LMFDB - Embedded newform 5415.2.a.z.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5415,2,Mod(1,5415)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5415, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("5415.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5415 = 3 \cdot 5 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5415.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$43.2389926945$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.8797896.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 8x^{3} + 5x^{2} + 13x - 4 $ x^5 - x^4 - 8x^3 + 5x^2 + 13*x - 4
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 285)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-1.38140$ of defining polynomial
Character	$\chi$	$=$	5415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.38140 q^{2} +1.00000 q^{3} -0.0917248 q^{4} +1.00000 q^{5} -1.38140 q^{6} -4.36264 q^{7} +2.88952 q^{8} +1.00000 q^{9} -1.38140 q^{10} -4.31625 q^{11} -0.0917248 q^{12} +6.36264 q^{13} +6.02657 q^{14} +1.00000 q^{15} -3.80814 q^{16} +5.71641 q^{17} -1.38140 q^{18} -0.0917248 q^{20} -4.36264 q^{21} +5.96248 q^{22} -0.579357 q^{23} +2.88952 q^{24} +1.00000 q^{25} -8.78938 q^{26} +1.00000 q^{27} +0.400163 q^{28} +3.55344 q^{29} -1.38140 q^{30} -1.18345 q^{31} -0.518458 q^{32} -4.31625 q^{33} -7.89667 q^{34} -4.36264 q^{35} -0.0917248 q^{36} +6.54609 q^{37} +6.36264 q^{39} +2.88952 q^{40} +0.762807 q^{41} +6.02657 q^{42} -6.36264 q^{43} +0.395907 q^{44} +1.00000 q^{45} +0.800326 q^{46} -2.73264 q^{47} -3.80814 q^{48} +12.0327 q^{49} -1.38140 q^{50} +5.71641 q^{51} -0.583613 q^{52} -5.13706 q^{53} -1.38140 q^{54} -4.31625 q^{55} -12.6059 q^{56} -4.90874 q^{58} -3.82968 q^{59} -0.0917248 q^{60} -12.0211 q^{61} +1.63482 q^{62} -4.36264 q^{63} +8.33247 q^{64} +6.36264 q^{65} +5.96248 q^{66} +4.00426 q^{67} -0.524337 q^{68} -0.579357 q^{69} +6.02657 q^{70} -3.07906 q^{71} +2.88952 q^{72} +8.08640 q^{73} -9.04280 q^{74} +1.00000 q^{75} +18.8303 q^{77} -8.78938 q^{78} -11.3367 q^{79} -3.80814 q^{80} +1.00000 q^{81} -1.05374 q^{82} +7.67889 q^{83} +0.400163 q^{84} +5.71641 q^{85} +8.78938 q^{86} +3.55344 q^{87} -12.4719 q^{88} -9.84186 q^{89} -1.38140 q^{90} -27.7579 q^{91} +0.0531414 q^{92} -1.18345 q^{93} +3.77487 q^{94} -0.518458 q^{96} -2.00000 q^{97} -16.6220 q^{98} -4.31625 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) $ 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * 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 $

$2$	−1.38140	−0.976800	−0.488400	−	0.872620i	$-0.662419\pi$
$2$	−1.38140	−0.976800	−0.488400	+	0.872620i	$0.662419\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.0917248	−0.0458624
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.38140	−0.563956
$7$	−4.36264	−1.64892	−0.824462	−	0.565917i	$-0.808522\pi$
$7$	−4.36264	−1.64892	−0.824462	+	0.565917i	$0.808522\pi$
$8$	2.88952	1.02160
$9$	1.00000	0.333333
$10$	−1.38140	−0.436838
$11$	−4.31625	−1.30140	−0.650699	−	0.759336i	$-0.725524\pi$
$11$	−4.31625	−1.30140	−0.650699	+	0.759336i	$0.725524\pi$
$12$	−0.0917248	−0.0264787
$13$	6.36264	1.76468	0.882340	−	0.470613i	$-0.155967\pi$
$13$	6.36264	1.76468	0.882340	+	0.470613i	$0.155967\pi$
$14$	6.02657	1.61067
$15$	1.00000	0.258199
$16$	−3.80814	−0.952034
$17$	5.71641	1.38643	0.693217	−	0.720729i	$-0.256193\pi$
$17$	5.71641	1.38643	0.693217	+	0.720729i	$0.256193\pi$
$18$	−1.38140	−0.325600
$19$	0	0
$19$	0	0
$20$	−0.0917248	−0.0205103
$21$	−4.36264	−0.952007
$22$	5.96248	1.27121
$23$	−0.579357	−0.120804	−0.0604021	−	0.998174i	$-0.519238\pi$
$23$	−0.579357	−0.120804	−0.0604021	+	0.998174i	$0.519238\pi$
$24$	2.88952	0.589820
$25$	1.00000	0.200000
$26$	−8.78938	−1.72374
$27$	1.00000	0.192450
$28$	0.400163	0.0756237
$29$	3.55344	0.659858	0.329929	−	0.944006i	$-0.392975\pi$
$29$	3.55344	0.659858	0.329929	+	0.944006i	$0.392975\pi$
$30$	−1.38140	−0.252209
$31$	−1.18345	−0.212554	−0.106277	−	0.994337i	$-0.533893\pi$
$31$	−1.18345	−0.212554	−0.106277	+	0.994337i	$0.533893\pi$
$32$	−0.518458	−0.0916514
$33$	−4.31625	−0.751363
$34$	−7.89667	−1.35427
$35$	−4.36264	−0.737421
$36$	−0.0917248	−0.0152875
$37$	6.54609	1.07617	0.538086	−	0.842890i	$-0.319148\pi$
$37$	6.54609	1.07617	0.538086	+	0.842890i	$0.319148\pi$
$38$	0	0
$39$	6.36264	1.01884
$40$	2.88952	0.456873
$41$	0.762807	0.119130	0.0595652	−	0.998224i	$-0.481029\pi$
$41$	0.762807	0.119130	0.0595652	+	0.998224i	$0.481029\pi$
$42$	6.02657	0.929920
$43$	−6.36264	−0.970294	−0.485147	−	0.874433i	$-0.661234\pi$
$43$	−6.36264	−0.970294	−0.485147	+	0.874433i	$0.661234\pi$
$44$	0.395907	0.0596853
$45$	1.00000	0.149071
$46$	0.800326	0.118002
$47$	−2.73264	−0.398596	−0.199298	−	0.979939i	$-0.563866\pi$
$47$	−2.73264	−0.398596	−0.199298	+	0.979939i	$0.563866\pi$
$48$	−3.80814	−0.549657
$49$	12.0327	1.71895
$50$	−1.38140	−0.195360
$51$	5.71641	0.800458
$52$	−0.583613	−0.0809325
$53$	−5.13706	−0.705629	−0.352814	−	0.935693i	$-0.614775\pi$
$53$	−5.13706	−0.705629	−0.352814	+	0.935693i	$0.614775\pi$
$54$	−1.38140	−0.187985
$55$	−4.31625	−0.582003
$56$	−12.6059	−1.68454
$57$	0	0
$58$	−4.90874	−0.644549
$59$	−3.82968	−0.498582	−0.249291	−	0.968429i	$-0.580198\pi$
$59$	−3.82968	−0.498582	−0.249291	+	0.968429i	$0.580198\pi$
$60$	−0.0917248	−0.0118416
$61$	−12.0211	−1.53914	−0.769569	−	0.638563i	$-0.779529\pi$
$61$	−12.0211	−1.53914	−0.769569	+	0.638563i	$0.779529\pi$
$62$	1.63482	0.207623
$63$	−4.36264	−0.549641
$64$	8.33247	1.04156
$65$	6.36264	0.789189
$66$	5.96248	0.733931
$67$	4.00426	0.489198	0.244599	−	0.969624i	$-0.421344\pi$
$67$	4.00426	0.489198	0.244599	+	0.969624i	$0.421344\pi$
$68$	−0.524337	−0.0635852
$69$	−0.579357	−0.0697464
$70$	6.02657	0.720313
$71$	−3.07906	−0.365417	−0.182708	−	0.983167i	$-0.558486\pi$
$71$	−3.07906	−0.365417	−0.182708	+	0.983167i	$0.558486\pi$
$72$	2.88952	0.340533
$73$	8.08640	0.946442	0.473221	−	0.880944i	$-0.343091\pi$
$73$	8.08640	0.946442	0.473221	+	0.880944i	$0.343091\pi$
$74$	−9.04280	−1.05120
$75$	1.00000	0.115470
$76$	0	0
$77$	18.8303	2.14591
$78$	−8.78938	−0.995201
$79$	−11.3367	−1.27548	−0.637741	−	0.770251i	$-0.720131\pi$
$79$	−11.3367	−1.27548	−0.637741	+	0.770251i	$0.720131\pi$
$80$	−3.80814	−0.425763
$81$	1.00000	0.111111
$82$	−1.05374	−0.116367
$83$	7.67889	0.842868	0.421434	−	0.906859i	$-0.361527\pi$
$83$	7.67889	0.842868	0.421434	+	0.906859i	$0.361527\pi$
$84$	0.400163	0.0436613
$85$	5.71641	0.620032
$86$	8.78938	0.947783
$87$	3.55344	0.380969
$88$	−12.4719	−1.32951
$89$	−9.84186	−1.04324	−0.521618	−	0.853179i	$-0.674671\pi$
$89$	−9.84186	−1.04324	−0.521618	+	0.853179i	$0.674671\pi$
$90$	−1.38140	−0.145613
$91$	−27.7579	−2.90982
$92$	0.0531414	0.00554038
$93$	−1.18345	−0.122718
$94$	3.77487	0.389348
$95$	0	0
$96$	−0.518458	−0.0529149
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−16.6220	−1.67907
$99$	−4.31625	−0.433799
$100$	−0.0917248	−0.00917248
$101$	−4.49970	−0.447737	−0.223868	−	0.974619i	$-0.571869\pi$
$101$	−4.49970	−0.447737	−0.223868	+	0.974619i	$0.571869\pi$
$102$	−7.89667	−0.781887
$103$	16.0717	1.58359	0.791796	−	0.610785i	$-0.209146\pi$
$103$	16.0717	1.58359	0.791796	+	0.610785i	$0.209146\pi$
$104$	18.3850	1.80279
$105$	−4.36264	−0.425750
$106$	7.09634	0.689258
$107$	−13.6789	−1.32239	−0.661194	−	0.750215i	$-0.729950\pi$
$107$	−13.6789	−1.32239	−0.661194	+	0.750215i	$0.729950\pi$
$108$	−0.0917248	−0.00882623
$109$	8.96674	0.858858	0.429429	−	0.903101i	$-0.358715\pi$
$109$	8.96674	0.858858	0.429429	+	0.903101i	$0.358715\pi$
$110$	5.96248	0.568500
$111$	6.54609	0.621328
$112$	16.6135	1.56983
$113$	−6.42952	−0.604838	−0.302419	−	0.953175i	$-0.597794\pi$
$113$	−6.42952	−0.604838	−0.302419	+	0.953175i	$0.597794\pi$
$114$	0	0
$115$	−0.579357	−0.0540253
$116$	−0.325939	−0.0302627
$117$	6.36264	0.588227
$118$	5.29033	0.487015
$119$	−24.9387	−2.28612
$120$	2.88952	0.263775
$121$	7.63001	0.693637
$122$	16.6059	1.50343
$123$	0.762807	0.0687800
$124$	0.108552	0.00974823
$125$	1.00000	0.0894427
$126$	6.02657	0.536890
$127$	6.18345	0.548692	0.274346	−	0.961631i	$-0.411539\pi$
$127$	6.18345	0.548692	0.274346	+	0.961631i	$0.411539\pi$
$128$	−10.4736	−0.925743
$129$	−6.36264	−0.560200
$130$	−8.78938	−0.770879
$131$	17.3974	1.52002	0.760010	−	0.649911i	$-0.225194\pi$
$131$	17.3974	1.52002	0.760010	+	0.649911i	$0.225194\pi$
$132$	0.395907	0.0344593
$133$	0	0
$134$	−5.53149	−0.477848
$135$	1.00000	0.0860663
$136$	16.5177	1.41638
$137$	15.7164	1.34274	0.671372	−	0.741121i	$-0.265705\pi$
$137$	15.7164	1.34274	0.671372	+	0.741121i	$0.265705\pi$
$138$	0.800326	0.0681282
$139$	6.55344	0.555856	0.277928	−	0.960602i	$-0.410352\pi$
$139$	6.55344	0.555856	0.277928	+	0.960602i	$0.410352\pi$
$140$	0.400163	0.0338199
$141$	−2.73264	−0.230130
$142$	4.25342	0.356939
$143$	−27.4628	−2.29655
$144$	−3.80814	−0.317345
$145$	3.55344	0.295097
$146$	−11.1706	−0.924484
$147$	12.0327	0.992437
$148$	−0.600439	−0.0493558
$149$	5.75120	0.471157	0.235578	−	0.971855i	$-0.424302\pi$
$149$	5.75120	0.471157	0.235578	+	0.971855i	$0.424302\pi$
$150$	−1.38140	−0.112791
$151$	12.6673	1.03085	0.515425	−	0.856935i	$-0.327634\pi$
$151$	12.6673	1.03085	0.515425	+	0.856935i	$0.327634\pi$
$152$	0	0
$153$	5.71641	0.462145
$154$	−26.0122	−2.09612
$155$	−1.18345	−0.0950570
$156$	−0.583613	−0.0467264
$157$	1.37887	0.110046	0.0550228	−	0.998485i	$-0.482477\pi$
$157$	1.37887	0.110046	0.0550228	+	0.998485i	$0.482477\pi$
$158$	15.6606	1.24589
$159$	−5.13706	−0.407395
$160$	−0.518458	−0.0409877
$161$	2.52753	0.199197
$162$	−1.38140	−0.108533
$163$	−11.6120	−0.909523	−0.454762	−	0.890613i	$-0.650276\pi$
$163$	−11.6120	−0.909523	−0.454762	+	0.890613i	$0.650276\pi$
$164$	−0.0699683	−0.00546361
$165$	−4.31625	−0.336020
$166$	−10.6076	−0.823313
$167$	20.3114	1.57174	0.785871	−	0.618390i	$-0.212215\pi$
$167$	20.3114	1.57174	0.785871	+	0.618390i	$0.212215\pi$
$168$	−12.6059	−0.972568
$169$	27.4832	2.11410
$170$	−7.89667	−0.605647
$171$	0	0
$172$	0.583613	0.0445000
$173$	12.2509	0.931419	0.465709	−	0.884938i	$-0.345799\pi$
$173$	12.2509	0.931419	0.465709	+	0.884938i	$0.345799\pi$
$174$	−4.90874	−0.372130
$175$	−4.36264	−0.329785
$176$	16.4369	1.23898
$177$	−3.82968	−0.287856
$178$	13.5956	1.01903
$179$	19.1840	1.43388	0.716941	−	0.697134i	$-0.245542\pi$
$179$	19.1840	1.43388	0.716941	+	0.697134i	$0.245542\pi$
$180$	−0.0917248	−0.00683677
$181$	3.22984	0.240072	0.120036	−	0.992770i	$-0.461699\pi$
$181$	3.22984	0.240072	0.120036	+	0.992770i	$0.461699\pi$
$182$	38.3449	2.84231
$183$	−12.0211	−0.888622
$184$	−1.67406	−0.123413
$185$	6.54609	0.481278
$186$	1.63482	0.119871
$187$	−24.6735	−1.80430
$188$	0.250651	0.0182806
$189$	−4.36264	−0.317336
$190$	0	0
$191$	27.5509	1.99352	0.996758	−	0.0804642i	$-0.0256403\pi$
$191$	27.5509	1.99352	0.996758	+	0.0804642i	$0.0256403\pi$
$192$	8.33247	0.601345
$193$	−22.2466	−1.60135	−0.800674	−	0.599100i	$-0.795525\pi$
$193$	−22.2466	−1.60135	−0.800674	+	0.599100i	$0.795525\pi$
$194$	2.76281	0.198358
$195$	6.36264	0.455638
$196$	−1.10369	−0.0788353
$197$	12.6627	0.902178	0.451089	−	0.892479i	$-0.351036\pi$
$197$	12.6627	0.902178	0.451089	+	0.892479i	$0.351036\pi$
$198$	5.96248	0.423735
$199$	−8.76955	−0.621657	−0.310829	−	0.950466i	$-0.600607\pi$
$199$	−8.76955	−0.621657	−0.310829	+	0.950466i	$0.600607\pi$
$200$	2.88952	0.204320
$201$	4.00426	0.282438
$202$	6.21590	0.437349
$203$	−15.5024	−1.08806
$204$	−0.524337	−0.0367109
$205$	0.762807	0.0532767
$206$	−22.2015	−1.54685
$207$	−0.579357	−0.0402681
$208$	−24.2298	−1.68004
$209$	0	0
$210$	6.02657	0.415873
$211$	−7.86778	−0.541640	−0.270820	−	0.962630i	$-0.587295\pi$
$211$	−7.86778	−0.541640	−0.270820	+	0.962630i	$0.587295\pi$
$212$	0.471196	0.0323618
$213$	−3.07906	−0.210973
$214$	18.8961	1.29171
$215$	−6.36264	−0.433929
$216$	2.88952	0.196607
$217$	5.16297	0.350485
$218$	−12.3867	−0.838932
$219$	8.08640	0.546429
$220$	0.395907	0.0266921
$221$	36.3715	2.44661
$222$	−9.04280	−0.606913
$223$	27.3535	1.83173	0.915864	−	0.401489i	$-0.131507\pi$
$223$	27.3535	1.83173	0.915864	+	0.401489i	$0.131507\pi$
$224$	2.26185	0.151126
$225$	1.00000	0.0666667
$226$	8.88176	0.590806
$227$	25.0922	1.66543	0.832713	−	0.553704i	$-0.186786\pi$
$227$	25.0922	1.66543	0.832713	+	0.553704i	$0.186786\pi$
$228$	0	0
$229$	4.98530	0.329438	0.164719	−	0.986341i	$-0.447328\pi$
$229$	4.98530	0.329438	0.164719	+	0.986341i	$0.447328\pi$
$230$	0.800326	0.0527719
$231$	18.8303	1.23894
$232$	10.2677	0.674109
$233$	12.7964	0.838321	0.419161	−	0.907912i	$-0.362324\pi$
$233$	12.7964	0.838321	0.419161	+	0.907912i	$0.362324\pi$
$234$	−8.78938	−0.574580
$235$	−2.73264	−0.178258
$236$	0.351277	0.0228662
$237$	−11.3367	−0.736400
$238$	34.4504	2.23309
$239$	12.8049	0.828283	0.414142	−	0.910212i	$-0.364082\pi$
$239$	12.8049	0.828283	0.414142	+	0.910212i	$0.364082\pi$
$240$	−3.80814	−0.245814
$241$	1.09279	0.0703927	0.0351964	−	0.999380i	$-0.488794\pi$
$241$	1.09279	0.0703927	0.0351964	+	0.999380i	$0.488794\pi$
$242$	−10.5401	−0.677544
$243$	1.00000	0.0641500
$244$	1.10263	0.0705886
$245$	12.0327	0.768739
$246$	−1.05374	−0.0671842
$247$	0	0
$248$	−3.41960	−0.217145
$249$	7.67889	0.486630
$250$	−1.38140	−0.0873676
$251$	6.09528	0.384731	0.192365	−	0.981323i	$-0.438384\pi$
$251$	6.09528	0.384731	0.192365	+	0.981323i	$0.438384\pi$
$252$	0.400163	0.0252079
$253$	2.50065	0.157214
$254$	−8.54184	−0.535963
$255$	5.71641	0.357976
$256$	−2.19670	−0.137293
$257$	−4.62032	−0.288207	−0.144104	−	0.989563i	$-0.546030\pi$
$257$	−4.62032	−0.288207	−0.144104	+	0.989563i	$0.546030\pi$
$258$	8.78938	0.547203
$259$	−28.5583	−1.77452
$260$	−0.583613	−0.0361941
$261$	3.55344	0.219953
$262$	−24.0329	−1.48476
$263$	−30.0495	−1.85293	−0.926465	−	0.376382i	$-0.877168\pi$
$263$	−30.0495	−1.85293	−0.926465	+	0.376382i	$0.877168\pi$
$264$	−12.4719	−0.767591
$265$	−5.13706	−0.315567
$266$	0	0
$267$	−9.84186	−0.602312
$268$	−0.367290	−0.0224358
$269$	0.211279	0.0128819	0.00644095	−	0.999979i	$-0.497950\pi$
$269$	0.211279	0.0128819	0.00644095	+	0.999979i	$0.497950\pi$
$270$	−1.38140	−0.0840695
$271$	−7.40727	−0.449960	−0.224980	−	0.974363i	$-0.572232\pi$
$271$	−7.40727	−0.449960	−0.224980	+	0.974363i	$0.572232\pi$
$272$	−21.7689	−1.31993
$273$	−27.7579	−1.67999
$274$	−21.7107	−1.31159
$275$	−4.31625	−0.260280
$276$	0.0531414	0.00319874
$277$	−29.0668	−1.74646	−0.873229	−	0.487310i	$-0.837978\pi$
$277$	−29.0668	−1.74646	−0.873229	+	0.487310i	$0.837978\pi$
$278$	−9.05295	−0.542960
$279$	−1.18345	−0.0708513
$280$	−12.6059	−0.753348
$281$	−11.4759	−0.684596	−0.342298	−	0.939592i	$-0.611205\pi$
$281$	−11.4759	−0.684596	−0.342298	+	0.939592i	$0.611205\pi$
$282$	3.77487	0.224790
$283$	−27.3324	−1.62475	−0.812373	−	0.583139i	$-0.801824\pi$
$283$	−27.3324	−1.62475	−0.812373	+	0.583139i	$0.801824\pi$
$284$	0.282426	0.0167589
$285$	0	0
$286$	37.9371	2.24327
$287$	−3.32785	−0.196437
$288$	−0.518458	−0.0305505
$289$	15.6774	0.922198
$290$	−4.90874	−0.288251
$291$	−2.00000	−0.117242
$292$	−0.741724	−0.0434061
$293$	−13.0211	−0.760698	−0.380349	−	0.924843i	$-0.624196\pi$
$293$	−13.0211	−0.760698	−0.380349	+	0.924843i	$0.624196\pi$
$294$	−16.6220	−0.969412
$295$	−3.82968	−0.222973
$296$	18.9150	1.09941
$297$	−4.31625	−0.250454
$298$	−7.94473	−0.460226
$299$	−3.68624	−0.213181
$300$	−0.0917248	−0.00529574
$301$	27.7579	1.59994
$302$	−17.4986	−1.00693
$303$	−4.49970	−0.258501
$304$	0	0
$305$	−12.0211	−0.688324
$306$	−7.89667	−0.451423
$307$	−4.02534	−0.229738	−0.114869	−	0.993381i	$-0.536645\pi$
$307$	−4.02534	−0.229738	−0.114869	+	0.993381i	$0.536645\pi$
$308$	−1.72720	−0.0984165
$309$	16.0717	0.914287
$310$	1.63482	0.0928516
$311$	15.3578	0.870860	0.435430	−	0.900223i	$-0.356596\pi$
$311$	15.3578	0.870860	0.435430	+	0.900223i	$0.356596\pi$
$312$	18.3850	1.04084
$313$	21.9600	1.24125	0.620625	−	0.784107i	$-0.286879\pi$
$313$	21.9600	1.24125	0.620625	+	0.784107i	$0.286879\pi$
$314$	−1.90477	−0.107493
$315$	−4.36264	−0.245807
$316$	1.03986	0.0584967
$317$	24.1279	1.35516	0.677580	−	0.735449i	$-0.263029\pi$
$317$	24.1279	1.35516	0.677580	+	0.735449i	$0.263029\pi$
$318$	7.09634	0.397943
$319$	−15.3375	−0.858738
$320$	8.33247	0.465799
$321$	−13.6789	−0.763481
$322$	−3.49154	−0.194576
$323$	0	0
$324$	−0.0917248	−0.00509582
$325$	6.36264	0.352936
$326$	16.0409	0.888422
$327$	8.96674	0.495862
$328$	2.20414	0.121703
$329$	11.9215	0.657255
$330$	5.96248	0.328224
$331$	24.8416	1.36542	0.682710	−	0.730690i	$-0.260801\pi$
$331$	24.8416	1.36542	0.682710	+	0.730690i	$0.260801\pi$
$332$	−0.704345	−0.0386560
$333$	6.54609	0.358724
$334$	−28.0582	−1.53528
$335$	4.00426	0.218776
$336$	16.6135	0.906343
$337$	−0.569303	−0.0310119	−0.0155059	−	0.999880i	$-0.504936\pi$
$337$	−0.569303	−0.0310119	−0.0155059	+	0.999880i	$0.504936\pi$
$338$	−37.9654	−2.06505
$339$	−6.42952	−0.349204
$340$	−0.524337	−0.0284362
$341$	5.10806	0.276617
$342$	0	0
$343$	−21.9557	−1.18550
$344$	−18.3850	−0.991251
$345$	−0.579357	−0.0311915
$346$	−16.9234	−0.909810
$347$	9.37365	0.503204	0.251602	−	0.967831i	$-0.419043\pi$
$347$	9.37365	0.503204	0.251602	+	0.967831i	$0.419043\pi$
$348$	−0.325939	−0.0174722
$349$	14.8297	0.793815	0.396907	−	0.917859i	$-0.370083\pi$
$349$	14.8297	0.793815	0.396907	+	0.917859i	$0.370083\pi$
$350$	6.02657	0.322134
$351$	6.36264	0.339613
$352$	2.23780	0.119275
$353$	31.2650	1.66407	0.832034	−	0.554725i	$-0.187176\pi$
$353$	31.2650	1.66407	0.832034	+	0.554725i	$0.187176\pi$
$354$	5.29033	0.281178
$355$	−3.07906	−0.163419
$356$	0.902743	0.0478453
$357$	−24.9387	−1.31989
$358$	−26.5009	−1.40061
$359$	10.8712	0.573761	0.286880	−	0.957966i	$-0.407382\pi$
$359$	10.8712	0.573761	0.286880	+	0.957966i	$0.407382\pi$
$360$	2.88952	0.152291
$361$	0	0
$362$	−4.46172	−0.234503
$363$	7.63001	0.400472
$364$	2.54609	0.133452
$365$	8.08640	0.423262
$366$	16.6059	0.868006
$367$	−18.7295	−0.977674	−0.488837	−	0.872375i	$-0.662579\pi$
$367$	−18.7295	−0.977674	−0.488837	+	0.872375i	$0.662579\pi$
$368$	2.20627	0.115010
$369$	0.762807	0.0397101
$370$	−9.04280	−0.470113
$371$	22.4111	1.16353
$372$	0.108552	0.00562815
$373$	−29.3275	−1.51852	−0.759259	−	0.650788i	$-0.774439\pi$
$373$	−29.3275	−1.51852	−0.759259	+	0.650788i	$0.774439\pi$
$374$	34.0840	1.76244
$375$	1.00000	0.0516398
$376$	−7.89600	−0.407205
$377$	22.6093	1.16444
$378$	6.02657	0.309973
$379$	10.6486	0.546980	0.273490	−	0.961875i	$-0.411822\pi$
$379$	10.6486	0.546980	0.273490	+	0.961875i	$0.411822\pi$
$380$	0	0
$381$	6.18345	0.316788
$382$	−38.0589	−1.94726
$383$	−9.27954	−0.474163	−0.237081	−	0.971490i	$-0.576191\pi$
$383$	−9.27954	−0.474163	−0.237081	+	0.971490i	$0.576191\pi$
$384$	−10.4736	−0.534478
$385$	18.8303	0.959679
$386$	30.7316	1.56420
$387$	−6.36264	−0.323431
$388$	0.183450	0.00931325
$389$	1.33247	0.0675591	0.0337796	−	0.999429i	$-0.489246\pi$
$389$	1.33247	0.0675591	0.0337796	+	0.999429i	$0.489246\pi$
$390$	−8.78938	−0.445067
$391$	−3.31184	−0.167487
$392$	34.7686	1.75608
$393$	17.3974	0.877584
$394$	−17.4923	−0.881247
$395$	−11.3367	−0.570413
$396$	0.395907	0.0198951
$397$	−31.6648	−1.58921	−0.794605	−	0.607127i	$-0.792322\pi$
$397$	−31.6648	−1.58921	−0.794605	+	0.607127i	$0.792322\pi$
$398$	12.1143	0.607235
$399$	0	0
$400$	−3.80814	−0.190407
$401$	4.88849	0.244120	0.122060	−	0.992523i	$-0.461050\pi$
$401$	4.88849	0.244120	0.122060	+	0.992523i	$0.461050\pi$
$402$	−5.53149	−0.275886
$403$	−7.52987	−0.375089
$404$	0.412734	0.0205343
$405$	1.00000	0.0496904
$406$	21.4151	1.06281
$407$	−28.2546	−1.40053
$408$	16.5177	0.817746
$409$	22.7881	1.12680	0.563400	−	0.826184i	$-0.309493\pi$
$409$	22.7881	1.12680	0.563400	+	0.826184i	$0.309493\pi$
$410$	−1.05374	−0.0520407
$411$	15.7164	0.775233
$412$	−1.47417	−0.0726274
$413$	16.7075	0.822124
$414$	0.800326	0.0393339
$415$	7.67889	0.376942
$416$	−3.29877	−0.161735
$417$	6.55344	0.320923
$418$	0	0
$419$	30.8809	1.50863	0.754316	−	0.656512i	$-0.227969\pi$
$419$	30.8809	1.50863	0.754316	+	0.656512i	$0.227969\pi$
$420$	0.400163	0.0195259
$421$	−26.5782	−1.29534	−0.647671	−	0.761920i	$-0.724257\pi$
$421$	−26.5782	−1.29534	−0.647671	+	0.761920i	$0.724257\pi$
$422$	10.8686	0.529074
$423$	−2.73264	−0.132865
$424$	−14.8436	−0.720869
$425$	5.71641	0.277287
$426$	4.25342	0.206079
$427$	52.4436	2.53792
$428$	1.25469	0.0606479
$429$	−27.4628	−1.32591
$430$	8.78938	0.423861
$431$	−16.4744	−0.793542	−0.396771	−	0.917918i	$-0.629869\pi$
$431$	−16.4744	−0.793542	−0.396771	+	0.917918i	$0.629869\pi$
$432$	−3.80814	−0.183219
$433$	36.8041	1.76869	0.884346	−	0.466832i	$-0.154605\pi$
$433$	36.8041	1.76869	0.884346	+	0.466832i	$0.154605\pi$
$434$	−7.13214	−0.342354
$435$	3.55344	0.170375
$436$	−0.822473	−0.0393893
$437$	0	0
$438$	−11.1706	−0.533751
$439$	−9.58280	−0.457362	−0.228681	−	0.973501i	$-0.573441\pi$
$439$	−9.58280	−0.457362	−0.228681	+	0.973501i	$0.573441\pi$
$440$	−12.4719	−0.594573
$441$	12.0327	0.572984
$442$	−50.2437	−2.38985
$443$	−22.2436	−1.05682	−0.528412	−	0.848988i	$-0.677212\pi$
$443$	−22.2436	−1.05682	−0.528412	+	0.848988i	$0.677212\pi$
$444$	−0.600439	−0.0284956
$445$	−9.84186	−0.466549
$446$	−37.7863	−1.78923
$447$	5.75120	0.272023
$448$	−36.3516	−1.71745
$449$	0.491188	0.0231806	0.0115903	−	0.999933i	$-0.496311\pi$
$449$	0.491188	0.0231806	0.0115903	+	0.999933i	$0.496311\pi$
$450$	−1.38140	−0.0651200
$451$	−3.29246	−0.155036
$452$	0.589747	0.0277393
$453$	12.6673	0.595161
$454$	−34.6624	−1.62679
$455$	−27.7579	−1.30131
$456$	0	0
$457$	13.2607	0.620311	0.310156	−	0.950686i	$-0.399619\pi$
$457$	13.2607	0.620311	0.310156	+	0.950686i	$0.399619\pi$
$458$	−6.88671	−0.321795
$459$	5.71641	0.266819
$460$	0.0531414	0.00247773
$461$	23.3734	1.08861	0.544305	−	0.838888i	$-0.316794\pi$
$461$	23.3734	1.08861	0.544305	+	0.838888i	$0.316794\pi$
$462$	−26.0122	−1.21020
$463$	−0.981649	−0.0456211	−0.0228105	−	0.999740i	$-0.507261\pi$
$463$	−0.981649	−0.0456211	−0.0228105	+	0.999740i	$0.507261\pi$
$464$	−13.5320	−0.628207
$465$	−1.18345	−0.0548812
$466$	−17.6770	−0.818872
$467$	−18.8498	−0.872264	−0.436132	−	0.899883i	$-0.643652\pi$
$467$	−18.8498	−0.872264	−0.436132	+	0.899883i	$0.643652\pi$
$468$	−0.583613	−0.0269775
$469$	−17.4691	−0.806650
$470$	3.77487	0.174122
$471$	1.37887	0.0635349
$472$	−11.0659	−0.509350
$473$	27.4628	1.26274
$474$	15.6606	0.719315
$475$	0	0
$476$	2.28750	0.104847
$477$	−5.13706	−0.235210
$478$	−17.6888	−0.809067
$479$	20.1591	0.921091	0.460546	−	0.887636i	$-0.347654\pi$
$479$	20.1591	0.921091	0.460546	+	0.887636i	$0.347654\pi$
$480$	−0.518458	−0.0236643
$481$	41.6505	1.89910
$482$	−1.50958	−0.0687596
$483$	2.52753	0.115007
$484$	−0.699861	−0.0318119
$485$	−2.00000	−0.0908153
$486$	−1.38140	−0.0626617
$487$	−2.79159	−0.126499	−0.0632494	−	0.997998i	$-0.520146\pi$
$487$	−2.79159	−0.126499	−0.0632494	+	0.997998i	$0.520146\pi$
$488$	−34.7350	−1.57238
$489$	−11.6120	−0.525114
$490$	−16.6220	−0.750904
$491$	5.77808	0.260761	0.130381	−	0.991464i	$-0.458380\pi$
$491$	5.77808	0.260761	0.130381	+	0.991464i	$0.458380\pi$
$492$	−0.0699683	−0.00315442
$493$	20.3129	0.914849
$494$	0	0
$495$	−4.31625	−0.194001
$496$	4.50674	0.202359
$497$	13.4328	0.602545
$498$	−10.6076	−0.475340
$499$	12.7958	0.572820	0.286410	−	0.958107i	$-0.407538\pi$
$499$	12.7958	0.572820	0.286410	+	0.958107i	$0.407538\pi$
$500$	−0.0917248	−0.00410206
$501$	20.3114	0.907446
$502$	−8.42004	−0.375805
$503$	31.6679	1.41200	0.706000	−	0.708212i	$-0.250498\pi$
$503$	31.6679	1.41200	0.706000	+	0.708212i	$0.250498\pi$
$504$	−12.6059	−0.561513
$505$	−4.49970	−0.200234
$506$	−3.45440	−0.153567
$507$	27.4832	1.22057
$508$	−0.567176	−0.0251644
$509$	5.48809	0.243256	0.121628	−	0.992576i	$-0.461189\pi$
$509$	5.48809	0.243256	0.121628	+	0.992576i	$0.461189\pi$
$510$	−7.89667	−0.349670
$511$	−35.2781	−1.56061
$512$	23.9817	1.05985
$513$	0	0
$514$	6.38252	0.281521
$515$	16.0717	0.708204
$516$	0.583613	0.0256921
$517$	11.7947	0.518732
$518$	39.4505	1.73336
$519$	12.2509	0.537755
$520$	18.3850	0.806234
$521$	−8.28086	−0.362791	−0.181396	−	0.983410i	$-0.558061\pi$
$521$	−8.28086	−0.362791	−0.181396	+	0.983410i	$0.558061\pi$
$522$	−4.90874	−0.214850
$523$	−11.5517	−0.505120	−0.252560	−	0.967581i	$-0.581272\pi$
$523$	−11.5517	−0.505120	−0.252560	+	0.967581i	$0.581272\pi$
$524$	−1.59578	−0.0697118
$525$	−4.36264	−0.190401
$526$	41.5104	1.80994
$527$	−6.76509	−0.294692
$528$	16.4369	0.715323
$529$	−22.6643	−0.985406
$530$	7.09634	0.308246
$531$	−3.82968	−0.166194
$532$	0	0
$533$	4.85347	0.210227
$534$	13.5956	0.588338
$535$	−13.6789	−0.591390
$536$	11.5704	0.499763
$537$	19.1840	0.827852
$538$	−0.291861	−0.0125830
$539$	−51.9360	−2.23704
$540$	−0.0917248	−0.00394721
$541$	−25.8749	−1.11245	−0.556224	−	0.831032i	$-0.687750\pi$
$541$	−25.8749	−1.11245	−0.556224	+	0.831032i	$0.687750\pi$
$542$	10.2324	0.439521
$543$	3.22984	0.138606
$544$	−2.96372	−0.127069
$545$	8.96674	0.384093
$546$	38.3449	1.64101
$547$	−6.40573	−0.273889	−0.136945	−	0.990579i	$-0.543728\pi$
$547$	−6.40573	−0.273889	−0.136945	+	0.990579i	$0.543728\pi$
$548$	−1.44159	−0.0615815
$549$	−12.0211	−0.513046
$550$	5.96248	0.254241
$551$	0	0
$552$	−1.67406	−0.0712528
$553$	49.4581	2.10317
$554$	40.1530	1.70594
$555$	6.54609	0.277866
$556$	−0.601113	−0.0254929
$557$	−3.52561	−0.149385	−0.0746925	−	0.997207i	$-0.523798\pi$
$557$	−3.52561	−0.149385	−0.0746925	+	0.997207i	$0.523798\pi$
$558$	1.63482	0.0692075
$559$	−40.4832	−1.71226
$560$	16.6135	0.702050
$561$	−24.6735	−1.04171
$562$	15.8529	0.668713
$563$	30.7179	1.29461	0.647303	−	0.762232i	$-0.275897\pi$
$563$	30.7179	1.29461	0.647303	+	0.762232i	$0.275897\pi$
$564$	0.250651	0.0105543
$565$	−6.42952	−0.270492
$566$	37.7571	1.58705
$567$	−4.36264	−0.183214
$568$	−8.89698	−0.373309
$569$	−9.17896	−0.384802	−0.192401	−	0.981316i	$-0.561627\pi$
$569$	−9.17896	−0.384802	−0.192401	+	0.981316i	$0.561627\pi$
$570$	0	0
$571$	−7.49001	−0.313447	−0.156724	−	0.987643i	$-0.550093\pi$
$571$	−7.49001	−0.313447	−0.156724	+	0.987643i	$0.550093\pi$
$572$	2.51902	0.105325
$573$	27.5509	1.15096
$574$	4.59711	0.191880
$575$	−0.579357	−0.0241609
$576$	8.33247	0.347186
$577$	32.6093	1.35754	0.678771	−	0.734350i	$-0.262513\pi$
$577$	32.6093	1.35754	0.678771	+	0.734350i	$0.262513\pi$
$578$	−21.6568	−0.900803
$579$	−22.2466	−0.924539
$580$	−0.325939	−0.0135339
$581$	−33.5003	−1.38983
$582$	2.76281	0.114522
$583$	22.1728	0.918304
$584$	23.3658	0.966883
$585$	6.36264	0.263063
$586$	17.9873	0.743050
$587$	−18.3895	−0.759015	−0.379508	−	0.925189i	$-0.623907\pi$
$587$	−18.3895	−0.759015	−0.379508	+	0.925189i	$0.623907\pi$
$588$	−1.10369	−0.0455156
$589$	0	0
$590$	5.29033	0.217800
$591$	12.6627	0.520873
$592$	−24.9284	−1.02455
$593$	0.417338	0.0171380	0.00856900	−	0.999963i	$-0.497272\pi$
$593$	0.417338	0.0171380	0.00856900	+	0.999963i	$0.497272\pi$
$594$	5.96248	0.244644
$595$	−24.9387	−1.02239
$596$	−0.527528	−0.0216084
$597$	−8.76955	−0.358914
$598$	5.09219	0.208235
$599$	38.9655	1.59209	0.796045	−	0.605238i	$-0.206922\pi$
$599$	38.9655	1.59209	0.796045	+	0.605238i	$0.206922\pi$
$600$	2.88952	0.117964
$601$	−10.0358	−0.409367	−0.204683	−	0.978828i	$-0.565617\pi$
$601$	−10.0358	−0.409367	−0.204683	+	0.978828i	$0.565617\pi$
$602$	−38.3449	−1.56282
$603$	4.00426	0.163066
$604$	−1.16191	−0.0472772
$605$	7.63001	0.310204
$606$	6.21590	0.252504
$607$	6.25423	0.253851	0.126926	−	0.991912i	$-0.459489\pi$
$607$	6.25423	0.253851	0.126926	+	0.991912i	$0.459489\pi$
$608$	0	0
$609$	−15.5024	−0.628189
$610$	16.6059	0.672354
$611$	−17.3868	−0.703394
$612$	−0.524337	−0.0211951
$613$	29.8743	1.20661	0.603306	−	0.797510i	$-0.293850\pi$
$613$	29.8743	1.20661	0.603306	+	0.797510i	$0.293850\pi$
$614$	5.56062	0.224408
$615$	0.762807	0.0307593
$616$	54.4103	2.19225
$617$	−30.6395	−1.23350	−0.616749	−	0.787160i	$-0.711551\pi$
$617$	−30.6395	−1.23350	−0.616749	+	0.787160i	$0.711551\pi$
$618$	−22.2015	−0.893076
$619$	21.1480	0.850011	0.425006	−	0.905191i	$-0.360272\pi$
$619$	21.1480	0.850011	0.425006	+	0.905191i	$0.360272\pi$
$620$	0.108552	0.00435954
$621$	−0.579357	−0.0232488
$622$	−21.2153	−0.850656
$623$	42.9365	1.72022
$624$	−24.2298	−0.969969
$625$	1.00000	0.0400000
$626$	−30.3356	−1.21245
$627$	0	0
$628$	−0.126476	−0.00504696
$629$	37.4202	1.49204
$630$	6.02657	0.240104
$631$	−26.0247	−1.03603	−0.518014	−	0.855372i	$-0.673329\pi$
$631$	−26.0247	−1.03603	−0.518014	+	0.855372i	$0.673329\pi$
$632$	−32.7577	−1.30303
$633$	−7.86778	−0.312716
$634$	−33.3304	−1.32372
$635$	6.18345	0.245383
$636$	0.471196	0.0186841
$637$	76.5595	3.03340
$638$	21.1873	0.838815
$639$	−3.07906	−0.121806
$640$	−10.4736	−0.414005
$641$	19.1996	0.758341	0.379170	−	0.925327i	$-0.376209\pi$
$641$	19.1996	0.758341	0.379170	+	0.925327i	$0.376209\pi$
$642$	18.8961	0.745768
$643$	8.54609	0.337025	0.168513	−	0.985700i	$-0.446104\pi$
$643$	8.54609	0.337025	0.168513	+	0.985700i	$0.446104\pi$
$644$	−0.231837	−0.00913566
$645$	−6.36264	−0.250529
$646$	0	0
$647$	−21.6966	−0.852983	−0.426492	−	0.904492i	$-0.640251\pi$
$647$	−21.6966	−0.852983	−0.426492	+	0.904492i	$0.640251\pi$
$648$	2.88952	0.113511
$649$	16.5299	0.648854
$650$	−8.78938	−0.344748
$651$	5.16297	0.202353
$652$	1.06511	0.0417129
$653$	−4.39011	−0.171798	−0.0858991	−	0.996304i	$-0.527376\pi$
$653$	−4.39011	−0.171798	−0.0858991	+	0.996304i	$0.527376\pi$
$654$	−12.3867	−0.484358
$655$	17.3974	0.679774
$656$	−2.90487	−0.113416
$657$	8.08640	0.315481
$658$	−16.4684	−0.642006
$659$	15.1465	0.590025	0.295013	−	0.955493i	$-0.404676\pi$
$659$	15.1465	0.590025	0.295013	+	0.955493i	$0.404676\pi$
$660$	0.395907	0.0154107
$661$	−7.31588	−0.284555	−0.142277	−	0.989827i	$-0.545443\pi$
$661$	−7.31588	−0.284555	−0.142277	+	0.989827i	$0.545443\pi$
$662$	−34.3163	−1.33374
$663$	36.3715	1.41255
$664$	22.1883	0.861072
$665$	0	0
$666$	−9.04280	−0.350401
$667$	−2.05871	−0.0797136
$668$	−1.86306	−0.0720839
$669$	27.3535	1.05755
$670$	−5.53149	−0.213700
$671$	51.8859	2.00303
$672$	2.26185	0.0872527
$673$	−39.7027	−1.53043	−0.765213	−	0.643777i	$-0.777366\pi$
$673$	−39.7027	−1.53043	−0.765213	+	0.643777i	$0.777366\pi$
$674$	0.786437	0.0302924
$675$	1.00000	0.0384900
$676$	−2.52090	−0.0969575
$677$	9.45197	0.363269	0.181634	−	0.983366i	$-0.441861\pi$
$677$	9.45197	0.363269	0.181634	+	0.983366i	$0.441861\pi$
$678$	8.88176	0.341102
$679$	8.72529	0.334846
$680$	16.5177	0.633423
$681$	25.0922	0.961535
$682$	−7.05630	−0.270200
$683$	6.27600	0.240145	0.120072	−	0.992765i	$-0.461687\pi$
$683$	6.27600	0.240145	0.120072	+	0.992765i	$0.461687\pi$
$684$	0	0
$685$	15.7164	0.600493
$686$	30.3297	1.15799
$687$	4.98530	0.190201
$688$	24.2298	0.923753
$689$	−32.6853	−1.24521
$690$	0.800326	0.0304679
$691$	−33.8913	−1.28929	−0.644643	−	0.764483i	$-0.722994\pi$
$691$	−33.8913	−1.28929	−0.644643	+	0.764483i	$0.722994\pi$
$692$	−1.12371	−0.0427171
$693$	18.8303	0.715302
$694$	−12.9488	−0.491529
$695$	6.55344	0.248586
$696$	10.2677	0.389197
$697$	4.36052	0.165166
$698$	−20.4858	−0.775398
$699$	12.7964	0.484005
$700$	0.400163	0.0151247
$701$	40.3040	1.52226	0.761131	−	0.648598i	$-0.224644\pi$
$701$	40.3040	1.52226	0.761131	+	0.648598i	$0.224644\pi$
$702$	−8.78938	−0.331734
$703$	0	0
$704$	−35.9650	−1.35548
$705$	−2.73264	−0.102917
$706$	−43.1896	−1.62546
$707$	19.6306	0.738284
$708$	0.351277	0.0132018
$709$	−5.27411	−0.198073	−0.0990367	−	0.995084i	$-0.531576\pi$
$709$	−5.27411	−0.198073	−0.0990367	+	0.995084i	$0.531576\pi$
$710$	4.25342	0.159628
$711$	−11.3367	−0.425161
$712$	−28.4382	−1.06577
$713$	0.685640	0.0256774
$714$	34.4504	1.28927
$715$	−27.4628	−1.02705
$716$	−1.75965	−0.0657613
$717$	12.8049	0.478209
$718$	−15.0175	−0.560450
$719$	23.7668	0.886353	0.443176	−	0.896434i	$-0.353851\pi$
$719$	23.7668	0.886353	0.443176	+	0.896434i	$0.353851\pi$
$720$	−3.80814	−0.141921
$721$	−70.1151	−2.61122
$722$	0	0
$723$	1.09279	0.0406413
$724$	−0.296257	−0.0110103
$725$	3.55344	0.131972
$726$	−10.5401	−0.391180
$727$	−33.8449	−1.25524	−0.627620	−	0.778520i	$-0.715971\pi$
$727$	−33.8449	−1.25524	−0.627620	+	0.778520i	$0.715971\pi$
$728$	−80.2070	−2.97267
$729$	1.00000	0.0370370
$730$	−11.1706	−0.413442
$731$	−36.3715	−1.34525
$732$	1.10263	0.0407544
$733$	24.6249	0.909542	0.454771	−	0.890608i	$-0.349721\pi$
$733$	24.6249	0.909542	0.454771	+	0.890608i	$0.349721\pi$
$734$	25.8731	0.954992
$735$	12.0327	0.443831
$736$	0.300372	0.0110719
$737$	−17.2834	−0.636641
$738$	−1.05374	−0.0387888
$739$	18.4593	0.679037	0.339518	−	0.940599i	$-0.389736\pi$
$739$	18.4593	0.679037	0.339518	+	0.940599i	$0.389736\pi$
$740$	−0.600439	−0.0220726
$741$	0	0
$742$	−30.9588	−1.13653
$743$	8.95728	0.328611	0.164305	−	0.986410i	$-0.447462\pi$
$743$	8.95728	0.328611	0.164305	+	0.986410i	$0.447462\pi$
$744$	−3.41960	−0.125368
$745$	5.75120	0.210708
$746$	40.5131	1.48329
$747$	7.67889	0.280956
$748$	2.26317	0.0827497
$749$	59.6761	2.18052
$750$	−1.38140	−0.0504417
$751$	29.2256	1.06646	0.533228	−	0.845972i	$-0.320979\pi$
$751$	29.2256	1.06646	0.533228	+	0.845972i	$0.320979\pi$
$752$	10.4063	0.379477
$753$	6.09528	0.222124
$754$	−31.2325	−1.13742
$755$	12.6673	0.461010
$756$	0.400163	0.0145538
$757$	18.6777	0.678853	0.339427	−	0.940633i	$-0.389767\pi$
$757$	18.6777	0.678853	0.339427	+	0.940633i	$0.389767\pi$
$758$	−14.7100	−0.534290
$759$	2.50065	0.0907678
$760$	0	0
$761$	41.5952	1.50782	0.753912	−	0.656975i	$-0.228164\pi$
$761$	41.5952	1.50782	0.753912	+	0.656975i	$0.228164\pi$
$762$	−8.54184	−0.309438
$763$	−39.1187	−1.41619
$764$	−2.52710	−0.0914274
$765$	5.71641	0.206677
$766$	12.8188	0.463162
$767$	−24.3669	−0.879838
$768$	−2.19670	−0.0792664
$769$	35.2509	1.27118	0.635590	−	0.772027i	$-0.280757\pi$
$769$	35.2509	1.27118	0.635590	+	0.772027i	$0.280757\pi$
$770$	−26.0122	−0.937414
$771$	−4.62032	−0.166397
$772$	2.04057	0.0734417
$773$	−47.9524	−1.72473	−0.862364	−	0.506290i	$-0.831017\pi$
$773$	−47.9524	−1.72473	−0.862364	+	0.506290i	$0.831017\pi$
$774$	8.78938	0.315928
$775$	−1.18345	−0.0425108
$776$	−5.77903	−0.207455
$777$	−28.5583	−1.02452
$778$	−1.84068	−0.0659917
$779$	0	0
$780$	−0.583613	−0.0208967
$781$	13.2900	0.475553
$782$	4.57499	0.163601
$783$	3.55344	0.126990
$784$	−45.8220	−1.63650
$785$	1.37887	0.0492139
$786$	−24.0329	−0.857224
$787$	5.26074	0.187525	0.0937626	−	0.995595i	$-0.470111\pi$
$787$	5.26074	0.187525	0.0937626	+	0.995595i	$0.470111\pi$
$788$	−1.16148	−0.0413761
$789$	−30.0495	−1.06979
$790$	15.6606	0.557179
$791$	28.0497	0.997333
$792$	−12.4719	−0.443169
$793$	−76.4857	−2.71609
$794$	43.7418	1.55234
$795$	−5.13706	−0.182193
$796$	0.804386	0.0285107
$797$	21.0174	0.744474	0.372237	−	0.928138i	$-0.378591\pi$
$797$	21.0174	0.744474	0.372237	+	0.928138i	$0.378591\pi$
$798$	0	0
$799$	−15.6209	−0.552627
$800$	−0.518458	−0.0183303
$801$	−9.84186	−0.347745
$802$	−6.75298	−0.238456
$803$	−34.9029	−1.23170
$804$	−0.367290	−0.0129533
$805$	2.52753	0.0890837
$806$	10.4018	0.366387
$807$	0.211279	0.00743737
$808$	−13.0020	−0.457407
$809$	35.3856	1.24409	0.622046	−	0.782981i	$-0.286302\pi$
$809$	35.3856	1.24409	0.622046	+	0.782981i	$0.286302\pi$
$810$	−1.38140	−0.0485376
$811$	−5.35046	−0.187880	−0.0939401	−	0.995578i	$-0.529946\pi$
$811$	−5.35046	−0.187880	−0.0939401	+	0.995578i	$0.529946\pi$
$812$	1.42196	0.0499009
$813$	−7.40727	−0.259784
$814$	39.0310	1.36803
$815$	−11.6120	−0.406751
$816$	−21.7689	−0.762063
$817$	0	0
$818$	−31.4796	−1.10066
$819$	−27.7579	−0.969941
$820$	−0.0699683	−0.00244340
$821$	7.63772	0.266558	0.133279	−	0.991079i	$-0.457449\pi$
$821$	7.63772	0.266558	0.133279	+	0.991079i	$0.457449\pi$
$822$	−21.7107	−0.757248
$823$	27.5732	0.961141	0.480570	−	0.876956i	$-0.340430\pi$
$823$	27.5732	0.961141	0.480570	+	0.876956i	$0.340430\pi$
$824$	46.4394	1.61779
$825$	−4.31625	−0.150273
$826$	−23.0798	−0.803051
$827$	19.0317	0.661797	0.330898	−	0.943666i	$-0.392648\pi$
$827$	19.0317	0.661797	0.330898	+	0.943666i	$0.392648\pi$
$828$	0.0531414	0.00184679
$829$	13.7455	0.477402	0.238701	−	0.971093i	$-0.423278\pi$
$829$	13.7455	0.477402	0.238701	+	0.971093i	$0.423278\pi$
$830$	−10.6076	−0.368197
$831$	−29.0668	−1.00832
$832$	53.0166	1.83802
$833$	68.7836	2.38321
$834$	−9.05295	−0.313478
$835$	20.3114	0.702905
$836$	0	0
$837$	−1.18345	−0.0409060
$838$	−42.6590	−1.47363
$839$	−34.3599	−1.18624	−0.593118	−	0.805115i	$-0.702103\pi$
$839$	−34.3599	−1.18624	−0.593118	+	0.805115i	$0.702103\pi$
$840$	−12.6059	−0.434946
$841$	−16.3730	−0.564588
$842$	36.7152	1.26529
$843$	−11.4759	−0.395251
$844$	0.721671	0.0248409
$845$	27.4832	0.945452
$846$	3.77487	0.129783
$847$	−33.2870	−1.14375
$848$	19.5626	0.671783
$849$	−27.3324	−0.938047
$850$	−7.89667	−0.270854
$851$	−3.79252	−0.130006
$852$	0.282426	0.00967575
$853$	45.4295	1.55548	0.777738	−	0.628588i	$-0.216367\pi$
$853$	45.4295	1.55548	0.777738	+	0.628588i	$0.216367\pi$
$854$	−72.4457	−2.47904
$855$	0	0
$856$	−39.5254	−1.35095
$857$	−13.8935	−0.474592	−0.237296	−	0.971437i	$-0.576261\pi$
$857$	−13.8935	−0.474592	−0.237296	+	0.971437i	$0.576261\pi$
$858$	37.9371	1.29515
$859$	−3.20666	−0.109410	−0.0547049	−	0.998503i	$-0.517422\pi$
$859$	−3.20666	−0.109410	−0.0547049	+	0.998503i	$0.517422\pi$
$860$	0.583613	0.0199010
$861$	−3.32785	−0.113413
$862$	22.7577	0.775132
$863$	−51.7277	−1.76083	−0.880416	−	0.474201i	$-0.842737\pi$
$863$	−51.7277	−1.76083	−0.880416	+	0.474201i	$0.842737\pi$
$864$	−0.518458	−0.0176383
$865$	12.2509	0.416543
$866$	−50.8413	−1.72766
$867$	15.6774	0.532431
$868$	−0.473573	−0.0160741
$869$	48.9321	1.65991
$870$	−4.90874	−0.166422
$871$	25.4777	0.863277
$872$	25.9095	0.877407
$873$	−2.00000	−0.0676897
$874$	0	0
$875$	−4.36264	−0.147484
$876$	−0.741724	−0.0250605
$877$	−17.0271	−0.574964	−0.287482	−	0.957786i	$-0.592818\pi$
$877$	−17.0271	−0.574964	−0.287482	+	0.957786i	$0.592818\pi$
$878$	13.2377	0.446751
$879$	−13.0211	−0.439189
$880$	16.4369	0.554087
$881$	12.9112	0.434990	0.217495	−	0.976061i	$-0.430211\pi$
$881$	12.9112	0.434990	0.217495	+	0.976061i	$0.430211\pi$
$882$	−16.6220	−0.559690
$883$	25.0205	0.842006	0.421003	−	0.907059i	$-0.361678\pi$
$883$	25.0205	0.842006	0.421003	+	0.907059i	$0.361678\pi$
$884$	−3.33617	−0.112208
$885$	−3.82968	−0.128733
$886$	30.7273	1.03230
$887$	−10.0727	−0.338207	−0.169104	−	0.985598i	$-0.554087\pi$
$887$	−10.0727	−0.338207	−0.169104	+	0.985598i	$0.554087\pi$
$888$	18.9150	0.634747
$889$	−26.9762	−0.904752
$890$	13.5956	0.455725
$891$	−4.31625	−0.144600
$892$	−2.50900	−0.0840075
$893$	0	0
$894$	−7.94473	−0.265712
$895$	19.1840	0.641251
$896$	45.6925	1.52648
$897$	−3.68624	−0.123080
$898$	−0.678528	−0.0226428
$899$	−4.20532	−0.140255
$900$	−0.0917248	−0.00305749
$901$	−29.3655	−0.978307
$902$	4.54822	0.151439
$903$	27.7579	0.923727
$904$	−18.5782	−0.617902
$905$	3.22984	0.107364
$906$	−17.4986	−0.581353
$907$	7.86462	0.261140	0.130570	−	0.991439i	$-0.458319\pi$
$907$	7.86462	0.261140	0.130570	+	0.991439i	$0.458319\pi$
$908$	−2.30158	−0.0763805
$909$	−4.49970	−0.149246
$910$	38.3449	1.27112
$911$	52.2665	1.73167	0.865833	−	0.500333i	$-0.166789\pi$
$911$	52.2665	1.73167	0.865833	+	0.500333i	$0.166789\pi$
$912$	0	0
$913$	−33.1440	−1.09691
$914$	−18.3184	−0.605920
$915$	−12.0211	−0.397404
$916$	−0.457276	−0.0151088
$917$	−75.8988	−2.50640
$918$	−7.89667	−0.260629
$919$	24.2225	0.799026	0.399513	−	0.916728i	$-0.369179\pi$
$919$	24.2225	0.799026	0.399513	+	0.916728i	$0.369179\pi$
$920$	−1.67406	−0.0551922
$921$	−4.02534	−0.132639
$922$	−32.2881	−1.06335
$923$	−19.5909	−0.644844
$924$	−1.72720	−0.0568208
$925$	6.54609	0.215234
$926$	1.35605	0.0445627
$927$	16.0717	0.527864
$928$	−1.84231	−0.0604769
$929$	−42.7987	−1.40418	−0.702089	−	0.712089i	$-0.747749\pi$
$929$	−42.7987	−1.40418	−0.702089	+	0.712089i	$0.747749\pi$
$930$	1.63482	0.0536079
$931$	0	0
$932$	−1.17375	−0.0384474
$933$	15.3578	0.502791
$934$	26.0392	0.852027
$935$	−24.6735	−0.806908
$936$	18.3850	0.600931
$937$	11.3557	0.370973	0.185487	−	0.982647i	$-0.440614\pi$
$937$	11.3557	0.370973	0.185487	+	0.982647i	$0.440614\pi$
$938$	24.1319	0.787935
$939$	21.9600	0.716636
$940$	0.250651	0.00817532
$941$	−44.1422	−1.43900	−0.719498	−	0.694495i	$-0.755628\pi$
$941$	−44.1422	−1.43900	−0.719498	+	0.694495i	$0.755628\pi$
$942$	−1.90477	−0.0620609
$943$	−0.441937	−0.0143915
$944$	14.5840	0.474667
$945$	−4.36264	−0.141917
$946$	−37.9371	−1.23344
$947$	−37.2381	−1.21008	−0.605038	−	0.796197i	$-0.706842\pi$
$947$	−37.2381	−1.21008	−0.605038	+	0.796197i	$0.706842\pi$
$948$	1.03986	0.0337731
$949$	51.4509	1.67017
$950$	0	0
$951$	24.1279	0.782402
$952$	−72.0607	−2.33550
$953$	39.2867	1.27262	0.636310	−	0.771434i	$-0.280460\pi$
$953$	39.2867	1.27262	0.636310	+	0.771434i	$0.280460\pi$
$954$	7.09634	0.229753
$955$	27.5509	0.891527
$956$	−1.17453	−0.0379871
$957$	−15.3375	−0.495792
$958$	−27.8478	−0.899721
$959$	−68.5651	−2.21408
$960$	8.33247	0.268929
$961$	−29.5994	−0.954821
$962$	−57.5361	−1.85504
$963$	−13.6789	−0.440796
$964$	−0.100236	−0.00322838
$965$	−22.2466	−0.716145
$966$	−3.49154	−0.112338
$967$	21.0858	0.678074	0.339037	−	0.940773i	$-0.389899\pi$
$967$	21.0858	0.678074	0.339037	+	0.940773i	$0.389899\pi$
$968$	22.0470	0.708618
$969$	0	0
$970$	2.76281	0.0887084
$971$	24.2451	0.778062	0.389031	−	0.921225i	$-0.372810\pi$
$971$	24.2451	0.778062	0.389031	+	0.921225i	$0.372810\pi$
$972$	−0.0917248	−0.00294208
$973$	−28.5903	−0.916564
$974$	3.85631	0.123564
$975$	6.36264	0.203768
$976$	45.7778	1.46531
$977$	51.4540	1.64616	0.823080	−	0.567926i	$-0.192254\pi$
$977$	51.4540	1.64616	0.823080	+	0.567926i	$0.192254\pi$
$978$	16.0409	0.512931
$979$	42.4799	1.35766
$980$	−1.10369	−0.0352562
$981$	8.96674	0.286286
$982$	−7.98186	−0.254711
$983$	−9.13493	−0.291359	−0.145679	−	0.989332i	$-0.546537\pi$
$983$	−9.13493	−0.291359	−0.145679	+	0.989332i	$0.546537\pi$
$984$	2.20414	0.0702655
$985$	12.6627	0.403466
$986$	−28.0604	−0.893624
$987$	11.9215	0.379466
$988$	0	0
$989$	3.68624	0.117216
$990$	5.96248	0.189500
$991$	17.7543	0.563983	0.281991	−	0.959417i	$-0.409005\pi$
$991$	17.7543	0.563983	0.281991	+	0.959417i	$0.409005\pi$
$992$	0.613569	0.0194808
$993$	24.8416	0.788325
$994$	−18.5561	−0.588565
$995$	−8.76955	−0.278014
$996$	−0.704345	−0.0223180
$997$	−56.2433	−1.78124	−0.890622	−	0.454745i	$-0.849730\pi$
$997$	−56.2433	−1.78124	−0.890622	+	0.454745i	$0.849730\pi$
$998$	−17.6762	−0.559531
$999$	6.54609	0.207109

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5415.2.a.z.1.2		5
19.8	odd	6		285.2.i.f.121.2	yes	10
19.12	odd	6		285.2.i.f.106.2	✓	10
19.18	odd	2		5415.2.a.y.1.4		5
57.8	even	6		855.2.k.i.406.4		10
57.50	even	6		855.2.k.i.676.4		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
285.2.i.f.106.2	✓	10	19.12	odd	6
285.2.i.f.121.2	yes	10	19.8	odd	6
855.2.k.i.406.4		10	57.8	even	6
855.2.k.i.676.4		10	57.50	even	6
5415.2.a.y.1.4		5	19.18	odd	2
5415.2.a.z.1.2		5	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 5415 = 3 \cdot 5 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5415.a (trivial)

\(f(q)\)	\(=\)	\(q-1.38140 q^{2} +1.00000 q^{3} -0.0917248 q^{4} +1.00000 q^{5} -1.38140 q^{6} -4.36264 q^{7} +2.88952 q^{8} +1.00000 q^{9} -1.38140 q^{10} -4.31625 q^{11} -0.0917248 q^{12} +6.36264 q^{13} +6.02657 q^{14} +1.00000 q^{15} -3.80814 q^{16} +5.71641 q^{17} -1.38140 q^{18} -0.0917248 q^{20} -4.36264 q^{21} +5.96248 q^{22} -0.579357 q^{23} +2.88952 q^{24} +1.00000 q^{25} -8.78938 q^{26} +1.00000 q^{27} +0.400163 q^{28} +3.55344 q^{29} -1.38140 q^{30} -1.18345 q^{31} -0.518458 q^{32} -4.31625 q^{33} -7.89667 q^{34} -4.36264 q^{35} -0.0917248 q^{36} +6.54609 q^{37} +6.36264 q^{39} +2.88952 q^{40} +0.762807 q^{41} +6.02657 q^{42} -6.36264 q^{43} +0.395907 q^{44} +1.00000 q^{45} +0.800326 q^{46} -2.73264 q^{47} -3.80814 q^{48} +12.0327 q^{49} -1.38140 q^{50} +5.71641 q^{51} -0.583613 q^{52} -5.13706 q^{53} -1.38140 q^{54} -4.31625 q^{55} -12.6059 q^{56} -4.90874 q^{58} -3.82968 q^{59} -0.0917248 q^{60} -12.0211 q^{61} +1.63482 q^{62} -4.36264 q^{63} +8.33247 q^{64} +6.36264 q^{65} +5.96248 q^{66} +4.00426 q^{67} -0.524337 q^{68} -0.579357 q^{69} +6.02657 q^{70} -3.07906 q^{71} +2.88952 q^{72} +8.08640 q^{73} -9.04280 q^{74} +1.00000 q^{75} +18.8303 q^{77} -8.78938 q^{78} -11.3367 q^{79} -3.80814 q^{80} +1.00000 q^{81} -1.05374 q^{82} +7.67889 q^{83} +0.400163 q^{84} +5.71641 q^{85} +8.78938 q^{86} +3.55344 q^{87} -12.4719 q^{88} -9.84186 q^{89} -1.38140 q^{90} -27.7579 q^{91} +0.0531414 q^{92} -1.18345 q^{93} +3.77487 q^{94} -0.518458 q^{96} -2.00000 q^{97} -16.6220 q^{98} -4.31625 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + q^{2} + 5 q^{3} + 7 q^{4} + 5 q^{5} + q^{6} + 2 q^{7} + 6 q^{8} + 5 q^{9} + q^{10} + 5 q^{11} + 7 q^{12} + 8 q^{13} + 4 q^{14} + 5 q^{15} + 7 q^{16} + 10 q^{17} + q^{18} + 7 q^{20} + 2 q^{21}+ \cdots + 5 q^{99}+O(q^{100}) \) 5 * q + q^2 + 5 * q^3 + 7 * q^4 + 5 * q^5 + q^6 + 2 * q^7 + 6 * q^8 + 5 * q^9 + q^10 + 5 * q^11 + 7 * q^12 + 8 * q^13 + 4 * q^14 + 5 * q^15 + 7 * q^16 + 10 * q^17 + q^18 + 7 * q^20 + 2 * q^21 - 2 * q^22 - 2 * q^23 + 6 * q^24 + 5 * q^25 - 2 * q^26 + 5 * q^27 + 10 * q^28 + 7 * q^29 + q^30 + 9 * q^31 + 23 * q^32 + 5 * q^33 - 25 * q^34 + 2 * q^35 + 7 * q^36 - 6 * q^37 + 8 * q^39 + 6 * q^40 - 12 * q^41 + 4 * q^42 - 8 * q^43 + 16 * q^44 + 5 * q^45 + 20 * q^46 + 6 * q^47 + 7 * q^48 + 15 * q^49 + q^50 + 10 * q^51 + 4 * q^52 - 8 * q^53 + q^54 + 5 * q^55 - 36 * q^56 + 38 * q^58 + q^59 + 7 * q^60 + 7 * q^61 + 15 * q^62 + 2 * q^63 + 14 * q^64 + 8 * q^65 - 2 * q^66 + 14 * q^67 - q^68 - 2 * q^69 + 4 * q^70 + 27 * q^71 + 6 * q^72 + 26 * q^73 - 18 * q^74 + 5 * q^75 + 14 * q^77 - 2 * q^78 - 23 * q^79 + 7 * q^80 + 5 * q^81 - 36 * q^82 - 12 * q^83 + 10 * q^84 + 10 * q^85 + 2 * q^86 + 7 * q^87 + 9 * q^89 + q^90 - 46 * q^91 - 52 * q^92 + 9 * q^93 - 45 * q^94 + 23 * q^96 - 10 * q^97 - 21 * q^98 + 5 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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