LMFDB - Embedded newform 3630.2.a.bm.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:	$0$
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			1.2
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -1.61803 q^{13} +1.23607 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.85410 q^{17} +1.00000 q^{18} +0.763932 q^{19} +1.00000 q^{20} -1.23607 q^{21} +1.38197 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.61803 q^{26} -1.00000 q^{27} +1.23607 q^{28} +6.09017 q^{29} -1.00000 q^{30} +2.85410 q^{31} +1.00000 q^{32} -3.85410 q^{34} +1.23607 q^{35} +1.00000 q^{36} +5.85410 q^{37} +0.763932 q^{38} +1.61803 q^{39} +1.00000 q^{40} +1.70820 q^{41} -1.23607 q^{42} +5.85410 q^{43} +1.00000 q^{45} +1.38197 q^{46} +13.6180 q^{47} -1.00000 q^{48} -5.47214 q^{49} +1.00000 q^{50} +3.85410 q^{51} -1.61803 q^{52} +8.47214 q^{53} -1.00000 q^{54} +1.23607 q^{56} -0.763932 q^{57} +6.09017 q^{58} +0.145898 q^{59} -1.00000 q^{60} +1.52786 q^{61} +2.85410 q^{62} +1.23607 q^{63} +1.00000 q^{64} -1.61803 q^{65} -9.32624 q^{67} -3.85410 q^{68} -1.38197 q^{69} +1.23607 q^{70} -15.4164 q^{71} +1.00000 q^{72} +4.47214 q^{73} +5.85410 q^{74} -1.00000 q^{75} +0.763932 q^{76} +1.61803 q^{78} -9.56231 q^{79} +1.00000 q^{80} +1.00000 q^{81} +1.70820 q^{82} +1.52786 q^{83} -1.23607 q^{84} -3.85410 q^{85} +5.85410 q^{86} -6.09017 q^{87} +5.70820 q^{89} +1.00000 q^{90} -2.00000 q^{91} +1.38197 q^{92} -2.85410 q^{93} +13.6180 q^{94} +0.763932 q^{95} -1.00000 q^{96} +4.29180 q^{97} -5.47214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$7$	1.23607	0.467190	0.233595	−	0.972334i	$-0.424951\pi$
$7$	1.23607	0.467190	0.233595	+	0.972334i	$0.424951\pi$
$8$	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
$13$	−1.61803	−0.448762	−0.224381	−	0.974502i	$-0.572036\pi$
$13$	−1.61803	−0.448762	−0.224381	+	0.974502i	$0.572036\pi$
$14$	1.23607	0.330353
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−3.85410	−0.934757	−0.467379	−	0.884057i	$-0.654801\pi$
$17$	−3.85410	−0.934757	−0.467379	+	0.884057i	$0.654801\pi$
$18$	1.00000	0.235702
$19$	0.763932	0.175258	0.0876290	−	0.996153i	$-0.472071\pi$
$19$	0.763932	0.175258	0.0876290	+	0.996153i	$0.472071\pi$
$20$	1.00000	0.223607
$21$	−1.23607	−0.269732
$22$	0	0
$23$	1.38197	0.288160	0.144080	−	0.989566i	$-0.453978\pi$
$23$	1.38197	0.288160	0.144080	+	0.989566i	$0.453978\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−1.61803	−0.317323
$27$	−1.00000	−0.192450
$28$	1.23607	0.233595
$29$	6.09017	1.13092	0.565458	−	0.824777i	$-0.308699\pi$
$29$	6.09017	1.13092	0.565458	+	0.824777i	$0.308699\pi$
$30$	−1.00000	−0.182574
$31$	2.85410	0.512612	0.256306	−	0.966596i	$-0.417495\pi$
$31$	2.85410	0.512612	0.256306	+	0.966596i	$0.417495\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−3.85410	−0.660973
$35$	1.23607	0.208934
$36$	1.00000	0.166667
$37$	5.85410	0.962408	0.481204	−	0.876609i	$-0.340200\pi$
$37$	5.85410	0.962408	0.481204	+	0.876609i	$0.340200\pi$
$38$	0.763932	0.123926
$39$	1.61803	0.259093
$40$	1.00000	0.158114
$41$	1.70820	0.266777	0.133388	−	0.991064i	$-0.457414\pi$
$41$	1.70820	0.266777	0.133388	+	0.991064i	$0.457414\pi$
$42$	−1.23607	−0.190729
$43$	5.85410	0.892742	0.446371	−	0.894848i	$-0.352716\pi$
$43$	5.85410	0.892742	0.446371	+	0.894848i	$0.352716\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	1.38197	0.203760
$47$	13.6180	1.98639	0.993197	−	0.116444i	$-0.0371497\pi$
$47$	13.6180	1.98639	0.993197	+	0.116444i	$0.0371497\pi$
$48$	−1.00000	−0.144338
$49$	−5.47214	−0.781734
$50$	1.00000	0.141421
$51$	3.85410	0.539682
$52$	−1.61803	−0.224381
$53$	8.47214	1.16374	0.581869	−	0.813283i	$-0.302322\pi$
$53$	8.47214	1.16374	0.581869	+	0.813283i	$0.302322\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.23607	0.165177
$57$	−0.763932	−0.101185
$58$	6.09017	0.799678
$59$	0.145898	0.0189943	0.00949715	−	0.999955i	$-0.496977\pi$
$59$	0.145898	0.0189943	0.00949715	+	0.999955i	$0.496977\pi$
$60$	−1.00000	−0.129099
$61$	1.52786	0.195623	0.0978115	−	0.995205i	$-0.468816\pi$
$61$	1.52786	0.195623	0.0978115	+	0.995205i	$0.468816\pi$
$62$	2.85410	0.362471
$63$	1.23607	0.155730
$64$	1.00000	0.125000
$65$	−1.61803	−0.200692
$66$	0	0
$67$	−9.32624	−1.13938	−0.569691	−	0.821859i	$-0.692937\pi$
$67$	−9.32624	−1.13938	−0.569691	+	0.821859i	$0.692937\pi$
$68$	−3.85410	−0.467379
$69$	−1.38197	−0.166369
$70$	1.23607	0.147738
$71$	−15.4164	−1.82959	−0.914796	−	0.403917i	$-0.867648\pi$
$71$	−15.4164	−1.82959	−0.914796	+	0.403917i	$0.867648\pi$
$72$	1.00000	0.117851
$73$	4.47214	0.523424	0.261712	−	0.965146i	$-0.415713\pi$
$73$	4.47214	0.523424	0.261712	+	0.965146i	$0.415713\pi$
$74$	5.85410	0.680526
$75$	−1.00000	−0.115470
$76$	0.763932	0.0876290
$77$	0	0
$78$	1.61803	0.183206
$79$	−9.56231	−1.07584	−0.537922	−	0.842995i	$-0.680790\pi$
$79$	−9.56231	−1.07584	−0.537922	+	0.842995i	$0.680790\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	1.70820	0.188640
$83$	1.52786	0.167705	0.0838524	−	0.996478i	$-0.473278\pi$
$83$	1.52786	0.167705	0.0838524	+	0.996478i	$0.473278\pi$
$84$	−1.23607	−0.134866
$85$	−3.85410	−0.418036
$86$	5.85410	0.631264
$87$	−6.09017	−0.652935
$88$	0	0
$89$	5.70820	0.605068	0.302534	−	0.953139i	$-0.402167\pi$
$89$	5.70820	0.605068	0.302534	+	0.953139i	$0.402167\pi$
$90$	1.00000	0.105409
$91$	−2.00000	−0.209657
$92$	1.38197	0.144080
$93$	−2.85410	−0.295957
$94$	13.6180	1.40459
$95$	0.763932	0.0783778
$96$	−1.00000	−0.102062
$97$	4.29180	0.435766	0.217883	−	0.975975i	$-0.430085\pi$
$97$	4.29180	0.435766	0.217883	+	0.975975i	$0.430085\pi$
$98$	−5.47214	−0.552769
$99$	0	0
$100$	1.00000	0.100000
$101$	−8.14590	−0.810547	−0.405274	−	0.914195i	$-0.632824\pi$
$101$	−8.14590	−0.810547	−0.405274	+	0.914195i	$0.632824\pi$
$102$	3.85410	0.381613
$103$	15.2361	1.50125	0.750627	−	0.660726i	$-0.229751\pi$
$103$	15.2361	1.50125	0.750627	+	0.660726i	$0.229751\pi$
$104$	−1.61803	−0.158661
$105$	−1.23607	−0.120628
$106$	8.47214	0.822887
$107$	−7.70820	−0.745180	−0.372590	−	0.927996i	$-0.621530\pi$
$107$	−7.70820	−0.745180	−0.372590	+	0.927996i	$0.621530\pi$
$108$	−1.00000	−0.0962250
$109$	−8.94427	−0.856706	−0.428353	−	0.903612i	$-0.640906\pi$
$109$	−8.94427	−0.856706	−0.428353	+	0.903612i	$0.640906\pi$
$110$	0	0
$111$	−5.85410	−0.555647
$112$	1.23607	0.116797
$113$	14.8541	1.39736	0.698678	−	0.715436i	$-0.253772\pi$
$113$	14.8541	1.39736	0.698678	+	0.715436i	$0.253772\pi$
$114$	−0.763932	−0.0715488
$115$	1.38197	0.128869
$116$	6.09017	0.565458
$117$	−1.61803	−0.149587
$118$	0.145898	0.0134310
$119$	−4.76393	−0.436709
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	1.52786	0.138326
$123$	−1.70820	−0.154024
$124$	2.85410	0.256306
$125$	1.00000	0.0894427
$126$	1.23607	0.110118
$127$	0.291796	0.0258927	0.0129464	−	0.999916i	$-0.495879\pi$
$127$	0.291796	0.0258927	0.0129464	+	0.999916i	$0.495879\pi$
$128$	1.00000	0.0883883
$129$	−5.85410	−0.515425
$130$	−1.61803	−0.141911
$131$	18.3820	1.60604	0.803020	−	0.595952i	$-0.203225\pi$
$131$	18.3820	1.60604	0.803020	+	0.595952i	$0.203225\pi$
$132$	0	0
$133$	0.944272	0.0818788
$134$	−9.32624	−0.805664
$135$	−1.00000	−0.0860663
$136$	−3.85410	−0.330487
$137$	11.6180	0.992596	0.496298	−	0.868152i	$-0.334692\pi$
$137$	11.6180	0.992596	0.496298	+	0.868152i	$0.334692\pi$
$138$	−1.38197	−0.117641
$139$	20.6525	1.75172	0.875860	−	0.482565i	$-0.160295\pi$
$139$	20.6525	1.75172	0.875860	+	0.482565i	$0.160295\pi$
$140$	1.23607	0.104467
$141$	−13.6180	−1.14685
$142$	−15.4164	−1.29372
$143$	0	0
$144$	1.00000	0.0833333
$145$	6.09017	0.505761
$146$	4.47214	0.370117
$147$	5.47214	0.451334
$148$	5.85410	0.481204
$149$	−7.85410	−0.643433	−0.321717	−	0.946836i	$-0.604260\pi$
$149$	−7.85410	−0.643433	−0.321717	+	0.946836i	$0.604260\pi$
$150$	−1.00000	−0.0816497
$151$	4.94427	0.402359	0.201180	−	0.979554i	$-0.435523\pi$
$151$	4.94427	0.402359	0.201180	+	0.979554i	$0.435523\pi$
$152$	0.763932	0.0619631
$153$	−3.85410	−0.311586
$154$	0	0
$155$	2.85410	0.229247
$156$	1.61803	0.129546
$157$	−5.61803	−0.448368	−0.224184	−	0.974547i	$-0.571972\pi$
$157$	−5.61803	−0.448368	−0.224184	+	0.974547i	$0.571972\pi$
$158$	−9.56231	−0.760736
$159$	−8.47214	−0.671884
$160$	1.00000	0.0790569
$161$	1.70820	0.134625
$162$	1.00000	0.0785674
$163$	−6.79837	−0.532490	−0.266245	−	0.963905i	$-0.585783\pi$
$163$	−6.79837	−0.532490	−0.266245	+	0.963905i	$0.585783\pi$
$164$	1.70820	0.133388
$165$	0	0
$166$	1.52786	0.118585
$167$	11.3262	0.876451	0.438225	−	0.898865i	$-0.355607\pi$
$167$	11.3262	0.876451	0.438225	+	0.898865i	$0.355607\pi$
$168$	−1.23607	−0.0953647
$169$	−10.3820	−0.798613
$170$	−3.85410	−0.295596
$171$	0.763932	0.0584193
$172$	5.85410	0.446371
$173$	−8.00000	−0.608229	−0.304114	−	0.952636i	$-0.598361\pi$
$173$	−8.00000	−0.608229	−0.304114	+	0.952636i	$0.598361\pi$
$174$	−6.09017	−0.461695
$175$	1.23607	0.0934380
$176$	0	0
$177$	−0.145898	−0.0109664
$178$	5.70820	0.427848
$179$	9.03444	0.675266	0.337633	−	0.941278i	$-0.390374\pi$
$179$	9.03444	0.675266	0.337633	+	0.941278i	$0.390374\pi$
$180$	1.00000	0.0745356
$181$	10.4721	0.778388	0.389194	−	0.921156i	$-0.372754\pi$
$181$	10.4721	0.778388	0.389194	+	0.921156i	$0.372754\pi$
$182$	−2.00000	−0.148250
$183$	−1.52786	−0.112943
$184$	1.38197	0.101880
$185$	5.85410	0.430402
$186$	−2.85410	−0.209273
$187$	0	0
$188$	13.6180	0.993197
$189$	−1.23607	−0.0899107
$190$	0.763932	0.0554215
$191$	25.7082	1.86018	0.930090	−	0.367331i	$-0.119728\pi$
$191$	25.7082	1.86018	0.930090	+	0.367331i	$0.119728\pi$
$192$	−1.00000	−0.0721688
$193$	8.94427	0.643823	0.321911	−	0.946770i	$-0.395675\pi$
$193$	8.94427	0.643823	0.321911	+	0.946770i	$0.395675\pi$
$194$	4.29180	0.308133
$195$	1.61803	0.115870
$196$	−5.47214	−0.390867
$197$	−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
$199$	9.27051	0.657169	0.328585	−	0.944475i	$-0.393428\pi$
$199$	9.27051	0.657169	0.328585	+	0.944475i	$0.393428\pi$
$200$	1.00000	0.0707107
$201$	9.32624	0.657822
$202$	−8.14590	−0.573143
$203$	7.52786	0.528352
$204$	3.85410	0.269841
$205$	1.70820	0.119306
$206$	15.2361	1.06155
$207$	1.38197	0.0960533
$208$	−1.61803	−0.112190
$209$	0	0
$210$	−1.23607	−0.0852968
$211$	2.29180	0.157774	0.0788869	−	0.996884i	$-0.474863\pi$
$211$	2.29180	0.157774	0.0788869	+	0.996884i	$0.474863\pi$
$212$	8.47214	0.581869
$213$	15.4164	1.05631
$214$	−7.70820	−0.526922
$215$	5.85410	0.399246
$216$	−1.00000	−0.0680414
$217$	3.52786	0.239487
$218$	−8.94427	−0.605783
$219$	−4.47214	−0.302199
$220$	0	0
$221$	6.23607	0.419483
$222$	−5.85410	−0.392902
$223$	−19.1246	−1.28068	−0.640339	−	0.768092i	$-0.721206\pi$
$223$	−19.1246	−1.28068	−0.640339	+	0.768092i	$0.721206\pi$
$224$	1.23607	0.0825883
$225$	1.00000	0.0666667
$226$	14.8541	0.988080
$227$	13.8885	0.921815	0.460908	−	0.887448i	$-0.347524\pi$
$227$	13.8885	0.921815	0.460908	+	0.887448i	$0.347524\pi$
$228$	−0.763932	−0.0505926
$229$	−15.1246	−0.999462	−0.499731	−	0.866181i	$-0.666568\pi$
$229$	−15.1246	−0.999462	−0.499731	+	0.866181i	$0.666568\pi$
$230$	1.38197	0.0911241
$231$	0	0
$232$	6.09017	0.399839
$233$	−23.9787	−1.57090	−0.785449	−	0.618927i	$-0.787568\pi$
$233$	−23.9787	−1.57090	−0.785449	+	0.618927i	$0.787568\pi$
$234$	−1.61803	−0.105774
$235$	13.6180	0.888343
$236$	0.145898	0.00949715
$237$	9.56231	0.621139
$238$	−4.76393	−0.308800
$239$	−27.7082	−1.79229	−0.896147	−	0.443757i	$-0.853645\pi$
$239$	−27.7082	−1.79229	−0.896147	+	0.443757i	$0.853645\pi$
$240$	−1.00000	−0.0645497
$241$	2.94427	0.189657	0.0948286	−	0.995494i	$-0.469770\pi$
$241$	2.94427	0.189657	0.0948286	+	0.995494i	$0.469770\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	1.52786	0.0978115
$245$	−5.47214	−0.349602
$246$	−1.70820	−0.108911
$247$	−1.23607	−0.0786491
$248$	2.85410	0.181236
$249$	−1.52786	−0.0968244
$250$	1.00000	0.0632456
$251$	18.3262	1.15674	0.578371	−	0.815774i	$-0.303689\pi$
$251$	18.3262	1.15674	0.578371	+	0.815774i	$0.303689\pi$
$252$	1.23607	0.0778650
$253$	0	0
$254$	0.291796	0.0183089
$255$	3.85410	0.241353
$256$	1.00000	0.0625000
$257$	12.4721	0.777990	0.388995	−	0.921240i	$-0.372822\pi$
$257$	12.4721	0.777990	0.388995	+	0.921240i	$0.372822\pi$
$258$	−5.85410	−0.364460
$259$	7.23607	0.449627
$260$	−1.61803	−0.100346
$261$	6.09017	0.376972
$262$	18.3820	1.13564
$263$	19.5623	1.20626	0.603132	−	0.797642i	$-0.293919\pi$
$263$	19.5623	1.20626	0.603132	+	0.797642i	$0.293919\pi$
$264$	0	0
$265$	8.47214	0.520439
$266$	0.944272	0.0578970
$267$	−5.70820	−0.349336
$268$	−9.32624	−0.569691
$269$	−5.32624	−0.324746	−0.162373	−	0.986729i	$-0.551915\pi$
$269$	−5.32624	−0.324746	−0.162373	+	0.986729i	$0.551915\pi$
$270$	−1.00000	−0.0608581
$271$	−6.79837	−0.412972	−0.206486	−	0.978450i	$-0.566203\pi$
$271$	−6.79837	−0.412972	−0.206486	+	0.978450i	$0.566203\pi$
$272$	−3.85410	−0.233689
$273$	2.00000	0.121046
$274$	11.6180	0.701871
$275$	0	0
$276$	−1.38197	−0.0831846
$277$	−32.0344	−1.92476	−0.962382	−	0.271702i	$-0.912414\pi$
$277$	−32.0344	−1.92476	−0.962382	+	0.271702i	$0.912414\pi$
$278$	20.6525	1.23865
$279$	2.85410	0.170871
$280$	1.23607	0.0738692
$281$	−23.8885	−1.42507	−0.712536	−	0.701636i	$-0.752453\pi$
$281$	−23.8885	−1.42507	−0.712536	+	0.701636i	$0.752453\pi$
$282$	−13.6180	−0.810942
$283$	3.03444	0.180379	0.0901894	−	0.995925i	$-0.471253\pi$
$283$	3.03444	0.180379	0.0901894	+	0.995925i	$0.471253\pi$
$284$	−15.4164	−0.914796
$285$	−0.763932	−0.0452514
$286$	0	0
$287$	2.11146	0.124635
$288$	1.00000	0.0589256
$289$	−2.14590	−0.126229
$290$	6.09017	0.357627
$291$	−4.29180	−0.251590
$292$	4.47214	0.261712
$293$	7.05573	0.412200	0.206100	−	0.978531i	$-0.433923\pi$
$293$	7.05573	0.412200	0.206100	+	0.978531i	$0.433923\pi$
$294$	5.47214	0.319141
$295$	0.145898	0.00849451
$296$	5.85410	0.340263
$297$	0	0
$298$	−7.85410	−0.454976
$299$	−2.23607	−0.129315
$300$	−1.00000	−0.0577350
$301$	7.23607	0.417080
$302$	4.94427	0.284511
$303$	8.14590	0.467970
$304$	0.763932	0.0438145
$305$	1.52786	0.0874852
$306$	−3.85410	−0.220324
$307$	−18.0902	−1.03246	−0.516230	−	0.856450i	$-0.672665\pi$
$307$	−18.0902	−1.03246	−0.516230	+	0.856450i	$0.672665\pi$
$308$	0	0
$309$	−15.2361	−0.866750
$310$	2.85410	0.162102
$311$	−4.18034	−0.237045	−0.118523	−	0.992951i	$-0.537816\pi$
$311$	−4.18034	−0.237045	−0.118523	+	0.992951i	$0.537816\pi$
$312$	1.61803	0.0916031
$313$	24.8328	1.40363	0.701817	−	0.712357i	$-0.252372\pi$
$313$	24.8328	1.40363	0.701817	+	0.712357i	$0.252372\pi$
$314$	−5.61803	−0.317044
$315$	1.23607	0.0696445
$316$	−9.56231	−0.537922
$317$	35.4164	1.98918	0.994592	−	0.103861i	$-0.0331197\pi$
$317$	35.4164	1.98918	0.994592	+	0.103861i	$0.0331197\pi$
$318$	−8.47214	−0.475094
$319$	0	0
$320$	1.00000	0.0559017
$321$	7.70820	0.430230
$322$	1.70820	0.0951945
$323$	−2.94427	−0.163824
$324$	1.00000	0.0555556
$325$	−1.61803	−0.0897524
$326$	−6.79837	−0.376527
$327$	8.94427	0.494619
$328$	1.70820	0.0943198
$329$	16.8328	0.928023
$330$	0	0
$331$	26.0689	1.43288	0.716438	−	0.697651i	$-0.245771\pi$
$331$	26.0689	1.43288	0.716438	+	0.697651i	$0.245771\pi$
$332$	1.52786	0.0838524
$333$	5.85410	0.320803
$334$	11.3262	0.619744
$335$	−9.32624	−0.509547
$336$	−1.23607	−0.0674330
$337$	−29.2361	−1.59259	−0.796295	−	0.604908i	$-0.793210\pi$
$337$	−29.2361	−1.59259	−0.796295	+	0.604908i	$0.793210\pi$
$338$	−10.3820	−0.564705
$339$	−14.8541	−0.806764
$340$	−3.85410	−0.209018
$341$	0	0
$342$	0.763932	0.0413087
$343$	−15.4164	−0.832408
$344$	5.85410	0.315632
$345$	−1.38197	−0.0744025
$346$	−8.00000	−0.430083
$347$	−29.4164	−1.57916	−0.789578	−	0.613651i	$-0.789700\pi$
$347$	−29.4164	−1.57916	−0.789578	+	0.613651i	$0.789700\pi$
$348$	−6.09017	−0.326467
$349$	−28.0000	−1.49881	−0.749403	−	0.662114i	$-0.769659\pi$
$349$	−28.0000	−1.49881	−0.749403	+	0.662114i	$0.769659\pi$
$350$	1.23607	0.0660706
$351$	1.61803	0.0863643
$352$	0	0
$353$	14.6180	0.778039	0.389020	−	0.921229i	$-0.372814\pi$
$353$	14.6180	0.778039	0.389020	+	0.921229i	$0.372814\pi$
$354$	−0.145898	−0.00775439
$355$	−15.4164	−0.818218
$356$	5.70820	0.302534
$357$	4.76393	0.252134
$358$	9.03444	0.477485
$359$	−10.1803	−0.537298	−0.268649	−	0.963238i	$-0.586577\pi$
$359$	−10.1803	−0.537298	−0.268649	+	0.963238i	$0.586577\pi$
$360$	1.00000	0.0527046
$361$	−18.4164	−0.969285
$362$	10.4721	0.550403
$363$	0	0
$364$	−2.00000	−0.104828
$365$	4.47214	0.234082
$366$	−1.52786	−0.0798627
$367$	21.7082	1.13316	0.566580	−	0.824007i	$-0.308266\pi$
$367$	21.7082	1.13316	0.566580	+	0.824007i	$0.308266\pi$
$368$	1.38197	0.0720400
$369$	1.70820	0.0889255
$370$	5.85410	0.304340
$371$	10.4721	0.543686
$372$	−2.85410	−0.147978
$373$	17.4164	0.901787	0.450894	−	0.892578i	$-0.351105\pi$
$373$	17.4164	0.901787	0.450894	+	0.892578i	$0.351105\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	13.6180	0.702296
$377$	−9.85410	−0.507512
$378$	−1.23607	−0.0635765
$379$	3.41641	0.175489	0.0877445	−	0.996143i	$-0.472034\pi$
$379$	3.41641	0.175489	0.0877445	+	0.996143i	$0.472034\pi$
$380$	0.763932	0.0391889
$381$	−0.291796	−0.0149492
$382$	25.7082	1.31535
$383$	−11.3262	−0.578744	−0.289372	−	0.957217i	$-0.593446\pi$
$383$	−11.3262	−0.578744	−0.289372	+	0.957217i	$0.593446\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	8.94427	0.455251
$387$	5.85410	0.297581
$388$	4.29180	0.217883
$389$	−15.5623	−0.789040	−0.394520	−	0.918887i	$-0.629089\pi$
$389$	−15.5623	−0.789040	−0.394520	+	0.918887i	$0.629089\pi$
$390$	1.61803	0.0819323
$391$	−5.32624	−0.269359
$392$	−5.47214	−0.276385
$393$	−18.3820	−0.927248
$394$	−22.0000	−1.10834
$395$	−9.56231	−0.481132
$396$	0	0
$397$	−23.4508	−1.17696	−0.588482	−	0.808510i	$-0.700274\pi$
$397$	−23.4508	−1.17696	−0.588482	+	0.808510i	$0.700274\pi$
$398$	9.27051	0.464689
$399$	−0.944272	−0.0472727
$400$	1.00000	0.0500000
$401$	−23.1246	−1.15479	−0.577394	−	0.816466i	$-0.695930\pi$
$401$	−23.1246	−1.15479	−0.577394	+	0.816466i	$0.695930\pi$
$402$	9.32624	0.465150
$403$	−4.61803	−0.230041
$404$	−8.14590	−0.405274
$405$	1.00000	0.0496904
$406$	7.52786	0.373602
$407$	0	0
$408$	3.85410	0.190806
$409$	−36.8541	−1.82232	−0.911159	−	0.412055i	$-0.864811\pi$
$409$	−36.8541	−1.82232	−0.911159	+	0.412055i	$0.864811\pi$
$410$	1.70820	0.0843622
$411$	−11.6180	−0.573075
$412$	15.2361	0.750627
$413$	0.180340	0.00887395
$414$	1.38197	0.0679199
$415$	1.52786	0.0749999
$416$	−1.61803	−0.0793306
$417$	−20.6525	−1.01136
$418$	0	0
$419$	17.7426	0.866785	0.433392	−	0.901205i	$-0.357316\pi$
$419$	17.7426	0.866785	0.433392	+	0.901205i	$0.357316\pi$
$420$	−1.23607	−0.0603139
$421$	4.00000	0.194948	0.0974740	−	0.995238i	$-0.468924\pi$
$421$	4.00000	0.194948	0.0974740	+	0.995238i	$0.468924\pi$
$422$	2.29180	0.111563
$423$	13.6180	0.662131
$424$	8.47214	0.411443
$425$	−3.85410	−0.186951
$426$	15.4164	0.746927
$427$	1.88854	0.0913930
$428$	−7.70820	−0.372590
$429$	0	0
$430$	5.85410	0.282310
$431$	−19.5279	−0.940624	−0.470312	−	0.882500i	$-0.655859\pi$
$431$	−19.5279	−0.940624	−0.470312	+	0.882500i	$0.655859\pi$
$432$	−1.00000	−0.0481125
$433$	−27.4164	−1.31755	−0.658774	−	0.752341i	$-0.728925\pi$
$433$	−27.4164	−1.31755	−0.658774	+	0.752341i	$0.728925\pi$
$434$	3.52786	0.169343
$435$	−6.09017	−0.292001
$436$	−8.94427	−0.428353
$437$	1.05573	0.0505023
$438$	−4.47214	−0.213687
$439$	19.9787	0.953532	0.476766	−	0.879030i	$-0.341809\pi$
$439$	19.9787	0.953532	0.476766	+	0.879030i	$0.341809\pi$
$440$	0	0
$441$	−5.47214	−0.260578
$442$	6.23607	0.296620
$443$	11.1246	0.528546	0.264273	−	0.964448i	$-0.414868\pi$
$443$	11.1246	0.528546	0.264273	+	0.964448i	$0.414868\pi$
$444$	−5.85410	−0.277823
$445$	5.70820	0.270595
$446$	−19.1246	−0.905577
$447$	7.85410	0.371486
$448$	1.23607	0.0583987
$449$	21.1246	0.996932	0.498466	−	0.866909i	$-0.333897\pi$
$449$	21.1246	0.996932	0.498466	+	0.866909i	$0.333897\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	14.8541	0.698678
$453$	−4.94427	−0.232302
$454$	13.8885	0.651822
$455$	−2.00000	−0.0937614
$456$	−0.763932	−0.0357744
$457$	1.70820	0.0799064	0.0399532	−	0.999202i	$-0.487279\pi$
$457$	1.70820	0.0799064	0.0399532	+	0.999202i	$0.487279\pi$
$458$	−15.1246	−0.706727
$459$	3.85410	0.179894
$460$	1.38197	0.0644345
$461$	−2.90983	−0.135524	−0.0677621	−	0.997702i	$-0.521586\pi$
$461$	−2.90983	−0.135524	−0.0677621	+	0.997702i	$0.521586\pi$
$462$	0	0
$463$	−18.0000	−0.836531	−0.418265	−	0.908325i	$-0.637362\pi$
$463$	−18.0000	−0.836531	−0.418265	+	0.908325i	$0.637362\pi$
$464$	6.09017	0.282729
$465$	−2.85410	−0.132356
$466$	−23.9787	−1.11079
$467$	28.2918	1.30919	0.654594	−	0.755981i	$-0.272840\pi$
$467$	28.2918	1.30919	0.654594	+	0.755981i	$0.272840\pi$
$468$	−1.61803	−0.0747936
$469$	−11.5279	−0.532307
$470$	13.6180	0.628153
$471$	5.61803	0.258865
$472$	0.145898	0.00671550
$473$	0	0
$474$	9.56231	0.439211
$475$	0.763932	0.0350516
$476$	−4.76393	−0.218354
$477$	8.47214	0.387912
$478$	−27.7082	−1.26734
$479$	−26.1803	−1.19621	−0.598105	−	0.801418i	$-0.704079\pi$
$479$	−26.1803	−1.19621	−0.598105	+	0.801418i	$0.704079\pi$
$480$	−1.00000	−0.0456435
$481$	−9.47214	−0.431892
$482$	2.94427	0.134108
$483$	−1.70820	−0.0777260
$484$	0	0
$485$	4.29180	0.194880
$486$	−1.00000	−0.0453609
$487$	−9.52786	−0.431749	−0.215874	−	0.976421i	$-0.569260\pi$
$487$	−9.52786	−0.431749	−0.215874	+	0.976421i	$0.569260\pi$
$488$	1.52786	0.0691632
$489$	6.79837	0.307433
$490$	−5.47214	−0.247206
$491$	11.9098	0.537483	0.268742	−	0.963212i	$-0.413392\pi$
$491$	11.9098	0.537483	0.268742	+	0.963212i	$0.413392\pi$
$492$	−1.70820	−0.0770118
$493$	−23.4721	−1.05713
$494$	−1.23607	−0.0556133
$495$	0	0
$496$	2.85410	0.128153
$497$	−19.0557	−0.854766
$498$	−1.52786	−0.0684652
$499$	−31.8885	−1.42753	−0.713764	−	0.700387i	$-0.753011\pi$
$499$	−31.8885	−1.42753	−0.713764	+	0.700387i	$0.753011\pi$
$500$	1.00000	0.0447214
$501$	−11.3262	−0.506019
$502$	18.3262	0.817940
$503$	22.3820	0.997963	0.498981	−	0.866613i	$-0.333708\pi$
$503$	22.3820	0.997963	0.498981	+	0.866613i	$0.333708\pi$
$504$	1.23607	0.0550588
$505$	−8.14590	−0.362488
$506$	0	0
$507$	10.3820	0.461079
$508$	0.291796	0.0129464
$509$	−13.5066	−0.598669	−0.299334	−	0.954148i	$-0.596765\pi$
$509$	−13.5066	−0.598669	−0.299334	+	0.954148i	$0.596765\pi$
$510$	3.85410	0.170663
$511$	5.52786	0.244538
$512$	1.00000	0.0441942
$513$	−0.763932	−0.0337284
$514$	12.4721	0.550122
$515$	15.2361	0.671381
$516$	−5.85410	−0.257712
$517$	0	0
$518$	7.23607	0.317935
$519$	8.00000	0.351161
$520$	−1.61803	−0.0709555
$521$	−19.3050	−0.845765	−0.422883	−	0.906184i	$-0.638982\pi$
$521$	−19.3050	−0.845765	−0.422883	+	0.906184i	$0.638982\pi$
$522$	6.09017	0.266559
$523$	−25.8885	−1.13203	−0.566013	−	0.824396i	$-0.691515\pi$
$523$	−25.8885	−1.13203	−0.566013	+	0.824396i	$0.691515\pi$
$524$	18.3820	0.803020
$525$	−1.23607	−0.0539464
$526$	19.5623	0.852957
$527$	−11.0000	−0.479168
$528$	0	0
$529$	−21.0902	−0.916964
$530$	8.47214	0.368006
$531$	0.145898	0.00633144
$532$	0.944272	0.0409394
$533$	−2.76393	−0.119719
$534$	−5.70820	−0.247018
$535$	−7.70820	−0.333255
$536$	−9.32624	−0.402832
$537$	−9.03444	−0.389865
$538$	−5.32624	−0.229630
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	34.7639	1.49462	0.747309	−	0.664477i	$-0.231345\pi$
$541$	34.7639	1.49462	0.747309	+	0.664477i	$0.231345\pi$
$542$	−6.79837	−0.292015
$543$	−10.4721	−0.449402
$544$	−3.85410	−0.165243
$545$	−8.94427	−0.383131
$546$	2.00000	0.0855921
$547$	2.85410	0.122033	0.0610163	−	0.998137i	$-0.480566\pi$
$547$	2.85410	0.122033	0.0610163	+	0.998137i	$0.480566\pi$
$548$	11.6180	0.496298
$549$	1.52786	0.0652076
$550$	0	0
$551$	4.65248	0.198202
$552$	−1.38197	−0.0588204
$553$	−11.8197	−0.502623
$554$	−32.0344	−1.36101
$555$	−5.85410	−0.248493
$556$	20.6525	0.875860
$557$	21.1246	0.895079	0.447539	−	0.894264i	$-0.352300\pi$
$557$	21.1246	0.895079	0.447539	+	0.894264i	$0.352300\pi$
$558$	2.85410	0.120824
$559$	−9.47214	−0.400629
$560$	1.23607	0.0522334
$561$	0	0
$562$	−23.8885	−1.00768
$563$	38.3607	1.61671	0.808355	−	0.588695i	$-0.200358\pi$
$563$	38.3607	1.61671	0.808355	+	0.588695i	$0.200358\pi$
$564$	−13.6180	−0.573423
$565$	14.8541	0.624917
$566$	3.03444	0.127547
$567$	1.23607	0.0519100
$568$	−15.4164	−0.646858
$569$	−43.3050	−1.81544	−0.907719	−	0.419579i	$-0.862178\pi$
$569$	−43.3050	−1.81544	−0.907719	+	0.419579i	$0.862178\pi$
$570$	−0.763932	−0.0319976
$571$	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
$573$	−25.7082	−1.07398
$574$	2.11146	0.0881305
$575$	1.38197	0.0576320
$576$	1.00000	0.0416667
$577$	9.41641	0.392010	0.196005	−	0.980603i	$-0.437203\pi$
$577$	9.41641	0.392010	0.196005	+	0.980603i	$0.437203\pi$
$578$	−2.14590	−0.0892576
$579$	−8.94427	−0.371711
$580$	6.09017	0.252881
$581$	1.88854	0.0783500
$582$	−4.29180	−0.177901
$583$	0	0
$584$	4.47214	0.185058
$585$	−1.61803	−0.0668975
$586$	7.05573	0.291469
$587$	22.5410	0.930367	0.465184	−	0.885214i	$-0.345988\pi$
$587$	22.5410	0.930367	0.465184	+	0.885214i	$0.345988\pi$
$588$	5.47214	0.225667
$589$	2.18034	0.0898393
$590$	0.145898	0.00600653
$591$	22.0000	0.904959
$592$	5.85410	0.240602
$593$	19.0344	0.781651	0.390825	−	0.920465i	$-0.372190\pi$
$593$	19.0344	0.781651	0.390825	+	0.920465i	$0.372190\pi$
$594$	0	0
$595$	−4.76393	−0.195302
$596$	−7.85410	−0.321717
$597$	−9.27051	−0.379417
$598$	−2.23607	−0.0914396
$599$	−30.6525	−1.25243	−0.626213	−	0.779652i	$-0.715396\pi$
$599$	−30.6525	−1.25243	−0.626213	+	0.779652i	$0.715396\pi$
$600$	−1.00000	−0.0408248
$601$	−45.7771	−1.86729	−0.933643	−	0.358204i	$-0.883389\pi$
$601$	−45.7771	−1.86729	−0.933643	+	0.358204i	$0.883389\pi$
$602$	7.23607	0.294920
$603$	−9.32624	−0.379794
$604$	4.94427	0.201180
$605$	0	0
$606$	8.14590	0.330904
$607$	37.7771	1.53332	0.766662	−	0.642051i	$-0.221916\pi$
$607$	37.7771	1.53332	0.766662	+	0.642051i	$0.221916\pi$
$608$	0.763932	0.0309815
$609$	−7.52786	−0.305044
$610$	1.52786	0.0618614
$611$	−22.0344	−0.891418
$612$	−3.85410	−0.155793
$613$	13.0557	0.527316	0.263658	−	0.964616i	$-0.415071\pi$
$613$	13.0557	0.527316	0.263658	+	0.964616i	$0.415071\pi$
$614$	−18.0902	−0.730060
$615$	−1.70820	−0.0688814
$616$	0	0
$617$	−22.3607	−0.900207	−0.450104	−	0.892976i	$-0.648613\pi$
$617$	−22.3607	−0.900207	−0.450104	+	0.892976i	$0.648613\pi$
$618$	−15.2361	−0.612885
$619$	−6.11146	−0.245640	−0.122820	−	0.992429i	$-0.539194\pi$
$619$	−6.11146	−0.245640	−0.122820	+	0.992429i	$0.539194\pi$
$620$	2.85410	0.114623
$621$	−1.38197	−0.0554564
$622$	−4.18034	−0.167616
$623$	7.05573	0.282682
$624$	1.61803	0.0647732
$625$	1.00000	0.0400000
$626$	24.8328	0.992519
$627$	0	0
$628$	−5.61803	−0.224184
$629$	−22.5623	−0.899618
$630$	1.23607	0.0492461
$631$	23.9787	0.954578	0.477289	−	0.878747i	$-0.341620\pi$
$631$	23.9787	0.954578	0.477289	+	0.878747i	$0.341620\pi$
$632$	−9.56231	−0.380368
$633$	−2.29180	−0.0910907
$634$	35.4164	1.40657
$635$	0.291796	0.0115796
$636$	−8.47214	−0.335942
$637$	8.85410	0.350812
$638$	0	0
$639$	−15.4164	−0.609864
$640$	1.00000	0.0395285
$641$	1.23607	0.0488217	0.0244109	−	0.999702i	$-0.492229\pi$
$641$	1.23607	0.0488217	0.0244109	+	0.999702i	$0.492229\pi$
$642$	7.70820	0.304219
$643$	1.32624	0.0523017	0.0261509	−	0.999658i	$-0.491675\pi$
$643$	1.32624	0.0523017	0.0261509	+	0.999658i	$0.491675\pi$
$644$	1.70820	0.0673127
$645$	−5.85410	−0.230505
$646$	−2.94427	−0.115841
$647$	18.0344	0.709007	0.354504	−	0.935055i	$-0.384650\pi$
$647$	18.0344	0.709007	0.354504	+	0.935055i	$0.384650\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−1.61803	−0.0634645
$651$	−3.52786	−0.138268
$652$	−6.79837	−0.266245
$653$	−16.2918	−0.637547	−0.318774	−	0.947831i	$-0.603271\pi$
$653$	−16.2918	−0.637547	−0.318774	+	0.947831i	$0.603271\pi$
$654$	8.94427	0.349749
$655$	18.3820	0.718243
$656$	1.70820	0.0666942
$657$	4.47214	0.174475
$658$	16.8328	0.656211
$659$	27.4164	1.06799	0.533996	−	0.845487i	$-0.320690\pi$
$659$	27.4164	1.06799	0.533996	+	0.845487i	$0.320690\pi$
$660$	0	0
$661$	−3.41641	−0.132883	−0.0664414	−	0.997790i	$-0.521165\pi$
$661$	−3.41641	−0.132883	−0.0664414	+	0.997790i	$0.521165\pi$
$662$	26.0689	1.01320
$663$	−6.23607	−0.242189
$664$	1.52786	0.0592926
$665$	0.944272	0.0366173
$666$	5.85410	0.226842
$667$	8.41641	0.325885
$668$	11.3262	0.438225
$669$	19.1246	0.739400
$670$	−9.32624	−0.360304
$671$	0	0
$672$	−1.23607	−0.0476824
$673$	−27.2361	−1.04987	−0.524937	−	0.851141i	$-0.675911\pi$
$673$	−27.2361	−1.04987	−0.524937	+	0.851141i	$0.675911\pi$
$674$	−29.2361	−1.12613
$675$	−1.00000	−0.0384900
$676$	−10.3820	−0.399306
$677$	−6.76393	−0.259959	−0.129980	−	0.991517i	$-0.541491\pi$
$677$	−6.76393	−0.259959	−0.129980	+	0.991517i	$0.541491\pi$
$678$	−14.8541	−0.570468
$679$	5.30495	0.203585
$680$	−3.85410	−0.147798
$681$	−13.8885	−0.532210
$682$	0	0
$683$	5.23607	0.200353	0.100176	−	0.994970i	$-0.468059\pi$
$683$	5.23607	0.200353	0.100176	+	0.994970i	$0.468059\pi$
$684$	0.763932	0.0292097
$685$	11.6180	0.443902
$686$	−15.4164	−0.588601
$687$	15.1246	0.577040
$688$	5.85410	0.223186
$689$	−13.7082	−0.522241
$690$	−1.38197	−0.0526105
$691$	−29.1246	−1.10795	−0.553976	−	0.832532i	$-0.686890\pi$
$691$	−29.1246	−1.10795	−0.553976	+	0.832532i	$0.686890\pi$
$692$	−8.00000	−0.304114
$693$	0	0
$694$	−29.4164	−1.11663
$695$	20.6525	0.783393
$696$	−6.09017	−0.230847
$697$	−6.58359	−0.249371
$698$	−28.0000	−1.05982
$699$	23.9787	0.906958
$700$	1.23607	0.0467190
$701$	−28.4721	−1.07538	−0.537689	−	0.843143i	$-0.680702\pi$
$701$	−28.4721	−1.07538	−0.537689	+	0.843143i	$0.680702\pi$
$702$	1.61803	0.0610688
$703$	4.47214	0.168670
$704$	0	0
$705$	−13.6180	−0.512885
$706$	14.6180	0.550157
$707$	−10.0689	−0.378679
$708$	−0.145898	−0.00548318
$709$	−38.9443	−1.46258	−0.731291	−	0.682065i	$-0.761082\pi$
$709$	−38.9443	−1.46258	−0.731291	+	0.682065i	$0.761082\pi$
$710$	−15.4164	−0.578567
$711$	−9.56231	−0.358614
$712$	5.70820	0.213924
$713$	3.94427	0.147714
$714$	4.76393	0.178286
$715$	0	0
$716$	9.03444	0.337633
$717$	27.7082	1.03478
$718$	−10.1803	−0.379927
$719$	−32.1803	−1.20012	−0.600062	−	0.799953i	$-0.704857\pi$
$719$	−32.1803	−1.20012	−0.600062	+	0.799953i	$0.704857\pi$
$720$	1.00000	0.0372678
$721$	18.8328	0.701371
$722$	−18.4164	−0.685388
$723$	−2.94427	−0.109499
$724$	10.4721	0.389194
$725$	6.09017	0.226183
$726$	0	0
$727$	−18.0689	−0.670138	−0.335069	−	0.942194i	$-0.608760\pi$
$727$	−18.0689	−0.670138	−0.335069	+	0.942194i	$0.608760\pi$
$728$	−2.00000	−0.0741249
$729$	1.00000	0.0370370
$730$	4.47214	0.165521
$731$	−22.5623	−0.834497
$732$	−1.52786	−0.0564715
$733$	10.7984	0.398847	0.199424	−	0.979913i	$-0.436093\pi$
$733$	10.7984	0.398847	0.199424	+	0.979913i	$0.436093\pi$
$734$	21.7082	0.801264
$735$	5.47214	0.201843
$736$	1.38197	0.0509399
$737$	0	0
$738$	1.70820	0.0628799
$739$	−27.7082	−1.01926	−0.509631	−	0.860393i	$-0.670218\pi$
$739$	−27.7082	−1.01926	−0.509631	+	0.860393i	$0.670218\pi$
$740$	5.85410	0.215201
$741$	1.23607	0.0454081
$742$	10.4721	0.384444
$743$	11.1459	0.408903	0.204452	−	0.978877i	$-0.434459\pi$
$743$	11.1459	0.408903	0.204452	+	0.978877i	$0.434459\pi$
$744$	−2.85410	−0.104636
$745$	−7.85410	−0.287752
$746$	17.4164	0.637660
$747$	1.52786	0.0559016
$748$	0	0
$749$	−9.52786	−0.348141
$750$	−1.00000	−0.0365148
$751$	−41.2705	−1.50598	−0.752991	−	0.658031i	$-0.771390\pi$
$751$	−41.2705	−1.50598	−0.752991	+	0.658031i	$0.771390\pi$
$752$	13.6180	0.496599
$753$	−18.3262	−0.667845
$754$	−9.85410	−0.358865
$755$	4.94427	0.179940
$756$	−1.23607	−0.0449554
$757$	10.9656	0.398550	0.199275	−	0.979944i	$-0.436141\pi$
$757$	10.9656	0.398550	0.199275	+	0.979944i	$0.436141\pi$
$758$	3.41641	0.124090
$759$	0	0
$760$	0.763932	0.0277107
$761$	35.5279	1.28788	0.643942	−	0.765074i	$-0.277298\pi$
$761$	35.5279	1.28788	0.643942	+	0.765074i	$0.277298\pi$
$762$	−0.291796	−0.0105707
$763$	−11.0557	−0.400244
$764$	25.7082	0.930090
$765$	−3.85410	−0.139345
$766$	−11.3262	−0.409234
$767$	−0.236068	−0.00852392
$768$	−1.00000	−0.0360844
$769$	−39.4508	−1.42263	−0.711317	−	0.702871i	$-0.751901\pi$
$769$	−39.4508	−1.42263	−0.711317	+	0.702871i	$0.751901\pi$
$770$	0	0
$771$	−12.4721	−0.449173
$772$	8.94427	0.321911
$773$	−4.29180	−0.154365	−0.0771826	−	0.997017i	$-0.524592\pi$
$773$	−4.29180	−0.154365	−0.0771826	+	0.997017i	$0.524592\pi$
$774$	5.85410	0.210421
$775$	2.85410	0.102522
$776$	4.29180	0.154067
$777$	−7.23607	−0.259592
$778$	−15.5623	−0.557936
$779$	1.30495	0.0467547
$780$	1.61803	0.0579349
$781$	0	0
$782$	−5.32624	−0.190466
$783$	−6.09017	−0.217645
$784$	−5.47214	−0.195433
$785$	−5.61803	−0.200516
$786$	−18.3820	−0.655663
$787$	−52.6869	−1.87809	−0.939043	−	0.343800i	$-0.888286\pi$
$787$	−52.6869	−1.87809	−0.939043	+	0.343800i	$0.888286\pi$
$788$	−22.0000	−0.783718
$789$	−19.5623	−0.696437
$790$	−9.56231	−0.340212
$791$	18.3607	0.652831
$792$	0	0
$793$	−2.47214	−0.0877881
$794$	−23.4508	−0.832240
$795$	−8.47214	−0.300476
$796$	9.27051	0.328585
$797$	51.1246	1.81093	0.905463	−	0.424425i	$-0.139524\pi$
$797$	51.1246	1.81093	0.905463	+	0.424425i	$0.139524\pi$
$798$	−0.944272	−0.0334269
$799$	−52.4853	−1.85680
$800$	1.00000	0.0353553
$801$	5.70820	0.201689
$802$	−23.1246	−0.816558
$803$	0	0
$804$	9.32624	0.328911
$805$	1.70820	0.0602063
$806$	−4.61803	−0.162663
$807$	5.32624	0.187492
$808$	−8.14590	−0.286572
$809$	56.4296	1.98396	0.991979	−	0.126404i	$-0.0403434\pi$
$809$	56.4296	1.98396	0.991979	+	0.126404i	$0.0403434\pi$
$810$	1.00000	0.0351364
$811$	2.11146	0.0741433	0.0370716	−	0.999313i	$-0.488197\pi$
$811$	2.11146	0.0741433	0.0370716	+	0.999313i	$0.488197\pi$
$812$	7.52786	0.264176
$813$	6.79837	0.238429
$814$	0	0
$815$	−6.79837	−0.238137
$816$	3.85410	0.134921
$817$	4.47214	0.156460
$818$	−36.8541	−1.28857
$819$	−2.00000	−0.0698857
$820$	1.70820	0.0596531
$821$	35.3050	1.23215	0.616076	−	0.787687i	$-0.288722\pi$
$821$	35.3050	1.23215	0.616076	+	0.787687i	$0.288722\pi$
$822$	−11.6180	−0.405225
$823$	−8.87539	−0.309377	−0.154688	−	0.987963i	$-0.549437\pi$
$823$	−8.87539	−0.309377	−0.154688	+	0.987963i	$0.549437\pi$
$824$	15.2361	0.530774
$825$	0	0
$826$	0.180340	0.00627483
$827$	34.1803	1.18857	0.594283	−	0.804256i	$-0.297436\pi$
$827$	34.1803	1.18857	0.594283	+	0.804256i	$0.297436\pi$
$828$	1.38197	0.0480266
$829$	−30.5410	−1.06073	−0.530367	−	0.847768i	$-0.677946\pi$
$829$	−30.5410	−1.06073	−0.530367	+	0.847768i	$0.677946\pi$
$830$	1.52786	0.0530329
$831$	32.0344	1.11126
$832$	−1.61803	−0.0560952
$833$	21.0902	0.730731
$834$	−20.6525	−0.715137
$835$	11.3262	0.391961
$836$	0	0
$837$	−2.85410	−0.0986522
$838$	17.7426	0.612910
$839$	7.81966	0.269965	0.134982	−	0.990848i	$-0.456902\pi$
$839$	7.81966	0.269965	0.134982	+	0.990848i	$0.456902\pi$
$840$	−1.23607	−0.0426484
$841$	8.09017	0.278971
$842$	4.00000	0.137849
$843$	23.8885	0.822765
$844$	2.29180	0.0788869
$845$	−10.3820	−0.357150
$846$	13.6180	0.468198
$847$	0	0
$848$	8.47214	0.290934
$849$	−3.03444	−0.104142
$850$	−3.85410	−0.132195
$851$	8.09017	0.277327
$852$	15.4164	0.528157
$853$	−19.5279	−0.668621	−0.334311	−	0.942463i	$-0.608503\pi$
$853$	−19.5279	−0.668621	−0.334311	+	0.942463i	$0.608503\pi$
$854$	1.88854	0.0646246
$855$	0.763932	0.0261259
$856$	−7.70820	−0.263461
$857$	−18.3262	−0.626012	−0.313006	−	0.949751i	$-0.601336\pi$
$857$	−18.3262	−0.626012	−0.313006	+	0.949751i	$0.601336\pi$
$858$	0	0
$859$	22.0689	0.752981	0.376490	−	0.926421i	$-0.377131\pi$
$859$	22.0689	0.752981	0.376490	+	0.926421i	$0.377131\pi$
$860$	5.85410	0.199623
$861$	−2.11146	−0.0719582
$862$	−19.5279	−0.665122
$863$	−32.8673	−1.11881	−0.559407	−	0.828893i	$-0.688971\pi$
$863$	−32.8673	−1.11881	−0.559407	+	0.828893i	$0.688971\pi$
$864$	−1.00000	−0.0340207
$865$	−8.00000	−0.272008
$866$	−27.4164	−0.931647
$867$	2.14590	0.0728785
$868$	3.52786	0.119744
$869$	0	0
$870$	−6.09017	−0.206476
$871$	15.0902	0.511311
$872$	−8.94427	−0.302891
$873$	4.29180	0.145255
$874$	1.05573	0.0357105
$875$	1.23607	0.0417867
$876$	−4.47214	−0.151099
$877$	42.2148	1.42549	0.712746	−	0.701422i	$-0.247451\pi$
$877$	42.2148	1.42549	0.712746	+	0.701422i	$0.247451\pi$
$878$	19.9787	0.674249
$879$	−7.05573	−0.237984
$880$	0	0
$881$	−45.3050	−1.52636	−0.763181	−	0.646184i	$-0.776364\pi$
$881$	−45.3050	−1.52636	−0.763181	+	0.646184i	$0.776364\pi$
$882$	−5.47214	−0.184256
$883$	−42.2148	−1.42064	−0.710320	−	0.703879i	$-0.751450\pi$
$883$	−42.2148	−1.42064	−0.710320	+	0.703879i	$0.751450\pi$
$884$	6.23607	0.209742
$885$	−0.145898	−0.00490431
$886$	11.1246	0.373739
$887$	−14.6869	−0.493138	−0.246569	−	0.969125i	$-0.579303\pi$
$887$	−14.6869	−0.493138	−0.246569	+	0.969125i	$0.579303\pi$
$888$	−5.85410	−0.196451
$889$	0.360680	0.0120968
$890$	5.70820	0.191339
$891$	0	0
$892$	−19.1246	−0.640339
$893$	10.4033	0.348132
$894$	7.85410	0.262680
$895$	9.03444	0.301988
$896$	1.23607	0.0412941
$897$	2.23607	0.0746601
$898$	21.1246	0.704937
$899$	17.3820	0.579721
$900$	1.00000	0.0333333
$901$	−32.6525	−1.08781
$902$	0	0
$903$	−7.23607	−0.240801
$904$	14.8541	0.494040
$905$	10.4721	0.348106
$906$	−4.94427	−0.164262
$907$	−5.49342	−0.182406	−0.0912030	−	0.995832i	$-0.529071\pi$
$907$	−5.49342	−0.182406	−0.0912030	+	0.995832i	$0.529071\pi$
$908$	13.8885	0.460908
$909$	−8.14590	−0.270182
$910$	−2.00000	−0.0662994
$911$	−13.6393	−0.451891	−0.225945	−	0.974140i	$-0.572547\pi$
$911$	−13.6393	−0.451891	−0.225945	+	0.974140i	$0.572547\pi$
$912$	−0.763932	−0.0252963
$913$	0	0
$914$	1.70820	0.0565024
$915$	−1.52786	−0.0505096
$916$	−15.1246	−0.499731
$917$	22.7214	0.750325
$918$	3.85410	0.127204
$919$	−34.7984	−1.14789	−0.573946	−	0.818893i	$-0.694588\pi$
$919$	−34.7984	−1.14789	−0.573946	+	0.818893i	$0.694588\pi$
$920$	1.38197	0.0455621
$921$	18.0902	0.596091
$922$	−2.90983	−0.0958301
$923$	24.9443	0.821051
$924$	0	0
$925$	5.85410	0.192482
$926$	−18.0000	−0.591517
$927$	15.2361	0.500418
$928$	6.09017	0.199920
$929$	−1.52786	−0.0501276	−0.0250638	−	0.999686i	$-0.507979\pi$
$929$	−1.52786	−0.0501276	−0.0250638	+	0.999686i	$0.507979\pi$
$930$	−2.85410	−0.0935897
$931$	−4.18034	−0.137005
$932$	−23.9787	−0.785449
$933$	4.18034	0.136858
$934$	28.2918	0.925736
$935$	0	0
$936$	−1.61803	−0.0528871
$937$	57.0132	1.86254	0.931269	−	0.364332i	$-0.118703\pi$
$937$	57.0132	1.86254	0.931269	+	0.364332i	$0.118703\pi$
$938$	−11.5279	−0.376398
$939$	−24.8328	−0.810388
$940$	13.6180	0.444171
$941$	−52.1591	−1.70034	−0.850168	−	0.526511i	$-0.823500\pi$
$941$	−52.1591	−1.70034	−0.850168	+	0.526511i	$0.823500\pi$
$942$	5.61803	0.183045
$943$	2.36068	0.0768743
$944$	0.145898	0.00474858
$945$	−1.23607	−0.0402093
$946$	0	0
$947$	1.88854	0.0613694	0.0306847	−	0.999529i	$-0.490231\pi$
$947$	1.88854	0.0613694	0.0306847	+	0.999529i	$0.490231\pi$
$948$	9.56231	0.310569
$949$	−7.23607	−0.234893
$950$	0.763932	0.0247852
$951$	−35.4164	−1.14846
$952$	−4.76393	−0.154400
$953$	34.3262	1.11194	0.555968	−	0.831204i	$-0.312348\pi$
$953$	34.3262	1.11194	0.555968	+	0.831204i	$0.312348\pi$
$954$	8.47214	0.274296
$955$	25.7082	0.831898
$956$	−27.7082	−0.896147
$957$	0	0
$958$	−26.1803	−0.845848
$959$	14.3607	0.463731
$960$	−1.00000	−0.0322749
$961$	−22.8541	−0.737229
$962$	−9.47214	−0.305394
$963$	−7.70820	−0.248393
$964$	2.94427	0.0948286
$965$	8.94427	0.287926
$966$	−1.70820	−0.0549606
$967$	−35.7771	−1.15051	−0.575257	−	0.817973i	$-0.695098\pi$
$967$	−35.7771	−1.15051	−0.575257	+	0.817973i	$0.695098\pi$
$968$	0	0
$969$	2.94427	0.0945836
$970$	4.29180	0.137801
$971$	0.583592	0.0187284	0.00936418	−	0.999956i	$-0.497019\pi$
$971$	0.583592	0.0187284	0.00936418	+	0.999956i	$0.497019\pi$
$972$	−1.00000	−0.0320750
$973$	25.5279	0.818386
$974$	−9.52786	−0.305292
$975$	1.61803	0.0518186
$976$	1.52786	0.0489057
$977$	37.0557	1.18552	0.592759	−	0.805380i	$-0.298039\pi$
$977$	37.0557	1.18552	0.592759	+	0.805380i	$0.298039\pi$
$978$	6.79837	0.217388
$979$	0	0
$980$	−5.47214	−0.174801
$981$	−8.94427	−0.285569
$982$	11.9098	0.380058
$983$	−42.2492	−1.34754	−0.673770	−	0.738941i	$-0.735326\pi$
$983$	−42.2492	−1.34754	−0.673770	+	0.738941i	$0.735326\pi$
$984$	−1.70820	−0.0544556
$985$	−22.0000	−0.700978
$986$	−23.4721	−0.747505
$987$	−16.8328	−0.535794
$988$	−1.23607	−0.0393246
$989$	8.09017	0.257252
$990$	0	0
$991$	53.3394	1.69438	0.847191	−	0.531289i	$-0.178292\pi$
$991$	53.3394	1.69438	0.847191	+	0.531289i	$0.178292\pi$
$992$	2.85410	0.0906178
$993$	−26.0689	−0.827271
$994$	−19.0557	−0.604411
$995$	9.27051	0.293895
$996$	−1.52786	−0.0484122
$997$	−10.5066	−0.332747	−0.166373	−	0.986063i	$-0.553206\pi$
$997$	−10.5066	−0.332747	−0.166373	+	0.986063i	$0.553206\pi$
$998$	−31.8885	−1.00941
$999$	−5.85410	−0.185216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bm.1.2		2
11.7	odd	10		330.2.m.c.181.1	yes	4
11.8	odd	10		330.2.m.c.31.1	✓	4
11.10	odd	2		3630.2.a.be.1.1		2
33.8	even	10		990.2.n.d.361.1		4
33.29	even	10		990.2.n.d.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.c.31.1	✓	4	11.8	odd	10
330.2.m.c.181.1	yes	4	11.7	odd	10
990.2.n.d.181.1		4	33.29	even	10
990.2.n.d.361.1		4	33.8	even	10
3630.2.a.be.1.1		2	11.10	odd	2
3630.2.a.bm.1.2		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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -1.61803 q^{13} +1.23607 q^{14} -1.00000 q^{15} +1.00000 q^{16} -3.85410 q^{17} +1.00000 q^{18} +0.763932 q^{19} +1.00000 q^{20} -1.23607 q^{21} +1.38197 q^{23} -1.00000 q^{24} +1.00000 q^{25} -1.61803 q^{26} -1.00000 q^{27} +1.23607 q^{28} +6.09017 q^{29} -1.00000 q^{30} +2.85410 q^{31} +1.00000 q^{32} -3.85410 q^{34} +1.23607 q^{35} +1.00000 q^{36} +5.85410 q^{37} +0.763932 q^{38} +1.61803 q^{39} +1.00000 q^{40} +1.70820 q^{41} -1.23607 q^{42} +5.85410 q^{43} +1.00000 q^{45} +1.38197 q^{46} +13.6180 q^{47} -1.00000 q^{48} -5.47214 q^{49} +1.00000 q^{50} +3.85410 q^{51} -1.61803 q^{52} +8.47214 q^{53} -1.00000 q^{54} +1.23607 q^{56} -0.763932 q^{57} +6.09017 q^{58} +0.145898 q^{59} -1.00000 q^{60} +1.52786 q^{61} +2.85410 q^{62} +1.23607 q^{63} +1.00000 q^{64} -1.61803 q^{65} -9.32624 q^{67} -3.85410 q^{68} -1.38197 q^{69} +1.23607 q^{70} -15.4164 q^{71} +1.00000 q^{72} +4.47214 q^{73} +5.85410 q^{74} -1.00000 q^{75} +0.763932 q^{76} +1.61803 q^{78} -9.56231 q^{79} +1.00000 q^{80} +1.00000 q^{81} +1.70820 q^{82} +1.52786 q^{83} -1.23607 q^{84} -3.85410 q^{85} +5.85410 q^{86} -6.09017 q^{87} +5.70820 q^{89} +1.00000 q^{90} -2.00000 q^{91} +1.38197 q^{92} -2.85410 q^{93} +13.6180 q^{94} +0.763932 q^{95} -1.00000 q^{96} +4.29180 q^{97} -5.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

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