LMFDB - Embedded newform 7803.2.a.bs.1.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [7803,2,Mod(1,7803)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("7803.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(7803, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 7803 = 3^{3} \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7803.a (trivial)

Newform invariants

comment:select newform

sage:traces = [10,0,0,12,2,0,0,0,0,0,-22,0,0,0,0,16,0,0,-10,-8,0,0,-28,0,8, 0,0,0,-6,0,0,0,0,0,0,0,0,0,0,0,-28,0,-8,-76,0,0,0,0,2,0,0,-4,0,0,42,64, 0,0,0,0,0,-52,0,-36,-32,0,18,0,0,-72,50,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(73)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$62.3072686972$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 16x^{8} + 86x^{6} - 170x^{4} + 73x^{2} - 8 $ x^10 - 16x^8 + 86x^6 - 170x^4 + 73x^2 - 8
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 459)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$2.60924$ of defining polynomial
Character	$\chi$	$=$	7803.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.60924 q^{2} +4.80812 q^{4} -2.94788 q^{5} +3.30360 q^{7} +7.32705 q^{8} -7.69173 q^{10} -6.06599 q^{11} -1.60601 q^{13} +8.61988 q^{14} +9.50178 q^{16} -0.742135 q^{19} -14.1738 q^{20} -15.8276 q^{22} -4.08401 q^{23} +3.69002 q^{25} -4.19047 q^{26} +15.8841 q^{28} -4.66836 q^{29} -9.07096 q^{31} +10.1383 q^{32} -9.73864 q^{35} -0.500659 q^{37} -1.93641 q^{38} -21.5993 q^{40} +4.53588 q^{41} -5.03817 q^{43} -29.1660 q^{44} -10.6561 q^{46} -7.27488 q^{47} +3.91379 q^{49} +9.62814 q^{50} -7.72191 q^{52} +1.02721 q^{53} +17.8818 q^{55} +24.2057 q^{56} -12.1809 q^{58} -3.06288 q^{59} +7.67019 q^{61} -23.6683 q^{62} +7.44967 q^{64} +4.73434 q^{65} -0.749419 q^{67} -25.4104 q^{70} +14.8158 q^{71} +3.54948 q^{73} -1.30634 q^{74} -3.56828 q^{76} -20.0396 q^{77} -1.15943 q^{79} -28.0101 q^{80} +11.8352 q^{82} +3.75916 q^{83} -13.1458 q^{86} -44.4458 q^{88} -3.43898 q^{89} -5.30563 q^{91} -19.6364 q^{92} -18.9819 q^{94} +2.18773 q^{95} -15.6128 q^{97} +10.2120 q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 12 q^{4} + 2 q^{5} - 22 q^{11} + 16 q^{16} - 10 q^{19} - 8 q^{20} - 28 q^{23} + 8 q^{25} - 6 q^{29} - 28 q^{41} - 8 q^{43} - 76 q^{44} + 2 q^{49} - 4 q^{52} + 42 q^{55} + 64 q^{56} - 52 q^{62} - 36 q^{64}+ \cdots - 38 q^{95}+O(q^{100}) $ 10 * q + 12 * q^4 + 2 * q^5 - 22 * q^11 + 16 * q^16 - 10 * q^19 - 8 * q^20 - 28 * q^23 + 8 * q^25 - 6 * q^29 - 28 * q^41 - 8 * q^43 - 76 * q^44 + 2 * q^49 - 4 * q^52 + 42 * q^55 + 64 * q^56 - 52 * q^62 - 36 * q^64 - 32 * q^65 + 18 * q^67 - 72 * q^70 + 50 * q^71 - 56 * q^74 - 28 * q^76 - 80 * q^80 - 56 * q^92 - 20 * q^94 - 38 * q^95

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.60924	1.84501	0.922505	−	0.385986i	$-0.126139\pi$
$2$	2.60924	1.84501	0.922505	+	0.385986i	$0.126139\pi$
$3$	0	0
$3$	0	0
$4$	4.80812	2.40406
$5$	−2.94788	−1.31833	−0.659167	−	0.751997i	$-0.729091\pi$
$5$	−2.94788	−1.31833	−0.659167	+	0.751997i	$0.729091\pi$
$6$	0	0
$7$	3.30360	1.24864	0.624322	−	0.781167i	$-0.285375\pi$
$7$	3.30360	1.24864	0.624322	+	0.781167i	$0.285375\pi$
$8$	7.32705	2.59050
$9$	0	0
$10$	−7.69173	−2.43234
$11$	−6.06599	−1.82896	−0.914482	−	0.404627i	$-0.867401\pi$
$11$	−6.06599	−1.82896	−0.914482	+	0.404627i	$0.867401\pi$
$12$	0	0
$13$	−1.60601	−0.445428	−0.222714	−	0.974884i	$-0.571492\pi$
$13$	−1.60601	−0.445428	−0.222714	+	0.974884i	$0.571492\pi$
$14$	8.61988	2.30376
$15$	0	0
$16$	9.50178	2.37545
$17$	0	0
$17$	0	0
$18$	0	0
$19$	−0.742135	−0.170258	−0.0851288	−	0.996370i	$-0.527130\pi$
$19$	−0.742135	−0.170258	−0.0851288	+	0.996370i	$0.527130\pi$
$20$	−14.1738	−3.16935
$21$	0	0
$22$	−15.8276	−3.37445
$23$	−4.08401	−0.851574	−0.425787	−	0.904823i	$-0.640003\pi$
$23$	−4.08401	−0.851574	−0.425787	+	0.904823i	$0.640003\pi$
$24$	0	0
$25$	3.69002	0.738004
$26$	−4.19047	−0.821819
$27$	0	0
$28$	15.8841	3.00182
$29$	−4.66836	−0.866892	−0.433446	−	0.901180i	$-0.642703\pi$
$29$	−4.66836	−0.866892	−0.433446	+	0.901180i	$0.642703\pi$
$30$	0	0
$31$	−9.07096	−1.62919	−0.814596	−	0.580029i	$-0.803041\pi$
$31$	−9.07096	−1.62919	−0.814596	+	0.580029i	$0.803041\pi$
$32$	10.1383	1.79221
$33$	0	0
$34$	0	0
$35$	−9.73864	−1.64613
$36$	0	0
$37$	−0.500659	−0.0823079	−0.0411539	−	0.999153i	$-0.513103\pi$
$37$	−0.500659	−0.0823079	−0.0411539	+	0.999153i	$0.513103\pi$
$38$	−1.93641	−0.314127
$39$	0	0
$40$	−21.5993	−3.41515
$41$	4.53588	0.708385	0.354193	−	0.935173i	$-0.384756\pi$
$41$	4.53588	0.708385	0.354193	+	0.935173i	$0.384756\pi$
$42$	0	0
$43$	−5.03817	−0.768313	−0.384157	−	0.923268i	$-0.625508\pi$
$43$	−5.03817	−0.768313	−0.384157	+	0.923268i	$0.625508\pi$
$44$	−29.1660	−4.39694
$45$	0	0
$46$	−10.6561	−1.57116
$47$	−7.27488	−1.06115	−0.530575	−	0.847638i	$-0.678024\pi$
$47$	−7.27488	−1.06115	−0.530575	+	0.847638i	$0.678024\pi$
$48$	0	0
$49$	3.91379	0.559113
$50$	9.62814	1.36162
$51$	0	0
$52$	−7.72191	−1.07084
$53$	1.02721	0.141097	0.0705487	−	0.997508i	$-0.477525\pi$
$53$	1.02721	0.141097	0.0705487	+	0.997508i	$0.477525\pi$
$54$	0	0
$55$	17.8818	2.41118
$56$	24.2057	3.23462
$57$	0	0
$58$	−12.1809	−1.59942
$59$	−3.06288	−0.398753	−0.199376	−	0.979923i	$-0.563892\pi$
$59$	−3.06288	−0.398753	−0.199376	+	0.979923i	$0.563892\pi$
$60$	0	0
$61$	7.67019	0.982068	0.491034	−	0.871140i	$-0.336619\pi$
$61$	7.67019	0.982068	0.491034	+	0.871140i	$0.336619\pi$
$62$	−23.6683	−3.00587
$63$	0	0
$64$	7.44967	0.931208
$65$	4.73434	0.587223
$66$	0	0
$67$	−0.749419	−0.0915561	−0.0457781	−	0.998952i	$-0.514577\pi$
$67$	−0.749419	−0.0915561	−0.0457781	+	0.998952i	$0.514577\pi$
$68$	0	0
$69$	0	0
$70$	−25.4104	−3.03713
$71$	14.8158	1.75832	0.879158	−	0.476530i	$-0.158106\pi$
$71$	14.8158	1.75832	0.879158	+	0.476530i	$0.158106\pi$
$72$	0	0
$73$	3.54948	0.415435	0.207717	−	0.978189i	$-0.433397\pi$
$73$	3.54948	0.415435	0.207717	+	0.978189i	$0.433397\pi$
$74$	−1.30634	−0.151859
$75$	0	0
$76$	−3.56828	−0.409309
$77$	−20.0396	−2.28372
$78$	0	0
$79$	−1.15943	−0.130446	−0.0652230	−	0.997871i	$-0.520776\pi$
$79$	−1.15943	−0.130446	−0.0652230	+	0.997871i	$0.520776\pi$
$80$	−28.0101	−3.13163
$81$	0	0
$82$	11.8352	1.30698
$83$	3.75916	0.412622	0.206311	−	0.978486i	$-0.433854\pi$
$83$	3.75916	0.412622	0.206311	+	0.978486i	$0.433854\pi$
$84$	0	0
$85$	0	0
$86$	−13.1458	−1.41755
$87$	0	0
$88$	−44.4458	−4.73794
$89$	−3.43898	−0.364531	−0.182265	−	0.983249i	$-0.558343\pi$
$89$	−3.43898	−0.364531	−0.182265	+	0.983249i	$0.558343\pi$
$90$	0	0
$91$	−5.30563	−0.556181
$92$	−19.6364	−2.04724
$93$	0	0
$94$	−18.9819	−1.95783
$95$	2.18773	0.224456
$96$	0	0
$97$	−15.6128	−1.58524	−0.792618	−	0.609719i	$-0.791282\pi$
$97$	−15.6128	−1.58524	−0.792618	+	0.609719i	$0.791282\pi$
$98$	10.2120	1.03157
$99$	0	0
$100$	17.7421	1.77421
$101$	0.786481	0.0782578	0.0391289	−	0.999234i	$-0.487542\pi$
$101$	0.786481	0.0782578	0.0391289	+	0.999234i	$0.487542\pi$
$102$	0	0
$103$	10.0923	0.994423	0.497211	−	0.867629i	$-0.334357\pi$
$103$	10.0923	0.994423	0.497211	+	0.867629i	$0.334357\pi$
$104$	−11.7673	−1.15388
$105$	0	0
$106$	2.68022	0.260326
$107$	−16.1738	−1.56358	−0.781789	−	0.623543i	$-0.785693\pi$
$107$	−16.1738	−1.56358	−0.781789	+	0.623543i	$0.785693\pi$
$108$	0	0
$109$	−13.3022	−1.27412	−0.637059	−	0.770815i	$-0.719849\pi$
$109$	−13.3022	−1.27412	−0.637059	+	0.770815i	$0.719849\pi$
$110$	46.6579	4.44866
$111$	0	0
$112$	31.3901	2.96609
$113$	−7.32021	−0.688627	−0.344314	−	0.938855i	$-0.611888\pi$
$113$	−7.32021	−0.688627	−0.344314	+	0.938855i	$0.611888\pi$
$114$	0	0
$115$	12.0392	1.12266
$116$	−22.4460	−2.08406
$117$	0	0
$118$	−7.99178	−0.735703
$119$	0	0
$120$	0	0
$121$	25.7962	2.34511
$122$	20.0134	1.81192
$123$	0	0
$124$	−43.6142	−3.91668
$125$	3.86167	0.345398
$126$	0	0
$127$	12.1675	1.07969	0.539846	−	0.841764i	$-0.318483\pi$
$127$	12.1675	1.07969	0.539846	+	0.841764i	$0.318483\pi$
$128$	−0.838650	−0.0741269
$129$	0	0
$130$	12.3530	1.08343
$131$	1.98757	0.173654	0.0868272	−	0.996223i	$-0.472327\pi$
$131$	1.98757	0.173654	0.0868272	+	0.996223i	$0.472327\pi$
$132$	0	0
$133$	−2.45172	−0.212591
$134$	−1.95541	−0.168922
$135$	0	0
$136$	0	0
$137$	−10.8410	−0.926206	−0.463103	−	0.886304i	$-0.653264\pi$
$137$	−10.8410	−0.926206	−0.463103	+	0.886304i	$0.653264\pi$
$138$	0	0
$139$	15.0567	1.27709	0.638546	−	0.769583i	$-0.279536\pi$
$139$	15.0567	1.27709	0.638546	+	0.769583i	$0.279536\pi$
$140$	−46.8245	−3.95740
$141$	0	0
$142$	38.6580	3.24411
$143$	9.74206	0.814672
$144$	0	0
$145$	13.7618	1.14285
$146$	9.26143	0.766481
$147$	0	0
$148$	−2.40723	−0.197873
$149$	−6.94955	−0.569329	−0.284665	−	0.958627i	$-0.591882\pi$
$149$	−6.94955	−0.569329	−0.284665	+	0.958627i	$0.591882\pi$
$150$	0	0
$151$	14.1742	1.15348	0.576740	−	0.816927i	$-0.304324\pi$
$151$	14.1742	1.15348	0.576740	+	0.816927i	$0.304324\pi$
$152$	−5.43766	−0.441053
$153$	0	0
$154$	−52.2881	−4.21349
$155$	26.7401	2.14782
$156$	0	0
$157$	9.63833	0.769223	0.384611	−	0.923079i	$-0.374335\pi$
$157$	9.63833	0.769223	0.384611	+	0.923079i	$0.374335\pi$
$158$	−3.02523	−0.240674
$159$	0	0
$160$	−29.8865	−2.36274
$161$	−13.4919	−1.06331
$162$	0	0
$163$	13.1122	1.02703	0.513514	−	0.858081i	$-0.328344\pi$
$163$	13.1122	1.02703	0.513514	+	0.858081i	$0.328344\pi$
$164$	21.8090	1.70300
$165$	0	0
$166$	9.80855	0.761291
$167$	−11.6752	−0.903455	−0.451727	−	0.892156i	$-0.649192\pi$
$167$	−11.6752	−0.903455	−0.451727	+	0.892156i	$0.649192\pi$
$168$	0	0
$169$	−10.4207	−0.801594
$170$	0	0
$171$	0	0
$172$	−24.2241	−1.84707
$173$	−22.7218	−1.72751	−0.863754	−	0.503913i	$-0.831893\pi$
$173$	−22.7218	−1.72751	−0.863754	+	0.503913i	$0.831893\pi$
$174$	0	0
$175$	12.1904	0.921504
$176$	−57.6377	−4.34460
$177$	0	0
$178$	−8.97311	−0.672563
$179$	−0.531696	−0.0397409	−0.0198704	−	0.999803i	$-0.506325\pi$
$179$	−0.531696	−0.0397409	−0.0198704	+	0.999803i	$0.506325\pi$
$180$	0	0
$181$	7.87988	0.585707	0.292853	−	0.956157i	$-0.405395\pi$
$181$	7.87988	0.585707	0.292853	+	0.956157i	$0.405395\pi$
$182$	−13.8437	−1.02616
$183$	0	0
$184$	−29.9237	−2.20601
$185$	1.47589	0.108509
$186$	0	0
$187$	0	0
$188$	−34.9785	−2.55107
$189$	0	0
$190$	5.70830	0.414124
$191$	−24.6325	−1.78234	−0.891171	−	0.453668i	$-0.850115\pi$
$191$	−24.6325	−1.78234	−0.891171	+	0.453668i	$0.850115\pi$
$192$	0	0
$193$	2.62349	0.188843	0.0944214	−	0.995532i	$-0.469900\pi$
$193$	2.62349	0.188843	0.0944214	+	0.995532i	$0.469900\pi$
$194$	−40.7374	−2.92477
$195$	0	0
$196$	18.8180	1.34414
$197$	11.7379	0.836291	0.418146	−	0.908380i	$-0.362680\pi$
$197$	11.7379	0.836291	0.418146	+	0.908380i	$0.362680\pi$
$198$	0	0
$199$	24.5477	1.74014	0.870071	−	0.492926i	$-0.164073\pi$
$199$	24.5477	1.74014	0.870071	+	0.492926i	$0.164073\pi$
$200$	27.0370	1.91180
$201$	0	0
$202$	2.05212	0.144386
$203$	−15.4224	−1.08244
$204$	0	0
$205$	−13.3712	−0.933888
$206$	26.3332	1.83472
$207$	0	0
$208$	−15.2600	−1.05809
$209$	4.50178	0.311395
$210$	0	0
$211$	−22.8230	−1.57120	−0.785599	−	0.618736i	$-0.787645\pi$
$211$	−22.8230	−1.57120	−0.785599	+	0.618736i	$0.787645\pi$
$212$	4.93893	0.339207
$213$	0	0
$214$	−42.2012	−2.88482
$215$	14.8519	1.01289
$216$	0	0
$217$	−29.9668	−2.03428
$218$	−34.7085	−2.35076
$219$	0	0
$220$	85.9779	5.79663
$221$	0	0
$222$	0	0
$223$	−18.1426	−1.21492	−0.607460	−	0.794350i	$-0.707812\pi$
$223$	−18.1426	−1.21492	−0.607460	+	0.794350i	$0.707812\pi$
$224$	33.4929	2.23784
$225$	0	0
$226$	−19.1002	−1.27052
$227$	−1.06204	−0.0704899	−0.0352449	−	0.999379i	$-0.511221\pi$
$227$	−1.06204	−0.0704899	−0.0352449	+	0.999379i	$0.511221\pi$
$228$	0	0
$229$	−1.11039	−0.0733765	−0.0366882	−	0.999327i	$-0.511681\pi$
$229$	−1.11039	−0.0733765	−0.0366882	+	0.999327i	$0.511681\pi$
$230$	31.4131	2.07132
$231$	0	0
$232$	−34.2053	−2.24569
$233$	1.70202	0.111503	0.0557516	−	0.998445i	$-0.482245\pi$
$233$	1.70202	0.111503	0.0557516	+	0.998445i	$0.482245\pi$
$234$	0	0
$235$	21.4455	1.39895
$236$	−14.7267	−0.958626
$237$	0	0
$238$	0	0
$239$	8.14337	0.526751	0.263375	−	0.964693i	$-0.415164\pi$
$239$	8.14337	0.526751	0.263375	+	0.964693i	$0.415164\pi$
$240$	0	0
$241$	7.35849	0.474002	0.237001	−	0.971509i	$-0.423836\pi$
$241$	7.35849	0.474002	0.237001	+	0.971509i	$0.423836\pi$
$242$	67.3084	4.32674
$243$	0	0
$244$	36.8792	2.36095
$245$	−11.5374	−0.737097
$246$	0	0
$247$	1.19188	0.0758375
$248$	−66.4634	−4.22043
$249$	0	0
$250$	10.0760	0.637263
$251$	−14.2157	−0.897289	−0.448644	−	0.893710i	$-0.648093\pi$
$251$	−14.2157	−0.897289	−0.448644	+	0.893710i	$0.648093\pi$
$252$	0	0
$253$	24.7735	1.55750
$254$	31.7479	1.99204
$255$	0	0
$256$	−17.0876	−1.06797
$257$	−10.0355	−0.625996	−0.312998	−	0.949754i	$-0.601333\pi$
$257$	−10.0355	−0.625996	−0.312998	+	0.949754i	$0.601333\pi$
$258$	0	0
$259$	−1.65398	−0.102773
$260$	22.7633	1.41172
$261$	0	0
$262$	5.18603	0.320394
$263$	−3.05298	−0.188255	−0.0941274	−	0.995560i	$-0.530006\pi$
$263$	−3.05298	−0.188255	−0.0941274	+	0.995560i	$0.530006\pi$
$264$	0	0
$265$	−3.02808	−0.186014
$266$	−6.39712	−0.392233
$267$	0	0
$268$	−3.60330	−0.220106
$269$	−0.715832	−0.0436451	−0.0218225	−	0.999762i	$-0.506947\pi$
$269$	−0.715832	−0.0436451	−0.0218225	+	0.999762i	$0.506947\pi$
$270$	0	0
$271$	−6.48834	−0.394139	−0.197069	−	0.980390i	$-0.563142\pi$
$271$	−6.48834	−0.394139	−0.197069	+	0.980390i	$0.563142\pi$
$272$	0	0
$273$	0	0
$274$	−28.2867	−1.70886
$275$	−22.3836	−1.34978
$276$	0	0
$277$	−8.80232	−0.528880	−0.264440	−	0.964402i	$-0.585187\pi$
$277$	−8.80232	−0.528880	−0.264440	+	0.964402i	$0.585187\pi$
$278$	39.2865	2.35625
$279$	0	0
$280$	−71.3555	−4.26431
$281$	22.4183	1.33737	0.668683	−	0.743548i	$-0.266858\pi$
$281$	22.4183	1.33737	0.668683	+	0.743548i	$0.266858\pi$
$282$	0	0
$283$	22.0106	1.30839	0.654197	−	0.756324i	$-0.273007\pi$
$283$	22.0106	1.30839	0.654197	+	0.756324i	$0.273007\pi$
$284$	71.2363	4.22710
$285$	0	0
$286$	25.4193	1.50308
$287$	14.9847	0.884521
$288$	0	0
$289$	0	0
$290$	35.9077	2.10858
$291$	0	0
$292$	17.0663	0.998730
$293$	−9.65322	−0.563947	−0.281974	−	0.959422i	$-0.590989\pi$
$293$	−9.65322	−0.563947	−0.281974	+	0.959422i	$0.590989\pi$
$294$	0	0
$295$	9.02901	0.525689
$296$	−3.66836	−0.213219
$297$	0	0
$298$	−18.1330	−1.05042
$299$	6.55897	0.379315
$300$	0	0
$301$	−16.6441	−0.959350
$302$	36.9839	2.12818
$303$	0	0
$304$	−7.05161	−0.404437
$305$	−22.6108	−1.29469
$306$	0	0
$307$	−2.26414	−0.129222	−0.0646108	−	0.997911i	$-0.520581\pi$
$307$	−2.26414	−0.129222	−0.0646108	+	0.997911i	$0.520581\pi$
$308$	−96.3528	−5.49021
$309$	0	0
$310$	69.7713	3.96275
$311$	16.9857	0.963169	0.481584	−	0.876400i	$-0.340061\pi$
$311$	16.9857	0.963169	0.481584	+	0.876400i	$0.340061\pi$
$312$	0	0
$313$	2.61460	0.147786	0.0738930	−	0.997266i	$-0.476458\pi$
$313$	2.61460	0.147786	0.0738930	+	0.997266i	$0.476458\pi$
$314$	25.1487	1.41922
$315$	0	0
$316$	−5.57467	−0.313600
$317$	−17.1609	−0.963853	−0.481927	−	0.876212i	$-0.660063\pi$
$317$	−17.1609	−0.963853	−0.481927	+	0.876212i	$0.660063\pi$
$318$	0	0
$319$	28.3182	1.58551
$320$	−21.9607	−1.22764
$321$	0	0
$322$	−35.2036	−1.96182
$323$	0	0
$324$	0	0
$325$	−5.92622	−0.328728
$326$	34.2129	1.89488
$327$	0	0
$328$	33.2346	1.83507
$329$	−24.0333	−1.32500
$330$	0	0
$331$	22.5719	1.24066	0.620332	−	0.784339i	$-0.286998\pi$
$331$	22.5719	1.24066	0.620332	+	0.784339i	$0.286998\pi$
$332$	18.0745	0.991968
$333$	0	0
$334$	−30.4634	−1.66688
$335$	2.20920	0.120702
$336$	0	0
$337$	6.76237	0.368370	0.184185	−	0.982892i	$-0.441035\pi$
$337$	6.76237	0.368370	0.184185	+	0.982892i	$0.441035\pi$
$338$	−27.1901	−1.47895
$339$	0	0
$340$	0	0
$341$	55.0243	2.97973
$342$	0	0
$343$	−10.1956	−0.550512
$344$	−36.9149	−1.99032
$345$	0	0
$346$	−59.2866	−3.18727
$347$	−10.8097	−0.580294	−0.290147	−	0.956982i	$-0.593704\pi$
$347$	−10.8097	−0.580294	−0.290147	+	0.956982i	$0.593704\pi$
$348$	0	0
$349$	−24.9056	−1.33317	−0.666583	−	0.745430i	$-0.732244\pi$
$349$	−24.9056	−1.33317	−0.666583	+	0.745430i	$0.732244\pi$
$350$	31.8075	1.70018
$351$	0	0
$352$	−61.4988	−3.27790
$353$	−7.53997	−0.401312	−0.200656	−	0.979662i	$-0.564307\pi$
$353$	−7.53997	−0.401312	−0.200656	+	0.979662i	$0.564307\pi$
$354$	0	0
$355$	−43.6754	−2.31805
$356$	−16.5350	−0.876354
$357$	0	0
$358$	−1.38732	−0.0733223
$359$	−21.4564	−1.13242	−0.566212	−	0.824260i	$-0.691592\pi$
$359$	−21.4564	−1.13242	−0.566212	+	0.824260i	$0.691592\pi$
$360$	0	0
$361$	−18.4492	−0.971012
$362$	20.5605	1.08063
$363$	0	0
$364$	−25.5101	−1.33709
$365$	−10.4634	−0.547682
$366$	0	0
$367$	−8.94128	−0.466731	−0.233365	−	0.972389i	$-0.574974\pi$
$367$	−8.94128	−0.466731	−0.233365	+	0.972389i	$0.574974\pi$
$368$	−38.8053	−2.02287
$369$	0	0
$370$	3.85094	0.200201
$371$	3.39348	0.176181
$372$	0	0
$373$	−23.4331	−1.21332	−0.606659	−	0.794962i	$-0.707491\pi$
$373$	−23.4331	−1.21332	−0.606659	+	0.794962i	$0.707491\pi$
$374$	0	0
$375$	0	0
$376$	−53.3035	−2.74892
$377$	7.49745	0.386138
$378$	0	0
$379$	15.7426	0.808642	0.404321	−	0.914617i	$-0.367508\pi$
$379$	15.7426	0.808642	0.404321	+	0.914617i	$0.367508\pi$
$380$	10.5189	0.539606
$381$	0	0
$382$	−64.2719	−3.28844
$383$	−2.47680	−0.126559	−0.0632793	−	0.997996i	$-0.520156\pi$
$383$	−2.47680	−0.126559	−0.0632793	+	0.997996i	$0.520156\pi$
$384$	0	0
$385$	59.0744	3.01071
$386$	6.84530	0.348417
$387$	0	0
$388$	−75.0680	−3.81100
$389$	17.9743	0.911332	0.455666	−	0.890151i	$-0.349401\pi$
$389$	17.9743	0.911332	0.455666	+	0.890151i	$0.349401\pi$
$390$	0	0
$391$	0	0
$392$	28.6765	1.44838
$393$	0	0
$394$	30.6270	1.54297
$395$	3.41786	0.171971
$396$	0	0
$397$	−12.5443	−0.629580	−0.314790	−	0.949161i	$-0.601934\pi$
$397$	−12.5443	−0.629580	−0.314790	+	0.949161i	$0.601934\pi$
$398$	64.0509	3.21058
$399$	0	0
$400$	35.0618	1.75309
$401$	14.8389	0.741021	0.370510	−	0.928828i	$-0.379183\pi$
$401$	14.8389	0.741021	0.370510	+	0.928828i	$0.379183\pi$
$402$	0	0
$403$	14.5681	0.725688
$404$	3.78150	0.188136
$405$	0	0
$406$	−40.2407	−1.99711
$407$	3.03699	0.150538
$408$	0	0
$409$	33.5394	1.65841	0.829207	−	0.558941i	$-0.188792\pi$
$409$	33.5394	1.65841	0.829207	+	0.558941i	$0.188792\pi$
$410$	−34.8887	−1.72303
$411$	0	0
$412$	48.5249	2.39065
$413$	−10.1185	−0.497900
$414$	0	0
$415$	−11.0816	−0.543973
$416$	−16.2822	−0.798303
$417$	0	0
$418$	11.7462	0.574526
$419$	34.8073	1.70045	0.850223	−	0.526423i	$-0.176467\pi$
$419$	34.8073	1.70045	0.850223	+	0.526423i	$0.176467\pi$
$420$	0	0
$421$	−39.1420	−1.90767	−0.953833	−	0.300337i	$-0.902901\pi$
$421$	−39.1420	−1.90767	−0.953833	+	0.300337i	$0.902901\pi$
$422$	−59.5505	−2.89887
$423$	0	0
$424$	7.52639	0.365514
$425$	0	0
$426$	0	0
$427$	25.3393	1.22625
$428$	−77.7655	−3.75894
$429$	0	0
$430$	38.7522	1.86880
$431$	18.9548	0.913022	0.456511	−	0.889718i	$-0.349099\pi$
$431$	18.9548	0.913022	0.456511	+	0.889718i	$0.349099\pi$
$432$	0	0
$433$	27.9754	1.34441	0.672206	−	0.740364i	$-0.265347\pi$
$433$	27.9754	1.34441	0.672206	+	0.740364i	$0.265347\pi$
$434$	−78.1906	−3.75327
$435$	0	0
$436$	−63.9585	−3.06305
$437$	3.03088	0.144987
$438$	0	0
$439$	13.6777	0.652801	0.326400	−	0.945232i	$-0.394164\pi$
$439$	13.6777	0.652801	0.326400	+	0.945232i	$0.394164\pi$
$440$	131.021	6.24618
$441$	0	0
$442$	0	0
$443$	−12.4388	−0.590987	−0.295493	−	0.955345i	$-0.595484\pi$
$443$	−12.4388	−0.590987	−0.295493	+	0.955345i	$0.595484\pi$
$444$	0	0
$445$	10.1377	0.480573
$446$	−47.3384	−2.24154
$447$	0	0
$448$	24.6107	1.16275
$449$	25.9018	1.22238	0.611190	−	0.791484i	$-0.290691\pi$
$449$	25.9018	1.22238	0.611190	+	0.791484i	$0.290691\pi$
$450$	0	0
$451$	−27.5146	−1.29561
$452$	−35.1964	−1.65550
$453$	0	0
$454$	−2.77111	−0.130055
$455$	15.6404	0.733233
$456$	0	0
$457$	15.7899	0.738620	0.369310	−	0.929306i	$-0.379594\pi$
$457$	15.7899	0.738620	0.369310	+	0.929306i	$0.379594\pi$
$458$	−2.89726	−0.135380
$459$	0	0
$460$	57.8858	2.69894
$461$	5.32484	0.248003	0.124001	−	0.992282i	$-0.460427\pi$
$461$	5.32484	0.248003	0.124001	+	0.992282i	$0.460427\pi$
$462$	0	0
$463$	−8.50127	−0.395088	−0.197544	−	0.980294i	$-0.563296\pi$
$463$	−8.50127	−0.395088	−0.197544	+	0.980294i	$0.563296\pi$
$464$	−44.3577	−2.05925
$465$	0	0
$466$	4.44098	0.205725
$467$	13.9040	0.643401	0.321701	−	0.946841i	$-0.395746\pi$
$467$	13.9040	0.643401	0.321701	+	0.946841i	$0.395746\pi$
$468$	0	0
$469$	−2.47578	−0.114321
$470$	55.9564	2.58108
$471$	0	0
$472$	−22.4419	−1.03297
$473$	30.5615	1.40522
$474$	0	0
$475$	−2.73849	−0.125651
$476$	0	0
$477$	0	0
$478$	21.2480	0.971860
$479$	38.7365	1.76991	0.884957	−	0.465672i	$-0.154187\pi$
$479$	38.7365	1.76991	0.884957	+	0.465672i	$0.154187\pi$
$480$	0	0
$481$	0.804066	0.0366622
$482$	19.2000	0.874538
$483$	0	0
$484$	124.031	5.63778
$485$	46.0246	2.08987
$486$	0	0
$487$	11.7126	0.530750	0.265375	−	0.964145i	$-0.414504\pi$
$487$	11.7126	0.530750	0.265375	+	0.964145i	$0.414504\pi$
$488$	56.1999	2.54405
$489$	0	0
$490$	−30.1038	−1.35995
$491$	−19.1773	−0.865460	−0.432730	−	0.901524i	$-0.642450\pi$
$491$	−19.1773	−0.865460	−0.432730	+	0.901524i	$0.642450\pi$
$492$	0	0
$493$	0	0
$494$	3.10990	0.139921
$495$	0	0
$496$	−86.1902	−3.87006
$497$	48.9456	2.19551
$498$	0	0
$499$	−31.5002	−1.41014	−0.705071	−	0.709136i	$-0.749085\pi$
$499$	−31.5002	−1.41014	−0.705071	+	0.709136i	$0.749085\pi$
$500$	18.5674	0.830359
$501$	0	0
$502$	−37.0922	−1.65551
$503$	12.5690	0.560425	0.280212	−	0.959938i	$-0.409595\pi$
$503$	12.5690	0.560425	0.280212	+	0.959938i	$0.409595\pi$
$504$	0	0
$505$	−2.31846	−0.103170
$506$	64.6400	2.87360
$507$	0	0
$508$	58.5028	2.59564
$509$	−14.9723	−0.663634	−0.331817	−	0.943344i	$-0.607662\pi$
$509$	−14.9723	−0.663634	−0.331817	+	0.943344i	$0.607662\pi$
$510$	0	0
$511$	11.7261	0.518730
$512$	−42.9082	−1.89629
$513$	0	0
$514$	−26.1849	−1.15497
$515$	−29.7509	−1.31098
$516$	0	0
$517$	44.1293	1.94081
$518$	−4.31562	−0.189618
$519$	0	0
$520$	34.6888	1.52120
$521$	−5.88454	−0.257806	−0.128903	−	0.991657i	$-0.541146\pi$
$521$	−5.88454	−0.257806	−0.128903	+	0.991657i	$0.541146\pi$
$522$	0	0
$523$	−19.0961	−0.835012	−0.417506	−	0.908674i	$-0.637096\pi$
$523$	−19.0961	−0.835012	−0.417506	+	0.908674i	$0.637096\pi$
$524$	9.55646	0.417476
$525$	0	0
$526$	−7.96595	−0.347332
$527$	0	0
$528$	0	0
$529$	−6.32090	−0.274822
$530$	−7.90098	−0.343197
$531$	0	0
$532$	−11.7882	−0.511082
$533$	−7.28468	−0.315535
$534$	0	0
$535$	47.6784	2.06132
$536$	−5.49103	−0.237177
$537$	0	0
$538$	−1.86778	−0.0805255
$539$	−23.7410	−1.02260
$540$	0	0
$541$	4.09222	0.175938	0.0879692	−	0.996123i	$-0.471962\pi$
$541$	4.09222	0.175938	0.0879692	+	0.996123i	$0.471962\pi$
$542$	−16.9296	−0.727190
$543$	0	0
$544$	0	0
$545$	39.2133	1.67971
$546$	0	0
$547$	−33.2481	−1.42159	−0.710794	−	0.703400i	$-0.751664\pi$
$547$	−33.2481	−1.42159	−0.710794	+	0.703400i	$0.751664\pi$
$548$	−52.1247	−2.22666
$549$	0	0
$550$	−58.4041	−2.49036
$551$	3.46455	0.147595
$552$	0	0
$553$	−3.83029	−0.162881
$554$	−22.9673	−0.975788
$555$	0	0
$556$	72.3944	3.07021
$557$	35.9740	1.52427	0.762133	−	0.647421i	$-0.224152\pi$
$557$	35.9740	1.52427	0.762133	+	0.647421i	$0.224152\pi$
$558$	0	0
$559$	8.09137	0.342228
$560$	−92.5344	−3.91029
$561$	0	0
$562$	58.4948	2.46745
$563$	−21.9711	−0.925971	−0.462985	−	0.886366i	$-0.653222\pi$
$563$	−21.9711	−0.925971	−0.462985	+	0.886366i	$0.653222\pi$
$564$	0	0
$565$	21.5791	0.907841
$566$	57.4309	2.41400
$567$	0	0
$568$	108.556	4.55493
$569$	−21.3880	−0.896631	−0.448315	−	0.893875i	$-0.647976\pi$
$569$	−21.3880	−0.896631	−0.448315	+	0.893875i	$0.647976\pi$
$570$	0	0
$571$	−30.0947	−1.25942	−0.629712	−	0.776829i	$-0.716827\pi$
$571$	−30.0947	−1.25942	−0.629712	+	0.776829i	$0.716827\pi$
$572$	46.8410	1.95852
$573$	0	0
$574$	39.0987	1.63195
$575$	−15.0701	−0.628465
$576$	0	0
$577$	21.6490	0.901260	0.450630	−	0.892711i	$-0.351199\pi$
$577$	21.6490	0.901260	0.450630	+	0.892711i	$0.351199\pi$
$578$	0	0
$579$	0	0
$580$	66.1683	2.74749
$581$	12.4188	0.515218
$582$	0	0
$583$	−6.23101	−0.258062
$584$	26.0072	1.07619
$585$	0	0
$586$	−25.1875	−1.04049
$587$	42.0603	1.73602	0.868008	−	0.496551i	$-0.165400\pi$
$587$	42.0603	1.73602	0.868008	+	0.496551i	$0.165400\pi$
$588$	0	0
$589$	6.73188	0.277382
$590$	23.5588	0.969902
$591$	0	0
$592$	−4.75715	−0.195518
$593$	32.3349	1.32784	0.663918	−	0.747806i	$-0.268893\pi$
$593$	32.3349	1.32784	0.663918	+	0.747806i	$0.268893\pi$
$594$	0	0
$595$	0	0
$596$	−33.4143	−1.36870
$597$	0	0
$598$	17.1139	0.699840
$599$	34.4979	1.40955	0.704773	−	0.709433i	$-0.251049\pi$
$599$	34.4979	1.40955	0.704773	+	0.709433i	$0.251049\pi$
$600$	0	0
$601$	14.4066	0.587658	0.293829	−	0.955858i	$-0.405070\pi$
$601$	14.4066	0.587658	0.293829	+	0.955858i	$0.405070\pi$
$602$	−43.4284	−1.77001
$603$	0	0
$604$	68.1513	2.77304
$605$	−76.0441	−3.09163
$606$	0	0
$607$	43.6878	1.77323	0.886617	−	0.462504i	$-0.153049\pi$
$607$	43.6878	1.77323	0.886617	+	0.462504i	$0.153049\pi$
$608$	−7.52399	−0.305138
$609$	0	0
$610$	−58.9971	−2.38872
$611$	11.6836	0.472666
$612$	0	0
$613$	−10.1396	−0.409536	−0.204768	−	0.978811i	$-0.565644\pi$
$613$	−10.1396	−0.409536	−0.204768	+	0.978811i	$0.565644\pi$
$614$	−5.90769	−0.238415
$615$	0	0
$616$	−146.831	−5.91600
$617$	−24.8202	−0.999222	−0.499611	−	0.866250i	$-0.666524\pi$
$617$	−24.8202	−0.999222	−0.499611	+	0.866250i	$0.666524\pi$
$618$	0	0
$619$	−28.4588	−1.14386	−0.571929	−	0.820303i	$-0.693805\pi$
$619$	−28.4588	−1.14386	−0.571929	+	0.820303i	$0.693805\pi$
$620$	128.570	5.16348
$621$	0	0
$622$	44.3196	1.77706
$623$	−11.3610	−0.455169
$624$	0	0
$625$	−29.8339	−1.19335
$626$	6.82211	0.272667
$627$	0	0
$628$	46.3423	1.84926
$629$	0	0
$630$	0	0
$631$	−28.1728	−1.12154	−0.560772	−	0.827971i	$-0.689495\pi$
$631$	−28.1728	−1.12154	−0.560772	+	0.827971i	$0.689495\pi$
$632$	−8.49520	−0.337921
$633$	0	0
$634$	−44.7769	−1.77832
$635$	−35.8684	−1.42339
$636$	0	0
$637$	−6.28560	−0.249044
$638$	73.8889	2.92529
$639$	0	0
$640$	2.47224	0.0977240
$641$	44.9354	1.77484	0.887421	−	0.460960i	$-0.152495\pi$
$641$	44.9354	1.77484	0.887421	+	0.460960i	$0.152495\pi$
$642$	0	0
$643$	2.49228	0.0982857	0.0491429	−	0.998792i	$-0.484351\pi$
$643$	2.49228	0.0982857	0.0491429	+	0.998792i	$0.484351\pi$
$644$	−64.8708	−2.55627
$645$	0	0
$646$	0	0
$647$	−17.6826	−0.695176	−0.347588	−	0.937647i	$-0.612999\pi$
$647$	−17.6826	−0.695176	−0.347588	+	0.937647i	$0.612999\pi$
$648$	0	0
$649$	18.5794	0.729304
$650$	−15.4629	−0.606506
$651$	0	0
$652$	63.0451	2.46904
$653$	−20.6116	−0.806594	−0.403297	−	0.915069i	$-0.632136\pi$
$653$	−20.6116	−0.806594	−0.403297	+	0.915069i	$0.632136\pi$
$654$	0	0
$655$	−5.85911	−0.228934
$656$	43.0989	1.68273
$657$	0	0
$658$	−62.7087	−2.44464
$659$	−19.1198	−0.744801	−0.372400	−	0.928072i	$-0.621465\pi$
$659$	−19.1198	−0.744801	−0.372400	+	0.928072i	$0.621465\pi$
$660$	0	0
$661$	−10.5164	−0.409041	−0.204521	−	0.978862i	$-0.565564\pi$
$661$	−10.5164	−0.409041	−0.204521	+	0.978862i	$0.565564\pi$
$662$	58.8955	2.28904
$663$	0	0
$664$	27.5436	1.06890
$665$	7.22738	0.280266
$666$	0	0
$667$	19.0656	0.738223
$668$	−56.1358	−2.17196
$669$	0	0
$670$	5.76433	0.222695
$671$	−46.5273	−1.79617
$672$	0	0
$673$	−42.6539	−1.64419	−0.822093	−	0.569353i	$-0.807194\pi$
$673$	−42.6539	−1.64419	−0.822093	+	0.569353i	$0.807194\pi$
$674$	17.6446	0.679646
$675$	0	0
$676$	−50.1041	−1.92708
$677$	−4.94952	−0.190226	−0.0951128	−	0.995467i	$-0.530321\pi$
$677$	−4.94952	−0.190226	−0.0951128	+	0.995467i	$0.530321\pi$
$678$	0	0
$679$	−51.5783	−1.97940
$680$	0	0
$681$	0	0
$682$	143.571	5.49763
$683$	16.2603	0.622183	0.311092	−	0.950380i	$-0.399305\pi$
$683$	16.2603	0.622183	0.311092	+	0.950380i	$0.399305\pi$
$684$	0	0
$685$	31.9579	1.22105
$686$	−26.6028	−1.01570
$687$	0	0
$688$	−47.8716	−1.82509
$689$	−1.64971	−0.0628488
$690$	0	0
$691$	7.66748	0.291685	0.145842	−	0.989308i	$-0.453411\pi$
$691$	7.66748	0.291685	0.145842	+	0.989308i	$0.453411\pi$
$692$	−109.249	−4.15303
$693$	0	0
$694$	−28.2050	−1.07065
$695$	−44.3854	−1.68363
$696$	0	0
$697$	0	0
$698$	−64.9847	−2.45971
$699$	0	0
$700$	58.6127	2.21535
$701$	8.05266	0.304145	0.152072	−	0.988369i	$-0.451405\pi$
$701$	8.05266	0.304145	0.152072	+	0.988369i	$0.451405\pi$
$702$	0	0
$703$	0.371557	0.0140135
$704$	−45.1896	−1.70315
$705$	0	0
$706$	−19.6736	−0.740425
$707$	2.59822	0.0977162
$708$	0	0
$709$	−9.11588	−0.342354	−0.171177	−	0.985240i	$-0.554757\pi$
$709$	−9.11588	−0.342354	−0.171177	+	0.985240i	$0.554757\pi$
$710$	−113.959	−4.27682
$711$	0	0
$712$	−25.1976	−0.944319
$713$	37.0458	1.38738
$714$	0	0
$715$	−28.7185	−1.07401
$716$	−2.55646	−0.0955394
$717$	0	0
$718$	−55.9847	−2.08933
$719$	22.2728	0.830634	0.415317	−	0.909677i	$-0.363671\pi$
$719$	22.2728	0.830634	0.415317	+	0.909677i	$0.363671\pi$
$720$	0	0
$721$	33.3409	1.24168
$722$	−48.1384	−1.79153
$723$	0	0
$724$	37.8874	1.40807
$725$	−17.2263	−0.639770
$726$	0	0
$727$	−10.0870	−0.374106	−0.187053	−	0.982350i	$-0.559894\pi$
$727$	−10.0870	−0.374106	−0.187053	+	0.982350i	$0.559894\pi$
$728$	−38.8746	−1.44079
$729$	0	0
$730$	−27.3016	−1.01048
$731$	0	0
$732$	0	0
$733$	−2.27909	−0.0841802	−0.0420901	−	0.999114i	$-0.513402\pi$
$733$	−2.27909	−0.0841802	−0.0420901	+	0.999114i	$0.513402\pi$
$734$	−23.3299	−0.861123
$735$	0	0
$736$	−41.4049	−1.52620
$737$	4.54597	0.167453
$738$	0	0
$739$	23.0008	0.846100	0.423050	−	0.906106i	$-0.360960\pi$
$739$	23.0008	0.846100	0.423050	+	0.906106i	$0.360960\pi$
$740$	7.09623	0.260863
$741$	0	0
$742$	8.85439	0.325055
$743$	−32.3634	−1.18730	−0.593650	−	0.804723i	$-0.702314\pi$
$743$	−32.3634	−1.18730	−0.593650	+	0.804723i	$0.702314\pi$
$744$	0	0
$745$	20.4865	0.750566
$746$	−61.1425	−2.23858
$747$	0	0
$748$	0	0
$749$	−53.4317	−1.95235
$750$	0	0
$751$	−2.18406	−0.0796974	−0.0398487	−	0.999206i	$-0.512688\pi$
$751$	−2.18406	−0.0796974	−0.0398487	+	0.999206i	$0.512688\pi$
$752$	−69.1244	−2.52071
$753$	0	0
$754$	19.5626	0.712429
$755$	−41.7839	−1.52067
$756$	0	0
$757$	−4.25848	−0.154777	−0.0773885	−	0.997001i	$-0.524658\pi$
$757$	−4.25848	−0.154777	−0.0773885	+	0.997001i	$0.524658\pi$
$758$	41.0761	1.49195
$759$	0	0
$760$	16.0296	0.581455
$761$	−26.7113	−0.968285	−0.484143	−	0.874989i	$-0.660868\pi$
$761$	−26.7113	−0.968285	−0.484143	+	0.874989i	$0.660868\pi$
$762$	0	0
$763$	−43.9451	−1.59092
$764$	−118.436	−4.28486
$765$	0	0
$766$	−6.46256	−0.233502
$767$	4.91902	0.177616
$768$	0	0
$769$	−14.6648	−0.528828	−0.264414	−	0.964409i	$-0.585178\pi$
$769$	−14.6648	−0.528828	−0.264414	+	0.964409i	$0.585178\pi$
$770$	154.139	5.55479
$771$	0	0
$772$	12.6140	0.453990
$773$	−21.0087	−0.755630	−0.377815	−	0.925881i	$-0.623325\pi$
$773$	−21.0087	−0.755630	−0.377815	+	0.925881i	$0.623325\pi$
$774$	0	0
$775$	−33.4720	−1.20235
$776$	−114.396	−4.10656
$777$	0	0
$778$	46.8992	1.68142
$779$	−3.36623	−0.120608
$780$	0	0
$781$	−89.8726	−3.21590
$782$	0	0
$783$	0	0
$784$	37.1880	1.32814
$785$	−28.4127	−1.01409
$786$	0	0
$787$	−13.3134	−0.474572	−0.237286	−	0.971440i	$-0.576258\pi$
$787$	−13.3134	−0.474572	−0.237286	+	0.971440i	$0.576258\pi$
$788$	56.4373	2.01049
$789$	0	0
$790$	8.91801	0.317289
$791$	−24.1831	−0.859850
$792$	0	0
$793$	−12.3184	−0.437441
$794$	−32.7311	−1.16158
$795$	0	0
$796$	118.028	4.18341
$797$	0.456366	0.0161653	0.00808266	−	0.999967i	$-0.497427\pi$
$797$	0.456366	0.0161653	0.00808266	+	0.999967i	$0.497427\pi$
$798$	0	0
$799$	0	0
$800$	37.4105	1.32266
$801$	0	0
$802$	38.7183	1.36719
$803$	−21.5311	−0.759815
$804$	0	0
$805$	39.7726	1.40180
$806$	38.0116	1.33890
$807$	0	0
$808$	5.76259	0.202727
$809$	−49.1828	−1.72918	−0.864588	−	0.502482i	$-0.832420\pi$
$809$	−49.1828	−1.72918	−0.864588	+	0.502482i	$0.832420\pi$
$810$	0	0
$811$	40.2083	1.41191	0.705953	−	0.708259i	$-0.250519\pi$
$811$	40.2083	1.41191	0.705953	+	0.708259i	$0.250519\pi$
$812$	−74.1527	−2.60225
$813$	0	0
$814$	7.92423	0.277744
$815$	−38.6533	−1.35397
$816$	0	0
$817$	3.73900	0.130811
$818$	87.5122	3.05979
$819$	0	0
$820$	−64.2905	−2.24512
$821$	−13.2638	−0.462908	−0.231454	−	0.972846i	$-0.574348\pi$
$821$	−13.2638	−0.462908	−0.231454	+	0.972846i	$0.574348\pi$
$822$	0	0
$823$	29.0218	1.01164	0.505819	−	0.862640i	$-0.331190\pi$
$823$	29.0218	1.01164	0.505819	+	0.862640i	$0.331190\pi$
$824$	73.9467	2.57606
$825$	0	0
$826$	−26.4017	−0.918631
$827$	−6.98830	−0.243007	−0.121504	−	0.992591i	$-0.538772\pi$
$827$	−6.98830	−0.243007	−0.121504	+	0.992591i	$0.538772\pi$
$828$	0	0
$829$	52.8012	1.83386	0.916931	−	0.399046i	$-0.130658\pi$
$829$	52.8012	1.83386	0.916931	+	0.399046i	$0.130658\pi$
$830$	−28.9145	−1.00364
$831$	0	0
$832$	−11.9643	−0.414786
$833$	0	0
$834$	0	0
$835$	34.4172	1.19106
$836$	21.6451	0.748612
$837$	0	0
$838$	90.8204	3.13734
$839$	−23.9485	−0.826795	−0.413398	−	0.910551i	$-0.635658\pi$
$839$	−23.9485	−0.826795	−0.413398	+	0.910551i	$0.635658\pi$
$840$	0	0
$841$	−7.20644	−0.248498
$842$	−102.131	−3.51966
$843$	0	0
$844$	−109.736	−3.77725
$845$	30.7191	1.05677
$846$	0	0
$847$	85.2203	2.92820
$848$	9.76028	0.335169
$849$	0	0
$850$	0	0
$851$	2.04470	0.0700912
$852$	0	0
$853$	47.1238	1.61349	0.806744	−	0.590901i	$-0.201228\pi$
$853$	47.1238	1.61349	0.806744	+	0.590901i	$0.201228\pi$
$854$	66.1162	2.26245
$855$	0	0
$856$	−118.506	−4.05046
$857$	−21.8156	−0.745206	−0.372603	−	0.927991i	$-0.621535\pi$
$857$	−21.8156	−0.745206	−0.372603	+	0.927991i	$0.621535\pi$
$858$	0	0
$859$	−12.6749	−0.432461	−0.216230	−	0.976342i	$-0.569376\pi$
$859$	−12.6749	−0.432461	−0.216230	+	0.976342i	$0.569376\pi$
$860$	71.4099	2.43506
$861$	0	0
$862$	49.4576	1.68453
$863$	26.0408	0.886439	0.443220	−	0.896413i	$-0.353836\pi$
$863$	26.0408	0.886439	0.443220	+	0.896413i	$0.353836\pi$
$864$	0	0
$865$	66.9813	2.27743
$866$	72.9945	2.48045
$867$	0	0
$868$	−144.084	−4.89053
$869$	7.03308	0.238581
$870$	0	0
$871$	1.20358	0.0407817
$872$	−97.4657	−3.30061
$873$	0	0
$874$	7.90830	0.267502
$875$	12.7574	0.431280
$876$	0	0
$877$	19.4601	0.657120	0.328560	−	0.944483i	$-0.393437\pi$
$877$	19.4601	0.657120	0.328560	+	0.944483i	$0.393437\pi$
$878$	35.6884	1.20442
$879$	0	0
$880$	169.909	5.72764
$881$	−0.550997	−0.0185636	−0.00928179	−	0.999957i	$-0.502955\pi$
$881$	−0.550997	−0.0185636	−0.00928179	+	0.999957i	$0.502955\pi$
$882$	0	0
$883$	−7.74903	−0.260776	−0.130388	−	0.991463i	$-0.541622\pi$
$883$	−7.74903	−0.260776	−0.130388	+	0.991463i	$0.541622\pi$
$884$	0	0
$885$	0	0
$886$	−32.4559	−1.09038
$887$	38.2265	1.28352	0.641760	−	0.766905i	$-0.278204\pi$
$887$	38.2265	1.28352	0.641760	+	0.766905i	$0.278204\pi$
$888$	0	0
$889$	40.1966	1.34815
$890$	26.4517	0.886662
$891$	0	0
$892$	−87.2319	−2.92074
$893$	5.39895	0.180669
$894$	0	0
$895$	1.56738	0.0523917
$896$	−2.77057	−0.0925581
$897$	0	0
$898$	67.5839	2.25530
$899$	42.3465	1.41233
$900$	0	0
$901$	0	0
$902$	−71.7920	−2.39041
$903$	0	0
$904$	−53.6356	−1.78389
$905$	−23.2290	−0.772157
$906$	0	0
$907$	−23.5471	−0.781867	−0.390934	−	0.920419i	$-0.627848\pi$
$907$	−23.5471	−0.781867	−0.390934	+	0.920419i	$0.627848\pi$
$908$	−5.10640	−0.169462
$909$	0	0
$910$	40.8095	1.35282
$911$	−55.5565	−1.84067	−0.920334	−	0.391133i	$-0.872083\pi$
$911$	−55.5565	−1.84067	−0.920334	+	0.391133i	$0.872083\pi$
$912$	0	0
$913$	−22.8030	−0.754670
$914$	41.1996	1.36276
$915$	0	0
$916$	−5.33888	−0.176401
$917$	6.56613	0.216833
$918$	0	0
$919$	20.0039	0.659869	0.329935	−	0.944004i	$-0.392973\pi$
$919$	20.0039	0.659869	0.329935	+	0.944004i	$0.392973\pi$
$920$	88.2117	2.90825
$921$	0	0
$922$	13.8938	0.457567
$923$	−23.7944	−0.783203
$924$	0	0
$925$	−1.84744	−0.0607435
$926$	−22.1818	−0.728940
$927$	0	0
$928$	−47.3292	−1.55366
$929$	23.9928	0.787177	0.393588	−	0.919287i	$-0.371233\pi$
$929$	23.9928	0.787177	0.393588	+	0.919287i	$0.371233\pi$
$930$	0	0
$931$	−2.90456	−0.0951931
$932$	8.18353	0.268061
$933$	0	0
$934$	36.2789	1.18708
$935$	0	0
$936$	0	0
$937$	13.6857	0.447093	0.223547	−	0.974693i	$-0.428236\pi$
$937$	13.6857	0.447093	0.223547	+	0.974693i	$0.428236\pi$
$938$	−6.45991	−0.210923
$939$	0	0
$940$	103.113	3.36316
$941$	−26.9334	−0.878002	−0.439001	−	0.898486i	$-0.644668\pi$
$941$	−26.9334	−0.878002	−0.439001	+	0.898486i	$0.644668\pi$
$942$	0	0
$943$	−18.5245	−0.603242
$944$	−29.1028	−0.947215
$945$	0	0
$946$	79.7421	2.59264
$947$	39.4644	1.28242	0.641210	−	0.767365i	$-0.278433\pi$
$947$	39.4644	1.28242	0.641210	+	0.767365i	$0.278433\pi$
$948$	0	0
$949$	−5.70051	−0.185046
$950$	−7.14538	−0.231827
$951$	0	0
$952$	0	0
$953$	7.64725	0.247719	0.123859	−	0.992300i	$-0.460473\pi$
$953$	7.64725	0.247719	0.123859	+	0.992300i	$0.460473\pi$
$954$	0	0
$955$	72.6136	2.34972
$956$	39.1543	1.26634
$957$	0	0
$958$	101.073	3.26551
$959$	−35.8142	−1.15650
$960$	0	0
$961$	51.2822	1.65427
$962$	2.09800	0.0676422
$963$	0	0
$964$	35.3805	1.13953
$965$	−7.73374	−0.248958
$966$	0	0
$967$	−1.80461	−0.0580323	−0.0290161	−	0.999579i	$-0.509237\pi$
$967$	−1.80461	−0.0580323	−0.0290161	+	0.999579i	$0.509237\pi$
$968$	189.010	6.07501
$969$	0	0
$970$	120.089	3.85583
$971$	22.6386	0.726508	0.363254	−	0.931690i	$-0.381666\pi$
$971$	22.6386	0.726508	0.363254	+	0.931690i	$0.381666\pi$
$972$	0	0
$973$	49.7413	1.59463
$974$	30.5611	0.979239
$975$	0	0
$976$	72.8805	2.33285
$977$	40.0443	1.28113	0.640566	−	0.767903i	$-0.278700\pi$
$977$	40.0443	1.28113	0.640566	+	0.767903i	$0.278700\pi$
$978$	0	0
$979$	20.8608	0.666714
$980$	−55.4732	−1.77203
$981$	0	0
$982$	−50.0381	−1.59678
$983$	−4.62495	−0.147513	−0.0737566	−	0.997276i	$-0.523499\pi$
$983$	−4.62495	−0.147513	−0.0737566	+	0.997276i	$0.523499\pi$
$984$	0	0
$985$	−34.6020	−1.10251
$986$	0	0
$987$	0	0
$988$	5.73070	0.182318
$989$	20.5759	0.654276
$990$	0	0
$991$	−29.3798	−0.933280	−0.466640	−	0.884447i	$-0.654536\pi$
$991$	−29.3798	−0.933280	−0.466640	+	0.884447i	$0.654536\pi$
$992$	−91.9641	−2.91986
$993$	0	0
$994$	127.711	4.05074
$995$	−72.3639	−2.29409
$996$	0	0
$997$	−34.0316	−1.07779	−0.538896	−	0.842373i	$-0.681158\pi$
$997$	−34.0316	−1.07779	−0.538896	+	0.842373i	$0.681158\pi$
$998$	−82.1915	−2.60173
$999$	0	0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7803.2.a.bs.1.10		10
3.2	odd	2		7803.2.a.br.1.1		10
17.2	even	8		459.2.f.b.55.10	yes	20
17.9	even	8		459.2.f.b.217.1	yes	20
17.16	even	2		7803.2.a.br.1.10		10
51.2	odd	8		459.2.f.b.55.1	✓	20
51.26	odd	8		459.2.f.b.217.10	yes	20
51.50	odd	2	inner	7803.2.a.bs.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
459.2.f.b.55.1	✓	20	51.2	odd	8
459.2.f.b.55.10	yes	20	17.2	even	8
459.2.f.b.217.1	yes	20	17.9	even	8
459.2.f.b.217.10	yes	20	51.26	odd	8
7803.2.a.br.1.1		10	3.2	odd	2
7803.2.a.br.1.10		10	17.16	even	2
7803.2.a.bs.1.1		10	51.50	odd	2	inner
7803.2.a.bs.1.10		10	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 7803 = 3^{3} \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7803.a (trivial)

\(f(q)\)	\(=\)	\(q+2.60924 q^{2} +4.80812 q^{4} -2.94788 q^{5} +3.30360 q^{7} +7.32705 q^{8} -7.69173 q^{10} -6.06599 q^{11} -1.60601 q^{13} +8.61988 q^{14} +9.50178 q^{16} -0.742135 q^{19} -14.1738 q^{20} -15.8276 q^{22} -4.08401 q^{23} +3.69002 q^{25} -4.19047 q^{26} +15.8841 q^{28} -4.66836 q^{29} -9.07096 q^{31} +10.1383 q^{32} -9.73864 q^{35} -0.500659 q^{37} -1.93641 q^{38} -21.5993 q^{40} +4.53588 q^{41} -5.03817 q^{43} -29.1660 q^{44} -10.6561 q^{46} -7.27488 q^{47} +3.91379 q^{49} +9.62814 q^{50} -7.72191 q^{52} +1.02721 q^{53} +17.8818 q^{55} +24.2057 q^{56} -12.1809 q^{58} -3.06288 q^{59} +7.67019 q^{61} -23.6683 q^{62} +7.44967 q^{64} +4.73434 q^{65} -0.749419 q^{67} -25.4104 q^{70} +14.8158 q^{71} +3.54948 q^{73} -1.30634 q^{74} -3.56828 q^{76} -20.0396 q^{77} -1.15943 q^{79} -28.0101 q^{80} +11.8352 q^{82} +3.75916 q^{83} -13.1458 q^{86} -44.4458 q^{88} -3.43898 q^{89} -5.30563 q^{91} -19.6364 q^{92} -18.9819 q^{94} +2.18773 q^{95} -15.6128 q^{97} +10.2120 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 12 q^{4} + 2 q^{5} - 22 q^{11} + 16 q^{16} - 10 q^{19} - 8 q^{20} - 28 q^{23} + 8 q^{25} - 6 q^{29} - 28 q^{41} - 8 q^{43} - 76 q^{44} + 2 q^{49} - 4 q^{52} + 42 q^{55} + 64 q^{56} - 52 q^{62} - 36 q^{64}+ \cdots - 38 q^{95}+O(q^{100}) \) 10 * q + 12 * q^4 + 2 * q^5 - 22 * q^11 + 16 * q^16 - 10 * q^19 - 8 * q^20 - 28 * q^23 + 8 * q^25 - 6 * q^29 - 28 * q^41 - 8 * q^43 - 76 * q^44 + 2 * q^49 - 4 * q^52 + 42 * q^55 + 64 * q^56 - 52 * q^62 - 36 * q^64 - 32 * q^65 + 18 * q^67 - 72 * q^70 + 50 * q^71 - 56 * q^74 - 28 * q^76 - 80 * q^80 - 56 * q^92 - 20 * q^94 - 38 * q^95

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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