LMFDB - Embedded newform 9025.2.a.ct.1.22

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9025,2,Mod(1,9025)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9025, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9025.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 9025 = 5^{2} \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9025.a (trivial)

Newform invariants

comment:select newform

sage:traces = [24,0,0,18,0,-12,0,0,12,0,12,0,0,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(14)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$72.0649878242$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 95)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	9025.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.32462 q^{2} +1.14858 q^{3} +3.40387 q^{4} +2.67001 q^{6} +0.143302 q^{7} +3.26348 q^{8} -1.68077 q^{9} -2.81557 q^{11} +3.90962 q^{12} +1.70854 q^{13} +0.333123 q^{14} +0.778610 q^{16} -3.55886 q^{17} -3.90715 q^{18} +0.164594 q^{21} -6.54515 q^{22} -7.19394 q^{23} +3.74836 q^{24} +3.97171 q^{26} -5.37623 q^{27} +0.487782 q^{28} -7.57154 q^{29} -4.84686 q^{31} -4.71698 q^{32} -3.23391 q^{33} -8.27302 q^{34} -5.72111 q^{36} +9.49127 q^{37} +1.96239 q^{39} +0.187320 q^{41} +0.382619 q^{42} -10.9943 q^{43} -9.58385 q^{44} -16.7232 q^{46} +3.67032 q^{47} +0.894296 q^{48} -6.97946 q^{49} -4.08764 q^{51} +5.81566 q^{52} +1.64322 q^{53} -12.4977 q^{54} +0.467663 q^{56} -17.6010 q^{58} +5.36637 q^{59} +10.1127 q^{61} -11.2671 q^{62} -0.240857 q^{63} -12.5224 q^{64} -7.51762 q^{66} +6.00805 q^{67} -12.1139 q^{68} -8.26281 q^{69} -0.540979 q^{71} -5.48514 q^{72} -10.4674 q^{73} +22.0636 q^{74} -0.403477 q^{77} +4.56183 q^{78} +11.6088 q^{79} -1.13273 q^{81} +0.435449 q^{82} -7.59579 q^{83} +0.560257 q^{84} -25.5576 q^{86} -8.69652 q^{87} -9.18856 q^{88} -1.44684 q^{89} +0.244837 q^{91} -24.4873 q^{92} -5.56701 q^{93} +8.53210 q^{94} -5.41783 q^{96} +8.80212 q^{97} -16.2246 q^{98} +4.73232 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots - 120 q^{96}+O(q^{100}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

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 $

$2$	2.32462	1.64376	0.821878	−	0.569663i	$-0.192926\pi$
$2$	2.32462	1.64376	0.821878	+	0.569663i	$0.192926\pi$
$3$	1.14858	0.663133	0.331566	−	0.943432i	$-0.392423\pi$
$3$	1.14858	0.663133	0.331566	+	0.943432i	$0.392423\pi$
$4$	3.40387	1.70194
$5$	0	0
$5$	0	0
$6$	2.67001	1.09003
$7$	0.143302	0.0541631	0.0270816	−	0.999633i	$-0.491379\pi$
$7$	0.143302	0.0541631	0.0270816	+	0.999633i	$0.491379\pi$
$8$	3.26348	1.15381
$9$	−1.68077	−0.560255
$10$	0	0
$11$	−2.81557	−0.848927	−0.424463	−	0.905445i	$-0.639537\pi$
$11$	−2.81557	−0.848927	−0.424463	+	0.905445i	$0.639537\pi$
$12$	3.90962	1.12861
$13$	1.70854	0.473864	0.236932	−	0.971526i	$-0.423858\pi$
$13$	1.70854	0.473864	0.236932	+	0.971526i	$0.423858\pi$
$14$	0.333123	0.0890310
$15$	0	0
$16$	0.778610	0.194653
$17$	−3.55886	−0.863151	−0.431576	−	0.902077i	$-0.642042\pi$
$17$	−3.55886	−0.863151	−0.431576	+	0.902077i	$0.642042\pi$
$18$	−3.90715	−0.920923
$19$	0	0
$19$	0	0
$20$	0	0
$21$	0.164594	0.0359173
$22$	−6.54515	−1.39543
$23$	−7.19394	−1.50004	−0.750020	−	0.661415i	$-0.769956\pi$
$23$	−7.19394	−1.50004	−0.750020	+	0.661415i	$0.769956\pi$
$24$	3.74836	0.765132
$25$	0	0
$26$	3.97171	0.778917
$27$	−5.37623	−1.03466
$28$	0.487782	0.0921822
$29$	−7.57154	−1.40600	−0.703000	−	0.711190i	$-0.748157\pi$
$29$	−7.57154	−1.40600	−0.703000	+	0.711190i	$0.748157\pi$
$30$	0	0
$31$	−4.84686	−0.870522	−0.435261	−	0.900304i	$-0.643344\pi$
$31$	−4.84686	−0.870522	−0.435261	+	0.900304i	$0.643344\pi$
$32$	−4.71698	−0.833852
$33$	−3.23391	−0.562951
$34$	−8.27302	−1.41881
$35$	0	0
$36$	−5.72111	−0.953519
$37$	9.49127	1.56035	0.780177	−	0.625559i	$-0.215129\pi$
$37$	9.49127	1.56035	0.780177	+	0.625559i	$0.215129\pi$
$38$	0	0
$39$	1.96239	0.314235
$40$	0	0
$41$	0.187320	0.0292545	0.0146272	−	0.999893i	$-0.495344\pi$
$41$	0.187320	0.0292545	0.0146272	+	0.999893i	$0.495344\pi$
$42$	0.382619	0.0590393
$43$	−10.9943	−1.67662	−0.838309	−	0.545196i	$-0.816455\pi$
$43$	−10.9943	−1.67662	−0.838309	+	0.545196i	$0.816455\pi$
$44$	−9.58385	−1.44482
$45$	0	0
$46$	−16.7232	−2.46570
$47$	3.67032	0.535371	0.267685	−	0.963506i	$-0.413741\pi$
$47$	3.67032	0.535371	0.267685	+	0.963506i	$0.413741\pi$
$48$	0.894296	0.129080
$49$	−6.97946	−0.997066
$50$	0	0
$51$	−4.08764	−0.572384
$52$	5.81566	0.806486
$53$	1.64322	0.225714	0.112857	−	0.993611i	$-0.464000\pi$
$53$	1.64322	0.225714	0.112857	+	0.993611i	$0.464000\pi$
$54$	−12.4977	−1.70072
$55$	0	0
$56$	0.467663	0.0624941
$57$	0	0
$58$	−17.6010	−2.31112
$59$	5.36637	0.698642	0.349321	−	0.937003i	$-0.386412\pi$
$59$	5.36637	0.698642	0.349321	+	0.937003i	$0.386412\pi$
$60$	0	0
$61$	10.1127	1.29480	0.647402	−	0.762148i	$-0.275855\pi$
$61$	10.1127	1.29480	0.647402	+	0.762148i	$0.275855\pi$
$62$	−11.2671	−1.43093
$63$	−0.240857	−0.0303452
$64$	−12.5224	−1.56530
$65$	0	0
$66$	−7.51762	−0.925355
$67$	6.00805	0.734001	0.367000	−	0.930221i	$-0.380385\pi$
$67$	6.00805	0.734001	0.367000	+	0.930221i	$0.380385\pi$
$68$	−12.1139	−1.46903
$69$	−8.26281	−0.994725
$70$	0	0
$71$	−0.540979	−0.0642024	−0.0321012	−	0.999485i	$-0.510220\pi$
$71$	−0.540979	−0.0642024	−0.0321012	+	0.999485i	$0.510220\pi$
$72$	−5.48514	−0.646430
$73$	−10.4674	−1.22512	−0.612559	−	0.790425i	$-0.709860\pi$
$73$	−10.4674	−1.22512	−0.612559	+	0.790425i	$0.709860\pi$
$74$	22.0636	2.56484
$75$	0	0
$76$	0	0
$77$	−0.403477	−0.0459805
$78$	4.56183	0.516525
$79$	11.6088	1.30610	0.653048	−	0.757317i	$-0.273490\pi$
$79$	11.6088	1.30610	0.653048	+	0.757317i	$0.273490\pi$
$80$	0	0
$81$	−1.13273	−0.125859
$82$	0.435449	0.0480873
$83$	−7.59579	−0.833746	−0.416873	−	0.908965i	$-0.636874\pi$
$83$	−7.59579	−0.833746	−0.416873	+	0.908965i	$0.636874\pi$
$84$	0.560257	0.0611290
$85$	0	0
$86$	−25.5576	−2.75595
$87$	−8.69652	−0.932365
$88$	−9.18856	−0.979504
$89$	−1.44684	−0.153365	−0.0766823	−	0.997056i	$-0.524433\pi$
$89$	−1.44684	−0.153365	−0.0766823	+	0.997056i	$0.524433\pi$
$90$	0	0
$91$	0.244837	0.0256659
$92$	−24.4873	−2.55297
$93$	−5.56701	−0.577272
$94$	8.53210	0.880019
$95$	0	0
$96$	−5.41783	−0.552955
$97$	8.80212	0.893720	0.446860	−	0.894604i	$-0.352542\pi$
$97$	8.80212	0.893720	0.446860	+	0.894604i	$0.352542\pi$
$98$	−16.2246	−1.63893
$99$	4.73232	0.475616
$100$	0	0
$101$	−2.87795	−0.286367	−0.143183	−	0.989696i	$-0.545734\pi$
$101$	−2.87795	−0.286367	−0.143183	+	0.989696i	$0.545734\pi$
$102$	−9.50222	−0.940860
$103$	1.19966	0.118206	0.0591032	−	0.998252i	$-0.481176\pi$
$103$	1.19966	0.118206	0.0591032	+	0.998252i	$0.481176\pi$
$104$	5.57578	0.546751
$105$	0	0
$106$	3.81987	0.371019
$107$	−4.09536	−0.395913	−0.197957	−	0.980211i	$-0.563430\pi$
$107$	−4.09536	−0.395913	−0.197957	+	0.980211i	$0.563430\pi$
$108$	−18.3000	−1.76092
$109$	16.1941	1.55111	0.775555	−	0.631280i	$-0.217470\pi$
$109$	16.1941	1.55111	0.775555	+	0.631280i	$0.217470\pi$
$110$	0	0
$111$	10.9015	1.03472
$112$	0.111576	0.0105430
$113$	3.11845	0.293359	0.146680	−	0.989184i	$-0.453141\pi$
$113$	3.11845	0.293359	0.146680	+	0.989184i	$0.453141\pi$
$114$	0	0
$115$	0	0
$116$	−25.7726	−2.39292
$117$	−2.87166	−0.265485
$118$	12.4748	1.14840
$119$	−0.509993	−0.0467509
$120$	0	0
$121$	−3.07255	−0.279323
$122$	23.5083	2.12834
$123$	0.215152	0.0193996
$124$	−16.4981	−1.48157
$125$	0	0
$126$	−0.559902	−0.0498801
$127$	−8.16019	−0.724100	−0.362050	−	0.932159i	$-0.617923\pi$
$127$	−8.16019	−0.724100	−0.362050	+	0.932159i	$0.617923\pi$
$128$	−19.6760	−1.73913
$129$	−12.6278	−1.11182
$130$	0	0
$131$	2.61996	0.228907	0.114453	−	0.993429i	$-0.463488\pi$
$131$	2.61996	0.228907	0.114453	+	0.993429i	$0.463488\pi$
$132$	−11.0078	−0.958108
$133$	0	0
$134$	13.9665	1.20652
$135$	0	0
$136$	−11.6143	−0.995916
$137$	12.3205	1.05261	0.526305	−	0.850296i	$-0.323577\pi$
$137$	12.3205	1.05261	0.526305	+	0.850296i	$0.323577\pi$
$138$	−19.2079	−1.63509
$139$	7.95376	0.674629	0.337314	−	0.941392i	$-0.390481\pi$
$139$	7.95376	0.674629	0.337314	+	0.941392i	$0.390481\pi$
$140$	0	0
$141$	4.21565	0.355022
$142$	−1.25757	−0.105533
$143$	−4.81052	−0.402276
$144$	−1.30866	−0.109055
$145$	0	0
$146$	−24.3328	−2.01380
$147$	−8.01647	−0.661187
$148$	32.3071	2.65562
$149$	−4.19620	−0.343766	−0.171883	−	0.985117i	$-0.554985\pi$
$149$	−4.19620	−0.343766	−0.171883	+	0.985117i	$0.554985\pi$
$150$	0	0
$151$	2.86140	0.232857	0.116429	−	0.993199i	$-0.462855\pi$
$151$	2.86140	0.232857	0.116429	+	0.993199i	$0.462855\pi$
$152$	0	0
$153$	5.98161	0.483585
$154$	−0.937933	−0.0755808
$155$	0	0
$156$	6.67974	0.534807
$157$	11.5244	0.919744	0.459872	−	0.887985i	$-0.347895\pi$
$157$	11.5244	0.919744	0.459872	+	0.887985i	$0.347895\pi$
$158$	26.9862	2.14690
$159$	1.88737	0.149678
$160$	0	0
$161$	−1.03091	−0.0812468
$162$	−2.63318	−0.206882
$163$	−18.9195	−1.48189	−0.740944	−	0.671567i	$-0.765621\pi$
$163$	−18.9195	−1.48189	−0.740944	+	0.671567i	$0.765621\pi$
$164$	0.637614	0.0497893
$165$	0	0
$166$	−17.6573	−1.37048
$167$	15.0690	1.16607	0.583036	−	0.812447i	$-0.301865\pi$
$167$	15.0690	1.16607	0.583036	+	0.812447i	$0.301865\pi$
$168$	0.537148	0.0414419
$169$	−10.0809	−0.775453
$170$	0	0
$171$	0	0
$172$	−37.4233	−2.85350
$173$	21.6950	1.64944	0.824719	−	0.565542i	$-0.191333\pi$
$173$	21.6950	1.64944	0.824719	+	0.565542i	$0.191333\pi$
$174$	−20.2161	−1.53258
$175$	0	0
$176$	−2.19223	−0.165246
$177$	6.16370	0.463292
$178$	−3.36336	−0.252094
$179$	−22.8790	−1.71006	−0.855028	−	0.518581i	$-0.826460\pi$
$179$	−22.8790	−1.71006	−0.855028	+	0.518581i	$0.826460\pi$
$180$	0	0
$181$	11.5660	0.859693	0.429847	−	0.902902i	$-0.358568\pi$
$181$	11.5660	0.859693	0.429847	+	0.902902i	$0.358568\pi$
$182$	0.569155	0.0421886
$183$	11.6153	0.858627
$184$	−23.4773	−1.73077
$185$	0	0
$186$	−12.9412	−0.948894
$187$	10.0202	0.732752
$188$	12.4933	0.911167
$189$	−0.770425	−0.0560402
$190$	0	0
$191$	7.28958	0.527455	0.263728	−	0.964597i	$-0.415048\pi$
$191$	7.28958	0.527455	0.263728	+	0.964597i	$0.415048\pi$
$192$	−14.3830	−1.03800
$193$	−26.1862	−1.88493	−0.942464	−	0.334308i	$-0.891497\pi$
$193$	−26.1862	−1.88493	−0.942464	+	0.334308i	$0.891497\pi$
$194$	20.4616	1.46906
$195$	0	0
$196$	−23.7572	−1.69694
$197$	2.28820	0.163027	0.0815136	−	0.996672i	$-0.474025\pi$
$197$	2.28820	0.163027	0.0815136	+	0.996672i	$0.474025\pi$
$198$	11.0009	0.781797
$199$	−12.2469	−0.868159	−0.434079	−	0.900875i	$-0.642926\pi$
$199$	−12.2469	−0.868159	−0.434079	+	0.900875i	$0.642926\pi$
$200$	0	0
$201$	6.90073	0.486740
$202$	−6.69015	−0.470717
$203$	−1.08502	−0.0761533
$204$	−13.9138	−0.974161
$205$	0	0
$206$	2.78877	0.194302
$207$	12.0913	0.840405
$208$	1.33029	0.0922388
$209$	0	0
$210$	0	0
$211$	−3.00309	−0.206741	−0.103371	−	0.994643i	$-0.532963\pi$
$211$	−3.00309	−0.206741	−0.103371	+	0.994643i	$0.532963\pi$
$212$	5.59332	0.384151
$213$	−0.621357	−0.0425747
$214$	−9.52016	−0.650785
$215$	0	0
$216$	−17.5452	−1.19380
$217$	−0.694565	−0.0471502
$218$	37.6451	2.54965
$219$	−12.0227	−0.812416
$220$	0	0
$221$	−6.08046	−0.409016
$222$	25.3418	1.70083
$223$	2.19363	0.146897	0.0734483	−	0.997299i	$-0.476600\pi$
$223$	2.19363	0.146897	0.0734483	+	0.997299i	$0.476600\pi$
$224$	−0.675953	−0.0451640
$225$	0	0
$226$	7.24922	0.482211
$227$	−6.44357	−0.427675	−0.213838	−	0.976869i	$-0.568596\pi$
$227$	−6.44357	−0.427675	−0.213838	+	0.976869i	$0.568596\pi$
$228$	0	0
$229$	−1.54321	−0.101978	−0.0509892	−	0.998699i	$-0.516237\pi$
$229$	−1.54321	−0.101978	−0.0509892	+	0.998699i	$0.516237\pi$
$230$	0	0
$231$	−0.463426	−0.0304912
$232$	−24.7096	−1.62226
$233$	−20.4612	−1.34046	−0.670228	−	0.742155i	$-0.733804\pi$
$233$	−20.4612	−1.34046	−0.670228	+	0.742155i	$0.733804\pi$
$234$	−6.67552	−0.436392
$235$	0	0
$236$	18.2665	1.18904
$237$	13.3337	0.866115
$238$	−1.18554	−0.0768472
$239$	6.24066	0.403675	0.201837	−	0.979419i	$-0.435309\pi$
$239$	6.24066	0.403675	0.201837	+	0.979419i	$0.435309\pi$
$240$	0	0
$241$	26.3148	1.69508	0.847542	−	0.530728i	$-0.178081\pi$
$241$	26.3148	1.69508	0.847542	+	0.530728i	$0.178081\pi$
$242$	−7.14253	−0.459139
$243$	14.8277	0.951195
$244$	34.4225	2.20368
$245$	0	0
$246$	0.500147	0.0318882
$247$	0	0
$248$	−15.8176	−1.00442
$249$	−8.72437	−0.552884
$250$	0	0
$251$	−10.7064	−0.675779	−0.337889	−	0.941186i	$-0.609713\pi$
$251$	−10.7064	−0.675779	−0.337889	+	0.941186i	$0.609713\pi$
$252$	−0.819847	−0.0516455
$253$	20.2551	1.27342
$254$	−18.9694	−1.19024
$255$	0	0
$256$	−20.6943	−1.29340
$257$	−13.5240	−0.843603	−0.421802	−	0.906688i	$-0.638602\pi$
$257$	−13.5240	−0.843603	−0.421802	+	0.906688i	$0.638602\pi$
$258$	−29.3550	−1.82756
$259$	1.36012	0.0845136
$260$	0	0
$261$	12.7260	0.787719
$262$	6.09042	0.376267
$263$	6.54056	0.403308	0.201654	−	0.979457i	$-0.435368\pi$
$263$	6.54056	0.403308	0.201654	+	0.979457i	$0.435368\pi$
$264$	−10.5538	−0.649541
$265$	0	0
$266$	0	0
$267$	−1.66181	−0.101701
$268$	20.4507	1.24922
$269$	−14.4220	−0.879327	−0.439663	−	0.898163i	$-0.644902\pi$
$269$	−14.4220	−0.879327	−0.439663	+	0.898163i	$0.644902\pi$
$270$	0	0
$271$	−2.18429	−0.132686	−0.0663431	−	0.997797i	$-0.521133\pi$
$271$	−2.18429	−0.132686	−0.0663431	+	0.997797i	$0.521133\pi$
$272$	−2.77097	−0.168015
$273$	0.281215	0.0170199
$274$	28.6405	1.73024
$275$	0	0
$276$	−28.1256	−1.69296
$277$	−15.9746	−0.959823	−0.479911	−	0.877317i	$-0.659331\pi$
$277$	−15.9746	−0.959823	−0.479911	+	0.877317i	$0.659331\pi$
$278$	18.4895	1.10893
$279$	8.14644	0.487714
$280$	0	0
$281$	14.2569	0.850496	0.425248	−	0.905077i	$-0.360187\pi$
$281$	14.2569	0.850496	0.425248	+	0.905077i	$0.360187\pi$
$282$	9.79980	0.583569
$283$	−7.06732	−0.420108	−0.210054	−	0.977690i	$-0.567364\pi$
$283$	−7.06732	−0.420108	−0.210054	+	0.977690i	$0.567364\pi$
$284$	−1.84142	−0.109268
$285$	0	0
$286$	−11.1826	−0.661244
$287$	0.0268434	0.00158451
$288$	7.92814	0.467170
$289$	−4.33449	−0.254970
$290$	0	0
$291$	10.1099	0.592655
$292$	−35.6298	−2.08507
$293$	−0.976745	−0.0570621	−0.0285310	−	0.999593i	$-0.509083\pi$
$293$	−0.976745	−0.0570621	−0.0285310	+	0.999593i	$0.509083\pi$
$294$	−18.6353	−1.08683
$295$	0	0
$296$	30.9745	1.80036
$297$	15.1372	0.878347
$298$	−9.75458	−0.565068
$299$	−12.2911	−0.710815
$300$	0	0
$301$	−1.57551	−0.0908108
$302$	6.65167	0.382760
$303$	−3.30555	−0.189899
$304$	0	0
$305$	0	0
$306$	13.9050	0.794896
$307$	−28.4670	−1.62470	−0.812350	−	0.583171i	$-0.801812\pi$
$307$	−28.4670	−1.62470	−0.812350	+	0.583171i	$0.801812\pi$
$308$	−1.37339	−0.0782559
$309$	1.37791	0.0783865
$310$	0	0
$311$	−25.5461	−1.44858	−0.724292	−	0.689493i	$-0.757833\pi$
$311$	−25.5461	−1.44858	−0.724292	+	0.689493i	$0.757833\pi$
$312$	6.40423	0.362568
$313$	−14.9513	−0.845098	−0.422549	−	0.906340i	$-0.638865\pi$
$313$	−14.9513	−0.845098	−0.422549	+	0.906340i	$0.638865\pi$
$314$	26.7898	1.51184
$315$	0	0
$316$	39.5150	2.22289
$317$	−22.5401	−1.26598	−0.632990	−	0.774160i	$-0.718173\pi$
$317$	−22.5401	−1.26598	−0.632990	+	0.774160i	$0.718173\pi$
$318$	4.38743	0.246035
$319$	21.3182	1.19359
$320$	0	0
$321$	−4.70384	−0.262543
$322$	−2.39647	−0.133550
$323$	0	0
$324$	−3.85568	−0.214204
$325$	0	0
$326$	−43.9806	−2.43586
$327$	18.6002	1.02859
$328$	0.611315	0.0337542
$329$	0.525964	0.0289973
$330$	0	0
$331$	10.8681	0.597365	0.298682	−	0.954353i	$-0.403453\pi$
$331$	10.8681	0.597365	0.298682	+	0.954353i	$0.403453\pi$
$332$	−25.8551	−1.41898
$333$	−15.9526	−0.874196
$334$	35.0297	1.91674
$335$	0	0
$336$	0.128154	0.00699140
$337$	7.70906	0.419939	0.209970	−	0.977708i	$-0.432663\pi$
$337$	7.70906	0.419939	0.209970	+	0.977708i	$0.432663\pi$
$338$	−23.4343	−1.27466
$339$	3.58179	0.194536
$340$	0	0
$341$	13.6467	0.739010
$342$	0	0
$343$	−2.00329	−0.108167
$344$	−35.8797	−1.93450
$345$	0	0
$346$	50.4327	2.71128
$347$	−20.2699	−1.08814	−0.544072	−	0.839039i	$-0.683118\pi$
$347$	−20.2699	−1.08814	−0.544072	+	0.839039i	$0.683118\pi$
$348$	−29.6019	−1.58683
$349$	19.0503	1.01974	0.509870	−	0.860252i	$-0.329694\pi$
$349$	19.0503	1.01974	0.509870	+	0.860252i	$0.329694\pi$
$350$	0	0
$351$	−9.18551	−0.490286
$352$	13.2810	0.707880
$353$	18.1667	0.966917	0.483459	−	0.875367i	$-0.339380\pi$
$353$	18.1667	0.966917	0.483459	+	0.875367i	$0.339380\pi$
$354$	14.3283	0.761540
$355$	0	0
$356$	−4.92486	−0.261017
$357$	−0.585767	−0.0310021
$358$	−53.1851	−2.81092
$359$	−16.1318	−0.851406	−0.425703	−	0.904863i	$-0.639973\pi$
$359$	−16.1318	−0.851406	−0.425703	+	0.904863i	$0.639973\pi$
$360$	0	0
$361$	0	0
$362$	26.8866	1.41313
$363$	−3.52907	−0.185228
$364$	0.833396	0.0436818
$365$	0	0
$366$	27.0012	1.41137
$367$	32.2616	1.68404	0.842021	−	0.539445i	$-0.181366\pi$
$367$	32.2616	1.68404	0.842021	+	0.539445i	$0.181366\pi$
$368$	−5.60127	−0.291987
$369$	−0.314841	−0.0163900
$370$	0	0
$371$	0.235477	0.0122254
$372$	−18.9494	−0.982480
$373$	−2.38037	−0.123251	−0.0616253	−	0.998099i	$-0.519628\pi$
$373$	−2.38037	−0.123251	−0.0616253	+	0.998099i	$0.519628\pi$
$374$	23.2933	1.20447
$375$	0	0
$376$	11.9780	0.617718
$377$	−12.9363	−0.666253
$378$	−1.79095	−0.0921164
$379$	−17.7215	−0.910291	−0.455145	−	0.890417i	$-0.650413\pi$
$379$	−17.7215	−0.910291	−0.455145	+	0.890417i	$0.650413\pi$
$380$	0	0
$381$	−9.37263	−0.480174
$382$	16.9455	0.867009
$383$	−10.6646	−0.544934	−0.272467	−	0.962165i	$-0.587840\pi$
$383$	−10.6646	−0.544934	−0.272467	+	0.962165i	$0.587840\pi$
$384$	−22.5994	−1.15327
$385$	0	0
$386$	−60.8732	−3.09836
$387$	18.4789	0.939333
$388$	29.9613	1.52105
$389$	22.7313	1.15252	0.576262	−	0.817265i	$-0.304511\pi$
$389$	22.7313	1.15252	0.576262	+	0.817265i	$0.304511\pi$
$390$	0	0
$391$	25.6022	1.29476
$392$	−22.7773	−1.15043
$393$	3.00923	0.151796
$394$	5.31919	0.267977
$395$	0	0
$396$	16.1082	0.809468
$397$	−20.4405	−1.02588	−0.512939	−	0.858425i	$-0.671443\pi$
$397$	−20.4405	−1.02588	−0.512939	+	0.858425i	$0.671443\pi$
$398$	−28.4694	−1.42704
$399$	0	0
$400$	0	0
$401$	−16.6972	−0.833817	−0.416908	−	0.908949i	$-0.636886\pi$
$401$	−16.6972	−0.833817	−0.416908	+	0.908949i	$0.636886\pi$
$402$	16.0416	0.800082
$403$	−8.28106	−0.412509
$404$	−9.79618	−0.487378
$405$	0	0
$406$	−2.52226	−0.125178
$407$	−26.7233	−1.32463
$408$	−13.3399	−0.660424
$409$	17.6846	0.874447	0.437224	−	0.899353i	$-0.355962\pi$
$409$	17.6846	0.874447	0.437224	+	0.899353i	$0.355962\pi$
$410$	0	0
$411$	14.1511	0.698021
$412$	4.08350	0.201180
$413$	0.769012	0.0378406
$414$	28.1078	1.38142
$415$	0	0
$416$	−8.05915	−0.395133
$417$	9.13552	0.447369
$418$	0	0
$419$	−37.9339	−1.85319	−0.926596	−	0.376059i	$-0.877279\pi$
$419$	−37.9339	−1.85319	−0.926596	+	0.376059i	$0.877279\pi$
$420$	0	0
$421$	−11.5822	−0.564481	−0.282241	−	0.959344i	$-0.591078\pi$
$421$	−11.5822	−0.564481	−0.282241	+	0.959344i	$0.591078\pi$
$422$	−6.98106	−0.339833
$423$	−6.16894	−0.299944
$424$	5.36262	0.260432
$425$	0	0
$426$	−1.44442	−0.0699825
$427$	1.44918	0.0701306
$428$	−13.9401	−0.673819
$429$	−5.52526	−0.266762
$430$	0	0
$431$	−31.7898	−1.53126	−0.765629	−	0.643282i	$-0.777572\pi$
$431$	−31.7898	−1.53126	−0.765629	+	0.643282i	$0.777572\pi$
$432$	−4.18599	−0.201398
$433$	4.08848	0.196480	0.0982399	−	0.995163i	$-0.468679\pi$
$433$	4.08848	0.196480	0.0982399	+	0.995163i	$0.468679\pi$
$434$	−1.61460	−0.0775034
$435$	0	0
$436$	55.1226	2.63989
$437$	0	0
$438$	−27.9481	−1.33541
$439$	11.7557	0.561070	0.280535	−	0.959844i	$-0.409488\pi$
$439$	11.7557	0.561070	0.280535	+	0.959844i	$0.409488\pi$
$440$	0	0
$441$	11.7308	0.558611
$442$	−14.1348	−0.672323
$443$	−7.88658	−0.374703	−0.187351	−	0.982293i	$-0.559990\pi$
$443$	−7.88658	−0.374703	−0.187351	+	0.982293i	$0.559990\pi$
$444$	37.1072	1.76103
$445$	0	0
$446$	5.09937	0.241462
$447$	−4.81967	−0.227962
$448$	−1.79449	−0.0847817
$449$	1.16079	0.0547812	0.0273906	−	0.999625i	$-0.491280\pi$
$449$	1.16079	0.0547812	0.0273906	+	0.999625i	$0.491280\pi$
$450$	0	0
$451$	−0.527413	−0.0248349
$452$	10.6148	0.499279
$453$	3.28654	0.154415
$454$	−14.9789	−0.702994
$455$	0	0
$456$	0	0
$457$	38.6888	1.80978	0.904892	−	0.425641i	$-0.139951\pi$
$457$	38.6888	1.80978	0.904892	+	0.425641i	$0.139951\pi$
$458$	−3.58739	−0.167628
$459$	19.1333	0.893065
$460$	0	0
$461$	−24.4994	−1.14105	−0.570525	−	0.821280i	$-0.693260\pi$
$461$	−24.4994	−1.14105	−0.570525	+	0.821280i	$0.693260\pi$
$462$	−1.07729	−0.0501201
$463$	−32.4849	−1.50970	−0.754852	−	0.655895i	$-0.772291\pi$
$463$	−32.4849	−1.50970	−0.754852	+	0.655895i	$0.772291\pi$
$464$	−5.89528	−0.273681
$465$	0	0
$466$	−47.5645	−2.20338
$467$	14.7020	0.680327	0.340163	−	0.940366i	$-0.389518\pi$
$467$	14.7020	0.680327	0.340163	+	0.940366i	$0.389518\pi$
$468$	−9.77475	−0.451838
$469$	0.860967	0.0397558
$470$	0	0
$471$	13.2366	0.609912
$472$	17.5130	0.806103
$473$	30.9553	1.42333
$474$	30.9957	1.42368
$475$	0	0
$476$	−1.73595	−0.0795672
$477$	−2.76187	−0.126457
$478$	14.5072	0.663543
$479$	−13.2196	−0.604020	−0.302010	−	0.953305i	$-0.597658\pi$
$479$	−13.2196	−0.604020	−0.302010	+	0.953305i	$0.597658\pi$
$480$	0	0
$481$	16.2162	0.739396
$482$	61.1720	2.78631
$483$	−1.18408	−0.0538774
$484$	−10.4586	−0.475390
$485$	0	0
$486$	34.4687	1.56353
$487$	9.66071	0.437769	0.218884	−	0.975751i	$-0.429758\pi$
$487$	9.66071	0.437769	0.218884	+	0.975751i	$0.429758\pi$
$488$	33.0027	1.49396
$489$	−21.7305	−0.982688
$490$	0	0
$491$	2.68634	0.121233	0.0606165	−	0.998161i	$-0.480693\pi$
$491$	2.68634	0.121233	0.0606165	+	0.998161i	$0.480693\pi$
$492$	0.732350	0.0330169
$493$	26.9461	1.21359
$494$	0	0
$495$	0	0
$496$	−3.77382	−0.169449
$497$	−0.0775234	−0.00347740
$498$	−20.2809	−0.908807
$499$	2.35546	0.105445	0.0527224	−	0.998609i	$-0.483210\pi$
$499$	2.35546	0.105445	0.0527224	+	0.998609i	$0.483210\pi$
$500$	0	0
$501$	17.3079	0.773260
$502$	−24.8882	−1.11082
$503$	13.7390	0.612590	0.306295	−	0.951937i	$-0.400911\pi$
$503$	13.7390	0.612590	0.306295	+	0.951937i	$0.400911\pi$
$504$	−0.786032	−0.0350127
$505$	0	0
$506$	47.0854	2.09320
$507$	−11.5787	−0.514228
$508$	−27.7763	−1.23237
$509$	36.3796	1.61250	0.806249	−	0.591577i	$-0.201494\pi$
$509$	36.3796	1.61250	0.806249	+	0.591577i	$0.201494\pi$
$510$	0	0
$511$	−1.50000	−0.0663562
$512$	−8.75464	−0.386904
$513$	0	0
$514$	−31.4382	−1.38668
$515$	0	0
$516$	−42.9836	−1.89225
$517$	−10.3340	−0.454491
$518$	3.16176	0.138920
$519$	24.9184	1.09380
$520$	0	0
$521$	−0.580423	−0.0254288	−0.0127144	−	0.999919i	$-0.504047\pi$
$521$	−0.580423	−0.0254288	−0.0127144	+	0.999919i	$0.504047\pi$
$522$	29.5831	1.29482
$523$	19.2463	0.841582	0.420791	−	0.907158i	$-0.361753\pi$
$523$	19.2463	0.841582	0.420791	+	0.907158i	$0.361753\pi$
$524$	8.91801	0.389585
$525$	0	0
$526$	15.2043	0.662941
$527$	17.2493	0.751392
$528$	−2.51795	−0.109580
$529$	28.7528	1.25012
$530$	0	0
$531$	−9.01961	−0.391418
$532$	0	0
$533$	0.320044	0.0138626
$534$	−3.86308	−0.167172
$535$	0	0
$536$	19.6072	0.846900
$537$	−26.2783	−1.13399
$538$	−33.5258	−1.44540
$539$	19.6512	0.846437
$540$	0	0
$541$	−31.9066	−1.37177	−0.685886	−	0.727709i	$-0.740585\pi$
$541$	−31.9066	−1.37177	−0.685886	+	0.727709i	$0.740585\pi$
$542$	−5.07765	−0.218104
$543$	13.2845	0.570091
$544$	16.7871	0.719741
$545$	0	0
$546$	0.653720	0.0279766
$547$	−3.43452	−0.146849	−0.0734246	−	0.997301i	$-0.523393\pi$
$547$	−3.43452	−0.146849	−0.0734246	+	0.997301i	$0.523393\pi$
$548$	41.9374	1.79148
$549$	−16.9972	−0.725421
$550$	0	0
$551$	0	0
$552$	−26.9655	−1.14773
$553$	1.66357	0.0707422
$554$	−37.1350	−1.57772
$555$	0	0
$556$	27.0736	1.14818
$557$	−6.83010	−0.289401	−0.144700	−	0.989476i	$-0.546222\pi$
$557$	−6.83010	−0.289401	−0.144700	+	0.989476i	$0.546222\pi$
$558$	18.9374	0.801684
$559$	−18.7842	−0.794488
$560$	0	0
$561$	11.5090	0.485912
$562$	33.1419	1.39801
$563$	−12.5628	−0.529460	−0.264730	−	0.964323i	$-0.585283\pi$
$563$	−12.5628	−0.529460	−0.264730	+	0.964323i	$0.585283\pi$
$564$	14.3495	0.604225
$565$	0	0
$566$	−16.4289	−0.690556
$567$	−0.162323	−0.00681692
$568$	−1.76547	−0.0740776
$569$	−3.47978	−0.145880	−0.0729400	−	0.997336i	$-0.523238\pi$
$569$	−3.47978	−0.145880	−0.0729400	+	0.997336i	$0.523238\pi$
$570$	0	0
$571$	−0.621524	−0.0260100	−0.0130050	−	0.999915i	$-0.504140\pi$
$571$	−0.621524	−0.0260100	−0.0130050	+	0.999915i	$0.504140\pi$
$572$	−16.3744	−0.684648
$573$	8.37266	0.349773
$574$	0.0624007	0.00260456
$575$	0	0
$576$	21.0473	0.876969
$577$	−3.85170	−0.160348	−0.0801742	−	0.996781i	$-0.525548\pi$
$577$	−3.85170	−0.160348	−0.0801742	+	0.996781i	$0.525548\pi$
$578$	−10.0761	−0.419109
$579$	−30.0770	−1.24996
$580$	0	0
$581$	−1.08849	−0.0451583
$582$	23.5018	0.974180
$583$	−4.62661	−0.191615
$584$	−34.1602	−1.41356
$585$	0	0
$586$	−2.27056	−0.0937961
$587$	−40.4333	−1.66886	−0.834431	−	0.551113i	$-0.814203\pi$
$587$	−40.4333	−1.66886	−0.834431	+	0.551113i	$0.814203\pi$
$588$	−27.2871	−1.12530
$589$	0	0
$590$	0	0
$591$	2.62817	0.108109
$592$	7.38999	0.303727
$593$	5.87362	0.241201	0.120600	−	0.992701i	$-0.461518\pi$
$593$	5.87362	0.241201	0.120600	+	0.992701i	$0.461518\pi$
$594$	35.1882	1.44379
$595$	0	0
$596$	−14.2833	−0.585068
$597$	−14.0665	−0.575704
$598$	−28.5723	−1.16841
$599$	13.3107	0.543862	0.271931	−	0.962317i	$-0.412338\pi$
$599$	13.3107	0.543862	0.271931	+	0.962317i	$0.412338\pi$
$600$	0	0
$601$	−5.16016	−0.210487	−0.105244	−	0.994446i	$-0.533562\pi$
$601$	−5.16016	−0.210487	−0.105244	+	0.994446i	$0.533562\pi$
$602$	−3.66246	−0.149271
$603$	−10.0981	−0.411228
$604$	9.73983	0.396308
$605$	0	0
$606$	−7.68417	−0.312148
$607$	30.5069	1.23824	0.619119	−	0.785297i	$-0.287490\pi$
$607$	30.5069	1.23824	0.619119	+	0.785297i	$0.287490\pi$
$608$	0	0
$609$	−1.24623	−0.0504998
$610$	0	0
$611$	6.27088	0.253693
$612$	20.3607	0.823031
$613$	45.5007	1.83776	0.918879	−	0.394540i	$-0.129096\pi$
$613$	45.5007	1.83776	0.918879	+	0.394540i	$0.129096\pi$
$614$	−66.1751	−2.67061
$615$	0	0
$616$	−1.31674	−0.0530530
$617$	−2.48247	−0.0999403	−0.0499701	−	0.998751i	$-0.515913\pi$
$617$	−2.48247	−0.0999403	−0.0499701	+	0.998751i	$0.515913\pi$
$618$	3.20312	0.128848
$619$	23.4945	0.944325	0.472162	−	0.881512i	$-0.343474\pi$
$619$	23.4945	0.944325	0.472162	+	0.881512i	$0.343474\pi$
$620$	0	0
$621$	38.6763	1.55203
$622$	−59.3850	−2.38112
$623$	−0.207335	−0.00830670
$624$	1.52794	0.0611666
$625$	0	0
$626$	−34.7562	−1.38914
$627$	0	0
$628$	39.2275	1.56535
$629$	−33.7781	−1.34682
$630$	0	0
$631$	−17.8197	−0.709392	−0.354696	−	0.934982i	$-0.615416\pi$
$631$	−17.8197	−0.709392	−0.354696	+	0.934982i	$0.615416\pi$
$632$	37.8852	1.50699
$633$	−3.44929	−0.137097
$634$	−52.3974	−2.08096
$635$	0	0
$636$	6.42437	0.254743
$637$	−11.9247	−0.472474
$638$	49.5568	1.96197
$639$	0.909259	0.0359697
$640$	0	0
$641$	−37.4631	−1.47970	−0.739852	−	0.672770i	$-0.765104\pi$
$641$	−37.4631	−1.47970	−0.739852	+	0.672770i	$0.765104\pi$
$642$	−10.9347	−0.431557
$643$	19.8886	0.784331	0.392165	−	0.919895i	$-0.371726\pi$
$643$	19.8886	0.784331	0.392165	+	0.919895i	$0.371726\pi$
$644$	−3.50908	−0.138277
$645$	0	0
$646$	0	0
$647$	23.0645	0.906759	0.453380	−	0.891318i	$-0.350218\pi$
$647$	23.0645	0.906759	0.453380	+	0.891318i	$0.350218\pi$
$648$	−3.69665	−0.145218
$649$	−15.1094	−0.593096
$650$	0	0
$651$	−0.797764	−0.0312668
$652$	−64.3995	−2.52208
$653$	26.9839	1.05596	0.527981	−	0.849256i	$-0.322949\pi$
$653$	26.9839	1.05596	0.527981	+	0.849256i	$0.322949\pi$
$654$	43.2384	1.69075
$655$	0	0
$656$	0.145849	0.00569446
$657$	17.5933	0.686379
$658$	1.22267	0.0476646
$659$	−13.4880	−0.525418	−0.262709	−	0.964875i	$-0.584616\pi$
$659$	−13.4880	−0.525418	−0.262709	+	0.964875i	$0.584616\pi$
$660$	0	0
$661$	21.9777	0.854835	0.427417	−	0.904054i	$-0.359423\pi$
$661$	21.9777	0.854835	0.427417	+	0.904054i	$0.359423\pi$
$662$	25.2642	0.981922
$663$	−6.98389	−0.271232
$664$	−24.7887	−0.961988
$665$	0	0
$666$	−37.0838	−1.43697
$667$	54.4692	2.10906
$668$	51.2928	1.98458
$669$	2.51956	0.0974119
$670$	0	0
$671$	−28.4732	−1.09919
$672$	−0.776386	−0.0299497
$673$	−23.1998	−0.894286	−0.447143	−	0.894462i	$-0.647559\pi$
$673$	−23.1998	−0.894286	−0.447143	+	0.894462i	$0.647559\pi$
$674$	17.9207	0.690278
$675$	0	0
$676$	−34.3141	−1.31977
$677$	28.7294	1.10416	0.552081	−	0.833791i	$-0.313834\pi$
$677$	28.7294	1.10416	0.552081	+	0.833791i	$0.313834\pi$
$678$	8.32631	0.319770
$679$	1.26136	0.0484066
$680$	0	0
$681$	−7.40096	−0.283605
$682$	31.7234	1.21475
$683$	24.0010	0.918374	0.459187	−	0.888340i	$-0.348141\pi$
$683$	24.0010	0.918374	0.459187	+	0.888340i	$0.348141\pi$
$684$	0	0
$685$	0	0
$686$	−4.65689	−0.177801
$687$	−1.77250	−0.0676252
$688$	−8.56028	−0.326358
$689$	2.80751	0.106958
$690$	0	0
$691$	37.3866	1.42226	0.711128	−	0.703063i	$-0.248185\pi$
$691$	37.3866	1.42226	0.711128	+	0.703063i	$0.248185\pi$
$692$	73.8470	2.80724
$693$	0.678151	0.0257608
$694$	−47.1198	−1.78864
$695$	0	0
$696$	−28.3809	−1.07578
$697$	−0.666647	−0.0252510
$698$	44.2848	1.67620
$699$	−23.5013	−0.888900
$700$	0	0
$701$	−2.32624	−0.0878609	−0.0439304	−	0.999035i	$-0.513988\pi$
$701$	−2.32624	−0.0878609	−0.0439304	+	0.999035i	$0.513988\pi$
$702$	−21.3528	−0.805911
$703$	0	0
$704$	35.2578	1.32883
$705$	0	0
$706$	42.2308	1.58938
$707$	−0.412416	−0.0155105
$708$	20.9805	0.788494
$709$	−24.3523	−0.914568	−0.457284	−	0.889321i	$-0.651178\pi$
$709$	−24.3523	−0.914568	−0.457284	+	0.889321i	$0.651178\pi$
$710$	0	0
$711$	−19.5117	−0.731747
$712$	−4.72173	−0.176954
$713$	34.8680	1.30582
$714$	−1.36169	−0.0509599
$715$	0	0
$716$	−77.8772	−2.91041
$717$	7.16789	0.267690
$718$	−37.5004	−1.39950
$719$	17.0622	0.636311	0.318155	−	0.948039i	$-0.396937\pi$
$719$	17.0622	0.636311	0.318155	+	0.948039i	$0.396937\pi$
$720$	0	0
$721$	0.171914	0.00640242
$722$	0	0
$723$	30.2246	1.12407
$724$	39.3692	1.46314
$725$	0	0
$726$	−8.20376	−0.304470
$727$	14.6251	0.542415	0.271207	−	0.962521i	$-0.412577\pi$
$727$	14.6251	0.542415	0.271207	+	0.962521i	$0.412577\pi$
$728$	0.799022	0.0296137
$729$	20.4289	0.756628
$730$	0	0
$731$	39.1273	1.44717
$732$	39.5370	1.46133
$733$	−33.5260	−1.23831	−0.619156	−	0.785268i	$-0.712525\pi$
$733$	−33.5260	−1.23831	−0.619156	+	0.785268i	$0.712525\pi$
$734$	74.9961	2.76816
$735$	0	0
$736$	33.9337	1.25081
$737$	−16.9161	−0.623113
$738$	−0.731887	−0.0269411
$739$	−15.2098	−0.559501	−0.279751	−	0.960073i	$-0.590252\pi$
$739$	−15.2098	−0.559501	−0.279751	+	0.960073i	$0.590252\pi$
$740$	0	0
$741$	0	0
$742$	0.547396	0.0200955
$743$	6.65799	0.244258	0.122129	−	0.992514i	$-0.461028\pi$
$743$	6.65799	0.244258	0.122129	+	0.992514i	$0.461028\pi$
$744$	−18.1678	−0.666064
$745$	0	0
$746$	−5.53345	−0.202594
$747$	12.7667	0.467110
$748$	34.1076	1.24710
$749$	−0.586873	−0.0214439
$750$	0	0
$751$	−7.81110	−0.285031	−0.142516	−	0.989793i	$-0.545519\pi$
$751$	−7.81110	−0.285031	−0.142516	+	0.989793i	$0.545519\pi$
$752$	2.85774	0.104211
$753$	−12.2971	−0.448131
$754$	−30.0720	−1.09516
$755$	0	0
$756$	−2.62243	−0.0953769
$757$	18.3846	0.668201	0.334100	−	0.942537i	$-0.391568\pi$
$757$	18.3846	0.668201	0.334100	+	0.942537i	$0.391568\pi$
$758$	−41.1958	−1.49630
$759$	23.2645	0.844449
$760$	0	0
$761$	22.4779	0.814822	0.407411	−	0.913245i	$-0.366432\pi$
$761$	22.4779	0.814822	0.407411	+	0.913245i	$0.366432\pi$
$762$	−21.7878	−0.789290
$763$	2.32064	0.0840129
$764$	24.8128	0.897696
$765$	0	0
$766$	−24.7911	−0.895739
$767$	9.16866	0.331061
$768$	−23.7691	−0.857694
$769$	5.51880	0.199013	0.0995065	−	0.995037i	$-0.468274\pi$
$769$	5.51880	0.199013	0.0995065	+	0.995037i	$0.468274\pi$
$770$	0	0
$771$	−15.5334	−0.559421
$772$	−89.1347	−3.20803
$773$	−33.1881	−1.19369	−0.596846	−	0.802356i	$-0.703580\pi$
$773$	−33.1881	−1.19369	−0.596846	+	0.802356i	$0.703580\pi$
$774$	42.9564	1.54404
$775$	0	0
$776$	28.7255	1.03119
$777$	1.56220	0.0560438
$778$	52.8418	1.89447
$779$	0	0
$780$	0	0
$781$	1.52317	0.0545031
$782$	59.5156	2.12827
$783$	40.7064	1.45473
$784$	−5.43428	−0.194081
$785$	0	0
$786$	6.99533	0.249515
$787$	−48.6451	−1.73401	−0.867005	−	0.498300i	$-0.833958\pi$
$787$	−48.6451	−1.73401	−0.867005	+	0.498300i	$0.833958\pi$
$788$	7.78873	0.277462
$789$	7.51235	0.267447
$790$	0	0
$791$	0.446881	0.0158892
$792$	15.4438	0.548772
$793$	17.2780	0.613561
$794$	−47.5164	−1.68630
$795$	0	0
$796$	−41.6869	−1.47755
$797$	−1.06027	−0.0375567	−0.0187784	−	0.999824i	$-0.505978\pi$
$797$	−1.06027	−0.0375567	−0.0187784	+	0.999824i	$0.505978\pi$
$798$	0	0
$799$	−13.0622	−0.462106
$800$	0	0
$801$	2.43180	0.0859233
$802$	−38.8146	−1.37059
$803$	29.4718	1.04004
$804$	23.4892	0.828400
$805$	0	0
$806$	−19.2503	−0.678064
$807$	−16.5648	−0.583110
$808$	−9.39213	−0.330414
$809$	−13.6192	−0.478826	−0.239413	−	0.970918i	$-0.576955\pi$
$809$	−13.6192	−0.478826	−0.239413	+	0.970918i	$0.576955\pi$
$810$	0	0
$811$	−22.3947	−0.786385	−0.393192	−	0.919456i	$-0.628629\pi$
$811$	−22.3947	−0.786385	−0.393192	+	0.919456i	$0.628629\pi$
$812$	−3.69326	−0.129608
$813$	−2.50883	−0.0879886
$814$	−62.1217	−2.17736
$815$	0	0
$816$	−3.18268	−0.111416
$817$	0	0
$818$	41.1100	1.43738
$819$	−0.411514	−0.0143795
$820$	0	0
$821$	−5.51937	−0.192627	−0.0963137	−	0.995351i	$-0.530705\pi$
$821$	−5.51937	−0.192627	−0.0963137	+	0.995351i	$0.530705\pi$
$822$	32.8959	1.14738
$823$	22.3523	0.779154	0.389577	−	0.920994i	$-0.372621\pi$
$823$	22.3523	0.779154	0.389577	+	0.920994i	$0.372621\pi$
$824$	3.91508	0.136388
$825$	0	0
$826$	1.78766	0.0622008
$827$	−4.48687	−0.156024	−0.0780118	−	0.996952i	$-0.524857\pi$
$827$	−4.48687	−0.156024	−0.0780118	+	0.996952i	$0.524857\pi$
$828$	41.1573	1.43032
$829$	−27.0312	−0.938832	−0.469416	−	0.882977i	$-0.655535\pi$
$829$	−27.0312	−0.938832	−0.469416	+	0.882977i	$0.655535\pi$
$830$	0	0
$831$	−18.3481	−0.636490
$832$	−21.3951	−0.741741
$833$	24.8390	0.860619
$834$	21.2367	0.735365
$835$	0	0
$836$	0	0
$837$	26.0578	0.900691
$838$	−88.1820	−3.04620
$839$	10.1152	0.349214	0.174607	−	0.984638i	$-0.444135\pi$
$839$	10.1152	0.349214	0.174607	+	0.984638i	$0.444135\pi$
$840$	0	0
$841$	28.3283	0.976837
$842$	−26.9242	−0.927870
$843$	16.3752	0.563991
$844$	−10.2221	−0.351861
$845$	0	0
$846$	−14.3405	−0.493035
$847$	−0.440303	−0.0151290
$848$	1.27943	0.0439358
$849$	−8.11738	−0.278588
$850$	0	0
$851$	−68.2796	−2.34059
$852$	−2.11502	−0.0724595
$853$	−27.6102	−0.945356	−0.472678	−	0.881235i	$-0.656713\pi$
$853$	−27.6102	−0.945356	−0.472678	+	0.881235i	$0.656713\pi$
$854$	3.36879	0.115278
$855$	0	0
$856$	−13.3651	−0.456810
$857$	−38.6174	−1.31915	−0.659573	−	0.751640i	$-0.729263\pi$
$857$	−38.6174	−1.31915	−0.659573	+	0.751640i	$0.729263\pi$
$858$	−12.8442	−0.438492
$859$	57.1723	1.95069	0.975346	−	0.220681i	$-0.0708280\pi$
$859$	57.1723	1.95069	0.975346	+	0.220681i	$0.0708280\pi$
$860$	0	0
$861$	0.0308317	0.00105074
$862$	−73.8992	−2.51702
$863$	−28.4419	−0.968173	−0.484087	−	0.875020i	$-0.660848\pi$
$863$	−28.4419	−0.968173	−0.484087	+	0.875020i	$0.660848\pi$
$864$	25.3596	0.862750
$865$	0	0
$866$	9.50417	0.322965
$867$	−4.97851	−0.169079
$868$	−2.36421	−0.0802466
$869$	−32.6855	−1.10878
$870$	0	0
$871$	10.2650	0.347816
$872$	52.8490	1.78969
$873$	−14.7943	−0.500711
$874$	0	0
$875$	0	0
$876$	−40.9236	−1.38268
$877$	−13.3300	−0.450121	−0.225060	−	0.974345i	$-0.572258\pi$
$877$	−13.3300	−0.450121	−0.225060	+	0.974345i	$0.572258\pi$
$878$	27.3276	0.922263
$879$	−1.12187	−0.0378397
$880$	0	0
$881$	−28.1384	−0.948007	−0.474004	−	0.880523i	$-0.657192\pi$
$881$	−28.1384	−0.948007	−0.474004	+	0.880523i	$0.657192\pi$
$882$	27.2698	0.918222
$883$	35.6238	1.19884	0.599418	−	0.800436i	$-0.295399\pi$
$883$	35.6238	1.19884	0.599418	+	0.800436i	$0.295399\pi$
$884$	−20.6971	−0.696120
$885$	0	0
$886$	−18.3333	−0.615920
$887$	59.1722	1.98681	0.993403	−	0.114672i	$-0.0365818\pi$
$887$	59.1722	1.98681	0.993403	+	0.114672i	$0.0365818\pi$
$888$	35.5767	1.19388
$889$	−1.16937	−0.0392195
$890$	0	0
$891$	3.18929	0.106845
$892$	7.46685	0.250009
$893$	0	0
$894$	−11.2039	−0.374715
$895$	0	0
$896$	−2.81961	−0.0941964
$897$	−14.1173	−0.471364
$898$	2.69841	0.0900470
$899$	36.6982	1.22395
$900$	0	0
$901$	−5.84800	−0.194825
$902$	−1.22604	−0.0408226
$903$	−1.80960	−0.0602196
$904$	10.1770	0.338482
$905$	0	0
$906$	7.63997	0.253821
$907$	46.2445	1.53552	0.767762	−	0.640735i	$-0.221370\pi$
$907$	46.2445	1.53552	0.767762	+	0.640735i	$0.221370\pi$
$908$	−21.9331	−0.727876
$909$	4.83716	0.160438
$910$	0	0
$911$	−48.8276	−1.61773	−0.808866	−	0.587994i	$-0.799918\pi$
$911$	−48.8276	−1.61773	−0.808866	+	0.587994i	$0.799918\pi$
$912$	0	0
$913$	21.3865	0.707790
$914$	89.9368	2.97485
$915$	0	0
$916$	−5.25291	−0.173561
$917$	0.375446	0.0123983
$918$	44.4777	1.46798
$919$	−9.60929	−0.316981	−0.158491	−	0.987360i	$-0.550663\pi$
$919$	−9.60929	−0.316981	−0.158491	+	0.987360i	$0.550663\pi$
$920$	0	0
$921$	−32.6967	−1.07739
$922$	−56.9519	−1.87561
$923$	−0.924285	−0.0304232
$924$	−1.57744	−0.0518941
$925$	0	0
$926$	−75.5153	−2.48159
$927$	−2.01635	−0.0662257
$928$	35.7148	1.17240
$929$	51.7174	1.69679	0.848396	−	0.529362i	$-0.177569\pi$
$929$	51.7174	1.69679	0.848396	+	0.529362i	$0.177569\pi$
$930$	0	0
$931$	0	0
$932$	−69.6473	−2.28137
$933$	−29.3417	−0.960604
$934$	34.1766	1.11829
$935$	0	0
$936$	−9.37158	−0.306320
$937$	11.4894	0.375341	0.187671	−	0.982232i	$-0.439906\pi$
$937$	11.4894	0.375341	0.187671	+	0.982232i	$0.439906\pi$
$938$	2.00142	0.0653488
$939$	−17.1728	−0.560412
$940$	0	0
$941$	−26.4897	−0.863540	−0.431770	−	0.901984i	$-0.642111\pi$
$941$	−26.4897	−0.863540	−0.431770	+	0.901984i	$0.642111\pi$
$942$	30.7702	1.00255
$943$	−1.34757	−0.0438829
$944$	4.17831	0.135992
$945$	0	0
$946$	71.9594	2.33960
$947$	−14.7018	−0.477745	−0.238873	−	0.971051i	$-0.576778\pi$
$947$	−14.7018	−0.477745	−0.238873	+	0.971051i	$0.576778\pi$
$948$	45.3861	1.47407
$949$	−17.8840	−0.580539
$950$	0	0
$951$	−25.8892	−0.839513
$952$	−1.66435	−0.0539419
$953$	5.85051	0.189517	0.0947583	−	0.995500i	$-0.469792\pi$
$953$	5.85051	0.189517	0.0947583	+	0.995500i	$0.469792\pi$
$954$	−6.42031	−0.207865
$955$	0	0
$956$	21.2424	0.687029
$957$	24.4857	0.791510
$958$	−30.7306	−0.992862
$959$	1.76555	0.0570127
$960$	0	0
$961$	−7.50793	−0.242191
$962$	37.6966	1.21539
$963$	6.88333	0.221812
$964$	89.5722	2.88493
$965$	0	0
$966$	−2.75254	−0.0885614
$967$	24.0705	0.774054	0.387027	−	0.922068i	$-0.373502\pi$
$967$	24.0705	0.774054	0.387027	+	0.922068i	$0.373502\pi$
$968$	−10.0272	−0.322287
$969$	0	0
$970$	0	0
$971$	−52.6618	−1.69000	−0.844999	−	0.534768i	$-0.820399\pi$
$971$	−52.6618	−1.69000	−0.844999	+	0.534768i	$0.820399\pi$
$972$	50.4715	1.61887
$973$	1.13979	0.0365400
$974$	22.4575	0.719585
$975$	0	0
$976$	7.87389	0.252037
$977$	−6.50872	−0.208232	−0.104116	−	0.994565i	$-0.533201\pi$
$977$	−6.50872	−0.208232	−0.104116	+	0.994565i	$0.533201\pi$
$978$	−50.5153	−1.61530
$979$	4.07368	0.130195
$980$	0	0
$981$	−27.2184	−0.869017
$982$	6.24474	0.199278
$983$	−1.24935	−0.0398480	−0.0199240	−	0.999801i	$-0.506342\pi$
$983$	−1.24935	−0.0398480	−0.0199240	+	0.999801i	$0.506342\pi$
$984$	0.702144	0.0223835
$985$	0	0
$986$	62.6395	1.99485
$987$	0.604111	0.0192291
$988$	0	0
$989$	79.0924	2.51499
$990$	0	0
$991$	−37.5958	−1.19427	−0.597134	−	0.802141i	$-0.703694\pi$
$991$	−37.5958	−1.19427	−0.597134	+	0.802141i	$0.703694\pi$
$992$	22.8626	0.725887
$993$	12.4829	0.396132
$994$	−0.180213	−0.00571600
$995$	0	0
$996$	−29.6966	−0.940974
$997$	−29.9308	−0.947918	−0.473959	−	0.880547i	$-0.657175\pi$
$997$	−29.9308	−0.947918	−0.473959	+	0.880547i	$0.657175\pi$
$998$	5.47555	0.173325
$999$	−51.0272	−1.61443

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.ct.1.22		24
5.2	odd	4		1805.2.b.l.1084.22		24
5.3	odd	4		1805.2.b.l.1084.3		24
5.4	even	2	inner	9025.2.a.ct.1.3		24
19.2	odd	18		475.2.l.f.251.7		48
19.10	odd	18		475.2.l.f.176.7		48
19.18	odd	2		9025.2.a.cu.1.3		24
95.2	even	36		95.2.p.a.4.2	✓	48
95.18	even	4		1805.2.b.k.1084.22		24
95.29	odd	18		475.2.l.f.176.2		48
95.37	even	4		1805.2.b.k.1084.3		24
95.48	even	36		95.2.p.a.24.2	yes	48
95.59	odd	18		475.2.l.f.251.2		48
95.67	even	36		95.2.p.a.24.7	yes	48
95.78	even	36		95.2.p.a.4.7	yes	48
95.94	odd	2		9025.2.a.cu.1.22		24
285.2	odd	36		855.2.da.b.289.7		48
285.143	odd	36		855.2.da.b.784.7		48
285.173	odd	36		855.2.da.b.289.2		48
285.257	odd	36		855.2.da.b.784.2		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.2	✓	48	95.2	even	36
95.2.p.a.4.7	yes	48	95.78	even	36
95.2.p.a.24.2	yes	48	95.48	even	36
95.2.p.a.24.7	yes	48	95.67	even	36
475.2.l.f.176.2		48	95.29	odd	18
475.2.l.f.176.7		48	19.10	odd	18
475.2.l.f.251.2		48	95.59	odd	18
475.2.l.f.251.7		48	19.2	odd	18
855.2.da.b.289.2		48	285.173	odd	36
855.2.da.b.289.7		48	285.2	odd	36
855.2.da.b.784.2		48	285.257	odd	36
855.2.da.b.784.7		48	285.143	odd	36
1805.2.b.k.1084.3		24	95.37	even	4
1805.2.b.k.1084.22		24	95.18	even	4
1805.2.b.l.1084.3		24	5.3	odd	4
1805.2.b.l.1084.22		24	5.2	odd	4
9025.2.a.ct.1.3		24	5.4	even	2	inner
9025.2.a.ct.1.22		24	1.1	even	1	trivial
9025.2.a.cu.1.3		24	19.18	odd	2
9025.2.a.cu.1.22		24	95.94	odd	2

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 9025 = 5^{2} \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.32462 q^{2} +1.14858 q^{3} +3.40387 q^{4} +2.67001 q^{6} +0.143302 q^{7} +3.26348 q^{8} -1.68077 q^{9} -2.81557 q^{11} +3.90962 q^{12} +1.70854 q^{13} +0.333123 q^{14} +0.778610 q^{16} -3.55886 q^{17} -3.90715 q^{18} +0.164594 q^{21} -6.54515 q^{22} -7.19394 q^{23} +3.74836 q^{24} +3.97171 q^{26} -5.37623 q^{27} +0.487782 q^{28} -7.57154 q^{29} -4.84686 q^{31} -4.71698 q^{32} -3.23391 q^{33} -8.27302 q^{34} -5.72111 q^{36} +9.49127 q^{37} +1.96239 q^{39} +0.187320 q^{41} +0.382619 q^{42} -10.9943 q^{43} -9.58385 q^{44} -16.7232 q^{46} +3.67032 q^{47} +0.894296 q^{48} -6.97946 q^{49} -4.08764 q^{51} +5.81566 q^{52} +1.64322 q^{53} -12.4977 q^{54} +0.467663 q^{56} -17.6010 q^{58} +5.36637 q^{59} +10.1127 q^{61} -11.2671 q^{62} -0.240857 q^{63} -12.5224 q^{64} -7.51762 q^{66} +6.00805 q^{67} -12.1139 q^{68} -8.26281 q^{69} -0.540979 q^{71} -5.48514 q^{72} -10.4674 q^{73} +22.0636 q^{74} -0.403477 q^{77} +4.56183 q^{78} +11.6088 q^{79} -1.13273 q^{81} +0.435449 q^{82} -7.59579 q^{83} +0.560257 q^{84} -25.5576 q^{86} -8.69652 q^{87} -9.18856 q^{88} -1.44684 q^{89} +0.244837 q^{91} -24.4873 q^{92} -5.56701 q^{93} +8.53210 q^{94} -5.41783 q^{96} +8.80212 q^{97} -16.2246 q^{98} +4.73232 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49}+ \cdots - 120 q^{96}+O(q^{100}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9 + 12 * q^11 - 24 * q^14 + 6 * q^16 - 6 * q^21 - 42 * q^24 - 12 * q^26 - 36 * q^29 - 42 * q^31 - 6 * q^34 - 6 * q^36 + 24 * q^39 - 60 * q^41 - 30 * q^44 - 6 * q^46 + 12 * q^49 - 30 * q^51 - 24 * q^54 - 18 * q^56 - 60 * q^59 + 30 * q^61 + 36 * q^66 - 66 * q^69 - 96 * q^71 + 24 * q^74 - 72 * q^79 - 96 * q^81 + 54 * q^84 - 108 * q^86 - 84 * q^89 - 96 * q^91 - 36 * q^94 - 120 * q^96

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