LMFDB - Embedded newform 9801.2.a.cp.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [9801,2,Mod(1,9801)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(9801, 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("9801.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 9801 = 3^{4} \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9801.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:	$78.2613790211$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 22 x^{16} + 42 x^{15} + 198 x^{14} - 357 x^{13} - 944 x^{12} + 1579 x^{11} + \cdots - 55 $ x^18 - 2x^17 - 22x^16 + 42x^15 + 198x^14 - 357x^13 - 944x^12 + 1579x^11 + 2594x^10 - 3897x^9 - 4219x^8 + 5363x^7 + 4035x^6 - 3886x^5 - 2173x^4 + 1303x^3 + 576x^2 - 155*x - 55
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-0.577812$ of defining polynomial
Character	$\chi$	$=$	9801.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.577812 q^{2} -1.66613 q^{4} -3.00443 q^{5} -1.16432 q^{7} +2.11834 q^{8} +1.73599 q^{10} -3.94617 q^{13} +0.672758 q^{14} +2.10827 q^{16} +0.314191 q^{17} +6.36839 q^{19} +5.00578 q^{20} +0.0855002 q^{23} +4.02659 q^{25} +2.28015 q^{26} +1.93991 q^{28} +7.69982 q^{29} +6.52884 q^{31} -5.45485 q^{32} -0.181543 q^{34} +3.49812 q^{35} -6.24309 q^{37} -3.67973 q^{38} -6.36439 q^{40} -5.80907 q^{41} -6.78458 q^{43} -0.0494030 q^{46} +0.327736 q^{47} -5.64436 q^{49} -2.32661 q^{50} +6.57485 q^{52} +2.42269 q^{53} -2.46642 q^{56} -4.44905 q^{58} +2.29603 q^{59} -13.6872 q^{61} -3.77244 q^{62} -1.06465 q^{64} +11.8560 q^{65} +11.6798 q^{67} -0.523483 q^{68} -2.02125 q^{70} -8.71765 q^{71} +2.94656 q^{73} +3.60733 q^{74} -10.6106 q^{76} -8.88719 q^{79} -6.33413 q^{80} +3.35655 q^{82} -4.95778 q^{83} -0.943963 q^{85} +3.92021 q^{86} -2.12862 q^{89} +4.59461 q^{91} -0.142455 q^{92} -0.189370 q^{94} -19.1334 q^{95} -0.0888392 q^{97} +3.26138 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 12 q^{4} + q^{5} + q^{7} + 6 q^{8} - 2 q^{10} + 3 q^{13} - 8 q^{16} + 20 q^{17} - 3 q^{19} + 5 q^{20} + 10 q^{23} + 7 q^{25} - 2 q^{26} + 19 q^{28} + 21 q^{29} + 6 q^{31} + 9 q^{32} - 4 q^{34}+ \cdots + 82 q^{98}+O(q^{100}) $ 18 * q + 2 * q^2 + 12 * q^4 + q^5 + q^7 + 6 * q^8 - 2 * q^10 + 3 * q^13 - 8 * q^16 + 20 * q^17 - 3 * q^19 + 5 * q^20 + 10 * q^23 + 7 * q^25 - 2 * q^26 + 19 * q^28 + 21 * q^29 + 6 * q^31 + 9 * q^32 - 4 * q^34 + 38 * q^35 + 7 * q^37 - 13 * q^38 + 20 * q^41 + 4 * q^43 + 8 * q^46 - 7 * q^47 + 7 * q^49 + 25 * q^50 - 19 * q^52 - 31 * q^53 + 57 * q^56 + 12 * q^58 + 12 * q^59 - 16 * q^61 + 19 * q^62 - 16 * q^64 + 42 * q^65 - 5 * q^67 + 51 * q^68 + 8 * q^70 - 13 * q^71 + 9 * q^74 - 8 * q^76 - 2 * q^79 - 46 * q^80 - 34 * q^82 + 36 * q^83 + 25 * q^85 - 26 * q^86 + 14 * q^89 - 15 * q^91 + 15 * q^92 + 4 * q^94 + 64 * q^95 - 16 * q^97 + 82 * q^98

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 $

$2$	−0.577812	−0.408575	−0.204287	−	0.978911i	$-0.565488\pi$
$2$	−0.577812	−0.408575	−0.204287	+	0.978911i	$0.565488\pi$
$3$	0	0
$3$	0	0
$4$	−1.66613	−0.833067
$5$	−3.00443	−1.34362	−0.671810	−	0.740723i	$-0.734483\pi$
$5$	−3.00443	−1.34362	−0.671810	+	0.740723i	$0.734483\pi$
$6$	0	0
$7$	−1.16432	−0.440072	−0.220036	−	0.975492i	$-0.570617\pi$
$7$	−1.16432	−0.440072	−0.220036	+	0.975492i	$0.570617\pi$
$8$	2.11834	0.748945
$9$	0	0
$10$	1.73599	0.548970
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−3.94617	−1.09447	−0.547236	−	0.836979i	$-0.684320\pi$
$13$	−3.94617	−1.09447	−0.547236	+	0.836979i	$0.684320\pi$
$14$	0.672758	0.179802
$15$	0	0
$16$	2.10827	0.527067
$17$	0.314191	0.0762024	0.0381012	−	0.999274i	$-0.487869\pi$
$17$	0.314191	0.0762024	0.0381012	+	0.999274i	$0.487869\pi$
$18$	0	0
$19$	6.36839	1.46101	0.730504	−	0.682908i	$-0.239285\pi$
$19$	6.36839	1.46101	0.730504	+	0.682908i	$0.239285\pi$
$20$	5.00578	1.11933
$21$	0	0
$22$	0	0
$23$	0.0855002	0.0178280	0.00891401	−	0.999960i	$-0.497163\pi$
$23$	0.0855002	0.0178280	0.00891401	+	0.999960i	$0.497163\pi$
$24$	0	0
$25$	4.02659	0.805317
$26$	2.28015	0.447173
$27$	0	0
$28$	1.93991	0.366609
$29$	7.69982	1.42982	0.714910	−	0.699216i	$-0.246468\pi$
$29$	7.69982	1.42982	0.714910	+	0.699216i	$0.246468\pi$
$30$	0	0
$31$	6.52884	1.17261	0.586307	−	0.810089i	$-0.300581\pi$
$31$	6.52884	1.17261	0.586307	+	0.810089i	$0.300581\pi$
$32$	−5.45485	−0.964291
$33$	0	0
$34$	−0.181543	−0.0311344
$35$	3.49812	0.591290
$36$	0	0
$37$	−6.24309	−1.02636	−0.513179	−	0.858282i	$-0.671532\pi$
$37$	−6.24309	−1.02636	−0.513179	+	0.858282i	$0.671532\pi$
$38$	−3.67973	−0.596931
$39$	0	0
$40$	−6.36439	−1.00630
$41$	−5.80907	−0.907224	−0.453612	−	0.891199i	$-0.649865\pi$
$41$	−5.80907	−0.907224	−0.453612	+	0.891199i	$0.649865\pi$
$42$	0	0
$43$	−6.78458	−1.03464	−0.517320	−	0.855792i	$-0.673070\pi$
$43$	−6.78458	−1.03464	−0.517320	+	0.855792i	$0.673070\pi$
$44$	0	0
$45$	0	0
$46$	−0.0494030	−0.00728408
$47$	0.327736	0.0478052	0.0239026	−	0.999714i	$-0.492391\pi$
$47$	0.327736	0.0478052	0.0239026	+	0.999714i	$0.492391\pi$
$48$	0	0
$49$	−5.64436	−0.806337
$50$	−2.32661	−0.329032
$51$	0	0
$52$	6.57485	0.911767
$53$	2.42269	0.332782	0.166391	−	0.986060i	$-0.446789\pi$
$53$	2.42269	0.332782	0.166391	+	0.986060i	$0.446789\pi$
$54$	0	0
$55$	0	0
$56$	−2.46642	−0.329589
$57$	0	0
$58$	−4.44905	−0.584189
$59$	2.29603	0.298918	0.149459	−	0.988768i	$-0.452247\pi$
$59$	2.29603	0.298918	0.149459	+	0.988768i	$0.452247\pi$
$60$	0	0
$61$	−13.6872	−1.75247	−0.876233	−	0.481887i	$-0.839951\pi$
$61$	−13.6872	−1.75247	−0.876233	+	0.481887i	$0.839951\pi$
$62$	−3.77244	−0.479100
$63$	0	0
$64$	−1.06465	−0.133081
$65$	11.8560	1.47055
$66$	0	0
$67$	11.6798	1.42691	0.713456	−	0.700700i	$-0.247129\pi$
$67$	11.6798	1.42691	0.713456	+	0.700700i	$0.247129\pi$
$68$	−0.523483	−0.0634817
$69$	0	0
$70$	−2.02125	−0.241586
$71$	−8.71765	−1.03459	−0.517297	−	0.855806i	$-0.673062\pi$
$71$	−8.71765	−1.03459	−0.517297	+	0.855806i	$0.673062\pi$
$72$	0	0
$73$	2.94656	0.344869	0.172434	−	0.985021i	$-0.444837\pi$
$73$	2.94656	0.344869	0.172434	+	0.985021i	$0.444837\pi$
$74$	3.60733	0.419344
$75$	0	0
$76$	−10.6106	−1.21712
$77$	0	0
$78$	0	0
$79$	−8.88719	−0.999887	−0.499944	−	0.866058i	$-0.666646\pi$
$79$	−8.88719	−0.999887	−0.499944	+	0.866058i	$0.666646\pi$
$80$	−6.33413	−0.708178
$81$	0	0
$82$	3.35655	0.370669
$83$	−4.95778	−0.544187	−0.272094	−	0.962271i	$-0.587716\pi$
$83$	−4.95778	−0.544187	−0.272094	+	0.962271i	$0.587716\pi$
$84$	0	0
$85$	−0.943963	−0.102387
$86$	3.92021	0.422728
$87$	0	0
$88$	0	0
$89$	−2.12862	−0.225634	−0.112817	−	0.993616i	$-0.535987\pi$
$89$	−2.12862	−0.225634	−0.112817	+	0.993616i	$0.535987\pi$
$90$	0	0
$91$	4.59461	0.481646
$92$	−0.142455	−0.0148519
$93$	0	0
$94$	−0.189370	−0.0195320
$95$	−19.1334	−1.96304
$96$	0	0
$97$	−0.0888392	−0.00902026	−0.00451013	−	0.999990i	$-0.501436\pi$
$97$	−0.0888392	−0.00902026	−0.00451013	+	0.999990i	$0.501436\pi$
$98$	3.26138	0.329449
$99$	0	0
$100$	−6.70883	−0.670883
$101$	2.05648	0.204628	0.102314	−	0.994752i	$-0.467375\pi$
$101$	2.05648	0.204628	0.102314	+	0.994752i	$0.467375\pi$
$102$	0	0
$103$	−3.01672	−0.297246	−0.148623	−	0.988894i	$-0.547484\pi$
$103$	−3.01672	−0.297246	−0.148623	+	0.988894i	$0.547484\pi$
$104$	−8.35932	−0.819698
$105$	0	0
$106$	−1.39986	−0.135967
$107$	−11.9929	−1.15939	−0.579697	−	0.814832i	$-0.696829\pi$
$107$	−11.9929	−1.15939	−0.579697	+	0.814832i	$0.696829\pi$
$108$	0	0
$109$	5.20013	0.498082	0.249041	−	0.968493i	$-0.419885\pi$
$109$	5.20013	0.498082	0.249041	+	0.968493i	$0.419885\pi$
$110$	0	0
$111$	0	0
$112$	−2.45470	−0.231947
$113$	−19.2276	−1.80878	−0.904388	−	0.426711i	$-0.859672\pi$
$113$	−19.2276	−1.80878	−0.904388	+	0.426711i	$0.859672\pi$
$114$	0	0
$115$	−0.256879	−0.0239541
$116$	−12.8289	−1.19114
$117$	0	0
$118$	−1.32667	−0.122130
$119$	−0.365818	−0.0335345
$120$	0	0
$121$	0	0
$122$	7.90863	0.716014
$123$	0	0
$124$	−10.8779	−0.976865
$125$	2.92455	0.261580
$126$	0	0
$127$	−13.1829	−1.16980	−0.584898	−	0.811107i	$-0.698865\pi$
$127$	−13.1829	−1.16980	−0.584898	+	0.811107i	$0.698865\pi$
$128$	11.5249	1.01866
$129$	0	0
$130$	−6.85053	−0.600831
$131$	17.9718	1.57020	0.785100	−	0.619369i	$-0.212611\pi$
$131$	17.9718	1.57020	0.785100	+	0.619369i	$0.212611\pi$
$132$	0	0
$133$	−7.41484	−0.642949
$134$	−6.74872	−0.583001
$135$	0	0
$136$	0.665561	0.0570714
$137$	16.4017	1.40130	0.700648	−	0.713507i	$-0.252895\pi$
$137$	16.4017	1.40130	0.700648	+	0.713507i	$0.252895\pi$
$138$	0	0
$139$	−11.9016	−1.00948	−0.504740	−	0.863271i	$-0.668412\pi$
$139$	−11.9016	−1.00948	−0.504740	+	0.863271i	$0.668412\pi$
$140$	−5.82833	−0.492584
$141$	0	0
$142$	5.03716	0.422709
$143$	0	0
$144$	0	0
$145$	−23.1336	−1.92114
$146$	−1.70256	−0.140905
$147$	0	0
$148$	10.4018	0.855024
$149$	4.53172	0.371253	0.185626	−	0.982620i	$-0.440569\pi$
$149$	4.53172	0.371253	0.185626	+	0.982620i	$0.440569\pi$
$150$	0	0
$151$	−2.93086	−0.238510	−0.119255	−	0.992864i	$-0.538051\pi$
$151$	−2.93086	−0.238510	−0.119255	+	0.992864i	$0.538051\pi$
$152$	13.4904	1.09422
$153$	0	0
$154$	0	0
$155$	−19.6154	−1.57555
$156$	0	0
$157$	−18.0536	−1.44084	−0.720419	−	0.693539i	$-0.756050\pi$
$157$	−18.0536	−1.44084	−0.720419	+	0.693539i	$0.756050\pi$
$158$	5.13513	0.408529
$159$	0	0
$160$	16.3887	1.29564
$161$	−0.0995496	−0.00784561
$162$	0	0
$163$	−5.82347	−0.456130	−0.228065	−	0.973646i	$-0.573240\pi$
$163$	−5.82347	−0.456130	−0.228065	+	0.973646i	$0.573240\pi$
$164$	9.67868	0.755778
$165$	0	0
$166$	2.86467	0.222341
$167$	5.02173	0.388593	0.194296	−	0.980943i	$-0.437758\pi$
$167$	5.02173	0.388593	0.194296	+	0.980943i	$0.437758\pi$
$168$	0	0
$169$	2.57227	0.197867
$170$	0.545433	0.0418328
$171$	0	0
$172$	11.3040	0.861923
$173$	15.5899	1.18528	0.592638	−	0.805469i	$-0.298087\pi$
$173$	15.5899	1.18528	0.592638	+	0.805469i	$0.298087\pi$
$174$	0	0
$175$	−4.68824	−0.354397
$176$	0	0
$177$	0	0
$178$	1.22994	0.0921882
$179$	−7.04887	−0.526857	−0.263428	−	0.964679i	$-0.584853\pi$
$179$	−7.04887	−0.526857	−0.263428	+	0.964679i	$0.584853\pi$
$180$	0	0
$181$	2.49770	0.185652	0.0928262	−	0.995682i	$-0.470410\pi$
$181$	2.49770	0.185652	0.0928262	+	0.995682i	$0.470410\pi$
$182$	−2.65482	−0.196788
$183$	0	0
$184$	0.181118	0.0133522
$185$	18.7569	1.37904
$186$	0	0
$187$	0	0
$188$	−0.546051	−0.0398249
$189$	0	0
$190$	11.0555	0.802050
$191$	11.8230	0.855481	0.427740	−	0.903902i	$-0.359310\pi$
$191$	11.8230	0.855481	0.427740	+	0.903902i	$0.359310\pi$
$192$	0	0
$193$	6.74666	0.485635	0.242817	−	0.970072i	$-0.421928\pi$
$193$	6.74666	0.485635	0.242817	+	0.970072i	$0.421928\pi$
$194$	0.0513324	0.00368545
$195$	0	0
$196$	9.40425	0.671732
$197$	20.6474	1.47107	0.735534	−	0.677488i	$-0.236931\pi$
$197$	20.6474	1.47107	0.735534	+	0.677488i	$0.236931\pi$
$198$	0	0
$199$	−13.2862	−0.941832	−0.470916	−	0.882178i	$-0.656077\pi$
$199$	−13.2862	−0.941832	−0.470916	+	0.882178i	$0.656077\pi$
$200$	8.52966	0.603138
$201$	0	0
$202$	−1.18826	−0.0836058
$203$	−8.96506	−0.629224
$204$	0	0
$205$	17.4529	1.21897
$206$	1.74309	0.121447
$207$	0	0
$208$	−8.31958	−0.576859
$209$	0	0
$210$	0	0
$211$	−8.34502	−0.574495	−0.287247	−	0.957856i	$-0.592740\pi$
$211$	−8.34502	−0.574495	−0.287247	+	0.957856i	$0.592740\pi$
$212$	−4.03653	−0.277230
$213$	0	0
$214$	6.92962	0.473699
$215$	20.3838	1.39016
$216$	0	0
$217$	−7.60166	−0.516034
$218$	−3.00470	−0.203504
$219$	0	0
$220$	0	0
$221$	−1.23985	−0.0834013
$222$	0	0
$223$	−0.383656	−0.0256915	−0.0128457	−	0.999917i	$-0.504089\pi$
$223$	−0.383656	−0.0256915	−0.0128457	+	0.999917i	$0.504089\pi$
$224$	6.35120	0.424357
$225$	0	0
$226$	11.1099	0.739020
$227$	−18.0140	−1.19563	−0.597817	−	0.801633i	$-0.703965\pi$
$227$	−18.0140	−1.19563	−0.597817	+	0.801633i	$0.703965\pi$
$228$	0	0
$229$	13.4279	0.887339	0.443669	−	0.896191i	$-0.353676\pi$
$229$	13.4279	0.887339	0.443669	+	0.896191i	$0.353676\pi$
$230$	0.148428	0.00978704
$231$	0	0
$232$	16.3108	1.07086
$233$	3.36965	0.220753	0.110377	−	0.993890i	$-0.464794\pi$
$233$	3.36965	0.220753	0.110377	+	0.993890i	$0.464794\pi$
$234$	0	0
$235$	−0.984658	−0.0642320
$236$	−3.82549	−0.249018
$237$	0	0
$238$	0.211374	0.0137014
$239$	23.1968	1.50048	0.750238	−	0.661168i	$-0.229939\pi$
$239$	23.1968	1.50048	0.750238	+	0.661168i	$0.229939\pi$
$240$	0	0
$241$	15.1641	0.976807	0.488404	−	0.872618i	$-0.337579\pi$
$241$	15.1641	0.976807	0.488404	+	0.872618i	$0.337579\pi$
$242$	0	0
$243$	0	0
$244$	22.8047	1.45992
$245$	16.9581	1.08341
$246$	0	0
$247$	−25.1308	−1.59903
$248$	13.8303	0.878223
$249$	0	0
$250$	−1.68984	−0.106875
$251$	0.582306	0.0367548	0.0183774	−	0.999831i	$-0.494150\pi$
$251$	0.582306	0.0367548	0.0183774	+	0.999831i	$0.494150\pi$
$252$	0	0
$253$	0	0
$254$	7.61725	0.477949
$255$	0	0
$256$	−4.52991	−0.283119
$257$	10.9714	0.684378	0.342189	−	0.939631i	$-0.388832\pi$
$257$	10.9714	0.684378	0.342189	+	0.939631i	$0.388832\pi$
$258$	0	0
$259$	7.26895	0.451671
$260$	−19.7537	−1.22507
$261$	0	0
$262$	−10.3843	−0.641544
$263$	14.3954	0.887656	0.443828	−	0.896112i	$-0.353620\pi$
$263$	14.3954	0.887656	0.443828	+	0.896112i	$0.353620\pi$
$264$	0	0
$265$	−7.27881	−0.447134
$266$	4.28439	0.262693
$267$	0	0
$268$	−19.4601	−1.18871
$269$	−0.488976	−0.0298134	−0.0149067	−	0.999889i	$-0.504745\pi$
$269$	−0.488976	−0.0298134	−0.0149067	+	0.999889i	$0.504745\pi$
$270$	0	0
$271$	21.9389	1.33270	0.666348	−	0.745641i	$-0.267857\pi$
$271$	21.9389	1.33270	0.666348	+	0.745641i	$0.267857\pi$
$272$	0.662397	0.0401637
$273$	0	0
$274$	−9.47712	−0.572534
$275$	0	0
$276$	0	0
$277$	2.86952	0.172413	0.0862065	−	0.996277i	$-0.472526\pi$
$277$	2.86952	0.172413	0.0862065	+	0.996277i	$0.472526\pi$
$278$	6.87689	0.412448
$279$	0	0
$280$	7.41019	0.442843
$281$	−18.1781	−1.08441	−0.542206	−	0.840245i	$-0.682411\pi$
$281$	−18.1781	−1.08441	−0.542206	+	0.840245i	$0.682411\pi$
$282$	0	0
$283$	−20.5371	−1.22080	−0.610402	−	0.792092i	$-0.708992\pi$
$283$	−20.5371	−1.22080	−0.610402	+	0.792092i	$0.708992\pi$
$284$	14.5248	0.861886
$285$	0	0
$286$	0	0
$287$	6.76362	0.399244
$288$	0	0
$289$	−16.9013	−0.994193
$290$	13.3668	0.784928
$291$	0	0
$292$	−4.90936	−0.287299
$293$	−0.860067	−0.0502456	−0.0251228	−	0.999684i	$-0.507998\pi$
$293$	−0.860067	−0.0502456	−0.0251228	+	0.999684i	$0.507998\pi$
$294$	0	0
$295$	−6.89826	−0.401632
$296$	−13.2250	−0.768685
$297$	0	0
$298$	−2.61848	−0.151684
$299$	−0.337398	−0.0195122
$300$	0	0
$301$	7.89943	0.455315
$302$	1.69349	0.0974493
$303$	0	0
$304$	13.4263	0.770049
$305$	41.1222	2.35465
$306$	0	0
$307$	3.48920	0.199139	0.0995696	−	0.995031i	$-0.468253\pi$
$307$	3.48920	0.199139	0.0995696	+	0.995031i	$0.468253\pi$
$308$	0	0
$309$	0	0
$310$	11.3340	0.643729
$311$	−10.8453	−0.614981	−0.307490	−	0.951551i	$-0.599489\pi$
$311$	−10.8453	−0.614981	−0.307490	+	0.951551i	$0.599489\pi$
$312$	0	0
$313$	−28.2811	−1.59854	−0.799270	−	0.600972i	$-0.794780\pi$
$313$	−28.2811	−1.59854	−0.799270	+	0.600972i	$0.794780\pi$
$314$	10.4316	0.588690
$315$	0	0
$316$	14.8072	0.832973
$317$	1.11253	0.0624857	0.0312429	−	0.999512i	$-0.490053\pi$
$317$	1.11253	0.0624857	0.0312429	+	0.999512i	$0.490053\pi$
$318$	0	0
$319$	0	0
$320$	3.19867	0.178811
$321$	0	0
$322$	0.0575209	0.00320552
$323$	2.00089	0.111332
$324$	0	0
$325$	−15.8896	−0.881396
$326$	3.36487	0.186363
$327$	0	0
$328$	−12.3056	−0.679461
$329$	−0.381589	−0.0210377
$330$	0	0
$331$	−12.3783	−0.680373	−0.340187	−	0.940358i	$-0.610490\pi$
$331$	−12.3783	−0.680373	−0.340187	+	0.940358i	$0.610490\pi$
$332$	8.26033	0.453344
$333$	0	0
$334$	−2.90161	−0.158769
$335$	−35.0911	−1.91723
$336$	0	0
$337$	13.4736	0.733955	0.366977	−	0.930230i	$-0.380393\pi$
$337$	13.4736	0.733955	0.366977	+	0.930230i	$0.380393\pi$
$338$	−1.48629	−0.0808434
$339$	0	0
$340$	1.57277	0.0852953
$341$	0	0
$342$	0	0
$343$	14.7221	0.794918
$344$	−14.3720	−0.774888
$345$	0	0
$346$	−9.00801	−0.484274
$347$	−9.73917	−0.522826	−0.261413	−	0.965227i	$-0.584188\pi$
$347$	−9.73917	−0.522826	−0.261413	+	0.965227i	$0.584188\pi$
$348$	0	0
$349$	−4.44019	−0.237678	−0.118839	−	0.992914i	$-0.537917\pi$
$349$	−4.44019	−0.237678	−0.118839	+	0.992914i	$0.537917\pi$
$350$	2.70892	0.144798
$351$	0	0
$352$	0	0
$353$	−32.5235	−1.73105	−0.865527	−	0.500863i	$-0.833016\pi$
$353$	−32.5235	−1.73105	−0.865527	+	0.500863i	$0.833016\pi$
$354$	0	0
$355$	26.1915	1.39010
$356$	3.54657	0.187968
$357$	0	0
$358$	4.07292	0.215260
$359$	27.7701	1.46565	0.732825	−	0.680417i	$-0.238201\pi$
$359$	27.7701	1.46565	0.732825	+	0.680417i	$0.238201\pi$
$360$	0	0
$361$	21.5564	1.13455
$362$	−1.44320	−0.0758529
$363$	0	0
$364$	−7.65523	−0.401243
$365$	−8.85273	−0.463373
$366$	0	0
$367$	1.17220	0.0611882	0.0305941	−	0.999532i	$-0.490260\pi$
$367$	1.17220	0.0611882	0.0305941	+	0.999532i	$0.490260\pi$
$368$	0.180257	0.00939655
$369$	0	0
$370$	−10.8380	−0.563439
$371$	−2.82079	−0.146448
$372$	0	0
$373$	21.7668	1.12704	0.563520	−	0.826102i	$-0.309447\pi$
$373$	21.7668	1.12704	0.563520	+	0.826102i	$0.309447\pi$
$374$	0	0
$375$	0	0
$376$	0.694254	0.0358034
$377$	−30.3848	−1.56490
$378$	0	0
$379$	−16.2469	−0.834545	−0.417273	−	0.908781i	$-0.637014\pi$
$379$	−16.2469	−0.834545	−0.417273	+	0.908781i	$0.637014\pi$
$380$	31.8787	1.63534
$381$	0	0
$382$	−6.83146	−0.349528
$383$	−6.19335	−0.316465	−0.158233	−	0.987402i	$-0.550580\pi$
$383$	−6.19335	−0.316465	−0.158233	+	0.987402i	$0.550580\pi$
$384$	0	0
$385$	0	0
$386$	−3.89830	−0.198418
$387$	0	0
$388$	0.148018	0.00751447
$389$	0.723213	0.0366684	0.0183342	−	0.999832i	$-0.494164\pi$
$389$	0.723213	0.0366684	0.0183342	+	0.999832i	$0.494164\pi$
$390$	0	0
$391$	0.0268633	0.00135854
$392$	−11.9566	−0.603902
$393$	0	0
$394$	−11.9303	−0.601041
$395$	26.7009	1.34347
$396$	0	0
$397$	4.08994	0.205268	0.102634	−	0.994719i	$-0.467273\pi$
$397$	4.08994	0.205268	0.102634	+	0.994719i	$0.467273\pi$
$398$	7.67691	0.384809
$399$	0	0
$400$	8.48912	0.424456
$401$	5.64627	0.281961	0.140981	−	0.990012i	$-0.454974\pi$
$401$	5.64627	0.281961	0.140981	+	0.990012i	$0.454974\pi$
$402$	0	0
$403$	−25.7639	−1.28339
$404$	−3.42638	−0.170469
$405$	0	0
$406$	5.18012	0.257085
$407$	0	0
$408$	0	0
$409$	9.44877	0.467212	0.233606	−	0.972331i	$-0.424947\pi$
$409$	9.44877	0.467212	0.233606	+	0.972331i	$0.424947\pi$
$410$	−10.0845	−0.498039
$411$	0	0
$412$	5.02625	0.247626
$413$	−2.67332	−0.131545
$414$	0	0
$415$	14.8953	0.731182
$416$	21.5258	1.05539
$417$	0	0
$418$	0	0
$419$	−0.151564	−0.00740438	−0.00370219	−	0.999993i	$-0.501178\pi$
$419$	−0.151564	−0.00740438	−0.00370219	+	0.999993i	$0.501178\pi$
$420$	0	0
$421$	16.9766	0.827387	0.413693	−	0.910416i	$-0.364239\pi$
$421$	16.9766	0.827387	0.413693	+	0.910416i	$0.364239\pi$
$422$	4.82185	0.234724
$423$	0	0
$424$	5.13208	0.249236
$425$	1.26512	0.0613671
$426$	0	0
$427$	15.9363	0.771211
$428$	19.9817	0.965852
$429$	0	0
$430$	−11.7780	−0.567986
$431$	25.3694	1.22200	0.610999	−	0.791631i	$-0.290768\pi$
$431$	25.3694	1.22200	0.610999	+	0.791631i	$0.290768\pi$
$432$	0	0
$433$	16.5347	0.794607	0.397303	−	0.917687i	$-0.369946\pi$
$433$	16.5347	0.794607	0.397303	+	0.917687i	$0.369946\pi$
$434$	4.39233	0.210839
$435$	0	0
$436$	−8.66410	−0.414935
$437$	0.544498	0.0260469
$438$	0	0
$439$	−39.2413	−1.87289	−0.936443	−	0.350819i	$-0.885903\pi$
$439$	−39.2413	−1.87289	−0.936443	+	0.350819i	$0.885903\pi$
$440$	0	0
$441$	0	0
$442$	0.716400	0.0340757
$443$	−32.1894	−1.52936	−0.764681	−	0.644409i	$-0.777104\pi$
$443$	−32.1894	−1.52936	−0.764681	+	0.644409i	$0.777104\pi$
$444$	0	0
$445$	6.39529	0.303166
$446$	0.221681	0.0104969
$447$	0	0
$448$	1.23960	0.0585654
$449$	25.8443	1.21967	0.609833	−	0.792530i	$-0.291236\pi$
$449$	25.8443	1.21967	0.609833	+	0.792530i	$0.291236\pi$
$450$	0	0
$451$	0	0
$452$	32.0357	1.50683
$453$	0	0
$454$	10.4087	0.488506
$455$	−13.8042	−0.647149
$456$	0	0
$457$	−12.7163	−0.594842	−0.297421	−	0.954746i	$-0.596127\pi$
$457$	−12.7163	−0.594842	−0.297421	+	0.954746i	$0.596127\pi$
$458$	−7.75879	−0.362544
$459$	0	0
$460$	0.427995	0.0199554
$461$	19.0217	0.885931	0.442965	−	0.896539i	$-0.353927\pi$
$461$	19.0217	0.885931	0.442965	+	0.896539i	$0.353927\pi$
$462$	0	0
$463$	−22.8667	−1.06271	−0.531353	−	0.847150i	$-0.678316\pi$
$463$	−22.8667	−1.06271	−0.531353	+	0.847150i	$0.678316\pi$
$464$	16.2333	0.753611
$465$	0	0
$466$	−1.94703	−0.0901942
$467$	−15.9228	−0.736821	−0.368411	−	0.929663i	$-0.620098\pi$
$467$	−15.9228	−0.736821	−0.368411	+	0.929663i	$0.620098\pi$
$468$	0	0
$469$	−13.5990	−0.627944
$470$	0.568947	0.0262436
$471$	0	0
$472$	4.86377	0.223873
$473$	0	0
$474$	0	0
$475$	25.6429	1.17658
$476$	0.609502	0.0279365
$477$	0	0
$478$	−13.4034	−0.613057
$479$	16.3900	0.748877	0.374438	−	0.927252i	$-0.377836\pi$
$479$	16.3900	0.748877	0.374438	+	0.927252i	$0.377836\pi$
$480$	0	0
$481$	24.6363	1.12332
$482$	−8.76202	−0.399099
$483$	0	0
$484$	0	0
$485$	0.266911	0.0121198
$486$	0	0
$487$	22.7865	1.03256	0.516278	−	0.856421i	$-0.327317\pi$
$487$	22.7865	1.03256	0.516278	+	0.856421i	$0.327317\pi$
$488$	−28.9941	−1.31250
$489$	0	0
$490$	−9.79858	−0.442655
$491$	43.6430	1.96958	0.984791	−	0.173745i	$-0.0555868\pi$
$491$	43.6430	1.96958	0.984791	+	0.173745i	$0.0555868\pi$
$492$	0	0
$493$	2.41921	0.108956
$494$	14.5209	0.653324
$495$	0	0
$496$	13.7645	0.618045
$497$	10.1501	0.455296
$498$	0	0
$499$	−20.1035	−0.899957	−0.449978	−	0.893039i	$-0.648568\pi$
$499$	−20.1035	−0.899957	−0.449978	+	0.893039i	$0.648568\pi$
$500$	−4.87269	−0.217913
$501$	0	0
$502$	−0.336463	−0.0150171
$503$	10.6083	0.473001	0.236500	−	0.971631i	$-0.424000\pi$
$503$	10.6083	0.473001	0.236500	+	0.971631i	$0.424000\pi$
$504$	0	0
$505$	−6.17856	−0.274942
$506$	0	0
$507$	0	0
$508$	21.9645	0.974517
$509$	44.4684	1.97103	0.985513	−	0.169601i	$-0.0542478\pi$
$509$	44.4684	1.97103	0.985513	+	0.169601i	$0.0542478\pi$
$510$	0	0
$511$	−3.43074	−0.151767
$512$	−20.4323	−0.902989
$513$	0	0
$514$	−6.33942	−0.279620
$515$	9.06350	0.399386
$516$	0	0
$517$	0	0
$518$	−4.20009	−0.184541
$519$	0	0
$520$	25.1150	1.10136
$521$	−16.9511	−0.742643	−0.371322	−	0.928504i	$-0.621095\pi$
$521$	−16.9511	−0.742643	−0.371322	+	0.928504i	$0.621095\pi$
$522$	0	0
$523$	30.2142	1.32117	0.660587	−	0.750749i	$-0.270307\pi$
$523$	30.2142	1.32117	0.660587	+	0.750749i	$0.270307\pi$
$524$	−29.9434	−1.30808
$525$	0	0
$526$	−8.31782	−0.362674
$527$	2.05130	0.0893560
$528$	0	0
$529$	−22.9927	−0.999682
$530$	4.20578	0.182688
$531$	0	0
$532$	12.3541	0.535619
$533$	22.9236	0.992931
$534$	0	0
$535$	36.0317	1.55779
$536$	24.7417	1.06868
$537$	0	0
$538$	0.282536	0.0121810
$539$	0	0
$540$	0	0
$541$	11.8312	0.508663	0.254332	−	0.967117i	$-0.418145\pi$
$541$	11.8312	0.508663	0.254332	+	0.967117i	$0.418145\pi$
$542$	−12.6766	−0.544506
$543$	0	0
$544$	−1.71386	−0.0734813
$545$	−15.6234	−0.669233
$546$	0	0
$547$	2.54581	0.108851	0.0544255	−	0.998518i	$-0.482667\pi$
$547$	2.54581	0.108851	0.0544255	+	0.998518i	$0.482667\pi$
$548$	−27.3275	−1.16737
$549$	0	0
$550$	0	0
$551$	49.0355	2.08898
$552$	0	0
$553$	10.3475	0.440022
$554$	−1.65805	−0.0704436
$555$	0	0
$556$	19.8297	0.840965
$557$	−9.67543	−0.409961	−0.204981	−	0.978766i	$-0.565713\pi$
$557$	−9.67543	−0.409961	−0.204981	+	0.978766i	$0.565713\pi$
$558$	0	0
$559$	26.7731	1.13238
$560$	7.37496	0.311649
$561$	0	0
$562$	10.5035	0.443064
$563$	23.9872	1.01094	0.505470	−	0.862844i	$-0.331319\pi$
$563$	23.9872	1.01094	0.505470	+	0.862844i	$0.331319\pi$
$564$	0	0
$565$	57.7678	2.43031
$566$	11.8666	0.498790
$567$	0	0
$568$	−18.4669	−0.774854
$569$	37.6191	1.57708	0.788538	−	0.614986i	$-0.210838\pi$
$569$	37.6191	1.57708	0.788538	+	0.614986i	$0.210838\pi$
$570$	0	0
$571$	−14.7548	−0.617469	−0.308735	−	0.951148i	$-0.599905\pi$
$571$	−14.7548	−0.617469	−0.308735	+	0.951148i	$0.599905\pi$
$572$	0	0
$573$	0	0
$574$	−3.90810	−0.163121
$575$	0.344274	0.0143572
$576$	0	0
$577$	−22.3068	−0.928644	−0.464322	−	0.885667i	$-0.653702\pi$
$577$	−22.3068	−0.928644	−0.464322	+	0.885667i	$0.653702\pi$
$578$	9.76577	0.406202
$579$	0	0
$580$	38.5436	1.60043
$581$	5.77245	0.239481
$582$	0	0
$583$	0	0
$584$	6.24181	0.258288
$585$	0	0
$586$	0.496957	0.0205291
$587$	2.50017	0.103193	0.0515965	−	0.998668i	$-0.483569\pi$
$587$	2.50017	0.103193	0.0515965	+	0.998668i	$0.483569\pi$
$588$	0	0
$589$	41.5782	1.71320
$590$	3.98590	0.164097
$591$	0	0
$592$	−13.1621	−0.540959
$593$	10.8953	0.447417	0.223708	−	0.974656i	$-0.428184\pi$
$593$	10.8953	0.447417	0.223708	+	0.974656i	$0.428184\pi$
$594$	0	0
$595$	1.09907	0.0450577
$596$	−7.55044	−0.309278
$597$	0	0
$598$	0.194953	0.00797221
$599$	36.8381	1.50516	0.752582	−	0.658499i	$-0.228808\pi$
$599$	36.8381	1.50516	0.752582	+	0.658499i	$0.228808\pi$
$600$	0	0
$601$	−15.4543	−0.630393	−0.315197	−	0.949026i	$-0.602070\pi$
$601$	−15.4543	−0.630393	−0.315197	+	0.949026i	$0.602070\pi$
$602$	−4.56438	−0.186030
$603$	0	0
$604$	4.88321	0.198695
$605$	0	0
$606$	0	0
$607$	−25.4769	−1.03408	−0.517038	−	0.855963i	$-0.672965\pi$
$607$	−25.4769	−1.03408	−0.517038	+	0.855963i	$0.672965\pi$
$608$	−34.7386	−1.40884
$609$	0	0
$610$	−23.7609	−0.962051
$611$	−1.29330	−0.0523214
$612$	0	0
$613$	−37.7740	−1.52568	−0.762839	−	0.646588i	$-0.776195\pi$
$613$	−37.7740	−1.52568	−0.762839	+	0.646588i	$0.776195\pi$
$614$	−2.01610	−0.0813633
$615$	0	0
$616$	0	0
$617$	−41.8928	−1.68654	−0.843271	−	0.537489i	$-0.819373\pi$
$617$	−41.8928	−1.68654	−0.843271	+	0.537489i	$0.819373\pi$
$618$	0	0
$619$	−5.98961	−0.240743	−0.120371	−	0.992729i	$-0.538409\pi$
$619$	−5.98961	−0.240743	−0.120371	+	0.992729i	$0.538409\pi$
$620$	32.6819	1.31254
$621$	0	0
$622$	6.26655	0.251266
$623$	2.47840	0.0992950
$624$	0	0
$625$	−28.9195	−1.15678
$626$	16.3411	0.653123
$627$	0	0
$628$	30.0798	1.20031
$629$	−1.96152	−0.0782109
$630$	0	0
$631$	−21.4994	−0.855878	−0.427939	−	0.903808i	$-0.640760\pi$
$631$	−21.4994	−0.855878	−0.427939	+	0.903808i	$0.640760\pi$
$632$	−18.8261	−0.748861
$633$	0	0
$634$	−0.642832	−0.0255301
$635$	39.6071	1.57176
$636$	0	0
$637$	22.2736	0.882512
$638$	0	0
$639$	0	0
$640$	−34.6257	−1.36870
$641$	−12.8370	−0.507031	−0.253516	−	0.967331i	$-0.581587\pi$
$641$	−12.8370	−0.507031	−0.253516	+	0.967331i	$0.581587\pi$
$642$	0	0
$643$	28.3556	1.11823	0.559117	−	0.829089i	$-0.311140\pi$
$643$	28.3556	1.11823	0.559117	+	0.829089i	$0.311140\pi$
$644$	0.165863	0.00653591
$645$	0	0
$646$	−1.15614	−0.0454876
$647$	17.4948	0.687792	0.343896	−	0.939008i	$-0.388253\pi$
$647$	17.4948	0.687792	0.343896	+	0.939008i	$0.388253\pi$
$648$	0	0
$649$	0	0
$650$	9.18120	0.360116
$651$	0	0
$652$	9.70268	0.379986
$653$	29.3022	1.14668	0.573342	−	0.819316i	$-0.305647\pi$
$653$	29.3022	1.14668	0.573342	+	0.819316i	$0.305647\pi$
$654$	0	0
$655$	−53.9949	−2.10975
$656$	−12.2471	−0.478168
$657$	0	0
$658$	0.220487	0.00859547
$659$	−27.5870	−1.07464	−0.537319	−	0.843379i	$-0.680563\pi$
$659$	−27.5870	−1.07464	−0.537319	+	0.843379i	$0.680563\pi$
$660$	0	0
$661$	29.7552	1.15734	0.578672	−	0.815560i	$-0.303571\pi$
$661$	29.7552	1.15734	0.578672	+	0.815560i	$0.303571\pi$
$662$	7.15234	0.277983
$663$	0	0
$664$	−10.5023	−0.407566
$665$	22.2774	0.863879
$666$	0	0
$667$	0.658336	0.0254909
$668$	−8.36687	−0.323724
$669$	0	0
$670$	20.2760	0.783332
$671$	0	0
$672$	0	0
$673$	9.65367	0.372122	0.186061	−	0.982538i	$-0.440428\pi$
$673$	9.65367	0.372122	0.186061	+	0.982538i	$0.440428\pi$
$674$	−7.78522	−0.299875
$675$	0	0
$676$	−4.28574	−0.164836
$677$	0.0981151	0.00377087	0.00188544	−	0.999998i	$-0.499400\pi$
$677$	0.0981151	0.00377087	0.00188544	+	0.999998i	$0.499400\pi$
$678$	0	0
$679$	0.103437	0.00396956
$680$	−1.99963	−0.0766823
$681$	0	0
$682$	0	0
$683$	−30.5246	−1.16799	−0.583996	−	0.811756i	$-0.698512\pi$
$683$	−30.5246	−1.16799	−0.583996	+	0.811756i	$0.698512\pi$
$684$	0	0
$685$	−49.2778	−1.88281
$686$	−8.50660	−0.324783
$687$	0	0
$688$	−14.3037	−0.545324
$689$	−9.56036	−0.364221
$690$	0	0
$691$	32.8017	1.24784	0.623918	−	0.781490i	$-0.285540\pi$
$691$	32.8017	1.24784	0.623918	+	0.781490i	$0.285540\pi$
$692$	−25.9748	−0.987413
$693$	0	0
$694$	5.62741	0.213614
$695$	35.7575	1.35636
$696$	0	0
$697$	−1.82515	−0.0691327
$698$	2.56560	0.0971093
$699$	0	0
$700$	7.81123	0.295237
$701$	8.74920	0.330453	0.165226	−	0.986256i	$-0.447165\pi$
$701$	8.74920	0.330453	0.165226	+	0.986256i	$0.447165\pi$
$702$	0	0
$703$	−39.7584	−1.49952
$704$	0	0
$705$	0	0
$706$	18.7925	0.707265
$707$	−2.39441	−0.0900509
$708$	0	0
$709$	26.7759	1.00559	0.502795	−	0.864406i	$-0.332305\pi$
$709$	26.7759	1.00559	0.502795	+	0.864406i	$0.332305\pi$
$710$	−15.1338	−0.567961
$711$	0	0
$712$	−4.50914	−0.168987
$713$	0.558217	0.0209054
$714$	0	0
$715$	0	0
$716$	11.7443	0.438907
$717$	0	0
$718$	−16.0459	−0.598828
$719$	15.0047	0.559582	0.279791	−	0.960061i	$-0.409735\pi$
$719$	15.0047	0.559582	0.279791	+	0.960061i	$0.409735\pi$
$720$	0	0
$721$	3.51242	0.130809
$722$	−12.4555	−0.463547
$723$	0	0
$724$	−4.16150	−0.154661
$725$	31.0040	1.15146
$726$	0	0
$727$	27.5325	1.02112	0.510562	−	0.859841i	$-0.329437\pi$
$727$	27.5325	1.02112	0.510562	+	0.859841i	$0.329437\pi$
$728$	9.73292	0.360726
$729$	0	0
$730$	5.11522	0.189323
$731$	−2.13165	−0.0788420
$732$	0	0
$733$	47.7397	1.76331	0.881653	−	0.471899i	$-0.156431\pi$
$733$	47.7397	1.76331	0.881653	+	0.471899i	$0.156431\pi$
$734$	−0.677309	−0.0249999
$735$	0	0
$736$	−0.466391	−0.0171914
$737$	0	0
$738$	0	0
$739$	1.48849	0.0547549	0.0273774	−	0.999625i	$-0.491284\pi$
$739$	1.48849	0.0547549	0.0273774	+	0.999625i	$0.491284\pi$
$740$	−31.2515	−1.14883
$741$	0	0
$742$	1.62989	0.0598350
$743$	18.1602	0.666232	0.333116	−	0.942886i	$-0.391900\pi$
$743$	18.1602	0.666232	0.333116	+	0.942886i	$0.391900\pi$
$744$	0	0
$745$	−13.6152	−0.498823
$746$	−12.5771	−0.460481
$747$	0	0
$748$	0	0
$749$	13.9635	0.510216
$750$	0	0
$751$	−4.39465	−0.160363	−0.0801816	−	0.996780i	$-0.525550\pi$
$751$	−4.39465	−0.160363	−0.0801816	+	0.996780i	$0.525550\pi$
$752$	0.690954	0.0251965
$753$	0	0
$754$	17.5567	0.639378
$755$	8.80557	0.320467
$756$	0	0
$757$	−13.7659	−0.500331	−0.250165	−	0.968203i	$-0.580485\pi$
$757$	−13.7659	−0.500331	−0.250165	+	0.968203i	$0.580485\pi$
$758$	9.38763	0.340974
$759$	0	0
$760$	−40.5309	−1.47021
$761$	31.1061	1.12760	0.563798	−	0.825913i	$-0.309340\pi$
$761$	31.1061	1.12760	0.563798	+	0.825913i	$0.309340\pi$
$762$	0	0
$763$	−6.05461	−0.219192
$764$	−19.6987	−0.712672
$765$	0	0
$766$	3.57859	0.129300
$767$	−9.06053	−0.327157
$768$	0	0
$769$	21.9353	0.791009	0.395504	−	0.918464i	$-0.370570\pi$
$769$	21.9353	0.791009	0.395504	+	0.918464i	$0.370570\pi$
$770$	0	0
$771$	0	0
$772$	−11.2408	−0.404566
$773$	12.7166	0.457385	0.228693	−	0.973499i	$-0.426555\pi$
$773$	12.7166	0.457385	0.228693	+	0.973499i	$0.426555\pi$
$774$	0	0
$775$	26.2889	0.944326
$776$	−0.188191	−0.00675568
$777$	0	0
$778$	−0.417881	−0.0149818
$779$	−36.9944	−1.32546
$780$	0	0
$781$	0	0
$782$	−0.0155220	−0.000555064 0
$783$	0	0
$784$	−11.8998	−0.424993
$785$	54.2409	1.93594
$786$	0	0
$787$	−17.2617	−0.615312	−0.307656	−	0.951498i	$-0.599545\pi$
$787$	−17.2617	−0.615312	−0.307656	+	0.951498i	$0.599545\pi$
$788$	−34.4014	−1.22550
$789$	0	0
$790$	−15.4281	−0.548908
$791$	22.3870	0.795991
$792$	0	0
$793$	54.0120	1.91802
$794$	−2.36321	−0.0838673
$795$	0	0
$796$	22.1365	0.784609
$797$	−35.2015	−1.24690	−0.623451	−	0.781863i	$-0.714270\pi$
$797$	−35.2015	−1.24690	−0.623451	+	0.781863i	$0.714270\pi$
$798$	0	0
$799$	0.102971	0.00364287
$800$	−21.9644	−0.776560
$801$	0	0
$802$	−3.26248	−0.115202
$803$	0	0
$804$	0	0
$805$	0.299090	0.0105415
$806$	14.8867	0.524362
$807$	0	0
$808$	4.35632	0.153255
$809$	19.0808	0.670845	0.335423	−	0.942068i	$-0.391121\pi$
$809$	19.0808	0.670845	0.335423	+	0.942068i	$0.391121\pi$
$810$	0	0
$811$	−31.0588	−1.09062	−0.545311	−	0.838234i	$-0.683588\pi$
$811$	−31.0588	−1.09062	−0.545311	+	0.838234i	$0.683588\pi$
$812$	14.9370	0.524185
$813$	0	0
$814$	0	0
$815$	17.4962	0.612865
$816$	0	0
$817$	−43.2069	−1.51162
$818$	−5.45961	−0.190891
$819$	0	0
$820$	−29.0789	−1.01548
$821$	−34.0085	−1.18691	−0.593453	−	0.804869i	$-0.702236\pi$
$821$	−34.0085	−1.18691	−0.593453	+	0.804869i	$0.702236\pi$
$822$	0	0
$823$	15.5560	0.542248	0.271124	−	0.962544i	$-0.412605\pi$
$823$	15.5560	0.542248	0.271124	+	0.962544i	$0.412605\pi$
$824$	−6.39042	−0.222621
$825$	0	0
$826$	1.54467	0.0537461
$827$	−16.0277	−0.557337	−0.278669	−	0.960387i	$-0.589893\pi$
$827$	−16.0277	−0.557337	−0.278669	+	0.960387i	$0.589893\pi$
$828$	0	0
$829$	19.0994	0.663351	0.331675	−	0.943394i	$-0.392386\pi$
$829$	19.0994	0.663351	0.331675	+	0.943394i	$0.392386\pi$
$830$	−8.60669	−0.298742
$831$	0	0
$832$	4.20130	0.145654
$833$	−1.77340	−0.0614448
$834$	0	0
$835$	−15.0874	−0.522122
$836$	0	0
$837$	0	0
$838$	0.0875755	0.00302524
$839$	−1.48792	−0.0513687	−0.0256844	−	0.999670i	$-0.508176\pi$
$839$	−1.48792	−0.0513687	−0.0256844	+	0.999670i	$0.508176\pi$
$840$	0	0
$841$	30.2872	1.04439
$842$	−9.80926	−0.338049
$843$	0	0
$844$	13.9039	0.478592
$845$	−7.72819	−0.265858
$846$	0	0
$847$	0	0
$848$	5.10768	0.175399
$849$	0	0
$850$	−0.730999	−0.0250731
$851$	−0.533785	−0.0182979
$852$	0	0
$853$	37.8021	1.29432	0.647159	−	0.762355i	$-0.275957\pi$
$853$	37.8021	1.29432	0.647159	+	0.762355i	$0.275957\pi$
$854$	−9.20818	−0.315097
$855$	0	0
$856$	−25.4049	−0.868322
$857$	−19.8270	−0.677276	−0.338638	−	0.940917i	$-0.609966\pi$
$857$	−19.8270	−0.677276	−0.338638	+	0.940917i	$0.609966\pi$
$858$	0	0
$859$	−15.7153	−0.536199	−0.268099	−	0.963391i	$-0.586396\pi$
$859$	−15.7153	−0.536199	−0.268099	+	0.963391i	$0.586396\pi$
$860$	−33.9621	−1.15810
$861$	0	0
$862$	−14.6587	−0.499278
$863$	−8.12774	−0.276671	−0.138336	−	0.990385i	$-0.544175\pi$
$863$	−8.12774	−0.276671	−0.138336	+	0.990385i	$0.544175\pi$
$864$	0	0
$865$	−46.8386	−1.59256
$866$	−9.55395	−0.324656
$867$	0	0
$868$	12.6654	0.429891
$869$	0	0
$870$	0	0
$871$	−46.0904	−1.56171
$872$	11.0156	0.373036
$873$	0	0
$874$	−0.314618	−0.0106421
$875$	−3.40511	−0.115114
$876$	0	0
$877$	−2.53353	−0.0855512	−0.0427756	−	0.999085i	$-0.513620\pi$
$877$	−2.53353	−0.0855512	−0.0427756	+	0.999085i	$0.513620\pi$
$878$	22.6741	0.765214
$879$	0	0
$880$	0	0
$881$	47.4109	1.59731	0.798657	−	0.601786i	$-0.205544\pi$
$881$	47.4109	1.59731	0.798657	+	0.601786i	$0.205544\pi$
$882$	0	0
$883$	26.5129	0.892231	0.446116	−	0.894975i	$-0.352807\pi$
$883$	26.5129	0.892231	0.446116	+	0.894975i	$0.352807\pi$
$884$	2.06575	0.0694789
$885$	0	0
$886$	18.5994	0.624859
$887$	47.8293	1.60595	0.802976	−	0.596011i	$-0.203249\pi$
$887$	47.8293	1.60595	0.802976	+	0.596011i	$0.203249\pi$
$888$	0	0
$889$	15.3491	0.514794
$890$	−3.69528	−0.123866
$891$	0	0
$892$	0.639221	0.0214027
$893$	2.08715	0.0698438
$894$	0	0
$895$	21.1778	0.707896
$896$	−13.4186	−0.448286
$897$	0	0
$898$	−14.9331	−0.498325
$899$	50.2709	1.67663
$900$	0	0
$901$	0.761187	0.0253588
$902$	0	0
$903$	0	0
$904$	−40.7304	−1.35467
$905$	−7.50415	−0.249446
$906$	0	0
$907$	47.4583	1.57583	0.787914	−	0.615785i	$-0.211161\pi$
$907$	47.4583	1.57583	0.787914	+	0.615785i	$0.211161\pi$
$908$	30.0138	0.996042
$909$	0	0
$910$	7.97621	0.264409
$911$	28.4322	0.942002	0.471001	−	0.882133i	$-0.343893\pi$
$911$	28.4322	0.942002	0.471001	+	0.882133i	$0.343893\pi$
$912$	0	0
$913$	0	0
$914$	7.34762	0.243038
$915$	0	0
$916$	−22.3726	−0.739212
$917$	−20.9249	−0.691001
$918$	0	0
$919$	38.3728	1.26580	0.632901	−	0.774233i	$-0.281864\pi$
$919$	38.3728	1.26580	0.632901	+	0.774233i	$0.281864\pi$
$920$	−0.544156	−0.0179403
$921$	0	0
$922$	−10.9910	−0.361969
$923$	34.4013	1.13233
$924$	0	0
$925$	−25.1383	−0.826543
$926$	13.2127	0.434195
$927$	0	0
$928$	−42.0014	−1.37876
$929$	−13.3877	−0.439235	−0.219618	−	0.975586i	$-0.570481\pi$
$929$	−13.3877	−0.439235	−0.219618	+	0.975586i	$0.570481\pi$
$930$	0	0
$931$	−35.9455	−1.17807
$932$	−5.61429	−0.183902
$933$	0	0
$934$	9.20041	0.301047
$935$	0	0
$936$	0	0
$937$	−24.6705	−0.805950	−0.402975	−	0.915211i	$-0.632024\pi$
$937$	−24.6705	−0.805950	−0.402975	+	0.915211i	$0.632024\pi$
$938$	7.85767	0.256562
$939$	0	0
$940$	1.64057	0.0535095
$941$	−8.30230	−0.270647	−0.135324	−	0.990801i	$-0.543207\pi$
$941$	−8.30230	−0.270647	−0.135324	+	0.990801i	$0.543207\pi$
$942$	0	0
$943$	−0.496676	−0.0161740
$944$	4.84065	0.157550
$945$	0	0
$946$	0	0
$947$	−37.9496	−1.23320	−0.616598	−	0.787278i	$-0.711490\pi$
$947$	−37.9496	−1.23320	−0.616598	+	0.787278i	$0.711490\pi$
$948$	0	0
$949$	−11.6276	−0.377449
$950$	−14.8168	−0.480719
$951$	0	0
$952$	−0.774926	−0.0251155
$953$	48.6705	1.57659	0.788297	−	0.615295i	$-0.210963\pi$
$953$	48.6705	1.57659	0.788297	+	0.615295i	$0.210963\pi$
$954$	0	0
$955$	−35.5213	−1.14944
$956$	−38.6490	−1.25000
$957$	0	0
$958$	−9.47032	−0.305972
$959$	−19.0969	−0.616670
$960$	0	0
$961$	11.6257	0.375023
$962$	−14.2352	−0.458960
$963$	0	0
$964$	−25.2655	−0.813746
$965$	−20.2698	−0.652509
$966$	0	0
$967$	10.9780	0.353029	0.176515	−	0.984298i	$-0.443518\pi$
$967$	10.9780	0.353029	0.176515	+	0.984298i	$0.443518\pi$
$968$	0	0
$969$	0	0
$970$	−0.154224	−0.00495185
$971$	−13.0636	−0.419231	−0.209615	−	0.977784i	$-0.567221\pi$
$971$	−13.0636	−0.419231	−0.209615	+	0.977784i	$0.567221\pi$
$972$	0	0
$973$	13.8573	0.444244
$974$	−13.1663	−0.421876
$975$	0	0
$976$	−28.8563	−0.923666
$977$	11.0763	0.354362	0.177181	−	0.984178i	$-0.443302\pi$
$977$	11.0763	0.354362	0.177181	+	0.984178i	$0.443302\pi$
$978$	0	0
$979$	0	0
$980$	−28.2544	−0.902554
$981$	0	0
$982$	−25.2175	−0.804721
$983$	26.4315	0.843033	0.421517	−	0.906821i	$-0.361498\pi$
$983$	26.4315	0.843033	0.421517	+	0.906821i	$0.361498\pi$
$984$	0	0
$985$	−62.0337	−1.97656
$986$	−1.39785	−0.0445166
$987$	0	0
$988$	41.8712	1.33210
$989$	−0.580083	−0.0184456
$990$	0	0
$991$	−18.9911	−0.603272	−0.301636	−	0.953423i	$-0.597533\pi$
$991$	−18.9911	−0.603272	−0.301636	+	0.953423i	$0.597533\pi$
$992$	−35.6138	−1.13074
$993$	0	0
$994$	−5.86487	−0.186022
$995$	39.9174	1.26547
$996$	0	0
$997$	22.1132	0.700331	0.350165	−	0.936688i	$-0.386125\pi$
$997$	22.1132	0.700331	0.350165	+	0.936688i	$0.386125\pi$
$998$	11.6161	0.367700
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9801.2.a.cp.1.8		18
3.2	odd	2		9801.2.a.cm.1.11		18
9.2	odd	6		1089.2.e.p.364.8		36
9.5	odd	6		1089.2.e.p.727.8		36
11.5	even	5		891.2.f.e.487.6		36
11.9	even	5		891.2.f.e.730.6		36
11.10	odd	2		9801.2.a.cn.1.11		18
33.5	odd	10		891.2.f.f.487.4		36
33.20	odd	10		891.2.f.f.730.4		36
33.32	even	2		9801.2.a.co.1.8		18
99.5	odd	30		99.2.m.b.25.4	yes	72
99.16	even	15		297.2.n.b.91.4		72
99.20	odd	30		99.2.m.b.4.4	✓	72
99.31	even	15		297.2.n.b.235.4		72
99.32	even	6		1089.2.e.o.727.11		36
99.38	odd	30		99.2.m.b.58.6	yes	72
99.49	even	15		297.2.n.b.289.6		72
99.65	even	6		1089.2.e.o.364.11		36
99.86	odd	30		99.2.m.b.70.6	yes	72
99.97	even	15		297.2.n.b.37.6		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	99.20	odd	30
99.2.m.b.25.4	yes	72	99.5	odd	30
99.2.m.b.58.6	yes	72	99.38	odd	30
99.2.m.b.70.6	yes	72	99.86	odd	30
297.2.n.b.37.6		72	99.97	even	15
297.2.n.b.91.4		72	99.16	even	15
297.2.n.b.235.4		72	99.31	even	15
297.2.n.b.289.6		72	99.49	even	15
891.2.f.e.487.6		36	11.5	even	5
891.2.f.e.730.6		36	11.9	even	5
891.2.f.f.487.4		36	33.5	odd	10
891.2.f.f.730.4		36	33.20	odd	10
1089.2.e.o.364.11		36	99.65	even	6
1089.2.e.o.727.11		36	99.32	even	6
1089.2.e.p.364.8		36	9.2	odd	6
1089.2.e.p.727.8		36	9.5	odd	6
9801.2.a.cm.1.11		18	3.2	odd	2
9801.2.a.cn.1.11		18	11.10	odd	2
9801.2.a.co.1.8		18	33.32	even	2
9801.2.a.cp.1.8		18	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:	\( N \)	\(=\)	\( 9801 = 3^{4} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9801.a (trivial)

\(f(q)\)	\(=\)	\(q-0.577812 q^{2} -1.66613 q^{4} -3.00443 q^{5} -1.16432 q^{7} +2.11834 q^{8} +1.73599 q^{10} -3.94617 q^{13} +0.672758 q^{14} +2.10827 q^{16} +0.314191 q^{17} +6.36839 q^{19} +5.00578 q^{20} +0.0855002 q^{23} +4.02659 q^{25} +2.28015 q^{26} +1.93991 q^{28} +7.69982 q^{29} +6.52884 q^{31} -5.45485 q^{32} -0.181543 q^{34} +3.49812 q^{35} -6.24309 q^{37} -3.67973 q^{38} -6.36439 q^{40} -5.80907 q^{41} -6.78458 q^{43} -0.0494030 q^{46} +0.327736 q^{47} -5.64436 q^{49} -2.32661 q^{50} +6.57485 q^{52} +2.42269 q^{53} -2.46642 q^{56} -4.44905 q^{58} +2.29603 q^{59} -13.6872 q^{61} -3.77244 q^{62} -1.06465 q^{64} +11.8560 q^{65} +11.6798 q^{67} -0.523483 q^{68} -2.02125 q^{70} -8.71765 q^{71} +2.94656 q^{73} +3.60733 q^{74} -10.6106 q^{76} -8.88719 q^{79} -6.33413 q^{80} +3.35655 q^{82} -4.95778 q^{83} -0.943963 q^{85} +3.92021 q^{86} -2.12862 q^{89} +4.59461 q^{91} -0.142455 q^{92} -0.189370 q^{94} -19.1334 q^{95} -0.0888392 q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 12 q^{4} + q^{5} + q^{7} + 6 q^{8} - 2 q^{10} + 3 q^{13} - 8 q^{16} + 20 q^{17} - 3 q^{19} + 5 q^{20} + 10 q^{23} + 7 q^{25} - 2 q^{26} + 19 q^{28} + 21 q^{29} + 6 q^{31} + 9 q^{32} - 4 q^{34}+ \cdots + 82 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 12 * q^4 + q^5 + q^7 + 6 * q^8 - 2 * q^10 + 3 * q^13 - 8 * q^16 + 20 * q^17 - 3 * q^19 + 5 * q^20 + 10 * q^23 + 7 * q^25 - 2 * q^26 + 19 * q^28 + 21 * q^29 + 6 * q^31 + 9 * q^32 - 4 * q^34 + 38 * q^35 + 7 * q^37 - 13 * q^38 + 20 * q^41 + 4 * q^43 + 8 * q^46 - 7 * q^47 + 7 * q^49 + 25 * q^50 - 19 * q^52 - 31 * q^53 + 57 * q^56 + 12 * q^58 + 12 * q^59 - 16 * q^61 + 19 * q^62 - 16 * q^64 + 42 * q^65 - 5 * q^67 + 51 * q^68 + 8 * q^70 - 13 * q^71 + 9 * q^74 - 8 * q^76 - 2 * q^79 - 46 * q^80 - 34 * q^82 + 36 * q^83 + 25 * q^85 - 26 * q^86 + 14 * q^89 - 15 * q^91 + 15 * q^92 + 4 * q^94 + 64 * q^95 - 16 * q^97 + 82 * q^98

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