	−0.749208	+	0.243432i
$429$	−22.8614	−	4.85935i	−1.10376	−	0.234612i
$430$	−17.5352	+	18.2375i	−0.845623	+	0.879488i
$431$	20.2153	−	4.29689i	0.973736	−	0.206974i	0.306542	−	0.951857i	$-0.400828\pi$
$431$	20.2153	−	4.29689i	0.973736	−	0.206974i	0.667195	+	0.744883i	$0.267495\pi$
$432$	−1.77141	−	1.02272i	−0.0852269	−	0.0492058i
$433$	−25.2950	−	8.21886i	−1.21560	−	0.394973i	−0.370124	−	0.928982i	$-0.620685\pi$
$433$	−25.2950	−	8.21886i	−1.21560	−	0.394973i	−0.845479	+	0.534009i	$0.820685\pi$
$434$	−10.2332	−	30.8694i	−0.491210	−	1.48178i
$435$	−0.455220	+	13.9026i	−0.0218261	+	0.666576i
$436$	−6.23791	+	2.77730i	−0.298742	+	0.133008i
$437$	9.49766	−	21.3321i	0.454335	−	1.02045i
$438$	23.4903	−	52.7601i	1.12241	−	2.52098i
$439$	10.7615	−	4.79134i	0.513620	−	0.228678i	−0.133525	−	0.991045i	$-0.542630\pi$
$439$	10.7615	−	4.79134i	0.513620	−	0.228678i	0.647145	+	0.762367i	$0.275963\pi$
$440$	−0.0721301	+	2.20287i	−0.00343867	+	0.105018i
$441$	−9.61673	+	17.1233i	−0.457939	+	0.815396i
$442$	−22.4211	−	7.28507i	−1.06646	−	0.346515i
$443$	0.871479	+	0.503149i	0.0414052	+	0.0239053i	0.520560	−	0.853825i	$-0.325723\pi$
$443$	0.871479	+	0.503149i	0.0414052	+	0.0239053i	−0.479154	+	0.877731i	$0.659057\pi$
$444$	−34.5397	+	7.34163i	−1.63918	+	0.348419i
$445$	−21.5320	+	22.3942i	−1.02071	+	1.06159i
$446$	16.9742	+	3.60798i	0.803753	+	0.170843i
$447$	−8.47257	+	2.75290i	−0.400739	+	0.130208i
$448$	−9.86902	−	13.4152i	−0.466267	−	0.633810i
$449$	29.0408			1.37052			0.685261	−	0.728298i	$-0.259688\pi$
$449$	29.0408			1.37052			0.685261	+	0.728298i	$0.259688\pi$
$450$	−7.41924	+	26.3052i	−0.349747	+	1.24004i
$451$	−6.46400	−	11.1960i	−0.304378	−	0.527198i
$452$	−22.8611	−	2.40279i	−1.07529	−	0.113018i
$453$	1.10572	−	5.20203i	0.0519515	−	0.244412i
$454$	7.56804	+	23.2920i	0.355186	+	1.09315i
$455$	−15.0054	−	17.5909i	−0.703465	−	0.824672i
$456$	1.51442	−	4.66090i	0.0709191	−	0.218267i
$457$	−11.1386	−	6.43087i	−0.521041	−	0.300823i	0.216319	−	0.976323i	$-0.430595\pi$
$457$	−11.1386	−	6.43087i	−0.521041	−	0.300823i	−0.737361	+	0.675499i	$0.763928\pi$
$458$	6.69923	+	31.5174i	0.313035	+	1.47271i
$459$	1.32501	+	0.589934i	0.0618464	+	0.0275358i
$460$	18.2646	−	1.31710i	0.851590	−	0.0614102i
$461$	−9.56290	−	6.94785i	−0.445389	−	0.323594i	0.342384	−	0.939560i	$-0.388766\pi$
$461$	−9.56290	−	6.94785i	−0.445389	−	0.323594i	−0.787772	+	0.615966i	$0.788766\pi$
$462$	23.0315	+	20.4913i	1.07152	+	0.953339i
$463$	−20.4731	−	28.1788i	−0.951465	−	1.30958i	−0.950873	−	0.309580i	$-0.899812\pi$
$463$	−20.4731	−	28.1788i	−0.951465	−	1.30958i	−0.000592125	−	1.00000i	$-0.500188\pi$
$464$	10.2978	−	4.58488i	0.478064	−	0.212848i
$465$	33.6696	+	4.65732i	1.56139	+	0.215978i
$466$	10.3772	+	4.62022i	0.480714	+	0.214028i
$467$	17.5658	−	15.8163i	0.812847	−	0.731891i	−0.153773	−	0.988106i	$-0.549142\pi$
$467$	17.5658	−	15.8163i	0.812847	−	0.731891i	0.966620	+	0.256215i	$0.0824757\pi$
$468$			19.6947i			0.910387i
$469$	2.23710	−	22.5737i	0.103299	−	1.04236i
$470$	−7.86152	+	5.32757i	−0.362625	+	0.245743i
$471$	56.6838	+	12.0485i	2.61185	+	0.555166i
$472$	−3.26221	−	2.93731i	−0.150155	−	0.135201i
$473$	−14.3342	−	1.50658i	−0.659086	−	0.0692727i
$474$	14.6795	−	25.4257i	0.674253	−	1.16784i
$475$	25.5528	+	1.67518i	1.17244	+	0.0768626i
$476$	9.90953	+	10.8750i	0.454203	+	0.498456i
$477$	12.6738	−	17.4440i	0.580294	−	0.798706i
$478$	1.65121	−	7.76833i	0.0755246	−	0.355315i
$479$	−6.77351	+	7.52274i	−0.309490	+	0.343723i	−0.877744	−	0.479130i	$-0.840952\pi$
$479$	−6.77351	+	7.52274i	−0.309490	+	0.343723i	0.568254	+	0.822853i	$0.307619\pi$
$480$	40.9062	−	7.30463i	1.86711	−	0.333409i
$481$	21.3371	+	23.6973i	0.972889	+	1.08050i
$482$			44.3376i			2.01952i
$483$	−16.9442	+	23.6154i	−0.770986	+	1.07454i
$484$	−7.03293	+	5.10972i	−0.319678	+	0.232260i
$485$	7.74578	−	6.52824i	0.351718	−	0.296432i
$486$	4.39789	−	41.8431i	0.199492	−	1.89804i
$487$	4.86270	−	10.9218i	0.220350	−	0.494914i	−0.769217	−	0.638988i	$-0.779354\pi$
$487$	4.86270	−	10.9218i	0.220350	−	0.494914i	0.989567	+	0.144074i	$0.0460202\pi$
$488$	3.41842	−	0.359291i	0.154745	−	0.0162643i
$489$	1.88954	+	1.37283i	0.0854480	+	0.0620816i
$490$	5.71734	+	29.9562i	0.258283	+	1.35328i
$491$	0.443578	−	0.322278i	0.0200184	−	0.0145442i	−0.577731	−	0.816227i	$-0.696062\pi$
$491$	0.443578	−	0.322278i	0.0200184	−	0.0145442i	0.597749	+	0.801683i	$0.296062\pi$
$492$	−16.7525	+	15.0840i	−0.755260	+	0.680039i
$493$	−6.92226	+	3.99657i	−0.311763	+	0.179996i
$494$	38.1468	−	8.10835i	1.71631	−	0.364812i
$495$	−14.4240	+	5.86418i	−0.648309	+	0.263575i
$496$	−8.51185	−	26.1968i	−0.382193	−	1.17627i
$497$	0.222045	+	37.3778i	0.00996010	+	1.67662i
$498$	−13.8861	+	19.1126i	−0.622252	+	0.856456i
$499$	−20.0243	+	34.6832i	−0.896412	+	1.55263i	−0.0643647	+	0.997926i	$0.520502\pi$
$499$	−20.0243	+	34.6832i	−0.896412	+	1.55263i	−0.832047	+	0.554705i	$0.812831\pi$
$500$	8.28751	+	18.2920i	0.370629	+	0.818041i
$501$	−2.20843	−	3.82511i	−0.0986654	−	0.170893i
$502$	2.09689	+	4.70968i	0.0935886	+	0.210203i
$503$	−11.8433	+	3.84812i	−0.528066	+	0.171579i	−0.560903	−	0.827882i	$-0.689546\pi$
$503$	−11.8433	+	3.84812i	−0.528066	+	0.171579i	0.0328365	+	0.999461i	$0.489546\pi$
$504$	−1.45875	+	2.56166i	−0.0649780	+	0.114105i
$505$	−20.1240	−	15.6522i	−0.895505	−	0.696515i
$506$	14.7531	+	16.3850i	0.655855	+	0.728401i
$507$	4.74574	−	2.73996i	0.210766	−	0.121686i
$508$	3.63790	+	17.1150i	0.161406	+	0.759354i
$509$	−1.34880	−	12.8330i	−0.0597846	−	0.568812i	−0.982881	−	0.184243i	$-0.941017\pi$
$509$	−1.34880	−	12.8330i	−0.0597846	−	0.568812i	0.923096	−	0.384569i	$-0.125650\pi$
$510$	−31.2210	+	9.02601i	−1.38249	+	0.399679i
$511$	29.8126	+	13.0618i	1.31883	+	0.577818i
$512$	−17.7546	−	24.4372i	−0.784652	−	1.07998i
$513$	−2.38620	+	0.250800i	−0.105353	+	0.0110731i
$514$	0.404698	−	3.85044i	0.0178504	−	0.169836i
$515$	−0.600764	−	3.36430i	−0.0264728	−	0.148249i
$516$	2.62704	+	24.9946i	0.115649	+	1.10033i
$517$	−5.14536	−	1.67183i	−0.226292	−	0.0735269i
$518$	−8.98894	−	41.0879i	−0.394951	−	1.80530i
$519$	−5.83490	+	17.9580i	−0.256124	+	0.788267i
$520$	−2.23665	−	2.65379i	−0.0980835	−	0.116377i
$521$	−26.2492	+	29.1527i	−1.15000	+	1.27720i	−0.194930	+	0.980817i	$0.562448\pi$
$521$	−26.2492	+	29.1527i	−1.15000	+	1.27720i	−0.955068	+	0.296386i	$0.904219\pi$
$522$	10.4879	+	9.44331i	0.459041	+	0.413322i
$523$	−3.13487	−	7.04103i	−0.137078	−	0.307883i	0.831943	−	0.554862i	$-0.187229\pi$
$523$	−3.13487	−	7.04103i	−0.137078	−	0.307883i	−0.969021	+	0.246979i	$0.920562\pi$
$524$	32.0670			1.40085
$525$	−30.7284	−	8.47003i	−1.34110	−	0.369662i
$526$	−57.3437			−2.50030
$527$	7.94433	+	17.8433i	0.346061	+	0.777265i
$528$	19.4038	+	17.4713i	0.844442	+	0.760339i
$529$	1.48030	−	1.64404i	0.0643610	−	0.0714801i
$530$	−2.40829	−	33.3964i	−0.104610	−	1.45065i
$531$	9.58297	−	29.4934i	0.415866	−	1.27990i
$532$	−23.1917	−	7.38341i	−1.00549	−	0.320112i
$533$	19.3608	+	6.29070i	0.838608	+	0.272480i
$534$	6.81768	+	64.8659i	0.295030	+	2.80702i
$535$	20.0974	+	2.77995i	0.868887	+	0.120188i
$536$	0.355920	−	3.38635i	0.0153734	−	0.146268i
$537$	−25.6112	+	2.69185i	−1.10520	+	0.116162i
$538$	27.3893	+	37.6981i	1.18083	+	1.62528i
$539$	−11.4711	+	13.0484i	−0.494095	+	0.562036i
$540$	−1.05556	−	1.55762i	−0.0454241	−	0.0670292i
$541$	−1.99892	−	19.0185i	−0.0859403	−	0.817668i	−0.949573	−	0.313546i	$-0.898483\pi$
$541$	−1.99892	−	19.0185i	−0.0859403	−	0.817668i	0.863633	−	0.504122i	$-0.168184\pi$
$542$	−4.88903	−	23.0011i	−0.210002	−	0.987981i
$543$	12.7932	−	7.38617i	0.549009	−	0.316971i
$544$	15.9774	+	17.7447i	0.685026	+	0.760799i
$545$	8.49599	+	0.278190i	0.363928	+	0.0119163i
$546$	−48.5420	+	0.288367i	−2.07740	+	0.0123410i
$547$	−17.8957	+	5.81466i	−0.765164	+	0.248617i	−0.665494	−	0.746404i	$-0.731779\pi$
$547$	−17.8957	+	5.81466i	−0.765164	+	0.248617i	−0.0996705	+	0.995020i	$0.531779\pi$
$548$	2.36606	+	5.31425i	0.101073	+	0.227014i
$549$	12.1412	+	21.0291i	0.518173	+	0.897501i
$550$	−11.2584	+	21.3980i	−0.480060	+	0.912413i
$551$	6.61134	−	11.4512i	0.281653	−	0.487837i
$552$	−2.56440	+	3.52959i	−0.109148	+	0.150229i
$553$	14.3783	+	8.18779i	0.611426	+	0.348180i
$554$	−11.2372	−	34.5846i	−0.477424	−	1.46936i
$555$	42.6766	+	10.5420i	1.81152	+	0.447481i
$556$	−13.4415	+	2.85709i	−0.570048	+	0.121167i
$557$	−2.99630	+	1.72991i	−0.126957	+	0.0732988i	−0.562134	−	0.827046i	$-0.690019\pi$
$557$	−2.99630	+	1.72991i	−0.126957	+	0.0732988i	0.435176	+	0.900345i	$0.356686\pi$
$558$	25.6279	−	23.0755i	1.08492	−	0.976863i
$559$	18.3612	−	13.3402i	0.776596	−	0.564230i
$560$	4.69166	+	25.4006i	0.198259	+	1.07337i
$561$	−14.9787	−	10.8826i	−0.632400	−	0.459466i
$562$	12.9983	−	1.36618i	0.548300	−	0.0576286i
$563$	13.0064	−	29.2128i	0.548153	−	1.23117i	−0.400919	−	0.916114i	$-0.631309\pi$
$563$	13.0064	−	29.2128i	0.548153	−	1.23117i	0.949072	−	0.315059i	$-0.102024\pi$
$564$	−0.986092	+	9.38204i	−0.0415220	+	0.395055i
$565$	24.3013	+	15.1117i	1.02236	+	0.635755i
$566$	−14.0545	+	10.2112i	−0.590753	+	0.429207i
$567$	25.1319	+	2.49062i	1.05544	+	0.104596i
$568$			5.61066i			0.235418i
$569$	−0.584954	−	0.649657i	−0.0245226	−	0.0272351i	0.730759	−	0.682636i	$-0.239166\pi$
$569$	−0.584954	−	0.649657i	−0.0245226	−	0.0272351i	−0.755281	+	0.655401i	$0.772500\pi$
$570$	37.2624	−	38.7547i	1.56075	−	1.62326i
$571$	−4.90001	+	5.44201i	−0.205059	+	0.227741i	−0.836898	−	0.547358i	$-0.815634\pi$
$571$	−4.90001	+	5.44201i	−0.205059	+	0.227741i	0.631839	+	0.775099i	$0.282300\pi$
$572$	−3.62246	+	17.0423i	−0.151463	+	0.712575i
$573$	−30.3578	+	41.7839i	−1.26822	+	1.74555i
$574$	−18.0849	−	19.8470i	−0.754850	−	0.828396i
$575$	−21.1737	−	8.44781i	−0.883006	−	0.352298i
$576$	8.83015	−	15.2943i	0.367923	−	0.637261i
$577$	22.7546	+	2.39160i	0.947286	+	0.0995638i	0.565556	−	0.824710i	$-0.308662\pi$
$577$	22.7546	+	2.39160i	0.947286	+	0.0995638i	0.381730	+	0.924274i	$0.375328\pi$
$578$	10.7363	+	9.66698i	0.446570	+	0.402093i
$579$	−4.48761	−	0.953872i	−0.186499	−	0.0396416i
$580$	10.3638	+	0.339349i	0.430334	+	0.0140907i
$581$	−10.8177	−	7.76178i	−0.448795	−	0.322013i
$582$		−	21.2675i		−	0.881564i
$583$	14.1755	−	12.7636i	0.587087	−	0.528616i
$584$	4.46326	+	1.98717i	0.184691	+	0.0822297i
$585$	10.7001	−	22.0600i	0.442394	−	0.912070i
$586$	−37.6683	+	16.7710i	−1.55606	+	0.692803i
$587$	15.5422	+	21.3920i	0.641496	+	0.882943i	0.998694	−	0.0510854i	$-0.0162681\pi$
$587$	15.5422	+	21.3920i	0.641496	+	0.882943i	−0.357199	+	0.934028i	$0.616268\pi$
$588$	26.4142	+	14.8346i	1.08930	+	0.611769i
$589$	−26.1399	−	18.9918i	−1.07708	−	0.782542i
$590$	−18.1368	−	44.6106i	−0.746680	−	1.83659i
$591$	−7.48419	−	3.33218i	−0.307858	−	0.137067i
$592$	−7.40659	−	34.8452i	−0.304409	−	1.43213i
$593$	−7.97900	−	4.60668i	−0.327658	−	0.189174i	0.327143	−	0.944975i	$-0.393914\pi$
$593$	−7.97900	−	4.60668i	−0.327658	−	0.189174i	−0.654801	+	0.755801i	$0.727248\pi$
$594$	0.700074	−	2.15461i	0.0287244	−	0.0884045i
$595$	−5.19130	−	17.5650i	−0.212822	−	0.720093i
$596$	2.05218	+	6.31597i	0.0840607	+	0.258712i
$597$	4.13952	−	19.4749i	0.169419	−	0.797054i
$598$	−34.5280	−	3.62904i	−1.41196	−	0.148402i
$599$	−6.03999	−	10.4616i	−0.246787	−	0.427448i	0.715845	−	0.698259i	$-0.246042\pi$
$599$	−6.03999	−	10.4616i	−0.246787	−	0.427448i	−0.962633	+	0.270811i	$0.912708\pi$
$600$	−4.60482	−	1.29876i	−0.187991	−	0.0530218i
$601$	−18.7934			−0.766597			−0.383299	−	0.923624i	$-0.625212\pi$
$601$	−18.7934			−0.766597			−0.383299	+	0.923624i	$0.625212\pi$
$602$	−29.7522	+	3.30589i	−1.21261	+	0.134738i
$603$	22.8772	−	7.43326i	0.931632	−	0.302706i
$604$	−3.87791	−	0.824275i	−0.157790	−	0.0335393i
$605$	10.6537	−	1.90243i	0.433134	−	0.0773448i
$606$	−52.3552	+	11.1284i	−2.12679	+	0.452062i
$607$	3.61582	+	2.08760i	0.146762	+	0.0847329i	0.571583	−	0.820544i	$-0.306330\pi$
$607$	3.61582	+	2.08760i	0.146762	+	0.0847329i	−0.424821	+	0.905277i	$0.639663\pi$
$608$	−37.5668	−	12.2062i	−1.52354	−	0.495027i
$609$	−10.9401	+	12.2963i	−0.443313	+	0.498270i
$610$	35.4614	+	12.8196i	1.43579	+	0.519052i
$611$	7.78259	−	3.46503i	0.314850	−	0.140180i
$612$	−6.34569	+	14.2527i	−0.256509	+	0.576129i
$613$	−9.06313	+	20.3561i	−0.366056	+	0.822176i	0.632798	+	0.774317i	$0.281907\pi$
$613$	−9.06313	+	20.3561i	−0.366056	+	0.822176i	−0.998854	+	0.0478591i	$0.984760\pi$
$614$	−36.3261	+	16.1734i	−1.46600	+	0.652706i
$615$	26.9595	−	7.79401i	1.08711	−	0.314285i
$616$	−1.73346	+	1.94836i	−0.0698432	+	0.0785016i
$617$	25.9217	+	8.42248i	1.04357	+	0.339076i	0.780142	−	0.625603i	$-0.215147\pi$
$617$	25.9217	+	8.42248i	1.04357	+	0.339076i	0.263428	+	0.964679i	$0.415147\pi$
$618$	−6.21373	−	3.58750i	−0.249953	−	0.144310i
$619$	18.5773	−	3.94873i	0.746685	−	0.158713i	0.181171	−	0.983452i	$-0.442011\pi$
$619$	18.5773	−	3.94873i	0.746685	−	0.158713i	0.565514	+	0.824739i	$0.308678\pi$
$620$	3.47185	−	25.0994i	0.139433	−	1.00802i
$621$	2.08930	+	0.444094i	0.0838407	+	0.0178209i
$622$	5.32621	−	1.73059i	0.213562	−	0.0693904i
$623$	−36.5335	+	4.05939i	−1.46369	+	0.162636i
$624$	−41.1148			−1.64591
$625$	0.655127	−	24.9914i	0.0262051	−	0.999657i
$626$	3.98421	+	6.90086i	0.159241	+	0.275814i
$627$	30.4602	+	3.20149i	1.21646	+	0.127855i
$628$	8.98170	−	42.2556i	0.358409	−	1.68618i
$629$	7.80592	+	24.0242i	0.311242	+	0.957906i
$630$	−26.6627	+	18.3007i	−1.06227	+	0.729119i
$631$	−10.1285	+	31.1724i	−0.403210	+	1.24095i	0.519170	+	0.854671i	$0.326241\pi$
$631$	−10.1285	+	31.1724i	−0.403210	+	1.24095i	−0.922380	+	0.386283i	$0.873759\pi$
$632$	2.15089	+	1.24182i	0.0855580	+	0.0493969i
$633$	11.2439	+	52.8986i	0.446906	+	2.10253i
$634$	−6.09715	−	2.71463i	−0.242149	−	0.107812i
$635$	5.22371	−	21.1470i	0.207297	−	0.839192i
$636$	−26.9088	−	19.5504i	−1.06700	−	0.775224i
$637$	−0.325029	−	27.3557i	−0.0128781	−	1.08387i
$638$	7.33850	+	10.1006i	0.290534	+	0.399886i
$639$	−36.2096	+	16.1215i	−1.43243	+	0.637758i
$640$	1.24236	+	6.95727i	0.0491086	+	0.275010i
$641$	35.9058	+	15.9863i	1.41820	+	0.631421i	0.965538	−	0.260263i	$-0.0838093\pi$
$641$	35.9058	+	15.9863i	1.41820	+	0.631421i	0.452658	+	0.891684i	$0.350476\pi$
$642$	31.6548	−	28.5021i	1.24931	−	1.12489i
$643$		−	28.8706i		−	1.13854i	−0.822149	−	0.569272i	$-0.807225\pi$
$643$		−	28.8706i		−	1.13854i	0.822149	−	0.569272i	$-0.192775\pi$
$644$	17.6044	+	12.6312i	0.693709	+	0.497740i
$645$	10.6370	−	29.4237i	0.418830	−	1.15856i
$646$	30.2186	+	6.42317i	1.18894	+	0.252716i
$647$	−3.87554	−	3.48955i	−0.152363	−	0.137188i	0.589424	−	0.807824i	$-0.299355\pi$
$647$	−3.87554	−	3.48955i	−0.152363	−	0.137188i	−0.741787	+	0.670636i	$0.766021\pi$
$648$	3.77011	+	0.396255i	0.148104	+	0.0155664i
$649$	13.7171	−	23.7588i	0.538444	−	0.932613i
$650$	−9.37142	−	36.9022i	−0.367577	−	1.44742i
$651$	27.0880	+	29.7272i	1.06166	+	1.16510i
$652$	1.02339	−	1.40858i	0.0400792	−	0.0551643i
$653$	4.81049	−	22.6316i	0.188249	−	0.885642i	−0.778047	−	0.628207i	$-0.783789\pi$
$653$	4.81049	−	22.6316i	0.188249	−	0.885642i	0.966296	−	0.257435i	$-0.0828774\pi$
$654$	11.9417	−	13.2626i	0.466959	−	0.518611i
$655$	−35.9183	−	17.4219i	−1.40344	−	0.680732i
$656$	−15.2174	−	16.9007i	−0.594141	−	0.659861i
$657$			34.5145i			1.34654i
$658$	−11.1818	−	1.10814i	−0.435913	−	0.0431997i
$659$	2.56376	−	1.86268i	0.0998698	−	0.0725596i	−0.536730	−	0.843754i	$-0.680340\pi$
$659$	2.56376	−	1.86268i	0.0998698	−	0.0725596i	0.636599	+	0.771195i	$0.280340\pi$
$660$	9.04600	+	22.2502i	0.352115	+	0.866088i
$661$	−0.812074	+	7.72636i	−0.0315860	+	0.300521i	0.967312	+	0.253589i	$0.0816110\pi$
$661$	−0.812074	+	7.72636i	−0.0315860	+	0.300521i	−0.998898	+	0.0469319i	$0.985056\pi$
$662$	−21.3411	+	47.9330i	−0.829447	+	1.86297i
$663$	28.9945	−	3.04744i	1.12605	−	0.118353i
$664$	−1.61684	−	1.17470i	−0.0627454	−	0.0455872i
$665$	21.9656	+	20.8702i	0.851791	+	0.809310i
$666$	36.0824	−	26.2154i	1.39816	−	1.01583i
$667$	−8.74776	+	7.87652i	−0.338715	+	0.304980i
$668$	−2.85147	+	1.64630i	−0.110327	+	0.0636972i
$669$	−20.9913	+	4.46184i	−0.811571	+	0.172505i
$670$	19.7255	−	31.7207i	0.762064	−	1.22548i
$671$	6.63817	+	20.4302i	0.256264	+	0.788699i
$672$	42.7248	+	24.3299i	1.64814	+	0.938546i
$673$	−1.93901	+	2.66881i	−0.0747432	+	0.102875i	−0.844752	−	0.535158i	$-0.820252\pi$
$673$	−1.93901	+	2.66881i	−0.0747432	+	0.102875i	0.770009	+	0.638034i	$0.220252\pi$
$674$	−25.4049	+	44.0027i	−0.978562	+	1.69492i
$675$	0.336086	+	2.31817i	0.0129359	+	0.0892265i
$676$	−2.04253	−	3.53777i	−0.0785589	−	0.136068i
$677$	6.65071	+	14.9377i	0.255608	+	0.574104i	0.995079	−	0.0990838i	$-0.0315912\pi$
$677$	6.65071	+	14.9377i	0.255608	+	0.574104i	−0.739471	+	0.673188i	$0.764925\pi$
$678$	57.1394	−	18.5657i	2.19443	−	0.713012i
$679$	11.9857	−	0.0712016i	0.459967	−	0.00273247i
$680$	−0.763558	−	2.64115i	−0.0292811	−	0.101284i
$681$	−20.2657	−	22.5073i	−0.776583	−	0.862483i
$682$	26.4208	−	15.2541i	1.01170	−	0.584108i
$683$	−8.14026	−	38.2969i	−0.311478	−	1.46539i	−0.803759	−	0.594955i	$-0.797170\pi$
$683$	−8.14026	−	38.2969i	−0.311478	−	1.46539i	0.492281	−	0.870436i	$-0.336163\pi$
$684$	−2.69775	−	25.6674i	−0.103151	−	0.981418i
$685$	0.236998	−	7.23797i	0.00905522	−	0.276549i
$686$	−17.4825	+	31.5666i	−0.667483	+	1.20522i
$687$	−23.4215	−	32.2369i	−0.893585	−	1.22991i
$688$	−25.2157	+	2.65028i	−0.961341	+	0.101041i
$689$	−3.13966	+	29.8719i	−0.119612	+	1.13803i
$690$	−42.2100	+	22.5613i	−1.60691	+	0.858895i
$691$	−3.74529	−	35.6340i	−0.142478	−	1.35558i	−0.799025	−	0.601298i	$-0.794650\pi$
$691$	−3.74529	−	35.6340i	−0.142478	−	1.35558i	0.656547	−	0.754285i	$-0.272016\pi$
$692$	13.3870	+	4.34969i	0.508896	+	0.165350i
$693$	−17.5550	−	5.58890i	−0.666861	−	0.212305i
$694$	14.6550	−	45.1033i	0.556295	−	1.71210i
$695$	16.6081	+	4.10253i	0.629982	+	0.155618i
$696$	−1.65308	+	1.83593i	−0.0626599	+	0.0695909i
$697$	11.9841	+	10.7906i	0.453931	+	0.408722i
$698$	22.6572	+	50.8890i	0.857589	+	1.92618i
$699$	−14.0475			−0.531325
$700$	−6.31408	+	22.9068i	−0.238650	+	0.865796i
$701$	4.06365			0.153482			0.0767409	−	0.997051i	$-0.475549\pi$
$701$	4.06365			0.153482			0.0767409	+	0.997051i	$0.475549\pi$
$702$	1.45097	+	3.25894i	0.0547635	+	0.123001i
$703$	−31.0540	−	27.9611i	−1.17122	−	1.05457i
$704$	10.4540	−	11.6104i	0.394002	−	0.437583i
$705$	6.20176	−	9.97309i	0.233572	−	0.375608i
$706$	1.05040	−	3.23279i	0.0395322	−	0.121668i
$707$	−6.44692	−	29.4685i	−0.242461	−	1.10828i
$708$	−45.4960	−	14.7825i	−1.70984	−	0.555562i
$709$	−3.10511	−	29.5431i	−0.116615	−	1.10952i	−0.883727	−	0.468003i	$-0.844974\pi$
$709$	−3.10511	−	29.5431i	−0.116615	−	1.10952i	0.767112	−	0.641513i	$-0.221693\pi$
$710$	−26.8615	+	55.3796i	−1.00809	+	2.07836i
$711$	−1.83401	+	17.4495i	−0.0687808	+	0.654406i
$712$	−5.48735	+	0.576744i	−0.205647	+	0.0216144i
$713$	16.9071	+	23.2706i	0.633175	+	0.871491i
$714$	−35.2218	−	15.4317i	−1.31814	−	0.577517i
$715$	13.3166	−	17.1210i	0.498011	−	0.640291i
$716$	2.00667	+	19.0922i	0.0749927	+	0.713507i
$717$	2.04198	+	9.60677i	0.0762592	+	0.358771i
$718$	18.3643	−	10.6026i	0.685350	−	0.395687i
$719$	8.36849	+	9.29415i	0.312092	+	0.346613i	0.878700	−	0.477374i	$-0.158411\pi$
$719$	8.36849	+	9.29415i	0.312092	+	0.346613i	−0.566608	+	0.823987i	$0.691745\pi$
$720$	−22.6744	+	15.3659i	−0.845026	+	0.572655i
$721$	2.00099	−	3.51387i	0.0745209	−	0.130863i
$722$	−13.3975	+	4.35310i	−0.498603	+	0.162006i
$723$	−22.3016	−	50.0901i	−0.829404	−	1.86287i
$724$	−5.50610	−	9.53685i	−0.204633	−	0.354434i
$725$	−11.4241	−	6.01074i	−0.424282	−	0.223233i
$726$	11.3605	−	19.6769i	0.421626	−	0.730278i
$727$	21.7358	−	29.9167i	0.806135	−	1.10955i	−0.185773	−	0.982593i	$-0.559479\pi$
$727$	21.7358	−	29.9167i	0.806135	−	1.10955i	0.991908	−	0.126957i	$-0.0405211\pi$
$728$	−0.0243945	−	4.10642i	−0.000904119	−	0.152194i
$729$	7.22919	+	22.2491i	0.267748	+	0.824043i
$730$	34.5405	+	40.9825i	1.27840	+	1.51683i
$731$	17.5859	−	3.73800i	0.650437	−	0.138255i
$732$	32.4392	−	18.7288i	1.19899	−	0.692236i
$733$	−24.2089	+	21.7978i	−0.894177	+	0.805120i	−0.981580	−	0.191053i	$-0.938810\pi$
$733$	−24.2089	+	21.7978i	−0.894177	+	0.805120i	0.0874030	+	0.996173i	$0.472143\pi$
$734$	−19.6428	+	14.2713i	−0.725030	+	0.526765i
$735$	−21.5269	−	30.9670i	−0.794032	−	1.14224i
$736$	28.4485	+	20.6690i	1.04863	+	0.761871i
$737$	21.1635	−	2.22437i	0.779566	−	0.0819357i
$738$	11.5809	−	26.0111i	0.426299	−	0.957483i
$739$	2.60085	−	24.7454i	0.0956737	−	0.910274i	−0.836428	−	0.548077i	$-0.815360\pi$
$739$	2.60085	−	24.7454i	0.0956737	−	0.910274i	0.932102	−	0.362197i	$-0.117973\pi$
$740$	7.85862	−	31.8138i	0.288889	−	1.16950i
$741$	−39.0176	+	28.3480i	−1.43335	+	1.04139i
$742$	23.0959	−	32.1892i	0.847877	−	1.18170i
$743$		−	37.2111i		−	1.36514i	−0.730819	−	0.682572i	$-0.760862\pi$
$743$		−	37.2111i		−	1.36514i	0.730819	−	0.682572i	$-0.239138\pi$
$744$	4.03944	+	4.48625i	0.148093	+	0.164474i
$745$	1.13280	−	8.18947i	0.0415026	−	0.300039i
$746$	16.9745	−	18.8520i	0.621479	−	0.690222i
$747$	2.93539	−	13.8099i	0.107400	−	0.505279i
$748$	−8.11259	+	11.1660i	−0.296626	+	0.408270i
$749$	16.1688	+	17.7442i	0.590796	+	0.648358i
$750$	−39.2336	−	34.8653i	−1.43261	−	1.27310i
$751$	−2.82557	+	4.89402i	−0.103106	+	0.178585i	−0.912963	−	0.408042i	$-0.866212\pi$
$751$	−2.82557	+	4.89402i	−0.103106	+	0.178585i	0.809857	+	0.586628i	$0.199545\pi$
$752$	−9.46504	−	0.994816i	−0.345154	−	0.0362772i
$753$	−4.73788	−	4.26601i	−0.172658	−	0.155462i
$754$	−19.2299	−	4.08745i	−0.700313	−	0.148856i
$755$	3.89582	+	3.03013i	0.141783	+	0.110278i
$756$	0.219558	−	2.21548i	0.00798523	−	0.0805761i
$757$			38.6504i			1.40477i	0.711796	+	0.702386i	$0.247882\pi$
$757$			38.6504i			1.40477i	−0.711796	+	0.702386i	$0.752118\pi$
$758$	−10.6001	+	9.54440i	−0.385014	+	0.346668i
$759$	−24.9087	−	11.0901i	−0.904130	−	0.402545i
$760$	3.27846	+	3.15223i	0.118922	+	0.114343i
$761$	−1.22835	+	0.546899i	−0.0445278	+	0.0198251i	−0.428880	−	0.903362i	$-0.641092\pi$
$761$	−1.22835	+	0.546899i	−0.0445278	+	0.0198251i	0.384352	+	0.923187i	$0.374425\pi$
$762$	−26.8806	−	36.9979i	−0.973780	−	1.34029i
$763$	7.51438	+	6.68558i	0.272039	+	0.242034i
$764$	31.1483	+	22.6306i	1.12691	+	0.818745i
$765$	14.8512	−	12.5168i	0.536948	−	0.452546i
$766$	12.2639	+	5.46026i	0.443114	+	0.197287i
$767$	8.98167	+	42.2554i	0.324309	+

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)

\(f(q)\)	\(=\)	\(q+(0.792476 + 1.77993i) q^{2} +(-1.79059 - 1.61225i) q^{3} +(-1.20187 + 1.33481i) q^{4} +(2.07142 - 0.842152i) q^{5} +(1.45070 - 4.46479i) q^{6} +(2.52107 + 0.802620i) q^{7} +(0.377701 + 0.122722i) q^{8} +(0.293262 + 2.79020i) q^{9} +O(q^{10})\)	\(q+(0.792476 + 1.77993i) q^{2} +(-1.79059 - 1.61225i) q^{3} +(-1.20187 + 1.33481i) q^{4} +(2.07142 - 0.842152i) q^{5} +(1.45070 - 4.46479i) q^{6} +(2.52107 + 0.802620i) q^{7} +(0.377701 + 0.122722i) q^{8} +(0.293262 + 2.79020i) q^{9} +(3.14052 + 3.01960i) q^{10} +(-0.259436 + 2.46837i) q^{11} +(4.30412 - 0.452381i) q^{12} +(-2.29720 - 3.16183i) q^{13} +(0.569281 + 5.12339i) q^{14} +(-5.06682 - 1.83170i) q^{15} +(0.456383 + 4.34220i) q^{16} +(-0.643690 - 3.02832i) q^{17} +(-4.73395 + 2.73315i) q^{18} +(3.42697 + 3.80604i) q^{19} +(-1.36546 + 3.77712i) q^{20} +(-3.22017 - 5.50177i) q^{21} +(-4.59912 + 1.49435i) q^{22} +(-1.85446 - 4.16518i) q^{23} +(-0.478447 - 0.828694i) q^{24} +(3.58156 - 3.48890i) q^{25} +(3.80736 - 6.59454i) q^{26} +(-0.275367 + 0.379010i) q^{27} +(-4.10135 + 2.40052i) q^{28} +(-0.797815 - 2.45542i) q^{29} +(-0.755029 - 10.4702i) q^{30} +(-6.17093 + 1.31167i) q^{31} +(-6.67927 + 3.85628i) q^{32} +(4.44418 - 4.00156i) q^{33} +(4.88009 - 3.54559i) q^{34} +(5.89813 - 0.460563i) q^{35} +(-4.07686 - 2.96201i) q^{36} +(-8.11444 + 0.852862i) q^{37} +(-4.05869 + 9.11597i) q^{38} +(-0.984323 + 9.36521i) q^{39} +(0.885727 - 0.0638719i) q^{40} +(-4.21399 + 3.06164i) q^{41} +(7.24085 - 10.0917i) q^{42} +5.80714i q^{43} +(-2.98301 - 3.31296i) q^{44} +(2.95724 + 5.53270i) q^{45} +(5.94411 - 6.60161i) q^{46} +(-0.453202 + 2.13215i) q^{47} +(6.18352 - 8.51089i) q^{48} +(5.71160 + 4.04692i) q^{49} +(9.04830 + 3.61005i) q^{50} +(-3.72984 + 6.46027i) q^{51} +(6.98140 + 0.733775i) q^{52} +(-5.71138 - 5.14255i) q^{53} +(-0.892832 - 0.189777i) q^{54} +(1.54134 + 5.33152i) q^{55} +(0.853711 + 0.612542i) q^{56} -12.3402i q^{57} +(3.73823 - 3.36592i) q^{58} +(-10.0978 - 4.49584i) q^{59} +(8.53466 - 4.56179i) q^{60} +(7.90679 - 3.52033i) q^{61} +(-7.22500 - 9.94436i) q^{62} +(-1.50013 + 7.26967i) q^{63} +(-5.09255 - 3.69995i) q^{64} +(-7.42122 - 4.61488i) q^{65} +(10.6444 + 4.73919i) q^{66} +(-1.78260 - 8.38650i) q^{67} +(4.81588 + 2.78045i) q^{68} +(-3.39475 + 10.4480i) q^{69} +(5.49389 + 10.1333i) q^{70} +(4.36571 + 13.4363i) q^{71} +(-0.231655 + 1.08985i) q^{72} +(12.2347 + 1.28592i) q^{73} +(-7.94853 - 13.7673i) q^{74} +(-12.0381 + 0.472808i) q^{75} -9.19914 q^{76} +(-2.63522 + 6.01471i) q^{77} +(-17.4495 + 5.66968i) q^{78} +(6.11718 + 1.30025i) q^{79} +(4.60215 + 8.61017i) q^{80} +(9.33690 - 1.98462i) q^{81} +(-8.78899 - 5.07433i) q^{82} +(-4.78601 - 1.55507i) q^{83} +(11.2141 + 2.31409i) q^{84} +(-3.88366 - 5.73084i) q^{85} +(-10.3363 + 4.60202i) q^{86} +(-2.53020 + 5.68293i) q^{87} +(-0.400913 + 0.900466i) q^{88} +(-12.6922 + 5.65094i) q^{89} +(-7.50428 + 9.64821i) q^{90} +(-3.25367 - 9.81498i) q^{91} +(7.78856 + 2.53066i) q^{92} +(13.1644 + 7.60044i) q^{93} +(-4.15423 + 0.883008i) q^{94} +(10.3040 + 4.99787i) q^{95} +(18.1771 + 3.86367i) q^{96} +(4.30851 - 1.39992i) q^{97} +(-2.67694 + 13.3733i) q^{98} -6.96332 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

Related objects

Downloads

Learn more