LMFDB - Embedded newform 1728.2.s.f.1151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1728,2,Mod(575,1728)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1728, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 1]))

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

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

chi := DirichletCharacter("1728.575");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1728 = 2^{6} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1728.s (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:	$13.7981494693$
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:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			1151.1
Root			$-1.02187 + 0.977642i$ of defining polynomial
Character	$\chi$	$=$	1728.1151
Dual form			1728.2.s.f.575.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.18614 - 1.26217i) q^{5} +(-1.10489 + 0.637910i) q^{7} +O(q^{10})$	$q+(-2.18614 - 1.26217i) q^{5} +(-1.10489 + 0.637910i) q^{7} +(-0.252704 - 0.437696i) q^{11} +(-1.18614 + 2.05446i) q^{13} -0.792287i q^{17} +4.70285i q^{19} +(1.61030 - 2.78912i) q^{23} +(0.686141 + 1.18843i) q^{25} +(2.18614 - 1.26217i) q^{29} +(7.04069 + 4.06494i) q^{31} +3.22060 q^{35} +6.74456 q^{37} +(-5.87228 - 3.39036i) q^{41} +(6.69391 - 3.86473i) q^{43} +(0.599485 + 1.03834i) q^{47} +(-2.68614 + 4.65253i) q^{49} +1.87953i q^{53} +1.27582i q^{55} +(6.18850 - 10.7188i) q^{59} +(-1.18614 - 2.05446i) q^{61} +(5.18614 - 2.99422i) q^{65} +(6.69391 + 3.86473i) q^{67} +11.8716 q^{71} +3.37228 q^{73} +(0.558422 + 0.322405i) q^{77} +(8.55691 - 4.94034i) q^{79} +(3.82009 + 6.61659i) q^{83} +(-1.00000 + 1.73205i) q^{85} +11.9769i q^{89} -3.02661i q^{91} +(5.93580 - 10.2811i) q^{95} +(-5.24456 - 9.08385i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{5}+O(q^{10}) $ 8 * q - 6 * q^5	$ 8 q - 6 q^{5} + 2 q^{13} - 6 q^{25} + 6 q^{29} + 8 q^{37} - 24 q^{41} - 10 q^{49} + 2 q^{61} + 30 q^{65} + 4 q^{73} - 30 q^{77} - 8 q^{85} + 4 q^{97}+O(q^{100}) $ 8 * q - 6 * q^5 + 2 * q^13 - 6 * q^25 + 6 * q^29 + 8 * q^37 - 24 * q^41 - 10 * q^49 + 2 * q^61 + 30 * q^65 + 4 * q^73 - 30 * q^77 - 8 * q^85 + 4 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times$.

$n$	$325$	$703$	$1217$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

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			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−2.18614	−	1.26217i	−0.977672	−	0.564459i	−0.0761054	−	0.997100i	$-0.524249\pi$
$5$	−2.18614	−	1.26217i	−0.977672	−	0.564459i	−0.901566	+	0.432641i	$0.857582\pi$
$6$		0			0
$7$	−1.10489	+	0.637910i	−0.417610	+	0.241107i	−0.694054	−	0.719923i	$-0.744177\pi$
$7$	−1.10489	+	0.637910i	−0.417610	+	0.241107i	0.276444	+	0.961030i	$0.410844\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−0.252704	−	0.437696i	−0.0761931	−	0.131970i	0.825411	−	0.564532i	$-0.190943\pi$
$11$	−0.252704	−	0.437696i	−0.0761931	−	0.131970i	−0.901605	+	0.432561i	$0.857610\pi$
$12$		0			0
$13$	−1.18614	+	2.05446i	−0.328976	+	0.569804i	−0.982309	−	0.187267i	$-0.940037\pi$
$13$	−1.18614	+	2.05446i	−0.328976	+	0.569804i	0.653333	+	0.757071i	$0.273370\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$		−	0.792287i		−	0.192158i	−0.995374	−	0.0960789i	$-0.969370\pi$
$17$		−	0.792287i		−	0.192158i	0.995374	−	0.0960789i	$-0.0306301\pi$
$18$		0			0
$19$			4.70285i			1.07891i	0.842015	+	0.539454i	$0.181369\pi$
$19$			4.70285i			1.07891i	−0.842015	+	0.539454i	$0.818631\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.61030	−	2.78912i	0.335771	−	0.581572i	−0.647862	−	0.761758i	$-0.724336\pi$
$23$	1.61030	−	2.78912i	0.335771	−	0.581572i	0.983633	+	0.180186i	$0.0576698\pi$
$24$		0			0
$25$	0.686141	+	1.18843i	0.137228	+	0.237686i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	2.18614	−	1.26217i	0.405956	−	0.234379i	−0.283095	−	0.959092i	$-0.591361\pi$
$29$	2.18614	−	1.26217i	0.405956	−	0.234379i	0.689051	+	0.724713i	$0.258028\pi$
$30$		0			0
$31$	7.04069	+	4.06494i	1.26455	+	0.730086i	0.973951	−	0.226761i	$-0.0728135\pi$
$31$	7.04069	+	4.06494i	1.26455	+	0.730086i	0.290595	+	0.956846i	$0.406147\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.22060			0.544381
$36$		0			0
$37$	6.74456			1.10880			0.554400	−	0.832251i	$-0.312948\pi$
$37$	6.74456			1.10880			0.554400	+	0.832251i	$0.312948\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−5.87228	−	3.39036i	−0.917096	−	0.529486i	−0.0343887	−	0.999409i	$-0.510948\pi$
$41$	−5.87228	−	3.39036i	−0.917096	−	0.529486i	−0.882708	+	0.469923i	$0.844282\pi$
$42$		0			0
$43$	6.69391	−	3.86473i	1.02081	−	0.589366i	0.106473	−	0.994316i	$-0.466044\pi$
$43$	6.69391	−	3.86473i	1.02081	−	0.589366i	0.914339	+	0.404950i	$0.132711\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	0.599485	+	1.03834i	0.0874439	+	0.151457i	0.906430	−	0.422356i	$-0.138797\pi$
$47$	0.599485	+	1.03834i	0.0874439	+	0.151457i	−0.818986	+	0.573813i	$0.805463\pi$
$48$		0			0
$49$	−2.68614	+	4.65253i	−0.383734	+	0.664647i
$50$		0			0
$51$		0			0
$52$		0			0
$53$			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
$56$		0			0
$57$		0			0
$58$		0			0
$59$	6.18850	−	10.7188i	0.805674	−	1.39547i	−0.110161	−	0.993914i	$-0.535137\pi$
$59$	6.18850	−	10.7188i	0.805674	−	1.39547i	0.915835	−	0.401555i	$-0.131530\pi$
$60$		0			0
$61$	−1.18614	−	2.05446i	−0.151870	−	0.263046i	0.780045	−	0.625723i	$-0.215196\pi$
$61$	−1.18614	−	2.05446i	−0.151870	−	0.263046i	−0.931915	+	0.362677i	$0.881863\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	5.18614	−	2.99422i	0.643262	−	0.371387i
$66$		0			0
$67$	6.69391	+	3.86473i	0.817791	+	0.472152i	0.849654	−	0.527340i	$-0.176811\pi$
$67$	6.69391	+	3.86473i	0.817791	+	0.472152i	−0.0318630	+	0.999492i	$0.510144\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	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	$0.436767\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	0.558422	+	0.322405i	0.0636381	+	0.0367415i
$78$		0			0
$79$	8.55691	−	4.94034i	0.962728	−	0.555831i	0.0657165	−	0.997838i	$-0.479067\pi$
$79$	8.55691	−	4.94034i	0.962728	−	0.555831i	0.897012	+	0.442007i	$0.145733\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	3.82009	+	6.61659i	0.419309	+	0.726265i	0.995870	−	0.0907894i	$-0.0289390\pi$
$83$	3.82009	+	6.61659i	0.419309	+	0.726265i	−0.576561	+	0.817054i	$0.695606\pi$
$84$		0			0
$85$	−1.00000	+	1.73205i	−0.108465	+	0.187867i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			11.9769i			1.26955i	0.772698	+	0.634773i	$0.218907\pi$
$89$			11.9769i			1.26955i	−0.772698	+	0.634773i	$0.781093\pi$
$90$		0			0
$91$		−	3.02661i		−	0.317274i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	5.93580	−	10.2811i	0.609000	−	1.05482i
$96$		0			0
$97$	−5.24456	−	9.08385i	−0.532505	−	0.922325i	−0.999280	−	0.0379490i	$-0.987918\pi$
$97$	−5.24456	−	9.08385i	−0.532505	−	0.922325i	0.466775	−	0.884376i	$-0.345416\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	1.06930	−	0.617359i	0.106399	−	0.0614295i	−0.445856	−	0.895105i	$-0.647101\pi$
$101$	1.06930	−	0.617359i	0.106399	−	0.0614295i	0.552255	+	0.833675i	$0.313767\pi$
$102$		0			0
$103$	0.411331	+	0.237482i	0.0405297	+	0.0233998i	0.520128	−	0.854088i	$-0.325884\pi$
$103$	0.411331	+	0.237482i	0.0405297	+	0.0233998i	−0.479598	+	0.877488i	$0.659218\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	12.5652			1.21472			0.607360	−	0.794427i	$-0.292229\pi$
$107$	12.5652			1.21472			0.607360	+	0.794427i	$0.292229\pi$
$108$		0			0
$109$	−13.4891			−1.29202			−0.646012	−	0.763327i	$-0.723564\pi$
$109$	−13.4891			−1.29202			−0.646012	+	0.763327i	$0.723564\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	6.30298	+	3.63903i	0.592935	+	0.342331i	0.766257	−	0.642534i	$-0.222117\pi$
$113$	6.30298	+	3.63903i	0.592935	+	0.342331i	−0.173322	+	0.984865i	$0.555450\pi$
$114$		0			0
$115$	−7.04069	+	4.06494i	−0.656548	+	0.379058i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	0.505408	+	0.875393i	0.0463307	+	0.0802471i
$120$		0			0
$121$	5.37228	−	9.30506i	0.488389	−	0.845915i
$122$		0			0
$123$		0			0
$124$		0			0
$125$			9.15759i			0.819080i
$126$		0			0
$127$			7.65492i			0.679265i	0.940558	+	0.339632i	$0.110303\pi$
$127$			7.65492i			0.679265i	−0.940558	+	0.339632i	$0.889697\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.82009	+	6.61659i	−0.333763	+	0.578094i	−0.983246	−	0.182282i	$-0.941652\pi$
$131$	−3.82009	+	6.61659i	−0.333763	+	0.578094i	0.649484	+	0.760375i	$0.274985\pi$
$132$		0			0
$133$	−3.00000	−	5.19615i	−0.260133	−	0.450564i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.75544	−	2.74555i	0.406284	−	0.234568i	−0.282908	−	0.959147i	$-0.591299\pi$
$137$	4.75544	−	2.74555i	0.406284	−	0.234568i	0.689192	+	0.724579i	$0.257966\pi$
$138$		0			0
$139$	13.3233	+	7.69219i	1.13006	+	0.652443i	0.943951	−	0.330085i	$-0.107077\pi$
$139$	13.3233	+	7.69219i	1.13006	+	0.652443i	0.186114	+	0.982528i	$0.440411\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	1.19897			0.100263
$144$		0			0
$145$	−6.37228			−0.529189
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−11.1861	−	6.45832i	−0.916404	−	0.529086i	−0.0339182	−	0.999425i	$-0.510799\pi$
$149$	−11.1861	−	6.45832i	−0.916404	−	0.529086i	−0.882486	+	0.470338i	$0.844132\pi$
$150$		0			0
$151$	−2.62112	+	1.51330i	−0.213304	+	0.123151i	−0.602846	−	0.797858i	$-0.705967\pi$
$151$	−2.62112	+	1.51330i	−0.213304	+	0.123151i	0.389542	+	0.921009i	$0.372633\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−10.2613	−	17.7731i	−0.824207	−	1.42757i
$156$		0			0
$157$	5.93070	−	10.2723i	0.473322	−	0.819817i	−0.526212	−	0.850353i	$-0.676388\pi$
$157$	5.93070	−	10.2723i	0.473322	−	0.819817i	0.999534	+	0.0305363i	$0.00972150\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$			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	$0.978158\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−8.74507	+	15.1469i	−0.676714	+	1.17210i	0.299251	+	0.954174i	$0.403263\pi$
$167$	−8.74507	+	15.1469i	−0.676714	+	1.17210i	−0.975965	+	0.217928i	$0.930070\pi$
$168$		0			0
$169$	3.68614	+	6.38458i	0.283549	+	0.491122i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	15.3030	−	8.83518i	1.16346	−	0.671726i	0.211333	−	0.977414i	$-0.432220\pi$
$173$	15.3030	−	8.83518i	1.16346	−	0.671726i	0.952132	+	0.305688i	$0.0988864\pi$
$174$		0			0
$175$	−1.51622	−	0.875393i	−0.114616	−	0.0661735i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−8.83915			−0.660669			−0.330334	−	0.943864i	$-0.607162\pi$
$179$	−8.83915			−0.660669			−0.330334	+	0.943864i	$0.607162\pi$
$180$		0			0
$181$	4.00000			0.297318			0.148659	−	0.988889i	$-0.452504\pi$
$181$	4.00000			0.297318			0.148659	+	0.988889i	$0.452504\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−14.7446	−	8.51278i	−1.08404	−	0.625872i
$186$		0			0
$187$	−0.346781	+	0.200214i	−0.0253591	+	0.0146411i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−7.54610	−	13.0702i	−0.546017	−	0.945728i	−0.998542	−	0.0539770i	$-0.982810\pi$
$191$	−7.54610	−	13.0702i	−0.546017	−	0.945728i	0.452526	−	0.891751i	$-0.350523\pi$
$192$		0			0
$193$	−3.87228	+	6.70699i	−0.278733	+	0.482780i	−0.971070	−	0.238795i	$-0.923248\pi$
$193$	−3.87228	+	6.70699i	−0.278733	+	0.482780i	0.692337	+	0.721574i	$0.256581\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			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	$0.151250\pi$
$199$			12.9073i			0.914973i	−0.889217	+	0.457486i	$0.848750\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−1.61030	+	2.78912i	−0.113021	+	0.195758i
$204$		0			0
$205$	8.55842	+	14.8236i	0.597746	+	1.03533i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	2.05842	−	1.18843i	0.142384	−	0.0822055i
$210$		0			0
$211$	−15.1863	−	8.76780i	−1.04547	−	0.603600i	−0.124090	−	0.992271i	$-0.539601\pi$
$211$	−15.1863	−	8.76780i	−1.04547	−	0.603600i	−0.921377	+	0.388671i	$0.872934\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−19.5118			−1.33069
$216$		0			0
$217$	−10.3723			−0.704116
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.62772	+	0.939764i	0.109492	+	0.0632154i
$222$		0			0
$223$	7.04069	−	4.06494i	0.471479	−	0.272209i	−0.245379	−	0.969427i	$-0.578913\pi$
$223$	7.04069	−	4.06494i	0.471479	−	0.272209i	0.716859	+	0.697218i	$0.245579\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	7.19932	+	12.4696i	0.477835	+	0.827635i	0.999677	−	0.0254070i	$-0.00808817\pi$
$227$	7.19932	+	12.4696i	0.477835	+	0.827635i	−0.521842	+	0.853042i	$0.674755\pi$
$228$		0			0
$229$	1.81386	−	3.14170i	0.119863	−	0.207609i	−0.799850	−	0.600200i	$-0.795088\pi$
$229$	1.81386	−	3.14170i	0.119863	−	0.207609i	0.919713	+	0.392591i	$0.128421\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$			4.84630i			0.317491i	0.987320	+	0.158746i	$0.0507450\pi$
$233$			4.84630i			0.317491i	−0.987320	+	0.158746i	$0.949255\pi$
$234$		0			0
$235$		−	3.02661i		−	0.197434i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	6.02987	−	10.4440i	0.390040	−	0.675569i	−0.602414	−	0.798184i	$-0.705794\pi$
$239$	6.02987	−	10.4440i	0.390040	−	0.675569i	0.992454	+	0.122614i	$0.0391278\pi$
$240$		0			0
$241$	3.24456	+	5.61975i	0.209001	+	0.362000i	0.951400	−	0.307958i	$-0.0996456\pi$
$241$	3.24456	+	5.61975i	0.209001	+	0.362000i	−0.742399	+	0.669958i	$0.766312\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	11.7446	−	6.78073i	0.750333	−	0.433205i
$246$		0			0
$247$	−9.66181	−	5.57825i	−0.614766	−	0.354935i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−11.1780			−0.705551			−0.352776	−	0.935708i	$-0.614762\pi$
$251$	−11.1780			−0.705551			−0.352776	+	0.935708i	$0.614762\pi$
$252$		0			0
$253$	−1.62772			−0.102334
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.9891	−	7.49927i	−0.810239	−	0.467792i	0.0367996	−	0.999323i	$-0.488284\pi$
$257$	−12.9891	−	7.49927i	−0.810239	−	0.467792i	−0.847039	+	0.531531i	$0.821617\pi$
$258$		0			0
$259$	−7.45202	+	4.30243i	−0.463046	+	0.267340i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	13.9873	+	24.2267i	0.862494	+	1.49388i	0.869514	+	0.493908i	$0.164432\pi$
$263$	13.9873	+	24.2267i	0.862494	+	1.49388i	−0.00701993	+	0.999975i	$0.502235\pi$
$264$		0			0
$265$	2.37228	−	4.10891i	0.145728	−	0.252408i
$266$		0			0
$267$		0			0
$268$		0			0
$269$		−	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	$-0.635920\pi$
$271$		−	29.9679i		−	1.82042i	0.414146	−	0.910211i	$-0.364080\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.346781	−	0.600642i	0.0209117	−	0.0362201i
$276$		0			0
$277$	3.18614	+	5.51856i	0.191437	+	0.331578i	0.945727	−	0.324963i	$-0.105352\pi$
$277$	3.18614	+	5.51856i	0.191437	+	0.331578i	−0.754290	+	0.656541i	$0.772019\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	19.9307	−	11.5070i	1.18897	−	0.686450i	0.230894	−	0.972979i	$-0.425835\pi$
$281$	19.9307	−	11.5070i	1.18897	−	0.686450i	0.958072	+	0.286529i	$0.0925014\pi$
$282$		0			0
$283$	−8.55691	−	4.94034i	−0.508656	−	0.293673i	0.223625	−	0.974675i	$-0.428211\pi$
$283$	−8.55691	−	4.94034i	−0.508656	−	0.293673i	−0.732281	+	0.681003i	$0.761544\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	8.65099			0.510652
$288$		0			0
$289$	16.3723			0.963075
$290$		0			0
$291$		0			0
$292$		0			0
$293$	−20.1861	−	11.6545i	−1.17929	−	0.680862i	−0.223437	−	0.974718i	$-0.571728\pi$
$293$	−20.1861	−	11.6545i	−1.17929	−	0.680862i	−0.955850	+	0.293857i	$0.905061\pi$
$294$		0			0
$295$	−27.0579	+	15.6219i	−1.57537	+	0.909540i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.82009	+	6.61659i	0.220921	+	0.382647i
$300$		0			0
$301$	−4.93070	+	8.54023i	−0.284201	+	0.492251i
$302$		0			0
$303$		0			0
$304$		0			0
$305$			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	$-0.0109140\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−9.56773	+	16.5718i	−0.542536	+	0.939700i	0.456221	+	0.889866i	$0.349203\pi$
$311$	−9.56773	+	16.5718i	−0.542536	+	0.939700i	−0.998758	+	0.0498340i	$0.984131\pi$
$312$		0			0
$313$	9.24456	+	16.0121i	0.522534	+	0.905055i	0.999656	+	0.0262180i	$0.00834640\pi$
$313$	9.24456	+	16.0121i	0.522534	+	0.905055i	−0.477123	+	0.878837i	$0.658320\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−28.1644	+	16.2607i	−1.58187	+	0.913293i	−0.587283	+	0.809381i	$0.699803\pi$
$317$	−28.1644	+	16.2607i	−1.58187	+	0.913293i	−0.994587	+	0.103911i	$0.966864\pi$
$318$		0			0
$319$	−1.10489	−	0.637910i	−0.0618621	−	0.0357161i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.72601			0.207321
$324$		0			0
$325$	−3.25544			−0.180579
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−1.32473	−	0.764836i	−0.0730350	−	0.0421667i
$330$		0			0
$331$	24.0254	−	13.8711i	1.32056	−	0.762424i	0.336739	−	0.941598i	$-0.390676\pi$
$331$	24.0254	−	13.8711i	1.32056	−	0.762424i	0.983817	+	0.179174i	$0.0573426\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−9.75588	−	16.8977i	−0.533021	−	0.923219i
$336$		0			0
$337$	7.87228	−	13.6352i	0.428830	−	0.742756i	−0.567939	−	0.823071i	$-0.692259\pi$
$337$	7.87228	−	13.6352i	0.428830	−	0.742756i	0.996770	+	0.0803144i	$0.0255924\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$		−	4.10891i		−	0.222510i
$342$		0			0
$343$		−	15.7848i		−	0.852300i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−3.47331	+	6.01594i	−0.186457	+	0.322953i	−0.944066	−	0.329755i	$-0.893034\pi$
$347$	−3.47331	+	6.01594i	−0.186457	+	0.322953i	0.757610	+	0.652708i	$0.226367\pi$
$348$		0			0
$349$	−2.81386	−	4.87375i	−0.150622	−	0.260886i	0.780834	−	0.624739i	$-0.214794\pi$
$349$	−2.81386	−	4.87375i	−0.150622	−	0.260886i	−0.931456	+	0.363853i	$0.881461\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−7.24456	+	4.18265i	−0.385589	+	0.222620i	−0.680247	−	0.732983i	$-0.738128\pi$
$353$	−7.24456	+	4.18265i	−0.385589	+	0.222620i	0.294658	+	0.955603i	$0.404794\pi$
$354$		0			0
$355$	−25.9530	−	14.9840i	−1.37744	−	0.795266i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−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
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−7.37228	−	4.25639i	−0.385883	−	0.222790i
$366$		0			0
$367$	5.52447	−	3.18955i	0.288375	−	0.166493i	−0.348834	−	0.937185i	$-0.613422\pi$
$367$	5.52447	−	3.18955i	0.288375	−	0.166493i	0.637209	+	0.770691i	$0.280089\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−1.19897	−	2.07668i	−0.0622474	−	0.107816i
$372$		0			0
$373$	−9.93070	+	17.2005i	−0.514192	+	0.890607i	0.485672	+	0.874141i	$0.338575\pi$
$373$	−9.93070	+	17.2005i	−0.514192	+	0.890607i	−0.999864	+	0.0164662i	$0.994758\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$			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	$-0.0530047\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.32550	+	7.49198i	−0.221023	+	0.382822i	−0.955119	−	0.296223i	$-0.904273\pi$
$383$	−4.32550	+	7.49198i	−0.221023	+	0.382822i	0.734096	+	0.679045i	$0.237606\pi$
$384$		0			0
$385$	−0.813859	−	1.40965i	−0.0414781	−	0.0718422i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	27.3030	−	15.7634i	1.38432	−	0.799235i	0.391649	−	0.920115i	$-0.371905\pi$
$389$	27.3030	−	15.7634i	1.38432	−	0.799235i	0.992667	+	0.120879i	$0.0385714\pi$
$390$		0			0
$391$	−2.20979	−	1.27582i	−0.111754	−	0.0645210i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−24.9422			−1.25498
$396$		0			0
$397$	18.7446			0.940763			0.470381	−	0.882463i	$-0.344116\pi$
$397$	18.7446			0.940763			0.470381	+	0.882463i	$0.344116\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−3.98913	−	2.30312i	−0.199207	−	0.115012i	0.397078	−	0.917785i	$-0.370024\pi$
$401$	−3.98913	−	2.30312i	−0.199207	−	0.115012i	−0.596286	+	0.802772i	$0.703357\pi$
$402$		0			0
$403$	−16.7025	+	9.64319i	−0.832011	+	0.480362i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−1.70438	−	2.95207i	−0.0844829	−	0.146329i
$408$		0			0
$409$	−6.87228	+	11.9031i	−0.339812	+	0.588572i	−0.984397	−	0.175960i	$-0.943697\pi$
$409$	−6.87228	+	11.9031i	−0.339812	+	0.588572i	0.644585	+	0.764533i	$0.277030\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$			15.7908i			0.777016i
$414$		0			0
$415$		−	19.2864i		−	0.946731i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−13.4819	+	23.3513i	−0.658634	+	1.14079i	0.322336	+	0.946625i	$0.395532\pi$
$419$	−13.4819	+	23.3513i	−0.658634	+	1.14079i	−0.980970	+	0.194162i	$0.937801\pi$
$420$		0			0
$421$	−5.30298	−	9.18504i	−0.258452	−	0.447651i	0.707376	−	0.706838i	$-0.249879\pi$
$421$	−5.30298	−	9.18504i	−0.258452	−	0.447651i	−0.965827	+	0.259186i	$0.916546\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.941578	−	0.543620i	0.0456732	−	0.0263695i
$426$		0			0
$427$	2.62112	+	1.51330i	0.126845	+	0.0732339i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−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	$0.566471\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	13.1168	+	7.57301i	0.627464	+	0.362266i
$438$		0			0
$439$	−5.65357	+	3.26409i	−0.269830	+	0.155786i	−0.628810	−	0.777559i	$-0.716458\pi$
$439$	−5.65357	+	3.26409i	−0.269830	+	0.155786i	0.358980	+	0.933345i	$0.383124\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−6.18850	−	10.7188i	−0.294025	−	0.509265i	0.680733	−	0.732532i	$-0.261661\pi$
$443$	−6.18850	−	10.7188i	−0.294025	−	0.509265i	−0.974758	+	0.223266i	$0.928328\pi$
$444$		0			0
$445$	15.1168	−	26.1831i	0.716607	−	1.24120i
$446$		0			0
$447$		0			0
$448$		0			0
$449$		−	19.4024i		−	0.915657i	−0.889041	−	0.457828i	$-0.848627\pi$
$449$		−	19.4024i		−	0.915657i	0.889041	−	0.457828i	$-0.151373\pi$
$450$		0			0
$451$			3.42703i			0.161373i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−3.82009	+	6.61659i	−0.179088	+	0.310190i
$456$		0			0
$457$	−19.9891	−	34.6222i	−0.935052	−	1.61956i	−0.774541	−	0.632523i	$-0.782019\pi$
$457$	−19.9891	−	34.6222i	−0.935052	−	1.61956i	−0.160510	−	0.987034i	$-0.551314\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	0.302985	−	0.174928i	0.0141114	−	0.00814722i	−0.492928	−	0.870070i	$-0.664073\pi$
$461$	0.302985	−	0.174928i	0.0141114	−	0.00814722i	0.507039	+	0.861923i	$0.330740\pi$
$462$		0			0
$463$	−4.13734	−	2.38870i	−0.192279	−	0.111012i	0.400770	−	0.916179i	$-0.368743\pi$
$463$	−4.13734	−	2.38870i	−0.192279	−	0.111012i	−0.593049	+	0.805167i	$0.702076\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−5.11313			−0.236608			−0.118304	−	0.992977i	$-0.537746\pi$
$467$	−5.11313			−0.236608			−0.118304	+	0.992977i	$0.537746\pi$
$468$		0			0
$469$	−9.86141			−0.455357
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.38316	−	1.95327i	−0.155558	−	0.0898113i
$474$		0			0
$475$	−5.58902	+	3.22682i	−0.256442	+	0.148057i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	6.53528	+	11.3194i	0.298605	+	0.517198i	0.975817	−	0.218589i	$-0.0701455\pi$
$479$	6.53528	+	11.3194i	0.298605	+	0.517198i	−0.677212	+	0.735788i	$0.736812\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$		0			0
$483$		0			0
$484$		0			0
$485$			26.4781i			1.20231i
$486$		0			0
$487$			42.8752i			1.94286i	0.237325	+	0.971430i	$0.423729\pi$
$487$			42.8752i			1.94286i	−0.237325	+	0.971430i	$0.576271\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	6.88206	−	11.9201i	0.310583	−	0.537946i	−0.667906	−	0.744246i	$-0.732809\pi$
$491$	6.88206	−	11.9201i	0.310583	−	0.537946i	0.978489	+	0.206300i	$0.0661423\pi$
$492$		0			0
$493$	−1.00000	−	1.73205i	−0.0450377	−	0.0780076i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−13.1168	+	7.57301i	−0.588371	+	0.339696i
$498$		0			0
$499$	−2.96790	−	1.71352i	−0.132861	−	0.0767076i	0.432096	−	0.901828i	$-0.357774\pi$
$499$	−2.96790	−	1.71352i	−0.132861	−	0.0767076i	−0.564958	+	0.825120i	$0.691107\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−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			0
$507$		0			0
$508$		0			0
$509$	12.8139	+	7.39809i	0.567964	+	0.327914i	0.756336	−	0.654183i	$-0.226988\pi$
$509$	12.8139	+	7.39809i	0.567964	+	0.327914i	−0.188372	+	0.982098i	$0.560321\pi$
$510$		0			0
$511$	−3.72601	+	2.15121i	−0.164829	+	0.0951641i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−0.599485	−	1.03834i	−0.0264165	−	0.0457547i
$516$		0			0
$517$	0.302985	−	0.524785i	0.0133252	−	0.0230800i
$518$		0			0
$519$		0			0
$520$		0			0
$521$			26.0357i			1.14064i	0.821421	+	0.570322i	$0.193181\pi$
$521$			26.0357i			1.14064i	−0.821421	+	0.570322i	$0.806819\pi$
$522$		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			0
$525$		0			0
$526$		0			0
$527$	3.22060	−	5.57825i	0.140292	−	0.242992i
$528$		0			0
$529$	6.31386	+	10.9359i	0.274516	+	0.475475i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	13.9307	−	8.04290i	0.603406	−	0.348376i
$534$		0			0
$535$	−27.4692	−	15.8593i	−1.18760	−	0.685659i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	2.71519			0.116952
$540$		0			0
$541$	8.97825			0.386005			0.193003	−	0.981198i	$-0.438177\pi$
$541$	8.97825			0.386005			0.193003	+	0.981198i	$0.438177\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	29.4891	+	17.0256i	1.26318	+	0.729295i
$546$		0			0
$547$	−19.2591	+	11.1192i	−0.823458	+	0.475424i	−0.851608	−	0.524180i	$-0.824372\pi$
$547$	−19.2591	+	11.1192i	−0.823458	+	0.475424i	0.0281494	+	0.999604i	$0.491039\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	5.93580	+	10.2811i	0.252873	+	0.437990i
$552$		0			0
$553$	−6.30298	+	10.9171i	−0.268030	+	0.464242i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	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
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−7.89288	+	13.6709i	−0.332645	+	0.576158i	−0.983030	−	0.183447i	$-0.941274\pi$
$563$	−7.89288	+	13.6709i	−0.332645	+	0.576158i	0.650384	+	0.759605i	$0.274608\pi$
$564$		0			0
$565$	−9.18614	−	15.9109i	−0.386464	−	0.669375i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	21.9891	−	12.6954i	0.921832	−	0.532220i	0.0376130	−	0.999292i	$-0.488025\pi$
$569$	21.9891	−	12.6954i	0.921832	−	0.532220i	0.884219	+	0.467072i	$0.154691\pi$
$570$		0			0
$571$	3.66146	+	2.11395i	0.153227	+	0.0884659i	0.574653	−	0.818397i	$-0.305137\pi$
$571$	3.66146	+	2.11395i	0.153227	+	0.0884659i	−0.421426	+	0.906863i	$0.638470\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	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	$0.269389\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−8.44158	−	4.87375i	−0.350216	−	0.202197i
$582$		0			0
$583$	0.822662	−	0.474964i	0.0340712	−	0.0196710i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	1.95708	+	3.38977i	0.0807774	+	0.139911i	0.903584	−	0.428411i	$-0.140926\pi$
$587$	1.95708	+	3.38977i	0.0807774	+	0.139911i	−0.822807	+	0.568321i	$0.807593\pi$
$588$		0			0
$589$	−19.1168	+	33.1113i	−0.787696	+	1.36433i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	8.80773i		−	0.361690i	−0.983512	−	0.180845i	$-0.942117\pi$
$593$		−	8.80773i		−	0.361690i	0.983512	−	0.180845i	$-0.0578833\pi$
$594$		0			0
$595$		−	2.55164i		−	0.104607i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	0.0940770	−	0.162946i	0.00384388	−	0.00665780i	−0.864097	−	0.503325i	$-0.832110\pi$
$599$	0.0940770	−	0.162946i	0.00384388	−	0.00665780i	0.867941	+	0.496667i	$0.165443\pi$
$600$		0			0
$601$	−7.98913	−	13.8376i	−0.325883	−	0.564446i	0.655807	−	0.754928i	$-0.272328\pi$
$601$	−7.98913	−	13.8376i	−0.325883	−	0.564446i	−0.981691	+	0.190482i	$0.938995\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−23.4891	+	13.5615i	−0.954969	+	0.551351i
$606$		0			0
$607$	3.44378	+	1.98827i	0.139779	+	0.0807013i	0.568259	−	0.822850i	$-0.307617\pi$
$607$	3.44378	+	1.98827i	0.139779	+	0.0807013i	−0.428480	+	0.903551i	$0.640951\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−2.84429			−0.115068
$612$		0			0
$613$	−4.23369			−0.170997			−0.0854985	−	0.996338i	$-0.527248\pi$
$613$	−4.23369			−0.170997			−0.0854985	+	0.996338i	$0.527248\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	4.24456	+	2.45060i	0.170880	+	0.0986574i	0.583001	−	0.812472i	$-0.301879\pi$
$617$	4.24456	+	2.45060i	0.170880	+	0.0986574i	−0.412121	+	0.911129i	$0.635212\pi$
$618$		0			0
$619$	−8.08103	+	4.66559i	−0.324804	+	0.187526i	−0.653532	−	0.756899i	$-0.726713\pi$
$619$	−8.08103	+	4.66559i	−0.324804	+	0.187526i	0.328728	+	0.944425i	$0.393380\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−7.64018	−	13.2332i	−0.306097	−	0.530176i
$624$		0			0
$625$	14.9891	−	25.9619i	0.599565	−	1.03848i
$626$		0			0
$627$		0			0
$628$		0			0
$629$		−	5.34363i		−	0.213064i
$630$		0			0
$631$		−	42.8752i		−	1.70683i	−0.521228	−	0.853417i	$-0.674526\pi$
$631$		−	42.8752i		−	1.70683i	0.521228	−	0.853417i	$-0.325474\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	9.66181	−	16.7347i	0.383417	−	0.664098i
$636$		0			0
$637$	−6.37228	−	11.0371i	−0.252479	−	0.437306i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−18.1277	+	10.4660i	−0.716002	+	0.413384i	−0.813279	−	0.581873i	$-0.802320\pi$
$641$	−18.1277	+	10.4660i	−0.716002	+	0.413384i	0.0972775	+	0.995257i	$0.468987\pi$
$642$		0			0
$643$	31.1307	+	17.9733i	1.22767	+	0.708798i	0.966543	−	0.256506i	$-0.0825713\pi$
$643$	31.1307	+	17.9733i	1.22767	+	0.708798i	0.261131	+	0.965303i	$0.415905\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	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
$650$		0			0
$651$		0			0
$652$		0			0
$653$	3.81386	+	2.20193i	0.149248	+	0.0861683i	0.572764	−	0.819720i	$-0.305871\pi$
$653$	3.81386	+	2.20193i	0.149248	+	0.0861683i	−0.423516	+	0.905888i	$0.639204\pi$
$654$		0			0
$655$	16.7025	−	9.64319i	0.652621	−	0.376791i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.02987	+	10.4440i	0.234891	+	0.406842i	0.959241	−	0.282590i	$-0.0911935\pi$
$659$	6.02987	+	10.4440i	0.234891	+	0.406842i	−0.724350	+	0.689432i	$0.757860\pi$
$660$		0			0
$661$	7.81386	−	13.5340i	0.303924	−	0.526412i	−0.673097	−	0.739554i	$-0.735036\pi$
$661$	7.81386	−	13.5340i	0.303924	−	0.526412i	0.977021	+	0.213142i	$0.0683698\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$			15.1460i			0.587338i
$666$		0			0
$667$		−	8.12989i		−	0.314791i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−0.599485	+	1.03834i	−0.0231429	+	0.0400846i
$672$		0			0
$673$	−14.9307	−	25.8607i	−0.575536	−	0.996858i	−0.995983	−	0.0895410i	$-0.971460\pi$
$673$	−14.9307	−	25.8607i	−0.575536	−	0.996858i	0.420447	−	0.907317i	$-0.361873\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−3.04755	+	1.75950i	−0.117127	+	0.0676232i	−0.557419	−	0.830231i	$-0.688208\pi$
$677$	−3.04755	+	1.75950i	−0.117127	+	0.0676232i	0.440292	+	0.897855i	$0.354875\pi$
$678$		0			0
$679$	11.5894	+	6.69112i	0.444759	+	0.256782i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	20.0172			0.765936			0.382968	−	0.923762i	$-0.374902\pi$
$683$	20.0172			0.765936			0.382968	+	0.923762i	$0.374902\pi$
$684$		0			0
$685$	−13.8614			−0.529617
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.86141	−	2.22938i	−0.147108	−	0.0849328i
$690$		0			0
$691$	17.3961	−	10.0436i	0.661777	−	0.382077i	−0.131177	−	0.991359i	$-0.541875\pi$
$691$	17.3961	−	10.0436i	0.661777	−	0.382077i	0.792954	+	0.609282i	$0.208542\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−19.4177	−	33.6324i	−0.736555	−	1.27575i
$696$		0			0
$697$	−2.68614	+	4.65253i	−0.101745	+	0.176227i
$698$		0			0
$699$		0			0
$700$		0			0
$701$		−	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
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−0.787639	+	1.36423i	−0.0296222	+	0.0513072i
$708$		0			0
$709$	11.9307	+	20.6646i	0.448067	+	0.776075i	0.998260	−	0.0589626i	$-0.0187793\pi$
$709$	11.9307	+	20.6646i	0.448067	+	0.776075i	−0.550193	+	0.835037i	$0.685446\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	22.6753	−	13.0916i	0.849195	−	0.490283i
$714$		0			0
$715$	−2.62112	−	1.51330i	−0.0980242	−	0.0565943i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	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
$722$		0			0
$723$		0			0
$724$		0			0
$725$	3.00000	+	1.73205i	0.111417	+	0.0643268i
$726$		0			0
$727$	32.9937	−	19.0489i	1.22367	−	0.706485i	0.257969	−	0.966153i	$-0.416947\pi$
$727$	32.9937	−	19.0489i	1.22367	−	0.706485i	0.965698	+	0.259668i	$0.0836133\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−3.06198	−	5.30350i	−0.113251	−	0.196157i
$732$		0			0
$733$	0.186141	−	0.322405i	0.00687526	−	0.0119083i	−0.862567	−	0.505942i	$-0.831145\pi$
$733$	0.186141	−	0.322405i	0.00687526	−	0.0119083i	0.869443	+	0.494034i	$0.164478\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$		−	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	$0.962127\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	10.5785	−	18.3226i	0.388089	−	0.672190i	−0.604103	−	0.796906i	$-0.706469\pi$
$743$	10.5785	−	18.3226i	0.388089	−	0.672190i	0.992193	+	0.124716i	$0.0398019\pi$
$744$		0			0
$745$	16.3030	+	28.2376i	0.597295	+	1.03455i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−13.8832	+	8.01544i	−0.507279	+	0.292878i
$750$		0			0
$751$	18.7832	+	10.8445i	0.685408	+	0.395721i	0.801890	−	0.597472i	$-0.203828\pi$
$751$	18.7832	+	10.8445i	0.685408	+	0.395721i	−0.116481	+	0.993193i	$0.537162\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	7.64018			0.278054
$756$		0			0
$757$	−14.0000			−0.508839			−0.254419	−	0.967094i	$-0.581884\pi$
$757$	−14.0000			−0.508839			−0.254419	+	0.967094i	$0.581884\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−15.0475	−	8.68771i	−0.545473	−	0.314929i	0.201821	−	0.979422i	$-0.435314\pi$
$761$	−15.0475	−	8.68771i	−0.545473	−	0.314929i	−0.747294	+	0.664493i	$0.768647\pi$
$762$		0			0
$763$	14.9040	−	8.60485i	0.539563	−	0.311517i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	14.6809	+	25.4280i	0.530095	+	0.918152i
$768$		0			0
$769$	−4.04755	+	7.01056i	−0.145958	+	0.252807i	−0.929730	−	0.368242i	$-0.879960\pi$
$769$	−4.04755	+	7.01056i	−0.145958	+	0.252807i	0.783772	+	0.621049i	$0.213293\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$		−	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
$776$		0			0
$777$		0			0
$778$		0			0
$779$	15.9444	−	27.6165i	0.571267	−	0.989463i
$780$		0			0
$781$	−3.00000	−	5.19615i	−0.107348	−	0.185933i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−25.9307	+	14.9711i	−0.925506	+	0.534341i
$786$		0			0
$787$	30.0903	+	17.3727i	1.07260	+	0.619268i	0.928892	−	0.370351i	$-0.120763\pi$
$787$	30.0903	+	17.3727i	1.07260	+	0.619268i	0.143712	+	0.989620i	$0.454096\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.28550			−0.330154
$792$		0			0
$793$	5.62772			0.199846
$794$		0			0
$795$		0			0
$796$		0			0
$797$	20.6970	+	11.9494i	0.733126	+	0.423270i	0.819565	−	0.572987i	$-0.194215\pi$
$797$	20.6970	+	11.9494i	0.733126	+	0.423270i	−0.0864387	+	0.996257i	$0.527549\pi$
$798$		0			0
$799$	0.822662	−	0.474964i	0.0291037	−	0.0168030i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−0.852189	−	1.47603i	−0.0300731	−	0.0520881i
$804$		0			0
$805$	5.18614	−	8.98266i	0.182787	−	0.316597i
$806$		0			0
$807$		0			0
$808$		0			0
$809$		−	35.8381i		−	1.26000i	−0.776595	−	0.630000i	$-0.783055\pi$
$809$		−	35.8381i		−	1.26000i	0.776595	−	0.630000i	$-0.216945\pi$
$810$		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			0
$813$		0			0
$814$		0			0
$815$	2.20979	−	3.82746i	0.0774054	−	0.134070i
$816$		0			0
$817$	18.1753	+	31.4805i	0.635872	+	1.10136i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−15.8139	+	9.13014i	−0.551907	+	0.318644i	−0.749891	−	0.661561i	$-0.769894\pi$
$821$	−15.8139	+	9.13014i	−0.551907	+	0.318644i	0.197983	+	0.980205i	$0.436561\pi$
$822$		0			0
$823$	12.1538	+	7.01701i	0.423656	+	0.244598i	0.696640	−	0.717421i	$-0.254677\pi$
$823$	12.1538	+	7.01701i	0.423656	+	0.244598i	−0.272984	+	0.962018i	$0.588011\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	47.4864			1.65126			0.825632	−	0.564210i	$-0.190819\pi$
$827$	47.4864			1.65126			0.825632	+	0.564210i	$0.190819\pi$
$828$		0			0
$829$	48.2337			1.67523			0.837613	−	0.546265i	$-0.183951\pi$
$829$	48.2337			1.67523			0.837613	+	0.546265i	$0.183951\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	3.68614	+	2.12819i	0.127717	+	0.0737376i
$834$		0			0
$835$	38.2359	−	22.0755i	1.32321	−	0.763954i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	21.3102	+	36.9104i	0.735711	+	1.27429i	0.954411	+	0.298496i	$0.0964850\pi$
$839$	21.3102	+	36.9104i	0.735711	+	1.27429i	−0.218700	+	0.975792i	$0.570182\pi$
$840$		0			0
$841$	−11.3139	+	19.5962i	−0.390133	+	0.675730i
$842$		0			0
$843$		0			0
$844$		0			0
$845$		−	18.6101i		−	0.640208i
$846$		0			0
$847$			13.7081i			0.471017i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	10.8608	−	18.8114i	0.372303	−	0.644847i
$852$		0			0
$853$	22.3030	+	38.6299i	0.763640	+	1.32266i	0.940963	+	0.338510i	$0.109923\pi$
$853$	22.3030	+	38.6299i	0.763640	+	1.32266i	−0.177323	+	0.984153i	$0.556744\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−32.5367	+	18.7851i	−1.11143	+	0.641685i	−0.939200	−	0.343371i	$-0.888431\pi$
$857$	−32.5367	+	18.7851i	−1.11143	+	0.641685i	−0.172232	+	0.985056i	$0.555098\pi$
$858$		0			0
$859$	1.58077	+	0.912661i	0.0539353	+	0.0311396i	0.526725	−	0.850036i	$-0.323420\pi$
$859$	1.58077	+	0.912661i	0.0539353	+	0.0311396i	−0.472790	+	0.881175i	$0.656753\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	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
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−4.32473	−	2.49689i	−0.146707	−	0.0847011i
$870$		0			0
$871$	−15.8798	+	9.16823i	−0.538068	+	0.310654i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−5.84172	−	10.1182i	−0.197486	−	0.342056i
$876$		0			0
$877$	10.8139	−	18.7302i	0.365158	−	0.632472i	−0.623643	−	0.781709i	$-0.714348\pi$
$877$	10.8139	−	18.7302i	0.365158	−	0.632472i	0.988802	+	0.149237i	$0.0476816\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$		−	52.9562i		−	1.78414i	−0.451898	−	0.892070i	$-0.649253\pi$
$881$		−	52.9562i		−	1.78414i	0.451898	−	0.892070i	$-0.350747\pi$
$882$		0			0
$883$			20.0127i			0.673481i	0.941597	+	0.336741i	$0.109325\pi$
$883$			20.0127i			0.673481i	−0.941597	+	0.336741i	$0.890675\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	9.75588	−	16.8977i	0.327571	−	0.567369i	−0.654459	−	0.756098i	$-0.727103\pi$
$887$	9.75588	−	16.8977i	0.327571	−	0.567369i	0.982029	+	0.188729i	$0.0604368\pi$
$888$		0			0
$889$	−4.88316	−	8.45787i	−0.163776	−	0.283668i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−4.88316	+	2.81929i	−0.163409	+	0.0943440i
$894$		0			0
$895$	19.3236	+	11.1565i	0.645917	+	0.372920i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	20.5226			0.684467
$900$		0			0
$901$	1.48913			0.0496100
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.74456	−	5.04868i	−0.290679	−	0.167824i
$906$		0			0
$907$	−25.8884	+	14.9467i	−0.859611	+	0.496297i	−0.863882	−	0.503694i	$-0.831974\pi$
$907$	−25.8884	+	14.9467i	−0.859611	+	0.496297i	0.00427097	+	0.999991i	$0.498641\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−17.9015	−	31.0063i	−0.593102	−	1.02728i	−0.993812	−	0.111078i	$-0.964570\pi$
$911$	−17.9015	−	31.0063i	−0.593102	−	1.02728i	0.400710	−	0.916205i	$-0.368764\pi$
$912$		0			0
$913$	1.93070	−	3.34408i	0.0638970	−	0.110673i
$914$		0			0
$915$		0			0
$916$		0			0
$917$		−	9.74749i		−	0.321891i
$918$		0			0
$919$		−	36.9711i		−	1.21956i	−0.792570	−	0.609781i	$-0.791257\pi$
$919$		−	36.9711i		−	1.21956i	0.792570	−	0.609781i	$-0.208743\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−14.0814	+	24.3897i	−0.463494	+	0.802796i
$924$		0			0
$925$	4.62772	+	8.01544i	0.152158	+	0.263546i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−16.0693	+	9.27761i	−0.527217	+	0.304389i	−0.739882	−	0.672736i	$-0.765119\pi$
$929$	−16.0693	+	9.27761i	−0.527217	+	0.304389i	0.212666	+	0.977125i	$0.431785\pi$
$930$		0			0
$931$	−21.8802	−	12.6325i	−0.717094	−	0.414014i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	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	$0.231565\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	11.6970	+	6.75327i	0.381312	+	0.220150i	0.678389	−	0.734703i	$-0.262678\pi$
$941$	11.6970	+	6.75327i	0.381312	+	0.220150i	−0.297077	+	0.954854i	$0.596012\pi$
$942$		0			0
$943$	−18.9123	+	10.9190i	−0.615869	+	0.355572i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−3.28515	−	5.69005i	−0.106753	−	0.184902i	0.807700	−	0.589594i	$-0.200712\pi$
$947$	−3.28515	−	5.69005i	−0.106753	−	0.184902i	−0.914453	+	0.404692i	$0.867379\pi$
$948$		0			0
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$		0			0
$952$		0			0
$953$		−	10.2997i		−	0.333641i	−0.985987	−	0.166821i	$-0.946650\pi$
$953$		−	10.2997i		−	0.333641i	0.985987	−	0.166821i	$-0.0533500\pi$
$954$		0			0
$955$			38.0978i			1.23282i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−3.50283	+	6.06709i	−0.113112	+	0.195916i
$960$		0			0
$961$	17.5475	+	30.3932i	0.566050	+	0.980427i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	16.9307	−	9.77495i	0.545019	−	0.314667i
$966$		0			0
$967$	40.5748	+	23.4259i	1.30480	+	0.753325i	0.981223	−	0.192878i	$-0.0617821\pi$
$967$	40.5748	+	23.4259i	1.30480	+	0.753325i	0.323574	+	0.946203i	$0.395115\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−37.0019			−1.18745			−0.593724	−	0.804669i	$-0.702343\pi$
$971$	−37.0019			−1.18745			−0.593724	+	0.804669i	$0.702343\pi$
$972$		0			0
$973$	−19.6277			−0.629236
$974$		0			0
$975$		0			0
$976$		0			0
$977$	47.3614	+	27.3441i	1.51523	+	0.874816i	0.999841	+	0.0178572i	$0.00568444\pi$
$977$	47.3614	+	27.3441i	1.51523	+	0.874816i	0.515385	+	0.856959i	$0.327649\pi$
$978$		0			0
$979$	5.24224	−	3.02661i	0.167543	−	0.0967307i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−17.2079	−	29.8050i	−0.548847	−	0.950631i	−0.998354	−	0.0573540i	$-0.981734\pi$
$983$	−17.2079	−	29.8050i	−0.548847	−	0.950631i	0.449507	−	0.893277i	$-0.351600\pi$
$984$		0			0
$985$	30.2337	−	52.3663i	0.963325	−	1.66853i
$986$		0			0
$987$		0			0
$988$		0			0
$989$		−	24.8935i		−	0.791568i
$990$		0			0
$991$		−	7.65492i		−	0.243167i	−0.992581	−	0.121583i	$-0.961203\pi$
$991$		−	7.65492i		−	0.243167i	0.992581	−	0.121583i	$-0.0387972\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	16.2912	−	28.2171i	0.516465	−	0.894543i
$996$		0			0
$997$	−12.0693	−	20.9046i	−0.382238	−	0.662056i	0.609143	−	0.793060i	$-0.291513\pi$
$997$	−12.0693	−	20.9046i	−0.382238	−	0.662056i	−0.991382	+	0.131004i	$0.958180\pi$
$998$		0			0
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.2.h.a.11.3	✓	8	72.43	odd	6
36.2.h.a.11.4	yes	8	72.61	even	6
36.2.h.a.23.3	yes	8	24.5	odd	2
36.2.h.a.23.4	yes	8	24.11	even	2
108.2.h.a.35.1		8	72.29	odd	6
108.2.h.a.35.2		8	72.11	even	6
108.2.h.a.71.1		8	8.3	odd	2
108.2.h.a.71.2		8	8.5	even	2
324.2.b.b.323.1		8	72.13	even	6
324.2.b.b.323.2		8	72.59	even	6
324.2.b.b.323.7		8	72.67	odd	6
324.2.b.b.323.8		8	72.5	odd	6
576.2.s.f.191.1		8	36.7	odd	6
576.2.s.f.191.4		8	9.7	even	3
576.2.s.f.383.1		8	3.2	odd	2
576.2.s.f.383.4		8	12.11	even	2
900.2.o.a.299.1		16	360.187	even	12
900.2.o.a.299.3		16	360.133	odd	12
900.2.o.a.299.6		16	360.277	odd	12
900.2.o.a.299.8		16	360.43	even	12
900.2.o.a.599.1		16	120.53	even	4
900.2.o.a.599.3		16	120.107	odd	4
900.2.o.a.599.6		16	120.83	odd	4
900.2.o.a.599.8		16	120.77	even	4
900.2.r.c.551.1		8	360.349	even	6
900.2.r.c.551.2		8	360.259	odd	6
900.2.r.c.851.1		8	120.59	even	2
900.2.r.c.851.2		8	120.29	odd	2
1728.2.s.f.575.1		8	36.11	even	6	inner
1728.2.s.f.575.2		8	9.2	odd	6	inner
1728.2.s.f.1151.1		8	1.1	even	1	trivial
1728.2.s.f.1151.2		8	4.3	odd	2	inner
5184.2.c.j.5183.1		8	9.5	odd	6
5184.2.c.j.5183.2		8	36.23	even	6
5184.2.c.j.5183.7		8	9.4	even	3
5184.2.c.j.5183.8		8	36.31	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:	\( N \)	\(=\)	\( 1728 = 2^{6} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1728.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.18614 - 1.26217i) q^{5} +(-1.10489 + 0.637910i) q^{7} +O(q^{10})\)	\(q+(-2.18614 - 1.26217i) q^{5} +(-1.10489 + 0.637910i) q^{7} +(-0.252704 - 0.437696i) q^{11} +(-1.18614 + 2.05446i) q^{13} -0.792287i q^{17} +4.70285i q^{19} +(1.61030 - 2.78912i) q^{23} +(0.686141 + 1.18843i) q^{25} +(2.18614 - 1.26217i) q^{29} +(7.04069 + 4.06494i) q^{31} +3.22060 q^{35} +6.74456 q^{37} +(-5.87228 - 3.39036i) q^{41} +(6.69391 - 3.86473i) q^{43} +(0.599485 + 1.03834i) q^{47} +(-2.68614 + 4.65253i) q^{49} +1.87953i q^{53} +1.27582i q^{55} +(6.18850 - 10.7188i) q^{59} +(-1.18614 - 2.05446i) q^{61} +(5.18614 - 2.99422i) q^{65} +(6.69391 + 3.86473i) q^{67} +11.8716 q^{71} +3.37228 q^{73} +(0.558422 + 0.322405i) q^{77} +(8.55691 - 4.94034i) q^{79} +(3.82009 + 6.61659i) q^{83} +(-1.00000 + 1.73205i) q^{85} +11.9769i q^{89} -3.02661i q^{91} +(5.93580 - 10.2811i) q^{95} +(-5.24456 - 9.08385i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{5}+O(q^{10}) \) 8 * q - 6 * q^5	\( 8 q - 6 q^{5} + 2 q^{13} - 6 q^{25} + 6 q^{29} + 8 q^{37} - 24 q^{41} - 10 q^{49} + 2 q^{61} + 30 q^{65} + 4 q^{73} - 30 q^{77} - 8 q^{85} + 4 q^{97}+O(q^{100}) \) 8 * q - 6 * q^5 + 2 * q^13 - 6 * q^25 + 6 * q^29 + 8 * q^37 - 24 * q^41 - 10 * q^49 + 2 * q^61 + 30 * q^65 + 4 * q^73 - 30 * q^77 - 8 * q^85 + 4 * q^97

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