LMFDB - Embedded newform 108.2.h.a.35.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [108,2,Mod(35,108)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(108, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("108.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 108 = 2^{2} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	108.h (of order $6$, degree $2$, not 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:	$0.862384341830$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.170772624.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 $ x^8 - 3x^7 + 5x^6 - 6x^5 + 6x^4 - 12x^3 + 20x^2 - 24*x + 16
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			35.2
Root			$0.335728 - 1.37379i$ of defining polynomial
Character	$\chi$	$=$	108.35
Dual form			108.2.h.a.71.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.335728 - 1.37379i) q^{2} +(-1.77457 - 0.922437i) q^{4} +(2.18614 - 1.26217i) q^{5} +(-1.10489 - 0.637910i) q^{7} +(-1.86301 + 2.12819i) q^{8} +O(q^{10})$	\(q+(0.335728 - 1.37379i) q^{2} +(-1.77457 - 0.922437i) q^{4} +(2.18614 - 1.26217i) q^{5} +(-1.10489 - 0.637910i) q^{7} +(-1.86301 + 2.12819i) q^{8} +(-1.00000 - 3.42703i) q^{10} +(0.252704 - 0.437696i) q^{11} +(1.18614 + 2.05446i) q^{13} +(-1.24730 + 1.30372i) q^{14} +(2.29822 + 3.27386i) q^{16} +0.792287i q^{17} +4.70285i q^{19} +(-5.04374 + 0.223233i) q^{20} +(-0.516461 - 0.494108i) q^{22} +(1.61030 + 2.78912i) q^{23} +(0.686141 - 1.18843i) q^{25} +(3.22060 - 0.939764i) q^{26} +(1.37228 + 2.15121i) q^{28} +(-2.18614 - 1.26217i) q^{29} +(7.04069 - 4.06494i) q^{31} +(5.26916 - 2.05813i) q^{32} +(1.08843 + 0.265993i) q^{34} -3.22060 q^{35} -6.74456 q^{37} +(6.46071 + 1.57888i) q^{38} +(-1.38665 + 7.00396i) q^{40} +(-5.87228 + 3.39036i) q^{41} +(-6.69391 - 3.86473i) q^{43} +(-0.852189 + 0.543620i) q^{44} +(4.37228 - 1.27582i) q^{46} +(0.599485 - 1.03834i) q^{47} +(-2.68614 - 4.65253i) q^{49} +(-1.40229 - 1.34160i) q^{50} +(-0.209786 - 4.73992i) q^{52} +1.87953i q^{53} -1.27582i q^{55} +(3.41602 - 1.16300i) q^{56} +(-2.46790 + 2.57954i) q^{58} +(-6.18850 - 10.7188i) q^{59} +(1.18614 - 2.05446i) q^{61} +(-3.22060 - 11.0371i) q^{62} +(-1.05842 - 7.92967i) q^{64} +(5.18614 + 2.99422i) q^{65} +(-6.69391 + 3.86473i) q^{67} +(0.730835 - 1.40597i) q^{68} +(-1.08125 + 4.42442i) q^{70} +11.8716 q^{71} +3.37228 q^{73} +(-2.26434 + 9.26558i) q^{74} +(4.33809 - 8.34556i) q^{76} +(-0.558422 + 0.322405i) q^{77} +(8.55691 + 4.94034i) q^{79} +(9.15640 + 4.25639i) q^{80} +(2.68614 + 9.20550i) q^{82} +(-3.82009 + 6.61659i) q^{83} +(1.00000 + 1.73205i) q^{85} +(-7.55665 + 7.89850i) q^{86} +(0.460714 + 1.35323i) q^{88} -11.9769i q^{89} -3.02661i q^{91} +(-0.284805 - 6.43491i) q^{92} +(-1.22519 - 1.17216i) q^{94} +(5.93580 + 10.2811i) q^{95} +(-5.24456 + 9.08385i) q^{97} +(-7.29339 + 2.12819i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) $ 8 * q + 3 * q^2 - q^4 + 6 * q^5	$ 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41} + 12 q^{46} - 10 q^{49} - 21 q^{50} + 16 q^{52} - 18 q^{56} + 4 q^{58} - 2 q^{61} + 26 q^{64} + 30 q^{65} + 15 q^{68} - 6 q^{70} + 4 q^{73} + 30 q^{74} - 3 q^{76} + 30 q^{77} + 10 q^{82} + 8 q^{85} - 21 q^{86} - 21 q^{88} - 24 q^{92} - 18 q^{94} + 4 q^{97}+O(q^{100}) $ 8 * q + 3 * q^2 - q^4 + 6 * q^5 - 8 * q^10 - 2 * q^13 - 12 * q^14 - q^16 - 18 * q^20 + 3 * q^22 - 6 * q^25 - 12 * q^28 - 6 * q^29 + 33 * q^32 + 7 * q^34 - 8 * q^37 + 27 * q^38 + 10 * q^40 - 24 * q^41 + 12 * q^46 - 10 * q^49 - 21 * q^50 + 16 * q^52 - 18 * q^56 + 4 * q^58 - 2 * q^61 + 26 * q^64 + 30 * q^65 + 15 * q^68 - 6 * q^70 + 4 * q^73 + 30 * q^74 - 3 * q^76 + 30 * q^77 + 10 * q^82 + 8 * q^85 - 21 * q^86 - 21 * q^88 - 24 * q^92 - 18 * q^94 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/108\mathbb{Z}\right)^\times$.

$n$	$29$	$55$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	0.335728	−	1.37379i	0.237396	−	0.971413i
$2$	0.335728	−	1.37379i	0.237396	−	0.971413i
$3$		0			0
$3$		0			0
$4$	−1.77457	−	0.922437i	−0.887287	−	0.461219i
$5$	2.18614	−	1.26217i	0.977672	−	0.564459i	0.0761054	−	0.997100i	$-0.475751\pi$
$5$	2.18614	−	1.26217i	0.977672	−	0.564459i	0.901566	+	0.432641i	$0.142418\pi$
$6$		0			0
$7$	−1.10489	−	0.637910i	−0.417610	−	0.241107i	0.276444	−	0.961030i	$-0.410844\pi$
$7$	−1.10489	−	0.637910i	−0.417610	−	0.241107i	−0.694054	+	0.719923i	$0.744177\pi$
$8$	−1.86301	+	2.12819i	−0.658672	+	0.752430i
$9$		0			0
$10$	−1.00000	−	3.42703i	−0.316228	−	1.08372i
$11$	0.252704	−	0.437696i	0.0761931	−	0.131970i	−0.825411	−	0.564532i	$-0.809057\pi$
$11$	0.252704	−	0.437696i	0.0761931	−	0.131970i	0.901605	+	0.432561i	$0.142390\pi$
$12$		0			0
$13$	1.18614	+	2.05446i	0.328976	+	0.569804i	0.982309	−	0.187267i	$-0.0599631\pi$
$13$	1.18614	+	2.05446i	0.328976	+	0.569804i	−0.653333	+	0.757071i	$0.726630\pi$
$14$	−1.24730	+	1.30372i	−0.333354	+	0.348434i
$15$		0			0
$16$	2.29822	+	3.27386i	0.574555	+	0.818466i
$17$			0.792287i			0.192158i	0.995374	+	0.0960789i	$0.0306301\pi$
$17$			0.792287i			0.192158i	−0.995374	+	0.0960789i	$0.969370\pi$
$18$		0			0
$19$			4.70285i			1.07891i	0.842015	+	0.539454i	$0.181369\pi$
$19$			4.70285i			1.07891i	−0.842015	+	0.539454i	$0.818631\pi$
$20$	−5.04374	+	0.223233i	−1.12781	+	0.0499164i
$21$		0			0
$22$	−0.516461	−	0.494108i	−0.110110	−	0.105344i
$23$	1.61030	+	2.78912i	0.335771	+	0.581572i	0.983633	−	0.180186i	$-0.0576698\pi$
$23$	1.61030	+	2.78912i	0.335771	+	0.581572i	−0.647862	+	0.761758i	$0.724336\pi$
$24$		0			0
$25$	0.686141	−	1.18843i	0.137228	−	0.237686i
$26$	3.22060	−	0.939764i	0.631612	−	0.184303i
$27$		0			0
$28$	1.37228	+	2.15121i	0.259337	+	0.406541i
$29$	−2.18614	−	1.26217i	−0.405956	−	0.234379i	0.283095	−	0.959092i	$-0.408639\pi$
$29$	−2.18614	−	1.26217i	−0.405956	−	0.234379i	−0.689051	+	0.724713i	$0.741972\pi$
$30$		0			0
$31$	7.04069	−	4.06494i	1.26455	−	0.730086i	0.290595	−	0.956846i	$-0.406147\pi$
$31$	7.04069	−	4.06494i	1.26455	−	0.730086i	0.973951	+	0.226761i	$0.0728135\pi$
$32$	5.26916	−	2.05813i	0.931466	−	0.363830i
$33$		0			0
$34$	1.08843	+	0.265993i	0.186665	+	0.0456175i
$35$	−3.22060			−0.544381
$36$		0			0
$37$	−6.74456			−1.10880			−0.554400	−	0.832251i	$-0.687052\pi$
$37$	−6.74456			−1.10880			−0.554400	+	0.832251i	$0.687052\pi$
$38$	6.46071	+	1.57888i	1.04807	+	0.256128i
$39$		0			0
$40$	−1.38665	+	7.00396i	−0.219249	+	1.10742i
$41$	−5.87228	+	3.39036i	−0.917096	+	0.529486i	−0.882708	−	0.469923i	$-0.844282\pi$
$41$	−5.87228	+	3.39036i	−0.917096	+	0.529486i	−0.0343887	+	0.999409i	$0.510948\pi$
$42$		0			0
$43$	−6.69391	−	3.86473i	−1.02081	−	0.589366i	−0.106473	−	0.994316i	$-0.533956\pi$
$43$	−6.69391	−	3.86473i	−1.02081	−	0.589366i	−0.914339	+	0.404950i	$0.867289\pi$
$44$	−0.852189	+	0.543620i	−0.128472	+	0.0819538i
$45$		0			0
$46$	4.37228	−	1.27582i	0.644658	−	0.188110i
$47$	0.599485	−	1.03834i	0.0874439	−	0.151457i	−0.818986	−	0.573813i	$-0.805463\pi$
$47$	0.599485	−	1.03834i	0.0874439	−	0.151457i	0.906430	+	0.422356i	$0.138797\pi$
$48$		0			0
$49$	−2.68614	−	4.65253i	−0.383734	−	0.664647i
$50$	−1.40229	−	1.34160i	−0.198314	−	0.189731i
$51$		0			0
$52$	−0.209786	−	4.73992i	−0.0290921	−	0.657309i
$53$			1.87953i			0.258173i	0.991633	+	0.129086i	$0.0412045\pi$
$53$			1.87953i			0.258173i	−0.991633	+	0.129086i	$0.958796\pi$
$54$		0			0
$55$		−	1.27582i		−	0.172032i
$56$	3.41602	−	1.16300i	0.456485	−	0.155412i
$57$		0			0
$58$	−2.46790	+	2.57954i	−0.324051	+	0.338711i
$59$	−6.18850	−	10.7188i	−0.805674	−	1.39547i	−0.915835	−	0.401555i	$-0.868470\pi$
$59$	−6.18850	−	10.7188i	−0.805674	−	1.39547i	0.110161	−	0.993914i	$-0.464863\pi$
$60$		0			0
$61$	1.18614	−	2.05446i	0.151870	−	0.263046i	−0.780045	−	0.625723i	$-0.784804\pi$
$61$	1.18614	−	2.05446i	0.151870	−	0.263046i	0.931915	+	0.362677i	$0.118137\pi$
$62$	−3.22060	−	11.0371i	−0.409017	−	1.40172i
$63$		0			0
$64$	−1.05842	−	7.92967i	−0.132303	−	0.991209i
$65$	5.18614	+	2.99422i	0.643262	+	0.371387i
$66$		0			0
$67$	−6.69391	+	3.86473i	−0.817791	+	0.472152i	−0.849654	−	0.527340i	$-0.823189\pi$
$67$	−6.69391	+	3.86473i	−0.817791	+	0.472152i	0.0318630	+	0.999492i	$0.489856\pi$
$68$	0.730835	−	1.40597i	0.0886268	−	0.170499i
$69$		0			0
$70$	−1.08125	+	4.42442i	−0.129234	+	0.528819i
$71$	11.8716			1.40890			0.704450	−	0.709754i	$-0.251194\pi$
$71$	11.8716			1.40890			0.704450	+	0.709754i	$0.251194\pi$
$72$		0			0
$73$	3.37228			0.394696			0.197348	−	0.980334i	$-0.436767\pi$
$73$	3.37228			0.394696			0.197348	+	0.980334i	$0.436767\pi$
$74$	−2.26434	+	9.26558i	−0.263224	+	1.07710i
$75$		0			0
$76$	4.33809	−	8.34556i	0.497613	−	0.957301i
$77$	−0.558422	+	0.322405i	−0.0636381	+	0.0367415i
$78$		0			0
$79$	8.55691	+	4.94034i	0.962728	+	0.555831i	0.897012	−	0.442007i	$-0.145733\pi$
$79$	8.55691	+	4.94034i	0.962728	+	0.555831i	0.0657165	+	0.997838i	$0.479067\pi$
$80$	9.15640	+	4.25639i	1.02372	+	0.475879i
$81$		0			0
$82$	2.68614	+	9.20550i	0.296635	+	1.01658i
$83$	−3.82009	+	6.61659i	−0.419309	+	0.726265i	−0.995870	−	0.0907894i	$-0.971061\pi$
$83$	−3.82009	+	6.61659i	−0.419309	+	0.726265i	0.576561	+	0.817054i	$0.304394\pi$
$84$		0			0
$85$	1.00000	+	1.73205i	0.108465	+	0.187867i
$86$	−7.55665	+	7.89850i	−0.814854	+	0.851717i
$87$		0			0
$88$	0.460714	+	1.35323i	0.0491122	+	0.144255i
$89$		−	11.9769i		−	1.26955i	−0.772698	−	0.634773i	$-0.781093\pi$
$89$		−	11.9769i		−	1.26955i	0.772698	−	0.634773i	$-0.218907\pi$
$90$		0			0
$91$		−	3.02661i		−	0.317274i
$92$	−0.284805	−	6.43491i	−0.0296930	−	0.670885i
$93$		0			0
$94$	−1.22519	−	1.17216i	−0.126369	−	0.120899i
$95$	5.93580	+	10.2811i	0.609000	+	1.05482i
$96$		0			0
$97$	−5.24456	+	9.08385i	−0.532505	+	0.922325i	0.466775	+	0.884376i	$0.345416\pi$
$97$	−5.24456	+	9.08385i	−0.532505	+	0.922325i	−0.999280	+	0.0379490i	$0.987918\pi$
$98$	−7.29339	+	2.12819i	−0.736744	+	0.214980i
$99$		0			0
$100$	−2.31386	+	1.47603i	−0.231386	+	0.147603i
$101$	−1.06930	−	0.617359i	−0.106399	−	0.0614295i	0.445856	−	0.895105i	$-0.352899\pi$
$101$	−1.06930	−	0.617359i	−0.106399	−	0.0614295i	−0.552255	+	0.833675i	$0.686233\pi$
$102$		0			0
$103$	0.411331	−	0.237482i	0.0405297	−	0.0233998i	−0.479598	−	0.877488i	$-0.659218\pi$
$103$	0.411331	−	0.237482i	0.0405297	−	0.0233998i	0.520128	+	0.854088i	$0.325884\pi$
$104$	−6.58207	−	1.30312i	−0.645425	−	0.127782i
$105$		0			0
$106$	2.58207	+	0.631011i	0.250793	+	0.0612892i
$107$	−12.5652			−1.21472			−0.607360	−	0.794427i	$-0.707771\pi$
$107$	−12.5652			−1.21472			−0.607360	+	0.794427i	$0.707771\pi$
$108$		0			0
$109$	13.4891			1.29202			0.646012	−	0.763327i	$-0.276436\pi$
$109$	13.4891			1.29202			0.646012	+	0.763327i	$0.276436\pi$
$110$	−1.75270	−	0.428329i	−0.167114	−	0.0408396i
$111$		0			0
$112$	−0.450854	−	5.08333i	−0.0426017	−	0.480329i
$113$	6.30298	−	3.63903i	0.592935	−	0.342331i	−0.173322	−	0.984865i	$-0.555450\pi$
$113$	6.30298	−	3.63903i	0.592935	−	0.342331i	0.766257	+	0.642534i	$0.222117\pi$
$114$		0			0
$115$	7.04069	+	4.06494i	0.656548	+	0.379058i
$116$	2.71519	+	4.25639i	0.252099	+	0.395196i
$117$		0			0
$118$	−16.8030	+	4.90307i	−1.54684	+	0.451364i
$119$	0.505408	−	0.875393i	0.0463307	−	0.0802471i
$120$		0			0
$121$	5.37228	+	9.30506i	0.488389	+	0.845915i
$122$	−2.42416	−	2.31924i	−0.219473	−	0.209974i
$123$		0			0
$124$	−16.2439	+	0.718945i	−1.45874	+	0.0645632i
$125$			9.15759i			0.819080i
$126$		0			0
$127$		−	7.65492i		−	0.679265i	−0.940558	−	0.339632i	$-0.889697\pi$
$127$		−	7.65492i		−	0.679265i	0.940558	−	0.339632i	$-0.110303\pi$
$128$	−11.2490	−	1.20817i	−0.994282	−	0.106788i
$129$		0			0
$130$	5.85455	−	6.11940i	0.513478	−	0.536707i
$131$	3.82009	+	6.61659i	0.333763	+	0.578094i	0.983246	−	0.182282i	$-0.0583483\pi$
$131$	3.82009	+	6.61659i	0.333763	+	0.578094i	−0.649484	+	0.760375i	$0.725015\pi$
$132$		0			0
$133$	3.00000	−	5.19615i	0.260133	−	0.450564i
$134$	3.06198	+	10.4935i	0.264514	+	0.906500i
$135$		0			0
$136$	−1.68614	−	1.47603i	−0.144585	−	0.126569i
$137$	4.75544	+	2.74555i	0.406284	+	0.234568i	0.689192	−	0.724579i	$-0.257966\pi$
$137$	4.75544	+	2.74555i	0.406284	+	0.234568i	−0.282908	+	0.959147i	$0.591299\pi$
$138$		0			0
$139$	−13.3233	+	7.69219i	−1.13006	+	0.652443i	−0.943951	−	0.330085i	$-0.892923\pi$
$139$	−13.3233	+	7.69219i	−1.13006	+	0.652443i	−0.186114	+	0.982528i	$0.559589\pi$
$140$	5.71519	+	2.97080i	0.483022	+	0.251079i
$141$		0			0
$142$	3.98563	−	16.3090i	0.334467	−	1.36862i
$143$	1.19897			0.100263
$144$		0			0
$145$	−6.37228			−0.529189
$146$	1.13217	−	4.63279i	0.0936991	−	0.383413i
$147$		0			0
$148$	11.9687	+	6.22144i	0.983823	+	0.511399i
$149$	11.1861	−	6.45832i	0.916404	−	0.529086i	0.0339182	−	0.999425i	$-0.489201\pi$
$149$	11.1861	−	6.45832i	0.916404	−	0.529086i	0.882486	+	0.470338i	$0.155868\pi$
$150$		0			0
$151$	−2.62112	−	1.51330i	−0.213304	−	0.123151i	0.389542	−	0.921009i	$-0.372633\pi$
$151$	−2.62112	−	1.51330i	−0.213304	−	0.123151i	−0.602846	+	0.797858i	$0.705967\pi$
$152$	−10.0086	−	8.76144i	−0.811804	−	0.710647i
$153$		0			0
$154$	0.255437	+	0.875393i	0.0205837	+	0.0705411i
$155$	10.2613	−	17.7731i	0.824207	−	1.42757i
$156$		0			0
$157$	−5.93070	−	10.2723i	−0.473322	−	0.819817i	0.526212	−	0.850353i	$-0.323612\pi$
$157$	−5.93070	−	10.2723i	−0.473322	−	0.819817i	−0.999534	+	0.0305363i	$0.990278\pi$
$158$	9.65976	−	10.0968i	0.768489	−	0.803255i
$159$		0			0
$160$	8.92143	−	11.1499i	0.705301	−	0.881480i
$161$		−	4.10891i		−	0.323828i
$162$		0			0
$163$			1.75079i			0.137132i	0.997647	+	0.0685660i	$0.0218424\pi$
$163$			1.75079i			0.137132i	−0.997647	+	0.0685660i	$0.978158\pi$
$164$	13.5482	−	0.599636i	1.05794	−	0.0468237i
$165$		0			0
$166$	7.80726	+	7.46936i	0.605961	+	0.579734i
$167$	−8.74507	−	15.1469i	−0.676714	−	1.17210i	−0.975965	−	0.217928i	$-0.930070\pi$
$167$	−8.74507	−	15.1469i	−0.676714	−	1.17210i	0.299251	−	0.954174i	$-0.403263\pi$
$168$		0			0
$169$	3.68614	−	6.38458i	0.283549	−	0.491122i
$170$	2.71519	−	0.792287i	0.208246	−	0.0607656i
$171$		0			0
$172$	8.31386	+	13.0330i	0.633926	+	0.993754i
$173$	−15.3030	−	8.83518i	−1.16346	−	0.671726i	−0.211333	−	0.977414i	$-0.567780\pi$
$173$	−15.3030	−	8.83518i	−1.16346	−	0.671726i	−0.952132	+	0.305688i	$0.901114\pi$
$174$		0			0
$175$	−1.51622	+	0.875393i	−0.114616	+	0.0661735i
$176$	2.01373	−	0.178603i	0.151790	−	0.0134627i
$177$		0			0
$178$	−16.4537	−	4.02098i	−1.23325	−	0.301385i
$179$	8.83915			0.660669			0.330334	−	0.943864i	$-0.392838\pi$
$179$	8.83915			0.660669			0.330334	+	0.943864i	$0.392838\pi$
$180$		0			0
$181$	−4.00000			−0.297318			−0.148659	−	0.988889i	$-0.547496\pi$
$181$	−4.00000			−0.297318			−0.148659	+	0.988889i	$0.547496\pi$
$182$	−4.15791	−	1.01612i	−0.308205	−	0.0753196i
$183$		0			0
$184$	−8.93580	−	1.76912i	−0.658756	−	0.130421i
$185$	−14.7446	+	8.51278i	−1.08404	+	0.625872i
$186$		0			0
$187$	0.346781	+	0.200214i	0.0253591	+	0.0146411i
$188$	−2.02163	+	1.28962i	−0.147443	+	0.0940552i
$189$		0			0
$190$	16.1168	−	4.70285i	1.16924	−	0.341181i
$191$	−7.54610	+	13.0702i	−0.546017	+	0.945728i	0.452526	+	0.891751i	$0.350523\pi$
$191$	−7.54610	+	13.0702i	−0.546017	+	0.945728i	−0.998542	+	0.0539770i	$0.982810\pi$
$192$		0			0
$193$	−3.87228	−	6.70699i	−0.278733	−	0.482780i	0.692337	−	0.721574i	$-0.256581\pi$
$193$	−3.87228	−	6.70699i	−0.278733	−	0.482780i	−0.971070	+	0.238795i	$0.923248\pi$
$194$	10.7185	+	10.2546i	0.769544	+	0.736238i
$195$		0			0
$196$	0.475083	+	10.7341i	0.0339345	+	0.766718i
$197$			23.9538i			1.70663i	0.521392	+	0.853317i	$0.325413\pi$
$197$			23.9538i			1.70663i	−0.521392	+	0.853317i	$0.674587\pi$
$198$		0			0
$199$		−	12.9073i		−	0.914973i	−0.889217	−	0.457486i	$-0.848750\pi$
$199$		−	12.9073i		−	0.914973i	0.889217	−	0.457486i	$-0.151250\pi$
$200$	1.25093	+	3.67429i	0.0884539	+	0.259812i
$201$		0			0
$202$	−1.20711	+	1.26172i	−0.0849321	+	0.0887743i
$203$	1.61030	+	2.78912i	0.113021	+	0.195758i
$204$		0			0
$205$	−8.55842	+	14.8236i	−0.597746	+	1.03533i
$206$	−0.188154	−	0.644810i	−0.0131093	−	0.0449261i
$207$		0			0
$208$	−4.00000	+	8.60485i	−0.277350	+	0.596639i
$209$	2.05842	+	1.18843i	0.142384	+	0.0822055i
$210$		0			0
$211$	15.1863	−	8.76780i	1.04547	−	0.603600i	0.124090	−	0.992271i	$-0.460399\pi$
$211$	15.1863	−	8.76780i	1.04547	−	0.603600i	0.921377	+	0.388671i	$0.127066\pi$
$212$	1.73375	−	3.33536i	0.119074	−	0.229073i
$213$		0			0
$214$	−4.21848	+	17.2618i	−0.288369	+	1.17999i
$215$	−19.5118			−1.33069
$216$		0			0
$217$	−10.3723			−0.704116
$218$	4.52868	−	18.5312i	0.306721	−	1.25509i
$219$		0			0
$220$	−1.17686	+	2.26404i	−0.0793442	+	0.152641i
$221$	−1.62772	+	0.939764i	−0.109492	+	0.0632154i
$222$		0			0
$223$	7.04069	+	4.06494i	0.471479	+	0.272209i	0.716859	−	0.697218i	$-0.245579\pi$
$223$	7.04069	+	4.06494i	0.471479	+	0.272209i	−0.245379	+	0.969427i	$0.578913\pi$
$224$	−7.13477	−	1.08724i	−0.476712	−	0.0726443i
$225$		0			0
$226$	−2.88316	−	9.88067i	−0.191785	−	0.657253i
$227$	−7.19932	+	12.4696i	−0.477835	+	0.827635i	−0.999677	−	0.0254070i	$-0.991912\pi$
$227$	−7.19932	+	12.4696i	−0.477835	+	0.827635i	0.521842	+	0.853042i	$0.325245\pi$
$228$		0			0
$229$	−1.81386	−	3.14170i	−0.119863	−	0.207609i	0.799850	−	0.600200i	$-0.204912\pi$
$229$	−1.81386	−	3.14170i	−0.119863	−	0.207609i	−0.919713	+	0.392591i	$0.871579\pi$
$230$	7.94812	−	8.30768i	0.524084	−	0.547792i
$231$		0			0
$232$	6.75893	−	2.30110i	0.443746	−	0.151075i
$233$		−	4.84630i		−	0.317491i	−0.987320	−	0.158746i	$-0.949255\pi$
$233$		−	4.84630i		−	0.317491i	0.987320	−	0.158746i	$-0.0507450\pi$
$234$		0			0
$235$		−	3.02661i		−	0.197434i
$236$	1.09453	+	24.7298i	0.0712477	+	1.60977i
$237$		0			0
$238$	−1.03292	−	0.988216i	−0.0669544	−	0.0640566i
$239$	6.02987	+	10.4440i	0.390040	+	0.675569i	0.992454	−	0.122614i	$-0.0391278\pi$
$239$	6.02987	+	10.4440i	0.390040	+	0.675569i	−0.602414	+	0.798184i	$0.705794\pi$
$240$		0			0
$241$	3.24456	−	5.61975i	0.209001	−	0.362000i	−0.742399	−	0.669958i	$-0.766312\pi$
$241$	3.24456	−	5.61975i	0.209001	−	0.362000i	0.951400	+	0.307958i	$0.0996456\pi$
$242$	14.5868	−	4.25639i	0.937674	−	0.273611i
$243$		0			0
$244$	−4.00000	+	2.55164i	−0.256074	+	0.163352i
$245$	−11.7446	−	6.78073i	−0.750333	−	0.433205i
$246$		0			0
$247$	−9.66181	+	5.57825i	−0.614766	+	0.354935i
$248$	−4.46585	+	22.5570i	−0.283582	+	1.43237i
$249$		0			0
$250$	12.5806	+	3.07446i	0.795665	+	0.194446i
$251$	11.1780			0.705551			0.352776	−	0.935708i	$-0.385238\pi$
$251$	11.1780			0.705551			0.352776	+	0.935708i	$0.385238\pi$
$252$		0			0
$253$	1.62772			0.102334
$254$	−10.5162	−	2.56997i	−0.659847	−	0.161255i
$255$		0			0
$256$	−5.43638	+	15.0481i	−0.339774	+	0.940507i
$257$	−12.9891	+	7.49927i	−0.810239	+	0.467792i	−0.847039	−	0.531531i	$-0.821617\pi$
$257$	−12.9891	+	7.49927i	−0.810239	+	0.467792i	0.0367996	+	0.999323i	$0.488284\pi$
$258$		0			0
$259$	7.45202	+	4.30243i	0.463046	+	0.267340i
$260$	−6.44121	−	10.0974i	−0.399467	−	0.626211i
$261$		0			0
$262$	10.3723	−	3.02661i	0.640802	−	0.186984i
$263$	13.9873	−	24.2267i	0.862494	−	1.49388i	−0.00701993	−	0.999975i	$-0.502235\pi$
$263$	13.9873	−	24.2267i	0.862494	−	1.49388i	0.869514	−	0.493908i	$-0.164432\pi$
$264$		0			0
$265$	2.37228	+	4.10891i	0.145728	+	0.252408i
$266$	−6.13121	−	5.86585i	−0.375929	−	0.359658i
$267$		0			0
$268$	15.4438	−	0.683534i	0.943380	−	0.0417535i
$269$		−	21.4843i		−	1.30992i	−0.755663	−	0.654961i	$-0.772685\pi$
$269$		−	21.4843i		−	1.30992i	0.755663	−	0.654961i	$-0.227315\pi$
$270$		0			0
$271$			29.9679i			1.82042i	0.414146	+	0.910211i	$0.364080\pi$
$271$			29.9679i			1.82042i	−0.414146	+	0.910211i	$0.635920\pi$
$272$	−2.59384	+	1.82085i	−0.157275	+	0.110405i
$273$		0			0
$274$	5.36834	−	5.61119i	0.324313	−	0.338984i
$275$	−0.346781	−	0.600642i	−0.0209117	−	0.0362201i
$276$		0			0
$277$	−3.18614	+	5.51856i	−0.191437	+	0.331578i	−0.945727	−	0.324963i	$-0.894648\pi$
$277$	−3.18614	+	5.51856i	−0.191437	+	0.331578i	0.754290	+	0.656541i	$0.227981\pi$
$278$	6.09442	+	20.8858i	0.365519	+	1.25265i
$279$		0			0
$280$	6.00000	−	6.85407i	0.358569	−	0.409609i
$281$	19.9307	+	11.5070i	1.18897	+	0.686450i	0.958072	−	0.286529i	$-0.0925014\pi$
$281$	19.9307	+	11.5070i	1.18897	+	0.686450i	0.230894	+	0.972979i	$0.425835\pi$
$282$		0			0
$283$	8.55691	−	4.94034i	0.508656	−	0.293673i	−0.223625	−	0.974675i	$-0.571789\pi$
$283$	8.55691	−	4.94034i	0.508656	−	0.293673i	0.732281	+	0.681003i	$0.238456\pi$
$284$	−21.0670	−	10.9508i	−1.25010	−	0.649811i
$285$		0			0
$286$	0.402528	−	1.64713i	0.0238020	−	0.0973967i
$287$	8.65099			0.510652
$288$		0			0
$289$	16.3723			0.963075
$290$	−2.13936	+	8.75415i	−0.125627	+	0.514061i
$291$		0			0
$292$	−5.98436	−	3.11072i	−0.350208	−	0.182041i
$293$	20.1861	−	11.6545i	1.17929	−	0.680862i	0.223437	−	0.974718i	$-0.428272\pi$
$293$	20.1861	−	11.6545i	1.17929	−	0.680862i	0.955850	+	0.293857i	$0.0949388\pi$
$294$		0			0
$295$	−27.0579	−	15.6219i	−1.57537	−	0.909540i
$296$	12.5652	−	14.3537i	0.730335	−	0.834294i
$297$		0			0
$298$	−5.11684	−	17.5356i	−0.296411	−	1.01581i
$299$	−3.82009	+	6.61659i	−0.220921	+	0.382647i
$300$		0			0
$301$	4.93070	+	8.54023i	0.284201	+	0.492251i
$302$	−2.95894	+	3.09279i	−0.170268	+	0.177970i
$303$		0			0
$304$	−15.3965	+	10.8082i	−0.883050	+	0.619892i
$305$		−	5.98844i		−	0.342897i
$306$		0			0
$307$		−	1.20128i		−	0.0685609i	−0.999412	−	0.0342805i	$-0.989086\pi$
$307$		−	1.20128i		−	0.0685609i	0.999412	−	0.0342805i	$-0.0109140\pi$
$308$	1.28836	−	0.0570221i	0.0734111	−	0.00324913i
$309$		0			0
$310$	−20.9714	−	20.0637i	−1.19110	−	1.13954i
$311$	−9.56773	−	16.5718i	−0.542536	−	0.939700i	−0.998758	−	0.0498340i	$-0.984131\pi$
$311$	−9.56773	−	16.5718i	−0.542536	−	0.939700i	0.456221	−	0.889866i	$-0.349203\pi$
$312$		0			0
$313$	9.24456	−	16.0121i	0.522534	−	0.905055i	−0.477123	−	0.878837i	$-0.658320\pi$
$313$	9.24456	−	16.0121i	0.522534	−	0.905055i	0.999656	−	0.0262180i	$-0.00834640\pi$
$314$	−16.1030	+	4.69882i	−0.908746	+	0.265170i
$315$		0			0
$316$	−10.6277	−	16.6602i	−0.597856	−	0.937210i
$317$	28.1644	+	16.2607i	1.58187	+	0.913293i	0.994587	+	0.103911i	$0.0331359\pi$
$317$	28.1644	+	16.2607i	1.58187	+	0.913293i	0.587283	+	0.809381i	$0.300197\pi$
$318$		0			0
$319$	−1.10489	+	0.637910i	−0.0618621	+	0.0357161i
$320$	−12.3224	−	15.9995i	−0.688846	−	0.894398i
$321$		0			0
$322$	−5.64476	−	1.37948i	−0.314570	−	0.0768753i
$323$	−3.72601			−0.207321
$324$		0			0
$325$	3.25544			0.180579
$326$	2.40520	+	0.587788i	0.133212	+	0.0325546i
$327$		0			0
$328$	3.72474	−	18.8136i	0.205664	−	1.03881i
$329$	−1.32473	+	0.764836i	−0.0730350	+	0.0421667i
$330$		0			0
$331$	−24.0254	−	13.8711i	−1.32056	−	0.762424i	−0.336739	−	0.941598i	$-0.609324\pi$
$331$	−24.0254	−	13.8711i	−1.32056	−	0.762424i	−0.983817	+	0.179174i	$0.942657\pi$
$332$	12.8824	−	8.21782i	0.707014	−	0.451012i
$333$		0			0
$334$	−23.7446	+	6.92860i	−1.29924	+	0.379116i
$335$	−9.75588	+	16.8977i	−0.533021	+	0.923219i
$336$		0			0
$337$	7.87228	+	13.6352i	0.428830	+	0.742756i	0.996770	−	0.0803144i	$-0.0255924\pi$
$337$	7.87228	+	13.6352i	0.428830	+	0.742756i	−0.567939	+	0.823071i	$0.692259\pi$
$338$	−7.53351	−	7.20745i	−0.409769	−	0.392034i
$339$		0			0
$340$	−0.176865	−	3.99609i	−0.00959184	−	0.216718i
$341$		−	4.10891i		−	0.222510i
$342$		0			0
$343$			15.7848i			0.852300i
$344$	20.6957	−	7.04593i	1.11584	−	0.379891i
$345$		0			0
$346$	−17.2753	+	18.0568i	−0.928725	+	0.970739i
$347$	3.47331	+	6.01594i	0.186457	+	0.322953i	0.944066	−	0.329755i	$-0.106966\pi$
$347$	3.47331	+	6.01594i	0.186457	+	0.322953i	−0.757610	+	0.652708i	$0.773633\pi$
$348$		0			0
$349$	2.81386	−	4.87375i	0.150622	−	0.260886i	−0.780834	−	0.624739i	$-0.785206\pi$
$349$	2.81386	−	4.87375i	0.150622	−	0.260886i	0.931456	+	0.363853i	$0.118539\pi$
$350$	0.693562	+	2.37686i	0.0370725	+	0.127049i
$351$		0			0
$352$	0.430703	−	2.82639i	0.0229566	−	0.150647i
$353$	−7.24456	−	4.18265i	−0.385589	−	0.222620i	0.294658	−	0.955603i	$-0.404794\pi$
$353$	−7.24456	−	4.18265i	−0.385589	−	0.222620i	−0.680247	+	0.732983i	$0.738128\pi$
$354$		0			0
$355$	25.9530	−	14.9840i	1.37744	−	0.795266i
$356$	−11.0479	+	21.2538i	−0.585539	+	1.12645i
$357$		0			0
$358$	2.96755	−	12.1431i	0.156840	−	0.641782i
$359$	−1.38712			−0.0732096			−0.0366048	−	0.999330i	$-0.511654\pi$
$359$	−1.38712			−0.0732096			−0.0366048	+	0.999330i	$0.511654\pi$
$360$		0			0
$361$	−3.11684			−0.164044
$362$	−1.34291	+	5.49514i	−0.0705820	+	0.288818i
$363$		0			0
$364$	−2.79185	+	5.37093i	−0.146333	+	0.281513i
$365$	7.37228	−	4.25639i	0.385883	−	0.222790i
$366$		0			0
$367$	5.52447	+	3.18955i	0.288375	+	0.166493i	0.637209	−	0.770691i	$-0.280089\pi$
$367$	5.52447	+	3.18955i	0.288375	+	0.166493i	−0.348834	+	0.937185i	$0.613422\pi$
$368$	−5.43039	+	11.6819i	−0.283079	+	0.608962i
$369$		0			0
$370$	6.74456	+	23.1138i	0.350633	+	1.20163i
$371$	1.19897	−	2.07668i	0.0622474	−	0.107816i
$372$		0			0
$373$	9.93070	+	17.2005i	0.514192	+	0.890607i	0.999864	+	0.0164662i	$0.00524158\pi$
$373$	9.93070	+	17.2005i	0.514192	+	0.890607i	−0.485672	+	0.874141i	$0.661425\pi$
$374$	0.391475	−	0.409185i	0.0202427	−	0.0211585i
$375$		0			0
$376$	1.09294	+	3.21025i	0.0563642	+	0.165556i
$377$		−	5.98844i		−	0.308420i
$378$		0			0
$379$		−	6.45364i		−	0.331501i	−0.986168	−	0.165751i	$-0.946995\pi$
$379$		−	6.45364i		−	0.331501i	0.986168	−	0.165751i	$-0.0530047\pi$
$380$	−1.04983	−	23.7200i	−0.0538553	−	1.21681i
$381$		0			0
$382$	15.4222	+	14.7548i	0.789071	+	0.754919i
$383$	−4.32550	−	7.49198i	−0.221023	−	0.382822i	0.734096	−	0.679045i	$-0.237606\pi$
$383$	−4.32550	−	7.49198i	−0.221023	−	0.382822i	−0.955119	+	0.296223i	$0.904273\pi$
$384$		0			0
$385$	−0.813859	+	1.40965i	−0.0414781	+	0.0718422i
$386$	−10.5140	+	3.06796i	−0.535148	+	0.156155i
$387$		0			0
$388$	17.6861	−	11.2822i	0.897878	−	0.572766i
$389$	−27.3030	−	15.7634i	−1.38432	−	0.799235i	−0.391649	−	0.920115i	$-0.628095\pi$
$389$	−27.3030	−	15.7634i	−1.38432	−	0.799235i	−0.992667	+	0.120879i	$0.961429\pi$
$390$		0			0
$391$	−2.20979	+	1.27582i	−0.111754	+	0.0645210i
$392$	14.9058	+	2.95106i	0.752856	+	0.149051i
$393$		0			0
$394$	32.9073	+	8.04195i	1.65785	+	0.405148i
$395$	24.9422			1.25498
$396$		0			0
$397$	−18.7446			−0.940763			−0.470381	−	0.882463i	$-0.655884\pi$
$397$	−18.7446			−0.940763			−0.470381	+	0.882463i	$0.655884\pi$
$398$	−17.7318	−	4.33334i	−0.888816	−	0.217211i
$399$		0			0
$400$	5.46766	−	0.484942i	0.273383	−	0.0242471i
$401$	−3.98913	+	2.30312i	−0.199207	+	0.115012i	−0.596286	−	0.802772i	$-0.703357\pi$
$401$	−3.98913	+	2.30312i	−0.199207	+	0.115012i	0.397078	+	0.917785i	$0.370024\pi$
$402$		0			0
$403$	16.7025	+	9.64319i	0.832011	+	0.480362i
$404$	1.32807	+	2.08191i	0.0660740	+	0.103579i
$405$		0			0
$406$	4.37228	−	1.27582i	0.216993	−	0.0633179i
$407$	−1.70438	+	2.95207i	−0.0844829	+	0.146329i
$408$		0			0
$409$	−6.87228	−	11.9031i	−0.339812	−	0.588572i	0.644585	−	0.764533i	$-0.277030\pi$
$409$	−6.87228	−	11.9031i	−0.339812	−	0.588572i	−0.984397	+	0.175960i	$0.943697\pi$
$410$	17.4912	+	16.7341i	0.863827	+	0.826441i
$411$		0			0
$412$	−0.948999	+	0.0420022i	−0.0467538	+	0.00206930i
$413$			15.7908i			0.777016i
$414$		0			0
$415$			19.2864i			0.946731i
$416$	10.4783	+	8.38403i	0.513741	+	0.411061i
$417$		0			0
$418$	2.32372	−	2.42884i	0.113657	−	0.118798i
$419$	13.4819	+	23.3513i	0.658634	+	1.14079i	0.980970	+	0.194162i	$0.0621986\pi$
$419$	13.4819	+	23.3513i	0.658634	+	1.14079i	−0.322336	+	0.946625i	$0.604468\pi$
$420$		0			0
$421$	5.30298	−	9.18504i	0.258452	−	0.447651i	−0.707376	−	0.706838i	$-0.750121\pi$
$421$	5.30298	−	9.18504i	0.258452	−	0.447651i	0.965827	+	0.259186i	$0.0834544\pi$
$422$	−6.94661	−	23.8063i	−0.338156	−	1.15887i
$423$		0			0
$424$	−4.00000	−	3.50157i	−0.194257	−	0.170051i
$425$	0.941578	+	0.543620i	0.0456732	+	0.0263695i
$426$		0			0
$427$	−2.62112	+	1.51330i	−0.126845	+	0.0732339i
$428$	22.2978	+	11.5906i	1.07780	+	0.560251i
$429$		0			0
$430$	−6.55065	+	26.8050i	−0.315901	+	1.29265i
$431$	−31.1952			−1.50262			−0.751310	−	0.659949i	$-0.770578\pi$
$431$	−31.1952			−1.50262			−0.751310	+	0.659949i	$0.770578\pi$
$432$		0			0
$433$	−8.62772			−0.414622			−0.207311	−	0.978275i	$-0.566471\pi$
$433$	−8.62772			−0.414622			−0.207311	+	0.978275i	$0.566471\pi$
$434$	−3.48227	+	14.2493i	−0.167154	+	0.683988i
$435$		0			0
$436$	−23.9374	−	12.4429i	−1.14640	−	0.595906i
$437$	−13.1168	+	7.57301i	−0.627464	+	0.362266i
$438$		0			0
$439$	−5.65357	−	3.26409i	−0.269830	−	0.155786i	0.358980	−	0.933345i	$-0.383124\pi$
$439$	−5.65357	−	3.26409i	−0.269830	−	0.155786i	−0.628810	+	0.777559i	$0.716458\pi$
$440$	2.71519	+	2.37686i	0.129442	+	0.113312i
$441$		0			0
$442$	0.744563	+	2.55164i	0.0354152	+	0.121369i
$443$	6.18850	−	10.7188i	0.294025	−	0.509265i	−0.680733	−	0.732532i	$-0.738339\pi$
$443$	6.18850	−	10.7188i	0.294025	−	0.509265i	0.974758	+	0.223266i	$0.0716719\pi$
$444$		0			0
$445$	−15.1168	−	26.1831i	−0.716607	−	1.24120i
$446$	7.94812	−	8.30768i	0.376354	−	0.393380i
$447$		0			0
$448$	−3.88898	+	9.43662i	−0.183737	+	0.445838i
$449$			19.4024i			0.915657i	0.889041	+	0.457828i	$0.151373\pi$
$449$			19.4024i			0.915657i	−0.889041	+	0.457828i	$0.848627\pi$
$450$		0			0
$451$			3.42703i			0.161373i
$452$	−14.5419	+	0.643616i	−0.683993	+	0.0302731i
$453$		0			0
$454$	14.7135	+	14.0767i	0.690540	+	0.660653i
$455$	−3.82009	−	6.61659i	−0.179088	−	0.310190i
$456$		0			0
$457$	−19.9891	+	34.6222i	−0.935052	+	1.61956i	−0.160510	+	0.987034i	$0.551314\pi$
$457$	−19.9891	+	34.6222i	−0.935052	+	1.61956i	−0.774541	+	0.632523i	$0.782019\pi$
$458$	−4.92498	+	1.43710i	−0.230129	+	0.0671511i
$459$		0			0
$460$	−8.74456	−	13.7081i	−0.407717	−	0.639145i
$461$	−0.302985	−	0.174928i	−0.0141114	−	0.00814722i	0.492928	−	0.870070i	$-0.335927\pi$
$461$	−0.302985	−	0.174928i	−0.0141114	−	0.00814722i	−0.507039	+	0.861923i	$0.669260\pi$
$462$		0			0
$463$	−4.13734	+	2.38870i	−0.192279	+	0.111012i	−0.593049	−	0.805167i	$-0.702076\pi$
$463$	−4.13734	+	2.38870i	−0.192279	+	0.111012i	0.400770	+	0.916179i	$0.368743\pi$
$464$	−0.892059	−	10.0579i	−0.0414128	−	0.466925i
$465$		0			0
$466$	−6.65777	−	1.62704i	−0.308415	−	0.0753711i
$467$	5.11313			0.236608			0.118304	−	0.992977i	$-0.462254\pi$
$467$	5.11313			0.236608			0.118304	+	0.992977i	$0.462254\pi$
$468$		0			0
$469$	9.86141			0.455357
$470$	−4.15791	−	1.01612i	−0.191790	−	0.0468700i
$471$		0			0
$472$	34.3409	+	6.79885i	1.58067	+	0.312942i
$473$	−3.38316	+	1.95327i	−0.155558	+	0.0898113i
$474$		0			0
$475$	5.58902	+	3.22682i	0.256442	+	0.148057i
$476$	−1.70438	+	1.08724i	−0.0781201	+	0.0498336i
$477$		0			0
$478$	16.3723	−	4.77739i	0.748851	−	0.218513i
$479$	6.53528	−	11.3194i	0.298605	−	0.517198i	−0.677212	−	0.735788i	$-0.736812\pi$
$479$	6.53528	−	11.3194i	0.298605	−	0.517198i	0.975817	+	0.218589i	$0.0701455\pi$
$480$		0			0
$481$	−8.00000	−	13.8564i	−0.364769	−	0.631798i
$482$	−6.63104	−	6.34404i	−0.302035	−	0.288963i
$483$		0			0
$484$	−0.950167	−	21.4681i	−0.0431894	−	0.975823i
$485$			26.4781i			1.20231i
$486$		0			0
$487$		−	42.8752i		−	1.94286i	−0.237325	−	0.971430i	$-0.576271\pi$
$487$		−	42.8752i		−	1.94286i	0.237325	−	0.971430i	$-0.423729\pi$
$488$	2.16249	+	6.35180i	0.0978915	+	0.287532i
$489$		0			0
$490$	−13.2582	+	13.8580i	−0.598946	+	0.626042i
$491$	−6.88206	−	11.9201i	−0.310583	−	0.537946i	0.667906	−	0.744246i	$-0.267191\pi$
$491$	−6.88206	−	11.9201i	−0.310583	−	0.537946i	−0.978489	+	0.206300i	$0.933858\pi$
$492$		0			0
$493$	1.00000	−	1.73205i	0.0450377	−	0.0780076i
$494$	4.41957	+	15.1460i	0.198846	+	0.681452i
$495$		0			0
$496$	29.4891	+	13.7081i	1.32410	+	0.615513i
$497$	−13.1168	−	7.57301i	−0.588371	−	0.339696i
$498$		0			0
$499$	2.96790	−	1.71352i	0.132861	−	0.0767076i	−0.432096	−	0.901828i	$-0.642226\pi$
$499$	2.96790	−	1.71352i	0.132861	−	0.0767076i	0.564958	+	0.825120i	$0.308893\pi$
$500$	8.44730	−	16.2508i	0.377775	−	0.726758i
$501$		0			0
$502$	3.75278	−	15.3562i	0.167495	−	0.685382i
$503$	−19.3236			−0.861597			−0.430799	−	0.902448i	$-0.641768\pi$
$503$	−19.3236			−0.861597			−0.430799	+	0.902448i	$0.641768\pi$
$504$		0			0
$505$	−3.11684			−0.138698
$506$	0.546471	−	2.23614i	0.0242936	−	0.0994084i
$507$		0			0
$508$	−7.06119	+	13.5842i	−0.313290	+	0.602702i
$509$	−12.8139	+	7.39809i	−0.567964	+	0.327914i	−0.756336	−	0.654183i	$-0.773012\pi$
$509$	−12.8139	+	7.39809i	−0.567964	+	0.327914i	0.188372	+	0.982098i	$0.439679\pi$
$510$		0			0
$511$	−3.72601	−	2.15121i	−0.164829	−	0.0951641i
$512$	18.8477	+	12.5205i	0.832960	+	0.553333i
$513$		0			0
$514$	5.94158	+	20.3620i	0.262072	+	0.898129i
$515$	0.599485	−	1.03834i	0.0264165	−	0.0457547i
$516$		0			0
$517$	−0.302985	−	0.524785i	−0.0133252	−	0.0230800i
$518$	8.41247	−	8.79303i	0.369623	−	0.386344i
$519$		0			0
$520$	−16.0341	+	5.45887i	−0.703141	+	0.239387i
$521$		−	26.0357i		−	1.14064i	−0.821421	−	0.570322i	$-0.806819\pi$
$521$		−	26.0357i		−	1.14064i	0.821421	−	0.570322i	$-0.193181\pi$
$522$		0			0
$523$		−	9.40571i		−	0.411283i	−0.978627	−	0.205641i	$-0.934072\pi$
$523$		−	9.40571i		−	0.411283i	0.978627	−	0.205641i	$-0.0659281\pi$
$524$	−0.675639	−	15.2654i	−0.0295154	−	0.666872i
$525$		0			0
$526$	−28.5864	−	27.3492i	−1.24643	−	1.19248i
$527$	3.22060	+	5.57825i	0.140292	+	0.242992i
$528$		0			0
$529$	6.31386	−	10.9359i	0.274516	−	0.475475i
$530$	6.44121	−	1.87953i	0.279788	−	0.0816415i
$531$		0			0
$532$	−10.1168	+	6.45364i	−0.438621	+	0.279801i
$533$	−13.9307	−	8.04290i	−0.603406	−	0.348376i
$534$		0			0
$535$	−27.4692	+	15.8593i	−1.18760	+	0.685659i
$536$	4.24589	−	21.4460i	0.183395	−	0.926324i
$537$		0			0
$538$	−29.5149	−	7.21290i	−1.27248	−	0.310970i
$539$	−2.71519			−0.116952
$540$		0			0
$541$	−8.97825			−0.386005			−0.193003	−	0.981198i	$-0.561823\pi$
$541$	−8.97825			−0.386005			−0.193003	+	0.981198i	$0.561823\pi$
$542$	41.1695	+	10.0611i	1.76838	+	0.432160i
$543$		0			0
$544$	1.63063	+	4.17469i	0.0699127	+	0.178988i
$545$	29.4891	−	17.0256i	1.26318	−	0.729295i
$546$		0			0
$547$	19.2591	+	11.1192i	0.823458	+	0.475424i	0.851608	−	0.524180i	$-0.175628\pi$
$547$	19.2591	+	11.1192i	0.823458	+	0.475424i	−0.0281494	+	0.999604i	$0.508961\pi$
$548$	−5.90627	−	9.25878i	−0.252303	−	0.395515i
$549$		0			0
$550$	−0.941578	+	0.274750i	−0.0401490	+	0.0117154i
$551$	5.93580	−	10.2811i	0.252873	−	0.437990i
$552$		0			0
$553$	−6.30298	−	10.9171i	−0.268030	−	0.464242i
$554$	6.51164	+	6.22981i	0.276653	+	0.264679i
$555$		0			0
$556$	30.7387	−	1.36048i	1.30361	−	0.0576971i
$557$		−	7.22316i		−	0.306055i	−0.988222	−	0.153027i	$-0.951098\pi$
$557$		−	7.22316i		−	0.306055i	0.988222	−	0.153027i	$-0.0489023\pi$
$558$		0			0
$559$		−	18.3365i		−	0.775549i
$560$	−7.40165	−	10.5438i	−0.312777	−	0.445558i
$561$		0			0
$562$	22.4994	−	23.5173i	0.949082	−	0.992017i
$563$	7.89288	+	13.6709i	0.332645	+	0.576158i	0.983030	−	0.183447i	$-0.0587255\pi$
$563$	7.89288	+	13.6709i	0.332645	+	0.576158i	−0.650384	+	0.759605i	$0.725392\pi$
$564$		0			0
$565$	9.18614	−	15.9109i	0.386464	−	0.669375i
$566$	−3.91416	−	13.4140i	−0.164525	−	0.563831i
$567$		0			0
$568$	−22.1168	+	25.2651i	−0.928002	+	1.06010i
$569$	21.9891	+	12.6954i	0.921832	+	0.532220i	0.884219	−	0.467072i	$-0.154691\pi$
$569$	21.9891	+	12.6954i	0.921832	+	0.532220i	0.0376130	+	0.999292i	$0.488025\pi$
$570$		0			0
$571$	−3.66146	+	2.11395i	−0.153227	+	0.0884659i	−0.574653	−	0.818397i	$-0.694863\pi$
$571$	−3.66146	+	2.11395i	−0.153227	+	0.0884659i	0.421426	+	0.906863i	$0.361530\pi$
$572$	−2.12766	−	1.10597i	−0.0889619	−	0.0462431i
$573$		0			0
$574$	2.90438	−	11.8846i	0.121227	−	0.496054i
$575$	4.41957			0.184309
$576$		0			0
$577$	31.8397			1.32550			0.662751	−	0.748840i	$-0.269389\pi$
$577$	31.8397			1.32550			0.662751	+	0.748840i	$0.269389\pi$
$578$	5.49664	−	22.4920i	0.228630	−	0.935544i
$579$		0			0
$580$	11.3081	+	5.87803i	0.469542	+	0.244072i
$581$	8.44158	−	4.87375i	0.350216	−	0.202197i
$582$		0			0
$583$	0.822662	+	0.474964i	0.0340712	+	0.0196710i
$584$	−6.28258	+	7.17687i	−0.259975	+	0.296981i
$585$		0			0
$586$	−9.23369	−	31.6442i	−0.381440	−	1.30721i
$587$	−1.95708	+	3.38977i	−0.0807774	+	0.139911i	−0.903584	−	0.428411i	$-0.859074\pi$
$587$	−1.95708	+	3.38977i	−0.0807774	+	0.139911i	0.822807	+	0.568321i	$0.192407\pi$
$588$		0			0
$589$	19.1168	+	33.1113i	0.787696	+	1.36433i
$590$	−30.5452	+	31.9270i	−1.25753	+	1.31441i
$591$		0			0
$592$	−15.5005	−	22.0808i	−0.637066	−	0.907515i
$593$			8.80773i			0.361690i	0.983512	+	0.180845i	$0.0578833\pi$
$593$			8.80773i			0.361690i	−0.983512	+	0.180845i	$0.942117\pi$
$594$		0			0
$595$		−	2.55164i		−	0.104607i
$596$	−25.8080	+	1.14225i	−1.05714	+	0.0467883i
$597$		0			0
$598$	7.80726	+	7.46936i	0.319263	+	0.305445i
$599$	0.0940770	+	0.162946i	0.00384388	+	0.00665780i	0.867941	−	0.496667i	$-0.165443\pi$
$599$	0.0940770	+	0.162946i	0.00384388	+	0.00665780i	−0.864097	+	0.503325i	$0.832110\pi$
$600$		0			0
$601$	−7.98913	+	13.8376i	−0.325883	+	0.564446i	−0.981691	−	0.190482i	$-0.938995\pi$
$601$	−7.98913	+	13.8376i	−0.325883	+	0.564446i	0.655807	+	0.754928i	$0.272328\pi$
$602$	13.3878	−	3.90653i	0.545647	−	0.159218i
$603$		0			0
$604$	3.25544	+	5.10328i	0.132462	+	0.207650i
$605$	23.4891	+	13.5615i	0.954969	+	0.551351i
$606$		0			0
$607$	3.44378	−	1.98827i	0.139779	−	0.0807013i	−0.428480	−	0.903551i	$-0.640951\pi$
$607$	3.44378	−	1.98827i	0.139779	−	0.0807013i	0.568259	+	0.822850i	$0.307617\pi$
$608$	9.67909	+	24.7801i	0.392539	+	1.00497i
$609$		0			0
$610$	−8.22683	−	2.01049i	−0.333095	−	0.0814023i
$611$	2.84429			0.115068
$612$		0			0
$613$	4.23369			0.170997			0.0854985	−	0.996338i	$-0.472752\pi$
$613$	4.23369			0.170997			0.0854985	+	0.996338i	$0.472752\pi$
$614$	−1.65031	−	0.403305i	−0.0666010	−	0.0162761i
$615$		0			0
$616$	0.354202	−	1.78907i	0.0142712	−	0.0720838i
$617$	4.24456	−	2.45060i	0.170880	−	0.0986574i	−0.412121	−	0.911129i	$-0.635212\pi$
$617$	4.24456	−	2.45060i	0.170880	−	0.0986574i	0.583001	+	0.812472i	$0.301879\pi$
$618$		0			0
$619$	8.08103	+	4.66559i	0.324804	+	0.187526i	0.653532	−	0.756899i	$-0.273287\pi$
$619$	8.08103	+	4.66559i	0.324804	+	0.187526i	−0.328728	+	0.944425i	$0.606620\pi$
$620$	−34.6040	+	22.0742i	−1.38973	+	0.886522i
$621$		0			0
$622$	−25.9783	+	7.58039i	−1.04163	+	0.303946i
$623$	−7.64018	+	13.2332i	−0.306097	+	0.530176i
$624$		0			0
$625$	14.9891	+	25.9619i	0.599565	+	1.03848i
$626$	−18.8935	−	18.0757i	−0.755135	−	0.722452i
$627$		0			0
$628$	1.04893	+	23.6996i	0.0418569	+	0.945717i
$629$		−	5.34363i		−	0.213064i
$630$		0			0
$631$			42.8752i			1.70683i	0.521228	+	0.853417i	$0.325474\pi$
$631$			42.8752i			1.70683i	−0.521228	+	0.853417i	$0.674526\pi$
$632$	−26.4556	+	9.00690i	−1.05235	+	0.358275i
$633$		0			0
$634$	31.7943	−	33.2326i	1.26271	−	1.31984i
$635$	−9.66181	−	16.7347i	−0.383417	−	0.664098i
$636$		0			0
$637$	6.37228	−	11.0371i	0.252479	−	0.437306i
$638$	0.505408	+	1.73205i	0.0200093	+	0.0685725i
$639$		0			0
$640$	−26.1168	+	11.5569i	−1.03236	+	0.456827i
$641$	−18.1277	−	10.4660i	−0.716002	−	0.413384i	0.0972775	−	0.995257i	$-0.468987\pi$
$641$	−18.1277	−	10.4660i	−0.716002	−	0.413384i	−0.813279	+	0.581873i	$0.802320\pi$
$642$		0			0
$643$	−31.1307	+	17.9733i	−1.22767	+	0.708798i	−0.966543	−	0.256506i	$-0.917429\pi$
$643$	−31.1307	+	17.9733i	−1.22767	+	0.708798i	−0.261131	+	0.965303i	$0.584095\pi$
$644$	−3.79021	+	7.29156i	−0.149355	+	0.287328i
$645$		0			0
$646$	−1.25093	+	5.11874i	−0.0492171	+	0.201394i
$647$	46.0993			1.81235			0.906174	−	0.422904i	$-0.138989\pi$
$647$	46.0993			1.81235			0.906174	+	0.422904i	$0.138989\pi$
$648$		0			0
$649$	−6.25544			−0.245547
$650$	1.09294	−	4.47227i	0.0428687	−	0.175417i
$651$		0			0
$652$	1.61499	−	3.10690i	0.0632479	−	0.121675i
$653$	−3.81386	+	2.20193i	−0.149248	+	0.0861683i	−0.572764	−	0.819720i	$-0.694129\pi$
$653$	−3.81386	+	2.20193i	−0.149248	+	0.0861683i	0.423516	+	0.905888i	$0.360796\pi$
$654$		0			0
$655$	16.7025	+	9.64319i	0.652621	+	0.376791i
$656$	−24.5954	−	11.4333i	−0.960288	−	0.446394i
$657$		0			0
$658$	0.605969	+	2.07668i	0.0236231	+	0.0809573i
$659$	−6.02987	+	10.4440i	−0.234891	+	0.406842i	−0.959241	−	0.282590i	$-0.908807\pi$
$659$	−6.02987	+	10.4440i	−0.234891	+	0.406842i	0.724350	+	0.689432i	$0.242140\pi$
$660$		0			0
$661$	−7.81386	−	13.5340i	−0.303924	−	0.526412i	0.673097	−	0.739554i	$-0.264964\pi$
$661$	−7.81386	−	13.5340i	−0.303924	−	0.526412i	−0.977021	+	0.213142i	$0.931630\pi$
$662$	−27.1219	+	28.3489i	−1.05412	+	1.10181i
$663$		0			0
$664$	−6.96454	−	20.4566i	−0.270276	−	0.793871i
$665$		−	15.1460i		−	0.587338i
$666$		0			0
$667$		−	8.12989i		−	0.314791i
$668$	1.54669	+	34.9461i	0.0598434	+	1.35210i
$669$		0			0
$670$	19.9385	+	19.0755i	0.770290	+	0.736952i
$671$	−0.599485	−	1.03834i	−0.0231429	−	0.0400846i
$672$		0			0
$673$	−14.9307	+	25.8607i	−0.575536	+	0.996858i	0.420447	+	0.907317i	$0.361873\pi$
$673$	−14.9307	+	25.8607i	−0.575536	+	0.996858i	−0.995983	+	0.0895410i	$0.971460\pi$
$674$	21.3748	−	6.23711i	0.823326	−	0.240244i
$675$		0			0
$676$	−12.4307	+	7.92967i	−0.478104	+	0.304987i
$677$	3.04755	+	1.75950i	0.117127	+	0.0676232i	0.557419	−	0.830231i	$-0.311792\pi$
$677$	3.04755	+	1.75950i	0.117127	+	0.0676232i	−0.440292	+	0.897855i	$0.645125\pi$
$678$		0			0
$679$	11.5894	−	6.69112i	0.444759	−	0.256782i
$680$	−5.54915	−	1.09863i	−0.212800	−	0.0421304i
$681$		0			0
$682$	−5.64476	−	1.37948i	−0.216149	−	0.0528229i
$683$	−20.0172			−0.765936			−0.382968	−	0.923762i	$-0.625098\pi$
$683$	−20.0172			−0.765936			−0.382968	+	0.923762i	$0.625098\pi$
$684$		0			0
$685$	13.8614			0.529617
$686$	21.6849	+	5.29941i	0.827935	+	0.202332i
$687$		0			0
$688$	−2.73146	−	30.7969i	−0.104136	−	1.17412i
$689$	−3.86141	+	2.22938i	−0.147108	+	0.0849328i
$690$		0			0
$691$	−17.3961	−	10.0436i	−0.661777	−	0.382077i	0.131177	−	0.991359i	$-0.458125\pi$
$691$	−17.3961	−	10.0436i	−0.661777	−	0.382077i	−0.792954	+	0.609282i	$0.791458\pi$
$692$	19.0064	+	29.7947i	0.722513	+	1.13263i
$693$		0			0
$694$	9.43070	−	2.75186i	0.357985	−	0.104459i
$695$	−19.4177	+	33.6324i	−0.736555	+	1.27575i
$696$		0			0
$697$	−2.68614	−	4.65253i	−0.101745	−	0.176227i
$698$	−5.75079	−	5.50189i	−0.217671	−	0.208250i
$699$		0			0
$700$	3.49815	−	0.154826i	0.132217	−	0.00585187i
$701$		−	32.7615i		−	1.23738i	−0.785634	−	0.618692i	$-0.787663\pi$
$701$		−	32.7615i		−	1.23738i	0.785634	−	0.618692i	$-0.212337\pi$
$702$		0			0
$703$		−	31.7187i		−	1.19629i
$704$	−3.73826	−	1.54059i	−0.140891	−	0.0580633i
$705$		0			0
$706$	−8.17827	+	8.54824i	−0.307793	+	0.321717i
$707$	0.787639	+	1.36423i	0.0296222	+	0.0513072i
$708$		0			0
$709$	−11.9307	+	20.6646i	−0.448067	+	0.776075i	−0.998260	−	0.0589626i	$-0.981221\pi$
$709$	−11.9307	+	20.6646i	−0.448067	+	0.776075i	0.550193	+	0.835037i	$0.314554\pi$
$710$	−11.8716	−	40.6844i	−0.445533	−	1.52686i
$711$		0			0
$712$	25.4891	+	22.3130i	0.955245	+	0.836215i
$713$	22.6753	+	13.0916i	0.849195	+	0.490283i
$714$		0			0
$715$	2.62112	−	1.51330i	0.0980242	−	0.0565943i
$716$	−15.6857	−	8.15356i	−0.586202	−	0.304713i
$717$		0			0
$718$	−0.465697	+	1.90561i	−0.0173797	+	0.0711168i
$719$	16.2912			0.607558			0.303779	−	0.952743i	$-0.401752\pi$
$719$	16.2912			0.607558			0.303779	+	0.952743i	$0.401752\pi$
$720$		0			0
$721$	−0.605969			−0.0225675
$722$	−1.04641	+	4.28187i	−0.0389434	+	0.159355i
$723$		0			0
$724$	7.09829	+	3.68975i	0.263806	+	0.137128i
$725$	−3.00000	+	1.73205i	−0.111417	+	0.0643268i
$726$		0			0
$727$	32.9937	+	19.0489i	1.22367	+	0.706485i	0.965698	−	0.259668i	$-0.0836133\pi$
$727$	32.9937	+	19.0489i	1.22367	+	0.706485i	0.257969	+	0.966153i	$0.416947\pi$
$728$	6.44121	+	5.63858i	0.238727	+	0.208980i
$729$		0			0
$730$	−3.37228	−	11.5569i	−0.124814	−	0.427741i
$731$	3.06198	−	5.30350i	0.113251	−	0.196157i
$732$		0			0
$733$	−0.186141	−	0.322405i	−0.00687526	−	0.0119083i	0.862567	−	0.505942i	$-0.168855\pi$
$733$	−0.186141	−	0.322405i	−0.00687526	−	0.0119083i	−0.869443	+	0.494034i	$0.835522\pi$
$734$	6.23648	−	6.51861i	0.230193	−	0.240606i
$735$		0			0
$736$	14.2253	+	11.3821i	0.524352	+	0.419551i
$737$			3.90653i			0.143899i
$738$		0			0
$739$			6.45364i			0.237401i	0.992930	+	0.118700i	$0.0378728\pi$
$739$			6.45364i			0.237401i	−0.992930	+	0.118700i	$0.962127\pi$
$740$	34.0178	−	1.50561i	1.25052	−	0.0553473i
$741$		0			0
$742$	−2.45038	−	2.34433i	−0.0899563	−	0.0860630i
$743$	10.5785	+	18.3226i	0.388089	+	0.672190i	0.992193	−	0.124716i	$-0.0398019\pi$
$743$	10.5785	+	18.3226i	0.388089	+	0.672190i	−0.604103	+	0.796906i	$0.706469\pi$
$744$		0			0
$745$	16.3030	−	28.2376i	0.597295	−	1.03455i
$746$	26.9638	−	7.86797i	0.987215	−	0.288067i
$747$		0			0
$748$	−0.430703	−	0.675178i	−0.0157481	−	0.0246870i
$749$	13.8832	+	8.01544i	0.507279	+	0.292878i
$750$		0			0
$751$	18.7832	−	10.8445i	0.685408	−	0.395721i	−0.116481	−	0.993193i	$-0.537162\pi$
$751$	18.7832	−	10.8445i	0.685408	−	0.395721i	0.801890	+	0.597472i	$0.203828\pi$
$752$	4.77713	−	0.423696i	0.174204	−	0.0154506i
$753$		0			0
$754$	−8.22683	−	2.01049i	−0.299604	−	0.0732177i
$755$	−7.64018			−0.278054
$756$		0			0
$757$	14.0000			0.508839			0.254419	−	0.967094i	$-0.418116\pi$
$757$	14.0000			0.508839			0.254419	+	0.967094i	$0.418116\pi$
$758$	−8.86592	−	2.16667i	−0.322025	−	0.0786970i
$759$		0			0
$760$	−32.9386	−	6.52122i	−1.19481	−	0.236549i
$761$	−15.0475	+	8.68771i	−0.545473	+	0.314929i	−0.747294	−	0.664493i	$-0.768647\pi$
$761$	−15.0475	+	8.68771i	−0.545473	+	0.314929i	0.201821	+	0.979422i	$0.435314\pi$
$762$		0			0
$763$	−14.9040	−	8.60485i	−0.539563	−	0.311517i
$764$	25.4476	−	16.2333i	0.920661	−	0.587299i
$765$		0			0
$766$	−11.7446	+	3.42703i	−0.424348	+	0.123824i
$767$	14.6809	−	25.4280i	0.530095	−	0.918152i
$768$		0			0
$769$	−4.04755	−	7.01056i	−0.145958	−	0.252807i	0.783772	−	0.621049i	$-0.213293\pi$
$769$	−4.04755	−	7.01056i	−0.145958	−	0.252807i	−0.929730	+	0.368242i	$0.879960\pi$
$770$	1.66332	+	1.59133i	0.0599417	+	0.0573474i
$771$		0			0
$772$	0.684870	+	15.4740i	0.0246490	+	0.556921i
$773$		−	0.699713i		−	0.0251669i	−0.999921	−	0.0125835i	$-0.995994\pi$
$773$		−	0.699713i		−	0.0251669i	0.999921	−	0.0125835i	$-0.00400555\pi$
$774$		0			0
$775$		−	11.1565i		−	0.400753i
$776$	−9.56155	−	28.0847i	−0.343240	−	1.00818i
$777$		0			0
$778$	−30.8219	+	32.2162i	−1.10502	+	1.15501i
$779$	−15.9444	−	27.6165i	−0.571267	−	0.989463i
$780$		0			0
$781$	3.00000	−	5.19615i	0.107348	−	0.185933i
$782$	1.01082	+	3.46410i	0.0361467	+	0.123876i
$783$		0			0
$784$	9.05842	−	19.4866i	0.323515	−	0.695950i
$785$	−25.9307	−	14.9711i	−0.925506	−	0.534341i
$786$		0			0
$787$	−30.0903	+	17.3727i	−1.07260	+	0.619268i	−0.928892	−	0.370351i	$-0.879237\pi$
$787$	−30.0903	+	17.3727i	−1.07260	+	0.619268i	−0.143712	+	0.989620i	$0.545904\pi$
$788$	22.0958	−	42.5077i	0.787132	−	1.51427i
$789$		0			0
$790$	8.37379	−	34.2652i	0.297926	−	1.21910i
$791$	−9.28550			−0.330154
$792$		0			0
$793$	5.62772			0.199846
$794$	−6.29308	+	25.7510i	−0.223333	+	0.913869i
$795$		0			0
$796$	−11.9062	+	22.9049i	−0.422003	+	0.811843i
$797$	−20.6970	+	11.9494i	−0.733126	+	0.423270i	−0.819565	−	0.572987i	$-0.805785\pi$
$797$	−20.6970	+	11.9494i	−0.733126	+	0.423270i	0.0864387	+	0.996257i	$0.472451\pi$
$798$		0			0
$799$	0.822662	+	0.474964i	0.0291037	+	0.0168030i
$800$	1.16944	−	7.67420i	0.0413461	−	0.271324i
$801$		0			0
$802$	1.82473	+	6.25343i	0.0644336	+	0.220816i
$803$	0.852189	−	1.47603i	0.0300731	−	0.0520881i
$804$		0			0
$805$	−5.18614	−	8.98266i	−0.182787	−	0.316597i
$806$	18.8552	−	19.7082i	0.664145	−	0.694190i
$807$		0			0
$808$	3.30596	−	1.12553i	0.116303	−	0.0395960i
$809$			35.8381i			1.26000i	0.776595	+	0.630000i	$0.216945\pi$
$809$			35.8381i			1.26000i	−0.776595	+	0.630000i	$0.783055\pi$
$810$		0			0
$811$			1.20128i			0.0421828i	0.999778	+	0.0210914i	$0.00671410\pi$
$811$			1.20128i			0.0421828i	−0.999778	+	0.0210914i	$0.993286\pi$
$812$	−0.284805	−	6.43491i	−0.00999471	−	0.225821i
$813$		0			0
$814$	3.48330	+	3.33254i	0.122090	+	0.116806i
$815$	2.20979	+	3.82746i	0.0774054	+	0.134070i
$816$		0			0
$817$	18.1753	−	31.4805i	0.635872	−	1.10136i
$818$	−18.6596	+	5.44482i	−0.652417	+	0.190374i
$819$		0			0
$820$	28.8614	−	18.4110i	1.00788	−	0.642940i
$821$	15.8139	+	9.13014i	0.551907	+	0.318644i	0.749891	−	0.661561i	$-0.230106\pi$
$821$	15.8139	+	9.13014i	0.551907	+	0.318644i	−0.197983	+	0.980205i	$0.563439\pi$
$822$		0			0
$823$	12.1538	−	7.01701i	0.423656	−	0.244598i	−0.272984	−	0.962018i	$-0.588011\pi$
$823$	12.1538	−	7.01701i	0.423656	−	0.244598i	0.696640	+	0.717421i	$0.254677\pi$
$824$	−0.260904	+	1.31782i	−0.00908902	+	0.0459085i
$825$		0			0
$826$	21.6932	+	5.30143i	0.754804	+	0.184460i
$827$	−47.4864			−1.65126			−0.825632	−	0.564210i	$-0.809181\pi$
$827$	−47.4864			−1.65126			−0.825632	+	0.564210i	$0.809181\pi$
$828$		0			0
$829$	−48.2337			−1.67523			−0.837613	−	0.546265i	$-0.816049\pi$
$829$	−48.2337			−1.67523			−0.837613	+	0.546265i	$0.816049\pi$
$830$	26.4954	+	6.47498i	0.919667	+	0.224750i
$831$		0			0
$832$	15.0357	−	11.5802i	0.521270	−	0.401471i
$833$	3.68614	−	2.12819i	0.127717	−	0.0737376i
$834$		0			0
$835$	−38.2359	−	22.0755i	−1.32321	−	0.763954i
$836$	−2.55657	−	4.00772i	−0.0884207	−	0.138610i
$837$		0			0
$838$	36.6060	−	10.6815i	1.26453	−	0.368987i
$839$	21.3102	−	36.9104i	0.735711	−	1.27429i	−0.218700	−	0.975792i	$-0.570182\pi$
$839$	21.3102	−	36.9104i	0.735711	−	1.27429i	0.954411	−	0.298496i	$-0.0964850\pi$
$840$		0			0
$841$	−11.3139	−	19.5962i	−0.390133	−	0.675730i
$842$	−10.8379	−	10.3688i	−0.373499	−	0.357334i
$843$		0			0
$844$	−35.0369	+	1.55071i	−1.20602	+	0.0533778i
$845$		−	18.6101i		−	0.640208i
$846$		0			0
$847$		−	13.7081i		−	0.471017i
$848$	−6.15332	+	4.31957i	−0.211306	+	0.148334i
$849$		0			0
$850$	1.06293	−	1.11102i	0.0364583	−	0.0381076i
$851$	−10.8608	−	18.8114i	−0.372303	−	0.644847i
$852$		0			0
$853$	−22.3030	+	38.6299i	−0.763640	+	1.32266i	0.177323	+	0.984153i	$0.443256\pi$
$853$	−22.3030	+	38.6299i	−0.763640	+	1.32266i	−0.940963	+	0.338510i	$0.890077\pi$
$854$	1.19897	+	4.10891i	0.0410279	+	0.140604i
$855$		0			0
$856$	23.4090	−	26.7411i	0.800102	−	0.913992i
$857$	−32.5367	−	18.7851i	−1.11143	−	0.641685i	−0.172232	−	0.985056i	$-0.555098\pi$
$857$	−32.5367	−	18.7851i	−1.11143	−	0.641685i	−0.939200	+	0.343371i	$0.888431\pi$
$858$		0			0
$859$	−1.58077	+	0.912661i	−0.0539353	+	0.0311396i	−0.526725	−	0.850036i	$-0.676580\pi$
$859$	−1.58077	+	0.912661i	−0.0539353	+	0.0311396i	0.472790	+	0.881175i	$0.343247\pi$
$860$	34.6251	+	17.9984i	1.18070	+	0.613740i
$861$		0			0
$862$	−10.4731	+	42.8555i	−0.356716	+	1.45967i
$863$	40.0344			1.36279			0.681393	−	0.731918i	$-0.261375\pi$
$863$	40.0344			1.36279			0.681393	+	0.731918i	$0.261375\pi$
$864$		0			0
$865$	−44.6060			−1.51665
$866$	−2.89657	+	11.8526i	−0.0984294	+	0.402769i
$867$		0			0
$868$	18.4064	+	9.56778i	0.624753	+	0.324752i
$869$	4.32473	−	2.49689i	0.146707	−	0.0847011i
$870$		0			0
$871$	−15.8798	−	9.16823i	−0.538068	−	0.310654i
$872$	−25.1303	+	28.7075i	−0.851020	+	0.972158i
$873$		0			0
$874$	6.00000	+	20.5622i	0.202953	+	0.695527i
$875$	5.84172	−	10.1182i	0.197486	−	0.342056i
$876$		0			0
$877$	−10.8139	−	18.7302i	−0.365158	−	0.632472i	0.623643	−	0.781709i	$-0.285652\pi$
$877$	−10.8139	−	18.7302i	−0.365158	−	0.632472i	−0.988802	+	0.149237i	$0.952318\pi$
$878$	−6.38222	+	6.67094i	−0.215389	+	0.225133i
$879$		0			0
$880$	4.17686	−	2.93212i	0.140802	−	0.0988416i
$881$			52.9562i			1.78414i	0.451898	+	0.892070i	$0.350747\pi$
$881$			52.9562i			1.78414i	−0.451898	+	0.892070i	$0.649253\pi$
$882$		0			0
$883$			20.0127i			0.673481i	0.941597	+	0.336741i	$0.109325\pi$
$883$			20.0127i			0.673481i	−0.941597	+	0.336741i	$0.890675\pi$
$884$	3.75538	−	0.166211i	0.126307	−	0.00559028i
$885$		0			0
$886$	−12.6477	−	12.1003i	−0.424907	−	0.406517i
$887$	9.75588	+	16.8977i	0.327571	+	0.567369i	0.982029	−	0.188729i	$-0.0604368\pi$
$887$	9.75588	+	16.8977i	0.327571	+	0.567369i	−0.654459	+	0.756098i	$0.727103\pi$
$888$		0			0
$889$	−4.88316	+	8.45787i	−0.163776	+	0.283668i
$890$	−41.0452	+	11.9769i	−1.37584	+	0.401466i
$891$		0			0
$892$	−8.74456	−	13.7081i	−0.292790	−	0.458982i
$893$	4.88316	+	2.81929i	0.163409	+	0.0943440i
$894$		0			0
$895$	19.3236	−	11.1565i	0.645917	−	0.372920i
$896$	11.6583	+	8.51076i	0.389475	+	0.284325i
$897$		0			0
$898$	26.6548	+	6.51394i	0.889481	+	0.217373i
$899$	−20.5226			−0.684467
$900$		0			0
$901$	−1.48913			−0.0496100
$902$	4.70801	+	1.15055i	0.156760	+	0.0383092i
$903$		0			0
$904$	−3.99793	+	20.1935i	−0.132969	+	0.671626i
$905$	−8.74456	+	5.04868i	−0.290679	+	0.167824i
$906$		0			0
$907$	25.8884	+	14.9467i	0.859611	+	0.496297i	0.863882	−	0.503694i	$-0.168026\pi$
$907$	25.8884	+	14.9467i	0.859611	+	0.496297i	−0.00427097	+	0.999991i	$0.501359\pi$
$908$	24.2781	−	15.4873i	0.805698	−	0.513963i
$909$		0			0
$910$	−10.3723	+	3.02661i	−0.343838	+	0.100331i
$911$	−17.9015	+	31.0063i	−0.593102	+	1.02728i	0.400710	+	0.916205i	$0.368764\pi$
$911$	−17.9015	+	31.0063i	−0.593102	+	1.02728i	−0.993812	+	0.111078i	$0.964570\pi$
$912$		0			0
$913$	1.93070	+	3.34408i	0.0638970	+	0.110673i
$914$	40.8525	+	39.0844i	1.35128	+	1.29280i
$915$		0			0
$916$	0.320808	+	7.24834i	0.0105998	+	0.239492i
$917$		−	9.74749i		−	0.321891i
$918$		0			0
$919$			36.9711i			1.21956i	0.792570	+	0.609781i	$0.208743\pi$
$919$			36.9711i			1.21956i	−0.792570	+	0.609781i	$0.791257\pi$
$920$	−21.7678	+	7.41094i	−0.717664	+	0.244332i
$921$		0			0
$922$	−0.342034	+	0.357508i	−0.0112643	+	0.0117739i
$923$	14.0814	+	24.3897i	0.463494	+	0.802796i
$924$		0			0
$925$	−4.62772	+	8.01544i	−0.152158	+	0.263546i
$926$	1.89253	+	6.48577i	0.0621925	+	0.213136i
$927$		0			0
$928$	−14.1168	−	2.15121i	−0.463408	−	0.0706170i
$929$	−16.0693	−	9.27761i	−0.527217	−	0.304389i	0.212666	−	0.977125i	$-0.431785\pi$
$929$	−16.0693	−	9.27761i	−0.527217	−	0.304389i	−0.739882	+	0.672736i	$0.765119\pi$
$930$		0			0
$931$	21.8802	−	12.6325i	0.717094	−	0.414014i
$932$	−4.47040	+	8.60011i	−0.146433	+	0.281706i
$933$		0			0
$934$	1.71662	−	7.02435i	0.0561697	−	0.229844i
$935$	1.01082			0.0330572
$936$		0			0
$937$	45.7228			1.49370			0.746850	−	0.664993i	$-0.231565\pi$
$937$	45.7228			1.49370			0.746850	+	0.664993i	$0.231565\pi$
$938$	3.31075	−	13.5475i	0.108100	−	0.442340i
$939$		0			0
$940$	−2.79185	+	5.37093i	−0.0910602	+	0.175181i
$941$	−11.6970	+	6.75327i	−0.381312	+	0.220150i	−0.678389	−	0.734703i	$-0.737322\pi$
$941$	−11.6970	+	6.75327i	−0.381312	+	0.220150i	0.297077	+	0.954854i	$0.403988\pi$
$942$		0			0
$943$	−18.9123	−	10.9190i	−0.615869	−	0.355572i
$944$	20.8694	−	44.8945i	0.679240	−	1.46119i
$945$		0			0
$946$	1.54755	+	5.30350i	0.0503151	+	0.172432i
$947$	3.28515	−	5.69005i	0.106753	−	0.184902i	−0.807700	−	0.589594i	$-0.799288\pi$
$947$	3.28515	−	5.69005i	0.106753	−	0.184902i	0.914453	+	0.404692i	$0.132621\pi$
$948$		0			0
$949$	4.00000	+	6.92820i	0.129845	+	0.224899i
$950$	6.30935	−	6.59477i	0.204702	−	0.213963i
$951$		0			0
$952$	0.921427	+	2.70647i	0.0298636	+	0.0877171i
$953$			10.2997i			0.333641i	0.985987	+	0.166821i	$0.0533500\pi$
$953$			10.2997i			0.333641i	−0.985987	+	0.166821i	$0.946650\pi$
$954$		0			0
$955$			38.0978i			1.23282i
$956$	−1.06647	−	24.0959i	−0.0344922	−	0.779317i
$957$		0			0
$958$	−13.3564	−	12.7783i	−0.431526	−	0.412849i
$959$	−3.50283	−	6.06709i	−0.113112	−	0.195916i
$960$		0			0
$961$	17.5475	−	30.3932i	0.566050	−	0.980427i
$962$	−21.7216	+	6.33830i	−0.700331	+	0.204355i
$963$		0			0
$964$	−10.9416	+	6.97975i	−0.352404	+	0.224802i
$965$	−16.9307	−	9.77495i	−0.545019	−	0.314667i
$966$		0			0
$967$	40.5748	−	23.4259i	1.30480	−	0.753325i	0.323574	−	0.946203i	$-0.395115\pi$
$967$	40.5748	−	23.4259i	1.30480	−	0.753325i	0.981223	+	0.192878i	$0.0617821\pi$
$968$	−29.8116	−	5.90213i	−0.958180	−	0.189702i
$969$		0			0
$970$	36.3752	+	8.88945i	1.16794	+	0.285423i
$971$	37.0019			1.18745			0.593724	−	0.804669i	$-0.297657\pi$
$971$	37.0019			1.18745			0.593724	+	0.804669i	$0.297657\pi$
$972$		0			0
$973$	19.6277			0.629236
$974$	−58.9013	−	14.3944i	−1.88732	−	0.461227i
$975$		0			0
$976$	9.45202	−	0.838325i	0.302552	−	0.0268341i
$977$	47.3614	−	27.3441i	1.51523	−	0.874816i	0.515385	−	0.856959i	$-0.327649\pi$
$977$	47.3614	−	27.3441i	1.51523	−	0.874816i	0.999841	−	0.0178572i	$-0.00568444\pi$
$978$		0			0
$979$	−5.24224	−	3.02661i	−0.167543	−	0.0967307i
$980$	14.5868	+	22.8665i	0.465958	+	0.730444i
$981$		0			0
$982$	−18.6861	+	5.45257i	−0.596299	+	0.173998i
$983$	−17.2079	+	29.8050i	−0.548847	+	0.950631i	0.449507	+	0.893277i	$0.351600\pi$
$983$	−17.2079	+	29.8050i	−0.548847	+	0.950631i	−0.998354	+	0.0573540i	$0.981734\pi$
$984$		0			0
$985$	30.2337	+	52.3663i	0.963325	+	1.66853i
$986$	−2.04374	−	1.95528i	−0.0650859	−	0.0622689i
$987$		0			0
$988$	22.2912	−	0.986595i	0.709177	−	0.0313878i
$989$		−	24.8935i		−	0.791568i
$990$		0			0
$991$			7.65492i			0.243167i	0.992581	+	0.121583i	$0.0387972\pi$
$991$			7.65492i			0.243167i	−0.992581	+	0.121583i	$0.961203\pi$
$992$	28.7324	−	35.9095i	0.912254	−	1.14013i
$993$		0			0
$994$	−14.8074	+	15.4773i	−0.469662	+	0.490909i
$995$	−16.2912	−	28.2171i	−0.516465	−	0.894543i
$996$		0			0
$997$	12.0693	−	20.9046i	0.382238	−	0.662056i	−0.609143	−	0.793060i	$-0.708487\pi$
$997$	12.0693	−	20.9046i	0.382238	−	0.662056i	0.991382	+	0.131004i	$0.0418200\pi$
$998$	−1.35760	−	4.65253i	−0.0429740	−	0.147273i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	108.2.h.a.35.2		8
3.2	odd	2		36.2.h.a.11.3	✓	8
4.3	odd	2	inner	108.2.h.a.35.1		8
8.3	odd	2		1728.2.s.f.575.2		8
8.5	even	2		1728.2.s.f.575.1		8
9.2	odd	6		324.2.b.b.323.7		8
9.4	even	3		36.2.h.a.23.4	yes	8
9.5	odd	6	inner	108.2.h.a.71.1		8
9.7	even	3		324.2.b.b.323.2		8
12.11	even	2		36.2.h.a.11.4	yes	8
15.2	even	4		900.2.o.a.299.1		16
15.8	even	4		900.2.o.a.299.8		16
15.14	odd	2		900.2.r.c.551.2		8
24.5	odd	2		576.2.s.f.191.1		8
24.11	even	2		576.2.s.f.191.4		8
36.7	odd	6		324.2.b.b.323.8		8
36.11	even	6		324.2.b.b.323.1		8
36.23	even	6	inner	108.2.h.a.71.2		8
36.31	odd	6		36.2.h.a.23.3	yes	8
45.4	even	6		900.2.r.c.851.1		8
45.13	odd	12		900.2.o.a.599.6		16
45.22	odd	12		900.2.o.a.599.3		16
60.23	odd	4		900.2.o.a.299.3		16
60.47	odd	4		900.2.o.a.299.6		16
60.59	even	2		900.2.r.c.551.1		8
72.5	odd	6		1728.2.s.f.1151.2		8
72.11	even	6		5184.2.c.j.5183.7		8
72.13	even	6		576.2.s.f.383.4		8
72.29	odd	6		5184.2.c.j.5183.8		8
72.43	odd	6		5184.2.c.j.5183.1		8
72.59	even	6		1728.2.s.f.1151.1		8
72.61	even	6		5184.2.c.j.5183.2		8
72.67	odd	6		576.2.s.f.383.1		8
180.67	even	12		900.2.o.a.599.8		16
180.103	even	12		900.2.o.a.599.1		16
180.139	odd	6		900.2.r.c.851.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.3	✓	8	3.2	odd	2
36.2.h.a.11.4	yes	8	12.11	even	2
36.2.h.a.23.3	yes	8	36.31	odd	6
36.2.h.a.23.4	yes	8	9.4	even	3
108.2.h.a.35.1		8	4.3	odd	2	inner
108.2.h.a.35.2		8	1.1	even	1	trivial
108.2.h.a.71.1		8	9.5	odd	6	inner
108.2.h.a.71.2		8	36.23	even	6	inner
324.2.b.b.323.1		8	36.11	even	6
324.2.b.b.323.2		8	9.7	even	3
324.2.b.b.323.7		8	9.2	odd	6
324.2.b.b.323.8		8	36.7	odd	6
576.2.s.f.191.1		8	24.5	odd	2
576.2.s.f.191.4		8	24.11	even	2
576.2.s.f.383.1		8	72.67	odd	6
576.2.s.f.383.4		8	72.13	even	6
900.2.o.a.299.1		16	15.2	even	4
900.2.o.a.299.3		16	60.23	odd	4
900.2.o.a.299.6		16	60.47	odd	4
900.2.o.a.299.8		16	15.8	even	4
900.2.o.a.599.1		16	180.103	even	12
900.2.o.a.599.3		16	45.22	odd	12
900.2.o.a.599.6		16	45.13	odd	12
900.2.o.a.599.8		16	180.67	even	12
900.2.r.c.551.1		8	60.59	even	2
900.2.r.c.551.2		8	15.14	odd	2
900.2.r.c.851.1		8	45.4	even	6
900.2.r.c.851.2		8	180.139	odd	6
1728.2.s.f.575.1		8	8.5	even	2
1728.2.s.f.575.2		8	8.3	odd	2
1728.2.s.f.1151.1		8	72.59	even	6
1728.2.s.f.1151.2		8	72.5	odd	6
5184.2.c.j.5183.1		8	72.43	odd	6
5184.2.c.j.5183.2		8	72.61	even	6
5184.2.c.j.5183.7		8	72.11	even	6
5184.2.c.j.5183.8		8	72.29	odd	6

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:	\( N \)	\(=\)	\( 108 = 2^{2} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	108.h (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.335728 - 1.37379i) q^{2} +(-1.77457 - 0.922437i) q^{4} +(2.18614 - 1.26217i) q^{5} +(-1.10489 - 0.637910i) q^{7} +(-1.86301 + 2.12819i) q^{8} +O(q^{10})\)	\(q+(0.335728 - 1.37379i) q^{2} +(-1.77457 - 0.922437i) q^{4} +(2.18614 - 1.26217i) q^{5} +(-1.10489 - 0.637910i) q^{7} +(-1.86301 + 2.12819i) q^{8} +(-1.00000 - 3.42703i) q^{10} +(0.252704 - 0.437696i) q^{11} +(1.18614 + 2.05446i) q^{13} +(-1.24730 + 1.30372i) q^{14} +(2.29822 + 3.27386i) q^{16} +0.792287i q^{17} +4.70285i q^{19} +(-5.04374 + 0.223233i) q^{20} +(-0.516461 - 0.494108i) q^{22} +(1.61030 + 2.78912i) q^{23} +(0.686141 - 1.18843i) q^{25} +(3.22060 - 0.939764i) q^{26} +(1.37228 + 2.15121i) q^{28} +(-2.18614 - 1.26217i) q^{29} +(7.04069 - 4.06494i) q^{31} +(5.26916 - 2.05813i) q^{32} +(1.08843 + 0.265993i) q^{34} -3.22060 q^{35} -6.74456 q^{37} +(6.46071 + 1.57888i) q^{38} +(-1.38665 + 7.00396i) q^{40} +(-5.87228 + 3.39036i) q^{41} +(-6.69391 - 3.86473i) q^{43} +(-0.852189 + 0.543620i) q^{44} +(4.37228 - 1.27582i) q^{46} +(0.599485 - 1.03834i) q^{47} +(-2.68614 - 4.65253i) q^{49} +(-1.40229 - 1.34160i) q^{50} +(-0.209786 - 4.73992i) q^{52} +1.87953i q^{53} -1.27582i q^{55} +(3.41602 - 1.16300i) q^{56} +(-2.46790 + 2.57954i) q^{58} +(-6.18850 - 10.7188i) q^{59} +(1.18614 - 2.05446i) q^{61} +(-3.22060 - 11.0371i) q^{62} +(-1.05842 - 7.92967i) q^{64} +(5.18614 + 2.99422i) q^{65} +(-6.69391 + 3.86473i) q^{67} +(0.730835 - 1.40597i) q^{68} +(-1.08125 + 4.42442i) q^{70} +11.8716 q^{71} +3.37228 q^{73} +(-2.26434 + 9.26558i) q^{74} +(4.33809 - 8.34556i) q^{76} +(-0.558422 + 0.322405i) q^{77} +(8.55691 + 4.94034i) q^{79} +(9.15640 + 4.25639i) q^{80} +(2.68614 + 9.20550i) q^{82} +(-3.82009 + 6.61659i) q^{83} +(1.00000 + 1.73205i) q^{85} +(-7.55665 + 7.89850i) q^{86} +(0.460714 + 1.35323i) q^{88} -11.9769i q^{89} -3.02661i q^{91} +(-0.284805 - 6.43491i) q^{92} +(-1.22519 - 1.17216i) q^{94} +(5.93580 + 10.2811i) q^{95} +(-5.24456 + 9.08385i) q^{97} +(-7.29339 + 2.12819i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 3 q^{2} - q^{4} + 6 q^{5}+O(q^{10}) \) 8 * q + 3 * q^2 - q^4 + 6 * q^5	\( 8 q + 3 q^{2} - q^{4} + 6 q^{5} - 8 q^{10} - 2 q^{13} - 12 q^{14} - q^{16} - 18 q^{20} + 3 q^{22} - 6 q^{25} - 12 q^{28} - 6 q^{29} + 33 q^{32} + 7 q^{34} - 8 q^{37} + 27 q^{38} + 10 q^{40} - 24 q^{41} + 12 q^{46} - 10 q^{49} - 21 q^{50} + 16 q^{52} - 18 q^{56} + 4 q^{58} - 2 q^{61} + 26 q^{64} + 30 q^{65} + 15 q^{68} - 6 q^{70} + 4 q^{73} + 30 q^{74} - 3 q^{76} + 30 q^{77} + 10 q^{82} + 8 q^{85} - 21 q^{86} - 21 q^{88} - 24 q^{92} - 18 q^{94} + 4 q^{97}+O(q^{100}) \) 8 * q + 3 * q^2 - q^4 + 6 * q^5 - 8 * q^10 - 2 * q^13 - 12 * q^14 - q^16 - 18 * q^20 + 3 * q^22 - 6 * q^25 - 12 * q^28 - 6 * q^29 + 33 * q^32 + 7 * q^34 - 8 * q^37 + 27 * q^38 + 10 * q^40 - 24 * q^41 + 12 * q^46 - 10 * q^49 - 21 * q^50 + 16 * q^52 - 18 * q^56 + 4 * q^58 - 2 * q^61 + 26 * q^64 + 30 * q^65 + 15 * q^68 - 6 * q^70 + 4 * q^73 + 30 * q^74 - 3 * q^76 + 30 * q^77 + 10 * q^82 + 8 * q^85 - 21 * q^86 - 21 * q^88 - 24 * q^92 - 18 * q^94 + 4 * q^97

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