LMFDB - Embedded newform 3630.2.a.bc.1.2

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:	$1$
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:	$\Z[a_1, \ldots, a_{7}]$
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			1.2
Root			$-0.618034$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +0.618034 q^{13} -3.61803 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.47214 q^{17} -1.00000 q^{18} -0.618034 q^{19} -1.00000 q^{20} -3.61803 q^{21} +4.85410 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.618034 q^{26} -1.00000 q^{27} +3.61803 q^{28} +3.70820 q^{29} -1.00000 q^{30} -9.23607 q^{31} -1.00000 q^{32} +6.47214 q^{34} -3.61803 q^{35} +1.00000 q^{36} -0.618034 q^{37} +0.618034 q^{38} -0.618034 q^{39} +1.00000 q^{40} -9.32624 q^{41} +3.61803 q^{42} +0.763932 q^{43} -1.00000 q^{45} -4.85410 q^{46} -2.61803 q^{47} -1.00000 q^{48} +6.09017 q^{49} -1.00000 q^{50} +6.47214 q^{51} +0.618034 q^{52} -6.09017 q^{53} +1.00000 q^{54} -3.61803 q^{56} +0.618034 q^{57} -3.70820 q^{58} -14.6180 q^{59} +1.00000 q^{60} +11.2361 q^{61} +9.23607 q^{62} +3.61803 q^{63} +1.00000 q^{64} -0.618034 q^{65} -8.18034 q^{67} -6.47214 q^{68} -4.85410 q^{69} +3.61803 q^{70} -0.291796 q^{71} -1.00000 q^{72} +10.9443 q^{73} +0.618034 q^{74} -1.00000 q^{75} -0.618034 q^{76} +0.618034 q^{78} -4.47214 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.32624 q^{82} -4.94427 q^{83} -3.61803 q^{84} +6.47214 q^{85} -0.763932 q^{86} -3.70820 q^{87} -5.14590 q^{89} +1.00000 q^{90} +2.23607 q^{91} +4.85410 q^{92} +9.23607 q^{93} +2.61803 q^{94} +0.618034 q^{95} +1.00000 q^{96} +14.9443 q^{97} -6.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 5 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 + 5 * 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} + 5 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - q^{13} - 5 q^{14} + 2 q^{15} + 2 q^{16} - 4 q^{17} - 2 q^{18} + q^{19} - 2 q^{20} - 5 q^{21} + 3 q^{23} + 2 q^{24} + 2 q^{25} + q^{26} - 2 q^{27} + 5 q^{28} - 6 q^{29} - 2 q^{30} - 14 q^{31} - 2 q^{32} + 4 q^{34} - 5 q^{35} + 2 q^{36} + q^{37} - q^{38} + q^{39} + 2 q^{40} - 3 q^{41} + 5 q^{42} + 6 q^{43} - 2 q^{45} - 3 q^{46} - 3 q^{47} - 2 q^{48} + q^{49} - 2 q^{50} + 4 q^{51} - q^{52} - q^{53} + 2 q^{54} - 5 q^{56} - q^{57} + 6 q^{58} - 27 q^{59} + 2 q^{60} + 18 q^{61} + 14 q^{62} + 5 q^{63} + 2 q^{64} + q^{65} + 6 q^{67} - 4 q^{68} - 3 q^{69} + 5 q^{70} - 14 q^{71} - 2 q^{72} + 4 q^{73} - q^{74} - 2 q^{75} + q^{76} - q^{78} - 2 q^{80} + 2 q^{81} + 3 q^{82} + 8 q^{83} - 5 q^{84} + 4 q^{85} - 6 q^{86} + 6 q^{87} - 17 q^{89} + 2 q^{90} + 3 q^{92} + 14 q^{93} + 3 q^{94} - q^{95} + 2 q^{96} + 12 q^{97} - q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - q^13 - 5 * q^14 + 2 * q^15 + 2 * q^16 - 4 * q^17 - 2 * q^18 + q^19 - 2 * q^20 - 5 * q^21 + 3 * q^23 + 2 * q^24 + 2 * q^25 + q^26 - 2 * q^27 + 5 * q^28 - 6 * q^29 - 2 * q^30 - 14 * q^31 - 2 * q^32 + 4 * q^34 - 5 * q^35 + 2 * q^36 + q^37 - q^38 + q^39 + 2 * q^40 - 3 * q^41 + 5 * q^42 + 6 * q^43 - 2 * q^45 - 3 * q^46 - 3 * q^47 - 2 * q^48 + q^49 - 2 * q^50 + 4 * q^51 - q^52 - q^53 + 2 * q^54 - 5 * q^56 - q^57 + 6 * q^58 - 27 * q^59 + 2 * q^60 + 18 * q^61 + 14 * q^62 + 5 * q^63 + 2 * q^64 + q^65 + 6 * q^67 - 4 * q^68 - 3 * q^69 + 5 * q^70 - 14 * q^71 - 2 * q^72 + 4 * q^73 - q^74 - 2 * q^75 + q^76 - q^78 - 2 * q^80 + 2 * q^81 + 3 * q^82 + 8 * q^83 - 5 * q^84 + 4 * q^85 - 6 * q^86 + 6 * q^87 - 17 * q^89 + 2 * q^90 + 3 * q^92 + 14 * q^93 + 3 * q^94 - q^95 + 2 * q^96 + 12 * q^97 - 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
$7$	3.61803	1.36749	0.683744	−	0.729722i	$-0.260350\pi$
$7$	3.61803	1.36749	0.683744	+	0.729722i	$0.260350\pi$
$8$	−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	$0.472685\pi$
$14$	−3.61803	−0.966960
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−6.47214	−1.56972	−0.784862	−	0.619671i	$-0.787266\pi$
$17$	−6.47214	−1.56972	−0.784862	+	0.619671i	$0.787266\pi$
$18$	−1.00000	−0.235702
$19$	−0.618034	−0.141787	−0.0708934	−	0.997484i	$-0.522585\pi$
$19$	−0.618034	−0.141787	−0.0708934	+	0.997484i	$0.522585\pi$
$20$	−1.00000	−0.223607
$21$	−3.61803	−0.789520
$22$	0	0
$23$	4.85410	1.01215	0.506075	−	0.862489i	$-0.331096\pi$
$23$	4.85410	1.01215	0.506075	+	0.862489i	$0.331096\pi$
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	−0.618034	−0.121206
$27$	−1.00000	−0.192450
$28$	3.61803	0.683744
$29$	3.70820	0.688596	0.344298	−	0.938860i	$-0.388117\pi$
$29$	3.70820	0.688596	0.344298	+	0.938860i	$0.388117\pi$
$30$	−1.00000	−0.182574
$31$	−9.23607	−1.65885	−0.829423	−	0.558620i	$-0.811331\pi$
$31$	−9.23607	−1.65885	−0.829423	+	0.558620i	$0.811331\pi$
$32$	−1.00000	−0.176777
$33$	0	0
$34$	6.47214	1.10996
$35$	−3.61803	−0.611559
$36$	1.00000	0.166667
$37$	−0.618034	−0.101604	−0.0508021	−	0.998709i	$-0.516178\pi$
$37$	−0.618034	−0.101604	−0.0508021	+	0.998709i	$0.516178\pi$
$38$	0.618034	0.100258
$39$	−0.618034	−0.0989646
$40$	1.00000	0.158114
$41$	−9.32624	−1.45651	−0.728257	−	0.685304i	$-0.759669\pi$
$41$	−9.32624	−1.45651	−0.728257	+	0.685304i	$0.759669\pi$
$42$	3.61803	0.558275
$43$	0.763932	0.116499	0.0582493	−	0.998302i	$-0.481448\pi$
$43$	0.763932	0.116499	0.0582493	+	0.998302i	$0.481448\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	−4.85410	−0.715698
$47$	−2.61803	−0.381880	−0.190940	−	0.981602i	$-0.561154\pi$
$47$	−2.61803	−0.381880	−0.190940	+	0.981602i	$0.561154\pi$
$48$	−1.00000	−0.144338
$49$	6.09017	0.870024
$50$	−1.00000	−0.141421
$51$	6.47214	0.906280
$52$	0.618034	0.0857059
$53$	−6.09017	−0.836549	−0.418275	−	0.908321i	$-0.637365\pi$
$53$	−6.09017	−0.836549	−0.418275	+	0.908321i	$0.637365\pi$
$54$	1.00000	0.136083
$55$	0	0
$56$	−3.61803	−0.483480
$57$	0.618034	0.0818606
$58$	−3.70820	−0.486911
$59$	−14.6180	−1.90311	−0.951553	−	0.307485i	$-0.900513\pi$
$59$	−14.6180	−1.90311	−0.951553	+	0.307485i	$0.900513\pi$
$60$	1.00000	0.129099
$61$	11.2361	1.43863	0.719316	−	0.694683i	$-0.244456\pi$
$61$	11.2361	1.43863	0.719316	+	0.694683i	$0.244456\pi$
$62$	9.23607	1.17298
$63$	3.61803	0.455829
$64$	1.00000	0.125000
$65$	−0.618034	−0.0766577
$66$	0	0
$67$	−8.18034	−0.999388	−0.499694	−	0.866202i	$-0.666554\pi$
$67$	−8.18034	−0.999388	−0.499694	+	0.866202i	$0.666554\pi$
$68$	−6.47214	−0.784862
$69$	−4.85410	−0.584365
$70$	3.61803	0.432438
$71$	−0.291796	−0.0346298	−0.0173149	−	0.999850i	$-0.505512\pi$
$71$	−0.291796	−0.0346298	−0.0173149	+	0.999850i	$0.505512\pi$
$72$	−1.00000	−0.117851
$73$	10.9443	1.28093	0.640465	−	0.767987i	$-0.278742\pi$
$73$	10.9443	1.28093	0.640465	+	0.767987i	$0.278742\pi$
$74$	0.618034	0.0718450
$75$	−1.00000	−0.115470
$76$	−0.618034	−0.0708934
$77$	0	0
$78$	0.618034	0.0699786
$79$	−4.47214	−0.503155	−0.251577	−	0.967837i	$-0.580949\pi$
$79$	−4.47214	−0.503155	−0.251577	+	0.967837i	$0.580949\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	9.32624	1.02991
$83$	−4.94427	−0.542704	−0.271352	−	0.962480i	$-0.587471\pi$
$83$	−4.94427	−0.542704	−0.271352	+	0.962480i	$0.587471\pi$
$84$	−3.61803	−0.394760
$85$	6.47214	0.702002
$86$	−0.763932	−0.0823769
$87$	−3.70820	−0.397561
$88$	0	0
$89$	−5.14590	−0.545464	−0.272732	−	0.962090i	$-0.587927\pi$
$89$	−5.14590	−0.545464	−0.272732	+	0.962090i	$0.587927\pi$
$90$	1.00000	0.105409
$91$	2.23607	0.234404
$92$	4.85410	0.506075
$93$	9.23607	0.957736
$94$	2.61803	0.270030
$95$	0.618034	0.0634089
$96$	1.00000	0.102062
$97$	14.9443	1.51736	0.758680	−	0.651463i	$-0.225844\pi$
$97$	14.9443	1.51736	0.758680	+	0.651463i	$0.225844\pi$
$98$	−6.09017	−0.615200
$99$	0	0
$100$	1.00000	0.100000
$101$	4.00000	0.398015	0.199007	−	0.979998i	$-0.436228\pi$
$101$	4.00000	0.398015	0.199007	+	0.979998i	$0.436228\pi$
$102$	−6.47214	−0.640837
$103$	−9.85410	−0.970954	−0.485477	−	0.874250i	$-0.661354\pi$
$103$	−9.85410	−0.970954	−0.485477	+	0.874250i	$0.661354\pi$
$104$	−0.618034	−0.0606032
$105$	3.61803	0.353084
$106$	6.09017	0.591530
$107$	17.8885	1.72935	0.864675	−	0.502331i	$-0.167524\pi$
$107$	17.8885	1.72935	0.864675	+	0.502331i	$0.167524\pi$
$108$	−1.00000	−0.0962250
$109$	4.00000	0.383131	0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000	0.383131	0.191565	+	0.981480i	$0.438644\pi$
$110$	0	0
$111$	0.618034	0.0586612
$112$	3.61803	0.341872
$113$	−12.4721	−1.17328	−0.586640	−	0.809848i	$-0.699550\pi$
$113$	−12.4721	−1.17328	−0.586640	+	0.809848i	$0.699550\pi$
$114$	−0.618034	−0.0578842
$115$	−4.85410	−0.452647
$116$	3.70820	0.344298
$117$	0.618034	0.0571373
$118$	14.6180	1.34570
$119$	−23.4164	−2.14658
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−11.2361	−1.01727
$123$	9.32624	0.840919
$124$	−9.23607	−0.829423
$125$	−1.00000	−0.0894427
$126$	−3.61803	−0.322320
$127$	12.6180	1.11967	0.559835	−	0.828604i	$-0.310865\pi$
$127$	12.6180	1.11967	0.559835	+	0.828604i	$0.310865\pi$
$128$	−1.00000	−0.0883883
$129$	−0.763932	−0.0672605
$130$	0.618034	0.0542052
$131$	20.9443	1.82991	0.914955	−	0.403556i	$-0.132226\pi$
$131$	20.9443	1.82991	0.914955	+	0.403556i	$0.132226\pi$
$132$	0	0
$133$	−2.23607	−0.193892
$134$	8.18034	0.706674
$135$	1.00000	0.0860663
$136$	6.47214	0.554981
$137$	15.4164	1.31711	0.658556	−	0.752531i	$-0.271167\pi$
$137$	15.4164	1.31711	0.658556	+	0.752531i	$0.271167\pi$
$138$	4.85410	0.413209
$139$	−7.61803	−0.646153	−0.323077	−	0.946373i	$-0.604717\pi$
$139$	−7.61803	−0.646153	−0.323077	+	0.946373i	$0.604717\pi$
$140$	−3.61803	−0.305780
$141$	2.61803	0.220478
$142$	0.291796	0.0244870
$143$	0	0
$144$	1.00000	0.0833333
$145$	−3.70820	−0.307950
$146$	−10.9443	−0.905754
$147$	−6.09017	−0.502309
$148$	−0.618034	−0.0508021
$149$	−8.94427	−0.732743	−0.366372	−	0.930469i	$-0.619400\pi$
$149$	−8.94427	−0.732743	−0.366372	+	0.930469i	$0.619400\pi$
$150$	1.00000	0.0816497
$151$	−12.4721	−1.01497	−0.507484	−	0.861661i	$-0.669424\pi$
$151$	−12.4721	−1.01497	−0.507484	+	0.861661i	$0.669424\pi$
$152$	0.618034	0.0501292
$153$	−6.47214	−0.523241
$154$	0	0
$155$	9.23607	0.741859
$156$	−0.618034	−0.0494823
$157$	−5.61803	−0.448368	−0.224184	−	0.974547i	$-0.571972\pi$
$157$	−5.61803	−0.448368	−0.224184	+	0.974547i	$0.571972\pi$
$158$	4.47214	0.355784
$159$	6.09017	0.482982
$160$	1.00000	0.0790569
$161$	17.5623	1.38410
$162$	−1.00000	−0.0785674
$163$	17.8885	1.40114	0.700569	−	0.713584i	$-0.252929\pi$
$163$	17.8885	1.40114	0.700569	+	0.713584i	$0.252929\pi$
$164$	−9.32624	−0.728257
$165$	0	0
$166$	4.94427	0.383750
$167$	−11.5623	−0.894718	−0.447359	−	0.894354i	$-0.647635\pi$
$167$	−11.5623	−0.894718	−0.447359	+	0.894354i	$0.647635\pi$
$168$	3.61803	0.279137
$169$	−12.6180	−0.970618
$170$	−6.47214	−0.496390
$171$	−0.618034	−0.0472622
$172$	0.763932	0.0582493
$173$	−24.5623	−1.86744	−0.933719	−	0.358007i	$-0.883456\pi$
$173$	−24.5623	−1.86744	−0.933719	+	0.358007i	$0.883456\pi$
$174$	3.70820	0.281118
$175$	3.61803	0.273498
$176$	0	0
$177$	14.6180	1.09876
$178$	5.14590	0.385701
$179$	−11.1459	−0.833084	−0.416542	−	0.909117i	$-0.636758\pi$
$179$	−11.1459	−0.833084	−0.416542	+	0.909117i	$0.636758\pi$
$180$	−1.00000	−0.0745356
$181$	−24.3607	−1.81072	−0.905358	−	0.424650i	$-0.860397\pi$
$181$	−24.3607	−1.81072	−0.905358	+	0.424650i	$0.860397\pi$
$182$	−2.23607	−0.165748
$183$	−11.2361	−0.830594
$184$	−4.85410	−0.357849
$185$	0.618034	0.0454388
$186$	−9.23607	−0.677221
$187$	0	0
$188$	−2.61803	−0.190940
$189$	−3.61803	−0.263173
$190$	−0.618034	−0.0448369
$191$	−13.7082	−0.991891	−0.495945	−	0.868354i	$-0.665178\pi$
$191$	−13.7082	−0.991891	−0.495945	+	0.868354i	$0.665178\pi$
$192$	−1.00000	−0.0721688
$193$	−3.70820	−0.266922	−0.133461	−	0.991054i	$-0.542609\pi$
$193$	−3.70820	−0.266922	−0.133461	+	0.991054i	$0.542609\pi$
$194$	−14.9443	−1.07294
$195$	0.618034	0.0442583
$196$	6.09017	0.435012
$197$	3.61803	0.257774	0.128887	−	0.991659i	$-0.458860\pi$
$197$	3.61803	0.257774	0.128887	+	0.991659i	$0.458860\pi$
$198$	0	0
$199$	−12.9443	−0.917595	−0.458798	−	0.888541i	$-0.651720\pi$
$199$	−12.9443	−0.917595	−0.458798	+	0.888541i	$0.651720\pi$
$200$	−1.00000	−0.0707107
$201$	8.18034	0.576997
$202$	−4.00000	−0.281439
$203$	13.4164	0.941647
$204$	6.47214	0.453140
$205$	9.32624	0.651373
$206$	9.85410	0.686568
$207$	4.85410	0.337383
$208$	0.618034	0.0428529
$209$	0	0
$210$	−3.61803	−0.249668
$211$	−23.4164	−1.61205	−0.806026	−	0.591880i	$-0.798386\pi$
$211$	−23.4164	−1.61205	−0.806026	+	0.591880i	$0.798386\pi$
$212$	−6.09017	−0.418275
$213$	0.291796	0.0199935
$214$	−17.8885	−1.22284
$215$	−0.763932	−0.0520997
$216$	1.00000	0.0680414
$217$	−33.4164	−2.26845
$218$	−4.00000	−0.270914
$219$	−10.9443	−0.739545
$220$	0	0
$221$	−4.00000	−0.269069
$222$	−0.618034	−0.0414797
$223$	7.61803	0.510141	0.255071	−	0.966922i	$-0.417901\pi$
$223$	7.61803	0.510141	0.255071	+	0.966922i	$0.417901\pi$
$224$	−3.61803	−0.241740
$225$	1.00000	0.0666667
$226$	12.4721	0.829634
$227$	−4.18034	−0.277459	−0.138729	−	0.990330i	$-0.544302\pi$
$227$	−4.18034	−0.277459	−0.138729	+	0.990330i	$0.544302\pi$
$228$	0.618034	0.0409303
$229$	−11.5279	−0.761783	−0.380891	−	0.924620i	$-0.624383\pi$
$229$	−11.5279	−0.761783	−0.380891	+	0.924620i	$0.624383\pi$
$230$	4.85410	0.320070
$231$	0	0
$232$	−3.70820	−0.243456
$233$	−16.2918	−1.06731	−0.533656	−	0.845702i	$-0.679182\pi$
$233$	−16.2918	−1.06731	−0.533656	+	0.845702i	$0.679182\pi$
$234$	−0.618034	−0.0404021
$235$	2.61803	0.170782
$236$	−14.6180	−0.951553
$237$	4.47214	0.290496
$238$	23.4164	1.51786
$239$	22.1803	1.43473	0.717363	−	0.696699i	$-0.245349\pi$
$239$	22.1803	1.43473	0.717363	+	0.696699i	$0.245349\pi$
$240$	1.00000	0.0645497
$241$	−25.6180	−1.65020	−0.825101	−	0.564985i	$-0.808882\pi$
$241$	−25.6180	−1.65020	−0.825101	+	0.564985i	$0.808882\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	11.2361	0.719316
$245$	−6.09017	−0.389087
$246$	−9.32624	−0.594619
$247$	−0.381966	−0.0243039
$248$	9.23607	0.586491
$249$	4.94427	0.313331
$250$	1.00000	0.0632456
$251$	11.5066	0.726289	0.363144	−	0.931733i	$-0.381703\pi$
$251$	11.5066	0.726289	0.363144	+	0.931733i	$0.381703\pi$
$252$	3.61803	0.227915
$253$	0	0
$254$	−12.6180	−0.791726
$255$	−6.47214	−0.405301
$256$	1.00000	0.0625000
$257$	−5.05573	−0.315368	−0.157684	−	0.987490i	$-0.550403\pi$
$257$	−5.05573	−0.315368	−0.157684	+	0.987490i	$0.550403\pi$
$258$	0.763932	0.0475603
$259$	−2.23607	−0.138943
$260$	−0.618034	−0.0383288
$261$	3.70820	0.229532
$262$	−20.9443	−1.29394
$263$	−8.14590	−0.502298	−0.251149	−	0.967948i	$-0.580808\pi$
$263$	−8.14590	−0.502298	−0.251149	+	0.967948i	$0.580808\pi$
$264$	0	0
$265$	6.09017	0.374116
$266$	2.23607	0.137102
$267$	5.14590	0.314924
$268$	−8.18034	−0.499694
$269$	−24.7639	−1.50988	−0.754942	−	0.655792i	$-0.772335\pi$
$269$	−24.7639	−1.50988	−0.754942	+	0.655792i	$0.772335\pi$
$270$	−1.00000	−0.0608581
$271$	0.652476	0.0396351	0.0198175	−	0.999804i	$-0.493691\pi$
$271$	0.652476	0.0396351	0.0198175	+	0.999804i	$0.493691\pi$
$272$	−6.47214	−0.392431
$273$	−2.23607	−0.135333
$274$	−15.4164	−0.931339
$275$	0	0
$276$	−4.85410	−0.292183
$277$	−8.27051	−0.496927	−0.248463	−	0.968641i	$-0.579926\pi$
$277$	−8.27051	−0.496927	−0.248463	+	0.968641i	$0.579926\pi$
$278$	7.61803	0.456899
$279$	−9.23607	−0.552949
$280$	3.61803	0.216219
$281$	7.88854	0.470591	0.235296	−	0.971924i	$-0.424394\pi$
$281$	7.88854	0.470591	0.235296	+	0.971924i	$0.424394\pi$
$282$	−2.61803	−0.155902
$283$	3.70820	0.220430	0.110215	−	0.993908i	$-0.464846\pi$
$283$	3.70820	0.220430	0.110215	+	0.993908i	$0.464846\pi$
$284$	−0.291796	−0.0173149
$285$	−0.618034	−0.0366092
$286$	0	0
$287$	−33.7426	−1.99177
$288$	−1.00000	−0.0589256
$289$	24.8885	1.46403
$290$	3.70820	0.217753
$291$	−14.9443	−0.876049
$292$	10.9443	0.640465
$293$	11.0344	0.644639	0.322319	−	0.946631i	$-0.395537\pi$
$293$	11.0344	0.644639	0.322319	+	0.946631i	$0.395537\pi$
$294$	6.09017	0.355186
$295$	14.6180	0.851095
$296$	0.618034	0.0359225
$297$	0	0
$298$	8.94427	0.518128
$299$	3.00000	0.173494
$300$	−1.00000	−0.0577350
$301$	2.76393	0.159310
$302$	12.4721	0.717691
$303$	−4.00000	−0.229794
$304$	−0.618034	−0.0354467
$305$	−11.2361	−0.643375
$306$	6.47214	0.369987
$307$	26.8328	1.53143	0.765715	−	0.643180i	$-0.222385\pi$
$307$	26.8328	1.53143	0.765715	+	0.643180i	$0.222385\pi$
$308$	0	0
$309$	9.85410	0.560580
$310$	−9.23607	−0.524573
$311$	−27.8885	−1.58141	−0.790707	−	0.612195i	$-0.790287\pi$
$311$	−27.8885	−1.58141	−0.790707	+	0.612195i	$0.790287\pi$
$312$	0.618034	0.0349893
$313$	5.70820	0.322647	0.161323	−	0.986902i	$-0.448424\pi$
$313$	5.70820	0.322647	0.161323	+	0.986902i	$0.448424\pi$
$314$	5.61803	0.317044
$315$	−3.61803	−0.203853
$316$	−4.47214	−0.251577
$317$	10.9098	0.612757	0.306379	−	0.951910i	$-0.400883\pi$
$317$	10.9098	0.612757	0.306379	+	0.951910i	$0.400883\pi$
$318$	−6.09017	−0.341520
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−17.8885	−0.998441
$322$	−17.5623	−0.978709
$323$	4.00000	0.222566
$324$	1.00000	0.0555556
$325$	0.618034	0.0342824
$326$	−17.8885	−0.990755
$327$	−4.00000	−0.221201
$328$	9.32624	0.514955
$329$	−9.47214	−0.522216
$330$	0	0
$331$	7.67376	0.421788	0.210894	−	0.977509i	$-0.432362\pi$
$331$	7.67376	0.421788	0.210894	+	0.977509i	$0.432362\pi$
$332$	−4.94427	−0.271352
$333$	−0.618034	−0.0338681
$334$	11.5623	0.632661
$335$	8.18034	0.446940
$336$	−3.61803	−0.197380
$337$	−20.0000	−1.08947	−0.544735	−	0.838608i	$-0.683370\pi$
$337$	−20.0000	−1.08947	−0.544735	+	0.838608i	$0.683370\pi$
$338$	12.6180	0.686331
$339$	12.4721	0.677393
$340$	6.47214	0.351001
$341$	0	0
$342$	0.618034	0.0334195
$343$	−3.29180	−0.177740
$344$	−0.763932	−0.0411885
$345$	4.85410	0.261336
$346$	24.5623	1.32048
$347$	3.81966	0.205050	0.102525	−	0.994730i	$-0.467308\pi$
$347$	3.81966	0.205050	0.102525	+	0.994730i	$0.467308\pi$
$348$	−3.70820	−0.198781
$349$	10.0000	0.535288	0.267644	−	0.963518i	$-0.413755\pi$
$349$	10.0000	0.535288	0.267644	+	0.963518i	$0.413755\pi$
$350$	−3.61803	−0.193392
$351$	−0.618034	−0.0329882
$352$	0	0
$353$	−24.6525	−1.31212	−0.656059	−	0.754709i	$-0.727778\pi$
$353$	−24.6525	−1.31212	−0.656059	+	0.754709i	$0.727778\pi$
$354$	−14.6180	−0.776940
$355$	0.291796	0.0154869
$356$	−5.14590	−0.272732
$357$	23.4164	1.23933
$358$	11.1459	0.589079
$359$	25.2361	1.33191	0.665954	−	0.745992i	$-0.268025\pi$
$359$	25.2361	1.33191	0.665954	+	0.745992i	$0.268025\pi$
$360$	1.00000	0.0527046
$361$	−18.6180	−0.979897
$362$	24.3607	1.28037
$363$	0	0
$364$	2.23607	0.117202
$365$	−10.9443	−0.572849
$366$	11.2361	0.587319
$367$	8.36068	0.436424	0.218212	−	0.975901i	$-0.429978\pi$
$367$	8.36068	0.436424	0.218212	+	0.975901i	$0.429978\pi$
$368$	4.85410	0.253038
$369$	−9.32624	−0.485505
$370$	−0.618034	−0.0321301
$371$	−22.0344	−1.14397
$372$	9.23607	0.478868
$373$	−13.8541	−0.717338	−0.358669	−	0.933465i	$-0.616769\pi$
$373$	−13.8541	−0.717338	−0.358669	+	0.933465i	$0.616769\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	2.61803	0.135015
$377$	2.29180	0.118034
$378$	3.61803	0.186092
$379$	−32.7426	−1.68188	−0.840938	−	0.541131i	$-0.817996\pi$
$379$	−32.7426	−1.68188	−0.840938	+	0.541131i	$0.817996\pi$
$380$	0.618034	0.0317045
$381$	−12.6180	−0.646441
$382$	13.7082	0.701373
$383$	−28.4508	−1.45377	−0.726885	−	0.686759i	$-0.759033\pi$
$383$	−28.4508	−1.45377	−0.726885	+	0.686759i	$0.759033\pi$
$384$	1.00000	0.0510310
$385$	0	0
$386$	3.70820	0.188743
$387$	0.763932	0.0388328
$388$	14.9443	0.758680
$389$	3.52786	0.178870	0.0894349	−	0.995993i	$-0.471494\pi$
$389$	3.52786	0.178870	0.0894349	+	0.995993i	$0.471494\pi$
$390$	−0.618034	−0.0312954
$391$	−31.4164	−1.58880
$392$	−6.09017	−0.307600
$393$	−20.9443	−1.05650
$394$	−3.61803	−0.182274
$395$	4.47214	0.225018
$396$	0	0
$397$	12.6738	0.636078	0.318039	−	0.948078i	$-0.396976\pi$
$397$	12.6738	0.636078	0.318039	+	0.948078i	$0.396976\pi$
$398$	12.9443	0.648838
$399$	2.23607	0.111943
$400$	1.00000	0.0500000
$401$	−1.67376	−0.0835837	−0.0417918	−	0.999126i	$-0.513307\pi$
$401$	−1.67376	−0.0835837	−0.0417918	+	0.999126i	$0.513307\pi$
$402$	−8.18034	−0.407998
$403$	−5.70820	−0.284346
$404$	4.00000	0.199007
$405$	−1.00000	−0.0496904
$406$	−13.4164	−0.665845
$407$	0	0
$408$	−6.47214	−0.320418
$409$	14.2148	0.702876	0.351438	−	0.936211i	$-0.385693\pi$
$409$	14.2148	0.702876	0.351438	+	0.936211i	$0.385693\pi$
$410$	−9.32624	−0.460590
$411$	−15.4164	−0.760435
$412$	−9.85410	−0.485477
$413$	−52.8885	−2.60248
$414$	−4.85410	−0.238566
$415$	4.94427	0.242705
$416$	−0.618034	−0.0303016
$417$	7.61803	0.373057
$418$	0	0
$419$	−11.2016	−0.547235	−0.273618	−	0.961839i	$-0.588220\pi$
$419$	−11.2016	−0.547235	−0.273618	+	0.961839i	$0.588220\pi$
$420$	3.61803	0.176542
$421$	26.9443	1.31318	0.656592	−	0.754246i	$-0.271997\pi$
$421$	26.9443	1.31318	0.656592	+	0.754246i	$0.271997\pi$
$422$	23.4164	1.13989
$423$	−2.61803	−0.127293
$424$	6.09017	0.295765
$425$	−6.47214	−0.313945
$426$	−0.291796	−0.0141376
$427$	40.6525	1.96731
$428$	17.8885	0.864675
$429$	0	0
$430$	0.763932	0.0368401
$431$	2.18034	0.105023	0.0525116	−	0.998620i	$-0.483277\pi$
$431$	2.18034	0.105023	0.0525116	+	0.998620i	$0.483277\pi$
$432$	−1.00000	−0.0481125
$433$	−33.1246	−1.59187	−0.795934	−	0.605384i	$-0.793020\pi$
$433$	−33.1246	−1.59187	−0.795934	+	0.605384i	$0.793020\pi$
$434$	33.4164	1.60404
$435$	3.70820	0.177795
$436$	4.00000	0.191565
$437$	−3.00000	−0.143509
$438$	10.9443	0.522938
$439$	20.1803	0.963155	0.481578	−	0.876403i	$-0.340064\pi$
$439$	20.1803	0.963155	0.481578	+	0.876403i	$0.340064\pi$
$440$	0	0
$441$	6.09017	0.290008
$442$	4.00000	0.190261
$443$	28.8328	1.36989	0.684944	−	0.728596i	$-0.259827\pi$
$443$	28.8328	1.36989	0.684944	+	0.728596i	$0.259827\pi$
$444$	0.618034	0.0293306
$445$	5.14590	0.243939
$446$	−7.61803	−0.360724
$447$	8.94427	0.423050
$448$	3.61803	0.170936
$449$	−18.6180	−0.878639	−0.439320	−	0.898331i	$-0.644780\pi$
$449$	−18.6180	−0.878639	−0.439320	+	0.898331i	$0.644780\pi$
$450$	−1.00000	−0.0471405
$451$	0	0
$452$	−12.4721	−0.586640
$453$	12.4721	0.585992
$454$	4.18034	0.196193
$455$	−2.23607	−0.104828
$456$	−0.618034	−0.0289421
$457$	9.88854	0.462567	0.231283	−	0.972886i	$-0.425708\pi$
$457$	9.88854	0.462567	0.231283	+	0.972886i	$0.425708\pi$
$458$	11.5279	0.538662
$459$	6.47214	0.302093
$460$	−4.85410	−0.226324
$461$	−24.7639	−1.15337	−0.576686	−	0.816966i	$-0.695654\pi$
$461$	−24.7639	−1.15337	−0.576686	+	0.816966i	$0.695654\pi$
$462$	0	0
$463$	−3.38197	−0.157173	−0.0785866	−	0.996907i	$-0.525041\pi$
$463$	−3.38197	−0.157173	−0.0785866	+	0.996907i	$0.525041\pi$
$464$	3.70820	0.172149
$465$	−9.23607	−0.428312
$466$	16.2918	0.754703
$467$	7.05573	0.326500	0.163250	−	0.986585i	$-0.447802\pi$
$467$	7.05573	0.326500	0.163250	+	0.986585i	$0.447802\pi$
$468$	0.618034	0.0285686
$469$	−29.5967	−1.36665
$470$	−2.61803	−0.120761
$471$	5.61803	0.258865
$472$	14.6180	0.672850
$473$	0	0
$474$	−4.47214	−0.205412
$475$	−0.618034	−0.0283573
$476$	−23.4164	−1.07329
$477$	−6.09017	−0.278850
$478$	−22.1803	−1.01451
$479$	−39.0132	−1.78256	−0.891278	−	0.453457i	$-0.850191\pi$
$479$	−39.0132	−1.78256	−0.891278	+	0.453457i	$0.850191\pi$
$480$	−1.00000	−0.0456435
$481$	−0.381966	−0.0174162
$482$	25.6180	1.16687
$483$	−17.5623	−0.799113
$484$	0	0
$485$	−14.9443	−0.678584
$486$	1.00000	0.0453609
$487$	40.3607	1.82892	0.914458	−	0.404680i	$-0.132617\pi$
$487$	40.3607	1.82892	0.914458	+	0.404680i	$0.132617\pi$
$488$	−11.2361	−0.508633
$489$	−17.8885	−0.808948
$490$	6.09017	0.275126
$491$	−2.32624	−0.104982	−0.0524908	−	0.998621i	$-0.516716\pi$
$491$	−2.32624	−0.104982	−0.0524908	+	0.998621i	$0.516716\pi$
$492$	9.32624	0.420459
$493$	−24.0000	−1.08091
$494$	0.381966	0.0171855
$495$	0	0
$496$	−9.23607	−0.414712
$497$	−1.05573	−0.0473559
$498$	−4.94427	−0.221558
$499$	−33.6869	−1.50803	−0.754017	−	0.656855i	$-0.771886\pi$
$499$	−33.6869	−1.50803	−0.754017	+	0.656855i	$0.771886\pi$
$500$	−1.00000	−0.0447214
$501$	11.5623	0.516566
$502$	−11.5066	−0.513564
$503$	−4.79837	−0.213949	−0.106974	−	0.994262i	$-0.534116\pi$
$503$	−4.79837	−0.213949	−0.106974	+	0.994262i	$0.534116\pi$
$504$	−3.61803	−0.161160
$505$	−4.00000	−0.177998
$506$	0	0
$507$	12.6180	0.560387
$508$	12.6180	0.559835
$509$	−25.4164	−1.12656	−0.563281	−	0.826265i	$-0.690461\pi$
$509$	−25.4164	−1.12656	−0.563281	+	0.826265i	$0.690461\pi$
$510$	6.47214	0.286591
$511$	39.5967	1.75166
$512$	−1.00000	−0.0441942
$513$	0.618034	0.0272869
$514$	5.05573	0.222999
$515$	9.85410	0.434224
$516$	−0.763932	−0.0336302
$517$	0	0
$518$	2.23607	0.0982472
$519$	24.5623	1.07817
$520$	0.618034	0.0271026
$521$	37.3262	1.63529	0.817646	−	0.575721i	$-0.195279\pi$
$521$	37.3262	1.63529	0.817646	+	0.575721i	$0.195279\pi$
$522$	−3.70820	−0.162304
$523$	2.29180	0.100213	0.0501066	−	0.998744i	$-0.484044\pi$
$523$	2.29180	0.100213	0.0501066	+	0.998744i	$0.484044\pi$
$524$	20.9443	0.914955
$525$	−3.61803	−0.157904
$526$	8.14590	0.355178
$527$	59.7771	2.60393
$528$	0	0
$529$	0.562306	0.0244481
$530$	−6.09017	−0.264540
$531$	−14.6180	−0.634369
$532$	−2.23607	−0.0969458
$533$	−5.76393	−0.249664
$534$	−5.14590	−0.222685
$535$	−17.8885	−0.773389
$536$	8.18034	0.353337
$537$	11.1459	0.480981
$538$	24.7639	1.06765
$539$	0	0
$540$	1.00000	0.0430331
$541$	−15.0557	−0.647296	−0.323648	−	0.946178i	$-0.604909\pi$
$541$	−15.0557	−0.647296	−0.323648	+	0.946178i	$0.604909\pi$
$542$	−0.652476	−0.0280262
$543$	24.3607	1.04542
$544$	6.47214	0.277491
$545$	−4.00000	−0.171341
$546$	2.23607	0.0956949
$547$	−19.2361	−0.822475	−0.411237	−	0.911528i	$-0.634903\pi$
$547$	−19.2361	−0.822475	−0.411237	+	0.911528i	$0.634903\pi$
$548$	15.4164	0.658556
$549$	11.2361	0.479544
$550$	0	0
$551$	−2.29180	−0.0976338
$552$	4.85410	0.206604
$553$	−16.1803	−0.688058
$554$	8.27051	0.351380
$555$	−0.618034	−0.0262341
$556$	−7.61803	−0.323077
$557$	13.6738	0.579376	0.289688	−	0.957121i	$-0.406448\pi$
$557$	13.6738	0.579376	0.289688	+	0.957121i	$0.406448\pi$
$558$	9.23607	0.390994
$559$	0.472136	0.0199692
$560$	−3.61803	−0.152890
$561$	0	0
$562$	−7.88854	−0.332758
$563$	45.3050	1.90938	0.954688	−	0.297608i	$-0.0961890\pi$
$563$	45.3050	1.90938	0.954688	+	0.297608i	$0.0961890\pi$
$564$	2.61803	0.110239
$565$	12.4721	0.524707
$566$	−3.70820	−0.155867
$567$	3.61803	0.151943
$568$	0.291796	0.0122435
$569$	14.8541	0.622716	0.311358	−	0.950293i	$-0.399216\pi$
$569$	14.8541	0.622716	0.311358	+	0.950293i	$0.399216\pi$
$570$	0.618034	0.0258866
$571$	−21.5066	−0.900022	−0.450011	−	0.893023i	$-0.648580\pi$
$571$	−21.5066	−0.900022	−0.450011	+	0.893023i	$0.648580\pi$
$572$	0	0
$573$	13.7082	0.572668
$574$	33.7426	1.40839
$575$	4.85410	0.202430
$576$	1.00000	0.0416667
$577$	−7.12461	−0.296601	−0.148301	−	0.988942i	$-0.547380\pi$
$577$	−7.12461	−0.296601	−0.148301	+	0.988942i	$0.547380\pi$
$578$	−24.8885	−1.03523
$579$	3.70820	0.154108
$580$	−3.70820	−0.153975
$581$	−17.8885	−0.742142
$582$	14.9443	0.619460
$583$	0	0
$584$	−10.9443	−0.452877
$585$	−0.618034	−0.0255526
$586$	−11.0344	−0.455829
$587$	34.8328	1.43770	0.718852	−	0.695163i	$-0.244668\pi$
$587$	34.8328	1.43770	0.718852	+	0.695163i	$0.244668\pi$
$588$	−6.09017	−0.251154
$589$	5.70820	0.235202
$590$	−14.6180	−0.601815
$591$	−3.61803	−0.148826
$592$	−0.618034	−0.0254010
$593$	−2.58359	−0.106095	−0.0530477	−	0.998592i	$-0.516894\pi$
$593$	−2.58359	−0.106095	−0.0530477	+	0.998592i	$0.516894\pi$
$594$	0	0
$595$	23.4164	0.959979
$596$	−8.94427	−0.366372
$597$	12.9443	0.529774
$598$	−3.00000	−0.122679
$599$	−4.29180	−0.175358	−0.0876790	−	0.996149i	$-0.527945\pi$
$599$	−4.29180	−0.175358	−0.0876790	+	0.996149i	$0.527945\pi$
$600$	1.00000	0.0408248
$601$	−35.0902	−1.43136	−0.715679	−	0.698429i	$-0.753883\pi$
$601$	−35.0902	−1.43136	−0.715679	+	0.698429i	$0.753883\pi$
$602$	−2.76393	−0.112649
$603$	−8.18034	−0.333129
$604$	−12.4721	−0.507484
$605$	0	0
$606$	4.00000	0.162489
$607$	−16.3607	−0.664060	−0.332030	−	0.943269i	$-0.607733\pi$
$607$	−16.3607	−0.664060	−0.332030	+	0.943269i	$0.607733\pi$
$608$	0.618034	0.0250646
$609$	−13.4164	−0.543660
$610$	11.2361	0.454935
$611$	−1.61803	−0.0654586
$612$	−6.47214	−0.261621
$613$	45.4164	1.83435	0.917176	−	0.398483i	$-0.130463\pi$
$613$	45.4164	1.83435	0.917176	+	0.398483i	$0.130463\pi$
$614$	−26.8328	−1.08288
$615$	−9.32624	−0.376070
$616$	0	0
$617$	23.0557	0.928189	0.464094	−	0.885786i	$-0.346380\pi$
$617$	23.0557	0.928189	0.464094	+	0.885786i	$0.346380\pi$
$618$	−9.85410	−0.396390
$619$	23.7426	0.954298	0.477149	−	0.878823i	$-0.341670\pi$
$619$	23.7426	0.954298	0.477149	+	0.878823i	$0.341670\pi$
$620$	9.23607	0.370929
$621$	−4.85410	−0.194788
$622$	27.8885	1.11823
$623$	−18.6180	−0.745916
$624$	−0.618034	−0.0247412
$625$	1.00000	0.0400000
$626$	−5.70820	−0.228146
$627$	0	0
$628$	−5.61803	−0.224184
$629$	4.00000	0.159490
$630$	3.61803	0.144146
$631$	1.70820	0.0680025	0.0340013	−	0.999422i	$-0.489175\pi$
$631$	1.70820	0.0680025	0.0340013	+	0.999422i	$0.489175\pi$
$632$	4.47214	0.177892
$633$	23.4164	0.930719
$634$	−10.9098	−0.433285
$635$	−12.6180	−0.500731
$636$	6.09017	0.241491
$637$	3.76393	0.149132
$638$	0	0
$639$	−0.291796	−0.0115433
$640$	1.00000	0.0395285
$641$	37.4508	1.47922	0.739610	−	0.673036i	$-0.235010\pi$
$641$	37.4508	1.47922	0.739610	+	0.673036i	$0.235010\pi$
$642$	17.8885	0.706005
$643$	−3.41641	−0.134730	−0.0673650	−	0.997728i	$-0.521459\pi$
$643$	−3.41641	−0.134730	−0.0673650	+	0.997728i	$0.521459\pi$
$644$	17.5623	0.692052
$645$	0.763932	0.0300798
$646$	−4.00000	−0.157378
$647$	−30.8328	−1.21216	−0.606082	−	0.795403i	$-0.707259\pi$
$647$	−30.8328	−1.21216	−0.606082	+	0.795403i	$0.707259\pi$
$648$	−1.00000	−0.0392837
$649$	0	0
$650$	−0.618034	−0.0242413
$651$	33.4164	1.30969
$652$	17.8885	0.700569
$653$	−15.8541	−0.620419	−0.310209	−	0.950668i	$-0.600399\pi$
$653$	−15.8541	−0.620419	−0.310209	+	0.950668i	$0.600399\pi$
$654$	4.00000	0.156412
$655$	−20.9443	−0.818360
$656$	−9.32624	−0.364128
$657$	10.9443	0.426977
$658$	9.47214	0.369262
$659$	28.2705	1.10126	0.550631	−	0.834749i	$-0.314387\pi$
$659$	28.2705	1.10126	0.550631	+	0.834749i	$0.314387\pi$
$660$	0	0
$661$	41.4853	1.61359	0.806795	−	0.590831i	$-0.201200\pi$
$661$	41.4853	1.61359	0.806795	+	0.590831i	$0.201200\pi$
$662$	−7.67376	−0.298249
$663$	4.00000	0.155347
$664$	4.94427	0.191875
$665$	2.23607	0.0867110
$666$	0.618034	0.0239483
$667$	18.0000	0.696963
$668$	−11.5623	−0.447359
$669$	−7.61803	−0.294530
$670$	−8.18034	−0.316034
$671$	0	0
$672$	3.61803	0.139569
$673$	−45.5967	−1.75763	−0.878813	−	0.477167i	$-0.841664\pi$
$673$	−45.5967	−1.75763	−0.878813	+	0.477167i	$0.841664\pi$
$674$	20.0000	0.770371
$675$	−1.00000	−0.0384900
$676$	−12.6180	−0.485309
$677$	14.3607	0.551926	0.275963	−	0.961168i	$-0.411003\pi$
$677$	14.3607	0.551926	0.275963	+	0.961168i	$0.411003\pi$
$678$	−12.4721	−0.478989
$679$	54.0689	2.07497
$680$	−6.47214	−0.248195
$681$	4.18034	0.160191
$682$	0	0
$683$	31.1246	1.19095	0.595475	−	0.803374i	$-0.296964\pi$
$683$	31.1246	1.19095	0.595475	+	0.803374i	$0.296964\pi$
$684$	−0.618034	−0.0236311
$685$	−15.4164	−0.589031
$686$	3.29180	0.125681
$687$	11.5279	0.439815
$688$	0.763932	0.0291246
$689$	−3.76393	−0.143394
$690$	−4.85410	−0.184793
$691$	−1.50658	−0.0573129	−0.0286565	−	0.999589i	$-0.509123\pi$
$691$	−1.50658	−0.0573129	−0.0286565	+	0.999589i	$0.509123\pi$
$692$	−24.5623	−0.933719
$693$	0	0
$694$	−3.81966	−0.144992
$695$	7.61803	0.288969
$696$	3.70820	0.140559
$697$	60.3607	2.28632
$698$	−10.0000	−0.378506
$699$	16.2918	0.616212
$700$	3.61803	0.136749
$701$	−20.0689	−0.757991	−0.378996	−	0.925398i	$-0.623730\pi$
$701$	−20.0689	−0.757991	−0.378996	+	0.925398i	$0.623730\pi$
$702$	0.618034	0.0233262
$703$	0.381966	0.0144061
$704$	0	0
$705$	−2.61803	−0.0986009
$706$	24.6525	0.927808
$707$	14.4721	0.544281
$708$	14.6180	0.549379
$709$	−24.6525	−0.925843	−0.462922	−	0.886399i	$-0.653199\pi$
$709$	−24.6525	−0.925843	−0.462922	+	0.886399i	$0.653199\pi$
$710$	−0.291796	−0.0109509
$711$	−4.47214	−0.167718
$712$	5.14590	0.192851
$713$	−44.8328	−1.67900
$714$	−23.4164	−0.876337
$715$	0	0
$716$	−11.1459	−0.416542
$717$	−22.1803	−0.828340
$718$	−25.2361	−0.941802
$719$	−23.8885	−0.890892	−0.445446	−	0.895309i	$-0.646955\pi$
$719$	−23.8885	−0.890892	−0.445446	+	0.895309i	$0.646955\pi$
$720$	−1.00000	−0.0372678
$721$	−35.6525	−1.32777
$722$	18.6180	0.692891
$723$	25.6180	0.952745
$724$	−24.3607	−0.905358
$725$	3.70820	0.137719
$726$	0	0
$727$	−46.6312	−1.72946	−0.864728	−	0.502241i	$-0.832509\pi$
$727$	−46.6312	−1.72946	−0.864728	+	0.502241i	$0.832509\pi$
$728$	−2.23607	−0.0828742
$729$	1.00000	0.0370370
$730$	10.9443	0.405066
$731$	−4.94427	−0.182871
$732$	−11.2361	−0.415297
$733$	−28.4721	−1.05164	−0.525821	−	0.850595i	$-0.676242\pi$
$733$	−28.4721	−1.05164	−0.525821	+	0.850595i	$0.676242\pi$
$734$	−8.36068	−0.308598
$735$	6.09017	0.224639
$736$	−4.85410	−0.178925
$737$	0	0
$738$	9.32624	0.343304
$739$	27.6180	1.01595	0.507973	−	0.861373i	$-0.330395\pi$
$739$	27.6180	1.01595	0.507973	+	0.861373i	$0.330395\pi$
$740$	0.618034	0.0227194
$741$	0.381966	0.0140319
$742$	22.0344	0.808910
$743$	−7.14590	−0.262158	−0.131079	−	0.991372i	$-0.541844\pi$
$743$	−7.14590	−0.262158	−0.131079	+	0.991372i	$0.541844\pi$
$744$	−9.23607	−0.338611
$745$	8.94427	0.327693
$746$	13.8541	0.507235
$747$	−4.94427	−0.180901
$748$	0	0
$749$	64.7214	2.36487
$750$	−1.00000	−0.0365148
$751$	−30.2492	−1.10381	−0.551905	−	0.833907i	$-0.686099\pi$
$751$	−30.2492	−1.10381	−0.551905	+	0.833907i	$0.686099\pi$
$752$	−2.61803	−0.0954699
$753$	−11.5066	−0.419323
$754$	−2.29180	−0.0834623
$755$	12.4721	0.453908
$756$	−3.61803	−0.131587
$757$	1.85410	0.0673885	0.0336942	−	0.999432i	$-0.489273\pi$
$757$	1.85410	0.0673885	0.0336942	+	0.999432i	$0.489273\pi$
$758$	32.7426	1.18927
$759$	0	0
$760$	−0.618034	−0.0224184
$761$	−7.88854	−0.285959	−0.142980	−	0.989726i	$-0.545668\pi$
$761$	−7.88854	−0.285959	−0.142980	+	0.989726i	$0.545668\pi$
$762$	12.6180	0.457103
$763$	14.4721	0.523926
$764$	−13.7082	−0.495945
$765$	6.47214	0.234001
$766$	28.4508	1.02797
$767$	−9.03444	−0.326215
$768$	−1.00000	−0.0360844
$769$	−34.7984	−1.25486	−0.627431	−	0.778672i	$-0.715893\pi$
$769$	−34.7984	−1.25486	−0.627431	+	0.778672i	$0.715893\pi$
$770$	0	0
$771$	5.05573	0.182078
$772$	−3.70820	−0.133461
$773$	3.79837	0.136618	0.0683090	−	0.997664i	$-0.478240\pi$
$773$	3.79837	0.136618	0.0683090	+	0.997664i	$0.478240\pi$
$774$	−0.763932	−0.0274590
$775$	−9.23607	−0.331769
$776$	−14.9443	−0.536468
$777$	2.23607	0.0802185
$778$	−3.52786	−0.126480
$779$	5.76393	0.206514
$780$	0.618034	0.0221292
$781$	0	0
$782$	31.4164	1.12345
$783$	−3.70820	−0.132520
$784$	6.09017	0.217506
$785$	5.61803	0.200516
$786$	20.9443	0.747057
$787$	−18.1803	−0.648059	−0.324030	−	0.946047i	$-0.605038\pi$
$787$	−18.1803	−0.648059	−0.324030	+	0.946047i	$0.605038\pi$
$788$	3.61803	0.128887
$789$	8.14590	0.290002
$790$	−4.47214	−0.159111
$791$	−45.1246	−1.60445
$792$	0	0
$793$	6.94427	0.246598
$794$	−12.6738	−0.449775
$795$	−6.09017	−0.215996
$796$	−12.9443	−0.458798
$797$	13.7426	0.486789	0.243395	−	0.969927i	$-0.421739\pi$
$797$	13.7426	0.486789	0.243395	+	0.969927i	$0.421739\pi$
$798$	−2.23607	−0.0791559
$799$	16.9443	0.599445
$800$	−1.00000	−0.0353553
$801$	−5.14590	−0.181821
$802$	1.67376	0.0591026
$803$	0	0
$804$	8.18034	0.288498
$805$	−17.5623	−0.618990
$806$	5.70820	0.201063
$807$	24.7639	0.871732
$808$	−4.00000	−0.140720
$809$	−3.49342	−0.122822	−0.0614111	−	0.998113i	$-0.519560\pi$
$809$	−3.49342	−0.122822	−0.0614111	+	0.998113i	$0.519560\pi$
$810$	1.00000	0.0351364
$811$	26.2705	0.922482	0.461241	−	0.887275i	$-0.347404\pi$
$811$	26.2705	0.922482	0.461241	+	0.887275i	$0.347404\pi$
$812$	13.4164	0.470824
$813$	−0.652476	−0.0228833
$814$	0	0
$815$	−17.8885	−0.626608
$816$	6.47214	0.226570
$817$	−0.472136	−0.0165179
$818$	−14.2148	−0.497008
$819$	2.23607	0.0781345
$820$	9.32624	0.325686
$821$	12.7639	0.445464	0.222732	−	0.974880i	$-0.428502\pi$
$821$	12.7639	0.445464	0.222732	+	0.974880i	$0.428502\pi$
$822$	15.4164	0.537709
$823$	32.9098	1.14716	0.573582	−	0.819148i	$-0.305553\pi$
$823$	32.9098	1.14716	0.573582	+	0.819148i	$0.305553\pi$
$824$	9.85410	0.343284
$825$	0	0
$826$	52.8885	1.84023
$827$	−9.70820	−0.337587	−0.168794	−	0.985651i	$-0.553987\pi$
$827$	−9.70820	−0.337587	−0.168794	+	0.985651i	$0.553987\pi$
$828$	4.85410	0.168692
$829$	−23.3050	−0.809414	−0.404707	−	0.914446i	$-0.632627\pi$
$829$	−23.3050	−0.809414	−0.404707	+	0.914446i	$0.632627\pi$
$830$	−4.94427	−0.171618
$831$	8.27051	0.286901
$832$	0.618034	0.0214265
$833$	−39.4164	−1.36570
$834$	−7.61803	−0.263791
$835$	11.5623	0.400130
$836$	0	0
$837$	9.23607	0.319245
$838$	11.2016	0.386954
$839$	33.1246	1.14359	0.571794	−	0.820397i	$-0.306248\pi$
$839$	33.1246	1.14359	0.571794	+	0.820397i	$0.306248\pi$
$840$	−3.61803	−0.124834
$841$	−15.2492	−0.525835
$842$	−26.9443	−0.928561
$843$	−7.88854	−0.271696
$844$	−23.4164	−0.806026
$845$	12.6180	0.434074
$846$	2.61803	0.0900099
$847$	0	0
$848$	−6.09017	−0.209137
$849$	−3.70820	−0.127265
$850$	6.47214	0.221992
$851$	−3.00000	−0.102839
$852$	0.291796	0.00999677
$853$	48.8115	1.67127	0.835637	−	0.549281i	$-0.185098\pi$
$853$	48.8115	1.67127	0.835637	+	0.549281i	$0.185098\pi$
$854$	−40.6525	−1.39110
$855$	0.618034	0.0211363
$856$	−17.8885	−0.611418
$857$	55.2361	1.88683	0.943414	−	0.331617i	$-0.107594\pi$
$857$	55.2361	1.88683	0.943414	+	0.331617i	$0.107594\pi$
$858$	0	0
$859$	51.0344	1.74127	0.870636	−	0.491927i	$-0.163707\pi$
$859$	51.0344	1.74127	0.870636	+	0.491927i	$0.163707\pi$
$860$	−0.763932	−0.0260499
$861$	33.7426	1.14995
$862$	−2.18034	−0.0742627
$863$	−0.145898	−0.00496643	−0.00248321	−	0.999997i	$-0.500790\pi$
$863$	−0.145898	−0.00496643	−0.00248321	+	0.999997i	$0.500790\pi$
$864$	1.00000	0.0340207
$865$	24.5623	0.835143
$866$	33.1246	1.12562
$867$	−24.8885	−0.845259
$868$	−33.4164	−1.13423
$869$	0	0
$870$	−3.70820	−0.125720
$871$	−5.05573	−0.171307
$872$	−4.00000	−0.135457
$873$	14.9443	0.505787
$874$	3.00000	0.101477
$875$	−3.61803	−0.122312
$876$	−10.9443	−0.369773
$877$	−23.3820	−0.789553	−0.394776	−	0.918777i	$-0.629178\pi$
$877$	−23.3820	−0.789553	−0.394776	+	0.918777i	$0.629178\pi$
$878$	−20.1803	−0.681053
$879$	−11.0344	−0.372182
$880$	0	0
$881$	7.79837	0.262734	0.131367	−	0.991334i	$-0.458063\pi$
$881$	7.79837	0.262734	0.131367	+	0.991334i	$0.458063\pi$
$882$	−6.09017	−0.205067
$883$	25.3050	0.851579	0.425790	−	0.904822i	$-0.359996\pi$
$883$	25.3050	0.851579	0.425790	+	0.904822i	$0.359996\pi$
$884$	−4.00000	−0.134535
$885$	−14.6180	−0.491380
$886$	−28.8328	−0.968657
$887$	1.25735	0.0422178	0.0211089	−	0.999777i	$-0.493280\pi$
$887$	1.25735	0.0422178	0.0211089	+	0.999777i	$0.493280\pi$
$888$	−0.618034	−0.0207399
$889$	45.6525	1.53113
$890$	−5.14590	−0.172491
$891$	0	0
$892$	7.61803	0.255071
$893$	1.61803	0.0541454
$894$	−8.94427	−0.299141
$895$	11.1459	0.372566
$896$	−3.61803	−0.120870
$897$	−3.00000	−0.100167
$898$	18.6180	0.621292
$899$	−34.2492	−1.14228
$900$	1.00000	0.0333333
$901$	39.4164	1.31315
$902$	0	0
$903$	−2.76393	−0.0919779
$904$	12.4721	0.414817
$905$	24.3607	0.809776
$906$	−12.4721	−0.414359
$907$	29.8885	0.992433	0.496216	−	0.868199i	$-0.334722\pi$
$907$	29.8885	0.992433	0.496216	+	0.868199i	$0.334722\pi$
$908$	−4.18034	−0.138729
$909$	4.00000	0.132672
$910$	2.23607	0.0741249
$911$	−10.6525	−0.352932	−0.176466	−	0.984307i	$-0.556467\pi$
$911$	−10.6525	−0.352932	−0.176466	+	0.984307i	$0.556467\pi$
$912$	0.618034	0.0204652
$913$	0	0
$914$	−9.88854	−0.327084
$915$	11.2361	0.371453
$916$	−11.5279	−0.380891
$917$	75.7771	2.50238
$918$	−6.47214	−0.213612
$919$	−18.0689	−0.596037	−0.298019	−	0.954560i	$-0.596326\pi$
$919$	−18.0689	−0.596037	−0.298019	+	0.954560i	$0.596326\pi$
$920$	4.85410	0.160035
$921$	−26.8328	−0.884171
$922$	24.7639	0.815557
$923$	−0.180340	−0.00593596
$924$	0	0
$925$	−0.618034	−0.0203208
$926$	3.38197	0.111138
$927$	−9.85410	−0.323651
$928$	−3.70820	−0.121728
$929$	−7.03444	−0.230793	−0.115396	−	0.993320i	$-0.536814\pi$
$929$	−7.03444	−0.230793	−0.115396	+	0.993320i	$0.536814\pi$
$930$	9.23607	0.302863
$931$	−3.76393	−0.123358
$932$	−16.2918	−0.533656
$933$	27.8885	0.913030
$934$	−7.05573	−0.230870
$935$	0	0
$936$	−0.618034	−0.0202011
$937$	48.3607	1.57987	0.789937	−	0.613188i	$-0.210113\pi$
$937$	48.3607	1.57987	0.789937	+	0.613188i	$0.210113\pi$
$938$	29.5967	0.966368
$939$	−5.70820	−0.186280
$940$	2.61803	0.0853909
$941$	11.0557	0.360406	0.180203	−	0.983629i	$-0.442324\pi$
$941$	11.0557	0.360406	0.180203	+	0.983629i	$0.442324\pi$
$942$	−5.61803	−0.183045
$943$	−45.2705	−1.47421
$944$	−14.6180	−0.475776
$945$	3.61803	0.117695
$946$	0	0
$947$	−3.30495	−0.107396	−0.0536982	−	0.998557i	$-0.517101\pi$
$947$	−3.30495	−0.107396	−0.0536982	+	0.998557i	$0.517101\pi$
$948$	4.47214	0.145248
$949$	6.76393	0.219567
$950$	0.618034	0.0200517
$951$	−10.9098	−0.353775
$952$	23.4164	0.758930
$953$	−44.7639	−1.45005	−0.725023	−	0.688725i	$-0.758171\pi$
$953$	−44.7639	−1.45005	−0.725023	+	0.688725i	$0.758171\pi$
$954$	6.09017	0.197177
$955$	13.7082	0.443587
$956$	22.1803	0.717363
$957$	0	0
$958$	39.0132	1.26046
$959$	55.7771	1.80114
$960$	1.00000	0.0322749
$961$	54.3050	1.75177
$962$	0.381966	0.0123151
$963$	17.8885	0.576450
$964$	−25.6180	−0.825101
$965$	3.70820	0.119371
$966$	17.5623	0.565058
$967$	−4.25735	−0.136907	−0.0684536	−	0.997654i	$-0.521807\pi$
$967$	−4.25735	−0.136907	−0.0684536	+	0.997654i	$0.521807\pi$
$968$	0	0
$969$	−4.00000	−0.128499
$970$	14.9443	0.479832
$971$	5.79837	0.186079	0.0930393	−	0.995662i	$-0.470342\pi$
$971$	5.79837	0.186079	0.0930393	+	0.995662i	$0.470342\pi$
$972$	−1.00000	−0.0320750
$973$	−27.5623	−0.883607
$974$	−40.3607	−1.29324
$975$	−0.618034	−0.0197929
$976$	11.2361	0.359658
$977$	−24.8328	−0.794472	−0.397236	−	0.917716i	$-0.630031\pi$
$977$	−24.8328	−0.794472	−0.397236	+	0.917716i	$0.630031\pi$
$978$	17.8885	0.572013
$979$	0	0
$980$	−6.09017	−0.194543
$981$	4.00000	0.127710
$982$	2.32624	0.0742332
$983$	−33.0344	−1.05364	−0.526818	−	0.849978i	$-0.676615\pi$
$983$	−33.0344	−1.05364	−0.526818	+	0.849978i	$0.676615\pi$
$984$	−9.32624	−0.297310
$985$	−3.61803	−0.115280
$986$	24.0000	0.764316
$987$	9.47214	0.301501
$988$	−0.381966	−0.0121520
$989$	3.70820	0.117914
$990$	0	0
$991$	8.94427	0.284124	0.142062	−	0.989858i	$-0.454627\pi$
$991$	8.94427	0.284124	0.142062	+	0.989858i	$0.454627\pi$
$992$	9.23607	0.293245
$993$	−7.67376	−0.243519
$994$	1.05573	0.0334857
$995$	12.9443	0.410361
$996$	4.94427	0.156665
$997$	−13.7771	−0.436325	−0.218162	−	0.975912i	$-0.570006\pi$
$997$	−13.7771	−0.436325	−0.218162	+	0.975912i	$0.570006\pi$
$998$	33.6869	1.06634
$999$	0.618034	0.0195537

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bc.1.2		2
11.3	even	5		330.2.m.d.31.1	✓	4
11.4	even	5		330.2.m.d.181.1	yes	4
11.10	odd	2		3630.2.a.bi.1.1		2
33.14	odd	10		990.2.n.a.361.1		4
33.26	odd	10		990.2.n.a.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.d.31.1	✓	4	11.3	even	5
330.2.m.d.181.1	yes	4	11.4	even	5
990.2.n.a.181.1		4	33.26	odd	10
990.2.n.a.361.1		4	33.14	odd	10
3630.2.a.bc.1.2		2	1.1	even	1	trivial
3630.2.a.bi.1.1		2	11.10	odd	2

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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.00000 q^{6} +3.61803 q^{7} -1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +0.618034 q^{13} -3.61803 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.47214 q^{17} -1.00000 q^{18} -0.618034 q^{19} -1.00000 q^{20} -3.61803 q^{21} +4.85410 q^{23} +1.00000 q^{24} +1.00000 q^{25} -0.618034 q^{26} -1.00000 q^{27} +3.61803 q^{28} +3.70820 q^{29} -1.00000 q^{30} -9.23607 q^{31} -1.00000 q^{32} +6.47214 q^{34} -3.61803 q^{35} +1.00000 q^{36} -0.618034 q^{37} +0.618034 q^{38} -0.618034 q^{39} +1.00000 q^{40} -9.32624 q^{41} +3.61803 q^{42} +0.763932 q^{43} -1.00000 q^{45} -4.85410 q^{46} -2.61803 q^{47} -1.00000 q^{48} +6.09017 q^{49} -1.00000 q^{50} +6.47214 q^{51} +0.618034 q^{52} -6.09017 q^{53} +1.00000 q^{54} -3.61803 q^{56} +0.618034 q^{57} -3.70820 q^{58} -14.6180 q^{59} +1.00000 q^{60} +11.2361 q^{61} +9.23607 q^{62} +3.61803 q^{63} +1.00000 q^{64} -0.618034 q^{65} -8.18034 q^{67} -6.47214 q^{68} -4.85410 q^{69} +3.61803 q^{70} -0.291796 q^{71} -1.00000 q^{72} +10.9443 q^{73} +0.618034 q^{74} -1.00000 q^{75} -0.618034 q^{76} +0.618034 q^{78} -4.47214 q^{79} -1.00000 q^{80} +1.00000 q^{81} +9.32624 q^{82} -4.94427 q^{83} -3.61803 q^{84} +6.47214 q^{85} -0.763932 q^{86} -3.70820 q^{87} -5.14590 q^{89} +1.00000 q^{90} +2.23607 q^{91} +4.85410 q^{92} +9.23607 q^{93} +2.61803 q^{94} +0.618034 q^{95} +1.00000 q^{96} +14.9443 q^{97} -6.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} + 2 q^{6} + 5 q^{7} - 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - q^{13} - 5 q^{14} + 2 q^{15} + 2 q^{16} - 4 q^{17} - 2 q^{18} + q^{19} - 2 q^{20} - 5 q^{21} + 3 q^{23} + 2 q^{24} + 2 q^{25} + q^{26} - 2 q^{27} + 5 q^{28} - 6 q^{29} - 2 q^{30} - 14 q^{31} - 2 q^{32} + 4 q^{34} - 5 q^{35} + 2 q^{36} + q^{37} - q^{38} + q^{39} + 2 q^{40} - 3 q^{41} + 5 q^{42} + 6 q^{43} - 2 q^{45} - 3 q^{46} - 3 q^{47} - 2 q^{48} + q^{49} - 2 q^{50} + 4 q^{51} - q^{52} - q^{53} + 2 q^{54} - 5 q^{56} - q^{57} + 6 q^{58} - 27 q^{59} + 2 q^{60} + 18 q^{61} + 14 q^{62} + 5 q^{63} + 2 q^{64} + q^{65} + 6 q^{67} - 4 q^{68} - 3 q^{69} + 5 q^{70} - 14 q^{71} - 2 q^{72} + 4 q^{73} - q^{74} - 2 q^{75} + q^{76} - q^{78} - 2 q^{80} + 2 q^{81} + 3 q^{82} + 8 q^{83} - 5 q^{84} + 4 q^{85} - 6 q^{86} + 6 q^{87} - 17 q^{89} + 2 q^{90} + 3 q^{92} + 14 q^{93} + 3 q^{94} - q^{95} + 2 q^{96} + 12 q^{97} - q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 + 2 * q^6 + 5 * q^7 - 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - q^13 - 5 * q^14 + 2 * q^15 + 2 * q^16 - 4 * q^17 - 2 * q^18 + q^19 - 2 * q^20 - 5 * q^21 + 3 * q^23 + 2 * q^24 + 2 * q^25 + q^26 - 2 * q^27 + 5 * q^28 - 6 * q^29 - 2 * q^30 - 14 * q^31 - 2 * q^32 + 4 * q^34 - 5 * q^35 + 2 * q^36 + q^37 - q^38 + q^39 + 2 * q^40 - 3 * q^41 + 5 * q^42 + 6 * q^43 - 2 * q^45 - 3 * q^46 - 3 * q^47 - 2 * q^48 + q^49 - 2 * q^50 + 4 * q^51 - q^52 - q^53 + 2 * q^54 - 5 * q^56 - q^57 + 6 * q^58 - 27 * q^59 + 2 * q^60 + 18 * q^61 + 14 * q^62 + 5 * q^63 + 2 * q^64 + q^65 + 6 * q^67 - 4 * q^68 - 3 * q^69 + 5 * q^70 - 14 * q^71 - 2 * q^72 + 4 * q^73 - q^74 - 2 * q^75 + q^76 - q^78 - 2 * q^80 + 2 * q^81 + 3 * q^82 + 8 * q^83 - 5 * q^84 + 4 * q^85 - 6 * q^86 + 6 * q^87 - 17 * q^89 + 2 * q^90 + 3 * q^92 + 14 * q^93 + 3 * q^94 - q^95 + 2 * q^96 + 12 * q^97 - q^98

Introduction

L-functions

Modular forms

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