LMFDB - Embedded newform 3025.2.a.bo.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3025,2,Mod(1,3025)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3025, 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("3025.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3025 = 5^{2} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3025.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:	$24.1547466114$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} - 34 x^{10} + 28 x^{9} + 340 x^{8} + 44 x^{7} - 884 x^{6} - 132 x^{5} + 761 x^{4} + \cdots - 8 $ x^12 - 2x^11 - 34x^10 + 28x^9 + 340x^8 + 44x^7 - 884x^6 - 132x^5 + 761x^4 - 142x^3 - 166x^2 + 72*x - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 605)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$0.236881$ of defining polynomial
Character	$\chi$	$=$	3025.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.02281 q^{2} +2.91475 q^{3} +2.09174 q^{4} +5.89598 q^{6} +3.21128 q^{7} +0.185581 q^{8} +5.49579 q^{9} +O(q^{10})$	\(q+2.02281 q^{2} +2.91475 q^{3} +2.09174 q^{4} +5.89598 q^{6} +3.21128 q^{7} +0.185581 q^{8} +5.49579 q^{9} +6.09692 q^{12} -0.648753 q^{13} +6.49579 q^{14} -3.80809 q^{16} +1.18847 q^{17} +11.1169 q^{18} +1.89096 q^{19} +9.36008 q^{21} -4.35986 q^{23} +0.540924 q^{24} -1.31230 q^{26} +7.27462 q^{27} +6.71717 q^{28} -4.16393 q^{29} +7.89984 q^{31} -8.07420 q^{32} +2.40405 q^{34} +11.4958 q^{36} +2.05849 q^{37} +3.82504 q^{38} -1.89096 q^{39} -3.30520 q^{41} +18.9336 q^{42} -10.9313 q^{43} -8.81916 q^{46} -2.91475 q^{47} -11.0997 q^{48} +3.31230 q^{49} +3.46410 q^{51} -1.35703 q^{52} +6.41836 q^{53} +14.7151 q^{54} +0.595953 q^{56} +5.51167 q^{57} -8.42283 q^{58} -3.71635 q^{59} -7.78694 q^{61} +15.9798 q^{62} +17.6485 q^{63} -8.71635 q^{64} +2.37993 q^{67} +2.48598 q^{68} -12.7079 q^{69} +15.7163 q^{71} +1.01992 q^{72} +5.71428 q^{73} +4.16393 q^{74} +3.95540 q^{76} -3.82504 q^{78} -15.2561 q^{79} +4.71635 q^{81} -6.68577 q^{82} +10.6367 q^{83} +19.5789 q^{84} -22.1120 q^{86} -12.1368 q^{87} +9.00000 q^{89} -2.08333 q^{91} -9.11972 q^{92} +23.0261 q^{93} -5.89598 q^{94} -23.5343 q^{96} -15.1381 q^{97} +6.70015 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 20 q^{4} + 20 q^{9}+O(q^{10}) $ 12 * q + 20 * q^4 + 20 * q^9	$ 12 q + 20 q^{4} + 20 q^{9} + 32 q^{14} + 36 q^{16} + 20 q^{26} + 8 q^{31} - 12 q^{34} + 92 q^{36} + 4 q^{49} + 48 q^{56} + 32 q^{59} - 28 q^{64} + 16 q^{69} + 112 q^{71} - 20 q^{81} - 56 q^{86} + 108 q^{89} + 72 q^{91}+O(q^{100}) $ 12 * q + 20 * q^4 + 20 * q^9 + 32 * q^14 + 36 * q^16 + 20 * q^26 + 8 * q^31 - 12 * q^34 + 92 * q^36 + 4 * q^49 + 48 * q^56 + 32 * q^59 - 28 * q^64 + 16 * q^69 + 112 * q^71 - 20 * q^81 - 56 * q^86 + 108 * q^89 + 72 * q^91

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 $

$2$	2.02281	1.43034	0.715170	−	0.698951i	$-0.246349\pi$
$2$	2.02281	1.43034	0.715170	+	0.698951i	$0.246349\pi$
$3$	2.91475	1.68283	0.841417	−	0.540386i	$-0.181722\pi$
$3$	2.91475	1.68283	0.841417	+	0.540386i	$0.181722\pi$
$4$	2.09174	1.04587
$5$	0	0
$5$	0	0
$6$	5.89598	2.40702
$7$	3.21128	1.21375	0.606874	−	0.794798i	$-0.292423\pi$
$7$	3.21128	1.21375	0.606874	+	0.794798i	$0.292423\pi$
$8$	0.185581	0.0656129
$9$	5.49579	1.83193
$10$	0	0
$11$	0	0
$11$	0	0
$12$	6.09692	1.76003
$13$	−0.648753	−0.179932	−0.0899659	−	0.995945i	$-0.528676\pi$
$13$	−0.648753	−0.179932	−0.0899659	+	0.995945i	$0.528676\pi$
$14$	6.49579	1.73607
$15$	0	0
$16$	−3.80809	−0.952023
$17$	1.18847	0.288247	0.144123	−	0.989560i	$-0.453964\pi$
$17$	1.18847	0.288247	0.144123	+	0.989560i	$0.453964\pi$
$18$	11.1169	2.62028
$19$	1.89096	0.433815	0.216908	−	0.976192i	$-0.430403\pi$
$19$	1.89096	0.433815	0.216908	+	0.976192i	$0.430403\pi$
$20$	0	0
$21$	9.36008	2.04254
$22$	0	0
$23$	−4.35986	−0.909095	−0.454547	−	0.890723i	$-0.650199\pi$
$23$	−4.35986	−0.909095	−0.454547	+	0.890723i	$0.650199\pi$
$24$	0.540924	0.110416
$25$	0	0
$26$	−1.31230	−0.257364
$27$	7.27462	1.40000
$28$	6.71717	1.26943
$29$	−4.16393	−0.773223	−0.386611	−	0.922243i	$-0.626355\pi$
$29$	−4.16393	−0.773223	−0.386611	+	0.922243i	$0.626355\pi$
$30$	0	0
$31$	7.89984	1.41885	0.709426	−	0.704779i	$-0.248954\pi$
$31$	7.89984	1.41885	0.709426	+	0.704779i	$0.248954\pi$
$32$	−8.07420	−1.42733
$33$	0	0
$34$	2.40405	0.412291
$35$	0	0
$36$	11.4958	1.91597
$37$	2.05849	0.338414	0.169207	−	0.985581i	$-0.445879\pi$
$37$	2.05849	0.338414	0.169207	+	0.985581i	$0.445879\pi$
$38$	3.82504	0.620503
$39$	−1.89096	−0.302795
$40$	0	0
$41$	−3.30520	−0.516185	−0.258092	−	0.966120i	$-0.583094\pi$
$41$	−3.30520	−0.516185	−0.258092	+	0.966120i	$0.583094\pi$
$42$	18.9336	2.92152
$43$	−10.9313	−1.66701	−0.833507	−	0.552509i	$-0.813670\pi$
$43$	−10.9313	−1.66701	−0.833507	+	0.552509i	$0.813670\pi$
$44$	0	0
$45$	0	0
$46$	−8.81916	−1.30031
$47$	−2.91475	−0.425161	−0.212580	−	0.977144i	$-0.568187\pi$
$47$	−2.91475	−0.425161	−0.212580	+	0.977144i	$0.568187\pi$
$48$	−11.0997	−1.60210
$49$	3.31230	0.473186
$50$	0	0
$51$	3.46410	0.485071
$52$	−1.35703	−0.188186
$53$	6.41836	0.881629	0.440815	−	0.897598i	$-0.354690\pi$
$53$	6.41836	0.881629	0.440815	+	0.897598i	$0.354690\pi$
$54$	14.7151	2.00248
$55$	0	0
$56$	0.595953	0.0796376
$57$	5.51167	0.730039
$58$	−8.42283	−1.10597
$59$	−3.71635	−0.483827	−0.241914	−	0.970298i	$-0.577775\pi$
$59$	−3.71635	−0.483827	−0.241914	+	0.970298i	$0.577775\pi$
$60$	0	0
$61$	−7.78694	−0.997015	−0.498508	−	0.866885i	$-0.666118\pi$
$61$	−7.78694	−0.997015	−0.498508	+	0.866885i	$0.666118\pi$
$62$	15.9798	2.02944
$63$	17.6485	2.22350
$64$	−8.71635	−1.08954
$65$	0	0
$66$	0	0
$67$	2.37993	0.290755	0.145377	−	0.989376i	$-0.453560\pi$
$67$	2.37993	0.290755	0.145377	+	0.989376i	$0.453560\pi$
$68$	2.48598	0.301469
$69$	−12.7079	−1.52986
$70$	0	0
$71$	15.7163	1.86519	0.932594	−	0.360928i	$-0.117540\pi$
$71$	15.7163	1.86519	0.932594	+	0.360928i	$0.117540\pi$
$72$	1.01992	0.120198
$73$	5.71428	0.668806	0.334403	−	0.942430i	$-0.391465\pi$
$73$	5.71428	0.668806	0.334403	+	0.942430i	$0.391465\pi$
$74$	4.16393	0.484047
$75$	0	0
$76$	3.95540	0.453715
$77$	0	0
$78$	−3.82504	−0.433100
$79$	−15.2561	−1.71644	−0.858221	−	0.513281i	$-0.828430\pi$
$79$	−15.2561	−1.71644	−0.858221	+	0.513281i	$0.828430\pi$
$80$	0	0
$81$	4.71635	0.524039
$82$	−6.68577	−0.738320
$83$	10.6367	1.16753	0.583766	−	0.811922i	$-0.301579\pi$
$83$	10.6367	1.16753	0.583766	+	0.811922i	$0.301579\pi$
$84$	19.5789	2.13623
$85$	0	0
$86$	−22.1120	−2.38440
$87$	−12.1368	−1.30121
$88$	0	0
$89$	9.00000	0.953998	0.476999	−	0.878904i	$-0.341725\pi$
$89$	9.00000	0.953998	0.476999	+	0.878904i	$0.341725\pi$
$90$	0	0
$91$	−2.08333	−0.218392
$92$	−9.11972	−0.950797
$93$	23.0261	2.38769
$94$	−5.89598	−0.608124
$95$	0	0
$96$	−23.5343	−2.40196
$97$	−15.1381	−1.53704	−0.768520	−	0.639826i	$-0.779006\pi$
$97$	−15.1381	−1.53704	−0.768520	+	0.639826i	$0.779006\pi$
$98$	6.70015	0.676817
$99$	0	0
$100$	0	0
$101$	−5.57817	−0.555049	−0.277524	−	0.960719i	$-0.589514\pi$
$101$	−5.57817	−0.555049	−0.277524	+	0.960719i	$0.589514\pi$
$102$	7.00721	0.693817
$103$	3.18217	0.313548	0.156774	−	0.987634i	$-0.449891\pi$
$103$	3.18217	0.313548	0.156774	+	0.987634i	$0.449891\pi$
$104$	−0.120397	−0.0118058
$105$	0	0
$106$	12.9831	1.26103
$107$	−3.96907	−0.383704	−0.191852	−	0.981424i	$-0.561449\pi$
$107$	−3.96907	−0.383704	−0.191852	+	0.981424i	$0.561449\pi$
$108$	15.2166	1.46422
$109$	−15.4150	−1.47649	−0.738243	−	0.674535i	$-0.764344\pi$
$109$	−15.4150	−1.47649	−0.738243	+	0.674535i	$0.764344\pi$
$110$	0	0
$111$	6.00000	0.569495
$112$	−12.2288	−1.15552
$113$	10.1353	0.953453	0.476727	−	0.879052i	$-0.341823\pi$
$113$	10.1353	0.953453	0.476727	+	0.879052i	$0.341823\pi$
$114$	11.1490	1.04420
$115$	0	0
$116$	−8.70988	−0.808692
$117$	−3.56541	−0.329623
$118$	−7.51745	−0.692038
$119$	3.81651	0.349859
$120$	0	0
$121$	0	0
$122$	−15.7515	−1.42607
$123$	−9.63383	−0.868653
$124$	16.5244	1.48394
$125$	0	0
$126$	35.6995	3.18037
$127$	16.4430	1.45908	0.729541	−	0.683937i	$-0.239734\pi$
$127$	16.4430	1.45908	0.729541	+	0.683937i	$0.239734\pi$
$128$	−1.48309	−0.131088
$129$	−31.8622	−2.80531
$130$	0	0
$131$	−14.0007	−1.22325	−0.611625	−	0.791148i	$-0.709484\pi$
$131$	−14.0007	−1.22325	−0.611625	+	0.791148i	$0.709484\pi$
$132$	0	0
$133$	6.07239	0.526543
$134$	4.81413	0.415878
$135$	0	0
$136$	0.220558	0.0189127
$137$	13.7715	1.17658	0.588291	−	0.808650i	$-0.299801\pi$
$137$	13.7715	1.17658	0.588291	+	0.808650i	$0.299801\pi$
$138$	−25.7057	−2.18821
$139$	−6.75472	−0.572928	−0.286464	−	0.958091i	$-0.592480\pi$
$139$	−6.75472	−0.572928	−0.286464	+	0.958091i	$0.592480\pi$
$140$	0	0
$141$	−8.49579	−0.715475
$142$	31.7911	2.66785
$143$	0	0
$144$	−20.9285	−1.74404
$145$	0	0
$146$	11.5589	0.956620
$147$	9.65455	0.796294
$148$	4.30584	0.353938
$149$	19.1969	1.57267	0.786335	−	0.617800i	$-0.211976\pi$
$149$	19.1969	1.57267	0.786335	+	0.617800i	$0.211976\pi$
$150$	0	0
$151$	3.29062	0.267787	0.133893	−	0.990996i	$-0.457252\pi$
$151$	3.29062	0.267787	0.133893	+	0.990996i	$0.457252\pi$
$152$	0.350926	0.0284639
$153$	6.53159	0.528048
$154$	0	0
$155$	0	0
$156$	−3.95540	−0.316685
$157$	−14.0144	−1.11847	−0.559236	−	0.829009i	$-0.688905\pi$
$157$	−14.0144	−1.11847	−0.559236	+	0.829009i	$0.688905\pi$
$158$	−30.8601	−2.45509
$159$	18.7079	1.48364
$160$	0	0
$161$	−14.0007	−1.10341
$162$	9.54026	0.749554
$163$	−10.3220	−0.808478	−0.404239	−	0.914653i	$-0.632464\pi$
$163$	−10.3220	−0.808478	−0.404239	+	0.914653i	$0.632464\pi$
$164$	−6.91362	−0.539863
$165$	0	0
$166$	21.5160	1.66997
$167$	−14.6058	−1.13023	−0.565115	−	0.825012i	$-0.691168\pi$
$167$	−14.6058	−1.13023	−0.565115	+	0.825012i	$0.691168\pi$
$168$	1.73706	0.134017
$169$	−12.5791	−0.967625
$170$	0	0
$171$	10.3923	0.794719
$172$	−22.8656	−1.74348
$173$	−2.20839	−0.167901	−0.0839503	−	0.996470i	$-0.526754\pi$
$173$	−2.20839	−0.167901	−0.0839503	+	0.996470i	$0.526754\pi$
$174$	−24.5505	−1.86117
$175$	0	0
$176$	0	0
$177$	−10.8322	−0.814201
$178$	18.2053	1.36454
$179$	10.8081	0.807835	0.403917	−	0.914795i	$-0.367648\pi$
$179$	10.8081	0.807835	0.403917	+	0.914795i	$0.367648\pi$
$180$	0	0
$181$	−3.36698	−0.250265	−0.125133	−	0.992140i	$-0.539936\pi$
$181$	−3.36698	−0.250265	−0.125133	+	0.992140i	$0.539936\pi$
$182$	−4.21417	−0.312375
$183$	−22.6970	−1.67781
$184$	−0.809109	−0.0596483
$185$	0	0
$186$	46.5773	3.41521
$187$	0	0
$188$	−6.09692	−0.444664
$189$	23.3608	1.69925
$190$	0	0
$191$	9.27523	0.671132	0.335566	−	0.942017i	$-0.391072\pi$
$191$	9.27523	0.671132	0.335566	+	0.942017i	$0.391072\pi$
$192$	−25.4060	−1.83352
$193$	4.86292	0.350041	0.175020	−	0.984565i	$-0.444001\pi$
$193$	4.86292	0.350041	0.175020	+	0.984565i	$0.444001\pi$
$194$	−30.6214	−2.19849
$195$	0	0
$196$	6.92849	0.494892
$197$	−11.8747	−0.846038	−0.423019	−	0.906121i	$-0.639030\pi$
$197$	−11.8747	−0.846038	−0.423019	+	0.906121i	$0.639030\pi$
$198$	0	0
$199$	−4.99158	−0.353844	−0.176922	−	0.984225i	$-0.556614\pi$
$199$	−4.99158	−0.353844	−0.176922	+	0.984225i	$0.556614\pi$
$200$	0	0
$201$	6.93691	0.489292
$202$	−11.2836	−0.793908
$203$	−13.3715	−0.938498
$204$	7.24602	0.507323
$205$	0	0
$206$	6.43691	0.448481
$207$	−23.9609	−1.66540
$208$	2.47051	0.171299
$209$	0	0
$210$	0	0
$211$	−1.57314	−0.108300	−0.0541499	−	0.998533i	$-0.517245\pi$
$211$	−1.57314	−0.108300	−0.0541499	+	0.998533i	$0.517245\pi$
$212$	13.4256	0.922071
$213$	45.8093	3.13880
$214$	−8.02865	−0.548827
$215$	0	0
$216$	1.35003	0.0918581
$217$	25.3686	1.72213
$218$	−31.1815	−2.11188
$219$	16.6557	1.12549
$220$	0	0
$221$	−0.771025	−0.0518647
$222$	12.1368	0.814571
$223$	3.31475	0.221972	0.110986	−	0.993822i	$-0.464599\pi$
$223$	3.31475	0.221972	0.110986	+	0.993822i	$0.464599\pi$
$224$	−25.9285	−1.73242
$225$	0	0
$226$	20.5018	1.36376
$227$	−2.84011	−0.188505	−0.0942525	−	0.995548i	$-0.530046\pi$
$227$	−2.84011	−0.188505	−0.0942525	+	0.995548i	$0.530046\pi$
$228$	11.5290	0.763528
$229$	−1.99158	−0.131608	−0.0658038	−	0.997833i	$-0.520961\pi$
$229$	−1.99158	−0.131608	−0.0658038	+	0.997833i	$0.520961\pi$
$230$	0	0
$231$	0	0
$232$	−0.772748	−0.0507334
$233$	20.2535	1.32685	0.663426	−	0.748242i	$-0.269102\pi$
$233$	20.2535	1.32685	0.663426	+	0.748242i	$0.269102\pi$
$234$	−7.21214	−0.471472
$235$	0	0
$236$	−7.77365	−0.506022
$237$	−44.4677	−2.88849
$238$	7.72006	0.500417
$239$	1.89096	0.122316	0.0611579	−	0.998128i	$-0.480521\pi$
$239$	1.89096	0.122316	0.0611579	+	0.998128i	$0.480521\pi$
$240$	0	0
$241$	4.00503	0.257986	0.128993	−	0.991645i	$-0.458825\pi$
$241$	4.00503	0.257986	0.128993	+	0.991645i	$0.458825\pi$
$242$	0	0
$243$	−8.07686	−0.518131
$244$	−16.2883	−1.04275
$245$	0	0
$246$	−19.4874	−1.24247
$247$	−1.22676	−0.0780572
$248$	1.46606	0.0930950
$249$	31.0034	1.96476
$250$	0	0
$251$	22.7079	1.43331	0.716656	−	0.697427i	$-0.245672\pi$
$251$	22.7079	1.43331	0.716656	+	0.697427i	$0.245672\pi$
$252$	36.9162	2.32550
$253$	0	0
$254$	33.2610	2.08698
$255$	0	0
$256$	14.4327	0.902044
$257$	−4.06296	−0.253441	−0.126720	−	0.991938i	$-0.540445\pi$
$257$	−4.06296	−0.253441	−0.126720	+	0.991938i	$0.540445\pi$
$258$	−64.4510	−4.01254
$259$	6.61039	0.410750
$260$	0	0
$261$	−22.8841	−1.41649
$262$	−28.3208	−1.74966
$263$	−12.3054	−0.758783	−0.379391	−	0.925236i	$-0.623867\pi$
$263$	−12.3054	−0.758783	−0.379391	+	0.925236i	$0.623867\pi$
$264$	0	0
$265$	0	0
$266$	12.2833	0.753135
$267$	26.2328	1.60542
$268$	4.97820	0.304092
$269$	−7.70793	−0.469961	−0.234980	−	0.972000i	$-0.575503\pi$
$269$	−7.70793	−0.469961	−0.234980	+	0.972000i	$0.575503\pi$
$270$	0	0
$271$	15.5739	0.946046	0.473023	−	0.881050i	$-0.343163\pi$
$271$	15.5739	0.946046	0.473023	+	0.881050i	$0.343163\pi$
$272$	−4.52581	−0.274418
$273$	−6.07239	−0.367518
$274$	27.8571	1.68291
$275$	0	0
$276$	−26.5817	−1.60003
$277$	20.3030	1.21989	0.609946	−	0.792443i	$-0.291191\pi$
$277$	20.3030	1.21989	0.609946	+	0.792443i	$0.291191\pi$
$278$	−13.6635	−0.819481
$279$	43.4159	2.59924
$280$	0	0
$281$	24.2196	1.44482	0.722409	−	0.691466i	$-0.243035\pi$
$281$	24.2196	1.44482	0.722409	+	0.691466i	$0.243035\pi$
$282$	−17.1853	−1.02337
$283$	−14.4372	−0.858204	−0.429102	−	0.903256i	$-0.641170\pi$
$283$	−14.4372	−0.858204	−0.429102	+	0.903256i	$0.641170\pi$
$284$	32.8746	1.95075
$285$	0	0
$286$	0	0
$287$	−10.6139	−0.626519
$288$	−44.3741	−2.61477
$289$	−15.5875	−0.916914
$290$	0	0
$291$	−44.1238	−2.58658
$292$	11.9528	0.699486
$293$	−15.1625	−0.885805	−0.442902	−	0.896570i	$-0.646051\pi$
$293$	−15.1625	−0.885805	−0.442902	+	0.896570i	$0.646051\pi$
$294$	19.5293	1.13897
$295$	0	0
$296$	0.382018	0.0222043
$297$	0	0
$298$	38.8316	2.24945
$299$	2.82848	0.163575
$300$	0	0
$301$	−35.1036	−2.02334
$302$	6.65628	0.383026
$303$	−16.2590	−0.934055
$304$	−7.20094	−0.413002
$305$	0	0
$306$	13.2121	0.755288
$307$	−8.04171	−0.458965	−0.229482	−	0.973313i	$-0.573703\pi$
$307$	−8.04171	−0.458965	−0.229482	+	0.973313i	$0.573703\pi$
$308$	0	0
$309$	9.27523	0.527650
$310$	0	0
$311$	22.2668	1.26264	0.631318	−	0.775524i	$-0.282514\pi$
$311$	22.2668	1.26264	0.631318	+	0.775524i	$0.282514\pi$
$312$	−0.350926	−0.0198673
$313$	2.35044	0.132855	0.0664273	−	0.997791i	$-0.478840\pi$
$313$	2.35044	0.132855	0.0664273	+	0.997791i	$0.478840\pi$
$314$	−28.3484	−1.59979
$315$	0	0
$316$	−31.9118	−1.79518
$317$	18.0233	1.01229	0.506146	−	0.862448i	$-0.331070\pi$
$317$	18.0233	1.01229	0.506146	+	0.862448i	$0.331070\pi$
$318$	37.8425	2.12210
$319$	0	0
$320$	0	0
$321$	−11.5689	−0.645710
$322$	−28.3208	−1.57825
$323$	2.24735	0.125046
$324$	9.86540	0.548078
$325$	0	0
$326$	−20.8793	−1.15640
$327$	−44.9309	−2.48468
$328$	−0.613382	−0.0338684
$329$	−9.36008	−0.516038
$330$	0	0
$331$	−3.09174	−0.169938	−0.0849688	−	0.996384i	$-0.527079\pi$
$331$	−3.09174	−0.169938	−0.0849688	+	0.996384i	$0.527079\pi$
$332$	22.2493	1.22109
$333$	11.3130	0.619951
$334$	−29.5447	−1.61661
$335$	0	0
$336$	−35.6441	−1.94454
$337$	−35.9458	−1.95809	−0.979046	−	0.203641i	$-0.934722\pi$
$337$	−35.9458	−1.95809	−0.979046	+	0.203641i	$0.934722\pi$
$338$	−25.4451	−1.38403
$339$	29.5420	1.60450
$340$	0	0
$341$	0	0
$342$	21.0216	1.13672
$343$	−11.8422	−0.639420
$344$	−2.02865	−0.109378
$345$	0	0
$346$	−4.46714	−0.240155
$347$	−12.2629	−0.658307	−0.329153	−	0.944276i	$-0.606763\pi$
$347$	−12.2629	−0.658307	−0.329153	+	0.944276i	$0.606763\pi$
$348$	−25.3872	−1.36089
$349$	17.6734	0.946034	0.473017	−	0.881053i	$-0.343165\pi$
$349$	17.6734	0.946034	0.473017	+	0.881053i	$0.343165\pi$
$350$	0	0
$351$	−4.71943	−0.251905
$352$	0	0
$353$	−18.7202	−0.996378	−0.498189	−	0.867068i	$-0.666001\pi$
$353$	−18.7202	−0.996378	−0.498189	+	0.867068i	$0.666001\pi$
$354$	−21.9115	−1.16458
$355$	0	0
$356$	18.8257	0.997760
$357$	11.1242	0.588755
$358$	21.8627	1.15548
$359$	37.2669	1.96687	0.983435	−	0.181263i	$-0.0580187\pi$
$359$	37.2669	1.96687	0.983435	+	0.181263i	$0.0580187\pi$
$360$	0	0
$361$	−15.4243	−0.811804
$362$	−6.81074	−0.357965
$363$	0	0
$364$	−4.35779	−0.228410
$365$	0	0
$366$	−45.9117	−2.39984
$367$	17.9988	0.939531	0.469765	−	0.882791i	$-0.344339\pi$
$367$	17.9988	0.939531	0.469765	+	0.882791i	$0.344339\pi$
$368$	16.6028	0.865479
$369$	−18.1647	−0.945615
$370$	0	0
$371$	20.6111	1.07008
$372$	48.1647	2.49722
$373$	−0.202607	−0.0104906	−0.00524531	−	0.999986i	$-0.501670\pi$
$373$	−0.202607	−0.0104906	−0.00524531	+	0.999986i	$0.501670\pi$
$374$	0	0
$375$	0	0
$376$	−0.540924	−0.0278960
$377$	2.70137	0.139127
$378$	47.2544	2.43050
$379$	−33.9832	−1.74560	−0.872799	−	0.488080i	$-0.837697\pi$
$379$	−33.9832	−1.74560	−0.872799	+	0.488080i	$0.837697\pi$
$380$	0	0
$381$	47.9273	2.45539
$382$	18.7620	0.959947
$383$	−7.14204	−0.364941	−0.182471	−	0.983211i	$-0.558409\pi$
$383$	−7.14204	−0.364941	−0.182471	+	0.983211i	$0.558409\pi$
$384$	−4.32284	−0.220599
$385$	0	0
$386$	9.83675	0.500677
$387$	−60.0764	−3.05385
$388$	−31.6650	−1.60755
$389$	13.2668	0.672654	0.336327	−	0.941745i	$-0.390815\pi$
$389$	13.2668	0.672654	0.336327	+	0.941745i	$0.390815\pi$
$390$	0	0
$391$	−5.18157	−0.262043
$392$	0.614701	0.0310471
$393$	−40.8087	−2.05853
$394$	−24.0202	−1.21012
$395$	0	0
$396$	0	0
$397$	33.5614	1.68440	0.842200	−	0.539165i	$-0.181260\pi$
$397$	33.5614	1.68440	0.842200	+	0.539165i	$0.181260\pi$
$398$	−10.0970	−0.506117
$399$	17.6995	0.886084
$400$	0	0
$401$	33.5909	1.67745	0.838726	−	0.544554i	$-0.183301\pi$
$401$	33.5909	1.67745	0.838726	+	0.544554i	$0.183301\pi$
$402$	14.0320	0.699853
$403$	−5.12505	−0.255297
$404$	−11.6681	−0.580510
$405$	0	0
$406$	−27.0480	−1.34237
$407$	0	0
$408$	0.642872	0.0318269
$409$	8.16896	0.403929	0.201964	−	0.979393i	$-0.435267\pi$
$409$	8.16896	0.403929	0.201964	+	0.979393i	$0.435267\pi$
$410$	0	0
$411$	40.1406	1.97999
$412$	6.65628	0.327931
$413$	−11.9342	−0.587245
$414$	−48.4683	−2.38209
$415$	0	0
$416$	5.23816	0.256822
$417$	−19.6883	−0.964142
$418$	0	0
$419$	19.5329	0.954243	0.477121	−	0.878837i	$-0.341680\pi$
$419$	19.5329	0.954243	0.477121	+	0.878837i	$0.341680\pi$
$420$	0	0
$421$	−23.9083	−1.16522	−0.582609	−	0.812753i	$-0.697968\pi$
$421$	−23.9083	−1.16522	−0.582609	+	0.812753i	$0.697968\pi$
$422$	−3.18217	−0.154905
$423$	−16.0189	−0.778865
$424$	1.19113	0.0578462
$425$	0	0
$426$	92.6633	4.48955
$427$	−25.0060	−1.21013
$428$	−8.30227	−0.401306
$429$	0	0
$430$	0	0
$431$	−7.56383	−0.364337	−0.182168	−	0.983267i	$-0.558312\pi$
$431$	−7.56383	−0.364337	−0.182168	+	0.983267i	$0.558312\pi$
$432$	−27.7024	−1.33283
$433$	−25.6194	−1.23119	−0.615595	−	0.788063i	$-0.711084\pi$
$433$	−25.6194	−1.23119	−0.615595	+	0.788063i	$0.711084\pi$
$434$	51.3157	2.46323
$435$	0	0
$436$	−32.2442	−1.54422
$437$	−8.24432	−0.394379
$438$	33.6913	1.60983
$439$	−20.4668	−0.976827	−0.488413	−	0.872612i	$-0.662424\pi$
$439$	−20.4668	−0.976827	−0.488413	+	0.872612i	$0.662424\pi$
$440$	0	0
$441$	18.2037	0.866844
$442$	−1.55963	−0.0741842
$443$	−10.1648	−0.482946	−0.241473	−	0.970408i	$-0.577631\pi$
$443$	−10.1648	−0.482946	−0.241473	+	0.970408i	$0.577631\pi$
$444$	12.5505	0.595619
$445$	0	0
$446$	6.70509	0.317495
$447$	55.9542	2.64654
$448$	−27.9906	−1.32243
$449$	−14.6995	−0.693713	−0.346857	−	0.937918i	$-0.612751\pi$
$449$	−14.6995	−0.693713	−0.346857	+	0.937918i	$0.612751\pi$
$450$	0	0
$451$	0	0
$452$	21.2006	0.997190
$453$	9.59134	0.450640
$454$	−5.74500	−0.269626
$455$	0	0
$456$	1.02286	0.0479000
$457$	−3.36281	−0.157305	−0.0786527	−	0.996902i	$-0.525062\pi$
$457$	−3.36281	−0.157305	−0.0786527	+	0.996902i	$0.525062\pi$
$458$	−4.02859	−0.188243
$459$	8.64568	0.403546
$460$	0	0
$461$	−1.41424	−0.0658677	−0.0329338	−	0.999458i	$-0.510485\pi$
$461$	−1.41424	−0.0658677	−0.0329338	+	0.999458i	$0.510485\pi$
$462$	0	0
$463$	15.4595	0.718465	0.359232	−	0.933248i	$-0.383039\pi$
$463$	15.4595	0.718465	0.359232	+	0.933248i	$0.383039\pi$
$464$	15.8566	0.736126
$465$	0	0
$466$	40.9690	1.89785
$467$	−18.6908	−0.864905	−0.432453	−	0.901657i	$-0.642352\pi$
$467$	−18.6908	−0.864905	−0.432453	+	0.901657i	$0.642352\pi$
$468$	−7.45793	−0.344743
$469$	7.64261	0.352903
$470$	0	0
$471$	−40.8486	−1.88220
$472$	−0.689685	−0.0317453
$473$	0	0
$474$	−89.9495	−4.13152
$475$	0	0
$476$	7.98317	0.365908
$477$	35.2740	1.61508
$478$	3.82504	0.174953
$479$	−29.8765	−1.36509	−0.682546	−	0.730842i	$-0.739127\pi$
$479$	−29.8765	−1.36509	−0.682546	+	0.730842i	$0.739127\pi$
$480$	0	0
$481$	−1.33545	−0.0608915
$482$	8.10139	0.369008
$483$	−40.8087	−1.85686
$484$	0	0
$485$	0	0
$486$	−16.3379	−0.741103
$487$	−0.934819	−0.0423607	−0.0211803	−	0.999776i	$-0.506742\pi$
$487$	−0.934819	−0.0423607	−0.0211803	+	0.999776i	$0.506742\pi$
$488$	−1.44511	−0.0654171
$489$	−30.0860	−1.36053
$490$	0	0
$491$	−32.8944	−1.48450	−0.742251	−	0.670121i	$-0.766242\pi$
$491$	−32.8944	−1.48450	−0.742251	+	0.670121i	$0.766242\pi$
$492$	−20.1515	−0.908500
$493$	−4.94871	−0.222879
$494$	−2.48151	−0.111648
$495$	0	0
$496$	−30.0833	−1.35078
$497$	50.4696	2.26387
$498$	62.7139	2.81028
$499$	8.99158	0.402519	0.201259	−	0.979538i	$-0.435497\pi$
$499$	8.99158	0.402519	0.201259	+	0.979538i	$0.435497\pi$
$500$	0	0
$501$	−42.5723	−1.90199
$502$	45.9337	2.05012
$503$	1.22096	0.0544400	0.0272200	−	0.999629i	$-0.491335\pi$
$503$	1.22096	0.0544400	0.0272200	+	0.999629i	$0.491335\pi$
$504$	3.27523	0.145890
$505$	0	0
$506$	0	0
$507$	−36.6650	−1.62835
$508$	34.3946	1.52601
$509$	24.1953	1.07244	0.536219	−	0.844079i	$-0.319852\pi$
$509$	24.1953	1.07244	0.536219	+	0.844079i	$0.319852\pi$
$510$	0	0
$511$	18.3501	0.811763
$512$	32.1607	1.42132
$513$	13.7560	0.607342
$514$	−8.21858	−0.362506
$515$	0	0
$516$	−66.6475	−2.93399
$517$	0	0
$518$	13.3715	0.587512
$519$	−6.43691	−0.282549
$520$	0	0
$521$	−4.85358	−0.212639	−0.106320	−	0.994332i	$-0.533907\pi$
$521$	−4.85358	−0.212639	−0.106320	+	0.994332i	$0.533907\pi$
$522$	−46.2901	−2.02606
$523$	7.33344	0.320669	0.160334	−	0.987063i	$-0.448743\pi$
$523$	7.33344	0.320669	0.160334	+	0.987063i	$0.448743\pi$
$524$	−29.2860	−1.27936
$525$	0	0
$526$	−24.8914	−1.08532
$527$	9.38873	0.408980
$528$	0	0
$529$	−3.99158	−0.173547
$530$	0	0
$531$	−20.4243	−0.886338
$532$	12.7019	0.550696
$533$	2.14426	0.0928781
$534$	53.0638	2.29630
$535$	0	0
$536$	0.441670	0.0190773
$537$	31.5029	1.35945
$538$	−15.5917	−0.672204
$539$	0	0
$540$	0	0
$541$	28.0803	1.20726	0.603632	−	0.797263i	$-0.293720\pi$
$541$	28.0803	1.20726	0.603632	+	0.797263i	$0.293720\pi$
$542$	31.5029	1.35317
$543$	−9.81391	−0.421155
$544$	−9.59595	−0.411423
$545$	0	0
$546$	−12.2833	−0.525675
$547$	23.3628	0.998921	0.499460	−	0.866337i	$-0.333532\pi$
$547$	23.3628	0.998921	0.499460	+	0.866337i	$0.333532\pi$
$548$	28.8065	1.23055
$549$	−42.7954	−1.82646
$550$	0	0
$551$	−7.87382	−0.335436
$552$	−2.35835	−0.100378
$553$	−48.9915	−2.08333
$554$	41.0691	1.74486
$555$	0	0
$556$	−14.1291	−0.599209
$557$	0.0340521	0.00144283	0.000721417	−	1.00000i	$-0.499770\pi$
$557$	0.0340521	0.00144283	0.000721417		1.00000i	$0.499770\pi$
$558$	87.8219	3.71780
$559$	7.09174	0.299949
$560$	0	0
$561$	0	0
$562$	48.9915	2.06658
$563$	23.6574	0.997041	0.498520	−	0.866878i	$-0.333877\pi$
$563$	23.6574	0.997041	0.498520	+	0.866878i	$0.333877\pi$
$564$	−17.7710	−0.748295
$565$	0	0
$566$	−29.2037	−1.22752
$567$	15.1455	0.636051
$568$	2.91666	0.122380
$569$	30.7352	1.28849	0.644244	−	0.764820i	$-0.277172\pi$
$569$	30.7352	1.28849	0.644244	+	0.764820i	$0.277172\pi$
$570$	0	0
$571$	−28.4768	−1.19172	−0.595860	−	0.803089i	$-0.703188\pi$
$571$	−28.4768	−1.19172	−0.595860	+	0.803089i	$0.703188\pi$
$572$	0	0
$573$	27.0350	1.12940
$574$	−21.4699	−0.896135
$575$	0	0
$576$	−47.9032	−1.99597
$577$	38.6132	1.60749	0.803745	−	0.594974i	$-0.202838\pi$
$577$	38.6132	1.60749	0.803745	+	0.594974i	$0.202838\pi$
$578$	−31.5306	−1.31150
$579$	14.1742	0.589060
$580$	0	0
$581$	34.1575	1.41709
$582$	−89.2539	−3.69969
$583$	0	0
$584$	1.06046	0.0438823
$585$	0	0
$586$	−30.6709	−1.26700
$587$	−14.2818	−0.589474	−0.294737	−	0.955578i	$-0.595232\pi$
$587$	−14.2818	−0.589474	−0.294737	+	0.955578i	$0.595232\pi$
$588$	20.1948	0.832821
$589$	14.9383	0.615520
$590$	0	0
$591$	−34.6119	−1.42374
$592$	−7.83893	−0.322178
$593$	36.4700	1.49764	0.748822	−	0.662771i	$-0.230620\pi$
$593$	36.4700	1.49764	0.748822	+	0.662771i	$0.230620\pi$
$594$	0	0
$595$	0	0
$596$	40.1550	1.64481
$597$	−14.5492	−0.595461
$598$	5.72146	0.233968
$599$	30.3410	1.23970	0.619849	−	0.784721i	$-0.287194\pi$
$599$	30.3410	1.23970	0.619849	+	0.784721i	$0.287194\pi$
$600$	0	0
$601$	37.8224	1.54281	0.771403	−	0.636347i	$-0.219555\pi$
$601$	37.8224	1.54281	0.771403	+	0.636347i	$0.219555\pi$
$602$	−71.0077	−2.89406
$603$	13.0796	0.532642
$604$	6.88313	0.280071
$605$	0	0
$606$	−32.8888	−1.33602
$607$	−31.0829	−1.26161	−0.630807	−	0.775940i	$-0.717276\pi$
$607$	−31.0829	−1.26161	−0.630807	+	0.775940i	$0.717276\pi$
$608$	−15.2680	−0.619198
$609$	−38.9747	−1.57934
$610$	0	0
$611$	1.89096	0.0764999
$612$	13.6624	0.552271
$613$	36.2674	1.46483	0.732414	−	0.680860i	$-0.238394\pi$
$613$	36.2674	1.46483	0.732414	+	0.680860i	$0.238394\pi$
$614$	−16.2668	−0.656475
$615$	0	0
$616$	0	0
$617$	1.28079	0.0515626	0.0257813	−	0.999668i	$-0.491793\pi$
$617$	1.28079	0.0515626	0.0257813	+	0.999668i	$0.491793\pi$
$618$	18.7620	0.754718
$619$	8.24079	0.331225	0.165613	−	0.986191i	$-0.447040\pi$
$619$	8.24079	0.331225	0.165613	+	0.986191i	$0.447040\pi$
$620$	0	0
$621$	−31.7163	−1.27273
$622$	45.0415	1.80600
$623$	28.9015	1.15791
$624$	7.20094	0.288268
$625$	0	0
$626$	4.75448	0.190027
$627$	0	0
$628$	−29.3146	−1.16978
$629$	2.44646	0.0975467
$630$	0	0
$631$	−12.4074	−0.493933	−0.246966	−	0.969024i	$-0.579434\pi$
$631$	−12.4074	−0.493933	−0.246966	+	0.969024i	$0.579434\pi$
$632$	−2.83124	−0.112621
$633$	−4.58533	−0.182251
$634$	36.4577	1.44792
$635$	0	0
$636$	39.1322	1.55169
$637$	−2.14887	−0.0851412
$638$	0	0
$639$	86.3738	3.41689
$640$	0	0
$641$	−5.42930	−0.214444	−0.107222	−	0.994235i	$-0.534196\pi$
$641$	−5.42930	−0.214444	−0.107222	+	0.994235i	$0.534196\pi$
$642$	−23.4015	−0.923585
$643$	2.08798	0.0823420	0.0411710	−	0.999152i	$-0.486891\pi$
$643$	2.08798	0.0823420	0.0411710	+	0.999152i	$0.486891\pi$
$644$	−29.2860	−1.15403
$645$	0	0
$646$	4.54595	0.178858
$647$	24.7631	0.973540	0.486770	−	0.873530i	$-0.338175\pi$
$647$	24.7631	0.973540	0.486770	+	0.873530i	$0.338175\pi$
$648$	0.875266	0.0343837
$649$	0	0
$650$	0	0
$651$	73.9432	2.89806
$652$	−21.5909	−0.845564
$653$	−6.89916	−0.269985	−0.134992	−	0.990847i	$-0.543101\pi$
$653$	−6.89916	−0.269985	−0.134992	+	0.990847i	$0.543101\pi$
$654$	−90.8864	−3.55394
$655$	0	0
$656$	12.5865	0.491420
$657$	31.4045	1.22521
$658$	−18.9336	−0.738110
$659$	−12.4567	−0.485246	−0.242623	−	0.970121i	$-0.578008\pi$
$659$	−12.4567	−0.485246	−0.242623	+	0.970121i	$0.578008\pi$
$660$	0	0
$661$	17.8173	0.693012	0.346506	−	0.938048i	$-0.387368\pi$
$661$	17.8173	0.693012	0.346506	+	0.938048i	$0.387368\pi$
$662$	−6.25400	−0.243069
$663$	−2.24735	−0.0872798
$664$	1.97398	0.0766052
$665$	0	0
$666$	22.8841	0.886741
$667$	18.1542	0.702933
$668$	−30.5516	−1.18208
$669$	9.66167	0.373542
$670$	0	0
$671$	0	0
$672$	−75.5752	−2.91538
$673$	−29.0771	−1.12084	−0.560419	−	0.828209i	$-0.689360\pi$
$673$	−29.0771	−1.12084	−0.560419	+	0.828209i	$0.689360\pi$
$674$	−72.7113	−2.80074
$675$	0	0
$676$	−26.3123	−1.01201
$677$	−40.8682	−1.57069	−0.785347	−	0.619056i	$-0.787515\pi$
$677$	−40.8682	−1.57069	−0.785347	+	0.619056i	$0.787515\pi$
$678$	59.7578	2.29499
$679$	−48.6126	−1.86558
$680$	0	0
$681$	−8.27824	−0.317223
$682$	0	0
$683$	17.2211	0.658948	0.329474	−	0.944165i	$-0.393129\pi$
$683$	17.2211	0.658948	0.329474	+	0.944165i	$0.393129\pi$
$684$	21.7380	0.831175
$685$	0	0
$686$	−23.9545	−0.914588
$687$	−5.80497	−0.221474
$688$	41.6276	1.58704
$689$	−4.16393	−0.158633
$690$	0	0
$691$	20.1406	0.766186	0.383093	−	0.923710i	$-0.374859\pi$
$691$	20.1406	0.766186	0.383093	+	0.923710i	$0.374859\pi$
$692$	−4.61938	−0.175603
$693$	0	0
$694$	−24.8055	−0.941603
$695$	0	0
$696$	−2.25237	−0.0853759
$697$	−3.92813	−0.148789
$698$	35.7498	1.35315
$699$	59.0341	2.23287
$700$	0	0
$701$	21.1666	0.799452	0.399726	−	0.916635i	$-0.369105\pi$
$701$	21.1666	0.799452	0.399726	+	0.916635i	$0.369105\pi$
$702$	−9.54650	−0.360309
$703$	3.89252	0.146809
$704$	0	0
$705$	0	0
$706$	−37.8674	−1.42516
$707$	−17.9131	−0.673690
$708$	−22.6583	−0.851551
$709$	20.5623	0.772233	0.386116	−	0.922450i	$-0.373816\pi$
$709$	20.5623	0.772233	0.386116	+	0.922450i	$0.373816\pi$
$710$	0	0
$711$	−83.8442	−3.14440
$712$	1.67023	0.0625946
$713$	−34.4422	−1.28987
$714$	22.5021	0.842119
$715$	0	0
$716$	22.6078	0.844892
$717$	5.51167	0.205837
$718$	75.3836	2.81329
$719$	−18.2500	−0.680609	−0.340305	−	0.940315i	$-0.610530\pi$
$719$	−18.2500	−0.680609	−0.340305	+	0.940315i	$0.610530\pi$
$720$	0	0
$721$	10.2188	0.380569
$722$	−31.2003	−1.16116
$723$	11.6737	0.434148
$724$	−7.04286	−0.261746
$725$	0	0
$726$	0	0
$727$	0.218345	0.00809798	0.00404899	−	0.999992i	$-0.498711\pi$
$727$	0.218345	0.00809798	0.00404899	+	0.999992i	$0.498711\pi$
$728$	−0.386627	−0.0143293
$729$	−37.6911	−1.39597
$730$	0	0
$731$	−12.9916	−0.480511
$732$	−47.4764	−1.75478
$733$	1.74365	0.0644033	0.0322016	−	0.999481i	$-0.489748\pi$
$733$	1.74365	0.0644033	0.0322016	+	0.999481i	$0.489748\pi$
$734$	36.4081	1.34385
$735$	0	0
$736$	35.2024	1.29758
$737$	0	0
$738$	−36.7436	−1.35255
$739$	30.3837	1.11768	0.558842	−	0.829274i	$-0.311246\pi$
$739$	30.3837	1.11768	0.558842	+	0.829274i	$0.311246\pi$
$740$	0	0
$741$	−3.57572	−0.131357
$742$	41.6923	1.53057
$743$	34.6653	1.27175	0.635873	−	0.771794i	$-0.280640\pi$
$743$	34.6653	1.27175	0.635873	+	0.771794i	$0.280640\pi$
$744$	4.27321	0.156664
$745$	0	0
$746$	−0.409835	−0.0150051
$747$	58.4572	2.13884
$748$	0	0
$749$	−12.7458	−0.465720
$750$	0	0
$751$	9.55888	0.348809	0.174404	−	0.984674i	$-0.444200\pi$
$751$	9.55888	0.348809	0.174404	+	0.984674i	$0.444200\pi$
$752$	11.0997	0.404763
$753$	66.1880	2.41203
$754$	5.46434	0.198999
$755$	0	0
$756$	48.8649	1.77720
$757$	6.26124	0.227569	0.113784	−	0.993505i	$-0.463703\pi$
$757$	6.26124	0.227569	0.113784	+	0.993505i	$0.463703\pi$
$758$	−68.7414	−2.49680
$759$	0	0
$760$	0	0
$761$	26.6660	0.966642	0.483321	−	0.875443i	$-0.339430\pi$
$761$	26.6660	0.966642	0.483321	+	0.875443i	$0.339430\pi$
$762$	96.9477	3.51205
$763$	−49.5018	−1.79208
$764$	19.4014	0.701919
$765$	0	0
$766$	−14.4470	−0.521990
$767$	2.41099	0.0870560
$768$	42.0678	1.51799
$769$	42.2399	1.52321	0.761605	−	0.648042i	$-0.224412\pi$
$769$	42.2399	1.52321	0.761605	+	0.648042i	$0.224412\pi$
$770$	0	0
$771$	−11.8425	−0.426498
$772$	10.1720	0.366098
$773$	46.2951	1.66512	0.832559	−	0.553937i	$-0.186875\pi$
$773$	46.2951	1.66512	0.832559	+	0.553937i	$0.186875\pi$
$774$	−121.523	−4.36805
$775$	0	0
$776$	−2.80935	−0.100850
$777$	19.2677	0.691224
$778$	26.8362	0.962124
$779$	−6.24998	−0.223929
$780$	0	0
$781$	0	0
$782$	−10.4813	−0.374811
$783$	−30.2910	−1.08251
$784$	−12.6136	−0.450484
$785$	0	0
$786$	−82.5481	−2.94439
$787$	49.1450	1.75183	0.875915	−	0.482465i	$-0.160258\pi$
$787$	49.1450	1.75183	0.875915	+	0.482465i	$0.160258\pi$
$788$	−24.8389	−0.884848
$789$	−35.8672	−1.27691
$790$	0	0
$791$	32.5474	1.15725
$792$	0	0
$793$	5.05180	0.179395
$794$	67.8883	2.40926
$795$	0	0
$796$	−10.4411	−0.370076
$797$	−43.6700	−1.54687	−0.773435	−	0.633875i	$-0.781463\pi$
$797$	−43.6700	−1.54687	−0.773435	+	0.633875i	$0.781463\pi$
$798$	35.8027	1.26740
$799$	−3.46410	−0.122551
$800$	0	0
$801$	49.4621	1.74766
$802$	67.9480	2.39933
$803$	0	0
$804$	14.5102	0.511737
$805$	0	0
$806$	−10.3670	−0.365161
$807$	−22.4667	−0.790866
$808$	−1.03520	−0.0364184
$809$	−39.5048	−1.38891	−0.694457	−	0.719534i	$-0.744355\pi$
$809$	−39.5048	−1.38891	−0.694457	+	0.719534i	$0.744355\pi$
$810$	0	0
$811$	46.5773	1.63555	0.817775	−	0.575538i	$-0.195207\pi$
$811$	46.5773	1.63555	0.817775	+	0.575538i	$0.195207\pi$
$812$	−27.9698	−0.981549
$813$	45.3940	1.59204
$814$	0	0
$815$	0	0
$816$	−13.1916	−0.461799
$817$	−20.6707	−0.723176
$818$	16.5242	0.577756
$819$	−11.4495	−0.400079
$820$	0	0
$821$	29.2072	1.01934	0.509669	−	0.860371i	$-0.329768\pi$
$821$	29.2072	1.01934	0.509669	+	0.860371i	$0.329768\pi$
$822$	81.1967	2.83206
$823$	−13.8818	−0.483890	−0.241945	−	0.970290i	$-0.577785\pi$
$823$	−13.8818	−0.483890	−0.241945	+	0.970290i	$0.577785\pi$
$824$	0.590551	0.0205728
$825$	0	0
$826$	−24.1406	−0.839960
$827$	−9.55026	−0.332095	−0.166048	−	0.986118i	$-0.553101\pi$
$827$	−9.55026	−0.332095	−0.166048	+	0.986118i	$0.553101\pi$
$828$	−50.1201	−1.74179
$829$	37.3241	1.29632	0.648160	−	0.761504i	$-0.275539\pi$
$829$	37.3241	1.29632	0.648160	+	0.761504i	$0.275539\pi$
$830$	0	0
$831$	59.1784	2.05288
$832$	5.65476	0.196044
$833$	3.93658	0.136394
$834$	−39.8257	−1.37905
$835$	0	0
$836$	0	0
$837$	57.4683	1.98640
$838$	39.5112	1.36489
$839$	−1.43270	−0.0494623	−0.0247311	−	0.999694i	$-0.507873\pi$
$839$	−1.43270	−0.0494623	−0.0247311	+	0.999694i	$0.507873\pi$
$840$	0	0
$841$	−11.6617	−0.402127
$842$	−48.3618	−1.66666
$843$	70.5940	2.43139
$844$	−3.29062	−0.113268
$845$	0	0
$846$	−32.4031	−1.11404
$847$	0	0
$848$	−24.4417	−0.839332
$849$	−42.0810	−1.44422
$850$	0	0
$851$	−8.97475	−0.307650
$852$	95.8213	3.28278
$853$	−28.1421	−0.963569	−0.481784	−	0.876290i	$-0.660011\pi$
$853$	−28.1421	−0.963569	−0.481784	+	0.876290i	$0.660011\pi$
$854$	−50.5823	−1.73089
$855$	0	0
$856$	−0.736584	−0.0251759
$857$	−4.04561	−0.138195	−0.0690977	−	0.997610i	$-0.522012\pi$
$857$	−4.04561	−0.138195	−0.0690977	+	0.997610i	$0.522012\pi$
$858$	0	0
$859$	−55.2064	−1.88362	−0.941808	−	0.336151i	$-0.890875\pi$
$859$	−55.2064	−1.88362	−0.941808	+	0.336151i	$0.890875\pi$
$860$	0	0
$861$	−30.9369	−1.05433
$862$	−15.3002	−0.521125
$863$	−30.1927	−1.02777	−0.513885	−	0.857859i	$-0.671794\pi$
$863$	−30.1927	−1.02777	−0.513885	+	0.857859i	$0.671794\pi$
$864$	−58.7367	−1.99826
$865$	0	0
$866$	−51.8231	−1.76102
$867$	−45.4338	−1.54301
$868$	53.0646	1.80113
$869$	0	0
$870$	0	0
$871$	−1.54399	−0.0523160
$872$	−2.86073	−0.0968766
$873$	−83.1958	−2.81575
$874$	−16.6767	−0.564096
$875$	0	0
$876$	34.8395	1.17712
$877$	30.9398	1.04476	0.522381	−	0.852712i	$-0.325044\pi$
$877$	30.9398	1.04476	0.522381	+	0.852712i	$0.325044\pi$
$878$	−41.4004	−1.39719
$879$	−44.1951	−1.49066
$880$	0	0
$881$	−8.25840	−0.278233	−0.139116	−	0.990276i	$-0.544426\pi$
$881$	−8.25840	−0.278233	−0.139116	+	0.990276i	$0.544426\pi$
$882$	36.8226	1.23988
$883$	−40.0289	−1.34708	−0.673539	−	0.739152i	$-0.735227\pi$
$883$	−40.0289	−1.34708	−0.673539	+	0.739152i	$0.735227\pi$
$884$	−1.61279	−0.0542439
$885$	0	0
$886$	−20.5615	−0.690777
$887$	−37.7350	−1.26702	−0.633509	−	0.773735i	$-0.718386\pi$
$887$	−37.7350	−1.26702	−0.633509	+	0.773735i	$0.718386\pi$
$888$	1.11349	0.0373662
$889$	52.8031	1.77096
$890$	0	0
$891$	0	0
$892$	6.93360	0.232154
$893$	−5.51167	−0.184441
$894$	113.185	3.78546
$895$	0	0
$896$	−4.76261	−0.159108
$897$	8.24432	0.275270
$898$	−29.7343	−0.992245
$899$	−32.8944	−1.09709
$900$	0	0
$901$	7.62803	0.254127
$902$	0	0
$903$	−102.318	−3.40494
$904$	1.88093	0.0625588
$905$	0	0
$906$	19.4014	0.644569
$907$	−33.5319	−1.11341	−0.556705	−	0.830710i	$-0.687935\pi$
$907$	−33.5319	−1.11341	−0.556705	+	0.830710i	$0.687935\pi$
$908$	−5.94079	−0.197152
$909$	−30.6565	−1.01681
$910$	0	0
$911$	−13.7828	−0.456646	−0.228323	−	0.973585i	$-0.573324\pi$
$911$	−13.7828	−0.456646	−0.228323	+	0.973585i	$0.573324\pi$
$912$	−20.9890	−0.695014
$913$	0	0
$914$	−6.80231	−0.225000
$915$	0	0
$916$	−4.16588	−0.137645
$917$	−44.9602	−1.48472
$918$	17.4885	0.577207
$919$	41.8128	1.37928	0.689639	−	0.724154i	$-0.257769\pi$
$919$	41.8128	1.37928	0.689639	+	0.724154i	$0.257769\pi$
$920$	0	0
$921$	−23.4396	−0.772361
$922$	−2.86073	−0.0942131
$923$	−10.1960	−0.335607
$924$	0	0
$925$	0	0
$926$	31.2716	1.02765
$927$	17.4885	0.574399
$928$	33.6204	1.10364
$929$	13.1028	0.429889	0.214944	−	0.976626i	$-0.431043\pi$
$929$	13.1028	0.429889	0.214944	+	0.976626i	$0.431043\pi$
$930$	0	0
$931$	6.26342	0.205275
$932$	42.3652	1.38772
$933$	64.9023	2.12481
$934$	−37.8078	−1.23711
$935$	0	0
$936$	−0.661674	−0.0216275
$937$	8.75544	0.286028	0.143014	−	0.989721i	$-0.454321\pi$
$937$	8.75544	0.286028	0.143014	+	0.989721i	$0.454321\pi$
$938$	15.4595	0.504771
$939$	6.85095	0.223572
$940$	0	0
$941$	−17.6529	−0.575468	−0.287734	−	0.957710i	$-0.592902\pi$
$941$	−17.6529	−0.575468	−0.287734	+	0.957710i	$0.592902\pi$
$942$	−82.6287	−2.69219
$943$	14.4102	0.469261
$944$	14.1522	0.460615
$945$	0	0
$946$	0	0
$947$	−56.2415	−1.82760	−0.913802	−	0.406159i	$-0.866868\pi$
$947$	−56.2415	−1.82760	−0.913802	+	0.406159i	$0.866868\pi$
$948$	−93.0150	−3.02099
$949$	−3.70716	−0.120340
$950$	0	0
$951$	52.5336	1.70352
$952$	0.708273	0.0229553
$953$	4.74388	0.153669	0.0768347	−	0.997044i	$-0.475519\pi$
$953$	4.74388	0.153669	0.0768347	+	0.997044i	$0.475519\pi$
$954$	71.3524	2.31012
$955$	0	0
$956$	3.95540	0.127927
$957$	0	0
$958$	−60.4344	−1.95255
$959$	44.2242	1.42807
$960$	0	0
$961$	31.4074	1.01314
$962$	−2.70137	−0.0870955
$963$	−21.8132	−0.702919
$964$	8.37749	0.269821
$965$	0	0
$966$	−82.5481	−2.65594
$967$	−33.8619	−1.08892	−0.544462	−	0.838785i	$-0.683266\pi$
$967$	−33.8619	−1.08892	−0.544462	+	0.838785i	$0.683266\pi$
$968$	0	0
$969$	6.55047	0.210431
$970$	0	0
$971$	−19.7828	−0.634862	−0.317431	−	0.948281i	$-0.602820\pi$
$971$	−19.7828	−0.634862	−0.317431	+	0.948281i	$0.602820\pi$
$972$	−16.8947	−0.541898
$973$	−21.6913	−0.695390
$974$	−1.89096	−0.0605902
$975$	0	0
$976$	29.6534	0.949182
$977$	6.66124	0.213112	0.106556	−	0.994307i	$-0.466018\pi$
$977$	6.66124	0.213112	0.106556	+	0.994307i	$0.466018\pi$
$978$	−60.8581	−1.94603
$979$	0	0
$980$	0	0
$981$	−84.7175	−2.70482
$982$	−66.5390	−2.12334
$983$	5.16210	0.164645	0.0823227	−	0.996606i	$-0.473766\pi$
$983$	5.16210	0.164645	0.0823227	+	0.996606i	$0.473766\pi$
$984$	−1.78786	−0.0569949
$985$	0	0
$986$	−10.0103	−0.318792
$987$	−27.2823	−0.868407
$988$	−2.56608	−0.0816378
$989$	47.6592	1.51547
$990$	0	0
$991$	−23.8830	−0.758669	−0.379334	−	0.925260i	$-0.623847\pi$
$991$	−23.8830	−0.758669	−0.379334	+	0.925260i	$0.623847\pi$
$992$	−63.7849	−2.02517
$993$	−9.01167	−0.285977
$994$	102.090	3.23810
$995$	0	0
$996$	64.8513	2.05489
$997$	−29.6423	−0.938780	−0.469390	−	0.882991i	$-0.655526\pi$
$997$	−29.6423	−0.938780	−0.469390	+	0.882991i	$0.655526\pi$
$998$	18.1882	0.575738
$999$	14.9747	0.473780

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3025.2.a.bo.1.10		12
5.2	odd	4		605.2.b.h.364.9	yes	12
5.3	odd	4		605.2.b.h.364.4	yes	12
5.4	even	2	inner	3025.2.a.bo.1.3		12
11.10	odd	2	inner	3025.2.a.bo.1.4		12
55.2	even	20		605.2.j.k.444.3		48
55.3	odd	20		605.2.j.k.9.3		48
55.7	even	20		605.2.j.k.269.9		48
55.8	even	20		605.2.j.k.9.9		48
55.13	even	20		605.2.j.k.444.10		48
55.17	even	20		605.2.j.k.124.10		48
55.18	even	20		605.2.j.k.269.4		48
55.27	odd	20		605.2.j.k.124.4		48
55.28	even	20		605.2.j.k.124.3		48
55.32	even	4		605.2.b.h.364.3	✓	12
55.37	odd	20		605.2.j.k.269.3		48
55.38	odd	20		605.2.j.k.124.9		48
55.42	odd	20		605.2.j.k.444.9		48
55.43	even	4		605.2.b.h.364.10	yes	12
55.47	odd	20		605.2.j.k.9.10		48
55.48	odd	20		605.2.j.k.269.10		48
55.52	even	20		605.2.j.k.9.4		48
55.53	odd	20		605.2.j.k.444.4		48
55.54	odd	2	inner	3025.2.a.bo.1.9		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
605.2.b.h.364.3	✓	12	55.32	even	4
605.2.b.h.364.4	yes	12	5.3	odd	4
605.2.b.h.364.9	yes	12	5.2	odd	4
605.2.b.h.364.10	yes	12	55.43	even	4
605.2.j.k.9.3		48	55.3	odd	20
605.2.j.k.9.4		48	55.52	even	20
605.2.j.k.9.9		48	55.8	even	20
605.2.j.k.9.10		48	55.47	odd	20
605.2.j.k.124.3		48	55.28	even	20
605.2.j.k.124.4		48	55.27	odd	20
605.2.j.k.124.9		48	55.38	odd	20
605.2.j.k.124.10		48	55.17	even	20
605.2.j.k.269.3		48	55.37	odd	20
605.2.j.k.269.4		48	55.18	even	20
605.2.j.k.269.9		48	55.7	even	20
605.2.j.k.269.10		48	55.48	odd	20
605.2.j.k.444.3		48	55.2	even	20
605.2.j.k.444.4		48	55.53	odd	20
605.2.j.k.444.9		48	55.42	odd	20
605.2.j.k.444.10		48	55.13	even	20
3025.2.a.bo.1.3		12	5.4	even	2	inner
3025.2.a.bo.1.4		12	11.10	odd	2	inner
3025.2.a.bo.1.9		12	55.54	odd	2	inner
3025.2.a.bo.1.10		12	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 3025 = 5^{2} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3025.a (trivial)

\(f(q)\)	\(=\)	\(q+2.02281 q^{2} +2.91475 q^{3} +2.09174 q^{4} +5.89598 q^{6} +3.21128 q^{7} +0.185581 q^{8} +5.49579 q^{9} +O(q^{10})\)	\(q+2.02281 q^{2} +2.91475 q^{3} +2.09174 q^{4} +5.89598 q^{6} +3.21128 q^{7} +0.185581 q^{8} +5.49579 q^{9} +6.09692 q^{12} -0.648753 q^{13} +6.49579 q^{14} -3.80809 q^{16} +1.18847 q^{17} +11.1169 q^{18} +1.89096 q^{19} +9.36008 q^{21} -4.35986 q^{23} +0.540924 q^{24} -1.31230 q^{26} +7.27462 q^{27} +6.71717 q^{28} -4.16393 q^{29} +7.89984 q^{31} -8.07420 q^{32} +2.40405 q^{34} +11.4958 q^{36} +2.05849 q^{37} +3.82504 q^{38} -1.89096 q^{39} -3.30520 q^{41} +18.9336 q^{42} -10.9313 q^{43} -8.81916 q^{46} -2.91475 q^{47} -11.0997 q^{48} +3.31230 q^{49} +3.46410 q^{51} -1.35703 q^{52} +6.41836 q^{53} +14.7151 q^{54} +0.595953 q^{56} +5.51167 q^{57} -8.42283 q^{58} -3.71635 q^{59} -7.78694 q^{61} +15.9798 q^{62} +17.6485 q^{63} -8.71635 q^{64} +2.37993 q^{67} +2.48598 q^{68} -12.7079 q^{69} +15.7163 q^{71} +1.01992 q^{72} +5.71428 q^{73} +4.16393 q^{74} +3.95540 q^{76} -3.82504 q^{78} -15.2561 q^{79} +4.71635 q^{81} -6.68577 q^{82} +10.6367 q^{83} +19.5789 q^{84} -22.1120 q^{86} -12.1368 q^{87} +9.00000 q^{89} -2.08333 q^{91} -9.11972 q^{92} +23.0261 q^{93} -5.89598 q^{94} -23.5343 q^{96} -15.1381 q^{97} +6.70015 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 20 q^{4} + 20 q^{9}+O(q^{10}) \) 12 * q + 20 * q^4 + 20 * q^9	\( 12 q + 20 q^{4} + 20 q^{9} + 32 q^{14} + 36 q^{16} + 20 q^{26} + 8 q^{31} - 12 q^{34} + 92 q^{36} + 4 q^{49} + 48 q^{56} + 32 q^{59} - 28 q^{64} + 16 q^{69} + 112 q^{71} - 20 q^{81} - 56 q^{86} + 108 q^{89} + 72 q^{91}+O(q^{100}) \) 12 * q + 20 * q^4 + 20 * q^9 + 32 * q^14 + 36 * q^16 + 20 * q^26 + 8 * q^31 - 12 * q^34 + 92 * q^36 + 4 * q^49 + 48 * q^56 + 32 * q^59 - 28 * q^64 + 16 * q^69 + 112 * q^71 - 20 * q^81 - 56 * q^86 + 108 * q^89 + 72 * q^91

Introduction

L-functions

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