LMFDB - Embedded newform 9801.2.a.cm.1.11

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:	$1$
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			1.11
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	$-0.434512\pi$
$2$	0.577812	0.408575	0.204287	+	0.978911i	$0.434512\pi$
$3$	0	0
$3$	0	0
$4$	−1.66613	−0.833067
$5$	3.00443	1.34362	0.671810	−	0.740723i	$-0.265517\pi$
$5$	3.00443	1.34362	0.671810	+	0.740723i	$0.265517\pi$
$6$	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	$-0.512131\pi$
$17$	−0.314191	−0.0762024	−0.0381012	+	0.999274i	$0.512131\pi$
$18$	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	$-0.502837\pi$
$23$	−0.0855002	−0.0178280	−0.00891401	+	0.999960i	$0.502837\pi$
$24$	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	$-0.753532\pi$
$29$	−7.69982	−1.42982	−0.714910	+	0.699216i	$0.753532\pi$
$30$	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	$-0.350135\pi$
$41$	5.80907	0.907224	0.453612	+	0.891199i	$0.350135\pi$
$42$	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	$-0.507609\pi$
$47$	−0.327736	−0.0478052	−0.0239026	+	0.999714i	$0.507609\pi$
$48$	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	$-0.553211\pi$
$53$	−2.42269	−0.332782	−0.166391	+	0.986060i	$0.553211\pi$
$54$	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	$-0.547753\pi$
$59$	−2.29603	−0.298918	−0.149459	+	0.988768i	$0.547753\pi$
$60$	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	$-0.326938\pi$
$71$	8.71765	1.03459	0.517297	+	0.855806i	$0.326938\pi$
$72$	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	$-0.412284\pi$
$83$	4.95778	0.544187	0.272094	+	0.962271i	$0.412284\pi$
$84$	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	$-0.464013\pi$
$89$	2.12862	0.225634	0.112817	+	0.993616i	$0.464013\pi$
$90$	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	$-0.532625\pi$
$101$	−2.05648	−0.204628	−0.102314	+	0.994752i	$0.532625\pi$
$102$	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	$-0.303171\pi$
$107$	11.9929	1.15939	0.579697	+	0.814832i	$0.303171\pi$
$108$	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	$-0.140328\pi$
$113$	19.2276	1.80878	0.904388	+	0.426711i	$0.140328\pi$
$114$	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	$-0.787389\pi$
$131$	−17.9718	−1.57020	−0.785100	+	0.619369i	$0.787389\pi$
$132$	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	$-0.747105\pi$
$137$	−16.4017	−1.40130	−0.700648	+	0.713507i	$0.747105\pi$
$138$	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	$-0.559431\pi$
$149$	−4.53172	−0.371253	−0.185626	+	0.982620i	$0.559431\pi$
$150$	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	$-0.562242\pi$
$167$	−5.02173	−0.388593	−0.194296	+	0.980943i	$0.562242\pi$
$168$	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	$-0.701913\pi$
$173$	−15.5899	−1.18528	−0.592638	+	0.805469i	$0.701913\pi$
$174$	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	$-0.415147\pi$
$179$	7.04887	0.526857	0.263428	+	0.964679i	$0.415147\pi$
$180$	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	$-0.640690\pi$
$191$	−11.8230	−0.855481	−0.427740	+	0.903902i	$0.640690\pi$
$192$	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	$-0.763069\pi$
$197$	−20.6474	−1.47107	−0.735534	+	0.677488i	$0.763069\pi$
$198$	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	$-0.296035\pi$
$227$	18.0140	1.19563	0.597817	+	0.801633i	$0.296035\pi$
$228$	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	$-0.535206\pi$
$233$	−3.36965	−0.220753	−0.110377	+	0.993890i	$0.535206\pi$
$234$	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	$-0.770061\pi$
$239$	−23.1968	−1.50048	−0.750238	+	0.661168i	$0.770061\pi$
$240$	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	$-0.505850\pi$
$251$	−0.582306	−0.0367548	−0.0183774	+	0.999831i	$0.505850\pi$
$252$	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	$-0.611168\pi$
$257$	−10.9714	−0.684378	−0.342189	+	0.939631i	$0.611168\pi$
$258$	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	$-0.646380\pi$
$263$	−14.3954	−0.887656	−0.443828	+	0.896112i	$0.646380\pi$
$264$	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	$-0.495255\pi$
$269$	0.488976	0.0298134	0.0149067	+	0.999889i	$0.495255\pi$
$270$	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	$-0.317589\pi$
$281$	18.1781	1.08441	0.542206	+	0.840245i	$0.317589\pi$
$282$	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	$-0.492002\pi$
$293$	0.860067	0.0502456	0.0251228	+	0.999684i	$0.492002\pi$
$294$	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	$-0.400511\pi$
$311$	10.8453	0.614981	0.307490	+	0.951551i	$0.400511\pi$
$312$	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	$-0.509947\pi$
$317$	−1.11253	−0.0624857	−0.0312429	+	0.999512i	$0.509947\pi$
$318$	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	$-0.415812\pi$
$347$	9.73917	0.522826	0.261413	+	0.965227i	$0.415812\pi$
$348$	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	$-0.166984\pi$
$353$	32.5235	1.73105	0.865527	+	0.500863i	$0.166984\pi$
$354$	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	$-0.761799\pi$
$359$	−27.7701	−1.46565	−0.732825	+	0.680417i	$0.761799\pi$
$360$	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	$-0.449420\pi$
$383$	6.19335	0.316465	0.158233	+	0.987402i	$0.449420\pi$
$384$	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	$-0.505836\pi$
$389$	−0.723213	−0.0366684	−0.0183342	+	0.999832i	$0.505836\pi$
$390$	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	$-0.545026\pi$
$401$	−5.64627	−0.281961	−0.140981	+	0.990012i	$0.545026\pi$
$402$	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	$-0.498822\pi$
$419$	0.151564	0.00740438	0.00370219	+	0.999993i	$0.498822\pi$
$420$	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	$-0.709232\pi$
$431$	−25.3694	−1.22200	−0.610999	+	0.791631i	$0.709232\pi$
$432$	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	$-0.222896\pi$
$443$	32.1894	1.52936	0.764681	+	0.644409i	$0.222896\pi$
$444$	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	$-0.708764\pi$
$449$	−25.8443	−1.21967	−0.609833	+	0.792530i	$0.708764\pi$
$450$	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	$-0.646073\pi$
$461$	−19.0217	−0.885931	−0.442965	+	0.896539i	$0.646073\pi$
$462$	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	$-0.379902\pi$
$467$	15.9228	0.736821	0.368411	+	0.929663i	$0.379902\pi$
$468$	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	$-0.622164\pi$
$479$	−16.3900	−0.748877	−0.374438	+	0.927252i	$0.622164\pi$
$480$	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	$-0.944413\pi$
$491$	−43.6430	−1.96958	−0.984791	+	0.173745i	$0.944413\pi$
$492$	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	$-0.576000\pi$
$503$	−10.6083	−0.473001	−0.236500	+	0.971631i	$0.576000\pi$
$504$	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	$-0.945752\pi$
$509$	−44.4684	−1.97103	−0.985513	+	0.169601i	$0.945752\pi$
$510$	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	$-0.378905\pi$
$521$	16.9511	0.742643	0.371322	+	0.928504i	$0.378905\pi$
$522$	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	$-0.434287\pi$
$557$	9.67543	0.409961	0.204981	+	0.978766i	$0.434287\pi$
$558$	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	$-0.668681\pi$
$563$	−23.9872	−1.01094	−0.505470	+	0.862844i	$0.668681\pi$
$564$	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	$-0.789162\pi$
$569$	−37.6191	−1.57708	−0.788538	+	0.614986i	$0.789162\pi$
$570$	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	$-0.516431\pi$
$587$	−2.50017	−0.103193	−0.0515965	+	0.998668i	$0.516431\pi$
$588$	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	$-0.571816\pi$
$593$	−10.8953	−0.447417	−0.223708	+	0.974656i	$0.571816\pi$
$594$	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	$-0.771192\pi$
$599$	−36.8381	−1.50516	−0.752582	+	0.658499i	$0.771192\pi$
$600$	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	$-0.180627\pi$
$617$	41.8928	1.68654	0.843271	+	0.537489i	$0.180627\pi$
$618$	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	$-0.418413\pi$
$641$	12.8370	0.507031	0.253516	+	0.967331i	$0.418413\pi$
$642$	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	$-0.611747\pi$
$647$	−17.4948	−0.687792	−0.343896	+	0.939008i	$0.611747\pi$
$648$	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	$-0.694353\pi$
$653$	−29.3022	−1.14668	−0.573342	+	0.819316i	$0.694353\pi$
$654$	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	$-0.319437\pi$
$659$	27.5870	1.07464	0.537319	+	0.843379i	$0.319437\pi$
$660$	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	$-0.500600\pi$
$677$	−0.0981151	−0.00377087	−0.00188544	+	0.999998i	$0.500600\pi$
$678$	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	$-0.301488\pi$
$683$	30.5246	1.16799	0.583996	+	0.811756i	$0.301488\pi$
$684$	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	$-0.552835\pi$
$701$	−8.74920	−0.330453	−0.165226	+	0.986256i	$0.552835\pi$
$702$	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	$-0.590265\pi$
$719$	−15.0047	−0.559582	−0.279791	+	0.960061i	$0.590265\pi$
$720$	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	$-0.608100\pi$
$743$	−18.1602	−0.666232	−0.333116	+	0.942886i	$0.608100\pi$
$744$	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	$-0.690660\pi$
$761$	−31.1061	−1.12760	−0.563798	+	0.825913i	$0.690660\pi$
$762$	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	$-0.573445\pi$
$773$	−12.7166	−0.457385	−0.228693	+	0.973499i	$0.573445\pi$
$774$	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	$-0.285730\pi$
$797$	35.2015	1.24690	0.623451	+	0.781863i	$0.285730\pi$
$798$	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	$-0.608879\pi$
$809$	−19.0808	−0.670845	−0.335423	+	0.942068i	$0.608879\pi$
$810$	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	$-0.297764\pi$
$821$	34.0085	1.18691	0.593453	+	0.804869i	$0.297764\pi$
$822$	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	$-0.410107\pi$
$827$	16.0277	0.557337	0.278669	+	0.960387i	$0.410107\pi$
$828$	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	$-0.491824\pi$
$839$	1.48792	0.0513687	0.0256844	+	0.999670i	$0.491824\pi$
$840$	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	$-0.390034\pi$
$857$	19.8270	0.677276	0.338638	+	0.940917i	$0.390034\pi$
$858$	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	$-0.455825\pi$
$863$	8.12774	0.276671	0.138336	+	0.990385i	$0.455825\pi$
$864$	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	$-0.794456\pi$
$881$	−47.4109	−1.59731	−0.798657	+	0.601786i	$0.794456\pi$
$882$	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	$-0.796751\pi$
$887$	−47.8293	−1.60595	−0.802976	+	0.596011i	$0.796751\pi$
$888$	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	$-0.656107\pi$
$911$	−28.4322	−0.942002	−0.471001	+	0.882133i	$0.656107\pi$
$912$	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	$-0.429519\pi$
$929$	13.3877	0.439235	0.219618	+	0.975586i	$0.429519\pi$
$930$	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	$-0.456793\pi$
$941$	8.30230	0.270647	0.135324	+	0.990801i	$0.456793\pi$
$942$	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	$-0.288510\pi$
$947$	37.9496	1.23320	0.616598	+	0.787278i	$0.288510\pi$
$948$	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	$-0.789037\pi$
$953$	−48.6705	−1.57659	−0.788297	+	0.615295i	$0.789037\pi$
$954$	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	$-0.432779\pi$
$971$	13.0636	0.419231	0.209615	+	0.977784i	$0.432779\pi$
$972$	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	$-0.556698\pi$
$977$	−11.0763	−0.354362	−0.177181	+	0.984178i	$0.556698\pi$
$978$	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	$-0.638502\pi$
$983$	−26.4315	−0.843033	−0.421517	+	0.906821i	$0.638502\pi$
$984$	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.cm.1.11		18
3.2	odd	2		9801.2.a.cp.1.8		18
9.4	even	3		1089.2.e.p.727.8		36
9.7	even	3		1089.2.e.p.364.8		36
11.5	even	5		891.2.f.f.487.4		36
11.9	even	5		891.2.f.f.730.4		36
11.10	odd	2		9801.2.a.co.1.8		18
33.5	odd	10		891.2.f.e.487.6		36
33.20	odd	10		891.2.f.e.730.6		36
33.32	even	2		9801.2.a.cn.1.11		18
99.5	odd	30		297.2.n.b.289.6		72
99.16	even	15		99.2.m.b.58.6	yes	72
99.20	odd	30		297.2.n.b.37.6		72
99.31	even	15		99.2.m.b.70.6	yes	72
99.38	odd	30		297.2.n.b.91.4		72
99.43	odd	6		1089.2.e.o.364.11		36
99.49	even	15		99.2.m.b.25.4	yes	72
99.76	odd	6		1089.2.e.o.727.11		36
99.86	odd	30		297.2.n.b.235.4		72
99.97	even	15		99.2.m.b.4.4	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	99.97	even	15
99.2.m.b.25.4	yes	72	99.49	even	15
99.2.m.b.58.6	yes	72	99.16	even	15
99.2.m.b.70.6	yes	72	99.31	even	15
297.2.n.b.37.6		72	99.20	odd	30
297.2.n.b.91.4		72	99.38	odd	30
297.2.n.b.235.4		72	99.86	odd	30
297.2.n.b.289.6		72	99.5	odd	30
891.2.f.e.487.6		36	33.5	odd	10
891.2.f.e.730.6		36	33.20	odd	10
891.2.f.f.487.4		36	11.5	even	5
891.2.f.f.730.4		36	11.9	even	5
1089.2.e.o.364.11		36	99.43	odd	6
1089.2.e.o.727.11		36	99.76	odd	6
1089.2.e.p.364.8		36	9.7	even	3
1089.2.e.p.727.8		36	9.4	even	3
9801.2.a.cm.1.11		18	1.1	even	1	trivial
9801.2.a.cn.1.11		18	33.32	even	2
9801.2.a.co.1.8		18	11.10	odd	2
9801.2.a.cp.1.8		18	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 9801 = 3^{4} \cdot 11^{2} \)
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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