LMFDB - Embedded newform 3630.2.a.bj.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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +5.61803 q^{13} +1.23607 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.09017 q^{17} +1.00000 q^{18} -3.23607 q^{19} -1.00000 q^{20} -1.23607 q^{21} +0.145898 q^{23} -1.00000 q^{24} +1.00000 q^{25} +5.61803 q^{26} -1.00000 q^{27} +1.23607 q^{28} -0.381966 q^{29} +1.00000 q^{30} -3.61803 q^{31} +1.00000 q^{32} +5.09017 q^{34} -1.23607 q^{35} +1.00000 q^{36} -8.61803 q^{37} -3.23607 q^{38} -5.61803 q^{39} -1.00000 q^{40} -3.23607 q^{41} -1.23607 q^{42} +11.0902 q^{43} -1.00000 q^{45} +0.145898 q^{46} +11.3262 q^{47} -1.00000 q^{48} -5.47214 q^{49} +1.00000 q^{50} -5.09017 q^{51} +5.61803 q^{52} -0.472136 q^{53} -1.00000 q^{54} +1.23607 q^{56} +3.23607 q^{57} -0.381966 q^{58} +2.90983 q^{59} +1.00000 q^{60} -3.61803 q^{62} +1.23607 q^{63} +1.00000 q^{64} -5.61803 q^{65} +6.09017 q^{67} +5.09017 q^{68} -0.145898 q^{69} -1.23607 q^{70} +1.52786 q^{71} +1.00000 q^{72} -13.4164 q^{73} -8.61803 q^{74} -1.00000 q^{75} -3.23607 q^{76} -5.61803 q^{78} +7.09017 q^{79} -1.00000 q^{80} +1.00000 q^{81} -3.23607 q^{82} +4.00000 q^{83} -1.23607 q^{84} -5.09017 q^{85} +11.0902 q^{86} +0.381966 q^{87} +12.7639 q^{89} -1.00000 q^{90} +6.94427 q^{91} +0.145898 q^{92} +3.61803 q^{93} +11.3262 q^{94} +3.23607 q^{95} -1.00000 q^{96} -12.6525 q^{97} -5.47214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} + 9 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 7 q^{23} - 2 q^{24} + 2 q^{25} + 9 q^{26} - 2 q^{27} - 2 q^{28} - 3 q^{29} + 2 q^{30} - 5 q^{31} + 2 q^{32} - q^{34} + 2 q^{35} + 2 q^{36} - 15 q^{37} - 2 q^{38} - 9 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 2 q^{45} + 7 q^{46} + 7 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + q^{51} + 9 q^{52} + 8 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 17 q^{59} + 2 q^{60} - 5 q^{62} - 2 q^{63} + 2 q^{64} - 9 q^{65} + q^{67} - q^{68} - 7 q^{69} + 2 q^{70} + 12 q^{71} + 2 q^{72} - 15 q^{74} - 2 q^{75} - 2 q^{76} - 9 q^{78} + 3 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{82} + 8 q^{83} + 2 q^{84} + q^{85} + 11 q^{86} + 3 q^{87} + 30 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 5 q^{93} + 7 q^{94} + 2 q^{95} - 2 q^{96} + 6 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 + 9 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 - q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 + 7 * q^23 - 2 * q^24 + 2 * q^25 + 9 * q^26 - 2 * q^27 - 2 * q^28 - 3 * q^29 + 2 * q^30 - 5 * q^31 + 2 * q^32 - q^34 + 2 * q^35 + 2 * q^36 - 15 * q^37 - 2 * q^38 - 9 * q^39 - 2 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 2 * q^45 + 7 * q^46 + 7 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + q^51 + 9 * q^52 + 8 * q^53 - 2 * q^54 - 2 * q^56 + 2 * q^57 - 3 * q^58 + 17 * q^59 + 2 * q^60 - 5 * q^62 - 2 * q^63 + 2 * q^64 - 9 * q^65 + q^67 - q^68 - 7 * q^69 + 2 * q^70 + 12 * q^71 + 2 * q^72 - 15 * q^74 - 2 * q^75 - 2 * q^76 - 9 * q^78 + 3 * q^79 - 2 * q^80 + 2 * q^81 - 2 * q^82 + 8 * q^83 + 2 * q^84 + q^85 + 11 * q^86 + 3 * q^87 + 30 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 5 * q^93 + 7 * q^94 + 2 * q^95 - 2 * q^96 + 6 * 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
$13$	5.61803	1.55816	0.779081	−	0.626923i	$-0.215686\pi$
$13$	5.61803	1.55816	0.779081	+	0.626923i	$0.215686\pi$
$14$	1.23607	0.330353
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	5.09017	1.23455	0.617274	−	0.786748i	$-0.288237\pi$
$17$	5.09017	1.23455	0.617274	+	0.786748i	$0.288237\pi$
$18$	1.00000	0.235702
$19$	−3.23607	−0.742405	−0.371202	−	0.928552i	$-0.621054\pi$
$19$	−3.23607	−0.742405	−0.371202	+	0.928552i	$0.621054\pi$
$20$	−1.00000	−0.223607
$21$	−1.23607	−0.269732
$22$	0	0
$23$	0.145898	0.0304218	0.0152109	−	0.999884i	$-0.495158\pi$
$23$	0.145898	0.0304218	0.0152109	+	0.999884i	$0.495158\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	5.61803	1.10179
$27$	−1.00000	−0.192450
$28$	1.23607	0.233595
$29$	−0.381966	−0.0709293	−0.0354647	−	0.999371i	$-0.511291\pi$
$29$	−0.381966	−0.0709293	−0.0354647	+	0.999371i	$0.511291\pi$
$30$	1.00000	0.182574
$31$	−3.61803	−0.649818	−0.324909	−	0.945745i	$-0.605334\pi$
$31$	−3.61803	−0.649818	−0.324909	+	0.945745i	$0.605334\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	5.09017	0.872957
$35$	−1.23607	−0.208934
$36$	1.00000	0.166667
$37$	−8.61803	−1.41680	−0.708398	−	0.705813i	$-0.750582\pi$
$37$	−8.61803	−1.41680	−0.708398	+	0.705813i	$0.750582\pi$
$38$	−3.23607	−0.524960
$39$	−5.61803	−0.899605
$40$	−1.00000	−0.158114
$41$	−3.23607	−0.505389	−0.252694	−	0.967546i	$-0.581317\pi$
$41$	−3.23607	−0.505389	−0.252694	+	0.967546i	$0.581317\pi$
$42$	−1.23607	−0.190729
$43$	11.0902	1.69124	0.845618	−	0.533789i	$-0.179232\pi$
$43$	11.0902	1.69124	0.845618	+	0.533789i	$0.179232\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	0.145898	0.0215115
$47$	11.3262	1.65210	0.826051	−	0.563596i	$-0.190582\pi$
$47$	11.3262	1.65210	0.826051	+	0.563596i	$0.190582\pi$
$48$	−1.00000	−0.144338
$49$	−5.47214	−0.781734
$50$	1.00000	0.141421
$51$	−5.09017	−0.712766
$52$	5.61803	0.779081
$53$	−0.472136	−0.0648529	−0.0324264	−	0.999474i	$-0.510323\pi$
$53$	−0.472136	−0.0648529	−0.0324264	+	0.999474i	$0.510323\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	1.23607	0.165177
$57$	3.23607	0.428628
$58$	−0.381966	−0.0501546
$59$	2.90983	0.378828	0.189414	−	0.981897i	$-0.439341\pi$
$59$	2.90983	0.378828	0.189414	+	0.981897i	$0.439341\pi$
$60$	1.00000	0.129099
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−3.61803	−0.459491
$63$	1.23607	0.155730
$64$	1.00000	0.125000
$65$	−5.61803	−0.696831
$66$	0	0
$67$	6.09017	0.744033	0.372016	−	0.928226i	$-0.378667\pi$
$67$	6.09017	0.744033	0.372016	+	0.928226i	$0.378667\pi$
$68$	5.09017	0.617274
$69$	−0.145898	−0.0175641
$70$	−1.23607	−0.147738
$71$	1.52786	0.181324	0.0906621	−	0.995882i	$-0.471102\pi$
$71$	1.52786	0.181324	0.0906621	+	0.995882i	$0.471102\pi$
$72$	1.00000	0.117851
$73$	−13.4164	−1.57027	−0.785136	−	0.619324i	$-0.787407\pi$
$73$	−13.4164	−1.57027	−0.785136	+	0.619324i	$0.787407\pi$
$74$	−8.61803	−1.00183
$75$	−1.00000	−0.115470
$76$	−3.23607	−0.371202
$77$	0	0
$78$	−5.61803	−0.636117
$79$	7.09017	0.797706	0.398853	−	0.917015i	$-0.369408\pi$
$79$	7.09017	0.797706	0.398853	+	0.917015i	$0.369408\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	−3.23607	−0.357364
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	−1.23607	−0.134866
$85$	−5.09017	−0.552106
$86$	11.0902	1.19588
$87$	0.381966	0.0409511
$88$	0	0
$89$	12.7639	1.35297	0.676487	−	0.736455i	$-0.263501\pi$
$89$	12.7639	1.35297	0.676487	+	0.736455i	$0.263501\pi$
$90$	−1.00000	−0.105409
$91$	6.94427	0.727957
$92$	0.145898	0.0152109
$93$	3.61803	0.375173
$94$	11.3262	1.16821
$95$	3.23607	0.332014
$96$	−1.00000	−0.102062
$97$	−12.6525	−1.28466	−0.642332	−	0.766426i	$-0.722033\pi$
$97$	−12.6525	−1.28466	−0.642332	+	0.766426i	$0.722033\pi$
$98$	−5.47214	−0.552769
$99$	0	0
$100$	1.00000	0.100000
$101$	13.3820	1.33156	0.665778	−	0.746150i	$-0.268100\pi$
$101$	13.3820	1.33156	0.665778	+	0.746150i	$0.268100\pi$
$102$	−5.09017	−0.504002
$103$	11.2361	1.10712	0.553561	−	0.832808i	$-0.313268\pi$
$103$	11.2361	1.10712	0.553561	+	0.832808i	$0.313268\pi$
$104$	5.61803	0.550894
$105$	1.23607	0.120628
$106$	−0.472136	−0.0458579
$107$	19.7082	1.90526	0.952632	−	0.304125i	$-0.0983642\pi$
$107$	19.7082	1.90526	0.952632	+	0.304125i	$0.0983642\pi$
$108$	−1.00000	−0.0962250
$109$	6.47214	0.619918	0.309959	−	0.950750i	$-0.399685\pi$
$109$	6.47214	0.619918	0.309959	+	0.950750i	$0.399685\pi$
$110$	0	0
$111$	8.61803	0.817988
$112$	1.23607	0.116797
$113$	0.562306	0.0528973	0.0264486	−	0.999650i	$-0.491580\pi$
$113$	0.562306	0.0528973	0.0264486	+	0.999650i	$0.491580\pi$
$114$	3.23607	0.303086
$115$	−0.145898	−0.0136051
$116$	−0.381966	−0.0354647
$117$	5.61803	0.519387
$118$	2.90983	0.267872
$119$	6.29180	0.576768
$120$	1.00000	0.0912871
$121$	0	0
$122$	0	0
$123$	3.23607	0.291786
$124$	−3.61803	−0.324909
$125$	−1.00000	−0.0894427
$126$	1.23607	0.110118
$127$	−16.6525	−1.47767	−0.738834	−	0.673887i	$-0.764623\pi$
$127$	−16.6525	−1.47767	−0.738834	+	0.673887i	$0.764623\pi$
$128$	1.00000	0.0883883
$129$	−11.0902	−0.976435
$130$	−5.61803	−0.492734
$131$	−5.61803	−0.490850	−0.245425	−	0.969416i	$-0.578927\pi$
$131$	−5.61803	−0.490850	−0.245425	+	0.969416i	$0.578927\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	6.09017	0.526111
$135$	1.00000	0.0860663
$136$	5.09017	0.436478
$137$	11.7984	1.00800	0.504002	−	0.863703i	$-0.331861\pi$
$137$	11.7984	1.00800	0.504002	+	0.863703i	$0.331861\pi$
$138$	−0.145898	−0.0124197
$139$	13.2361	1.12267	0.561334	−	0.827589i	$-0.310288\pi$
$139$	13.2361	1.12267	0.561334	+	0.827589i	$0.310288\pi$
$140$	−1.23607	−0.104467
$141$	−11.3262	−0.953841
$142$	1.52786	0.128216
$143$	0	0
$144$	1.00000	0.0833333
$145$	0.381966	0.0317206
$146$	−13.4164	−1.11035
$147$	5.47214	0.451334
$148$	−8.61803	−0.708398
$149$	−5.38197	−0.440908	−0.220454	−	0.975397i	$-0.570754\pi$
$149$	−5.38197	−0.440908	−0.220454	+	0.975397i	$0.570754\pi$
$150$	−1.00000	−0.0816497
$151$	3.05573	0.248672	0.124336	−	0.992240i	$-0.460320\pi$
$151$	3.05573	0.248672	0.124336	+	0.992240i	$0.460320\pi$
$152$	−3.23607	−0.262480
$153$	5.09017	0.411516
$154$	0	0
$155$	3.61803	0.290607
$156$	−5.61803	−0.449803
$157$	24.2705	1.93700	0.968499	−	0.249018i	$-0.0801079\pi$
$157$	24.2705	1.93700	0.968499	+	0.249018i	$0.0801079\pi$
$158$	7.09017	0.564064
$159$	0.472136	0.0374428
$160$	−1.00000	−0.0790569
$161$	0.180340	0.0142128
$162$	1.00000	0.0785674
$163$	−5.85410	−0.458529	−0.229264	−	0.973364i	$-0.573632\pi$
$163$	−5.85410	−0.458529	−0.229264	+	0.973364i	$0.573632\pi$
$164$	−3.23607	−0.252694
$165$	0	0
$166$	4.00000	0.310460
$167$	20.2705	1.56858	0.784290	−	0.620395i	$-0.213028\pi$
$167$	20.2705	1.56858	0.784290	+	0.620395i	$0.213028\pi$
$168$	−1.23607	−0.0953647
$169$	18.5623	1.42787
$170$	−5.09017	−0.390398
$171$	−3.23607	−0.247468
$172$	11.0902	0.845618
$173$	−18.4721	−1.40441	−0.702205	−	0.711975i	$-0.747801\pi$
$173$	−18.4721	−1.40441	−0.702205	+	0.711975i	$0.747801\pi$
$174$	0.381966	0.0289568
$175$	1.23607	0.0934380
$176$	0	0
$177$	−2.90983	−0.218716
$178$	12.7639	0.956697
$179$	24.8541	1.85768	0.928841	−	0.370478i	$-0.120806\pi$
$179$	24.8541	1.85768	0.928841	+	0.370478i	$0.120806\pi$
$180$	−1.00000	−0.0745356
$181$	−13.8885	−1.03233	−0.516164	−	0.856490i	$-0.672640\pi$
$181$	−13.8885	−1.03233	−0.516164	+	0.856490i	$0.672640\pi$
$182$	6.94427	0.514744
$183$	0	0
$184$	0.145898	0.0107557
$185$	8.61803	0.633610
$186$	3.61803	0.265287
$187$	0	0
$188$	11.3262	0.826051
$189$	−1.23607	−0.0899107
$190$	3.23607	0.234769
$191$	4.76393	0.344706	0.172353	−	0.985035i	$-0.444863\pi$
$191$	4.76393	0.344706	0.172353	+	0.985035i	$0.444863\pi$
$192$	−1.00000	−0.0721688
$193$	−3.05573	−0.219956	−0.109978	−	0.993934i	$-0.535078\pi$
$193$	−3.05573	−0.219956	−0.109978	+	0.993934i	$0.535078\pi$
$194$	−12.6525	−0.908395
$195$	5.61803	0.402316
$196$	−5.47214	−0.390867
$197$	−6.94427	−0.494759	−0.247379	−	0.968919i	$-0.579569\pi$
$197$	−6.94427	−0.494759	−0.247379	+	0.968919i	$0.579569\pi$
$198$	0	0
$199$	−20.9787	−1.48714	−0.743571	−	0.668657i	$-0.766869\pi$
$199$	−20.9787	−1.48714	−0.743571	+	0.668657i	$0.766869\pi$
$200$	1.00000	0.0707107
$201$	−6.09017	−0.429567
$202$	13.3820	0.941552
$203$	−0.472136	−0.0331374
$204$	−5.09017	−0.356383
$205$	3.23607	0.226017
$206$	11.2361	0.782854
$207$	0.145898	0.0101406
$208$	5.61803	0.389541
$209$	0	0
$210$	1.23607	0.0852968
$211$	−20.7639	−1.42945	−0.714724	−	0.699407i	$-0.753448\pi$
$211$	−20.7639	−1.42945	−0.714724	+	0.699407i	$0.753448\pi$
$212$	−0.472136	−0.0324264
$213$	−1.52786	−0.104688
$214$	19.7082	1.34723
$215$	−11.0902	−0.756343
$216$	−1.00000	−0.0680414
$217$	−4.47214	−0.303588
$218$	6.47214	0.438348
$219$	13.4164	0.906597
$220$	0	0
$221$	28.5967	1.92363
$222$	8.61803	0.578405
$223$	2.76393	0.185087	0.0925433	−	0.995709i	$-0.470500\pi$
$223$	2.76393	0.185087	0.0925433	+	0.995709i	$0.470500\pi$
$224$	1.23607	0.0825883
$225$	1.00000	0.0666667
$226$	0.562306	0.0374040
$227$	−24.3607	−1.61688	−0.808438	−	0.588582i	$-0.799686\pi$
$227$	−24.3607	−1.61688	−0.808438	+	0.588582i	$0.799686\pi$
$228$	3.23607	0.214314
$229$	5.23607	0.346009	0.173005	−	0.984921i	$-0.444652\pi$
$229$	5.23607	0.346009	0.173005	+	0.984921i	$0.444652\pi$
$230$	−0.145898	−0.00962023
$231$	0	0
$232$	−0.381966	−0.0250773
$233$	−24.5623	−1.60913	−0.804565	−	0.593864i	$-0.797602\pi$
$233$	−24.5623	−1.60913	−0.804565	+	0.593864i	$0.797602\pi$
$234$	5.61803	0.367262
$235$	−11.3262	−0.738842
$236$	2.90983	0.189414
$237$	−7.09017	−0.460556
$238$	6.29180	0.407837
$239$	1.23607	0.0799546	0.0399773	−	0.999201i	$-0.487271\pi$
$239$	1.23607	0.0799546	0.0399773	+	0.999201i	$0.487271\pi$
$240$	1.00000	0.0645497
$241$	11.8885	0.765808	0.382904	−	0.923788i	$-0.374924\pi$
$241$	11.8885	0.765808	0.382904	+	0.923788i	$0.374924\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	5.47214	0.349602
$246$	3.23607	0.206324
$247$	−18.1803	−1.15679
$248$	−3.61803	−0.229745
$249$	−4.00000	−0.253490
$250$	−1.00000	−0.0632456
$251$	10.6180	0.670204	0.335102	−	0.942182i	$-0.391229\pi$
$251$	10.6180	0.670204	0.335102	+	0.942182i	$0.391229\pi$
$252$	1.23607	0.0778650
$253$	0	0
$254$	−16.6525	−1.04487
$255$	5.09017	0.318759
$256$	1.00000	0.0625000
$257$	−14.3607	−0.895795	−0.447897	−	0.894085i	$-0.647827\pi$
$257$	−14.3607	−0.895795	−0.447897	+	0.894085i	$0.647827\pi$
$258$	−11.0902	−0.690444
$259$	−10.6525	−0.661913
$260$	−5.61803	−0.348416
$261$	−0.381966	−0.0236431
$262$	−5.61803	−0.347083
$263$	0.145898	0.00899646	0.00449823	−	0.999990i	$-0.498568\pi$
$263$	0.145898	0.00899646	0.00449823	+	0.999990i	$0.498568\pi$
$264$	0	0
$265$	0.472136	0.0290031
$266$	−4.00000	−0.245256
$267$	−12.7639	−0.781140
$268$	6.09017	0.372016
$269$	27.7984	1.69490	0.847448	−	0.530878i	$-0.178138\pi$
$269$	27.7984	1.69490	0.847448	+	0.530878i	$0.178138\pi$
$270$	1.00000	0.0608581
$271$	−8.61803	−0.523508	−0.261754	−	0.965135i	$-0.584301\pi$
$271$	−8.61803	−0.523508	−0.261754	+	0.965135i	$0.584301\pi$
$272$	5.09017	0.308637
$273$	−6.94427	−0.420286
$274$	11.7984	0.712766
$275$	0	0
$276$	−0.145898	−0.00878203
$277$	14.5066	0.871616	0.435808	−	0.900040i	$-0.356463\pi$
$277$	14.5066	0.871616	0.435808	+	0.900040i	$0.356463\pi$
$278$	13.2361	0.793847
$279$	−3.61803	−0.216606
$280$	−1.23607	−0.0738692
$281$	−16.4721	−0.982645	−0.491323	−	0.870978i	$-0.663486\pi$
$281$	−16.4721	−0.982645	−0.491323	+	0.870978i	$0.663486\pi$
$282$	−11.3262	−0.674468
$283$	−6.67376	−0.396714	−0.198357	−	0.980130i	$-0.563561\pi$
$283$	−6.67376	−0.396714	−0.198357	+	0.980130i	$0.563561\pi$
$284$	1.52786	0.0906621
$285$	−3.23607	−0.191688
$286$	0	0
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	8.90983	0.524108
$290$	0.381966	0.0224298
$291$	12.6525	0.741701
$292$	−13.4164	−0.785136
$293$	−20.0000	−1.16841	−0.584206	−	0.811605i	$-0.698594\pi$
$293$	−20.0000	−1.16841	−0.584206	+	0.811605i	$0.698594\pi$
$294$	5.47214	0.319141
$295$	−2.90983	−0.169417
$296$	−8.61803	−0.500913
$297$	0	0
$298$	−5.38197	−0.311769
$299$	0.819660	0.0474022
$300$	−1.00000	−0.0577350
$301$	13.7082	0.790128
$302$	3.05573	0.175837
$303$	−13.3820	−0.768774
$304$	−3.23607	−0.185601
$305$	0	0
$306$	5.09017	0.290986
$307$	22.4508	1.28134	0.640669	−	0.767817i	$-0.278657\pi$
$307$	22.4508	1.28134	0.640669	+	0.767817i	$0.278657\pi$
$308$	0	0
$309$	−11.2361	−0.639198
$310$	3.61803	0.205491
$311$	4.76393	0.270138	0.135069	−	0.990836i	$-0.456874\pi$
$311$	4.76393	0.270138	0.135069	+	0.990836i	$0.456874\pi$
$312$	−5.61803	−0.318059
$313$	−0.472136	−0.0266867	−0.0133434	−	0.999911i	$-0.504247\pi$
$313$	−0.472136	−0.0266867	−0.0133434	+	0.999911i	$0.504247\pi$
$314$	24.2705	1.36966
$315$	−1.23607	−0.0696445
$316$	7.09017	0.398853
$317$	−0.583592	−0.0327778	−0.0163889	−	0.999866i	$-0.505217\pi$
$317$	−0.583592	−0.0327778	−0.0163889	+	0.999866i	$0.505217\pi$
$318$	0.472136	0.0264761
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−19.7082	−1.10000
$322$	0.180340	0.0100499
$323$	−16.4721	−0.916534
$324$	1.00000	0.0555556
$325$	5.61803	0.311632
$326$	−5.85410	−0.324229
$327$	−6.47214	−0.357910
$328$	−3.23607	−0.178682
$329$	14.0000	0.771845
$330$	0	0
$331$	4.76393	0.261849	0.130925	−	0.991392i	$-0.458205\pi$
$331$	4.76393	0.261849	0.130925	+	0.991392i	$0.458205\pi$
$332$	4.00000	0.219529
$333$	−8.61803	−0.472265
$334$	20.2705	1.10915
$335$	−6.09017	−0.332742
$336$	−1.23607	−0.0674330
$337$	−10.7639	−0.586349	−0.293174	−	0.956059i	$-0.594712\pi$
$337$	−10.7639	−0.586349	−0.293174	+	0.956059i	$0.594712\pi$
$338$	18.5623	1.00966
$339$	−0.562306	−0.0305403
$340$	−5.09017	−0.276053
$341$	0	0
$342$	−3.23607	−0.174987
$343$	−15.4164	−0.832408
$344$	11.0902	0.597942
$345$	0.145898	0.00785489
$346$	−18.4721	−0.993068
$347$	0.111456	0.00598328	0.00299164	−	0.999996i	$-0.499048\pi$
$347$	0.111456	0.00598328	0.00299164	+	0.999996i	$0.499048\pi$
$348$	0.381966	0.0204755
$349$	15.4164	0.825221	0.412611	−	0.910907i	$-0.364617\pi$
$349$	15.4164	0.825221	0.412611	+	0.910907i	$0.364617\pi$
$350$	1.23607	0.0660706
$351$	−5.61803	−0.299868
$352$	0	0
$353$	21.3820	1.13805	0.569024	−	0.822321i	$-0.307321\pi$
$353$	21.3820	1.13805	0.569024	+	0.822321i	$0.307321\pi$
$354$	−2.90983	−0.154656
$355$	−1.52786	−0.0810906
$356$	12.7639	0.676487
$357$	−6.29180	−0.332997
$358$	24.8541	1.31358
$359$	10.1803	0.537298	0.268649	−	0.963238i	$-0.413423\pi$
$359$	10.1803	0.537298	0.268649	+	0.963238i	$0.413423\pi$
$360$	−1.00000	−0.0527046
$361$	−8.52786	−0.448835
$362$	−13.8885	−0.729966
$363$	0	0
$364$	6.94427	0.363979
$365$	13.4164	0.702247
$366$	0	0
$367$	−31.2361	−1.63051	−0.815255	−	0.579103i	$-0.803403\pi$
$367$	−31.2361	−1.63051	−0.815255	+	0.579103i	$0.803403\pi$
$368$	0.145898	0.00760546
$369$	−3.23607	−0.168463
$370$	8.61803	0.448030
$371$	−0.583592	−0.0302986
$372$	3.61803	0.187586
$373$	−20.4721	−1.06001	−0.530004	−	0.847995i	$-0.677809\pi$
$373$	−20.4721	−1.06001	−0.530004	+	0.847995i	$0.677809\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	11.3262	0.584106
$377$	−2.14590	−0.110519
$378$	−1.23607	−0.0635765
$379$	32.3607	1.66226	0.831128	−	0.556081i	$-0.187696\pi$
$379$	32.3607	1.66226	0.831128	+	0.556081i	$0.187696\pi$
$380$	3.23607	0.166007
$381$	16.6525	0.853132
$382$	4.76393	0.243744
$383$	15.3262	0.783134	0.391567	−	0.920150i	$-0.371933\pi$
$383$	15.3262	0.783134	0.391567	+	0.920150i	$0.371933\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−3.05573	−0.155532
$387$	11.0902	0.563745
$388$	−12.6525	−0.642332
$389$	0.145898	0.00739732	0.00369866	−	0.999993i	$-0.498823\pi$
$389$	0.145898	0.00739732	0.00369866	+	0.999993i	$0.498823\pi$
$390$	5.61803	0.284480
$391$	0.742646	0.0375572
$392$	−5.47214	−0.276385
$393$	5.61803	0.283392
$394$	−6.94427	−0.349847
$395$	−7.09017	−0.356745
$396$	0	0
$397$	26.7984	1.34497	0.672486	−	0.740110i	$-0.265227\pi$
$397$	26.7984	1.34497	0.672486	+	0.740110i	$0.265227\pi$
$398$	−20.9787	−1.05157
$399$	4.00000	0.200250
$400$	1.00000	0.0500000
$401$	−36.0689	−1.80119	−0.900597	−	0.434655i	$-0.856870\pi$
$401$	−36.0689	−1.80119	−0.900597	+	0.434655i	$0.856870\pi$
$402$	−6.09017	−0.303750
$403$	−20.3262	−1.01252
$404$	13.3820	0.665778
$405$	−1.00000	−0.0496904
$406$	−0.472136	−0.0234317
$407$	0	0
$408$	−5.09017	−0.252001
$409$	−33.9787	−1.68014	−0.840070	−	0.542479i	$-0.817486\pi$
$409$	−33.9787	−1.68014	−0.840070	+	0.542479i	$0.817486\pi$
$410$	3.23607	0.159818
$411$	−11.7984	−0.581971
$412$	11.2361	0.553561
$413$	3.59675	0.176984
$414$	0.145898	0.00717050
$415$	−4.00000	−0.196352
$416$	5.61803	0.275447
$417$	−13.2361	−0.648173
$418$	0	0
$419$	16.1459	0.788779	0.394389	−	0.918943i	$-0.370956\pi$
$419$	16.1459	0.788779	0.394389	+	0.918943i	$0.370956\pi$
$420$	1.23607	0.0603139
$421$	6.47214	0.315433	0.157716	−	0.987484i	$-0.449587\pi$
$421$	6.47214	0.315433	0.157716	+	0.987484i	$0.449587\pi$
$422$	−20.7639	−1.01077
$423$	11.3262	0.550701
$424$	−0.472136	−0.0229289
$425$	5.09017	0.246910
$426$	−1.52786	−0.0740253
$427$	0	0
$428$	19.7082	0.952632
$429$	0	0
$430$	−11.0902	−0.534815
$431$	−22.3607	−1.07708	−0.538538	−	0.842601i	$-0.681023\pi$
$431$	−22.3607	−1.07708	−0.538538	+	0.842601i	$0.681023\pi$
$432$	−1.00000	−0.0481125
$433$	30.8328	1.48173	0.740865	−	0.671654i	$-0.234416\pi$
$433$	30.8328	1.48173	0.740865	+	0.671654i	$0.234416\pi$
$434$	−4.47214	−0.214669
$435$	−0.381966	−0.0183139
$436$	6.47214	0.309959
$437$	−0.472136	−0.0225853
$438$	13.4164	0.641061
$439$	17.3262	0.826936	0.413468	−	0.910519i	$-0.364317\pi$
$439$	17.3262	0.826936	0.413468	+	0.910519i	$0.364317\pi$
$440$	0	0
$441$	−5.47214	−0.260578
$442$	28.5967	1.36021
$443$	12.6525	0.601137	0.300569	−	0.953760i	$-0.402824\pi$
$443$	12.6525	0.601137	0.300569	+	0.953760i	$0.402824\pi$
$444$	8.61803	0.408994
$445$	−12.7639	−0.605068
$446$	2.76393	0.130876
$447$	5.38197	0.254558
$448$	1.23607	0.0583987
$449$	29.1246	1.37448	0.687238	−	0.726433i	$-0.258823\pi$
$449$	29.1246	1.37448	0.687238	+	0.726433i	$0.258823\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	0.562306	0.0264486
$453$	−3.05573	−0.143571
$454$	−24.3607	−1.14330
$455$	−6.94427	−0.325552
$456$	3.23607	0.151543
$457$	−26.6525	−1.24675	−0.623375	−	0.781923i	$-0.714239\pi$
$457$	−26.6525	−1.24675	−0.623375	+	0.781923i	$0.714239\pi$
$458$	5.23607	0.244665
$459$	−5.09017	−0.237589
$460$	−0.145898	−0.00680253
$461$	−28.2148	−1.31409	−0.657047	−	0.753850i	$-0.728195\pi$
$461$	−28.2148	−1.31409	−0.657047	+	0.753850i	$0.728195\pi$
$462$	0	0
$463$	−23.8885	−1.11019	−0.555097	−	0.831785i	$-0.687319\pi$
$463$	−23.8885	−1.11019	−0.555097	+	0.831785i	$0.687319\pi$
$464$	−0.381966	−0.0177323
$465$	−3.61803	−0.167782
$466$	−24.5623	−1.13783
$467$	−38.5410	−1.78347	−0.891733	−	0.452562i	$-0.850510\pi$
$467$	−38.5410	−1.78347	−0.891733	+	0.452562i	$0.850510\pi$
$468$	5.61803	0.259694
$469$	7.52786	0.347604
$470$	−11.3262	−0.522440
$471$	−24.2705	−1.11833
$472$	2.90983	0.133936
$473$	0	0
$474$	−7.09017	−0.325662
$475$	−3.23607	−0.148481
$476$	6.29180	0.288384
$477$	−0.472136	−0.0216176
$478$	1.23607	0.0565364
$479$	17.2361	0.787536	0.393768	−	0.919210i	$-0.371171\pi$
$479$	17.2361	0.787536	0.393768	+	0.919210i	$0.371171\pi$
$480$	1.00000	0.0456435
$481$	−48.4164	−2.20760
$482$	11.8885	0.541508
$483$	−0.180340	−0.00820575
$484$	0	0
$485$	12.6525	0.574519
$486$	−1.00000	−0.0453609
$487$	−15.4164	−0.698584	−0.349292	−	0.937014i	$-0.613578\pi$
$487$	−15.4164	−0.698584	−0.349292	+	0.937014i	$0.613578\pi$
$488$	0	0
$489$	5.85410	0.264732
$490$	5.47214	0.247206
$491$	−1.03444	−0.0466837	−0.0233419	−	0.999728i	$-0.507431\pi$
$491$	−1.03444	−0.0466837	−0.0233419	+	0.999728i	$0.507431\pi$
$492$	3.23607	0.145893
$493$	−1.94427	−0.0875656
$494$	−18.1803	−0.817972
$495$	0	0
$496$	−3.61803	−0.162455
$497$	1.88854	0.0847128
$498$	−4.00000	−0.179244
$499$	−23.5279	−1.05325	−0.526626	−	0.850097i	$-0.676543\pi$
$499$	−23.5279	−1.05325	−0.526626	+	0.850097i	$0.676543\pi$
$500$	−1.00000	−0.0447214
$501$	−20.2705	−0.905620
$502$	10.6180	0.473906
$503$	−8.67376	−0.386744	−0.193372	−	0.981126i	$-0.561942\pi$
$503$	−8.67376	−0.386744	−0.193372	+	0.981126i	$0.561942\pi$
$504$	1.23607	0.0550588
$505$	−13.3820	−0.595490
$506$	0	0
$507$	−18.5623	−0.824381
$508$	−16.6525	−0.738834
$509$	−15.7984	−0.700251	−0.350125	−	0.936703i	$-0.613861\pi$
$509$	−15.7984	−0.700251	−0.350125	+	0.936703i	$0.613861\pi$
$510$	5.09017	0.225397
$511$	−16.5836	−0.733615
$512$	1.00000	0.0441942
$513$	3.23607	0.142876
$514$	−14.3607	−0.633422
$515$	−11.2361	−0.495120
$516$	−11.0902	−0.488218
$517$	0	0
$518$	−10.6525	−0.468043
$519$	18.4721	0.810837
$520$	−5.61803	−0.246367
$521$	42.3607	1.85586	0.927928	−	0.372761i	$-0.121589\pi$
$521$	42.3607	1.85586	0.927928	+	0.372761i	$0.121589\pi$
$522$	−0.381966	−0.0167182
$523$	−14.8328	−0.648594	−0.324297	−	0.945955i	$-0.605128\pi$
$523$	−14.8328	−0.648594	−0.324297	+	0.945955i	$0.605128\pi$
$524$	−5.61803	−0.245425
$525$	−1.23607	−0.0539464
$526$	0.145898	0.00636146
$527$	−18.4164	−0.802231
$528$	0	0
$529$	−22.9787	−0.999075
$530$	0.472136	0.0205083
$531$	2.90983	0.126276
$532$	−4.00000	−0.173422
$533$	−18.1803	−0.787478
$534$	−12.7639	−0.552349
$535$	−19.7082	−0.852060
$536$	6.09017	0.263055
$537$	−24.8541	−1.07253
$538$	27.7984	1.19847
$539$	0	0
$540$	1.00000	0.0430331
$541$	−32.0689	−1.37875	−0.689374	−	0.724405i	$-0.742115\pi$
$541$	−32.0689	−1.37875	−0.689374	+	0.724405i	$0.742115\pi$
$542$	−8.61803	−0.370176
$543$	13.8885	0.596014
$544$	5.09017	0.218239
$545$	−6.47214	−0.277236
$546$	−6.94427	−0.297187
$547$	18.6738	0.798432	0.399216	−	0.916857i	$-0.369282\pi$
$547$	18.6738	0.798432	0.399216	+	0.916857i	$0.369282\pi$
$548$	11.7984	0.504002
$549$	0	0
$550$	0	0
$551$	1.23607	0.0526583
$552$	−0.145898	−0.00620983
$553$	8.76393	0.372680
$554$	14.5066	0.616325
$555$	−8.61803	−0.365815
$556$	13.2361	0.561334
$557$	5.12461	0.217137	0.108568	−	0.994089i	$-0.465373\pi$
$557$	5.12461	0.217137	0.108568	+	0.994089i	$0.465373\pi$
$558$	−3.61803	−0.153164
$559$	62.3050	2.63522
$560$	−1.23607	−0.0522334
$561$	0	0
$562$	−16.4721	−0.694835
$563$	34.9443	1.47273	0.736363	−	0.676587i	$-0.236542\pi$
$563$	34.9443	1.47273	0.736363	+	0.676587i	$0.236542\pi$
$564$	−11.3262	−0.476921
$565$	−0.562306	−0.0236564
$566$	−6.67376	−0.280519
$567$	1.23607	0.0519100
$568$	1.52786	0.0641078
$569$	1.41641	0.0593789	0.0296895	−	0.999559i	$-0.490548\pi$
$569$	1.41641	0.0593789	0.0296895	+	0.999559i	$0.490548\pi$
$570$	−3.23607	−0.135544
$571$	16.3607	0.684673	0.342337	−	0.939577i	$-0.388782\pi$
$571$	16.3607	0.684673	0.342337	+	0.939577i	$0.388782\pi$
$572$	0	0
$573$	−4.76393	−0.199016
$574$	−4.00000	−0.166957
$575$	0.145898	0.00608437
$576$	1.00000	0.0416667
$577$	34.9443	1.45475	0.727375	−	0.686241i	$-0.240740\pi$
$577$	34.9443	1.45475	0.727375	+	0.686241i	$0.240740\pi$
$578$	8.90983	0.370600
$579$	3.05573	0.126992
$580$	0.381966	0.0158603
$581$	4.94427	0.205123
$582$	12.6525	0.524462
$583$	0	0
$584$	−13.4164	−0.555175
$585$	−5.61803	−0.232277
$586$	−20.0000	−0.826192
$587$	−39.7082	−1.63893	−0.819466	−	0.573127i	$-0.805730\pi$
$587$	−39.7082	−1.63893	−0.819466	+	0.573127i	$0.805730\pi$
$588$	5.47214	0.225667
$589$	11.7082	0.482428
$590$	−2.90983	−0.119796
$591$	6.94427	0.285649
$592$	−8.61803	−0.354199
$593$	−33.3262	−1.36854	−0.684272	−	0.729227i	$-0.739880\pi$
$593$	−33.3262	−1.36854	−0.684272	+	0.729227i	$0.739880\pi$
$594$	0	0
$595$	−6.29180	−0.257938
$596$	−5.38197	−0.220454
$597$	20.9787	0.858602
$598$	0.819660	0.0335184
$599$	−4.18034	−0.170804	−0.0854020	−	0.996347i	$-0.527217\pi$
$599$	−4.18034	−0.170804	−0.0854020	+	0.996347i	$0.527217\pi$
$600$	−1.00000	−0.0408248
$601$	−1.05573	−0.0430640	−0.0215320	−	0.999768i	$-0.506854\pi$
$601$	−1.05573	−0.0430640	−0.0215320	+	0.999768i	$0.506854\pi$
$602$	13.7082	0.558705
$603$	6.09017	0.248011
$604$	3.05573	0.124336
$605$	0	0
$606$	−13.3820	−0.543605
$607$	4.47214	0.181518	0.0907592	−	0.995873i	$-0.471071\pi$
$607$	4.47214	0.181518	0.0907592	+	0.995873i	$0.471071\pi$
$608$	−3.23607	−0.131240
$609$	0.472136	0.0191319
$610$	0	0
$611$	63.6312	2.57424
$612$	5.09017	0.205758
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	22.4508	0.906043
$615$	−3.23607	−0.130491
$616$	0	0
$617$	−18.3607	−0.739173	−0.369587	−	0.929196i	$-0.620501\pi$
$617$	−18.3607	−0.739173	−0.369587	+	0.929196i	$0.620501\pi$
$618$	−11.2361	−0.451981
$619$	18.4721	0.742458	0.371229	−	0.928541i	$-0.378937\pi$
$619$	18.4721	0.742458	0.371229	+	0.928541i	$0.378937\pi$
$620$	3.61803	0.145304
$621$	−0.145898	−0.00585469
$622$	4.76393	0.191016
$623$	15.7771	0.632096
$624$	−5.61803	−0.224901
$625$	1.00000	0.0400000
$626$	−0.472136	−0.0188703
$627$	0	0
$628$	24.2705	0.968499
$629$	−43.8673	−1.74910
$630$	−1.23607	−0.0492461
$631$	−21.3262	−0.848984	−0.424492	−	0.905432i	$-0.639547\pi$
$631$	−21.3262	−0.848984	−0.424492	+	0.905432i	$0.639547\pi$
$632$	7.09017	0.282032
$633$	20.7639	0.825292
$634$	−0.583592	−0.0231774
$635$	16.6525	0.660833
$636$	0.472136	0.0187214
$637$	−30.7426	−1.21807
$638$	0	0
$639$	1.52786	0.0604414
$640$	−1.00000	−0.0395285
$641$	−10.1803	−0.402099	−0.201050	−	0.979581i	$-0.564435\pi$
$641$	−10.1803	−0.402099	−0.201050	+	0.979581i	$0.564435\pi$
$642$	−19.7082	−0.777821
$643$	19.7984	0.780772	0.390386	−	0.920651i	$-0.372342\pi$
$643$	19.7984	0.780772	0.390386	+	0.920651i	$0.372342\pi$
$644$	0.180340	0.00710639
$645$	11.0902	0.436675
$646$	−16.4721	−0.648088
$647$	−14.6180	−0.574694	−0.287347	−	0.957827i	$-0.592773\pi$
$647$	−14.6180	−0.574694	−0.287347	+	0.957827i	$0.592773\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	5.61803	0.220357
$651$	4.47214	0.175277
$652$	−5.85410	−0.229264
$653$	−42.5410	−1.66476	−0.832379	−	0.554206i	$-0.813022\pi$
$653$	−42.5410	−1.66476	−0.832379	+	0.554206i	$0.813022\pi$
$654$	−6.47214	−0.253081
$655$	5.61803	0.219515
$656$	−3.23607	−0.126347
$657$	−13.4164	−0.523424
$658$	14.0000	0.545777
$659$	11.4164	0.444720	0.222360	−	0.974965i	$-0.428624\pi$
$659$	11.4164	0.444720	0.222360	+	0.974965i	$0.428624\pi$
$660$	0	0
$661$	−36.3607	−1.41427	−0.707133	−	0.707080i	$-0.750012\pi$
$661$	−36.3607	−1.41427	−0.707133	+	0.707080i	$0.750012\pi$
$662$	4.76393	0.185155
$663$	−28.5967	−1.11061
$664$	4.00000	0.155230
$665$	4.00000	0.155113
$666$	−8.61803	−0.333942
$667$	−0.0557281	−0.00215780
$668$	20.2705	0.784290
$669$	−2.76393	−0.106860
$670$	−6.09017	−0.235284
$671$	0	0
$672$	−1.23607	−0.0476824
$673$	−2.29180	−0.0883422	−0.0441711	−	0.999024i	$-0.514065\pi$
$673$	−2.29180	−0.0883422	−0.0441711	+	0.999024i	$0.514065\pi$
$674$	−10.7639	−0.414611
$675$	−1.00000	−0.0384900
$676$	18.5623	0.713935
$677$	22.7639	0.874889	0.437444	−	0.899245i	$-0.355884\pi$
$677$	22.7639	0.874889	0.437444	+	0.899245i	$0.355884\pi$
$678$	−0.562306	−0.0215952
$679$	−15.6393	−0.600182
$680$	−5.09017	−0.195199
$681$	24.3607	0.933503
$682$	0	0
$683$	−19.1246	−0.731783	−0.365891	−	0.930658i	$-0.619236\pi$
$683$	−19.1246	−0.731783	−0.365891	+	0.930658i	$0.619236\pi$
$684$	−3.23607	−0.123734
$685$	−11.7984	−0.450793
$686$	−15.4164	−0.588601
$687$	−5.23607	−0.199768
$688$	11.0902	0.422809
$689$	−2.65248	−0.101051
$690$	0.145898	0.00555424
$691$	10.6525	0.405239	0.202620	−	0.979258i	$-0.435054\pi$
$691$	10.6525	0.405239	0.202620	+	0.979258i	$0.435054\pi$
$692$	−18.4721	−0.702205
$693$	0	0
$694$	0.111456	0.00423082
$695$	−13.2361	−0.502073
$696$	0.381966	0.0144784
$697$	−16.4721	−0.623927
$698$	15.4164	0.583520
$699$	24.5623	0.929032
$700$	1.23607	0.0467190
$701$	−12.4721	−0.471066	−0.235533	−	0.971866i	$-0.575684\pi$
$701$	−12.4721	−0.471066	−0.235533	+	0.971866i	$0.575684\pi$
$702$	−5.61803	−0.212039
$703$	27.8885	1.05184
$704$	0	0
$705$	11.3262	0.426571
$706$	21.3820	0.804721
$707$	16.5410	0.622089
$708$	−2.90983	−0.109358
$709$	−37.4164	−1.40520	−0.702601	−	0.711584i	$-0.747978\pi$
$709$	−37.4164	−1.40520	−0.702601	+	0.711584i	$0.747978\pi$
$710$	−1.52786	−0.0573397
$711$	7.09017	0.265902
$712$	12.7639	0.478349
$713$	−0.527864	−0.0197687
$714$	−6.29180	−0.235465
$715$	0	0
$716$	24.8541	0.928841
$717$	−1.23607	−0.0461618
$718$	10.1803	0.379927
$719$	9.34752	0.348604	0.174302	−	0.984692i	$-0.444233\pi$
$719$	9.34752	0.348604	0.174302	+	0.984692i	$0.444233\pi$
$720$	−1.00000	−0.0372678
$721$	13.8885	0.517236
$722$	−8.52786	−0.317374
$723$	−11.8885	−0.442140
$724$	−13.8885	−0.516164
$725$	−0.381966	−0.0141859
$726$	0	0
$727$	−27.8197	−1.03177	−0.515887	−	0.856657i	$-0.672538\pi$
$727$	−27.8197	−1.03177	−0.515887	+	0.856657i	$0.672538\pi$
$728$	6.94427	0.257372
$729$	1.00000	0.0370370
$730$	13.4164	0.496564
$731$	56.4508	2.08791
$732$	0	0
$733$	35.6738	1.31764	0.658820	−	0.752300i	$-0.271056\pi$
$733$	35.6738	1.31764	0.658820	+	0.752300i	$0.271056\pi$
$734$	−31.2361	−1.15294
$735$	−5.47214	−0.201843
$736$	0.145898	0.00537787
$737$	0	0
$738$	−3.23607	−0.119121
$739$	−49.0132	−1.80298	−0.901489	−	0.432802i	$-0.857525\pi$
$739$	−49.0132	−1.80298	−0.901489	+	0.432802i	$0.857525\pi$
$740$	8.61803	0.316805
$741$	18.1803	0.667871
$742$	−0.583592	−0.0214243
$743$	−13.7984	−0.506213	−0.253107	−	0.967438i	$-0.581452\pi$
$743$	−13.7984	−0.506213	−0.253107	+	0.967438i	$0.581452\pi$
$744$	3.61803	0.132644
$745$	5.38197	0.197180
$746$	−20.4721	−0.749538
$747$	4.00000	0.146352
$748$	0	0
$749$	24.3607	0.890120
$750$	1.00000	0.0365148
$751$	0.0344419	0.00125680	0.000628401	−	1.00000i	$-0.499800\pi$
$751$	0.0344419	0.00125680	0.000628401		1.00000i	$0.499800\pi$
$752$	11.3262	0.413025
$753$	−10.6180	−0.386943
$754$	−2.14590	−0.0781490
$755$	−3.05573	−0.111209
$756$	−1.23607	−0.0449554
$757$	−47.1459	−1.71355	−0.856773	−	0.515693i	$-0.827534\pi$
$757$	−47.1459	−1.71355	−0.856773	+	0.515693i	$0.827534\pi$
$758$	32.3607	1.17539
$759$	0	0
$760$	3.23607	0.117385
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	16.6525	0.603256
$763$	8.00000	0.289619
$764$	4.76393	0.172353
$765$	−5.09017	−0.184035
$766$	15.3262	0.553759
$767$	16.3475	0.590275
$768$	−1.00000	−0.0360844
$769$	31.4508	1.13415	0.567073	−	0.823667i	$-0.308076\pi$
$769$	31.4508	1.13415	0.567073	+	0.823667i	$0.308076\pi$
$770$	0	0
$771$	14.3607	0.517187
$772$	−3.05573	−0.109978
$773$	−29.5967	−1.06452	−0.532261	−	0.846581i	$-0.678657\pi$
$773$	−29.5967	−1.06452	−0.532261	+	0.846581i	$0.678657\pi$
$774$	11.0902	0.398628
$775$	−3.61803	−0.129964
$776$	−12.6525	−0.454197
$777$	10.6525	0.382155
$778$	0.145898	0.00523070
$779$	10.4721	0.375203
$780$	5.61803	0.201158
$781$	0	0
$782$	0.742646	0.0265570
$783$	0.381966	0.0136504
$784$	−5.47214	−0.195433
$785$	−24.2705	−0.866252
$786$	5.61803	0.200389
$787$	−8.03444	−0.286397	−0.143198	−	0.989694i	$-0.545739\pi$
$787$	−8.03444	−0.286397	−0.143198	+	0.989694i	$0.545739\pi$
$788$	−6.94427	−0.247379
$789$	−0.145898	−0.00519411
$790$	−7.09017	−0.252257
$791$	0.695048	0.0247131
$792$	0	0
$793$	0	0
$794$	26.7984	0.951039
$795$	−0.472136	−0.0167449
$796$	−20.9787	−0.743571
$797$	−8.29180	−0.293710	−0.146855	−	0.989158i	$-0.546915\pi$
$797$	−8.29180	−0.293710	−0.146855	+	0.989158i	$0.546915\pi$
$798$	4.00000	0.141598
$799$	57.6525	2.03960
$800$	1.00000	0.0353553
$801$	12.7639	0.450991
$802$	−36.0689	−1.27364
$803$	0	0
$804$	−6.09017	−0.214784
$805$	−0.180340	−0.00635615
$806$	−20.3262	−0.715961
$807$	−27.7984	−0.978549
$808$	13.3820	0.470776
$809$	28.6525	1.00737	0.503684	−	0.863888i	$-0.331978\pi$
$809$	28.6525	1.00737	0.503684	+	0.863888i	$0.331978\pi$
$810$	−1.00000	−0.0351364
$811$	−31.4164	−1.10318	−0.551590	−	0.834116i	$-0.685979\pi$
$811$	−31.4164	−1.10318	−0.551590	+	0.834116i	$0.685979\pi$
$812$	−0.472136	−0.0165687
$813$	8.61803	0.302248
$814$	0	0
$815$	5.85410	0.205060
$816$	−5.09017	−0.178192
$817$	−35.8885	−1.25558
$818$	−33.9787	−1.18804
$819$	6.94427	0.242652
$820$	3.23607	0.113008
$821$	19.3050	0.673747	0.336874	−	0.941550i	$-0.390630\pi$
$821$	19.3050	0.673747	0.336874	+	0.941550i	$0.390630\pi$
$822$	−11.7984	−0.411516
$823$	−17.2361	−0.600812	−0.300406	−	0.953811i	$-0.597122\pi$
$823$	−17.2361	−0.600812	−0.300406	+	0.953811i	$0.597122\pi$
$824$	11.2361	0.391427
$825$	0	0
$826$	3.59675	0.125147
$827$	43.7082	1.51988	0.759942	−	0.649991i	$-0.225228\pi$
$827$	43.7082	1.51988	0.759942	+	0.649991i	$0.225228\pi$
$828$	0.145898	0.00507031
$829$	−13.5967	−0.472235	−0.236117	−	0.971725i	$-0.575875\pi$
$829$	−13.5967	−0.472235	−0.236117	+	0.971725i	$0.575875\pi$
$830$	−4.00000	−0.138842
$831$	−14.5066	−0.503228
$832$	5.61803	0.194770
$833$	−27.8541	−0.965087
$834$	−13.2361	−0.458328
$835$	−20.2705	−0.701490
$836$	0	0
$837$	3.61803	0.125058
$838$	16.1459	0.557751
$839$	−54.6525	−1.88681	−0.943407	−	0.331639i	$-0.892399\pi$
$839$	−54.6525	−1.88681	−0.943407	+	0.331639i	$0.892399\pi$
$840$	1.23607	0.0426484
$841$	−28.8541	−0.994969
$842$	6.47214	0.223045
$843$	16.4721	0.567330
$844$	−20.7639	−0.714724
$845$	−18.5623	−0.638563
$846$	11.3262	0.389404
$847$	0	0
$848$	−0.472136	−0.0162132
$849$	6.67376	0.229043
$850$	5.09017	0.174591
$851$	−1.25735	−0.0431015
$852$	−1.52786	−0.0523438
$853$	−36.4721	−1.24878	−0.624391	−	0.781112i	$-0.714653\pi$
$853$	−36.4721	−1.24878	−0.624391	+	0.781112i	$0.714653\pi$
$854$	0	0
$855$	3.23607	0.110671
$856$	19.7082	0.673613
$857$	−45.1591	−1.54260	−0.771302	−	0.636469i	$-0.780394\pi$
$857$	−45.1591	−1.54260	−0.771302	+	0.636469i	$0.780394\pi$
$858$	0	0
$859$	21.1246	0.720762	0.360381	−	0.932805i	$-0.382647\pi$
$859$	21.1246	0.720762	0.360381	+	0.932805i	$0.382647\pi$
$860$	−11.0902	−0.378172
$861$	4.00000	0.136320
$862$	−22.3607	−0.761608
$863$	47.3394	1.61145	0.805726	−	0.592289i	$-0.201775\pi$
$863$	47.3394	1.61145	0.805726	+	0.592289i	$0.201775\pi$
$864$	−1.00000	−0.0340207
$865$	18.4721	0.628071
$866$	30.8328	1.04774
$867$	−8.90983	−0.302594
$868$	−4.47214	−0.151794
$869$	0	0
$870$	−0.381966	−0.0129499
$871$	34.2148	1.15932
$872$	6.47214	0.219174
$873$	−12.6525	−0.428221
$874$	−0.472136	−0.0159702
$875$	−1.23607	−0.0417867
$876$	13.4164	0.453298
$877$	48.0344	1.62201	0.811004	−	0.585041i	$-0.198921\pi$
$877$	48.0344	1.62201	0.811004	+	0.585041i	$0.198921\pi$
$878$	17.3262	0.584732
$879$	20.0000	0.674583
$880$	0	0
$881$	8.00000	0.269527	0.134763	−	0.990878i	$-0.456973\pi$
$881$	8.00000	0.269527	0.134763	+	0.990878i	$0.456973\pi$
$882$	−5.47214	−0.184256
$883$	−20.3262	−0.684032	−0.342016	−	0.939694i	$-0.611110\pi$
$883$	−20.3262	−0.684032	−0.342016	+	0.939694i	$0.611110\pi$
$884$	28.5967	0.961813
$885$	2.90983	0.0978129
$886$	12.6525	0.425068
$887$	13.4508	0.451635	0.225818	−	0.974170i	$-0.427495\pi$
$887$	13.4508	0.451635	0.225818	+	0.974170i	$0.427495\pi$
$888$	8.61803	0.289202
$889$	−20.5836	−0.690352
$890$	−12.7639	−0.427848
$891$	0	0
$892$	2.76393	0.0925433
$893$	−36.6525	−1.22653
$894$	5.38197	0.180000
$895$	−24.8541	−0.830781
$896$	1.23607	0.0412941
$897$	−0.819660	−0.0273677
$898$	29.1246	0.971901
$899$	1.38197	0.0460911
$900$	1.00000	0.0333333
$901$	−2.40325	−0.0800639
$902$	0	0
$903$	−13.7082	−0.456180
$904$	0.562306	0.0187020
$905$	13.8885	0.461671
$906$	−3.05573	−0.101520
$907$	14.5066	0.481683	0.240842	−	0.970564i	$-0.422577\pi$
$907$	14.5066	0.481683	0.240842	+	0.970564i	$0.422577\pi$
$908$	−24.3607	−0.808438
$909$	13.3820	0.443852
$910$	−6.94427	−0.230200
$911$	12.4721	0.413220	0.206610	−	0.978423i	$-0.433757\pi$
$911$	12.4721	0.413220	0.206610	+	0.978423i	$0.433757\pi$
$912$	3.23607	0.107157
$913$	0	0
$914$	−26.6525	−0.881586
$915$	0	0
$916$	5.23607	0.173005
$917$	−6.94427	−0.229320
$918$	−5.09017	−0.168001
$919$	−45.3394	−1.49561	−0.747804	−	0.663919i	$-0.768892\pi$
$919$	−45.3394	−1.49561	−0.747804	+	0.663919i	$0.768892\pi$
$920$	−0.145898	−0.00481012
$921$	−22.4508	−0.739781
$922$	−28.2148	−0.929204
$923$	8.58359	0.282532
$924$	0	0
$925$	−8.61803	−0.283359
$926$	−23.8885	−0.785026
$927$	11.2361	0.369041
$928$	−0.381966	−0.0125386
$929$	−21.5279	−0.706306	−0.353153	−	0.935566i	$-0.614891\pi$
$929$	−21.5279	−0.706306	−0.353153	+	0.935566i	$0.614891\pi$
$930$	−3.61803	−0.118640
$931$	17.7082	0.580363
$932$	−24.5623	−0.804565
$933$	−4.76393	−0.155964
$934$	−38.5410	−1.26110
$935$	0	0
$936$	5.61803	0.183631
$937$	−11.3475	−0.370707	−0.185354	−	0.982672i	$-0.559343\pi$
$937$	−11.3475	−0.370707	−0.185354	+	0.982672i	$0.559343\pi$
$938$	7.52786	0.245793
$939$	0.472136	0.0154076
$940$	−11.3262	−0.369421
$941$	47.9787	1.56406	0.782031	−	0.623240i	$-0.214184\pi$
$941$	47.9787	1.56406	0.782031	+	0.623240i	$0.214184\pi$
$942$	−24.2705	−0.790776
$943$	−0.472136	−0.0153749
$944$	2.90983	0.0947069
$945$	1.23607	0.0402093
$946$	0	0
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	−7.09017	−0.230278
$949$	−75.3738	−2.44674
$950$	−3.23607	−0.104992
$951$	0.583592	0.0189243
$952$	6.29180	0.203918
$953$	−7.78522	−0.252188	−0.126094	−	0.992018i	$-0.540244\pi$
$953$	−7.78522	−0.252188	−0.126094	+	0.992018i	$0.540244\pi$
$954$	−0.472136	−0.0152860
$955$	−4.76393	−0.154157
$956$	1.23607	0.0399773
$957$	0	0
$958$	17.2361	0.556872
$959$	14.5836	0.470929
$960$	1.00000	0.0322749
$961$	−17.9098	−0.577736
$962$	−48.4164	−1.56101
$963$	19.7082	0.635088
$964$	11.8885	0.382904
$965$	3.05573	0.0983674
$966$	−0.180340	−0.00580234
$967$	−9.30495	−0.299227	−0.149614	−	0.988745i	$-0.547803\pi$
$967$	−9.30495	−0.299227	−0.149614	+	0.988745i	$0.547803\pi$
$968$	0	0
$969$	16.4721	0.529161
$970$	12.6525	0.406247
$971$	−36.3607	−1.16687	−0.583435	−	0.812160i	$-0.698292\pi$
$971$	−36.3607	−1.16687	−0.583435	+	0.812160i	$0.698292\pi$
$972$	−1.00000	−0.0320750
$973$	16.3607	0.524499
$974$	−15.4164	−0.493974
$975$	−5.61803	−0.179921
$976$	0	0
$977$	−24.8328	−0.794472	−0.397236	−	0.917716i	$-0.630031\pi$
$977$	−24.8328	−0.794472	−0.397236	+	0.917716i	$0.630031\pi$
$978$	5.85410	0.187194
$979$	0	0
$980$	5.47214	0.174801
$981$	6.47214	0.206639
$982$	−1.03444	−0.0330104
$983$	47.1935	1.50524	0.752619	−	0.658456i	$-0.228790\pi$
$983$	47.1935	1.50524	0.752619	+	0.658456i	$0.228790\pi$
$984$	3.23607	0.103162
$985$	6.94427	0.221263
$986$	−1.94427	−0.0619182
$987$	−14.0000	−0.445625
$988$	−18.1803	−0.578394
$989$	1.61803	0.0514505
$990$	0	0
$991$	−59.5197	−1.89071	−0.945353	−	0.326048i	$-0.894283\pi$
$991$	−59.5197	−1.89071	−0.945353	+	0.326048i	$0.894283\pi$
$992$	−3.61803	−0.114873
$993$	−4.76393	−0.151179
$994$	1.88854	0.0599010
$995$	20.9787	0.665070
$996$	−4.00000	−0.126745
$997$	4.03444	0.127772	0.0638860	−	0.997957i	$-0.479651\pi$
$997$	4.03444	0.127772	0.0638860	+	0.997957i	$0.479651\pi$
$998$	−23.5279	−0.744762
$999$	8.61803	0.272663

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.b.31.1	✓	4	11.3	even	5
330.2.m.b.181.1	yes	4	11.4	even	5
990.2.n.e.181.1		4	33.26	odd	10
990.2.n.e.361.1		4	33.14	odd	10
3630.2.a.bb.1.1		2	11.10	odd	2
3630.2.a.bj.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +5.61803 q^{13} +1.23607 q^{14} +1.00000 q^{15} +1.00000 q^{16} +5.09017 q^{17} +1.00000 q^{18} -3.23607 q^{19} -1.00000 q^{20} -1.23607 q^{21} +0.145898 q^{23} -1.00000 q^{24} +1.00000 q^{25} +5.61803 q^{26} -1.00000 q^{27} +1.23607 q^{28} -0.381966 q^{29} +1.00000 q^{30} -3.61803 q^{31} +1.00000 q^{32} +5.09017 q^{34} -1.23607 q^{35} +1.00000 q^{36} -8.61803 q^{37} -3.23607 q^{38} -5.61803 q^{39} -1.00000 q^{40} -3.23607 q^{41} -1.23607 q^{42} +11.0902 q^{43} -1.00000 q^{45} +0.145898 q^{46} +11.3262 q^{47} -1.00000 q^{48} -5.47214 q^{49} +1.00000 q^{50} -5.09017 q^{51} +5.61803 q^{52} -0.472136 q^{53} -1.00000 q^{54} +1.23607 q^{56} +3.23607 q^{57} -0.381966 q^{58} +2.90983 q^{59} +1.00000 q^{60} -3.61803 q^{62} +1.23607 q^{63} +1.00000 q^{64} -5.61803 q^{65} +6.09017 q^{67} +5.09017 q^{68} -0.145898 q^{69} -1.23607 q^{70} +1.52786 q^{71} +1.00000 q^{72} -13.4164 q^{73} -8.61803 q^{74} -1.00000 q^{75} -3.23607 q^{76} -5.61803 q^{78} +7.09017 q^{79} -1.00000 q^{80} +1.00000 q^{81} -3.23607 q^{82} +4.00000 q^{83} -1.23607 q^{84} -5.09017 q^{85} +11.0902 q^{86} +0.381966 q^{87} +12.7639 q^{89} -1.00000 q^{90} +6.94427 q^{91} +0.145898 q^{92} +3.61803 q^{93} +11.3262 q^{94} +3.23607 q^{95} -1.00000 q^{96} -12.6525 q^{97} -5.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 9 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 7 q^{23} - 2 q^{24} + 2 q^{25} + 9 q^{26} - 2 q^{27} - 2 q^{28} - 3 q^{29} + 2 q^{30} - 5 q^{31} + 2 q^{32} - q^{34} + 2 q^{35} + 2 q^{36} - 15 q^{37} - 2 q^{38} - 9 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 2 q^{45} + 7 q^{46} + 7 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + q^{51} + 9 q^{52} + 8 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 17 q^{59} + 2 q^{60} - 5 q^{62} - 2 q^{63} + 2 q^{64} - 9 q^{65} + q^{67} - q^{68} - 7 q^{69} + 2 q^{70} + 12 q^{71} + 2 q^{72} - 15 q^{74} - 2 q^{75} - 2 q^{76} - 9 q^{78} + 3 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{82} + 8 q^{83} + 2 q^{84} + q^{85} + 11 q^{86} + 3 q^{87} + 30 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 5 q^{93} + 7 q^{94} + 2 q^{95} - 2 q^{96} + 6 q^{97} - 2 q^{98}+O(q^{100}) \) 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 + 9 * q^13 - 2 * q^14 + 2 * q^15 + 2 * q^16 - q^17 + 2 * q^18 - 2 * q^19 - 2 * q^20 + 2 * q^21 + 7 * q^23 - 2 * q^24 + 2 * q^25 + 9 * q^26 - 2 * q^27 - 2 * q^28 - 3 * q^29 + 2 * q^30 - 5 * q^31 + 2 * q^32 - q^34 + 2 * q^35 + 2 * q^36 - 15 * q^37 - 2 * q^38 - 9 * q^39 - 2 * q^40 - 2 * q^41 + 2 * q^42 + 11 * q^43 - 2 * q^45 + 7 * q^46 + 7 * q^47 - 2 * q^48 - 2 * q^49 + 2 * q^50 + q^51 + 9 * q^52 + 8 * q^53 - 2 * q^54 - 2 * q^56 + 2 * q^57 - 3 * q^58 + 17 * q^59 + 2 * q^60 - 5 * q^62 - 2 * q^63 + 2 * q^64 - 9 * q^65 + q^67 - q^68 - 7 * q^69 + 2 * q^70 + 12 * q^71 + 2 * q^72 - 15 * q^74 - 2 * q^75 - 2 * q^76 - 9 * q^78 + 3 * q^79 - 2 * q^80 + 2 * q^81 - 2 * q^82 + 8 * q^83 + 2 * q^84 + q^85 + 11 * q^86 + 3 * q^87 + 30 * q^89 - 2 * q^90 - 4 * q^91 + 7 * q^92 + 5 * q^93 + 7 * q^94 + 2 * q^95 - 2 * q^96 + 6 * q^97 - 2 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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