LMFDB - Embedded newform 900.2.w.c.469.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(109,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("900.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.w (of order $10$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			469.2
Character	$\chi$	$=$	900.469
Dual form			900.2.w.c.829.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.28878 - 1.82730i) q^{5} +2.44380i q^{7} +O(q^{10})$	$q+(-1.28878 - 1.82730i) q^{5} +2.44380i q^{7} +(0.178298 + 0.548744i) q^{11} +(-6.13093 - 1.99206i) q^{13} +(-1.11545 + 1.53529i) q^{17} +(6.69438 + 4.86375i) q^{19} +(-4.00298 + 1.30065i) q^{23} +(-1.67807 + 4.71000i) q^{25} +(-5.28988 + 3.84332i) q^{29} +(-3.93738 - 2.86068i) q^{31} +(4.46557 - 3.14954i) q^{35} +(-0.207335 - 0.0673673i) q^{37} +(-1.99456 + 6.13862i) q^{41} +3.42419i q^{43} +(-5.65351 - 7.78140i) q^{47} +1.02783 q^{49} +(8.22441 + 11.3199i) q^{53} +(0.772933 - 1.03302i) q^{55} +(-3.72459 + 11.4631i) q^{59} +(-1.48657 - 4.57520i) q^{61} +(4.26136 + 13.7704i) q^{65} +(2.27528 - 3.13165i) q^{67} +(-5.24443 + 3.81030i) q^{71} +(-9.55897 + 3.10590i) q^{73} +(-1.34102 + 0.435724i) q^{77} +(-3.83854 + 2.78887i) q^{79} +(2.01856 - 2.77831i) q^{83} +(4.24301 + 0.0596122i) q^{85} +(-1.75719 - 5.40807i) q^{89} +(4.86820 - 14.9828i) q^{91} +(0.259929 - 18.5010i) q^{95} +(-3.87042 - 5.32717i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 2 q^{5}+O(q^{10}) $ 24 * q + 2 * q^5	$ 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) $ 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{10}\right)$

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
$5$	−1.28878	−	1.82730i	−0.576362	−	0.817194i
$5$	−1.28878	−	1.82730i	−0.576362	−	0.817194i
$6$		0			0
$7$			2.44380i			0.923670i	0.886966	+	0.461835i	$0.152809\pi$
$7$			2.44380i			0.923670i	−0.886966	+	0.461835i	$0.847191\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	0.178298	+	0.548744i	0.0537588	+	0.165452i	0.974331	−	0.225120i	$-0.0722773\pi$
$11$	0.178298	+	0.548744i	0.0537588	+	0.165452i	−0.920572	+	0.390572i	$0.872277\pi$
$12$		0			0
$13$	−6.13093	−	1.99206i	−1.70042	−	0.552498i	−0.711723	−	0.702460i	$-0.752085\pi$
$13$	−6.13093	−	1.99206i	−1.70042	−	0.552498i	−0.988692	+	0.149962i	$0.952085\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−1.11545	+	1.53529i	−0.270537	+	0.372362i	−0.922571	−	0.385828i	$-0.873916\pi$
$17$	−1.11545	+	1.53529i	−0.270537	+	0.372362i	0.652034	+	0.758190i	$0.273916\pi$
$18$		0			0
$19$	6.69438	+	4.86375i	1.53580	+	1.11582i	0.952905	+	0.303269i	$0.0980782\pi$
$19$	6.69438	+	4.86375i	1.53580	+	1.11582i	0.582890	+	0.812551i	$0.301922\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−4.00298	+	1.30065i	−0.834678	+	0.271203i	−0.695015	−	0.718996i	$-0.744602\pi$
$23$	−4.00298	+	1.30065i	−0.834678	+	0.271203i	−0.139664	+	0.990199i	$0.544602\pi$
$24$		0			0
$25$	−1.67807	+	4.71000i	−0.335613	+	0.942000i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−5.28988	+	3.84332i	−0.982306	+	0.713687i	−0.958223	−	0.286023i	$-0.907667\pi$
$29$	−5.28988	+	3.84332i	−0.982306	+	0.713687i	−0.0240828	+	0.999710i	$0.507667\pi$
$30$		0			0
$31$	−3.93738	−	2.86068i	−0.707175	−	0.513793i	0.175086	−	0.984553i	$-0.443980\pi$
$31$	−3.93738	−	2.86068i	−0.707175	−	0.513793i	−0.882261	+	0.470760i	$0.843980\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	4.46557	−	3.14954i	0.754818	−	0.532369i
$36$		0			0
$37$	−0.207335	−	0.0673673i	−0.0340857	−	0.0110751i	0.291925	−	0.956441i	$-0.405704\pi$
$37$	−0.207335	−	0.0673673i	−0.0340857	−	0.0110751i	−0.326010	+	0.945366i	$0.605704\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.99456	+	6.13862i	−0.311498	+	0.958691i	0.665675	+	0.746242i	$0.268144\pi$
$41$	−1.99456	+	6.13862i	−0.311498	+	0.958691i	−0.977172	+	0.212449i	$0.931856\pi$
$42$		0			0
$43$			3.42419i			0.522184i	0.965314	+	0.261092i	$0.0840825\pi$
$43$			3.42419i			0.522184i	−0.965314	+	0.261092i	$0.915917\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−5.65351	−	7.78140i	−0.824650	−	1.13503i	−0.988895	−	0.148614i	$-0.952519\pi$
$47$	−5.65351	−	7.78140i	−0.824650	−	1.13503i	0.164245	−	0.986419i	$-0.447481\pi$
$48$		0			0
$49$	1.02783			0.146833
$50$		0			0
$51$		0			0
$52$		0			0
$53$	8.22441	+	11.3199i	1.12971	+	1.55491i	0.788620	+	0.614881i	$0.210796\pi$
$53$	8.22441	+	11.3199i	1.12971	+	1.55491i	0.341090	+	0.940031i	$0.389204\pi$
$54$		0			0
$55$	0.772933	−	1.03302i	0.104222	−	0.139292i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−3.72459	+	11.4631i	−0.484901	+	1.49237i	0.347224	+	0.937782i	$0.387124\pi$
$59$	−3.72459	+	11.4631i	−0.484901	+	1.49237i	−0.832125	+	0.554589i	$0.812876\pi$
$60$		0			0
$61$	−1.48657	−	4.57520i	−0.190336	−	0.585795i	0.809663	−	0.586895i	$-0.199650\pi$
$61$	−1.48657	−	4.57520i	−0.190336	−	0.585795i	−0.999999	+	0.00110016i	$0.999650\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	4.26136	+	13.7704i	0.528556	+	1.70801i
$66$		0			0
$67$	2.27528	−	3.13165i	0.277970	−	0.382592i	−0.647090	−	0.762413i	$-0.724014\pi$
$67$	2.27528	−	3.13165i	0.277970	−	0.382592i	0.925060	+	0.379821i	$0.124014\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−5.24443	+	3.81030i	−0.622399	+	0.452200i	−0.853759	−	0.520669i	$-0.825683\pi$
$71$	−5.24443	+	3.81030i	−0.622399	+	0.452200i	0.231359	+	0.972868i	$0.425683\pi$
$72$		0			0
$73$	−9.55897	+	3.10590i	−1.11879	+	0.363518i	−0.809307	−	0.587386i	$-0.800157\pi$
$73$	−9.55897	+	3.10590i	−1.11879	+	0.363518i	−0.309486	+	0.950904i	$0.600157\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.34102	+	0.435724i	−0.152824	+	0.0496554i
$78$		0			0
$79$	−3.83854	+	2.78887i	−0.431870	+	0.313772i	−0.782396	−	0.622781i	$-0.786003\pi$
$79$	−3.83854	+	2.78887i	−0.431870	+	0.313772i	0.350526	+	0.936553i	$0.386003\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	2.01856	−	2.77831i	0.221566	−	0.304959i	−0.683735	−	0.729730i	$-0.739646\pi$
$83$	2.01856	−	2.77831i	0.221566	−	0.304959i	0.905301	+	0.424772i	$0.139646\pi$
$84$		0			0
$85$	4.24301	+	0.0596122i	0.460220	+	0.00646585i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.75719	−	5.40807i	−0.186262	−	0.573254i	0.813706	−	0.581276i	$-0.197446\pi$
$89$	−1.75719	−	5.40807i	−0.186262	−	0.573254i	−0.999968	+	0.00802201i	$0.997446\pi$
$90$		0			0
$91$	4.86820	−	14.9828i	0.510326	−	1.57062i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	0.259929	−	18.5010i	0.0266682	−	1.89816i
$96$		0			0
$97$	−3.87042	−	5.32717i	−0.392982	−	0.540893i	0.565984	−	0.824416i	$-0.308497\pi$
$97$	−3.87042	−	5.32717i	−0.392982	−	0.540893i	−0.958965	+	0.283524i	$0.908497\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	12.0363			1.19766			0.598828	−	0.800877i	$-0.295633\pi$
$101$	12.0363			1.19766			0.598828	+	0.800877i	$0.295633\pi$
$102$		0			0
$103$	−3.40107	−	4.68117i	−0.335117	−	0.461249i	0.607890	−	0.794021i	$-0.292016\pi$
$103$	−3.40107	−	4.68117i	−0.335117	−	0.461249i	−0.943007	+	0.332772i	$0.892016\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.07081i		−	0.393540i	−0.980450	−	0.196770i	$-0.936955\pi$
$107$		−	4.07081i		−	0.393540i	0.980450	−	0.196770i	$-0.0630453\pi$
$108$		0			0
$109$	0.450471	−	1.38641i	0.0431473	−	0.132794i	−0.927162	−	0.374660i	$-0.877759\pi$
$109$	0.450471	−	1.38641i	0.0431473	−	0.132794i	0.970310	+	0.241866i	$0.0777595\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−5.57114	−	1.81017i	−0.524089	−	0.170287i	0.0350111	−	0.999387i	$-0.488853\pi$
$113$	−5.57114	−	1.81017i	−0.524089	−	0.170287i	−0.559100	+	0.829100i	$0.688853\pi$
$114$		0			0
$115$	7.53565	+	5.63839i	0.702703	+	0.525783i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−3.75194	−	2.72595i	−0.343940	−	0.249887i
$120$		0			0
$121$	8.62986	−	6.26996i	0.784532	−	0.569996i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.7693	−	3.00384i	0.963232	−	0.268672i
$126$		0			0
$127$	−14.5373	+	4.72346i	−1.28998	+	0.419139i	−0.872084	−	0.489357i	$-0.837232\pi$
$127$	−14.5373	+	4.72346i	−1.28998	+	0.419139i	−0.417894	+	0.908496i	$0.637232\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−3.03698	−	2.20650i	−0.265343	−	0.192783i	0.447156	−	0.894456i	$-0.352437\pi$
$131$	−3.03698	−	2.20650i	−0.265343	−	0.192783i	−0.712499	+	0.701673i	$0.752437\pi$
$132$		0			0
$133$	−11.8860	+	16.3597i	−1.03065	+	1.41857i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−19.2599	−	6.25793i	−1.64549	−	0.534651i	−0.667732	−	0.744402i	$-0.732735\pi$
$137$	−19.2599	−	6.25793i	−1.64549	−	0.534651i	−0.977755	+	0.209751i	$0.932735\pi$
$138$		0			0
$139$	0.287036	+	0.883406i	0.0243461	+	0.0749295i	0.962491	−	0.271312i	$-0.0874576\pi$
$139$	0.287036	+	0.883406i	0.0243461	+	0.0749295i	−0.938145	+	0.346242i	$0.887458\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	3.71949i		−	0.311040i
$144$		0			0
$145$	13.8404	+	4.71299i	1.14938	+	0.391393i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	13.1432			1.07673			0.538364	−	0.842712i	$-0.319042\pi$
$149$	13.1432			1.07673			0.538364	+	0.842712i	$0.319042\pi$
$150$		0			0
$151$	17.5864			1.43116			0.715580	−	0.698531i	$-0.246163\pi$
$151$	17.5864			1.43116			0.715580	+	0.698531i	$0.246163\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−0.152881	+	10.8816i	−0.0122797	+	0.874030i
$156$		0			0
$157$			8.68198i			0.692897i	0.938069	+	0.346449i	$0.112613\pi$
$157$			8.68198i			0.692897i	−0.938069	+	0.346449i	$0.887387\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−3.17852	−	9.78248i	−0.250503	−	0.770968i
$162$		0			0
$163$	1.33900	+	0.435068i	0.104879	+	0.0340771i	0.360986	−	0.932571i	$-0.382440\pi$
$163$	1.33900	+	0.435068i	0.104879	+	0.0340771i	−0.256108	+	0.966648i	$0.582440\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	5.18118	−	7.13128i	0.400932	−	0.551835i	−0.560046	−	0.828462i	$-0.689216\pi$
$167$	5.18118	−	7.13128i	0.400932	−	0.551835i	0.960978	+	0.276626i	$0.0892164\pi$
$168$		0			0
$169$	23.1028	+	16.7852i	1.77714	+	1.29117i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	7.51629	−	2.44219i	0.571453	−	0.185676i	−0.00901487	−	0.999959i	$-0.502870\pi$
$173$	7.51629	−	2.44219i	0.571453	−	0.185676i	0.580468	+	0.814283i	$0.302870\pi$
$174$		0			0
$175$	−11.5103	−	4.10086i	−0.870097	−	0.309996i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	9.29450	−	6.75285i	0.694704	−	0.504732i	−0.183499	−	0.983020i	$-0.558742\pi$
$179$	9.29450	−	6.75285i	0.694704	−	0.504732i	0.878203	+	0.478288i	$0.158742\pi$
$180$		0			0
$181$	−3.17383	−	2.30592i	−0.235909	−	0.171398i	0.463550	−	0.886071i	$-0.346576\pi$
$181$	−3.17383	−	2.30592i	−0.235909	−	0.171398i	−0.699459	+	0.714673i	$0.746576\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	0.144110	+	0.465686i	0.0105952	+	0.0342379i
$186$		0			0
$187$	−1.04136	−	0.338359i	−0.0761520	−	0.0247433i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	7.89402	−	24.2953i	0.571191	−	1.75795i	−0.0776060	−	0.996984i	$-0.524728\pi$
$191$	7.89402	−	24.2953i	0.571191	−	1.75795i	0.648797	−	0.760961i	$-0.275272\pi$
$192$		0			0
$193$		−	0.421651i		−	0.0303511i	−0.999885	−	0.0151756i	$-0.995169\pi$
$193$		−	0.421651i		−	0.0303511i	0.999885	−	0.0151756i	$-0.00483071\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	4.24463	+	5.84224i	0.302418	+	0.416242i	0.932998	−	0.359882i	$-0.117183\pi$
$197$	4.24463	+	5.84224i	0.302418	+	0.416242i	−0.630580	+	0.776124i	$0.717183\pi$
$198$		0			0
$199$	−3.93505			−0.278949			−0.139474	−	0.990226i	$-0.544541\pi$
$199$	−3.93505			−0.278949			−0.139474	+	0.990226i	$0.544541\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−9.39232	−	12.9274i	−0.659211	−	0.907327i
$204$		0			0
$205$	13.7877	−	4.26670i	0.962972	−	0.297999i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−1.47536	+	4.54069i	−0.102053	+	0.314086i
$210$		0			0
$211$	−7.65156	−	23.5491i	−0.526755	−	1.62119i	−0.760819	−	0.648964i	$-0.775202\pi$
$211$	−7.65156	−	23.5491i	−0.526755	−	1.62119i	0.234064	−	0.972221i	$-0.424798\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	6.25702	−	4.41304i	0.426726	−	0.300967i
$216$		0			0
$217$	6.99093	−	9.62219i	0.474575	−	0.653197i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	9.89715	−	7.19070i	0.665755	−	0.483699i
$222$		0			0
$223$	18.7098	−	6.07919i	1.25290	−	0.407093i	0.393942	−	0.919135i	$-0.371111\pi$
$223$	18.7098	−	6.07919i	1.25290	−	0.407093i	0.858960	+	0.512043i	$0.171111\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	25.0839	−	8.15025i	1.66488	−	0.540951i	0.682991	−	0.730427i	$-0.260679\pi$
$227$	25.0839	−	8.15025i	1.66488	−	0.540951i	0.981885	+	0.189476i	$0.0606789\pi$
$228$		0			0
$229$	−12.9614	+	9.41703i	−0.856515	+	0.622295i	−0.926935	−	0.375223i	$-0.877566\pi$
$229$	−12.9614	+	9.41703i	−0.856515	+	0.622295i	0.0704195	+	0.997517i	$0.477566\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	−17.2285	+	23.7129i	−1.12867	+	1.55349i	−0.338109	+	0.941107i	$0.609787\pi$
$233$	−17.2285	+	23.7129i	−1.12867	+	1.55349i	−0.790564	+	0.612379i	$0.790213\pi$
$234$		0			0
$235$	−6.93280	+	20.3592i	−0.452246	+	1.32809i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	7.98989	+	24.5904i	0.516823	+	1.59062i	0.779940	+	0.625854i	$0.215250\pi$
$239$	7.98989	+	24.5904i	0.516823	+	1.59062i	−0.263117	+	0.964764i	$0.584750\pi$
$240$		0			0
$241$	−2.88671	+	8.88437i	−0.185949	+	0.572292i	−0.999963	−	0.00855232i	$-0.997278\pi$
$241$	−2.88671	+	8.88437i	−0.185949	+	0.572292i	0.814014	+	0.580845i	$0.197278\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−1.32465	−	1.87816i	−0.0846289	−	0.119991i
$246$		0			0
$247$	−31.3539	−	43.1549i	−1.99500	−	2.74588i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	13.5088			0.852666			0.426333	−	0.904566i	$-0.359805\pi$
$251$	13.5088			0.852666			0.426333	+	0.904566i	$0.359805\pi$
$252$		0			0
$253$	−1.42744	−	1.96471i	−0.0897425	−	0.123520i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			13.0662i			0.815044i	0.913195	+	0.407522i	$0.133607\pi$
$257$			13.0662i			0.815044i	−0.913195	+	0.407522i	$0.866393\pi$
$258$		0			0
$259$	0.164632	−	0.506686i	0.0102298	−	0.0314839i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	4.21380	+	1.36915i	0.259834	+	0.0844251i	0.436037	−	0.899929i	$-0.356382\pi$
$263$	4.21380	+	1.36915i	0.259834	+	0.0844251i	−0.176203	+	0.984354i	$0.556382\pi$
$264$		0			0
$265$	10.0854	−	29.6174i	0.619543	−	1.81938i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−22.6936	−	16.4879i	−1.38366	−	1.00528i	−0.996528	−	0.0832584i	$-0.973467\pi$
$269$	−22.6936	−	16.4879i	−1.38366	−	1.00528i	−0.387127	−	0.922026i	$-0.626533\pi$
$270$		0			0
$271$	−4.84207	+	3.51797i	−0.294135	+	0.213701i	−0.725059	−	0.688687i	$-0.758188\pi$
$271$	−4.84207	+	3.51797i	−0.294135	+	0.213701i	0.430924	+	0.902388i	$0.358188\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−2.88378	−	0.0810472i	−0.173898	−	0.00488733i
$276$		0			0
$277$	4.82254	−	1.56694i	0.289758	−	0.0941481i	−0.160531	−	0.987031i	$-0.551321\pi$
$277$	4.82254	−	1.56694i	0.289758	−	0.0941481i	0.450290	+	0.892883i	$0.351321\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14.6885	−	10.6718i	−0.876239	−	0.636625i	0.0560144	−	0.998430i	$-0.482161\pi$
$281$	−14.6885	−	10.6718i	−0.876239	−	0.636625i	−0.932254	+	0.361805i	$0.882161\pi$
$282$		0			0
$283$	−2.76092	+	3.80009i	−0.164120	+	0.225892i	−0.883154	−	0.469083i	$-0.844584\pi$
$283$	−2.76092	+	3.80009i	−0.164120	+	0.225892i	0.719034	+	0.694975i	$0.244584\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−15.0016	−	4.87430i	−0.885514	−	0.287721i
$288$		0			0
$289$	4.14041	+	12.7429i	0.243554	+	0.749581i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	9.60771i		−	0.561288i	−0.959812	−	0.280644i	$-0.909452\pi$
$293$		−	9.60771i		−	0.561288i	0.959812	−	0.280644i	$-0.0905481\pi$
$294$		0			0
$295$	25.7468	−	7.96754i	1.49904	−	0.463888i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	27.1329			1.56914
$300$		0			0
$301$	−8.36804			−0.482326
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−6.44441	+	8.61287i	−0.369006	+	0.493172i
$306$		0			0
$307$		−	13.5400i		−	0.772771i	−0.922337	−	0.386386i	$-0.873723\pi$
$307$		−	13.5400i		−	0.772771i	0.922337	−	0.386386i	$-0.126277\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	0.916931	+	2.82202i	0.0519944	+	0.160022i	0.973682	−	0.227910i	$-0.0731893\pi$
$311$	0.916931	+	2.82202i	0.0519944	+	0.160022i	−0.921688	+	0.387933i	$0.873189\pi$
$312$		0			0
$313$	−13.3203	−	4.32802i	−0.752906	−	0.244634i	−0.0926747	−	0.995696i	$-0.529542\pi$
$313$	−13.3203	−	4.32802i	−0.752906	−	0.244634i	−0.660231	+	0.751063i	$0.729542\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−15.8806	+	21.8577i	−0.891941	+	1.22765i	0.0810273	+	0.996712i	$0.474180\pi$
$317$	−15.8806	+	21.8577i	−0.891941	+	1.22765i	−0.972968	+	0.230939i	$0.925820\pi$
$318$		0			0
$319$	−3.05217	−	2.21753i	−0.170889	−	0.124158i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−14.9345	+	4.85252i	−0.830979	+	0.270001i
$324$		0			0
$325$	19.6707	−	25.5339i	1.09114	−	1.41636i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	19.0162	−	13.8161i	1.04840	−	0.761705i
$330$		0			0
$331$	5.38394	+	3.91166i	0.295928	+	0.215004i	0.725835	−	0.687869i	$-0.241454\pi$
$331$	5.38394	+	3.91166i	0.295928	+	0.215004i	−0.429907	+	0.902873i	$0.641454\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−8.65482	−	0.121596i	−0.472863	−	0.00664348i
$336$		0			0
$337$	−18.2629	−	5.93398i	−0.994844	−	0.323245i	−0.234041	−	0.972227i	$-0.575195\pi$
$337$	−18.2629	−	5.93398i	−0.994844	−	0.323245i	−0.760804	+	0.648982i	$0.775195\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	0.867752	−	2.67067i	0.0469914	−	0.144625i
$342$		0			0
$343$			19.6184i			1.05930i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.85076	+	13.5584i	0.528816	+	0.727853i	0.986949	−	0.161030i	$-0.0514817\pi$
$347$	9.85076	+	13.5584i	0.528816	+	0.727853i	−0.458133	+	0.888884i	$0.651482\pi$
$348$		0			0
$349$	−22.9371			−1.22780			−0.613898	−	0.789385i	$-0.710399\pi$
$349$	−22.9371			−1.22780			−0.613898	+	0.789385i	$0.710399\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	−4.12280	−	5.67455i	−0.219434	−	0.302026i	0.685081	−	0.728467i	$-0.259767\pi$
$353$	−4.12280	−	5.67455i	−0.219434	−	0.302026i	−0.904515	+	0.426442i	$0.859767\pi$
$354$		0			0
$355$	13.7215	+	4.67250i	0.728262	+	0.247991i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−4.61051	+	14.1897i	−0.243333	+	0.748903i	0.752573	+	0.658509i	$0.228813\pi$
$359$	−4.61051	+	14.1897i	−0.243333	+	0.748903i	−0.995906	+	0.0903940i	$0.971187\pi$
$360$		0			0
$361$	15.2873	+	47.0494i	0.804594	+	2.47629i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	17.9949	+	13.4643i	0.941894	+	0.704753i
$366$		0			0
$367$	0.400262	−	0.550914i	0.0208935	−	0.0287575i	−0.798442	−	0.602071i	$-0.794342\pi$
$367$	0.400262	−	0.550914i	0.0208935	−	0.0287575i	0.819336	+	0.573314i	$0.194342\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−27.6637	+	20.0988i	−1.43623	+	1.04348i
$372$		0			0
$373$	−27.2355	+	8.84935i	−1.41020	+	0.458202i	−0.912475	−	0.409133i	$-0.865831\pi$
$373$	−27.2355	+	8.84935i	−1.41020	+	0.458202i	−0.497725	+	0.867335i	$0.665831\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	40.0880	−	13.0254i	2.06464	−	0.670842i
$378$		0			0
$379$	−17.7191	+	12.8737i	−0.910167	+	0.661275i	−0.941057	−	0.338247i	$-0.890166\pi$
$379$	−17.7191	+	12.8737i	−0.910167	+	0.661275i	0.0308898	+	0.999523i	$0.490166\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−2.68378	+	3.69391i	−0.137135	+	0.188750i	−0.872061	−	0.489397i	$-0.837217\pi$
$383$	−2.68378	+	3.69391i	−0.137135	+	0.188750i	0.734926	+	0.678147i	$0.237217\pi$
$384$		0			0
$385$	2.52449	+	1.88890i	0.128660	+	0.0962671i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	6.71865	+	20.6779i	0.340649	+	1.04841i	0.963872	+	0.266366i	$0.0858229\pi$
$389$	6.71865	+	20.6779i	0.340649	+	1.04841i	−0.623223	+	0.782044i	$0.714177\pi$
$390$		0			0
$391$	2.46826	−	7.59653i	0.124825	−	0.384173i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	10.0432	+	3.41993i	0.505326	+	0.172075i
$396$		0			0
$397$	9.18318	+	12.6396i	0.460891	+	0.634361i	0.974693	−	0.223547i	$-0.0717636\pi$
$397$	9.18318	+	12.6396i	0.460891	+	0.634361i	−0.513803	+	0.857908i	$0.671764\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	19.9417			0.995841			0.497920	−	0.867223i	$-0.334097\pi$
$401$	19.9417			0.995841			0.497920	+	0.867223i	$0.334097\pi$
$402$		0			0
$403$	18.4412	+	25.3821i	0.918622	+	1.26437i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	0.125785i		−	0.00623495i
$408$		0			0
$409$	5.32001	−	16.3733i	0.263058	−	0.809608i	−0.729077	−	0.684432i	$-0.760050\pi$
$409$	5.32001	−	16.3733i	0.263058	−	0.809608i	0.992134	−	0.125176i	$-0.0399497\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−28.0136	−	9.10217i	−1.37846	−	0.447888i
$414$		0			0
$415$	−7.67830	−	0.107876i	−0.376913	−	0.00529543i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−10.6230	−	7.71804i	−0.518966	−	0.377051i	0.297248	−	0.954800i	$-0.403931\pi$
$419$	−10.6230	−	7.71804i	−0.518966	−	0.377051i	−0.816214	+	0.577749i	$0.803931\pi$
$420$		0			0
$421$	−13.7712	+	10.0054i	−0.671169	+	0.487633i	−0.870416	−	0.492317i	$-0.836150\pi$
$421$	−13.7712	+	10.0054i	−0.671169	+	0.487633i	0.199248	+	0.979949i	$0.436150\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−5.35940	−	7.83010i	−0.259969	−	0.379816i
$426$		0			0
$427$	11.1809	−	3.63289i	0.541081	−	0.175808i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−10.1246	−	7.35594i	−0.487684	−	0.354323i	0.316609	−	0.948556i	$-0.397456\pi$
$431$	−10.1246	−	7.35594i	−0.487684	−	0.354323i	−0.804293	+	0.594233i	$0.797456\pi$
$432$		0			0
$433$	12.1949	−	16.7848i	0.586048	−	0.806626i	−0.408294	−	0.912850i	$-0.633876\pi$
$433$	12.1949	−	16.7848i	0.586048	−	0.806626i	0.994342	+	0.106225i	$0.0338763\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−33.1234	−	10.7625i	−1.58451	−	0.514838i
$438$		0			0
$439$	10.2225	+	31.4615i	0.487891	+	1.50157i	0.827749	+	0.561098i	$0.189621\pi$
$439$	10.2225	+	31.4615i	0.487891	+	1.50157i	−0.339858	+	0.940477i	$0.610379\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			23.4802i			1.11558i	0.829984	+	0.557788i	$0.188350\pi$
$443$			23.4802i			1.11558i	−0.829984	+	0.557788i	$0.811650\pi$
$444$		0			0
$445$	−7.61754	+	10.1808i	−0.361106	+	0.482614i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−31.6965			−1.49585			−0.747925	−	0.663783i	$-0.768950\pi$
$449$	−31.6965			−1.49585			−0.747925	+	0.663783i	$0.768950\pi$
$450$		0			0
$451$	−3.72415			−0.175363
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−33.6522	+	10.4139i	−1.57764	+	0.488212i
$456$		0			0
$457$			28.2267i			1.32039i	0.751094	+	0.660196i	$0.229527\pi$
$457$			28.2267i			1.32039i	−0.751094	+	0.660196i	$0.770473\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	1.52737	+	4.70075i	0.0711365	+	0.218936i	0.980304	−	0.197495i	$-0.0632807\pi$
$461$	1.52737	+	4.70075i	0.0711365	+	0.218936i	−0.909167	+	0.416431i	$0.863281\pi$
$462$		0			0
$463$	17.5435	+	5.70022i	0.815314	+	0.264912i	0.686847	−	0.726802i	$-0.258994\pi$
$463$	17.5435	+	5.70022i	0.815314	+	0.264912i	0.128467	+	0.991714i	$0.458994\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−10.1693	+	13.9969i	−0.470581	+	0.647699i	−0.976661	−	0.214788i	$-0.931094\pi$
$467$	−10.1693	+	13.9969i	−0.470581	+	0.647699i	0.506080	+	0.862487i	$0.331094\pi$
$468$		0			0
$469$	7.65314	+	5.56033i	0.353389	+	0.256752i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−1.87900	+	0.610525i	−0.0863966	+	0.0280719i
$474$		0			0
$475$	−34.1419	+	23.3688i	−1.56654	+	1.07223i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	27.8105	−	20.2055i	1.27069	−	0.923212i	0.271463	−	0.962449i	$-0.412493\pi$
$479$	27.8105	−	20.2055i	1.27069	−	0.923212i	0.999230	+	0.0392366i	$0.0124926\pi$
$480$		0			0
$481$	1.13696	+	0.826049i	0.0518408	+	0.0376646i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−4.74622	+	13.9380i	−0.215515	+	0.632892i
$486$		0			0
$487$	−4.79530	−	1.55809i	−0.217296	−	0.0706037i	0.198346	−	0.980132i	$-0.436443\pi$
$487$	−4.79530	−	1.55809i	−0.217296	−	0.0706037i	−0.415642	+	0.909528i	$0.636443\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.03949	−	24.7430i	0.362817	−	1.11664i	−0.588520	−	0.808483i	$-0.700289\pi$
$491$	8.03949	−	24.7430i	0.362817	−	1.11664i	0.951337	−	0.308153i	$-0.0997110\pi$
$492$		0			0
$493$		−	12.4085i		−	0.558852i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−9.31162	−	12.8163i	−0.417683	−	0.574892i
$498$		0			0
$499$	−2.49658			−0.111762			−0.0558812	−	0.998437i	$-0.517797\pi$
$499$	−2.49658			−0.111762			−0.0558812	+	0.998437i	$0.517797\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−8.38184	−	11.5366i	−0.373728	−	0.514392i	0.580181	−	0.814487i	$-0.302982\pi$
$503$	−8.38184	−	11.5366i	−0.373728	−	0.514392i	−0.953909	+	0.300095i	$0.902982\pi$
$504$		0			0
$505$	−15.5122	−	21.9940i	−0.690284	−	0.978718i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−4.82569	+	14.8520i	−0.213895	+	0.658301i	0.785335	+	0.619071i	$0.212491\pi$
$509$	−4.82569	+	14.8520i	−0.213895	+	0.658301i	−0.999230	+	0.0392303i	$0.987509\pi$
$510$		0			0
$511$	−7.59020	−	23.3602i	−0.335771	−	1.03340i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−4.17067	+	12.2478i	−0.183781	+	0.539703i
$516$		0			0
$517$	3.26198	−	4.48974i	0.143462	−	0.197458i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	11.6277	−	8.44804i	0.509420	−	0.370115i	−0.303183	−	0.952932i	$-0.598049\pi$
$521$	11.6277	−	8.44804i	0.509420	−	0.370115i	0.812604	+	0.582817i	$0.198049\pi$
$522$		0			0
$523$	−4.19878	+	1.36427i	−0.183600	+	0.0596552i	−0.399374	−	0.916788i	$-0.630772\pi$
$523$	−4.19878	+	1.36427i	−0.183600	+	0.0596552i	0.215774	+	0.976443i	$0.430772\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	8.78393	−	2.85407i	0.382634	−	0.124325i
$528$		0			0
$529$	−4.27526	+	3.10615i	−0.185881	+	0.135050i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	24.4570	−	33.6622i	1.05935	−	1.45807i
$534$		0			0
$535$	−7.43861	+	5.24640i	−0.321599	+	0.226822i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	0.183260	+	0.564015i	0.00789355	+	0.0242939i
$540$		0			0
$541$	11.1361	−	34.2734i	0.478778	−	1.47353i	−0.362016	−	0.932172i	$-0.617912\pi$
$541$	11.1361	−	34.2734i	0.478778	−	1.47353i	0.840794	−	0.541355i	$-0.182088\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−3.11395	+	0.963635i	−0.133387	+	0.0412776i
$546$		0			0
$547$	7.11410	+	9.79172i	0.304177	+	0.418664i	0.933554	−	0.358436i	$-0.116690\pi$
$547$	7.11410	+	9.79172i	0.304177	+	0.418664i	−0.629377	+	0.777100i	$0.716690\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	−54.1054			−2.30497
$552$		0			0
$553$	−6.81544	−	9.38064i	−0.289822	−	0.398906i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			24.0437i			1.01876i	0.860541	+	0.509382i	$0.170126\pi$
$557$			24.0437i			1.01876i	−0.860541	+	0.509382i	$0.829874\pi$
$558$		0			0
$559$	6.82119	−	20.9935i	0.288506	−	0.887929i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	18.0159	+	5.85371i	0.759278	+	0.246704i	0.662969	−	0.748647i	$-0.269296\pi$
$563$	18.0159	+	5.85371i	0.759278	+	0.246704i	0.0963092	+	0.995351i	$0.469296\pi$
$564$		0			0
$565$	3.87227	+	12.5131i	0.162908	+	0.526430i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	25.2591	+	18.3518i	1.05892	+	0.769348i	0.973888	−	0.227030i	$-0.0729016\pi$
$569$	25.2591	+	18.3518i	1.05892	+	0.769348i	0.0850293	+	0.996378i	$0.472902\pi$
$570$		0			0
$571$	0.0316916	−	0.0230253i	0.00132625	−	0.000963578i	−0.587122	−	0.809499i	$-0.699739\pi$
$571$	0.0316916	−	0.0230253i	0.00132625	−	0.000963578i	0.588448	+	0.808535i	$0.299739\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	0.591223	−	21.0366i	0.0246557	−	0.877286i
$576$		0			0
$577$	−19.1443	+	6.22035i	−0.796986	+	0.258957i	−0.679076	−	0.734068i	$-0.737619\pi$
$577$	−19.1443	+	6.22035i	−0.796986	+	0.258957i	−0.117910	+	0.993024i	$0.537619\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	6.78964	+	4.93296i	0.281682	+	0.204654i
$582$		0			0
$583$	−4.74535	+	6.53141i	−0.196532	+	0.270503i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−9.48143	−	3.08070i	−0.391341	−	0.127154i	0.106736	−	0.994287i	$-0.465960\pi$
$587$	−9.48143	−	3.08070i	−0.391341	−	0.127154i	−0.498076	+	0.867133i	$0.665960\pi$
$588$		0			0
$589$	−12.4447	−	38.3009i	−0.512776	−	1.57816i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			20.3619i			0.836163i	0.908410	+	0.418082i	$0.137297\pi$
$593$			20.3619i			0.836163i	−0.908410	+	0.418082i	$0.862703\pi$
$594$		0			0
$595$	−0.145680	+	10.3691i	−0.00597231	+	0.425091i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−24.1075			−0.985007			−0.492503	−	0.870311i	$-0.663918\pi$
$599$	−24.1075			−0.985007			−0.492503	+	0.870311i	$0.663918\pi$
$600$		0			0
$601$	37.2054			1.51764			0.758820	−	0.651300i	$-0.225776\pi$
$601$	37.2054			1.51764			0.758820	+	0.651300i	$0.225776\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−22.5791	−	7.68873i	−0.917973	−	0.312591i
$606$		0			0
$607$			40.5752i			1.64690i	0.567392	+	0.823448i	$0.307952\pi$
$607$			40.5752i			1.64690i	−0.567392	+	0.823448i	$0.692048\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	19.1603	+	58.9694i	0.775143	+	2.38565i
$612$		0			0
$613$	4.88423	+	1.58698i	0.197272	+	0.0640977i	0.405987	−	0.913879i	$-0.366928\pi$
$613$	4.88423	+	1.58698i	0.197272	+	0.0640977i	−0.208714	+	0.977977i	$0.566928\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−9.62895	+	13.2531i	−0.387647	+	0.533550i	−0.957590	−	0.288134i	$-0.906965\pi$
$617$	−9.62895	+	13.2531i	−0.387647	+	0.533550i	0.569943	+	0.821684i	$0.306965\pi$
$618$		0			0
$619$	14.9251	+	10.8437i	0.599892	+	0.435847i	0.845841	−	0.533436i	$-0.179099\pi$
$619$	14.9251	+	10.8437i	0.599892	+	0.435847i	−0.245948	+	0.969283i	$0.579099\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	13.2163	−	4.29422i	0.529498	−	0.172044i
$624$		0			0
$625$	−19.3682	−	15.8074i	−0.774727	−	0.632296i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	0.334701	−	0.243174i	0.0133454	−	0.00969600i
$630$		0			0
$631$	−31.1970	−	22.6659i	−1.24193	−	0.902316i	−0.244206	−	0.969723i	$-0.578527\pi$
$631$	−31.1970	−	22.6659i	−1.24193	−	0.902316i	−0.997726	+	0.0674068i	$0.978527\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	27.3667	+	20.4765i	1.08601	+	0.812587i
$636$		0			0
$637$	−6.30156	−	2.04750i	−0.249677	−	0.0811249i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	−5.87099	+	18.0690i	−0.231890	+	0.713684i	0.765629	+	0.643283i	$0.222428\pi$
$641$	−5.87099	+	18.0690i	−0.231890	+	0.713684i	−0.997519	+	0.0704016i	$0.977572\pi$
$642$		0			0
$643$		−	37.6504i		−	1.48479i	−0.669964	−	0.742393i	$-0.733691\pi$
$643$		−	37.6504i		−	1.48479i	0.669964	−	0.742393i	$-0.266309\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−3.37070	−	4.63937i	−0.132516	−	0.182392i	0.737603	−	0.675235i	$-0.235958\pi$
$647$	−3.37070	−	4.63937i	−0.132516	−	0.182392i	−0.870118	+	0.492843i	$0.835958\pi$
$648$		0			0
$649$	−6.95440			−0.272984
$650$		0			0
$651$		0			0
$652$		0			0
$653$	23.5590	+	32.4262i	0.921936	+	1.26894i	0.962923	+	0.269777i	$0.0869499\pi$
$653$	23.5590	+	32.4262i	0.921936	+	1.26894i	−0.0409866	+	0.999160i	$0.513050\pi$
$654$		0			0
$655$	−0.117920	+	8.39319i	−0.00460751	+	0.327949i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−9.75714	+	30.0294i	−0.380084	+	1.16978i	0.559900	+	0.828560i	$0.310840\pi$
$659$	−9.75714	+	30.0294i	−0.380084	+	1.16978i	−0.939984	+	0.341218i	$0.889160\pi$
$660$		0			0
$661$	9.68781	+	29.8160i	0.376812	+	1.15971i	0.942248	+	0.334916i	$0.108708\pi$
$661$	9.68781	+	29.8160i	0.376812	+	1.15971i	−0.565436	+	0.824792i	$0.691292\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	45.2127	+	0.635215i	1.75327	+	0.0246326i
$666$		0			0
$667$	16.1765	−	22.2650i	0.626355	−	0.862103i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	2.24556	−	1.63150i	0.0866889	−	0.0629832i
$672$		0			0
$673$	−4.25575	+	1.38278i	−0.164047	+	0.0533021i	−0.389889	−	0.920862i	$-0.627487\pi$
$673$	−4.25575	+	1.38278i	−0.164047	+	0.0533021i	0.225842	+	0.974164i	$0.427487\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	13.3935	−	4.35181i	0.514754	−	0.167254i	−0.0401092	−	0.999195i	$-0.512771\pi$
$677$	13.3935	−	4.35181i	0.514754	−	0.167254i	0.554863	+	0.831942i	$0.312771\pi$
$678$		0			0
$679$	13.0186	−	9.45854i	0.499607	−	0.362985i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	6.95685	−	9.57528i	0.266196	−	0.366388i	−0.654905	−	0.755711i	$-0.727291\pi$
$683$	6.95685	−	9.57528i	0.266196	−	0.366388i	0.921101	+	0.389324i	$0.127291\pi$
$684$		0			0
$685$	13.3868	+	43.2588i	0.511482	+	1.65284i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−27.8733	−	85.7853i	−1.06189	−	3.26816i
$690$		0			0
$691$	−11.6676	+	35.9091i	−0.443855	+	1.36605i	0.439879	+	0.898057i	$0.355021\pi$
$691$	−11.6676	+	35.9091i	−0.443855	+	1.36605i	−0.883734	+	0.467989i	$0.844979\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	1.24432	−	1.66302i	0.0471998	−	0.0630820i
$696$		0			0
$697$	−7.19971	−	9.90956i	−0.272709	−	0.375351i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	39.1678			1.47935			0.739674	−	0.672965i	$-0.234980\pi$
$701$	39.1678			1.47935			0.739674	+	0.672965i	$0.234980\pi$
$702$		0			0
$703$	−1.06032	−	1.45941i	−0.0399908	−	0.0550426i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			29.4143i			1.10624i
$708$		0			0
$709$	13.1296	−	40.4089i	0.493094	−	1.51759i	−0.326812	−	0.945089i	$-0.605974\pi$
$709$	13.1296	−	40.4089i	0.493094	−	1.51759i	0.819906	−	0.572498i	$-0.194026\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	19.4820	+	6.33008i	0.729606	+	0.237063i
$714$		0			0
$715$	−6.79664	+	4.79362i	−0.254180	+	0.179271i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−24.0261	−	17.4560i	−0.896022	−	0.650998i	0.0414189	−	0.999142i	$-0.486812\pi$
$719$	−24.0261	−	17.4560i	−0.896022	−	0.650998i	−0.937441	+	0.348143i	$0.886812\pi$
$720$		0			0
$721$	11.4399	−	8.31154i	0.426042	−	0.309538i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−9.22527	−	31.3647i	−0.342618	−	1.16485i
$726$		0			0
$727$	39.8796	−	12.9577i	1.47905	−	0.480573i	0.545222	−	0.838292i	$-0.316445\pi$
$727$	39.8796	−	12.9577i	1.47905	−	0.480573i	0.933829	+	0.357719i	$0.116445\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−5.25712	−	3.81952i	−0.194441	−	0.141270i
$732$		0			0
$733$	17.1695	−	23.6317i	0.634168	−	0.872858i	−0.364119	−	0.931352i	$-0.618630\pi$
$733$	17.1695	−	23.6317i	0.634168	−	0.872858i	0.998288	+	0.0584945i	$0.0186300\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	2.12415	+	0.690179i	0.0782441	+	0.0254231i
$738$		0			0
$739$	−8.00979	−	24.6516i	−0.294645	−	0.906824i	−0.983340	−	0.181773i	$-0.941816\pi$
$739$	−8.00979	−	24.6516i	−0.294645	−	0.906824i	0.688695	−	0.725051i	$-0.258184\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$			9.22935i			0.338592i	0.985565	+	0.169296i	$0.0541494\pi$
$743$			9.22935i			0.338592i	−0.985565	+	0.169296i	$0.945851\pi$
$744$		0			0
$745$	−16.9387	−	24.0165i	−0.620586	−	0.879897i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	9.94826			0.363502
$750$		0			0
$751$	−37.2805			−1.36038			−0.680192	−	0.733034i	$-0.738103\pi$
$751$	−37.2805			−1.36038			−0.680192	+	0.733034i	$0.738103\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−22.6651	−	32.1356i	−0.824866	−	1.16954i
$756$		0			0
$757$			27.6758i			1.00589i	0.864317	+	0.502947i	$0.167751\pi$
$757$			27.6758i			1.00589i	−0.864317	+	0.502947i	$0.832249\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	4.21264	+	12.9652i	0.152708	+	0.469988i	0.997921	−	0.0644416i	$-0.0205266\pi$
$761$	4.21264	+	12.9652i	0.152708	+	0.469988i	−0.845213	+	0.534429i	$0.820527\pi$
$762$		0			0
$763$	3.38811	+	1.10086i	0.122658	+	0.0398539i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	45.6705	−	62.8600i	1.64906	−	2.26974i
$768$		0			0
$769$	−24.6838	−	17.9339i	−0.890122	−	0.646712i	0.0457876	−	0.998951i	$-0.485420\pi$
$769$	−24.6838	−	17.9339i	−0.890122	−	0.646712i	−0.935910	+	0.352239i	$0.885420\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−8.03172	+	2.60967i	−0.288881	+	0.0938631i	−0.449873	−	0.893093i	$-0.648531\pi$
$773$	−8.03172	+	2.60967i	−0.288881	+	0.0938631i	0.160992	+	0.986956i	$0.448531\pi$
$774$		0			0
$775$	20.0810	−	13.7447i	0.721330	−	0.493723i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−43.2090	+	31.3932i	−1.54812	+	1.12478i
$780$		0			0
$781$	−3.02595	−	2.19848i	−0.108277	−	0.0786678i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	15.8646	−	11.1892i	0.566232	−	0.399360i
$786$		0			0
$787$	38.8560	+	12.6251i	1.38507	+	0.450036i	0.904332	−	0.426829i	$-0.140369\pi$
$787$	38.8560	+	12.6251i	1.38507	+	0.450036i	0.480736	+	0.876865i	$0.340369\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	4.42371	−	13.6148i	0.157289	−	0.484086i
$792$		0			0
$793$			31.0116i			1.10125i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−17.3703	−	23.9082i	−0.615288	−	0.846871i	0.381712	−	0.924281i	$-0.375335\pi$
$797$	−17.3703	−	23.9082i	−0.615288	−	0.846871i	−0.996999	+	0.0774107i	$0.975335\pi$
$798$		0			0
$799$	18.2529			0.645742
$800$		0			0
$801$		0			0
$802$		0			0
$803$	−3.40868	−	4.69165i	−0.120290	−	0.165565i
$804$		0			0
$805$	−13.7791	+	18.4156i	−0.485650	+	0.649066i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	7.69396	−	23.6796i	0.270505	−	0.832529i	−0.719869	−	0.694110i	$-0.755798\pi$
$809$	7.69396	−	23.6796i	0.270505	−	0.832529i	0.990374	−	0.138419i	$-0.0442020\pi$
$810$		0			0
$811$	7.52723	+	23.1664i	0.264317	+	0.813483i	0.991850	+	0.127411i	$0.0406667\pi$
$811$	7.52723	+	23.1664i	0.264317	+	0.813483i	−0.727533	+	0.686072i	$0.759333\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.930684	−	3.00747i	−0.0326004	−	0.105347i
$816$		0			0
$817$	−16.6544	+	22.9228i	−0.582663	+	0.801967i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−44.8023	+	32.5508i	−1.56361	+	1.13603i	−0.630642	+	0.776074i	$0.717208\pi$
$821$	−44.8023	+	32.5508i	−1.56361	+	1.13603i	−0.932969	+	0.359956i	$0.882792\pi$
$822$		0			0
$823$	16.6101	−	5.39695i	0.578992	−	0.188126i	−0.00485678	−	0.999988i	$-0.501546\pi$
$823$	16.6101	−	5.39695i	0.578992	−	0.188126i	0.583849	+	0.811862i	$0.301546\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.2394	−	7.22601i	0.773338	−	0.251273i	0.104345	−	0.994541i	$-0.466725\pi$
$827$	22.2394	−	7.22601i	0.773338	−	0.251273i	0.668993	+	0.743268i	$0.266725\pi$
$828$		0			0
$829$	29.1866	−	21.2053i	1.01369	−	0.736491i	0.0487125	−	0.998813i	$-0.484488\pi$
$829$	29.1866	−	21.2053i	1.01369	−	0.736491i	0.964980	+	0.262322i	$0.0844882\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.14650	+	1.57802i	−0.0397237	+	0.0546750i
$834$		0			0
$835$	−19.7084	−	0.276893i	−0.682039	−	0.00958229i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	5.88419	+	18.1097i	0.203145	+	0.625215i	0.999784	+	0.0207608i	$0.00660885\pi$
$839$	5.88419	+	18.1097i	0.203145	+	0.625215i	−0.796640	+	0.604454i	$0.793391\pi$
$840$		0			0
$841$	4.25019	−	13.0808i	0.146558	−	0.451060i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	0.897036	−	63.8483i	0.0308590	−	2.19645i
$846$		0			0
$847$	15.3225	+	21.0897i	0.526489	+	0.724649i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	0.917579			0.0314542
$852$		0			0
$853$	−10.6095	−	14.6027i	−0.363261	−	0.499986i	0.587793	−	0.809012i	$-0.299997\pi$
$853$	−10.6095	−	14.6027i	−0.363261	−	0.499986i	−0.951054	+	0.309026i	$0.899997\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	12.4435i		−	0.425061i	−0.977154	−	0.212531i	$-0.931829\pi$
$857$		−	12.4435i		−	0.425061i	0.977154	−	0.212531i	$-0.0681705\pi$
$858$		0			0
$859$	−14.2156	+	43.7511i	−0.485029	+	1.49277i	0.346909	+	0.937899i	$0.387231\pi$
$859$	−14.2156	+	43.7511i	−0.485029	+	1.49277i	−0.831938	+	0.554868i	$0.812769\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	45.0298	+	14.6311i	1.53283	+	0.498048i	0.949388	−	0.314105i	$-0.101704\pi$
$863$	45.0298	+	14.6311i	1.53283	+	0.498048i	0.583445	+	0.812153i	$0.301704\pi$
$864$		0			0
$865$	−14.1495	−	10.5871i	−0.481098	−	0.359972i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−2.21478	−	1.60913i	−0.0751311	−	0.0545860i
$870$		0			0
$871$	−20.1880	+	14.6675i	−0.684045	+	0.496988i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	7.34079	+	26.3179i	0.248164	+	0.889709i
$876$		0			0
$877$	30.3934	−	9.87543i	1.02631	−	0.333470i	0.252982	−	0.967471i	$-0.418589\pi$
$877$	30.3934	−	9.87543i	1.02631	−	0.333470i	0.773332	+	0.634001i	$0.218589\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−6.41518	−	4.66090i	−0.216133	−	0.157030i	0.474451	−	0.880282i	$-0.342647\pi$
$881$	−6.41518	−	4.66090i	−0.216133	−	0.157030i	−0.690584	+	0.723252i	$0.742647\pi$
$882$		0			0
$883$	21.8953	−	30.1363i	0.736836	−	1.01417i	−0.261958	−	0.965079i	$-0.584368\pi$
$883$	21.8953	−	30.1363i	0.736836	−	1.01417i	0.998794	−	0.0490886i	$-0.0156317\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−15.6114	−	5.07245i	−0.524179	−	0.170316i	0.0349619	−	0.999389i	$-0.488869\pi$
$887$	−15.6114	−	5.07245i	−0.524179	−	0.170316i	−0.559141	+	0.829072i	$0.688869\pi$
$888$		0			0
$889$	−11.5432	−	35.5263i	−0.387147	−	1.19151i
$890$		0			0
$891$		0			0
$892$		0			0
$893$		−	79.5889i		−	2.66334i
$894$		0			0
$895$	−24.3181	−	8.28089i	−0.812865	−	0.276800i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	31.8228			1.06135
$900$		0			0
$901$	−26.5533			−0.884619
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−0.123233	+	8.77139i	−0.00409642	+	0.291571i
$906$		0			0
$907$		−	1.85782i		−	0.0616880i	−0.999524	−	0.0308440i	$-0.990181\pi$
$907$		−	1.85782i		−	0.0616880i	0.999524	−	0.0308440i	$-0.00981950\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	6.95487	+	21.4049i	0.230425	+	0.709176i	0.997695	+	0.0678519i	$0.0216145\pi$
$911$	6.95487	+	21.4049i	0.230425	+	0.709176i	−0.767270	+	0.641324i	$0.778385\pi$
$912$		0			0
$913$	1.88448	+	0.612306i	0.0623673	+	0.0202644i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5.39225	−	7.42179i	0.178068	−	0.245089i
$918$		0			0
$919$	16.9124	+	12.2876i	0.557890	+	0.405331i	0.830686	−	0.556741i	$-0.187948\pi$
$919$	16.9124	+	12.2876i	0.557890	+	0.405331i	−0.272796	+	0.962072i	$0.587948\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	39.7436	−	12.9135i	1.30818	−	0.425052i
$924$		0			0
$925$	0.665222	−	0.863502i	0.0218724	−	0.0283918i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−11.3058	+	8.21417i	−0.370933	+	0.269498i	−0.757598	−	0.652722i	$-0.773627\pi$
$929$	−11.3058	+	8.21417i	−0.370933	+	0.269498i	0.386665	+	0.922220i	$0.373627\pi$
$930$		0			0
$931$	6.88068	+	4.99911i	0.225505	+	0.163839i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	0.723808	+	2.33896i	0.0236710	+	0.0764921i
$936$		0			0
$937$	31.1551	+	10.1229i	1.01779	+	0.330701i	0.769954	−	0.638100i	$-0.220279\pi$
$937$	31.1551	+	10.1229i	1.01779	+	0.330701i	0.247840	+	0.968801i	$0.420279\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	7.99456	−	24.6047i	0.260615	−	0.802091i	−0.732056	−	0.681244i	$-0.761439\pi$
$941$	7.99456	−	24.6047i	0.260615	−	0.802091i	0.992671	−	0.120847i	$-0.0385609\pi$
$942$		0			0
$943$		−	27.1669i		−	0.884677i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−32.7818	−	45.1202i	−1.06526	−	1.46621i	−0.874780	−	0.484521i	$-0.838994\pi$
$947$	−32.7818	−	45.1202i	−1.06526	−	1.46621i	−0.190485	−	0.981690i	$-0.561006\pi$
$948$		0			0
$949$	64.7925			2.10325
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−14.6533	−	20.1685i	−0.474666	−	0.653322i	0.502803	−	0.864401i	$-0.332302\pi$
$953$	−14.6533	−	20.1685i	−0.474666	−	0.653322i	−0.977469	+	0.211079i	$0.932302\pi$
$954$		0			0
$955$	−54.5685	+	16.8866i	−1.76580	+	0.546439i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	15.2931	−	47.0675i	0.493841	−	1.51989i
$960$		0			0
$961$	−2.26000	−	6.95558i	−0.0729034	−	0.224373i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−0.770484	+	0.543417i	−0.0248028	+	0.0174932i
$966$		0			0
$967$	5.10669	−	7.02876i	0.164220	−	0.226030i	−0.718974	−	0.695037i	$-0.755388\pi$
$967$	5.10669	−	7.02876i	0.164220	−	0.226030i	0.883194	+	0.469007i	$0.155388\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.9663	−	14.5064i	0.640750	−	0.465532i	−0.219358	−	0.975645i	$-0.570396\pi$
$971$	19.9663	−	14.5064i	0.640750	−	0.465532i	0.860108	+	0.510112i	$0.170396\pi$
$972$		0			0
$973$	−2.15887	+	0.701459i	−0.0692102	+	0.0224877i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	33.8554	−	11.0003i	1.08313	−	0.351930i	0.287542	−	0.957768i	$-0.407162\pi$
$977$	33.8554	−	11.0003i	1.08313	−	0.351930i	0.795588	+	0.605838i	$0.207162\pi$
$978$		0			0
$979$	2.65434	−	1.92849i	0.0848332	−	0.0616349i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	3.49217	−	4.80656i	0.111383	−	0.153305i	−0.749686	−	0.661794i	$-0.769795\pi$
$983$	3.49217	−	4.80656i	0.111383	−	0.153305i	0.861069	+	0.508488i	$0.169795\pi$
$984$		0			0
$985$	5.20511	−	15.2856i	0.165849	−	0.487040i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−4.45365	−	13.7069i	−0.141618	−	0.435855i
$990$		0			0
$991$	1.30614	−	4.01987i	0.0414908	−	0.127695i	−0.928166	−	0.372168i	$-0.878615\pi$
$991$	1.30614	−	4.01987i	0.0414908	−	0.127695i	0.969656	+	0.244472i	$0.0786147\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	5.07144	+	7.19053i	0.160775	+	0.227955i
$996$		0			0
$997$	7.37405	+	10.1495i	0.233538	+	0.321438i	0.909661	−	0.415351i	$-0.136341\pi$
$997$	7.37405	+	10.1495i	0.233538	+	0.321438i	−0.676123	+	0.736789i	$0.736341\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.w.c.469.2		24
3.2	odd	2		300.2.o.a.169.6	✓	24
15.2	even	4		1500.2.m.d.901.3		24
15.8	even	4		1500.2.m.c.901.4		24
15.14	odd	2		1500.2.o.c.349.1		24
25.4	even	10	inner	900.2.w.c.829.2		24
75.2	even	20		7500.2.a.m.1.5		12
75.11	odd	10		7500.2.d.g.1249.8		24
75.14	odd	10		7500.2.d.g.1249.17		24
75.23	even	20		7500.2.a.n.1.8		12
75.29	odd	10		300.2.o.a.229.6	yes	24
75.47	even	20		1500.2.m.d.601.3		24
75.53	even	20		1500.2.m.c.601.4		24
75.71	odd	10		1500.2.o.c.649.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.6	✓	24	3.2	odd	2
300.2.o.a.229.6	yes	24	75.29	odd	10
900.2.w.c.469.2		24	1.1	even	1	trivial
900.2.w.c.829.2		24	25.4	even	10	inner
1500.2.m.c.601.4		24	75.53	even	20
1500.2.m.c.901.4		24	15.8	even	4
1500.2.m.d.601.3		24	75.47	even	20
1500.2.m.d.901.3		24	15.2	even	4
1500.2.o.c.349.1		24	15.14	odd	2
1500.2.o.c.649.1		24	75.71	odd	10
7500.2.a.m.1.5		12	75.2	even	20
7500.2.a.n.1.8		12	75.23	even	20
7500.2.d.g.1249.8		24	75.11	odd	10
7500.2.d.g.1249.17		24	75.14	odd	10

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:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.28878 - 1.82730i) q^{5} +2.44380i q^{7} +O(q^{10})\)	\(q+(-1.28878 - 1.82730i) q^{5} +2.44380i q^{7} +(0.178298 + 0.548744i) q^{11} +(-6.13093 - 1.99206i) q^{13} +(-1.11545 + 1.53529i) q^{17} +(6.69438 + 4.86375i) q^{19} +(-4.00298 + 1.30065i) q^{23} +(-1.67807 + 4.71000i) q^{25} +(-5.28988 + 3.84332i) q^{29} +(-3.93738 - 2.86068i) q^{31} +(4.46557 - 3.14954i) q^{35} +(-0.207335 - 0.0673673i) q^{37} +(-1.99456 + 6.13862i) q^{41} +3.42419i q^{43} +(-5.65351 - 7.78140i) q^{47} +1.02783 q^{49} +(8.22441 + 11.3199i) q^{53} +(0.772933 - 1.03302i) q^{55} +(-3.72459 + 11.4631i) q^{59} +(-1.48657 - 4.57520i) q^{61} +(4.26136 + 13.7704i) q^{65} +(2.27528 - 3.13165i) q^{67} +(-5.24443 + 3.81030i) q^{71} +(-9.55897 + 3.10590i) q^{73} +(-1.34102 + 0.435724i) q^{77} +(-3.83854 + 2.78887i) q^{79} +(2.01856 - 2.77831i) q^{83} +(4.24301 + 0.0596122i) q^{85} +(-1.75719 - 5.40807i) q^{89} +(4.86820 - 14.9828i) q^{91} +(0.259929 - 18.5010i) q^{95} +(-3.87042 - 5.32717i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 24 * q + 2 * q^5	\( 24 q + 2 q^{5} + 6 q^{11} - 10 q^{17} + 10 q^{19} - 40 q^{23} - 4 q^{25} - 4 q^{29} + 6 q^{31} + 6 q^{35} + 10 q^{41} + 40 q^{47} - 56 q^{49} + 60 q^{53} - 62 q^{55} + 36 q^{59} - 12 q^{61} + 20 q^{67} - 40 q^{71} + 60 q^{73} + 40 q^{77} + 8 q^{79} + 50 q^{83} + 34 q^{85} - 30 q^{91} + 60 q^{95} - 40 q^{97}+O(q^{100}) \) 24 * q + 2 * q^5 + 6 * q^11 - 10 * q^17 + 10 * q^19 - 40 * q^23 - 4 * q^25 - 4 * q^29 + 6 * q^31 + 6 * q^35 + 10 * q^41 + 40 * q^47 - 56 * q^49 + 60 * q^53 - 62 * q^55 + 36 * q^59 - 12 * q^61 + 20 * q^67 - 40 * q^71 + 60 * q^73 + 40 * q^77 + 8 * q^79 + 50 * q^83 + 34 * q^85 - 30 * q^91 + 60 * q^95 - 40 * q^97

Introduction

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