LMFDB - Embedded newform 9025.2.a.ct.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9025,2,Mod(1,9025)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			1.9
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)

$f(q)$	$=$	$q-1.04740 q^{2} +0.531453 q^{3} -0.902948 q^{4} -0.556645 q^{6} +2.74033 q^{7} +3.04056 q^{8} -2.71756 q^{9} +O(q^{10})$	\(q-1.04740 q^{2} +0.531453 q^{3} -0.902948 q^{4} -0.556645 q^{6} +2.74033 q^{7} +3.04056 q^{8} -2.71756 q^{9} +0.832835 q^{11} -0.479874 q^{12} +0.610831 q^{13} -2.87023 q^{14} -1.37879 q^{16} -4.83841 q^{17} +2.84638 q^{18} +1.45636 q^{21} -0.872314 q^{22} -3.75094 q^{23} +1.61591 q^{24} -0.639786 q^{26} -3.03861 q^{27} -2.47437 q^{28} +3.97516 q^{29} +6.92676 q^{31} -4.63696 q^{32} +0.442613 q^{33} +5.06777 q^{34} +2.45381 q^{36} +4.33071 q^{37} +0.324628 q^{39} -5.31691 q^{41} -1.52539 q^{42} +10.4585 q^{43} -0.752007 q^{44} +3.92874 q^{46} -3.40016 q^{47} -0.732762 q^{48} +0.509407 q^{49} -2.57139 q^{51} -0.551549 q^{52} -13.6679 q^{53} +3.18265 q^{54} +8.33212 q^{56} -4.16359 q^{58} -10.0173 q^{59} +9.07245 q^{61} -7.25511 q^{62} -7.44700 q^{63} +7.61435 q^{64} -0.463594 q^{66} +10.9346 q^{67} +4.36883 q^{68} -1.99345 q^{69} +0.677726 q^{71} -8.26288 q^{72} -7.01343 q^{73} -4.53600 q^{74} +2.28224 q^{77} -0.340016 q^{78} -3.47957 q^{79} +6.53779 q^{81} +5.56894 q^{82} +4.97485 q^{83} -1.31501 q^{84} -10.9542 q^{86} +2.11261 q^{87} +2.53228 q^{88} +5.88868 q^{89} +1.67388 q^{91} +3.38690 q^{92} +3.68125 q^{93} +3.56134 q^{94} -2.46433 q^{96} -12.4387 q^{97} -0.533555 q^{98} -2.26328 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	$ 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}+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

Display 100 coefficients 10 coefficients

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 $

$2$	−1.04740	−0.740625	−0.370313	−	0.928907i	$-0.620749\pi$
$2$	−1.04740	−0.740625	−0.370313	+	0.928907i	$0.620749\pi$
$3$	0.531453	0.306835	0.153417	−	0.988161i	$-0.450972\pi$
$3$	0.531453	0.306835	0.153417	+	0.988161i	$0.450972\pi$
$4$	−0.902948	−0.451474
$5$	0	0
$5$	0	0
$6$	−0.556645	−0.227250
$7$	2.74033	1.03575	0.517874	−	0.855457i	$-0.326724\pi$
$7$	2.74033	1.03575	0.517874	+	0.855457i	$0.326724\pi$
$8$	3.04056	1.07500
$9$	−2.71756	−0.905853
$10$	0	0
$11$	0.832835	0.251109	0.125555	−	0.992087i	$-0.459929\pi$
$11$	0.832835	0.251109	0.125555	+	0.992087i	$0.459929\pi$
$12$	−0.479874	−0.138528
$13$	0.610831	0.169414	0.0847071	−	0.996406i	$-0.473005\pi$
$13$	0.610831	0.169414	0.0847071	+	0.996406i	$0.473005\pi$
$14$	−2.87023	−0.767101
$15$	0	0
$16$	−1.37879	−0.344697
$17$	−4.83841	−1.17349	−0.586744	−	0.809773i	$-0.699590\pi$
$17$	−4.83841	−1.17349	−0.586744	+	0.809773i	$0.699590\pi$
$18$	2.84638	0.670897
$19$	0	0
$19$	0	0
$20$	0	0
$21$	1.45636	0.317803
$22$	−0.872314	−0.185978
$23$	−3.75094	−0.782124	−0.391062	−	0.920364i	$-0.627892\pi$
$23$	−3.75094	−0.782124	−0.391062	+	0.920364i	$0.627892\pi$
$24$	1.61591	0.329847
$25$	0	0
$26$	−0.639786	−0.125472
$27$	−3.03861	−0.584781
$28$	−2.47437	−0.467613
$29$	3.97516	0.738168	0.369084	−	0.929396i	$-0.379671\pi$
$29$	3.97516	0.738168	0.369084	+	0.929396i	$0.379671\pi$
$30$	0	0
$31$	6.92676	1.24408	0.622042	−	0.782984i	$-0.286303\pi$
$31$	6.92676	1.24408	0.622042	+	0.782984i	$0.286303\pi$
$32$	−4.63696	−0.819707
$33$	0.442613	0.0770490
$34$	5.06777	0.869115
$35$	0	0
$36$	2.45381	0.408969
$37$	4.33071	0.711965	0.355982	−	0.934493i	$-0.384146\pi$
$37$	4.33071	0.711965	0.355982	+	0.934493i	$0.384146\pi$
$38$	0	0
$39$	0.324628	0.0519821
$40$	0	0
$41$	−5.31691	−0.830361	−0.415181	−	0.909739i	$-0.636282\pi$
$41$	−5.31691	−0.830361	−0.415181	+	0.909739i	$0.636282\pi$
$42$	−1.52539	−0.235373
$43$	10.4585	1.59490	0.797450	−	0.603385i	$-0.206182\pi$
$43$	10.4585	1.59490	0.797450	+	0.603385i	$0.206182\pi$
$44$	−0.752007	−0.113369
$45$	0	0
$46$	3.92874	0.579261
$47$	−3.40016	−0.495965	−0.247982	−	0.968765i	$-0.579768\pi$
$47$	−3.40016	−0.495965	−0.247982	+	0.968765i	$0.579768\pi$
$48$	−0.732762	−0.105765
$49$	0.509407	0.0727725
$50$	0	0
$51$	−2.57139	−0.360066
$52$	−0.551549	−0.0764861
$53$	−13.6679	−1.87743	−0.938716	−	0.344692i	$-0.887983\pi$
$53$	−13.6679	−1.87743	−0.938716	+	0.344692i	$0.887983\pi$
$54$	3.18265	0.433104
$55$	0	0
$56$	8.33212	1.11343
$57$	0	0
$58$	−4.16359	−0.546706
$59$	−10.0173	−1.30414	−0.652068	−	0.758160i	$-0.726098\pi$
$59$	−10.0173	−1.30414	−0.652068	+	0.758160i	$0.726098\pi$
$60$	0	0
$61$	9.07245	1.16161	0.580804	−	0.814043i	$-0.302738\pi$
$61$	9.07245	1.16161	0.580804	+	0.814043i	$0.302738\pi$
$62$	−7.25511	−0.921400
$63$	−7.44700	−0.938234
$64$	7.61435	0.951793
$65$	0	0
$66$	−0.463594	−0.0570645
$67$	10.9346	1.33587	0.667935	−	0.744220i	$-0.267179\pi$
$67$	10.9346	1.33587	0.667935	+	0.744220i	$0.267179\pi$
$68$	4.36883	0.529799
$69$	−1.99345	−0.239983
$70$	0	0
$71$	0.677726	0.0804313	0.0402157	−	0.999191i	$-0.487196\pi$
$71$	0.677726	0.0804313	0.0402157	+	0.999191i	$0.487196\pi$
$72$	−8.26288	−0.973790
$73$	−7.01343	−0.820859	−0.410430	−	0.911892i	$-0.634621\pi$
$73$	−7.01343	−0.820859	−0.410430	+	0.911892i	$0.634621\pi$
$74$	−4.53600	−0.527299
$75$	0	0
$76$	0	0
$77$	2.28224	0.260086
$78$	−0.340016	−0.0384993
$79$	−3.47957	−0.391482	−0.195741	−	0.980656i	$-0.562711\pi$
$79$	−3.47957	−0.391482	−0.195741	+	0.980656i	$0.562711\pi$
$80$	0	0
$81$	6.53779	0.726421
$82$	5.56894	0.614987
$83$	4.97485	0.546060	0.273030	−	0.962005i	$-0.411974\pi$
$83$	4.97485	0.546060	0.273030	+	0.962005i	$0.411974\pi$
$84$	−1.31501	−0.143480
$85$	0	0
$86$	−10.9542	−1.18122
$87$	2.11261	0.226495
$88$	2.53228	0.269942
$89$	5.88868	0.624198	0.312099	−	0.950050i	$-0.398968\pi$
$89$	5.88868	0.624198	0.312099	+	0.950050i	$0.398968\pi$
$90$	0	0
$91$	1.67388	0.175470
$92$	3.38690	0.353109
$93$	3.68125	0.381728
$94$	3.56134	0.367324
$95$	0	0
$96$	−2.46433	−0.251514
$97$	−12.4387	−1.26296	−0.631482	−	0.775391i	$-0.717553\pi$
$97$	−12.4387	−1.26296	−0.631482	+	0.775391i	$0.717553\pi$
$98$	−0.533555	−0.0538972
$99$	−2.26328	−0.227468
$100$	0	0
$101$	−17.7372	−1.76492	−0.882460	−	0.470387i	$-0.844114\pi$
$101$	−17.7372	−1.76492	−0.882460	+	0.470387i	$0.844114\pi$
$102$	2.69328	0.266674
$103$	−5.21849	−0.514193	−0.257097	−	0.966386i	$-0.582766\pi$
$103$	−5.21849	−0.514193	−0.257097	+	0.966386i	$0.582766\pi$
$104$	1.85727	0.182120
$105$	0	0
$106$	14.3158	1.39047
$107$	−15.1871	−1.46819	−0.734097	−	0.679044i	$-0.762394\pi$
$107$	−15.1871	−1.46819	−0.734097	+	0.679044i	$0.762394\pi$
$108$	2.74371	0.264014
$109$	−3.92257	−0.375714	−0.187857	−	0.982196i	$-0.560154\pi$
$109$	−3.92257	−0.375714	−0.187857	+	0.982196i	$0.560154\pi$
$110$	0	0
$111$	2.30157	0.218455
$112$	−3.77834	−0.357019
$113$	3.97342	0.373788	0.186894	−	0.982380i	$-0.440158\pi$
$113$	3.97342	0.373788	0.186894	+	0.982380i	$0.440158\pi$
$114$	0	0
$115$	0	0
$116$	−3.58936	−0.333264
$117$	−1.65997	−0.153464
$118$	10.4921	0.965877
$119$	−13.2588	−1.21544
$120$	0	0
$121$	−10.3064	−0.936944
$122$	−9.50251	−0.860317
$123$	−2.82569	−0.254784
$124$	−6.25451	−0.561671
$125$	0	0
$126$	7.80001	0.694880
$127$	9.18497	0.815034	0.407517	−	0.913198i	$-0.366395\pi$
$127$	9.18497	0.815034	0.407517	+	0.913198i	$0.366395\pi$
$128$	1.29864	0.114785
$129$	5.55818	0.489371
$130$	0	0
$131$	−3.73904	−0.326682	−0.163341	−	0.986570i	$-0.552227\pi$
$131$	−3.73904	−0.326682	−0.163341	+	0.986570i	$0.552227\pi$
$132$	−0.399656	−0.0347856
$133$	0	0
$134$	−11.4529	−0.989379
$135$	0	0
$136$	−14.7115	−1.26150
$137$	−2.36335	−0.201914	−0.100957	−	0.994891i	$-0.532191\pi$
$137$	−2.36335	−0.201914	−0.100957	+	0.994891i	$0.532191\pi$
$138$	2.08794	0.177737
$139$	2.44279	0.207195	0.103597	−	0.994619i	$-0.466965\pi$
$139$	2.44279	0.207195	0.103597	+	0.994619i	$0.466965\pi$
$140$	0	0
$141$	−1.80703	−0.152179
$142$	−0.709852	−0.0595695
$143$	0.508722	0.0425415
$144$	3.74694	0.312245
$145$	0	0
$146$	7.34588	0.607949
$147$	0.270726	0.0223291
$148$	−3.91041	−0.321433
$149$	14.2687	1.16894	0.584468	−	0.811417i	$-0.301303\pi$
$149$	14.2687	1.16894	0.584468	+	0.811417i	$0.301303\pi$
$150$	0	0
$151$	−2.34319	−0.190686	−0.0953432	−	0.995444i	$-0.530395\pi$
$151$	−2.34319	−0.190686	−0.0953432	+	0.995444i	$0.530395\pi$
$152$	0	0
$153$	13.1487	1.06301
$154$	−2.39043	−0.192626
$155$	0	0
$156$	−0.293122	−0.0234686
$157$	16.1747	1.29088	0.645442	−	0.763809i	$-0.276673\pi$
$157$	16.1747	1.29088	0.645442	+	0.763809i	$0.276673\pi$
$158$	3.64451	0.289941
$159$	−7.26385	−0.576061
$160$	0	0
$161$	−10.2788	−0.810083
$162$	−6.84770	−0.538006
$163$	16.0258	1.25524	0.627618	−	0.778521i	$-0.284030\pi$
$163$	16.0258	1.25524	0.627618	+	0.778521i	$0.284030\pi$
$164$	4.80089	0.374886
$165$	0	0
$166$	−5.21067	−0.404426
$167$	7.57646	0.586284	0.293142	−	0.956069i	$-0.405299\pi$
$167$	7.57646	0.586284	0.293142	+	0.956069i	$0.405299\pi$
$168$	4.42813	0.341638
$169$	−12.6269	−0.971299
$170$	0	0
$171$	0	0
$172$	−9.44344	−0.720056
$173$	−8.86205	−0.673769	−0.336885	−	0.941546i	$-0.609373\pi$
$173$	−8.86205	−0.673769	−0.336885	+	0.941546i	$0.609373\pi$
$174$	−2.21275	−0.167748
$175$	0	0
$176$	−1.14830	−0.0865567
$177$	−5.32370	−0.400154
$178$	−6.16782	−0.462297
$179$	−5.46546	−0.408508	−0.204254	−	0.978918i	$-0.565477\pi$
$179$	−5.46546	−0.408508	−0.204254	+	0.978918i	$0.565477\pi$
$180$	0	0
$181$	−18.8164	−1.39861	−0.699306	−	0.714822i	$-0.746508\pi$
$181$	−18.8164	−1.39861	−0.699306	+	0.714822i	$0.746508\pi$
$182$	−1.75323	−0.129958
$183$	4.82158	0.356422
$184$	−11.4049	−0.840782
$185$	0	0
$186$	−3.85575	−0.282717
$187$	−4.02960	−0.294674
$188$	3.07017	0.223915
$189$	−8.32680	−0.605686
$190$	0	0
$191$	−17.2606	−1.24893	−0.624465	−	0.781053i	$-0.714683\pi$
$191$	−17.2606	−1.24893	−0.624465	+	0.781053i	$0.714683\pi$
$192$	4.04667	0.292043
$193$	7.47422	0.538006	0.269003	−	0.963139i	$-0.413306\pi$
$193$	7.47422	0.538006	0.269003	+	0.963139i	$0.413306\pi$
$194$	13.0284	0.935383
$195$	0	0
$196$	−0.459968	−0.0328549
$197$	−12.2080	−0.869784	−0.434892	−	0.900483i	$-0.643213\pi$
$197$	−12.2080	−0.869784	−0.434892	+	0.900483i	$0.643213\pi$
$198$	2.37056	0.168469
$199$	−7.75788	−0.549942	−0.274971	−	0.961453i	$-0.588668\pi$
$199$	−7.75788	−0.549942	−0.274971	+	0.961453i	$0.588668\pi$
$200$	0	0
$201$	5.81121	0.409891
$202$	18.5780	1.30715
$203$	10.8932	0.764556
$204$	2.32183	0.162561
$205$	0	0
$206$	5.46586	0.380825
$207$	10.1934	0.708489
$208$	−0.842208	−0.0583966
$209$	0	0
$210$	0	0
$211$	−10.0571	−0.692359	−0.346179	−	0.938168i	$-0.612521\pi$
$211$	−10.0571	−0.692359	−0.346179	+	0.938168i	$0.612521\pi$
$212$	12.3414	0.847612
$213$	0.360180	0.0246791
$214$	15.9070	1.08738
$215$	0	0
$216$	−9.23907	−0.628639
$217$	18.9816	1.28856
$218$	4.10851	0.278264
$219$	−3.72731	−0.251868
$220$	0	0
$221$	−2.95545	−0.198805
$222$	−2.41067	−0.161794
$223$	28.3213	1.89654	0.948268	−	0.317470i	$-0.102833\pi$
$223$	28.3213	1.89654	0.948268	+	0.317470i	$0.102833\pi$
$224$	−12.7068	−0.849009
$225$	0	0
$226$	−4.16177	−0.276837
$227$	−15.8786	−1.05390	−0.526949	−	0.849897i	$-0.676664\pi$
$227$	−15.8786	−1.05390	−0.526949	+	0.849897i	$0.676664\pi$
$228$	0	0
$229$	11.3865	0.752438	0.376219	−	0.926531i	$-0.377224\pi$
$229$	11.3865	0.752438	0.376219	+	0.926531i	$0.377224\pi$
$230$	0	0
$231$	1.21291	0.0798033
$232$	12.0867	0.793530
$233$	15.8642	1.03930	0.519651	−	0.854379i	$-0.326062\pi$
$233$	15.8642	1.03930	0.519651	+	0.854379i	$0.326062\pi$
$234$	1.73866	0.113660
$235$	0	0
$236$	9.04506	0.588783
$237$	−1.84923	−0.120120
$238$	13.8873	0.900183
$239$	20.8648	1.34963	0.674817	−	0.737985i	$-0.264222\pi$
$239$	20.8648	1.34963	0.674817	+	0.737985i	$0.264222\pi$
$240$	0	0
$241$	−28.4290	−1.83127	−0.915636	−	0.402008i	$-0.868312\pi$
$241$	−28.4290	−1.83127	−0.915636	+	0.402008i	$0.868312\pi$
$242$	10.7949	0.693925
$243$	12.5904	0.807673
$244$	−8.19195	−0.524436
$245$	0	0
$246$	2.95963	0.188699
$247$	0	0
$248$	21.0612	1.33739
$249$	2.64390	0.167550
$250$	0	0
$251$	24.8136	1.56622	0.783109	−	0.621884i	$-0.213632\pi$
$251$	24.8136	1.56622	0.783109	+	0.621884i	$0.213632\pi$
$252$	6.72426	0.423588
$253$	−3.12391	−0.196399
$254$	−9.62036	−0.603635
$255$	0	0
$256$	−16.5889	−1.03681
$257$	−5.44223	−0.339477	−0.169739	−	0.985489i	$-0.554292\pi$
$257$	−5.44223	−0.339477	−0.169739	+	0.985489i	$0.554292\pi$
$258$	−5.82165	−0.362440
$259$	11.8676	0.737415
$260$	0	0
$261$	−10.8027	−0.668671
$262$	3.91628	0.241949
$263$	19.5197	1.20363	0.601817	−	0.798634i	$-0.294444\pi$
$263$	19.5197	1.20363	0.601817	+	0.798634i	$0.294444\pi$
$264$	1.34579	0.0828276
$265$	0	0
$266$	0	0
$267$	3.12956	0.191526
$268$	−9.87334	−0.603110
$269$	−18.5848	−1.13314	−0.566568	−	0.824015i	$-0.691729\pi$
$269$	−18.5848	−1.13314	−0.566568	+	0.824015i	$0.691729\pi$
$270$	0	0
$271$	1.89214	0.114939	0.0574696	−	0.998347i	$-0.481697\pi$
$271$	1.89214	0.114939	0.0574696	+	0.998347i	$0.481697\pi$
$272$	6.67115	0.404498
$273$	0.889588	0.0538403
$274$	2.47538	0.149543
$275$	0	0
$276$	1.79998	0.108346
$277$	6.77887	0.407303	0.203652	−	0.979043i	$-0.434719\pi$
$277$	6.77887	0.407303	0.203652	+	0.979043i	$0.434719\pi$
$278$	−2.55859	−0.153454
$279$	−18.8239	−1.12696
$280$	0	0
$281$	12.2861	0.732927	0.366464	−	0.930432i	$-0.380568\pi$
$281$	12.2861	0.732927	0.366464	+	0.930432i	$0.380568\pi$
$282$	1.89268	0.112708
$283$	−25.6667	−1.52572	−0.762862	−	0.646561i	$-0.776207\pi$
$283$	−25.6667	−1.52572	−0.762862	+	0.646561i	$0.776207\pi$
$284$	−0.611952	−0.0363126
$285$	0	0
$286$	−0.532837	−0.0315073
$287$	−14.5701	−0.860044
$288$	12.6012	0.742534
$289$	6.41023	0.377072
$290$	0	0
$291$	−6.61061	−0.387521
$292$	6.33276	0.370597
$293$	−28.1121	−1.64232	−0.821162	−	0.570695i	$-0.806674\pi$
$293$	−28.1121	−1.64232	−0.821162	+	0.570695i	$0.806674\pi$
$294$	−0.283559	−0.0165375
$295$	0	0
$296$	13.1678	0.765361
$297$	−2.53067	−0.146844
$298$	−14.9451	−0.865744
$299$	−2.29119	−0.132503
$300$	0	0
$301$	28.6596	1.65191
$302$	2.45427	0.141227
$303$	−9.42651	−0.541539
$304$	0	0
$305$	0	0
$306$	−13.7719	−0.787290
$307$	−2.57676	−0.147064	−0.0735319	−	0.997293i	$-0.523427\pi$
$307$	−2.57676	−0.147064	−0.0735319	+	0.997293i	$0.523427\pi$
$308$	−2.06075	−0.117422
$309$	−2.77338	−0.157772
$310$	0	0
$311$	14.6367	0.829974	0.414987	−	0.909827i	$-0.363786\pi$
$311$	14.6367	0.829974	0.414987	+	0.909827i	$0.363786\pi$
$312$	0.987050	0.0558807
$313$	−1.49408	−0.0844507	−0.0422253	−	0.999108i	$-0.513445\pi$
$313$	−1.49408	−0.0844507	−0.0422253	+	0.999108i	$0.513445\pi$
$314$	−16.9415	−0.956062
$315$	0	0
$316$	3.14187	0.176744
$317$	5.64234	0.316905	0.158453	−	0.987367i	$-0.449349\pi$
$317$	5.64234	0.316905	0.158453	+	0.987367i	$0.449349\pi$
$318$	7.60818	0.426646
$319$	3.31065	0.185361
$320$	0	0
$321$	−8.07124	−0.450493
$322$	10.7660	0.599968
$323$	0	0
$324$	−5.90329	−0.327960
$325$	0	0
$326$	−16.7854	−0.929660
$327$	−2.08466	−0.115282
$328$	−16.1663	−0.892637
$329$	−9.31757	−0.513694
$330$	0	0
$331$	−31.8920	−1.75294	−0.876472	−	0.481452i	$-0.840110\pi$
$331$	−31.8920	−1.75294	−0.876472	+	0.481452i	$0.840110\pi$
$332$	−4.49203	−0.246532
$333$	−11.7690	−0.644935
$334$	−7.93561	−0.434217
$335$	0	0
$336$	−2.00801	−0.109546
$337$	15.3378	0.835504	0.417752	−	0.908561i	$-0.362818\pi$
$337$	15.3378	0.835504	0.417752	+	0.908561i	$0.362818\pi$
$338$	13.2254	0.719369
$339$	2.11169	0.114691
$340$	0	0
$341$	5.76886	0.312401
$342$	0	0
$343$	−17.7864	−0.960373
$344$	31.7995	1.71452
$345$	0	0
$346$	9.28214	0.499011
$347$	0.0826977	0.00443945	0.00221972	−	0.999998i	$-0.499293\pi$
$347$	0.0826977	0.00443945	0.00221972	+	0.999998i	$0.499293\pi$
$348$	−1.90758	−0.102257
$349$	−4.64333	−0.248552	−0.124276	−	0.992248i	$-0.539661\pi$
$349$	−4.64333	−0.248552	−0.124276	+	0.992248i	$0.539661\pi$
$350$	0	0
$351$	−1.85608	−0.0990702
$352$	−3.86183	−0.205836
$353$	−3.99402	−0.212580	−0.106290	−	0.994335i	$-0.533897\pi$
$353$	−3.99402	−0.212580	−0.106290	+	0.994335i	$0.533897\pi$
$354$	5.57606	0.296364
$355$	0	0
$356$	−5.31717	−0.281809
$357$	−7.04645	−0.372938
$358$	5.72454	0.302551
$359$	30.2198	1.59494	0.797471	−	0.603358i	$-0.206171\pi$
$359$	30.2198	1.59494	0.797471	+	0.603358i	$0.206171\pi$
$360$	0	0
$361$	0	0
$362$	19.7084	1.03585
$363$	−5.47736	−0.287487
$364$	−1.51143	−0.0792202
$365$	0	0
$366$	−5.05014	−0.263975
$367$	−18.1399	−0.946896	−0.473448	−	0.880822i	$-0.656991\pi$
$367$	−18.1399	−0.946896	−0.473448	+	0.880822i	$0.656991\pi$
$368$	5.17175	0.269596
$369$	14.4490	0.752185
$370$	0	0
$371$	−37.4546	−1.94455
$372$	−3.32398	−0.172340
$373$	−25.2151	−1.30559	−0.652794	−	0.757536i	$-0.726403\pi$
$373$	−25.2151	−1.30559	−0.652794	+	0.757536i	$0.726403\pi$
$374$	4.22061	0.218243
$375$	0	0
$376$	−10.3384	−0.533161
$377$	2.42815	0.125056
$378$	8.72152	0.448586
$379$	27.5634	1.41584	0.707918	−	0.706294i	$-0.249634\pi$
$379$	27.5634	1.41584	0.707918	+	0.706294i	$0.249634\pi$
$380$	0	0
$381$	4.88138	0.250081
$382$	18.0788	0.924990
$383$	18.3237	0.936296	0.468148	−	0.883650i	$-0.344921\pi$
$383$	18.3237	0.936296	0.468148	+	0.883650i	$0.344921\pi$
$384$	0.690166	0.0352199
$385$	0	0
$386$	−7.82852	−0.398461
$387$	−28.4215	−1.44474
$388$	11.2315	0.570195
$389$	−7.18503	−0.364296	−0.182148	−	0.983271i	$-0.558305\pi$
$389$	−7.18503	−0.364296	−0.182148	+	0.983271i	$0.558305\pi$
$390$	0	0
$391$	18.1486	0.917813
$392$	1.54888	0.0782303
$393$	−1.98713	−0.100237
$394$	12.7867	0.644184
$395$	0	0
$396$	2.04362	0.102696
$397$	11.7242	0.588423	0.294211	−	0.955740i	$-0.404943\pi$
$397$	11.7242	0.588423	0.294211	+	0.955740i	$0.404943\pi$
$398$	8.12562	0.407301
$399$	0	0
$400$	0	0
$401$	−39.2123	−1.95817	−0.979085	−	0.203451i	$-0.934784\pi$
$401$	−39.2123	−1.95817	−0.979085	+	0.203451i	$0.934784\pi$
$402$	−6.08667	−0.303576
$403$	4.23108	0.210765
$404$	16.0158	0.796816
$405$	0	0
$406$	−11.4096	−0.566249
$407$	3.60677	0.178781
$408$	−7.81845	−0.387071
$409$	−8.87630	−0.438905	−0.219452	−	0.975623i	$-0.570427\pi$
$409$	−8.87630	−0.438905	−0.219452	+	0.975623i	$0.570427\pi$
$410$	0	0
$411$	−1.25601	−0.0619543
$412$	4.71203	0.232145
$413$	−27.4506	−1.35076
$414$	−10.6766	−0.524725
$415$	0	0
$416$	−2.83240	−0.138870
$417$	1.29823	0.0635745
$418$	0	0
$419$	−7.80196	−0.381151	−0.190575	−	0.981673i	$-0.561035\pi$
$419$	−7.80196	−0.381151	−0.190575	+	0.981673i	$0.561035\pi$
$420$	0	0
$421$	−34.5570	−1.68421	−0.842104	−	0.539316i	$-0.818683\pi$
$421$	−34.5570	−1.68421	−0.842104	+	0.539316i	$0.818683\pi$
$422$	10.5338	0.512779
$423$	9.24014	0.449271
$424$	−41.5580	−2.01824
$425$	0	0
$426$	−0.377253	−0.0182780
$427$	24.8615	1.20313
$428$	13.7132	0.662851
$429$	0.270362	0.0130532
$430$	0	0
$431$	−2.83951	−0.136775	−0.0683873	−	0.997659i	$-0.521785\pi$
$431$	−2.83951	−0.136775	−0.0683873	+	0.997659i	$0.521785\pi$
$432$	4.18961	0.201573
$433$	−21.8527	−1.05018	−0.525088	−	0.851048i	$-0.675967\pi$
$433$	−21.8527	−1.05018	−0.525088	+	0.851048i	$0.675967\pi$
$434$	−19.8814	−0.954338
$435$	0	0
$436$	3.54188	0.169625
$437$	0	0
$438$	3.90399	0.186540
$439$	−32.5760	−1.55477	−0.777383	−	0.629027i	$-0.783453\pi$
$439$	−32.5760	−1.55477	−0.777383	+	0.629027i	$0.783453\pi$
$440$	0	0
$441$	−1.38434	−0.0659212
$442$	3.09555	0.147240
$443$	−7.76173	−0.368771	−0.184385	−	0.982854i	$-0.559029\pi$
$443$	−7.76173	−0.368771	−0.184385	+	0.982854i	$0.559029\pi$
$444$	−2.07820	−0.0986269
$445$	0	0
$446$	−29.6638	−1.40462
$447$	7.58313	0.358670
$448$	20.8658	0.985817
$449$	−22.9821	−1.08459	−0.542296	−	0.840187i	$-0.682445\pi$
$449$	−22.9821	−1.08459	−0.542296	+	0.840187i	$0.682445\pi$
$450$	0	0
$451$	−4.42811	−0.208511
$452$	−3.58779	−0.168756
$453$	−1.24530	−0.0585092
$454$	16.6312	0.780543
$455$	0	0
$456$	0	0
$457$	−3.38866	−0.158515	−0.0792573	−	0.996854i	$-0.525255\pi$
$457$	−3.38866	−0.158515	−0.0792573	+	0.996854i	$0.525255\pi$
$458$	−11.9262	−0.557275
$459$	14.7021	0.686234
$460$	0	0
$461$	−10.8529	−0.505471	−0.252735	−	0.967535i	$-0.581330\pi$
$461$	−10.8529	−0.505471	−0.252735	+	0.967535i	$0.581330\pi$
$462$	−1.27040	−0.0591044
$463$	−7.31171	−0.339804	−0.169902	−	0.985461i	$-0.554345\pi$
$463$	−7.31171	−0.339804	−0.169902	+	0.985461i	$0.554345\pi$
$464$	−5.48090	−0.254445
$465$	0	0
$466$	−16.6163	−0.769733
$467$	10.8418	0.501699	0.250850	−	0.968026i	$-0.419290\pi$
$467$	10.8418	0.501699	0.250850	+	0.968026i	$0.419290\pi$
$468$	1.49887	0.0692851
$469$	29.9643	1.38362
$470$	0	0
$471$	8.59612	0.396088
$472$	−30.4580	−1.40194
$473$	8.71018	0.400494
$474$	1.93688	0.0889640
$475$	0	0
$476$	11.9720	0.548738
$477$	37.1433	1.70068
$478$	−21.8539	−0.999574
$479$	3.44738	0.157515	0.0787574	−	0.996894i	$-0.474905\pi$
$479$	3.44738	0.157515	0.0787574	+	0.996894i	$0.474905\pi$
$480$	0	0
$481$	2.64533	0.120617
$482$	29.7766	1.35629
$483$	−5.46270	−0.248561
$484$	9.30613	0.423006
$485$	0	0
$486$	−13.1872	−0.598183
$487$	26.9972	1.22336	0.611680	−	0.791106i	$-0.290494\pi$
$487$	26.9972	1.22336	0.611680	+	0.791106i	$0.290494\pi$
$488$	27.5853	1.24873
$489$	8.51695	0.385150
$490$	0	0
$491$	0.243979	0.0110106	0.00550530	−	0.999985i	$-0.498248\pi$
$491$	0.243979	0.0110106	0.00550530	+	0.999985i	$0.498248\pi$
$492$	2.55145	0.115028
$493$	−19.2334	−0.866231
$494$	0	0
$495$	0	0
$496$	−9.55055	−0.428832
$497$	1.85719	0.0833065
$498$	−2.76923	−0.124092
$499$	−3.24868	−0.145431	−0.0727155	−	0.997353i	$-0.523167\pi$
$499$	−3.24868	−0.145431	−0.0727155	+	0.997353i	$0.523167\pi$
$500$	0	0
$501$	4.02653	0.179892
$502$	−25.9898	−1.15998
$503$	−7.12545	−0.317708	−0.158854	−	0.987302i	$-0.550780\pi$
$503$	−7.12545	−0.317708	−0.158854	+	0.987302i	$0.550780\pi$
$504$	−22.6430	−1.00860
$505$	0	0
$506$	3.27199	0.145458
$507$	−6.71060	−0.298028
$508$	−8.29355	−0.367967
$509$	−1.73022	−0.0766907	−0.0383453	−	0.999265i	$-0.512209\pi$
$509$	−1.73022	−0.0766907	−0.0383453	+	0.999265i	$0.512209\pi$
$510$	0	0
$511$	−19.2191	−0.850203
$512$	14.7780	0.653100
$513$	0	0
$514$	5.70021	0.251426
$515$	0	0
$516$	−5.01875	−0.220938
$517$	−2.83178	−0.124541
$518$	−12.4301	−0.546149
$519$	−4.70977	−0.206736
$520$	0	0
$521$	−12.8033	−0.560922	−0.280461	−	0.959865i	$-0.590487\pi$
$521$	−12.8033	−0.560922	−0.280461	+	0.959865i	$0.590487\pi$
$522$	11.3148	0.495235
$523$	8.71641	0.381142	0.190571	−	0.981673i	$-0.438966\pi$
$523$	8.71641	0.381142	0.190571	+	0.981673i	$0.438966\pi$
$524$	3.37616	0.147488
$525$	0	0
$526$	−20.4449	−0.891441
$527$	−33.5145	−1.45992
$528$	−0.610270	−0.0265586
$529$	−8.93048	−0.388282
$530$	0	0
$531$	27.2225	1.18136
$532$	0	0
$533$	−3.24773	−0.140675
$534$	−3.27790	−0.141849
$535$	0	0
$536$	33.2471	1.43606
$537$	−2.90463	−0.125344
$538$	19.4658	0.839230
$539$	0.424253	0.0182739
$540$	0	0
$541$	11.0154	0.473588	0.236794	−	0.971560i	$-0.423903\pi$
$541$	11.0154	0.473588	0.236794	+	0.971560i	$0.423903\pi$
$542$	−1.98183	−0.0851268
$543$	−10.0000	−0.429143
$544$	22.4355	0.961916
$545$	0	0
$546$	−0.931757	−0.0398755
$547$	−18.3959	−0.786551	−0.393275	−	0.919421i	$-0.628658\pi$
$547$	−18.3959	−0.786551	−0.393275	+	0.919421i	$0.628658\pi$
$548$	2.13398	0.0911591
$549$	−24.6549	−1.05225
$550$	0	0
$551$	0	0
$552$	−6.06118	−0.257981
$553$	−9.53516	−0.405476
$554$	−7.10021	−0.301659
$555$	0	0
$556$	−2.20571	−0.0935431
$557$	−0.202098	−0.00856316	−0.00428158	−	0.999991i	$-0.501363\pi$
$557$	−0.202098	−0.00856316	−0.00428158	+	0.999991i	$0.501363\pi$
$558$	19.7162	0.834653
$559$	6.38835	0.270199
$560$	0	0
$561$	−2.14154	−0.0904161
$562$	−12.8685	−0.542824
$563$	−6.76375	−0.285058	−0.142529	−	0.989791i	$-0.545523\pi$
$563$	−6.76375	−0.285058	−0.142529	+	0.989791i	$0.545523\pi$
$564$	1.63165	0.0687049
$565$	0	0
$566$	26.8833	1.12999
$567$	17.9157	0.752389
$568$	2.06066	0.0864636
$569$	−7.15701	−0.300038	−0.150019	−	0.988683i	$-0.547933\pi$
$569$	−7.15701	−0.300038	−0.150019	+	0.988683i	$0.547933\pi$
$570$	0	0
$571$	−18.3153	−0.766471	−0.383236	−	0.923651i	$-0.625190\pi$
$571$	−18.3153	−0.766471	−0.383236	+	0.923651i	$0.625190\pi$
$572$	−0.459349	−0.0192064
$573$	−9.17318	−0.383215
$574$	15.2607	0.636971
$575$	0	0
$576$	−20.6924	−0.862184
$577$	21.5794	0.898364	0.449182	−	0.893440i	$-0.351716\pi$
$577$	21.5794	0.898364	0.449182	+	0.893440i	$0.351716\pi$
$578$	−6.71409	−0.279269
$579$	3.97220	0.165079
$580$	0	0
$581$	13.6327	0.565581
$582$	6.92397	0.287008
$583$	−11.3831	−0.471441
$584$	−21.3247	−0.882423
$585$	0	0
$586$	29.4446	1.21635
$587$	−28.9431	−1.19461	−0.597305	−	0.802014i	$-0.703762\pi$
$587$	−28.9431	−1.19461	−0.597305	+	0.802014i	$0.703762\pi$
$588$	−0.244452	−0.0100810
$589$	0	0
$590$	0	0
$591$	−6.48798	−0.266880
$592$	−5.97114	−0.245412
$593$	−17.8231	−0.731907	−0.365954	−	0.930633i	$-0.619257\pi$
$593$	−17.8231	−0.731907	−0.365954	+	0.930633i	$0.619257\pi$
$594$	2.65063	0.108756
$595$	0	0
$596$	−12.8839	−0.527744
$597$	−4.12295	−0.168741
$598$	2.39980	0.0981350
$599$	8.55080	0.349376	0.174688	−	0.984624i	$-0.444108\pi$
$599$	8.55080	0.349376	0.174688	+	0.984624i	$0.444108\pi$
$600$	0	0
$601$	4.19029	0.170925	0.0854627	−	0.996341i	$-0.472763\pi$
$601$	4.19029	0.170925	0.0854627	+	0.996341i	$0.472763\pi$
$602$	−30.0182	−1.22345
$603$	−29.7153	−1.21010
$604$	2.11578	0.0860899
$605$	0	0
$606$	9.87335	0.401077
$607$	7.59458	0.308254	0.154127	−	0.988051i	$-0.450743\pi$
$607$	7.59458	0.308254	0.154127	+	0.988051i	$0.450743\pi$
$608$	0	0
$609$	5.78925	0.234592
$610$	0	0
$611$	−2.07693	−0.0840234
$612$	−11.8726	−0.479920
$613$	−17.9449	−0.724788	−0.362394	−	0.932025i	$-0.618041\pi$
$613$	−17.9449	−0.724788	−0.362394	+	0.932025i	$0.618041\pi$
$614$	2.69891	0.108919
$615$	0	0
$616$	6.93929	0.279592
$617$	−40.5840	−1.63385	−0.816924	−	0.576745i	$-0.804323\pi$
$617$	−40.5840	−1.63385	−0.816924	+	0.576745i	$0.804323\pi$
$618$	2.90485	0.116850
$619$	−25.5608	−1.02738	−0.513688	−	0.857977i	$-0.671721\pi$
$619$	−25.5608	−1.02738	−0.513688	+	0.857977i	$0.671721\pi$
$620$	0	0
$621$	11.3976	0.457372
$622$	−15.3306	−0.614700
$623$	16.1369	0.646512
$624$	−0.447594	−0.0179181
$625$	0	0
$626$	1.56491	0.0625463
$627$	0	0
$628$	−14.6049	−0.582801
$629$	−20.9538	−0.835481
$630$	0	0
$631$	4.63486	0.184511	0.0922555	−	0.995735i	$-0.470592\pi$
$631$	4.63486	0.184511	0.0922555	+	0.995735i	$0.470592\pi$
$632$	−10.5798	−0.420842
$633$	−5.34487	−0.212440
$634$	−5.90980	−0.234708
$635$	0	0
$636$	6.55888	0.260077
$637$	0.311162	0.0123287
$638$	−3.46758	−0.137283
$639$	−1.84176	−0.0728589
$640$	0	0
$641$	−23.2079	−0.916658	−0.458329	−	0.888783i	$-0.651552\pi$
$641$	−23.2079	−0.916658	−0.458329	+	0.888783i	$0.651552\pi$
$642$	8.45384	0.333646
$643$	−15.2454	−0.601219	−0.300610	−	0.953747i	$-0.597190\pi$
$643$	−15.2454	−0.601219	−0.300610	+	0.953747i	$0.597190\pi$
$644$	9.28122	0.365731
$645$	0	0
$646$	0	0
$647$	−17.6749	−0.694872	−0.347436	−	0.937704i	$-0.612948\pi$
$647$	−17.6749	−0.694872	−0.347436	+	0.937704i	$0.612948\pi$
$648$	19.8785	0.780902
$649$	−8.34273	−0.327481
$650$	0	0
$651$	10.0878	0.395374
$652$	−14.4704	−0.566706
$653$	6.86456	0.268631	0.134315	−	0.990939i	$-0.457116\pi$
$653$	6.86456	0.268631	0.134315	+	0.990939i	$0.457116\pi$
$654$	2.18348	0.0853809
$655$	0	0
$656$	7.33089	0.286223
$657$	19.0594	0.743578
$658$	9.75924	0.380455
$659$	−27.3966	−1.06722	−0.533611	−	0.845730i	$-0.679165\pi$
$659$	−27.3966	−1.06722	−0.533611	+	0.845730i	$0.679165\pi$
$660$	0	0
$661$	−28.5502	−1.11048	−0.555238	−	0.831692i	$-0.687373\pi$
$661$	−28.5502	−1.11048	−0.555238	+	0.831692i	$0.687373\pi$
$662$	33.4038	1.29828
$663$	−1.57068	−0.0610003
$664$	15.1263	0.587014
$665$	0	0
$666$	12.3268	0.477655
$667$	−14.9106	−0.577339
$668$	−6.84115	−0.264692
$669$	15.0515	0.581923
$670$	0	0
$671$	7.55586	0.291691
$672$	−6.75307	−0.260505
$673$	45.1688	1.74113	0.870565	−	0.492054i	$-0.163754\pi$
$673$	45.1688	1.74113	0.870565	+	0.492054i	$0.163754\pi$
$674$	−16.0649	−0.618796
$675$	0	0
$676$	11.4014	0.438516
$677$	−46.9628	−1.80493	−0.902463	−	0.430767i	$-0.858243\pi$
$677$	−46.9628	−1.80493	−0.902463	+	0.430767i	$0.858243\pi$
$678$	−2.21179	−0.0849432
$679$	−34.0863	−1.30811
$680$	0	0
$681$	−8.43871	−0.323372
$682$	−6.04231	−0.231372
$683$	19.4215	0.743142	0.371571	−	0.928405i	$-0.378819\pi$
$683$	19.4215	0.743142	0.371571	+	0.928405i	$0.378819\pi$
$684$	0	0
$685$	0	0
$686$	18.6295	0.711277
$687$	6.05137	0.230874
$688$	−14.4200	−0.549758
$689$	−8.34879	−0.318063
$690$	0	0
$691$	−17.8669	−0.679688	−0.339844	−	0.940482i	$-0.610374\pi$
$691$	−17.8669	−0.679688	−0.339844	+	0.940482i	$0.610374\pi$
$692$	8.00197	0.304189
$693$	−6.20213	−0.235599
$694$	−0.0866178	−0.00328797
$695$	0	0
$696$	6.42350	0.243482
$697$	25.7254	0.974418
$698$	4.86343	0.184084
$699$	8.43110	0.318894
$700$	0	0
$701$	4.30484	0.162591	0.0812957	−	0.996690i	$-0.474094\pi$
$701$	4.30484	0.162591	0.0812957	+	0.996690i	$0.474094\pi$
$702$	1.94406	0.0733739
$703$	0	0
$704$	6.34150	0.239004
$705$	0	0
$706$	4.18335	0.157442
$707$	−48.6059	−1.82801
$708$	4.80703	0.180659
$709$	35.1319	1.31941	0.659703	−	0.751526i	$-0.270682\pi$
$709$	35.1319	1.31941	0.659703	+	0.751526i	$0.270682\pi$
$710$	0	0
$711$	9.45592	0.354625
$712$	17.9048	0.671012
$713$	−25.9818	−0.973028
$714$	7.38047	0.276207
$715$	0	0
$716$	4.93502	0.184431
$717$	11.0887	0.414114
$718$	−31.6523	−1.18125
$719$	29.4030	1.09655	0.548273	−	0.836299i	$-0.315285\pi$
$719$	29.4030	1.09655	0.548273	+	0.836299i	$0.315285\pi$
$720$	0	0
$721$	−14.3004	−0.532574
$722$	0	0
$723$	−15.1087	−0.561898
$724$	16.9902	0.631437
$725$	0	0
$726$	5.73700	0.212920
$727$	−22.5569	−0.836589	−0.418294	−	0.908312i	$-0.637372\pi$
$727$	−22.5569	−0.836589	−0.418294	+	0.908312i	$0.637372\pi$
$728$	5.08952	0.188630
$729$	−12.9222	−0.478599
$730$	0	0
$731$	−50.6023	−1.87159
$732$	−4.35364	−0.160915
$733$	−37.9002	−1.39988	−0.699938	−	0.714204i	$-0.746789\pi$
$733$	−37.9002	−1.39988	−0.699938	+	0.714204i	$0.746789\pi$
$734$	18.9998	0.701295
$735$	0	0
$736$	17.3929	0.641113
$737$	9.10669	0.335449
$738$	−15.1339	−0.557087
$739$	−26.0215	−0.957218	−0.478609	−	0.878028i	$-0.658859\pi$
$739$	−26.0215	−0.957218	−0.478609	+	0.878028i	$0.658859\pi$
$740$	0	0
$741$	0	0
$742$	39.2300	1.44018
$743$	50.3874	1.84854	0.924268	−	0.381744i	$-0.124677\pi$
$743$	50.3874	1.84854	0.924268	+	0.381744i	$0.124677\pi$
$744$	11.1930	0.410357
$745$	0	0
$746$	26.4103	0.966951
$747$	−13.5194	−0.494650
$748$	3.63852	0.133037
$749$	−41.6177	−1.52068
$750$	0	0
$751$	−27.1857	−0.992021	−0.496011	−	0.868316i	$-0.665202\pi$
$751$	−27.1857	−0.992021	−0.496011	+	0.868316i	$0.665202\pi$
$752$	4.68811	0.170958
$753$	13.1873	0.480570
$754$	−2.54325	−0.0926197
$755$	0	0
$756$	7.51867	0.273451
$757$	−32.8983	−1.19571	−0.597855	−	0.801605i	$-0.703980\pi$
$757$	−32.8983	−1.19571	−0.597855	+	0.801605i	$0.703980\pi$
$758$	−28.8700	−1.04860
$759$	−1.66021	−0.0602619
$760$	0	0
$761$	3.47213	0.125865	0.0629323	−	0.998018i	$-0.479955\pi$
$761$	3.47213	0.125865	0.0629323	+	0.998018i	$0.479955\pi$
$762$	−5.11277	−0.185216
$763$	−10.7491	−0.389145
$764$	15.5854	0.563859
$765$	0	0
$766$	−19.1923	−0.693445
$767$	−6.11886	−0.220939
$768$	−8.81622	−0.318128
$769$	−31.6735	−1.14218	−0.571089	−	0.820888i	$-0.693479\pi$
$769$	−31.6735	−1.14218	−0.571089	+	0.820888i	$0.693479\pi$
$770$	0	0
$771$	−2.89229	−0.104163
$772$	−6.74883	−0.242896
$773$	−35.0686	−1.26133	−0.630665	−	0.776056i	$-0.717218\pi$
$773$	−35.0686	−1.26133	−0.630665	+	0.776056i	$0.717218\pi$
$774$	29.7687	1.07001
$775$	0	0
$776$	−37.8207	−1.35768
$777$	6.30706	0.226265
$778$	7.52562	0.269807
$779$	0	0
$780$	0	0
$781$	0.564435	0.0201971
$782$	−19.0089	−0.679755
$783$	−12.0790	−0.431667
$784$	−0.702366	−0.0250845
$785$	0	0
$786$	2.08132	0.0742383
$787$	42.1829	1.50366	0.751829	−	0.659358i	$-0.229172\pi$
$787$	42.1829	1.50366	0.751829	+	0.659358i	$0.229172\pi$
$788$	11.0232	0.392685
$789$	10.3738	0.369316
$790$	0	0
$791$	10.8885	0.387150
$792$	−6.88162	−0.244528
$793$	5.54174	0.196793
$794$	−12.2800	−0.435801
$795$	0	0
$796$	7.00496	0.248284
$797$	−20.4194	−0.723291	−0.361646	−	0.932316i	$-0.617785\pi$
$797$	−20.4194	−0.723291	−0.361646	+	0.932316i	$0.617785\pi$
$798$	0	0
$799$	16.4514	0.582008
$800$	0	0
$801$	−16.0028	−0.565432
$802$	41.0711	1.45027
$803$	−5.84103	−0.206125
$804$	−5.24722	−0.185055
$805$	0	0
$806$	−4.43165	−0.156098
$807$	−9.87696	−0.347685
$808$	−53.9310	−1.89729
$809$	28.5536	1.00389	0.501946	−	0.864899i	$-0.332618\pi$
$809$	28.5536	1.00389	0.501946	+	0.864899i	$0.332618\pi$
$810$	0	0
$811$	1.61158	0.0565904	0.0282952	−	0.999600i	$-0.490992\pi$
$811$	1.61158	0.0565904	0.0282952	+	0.999600i	$0.490992\pi$
$812$	−9.83603	−0.345177
$813$	1.00558	0.0352673
$814$	−3.77774	−0.132410
$815$	0	0
$816$	3.54540	0.124114
$817$	0	0
$818$	9.29706	0.325064
$819$	−4.54886	−0.158950
$820$	0	0
$821$	−8.04886	−0.280907	−0.140454	−	0.990087i	$-0.544856\pi$
$821$	−8.04886	−0.280907	−0.140454	+	0.990087i	$0.544856\pi$
$822$	1.31555	0.0458849
$823$	37.3423	1.30167	0.650835	−	0.759219i	$-0.274419\pi$
$823$	37.3423	1.30167	0.650835	+	0.759219i	$0.274419\pi$
$824$	−15.8671	−0.552757
$825$	0	0
$826$	28.7518	1.00040
$827$	−10.9302	−0.380082	−0.190041	−	0.981776i	$-0.560862\pi$
$827$	−10.9302	−0.380082	−0.190041	+	0.981776i	$0.560862\pi$
$828$	−9.20409	−0.319864
$829$	−33.6375	−1.16828	−0.584139	−	0.811654i	$-0.698568\pi$
$829$	−33.6375	−1.16828	−0.584139	+	0.811654i	$0.698568\pi$
$830$	0	0
$831$	3.60265	0.124975
$832$	4.65108	0.161247
$833$	−2.46472	−0.0853976
$834$	−1.35977	−0.0470849
$835$	0	0
$836$	0	0
$837$	−21.0478	−0.727517
$838$	8.17179	0.282290
$839$	−13.8735	−0.478965	−0.239483	−	0.970901i	$-0.576978\pi$
$839$	−13.8735	−0.478965	−0.239483	+	0.970901i	$0.576978\pi$
$840$	0	0
$841$	−13.1981	−0.455108
$842$	36.1951	1.24737
$843$	6.52948	0.224887
$844$	9.08103	0.312582
$845$	0	0
$846$	−9.67815	−0.332741
$847$	−28.2429	−0.970437
$848$	18.8452	0.647146
$849$	−13.6406	−0.468145
$850$	0	0
$851$	−16.2442	−0.556845
$852$	−0.325224	−0.0111420
$853$	29.5477	1.01169	0.505846	−	0.862624i	$-0.331180\pi$
$853$	29.5477	1.01169	0.505846	+	0.862624i	$0.331180\pi$
$854$	−26.0400	−0.891071
$855$	0	0
$856$	−46.1773	−1.57831
$857$	4.28588	0.146403	0.0732014	−	0.997317i	$-0.476678\pi$
$857$	4.28588	0.146403	0.0732014	+	0.997317i	$0.476678\pi$
$858$	−0.283178	−0.00966753
$859$	−34.9764	−1.19338	−0.596689	−	0.802472i	$-0.703517\pi$
$859$	−34.9764	−1.19338	−0.596689	+	0.802472i	$0.703517\pi$
$860$	0	0
$861$	−7.74331	−0.263891
$862$	2.97412	0.101299
$863$	20.0305	0.681848	0.340924	−	0.940091i	$-0.389260\pi$
$863$	20.0305	0.681848	0.340924	+	0.940091i	$0.389260\pi$
$864$	14.0899	0.479349
$865$	0	0
$866$	22.8886	0.777786
$867$	3.40674	0.115699
$868$	−17.1394	−0.581750
$869$	−2.89791	−0.0983047
$870$	0	0
$871$	6.67917	0.226315
$872$	−11.9268	−0.403892
$873$	33.8030	1.14406
$874$	0	0
$875$	0	0
$876$	3.36556	0.113712
$877$	45.5920	1.53953	0.769766	−	0.638326i	$-0.220373\pi$
$877$	45.5920	1.53953	0.769766	+	0.638326i	$0.220373\pi$
$878$	34.1202	1.15150
$879$	−14.9402	−0.503922
$880$	0	0
$881$	−17.2730	−0.581941	−0.290971	−	0.956732i	$-0.593978\pi$
$881$	−17.2730	−0.581941	−0.290971	+	0.956732i	$0.593978\pi$
$882$	1.44997	0.0488229
$883$	35.1932	1.18434	0.592172	−	0.805812i	$-0.298271\pi$
$883$	35.1932	1.18434	0.592172	+	0.805812i	$0.298271\pi$
$884$	2.66862	0.0897554
$885$	0	0
$886$	8.12966	0.273121
$887$	3.16110	0.106139	0.0530697	−	0.998591i	$-0.483099\pi$
$887$	3.16110	0.106139	0.0530697	+	0.998591i	$0.483099\pi$
$888$	6.99805	0.234839
$889$	25.1698	0.844169
$890$	0	0
$891$	5.44491	0.182411
$892$	−25.5727	−0.856237
$893$	0	0
$894$	−7.94259	−0.265640
$895$	0	0
$896$	3.55870	0.118888
$897$	−1.21766	−0.0406565
$898$	24.0715	0.803277
$899$	27.5350	0.918343
$900$	0	0
$901$	66.1310	2.20314
$902$	4.63801	0.154429
$903$	15.2312	0.506864
$904$	12.0814	0.401822
$905$	0	0
$906$	1.30433	0.0433334
$907$	−15.9313	−0.528991	−0.264495	−	0.964387i	$-0.585205\pi$
$907$	−15.9313	−0.528991	−0.264495	+	0.964387i	$0.585205\pi$
$908$	14.3375	0.475807
$909$	48.2019	1.59876
$910$	0	0
$911$	−0.0577380	−0.00191294	−0.000956472	−	1.00000i	$-0.500304\pi$
$911$	−0.0577380	−0.00191294	−0.000956472		1.00000i	$0.500304\pi$
$912$	0	0
$913$	4.14323	0.137121
$914$	3.54929	0.117400
$915$	0	0
$916$	−10.2814	−0.339706
$917$	−10.2462	−0.338360
$918$	−15.3990	−0.508242
$919$	50.0489	1.65096	0.825481	−	0.564430i	$-0.190904\pi$
$919$	50.0489	1.65096	0.825481	+	0.564430i	$0.190904\pi$
$920$	0	0
$921$	−1.36943	−0.0451242
$922$	11.3674	0.374365
$923$	0.413977	0.0136262
$924$	−1.09519	−0.0360291
$925$	0	0
$926$	7.65831	0.251668
$927$	14.1816	0.465783
$928$	−18.4327	−0.605081
$929$	−16.9850	−0.557259	−0.278629	−	0.960399i	$-0.589880\pi$
$929$	−16.9850	−0.557259	−0.278629	+	0.960399i	$0.589880\pi$
$930$	0	0
$931$	0	0
$932$	−14.3246	−0.469218
$933$	7.77874	0.254665
$934$	−11.3557	−0.371571
$935$	0	0
$936$	−5.04723	−0.164974
$937$	33.6925	1.10069	0.550344	−	0.834938i	$-0.314497\pi$
$937$	33.6925	1.10069	0.550344	+	0.834938i	$0.314497\pi$
$938$	−31.3847	−1.02475
$939$	−0.794036	−0.0259124
$940$	0	0
$941$	27.1733	0.885823	0.442911	−	0.896565i	$-0.353946\pi$
$941$	27.1733	0.885823	0.442911	+	0.896565i	$0.353946\pi$
$942$	−9.00360	−0.293353
$943$	19.9434	0.649446
$944$	13.8117	0.449532
$945$	0	0
$946$	−9.12306	−0.296616
$947$	33.2962	1.08198	0.540991	−	0.841028i	$-0.318049\pi$
$947$	33.2962	1.08198	0.540991	+	0.841028i	$0.318049\pi$
$948$	1.66975	0.0542311
$949$	−4.28402	−0.139065
$950$	0	0
$951$	2.99864	0.0972376
$952$	−40.3142	−1.30659
$953$	−30.4086	−0.985030	−0.492515	−	0.870304i	$-0.663922\pi$
$953$	−30.4086	−0.985030	−0.492515	+	0.870304i	$0.663922\pi$
$954$	−38.9040	−1.25956
$955$	0	0
$956$	−18.8399	−0.609325
$957$	1.75946	0.0568751
$958$	−3.61079	−0.116659
$959$	−6.47635	−0.209132
$960$	0	0
$961$	16.9801	0.547744
$962$	−2.77073	−0.0893319
$963$	41.2719	1.32997
$964$	25.6699	0.826772
$965$	0	0
$966$	5.72165	0.184091
$967$	58.9180	1.89467	0.947337	−	0.320239i	$-0.103763\pi$
$967$	58.9180	1.89467	0.947337	+	0.320239i	$0.103763\pi$
$968$	−31.3371	−1.00721
$969$	0	0
$970$	0	0
$971$	40.8679	1.31151	0.655757	−	0.754972i	$-0.272349\pi$
$971$	40.8679	1.31151	0.655757	+	0.754972i	$0.272349\pi$
$972$	−11.3684	−0.364643
$973$	6.69405	0.214601
$974$	−28.2769	−0.906051
$975$	0	0
$976$	−12.5090	−0.400403
$977$	−35.9431	−1.14992	−0.574961	−	0.818181i	$-0.694983\pi$
$977$	−35.9431	−1.14992	−0.574961	+	0.818181i	$0.694983\pi$
$978$	−8.92068	−0.285252
$979$	4.90430	0.156742
$980$	0	0
$981$	10.6598	0.340342
$982$	−0.255544	−0.00815474
$983$	−10.0666	−0.321074	−0.160537	−	0.987030i	$-0.551323\pi$
$983$	−10.0666	−0.321074	−0.160537	+	0.987030i	$0.551323\pi$
$984$	−8.59165	−0.273892
$985$	0	0
$986$	20.1452	0.641553
$987$	−4.95185	−0.157619
$988$	0	0
$989$	−39.2290	−1.24741
$990$	0	0
$991$	18.0301	0.572745	0.286372	−	0.958118i	$-0.407551\pi$
$991$	18.0301	0.572745	0.286372	+	0.958118i	$0.407551\pi$
$992$	−32.1191	−1.01978
$993$	−16.9491	−0.537864
$994$	−1.94523	−0.0616989
$995$	0	0
$996$	−2.38730	−0.0756446
$997$	−18.7246	−0.593014	−0.296507	−	0.955031i	$-0.595822\pi$
$997$	−18.7246	−0.593014	−0.296507	+	0.955031i	$0.595822\pi$
$998$	3.40268	0.107710
$999$	−13.1594	−0.416344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.ct.1.9		24
5.2	odd	4		1805.2.b.l.1084.9		24
5.3	odd	4		1805.2.b.l.1084.16		24
5.4	even	2	inner	9025.2.a.ct.1.16		24
19.2	odd	18		475.2.l.f.251.3		48
19.10	odd	18		475.2.l.f.176.3		48
19.18	odd	2		9025.2.a.cu.1.16		24
95.2	even	36		95.2.p.a.4.6	yes	48
95.18	even	4		1805.2.b.k.1084.9		24
95.29	odd	18		475.2.l.f.176.6		48
95.37	even	4		1805.2.b.k.1084.16		24
95.48	even	36		95.2.p.a.24.6	yes	48
95.59	odd	18		475.2.l.f.251.6		48
95.67	even	36		95.2.p.a.24.3	yes	48
95.78	even	36		95.2.p.a.4.3	✓	48
95.94	odd	2		9025.2.a.cu.1.9		24
285.2	odd	36		855.2.da.b.289.3		48
285.143	odd	36		855.2.da.b.784.3		48
285.173	odd	36		855.2.da.b.289.6		48
285.257	odd	36		855.2.da.b.784.6		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
95.2.p.a.4.3	✓	48	95.78	even	36
95.2.p.a.4.6	yes	48	95.2	even	36
95.2.p.a.24.3	yes	48	95.67	even	36
95.2.p.a.24.6	yes	48	95.48	even	36
475.2.l.f.176.3		48	19.10	odd	18
475.2.l.f.176.6		48	95.29	odd	18
475.2.l.f.251.3		48	19.2	odd	18
475.2.l.f.251.6		48	95.59	odd	18
855.2.da.b.289.3		48	285.2	odd	36
855.2.da.b.289.6		48	285.173	odd	36
855.2.da.b.784.3		48	285.143	odd	36
855.2.da.b.784.6		48	285.257	odd	36
1805.2.b.k.1084.9		24	95.18	even	4
1805.2.b.k.1084.16		24	95.37	even	4
1805.2.b.l.1084.9		24	5.2	odd	4
1805.2.b.l.1084.16		24	5.3	odd	4
9025.2.a.ct.1.9		24	1.1	even	1	trivial
9025.2.a.ct.1.16		24	5.4	even	2	inner
9025.2.a.cu.1.9		24	95.94	odd	2
9025.2.a.cu.1.16		24	19.18	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-1.04740 q^{2} +0.531453 q^{3} -0.902948 q^{4} -0.556645 q^{6} +2.74033 q^{7} +3.04056 q^{8} -2.71756 q^{9} +O(q^{10})\)	\(q-1.04740 q^{2} +0.531453 q^{3} -0.902948 q^{4} -0.556645 q^{6} +2.74033 q^{7} +3.04056 q^{8} -2.71756 q^{9} +0.832835 q^{11} -0.479874 q^{12} +0.610831 q^{13} -2.87023 q^{14} -1.37879 q^{16} -4.83841 q^{17} +2.84638 q^{18} +1.45636 q^{21} -0.872314 q^{22} -3.75094 q^{23} +1.61591 q^{24} -0.639786 q^{26} -3.03861 q^{27} -2.47437 q^{28} +3.97516 q^{29} +6.92676 q^{31} -4.63696 q^{32} +0.442613 q^{33} +5.06777 q^{34} +2.45381 q^{36} +4.33071 q^{37} +0.324628 q^{39} -5.31691 q^{41} -1.52539 q^{42} +10.4585 q^{43} -0.752007 q^{44} +3.92874 q^{46} -3.40016 q^{47} -0.732762 q^{48} +0.509407 q^{49} -2.57139 q^{51} -0.551549 q^{52} -13.6679 q^{53} +3.18265 q^{54} +8.33212 q^{56} -4.16359 q^{58} -10.0173 q^{59} +9.07245 q^{61} -7.25511 q^{62} -7.44700 q^{63} +7.61435 q^{64} -0.463594 q^{66} +10.9346 q^{67} +4.36883 q^{68} -1.99345 q^{69} +0.677726 q^{71} -8.26288 q^{72} -7.01343 q^{73} -4.53600 q^{74} +2.28224 q^{77} -0.340016 q^{78} -3.47957 q^{79} +6.53779 q^{81} +5.56894 q^{82} +4.97485 q^{83} -1.31501 q^{84} -10.9542 q^{86} +2.11261 q^{87} +2.53228 q^{88} +5.88868 q^{89} +1.67388 q^{91} +3.38690 q^{92} +3.68125 q^{93} +3.56134 q^{94} -2.46433 q^{96} -12.4387 q^{97} -0.533555 q^{98} -2.26328 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q + 18 * q^4 - 12 * q^6 + 12 * q^9	\( 24 q + 18 q^{4} - 12 q^{6} + 12 q^{9} + 12 q^{11} - 24 q^{14} + 6 q^{16} - 6 q^{21} - 42 q^{24} - 12 q^{26} - 36 q^{29} - 42 q^{31} - 6 q^{34} - 6 q^{36} + 24 q^{39} - 60 q^{41} - 30 q^{44} - 6 q^{46} + 12 q^{49} - 30 q^{51} - 24 q^{54} - 18 q^{56} - 60 q^{59} + 30 q^{61} + 36 q^{66} - 66 q^{69} - 96 q^{71} + 24 q^{74} - 72 q^{79} - 96 q^{81} + 54 q^{84} - 108 q^{86} - 84 q^{89} - 96 q^{91} - 36 q^{94} - 120 q^{96}+O(q^{100}) \) 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

Introduction

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