LMFDB - Embedded newform 900.2.w.c.469.3

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			469.3
Character	$\chi$	$=$	900.469
Dual form			900.2.w.c.829.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.892889 + 2.05006i) q^{5} -4.13266i q^{7} +O(q^{10})$	$q+(-0.892889 + 2.05006i) q^{5} -4.13266i q^{7} +(1.16386 + 3.58198i) q^{11} +(0.664470 + 0.215899i) q^{13} +(3.11086 - 4.28173i) q^{17} +(4.63966 + 3.37091i) q^{19} +(-5.19894 + 1.68924i) q^{23} +(-3.40550 - 3.66095i) q^{25} +(5.68284 - 4.12883i) q^{29} +(8.16460 + 5.93193i) q^{31} +(8.47220 + 3.69001i) q^{35} +(5.50175 + 1.78763i) q^{37} +(2.03813 - 6.27271i) q^{41} -4.79668i q^{43} +(5.68611 + 7.82626i) q^{47} -10.0789 q^{49} +(1.99634 + 2.74773i) q^{53} +(-8.38247 - 0.812336i) q^{55} +(0.230309 - 0.708820i) q^{59} +(3.64886 + 11.2300i) q^{61} +(-1.03591 + 1.16943i) q^{65} +(-2.81995 + 3.88133i) q^{67} +(-2.54239 + 1.84715i) q^{71} +(10.2213 - 3.32110i) q^{73} +(14.8031 - 4.80982i) q^{77} +(-7.38222 + 5.36349i) q^{79} +(4.96148 - 6.82889i) q^{83} +(6.00015 + 10.2006i) q^{85} +(-1.04690 - 3.22202i) q^{89} +(0.892239 - 2.74603i) q^{91} +(-11.0533 + 6.50174i) q^{95} +(-6.13358 - 8.44215i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	−0.892889	+	2.05006i	−0.399312	+	0.916815i
$5$	−0.892889	+	2.05006i	−0.399312	+	0.916815i
$6$		0			0
$7$		−	4.13266i		−	1.56200i	−0.624532	−	0.780999i	$-0.714710\pi$
$7$		−	4.13266i		−	1.56200i	0.624532	−	0.780999i	$-0.285290\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	1.16386	+	3.58198i	0.350916	+	1.08001i	0.958340	+	0.285630i	$0.0922029\pi$
$11$	1.16386	+	3.58198i	0.350916	+	1.08001i	−0.607424	+	0.794378i	$0.707797\pi$
$12$		0			0
$13$	0.664470	+	0.215899i	0.184291	+	0.0598797i	0.399709	−	0.916642i	$-0.369111\pi$
$13$	0.664470	+	0.215899i	0.184291	+	0.0598797i	−0.215418	+	0.976522i	$0.569111\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	3.11086	−	4.28173i	0.754494	−	1.03847i	−0.243159	−	0.969987i	$-0.578184\pi$
$17$	3.11086	−	4.28173i	0.754494	−	1.03847i	0.997652	−	0.0684847i	$-0.0218164\pi$
$18$		0			0
$19$	4.63966	+	3.37091i	1.06441	+	0.773340i	0.974899	−	0.222646i	$-0.0714692\pi$
$19$	4.63966	+	3.37091i	1.06441	+	0.773340i	0.0895120	+	0.995986i	$0.471469\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−5.19894	+	1.68924i	−1.08405	+	0.352231i	−0.795946	−	0.605367i	$-0.793026\pi$
$23$	−5.19894	+	1.68924i	−1.08405	+	0.352231i	−0.288108	+	0.957598i	$0.593026\pi$
$24$		0			0
$25$	−3.40550	−	3.66095i	−0.681100	−	0.732191i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	5.68284	−	4.12883i	1.05528	−	0.766704i	0.0820685	−	0.996627i	$-0.473847\pi$
$29$	5.68284	−	4.12883i	1.05528	−	0.766704i	0.973209	+	0.229923i	$0.0738474\pi$
$30$		0			0
$31$	8.16460	+	5.93193i	1.46641	+	1.06541i	0.981636	+	0.190764i	$0.0610964\pi$
$31$	8.16460	+	5.93193i	1.46641	+	1.06541i	0.484769	+	0.874642i	$0.338904\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	8.47220	+	3.69001i	1.43206	+	0.623725i
$36$		0			0
$37$	5.50175	+	1.78763i	0.904482	+	0.293884i	0.724086	−	0.689710i	$-0.242262\pi$
$37$	5.50175	+	1.78763i	0.904482	+	0.293884i	0.180396	+	0.983594i	$0.442262\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	2.03813	−	6.27271i	0.318302	−	0.979633i	−0.656072	−	0.754698i	$-0.727783\pi$
$41$	2.03813	−	6.27271i	0.318302	−	0.979633i	0.974374	−	0.224935i	$-0.0722168\pi$
$42$		0			0
$43$		−	4.79668i		−	0.731488i	−0.930716	−	0.365744i	$-0.880815\pi$
$43$		−	4.79668i		−	0.731488i	0.930716	−	0.365744i	$-0.119185\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	5.68611	+	7.82626i	0.829405	+	1.14158i	0.988033	+	0.154239i	$0.0492927\pi$
$47$	5.68611	+	7.82626i	0.829405	+	1.14158i	−0.158629	+	0.987338i	$0.550707\pi$
$48$		0			0
$49$	−10.0789			−1.43984
$50$		0			0
$51$		0			0
$52$		0			0
$53$	1.99634	+	2.74773i	0.274219	+	0.377429i	0.923808	−	0.382856i	$-0.125059\pi$
$53$	1.99634	+	2.74773i	0.274219	+	0.377429i	−0.649590	+	0.760285i	$0.725059\pi$
$54$		0			0
$55$	−8.38247	−	0.812336i	−1.13029	−	0.109535i
$56$		0			0
$57$		0			0
$58$		0			0
$59$	0.230309	−	0.708820i	0.0299837	−	0.0922804i	−0.934945	−	0.354793i	$-0.884551\pi$
$59$	0.230309	−	0.708820i	0.0299837	−	0.0922804i	0.964928	+	0.262513i	$0.0845512\pi$
$60$		0			0
$61$	3.64886	+	11.2300i	0.467188	+	1.43786i	0.856210	+	0.516629i	$0.172813\pi$
$61$	3.64886	+	11.2300i	0.467188	+	1.43786i	−0.389021	+	0.921229i	$0.627187\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	−1.03591	+	1.16943i	−0.128488	+	0.145050i
$66$		0			0
$67$	−2.81995	+	3.88133i	−0.344512	+	0.474180i	−0.945752	−	0.324888i	$-0.894673\pi$
$67$	−2.81995	+	3.88133i	−0.344512	+	0.474180i	0.601241	+	0.799068i	$0.294673\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	−2.54239	+	1.84715i	−0.301726	+	0.219217i	−0.728338	−	0.685218i	$-0.759707\pi$
$71$	−2.54239	+	1.84715i	−0.301726	+	0.219217i	0.426612	+	0.904435i	$0.359707\pi$
$72$		0			0
$73$	10.2213	−	3.32110i	1.19631	−	0.388706i	0.357910	−	0.933756i	$-0.383490\pi$
$73$	10.2213	−	3.32110i	1.19631	−	0.388706i	0.838403	+	0.545051i	$0.183490\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	14.8031	−	4.80982i	1.68697	−	0.548130i
$78$		0			0
$79$	−7.38222	+	5.36349i	−0.830564	+	0.603440i	−0.919719	−	0.392578i	$-0.871583\pi$
$79$	−7.38222	+	5.36349i	−0.830564	+	0.603440i	0.0891546	+	0.996018i	$0.471583\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	4.96148	−	6.82889i	0.544593	−	0.749569i	−0.444673	−	0.895693i	$-0.646680\pi$
$83$	4.96148	−	6.82889i	0.544593	−	0.749569i	0.989266	+	0.146125i	$0.0466800\pi$
$84$		0			0
$85$	6.00015	+	10.2006i	0.650808	+	1.10641i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−1.04690	−	3.22202i	−0.110971	−	0.341533i	0.880114	−	0.474761i	$-0.157466\pi$
$89$	−1.04690	−	3.22202i	−0.110971	−	0.341533i	−0.991085	+	0.133228i	$0.957466\pi$
$90$		0			0
$91$	0.892239	−	2.74603i	0.0935321	−	0.287862i
$92$		0			0
$93$		0			0
$94$		0			0
$95$	−11.0533	+	6.50174i	−1.13404	+	0.667064i
$96$		0			0
$97$	−6.13358	−	8.44215i	−0.622771	−	0.857170i	0.374780	−	0.927114i	$-0.377718\pi$
$97$	−6.13358	−	8.44215i	−0.622771	−	0.857170i	−0.997551	+	0.0699435i	$0.977718\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	−7.10799			−0.707272			−0.353636	−	0.935383i	$-0.615055\pi$
$101$	−7.10799			−0.707272			−0.353636	+	0.935383i	$0.615055\pi$
$102$		0			0
$103$	−7.17630	−	9.87733i	−0.707102	−	0.973243i	−0.999855	−	0.0170543i	$-0.994571\pi$
$103$	−7.17630	−	9.87733i	−0.707102	−	0.973243i	0.292752	−	0.956188i	$-0.405429\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	4.04303i		−	0.390855i	−0.980718	−	0.195427i	$-0.937391\pi$
$107$		−	4.04303i		−	0.390855i	0.980718	−	0.195427i	$-0.0626094\pi$
$108$		0			0
$109$	0.239122	−	0.735942i	0.0229037	−	0.0704904i	−0.938951	−	0.344050i	$-0.888201\pi$
$109$	0.239122	−	0.735942i	0.0229037	−	0.0704904i	0.961855	+	0.273560i	$0.0882010\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	1.08366	+	0.352104i	0.101943	+	0.0331231i	0.359544	−	0.933128i	$-0.382932\pi$
$113$	1.08366	+	0.352104i	0.101943	+	0.0331231i	−0.257602	+	0.966251i	$0.582932\pi$
$114$		0			0
$115$	1.17904	−	12.1665i	0.109946	−	1.13453i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−17.6949	−	12.8561i	−1.62209	−	1.17852i
$120$		0			0
$121$	−2.57684	+	1.87218i	−0.234258	+	0.170198i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	10.5459	−	3.71265i	0.943255	−	0.332070i
$126$		0			0
$127$	0.511543	−	0.166210i	0.0453921	−	0.0147488i	−0.286233	−	0.958160i	$-0.592403\pi$
$127$	0.511543	−	0.166210i	0.0453921	−	0.0147488i	0.331625	+	0.943411i	$0.392403\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−5.43855	−	3.95134i	−0.475169	−	0.345230i	0.324284	−	0.945960i	$-0.394877\pi$
$131$	−5.43855	−	3.95134i	−0.475169	−	0.345230i	−0.799452	+	0.600730i	$0.794877\pi$
$132$		0			0
$133$	13.9308	−	19.1741i	1.20796	−	1.66261i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.174404	+	0.0566672i	0.0149003	+	0.00484140i	0.316458	−	0.948607i	$-0.397506\pi$
$137$	0.174404	+	0.0566672i	0.0149003	+	0.00484140i	−0.301557	+	0.953448i	$0.597506\pi$
$138$		0			0
$139$	−2.54014	−	7.81775i	−0.215452	−	0.663093i	−0.999121	−	0.0419144i	$-0.986654\pi$
$139$	−2.54014	−	7.81775i	−0.215452	−	0.663093i	0.783669	−	0.621178i	$-0.213346\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$			2.63140i			0.220048i
$144$		0			0
$145$	3.39020	+	15.3368i	0.281541	+	1.27365i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	5.53790			0.453682			0.226841	−	0.973932i	$-0.427160\pi$
$149$	5.53790			0.453682			0.226841	+	0.973932i	$0.427160\pi$
$150$		0			0
$151$	12.8736			1.04764			0.523821	−	0.851828i	$-0.324506\pi$
$151$	12.8736			1.04764			0.523821	+	0.851828i	$0.324506\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−19.4509	+	11.4414i	−1.56233	+	0.918993i
$156$		0			0
$157$			14.6395i			1.16836i	0.811625	+	0.584179i	$0.198583\pi$
$157$			14.6395i			1.16836i	−0.811625	+	0.584179i	$0.801417\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	6.98105	+	21.4855i	0.550184	+	1.69329i
$162$		0			0
$163$	−4.22672	−	1.37334i	−0.331062	−	0.107569i	0.138769	−	0.990325i	$-0.455685\pi$
$163$	−4.22672	−	1.37334i	−0.331062	−	0.107569i	−0.469832	+	0.882756i	$0.655685\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−13.9690	+	19.2267i	−1.08095	+	1.48780i	−0.222487	+	0.974936i	$0.571417\pi$
$167$	−13.9690	+	19.2267i	−1.08095	+	1.48780i	−0.858467	+	0.512869i	$0.828583\pi$
$168$		0			0
$169$	−10.1223	−	7.35429i	−0.778639	−	0.565715i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−14.3484	+	4.66207i	−1.09089	+	0.354451i	−0.798589	−	0.601877i	$-0.794420\pi$
$173$	−14.3484	+	4.66207i	−1.09089	+	0.354451i	−0.292298	+	0.956327i	$0.594420\pi$
$174$		0			0
$175$	−15.1295	+	14.0738i	−1.14368	+	1.06388i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−13.5238	+	9.82561i	−1.01082	+	0.734401i	−0.964380	−	0.264521i	$-0.914786\pi$
$179$	−13.5238	+	9.82561i	−1.01082	+	0.734401i	−0.0464356	+	0.998921i	$0.514786\pi$
$180$		0			0
$181$	−8.40755	−	6.10844i	−0.624928	−	0.454037i	0.229711	−	0.973259i	$-0.426222\pi$
$181$	−8.40755	−	6.10844i	−0.624928	−	0.454037i	−0.854639	+	0.519222i	$0.826222\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−8.57720	+	9.68277i	−0.630608	+	0.711892i
$186$		0			0
$187$	18.9576	+	6.15971i	1.38632	+	0.450443i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	6.10485	−	18.7888i	0.441732	−	1.35951i	−0.444297	−	0.895880i	$-0.646546\pi$
$191$	6.10485	−	18.7888i	0.441732	−	1.35951i	0.886029	−	0.463631i	$-0.153454\pi$
$192$		0			0
$193$		−	2.23549i		−	0.160914i	−0.996758	−	0.0804571i	$-0.974362\pi$
$193$		−	2.23549i		−	0.160914i	0.996758	−	0.0804571i	$-0.0256380\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−13.3761	−	18.4106i	−0.953008	−	1.31170i	−0.950178	−	0.311706i	$-0.899099\pi$
$197$	−13.3761	−	18.4106i	−0.953008	−	1.31170i	−0.00282909	−	0.999996i	$-0.500901\pi$
$198$		0			0
$199$	−22.8171			−1.61746			−0.808731	−	0.588179i	$-0.799845\pi$
$199$	−22.8171			−1.61746			−0.808731	+	0.588179i	$0.799845\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	−17.0630	−	23.4853i	−1.19759	−	1.64834i
$204$		0			0
$205$	11.0396	+	9.77912i	0.771040	+	0.683003i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	−6.67464	+	20.5424i	−0.461695	+	1.42095i
$210$		0			0
$211$	6.21019	+	19.1130i	0.427527	+	1.31579i	0.900554	+	0.434745i	$0.143161\pi$
$211$	6.21019	+	19.1130i	0.427527	+	1.31579i	−0.473027	+	0.881048i	$0.656839\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	9.83349	+	4.28291i	0.670639	+	0.292092i
$216$		0			0
$217$	24.5146	−	33.7415i	1.66416	−	2.29052i
$218$		0			0
$219$		0			0
$220$		0			0
$221$	2.99149	−	2.17345i	0.201230	−	0.146202i
$222$		0			0
$223$	−12.7621	+	4.14665i	−0.854612	+	0.277680i	−0.703377	−	0.710817i	$-0.748325\pi$
$223$	−12.7621	+	4.14665i	−0.854612	+	0.277680i	−0.151236	+	0.988498i	$0.548325\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	17.5862	−	5.71411i	1.16724	−	0.379259i	0.339628	−	0.940560i	$-0.389699\pi$
$227$	17.5862	−	5.71411i	1.16724	−	0.379259i	0.827612	+	0.561301i	$0.189699\pi$
$228$		0			0
$229$	−15.7050	+	11.4104i	−1.03782	+	0.754017i	−0.969858	−	0.243671i	$-0.921648\pi$
$229$	−15.7050	+	11.4104i	−1.03782	+	0.754017i	−0.0679579	+	0.997688i	$0.521648\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	7.16114	−	9.85646i	0.469142	−	0.645718i	−0.507231	−	0.861810i	$-0.669331\pi$
$233$	7.16114	−	9.85646i	0.469142	−	0.645718i	0.976373	+	0.216092i	$0.0693311\pi$
$234$		0			0
$235$	−21.1214	+	4.66889i	−1.37781	+	0.304565i
$236$		0			0
$237$		0			0
$238$		0			0
$239$	1.39823	+	4.30330i	0.0904438	+	0.278357i	0.986040	−	0.166512i	$-0.0532503\pi$
$239$	1.39823	+	4.30330i	0.0904438	+	0.278357i	−0.895596	+	0.444869i	$0.853250\pi$
$240$		0			0
$241$	2.78479	−	8.57071i	0.179384	−	0.552088i	−0.820422	−	0.571758i	$-0.806262\pi$
$241$	2.78479	−	8.57071i	0.179384	−	0.552088i	0.999807	+	0.0196702i	$0.00626163\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	8.99932	−	20.6623i	0.574945	−	1.32007i
$246$		0			0
$247$	2.35514	+	3.24157i	0.149854	+	0.206256i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−3.16965			−0.200066			−0.100033	−	0.994984i	$-0.531895\pi$
$251$	−3.16965			−0.200066			−0.100033	+	0.994984i	$0.531895\pi$
$252$		0			0
$253$	−12.1016	−	16.6565i	−0.760824	−	1.04718i
$254$		0			0
$255$		0			0
$256$		0			0
$257$			3.25241i			0.202880i	0.994842	+	0.101440i	$0.0323450\pi$
$257$			3.25241i			0.202880i	−0.994842	+	0.101440i	$0.967655\pi$
$258$		0			0
$259$	7.38766	−	22.7369i	0.459047	−	1.41280i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	10.5187	+	3.41774i	0.648612	+	0.210747i	0.614802	−	0.788682i	$-0.289236\pi$
$263$	10.5187	+	3.41774i	0.648612	+	0.210747i	0.0338097	+	0.999428i	$0.489236\pi$
$264$		0			0
$265$	−7.41552	+	1.63920i	−0.455532	+	0.100696i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	−20.0279	−	14.5511i	−1.22112	−	0.887197i	−0.224929	−	0.974375i	$-0.572215\pi$
$269$	−20.0279	−	14.5511i	−1.22112	−	0.887197i	−0.996193	+	0.0871780i	$0.972215\pi$
$270$		0			0
$271$	−0.202420	+	0.147067i	−0.0122962	+	0.00893369i	−0.593916	−	0.804527i	$-0.702419\pi$
$271$	−0.202420	+	0.147067i	−0.0122962	+	0.00893369i	0.581620	+	0.813460i	$0.302419\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	9.14996	−	16.4593i	0.551763	−	0.992530i
$276$		0			0
$277$	8.43658	−	2.74121i	0.506905	−	0.164703i	−0.0443894	−	0.999014i	$-0.514134\pi$
$277$	8.43658	−	2.74121i	0.506905	−	0.164703i	0.551294	+	0.834311i	$0.314134\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	15.9683	+	11.6016i	0.952588	+	0.692096i	0.951418	−	0.307904i	$-0.0996274\pi$
$281$	15.9683	+	11.6016i	0.952588	+	0.692096i	0.00117050	+	0.999999i	$0.499627\pi$
$282$		0			0
$283$	−15.5421	+	21.3919i	−0.923882	+	1.27162i	0.0383159	+	0.999266i	$0.487801\pi$
$283$	−15.5421	+	21.3919i	−0.923882	+	1.27162i	−0.962198	+	0.272349i	$0.912199\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−25.9230	−	8.42289i	−1.53019	−	0.497187i
$288$		0			0
$289$	−3.40247	−	10.4717i	−0.200145	−	0.615983i
$290$		0			0
$291$		0			0
$292$		0			0
$293$		−	19.1882i		−	1.12099i	−0.828158	−	0.560494i	$-0.810611\pi$
$293$		−	19.1882i		−	1.12099i	0.828158	−	0.560494i	$-0.189389\pi$
$294$		0			0
$295$	1.24748	+	1.10505i	0.0726312	+	0.0643382i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	−3.81925			−0.220873
$300$		0			0
$301$	−19.8231			−1.14258
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−26.2803	−	2.54679i	−1.50480	−	0.145829i
$306$		0			0
$307$			9.26979i			0.529055i	0.964378	+	0.264527i	$0.0852160\pi$
$307$			9.26979i			0.529055i	−0.964378	+	0.264527i	$0.914784\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	7.69255	+	23.6752i	0.436204	+	1.34250i	0.891847	+	0.452336i	$0.149409\pi$
$311$	7.69255	+	23.6752i	0.436204	+	1.34250i	−0.455643	+	0.890163i	$0.650591\pi$
$312$		0			0
$313$	5.75115	+	1.86866i	0.325074	+	0.105623i	0.467008	−	0.884253i	$-0.345332\pi$
$313$	5.75115	+	1.86866i	0.325074	+	0.105623i	−0.141934	+	0.989876i	$0.545332\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	8.45614	−	11.6389i	0.474944	−	0.653705i	−0.502579	−	0.864531i	$-0.667616\pi$
$317$	8.45614	−	11.6389i	0.474944	−	0.653705i	0.977523	+	0.210827i	$0.0676155\pi$
$318$		0			0
$319$	21.4034	+	15.5505i	1.19836	+	0.870659i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	28.8666	−	9.37934i	1.60618	−	0.521881i
$324$		0			0
$325$	−1.47245	−	3.16784i	−0.0816771	−	0.175720i
$326$		0			0
$327$		0			0
$328$		0			0
$329$	32.3433	−	23.4988i	1.78314	−	1.29553i
$330$		0			0
$331$	−0.863126	−	0.627098i	−0.0474417	−	0.0344684i	0.563812	−	0.825903i	$-0.309334\pi$
$331$	−0.863126	−	0.627098i	−0.0474417	−	0.0344684i	−0.611253	+	0.791435i	$0.709334\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	−5.43906	−	9.24667i	−0.297168	−	0.505200i
$336$		0			0
$337$	−13.8873	−	4.51226i	−0.756490	−	0.245799i	−0.0947186	−	0.995504i	$-0.530195\pi$
$337$	−13.8873	−	4.51226i	−0.756490	−	0.245799i	−0.661772	+	0.749705i	$0.730195\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	−11.7456	+	36.1493i	−0.636062	+	1.95760i
$342$		0			0
$343$			12.7239i			0.687029i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	9.48995	+	13.0618i	0.509447	+	0.701194i	0.983826	−	0.179127i	$-0.0573273\pi$
$347$	9.48995	+	13.0618i	0.509447	+	0.701194i	−0.474379	+	0.880321i	$0.657327\pi$
$348$		0			0
$349$	22.2622			1.19167			0.595834	−	0.803108i	$-0.296822\pi$
$349$	22.2622			1.19167			0.595834	+	0.803108i	$0.296822\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	5.60158	+	7.70991i	0.298142	+	0.410357i	0.931637	−	0.363389i	$-0.118381\pi$
$353$	5.60158	+	7.70991i	0.298142	+	0.410357i	−0.633496	+	0.773746i	$0.718381\pi$
$354$		0			0
$355$	−1.51670	−	6.86135i	−0.0804983	−	0.364162i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−5.18753	+	15.9656i	−0.273788	+	0.842632i	0.715750	+	0.698357i	$0.246085\pi$
$359$	−5.18753	+	15.9656i	−0.273788	+	0.842632i	−0.989538	+	0.144275i	$0.953915\pi$
$360$		0			0
$361$	4.29210	+	13.2097i	0.225900	+	0.695248i
$362$		0			0
$363$		0			0
$364$		0			0
$365$	−2.31803	+	23.9197i	−0.121331	+	1.25201i
$366$		0			0
$367$	19.0893	−	26.2741i	0.996452	−	1.37150i	0.0689751	−	0.997618i	$-0.478027\pi$
$367$	19.0893	−	26.2741i	0.996452	−	1.37150i	0.927477	−	0.373880i	$-0.121973\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	11.3554	−	8.25020i	0.589544	−	0.428329i
$372$		0			0
$373$	−13.5918	+	4.41623i	−0.703755	+	0.228664i	−0.638966	−	0.769235i	$-0.720637\pi$
$373$	−13.5918	+	4.41623i	−0.703755	+	0.228664i	−0.0647890	+	0.997899i	$0.520637\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	4.66749	−	1.51656i	0.240388	−	0.0781068i
$378$		0			0
$379$	−2.60155	+	1.89014i	−0.133633	+	0.0970897i	−0.652593	−	0.757708i	$-0.726319\pi$
$379$	−2.60155	+	1.89014i	−0.133633	+	0.0970897i	0.518961	+	0.854798i	$0.326319\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	−7.26491	+	9.99929i	−0.371220	+	0.510940i	−0.953232	−	0.302240i	$-0.902266\pi$
$383$	−7.26491	+	9.99929i	−0.371220	+	0.510940i	0.582012	+	0.813180i	$0.302266\pi$
$384$		0			0
$385$	−3.35711	+	34.6419i	−0.171094	+	1.76551i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	7.14594	+	21.9930i	0.362314	+	1.11509i	0.951646	+	0.307196i	$0.0993908\pi$
$389$	7.14594	+	21.9930i	0.362314	+	1.11509i	−0.589332	+	0.807891i	$0.700609\pi$
$390$		0			0
$391$	−8.94031	+	27.5154i	−0.452131	+	1.39152i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	−4.40399	−	19.9230i	−0.221589	−	1.00243i
$396$		0			0
$397$	−1.25095	−	1.72179i	−0.0627834	−	0.0864140i	0.776471	−	0.630153i	$-0.217008\pi$
$397$	−1.25095	−	1.72179i	−0.0627834	−	0.0864140i	−0.839254	+	0.543739i	$0.817008\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	33.8250			1.68914			0.844569	−	0.535447i	$-0.179857\pi$
$401$	33.8250			1.68914			0.844569	+	0.535447i	$0.179857\pi$
$402$		0			0
$403$	4.14443	+	5.70432i	0.206449	+	0.284153i
$404$		0			0
$405$		0			0
$406$		0			0
$407$			21.7877i			1.07998i
$408$		0			0
$409$	10.7434	−	33.0647i	0.531226	−	1.63495i	−0.220439	−	0.975401i	$-0.570749\pi$
$409$	10.7434	−	33.0647i	0.531226	−	1.63495i	0.751665	−	0.659545i	$-0.229251\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−2.92931	−	0.951790i	−0.144142	−	0.0468345i
$414$		0			0
$415$	9.56960	+	16.2688i	0.469753	+	0.798603i
$416$		0			0
$417$		0			0
$418$		0			0
$419$	5.49925	+	3.99544i	0.268656	+	0.195190i	0.713954	−	0.700192i	$-0.246902\pi$
$419$	5.49925	+	3.99544i	0.268656	+	0.195190i	−0.445298	+	0.895382i	$0.646902\pi$
$420$		0			0
$421$	8.75730	−	6.36255i	0.426805	−	0.310092i	−0.353565	−	0.935410i	$-0.615031\pi$
$421$	8.75730	−	6.36255i	0.426805	−	0.310092i	0.780370	+	0.625318i	$0.215031\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−26.2692	+	3.19271i	−1.27424	+	0.154869i
$426$		0			0
$427$	46.4099	−	15.0795i	2.24593	−	0.729747i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−8.40317	−	6.10526i	−0.404767	−	0.294080i	0.366713	−	0.930334i	$-0.380483\pi$
$431$	−8.40317	−	6.10526i	−0.404767	−	0.294080i	−0.771480	+	0.636254i	$0.780483\pi$
$432$		0			0
$433$	9.20630	−	12.6714i	0.442427	−	0.608948i	−0.528323	−	0.849044i	$-0.677179\pi$
$433$	9.20630	−	12.6714i	0.442427	−	0.608948i	0.970749	+	0.240096i	$0.0771789\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	−29.8156	−	9.68768i	−1.42627	−	0.463425i
$438$		0			0
$439$	−6.80071	−	20.9304i	−0.324580	−	0.998955i	−0.971630	−	0.236507i	$-0.923997\pi$
$439$	−6.80071	−	20.9304i	−0.324580	−	0.998955i	0.647050	−	0.762448i	$-0.276003\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$			29.4447i			1.39896i	0.714652	+	0.699480i	$0.246585\pi$
$443$			29.4447i			1.39896i	−0.714652	+	0.699480i	$0.753415\pi$
$444$		0			0
$445$	7.54010	+	0.730702i	0.357435	+	0.0346386i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	27.3445			1.29047			0.645234	−	0.763985i	$-0.276760\pi$
$449$	27.3445			1.29047			0.645234	+	0.763985i	$0.276760\pi$
$450$		0			0
$451$	24.8408			1.16971
$452$		0			0
$453$		0			0
$454$		0			0
$455$	4.83286	+	4.28104i	0.226568	+	0.200698i
$456$		0			0
$457$			33.6394i			1.57359i	0.617217	+	0.786793i	$0.288260\pi$
$457$			33.6394i			1.57359i	−0.617217	+	0.786793i	$0.711740\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	−7.86199	−	24.1967i	−0.366169	−	1.12695i	−0.949246	−	0.314536i	$-0.898151\pi$
$461$	−7.86199	−	24.1967i	−0.366169	−	1.12695i	0.583076	−	0.812417i	$-0.301849\pi$
$462$		0			0
$463$	−7.45749	−	2.42308i	−0.346579	−	0.112610i	0.130555	−	0.991441i	$-0.458324\pi$
$463$	−7.45749	−	2.42308i	−0.346579	−	0.112610i	−0.477134	+	0.878831i	$0.658324\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	6.34847	−	8.73792i	0.293772	−	0.404343i	−0.636463	−	0.771307i	$-0.719603\pi$
$467$	6.34847	−	8.73792i	0.293772	−	0.404343i	0.930235	+	0.366965i	$0.119603\pi$
$468$		0			0
$469$	16.0402	+	11.6539i	0.740668	+	0.538127i
$470$		0			0
$471$		0			0
$472$		0			0
$473$	17.1816	−	5.58265i	0.790012	−	0.256691i
$474$		0			0
$475$	−3.45961	−	28.4652i	−0.158738	−	1.30607i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	−18.3447	+	13.3282i	−0.838191	+	0.608981i	−0.921865	−	0.387512i	$-0.873335\pi$
$479$	−18.3447	+	13.3282i	−0.838191	+	0.608981i	0.0836740	+	0.996493i	$0.473335\pi$
$480$		0			0
$481$	3.26980	+	2.37565i	0.149090	+	0.108320i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	22.7835	−	5.03631i	1.03455	−	0.228687i
$486$		0			0
$487$	4.74184	+	1.54072i	0.214873	+	0.0698166i	0.414476	−	0.910060i	$-0.363965\pi$
$487$	4.74184	+	1.54072i	0.214873	+	0.0698166i	−0.199602	+	0.979877i	$0.563965\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	8.17443	−	25.1583i	0.368907	−	1.13538i	−0.578592	−	0.815617i	$-0.696397\pi$
$491$	8.17443	−	25.1583i	0.368907	−	1.13538i	0.947498	−	0.319761i	$-0.103603\pi$
$492$		0			0
$493$		−	37.1766i		−	1.67435i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	7.63365	+	10.5068i	0.342416	+	0.471295i
$498$		0			0
$499$	−38.0875			−1.70503			−0.852516	−	0.522702i	$-0.824924\pi$
$499$	−38.0875			−1.70503			−0.852516	+	0.522702i	$0.824924\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	1.38481	+	1.90603i	0.0617456	+	0.0849856i	0.838773	−	0.544481i	$-0.183273\pi$
$503$	1.38481	+	1.90603i	0.0617456	+	0.0849856i	−0.777027	+	0.629467i	$0.783273\pi$
$504$		0			0
$505$	6.34665	−	14.5718i	0.282422	−	0.648438i
$506$		0			0
$507$		0			0
$508$		0			0
$509$	−9.02282	+	27.7694i	−0.399929	+	1.23086i	0.525126	+	0.851024i	$0.324018\pi$
$509$	−9.02282	+	27.7694i	−0.399929	+	1.23086i	−0.925056	+	0.379832i	$0.875982\pi$
$510$		0			0
$511$	−13.7250	−	42.2412i	−0.607158	−	1.86864i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	26.6568	−	5.89249i	1.17464	−	0.259654i
$516$		0			0
$517$	−21.4157	+	29.4762i	−0.941862	+	1.29636i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	−34.4787	+	25.0503i	−1.51054	+	1.09747i	−0.544604	+	0.838693i	$0.683320\pi$
$521$	−34.4787	+	25.0503i	−1.51054	+	1.09747i	−0.965937	+	0.258779i	$0.916680\pi$
$522$		0			0
$523$	19.6631	−	6.38893i	0.859808	−	0.279368i	0.154259	−	0.988030i	$-0.450701\pi$
$523$	19.6631	−	6.38893i	0.859808	−	0.279368i	0.705548	+	0.708662i	$0.250701\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	50.7978	−	16.5052i	2.21279	−	0.718978i
$528$		0			0
$529$	5.56809	−	4.04545i	0.242091	−	0.175889i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	2.70855	−	3.72800i	0.117320	−	0.161478i
$534$		0			0
$535$	8.28846	+	3.60998i	0.358342	+	0.156073i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−11.7304	−	36.1023i	−0.505262	−	1.55504i
$540$		0			0
$541$	3.69426	−	11.3698i	0.158829	−	0.488824i	−0.839700	−	0.543050i	$-0.817269\pi$
$541$	3.69426	−	11.3698i	0.158829	−	0.488824i	0.998529	+	0.0542264i	$0.0172693\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	1.29522	+	1.14733i	0.0554810	+	0.0491462i
$546$		0			0
$547$	−15.6366	−	21.5220i	−0.668575	−	0.920214i	0.331152	−	0.943577i	$-0.392563\pi$
$547$	−15.6366	−	21.5220i	−0.668575	−	0.920214i	−0.999727	+	0.0233630i	$0.992563\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	40.2844			1.71617
$552$		0			0
$553$	22.1655	+	30.5082i	0.942573	+	1.29734i
$554$		0			0
$555$		0			0
$556$		0			0
$557$			28.3420i			1.20089i	0.799667	+	0.600444i	$0.205010\pi$
$557$			28.3420i			1.20089i	−0.799667	+	0.600444i	$0.794990\pi$
$558$		0			0
$559$	1.03560	−	3.18725i	0.0438013	−	0.134806i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	3.85764	+	1.25342i	0.162580	+	0.0528255i	0.389176	−	0.921163i	$-0.372760\pi$
$563$	3.85764	+	1.25342i	0.162580	+	0.0528255i	−0.226596	+	0.973989i	$0.572760\pi$
$564$		0			0
$565$	−1.68943	+	1.90719i	−0.0710747	+	0.0802360i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−1.59124	−	1.15610i	−0.0667081	−	0.0484663i	0.553931	−	0.832562i	$-0.313127\pi$
$569$	−1.59124	−	1.15610i	−0.0667081	−	0.0484663i	−0.620640	+	0.784096i	$0.713127\pi$
$570$		0			0
$571$	−4.17273	+	3.03167i	−0.174623	+	0.126871i	−0.671664	−	0.740856i	$-0.734420\pi$
$571$	−4.17273	+	3.03167i	−0.174623	+	0.126871i	0.497040	+	0.867727i	$0.334420\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	23.8892	+	13.2804i	0.996249	+	0.553831i
$576$		0			0
$577$	−36.7286	+	11.9338i	−1.52903	+	0.496812i	−0.948325	−	0.317301i	$-0.897224\pi$
$577$	−36.7286	+	11.9338i	−1.52903	+	0.496812i	−0.580706	+	0.814113i	$0.697224\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	−28.2215	−	20.5041i	−1.17083	−	0.850654i
$582$		0			0
$583$	−7.51885	+	10.3488i	−0.311399	+	0.428604i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−25.8420	−	8.39659i	−1.06662	−	0.346564i	−0.277447	−	0.960741i	$-0.589488\pi$
$587$	−25.8420	−	8.39659i	−1.06662	−	0.346564i	−0.789168	+	0.614177i	$0.789488\pi$
$588$		0			0
$589$	17.8850	+	55.0443i	0.736937	+	2.26806i
$590$		0			0
$591$		0			0
$592$		0			0
$593$		−	30.3486i		−	1.24627i	−0.782114	−	0.623135i	$-0.785859\pi$
$593$		−	30.3486i		−	1.24627i	0.782114	−	0.623135i	$-0.214141\pi$
$594$		0			0
$595$	42.1554	−	24.7966i	1.72820	−	1.01656i
$596$		0			0
$597$		0			0
$598$		0			0
$599$	−26.9205			−1.09994			−0.549971	−	0.835184i	$-0.685361\pi$
$599$	−26.9205			−1.09994			−0.549971	+	0.835184i	$0.685361\pi$
$600$		0			0
$601$	−16.9133			−0.689910			−0.344955	−	0.938619i	$-0.612106\pi$
$601$	−16.9133			−0.689910			−0.344955	+	0.938619i	$0.612106\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	−1.53726	−	6.95432i	−0.0624983	−	0.282733i
$606$		0			0
$607$			18.9715i			0.770028i	0.922911	+	0.385014i	$0.125803\pi$
$607$			18.9715i			0.770028i	−0.922911	+	0.385014i	$0.874197\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	2.08857	+	6.42795i	0.0844944	+	0.260047i
$612$		0			0
$613$	−5.19102	−	1.68666i	−0.209663	−	0.0681237i	0.202302	−	0.979323i	$-0.435158\pi$
$613$	−5.19102	−	1.68666i	−0.209663	−	0.0681237i	−0.411966	+	0.911199i	$0.635158\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−6.99287	+	9.62485i	−0.281522	+	0.387482i	−0.926237	−	0.376941i	$-0.876976\pi$
$617$	−6.99287	+	9.62485i	−0.281522	+	0.387482i	0.644715	+	0.764423i	$0.276976\pi$
$618$		0			0
$619$	−10.6888	−	7.76586i	−0.429619	−	0.312136i	0.351878	−	0.936046i	$-0.385543\pi$
$619$	−10.6888	−	7.76586i	−0.429619	−	0.312136i	−0.781496	+	0.623910i	$0.785543\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−13.3155	+	4.32647i	−0.533475	+	0.173336i
$624$		0			0
$625$	−1.80517	+	24.9347i	−0.0722066	+	0.997390i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	24.7693	−	17.9959i	0.987616	−	0.717545i
$630$		0			0
$631$	9.39932	+	6.82900i	0.374181	+	0.271858i	0.758943	−	0.651158i	$-0.225716\pi$
$631$	9.39932	+	6.82900i	0.374181	+	0.271858i	−0.384762	+	0.923016i	$0.625716\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	−0.116010	+	1.19710i	−0.00460371	+	0.0475055i
$636$		0			0
$637$	−6.69711	−	2.17602i	−0.265349	−	0.0862172i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	10.7784	−	33.1725i	0.425721	−	1.31023i	−0.476582	−	0.879130i	$-0.658124\pi$
$641$	10.7784	−	33.1725i	0.425721	−	1.31023i	0.902303	−	0.431103i	$-0.141876\pi$
$642$		0			0
$643$			2.90629i			0.114613i	0.998357	+	0.0573065i	$0.0182512\pi$
$643$			2.90629i			0.114613i	−0.998357	+	0.0573065i	$0.981749\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7.13583	−	9.82163i	−0.280538	−	0.386128i	0.645374	−	0.763867i	$-0.276702\pi$
$647$	−7.13583	−	9.82163i	−0.280538	−	0.386128i	−0.925912	+	0.377739i	$0.876702\pi$
$648$		0			0
$649$	2.80702			0.110185
$650$		0			0
$651$		0			0
$652$		0			0
$653$	15.3404	+	21.1143i	0.600318	+	0.826266i	0.995737	−	0.0922343i	$-0.0294009\pi$
$653$	15.3404	+	21.1143i	0.600318	+	0.826266i	−0.395420	+	0.918500i	$0.629401\pi$
$654$		0			0
$655$	12.9565	−	7.62126i	0.506253	−	0.297787i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	6.59035	−	20.2830i	0.256724	−	0.790114i	−0.736761	−	0.676153i	$-0.763646\pi$
$659$	6.59035	−	20.2830i	0.256724	−	0.790114i	0.993485	−	0.113962i	$-0.0363541\pi$
$660$		0			0
$661$	−9.79161	−	30.1355i	−0.380850	−	1.17213i	−0.939447	−	0.342695i	$-0.888660\pi$
$661$	−9.79161	−	30.1355i	−0.380850	−	1.17213i	0.558597	−	0.829439i	$-0.311340\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	26.8695	+	45.6794i	1.04195	+	1.77137i
$666$		0			0
$667$	−22.5702	+	31.0652i	−0.873922	+	1.20285i
$668$		0			0
$669$		0			0
$670$		0			0
$671$	−35.9790	+	26.1403i	−1.38895	+	1.00913i
$672$		0			0
$673$	−1.88857	+	0.613635i	−0.0727992	+	0.0236539i	−0.345190	−	0.938533i	$-0.612186\pi$
$673$	−1.88857	+	0.613635i	−0.0727992	+	0.0236539i	0.272391	+	0.962187i	$0.412186\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	37.5057	−	12.1864i	1.44146	−	0.468360i	0.519110	−	0.854708i	$-0.326264\pi$
$677$	37.5057	−	12.1864i	1.44146	−	0.468360i	0.922353	+	0.386348i	$0.126264\pi$
$678$		0			0
$679$	−34.8885	+	25.3480i	−1.33890	+	0.972767i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−7.22768	+	9.94805i	−0.276559	+	0.380651i	−0.924590	−	0.380962i	$-0.875593\pi$
$683$	−7.22768	+	9.94805i	−0.276559	+	0.380651i	0.648031	+	0.761614i	$0.275593\pi$
$684$		0			0
$685$	−0.271894	+	0.306940i	−0.0103885	+	0.0117276i
$686$		0			0
$687$		0			0
$688$		0			0
$689$	0.733276	+	2.25679i	0.0279356	+	0.0859769i
$690$		0			0
$691$	4.85334	−	14.9371i	0.184630	−	0.568232i	−0.815312	−	0.579022i	$-0.803435\pi$
$691$	4.85334	−	14.9371i	0.184630	−	0.568232i	0.999942	+	0.0107896i	$0.00343451\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	18.2949	+	1.77294i	0.693966	+	0.0672514i
$696$		0			0
$697$	−20.5177	−	28.2402i	−0.777164	−	1.06967i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	26.4222			0.997953			0.498976	−	0.866616i	$-0.333709\pi$
$701$	26.4222			0.997953			0.498976	+	0.866616i	$0.333709\pi$
$702$		0			0
$703$	19.5003	+	26.8399i	0.735469	+	1.01229i
$704$		0			0
$705$		0			0
$706$		0			0
$707$			29.3749i			1.10476i
$708$		0			0
$709$	−15.0638	+	46.3616i	−0.565733	+	1.74115i	0.100030	+	0.994984i	$0.468106\pi$
$709$	−15.0638	+	46.3616i	−0.565733	+	1.74115i	−0.665763	+	0.746163i	$0.731894\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−52.4677	−	17.0478i	−1.96493	−	0.638445i
$714$		0			0
$715$	−5.39452	−	2.34954i	−0.201744	−	0.0878680i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	27.7117	+	20.1337i	1.03347	+	0.750861i	0.969001	−	0.247058i	$-0.0794639\pi$
$719$	27.7117	+	20.1337i	1.03347	+	0.750861i	0.0644713	+	0.997920i	$0.479464\pi$
$720$		0			0
$721$	−40.8197	+	29.6572i	−1.52020	+	1.10449i
$722$		0			0
$723$		0			0
$724$		0			0
$725$	−34.4684	−	6.74391i	−1.28012	−	0.250463i
$726$		0			0
$727$	−20.3168	+	6.60134i	−0.753510	+	0.244830i	−0.660491	−	0.750834i	$-0.729652\pi$
$727$	−20.3168	+	6.60134i	−0.753510	+	0.244830i	−0.0930190	+	0.995664i	$0.529652\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−20.5381	−	14.9218i	−0.759629	−	0.551903i
$732$		0			0
$733$	18.3875	−	25.3083i	0.679159	−	0.934782i	−0.320765	−	0.947159i	$-0.603940\pi$
$733$	18.3875	−	25.3083i	0.679159	−	0.934782i	0.999923	+	0.0123772i	$0.00393990\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−17.1849	−	5.58370i	−0.633013	−	0.205678i
$738$		0			0
$739$	−0.406330	−	1.25056i	−0.0149471	−	0.0460025i	0.943305	−	0.331928i	$-0.107699\pi$
$739$	−0.406330	−	1.25056i	−0.0149471	−	0.0460025i	−0.958252	+	0.285925i	$0.907699\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$		−	8.76431i		−	0.321531i	−0.986993	−	0.160766i	$-0.948604\pi$
$743$		−	8.76431i		−	0.321531i	0.986993	−	0.160766i	$-0.0513963\pi$
$744$		0			0
$745$	−4.94473	+	11.3530i	−0.181161	+	0.415943i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	−16.7085			−0.610515
$750$		0			0
$751$	44.6570			1.62956			0.814779	−	0.579772i	$-0.196858\pi$
$751$	44.6570			1.62956			0.814779	+	0.579772i	$0.196858\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	−11.4947	+	26.3917i	−0.418336	+	0.960494i
$756$		0			0
$757$		−	7.70729i		−	0.280126i	−0.990143	−	0.140063i	$-0.955269\pi$
$757$		−	7.70729i		−	0.280126i	0.990143	−	0.140063i	$-0.0447305\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−12.2344	−	37.6537i	−0.443498	−	1.36495i	−0.884123	−	0.467254i	$-0.845243\pi$
$761$	−12.2344	−	37.6537i	−0.443498	−	1.36495i	0.440625	−	0.897691i	$-0.354757\pi$
$762$		0			0
$763$	−3.04140	−	0.988210i	−0.110106	−	0.0357756i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	0.306068	−	0.421266i	0.0110515	−	0.0152110i
$768$		0			0
$769$	23.7336	+	17.2435i	0.855855	+	0.621815i	0.926754	−	0.375668i	$-0.122587\pi$
$769$	23.7336	+	17.2435i	0.855855	+	0.621815i	−0.0708991	+	0.997483i	$0.522587\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	−10.3762	+	3.37142i	−0.373205	+	0.121262i	−0.489613	−	0.871940i	$-0.662862\pi$
$773$	−10.3762	+	3.37142i	−0.373205	+	0.121262i	0.116408	+	0.993201i	$0.462862\pi$
$774$		0			0
$775$	−6.08801	−	50.0914i	−0.218688	−	1.79934i
$776$		0			0
$777$		0			0
$778$		0			0
$779$	30.6010	−	22.2329i	1.09639	−	0.796577i
$780$		0			0
$781$	−9.57543	−	6.95696i	−0.342636	−	0.248940i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	−30.0118	−	13.0714i	−1.07117	−	0.466539i
$786$		0			0
$787$	−35.8619	−	11.6522i	−1.27834	−	0.415358i	−0.410344	−	0.911931i	$-0.634591\pi$
$787$	−35.8619	−	11.6522i	−1.27834	−	0.415358i	−0.867995	+	0.496573i	$0.834591\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	1.45512	−	4.47841i	0.0517383	−	0.159234i
$792$		0			0
$793$			8.24980i			0.292959i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−28.9432	−	39.8369i	−1.02522	−	1.41110i	−0.908477	−	0.417935i	$-0.862754\pi$
$797$	−28.9432	−	39.8369i	−1.02522	−	1.41110i	−0.116745	−	0.993162i	$-0.537246\pi$
$798$		0			0
$799$	51.1986			1.81128
$800$		0			0
$801$		0			0
$802$		0			0
$803$	23.7922	+	32.7472i	0.839610	+	1.15562i
$804$		0			0
$805$	−50.2798	−	4.87256i	−1.77213	−	0.171735i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	8.33675	−	25.6579i	0.293105	−	0.902083i	−0.690747	−	0.723097i	$-0.742718\pi$
$809$	8.33675	−	25.6579i	0.293105	−	0.902083i	0.983852	−	0.178987i	$-0.0572819\pi$
$810$		0			0
$811$	2.52546	+	7.77257i	0.0886809	+	0.272932i	0.985555	−	0.169353i	$-0.0541679\pi$
$811$	2.52546	+	7.77257i	0.0886809	+	0.272932i	−0.896875	+	0.442285i	$0.854168\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	6.58943	−	7.43879i	0.230818	−	0.260569i
$816$		0			0
$817$	16.1692	−	22.2550i	0.565689	−	0.778604i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	−35.4256	+	25.7382i	−1.23636	+	0.898269i	−0.997350	−	0.0727478i	$-0.976823\pi$
$821$	−35.4256	+	25.7382i	−1.23636	+	0.898269i	−0.239011	+	0.971017i	$0.576823\pi$
$822$		0			0
$823$	15.6512	−	5.08540i	0.545568	−	0.177266i	−0.0232493	−	0.999730i	$-0.507401\pi$
$823$	15.6512	−	5.08540i	0.545568	−	0.177266i	0.568817	+	0.822464i	$0.307401\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−3.82167	+	1.24174i	−0.132893	+	0.0431794i	−0.374708	−	0.927143i	$-0.622257\pi$
$827$	−3.82167	+	1.24174i	−0.132893	+	0.0431794i	0.241816	+	0.970322i	$0.422257\pi$
$828$		0			0
$829$	30.3103	−	22.0217i	1.05272	−	0.764847i	0.0799935	−	0.996795i	$-0.474510\pi$
$829$	30.3103	−	22.0217i	1.05272	−	0.764847i	0.972728	+	0.231948i	$0.0745101\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−31.3539	+	43.1550i	−1.08635	+	1.49523i
$834$		0			0
$835$	−26.9431	−	45.8046i	−0.932404	−	1.58513i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	−3.58335	−	11.0284i	−0.123711	−	0.380743i	0.869953	−	0.493135i	$-0.164149\pi$
$839$	−3.58335	−	11.0284i	−0.123711	−	0.380743i	−0.993664	+	0.112391i	$0.964149\pi$
$840$		0			0
$841$	6.28600	−	19.3463i	0.216759	−	0.667114i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	24.1148	−	14.1848i	0.829576	−	0.487972i
$846$		0			0
$847$	7.73709	+	10.6492i	0.265849	+	0.365910i
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−31.6230			−1.08402
$852$		0			0
$853$	0.777036	+	1.06950i	0.0266052	+	0.0366189i	0.822112	−	0.569325i	$-0.192795\pi$
$853$	0.777036	+	1.06950i	0.0266052	+	0.0366189i	−0.795507	+	0.605944i	$0.792795\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$			15.5623i			0.531598i	0.964028	+	0.265799i	$0.0856358\pi$
$857$			15.5623i			0.531598i	−0.964028	+	0.265799i	$0.914364\pi$
$858$		0			0
$859$	8.46169	−	26.0424i	0.288709	−	0.888556i	−0.696553	−	0.717505i	$-0.745284\pi$
$859$	8.46169	−	26.0424i	0.288709	−	0.888556i	0.985262	−	0.171050i	$-0.0547161\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	−30.4617	−	9.89760i	−1.03693	−	0.336918i	−0.259402	−	0.965769i	$-0.583525\pi$
$863$	−30.4617	−	9.89760i	−1.03693	−	0.336918i	−0.777526	+	0.628851i	$0.783525\pi$
$864$		0			0
$865$	3.25398	−	33.5777i	0.110639	−	1.14168i
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−27.8038	−	20.2006i	−0.943178	−	0.685259i
$870$		0			0
$871$	−2.71175	+	1.97020i	−0.0918842	+	0.0667578i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−15.3431	−	43.5827i	−0.518692	−	1.47336i
$876$		0			0
$877$	−4.08119	+	1.32606i	−0.137812	+	0.0447778i	−0.377111	−	0.926168i	$-0.623082\pi$
$877$	−4.08119	+	1.32606i	−0.137812	+	0.0447778i	0.239299	+	0.970946i	$0.423082\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	−43.7520	−	31.7877i	−1.47404	−	1.07095i	−0.979417	−	0.201848i	$-0.935305\pi$
$881$	−43.7520	−	31.7877i	−1.47404	−	1.07095i	−0.494625	−	0.869106i	$-0.664695\pi$
$882$		0			0
$883$	−18.6340	+	25.6474i	−0.627083	+	0.863105i	−0.997845	−	0.0656228i	$-0.979097\pi$
$883$	−18.6340	+	25.6474i	−0.627083	+	0.863105i	0.370762	+	0.928728i	$0.379097\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−5.11670	−	1.66252i	−0.171802	−	0.0558218i	0.221853	−	0.975080i	$-0.428789\pi$
$887$	−5.11670	−	1.66252i	−0.171802	−	0.0558218i	−0.393655	+	0.919258i	$0.628789\pi$
$888$		0			0
$889$	−0.686891	−	2.11403i	−0.0230376	−	0.0709024i
$890$		0			0
$891$		0			0
$892$		0			0
$893$			55.4786i			1.85652i
$894$		0			0
$895$	−8.06785	−	36.4978i	−0.269678	−	1.21999i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	70.8900			2.36432
$900$		0			0
$901$	17.9753			0.598846
$902$		0			0
$903$		0			0
$904$		0			0
$905$	20.0297	−	11.7818i	0.665809	−	0.391641i
$906$		0			0
$907$			45.7593i			1.51941i	0.650266	+	0.759706i	$0.274657\pi$
$907$			45.7593i			1.51941i	−0.650266	+	0.759706i	$0.725343\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−0.669870	−	2.06165i	−0.0221938	−	0.0683054i	0.939346	−	0.342970i	$-0.111433\pi$
$911$	−0.669870	−	2.06165i	−0.0221938	−	0.0683054i	−0.961540	+	0.274665i	$0.911433\pi$
$912$		0			0
$913$	30.2354	+	9.82408i	1.00065	+	0.325130i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−16.3295	+	22.4757i	−0.539249	+	0.742213i
$918$		0			0
$919$	−15.9053	−	11.5559i	−0.524666	−	0.381192i	0.293693	−	0.955900i	$-0.405116\pi$
$919$	−15.9053	−	11.5559i	−0.524666	−	0.381192i	−0.818359	+	0.574708i	$0.805116\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	−2.08814	+	0.678477i	−0.0687319	+	0.0223324i
$924$		0			0
$925$	−12.1918	−	26.2294i	−0.400863	−	0.862418i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	−35.2728	+	25.6272i	−1.15726	+	0.840800i	−0.989429	−	0.145016i	$-0.953677\pi$
$929$	−35.2728	+	25.6272i	−1.15726	+	0.840800i	−0.167832	+	0.985816i	$0.553677\pi$
$930$		0			0
$931$	−46.7626	−	33.9750i	−1.53258	−	1.11349i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−29.5549	+	33.3644i	−0.966547	+	1.09113i
$936$		0			0
$937$	−40.0143	−	13.0014i	−1.30721	−	0.424738i	−0.429126	−	0.903245i	$-0.641178\pi$
$937$	−40.0143	−	13.0014i	−1.30721	−	0.424738i	−0.878084	+	0.478506i	$0.841178\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−15.1162	+	46.5228i	−0.492773	+	1.51660i	0.327625	+	0.944808i	$0.393752\pi$
$941$	−15.1162	+	46.5228i	−0.492773	+	1.51660i	−0.820399	+	0.571792i	$0.806248\pi$
$942$		0			0
$943$			36.0544i			1.17409i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	4.18115	+	5.75486i	0.135869	+	0.187008i	0.871530	−	0.490342i	$-0.163128\pi$
$947$	4.18115	+	5.75486i	0.135869	+	0.187008i	−0.735661	+	0.677350i	$0.763128\pi$
$948$		0			0
$949$	7.50878			0.243745
$950$		0			0
$951$		0			0
$952$		0			0
$953$	−13.0707	−	17.9903i	−0.423402	−	0.582762i	0.543021	−	0.839719i	$-0.317280\pi$
$953$	−13.0707	−	17.9903i	−0.423402	−	0.582762i	−0.966423	+	0.256957i	$0.917280\pi$
$954$		0			0
$955$	33.0672	+	29.2916i	1.07003	+	0.947855i
$956$		0			0
$957$		0			0
$958$		0			0
$959$	0.234186	−	0.720751i	0.00756226	−	0.0232743i
$960$		0			0
$961$	21.8934	+	67.3809i	0.706238	+	2.17358i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	4.58290	+	1.99605i	0.147529	+	0.0642550i
$966$		0			0
$967$	−8.17914	+	11.2576i	−0.263023	+	0.362021i	−0.920019	−	0.391874i	$-0.871827\pi$
$967$	−8.17914	+	11.2576i	−0.263023	+	0.362021i	0.656996	+	0.753894i	$0.271827\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	19.6548	−	14.2801i	0.630754	−	0.458270i	−0.225907	−	0.974149i	$-0.572535\pi$
$971$	19.6548	−	14.2801i	0.630754	−	0.458270i	0.856661	+	0.515879i	$0.172535\pi$
$972$		0			0
$973$	−32.3081	+	10.4975i	−1.03575	+	0.336535i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−44.0637	+	14.3172i	−1.40972	+	0.458047i	−0.912322	−	0.409473i	$-0.865713\pi$
$977$	−44.0637	+	14.3172i	−1.40972	+	0.458047i	−0.497402	+	0.867520i	$0.665713\pi$
$978$		0			0
$979$	10.3228	−	7.49993i	0.329917	−	0.239699i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−24.1334	+	33.2168i	−0.769736	+	1.05945i	0.226605	+	0.973987i	$0.427237\pi$
$983$	−24.1334	+	33.2168i	−0.769736	+	1.05945i	−0.996341	+	0.0854644i	$0.972763\pi$
$984$		0			0
$985$	49.6863	−	10.9832i	1.58314	−	0.349953i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	8.10275	+	24.9377i	0.257652	+	0.792972i
$990$		0			0
$991$	6.26579	−	19.2841i	0.199039	−	0.612580i	−0.800866	−	0.598843i	$-0.795627\pi$
$991$	6.26579	−	19.2841i	0.199039	−	0.612580i	0.999906	−	0.0137370i	$-0.00437276\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	20.3731	−	46.7765i	0.645872	−	1.48291i
$996$		0			0
$997$	−14.3204	−	19.7104i	−0.453533	−	0.624234i	0.519619	−	0.854398i	$-0.326074\pi$
$997$	−14.3204	−	19.7104i	−0.453533	−	0.624234i	−0.973152	+	0.230164i	$0.926074\pi$
$998$		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.469.3		24
3.2	odd	2		300.2.o.a.169.5	✓	24
15.2	even	4		1500.2.m.d.901.6		24
15.8	even	4		1500.2.m.c.901.1		24
15.14	odd	2		1500.2.o.c.349.2		24
25.4	even	10	inner	900.2.w.c.829.3		24
75.2	even	20		7500.2.a.m.1.12		12
75.11	odd	10		7500.2.d.g.1249.1		24
75.14	odd	10		7500.2.d.g.1249.24		24
75.23	even	20		7500.2.a.n.1.1		12
75.29	odd	10		300.2.o.a.229.5	yes	24
75.47	even	20		1500.2.m.d.601.6		24
75.53	even	20		1500.2.m.c.601.1		24
75.71	odd	10		1500.2.o.c.649.2		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.o.a.169.5	✓	24	3.2	odd	2
300.2.o.a.229.5	yes	24	75.29	odd	10
900.2.w.c.469.3		24	1.1	even	1	trivial
900.2.w.c.829.3		24	25.4	even	10	inner
1500.2.m.c.601.1		24	75.53	even	20
1500.2.m.c.901.1		24	15.8	even	4
1500.2.m.d.601.6		24	75.47	even	20
1500.2.m.d.901.6		24	15.2	even	4
1500.2.o.c.349.2		24	15.14	odd	2
1500.2.o.c.649.2		24	75.71	odd	10
7500.2.a.m.1.12		12	75.2	even	20
7500.2.a.n.1.1		12	75.23	even	20
7500.2.d.g.1249.1		24	75.11	odd	10
7500.2.d.g.1249.24		24	75.14	odd	10

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.892889 + 2.05006i) q^{5} -4.13266i q^{7} +O(q^{10})\)	\(q+(-0.892889 + 2.05006i) q^{5} -4.13266i q^{7} +(1.16386 + 3.58198i) q^{11} +(0.664470 + 0.215899i) q^{13} +(3.11086 - 4.28173i) q^{17} +(4.63966 + 3.37091i) q^{19} +(-5.19894 + 1.68924i) q^{23} +(-3.40550 - 3.66095i) q^{25} +(5.68284 - 4.12883i) q^{29} +(8.16460 + 5.93193i) q^{31} +(8.47220 + 3.69001i) q^{35} +(5.50175 + 1.78763i) q^{37} +(2.03813 - 6.27271i) q^{41} -4.79668i q^{43} +(5.68611 + 7.82626i) q^{47} -10.0789 q^{49} +(1.99634 + 2.74773i) q^{53} +(-8.38247 - 0.812336i) q^{55} +(0.230309 - 0.708820i) q^{59} +(3.64886 + 11.2300i) q^{61} +(-1.03591 + 1.16943i) q^{65} +(-2.81995 + 3.88133i) q^{67} +(-2.54239 + 1.84715i) q^{71} +(10.2213 - 3.32110i) q^{73} +(14.8031 - 4.80982i) q^{77} +(-7.38222 + 5.36349i) q^{79} +(4.96148 - 6.82889i) q^{83} +(6.00015 + 10.2006i) q^{85} +(-1.04690 - 3.22202i) q^{89} +(0.892239 - 2.74603i) q^{91} +(-11.0533 + 6.50174i) q^{95} +(-6.13358 - 8.44215i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 2 q^{5}+O(q^{10}) \) 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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