LMFDB - Embedded newform 9025.2.a.ct.1.16

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			1.16
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	$-0.379251\pi$
$2$	1.04740	0.740625	0.370313	+	0.928907i	$0.379251\pi$
$3$	−0.531453	−0.306835	−0.153417	−	0.988161i	$-0.549028\pi$
$3$	−0.531453	−0.306835	−0.153417	+	0.988161i	$0.549028\pi$
$4$	−0.902948	−0.451474
$5$	0	0
$5$	0	0
$6$	−0.556645	−0.227250
$7$	−2.74033	−1.03575	−0.517874	−	0.855457i	$-0.673276\pi$
$7$	−2.74033	−1.03575	−0.517874	+	0.855457i	$0.673276\pi$
$8$	−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	$-0.526995\pi$
$13$	−0.610831	−0.169414	−0.0847071	+	0.996406i	$0.526995\pi$
$14$	−2.87023	−0.767101
$15$	0	0
$16$	−1.37879	−0.344697
$17$	4.83841	1.17349	0.586744	−	0.809773i	$-0.300410\pi$
$17$	4.83841	1.17349	0.586744	+	0.809773i	$0.300410\pi$
$18$	−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	$-0.372108\pi$
$23$	3.75094	0.782124	0.391062	+	0.920364i	$0.372108\pi$
$24$	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	$-0.615854\pi$
$37$	−4.33071	−0.711965	−0.355982	+	0.934493i	$0.615854\pi$
$38$	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	$-0.793818\pi$
$43$	−10.4585	−1.59490	−0.797450	+	0.603385i	$0.793818\pi$
$44$	−0.752007	−0.113369
$45$	0	0
$46$	3.92874	0.579261
$47$	3.40016	0.495965	0.247982	−	0.968765i	$-0.420232\pi$
$47$	3.40016	0.495965	0.247982	+	0.968765i	$0.420232\pi$
$48$	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	$-0.112017\pi$
$53$	13.6679	1.87743	0.938716	+	0.344692i	$0.112017\pi$
$54$	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	$-0.732821\pi$
$67$	−10.9346	−1.33587	−0.667935	+	0.744220i	$0.732821\pi$
$68$	−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	$-0.365379\pi$
$73$	7.01343	0.820859	0.410430	+	0.911892i	$0.365379\pi$
$74$	−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	$-0.588026\pi$
$83$	−4.97485	−0.546060	−0.273030	+	0.962005i	$0.588026\pi$
$84$	−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	$-0.282447\pi$
$97$	12.4387	1.26296	0.631482	+	0.775391i	$0.282447\pi$
$98$	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	$-0.417234\pi$
$103$	5.21849	0.514193	0.257097	+	0.966386i	$0.417234\pi$
$104$	1.85727	0.182120
$105$	0	0
$106$	14.3158	1.39047
$107$	15.1871	1.46819	0.734097	−	0.679044i	$-0.237606\pi$
$107$	15.1871	1.46819	0.734097	+	0.679044i	$0.237606\pi$
$108$	−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	$-0.559842\pi$
$113$	−3.97342	−0.373788	−0.186894	+	0.982380i	$0.559842\pi$
$114$	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	$-0.633605\pi$
$127$	−9.18497	−0.815034	−0.407517	+	0.913198i	$0.633605\pi$
$128$	−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	$-0.467809\pi$
$137$	2.36335	0.201914	0.100957	+	0.994891i	$0.467809\pi$
$138$	−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	$-0.723327\pi$
$157$	−16.1747	−1.29088	−0.645442	+	0.763809i	$0.723327\pi$
$158$	−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	$-0.715970\pi$
$163$	−16.0258	−1.25524	−0.627618	+	0.778521i	$0.715970\pi$
$164$	4.80089	0.374886
$165$	0	0
$166$	−5.21067	−0.404426
$167$	−7.57646	−0.586284	−0.293142	−	0.956069i	$-0.594701\pi$
$167$	−7.57646	−0.586284	−0.293142	+	0.956069i	$0.594701\pi$
$168$	−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	$-0.390627\pi$
$173$	8.86205	0.673769	0.336885	+	0.941546i	$0.390627\pi$
$174$	−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	$-0.586694\pi$
$193$	−7.47422	−0.538006	−0.269003	+	0.963139i	$0.586694\pi$
$194$	13.0284	0.935383
$195$	0	0
$196$	−0.459968	−0.0328549
$197$	12.2080	0.869784	0.434892	−	0.900483i	$-0.356787\pi$
$197$	12.2080	0.869784	0.434892	+	0.900483i	$0.356787\pi$
$198$	−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	$-0.897167\pi$
$223$	−28.3213	−1.89654	−0.948268	+	0.317470i	$0.897167\pi$
$224$	−12.7068	−0.849009
$225$	0	0
$226$	−4.16177	−0.276837
$227$	15.8786	1.05390	0.526949	−	0.849897i	$-0.323336\pi$
$227$	15.8786	1.05390	0.526949	+	0.849897i	$0.323336\pi$
$228$	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	$-0.673938\pi$
$233$	−15.8642	−1.03930	−0.519651	+	0.854379i	$0.673938\pi$
$234$	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	$-0.445708\pi$
$257$	5.44223	0.339477	0.169739	+	0.985489i	$0.445708\pi$
$258$	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	$-0.705556\pi$
$263$	−19.5197	−1.20363	−0.601817	+	0.798634i	$0.705556\pi$
$264$	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	$-0.565281\pi$
$277$	−6.77887	−0.407303	−0.203652	+	0.979043i	$0.565281\pi$
$278$	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	$-0.223793\pi$
$283$	25.6667	1.52572	0.762862	+	0.646561i	$0.223793\pi$
$284$	−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	$-0.193326\pi$
$293$	28.1121	1.64232	0.821162	+	0.570695i	$0.193326\pi$
$294$	−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	$-0.476573\pi$
$307$	2.57676	0.147064	0.0735319	+	0.997293i	$0.476573\pi$
$308$	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	$-0.486555\pi$
$313$	1.49408	0.0844507	0.0422253	+	0.999108i	$0.486555\pi$
$314$	−16.9415	−0.956062
$315$	0	0
$316$	3.14187	0.176744
$317$	−5.64234	−0.316905	−0.158453	−	0.987367i	$-0.550651\pi$
$317$	−5.64234	−0.316905	−0.158453	+	0.987367i	$0.550651\pi$
$318$	−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	$-0.637182\pi$
$337$	−15.3378	−0.835504	−0.417752	+	0.908561i	$0.637182\pi$
$338$	−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	$-0.500707\pi$
$347$	−0.0826977	−0.00443945	−0.00221972	+	0.999998i	$0.500707\pi$
$348$	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	$-0.466103\pi$
$353$	3.99402	0.212580	0.106290	+	0.994335i	$0.466103\pi$
$354$	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	$-0.343009\pi$
$367$	18.1399	0.946896	0.473448	+	0.880822i	$0.343009\pi$
$368$	−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	$-0.273597\pi$
$373$	25.2151	1.30559	0.652794	+	0.757536i	$0.273597\pi$
$374$	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	$-0.655079\pi$
$383$	−18.3237	−0.936296	−0.468148	+	0.883650i	$0.655079\pi$
$384$	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	$-0.595057\pi$
$397$	−11.7242	−0.588423	−0.294211	+	0.955740i	$0.595057\pi$
$398$	−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	$-0.324033\pi$
$433$	21.8527	1.05018	0.525088	+	0.851048i	$0.324033\pi$
$434$	−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	$-0.440971\pi$
$443$	7.76173	0.368771	0.184385	+	0.982854i	$0.440971\pi$
$444$	−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	$-0.474745\pi$
$457$	3.38866	0.158515	0.0792573	+	0.996854i	$0.474745\pi$
$458$	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	$-0.445655\pi$
$463$	7.31171	0.339804	0.169902	+	0.985461i	$0.445655\pi$
$464$	−5.48090	−0.254445
$465$	0	0
$466$	−16.6163	−0.769733
$467$	−10.8418	−0.501699	−0.250850	−	0.968026i	$-0.580710\pi$
$467$	−10.8418	−0.501699	−0.250850	+	0.968026i	$0.580710\pi$
$468$	−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	$-0.709506\pi$
$487$	−26.9972	−1.22336	−0.611680	+	0.791106i	$0.709506\pi$
$488$	−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	$-0.449220\pi$
$503$	7.12545	0.317708	0.158854	+	0.987302i	$0.449220\pi$
$504$	−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	$-0.561034\pi$
$523$	−8.71641	−0.381142	−0.190571	+	0.981673i	$0.561034\pi$
$524$	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	$-0.371342\pi$
$547$	18.3959	0.786551	0.393275	+	0.919421i	$0.371342\pi$
$548$	−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	$-0.498637\pi$
$557$	0.202098	0.00856316	0.00428158	+	0.999991i	$0.498637\pi$
$558$	−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	$-0.454477\pi$
$563$	6.76375	0.285058	0.142529	+	0.989791i	$0.454477\pi$
$564$	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	$-0.648284\pi$
$577$	−21.5794	−0.898364	−0.449182	+	0.893440i	$0.648284\pi$
$578$	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	$-0.296238\pi$
$587$	28.9431	1.19461	0.597305	+	0.802014i	$0.296238\pi$
$588$	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	$-0.380743\pi$
$593$	17.8231	0.731907	0.365954	+	0.930633i	$0.380743\pi$
$594$	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	$-0.549257\pi$
$607$	−7.59458	−0.308254	−0.154127	+	0.988051i	$0.549257\pi$
$608$	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	$-0.381959\pi$
$613$	17.9449	0.724788	0.362394	+	0.932025i	$0.381959\pi$
$614$	2.69891	0.108919
$615$	0	0
$616$	6.93929	0.279592
$617$	40.5840	1.63385	0.816924	−	0.576745i	$-0.195677\pi$
$617$	40.5840	1.63385	0.816924	+	0.576745i	$0.195677\pi$
$618$	−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	$-0.402810\pi$
$643$	15.2454	0.601219	0.300610	+	0.953747i	$0.402810\pi$
$644$	9.28122	0.365731
$645$	0	0
$646$	0	0
$647$	17.6749	0.694872	0.347436	−	0.937704i	$-0.387052\pi$
$647$	17.6749	0.694872	0.347436	+	0.937704i	$0.387052\pi$
$648$	−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	$-0.542884\pi$
$653$	−6.86456	−0.268631	−0.134315	+	0.990939i	$0.542884\pi$
$654$	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	$-0.836246\pi$
$673$	−45.1688	−1.74113	−0.870565	+	0.492054i	$0.836246\pi$
$674$	−16.0649	−0.618796
$675$	0	0
$676$	11.4014	0.438516
$677$	46.9628	1.80493	0.902463	−	0.430767i	$-0.141757\pi$
$677$	46.9628	1.80493	0.902463	+	0.430767i	$0.141757\pi$
$678$	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	$-0.621181\pi$
$683$	−19.4215	−0.743142	−0.371571	+	0.928405i	$0.621181\pi$
$684$	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	$-0.362628\pi$
$727$	22.5569	0.836589	0.418294	+	0.908312i	$0.362628\pi$
$728$	−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	$-0.253211\pi$
$733$	37.9002	1.39988	0.699938	+	0.714204i	$0.253211\pi$
$734$	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	$-0.875323\pi$
$743$	−50.3874	−1.84854	−0.924268	+	0.381744i	$0.875323\pi$
$744$	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	$-0.296020\pi$
$757$	32.8983	1.19571	0.597855	+	0.801605i	$0.296020\pi$
$758$	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	$-0.282782\pi$
$773$	35.0686	1.26133	0.630665	+	0.776056i	$0.282782\pi$
$774$	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	$-0.770828\pi$
$787$	−42.1829	−1.50366	−0.751829	+	0.659358i	$0.770828\pi$
$788$	−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	$-0.382215\pi$
$797$	20.4194	0.723291	0.361646	+	0.932316i	$0.382215\pi$
$798$	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	$-0.725581\pi$
$823$	−37.3423	−1.30167	−0.650835	+	0.759219i	$0.725581\pi$
$824$	−15.8671	−0.552757
$825$	0	0
$826$	28.7518	1.00040
$827$	10.9302	0.380082	0.190041	−	0.981776i	$-0.439138\pi$
$827$	10.9302	0.380082	0.190041	+	0.981776i	$0.439138\pi$
$828$	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	$-0.668820\pi$
$853$	−29.5477	−1.01169	−0.505846	+	0.862624i	$0.668820\pi$
$854$	−26.0400	−0.891071
$855$	0	0
$856$	−46.1773	−1.57831
$857$	−4.28588	−0.146403	−0.0732014	−	0.997317i	$-0.523322\pi$
$857$	−4.28588	−0.146403	−0.0732014	+	0.997317i	$0.523322\pi$
$858$	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	$-0.610740\pi$
$863$	−20.0305	−0.681848	−0.340924	+	0.940091i	$0.610740\pi$
$864$	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	$-0.779627\pi$
$877$	−45.5920	−1.53953	−0.769766	+	0.638326i	$0.779627\pi$
$878$	−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	$-0.701729\pi$
$883$	−35.1932	−1.18434	−0.592172	+	0.805812i	$0.701729\pi$
$884$	2.66862	0.0897554
$885$	0	0
$886$	8.12966	0.273121
$887$	−3.16110	−0.106139	−0.0530697	−	0.998591i	$-0.516901\pi$
$887$	−3.16110	−0.106139	−0.0530697	+	0.998591i	$0.516901\pi$
$888$	−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	$-0.414795\pi$
$907$	15.9313	0.528991	0.264495	+	0.964387i	$0.414795\pi$
$908$	−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	$-0.685503\pi$
$937$	−33.6925	−1.10069	−0.550344	+	0.834938i	$0.685503\pi$
$938$	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	$-0.681951\pi$
$947$	−33.2962	−1.08198	−0.540991	+	0.841028i	$0.681951\pi$
$948$	−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	$-0.336078\pi$
$953$	30.4086	0.985030	0.492515	+	0.870304i	$0.336078\pi$
$954$	−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	$-0.896237\pi$
$967$	−58.9180	−1.89467	−0.947337	+	0.320239i	$0.896237\pi$
$968$	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	$-0.305017\pi$
$977$	35.9431	1.14992	0.574961	+	0.818181i	$0.305017\pi$
$978$	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	$-0.448677\pi$
$983$	10.0666	0.321074	0.160537	+	0.987030i	$0.448677\pi$
$984$	−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	$-0.404178\pi$
$997$	18.7246	0.593014	0.296507	+	0.955031i	$0.404178\pi$
$998$	−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.1.16		24
5.2	odd	4		1805.2.b.l.1084.16		24
5.3	odd	4		1805.2.b.l.1084.9		24
5.4	even	2	inner	9025.2.a.ct.1.9		24
19.2	odd	18		475.2.l.f.251.6		48
19.10	odd	18		475.2.l.f.176.6		48
19.18	odd	2		9025.2.a.cu.1.9		24
95.2	even	36		95.2.p.a.4.3	✓	48
95.18	even	4		1805.2.b.k.1084.16		24
95.29	odd	18		475.2.l.f.176.3		48
95.37	even	4		1805.2.b.k.1084.9		24
95.48	even	36		95.2.p.a.24.3	yes	48
95.59	odd	18		475.2.l.f.251.3		48
95.67	even	36		95.2.p.a.24.6	yes	48
95.78	even	36		95.2.p.a.4.6	yes	48
95.94	odd	2		9025.2.a.cu.1.16		24
285.2	odd	36		855.2.da.b.289.6		48
285.143	odd	36		855.2.da.b.784.6		48
285.173	odd	36		855.2.da.b.289.3		48
285.257	odd	36		855.2.da.b.784.3		48

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

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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