LMFDB - Embedded newform 650.2.m.c.101.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [650,2,Mod(101,650)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(650, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("650.101"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 650 = 2 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	650.m (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,2,4,0,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$5.19027613138$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.3
Root			$0.665665 - 1.24775i$ of defining polynomial
Character	$\chi$	$=$	650.101
Dual form			650.2.m.c.251.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(-0.913419 - 1.58209i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.58209 - 0.913419i) q^{6} +(-3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(-0.168669 + 0.292144i) q^{9} +(-4.24026 + 2.44811i) q^{11} -1.82684 q^{12} +(2.87423 - 2.17688i) q^{13} -3.99102 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31414 + 5.74026i) q^{17} +0.337339i q^{18} +(1.81414 + 1.04739i) q^{19} +7.29094i q^{21} +(-2.44811 + 4.24026i) q^{22} +(0.495508 + 0.858244i) q^{23} +(-1.58209 + 0.913419i) q^{24} +(1.40072 - 3.32235i) q^{26} -4.86425 q^{27} +(-3.45632 + 1.99551i) q^{28} +(-2.92163 - 5.06040i) q^{29} -10.8179i q^{31} +(-0.866025 - 0.500000i) q^{32} +(7.74627 + 4.47231i) q^{33} +6.62828i q^{34} +(0.168669 + 0.292144i) q^{36} +(2.85782 - 1.64996i) q^{37} +2.09479 q^{38} +(-6.06939 - 2.55889i) q^{39} +(-4.48652 + 2.59030i) q^{41} +(3.64547 + 6.31414i) q^{42} +(-0.567874 + 0.983586i) q^{43} +4.89623i q^{44} +(0.858244 + 0.495508i) q^{46} -1.61186i q^{47} +(-0.913419 + 1.58209i) q^{48} +(4.46410 + 7.73205i) q^{49} +12.1088 q^{51} +(-0.448114 - 3.57760i) q^{52} +0.549905 q^{53} +(-4.21257 + 2.43213i) q^{54} +(-1.99551 + 3.45632i) q^{56} -3.82684i q^{57} +(-5.06040 - 2.92163i) q^{58} +(-3.00000 - 1.73205i) q^{59} +(0.685861 - 1.18795i) q^{61} +(-5.40893 - 9.36854i) q^{62} +(1.16595 - 0.673162i) q^{63} -1.00000 q^{64} +8.94462 q^{66} +(-3.13575 + 1.81042i) q^{67} +(3.31414 + 5.74026i) q^{68} +(0.905212 - 1.56787i) q^{69} +(-5.19615 - 3.00000i) q^{71} +(0.292144 + 0.168669i) q^{72} -8.94462i q^{73} +(1.64996 - 2.85782i) q^{74} +(1.81414 - 1.04739i) q^{76} +19.5409 q^{77} +(-6.53569 + 0.818632i) q^{78} +2.55231 q^{79} +(4.94911 + 8.57211i) q^{81} +(-2.59030 + 4.48652i) q^{82} -16.4207i q^{83} +(6.31414 + 3.64547i) q^{84} +1.13575i q^{86} +(-5.33734 + 9.24454i) q^{87} +(2.44811 + 4.24026i) q^{88} +(2.98652 - 1.72427i) q^{89} +(-14.2782 + 1.78843i) q^{91} +0.991015 q^{92} +(-17.1148 + 9.88124i) q^{93} +(-0.805932 - 1.39592i) q^{94} +1.82684i q^{96} +(10.0910 + 5.82606i) q^{97} +(7.73205 + 4.46410i) q^{98} -1.65169i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} - 6 q^{11} + 4 q^{12} + 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 40 q^{27} + 42 q^{33} + 4 q^{36} + 30 q^{37} + 12 q^{38}+ \cdots + 48 q^{98}+O(q^{100}) $ 8 * q + 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 - 6 * q^11 + 4 * q^12 + 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 - 6 * q^22 - 12 * q^23 - 6 * q^24 - 40 * q^27 + 42 * q^33 + 4 * q^36 + 30 * q^37 + 12 * q^38 - 40 * q^39 + 12 * q^41 + 6 * q^42 - 4 * q^43 + 2 * q^48 + 8 * q^49 + 10 * q^52 - 60 * q^53 + 36 * q^54 - 24 * q^59 + 26 * q^61 - 18 * q^62 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 24 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^72 + 6 * q^74 - 6 * q^76 + 60 * q^77 + 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 48 * q^87 + 6 * q^88 - 24 * q^89 - 66 * q^91 - 24 * q^92 - 48 * q^93 + 6 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/650\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.913419	−	1.58209i	−0.527363	−	0.913419i	−0.999491	−	0.0318895i	$-0.989848\pi$
$3$	−0.913419	−	1.58209i	−0.527363	−	0.913419i	0.472129	−	0.881530i	$-0.343486\pi$
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−1.58209	−	0.913419i	−0.645885	−	0.372902i
$7$	−3.45632	−	1.99551i	−1.30637	−	0.754231i	−0.324879	−	0.945756i	$-0.605323\pi$
$7$	−3.45632	−	1.99551i	−1.30637	−	0.754231i	−0.981488	+	0.191525i	$0.938657\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.168669	+	0.292144i	−0.0562231	+	0.0973812i
$10$		0			0
$11$	−4.24026	+	2.44811i	−1.27849	+	0.738134i	−0.976570	−	0.215200i	$-0.930960\pi$
$11$	−4.24026	+	2.44811i	−1.27849	+	0.738134i	−0.301916	+	0.953335i	$0.597626\pi$
$12$	−1.82684			−0.527363
$13$	2.87423	−	2.17688i	0.797169	−	0.603757i
$13$	2.87423	−	2.17688i	0.797169	−	0.603757i
$14$	−3.99102			−1.06664
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−3.31414	+	5.74026i	−0.803797	+	1.39222i	0.113303	+	0.993560i	$0.463857\pi$
$17$	−3.31414	+	5.74026i	−0.803797	+	1.39222i	−0.917100	+	0.398657i	$0.869477\pi$
$18$			0.337339i			0.0795115i
$19$	1.81414	+	1.04739i	0.416192	+	0.240289i	0.693447	−	0.720508i	$-0.256091\pi$
$19$	1.81414	+	1.04739i	0.416192	+	0.240289i	−0.277255	+	0.960796i	$0.589425\pi$
$20$		0			0
$21$			7.29094i			1.59101i
$22$	−2.44811	+	4.24026i	−0.521940	+	0.904026i
$23$	0.495508	+	0.858244i	0.103320	+	0.178956i	0.913051	−	0.407846i	$-0.133720\pi$
$23$	0.495508	+	0.858244i	0.103320	+	0.178956i	−0.809730	+	0.586802i	$0.800387\pi$
$24$	−1.58209	+	0.913419i	−0.322942	+	0.186451i
$25$		0			0
$26$	1.40072	−	3.32235i	0.274704	−	0.651566i
$27$	−4.86425			−0.936126
$28$	−3.45632	+	1.99551i	−0.653183	+	0.377115i
$29$	−2.92163	−	5.06040i	−0.542532	−	0.939694i	−0.998758	−	0.0498293i	$-0.984132\pi$
$29$	−2.92163	−	5.06040i	−0.542532	−	0.939694i	0.456225	−	0.889864i	$-0.349201\pi$
$30$		0			0
$31$		−	10.8179i		−	1.94294i	−0.237155	−	0.971472i	$-0.576215\pi$
$31$		−	10.8179i		−	1.94294i	0.237155	−	0.971472i	$-0.423785\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	7.74627	+	4.47231i	1.34845	+	0.778529i
$34$			6.62828i			1.13674i
$35$		0			0
$36$	0.168669	+	0.292144i	0.0281115	+	0.0486906i
$37$	2.85782	−	1.64996i	0.469822	−	0.271252i	−0.246343	−	0.969183i	$-0.579229\pi$
$37$	2.85782	−	1.64996i	0.469822	−	0.271252i	0.716165	+	0.697931i	$0.245896\pi$
$38$	2.09479			0.339819
$39$	−6.06939	−	2.55889i	−0.971880	−	0.409750i
$40$		0			0
$41$	−4.48652	+	2.59030i	−0.700677	+	0.404536i	−0.807600	−	0.589731i	$-0.799234\pi$
$41$	−4.48652	+	2.59030i	−0.700677	+	0.404536i	0.106922	+	0.994267i	$0.465900\pi$
$42$	3.64547	+	6.31414i	0.562508	+	0.974293i
$43$	−0.567874	+	0.983586i	−0.0866000	+	0.149996i	−0.906072	−	0.423124i	$-0.860934\pi$
$43$	−0.567874	+	0.983586i	−0.0866000	+	0.149996i	0.819472	+	0.573119i	$0.194267\pi$
$44$			4.89623i			0.738134i
$45$		0			0
$46$	0.858244	+	0.495508i	0.126541	+	0.0730586i
$47$		−	1.61186i		−	0.235115i	−0.993066	−	0.117557i	$-0.962494\pi$
$47$		−	1.61186i		−	0.235115i	0.993066	−	0.117557i	$-0.0375064\pi$
$48$	−0.913419	+	1.58209i	−0.131841	+	0.228355i
$49$	4.46410	+	7.73205i	0.637729	+	1.10458i
$50$		0			0
$51$	12.1088			1.69557
$52$	−0.448114	−	3.57760i	−0.0621422	−	0.496123i
$53$	0.549905			0.0755352			0.0377676	−	0.999287i	$-0.487975\pi$
$53$	0.549905			0.0755352			0.0377676	+	0.999287i	$0.487975\pi$
$54$	−4.21257	+	2.43213i	−0.573258	+	0.330970i
$55$		0			0
$56$	−1.99551	+	3.45632i	−0.266661	+	0.461870i
$57$		−	3.82684i		−	0.506877i
$58$	−5.06040	−	2.92163i	−0.664464	−	0.383628i
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	0.291839	−	0.956467i	$-0.405733\pi$
$59$	−3.00000	−	1.73205i	−0.390567	−	0.225494i	−0.682406	+	0.730974i	$0.739066\pi$
$60$		0			0
$61$	0.685861	−	1.18795i	0.0878155	−	0.152101i	−0.818772	−	0.574119i	$-0.805345\pi$
$61$	0.685861	−	1.18795i	0.0878155	−	0.152101i	0.906587	+	0.422018i	$0.138678\pi$
$62$	−5.40893	−	9.36854i	−0.686934	−	1.18981i
$63$	1.16595	−	0.673162i	0.146896	−	0.0848104i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	8.94462			1.10101
$67$	−3.13575	+	1.81042i	−0.383093	+	0.221179i	−0.679163	−	0.733988i	$-0.737657\pi$
$67$	−3.13575	+	1.81042i	−0.383093	+	0.221179i	0.296070	+	0.955166i	$0.404324\pi$
$68$	3.31414	+	5.74026i	0.401898	+	0.696108i
$69$	0.905212	−	1.56787i	0.108975	−	0.188750i
$70$		0			0
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	0.158901	−	0.987294i	$-0.449205\pi$
$71$	−5.19615	−	3.00000i	−0.616670	−	0.356034i	−0.775571	+	0.631260i	$0.782538\pi$
$72$	0.292144	+	0.168669i	0.0344295	+	0.0198779i
$73$		−	8.94462i		−	1.04689i	−0.852060	−	0.523444i	$-0.824647\pi$
$73$		−	8.94462i		−	1.04689i	0.852060	−	0.523444i	$-0.175353\pi$
$74$	1.64996	−	2.85782i	0.191804	−	0.332215i
$75$		0			0
$76$	1.81414	−	1.04739i	0.208096	−	0.120144i
$77$	19.5409			2.22689
$78$	−6.53569	+	0.818632i	−0.740021	+	0.0926918i
$79$	2.55231			0.287158			0.143579	−	0.989639i	$-0.454139\pi$
$79$	2.55231			0.287158			0.143579	+	0.989639i	$0.454139\pi$
$80$		0			0
$81$	4.94911	+	8.57211i	0.549901	+	0.952456i
$82$	−2.59030	+	4.48652i	−0.286050	+	0.495454i
$83$		−	16.4207i		−	1.80241i	−0.433393	−	0.901205i	$-0.642684\pi$
$83$		−	16.4207i		−	1.80241i	0.433393	−	0.901205i	$-0.357316\pi$
$84$	6.31414	+	3.64547i	0.688929	+	0.397753i
$85$		0			0
$86$			1.13575i			0.122471i
$87$	−5.33734	+	9.24454i	−0.572223	+	0.991119i
$88$	2.44811	+	4.24026i	0.260970	+	0.452013i
$89$	2.98652	−	1.72427i	0.316571	−	0.182772i	−0.333292	−	0.942824i	$-0.608160\pi$
$89$	2.98652	−	1.72427i	0.316571	−	0.182772i	0.649863	+	0.760051i	$0.274826\pi$
$90$		0			0
$91$	−14.2782	+	1.78843i	−1.49677	+	0.187478i
$92$	0.991015			0.103320
$93$	−17.1148	+	9.88124i	−1.77472	+	1.02464i
$94$	−0.805932	−	1.39592i	−0.0831256	−	0.143978i
$95$		0			0
$96$			1.82684i			0.186451i
$97$	10.0910	+	5.82606i	1.02459	+	0.591547i	0.915430	−	0.402477i	$-0.131851\pi$
$97$	10.0910	+	5.82606i	1.02459	+	0.591547i	0.109159	+	0.994024i	$0.465184\pi$
$98$	7.73205	+	4.46410i	0.781055	+	0.450942i
$99$		−	1.65169i		−	0.166001i
$100$		0			0
$101$	1.03961	+	1.80066i	0.103445	+	0.179173i	0.913102	−	0.407731i	$-0.133680\pi$
$101$	1.03961	+	1.80066i	0.103445	+	0.179173i	−0.809657	+	0.586904i	$0.800347\pi$
$102$	10.4865	−	6.05440i	1.03832	−	0.599475i
$103$	2.26795			0.223468			0.111734	−	0.993738i	$-0.464360\pi$
$103$	2.26795			0.223468			0.111734	+	0.993738i	$0.464360\pi$
$104$	−2.17688	−	2.87423i	−0.213460	−	0.281842i
$105$		0			0
$106$	0.476231	−	0.274952i	0.0462557	−	0.0267057i
$107$	−1.25076	−	2.16638i	−0.120915	−	0.209431i	0.799214	−	0.601047i	$-0.205250\pi$
$107$	−1.25076	−	2.16638i	−0.120915	−	0.209431i	−0.920129	+	0.391616i	$0.871916\pi$
$108$	−2.43213	+	4.21257i	−0.234031	+	0.405354i
$109$		−	15.6357i		−	1.49763i	−0.662780	−	0.748815i	$-0.730623\pi$
$109$		−	15.6357i		−	1.49763i	0.662780	−	0.748815i	$-0.269377\pi$
$110$		0			0
$111$	−5.22077	−	3.01421i	−0.495534	−	0.286097i
$112$			3.99102i			0.377115i
$113$	8.55889	−	14.8244i	0.805153	−	1.39457i	−0.111035	−	0.993816i	$-0.535417\pi$
$113$	8.55889	−	14.8244i	0.805153	−	1.39457i	0.916188	−	0.400749i	$-0.131250\pi$
$114$	−1.91342	−	3.31414i	−0.179208	−	0.310398i
$115$		0			0
$116$	−5.84325			−0.542532
$117$	0.151166	+	1.20686i	0.0139753	+	0.111574i
$118$	−3.46410			−0.318896
$119$	22.9095	−	13.2268i	2.10011	−	1.21250i
$120$		0			0
$121$	6.48652	−	11.2350i	0.589684	−	1.02136i
$122$		−	1.37172i		−	0.124190i
$123$	8.19615	+	4.73205i	0.739022	+	0.426675i
$124$	−9.36854	−	5.40893i	−0.841319	−	0.485736i
$125$		0			0
$126$	0.673162	−	1.16595i	0.0599700	−	0.103871i
$127$	−4.06218	−	7.03590i	−0.360460	−	0.624335i	0.627577	−	0.778555i	$-0.284047\pi$
$127$	−4.06218	−	7.03590i	−0.360460	−	0.624335i	−0.988037	+	0.154220i	$0.950714\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.07483			0.182678
$130$		0			0
$131$	14.1773			1.23868			0.619340	−	0.785123i	$-0.287400\pi$
$131$	14.1773			1.23868			0.619340	+	0.785123i	$0.287400\pi$
$132$	7.74627	−	4.47231i	0.674226	−	0.389264i
$133$	−4.18016	−	7.24026i	−0.362466	−	0.627810i
$134$	−1.81042	+	3.13575i	−0.156397	+	0.270887i
$135$		0			0
$136$	5.74026	+	3.31414i	0.492223	+	0.284185i
$137$	−12.1386	−	7.00821i	−1.03707	−	0.598752i	−0.118067	−	0.993006i	$-0.537670\pi$
$137$	−12.1386	−	7.00821i	−1.03707	−	0.598752i	−0.919001	+	0.394254i	$0.871003\pi$
$138$		−	1.81042i		−	0.154114i
$139$	−7.99473	+	13.8473i	−0.678104	+	1.17451i	0.297447	+	0.954738i	$0.403865\pi$
$139$	−7.99473	+	13.8473i	−0.678104	+	1.17451i	−0.975551	+	0.219772i	$0.929469\pi$
$140$		0			0
$141$	−2.55011	+	1.47231i	−0.214758	+	0.123991i
$142$	−6.00000			−0.503509
$143$	−6.85824	+	16.2670i	−0.573515	+	1.36031i
$144$	0.337339			0.0281115
$145$		0			0
$146$	−4.47231	−	7.74627i	−0.370131	−	0.641085i
$147$	8.15519	−	14.1252i	0.672629	−	1.16503i
$148$		−	3.29992i		−	0.271252i
$149$	6.49253	+	3.74846i	0.531889	+	0.307086i	0.741785	−	0.670637i	$-0.233979\pi$
$149$	6.49253	+	3.74846i	0.531889	+	0.307086i	−0.209896	+	0.977724i	$0.567313\pi$
$150$		0			0
$151$			4.24913i			0.345789i	0.984940	+	0.172895i	$0.0553120\pi$
$151$			4.24913i			0.345789i	−0.984940	+	0.172895i	$0.944688\pi$
$152$	1.04739	−	1.81414i	0.0849549	−	0.147146i
$153$	−1.11799	−	1.93641i	−0.0903839	−	0.156549i
$154$	16.9229	−	9.77046i	1.36369	−	0.787326i
$155$		0			0
$156$	−5.25076	+	3.97680i	−0.420397	+	0.318399i
$157$	22.7526			1.81586			0.907929	−	0.419124i	$-0.137663\pi$
$157$	22.7526			1.81586			0.907929	+	0.419124i	$0.137663\pi$
$158$	2.21037	−	1.27616i	0.175847	−	0.101526i
$159$	−0.502293	−	0.869998i	−0.0398345	−	0.0689953i
$160$		0			0
$161$		−	3.95516i		−	0.311710i
$162$	8.57211	+	4.94911i	0.673488	+	0.388839i
$163$	−4.51630	−	2.60749i	−0.353744	−	0.204234i	0.312589	−	0.949888i	$-0.398804\pi$
$163$	−4.51630	−	2.60749i	−0.353744	−	0.204234i	−0.666333	+	0.745654i	$0.732137\pi$
$164$			5.18059i			0.404536i
$165$		0			0
$166$	−8.21037	−	14.2208i	−0.637248	−	1.10375i
$167$	5.80624	−	3.35224i	0.449301	−	0.259404i	−0.258234	−	0.966082i	$-0.583141\pi$
$167$	5.80624	−	3.35224i	0.449301	−	0.259404i	0.707535	+	0.706679i	$0.249807\pi$
$168$	7.29094			0.562508
$169$	3.52242	−	12.5137i	0.270955	−	0.962592i
$170$		0			0
$171$	−0.611979	+	0.353326i	−0.0467992	+	0.0270195i
$172$	0.567874	+	0.983586i	0.0433000	+	0.0749978i
$173$	−9.77046	+	16.9229i	−0.742834	+	1.28663i	0.208365	+	0.978051i	$0.433186\pi$
$173$	−9.77046	+	16.9229i	−0.742834	+	1.28663i	−0.951200	+	0.308576i	$0.900148\pi$
$174$			10.6747i			0.809245i
$175$		0			0
$176$	4.24026	+	2.44811i	0.319621	+	0.184534i
$177$			6.32835i			0.475668i
$178$	1.72427	−	2.98652i	0.129239	−	0.223849i
$179$	4.48950	+	7.77604i	0.335561	+	0.581209i	0.983592	−	0.180405i	$-0.0577408\pi$
$179$	4.48950	+	7.77604i	0.335561	+	0.581209i	−0.648031	+	0.761614i	$0.724407\pi$
$180$		0			0
$181$	−5.55648			−0.413010			−0.206505	−	0.978446i	$-0.566209\pi$
$181$	−5.55648			−0.413010			−0.206505	+	0.978446i	$0.566209\pi$
$182$	−11.4711	+	8.68795i	−0.850295	+	0.643993i
$183$	−2.50591			−0.185242
$184$	0.858244	−	0.495508i	0.0632706	−	0.0365293i
$185$		0			0
$186$	−9.88124	+	17.1148i	−0.724527	+	1.25492i
$187$		−	32.4536i		−	2.37324i
$188$	−1.39592	−	0.805932i	−0.101808	−	0.0587787i
$189$	16.8124	+	9.70665i	1.22292	+	0.706055i
$190$		0			0
$191$	−5.09316	+	8.82161i	−0.368528	+	0.638309i	−0.989336	−	0.145654i	$-0.953471\pi$
$191$	−5.09316	+	8.82161i	−0.368528	+	0.638309i	0.620808	+	0.783963i	$0.286805\pi$
$192$	0.913419	+	1.58209i	0.0659204	+	0.114177i
$193$	−7.04839	+	4.06939i	−0.507354	+	0.292921i	−0.731745	−	0.681578i	$-0.761294\pi$
$193$	−7.04839	+	4.06939i	−0.507354	+	0.292921i	0.224391	+	0.974499i	$0.427961\pi$
$194$	11.6521			0.836574
$195$		0			0
$196$	8.92820			0.637729
$197$	−12.5405	+	7.24026i	−0.893473	+	0.515847i	−0.875077	−	0.483984i	$-0.839189\pi$
$197$	−12.5405	+	7.24026i	−0.893473	+	0.515847i	−0.0183962	+	0.999831i	$0.505856\pi$
$198$	−0.825843	−	1.43040i	−0.0586901	−	0.101654i
$199$	−5.62828	+	9.74846i	−0.398978	+	0.691050i	−0.993600	−	0.112955i	$-0.963968\pi$
$199$	−5.62828	+	9.74846i	−0.398978	+	0.691050i	0.594622	+	0.804005i	$0.297302\pi$
$200$		0			0
$201$	5.72850	+	3.30735i	0.404058	+	0.233283i
$202$	1.80066	+	1.03961i	0.126694	+	0.0731469i
$203$			23.3205i			1.63678i
$204$	6.05440	−	10.4865i	0.423893	−	0.734203i
$205$		0			0
$206$	1.96410	−	1.13397i	0.136845	−	0.0790078i
$207$	−0.334308			−0.0232360
$208$	−3.32235	−	1.40072i	−0.230363	−	0.0971225i
$209$	−10.2566			−0.709461
$210$		0			0
$211$	−4.79257	−	8.30097i	−0.329934	−	0.571463i	0.652564	−	0.757733i	$-0.273693\pi$
$211$	−4.79257	−	8.30097i	−0.329934	−	0.571463i	−0.982498	+	0.186271i	$0.940360\pi$
$212$	0.274952	−	0.476231i	0.0188838	−	0.0327077i
$213$			10.9610i			0.751037i
$214$	−2.16638	−	1.25076i	−0.148090	−	0.0855000i
$215$		0			0
$216$			4.86425i			0.330970i
$217$	−21.5871	+	37.3900i	−1.46543	+	2.53820i
$218$	−7.81785	−	13.5409i	−0.529492	−	0.917107i
$219$	−14.1512	+	8.17018i	−0.956248	+	0.552090i
$220$		0			0
$221$	2.97022	+	23.7133i	0.199799	+	1.59513i
$222$	−6.02843			−0.404602
$223$	23.5660	−	13.6058i	1.57809	−	0.911113i	0.582968	−	0.812495i	$-0.301891\pi$
$223$	23.5660	−	13.6058i	1.57809	−	0.911113i	0.995125	−	0.0986181i	$-0.0314422\pi$
$224$	1.99551	+	3.45632i	0.133330	+	0.230935i
$225$		0			0
$226$		−	17.1178i		−	1.13866i
$227$	−5.48052	−	3.16418i	−0.363755	−	0.210014i	0.306972	−	0.951719i	$-0.400684\pi$
$227$	−5.48052	−	3.16418i	−0.363755	−	0.210014i	−0.670726	+	0.741705i	$0.734018\pi$
$228$	−3.31414	−	1.91342i	−0.219484	−	0.126719i
$229$			2.50152i			0.165305i	0.996578	+	0.0826524i	$0.0263391\pi$
$229$			2.50152i			0.165305i	−0.996578	+	0.0826524i	$0.973661\pi$
$230$		0			0
$231$	−17.8491	−	30.9155i	−1.17438	−	2.03409i
$232$	−5.06040	+	2.92163i	−0.332232	+	0.191814i
$233$	−9.17903			−0.601339			−0.300669	−	0.953728i	$-0.597210\pi$
$233$	−9.17903			−0.601339			−0.300669	+	0.953728i	$0.597210\pi$
$234$	0.734344	+	0.969589i	0.0480056	+	0.0633840i
$235$		0			0
$236$	−3.00000	+	1.73205i	−0.195283	+	0.112747i
$237$	−2.33133	−	4.03798i	−0.151436	−	0.262295i
$238$	13.2268	−	22.9095i	0.857365	−	1.48500i
$239$			6.54030i			0.423057i	0.977372	+	0.211528i	$0.0678441\pi$
$239$			6.54030i			0.423057i	−0.977372	+	0.211528i	$0.932156\pi$
$240$		0			0
$241$	7.86571	+	4.54127i	0.506675	+	0.292529i	0.731466	−	0.681878i	$-0.238837\pi$
$241$	7.86571	+	4.54127i	0.506675	+	0.292529i	−0.224791	+	0.974407i	$0.572170\pi$
$242$		−	12.9730i		−	0.833939i
$243$	1.74484	−	3.02216i	0.111932	−	0.193872i
$244$	−0.685861	−	1.18795i	−0.0439077	−	0.0760504i
$245$		0			0
$246$	9.46410			0.603409
$247$	7.49430	−	0.938703i	0.476851	−	0.0597283i
$248$	−10.8179			−0.686934
$249$	−25.9791	+	14.9990i	−1.64636	+	0.950524i
$250$		0			0
$251$	−4.81414	+	8.33833i	−0.303866	+	0.526311i	−0.977008	−	0.213202i	$-0.931611\pi$
$251$	−4.81414	+	8.33833i	−0.303866	+	0.526311i	0.673142	+	0.739513i	$0.264944\pi$
$252$		−	1.34632i		−	0.0848104i
$253$	−4.20216	−	2.42612i	−0.264188	−	0.152529i
$254$	−7.03590	−	4.06218i	−0.441472	−	0.254884i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.41113	+	12.8364i	0.462293	+	0.800716i	0.999075	−	0.0430058i	$-0.0136934\pi$
$257$	7.41113	+	12.8364i	0.462293	+	0.800716i	−0.536781	+	0.843721i	$0.680360\pi$
$258$	1.79685	−	1.03741i	0.111867	−	0.0645866i
$259$	−13.1700			−0.818347
$260$		0			0
$261$	1.97115			0.122011
$262$	12.2779	−	7.08867i	0.758533	−	0.437939i
$263$	5.51673	+	9.55525i	0.340176	+	0.589202i	0.984465	−	0.175580i	$-0.0561801\pi$
$263$	5.51673	+	9.55525i	0.340176	+	0.589202i	−0.644289	+	0.764782i	$0.722847\pi$
$264$	4.47231	−	7.74627i	0.275252	−	0.476750i
$265$		0			0
$266$	−7.24026	−	4.18016i	−0.443929	−	0.256302i
$267$	−5.45589	−	3.14996i	−0.333895	−	0.192775i
$268$			3.62085i			0.221179i
$269$	1.30515	−	2.26059i	0.0795767	−	0.137831i	−0.823491	−	0.567330i	$-0.807976\pi$
$269$	1.30515	−	2.26059i	0.0795767	−	0.137831i	0.903067	+	0.429499i	$0.141310\pi$
$270$		0			0
$271$	24.8459	−	14.3448i	1.50928	−	0.871383i	0.509337	−	0.860567i	$-0.329891\pi$
$271$	24.8459	−	14.3448i	1.50928	−	0.871383i	0.999942	−	0.0108156i	$-0.00344279\pi$
$272$	6.62828			0.401898
$273$	15.8715	+	20.9559i	0.960585	+	1.26831i
$274$	−14.0164			−0.846763
$275$		0			0
$276$	−0.905212	−	1.56787i	−0.0544874	−	0.0943749i
$277$	−2.35035	+	4.07092i	−0.141219	+	0.244598i	−0.927956	−	0.372690i	$-0.878435\pi$
$277$	−2.35035	+	4.07092i	−0.141219	+	0.244598i	0.786737	+	0.617288i	$0.211769\pi$
$278$			15.9895i			0.958984i
$279$	3.16037	+	1.82464i	0.189206	+	0.109238i
$280$		0			0
$281$			3.32418i			0.198304i	0.995072	+	0.0991521i	$0.0316130\pi$
$281$			3.32418i			0.198304i	−0.995072	+	0.0991521i	$0.968387\pi$
$282$	−1.47231	+	2.55011i	−0.0876747	+	0.151857i
$283$	−12.9886	−	22.4969i	−0.772093	−	1.33730i	−0.936414	−	0.350897i	$-0.885877\pi$
$283$	−12.9886	−	22.4969i	−0.772093	−	1.33730i	0.164322	−	0.986407i	$-0.447457\pi$
$284$	−5.19615	+	3.00000i	−0.308335	+	0.178017i
$285$		0			0
$286$	2.19407	+	17.5167i	0.129738	+	1.03579i
$287$	20.6758			1.22045
$288$	0.292144	−	0.168669i	0.0172147	−	0.00993893i
$289$	−13.4670	−	23.3256i	−0.792179	−	1.37209i
$290$		0			0
$291$		−	21.2865i		−	1.24784i
$292$	−7.74627	−	4.47231i	−0.453316	−	0.261722i
$293$	−0.824857	−	0.476231i	−0.0481886	−	0.0278217i	0.475712	−	0.879601i	$-0.342190\pi$
$293$	−0.824857	−	0.476231i	−0.0481886	−	0.0278217i	−0.523901	+	0.851779i	$0.675524\pi$
$294$		−	16.3104i		−	0.951241i
$295$		0			0
$296$	−1.64996	−	2.85782i	−0.0959021	−	0.166107i
$297$	20.6257	−	11.9082i	1.19682	−	0.690986i
$298$	7.49693			0.434285
$299$	3.29250	+	1.38814i	0.190410	+	0.0802779i
$300$		0			0
$301$	3.92551	−	2.26639i	0.226263	−	0.130633i
$302$	2.12456	+	3.67985i	0.122255	+	0.211752i
$303$	1.89920	−	3.28952i	0.109106	−	0.188978i
$304$		−	2.09479i		−	0.120144i
$305$		0			0
$306$	−1.93641	−	1.11799i	−0.110697	−	0.0639111i
$307$			32.5819i			1.85955i	0.368133	+	0.929773i	$0.379997\pi$
$307$			32.5819i			1.85955i	−0.368133	+	0.929773i	$0.620003\pi$
$308$	9.77046	−	16.9229i	0.556724	−	0.964274i
$309$	−2.07159	−	3.58810i	−0.117849	−	0.204120i
$310$		0			0
$311$	18.2831			1.03674			0.518370	−	0.855157i	$-0.326539\pi$
$311$	18.2831			1.03674			0.518370	+	0.855157i	$0.326539\pi$
$312$	−2.55889	+	6.06939i	−0.144869	+	0.343612i
$313$	16.0968			0.909844			0.454922	−	0.890531i	$-0.349667\pi$
$313$	16.0968			0.909844			0.454922	+	0.890531i	$0.349667\pi$
$314$	19.7044	−	11.3763i	1.11198	−	0.642003i
$315$		0			0
$316$	1.27616	−	2.21037i	0.0717894	−	0.124343i
$317$			7.38961i			0.415042i	0.978231	+	0.207521i	$0.0665395\pi$
$317$			7.38961i			0.415042i	−0.978231	+	0.207521i	$0.933460\pi$
$318$	−0.869998	−	0.502293i	−0.0487870	−	0.0281672i
$319$	24.7769	+	14.3049i	1.38724	+	0.800923i
$320$		0			0
$321$	−2.28493	+	3.95762i	−0.127532	+	0.220893i
$322$	−1.97758	−	3.42527i	−0.110206	−	0.190883i
$323$	−12.0246	+	6.94242i	−0.669068	+	0.386286i
$324$	9.89822			0.549901
$325$		0			0
$326$	−5.21497			−0.288831
$327$	−24.7371	+	14.2820i	−1.36796	+	0.789794i
$328$	2.59030	+	4.48652i	0.143025	+	0.247727i
$329$	−3.21649	+	5.57112i	−0.177331	+	0.307146i
$330$		0			0
$331$	−16.8848	−	9.74846i	−0.928074	−	0.535824i	−0.0418724	−	0.999123i	$-0.513332\pi$
$331$	−16.8848	−	9.74846i	−0.928074	−	0.535824i	−0.886202	+	0.463299i	$0.846666\pi$
$332$	−14.2208	−	8.21037i	−0.780466	−	0.450602i
$333$			1.11319i			0.0610025i
$334$	3.35224	−	5.80624i	0.183426	−	0.317704i
$335$		0			0
$336$	6.31414	−	3.64547i	0.344465	−	0.198877i
$337$	−27.8865			−1.51908			−0.759538	−	0.650463i	$-0.774575\pi$
$337$	−27.8865			−1.51908			−0.759538	+	0.650463i	$0.774575\pi$
$338$	−3.20634	−	12.5984i	−0.174402	−	0.685262i
$339$	−31.2714			−1.69843
$340$		0			0
$341$	26.4833	+	45.8705i	1.43415	+	2.48403i
$342$	−0.353326	+	0.611979i	−0.0191057	+	0.0330920i
$343$		−	7.69549i		−	0.415517i
$344$	0.983586	+	0.567874i	0.0530314	+	0.0306177i
$345$		0			0
$346$			19.5409i			1.05053i
$347$	10.0940	−	17.4833i	0.541875	−	0.938555i	−0.456922	−	0.889507i	$-0.651048\pi$
$347$	10.0940	−	17.4833i	0.541875	−	0.938555i	0.998796	−	0.0490478i	$-0.0156187\pi$
$348$	5.33734	+	9.24454i	0.286111	+	0.495559i
$349$	−30.8885	+	17.8335i	−1.65342	+	0.954605i	−0.677774	+	0.735270i	$0.737055\pi$
$349$	−30.8885	+	17.8335i	−1.65342	+	0.954605i	−0.975650	+	0.219335i	$0.929611\pi$
$350$		0			0
$351$	−13.9810	+	10.5889i	−0.746250	+	0.565192i
$352$	4.89623			0.260970
$353$	22.1506	−	12.7886i	1.17896	−	0.680671i	0.223184	−	0.974776i	$-0.428355\pi$
$353$	22.1506	−	12.7886i	1.17896	−	0.680671i	0.955773	+	0.294105i	$0.0950217\pi$
$354$	3.16418	+	5.48052i	0.168174	+	0.291286i
$355$		0			0
$356$		−	3.44854i		−	0.182772i
$357$	−41.8519	−	24.1632i	−2.21504	−	1.27885i
$358$	7.77604	+	4.48950i	0.410977	+	0.237277i
$359$		−	24.2487i		−	1.27980i	−0.768459	−	0.639899i	$-0.778976\pi$
$359$		−	24.2487i		−	1.27980i	0.768459	−	0.639899i	$-0.221024\pi$
$360$		0			0
$361$	−7.30593	−	12.6542i	−0.384523	−	0.666013i
$362$	−4.81205	+	2.77824i	−0.252916	+	0.146021i
$363$	−23.6997			−1.24391
$364$	−5.59030	+	13.2595i	−0.293011	+	0.694988i
$365$		0			0
$366$	−2.17018	+	1.25296i	−0.113437	+	0.0654931i
$367$	1.47966	+	2.56285i	0.0772378	+	0.133780i	0.902057	−	0.431616i	$-0.142057\pi$
$367$	1.47966	+	2.56285i	0.0772378	+	0.133780i	−0.824819	+	0.565396i	$0.808723\pi$
$368$	0.495508	−	0.858244i	0.0258301	−	0.0447391i
$369$		−	1.74761i		−	0.0909771i
$370$		0			0
$371$	−1.90065	−	1.09734i	−0.0986766	−	0.0569710i
$372$			19.7625i			1.02464i
$373$	−2.91179	+	5.04337i	−0.150767	+	0.261136i	−0.931510	−	0.363717i	$-0.881508\pi$
$373$	−2.91179	+	5.04337i	−0.150767	+	0.261136i	0.780743	+	0.624853i	$0.214841\pi$
$374$	−16.2268	−	28.1056i	−0.839067	−	1.45331i
$375$		0			0
$376$	−1.61186			−0.0831256
$377$	−19.4133	−	8.18476i	−0.999836	−	0.421537i
$378$	19.4133			0.998513
$379$	−0.503185	+	0.290514i	−0.0258469	+	0.0149227i	−0.512868	−	0.858468i	$-0.671417\pi$
$379$	−0.503185	+	0.290514i	−0.0258469	+	0.0149227i	0.487021	+	0.873390i	$0.338084\pi$
$380$		0			0
$381$	−7.42094	+	12.8534i	−0.380186	+	0.658502i
$382$			10.1863i			0.521177i
$383$	13.2514	+	7.65070i	0.677115	+	0.390933i	0.798767	−	0.601640i	$-0.205486\pi$
$383$	13.2514	+	7.65070i	0.677115	+	0.390933i	−0.121652	+	0.992573i	$0.538819\pi$
$384$	1.58209	+	0.913419i	0.0807356	+	0.0466127i
$385$		0			0
$386$	−4.06939	+	7.04839i	−0.207126	+	0.358754i
$387$	−0.191566	−	0.331802i	−0.00973783	−	0.0168664i
$388$	10.0910	−	5.82606i	0.512295	−	0.295773i
$389$	−19.7281			−1.00025			−0.500127	−	0.865952i	$-0.666713\pi$
$389$	−19.7281			−1.00025			−0.500127	+	0.865952i	$0.666713\pi$
$390$		0			0
$391$	−6.56873			−0.332195
$392$	7.73205	−	4.46410i	0.390528	−	0.225471i
$393$	−12.9498	−	22.4298i	−0.653233	−	1.13143i
$394$	−7.24026	+	12.5405i	−0.364759	+	0.631781i
$395$		0			0
$396$	−1.43040	−	0.825843i	−0.0718804	−	0.0415002i
$397$	0.716063	+	0.413419i	0.0359382	+	0.0207489i	0.517861	−	0.855465i	$-0.326728\pi$
$397$	0.716063	+	0.413419i	0.0359382	+	0.0207489i	−0.481923	+	0.876213i	$0.660062\pi$
$398$			11.2566i			0.564240i
$399$	−7.63649	+	13.2268i	−0.382302	+	0.662167i
$400$		0			0
$401$	27.3668	−	15.8002i	1.36663	−	0.789026i	0.376137	−	0.926564i	$-0.377252\pi$
$401$	27.3668	−	15.8002i	1.36663	−	0.789026i	0.990496	+	0.137538i	$0.0439189\pi$
$402$	6.61471			0.329912
$403$	−23.5491	−	31.0930i	−1.17307	−	1.54885i
$404$	2.07923			0.103445
$405$		0			0
$406$	11.6603	+	20.1962i	0.578689	+	1.00232i
$407$	−8.07859	+	13.9925i	−0.400441	+	0.693584i
$408$		−	12.1088i		−	0.599475i
$409$	18.9951	+	10.9668i	0.939247	+	0.542274i	0.889724	−	0.456499i	$-0.150897\pi$
$409$	18.9951	+	10.9668i	0.939247	+	0.542274i	0.0495227	+	0.998773i	$0.484230\pi$
$410$		0			0
$411$			25.6057i			1.26304i
$412$	1.13397	−	1.96410i	0.0558669	−	0.0967643i
$413$	6.91264	+	11.9730i	0.340149	+	0.589155i
$414$	−0.289519	+	0.167154i	−0.0142291	+	0.00821516i
$415$		0			0
$416$	−3.57760	+	0.448114i	−0.175406	+	0.0219706i
$417$	29.2102			1.43043
$418$	−8.88244	+	5.12828i	−0.434454	+	0.250832i
$419$	15.2814	+	26.4681i	0.746545	+	1.29305i	0.949470	+	0.313859i	$0.101622\pi$
$419$	15.2814	+	26.4681i	0.746545	+	1.29305i	−0.202925	+	0.979194i	$0.565045\pi$
$420$		0			0
$421$		−	21.4565i		−	1.04573i	−0.852417	−	0.522863i	$-0.824864\pi$
$421$		−	21.4565i		−	1.04573i	0.852417	−	0.522863i	$-0.175136\pi$
$422$	−8.30097	−	4.79257i	−0.404085	−	0.233299i
$423$	0.470896	+	0.271872i	0.0228958	+	0.0132189i
$424$		−	0.549905i		−	0.0267057i
$425$		0			0
$426$	5.48052	+	9.49253i	0.265532	+	0.459915i
$427$	−4.74111	+	2.73728i	−0.229438	+	0.132466i
$428$	−2.50152			−0.120915
$429$	32.0002	−	4.00821i	1.54499	−	0.193518i
$430$		0			0
$431$	−7.93641	+	4.58209i	−0.382283	+	0.220711i	−0.678811	−	0.734313i	$-0.737505\pi$
$431$	−7.93641	+	4.58209i	−0.382283	+	0.220711i	0.296528	+	0.955024i	$0.404171\pi$
$432$	2.43213	+	4.21257i	0.117016	+	0.202677i
$433$	−5.04839	+	8.74407i	−0.242610	+	0.420213i	−0.961457	−	0.274955i	$-0.911337\pi$
$433$	−5.04839	+	8.74407i	−0.242610	+	0.420213i	0.718847	+	0.695168i	$0.244670\pi$
$434$			43.1742i			2.07243i
$435$		0			0
$436$	−13.5409	−	7.81785i	−0.648492	−	0.374407i
$437$			2.07597i			0.0993069i
$438$	−8.17018	+	14.1512i	−0.390387	+	0.676169i
$439$	13.2648	+	22.9752i	0.633093	+	1.09655i	0.986916	+	0.161236i	$0.0515481\pi$
$439$	13.2648	+	22.9752i	0.633093	+	1.09655i	−0.353823	+	0.935312i	$0.615119\pi$
$440$		0			0
$441$	−3.01183			−0.143420
$442$	14.4289	+	19.0512i	0.686315	+	0.906174i
$443$	−12.9851			−0.616939			−0.308469	−	0.951234i	$-0.599817\pi$
$443$	−12.9851			−0.616939			−0.308469	+	0.951234i	$0.599817\pi$
$444$	−5.22077	+	3.01421i	−0.247767	+	0.143048i
$445$		0			0
$446$	13.6058	−	23.5660i	0.644254	−	1.11588i
$447$		−	13.6957i		−	0.647783i
$448$	3.45632	+	1.99551i	0.163296	+	0.0942789i
$449$	−27.5283	−	15.8935i	−1.29914	−	0.750059i	−0.318885	−	0.947793i	$-0.603308\pi$
$449$	−27.5283	−	15.8935i	−1.29914	−	0.750059i	−0.980256	+	0.197734i	$0.936642\pi$
$450$		0			0
$451$	12.6827	−	21.9670i	0.597204	−	1.03439i
$452$	−8.55889	−	14.8244i	−0.402576	−	0.697283i
$453$	6.72250	−	3.88124i	0.315850	−	0.182356i
$454$	−6.32835			−0.297004
$455$		0			0
$456$	−3.82684			−0.179208
$457$	6.42293	−	3.70828i	0.300452	−	0.173466i	−0.342194	−	0.939629i	$-0.611170\pi$
$457$	6.42293	−	3.70828i	0.300452	−	0.173466i	0.642646	+	0.766163i	$0.277837\pi$
$458$	1.25076	+	2.16638i	0.0584441	+	0.101228i
$459$	16.1208	−	27.9221i	0.752455	−	1.30329i
$460$		0			0
$461$	−34.6924	−	20.0296i	−1.61578	−	0.932873i	−0.987994	−	0.154491i	$-0.950626\pi$
$461$	−34.6924	−	20.0296i	−1.61578	−	0.932873i	−0.627790	−	0.778383i	$-0.716040\pi$
$462$	−30.9155	−	17.8491i	−1.43832	−	0.830413i
$463$			22.6119i			1.05086i	0.850836	+	0.525431i	$0.176096\pi$
$463$			22.6119i			1.05086i	−0.850836	+	0.525431i	$0.823904\pi$
$464$	−2.92163	+	5.06040i	−0.135633	+	0.234923i
$465$		0			0
$466$	−7.94928	+	4.58952i	−0.368243	+	0.212605i
$467$	7.72244			0.357352			0.178676	−	0.983908i	$-0.442819\pi$
$467$	7.72244			0.357352			0.178676	+	0.983908i	$0.442819\pi$
$468$	1.12076	+	0.472517i	0.0518069	+	0.0218421i
$469$	14.4509			0.667279
$470$		0			0
$471$	−20.7827	−	35.9967i	−0.957616	−	1.65864i
$472$	−1.73205	+	3.00000i	−0.0797241	+	0.138086i
$473$		−	5.56088i		−	0.255690i
$474$	−4.03798	−	2.33133i	−0.185471	−	0.107082i
$475$		0			0
$476$		−	26.4536i		−	1.21250i
$477$	−0.0927520	+	0.160651i	−0.00424682	+	0.00735571i
$478$	3.27015	+	5.66406i	0.149573	+	0.259068i
$479$	4.32100	−	2.49473i	0.197431	−	0.113987i	−0.398025	−	0.917374i	$-0.630304\pi$
$479$	4.32100	−	2.49473i	0.197431	−	0.113987i	0.595457	+	0.803387i	$0.296971\pi$
$480$		0			0
$481$	4.62227	−	10.9635i	0.210757	−	0.499892i
$482$	9.08254			0.413699
$483$	−6.25741	+	3.61272i	−0.284722	+	0.164384i
$484$	−6.48652	−	11.2350i	−0.294842	−	0.510681i
$485$		0			0
$486$		−	3.48969i		−	0.158295i
$487$	−22.3741	−	12.9177i	−1.01387	−	0.585357i	−0.101546	−	0.994831i	$-0.532379\pi$
$487$	−22.3741	−	12.9177i	−1.01387	−	0.585357i	−0.912322	+	0.409474i	$0.865712\pi$
$488$	−1.18795	−	0.685861i	−0.0537758	−	0.0310475i
$489$			9.52691i			0.430822i
$490$		0			0
$491$	8.75076	+	15.1568i	0.394916	+	0.684015i	0.993090	−	0.117351i	$-0.0374403\pi$
$491$	8.75076	+	15.1568i	0.394916	+	0.684015i	−0.598174	+	0.801366i	$0.704107\pi$
$492$	8.19615	−	4.73205i	0.369511	−	0.213337i
$493$	38.7307			1.74434
$494$	6.02091	−	4.56009i	0.270893	−	0.205168i
$495$		0			0
$496$	−9.36854	+	5.40893i	−0.420660	+	0.242868i
$497$	11.9730	+	20.7379i	0.537065	+	0.930223i
$498$	−14.9990	+	25.9791i	−0.672122	+	1.16415i
$499$		−	19.0519i		−	0.852878i	−0.904516	−	0.426439i	$-0.859768\pi$
$499$		−	19.0519i		−	0.852878i	0.904516	−	0.426439i	$-0.140232\pi$
$500$		0			0
$501$	−10.6071	−	6.12399i	−0.473889	−	0.273600i
$502$			9.62828i			0.429731i
$503$	−1.96384	+	3.40148i	−0.0875635	+	0.151664i	−0.906481	−	0.422247i	$-0.861241\pi$
$503$	−1.96384	+	3.40148i	−0.0875635	+	0.151664i	0.818917	+	0.573912i	$0.194575\pi$
$504$	−0.673162	−	1.16595i	−0.0299850	−	0.0519355i
$505$		0			0
$506$	−4.85224			−0.215708
$507$	−23.0152	+	5.85747i	−1.02214	+	0.260139i
$508$	−8.12436			−0.360460
$509$	−36.9221	+	21.3170i	−1.63654	+	0.944858i	−0.654530	+	0.756036i	$0.727134\pi$
$509$	−36.9221	+	21.3170i	−1.63654	+	0.944858i	−0.982011	+	0.188822i	$0.939533\pi$
$510$		0			0
$511$	−17.8491	+	30.9155i	−0.789596	+	1.36762i
$512$			1.00000i			0.0441942i
$513$	−8.82443	−	5.09479i	−0.389608	−	0.224940i
$514$	12.8364	+	7.41113i	0.566191	+	0.326891i
$515$		0			0
$516$	1.03741	−	1.79685i	0.0456696	−	0.0791021i
$517$	3.94603	+	6.83472i	0.173546	+	0.300591i
$518$	−11.4056	+	6.58502i	−0.501133	+	0.289329i
$519$	35.6981			1.56697
$520$		0			0
$521$	32.4921			1.42351			0.711753	−	0.702430i	$-0.247902\pi$
$521$	32.4921			1.42351			0.711753	+	0.702430i	$0.247902\pi$
$522$	1.70707	−	0.985577i	0.0747164	−	0.0431375i
$523$	5.31194	+	9.20055i	0.232275	+	0.402312i	0.958477	−	0.285169i	$-0.0920498\pi$
$523$	5.31194	+	9.20055i	0.232275	+	0.402312i	−0.726202	+	0.687481i	$0.758716\pi$
$524$	7.08867	−	12.2779i	0.309670	−	0.536364i
$525$		0			0
$526$	9.55525	+	5.51673i	0.416629	+	0.240541i
$527$	62.0973	+	35.8519i	2.70500	+	1.56173i
$528$		−	8.94462i		−	0.389264i
$529$	11.0089	−	19.0681i	0.478650	−	0.829046i
$530$		0			0
$531$	1.01202	−	0.584287i	0.0439177	−	0.0253559i
$532$	−8.36033			−0.362466
$533$	−7.25656	+	17.2117i	−0.314316	+	0.745522i
$534$	−6.29992			−0.272624
$535$		0			0
$536$	1.81042	+	3.13575i	0.0781984	+	0.135444i
$537$	8.20159	−	14.2056i	0.353925	−	0.613016i
$538$		−	2.61031i		−	0.112538i
$539$	−37.8579	−	21.8573i	−1.63065	−	0.941459i
$540$		0			0
$541$		−	36.2860i		−	1.56006i	−0.625743	−	0.780029i	$-0.715204\pi$
$541$		−	36.2860i		−	1.56006i	0.625743	−	0.780029i	$-0.284796\pi$
$542$	14.3448	−	24.8459i	0.616161	−	1.06722i
$543$	5.07540	+	8.79085i	0.217806	+	0.377251i
$544$	5.74026	−	3.31414i	0.246112	−	0.142093i
$545$		0			0
$546$	24.2230	+	10.2126i	1.03665	+	0.437057i
$547$	21.3774			0.914030			0.457015	−	0.889459i	$-0.348919\pi$
$547$	21.3774			0.914030			0.457015	+	0.889459i	$0.348919\pi$
$548$	−12.1386	+	7.00821i	−0.518534	+	0.299376i
$549$	0.231367	+	0.400740i	0.00987451	+	0.0171032i
$550$		0			0
$551$		−	12.2404i		−	0.521457i
$552$	−1.56787	−	0.905212i	−0.0667331	−	0.0385284i
$553$	−8.82161	−	5.09316i	−0.375133	−	0.216583i
$554$			4.70070i			0.199714i
$555$		0			0
$556$	7.99473	+	13.8473i	0.339052	+	0.587255i
$557$	−25.0600	+	14.4684i	−1.06183	+	0.613045i	−0.925937	−	0.377679i	$-0.876722\pi$
$557$	−25.0600	+	14.4684i	−1.06183	+	0.613045i	−0.135889	+	0.990724i	$0.543389\pi$
$558$	3.64928			0.154486
$559$	0.508944	+	4.06325i	0.0215261	+	0.171857i
$560$		0			0
$561$	−51.3444	+	29.6437i	−2.16776	+	1.25156i
$562$	1.66209	+	2.87883i	0.0701111	+	0.121436i
$563$	9.18717	−	15.9126i	0.387193	−	0.670638i	−0.604878	−	0.796318i	$-0.706778\pi$
$563$	9.18717	−	15.9126i	0.387193	−	0.670638i	0.992071	+	0.125680i	$0.0401114\pi$
$564$			2.94462i			0.123991i
$565$		0			0
$566$	−22.4969	−	12.9886i	−0.945616	−	0.545952i
$567$		−	39.5039i		−	1.65901i
$568$	−3.00000	+	5.19615i	−0.125877	+	0.218026i
$569$	−1.40280	−	2.42973i	−0.0588086	−	0.101860i	0.835122	−	0.550064i	$-0.185397\pi$
$569$	−1.40280	−	2.42973i	−0.0588086	−	0.101860i	−0.893931	+	0.448205i	$0.852064\pi$
$570$		0			0
$571$	−0.119334			−0.00499398			−0.00249699	−	0.999997i	$-0.500795\pi$
$571$	−0.119334			−0.00499398			−0.00249699	+	0.999997i	$0.500795\pi$
$572$	10.6585	+	14.0729i	0.445653	+	0.588417i
$573$	18.6088			0.777392
$574$	17.9058	−	10.3379i	0.747373	−	0.431496i
$575$		0			0
$576$	0.168669	−	0.292144i	0.00702789	−	0.0121727i
$577$		−	27.6701i		−	1.15192i	−0.817478	−	0.575960i	$-0.804628\pi$
$577$		−	27.6701i		−	1.15192i	0.817478	−	0.575960i	$-0.195372\pi$
$578$	−23.3256	−	13.4670i	−0.970217	−	0.560155i
$579$	12.8763	+	7.43412i	0.535119	+	0.308951i
$580$		0			0
$581$	−32.7677	+	56.7553i	−1.35943	+	2.35461i
$582$	−10.6433	−	18.4347i	−0.441178	−	0.764142i
$583$	−2.33174	+	1.34623i	−0.0965707	+	0.0557551i
$584$	−8.94462			−0.370131
$585$		0			0
$586$	−0.952463			−0.0393459
$587$	−15.5195	+	8.96018i	−0.640558	+	0.369826i	−0.784829	−	0.619712i	$-0.787249\pi$
$587$	−15.5195	+	8.96018i	−0.640558	+	0.369826i	0.144272	+	0.989538i	$0.453916\pi$
$588$	−8.15519	−	14.1252i	−0.336314	−	0.582514i
$589$	11.3306	−	19.6251i	0.466867	−	0.808638i
$590$		0			0
$591$	22.9095	+	13.2268i	0.942369	+	0.544077i
$592$	−2.85782	−	1.64996i	−0.117456	−	0.0678130i
$593$		−	22.0640i		−	0.906058i	−0.891496	−	0.453029i	$-0.850343\pi$
$593$		−	22.0640i		−	0.906058i	0.891496	−	0.453029i	$-0.149657\pi$
$594$	11.9082	−	20.6257i	0.488601	−	0.846282i
$595$		0			0
$596$	6.49253	−	3.74846i	0.265944	−	0.153543i
$597$	20.5639			0.841625
$598$	3.54545	−	0.444088i	0.144984	−	0.0181601i
$599$	47.3354			1.93407			0.967035	−	0.254642i	$-0.0819577\pi$
$599$	47.3354			1.93407			0.967035	+	0.254642i	$0.0819577\pi$
$600$		0			0
$601$	13.4610	+	23.3152i	0.549087	+	0.951046i	0.998337	+	0.0576406i	$0.0183577\pi$
$601$	13.4610	+	23.3152i	0.549087	+	0.951046i	−0.449251	+	0.893406i	$0.648309\pi$
$602$	2.26639	−	3.92551i	0.0923713	−	0.159992i
$603$		−	1.22145i		−	0.0497414i
$604$	3.67985	+	2.12456i	0.149731	+	0.0864473i
$605$		0			0
$606$		−	3.79841i		−	0.154300i
$607$	9.85548	−	17.0702i	0.400022	−	0.692858i	−0.593706	−	0.804682i	$-0.702336\pi$
$607$	9.85548	−	17.0702i	0.400022	−	0.692858i	0.993728	+	0.111824i	$0.0356692\pi$
$608$	−1.04739	−	1.81414i	−0.0424774	−	0.0735731i
$609$	36.8951	−	21.3014i	1.49507	−	0.863176i
$610$		0			0
$611$	−3.50883	−	4.63287i	−0.141952	−	0.187426i
$612$	−2.23597			−0.0903839
$613$	−12.6840	+	7.32308i	−0.512300	+	0.295777i	−0.733779	−	0.679389i	$-0.762245\pi$
$613$	−12.6840	+	7.32308i	−0.512300	+	0.295777i	0.221479	+	0.975165i	$0.428912\pi$
$614$	16.2909	+	28.2167i	0.657449	+	1.13873i
$615$		0			0
$616$		−	19.5409i		−	0.787326i
$617$	4.08821	+	2.36033i	0.164585	+	0.0950233i	0.580030	−	0.814595i	$-0.303041\pi$
$617$	4.08821	+	2.36033i	0.164585	+	0.0950233i	−0.415445	+	0.909618i	$0.636374\pi$
$618$	−3.58810	−	2.07159i	−0.144334	−	0.0833315i
$619$		−	25.6874i		−	1.03246i	−0.856449	−	0.516231i	$-0.827335\pi$
$619$		−	25.6874i		−	1.03246i	0.856449	−	0.516231i	$-0.172665\pi$
$620$		0			0
$621$	−2.41027	−	4.17472i	−0.0967210	−	0.167526i
$622$	15.8336	−	9.14155i	0.634870	−	0.366543i
$623$	−13.7632			−0.551410
$624$	0.818632	+	6.53569i	0.0327715	+	0.261637i
$625$		0			0
$626$	13.9402	−	8.04839i	0.557163	−	0.321678i
$627$	9.36854	+	16.2268i	0.374143	+	0.648035i
$628$	11.3763	−	19.7044i	0.453964	−	0.786290i
$629$			21.8728i			0.872126i
$630$		0			0
$631$	24.3662	+	14.0678i	0.970003	+	0.560032i	0.899237	−	0.437461i	$-0.144122\pi$
$631$	24.3662	+	14.0678i	0.970003	+	0.560032i	0.0707660	+	0.997493i	$0.477456\pi$
$632$		−	2.55231i		−	0.101526i
$633$	−8.75525	+	15.1645i	−0.347990	+	0.602736i
$634$	3.69481	+	6.39959i	0.146739	+	0.254160i
$635$		0			0
$636$	−1.00459			−0.0398345
$637$	29.6626	+	12.5059i	1.17527	+	0.495502i
$638$	28.6099			1.13268
$639$	1.75286	−	1.01202i	0.0693422	−	0.0400347i
$640$		0			0
$641$	6.86874	−	11.8970i	0.271299	−	0.469904i	−0.697896	−	0.716199i	$-0.745880\pi$
$641$	6.86874	−	11.8970i	0.271299	−	0.469904i	0.969195	+	0.246296i	$0.0792134\pi$
$642$			4.56986i			0.180358i
$643$	−10.0859	−	5.82308i	−0.397748	−	0.229640i	0.287764	−	0.957701i	$-0.407088\pi$
$643$	−10.0859	−	5.82308i	−0.397748	−	0.229640i	−0.685512	+	0.728061i	$0.740422\pi$
$644$	−3.42527	−	1.97758i	−0.134974	−	0.0779275i
$645$		0			0
$646$	−6.94242	+	12.0246i	−0.273146	+	0.473102i
$647$	−17.2324	−	29.8473i	−0.677474	−	1.17342i	−0.975739	−	0.218936i	$-0.929741\pi$
$647$	−17.2324	−	29.8473i	−0.677474	−	1.17342i	0.298265	−	0.954483i	$-0.403592\pi$
$648$	8.57211	−	4.94911i	0.336744	−	0.194419i
$649$	16.9610			0.665779
$650$		0			0
$651$	78.8723			3.09125
$652$	−4.51630	+	2.60749i	−0.176872	+	0.102117i
$653$	−2.43255	−	4.21330i	−0.0951931	−	0.164879i	0.814496	−	0.580169i	$-0.197014\pi$
$653$	−2.43255	−	4.21330i	−0.0951931	−	0.164879i	−0.909689	+	0.415290i	$0.863680\pi$
$654$	−14.2820	+	24.7371i	−0.558469	+	0.967296i
$655$		0			0
$656$	4.48652	+	2.59030i	0.175169	+	0.101134i
$657$	2.61311	+	1.50868i	0.101947	+	0.0588593i
$658$			6.43298i			0.250784i
$659$	8.82145	−	15.2792i	0.343635	−	0.595193i	−0.641470	−	0.767148i	$-0.721675\pi$
$659$	8.82145	−	15.2792i	0.343635	−	0.595193i	0.985105	+	0.171955i	$0.0550083\pi$
$660$		0			0
$661$	3.16552	−	1.82762i	0.123125	−	0.0710860i	−0.437173	−	0.899378i	$-0.644020\pi$
$661$	3.16552	−	1.82762i	0.123125	−	0.0710860i	0.560297	+	0.828292i	$0.310687\pi$
$662$	−19.4969			−0.757770
$663$	34.8035	−	26.3593i	1.35166	−	1.02371i
$664$	−16.4207			−0.637248
$665$		0			0
$666$	0.556596	+	0.964052i	0.0215677	+	0.0373563i
$667$	2.89538	−	5.01494i	0.112109	−	0.194179i
$668$		−	6.70447i		−	0.259404i
$669$	−43.0512	−	24.8556i	−1.66446	−	0.960974i
$670$		0			0
$671$			6.71626i			0.259278i
$672$	3.64547	−	6.31414i	0.140627	−	0.243573i
$673$	−15.4685	−	26.7922i	−0.596267	−	1.03276i	−0.993367	−	0.114989i	$-0.963317\pi$
$673$	−15.4685	−	26.7922i	−0.596267	−	1.03276i	0.397100	−	0.917775i	$-0.370017\pi$
$674$	−24.1505	+	13.9433i	−0.930241	+	0.537075i
$675$		0			0
$676$	−9.07597	−	9.30735i	−0.349076	−	0.357975i
$677$	25.6685			0.986522			0.493261	−	0.869881i	$-0.335805\pi$
$677$	25.6685			0.986522			0.493261	+	0.869881i	$0.335805\pi$
$678$	−27.0818	+	15.6357i	−1.04007	+	0.600486i
$679$	−23.2519	−	40.2735i	−0.892326	−	1.54555i
$680$		0			0
$681$			11.5609i			0.443014i
$682$	45.8705	+	26.4833i	1.75647	+	1.01410i
$683$	26.3774	+	15.2290i	1.00930	+	0.582721i	0.910987	−	0.412435i	$-0.135321\pi$
$683$	26.3774	+	15.2290i	1.00930	+	0.582721i	0.0983147	+	0.995155i	$0.468655\pi$
$684$			0.706653i			0.0270195i
$685$		0			0
$686$	−3.84774	−	6.66449i	−0.146908	−	0.254451i
$687$	3.95762	−	2.28493i	0.150993	−	0.0871756i
$688$	1.13575			0.0433000
$689$	1.58055	−	1.19707i	0.0602143	−	0.0456049i
$690$		0			0
$691$	−5.41546	+	3.12662i	−0.206014	+	0.118942i	−0.599458	−	0.800407i	$-0.704617\pi$
$691$	−5.41546	+	3.12662i	−0.206014	+	0.118942i	0.393444	+	0.919349i	$0.371284\pi$
$692$	9.77046	+	16.9229i	0.371417	+	0.643313i
$693$	−3.29595	+	5.70876i	−0.125203	+	0.216858i
$694$		−	20.1880i		−	0.766327i
$695$		0			0
$696$	9.24454	+	5.33734i	0.350413	+	0.202311i
$697$		−	34.3384i		−	1.30066i
$698$	−17.8335	+	30.8885i	−0.675008	+	1.16915i
$699$	8.38431	+	14.5220i	0.317124	+	0.549274i
$700$		0			0
$701$	9.17903			0.346687			0.173344	−	0.984861i	$-0.444543\pi$
$701$	9.17903			0.346687			0.173344	+	0.984861i	$0.444543\pi$
$702$	−6.81346	+	16.1607i	−0.257157	+	0.609947i
$703$	6.91264			0.260715
$704$	4.24026	−	2.44811i	0.159811	−	0.0922668i
$705$		0			0
$706$	12.7886	−	22.1506i	0.481307	−	0.833648i
$707$		−	8.29822i		−	0.312087i
$708$	5.48052	+	3.16418i	0.205970	+	0.118917i
$709$	30.0521	+	17.3506i	1.12863	+	0.651614i	0.943590	−	0.331117i	$-0.107425\pi$
$709$	30.0521	+	17.3506i	1.12863	+	0.651614i	0.185039	+	0.982731i	$0.440759\pi$
$710$		0			0
$711$	−0.430497	+	0.745642i	−0.0161449	+	0.0279638i
$712$	−1.72427	−	2.98652i	−0.0646197	−	0.111925i
$713$	9.28436	−	5.36033i	0.347702	−	0.200746i
$714$	−48.3264			−1.80857
$715$		0			0
$716$	8.97900			0.335561
$717$	10.3473	−	5.97403i	0.386428	−	0.223104i
$718$	−12.1244	−	21.0000i	−0.452477	−	0.783713i
$719$	9.12761	−	15.8095i	0.340403	−	0.589595i	−0.644105	−	0.764937i	$-0.722770\pi$
$719$	9.12761	−	15.8095i	0.340403	−	0.589595i	0.984507	+	0.175343i	$0.0561033\pi$
$720$		0			0
$721$	−7.83876	−	4.52571i	−0.291931	−	0.168546i
$722$	−12.6542	−	7.30593i	−0.470942	−	0.271899i
$723$		−	16.5923i		−	0.617076i
$724$	−2.77824	+	4.81205i	−0.103253	+	0.178839i
$725$		0			0
$726$	−20.5245	+	11.8498i	−0.761736	+	0.439788i
$727$	−4.76025			−0.176548			−0.0882740	−	0.996096i	$-0.528135\pi$
$727$	−4.76025			−0.176548			−0.0882740	+	0.996096i	$0.528135\pi$
$728$	1.78843	+	14.2782i	0.0662836	+	0.529187i
$729$	23.3196			0.863687
$730$		0			0
$731$	−3.76403	−	6.51948i	−0.139218	−	0.241132i
$732$	−1.25296	+	2.17018i	−0.0463106	+	0.0802123i
$733$		−	1.44352i		−	0.0533176i	−0.999645	−	0.0266588i	$-0.991513\pi$
$733$		−	1.44352i		−	0.0533176i	0.999645	−	0.0266588i	$-0.00848676\pi$
$734$	2.56285	+	1.47966i	0.0945966	+	0.0546154i
$735$		0			0
$736$		−	0.991015i		−	0.0365293i
$737$	8.86425	−	15.3533i	0.326519	−	0.565547i
$738$	−0.873806	−	1.51348i	−0.0321653	−	0.0557119i
$739$	−27.0111	+	15.5949i	−0.993621	+	0.573667i	−0.906355	−	0.422518i	$-0.861146\pi$
$739$	−27.0111	+	15.5949i	−0.993621	+	0.573667i	−0.0872663	+	0.996185i	$0.527813\pi$
$740$		0			0
$741$	−8.33055	−	10.9992i	−0.306031	−	0.404067i
$742$	−2.19468			−0.0805691
$743$	20.8591	−	12.0430i	0.765246	−	0.441815i	−0.0659301	−	0.997824i	$-0.521001\pi$
$743$	20.8591	−	12.0430i	0.765246	−	0.441815i	0.831176	+	0.556009i	$0.187668\pi$
$744$	9.88124	+	17.1148i	0.362264	+	0.627459i
$745$		0			0
$746$			5.82358i			0.213216i
$747$	4.79721	+	2.76967i	0.175521	+	0.101337i
$748$	−28.1056	−	16.2268i	−1.02764	−	0.593310i
$749$			9.98359i			0.364792i
$750$		0			0
$751$	−0.944617	−	1.63612i	−0.0344696	−	0.0597030i	0.848276	−	0.529554i	$-0.177641\pi$
$751$	−0.944617	−	1.63612i	−0.0344696	−	0.0597030i	−0.882746	+	0.469851i	$0.844308\pi$
$752$	−1.39592	+	0.805932i	−0.0509038	+	0.0293893i
$753$	17.5893			0.640990
$754$	−20.9048	+	2.61844i	−0.761308	+	0.0953580i
$755$		0			0
$756$	16.8124	−	9.70665i	0.611462	−	0.353028i
$757$	−11.7385	−	20.3317i	−0.426642	−	0.738966i	0.569930	−	0.821693i	$-0.306970\pi$
$757$	−11.7385	−	20.3317i	−0.426642	−	0.738966i	−0.996572	+	0.0827270i	$0.973637\pi$
$758$	−0.290514	+	0.503185i	−0.0105520	+	0.0182765i
$759$			8.86425i			0.321752i
$760$		0			0
$761$	−20.4760	−	11.8218i	−0.742253	−	0.428540i	0.0806347	−	0.996744i	$-0.474305\pi$
$761$	−20.4760	−	11.8218i	−0.742253	−	0.428540i	−0.822888	+	0.568204i	$0.807639\pi$
$762$			14.8419i			0.537665i
$763$	−31.2012	+	54.0420i	−1.12956	+	1.95645i
$764$	5.09316	+	8.82161i	0.184264	+	0.319155i
$765$		0			0
$766$	15.3014			0.552862
$767$	−12.3932	+	1.55231i	−0.447491	+	0.0560507i
$768$	1.82684			0.0659204
$769$	33.5563	−	19.3738i	1.21007	−	0.698636i	0.247298	−	0.968940i	$-0.420457\pi$
$769$	33.5563	−	19.3738i	1.21007	−	0.698636i	0.962775	+	0.270304i	$0.0871241\pi$
$770$		0			0
$771$	13.5389	−	23.4501i	0.487593	−	0.844535i
$772$			8.13878i			0.292921i
$773$	6.16020	+	3.55660i	0.221567	+	0.127922i	0.606676	−	0.794949i	$-0.292503\pi$
$773$	6.16020	+	3.55660i	0.221567	+	0.127922i	−0.385109	+	0.922871i	$0.625836\pi$
$774$	−0.331802	−	0.191566i	−0.0119264	−	0.00688569i
$775$		0			0
$776$	5.82606	−	10.0910i	0.209143	−	0.362247i
$777$	12.0298	+	20.8362i	0.431566	+	0.747494i
$778$	−17.0850	+	9.86404i	−0.612528	+	0.353643i
$779$	−10.8522			−0.388822
$780$		0			0
$781$	29.3774			1.05120
$782$	−5.68868	+	3.28436i	−0.203427	+	0.117449i
$783$	14.2115	+	24.6151i	0.507878	+	0.879671i
$784$	4.46410	−	7.73205i	0.159432	−	0.276145i
$785$		0			0
$786$	−22.4298	−	12.9498i	−0.800044	−	0.461906i
$787$	−2.28033	−	1.31655i	−0.0812848	−	0.0469298i	0.458807	−	0.888536i	$-0.348277\pi$
$787$	−2.28033	−	1.31655i	−0.0812848	−	0.0469298i	−0.540092	+	0.841606i	$0.681610\pi$
$788$			14.4805i			0.515847i
$789$	10.0782	−	17.4559i	0.358792	−	0.621446i
$790$		0			0
$791$	−59.1645	+	34.1587i	−2.10365	+	1.21454i
$792$	−1.65169			−0.0586901
$793$	−0.614687	−	4.90747i	−0.0218282	−	0.174269i
$794$	0.826838			0.0293434
$795$		0			0
$796$	5.62828	+	9.74846i	0.199489	+	0.345525i
$797$	1.25953	−	2.18158i	0.0446150	−	0.0772754i	−0.842856	−	0.538140i	$-0.819127\pi$
$797$	1.25953	−	2.18158i	0.0446150	−	0.0772754i	0.887471	+	0.460864i	$0.152461\pi$
$798$			15.2730i			0.540657i
$799$	9.25252	+	5.34194i	0.327331	+	0.188984i
$800$		0			0
$801$			1.16333i			0.0411041i
$802$	15.8002	−	27.3668i	0.557926	−	0.966356i
$803$	21.8974	+	37.9275i	0.772744	+	1.33843i
$804$	5.72850	−	3.30735i	0.202029	−	0.116641i
$805$		0			0
$806$	−35.9407	−	15.1528i	−1.26596	−	0.533734i
$807$	−4.76861			−0.167863
$808$	1.80066	−	1.03961i	0.0633471	−	0.0365735i
$809$	−4.35078	−	7.53576i	−0.152965	−	0.264943i	0.779351	−	0.626587i	$-0.215549\pi$
$809$	−4.35078	−	7.53576i	−0.152965	−	0.264943i	−0.932316	+	0.361644i	$0.882216\pi$
$810$		0			0
$811$			40.3063i			1.41535i	0.706540	+	0.707673i	$0.250255\pi$
$811$			40.3063i			1.41535i	−0.706540	+	0.707673i	$0.749745\pi$
$812$	20.1962	+	11.6603i	0.708746	+	0.409195i
$813$	−45.3894	−	26.2056i	−1.59188	−	0.919070i
$814$			16.1572i			0.566309i
$815$		0			0
$816$	−6.05440	−	10.4865i	−0.211946	−	0.367102i
$817$	−2.06040	+	1.18958i	−0.0720844	+	0.0416180i
$818$	21.9336			0.766892
$819$	1.88582	−	4.47295i	0.0658960	−	0.156298i
$820$		0			0
$821$	29.2880	−	16.9095i	1.02216	−	0.590144i	0.107431	−	0.994213i	$-0.465738\pi$
$821$	29.2880	−	16.9095i	1.02216	−	0.590144i	0.914729	+	0.404068i	$0.132404\pi$
$822$	12.8029	+	22.1752i	0.446551	+	0.773449i
$823$	24.1874	−	41.8938i	0.843119	−	1.46033i	−0.0441253	−	0.999026i	$-0.514050\pi$
$823$	24.1874	−	41.8938i	0.843119	−	1.46033i	0.887245	−	0.461299i	$-0.152617\pi$
$824$		−	2.26795i		−	0.0790078i
$825$		0			0
$826$	11.9730	+	6.91264i	0.416596	+	0.240522i
$827$			15.1331i			0.526228i	0.964765	+	0.263114i	$0.0847495\pi$
$827$			15.1331i			0.526228i	−0.964765	+	0.263114i	$0.915250\pi$
$828$	−0.167154	+	0.289519i	−0.00580900	+	0.0100615i
$829$	−4.22458	−	7.31719i	−0.146726	−	0.254137i	0.783290	−	0.621657i	$-0.213540\pi$
$829$	−4.22458	−	7.31719i	−0.146726	−	0.254137i	−0.930015	+	0.367520i	$0.880207\pi$
$830$		0			0
$831$	8.58742			0.297894
$832$	−2.87423	+	2.17688i	−0.0996461	+	0.0754696i
$833$	−59.1786			−2.05042
$834$	25.2967	−	14.6051i	0.875954	−	0.505733i
$835$		0			0
$836$	−5.12828	+	8.88244i	−0.177365	+	0.307206i
$837$			52.6208i			1.81884i
$838$	26.4681	+	15.2814i	0.914327	+	0.527887i
$839$	−15.7792	−	9.11014i	−0.544759	−	0.314517i	0.202246	−	0.979335i	$-0.435176\pi$
$839$	−15.7792	−	9.11014i	−0.544759	−	0.314517i	−0.747006	+	0.664818i	$0.768509\pi$
$840$		0			0
$841$	−2.57180	+	4.45448i	−0.0886826	+	0.153603i
$842$	−10.7282	−	18.5819i	−0.369720	−	0.640373i
$843$	5.25915	−	3.03637i	0.181135	−	0.104578i
$844$	−9.58514			−0.329934
$845$		0			0
$846$	0.543744			0.0186943
$847$	−44.8390	+	25.8878i	−1.54069	+	0.889516i
$848$	−0.274952	−	0.476231i	−0.00944190	−	0.0163538i
$849$	−23.7281	+	41.0983i	−0.814346	+	1.41049i
$850$		0			0
$851$	2.83214	+	1.63514i	0.0970846	+	0.0560518i
$852$	9.49253	+	5.48052i	0.325209	+	0.187759i
$853$		−	37.4425i		−	1.28201i	−0.767539	−	0.641003i	$-0.778519\pi$
$853$		−	37.4425i		−	1.28201i	0.767539	−	0.641003i	$-0.221481\pi$
$854$	−2.73728	+	4.74111i	−0.0936678	+	0.162237i
$855$		0			0
$856$	−2.16638	+	1.25076i	−0.0740452	+	0.0427500i
$857$	28.6086			0.977251			0.488626	−	0.872494i	$-0.337498\pi$
$857$	28.6086			0.977251			0.488626	+	0.872494i	$0.337498\pi$
$858$	25.7089	−	19.4713i	0.877688	−	0.664740i
$859$	−22.4266			−0.765186			−0.382593	−	0.923917i	$-0.624969\pi$
$859$	−22.4266			−0.765186			−0.382593	+	0.923917i	$0.624969\pi$
$860$		0			0
$861$	−18.8857	−	32.7110i	−0.643622	−	1.11479i
$862$	−4.58209	+	7.93641i	−0.156067	+	0.270315i
$863$			3.08381i			0.104974i	0.998622	+	0.0524871i	$0.0167148\pi$
$863$			3.08381i			0.104974i	−0.998622	+	0.0524871i	$0.983285\pi$
$864$	4.21257	+	2.43213i	0.143314	+	0.0827426i
$865$		0			0
$866$			10.0968i			0.343102i
$867$	−24.6021	+	42.6121i	−0.835531	+	1.44718i
$868$	21.5871	+	37.3900i	0.732714	+	1.26910i
$869$	−10.8225	+	6.24835i	−0.367127	+	0.211961i
$870$		0			0
$871$	−5.07180	+	12.0297i	−0.171851	+	0.407611i
$872$	−15.6357			−0.529492
$873$	−3.40409	+	1.96535i	−0.115211	+	0.0665172i
$874$	1.03798	+	1.79784i	0.0351103	+	0.0608128i
$875$		0			0
$876$			16.3404i			0.552090i
$877$	−33.0587	−	19.0864i	−1.11631	−	0.644503i	−0.175855	−	0.984416i	$-0.556269\pi$
$877$	−33.0587	−	19.0864i	−1.11631	−	0.644503i	−0.940457	+	0.339913i	$0.889602\pi$
$878$	22.9752	+	13.2648i	0.775377	+	0.447664i
$879$			1.74000i			0.0586886i
$880$		0			0
$881$	−11.9835	−	20.7561i	−0.403736	−	0.699291i	0.590438	−	0.807083i	$-0.298955\pi$
$881$	−11.9835	−	20.7561i	−0.403736	−	0.699291i	−0.994173	+	0.107792i	$0.965622\pi$
$882$	−2.60832	+	1.50591i	−0.0878267	+	0.0507067i
$883$	−19.7537			−0.664765			−0.332383	−	0.943145i	$-0.607853\pi$
$883$	−19.7537			−0.664765			−0.332383	+	0.943145i	$0.607853\pi$
$884$	22.0214	+	9.28436i	0.740661	+	0.312267i
$885$		0			0
$886$	−11.2454	+	6.49253i	−0.377796	+	0.218121i
$887$	10.0846	+	17.4670i	0.338608	+	0.586486i	0.984171	−	0.177221i	$-0.0567107\pi$
$887$	10.0846	+	17.4670i	0.338608	+	0.586486i	−0.645563	+	0.763707i	$0.723377\pi$
$888$	−3.01421	+	5.22077i	−0.101150	+	0.175198i
$889$			32.4244i			1.08748i
$890$		0			0
$891$	−41.9710	−	24.2320i	−1.40608	−	0.811801i
$892$		−	27.2116i		−	0.911113i
$893$	1.68826	−	2.92415i	0.0564954	−	0.0978529i
$894$	−6.84784	−	11.8608i	−0.229026	−	0.396685i
$895$		0			0
$896$	3.99102			0.133330
$897$	−0.811276	−	6.47697i	−0.0270877	−	0.216260i
$898$	−31.7869			−1.06074
$899$	−54.7427	+	31.6057i	−1.82577	+	1.05411i
$900$		0			0
$901$	−1.82246	+	3.15659i	−0.0607150	+	0.105161i
$902$		−	25.3654i		−	0.844574i
$903$	−7.17127	−	4.14033i	−0.238645	−	0.137782i
$904$	−14.8244	−	8.55889i	−0.493053	−	0.284664i
$905$		0			0
$906$	3.88124	−	6.72250i	0.128945	−	0.223340i
$907$	11.9528	+	20.7029i	0.396887	+	0.687428i	0.993340	−	0.115220i	$-0.0367571\pi$
$907$	11.9528	+	20.7029i	0.396887	+	0.687428i	−0.596453	+	0.802648i	$0.703424\pi$
$908$	−5.48052	+	3.16418i	−0.181877	+	0.105007i
$909$	−0.701403			−0.0232641
$910$		0			0
$911$	−26.3025			−0.871439			−0.435720	−	0.900082i	$-0.643506\pi$
$911$	−26.3025			−0.871439			−0.435720	+	0.900082i	$0.643506\pi$
$912$	−3.31414	+	1.91342i	−0.109742	+	0.0633596i
$913$	40.1998	+	69.6281i	1.33042	+	2.30436i
$914$	3.70828	−	6.42293i	0.122659	−	0.212452i
$915$		0			0
$916$	2.16638	+	1.25076i	0.0715791	+	0.0413262i
$917$	−49.0014	−	28.2910i	−1.61817	−	0.934250i
$918$		−	32.2416i		−	1.06413i
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	−0.996335	−	0.0855332i	$-0.972741\pi$
$919$	−12.8564	+	22.2679i	−0.424094	+	0.734552i	0.572242	+	0.820085i	$0.306074\pi$
$920$		0			0
$921$	51.5474	−	29.7609i	1.69855	−	0.980655i
$922$	−40.0593			−1.31928
$923$	−21.4656	+	2.68868i	−0.706548	+	0.0884991i
$924$	−35.6981			−1.17438
$925$		0			0
$926$	11.3059	+	19.5824i	0.371536	+	0.643519i
$927$	−0.382533	+	0.662567i	−0.0125640	+	0.0217616i
$928$			5.84325i			0.191814i
$929$	22.9610	+	13.2566i	0.753327	+	0.434934i	0.826895	−	0.562357i	$-0.190105\pi$
$929$	22.9610	+	13.2566i	0.753327	+	0.434934i	−0.0735678	+	0.997290i	$0.523439\pi$
$930$		0			0
$931$			18.7027i			0.612956i
$932$	−4.58952	+	7.94928i	−0.150335	+	0.260387i
$933$	−16.7001	−	28.9255i	−0.546738	−	0.946977i
$934$	6.68783	−	3.86122i	0.218833	−	0.126343i
$935$		0			0
$936$	1.20686	−	0.151166i	0.0394475	−	0.00494102i
$937$	−24.3940			−0.796918			−0.398459	−	0.917186i	$-0.630455\pi$
$937$	−24.3940			−0.796918			−0.398459	+	0.917186i	$0.630455\pi$
$938$	12.5148	−	7.22543i	0.408623	−	0.235919i
$939$	−14.7031	−	25.4665i	−0.479818	−	0.831069i
$940$		0			0
$941$			3.13575i			0.102222i	0.998693	+	0.0511112i	$0.0162763\pi$
$941$			3.13575i			0.102222i	−0.998693	+	0.0511112i	$0.983724\pi$
$942$	−35.9967	−	20.7827i	−1.17284	−	0.677137i
$943$	−4.44621	−	2.56702i	−0.144789	−	0.0835937i
$944$			3.46410i			0.112747i
$945$		0			0
$946$	−2.78044	−	4.81586i	−0.0903999	−	0.156577i
$947$	−16.2718	+	9.39450i	−0.528761	+	0.305280i	−0.740512	−	0.672043i	$-0.765417\pi$
$947$	−16.2718	+	9.39450i	−0.528761	+	0.305280i	0.211751	+	0.977324i	$0.432084\pi$
$948$	−4.66266			−0.151436
$949$	−19.4713	−	25.7089i	−0.632066	−	0.834546i
$950$		0			0
$951$	11.6910	−	6.74981i	0.379107	−	0.218878i
$952$	−13.2268	−	22.9095i	−0.428682	−	0.742500i
$953$	3.80667	−	6.59335i	0.123310	−	0.213579i	−0.797761	−	0.602974i	$-0.793982\pi$
$953$	3.80667	−	6.59335i	0.123310	−	0.213579i	0.921071	+	0.389394i	$0.127316\pi$
$954$			0.185504i			0.00600591i
$955$		0			0
$956$	5.66406	+	3.27015i	0.183189	+	0.105764i
$957$		−	52.2656i		−	1.68951i
$958$	2.49473	−	4.32100i	0.0806011	−	0.139605i
$959$	27.9699	+	48.4452i	0.903194	+	1.56438i
$960$		0			0
$961$	−86.0260			−2.77503
$962$	−1.47874	−	11.8058i	−0.0476766	−	0.380634i
$963$	0.843858			0.0271929
$964$	7.86571	−	4.54127i	0.253338	−	0.146265i
$965$		0			0
$966$	−3.61272	+	6.25741i	−0.116237	+	0.201329i
$967$		−	22.5849i		−	0.726282i	−0.931734	−	0.363141i	$-0.881704\pi$
$967$		−	22.5849i		−	0.726282i	0.931734	−	0.363141i	$-0.118296\pi$
$968$	−11.2350	−	6.48652i	−0.361106	−	0.208485i
$969$	21.9670	+	12.6827i	0.705683	+	0.407426i
$970$		0			0
$971$	16.3491	−	28.3174i	0.524666	−	0.908748i	−0.474921	−	0.880028i	$-0.657524\pi$
$971$	16.3491	−	28.3174i	0.524666	−	0.908748i	0.999587	−	0.0287200i	$-0.00914313\pi$
$972$	−1.74484	−	3.02216i	−0.0559659	−	0.0969358i
$973$	55.2647	−	31.9071i	1.77170	−	1.02289i
$974$	−25.8354			−0.827820
$975$		0			0
$976$	−1.37172			−0.0439077
$977$	−42.3066	+	24.4258i	−1.35351	+	0.781449i	−0.988739	−	0.149648i	$-0.952186\pi$
$977$	−42.3066	+	24.4258i	−1.35351	+	0.781449i	−0.364770	+	0.931098i	$0.618853\pi$
$978$	4.76346	+	8.25055i	0.152319	+	0.263823i
$979$	−8.44242	+	14.6227i	−0.269821	+	0.467343i
$980$		0			0
$981$	4.56787	+	2.63726i	0.145841	+	0.0842013i
$982$	15.1568	+	8.75076i	0.483672	+	0.279248i
$983$		−	16.3881i		−	0.522700i	−0.965244	−	0.261350i	$-0.915832\pi$
$983$		−	16.3881i		−	0.522700i	0.965244	−	0.261350i	$-0.0841677\pi$
$984$	4.73205	−	8.19615i	0.150852	−	0.261284i
$985$		0			0
$986$	33.5418	−	19.3654i	1.06819	−	0.616718i
$987$	11.7520			0.374071
$988$	2.93421	−	6.95961i	0.0933497	−	0.221415i
$989$	−1.12554			−0.0357902
$990$		0			0
$991$	21.8977	+	37.9279i	0.695603	+	1.20482i	0.969977	+	0.243197i	$0.0781962\pi$
$991$	21.8977	+	37.9279i	0.695603	+	1.20482i	−0.274373	+	0.961623i	$0.588470\pi$
$992$	−5.40893	+	9.36854i	−0.171734	+	0.297451i
$993$			35.6177i			1.13029i
$994$	20.7379	+	11.9730i	0.657767	+	0.379762i
$995$		0			0
$996$			29.9980i			0.950524i
$997$	−22.5569	+	39.0697i	−0.714384	+	1.23735i	0.248812	+	0.968552i	$0.419960\pi$
$997$	−22.5569	+	39.0697i	−0.714384	+	1.23735i	−0.963196	+	0.268798i	$0.913373\pi$
$998$	−9.52593	−	16.4994i	−0.301538	−	0.522279i
$999$	−13.9012	+	8.02583i	−0.439813	+	0.253926i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	650.2.m.c.101.3		8
5.2	odd	4		650.2.n.e.49.2		8
5.3	odd	4		650.2.n.d.49.3		8
5.4	even	2		130.2.l.b.101.2	✓	8
13.2	odd	12		8450.2.a.cm.1.4		4
13.4	even	6	inner	650.2.m.c.251.3		8
13.11	odd	12		8450.2.a.ci.1.4		4
15.14	odd	2		1170.2.bs.g.361.4		8
20.19	odd	2		1040.2.da.d.881.1		8
65.4	even	6		130.2.l.b.121.2	yes	8
65.9	even	6		1690.2.l.j.1161.4		8
65.17	odd	12		650.2.n.d.199.3		8
65.19	odd	12		1690.2.e.t.191.4		8
65.24	odd	12		1690.2.a.u.1.1		4
65.29	even	6		1690.2.d.k.1351.1		8
65.34	odd	4		1690.2.e.s.991.4		8
65.43	odd	12		650.2.n.e.199.2		8
65.44	odd	4		1690.2.e.t.991.4		8
65.49	even	6		1690.2.d.k.1351.5		8
65.54	odd	12		1690.2.a.t.1.1		4
65.59	odd	12		1690.2.e.s.191.4		8
65.64	even	2		1690.2.l.j.361.4		8
195.134	odd	6		1170.2.bs.g.901.4		8
260.199	odd	6		1040.2.da.d.641.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.l.b.101.2	✓	8	5.4	even	2
130.2.l.b.121.2	yes	8	65.4	even	6
650.2.m.c.101.3		8	1.1	even	1	trivial
650.2.m.c.251.3		8	13.4	even	6	inner
650.2.n.d.49.3		8	5.3	odd	4
650.2.n.d.199.3		8	65.17	odd	12
650.2.n.e.49.2		8	5.2	odd	4
650.2.n.e.199.2		8	65.43	odd	12
1040.2.da.d.641.1		8	260.199	odd	6
1040.2.da.d.881.1		8	20.19	odd	2
1170.2.bs.g.361.4		8	15.14	odd	2
1170.2.bs.g.901.4		8	195.134	odd	6
1690.2.a.t.1.1		4	65.54	odd	12
1690.2.a.u.1.1		4	65.24	odd	12
1690.2.d.k.1351.1		8	65.29	even	6
1690.2.d.k.1351.5		8	65.49	even	6
1690.2.e.s.191.4		8	65.59	odd	12
1690.2.e.s.991.4		8	65.34	odd	4
1690.2.e.t.191.4		8	65.19	odd	12
1690.2.e.t.991.4		8	65.44	odd	4
1690.2.l.j.361.4		8	65.64	even	2
1690.2.l.j.1161.4		8	65.9	even	6
8450.2.a.ci.1.4		4	13.11	odd	12
8450.2.a.cm.1.4		4	13.2	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 650 = 2 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	650.m (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.913419 - 1.58209i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-1.58209 - 0.913419i) q^{6} +(-3.45632 - 1.99551i) q^{7} -1.00000i q^{8} +(-0.168669 + 0.292144i) q^{9} +(-4.24026 + 2.44811i) q^{11} -1.82684 q^{12} +(2.87423 - 2.17688i) q^{13} -3.99102 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-3.31414 + 5.74026i) q^{17} +0.337339i q^{18} +(1.81414 + 1.04739i) q^{19} +7.29094i q^{21} +(-2.44811 + 4.24026i) q^{22} +(0.495508 + 0.858244i) q^{23} +(-1.58209 + 0.913419i) q^{24} +(1.40072 - 3.32235i) q^{26} -4.86425 q^{27} +(-3.45632 + 1.99551i) q^{28} +(-2.92163 - 5.06040i) q^{29} -10.8179i q^{31} +(-0.866025 - 0.500000i) q^{32} +(7.74627 + 4.47231i) q^{33} +6.62828i q^{34} +(0.168669 + 0.292144i) q^{36} +(2.85782 - 1.64996i) q^{37} +2.09479 q^{38} +(-6.06939 - 2.55889i) q^{39} +(-4.48652 + 2.59030i) q^{41} +(3.64547 + 6.31414i) q^{42} +(-0.567874 + 0.983586i) q^{43} +4.89623i q^{44} +(0.858244 + 0.495508i) q^{46} -1.61186i q^{47} +(-0.913419 + 1.58209i) q^{48} +(4.46410 + 7.73205i) q^{49} +12.1088 q^{51} +(-0.448114 - 3.57760i) q^{52} +0.549905 q^{53} +(-4.21257 + 2.43213i) q^{54} +(-1.99551 + 3.45632i) q^{56} -3.82684i q^{57} +(-5.06040 - 2.92163i) q^{58} +(-3.00000 - 1.73205i) q^{59} +(0.685861 - 1.18795i) q^{61} +(-5.40893 - 9.36854i) q^{62} +(1.16595 - 0.673162i) q^{63} -1.00000 q^{64} +8.94462 q^{66} +(-3.13575 + 1.81042i) q^{67} +(3.31414 + 5.74026i) q^{68} +(0.905212 - 1.56787i) q^{69} +(-5.19615 - 3.00000i) q^{71} +(0.292144 + 0.168669i) q^{72} -8.94462i q^{73} +(1.64996 - 2.85782i) q^{74} +(1.81414 - 1.04739i) q^{76} +19.5409 q^{77} +(-6.53569 + 0.818632i) q^{78} +2.55231 q^{79} +(4.94911 + 8.57211i) q^{81} +(-2.59030 + 4.48652i) q^{82} -16.4207i q^{83} +(6.31414 + 3.64547i) q^{84} +1.13575i q^{86} +(-5.33734 + 9.24454i) q^{87} +(2.44811 + 4.24026i) q^{88} +(2.98652 - 1.72427i) q^{89} +(-14.2782 + 1.78843i) q^{91} +0.991015 q^{92} +(-17.1148 + 9.88124i) q^{93} +(-0.805932 - 1.39592i) q^{94} +1.82684i q^{96} +(10.0910 + 5.82606i) q^{97} +(7.73205 + 4.46410i) q^{98} -1.65169i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 2 q^{3} + 4 q^{4} - 6 q^{6} - 4 q^{9} - 6 q^{11} + 4 q^{12} + 2 q^{13} - 4 q^{16} - 6 q^{17} - 6 q^{19} - 6 q^{22} - 12 q^{23} - 6 q^{24} - 40 q^{27} + 42 q^{33} + 4 q^{36} + 30 q^{37} + 12 q^{38}+ \cdots + 48 q^{98}+O(q^{100}) \) 8 * q + 2 * q^3 + 4 * q^4 - 6 * q^6 - 4 * q^9 - 6 * q^11 + 4 * q^12 + 2 * q^13 - 4 * q^16 - 6 * q^17 - 6 * q^19 - 6 * q^22 - 12 * q^23 - 6 * q^24 - 40 * q^27 + 42 * q^33 + 4 * q^36 + 30 * q^37 + 12 * q^38 - 40 * q^39 + 12 * q^41 + 6 * q^42 - 4 * q^43 + 2 * q^48 + 8 * q^49 + 10 * q^52 - 60 * q^53 + 36 * q^54 - 24 * q^59 + 26 * q^61 - 18 * q^62 - 12 * q^63 - 8 * q^64 - 12 * q^66 - 24 * q^67 + 6 * q^68 + 12 * q^69 - 12 * q^72 + 6 * q^74 - 6 * q^76 + 60 * q^77 + 6 * q^78 + 20 * q^79 - 28 * q^81 + 30 * q^84 - 48 * q^87 + 6 * q^88 - 24 * q^89 - 66 * q^91 - 24 * q^92 - 48 * q^93 + 6 * q^97 + 48 * q^98

Introduction

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