LMFDB - Embedded newform 612.2.w.a.325.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [612,2,Mod(145,612)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(612, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 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("612.145");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 612 = 2^{2} \cdot 3^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	612.w (of order $8$, degree $4$, 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:	$4.88684460370$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 68)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			325.1
Root			$0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	612.325
Dual form			612.2.w.a.145.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.292893 - 0.707107i) q^{5} +(0.707107 - 1.70711i) q^{7} +O(q^{10})$	$q+(-0.292893 - 0.707107i) q^{5} +(0.707107 - 1.70711i) q^{7} +(2.70711 + 1.12132i) q^{11} +1.17157i q^{13} +(3.00000 - 2.82843i) q^{17} +(-3.82843 - 3.82843i) q^{19} +(-1.29289 - 0.535534i) q^{23} +(3.12132 - 3.12132i) q^{25} +(-2.29289 - 5.53553i) q^{29} +(9.53553 - 3.94975i) q^{31} -1.41421 q^{35} +(4.53553 - 1.87868i) q^{37} +(-3.12132 + 7.53553i) q^{41} +(-3.00000 + 3.00000i) q^{43} -7.65685i q^{47} +(2.53553 + 2.53553i) q^{49} +(9.82843 + 9.82843i) q^{53} -2.24264i q^{55} +(4.17157 - 4.17157i) q^{59} +(0.292893 - 0.707107i) q^{61} +(0.828427 - 0.343146i) q^{65} -11.3137 q^{67} +(-7.53553 + 3.12132i) q^{71} +(1.94975 + 4.70711i) q^{73} +(3.82843 - 3.82843i) q^{77} +(-8.36396 - 3.46447i) q^{79} +(-5.82843 - 5.82843i) q^{83} +(-2.87868 - 1.29289i) q^{85} +5.17157i q^{89} +(2.00000 + 0.828427i) q^{91} +(-1.58579 + 3.82843i) q^{95} +(5.12132 + 12.3640i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{5}+O(q^{10}) $ 4 * q - 4 * q^5	$ 4 q - 4 q^{5} + 8 q^{11} + 12 q^{17} - 4 q^{19} - 8 q^{23} + 4 q^{25} - 12 q^{29} + 24 q^{31} + 4 q^{37} - 4 q^{41} - 12 q^{43} - 4 q^{49} + 28 q^{53} + 28 q^{59} + 4 q^{61} - 8 q^{65} - 16 q^{71} - 12 q^{73} + 4 q^{77} - 8 q^{79} - 12 q^{83} - 20 q^{85} + 8 q^{91} - 12 q^{95} + 12 q^{97}+O(q^{100}) $ 4 * q - 4 * q^5 + 8 * q^11 + 12 * q^17 - 4 * q^19 - 8 * q^23 + 4 * q^25 - 12 * q^29 + 24 * q^31 + 4 * q^37 - 4 * q^41 - 12 * q^43 - 4 * q^49 + 28 * q^53 + 28 * q^59 + 4 * q^61 - 8 * q^65 - 16 * q^71 - 12 * q^73 + 4 * q^77 - 8 * q^79 - 12 * q^83 - 20 * q^85 + 8 * q^91 - 12 * q^95 + 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/612\mathbb{Z}\right)^\times$.

$n$	$37$	$137$	$307$
$\chi(n)$	$e\left(\frac{7}{8}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.292893	−	0.707107i	−0.130986	−	0.316228i	0.844756	−	0.535151i	$-0.179745\pi$
$5$	−0.292893	−	0.707107i	−0.130986	−	0.316228i	−0.975742	+	0.218924i	$0.929745\pi$
$6$		0			0
$7$	0.707107	−	1.70711i	0.267261	−	0.645226i	−0.732091	−	0.681207i	$-0.761456\pi$
$7$	0.707107	−	1.70711i	0.267261	−	0.645226i	0.999352	+	0.0359809i	$0.0114555\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	2.70711	+	1.12132i	0.816223	+	0.338091i	0.751434	−	0.659808i	$-0.229362\pi$
$11$	2.70711	+	1.12132i	0.816223	+	0.338091i	0.0647893	+	0.997899i	$0.479362\pi$
$12$		0			0
$13$			1.17157i			0.324936i	0.986714	+	0.162468i	$0.0519454\pi$
$13$			1.17157i			0.324936i	−0.986714	+	0.162468i	$0.948055\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.00000	−	2.82843i	0.727607	−	0.685994i
$17$	3.00000	−	2.82843i	0.727607	−	0.685994i
$18$		0			0
$19$	−3.82843	−	3.82843i	−0.878301	−	0.878301i	0.115057	−	0.993359i	$-0.463295\pi$
$19$	−3.82843	−	3.82843i	−0.878301	−	0.878301i	−0.993359	+	0.115057i	$0.963295\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−1.29289	−	0.535534i	−0.269587	−	0.111667i	0.243795	−	0.969827i	$-0.421608\pi$
$23$	−1.29289	−	0.535534i	−0.269587	−	0.111667i	−0.513382	+	0.858160i	$0.671608\pi$
$24$		0			0
$25$	3.12132	−	3.12132i	0.624264	−	0.624264i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−2.29289	−	5.53553i	−0.425780	−	1.02792i	−0.980612	−	0.195961i	$-0.937218\pi$
$29$	−2.29289	−	5.53553i	−0.425780	−	1.02792i	0.554832	−	0.831962i	$-0.312782\pi$
$30$		0			0
$31$	9.53553	−	3.94975i	1.71263	−	0.709396i	0.712664	−	0.701506i	$-0.247489\pi$
$31$	9.53553	−	3.94975i	1.71263	−	0.709396i	0.999969	−	0.00788961i	$-0.00251137\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.41421			−0.239046
$36$		0			0
$37$	4.53553	−	1.87868i	0.745637	−	0.308853i	0.0226771	−	0.999743i	$-0.492781\pi$
$37$	4.53553	−	1.87868i	0.745637	−	0.308853i	0.722960	+	0.690890i	$0.242781\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−3.12132	+	7.53553i	−0.487468	+	1.17685i	0.468521	+	0.883452i	$0.344787\pi$
$41$	−3.12132	+	7.53553i	−0.487468	+	1.17685i	−0.955990	+	0.293400i	$0.905213\pi$
$42$		0			0
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	−0.897833	−	0.440337i	$-0.854859\pi$
$43$	−3.00000	+	3.00000i	−0.457496	+	0.457496i	0.440337	+	0.897833i	$0.354859\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$		−	7.65685i		−	1.11687i	−0.829549	−	0.558433i	$-0.811403\pi$
$47$		−	7.65685i		−	1.11687i	0.829549	−	0.558433i	$-0.188597\pi$
$48$		0			0
$49$	2.53553	+	2.53553i	0.362219	+	0.362219i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	9.82843	+	9.82843i	1.35004	+	1.35004i	0.885612	+	0.464427i	$0.153740\pi$
$53$	9.82843	+	9.82843i	1.35004	+	1.35004i	0.464427	+	0.885612i	$0.346260\pi$
$54$		0			0
$55$		−	2.24264i		−	0.302398i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	4.17157	−	4.17157i	0.543093	−	0.543093i	−0.381342	−	0.924434i	$-0.624538\pi$
$59$	4.17157	−	4.17157i	0.543093	−	0.543093i	0.924434	+	0.381342i	$0.124538\pi$
$60$		0			0
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	−0.904019	−	0.427492i	$-0.859397\pi$
$61$	0.292893	−	0.707107i	0.0375011	−	0.0905357i	0.941520	+	0.336956i	$0.109397\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	0.828427	−	0.343146i	0.102754	−	0.0425620i
$66$		0			0
$67$	−11.3137			−1.38219			−0.691095	−	0.722764i	$-0.742871\pi$
$67$	−11.3137			−1.38219			−0.691095	+	0.722764i	$0.742871\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−7.53553	+	3.12132i	−0.894303	+	0.370433i	−0.782027	−	0.623244i	$-0.785814\pi$
$71$	−7.53553	+	3.12132i	−0.894303	+	0.370433i	−0.112276	+	0.993677i	$0.535814\pi$
$72$		0			0
$73$	1.94975	+	4.70711i	0.228201	+	0.550925i	0.995958	−	0.0898150i	$-0.0286276\pi$
$73$	1.94975	+	4.70711i	0.228201	+	0.550925i	−0.767758	+	0.640740i	$0.778628\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3.82843	−	3.82843i	0.436290	−	0.436290i
$78$		0			0
$79$	−8.36396	−	3.46447i	−0.941019	−	0.389783i	−0.141171	−	0.989985i	$-0.545087\pi$
$79$	−8.36396	−	3.46447i	−0.941019	−	0.389783i	−0.799848	+	0.600202i	$0.795087\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−5.82843	−	5.82843i	−0.639753	−	0.639753i	0.310741	−	0.950494i	$-0.399423\pi$
$83$	−5.82843	−	5.82843i	−0.639753	−	0.639753i	−0.950494	+	0.310741i	$0.899423\pi$
$84$		0			0
$85$	−2.87868	−	1.29289i	−0.312237	−	0.140234i
$86$		0			0
$87$		0			0
$88$		0			0
$89$			5.17157i			0.548186i	0.961703	+	0.274093i	$0.0883776\pi$
$89$			5.17157i			0.548186i	−0.961703	+	0.274093i	$0.911622\pi$
$90$		0			0
$91$	2.00000	+	0.828427i	0.209657	+	0.0868428i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−1.58579	+	3.82843i	−0.162698	+	0.392788i
$96$		0			0
$97$	5.12132	+	12.3640i	0.519991	+	1.25537i	0.937908	+	0.346885i	$0.112760\pi$
$97$	5.12132	+	12.3640i	0.519991	+	1.25537i	−0.417917	+	0.908485i	$0.637240\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.17157			−0.713598			−0.356799	−	0.934181i	$-0.616132\pi$
$101$	−7.17157			−0.713598			−0.356799	+	0.934181i	$0.616132\pi$
$102$		0			0
$103$	4.00000			0.394132			0.197066	−	0.980390i	$-0.436859\pi$
$103$	4.00000			0.394132			0.197066	+	0.980390i	$0.436859\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	3.53553	+	8.53553i	0.341793	+	0.825161i	0.997535	+	0.0701759i	$0.0223560\pi$
$107$	3.53553	+	8.53553i	0.341793	+	0.825161i	−0.655742	+	0.754985i	$0.727644\pi$
$108$		0			0
$109$	−2.53553	+	6.12132i	−0.242860	+	0.586316i	−0.997565	−	0.0697487i	$-0.977780\pi$
$109$	−2.53553	+	6.12132i	−0.242860	+	0.586316i	0.754704	+	0.656065i	$0.227780\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−6.53553	−	2.70711i	−0.614811	−	0.254663i	0.0534728	−	0.998569i	$-0.482971\pi$
$113$	−6.53553	−	2.70711i	−0.614811	−	0.254663i	−0.668284	+	0.743906i	$0.732971\pi$
$114$		0			0
$115$			1.07107i			0.0998776i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−2.70711	−	7.12132i	−0.248160	−	0.652810i
$120$		0			0
$121$	−1.70711	−	1.70711i	−0.155192	−	0.155192i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−6.65685	−	2.75736i	−0.595407	−	0.246626i
$126$		0			0
$127$	−5.82843	+	5.82843i	−0.517189	+	0.517189i	−0.916720	−	0.399531i	$-0.869173\pi$
$127$	−5.82843	+	5.82843i	−0.517189	+	0.517189i	0.399531	+	0.916720i	$0.369173\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	5.87868	+	14.1924i	0.513623	+	1.23999i	0.941761	+	0.336282i	$0.109169\pi$
$131$	5.87868	+	14.1924i	0.513623	+	1.23999i	−0.428139	+	0.903713i	$0.640831\pi$
$132$		0			0
$133$	−9.24264	+	3.82843i	−0.801439	+	0.331967i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	16.1421			1.37912			0.689558	−	0.724231i	$-0.257805\pi$
$137$	16.1421			1.37912			0.689558	+	0.724231i	$0.257805\pi$
$138$		0			0
$139$	−5.29289	+	2.19239i	−0.448937	+	0.185956i	−0.595685	−	0.803218i	$-0.703119\pi$
$139$	−5.29289	+	2.19239i	−0.448937	+	0.185956i	0.146748	+	0.989174i	$0.453119\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−1.31371	+	3.17157i	−0.109858	+	0.265220i
$144$		0			0
$145$	−3.24264	+	3.24264i	−0.269287	+	0.269287i
$146$		0			0
$147$		0			0
$148$		0			0
$149$			1.65685i			0.135735i	0.997694	+	0.0678674i	$0.0216195\pi$
$149$			1.65685i			0.135735i	−0.997694	+	0.0678674i	$0.978381\pi$
$150$		0			0
$151$	−12.3137	−	12.3137i	−1.00208	−	1.00208i	−0.999998	−	0.00207754i	$-0.999339\pi$
$151$	−12.3137	−	12.3137i	−1.00208	−	1.00208i	−0.00207754	−	0.999998i	$-0.500661\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−5.58579	−	5.58579i	−0.448661	−	0.448661i
$156$		0			0
$157$			13.6569i			1.08994i	0.838457	+	0.544968i	$0.183458\pi$
$157$			13.6569i			1.08994i	−0.838457	+	0.544968i	$0.816542\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−1.82843	+	1.82843i	−0.144100	+	0.144100i
$162$		0			0
$163$	−5.29289	+	12.7782i	−0.414571	+	1.00086i	0.569323	+	0.822114i	$0.307205\pi$
$163$	−5.29289	+	12.7782i	−0.414571	+	1.00086i	−0.983895	+	0.178750i	$0.942795\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	3.29289	−	1.36396i	0.254812	−	0.105546i	−0.251621	−	0.967826i	$-0.580964\pi$
$167$	3.29289	−	1.36396i	0.254812	−	0.105546i	0.506433	+	0.862279i	$0.330964\pi$
$168$		0			0
$169$	11.6274			0.894417
$170$		0			0
$171$		0			0
$172$		0			0
$173$	11.6066	−	4.80761i	0.882434	−	0.365516i	0.104993	−	0.994473i	$-0.466518\pi$
$173$	11.6066	−	4.80761i	0.882434	−	0.365516i	0.777440	+	0.628957i	$0.216518\pi$
$174$		0			0
$175$	−3.12132	−	7.53553i	−0.235950	−	0.569633i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.0000	+	13.0000i	−0.971666	+	0.971666i	−0.999609	−	0.0279439i	$-0.991104\pi$
$179$	−13.0000	+	13.0000i	−0.971666	+	0.971666i	0.0279439	+	0.999609i	$0.491104\pi$
$180$		0			0
$181$	8.53553	+	3.53553i	0.634441	+	0.262794i	0.676639	−	0.736315i	$-0.263436\pi$
$181$	8.53553	+	3.53553i	0.634441	+	0.262794i	−0.0421975	+	0.999109i	$0.513436\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−2.65685	−	2.65685i	−0.195336	−	0.195336i
$186$		0			0
$187$	11.2929	−	4.29289i	0.825818	−	0.313927i
$188$		0			0
$189$		0			0
$190$		0			0
$191$		−	11.6569i		−	0.843460i	−0.906721	−	0.421730i	$-0.861423\pi$
$191$		−	11.6569i		−	0.843460i	0.906721	−	0.421730i	$-0.138577\pi$
$192$		0			0
$193$	−3.94975	−	1.63604i	−0.284309	−	0.117765i	0.235972	−	0.971760i	$-0.424173\pi$
$193$	−3.94975	−	1.63604i	−0.284309	−	0.117765i	−0.520281	+	0.853995i	$0.674173\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−9.60660	+	23.1924i	−0.684442	+	1.65239i	0.0712470	+	0.997459i	$0.477302\pi$
$197$	−9.60660	+	23.1924i	−0.684442	+	1.65239i	−0.755689	+	0.654931i	$0.772698\pi$
$198$		0			0
$199$	−5.53553	−	13.3640i	−0.392404	−	0.947346i	−0.989415	−	0.145113i	$-0.953645\pi$
$199$	−5.53553	−	13.3640i	−0.392404	−	0.947346i	0.597011	−	0.802233i	$-0.296355\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−11.0711			−0.777037
$204$		0			0
$205$	6.24264			0.436005
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.07107	−	14.6569i	−0.419945	−	1.01384i
$210$		0			0
$211$	−6.12132	+	14.7782i	−0.421409	+	1.01737i	0.560523	+	0.828139i	$0.310600\pi$
$211$	−6.12132	+	14.7782i	−0.421409	+	1.01737i	−0.981932	+	0.189233i	$0.939400\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	3.00000	+	1.24264i	0.204598	+	0.0847474i
$216$		0			0
$217$		−	19.0711i		−	1.29463i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	3.31371	+	3.51472i	0.222904	+	0.236426i
$222$		0			0
$223$	17.8284	+	17.8284i	1.19388	+	1.19388i	0.975969	+	0.217911i	$0.0699243\pi$
$223$	17.8284	+	17.8284i	1.19388	+	1.19388i	0.217911	+	0.975969i	$0.430076\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−19.4350	−	8.05025i	−1.28995	−	0.534314i	−0.370978	−	0.928642i	$-0.620978\pi$
$227$	−19.4350	−	8.05025i	−1.28995	−	0.534314i	−0.918970	+	0.394328i	$0.870978\pi$
$228$		0			0
$229$	8.65685	−	8.65685i	0.572061	−	0.572061i	−0.360643	−	0.932704i	$-0.617443\pi$
$229$	8.65685	−	8.65685i	0.572061	−	0.572061i	0.932704	+	0.360643i	$0.117443\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	9.70711	+	23.4350i	0.635934	+	1.53528i	0.832051	+	0.554699i	$0.187167\pi$
$233$	9.70711	+	23.4350i	0.635934	+	1.53528i	−0.196117	+	0.980580i	$0.562833\pi$
$234$		0			0
$235$	−5.41421	+	2.24264i	−0.353184	+	0.146294i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	22.6274			1.46365			0.731823	−	0.681495i	$-0.238670\pi$
$239$	22.6274			1.46365			0.731823	+	0.681495i	$0.238670\pi$
$240$		0			0
$241$	−13.6066	+	5.63604i	−0.876478	+	0.363049i	−0.775130	−	0.631802i	$-0.782316\pi$
$241$	−13.6066	+	5.63604i	−0.876478	+	0.363049i	−0.101348	+	0.994851i	$0.532316\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	1.05025	−	2.53553i	0.0670982	−	0.161989i
$246$		0			0
$247$	4.48528	−	4.48528i	0.285392	−	0.285392i
$248$		0			0
$249$		0			0
$250$		0			0
$251$		−	10.9706i		−	0.692456i	−0.938150	−	0.346228i	$-0.887462\pi$
$251$		−	10.9706i		−	0.692456i	0.938150	−	0.346228i	$-0.112538\pi$
$252$		0			0
$253$	−2.89949	−	2.89949i	−0.182290	−	0.182290i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.65685	−	8.65685i	−0.540000	−	0.540000i	0.383529	−	0.923529i	$-0.374709\pi$
$257$	−8.65685	−	8.65685i	−0.540000	−	0.540000i	−0.923529	+	0.383529i	$0.874709\pi$
$258$		0			0
$259$		−	9.07107i		−	0.563649i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	20.6569	−	20.6569i	1.27376	−	1.27376i	0.329655	−	0.944102i	$-0.393068\pi$
$263$	20.6569	−	20.6569i	1.27376	−	1.27376i	0.944102	−	0.329655i	$-0.106932\pi$
$264$		0			0
$265$	4.07107	−	9.82843i	0.250084	−	0.603755i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	18.7782	−	7.77817i	1.14493	−	0.474244i	0.272097	−	0.962270i	$-0.412283\pi$
$269$	18.7782	−	7.77817i	1.14493	−	0.474244i	0.872829	+	0.488026i	$0.162283\pi$
$270$		0			0
$271$	11.3137			0.687259			0.343629	−	0.939105i	$-0.388344\pi$
$271$	11.3137			0.687259			0.343629	+	0.939105i	$0.388344\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	11.9497	−	4.94975i	0.720597	−	0.298481i
$276$		0			0
$277$	−4.05025	−	9.77817i	−0.243356	−	0.587514i	0.754256	−	0.656581i	$-0.227998\pi$
$277$	−4.05025	−	9.77817i	−0.243356	−	0.587514i	−0.997612	+	0.0690669i	$0.977998\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	0.656854	−	0.656854i	0.0391846	−	0.0391846i	−0.687243	−	0.726428i	$-0.741179\pi$
$281$	0.656854	−	0.656854i	0.0391846	−	0.0391846i	0.726428	+	0.687243i	$0.241179\pi$
$282$		0			0
$283$	1.29289	+	0.535534i	0.0768545	+	0.0318342i	0.420780	−	0.907163i	$-0.361757\pi$
$283$	1.29289	+	0.535534i	0.0768545	+	0.0318342i	−0.343925	+	0.938997i	$0.611757\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	10.6569	+	10.6569i	0.629054	+	0.629054i
$288$		0			0
$289$	1.00000	−	16.9706i	0.0588235	−	0.998268i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			8.00000i			0.467365i	0.972313	+	0.233682i	$0.0750776\pi$
$293$			8.00000i			0.467365i	−0.972313	+	0.233682i	$0.924922\pi$
$294$		0			0
$295$	−4.17157	−	1.72792i	−0.242878	−	0.100604i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	0.627417	−	1.51472i	0.0362845	−	0.0875984i
$300$		0			0
$301$	3.00000	+	7.24264i	0.172917	+	0.417459i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−0.585786			−0.0335420
$306$		0			0
$307$	17.6569			1.00773			0.503865	−	0.863782i	$-0.331911\pi$
$307$	17.6569			1.00773			0.503865	+	0.863782i	$0.331911\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−3.77817	−	9.12132i	−0.214241	−	0.517223i	0.779826	−	0.625996i	$-0.215308\pi$
$311$	−3.77817	−	9.12132i	−0.214241	−	0.517223i	−0.994067	+	0.108774i	$0.965308\pi$
$312$		0			0
$313$	−3.02082	+	7.29289i	−0.170747	+	0.412219i	−0.985969	−	0.166930i	$-0.946615\pi$
$313$	−3.02082	+	7.29289i	−0.170747	+	0.412219i	0.815222	+	0.579148i	$0.196615\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−29.8492	−	12.3640i	−1.67650	−	0.694429i	−0.677351	−	0.735660i	$-0.736872\pi$
$317$	−29.8492	−	12.3640i	−1.67650	−	0.694429i	−0.999150	+	0.0412309i	$0.986872\pi$
$318$		0			0
$319$		−	17.5563i		−	0.982967i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−22.3137	−	0.656854i	−1.24157	−	0.0365483i
$324$		0			0
$325$	3.65685	+	3.65685i	0.202846	+	0.202846i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−13.0711	−	5.41421i	−0.720631	−	0.298495i
$330$		0			0
$331$	−2.31371	+	2.31371i	−0.127173	+	0.127173i	−0.767828	−	0.640656i	$-0.778663\pi$
$331$	−2.31371	+	2.31371i	−0.127173	+	0.127173i	0.640656	+	0.767828i	$0.278663\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	3.31371	+	8.00000i	0.181047	+	0.437087i
$336$		0			0
$337$	0.0502525	−	0.0208153i	0.00273743	−	0.00113388i	−0.381314	−	0.924445i	$-0.624528\pi$
$337$	0.0502525	−	0.0208153i	0.00273743	−	0.00113388i	0.384052	+	0.923312i	$0.374528\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	30.2426			1.63773
$342$		0			0
$343$	18.0711	−	7.48528i	0.975746	−	0.404167i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−11.1924	+	27.0208i	−0.600839	+	1.45055i	0.271880	+	0.962331i	$0.412354\pi$
$347$	−11.1924	+	27.0208i	−0.600839	+	1.45055i	−0.872719	+	0.488222i	$0.837646\pi$
$348$		0			0
$349$	14.1716	−	14.1716i	0.758587	−	0.758587i	−0.217478	−	0.976065i	$-0.569783\pi$
$349$	14.1716	−	14.1716i	0.758587	−	0.758587i	0.976065	+	0.217478i	$0.0697831\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$		−	7.31371i		−	0.389269i	−0.980876	−	0.194635i	$-0.937648\pi$
$353$		−	7.31371i		−	0.389269i	0.980876	−	0.194635i	$-0.0623521\pi$
$354$		0			0
$355$	4.41421	+	4.41421i	0.234282	+	0.234282i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	4.51472	+	4.51472i	0.238278	+	0.238278i	0.816137	−	0.577859i	$-0.196112\pi$
$359$	4.51472	+	4.51472i	0.238278	+	0.238278i	−0.577859	+	0.816137i	$0.696112\pi$
$360$		0			0
$361$			10.3137i			0.542827i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	2.75736	−	2.75736i	0.144327	−	0.144327i
$366$		0			0
$367$	3.53553	−	8.53553i	0.184553	−	0.445551i	−0.804342	−	0.594167i	$-0.797482\pi$
$367$	3.53553	−	8.53553i	0.184553	−	0.445551i	0.988895	+	0.148616i	$0.0474818\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	23.7279	−	9.82843i	1.23189	−	0.510267i
$372$		0			0
$373$	1.51472			0.0784292			0.0392146	−	0.999231i	$-0.487514\pi$
$373$	1.51472			0.0784292			0.0392146	+	0.999231i	$0.487514\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	6.48528	−	2.68629i	0.334009	−	0.138351i
$378$		0			0
$379$	−5.87868	−	14.1924i	−0.301967	−	0.729014i	−0.999917	−	0.0128672i	$-0.995904\pi$
$379$	−5.87868	−	14.1924i	−0.301967	−	0.729014i	0.697950	−	0.716147i	$-0.254096\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−4.31371	+	4.31371i	−0.220420	+	0.220420i	−0.808675	−	0.588255i	$-0.799815\pi$
$383$	−4.31371	+	4.31371i	−0.220420	+	0.220420i	0.588255	+	0.808675i	$0.299815\pi$
$384$		0			0
$385$	−3.82843	−	1.58579i	−0.195115	−	0.0808192i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−15.4853	−	15.4853i	−0.785135	−	0.785135i	0.195557	−	0.980692i	$-0.437348\pi$
$389$	−15.4853	−	15.4853i	−0.785135	−	0.785135i	−0.980692	+	0.195557i	$0.937348\pi$
$390$		0			0
$391$	−5.39340	+	2.05025i	−0.272756	+	0.103686i
$392$		0			0
$393$		0			0
$394$		0			0
$395$			6.92893i			0.348632i
$396$		0			0
$397$	−22.7782	−	9.43503i	−1.14320	−	0.473531i	−0.270955	−	0.962592i	$-0.587339\pi$
$397$	−22.7782	−	9.43503i	−1.14320	−	0.473531i	−0.872249	+	0.489062i	$0.837339\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−1.46447	+	3.53553i	−0.0731319	+	0.176556i	−0.956218	−	0.292654i	$-0.905461\pi$
$401$	−1.46447	+	3.53553i	−0.0731319	+	0.176556i	0.883086	+	0.469211i	$0.155461\pi$
$402$		0			0
$403$	4.62742	+	11.1716i	0.230508	+	0.556496i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	14.3848			0.713027
$408$		0			0
$409$	−0.343146			−0.0169675			−0.00848373	−	0.999964i	$-0.502700\pi$
$409$	−0.343146			−0.0169675			−0.00848373	+	0.999964i	$0.502700\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−4.17157	−	10.0711i	−0.205270	−	0.495565i
$414$		0			0
$415$	−2.41421	+	5.82843i	−0.118509	+	0.286106i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	26.3640	+	10.9203i	1.28796	+	0.533492i	0.918378	−	0.395705i	$-0.129500\pi$
$419$	26.3640	+	10.9203i	1.28796	+	0.533492i	0.369586	+	0.929197i	$0.379500\pi$
$420$		0			0
$421$			6.82843i			0.332797i	0.986059	+	0.166399i	$0.0532138\pi$
$421$			6.82843i			0.332797i	−0.986059	+	0.166399i	$0.946786\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	0.535534	−	18.1924i	0.0259772	−	0.882460i
$426$		0			0
$427$	−1.00000	−	1.00000i	−0.0483934	−	0.0483934i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−12.1213	−	5.02082i	−0.583863	−	0.241844i	0.0711447	−	0.997466i	$-0.477335\pi$
$431$	−12.1213	−	5.02082i	−0.583863	−	0.241844i	−0.655008	+	0.755622i	$0.727335\pi$
$432$		0			0
$433$	0.171573	−	0.171573i	0.00824527	−	0.00824527i	−0.702972	−	0.711217i	$-0.748144\pi$
$433$	0.171573	−	0.171573i	0.00824527	−	0.00824527i	0.711217	+	0.702972i	$0.248144\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.89949	+	7.00000i	0.138702	+	0.334855i
$438$		0			0
$439$	29.6777	−	12.2929i	1.41644	−	0.586708i	0.462475	−	0.886632i	$-0.346962\pi$
$439$	29.6777	−	12.2929i	1.41644	−	0.586708i	0.953963	+	0.299925i	$0.0969615\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	10.3431			0.491418			0.245709	−	0.969344i	$-0.420979\pi$
$443$	10.3431			0.491418			0.245709	+	0.969344i	$0.420979\pi$
$444$		0			0
$445$	3.65685	−	1.51472i	0.173352	−	0.0718045i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−1.60660	+	3.87868i	−0.0758202	+	0.183046i	−0.957245	−	0.289278i	$-0.906585\pi$
$449$	−1.60660	+	3.87868i	−0.0758202	+	0.183046i	0.881425	+	0.472324i	$0.156585\pi$
$450$		0			0
$451$	−16.8995	+	16.8995i	−0.795766	+	0.795766i
$452$		0			0
$453$		0			0
$454$		0			0
$455$		−	1.65685i		−	0.0776745i
$456$		0			0
$457$	3.00000	+	3.00000i	0.140334	+	0.140334i	0.773784	−	0.633450i	$-0.218362\pi$
$457$	3.00000	+	3.00000i	0.140334	+	0.140334i	−0.633450	+	0.773784i	$0.718362\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	11.4853	+	11.4853i	0.534923	+	0.534923i	0.922033	−	0.387110i	$-0.126527\pi$
$461$	11.4853	+	11.4853i	0.534923	+	0.534923i	−0.387110	+	0.922033i	$0.626527\pi$
$462$		0			0
$463$		−	3.65685i		−	0.169948i	−0.996383	−	0.0849742i	$-0.972919\pi$
$463$		−	3.65685i		−	0.169948i	0.996383	−	0.0849742i	$-0.0270808\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−13.9706	+	13.9706i	−0.646481	+	0.646481i	−0.952141	−	0.305660i	$-0.901123\pi$
$467$	−13.9706	+	13.9706i	−0.646481	+	0.646481i	0.305660	+	0.952141i	$0.401123\pi$
$468$		0			0
$469$	−8.00000	+	19.3137i	−0.369406	+	0.891824i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−11.4853	+	4.75736i	−0.528094	+	0.218744i
$474$		0			0
$475$	−23.8995			−1.09658
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−32.8492	+	13.6066i	−1.50092	+	0.621702i	−0.973661	−	0.228003i	$-0.926780\pi$
$479$	−32.8492	+	13.6066i	−1.50092	+	0.621702i	−0.527260	+	0.849704i	$0.676780\pi$
$480$		0			0
$481$	2.20101	+	5.31371i	0.100357	+	0.242284i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	7.24264	−	7.24264i	0.328871	−	0.328871i
$486$		0			0
$487$	22.6066	+	9.36396i	1.02440	+	0.424322i	0.830689	−	0.556737i	$-0.187947\pi$
$487$	22.6066	+	9.36396i	1.02440	+	0.424322i	0.193714	+	0.981058i	$0.437947\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−22.7990	−	22.7990i	−1.02890	−	1.02890i	−0.999570	−	0.0293344i	$-0.990661\pi$
$491$	−22.7990	−	22.7990i	−1.02890	−	1.02890i	−0.0293344	−	0.999570i	$-0.509339\pi$
$492$		0			0
$493$	−22.5355	−	10.1213i	−1.01495	−	0.455841i
$494$		0			0
$495$		0			0
$496$		0			0
$497$			15.0711i			0.676030i
$498$		0			0
$499$	1.63604	+	0.677670i	0.0732392	+	0.0303367i	0.419002	−	0.907985i	$-0.362380\pi$
$499$	1.63604	+	0.677670i	0.0732392	+	0.0303367i	−0.345763	+	0.938322i	$0.612380\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.70711	+	21.0208i	−0.388231	+	0.937272i	0.602084	+	0.798433i	$0.294337\pi$
$503$	−8.70711	+	21.0208i	−0.388231	+	0.937272i	−0.990315	+	0.138839i	$0.955663\pi$
$504$		0			0
$505$	2.10051	+	5.07107i	0.0934712	+	0.225660i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−29.3137			−1.29931			−0.649654	−	0.760230i	$-0.725086\pi$
$509$	−29.3137			−1.29931			−0.649654	+	0.760230i	$0.725086\pi$
$510$		0			0
$511$	9.41421			0.416460
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.17157	−	2.82843i	−0.0516257	−	0.124635i
$516$		0			0
$517$	8.58579	−	20.7279i	0.377602	−	0.911613i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	3.46447	+	1.43503i	0.151781	+	0.0628698i	0.457281	−	0.889322i	$-0.348823\pi$
$521$	3.46447	+	1.43503i	0.151781	+	0.0628698i	−0.305500	+	0.952192i	$0.598823\pi$
$522$		0			0
$523$			34.0000i			1.48672i	0.668894	+	0.743358i	$0.266768\pi$
$523$			34.0000i			1.48672i	−0.668894	+	0.743358i	$0.733232\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	17.4350	−	38.8198i	0.759482	−	1.69102i
$528$		0			0
$529$	−14.8787	−	14.8787i	−0.646899	−	0.646899i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−8.82843	−	3.65685i	−0.382402	−	0.158396i
$534$		0			0
$535$	5.00000	−	5.00000i	0.216169	−	0.216169i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	4.02082	+	9.70711i	0.173189	+	0.418115i
$540$		0			0
$541$	21.0208	−	8.70711i	0.903755	−	0.374348i	0.118093	−	0.993003i	$-0.462322\pi$
$541$	21.0208	−	8.70711i	0.903755	−	0.374348i	0.785663	+	0.618655i	$0.212322\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	5.07107			0.217221
$546$		0			0
$547$	−30.6066	+	12.6777i	−1.30864	+	0.542058i	−0.924488	−	0.381210i	$-0.875507\pi$
$547$	−30.6066	+	12.6777i	−1.30864	+	0.542058i	−0.384155	+	0.923268i	$0.625507\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−12.4142	+	29.9706i	−0.528863	+	1.27679i
$552$		0			0
$553$	−11.8284	+	11.8284i	−0.502996	+	0.502996i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	17.1716i		−	0.727583i	−0.931480	−	0.363791i	$-0.881482\pi$
$557$		−	17.1716i		−	0.727583i	0.931480	−	0.363791i	$-0.118518\pi$
$558$		0			0
$559$	−3.51472	−	3.51472i	−0.148657	−	0.148657i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	29.2843	+	29.2843i	1.23418	+	1.23418i	0.962342	+	0.271843i	$0.0876333\pi$
$563$	29.2843	+	29.2843i	1.23418	+	1.23418i	0.271843	+	0.962342i	$0.412367\pi$
$564$		0			0
$565$			5.41421i			0.227778i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	2.51472	−	2.51472i	0.105422	−	0.105422i	−0.652428	−	0.757851i	$-0.726250\pi$
$569$	2.51472	−	2.51472i	0.105422	−	0.105422i	0.757851	+	0.652428i	$0.226250\pi$
$570$		0			0
$571$	−16.4645	+	39.7487i	−0.689016	+	1.66343i	0.0577369	+	0.998332i	$0.481612\pi$
$571$	−16.4645	+	39.7487i	−0.689016	+	1.66343i	−0.746753	+	0.665101i	$0.768388\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−5.70711	+	2.36396i	−0.238003	+	0.0985840i
$576$		0			0
$577$	−37.7990			−1.57359			−0.786796	−	0.617213i	$-0.788262\pi$
$577$	−37.7990			−1.57359			−0.786796	+	0.617213i	$0.788262\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−14.0711	+	5.82843i	−0.583766	+	0.241804i
$582$		0			0
$583$	15.5858	+	37.6274i	0.645497	+	1.55837i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	9.34315	−	9.34315i	0.385633	−	0.385633i	−0.487494	−	0.873127i	$-0.662089\pi$
$587$	9.34315	−	9.34315i	0.385633	−	0.385633i	0.873127	+	0.487494i	$0.162089\pi$
$588$		0			0
$589$	−51.6274	−	21.3848i	−2.12727	−	0.881144i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	6.51472	+	6.51472i	0.267527	+	0.267527i	0.828103	−	0.560576i	$-0.189420\pi$
$593$	6.51472	+	6.51472i	0.267527	+	0.267527i	−0.560576	+	0.828103i	$0.689420\pi$
$594$		0			0
$595$	−4.24264	+	4.00000i	−0.173931	+	0.163984i
$596$		0			0
$597$		0			0
$598$		0			0
$599$		−	14.6863i		−	0.600066i	−0.953929	−	0.300033i	$-0.903002\pi$
$599$		−	14.6863i		−	0.600066i	0.953929	−	0.300033i	$-0.0969976\pi$
$600$		0			0
$601$	−7.94975	−	3.29289i	−0.324277	−	0.134320i	0.214606	−	0.976701i	$-0.431153\pi$
$601$	−7.94975	−	3.29289i	−0.324277	−	0.134320i	−0.538883	+	0.842381i	$0.681153\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−0.707107	+	1.70711i	−0.0287480	+	0.0694038i
$606$		0			0
$607$	13.2929	+	32.0919i	0.539542	+	1.30257i	0.925043	+	0.379862i	$0.124029\pi$
$607$	13.2929	+	32.0919i	0.539542	+	1.30257i	−0.385501	+	0.922707i	$0.625971\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	8.97056			0.362910
$612$		0			0
$613$	11.6569			0.470816			0.235408	−	0.971897i	$-0.424357\pi$
$613$	11.6569			0.470816			0.235408	+	0.971897i	$0.424357\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	9.50610	+	22.9497i	0.382701	+	0.923922i	0.991441	+	0.130553i	$0.0416751\pi$
$617$	9.50610	+	22.9497i	0.382701	+	0.923922i	−0.608740	+	0.793370i	$0.708325\pi$
$618$		0			0
$619$	0.363961	−	0.878680i	0.0146288	−	0.0353171i	−0.916396	−	0.400272i	$-0.868916\pi$
$619$	0.363961	−	0.878680i	0.0146288	−	0.0353171i	0.931025	+	0.364955i	$0.118916\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	8.82843	+	3.65685i	0.353703	+	0.146509i
$624$		0			0
$625$		−	16.5563i		−	0.662254i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	8.29289	−	18.4645i	0.330659	−	0.736226i
$630$		0			0
$631$	−12.3137	−	12.3137i	−0.490201	−	0.490201i	0.418168	−	0.908369i	$-0.362672\pi$
$631$	−12.3137	−	12.3137i	−0.490201	−	0.490201i	−0.908369	+	0.418168i	$0.862672\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	5.82843	+	2.41421i	0.231294	+	0.0958051i
$636$		0			0
$637$	−2.97056	+	2.97056i	−0.117698	+	0.117698i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−0.920310	−	2.22183i	−0.0363501	−	0.0877568i	0.904662	−	0.426130i	$-0.140123\pi$
$641$	−0.920310	−	2.22183i	−0.0363501	−	0.0877568i	−0.941012	+	0.338373i	$0.890123\pi$
$642$		0			0
$643$	−2.12132	+	0.878680i	−0.0836567	+	0.0346517i	−0.424119	−	0.905606i	$-0.639416\pi$
$643$	−2.12132	+	0.878680i	−0.0836567	+	0.0346517i	0.340463	+	0.940258i	$0.389416\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	0.970563			0.0381568			0.0190784	−	0.999818i	$-0.493927\pi$
$647$	0.970563			0.0381568			0.0190784	+	0.999818i	$0.493927\pi$
$648$		0			0
$649$	15.9706	−	6.61522i	0.626899	−	0.259670i
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−7.74874	+	18.7071i	−0.303232	+	0.732066i	0.696661	+	0.717401i	$0.254668\pi$
$653$	−7.74874	+	18.7071i	−0.303232	+	0.732066i	−0.999892	+	0.0146651i	$0.995332\pi$
$654$		0			0
$655$	8.31371	−	8.31371i	0.324843	−	0.324843i
$656$		0			0
$657$		0			0
$658$		0			0
$659$		−	25.3137i		−	0.986082i	−0.870006	−	0.493041i	$-0.835885\pi$
$659$		−	25.3137i		−	0.986082i	0.870006	−	0.493041i	$-0.164115\pi$
$660$		0			0
$661$	9.00000	+	9.00000i	0.350059	+	0.350059i	0.860132	−	0.510072i	$-0.170381\pi$
$661$	9.00000	+	9.00000i	0.350059	+	0.350059i	−0.510072	+	0.860132i	$0.670381\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	5.41421	+	5.41421i	0.209954	+	0.209954i
$666$		0			0
$667$			8.38478i			0.324660i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	1.58579	−	1.58579i	0.0612186	−	0.0612186i
$672$		0			0
$673$	−6.67767	+	16.1213i	−0.257405	+	0.621431i	−0.998765	−	0.0496762i	$-0.984181\pi$
$673$	−6.67767	+	16.1213i	−0.257405	+	0.621431i	0.741360	+	0.671107i	$0.234181\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−13.3640	+	5.53553i	−0.513619	+	0.212748i	−0.624411	−	0.781096i	$-0.714661\pi$
$677$	−13.3640	+	5.53553i	−0.513619	+	0.212748i	0.110793	+	0.993844i	$0.464661\pi$
$678$		0			0
$679$	24.7279			0.948971
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−14.3640	+	5.94975i	−0.549622	+	0.227661i	−0.640173	−	0.768231i	$-0.721137\pi$
$683$	−14.3640	+	5.94975i	−0.549622	+	0.227661i	0.0905510	+	0.995892i	$0.471137\pi$
$684$		0			0
$685$	−4.72792	−	11.4142i	−0.180645	−	0.436115i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−11.5147	+	11.5147i	−0.438676	+	0.438676i
$690$		0			0
$691$	1.29289	+	0.535534i	0.0491840	+	0.0203727i	0.407140	−	0.913366i	$-0.366526\pi$
$691$	1.29289	+	0.535534i	0.0491840	+	0.0203727i	−0.357956	+	0.933739i	$0.616526\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.10051	+	3.10051i	0.117609	+	0.117609i
$696$		0			0
$697$	11.9497	+	31.4350i	0.452629	+	1.19069i
$698$		0			0
$699$		0			0
$700$		0			0
$701$			36.4853i			1.37803i	0.724747	+	0.689015i	$0.241957\pi$
$701$			36.4853i			1.37803i	−0.724747	+	0.689015i	$0.758043\pi$
$702$		0			0
$703$	−24.5563	−	10.1716i	−0.926160	−	0.383628i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−5.07107	+	12.2426i	−0.190717	+	0.460432i
$708$		0			0
$709$	1.12132	+	2.70711i	0.0421121	+	0.101668i	0.943536	−	0.331270i	$-0.107477\pi$
$709$	1.12132	+	2.70711i	0.0421121	+	0.101668i	−0.901424	+	0.432937i	$0.857477\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−14.4437			−0.540919
$714$		0			0
$715$	2.62742			0.0982598
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−18.1213	−	43.7487i	−0.675811	−	1.63155i	−0.771567	−	0.636148i	$-0.780527\pi$
$719$	−18.1213	−	43.7487i	−0.675811	−	1.63155i	0.0957560	−	0.995405i	$-0.469473\pi$
$720$		0			0
$721$	2.82843	−	6.82843i	0.105336	−	0.254304i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−24.4350	−	10.1213i	−0.907494	−	0.375896i
$726$		0			0
$727$		−	8.34315i		−	0.309430i	−0.987959	−	0.154715i	$-0.950554\pi$
$727$		−	8.34315i		−	0.309430i	0.987959	−	0.154715i	$-0.0494460\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.514719	+	17.4853i	−0.0190376	+	0.646716i
$732$		0			0
$733$	14.6569	+	14.6569i	0.541363	+	0.541363i	0.923928	−	0.382565i	$-0.124959\pi$
$733$	14.6569	+	14.6569i	0.541363	+	0.541363i	−0.382565	+	0.923928i	$0.624959\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−30.6274	−	12.6863i	−1.12818	−	0.467306i
$738$		0			0
$739$	21.9706	−	21.9706i	0.808200	−	0.808200i	−0.176161	−	0.984361i	$-0.556368\pi$
$739$	21.9706	−	21.9706i	0.808200	−	0.808200i	0.984361	+	0.176161i	$0.0563680\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	−1.97918	−	4.77817i	−0.0726092	−	0.175294i	0.883408	−	0.468605i	$-0.155243\pi$
$743$	−1.97918	−	4.77817i	−0.0726092	−	0.175294i	−0.956017	+	0.293310i	$0.905243\pi$
$744$		0			0
$745$	1.17157	−	0.485281i	0.0429231	−	0.0177793i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	17.0711			0.623763
$750$		0			0
$751$	30.3640	−	12.5772i	1.10800	−	0.458947i	0.247749	−	0.968824i	$-0.420309\pi$
$751$	30.3640	−	12.5772i	1.10800	−	0.458947i	0.860247	+	0.509877i	$0.170309\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−5.10051	+	12.3137i	−0.185626	+	0.448142i
$756$		0			0
$757$	−33.0000	+	33.0000i	−1.19941	+	1.19941i	−0.225061	+	0.974345i	$0.572258\pi$
$757$	−33.0000	+	33.0000i	−1.19941	+	1.19941i	−0.974345	+	0.225061i	$0.927742\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$		−	46.1421i		−	1.67265i	−0.548233	−	0.836326i	$-0.684699\pi$
$761$		−	46.1421i		−	1.67265i	0.548233	−	0.836326i	$-0.315301\pi$
$762$		0			0
$763$	8.65685	+	8.65685i	0.313399	+	0.313399i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	4.88730	+	4.88730i	0.176470	+	0.176470i
$768$		0			0
$769$		−	35.7990i		−	1.29094i	−0.763784	−	0.645472i	$-0.776661\pi$
$769$		−	35.7990i		−	1.29094i	0.763784	−	0.645472i	$-0.223339\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	24.7990	−	24.7990i	0.891958	−	0.891958i	−0.102750	−	0.994707i	$-0.532764\pi$
$773$	24.7990	−	24.7990i	0.891958	−	0.891958i	0.994707	+	0.102750i	$0.0327640\pi$
$774$		0			0
$775$	17.4350	−	42.0919i	0.626285	−	1.51199i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	40.7990	−	16.8995i	1.46178	−	0.605487i
$780$		0			0
$781$	−23.8995			−0.855191
$782$		0			0
$783$		0			0
$784$		0			0
$785$	9.65685	−	4.00000i	0.344668	−	0.142766i
$786$		0			0
$787$	−11.3934	−	27.5061i	−0.406131	−	0.980486i	−0.986146	−	0.165881i	$-0.946953\pi$
$787$	−11.3934	−	27.5061i	−0.406131	−	0.980486i	0.580015	−	0.814606i	$-0.303047\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−9.24264	+	9.24264i	−0.328630	+	0.328630i
$792$		0			0
$793$	0.828427	+	0.343146i	0.0294183	+	0.0121855i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	11.6863	+	11.6863i	0.413950	+	0.413950i	0.883112	−	0.469162i	$-0.155444\pi$
$797$	11.6863	+	11.6863i	0.413950	+	0.413950i	−0.469162	+	0.883112i	$0.655444\pi$
$798$		0			0
$799$	−21.6569	−	22.9706i	−0.766164	−	0.812640i
$800$		0			0
$801$		0			0
$802$		0			0
$803$			14.9289i			0.526831i
$804$		0			0
$805$	1.82843	+	0.757359i	0.0644436	+	0.0266934i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	13.5061	−	32.6066i	0.474849	−	1.14639i	−0.487146	−	0.873321i	$-0.661962\pi$
$809$	13.5061	−	32.6066i	0.474849	−	1.14639i	0.961995	−	0.273067i	$-0.0880379\pi$
$810$		0			0
$811$	−2.02082	−	4.87868i	−0.0709604	−	0.171314i	0.884420	−	0.466692i	$-0.154554\pi$
$811$	−2.02082	−	4.87868i	−0.0709604	−	0.171314i	−0.955380	+	0.295378i	$0.904554\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	10.5858			0.370804
$816$		0			0
$817$	22.9706			0.803638
$818$		0			0
$819$		0			0
$820$		0			0
$821$	12.5355	+	30.2635i	0.437493	+	1.05620i	0.976812	+	0.214100i	$0.0686819\pi$
$821$	12.5355	+	30.2635i	0.437493	+	1.05620i	−0.539319	+	0.842102i	$0.681318\pi$
$822$		0			0
$823$	−15.9203	+	38.4350i	−0.554947	+	1.33976i	0.358776	+	0.933424i	$0.383194\pi$
$823$	−15.9203	+	38.4350i	−0.554947	+	1.33976i	−0.913723	+	0.406337i	$0.866806\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−22.6066	−	9.36396i	−0.786109	−	0.325617i	−0.0467307	−	0.998908i	$-0.514880\pi$
$827$	−22.6066	−	9.36396i	−0.786109	−	0.325617i	−0.739378	+	0.673291i	$0.764880\pi$
$828$		0			0
$829$		−	18.3431i		−	0.637084i	−0.947909	−	0.318542i	$-0.896807\pi$
$829$		−	18.3431i		−	0.637084i	0.947909	−	0.318542i	$-0.103193\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	14.7782	+	0.435029i	0.512033	+	0.0150729i
$834$		0			0
$835$	−1.92893	−	1.92893i	−0.0667535	−	0.0667535i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	37.6777	+	15.6066i	1.30078	+	0.538800i	0.922180	−	0.386762i	$-0.126406\pi$
$839$	37.6777	+	15.6066i	1.30078	+	0.538800i	0.378598	+	0.925561i	$0.376406\pi$
$840$		0			0
$841$	−4.87868	+	4.87868i	−0.168230	+	0.168230i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−3.40559	−	8.22183i	−0.117156	−	0.282839i
$846$		0			0
$847$	−4.12132	+	1.70711i	−0.141610	+	0.0586569i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−6.87006			−0.235503
$852$		0			0
$853$	9.70711	−	4.02082i	0.332365	−	0.137670i	−0.210259	−	0.977646i	$-0.567431\pi$
$853$	9.70711	−	4.02082i	0.332365	−	0.137670i	0.542624	+	0.839976i	$0.317431\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	2.05025	−	4.94975i	0.0700353	−	0.169080i	−0.884986	−	0.465618i	$-0.845832\pi$
$857$	2.05025	−	4.94975i	0.0700353	−	0.169080i	0.955021	+	0.296538i	$0.0958321\pi$
$858$		0			0
$859$	6.17157	−	6.17157i	0.210571	−	0.210571i	−0.593939	−	0.804510i	$-0.702428\pi$
$859$	6.17157	−	6.17157i	0.210571	−	0.210571i	0.804510	+	0.593939i	$0.202428\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$			14.0000i			0.476566i	0.971196	+	0.238283i	$0.0765845\pi$
$863$			14.0000i			0.476566i	−0.971196	+	0.238283i	$0.923415\pi$
$864$		0			0
$865$	−6.79899	−	6.79899i	−0.231173	−	0.231173i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−18.7574	−	18.7574i	−0.636300	−	0.636300i
$870$		0			0
$871$		−	13.2548i		−	0.449123i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−9.41421	+	9.41421i	−0.318259	+	0.318259i
$876$		0			0
$877$	1.94975	−	4.70711i	0.0658383	−	0.158948i	−0.887536	−	0.460739i	$-0.847585\pi$
$877$	1.94975	−	4.70711i	0.0658383	−	0.158948i	0.953374	+	0.301791i	$0.0975845\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.29289	−	0.949747i	0.0772495	−	0.0319978i	−0.343724	−	0.939071i	$-0.611688\pi$
$881$	2.29289	−	0.949747i	0.0772495	−	0.0319978i	0.420974	+	0.907073i	$0.361688\pi$
$882$		0			0
$883$	25.6569			0.863422			0.431711	−	0.902012i	$-0.357910\pi$
$883$	25.6569			0.863422			0.431711	+	0.902012i	$0.357910\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	41.5772	−	17.2218i	1.39602	−	0.578252i	0.447308	−	0.894380i	$-0.352383\pi$
$887$	41.5772	−	17.2218i	1.39602	−	0.578252i	0.948717	+	0.316128i	$0.102383\pi$
$888$		0			0
$889$	5.82843	+	14.0711i	0.195479	+	0.471928i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	−29.3137	+	29.3137i	−0.980946	+	0.980946i
$894$		0			0
$895$	13.0000	+	5.38478i	0.434542	+	0.179993i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−43.7279	−	43.7279i	−1.45841	−	1.45841i
$900$		0			0
$901$	57.2843	+	1.68629i	1.90842	+	0.0561785i
$902$		0			0
$903$		0			0
$904$		0			0
$905$		−	7.07107i		−	0.235050i
$906$		0			0
$907$	41.0919	+	17.0208i	1.36443	+	0.565167i	0.940273	−	0.340420i	$-0.110569\pi$
$907$	41.0919	+	17.0208i	1.36443	+	0.565167i	0.424160	+	0.905587i	$0.360569\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−21.1924	+	51.1630i	−0.702135	+	1.69510i	0.0166400	+	0.999862i	$0.494703\pi$
$911$	−21.1924	+	51.1630i	−0.702135	+	1.69510i	−0.718775	+	0.695243i	$0.755297\pi$
$912$		0			0
$913$	−9.24264	−	22.3137i	−0.305887	−	0.738476i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	28.3848			0.937348
$918$		0			0
$919$	−25.6569			−0.846342			−0.423171	−	0.906050i	$-0.639083\pi$
$919$	−25.6569			−0.846342			−0.423171	+	0.906050i	$0.639083\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−3.65685	−	8.82843i	−0.120367	−	0.290591i
$924$		0			0
$925$	8.29289	−	20.0208i	0.272669	−	0.658280i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	24.9203	+	10.3223i	0.817609	+	0.338665i	0.751985	−	0.659180i	$-0.229096\pi$
$929$	24.9203	+	10.3223i	0.817609	+	0.338665i	0.0656235	+	0.997844i	$0.479096\pi$
$930$		0			0
$931$		−	19.4142i		−	0.636275i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−6.34315	−	6.72792i	−0.207443	−	0.220027i
$936$		0			0
$937$	33.4853	+	33.4853i	1.09392	+	1.09392i	0.995106	+	0.0988102i	$0.0315037\pi$
$937$	33.4853	+	33.4853i	1.09392	+	1.09392i	0.0988102	+	0.995106i	$0.468496\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−13.3640	−	5.53553i	−0.435653	−	0.180453i	0.154068	−	0.988060i	$-0.450762\pi$
$941$	−13.3640	−	5.53553i	−0.435653	−	0.180453i	−0.589721	+	0.807607i	$0.700762\pi$
$942$		0			0
$943$	8.07107	−	8.07107i	0.262830	−	0.262830i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.36396	+	10.5355i	0.141810	+	0.342359i	0.978788	−	0.204878i	$-0.0656797\pi$
$947$	4.36396	+	10.5355i	0.141810	+	0.342359i	−0.836978	+	0.547237i	$0.815680\pi$
$948$		0			0
$949$	−5.51472	+	2.28427i	−0.179015	+	0.0741506i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	16.1421			0.522895			0.261448	−	0.965218i	$-0.415800\pi$
$953$	16.1421			0.522895			0.261448	+	0.965218i	$0.415800\pi$
$954$		0			0
$955$	−8.24264	+	3.41421i	−0.266726	+	0.110481i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	11.4142	−	27.5563i	0.368584	−	0.889841i
$960$		0			0
$961$	53.4056	−	53.4056i	1.72276	−	1.72276i
$962$		0			0
$963$		0			0
$964$		0			0
$965$			3.27208i			0.105332i
$966$		0			0
$967$	−34.6569	−	34.6569i	−1.11449	−	1.11449i	−0.992536	−	0.121953i	$-0.961084\pi$
$967$	−34.6569	−	34.6569i	−1.11449	−	1.11449i	−0.121953	−	0.992536i	$-0.538916\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−3.68629	−	3.68629i	−0.118299	−	0.118299i	0.645479	−	0.763778i	$-0.276658\pi$
$971$	−3.68629	−	3.68629i	−0.118299	−	0.118299i	−0.763778	+	0.645479i	$0.776658\pi$
$972$		0			0
$973$			10.5858i			0.339365i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.14214	−	1.14214i	0.0365402	−	0.0365402i	−0.688601	−	0.725141i	$-0.741775\pi$
$977$	1.14214	−	1.14214i	0.0365402	−	0.0365402i	0.725141	+	0.688601i	$0.241775\pi$
$978$		0			0
$979$	−5.79899	+	14.0000i	−0.185337	+	0.447442i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	24.9497	−	10.3345i	0.795773	−	0.329620i	0.0525112	−	0.998620i	$-0.483277\pi$
$983$	24.9497	−	10.3345i	0.795773	−	0.329620i	0.743262	+	0.669000i	$0.233277\pi$
$984$		0			0
$985$	19.2132			0.612184
$986$		0			0
$987$		0			0
$988$		0			0
$989$	5.48528	−	2.27208i	0.174422	−	0.0722479i
$990$		0			0
$991$	1.92031	+	4.63604i	0.0610007	+	0.147269i	0.951441	−	0.307832i	$-0.0996034\pi$
$991$	1.92031	+	4.63604i	0.0610007	+	0.147269i	−0.890440	+	0.455100i	$0.849603\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.82843	+	7.82843i	−0.248178	+	0.248178i
$996$		0			0
$997$	17.8492	+	7.39340i	0.565291	+	0.234151i	0.646980	−	0.762507i	$-0.276032\pi$
$997$	17.8492	+	7.39340i	0.565291	+	0.234151i	−0.0816893	+	0.996658i	$0.526032\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	612.2.w.a.325.1		4
3.2	odd	2		68.2.h.a.53.1	yes	4
12.11	even	2		272.2.v.c.257.1		4
17.9	even	8	inner	612.2.w.a.145.1		4
51.2	odd	8		1156.2.h.c.977.1		4
51.5	even	16		1156.2.b.d.577.3		4
51.8	odd	8		1156.2.h.b.757.1		4
51.11	even	16		1156.2.e.f.905.2		8
51.14	even	16		1156.2.a.g.1.2		4
51.20	even	16		1156.2.a.g.1.3		4
51.23	even	16		1156.2.e.f.905.3		8
51.26	odd	8		68.2.h.a.9.1	✓	4
51.29	even	16		1156.2.b.d.577.2		4
51.32	odd	8		1156.2.h.a.977.1		4
51.38	odd	4		1156.2.h.a.1001.1		4
51.41	even	16		1156.2.e.f.829.2		8
51.44	even	16		1156.2.e.f.829.3		8
51.47	odd	4		1156.2.h.c.1001.1		4
51.50	odd	2		1156.2.h.b.733.1		4
204.71	odd	16		4624.2.a.bl.1.2		4
204.167	odd	16		4624.2.a.bl.1.3		4
204.179	even	8		272.2.v.c.145.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
68.2.h.a.9.1	✓	4	51.26	odd	8
68.2.h.a.53.1	yes	4	3.2	odd	2
272.2.v.c.145.1		4	204.179	even	8
272.2.v.c.257.1		4	12.11	even	2
612.2.w.a.145.1		4	17.9	even	8	inner
612.2.w.a.325.1		4	1.1	even	1	trivial
1156.2.a.g.1.2		4	51.14	even	16
1156.2.a.g.1.3		4	51.20	even	16
1156.2.b.d.577.2		4	51.29	even	16
1156.2.b.d.577.3		4	51.5	even	16
1156.2.e.f.829.2		8	51.41	even	16
1156.2.e.f.829.3		8	51.44	even	16
1156.2.e.f.905.2		8	51.11	even	16
1156.2.e.f.905.3		8	51.23	even	16
1156.2.h.a.977.1		4	51.32	odd	8
1156.2.h.a.1001.1		4	51.38	odd	4
1156.2.h.b.733.1		4	51.50	odd	2
1156.2.h.b.757.1		4	51.8	odd	8
1156.2.h.c.977.1		4	51.2	odd	8
1156.2.h.c.1001.1		4	51.47	odd	4
4624.2.a.bl.1.2		4	204.71	odd	16
4624.2.a.bl.1.3		4	204.167	odd	16

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:	\( N \)	\(=\)	\( 612 = 2^{2} \cdot 3^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	612.w (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.292893 - 0.707107i) q^{5} +(0.707107 - 1.70711i) q^{7} +O(q^{10})\)	\(q+(-0.292893 - 0.707107i) q^{5} +(0.707107 - 1.70711i) q^{7} +(2.70711 + 1.12132i) q^{11} +1.17157i q^{13} +(3.00000 - 2.82843i) q^{17} +(-3.82843 - 3.82843i) q^{19} +(-1.29289 - 0.535534i) q^{23} +(3.12132 - 3.12132i) q^{25} +(-2.29289 - 5.53553i) q^{29} +(9.53553 - 3.94975i) q^{31} -1.41421 q^{35} +(4.53553 - 1.87868i) q^{37} +(-3.12132 + 7.53553i) q^{41} +(-3.00000 + 3.00000i) q^{43} -7.65685i q^{47} +(2.53553 + 2.53553i) q^{49} +(9.82843 + 9.82843i) q^{53} -2.24264i q^{55} +(4.17157 - 4.17157i) q^{59} +(0.292893 - 0.707107i) q^{61} +(0.828427 - 0.343146i) q^{65} -11.3137 q^{67} +(-7.53553 + 3.12132i) q^{71} +(1.94975 + 4.70711i) q^{73} +(3.82843 - 3.82843i) q^{77} +(-8.36396 - 3.46447i) q^{79} +(-5.82843 - 5.82843i) q^{83} +(-2.87868 - 1.29289i) q^{85} +5.17157i q^{89} +(2.00000 + 0.828427i) q^{91} +(-1.58579 + 3.82843i) q^{95} +(5.12132 + 12.3640i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{5}+O(q^{10}) \) 4 * q - 4 * q^5	\( 4 q - 4 q^{5} + 8 q^{11} + 12 q^{17} - 4 q^{19} - 8 q^{23} + 4 q^{25} - 12 q^{29} + 24 q^{31} + 4 q^{37} - 4 q^{41} - 12 q^{43} - 4 q^{49} + 28 q^{53} + 28 q^{59} + 4 q^{61} - 8 q^{65} - 16 q^{71} - 12 q^{73} + 4 q^{77} - 8 q^{79} - 12 q^{83} - 20 q^{85} + 8 q^{91} - 12 q^{95} + 12 q^{97}+O(q^{100}) \) 4 * q - 4 * q^5 + 8 * q^11 + 12 * q^17 - 4 * q^19 - 8 * q^23 + 4 * q^25 - 12 * q^29 + 24 * q^31 + 4 * q^37 - 4 * q^41 - 12 * q^43 - 4 * q^49 + 28 * q^53 + 28 * q^59 + 4 * q^61 - 8 * q^65 - 16 * q^71 - 12 * q^73 + 4 * q^77 - 8 * q^79 - 12 * q^83 - 20 * q^85 + 8 * q^91 - 12 * q^95 + 12 * q^97

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