LMFDB - Embedded newform 1260.2.s.c.541.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1260,2,Mod(361,1260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1260, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))

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

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

chi := DirichletCharacter("1260.361");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1260.s (of order $3$, degree $2$, 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:	$10.0611506547$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 140)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			541.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	1260.541
Dual form			1260.2.s.c.361.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})$	$q+(-0.500000 + 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +(3.00000 + 5.19615i) q^{11} +2.00000 q^{13} +(-3.00000 - 5.19615i) q^{17} +(-4.00000 + 6.92820i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.00000 + 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} +3.00000 q^{41} +5.00000 q^{43} +(5.50000 + 4.33013i) q^{49} +(6.00000 + 10.3923i) q^{53} -6.00000 q^{55} +(0.500000 - 0.866025i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(3.50000 + 6.06218i) q^{67} +(5.00000 + 8.66025i) q^{73} +(3.00000 + 15.5885i) q^{77} +(2.00000 - 3.46410i) q^{79} -3.00000 q^{83} +6.00000 q^{85} +(-1.50000 + 2.59808i) q^{89} +(5.00000 + 1.73205i) q^{91} +(-4.00000 - 6.92820i) q^{95} -10.0000 q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{5} + 5 q^{7}+O(q^{10}) $ 2 * q - q^5 + 5 * q^7	$ 2 q - q^{5} + 5 q^{7} + 6 q^{11} + 4 q^{13} - 6 q^{17} - 8 q^{19} + 3 q^{23} - q^{25} - 6 q^{29} - 2 q^{31} - 4 q^{35} - 8 q^{37} + 6 q^{41} + 10 q^{43} + 11 q^{49} + 12 q^{53} - 12 q^{55} + q^{61} - 2 q^{65} + 7 q^{67} + 10 q^{73} + 6 q^{77} + 4 q^{79} - 6 q^{83} + 12 q^{85} - 3 q^{89} + 10 q^{91} - 8 q^{95} - 20 q^{97}+O(q^{100}) $ 2 * q - q^5 + 5 * q^7 + 6 * q^11 + 4 * q^13 - 6 * q^17 - 8 * q^19 + 3 * q^23 - q^25 - 6 * q^29 - 2 * q^31 - 4 * q^35 - 8 * q^37 + 6 * q^41 + 10 * q^43 + 11 * q^49 + 12 * q^53 - 12 * q^55 + q^61 - 2 * q^65 + 7 * q^67 + 10 * q^73 + 6 * q^77 + 4 * q^79 - 6 * q^83 + 12 * q^85 - 3 * q^89 + 10 * q^91 - 8 * q^95 - 20 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1260\mathbb{Z}\right)^\times$.

$n$	$281$	$631$	$757$	$1081$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i
$6$		0			0
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$7$	2.50000	+	0.866025i	0.944911	+	0.327327i
$8$		0			0
$9$		0			0
$10$		0			0
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.821541	+	0.570149i	$0.193114\pi$
$11$	3.00000	+	5.19615i	0.904534	+	1.56670i	0.0829925	+	0.996550i	$0.473552\pi$
$12$		0			0
$13$	2.00000			0.554700			0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000			0.554700			0.277350	+	0.960769i	$0.410544\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	−0.957892	−	0.287129i	$-0.907299\pi$
$17$	−3.00000	−	5.19615i	−0.727607	−	1.26025i	0.230285	−	0.973123i	$-0.426034\pi$
$18$		0			0
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.114708	+	0.993399i	$0.536593\pi$
$19$	−4.00000	+	6.92820i	−0.917663	+	1.58944i	−0.802955	+	0.596040i	$0.796740\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	−0.666190	−	0.745782i	$-0.732076\pi$
$23$	1.50000	−	2.59808i	0.312772	−	0.541736i	0.978961	+	0.204046i	$0.0654092\pi$
$24$		0			0
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3.00000			−0.557086			−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000			−0.557086			−0.278543	+	0.960424i	$0.589851\pi$
$30$		0			0
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	0.762140	−	0.647412i	$-0.224149\pi$
$31$	−1.00000	−	1.73205i	−0.179605	−	0.311086i	−0.941745	+	0.336327i	$0.890815\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−2.00000	+	1.73205i	−0.338062	+	0.292770i
$36$		0			0
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	0.323640	+	0.946180i	$0.395093\pi$
$37$	−4.00000	+	6.92820i	−0.657596	+	1.13899i	−0.981236	+	0.192809i	$0.938240\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	3.00000			0.468521			0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000			0.468521			0.234261	+	0.972174i	$0.424733\pi$
$42$		0			0
$43$	5.00000			0.762493			0.381246	−	0.924473i	$-0.375495\pi$
$43$	5.00000			0.762493			0.381246	+	0.924473i	$0.375495\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$		0			0
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	0.902557	+	0.430570i	$0.141688\pi$
$53$	6.00000	+	10.3923i	0.824163	+	1.42749i	−0.0783936	+	0.996922i	$0.524979\pi$
$54$		0			0
$55$	−6.00000			−0.809040
$56$		0			0
$57$		0			0
$58$		0			0
$59$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$59$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.00000	+	1.73205i	−0.124035	+	0.214834i
$66$		0			0
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	0.996659	−	0.0816792i	$-0.0260283\pi$
$67$	3.50000	+	6.06218i	0.427593	+	0.740613i	−0.569066	+	0.822292i	$0.692695\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	0.994850	+	0.101361i	$0.0323196\pi$
$73$	5.00000	+	8.66025i	0.585206	+	1.01361i	−0.409644	+	0.912245i	$0.634347\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.00000	+	15.5885i	0.341882	+	1.77647i
$78$		0			0
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	−0.731307	−	0.682048i	$-0.761089\pi$
$79$	2.00000	−	3.46410i	0.225018	−	0.389742i	0.956325	+	0.292306i	$0.0944227\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−3.00000			−0.329293			−0.164646	−	0.986353i	$-0.552648\pi$
$83$	−3.00000			−0.329293			−0.164646	+	0.986353i	$0.552648\pi$
$84$		0			0
$85$	6.00000			0.650791
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	−0.934508	−	0.355942i	$-0.884160\pi$
$89$	−1.50000	+	2.59808i	−0.159000	+	0.275396i	0.775509	+	0.631337i	$0.217494\pi$
$90$		0			0
$91$	5.00000	+	1.73205i	0.524142	+	0.181568i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−4.00000	−	6.92820i	−0.410391	−	0.710819i
$96$		0			0
$97$	−10.0000			−1.01535			−0.507673	−	0.861550i	$-0.669494\pi$
$97$	−10.0000			−1.01535			−0.507673	+	0.861550i	$0.669494\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	0.781697	−	0.623658i	$-0.214354\pi$
$101$	−1.50000	−	2.59808i	−0.149256	−	0.258518i	−0.930953	+	0.365140i	$0.881021\pi$
$102$		0			0
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	−0.929377	−	0.369132i	$-0.879655\pi$
$107$	−1.50000	+	2.59808i	−0.145010	+	0.251166i	0.784366	+	0.620298i	$0.212988\pi$
$108$		0			0
$109$	−8.50000	−	14.7224i	−0.814152	−	1.41015i	−0.909935	−	0.414751i	$-0.863869\pi$
$109$	−8.50000	−	14.7224i	−0.814152	−	1.41015i	0.0957826	−	0.995402i	$-0.469465\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.0000			1.12887			0.564433	−	0.825479i	$-0.309095\pi$
$113$	12.0000			1.12887			0.564433	+	0.825479i	$0.309095\pi$
$114$		0			0
$115$	1.50000	+	2.59808i	0.139876	+	0.242272i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.00000	−	15.5885i	−0.275010	−	1.42899i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.00000			0.0894427
$126$		0			0
$127$	8.00000			0.709885			0.354943	−	0.934888i	$-0.384500\pi$
$127$	8.00000			0.709885			0.354943	+	0.934888i	$0.384500\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	−0.475380	−	0.879781i	$-0.657689\pi$
$131$	6.00000	−	10.3923i	0.524222	−	0.907980i	0.999602	−	0.0281993i	$-0.00897729\pi$
$132$		0			0
$133$	−16.0000	+	13.8564i	−1.38738	+	1.20150i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	−0.999893	−	0.0146279i	$-0.995344\pi$
$137$	−6.00000	−	10.3923i	−0.512615	−	0.887875i	0.487278	−	0.873247i	$-0.337990\pi$
$138$		0			0
$139$	2.00000			0.169638			0.0848189	−	0.996396i	$-0.472969\pi$
$139$	2.00000			0.169638			0.0848189	+	0.996396i	$0.472969\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	6.00000	+	10.3923i	0.501745	+	0.869048i
$144$		0			0
$145$	1.50000	−	2.59808i	0.124568	−	0.215758i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	0.376061	+	0.926595i	$0.377278\pi$
$149$	−7.50000	+	12.9904i	−0.614424	+	1.06421i	−0.990485	+	0.137619i	$0.956055\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	2.00000			0.160644
$156$		0			0
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	−0.997609	−	0.0691164i	$-0.977982\pi$
$157$	−7.00000	−	12.1244i	−0.558661	−	0.967629i	0.438948	−	0.898513i	$-0.355351\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.00000	−	5.19615i	0.472866	−	0.409514i
$162$		0			0
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	21.0000			1.62503			0.812514	−	0.582941i	$-0.198098\pi$
$167$	21.0000			1.62503			0.812514	+	0.582941i	$0.198098\pi$
$168$		0			0
$169$	−9.00000			−0.692308
$170$		0			0
$171$		0			0
$172$		0			0
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$		0			0
$175$	−0.500000	−	2.59808i	−0.0377964	−	0.196396i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	0.731858	−	0.681457i	$-0.238654\pi$
$179$	−3.00000	−	5.19615i	−0.224231	−	0.388379i	−0.956088	+	0.293079i	$0.905320\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−4.00000	−	6.92820i	−0.294086	−	0.509372i
$186$		0			0
$187$	18.0000	−	31.1769i	1.31629	−	2.27988i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$		0			0
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	18.0000			1.28245			0.641223	−	0.767354i	$-0.278427\pi$
$197$	18.0000			1.28245			0.641223	+	0.767354i	$0.278427\pi$
$198$		0			0
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	−0.965272	−	0.261245i	$-0.915867\pi$
$199$	−10.0000	−	17.3205i	−0.708881	−	1.22782i	0.256391	−	0.966573i	$-0.417466\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−7.50000	−	2.59808i	−0.526397	−	0.182349i
$204$		0			0
$205$	−1.50000	+	2.59808i	−0.104765	+	0.181458i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−48.0000			−3.32023
$210$		0			0
$211$	−4.00000			−0.275371			−0.137686	−	0.990476i	$-0.543966\pi$
$211$	−4.00000			−0.275371			−0.137686	+	0.990476i	$0.543966\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−2.50000	+	4.33013i	−0.170499	+	0.295312i
$216$		0			0
$217$	−1.00000	−	5.19615i	−0.0678844	−	0.352738i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$		0			0
$223$	8.00000			0.535720			0.267860	−	0.963458i	$-0.413684\pi$
$223$	8.00000			0.535720			0.267860	+	0.963458i	$0.413684\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	−0.897173	−	0.441679i	$-0.854383\pi$
$229$	−1.00000	+	1.73205i	−0.0660819	+	0.114457i	0.831092	+	0.556136i	$0.187717\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−6.00000			−0.388108			−0.194054	−	0.980991i	$-0.562164\pi$
$239$	−6.00000			−0.388108			−0.194054	+	0.980991i	$0.562164\pi$
$240$		0			0
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	−0.892058	−	0.451920i	$-0.850739\pi$
$241$	−13.0000	−	22.5167i	−0.837404	−	1.45043i	0.0546547	−	0.998505i	$-0.482594\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−6.50000	+	2.59808i	−0.415270	+	0.165985i
$246$		0			0
$247$	−8.00000	+	13.8564i	−0.509028	+	0.881662i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$	18.0000			1.13165
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−12.0000	+	20.7846i	−0.748539	+	1.29651i	0.199983	+	0.979799i	$0.435911\pi$
$257$	−12.0000	+	20.7846i	−0.748539	+	1.29651i	−0.948523	+	0.316709i	$0.897422\pi$
$258$		0			0
$259$	−16.0000	+	13.8564i	−0.994192	+	0.860995i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	0.816066	−	0.577959i	$-0.196151\pi$
$263$	−1.50000	−	2.59808i	−0.0924940	−	0.160204i	−0.908560	+	0.417755i	$0.862817\pi$
$264$		0			0
$265$	−12.0000			−0.737154
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	0.541533	−	0.840679i	$-0.317844\pi$
$269$	−7.50000	−	12.9904i	−0.457283	−	0.792038i	−0.998816	+	0.0486418i	$0.984511\pi$
$270$		0			0
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	−0.513905	−	0.857847i	$-0.671801\pi$
$271$	8.00000	−	13.8564i	0.485965	−	0.841717i	0.999870	+	0.0161307i	$0.00513477\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	3.00000	−	5.19615i	0.180907	−	0.313340i
$276$		0			0
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	0.980373	+	0.197153i	$0.0631696\pi$
$277$	11.0000	+	19.0526i	0.660926	+	1.14476i	−0.319447	+	0.947604i	$0.603497\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$		0			0
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	−0.993626	−	0.112728i	$-0.964041\pi$
$283$	−10.0000	−	17.3205i	−0.594438	−	1.02960i	0.399188	−	0.916869i	$-0.369292\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	7.50000	+	2.59808i	0.442711	+	0.153360i
$288$		0			0
$289$	−9.50000	+	16.4545i	−0.558824	+	0.967911i
$290$		0			0
$291$		0			0
$292$		0			0
$293$	12.0000			0.701047			0.350524	−	0.936554i	$-0.386004\pi$
$293$	12.0000			0.701047			0.350524	+	0.936554i	$0.386004\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$		0			0
$298$		0			0
$299$	3.00000	−	5.19615i	0.173494	−	0.300501i
$300$		0			0
$301$	12.5000	+	4.33013i	0.720488	+	0.249584i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	0.500000	+	0.866025i	0.0286299	+	0.0495885i
$306$		0			0
$307$	−19.0000			−1.08439			−0.542194	−	0.840254i	$-0.682406\pi$
$307$	−19.0000			−1.08439			−0.542194	+	0.840254i	$0.682406\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$311$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$312$		0			0
$313$	2.00000	−	3.46410i	0.113047	−	0.195803i	−0.803951	−	0.594696i	$-0.797272\pi$
$313$	2.00000	−	3.46410i	0.113047	−	0.195803i	0.916997	+	0.398894i	$0.130606\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	−0.494489	−	0.869184i	$-0.664645\pi$
$317$	9.00000	−	15.5885i	0.505490	−	0.875535i	0.999980	−	0.00635137i	$-0.00202172\pi$
$318$		0			0
$319$	−9.00000	−	15.5885i	−0.503903	−	0.872786i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	48.0000			2.67079
$324$		0			0
$325$	−1.00000	−	1.73205i	−0.0554700	−	0.0960769i
$326$		0			0
$327$		0			0
$328$		0			0
$329$		0			0
$330$		0			0
$331$	11.0000	−	19.0526i	0.604615	−	1.04722i	−0.387498	−	0.921871i	$-0.626660\pi$
$331$	11.0000	−	19.0526i	0.604615	−	1.04722i	0.992112	−	0.125353i	$-0.0400062\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−7.00000			−0.382451
$336$		0			0
$337$	20.0000			1.08947			0.544735	−	0.838608i	$-0.316630\pi$
$337$	20.0000			1.08947			0.544735	+	0.838608i	$0.316630\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$		0			0
$343$	10.0000	+	15.5885i	0.539949	+	0.841698i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	−0.959090	−	0.283101i	$-0.908637\pi$
$347$	−13.5000	−	23.3827i	−0.724718	−	1.25525i	0.234372	−	0.972147i	$-0.424697\pi$
$348$		0			0
$349$	−1.00000			−0.0535288			−0.0267644	−	0.999642i	$-0.508520\pi$
$349$	−1.00000			−0.0535288			−0.0267644	+	0.999642i	$0.508520\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	0.661004	−	0.750382i	$-0.270130\pi$
$353$	−6.00000	−	10.3923i	−0.319348	−	0.553127i	−0.980352	+	0.197256i	$0.936797\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		0			0
$358$		0			0
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	−22.5000	−	38.9711i	−1.18421	−	2.05111i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−10.0000			−0.523424
$366$		0			0
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	0.793370	−	0.608740i	$-0.208325\pi$
$367$	−2.50000	−	4.33013i	−0.130499	−	0.226031i	−0.923869	+	0.382709i	$0.874991\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	6.00000	+	31.1769i	0.311504	+	1.61862i
$372$		0			0
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	−0.581122	−	0.813816i	$-0.697386\pi$
$373$	8.00000	−	13.8564i	0.414224	−	0.717458i	0.995347	+	0.0963587i	$0.0307196\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−6.00000			−0.309016
$378$		0			0
$379$	8.00000			0.410932			0.205466	−	0.978664i	$-0.434129\pi$
$379$	8.00000			0.410932			0.205466	+	0.978664i	$0.434129\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	1.50000	−	2.59808i	0.0766464	−	0.132755i	−0.825155	−	0.564907i	$-0.808912\pi$
$383$	1.50000	−	2.59808i	0.0766464	−	0.132755i	0.901801	+	0.432151i	$0.142245\pi$
$384$		0			0
$385$	−15.0000	−	5.19615i	−0.764471	−	0.264820i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	0.932002	−	0.362454i	$-0.118061\pi$
$389$	3.00000	+	5.19615i	0.152106	+	0.263455i	−0.779895	+	0.625910i	$0.784728\pi$
$390$		0			0
$391$	−18.0000			−0.910299
$392$		0			0
$393$		0			0
$394$		0			0
$395$	2.00000	+	3.46410i	0.100631	+	0.174298i
$396$		0			0
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	0.330075	+	0.943955i	$0.392926\pi$
$397$	−13.0000	+	22.5167i	−0.652451	+	1.13008i	−0.982526	+	0.186124i	$0.940407\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	−0.826139	−	0.563466i	$-0.809468\pi$
$401$	1.50000	−	2.59808i	0.0749064	−	0.129742i	0.901046	+	0.433724i	$0.142801\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−48.0000			−2.37927
$408$		0			0
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	0.697406	−	0.716677i	$-0.254338\pi$
$409$	−5.50000	−	9.52628i	−0.271957	−	0.471044i	−0.969363	+	0.245633i	$0.921004\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$		0			0
$414$		0			0
$415$	1.50000	−	2.59808i	0.0736321	−	0.127535i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$		0			0
$421$	23.0000			1.12095			0.560476	−	0.828171i	$-0.310618\pi$
$421$	23.0000			1.12095			0.560476	+	0.828171i	$0.310618\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−3.00000	+	5.19615i	−0.145521	+	0.252050i
$426$		0			0
$427$	2.00000	−	1.73205i	0.0967868	−	0.0838198i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$		0			0
$433$	−28.0000			−1.34559			−0.672797	−	0.739827i	$-0.734907\pi$
$433$	−28.0000			−1.34559			−0.672797	+	0.739827i	$0.734907\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	12.0000	+	20.7846i	0.574038	+	0.994263i
$438$		0			0
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	−0.310228	−	0.950662i	$-0.600405\pi$
$439$	14.0000	−	24.2487i	0.668184	−	1.15733i	0.978412	−	0.206666i	$-0.0662612\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	−0.739100	−	0.673596i	$-0.764749\pi$
$443$	4.50000	−	7.79423i	0.213801	−	0.370315i	0.952901	+	0.303281i	$0.0980821\pi$
$444$		0			0
$445$	−1.50000	−	2.59808i	−0.0711068	−	0.123161i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	9.00000			0.424736			0.212368	−	0.977190i	$-0.431882\pi$
$449$	9.00000			0.424736			0.212368	+	0.977190i	$0.431882\pi$
$450$		0			0
$451$	9.00000	+	15.5885i	0.423793	+	0.734032i
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−4.00000	+	3.46410i	−0.187523	+	0.162400i
$456$		0			0
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	−0.815449	−	0.578829i	$-0.803510\pi$
$457$	2.00000	−	3.46410i	0.0935561	−	0.162044i	0.909005	+	0.416785i	$0.136843\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−30.0000			−1.39724			−0.698620	−	0.715493i	$-0.746202\pi$
$461$	−30.0000			−1.39724			−0.698620	+	0.715493i	$0.746202\pi$
$462$		0			0
$463$	29.0000			1.34774			0.673872	−	0.738848i	$-0.264630\pi$
$463$	29.0000			1.34774			0.673872	+	0.738848i	$0.264630\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	−0.177492	−	0.984122i	$-0.556798\pi$
$467$	16.5000	−	28.5788i	0.763529	−	1.32247i	0.941021	−	0.338349i	$-0.109868\pi$
$468$		0			0
$469$	3.50000	+	18.1865i	0.161615	+	0.839776i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	15.0000	+	25.9808i	0.689701	+	1.19460i
$474$		0			0
$475$	8.00000			0.367065
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	−0.973321	−	0.229447i	$-0.926308\pi$
$479$	−15.0000	−	25.9808i	−0.685367	−	1.18709i	0.287954	−	0.957644i	$-0.407025\pi$
$480$		0			0
$481$	−8.00000	+	13.8564i	−0.364769	+	0.631798i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	5.00000	−	8.66025i	0.227038	−	0.393242i
$486$		0			0
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	0.761052	−	0.648691i	$-0.224683\pi$
$487$	−4.00000	−	6.92820i	−0.181257	−	0.313947i	−0.942309	+	0.334744i	$0.891350\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−6.00000			−0.270776			−0.135388	−	0.990793i	$-0.543228\pi$
$491$	−6.00000			−0.270776			−0.135388	+	0.990793i	$0.543228\pi$
$492$		0			0
$493$	9.00000	+	15.5885i	0.405340	+	0.702069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$		0			0
$498$		0			0
$499$	−1.00000	+	1.73205i	−0.0447661	+	0.0775372i	−0.887540	−	0.460730i	$-0.847588\pi$
$499$	−1.00000	+	1.73205i	−0.0447661	+	0.0775372i	0.842774	+	0.538267i	$0.180921\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	9.00000			0.401290			0.200645	−	0.979664i	$-0.435696\pi$
$503$	9.00000			0.401290			0.200645	+	0.979664i	$0.435696\pi$
$504$		0			0
$505$	3.00000			0.133498
$506$		0			0
$507$		0			0
$508$		0			0
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	−0.00339621	−	0.999994i	$-0.501081\pi$
$509$	19.5000	−	33.7750i	0.864322	−	1.49705i	0.867719	−	0.497056i	$-0.165586\pi$
$510$		0			0
$511$	5.00000	+	25.9808i	0.221187	+	1.14932i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	3.50000	+	6.06218i	0.154228	+	0.267131i
$516$		0			0
$517$		0			0
$518$		0			0
$519$		0			0
$520$		0			0
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	0.981347	+	0.192244i	$0.0615766\pi$
$521$	15.0000	+	25.9808i	0.657162	+	1.13824i	−0.324185	+	0.945994i	$0.605090\pi$
$522$		0			0
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.244507	+	0.969648i	$0.578626\pi$
$523$	−22.0000	+	38.1051i	−0.961993	+	1.66622i	−0.717486	+	0.696573i	$0.754707\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$		0			0
$529$	7.00000	+	12.1244i	0.304348	+	0.527146i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	6.00000			0.259889
$534$		0			0
$535$	−1.50000	−	2.59808i	−0.0648507	−	0.112325i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−6.00000	+	41.5692i	−0.258438	+	1.79051i
$540$		0			0
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	−0.988847	−	0.148933i	$-0.952416\pi$
$541$	−8.50000	+	14.7224i	−0.365444	+	0.632967i	0.623404	+	0.781900i	$0.285749\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	17.0000			0.728200
$546$		0			0
$547$	−19.0000			−0.812381			−0.406191	−	0.913788i	$-0.633143\pi$
$547$	−19.0000			−0.812381			−0.406191	+	0.913788i	$0.633143\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	12.0000	−	20.7846i	0.511217	−	0.885454i
$552$		0			0
$553$	8.00000	−	6.92820i	0.340195	−	0.294617i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$		0			0
$559$	10.0000			0.422955
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	0.755482	−	0.655169i	$-0.227403\pi$
$563$	−4.50000	−	7.79423i	−0.189652	−	0.328488i	−0.945134	+	0.326682i	$0.894069\pi$
$564$		0			0
$565$	−6.00000	+	10.3923i	−0.252422	+	0.437208i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	−0.990668	−	0.136295i	$-0.956481\pi$
$569$	−9.00000	+	15.5885i	−0.377300	+	0.653502i	0.613369	+	0.789797i	$0.289814\pi$
$570$		0			0
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	0.983444	−	0.181210i	$-0.0580014\pi$
$571$	8.00000	+	13.8564i	0.334790	+	0.579873i	−0.648655	+	0.761083i	$0.724668\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−3.00000			−0.125109
$576$		0			0
$577$	5.00000	+	8.66025i	0.208153	+	0.360531i	0.951133	−	0.308783i	$-0.0999216\pi$
$577$	5.00000	+	8.66025i	0.208153	+	0.360531i	−0.742980	+	0.669314i	$0.766588\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−7.50000	−	2.59808i	−0.311152	−	0.107786i
$582$		0			0
$583$	−36.0000	+	62.3538i	−1.49097	+	2.58243i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−12.0000			−0.495293			−0.247647	−	0.968850i	$-0.579657\pi$
$587$	−12.0000			−0.495293			−0.247647	+	0.968850i	$0.579657\pi$
$588$		0			0
$589$	16.0000			0.659269
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	−0.962522	−	0.271205i	$-0.912578\pi$
$593$	−6.00000	+	10.3923i	−0.246390	+	0.426761i	0.716131	+	0.697966i	$0.245911\pi$
$594$		0			0
$595$	15.0000	+	5.19615i	0.614940	+	0.213021i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−22.0000			−0.897399			−0.448699	−	0.893683i	$-0.648113\pi$
$601$	−22.0000			−0.897399			−0.448699	+	0.893683i	$0.648113\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−12.5000	−	21.6506i	−0.508197	−	0.880223i
$606$		0			0
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.0134214	−	0.999910i	$-0.495728\pi$
$607$	21.5000	−	37.2391i	0.872658	−	1.51149i	0.859237	−	0.511578i	$-0.170939\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$		0			0
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	0.845124	−	0.534570i	$-0.179527\pi$
$613$	−1.00000	−	1.73205i	−0.0403896	−	0.0699569i	−0.885514	+	0.464614i	$0.846193\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	12.0000			0.483102			0.241551	−	0.970388i	$-0.422344\pi$
$617$	12.0000			0.483102			0.241551	+	0.970388i	$0.422344\pi$
$618$		0			0
$619$	−7.00000	−	12.1244i	−0.281354	−	0.487319i	0.690365	−	0.723462i	$-0.257450\pi$
$619$	−7.00000	−	12.1244i	−0.281354	−	0.487319i	−0.971718	+	0.236143i	$0.924117\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−6.00000	+	5.19615i	−0.240385	+	0.208179i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	48.0000			1.91389
$630$		0			0
$631$	38.0000			1.51276			0.756378	−	0.654135i	$-0.226967\pi$
$631$	38.0000			1.51276			0.756378	+	0.654135i	$0.226967\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−4.00000	+	6.92820i	−0.158735	+	0.274937i
$636$		0			0
$637$	11.0000	+	8.66025i	0.435836	+	0.343132i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	−0.937451	−	0.348117i	$-0.886821\pi$
$641$	−19.5000	−	33.7750i	−0.770204	−	1.33403i	0.167247	−	0.985915i	$-0.446512\pi$
$642$		0			0
$643$	20.0000			0.788723			0.394362	−	0.918955i	$-0.370966\pi$
$643$	20.0000			0.788723			0.394362	+	0.918955i	$0.370966\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	0.995194	−	0.0979182i	$-0.0312184\pi$
$647$	10.5000	+	18.1865i	0.412798	+	0.714986i	−0.582397	+	0.812905i	$0.697885\pi$
$648$		0			0
$649$		0			0
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−21.0000	+	36.3731i	−0.821794	+	1.42339i	0.0825519	+	0.996587i	$0.473693\pi$
$653$	−21.0000	+	36.3731i	−0.821794	+	1.42339i	−0.904345	+	0.426801i	$0.859640\pi$
$654$		0			0
$655$	6.00000	+	10.3923i	0.234439	+	0.406061i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−12.0000			−0.467454			−0.233727	−	0.972302i	$-0.575092\pi$
$659$	−12.0000			−0.467454			−0.233727	+	0.972302i	$0.575092\pi$
$660$		0			0
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	0.999874	−	0.0158695i	$-0.00505163\pi$
$661$	12.5000	+	21.6506i	0.486194	+	0.842112i	−0.513680	+	0.857982i	$0.671718\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−4.00000	−	20.7846i	−0.155113	−	0.805993i
$666$		0			0
$667$	−4.50000	+	7.79423i	−0.174241	+	0.301794i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	6.00000			0.231627
$672$		0			0
$673$	32.0000			1.23351			0.616755	−	0.787155i	$-0.288447\pi$
$673$	32.0000			1.23351			0.616755	+	0.787155i	$0.288447\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	−0.985517	−	0.169580i	$-0.945759\pi$
$677$	−9.00000	+	15.5885i	−0.345898	+	0.599113i	0.639618	+	0.768693i	$0.279092\pi$
$678$		0			0
$679$	−25.0000	−	8.66025i	−0.959412	−	0.332350i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.50000	−	12.9904i	−0.286980	−	0.497063i	0.686108	−	0.727500i	$-0.259318\pi$
$683$	−7.50000	−	12.9904i	−0.286980	−	0.497063i	−0.973087	+	0.230437i	$0.925985\pi$
$684$		0			0
$685$	12.0000			0.458496
$686$		0			0
$687$		0			0
$688$		0			0
$689$	12.0000	+	20.7846i	0.457164	+	0.791831i
$690$		0			0
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	−0.967901	−	0.251330i	$-0.919132\pi$
$691$	−7.00000	+	12.1244i	−0.266293	+	0.461232i	0.701609	+	0.712562i	$0.252465\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	−1.00000	+	1.73205i	−0.0379322	+	0.0657004i
$696$		0			0
$697$	−9.00000	−	15.5885i	−0.340899	−	0.590455i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−27.0000			−1.01978			−0.509888	−	0.860241i	$-0.670313\pi$
$701$	−27.0000			−1.01978			−0.509888	+	0.860241i	$0.670313\pi$
$702$		0			0
$703$	−32.0000	−	55.4256i	−1.20690	−	2.09042i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−1.50000	−	7.79423i	−0.0564133	−	0.293132i
$708$		0			0
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	−0.856484	−	0.516174i	$-0.827356\pi$
$709$	0.500000	−	0.866025i	0.0187779	−	0.0325243i	0.875262	+	0.483650i	$0.160689\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−6.00000			−0.224702
$714$		0			0
$715$	−12.0000			−0.448775
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	0.438141	+	0.898906i	$0.355637\pi$
$719$	−15.0000	+	25.9808i	−0.559406	+	0.968919i	−0.997546	+	0.0700124i	$0.977696\pi$
$720$		0			0
$721$	14.0000	−	12.1244i	0.521387	−	0.451535i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	1.50000	+	2.59808i	0.0557086	+	0.0964901i
$726$		0			0
$727$	23.0000			0.853023			0.426511	−	0.904482i	$-0.359742\pi$
$727$	23.0000			0.853023			0.426511	+	0.904482i	$0.359742\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−15.0000	−	25.9808i	−0.554795	−	0.960933i
$732$		0			0
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	−0.883902	−	0.467671i	$-0.845093\pi$
$733$	−1.00000	+	1.73205i	−0.0369358	+	0.0639748i	0.846967	+	0.531646i	$0.178426\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−21.0000	+	36.3731i	−0.773545	+	1.33982i
$738$		0			0
$739$	23.0000	+	39.8372i	0.846069	+	1.46543i	0.884690	+	0.466180i	$0.154370\pi$
$739$	23.0000	+	39.8372i	0.846069	+	1.46543i	−0.0386212	+	0.999254i	$0.512297\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	39.0000			1.43077			0.715386	−	0.698730i	$-0.246251\pi$
$743$	39.0000			1.43077			0.715386	+	0.698730i	$0.246251\pi$
$744$		0			0
$745$	−7.50000	−	12.9904i	−0.274779	−	0.475931i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−6.00000	+	5.19615i	−0.219235	+	0.189863i
$750$		0			0
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	−0.988761	−	0.149505i	$-0.952232\pi$
$751$	−10.0000	+	17.3205i	−0.364905	+	0.632034i	0.623856	+	0.781540i	$0.285565\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−10.0000			−0.363937
$756$		0			0
$757$	2.00000			0.0726912			0.0363456	−	0.999339i	$-0.488428\pi$
$757$	2.00000			0.0726912			0.0363456	+	0.999339i	$0.488428\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	−0.454935	−	0.890525i	$-0.650337\pi$
$761$	15.0000	−	25.9808i	0.543750	−	0.941802i	0.998684	−	0.0512772i	$-0.0163292\pi$
$762$		0			0
$763$	−8.50000	−	44.1673i	−0.307721	−	1.59896i
$764$		0			0
$765$		0			0
$766$		0			0
$767$		0			0
$768$		0			0
$769$	−34.0000			−1.22607			−0.613036	−	0.790055i	$-0.710052\pi$
$769$	−34.0000			−1.22607			−0.613036	+	0.790055i	$0.710052\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−21.0000	−	36.3731i	−0.755318	−	1.30825i	−0.945216	−	0.326445i	$-0.894149\pi$
$773$	−21.0000	−	36.3731i	−0.755318	−	1.30825i	0.189899	−	0.981804i	$-0.439184\pi$
$774$		0			0
$775$	−1.00000	+	1.73205i	−0.0359211	+	0.0622171i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−12.0000	+	20.7846i	−0.429945	+	0.744686i
$780$		0			0
$781$		0			0
$782$		0			0
$783$		0			0
$784$		0			0
$785$	14.0000			0.499681
$786$		0			0
$787$	15.5000	+	26.8468i	0.552515	+	0.956985i	0.998092	+	0.0617409i	$0.0196653\pi$
$787$	15.5000	+	26.8468i	0.552515	+	0.956985i	−0.445577	+	0.895244i	$0.647001\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	30.0000	+	10.3923i	1.06668	+	0.369508i
$792$		0			0
$793$	1.00000	−	1.73205i	0.0355110	−	0.0615069i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	12.0000			0.425062			0.212531	−	0.977154i	$-0.431829\pi$
$797$	12.0000			0.425062			0.212531	+	0.977154i	$0.431829\pi$
$798$		0			0
$799$		0			0
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−30.0000	+	51.9615i	−1.05868	+	1.83368i
$804$		0			0
$805$	1.50000	+	7.79423i	0.0528681	+	0.274710i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−25.5000	−	44.1673i	−0.896532	−	1.55284i	−0.831897	−	0.554930i	$-0.812745\pi$
$809$	−25.5000	−	44.1673i	−0.896532	−	1.55284i	−0.0646355	−	0.997909i	$-0.520588\pi$
$810$		0			0
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	8.00000	+	13.8564i	0.280228	+	0.485369i
$816$		0			0
$817$	−20.0000	+	34.6410i	−0.699711	+	1.21194i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	−0.665144	−	0.746715i	$-0.731630\pi$
$821$	9.00000	−	15.5885i	0.314102	−	0.544041i	0.979246	+	0.202674i	$0.0649632\pi$
$822$		0			0
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	0.877555	+	0.479477i	$0.159174\pi$
$823$	24.5000	+	42.4352i	0.854016	+	1.47920i	−0.0235383	+	0.999723i	$0.507493\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	45.0000			1.56480			0.782402	−	0.622774i	$-0.213994\pi$
$827$	45.0000			1.56480			0.782402	+	0.622774i	$0.213994\pi$
$828$		0			0
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	0.939696	−	0.342012i	$-0.111108\pi$
$829$	5.00000	+	8.66025i	0.173657	+	0.300783i	−0.766039	+	0.642795i	$0.777775\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	6.00000	−	41.5692i	0.207888	−	1.44029i
$834$		0			0
$835$	−10.5000	+	18.1865i	−0.363367	+	0.629371i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	42.0000			1.45000			0.725001	−	0.688748i	$-0.241839\pi$
$839$	42.0000			1.45000			0.725001	+	0.688748i	$0.241839\pi$
$840$		0			0
$841$	−20.0000			−0.689655
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.50000	−	7.79423i	0.154805	−	0.268130i
$846$		0			0
$847$	−50.0000	+	43.3013i	−1.71802	+	1.48785i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	12.0000	+	20.7846i	0.411355	+	0.712487i
$852$		0			0
$853$	32.0000			1.09566			0.547830	−	0.836590i	$-0.315454\pi$
$853$	32.0000			1.09566			0.547830	+	0.836590i	$0.315454\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	0.962048	+	0.272882i	$0.0879768\pi$
$857$	21.0000	+	36.3731i	0.717346	+	1.24248i	−0.244701	+	0.969599i	$0.578690\pi$
$858$		0			0
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	−0.829887	−	0.557931i	$-0.811595\pi$
$859$	2.00000	−	3.46410i	0.0682391	−	0.118194i	0.898126	+	0.439738i	$0.144929\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	16.5000	−	28.5788i	0.561667	−	0.972835i	−0.435685	−	0.900099i	$-0.643494\pi$
$863$	16.5000	−	28.5788i	0.561667	−	0.972835i	0.997351	−	0.0727356i	$-0.0231729\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$		0			0
$868$		0			0
$869$	24.0000			0.814144
$870$		0			0
$871$	7.00000	+	12.1244i	0.237186	+	0.410818i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	2.50000	+	0.866025i	0.0845154	+	0.0292770i
$876$		0			0
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	−0.301014	−	0.953620i	$-0.597325\pi$
$877$	20.0000	−	34.6410i	0.675352	−	1.16974i	0.976366	−	0.216124i	$-0.0693416\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−9.00000			−0.303218			−0.151609	−	0.988441i	$-0.548445\pi$
$881$	−9.00000			−0.303218			−0.151609	+	0.988441i	$0.548445\pi$
$882$		0			0
$883$	−28.0000			−0.942275			−0.471138	−	0.882060i	$-0.656156\pi$
$883$	−28.0000			−0.942275			−0.471138	+	0.882060i	$0.656156\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	28.5000	−	49.3634i	0.956936	−	1.65746i	0.227063	−	0.973880i	$-0.427088\pi$
$887$	28.5000	−	49.3634i	0.956936	−	1.65746i	0.729873	−	0.683582i	$-0.239579\pi$
$888$		0			0
$889$	20.0000	+	6.92820i	0.670778	+	0.232364i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		0			0
$894$		0			0
$895$	6.00000			0.200558
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.00000	+	5.19615i	0.100056	+	0.173301i
$900$		0			0
$901$	36.0000	−	62.3538i	1.19933	−	2.07731i
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−8.50000	+	14.7224i	−0.282550	+	0.489390i
$906$		0			0
$907$	−11.5000	−	19.9186i	−0.381851	−	0.661386i	0.609476	−	0.792805i	$-0.291380\pi$
$907$	−11.5000	−	19.9186i	−0.381851	−	0.661386i	−0.991327	+	0.131419i	$0.958047\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	−9.00000	−	15.5885i	−0.297857	−	0.515903i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	24.0000	−	20.7846i	0.792550	−	0.686368i
$918$		0			0
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	−0.924427	−	0.381358i	$-0.875456\pi$
$919$	−4.00000	+	6.92820i	−0.131948	+	0.228540i	0.792480	+	0.609898i	$0.208790\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	8.00000			0.263038
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−22.5000	+	38.9711i	−0.738201	+	1.27860i	0.215104	+	0.976591i	$0.430991\pi$
$929$	−22.5000	+	38.9711i	−0.738201	+	1.27860i	−0.953305	+	0.302010i	$0.902342\pi$
$930$		0			0
$931$	−52.0000	+	20.7846i	−1.70423	+	0.681188i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	18.0000	+	31.1769i	0.588663	+	1.01959i
$936$		0			0
$937$	44.0000			1.43742			0.718709	−	0.695311i	$-0.244734\pi$
$937$	44.0000			1.43742			0.718709	+	0.695311i	$0.244734\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.851146	+	0.524929i	$0.175908\pi$
$941$	27.0000	+	46.7654i	0.880175	+	1.52451i	0.0290288	+	0.999579i	$0.490759\pi$
$942$		0			0
$943$	4.50000	−	7.79423i	0.146540	−	0.253815i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.50000	−	7.79423i	0.146230	−	0.253278i	−0.783601	−	0.621264i	$-0.786619\pi$
$947$	4.50000	−	7.79423i	0.146230	−	0.253278i	0.929831	+	0.367986i	$0.119953\pi$
$948$		0			0
$949$	10.0000	+	17.3205i	0.324614	+	0.562247i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−36.0000			−1.16615			−0.583077	−	0.812417i	$-0.698151\pi$
$953$	−36.0000			−1.16615			−0.583077	+	0.812417i	$0.698151\pi$
$954$		0			0
$955$	−9.00000	−	15.5885i	−0.291233	−	0.504431i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−6.00000	−	31.1769i	−0.193750	−	1.00676i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	2.00000			0.0643823
$966$		0			0
$967$	−7.00000			−0.225105			−0.112552	−	0.993646i	$-0.535903\pi$
$967$	−7.00000			−0.225105			−0.112552	+	0.993646i	$0.535903\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	−0.946094	−	0.323891i	$-0.895009\pi$
$971$	−6.00000	+	10.3923i	−0.192549	+	0.333505i	0.753545	+	0.657396i	$0.228342\pi$
$972$		0			0
$973$	5.00000	+	1.73205i	0.160293	+	0.0555270i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	−0.868227	−	0.496167i	$-0.834741\pi$
$977$	−27.0000	−	46.7654i	−0.863807	−	1.49616i	0.00442082	−	0.999990i	$-0.498593\pi$
$978$		0			0
$979$	−18.0000			−0.575282
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	−0.989122	−	0.147100i	$-0.953006\pi$
$983$	−19.5000	−	33.7750i	−0.621953	−	1.07725i	0.367168	−	0.930155i	$-0.380327\pi$
$984$		0			0
$985$	−9.00000	+	15.5885i	−0.286764	+	0.496690i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	7.50000	−	12.9904i	0.238486	−	0.413070i
$990$		0			0
$991$	−13.0000	−	22.5167i	−0.412959	−	0.715265i	0.582253	−	0.813008i	$-0.302171\pi$
$991$	−13.0000	−	22.5167i	−0.412959	−	0.715265i	−0.995212	+	0.0977423i	$0.968838\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	20.0000			0.634043
$996$		0			0
$997$	−16.0000	−	27.7128i	−0.506725	−	0.877674i	−0.999970	−	0.00778294i	$-0.997523\pi$
$997$	−16.0000	−	27.7128i	−0.506725	−	0.877674i	0.493245	−	0.869891i	$-0.335811\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1260.2.s.c.541.1		2
3.2	odd	2		140.2.i.a.121.1	yes	2
7.2	even	3		8820.2.a.p.1.1		1
7.4	even	3	inner	1260.2.s.c.361.1		2
7.5	odd	6		8820.2.a.a.1.1		1
12.11	even	2		560.2.q.f.401.1		2
15.2	even	4		700.2.r.a.149.1		4
15.8	even	4		700.2.r.a.149.2		4
15.14	odd	2		700.2.i.b.401.1		2
21.2	odd	6		980.2.a.g.1.1		1
21.5	even	6		980.2.a.e.1.1		1
21.11	odd	6		140.2.i.a.81.1	✓	2
21.17	even	6		980.2.i.f.361.1		2
21.20	even	2		980.2.i.f.961.1		2
84.11	even	6		560.2.q.f.81.1		2
84.23	even	6		3920.2.a.k.1.1		1
84.47	odd	6		3920.2.a.w.1.1		1
105.2	even	12		4900.2.e.m.2549.1		2
105.23	even	12		4900.2.e.m.2549.2		2
105.32	even	12		700.2.r.a.249.2		4
105.44	odd	6		4900.2.a.i.1.1		1
105.47	odd	12		4900.2.e.n.2549.2		2
105.53	even	12		700.2.r.a.249.1		4
105.68	odd	12		4900.2.e.n.2549.1		2
105.74	odd	6		700.2.i.b.501.1		2
105.89	even	6		4900.2.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
140.2.i.a.81.1	✓	2	21.11	odd	6
140.2.i.a.121.1	yes	2	3.2	odd	2
560.2.q.f.81.1		2	84.11	even	6
560.2.q.f.401.1		2	12.11	even	2
700.2.i.b.401.1		2	15.14	odd	2
700.2.i.b.501.1		2	105.74	odd	6
700.2.r.a.149.1		4	15.2	even	4
700.2.r.a.149.2		4	15.8	even	4
700.2.r.a.249.1		4	105.53	even	12
700.2.r.a.249.2		4	105.32	even	12
980.2.a.e.1.1		1	21.5	even	6
980.2.a.g.1.1		1	21.2	odd	6
980.2.i.f.361.1		2	21.17	even	6
980.2.i.f.961.1		2	21.20	even	2
1260.2.s.c.361.1		2	7.4	even	3	inner
1260.2.s.c.541.1		2	1.1	even	1	trivial
3920.2.a.k.1.1		1	84.23	even	6
3920.2.a.w.1.1		1	84.47	odd	6
4900.2.a.i.1.1		1	105.44	odd	6
4900.2.a.q.1.1		1	105.89	even	6
4900.2.e.m.2549.1		2	105.2	even	12
4900.2.e.m.2549.2		2	105.23	even	12
4900.2.e.n.2549.1		2	105.68	odd	12
4900.2.e.n.2549.2		2	105.47	odd	12
8820.2.a.a.1.1		1	7.5	odd	6
8820.2.a.p.1.1		1	7.2	even	3

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:	\( N \)	\(=\)	\( 1260 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1260.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{5} +(2.50000 + 0.866025i) q^{7} +(3.00000 + 5.19615i) q^{11} +2.00000 q^{13} +(-3.00000 - 5.19615i) q^{17} +(-4.00000 + 6.92820i) q^{19} +(1.50000 - 2.59808i) q^{23} +(-0.500000 - 0.866025i) q^{25} -3.00000 q^{29} +(-1.00000 - 1.73205i) q^{31} +(-2.00000 + 1.73205i) q^{35} +(-4.00000 + 6.92820i) q^{37} +3.00000 q^{41} +5.00000 q^{43} +(5.50000 + 4.33013i) q^{49} +(6.00000 + 10.3923i) q^{53} -6.00000 q^{55} +(0.500000 - 0.866025i) q^{61} +(-1.00000 + 1.73205i) q^{65} +(3.50000 + 6.06218i) q^{67} +(5.00000 + 8.66025i) q^{73} +(3.00000 + 15.5885i) q^{77} +(2.00000 - 3.46410i) q^{79} -3.00000 q^{83} +6.00000 q^{85} +(-1.50000 + 2.59808i) q^{89} +(5.00000 + 1.73205i) q^{91} +(-4.00000 - 6.92820i) q^{95} -10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{5} + 5 q^{7}+O(q^{10}) \) 2 * q - q^5 + 5 * q^7	\( 2 q - q^{5} + 5 q^{7} + 6 q^{11} + 4 q^{13} - 6 q^{17} - 8 q^{19} + 3 q^{23} - q^{25} - 6 q^{29} - 2 q^{31} - 4 q^{35} - 8 q^{37} + 6 q^{41} + 10 q^{43} + 11 q^{49} + 12 q^{53} - 12 q^{55} + q^{61} - 2 q^{65} + 7 q^{67} + 10 q^{73} + 6 q^{77} + 4 q^{79} - 6 q^{83} + 12 q^{85} - 3 q^{89} + 10 q^{91} - 8 q^{95} - 20 q^{97}+O(q^{100}) \) 2 * q - q^5 + 5 * q^7 + 6 * q^11 + 4 * q^13 - 6 * q^17 - 8 * q^19 + 3 * q^23 - q^25 - 6 * q^29 - 2 * q^31 - 4 * q^35 - 8 * q^37 + 6 * q^41 + 10 * q^43 + 11 * q^49 + 12 * q^53 - 12 * q^55 + q^61 - 2 * q^65 + 7 * q^67 + 10 * q^73 + 6 * q^77 + 4 * q^79 - 6 * q^83 + 12 * q^85 - 3 * q^89 + 10 * q^91 - 8 * q^95 - 20 * q^97

Introduction

L-functions

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