LMFDB - Embedded newform 3450.2.d.ba.2899.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3450,2,Mod(2899,3450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3450, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

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

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

chi := DirichletCharacter("3450.2899");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3450.d (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$27.5483886973$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.181494784.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 12x^{3} + 49x^{2} - 14x + 2 $ x^6 - 2x^5 + 2x^4 + 12x^3 + 49x^2 - 14*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			2899.6
Root			$2.38150 - 2.38150i$ of defining polynomial
Character	$\chi$	$=$	3450.2899
Dual form			3450.2.d.ba.2899.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.76300i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.76300i q^{7} -1.00000i q^{8} -1.00000 q^{9} +3.18291 q^{11} -1.00000i q^{12} -6.34310i q^{13} -3.76300 q^{14} +1.00000 q^{16} +2.58010i q^{17} -1.00000i q^{18} +6.34310 q^{19} -3.76300 q^{21} +3.18291i q^{22} -1.00000i q^{23} +1.00000 q^{24} +6.34310 q^{26} -1.00000i q^{27} -3.76300i q^{28} +1.00000 q^{29} +6.00000 q^{31} +1.00000i q^{32} +3.18291i q^{33} -2.58010 q^{34} +1.00000 q^{36} -2.58010i q^{37} +6.34310i q^{38} +6.34310 q^{39} +12.3431 q^{41} -3.76300i q^{42} +10.3431i q^{43} -3.18291 q^{44} +1.00000 q^{46} -3.34310i q^{47} +1.00000i q^{48} -7.16019 q^{49} -2.58010 q^{51} +6.34310i q^{52} +7.16019i q^{53} +1.00000 q^{54} +3.76300 q^{56} +6.34310i q^{57} +1.00000i q^{58} +4.36581 q^{59} -1.52601 q^{61} +6.00000i q^{62} -3.76300i q^{63} -1.00000 q^{64} -3.18291 q^{66} -10.6862i q^{67} -2.58010i q^{68} +1.00000 q^{69} +1.81709 q^{71} +1.00000i q^{72} +8.52601i q^{73} +2.58010 q^{74} -6.34310 q^{76} +11.9773i q^{77} +6.34310i q^{78} +3.18291 q^{79} +1.00000 q^{81} +12.3431i q^{82} -7.28901i q^{83} +3.76300 q^{84} -10.3431 q^{86} +1.00000i q^{87} -3.18291i q^{88} -4.58010 q^{89} +23.8691 q^{91} +1.00000i q^{92} +6.00000i q^{93} +3.34310 q^{94} -1.00000 q^{96} -11.5260i q^{97} -7.16019i q^{98} -3.18291 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	$ 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 2 q^{14} + 6 q^{16} + 2 q^{19} + 2 q^{21} + 6 q^{24} + 2 q^{26} + 6 q^{29} + 36 q^{31} - 4 q^{34} + 6 q^{36} + 2 q^{39} + 38 q^{41} - 6 q^{44} + 6 q^{46} - 20 q^{49} - 4 q^{51} + 6 q^{54} - 2 q^{56} + 40 q^{61} - 6 q^{64} - 6 q^{66} + 6 q^{69} + 24 q^{71} + 4 q^{74} - 2 q^{76} + 6 q^{79} + 6 q^{81} - 2 q^{84} - 26 q^{86} - 16 q^{89} + 58 q^{91} - 16 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) $ 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 6 * q^11 + 2 * q^14 + 6 * q^16 + 2 * q^19 + 2 * q^21 + 6 * q^24 + 2 * q^26 + 6 * q^29 + 36 * q^31 - 4 * q^34 + 6 * q^36 + 2 * q^39 + 38 * q^41 - 6 * q^44 + 6 * q^46 - 20 * q^49 - 4 * q^51 + 6 * q^54 - 2 * q^56 + 40 * q^61 - 6 * q^64 - 6 * q^66 + 6 * q^69 + 24 * q^71 + 4 * q^74 - 2 * q^76 + 6 * q^79 + 6 * q^81 - 2 * q^84 - 26 * q^86 - 16 * q^89 + 58 * q^91 - 16 * q^94 - 6 * q^96 - 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/3450\mathbb{Z}\right)^\times$.

$n$	$277$	$1151$	$1201$
$\chi(n)$	$-1$	$1$	$1$

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 $

$2$	1.00000i	0.707107i
$2$	1.00000i	0.707107i
$3$	1.00000i	0.577350i
$3$	1.00000i	0.577350i
$4$	−1.00000	−0.500000
$5$	0	0
$5$	0	0
$6$	−1.00000	−0.408248
$7$	3.76300i	1.42228i	0.703050	+	0.711141i	$0.251821\pi$
$7$	3.76300i	1.42228i	−0.703050	+	0.711141i	$0.748179\pi$
$8$	− 1.00000i	− 0.353553i
$9$	−1.00000	−0.333333
$10$	0	0
$11$	3.18291	0.959682	0.479841	−	0.877355i	$-0.340694\pi$
$11$	3.18291	0.959682	0.479841	+	0.877355i	$0.340694\pi$
$12$	− 1.00000i	− 0.288675i
$13$	− 6.34310i	− 1.75926i	−0.475659	−	0.879630i	$-0.657790\pi$
$13$	− 6.34310i	− 1.75926i	0.475659	−	0.879630i	$-0.342210\pi$
$14$	−3.76300	−1.00570
$15$	0	0
$16$	1.00000	0.250000
$17$	2.58010i	0.625765i	0.949792	+	0.312883i	$0.101295\pi$
$17$	2.58010i	0.625765i	−0.949792	+	0.312883i	$0.898705\pi$
$18$	− 1.00000i	− 0.235702i
$19$	6.34310	1.45521	0.727603	−	0.685998i	$-0.240634\pi$
$19$	6.34310	1.45521	0.727603	+	0.685998i	$0.240634\pi$
$20$	0	0
$21$	−3.76300	−0.821155
$22$	3.18291i	0.678598i
$23$	− 1.00000i	− 0.208514i
$23$	− 1.00000i	− 0.208514i
$24$	1.00000	0.204124
$25$	0	0
$26$	6.34310	1.24398
$27$	− 1.00000i	− 0.192450i
$28$	− 3.76300i	− 0.711141i
$29$	1.00000	0.185695	0.0928477	−	0.995680i	$-0.470403\pi$
$29$	1.00000	0.185695	0.0928477	+	0.995680i	$0.470403\pi$
$30$	0	0
$31$	6.00000	1.07763	0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000	1.07763	0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000i	0.176777i
$33$	3.18291i	0.554073i
$34$	−2.58010	−0.442483
$35$	0	0
$36$	1.00000	0.166667
$37$	− 2.58010i	− 0.424165i	−0.977252	−	0.212083i	$-0.931975\pi$
$37$	− 2.58010i	− 0.424165i	0.977252	−	0.212083i	$-0.0680246\pi$
$38$	6.34310i	1.02899i
$39$	6.34310	1.01571
$40$	0	0
$41$	12.3431	1.92767	0.963834	−	0.266503i	$-0.0858681\pi$
$41$	12.3431	1.92767	0.963834	+	0.266503i	$0.0858681\pi$
$42$	− 3.76300i	− 0.580644i
$43$	10.3431i	1.57731i	0.614837	+	0.788654i	$0.289222\pi$
$43$	10.3431i	1.57731i	−0.614837	+	0.788654i	$0.710778\pi$
$44$	−3.18291	−0.479841
$45$	0	0
$46$	1.00000	0.147442
$47$	− 3.34310i	− 0.487641i	−0.969820	−	0.243821i	$-0.921599\pi$
$47$	− 3.34310i	− 0.487641i	0.969820	−	0.243821i	$-0.0784008\pi$
$48$	1.00000i	0.144338i
$49$	−7.16019	−1.02288
$50$	0	0
$51$	−2.58010	−0.361286
$52$	6.34310i	0.879630i
$53$	7.16019i	0.983528i	0.870728	+	0.491764i	$0.163648\pi$
$53$	7.16019i	0.983528i	−0.870728	+	0.491764i	$0.836352\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	3.76300	0.502852
$57$	6.34310i	0.840164i
$58$	1.00000i	0.131306i
$59$	4.36581	0.568380	0.284190	−	0.958768i	$-0.408275\pi$
$59$	4.36581	0.568380	0.284190	+	0.958768i	$0.408275\pi$
$60$	0	0
$61$	−1.52601	−0.195385	−0.0976926	−	0.995217i	$-0.531146\pi$
$61$	−1.52601	−0.195385	−0.0976926	+	0.995217i	$0.531146\pi$
$62$	6.00000i	0.762001i
$63$	− 3.76300i	− 0.474094i
$64$	−1.00000	−0.125000
$65$	0	0
$66$	−3.18291	−0.391789
$67$	− 10.6862i	− 1.30553i	−0.757562	−	0.652764i	$-0.773610\pi$
$67$	− 10.6862i	− 1.30553i	0.757562	−	0.652764i	$-0.226390\pi$
$68$	− 2.58010i	− 0.312883i
$69$	1.00000	0.120386
$70$	0	0
$71$	1.81709	0.215649	0.107825	−	0.994170i	$-0.465611\pi$
$71$	1.81709	0.215649	0.107825	+	0.994170i	$0.465611\pi$
$72$	1.00000i	0.117851i
$73$	8.52601i	0.997894i	0.866633	+	0.498947i	$0.166280\pi$
$73$	8.52601i	0.997894i	−0.866633	+	0.498947i	$0.833720\pi$
$74$	2.58010	0.299930
$75$	0	0
$76$	−6.34310	−0.727603
$77$	11.9773i	1.36494i
$78$	6.34310i	0.718215i
$79$	3.18291	0.358105	0.179052	−	0.983840i	$-0.442697\pi$
$79$	3.18291	0.358105	0.179052	+	0.983840i	$0.442697\pi$
$80$	0	0
$81$	1.00000	0.111111
$82$	12.3431i	1.36307i
$83$	− 7.28901i	− 0.800073i	−0.916499	−	0.400036i	$-0.868997\pi$
$83$	− 7.28901i	− 0.800073i	0.916499	−	0.400036i	$-0.131003\pi$
$84$	3.76300	0.410577
$85$	0	0
$86$	−10.3431	−1.11533
$87$	1.00000i	0.107211i
$88$	− 3.18291i	− 0.339299i
$89$	−4.58010	−0.485489	−0.242745	−	0.970090i	$-0.578048\pi$
$89$	−4.58010	−0.485489	−0.242745	+	0.970090i	$0.578048\pi$
$90$	0	0
$91$	23.8691	2.50216
$92$	1.00000i	0.104257i
$93$	6.00000i	0.622171i
$94$	3.34310	0.344814
$95$	0	0
$96$	−1.00000	−0.102062
$97$	− 11.5260i	− 1.17029i	−0.810929	−	0.585144i	$-0.801038\pi$
$97$	− 11.5260i	− 1.17029i	0.810929	−	0.585144i	$-0.198962\pi$
$98$	− 7.16019i	− 0.723289i
$99$	−3.18291	−0.319894
$100$	0	0
$101$	−7.70891	−0.767066	−0.383533	−	0.923527i	$-0.625293\pi$
$101$	−7.70891	−0.767066	−0.383533	+	0.923527i	$0.625293\pi$
$102$	− 2.58010i	− 0.255468i
$103$	3.39719i	0.334735i	0.985895	+	0.167368i	$0.0535267\pi$
$103$	3.39719i	0.334735i	−0.985895	+	0.167368i	$0.946473\pi$
$104$	−6.34310	−0.621992
$105$	0	0
$106$	−7.16019	−0.695459
$107$	− 6.68620i	− 0.646379i	−0.946334	−	0.323190i	$-0.895245\pi$
$107$	− 6.68620i	− 0.646379i	0.946334	−	0.323190i	$-0.104755\pi$
$108$	1.00000i	0.0962250i
$109$	−5.78572	−0.554171	−0.277086	−	0.960845i	$-0.589369\pi$
$109$	−5.78572	−0.554171	−0.277086	+	0.960845i	$0.589369\pi$
$110$	0	0
$111$	2.58010	0.244892
$112$	3.76300i	0.355570i
$113$	− 0.580097i	− 0.0545709i	−0.999628	−	0.0272855i	$-0.991314\pi$
$113$	− 0.580097i	− 0.0545709i	0.999628	−	0.0272855i	$-0.00868631\pi$
$114$	−6.34310	−0.594086
$115$	0	0
$116$	−1.00000	−0.0928477
$117$	6.34310i	0.586420i
$118$	4.36581i	0.401906i
$119$	−9.70891	−0.890015
$120$	0	0
$121$	−0.869107	−0.0790097
$122$	− 1.52601i	− 0.138158i
$123$	12.3431i	1.11294i
$124$	−6.00000	−0.538816
$125$	0	0
$126$	3.76300	0.335235
$127$	14.3204i	1.27073i	0.772212	+	0.635364i	$0.219150\pi$
$127$	14.3204i	1.27073i	−0.772212	+	0.635364i	$0.780850\pi$
$128$	− 1.00000i	− 0.0883883i
$129$	−10.3431	−0.910659
$130$	0	0
$131$	15.8918	1.38847	0.694237	−	0.719746i	$-0.255742\pi$
$131$	15.8918	1.38847	0.694237	+	0.719746i	$0.255742\pi$
$132$	− 3.18291i	− 0.277036i
$133$	23.8691i	2.06971i
$134$	10.6862	0.923147
$135$	0	0
$136$	2.58010	0.221241
$137$	15.4199i	1.31741i	0.752401	+	0.658706i	$0.228896\pi$
$137$	15.4199i	1.31741i	−0.752401	+	0.658706i	$0.771104\pi$
$138$	1.00000i	0.0851257i
$139$	−3.02271	−0.256383	−0.128192	−	0.991749i	$-0.540917\pi$
$139$	−3.02271	−0.256383	−0.128192	+	0.991749i	$0.540917\pi$
$140$	0	0
$141$	3.34310	0.281540
$142$	1.81709i	0.152487i
$143$	− 20.1895i	− 1.68833i
$144$	−1.00000	−0.0833333
$145$	0	0
$146$	−8.52601	−0.705617
$147$	− 7.16019i	− 0.590563i
$148$	2.58010i	0.212083i
$149$	−16.6862	−1.36699	−0.683493	−	0.729957i	$-0.739540\pi$
$149$	−16.6862	−1.36699	−0.683493	+	0.729957i	$0.739540\pi$
$150$	0	0
$151$	−7.16019	−0.582688	−0.291344	−	0.956618i	$-0.594102\pi$
$151$	−7.16019	−0.582688	−0.291344	+	0.956618i	$0.594102\pi$
$152$	− 6.34310i	− 0.514493i
$153$	− 2.58010i	− 0.208588i
$154$	−11.9773	−0.965157
$155$	0	0
$156$	−6.34310	−0.507854
$157$	− 22.2122i	− 1.77273i	−0.462990	−	0.886364i	$-0.653223\pi$
$157$	− 22.2122i	− 1.77273i	0.462990	−	0.886364i	$-0.346777\pi$
$158$	3.18291i	0.253218i
$159$	−7.16019	−0.567840
$160$	0	0
$161$	3.76300	0.296566
$162$	1.00000i	0.0785674i
$163$	− 8.68620i	− 0.680356i	−0.940361	−	0.340178i	$-0.889513\pi$
$163$	− 8.68620i	− 0.680356i	0.940361	−	0.340178i	$-0.110487\pi$
$164$	−12.3431	−0.963834
$165$	0	0
$166$	7.28901	0.565737
$167$	25.2349i	1.95274i	0.216113	+	0.976368i	$0.430662\pi$
$167$	25.2349i	1.95274i	−0.216113	+	0.976368i	$0.569338\pi$
$168$	3.76300i	0.290322i
$169$	−27.2349	−2.09499
$170$	0	0
$171$	−6.34310	−0.485069
$172$	− 10.3431i	− 0.788654i
$173$	0.817094i	0.0621225i	0.999517	+	0.0310612i	$0.00988869\pi$
$173$	0.817094i	0.0621225i	−0.999517	+	0.0310612i	$0.990111\pi$
$174$	−1.00000	−0.0758098
$175$	0	0
$176$	3.18291	0.239921
$177$	4.36581i	0.328155i
$178$	− 4.58010i	− 0.343293i
$179$	3.16019	0.236204	0.118102	−	0.993001i	$-0.462319\pi$
$179$	3.16019	0.236204	0.118102	+	0.993001i	$0.462319\pi$
$180$	0	0
$181$	3.37448	0.250823	0.125411	−	0.992105i	$-0.459975\pi$
$181$	3.37448	0.250823	0.125411	+	0.992105i	$0.459975\pi$
$182$	23.8691i	1.76930i
$183$	− 1.52601i	− 0.112806i
$184$	−1.00000	−0.0737210
$185$	0	0
$186$	−6.00000	−0.439941
$187$	8.21221i	0.600536i
$188$	3.34310i	0.243821i
$189$	3.76300	0.273718
$190$	0	0
$191$	−11.8691	−0.858818	−0.429409	−	0.903110i	$-0.641278\pi$
$191$	−11.8691	−0.858818	−0.429409	+	0.903110i	$0.641278\pi$
$192$	− 1.00000i	− 0.0721688i
$193$	− 2.97729i	− 0.214310i	−0.994242	−	0.107155i	$-0.965826\pi$
$193$	− 2.97729i	− 0.214310i	0.994242	−	0.107155i	$-0.0341741\pi$
$194$	11.5260	0.827519
$195$	0	0
$196$	7.16019	0.511442
$197$	24.8918i	1.77347i	0.462279	+	0.886734i	$0.347032\pi$
$197$	24.8918i	1.77347i	−0.462279	+	0.886734i	$0.652968\pi$
$198$	− 3.18291i	− 0.226199i
$199$	−22.4492	−1.59138	−0.795691	−	0.605703i	$-0.792892\pi$
$199$	−22.4492	−1.59138	−0.795691	+	0.605703i	$0.792892\pi$
$200$	0	0
$201$	10.6862	0.753746
$202$	− 7.70891i	− 0.542397i
$203$	3.76300i	0.264111i
$204$	2.58010	0.180643
$205$	0	0
$206$	−3.39719	−0.236693
$207$	1.00000i	0.0695048i
$208$	− 6.34310i	− 0.439815i
$209$	20.1895	1.39654
$210$	0	0
$211$	19.5553	1.34624	0.673121	−	0.739532i	$-0.264953\pi$
$211$	19.5553	1.34624	0.673121	+	0.739532i	$0.264953\pi$
$212$	− 7.16019i	− 0.491764i
$213$	1.81709i	0.124505i
$214$	6.68620	0.457059
$215$	0	0
$216$	−1.00000	−0.0680414
$217$	22.5780i	1.53270i
$218$	− 5.78572i	− 0.391858i
$219$	−8.52601	−0.576134
$220$	0	0
$221$	16.3658	1.10088
$222$	2.58010i	0.173165i
$223$	28.8984i	1.93518i	0.252525	+	0.967590i	$0.418739\pi$
$223$	28.8984i	1.93518i	−0.252525	+	0.967590i	$0.581261\pi$
$224$	−3.76300	−0.251426
$225$	0	0
$226$	0.580097	0.0385875
$227$	− 17.6321i	− 1.17028i	−0.810931	−	0.585142i	$-0.801039\pi$
$227$	− 17.6321i	− 1.17028i	0.810931	−	0.585142i	$-0.198961\pi$
$228$	− 6.34310i	− 0.420082i
$229$	11.8918	0.785834	0.392917	−	0.919574i	$-0.371466\pi$
$229$	11.8918	0.785834	0.392917	+	0.919574i	$0.371466\pi$
$230$	0	0
$231$	−11.9773	−0.788048
$232$	− 1.00000i	− 0.0656532i
$233$	9.02930i	0.591529i	0.955261	+	0.295765i	$0.0955744\pi$
$233$	9.02930i	0.591529i	−0.955261	+	0.295765i	$0.904426\pi$
$234$	−6.34310	−0.414661
$235$	0	0
$236$	−4.36581	−0.284190
$237$	3.18291i	0.206752i
$238$	− 9.70891i	− 0.629335i
$239$	20.0747	1.29853	0.649263	−	0.760564i	$-0.275077\pi$
$239$	20.0747	1.29853	0.649263	+	0.760564i	$0.275077\pi$
$240$	0	0
$241$	−23.0066	−1.48198	−0.740992	−	0.671514i	$-0.765645\pi$
$241$	−23.0066	−1.48198	−0.740992	+	0.671514i	$0.765645\pi$
$242$	− 0.869107i	− 0.0558683i
$243$	1.00000i	0.0641500i
$244$	1.52601	0.0976926
$245$	0	0
$246$	−12.3431	−0.786967
$247$	− 40.2349i	− 2.56009i
$248$	− 6.00000i	− 0.381000i
$249$	7.28901	0.461922
$250$	0	0
$251$	−10.9459	−0.690900	−0.345450	−	0.938437i	$-0.612274\pi$
$251$	−10.9459	−0.690900	−0.345450	+	0.938437i	$0.612274\pi$
$252$	3.76300i	0.237047i
$253$	− 3.18291i	− 0.200108i
$254$	−14.3204	−0.898541
$255$	0	0
$256$	1.00000	0.0625000
$257$	16.3204i	1.01804i	0.860755	+	0.509019i	$0.169992\pi$
$257$	16.3204i	1.01804i	−0.860755	+	0.509019i	$0.830008\pi$
$258$	− 10.3431i	− 0.643933i
$259$	9.70891	0.603282
$260$	0	0
$261$	−1.00000	−0.0618984
$262$	15.8918i	0.981800i
$263$	29.0066i	1.78862i	0.447445	+	0.894311i	$0.352334\pi$
$263$	29.0066i	1.78862i	−0.447445	+	0.894311i	$0.647666\pi$
$264$	3.18291	0.195894
$265$	0	0
$266$	−23.8691	−1.46351
$267$	− 4.58010i	− 0.280297i
$268$	10.6862i	0.652764i
$269$	26.1895	1.59680	0.798401	−	0.602126i	$-0.205680\pi$
$269$	26.1895	1.59680	0.798401	+	0.602126i	$0.205680\pi$
$270$	0	0
$271$	6.36581	0.386696	0.193348	−	0.981130i	$-0.438065\pi$
$271$	6.36581	0.386696	0.193348	+	0.981130i	$0.438065\pi$
$272$	2.58010i	0.156441i
$273$	23.8691i	1.44462i
$274$	−15.4199	−0.931550
$275$	0	0
$276$	−1.00000	−0.0601929
$277$	9.50329i	0.570998i	0.958379	+	0.285499i	$0.0921593\pi$
$277$	9.50329i	0.570998i	−0.958379	+	0.285499i	$0.907841\pi$
$278$	− 3.02271i	− 0.181290i
$279$	−6.00000	−0.359211
$280$	0	0
$281$	27.2663	1.62657	0.813285	−	0.581865i	$-0.197677\pi$
$281$	27.2663	1.62657	0.813285	+	0.581865i	$0.197677\pi$
$282$	3.34310i	0.199079i
$283$	− 10.3204i	− 0.613483i	−0.951793	−	0.306742i	$-0.900761\pi$
$283$	− 10.3204i	− 0.613483i	0.951793	−	0.306742i	$-0.0992388\pi$
$284$	−1.81709	−0.107825
$285$	0	0
$286$	20.1895	1.19383
$287$	46.4471i	2.74169i
$288$	− 1.00000i	− 0.0589256i
$289$	10.3431	0.608418
$290$	0	0
$291$	11.5260	0.675666
$292$	− 8.52601i	− 0.498947i
$293$	8.36581i	0.488736i	0.969683	+	0.244368i	$0.0785805\pi$
$293$	8.36581i	0.488736i	−0.969683	+	0.244368i	$0.921420\pi$
$294$	7.16019	0.417591
$295$	0	0
$296$	−2.58010	−0.149965
$297$	− 3.18291i	− 0.184691i
$298$	− 16.6862i	− 0.966606i
$299$	−6.34310	−0.366831
$300$	0	0
$301$	−38.9211	−2.24338
$302$	− 7.16019i	− 0.412023i
$303$	− 7.70891i	− 0.442865i
$304$	6.34310	0.363802
$305$	0	0
$306$	2.58010	0.147494
$307$	− 33.7089i	− 1.92387i	−0.273280	−	0.961935i	$-0.588108\pi$
$307$	− 33.7089i	− 1.92387i	0.273280	−	0.961935i	$-0.411892\pi$
$308$	− 11.9773i	− 0.682469i
$309$	−3.39719	−0.193259
$310$	0	0
$311$	−1.86252	−0.105614	−0.0528069	−	0.998605i	$-0.516817\pi$
$311$	−1.86252	−0.105614	−0.0528069	+	0.998605i	$0.516817\pi$
$312$	− 6.34310i	− 0.359107i
$313$	− 26.8984i	− 1.52039i	−0.649696	−	0.760194i	$-0.725104\pi$
$313$	− 26.8984i	− 1.52039i	0.649696	−	0.760194i	$-0.274896\pi$
$314$	22.2122	1.25351
$315$	0	0
$316$	−3.18291	−0.179052
$317$	11.0000i	0.617822i	0.951091	+	0.308911i	$0.0999645\pi$
$317$	11.0000i	0.617822i	−0.951091	+	0.308911i	$0.900036\pi$
$318$	− 7.16019i	− 0.401524i
$319$	3.18291	0.178209
$320$	0	0
$321$	6.68620	0.373187
$322$	3.76300i	0.209704i
$323$	16.3658i	0.910618i
$324$	−1.00000	−0.0555556
$325$	0	0
$326$	8.68620	0.481084
$327$	− 5.78572i	− 0.319951i
$328$	− 12.3431i	− 0.681534i
$329$	12.5801	0.693563
$330$	0	0
$331$	−6.18291	−0.339843	−0.169922	−	0.985458i	$-0.554351\pi$
$331$	−6.18291	−0.339843	−0.169922	+	0.985458i	$0.554351\pi$
$332$	7.28901i	0.400036i
$333$	2.58010i	0.141388i
$334$	−25.2349	−1.38079
$335$	0	0
$336$	−3.76300	−0.205289
$337$	15.1602i	0.825828i	0.910770	+	0.412914i	$0.135489\pi$
$337$	15.1602i	0.825828i	−0.910770	+	0.412914i	$0.864511\pi$
$338$	− 27.2349i	− 1.48138i
$339$	0.580097	0.0315065
$340$	0	0
$341$	19.0974	1.03418
$342$	− 6.34310i	− 0.342996i
$343$	− 0.602810i	− 0.0325487i
$344$	10.3431	0.557663
$345$	0	0
$346$	−0.817094	−0.0439272
$347$	− 29.8918i	− 1.60468i	−0.596869	−	0.802338i	$-0.703589\pi$
$347$	− 29.8918i	− 1.60468i	0.596869	−	0.802338i	$-0.296411\pi$
$348$	− 1.00000i	− 0.0536056i
$349$	−7.02930	−0.376270	−0.188135	−	0.982143i	$-0.560244\pi$
$349$	−7.02930	−0.376270	−0.188135	+	0.982143i	$0.560244\pi$
$350$	0	0
$351$	−6.34310	−0.338570
$352$	3.18291i	0.169649i
$353$	26.2349i	1.39634i	0.715930	+	0.698172i	$0.246003\pi$
$353$	26.2349i	1.39634i	−0.715930	+	0.698172i	$0.753997\pi$
$354$	−4.36581	−0.232040
$355$	0	0
$356$	4.58010	0.242745
$357$	− 9.70891i	− 0.513850i
$358$	3.16019i	0.167021i
$359$	−19.5033	−1.02934	−0.514672	−	0.857387i	$-0.672086\pi$
$359$	−19.5033	−1.02934	−0.514672	+	0.857387i	$0.672086\pi$
$360$	0	0
$361$	21.2349	1.11763
$362$	3.37448i	0.177359i
$363$	− 0.869107i	− 0.0456163i
$364$	−23.8691	−1.25108
$365$	0	0
$366$	1.52601	0.0797656
$367$	− 33.5033i	− 1.74886i	−0.485154	−	0.874429i	$-0.661236\pi$
$367$	− 33.5033i	− 1.74886i	0.485154	−	0.874429i	$-0.338764\pi$
$368$	− 1.00000i	− 0.0521286i
$369$	−12.3431	−0.642556
$370$	0	0
$371$	−26.9438	−1.39885
$372$	− 6.00000i	− 0.311086i
$373$	− 10.1515i	− 0.525626i	−0.964847	−	0.262813i	$-0.915350\pi$
$373$	− 10.1515i	− 0.525626i	0.964847	−	0.262813i	$-0.0846503\pi$
$374$	−8.21221	−0.424643
$375$	0	0
$376$	−3.34310	−0.172407
$377$	− 6.34310i	− 0.326686i
$378$	3.76300i	0.193548i
$379$	−20.5780	−1.05702	−0.528511	−	0.848926i	$-0.677249\pi$
$379$	−20.5780	−1.05702	−0.528511	+	0.848926i	$0.677249\pi$
$380$	0	0
$381$	−14.3204	−0.733656
$382$	− 11.8691i	− 0.607276i
$383$	1.22833i	0.0627648i	0.999507	+	0.0313824i	$0.00999097\pi$
$383$	1.22833i	0.0627648i	−0.999507	+	0.0313824i	$0.990009\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	2.97729	0.151540
$387$	− 10.3431i	− 0.525769i
$388$	11.5260i	0.585144i
$389$	−35.3724	−1.79345	−0.896726	−	0.442586i	$-0.854061\pi$
$389$	−35.3724	−1.79345	−0.896726	+	0.442586i	$0.854061\pi$
$390$	0	0
$391$	2.58010	0.130481
$392$	7.16019i	0.361644i
$393$	15.8918i	0.801636i
$394$	−24.8918	−1.25403
$395$	0	0
$396$	3.18291	0.159947
$397$	− 31.0066i	− 1.55618i	−0.628155	−	0.778088i	$-0.716190\pi$
$397$	− 31.0066i	− 1.55618i	0.628155	−	0.778088i	$-0.283810\pi$
$398$	− 22.4492i	− 1.12528i
$399$	−23.8691	−1.19495
$400$	0	0
$401$	15.2056	0.759332	0.379666	−	0.925124i	$-0.376039\pi$
$401$	15.2056	0.759332	0.379666	+	0.925124i	$0.376039\pi$
$402$	10.6862i	0.532979i
$403$	− 38.0586i	− 1.89583i
$404$	7.70891	0.383533
$405$	0	0
$406$	−3.76300	−0.186755
$407$	− 8.21221i	− 0.407064i
$408$	2.58010i	0.127734i
$409$	2.57143	0.127149	0.0635746	−	0.997977i	$-0.479750\pi$
$409$	2.57143	0.127149	0.0635746	+	0.997977i	$0.479750\pi$
$410$	0	0
$411$	−15.4199	−0.760608
$412$	− 3.39719i	− 0.167368i
$413$	16.4286i	0.808397i
$414$	−1.00000	−0.0491473
$415$	0	0
$416$	6.34310	0.310996
$417$	− 3.02271i	− 0.148023i
$418$	20.1895i	0.987500i
$419$	19.0768	0.931963	0.465981	−	0.884795i	$-0.345701\pi$
$419$	19.0768	0.931963	0.465981	+	0.884795i	$0.345701\pi$
$420$	0	0
$421$	−15.8918	−0.774520	−0.387260	−	0.921971i	$-0.626578\pi$
$421$	−15.8918	−0.774520	−0.387260	+	0.921971i	$0.626578\pi$
$422$	19.5553i	0.951937i
$423$	3.34310i	0.162547i
$424$	7.16019	0.347730
$425$	0	0
$426$	−1.81709	−0.0880385
$427$	− 5.74237i	− 0.277893i
$428$	6.68620i	0.323190i
$429$	20.1895	0.974758
$430$	0	0
$431$	−24.2122	−1.16626	−0.583130	−	0.812379i	$-0.698172\pi$
$431$	−24.2122	−1.16626	−0.583130	+	0.812379i	$0.698172\pi$
$432$	− 1.00000i	− 0.0481125i
$433$	− 12.2122i	− 0.586881i	−0.955977	−	0.293441i	$-0.905200\pi$
$433$	− 12.2122i	− 0.586881i	0.955977	−	0.293441i	$-0.0948003\pi$
$434$	−22.5780	−1.08378
$435$	0	0
$436$	5.78572	0.277086
$437$	− 6.34310i	− 0.303432i
$438$	− 8.52601i	− 0.407388i
$439$	0.794381	0.0379137	0.0189569	−	0.999820i	$-0.493965\pi$
$439$	0.794381	0.0379137	0.0189569	+	0.999820i	$0.493965\pi$
$440$	0	0
$441$	7.16019	0.340962
$442$	16.3658i	0.778442i
$443$	14.2122i	0.675242i	0.941282	+	0.337621i	$0.109622\pi$
$443$	14.2122i	0.675242i	−0.941282	+	0.337621i	$0.890378\pi$
$444$	−2.58010	−0.122446
$445$	0	0
$446$	−28.8984	−1.36838
$447$	− 16.6862i	− 0.789230i
$448$	− 3.76300i	− 0.177785i
$449$	−1.05201	−0.0496476	−0.0248238	−	0.999692i	$-0.507902\pi$
$449$	−1.05201	−0.0496476	−0.0248238	+	0.999692i	$0.507902\pi$
$450$	0	0
$451$	39.2869	1.84995
$452$	0.580097i	0.0272855i
$453$	− 7.16019i	− 0.336415i
$454$	17.6321	0.827516
$455$	0	0
$456$	6.34310	0.297043
$457$	0.686200i	0.0320991i	0.999871	+	0.0160495i	$0.00510895\pi$
$457$	0.686200i	0.0320991i	−0.999871	+	0.0160495i	$0.994891\pi$
$458$	11.8918i	0.555668i
$459$	2.58010	0.120429
$460$	0	0
$461$	−29.5780	−1.37759	−0.688793	−	0.724958i	$-0.741859\pi$
$461$	−29.5780	−1.37759	−0.688793	+	0.724958i	$0.741859\pi$
$462$	− 11.9773i	− 0.557234i
$463$	− 12.0000i	− 0.557687i	−0.960337	−	0.278844i	$-0.910049\pi$
$463$	− 12.0000i	− 0.557687i	0.960337	−	0.278844i	$-0.0899511\pi$
$464$	1.00000	0.0464238
$465$	0	0
$466$	−9.02930	−0.418274
$467$	29.2890i	1.35533i	0.735369	+	0.677667i	$0.237009\pi$
$467$	29.2890i	1.35533i	−0.735369	+	0.677667i	$0.762991\pi$
$468$	− 6.34310i	− 0.293210i
$469$	40.2122	1.85683
$470$	0	0
$471$	22.2122	1.02348
$472$	− 4.36581i	− 0.200953i
$473$	32.9211i	1.51371i
$474$	−3.18291	−0.146196
$475$	0	0
$476$	9.70891	0.445007
$477$	− 7.16019i	− 0.327843i
$478$	20.0747i	0.918197i
$479$	−15.9145	−0.727154	−0.363577	−	0.931564i	$-0.618445\pi$
$479$	−15.9145	−0.727154	−0.363577	+	0.931564i	$0.618445\pi$
$480$	0	0
$481$	−16.3658	−0.746217
$482$	− 23.0066i	− 1.04792i
$483$	3.76300i	0.171223i
$484$	0.869107	0.0395049
$485$	0	0
$486$	−1.00000	−0.0453609
$487$	− 38.9438i	− 1.76471i	−0.470581	−	0.882357i	$-0.655956\pi$
$487$	− 38.9438i	− 1.76471i	0.470581	−	0.882357i	$-0.344044\pi$
$488$	1.52601i	0.0690791i
$489$	8.68620	0.392804
$490$	0	0
$491$	27.4806	1.24018	0.620091	−	0.784530i	$-0.287096\pi$
$491$	27.4806	1.24018	0.620091	+	0.784530i	$0.287096\pi$
$492$	− 12.3431i	− 0.556470i
$493$	2.58010i	0.116202i
$494$	40.2349	1.81025
$495$	0	0
$496$	6.00000	0.269408
$497$	6.83773i	0.306714i
$498$	7.28901i	0.326628i
$499$	−6.97729	−0.312346	−0.156173	−	0.987730i	$-0.549916\pi$
$499$	−6.97729	−0.312346	−0.156173	+	0.987730i	$0.549916\pi$
$500$	0	0
$501$	−25.2349	−1.12741
$502$	− 10.9459i	− 0.488540i
$503$	7.65690i	0.341404i	0.985323	+	0.170702i	$0.0546036\pi$
$503$	7.65690i	0.341404i	−0.985323	+	0.170702i	$0.945396\pi$
$504$	−3.76300	−0.167617
$505$	0	0
$506$	3.18291	0.141497
$507$	− 27.2349i	− 1.20955i
$508$	− 14.3204i	− 0.635364i
$509$	34.6073	1.53394	0.766971	−	0.641681i	$-0.221763\pi$
$509$	34.6073	1.53394	0.766971	+	0.641681i	$0.221763\pi$
$510$	0	0
$511$	−32.0834	−1.41929
$512$	1.00000i	0.0441942i
$513$	− 6.34310i	− 0.280055i
$514$	−16.3204	−0.719861
$515$	0	0
$516$	10.3431	0.455330
$517$	− 10.6408i	− 0.467981i
$518$	9.70891i	0.426585i
$519$	−0.817094	−0.0358664
$520$	0	0
$521$	25.4199	1.11367	0.556833	−	0.830624i	$-0.312016\pi$
$521$	25.4199	1.11367	0.556833	+	0.830624i	$0.312016\pi$
$522$	− 1.00000i	− 0.0437688i
$523$	25.8691i	1.13118i	0.824688	+	0.565589i	$0.191351\pi$
$523$	25.8691i	1.13118i	−0.824688	+	0.565589i	$0.808649\pi$
$524$	−15.8918	−0.694237
$525$	0	0
$526$	−29.0066	−1.26475
$527$	15.4806i	0.674345i
$528$	3.18291i	0.138518i
$529$	−1.00000	−0.0434783
$530$	0	0
$531$	−4.36581	−0.189460
$532$	− 23.8691i	− 1.03486i
$533$	− 78.2935i	− 3.39127i
$534$	4.58010	0.198200
$535$	0	0
$536$	−10.6862	−0.461574
$537$	3.16019i	0.136372i
$538$	26.1895i	1.12911i
$539$	−22.7902	−0.981645
$540$	0	0
$541$	34.6007	1.48760	0.743801	−	0.668401i	$-0.233021\pi$
$541$	34.6007	1.48760	0.743801	+	0.668401i	$0.233021\pi$
$542$	6.36581i	0.273435i
$543$	3.37448i	0.144813i
$544$	−2.58010	−0.110621
$545$	0	0
$546$	−23.8691	−1.02150
$547$	3.55531i	0.152014i	0.997107	+	0.0760070i	$0.0242171\pi$
$547$	3.55531i	0.152014i	−0.997107	+	0.0760070i	$0.975783\pi$
$548$	− 15.4199i	− 0.658706i
$549$	1.52601	0.0651284
$550$	0	0
$551$	6.34310	0.270225
$552$	− 1.00000i	− 0.0425628i
$553$	11.9773i	0.509326i
$554$	−9.50329	−0.403756
$555$	0	0
$556$	3.02271	0.128192
$557$	− 15.2642i	− 0.646766i	−0.946268	−	0.323383i	$-0.895180\pi$
$557$	− 15.2642i	− 0.646766i	0.946268	−	0.323383i	$-0.104820\pi$
$558$	− 6.00000i	− 0.254000i
$559$	65.6073	2.77489
$560$	0	0
$561$	−8.21221	−0.346720
$562$	27.2663i	1.15016i
$563$	13.5487i	0.571010i	0.958377	+	0.285505i	$0.0921614\pi$
$563$	13.5487i	0.571010i	−0.958377	+	0.285505i	$0.907839\pi$
$564$	−3.34310	−0.140770
$565$	0	0
$566$	10.3204	0.433798
$567$	3.76300i	0.158031i
$568$	− 1.81709i	− 0.0762436i
$569$	18.4740	0.774470	0.387235	−	0.921981i	$-0.373430\pi$
$569$	18.4740	0.774470	0.387235	+	0.921981i	$0.373430\pi$
$570$	0	0
$571$	−9.89182	−0.413960	−0.206980	−	0.978345i	$-0.566363\pi$
$571$	−9.89182	−0.413960	−0.206980	+	0.978345i	$0.566363\pi$
$572$	20.1895i	0.844165i
$573$	− 11.8691i	− 0.495839i
$574$	−46.4471	−1.93867
$575$	0	0
$576$	1.00000	0.0416667
$577$	− 29.5033i	− 1.22824i	−0.789213	−	0.614119i	$-0.789511\pi$
$577$	− 29.5033i	− 1.22824i	0.789213	−	0.614119i	$-0.210489\pi$
$578$	10.3431i	0.430216i
$579$	2.97729	0.123732
$580$	0	0
$581$	27.4286	1.13793
$582$	11.5260i	0.477768i
$583$	22.7902i	0.943875i
$584$	8.52601	0.352809
$585$	0	0
$586$	−8.36581	−0.345589
$587$	14.4740i	0.597406i	0.954346	+	0.298703i	$0.0965539\pi$
$587$	14.4740i	0.597406i	−0.954346	+	0.298703i	$0.903446\pi$
$588$	7.16019i	0.295281i
$589$	38.0586	1.56818
$590$	0	0
$591$	−24.8918	−1.02391
$592$	− 2.58010i	− 0.106041i
$593$	− 5.86911i	− 0.241015i	−0.992712	−	0.120508i	$-0.961548\pi$
$593$	− 5.86911i	− 0.241015i	0.992712	−	0.120508i	$-0.0384522\pi$
$594$	3.18291	0.130596
$595$	0	0
$596$	16.6862	0.683493
$597$	− 22.4492i	− 0.918785i
$598$	− 6.34310i	− 0.259389i
$599$	3.95457	0.161580	0.0807898	−	0.996731i	$-0.474256\pi$
$599$	3.95457	0.161580	0.0807898	+	0.996731i	$0.474256\pi$
$600$	0	0
$601$	9.23492	0.376700	0.188350	−	0.982102i	$-0.439686\pi$
$601$	9.23492	0.376700	0.188350	+	0.982102i	$0.439686\pi$
$602$	− 38.9211i	− 1.58631i
$603$	10.6862i	0.435176i
$604$	7.16019	0.291344
$605$	0	0
$606$	7.70891	0.313153
$607$	48.7448i	1.97849i	0.146266	+	0.989245i	$0.453274\pi$
$607$	48.7448i	1.97849i	−0.146266	+	0.989245i	$0.546726\pi$
$608$	6.34310i	0.257247i
$609$	−3.76300	−0.152485
$610$	0	0
$611$	−21.2056	−0.857888
$612$	2.58010i	0.104294i
$613$	− 3.67754i	− 0.148534i	−0.997238	−	0.0742671i	$-0.976338\pi$
$613$	− 3.67754i	− 0.148534i	0.997238	−	0.0742671i	$-0.0236617\pi$
$614$	33.7089	1.36038
$615$	0	0
$616$	11.9773	0.482579
$617$	0.794381i	0.0319806i	0.999872	+	0.0159903i	$0.00509008\pi$
$617$	0.794381i	0.0319806i	−0.999872	+	0.0159903i	$0.994910\pi$
$618$	− 3.39719i	− 0.136655i
$619$	4.57802	0.184006	0.0920031	−	0.995759i	$-0.470673\pi$
$619$	4.57802	0.184006	0.0920031	+	0.995759i	$0.470673\pi$
$620$	0	0
$621$	−1.00000	−0.0401286
$622$	− 1.86252i	− 0.0746802i
$623$	− 17.2349i	− 0.690502i
$624$	6.34310	0.253927
$625$	0	0
$626$	26.8984	1.07508
$627$	20.1895i	0.806291i
$628$	22.2122i	0.886364i
$629$	6.65690	0.265428
$630$	0	0
$631$	−31.1808	−1.24129	−0.620645	−	0.784092i	$-0.713129\pi$
$631$	−31.1808	−1.24129	−0.620645	+	0.784092i	$0.713129\pi$
$632$	− 3.18291i	− 0.126609i
$633$	19.5553i	0.777254i
$634$	−11.0000	−0.436866
$635$	0	0
$636$	7.16019	0.283920
$637$	45.4178i	1.79952i
$638$	3.18291i	0.126012i
$639$	−1.81709	−0.0718831
$640$	0	0
$641$	46.7295	1.84571	0.922853	−	0.385152i	$-0.125851\pi$
$641$	46.7295	1.84571	0.922853	+	0.385152i	$0.125851\pi$
$642$	6.68620i	0.263883i
$643$	4.81709i	0.189968i	0.995479	+	0.0949838i	$0.0302799\pi$
$643$	4.81709i	0.189968i	−0.995479	+	0.0949838i	$0.969720\pi$
$644$	−3.76300	−0.148283
$645$	0	0
$646$	−16.3658	−0.643904
$647$	− 19.4967i	− 0.766495i	−0.923646	−	0.383247i	$-0.874806\pi$
$647$	− 19.4967i	− 0.766495i	0.923646	−	0.383247i	$-0.125194\pi$
$648$	− 1.00000i	− 0.0392837i
$649$	13.8960	0.545465
$650$	0	0
$651$	−22.5780	−0.884902
$652$	8.68620i	0.340178i
$653$	− 30.5260i	− 1.19457i	−0.802027	−	0.597287i	$-0.796245\pi$
$653$	− 30.5260i	− 1.19457i	0.802027	−	0.597287i	$-0.203755\pi$
$654$	5.78572	0.226239
$655$	0	0
$656$	12.3431	0.481917
$657$	− 8.52601i	− 0.332631i
$658$	12.5801i	0.490423i
$659$	2.49463	0.0971769	0.0485885	−	0.998819i	$-0.484528\pi$
$659$	2.49463	0.0971769	0.0485885	+	0.998819i	$0.484528\pi$
$660$	0	0
$661$	−16.7337	−0.650866	−0.325433	−	0.945565i	$-0.605510\pi$
$661$	−16.7337	−0.650866	−0.325433	+	0.945565i	$0.605510\pi$
$662$	− 6.18291i	− 0.240305i
$663$	16.3658i	0.635596i
$664$	−7.28901	−0.282868
$665$	0	0
$666$	−2.58010	−0.0999767
$667$	− 1.00000i	− 0.0387202i
$668$	− 25.2349i	− 0.976368i
$669$	−28.8984	−1.11728
$670$	0	0
$671$	−4.85714	−0.187508
$672$	− 3.76300i	− 0.145161i
$673$	2.73821i	0.105550i	0.998606	+	0.0527752i	$0.0168067\pi$
$673$	2.73821i	0.105550i	−0.998606	+	0.0527752i	$0.983193\pi$
$674$	−15.1602	−0.583949
$675$	0	0
$676$	27.2349	1.04750
$677$	− 38.1040i	− 1.46446i	−0.681059	−	0.732228i	$-0.738480\pi$
$677$	− 38.1040i	− 1.46446i	0.681059	−	0.732228i	$-0.261520\pi$
$678$	0.580097i	0.0222785i
$679$	43.3724	1.66448
$680$	0	0
$681$	17.6321	0.675664
$682$	19.0974i	0.731279i
$683$	− 24.6234i	− 0.942190i	−0.882082	−	0.471095i	$-0.843859\pi$
$683$	− 24.6234i	− 0.942190i	0.882082	−	0.471095i	$-0.156141\pi$
$684$	6.34310	0.242534
$685$	0	0
$686$	0.602810	0.0230154
$687$	11.8918i	0.453701i
$688$	10.3431i	0.394327i
$689$	45.4178	1.73028
$690$	0	0
$691$	43.2935	1.64696	0.823482	−	0.567343i	$-0.192029\pi$
$691$	43.2935	1.64696	0.823482	+	0.567343i	$0.192029\pi$
$692$	− 0.817094i	− 0.0310612i
$693$	− 11.9773i	− 0.454980i
$694$	29.8918	1.13468
$695$	0	0
$696$	1.00000	0.0379049
$697$	31.8464i	1.20627i
$698$	− 7.02930i	− 0.266063i
$699$	−9.02930	−0.341520
$700$	0	0
$701$	9.00659	0.340174	0.170087	−	0.985429i	$-0.445595\pi$
$701$	9.00659	0.340174	0.170087	+	0.985429i	$0.445595\pi$
$702$	− 6.34310i	− 0.239405i
$703$	− 16.3658i	− 0.617248i
$704$	−3.18291	−0.119960
$705$	0	0
$706$	−26.2349	−0.987364
$707$	− 29.0087i	− 1.09098i
$708$	− 4.36581i	− 0.164077i
$709$	−22.3183	−0.838182	−0.419091	−	0.907944i	$-0.637651\pi$
$709$	−22.3183	−0.838182	−0.419091	+	0.907944i	$0.637651\pi$
$710$	0	0
$711$	−3.18291	−0.119368
$712$	4.58010i	0.171646i
$713$	− 6.00000i	− 0.224702i
$714$	9.70891	0.363347
$715$	0	0
$716$	−3.16019	−0.118102
$717$	20.0747i	0.749704i
$718$	− 19.5033i	− 0.727856i
$719$	32.1829	1.20022	0.600110	−	0.799918i	$-0.295123\pi$
$719$	32.1829	1.20022	0.600110	+	0.799918i	$0.295123\pi$
$720$	0	0
$721$	−12.7836	−0.476088
$722$	21.2349i	0.790282i
$723$	− 23.0066i	− 0.855624i
$724$	−3.37448	−0.125411
$725$	0	0
$726$	0.869107	0.0322556
$727$	− 32.3658i	− 1.20038i	−0.799857	−	0.600191i	$-0.795091\pi$
$727$	− 32.3658i	− 1.20038i	0.799857	−	0.600191i	$-0.204909\pi$
$728$	− 23.8691i	− 0.884648i
$729$	−1.00000	−0.0370370
$730$	0	0
$731$	−26.6862	−0.987025
$732$	1.52601i	0.0564028i
$733$	− 34.6841i	− 1.28109i	−0.767922	−	0.640544i	$-0.778709\pi$
$733$	− 34.6841i	− 1.28109i	0.767922	−	0.640544i	$-0.221291\pi$
$734$	33.5033	1.23663
$735$	0	0
$736$	1.00000	0.0368605
$737$	− 34.0132i	− 1.25289i
$738$	− 12.3431i	− 0.454356i
$739$	−45.1441	−1.66065	−0.830326	−	0.557278i	$-0.811846\pi$
$739$	−45.1441	−1.66065	−0.830326	+	0.557278i	$0.811846\pi$
$740$	0	0
$741$	40.2349	1.47807
$742$	− 26.9438i	− 0.989139i
$743$	3.02930i	0.111134i	0.998455	+	0.0555671i	$0.0176967\pi$
$743$	3.02930i	0.111134i	−0.998455	+	0.0555671i	$0.982303\pi$
$744$	6.00000	0.219971
$745$	0	0
$746$	10.1515	0.371674
$747$	7.28901i	0.266691i
$748$	− 8.21221i	− 0.300268i
$749$	25.1602	0.919333
$750$	0	0
$751$	−12.3410	−0.450330	−0.225165	−	0.974321i	$-0.572292\pi$
$751$	−12.3410	−0.450330	−0.225165	+	0.974321i	$0.572292\pi$
$752$	− 3.34310i	− 0.121910i
$753$	− 10.9459i	− 0.398891i
$754$	6.34310	0.231002
$755$	0	0
$756$	−3.76300	−0.136859
$757$	6.00208i	0.218149i	0.994034	+	0.109075i	$0.0347887\pi$
$757$	6.00208i	0.218149i	−0.994034	+	0.109075i	$0.965211\pi$
$758$	− 20.5780i	− 0.747427i
$759$	3.18291	0.115532
$760$	0	0
$761$	−26.2977	−0.953290	−0.476645	−	0.879096i	$-0.658147\pi$
$761$	−26.2977	−0.953290	−0.476645	+	0.879096i	$0.658147\pi$
$762$	− 14.3204i	− 0.518773i
$763$	− 21.7717i	− 0.788187i
$764$	11.8691	0.429409
$765$	0	0
$766$	−1.22833	−0.0443814
$767$	− 27.6928i	− 0.999929i
$768$	1.00000i	0.0360844i
$769$	45.8918	1.65490	0.827451	−	0.561538i	$-0.189790\pi$
$769$	45.8918	1.65490	0.827451	+	0.561538i	$0.189790\pi$
$770$	0	0
$771$	−16.3204	−0.587764
$772$	2.97729i	0.107155i
$773$	− 37.5846i	− 1.35182i	−0.736982	−	0.675912i	$-0.763750\pi$
$773$	− 37.5846i	− 1.35182i	0.736982	−	0.675912i	$-0.236250\pi$
$774$	10.3431	0.371775
$775$	0	0
$776$	−11.5260	−0.413760
$777$	9.70891i	0.348305i
$778$	− 35.3724i	− 1.26816i
$779$	78.2935	2.80516
$780$	0	0
$781$	5.78364	0.206955
$782$	2.58010i	0.0922641i
$783$	− 1.00000i	− 0.0357371i
$784$	−7.16019	−0.255721
$785$	0	0
$786$	−15.8918	−0.566842
$787$	− 20.9211i	− 0.745757i	−0.927880	−	0.372879i	$-0.878371\pi$
$787$	− 20.9211i	− 0.745757i	0.927880	−	0.372879i	$-0.121629\pi$
$788$	− 24.8918i	− 0.886734i
$789$	−29.0066	−1.03266
$790$	0	0
$791$	2.18291	0.0776152
$792$	3.18291i	0.113100i
$793$	9.67961i	0.343733i
$794$	31.0066	1.10038
$795$	0	0
$796$	22.4492	0.795691
$797$	46.5326i	1.64827i	0.566394	+	0.824135i	$0.308338\pi$
$797$	46.5326i	1.64827i	−0.566394	+	0.824135i	$0.691662\pi$
$798$	− 23.8691i	− 0.844957i
$799$	8.62552	0.305149
$800$	0	0
$801$	4.58010	0.161830
$802$	15.2056i	0.536929i
$803$	27.1375i	0.957661i
$804$	−10.6862	−0.376873
$805$	0	0
$806$	38.0586	1.34056
$807$	26.1895i	0.921914i
$808$	7.70891i	0.271199i
$809$	−26.1895	−0.920774	−0.460387	−	0.887718i	$-0.652289\pi$
$809$	−26.1895	−0.920774	−0.460387	+	0.887718i	$0.652289\pi$
$810$	0	0
$811$	10.4112	0.365588	0.182794	−	0.983151i	$-0.441486\pi$
$811$	10.4112	0.365588	0.182794	+	0.983151i	$0.441486\pi$
$812$	− 3.76300i	− 0.132056i
$813$	6.36581i	0.223259i
$814$	8.21221	0.287838
$815$	0	0
$816$	−2.58010	−0.0903215
$817$	65.6073i	2.29531i
$818$	2.57143i	0.0899080i
$819$	−23.8691	−0.834054
$820$	0	0
$821$	32.8171	1.14532	0.572662	−	0.819791i	$-0.305911\pi$
$821$	32.8171	1.14532	0.572662	+	0.819791i	$0.305911\pi$
$822$	− 15.4199i	− 0.537831i
$823$	20.5780i	0.717305i	0.933471	+	0.358652i	$0.116764\pi$
$823$	20.5780i	0.717305i	−0.933471	+	0.358652i	$0.883236\pi$
$824$	3.39719	0.118347
$825$	0	0
$826$	−16.4286	−0.571623
$827$	21.1982i	0.737132i	0.929602	+	0.368566i	$0.120151\pi$
$827$	21.1982i	0.737132i	−0.929602	+	0.368566i	$0.879849\pi$
$828$	− 1.00000i	− 0.0347524i
$829$	3.29109	0.114304	0.0571521	−	0.998365i	$-0.481798\pi$
$829$	3.29109	0.114304	0.0571521	+	0.998365i	$0.481798\pi$
$830$	0	0
$831$	−9.50329	−0.329666
$832$	6.34310i	0.219907i
$833$	− 18.4740i	− 0.640086i
$834$	3.02271	0.104668
$835$	0	0
$836$	−20.1895	−0.698268
$837$	− 6.00000i	− 0.207390i
$838$	19.0768i	0.658997i
$839$	20.0813	0.693284	0.346642	−	0.937998i	$-0.387322\pi$
$839$	20.0813	0.693284	0.346642	+	0.937998i	$0.387322\pi$
$840$	0	0
$841$	−28.0000	−0.965517
$842$	− 15.8918i	− 0.547668i
$843$	27.2663i	0.939101i
$844$	−19.5553	−0.673121
$845$	0	0
$846$	−3.34310	−0.114938
$847$	− 3.27045i	− 0.112374i
$848$	7.16019i	0.245882i
$849$	10.3204	0.354195
$850$	0	0
$851$	−2.58010	−0.0884446
$852$	− 1.81709i	− 0.0622526i
$853$	32.9211i	1.12720i	0.826049	+	0.563599i	$0.190584\pi$
$853$	32.9211i	1.12720i	−0.826049	+	0.563599i	$0.809416\pi$
$854$	5.74237	0.196500
$855$	0	0
$856$	−6.68620	−0.228530
$857$	46.5780i	1.59107i	0.605904	+	0.795537i	$0.292811\pi$
$857$	46.5780i	1.59107i	−0.605904	+	0.795537i	$0.707189\pi$
$858$	20.1895i	0.689258i
$859$	42.0132	1.43347	0.716736	−	0.697345i	$-0.245635\pi$
$859$	42.0132	1.43347	0.716736	+	0.697345i	$0.245635\pi$
$860$	0	0
$861$	−46.4471	−1.58291
$862$	− 24.2122i	− 0.824671i
$863$	15.5553i	0.529509i	0.964316	+	0.264754i	$0.0852909\pi$
$863$	15.5553i	0.529509i	−0.964316	+	0.264754i	$0.914709\pi$
$864$	1.00000	0.0340207
$865$	0	0
$866$	12.2122	0.414988
$867$	10.3431i	0.351270i
$868$	− 22.5780i	− 0.766348i
$869$	10.1309	0.343667
$870$	0	0
$871$	−67.7836	−2.29676
$872$	5.78572i	0.195929i
$873$	11.5260i	0.390096i
$874$	6.34310	0.214559
$875$	0	0
$876$	8.52601	0.288067
$877$	− 14.0000i	− 0.472746i	−0.971662	−	0.236373i	$-0.924041\pi$
$877$	− 14.0000i	− 0.472746i	0.971662	−	0.236373i	$-0.0759588\pi$
$878$	0.794381i	0.0268091i
$879$	−8.36581	−0.282172
$880$	0	0
$881$	10.4740	0.352878	0.176439	−	0.984312i	$-0.443542\pi$
$881$	10.4740	0.352878	0.176439	+	0.984312i	$0.443542\pi$
$882$	7.16019i	0.241096i
$883$	35.8757i	1.20731i	0.797244	+	0.603657i	$0.206290\pi$
$883$	35.8757i	1.20731i	−0.797244	+	0.603657i	$0.793710\pi$
$884$	−16.3658	−0.550442
$885$	0	0
$886$	−14.2122	−0.477468
$887$	− 7.29767i	− 0.245032i	−0.992467	−	0.122516i	$-0.960904\pi$
$887$	− 7.29767i	− 0.245032i	0.992467	−	0.122516i	$-0.0390963\pi$
$888$	− 2.58010i	− 0.0865824i
$889$	−53.8877	−1.80733
$890$	0	0
$891$	3.18291	0.106631
$892$	− 28.8984i	− 0.967590i
$893$	− 21.2056i	− 0.709619i
$894$	16.6862	0.558070
$895$	0	0
$896$	3.76300	0.125713
$897$	− 6.34310i	− 0.211790i
$898$	− 1.05201i	− 0.0351061i
$899$	6.00000	0.200111
$900$	0	0
$901$	−18.4740	−0.615458
$902$	39.2869i	1.30811i
$903$	− 38.9211i	− 1.29521i
$904$	−0.580097	−0.0192937
$905$	0	0
$906$	7.16019	0.237882
$907$	− 40.7089i	− 1.35172i	−0.737031	−	0.675859i	$-0.763773\pi$
$907$	− 40.7089i	− 1.35172i	0.737031	−	0.675859i	$-0.236227\pi$
$908$	17.6321i	0.585142i
$909$	7.70891	0.255689
$910$	0	0
$911$	22.7089	0.752380	0.376190	−	0.926543i	$-0.377234\pi$
$911$	22.7089	0.752380	0.376190	+	0.926543i	$0.377234\pi$
$912$	6.34310i	0.210041i
$913$	− 23.2002i	− 0.767816i
$914$	−0.686200	−0.0226975
$915$	0	0
$916$	−11.8918	−0.392917
$917$	59.8010i	1.97480i
$918$	2.58010i	0.0851559i
$919$	26.5801	0.876796	0.438398	−	0.898781i	$-0.355546\pi$
$919$	26.5801	0.876796	0.438398	+	0.898781i	$0.355546\pi$
$920$	0	0
$921$	33.7089	1.11075
$922$	− 29.5780i	− 0.974100i
$923$	− 11.5260i	− 0.379383i
$924$	11.9773	0.394024
$925$	0	0
$926$	12.0000	0.394344
$927$	− 3.39719i	− 0.111578i
$928$	1.00000i	0.0328266i
$929$	−36.5553	−1.19934	−0.599670	−	0.800247i	$-0.704702\pi$
$929$	−36.5553	−1.19934	−0.599670	+	0.800247i	$0.704702\pi$
$930$	0	0
$931$	−45.4178	−1.48851
$932$	− 9.02930i	− 0.295765i
$933$	− 1.86252i	− 0.0609761i
$934$	−29.2890	−0.958366
$935$	0	0
$936$	6.34310	0.207331
$937$	19.3724i	0.632869i	0.948614	+	0.316434i	$0.102486\pi$
$937$	19.3724i	0.632869i	−0.948614	+	0.316434i	$0.897514\pi$
$938$	40.2122i	1.31298i
$939$	26.8984	0.877796
$940$	0	0
$941$	−36.3204	−1.18401	−0.592005	−	0.805934i	$-0.701664\pi$
$941$	−36.3204	−1.18401	−0.592005	+	0.805934i	$0.701664\pi$
$942$	22.2122i	0.723713i
$943$	− 12.3431i	− 0.401947i
$944$	4.36581	0.142095
$945$	0	0
$946$	−32.9211	−1.07036
$947$	− 5.63419i	− 0.183086i	−0.995801	−	0.0915432i	$-0.970820\pi$
$947$	− 5.63419i	− 0.183086i	0.995801	−	0.0915432i	$-0.0291800\pi$
$948$	− 3.18291i	− 0.103376i
$949$	54.0813	1.75555
$950$	0	0
$951$	−11.0000	−0.356699
$952$	9.70891i	0.314668i
$953$	− 28.9005i	− 0.936179i	−0.883681	−	0.468089i	$-0.844943\pi$
$953$	− 28.9005i	− 0.936179i	0.883681	−	0.468089i	$-0.155057\pi$
$954$	7.16019	0.231820
$955$	0	0
$956$	−20.0747	−0.649263
$957$	3.18291i	0.102889i
$958$	− 15.9145i	− 0.514175i
$959$	−58.0251	−1.87373
$960$	0	0
$961$	5.00000	0.161290
$962$	− 16.3658i	− 0.527655i
$963$	6.68620i	0.215460i
$964$	23.0066	0.740992
$965$	0	0
$966$	−3.76300	−0.121073
$967$	− 12.3658i	− 0.397658i	−0.980034	−	0.198829i	$-0.936286\pi$
$967$	− 12.3658i	− 0.397658i	0.980034	−	0.198829i	$-0.0637138\pi$
$968$	0.869107i	0.0279341i
$969$	−16.3658	−0.525746
$970$	0	0
$971$	−33.9125	−1.08830	−0.544151	−	0.838987i	$-0.683148\pi$
$971$	−33.9125	−1.08830	−0.544151	+	0.838987i	$0.683148\pi$
$972$	− 1.00000i	− 0.0320750i
$973$	− 11.3745i	− 0.364649i
$974$	38.9438	1.24784
$975$	0	0
$976$	−1.52601	−0.0488463
$977$	− 41.3703i	− 1.32355i	−0.749701	−	0.661777i	$-0.769803\pi$
$977$	− 41.3703i	− 1.32355i	0.749701	−	0.661777i	$-0.230197\pi$
$978$	8.68620i	0.277754i
$979$	−14.5780	−0.465916
$980$	0	0
$981$	5.78572	0.184724
$982$	27.4806i	0.876941i
$983$	1.91453i	0.0610641i	0.999534	+	0.0305320i	$0.00972016\pi$
$983$	1.91453i	0.0610641i	−0.999534	+	0.0305320i	$0.990280\pi$
$984$	12.3431	0.393484
$985$	0	0
$986$	−2.58010	−0.0821670
$987$	12.5801i	0.400429i
$988$	40.2349i	1.28004i
$989$	10.3431	0.328891
$990$	0	0
$991$	3.31380	0.105266	0.0526332	−	0.998614i	$-0.483239\pi$
$991$	3.31380	0.105266	0.0526332	+	0.998614i	$0.483239\pi$
$992$	6.00000i	0.190500i
$993$	− 6.18291i	− 0.196209i
$994$	−6.83773	−0.216880
$995$	0	0
$996$	−7.28901	−0.230961
$997$	8.70891i	0.275814i	0.990445	+	0.137907i	$0.0440375\pi$
$997$	8.70891i	0.275814i	−0.990445	+	0.137907i	$0.955962\pi$
$998$	− 6.97729i	− 0.220862i
$999$	−2.58010	−0.0816307

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3450.2.d.ba.2899.6		6
5.2	odd	4		3450.2.a.bp.1.1	✓	3
5.3	odd	4		3450.2.a.bs.1.3	yes	3
5.4	even	2	inner	3450.2.d.ba.2899.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
3450.2.a.bp.1.1	✓	3	5.2	odd	4
3450.2.a.bs.1.3	yes	3	5.3	odd	4
3450.2.d.ba.2899.1		6	5.4	even	2	inner
3450.2.d.ba.2899.6		6	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:	\( N \)	\(=\)	\( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3450.d (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.76300i q^{7} -1.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +1.00000i q^{3} -1.00000 q^{4} -1.00000 q^{6} +3.76300i q^{7} -1.00000i q^{8} -1.00000 q^{9} +3.18291 q^{11} -1.00000i q^{12} -6.34310i q^{13} -3.76300 q^{14} +1.00000 q^{16} +2.58010i q^{17} -1.00000i q^{18} +6.34310 q^{19} -3.76300 q^{21} +3.18291i q^{22} -1.00000i q^{23} +1.00000 q^{24} +6.34310 q^{26} -1.00000i q^{27} -3.76300i q^{28} +1.00000 q^{29} +6.00000 q^{31} +1.00000i q^{32} +3.18291i q^{33} -2.58010 q^{34} +1.00000 q^{36} -2.58010i q^{37} +6.34310i q^{38} +6.34310 q^{39} +12.3431 q^{41} -3.76300i q^{42} +10.3431i q^{43} -3.18291 q^{44} +1.00000 q^{46} -3.34310i q^{47} +1.00000i q^{48} -7.16019 q^{49} -2.58010 q^{51} +6.34310i q^{52} +7.16019i q^{53} +1.00000 q^{54} +3.76300 q^{56} +6.34310i q^{57} +1.00000i q^{58} +4.36581 q^{59} -1.52601 q^{61} +6.00000i q^{62} -3.76300i q^{63} -1.00000 q^{64} -3.18291 q^{66} -10.6862i q^{67} -2.58010i q^{68} +1.00000 q^{69} +1.81709 q^{71} +1.00000i q^{72} +8.52601i q^{73} +2.58010 q^{74} -6.34310 q^{76} +11.9773i q^{77} +6.34310i q^{78} +3.18291 q^{79} +1.00000 q^{81} +12.3431i q^{82} -7.28901i q^{83} +3.76300 q^{84} -10.3431 q^{86} +1.00000i q^{87} -3.18291i q^{88} -4.58010 q^{89} +23.8691 q^{91} +1.00000i q^{92} +6.00000i q^{93} +3.34310 q^{94} -1.00000 q^{96} -11.5260i q^{97} -7.16019i q^{98} -3.18291 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9}+O(q^{10}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9	\( 6 q - 6 q^{4} - 6 q^{6} - 6 q^{9} + 6 q^{11} + 2 q^{14} + 6 q^{16} + 2 q^{19} + 2 q^{21} + 6 q^{24} + 2 q^{26} + 6 q^{29} + 36 q^{31} - 4 q^{34} + 6 q^{36} + 2 q^{39} + 38 q^{41} - 6 q^{44} + 6 q^{46} - 20 q^{49} - 4 q^{51} + 6 q^{54} - 2 q^{56} + 40 q^{61} - 6 q^{64} - 6 q^{66} + 6 q^{69} + 24 q^{71} + 4 q^{74} - 2 q^{76} + 6 q^{79} + 6 q^{81} - 2 q^{84} - 26 q^{86} - 16 q^{89} + 58 q^{91} - 16 q^{94} - 6 q^{96} - 6 q^{99}+O(q^{100}) \) 6 * q - 6 * q^4 - 6 * q^6 - 6 * q^9 + 6 * q^11 + 2 * q^14 + 6 * q^16 + 2 * q^19 + 2 * q^21 + 6 * q^24 + 2 * q^26 + 6 * q^29 + 36 * q^31 - 4 * q^34 + 6 * q^36 + 2 * q^39 + 38 * q^41 - 6 * q^44 + 6 * q^46 - 20 * q^49 - 4 * q^51 + 6 * q^54 - 2 * q^56 + 40 * q^61 - 6 * q^64 - 6 * q^66 + 6 * q^69 + 24 * q^71 + 4 * q^74 - 2 * q^76 + 6 * q^79 + 6 * q^81 - 2 * q^84 - 26 * q^86 - 16 * q^89 + 58 * q^91 - 16 * q^94 - 6 * q^96 - 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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