LMFDB - Embedded newform 900.2.w.c.289.5

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			289.5
Character	$\chi$	$=$	900.289
Dual form			900.2.w.c.109.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.98828 - 1.02311i) q^{5} +3.54704i q^{7} +O(q^{10})$	$q+(1.98828 - 1.02311i) q^{5} +3.54704i q^{7} +(-1.78482 + 1.29675i) q^{11} +(-4.21895 + 5.80689i) q^{13} +(-6.05378 + 1.96699i) q^{17} +(0.715151 + 2.20101i) q^{19} +(1.27899 + 1.76038i) q^{23} +(2.90649 - 4.06845i) q^{25} +(0.262008 - 0.806379i) q^{29} +(-1.32905 - 4.09040i) q^{31} +(3.62901 + 7.05250i) q^{35} +(4.24968 - 5.84918i) q^{37} +(-1.08778 - 0.790317i) q^{41} +8.18973i q^{43} +(5.75820 + 1.87095i) q^{47} -5.58150 q^{49} +(-11.3730 - 3.69530i) q^{53} +(-2.22201 + 4.40437i) q^{55} +(10.0896 + 7.33050i) q^{59} +(5.59873 - 4.06772i) q^{61} +(-2.44736 + 15.8622i) q^{65} +(4.50239 - 1.46291i) q^{67} +(-4.25799 + 13.1047i) q^{71} +(-0.640196 - 0.881155i) q^{73} +(-4.59963 - 6.33085i) q^{77} +(1.80542 - 5.55650i) q^{79} +(11.9145 - 3.87127i) q^{83} +(-10.0241 + 10.1046i) q^{85} +(5.68424 - 4.12984i) q^{89} +(-20.5973 - 14.9648i) q^{91} +(3.67379 + 3.64454i) q^{95} +(17.2564 + 5.60695i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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
$5$	1.98828	−	1.02311i	0.889185	−	0.457549i
$5$	1.98828	−	1.02311i	0.889185	−	0.457549i
$6$		0			0
$7$			3.54704i			1.34066i	0.742065	+	0.670328i	$0.233846\pi$
$7$			3.54704i			1.34066i	−0.742065	+	0.670328i	$0.766154\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−1.78482	+	1.29675i	−0.538145	+	0.390985i	−0.823396	−	0.567468i	$-0.807923\pi$
$11$	−1.78482	+	1.29675i	−0.538145	+	0.390985i	0.285251	+	0.958453i	$0.407923\pi$
$12$		0			0
$13$	−4.21895	+	5.80689i	−1.17013	+	1.61054i	−0.507301	+	0.861769i	$0.669357\pi$
$13$	−4.21895	+	5.80689i	−1.17013	+	1.61054i	−0.662827	+	0.748773i	$0.730643\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−6.05378	+	1.96699i	−1.46826	+	0.477066i	−0.930581	−	0.366086i	$-0.880698\pi$
$17$	−6.05378	+	1.96699i	−1.46826	+	0.477066i	−0.537676	+	0.843151i	$0.680698\pi$
$18$		0			0
$19$	0.715151	+	2.20101i	0.164067	+	0.504946i	0.998966	−	0.0454566i	$-0.0144743\pi$
$19$	0.715151	+	2.20101i	0.164067	+	0.504946i	−0.834899	+	0.550402i	$0.814474\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	1.27899	+	1.76038i	0.266687	+	0.367064i	0.921268	−	0.388929i	$-0.127155\pi$
$23$	1.27899	+	1.76038i	0.266687	+	0.367064i	−0.654580	+	0.755992i	$0.727155\pi$
$24$		0			0
$25$	2.90649	−	4.06845i	0.581298	−	0.813691i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	0.262008	−	0.806379i	0.0486538	−	0.149741i	−0.923778	−	0.382928i	$-0.874916\pi$
$29$	0.262008	−	0.806379i	0.0486538	−	0.149741i	0.972432	+	0.233188i	$0.0749156\pi$
$30$		0			0
$31$	−1.32905	−	4.09040i	−0.238705	−	0.734657i	−0.996608	−	0.0822910i	$-0.973776\pi$
$31$	−1.32905	−	4.09040i	−0.238705	−	0.734657i	0.757904	−	0.652367i	$-0.226224\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	3.62901	+	7.05250i	0.613415	+	1.19209i
$36$		0			0
$37$	4.24968	−	5.84918i	0.698643	−	0.961599i	−0.301325	−	0.953522i	$-0.597429\pi$
$37$	4.24968	−	5.84918i	0.698643	−	0.961599i	0.999967	−	0.00807756i	$-0.00257119\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	−1.08778	−	0.790317i	−0.169882	−	0.123427i	0.499595	−	0.866259i	$-0.333482\pi$
$41$	−1.08778	−	0.790317i	−0.169882	−	0.123427i	−0.669478	+	0.742832i	$0.733482\pi$
$42$		0			0
$43$			8.18973i			1.24892i	0.781056	+	0.624461i	$0.214681\pi$
$43$			8.18973i			1.24892i	−0.781056	+	0.624461i	$0.785319\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.75820	+	1.87095i	0.839920	+	0.272907i	0.697218	−	0.716859i	$-0.254421\pi$
$47$	5.75820	+	1.87095i	0.839920	+	0.272907i	0.142702	+	0.989766i	$0.454421\pi$
$48$		0			0
$49$	−5.58150			−0.797357
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−11.3730	−	3.69530i	−1.56220	−	0.507589i	−0.604805	−	0.796374i	$-0.706749\pi$
$53$	−11.3730	−	3.69530i	−1.56220	−	0.507589i	−0.957394	+	0.288785i	$0.906749\pi$
$54$		0			0
$55$	−2.22201	+	4.40437i	−0.299615	+	0.593886i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	10.0896	+	7.33050i	1.31355	+	0.954350i	0.999989	+	0.00478202i	$0.00152217\pi$
$59$	10.0896	+	7.33050i	1.31355	+	0.954350i	0.313561	+	0.949568i	$0.398478\pi$
$60$		0			0
$61$	5.59873	−	4.06772i	0.716844	−	0.520818i	−0.168530	−	0.985696i	$-0.553902\pi$
$61$	5.59873	−	4.06772i	0.716844	−	0.520818i	0.885374	+	0.464879i	$0.153902\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−2.44736	+	15.8622i	−0.303558	+	1.96746i
$66$		0			0
$67$	4.50239	−	1.46291i	0.550054	−	0.178723i	−0.0207870	−	0.999784i	$-0.506617\pi$
$67$	4.50239	−	1.46291i	0.550054	−	0.178723i	0.570841	+	0.821060i	$0.306617\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−4.25799	+	13.1047i	−0.505330	+	1.55525i	0.294884	+	0.955533i	$0.404719\pi$
$71$	−4.25799	+	13.1047i	−0.505330	+	1.55525i	−0.800214	+	0.599714i	$0.795281\pi$
$72$		0			0
$73$	−0.640196	−	0.881155i	−0.0749293	−	0.103131i	0.769907	−	0.638156i	$-0.220302\pi$
$73$	−0.640196	−	0.881155i	−0.0749293	−	0.103131i	−0.844837	+	0.535024i	$0.820302\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−4.59963	−	6.33085i	−0.524176	−	0.721467i
$78$		0			0
$79$	1.80542	−	5.55650i	0.203125	−	0.625156i	−0.796660	−	0.604428i	$-0.793402\pi$
$79$	1.80542	−	5.55650i	0.203125	−	0.625156i	0.999785	−	0.0207276i	$-0.00659828\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	11.9145	−	3.87127i	1.30779	−	0.424927i	0.429505	−	0.903064i	$-0.358688\pi$
$83$	11.9145	−	3.87127i	1.30779	−	0.424927i	0.878285	+	0.478137i	$0.158688\pi$
$84$		0			0
$85$	−10.0241	+	10.1046i	−1.08727	+	1.09600i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	5.68424	−	4.12984i	0.602528	−	0.437762i	−0.244247	−	0.969713i	$-0.578541\pi$
$89$	5.68424	−	4.12984i	0.602528	−	0.437762i	0.846775	+	0.531951i	$0.178541\pi$
$90$		0			0
$91$	−20.5973	−	14.9648i	−2.15918	−	1.56874i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	3.67379	+	3.64454i	0.376923	+	0.373921i
$96$		0			0
$97$	17.2564	+	5.60695i	1.75212	+	0.569299i	0.996337	−	0.0855183i	$-0.0272546\pi$
$97$	17.2564	+	5.60695i	1.75212	+	0.569299i	0.755787	+	0.654818i	$0.227255\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−5.97473			−0.594508			−0.297254	−	0.954798i	$-0.596071\pi$
$101$	−5.97473			−0.594508			−0.297254	+	0.954798i	$0.596071\pi$
$102$		0			0
$103$	−0.437076	−	0.142014i	−0.0430663	−	0.0139931i	0.287405	−	0.957809i	$-0.407208\pi$
$103$	−0.437076	−	0.142014i	−0.0430663	−	0.0139931i	−0.330471	+	0.943816i	$0.607208\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			2.47862i			0.239617i	0.992797	+	0.119809i	$0.0382281\pi$
$107$			2.47862i			0.239617i	−0.992797	+	0.119809i	$0.961772\pi$
$108$		0			0
$109$	−2.70314	−	1.96394i	−0.258914	−	0.188112i	0.450754	−	0.892648i	$-0.351155\pi$
$109$	−2.70314	−	1.96394i	−0.258914	−	0.188112i	−0.709668	+	0.704536i	$0.751155\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	−10.3438	+	14.2370i	−0.973059	+	1.33930i	−0.0325728	+	0.999469i	$0.510370\pi$
$113$	−10.3438	+	14.2370i	−0.973059	+	1.33930i	−0.940486	+	0.339832i	$0.889630\pi$
$114$		0			0
$115$	4.34404	+	2.19157i	0.405084	+	0.204365i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−6.97700	−	21.4730i	−0.639581	−	1.96843i
$120$		0			0
$121$	−1.89515	+	5.83267i	−0.172286	+	0.530243i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	1.61643	−	11.0629i	0.144578	−	0.989493i
$126$		0			0
$127$	7.29555	+	10.0415i	0.647376	+	0.891036i	0.998982	−	0.0451118i	$-0.0143644\pi$
$127$	7.29555	+	10.0415i	0.647376	+	0.891036i	−0.351606	+	0.936148i	$0.614364\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−4.88963	−	15.0487i	−0.427209	−	1.31481i	−0.900863	−	0.434104i	$-0.857065\pi$
$131$	−4.88963	−	15.0487i	−0.427209	−	1.31481i	0.473654	−	0.880711i	$-0.342935\pi$
$132$		0			0
$133$	−7.80706	+	2.53667i	−0.676958	+	0.219957i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.34663	−	5.98262i	0.371358	−	0.511130i	−0.581912	−	0.813252i	$-0.697695\pi$
$137$	4.34663	−	5.98262i	0.371358	−	0.511130i	0.953269	+	0.302122i	$0.0976950\pi$
$138$		0			0
$139$	3.18667	−	2.31525i	0.270290	−	0.196377i	−0.444381	−	0.895838i	$-0.646576\pi$
$139$	3.18667	−	2.31525i	0.270290	−	0.196377i	0.714671	+	0.699461i	$0.246576\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$		−	15.8352i		−	1.32421i
$144$		0			0
$145$	−0.304069	−	1.87137i	−0.0252516	−	0.155409i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	3.92892			0.321870			0.160935	−	0.986965i	$-0.448549\pi$
$149$	3.92892			0.321870			0.160935	+	0.986965i	$0.448549\pi$
$150$		0			0
$151$	7.93418			0.645674			0.322837	−	0.946455i	$-0.395363\pi$
$151$	7.93418			0.645674			0.322837	+	0.946455i	$0.395363\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−6.82745	−	6.77308i	−0.548394	−	0.544027i
$156$		0			0
$157$			6.09738i			0.486624i	0.969948	+	0.243312i	$0.0782339\pi$
$157$			6.09738i			0.486624i	−0.969948	+	0.243312i	$0.921766\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−6.24413	+	4.53662i	−0.492106	+	0.357536i
$162$		0			0
$163$	−0.00150257	+	0.00206811i	−0.000117690	+	0.000161987i	−0.809076	−	0.587704i	$-0.800032\pi$
$163$	−0.00150257	+	0.00206811i	−0.000117690	+	0.000161987i	0.808958	+	0.587866i	$0.200032\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	9.60630	−	3.12128i	0.743358	−	0.241532i	0.0872372	−	0.996188i	$-0.472196\pi$
$167$	9.60630	−	3.12128i	0.743358	−	0.241532i	0.656121	+	0.754656i	$0.272196\pi$
$168$		0			0
$169$	−11.9032	−	36.6343i	−0.915631	−	2.81802i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−3.63244	−	4.99963i	−0.276169	−	0.380115i	0.648291	−	0.761393i	$-0.275484\pi$
$173$	−3.63244	−	4.99963i	−0.276169	−	0.380115i	−0.924460	+	0.381278i	$0.875484\pi$
$174$		0			0
$175$	14.4310	+	10.3094i	1.09088	+	0.779321i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	4.45991	−	13.7262i	0.333349	−	1.02594i	−0.634181	−	0.773185i	$-0.718662\pi$
$179$	4.45991	−	13.7262i	0.333349	−	1.02594i	0.967530	−	0.252758i	$-0.0813376\pi$
$180$		0			0
$181$	2.08366	+	6.41283i	0.154877	+	0.476662i	0.998148	−	0.0608258i	$-0.0193734\pi$
$181$	2.08366	+	6.41283i	0.154877	+	0.476662i	−0.843272	+	0.537488i	$0.819373\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	2.46518	−	15.9777i	0.181244	−	1.17470i
$186$		0			0
$187$	8.25424	−	11.3610i	0.603610	−	0.830798i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	12.4512	+	9.04634i	0.900938	+	0.654570i	0.938707	−	0.344717i	$-0.112025\pi$
$191$	12.4512	+	9.04634i	0.900938	+	0.654570i	−0.0377687	+	0.999287i	$0.512025\pi$
$192$		0			0
$193$			16.3875i			1.17960i	0.807550	+	0.589799i	$0.200793\pi$
$193$			16.3875i			1.17960i	−0.807550	+	0.589799i	$0.799207\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	9.36824	+	3.04392i	0.667459	+	0.216871i	0.623097	−	0.782145i	$-0.285874\pi$
$197$	9.36824	+	3.04392i	0.667459	+	0.216871i	0.0443625	+	0.999015i	$0.485874\pi$
$198$		0			0
$199$	4.96275			0.351800			0.175900	−	0.984408i	$-0.443716\pi$
$199$	4.96275			0.351800			0.175900	+	0.984408i	$0.443716\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	2.86026	+	0.929355i	0.200751	+	0.0652279i
$204$		0			0
$205$	−2.97139	−	0.458452i	−0.207531	−	0.0320197i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−4.13058	−	3.00104i	−0.285718	−	0.207586i
$210$		0			0
$211$	−2.83140	+	2.05713i	−0.194921	+	0.141619i	−0.680965	−	0.732316i	$-0.738440\pi$
$211$	−2.83140	+	2.05713i	−0.194921	+	0.141619i	0.486044	+	0.873934i	$0.338440\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	8.37900	+	16.2835i	0.571443	+	1.11052i
$216$		0			0
$217$	14.5088	−	4.71420i	0.984923	−	0.320021i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	14.1185	−	43.4523i	0.949714	−	2.92292i
$222$		0			0
$223$	−13.5653	−	18.6710i	−0.908397	−	1.25030i	−0.967711	−	0.252062i	$-0.918891\pi$
$223$	−13.5653	−	18.6710i	−0.908397	−	1.25030i	0.0593138	−	0.998239i	$-0.481109\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	3.43889	+	4.73323i	0.228247	+	0.314155i	0.907745	−	0.419522i	$-0.137802\pi$
$227$	3.43889	+	4.73323i	0.228247	+	0.314155i	−0.679498	+	0.733677i	$0.737802\pi$
$228$		0			0
$229$	1.97484	−	6.07793i	0.130501	−	0.401641i	−0.864362	−	0.502870i	$-0.832277\pi$
$229$	1.97484	−	6.07793i	0.130501	−	0.401641i	0.994863	+	0.101229i	$0.0322775\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	4.32076	−	1.40390i	0.283062	−	0.0919725i	−0.164045	−	0.986453i	$-0.552454\pi$
$233$	4.32076	−	1.40390i	0.283062	−	0.0919725i	0.447107	+	0.894480i	$0.352454\pi$
$234$		0			0
$235$	13.3631	−	2.17130i	0.871712	−	0.141640i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	−18.6407	+	13.5432i	−1.20576	+	0.876040i	−0.994839	−	0.101463i	$-0.967648\pi$
$239$	−18.6407	+	13.5432i	−1.20576	+	0.876040i	−0.210926	+	0.977502i	$0.567648\pi$
$240$		0			0
$241$	−13.3064	−	9.66766i	−0.857140	−	0.622749i	0.0699655	−	0.997549i	$-0.477711\pi$
$241$	−13.3064	−	9.66766i	−0.857140	−	0.622749i	−0.927105	+	0.374801i	$0.877711\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	−11.0976	+	5.71049i	−0.708997	+	0.364830i
$246$		0			0
$247$	−15.7982	−	5.13315i	−1.00522	−	0.326614i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−4.66327			−0.294343			−0.147171	−	0.989111i	$-0.547017\pi$
$251$	−4.66327			−0.294343			−0.147171	+	0.989111i	$0.547017\pi$
$252$		0			0
$253$	−4.56554	−	1.48343i	−0.287033	−	0.0932627i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	5.78734i		−	0.361004i	−0.983575	−	0.180502i	$-0.942228\pi$
$257$		−	5.78734i		−	0.361004i	0.983575	−	0.180502i	$-0.0577723\pi$
$258$		0			0
$259$	20.7473	+	15.0738i	1.28917	+	0.936639i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	−13.4896	+	18.5668i	−0.831803	+	1.14488i	0.155781	+	0.987792i	$0.450210\pi$
$263$	−13.4896	+	18.5668i	−0.831803	+	1.14488i	−0.987585	+	0.157087i	$0.949790\pi$
$264$		0			0
$265$	−26.3933	+	4.28852i	−1.62133	+	0.263442i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−1.39366	−	4.28923i	−0.0849727	−	0.261519i	0.899538	−	0.436842i	$-0.143903\pi$
$269$	−1.39366	−	4.28923i	−0.0849727	−	0.261519i	−0.984511	+	0.175323i	$0.943903\pi$
$270$		0			0
$271$	−3.06895	+	9.44525i	−0.186425	+	0.573758i	−0.999970	−	0.00774433i	$-0.997535\pi$
$271$	−3.06895	+	9.44525i	−0.186425	+	0.573758i	0.813545	+	0.581502i	$0.197535\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	0.0881931	+	11.0305i	0.00531824	+	0.665163i
$276$		0			0
$277$	−13.5280	−	18.6197i	−0.812821	−	1.11875i	−0.990882	−	0.134732i	$-0.956983\pi$
$277$	−13.5280	−	18.6197i	−0.812821	−	1.11875i	0.178061	−	0.984019i	$-0.443017\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−0.226820	−	0.698080i	−0.0135309	−	0.0416439i	0.944063	−	0.329765i	$-0.106969\pi$
$281$	−0.226820	−	0.698080i	−0.0135309	−	0.0416439i	−0.957594	+	0.288121i	$0.906969\pi$
$282$		0			0
$283$	−20.4402	+	6.64144i	−1.21505	+	0.394793i	−0.845276	−	0.534330i	$-0.820564\pi$
$283$	−20.4402	+	6.64144i	−1.21505	+	0.394793i	−0.369771	+	0.929123i	$0.620564\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	2.80329	−	3.85839i	0.165473	−	0.227754i
$288$		0			0
$289$	19.0259	−	13.8231i	1.11917	−	0.813126i
$290$		0			0
$291$		0			0
$292$		0			0
$293$			26.5961i			1.55376i	0.629649	+	0.776880i	$0.283199\pi$
$293$			26.5961i			1.55376i	−0.629649	+	0.776880i	$0.716801\pi$
$294$		0			0
$295$	27.5608	+	4.25233i	1.60465	+	0.247580i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−15.6183			−0.903230
$300$		0			0
$301$	−29.0493			−1.67437
$302$		0			0
$303$		0			0
$304$		0			0
$305$	6.97011	−	13.8159i	0.399107	−	0.791094i
$306$		0			0
$307$		−	12.1736i		−	0.694785i	−0.937720	−	0.347393i	$-0.887067\pi$
$307$		−	12.1736i		−	0.694785i	0.937720	−	0.347393i	$-0.112933\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−20.0330	+	14.5548i	−1.13597	+	0.825327i	−0.986552	−	0.163447i	$-0.947739\pi$
$311$	−20.0330	+	14.5548i	−1.13597	+	0.825327i	−0.149414	+	0.988775i	$0.547739\pi$
$312$		0			0
$313$	8.72589	−	12.0102i	0.493216	−	0.678854i	−0.487761	−	0.872977i	$-0.662186\pi$
$313$	8.72589	−	12.0102i	0.493216	−	0.678854i	0.980977	+	0.194123i	$0.0621862\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	−1.84725	+	0.600207i	−0.103752	+	0.0337110i	−0.360433	−	0.932785i	$-0.617371\pi$
$317$	−1.84725	+	0.600207i	−0.103752	+	0.0337110i	0.256681	+	0.966496i	$0.417371\pi$
$318$		0			0
$319$	0.578034	+	1.77901i	0.0323637	+	0.0996052i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−8.65873	−	11.9177i	−0.481785	−	0.663120i
$324$		0			0
$325$	11.3627	+	34.0423i	0.630290	+	1.88833i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	−6.63635	+	20.4246i	−0.365874	+	1.12604i
$330$		0			0
$331$	−8.56924	−	26.3734i	−0.471008	−	1.44961i	−0.851266	−	0.524734i	$-0.824165\pi$
$331$	−8.56924	−	26.3734i	−0.471008	−	1.44961i	0.380258	−	0.924880i	$-0.375835\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	7.45527	−	7.51512i	0.407325	−	0.410595i
$336$		0			0
$337$	−6.40119	+	8.81048i	−0.348695	+	0.479937i	−0.946956	−	0.321364i	$-0.895859\pi$
$337$	−6.40119	+	8.81048i	−0.348695	+	0.479937i	0.598261	+	0.801301i	$0.295859\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	7.67636	+	5.57720i	0.415698	+	0.302022i
$342$		0			0
$343$			5.03148i			0.271675i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	21.7353	+	7.06224i	1.16681	+	0.379121i	0.827453	−	0.561536i	$-0.189789\pi$
$347$	21.7353	+	7.06224i	1.16681	+	0.379121i	0.339361	+	0.940656i	$0.389789\pi$
$348$		0			0
$349$	28.8539			1.54451			0.772256	−	0.635311i	$-0.219128\pi$
$349$	28.8539			1.54451			0.772256	+	0.635311i	$0.219128\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	25.9079	+	8.41799i	1.37894	+	0.448045i	0.902321	−	0.431065i	$-0.141862\pi$
$353$	25.9079	+	8.41799i	1.37894	+	0.448045i	0.476619	+	0.879110i	$0.341862\pi$
$354$		0			0
$355$	4.94153	+	30.4123i	0.262269	+	1.61412i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	19.3648	+	14.0694i	1.02204	+	0.742553i	0.966699	−	0.255915i	$-0.0823766\pi$
$359$	19.3648	+	14.0694i	1.02204	+	0.742553i	0.0553373	+	0.998468i	$0.482377\pi$
$360$		0			0
$361$	11.0383	−	8.01981i	0.580965	−	0.422096i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.17441	−	1.09699i	−0.113814	−	0.0574190i
$366$		0			0
$367$	−6.38465	+	2.07450i	−0.333276	+	0.108288i	−0.470875	−	0.882200i	$-0.656062\pi$
$367$	−6.38465	+	2.07450i	−0.333276	+	0.108288i	0.137599	+	0.990488i	$0.456062\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	13.1074	−	40.3404i	0.680502	−	2.09437i
$372$		0			0
$373$	−7.99923	−	11.0100i	−0.414184	−	0.570076i	0.550048	−	0.835133i	$-0.314609\pi$
$373$	−7.99923	−	11.0100i	−0.414184	−	0.570076i	−0.964233	+	0.265057i	$0.914609\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	3.57715	+	4.92353i	0.184233	+	0.253575i
$378$		0			0
$379$	−0.137272	+	0.422481i	−0.00705120	+	0.0217014i	−0.954520	−	0.298146i	$-0.903632\pi$
$379$	−0.137272	+	0.422481i	−0.00705120	+	0.0217014i	0.947469	+	0.319848i	$0.103632\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	9.72980	−	3.16140i	0.497170	−	0.161540i	−0.0496897	−	0.998765i	$-0.515823\pi$
$383$	9.72980	−	3.16140i	0.497170	−	0.161540i	0.546859	+	0.837224i	$0.315823\pi$
$384$		0			0
$385$	−15.6225	−	7.88155i	−0.796196	−	0.401681i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	19.5834	−	14.2282i	0.992919	−	0.721398i	0.0323607	−	0.999476i	$-0.489697\pi$
$389$	19.5834	−	14.2282i	0.992919	−	0.721398i	0.960558	+	0.278078i	$0.0896975\pi$
$390$		0			0
$391$	−11.2054	−	8.14117i	−0.566679	−	0.411717i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−2.09525	−	12.8950i	−0.105423	−	0.648818i
$396$		0			0
$397$	−2.58871	−	0.841124i	−0.129924	−	0.0422148i	0.243333	−	0.969943i	$-0.421759\pi$
$397$	−2.58871	−	0.841124i	−0.129924	−	0.0422148i	−0.373257	+	0.927728i	$0.621759\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	−31.3538			−1.56573			−0.782867	−	0.622189i	$-0.786244\pi$
$401$	−31.3538			−1.56573			−0.782867	+	0.622189i	$0.786244\pi$
$402$		0			0
$403$	29.3597	+	9.53955i	1.46251	+	0.475199i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			15.9505i			0.790639i
$408$		0			0
$409$	2.68805	+	1.95298i	0.132916	+	0.0965688i	0.652256	−	0.757998i	$-0.273823\pi$
$409$	2.68805	+	1.95298i	0.132916	+	0.0965688i	−0.519341	+	0.854567i	$0.673823\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−26.0016	+	35.7881i	−1.27945	+	1.76102i
$414$		0			0
$415$	19.7287	−	19.8870i	0.968442	−	0.976216i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	−3.41347	−	10.5056i	−0.166759	−	0.513231i	0.832403	−	0.554171i	$-0.186965\pi$
$419$	−3.41347	−	10.5056i	−0.166759	−	0.513231i	−0.999162	+	0.0409399i	$0.986965\pi$
$420$		0			0
$421$	−7.56044	+	23.2686i	−0.368473	+	1.13404i	0.579304	+	0.815111i	$0.303324\pi$
$421$	−7.56044	+	23.2686i	−0.368473	+	1.13404i	−0.947777	+	0.318932i	$0.896676\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−9.59264	+	30.3466i	−0.465312	+	1.47202i
$426$		0			0
$427$	14.4284	+	19.8589i	0.698237	+	0.961041i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−0.354621	−	1.09141i	−0.0170815	−	0.0525715i	0.942152	−	0.335185i	$-0.108799\pi$
$431$	−0.354621	−	1.09141i	−0.0170815	−	0.0525715i	−0.959234	+	0.282613i	$0.908799\pi$
$432$		0			0
$433$	−5.56802	+	1.80916i	−0.267582	+	0.0869427i	−0.439735	−	0.898128i	$-0.644928\pi$
$433$	−5.56802	+	1.80916i	−0.267582	+	0.0869427i	0.172153	+	0.985070i	$0.444928\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−2.95993	+	4.07400i	−0.141593	+	0.194886i
$438$		0			0
$439$	−16.4473	+	11.9497i	−0.784988	+	0.570328i	−0.906472	−	0.422266i	$-0.861235\pi$
$439$	−16.4473	+	11.9497i	−0.784988	+	0.570328i	0.121484	+	0.992593i	$0.461235\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			17.5912i			0.835783i	0.908497	+	0.417891i	$0.137231\pi$
$443$			17.5912i			0.835783i	−0.908497	+	0.417891i	$0.862769\pi$
$444$		0			0
$445$	7.07656	−	14.0269i	0.335461	−	0.664937i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−2.83956			−0.134007			−0.0670037	−	0.997753i	$-0.521344\pi$
$449$	−2.83956			−0.134007			−0.0670037	+	0.997753i	$0.521344\pi$
$450$		0			0
$451$	2.96634			0.139679
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−56.2637	−	8.68088i	−2.63768	−	0.406966i
$456$		0			0
$457$		−	8.12004i		−	0.379840i	−0.981800	−	0.189920i	$-0.939177\pi$
$457$		−	8.12004i		−	0.379840i	0.981800	−	0.189920i	$-0.0608228\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	14.5629	−	10.5806i	0.678261	−	0.492786i	−0.194519	−	0.980899i	$-0.562315\pi$
$461$	14.5629	−	10.5806i	0.678261	−	0.492786i	0.872780	+	0.488113i	$0.162315\pi$
$462$		0			0
$463$	−16.8529	+	23.1960i	−0.783219	+	1.07801i	0.211700	+	0.977335i	$0.432100\pi$
$463$	−16.8529	+	23.1960i	−0.783219	+	1.07801i	−0.994919	+	0.100674i	$0.967900\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	19.0638	−	6.19421i	0.882169	−	0.286634i	0.167311	−	0.985904i	$-0.446491\pi$
$467$	19.0638	−	6.19421i	0.882169	−	0.286634i	0.714858	+	0.699270i	$0.246491\pi$
$468$		0			0
$469$	5.18902	+	15.9702i	0.239607	+	0.737433i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	−10.6200	−	14.6172i	−0.488310	−	0.672101i
$474$		0			0
$475$	11.0333	+	3.48765i	0.506241	+	0.160024i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−4.78232	+	14.7185i	−0.218510	+	0.672505i	0.780376	+	0.625311i	$0.215028\pi$
$479$	−4.78232	+	14.7185i	−0.218510	+	0.672505i	−0.998886	+	0.0471937i	$0.984972\pi$
$480$		0			0
$481$	16.0364	+	49.3548i	0.731195	+	2.25039i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	40.0471	−	6.50704i	1.81844	−	0.295470i
$486$		0			0
$487$	−22.0222	+	30.3110i	−0.997923	+	1.37352i	−0.0713312	+	0.997453i	$0.522725\pi$
$487$	−22.0222	+	30.3110i	−0.997923	+	1.37352i	−0.926591	+	0.376070i	$0.877275\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	32.3517	+	23.5049i	1.46001	+	1.06076i	0.983360	+	0.181667i	$0.0581494\pi$
$491$	32.3517	+	23.5049i	1.46001	+	1.06076i	0.476651	+	0.879093i	$0.341851\pi$
$492$		0			0
$493$			5.39701i			0.243069i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−46.4831	−	15.1033i	−2.08505	−	0.677474i
$498$		0			0
$499$	−28.3040			−1.26706			−0.633530	−	0.773718i	$-0.718395\pi$
$499$	−28.3040			−1.26706			−0.633530	+	0.773718i	$0.718395\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−31.0839	−	10.0998i	−1.38596	−	0.450327i	−0.481338	−	0.876535i	$-0.659849\pi$
$503$	−31.0839	−	10.0998i	−1.38596	−	0.450327i	−0.904625	+	0.426208i	$0.859849\pi$
$504$		0			0
$505$	−11.8794	+	6.11281i	−0.528627	+	0.272016i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−13.8620	−	10.0713i	−0.614422	−	0.446404i	0.236547	−	0.971620i	$-0.423984\pi$
$509$	−13.8620	−	10.0713i	−0.614422	−	0.446404i	−0.850969	+	0.525217i	$0.823984\pi$
$510$		0			0
$511$	3.12549	−	2.27080i	0.138264	−	0.100454i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	−1.01432	+	0.164812i	−0.0446964	+	0.00726250i
$516$		0			0
$517$	−12.7035	+	4.12763i	−0.558701	+	0.181533i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−6.22259	+	19.1512i	−0.272617	+	0.839028i	0.717223	+	0.696843i	$0.245413\pi$
$521$	−6.22259	+	19.1512i	−0.272617	+	0.839028i	−0.989840	+	0.142185i	$0.954587\pi$
$522$		0			0
$523$	−16.4036	−	22.5777i	−0.717281	−	0.987253i	−0.999610	−	0.0279349i	$-0.991107\pi$
$523$	−16.4036	−	22.5777i	−0.717281	−	0.987253i	0.282329	−	0.959318i	$-0.408893\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	16.0916	+	22.1482i	0.700960	+	0.964789i
$528$		0			0
$529$	5.64428	−	17.3713i	0.245403	−	0.755274i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	9.17857	−	2.98230i	0.397568	−	0.129178i
$534$		0			0
$535$	2.53590	+	4.92818i	0.109636	+	0.213064i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	9.96200	−	7.23781i	0.429094	−	0.311755i
$540$		0			0
$541$	9.00089	+	6.53953i	0.386979	+	0.281156i	0.764216	−	0.644960i	$-0.223126\pi$
$541$	9.00089	+	6.53953i	0.386979	+	0.281156i	−0.377238	+	0.926116i	$0.623126\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	−7.38392	−	1.13926i	−0.316292	−	0.0488004i
$546$		0			0
$547$	26.4684	+	8.60009i	1.13171	+	0.367713i	0.814224	−	0.580551i	$-0.197163\pi$
$547$	26.4684	+	8.60009i	1.13171	+	0.367713i	0.317482	+	0.948264i	$0.397163\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	1.96222			0.0835935
$552$		0			0
$553$	19.7091	+	6.40389i	0.838118	+	0.272321i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			6.36580i			0.269728i	0.990864	+	0.134864i	$0.0430597\pi$
$557$			6.36580i			0.269728i	−0.990864	+	0.134864i	$0.956940\pi$
$558$		0			0
$559$	−47.5569	−	34.5521i	−2.01144	−	1.46140i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	10.0676	−	13.8569i	0.424301	−	0.584000i	−0.542333	−	0.840164i	$-0.682459\pi$
$563$	10.0676	−	13.8569i	0.424301	−	0.584000i	0.966633	+	0.256164i	$0.0824587\pi$
$564$		0			0
$565$	−6.00028	+	38.8898i	−0.252434	+	1.63611i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	4.75461	+	14.6332i	0.199324	+	0.613455i	0.999899	+	0.0142229i	$0.00452743\pi$
$569$	4.75461	+	14.6332i	0.199324	+	0.613455i	−0.800575	+	0.599232i	$0.795473\pi$
$570$		0			0
$571$	2.63760	−	8.11770i	0.110380	−	0.339715i	−0.880575	−	0.473906i	$-0.842844\pi$
$571$	2.63760	−	8.11770i	0.110380	−	0.339715i	0.990955	+	0.134191i	$0.0428435\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	10.8794	−	0.0869850i	0.453701	−	0.00362752i
$576$		0			0
$577$	1.35494	+	1.86491i	0.0564068	+	0.0776374i	0.836289	−	0.548290i	$-0.184721\pi$
$577$	1.35494	+	1.86491i	0.0564068	+	0.0776374i	−0.779882	+	0.625927i	$0.784721\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	13.7315	+	42.2614i	0.569681	+	1.75330i
$582$		0			0
$583$	25.0907	−	8.15245i	1.03915	−	0.337640i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−0.540303	+	0.743663i	−0.0223007	+	0.0306943i	−0.820022	−	0.572332i	$-0.806039\pi$
$587$	−0.540303	+	0.743663i	−0.0223007	+	0.0306943i	0.797721	+	0.603027i	$0.206039\pi$
$588$		0			0
$589$	8.05253	−	5.85051i	0.331799	−	0.241066i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	25.5925i		−	1.05096i	−0.850807	−	0.525478i	$-0.823886\pi$
$593$		−	25.5925i		−	1.05096i	0.850807	−	0.525478i	$-0.176114\pi$
$594$		0			0
$595$	−35.8415	−	35.5560i	−1.46936	−	1.45766i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−37.0204			−1.51261			−0.756307	−	0.654217i	$-0.772998\pi$
$599$	−37.0204			−1.51261			−0.756307	+	0.654217i	$0.772998\pi$
$600$		0			0
$601$	33.4191			1.36319			0.681597	−	0.731728i	$-0.261286\pi$
$601$	33.4191			1.36319			0.681597	+	0.731728i	$0.261286\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	2.19938	+	13.5359i	0.0894176	+	0.550313i
$606$		0			0
$607$			4.34502i			0.176359i	0.996105	+	0.0881795i	$0.0281049\pi$
$607$			4.34502i			0.176359i	−0.996105	+	0.0881795i	$0.971895\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−35.1580	+	25.5438i	−1.42234	+	1.03339i
$612$		0			0
$613$	−2.32761	+	3.20367i	−0.0940111	+	0.129395i	−0.853431	−	0.521205i	$-0.825483\pi$
$613$	−2.32761	+	3.20367i	−0.0940111	+	0.129395i	0.759420	+	0.650600i	$0.225483\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	19.2721	−	6.26189i	0.775866	−	0.252094i	0.105792	−	0.994388i	$-0.466262\pi$
$617$	19.2721	−	6.26189i	0.775866	−	0.252094i	0.670074	+	0.742294i	$0.266262\pi$
$618$		0			0
$619$	4.65930	+	14.3398i	0.187273	+	0.576367i	0.999980	−	0.00630532i	$-0.00200706\pi$
$619$	4.65930	+	14.3398i	0.187273	+	0.576367i	−0.812707	+	0.582672i	$0.802007\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	14.6487	+	20.1622i	0.586888	+	0.807782i
$624$		0			0
$625$	−8.10462	−	23.6498i	−0.324185	−	0.945994i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−14.2213	+	43.7687i	−0.567041	+	1.74517i
$630$		0			0
$631$	−0.755761	−	2.32599i	−0.0300864	−	0.0925963i	0.934886	−	0.354949i	$-0.115502\pi$
$631$	−0.755761	−	2.32599i	−0.0300864	−	0.0925963i	−0.964972	+	0.262352i	$0.915502\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	24.7791	+	12.5011i	0.983329	+	0.496090i
$636$		0			0
$637$	23.5481	−	32.4112i	0.933009	−	1.28418i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.8353	+	7.87228i	0.427967	+	0.310936i	0.780836	−	0.624737i	$-0.214794\pi$
$641$	10.8353	+	7.87228i	0.427967	+	0.310936i	−0.352868	+	0.935673i	$0.614794\pi$
$642$		0			0
$643$		−	35.4836i		−	1.39934i	−0.714467	−	0.699669i	$-0.753331\pi$
$643$		−	35.4836i		−	1.39934i	0.714467	−	0.699669i	$-0.246669\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−21.2886	−	6.91707i	−0.836940	−	0.271938i	−0.140974	−	0.990013i	$-0.545023\pi$
$647$	−21.2886	−	6.91707i	−0.836940	−	0.271938i	−0.695966	+	0.718075i	$0.745023\pi$
$648$		0			0
$649$	−27.5140			−1.08002
$650$		0			0
$651$		0			0
$652$		0			0
$653$	18.0021	+	5.84923i	0.704476	+	0.228898i	0.639279	−	0.768974i	$-0.279233\pi$
$653$	18.0021	+	5.84923i	0.704476	+	0.228898i	0.0651961	+	0.997872i	$0.479233\pi$
$654$		0			0
$655$	−25.1185	−	24.9184i	−0.981460	−	0.973644i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−4.58371	−	3.33026i	−0.178556	−	0.129729i	0.494917	−	0.868940i	$-0.335198\pi$
$659$	−4.58371	−	3.33026i	−0.178556	−	0.129729i	−0.673473	+	0.739212i	$0.735198\pi$
$660$		0			0
$661$	20.4225	−	14.8378i	0.794342	−	0.577123i	−0.114907	−	0.993376i	$-0.536657\pi$
$661$	20.4225	−	14.8378i	0.794342	−	0.577123i	0.909249	+	0.416253i	$0.136657\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	−12.9273	+	13.0311i	−0.501300	+	0.505324i
$666$		0			0
$667$	1.75464	−	0.570116i	0.0679398	−	0.0220750i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−4.71794	+	14.5203i	−0.182134	+	0.560551i
$672$		0			0
$673$	−7.74044	−	10.6538i	−0.298372	−	0.410674i	0.633339	−	0.773875i	$-0.281684\pi$
$673$	−7.74044	−	10.6538i	−0.298372	−	0.410674i	−0.931711	+	0.363201i	$0.881684\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−15.8487	−	21.8139i	−0.609115	−	0.838375i	0.387389	−	0.921916i	$-0.373377\pi$
$677$	−15.8487	−	21.8139i	−0.609115	−	0.838375i	−0.996504	+	0.0835409i	$0.973377\pi$
$678$		0			0
$679$	−19.8881	+	61.2092i	−0.763234	+	2.34899i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	49.2454	−	16.0008i	1.88432	−	0.612254i	0.899996	−	0.435897i	$-0.143569\pi$
$683$	49.2454	−	16.0008i	1.88432	−	0.612254i	0.984326	−	0.176356i	$-0.0564311\pi$
$684$		0			0
$685$	2.52142	−	16.3422i	0.0963386	−	0.624403i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	69.4403	−	50.4513i	2.64546	−	1.92204i
$690$		0			0
$691$	3.00647	+	2.18432i	0.114371	+	0.0830956i	0.643501	−	0.765446i	$-0.277481\pi$
$691$	3.00647	+	2.18432i	0.114371	+	0.0830956i	−0.529129	+	0.848541i	$0.677481\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	3.96722	−	7.86367i	0.150485	−	0.298286i
$696$		0			0
$697$	8.13972	+	2.64475i	0.308314	+	0.100177i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	28.4299			1.07378			0.536890	−	0.843652i	$-0.319599\pi$
$701$	28.4299			1.07378			0.536890	+	0.843652i	$0.319599\pi$
$702$		0			0
$703$	15.9132	+	5.17053i	0.600180	+	0.195010i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	21.1926i		−	0.797030i
$708$		0			0
$709$	33.1126	+	24.0577i	1.24357	+	0.903507i	0.997831	−	0.0658288i	$-0.0209691\pi$
$709$	33.1126	+	24.0577i	1.24357	+	0.903507i	0.245740	+	0.969336i	$0.420969\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	5.50080	−	7.57120i	0.206007	−	0.283544i
$714$		0			0
$715$	−16.2012	−	31.4848i	−0.605890	−	1.17746i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.46368	+	4.50475i	0.0545861	+	0.167999i	0.974633	−	0.223810i	$-0.0718495\pi$
$719$	1.46368	+	4.50475i	0.0545861	+	0.167999i	−0.920047	+	0.391809i	$0.871849\pi$
$720$		0			0
$721$	0.503731	−	1.55032i	0.0187599	−	0.0577371i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−2.51919	−	3.40970i	−0.0935604	−	0.126633i
$726$		0			0
$727$	−3.27447	−	4.50692i	−0.121443	−	0.167153i	0.743967	−	0.668217i	$-0.232942\pi$
$727$	−3.27447	−	4.50692i	−0.121443	−	0.167153i	−0.865410	+	0.501064i	$0.832942\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−16.1091	−	49.5788i	−0.595818	−	1.83374i
$732$		0			0
$733$	28.8738	−	9.38166i	1.06648	−	0.346520i	0.277363	−	0.960765i	$-0.410540\pi$
$733$	28.8738	−	9.38166i	1.06648	−	0.346520i	0.789115	+	0.614246i	$0.210540\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−6.13894	+	8.44952i	−0.226131	+	0.311242i
$738$		0			0
$739$	39.6127	−	28.7803i	1.45718	−	1.05870i	0.473089	−	0.881015i	$-0.343139\pi$
$739$	39.6127	−	28.7803i	1.45718	−	1.05870i	0.984087	−	0.177686i	$-0.0568611\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	45.5953i		−	1.67273i	−0.548174	−	0.836364i	$-0.684677\pi$
$743$		−	45.5953i		−	1.67273i	0.548174	−	0.836364i	$-0.315323\pi$
$744$		0			0
$745$	7.81178	−	4.01972i	0.286201	−	0.147271i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−8.79176			−0.321244
$750$		0			0
$751$	−27.9100			−1.01845			−0.509225	−	0.860633i	$-0.670068\pi$
$751$	−27.9100			−1.01845			−0.509225	+	0.860633i	$0.670068\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	15.7753	−	8.11754i	0.574123	−	0.295427i
$756$		0			0
$757$		−	27.6680i		−	1.00561i	−0.864400	−	0.502804i	$-0.832302\pi$
$757$		−	27.6680i		−	1.00561i	0.864400	−	0.502804i	$-0.167698\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−9.80362	+	7.12275i	−0.355381	+	0.258199i	−0.751123	−	0.660162i	$-0.770487\pi$
$761$	−9.80362	+	7.12275i	−0.355381	+	0.258199i	0.395742	+	0.918362i	$0.370487\pi$
$762$		0			0
$763$	6.96619	−	9.58814i	0.252193	−	0.347114i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	−85.1349	+	27.6620i	−3.07404	+	0.998817i
$768$		0			0
$769$	3.13398	+	9.64540i	0.113014	+	0.347822i	0.991528	−	0.129896i	$-0.0414642\pi$
$769$	3.13398	+	9.64540i	0.113014	+	0.347822i	−0.878513	+	0.477718i	$0.841464\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−29.4908	−	40.5906i	−1.06071	−	1.45994i	−0.879140	−	0.476563i	$-0.841882\pi$
$773$	−29.4908	−	40.5906i	−1.06071	−	1.45994i	−0.181569	−	0.983378i	$-0.558118\pi$
$774$		0			0
$775$	−20.5045	−	6.48153i	−0.736542	−	0.232823i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	0.961568	−	2.95940i	0.0344518	−	0.106032i
$780$		0			0
$781$	−9.39383	−	28.9112i	−0.336138	−	1.03453i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	6.23829	+	12.1233i	0.222654	+	0.432699i
$786$		0			0
$787$	−9.08606	+	12.5059i	−0.323883	+	0.445787i	−0.939648	−	0.342143i	$-0.888847\pi$
$787$	−9.08606	+	12.5059i	−0.323883	+	0.445787i	0.615765	+	0.787930i	$0.288847\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	−50.4991	−	36.6897i	−1.79554	−	1.30454i
$792$		0			0
$793$			49.6727i			1.76393i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	5.45087	+	1.77110i	0.193080	+	0.0627354i	0.403961	−	0.914776i	$-0.367633\pi$
$797$	5.45087	+	1.77110i	0.193080	+	0.0627354i	−0.210881	+	0.977512i	$0.567633\pi$
$798$		0			0
$799$	−38.5390			−1.36341
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.28528	+	0.742531i	0.0806457	+	0.0262034i
$804$		0			0
$805$	−7.77359	+	15.4085i	−0.273983	+	0.543078i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	22.9907	+	16.7038i	0.808312	+	0.587273i	0.913341	−	0.407196i	$-0.133494\pi$
$809$	22.9907	+	16.7038i	0.808312	+	0.587273i	−0.105029	+	0.994469i	$0.533494\pi$
$810$		0			0
$811$	9.86048	−	7.16406i	0.346248	−	0.251564i	−0.401045	−	0.916058i	$-0.631353\pi$
$811$	9.86048	−	7.16406i	0.346248	−	0.251564i	0.747293	+	0.664494i	$0.231353\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−0.000871621		0.00564927i	−3.05315e−5		0.000197885i
$816$		0			0
$817$	−18.0257	+	5.85689i	−0.630638	+	0.204907i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−4.51854	+	13.9066i	−0.157698	+	0.485345i	−0.998424	−	0.0561157i	$-0.982128\pi$
$821$	−4.51854	+	13.9066i	−0.157698	+	0.485345i	0.840726	+	0.541461i	$0.182128\pi$
$822$		0			0
$823$	12.7201	+	17.5077i	0.443394	+	0.610280i	0.970962	−	0.239233i	$-0.0768960\pi$
$823$	12.7201	+	17.5077i	0.443394	+	0.610280i	−0.527568	+	0.849513i	$0.676896\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.56096	+	9.03038i	0.228147	+	0.314017i	0.907709	−	0.419601i	$-0.137830\pi$
$827$	6.56096	+	9.03038i	0.228147	+	0.314017i	−0.679562	+	0.733618i	$0.737830\pi$
$828$		0			0
$829$	−8.60563	+	26.4854i	−0.298886	+	0.919876i	0.683003	+	0.730416i	$0.260674\pi$
$829$	−8.60563	+	26.4854i	−0.298886	+	0.919876i	−0.981888	+	0.189460i	$0.939326\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	33.7892	−	10.9788i	1.17073	−	0.380392i
$834$		0			0
$835$	15.9066	−	16.0343i	0.550470	−	0.554889i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	15.3556	−	11.1565i	0.530133	−	0.385164i	−0.290274	−	0.956943i	$-0.593747\pi$
$839$	15.3556	−	11.1565i	0.530133	−	0.385164i	0.820408	+	0.571779i	$0.193747\pi$
$840$		0			0
$841$	22.8799	+	16.6232i	0.788962	+	0.573214i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	−61.1478	−	60.6608i	−2.10355	−	2.08680i
$846$		0			0
$847$	−20.6887	−	6.72218i	−0.710873	−	0.230977i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	15.7320			0.539287
$852$		0			0
$853$	15.6987	+	5.10082i	0.537513	+	0.174649i	0.565179	−	0.824969i	$-0.308807\pi$
$853$	15.6987	+	5.10082i	0.537513	+	0.174649i	−0.0276653	+	0.999617i	$0.508807\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	28.7615i		−	0.982475i	−0.871026	−	0.491237i	$-0.836545\pi$
$857$		−	28.7615i		−	0.982475i	0.871026	−	0.491237i	$-0.163455\pi$
$858$		0			0
$859$	−12.2446	−	8.89622i	−0.417780	−	0.303535i	0.358964	−	0.933351i	$-0.383130\pi$
$859$	−12.2446	−	8.89622i	−0.417780	−	0.303535i	−0.776744	+	0.629816i	$0.783130\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−25.3024	+	34.8258i	−0.861305	+	1.18549i	0.119951	+	0.992780i	$0.461726\pi$
$863$	−25.3024	+	34.8258i	−0.861305	+	1.18549i	−0.981257	+	0.192705i	$0.938274\pi$
$864$		0			0
$865$	−12.3375	−	6.22426i	−0.419487	−	0.211631i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	3.98305	+	12.2586i	0.135116	+	0.415843i
$870$		0			0
$871$	−10.5004	+	32.3168i	−0.355792	+	1.09501i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	39.2405	+	5.73356i	1.32657	+	0.193830i
$876$		0			0
$877$	−29.7980	−	41.0134i	−1.00621	−	1.38492i	−0.921439	−	0.388523i	$-0.872985\pi$
$877$	−29.7980	−	41.0134i	−1.00621	−	1.38492i	−0.0847668	−	0.996401i	$-0.527015\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	0.818966	+	2.52052i	0.0275917	+	0.0849184i	0.963904	−	0.266250i	$-0.0857846\pi$
$881$	0.818966	+	2.52052i	0.0275917	+	0.0849184i	−0.936312	+	0.351168i	$0.885785\pi$
$882$		0			0
$883$	32.1189	−	10.4361i	1.08089	−	0.351201i	0.286168	−	0.958179i	$-0.407618\pi$
$883$	32.1189	−	10.4361i	1.08089	−	0.351201i	0.794719	+	0.606978i	$0.207618\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−2.54153	+	3.49811i	−0.0853361	+	0.117455i	−0.849551	−	0.527507i	$-0.823127\pi$
$887$	−2.54153	+	3.49811i	−0.0853361	+	0.117455i	0.764215	+	0.644962i	$0.223127\pi$
$888$		0			0
$889$	−35.6175	+	25.8776i	−1.19457	+	0.867908i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			14.0119i			0.468889i
$894$		0			0
$895$	−5.17586	−	31.8544i	−0.173010	−	1.06478i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	−3.64664			−0.121622
$900$		0			0
$901$	76.1182			2.53586
$902$		0			0
$903$		0			0
$904$		0			0
$905$	10.7039	+	10.6187i	0.355810	+	0.352977i
$906$		0			0
$907$			47.2507i			1.56893i	0.620171	+	0.784467i	$0.287063\pi$
$907$			47.2507i			1.56893i	−0.620171	+	0.784467i	$0.712937\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	41.1586	−	29.9035i	1.36365	−	0.990747i	0.365443	−	0.930834i	$-0.380918\pi$
$911$	41.1586	−	29.9035i	1.36365	−	0.990747i	0.998204	−	0.0599132i	$-0.0190824\pi$
$912$		0			0
$913$	−16.2453	+	22.3597i	−0.537641	+	0.739999i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	53.3785	−	17.3437i	1.76271	−	0.572740i
$918$		0			0
$919$	11.3396	+	34.8998i	0.374060	+	1.15124i	0.944111	+	0.329629i	$0.106924\pi$
$919$	11.3396	+	34.8998i	0.374060	+	1.15124i	−0.570051	+	0.821610i	$0.693076\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−58.1336	−	80.0140i	−1.91349	−	2.63369i
$924$		0			0
$925$	−11.4455	−	34.2902i	−0.376324	−	1.12745i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	14.9269	−	45.9401i	0.489734	−	1.50725i	−0.335271	−	0.942122i	$-0.608828\pi$
$929$	14.9269	−	45.9401i	0.489734	−	1.50725i	0.825005	−	0.565125i	$-0.191172\pi$
$930$		0			0
$931$	−3.99161	−	12.2849i	−0.130820	−	0.402622i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	4.78817	−	31.0338i	0.156590	−	1.01491i
$936$		0			0
$937$	−5.57420	+	7.67223i	−0.182101	+	0.250641i	−0.890302	−	0.455370i	$-0.849507\pi$
$937$	−5.57420	+	7.67223i	−0.182101	+	0.250641i	0.708201	+	0.706011i	$0.249507\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−17.2272	−	12.5163i	−0.561590	−	0.408019i	0.270450	−	0.962734i	$-0.412827\pi$
$941$	−17.2272	−	12.5163i	−0.561590	−	0.408019i	−0.832041	+	0.554715i	$0.812827\pi$
$942$		0			0
$943$		−	2.92570i		−	0.0952740i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−29.9695	−	9.73768i	−0.973877	−	0.316432i	−0.221497	−	0.975161i	$-0.571094\pi$
$947$	−29.9695	−	9.73768i	−0.973877	−	0.316432i	−0.752380	+	0.658729i	$0.771094\pi$
$948$		0			0
$949$	7.81773			0.253774
$950$		0			0
$951$		0			0
$952$		0			0
$953$	10.6646	+	3.46513i	0.345460	+	0.112247i	0.476608	−	0.879116i	$-0.341866\pi$
$953$	10.6646	+	3.46513i	0.345460	+	0.112247i	−0.131148	+	0.991363i	$0.541866\pi$
$954$		0			0
$955$	34.0119	+	5.24766i	1.10060	+	0.169810i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	21.2206	+	15.4177i	0.685249	+	0.497863i
$960$		0			0
$961$	10.1145	−	7.34864i	0.326275	−	0.237053i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	16.7662	+	32.5829i	0.539724	+	1.04888i
$966$		0			0
$967$	33.8782	−	11.0077i	1.08945	−	0.353984i	0.291417	−	0.956596i	$-0.405873\pi$
$967$	33.8782	−	11.0077i	1.08945	−	0.353984i	0.798034	+	0.602612i	$0.205873\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	−13.2227	+	40.6953i	−0.424337	+	1.30598i	0.479290	+	0.877656i	$0.340894\pi$
$971$	−13.2227	+	40.6953i	−0.424337	+	1.30598i	−0.903628	+	0.428319i	$0.859106\pi$
$972$		0			0
$973$	8.21228	+	11.3032i	0.263274	+	0.362365i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.9119	−	32.9119i	−0.765009	−	1.05294i	−0.996781	−	0.0801740i	$-0.974452\pi$
$977$	−23.9119	−	32.9119i	−0.765009	−	1.05294i	0.231772	−	0.972770i	$-0.425548\pi$
$978$		0			0
$979$	−4.78999	+	14.7421i	−0.153089	+	0.471159i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	46.5713	−	15.1319i	1.48539	−	0.482634i	0.549674	−	0.835379i	$-0.314752\pi$
$983$	46.5713	−	15.1319i	1.48539	−	0.482634i	0.935719	+	0.352746i	$0.114752\pi$
$984$		0			0
$985$	21.7409	−	3.53257i	0.692723	−	0.112557i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−14.4170	+	10.4746i	−0.458434	+	0.333072i
$990$		0			0
$991$	1.99334	+	1.44825i	0.0633206	+	0.0460051i	0.618995	−	0.785395i	$-0.287540\pi$
$991$	1.99334	+	1.44825i	0.0633206	+	0.0460051i	−0.555675	+	0.831400i	$0.687540\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	9.86732	−	5.07744i	0.312815	−	0.160966i
$996$		0			0
$997$	−51.5975	−	16.7650i	−1.63411	−	0.530954i	−0.658899	−	0.752232i	$-0.728977\pi$
$997$	−51.5975	−	16.7650i	−1.63411	−	0.530954i	−0.975211	+	0.221277i	$0.928977\pi$
$998$		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.289.5		24
3.2	odd	2		300.2.o.a.289.4	yes	24
15.2	even	4		1500.2.m.c.301.1		24
15.8	even	4		1500.2.m.d.301.6		24
15.14	odd	2		1500.2.o.c.949.3		24
25.9	even	10	inner	900.2.w.c.109.5		24
75.29	odd	10		7500.2.d.g.1249.2		24
75.38	even	20		1500.2.m.d.1201.6		24
75.41	odd	10		1500.2.o.c.49.3		24
75.47	even	20		7500.2.a.n.1.2		12
75.53	even	20		7500.2.a.m.1.11		12
75.59	odd	10		300.2.o.a.109.4	✓	24
75.62	even	20		1500.2.m.c.1201.1		24
75.71	odd	10		7500.2.d.g.1249.23		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.109.4	✓	24	75.59	odd	10
300.2.o.a.289.4	yes	24	3.2	odd	2
900.2.w.c.109.5		24	25.9	even	10	inner
900.2.w.c.289.5		24	1.1	even	1	trivial
1500.2.m.c.301.1		24	15.2	even	4
1500.2.m.c.1201.1		24	75.62	even	20
1500.2.m.d.301.6		24	15.8	even	4
1500.2.m.d.1201.6		24	75.38	even	20
1500.2.o.c.49.3		24	75.41	odd	10
1500.2.o.c.949.3		24	15.14	odd	2
7500.2.a.m.1.11		12	75.53	even	20
7500.2.a.n.1.2		12	75.47	even	20
7500.2.d.g.1249.2		24	75.29	odd	10
7500.2.d.g.1249.23		24	75.71	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)

\(f(q)\)	\(=\)	\(q+(1.98828 - 1.02311i) q^{5} +3.54704i q^{7} +O(q^{10})\)	\(q+(1.98828 - 1.02311i) q^{5} +3.54704i q^{7} +(-1.78482 + 1.29675i) q^{11} +(-4.21895 + 5.80689i) q^{13} +(-6.05378 + 1.96699i) q^{17} +(0.715151 + 2.20101i) q^{19} +(1.27899 + 1.76038i) q^{23} +(2.90649 - 4.06845i) q^{25} +(0.262008 - 0.806379i) q^{29} +(-1.32905 - 4.09040i) q^{31} +(3.62901 + 7.05250i) q^{35} +(4.24968 - 5.84918i) q^{37} +(-1.08778 - 0.790317i) q^{41} +8.18973i q^{43} +(5.75820 + 1.87095i) q^{47} -5.58150 q^{49} +(-11.3730 - 3.69530i) q^{53} +(-2.22201 + 4.40437i) q^{55} +(10.0896 + 7.33050i) q^{59} +(5.59873 - 4.06772i) q^{61} +(-2.44736 + 15.8622i) q^{65} +(4.50239 - 1.46291i) q^{67} +(-4.25799 + 13.1047i) q^{71} +(-0.640196 - 0.881155i) q^{73} +(-4.59963 - 6.33085i) q^{77} +(1.80542 - 5.55650i) q^{79} +(11.9145 - 3.87127i) q^{83} +(-10.0241 + 10.1046i) q^{85} +(5.68424 - 4.12984i) q^{89} +(-20.5973 - 14.9648i) q^{91} +(3.67379 + 3.64454i) q^{95} +(17.2564 + 5.60695i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 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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