LMFDB - Embedded newform 9409.2.a.o.1.105

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [9409,2,Mod(1,9409)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9409, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("9409.1"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 9409 = 97^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	9409.a (trivial)

Newform invariants

comment:select newform

sage:traces = [128,16,16,144,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	yes
Analytic conductor:	$75.1312432618$
Analytic rank:	$0$
Dimension:	$128$
Twist minimal:	no (minimal twist has level 97)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.105
Character	$\chi$	$=$	9409.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+2.05447 q^{2} -2.21611 q^{3} +2.22085 q^{4} -0.0918616 q^{5} -4.55293 q^{6} -1.32243 q^{7} +0.453730 q^{8} +1.91113 q^{9} -0.188727 q^{10} +2.06984 q^{11} -4.92164 q^{12} -5.93749 q^{13} -2.71689 q^{14} +0.203575 q^{15} -3.50953 q^{16} -3.69766 q^{17} +3.92636 q^{18} -2.93819 q^{19} -0.204011 q^{20} +2.93064 q^{21} +4.25242 q^{22} -6.94438 q^{23} -1.00551 q^{24} -4.99156 q^{25} -12.1984 q^{26} +2.41306 q^{27} -2.93691 q^{28} +1.96584 q^{29} +0.418239 q^{30} +2.48771 q^{31} -8.11768 q^{32} -4.58698 q^{33} -7.59673 q^{34} +0.121480 q^{35} +4.24433 q^{36} -3.87243 q^{37} -6.03642 q^{38} +13.1581 q^{39} -0.0416803 q^{40} +8.20619 q^{41} +6.02091 q^{42} +2.28270 q^{43} +4.59679 q^{44} -0.175559 q^{45} -14.2670 q^{46} -6.56975 q^{47} +7.77748 q^{48} -5.25119 q^{49} -10.2550 q^{50} +8.19440 q^{51} -13.1863 q^{52} +13.6650 q^{53} +4.95755 q^{54} -0.190139 q^{55} -0.600024 q^{56} +6.51133 q^{57} +4.03876 q^{58} +14.1905 q^{59} +0.452110 q^{60} +14.3342 q^{61} +5.11092 q^{62} -2.52733 q^{63} -9.65848 q^{64} +0.545427 q^{65} -9.42381 q^{66} -0.0774098 q^{67} -8.21194 q^{68} +15.3895 q^{69} +0.249578 q^{70} +0.356995 q^{71} +0.867135 q^{72} -6.29602 q^{73} -7.95580 q^{74} +11.0618 q^{75} -6.52527 q^{76} -2.73721 q^{77} +27.0329 q^{78} +0.920565 q^{79} +0.322391 q^{80} -11.0810 q^{81} +16.8594 q^{82} +0.398150 q^{83} +6.50851 q^{84} +0.339673 q^{85} +4.68973 q^{86} -4.35651 q^{87} +0.939146 q^{88} -3.85681 q^{89} -0.360681 q^{90} +7.85189 q^{91} -15.4224 q^{92} -5.51302 q^{93} -13.4974 q^{94} +0.269907 q^{95} +17.9896 q^{96} -10.7884 q^{98} +3.95572 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 16 q^{2} + 16 q^{3} + 144 q^{4} + 32 q^{6} + 48 q^{8} + 144 q^{9} + 64 q^{11} + 32 q^{12} + 176 q^{16} + 48 q^{18} + 32 q^{22} + 144 q^{24} + 128 q^{25} + 64 q^{27} + 96 q^{31} + 112 q^{32} + 16 q^{33}+ \cdots + 304 q^{99}+O(q^{100}) $ 128 * q + 16 * q^2 + 16 * q^3 + 144 * q^4 + 32 * q^6 + 48 * q^8 + 144 * q^9 + 64 * q^11 + 32 * q^12 + 176 * q^16 + 48 * q^18 + 32 * q^22 + 144 * q^24 + 128 * q^25 + 64 * q^27 + 96 * q^31 + 112 * q^32 + 16 * q^33 + 144 * q^35 + 224 * q^36 + 64 * q^43 + 160 * q^44 + 224 * q^47 + 64 * q^48 + 128 * q^49 + 144 * q^50 + 96 * q^53 + 96 * q^54 + 112 * q^61 + 112 * q^62 + 240 * q^64 + 64 * q^65 + 16 * q^70 + 304 * q^72 - 32 * q^73 + 48 * q^75 + 96 * q^79 + 112 * q^81 + 96 * q^86 - 32 * q^88 + 192 * q^89 + 128 * q^91 + 128 * q^94 + 208 * q^95 + 352 * q^96 + 208 * q^98 + 304 * 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 $

$2$	2.05447	1.45273	0.726365	−	0.687309i	$-0.241208\pi$
$2$	2.05447	1.45273	0.726365	+	0.687309i	$0.241208\pi$
$3$	−2.21611	−1.27947	−0.639735	−	0.768596i	$-0.720956\pi$
$3$	−2.21611	−1.27947	−0.639735	+	0.768596i	$0.720956\pi$
$4$	2.22085	1.11042
$5$	−0.0918616	−0.0410818	−0.0205409	−	0.999789i	$-0.506539\pi$
$5$	−0.0918616	−0.0410818	−0.0205409	+	0.999789i	$0.506539\pi$
$6$	−4.55293	−1.85872
$7$	−1.32243	−0.499830	−0.249915	−	0.968268i	$-0.580403\pi$
$7$	−1.32243	−0.499830	−0.249915	+	0.968268i	$0.580403\pi$
$8$	0.453730	0.160418
$9$	1.91113	0.637043
$10$	−0.188727	−0.0596807
$11$	2.06984	0.624079	0.312040	−	0.950069i	$-0.398988\pi$
$11$	2.06984	0.624079	0.312040	+	0.950069i	$0.398988\pi$
$12$	−4.92164	−1.42075
$13$	−5.93749	−1.64676	−0.823381	−	0.567488i	$-0.807915\pi$
$13$	−5.93749	−1.64676	−0.823381	+	0.567488i	$0.807915\pi$
$14$	−2.71689	−0.726118
$15$	0.203575	0.0525629
$16$	−3.50953	−0.877381
$17$	−3.69766	−0.896814	−0.448407	−	0.893830i	$-0.648008\pi$
$17$	−3.69766	−0.896814	−0.448407	+	0.893830i	$0.648008\pi$
$18$	3.92636	0.925451
$19$	−2.93819	−0.674066	−0.337033	−	0.941493i	$-0.609423\pi$
$19$	−2.93819	−0.674066	−0.337033	+	0.941493i	$0.609423\pi$
$20$	−0.204011	−0.0456182
$21$	2.93064	0.639518
$22$	4.25242	0.906618
$23$	−6.94438	−1.44800	−0.724001	−	0.689799i	$-0.757699\pi$
$23$	−6.94438	−1.44800	−0.724001	+	0.689799i	$0.757699\pi$
$24$	−1.00551	−0.205249
$25$	−4.99156	−0.998312
$26$	−12.1984	−2.39230
$27$	2.41306	0.464393
$28$	−2.93691	−0.555024
$29$	1.96584	0.365047	0.182524	−	0.983201i	$-0.441573\pi$
$29$	1.96584	0.365047	0.182524	+	0.983201i	$0.441573\pi$
$30$	0.418239	0.0763597
$31$	2.48771	0.446805	0.223403	−	0.974726i	$-0.428284\pi$
$31$	2.48771	0.446805	0.223403	+	0.974726i	$0.428284\pi$
$32$	−8.11768	−1.43502
$33$	−4.58698	−0.798490
$34$	−7.59673	−1.30283
$35$	0.121480	0.0205339
$36$	4.24433	0.707388
$37$	−3.87243	−0.636624	−0.318312	−	0.947986i	$-0.603116\pi$
$37$	−3.87243	−0.636624	−0.318312	+	0.947986i	$0.603116\pi$
$38$	−6.03642	−0.979236
$39$	13.1581	2.10698
$40$	−0.0416803	−0.00659024
$41$	8.20619	1.28159	0.640796	−	0.767711i	$-0.278604\pi$
$41$	8.20619	1.28159	0.640796	+	0.767711i	$0.278604\pi$
$42$	6.02091	0.929046
$43$	2.28270	0.348108	0.174054	−	0.984736i	$-0.444313\pi$
$43$	2.28270	0.348108	0.174054	+	0.984736i	$0.444313\pi$
$44$	4.59679	0.692993
$45$	−0.175559	−0.0261708
$46$	−14.2670	−2.10356
$47$	−6.56975	−0.958296	−0.479148	−	0.877734i	$-0.659054\pi$
$47$	−6.56975	−0.958296	−0.479148	+	0.877734i	$0.659054\pi$
$48$	7.77748	1.12258
$49$	−5.25119	−0.750170
$50$	−10.2550	−1.45028
$51$	8.19440	1.14745
$52$	−13.1863	−1.82861
$53$	13.6650	1.87703	0.938517	−	0.345234i	$-0.112200\pi$
$53$	13.6650	1.87703	0.938517	+	0.345234i	$0.112200\pi$
$54$	4.95755	0.674638
$55$	−0.190139	−0.0256383
$56$	−0.600024	−0.0801816
$57$	6.51133	0.862447
$58$	4.03876	0.530315
$59$	14.1905	1.84745	0.923725	−	0.383057i	$-0.125129\pi$
$59$	14.1905	1.84745	0.923725	+	0.383057i	$0.125129\pi$
$60$	0.452110	0.0583671
$61$	14.3342	1.83530	0.917651	−	0.397387i	$-0.130083\pi$
$61$	14.3342	1.83530	0.917651	+	0.397387i	$0.130083\pi$
$62$	5.11092	0.649088
$63$	−2.52733	−0.318413
$64$	−9.65848	−1.20731
$65$	0.545427	0.0676519
$66$	−9.42381	−1.15999
$67$	−0.0774098	−0.00945711	−0.00472856	−	0.999989i	$-0.501505\pi$
$67$	−0.0774098	−0.00945711	−0.00472856	+	0.999989i	$0.501505\pi$
$68$	−8.21194	−0.995844
$69$	15.3895	1.85268
$70$	0.249578	0.0298302
$71$	0.356995	0.0423675	0.0211838	−	0.999776i	$-0.493256\pi$
$71$	0.356995	0.0423675	0.0211838	+	0.999776i	$0.493256\pi$
$72$	0.867135	0.102193
$73$	−6.29602	−0.736893	−0.368447	−	0.929649i	$-0.620110\pi$
$73$	−6.29602	−0.736893	−0.368447	+	0.929649i	$0.620110\pi$
$74$	−7.95580	−0.924843
$75$	11.0618	1.27731
$76$	−6.52527	−0.748500
$77$	−2.73721	−0.311934
$78$	27.0329	3.06088
$79$	0.920565	0.103572	0.0517858	−	0.998658i	$-0.483509\pi$
$79$	0.920565	0.103572	0.0517858	+	0.998658i	$0.483509\pi$
$80$	0.322391	0.0360444
$81$	−11.0810	−1.23122
$82$	16.8594	1.86181
$83$	0.398150	0.0437027	0.0218513	−	0.999761i	$-0.493044\pi$
$83$	0.398150	0.0437027	0.0218513	+	0.999761i	$0.493044\pi$
$84$	6.50851	0.710136
$85$	0.339673	0.0368427
$86$	4.68973	0.505707
$87$	−4.35651	−0.467067
$88$	0.939146	0.100113
$89$	−3.85681	−0.408821	−0.204410	−	0.978885i	$-0.565528\pi$
$89$	−3.85681	−0.408821	−0.204410	+	0.978885i	$0.565528\pi$
$90$	−0.360681	−0.0380192
$91$	7.85189	0.823102
$92$	−15.4224	−1.60790
$93$	−5.51302	−0.571674
$94$	−13.4974	−1.39215
$95$	0.269907	0.0276918
$96$	17.9896	1.83606
$97$	0	0
$97$	0	0
$98$	−10.7884	−1.08979
$99$	3.95572	0.397565
$100$	−11.0855	−1.10855
$101$	10.4636	1.04117	0.520583	−	0.853811i	$-0.325715\pi$
$101$	10.4636	1.04117	0.520583	+	0.853811i	$0.325715\pi$
$102$	16.8352	1.66693
$103$	−7.23695	−0.713078	−0.356539	−	0.934280i	$-0.616043\pi$
$103$	−7.23695	−0.713078	−0.356539	+	0.934280i	$0.616043\pi$
$104$	−2.69401	−0.264170
$105$	−0.269213	−0.0262725
$106$	28.0744	2.72682
$107$	−13.6099	−1.31572	−0.657860	−	0.753140i	$-0.728538\pi$
$107$	−13.6099	−1.31572	−0.657860	+	0.753140i	$0.728538\pi$
$108$	5.35904	0.515674
$109$	16.1352	1.54547	0.772735	−	0.634729i	$-0.218888\pi$
$109$	16.1352	1.54547	0.772735	+	0.634729i	$0.218888\pi$
$110$	−0.390634	−0.0372455
$111$	8.58172	0.814541
$112$	4.64109	0.438542
$113$	−9.70471	−0.912942	−0.456471	−	0.889738i	$-0.650887\pi$
$113$	−9.70471	−0.912942	−0.456471	+	0.889738i	$0.650887\pi$
$114$	13.3773	1.25290
$115$	0.637922	0.0594865
$116$	4.36583	0.405357
$117$	−11.3473	−1.04906
$118$	29.1540	2.68385
$119$	4.88988	0.448254
$120$	0.0923681	0.00843201
$121$	−6.71578	−0.610525
$122$	29.4491	2.66620
$123$	−18.1858	−1.63976
$124$	5.52482	0.496144
$125$	0.917841	0.0820942
$126$	−5.19232	−0.462568
$127$	−0.771841	−0.0684898	−0.0342449	−	0.999413i	$-0.510903\pi$
$127$	−0.771841	−0.0684898	−0.0342449	+	0.999413i	$0.510903\pi$
$128$	−3.60771	−0.318879
$129$	−5.05870	−0.445394
$130$	1.12056	0.0982800
$131$	−20.2278	−1.76731	−0.883655	−	0.468139i	$-0.844925\pi$
$131$	−20.2278	−1.76731	−0.883655	+	0.468139i	$0.844925\pi$
$132$	−10.1870	−0.886663
$133$	3.88553	0.336919
$134$	−0.159036	−0.0137386
$135$	−0.221667	−0.0190781
$136$	−1.67774	−0.143865
$137$	−0.113820	−0.00972428	−0.00486214	−	0.999988i	$-0.501548\pi$
$137$	−0.113820	−0.00972428	−0.00486214	+	0.999988i	$0.501548\pi$
$138$	31.6172	2.69144
$139$	10.8614	0.921250	0.460625	−	0.887595i	$-0.347625\pi$
$139$	10.8614	0.921250	0.460625	+	0.887595i	$0.347625\pi$
$140$	0.269789	0.0228014
$141$	14.5593	1.22611
$142$	0.733436	0.0615486
$143$	−12.2896	−1.02771
$144$	−6.70715	−0.558929
$145$	−0.180585	−0.0149968
$146$	−12.9350	−1.07051
$147$	11.6372	0.959819
$148$	−8.60009	−0.706923
$149$	6.68892	0.547978	0.273989	−	0.961733i	$-0.411657\pi$
$149$	6.68892	0.547978	0.273989	+	0.961733i	$0.411657\pi$
$150$	22.7262	1.85559
$151$	−15.1372	−1.23185	−0.615924	−	0.787806i	$-0.711217\pi$
$151$	−15.1372	−1.23185	−0.615924	+	0.787806i	$0.711217\pi$
$152$	−1.33314	−0.108132
$153$	−7.06669	−0.571308
$154$	−5.62351	−0.453155
$155$	−0.228525	−0.0183556
$156$	29.2222	2.33965
$157$	−13.7796	−1.09973	−0.549866	−	0.835253i	$-0.685321\pi$
$157$	−13.7796	−1.09973	−0.549866	+	0.835253i	$0.685321\pi$
$158$	1.89127	0.150462
$159$	−30.2831	−2.40161
$160$	0.745703	0.0589530
$161$	9.18343	0.723755
$162$	−22.7655	−1.78863
$163$	13.8374	1.08383	0.541915	−	0.840434i	$-0.317700\pi$
$163$	13.8374	1.08383	0.541915	+	0.840434i	$0.317700\pi$
$164$	18.2247	1.42311
$165$	0.421367	0.0328034
$166$	0.817988	0.0634882
$167$	10.4933	0.812000	0.406000	−	0.913873i	$-0.366923\pi$
$167$	10.4933	0.812000	0.406000	+	0.913873i	$0.366923\pi$
$168$	1.32972	0.102590
$169$	22.2538	1.71183
$170$	0.697848	0.0535225
$171$	−5.61525	−0.429409
$172$	5.06953	0.386548
$173$	−19.6933	−1.49725	−0.748625	−	0.662994i	$-0.769286\pi$
$173$	−19.6933	−1.49725	−0.748625	+	0.662994i	$0.769286\pi$
$174$	−8.95032	−0.678522
$175$	6.60097	0.498987
$176$	−7.26414	−0.547555
$177$	−31.4477	−2.36376
$178$	−7.92370	−0.593906
$179$	−11.0637	−0.826939	−0.413469	−	0.910518i	$-0.635683\pi$
$179$	−11.0637	−0.826939	−0.413469	+	0.910518i	$0.635683\pi$
$180$	−0.389891	−0.0290608
$181$	16.8315	1.25108	0.625538	−	0.780194i	$-0.284880\pi$
$181$	16.8315	1.25108	0.625538	+	0.780194i	$0.284880\pi$
$182$	16.1315	1.19574
$183$	−31.7660	−2.34821
$184$	−3.15087	−0.232285
$185$	0.355728	0.0261536
$186$	−11.3263	−0.830488
$187$	−7.65354	−0.559683
$188$	−14.5904	−1.06412
$189$	−3.19109	−0.232118
$190$	0.554515	0.0402288
$191$	8.24081	0.596284	0.298142	−	0.954521i	$-0.403633\pi$
$191$	8.24081	0.596284	0.298142	+	0.954521i	$0.403633\pi$
$192$	21.4042	1.54472
$193$	13.7309	0.988369	0.494185	−	0.869357i	$-0.335467\pi$
$193$	13.7309	0.988369	0.494185	+	0.869357i	$0.335467\pi$
$194$	0	0
$195$	−1.20873	−0.0865586
$196$	−11.6621	−0.833007
$197$	3.21894	0.229340	0.114670	−	0.993404i	$-0.463419\pi$
$197$	3.21894	0.229340	0.114670	+	0.993404i	$0.463419\pi$
$198$	8.12691	0.577555
$199$	18.7217	1.32714	0.663571	−	0.748113i	$-0.269040\pi$
$199$	18.7217	1.32714	0.663571	+	0.748113i	$0.269040\pi$
$200$	−2.26482	−0.160147
$201$	0.171548	0.0121001
$202$	21.4971	1.51253
$203$	−2.59968	−0.182462
$204$	18.1985	1.27415
$205$	−0.753834	−0.0526501
$206$	−14.8681	−1.03591
$207$	−13.2716	−0.922439
$208$	20.8378	1.44484
$209$	−6.08156	−0.420670
$210$	−0.553091	−0.0381669
$211$	8.22855	0.566477	0.283239	−	0.959049i	$-0.408591\pi$
$211$	8.22855	0.566477	0.283239	+	0.959049i	$0.408591\pi$
$212$	30.3479	2.08430
$213$	−0.791139	−0.0542080
$214$	−27.9612	−1.91139
$215$	−0.209692	−0.0143009
$216$	1.09488	0.0744968
$217$	−3.28981	−0.223327
$218$	33.1492	2.24515
$219$	13.9526	0.942832
$220$	−0.422269	−0.0284694
$221$	21.9548	1.47684
$222$	17.6309	1.18331
$223$	10.7548	0.720194	0.360097	−	0.932915i	$-0.382744\pi$
$223$	10.7548	0.720194	0.360097	+	0.932915i	$0.382744\pi$
$224$	10.7350	0.717264
$225$	−9.53951	−0.635967
$226$	−19.9380	−1.32626
$227$	−1.25190	−0.0830913	−0.0415456	−	0.999137i	$-0.513228\pi$
$227$	−1.25190	−0.0830913	−0.0415456	+	0.999137i	$0.513228\pi$
$228$	14.4607	0.957683
$229$	5.93649	0.392294	0.196147	−	0.980574i	$-0.437157\pi$
$229$	5.93649	0.392294	0.196147	+	0.980574i	$0.437157\pi$
$230$	1.31059	0.0864178
$231$	6.06594	0.399110
$232$	0.891959	0.0585600
$233$	1.69556	0.111080	0.0555398	−	0.998456i	$-0.482312\pi$
$233$	1.69556	0.111080	0.0555398	+	0.998456i	$0.482312\pi$
$234$	−23.3127	−1.52400
$235$	0.603508	0.0393685
$236$	31.5150	2.05145
$237$	−2.04007	−0.132517
$238$	10.0461	0.651193
$239$	−12.8816	−0.833243	−0.416621	−	0.909080i	$-0.636786\pi$
$239$	−12.8816	−0.833243	−0.416621	+	0.909080i	$0.636786\pi$
$240$	−0.714452	−0.0461177
$241$	1.58717	0.102238	0.0511192	−	0.998693i	$-0.483721\pi$
$241$	1.58717	0.102238	0.0511192	+	0.998693i	$0.483721\pi$
$242$	−13.7974	−0.886929
$243$	17.3174	1.11091
$244$	31.8340	2.03797
$245$	0.482383	0.0308183
$246$	−37.3622	−2.38213
$247$	17.4454	1.11003
$248$	1.12875	0.0716755
$249$	−0.882343	−0.0559162
$250$	1.88568	0.119261
$251$	0.901773	0.0569194	0.0284597	−	0.999595i	$-0.490940\pi$
$251$	0.901773	0.0569194	0.0284597	+	0.999595i	$0.490940\pi$
$252$	−5.61281	−0.353574
$253$	−14.3737	−0.903668
$254$	−1.58573	−0.0994973
$255$	−0.752751	−0.0471391
$256$	11.9050	0.744064
$257$	−3.28396	−0.204848	−0.102424	−	0.994741i	$-0.532660\pi$
$257$	−3.28396	−0.204848	−0.102424	+	0.994741i	$0.532660\pi$
$258$	−10.3929	−0.647037
$259$	5.12101	0.318204
$260$	1.21131	0.0751224
$261$	3.75697	0.232551
$262$	−41.5574	−2.56742
$263$	−19.7553	−1.21817	−0.609083	−	0.793106i	$-0.708462\pi$
$263$	−19.7553	−1.21817	−0.609083	+	0.793106i	$0.708462\pi$
$264$	−2.08125	−0.128092
$265$	−1.25529	−0.0771119
$266$	7.98272	0.489452
$267$	8.54709	0.523074
$268$	−0.171916	−0.0105014
$269$	15.0580	0.918101	0.459050	−	0.888410i	$-0.348190\pi$
$269$	15.0580	0.918101	0.459050	+	0.888410i	$0.348190\pi$
$270$	−0.455409	−0.0277153
$271$	−20.3486	−1.23609	−0.618045	−	0.786143i	$-0.712075\pi$
$271$	−20.3486	−1.23609	−0.618045	+	0.786143i	$0.712075\pi$
$272$	12.9770	0.786848
$273$	−17.4006	−1.05313
$274$	−0.233839	−0.0141267
$275$	−10.3317	−0.623026
$276$	34.1777	2.05726
$277$	−19.5762	−1.17622	−0.588111	−	0.808780i	$-0.700128\pi$
$277$	−19.5762	−1.17622	−0.588111	+	0.808780i	$0.700128\pi$
$278$	22.3144	1.33833
$279$	4.75433	0.284634
$280$	0.0551192	0.00329400
$281$	22.7095	1.35474	0.677368	−	0.735645i	$-0.263121\pi$
$281$	22.7095	1.35474	0.677368	+	0.735645i	$0.263121\pi$
$282$	29.9116	1.78121
$283$	21.4831	1.27704	0.638518	−	0.769607i	$-0.279548\pi$
$283$	21.4831	1.27704	0.638518	+	0.769607i	$0.279548\pi$
$284$	0.792832	0.0470459
$285$	−0.598142	−0.0354309
$286$	−25.2487	−1.49299
$287$	−10.8521	−0.640578
$288$	−15.5139	−0.914166
$289$	−3.32733	−0.195725
$290$	−0.371007	−0.0217863
$291$	0	0
$292$	−13.9825	−0.818264
$293$	18.5065	1.08116	0.540581	−	0.841292i	$-0.318204\pi$
$293$	18.5065	1.08116	0.540581	+	0.841292i	$0.318204\pi$
$294$	23.9083	1.39436
$295$	−1.30357	−0.0758965
$296$	−1.75704	−0.102126
$297$	4.99463	0.289818
$298$	13.7422	0.796064
$299$	41.2321	2.38452
$300$	24.5667	1.41836
$301$	−3.01870	−0.173995
$302$	−31.0989	−1.78954
$303$	−23.1884	−1.33214
$304$	10.3116	0.591413
$305$	−1.31676	−0.0753975
$306$	−14.5183	−0.829957
$307$	−7.87868	−0.449660	−0.224830	−	0.974398i	$-0.572183\pi$
$307$	−7.87868	−0.449660	−0.224830	+	0.974398i	$0.572183\pi$
$308$	−6.07892	−0.346379
$309$	16.0379	0.912362
$310$	−0.469498	−0.0266657
$311$	4.25480	0.241268	0.120634	−	0.992697i	$-0.461507\pi$
$311$	4.25480	0.241268	0.120634	+	0.992697i	$0.461507\pi$
$312$	5.97022	0.337997
$313$	18.0085	1.01790	0.508951	−	0.860795i	$-0.330033\pi$
$313$	18.0085	1.01790	0.508951	+	0.860795i	$0.330033\pi$
$314$	−28.3098	−1.59761
$315$	0.232164	0.0130810
$316$	2.04444	0.115009
$317$	9.06236	0.508993	0.254497	−	0.967074i	$-0.418090\pi$
$317$	9.06236	0.508993	0.254497	+	0.967074i	$0.418090\pi$
$318$	−62.2158	−3.48889
$319$	4.06896	0.227818
$320$	0.887244	0.0495984
$321$	30.1610	1.68342
$322$	18.8671	1.05142
$323$	10.8644	0.604512
$324$	−24.6092	−1.36718
$325$	29.6373	1.64398
$326$	28.4285	1.57451
$327$	−35.7573	−1.97738
$328$	3.72339	0.205590
$329$	8.68801	0.478985
$330$	0.865687	0.0476545
$331$	29.8066	1.63832	0.819158	−	0.573567i	$-0.194441\pi$
$331$	29.8066	1.63832	0.819158	+	0.573567i	$0.194441\pi$
$332$	0.884232	0.0485285
$333$	−7.40071	−0.405557
$334$	21.5583	1.17962
$335$	0.00711099	0.000388515 0
$336$	−10.2851	−0.561101
$337$	9.69690	0.528224	0.264112	−	0.964492i	$-0.414921\pi$
$337$	9.69690	0.528224	0.264112	+	0.964492i	$0.414921\pi$
$338$	45.7197	2.48682
$339$	21.5067	1.16808
$340$	0.754362	0.0409110
$341$	5.14915	0.278842
$342$	−11.5364	−0.623815
$343$	16.2013	0.874788
$344$	1.03573	0.0558426
$345$	−1.41370	−0.0761112
$346$	−40.4592	−2.17510
$347$	19.9111	1.06889	0.534443	−	0.845205i	$-0.320522\pi$
$347$	19.9111	1.06889	0.534443	+	0.845205i	$0.320522\pi$
$348$	−9.67515	−0.518643
$349$	34.2702	1.83444	0.917220	−	0.398380i	$-0.130428\pi$
$349$	34.2702	1.83444	0.917220	+	0.398380i	$0.130428\pi$
$350$	13.5615	0.724893
$351$	−14.3275	−0.764745
$352$	−16.8023	−0.895563
$353$	−0.0453434	−0.00241339	−0.00120669	−	0.999999i	$-0.500384\pi$
$353$	−0.0453434	−0.00241339	−0.00120669	+	0.999999i	$0.500384\pi$
$354$	−64.6084	−3.43390
$355$	−0.0327941	−0.00174053
$356$	−8.56539	−0.453965
$357$	−10.8365	−0.573528
$358$	−22.7300	−1.20132
$359$	−14.7168	−0.776721	−0.388360	−	0.921508i	$-0.626958\pi$
$359$	−14.7168	−0.776721	−0.388360	+	0.921508i	$0.626958\pi$
$360$	−0.0796565	−0.00419826
$361$	−10.3671	−0.545635
$362$	34.5798	1.81748
$363$	14.8829	0.781149
$364$	17.4379	0.913993
$365$	0.578362	0.0302729
$366$	−65.2624	−3.41132
$367$	3.74113	0.195285	0.0976427	−	0.995222i	$-0.468870\pi$
$367$	3.74113	0.195285	0.0976427	+	0.995222i	$0.468870\pi$
$368$	24.3715	1.27045
$369$	15.6831	0.816429
$370$	0.730833	0.0379942
$371$	−18.0710	−0.938198
$372$	−12.2436	−0.634801
$373$	−25.2354	−1.30664	−0.653320	−	0.757082i	$-0.726624\pi$
$373$	−25.2354	−1.30664	−0.653320	+	0.757082i	$0.726624\pi$
$374$	−15.7240	−0.813068
$375$	−2.03403	−0.105037
$376$	−2.98089	−0.153728
$377$	−11.6721	−0.601146
$378$	−6.55600	−0.337204
$379$	34.2740	1.76054	0.880269	−	0.474475i	$-0.157362\pi$
$379$	34.2740	1.76054	0.880269	+	0.474475i	$0.157362\pi$
$380$	0.599422	0.0307497
$381$	1.71048	0.0876307
$382$	16.9305	0.866240
$383$	4.63704	0.236942	0.118471	−	0.992958i	$-0.462201\pi$
$383$	4.63704	0.236942	0.118471	+	0.992958i	$0.462201\pi$
$384$	7.99506	0.407996
$385$	0.251444	0.0128148
$386$	28.2097	1.43583
$387$	4.36252	0.221760
$388$	0	0
$389$	−14.5149	−0.735935	−0.367968	−	0.929839i	$-0.619946\pi$
$389$	−14.5149	−0.735935	−0.367968	+	0.929839i	$0.619946\pi$
$390$	−2.48329	−0.125746
$391$	25.6779	1.29859
$392$	−2.38262	−0.120340
$393$	44.8269	2.26122
$394$	6.61322	0.333169
$395$	−0.0845646	−0.00425491
$396$	8.78506	0.441466
$397$	−20.4339	−1.02555	−0.512773	−	0.858524i	$-0.671382\pi$
$397$	−20.4339	−1.02555	−0.512773	+	0.858524i	$0.671382\pi$
$398$	38.4631	1.92798
$399$	−8.61076	−0.431077
$400$	17.5180	0.875901
$401$	−20.6904	−1.03323	−0.516614	−	0.856219i	$-0.672808\pi$
$401$	−20.6904	−1.03323	−0.516614	+	0.856219i	$0.672808\pi$
$402$	0.352441	0.0175782
$403$	−14.7707	−0.735783
$404$	23.2381	1.15614
$405$	1.01792	0.0505807
$406$	−5.34096	−0.265067
$407$	−8.01530	−0.397304
$408$	3.71804	0.184071
$409$	−19.7326	−0.975712	−0.487856	−	0.872924i	$-0.662221\pi$
$409$	−19.7326	−0.975712	−0.487856	+	0.872924i	$0.662221\pi$
$410$	−1.54873	−0.0764863
$411$	0.252237	0.0124419
$412$	−16.0722	−0.791820
$413$	−18.7659	−0.923411
$414$	−27.2661	−1.34006
$415$	−0.0365747	−0.00179538
$416$	48.1986	2.36313
$417$	−24.0700	−1.17871
$418$	−12.4944	−0.611121
$419$	22.4831	1.09837	0.549185	−	0.835701i	$-0.314938\pi$
$419$	22.4831	1.09837	0.549185	+	0.835701i	$0.314938\pi$
$420$	−0.597882	−0.0291737
$421$	−25.0043	−1.21864	−0.609318	−	0.792926i	$-0.708557\pi$
$421$	−25.0043	−1.21864	−0.609318	+	0.792926i	$0.708557\pi$
$422$	16.9053	0.822938
$423$	−12.5556	−0.610476
$424$	6.20022	0.301109
$425$	18.4571	0.895300
$426$	−1.62537	−0.0787495
$427$	−18.9559	−0.917340
$428$	−30.2256	−1.46101
$429$	27.2351	1.31492
$430$	−0.430807	−0.0207753
$431$	−9.15160	−0.440817	−0.220409	−	0.975408i	$-0.570739\pi$
$431$	−9.15160	−0.440817	−0.220409	+	0.975408i	$0.570739\pi$
$432$	−8.46868	−0.407450
$433$	−8.30684	−0.399201	−0.199601	−	0.979877i	$-0.563964\pi$
$433$	−8.30684	−0.399201	−0.199601	+	0.979877i	$0.563964\pi$
$434$	−6.75882	−0.324434
$435$	0.400196	0.0191879
$436$	35.8338	1.71613
$437$	20.4039	0.976049
$438$	28.6653	1.36968
$439$	8.98024	0.428603	0.214302	−	0.976768i	$-0.431252\pi$
$439$	8.98024	0.428603	0.214302	+	0.976768i	$0.431252\pi$
$440$	−0.0862715	−0.00411283
$441$	−10.0357	−0.477890
$442$	45.1055	2.14545
$443$	19.6719	0.934642	0.467321	−	0.884088i	$-0.345219\pi$
$443$	19.6719	0.934642	0.467321	+	0.884088i	$0.345219\pi$
$444$	19.0587	0.904487
$445$	0.354293	0.0167951
$446$	22.0954	1.04625
$447$	−14.8234	−0.701121
$448$	12.7726	0.603450
$449$	−21.6358	−1.02106	−0.510528	−	0.859861i	$-0.670550\pi$
$449$	−21.6358	−1.02106	−0.510528	+	0.859861i	$0.670550\pi$
$450$	−19.5986	−0.923889
$451$	16.9855	0.799815
$452$	−21.5527	−1.01375
$453$	33.5456	1.57611
$454$	−2.57198	−0.120709
$455$	−0.721288	−0.0338145
$456$	2.95438	0.138352
$457$	−32.0557	−1.49950	−0.749752	−	0.661719i	$-0.769827\pi$
$457$	−32.0557	−1.49950	−0.749752	+	0.661719i	$0.769827\pi$
$458$	12.1963	0.569898
$459$	−8.92266	−0.416474
$460$	1.41673	0.0660553
$461$	−39.3572	−1.83305	−0.916524	−	0.399979i	$-0.869017\pi$
$461$	−39.3572	−1.83305	−0.916524	+	0.399979i	$0.869017\pi$
$462$	12.4623	0.579798
$463$	24.9451	1.15930	0.579649	−	0.814866i	$-0.303190\pi$
$463$	24.9451	1.15930	0.579649	+	0.814866i	$0.303190\pi$
$464$	−6.89916	−0.320286
$465$	0.506435	0.0234854
$466$	3.48347	0.161369
$467$	16.1696	0.748241	0.374121	−	0.927380i	$-0.377945\pi$
$467$	16.1696	0.748241	0.374121	+	0.927380i	$0.377945\pi$
$468$	−25.2006	−1.16490
$469$	0.102369	0.00472695
$470$	1.23989	0.0571918
$471$	30.5370	1.40707
$472$	6.43866	0.296363
$473$	4.72481	0.217247
$474$	−4.19126	−0.192511
$475$	14.6661	0.672928
$476$	10.8597	0.497753
$477$	26.1156	1.19575
$478$	−26.4649	−1.21048
$479$	0.245847	0.0112330	0.00561651	−	0.999984i	$-0.498212\pi$
$479$	0.245847	0.0112330	0.00561651	+	0.999984i	$0.498212\pi$
$480$	−1.65256	−0.0754286
$481$	22.9925	1.04837
$482$	3.26079	0.148525
$483$	−20.3514	−0.926023
$484$	−14.9147	−0.677943
$485$	0	0
$486$	35.5782	1.61386
$487$	−31.5961	−1.43175	−0.715877	−	0.698226i	$-0.753973\pi$
$487$	−31.5961	−1.43175	−0.715877	+	0.698226i	$0.753973\pi$
$488$	6.50384	0.294415
$489$	−30.6652	−1.38673
$490$	0.991041	0.0447707
$491$	−12.8493	−0.579882	−0.289941	−	0.957044i	$-0.593636\pi$
$491$	−12.8493	−0.579882	−0.289941	+	0.957044i	$0.593636\pi$
$492$	−40.3879	−1.82083
$493$	−7.26900	−0.327379
$494$	35.8412	1.61257
$495$	−0.363379	−0.0163327
$496$	−8.73067	−0.392019
$497$	−0.472100	−0.0211766
$498$	−1.81275	−0.0812312
$499$	−22.7533	−1.01858	−0.509288	−	0.860596i	$-0.670091\pi$
$499$	−22.7533	−1.01858	−0.509288	+	0.860596i	$0.670091\pi$
$500$	2.03839	0.0911595
$501$	−23.2544	−1.03893
$502$	1.85267	0.0826886
$503$	31.8687	1.42095	0.710477	−	0.703720i	$-0.248479\pi$
$503$	31.8687	1.42095	0.710477	+	0.703720i	$0.248479\pi$
$504$	−1.14672	−0.0510791
$505$	−0.961203	−0.0427730
$506$	−29.5304	−1.31279
$507$	−49.3167	−2.19023
$508$	−1.71414	−0.0760528
$509$	−13.0345	−0.577745	−0.288872	−	0.957368i	$-0.593280\pi$
$509$	−13.0345	−0.577745	−0.288872	+	0.957368i	$0.593280\pi$
$510$	−1.54651	−0.0684804
$511$	8.32602	0.368321
$512$	31.6739	1.39980
$513$	−7.09001	−0.313032
$514$	−6.74679	−0.297588
$515$	0.664798	0.0292945
$516$	−11.2346	−0.494576
$517$	−13.5983	−0.598053
$518$	10.5210	0.462264
$519$	43.6423	1.91569
$520$	0.247477	0.0108526
$521$	7.82851	0.342973	0.171487	−	0.985186i	$-0.445143\pi$
$521$	7.82851	0.342973	0.171487	+	0.985186i	$0.445143\pi$
$522$	7.71858	0.337833
$523$	−29.5671	−1.29288	−0.646439	−	0.762965i	$-0.723743\pi$
$523$	−29.5671	−1.29288	−0.646439	+	0.762965i	$0.723743\pi$
$524$	−44.9229	−1.96247
$525$	−14.6285	−0.638438
$526$	−40.5868	−1.76967
$527$	−9.19869	−0.400701
$528$	16.0981	0.700580
$529$	25.2243	1.09671
$530$	−2.57896	−0.112023
$531$	27.1199	1.17690
$532$	8.62919	0.374123
$533$	−48.7242	−2.11048
$534$	17.5598	0.759885
$535$	1.25023	0.0540521
$536$	−0.0351231	−0.00151709
$537$	24.5183	1.05804
$538$	30.9362	1.33375
$539$	−10.8691	−0.468165
$540$	−0.492290	−0.0211848
$541$	29.1374	1.25271	0.626357	−	0.779537i	$-0.284545\pi$
$541$	29.1374	1.25271	0.626357	+	0.779537i	$0.284545\pi$
$542$	−41.8056	−1.79570
$543$	−37.3004	−1.60071
$544$	30.0164	1.28694
$545$	−1.48220	−0.0634906
$546$	−35.7491	−1.52992
$547$	30.3740	1.29870	0.649350	−	0.760490i	$-0.275041\pi$
$547$	30.3740	1.29870	0.649350	+	0.760490i	$0.275041\pi$
$548$	−0.252777	−0.0107981
$549$	27.3944	1.16917
$550$	−21.2262	−0.905088
$551$	−5.77600	−0.246066
$552$	6.98266	0.297202
$553$	−1.21738	−0.0517682
$554$	−40.2188	−1.70873
$555$	−0.788331	−0.0334628
$556$	24.1215	1.02298
$557$	−19.5730	−0.829334	−0.414667	−	0.909973i	$-0.636102\pi$
$557$	−19.5730	−0.829334	−0.414667	+	0.909973i	$0.636102\pi$
$558$	9.76762	0.413497
$559$	−13.5535	−0.573251
$560$	−0.426338	−0.0180161
$561$	16.9611	0.716097
$562$	46.6560	1.96806
$563$	−29.2259	−1.23172	−0.615862	−	0.787854i	$-0.711192\pi$
$563$	−29.2259	−1.23172	−0.615862	+	0.787854i	$0.711192\pi$
$564$	32.3339	1.36150
$565$	0.891490	0.0375053
$566$	44.1363	1.85519
$567$	14.6538	0.615401
$568$	0.161979	0.00679650
$569$	34.0713	1.42834	0.714171	−	0.699972i	$-0.246804\pi$
$569$	34.0713	1.42834	0.714171	+	0.699972i	$0.246804\pi$
$570$	−1.22886	−0.0514715
$571$	−45.8453	−1.91856	−0.959282	−	0.282449i	$-0.908853\pi$
$571$	−45.8453	−1.91856	−0.959282	+	0.282449i	$0.908853\pi$
$572$	−27.2934	−1.14120
$573$	−18.2625	−0.762928
$574$	−22.2953	−0.930587
$575$	34.6633	1.44556
$576$	−18.4586	−0.769108
$577$	15.2675	0.635595	0.317798	−	0.948159i	$-0.397057\pi$
$577$	15.2675	0.635595	0.317798	+	0.948159i	$0.397057\pi$
$578$	−6.83591	−0.284336
$579$	−30.4291	−1.26459
$580$	−0.401053	−0.0166528
$581$	−0.526524	−0.0218439
$582$	0	0
$583$	28.2843	1.17142
$584$	−2.85669	−0.118211
$585$	1.04238	0.0430972
$586$	38.0211	1.57064
$587$	−24.1337	−0.996106	−0.498053	−	0.867147i	$-0.665952\pi$
$587$	−24.1337	−0.996106	−0.498053	+	0.867147i	$0.665952\pi$
$588$	25.8445	1.06581
$589$	−7.30935	−0.301176
$590$	−2.67814	−0.110257
$591$	−7.13352	−0.293434
$592$	13.5904	0.558562
$593$	30.5103	1.25291	0.626454	−	0.779458i	$-0.284505\pi$
$593$	30.5103	1.25291	0.626454	+	0.779458i	$0.284505\pi$
$594$	10.2613	0.421027
$595$	−0.449192	−0.0184151
$596$	14.8551	0.608488
$597$	−41.4892	−1.69804
$598$	84.7102	3.46406
$599$	−0.124091	−0.00507020	−0.00253510	−	0.999997i	$-0.500807\pi$
$599$	−0.124091	−0.00507020	−0.00253510	+	0.999997i	$0.500807\pi$
$600$	5.01908	0.204903
$601$	−9.01984	−0.367927	−0.183963	−	0.982933i	$-0.558893\pi$
$601$	−9.01984	−0.367927	−0.183963	+	0.982933i	$0.558893\pi$
$602$	−6.20183	−0.252768
$603$	−0.147940	−0.00602458
$604$	−33.6174	−1.36787
$605$	0.616922	0.0250815
$606$	−47.6400	−1.93524
$607$	−9.63884	−0.391228	−0.195614	−	0.980681i	$-0.562670\pi$
$607$	−9.63884	−0.391228	−0.195614	+	0.980681i	$0.562670\pi$
$608$	23.8512	0.967296
$609$	5.76116	0.233454
$610$	−2.70525	−0.109532
$611$	39.0078	1.57809
$612$	−15.6941	−0.634395
$613$	−14.2643	−0.576131	−0.288066	−	0.957611i	$-0.593012\pi$
$613$	−14.2643	−0.576131	−0.288066	+	0.957611i	$0.593012\pi$
$614$	−16.1865	−0.653235
$615$	1.67058	0.0673642
$616$	−1.24195	−0.0500396
$617$	17.5809	0.707779	0.353890	−	0.935287i	$-0.384859\pi$
$617$	17.5809	0.707779	0.353890	+	0.935287i	$0.384859\pi$
$618$	32.9493	1.32542
$619$	37.2591	1.49757	0.748785	−	0.662813i	$-0.230638\pi$
$619$	37.2591	1.49757	0.748785	+	0.662813i	$0.230638\pi$
$620$	−0.507519	−0.0203825
$621$	−16.7572	−0.672442
$622$	8.74137	0.350497
$623$	5.10034	0.204341
$624$	−46.1787	−1.84863
$625$	24.8735	0.994940
$626$	36.9980	1.47874
$627$	13.4774	0.538235
$628$	−30.6024	−1.22117
$629$	14.3189	0.570933
$630$	0.476975	0.0190031
$631$	−13.2847	−0.528855	−0.264428	−	0.964406i	$-0.585183\pi$
$631$	−13.2847	−0.528855	−0.264428	+	0.964406i	$0.585183\pi$
$632$	0.417688	0.0166147
$633$	−18.2354	−0.724790
$634$	18.6184	0.739430
$635$	0.0709026	0.00281368
$636$	−67.2543	−2.66680
$637$	31.1789	1.23535
$638$	8.35957	0.330959
$639$	0.682263	0.0269899
$640$	0.331410	0.0131001
$641$	−13.2345	−0.522732	−0.261366	−	0.965240i	$-0.584173\pi$
$641$	−13.2345	−0.522732	−0.261366	+	0.965240i	$0.584173\pi$
$642$	61.9649	2.44556
$643$	19.9672	0.787430	0.393715	−	0.919233i	$-0.371190\pi$
$643$	19.9672	0.787430	0.393715	+	0.919233i	$0.371190\pi$
$644$	20.3950	0.803676
$645$	0.464700	0.0182976
$646$	22.3206	0.878192
$647$	20.4095	0.802379	0.401190	−	0.915995i	$-0.368597\pi$
$647$	20.4095	0.802379	0.401190	+	0.915995i	$0.368597\pi$
$648$	−5.02777	−0.197509
$649$	29.3721	1.15295
$650$	60.8890	2.38826
$651$	7.29057	0.285740
$652$	30.7308	1.20351
$653$	19.9143	0.779307	0.389653	−	0.920962i	$-0.372595\pi$
$653$	19.9143	0.779307	0.389653	+	0.920962i	$0.372595\pi$
$654$	−73.4622	−2.87260
$655$	1.85816	0.0726042
$656$	−28.7998	−1.12444
$657$	−12.0325	−0.469432
$658$	17.8493	0.695837
$659$	−35.4757	−1.38194	−0.690969	−	0.722884i	$-0.742816\pi$
$659$	−35.4757	−1.38194	−0.690969	+	0.722884i	$0.742816\pi$
$660$	0.935793	0.0364257
$661$	−13.1135	−0.510057	−0.255028	−	0.966934i	$-0.582085\pi$
$661$	−13.1135	−0.510057	−0.255028	+	0.966934i	$0.582085\pi$
$662$	61.2367	2.38003
$663$	−48.6542	−1.88957
$664$	0.180652	0.00701068
$665$	−0.356932	−0.0138412
$666$	−15.2045	−0.589164
$667$	−13.6515	−0.528589
$668$	23.3041	0.901665
$669$	−23.8338	−0.921467
$670$	0.0146093	0.000564407 0
$671$	29.6694	1.14537
$672$	−23.7900	−0.917718
$673$	4.91397	0.189420	0.0947099	−	0.995505i	$-0.469808\pi$
$673$	4.91397	0.189420	0.0947099	+	0.995505i	$0.469808\pi$
$674$	19.9220	0.767367
$675$	−12.0449	−0.463609
$676$	49.4223	1.90086
$677$	−2.10971	−0.0810828	−0.0405414	−	0.999178i	$-0.512908\pi$
$677$	−2.10971	−0.0810828	−0.0405414	+	0.999178i	$0.512908\pi$
$678$	44.1848	1.69691
$679$	0	0
$680$	0.154120	0.00591022
$681$	2.77434	0.106313
$682$	10.5788	0.405082
$683$	−22.2737	−0.852278	−0.426139	−	0.904658i	$-0.640127\pi$
$683$	−22.2737	−0.852278	−0.426139	+	0.904658i	$0.640127\pi$
$684$	−12.4706	−0.476826
$685$	0.0104557	0.000399491 0
$686$	33.2851	1.27083
$687$	−13.1559	−0.501929
$688$	−8.01118	−0.305423
$689$	−81.1358	−3.09103
$690$	−2.90441	−0.110569
$691$	39.1525	1.48943	0.744716	−	0.667381i	$-0.232585\pi$
$691$	39.1525	1.48943	0.744716	+	0.667381i	$0.232585\pi$
$692$	−43.7358	−1.66258
$693$	−5.23115	−0.198715
$694$	40.9068	1.55280
$695$	−0.997744	−0.0378466
$696$	−1.97668	−0.0749257
$697$	−30.3437	−1.14935
$698$	70.4071	2.66495
$699$	−3.75753	−0.142123
$700$	14.6598	0.554087
$701$	−48.1568	−1.81886	−0.909429	−	0.415859i	$-0.863481\pi$
$701$	−48.1568	−1.81886	−0.909429	+	0.415859i	$0.863481\pi$
$702$	−29.4354	−1.11097
$703$	11.3779	0.429127
$704$	−19.9915	−0.753457
$705$	−1.33744	−0.0503708
$706$	−0.0931567	−0.00350600
$707$	−13.8373	−0.520406
$708$	−69.8407	−2.62477
$709$	−37.0841	−1.39272	−0.696361	−	0.717692i	$-0.745199\pi$
$709$	−37.0841	−1.39272	−0.696361	+	0.717692i	$0.745199\pi$
$710$	−0.0673746	−0.00252852
$711$	1.75932	0.0659795
$712$	−1.74995	−0.0655820
$713$	−17.2756	−0.646975
$714$	−22.2633	−0.833181
$715$	1.12895	0.0422202
$716$	−24.5708	−0.918254
$717$	28.5470	1.06611
$718$	−30.2351	−1.12837
$719$	38.0518	1.41909	0.709546	−	0.704659i	$-0.248900\pi$
$719$	38.0518	1.41909	0.709546	+	0.704659i	$0.248900\pi$
$720$	0.616130	0.0229618
$721$	9.57034	0.356418
$722$	−21.2988	−0.792660
$723$	−3.51733	−0.130811
$724$	37.3803	1.38923
$725$	−9.81261	−0.364431
$726$	30.5764	1.13480
$727$	41.0730	1.52331	0.761657	−	0.647981i	$-0.224386\pi$
$727$	41.0730	1.52331	0.761657	+	0.647981i	$0.224386\pi$
$728$	3.56264	0.132040
$729$	−5.13438	−0.190162
$730$	1.18823	0.0439783
$731$	−8.44063	−0.312188
$732$	−70.5476	−2.60752
$733$	2.41093	0.0890498	0.0445249	−	0.999008i	$-0.485823\pi$
$733$	2.41093	0.0890498	0.0445249	+	0.999008i	$0.485823\pi$
$734$	7.68604	0.283697
$735$	−1.06901	−0.0394311
$736$	56.3722	2.07791
$737$	−0.160226	−0.00590198
$738$	32.2204	1.18605
$739$	52.7638	1.94095	0.970473	−	0.241209i	$-0.0775438\pi$
$739$	52.7638	1.94095	0.970473	+	0.241209i	$0.0775438\pi$
$740$	0.790018	0.0290417
$741$	−38.6610	−1.42025
$742$	−37.1263	−1.36295
$743$	37.4433	1.37366	0.686830	−	0.726818i	$-0.259002\pi$
$743$	37.4433	1.37366	0.686830	+	0.726818i	$0.259002\pi$
$744$	−2.50142	−0.0917066
$745$	−0.614455	−0.0225119
$746$	−51.8454	−1.89820
$747$	0.760916	0.0278405
$748$	−16.9974	−0.621485
$749$	17.9981	0.657637
$750$	−4.17886	−0.152590
$751$	−18.5087	−0.675390	−0.337695	−	0.941256i	$-0.609647\pi$
$751$	−18.5087	−0.675390	−0.337695	+	0.941256i	$0.609647\pi$
$752$	23.0567	0.840791
$753$	−1.99843	−0.0728267
$754$	−23.9801	−0.873303
$755$	1.39053	0.0506065
$756$	−7.08693	−0.257749
$757$	12.2326	0.444600	0.222300	−	0.974978i	$-0.428644\pi$
$757$	12.2326	0.444600	0.222300	+	0.974978i	$0.428644\pi$
$758$	70.4150	2.55759
$759$	31.8537	1.15622
$760$	0.122465	0.00444226
$761$	15.2179	0.551648	0.275824	−	0.961208i	$-0.411049\pi$
$761$	15.2179	0.551648	0.275824	+	0.961208i	$0.411049\pi$
$762$	3.51414	0.127304
$763$	−21.3376	−0.772472
$764$	18.3016	0.662129
$765$	0.649158	0.0234704
$766$	9.52666	0.344212
$767$	−84.2561	−3.04231
$768$	−26.3828	−0.952008
$769$	−11.3160	−0.408066	−0.204033	−	0.978964i	$-0.565405\pi$
$769$	−11.3160	−0.408066	−0.204033	+	0.978964i	$0.565405\pi$
$770$	0.516585	0.0186164
$771$	7.27760	0.262096
$772$	30.4942	1.09751
$773$	−4.09044	−0.147123	−0.0735614	−	0.997291i	$-0.523436\pi$
$773$	−4.09044	−0.147123	−0.0735614	+	0.997291i	$0.523436\pi$
$774$	8.96268	0.322157
$775$	−12.4175	−0.446051
$776$	0	0
$777$	−11.3487	−0.407132
$778$	−29.8205	−1.06912
$779$	−24.1113	−0.863878
$780$	−2.68440	−0.0961168
$781$	0.738921	0.0264407
$782$	52.7545	1.88650
$783$	4.74368	0.169525
$784$	18.4292	0.658185
$785$	1.26582	0.0451789
$786$	92.0956	3.28494
$787$	34.7587	1.23901	0.619507	−	0.784991i	$-0.287333\pi$
$787$	34.7587	1.23901	0.619507	+	0.784991i	$0.287333\pi$
$788$	7.14879	0.254665
$789$	43.7799	1.55861
$790$	−0.173735	−0.00618123
$791$	12.8338	0.456316
$792$	1.79483	0.0637764
$793$	−85.1090	−3.02231
$794$	−41.9808	−1.48984
$795$	2.78186	0.0986623
$796$	41.5780	1.47369
$797$	−8.28837	−0.293589	−0.146794	−	0.989167i	$-0.546896\pi$
$797$	−8.28837	−0.293589	−0.146794	+	0.989167i	$0.546896\pi$
$798$	−17.6905	−0.626239
$799$	24.2927	0.859413
$800$	40.5199	1.43259
$801$	−7.37085	−0.260436
$802$	−42.5077	−1.50100
$803$	−13.0317	−0.459880
$804$	0.380983	0.0134362
$805$	−0.843604	−0.0297331
$806$	−30.3460	−1.06889
$807$	−33.3701	−1.17468
$808$	4.74764	0.167021
$809$	37.3272	1.31235	0.656176	−	0.754608i	$-0.272173\pi$
$809$	37.3272	1.31235	0.656176	+	0.754608i	$0.272173\pi$
$810$	2.09128	0.0734801
$811$	47.4210	1.66518	0.832588	−	0.553893i	$-0.186858\pi$
$811$	47.4210	1.66518	0.832588	+	0.553893i	$0.186858\pi$
$812$	−5.77349	−0.202610
$813$	45.0947	1.58154
$814$	−16.4672	−0.577175
$815$	−1.27113	−0.0445256
$816$	−28.7585	−1.00675
$817$	−6.70699	−0.234648
$818$	−40.5400	−1.41745
$819$	15.0060	0.524351
$820$	−1.67415	−0.0584639
$821$	19.5356	0.681797	0.340898	−	0.940100i	$-0.389269\pi$
$821$	19.5356	0.681797	0.340898	+	0.940100i	$0.389269\pi$
$822$	0.518213	0.0180747
$823$	11.5968	0.404240	0.202120	−	0.979361i	$-0.435217\pi$
$823$	11.5968	0.404240	0.202120	+	0.979361i	$0.435217\pi$
$824$	−3.28362	−0.114390
$825$	22.8962	0.797143
$826$	−38.5541	−1.34147
$827$	7.06876	0.245805	0.122903	−	0.992419i	$-0.460780\pi$
$827$	7.06876	0.245805	0.122903	+	0.992419i	$0.460780\pi$
$828$	−29.4742	−1.02430
$829$	−41.1047	−1.42763	−0.713813	−	0.700337i	$-0.753033\pi$
$829$	−41.1047	−1.42763	−0.713813	+	0.700337i	$0.753033\pi$
$830$	−0.0751417	−0.00260821
$831$	43.3830	1.50494
$832$	57.3471	1.98815
$833$	19.4171	0.672762
$834$	−49.4510	−1.71235
$835$	−0.963936	−0.0333584
$836$	−13.5062	−0.467123
$837$	6.00298	0.207493
$838$	46.1908	1.59564
$839$	−9.05827	−0.312726	−0.156363	−	0.987700i	$-0.549977\pi$
$839$	−9.05827	−0.312726	−0.156363	+	0.987700i	$0.549977\pi$
$840$	−0.122150	−0.00421457
$841$	−25.1355	−0.866741
$842$	−51.3707	−1.77035
$843$	−50.3267	−1.73334
$844$	18.2744	0.629030
$845$	−2.04427	−0.0703249
$846$	−25.7952	−0.886856
$847$	8.88112	0.305159
$848$	−47.9577	−1.64687
$849$	−47.6087	−1.63393
$850$	37.9195	1.30063
$851$	26.8916	0.921833
$852$	−1.75700	−0.0601939
$853$	31.5504	1.08027	0.540133	−	0.841580i	$-0.318374\pi$
$853$	31.5504	1.08027	0.540133	+	0.841580i	$0.318374\pi$
$854$	−38.9443	−1.33265
$855$	0.515826	0.0176409
$856$	−6.17522	−0.211065
$857$	−22.9673	−0.784547	−0.392273	−	0.919849i	$-0.628311\pi$
$857$	−22.9673	−0.784547	−0.392273	+	0.919849i	$0.628311\pi$
$858$	55.9538	1.91023
$859$	10.8958	0.371760	0.185880	−	0.982572i	$-0.440486\pi$
$859$	10.8958	0.371760	0.185880	+	0.982572i	$0.440486\pi$
$860$	−0.465695	−0.0158801
$861$	24.0494	0.819601
$862$	−18.8017	−0.640388
$863$	−24.7321	−0.841891	−0.420945	−	0.907086i	$-0.638302\pi$
$863$	−24.7321	−0.841891	−0.420945	+	0.907086i	$0.638302\pi$
$864$	−19.5884	−0.666411
$865$	1.80905	0.0615097
$866$	−17.0662	−0.579932
$867$	7.37372	0.250425
$868$	−7.30617	−0.247988
$869$	1.90542	0.0646369
$870$	0.822191	0.0278749
$871$	0.459620	0.0155736
$872$	7.32101	0.247921
$873$	0	0
$874$	41.9191	1.41794
$875$	−1.21378	−0.0410332
$876$	30.9867	1.04694
$877$	2.25839	0.0762603	0.0381301	−	0.999273i	$-0.487860\pi$
$877$	2.25839	0.0762603	0.0381301	+	0.999273i	$0.487860\pi$
$878$	18.4496	0.622645
$879$	−41.0124	−1.38331
$880$	0.667296	0.0224945
$881$	−31.9329	−1.07585	−0.537924	−	0.842993i	$-0.680791\pi$
$881$	−31.9329	−1.07585	−0.537924	+	0.842993i	$0.680791\pi$
$882$	−20.6180	−0.694245
$883$	−9.71072	−0.326792	−0.163396	−	0.986561i	$-0.552245\pi$
$883$	−9.71072	−0.326792	−0.163396	+	0.986561i	$0.552245\pi$
$884$	48.7583	1.63992
$885$	2.88884	0.0971073
$886$	40.4154	1.35778
$887$	−29.6172	−0.994447	−0.497224	−	0.867622i	$-0.665647\pi$
$887$	−29.6172	−0.994447	−0.497224	+	0.867622i	$0.665647\pi$
$888$	3.89378	0.130667
$889$	1.02070	0.0342333
$890$	0.727884	0.0243987
$891$	−22.9358	−0.768378
$892$	23.8848	0.799722
$893$	19.3031	0.645955
$894$	−30.4542	−1.01854
$895$	1.01633	0.0339721
$896$	4.77093	0.159385
$897$	−91.3748	−3.05092
$898$	−44.4501	−1.48332
$899$	4.89043	0.163105
$900$	−21.1858	−0.706194
$901$	−50.5285	−1.68335
$902$	34.8962	1.16191
$903$	6.68976	0.222621
$904$	−4.40331	−0.146452
$905$	−1.54617	−0.0513964
$906$	68.9185	2.28966
$907$	−2.24731	−0.0746208	−0.0373104	−	0.999304i	$-0.511879\pi$
$907$	−2.24731	−0.0746208	−0.0373104	+	0.999304i	$0.511879\pi$
$908$	−2.78027	−0.0922666
$909$	19.9973	0.663267
$910$	−1.48186	−0.0491233
$911$	−9.21236	−0.305219	−0.152610	−	0.988287i	$-0.548768\pi$
$911$	−9.21236	−0.305219	−0.152610	+	0.988287i	$0.548768\pi$
$912$	−22.8517	−0.756695
$913$	0.824105	0.0272739
$914$	−65.8575	−2.17837
$915$	2.91808	0.0964688
$916$	13.1841	0.435613
$917$	26.7498	0.883355
$918$	−18.3313	−0.605024
$919$	29.8530	0.984760	0.492380	−	0.870380i	$-0.336127\pi$
$919$	29.8530	0.984760	0.492380	+	0.870380i	$0.336127\pi$
$920$	0.289444	0.00954268
$921$	17.4600	0.575326
$922$	−80.8583	−2.66292
$923$	−2.11965	−0.0697693
$924$	13.4715	0.443181
$925$	19.3295	0.635550
$926$	51.2490	1.68415
$927$	−13.8307	−0.454261
$928$	−15.9580	−0.523849
$929$	−41.4723	−1.36066	−0.680332	−	0.732904i	$-0.738164\pi$
$929$	−41.4723	−1.36066	−0.680332	+	0.732904i	$0.738164\pi$
$930$	1.04046	0.0341179
$931$	15.4290	0.505664
$932$	3.76557	0.123345
$933$	−9.42910	−0.308695
$934$	33.2200	1.08699
$935$	0.703067	0.0229927
$936$	−5.14860	−0.168287
$937$	−40.3210	−1.31723	−0.658614	−	0.752481i	$-0.728857\pi$
$937$	−40.3210	−1.31723	−0.658614	+	0.752481i	$0.728857\pi$
$938$	0.210314	0.00686698
$939$	−39.9088	−1.30237
$940$	1.34030	0.0437158
$941$	−10.1881	−0.332122	−0.166061	−	0.986115i	$-0.553105\pi$
$941$	−10.1881	−0.332122	−0.166061	+	0.986115i	$0.553105\pi$
$942$	62.7375	2.04410
$943$	−56.9869	−1.85575
$944$	−49.8020	−1.62092
$945$	0.293139	0.00953580
$946$	9.70698	0.315601
$947$	−7.60664	−0.247183	−0.123591	−	0.992333i	$-0.539441\pi$
$947$	−7.60664	−0.247183	−0.123591	+	0.992333i	$0.539441\pi$
$948$	−4.53069	−0.147150
$949$	37.3825	1.21349
$950$	30.1311	0.977583
$951$	−20.0832	−0.651241
$952$	2.21868	0.0719079
$953$	30.9970	1.00409	0.502046	−	0.864841i	$-0.332581\pi$
$953$	30.9970	1.00409	0.502046	+	0.864841i	$0.332581\pi$
$954$	53.6537	1.73710
$955$	−0.757015	−0.0244964
$956$	−28.6081	−0.925253
$957$	−9.01726	−0.291487
$958$	0.505085	0.0163186
$959$	0.150518	0.00486049
$960$	−1.96623	−0.0634597
$961$	−24.8113	−0.800365
$962$	47.2375	1.52300
$963$	−26.0103	−0.838170
$964$	3.52486	0.113528
$965$	−1.26134	−0.0406040
$966$	−41.8115	−1.34526
$967$	11.6596	0.374948	0.187474	−	0.982270i	$-0.439970\pi$
$967$	11.6596	0.374948	0.187474	+	0.982270i	$0.439970\pi$
$968$	−3.04715	−0.0979390
$969$	−24.0767	−0.773454
$970$	0	0
$971$	−39.3179	−1.26177	−0.630885	−	0.775876i	$-0.717308\pi$
$971$	−39.3179	−1.26177	−0.630885	+	0.775876i	$0.717308\pi$
$972$	38.4595	1.23359
$973$	−14.3634	−0.460468
$974$	−64.9132	−2.07995
$975$	−65.6795	−2.10343
$976$	−50.3061	−1.61026
$977$	−42.3157	−1.35380	−0.676899	−	0.736076i	$-0.736677\pi$
$977$	−42.3157	−1.35380	−0.676899	+	0.736076i	$0.736677\pi$
$978$	−63.0007	−2.01454
$979$	−7.98296	−0.255136
$980$	1.07130	0.0342214
$981$	30.8364	0.984530
$982$	−26.3986	−0.842413
$983$	−26.3186	−0.839433	−0.419716	−	0.907655i	$-0.637870\pi$
$983$	−26.3186	−0.839433	−0.419716	+	0.907655i	$0.637870\pi$
$984$	−8.25143	−0.263046
$985$	−0.295697	−0.00942170
$986$	−14.9339	−0.475594
$987$	−19.2536	−0.612847
$988$	38.7437	1.23260
$989$	−15.8519	−0.504061
$990$	−0.746551	−0.0237270
$991$	19.7307	0.626766	0.313383	−	0.949627i	$-0.398538\pi$
$991$	19.7307	0.626766	0.313383	+	0.949627i	$0.398538\pi$
$992$	−20.1944	−0.641173
$993$	−66.0545	−2.09618
$994$	−0.969915	−0.0307638
$995$	−1.71980	−0.0545214
$996$	−1.95955	−0.0620908
$997$	−1.76471	−0.0558888	−0.0279444	−	0.999609i	$-0.508896\pi$
$997$	−1.76471	−0.0558888	−0.0279444	+	0.999609i	$0.508896\pi$
$998$	−46.7459	−1.47972
$999$	−9.34440	−0.295644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	9409.2.a.o.1.105		128
97.60	odd	96		97.2.k.a.11.7	✓	128
97.76	odd	96		97.2.k.a.53.7	yes	128
97.96	even	2	inner	9409.2.a.o.1.106		128
291.173	even	96		873.2.bu.d.829.2		128
291.254	even	96		873.2.bu.d.496.2		128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
97.2.k.a.11.7	✓	128	97.60	odd	96
97.2.k.a.53.7	yes	128	97.76	odd	96
873.2.bu.d.496.2		128	291.254	even	96
873.2.bu.d.829.2		128	291.173	even	96
9409.2.a.o.1.105		128	1.1	even	1	trivial
9409.2.a.o.1.106		128	97.96	even	2	inner

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:	\( N \)	\(=\)	\( 9409 = 97^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	9409.a (trivial)

\(f(q)\)	\(=\)	\(q+2.05447 q^{2} -2.21611 q^{3} +2.22085 q^{4} -0.0918616 q^{5} -4.55293 q^{6} -1.32243 q^{7} +0.453730 q^{8} +1.91113 q^{9} -0.188727 q^{10} +2.06984 q^{11} -4.92164 q^{12} -5.93749 q^{13} -2.71689 q^{14} +0.203575 q^{15} -3.50953 q^{16} -3.69766 q^{17} +3.92636 q^{18} -2.93819 q^{19} -0.204011 q^{20} +2.93064 q^{21} +4.25242 q^{22} -6.94438 q^{23} -1.00551 q^{24} -4.99156 q^{25} -12.1984 q^{26} +2.41306 q^{27} -2.93691 q^{28} +1.96584 q^{29} +0.418239 q^{30} +2.48771 q^{31} -8.11768 q^{32} -4.58698 q^{33} -7.59673 q^{34} +0.121480 q^{35} +4.24433 q^{36} -3.87243 q^{37} -6.03642 q^{38} +13.1581 q^{39} -0.0416803 q^{40} +8.20619 q^{41} +6.02091 q^{42} +2.28270 q^{43} +4.59679 q^{44} -0.175559 q^{45} -14.2670 q^{46} -6.56975 q^{47} +7.77748 q^{48} -5.25119 q^{49} -10.2550 q^{50} +8.19440 q^{51} -13.1863 q^{52} +13.6650 q^{53} +4.95755 q^{54} -0.190139 q^{55} -0.600024 q^{56} +6.51133 q^{57} +4.03876 q^{58} +14.1905 q^{59} +0.452110 q^{60} +14.3342 q^{61} +5.11092 q^{62} -2.52733 q^{63} -9.65848 q^{64} +0.545427 q^{65} -9.42381 q^{66} -0.0774098 q^{67} -8.21194 q^{68} +15.3895 q^{69} +0.249578 q^{70} +0.356995 q^{71} +0.867135 q^{72} -6.29602 q^{73} -7.95580 q^{74} +11.0618 q^{75} -6.52527 q^{76} -2.73721 q^{77} +27.0329 q^{78} +0.920565 q^{79} +0.322391 q^{80} -11.0810 q^{81} +16.8594 q^{82} +0.398150 q^{83} +6.50851 q^{84} +0.339673 q^{85} +4.68973 q^{86} -4.35651 q^{87} +0.939146 q^{88} -3.85681 q^{89} -0.360681 q^{90} +7.85189 q^{91} -15.4224 q^{92} -5.51302 q^{93} -13.4974 q^{94} +0.269907 q^{95} +17.9896 q^{96} -10.7884 q^{98} +3.95572 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 16 q^{2} + 16 q^{3} + 144 q^{4} + 32 q^{6} + 48 q^{8} + 144 q^{9} + 64 q^{11} + 32 q^{12} + 176 q^{16} + 48 q^{18} + 32 q^{22} + 144 q^{24} + 128 q^{25} + 64 q^{27} + 96 q^{31} + 112 q^{32} + 16 q^{33}+ \cdots + 304 q^{99}+O(q^{100}) \) 128 * q + 16 * q^2 + 16 * q^3 + 144 * q^4 + 32 * q^6 + 48 * q^8 + 144 * q^9 + 64 * q^11 + 32 * q^12 + 176 * q^16 + 48 * q^18 + 32 * q^22 + 144 * q^24 + 128 * q^25 + 64 * q^27 + 96 * q^31 + 112 * q^32 + 16 * q^33 + 144 * q^35 + 224 * q^36 + 64 * q^43 + 160 * q^44 + 224 * q^47 + 64 * q^48 + 128 * q^49 + 144 * q^50 + 96 * q^53 + 96 * q^54 + 112 * q^61 + 112 * q^62 + 240 * q^64 + 64 * q^65 + 16 * q^70 + 304 * q^72 - 32 * q^73 + 48 * q^75 + 96 * q^79 + 112 * q^81 + 96 * q^86 - 32 * q^88 + 192 * q^89 + 128 * q^91 + 128 * q^94 + 208 * q^95 + 352 * q^96 + 208 * q^98 + 304 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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