LMFDB - Embedded newform 900.2.w.c.469.4

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			469.4
Character	$\chi$	$=$	900.469
Dual form			900.2.w.c.829.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.900274 + 2.04683i) q^{5} +0.957526i q^{7} +O(q^{10})$	$q+(0.900274 + 2.04683i) q^{5} +0.957526i q^{7} +(1.67360 + 5.15082i) q^{11} +(-1.92371 - 0.625052i) q^{13} +(-0.377867 + 0.520090i) q^{17} +(-4.07829 - 2.96305i) q^{19} +(3.34734 - 1.08762i) q^{23} +(-3.37901 + 3.68541i) q^{25} +(-8.20405 + 5.96059i) q^{29} +(-2.98671 - 2.16997i) q^{31} +(-1.95989 + 0.862036i) q^{35} +(10.7615 + 3.49663i) q^{37} +(-1.08859 + 3.35035i) q^{41} +0.766348i q^{43} +(-2.90026 - 3.99186i) q^{47} +6.08314 q^{49} +(3.49517 + 4.81069i) q^{53} +(-9.03615 + 8.06273i) q^{55} +(1.45818 - 4.48783i) q^{59} +(1.34263 + 4.13219i) q^{61} +(-0.452494 - 4.50023i) q^{65} +(-5.59441 + 7.70005i) q^{67} +(-9.66368 + 7.02107i) q^{71} +(5.16713 - 1.67890i) q^{73} +(-4.93205 + 1.60252i) q^{77} +(9.58637 - 6.96491i) q^{79} +(0.819420 - 1.12784i) q^{83} +(-1.40472 - 0.305206i) q^{85} +(-0.527839 - 1.62452i) q^{89} +(0.598504 - 1.84200i) q^{91} +(2.39328 - 11.0151i) q^{95} +(8.57451 + 11.8018i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	0.900274	+	2.04683i	0.402615	+	0.915370i
$5$	0.900274	+	2.04683i	0.402615	+	0.915370i
$6$		0			0
$7$			0.957526i			0.361911i	0.983491	+	0.180955i	$0.0579190\pi$
$7$			0.957526i			0.361911i	−0.983491	+	0.180955i	$0.942081\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.67360	+	5.15082i	0.504611	+	1.55303i	0.801424	+	0.598096i	$0.204076\pi$
$11$	1.67360	+	5.15082i	0.504611	+	1.55303i	−0.296814	+	0.954935i	$0.595924\pi$
$12$		0			0
$13$	−1.92371	−	0.625052i	−0.533542	−	0.173358i	0.0298404	−	0.999555i	$-0.490500\pi$
$13$	−1.92371	−	0.625052i	−0.533542	−	0.173358i	−0.563382	+	0.826196i	$0.690500\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−0.377867	+	0.520090i	−0.0916463	+	0.126140i	−0.852378	−	0.522926i	$-0.824840\pi$
$17$	−0.377867	+	0.520090i	−0.0916463	+	0.126140i	0.760732	+	0.649067i	$0.224840\pi$
$18$		0			0
$19$	−4.07829	−	2.96305i	−0.935625	−	0.679771i	0.0117388	−	0.999931i	$-0.496263\pi$
$19$	−4.07829	−	2.96305i	−0.935625	−	0.679771i	−0.947364	+	0.320160i	$0.896263\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	3.34734	−	1.08762i	0.697969	−	0.226784i	0.0615235	−	0.998106i	$-0.480404\pi$
$23$	3.34734	−	1.08762i	0.697969	−	0.226784i	0.636445	+	0.771322i	$0.280404\pi$
$24$		0			0
$25$	−3.37901	+	3.68541i	−0.675803	+	0.737083i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−8.20405	+	5.96059i	−1.52345	+	1.10685i	−0.563712	+	0.825972i	$0.690627\pi$
$29$	−8.20405	+	5.96059i	−1.52345	+	1.10685i	−0.959742	+	0.280882i	$0.909373\pi$
$30$		0			0
$31$	−2.98671	−	2.16997i	−0.536429	−	0.389738i	0.286328	−	0.958132i	$-0.407565\pi$
$31$	−2.98671	−	2.16997i	−0.536429	−	0.389738i	−0.822757	+	0.568393i	$0.807565\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1.95989	+	0.862036i	−0.331282	+	0.145711i
$36$		0			0
$37$	10.7615	+	3.49663i	1.76918	+	0.574842i	0.998084	−	0.0618753i	$-0.0197081\pi$
$37$	10.7615	+	3.49663i	1.76918	+	0.574842i	0.771097	+	0.636717i	$0.219708\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.08859	+	3.35035i	−0.170010	+	0.523237i	−0.999370	−	0.0354770i	$-0.988705\pi$
$41$	−1.08859	+	3.35035i	−0.170010	+	0.523237i	0.829361	+	0.558714i	$0.188705\pi$
$42$		0			0
$43$			0.766348i			0.116867i	0.998291	+	0.0584335i	$0.0186106\pi$
$43$			0.766348i			0.116867i	−0.998291	+	0.0584335i	$0.981389\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−2.90026	−	3.99186i	−0.423046	−	0.582273i	0.543293	−	0.839543i	$-0.317177\pi$
$47$	−2.90026	−	3.99186i	−0.423046	−	0.582273i	−0.966340	+	0.257270i	$0.917177\pi$
$48$		0			0
$49$	6.08314			0.869021
$50$		0			0
$51$		0			0
$52$		0			0
$53$	3.49517	+	4.81069i	0.480099	+	0.660799i	0.978524	−	0.206134i	$-0.0660881\pi$
$53$	3.49517	+	4.81069i	0.480099	+	0.660799i	−0.498425	+	0.866933i	$0.666088\pi$
$54$		0			0
$55$	−9.03615	+	8.06273i	−1.21843	+	1.08718i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	1.45818	−	4.48783i	0.189839	−	0.584265i	−0.810159	−	0.586210i	$-0.800619\pi$
$59$	1.45818	−	4.48783i	0.189839	−	0.584265i	0.999998	+	0.00194529i	$0.000619206\pi$
$60$		0			0
$61$	1.34263	+	4.13219i	0.171906	+	0.529073i	0.999479	−	0.0322858i	$-0.0102787\pi$
$61$	1.34263	+	4.13219i	0.171906	+	0.529073i	−0.827572	+	0.561359i	$0.810279\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−0.452494	−	4.50023i	−0.0561249	−	0.558184i
$66$		0			0
$67$	−5.59441	+	7.70005i	−0.683466	+	0.940711i	−0.999969	−	0.00788103i	$-0.997491\pi$
$67$	−5.59441	+	7.70005i	−0.683466	+	0.940711i	0.316503	+	0.948592i	$0.397491\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−9.66368	+	7.02107i	−1.14687	+	0.833248i	−0.988061	−	0.154062i	$-0.950765\pi$
$71$	−9.66368	+	7.02107i	−1.14687	+	0.833248i	−0.158806	+	0.987310i	$0.550765\pi$
$72$		0			0
$73$	5.16713	−	1.67890i	0.604766	−	0.196500i	0.00940128	−	0.999956i	$-0.497007\pi$
$73$	5.16713	−	1.67890i	0.604766	−	0.196500i	0.595365	+	0.803455i	$0.297007\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.93205	+	1.60252i	−0.562059	+	0.182624i
$78$		0			0
$79$	9.58637	−	6.96491i	1.07855	−	0.783613i	0.101122	−	0.994874i	$-0.467757\pi$
$79$	9.58637	−	6.96491i	1.07855	−	0.783613i	0.977430	+	0.211261i	$0.0677569\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	0.819420	−	1.12784i	0.0899431	−	0.123796i	−0.761674	−	0.647960i	$-0.775622\pi$
$83$	0.819420	−	1.12784i	0.0899431	−	0.123796i	0.851617	+	0.524164i	$0.175622\pi$
$84$		0			0
$85$	−1.40472	−	0.305206i	−0.152363	−	0.0331043i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−0.527839	−	1.62452i	−0.0559508	−	0.172199i	0.919176	−	0.393847i	$-0.128856\pi$
$89$	−0.527839	−	1.62452i	−0.0559508	−	0.172199i	−0.975127	+	0.221649i	$0.928856\pi$
$90$		0			0
$91$	0.598504	−	1.84200i	0.0627402	−	0.193095i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	2.39328	−	11.0151i	0.245545	−	1.13013i
$96$		0			0
$97$	8.57451	+	11.8018i	0.870610	+	1.19829i	0.978934	+	0.204176i	$0.0654514\pi$
$97$	8.57451	+	11.8018i	0.870610	+	1.19829i	−0.108325	+	0.994116i	$0.534549\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	10.2832			1.02322			0.511610	−	0.859218i	$-0.329049\pi$
$101$	10.2832			1.02322			0.511610	+	0.859218i	$0.329049\pi$
$102$		0			0
$103$	−8.22008	−	11.3140i	−0.809949	−	1.11480i	−0.991331	−	0.131386i	$-0.958057\pi$
$103$	−8.22008	−	11.3140i	−0.809949	−	1.11480i	0.181383	−	0.983413i	$-0.441943\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			9.06727i			0.876566i	0.898837	+	0.438283i	$0.144413\pi$
$107$			9.06727i			0.876566i	−0.898837	+	0.438283i	$0.855587\pi$
$108$		0			0
$109$	−0.734025	+	2.25910i	−0.0703068	+	0.216382i	−0.980036	−	0.198820i	$-0.936289\pi$
$109$	−0.734025	+	2.25910i	−0.0703068	+	0.216382i	0.909729	+	0.415202i	$0.136289\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	12.7797	+	4.15238i	1.20221	+	0.390623i	0.840575	−	0.541696i	$-0.182218\pi$
$113$	12.7797	+	4.15238i	1.20221	+	0.390623i	0.361638	+	0.932318i	$0.382218\pi$
$114$		0			0
$115$	5.23969	+	5.87228i	0.488604	+	0.547593i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−0.498000	−	0.361818i	−0.0456515	−	0.0331678i
$120$		0			0
$121$	−14.8308	+	10.7752i	−1.34826	+	0.979567i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−10.5854	−	3.59838i	−0.946791	−	0.321849i
$126$		0			0
$127$	13.5648	−	4.40749i	1.20369	−	0.391101i	0.362570	−	0.931957i	$-0.381899\pi$
$127$	13.5648	−	4.40749i	1.20369	−	0.391101i	0.841116	+	0.540855i	$0.181899\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−0.104093	−	0.0756282i	−0.00909468	−	0.00660767i	0.583229	−	0.812308i	$-0.301789\pi$
$131$	−0.104093	−	0.0756282i	−0.00909468	−	0.00660767i	−0.592323	+	0.805700i	$0.701789\pi$
$132$		0			0
$133$	2.83720	−	3.90507i	0.246017	−	0.338613i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	13.0316	+	4.23423i	1.11337	+	0.361754i	0.807232	−	0.590234i	$-0.200965\pi$
$137$	13.0316	+	4.23423i	1.11337	+	0.361754i	0.306133	+	0.951989i	$0.400965\pi$
$138$		0			0
$139$	−7.25318	−	22.3230i	−0.615206	−	1.89341i	−0.398475	−	0.917179i	$-0.630461\pi$
$139$	−7.25318	−	22.3230i	−0.615206	−	1.89341i	−0.216731	−	0.976231i	$-0.569539\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	10.9548i		−	0.916086i
$144$		0			0
$145$	−19.5862	−	11.4261i	−1.62655	−	0.948888i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	−10.6938			−0.876071			−0.438035	−	0.898958i	$-0.644326\pi$
$149$	−10.6938			−0.876071			−0.438035	+	0.898958i	$0.644326\pi$
$150$		0			0
$151$	7.37520			0.600185			0.300092	−	0.953910i	$-0.402982\pi$
$151$	7.37520			0.600185			0.300092	+	0.953910i	$0.402982\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	1.75270	−	8.06685i	0.140780	−	0.647945i
$156$		0			0
$157$		−	13.0329i		−	1.04014i	−0.854124	−	0.520070i	$-0.825906\pi$
$157$		−	13.0329i		−	1.04014i	0.854124	−	0.520070i	$-0.174094\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	1.04142	+	3.20517i	0.0820755	+	0.252603i
$162$		0			0
$163$	7.03403	+	2.28549i	0.550948	+	0.179014i	0.571244	−	0.820780i	$-0.306461\pi$
$163$	7.03403	+	2.28549i	0.550948	+	0.179014i	−0.0202964	+	0.999794i	$0.506461\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.8301	−	16.2827i	0.915438	−	1.25999i	−0.0498368	−	0.998757i	$-0.515870\pi$
$167$	11.8301	−	16.2827i	0.915438	−	1.25999i	0.965275	−	0.261235i	$-0.0841299\pi$
$168$		0			0
$169$	−7.20724	−	5.23637i	−0.554403	−	0.402798i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−2.11241	+	0.686365i	−0.160604	+	0.0521833i	−0.388215	−	0.921569i	$-0.626908\pi$
$173$	−2.11241	+	0.686365i	−0.160604	+	0.0521833i	0.227612	+	0.973752i	$0.426908\pi$
$174$		0			0
$175$	−3.52888	−	3.23549i	−0.266758	−	0.244580i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	0.0312215	−	0.0226837i	0.00233360	−	0.00169546i	−0.586618	−	0.809864i	$-0.699541\pi$
$179$	0.0312215	−	0.0226837i	0.00233360	−	0.00169546i	0.588951	+	0.808168i	$0.299541\pi$
$180$		0			0
$181$	−0.118881	−	0.0863720i	−0.00883634	−	0.00641998i	0.583358	−	0.812215i	$-0.301738\pi$
$181$	−0.118881	−	0.0863720i	−0.00883634	−	0.00641998i	−0.592195	+	0.805795i	$0.701738\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.53131	+	25.1749i	0.186106	+	1.85089i
$186$		0			0
$187$	−3.31129	−	1.07590i	−0.242146	−	0.0786779i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	0.142049	−	0.437183i	0.0102783	−	0.0316335i	−0.945786	−	0.324791i	$-0.894706\pi$
$191$	0.142049	−	0.437183i	0.0102783	−	0.0316335i	0.956064	+	0.293158i	$0.0947060\pi$
$192$		0			0
$193$		−	19.0231i		−	1.36932i	−0.728864	−	0.684658i	$-0.759952\pi$
$193$		−	19.0231i		−	1.36932i	0.728864	−	0.684658i	$-0.240048\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−7.12107	−	9.80131i	−0.507355	−	0.698315i	0.476115	−	0.879383i	$-0.342045\pi$
$197$	−7.12107	−	9.80131i	−0.507355	−	0.698315i	−0.983471	+	0.181068i	$0.942045\pi$
$198$		0			0
$199$	−16.4872			−1.16875			−0.584375	−	0.811484i	$-0.698660\pi$
$199$	−16.4872			−1.16875			−0.584375	+	0.811484i	$0.698660\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−5.70742	−	7.85559i	−0.400583	−	0.551355i
$204$		0			0
$205$	−7.83763	+	0.788066i	−0.547404	+	0.0550409i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	8.43672	−	25.9656i	0.583580	−	1.79607i
$210$		0			0
$211$	5.61985	+	17.2961i	0.386887	+	1.19071i	0.935102	+	0.354378i	$0.115307\pi$
$211$	5.61985	+	17.2961i	0.386887	+	1.19071i	−0.548216	+	0.836337i	$0.684693\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−1.56858	+	0.689923i	−0.106976	+	0.0470524i
$216$		0			0
$217$	2.07780	−	2.85985i	0.141051	−	0.194139i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	1.05199	−	0.764316i	0.0707646	−	0.0514135i
$222$		0			0
$223$	22.3596	−	7.26507i	1.49731	−	0.486505i	0.558077	−	0.829789i	$-0.311539\pi$
$223$	22.3596	−	7.26507i	1.49731	−	0.486505i	0.939231	+	0.343284i	$0.111539\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	18.7171	−	6.08155i	1.24230	−	0.403647i	0.387142	−	0.922020i	$-0.373462\pi$
$227$	18.7171	−	6.08155i	1.24230	−	0.403647i	0.855154	+	0.518373i	$0.173462\pi$
$228$		0			0
$229$	4.29343	−	3.11936i	0.283718	−	0.206133i	−0.436819	−	0.899549i	$-0.643895\pi$
$229$	4.29343	−	3.11936i	0.283718	−	0.206133i	0.720538	+	0.693416i	$0.243895\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	13.6774	−	18.8253i	0.896034	−	1.23329i	−0.0756813	−	0.997132i	$-0.524113\pi$
$233$	13.6774	−	18.8253i	0.896034	−	1.23329i	0.971716	−	0.236154i	$-0.0758868\pi$
$234$		0			0
$235$	5.55963	−	9.53010i	0.362670	−	0.621675i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−4.65842	−	14.3371i	−0.301328	−	0.927392i	−0.981022	−	0.193897i	$-0.937887\pi$
$239$	−4.65842	−	14.3371i	−0.301328	−	0.927392i	0.679694	−	0.733496i	$-0.262113\pi$
$240$		0			0
$241$	−5.84454	+	17.9877i	−0.376480	+	1.15869i	0.565995	+	0.824409i	$0.308492\pi$
$241$	−5.84454	+	17.9877i	−0.376480	+	1.15869i	−0.942475	+	0.334278i	$0.891508\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	5.47650	+	12.4512i	0.349880	+	0.795475i
$246$		0			0
$247$	5.99340	+	8.24921i	0.381351	+	0.524885i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	4.56761			0.288305			0.144153	−	0.989555i	$-0.453954\pi$
$251$	4.56761			0.288305			0.144153	+	0.989555i	$0.453954\pi$
$252$		0			0
$253$	11.2042	+	15.4213i	0.704405	+	0.969530i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			20.2556i			1.26351i	0.775169	+	0.631754i	$0.217665\pi$
$257$			20.2556i			1.26351i	−0.775169	+	0.631754i	$0.782335\pi$
$258$		0			0
$259$	−3.34811	+	10.3044i	−0.208042	+	0.640286i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−29.2724	−	9.51119i	−1.80502	−	0.586485i	−0.805038	−	0.593223i	$-0.797855\pi$
$263$	−29.2724	−	9.51119i	−1.80502	−	0.586485i	−0.999977	+	0.00673789i	$0.997855\pi$
$264$		0			0
$265$	−6.70005	+	11.4850i	−0.411581	+	0.705515i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	21.5796	+	15.6785i	1.31573	+	0.955936i	0.999975	+	0.00709610i	$0.00225878\pi$
$269$	21.5796	+	15.6785i	1.31573	+	0.955936i	0.315758	+	0.948840i	$0.397741\pi$
$270$		0			0
$271$	4.47342	−	3.25013i	0.271741	−	0.197431i	−0.443566	−	0.896242i	$-0.646287\pi$
$271$	4.47342	−	3.25013i	0.271741	−	0.197431i	0.715307	+	0.698810i	$0.246287\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	−24.6380	−	11.2368i	−1.48573	−	0.677603i
$276$		0			0
$277$	29.4098	−	9.55583i	1.76706	−	0.574154i	0.769172	−	0.639041i	$-0.220669\pi$
$277$	29.4098	−	9.55583i	1.76706	−	0.574154i	0.997893	+	0.0648872i	$0.0206688\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−13.6310	−	9.90352i	−0.813159	−	0.590795i	0.101586	−	0.994827i	$-0.467608\pi$
$281$	−13.6310	−	9.90352i	−0.813159	−	0.590795i	−0.914745	+	0.404032i	$0.867608\pi$
$282$		0			0
$283$	6.62008	−	9.11176i	0.393523	−	0.541638i	−0.565581	−	0.824693i	$-0.691348\pi$
$283$	6.62008	−	9.11176i	0.393523	−	0.541638i	0.959104	+	0.283055i	$0.0913480\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−3.20805	−	1.04236i	−0.189365	−	0.0615285i
$288$		0			0
$289$	5.12558	+	15.7749i	0.301505	+	0.927936i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	11.1995i		−	0.654284i	−0.944975	−	0.327142i	$-0.893914\pi$
$293$		−	11.1995i		−	0.654284i	0.944975	−	0.327142i	$-0.106086\pi$
$294$		0			0
$295$	10.4986	−	1.05562i	0.611251	−	0.0614607i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−7.11914			−0.411710
$300$		0			0
$301$	−0.733798			−0.0422954
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−7.24916	+	6.46824i	−0.415086	+	0.370371i
$306$		0			0
$307$			24.1289i			1.37711i	0.725185	+	0.688554i	$0.241754\pi$
$307$			24.1289i			1.37711i	−0.725185	+	0.688554i	$0.758246\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−0.640628	−	1.97165i	−0.0363267	−	0.111802i	0.931249	−	0.364384i	$-0.118720\pi$
$311$	−0.640628	−	1.97165i	−0.0363267	−	0.111802i	−0.967576	+	0.252582i	$0.918720\pi$
$312$		0			0
$313$	8.10268	+	2.63272i	0.457991	+	0.148810i	0.528921	−	0.848671i	$-0.322597\pi$
$313$	8.10268	+	2.63272i	0.457991	+	0.148810i	−0.0709303	+	0.997481i	$0.522597\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−7.99798	+	11.0083i	−0.449211	+	0.618286i	−0.972228	−	0.234036i	$-0.924806\pi$
$317$	−7.99798	+	11.0083i	−0.449211	+	0.618286i	0.523017	+	0.852322i	$0.324806\pi$
$318$		0			0
$319$	−44.4323	−	32.2819i	−2.48773	−	1.80744i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	3.08211	−	1.00144i	0.171493	−	0.0557215i
$324$		0			0
$325$	8.80382	−	4.97761i	0.488348	−	0.276108i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	3.82231	−	2.77707i	0.210731	−	0.153105i
$330$		0			0
$331$	18.3097	+	13.3028i	1.00639	+	0.731187i	0.963449	−	0.267891i	$-0.0863266\pi$
$331$	18.3097	+	13.3028i	1.00639	+	0.731187i	0.0429430	+	0.999078i	$0.486327\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−20.7972	−	4.51865i	−1.13627	−	0.246880i
$336$		0			0
$337$	−34.2285	−	11.1215i	−1.86455	−	0.605828i	−0.993385	−	0.114831i	$-0.963367\pi$
$337$	−34.2285	−	11.1215i	−1.86455	−	0.605828i	−0.871161	−	0.490997i	$-0.836633\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	6.17857	−	19.0157i	0.334588	−	1.02976i
$342$		0			0
$343$			12.5275i			0.676419i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	5.26858	+	7.25158i	0.282832	+	0.389285i	0.926669	−	0.375877i	$-0.122659\pi$
$347$	5.26858	+	7.25158i	0.282832	+	0.389285i	−0.643837	+	0.765162i	$0.722659\pi$
$348$		0			0
$349$	11.8276			0.633114			0.316557	−	0.948573i	$-0.397473\pi$
$349$	11.8276			0.633114			0.316557	+	0.948573i	$0.397473\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	13.5712	+	18.6791i	0.722320	+	0.994188i	0.999444	+	0.0333537i	$0.0106188\pi$
$353$	13.5712	+	18.6791i	0.722320	+	0.994188i	−0.277124	+	0.960834i	$0.589381\pi$
$354$		0			0
$355$	−23.0709	−	13.4590i	−1.22448	−	0.714330i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	6.52607	−	20.0852i	0.344433	−	1.06005i	−0.617454	−	0.786607i	$-0.711836\pi$
$359$	6.52607	−	20.0852i	0.344433	−	1.06005i	0.961887	−	0.273448i	$-0.0881641\pi$
$360$		0			0
$361$	1.98147	+	6.09833i	0.104288	+	0.320965i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	8.08825	+	9.06475i	0.423358	+	0.474471i
$366$		0			0
$367$	−4.93178	+	6.78801i	−0.257437	+	0.354331i	−0.918098	−	0.396353i	$-0.870276\pi$
$367$	−4.93178	+	6.78801i	−0.257437	+	0.354331i	0.660662	+	0.750684i	$0.270276\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−4.60636	+	3.34672i	−0.239150	+	0.173753i
$372$		0			0
$373$	−6.01888	+	1.95565i	−0.311646	+	0.101260i	−0.460664	−	0.887575i	$-0.652389\pi$
$373$	−6.01888	+	1.95565i	−0.311646	+	0.101260i	0.149018	+	0.988834i	$0.452389\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	19.5079	−	6.33850i	1.00471	−	0.326450i
$378$		0			0
$379$	12.1990	−	8.86310i	0.626621	−	0.455267i	−0.228607	−	0.973519i	$-0.573417\pi$
$379$	12.1990	−	8.86310i	0.626621	−	0.455267i	0.855228	+	0.518252i	$0.173417\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−19.1490	+	26.3563i	−0.978466	+	1.34674i	−0.0408145	+	0.999167i	$0.512995\pi$
$383$	−19.1490	+	26.3563i	−0.978466	+	1.34674i	−0.937652	+	0.347576i	$0.887005\pi$
$384$		0			0
$385$	−7.72028	−	8.65235i	−0.393462	−	0.440965i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	−1.69084	−	5.20388i	−0.0857292	−	0.263847i	0.898998	−	0.437953i	$-0.144296\pi$
$389$	−1.69084	−	5.20388i	−0.0857292	−	0.263847i	−0.984727	+	0.174106i	$0.944296\pi$
$390$		0			0
$391$	−0.699192	+	2.15189i	−0.0353597	+	0.108826i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	22.8863	+	13.3513i	1.15154	+	0.671779i
$396$		0			0
$397$	−8.38686	−	11.5435i	−0.420925	−	0.579353i	0.544916	−	0.838491i	$-0.316562\pi$
$397$	−8.38686	−	11.5435i	−0.420925	−	0.579353i	−0.965840	+	0.259138i	$0.916562\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−17.8291			−0.890342			−0.445171	−	0.895446i	$-0.646857\pi$
$401$	−17.8291			−0.890342			−0.445171	+	0.895446i	$0.646857\pi$
$402$		0			0
$403$	4.38923	+	6.04125i	0.218643	+	0.300936i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			61.2826i			3.03767i
$408$		0			0
$409$	−7.42964	+	22.8661i	−0.367372	+	1.13065i	0.581110	+	0.813825i	$0.302618\pi$
$409$	−7.42964	+	22.8661i	−0.367372	+	1.13065i	−0.948482	+	0.316830i	$0.897382\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	4.29721	+	1.39625i	0.211452	+	0.0687049i
$414$		0			0
$415$	3.04619	+	0.661852i	0.149531	+	0.0324890i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	22.7180	+	16.5056i	1.10984	+	0.806349i	0.982639	−	0.185527i	$-0.0593992\pi$
$419$	22.7180	+	16.5056i	1.10984	+	0.806349i	0.127206	+	0.991876i	$0.459399\pi$
$420$		0			0
$421$	−16.3383	+	11.8704i	−0.796278	+	0.578530i	−0.909820	−	0.415003i	$-0.863780\pi$
$421$	−16.3383	+	11.8704i	−0.796278	+	0.578530i	0.113542	+	0.993533i	$0.463780\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−0.639926	−	3.14999i	−0.0310410	−	0.152797i
$426$		0			0
$427$	−3.95668	+	1.28560i	−0.191477	+	0.0622148i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−3.35912	−	2.44055i	−0.161803	−	0.117557i	0.503937	−	0.863740i	$-0.331884\pi$
$431$	−3.35912	−	2.44055i	−0.161803	−	0.117557i	−0.665741	+	0.746183i	$0.731884\pi$
$432$		0			0
$433$	17.8217	−	24.5295i	0.856456	−	1.17881i	−0.125947	−	0.992037i	$-0.540197\pi$
$433$	17.8217	−	24.5295i	0.856456	−	1.17881i	0.982403	−	0.186773i	$-0.0598030\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−16.8741	−	5.48273i	−0.807198	−	0.262275i
$438$		0			0
$439$	0.984067	+	3.02865i	0.0469670	+	0.144549i	0.971790	−	0.235849i	$-0.0757870\pi$
$439$	0.984067	+	3.02865i	0.0469670	+	0.144549i	−0.924823	+	0.380398i	$0.875787\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			30.4607i			1.44723i	0.690204	+	0.723615i	$0.257521\pi$
$443$			30.4607i			1.44723i	−0.690204	+	0.723615i	$0.742479\pi$
$444$		0			0
$445$	2.84992	−	2.54291i	0.135099	−	0.120545i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	1.35787			0.0640820			0.0320410	−	0.999487i	$-0.489799\pi$
$449$	1.35787			0.0640820			0.0320410	+	0.999487i	$0.489799\pi$
$450$		0			0
$451$	−19.0789			−0.898392
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.30909	−	0.433275i	0.202013	−	0.0203122i
$456$		0			0
$457$			9.89208i			0.462732i	0.972867	+	0.231366i	$0.0743195\pi$
$457$			9.89208i			0.462732i	−0.972867	+	0.231366i	$0.925680\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	6.51515	+	20.0516i	0.303441	+	0.933894i	0.980255	+	0.197740i	$0.0633602\pi$
$461$	6.51515	+	20.0516i	0.303441	+	0.933894i	−0.676814	+	0.736154i	$0.736640\pi$
$462$		0			0
$463$	0.488978	+	0.158879i	0.0227248	+	0.00738372i	0.320357	−	0.947297i	$-0.396197\pi$
$463$	0.488978	+	0.158879i	0.0227248	+	0.00738372i	−0.297633	+	0.954681i	$0.596197\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10.9175	−	15.0267i	0.505202	−	0.695352i	−0.477899	−	0.878415i	$-0.658601\pi$
$467$	10.9175	−	15.0267i	0.505202	−	0.695352i	0.983101	+	0.183063i	$0.0586014\pi$
$468$		0			0
$469$	−7.37300	−	5.35680i	−0.340453	−	0.247354i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−3.94732	+	1.28256i	−0.181498	+	0.0589723i
$474$		0			0
$475$	24.7007	−	5.01800i	1.13335	−	0.230241i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.3847	+	13.3573i	−0.840017	+	0.610308i	−0.922376	−	0.386294i	$-0.873755\pi$
$479$	−18.3847	+	13.3573i	−0.840017	+	0.610308i	0.0823581	+	0.996603i	$0.473755\pi$
$480$		0			0
$481$	−18.5165	−	13.4530i	−0.844279	−	0.613404i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	−16.4369	+	28.1754i	−0.746359	+	1.27938i
$486$		0			0
$487$	−25.2840	−	8.21528i	−1.14573	−	0.372270i	−0.326196	−	0.945302i	$-0.605767\pi$
$487$	−25.2840	−	8.21528i	−1.14573	−	0.372270i	−0.819533	+	0.573032i	$0.805767\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−1.66601	+	5.12746i	−0.0751860	+	0.231399i	−0.981586	−	0.191022i	$-0.938820\pi$
$491$	−1.66601	+	5.12746i	−0.0751860	+	0.231399i	0.906400	+	0.422421i	$0.138820\pi$
$492$		0			0
$493$		−	6.51915i		−	0.293608i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−6.72286	−	9.25323i	−0.301562	−	0.415064i
$498$		0			0
$499$	14.5574			0.651677			0.325839	−	0.945425i	$-0.394353\pi$
$499$	14.5574			0.651677			0.325839	+	0.945425i	$0.394353\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−19.9353	−	27.4386i	−0.888873	−	1.22343i	−0.973883	−	0.227049i	$-0.927092\pi$
$503$	−19.9353	−	27.4386i	−0.888873	−	1.22343i	0.0850104	−	0.996380i	$-0.472908\pi$
$504$		0			0
$505$	9.25773	+	21.0480i	0.411963	+	0.936624i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−5.18882	+	15.9695i	−0.229990	+	0.707838i	0.767756	+	0.640742i	$0.221373\pi$
$509$	−5.18882	+	15.9695i	−0.229990	+	0.707838i	−0.997747	+	0.0670956i	$0.978627\pi$
$510$		0			0
$511$	1.60759	+	4.94766i	0.0711157	+	0.218872i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	15.7574	−	27.0108i	0.694355	−	1.19024i
$516$		0			0
$517$	15.7075	−	21.6195i	0.690815	−	0.950825i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−13.8271	+	10.0460i	−0.605777	+	0.440123i	−0.847925	−	0.530117i	$-0.822148\pi$
$521$	−13.8271	+	10.0460i	−0.605777	+	0.440123i	0.242148	+	0.970239i	$0.422148\pi$
$522$		0			0
$523$	−19.6398	+	6.38135i	−0.858788	+	0.279037i	−0.705122	−	0.709086i	$-0.749108\pi$
$523$	−19.6398	+	6.38135i	−0.858788	+	0.279037i	−0.153666	+	0.988123i	$0.549108\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	2.25716	−	0.733396i	0.0983234	−	0.0319472i
$528$		0			0
$529$	−8.58561	+	6.23781i	−0.373287	+	0.271209i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	4.18829	−	5.76468i	0.181415	−	0.249696i
$534$		0			0
$535$	−18.5591	+	8.16303i	−0.802382	+	0.352918i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	10.1808	+	31.3332i	0.438517	+	1.34962i
$540$		0			0
$541$	−3.75968	+	11.5711i	−0.161641	+	0.497480i	−0.998773	−	0.0495207i	$-0.984231\pi$
$541$	−3.75968	+	11.5711i	−0.161641	+	0.497480i	0.837132	+	0.547001i	$0.184231\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−5.28481	+	0.531383i	−0.226376	+	0.0227619i
$546$		0			0
$547$	6.56378	+	9.03427i	0.280647	+	0.386278i	0.925948	−	0.377651i	$-0.123268\pi$
$547$	6.56378	+	9.03427i	0.280647	+	0.386278i	−0.645301	+	0.763928i	$0.723268\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	51.1201			2.17779
$552$		0			0
$553$	6.66908	+	9.17921i	0.283598	+	0.390340i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			12.9282i			0.547787i	0.961760	+	0.273894i	$0.0883116\pi$
$557$			12.9282i			0.547787i	−0.961760	+	0.273894i	$0.911688\pi$
$558$		0			0
$559$	0.479007	−	1.47423i	0.0202598	−	0.0623534i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	30.1722	+	9.80354i	1.27161	+	0.413170i	0.865616	−	0.500708i	$-0.166927\pi$
$563$	30.1722	+	9.80354i	1.27161	+	0.413170i	0.405989	+	0.913878i	$0.366927\pi$
$564$		0			0
$565$	3.00603	+	29.8961i	0.126465	+	1.25774i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−23.3050	−	16.9321i	−0.976997	−	0.709830i	−0.0199619	−	0.999801i	$-0.506354\pi$
$569$	−23.3050	−	16.9321i	−0.976997	−	0.709830i	−0.957036	+	0.289971i	$0.906354\pi$
$570$		0			0
$571$	14.6999	−	10.6801i	0.615173	−	0.446950i	−0.236059	−	0.971739i	$-0.575856\pi$
$571$	14.6999	−	10.6801i	0.615173	−	0.446950i	0.851232	+	0.524789i	$0.175856\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−7.30239	+	16.0114i	−0.304531	+	0.667722i
$576$		0			0
$577$	38.7990	−	12.6065i	1.61522	−	0.524817i	0.644414	−	0.764677i	$-0.277101\pi$
$577$	38.7990	−	12.6065i	1.61522	−	0.524817i	0.970808	+	0.239859i	$0.0771014\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	1.07993	+	0.784616i	0.0448031	+	0.0325514i
$582$		0			0
$583$	−18.9295	+	26.0542i	−0.783979	+	1.07905i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−8.75436	−	2.84446i	−0.361331	−	0.117404i	0.122725	−	0.992441i	$-0.460837\pi$
$587$	−8.75436	−	2.84446i	−0.361331	−	0.117404i	−0.484056	+	0.875037i	$0.660837\pi$
$588$		0			0
$589$	5.75094	+	17.6996i	0.236963	+	0.729298i
$590$		0			0
$591$		0			0
$592$		0			0
$593$			12.3856i			0.508614i	0.967124	+	0.254307i	$0.0818474\pi$
$593$			12.3856i			0.508614i	−0.967124	+	0.254307i	$0.918153\pi$
$594$		0			0
$595$	0.292243	−	1.34505i	0.0119808	−	0.0551419i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−18.1732			−0.742536			−0.371268	−	0.928526i	$-0.621077\pi$
$599$	−18.1732			−0.742536			−0.371268	+	0.928526i	$0.621077\pi$
$600$		0			0
$601$	29.8155			1.21620			0.608099	−	0.793861i	$-0.291932\pi$
$601$	29.8155			1.21620			0.608099	+	0.793861i	$0.291932\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−35.4069	−	20.6555i	−1.43950	−	0.839767i
$606$		0			0
$607$			9.16747i			0.372096i	0.982541	+	0.186048i	$0.0595680\pi$
$607$			9.16747i			0.372096i	−0.982541	+	0.186048i	$0.940432\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	3.08414	+	9.49201i	0.124771	+	0.384006i
$612$		0			0
$613$	−13.3662	−	4.34294i	−0.539855	−	0.175410i	0.0263819	−	0.999652i	$-0.491601\pi$
$613$	−13.3662	−	4.34294i	−0.539855	−	0.175410i	−0.566237	+	0.824242i	$0.691601\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	21.2980	−	29.3141i	0.857424	−	1.18014i	−0.124754	−	0.992188i	$-0.539814\pi$
$617$	21.2980	−	29.3141i	0.857424	−	1.18014i	0.982178	−	0.187955i	$-0.0601859\pi$
$618$		0			0
$619$	20.7716	+	15.0915i	0.834882	+	0.606577i	0.920936	−	0.389713i	$-0.127426\pi$
$619$	20.7716	+	15.0915i	0.834882	+	0.606577i	−0.0860542	+	0.996290i	$0.527426\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	1.55552	−	0.505419i	0.0623206	−	0.0202492i
$624$		0			0
$625$	−2.16453	−	24.9061i	−0.0865814	−	0.996245i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−5.88498	+	4.27569i	−0.234650	+	0.170483i
$630$		0			0
$631$	19.9603	+	14.5020i	0.794608	+	0.577317i	0.909327	−	0.416081i	$-0.136597\pi$
$631$	19.9603	+	14.5020i	0.794608	+	0.577317i	−0.114719	+	0.993398i	$0.536597\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	21.2334	+	23.7970i	0.842624	+	0.944354i
$636$		0			0
$637$	−11.7022	−	3.80228i	−0.463659	−	0.150652i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	9.25128	−	28.4725i	0.365404	−	1.12460i	−0.584324	−	0.811520i	$-0.698640\pi$
$641$	9.25128	−	28.4725i	0.365404	−	1.12460i	0.949728	−	0.313077i	$-0.101360\pi$
$642$		0			0
$643$			10.1343i			0.399658i	0.979831	+	0.199829i	$0.0640387\pi$
$643$			10.1343i			0.399658i	−0.979831	+	0.199829i	$0.935961\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−26.6027	−	36.6155i	−1.04586	−	1.43950i	−0.892343	−	0.451358i	$-0.850940\pi$
$647$	−26.6027	−	36.6155i	−1.04586	−	1.43950i	−0.153518	−	0.988146i	$-0.549060\pi$
$648$		0			0
$649$	25.5564			1.00318
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−19.3880	−	26.6853i	−0.758711	−	1.04428i	−0.997320	−	0.0731608i	$-0.976691\pi$
$653$	−19.3880	−	26.6853i	−0.758711	−	1.04428i	0.238609	−	0.971116i	$-0.423309\pi$
$654$		0			0
$655$	0.0610855	−	0.281147i	0.00238681	−	0.0109853i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	0.789392	−	2.42950i	0.0307504	−	0.0946398i	−0.934503	−	0.355954i	$-0.884156\pi$
$659$	0.789392	−	2.42950i	0.0307504	−	0.0946398i	0.965254	+	0.261314i	$0.0841559\pi$
$660$		0			0
$661$	−14.0332	−	43.1898i	−0.545829	−	1.67989i	−0.719011	−	0.694999i	$-0.755405\pi$
$661$	−14.0332	−	43.1898i	−0.545829	−	1.67989i	0.173182	−	0.984890i	$-0.444595\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	10.5473	+	2.29163i	0.409006	+	0.0888656i
$666$		0			0
$667$	−20.9789	+	28.8750i	−0.812307	+	1.11804i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−19.0372	+	13.8313i	−0.734922	+	0.533952i
$672$		0			0
$673$	−10.7875	+	3.50508i	−0.415828	+	0.135111i	−0.509456	−	0.860496i	$-0.670153\pi$
$673$	−10.7875	+	3.50508i	−0.415828	+	0.135111i	0.0936282	+	0.995607i	$0.470153\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	14.7113	−	4.78000i	0.565402	−	0.183710i	−0.0123484	−	0.999924i	$-0.503931\pi$
$677$	14.7113	−	4.78000i	0.565402	−	0.183710i	0.577750	+	0.816213i	$0.303931\pi$
$678$		0			0
$679$	−11.3005	+	8.21032i	−0.433675	+	0.315083i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−3.99284	+	5.49567i	−0.152782	+	0.210286i	−0.878546	−	0.477657i	$-0.841486\pi$
$683$	−3.99284	+	5.49567i	−0.152782	+	0.210286i	0.725765	+	0.687943i	$0.241486\pi$
$684$		0			0
$685$	3.06528	+	30.4854i	0.117118	+	1.16479i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−3.71677	−	11.4390i	−0.141598	−	0.435793i
$690$		0			0
$691$	13.0774	−	40.2482i	0.497489	−	1.53111i	−0.315552	−	0.948908i	$-0.602190\pi$
$691$	13.0774	−	40.2482i	0.497489	−	1.53111i	0.813041	−	0.582206i	$-0.197810\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	39.1615	−	34.9428i	1.48548	−	1.32546i
$696$		0			0
$697$	−1.33114	−	1.83215i	−0.0504205	−	0.0693978i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	−32.2924			−1.21967			−0.609834	−	0.792529i	$-0.708764\pi$
$701$	−32.2924			−1.21967			−0.609834	+	0.792529i	$0.708764\pi$
$702$		0			0
$703$	−33.5279	−	46.1472i	−1.26453	−	1.74047i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			9.84647i			0.370314i
$708$		0			0
$709$	0.667116	−	2.05317i	0.0250541	−	0.0771085i	−0.937748	−	0.347317i	$-0.887093\pi$
$709$	0.667116	−	2.05317i	0.0250541	−	0.0771085i	0.962802	+	0.270209i	$0.0870927\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−12.3576	−	4.01524i	−0.462797	−	0.150372i
$714$		0			0
$715$	22.4226	−	9.86231i	0.838557	−	0.368830i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	−1.28757	−	0.935472i	−0.0480181	−	0.0348872i	0.563517	−	0.826104i	$-0.309448\pi$
$719$	−1.28757	−	0.935472i	−0.0480181	−	0.0348872i	−0.611535	+	0.791217i	$0.709448\pi$
$720$		0			0
$721$	10.8334	−	7.87094i	0.403458	−	0.293129i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	5.75436	−	50.3762i	0.213711	−	1.87093i
$726$		0			0
$727$	−1.27424	+	0.414026i	−0.0472589	+	0.0153554i	−0.332551	−	0.943085i	$-0.607909\pi$
$727$	−1.27424	+	0.414026i	−0.0472589	+	0.0153554i	0.285292	+	0.958441i	$0.407909\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−0.398570	−	0.289578i	−0.0147416	−	0.0107104i
$732$		0			0
$733$	−25.7748	+	35.4759i	−0.952013	+	1.31033i	−0.00138578	+	0.999999i	$0.500441\pi$
$733$	−25.7748	+	35.4759i	−0.952013	+	1.31033i	−0.950627	+	0.310335i	$0.899559\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−49.0244	−	15.9290i	−1.80584	−	0.586752i
$738$		0			0
$739$	−5.67584	−	17.4684i	−0.208789	−	0.642587i	−0.999536	−	0.0304443i	$-0.990308\pi$
$739$	−5.67584	−	17.4684i	−0.208789	−	0.642587i	0.790747	−	0.612143i	$-0.209692\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	21.5051i		−	0.788947i	−0.918907	−	0.394474i	$-0.870927\pi$
$743$		−	21.5051i		−	0.788947i	0.918907	−	0.394474i	$-0.129073\pi$
$744$		0			0
$745$	−9.62736	−	21.8884i	−0.352719	−	0.801929i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.68215			−0.317239
$750$		0			0
$751$	−7.02810			−0.256459			−0.128230	−	0.991745i	$-0.540929\pi$
$751$	−7.02810			−0.256459			−0.128230	+	0.991745i	$0.540929\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	6.63970	+	15.0958i	0.241643	+	0.549391i
$756$		0			0
$757$			5.39361i			0.196034i	0.995185	+	0.0980171i	$0.0312500\pi$
$757$			5.39361i			0.196034i	−0.995185	+	0.0980171i	$0.968750\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	6.22670	+	19.1638i	0.225718	+	0.694688i	0.998218	+	0.0596731i	$0.0190058\pi$
$761$	6.22670	+	19.1638i	0.225718	+	0.694688i	−0.772500	+	0.635014i	$0.780994\pi$
$762$		0			0
$763$	−2.16314	−	0.702848i	−0.0783111	−	0.0254448i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−5.61025	+	7.72184i	−0.202574	+	0.278820i
$768$		0			0
$769$	25.0121	+	18.1724i	0.901960	+	0.655312i	0.938969	−	0.344003i	$-0.111783\pi$
$769$	25.0121	+	18.1724i	0.901960	+	0.655312i	−0.0370088	+	0.999315i	$0.511783\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	30.4255	−	9.88584i	1.09433	−	0.355569i	0.294411	−	0.955679i	$-0.404876\pi$
$773$	30.4255	−	9.88584i	1.09433	−	0.355569i	0.799918	+	0.600110i	$0.204876\pi$
$774$		0			0
$775$	18.0894	−	3.67489i	0.649790	−	0.132006i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	14.3669	−	10.4381i	0.514747	−	0.373985i
$780$		0			0
$781$	−52.3375	−	38.0254i	−1.87278	−	1.36066i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	26.6761	−	11.7332i	0.952112	−	0.418776i
$786$		0			0
$787$	23.2267	+	7.54681i	0.827942	+	0.269015i	0.692178	−	0.721726i	$-0.256651\pi$
$787$	23.2267	+	7.54681i	0.827942	+	0.269015i	0.135764	+	0.990741i	$0.456651\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−3.97601	+	12.2369i	−0.141371	+	0.435094i
$792$		0			0
$793$		−	8.78837i		−	0.312084i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−29.1765	−	40.1580i	−1.03348	−	1.42247i	−0.902300	−	0.431110i	$-0.858122\pi$
$797$	−29.1765	−	40.1580i	−1.03348	−	1.42247i	−0.131184	−	0.991358i	$-0.541878\pi$
$798$		0			0
$799$	3.17204			0.112219
$800$		0			0
$801$		0			0
$802$		0			0
$803$	17.2954	+	23.8051i	0.610343	+	0.840065i
$804$		0			0
$805$	−5.62286	+	5.01714i	−0.198180	+	0.176831i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−5.82162	+	17.9171i	−0.204677	+	0.629932i	0.795049	+	0.606545i	$0.207445\pi$
$809$	−5.82162	+	17.9171i	−0.204677	+	0.629932i	−0.999726	+	0.0233871i	$0.992555\pi$
$810$		0			0
$811$	5.77928	+	17.7868i	0.202938	+	0.624578i	0.999792	+	0.0204064i	$0.00649600\pi$
$811$	5.77928	+	17.7868i	0.202938	+	0.624578i	−0.796854	+	0.604172i	$0.793504\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	1.65454	+	16.4550i	0.0579559	+	0.576394i
$816$		0			0
$817$	2.27073	−	3.12539i	0.0794428	−	0.109344i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	29.7103	−	21.5858i	1.03690	−	0.753350i	0.0672202	−	0.997738i	$-0.478587\pi$
$821$	29.7103	−	21.5858i	1.03690	−	0.753350i	0.969678	+	0.244388i	$0.0785870\pi$
$822$		0			0
$823$	−38.5327	+	12.5200i	−1.34317	+	0.436421i	−0.890388	−	0.455202i	$-0.849567\pi$
$823$	−38.5327	+	12.5200i	−1.34317	+	0.436421i	−0.452779	+	0.891623i	$0.649567\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−10.6264	+	3.45274i	−0.369517	+	0.120063i	−0.487889	−	0.872906i	$-0.662233\pi$
$827$	−10.6264	+	3.45274i	−0.369517	+	0.120063i	0.118371	+	0.992969i	$0.462233\pi$
$828$		0			0
$829$	29.8314	−	21.6738i	1.03609	−	0.752762i	0.0665703	−	0.997782i	$-0.478794\pi$
$829$	29.8314	−	21.6738i	1.03609	−	0.752762i	0.969518	+	0.245019i	$0.0787943\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−2.29862	+	3.16378i	−0.0796425	+	0.109618i
$834$		0			0
$835$	43.9782	+	9.55524i	1.52193	+	0.330673i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.53480	−	10.8790i	−0.122035	−	0.375585i	0.871314	−	0.490725i	$-0.163268\pi$
$839$	−3.53480	−	10.8790i	−0.122035	−	0.375585i	−0.993349	+	0.115140i	$0.963268\pi$
$840$		0			0
$841$	22.8163	−	70.2213i	0.786769	−	2.42143i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.22945	−	19.4662i	0.145498	−	0.669656i
$846$		0			0
$847$	−10.3176	−	14.2009i	−0.354516	−	0.487950i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	39.8254			1.36520
$852$		0			0
$853$	14.4849	+	19.9368i	0.495954	+	0.682623i	0.981472	−	0.191604i	$-0.0613689\pi$
$853$	14.4849	+	19.9368i	0.495954	+	0.682623i	−0.485518	+	0.874227i	$0.661369\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			11.2342i			0.383752i	0.981419	+	0.191876i	$0.0614571\pi$
$857$			11.2342i			0.383752i	−0.981419	+	0.191876i	$0.938543\pi$
$858$		0			0
$859$	4.79573	−	14.7597i	0.163628	−	0.503595i	−0.835305	−	0.549788i	$-0.814709\pi$
$859$	4.79573	−	14.7597i	0.163628	−	0.503595i	0.998933	+	0.0461922i	$0.0147087\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	18.5636	+	6.03168i	0.631912	+	0.205321i	0.607422	−	0.794379i	$-0.292204\pi$
$863$	18.5636	+	6.03168i	0.631912	+	0.205321i	0.0244902	+	0.999700i	$0.492204\pi$
$864$		0			0
$865$	−3.30662	−	3.70583i	−0.112429	−	0.126002i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	51.9188	+	37.7212i	1.76123	+	1.27960i
$870$		0			0
$871$	15.5750	−	11.3159i	0.527738	−	0.383424i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	3.44554	−	10.1358i	0.116481	−	0.342654i
$876$		0			0
$877$	−13.0638	+	4.24470i	−0.441134	+	0.143333i	−0.521159	−	0.853460i	$-0.674500\pi$
$877$	−13.0638	+	4.24470i	−0.441134	+	0.143333i	0.0800245	+	0.996793i	$0.474500\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−42.4014	−	30.8064i	−1.42854	−	1.03789i	−0.990286	−	0.139042i	$-0.955598\pi$
$881$	−42.4014	−	30.8064i	−1.42854	−	1.03789i	−0.438253	−	0.898852i	$-0.644402\pi$
$882$		0			0
$883$	−9.81699	+	13.5119i	−0.330368	+	0.454713i	−0.941597	−	0.336741i	$-0.890675\pi$
$883$	−9.81699	+	13.5119i	−0.330368	+	0.454713i	0.611229	+	0.791454i	$0.290675\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−24.6331	−	8.00379i	−0.827099	−	0.268741i	−0.135276	−	0.990808i	$-0.543192\pi$
$887$	−24.6331	−	8.00379i	−0.827099	−	0.268741i	−0.691823	+	0.722067i	$0.743192\pi$
$888$		0			0
$889$	4.22028	+	12.9887i	0.141544	+	0.435627i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			24.8736i			0.832364i
$894$		0			0
$895$	0.0745376	+	0.0434835i	0.00249152	+	0.00145349i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	37.4374			1.24861
$900$		0			0
$901$	−3.82270			−0.127353
$902$		0			0
$903$		0			0
$904$		0			0
$905$	0.0697633	−	0.321087i	0.00231901	−	0.0106733i
$906$		0			0
$907$		−	4.74821i		−	0.157662i	−0.996888	−	0.0788308i	$-0.974881\pi$
$907$		−	4.74821i		−	0.157662i	0.996888	−	0.0788308i	$-0.0251187\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	3.79559	+	11.6816i	0.125753	+	0.387029i	0.994038	−	0.109038i	$-0.0347770\pi$
$911$	3.79559	+	11.6816i	0.125753	+	0.387029i	−0.868284	+	0.496067i	$0.834777\pi$
$912$		0			0
$913$	7.18067	+	2.33314i	0.237645	+	0.0772156i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	0.0724160	−	0.0996721i	0.00239139	−	0.00329146i
$918$		0			0
$919$	16.7306	+	12.1555i	0.551893	+	0.400974i	0.828483	−	0.560014i	$-0.189204\pi$
$919$	16.7306	+	12.1555i	0.551893	+	0.400974i	−0.276590	+	0.960988i	$0.589204\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	22.9787	−	7.46622i	0.756352	−	0.245754i
$924$		0			0
$925$	−49.2498	+	27.8455i	−1.61932	+	0.915553i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−19.4753	+	14.1496i	−0.638964	+	0.464235i	−0.859494	−	0.511145i	$-0.829221\pi$
$929$	−19.4753	+	14.1496i	−0.638964	+	0.464235i	0.220530	+	0.975380i	$0.429221\pi$
$930$		0			0
$931$	−24.8088	−	18.0247i	−0.813077	−	0.590735i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−0.778879	−	7.74625i	−0.0254721	−	0.253330i
$936$		0			0
$937$	−42.6067	−	13.8438i	−1.39190	−	0.452256i	−0.485338	−	0.874327i	$-0.661303\pi$
$937$	−42.6067	−	13.8438i	−1.39190	−	0.452256i	−0.906563	+	0.422071i	$0.861303\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	14.5501	−	44.7806i	0.474319	−	1.45980i	−0.372554	−	0.928010i	$-0.621518\pi$
$941$	14.5501	−	44.7806i	0.474319	−	1.45980i	0.846874	−	0.531794i	$-0.178482\pi$
$942$		0			0
$943$			12.3987i			0.403759i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	10.5656	+	14.5424i	0.343337	+	0.472563i	0.945412	−	0.325876i	$-0.105659\pi$
$947$	10.5656	+	14.5424i	0.343337	+	0.472563i	−0.602075	+	0.798439i	$0.705659\pi$
$948$		0			0
$949$	−10.9895			−0.356733
$950$		0			0
$951$		0			0
$952$		0			0
$953$	21.1318	+	29.0854i	0.684526	+	0.942169i	0.999977	−	0.00677250i	$-0.00215577\pi$
$953$	21.1318	+	29.0854i	0.684526	+	0.942169i	−0.315451	+	0.948942i	$0.602156\pi$
$954$		0			0
$955$	1.02272	−	0.102834i	0.0330945	−	0.00332762i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	−4.05438	+	12.4781i	−0.130923	+	0.402939i
$960$		0			0
$961$	−5.36787	−	16.5206i	−0.173157	−	0.532923i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	38.9371	−	17.1260i	1.25343	−	0.551307i
$966$		0			0
$967$	5.64225	−	7.76589i	0.181443	−	0.249734i	−0.708601	−	0.705609i	$-0.750674\pi$
$967$	5.64225	−	7.76589i	0.181443	−	0.249734i	0.890044	+	0.455875i	$0.150674\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−22.5625	+	16.3926i	−0.724066	+	0.526065i	−0.887681	−	0.460460i	$-0.847685\pi$
$971$	−22.5625	+	16.3926i	−0.724066	+	0.526065i	0.163615	+	0.986524i	$0.447685\pi$
$972$		0			0
$973$	21.3748	−	6.94511i	0.685246	−	0.222650i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	53.9664	−	17.5347i	1.72654	−	0.560986i	0.733595	−	0.679587i	$-0.237841\pi$
$977$	53.9664	−	17.5347i	1.72654	−	0.560986i	0.992942	+	0.118601i	$0.0378409\pi$
$978$		0			0
$979$	7.48423	−	5.43761i	0.239197	−	0.173787i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−6.61324	+	9.10235i	−0.210930	+	0.290320i	−0.901352	−	0.433086i	$-0.857425\pi$
$983$	−6.61324	+	9.10235i	−0.210930	+	0.290320i	0.690423	+	0.723406i	$0.257425\pi$
$984$		0			0
$985$	13.6507	−	23.3995i	0.434947	−	0.745569i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	0.833493	+	2.56523i	0.0265035	+	0.0815695i
$990$		0			0
$991$	10.6488	−	32.7735i	0.338269	−	1.04109i	−0.626820	−	0.779164i	$-0.715644\pi$
$991$	10.6488	−	32.7735i	0.338269	−	1.04109i	0.965089	−	0.261921i	$-0.0843561\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−14.8430	−	33.7466i	−0.470556	−	1.06984i
$996$		0			0
$997$	−30.0889	−	41.4138i	−0.952924	−	1.31159i	−0.950216	−	0.311591i	$-0.899138\pi$
$997$	−30.0889	−	41.4138i	−0.952924	−	1.31159i	−0.00270782	−	0.999996i	$-0.500862\pi$
$998$		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.469.4		24
3.2	odd	2		300.2.o.a.169.2	✓	24
15.2	even	4		1500.2.m.c.901.3		24
15.8	even	4		1500.2.m.d.901.4		24
15.14	odd	2		1500.2.o.c.349.5		24
25.4	even	10	inner	900.2.w.c.829.4		24
75.2	even	20		7500.2.a.n.1.5		12
75.11	odd	10		7500.2.d.g.1249.20		24
75.14	odd	10		7500.2.d.g.1249.5		24
75.23	even	20		7500.2.a.m.1.8		12
75.29	odd	10		300.2.o.a.229.2	yes	24
75.47	even	20		1500.2.m.c.601.3		24
75.53	even	20		1500.2.m.d.601.4		24
75.71	odd	10		1500.2.o.c.649.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.2	✓	24	3.2	odd	2
300.2.o.a.229.2	yes	24	75.29	odd	10
900.2.w.c.469.4		24	1.1	even	1	trivial
900.2.w.c.829.4		24	25.4	even	10	inner
1500.2.m.c.601.3		24	75.47	even	20
1500.2.m.c.901.3		24	15.2	even	4
1500.2.m.d.601.4		24	75.53	even	20
1500.2.m.d.901.4		24	15.8	even	4
1500.2.o.c.349.5		24	15.14	odd	2
1500.2.o.c.649.5		24	75.71	odd	10
7500.2.a.m.1.8		12	75.23	even	20
7500.2.a.n.1.5		12	75.2	even	20
7500.2.d.g.1249.5		24	75.14	odd	10
7500.2.d.g.1249.20		24	75.11	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)

\(f(q)\)	\(=\)	\(q+(0.900274 + 2.04683i) q^{5} +0.957526i q^{7} +O(q^{10})\)	\(q+(0.900274 + 2.04683i) q^{5} +0.957526i q^{7} +(1.67360 + 5.15082i) q^{11} +(-1.92371 - 0.625052i) q^{13} +(-0.377867 + 0.520090i) q^{17} +(-4.07829 - 2.96305i) q^{19} +(3.34734 - 1.08762i) q^{23} +(-3.37901 + 3.68541i) q^{25} +(-8.20405 + 5.96059i) q^{29} +(-2.98671 - 2.16997i) q^{31} +(-1.95989 + 0.862036i) q^{35} +(10.7615 + 3.49663i) q^{37} +(-1.08859 + 3.35035i) q^{41} +0.766348i q^{43} +(-2.90026 - 3.99186i) q^{47} +6.08314 q^{49} +(3.49517 + 4.81069i) q^{53} +(-9.03615 + 8.06273i) q^{55} +(1.45818 - 4.48783i) q^{59} +(1.34263 + 4.13219i) q^{61} +(-0.452494 - 4.50023i) q^{65} +(-5.59441 + 7.70005i) q^{67} +(-9.66368 + 7.02107i) q^{71} +(5.16713 - 1.67890i) q^{73} +(-4.93205 + 1.60252i) q^{77} +(9.58637 - 6.96491i) q^{79} +(0.819420 - 1.12784i) q^{83} +(-1.40472 - 0.305206i) q^{85} +(-0.527839 - 1.62452i) q^{89} +(0.598504 - 1.84200i) q^{91} +(2.39328 - 11.0151i) q^{95} +(8.57451 + 11.8018i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 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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