LMFDB - Embedded newform 10000.2.a.bj.1.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [10000,2,Mod(1,10000)] 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("10000.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(10000, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$N$	$=$	$10000 = 2^{4} \cdot 5^{4}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	10000.a (trivial)

Newform invariants

comment:select newform

sage:traces = [8,0,0,0,0,0,0,0,4,0,-16,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	yes
Analytic conductor:	$79.8504020213$
Analytic rank:	$1$
Dimension:	$8$
Coefficient field:	8.8.14884000000.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$x^{8} - 11x^{6} + 36x^{4} - 31x^{2} + 1$ x^8 - 11x^6 + 36x^4 - 31*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$1$
Twist minimal:	no (minimal twist has level 25)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-2.08529$ of defining polynomial
Character	$\chi$	$=$	10000.1

$q$ -expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	$q+2.19849 q^{3} -0.992398 q^{7} +1.83337 q^{9} -2.00000 q^{11} -3.37406 q^{13} +2.89451 q^{17} +2.58448 q^{19} -2.18178 q^{21} +4.54963 q^{23} -2.56484 q^{27} -5.38430 q^{29} -0.136538 q^{31} -4.39698 q^{33} -2.14910 q^{37} -7.41785 q^{39} +8.63318 q^{41} -4.64398 q^{43} -9.92630 q^{47} -6.01515 q^{49} +6.36356 q^{51} +7.56521 q^{53} +5.68196 q^{57} -4.91775 q^{59} -2.76972 q^{61} -1.81943 q^{63} -2.18577 q^{67} +10.0023 q^{69} -9.64254 q^{71} +0.775929 q^{73} +1.98480 q^{77} -15.8508 q^{79} -11.1389 q^{81} +1.77110 q^{83} -11.8373 q^{87} +14.5080 q^{89} +3.34841 q^{91} -0.300177 q^{93} -17.0291 q^{97} -3.66673 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$8 q + 4 q^{9} - 16 q^{11} - 10 q^{19} + 6 q^{21} + 20 q^{29} - 16 q^{31} - 18 q^{39} + 26 q^{41} - 14 q^{49} + 4 q^{51} - 30 q^{59} + 6 q^{61} + 8 q^{69} - 46 q^{71} - 10 q^{79} - 32 q^{81} + 30 q^{89}+ \cdots - 8 q^{99}+O(q^{100})$ 8 * q + 4 * q^9 - 16 * q^11 - 10 * q^19 + 6 * q^21 + 20 * q^29 - 16 * q^31 - 18 * q^39 + 26 * q^41 - 14 * q^49 + 4 * q^51 - 30 * q^59 + 6 * q^61 + 8 * q^69 - 46 * q^71 - 10 * q^79 - 32 * q^81 + 30 * q^89 + 14 * q^91 - 8 * q^99

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	0
$2$	0	0
$3$	2.19849	1.26930	0.634650	−	0.772800i	$-0.281144\pi$
$3$	2.19849	1.26930	0.634650	+	0.772800i	$0.281144\pi$
$4$	0	0
$5$	0	0
$5$	0	0
$6$	0	0
$7$	−0.992398	−0.375091	−0.187546	−	0.982256i	$-0.560053\pi$
$7$	−0.992398	−0.375091	−0.187546	+	0.982256i	$0.560053\pi$
$8$	0	0
$9$	1.83337	0.611122
$10$	0	0
$11$	−2.00000	−0.603023	−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000	−0.603023	−0.301511	+	0.953463i	$0.597491\pi$
$12$	0	0
$13$	−3.37406	−0.935796	−0.467898	−	0.883782i	$-0.654989\pi$
$13$	−3.37406	−0.935796	−0.467898	+	0.883782i	$0.654989\pi$
$14$	0	0
$15$	0	0
$16$	0	0
$17$	2.89451	0.702022	0.351011	−	0.936371i	$-0.385838\pi$
$17$	2.89451	0.702022	0.351011	+	0.936371i	$0.385838\pi$
$18$	0	0
$19$	2.58448	0.592921	0.296460	−	0.955045i	$-0.404194\pi$
$19$	2.58448	0.592921	0.296460	+	0.955045i	$0.404194\pi$
$20$	0	0
$21$	−2.18178	−0.476103
$22$	0	0
$23$	4.54963	0.948664	0.474332	−	0.880346i	$-0.342690\pi$
$23$	4.54963	0.948664	0.474332	+	0.880346i	$0.342690\pi$
$24$	0	0
$25$	0	0
$26$	0	0
$27$	−2.56484	−0.493603
$28$	0	0
$29$	−5.38430	−0.999839	−0.499919	−	0.866072i	$-0.666637\pi$
$29$	−5.38430	−0.999839	−0.499919	+	0.866072i	$0.666637\pi$
$30$	0	0
$31$	−0.136538	−0.0245229	−0.0122614	−	0.999925i	$-0.503903\pi$
$31$	−0.136538	−0.0245229	−0.0122614	+	0.999925i	$0.503903\pi$
$32$	0	0
$33$	−4.39698	−0.765417
$34$	0	0
$35$	0	0
$36$	0	0
$37$	−2.14910	−0.353311	−0.176655	−	0.984273i	$-0.556528\pi$
$37$	−2.14910	−0.353311	−0.176655	+	0.984273i	$0.556528\pi$
$38$	0	0
$39$	−7.41785	−1.18781
$40$	0	0
$41$	8.63318	1.34828	0.674138	−	0.738605i	$-0.264515\pi$
$41$	8.63318	1.34828	0.674138	+	0.738605i	$0.264515\pi$
$42$	0	0
$43$	−4.64398	−0.708200	−0.354100	−	0.935208i	$-0.615213\pi$
$43$	−4.64398	−0.708200	−0.354100	+	0.935208i	$0.615213\pi$
$44$	0	0
$45$	0	0
$46$	0	0
$47$	−9.92630	−1.44790	−0.723950	−	0.689853i	$-0.757675\pi$
$47$	−9.92630	−1.44790	−0.723950	+	0.689853i	$0.757675\pi$
$48$	0	0
$49$	−6.01515	−0.859306
$50$	0	0
$51$	6.36356	0.891077
$52$	0	0
$53$	7.56521	1.03916	0.519581	−	0.854421i	$-0.326088\pi$
$53$	7.56521	1.03916	0.519581	+	0.854421i	$0.326088\pi$
$54$	0	0
$55$	0	0
$56$	0	0
$57$	5.68196	0.752594
$58$	0	0
$59$	−4.91775	−0.640237	−0.320118	−	0.947378i	$-0.603723\pi$
$59$	−4.91775	−0.640237	−0.320118	+	0.947378i	$0.603723\pi$
$60$	0	0
$61$	−2.76972	−0.354626	−0.177313	−	0.984155i	$-0.556740\pi$
$61$	−2.76972	−0.354626	−0.177313	+	0.984155i	$0.556740\pi$
$62$	0	0
$63$	−1.81943	−0.229227
$64$	0	0
$65$	0	0
$66$	0	0
$67$	−2.18577	−0.267035	−0.133517	−	0.991046i	$-0.542627\pi$
$67$	−2.18577	−0.267035	−0.133517	+	0.991046i	$0.542627\pi$
$68$	0	0
$69$	10.0023	1.20414
$70$	0	0
$71$	−9.64254	−1.14436	−0.572179	−	0.820128i	$-0.693902\pi$
$71$	−9.64254	−1.14436	−0.572179	+	0.820128i	$0.693902\pi$
$72$	0	0
$73$	0.775929	0.0908157	0.0454078	−	0.998969i	$-0.485541\pi$
$73$	0.775929	0.0908157	0.0454078	+	0.998969i	$0.485541\pi$
$74$	0	0
$75$	0	0
$76$	0	0
$77$	1.98480	0.226189
$78$	0	0
$79$	−15.8508	−1.78336	−0.891679	−	0.452667i	$-0.850473\pi$
$79$	−15.8508	−1.78336	−0.891679	+	0.452667i	$0.850473\pi$
$80$	0	0
$81$	−11.1389	−1.23765
$82$	0	0
$83$	1.77110	0.194404	0.0972019	−	0.995265i	$-0.469011\pi$
$83$	1.77110	0.194404	0.0972019	+	0.995265i	$0.469011\pi$
$84$	0	0
$85$	0	0
$86$	0	0
$87$	−11.8373	−1.26909
$88$	0	0
$89$	14.5080	1.53785	0.768923	−	0.639341i	$-0.220793\pi$
$89$	14.5080	1.53785	0.768923	+	0.639341i	$0.220793\pi$
$90$	0	0
$91$	3.34841	0.351009
$92$	0	0
$93$	−0.300177	−0.0311269
$94$	0	0
$95$	0	0
$96$	0	0
$97$	−17.0291	−1.72904	−0.864522	−	0.502595i	$-0.832379\pi$
$97$	−17.0291	−1.72904	−0.864522	+	0.502595i	$0.832379\pi$
$98$	0	0
$99$	−3.66673	−0.368520
$100$	0	0
$101$	−2.54716	−0.253452	−0.126726	−	0.991938i	$-0.540447\pi$
$101$	−2.54716	−0.253452	−0.126726	+	0.991938i	$0.540447\pi$
$102$	0	0
$103$	−10.1654	−1.00163	−0.500815	−	0.865555i	$-0.666966\pi$
$103$	−10.1654	−1.00163	−0.500815	+	0.865555i	$0.666966\pi$
$104$	0	0
$105$	0	0
$106$	0	0
$107$	4.81720	0.465697	0.232848	−	0.972513i	$-0.425195\pi$
$107$	4.81720	0.465697	0.232848	+	0.972513i	$0.425195\pi$
$108$	0	0
$109$	16.2743	1.55879	0.779397	−	0.626531i	$-0.215526\pi$
$109$	16.2743	1.55879	0.779397	+	0.626531i	$0.215526\pi$
$110$	0	0
$111$	−4.72479	−0.448457
$112$	0	0
$113$	6.75704	0.635649	0.317825	−	0.948150i	$-0.397048\pi$
$113$	6.75704	0.635649	0.317825	+	0.948150i	$0.397048\pi$
$114$	0	0
$115$	0	0
$116$	0	0
$117$	−6.18589	−0.571886
$118$	0	0
$119$	−2.87251	−0.263322
$120$	0	0
$121$	−7.00000	−0.636364
$122$	0	0
$123$	18.9800	1.71137
$124$	0	0
$125$	0	0
$126$	0	0
$127$	1.49081	0.132288	0.0661441	−	0.997810i	$-0.478930\pi$
$127$	1.49081	0.132288	0.0661441	+	0.997810i	$0.478930\pi$
$128$	0	0
$129$	−10.2097	−0.898918
$130$	0	0
$131$	−14.1147	−1.23320	−0.616602	−	0.787275i	$-0.711491\pi$
$131$	−14.1147	−1.23320	−0.616602	+	0.787275i	$0.711491\pi$
$132$	0	0
$133$	−2.56484	−0.222399
$134$	0	0
$135$	0	0
$136$	0	0
$137$	−0.689447	−0.0589035	−0.0294517	−	0.999566i	$-0.509376\pi$
$137$	−0.689447	−0.0589035	−0.0294517	+	0.999566i	$0.509376\pi$
$138$	0	0
$139$	16.5719	1.40561	0.702803	−	0.711384i	$-0.251931\pi$
$139$	16.5719	1.40561	0.702803	+	0.711384i	$0.251931\pi$
$140$	0	0
$141$	−21.8229	−1.83782
$142$	0	0
$143$	6.74812	0.564307
$144$	0	0
$145$	0	0
$146$	0	0
$147$	−13.2242	−1.09072
$148$	0	0
$149$	3.21156	0.263101	0.131551	−	0.991309i	$-0.458004\pi$
$149$	3.21156	0.263101	0.131551	+	0.991309i	$0.458004\pi$
$150$	0	0
$151$	−17.6863	−1.43929	−0.719647	−	0.694340i	$-0.755696\pi$
$151$	−17.6863	−1.43929	−0.719647	+	0.694340i	$0.755696\pi$
$152$	0	0
$153$	5.30670	0.429021
$154$	0	0
$155$	0	0
$156$	0	0
$157$	1.65512	0.132093	0.0660465	−	0.997817i	$-0.478961\pi$
$157$	1.65512	0.132093	0.0660465	+	0.997817i	$0.478961\pi$
$158$	0	0
$159$	16.6321	1.31901
$160$	0	0
$161$	−4.51505	−0.355836
$162$	0	0
$163$	−0.892934	−0.0699400	−0.0349700	−	0.999388i	$-0.511134\pi$
$163$	−0.892934	−0.0699400	−0.0349700	+	0.999388i	$0.511134\pi$
$164$	0	0
$165$	0	0
$166$	0	0
$167$	−5.19558	−0.402046	−0.201023	−	0.979587i	$-0.564427\pi$
$167$	−5.19558	−0.402046	−0.201023	+	0.979587i	$0.564427\pi$
$168$	0	0
$169$	−1.61570	−0.124285
$170$	0	0
$171$	4.73830	0.362347
$172$	0	0
$173$	−5.76465	−0.438278	−0.219139	−	0.975694i	$-0.570325\pi$
$173$	−5.76465	−0.438278	−0.219139	+	0.975694i	$0.570325\pi$
$174$	0	0
$175$	0	0
$176$	0	0
$177$	−10.8116	−0.812652
$178$	0	0
$179$	−8.66887	−0.647942	−0.323971	−	0.946067i	$-0.605018\pi$
$179$	−8.66887	−0.647942	−0.323971	+	0.946067i	$0.605018\pi$
$180$	0	0
$181$	14.2909	1.06223	0.531116	−	0.847299i	$-0.321773\pi$
$181$	14.2909	1.06223	0.531116	+	0.847299i	$0.321773\pi$
$182$	0	0
$183$	−6.08920	−0.450127
$184$	0	0
$185$	0	0
$186$	0	0
$187$	−5.78902	−0.423335
$188$	0	0
$189$	2.54534	0.185146
$190$	0	0
$191$	1.26636	0.0916305	0.0458153	−	0.998950i	$-0.485411\pi$
$191$	1.26636	0.0916305	0.0458153	+	0.998950i	$0.485411\pi$
$192$	0	0
$193$	21.1730	1.52406	0.762031	−	0.647540i	$-0.224202\pi$
$193$	21.1730	1.52406	0.762031	+	0.647540i	$0.224202\pi$
$194$	0	0
$195$	0	0
$196$	0	0
$197$	−12.2013	−0.869308	−0.434654	−	0.900597i	$-0.643129\pi$
$197$	−12.2013	−0.869308	−0.434654	+	0.900597i	$0.643129\pi$
$198$	0	0
$199$	−10.4065	−0.737695	−0.368848	−	0.929490i	$-0.620248\pi$
$199$	−10.4065	−0.737695	−0.368848	+	0.929490i	$0.620248\pi$
$200$	0	0
$201$	−4.80540	−0.338947
$202$	0	0
$203$	5.34337	0.375031
$204$	0	0
$205$	0	0
$206$	0	0
$207$	8.34114	0.579749
$208$	0	0
$209$	−5.16896	−0.357545
$210$	0	0
$211$	8.65769	0.596020	0.298010	−	0.954563i	$-0.403677\pi$
$211$	8.65769	0.596020	0.298010	+	0.954563i	$0.403677\pi$
$212$	0	0
$213$	−21.1990	−1.45253
$214$	0	0
$215$	0	0
$216$	0	0
$217$	0.135500	0.00919832
$218$	0	0
$219$	1.70587	0.115272
$220$	0	0
$221$	−9.76626	−0.656950
$222$	0	0
$223$	−28.3434	−1.89801	−0.949007	−	0.315256i	$-0.897909\pi$
$223$	−28.3434	−1.89801	−0.949007	+	0.315256i	$0.897909\pi$
$224$	0	0
$225$	0	0
$226$	0	0
$227$	−22.2415	−1.47622	−0.738109	−	0.674682i	$-0.764281\pi$
$227$	−22.2415	−1.47622	−0.738109	+	0.674682i	$0.764281\pi$
$228$	0	0
$229$	2.47559	0.163592	0.0817958	−	0.996649i	$-0.473934\pi$
$229$	2.47559	0.163592	0.0817958	+	0.996649i	$0.473934\pi$
$230$	0	0
$231$	4.36356	0.287101
$232$	0	0
$233$	5.95605	0.390194	0.195097	−	0.980784i	$-0.437498\pi$
$233$	5.95605	0.390194	0.195097	+	0.980784i	$0.437498\pi$
$234$	0	0
$235$	0	0
$236$	0	0
$237$	−34.8479	−2.26362
$238$	0	0
$239$	7.03243	0.454890	0.227445	−	0.973791i	$-0.426963\pi$
$239$	7.03243	0.454890	0.227445	+	0.973791i	$0.426963\pi$
$240$	0	0
$241$	1.17976	0.0759953	0.0379976	−	0.999278i	$-0.487902\pi$
$241$	1.17976	0.0759953	0.0379976	+	0.999278i	$0.487902\pi$
$242$	0	0
$243$	−16.7942	−1.07735
$244$	0	0
$245$	0	0
$246$	0	0
$247$	−8.72020	−0.554853
$248$	0	0
$249$	3.89375	0.246757
$250$	0	0
$251$	−4.60867	−0.290897	−0.145448	−	0.989366i	$-0.546462\pi$
$251$	−4.60867	−0.290897	−0.145448	+	0.989366i	$0.546462\pi$
$252$	0	0
$253$	−9.09927	−0.572066
$254$	0	0
$255$	0	0
$256$	0	0
$257$	−9.75542	−0.608526	−0.304263	−	0.952588i	$-0.598410\pi$
$257$	−9.75542	−0.608526	−0.304263	+	0.952588i	$0.598410\pi$
$258$	0	0
$259$	2.13277	0.132524
$260$	0	0
$261$	−9.87138	−0.611023
$262$	0	0
$263$	−0.995828	−0.0614054	−0.0307027	−	0.999529i	$-0.509775\pi$
$263$	−0.995828	−0.0614054	−0.0307027	+	0.999529i	$0.509775\pi$
$264$	0	0
$265$	0	0
$266$	0	0
$267$	31.8958	1.95199
$268$	0	0
$269$	−3.28853	−0.200506	−0.100253	−	0.994962i	$-0.531965\pi$
$269$	−3.28853	−0.200506	−0.100253	+	0.994962i	$0.531965\pi$
$270$	0	0
$271$	−12.1500	−0.738063	−0.369031	−	0.929417i	$-0.620311\pi$
$271$	−12.1500	−0.738063	−0.369031	+	0.929417i	$0.620311\pi$
$272$	0	0
$273$	7.36146	0.445536
$274$	0	0
$275$	0	0
$276$	0	0
$277$	−11.8666	−0.712993	−0.356496	−	0.934297i	$-0.616029\pi$
$277$	−11.8666	−0.712993	−0.356496	+	0.934297i	$0.616029\pi$
$278$	0	0
$279$	−0.250324	−0.0149865
$280$	0	0
$281$	−24.6416	−1.47000	−0.734998	−	0.678070i	$-0.762817\pi$
$281$	−24.6416	−1.47000	−0.734998	+	0.678070i	$0.762817\pi$
$282$	0	0
$283$	3.36343	0.199935	0.0999675	−	0.994991i	$-0.468126\pi$
$283$	3.36343	0.199935	0.0999675	+	0.994991i	$0.468126\pi$
$284$	0	0
$285$	0	0
$286$	0	0
$287$	−8.56755	−0.505727
$288$	0	0
$289$	−8.62180	−0.507165
$290$	0	0
$291$	−37.4383	−2.19467
$292$	0	0
$293$	−8.96340	−0.523647	−0.261824	−	0.965116i	$-0.584324\pi$
$293$	−8.96340	−0.523647	−0.261824	+	0.965116i	$0.584324\pi$
$294$	0	0
$295$	0	0
$296$	0	0
$297$	5.12967	0.297654
$298$	0	0
$299$	−15.3507	−0.887756
$300$	0	0
$301$	4.60867	0.265640
$302$	0	0
$303$	−5.59991	−0.321706
$304$	0	0
$305$	0	0
$306$	0	0
$307$	−9.48133	−0.541128	−0.270564	−	0.962702i	$-0.587210\pi$
$307$	−9.48133	−0.541128	−0.270564	+	0.962702i	$0.587210\pi$
$308$	0	0
$309$	−22.3486	−1.27137
$310$	0	0
$311$	−29.3320	−1.66327	−0.831633	−	0.555325i	$-0.812594\pi$
$311$	−29.3320	−1.66327	−0.831633	+	0.555325i	$0.812594\pi$
$312$	0	0
$313$	18.8901	1.06773	0.533865	−	0.845570i	$-0.320739\pi$
$313$	18.8901	1.06773	0.533865	+	0.845570i	$0.320739\pi$
$314$	0	0
$315$	0	0
$316$	0	0
$317$	22.7893	1.27998	0.639988	−	0.768385i	$-0.278939\pi$
$317$	22.7893	1.27998	0.639988	+	0.768385i	$0.278939\pi$
$318$	0	0
$319$	10.7686	0.602925
$320$	0	0
$321$	10.5906	0.591109
$322$	0	0
$323$	7.48081	0.416244
$324$	0	0
$325$	0	0
$326$	0	0
$327$	35.7789	1.97858
$328$	0	0
$329$	9.85084	0.543094
$330$	0	0
$331$	−2.96299	−0.162861	−0.0814304	−	0.996679i	$-0.525949\pi$
$331$	−2.96299	−0.162861	−0.0814304	+	0.996679i	$0.525949\pi$
$332$	0	0
$333$	−3.94010	−0.215916
$334$	0	0
$335$	0	0
$336$	0	0
$337$	−18.8123	−1.02477	−0.512385	−	0.858756i	$-0.671238\pi$
$337$	−18.8123	−1.02477	−0.512385	+	0.858756i	$0.671238\pi$
$338$	0	0
$339$	14.8553	0.806829
$340$	0	0
$341$	0.273075	0.0147879
$342$	0	0
$343$	12.9162	0.697410
$344$	0	0
$345$	0	0
$346$	0	0
$347$	22.7382	1.22065	0.610325	−	0.792151i	$-0.291039\pi$
$347$	22.7382	1.22065	0.610325	+	0.792151i	$0.291039\pi$
$348$	0	0
$349$	1.93849	0.103765	0.0518824	−	0.998653i	$-0.483478\pi$
$349$	1.93849	0.103765	0.0518824	+	0.998653i	$0.483478\pi$
$350$	0	0
$351$	8.65392	0.461912
$352$	0	0
$353$	5.24945	0.279400	0.139700	−	0.990194i	$-0.455386\pi$
$353$	5.24945	0.279400	0.139700	+	0.990194i	$0.455386\pi$
$354$	0	0
$355$	0	0
$356$	0	0
$357$	−6.31519	−0.334235
$358$	0	0
$359$	−22.5937	−1.19245	−0.596226	−	0.802817i	$-0.703334\pi$
$359$	−22.5937	−1.19245	−0.596226	+	0.802817i	$0.703334\pi$
$360$	0	0
$361$	−12.3205	−0.648445
$362$	0	0
$363$	−15.3894	−0.807736
$364$	0	0
$365$	0	0
$366$	0	0
$367$	7.29872	0.380990	0.190495	−	0.981688i	$-0.438991\pi$
$367$	7.29872	0.380990	0.190495	+	0.981688i	$0.438991\pi$
$368$	0	0
$369$	15.8278	0.823961
$370$	0	0
$371$	−7.50770	−0.389781
$372$	0	0
$373$	−22.3074	−1.15503	−0.577516	−	0.816380i	$-0.695978\pi$
$373$	−22.3074	−1.15503	−0.577516	+	0.816380i	$0.695978\pi$
$374$	0	0
$375$	0	0
$376$	0	0
$377$	18.1669	0.935645
$378$	0	0
$379$	32.9466	1.69235	0.846177	−	0.532903i	$-0.178899\pi$
$379$	32.9466	1.69235	0.846177	+	0.532903i	$0.178899\pi$
$380$	0	0
$381$	3.27754	0.167913
$382$	0	0
$383$	20.7002	1.05773	0.528865	−	0.848706i	$-0.322618\pi$
$383$	20.7002	1.05773	0.528865	+	0.848706i	$0.322618\pi$
$384$	0	0
$385$	0	0
$386$	0	0
$387$	−8.51410	−0.432796
$388$	0	0
$389$	−1.14446	−0.0580263	−0.0290132	−	0.999579i	$-0.509236\pi$
$389$	−1.14446	−0.0580263	−0.0290132	+	0.999579i	$0.509236\pi$
$390$	0	0
$391$	13.1690	0.665983
$392$	0	0
$393$	−31.0310	−1.56531
$394$	0	0
$395$	0	0
$396$	0	0
$397$	−4.68513	−0.235140	−0.117570	−	0.993065i	$-0.537510\pi$
$397$	−4.68513	−0.235140	−0.117570	+	0.993065i	$0.537510\pi$
$398$	0	0
$399$	−5.63877	−0.282292
$400$	0	0
$401$	−24.0851	−1.20275	−0.601376	−	0.798966i	$-0.705381\pi$
$401$	−24.0851	−1.20275	−0.601376	+	0.798966i	$0.705381\pi$
$402$	0	0
$403$	0.460687	0.0229484
$404$	0	0
$405$	0	0
$406$	0	0
$407$	4.29821	0.213054
$408$	0	0
$409$	−1.89934	−0.0939165	−0.0469583	−	0.998897i	$-0.514953\pi$
$409$	−1.89934	−0.0939165	−0.0469583	+	0.998897i	$0.514953\pi$
$410$	0	0
$411$	−1.51574	−0.0747661
$412$	0	0
$413$	4.88037	0.240147
$414$	0	0
$415$	0	0
$416$	0	0
$417$	36.4331	1.78414
$418$	0	0
$419$	2.32806	0.113733	0.0568666	−	0.998382i	$-0.481889\pi$
$419$	2.32806	0.113733	0.0568666	+	0.998382i	$0.481889\pi$
$420$	0	0
$421$	−23.9501	−1.16725	−0.583627	−	0.812022i	$-0.698367\pi$
$421$	−23.9501	−1.16725	−0.583627	+	0.812022i	$0.698367\pi$
$422$	0	0
$423$	−18.1985	−0.884843
$424$	0	0
$425$	0	0
$426$	0	0
$427$	2.74866	0.133017
$428$	0	0
$429$	14.8357	0.716274
$430$	0	0
$431$	−1.19227	−0.0574294	−0.0287147	−	0.999588i	$-0.509141\pi$
$431$	−1.19227	−0.0574294	−0.0287147	+	0.999588i	$0.509141\pi$
$432$	0	0
$433$	25.6138	1.23092	0.615461	−	0.788167i	$-0.288970\pi$
$433$	25.6138	1.23092	0.615461	+	0.788167i	$0.288970\pi$
$434$	0	0
$435$	0	0
$436$	0	0
$437$	11.7584	0.562483
$438$	0	0
$439$	−19.3741	−0.924676	−0.462338	−	0.886704i	$-0.652989\pi$
$439$	−19.3741	−0.924676	−0.462338	+	0.886704i	$0.652989\pi$
$440$	0	0
$441$	−11.0280	−0.525141
$442$	0	0
$443$	2.46263	0.117003	0.0585016	−	0.998287i	$-0.481368\pi$
$443$	2.46263	0.117003	0.0585016	+	0.998287i	$0.481368\pi$
$444$	0	0
$445$	0	0
$446$	0	0
$447$	7.06059	0.333955
$448$	0	0
$449$	−14.3585	−0.677618	−0.338809	−	0.940855i	$-0.610024\pi$
$449$	−14.3585	−0.677618	−0.338809	+	0.940855i	$0.610024\pi$
$450$	0	0
$451$	−17.2664	−0.813041
$452$	0	0
$453$	−38.8833	−1.82690
$454$	0	0
$455$	0	0
$456$	0	0
$457$	25.1964	1.17864	0.589319	−	0.807901i	$-0.299396\pi$
$457$	25.1964	1.17864	0.589319	+	0.807901i	$0.299396\pi$
$458$	0	0
$459$	−7.42395	−0.346520
$460$	0	0
$461$	28.8255	1.34254	0.671269	−	0.741214i	$-0.265749\pi$
$461$	28.8255	1.34254	0.671269	+	0.741214i	$0.265749\pi$
$462$	0	0
$463$	31.8796	1.48157	0.740786	−	0.671742i	$-0.234453\pi$
$463$	31.8796	1.48157	0.740786	+	0.671742i	$0.234453\pi$
$464$	0	0
$465$	0	0
$466$	0	0
$467$	43.0996	1.99441	0.997206	−	0.0747039i	$-0.0238012\pi$
$467$	43.0996	1.99441	0.997206	+	0.0747039i	$0.0238012\pi$
$468$	0	0
$469$	2.16916	0.100162
$470$	0	0
$471$	3.63877	0.167666
$472$	0	0
$473$	9.28795	0.427060
$474$	0	0
$475$	0	0
$476$	0	0
$477$	13.8698	0.635054
$478$	0	0
$479$	−21.0263	−0.960717	−0.480359	−	0.877072i	$-0.659494\pi$
$479$	−21.0263	−0.960717	−0.480359	+	0.877072i	$0.659494\pi$
$480$	0	0
$481$	7.25121	0.330627
$482$	0	0
$483$	−9.92630	−0.451662
$484$	0	0
$485$	0	0
$486$	0	0
$487$	−27.9190	−1.26513	−0.632565	−	0.774507i	$-0.717998\pi$
$487$	−27.9190	−1.26513	−0.632565	+	0.774507i	$0.717998\pi$
$488$	0	0
$489$	−1.96311	−0.0887748
$490$	0	0
$491$	−14.9611	−0.675183	−0.337591	−	0.941293i	$-0.609612\pi$
$491$	−14.9611	−0.675183	−0.337591	+	0.941293i	$0.609612\pi$
$492$	0	0
$493$	−15.5849	−0.701909
$494$	0	0
$495$	0	0
$496$	0	0
$497$	9.56924	0.429239
$498$	0	0
$499$	44.3253	1.98427	0.992137	−	0.125160i	$-0.0399443\pi$
$499$	44.3253	1.98427	0.992137	+	0.125160i	$0.0399443\pi$
$500$	0	0
$501$	−11.4224	−0.510316
$502$	0	0
$503$	23.6212	1.05322	0.526609	−	0.850108i	$-0.323463\pi$
$503$	23.6212	1.05322	0.526609	+	0.850108i	$0.323463\pi$
$504$	0	0
$505$	0	0
$506$	0	0
$507$	−3.55211	−0.157755
$508$	0	0
$509$	−26.7154	−1.18414	−0.592070	−	0.805886i	$-0.701689\pi$
$509$	−26.7154	−1.18414	−0.592070	+	0.805886i	$0.701689\pi$
$510$	0	0
$511$	−0.770031	−0.0340642
$512$	0	0
$513$	−6.62877	−0.292667
$514$	0	0
$515$	0	0
$516$	0	0
$517$	19.8526	0.873116
$518$	0	0
$519$	−12.6735	−0.556306
$520$	0	0
$521$	32.7073	1.43293	0.716466	−	0.697622i	$-0.245759\pi$
$521$	32.7073	1.43293	0.716466	+	0.697622i	$0.245759\pi$
$522$	0	0
$523$	−0.235966	−0.0103181	−0.00515904	−	0.999987i	$-0.501642\pi$
$523$	−0.235966	−0.0103181	−0.00515904	+	0.999987i	$0.501642\pi$
$524$	0	0
$525$	0	0
$526$	0	0
$527$	−0.395210	−0.0172156
$528$	0	0
$529$	−2.30084	−0.100037
$530$	0	0
$531$	−9.01604	−0.391263
$532$	0	0
$533$	−29.1289	−1.26171
$534$	0	0
$535$	0	0
$536$	0	0
$537$	−19.0584	−0.822432
$538$	0	0
$539$	12.0303	0.518181
$540$	0	0
$541$	−33.5572	−1.44274	−0.721369	−	0.692551i	$-0.756487\pi$
$541$	−33.5572	−1.44274	−0.721369	+	0.692551i	$0.756487\pi$
$542$	0	0
$543$	31.4183	1.34829
$544$	0	0
$545$	0	0
$546$	0	0
$547$	−38.5125	−1.64668	−0.823338	−	0.567552i	$-0.807891\pi$
$547$	−38.5125	−1.64668	−0.823338	+	0.567552i	$0.807891\pi$
$548$	0	0
$549$	−5.07790	−0.216720
$550$	0	0
$551$	−13.9156	−0.592825
$552$	0	0
$553$	15.7303	0.668922
$554$	0	0
$555$	0	0
$556$	0	0
$557$	4.33445	0.183657	0.0918283	−	0.995775i	$-0.470729\pi$
$557$	4.33445	0.183657	0.0918283	+	0.995775i	$0.470729\pi$
$558$	0	0
$559$	15.6691	0.662731
$560$	0	0
$561$	−12.7271	−0.537339
$562$	0	0
$563$	34.9018	1.47094	0.735468	−	0.677559i	$-0.236962\pi$
$563$	34.9018	1.47094	0.735468	+	0.677559i	$0.236962\pi$
$564$	0	0
$565$	0	0
$566$	0	0
$567$	11.0542	0.464233
$568$	0	0
$569$	−41.9646	−1.75925	−0.879623	−	0.475671i	$-0.842205\pi$
$569$	−41.9646	−1.75925	−0.879623	+	0.475671i	$0.842205\pi$
$570$	0	0
$571$	13.8332	0.578900	0.289450	−	0.957193i	$-0.406528\pi$
$571$	13.8332	0.578900	0.289450	+	0.957193i	$0.406528\pi$
$572$	0	0
$573$	2.78408	0.116307
$574$	0	0
$575$	0	0
$576$	0	0
$577$	12.7793	0.532008	0.266004	−	0.963972i	$-0.414296\pi$
$577$	12.7793	0.532008	0.266004	+	0.963972i	$0.414296\pi$
$578$	0	0
$579$	46.5486	1.93449
$580$	0	0
$581$	−1.75764	−0.0729191
$582$	0	0
$583$	−15.1304	−0.626638
$584$	0	0
$585$	0	0
$586$	0	0
$587$	−12.1870	−0.503009	−0.251505	−	0.967856i	$-0.580925\pi$
$587$	−12.1870	−0.503009	−0.251505	+	0.967856i	$0.580925\pi$
$588$	0	0
$589$	−0.352879	−0.0145401
$590$	0	0
$591$	−26.8245	−1.10341
$592$	0	0
$593$	31.2580	1.28361	0.641807	−	0.766866i	$-0.278185\pi$
$593$	31.2580	1.28361	0.641807	+	0.766866i	$0.278185\pi$
$594$	0	0
$595$	0	0
$596$	0	0
$597$	−22.8785	−0.936356
$598$	0	0
$599$	33.3707	1.36349	0.681746	−	0.731589i	$-0.261221\pi$
$599$	33.3707	1.36349	0.681746	+	0.731589i	$0.261221\pi$
$600$	0	0
$601$	−46.8052	−1.90922	−0.954611	−	0.297854i	$-0.903729\pi$
$601$	−46.8052	−1.90922	−0.954611	+	0.297854i	$0.903729\pi$
$602$	0	0
$603$	−4.00732	−0.163191
$604$	0	0
$605$	0	0
$606$	0	0
$607$	30.7401	1.24770	0.623851	−	0.781543i	$-0.285567\pi$
$607$	30.7401	1.24770	0.623851	+	0.781543i	$0.285567\pi$
$608$	0	0
$609$	11.7473	0.476027
$610$	0	0
$611$	33.4919	1.35494
$612$	0	0
$613$	38.2895	1.54650	0.773248	−	0.634103i	$-0.218631\pi$
$613$	38.2895	1.54650	0.773248	+	0.634103i	$0.218631\pi$
$614$	0	0
$615$	0	0
$616$	0	0
$617$	−0.425306	−0.0171222	−0.00856109	−	0.999963i	$-0.502725\pi$
$617$	−0.425306	−0.0171222	−0.00856109	+	0.999963i	$0.502725\pi$
$618$	0	0
$619$	−7.51147	−0.301912	−0.150956	−	0.988541i	$-0.548235\pi$
$619$	−7.51147	−0.301912	−0.150956	+	0.988541i	$0.548235\pi$
$620$	0	0
$621$	−11.6691	−0.468263
$622$	0	0
$623$	−14.3977	−0.576833
$624$	0	0
$625$	0	0
$626$	0	0
$627$	−11.3639	−0.453831
$628$	0	0
$629$	−6.22061	−0.248032
$630$	0	0
$631$	11.2716	0.448714	0.224357	−	0.974507i	$-0.427972\pi$
$631$	11.2716	0.448714	0.224357	+	0.974507i	$0.427972\pi$
$632$	0	0
$633$	19.0338	0.756528
$634$	0	0
$635$	0	0
$636$	0	0
$637$	20.2955	0.804136
$638$	0	0
$639$	−17.6783	−0.699343
$640$	0	0
$641$	26.0825	1.03020	0.515099	−	0.857131i	$-0.327755\pi$
$641$	26.0825	1.03020	0.515099	+	0.857131i	$0.327755\pi$
$642$	0	0
$643$	−31.9492	−1.25995	−0.629977	−	0.776614i	$-0.716936\pi$
$643$	−31.9492	−1.25995	−0.629977	+	0.776614i	$0.716936\pi$
$644$	0	0
$645$	0	0
$646$	0	0
$647$	−7.39433	−0.290701	−0.145351	−	0.989380i	$-0.546431\pi$
$647$	−7.39433	−0.290701	−0.145351	+	0.989380i	$0.546431\pi$
$648$	0	0
$649$	9.83550	0.386077
$650$	0	0
$651$	0.297895	0.0116754
$652$	0	0
$653$	−18.6853	−0.731212	−0.365606	−	0.930770i	$-0.619138\pi$
$653$	−18.6853	−0.731212	−0.365606	+	0.930770i	$0.619138\pi$
$654$	0	0
$655$	0	0
$656$	0	0
$657$	1.42256	0.0554994
$658$	0	0
$659$	−9.80157	−0.381815	−0.190907	−	0.981608i	$-0.561143\pi$
$659$	−9.80157	−0.381815	−0.190907	+	0.981608i	$0.561143\pi$
$660$	0	0
$661$	−28.1585	−1.09524	−0.547619	−	0.836728i	$-0.684466\pi$
$661$	−28.1585	−1.09524	−0.547619	+	0.836728i	$0.684466\pi$
$662$	0	0
$663$	−21.4710	−0.833866
$664$	0	0
$665$	0	0
$666$	0	0
$667$	−24.4966	−0.948511
$668$	0	0
$669$	−62.3127	−2.40915
$670$	0	0
$671$	5.53943	0.213847
$672$	0	0
$673$	39.0253	1.50432	0.752158	−	0.658983i	$-0.229013\pi$
$673$	39.0253	1.50432	0.752158	+	0.658983i	$0.229013\pi$
$674$	0	0
$675$	0	0
$676$	0	0
$677$	−5.03533	−0.193523	−0.0967617	−	0.995308i	$-0.530848\pi$
$677$	−5.03533	−0.193523	−0.0967617	+	0.995308i	$0.530848\pi$
$678$	0	0
$679$	16.8997	0.648549
$680$	0	0
$681$	−48.8977	−1.87376
$682$	0	0
$683$	−30.3312	−1.16059	−0.580295	−	0.814406i	$-0.697063\pi$
$683$	−30.3312	−1.16059	−0.580295	+	0.814406i	$0.697063\pi$
$684$	0	0
$685$	0	0
$686$	0	0
$687$	5.44257	0.207647
$688$	0	0
$689$	−25.5255	−0.972444
$690$	0	0
$691$	21.2329	0.807739	0.403869	−	0.914817i	$-0.367665\pi$
$691$	21.2329	0.807739	0.403869	+	0.914817i	$0.367665\pi$
$692$	0	0
$693$	3.63886	0.138229
$694$	0	0
$695$	0	0
$696$	0	0
$697$	24.9888	0.946520
$698$	0	0
$699$	13.0943	0.495273
$700$	0	0
$701$	32.7698	1.23770	0.618849	−	0.785510i	$-0.287599\pi$
$701$	32.7698	1.23770	0.618849	+	0.785510i	$0.287599\pi$
$702$	0	0
$703$	−5.55432	−0.209485
$704$	0	0
$705$	0	0
$706$	0	0
$707$	2.52780	0.0950676
$708$	0	0
$709$	19.8459	0.745330	0.372665	−	0.927966i	$-0.378444\pi$
$709$	19.8459	0.745330	0.372665	+	0.927966i	$0.378444\pi$
$710$	0	0
$711$	−29.0604	−1.08985
$712$	0	0
$713$	−0.621196	−0.0232640
$714$	0	0
$715$	0	0
$716$	0	0
$717$	15.4607	0.577392
$718$	0	0
$719$	−24.2201	−0.903258	−0.451629	−	0.892206i	$-0.649157\pi$
$719$	−24.2201	−0.903258	−0.451629	+	0.892206i	$0.649157\pi$
$720$	0	0
$721$	10.0882	0.375703
$722$	0	0
$723$	2.59370	0.0964608
$724$	0	0
$725$	0	0
$726$	0	0
$727$	−5.86510	−0.217524	−0.108762	−	0.994068i	$-0.534689\pi$
$727$	−5.86510	−0.217524	−0.108762	+	0.994068i	$0.534689\pi$
$728$	0	0
$729$	−3.50531	−0.129826
$730$	0	0
$731$	−13.4420	−0.497172
$732$	0	0
$733$	34.5015	1.27434	0.637171	−	0.770723i	$-0.280105\pi$
$733$	34.5015	1.27434	0.637171	+	0.770723i	$0.280105\pi$
$734$	0	0
$735$	0	0
$736$	0	0
$737$	4.37155	0.161028
$738$	0	0
$739$	−39.5712	−1.45565	−0.727826	−	0.685762i	$-0.759469\pi$
$739$	−39.5712	−1.45565	−0.727826	+	0.685762i	$0.759469\pi$
$740$	0	0
$741$	−19.1713	−0.704275
$742$	0	0
$743$	29.7058	1.08980	0.544900	−	0.838501i	$-0.316567\pi$
$743$	29.7058	1.08980	0.544900	+	0.838501i	$0.316567\pi$
$744$	0	0
$745$	0	0
$746$	0	0
$747$	3.24708	0.118804
$748$	0	0
$749$	−4.78058	−0.174679
$750$	0	0
$751$	−26.8870	−0.981122	−0.490561	−	0.871407i	$-0.663208\pi$
$751$	−26.8870	−0.981122	−0.490561	+	0.871407i	$0.663208\pi$
$752$	0	0
$753$	−10.1321	−0.369235
$754$	0	0
$755$	0	0
$756$	0	0
$757$	44.6792	1.62389	0.811947	−	0.583731i	$-0.198408\pi$
$757$	44.6792	1.62389	0.811947	+	0.583731i	$0.198408\pi$
$758$	0	0
$759$	−20.0047	−0.726123
$760$	0	0
$761$	20.3080	0.736163	0.368081	−	0.929794i	$-0.380015\pi$
$761$	20.3080	0.736163	0.368081	+	0.929794i	$0.380015\pi$
$762$	0	0
$763$	−16.1506	−0.584690
$764$	0	0
$765$	0	0
$766$	0	0
$767$	16.5928	0.599131
$768$	0	0
$769$	26.0577	0.939665	0.469832	−	0.882756i	$-0.344314\pi$
$769$	26.0577	0.939665	0.469832	+	0.882756i	$0.344314\pi$
$770$	0	0
$771$	−21.4472	−0.772402
$772$	0	0
$773$	13.7305	0.493851	0.246926	−	0.969034i	$-0.420580\pi$
$773$	13.7305	0.493851	0.246926	+	0.969034i	$0.420580\pi$
$774$	0	0
$775$	0	0
$776$	0	0
$777$	4.68887	0.168212
$778$	0	0
$779$	22.3123	0.799421
$780$	0	0
$781$	19.2851	0.690074
$782$	0	0
$783$	13.8098	0.493523
$784$	0	0
$785$	0	0
$786$	0	0
$787$	19.6660	0.701018	0.350509	−	0.936559i	$-0.386009\pi$
$787$	19.6660	0.701018	0.350509	+	0.936559i	$0.386009\pi$
$788$	0	0
$789$	−2.18932	−0.0779418
$790$	0	0
$791$	−6.70568	−0.238427
$792$	0	0
$793$	9.34520	0.331858
$794$	0	0
$795$	0	0
$796$	0	0
$797$	10.9441	0.387660	0.193830	−	0.981035i	$-0.437909\pi$
$797$	10.9441	0.387660	0.193830	+	0.981035i	$0.437909\pi$
$798$	0	0
$799$	−28.7318	−1.01646
$800$	0	0
$801$	26.5985	0.939812
$802$	0	0
$803$	−1.55186	−0.0547639
$804$	0	0
$805$	0	0
$806$	0	0
$807$	−7.22982	−0.254502
$808$	0	0
$809$	16.4427	0.578096	0.289048	−	0.957315i	$-0.406661\pi$
$809$	16.4427	0.578096	0.289048	+	0.957315i	$0.406661\pi$
$810$	0	0
$811$	−22.6473	−0.795253	−0.397627	−	0.917547i	$-0.630166\pi$
$811$	−22.6473	−0.795253	−0.397627	+	0.917547i	$0.630166\pi$
$812$	0	0
$813$	−26.7118	−0.936823
$814$	0	0
$815$	0	0
$816$	0	0
$817$	−12.0023	−0.419906
$818$	0	0
$819$	6.13887	0.214509
$820$	0	0
$821$	−39.7792	−1.38830	−0.694151	−	0.719829i	$-0.744220\pi$
$821$	−39.7792	−1.38830	−0.694151	+	0.719829i	$0.744220\pi$
$822$	0	0
$823$	−16.5602	−0.577252	−0.288626	−	0.957442i	$-0.593198\pi$
$823$	−16.5602	−0.577252	−0.288626	+	0.957442i	$0.593198\pi$
$824$	0	0
$825$	0	0
$826$	0	0
$827$	26.0361	0.905365	0.452683	−	0.891672i	$-0.350467\pi$
$827$	26.0361	0.905365	0.452683	+	0.891672i	$0.350467\pi$
$828$	0	0
$829$	5.14357	0.178644	0.0893218	−	0.996003i	$-0.471530\pi$
$829$	5.14357	0.178644	0.0893218	+	0.996003i	$0.471530\pi$
$830$	0	0
$831$	−26.0885	−0.905002
$832$	0	0
$833$	−17.4109	−0.603252
$834$	0	0
$835$	0	0
$836$	0	0
$837$	0.350197	0.0121046
$838$	0	0
$839$	−38.5664	−1.33146	−0.665730	−	0.746193i	$-0.731880\pi$
$839$	−38.5664	−1.33146	−0.665730	+	0.746193i	$0.731880\pi$
$840$	0	0
$841$	−0.00936035	−0.000322771 0
$842$	0	0
$843$	−54.1744	−1.86586
$844$	0	0
$845$	0	0
$846$	0	0
$847$	6.94679	0.238694
$848$	0	0
$849$	7.39447	0.253777
$850$	0	0
$851$	−9.77764	−0.335173
$852$	0	0
$853$	9.14763	0.313209	0.156604	−	0.987661i	$-0.449945\pi$
$853$	9.14763	0.313209	0.156604	+	0.987661i	$0.449945\pi$
$854$	0	0
$855$	0	0
$856$	0	0
$857$	−13.6712	−0.466998	−0.233499	−	0.972357i	$-0.575018\pi$
$857$	−13.6712	−0.466998	−0.233499	+	0.972357i	$0.575018\pi$
$858$	0	0
$859$	35.6556	1.21655	0.608277	−	0.793725i	$-0.291861\pi$
$859$	35.6556	1.21655	0.608277	+	0.793725i	$0.291861\pi$
$860$	0	0
$861$	−18.8357	−0.641919
$862$	0	0
$863$	−33.9333	−1.15510	−0.577552	−	0.816354i	$-0.695992\pi$
$863$	−33.9333	−1.15510	−0.577552	+	0.816354i	$0.695992\pi$
$864$	0	0
$865$	0	0
$866$	0	0
$867$	−18.9550	−0.643744
$868$	0	0
$869$	31.7017	1.07541
$870$	0	0
$871$	7.37494	0.249890
$872$	0	0
$873$	−31.2206	−1.05666
$874$	0	0
$875$	0	0
$876$	0	0
$877$	28.6991	0.969099	0.484550	−	0.874764i	$-0.338983\pi$
$877$	28.6991	0.969099	0.484550	+	0.874764i	$0.338983\pi$
$878$	0	0
$879$	−19.7060	−0.664665
$880$	0	0
$881$	8.33039	0.280658	0.140329	−	0.990105i	$-0.455184\pi$
$881$	8.33039	0.280658	0.140329	+	0.990105i	$0.455184\pi$
$882$	0	0
$883$	50.3165	1.69329	0.846643	−	0.532161i	$-0.178620\pi$
$883$	50.3165	1.69329	0.846643	+	0.532161i	$0.178620\pi$
$884$	0	0
$885$	0	0
$886$	0	0
$887$	−12.1186	−0.406903	−0.203452	−	0.979085i	$-0.565216\pi$
$887$	−12.1186	−0.406903	−0.203452	+	0.979085i	$0.565216\pi$
$888$	0	0
$889$	−1.47948	−0.0496202
$890$	0	0
$891$	22.2777	0.746332
$892$	0	0
$893$	−25.6543	−0.858490
$894$	0	0
$895$	0	0
$896$	0	0
$897$	−33.7485	−1.12683
$898$	0	0
$899$	0.735159	0.0245189
$900$	0	0
$901$	21.8976	0.729514
$902$	0	0
$903$	10.1321	0.337176
$904$	0	0
$905$	0	0
$906$	0	0
$907$	31.9105	1.05957	0.529786	−	0.848132i	$-0.322272\pi$
$907$	31.9105	1.05957	0.529786	+	0.848132i	$0.322272\pi$
$908$	0	0
$909$	−4.66988	−0.154890
$910$	0	0
$911$	24.6880	0.817949	0.408975	−	0.912546i	$-0.365886\pi$
$911$	24.6880	0.817949	0.408975	+	0.912546i	$0.365886\pi$
$912$	0	0
$913$	−3.54220	−0.117230
$914$	0	0
$915$	0	0
$916$	0	0
$917$	14.0074	0.462565
$918$	0	0
$919$	19.4850	0.642752	0.321376	−	0.946952i	$-0.395855\pi$
$919$	19.4850	0.642752	0.321376	+	0.946952i	$0.395855\pi$
$920$	0	0
$921$	−20.8446	−0.686854
$922$	0	0
$923$	32.5345	1.07089
$924$	0	0
$925$	0	0
$926$	0	0
$927$	−18.6369	−0.612118
$928$	0	0
$929$	11.7642	0.385972	0.192986	−	0.981201i	$-0.438183\pi$
$929$	11.7642	0.385972	0.192986	+	0.981201i	$0.438183\pi$
$930$	0	0
$931$	−15.5460	−0.509501
$932$	0	0
$933$	−64.4862	−2.11118
$934$	0	0
$935$	0	0
$936$	0	0
$937$	−21.0683	−0.688271	−0.344136	−	0.938920i	$-0.611828\pi$
$937$	−21.0683	−0.688271	−0.344136	+	0.938920i	$0.611828\pi$
$938$	0	0
$939$	41.5296	1.35527
$940$	0	0
$941$	−2.24706	−0.0732521	−0.0366261	−	0.999329i	$-0.511661\pi$
$941$	−2.24706	−0.0732521	−0.0366261	+	0.999329i	$0.511661\pi$
$942$	0	0
$943$	39.2778	1.27906
$944$	0	0
$945$	0	0
$946$	0	0
$947$	6.75625	0.219549	0.109774	−	0.993957i	$-0.464987\pi$
$947$	6.75625	0.219549	0.109774	+	0.993957i	$0.464987\pi$
$948$	0	0
$949$	−2.61803	−0.0849850
$950$	0	0
$951$	50.1021	1.62467
$952$	0	0
$953$	59.9534	1.94208	0.971040	−	0.238918i	$-0.0767926\pi$
$953$	59.9534	1.94208	0.971040	+	0.238918i	$0.0767926\pi$
$954$	0	0
$955$	0	0
$956$	0	0
$957$	23.6747	0.765293
$958$	0	0
$959$	0.684206	0.0220942
$960$	0	0
$961$	−30.9814	−0.999399
$962$	0	0
$963$	8.83169	0.284597
$964$	0	0
$965$	0	0
$966$	0	0
$967$	9.05599	0.291221	0.145610	−	0.989342i	$-0.453485\pi$
$967$	9.05599	0.291221	0.145610	+	0.989342i	$0.453485\pi$
$968$	0	0
$969$	16.4465	0.528338
$970$	0	0
$971$	−47.3508	−1.51956	−0.759780	−	0.650180i	$-0.774693\pi$
$971$	−47.3508	−1.51956	−0.759780	+	0.650180i	$0.774693\pi$
$972$	0	0
$973$	−16.4459	−0.527231
$974$	0	0
$975$	0	0
$976$	0	0
$977$	−4.74467	−0.151795	−0.0758977	−	0.997116i	$-0.524182\pi$
$977$	−4.74467	−0.151795	−0.0758977	+	0.997116i	$0.524182\pi$
$978$	0	0
$979$	−29.0160	−0.927357
$980$	0	0
$981$	29.8367	0.952613
$982$	0	0
$983$	−18.5656	−0.592150	−0.296075	−	0.955165i	$-0.595678\pi$
$983$	−18.5656	−0.592150	−0.296075	+	0.955165i	$0.595678\pi$
$984$	0	0
$985$	0	0
$986$	0	0
$987$	21.6570	0.689350
$988$	0	0
$989$	−21.1284	−0.671843
$990$	0	0
$991$	39.7199	1.26174	0.630871	−	0.775887i	$-0.282698\pi$
$991$	39.7199	1.26174	0.630871	+	0.775887i	$0.282698\pi$
$992$	0	0
$993$	−6.51411	−0.206719
$994$	0	0
$995$	0	0
$996$	0	0
$997$	30.2914	0.959338	0.479669	−	0.877449i	$-0.340757\pi$
$997$	30.2914	0.959338	0.479669	+	0.877449i	$0.340757\pi$
$998$	0	0
$999$	5.51210	0.174395

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10000.2.a.bj.1.7		8
4.3	odd	2		625.2.a.f.1.2		8
5.4	even	2	inner	10000.2.a.bj.1.2		8
12.11	even	2		5625.2.a.x.1.7		8
20.3	even	4		625.2.b.c.624.7		8
20.7	even	4		625.2.b.c.624.2		8
20.19	odd	2		625.2.a.f.1.7		8
25.2	odd	20		400.2.y.c.129.1		8
25.13	odd	20		400.2.y.c.369.1		8
60.59	even	2		5625.2.a.x.1.2		8
100.3	even	20		625.2.e.i.249.2		8
100.11	odd	10		125.2.d.b.101.1		16
100.19	odd	10		625.2.d.o.251.1		16
100.23	even	20		125.2.e.b.24.2		8
100.27	even	20		25.2.e.a.4.1	✓	8
100.31	odd	10		625.2.d.o.251.4		16
100.39	odd	10		125.2.d.b.101.4		16
100.47	even	20		625.2.e.a.249.1		8
100.59	odd	10		125.2.d.b.26.4		16
100.63	even	20		25.2.e.a.19.1	yes	8
100.67	even	20		625.2.e.i.374.2		8
100.71	odd	10		625.2.d.o.376.4		16
100.79	odd	10		625.2.d.o.376.1		16
100.83	even	20		625.2.e.a.374.1		8
100.87	even	20		125.2.e.b.99.2		8
100.91	odd	10		125.2.d.b.26.1		16
300.227	odd	20		225.2.m.a.154.2		8
300.263	odd	20		225.2.m.a.19.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.2.e.a.4.1	✓	8	100.27	even	20
25.2.e.a.19.1	yes	8	100.63	even	20
125.2.d.b.26.1		16	100.91	odd	10
125.2.d.b.26.4		16	100.59	odd	10
125.2.d.b.101.1		16	100.11	odd	10
125.2.d.b.101.4		16	100.39	odd	10
125.2.e.b.24.2		8	100.23	even	20
125.2.e.b.99.2		8	100.87	even	20
225.2.m.a.19.2		8	300.263	odd	20
225.2.m.a.154.2		8	300.227	odd	20
400.2.y.c.129.1		8	25.2	odd	20
400.2.y.c.369.1		8	25.13	odd	20
625.2.a.f.1.2		8	4.3	odd	2
625.2.a.f.1.7		8	20.19	odd	2
625.2.b.c.624.2		8	20.7	even	4
625.2.b.c.624.7		8	20.3	even	4
625.2.d.o.251.1		16	100.19	odd	10
625.2.d.o.251.4		16	100.31	odd	10
625.2.d.o.376.1		16	100.79	odd	10
625.2.d.o.376.4		16	100.71	odd	10
625.2.e.a.249.1		8	100.47	even	20
625.2.e.a.374.1		8	100.83	even	20
625.2.e.i.249.2		8	100.3	even	20
625.2.e.i.374.2		8	100.67	even	20
5625.2.a.x.1.2		8	60.59	even	2
5625.2.a.x.1.7		8	12.11	even	2
10000.2.a.bj.1.2		8	5.4	even	2	inner
10000.2.a.bj.1.7		8	1.1	even	1	trivial

Overview	Random
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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

Introduction

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Fields

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Database

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	10000.2.a.bj.1.7

Level	$10000$
Weight	$2$
Character	10000.1
Self dual	yes
Analytic conductor	$79.850$
Analytic rank	$1$
Dimension	$8$
Inner twists	$2$