LMFDB - Embedded newform 8670.2.a.bs.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [8670,2,Mod(1,8670)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("8670.1"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(8670, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8670.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3,3,3,3,3,3,-6,3,3,3,-12,3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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

Self dual:	yes
Analytic conductor:	$69.2302985525$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	$\Q(\zeta_{18})^+$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 3x - 1 $ x^3 - 3*x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.87939$ of defining polynomial
Character	$\chi$	$=$	8670.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -0.120615 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.53209 q^{11} +1.00000 q^{12} +2.71688 q^{13} -0.120615 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -5.12836 q^{19} +1.00000 q^{20} -0.120615 q^{21} -5.53209 q^{22} -6.10607 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.71688 q^{26} +1.00000 q^{27} -0.120615 q^{28} +1.75877 q^{29} +1.00000 q^{30} -9.06418 q^{31} +1.00000 q^{32} -5.53209 q^{33} -0.120615 q^{35} +1.00000 q^{36} -3.69459 q^{37} -5.12836 q^{38} +2.71688 q^{39} +1.00000 q^{40} -8.06418 q^{41} -0.120615 q^{42} +1.06418 q^{43} -5.53209 q^{44} +1.00000 q^{45} -6.10607 q^{46} +0.248970 q^{47} +1.00000 q^{48} -6.98545 q^{49} +1.00000 q^{50} +2.71688 q^{52} -7.29086 q^{53} +1.00000 q^{54} -5.53209 q^{55} -0.120615 q^{56} -5.12836 q^{57} +1.75877 q^{58} -9.04963 q^{59} +1.00000 q^{60} -13.5175 q^{61} -9.06418 q^{62} -0.120615 q^{63} +1.00000 q^{64} +2.71688 q^{65} -5.53209 q^{66} -3.17705 q^{67} -6.10607 q^{69} -0.120615 q^{70} +13.0351 q^{71} +1.00000 q^{72} +13.2763 q^{73} -3.69459 q^{74} +1.00000 q^{75} -5.12836 q^{76} +0.667252 q^{77} +2.71688 q^{78} +6.45336 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.06418 q^{82} +6.61081 q^{83} -0.120615 q^{84} +1.06418 q^{86} +1.75877 q^{87} -5.53209 q^{88} +10.4165 q^{89} +1.00000 q^{90} -0.327696 q^{91} -6.10607 q^{92} -9.06418 q^{93} +0.248970 q^{94} -5.12836 q^{95} +1.00000 q^{96} -9.27631 q^{97} -6.98545 q^{98} -5.53209 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 12 q^{11} + 3 q^{12} - 6 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{18} + 3 q^{19} + 3 q^{20} - 6 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 12 * q^11 + 3 * q^12 - 6 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^18 + 3 * q^19 + 3 * q^20 - 6 * q^21 - 12 * q^22 - 6 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 6 * q^28 - 6 * q^29 + 3 * q^30 - 18 * q^31 + 3 * q^32 - 12 * q^33 - 6 * q^35 + 3 * q^36 - 9 * q^37 + 3 * q^38 + 3 * q^40 - 15 * q^41 - 6 * q^42 - 6 * q^43 - 12 * q^44 + 3 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 - 6 * q^53 + 3 * q^54 - 12 * q^55 - 6 * q^56 + 3 * q^57 - 6 * q^58 + 3 * q^60 - 18 * q^61 - 18 * q^62 - 6 * q^63 + 3 * q^64 - 12 * q^66 - 30 * q^67 - 6 * q^69 - 6 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 + 21 * q^77 + 6 * q^79 + 3 * q^80 + 3 * q^81 - 15 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^86 - 6 * q^87 - 12 * q^88 + 6 * q^89 + 3 * q^90 + 3 * q^91 - 6 * q^92 - 18 * q^93 - 12 * q^94 + 3 * q^95 + 3 * q^96 + 6 * q^97 - 3 * q^98 - 12 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	−0.120615	−0.0455881	−0.0227940	−	0.999740i	$-0.507256\pi$
$7$	−0.120615	−0.0455881	−0.0227940	+	0.999740i	$0.507256\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−5.53209	−1.66799	−0.833994	−	0.551774i	$-0.813951\pi$
$11$	−5.53209	−1.66799	−0.833994	+	0.551774i	$0.813951\pi$
$12$	1.00000	0.288675
$13$	2.71688	0.753527	0.376764	−	0.926309i	$-0.377037\pi$
$13$	2.71688	0.753527	0.376764	+	0.926309i	$0.377037\pi$
$14$	−0.120615	−0.0322357
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0	0
$17$	0	0
$18$	1.00000	0.235702
$19$	−5.12836	−1.17653	−0.588263	−	0.808670i	$-0.700188\pi$
$19$	−5.12836	−1.17653	−0.588263	+	0.808670i	$0.700188\pi$
$20$	1.00000	0.223607
$21$	−0.120615	−0.0263203
$22$	−5.53209	−1.17945
$23$	−6.10607	−1.27320	−0.636601	−	0.771193i	$-0.719660\pi$
$23$	−6.10607	−1.27320	−0.636601	+	0.771193i	$0.719660\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	2.71688	0.532824
$27$	1.00000	0.192450
$28$	−0.120615	−0.0227940
$29$	1.75877	0.326595	0.163298	−	0.986577i	$-0.447787\pi$
$29$	1.75877	0.326595	0.163298	+	0.986577i	$0.447787\pi$
$30$	1.00000	0.182574
$31$	−9.06418	−1.62797	−0.813987	−	0.580883i	$-0.802707\pi$
$31$	−9.06418	−1.62797	−0.813987	+	0.580883i	$0.802707\pi$
$32$	1.00000	0.176777
$33$	−5.53209	−0.963013
$34$	0	0
$35$	−0.120615	−0.0203876
$36$	1.00000	0.166667
$37$	−3.69459	−0.607387	−0.303694	−	0.952770i	$-0.598220\pi$
$37$	−3.69459	−0.607387	−0.303694	+	0.952770i	$0.598220\pi$
$38$	−5.12836	−0.831929
$39$	2.71688	0.435049
$40$	1.00000	0.158114
$41$	−8.06418	−1.25941	−0.629706	−	0.776833i	$-0.716825\pi$
$41$	−8.06418	−1.25941	−0.629706	+	0.776833i	$0.716825\pi$
$42$	−0.120615	−0.0186113
$43$	1.06418	0.162286	0.0811428	−	0.996702i	$-0.474143\pi$
$43$	1.06418	0.162286	0.0811428	+	0.996702i	$0.474143\pi$
$44$	−5.53209	−0.833994
$45$	1.00000	0.149071
$46$	−6.10607	−0.900290
$47$	0.248970	0.0363161	0.0181580	−	0.999835i	$-0.494220\pi$
$47$	0.248970	0.0363161	0.0181580	+	0.999835i	$0.494220\pi$
$48$	1.00000	0.144338
$49$	−6.98545	−0.997922
$50$	1.00000	0.141421
$51$	0	0
$52$	2.71688	0.376764
$53$	−7.29086	−1.00148	−0.500738	−	0.865599i	$-0.666938\pi$
$53$	−7.29086	−1.00148	−0.500738	+	0.865599i	$0.666938\pi$
$54$	1.00000	0.136083
$55$	−5.53209	−0.745947
$56$	−0.120615	−0.0161178
$57$	−5.12836	−0.679267
$58$	1.75877	0.230938
$59$	−9.04963	−1.17816	−0.589081	−	0.808074i	$-0.700510\pi$
$59$	−9.04963	−1.17816	−0.589081	+	0.808074i	$0.700510\pi$
$60$	1.00000	0.129099
$61$	−13.5175	−1.73074	−0.865372	−	0.501130i	$-0.832918\pi$
$61$	−13.5175	−1.73074	−0.865372	+	0.501130i	$0.832918\pi$
$62$	−9.06418	−1.15115
$63$	−0.120615	−0.0151960
$64$	1.00000	0.125000
$65$	2.71688	0.336988
$66$	−5.53209	−0.680953
$67$	−3.17705	−0.388139	−0.194069	−	0.980988i	$-0.562169\pi$
$67$	−3.17705	−0.388139	−0.194069	+	0.980988i	$0.562169\pi$
$68$	0	0
$69$	−6.10607	−0.735084
$70$	−0.120615	−0.0144162
$71$	13.0351	1.54698	0.773490	−	0.633809i	$-0.218509\pi$
$71$	13.0351	1.54698	0.773490	+	0.633809i	$0.218509\pi$
$72$	1.00000	0.117851
$73$	13.2763	1.55387	0.776937	−	0.629578i	$-0.216772\pi$
$73$	13.2763	1.55387	0.776937	+	0.629578i	$0.216772\pi$
$74$	−3.69459	−0.429488
$75$	1.00000	0.115470
$76$	−5.12836	−0.588263
$77$	0.667252	0.0760404
$78$	2.71688	0.307626
$79$	6.45336	0.726060	0.363030	−	0.931777i	$-0.381742\pi$
$79$	6.45336	0.726060	0.363030	+	0.931777i	$0.381742\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−8.06418	−0.890539
$83$	6.61081	0.725631	0.362816	−	0.931861i	$-0.381815\pi$
$83$	6.61081	0.725631	0.362816	+	0.931861i	$0.381815\pi$
$84$	−0.120615	−0.0131601
$85$	0	0
$86$	1.06418	0.114753
$87$	1.75877	0.188560
$88$	−5.53209	−0.589723
$89$	10.4165	1.10415	0.552075	−	0.833795i	$-0.313836\pi$
$89$	10.4165	1.10415	0.552075	+	0.833795i	$0.313836\pi$
$90$	1.00000	0.105409
$91$	−0.327696	−0.0343519
$92$	−6.10607	−0.636601
$93$	−9.06418	−0.939911
$94$	0.248970	0.0256793
$95$	−5.12836	−0.526158
$96$	1.00000	0.102062
$97$	−9.27631	−0.941867	−0.470933	−	0.882169i	$-0.656083\pi$
$97$	−9.27631	−0.941867	−0.470933	+	0.882169i	$0.656083\pi$
$98$	−6.98545	−0.705637
$99$	−5.53209	−0.555996
$100$	1.00000	0.100000
$101$	−4.73917	−0.471565	−0.235783	−	0.971806i	$-0.575765\pi$
$101$	−4.73917	−0.471565	−0.235783	+	0.971806i	$0.575765\pi$
$102$	0	0
$103$	15.9905	1.57559	0.787796	−	0.615937i	$-0.211222\pi$
$103$	15.9905	1.57559	0.787796	+	0.615937i	$0.211222\pi$
$104$	2.71688	0.266412
$105$	−0.120615	−0.0117708
$106$	−7.29086	−0.708151
$107$	3.30541	0.319546	0.159773	−	0.987154i	$-0.448924\pi$
$107$	3.30541	0.319546	0.159773	+	0.987154i	$0.448924\pi$
$108$	1.00000	0.0962250
$109$	−6.90673	−0.661544	−0.330772	−	0.943711i	$-0.607309\pi$
$109$	−6.90673	−0.661544	−0.330772	+	0.943711i	$0.607309\pi$
$110$	−5.53209	−0.527464
$111$	−3.69459	−0.350675
$112$	−0.120615	−0.0113970
$113$	16.3405	1.53718	0.768592	−	0.639739i	$-0.220958\pi$
$113$	16.3405	1.53718	0.768592	+	0.639739i	$0.220958\pi$
$114$	−5.12836	−0.480315
$115$	−6.10607	−0.569394
$116$	1.75877	0.163298
$117$	2.71688	0.251176
$118$	−9.04963	−0.833086
$119$	0	0
$120$	1.00000	0.0912871
$121$	19.6040	1.78218
$122$	−13.5175	−1.22382
$123$	−8.06418	−0.727122
$124$	−9.06418	−0.813987
$125$	1.00000	0.0894427
$126$	−0.120615	−0.0107452
$127$	−6.17705	−0.548125	−0.274062	−	0.961712i	$-0.588367\pi$
$127$	−6.17705	−0.548125	−0.274062	+	0.961712i	$0.588367\pi$
$128$	1.00000	0.0883883
$129$	1.06418	0.0936956
$130$	2.71688	0.238286
$131$	−12.4311	−1.08611	−0.543054	−	0.839698i	$-0.682732\pi$
$131$	−12.4311	−1.08611	−0.543054	+	0.839698i	$0.682732\pi$
$132$	−5.53209	−0.481507
$133$	0.618555	0.0536356
$134$	−3.17705	−0.274455
$135$	1.00000	0.0860663
$136$	0	0
$137$	18.7101	1.59851	0.799255	−	0.600992i	$-0.205228\pi$
$137$	18.7101	1.59851	0.799255	+	0.600992i	$0.205228\pi$
$138$	−6.10607	−0.519783
$139$	−10.5175	−0.892086	−0.446043	−	0.895011i	$-0.647167\pi$
$139$	−10.5175	−0.892086	−0.446043	+	0.895011i	$0.647167\pi$
$140$	−0.120615	−0.0101938
$141$	0.248970	0.0209671
$142$	13.0351	1.09388
$143$	−15.0300	−1.25687
$144$	1.00000	0.0833333
$145$	1.75877	0.146058
$146$	13.2763	1.09876
$147$	−6.98545	−0.576150
$148$	−3.69459	−0.303694
$149$	5.06418	0.414874	0.207437	−	0.978248i	$-0.433488\pi$
$149$	5.06418	0.414874	0.207437	+	0.978248i	$0.433488\pi$
$150$	1.00000	0.0816497
$151$	−5.43376	−0.442193	−0.221097	−	0.975252i	$-0.570964\pi$
$151$	−5.43376	−0.442193	−0.221097	+	0.975252i	$0.570964\pi$
$152$	−5.12836	−0.415965
$153$	0	0
$154$	0.667252	0.0537687
$155$	−9.06418	−0.728052
$156$	2.71688	0.217525
$157$	−8.09152	−0.645774	−0.322887	−	0.946438i	$-0.604653\pi$
$157$	−8.09152	−0.645774	−0.322887	+	0.946438i	$0.604653\pi$
$158$	6.45336	0.513402
$159$	−7.29086	−0.578203
$160$	1.00000	0.0790569
$161$	0.736482	0.0580429
$162$	1.00000	0.0785674
$163$	−14.9905	−1.17415	−0.587073	−	0.809534i	$-0.699720\pi$
$163$	−14.9905	−1.17415	−0.587073	+	0.809534i	$0.699720\pi$
$164$	−8.06418	−0.629706
$165$	−5.53209	−0.430673
$166$	6.61081	0.513099
$167$	14.3996	1.11428	0.557138	−	0.830420i	$-0.311900\pi$
$167$	14.3996	1.11428	0.557138	+	0.830420i	$0.311900\pi$
$168$	−0.120615	−0.00930563
$169$	−5.61856	−0.432197
$170$	0	0
$171$	−5.12836	−0.392175
$172$	1.06418	0.0811428
$173$	−16.5202	−1.25601	−0.628005	−	0.778209i	$-0.716128\pi$
$173$	−16.5202	−1.25601	−0.628005	+	0.778209i	$0.716128\pi$
$174$	1.75877	0.133332
$175$	−0.120615	−0.00911762
$176$	−5.53209	−0.416997
$177$	−9.04963	−0.680212
$178$	10.4165	0.780752
$179$	−3.94862	−0.295133	−0.147567	−	0.989052i	$-0.547144\pi$
$179$	−3.94862	−0.295133	−0.147567	+	0.989052i	$0.547144\pi$
$180$	1.00000	0.0745356
$181$	−4.93582	−0.366877	−0.183438	−	0.983031i	$-0.558723\pi$
$181$	−4.93582	−0.366877	−0.183438	+	0.983031i	$0.558723\pi$
$182$	−0.327696	−0.0242904
$183$	−13.5175	−0.999245
$184$	−6.10607	−0.450145
$185$	−3.69459	−0.271632
$186$	−9.06418	−0.664618
$187$	0	0
$188$	0.248970	0.0181580
$189$	−0.120615	−0.00877343
$190$	−5.12836	−0.372050
$191$	−3.63041	−0.262688	−0.131344	−	0.991337i	$-0.541929\pi$
$191$	−3.63041	−0.262688	−0.131344	+	0.991337i	$0.541929\pi$
$192$	1.00000	0.0721688
$193$	13.7743	0.991492	0.495746	−	0.868467i	$-0.334895\pi$
$193$	13.7743	0.991492	0.495746	+	0.868467i	$0.334895\pi$
$194$	−9.27631	−0.666000
$195$	2.71688	0.194560
$196$	−6.98545	−0.498961
$197$	15.5476	1.10772	0.553859	−	0.832610i	$-0.313155\pi$
$197$	15.5476	1.10772	0.553859	+	0.832610i	$0.313155\pi$
$198$	−5.53209	−0.393148
$199$	10.6209	0.752897	0.376449	−	0.926438i	$-0.377145\pi$
$199$	10.6209	0.752897	0.376449	+	0.926438i	$0.377145\pi$
$200$	1.00000	0.0707107
$201$	−3.17705	−0.224092
$202$	−4.73917	−0.333447
$203$	−0.212134	−0.0148889
$204$	0	0
$205$	−8.06418	−0.563227
$206$	15.9905	1.11411
$207$	−6.10607	−0.424401
$208$	2.71688	0.188382
$209$	28.3705	1.96243
$210$	−0.120615	−0.00832321
$211$	−15.8111	−1.08848	−0.544240	−	0.838929i	$-0.683182\pi$
$211$	−15.8111	−1.08848	−0.544240	+	0.838929i	$0.683182\pi$
$212$	−7.29086	−0.500738
$213$	13.0351	0.893149
$214$	3.30541	0.225953
$215$	1.06418	0.0725763
$216$	1.00000	0.0680414
$217$	1.09327	0.0742162
$218$	−6.90673	−0.467783
$219$	13.2763	0.897130
$220$	−5.53209	−0.372973
$221$	0	0
$222$	−3.69459	−0.247965
$223$	−20.3337	−1.36164	−0.680822	−	0.732449i	$-0.738377\pi$
$223$	−20.3337	−1.36164	−0.680822	+	0.732449i	$0.738377\pi$
$224$	−0.120615	−0.00805891
$225$	1.00000	0.0666667
$226$	16.3405	1.08695
$227$	0.650015	0.0431430	0.0215715	−	0.999767i	$-0.493133\pi$
$227$	0.650015	0.0431430	0.0215715	+	0.999767i	$0.493133\pi$
$228$	−5.12836	−0.339634
$229$	16.4688	1.08829	0.544146	−	0.838991i	$-0.316854\pi$
$229$	16.4688	1.08829	0.544146	+	0.838991i	$0.316854\pi$
$230$	−6.10607	−0.402622
$231$	0.667252	0.0439019
$232$	1.75877	0.115469
$233$	4.34049	0.284355	0.142177	−	0.989841i	$-0.454590\pi$
$233$	4.34049	0.284355	0.142177	+	0.989841i	$0.454590\pi$
$234$	2.71688	0.177608
$235$	0.248970	0.0162410
$236$	−9.04963	−0.589081
$237$	6.45336	0.419191
$238$	0	0
$239$	7.36009	0.476085	0.238042	−	0.971255i	$-0.423494\pi$
$239$	7.36009	0.476085	0.238042	+	0.971255i	$0.423494\pi$
$240$	1.00000	0.0645497
$241$	−12.0077	−0.773487	−0.386743	−	0.922187i	$-0.626400\pi$
$241$	−12.0077	−0.773487	−0.386743	+	0.922187i	$0.626400\pi$
$242$	19.6040	1.26019
$243$	1.00000	0.0641500
$244$	−13.5175	−0.865372
$245$	−6.98545	−0.446284
$246$	−8.06418	−0.514153
$247$	−13.9331	−0.886544
$248$	−9.06418	−0.575576
$249$	6.61081	0.418943
$250$	1.00000	0.0632456
$251$	−2.01455	−0.127157	−0.0635786	−	0.997977i	$-0.520251\pi$
$251$	−2.01455	−0.127157	−0.0635786	+	0.997977i	$0.520251\pi$
$252$	−0.120615	−0.00759802
$253$	33.7793	2.12369
$254$	−6.17705	−0.387583
$255$	0	0
$256$	1.00000	0.0625000
$257$	20.0838	1.25279	0.626396	−	0.779505i	$-0.284529\pi$
$257$	20.0838	1.25279	0.626396	+	0.779505i	$0.284529\pi$
$258$	1.06418	0.0662528
$259$	0.445622	0.0276896
$260$	2.71688	0.168494
$261$	1.75877	0.108865
$262$	−12.4311	−0.767994
$263$	28.2208	1.74017	0.870085	−	0.492902i	$-0.164064\pi$
$263$	28.2208	1.74017	0.870085	+	0.492902i	$0.164064\pi$
$264$	−5.53209	−0.340477
$265$	−7.29086	−0.447874
$266$	0.618555	0.0379261
$267$	10.4165	0.637481
$268$	−3.17705	−0.194069
$269$	−11.1034	−0.676985	−0.338492	−	0.940969i	$-0.609917\pi$
$269$	−11.1034	−0.676985	−0.338492	+	0.940969i	$0.609917\pi$
$270$	1.00000	0.0608581
$271$	−13.1925	−0.801389	−0.400695	−	0.916212i	$-0.631231\pi$
$271$	−13.1925	−0.801389	−0.400695	+	0.916212i	$0.631231\pi$
$272$	0	0
$273$	−0.327696	−0.0198331
$274$	18.7101	1.13032
$275$	−5.53209	−0.333598
$276$	−6.10607	−0.367542
$277$	16.8007	1.00945	0.504727	−	0.863279i	$-0.331593\pi$
$277$	16.8007	1.00945	0.504727	+	0.863279i	$0.331593\pi$
$278$	−10.5175	−0.630800
$279$	−9.06418	−0.542658
$280$	−0.120615	−0.00720811
$281$	7.90167	0.471374	0.235687	−	0.971829i	$-0.424266\pi$
$281$	7.90167	0.471374	0.235687	+	0.971829i	$0.424266\pi$
$282$	0.248970	0.0148260
$283$	−24.6946	−1.46794	−0.733971	−	0.679181i	$-0.762335\pi$
$283$	−24.6946	−1.46794	−0.733971	+	0.679181i	$0.762335\pi$
$284$	13.0351	0.773490
$285$	−5.12836	−0.303778
$286$	−15.0300	−0.888744
$287$	0.972659	0.0574142
$288$	1.00000	0.0589256
$289$	0	0
$290$	1.75877	0.103279
$291$	−9.27631	−0.543787
$292$	13.2763	0.776937
$293$	−0.394238	−0.0230316	−0.0115158	−	0.999934i	$-0.503666\pi$
$293$	−0.394238	−0.0230316	−0.0115158	+	0.999934i	$0.503666\pi$
$294$	−6.98545	−0.407400
$295$	−9.04963	−0.526890
$296$	−3.69459	−0.214744
$297$	−5.53209	−0.321004
$298$	5.06418	0.293360
$299$	−16.5895	−0.959393
$300$	1.00000	0.0577350
$301$	−0.128356	−0.00739829
$302$	−5.43376	−0.312678
$303$	−4.73917	−0.272258
$304$	−5.12836	−0.294131
$305$	−13.5175	−0.774012
$306$	0	0
$307$	6.99050	0.398969	0.199485	−	0.979901i	$-0.436073\pi$
$307$	6.99050	0.398969	0.199485	+	0.979901i	$0.436073\pi$
$308$	0.667252	0.0380202
$309$	15.9905	0.909668
$310$	−9.06418	−0.514811
$311$	−20.3696	−1.15505	−0.577527	−	0.816372i	$-0.695982\pi$
$311$	−20.3696	−1.15505	−0.577527	+	0.816372i	$0.695982\pi$
$312$	2.71688	0.153813
$313$	18.3405	1.03667	0.518333	−	0.855179i	$-0.326553\pi$
$313$	18.3405	1.03667	0.518333	+	0.855179i	$0.326553\pi$
$314$	−8.09152	−0.456631
$315$	−0.120615	−0.00679587
$316$	6.45336	0.363030
$317$	9.49794	0.533457	0.266729	−	0.963772i	$-0.414057\pi$
$317$	9.49794	0.533457	0.266729	+	0.963772i	$0.414057\pi$
$318$	−7.29086	−0.408851
$319$	−9.72967	−0.544757
$320$	1.00000	0.0559017
$321$	3.30541	0.184490
$322$	0.736482	0.0410425
$323$	0	0
$324$	1.00000	0.0555556
$325$	2.71688	0.150705
$326$	−14.9905	−0.830247
$327$	−6.90673	−0.381943
$328$	−8.06418	−0.445270
$329$	−0.0300295	−0.00165558
$330$	−5.53209	−0.304531
$331$	−25.9394	−1.42576	−0.712880	−	0.701286i	$-0.752610\pi$
$331$	−25.9394	−1.42576	−0.712880	+	0.701286i	$0.752610\pi$
$332$	6.61081	0.362816
$333$	−3.69459	−0.202462
$334$	14.3996	0.787912
$335$	−3.17705	−0.173581
$336$	−0.120615	−0.00658007
$337$	−24.4688	−1.33290	−0.666451	−	0.745548i	$-0.732188\pi$
$337$	−24.4688	−1.33290	−0.666451	+	0.745548i	$0.732188\pi$
$338$	−5.61856	−0.305609
$339$	16.3405	0.887494
$340$	0	0
$341$	50.1438	2.71544
$342$	−5.12836	−0.277310
$343$	1.68685	0.0910814
$344$	1.06418	0.0573766
$345$	−6.10607	−0.328740
$346$	−16.5202	−0.888133
$347$	−28.5134	−1.53068	−0.765340	−	0.643626i	$-0.777429\pi$
$347$	−28.5134	−1.53068	−0.765340	+	0.643626i	$0.777429\pi$
$348$	1.75877	0.0942800
$349$	14.0000	0.749403	0.374701	−	0.927146i	$-0.377745\pi$
$349$	14.0000	0.749403	0.374701	+	0.927146i	$0.377745\pi$
$350$	−0.120615	−0.00644713
$351$	2.71688	0.145016
$352$	−5.53209	−0.294861
$353$	−15.6168	−0.831198	−0.415599	−	0.909548i	$-0.636428\pi$
$353$	−15.6168	−0.831198	−0.415599	+	0.909548i	$0.636428\pi$
$354$	−9.04963	−0.480982
$355$	13.0351	0.691830
$356$	10.4165	0.552075
$357$	0	0
$358$	−3.94862	−0.208691
$359$	−26.6810	−1.40817	−0.704084	−	0.710117i	$-0.748642\pi$
$359$	−26.6810	−1.40817	−0.704084	+	0.710117i	$0.748642\pi$
$360$	1.00000	0.0527046
$361$	7.30003	0.384212
$362$	−4.93582	−0.259421
$363$	19.6040	1.02894
$364$	−0.327696	−0.0171759
$365$	13.2763	0.694914
$366$	−13.5175	−0.706573
$367$	8.96585	0.468014	0.234007	−	0.972235i	$-0.424816\pi$
$367$	8.96585	0.468014	0.234007	+	0.972235i	$0.424816\pi$
$368$	−6.10607	−0.318301
$369$	−8.06418	−0.419804
$370$	−3.69459	−0.192073
$371$	0.879385	0.0456554
$372$	−9.06418	−0.469956
$373$	−12.2591	−0.634751	−0.317375	−	0.948300i	$-0.602802\pi$
$373$	−12.2591	−0.634751	−0.317375	+	0.948300i	$0.602802\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	0.248970	0.0128397
$377$	4.77837	0.246099
$378$	−0.120615	−0.00620375
$379$	37.1634	1.90896	0.954479	−	0.298279i	$-0.0964125\pi$
$379$	37.1634	1.90896	0.954479	+	0.298279i	$0.0964125\pi$
$380$	−5.12836	−0.263079
$381$	−6.17705	−0.316460
$382$	−3.63041	−0.185748
$383$	17.1830	0.878012	0.439006	−	0.898484i	$-0.355331\pi$
$383$	17.1830	0.878012	0.439006	+	0.898484i	$0.355331\pi$
$384$	1.00000	0.0510310
$385$	0.667252	0.0340063
$386$	13.7743	0.701091
$387$	1.06418	0.0540952
$388$	−9.27631	−0.470933
$389$	−0.710074	−0.0360022	−0.0180011	−	0.999838i	$-0.505730\pi$
$389$	−0.710074	−0.0360022	−0.0180011	+	0.999838i	$0.505730\pi$
$390$	2.71688	0.137575
$391$	0	0
$392$	−6.98545	−0.352819
$393$	−12.4311	−0.627065
$394$	15.5476	0.783275
$395$	6.45336	0.324704
$396$	−5.53209	−0.277998
$397$	7.24392	0.363562	0.181781	−	0.983339i	$-0.441814\pi$
$397$	7.24392	0.363562	0.181781	+	0.983339i	$0.441814\pi$
$398$	10.6209	0.532379
$399$	0.618555	0.0309665
$400$	1.00000	0.0500000
$401$	−14.2267	−0.710447	−0.355223	−	0.934781i	$-0.615595\pi$
$401$	−14.2267	−0.710447	−0.355223	+	0.934781i	$0.615595\pi$
$402$	−3.17705	−0.158457
$403$	−24.6263	−1.22672
$404$	−4.73917	−0.235783
$405$	1.00000	0.0496904
$406$	−0.212134	−0.0105280
$407$	20.4388	1.01311
$408$	0	0
$409$	25.1310	1.24265	0.621325	−	0.783553i	$-0.286595\pi$
$409$	25.1310	1.24265	0.621325	+	0.783553i	$0.286595\pi$
$410$	−8.06418	−0.398261
$411$	18.7101	0.922900
$412$	15.9905	0.787796
$413$	1.09152	0.0537101
$414$	−6.10607	−0.300097
$415$	6.61081	0.324512
$416$	2.71688	0.133206
$417$	−10.5175	−0.515046
$418$	28.3705	1.38765
$419$	−37.2148	−1.81806	−0.909032	−	0.416727i	$-0.863177\pi$
$419$	−37.2148	−1.81806	−0.909032	+	0.416727i	$0.863177\pi$
$420$	−0.120615	−0.00588540
$421$	3.50744	0.170942	0.0854710	−	0.996341i	$-0.472761\pi$
$421$	3.50744	0.170942	0.0854710	+	0.996341i	$0.472761\pi$
$422$	−15.8111	−0.769672
$423$	0.248970	0.0121054
$424$	−7.29086	−0.354075
$425$	0	0
$426$	13.0351	0.631552
$427$	1.63041	0.0789013
$428$	3.30541	0.159773
$429$	−15.0300	−0.725657
$430$	1.06418	0.0513192
$431$	−17.8135	−0.858044	−0.429022	−	0.903294i	$-0.641142\pi$
$431$	−17.8135	−0.858044	−0.429022	+	0.903294i	$0.641142\pi$
$432$	1.00000	0.0481125
$433$	−10.5371	−0.506383	−0.253191	−	0.967416i	$-0.581480\pi$
$433$	−10.5371	−0.506383	−0.253191	+	0.967416i	$0.581480\pi$
$434$	1.09327	0.0524788
$435$	1.75877	0.0843266
$436$	−6.90673	−0.330772
$437$	31.3141	1.49796
$438$	13.2763	0.634367
$439$	−38.4789	−1.83650	−0.918250	−	0.396001i	$-0.870398\pi$
$439$	−38.4789	−1.83650	−0.918250	+	0.396001i	$0.870398\pi$
$440$	−5.53209	−0.263732
$441$	−6.98545	−0.332641
$442$	0	0
$443$	29.2026	1.38746	0.693730	−	0.720236i	$-0.255966\pi$
$443$	29.2026	1.38746	0.693730	+	0.720236i	$0.255966\pi$
$444$	−3.69459	−0.175338
$445$	10.4165	0.493791
$446$	−20.3337	−0.962828
$447$	5.06418	0.239527
$448$	−0.120615	−0.00569851
$449$	−31.4201	−1.48281	−0.741404	−	0.671059i	$-0.765840\pi$
$449$	−31.4201	−1.48281	−0.741404	+	0.671059i	$0.765840\pi$
$450$	1.00000	0.0471405
$451$	44.6117	2.10069
$452$	16.3405	0.768592
$453$	−5.43376	−0.255300
$454$	0.650015	0.0305067
$455$	−0.327696	−0.0153626
$456$	−5.12836	−0.240157
$457$	26.6364	1.24600	0.622999	−	0.782223i	$-0.285914\pi$
$457$	26.6364	1.24600	0.622999	+	0.782223i	$0.285914\pi$
$458$	16.4688	0.769539
$459$	0	0
$460$	−6.10607	−0.284697
$461$	20.9804	0.977155	0.488577	−	0.872521i	$-0.337516\pi$
$461$	20.9804	0.977155	0.488577	+	0.872521i	$0.337516\pi$
$462$	0.667252	0.0310434
$463$	−9.02734	−0.419536	−0.209768	−	0.977751i	$-0.567271\pi$
$463$	−9.02734	−0.419536	−0.209768	+	0.977751i	$0.567271\pi$
$464$	1.75877	0.0816489
$465$	−9.06418	−0.420341
$466$	4.34049	0.201069
$467$	30.0993	1.39283	0.696414	−	0.717640i	$-0.254778\pi$
$467$	30.0993	1.39283	0.696414	+	0.717640i	$0.254778\pi$
$468$	2.71688	0.125588
$469$	0.383199	0.0176945
$470$	0.248970	0.0114841
$471$	−8.09152	−0.372838
$472$	−9.04963	−0.416543
$473$	−5.88713	−0.270690
$474$	6.45336	0.296413
$475$	−5.12836	−0.235305
$476$	0	0
$477$	−7.29086	−0.333826
$478$	7.36009	0.336643
$479$	−39.3310	−1.79708	−0.898539	−	0.438893i	$-0.855371\pi$
$479$	−39.3310	−1.79708	−0.898539	+	0.438893i	$0.855371\pi$
$480$	1.00000	0.0456435
$481$	−10.0378	−0.457683
$482$	−12.0077	−0.546938
$483$	0.736482	0.0335111
$484$	19.6040	0.891091
$485$	−9.27631	−0.421216
$486$	1.00000	0.0453609
$487$	36.2864	1.64429	0.822147	−	0.569275i	$-0.192776\pi$
$487$	36.2864	1.64429	0.822147	+	0.569275i	$0.192776\pi$
$488$	−13.5175	−0.611910
$489$	−14.9905	−0.677894
$490$	−6.98545	−0.315571
$491$	18.0368	0.813991	0.406996	−	0.913430i	$-0.366576\pi$
$491$	18.0368	0.813991	0.406996	+	0.913430i	$0.366576\pi$
$492$	−8.06418	−0.363561
$493$	0	0
$494$	−13.9331	−0.626881
$495$	−5.53209	−0.248649
$496$	−9.06418	−0.406994
$497$	−1.57222	−0.0705239
$498$	6.61081	0.296238
$499$	−1.66725	−0.0746364	−0.0373182	−	0.999303i	$-0.511882\pi$
$499$	−1.66725	−0.0746364	−0.0373182	+	0.999303i	$0.511882\pi$
$500$	1.00000	0.0447214
$501$	14.3996	0.643327
$502$	−2.01455	−0.0899137
$503$	32.1762	1.43467	0.717334	−	0.696730i	$-0.245362\pi$
$503$	32.1762	1.43467	0.717334	+	0.696730i	$0.245362\pi$
$504$	−0.120615	−0.00537261
$505$	−4.73917	−0.210890
$506$	33.7793	1.50167
$507$	−5.61856	−0.249529
$508$	−6.17705	−0.274062
$509$	−17.5229	−0.776690	−0.388345	−	0.921514i	$-0.626953\pi$
$509$	−17.5229	−0.776690	−0.388345	+	0.921514i	$0.626953\pi$
$510$	0	0
$511$	−1.60132	−0.0708382
$512$	1.00000	0.0441942
$513$	−5.12836	−0.226422
$514$	20.0838	0.885857
$515$	15.9905	0.704626
$516$	1.06418	0.0468478
$517$	−1.37733	−0.0605747
$518$	0.445622	0.0195795
$519$	−16.5202	−0.725158
$520$	2.71688	0.119143
$521$	−16.9317	−0.741791	−0.370896	−	0.928675i	$-0.620949\pi$
$521$	−16.9317	−0.741791	−0.370896	+	0.928675i	$0.620949\pi$
$522$	1.75877	0.0769793
$523$	−0.906726	−0.0396484	−0.0198242	−	0.999803i	$-0.506311\pi$
$523$	−0.906726	−0.0396484	−0.0198242	+	0.999803i	$0.506311\pi$
$524$	−12.4311	−0.543054
$525$	−0.120615	−0.00526406
$526$	28.2208	1.23049
$527$	0	0
$528$	−5.53209	−0.240753
$529$	14.2841	0.621046
$530$	−7.29086	−0.316695
$531$	−9.04963	−0.392720
$532$	0.618555	0.0268178
$533$	−21.9094	−0.949002
$534$	10.4165	0.450767
$535$	3.30541	0.142905
$536$	−3.17705	−0.137228
$537$	−3.94862	−0.170395
$538$	−11.1034	−0.478701
$539$	38.6441	1.66452
$540$	1.00000	0.0430331
$541$	38.4843	1.65457	0.827285	−	0.561782i	$-0.189884\pi$
$541$	38.4843	1.65457	0.827285	+	0.561782i	$0.189884\pi$
$542$	−13.1925	−0.566668
$543$	−4.93582	−0.211816
$544$	0	0
$545$	−6.90673	−0.295852
$546$	−0.327696	−0.0140241
$547$	−15.6750	−0.670214	−0.335107	−	0.942180i	$-0.608773\pi$
$547$	−15.6750	−0.670214	−0.335107	+	0.942180i	$0.608773\pi$
$548$	18.7101	0.799255
$549$	−13.5175	−0.576915
$550$	−5.53209	−0.235889
$551$	−9.01960	−0.384248
$552$	−6.10607	−0.259891
$553$	−0.778371	−0.0330997
$554$	16.8007	0.713792
$555$	−3.69459	−0.156827
$556$	−10.5175	−0.446043
$557$	−42.1962	−1.78791	−0.893954	−	0.448158i	$-0.852080\pi$
$557$	−42.1962	−1.78791	−0.893954	+	0.448158i	$0.852080\pi$
$558$	−9.06418	−0.383717
$559$	2.89124	0.122287
$560$	−0.120615	−0.00509690
$561$	0	0
$562$	7.90167	0.333312
$563$	2.36959	0.0998661	0.0499331	−	0.998753i	$-0.484099\pi$
$563$	2.36959	0.0998661	0.0499331	+	0.998753i	$0.484099\pi$
$564$	0.248970	0.0104835
$565$	16.3405	0.687450
$566$	−24.6946	−1.03799
$567$	−0.120615	−0.00506534
$568$	13.0351	0.546940
$569$	−18.2317	−0.764314	−0.382157	−	0.924097i	$-0.624819\pi$
$569$	−18.2317	−0.764314	−0.382157	+	0.924097i	$0.624819\pi$
$570$	−5.12836	−0.214803
$571$	−20.4858	−0.857302	−0.428651	−	0.903470i	$-0.641011\pi$
$571$	−20.4858	−0.857302	−0.428651	+	0.903470i	$0.641011\pi$
$572$	−15.0300	−0.628437
$573$	−3.63041	−0.151663
$574$	0.972659	0.0405980
$575$	−6.10607	−0.254641
$576$	1.00000	0.0416667
$577$	−45.0114	−1.87385	−0.936924	−	0.349534i	$-0.886340\pi$
$577$	−45.0114	−1.87385	−0.936924	+	0.349534i	$0.886340\pi$
$578$	0	0
$579$	13.7743	0.572438
$580$	1.75877	0.0730290
$581$	−0.797362	−0.0330801
$582$	−9.27631	−0.384515
$583$	40.3337	1.67045
$584$	13.2763	0.549378
$585$	2.71688	0.112329
$586$	−0.394238	−0.0162858
$587$	−37.6323	−1.55325	−0.776625	−	0.629963i	$-0.783070\pi$
$587$	−37.6323	−1.55325	−0.776625	+	0.629963i	$0.783070\pi$
$588$	−6.98545	−0.288075
$589$	46.4843	1.91535
$590$	−9.04963	−0.372567
$591$	15.5476	0.639542
$592$	−3.69459	−0.151847
$593$	2.52166	0.103552	0.0517761	−	0.998659i	$-0.483512\pi$
$593$	2.52166	0.103552	0.0517761	+	0.998659i	$0.483512\pi$
$594$	−5.53209	−0.226984
$595$	0	0
$596$	5.06418	0.207437
$597$	10.6209	0.434685
$598$	−16.5895	−0.678393
$599$	12.7101	0.519320	0.259660	−	0.965700i	$-0.416390\pi$
$599$	12.7101	0.519320	0.259660	+	0.965700i	$0.416390\pi$
$600$	1.00000	0.0408248
$601$	−21.7306	−0.886410	−0.443205	−	0.896420i	$-0.646159\pi$
$601$	−21.7306	−0.886410	−0.443205	+	0.896420i	$0.646159\pi$
$602$	−0.128356	−0.00523138
$603$	−3.17705	−0.129380
$604$	−5.43376	−0.221097
$605$	19.6040	0.797016
$606$	−4.73917	−0.192516
$607$	33.3878	1.35517	0.677584	−	0.735446i	$-0.263027\pi$
$607$	33.3878	1.35517	0.677584	+	0.735446i	$0.263027\pi$
$608$	−5.12836	−0.207982
$609$	−0.212134	−0.00859609
$610$	−13.5175	−0.547309
$611$	0.676423	0.0273651
$612$	0	0
$613$	−35.6827	−1.44121	−0.720606	−	0.693345i	$-0.756136\pi$
$613$	−35.6827	−1.44121	−0.720606	+	0.693345i	$0.756136\pi$
$614$	6.99050	0.282114
$615$	−8.06418	−0.325179
$616$	0.667252	0.0268843
$617$	−6.31139	−0.254087	−0.127044	−	0.991897i	$-0.540549\pi$
$617$	−6.31139	−0.254087	−0.127044	+	0.991897i	$0.540549\pi$
$618$	15.9905	0.643232
$619$	−3.73742	−0.150219	−0.0751097	−	0.997175i	$-0.523931\pi$
$619$	−3.73742	−0.150219	−0.0751097	+	0.997175i	$0.523931\pi$
$620$	−9.06418	−0.364026
$621$	−6.10607	−0.245028
$622$	−20.3696	−0.816746
$623$	−1.25639	−0.0503361
$624$	2.71688	0.108762
$625$	1.00000	0.0400000
$626$	18.3405	0.733033
$627$	28.3705	1.13301
$628$	−8.09152	−0.322887
$629$	0	0
$630$	−0.120615	−0.00480541
$631$	12.8384	0.511090	0.255545	−	0.966797i	$-0.417745\pi$
$631$	12.8384	0.511090	0.255545	+	0.966797i	$0.417745\pi$
$632$	6.45336	0.256701
$633$	−15.8111	−0.628434
$634$	9.49794	0.377211
$635$	−6.17705	−0.245129
$636$	−7.29086	−0.289101
$637$	−18.9786	−0.751961
$638$	−9.72967	−0.385202
$639$	13.0351	0.515660
$640$	1.00000	0.0395285
$641$	22.4902	0.888309	0.444155	−	0.895950i	$-0.353504\pi$
$641$	22.4902	0.888309	0.444155	+	0.895950i	$0.353504\pi$
$642$	3.30541	0.130454
$643$	−22.8621	−0.901595	−0.450798	−	0.892626i	$-0.648860\pi$
$643$	−22.8621	−0.901595	−0.450798	+	0.892626i	$0.648860\pi$
$644$	0.736482	0.0290214
$645$	1.06418	0.0419020
$646$	0	0
$647$	21.0104	0.826005	0.413003	−	0.910730i	$-0.364480\pi$
$647$	21.0104	0.826005	0.413003	+	0.910730i	$0.364480\pi$
$648$	1.00000	0.0392837
$649$	50.0634	1.96516
$650$	2.71688	0.106565
$651$	1.09327	0.0428488
$652$	−14.9905	−0.587073
$653$	26.1807	1.02453	0.512264	−	0.858828i	$-0.328807\pi$
$653$	26.1807	1.02453	0.512264	+	0.858828i	$0.328807\pi$
$654$	−6.90673	−0.270074
$655$	−12.4311	−0.485722
$656$	−8.06418	−0.314853
$657$	13.2763	0.517958
$658$	−0.0300295	−0.00117067
$659$	19.2276	0.749002	0.374501	−	0.927227i	$-0.377814\pi$
$659$	19.2276	0.749002	0.374501	+	0.927227i	$0.377814\pi$
$660$	−5.53209	−0.215336
$661$	43.0114	1.67295	0.836474	−	0.548007i	$-0.184613\pi$
$661$	43.0114	1.67295	0.836474	+	0.548007i	$0.184613\pi$
$662$	−25.9394	−1.00817
$663$	0	0
$664$	6.61081	0.256549
$665$	0.618555	0.0239865
$666$	−3.69459	−0.143163
$667$	−10.7392	−0.415822
$668$	14.3996	0.557138
$669$	−20.3337	−0.786146
$670$	−3.17705	−0.122740
$671$	74.7802	2.88686
$672$	−0.120615	−0.00465282
$673$	6.73917	0.259776	0.129888	−	0.991529i	$-0.458538\pi$
$673$	6.73917	0.259776	0.129888	+	0.991529i	$0.458538\pi$
$674$	−24.4688	−0.942505
$675$	1.00000	0.0384900
$676$	−5.61856	−0.216098
$677$	29.9240	1.15007	0.575036	−	0.818128i	$-0.304988\pi$
$677$	29.9240	1.15007	0.575036	+	0.818128i	$0.304988\pi$
$678$	16.3405	0.627553
$679$	1.11886	0.0429379
$680$	0	0
$681$	0.650015	0.0249086
$682$	50.1438	1.92011
$683$	−12.2121	−0.467284	−0.233642	−	0.972323i	$-0.575064\pi$
$683$	−12.2121	−0.467284	−0.233642	+	0.972323i	$0.575064\pi$
$684$	−5.12836	−0.196088
$685$	18.7101	0.714875
$686$	1.68685	0.0644043
$687$	16.4688	0.628326
$688$	1.06418	0.0405714
$689$	−19.8084	−0.754640
$690$	−6.10607	−0.232454
$691$	40.2154	1.52987	0.764934	−	0.644109i	$-0.222772\pi$
$691$	40.2154	1.52987	0.764934	+	0.644109i	$0.222772\pi$
$692$	−16.5202	−0.628005
$693$	0.667252	0.0253468
$694$	−28.5134	−1.08235
$695$	−10.5175	−0.398953
$696$	1.75877	0.0666660
$697$	0	0
$698$	14.0000	0.529908
$699$	4.34049	0.164172
$700$	−0.120615	−0.00455881
$701$	32.6946	1.23486	0.617429	−	0.786627i	$-0.288174\pi$
$701$	32.6946	1.23486	0.617429	+	0.786627i	$0.288174\pi$
$702$	2.71688	0.102542
$703$	18.9472	0.714607
$704$	−5.53209	−0.208498
$705$	0.248970	0.00937676
$706$	−15.6168	−0.587746
$707$	0.571614	0.0214978
$708$	−9.04963	−0.340106
$709$	−10.3114	−0.387253	−0.193626	−	0.981075i	$-0.562025\pi$
$709$	−10.3114	−0.387253	−0.193626	+	0.981075i	$0.562025\pi$
$710$	13.0351	0.489198
$711$	6.45336	0.242020
$712$	10.4165	0.390376
$713$	55.3465	2.07274
$714$	0	0
$715$	−15.0300	−0.562091
$716$	−3.94862	−0.147567
$717$	7.36009	0.274868
$718$	−26.6810	−0.995725
$719$	−29.0642	−1.08391	−0.541955	−	0.840407i	$-0.682316\pi$
$719$	−29.0642	−1.08391	−0.541955	+	0.840407i	$0.682316\pi$
$720$	1.00000	0.0372678
$721$	−1.92869	−0.0718282
$722$	7.30003	0.271679
$723$	−12.0077	−0.446573
$724$	−4.93582	−0.183438
$725$	1.75877	0.0653191
$726$	19.6040	0.727573
$727$	−29.2540	−1.08497	−0.542486	−	0.840065i	$-0.682517\pi$
$727$	−29.2540	−1.08497	−0.542486	+	0.840065i	$0.682517\pi$
$728$	−0.327696	−0.0121452
$729$	1.00000	0.0370370
$730$	13.2763	0.491378
$731$	0	0
$732$	−13.5175	−0.499623
$733$	7.50805	0.277316	0.138658	−	0.990340i	$-0.455721\pi$
$733$	7.50805	0.277316	0.138658	+	0.990340i	$0.455721\pi$
$734$	8.96585	0.330936
$735$	−6.98545	−0.257662
$736$	−6.10607	−0.225073
$737$	17.5757	0.647410
$738$	−8.06418	−0.296846
$739$	−2.13753	−0.0786302	−0.0393151	−	0.999227i	$-0.512518\pi$
$739$	−2.13753	−0.0786302	−0.0393151	+	0.999227i	$0.512518\pi$
$740$	−3.69459	−0.135816
$741$	−13.9331	−0.511846
$742$	0.879385	0.0322832
$743$	−46.7347	−1.71453	−0.857265	−	0.514875i	$-0.827838\pi$
$743$	−46.7347	−1.71453	−0.857265	+	0.514875i	$0.827838\pi$
$744$	−9.06418	−0.332309
$745$	5.06418	0.185537
$746$	−12.2591	−0.448837
$747$	6.61081	0.241877
$748$	0	0
$749$	−0.398681	−0.0145675
$750$	1.00000	0.0365148
$751$	22.6810	0.827641	0.413820	−	0.910359i	$-0.364194\pi$
$751$	22.6810	0.827641	0.413820	+	0.910359i	$0.364194\pi$
$752$	0.248970	0.00907901
$753$	−2.01455	−0.0734142
$754$	4.77837	0.174018
$755$	−5.43376	−0.197755
$756$	−0.120615	−0.00438672
$757$	−21.2071	−0.770784	−0.385392	−	0.922753i	$-0.625934\pi$
$757$	−21.2071	−0.770784	−0.385392	+	0.922753i	$0.625934\pi$
$758$	37.1634	1.34984
$759$	33.7793	1.22611
$760$	−5.12836	−0.186025
$761$	−52.0779	−1.88782	−0.943911	−	0.330199i	$-0.892884\pi$
$761$	−52.0779	−1.88782	−0.943911	+	0.330199i	$0.892884\pi$
$762$	−6.17705	−0.223771
$763$	0.833053	0.0301585
$764$	−3.63041	−0.131344
$765$	0	0
$766$	17.1830	0.620848
$767$	−24.5868	−0.887777
$768$	1.00000	0.0360844
$769$	−2.52940	−0.0912125	−0.0456063	−	0.998959i	$-0.514522\pi$
$769$	−2.52940	−0.0912125	−0.0456063	+	0.998959i	$0.514522\pi$
$770$	0.667252	0.0240461
$771$	20.0838	0.723300
$772$	13.7743	0.495746
$773$	25.6655	0.923124	0.461562	−	0.887108i	$-0.347289\pi$
$773$	25.6655	0.923124	0.461562	+	0.887108i	$0.347289\pi$
$774$	1.06418	0.0382511
$775$	−9.06418	−0.325595
$776$	−9.27631	−0.333000
$777$	0.445622	0.0159866
$778$	−0.710074	−0.0254574
$779$	41.3560	1.48173
$780$	2.71688	0.0972800
$781$	−72.1112	−2.58034
$782$	0	0
$783$	1.75877	0.0628533
$784$	−6.98545	−0.249480
$785$	−8.09152	−0.288799
$786$	−12.4311	−0.443402
$787$	−38.9121	−1.38707	−0.693533	−	0.720425i	$-0.743947\pi$
$787$	−38.9121	−1.38707	−0.693533	+	0.720425i	$0.743947\pi$
$788$	15.5476	0.553859
$789$	28.2208	1.00469
$790$	6.45336	0.229600
$791$	−1.97090	−0.0700773
$792$	−5.53209	−0.196574
$793$	−36.7256	−1.30416
$794$	7.24392	0.257077
$795$	−7.29086	−0.258580
$796$	10.6209	0.376449
$797$	9.59358	0.339822	0.169911	−	0.985459i	$-0.445652\pi$
$797$	9.59358	0.339822	0.169911	+	0.985459i	$0.445652\pi$
$798$	0.618555	0.0218966
$799$	0	0
$800$	1.00000	0.0353553
$801$	10.4165	0.368050
$802$	−14.2267	−0.502362
$803$	−73.4457	−2.59184
$804$	−3.17705	−0.112046
$805$	0.736482	0.0259576
$806$	−24.6263	−0.867424
$807$	−11.1034	−0.390857
$808$	−4.73917	−0.166723
$809$	−0.153333	−0.00539089	−0.00269544	−	0.999996i	$-0.500858\pi$
$809$	−0.153333	−0.00539089	−0.00269544	+	0.999996i	$0.500858\pi$
$810$	1.00000	0.0351364
$811$	39.3441	1.38156	0.690779	−	0.723066i	$-0.257268\pi$
$811$	39.3441	1.38156	0.690779	+	0.723066i	$0.257268\pi$
$812$	−0.212134	−0.00744443
$813$	−13.1925	−0.462682
$814$	20.4388	0.716380
$815$	−14.9905	−0.525094
$816$	0	0
$817$	−5.45748	−0.190933
$818$	25.1310	0.878686
$819$	−0.327696	−0.0114506
$820$	−8.06418	−0.281613
$821$	43.7844	1.52808	0.764042	−	0.645166i	$-0.223212\pi$
$821$	43.7844	1.52808	0.764042	+	0.645166i	$0.223212\pi$
$822$	18.7101	0.652589
$823$	28.1094	0.979831	0.489915	−	0.871770i	$-0.337028\pi$
$823$	28.1094	0.979831	0.489915	+	0.871770i	$0.337028\pi$
$824$	15.9905	0.557056
$825$	−5.53209	−0.192603
$826$	1.09152	0.0379788
$827$	−8.29591	−0.288477	−0.144239	−	0.989543i	$-0.546073\pi$
$827$	−8.29591	−0.288477	−0.144239	+	0.989543i	$0.546073\pi$
$828$	−6.10607	−0.212200
$829$	−14.8520	−0.515833	−0.257916	−	0.966167i	$-0.583036\pi$
$829$	−14.8520	−0.515833	−0.257916	+	0.966167i	$0.583036\pi$
$830$	6.61081	0.229465
$831$	16.8007	0.582808
$832$	2.71688	0.0941909
$833$	0	0
$834$	−10.5175	−0.364193
$835$	14.3996	0.498319
$836$	28.3705	0.981215
$837$	−9.06418	−0.313304
$838$	−37.2148	−1.28556
$839$	−53.4884	−1.84663	−0.923313	−	0.384048i	$-0.874530\pi$
$839$	−53.4884	−1.84663	−0.923313	+	0.384048i	$0.874530\pi$
$840$	−0.120615	−0.00416160
$841$	−25.9067	−0.893335
$842$	3.50744	0.120874
$843$	7.90167	0.272148
$844$	−15.8111	−0.544240
$845$	−5.61856	−0.193284
$846$	0.248970	0.00855978
$847$	−2.36453	−0.0812463
$848$	−7.29086	−0.250369
$849$	−24.6946	−0.847516
$850$	0	0
$851$	22.5594	0.773327
$852$	13.0351	0.446575
$853$	−28.0164	−0.959264	−0.479632	−	0.877470i	$-0.659230\pi$
$853$	−28.0164	−0.959264	−0.479632	+	0.877470i	$0.659230\pi$
$854$	1.63041	0.0557917
$855$	−5.12836	−0.175386
$856$	3.30541	0.112976
$857$	25.0487	0.855647	0.427824	−	0.903862i	$-0.359280\pi$
$857$	25.0487	0.855647	0.427824	+	0.903862i	$0.359280\pi$
$858$	−15.0300	−0.513117
$859$	−30.3500	−1.03553	−0.517764	−	0.855523i	$-0.673235\pi$
$859$	−30.3500	−1.03553	−0.517764	+	0.855523i	$0.673235\pi$
$860$	1.06418	0.0362882
$861$	0.972659	0.0331481
$862$	−17.8135	−0.606729
$863$	−31.5631	−1.07442	−0.537209	−	0.843449i	$-0.680522\pi$
$863$	−31.5631	−1.07442	−0.537209	+	0.843449i	$0.680522\pi$
$864$	1.00000	0.0340207
$865$	−16.5202	−0.561705
$866$	−10.5371	−0.358067
$867$	0	0
$868$	1.09327	0.0371081
$869$	−35.7006	−1.21106
$870$	1.75877	0.0596279
$871$	−8.63167	−0.292473
$872$	−6.90673	−0.233891
$873$	−9.27631	−0.313956
$874$	31.3141	1.05921
$875$	−0.120615	−0.00407752
$876$	13.2763	0.448565
$877$	−29.5699	−0.998503	−0.499252	−	0.866457i	$-0.666392\pi$
$877$	−29.5699	−0.998503	−0.499252	+	0.866457i	$0.666392\pi$
$878$	−38.4789	−1.29860
$879$	−0.394238	−0.0132973
$880$	−5.53209	−0.186487
$881$	52.6587	1.77412	0.887058	−	0.461658i	$-0.152745\pi$
$881$	52.6587	1.77412	0.887058	+	0.461658i	$0.152745\pi$
$882$	−6.98545	−0.235212
$883$	−38.2668	−1.28778	−0.643890	−	0.765118i	$-0.722681\pi$
$883$	−38.2668	−1.28778	−0.643890	+	0.765118i	$0.722681\pi$
$884$	0	0
$885$	−9.04963	−0.304200
$886$	29.2026	0.981082
$887$	21.9614	0.737392	0.368696	−	0.929550i	$-0.379804\pi$
$887$	21.9614	0.737392	0.368696	+	0.929550i	$0.379804\pi$
$888$	−3.69459	−0.123982
$889$	0.745044	0.0249880
$890$	10.4165	0.349163
$891$	−5.53209	−0.185332
$892$	−20.3337	−0.680822
$893$	−1.27681	−0.0427268
$894$	5.06418	0.169371
$895$	−3.94862	−0.131988
$896$	−0.120615	−0.00402946
$897$	−16.5895	−0.553906
$898$	−31.4201	−1.04850
$899$	−15.9418	−0.531689
$900$	1.00000	0.0333333
$901$	0	0
$902$	44.6117	1.48541
$903$	−0.128356	−0.00427141
$904$	16.3405	0.543477
$905$	−4.93582	−0.164072
$906$	−5.43376	−0.180525
$907$	31.8871	1.05879	0.529397	−	0.848374i	$-0.322418\pi$
$907$	31.8871	1.05879	0.529397	+	0.848374i	$0.322418\pi$
$908$	0.650015	0.0215715
$909$	−4.73917	−0.157188
$910$	−0.327696	−0.0108630
$911$	−43.8052	−1.45133	−0.725666	−	0.688047i	$-0.758468\pi$
$911$	−43.8052	−1.45133	−0.725666	+	0.688047i	$0.758468\pi$
$912$	−5.12836	−0.169817
$913$	−36.5716	−1.21034
$914$	26.6364	0.881054
$915$	−13.5175	−0.446876
$916$	16.4688	0.544146
$917$	1.49937	0.0495136
$918$	0	0
$919$	−55.9627	−1.84604	−0.923019	−	0.384754i	$-0.874286\pi$
$919$	−55.9627	−1.84604	−0.923019	+	0.384754i	$0.874286\pi$
$920$	−6.10607	−0.201311
$921$	6.99050	0.230345
$922$	20.9804	0.690953
$923$	35.4148	1.16569
$924$	0.667252	0.0219510
$925$	−3.69459	−0.121477
$926$	−9.02734	−0.296657
$927$	15.9905	0.525197
$928$	1.75877	0.0577345
$929$	49.6067	1.62754	0.813771	−	0.581185i	$-0.197411\pi$
$929$	49.6067	1.62754	0.813771	+	0.581185i	$0.197411\pi$
$930$	−9.06418	−0.297226
$931$	35.8239	1.17408
$932$	4.34049	0.142177
$933$	−20.3696	−0.666870
$934$	30.0993	0.984878
$935$	0	0
$936$	2.71688	0.0888040
$937$	−26.1676	−0.854857	−0.427428	−	0.904049i	$-0.640580\pi$
$937$	−26.1676	−0.854857	−0.427428	+	0.904049i	$0.640580\pi$
$938$	0.383199	0.0125119
$939$	18.3405	0.598519
$940$	0.248970	0.00812052
$941$	−23.7606	−0.774575	−0.387287	−	0.921959i	$-0.626588\pi$
$941$	−23.7606	−0.774575	−0.387287	+	0.921959i	$0.626588\pi$
$942$	−8.09152	−0.263636
$943$	49.2404	1.60349
$944$	−9.04963	−0.294540
$945$	−0.120615	−0.00392360
$946$	−5.88713	−0.191407
$947$	16.9121	0.549570	0.274785	−	0.961506i	$-0.411393\pi$
$947$	16.9121	0.549570	0.274785	+	0.961506i	$0.411393\pi$
$948$	6.45336	0.209595
$949$	36.0702	1.17089
$950$	−5.12836	−0.166386
$951$	9.49794	0.307992
$952$	0	0
$953$	−45.4647	−1.47275	−0.736373	−	0.676575i	$-0.763463\pi$
$953$	−45.4647	−1.47275	−0.736373	+	0.676575i	$0.763463\pi$
$954$	−7.29086	−0.236050
$955$	−3.63041	−0.117477
$956$	7.36009	0.238042
$957$	−9.72967	−0.314516
$958$	−39.3310	−1.27073
$959$	−2.25671	−0.0728730
$960$	1.00000	0.0322749
$961$	51.1593	1.65030
$962$	−10.0378	−0.323631
$963$	3.30541	0.106515
$964$	−12.0077	−0.386743
$965$	13.7743	0.443409
$966$	0.736482	0.0236959
$967$	−0.562118	−0.0180765	−0.00903825	−	0.999959i	$-0.502877\pi$
$967$	−0.562118	−0.0180765	−0.00903825	+	0.999959i	$0.502877\pi$
$968$	19.6040	0.630097
$969$	0	0
$970$	−9.27631	−0.297844
$971$	39.7101	1.27436	0.637178	−	0.770716i	$-0.280101\pi$
$971$	39.7101	1.27436	0.637178	+	0.770716i	$0.280101\pi$
$972$	1.00000	0.0320750
$973$	1.26857	0.0406685
$974$	36.2864	1.16269
$975$	2.71688	0.0870098
$976$	−13.5175	−0.432686
$977$	−24.4379	−0.781837	−0.390919	−	0.920425i	$-0.627843\pi$
$977$	−24.4379	−0.781837	−0.390919	+	0.920425i	$0.627843\pi$
$978$	−14.9905	−0.479343
$979$	−57.6252	−1.84171
$980$	−6.98545	−0.223142
$981$	−6.90673	−0.220515
$982$	18.0368	0.575579
$983$	−8.03096	−0.256148	−0.128074	−	0.991765i	$-0.540879\pi$
$983$	−8.03096	−0.256148	−0.128074	+	0.991765i	$0.540879\pi$
$984$	−8.06418	−0.257077
$985$	15.5476	0.495387
$986$	0	0
$987$	−0.0300295	−0.000955849 0
$988$	−13.9331	−0.443272
$989$	−6.49794	−0.206622
$990$	−5.53209	−0.175821
$991$	−27.8479	−0.884619	−0.442309	−	0.896863i	$-0.645841\pi$
$991$	−27.8479	−0.884619	−0.442309	+	0.896863i	$0.645841\pi$
$992$	−9.06418	−0.287788
$993$	−25.9394	−0.823163
$994$	−1.57222	−0.0498679
$995$	10.6209	0.336706
$996$	6.61081	0.209472
$997$	−36.7847	−1.16498	−0.582491	−	0.812837i	$-0.697922\pi$
$997$	−36.7847	−1.16498	−0.582491	+	0.812837i	$0.697922\pi$
$998$	−1.66725	−0.0527759
$999$	−3.69459	−0.116892

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8670.2.a.bs.1.3	yes	3
17.16	even	2		8670.2.a.bp.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8670.2.a.bp.1.1	✓	3	17.16	even	2
8670.2.a.bs.1.3	yes	3	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 8670 = 2 \cdot 3 \cdot 5 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8670.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} -0.120615 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -5.53209 q^{11} +1.00000 q^{12} +2.71688 q^{13} -0.120615 q^{14} +1.00000 q^{15} +1.00000 q^{16} +1.00000 q^{18} -5.12836 q^{19} +1.00000 q^{20} -0.120615 q^{21} -5.53209 q^{22} -6.10607 q^{23} +1.00000 q^{24} +1.00000 q^{25} +2.71688 q^{26} +1.00000 q^{27} -0.120615 q^{28} +1.75877 q^{29} +1.00000 q^{30} -9.06418 q^{31} +1.00000 q^{32} -5.53209 q^{33} -0.120615 q^{35} +1.00000 q^{36} -3.69459 q^{37} -5.12836 q^{38} +2.71688 q^{39} +1.00000 q^{40} -8.06418 q^{41} -0.120615 q^{42} +1.06418 q^{43} -5.53209 q^{44} +1.00000 q^{45} -6.10607 q^{46} +0.248970 q^{47} +1.00000 q^{48} -6.98545 q^{49} +1.00000 q^{50} +2.71688 q^{52} -7.29086 q^{53} +1.00000 q^{54} -5.53209 q^{55} -0.120615 q^{56} -5.12836 q^{57} +1.75877 q^{58} -9.04963 q^{59} +1.00000 q^{60} -13.5175 q^{61} -9.06418 q^{62} -0.120615 q^{63} +1.00000 q^{64} +2.71688 q^{65} -5.53209 q^{66} -3.17705 q^{67} -6.10607 q^{69} -0.120615 q^{70} +13.0351 q^{71} +1.00000 q^{72} +13.2763 q^{73} -3.69459 q^{74} +1.00000 q^{75} -5.12836 q^{76} +0.667252 q^{77} +2.71688 q^{78} +6.45336 q^{79} +1.00000 q^{80} +1.00000 q^{81} -8.06418 q^{82} +6.61081 q^{83} -0.120615 q^{84} +1.06418 q^{86} +1.75877 q^{87} -5.53209 q^{88} +10.4165 q^{89} +1.00000 q^{90} -0.327696 q^{91} -6.10607 q^{92} -9.06418 q^{93} +0.248970 q^{94} -5.12836 q^{95} +1.00000 q^{96} -9.27631 q^{97} -6.98545 q^{98} -5.53209 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{3} + 3 q^{4} + 3 q^{5} + 3 q^{6} - 6 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 12 q^{11} + 3 q^{12} - 6 q^{14} + 3 q^{15} + 3 q^{16} + 3 q^{18} + 3 q^{19} + 3 q^{20} - 6 q^{21} - 12 q^{22}+ \cdots - 12 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^3 + 3 * q^4 + 3 * q^5 + 3 * q^6 - 6 * q^7 + 3 * q^8 + 3 * q^9 + 3 * q^10 - 12 * q^11 + 3 * q^12 - 6 * q^14 + 3 * q^15 + 3 * q^16 + 3 * q^18 + 3 * q^19 + 3 * q^20 - 6 * q^21 - 12 * q^22 - 6 * q^23 + 3 * q^24 + 3 * q^25 + 3 * q^27 - 6 * q^28 - 6 * q^29 + 3 * q^30 - 18 * q^31 + 3 * q^32 - 12 * q^33 - 6 * q^35 + 3 * q^36 - 9 * q^37 + 3 * q^38 + 3 * q^40 - 15 * q^41 - 6 * q^42 - 6 * q^43 - 12 * q^44 + 3 * q^45 - 6 * q^46 - 12 * q^47 + 3 * q^48 - 3 * q^49 + 3 * q^50 - 6 * q^53 + 3 * q^54 - 12 * q^55 - 6 * q^56 + 3 * q^57 - 6 * q^58 + 3 * q^60 - 18 * q^61 - 18 * q^62 - 6 * q^63 + 3 * q^64 - 12 * q^66 - 30 * q^67 - 6 * q^69 - 6 * q^70 - 6 * q^71 + 3 * q^72 + 6 * q^73 - 9 * q^74 + 3 * q^75 + 3 * q^76 + 21 * q^77 + 6 * q^79 + 3 * q^80 + 3 * q^81 - 15 * q^82 + 24 * q^83 - 6 * q^84 - 6 * q^86 - 6 * q^87 - 12 * q^88 + 6 * q^89 + 3 * q^90 + 3 * q^91 - 6 * q^92 - 18 * q^93 - 12 * q^94 + 3 * q^95 + 3 * q^96 + 6 * q^97 - 3 * q^98 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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