LMFDB - Embedded newform 9801.2.a.cn.1.10

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			1.10
Root			$-0.285148$ 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)

$f(q)$	$=$	$q+0.285148 q^{2} -1.91869 q^{4} -2.70873 q^{5} +4.07334 q^{7} -1.11741 q^{8} -0.772391 q^{10} -3.85096 q^{13} +1.16150 q^{14} +3.51875 q^{16} -4.32020 q^{17} +1.62229 q^{19} +5.19722 q^{20} +1.86423 q^{23} +2.33724 q^{25} -1.09809 q^{26} -7.81547 q^{28} +3.55334 q^{29} -4.86459 q^{31} +3.23818 q^{32} -1.23190 q^{34} -11.0336 q^{35} +7.74449 q^{37} +0.462595 q^{38} +3.02676 q^{40} +6.87214 q^{41} -0.984991 q^{43} +0.531584 q^{46} -5.86635 q^{47} +9.59206 q^{49} +0.666460 q^{50} +7.38879 q^{52} +1.57183 q^{53} -4.55158 q^{56} +1.01323 q^{58} -11.3625 q^{59} +8.60748 q^{61} -1.38713 q^{62} -6.11414 q^{64} +10.4312 q^{65} -1.74056 q^{67} +8.28914 q^{68} -3.14621 q^{70} +5.74136 q^{71} +4.04662 q^{73} +2.20833 q^{74} -3.11268 q^{76} +4.28015 q^{79} -9.53137 q^{80} +1.95958 q^{82} -6.50019 q^{83} +11.7023 q^{85} -0.280869 q^{86} -9.26243 q^{89} -15.6862 q^{91} -3.57689 q^{92} -1.67278 q^{94} -4.39436 q^{95} -7.41268 q^{97} +2.73516 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	0.285148	0.201630	0.100815	−	0.994905i	$-0.467855\pi$
$2$	0.285148	0.201630	0.100815	+	0.994905i	$0.467855\pi$
$3$	0	0
$3$	0	0
$4$	−1.91869	−0.959345
$5$	−2.70873	−1.21138	−0.605691	−	0.795700i	$-0.707103\pi$
$5$	−2.70873	−1.21138	−0.605691	+	0.795700i	$0.707103\pi$
$6$	0	0
$7$	4.07334	1.53958	0.769788	−	0.638300i	$-0.220362\pi$
$7$	4.07334	1.53958	0.769788	+	0.638300i	$0.220362\pi$
$8$	−1.11741	−0.395063
$9$	0	0
$10$	−0.772391	−0.244251
$11$	0	0
$11$	0	0
$12$	0	0
$13$	−3.85096	−1.06806	−0.534032	−	0.845465i	$-0.679324\pi$
$13$	−3.85096	−1.06806	−0.534032	+	0.845465i	$0.679324\pi$
$14$	1.16150	0.310425
$15$	0	0
$16$	3.51875	0.879688
$17$	−4.32020	−1.04780	−0.523902	−	0.851779i	$-0.675524\pi$
$17$	−4.32020	−1.04780	−0.523902	+	0.851779i	$0.675524\pi$
$18$	0	0
$19$	1.62229	0.372180	0.186090	−	0.982533i	$-0.440418\pi$
$19$	1.62229	0.372180	0.186090	+	0.982533i	$0.440418\pi$
$20$	5.19722	1.16213
$21$	0	0
$22$	0	0
$23$	1.86423	0.388720	0.194360	−	0.980930i	$-0.437737\pi$
$23$	1.86423	0.388720	0.194360	+	0.980930i	$0.437737\pi$
$24$	0	0
$25$	2.33724	0.467448
$26$	−1.09809	−0.215354
$27$	0	0
$28$	−7.81547	−1.47698
$29$	3.55334	0.659840	0.329920	−	0.944009i	$-0.392978\pi$
$29$	3.55334	0.659840	0.329920	+	0.944009i	$0.392978\pi$
$30$	0	0
$31$	−4.86459	−0.873706	−0.436853	−	0.899533i	$-0.643907\pi$
$31$	−4.86459	−0.873706	−0.436853	+	0.899533i	$0.643907\pi$
$32$	3.23818	0.572435
$33$	0	0
$34$	−1.23190	−0.211269
$35$	−11.0336	−1.86502
$36$	0	0
$37$	7.74449	1.27319	0.636593	−	0.771200i	$-0.280343\pi$
$37$	7.74449	1.27319	0.636593	+	0.771200i	$0.280343\pi$
$38$	0.462595	0.0750427
$39$	0	0
$40$	3.02676	0.478573
$41$	6.87214	1.07325	0.536624	−	0.843821i	$-0.319699\pi$
$41$	6.87214	1.07325	0.536624	+	0.843821i	$0.319699\pi$
$42$	0	0
$43$	−0.984991	−0.150210	−0.0751049	−	0.997176i	$-0.523929\pi$
$43$	−0.984991	−0.150210	−0.0751049	+	0.997176i	$0.523929\pi$
$44$	0	0
$45$	0	0
$46$	0.531584	0.0783777
$47$	−5.86635	−0.855695	−0.427847	−	0.903851i	$-0.640728\pi$
$47$	−5.86635	−0.855695	−0.427847	+	0.903851i	$0.640728\pi$
$48$	0	0
$49$	9.59206	1.37029
$50$	0.666460	0.0942517
$51$	0	0
$52$	7.38879	1.02464
$53$	1.57183	0.215907	0.107953	−	0.994156i	$-0.465570\pi$
$53$	1.57183	0.215907	0.107953	+	0.994156i	$0.465570\pi$
$54$	0	0
$55$	0	0
$56$	−4.55158	−0.608230
$57$	0	0
$58$	1.01323	0.133044
$59$	−11.3625	−1.47927	−0.739635	−	0.673008i	$-0.765002\pi$
$59$	−11.3625	−1.47927	−0.739635	+	0.673008i	$0.765002\pi$
$60$	0	0
$61$	8.60748	1.10207	0.551037	−	0.834481i	$-0.314232\pi$
$61$	8.60748	1.10207	0.551037	+	0.834481i	$0.314232\pi$
$62$	−1.38713	−0.176166
$63$	0	0
$64$	−6.11414	−0.764268
$65$	10.4312	1.29383
$66$	0	0
$67$	−1.74056	−0.212644	−0.106322	−	0.994332i	$-0.533907\pi$
$67$	−1.74056	−0.212644	−0.106322	+	0.994332i	$0.533907\pi$
$68$	8.28914	1.00521
$69$	0	0
$70$	−3.14621	−0.376044
$71$	5.74136	0.681374	0.340687	−	0.940177i	$-0.389340\pi$
$71$	5.74136	0.681374	0.340687	+	0.940177i	$0.389340\pi$
$72$	0	0
$73$	4.04662	0.473622	0.236811	−	0.971556i	$-0.423898\pi$
$73$	4.04662	0.473622	0.236811	+	0.971556i	$0.423898\pi$
$74$	2.20833	0.256713
$75$	0	0
$76$	−3.11268	−0.357049
$77$	0	0
$78$	0	0
$79$	4.28015	0.481554	0.240777	−	0.970580i	$-0.422598\pi$
$79$	4.28015	0.481554	0.240777	+	0.970580i	$0.422598\pi$
$80$	−9.53137	−1.06564
$81$	0	0
$82$	1.95958	0.216400
$83$	−6.50019	−0.713488	−0.356744	−	0.934202i	$-0.616113\pi$
$83$	−6.50019	−0.713488	−0.356744	+	0.934202i	$0.616113\pi$
$84$	0	0
$85$	11.7023	1.26929
$86$	−0.280869	−0.0302868
$87$	0	0
$88$	0	0
$89$	−9.26243	−0.981816	−0.490908	−	0.871211i	$-0.663335\pi$
$89$	−9.26243	−0.981816	−0.490908	+	0.871211i	$0.663335\pi$
$90$	0	0
$91$	−15.6862	−1.64436
$92$	−3.57689	−0.372916
$93$	0	0
$94$	−1.67278	−0.172534
$95$	−4.39436	−0.450852
$96$	0	0
$97$	−7.41268	−0.752644	−0.376322	−	0.926489i	$-0.622811\pi$
$97$	−7.41268	−0.752644	−0.376322	+	0.926489i	$0.622811\pi$
$98$	2.73516	0.276293
$99$	0	0
$100$	−4.48444	−0.448444
$101$	−13.7176	−1.36495	−0.682476	−	0.730908i	$-0.739097\pi$
$101$	−13.7176	−1.36495	−0.682476	+	0.730908i	$0.739097\pi$
$102$	0	0
$103$	5.07525	0.500079	0.250039	−	0.968236i	$-0.419556\pi$
$103$	5.07525	0.500079	0.250039	+	0.968236i	$0.419556\pi$
$104$	4.30309	0.421953
$105$	0	0
$106$	0.448203	0.0435334
$107$	−2.77898	−0.268654	−0.134327	−	0.990937i	$-0.542887\pi$
$107$	−2.77898	−0.268654	−0.134327	+	0.990937i	$0.542887\pi$
$108$	0	0
$109$	17.3573	1.66253	0.831263	−	0.555879i	$-0.187618\pi$
$109$	17.3573	1.66253	0.831263	+	0.555879i	$0.187618\pi$
$110$	0	0
$111$	0	0
$112$	14.3331	1.35435
$113$	−0.943654	−0.0887715	−0.0443858	−	0.999014i	$-0.514133\pi$
$113$	−0.943654	−0.0887715	−0.0443858	+	0.999014i	$0.514133\pi$
$114$	0	0
$115$	−5.04972	−0.470888
$116$	−6.81777	−0.633014
$117$	0	0
$118$	−3.24000	−0.298266
$119$	−17.5976	−1.61317
$120$	0	0
$121$	0	0
$122$	2.45441	0.222212
$123$	0	0
$124$	9.33364	0.838186
$125$	7.21271	0.645125
$126$	0	0
$127$	−2.45040	−0.217438	−0.108719	−	0.994073i	$-0.534675\pi$
$127$	−2.45040	−0.217438	−0.108719	+	0.994073i	$0.534675\pi$
$128$	−8.21980	−0.726535
$129$	0	0
$130$	2.97444	0.260876
$131$	3.99737	0.349252	0.174626	−	0.984635i	$-0.444128\pi$
$131$	3.99737	0.349252	0.174626	+	0.984635i	$0.444128\pi$
$132$	0	0
$133$	6.60815	0.572999
$134$	−0.496319	−0.0428754
$135$	0	0
$136$	4.82743	0.413949
$137$	−1.08926	−0.0930615	−0.0465307	−	0.998917i	$-0.514817\pi$
$137$	−1.08926	−0.0930615	−0.0465307	+	0.998917i	$0.514817\pi$
$138$	0	0
$139$	−2.88493	−0.244696	−0.122348	−	0.992487i	$-0.539042\pi$
$139$	−2.88493	−0.244696	−0.122348	+	0.992487i	$0.539042\pi$
$140$	21.1700	1.78919
$141$	0	0
$142$	1.63714	0.137386
$143$	0	0
$144$	0	0
$145$	−9.62506	−0.799318
$146$	1.15389	0.0954965
$147$	0	0
$148$	−14.8593	−1.22142
$149$	20.1748	1.65279	0.826393	−	0.563094i	$-0.190389\pi$
$149$	20.1748	1.65279	0.826393	+	0.563094i	$0.190389\pi$
$150$	0	0
$151$	11.0784	0.901544	0.450772	−	0.892639i	$-0.351149\pi$
$151$	11.0784	0.901544	0.450772	+	0.892639i	$0.351149\pi$
$152$	−1.81276	−0.147035
$153$	0	0
$154$	0	0
$155$	13.1769	1.05839
$156$	0	0
$157$	0.332784	0.0265591	0.0132795	−	0.999912i	$-0.495773\pi$
$157$	0.332784	0.0265591	0.0132795	+	0.999912i	$0.495773\pi$
$158$	1.22048	0.0970959
$159$	0	0
$160$	−8.77138	−0.693438
$161$	7.59365	0.598464
$162$	0	0
$163$	13.3380	1.04472	0.522358	−	0.852726i	$-0.325053\pi$
$163$	13.3380	1.04472	0.522358	+	0.852726i	$0.325053\pi$
$164$	−13.1855	−1.02962
$165$	0	0
$166$	−1.85352	−0.143861
$167$	−18.9152	−1.46370	−0.731849	−	0.681467i	$-0.761342\pi$
$167$	−18.9152	−1.46370	−0.731849	+	0.681467i	$0.761342\pi$
$168$	0	0
$169$	1.82986	0.140759
$170$	3.33689	0.255928
$171$	0	0
$172$	1.88989	0.144103
$173$	−1.51409	−0.115114	−0.0575570	−	0.998342i	$-0.518331\pi$
$173$	−1.51409	−0.115114	−0.0575570	+	0.998342i	$0.518331\pi$
$174$	0	0
$175$	9.52036	0.719671
$176$	0	0
$177$	0	0
$178$	−2.64117	−0.197964
$179$	−13.1892	−0.985810	−0.492905	−	0.870083i	$-0.664065\pi$
$179$	−13.1892	−0.985810	−0.492905	+	0.870083i	$0.664065\pi$
$180$	0	0
$181$	2.79883	0.208035	0.104018	−	0.994575i	$-0.466830\pi$
$181$	2.79883	0.208035	0.104018	+	0.994575i	$0.466830\pi$
$182$	−4.47290	−0.331554
$183$	0	0
$184$	−2.08311	−0.153569
$185$	−20.9778	−1.54232
$186$	0	0
$187$	0	0
$188$	11.2557	0.820907
$189$	0	0
$190$	−1.25305	−0.0909055
$191$	16.7416	1.21138	0.605688	−	0.795702i	$-0.292898\pi$
$191$	16.7416	1.21138	0.605688	+	0.795702i	$0.292898\pi$
$192$	0	0
$193$	22.0394	1.58643	0.793214	−	0.608942i	$-0.208406\pi$
$193$	22.0394	1.58643	0.793214	+	0.608942i	$0.208406\pi$
$194$	−2.11371	−0.151756
$195$	0	0
$196$	−18.4042	−1.31459
$197$	18.2247	1.29845	0.649227	−	0.760595i	$-0.275093\pi$
$197$	18.2247	1.29845	0.649227	+	0.760595i	$0.275093\pi$
$198$	0	0
$199$	−25.0958	−1.77899	−0.889497	−	0.456942i	$-0.848945\pi$
$199$	−25.0958	−1.77899	−0.889497	+	0.456942i	$0.848945\pi$
$200$	−2.61165	−0.184672
$201$	0	0
$202$	−3.91155	−0.275216
$203$	14.4740	1.01587
$204$	0	0
$205$	−18.6148	−1.30011
$206$	1.44720	0.100831
$207$	0	0
$208$	−13.5506	−0.939563
$209$	0	0
$210$	0	0
$211$	−8.27002	−0.569332	−0.284666	−	0.958627i	$-0.591883\pi$
$211$	−8.27002	−0.569332	−0.284666	+	0.958627i	$0.591883\pi$
$212$	−3.01585	−0.207129
$213$	0	0
$214$	−0.792421	−0.0541688
$215$	2.66808	0.181961
$216$	0	0
$217$	−19.8151	−1.34514
$218$	4.94940	0.335216
$219$	0	0
$220$	0	0
$221$	16.6369	1.11912
$222$	0	0
$223$	−7.35208	−0.492332	−0.246166	−	0.969228i	$-0.579171\pi$
$223$	−7.35208	−0.492332	−0.246166	+	0.969228i	$0.579171\pi$
$224$	13.1902	0.881308
$225$	0	0
$226$	−0.269081	−0.0178990
$227$	−18.9412	−1.25717	−0.628586	−	0.777740i	$-0.716366\pi$
$227$	−18.9412	−1.25717	−0.628586	+	0.777740i	$0.716366\pi$
$228$	0	0
$229$	−7.85945	−0.519367	−0.259683	−	0.965694i	$-0.583618\pi$
$229$	−7.85945	−0.519367	−0.259683	+	0.965694i	$0.583618\pi$
$230$	−1.43992	−0.0949454
$231$	0	0
$232$	−3.97054	−0.260678
$233$	−6.56942	−0.430377	−0.215188	−	0.976573i	$-0.569037\pi$
$233$	−6.56942	−0.430377	−0.215188	+	0.976573i	$0.569037\pi$
$234$	0	0
$235$	15.8904	1.03657
$236$	21.8011	1.41913
$237$	0	0
$238$	−5.01794	−0.325265
$239$	−25.5463	−1.65245	−0.826226	−	0.563339i	$-0.809516\pi$
$239$	−25.5463	−1.65245	−0.826226	+	0.563339i	$0.809516\pi$
$240$	0	0
$241$	2.98198	0.192086	0.0960432	−	0.995377i	$-0.469381\pi$
$241$	2.98198	0.192086	0.0960432	+	0.995377i	$0.469381\pi$
$242$	0	0
$243$	0	0
$244$	−16.5151	−1.05727
$245$	−25.9823	−1.65995
$246$	0	0
$247$	−6.24738	−0.397511
$248$	5.43573	0.345169
$249$	0	0
$250$	2.05669	0.130077
$251$	−11.6685	−0.736510	−0.368255	−	0.929725i	$-0.620045\pi$
$251$	−11.6685	−0.736510	−0.368255	+	0.929725i	$0.620045\pi$
$252$	0	0
$253$	0	0
$254$	−0.698728	−0.0438421
$255$	0	0
$256$	9.88443	0.617777
$257$	−20.7245	−1.29276	−0.646378	−	0.763017i	$-0.723717\pi$
$257$	−20.7245	−1.29276	−0.646378	+	0.763017i	$0.723717\pi$
$258$	0	0
$259$	31.5459	1.96017
$260$	−20.0143	−1.24123
$261$	0	0
$262$	1.13984	0.0704198
$263$	9.08545	0.560233	0.280117	−	0.959966i	$-0.409627\pi$
$263$	9.08545	0.560233	0.280117	+	0.959966i	$0.409627\pi$
$264$	0	0
$265$	−4.25766	−0.261546
$266$	1.88430	0.115534
$267$	0	0
$268$	3.33960	0.203999
$269$	−7.94129	−0.484189	−0.242094	−	0.970253i	$-0.577834\pi$
$269$	−7.94129	−0.484189	−0.242094	+	0.970253i	$0.577834\pi$
$270$	0	0
$271$	−3.72364	−0.226195	−0.113097	−	0.993584i	$-0.536077\pi$
$271$	−3.72364	−0.226195	−0.113097	+	0.993584i	$0.536077\pi$
$272$	−15.2017	−0.921741
$273$	0	0
$274$	−0.310600	−0.0187640
$275$	0	0
$276$	0	0
$277$	3.90064	0.234367	0.117183	−	0.993110i	$-0.462614\pi$
$277$	3.90064	0.234367	0.117183	+	0.993110i	$0.462614\pi$
$278$	−0.822632	−0.0493382
$279$	0	0
$280$	12.3290	0.736799
$281$	0.0396231	0.00236371	0.00118186	−	0.999999i	$-0.499624\pi$
$281$	0.0396231	0.00236371	0.00118186	+	0.999999i	$0.499624\pi$
$282$	0	0
$283$	−6.39387	−0.380076	−0.190038	−	0.981777i	$-0.560861\pi$
$283$	−6.39387	−0.380076	−0.190038	+	0.981777i	$0.560861\pi$
$284$	−11.0159	−0.653673
$285$	0	0
$286$	0	0
$287$	27.9925	1.65235
$288$	0	0
$289$	1.66417	0.0978923
$290$	−2.74457	−0.161167
$291$	0	0
$292$	−7.76422	−0.454367
$293$	−23.4074	−1.36748	−0.683738	−	0.729728i	$-0.739647\pi$
$293$	−23.4074	−1.36748	−0.683738	+	0.729728i	$0.739647\pi$
$294$	0	0
$295$	30.7780	1.79196
$296$	−8.65375	−0.502989
$297$	0	0
$298$	5.75282	0.333252
$299$	−7.17909	−0.415177
$300$	0	0
$301$	−4.01220	−0.231259
$302$	3.15898	0.181779
$303$	0	0
$304$	5.70845	0.327402
$305$	−23.3154	−1.33503
$306$	0	0
$307$	−29.1494	−1.66365	−0.831823	−	0.555042i	$-0.812702\pi$
$307$	−29.1494	−1.66365	−0.831823	+	0.555042i	$0.812702\pi$
$308$	0	0
$309$	0	0
$310$	3.75737	0.213404
$311$	19.7057	1.11741	0.558705	−	0.829367i	$-0.311299\pi$
$311$	19.7057	1.11741	0.558705	+	0.829367i	$0.311299\pi$
$312$	0	0
$313$	1.33838	0.0756495	0.0378248	−	0.999284i	$-0.487957\pi$
$313$	1.33838	0.0756495	0.0378248	+	0.999284i	$0.487957\pi$
$314$	0.0948929	0.00535511
$315$	0	0
$316$	−8.21228	−0.461977
$317$	−4.00089	−0.224712	−0.112356	−	0.993668i	$-0.535840\pi$
$317$	−4.00089	−0.224712	−0.112356	+	0.993668i	$0.535840\pi$
$318$	0	0
$319$	0	0
$320$	16.5616	0.925821
$321$	0	0
$322$	2.16532	0.120668
$323$	−7.00864	−0.389971
$324$	0	0
$325$	−9.00060	−0.499264
$326$	3.80332	0.210646
$327$	0	0
$328$	−7.67899	−0.424001
$329$	−23.8956	−1.31741
$330$	0	0
$331$	3.18033	0.174807	0.0874034	−	0.996173i	$-0.472143\pi$
$331$	3.18033	0.174807	0.0874034	+	0.996173i	$0.472143\pi$
$332$	12.4718	0.684481
$333$	0	0
$334$	−5.39362	−0.295126
$335$	4.71472	0.257593
$336$	0	0
$337$	18.1978	0.991298	0.495649	−	0.868523i	$-0.334930\pi$
$337$	18.1978	0.991298	0.495649	+	0.868523i	$0.334930\pi$
$338$	0.521783	0.0283812
$339$	0	0
$340$	−22.4531	−1.21769
$341$	0	0
$342$	0	0
$343$	10.5583	0.570096
$344$	1.10064	0.0593424
$345$	0	0
$346$	−0.431740	−0.0232105
$347$	−27.4141	−1.47167	−0.735833	−	0.677163i	$-0.763209\pi$
$347$	−27.4141	−1.47167	−0.735833	+	0.677163i	$0.763209\pi$
$348$	0	0
$349$	−22.9055	−1.22610	−0.613052	−	0.790042i	$-0.710059\pi$
$349$	−22.9055	−1.22610	−0.613052	+	0.790042i	$0.710059\pi$
$350$	2.71471	0.145108
$351$	0	0
$352$	0	0
$353$	29.7047	1.58102	0.790511	−	0.612448i	$-0.209815\pi$
$353$	29.7047	1.58102	0.790511	+	0.612448i	$0.209815\pi$
$354$	0	0
$355$	−15.5518	−0.825405
$356$	17.7717	0.941900
$357$	0	0
$358$	−3.76089	−0.198769
$359$	−36.8574	−1.94526	−0.972631	−	0.232356i	$-0.925356\pi$
$359$	−36.8574	−1.94526	−0.972631	+	0.232356i	$0.925356\pi$
$360$	0	0
$361$	−16.3682	−0.861482
$362$	0.798082	0.0419462
$363$	0	0
$364$	30.0970	1.57751
$365$	−10.9612	−0.573737
$366$	0	0
$367$	−24.8606	−1.29771	−0.648857	−	0.760910i	$-0.724753\pi$
$367$	−24.8606	−1.29771	−0.648857	+	0.760910i	$0.724753\pi$
$368$	6.55978	0.341952
$369$	0	0
$370$	−5.98177	−0.310978
$371$	6.40257	0.332405
$372$	0	0
$373$	−18.2790	−0.946453	−0.473227	−	0.880941i	$-0.656911\pi$
$373$	−18.2790	−0.946453	−0.473227	+	0.880941i	$0.656911\pi$
$374$	0	0
$375$	0	0
$376$	6.55511	0.338054
$377$	−13.6838	−0.704750
$378$	0	0
$379$	−31.4593	−1.61595	−0.807977	−	0.589213i	$-0.799438\pi$
$379$	−31.4593	−1.61595	−0.807977	+	0.589213i	$0.799438\pi$
$380$	8.43142	0.432523
$381$	0	0
$382$	4.77383	0.244250
$383$	12.4318	0.635234	0.317617	−	0.948219i	$-0.397117\pi$
$383$	12.4318	0.635234	0.317617	+	0.948219i	$0.397117\pi$
$384$	0	0
$385$	0	0
$386$	6.28449	0.319872
$387$	0	0
$388$	14.2226	0.722045
$389$	−7.31968	−0.371123	−0.185561	−	0.982633i	$-0.559410\pi$
$389$	−7.31968	−0.371123	−0.185561	+	0.982633i	$0.559410\pi$
$390$	0	0
$391$	−8.05388	−0.407302
$392$	−10.7182	−0.541353
$393$	0	0
$394$	5.19673	0.261808
$395$	−11.5938	−0.583346
$396$	0	0
$397$	34.2087	1.71688	0.858442	−	0.512911i	$-0.171433\pi$
$397$	34.2087	1.71688	0.858442	+	0.512911i	$0.171433\pi$
$398$	−7.15602	−0.358699
$399$	0	0
$400$	8.22417	0.411208
$401$	−7.47577	−0.373322	−0.186661	−	0.982424i	$-0.559767\pi$
$401$	−7.47577	−0.373322	−0.186661	+	0.982424i	$0.559767\pi$
$402$	0	0
$403$	18.7333	0.933173
$404$	26.3198	1.30946
$405$	0	0
$406$	4.12723	0.204831
$407$	0	0
$408$	0	0
$409$	−2.41020	−0.119177	−0.0595883	−	0.998223i	$-0.518979\pi$
$409$	−2.41020	−0.119177	−0.0595883	+	0.998223i	$0.518979\pi$
$410$	−5.30798	−0.262143
$411$	0	0
$412$	−9.73783	−0.479748
$413$	−46.2832	−2.27745
$414$	0	0
$415$	17.6073	0.864307
$416$	−12.4701	−0.611397
$417$	0	0
$418$	0	0
$419$	11.2018	0.547242	0.273621	−	0.961838i	$-0.411779\pi$
$419$	11.2018	0.547242	0.273621	+	0.961838i	$0.411779\pi$
$420$	0	0
$421$	−6.90486	−0.336522	−0.168261	−	0.985742i	$-0.553815\pi$
$421$	−6.90486	−0.336522	−0.168261	+	0.985742i	$0.553815\pi$
$422$	−2.35818	−0.114795
$423$	0	0
$424$	−1.75637	−0.0852969
$425$	−10.0974	−0.489793
$426$	0	0
$427$	35.0611	1.69673
$428$	5.33200	0.257732
$429$	0	0
$430$	0.760798	0.0366890
$431$	−29.1806	−1.40558	−0.702789	−	0.711398i	$-0.748062\pi$
$431$	−29.1806	−1.40558	−0.702789	+	0.711398i	$0.748062\pi$
$432$	0	0
$433$	−36.5360	−1.75581	−0.877903	−	0.478838i	$-0.841058\pi$
$433$	−36.5360	−1.75581	−0.877903	+	0.478838i	$0.841058\pi$
$434$	−5.65025	−0.271220
$435$	0	0
$436$	−33.3033	−1.59494
$437$	3.02434	0.144674
$438$	0	0
$439$	21.4975	1.02602	0.513009	−	0.858383i	$-0.328531\pi$
$439$	21.4975	1.02602	0.513009	+	0.858383i	$0.328531\pi$
$440$	0	0
$441$	0	0
$442$	4.74399	0.225649
$443$	33.4450	1.58902	0.794510	−	0.607251i	$-0.207728\pi$
$443$	33.4450	1.58902	0.794510	+	0.607251i	$0.207728\pi$
$444$	0	0
$445$	25.0895	1.18935
$446$	−2.09643	−0.0992690
$447$	0	0
$448$	−24.9050	−1.17665
$449$	−39.5333	−1.86569	−0.932846	−	0.360276i	$-0.882682\pi$
$449$	−39.5333	−1.86569	−0.932846	+	0.360276i	$0.882682\pi$
$450$	0	0
$451$	0	0
$452$	1.81058	0.0851625
$453$	0	0
$454$	−5.40105	−0.253484
$455$	42.4898	1.99195
$456$	0	0
$457$	−37.5123	−1.75475	−0.877376	−	0.479803i	$-0.840708\pi$
$457$	−37.5123	−1.75475	−0.877376	+	0.479803i	$0.840708\pi$
$458$	−2.24111	−0.104720
$459$	0	0
$460$	9.68884	0.451745
$461$	19.3653	0.901932	0.450966	−	0.892541i	$-0.351080\pi$
$461$	19.3653	0.901932	0.450966	+	0.892541i	$0.351080\pi$
$462$	0	0
$463$	−14.3493	−0.666867	−0.333434	−	0.942774i	$-0.608207\pi$
$463$	−14.3493	−0.666867	−0.333434	+	0.942774i	$0.608207\pi$
$464$	12.5033	0.580453
$465$	0	0
$466$	−1.87326	−0.0867770
$467$	22.3209	1.03289	0.516445	−	0.856320i	$-0.327255\pi$
$467$	22.3209	1.03289	0.516445	+	0.856320i	$0.327255\pi$
$468$	0	0
$469$	−7.08990	−0.327381
$470$	4.53112	0.209005
$471$	0	0
$472$	12.6965	0.584406
$473$	0	0
$474$	0	0
$475$	3.79169	0.173975
$476$	33.7644	1.54759
$477$	0	0
$478$	−7.28448	−0.333184
$479$	−23.2616	−1.06285	−0.531426	−	0.847105i	$-0.678343\pi$
$479$	−23.2616	−1.06285	−0.531426	+	0.847105i	$0.678343\pi$
$480$	0	0
$481$	−29.8237	−1.35984
$482$	0.850308	0.0387305
$483$	0	0
$484$	0	0
$485$	20.0790	0.911740
$486$	0	0
$487$	0.270802	0.0122712	0.00613559	−	0.999981i	$-0.498047\pi$
$487$	0.270802	0.0122712	0.00613559	+	0.999981i	$0.498047\pi$
$488$	−9.61807	−0.435389
$489$	0	0
$490$	−7.40882	−0.334696
$491$	−4.20656	−0.189839	−0.0949196	−	0.995485i	$-0.530259\pi$
$491$	−4.20656	−0.189839	−0.0949196	+	0.995485i	$0.530259\pi$
$492$	0	0
$493$	−15.3512	−0.691382
$494$	−1.78143	−0.0801504
$495$	0	0
$496$	−17.1173	−0.768589
$497$	23.3865	1.04903
$498$	0	0
$499$	−15.3642	−0.687798	−0.343899	−	0.939007i	$-0.611748\pi$
$499$	−15.3642	−0.687798	−0.343899	+	0.939007i	$0.611748\pi$
$500$	−13.8390	−0.618897
$501$	0	0
$502$	−3.32726	−0.148503
$503$	3.91570	0.174592	0.0872961	−	0.996182i	$-0.472177\pi$
$503$	3.91570	0.174592	0.0872961	+	0.996182i	$0.472177\pi$
$504$	0	0
$505$	37.1573	1.65348
$506$	0	0
$507$	0	0
$508$	4.70156	0.208598
$509$	−28.5494	−1.26543	−0.632715	−	0.774385i	$-0.718059\pi$
$509$	−28.5494	−1.26543	−0.632715	+	0.774385i	$0.718059\pi$
$510$	0	0
$511$	16.4833	0.729176
$512$	19.2581	0.851097
$513$	0	0
$514$	−5.90954	−0.260659
$515$	−13.7475	−0.605787
$516$	0	0
$517$	0	0
$518$	8.99526	0.395229
$519$	0	0
$520$	−11.6559	−0.511146
$521$	14.2748	0.625388	0.312694	−	0.949854i	$-0.398768\pi$
$521$	14.2748	0.625388	0.312694	+	0.949854i	$0.398768\pi$
$522$	0	0
$523$	33.1573	1.44987	0.724934	−	0.688818i	$-0.241870\pi$
$523$	33.1573	1.44987	0.724934	+	0.688818i	$0.241870\pi$
$524$	−7.66972	−0.335053
$525$	0	0
$526$	2.59070	0.112960
$527$	21.0160	0.915472
$528$	0	0
$529$	−19.5246	−0.848897
$530$	−1.21406	−0.0527356
$531$	0	0
$532$	−12.6790	−0.549704
$533$	−26.4643	−1.14630
$534$	0	0
$535$	7.52751	0.325443
$536$	1.94492	0.0840077
$537$	0	0
$538$	−2.26444	−0.0976271
$539$	0	0
$540$	0	0
$541$	28.4609	1.22363	0.611815	−	0.791001i	$-0.290440\pi$
$541$	28.4609	1.22363	0.611815	+	0.791001i	$0.290440\pi$
$542$	−1.06179	−0.0456077
$543$	0	0
$544$	−13.9896	−0.599800
$545$	−47.0163	−2.01396
$546$	0	0
$547$	30.7466	1.31463	0.657316	−	0.753615i	$-0.271692\pi$
$547$	30.7466	1.31463	0.657316	+	0.753615i	$0.271692\pi$
$548$	2.08995	0.0892781
$549$	0	0
$550$	0	0
$551$	5.76457	0.245579
$552$	0	0
$553$	17.4345	0.741389
$554$	1.11226	0.0472554
$555$	0	0
$556$	5.53528	0.234748
$557$	−7.29459	−0.309082	−0.154541	−	0.987986i	$-0.549390\pi$
$557$	−7.29459	−0.309082	−0.154541	+	0.987986i	$0.549390\pi$
$558$	0	0
$559$	3.79316	0.160433
$560$	−38.8245	−1.64063
$561$	0	0
$562$	0.0112985	0.000476597 0
$563$	−36.5734	−1.54139	−0.770693	−	0.637206i	$-0.780090\pi$
$563$	−36.5734	−1.54139	−0.770693	+	0.637206i	$0.780090\pi$
$564$	0	0
$565$	2.55611	0.107536
$566$	−1.82320	−0.0766349
$567$	0	0
$568$	−6.41545	−0.269186
$569$	0.151484	0.00635053	0.00317527	−	0.999995i	$-0.498989\pi$
$569$	0.151484	0.00635053	0.00317527	+	0.999995i	$0.498989\pi$
$570$	0	0
$571$	−43.2254	−1.80893	−0.904463	−	0.426552i	$-0.859728\pi$
$571$	−43.2254	−1.80893	−0.904463	+	0.426552i	$0.859728\pi$
$572$	0	0
$573$	0	0
$574$	7.98203	0.333163
$575$	4.35716	0.181706
$576$	0	0
$577$	29.1251	1.21250	0.606248	−	0.795276i	$-0.292674\pi$
$577$	29.1251	1.21250	0.606248	+	0.795276i	$0.292674\pi$
$578$	0.474535	0.0197381
$579$	0	0
$580$	18.4675	0.766822
$581$	−26.4774	−1.09847
$582$	0	0
$583$	0	0
$584$	−4.52173	−0.187111
$585$	0	0
$586$	−6.67459	−0.275725
$587$	22.6949	0.936718	0.468359	−	0.883538i	$-0.344845\pi$
$587$	22.6949	0.936718	0.468359	+	0.883538i	$0.344845\pi$
$588$	0	0
$589$	−7.89180	−0.325176
$590$	8.77629	0.361314
$591$	0	0
$592$	27.2509	1.12001
$593$	−22.9308	−0.941656	−0.470828	−	0.882225i	$-0.656045\pi$
$593$	−22.9308	−0.941656	−0.470828	+	0.882225i	$0.656045\pi$
$594$	0	0
$595$	47.6673	1.95417
$596$	−38.7092	−1.58559
$597$	0	0
$598$	−2.04710	−0.0837123
$599$	12.5007	0.510764	0.255382	−	0.966840i	$-0.417799\pi$
$599$	12.5007	0.510764	0.255382	+	0.966840i	$0.417799\pi$
$600$	0	0
$601$	−22.4788	−0.916930	−0.458465	−	0.888712i	$-0.651601\pi$
$601$	−22.4788	−0.916930	−0.458465	+	0.888712i	$0.651601\pi$
$602$	−1.14407	−0.0466289
$603$	0	0
$604$	−21.2559	−0.864892
$605$	0	0
$606$	0	0
$607$	−26.7047	−1.08391	−0.541956	−	0.840407i	$-0.682316\pi$
$607$	−26.7047	−1.08391	−0.541956	+	0.840407i	$0.682316\pi$
$608$	5.25329	0.213049
$609$	0	0
$610$	−6.64834	−0.269183
$611$	22.5911	0.913936
$612$	0	0
$613$	43.4844	1.75632	0.878160	−	0.478367i	$-0.158771\pi$
$613$	43.4844	1.75632	0.878160	+	0.478367i	$0.158771\pi$
$614$	−8.31191	−0.335441
$615$	0	0
$616$	0	0
$617$	−41.4255	−1.66773	−0.833864	−	0.551969i	$-0.813877\pi$
$617$	−41.4255	−1.66773	−0.833864	+	0.551969i	$0.813877\pi$
$618$	0	0
$619$	8.91175	0.358194	0.179097	−	0.983831i	$-0.442682\pi$
$619$	8.91175	0.358194	0.179097	+	0.983831i	$0.442682\pi$
$620$	−25.2824	−1.01536
$621$	0	0
$622$	5.61906	0.225304
$623$	−37.7290	−1.51158
$624$	0	0
$625$	−31.2235	−1.24894
$626$	0.381636	0.0152532
$627$	0	0
$628$	−0.638510	−0.0254793
$629$	−33.4578	−1.33405
$630$	0	0
$631$	−5.67049	−0.225739	−0.112869	−	0.993610i	$-0.536004\pi$
$631$	−5.67049	−0.225739	−0.112869	+	0.993610i	$0.536004\pi$
$632$	−4.78267	−0.190244
$633$	0	0
$634$	−1.14085	−0.0453089
$635$	6.63749	0.263401
$636$	0	0
$637$	−36.9386	−1.46356
$638$	0	0
$639$	0	0
$640$	22.2653	0.880112
$641$	−26.8182	−1.05926	−0.529628	−	0.848230i	$-0.677668\pi$
$641$	−26.8182	−1.05926	−0.529628	+	0.848230i	$0.677668\pi$
$642$	0	0
$643$	14.1385	0.557566	0.278783	−	0.960354i	$-0.410069\pi$
$643$	14.1385	0.557566	0.278783	+	0.960354i	$0.410069\pi$
$644$	−14.5699	−0.574133
$645$	0	0
$646$	−1.99850	−0.0786301
$647$	1.27403	0.0500875	0.0250437	−	0.999686i	$-0.492027\pi$
$647$	1.27403	0.0500875	0.0250437	+	0.999686i	$0.492027\pi$
$648$	0	0
$649$	0	0
$650$	−2.56651	−0.100667
$651$	0	0
$652$	−25.5916	−1.00224
$653$	4.82833	0.188947	0.0944736	−	0.995527i	$-0.469883\pi$
$653$	4.82833	0.188947	0.0944736	+	0.995527i	$0.469883\pi$
$654$	0	0
$655$	−10.8278	−0.423078
$656$	24.1814	0.944124
$657$	0	0
$658$	−6.81379	−0.265629
$659$	−22.1777	−0.863921	−0.431961	−	0.901892i	$-0.642178\pi$
$659$	−22.1777	−0.863921	−0.431961	+	0.901892i	$0.642178\pi$
$660$	0	0
$661$	−27.3975	−1.06564	−0.532820	−	0.846229i	$-0.678868\pi$
$661$	−27.3975	−1.06564	−0.532820	+	0.846229i	$0.678868\pi$
$662$	0.906866	0.0352464
$663$	0	0
$664$	7.26336	0.281873
$665$	−17.8997	−0.694121
$666$	0	0
$667$	6.62427	0.256493
$668$	36.2923	1.40419
$669$	0	0
$670$	1.34440	0.0519385
$671$	0	0
$672$	0	0
$673$	−35.2435	−1.35854	−0.679269	−	0.733889i	$-0.737703\pi$
$673$	−35.2435	−1.35854	−0.679269	+	0.733889i	$0.737703\pi$
$674$	5.18907	0.199876
$675$	0	0
$676$	−3.51094	−0.135036
$677$	−44.0500	−1.69298	−0.846489	−	0.532406i	$-0.821288\pi$
$677$	−44.0500	−1.69298	−0.846489	+	0.532406i	$0.821288\pi$
$678$	0	0
$679$	−30.1943	−1.15875
$680$	−13.0762	−0.501450
$681$	0	0
$682$	0	0
$683$	−42.2845	−1.61797	−0.808985	−	0.587829i	$-0.799983\pi$
$683$	−42.2845	−1.61797	−0.808985	+	0.587829i	$0.799983\pi$
$684$	0	0
$685$	2.95051	0.112733
$686$	3.01069	0.114949
$687$	0	0
$688$	−3.46594	−0.132138
$689$	−6.05303	−0.230602
$690$	0	0
$691$	−8.46688	−0.322095	−0.161048	−	0.986947i	$-0.551487\pi$
$691$	−8.46688	−0.322095	−0.161048	+	0.986947i	$0.551487\pi$
$692$	2.90507	0.110434
$693$	0	0
$694$	−7.81709	−0.296733
$695$	7.81450	0.296421
$696$	0	0
$697$	−29.6891	−1.12455
$698$	−6.53147	−0.247220
$699$	0	0
$700$	−18.2666	−0.690413
$701$	43.5518	1.64493	0.822465	−	0.568816i	$-0.192599\pi$
$701$	43.5518	1.64493	0.822465	+	0.568816i	$0.192599\pi$
$702$	0	0
$703$	12.5638	0.473854
$704$	0	0
$705$	0	0
$706$	8.47025	0.318782
$707$	−55.8764	−2.10145
$708$	0	0
$709$	−6.02729	−0.226360	−0.113180	−	0.993575i	$-0.536104\pi$
$709$	−6.02729	−0.226360	−0.113180	+	0.993575i	$0.536104\pi$
$710$	−4.43458	−0.166427
$711$	0	0
$712$	10.3499	0.387880
$713$	−9.06874	−0.339627
$714$	0	0
$715$	0	0
$716$	25.3061	0.945732
$717$	0	0
$718$	−10.5098	−0.392224
$719$	−40.4066	−1.50691	−0.753457	−	0.657498i	$-0.771615\pi$
$719$	−40.4066	−1.50691	−0.753457	+	0.657498i	$0.771615\pi$
$720$	0	0
$721$	20.6732	0.769909
$722$	−4.66735	−0.173701
$723$	0	0
$724$	−5.37009	−0.199578
$725$	8.30501	0.308441
$726$	0	0
$727$	18.7206	0.694310	0.347155	−	0.937808i	$-0.387148\pi$
$727$	18.7206	0.694310	0.347155	+	0.937808i	$0.387148\pi$
$728$	17.5279	0.649628
$729$	0	0
$730$	−3.12558	−0.115683
$731$	4.25536	0.157390
$732$	0	0
$733$	−0.564191	−0.0208389	−0.0104194	−	0.999946i	$-0.503317\pi$
$733$	−0.564191	−0.0208389	−0.0104194	+	0.999946i	$0.503317\pi$
$734$	−7.08897	−0.261659
$735$	0	0
$736$	6.03673	0.222517
$737$	0	0
$738$	0	0
$739$	−1.94812	−0.0716629	−0.0358315	−	0.999358i	$-0.511408\pi$
$739$	−1.94812	−0.0716629	−0.0358315	+	0.999358i	$0.511408\pi$
$740$	40.2498	1.47961
$741$	0	0
$742$	1.82568	0.0670229
$743$	−27.2627	−1.00017	−0.500086	−	0.865976i	$-0.666698\pi$
$743$	−27.2627	−1.00017	−0.500086	+	0.865976i	$0.666698\pi$
$744$	0	0
$745$	−54.6482	−2.00216
$746$	−5.21224	−0.190834
$747$	0	0
$748$	0	0
$749$	−11.3197	−0.413613
$750$	0	0
$751$	30.3063	1.10589	0.552946	−	0.833217i	$-0.313504\pi$
$751$	30.3063	1.10589	0.552946	+	0.833217i	$0.313504\pi$
$752$	−20.6422	−0.752745
$753$	0	0
$754$	−3.90191	−0.142099
$755$	−30.0083	−1.09211
$756$	0	0
$757$	11.1070	0.403689	0.201845	−	0.979418i	$-0.435306\pi$
$757$	11.1070	0.403689	0.201845	+	0.979418i	$0.435306\pi$
$758$	−8.97056	−0.325826
$759$	0	0
$760$	4.91030	0.178115
$761$	−33.3410	−1.20861	−0.604304	−	0.796754i	$-0.706549\pi$
$761$	−33.3410	−1.20861	−0.604304	+	0.796754i	$0.706549\pi$
$762$	0	0
$763$	70.7020	2.55959
$764$	−32.1219	−1.16213
$765$	0	0
$766$	3.54490	0.128082
$767$	43.7565	1.57995
$768$	0	0
$769$	51.9401	1.87301	0.936504	−	0.350656i	$-0.114041\pi$
$769$	51.9401	1.87301	0.936504	+	0.350656i	$0.114041\pi$
$770$	0	0
$771$	0	0
$772$	−42.2867	−1.52193
$773$	7.72276	0.277768	0.138884	−	0.990309i	$-0.455648\pi$
$773$	7.72276	0.277768	0.138884	+	0.990309i	$0.455648\pi$
$774$	0	0
$775$	−11.3697	−0.408412
$776$	8.28299	0.297342
$777$	0	0
$778$	−2.08720	−0.0748296
$779$	11.1486	0.399441
$780$	0	0
$781$	0	0
$782$	−2.29655	−0.0821244
$783$	0	0
$784$	33.7521	1.20543
$785$	−0.901424	−0.0321732
$786$	0	0
$787$	19.7063	0.702454	0.351227	−	0.936290i	$-0.385764\pi$
$787$	19.7063	0.702454	0.351227	+	0.936290i	$0.385764\pi$
$788$	−34.9675	−1.24567
$789$	0	0
$790$	−3.30595	−0.117620
$791$	−3.84382	−0.136670
$792$	0	0
$793$	−33.1470	−1.17709
$794$	9.75455	0.346176
$795$	0	0
$796$	48.1510	1.70667
$797$	−14.0258	−0.496818	−0.248409	−	0.968655i	$-0.579908\pi$
$797$	−14.0258	−0.496818	−0.248409	+	0.968655i	$0.579908\pi$
$798$	0	0
$799$	25.3438	0.896600
$800$	7.56841	0.267584
$801$	0	0
$802$	−2.13170	−0.0752731
$803$	0	0
$804$	0	0
$805$	−20.5692	−0.724968
$806$	5.34178	0.188156
$807$	0	0
$808$	15.3282	0.539243
$809$	−20.9298	−0.735854	−0.367927	−	0.929855i	$-0.619932\pi$
$809$	−20.9298	−0.735854	−0.367927	+	0.929855i	$0.619932\pi$
$810$	0	0
$811$	−1.94293	−0.0682255	−0.0341127	−	0.999418i	$-0.510861\pi$
$811$	−1.94293	−0.0682255	−0.0341127	+	0.999418i	$0.510861\pi$
$812$	−27.7711	−0.974573
$813$	0	0
$814$	0	0
$815$	−36.1292	−1.26555
$816$	0	0
$817$	−1.59795	−0.0559050
$818$	−0.687264	−0.0240296
$819$	0	0
$820$	35.7161	1.24726
$821$	10.8418	0.378380	0.189190	−	0.981940i	$-0.439414\pi$
$821$	10.8418	0.378380	0.189190	+	0.981940i	$0.439414\pi$
$822$	0	0
$823$	47.6678	1.66160	0.830798	−	0.556575i	$-0.187885\pi$
$823$	47.6678	1.66160	0.830798	+	0.556575i	$0.187885\pi$
$824$	−5.67112	−0.197563
$825$	0	0
$826$	−13.1976	−0.459203
$827$	37.4150	1.30105	0.650524	−	0.759486i	$-0.274549\pi$
$827$	37.4150	1.30105	0.650524	+	0.759486i	$0.274549\pi$
$828$	0	0
$829$	10.7069	0.371866	0.185933	−	0.982562i	$-0.440469\pi$
$829$	10.7069	0.371866	0.185933	+	0.982562i	$0.440469\pi$
$830$	5.02068	0.174271
$831$	0	0
$832$	23.5453	0.816287
$833$	−41.4397	−1.43580
$834$	0	0
$835$	51.2361	1.77310
$836$	0	0
$837$	0	0
$838$	3.19416	0.110341
$839$	−15.3615	−0.530338	−0.265169	−	0.964202i	$-0.585428\pi$
$839$	−15.3615	−0.530338	−0.265169	+	0.964202i	$0.585428\pi$
$840$	0	0
$841$	−16.3737	−0.564612
$842$	−1.96891	−0.0678531
$843$	0	0
$844$	15.8676	0.546186
$845$	−4.95661	−0.170513
$846$	0	0
$847$	0	0
$848$	5.53087	0.189931
$849$	0	0
$850$	−2.87924	−0.0987572
$851$	14.4375	0.494913
$852$	0	0
$853$	−41.4642	−1.41971	−0.709854	−	0.704349i	$-0.751239\pi$
$853$	−41.4642	−1.41971	−0.709854	+	0.704349i	$0.751239\pi$
$854$	9.99763	0.342112
$855$	0	0
$856$	3.10525	0.106135
$857$	18.4055	0.628719	0.314359	−	0.949304i	$-0.398210\pi$
$857$	18.4055	0.628719	0.314359	+	0.949304i	$0.398210\pi$
$858$	0	0
$859$	−15.0485	−0.513449	−0.256725	−	0.966485i	$-0.582643\pi$
$859$	−15.0485	−0.513449	−0.256725	+	0.966485i	$0.582643\pi$
$860$	−5.11922	−0.174564
$861$	0	0
$862$	−8.32079	−0.283407
$863$	14.4298	0.491196	0.245598	−	0.969372i	$-0.421016\pi$
$863$	14.4298	0.491196	0.245598	+	0.969372i	$0.421016\pi$
$864$	0	0
$865$	4.10126	0.139447
$866$	−10.4182	−0.354024
$867$	0	0
$868$	38.0191	1.29045
$869$	0	0
$870$	0	0
$871$	6.70283	0.227117
$872$	−19.3952	−0.656803
$873$	0	0
$874$	0.862385	0.0291706
$875$	29.3798	0.993218
$876$	0	0
$877$	24.0754	0.812967	0.406484	−	0.913658i	$-0.366755\pi$
$877$	24.0754	0.812967	0.406484	+	0.913658i	$0.366755\pi$
$878$	6.12996	0.206876
$879$	0	0
$880$	0	0
$881$	10.0956	0.340129	0.170064	−	0.985433i	$-0.445602\pi$
$881$	10.0956	0.340129	0.170064	+	0.985433i	$0.445602\pi$
$882$	0	0
$883$	50.7198	1.70686	0.853429	−	0.521209i	$-0.174519\pi$
$883$	50.7198	1.70686	0.853429	+	0.521209i	$0.174519\pi$
$884$	−31.9211	−1.07362
$885$	0	0
$886$	9.53679	0.320395
$887$	−2.57271	−0.0863831	−0.0431915	−	0.999067i	$-0.513753\pi$
$887$	−2.57271	−0.0863831	−0.0431915	+	0.999067i	$0.513753\pi$
$888$	0	0
$889$	−9.98131	−0.334762
$890$	7.15422	0.239810
$891$	0	0
$892$	14.1064	0.472316
$893$	−9.51694	−0.318472
$894$	0	0
$895$	35.7261	1.19419
$896$	−33.4820	−1.11856
$897$	0	0
$898$	−11.2729	−0.376180
$899$	−17.2856	−0.576506
$900$	0	0
$901$	−6.79061	−0.226228
$902$	0	0
$903$	0	0
$904$	1.05445	0.0350704
$905$	−7.58129	−0.252010
$906$	0	0
$907$	10.2949	0.341835	0.170918	−	0.985285i	$-0.445327\pi$
$907$	10.2949	0.341835	0.170918	+	0.985285i	$0.445327\pi$
$908$	36.3423	1.20606
$909$	0	0
$910$	12.1159	0.401638
$911$	15.6025	0.516935	0.258468	−	0.966020i	$-0.416782\pi$
$911$	15.6025	0.516935	0.258468	+	0.966020i	$0.416782\pi$
$912$	0	0
$913$	0	0
$914$	−10.6966	−0.353811
$915$	0	0
$916$	15.0798	0.498252
$917$	16.2826	0.537700
$918$	0	0
$919$	−11.2124	−0.369864	−0.184932	−	0.982751i	$-0.559206\pi$
$919$	−11.2124	−0.369864	−0.184932	+	0.982751i	$0.559206\pi$
$920$	5.64259	0.186031
$921$	0	0
$922$	5.52198	0.181857
$923$	−22.1097	−0.727751
$924$	0	0
$925$	18.1007	0.595148
$926$	−4.09167	−0.134461
$927$	0	0
$928$	11.5064	0.377715
$929$	−23.5275	−0.771912	−0.385956	−	0.922517i	$-0.626128\pi$
$929$	−23.5275	−0.771912	−0.385956	+	0.922517i	$0.626128\pi$
$930$	0	0
$931$	15.5611	0.509996
$932$	12.6047	0.412880
$933$	0	0
$934$	6.36478	0.208262
$935$	0	0
$936$	0	0
$937$	−18.6555	−0.609448	−0.304724	−	0.952441i	$-0.598564\pi$
$937$	−18.6555	−0.609448	−0.304724	+	0.952441i	$0.598564\pi$
$938$	−2.02167	−0.0660100
$939$	0	0
$940$	−30.4887	−0.994432
$941$	−32.4926	−1.05923	−0.529615	−	0.848238i	$-0.677663\pi$
$941$	−32.4926	−1.05923	−0.529615	+	0.848238i	$0.677663\pi$
$942$	0	0
$943$	12.8113	0.417193
$944$	−39.9818	−1.30130
$945$	0	0
$946$	0	0
$947$	3.84273	0.124872	0.0624360	−	0.998049i	$-0.480113\pi$
$947$	3.84273	0.124872	0.0624360	+	0.998049i	$0.480113\pi$
$948$	0	0
$949$	−15.5834	−0.505858
$950$	1.08119	0.0350786
$951$	0	0
$952$	19.6637	0.637306
$953$	19.0891	0.618358	0.309179	−	0.951004i	$-0.399946\pi$
$953$	19.0891	0.618358	0.309179	+	0.951004i	$0.399946\pi$
$954$	0	0
$955$	−45.3484	−1.46744
$956$	49.0154	1.58527
$957$	0	0
$958$	−6.63302	−0.214303
$959$	−4.43691	−0.143275
$960$	0	0
$961$	−7.33576	−0.236638
$962$	−8.50417	−0.274186
$963$	0	0
$964$	−5.72150	−0.184277
$965$	−59.6988	−1.92177
$966$	0	0
$967$	−26.5627	−0.854198	−0.427099	−	0.904205i	$-0.640464\pi$
$967$	−26.5627	−0.854198	−0.427099	+	0.904205i	$0.640464\pi$
$968$	0	0
$969$	0	0
$970$	5.72549	0.183834
$971$	51.1079	1.64013	0.820066	−	0.572269i	$-0.193937\pi$
$971$	51.1079	1.64013	0.820066	+	0.572269i	$0.193937\pi$
$972$	0	0
$973$	−11.7513	−0.376728
$974$	0.0772186	0.00247424
$975$	0	0
$976$	30.2876	0.969482
$977$	21.1746	0.677435	0.338717	−	0.940888i	$-0.390007\pi$
$977$	21.1746	0.677435	0.338717	+	0.940888i	$0.390007\pi$
$978$	0	0
$979$	0	0
$980$	49.8521	1.59247
$981$	0	0
$982$	−1.19949	−0.0382774
$983$	−50.8354	−1.62140	−0.810699	−	0.585463i	$-0.800913\pi$
$983$	−50.8354	−1.62140	−0.810699	+	0.585463i	$0.800913\pi$
$984$	0	0
$985$	−49.3658	−1.57292
$986$	−4.37736	−0.139404
$987$	0	0
$988$	11.9868	0.381351
$989$	−1.83625	−0.0583895
$990$	0	0
$991$	−13.1480	−0.417662	−0.208831	−	0.977952i	$-0.566966\pi$
$991$	−13.1480	−0.417662	−0.208831	+	0.977952i	$0.566966\pi$
$992$	−15.7524	−0.500140
$993$	0	0
$994$	6.66862	0.211516
$995$	67.9778	2.15504
$996$	0	0
$997$	37.2087	1.17841	0.589205	−	0.807983i	$-0.299441\pi$
$997$	37.2087	1.17841	0.589205	+	0.807983i	$0.299441\pi$
$998$	−4.38109	−0.138681
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9801.2.a.cn.1.10		18
3.2	odd	2		9801.2.a.co.1.9		18
9.2	odd	6		1089.2.e.o.364.10		36
9.5	odd	6		1089.2.e.o.727.10		36
11.7	odd	10		891.2.f.e.82.5		36
11.8	odd	10		891.2.f.e.163.5		36
11.10	odd	2		9801.2.a.cp.1.9		18
33.8	even	10		891.2.f.f.163.5		36
33.29	even	10		891.2.f.f.82.5		36
33.32	even	2		9801.2.a.cm.1.10		18
99.7	odd	30		297.2.n.b.280.5		72
99.29	even	30		99.2.m.b.49.5	yes	72
99.32	even	6		1089.2.e.p.727.9		36
99.40	odd	30		297.2.n.b.181.5		72
99.41	even	30		99.2.m.b.97.5	yes	72
99.52	odd	30		297.2.n.b.64.5		72
99.65	even	6		1089.2.e.p.364.9		36
99.74	even	30		99.2.m.b.31.5	yes	72
99.85	odd	30		297.2.n.b.262.5		72
99.95	even	30		99.2.m.b.16.5	✓	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	99.95	even	30
99.2.m.b.31.5	yes	72	99.74	even	30
99.2.m.b.49.5	yes	72	99.29	even	30
99.2.m.b.97.5	yes	72	99.41	even	30
297.2.n.b.64.5		72	99.52	odd	30
297.2.n.b.181.5		72	99.40	odd	30
297.2.n.b.262.5		72	99.85	odd	30
297.2.n.b.280.5		72	99.7	odd	30
891.2.f.e.82.5		36	11.7	odd	10
891.2.f.e.163.5		36	11.8	odd	10
891.2.f.f.82.5		36	33.29	even	10
891.2.f.f.163.5		36	33.8	even	10
1089.2.e.o.364.10		36	9.2	odd	6
1089.2.e.o.727.10		36	9.5	odd	6
1089.2.e.p.364.9		36	99.65	even	6
1089.2.e.p.727.9		36	99.32	even	6
9801.2.a.cm.1.10		18	33.32	even	2
9801.2.a.cn.1.10		18	1.1	even	1	trivial
9801.2.a.co.1.9		18	3.2	odd	2
9801.2.a.cp.1.9		18	11.10	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)

\(f(q)\)	\(=\)	\(q+0.285148 q^{2} -1.91869 q^{4} -2.70873 q^{5} +4.07334 q^{7} -1.11741 q^{8} -0.772391 q^{10} -3.85096 q^{13} +1.16150 q^{14} +3.51875 q^{16} -4.32020 q^{17} +1.62229 q^{19} +5.19722 q^{20} +1.86423 q^{23} +2.33724 q^{25} -1.09809 q^{26} -7.81547 q^{28} +3.55334 q^{29} -4.86459 q^{31} +3.23818 q^{32} -1.23190 q^{34} -11.0336 q^{35} +7.74449 q^{37} +0.462595 q^{38} +3.02676 q^{40} +6.87214 q^{41} -0.984991 q^{43} +0.531584 q^{46} -5.86635 q^{47} +9.59206 q^{49} +0.666460 q^{50} +7.38879 q^{52} +1.57183 q^{53} -4.55158 q^{56} +1.01323 q^{58} -11.3625 q^{59} +8.60748 q^{61} -1.38713 q^{62} -6.11414 q^{64} +10.4312 q^{65} -1.74056 q^{67} +8.28914 q^{68} -3.14621 q^{70} +5.74136 q^{71} +4.04662 q^{73} +2.20833 q^{74} -3.11268 q^{76} +4.28015 q^{79} -9.53137 q^{80} +1.95958 q^{82} -6.50019 q^{83} +11.7023 q^{85} -0.280869 q^{86} -9.26243 q^{89} -15.6862 q^{91} -3.57689 q^{92} -1.67278 q^{94} -4.39436 q^{95} -7.41268 q^{97} +2.73516 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 12 q^{4} + q^{5} - q^{7} - 6 q^{8} + 2 q^{10} - 3 q^{13} - 8 q^{16} - 20 q^{17} + 3 q^{19} + 5 q^{20} + 10 q^{23} + 7 q^{25} - 2 q^{26} - 19 q^{28} - 21 q^{29} + 6 q^{31} - 9 q^{32} - 4 q^{34}+ \cdots - 82 q^{98}+O(q^{100}) \) 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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