LMFDB - Embedded newform 9801.2.a.cp.1.9

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			1.9
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	$-0.532145\pi$
$2$	−0.285148	−0.201630	−0.100815	+	0.994905i	$0.532145\pi$
$3$	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	$-0.779638\pi$
$7$	−4.07334	−1.53958	−0.769788	+	0.638300i	$0.779638\pi$
$8$	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	$-0.320676\pi$
$13$	3.85096	1.06806	0.534032	+	0.845465i	$0.320676\pi$
$14$	1.16150	0.310425
$15$	0	0
$16$	3.51875	0.879688
$17$	4.32020	1.04780	0.523902	−	0.851779i	$-0.324476\pi$
$17$	4.32020	1.04780	0.523902	+	0.851779i	$0.324476\pi$
$18$	0	0
$19$	−1.62229	−0.372180	−0.186090	−	0.982533i	$-0.559582\pi$
$19$	−1.62229	−0.372180	−0.186090	+	0.982533i	$0.559582\pi$
$20$	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	$-0.607022\pi$
$29$	−3.55334	−0.659840	−0.329920	+	0.944009i	$0.607022\pi$
$30$	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	$-0.680301\pi$
$41$	−6.87214	−1.07325	−0.536624	+	0.843821i	$0.680301\pi$
$42$	0	0
$43$	0.984991	0.150210	0.0751049	−	0.997176i	$-0.476071\pi$
$43$	0.984991	0.150210	0.0751049	+	0.997176i	$0.476071\pi$
$44$	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	$-0.685768\pi$
$61$	−8.60748	−1.10207	−0.551037	+	0.834481i	$0.685768\pi$
$62$	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	$-0.576102\pi$
$73$	−4.04662	−0.473622	−0.236811	+	0.971556i	$0.576102\pi$
$74$	−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	$-0.577402\pi$
$79$	−4.28015	−0.481554	−0.240777	+	0.970580i	$0.577402\pi$
$80$	−9.53137	−1.06564
$81$	0	0
$82$	1.95958	0.216400
$83$	6.50019	0.713488	0.356744	−	0.934202i	$-0.383887\pi$
$83$	6.50019	0.713488	0.356744	+	0.934202i	$0.383887\pi$
$84$	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	$-0.260903\pi$
$101$	13.7176	1.36495	0.682476	+	0.730908i	$0.260903\pi$
$102$	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	$-0.457113\pi$
$107$	2.77898	0.268654	0.134327	+	0.990937i	$0.457113\pi$
$108$	0	0
$109$	−17.3573	−1.66253	−0.831263	−	0.555879i	$-0.812382\pi$
$109$	−17.3573	−1.66253	−0.831263	+	0.555879i	$0.812382\pi$
$110$	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	$-0.465325\pi$
$127$	2.45040	0.217438	0.108719	+	0.994073i	$0.465325\pi$
$128$	8.21980	0.726535
$129$	0	0
$130$	2.97444	0.260876
$131$	−3.99737	−0.349252	−0.174626	−	0.984635i	$-0.555872\pi$
$131$	−3.99737	−0.349252	−0.174626	+	0.984635i	$0.555872\pi$
$132$	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	$-0.460958\pi$
$139$	2.88493	0.244696	0.122348	+	0.992487i	$0.460958\pi$
$140$	−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	$-0.809611\pi$
$149$	−20.1748	−1.65279	−0.826393	+	0.563094i	$0.809611\pi$
$150$	0	0
$151$	−11.0784	−0.901544	−0.450772	−	0.892639i	$-0.648851\pi$
$151$	−11.0784	−0.901544	−0.450772	+	0.892639i	$0.648851\pi$
$152$	−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	$-0.238658\pi$
$167$	18.9152	1.46370	0.731849	+	0.681467i	$0.238658\pi$
$168$	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	$-0.481669\pi$
$173$	1.51409	0.115114	0.0575570	+	0.998342i	$0.481669\pi$
$174$	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	$-0.791594\pi$
$193$	−22.0394	−1.58643	−0.793214	+	0.608942i	$0.791594\pi$
$194$	2.11371	0.151756
$195$	0	0
$196$	−18.4042	−1.31459
$197$	−18.2247	−1.29845	−0.649227	−	0.760595i	$-0.724907\pi$
$197$	−18.2247	−1.29845	−0.649227	+	0.760595i	$0.724907\pi$
$198$	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	$-0.408117\pi$
$211$	8.27002	0.569332	0.284666	+	0.958627i	$0.408117\pi$
$212$	−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	$-0.283634\pi$
$227$	18.9412	1.25717	0.628586	+	0.777740i	$0.283634\pi$
$228$	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	$-0.430963\pi$
$233$	6.56942	0.430377	0.215188	+	0.976573i	$0.430963\pi$
$234$	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	$-0.190484\pi$
$239$	25.5463	1.65245	0.826226	+	0.563339i	$0.190484\pi$
$240$	0	0
$241$	−2.98198	−0.192086	−0.0960432	−	0.995377i	$-0.530619\pi$
$241$	−2.98198	−0.192086	−0.0960432	+	0.995377i	$0.530619\pi$
$242$	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	$-0.590373\pi$
$263$	−9.08545	−0.560233	−0.280117	+	0.959966i	$0.590373\pi$
$264$	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	$-0.463923\pi$
$271$	3.72364	0.226195	0.113097	+	0.993584i	$0.463923\pi$
$272$	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	$-0.537386\pi$
$277$	−3.90064	−0.234367	−0.117183	+	0.993110i	$0.537386\pi$
$278$	−0.822632	−0.0493382
$279$	0	0
$280$	12.3290	0.736799
$281$	−0.0396231	−0.00236371	−0.00118186	−	0.999999i	$-0.500376\pi$
$281$	−0.0396231	−0.00236371	−0.00118186	+	0.999999i	$0.500376\pi$
$282$	0	0
$283$	6.39387	0.380076	0.190038	−	0.981777i	$-0.439139\pi$
$283$	6.39387	0.380076	0.190038	+	0.981777i	$0.439139\pi$
$284$	−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	$-0.260353\pi$
$293$	23.4074	1.36748	0.683738	+	0.729728i	$0.260353\pi$
$294$	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	$-0.187298\pi$
$307$	29.1494	1.66365	0.831823	+	0.555042i	$0.187298\pi$
$308$	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	$-0.665070\pi$
$337$	−18.1978	−0.991298	−0.495649	+	0.868523i	$0.665070\pi$
$338$	−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	$-0.236791\pi$
$347$	27.4141	1.47167	0.735833	+	0.677163i	$0.236791\pi$
$348$	0	0
$349$	22.9055	1.22610	0.613052	−	0.790042i	$-0.289941\pi$
$349$	22.9055	1.22610	0.613052	+	0.790042i	$0.289941\pi$
$350$	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	$-0.0746436\pi$
$359$	36.8574	1.94526	0.972631	+	0.232356i	$0.0746436\pi$
$360$	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	$-0.343089\pi$
$373$	18.2790	0.946453	0.473227	+	0.880941i	$0.343089\pi$
$374$	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	$-0.481021\pi$
$409$	2.41020	0.119177	0.0595883	+	0.998223i	$0.481021\pi$
$410$	−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	$-0.251938\pi$
$431$	29.1806	1.40558	0.702789	+	0.711398i	$0.251938\pi$
$432$	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	$-0.671469\pi$
$439$	−21.4975	−1.02602	−0.513009	+	0.858383i	$0.671469\pi$
$440$	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	$-0.159292\pi$
$457$	37.5123	1.75475	0.877376	+	0.479803i	$0.159292\pi$
$458$	2.24111	0.104720
$459$	0	0
$460$	9.68884	0.451745
$461$	−19.3653	−0.901932	−0.450966	−	0.892541i	$-0.648920\pi$
$461$	−19.3653	−0.901932	−0.450966	+	0.892541i	$0.648920\pi$
$462$	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	$-0.321657\pi$
$479$	23.2616	1.06285	0.531426	+	0.847105i	$0.321657\pi$
$480$	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	$-0.469741\pi$
$491$	4.20656	0.189839	0.0949196	+	0.995485i	$0.469741\pi$
$492$	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	$-0.527823\pi$
$503$	−3.91570	−0.174592	−0.0872961	+	0.996182i	$0.527823\pi$
$504$	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	$-0.758130\pi$
$523$	−33.1573	−1.44987	−0.724934	+	0.688818i	$0.758130\pi$
$524$	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	$-0.709560\pi$
$541$	−28.4609	−1.22363	−0.611815	+	0.791001i	$0.709560\pi$
$542$	−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	$-0.728308\pi$
$547$	−30.7466	−1.31463	−0.657316	+	0.753615i	$0.728308\pi$
$548$	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	$-0.450610\pi$
$557$	7.29459	0.309082	0.154541	+	0.987986i	$0.450610\pi$
$558$	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	$-0.219910\pi$
$563$	36.5734	1.54139	0.770693	+	0.637206i	$0.219910\pi$
$564$	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	$-0.501011\pi$
$569$	−0.151484	−0.00635053	−0.00317527	+	0.999995i	$0.501011\pi$
$570$	0	0
$571$	43.2254	1.80893	0.904463	−	0.426552i	$-0.140272\pi$
$571$	43.2254	1.80893	0.904463	+	0.426552i	$0.140272\pi$
$572$	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	$-0.343955\pi$
$593$	22.9308	0.941656	0.470828	+	0.882225i	$0.343955\pi$
$594$	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	$-0.348399\pi$
$601$	22.4788	0.916930	0.458465	+	0.888712i	$0.348399\pi$
$602$	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	$-0.317684\pi$
$607$	26.7047	1.08391	0.541956	+	0.840407i	$0.317684\pi$
$608$	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	$-0.841229\pi$
$613$	−43.4844	−1.75632	−0.878160	+	0.478367i	$0.841229\pi$
$614$	−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	$-0.357822\pi$
$659$	22.1777	0.863921	0.431961	+	0.901892i	$0.357822\pi$
$660$	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	$-0.262297\pi$
$673$	35.2435	1.35854	0.679269	+	0.733889i	$0.262297\pi$
$674$	5.18907	0.199876
$675$	0	0
$676$	−3.51094	−0.135036
$677$	44.0500	1.69298	0.846489	−	0.532406i	$-0.178712\pi$
$677$	44.0500	1.69298	0.846489	+	0.532406i	$0.178712\pi$
$678$	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	$-0.807401\pi$
$701$	−43.5518	−1.64493	−0.822465	+	0.568816i	$0.807401\pi$
$702$	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	$-0.496683\pi$
$733$	0.564191	0.0208389	0.0104194	+	0.999946i	$0.496683\pi$
$734$	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	$-0.488592\pi$
$739$	1.94812	0.0716629	0.0358315	+	0.999358i	$0.488592\pi$
$740$	40.2498	1.47961
$741$	0	0
$742$	1.82568	0.0670229
$743$	27.2627	1.00017	0.500086	−	0.865976i	$-0.333302\pi$
$743$	27.2627	1.00017	0.500086	+	0.865976i	$0.333302\pi$
$744$	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	$-0.293451\pi$
$761$	33.3410	1.20861	0.604304	+	0.796754i	$0.293451\pi$
$762$	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	$-0.885959\pi$
$769$	−51.9401	−1.87301	−0.936504	+	0.350656i	$0.885959\pi$
$770$	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	$-0.614236\pi$
$787$	−19.7063	−0.702454	−0.351227	+	0.936290i	$0.614236\pi$
$788$	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	$-0.380068\pi$
$809$	20.9298	0.735854	0.367927	+	0.929855i	$0.380068\pi$
$810$	0	0
$811$	1.94293	0.0682255	0.0341127	−	0.999418i	$-0.489139\pi$
$811$	1.94293	0.0682255	0.0341127	+	0.999418i	$0.489139\pi$
$812$	−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	$-0.560586\pi$
$821$	−10.8418	−0.378380	−0.189190	+	0.981940i	$0.560586\pi$
$822$	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	$-0.725451\pi$
$827$	−37.4150	−1.30105	−0.650524	+	0.759486i	$0.725451\pi$
$828$	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	$-0.248761\pi$
$853$	41.4642	1.41971	0.709854	+	0.704349i	$0.248761\pi$
$854$	−9.99763	−0.342112
$855$	0	0
$856$	3.10525	0.106135
$857$	−18.4055	−0.628719	−0.314359	−	0.949304i	$-0.601790\pi$
$857$	−18.4055	−0.628719	−0.314359	+	0.949304i	$0.601790\pi$
$858$	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	$-0.633245\pi$
$877$	−24.0754	−0.812967	−0.406484	+	0.913658i	$0.633245\pi$
$878$	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	$-0.486247\pi$
$887$	2.57271	0.0863831	0.0431915	+	0.999067i	$0.486247\pi$
$888$	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	$-0.440794\pi$
$919$	11.2124	0.369864	0.184932	+	0.982751i	$0.440794\pi$
$920$	−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	$-0.401436\pi$
$937$	18.6555	0.609448	0.304724	+	0.952441i	$0.401436\pi$
$938$	−2.02167	−0.0660100
$939$	0	0
$940$	−30.4887	−0.994432
$941$	32.4926	1.05923	0.529615	−	0.848238i	$-0.322337\pi$
$941$	32.4926	1.05923	0.529615	+	0.848238i	$0.322337\pi$
$942$	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	$-0.600054\pi$
$953$	−19.0891	−0.618358	−0.309179	+	0.951004i	$0.600054\pi$
$954$	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	$-0.359536\pi$
$967$	26.5627	0.854198	0.427099	+	0.904205i	$0.359536\pi$
$968$	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	$-0.700559\pi$
$997$	−37.2087	−1.17841	−0.589205	+	0.807983i	$0.700559\pi$
$998$	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.cp.1.9		18
3.2	odd	2		9801.2.a.cm.1.10		18
9.2	odd	6		1089.2.e.p.364.9		36
9.5	odd	6		1089.2.e.p.727.9		36
11.3	even	5		891.2.f.e.163.5		36
11.4	even	5		891.2.f.e.82.5		36
11.10	odd	2		9801.2.a.cn.1.10		18
33.14	odd	10		891.2.f.f.163.5		36
33.26	odd	10		891.2.f.f.82.5		36
33.32	even	2		9801.2.a.co.1.9		18
99.4	even	15		297.2.n.b.181.5		72
99.14	odd	30		99.2.m.b.97.5	yes	72
99.25	even	15		297.2.n.b.64.5		72
99.32	even	6		1089.2.e.o.727.10		36
99.47	odd	30		99.2.m.b.31.5	yes	72
99.58	even	15		297.2.n.b.262.5		72
99.59	odd	30		99.2.m.b.16.5	✓	72
99.65	even	6		1089.2.e.o.364.10		36
99.70	even	15		297.2.n.b.280.5		72
99.92	odd	30		99.2.m.b.49.5	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.16.5	✓	72	99.59	odd	30
99.2.m.b.31.5	yes	72	99.47	odd	30
99.2.m.b.49.5	yes	72	99.92	odd	30
99.2.m.b.97.5	yes	72	99.14	odd	30
297.2.n.b.64.5		72	99.25	even	15
297.2.n.b.181.5		72	99.4	even	15
297.2.n.b.262.5		72	99.58	even	15
297.2.n.b.280.5		72	99.70	even	15
891.2.f.e.82.5		36	11.4	even	5
891.2.f.e.163.5		36	11.3	even	5
891.2.f.f.82.5		36	33.26	odd	10
891.2.f.f.163.5		36	33.14	odd	10
1089.2.e.o.364.10		36	99.65	even	6
1089.2.e.o.727.10		36	99.32	even	6
1089.2.e.p.364.9		36	9.2	odd	6
1089.2.e.p.727.9		36	9.5	odd	6
9801.2.a.cm.1.10		18	3.2	odd	2
9801.2.a.cn.1.10		18	11.10	odd	2
9801.2.a.co.1.9		18	33.32	even	2
9801.2.a.cp.1.9		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)

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