LMFDB - Embedded newform 3630.2.a.bm.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$28.9856959337$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +0.618034 q^{13} -3.23607 q^{14} -1.00000 q^{15} +1.00000 q^{16} +2.85410 q^{17} +1.00000 q^{18} +5.23607 q^{19} +1.00000 q^{20} +3.23607 q^{21} +3.61803 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.618034 q^{26} -1.00000 q^{27} -3.23607 q^{28} -5.09017 q^{29} -1.00000 q^{30} -3.85410 q^{31} +1.00000 q^{32} +2.85410 q^{34} -3.23607 q^{35} +1.00000 q^{36} -0.854102 q^{37} +5.23607 q^{38} -0.618034 q^{39} +1.00000 q^{40} -11.7082 q^{41} +3.23607 q^{42} -0.854102 q^{43} +1.00000 q^{45} +3.61803 q^{46} +11.3820 q^{47} -1.00000 q^{48} +3.47214 q^{49} +1.00000 q^{50} -2.85410 q^{51} +0.618034 q^{52} -0.472136 q^{53} -1.00000 q^{54} -3.23607 q^{56} -5.23607 q^{57} -5.09017 q^{58} +6.85410 q^{59} -1.00000 q^{60} +10.4721 q^{61} -3.85410 q^{62} -3.23607 q^{63} +1.00000 q^{64} +0.618034 q^{65} +6.32624 q^{67} +2.85410 q^{68} -3.61803 q^{69} -3.23607 q^{70} +11.4164 q^{71} +1.00000 q^{72} -4.47214 q^{73} -0.854102 q^{74} -1.00000 q^{75} +5.23607 q^{76} -0.618034 q^{78} +10.5623 q^{79} +1.00000 q^{80} +1.00000 q^{81} -11.7082 q^{82} +10.4721 q^{83} +3.23607 q^{84} +2.85410 q^{85} -0.854102 q^{86} +5.09017 q^{87} -7.70820 q^{89} +1.00000 q^{90} -2.00000 q^{91} +3.61803 q^{92} +3.85410 q^{93} +11.3820 q^{94} +5.23607 q^{95} -1.00000 q^{96} +17.7082 q^{97} +3.47214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - q^{13} - 2 q^{14} - 2 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} + 6 q^{19} + 2 q^{20} + 2 q^{21} + 5 q^{23} - 2 q^{24} + 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + q^{29} - 2 q^{30} - q^{31} + 2 q^{32} - q^{34} - 2 q^{35} + 2 q^{36} + 5 q^{37} + 6 q^{38} + q^{39} + 2 q^{40} - 10 q^{41} + 2 q^{42} + 5 q^{43} + 2 q^{45} + 5 q^{46} + 25 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + q^{51} - q^{52} + 8 q^{53} - 2 q^{54} - 2 q^{56} - 6 q^{57} + q^{58} + 7 q^{59} - 2 q^{60} + 12 q^{61} - q^{62} - 2 q^{63} + 2 q^{64} - q^{65} - 3 q^{67} - q^{68} - 5 q^{69} - 2 q^{70} - 4 q^{71} + 2 q^{72} + 5 q^{74} - 2 q^{75} + 6 q^{76} + q^{78} + q^{79} + 2 q^{80} + 2 q^{81} - 10 q^{82} + 12 q^{83} + 2 q^{84} - q^{85} + 5 q^{86} - q^{87} - 2 q^{89} + 2 q^{90} - 4 q^{91} + 5 q^{92} + q^{93} + 25 q^{94} + 6 q^{95} - 2 q^{96} + 22 q^{97} - 2 q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - q^13 - 2 * q^14 - 2 * q^15 + 2 * q^16 - q^17 + 2 * q^18 + 6 * q^19 + 2 * q^20 + 2 * q^21 + 5 * q^23 - 2 * q^24 + 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + q^29 - 2 * q^30 - q^31 + 2 * q^32 - q^34 - 2 * q^35 + 2 * q^36 + 5 * q^37 + 6 * q^38 + q^39 + 2 * q^40 - 10 * q^41 + 2 * q^42 + 5 * q^43 + 2 * q^45 + 5 * q^46 + 25 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + q^51 - q^52 + 8 * q^53 - 2 * q^54 - 2 * q^56 - 6 * q^57 + q^58 + 7 * q^59 - 2 * q^60 + 12 * q^61 - q^62 - 2 * q^63 + 2 * q^64 - q^65 - 3 * q^67 - q^68 - 5 * q^69 - 2 * q^70 - 4 * q^71 + 2 * q^72 + 5 * q^74 - 2 * q^75 + 6 * q^76 + q^78 + q^79 + 2 * q^80 + 2 * q^81 - 10 * q^82 + 12 * q^83 + 2 * q^84 - q^85 + 5 * q^86 - q^87 - 2 * q^89 + 2 * q^90 - 4 * q^91 + 5 * q^92 + q^93 + 25 * q^94 + 6 * q^95 - 2 * q^96 + 22 * q^97 - 2 * q^98

Display 100 coefficients 10 coefficients

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
$7$	−3.23607	−1.22312	−0.611559	−	0.791199i	$-0.709457\pi$
$7$	−3.23607	−1.22312	−0.611559	+	0.791199i	$0.709457\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	0.618034	0.171412	0.0857059	−	0.996320i	$-0.472685\pi$
$13$	0.618034	0.171412	0.0857059	+	0.996320i	$0.472685\pi$
$14$	−3.23607	−0.864876
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	2.85410	0.692221	0.346111	−	0.938194i	$-0.387502\pi$
$17$	2.85410	0.692221	0.346111	+	0.938194i	$0.387502\pi$
$18$	1.00000	0.235702
$19$	5.23607	1.20124	0.600618	−	0.799536i	$-0.294921\pi$
$19$	5.23607	1.20124	0.600618	+	0.799536i	$0.294921\pi$
$20$	1.00000	0.223607
$21$	3.23607	0.706168
$22$	0	0
$23$	3.61803	0.754412	0.377206	−	0.926129i	$-0.376885\pi$
$23$	3.61803	0.754412	0.377206	+	0.926129i	$0.376885\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	0.618034	0.121206
$27$	−1.00000	−0.192450
$28$	−3.23607	−0.611559
$29$	−5.09017	−0.945221	−0.472610	−	0.881271i	$-0.656688\pi$
$29$	−5.09017	−0.945221	−0.472610	+	0.881271i	$0.656688\pi$
$30$	−1.00000	−0.182574
$31$	−3.85410	−0.692217	−0.346109	−	0.938194i	$-0.612497\pi$
$31$	−3.85410	−0.692217	−0.346109	+	0.938194i	$0.612497\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	2.85410	0.489474
$35$	−3.23607	−0.546995
$36$	1.00000	0.166667
$37$	−0.854102	−0.140413	−0.0702067	−	0.997532i	$-0.522366\pi$
$37$	−0.854102	−0.140413	−0.0702067	+	0.997532i	$0.522366\pi$
$38$	5.23607	0.849402
$39$	−0.618034	−0.0989646
$40$	1.00000	0.158114
$41$	−11.7082	−1.82851	−0.914257	−	0.405134i	$-0.867225\pi$
$41$	−11.7082	−1.82851	−0.914257	+	0.405134i	$0.867225\pi$
$42$	3.23607	0.499336
$43$	−0.854102	−0.130249	−0.0651247	−	0.997877i	$-0.520745\pi$
$43$	−0.854102	−0.130249	−0.0651247	+	0.997877i	$0.520745\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	3.61803	0.533450
$47$	11.3820	1.66023	0.830115	−	0.557592i	$-0.188275\pi$
$47$	11.3820	1.66023	0.830115	+	0.557592i	$0.188275\pi$
$48$	−1.00000	−0.144338
$49$	3.47214	0.496019
$50$	1.00000	0.141421
$51$	−2.85410	−0.399654
$52$	0.618034	0.0857059
$53$	−0.472136	−0.0648529	−0.0324264	−	0.999474i	$-0.510323\pi$
$53$	−0.472136	−0.0648529	−0.0324264	+	0.999474i	$0.510323\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.23607	−0.432438
$57$	−5.23607	−0.693534
$58$	−5.09017	−0.668372
$59$	6.85410	0.892328	0.446164	−	0.894951i	$-0.352790\pi$
$59$	6.85410	0.892328	0.446164	+	0.894951i	$0.352790\pi$
$60$	−1.00000	−0.129099
$61$	10.4721	1.34082	0.670410	−	0.741991i	$-0.266118\pi$
$61$	10.4721	1.34082	0.670410	+	0.741991i	$0.266118\pi$
$62$	−3.85410	−0.489471
$63$	−3.23607	−0.407706
$64$	1.00000	0.125000
$65$	0.618034	0.0766577
$66$	0	0
$67$	6.32624	0.772873	0.386436	−	0.922316i	$-0.373706\pi$
$67$	6.32624	0.772873	0.386436	+	0.922316i	$0.373706\pi$
$68$	2.85410	0.346111
$69$	−3.61803	−0.435560
$70$	−3.23607	−0.386784
$71$	11.4164	1.35488	0.677439	−	0.735579i	$-0.263090\pi$
$71$	11.4164	1.35488	0.677439	+	0.735579i	$0.263090\pi$
$72$	1.00000	0.117851
$73$	−4.47214	−0.523424	−0.261712	−	0.965146i	$-0.584287\pi$
$73$	−4.47214	−0.523424	−0.261712	+	0.965146i	$0.584287\pi$
$74$	−0.854102	−0.0992873
$75$	−1.00000	−0.115470
$76$	5.23607	0.600618
$77$	0	0
$78$	−0.618034	−0.0699786
$79$	10.5623	1.18835	0.594176	−	0.804335i	$-0.297478\pi$
$79$	10.5623	1.18835	0.594176	+	0.804335i	$0.297478\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−11.7082	−1.29295
$83$	10.4721	1.14947	0.574733	−	0.818341i	$-0.305106\pi$
$83$	10.4721	1.14947	0.574733	+	0.818341i	$0.305106\pi$
$84$	3.23607	0.353084
$85$	2.85410	0.309571
$86$	−0.854102	−0.0921002
$87$	5.09017	0.545724
$88$	0	0
$89$	−7.70820	−0.817068	−0.408534	−	0.912743i	$-0.633960\pi$
$89$	−7.70820	−0.817068	−0.408534	+	0.912743i	$0.633960\pi$
$90$	1.00000	0.105409
$91$	−2.00000	−0.209657
$92$	3.61803	0.377206
$93$	3.85410	0.399652
$94$	11.3820	1.17396
$95$	5.23607	0.537209
$96$	−1.00000	−0.102062
$97$	17.7082	1.79800	0.898998	−	0.437953i	$-0.144296\pi$
$97$	17.7082	1.79800	0.898998	+	0.437953i	$0.144296\pi$
$98$	3.47214	0.350739
$99$	0	0
$100$	1.00000	0.100000
$101$	−14.8541	−1.47804	−0.739019	−	0.673684i	$-0.764711\pi$
$101$	−14.8541	−1.47804	−0.739019	+	0.673684i	$0.764711\pi$
$102$	−2.85410	−0.282598
$103$	10.7639	1.06060	0.530301	−	0.847810i	$-0.322079\pi$
$103$	10.7639	1.06060	0.530301	+	0.847810i	$0.322079\pi$
$104$	0.618034	0.0606032
$105$	3.23607	0.315808
$106$	−0.472136	−0.0458579
$107$	5.70820	0.551833	0.275916	−	0.961182i	$-0.411019\pi$
$107$	5.70820	0.551833	0.275916	+	0.961182i	$0.411019\pi$
$108$	−1.00000	−0.0962250
$109$	8.94427	0.856706	0.428353	−	0.903612i	$-0.359094\pi$
$109$	8.94427	0.856706	0.428353	+	0.903612i	$0.359094\pi$
$110$	0	0
$111$	0.854102	0.0810678
$112$	−3.23607	−0.305780
$113$	8.14590	0.766302	0.383151	−	0.923686i	$-0.374839\pi$
$113$	8.14590	0.766302	0.383151	+	0.923686i	$0.374839\pi$
$114$	−5.23607	−0.490403
$115$	3.61803	0.337383
$116$	−5.09017	−0.472610
$117$	0.618034	0.0571373
$118$	6.85410	0.630971
$119$	−9.23607	−0.846669
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	10.4721	0.948103
$123$	11.7082	1.05569
$124$	−3.85410	−0.346109
$125$	1.00000	0.0894427
$126$	−3.23607	−0.288292
$127$	13.7082	1.21641	0.608203	−	0.793781i	$-0.291891\pi$
$127$	13.7082	1.21641	0.608203	+	0.793781i	$0.291891\pi$
$128$	1.00000	0.0883883
$129$	0.854102	0.0751995
$130$	0.618034	0.0542052
$131$	20.6180	1.80141	0.900703	−	0.434435i	$-0.143052\pi$
$131$	20.6180	1.80141	0.900703	+	0.434435i	$0.143052\pi$
$132$	0	0
$133$	−16.9443	−1.46925
$134$	6.32624	0.546504
$135$	−1.00000	−0.0860663
$136$	2.85410	0.244737
$137$	9.38197	0.801555	0.400778	−	0.916175i	$-0.368740\pi$
$137$	9.38197	0.801555	0.400778	+	0.916175i	$0.368740\pi$
$138$	−3.61803	−0.307988
$139$	−10.6525	−0.903531	−0.451766	−	0.892137i	$-0.649206\pi$
$139$	−10.6525	−0.903531	−0.451766	+	0.892137i	$0.649206\pi$
$140$	−3.23607	−0.273498
$141$	−11.3820	−0.958534
$142$	11.4164	0.958044
$143$	0	0
$144$	1.00000	0.0833333
$145$	−5.09017	−0.422716
$146$	−4.47214	−0.370117
$147$	−3.47214	−0.286377
$148$	−0.854102	−0.0702067
$149$	−1.14590	−0.0938756	−0.0469378	−	0.998898i	$-0.514946\pi$
$149$	−1.14590	−0.0938756	−0.0469378	+	0.998898i	$0.514946\pi$
$150$	−1.00000	−0.0816497
$151$	−12.9443	−1.05339	−0.526695	−	0.850054i	$-0.676569\pi$
$151$	−12.9443	−1.05339	−0.526695	+	0.850054i	$0.676569\pi$
$152$	5.23607	0.424701
$153$	2.85410	0.230740
$154$	0	0
$155$	−3.85410	−0.309569
$156$	−0.618034	−0.0494823
$157$	−3.38197	−0.269910	−0.134955	−	0.990852i	$-0.543089\pi$
$157$	−3.38197	−0.269910	−0.134955	+	0.990852i	$0.543089\pi$
$158$	10.5623	0.840292
$159$	0.472136	0.0374428
$160$	1.00000	0.0790569
$161$	−11.7082	−0.922736
$162$	1.00000	0.0785674
$163$	17.7984	1.39408	0.697038	−	0.717034i	$-0.254501\pi$
$163$	17.7984	1.39408	0.697038	+	0.717034i	$0.254501\pi$
$164$	−11.7082	−0.914257
$165$	0	0
$166$	10.4721	0.812795
$167$	−4.32624	−0.334774	−0.167387	−	0.985891i	$-0.553533\pi$
$167$	−4.32624	−0.334774	−0.167387	+	0.985891i	$0.553533\pi$
$168$	3.23607	0.249668
$169$	−12.6180	−0.970618
$170$	2.85410	0.218900
$171$	5.23607	0.400412
$172$	−0.854102	−0.0651247
$173$	−8.00000	−0.608229	−0.304114	−	0.952636i	$-0.598361\pi$
$173$	−8.00000	−0.608229	−0.304114	+	0.952636i	$0.598361\pi$
$174$	5.09017	0.385885
$175$	−3.23607	−0.244624
$176$	0	0
$177$	−6.85410	−0.515186
$178$	−7.70820	−0.577754
$179$	−20.0344	−1.49744	−0.748722	−	0.662884i	$-0.769332\pi$
$179$	−20.0344	−1.49744	−0.748722	+	0.662884i	$0.769332\pi$
$180$	1.00000	0.0745356
$181$	1.52786	0.113565	0.0567826	−	0.998387i	$-0.481916\pi$
$181$	1.52786	0.113565	0.0567826	+	0.998387i	$0.481916\pi$
$182$	−2.00000	−0.148250
$183$	−10.4721	−0.774123
$184$	3.61803	0.266725
$185$	−0.854102	−0.0627948
$186$	3.85410	0.282596
$187$	0	0
$188$	11.3820	0.830115
$189$	3.23607	0.235389
$190$	5.23607	0.379864
$191$	12.2918	0.889403	0.444702	−	0.895679i	$-0.353310\pi$
$191$	12.2918	0.889403	0.444702	+	0.895679i	$0.353310\pi$
$192$	−1.00000	−0.0721688
$193$	−8.94427	−0.643823	−0.321911	−	0.946770i	$-0.604325\pi$
$193$	−8.94427	−0.643823	−0.321911	+	0.946770i	$0.604325\pi$
$194$	17.7082	1.27137
$195$	−0.618034	−0.0442583
$196$	3.47214	0.248010
$197$	−22.0000	−1.56744	−0.783718	−	0.621117i	$-0.786679\pi$
$197$	−22.0000	−1.56744	−0.783718	+	0.621117i	$0.786679\pi$
$198$	0	0
$199$	−24.2705	−1.72049	−0.860245	−	0.509880i	$-0.829690\pi$
$199$	−24.2705	−1.72049	−0.860245	+	0.509880i	$0.829690\pi$
$200$	1.00000	0.0707107
$201$	−6.32624	−0.446218
$202$	−14.8541	−1.04513
$203$	16.4721	1.15612
$204$	−2.85410	−0.199827
$205$	−11.7082	−0.817736
$206$	10.7639	0.749959
$207$	3.61803	0.251471
$208$	0.618034	0.0428529
$209$	0	0
$210$	3.23607	0.223310
$211$	15.7082	1.08140	0.540699	−	0.841216i	$-0.318160\pi$
$211$	15.7082	1.08140	0.540699	+	0.841216i	$0.318160\pi$
$212$	−0.472136	−0.0324264
$213$	−11.4164	−0.782239
$214$	5.70820	0.390205
$215$	−0.854102	−0.0582493
$216$	−1.00000	−0.0680414
$217$	12.4721	0.846664
$218$	8.94427	0.605783
$219$	4.47214	0.302199
$220$	0	0
$221$	1.76393	0.118655
$222$	0.854102	0.0573236
$223$	21.1246	1.41461	0.707304	−	0.706909i	$-0.249911\pi$
$223$	21.1246	1.41461	0.707304	+	0.706909i	$0.249911\pi$
$224$	−3.23607	−0.216219
$225$	1.00000	0.0666667
$226$	8.14590	0.541857
$227$	−21.8885	−1.45279	−0.726397	−	0.687276i	$-0.758807\pi$
$227$	−21.8885	−1.45279	−0.726397	+	0.687276i	$0.758807\pi$
$228$	−5.23607	−0.346767
$229$	25.1246	1.66028	0.830141	−	0.557554i	$-0.188260\pi$
$229$	25.1246	1.66028	0.830141	+	0.557554i	$0.188260\pi$
$230$	3.61803	0.238566
$231$	0	0
$232$	−5.09017	−0.334186
$233$	22.9787	1.50539	0.752693	−	0.658372i	$-0.228755\pi$
$233$	22.9787	1.50539	0.752693	+	0.658372i	$0.228755\pi$
$234$	0.618034	0.0404021
$235$	11.3820	0.742478
$236$	6.85410	0.446164
$237$	−10.5623	−0.686095
$238$	−9.23607	−0.598685
$239$	−14.2918	−0.924459	−0.462230	−	0.886760i	$-0.652950\pi$
$239$	−14.2918	−0.924459	−0.462230	+	0.886760i	$0.652950\pi$
$240$	−1.00000	−0.0645497
$241$	−14.9443	−0.962645	−0.481323	−	0.876544i	$-0.659843\pi$
$241$	−14.9443	−0.962645	−0.481323	+	0.876544i	$0.659843\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	10.4721	0.670410
$245$	3.47214	0.221827
$246$	11.7082	0.746488
$247$	3.23607	0.205906
$248$	−3.85410	−0.244736
$249$	−10.4721	−0.663645
$250$	1.00000	0.0632456
$251$	2.67376	0.168766	0.0843832	−	0.996433i	$-0.473108\pi$
$251$	2.67376	0.168766	0.0843832	+	0.996433i	$0.473108\pi$
$252$	−3.23607	−0.203853
$253$	0	0
$254$	13.7082	0.860129
$255$	−2.85410	−0.178731
$256$	1.00000	0.0625000
$257$	3.52786	0.220062	0.110031	−	0.993928i	$-0.464905\pi$
$257$	3.52786	0.220062	0.110031	+	0.993928i	$0.464905\pi$
$258$	0.854102	0.0531741
$259$	2.76393	0.171742
$260$	0.618034	0.0383288
$261$	−5.09017	−0.315074
$262$	20.6180	1.27379
$263$	−0.562306	−0.0346733	−0.0173366	−	0.999850i	$-0.505519\pi$
$263$	−0.562306	−0.0346733	−0.0173366	+	0.999850i	$0.505519\pi$
$264$	0	0
$265$	−0.472136	−0.0290031
$266$	−16.9443	−1.03892
$267$	7.70820	0.471734
$268$	6.32624	0.386436
$269$	10.3262	0.629602	0.314801	−	0.949158i	$-0.398062\pi$
$269$	10.3262	0.629602	0.314801	+	0.949158i	$0.398062\pi$
$270$	−1.00000	−0.0608581
$271$	17.7984	1.08117	0.540587	−	0.841288i	$-0.318202\pi$
$271$	17.7984	1.08117	0.540587	+	0.841288i	$0.318202\pi$
$272$	2.85410	0.173055
$273$	2.00000	0.121046
$274$	9.38197	0.566785
$275$	0	0
$276$	−3.61803	−0.217780
$277$	−2.96556	−0.178183	−0.0890916	−	0.996023i	$-0.528396\pi$
$277$	−2.96556	−0.178183	−0.0890916	+	0.996023i	$0.528396\pi$
$278$	−10.6525	−0.638893
$279$	−3.85410	−0.230739
$280$	−3.23607	−0.193392
$281$	11.8885	0.709211	0.354606	−	0.935016i	$-0.384615\pi$
$281$	11.8885	0.709211	0.354606	+	0.935016i	$0.384615\pi$
$282$	−11.3820	−0.677786
$283$	−26.0344	−1.54759	−0.773793	−	0.633438i	$-0.781643\pi$
$283$	−26.0344	−1.54759	−0.773793	+	0.633438i	$0.781643\pi$
$284$	11.4164	0.677439
$285$	−5.23607	−0.310158
$286$	0	0
$287$	37.8885	2.23649
$288$	1.00000	0.0589256
$289$	−8.85410	−0.520830
$290$	−5.09017	−0.298905
$291$	−17.7082	−1.03807
$292$	−4.47214	−0.261712
$293$	24.9443	1.45726	0.728630	−	0.684908i	$-0.240157\pi$
$293$	24.9443	1.45726	0.728630	+	0.684908i	$0.240157\pi$
$294$	−3.47214	−0.202499
$295$	6.85410	0.399061
$296$	−0.854102	−0.0496437
$297$	0	0
$298$	−1.14590	−0.0663801
$299$	2.23607	0.129315
$300$	−1.00000	−0.0577350
$301$	2.76393	0.159310
$302$	−12.9443	−0.744859
$303$	14.8541	0.853346
$304$	5.23607	0.300309
$305$	10.4721	0.599633
$306$	2.85410	0.163158
$307$	−6.90983	−0.394365	−0.197182	−	0.980367i	$-0.563179\pi$
$307$	−6.90983	−0.394365	−0.197182	+	0.980367i	$0.563179\pi$
$308$	0	0
$309$	−10.7639	−0.612339
$310$	−3.85410	−0.218898
$311$	18.1803	1.03091	0.515456	−	0.856916i	$-0.327622\pi$
$311$	18.1803	1.03091	0.515456	+	0.856916i	$0.327622\pi$
$312$	−0.618034	−0.0349893
$313$	−28.8328	−1.62973	−0.814864	−	0.579653i	$-0.803188\pi$
$313$	−28.8328	−1.62973	−0.814864	+	0.579653i	$0.803188\pi$
$314$	−3.38197	−0.190855
$315$	−3.23607	−0.182332
$316$	10.5623	0.594176
$317$	8.58359	0.482103	0.241051	−	0.970512i	$-0.422508\pi$
$317$	8.58359	0.482103	0.241051	+	0.970512i	$0.422508\pi$
$318$	0.472136	0.0264761
$319$	0	0
$320$	1.00000	0.0559017
$321$	−5.70820	−0.318601
$322$	−11.7082	−0.652473
$323$	14.9443	0.831522
$324$	1.00000	0.0555556
$325$	0.618034	0.0342824
$326$	17.7984	0.985761
$327$	−8.94427	−0.494619
$328$	−11.7082	−0.646477
$329$	−36.8328	−2.03066
$330$	0	0
$331$	−32.0689	−1.76267	−0.881333	−	0.472496i	$-0.843353\pi$
$331$	−32.0689	−1.76267	−0.881333	+	0.472496i	$0.843353\pi$
$332$	10.4721	0.574733
$333$	−0.854102	−0.0468045
$334$	−4.32624	−0.236721
$335$	6.32624	0.345639
$336$	3.23607	0.176542
$337$	−24.7639	−1.34898	−0.674489	−	0.738285i	$-0.735636\pi$
$337$	−24.7639	−1.34898	−0.674489	+	0.738285i	$0.735636\pi$
$338$	−12.6180	−0.686331
$339$	−8.14590	−0.442424
$340$	2.85410	0.154785
$341$	0	0
$342$	5.23607	0.283134
$343$	11.4164	0.616428
$344$	−0.854102	−0.0460501
$345$	−3.61803	−0.194788
$346$	−8.00000	−0.430083
$347$	−2.58359	−0.138694	−0.0693472	−	0.997593i	$-0.522092\pi$
$347$	−2.58359	−0.138694	−0.0693472	+	0.997593i	$0.522092\pi$
$348$	5.09017	0.272862
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	−3.23607	−0.172975
$351$	−0.618034	−0.0329882
$352$	0	0
$353$	12.3820	0.659026	0.329513	−	0.944151i	$-0.393116\pi$
$353$	12.3820	0.659026	0.329513	+	0.944151i	$0.393116\pi$
$354$	−6.85410	−0.364291
$355$	11.4164	0.605920
$356$	−7.70820	−0.408534
$357$	9.23607	0.488825
$358$	−20.0344	−1.05885
$359$	12.1803	0.642854	0.321427	−	0.946934i	$-0.395838\pi$
$359$	12.1803	0.642854	0.321427	+	0.946934i	$0.395838\pi$
$360$	1.00000	0.0527046
$361$	8.41641	0.442969
$362$	1.52786	0.0803028
$363$	0	0
$364$	−2.00000	−0.104828
$365$	−4.47214	−0.234082
$366$	−10.4721	−0.547387
$367$	8.29180	0.432828	0.216414	−	0.976302i	$-0.430564\pi$
$367$	8.29180	0.432828	0.216414	+	0.976302i	$0.430564\pi$
$368$	3.61803	0.188603
$369$	−11.7082	−0.609505
$370$	−0.854102	−0.0444026
$371$	1.52786	0.0793227
$372$	3.85410	0.199826
$373$	−9.41641	−0.487563	−0.243782	−	0.969830i	$-0.578388\pi$
$373$	−9.41641	−0.487563	−0.243782	+	0.969830i	$0.578388\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	11.3820	0.586980
$377$	−3.14590	−0.162022
$378$	3.23607	0.166445
$379$	−23.4164	−1.20282	−0.601410	−	0.798941i	$-0.705394\pi$
$379$	−23.4164	−1.20282	−0.601410	+	0.798941i	$0.705394\pi$
$380$	5.23607	0.268605
$381$	−13.7082	−0.702293
$382$	12.2918	0.628903
$383$	4.32624	0.221060	0.110530	−	0.993873i	$-0.464745\pi$
$383$	4.32624	0.221060	0.110530	+	0.993873i	$0.464745\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−8.94427	−0.455251
$387$	−0.854102	−0.0434164
$388$	17.7082	0.898998
$389$	4.56231	0.231318	0.115659	−	0.993289i	$-0.463102\pi$
$389$	4.56231	0.231318	0.115659	+	0.993289i	$0.463102\pi$
$390$	−0.618034	−0.0312954
$391$	10.3262	0.522220
$392$	3.47214	0.175369
$393$	−20.6180	−1.04004
$394$	−22.0000	−1.10834
$395$	10.5623	0.531447
$396$	0	0
$397$	32.4508	1.62866	0.814331	−	0.580401i	$-0.197104\pi$
$397$	32.4508	1.62866	0.814331	+	0.580401i	$0.197104\pi$
$398$	−24.2705	−1.21657
$399$	16.9443	0.848275
$400$	1.00000	0.0500000
$401$	17.1246	0.855162	0.427581	−	0.903977i	$-0.359366\pi$
$401$	17.1246	0.855162	0.427581	+	0.903977i	$0.359366\pi$
$402$	−6.32624	−0.315524
$403$	−2.38197	−0.118654
$404$	−14.8541	−0.739019
$405$	1.00000	0.0496904
$406$	16.4721	0.817498
$407$	0	0
$408$	−2.85410	−0.141299
$409$	−30.1459	−1.49062	−0.745309	−	0.666719i	$-0.767698\pi$
$409$	−30.1459	−1.49062	−0.745309	+	0.666719i	$0.767698\pi$
$410$	−11.7082	−0.578227
$411$	−9.38197	−0.462778
$412$	10.7639	0.530301
$413$	−22.1803	−1.09142
$414$	3.61803	0.177817
$415$	10.4721	0.514057
$416$	0.618034	0.0303016
$417$	10.6525	0.521654
$418$	0	0
$419$	−24.7426	−1.20876	−0.604379	−	0.796697i	$-0.706579\pi$
$419$	−24.7426	−1.20876	−0.604379	+	0.796697i	$0.706579\pi$
$420$	3.23607	0.157904
$421$	4.00000	0.194948	0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000	0.194948	0.0974740	+	0.995238i	$0.468924\pi$
$422$	15.7082	0.764663
$423$	11.3820	0.553410
$424$	−0.472136	−0.0229289
$425$	2.85410	0.138444
$426$	−11.4164	−0.553127
$427$	−33.8885	−1.63998
$428$	5.70820	0.275916
$429$	0	0
$430$	−0.854102	−0.0411885
$431$	−28.4721	−1.37145	−0.685727	−	0.727859i	$-0.740516\pi$
$431$	−28.4721	−1.37145	−0.685727	+	0.727859i	$0.740516\pi$
$432$	−1.00000	−0.0481125
$433$	−0.583592	−0.0280456	−0.0140228	−	0.999902i	$-0.504464\pi$
$433$	−0.583592	−0.0280456	−0.0140228	+	0.999902i	$0.504464\pi$
$434$	12.4721	0.598682
$435$	5.09017	0.244055
$436$	8.94427	0.428353
$437$	18.9443	0.906227
$438$	4.47214	0.213687
$439$	−26.9787	−1.28762	−0.643812	−	0.765184i	$-0.722648\pi$
$439$	−26.9787	−1.28762	−0.643812	+	0.765184i	$0.722648\pi$
$440$	0	0
$441$	3.47214	0.165340
$442$	1.76393	0.0839017
$443$	−29.1246	−1.38375	−0.691876	−	0.722016i	$-0.743216\pi$
$443$	−29.1246	−1.38375	−0.691876	+	0.722016i	$0.743216\pi$
$444$	0.854102	0.0405339
$445$	−7.70820	−0.365404
$446$	21.1246	1.00028
$447$	1.14590	0.0541991
$448$	−3.23607	−0.152890
$449$	−19.1246	−0.902546	−0.451273	−	0.892386i	$-0.649030\pi$
$449$	−19.1246	−0.902546	−0.451273	+	0.892386i	$0.649030\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	8.14590	0.383151
$453$	12.9443	0.608175
$454$	−21.8885	−1.02728
$455$	−2.00000	−0.0937614
$456$	−5.23607	−0.245201
$457$	−11.7082	−0.547687	−0.273843	−	0.961774i	$-0.588295\pi$
$457$	−11.7082	−0.547687	−0.273843	+	0.961774i	$0.588295\pi$
$458$	25.1246	1.17400
$459$	−2.85410	−0.133218
$460$	3.61803	0.168692
$461$	−14.0902	−0.656245	−0.328122	−	0.944635i	$-0.606416\pi$
$461$	−14.0902	−0.656245	−0.328122	+	0.944635i	$0.606416\pi$
$462$	0	0
$463$	−18.0000	−0.836531	−0.418265	−	0.908325i	$-0.637362\pi$
$463$	−18.0000	−0.836531	−0.418265	+	0.908325i	$0.637362\pi$
$464$	−5.09017	−0.236305
$465$	3.85410	0.178730
$466$	22.9787	1.06447
$467$	41.7082	1.93003	0.965013	−	0.262203i	$-0.0844490\pi$
$467$	41.7082	1.93003	0.965013	+	0.262203i	$0.0844490\pi$
$468$	0.618034	0.0285686
$469$	−20.4721	−0.945315
$470$	11.3820	0.525011
$471$	3.38197	0.155833
$472$	6.85410	0.315486
$473$	0	0
$474$	−10.5623	−0.485143
$475$	5.23607	0.240247
$476$	−9.23607	−0.423334
$477$	−0.472136	−0.0216176
$478$	−14.2918	−0.653692
$479$	−3.81966	−0.174525	−0.0872624	−	0.996185i	$-0.527812\pi$
$479$	−3.81966	−0.174525	−0.0872624	+	0.996185i	$0.527812\pi$
$480$	−1.00000	−0.0456435
$481$	−0.527864	−0.0240685
$482$	−14.9443	−0.680693
$483$	11.7082	0.532742
$484$	0	0
$485$	17.7082	0.804088
$486$	−1.00000	−0.0453609
$487$	−18.4721	−0.837052	−0.418526	−	0.908205i	$-0.637453\pi$
$487$	−18.4721	−0.837052	−0.418526	+	0.908205i	$0.637453\pi$
$488$	10.4721	0.474051
$489$	−17.7984	−0.804870
$490$	3.47214	0.156855
$491$	23.0902	1.04204	0.521022	−	0.853543i	$-0.325551\pi$
$491$	23.0902	1.04204	0.521022	+	0.853543i	$0.325551\pi$
$492$	11.7082	0.527847
$493$	−14.5279	−0.654302
$494$	3.23607	0.145598
$495$	0	0
$496$	−3.85410	−0.173054
$497$	−36.9443	−1.65718
$498$	−10.4721	−0.469268
$499$	3.88854	0.174075	0.0870376	−	0.996205i	$-0.472260\pi$
$499$	3.88854	0.174075	0.0870376	+	0.996205i	$0.472260\pi$
$500$	1.00000	0.0447214
$501$	4.32624	0.193282
$502$	2.67376	0.119336
$503$	24.6180	1.09766	0.548832	−	0.835933i	$-0.315073\pi$
$503$	24.6180	1.09766	0.548832	+	0.835933i	$0.315073\pi$
$504$	−3.23607	−0.144146
$505$	−14.8541	−0.660999
$506$	0	0
$507$	12.6180	0.560387
$508$	13.7082	0.608203
$509$	24.5066	1.08623	0.543117	−	0.839657i	$-0.317244\pi$
$509$	24.5066	1.08623	0.543117	+	0.839657i	$0.317244\pi$
$510$	−2.85410	−0.126382
$511$	14.4721	0.640210
$512$	1.00000	0.0441942
$513$	−5.23607	−0.231178
$514$	3.52786	0.155607
$515$	10.7639	0.474316
$516$	0.854102	0.0375997
$517$	0	0
$518$	2.76393	0.121440
$519$	8.00000	0.351161
$520$	0.618034	0.0271026
$521$	43.3050	1.89722	0.948612	−	0.316441i	$-0.102488\pi$
$521$	43.3050	1.89722	0.948612	+	0.316441i	$0.102488\pi$
$522$	−5.09017	−0.222791
$523$	9.88854	0.432396	0.216198	−	0.976350i	$-0.430634\pi$
$523$	9.88854	0.432396	0.216198	+	0.976350i	$0.430634\pi$
$524$	20.6180	0.900703
$525$	3.23607	0.141234
$526$	−0.562306	−0.0245177
$527$	−11.0000	−0.479168
$528$	0	0
$529$	−9.90983	−0.430862
$530$	−0.472136	−0.0205083
$531$	6.85410	0.297443
$532$	−16.9443	−0.734627
$533$	−7.23607	−0.313429
$534$	7.70820	0.333567
$535$	5.70820	0.246787
$536$	6.32624	0.273252
$537$	20.0344	0.864550
$538$	10.3262	0.445196
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	39.2361	1.68689	0.843445	−	0.537215i	$-0.180524\pi$
$541$	39.2361	1.68689	0.843445	+	0.537215i	$0.180524\pi$
$542$	17.7984	0.764506
$543$	−1.52786	−0.0655669
$544$	2.85410	0.122369
$545$	8.94427	0.383131
$546$	2.00000	0.0855921
$547$	−3.85410	−0.164790	−0.0823948	−	0.996600i	$-0.526257\pi$
$547$	−3.85410	−0.164790	−0.0823948	+	0.996600i	$0.526257\pi$
$548$	9.38197	0.400778
$549$	10.4721	0.446940
$550$	0	0
$551$	−26.6525	−1.13543
$552$	−3.61803	−0.153994
$553$	−34.1803	−1.45350
$554$	−2.96556	−0.125994
$555$	0.854102	0.0362546
$556$	−10.6525	−0.451766
$557$	−19.1246	−0.810336	−0.405168	−	0.914242i	$-0.632787\pi$
$557$	−19.1246	−0.810336	−0.405168	+	0.914242i	$0.632787\pi$
$558$	−3.85410	−0.163157
$559$	−0.527864	−0.0223263
$560$	−3.23607	−0.136749
$561$	0	0
$562$	11.8885	0.501488
$563$	−6.36068	−0.268071	−0.134035	−	0.990977i	$-0.542794\pi$
$563$	−6.36068	−0.268071	−0.134035	+	0.990977i	$0.542794\pi$
$564$	−11.3820	−0.479267
$565$	8.14590	0.342701
$566$	−26.0344	−1.09431
$567$	−3.23607	−0.135902
$568$	11.4164	0.479022
$569$	19.3050	0.809306	0.404653	−	0.914470i	$-0.367392\pi$
$569$	19.3050	0.809306	0.404653	+	0.914470i	$0.367392\pi$
$570$	−5.23607	−0.219315
$571$	12.0000	0.502184	0.251092	−	0.967963i	$-0.419210\pi$
$571$	12.0000	0.502184	0.251092	+	0.967963i	$0.419210\pi$
$572$	0	0
$573$	−12.2918	−0.513497
$574$	37.8885	1.58144
$575$	3.61803	0.150882
$576$	1.00000	0.0416667
$577$	−17.4164	−0.725055	−0.362527	−	0.931973i	$-0.618086\pi$
$577$	−17.4164	−0.725055	−0.362527	+	0.931973i	$0.618086\pi$
$578$	−8.85410	−0.368282
$579$	8.94427	0.371711
$580$	−5.09017	−0.211358
$581$	−33.8885	−1.40593
$582$	−17.7082	−0.734029
$583$	0	0
$584$	−4.47214	−0.185058
$585$	0.618034	0.0255526
$586$	24.9443	1.03044
$587$	−44.5410	−1.83840	−0.919202	−	0.393786i	$-0.871165\pi$
$587$	−44.5410	−1.83840	−0.919202	+	0.393786i	$0.871165\pi$
$588$	−3.47214	−0.143188
$589$	−20.1803	−0.831516
$590$	6.85410	0.282179
$591$	22.0000	0.904959
$592$	−0.854102	−0.0351034
$593$	−10.0344	−0.412065	−0.206033	−	0.978545i	$-0.566055\pi$
$593$	−10.0344	−0.412065	−0.206033	+	0.978545i	$0.566055\pi$
$594$	0	0
$595$	−9.23607	−0.378642
$596$	−1.14590	−0.0469378
$597$	24.2705	0.993326
$598$	2.23607	0.0914396
$599$	0.652476	0.0266594	0.0133297	−	0.999911i	$-0.495757\pi$
$599$	0.652476	0.0266594	0.0133297	+	0.999911i	$0.495757\pi$
$600$	−1.00000	−0.0408248
$601$	25.7771	1.05147	0.525735	−	0.850649i	$-0.323790\pi$
$601$	25.7771	1.05147	0.525735	+	0.850649i	$0.323790\pi$
$602$	2.76393	0.112649
$603$	6.32624	0.257624
$604$	−12.9443	−0.526695
$605$	0	0
$606$	14.8541	0.603407
$607$	−33.7771	−1.37097	−0.685485	−	0.728087i	$-0.740410\pi$
$607$	−33.7771	−1.37097	−0.685485	+	0.728087i	$0.740410\pi$
$608$	5.23607	0.212351
$609$	−16.4721	−0.667485
$610$	10.4721	0.424004
$611$	7.03444	0.284583
$612$	2.85410	0.115370
$613$	30.9443	1.24983	0.624914	−	0.780694i	$-0.285134\pi$
$613$	30.9443	1.24983	0.624914	+	0.780694i	$0.285134\pi$
$614$	−6.90983	−0.278858
$615$	11.7082	0.472120
$616$	0	0
$617$	22.3607	0.900207	0.450104	−	0.892976i	$-0.351387\pi$
$617$	22.3607	0.900207	0.450104	+	0.892976i	$0.351387\pi$
$618$	−10.7639	−0.432989
$619$	−41.8885	−1.68364	−0.841821	−	0.539756i	$-0.818516\pi$
$619$	−41.8885	−1.68364	−0.841821	+	0.539756i	$0.818516\pi$
$620$	−3.85410	−0.154784
$621$	−3.61803	−0.145187
$622$	18.1803	0.728965
$623$	24.9443	0.999371
$624$	−0.618034	−0.0247412
$625$	1.00000	0.0400000
$626$	−28.8328	−1.15239
$627$	0	0
$628$	−3.38197	−0.134955
$629$	−2.43769	−0.0971972
$630$	−3.23607	−0.128928
$631$	−22.9787	−0.914768	−0.457384	−	0.889269i	$-0.651214\pi$
$631$	−22.9787	−0.914768	−0.457384	+	0.889269i	$0.651214\pi$
$632$	10.5623	0.420146
$633$	−15.7082	−0.624345
$634$	8.58359	0.340898
$635$	13.7082	0.543993
$636$	0.472136	0.0187214
$637$	2.14590	0.0850236
$638$	0	0
$639$	11.4164	0.451626
$640$	1.00000	0.0395285
$641$	−3.23607	−0.127817	−0.0639085	−	0.997956i	$-0.520357\pi$
$641$	−3.23607	−0.127817	−0.0639085	+	0.997956i	$0.520357\pi$
$642$	−5.70820	−0.225285
$643$	−14.3262	−0.564972	−0.282486	−	0.959271i	$-0.591159\pi$
$643$	−14.3262	−0.564972	−0.282486	+	0.959271i	$0.591159\pi$
$644$	−11.7082	−0.461368
$645$	0.854102	0.0336302
$646$	14.9443	0.587975
$647$	−11.0344	−0.433809	−0.216904	−	0.976193i	$-0.569596\pi$
$647$	−11.0344	−0.433809	−0.216904	+	0.976193i	$0.569596\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	0.618034	0.0242413
$651$	−12.4721	−0.488822
$652$	17.7984	0.697038
$653$	−29.7082	−1.16257	−0.581286	−	0.813699i	$-0.697450\pi$
$653$	−29.7082	−1.16257	−0.581286	+	0.813699i	$0.697450\pi$
$654$	−8.94427	−0.349749
$655$	20.6180	0.805613
$656$	−11.7082	−0.457129
$657$	−4.47214	−0.174475
$658$	−36.8328	−1.43589
$659$	0.583592	0.0227335	0.0113668	−	0.999935i	$-0.496382\pi$
$659$	0.583592	0.0227335	0.0113668	+	0.999935i	$0.496382\pi$
$660$	0	0
$661$	23.4164	0.910793	0.455396	−	0.890289i	$-0.349498\pi$
$661$	23.4164	0.910793	0.455396	+	0.890289i	$0.349498\pi$
$662$	−32.0689	−1.24639
$663$	−1.76393	−0.0685054
$664$	10.4721	0.406398
$665$	−16.9443	−0.657071
$666$	−0.854102	−0.0330958
$667$	−18.4164	−0.713086
$668$	−4.32624	−0.167387
$669$	−21.1246	−0.816725
$670$	6.32624	0.244404
$671$	0	0
$672$	3.23607	0.124834
$673$	−22.7639	−0.877485	−0.438743	−	0.898613i	$-0.644576\pi$
$673$	−22.7639	−0.877485	−0.438743	+	0.898613i	$0.644576\pi$
$674$	−24.7639	−0.953871
$675$	−1.00000	−0.0384900
$676$	−12.6180	−0.485309
$677$	−11.2361	−0.431837	−0.215919	−	0.976411i	$-0.569275\pi$
$677$	−11.2361	−0.431837	−0.215919	+	0.976411i	$0.569275\pi$
$678$	−8.14590	−0.312841
$679$	−57.3050	−2.19916
$680$	2.85410	0.109450
$681$	21.8885	0.838771
$682$	0	0
$683$	0.763932	0.0292310	0.0146155	−	0.999893i	$-0.495348\pi$
$683$	0.763932	0.0292310	0.0146155	+	0.999893i	$0.495348\pi$
$684$	5.23607	0.200206
$685$	9.38197	0.358466
$686$	11.4164	0.435880
$687$	−25.1246	−0.958564
$688$	−0.854102	−0.0325623
$689$	−0.291796	−0.0111165
$690$	−3.61803	−0.137736
$691$	11.1246	0.423200	0.211600	−	0.977356i	$-0.432133\pi$
$691$	11.1246	0.423200	0.211600	+	0.977356i	$0.432133\pi$
$692$	−8.00000	−0.304114
$693$	0	0
$694$	−2.58359	−0.0980718
$695$	−10.6525	−0.404071
$696$	5.09017	0.192942
$697$	−33.4164	−1.26574
$698$	−28.0000	−1.05982
$699$	−22.9787	−0.869135
$700$	−3.23607	−0.122312
$701$	−19.5279	−0.737557	−0.368779	−	0.929517i	$-0.620224\pi$
$701$	−19.5279	−0.737557	−0.368779	+	0.929517i	$0.620224\pi$
$702$	−0.618034	−0.0233262
$703$	−4.47214	−0.168670
$704$	0	0
$705$	−11.3820	−0.428670
$706$	12.3820	0.466001
$707$	48.0689	1.80782
$708$	−6.85410	−0.257593
$709$	−21.0557	−0.790764	−0.395382	−	0.918517i	$-0.629388\pi$
$709$	−21.0557	−0.790764	−0.395382	+	0.918517i	$0.629388\pi$
$710$	11.4164	0.428450
$711$	10.5623	0.396117
$712$	−7.70820	−0.288877
$713$	−13.9443	−0.522217
$714$	9.23607	0.345651
$715$	0	0
$716$	−20.0344	−0.748722
$717$	14.2918	0.533737
$718$	12.1803	0.454566
$719$	−9.81966	−0.366212	−0.183106	−	0.983093i	$-0.558615\pi$
$719$	−9.81966	−0.366212	−0.183106	+	0.983093i	$0.558615\pi$
$720$	1.00000	0.0372678
$721$	−34.8328	−1.29724
$722$	8.41641	0.313226
$723$	14.9443	0.555783
$724$	1.52786	0.0567826
$725$	−5.09017	−0.189044
$726$	0	0
$727$	40.0689	1.48607	0.743036	−	0.669251i	$-0.233385\pi$
$727$	40.0689	1.48607	0.743036	+	0.669251i	$0.233385\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	−4.47214	−0.165521
$731$	−2.43769	−0.0901614
$732$	−10.4721	−0.387061
$733$	−13.7984	−0.509655	−0.254827	−	0.966987i	$-0.582019\pi$
$733$	−13.7984	−0.509655	−0.254827	+	0.966987i	$0.582019\pi$
$734$	8.29180	0.306056
$735$	−3.47214	−0.128072
$736$	3.61803	0.133363
$737$	0	0
$738$	−11.7082	−0.430985
$739$	−14.2918	−0.525732	−0.262866	−	0.964832i	$-0.584668\pi$
$739$	−14.2918	−0.525732	−0.262866	+	0.964832i	$0.584668\pi$
$740$	−0.854102	−0.0313974
$741$	−3.23607	−0.118880
$742$	1.52786	0.0560897
$743$	17.8541	0.655003	0.327502	−	0.944851i	$-0.393793\pi$
$743$	17.8541	0.655003	0.327502	+	0.944851i	$0.393793\pi$
$744$	3.85410	0.141298
$745$	−1.14590	−0.0419825
$746$	−9.41641	−0.344759
$747$	10.4721	0.383155
$748$	0	0
$749$	−18.4721	−0.674957
$750$	−1.00000	−0.0365148
$751$	−7.72949	−0.282053	−0.141027	−	0.990006i	$-0.545040\pi$
$751$	−7.72949	−0.282053	−0.141027	+	0.990006i	$0.545040\pi$
$752$	11.3820	0.415058
$753$	−2.67376	−0.0974373
$754$	−3.14590	−0.114567
$755$	−12.9443	−0.471090
$756$	3.23607	0.117695
$757$	40.0344	1.45508	0.727538	−	0.686067i	$-0.240664\pi$
$757$	40.0344	1.45508	0.727538	+	0.686067i	$0.240664\pi$
$758$	−23.4164	−0.850522
$759$	0	0
$760$	5.23607	0.189932
$761$	44.4721	1.61211	0.806057	−	0.591838i	$-0.201598\pi$
$761$	44.4721	1.61211	0.806057	+	0.591838i	$0.201598\pi$
$762$	−13.7082	−0.496596
$763$	−28.9443	−1.04785
$764$	12.2918	0.444702
$765$	2.85410	0.103190
$766$	4.32624	0.156313
$767$	4.23607	0.152956
$768$	−1.00000	−0.0360844
$769$	16.4508	0.593233	0.296616	−	0.954997i	$-0.404142\pi$
$769$	16.4508	0.593233	0.296616	+	0.954997i	$0.404142\pi$
$770$	0	0
$771$	−3.52786	−0.127053
$772$	−8.94427	−0.321911
$773$	−17.7082	−0.636920	−0.318460	−	0.947936i	$-0.603166\pi$
$773$	−17.7082	−0.636920	−0.318460	+	0.947936i	$0.603166\pi$
$774$	−0.854102	−0.0307001
$775$	−3.85410	−0.138443
$776$	17.7082	0.635687
$777$	−2.76393	−0.0991555
$778$	4.56231	0.163567
$779$	−61.3050	−2.19648
$780$	−0.618034	−0.0221292
$781$	0	0
$782$	10.3262	0.369266
$783$	5.09017	0.181908
$784$	3.47214	0.124005
$785$	−3.38197	−0.120708
$786$	−20.6180	−0.735421
$787$	7.68692	0.274009	0.137005	−	0.990570i	$-0.456253\pi$
$787$	7.68692	0.274009	0.137005	+	0.990570i	$0.456253\pi$
$788$	−22.0000	−0.783718
$789$	0.562306	0.0200186
$790$	10.5623	0.375790
$791$	−26.3607	−0.937278
$792$	0	0
$793$	6.47214	0.229832
$794$	32.4508	1.15164
$795$	0.472136	0.0167449
$796$	−24.2705	−0.860245
$797$	10.8754	0.385226	0.192613	−	0.981275i	$-0.438304\pi$
$797$	10.8754	0.385226	0.192613	+	0.981275i	$0.438304\pi$
$798$	16.9443	0.599821
$799$	32.4853	1.14925
$800$	1.00000	0.0353553
$801$	−7.70820	−0.272356
$802$	17.1246	0.604691
$803$	0	0
$804$	−6.32624	−0.223109
$805$	−11.7082	−0.412660
$806$	−2.38197	−0.0839012
$807$	−10.3262	−0.363501
$808$	−14.8541	−0.522565
$809$	−46.4296	−1.63238	−0.816188	−	0.577786i	$-0.803917\pi$
$809$	−46.4296	−1.63238	−0.816188	+	0.577786i	$0.803917\pi$
$810$	1.00000	0.0351364
$811$	37.8885	1.33045	0.665223	−	0.746644i	$-0.268336\pi$
$811$	37.8885	1.33045	0.665223	+	0.746644i	$0.268336\pi$
$812$	16.4721	0.578059
$813$	−17.7984	−0.624216
$814$	0	0
$815$	17.7984	0.623450
$816$	−2.85410	−0.0999136
$817$	−4.47214	−0.156460
$818$	−30.1459	−1.05403
$819$	−2.00000	−0.0698857
$820$	−11.7082	−0.408868
$821$	−27.3050	−0.952949	−0.476475	−	0.879188i	$-0.658086\pi$
$821$	−27.3050	−0.952949	−0.476475	+	0.879188i	$0.658086\pi$
$822$	−9.38197	−0.327234
$823$	−49.1246	−1.71238	−0.856188	−	0.516664i	$-0.827174\pi$
$823$	−49.1246	−1.71238	−0.856188	+	0.516664i	$0.827174\pi$
$824$	10.7639	0.374979
$825$	0	0
$826$	−22.1803	−0.771753
$827$	11.8197	0.411010	0.205505	−	0.978656i	$-0.434116\pi$
$827$	11.8197	0.411010	0.205505	+	0.978656i	$0.434116\pi$
$828$	3.61803	0.125735
$829$	36.5410	1.26912	0.634561	−	0.772873i	$-0.281181\pi$
$829$	36.5410	1.26912	0.634561	+	0.772873i	$0.281181\pi$
$830$	10.4721	0.363493
$831$	2.96556	0.102874
$832$	0.618034	0.0214265
$833$	9.90983	0.343355
$834$	10.6525	0.368865
$835$	−4.32624	−0.149716
$836$	0	0
$837$	3.85410	0.133217
$838$	−24.7426	−0.854721
$839$	30.1803	1.04194	0.520971	−	0.853575i	$-0.325570\pi$
$839$	30.1803	1.04194	0.520971	+	0.853575i	$0.325570\pi$
$840$	3.23607	0.111655
$841$	−3.09017	−0.106558
$842$	4.00000	0.137849
$843$	−11.8885	−0.409463
$844$	15.7082	0.540699
$845$	−12.6180	−0.434074
$846$	11.3820	0.391320
$847$	0	0
$848$	−0.472136	−0.0162132
$849$	26.0344	0.893500
$850$	2.85410	0.0978949
$851$	−3.09017	−0.105930
$852$	−11.4164	−0.391120
$853$	−28.4721	−0.974867	−0.487434	−	0.873160i	$-0.662067\pi$
$853$	−28.4721	−0.974867	−0.487434	+	0.873160i	$0.662067\pi$
$854$	−33.8885	−1.15964
$855$	5.23607	0.179070
$856$	5.70820	0.195102
$857$	−2.67376	−0.0913340	−0.0456670	−	0.998957i	$-0.514541\pi$
$857$	−2.67376	−0.0913340	−0.0456670	+	0.998957i	$0.514541\pi$
$858$	0	0
$859$	−36.0689	−1.23065	−0.615327	−	0.788272i	$-0.710976\pi$
$859$	−36.0689	−1.23065	−0.615327	+	0.788272i	$0.710976\pi$
$860$	−0.854102	−0.0291246
$861$	−37.8885	−1.29124
$862$	−28.4721	−0.969765
$863$	49.8673	1.69750	0.848751	−	0.528793i	$-0.177355\pi$
$863$	49.8673	1.69750	0.848751	+	0.528793i	$0.177355\pi$
$864$	−1.00000	−0.0340207
$865$	−8.00000	−0.272008
$866$	−0.583592	−0.0198313
$867$	8.85410	0.300701
$868$	12.4721	0.423332
$869$	0	0
$870$	5.09017	0.172573
$871$	3.90983	0.132480
$872$	8.94427	0.302891
$873$	17.7082	0.599332
$874$	18.9443	0.640800
$875$	−3.23607	−0.109399
$876$	4.47214	0.151099
$877$	−9.21478	−0.311161	−0.155581	−	0.987823i	$-0.549725\pi$
$877$	−9.21478	−0.311161	−0.155581	+	0.987823i	$0.549725\pi$
$878$	−26.9787	−0.910487
$879$	−24.9443	−0.841349
$880$	0	0
$881$	17.3050	0.583019	0.291509	−	0.956568i	$-0.405843\pi$
$881$	17.3050	0.583019	0.291509	+	0.956568i	$0.405843\pi$
$882$	3.47214	0.116913
$883$	9.21478	0.310102	0.155051	−	0.987906i	$-0.450446\pi$
$883$	9.21478	0.310102	0.155051	+	0.987906i	$0.450446\pi$
$884$	1.76393	0.0593275
$885$	−6.85410	−0.230398
$886$	−29.1246	−0.978460
$887$	45.6869	1.53402	0.767008	−	0.641637i	$-0.221744\pi$
$887$	45.6869	1.53402	0.767008	+	0.641637i	$0.221744\pi$
$888$	0.854102	0.0286618
$889$	−44.3607	−1.48781
$890$	−7.70820	−0.258380
$891$	0	0
$892$	21.1246	0.707304
$893$	59.5967	1.99433
$894$	1.14590	0.0383246
$895$	−20.0344	−0.669678
$896$	−3.23607	−0.108109
$897$	−2.23607	−0.0746601
$898$	−19.1246	−0.638197
$899$	19.6180	0.654298
$900$	1.00000	0.0333333
$901$	−1.34752	−0.0448925
$902$	0	0
$903$	−2.76393	−0.0919779
$904$	8.14590	0.270929
$905$	1.52786	0.0507879
$906$	12.9443	0.430045
$907$	−43.5066	−1.44461	−0.722306	−	0.691573i	$-0.756918\pi$
$907$	−43.5066	−1.44461	−0.722306	+	0.691573i	$0.756918\pi$
$908$	−21.8885	−0.726397
$909$	−14.8541	−0.492679
$910$	−2.00000	−0.0662994
$911$	−58.3607	−1.93358	−0.966788	−	0.255580i	$-0.917733\pi$
$911$	−58.3607	−1.93358	−0.966788	+	0.255580i	$0.917733\pi$
$912$	−5.23607	−0.173384
$913$	0	0
$914$	−11.7082	−0.387273
$915$	−10.4721	−0.346198
$916$	25.1246	0.830141
$917$	−66.7214	−2.20333
$918$	−2.85410	−0.0941994
$919$	−10.2016	−0.336521	−0.168260	−	0.985743i	$-0.553815\pi$
$919$	−10.2016	−0.336521	−0.168260	+	0.985743i	$0.553815\pi$
$920$	3.61803	0.119283
$921$	6.90983	0.227687
$922$	−14.0902	−0.464035
$923$	7.05573	0.232242
$924$	0	0
$925$	−0.854102	−0.0280827
$926$	−18.0000	−0.591517
$927$	10.7639	0.353534
$928$	−5.09017	−0.167093
$929$	−10.4721	−0.343580	−0.171790	−	0.985134i	$-0.554955\pi$
$929$	−10.4721	−0.343580	−0.171790	+	0.985134i	$0.554955\pi$
$930$	3.85410	0.126381
$931$	18.1803	0.595837
$932$	22.9787	0.752693
$933$	−18.1803	−0.595198
$934$	41.7082	1.36473
$935$	0	0
$936$	0.618034	0.0202011
$937$	−19.0132	−0.621133	−0.310566	−	0.950552i	$-0.600519\pi$
$937$	−19.0132	−0.621133	−0.310566	+	0.950552i	$0.600519\pi$
$938$	−20.4721	−0.668439
$939$	28.8328	0.940923
$940$	11.3820	0.371239
$941$	17.1591	0.559369	0.279685	−	0.960092i	$-0.409770\pi$
$941$	17.1591	0.559369	0.279685	+	0.960092i	$0.409770\pi$
$942$	3.38197	0.110190
$943$	−42.3607	−1.37945
$944$	6.85410	0.223082
$945$	3.23607	0.105269
$946$	0	0
$947$	−33.8885	−1.10123	−0.550615	−	0.834759i	$-0.685607\pi$
$947$	−33.8885	−1.10123	−0.550615	+	0.834759i	$0.685607\pi$
$948$	−10.5623	−0.343048
$949$	−2.76393	−0.0897210
$950$	5.23607	0.169880
$951$	−8.58359	−0.278342
$952$	−9.23607	−0.299343
$953$	18.6738	0.604902	0.302451	−	0.953165i	$-0.402195\pi$
$953$	18.6738	0.604902	0.302451	+	0.953165i	$0.402195\pi$
$954$	−0.472136	−0.0152860
$955$	12.2918	0.397753
$956$	−14.2918	−0.462230
$957$	0	0
$958$	−3.81966	−0.123408
$959$	−30.3607	−0.980397
$960$	−1.00000	−0.0322749
$961$	−16.1459	−0.520835
$962$	−0.527864	−0.0170190
$963$	5.70820	0.183944
$964$	−14.9443	−0.481323
$965$	−8.94427	−0.287926
$966$	11.7082	0.376705
$967$	35.7771	1.15051	0.575257	−	0.817973i	$-0.304902\pi$
$967$	35.7771	1.15051	0.575257	+	0.817973i	$0.304902\pi$
$968$	0	0
$969$	−14.9443	−0.480079
$970$	17.7082	0.568576
$971$	27.4164	0.879834	0.439917	−	0.898038i	$-0.355008\pi$
$971$	27.4164	0.879834	0.439917	+	0.898038i	$0.355008\pi$
$972$	−1.00000	−0.0320750
$973$	34.4721	1.10513
$974$	−18.4721	−0.591885
$975$	−0.618034	−0.0197929
$976$	10.4721	0.335205
$977$	54.9443	1.75782	0.878911	−	0.476985i	$-0.158270\pi$
$977$	54.9443	1.75782	0.878911	+	0.476985i	$0.158270\pi$
$978$	−17.7984	−0.569129
$979$	0	0
$980$	3.47214	0.110913
$981$	8.94427	0.285569
$982$	23.0902	0.736837
$983$	38.2492	1.21996	0.609980	−	0.792417i	$-0.291177\pi$
$983$	38.2492	1.21996	0.609980	+	0.792417i	$0.291177\pi$
$984$	11.7082	0.373244
$985$	−22.0000	−0.700978
$986$	−14.5279	−0.462661
$987$	36.8328	1.17240
$988$	3.23607	0.102953
$989$	−3.09017	−0.0982617
$990$	0	0
$991$	−38.3394	−1.21789	−0.608945	−	0.793212i	$-0.708407\pi$
$991$	−38.3394	−1.21789	−0.608945	+	0.793212i	$0.708407\pi$
$992$	−3.85410	−0.122368
$993$	32.0689	1.01768
$994$	−36.9443	−1.17180
$995$	−24.2705	−0.769427
$996$	−10.4721	−0.331822
$997$	27.5066	0.871142	0.435571	−	0.900154i	$-0.356546\pi$
$997$	27.5066	0.871142	0.435571	+	0.900154i	$0.356546\pi$
$998$	3.88854	0.123090
$999$	0.854102	0.0270226

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bm.1.1		2
11.2	odd	10		330.2.m.c.301.1	yes	4
11.6	odd	10		330.2.m.c.91.1	✓	4
11.10	odd	2		3630.2.a.be.1.2		2
33.2	even	10		990.2.n.d.631.1		4
33.17	even	10		990.2.n.d.91.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.c.91.1	✓	4	11.6	odd	10
330.2.m.c.301.1	yes	4	11.2	odd	10
990.2.n.d.91.1		4	33.17	even	10
990.2.n.d.631.1		4	33.2	even	10
3630.2.a.be.1.2		2	11.10	odd	2
3630.2.a.bm.1.1		2	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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +0.618034 q^{13} -3.23607 q^{14} -1.00000 q^{15} +1.00000 q^{16} +2.85410 q^{17} +1.00000 q^{18} +5.23607 q^{19} +1.00000 q^{20} +3.23607 q^{21} +3.61803 q^{23} -1.00000 q^{24} +1.00000 q^{25} +0.618034 q^{26} -1.00000 q^{27} -3.23607 q^{28} -5.09017 q^{29} -1.00000 q^{30} -3.85410 q^{31} +1.00000 q^{32} +2.85410 q^{34} -3.23607 q^{35} +1.00000 q^{36} -0.854102 q^{37} +5.23607 q^{38} -0.618034 q^{39} +1.00000 q^{40} -11.7082 q^{41} +3.23607 q^{42} -0.854102 q^{43} +1.00000 q^{45} +3.61803 q^{46} +11.3820 q^{47} -1.00000 q^{48} +3.47214 q^{49} +1.00000 q^{50} -2.85410 q^{51} +0.618034 q^{52} -0.472136 q^{53} -1.00000 q^{54} -3.23607 q^{56} -5.23607 q^{57} -5.09017 q^{58} +6.85410 q^{59} -1.00000 q^{60} +10.4721 q^{61} -3.85410 q^{62} -3.23607 q^{63} +1.00000 q^{64} +0.618034 q^{65} +6.32624 q^{67} +2.85410 q^{68} -3.61803 q^{69} -3.23607 q^{70} +11.4164 q^{71} +1.00000 q^{72} -4.47214 q^{73} -0.854102 q^{74} -1.00000 q^{75} +5.23607 q^{76} -0.618034 q^{78} +10.5623 q^{79} +1.00000 q^{80} +1.00000 q^{81} -11.7082 q^{82} +10.4721 q^{83} +3.23607 q^{84} +2.85410 q^{85} -0.854102 q^{86} +5.09017 q^{87} -7.70820 q^{89} +1.00000 q^{90} -2.00000 q^{91} +3.61803 q^{92} +3.85410 q^{93} +11.3820 q^{94} +5.23607 q^{95} -1.00000 q^{96} +17.7082 q^{97} +3.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - q^{13} - 2 q^{14} - 2 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} + 6 q^{19} + 2 q^{20} + 2 q^{21} + 5 q^{23} - 2 q^{24} + 2 q^{25} - q^{26} - 2 q^{27} - 2 q^{28} + q^{29} - 2 q^{30} - q^{31} + 2 q^{32} - q^{34} - 2 q^{35} + 2 q^{36} + 5 q^{37} + 6 q^{38} + q^{39} + 2 q^{40} - 10 q^{41} + 2 q^{42} + 5 q^{43} + 2 q^{45} + 5 q^{46} + 25 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + q^{51} - q^{52} + 8 q^{53} - 2 q^{54} - 2 q^{56} - 6 q^{57} + q^{58} + 7 q^{59} - 2 q^{60} + 12 q^{61} - q^{62} - 2 q^{63} + 2 q^{64} - q^{65} - 3 q^{67} - q^{68} - 5 q^{69} - 2 q^{70} - 4 q^{71} + 2 q^{72} + 5 q^{74} - 2 q^{75} + 6 q^{76} + q^{78} + q^{79} + 2 q^{80} + 2 q^{81} - 10 q^{82} + 12 q^{83} + 2 q^{84} - q^{85} + 5 q^{86} - q^{87} - 2 q^{89} + 2 q^{90} - 4 q^{91} + 5 q^{92} + q^{93} + 25 q^{94} + 6 q^{95} - 2 q^{96} + 22 q^{97} - 2 q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - q^13 - 2 * q^14 - 2 * q^15 + 2 * q^16 - q^17 + 2 * q^18 + 6 * q^19 + 2 * q^20 + 2 * q^21 + 5 * q^23 - 2 * q^24 + 2 * q^25 - q^26 - 2 * q^27 - 2 * q^28 + q^29 - 2 * q^30 - q^31 + 2 * q^32 - q^34 - 2 * q^35 + 2 * q^36 + 5 * q^37 + 6 * q^38 + q^39 + 2 * q^40 - 10 * q^41 + 2 * q^42 + 5 * q^43 + 2 * q^45 + 5 * q^46 + 25 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + q^51 - q^52 + 8 * q^53 - 2 * q^54 - 2 * q^56 - 6 * q^57 + q^58 + 7 * q^59 - 2 * q^60 + 12 * q^61 - q^62 - 2 * q^63 + 2 * q^64 - q^65 - 3 * q^67 - q^68 - 5 * q^69 - 2 * q^70 - 4 * q^71 + 2 * q^72 + 5 * q^74 - 2 * q^75 + 6 * q^76 + q^78 + q^79 + 2 * q^80 + 2 * q^81 - 10 * q^82 + 12 * q^83 + 2 * q^84 - q^85 + 5 * q^86 - q^87 - 2 * q^89 + 2 * q^90 - 4 * q^91 + 5 * q^92 + q^93 + 25 * q^94 + 6 * q^95 - 2 * q^96 + 22 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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