LMFDB - Embedded newform 9025.2.a.cv.1.20

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:	$0$
Dimension:	$40$
Twist minimal:	no (minimal twist has level 1805)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-0.113485 q^{2} -1.07621 q^{3} -1.98712 q^{4} +0.122133 q^{6} +1.50555 q^{7} +0.452479 q^{8} -1.84178 q^{9} +O(q^{10})$	\(q-0.113485 q^{2} -1.07621 q^{3} -1.98712 q^{4} +0.122133 q^{6} +1.50555 q^{7} +0.452479 q^{8} -1.84178 q^{9} -0.314502 q^{11} +2.13855 q^{12} +5.17028 q^{13} -0.170857 q^{14} +3.92289 q^{16} -6.53710 q^{17} +0.209015 q^{18} -1.62028 q^{21} +0.0356913 q^{22} +5.96878 q^{23} -0.486960 q^{24} -0.586750 q^{26} +5.21075 q^{27} -2.99170 q^{28} +6.64674 q^{29} -7.01474 q^{31} -1.35015 q^{32} +0.338469 q^{33} +0.741863 q^{34} +3.65984 q^{36} -1.92182 q^{37} -5.56429 q^{39} +1.75303 q^{41} +0.183877 q^{42} +0.0943416 q^{43} +0.624953 q^{44} -0.677368 q^{46} -0.794179 q^{47} -4.22184 q^{48} -4.73333 q^{49} +7.03526 q^{51} -10.2740 q^{52} +6.17127 q^{53} -0.591343 q^{54} +0.681228 q^{56} -0.754306 q^{58} -12.6295 q^{59} +7.61655 q^{61} +0.796068 q^{62} -2.77289 q^{63} -7.69256 q^{64} -0.0384111 q^{66} +14.5501 q^{67} +12.9900 q^{68} -6.42364 q^{69} +2.29699 q^{71} -0.833367 q^{72} +8.53778 q^{73} +0.218098 q^{74} -0.473497 q^{77} +0.631464 q^{78} +8.30254 q^{79} -0.0824966 q^{81} -0.198943 q^{82} +3.71479 q^{83} +3.21969 q^{84} -0.0107064 q^{86} -7.15326 q^{87} -0.142305 q^{88} -2.77358 q^{89} +7.78410 q^{91} -11.8607 q^{92} +7.54930 q^{93} +0.0901275 q^{94} +1.45304 q^{96} -6.44264 q^{97} +0.537163 q^{98} +0.579244 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) $ 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9	$ 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) $ 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9 + 20 * q^11 + 40 * q^16 + 92 * q^24 + 76 * q^26 + 156 * q^36 + 80 * q^39 + 48 * q^44 + 72 * q^49 + 32 * q^54 + 80 * q^61 + 72 * q^64 + 16 * q^66 + 100 * q^74 + 40 * q^81 + 380 * q^96 + 128 * q^99

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 $

$2$	−0.113485	−0.0802461	−0.0401230	−	0.999195i	$-0.512775\pi$
$2$	−0.113485	−0.0802461	−0.0401230	+	0.999195i	$0.512775\pi$
$3$	−1.07621	−0.621348	−0.310674	−	0.950517i	$-0.600555\pi$
$3$	−1.07621	−0.621348	−0.310674	+	0.950517i	$0.600555\pi$
$4$	−1.98712	−0.993561
$5$	0	0
$5$	0	0
$6$	0.122133	0.0498607
$7$	1.50555	0.569043	0.284521	−	0.958670i	$-0.408165\pi$
$7$	1.50555	0.569043	0.284521	+	0.958670i	$0.408165\pi$
$8$	0.452479	0.159975
$9$	−1.84178	−0.613927
$10$	0	0
$11$	−0.314502	−0.0948258	−0.0474129	−	0.998875i	$-0.515098\pi$
$11$	−0.314502	−0.0948258	−0.0474129	+	0.998875i	$0.515098\pi$
$12$	2.13855	0.617346
$13$	5.17028	1.43398	0.716989	−	0.697084i	$-0.245520\pi$
$13$	5.17028	1.43398	0.716989	+	0.697084i	$0.245520\pi$
$14$	−0.170857	−0.0456635
$15$	0	0
$16$	3.92289	0.980723
$17$	−6.53710	−1.58548	−0.792740	−	0.609560i	$-0.791346\pi$
$17$	−6.53710	−1.58548	−0.792740	+	0.609560i	$0.791346\pi$
$18$	0.209015	0.0492652
$19$	0	0
$19$	0	0
$20$	0	0
$21$	−1.62028	−0.353573
$22$	0.0356913	0.00760940
$23$	5.96878	1.24458	0.622288	−	0.782788i	$-0.286203\pi$
$23$	5.96878	1.24458	0.622288	+	0.782788i	$0.286203\pi$
$24$	−0.486960	−0.0994003
$25$	0	0
$26$	−0.586750	−0.115071
$27$	5.21075	1.00281
$28$	−2.99170	−0.565379
$29$	6.64674	1.23427	0.617134	−	0.786858i	$-0.288294\pi$
$29$	6.64674	1.23427	0.617134	+	0.786858i	$0.288294\pi$
$30$	0	0
$31$	−7.01474	−1.25988	−0.629942	−	0.776642i	$-0.716921\pi$
$31$	−7.01474	−1.25988	−0.629942	+	0.776642i	$0.716921\pi$
$32$	−1.35015	−0.238675
$33$	0.338469	0.0589198
$34$	0.741863	0.127228
$35$	0	0
$36$	3.65984	0.609974
$37$	−1.92182	−0.315945	−0.157972	−	0.987444i	$-0.550496\pi$
$37$	−1.92182	−0.315945	−0.157972	+	0.987444i	$0.550496\pi$
$38$	0	0
$39$	−5.56429	−0.890999
$40$	0	0
$41$	1.75303	0.273778	0.136889	−	0.990586i	$-0.456290\pi$
$41$	1.75303	0.273778	0.136889	+	0.990586i	$0.456290\pi$
$42$	0.183877	0.0283729
$43$	0.0943416	0.0143870	0.00719348	−	0.999974i	$-0.497710\pi$
$43$	0.0943416	0.0143870	0.00719348	+	0.999974i	$0.497710\pi$
$44$	0.624953	0.0942152
$45$	0	0
$46$	−0.677368	−0.0998724
$47$	−0.794179	−0.115843	−0.0579215	−	0.998321i	$-0.518447\pi$
$47$	−0.794179	−0.115843	−0.0579215	+	0.998321i	$0.518447\pi$
$48$	−4.22184	−0.609370
$49$	−4.73333	−0.676190
$50$	0	0
$51$	7.03526	0.985134
$52$	−10.2740	−1.42474
$53$	6.17127	0.847689	0.423844	−	0.905735i	$-0.360680\pi$
$53$	6.17127	0.847689	0.423844	+	0.905735i	$0.360680\pi$
$54$	−0.591343	−0.0804716
$55$	0	0
$56$	0.681228	0.0910329
$57$	0	0
$58$	−0.754306	−0.0990452
$59$	−12.6295	−1.64422	−0.822109	−	0.569330i	$-0.807203\pi$
$59$	−12.6295	−1.64422	−0.822109	+	0.569330i	$0.807203\pi$
$60$	0	0
$61$	7.61655	0.975199	0.487599	−	0.873067i	$-0.337873\pi$
$61$	7.61655	0.975199	0.487599	+	0.873067i	$0.337873\pi$
$62$	0.796068	0.101101
$63$	−2.77289	−0.349351
$64$	−7.69256	−0.961570
$65$	0	0
$66$	−0.0384111	−0.00472808
$67$	14.5501	1.77758	0.888790	−	0.458314i	$-0.151546\pi$
$67$	14.5501	1.77758	0.888790	+	0.458314i	$0.151546\pi$
$68$	12.9900	1.57527
$69$	−6.42364	−0.773315
$70$	0	0
$71$	2.29699	0.272602	0.136301	−	0.990667i	$-0.456479\pi$
$71$	2.29699	0.272602	0.136301	+	0.990667i	$0.456479\pi$
$72$	−0.833367	−0.0982133
$73$	8.53778	0.999272	0.499636	−	0.866236i	$-0.333467\pi$
$73$	8.53778	0.999272	0.499636	+	0.866236i	$0.333467\pi$
$74$	0.218098	0.0253533
$75$	0	0
$76$	0	0
$77$	−0.473497	−0.0539600
$78$	0.631464	0.0714992
$79$	8.30254	0.934109	0.467054	−	0.884229i	$-0.345315\pi$
$79$	8.30254	0.934109	0.467054	+	0.884229i	$0.345315\pi$
$80$	0	0
$81$	−0.0824966	−0.00916629
$82$	−0.198943	−0.0219696
$83$	3.71479	0.407751	0.203875	−	0.978997i	$-0.434646\pi$
$83$	3.71479	0.407751	0.203875	+	0.978997i	$0.434646\pi$
$84$	3.21969	0.351297
$85$	0	0
$86$	−0.0107064	−0.00115450
$87$	−7.15326	−0.766910
$88$	−0.142305	−0.0151698
$89$	−2.77358	−0.293999	−0.147000	−	0.989137i	$-0.546962\pi$
$89$	−2.77358	−0.293999	−0.147000	+	0.989137i	$0.546962\pi$
$90$	0	0
$91$	7.78410	0.815995
$92$	−11.8607	−1.23656
$93$	7.54930	0.782826
$94$	0.0901275	0.00929594
$95$	0	0
$96$	1.45304	0.148300
$97$	−6.44264	−0.654151	−0.327075	−	0.944998i	$-0.606063\pi$
$97$	−6.44264	−0.654151	−0.327075	+	0.944998i	$0.606063\pi$
$98$	0.537163	0.0542616
$99$	0.579244	0.0582162
$100$	0	0
$101$	−9.46719	−0.942021	−0.471010	−	0.882128i	$-0.656111\pi$
$101$	−9.46719	−0.942021	−0.471010	+	0.882128i	$0.656111\pi$
$102$	−0.798397	−0.0790531
$103$	−13.4778	−1.32800	−0.664002	−	0.747731i	$-0.731143\pi$
$103$	−13.4778	−1.32800	−0.664002	+	0.747731i	$0.731143\pi$
$104$	2.33944	0.229401
$105$	0	0
$106$	−0.700347	−0.0680237
$107$	−9.97967	−0.964771	−0.482385	−	0.875959i	$-0.660230\pi$
$107$	−9.97967	−0.964771	−0.482385	+	0.875959i	$0.660230\pi$
$108$	−10.3544	−0.996352
$109$	−8.18121	−0.783618	−0.391809	−	0.920047i	$-0.628151\pi$
$109$	−8.18121	−0.783618	−0.391809	+	0.920047i	$0.628151\pi$
$110$	0	0
$111$	2.06827	0.196312
$112$	5.90610	0.558074
$113$	−14.1535	−1.33145	−0.665724	−	0.746198i	$-0.731877\pi$
$113$	−14.1535	−1.33145	−0.665724	+	0.746198i	$0.731877\pi$
$114$	0	0
$115$	0	0
$116$	−13.2079	−1.22632
$117$	−9.52253	−0.880358
$118$	1.43326	0.131942
$119$	−9.84190	−0.902206
$120$	0	0
$121$	−10.9011	−0.991008
$122$	−0.864364	−0.0782559
$123$	−1.88663	−0.170111
$124$	13.9391	1.25177
$125$	0	0
$126$	0.314681	0.0280340
$127$	−18.5751	−1.64828	−0.824138	−	0.566388i	$-0.808340\pi$
$127$	−18.5751	−1.64828	−0.824138	+	0.566388i	$0.808340\pi$
$128$	3.57329	0.315837
$129$	−0.101531	−0.00893930
$130$	0	0
$131$	18.3046	1.59928	0.799642	−	0.600477i	$-0.205023\pi$
$131$	18.3046	1.59928	0.799642	+	0.600477i	$0.205023\pi$
$132$	−0.672578	−0.0585404
$133$	0	0
$134$	−1.65122	−0.142644
$135$	0	0
$136$	−2.95790	−0.253638
$137$	2.57199	0.219740	0.109870	−	0.993946i	$-0.464957\pi$
$137$	2.57199	0.219740	0.109870	+	0.993946i	$0.464957\pi$
$138$	0.728987	0.0620555
$139$	−2.00421	−0.169994	−0.0849972	−	0.996381i	$-0.527088\pi$
$139$	−2.00421	−0.169994	−0.0849972	+	0.996381i	$0.527088\pi$
$140$	0	0
$141$	0.854700	0.0719788
$142$	−0.260674	−0.0218753
$143$	−1.62606	−0.135978
$144$	−7.22511	−0.602093
$145$	0	0
$146$	−0.968911	−0.0801876
$147$	5.09404	0.420149
$148$	3.81888	0.313910
$149$	8.49666	0.696074	0.348037	−	0.937481i	$-0.386848\pi$
$149$	8.49666	0.696074	0.348037	+	0.937481i	$0.386848\pi$
$150$	0	0
$151$	16.1197	1.31180	0.655901	−	0.754847i	$-0.272289\pi$
$151$	16.1197	1.31180	0.655901	+	0.754847i	$0.272289\pi$
$152$	0	0
$153$	12.0399	0.973369
$154$	0.0537348	0.00433008
$155$	0	0
$156$	11.0569	0.885261
$157$	−6.46789	−0.516194	−0.258097	−	0.966119i	$-0.583095\pi$
$157$	−6.46789	−0.516194	−0.258097	+	0.966119i	$0.583095\pi$
$158$	−0.942215	−0.0749586
$159$	−6.64155	−0.526709
$160$	0	0
$161$	8.98627	0.708218
$162$	0.00936214	0.000735559 0
$163$	−17.1020	−1.33953	−0.669767	−	0.742571i	$-0.733606\pi$
$163$	−17.1020	−1.33953	−0.669767	+	0.742571i	$0.733606\pi$
$164$	−3.48349	−0.272015
$165$	0	0
$166$	−0.421573	−0.0327204
$167$	0.904143	0.0699647	0.0349823	−	0.999388i	$-0.488863\pi$
$167$	0.904143	0.0699647	0.0349823	+	0.999388i	$0.488863\pi$
$168$	−0.733141	−0.0565631
$169$	13.7318	1.05629
$170$	0	0
$171$	0	0
$172$	−0.187468	−0.0142943
$173$	10.5529	0.802326	0.401163	−	0.916007i	$-0.368606\pi$
$173$	10.5529	0.802326	0.401163	+	0.916007i	$0.368606\pi$
$174$	0.811788	0.0615415
$175$	0	0
$176$	−1.23376	−0.0929979
$177$	13.5919	1.02163
$178$	0.314760	0.0235923
$179$	2.54363	0.190120	0.0950601	−	0.995472i	$-0.469696\pi$
$179$	2.54363	0.190120	0.0950601	+	0.995472i	$0.469696\pi$
$180$	0	0
$181$	6.28754	0.467349	0.233674	−	0.972315i	$-0.424925\pi$
$181$	6.28754	0.467349	0.233674	+	0.972315i	$0.424925\pi$
$182$	−0.883379	−0.0654804
$183$	−8.19697	−0.605937
$184$	2.70075	0.199102
$185$	0	0
$186$	−0.856733	−0.0628187
$187$	2.05593	0.150344
$188$	1.57813	0.115097
$189$	7.84503	0.570642
$190$	0	0
$191$	22.6478	1.63873	0.819367	−	0.573269i	$-0.194325\pi$
$191$	22.6478	1.63873	0.819367	+	0.573269i	$0.194325\pi$
$192$	8.27878	0.597470
$193$	−8.73921	−0.629062	−0.314531	−	0.949247i	$-0.601847\pi$
$193$	−8.73921	−0.629062	−0.314531	+	0.949247i	$0.601847\pi$
$194$	0.731143	0.0524930
$195$	0	0
$196$	9.40570	0.671836
$197$	19.9939	1.42450	0.712252	−	0.701924i	$-0.247676\pi$
$197$	19.9939	1.42450	0.712252	+	0.701924i	$0.247676\pi$
$198$	−0.0657355	−0.00467162
$199$	2.87202	0.203592	0.101796	−	0.994805i	$-0.467541\pi$
$199$	2.87202	0.203592	0.101796	+	0.994805i	$0.467541\pi$
$200$	0	0
$201$	−15.6589	−1.10450
$202$	1.07439	0.0755935
$203$	10.0070	0.702352
$204$	−13.9799	−0.978790
$205$	0	0
$206$	1.52953	0.106567
$207$	−10.9932	−0.764080
$208$	20.2825	1.40634
$209$	0	0
$210$	0	0
$211$	−21.7010	−1.49396	−0.746979	−	0.664848i	$-0.768497\pi$
$211$	−21.7010	−1.49396	−0.746979	+	0.664848i	$0.768497\pi$
$212$	−12.2631	−0.842230
$213$	−2.47203	−0.169381
$214$	1.13254	0.0774191
$215$	0	0
$216$	2.35776	0.160425
$217$	−10.5610	−0.716928
$218$	0.928445	0.0628822
$219$	−9.18841	−0.620895
$220$	0	0
$221$	−33.7986	−2.27354
$222$	−0.234718	−0.0157532
$223$	−10.3957	−0.696147	−0.348074	−	0.937467i	$-0.613164\pi$
$223$	−10.3957	−0.696147	−0.348074	+	0.937467i	$0.613164\pi$
$224$	−2.03271	−0.135816
$225$	0	0
$226$	1.60621	0.106844
$227$	3.48770	0.231487	0.115743	−	0.993279i	$-0.463075\pi$
$227$	3.48770	0.231487	0.115743	+	0.993279i	$0.463075\pi$
$228$	0	0
$229$	14.2418	0.941123	0.470562	−	0.882367i	$-0.344051\pi$
$229$	14.2418	0.941123	0.470562	+	0.882367i	$0.344051\pi$
$230$	0	0
$231$	0.509580	0.0335279
$232$	3.00751	0.197453
$233$	−4.69025	−0.307269	−0.153634	−	0.988128i	$-0.549098\pi$
$233$	−4.69025	−0.307269	−0.153634	+	0.988128i	$0.549098\pi$
$234$	1.08067	0.0706453
$235$	0	0
$236$	25.0963	1.63363
$237$	−8.93524	−0.580406
$238$	1.11691	0.0723985
$239$	11.4369	0.739793	0.369896	−	0.929073i	$-0.379393\pi$
$239$	11.4369	0.739793	0.369896	+	0.929073i	$0.379393\pi$
$240$	0	0
$241$	23.9346	1.54176	0.770880	−	0.636980i	$-0.219817\pi$
$241$	23.9346	1.54176	0.770880	+	0.636980i	$0.219817\pi$
$242$	1.23711	0.0795245
$243$	−15.5435	−0.997114
$244$	−15.1350	−0.968919
$245$	0	0
$246$	0.214104	0.0136508
$247$	0	0
$248$	−3.17402	−0.201550
$249$	−3.99787	−0.253355
$250$	0	0
$251$	17.5359	1.10686	0.553429	−	0.832896i	$-0.313319\pi$
$251$	17.5359	1.10686	0.553429	+	0.832896i	$0.313319\pi$
$252$	5.51006	0.347101
$253$	−1.87719	−0.118018
$254$	2.10800	0.132268
$255$	0	0
$256$	14.9796	0.936226
$257$	−20.9190	−1.30489	−0.652446	−	0.757836i	$-0.726257\pi$
$257$	−20.9190	−1.30489	−0.652446	+	0.757836i	$0.726257\pi$
$258$	0.0115223	0.000717344 0
$259$	−2.89338	−0.179786
$260$	0	0
$261$	−12.2418	−0.757751
$262$	−2.07730	−0.128336
$263$	−19.4145	−1.19715	−0.598575	−	0.801067i	$-0.704266\pi$
$263$	−19.4145	−1.19715	−0.598575	+	0.801067i	$0.704266\pi$
$264$	0.153150	0.00942572
$265$	0	0
$266$	0	0
$267$	2.98494	0.182676
$268$	−28.9129	−1.76613
$269$	3.01230	0.183663	0.0918317	−	0.995775i	$-0.470728\pi$
$269$	3.01230	0.183663	0.0918317	+	0.995775i	$0.470728\pi$
$270$	0	0
$271$	19.1729	1.16467	0.582334	−	0.812949i	$-0.302139\pi$
$271$	19.1729	1.16467	0.582334	+	0.812949i	$0.302139\pi$
$272$	−25.6443	−1.55492
$273$	−8.37729	−0.507017
$274$	−0.291882	−0.0176333
$275$	0	0
$276$	12.7645	0.768335
$277$	20.7927	1.24931	0.624656	−	0.780900i	$-0.285239\pi$
$277$	20.7927	1.24931	0.624656	+	0.780900i	$0.285239\pi$
$278$	0.227447	0.0136414
$279$	12.9196	0.773477
$280$	0	0
$281$	−13.8711	−0.827482	−0.413741	−	0.910395i	$-0.635778\pi$
$281$	−13.8711	−0.827482	−0.413741	+	0.910395i	$0.635778\pi$
$282$	−0.0969957	−0.00577601
$283$	−25.6745	−1.52619	−0.763094	−	0.646287i	$-0.776321\pi$
$283$	−25.6745	−1.52619	−0.763094	+	0.646287i	$0.776321\pi$
$284$	−4.56439	−0.270847
$285$	0	0
$286$	0.184534	0.0109117
$287$	2.63927	0.155791
$288$	2.48668	0.146529
$289$	25.7337	1.51374
$290$	0	0
$291$	6.93360	0.406455
$292$	−16.9656	−0.992837
$293$	21.3740	1.24868	0.624340	−	0.781153i	$-0.285368\pi$
$293$	21.3740	1.24868	0.624340	+	0.781153i	$0.285368\pi$
$294$	−0.578097	−0.0337153
$295$	0	0
$296$	−0.869581	−0.0505434
$297$	−1.63879	−0.0950923
$298$	−0.964244	−0.0558572
$299$	30.8603	1.78470
$300$	0	0
$301$	0.142036	0.00818680
$302$	−1.82934	−0.105267
$303$	10.1886	0.585322
$304$	0	0
$305$	0	0
$306$	−1.36635	−0.0781090
$307$	29.9590	1.70985	0.854924	−	0.518753i	$-0.173604\pi$
$307$	29.9590	1.70985	0.854924	+	0.518753i	$0.173604\pi$
$308$	0.940896	0.0536125
$309$	14.5049	0.825152
$310$	0	0
$311$	−15.0057	−0.850898	−0.425449	−	0.904982i	$-0.639884\pi$
$311$	−15.0057	−0.850898	−0.425449	+	0.904982i	$0.639884\pi$
$312$	−2.51772	−0.142538
$313$	−6.22859	−0.352061	−0.176030	−	0.984385i	$-0.556326\pi$
$313$	−6.22859	−0.352061	−0.176030	+	0.984385i	$0.556326\pi$
$314$	0.734009	0.0414225
$315$	0	0
$316$	−16.4982	−0.928094
$317$	25.3086	1.42147	0.710737	−	0.703458i	$-0.248362\pi$
$317$	25.3086	1.42147	0.710737	+	0.703458i	$0.248362\pi$
$318$	0.753717	0.0422664
$319$	−2.09041	−0.117041
$320$	0	0
$321$	10.7402	0.599458
$322$	−1.01981	−0.0568317
$323$	0	0
$324$	0.163931	0.00910727
$325$	0	0
$326$	1.94083	0.107492
$327$	8.80466	0.486899
$328$	0.793211	0.0437978
$329$	−1.19567	−0.0659196
$330$	0	0
$331$	20.8596	1.14654	0.573272	−	0.819365i	$-0.305674\pi$
$331$	20.8596	1.14654	0.573272	+	0.819365i	$0.305674\pi$
$332$	−7.38173	−0.405125
$333$	3.53957	0.193967
$334$	−0.102607	−0.00561439
$335$	0	0
$336$	−6.35617	−0.346758
$337$	−22.3057	−1.21507	−0.607533	−	0.794294i	$-0.707841\pi$
$337$	−22.3057	−1.21507	−0.607533	+	0.794294i	$0.707841\pi$
$338$	−1.55836	−0.0847634
$339$	15.2321	0.827292
$340$	0	0
$341$	2.20615	0.119470
$342$	0	0
$343$	−17.6651	−0.953824
$344$	0.0426876	0.00230156
$345$	0	0
$346$	−1.19760	−0.0643835
$347$	2.40870	0.129306	0.0646529	−	0.997908i	$-0.479406\pi$
$347$	2.40870	0.129306	0.0646529	+	0.997908i	$0.479406\pi$
$348$	14.2144	0.761971
$349$	15.5260	0.831088	0.415544	−	0.909573i	$-0.363591\pi$
$349$	15.5260	0.831088	0.415544	+	0.909573i	$0.363591\pi$
$350$	0	0
$351$	26.9411	1.43801
$352$	0.424624	0.0226325
$353$	3.52309	0.187515	0.0937576	−	0.995595i	$-0.470112\pi$
$353$	3.52309	0.187515	0.0937576	+	0.995595i	$0.470112\pi$
$354$	−1.54248	−0.0819819
$355$	0	0
$356$	5.51144	0.292106
$357$	10.5919	0.560583
$358$	−0.288665	−0.0152564
$359$	10.8027	0.570142	0.285071	−	0.958506i	$-0.407983\pi$
$359$	10.8027	0.570142	0.285071	+	0.958506i	$0.407983\pi$
$360$	0	0
$361$	0	0
$362$	−0.713542	−0.0375029
$363$	11.7318	0.615760
$364$	−15.4679	−0.810741
$365$	0	0
$366$	0.930234	0.0486241
$367$	−15.5752	−0.813017	−0.406508	−	0.913647i	$-0.633254\pi$
$367$	−15.5752	−0.813017	−0.406508	+	0.913647i	$0.633254\pi$
$368$	23.4149	1.22059
$369$	−3.22871	−0.168080
$370$	0	0
$371$	9.29113	0.482371
$372$	−15.0014	−0.777785
$373$	1.61712	0.0837313	0.0418657	−	0.999123i	$-0.486670\pi$
$373$	1.61712	0.0837313	0.0418657	+	0.999123i	$0.486670\pi$
$374$	−0.233317	−0.0120645
$375$	0	0
$376$	−0.359349	−0.0185320
$377$	34.3655	1.76991
$378$	−0.890294	−0.0457918
$379$	18.0335	0.926316	0.463158	−	0.886276i	$-0.346716\pi$
$379$	18.0335	0.926316	0.463158	+	0.886276i	$0.346716\pi$
$380$	0	0
$381$	19.9907	1.02415
$382$	−2.57018	−0.131502
$383$	26.2750	1.34259	0.671294	−	0.741191i	$-0.265739\pi$
$383$	26.2750	1.34259	0.671294	+	0.741191i	$0.265739\pi$
$384$	−3.84559	−0.196244
$385$	0	0
$386$	0.991770	0.0504798
$387$	−0.173757	−0.00883254
$388$	12.8023	0.649938
$389$	9.94513	0.504238	0.252119	−	0.967696i	$-0.418873\pi$
$389$	9.94513	0.504238	0.252119	+	0.967696i	$0.418873\pi$
$390$	0	0
$391$	−39.0185	−1.97325
$392$	−2.14173	−0.108174
$393$	−19.6996	−0.993711
$394$	−2.26900	−0.114311
$395$	0	0
$396$	−1.15103	−0.0578413
$397$	21.6194	1.08505	0.542524	−	0.840040i	$-0.317469\pi$
$397$	21.6194	1.08505	0.542524	+	0.840040i	$0.317469\pi$
$398$	−0.325932	−0.0163375
$399$	0	0
$400$	0	0
$401$	−10.1889	−0.508808	−0.254404	−	0.967098i	$-0.581879\pi$
$401$	−10.1889	−0.508808	−0.254404	+	0.967098i	$0.581879\pi$
$402$	1.77705	0.0886314
$403$	−36.2682	−1.80665
$404$	18.8125	0.935955
$405$	0	0
$406$	−1.13564	−0.0563610
$407$	0.604415	0.0299597
$408$	3.18331	0.157597
$409$	−29.5673	−1.46201	−0.731003	−	0.682374i	$-0.760948\pi$
$409$	−29.5673	−1.46201	−0.731003	+	0.682374i	$0.760948\pi$
$410$	0	0
$411$	−2.76799	−0.136535
$412$	26.7820	1.31945
$413$	−19.0143	−0.935631
$414$	1.24756	0.0613144
$415$	0	0
$416$	−6.98064	−0.342254
$417$	2.15694	0.105626
$418$	0	0
$419$	38.4410	1.87797	0.938984	−	0.343961i	$-0.111769\pi$
$419$	38.4410	1.87797	0.938984	+	0.343961i	$0.111769\pi$
$420$	0	0
$421$	−32.1388	−1.56635	−0.783175	−	0.621801i	$-0.786401\pi$
$421$	−32.1388	−1.56635	−0.783175	+	0.621801i	$0.786401\pi$
$422$	2.46274	0.119884
$423$	1.46270	0.0711191
$424$	2.79237	0.135609
$425$	0	0
$426$	0.280539	0.0135921
$427$	11.4671	0.554930
$428$	19.8308	0.958558
$429$	1.74998	0.0844897
$430$	0	0
$431$	−3.32723	−0.160267	−0.0801334	−	0.996784i	$-0.525535\pi$
$431$	−3.32723	−0.160267	−0.0801334	+	0.996784i	$0.525535\pi$
$432$	20.4412	0.983479
$433$	4.80891	0.231101	0.115551	−	0.993302i	$-0.463137\pi$
$433$	4.80891	0.231101	0.115551	+	0.993302i	$0.463137\pi$
$434$	1.19852	0.0575307
$435$	0	0
$436$	16.2571	0.778572
$437$	0	0
$438$	1.04275	0.0498244
$439$	2.48577	0.118640	0.0593198	−	0.998239i	$-0.481107\pi$
$439$	2.48577	0.118640	0.0593198	+	0.998239i	$0.481107\pi$
$440$	0	0
$441$	8.71776	0.415132
$442$	3.83564	0.182443
$443$	−5.25211	−0.249535	−0.124768	−	0.992186i	$-0.539819\pi$
$443$	−5.25211	−0.249535	−0.124768	+	0.992186i	$0.539819\pi$
$444$	−4.10990	−0.195047
$445$	0	0
$446$	1.17976	0.0558631
$447$	−9.14415	−0.432504
$448$	−11.5815	−0.547175
$449$	−23.6384	−1.11557	−0.557783	−	0.829987i	$-0.688348\pi$
$449$	−23.6384	−1.11557	−0.557783	+	0.829987i	$0.688348\pi$
$450$	0	0
$451$	−0.551333	−0.0259612
$452$	28.1247	1.32287
$453$	−17.3481	−0.815085
$454$	−0.395802	−0.0185759
$455$	0	0
$456$	0	0
$457$	17.5786	0.822291	0.411145	−	0.911570i	$-0.365129\pi$
$457$	17.5786	0.822291	0.411145	+	0.911570i	$0.365129\pi$
$458$	−1.61623	−0.0755214
$459$	−34.0632	−1.58993
$460$	0	0
$461$	3.04030	0.141601	0.0708004	−	0.997491i	$-0.477445\pi$
$461$	3.04030	0.141601	0.0708004	+	0.997491i	$0.477445\pi$
$462$	−0.0578297	−0.00269048
$463$	−16.7690	−0.779321	−0.389660	−	0.920959i	$-0.627408\pi$
$463$	−16.7690	−0.779321	−0.389660	+	0.920959i	$0.627408\pi$
$464$	26.0744	1.21048
$465$	0	0
$466$	0.532274	0.0246571
$467$	21.9836	1.01728	0.508639	−	0.860980i	$-0.330149\pi$
$467$	21.9836	1.01728	0.508639	+	0.860980i	$0.330149\pi$
$468$	18.9224	0.874689
$469$	21.9059	1.01152
$470$	0	0
$471$	6.96078	0.320736
$472$	−5.71457	−0.263035
$473$	−0.0296706	−0.00136426
$474$	1.01402	0.0465753
$475$	0	0
$476$	19.5571	0.896396
$477$	−11.3661	−0.520419
$478$	−1.29792	−0.0593655
$479$	17.8638	0.816219	0.408109	−	0.912933i	$-0.366188\pi$
$479$	17.8638	0.816219	0.408109	+	0.912933i	$0.366188\pi$
$480$	0	0
$481$	−9.93634	−0.453058
$482$	−2.71622	−0.123720
$483$	−9.67108	−0.440049
$484$	21.6618	0.984627
$485$	0	0
$486$	1.76395	0.0800145
$487$	11.0841	0.502270	0.251135	−	0.967952i	$-0.419196\pi$
$487$	11.0841	0.502270	0.251135	+	0.967952i	$0.419196\pi$
$488$	3.44633	0.156008
$489$	18.4053	0.832316
$490$	0	0
$491$	−9.61186	−0.433777	−0.216889	−	0.976196i	$-0.569591\pi$
$491$	−9.61186	−0.433777	−0.216889	+	0.976196i	$0.569591\pi$
$492$	3.74895	0.169016
$493$	−43.4504	−1.95691
$494$	0	0
$495$	0	0
$496$	−27.5181	−1.23560
$497$	3.45822	0.155122
$498$	0.453699	0.0203307
$499$	−3.45169	−0.154519	−0.0772594	−	0.997011i	$-0.524617\pi$
$499$	−3.45169	−0.154519	−0.0772594	+	0.997011i	$0.524617\pi$
$500$	0	0
$501$	−0.973043	−0.0434724
$502$	−1.99007	−0.0888210
$503$	34.6220	1.54372	0.771859	−	0.635793i	$-0.219327\pi$
$503$	34.6220	1.54372	0.771859	+	0.635793i	$0.219327\pi$
$504$	−1.25467	−0.0558876
$505$	0	0
$506$	0.213033	0.00947049
$507$	−14.7783	−0.656326
$508$	36.9110	1.63766
$509$	35.2230	1.56123	0.780616	−	0.625011i	$-0.214906\pi$
$509$	35.2230	1.56123	0.780616	+	0.625011i	$0.214906\pi$
$510$	0	0
$511$	12.8540	0.568628
$512$	−8.84654	−0.390965
$513$	0	0
$514$	2.37399	0.104712
$515$	0	0
$516$	0.201754	0.00888174
$517$	0.249771	0.0109849
$518$	0.328356	0.0144271
$519$	−11.3571	−0.498523
$520$	0	0
$521$	45.1472	1.97793	0.988967	−	0.148139i	$-0.0473282\pi$
$521$	45.1472	1.97793	0.988967	+	0.148139i	$0.0473282\pi$
$522$	1.38927	0.0608065
$523$	11.8077	0.516315	0.258158	−	0.966103i	$-0.416885\pi$
$523$	11.8077	0.516315	0.258158	+	0.966103i	$0.416885\pi$
$524$	−36.3735	−1.58899
$525$	0	0
$526$	2.20326	0.0960665
$527$	45.8560	1.99752
$528$	1.32778	0.0577840
$529$	12.6264	0.548972
$530$	0	0
$531$	23.2607	1.00943
$532$	0	0
$533$	9.06368	0.392592
$534$	−0.338747	−0.0146590
$535$	0	0
$536$	6.58362	0.284369
$537$	−2.73747	−0.118131
$538$	−0.341852	−0.0147383
$539$	1.48864	0.0641203
$540$	0	0
$541$	16.4508	0.707274	0.353637	−	0.935383i	$-0.384945\pi$
$541$	16.4508	0.707274	0.353637	+	0.935383i	$0.384945\pi$
$542$	−2.17583	−0.0934601
$543$	−6.76668	−0.290386
$544$	8.82605	0.378414
$545$	0	0
$546$	0.950697	0.0406861
$547$	−36.6728	−1.56802	−0.784009	−	0.620750i	$-0.786828\pi$
$547$	−36.6728	−1.56802	−0.784009	+	0.620750i	$0.786828\pi$
$548$	−5.11085	−0.218325
$549$	−14.0280	−0.598701
$550$	0	0
$551$	0	0
$552$	−2.90656	−0.123711
$553$	12.4999	0.531548
$554$	−2.35966	−0.100252
$555$	0	0
$556$	3.98260	0.168900
$557$	26.8747	1.13872	0.569360	−	0.822089i	$-0.307191\pi$
$557$	26.8747	1.13872	0.569360	+	0.822089i	$0.307191\pi$
$558$	−1.46618	−0.0620685
$559$	0.487773	0.0206306
$560$	0	0
$561$	−2.21260	−0.0934161
$562$	1.57417	0.0664022
$563$	−3.21769	−0.135609	−0.0678046	−	0.997699i	$-0.521599\pi$
$563$	−3.21769	−0.135609	−0.0678046	+	0.997699i	$0.521599\pi$
$564$	−1.69839	−0.0715152
$565$	0	0
$566$	2.91367	0.122471
$567$	−0.124202	−0.00521601
$568$	1.03934	0.0436096
$569$	−14.0358	−0.588410	−0.294205	−	0.955742i	$-0.595055\pi$
$569$	−14.0358	−0.588410	−0.294205	+	0.955742i	$0.595055\pi$
$570$	0	0
$571$	−0.475134	−0.0198837	−0.00994187	−	0.999951i	$-0.503165\pi$
$571$	−0.475134	−0.0198837	−0.00994187	+	0.999951i	$0.503165\pi$
$572$	3.23118	0.135103
$573$	−24.3736	−1.01822
$574$	−0.299518	−0.0125017
$575$	0	0
$576$	14.1680	0.590334
$577$	6.46828	0.269278	0.134639	−	0.990895i	$-0.457013\pi$
$577$	6.46828	0.269278	0.134639	+	0.990895i	$0.457013\pi$
$578$	−2.92039	−0.121472
$579$	9.40518	0.390866
$580$	0	0
$581$	5.59278	0.232028
$582$	−0.786860	−0.0326164
$583$	−1.94087	−0.0803828
$584$	3.86316	0.159859
$585$	0	0
$586$	−2.42563	−0.100202
$587$	16.8347	0.694843	0.347421	−	0.937709i	$-0.387057\pi$
$587$	16.8347	0.694843	0.347421	+	0.937709i	$0.387057\pi$
$588$	−10.1225	−0.417444
$589$	0	0
$590$	0	0
$591$	−21.5175	−0.885112
$592$	−7.53908	−0.309854
$593$	15.1827	0.623477	0.311739	−	0.950168i	$-0.399089\pi$
$593$	15.1827	0.623477	0.311739	+	0.950168i	$0.399089\pi$
$594$	0.185978	0.00763078
$595$	0	0
$596$	−16.8839	−0.691591
$597$	−3.09089	−0.126502
$598$	−3.50218	−0.143215
$599$	−21.5126	−0.878982	−0.439491	−	0.898247i	$-0.644841\pi$
$599$	−21.5126	−0.878982	−0.439491	+	0.898247i	$0.644841\pi$
$600$	0	0
$601$	−26.0308	−1.06182	−0.530910	−	0.847428i	$-0.678150\pi$
$601$	−26.0308	−1.06182	−0.530910	+	0.847428i	$0.678150\pi$
$602$	−0.0161189	−0.000656958 0
$603$	−26.7982	−1.09131
$604$	−32.0318	−1.30335
$605$	0	0
$606$	−1.15626	−0.0469698
$607$	12.8904	0.523204	0.261602	−	0.965176i	$-0.415749\pi$
$607$	12.8904	0.523204	0.261602	+	0.965176i	$0.415749\pi$
$608$	0	0
$609$	−10.7696	−0.436404
$610$	0	0
$611$	−4.10613	−0.166116
$612$	−23.9248	−0.967101
$613$	21.7499	0.878472	0.439236	−	0.898372i	$-0.355249\pi$
$613$	21.7499	0.878472	0.439236	+	0.898372i	$0.355249\pi$
$614$	−3.39990	−0.137209
$615$	0	0
$616$	−0.214247	−0.00863227
$617$	18.5508	0.746828	0.373414	−	0.927665i	$-0.378187\pi$
$617$	18.5508	0.746828	0.373414	+	0.927665i	$0.378187\pi$
$618$	−1.64608	−0.0662152
$619$	15.5031	0.623121	0.311561	−	0.950226i	$-0.399148\pi$
$619$	15.5031	0.623121	0.311561	+	0.950226i	$0.399148\pi$
$620$	0	0
$621$	31.1018	1.24807
$622$	1.70293	0.0682812
$623$	−4.17575	−0.167298
$624$	−21.8281	−0.873823
$625$	0	0
$626$	0.706852	0.0282515
$627$	0	0
$628$	12.8525	0.512870
$629$	12.5631	0.500924
$630$	0	0
$631$	28.1737	1.12158	0.560789	−	0.827959i	$-0.310498\pi$
$631$	28.1737	1.12158	0.560789	+	0.827959i	$0.310498\pi$
$632$	3.75672	0.149434
$633$	23.3547	0.928267
$634$	−2.87215	−0.114068
$635$	0	0
$636$	13.1976	0.523318
$637$	−24.4727	−0.969642
$638$	0.237230	0.00939204
$639$	−4.23055	−0.167358
$640$	0	0
$641$	23.5724	0.931055	0.465528	−	0.885033i	$-0.345865\pi$
$641$	23.5724	0.931055	0.465528	+	0.885033i	$0.345865\pi$
$642$	−1.21885	−0.0481042
$643$	44.2053	1.74329	0.871644	−	0.490140i	$-0.163054\pi$
$643$	44.2053	1.74329	0.871644	+	0.490140i	$0.163054\pi$
$644$	−17.8568	−0.703657
$645$	0	0
$646$	0	0
$647$	−21.2728	−0.836319	−0.418160	−	0.908374i	$-0.637325\pi$
$647$	−21.2728	−0.836319	−0.418160	+	0.908374i	$0.637325\pi$
$648$	−0.0373280	−0.00146638
$649$	3.97199	0.155914
$650$	0	0
$651$	11.3658	0.445461
$652$	33.9838	1.33091
$653$	−27.6776	−1.08311	−0.541555	−	0.840666i	$-0.682164\pi$
$653$	−27.6776	−1.08311	−0.541555	+	0.840666i	$0.682164\pi$
$654$	−0.999198	−0.0390717
$655$	0	0
$656$	6.87697	0.268500
$657$	−15.7247	−0.613480
$658$	0.135691	0.00528979
$659$	−19.3063	−0.752065	−0.376033	−	0.926606i	$-0.622712\pi$
$659$	−19.3063	−0.752065	−0.376033	+	0.926606i	$0.622712\pi$
$660$	0	0
$661$	19.9967	0.777781	0.388891	−	0.921284i	$-0.372858\pi$
$661$	19.9967	0.777781	0.388891	+	0.921284i	$0.372858\pi$
$662$	−2.36725	−0.0920057
$663$	36.3743	1.41266
$664$	1.68086	0.0652301
$665$	0	0
$666$	−0.401688	−0.0155651
$667$	39.6729	1.53614
$668$	−1.79664	−0.0695141
$669$	11.1879	0.432549
$670$	0	0
$671$	−2.39542	−0.0924741
$672$	2.18761	0.0843890
$673$	24.0044	0.925300	0.462650	−	0.886541i	$-0.346899\pi$
$673$	24.0044	0.925300	0.462650	+	0.886541i	$0.346899\pi$
$674$	2.53136	0.0975043
$675$	0	0
$676$	−27.2868	−1.04949
$677$	18.1589	0.697901	0.348951	−	0.937141i	$-0.386538\pi$
$677$	18.1589	0.697901	0.348951	+	0.937141i	$0.386538\pi$
$678$	−1.72861	−0.0663870
$679$	−9.69968	−0.372240
$680$	0	0
$681$	−3.75348	−0.143834
$682$	−0.250365	−0.00958696
$683$	48.8671	1.86985	0.934924	−	0.354849i	$-0.115468\pi$
$683$	48.8671	1.86985	0.934924	+	0.354849i	$0.115468\pi$
$684$	0	0
$685$	0	0
$686$	2.00472	0.0765406
$687$	−15.3271	−0.584765
$688$	0.370092	0.0141096
$689$	31.9072	1.21557
$690$	0	0
$691$	18.9182	0.719682	0.359841	−	0.933014i	$-0.382831\pi$
$691$	18.9182	0.719682	0.359841	+	0.933014i	$0.382831\pi$
$692$	−20.9700	−0.797159
$693$	0.872078	0.0331275
$694$	−0.273352	−0.0103763
$695$	0	0
$696$	−3.23670	−0.122687
$697$	−11.4598	−0.434069
$698$	−1.76197	−0.0666915
$699$	5.04768	0.190921
$700$	0	0
$701$	33.6317	1.27025	0.635126	−	0.772408i	$-0.280948\pi$
$701$	33.6317	1.27025	0.635126	+	0.772408i	$0.280948\pi$
$702$	−3.05741	−0.115394
$703$	0	0
$704$	2.41932	0.0911817
$705$	0	0
$706$	−0.399818	−0.0150474
$707$	−14.2533	−0.536050
$708$	−27.0088	−1.01505
$709$	24.8928	0.934868	0.467434	−	0.884028i	$-0.345179\pi$
$709$	24.8928	0.934868	0.467434	+	0.884028i	$0.345179\pi$
$710$	0	0
$711$	−15.2915	−0.573475
$712$	−1.25499	−0.0470326
$713$	−41.8694	−1.56802
$714$	−1.20202	−0.0449846
$715$	0	0
$716$	−5.05451	−0.188896
$717$	−12.3085	−0.459668
$718$	−1.22594	−0.0457517
$719$	−4.93432	−0.184019	−0.0920095	−	0.995758i	$-0.529329\pi$
$719$	−4.93432	−0.184019	−0.0920095	+	0.995758i	$0.529329\pi$
$720$	0	0
$721$	−20.2914	−0.755691
$722$	0	0
$723$	−25.7585	−0.957969
$724$	−12.4941	−0.464340
$725$	0	0
$726$	−1.33139	−0.0494124
$727$	−29.3061	−1.08690	−0.543452	−	0.839440i	$-0.682883\pi$
$727$	−29.3061	−1.08690	−0.543452	+	0.839440i	$0.682883\pi$
$728$	3.52214	0.130539
$729$	16.9755	0.628721
$730$	0	0
$731$	−0.616720	−0.0228102
$732$	16.2884	0.602036
$733$	15.7183	0.580567	0.290284	−	0.956941i	$-0.406250\pi$
$733$	15.7183	0.580567	0.290284	+	0.956941i	$0.406250\pi$
$734$	1.76755	0.0652414
$735$	0	0
$736$	−8.05874	−0.297049
$737$	−4.57604	−0.168561
$738$	0.366410	0.0134877
$739$	5.49827	0.202257	0.101129	−	0.994873i	$-0.467755\pi$
$739$	5.49827	0.202257	0.101129	+	0.994873i	$0.467755\pi$
$740$	0	0
$741$	0	0
$742$	−1.05440	−0.0387084
$743$	−19.2065	−0.704618	−0.352309	−	0.935884i	$-0.614603\pi$
$743$	−19.2065	−0.704618	−0.352309	+	0.935884i	$0.614603\pi$
$744$	3.41590	0.125233
$745$	0	0
$746$	−0.183519	−0.00671911
$747$	−6.84182	−0.250329
$748$	−4.08538	−0.149376
$749$	−15.0248	−0.548996
$750$	0	0
$751$	−13.7467	−0.501623	−0.250811	−	0.968036i	$-0.580697\pi$
$751$	−13.7467	−0.501623	−0.250811	+	0.968036i	$0.580697\pi$
$752$	−3.11548	−0.113610
$753$	−18.8723	−0.687744
$754$	−3.89997	−0.142029
$755$	0	0
$756$	−15.5890	−0.566967
$757$	−29.9965	−1.09024	−0.545121	−	0.838357i	$-0.683516\pi$
$757$	−29.9965	−1.09024	−0.545121	+	0.838357i	$0.683516\pi$
$758$	−2.04653	−0.0743332
$759$	2.02024	0.0733302
$760$	0	0
$761$	37.1297	1.34595	0.672976	−	0.739664i	$-0.265016\pi$
$761$	37.1297	1.34595	0.672976	+	0.739664i	$0.265016\pi$
$762$	−2.26864	−0.0821843
$763$	−12.3172	−0.445912
$764$	−45.0038	−1.62818
$765$	0	0
$766$	−2.98182	−0.107737
$767$	−65.2980	−2.35777
$768$	−16.1211	−0.581722
$769$	−8.35052	−0.301127	−0.150564	−	0.988600i	$-0.548109\pi$
$769$	−8.35052	−0.301127	−0.150564	+	0.988600i	$0.548109\pi$
$770$	0	0
$771$	22.5131	0.810791
$772$	17.3659	0.625011
$773$	20.9026	0.751816	0.375908	−	0.926657i	$-0.377331\pi$
$773$	20.9026	0.751816	0.375908	+	0.926657i	$0.377331\pi$
$774$	0.0197188	0.000708777 0
$775$	0	0
$776$	−2.91516	−0.104648
$777$	3.11388	0.111710
$778$	−1.12862	−0.0404631
$779$	0	0
$780$	0	0
$781$	−0.722406	−0.0258497
$782$	4.42802	0.158346
$783$	34.6345	1.23774
$784$	−18.5684	−0.663155
$785$	0	0
$786$	2.23561	0.0797414
$787$	43.9642	1.56716	0.783578	−	0.621294i	$-0.213393\pi$
$787$	43.9642	1.56716	0.783578	+	0.621294i	$0.213393\pi$
$788$	−39.7302	−1.41533
$789$	20.8940	0.743846
$790$	0	0
$791$	−21.3087	−0.757651
$792$	0.262095	0.00931316
$793$	39.3797	1.39841
$794$	−2.45348	−0.0870708
$795$	0	0
$796$	−5.70706	−0.202281
$797$	−16.3576	−0.579416	−0.289708	−	0.957115i	$-0.593558\pi$
$797$	−16.3576	−0.579416	−0.289708	+	0.957115i	$0.593558\pi$
$798$	0	0
$799$	5.19163	0.183667
$800$	0	0
$801$	5.10833	0.180494
$802$	1.15629	0.0408299
$803$	−2.68515	−0.0947568
$804$	31.1162	1.09738
$805$	0	0
$806$	4.11590	0.144976
$807$	−3.24186	−0.114119
$808$	−4.28370	−0.150700
$809$	6.79371	0.238854	0.119427	−	0.992843i	$-0.461894\pi$
$809$	6.79371	0.238854	0.119427	+	0.992843i	$0.461894\pi$
$810$	0	0
$811$	10.6600	0.374324	0.187162	−	0.982329i	$-0.440071\pi$
$811$	10.6600	0.374324	0.187162	+	0.982329i	$0.440071\pi$
$812$	−19.8851	−0.697829
$813$	−20.6339	−0.723664
$814$	−0.0685921	−0.00240415
$815$	0	0
$816$	27.5986	0.966143
$817$	0	0
$818$	3.35544	0.117320
$819$	−14.3366	−0.500962
$820$	0	0
$821$	20.7381	0.723766	0.361883	−	0.932224i	$-0.382134\pi$
$821$	20.7381	0.723766	0.361883	+	0.932224i	$0.382134\pi$
$822$	0.314126	0.0109564
$823$	−13.9819	−0.487377	−0.243689	−	0.969854i	$-0.578357\pi$
$823$	−13.9819	−0.487377	−0.243689	+	0.969854i	$0.578357\pi$
$824$	−6.09840	−0.212448
$825$	0	0
$826$	2.15784	0.0750807
$827$	33.1980	1.15441	0.577203	−	0.816601i	$-0.304144\pi$
$827$	33.1980	1.15441	0.577203	+	0.816601i	$0.304144\pi$
$828$	21.8448	0.759159
$829$	8.68051	0.301487	0.150743	−	0.988573i	$-0.451833\pi$
$829$	8.68051	0.301487	0.150743	+	0.988573i	$0.451833\pi$
$830$	0	0
$831$	−22.3772	−0.776257
$832$	−39.7727	−1.37887
$833$	30.9423	1.07209
$834$	−0.244780	−0.00847604
$835$	0	0
$836$	0	0
$837$	−36.5521	−1.26342
$838$	−4.36249	−0.150700
$839$	12.2248	0.422049	0.211024	−	0.977481i	$-0.432320\pi$
$839$	12.2248	0.422049	0.211024	+	0.977481i	$0.432320\pi$
$840$	0	0
$841$	15.1791	0.523418
$842$	3.64728	0.125693
$843$	14.9282	0.514154
$844$	43.1225	1.48434
$845$	0	0
$846$	−0.165995	−0.00570703
$847$	−16.4121	−0.563926
$848$	24.2092	0.831348
$849$	27.6310	0.948293
$850$	0	0
$851$	−11.4709	−0.393218
$852$	4.91222	0.168290
$853$	−19.6824	−0.673911	−0.336956	−	0.941521i	$-0.609397\pi$
$853$	−19.6824	−0.673911	−0.336956	+	0.941521i	$0.609397\pi$
$854$	−1.30134	−0.0445310
$855$	0	0
$856$	−4.51559	−0.154340
$857$	−45.3053	−1.54760	−0.773800	−	0.633430i	$-0.781646\pi$
$857$	−45.3053	−1.54760	−0.773800	+	0.633430i	$0.781646\pi$
$858$	−0.198596	−0.00677997
$859$	31.1076	1.06138	0.530689	−	0.847567i	$-0.321933\pi$
$859$	31.1076	1.06138	0.530689	+	0.847567i	$0.321933\pi$
$860$	0	0
$861$	−2.84040	−0.0968006
$862$	0.377590	0.0128608
$863$	−41.0858	−1.39858	−0.699289	−	0.714839i	$-0.746500\pi$
$863$	−41.0858	−1.39858	−0.699289	+	0.714839i	$0.746500\pi$
$864$	−7.03528	−0.239345
$865$	0	0
$866$	−0.545740	−0.0185450
$867$	−27.6947	−0.940561
$868$	20.9860	0.712311
$869$	−2.61116	−0.0885777
$870$	0	0
$871$	75.2283	2.54901
$872$	−3.70182	−0.125360
$873$	11.8659	0.401601
$874$	0	0
$875$	0	0
$876$	18.2585	0.616897
$877$	12.1276	0.409520	0.204760	−	0.978812i	$-0.434359\pi$
$877$	12.1276	0.409520	0.204760	+	0.978812i	$0.434359\pi$
$878$	−0.282098	−0.00952036
$879$	−23.0028	−0.775865
$880$	0	0
$881$	−35.6584	−1.20136	−0.600680	−	0.799489i	$-0.705104\pi$
$881$	−35.6584	−1.20136	−0.600680	+	0.799489i	$0.705104\pi$
$882$	−0.989336	−0.0333127
$883$	−1.13310	−0.0381318	−0.0190659	−	0.999818i	$-0.506069\pi$
$883$	−1.13310	−0.0381318	−0.0190659	+	0.999818i	$0.506069\pi$
$884$	67.1620	2.25890
$885$	0	0
$886$	0.596036	0.0200242
$887$	12.9644	0.435301	0.217650	−	0.976027i	$-0.430161\pi$
$887$	12.9644	0.435301	0.217650	+	0.976027i	$0.430161\pi$
$888$	0.935848	0.0314050
$889$	−27.9657	−0.937940
$890$	0	0
$891$	0.0259453	0.000869201 0
$892$	20.6575	0.691664
$893$	0	0
$894$	1.03773	0.0347067
$895$	0	0
$896$	5.37975	0.179725
$897$	−33.2120	−1.10892
$898$	2.68261	0.0895197
$899$	−46.6251	−1.55503
$900$	0	0
$901$	−40.3422	−1.34399
$902$	0.0625680	0.00208329
$903$	−0.152860	−0.00508685
$904$	−6.40416	−0.212999
$905$	0	0
$906$	1.96875	0.0654073
$907$	−8.58894	−0.285191	−0.142596	−	0.989781i	$-0.545545\pi$
$907$	−8.58894	−0.285191	−0.142596	+	0.989781i	$0.545545\pi$
$908$	−6.93048	−0.229996
$909$	17.4365	0.578332
$910$	0	0
$911$	−22.6445	−0.750246	−0.375123	−	0.926975i	$-0.622400\pi$
$911$	−22.6445	−0.750246	−0.375123	+	0.926975i	$0.622400\pi$
$912$	0	0
$913$	−1.16831	−0.0386653
$914$	−1.99491	−0.0659856
$915$	0	0
$916$	−28.3001	−0.935063
$917$	27.5585	0.910061
$918$	3.86567	0.127586
$919$	−20.0503	−0.661397	−0.330698	−	0.943736i	$-0.607284\pi$
$919$	−20.0503	−0.661397	−0.330698	+	0.943736i	$0.607284\pi$
$920$	0	0
$921$	−32.2420	−1.06241
$922$	−0.345028	−0.0113629
$923$	11.8761	0.390906
$924$	−1.01260	−0.0333120
$925$	0	0
$926$	1.90303	0.0625374
$927$	24.8231	0.815298
$928$	−8.97408	−0.294588
$929$	59.6067	1.95563	0.977815	−	0.209468i	$-0.0671732\pi$
$929$	59.6067	1.95563	0.977815	+	0.209468i	$0.0671732\pi$
$930$	0	0
$931$	0	0
$932$	9.32010	0.305290
$933$	16.1493	0.528703
$934$	−2.49481	−0.0816326
$935$	0	0
$936$	−4.30874	−0.140836
$937$	−1.03896	−0.0339415	−0.0169707	−	0.999856i	$-0.505402\pi$
$937$	−1.03896	−0.0339415	−0.0169707	+	0.999856i	$0.505402\pi$
$938$	−2.48599	−0.0811705
$939$	6.70324	0.218752
$940$	0	0
$941$	−2.96197	−0.0965574	−0.0482787	−	0.998834i	$-0.515374\pi$
$941$	−2.96197	−0.0965574	−0.0482787	+	0.998834i	$0.515374\pi$
$942$	−0.789945	−0.0257378
$943$	10.4635	0.340738
$944$	−49.5441	−1.61252
$945$	0	0
$946$	0.00336717	0.000109476 0
$947$	21.4691	0.697653	0.348826	−	0.937187i	$-0.386580\pi$
$947$	21.4691	0.697653	0.348826	+	0.937187i	$0.386580\pi$
$948$	17.7554	0.576669
$949$	44.1427	1.43293
$950$	0	0
$951$	−27.2373	−0.883230
$952$	−4.45325	−0.144331
$953$	20.2543	0.656101	0.328051	−	0.944660i	$-0.393608\pi$
$953$	20.2543	0.656101	0.328051	+	0.944660i	$0.393608\pi$
$954$	1.28989	0.0417616
$955$	0	0
$956$	−22.7265	−0.735029
$957$	2.24971	0.0727229
$958$	−2.02728	−0.0654984
$959$	3.87225	0.125041
$960$	0	0
$961$	18.2065	0.587307
$962$	1.12763	0.0363561
$963$	18.3804	0.592299
$964$	−47.5609	−1.53183
$965$	0	0
$966$	1.09752	0.0353122
$967$	−61.2295	−1.96901	−0.984504	−	0.175363i	$-0.943890\pi$
$967$	−61.2295	−1.96901	−0.984504	+	0.175363i	$0.943890\pi$
$968$	−4.93251	−0.158537
$969$	0	0
$970$	0	0
$971$	21.6739	0.695550	0.347775	−	0.937578i	$-0.386937\pi$
$971$	21.6739	0.695550	0.347775	+	0.937578i	$0.386937\pi$
$972$	30.8868	0.990693
$973$	−3.01742	−0.0967341
$974$	−1.25788	−0.0403052
$975$	0	0
$976$	29.8789	0.956400
$977$	22.5832	0.722499	0.361250	−	0.932469i	$-0.382350\pi$
$977$	22.5832	0.722499	0.361250	+	0.932469i	$0.382350\pi$
$978$	−2.08873	−0.0667901
$979$	0.872296	0.0278787
$980$	0	0
$981$	15.0680	0.481084
$982$	1.09080	0.0348089
$983$	−4.45933	−0.142231	−0.0711153	−	0.997468i	$-0.522656\pi$
$983$	−4.45933	−0.142231	−0.0711153	+	0.997468i	$0.522656\pi$
$984$	−0.853658	−0.0272136
$985$	0	0
$986$	4.93097	0.157034
$987$	1.28679	0.0409590
$988$	0	0
$989$	0.563104	0.0179057
$990$	0	0
$991$	24.5724	0.780568	0.390284	−	0.920695i	$-0.372377\pi$
$991$	24.5724	0.780568	0.390284	+	0.920695i	$0.372377\pi$
$992$	9.47093	0.300702
$993$	−22.4492	−0.712403
$994$	−0.392456	−0.0124480
$995$	0	0
$996$	7.94426	0.251723
$997$	37.5241	1.18840	0.594199	−	0.804318i	$-0.297469\pi$
$997$	37.5241	1.18840	0.594199	+	0.804318i	$0.297469\pi$
$998$	0.391715	0.0123995
$999$	−10.0141	−0.316832

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9025.2.a.cv.1.20		40
5.2	odd	4		1805.2.b.m.1084.19	✓	40
5.3	odd	4		1805.2.b.m.1084.22	yes	40
5.4	even	2	inner	9025.2.a.cv.1.21		40
19.18	odd	2	inner	9025.2.a.cv.1.22		40
95.18	even	4		1805.2.b.m.1084.20	yes	40
95.37	even	4		1805.2.b.m.1084.21	yes	40
95.94	odd	2	inner	9025.2.a.cv.1.19		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1805.2.b.m.1084.19	✓	40	5.2	odd	4
1805.2.b.m.1084.20	yes	40	95.18	even	4
1805.2.b.m.1084.21	yes	40	95.37	even	4
1805.2.b.m.1084.22	yes	40	5.3	odd	4
9025.2.a.cv.1.19		40	95.94	odd	2	inner
9025.2.a.cv.1.20		40	1.1	even	1	trivial
9025.2.a.cv.1.21		40	5.4	even	2	inner
9025.2.a.cv.1.22		40	19.18	odd	2	inner

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)

\(f(q)\)	\(=\)	\(q-0.113485 q^{2} -1.07621 q^{3} -1.98712 q^{4} +0.122133 q^{6} +1.50555 q^{7} +0.452479 q^{8} -1.84178 q^{9} +O(q^{10})\)	\(q-0.113485 q^{2} -1.07621 q^{3} -1.98712 q^{4} +0.122133 q^{6} +1.50555 q^{7} +0.452479 q^{8} -1.84178 q^{9} -0.314502 q^{11} +2.13855 q^{12} +5.17028 q^{13} -0.170857 q^{14} +3.92289 q^{16} -6.53710 q^{17} +0.209015 q^{18} -1.62028 q^{21} +0.0356913 q^{22} +5.96878 q^{23} -0.486960 q^{24} -0.586750 q^{26} +5.21075 q^{27} -2.99170 q^{28} +6.64674 q^{29} -7.01474 q^{31} -1.35015 q^{32} +0.338469 q^{33} +0.741863 q^{34} +3.65984 q^{36} -1.92182 q^{37} -5.56429 q^{39} +1.75303 q^{41} +0.183877 q^{42} +0.0943416 q^{43} +0.624953 q^{44} -0.677368 q^{46} -0.794179 q^{47} -4.22184 q^{48} -4.73333 q^{49} +7.03526 q^{51} -10.2740 q^{52} +6.17127 q^{53} -0.591343 q^{54} +0.681228 q^{56} -0.754306 q^{58} -12.6295 q^{59} +7.61655 q^{61} +0.796068 q^{62} -2.77289 q^{63} -7.69256 q^{64} -0.0384111 q^{66} +14.5501 q^{67} +12.9900 q^{68} -6.42364 q^{69} +2.29699 q^{71} -0.833367 q^{72} +8.53778 q^{73} +0.218098 q^{74} -0.473497 q^{77} +0.631464 q^{78} +8.30254 q^{79} -0.0824966 q^{81} -0.198943 q^{82} +3.71479 q^{83} +3.21969 q^{84} -0.0107064 q^{86} -7.15326 q^{87} -0.142305 q^{88} -2.77358 q^{89} +7.78410 q^{91} -11.8607 q^{92} +7.54930 q^{93} +0.0901275 q^{94} +1.45304 q^{96} -6.44264 q^{97} +0.537163 q^{98} +0.579244 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9}+O(q^{10}) \) 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9	\( 40 q + 48 q^{4} + 20 q^{6} + 52 q^{9} + 20 q^{11} + 40 q^{16} + 92 q^{24} + 76 q^{26} + 156 q^{36} + 80 q^{39} + 48 q^{44} + 72 q^{49} + 32 q^{54} + 80 q^{61} + 72 q^{64} + 16 q^{66} + 100 q^{74} + 40 q^{81} + 380 q^{96} + 128 q^{99}+O(q^{100}) \) 40 * q + 48 * q^4 + 20 * q^6 + 52 * q^9 + 20 * q^11 + 40 * q^16 + 92 * q^24 + 76 * q^26 + 156 * q^36 + 80 * q^39 + 48 * q^44 + 72 * q^49 + 32 * q^54 + 80 * q^61 + 72 * q^64 + 16 * q^66 + 100 * q^74 + 40 * q^81 + 380 * q^96 + 128 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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