LMFDB - Embedded newform 3630.2.a.bj.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

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

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +3.38197 q^{13} -3.23607 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.09017 q^{17} +1.00000 q^{18} +1.23607 q^{19} -1.00000 q^{20} +3.23607 q^{21} +6.85410 q^{23} -1.00000 q^{24} +1.00000 q^{25} +3.38197 q^{26} -1.00000 q^{27} -3.23607 q^{28} -2.61803 q^{29} +1.00000 q^{30} -1.38197 q^{31} +1.00000 q^{32} -6.09017 q^{34} +3.23607 q^{35} +1.00000 q^{36} -6.38197 q^{37} +1.23607 q^{38} -3.38197 q^{39} -1.00000 q^{40} +1.23607 q^{41} +3.23607 q^{42} -0.0901699 q^{43} -1.00000 q^{45} +6.85410 q^{46} -4.32624 q^{47} -1.00000 q^{48} +3.47214 q^{49} +1.00000 q^{50} +6.09017 q^{51} +3.38197 q^{52} +8.47214 q^{53} -1.00000 q^{54} -3.23607 q^{56} -1.23607 q^{57} -2.61803 q^{58} +14.0902 q^{59} +1.00000 q^{60} -1.38197 q^{62} -3.23607 q^{63} +1.00000 q^{64} -3.38197 q^{65} -5.09017 q^{67} -6.09017 q^{68} -6.85410 q^{69} +3.23607 q^{70} +10.4721 q^{71} +1.00000 q^{72} +13.4164 q^{73} -6.38197 q^{74} -1.00000 q^{75} +1.23607 q^{76} -3.38197 q^{78} -4.09017 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.23607 q^{82} +4.00000 q^{83} +3.23607 q^{84} +6.09017 q^{85} -0.0901699 q^{86} +2.61803 q^{87} +17.2361 q^{89} -1.00000 q^{90} -10.9443 q^{91} +6.85410 q^{92} +1.38197 q^{93} -4.32624 q^{94} -1.23607 q^{95} -1.00000 q^{96} +18.6525 q^{97} +3.47214 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 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
$7$	−3.23607	−1.22312	−0.611559	−	0.791199i	$-0.709457\pi$
$7$	−3.23607	−1.22312	−0.611559	+	0.791199i	$0.709457\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	3.38197	0.937989	0.468994	−	0.883201i	$-0.344616\pi$
$13$	3.38197	0.937989	0.468994	+	0.883201i	$0.344616\pi$
$14$	−3.23607	−0.864876
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−6.09017	−1.47708	−0.738542	−	0.674208i	$-0.764485\pi$
$17$	−6.09017	−1.47708	−0.738542	+	0.674208i	$0.764485\pi$
$18$	1.00000	0.235702
$19$	1.23607	0.283573	0.141787	−	0.989897i	$-0.454715\pi$
$19$	1.23607	0.283573	0.141787	+	0.989897i	$0.454715\pi$
$20$	−1.00000	−0.223607
$21$	3.23607	0.706168
$22$	0	0
$23$	6.85410	1.42918	0.714590	−	0.699544i	$-0.246614\pi$
$23$	6.85410	1.42918	0.714590	+	0.699544i	$0.246614\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	3.38197	0.663258
$27$	−1.00000	−0.192450
$28$	−3.23607	−0.611559
$29$	−2.61803	−0.486157	−0.243078	−	0.970007i	$-0.578157\pi$
$29$	−2.61803	−0.486157	−0.243078	+	0.970007i	$0.578157\pi$
$30$	1.00000	0.182574
$31$	−1.38197	−0.248208	−0.124104	−	0.992269i	$-0.539606\pi$
$31$	−1.38197	−0.248208	−0.124104	+	0.992269i	$0.539606\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−6.09017	−1.04446
$35$	3.23607	0.546995
$36$	1.00000	0.166667
$37$	−6.38197	−1.04919	−0.524594	−	0.851352i	$-0.675783\pi$
$37$	−6.38197	−1.04919	−0.524594	+	0.851352i	$0.675783\pi$
$38$	1.23607	0.200517
$39$	−3.38197	−0.541548
$40$	−1.00000	−0.158114
$41$	1.23607	0.193041	0.0965207	−	0.995331i	$-0.469229\pi$
$41$	1.23607	0.193041	0.0965207	+	0.995331i	$0.469229\pi$
$42$	3.23607	0.499336
$43$	−0.0901699	−0.0137508	−0.00687539	−	0.999976i	$-0.502189\pi$
$43$	−0.0901699	−0.0137508	−0.00687539	+	0.999976i	$0.502189\pi$
$44$	0	0
$45$	−1.00000	−0.149071
$46$	6.85410	1.01058
$47$	−4.32624	−0.631047	−0.315523	−	0.948918i	$-0.602180\pi$
$47$	−4.32624	−0.631047	−0.315523	+	0.948918i	$0.602180\pi$
$48$	−1.00000	−0.144338
$49$	3.47214	0.496019
$50$	1.00000	0.141421
$51$	6.09017	0.852794
$52$	3.38197	0.468994
$53$	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
$56$	−3.23607	−0.432438
$57$	−1.23607	−0.163721
$58$	−2.61803	−0.343765
$59$	14.0902	1.83438	0.917192	−	0.398446i	$-0.130450\pi$
$59$	14.0902	1.83438	0.917192	+	0.398446i	$0.130450\pi$
$60$	1.00000	0.129099
$61$	0	0		−	1.00000i	$-0.5\pi$
$61$	0	0			1.00000i	$0.5\pi$
$62$	−1.38197	−0.175510
$63$	−3.23607	−0.407706
$64$	1.00000	0.125000
$65$	−3.38197	−0.419481
$66$	0	0
$67$	−5.09017	−0.621863	−0.310932	−	0.950432i	$-0.600641\pi$
$67$	−5.09017	−0.621863	−0.310932	+	0.950432i	$0.600641\pi$
$68$	−6.09017	−0.738542
$69$	−6.85410	−0.825137
$70$	3.23607	0.386784
$71$	10.4721	1.24281	0.621407	−	0.783488i	$-0.286561\pi$
$71$	10.4721	1.24281	0.621407	+	0.783488i	$0.286561\pi$
$72$	1.00000	0.117851
$73$	13.4164	1.57027	0.785136	−	0.619324i	$-0.212593\pi$
$73$	13.4164	1.57027	0.785136	+	0.619324i	$0.212593\pi$
$74$	−6.38197	−0.741888
$75$	−1.00000	−0.115470
$76$	1.23607	0.141787
$77$	0	0
$78$	−3.38197	−0.382932
$79$	−4.09017	−0.460180	−0.230090	−	0.973169i	$-0.573902\pi$
$79$	−4.09017	−0.460180	−0.230090	+	0.973169i	$0.573902\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.23607	0.136501
$83$	4.00000	0.439057	0.219529	−	0.975606i	$-0.429548\pi$
$83$	4.00000	0.439057	0.219529	+	0.975606i	$0.429548\pi$
$84$	3.23607	0.353084
$85$	6.09017	0.660572
$86$	−0.0901699	−0.00972328
$87$	2.61803	0.280683
$88$	0	0
$89$	17.2361	1.82702	0.913510	−	0.406817i	$-0.133361\pi$
$89$	17.2361	1.82702	0.913510	+	0.406817i	$0.133361\pi$
$90$	−1.00000	−0.105409
$91$	−10.9443	−1.14727
$92$	6.85410	0.714590
$93$	1.38197	0.143303
$94$	−4.32624	−0.446217
$95$	−1.23607	−0.126818
$96$	−1.00000	−0.102062
$97$	18.6525	1.89387	0.946936	−	0.321422i	$-0.104161\pi$
$97$	18.6525	1.89387	0.946936	+	0.321422i	$0.104161\pi$
$98$	3.47214	0.350739
$99$	0	0
$100$	1.00000	0.100000
$101$	15.6180	1.55405	0.777026	−	0.629468i	$-0.216727\pi$
$101$	15.6180	1.55405	0.777026	+	0.629468i	$0.216727\pi$
$102$	6.09017	0.603017
$103$	6.76393	0.666470	0.333235	−	0.942844i	$-0.391860\pi$
$103$	6.76393	0.666470	0.333235	+	0.942844i	$0.391860\pi$
$104$	3.38197	0.331629
$105$	−3.23607	−0.315808
$106$	8.47214	0.822887
$107$	6.29180	0.608251	0.304125	−	0.952632i	$-0.401636\pi$
$107$	6.29180	0.608251	0.304125	+	0.952632i	$0.401636\pi$
$108$	−1.00000	−0.0962250
$109$	−2.47214	−0.236788	−0.118394	−	0.992967i	$-0.537775\pi$
$109$	−2.47214	−0.236788	−0.118394	+	0.992967i	$0.537775\pi$
$110$	0	0
$111$	6.38197	0.605749
$112$	−3.23607	−0.305780
$113$	−19.5623	−1.84027	−0.920133	−	0.391605i	$-0.871920\pi$
$113$	−19.5623	−1.84027	−0.920133	+	0.391605i	$0.871920\pi$
$114$	−1.23607	−0.115768
$115$	−6.85410	−0.639148
$116$	−2.61803	−0.243078
$117$	3.38197	0.312663
$118$	14.0902	1.29711
$119$	19.7082	1.80665
$120$	1.00000	0.0912871
$121$	0	0
$122$	0	0
$123$	−1.23607	−0.111452
$124$	−1.38197	−0.124104
$125$	−1.00000	−0.0894427
$126$	−3.23607	−0.288292
$127$	14.6525	1.30020	0.650098	−	0.759850i	$-0.274728\pi$
$127$	14.6525	1.30020	0.650098	+	0.759850i	$0.274728\pi$
$128$	1.00000	0.0883883
$129$	0.0901699	0.00793902
$130$	−3.38197	−0.296618
$131$	−3.38197	−0.295484	−0.147742	−	0.989026i	$-0.547200\pi$
$131$	−3.38197	−0.295484	−0.147742	+	0.989026i	$0.547200\pi$
$132$	0	0
$133$	−4.00000	−0.346844
$134$	−5.09017	−0.439724
$135$	1.00000	0.0860663
$136$	−6.09017	−0.522228
$137$	−12.7984	−1.09344	−0.546719	−	0.837316i	$-0.684124\pi$
$137$	−12.7984	−1.09344	−0.546719	+	0.837316i	$0.684124\pi$
$138$	−6.85410	−0.583460
$139$	8.76393	0.743347	0.371674	−	0.928364i	$-0.378784\pi$
$139$	8.76393	0.743347	0.371674	+	0.928364i	$0.378784\pi$
$140$	3.23607	0.273498
$141$	4.32624	0.364335
$142$	10.4721	0.878802
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.61803	0.217416
$146$	13.4164	1.11035
$147$	−3.47214	−0.286377
$148$	−6.38197	−0.524594
$149$	−7.61803	−0.624094	−0.312047	−	0.950067i	$-0.601015\pi$
$149$	−7.61803	−0.624094	−0.312047	+	0.950067i	$0.601015\pi$
$150$	−1.00000	−0.0816497
$151$	20.9443	1.70442	0.852210	−	0.523199i	$-0.175262\pi$
$151$	20.9443	1.70442	0.852210	+	0.523199i	$0.175262\pi$
$152$	1.23607	0.100258
$153$	−6.09017	−0.492361
$154$	0	0
$155$	1.38197	0.111002
$156$	−3.38197	−0.270774
$157$	−9.27051	−0.739867	−0.369934	−	0.929058i	$-0.620620\pi$
$157$	−9.27051	−0.739867	−0.369934	+	0.929058i	$0.620620\pi$
$158$	−4.09017	−0.325396
$159$	−8.47214	−0.671884
$160$	−1.00000	−0.0790569
$161$	−22.1803	−1.74806
$162$	1.00000	0.0785674
$163$	0.854102	0.0668984	0.0334492	−	0.999440i	$-0.489351\pi$
$163$	0.854102	0.0668984	0.0334492	+	0.999440i	$0.489351\pi$
$164$	1.23607	0.0965207
$165$	0	0
$166$	4.00000	0.310460
$167$	−13.2705	−1.02690	−0.513451	−	0.858119i	$-0.671633\pi$
$167$	−13.2705	−1.02690	−0.513451	+	0.858119i	$0.671633\pi$
$168$	3.23607	0.249668
$169$	−1.56231	−0.120177
$170$	6.09017	0.467095
$171$	1.23607	0.0945245
$172$	−0.0901699	−0.00687539
$173$	−9.52786	−0.724390	−0.362195	−	0.932102i	$-0.617973\pi$
$173$	−9.52786	−0.724390	−0.362195	+	0.932102i	$0.617973\pi$
$174$	2.61803	0.198473
$175$	−3.23607	−0.244624
$176$	0	0
$177$	−14.0902	−1.05908
$178$	17.2361	1.29190
$179$	18.1459	1.35629	0.678144	−	0.734929i	$-0.262785\pi$
$179$	18.1459	1.35629	0.678144	+	0.734929i	$0.262785\pi$
$180$	−1.00000	−0.0745356
$181$	21.8885	1.62696	0.813481	−	0.581591i	$-0.197570\pi$
$181$	21.8885	1.62696	0.813481	+	0.581591i	$0.197570\pi$
$182$	−10.9443	−0.811243
$183$	0	0
$184$	6.85410	0.505291
$185$	6.38197	0.469211
$186$	1.38197	0.101331
$187$	0	0
$188$	−4.32624	−0.315523
$189$	3.23607	0.235389
$190$	−1.23607	−0.0896738
$191$	9.23607	0.668298	0.334149	−	0.942520i	$-0.391551\pi$
$191$	9.23607	0.668298	0.334149	+	0.942520i	$0.391551\pi$
$192$	−1.00000	−0.0721688
$193$	−20.9443	−1.50760	−0.753801	−	0.657103i	$-0.771782\pi$
$193$	−20.9443	−1.50760	−0.753801	+	0.657103i	$0.771782\pi$
$194$	18.6525	1.33917
$195$	3.38197	0.242188
$196$	3.47214	0.248010
$197$	10.9443	0.779747	0.389874	−	0.920868i	$-0.372519\pi$
$197$	10.9443	0.779747	0.389874	+	0.920868i	$0.372519\pi$
$198$	0	0
$199$	25.9787	1.84158	0.920791	−	0.390056i	$-0.127544\pi$
$199$	25.9787	1.84158	0.920791	+	0.390056i	$0.127544\pi$
$200$	1.00000	0.0707107
$201$	5.09017	0.359033
$202$	15.6180	1.09888
$203$	8.47214	0.594627
$204$	6.09017	0.426397
$205$	−1.23607	−0.0863307
$206$	6.76393	0.471265
$207$	6.85410	0.476393
$208$	3.38197	0.234497
$209$	0	0
$210$	−3.23607	−0.223310
$211$	−25.2361	−1.73732	−0.868661	−	0.495406i	$-0.835019\pi$
$211$	−25.2361	−1.73732	−0.868661	+	0.495406i	$0.835019\pi$
$212$	8.47214	0.581869
$213$	−10.4721	−0.717539
$214$	6.29180	0.430098
$215$	0.0901699	0.00614954
$216$	−1.00000	−0.0680414
$217$	4.47214	0.303588
$218$	−2.47214	−0.167434
$219$	−13.4164	−0.906597
$220$	0	0
$221$	−20.5967	−1.38549
$222$	6.38197	0.428330
$223$	7.23607	0.484563	0.242281	−	0.970206i	$-0.422104\pi$
$223$	7.23607	0.484563	0.242281	+	0.970206i	$0.422104\pi$
$224$	−3.23607	−0.216219
$225$	1.00000	0.0666667
$226$	−19.5623	−1.30127
$227$	20.3607	1.35139	0.675693	−	0.737183i	$-0.263845\pi$
$227$	20.3607	1.35139	0.675693	+	0.737183i	$0.263845\pi$
$228$	−1.23607	−0.0818606
$229$	0.763932	0.0504820	0.0252410	−	0.999681i	$-0.491965\pi$
$229$	0.763932	0.0504820	0.0252410	+	0.999681i	$0.491965\pi$
$230$	−6.85410	−0.451946
$231$	0	0
$232$	−2.61803	−0.171882
$233$	−4.43769	−0.290723	−0.145362	−	0.989379i	$-0.546435\pi$
$233$	−4.43769	−0.290723	−0.145362	+	0.989379i	$0.546435\pi$
$234$	3.38197	0.221086
$235$	4.32624	0.282213
$236$	14.0902	0.917192
$237$	4.09017	0.265685
$238$	19.7082	1.27749
$239$	−3.23607	−0.209324	−0.104662	−	0.994508i	$-0.533376\pi$
$239$	−3.23607	−0.209324	−0.104662	+	0.994508i	$0.533376\pi$
$240$	1.00000	0.0645497
$241$	−23.8885	−1.53880	−0.769398	−	0.638769i	$-0.779444\pi$
$241$	−23.8885	−1.53880	−0.769398	+	0.638769i	$0.779444\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	0	0
$245$	−3.47214	−0.221827
$246$	−1.23607	−0.0788088
$247$	4.18034	0.265989
$248$	−1.38197	−0.0877549
$249$	−4.00000	−0.253490
$250$	−1.00000	−0.0632456
$251$	8.38197	0.529065	0.264533	−	0.964377i	$-0.414782\pi$
$251$	8.38197	0.529065	0.264533	+	0.964377i	$0.414782\pi$
$252$	−3.23607	−0.203853
$253$	0	0
$254$	14.6525	0.919378
$255$	−6.09017	−0.381381
$256$	1.00000	0.0625000
$257$	30.3607	1.89385	0.946924	−	0.321459i	$-0.104173\pi$
$257$	30.3607	1.89385	0.946924	+	0.321459i	$0.104173\pi$
$258$	0.0901699	0.00561374
$259$	20.6525	1.28328
$260$	−3.38197	−0.209741
$261$	−2.61803	−0.162052
$262$	−3.38197	−0.208939
$263$	6.85410	0.422642	0.211321	−	0.977417i	$-0.432223\pi$
$263$	6.85410	0.422642	0.211321	+	0.977417i	$0.432223\pi$
$264$	0	0
$265$	−8.47214	−0.520439
$266$	−4.00000	−0.245256
$267$	−17.2361	−1.05483
$268$	−5.09017	−0.310932
$269$	3.20163	0.195207	0.0976033	−	0.995225i	$-0.468882\pi$
$269$	3.20163	0.195207	0.0976033	+	0.995225i	$0.468882\pi$
$270$	1.00000	0.0608581
$271$	−6.38197	−0.387677	−0.193838	−	0.981033i	$-0.562094\pi$
$271$	−6.38197	−0.387677	−0.193838	+	0.981033i	$0.562094\pi$
$272$	−6.09017	−0.369271
$273$	10.9443	0.662377
$274$	−12.7984	−0.773178
$275$	0	0
$276$	−6.85410	−0.412568
$277$	−23.5066	−1.41237	−0.706187	−	0.708026i	$-0.749586\pi$
$277$	−23.5066	−1.41237	−0.706187	+	0.708026i	$0.749586\pi$
$278$	8.76393	0.525626
$279$	−1.38197	−0.0827361
$280$	3.23607	0.193392
$281$	−7.52786	−0.449075	−0.224537	−	0.974465i	$-0.572087\pi$
$281$	−7.52786	−0.449075	−0.224537	+	0.974465i	$0.572087\pi$
$282$	4.32624	0.257624
$283$	−22.3262	−1.32716	−0.663579	−	0.748107i	$-0.730963\pi$
$283$	−22.3262	−1.32716	−0.663579	+	0.748107i	$0.730963\pi$
$284$	10.4721	0.621407
$285$	1.23607	0.0732183
$286$	0	0
$287$	−4.00000	−0.236113
$288$	1.00000	0.0589256
$289$	20.0902	1.18177
$290$	2.61803	0.153736
$291$	−18.6525	−1.09343
$292$	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	$0.698594\pi$
$294$	−3.47214	−0.202499
$295$	−14.0902	−0.820361
$296$	−6.38197	−0.370944
$297$	0	0
$298$	−7.61803	−0.441301
$299$	23.1803	1.34055
$300$	−1.00000	−0.0577350
$301$	0.291796	0.0168188
$302$	20.9443	1.20521
$303$	−15.6180	−0.897233
$304$	1.23607	0.0708934
$305$	0	0
$306$	−6.09017	−0.348152
$307$	−33.4508	−1.90914	−0.954570	−	0.297985i	$-0.903685\pi$
$307$	−33.4508	−1.90914	−0.954570	+	0.297985i	$0.903685\pi$
$308$	0	0
$309$	−6.76393	−0.384787
$310$	1.38197	0.0784904
$311$	9.23607	0.523729	0.261865	−	0.965105i	$-0.415663\pi$
$311$	9.23607	0.523729	0.261865	+	0.965105i	$0.415663\pi$
$312$	−3.38197	−0.191466
$313$	8.47214	0.478873	0.239437	−	0.970912i	$-0.423037\pi$
$313$	8.47214	0.478873	0.239437	+	0.970912i	$0.423037\pi$
$314$	−9.27051	−0.523165
$315$	3.23607	0.182332
$316$	−4.09017	−0.230090
$317$	−27.4164	−1.53986	−0.769929	−	0.638129i	$-0.779709\pi$
$317$	−27.4164	−1.53986	−0.769929	+	0.638129i	$0.779709\pi$
$318$	−8.47214	−0.475094
$319$	0	0
$320$	−1.00000	−0.0559017
$321$	−6.29180	−0.351174
$322$	−22.1803	−1.23606
$323$	−7.52786	−0.418862
$324$	1.00000	0.0555556
$325$	3.38197	0.187598
$326$	0.854102	0.0473043
$327$	2.47214	0.136709
$328$	1.23607	0.0682504
$329$	14.0000	0.771845
$330$	0	0
$331$	9.23607	0.507660	0.253830	−	0.967249i	$-0.418310\pi$
$331$	9.23607	0.507660	0.253830	+	0.967249i	$0.418310\pi$
$332$	4.00000	0.219529
$333$	−6.38197	−0.349730
$334$	−13.2705	−0.726130
$335$	5.09017	0.278106
$336$	3.23607	0.176542
$337$	−15.2361	−0.829962	−0.414981	−	0.909830i	$-0.636212\pi$
$337$	−15.2361	−0.829962	−0.414981	+	0.909830i	$0.636212\pi$
$338$	−1.56231	−0.0849782
$339$	19.5623	1.06248
$340$	6.09017	0.330286
$341$	0	0
$342$	1.23607	0.0668389
$343$	11.4164	0.616428
$344$	−0.0901699	−0.00486164
$345$	6.85410	0.369012
$346$	−9.52786	−0.512221
$347$	35.8885	1.92660	0.963299	−	0.268431i	$-0.0865050\pi$
$347$	35.8885	1.92660	0.963299	+	0.268431i	$0.0865050\pi$
$348$	2.61803	0.140341
$349$	−11.4164	−0.611106	−0.305553	−	0.952175i	$-0.598841\pi$
$349$	−11.4164	−0.611106	−0.305553	+	0.952175i	$0.598841\pi$
$350$	−3.23607	−0.172975
$351$	−3.38197	−0.180516
$352$	0	0
$353$	23.6180	1.25706	0.628531	−	0.777785i	$-0.283657\pi$
$353$	23.6180	1.25706	0.628531	+	0.777785i	$0.283657\pi$
$354$	−14.0902	−0.748884
$355$	−10.4721	−0.555803
$356$	17.2361	0.913510
$357$	−19.7082	−1.04307
$358$	18.1459	0.959041
$359$	−12.1803	−0.642854	−0.321427	−	0.946934i	$-0.604162\pi$
$359$	−12.1803	−0.642854	−0.321427	+	0.946934i	$0.604162\pi$
$360$	−1.00000	−0.0527046
$361$	−17.4721	−0.919586
$362$	21.8885	1.15044
$363$	0	0
$364$	−10.9443	−0.573636
$365$	−13.4164	−0.702247
$366$	0	0
$367$	−26.7639	−1.39707	−0.698533	−	0.715578i	$-0.746163\pi$
$367$	−26.7639	−1.39707	−0.698533	+	0.715578i	$0.746163\pi$
$368$	6.85410	0.357295
$369$	1.23607	0.0643471
$370$	6.38197	0.331783
$371$	−27.4164	−1.42339
$372$	1.38197	0.0716516
$373$	−11.5279	−0.596890	−0.298445	−	0.954427i	$-0.596468\pi$
$373$	−11.5279	−0.596890	−0.298445	+	0.954427i	$0.596468\pi$
$374$	0	0
$375$	1.00000	0.0516398
$376$	−4.32624	−0.223109
$377$	−8.85410	−0.456009
$378$	3.23607	0.166445
$379$	−12.3607	−0.634925	−0.317463	−	0.948271i	$-0.602831\pi$
$379$	−12.3607	−0.634925	−0.317463	+	0.948271i	$0.602831\pi$
$380$	−1.23607	−0.0634089
$381$	−14.6525	−0.750669
$382$	9.23607	0.472558
$383$	−0.326238	−0.0166700	−0.00833499	−	0.999965i	$-0.502653\pi$
$383$	−0.326238	−0.0166700	−0.00833499	+	0.999965i	$0.502653\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−20.9443	−1.06604
$387$	−0.0901699	−0.00458360
$388$	18.6525	0.946936
$389$	6.85410	0.347517	0.173758	−	0.984788i	$-0.444409\pi$
$389$	6.85410	0.347517	0.173758	+	0.984788i	$0.444409\pi$
$390$	3.38197	0.171253
$391$	−41.7426	−2.11102
$392$	3.47214	0.175369
$393$	3.38197	0.170598
$394$	10.9443	0.551364
$395$	4.09017	0.205799
$396$	0	0
$397$	2.20163	0.110496	0.0552482	−	0.998473i	$-0.482405\pi$
$397$	2.20163	0.110496	0.0552482	+	0.998473i	$0.482405\pi$
$398$	25.9787	1.30220
$399$	4.00000	0.200250
$400$	1.00000	0.0500000
$401$	22.0689	1.10207	0.551034	−	0.834483i	$-0.314234\pi$
$401$	22.0689	1.10207	0.551034	+	0.834483i	$0.314234\pi$
$402$	5.09017	0.253875
$403$	−4.67376	−0.232817
$404$	15.6180	0.777026
$405$	−1.00000	−0.0496904
$406$	8.47214	0.420465
$407$	0	0
$408$	6.09017	0.301508
$409$	12.9787	0.641756	0.320878	−	0.947121i	$-0.396022\pi$
$409$	12.9787	0.641756	0.320878	+	0.947121i	$0.396022\pi$
$410$	−1.23607	−0.0610450
$411$	12.7984	0.631297
$412$	6.76393	0.333235
$413$	−45.5967	−2.24367
$414$	6.85410	0.336861
$415$	−4.00000	−0.196352
$416$	3.38197	0.165815
$417$	−8.76393	−0.429172
$418$	0	0
$419$	22.8541	1.11650	0.558248	−	0.829674i	$-0.311474\pi$
$419$	22.8541	1.11650	0.558248	+	0.829674i	$0.311474\pi$
$420$	−3.23607	−0.157904
$421$	−2.47214	−0.120485	−0.0602423	−	0.998184i	$-0.519187\pi$
$421$	−2.47214	−0.120485	−0.0602423	+	0.998184i	$0.519187\pi$
$422$	−25.2361	−1.22847
$423$	−4.32624	−0.210349
$424$	8.47214	0.411443
$425$	−6.09017	−0.295417
$426$	−10.4721	−0.507377
$427$	0	0
$428$	6.29180	0.304125
$429$	0	0
$430$	0.0901699	0.00434838
$431$	22.3607	1.07708	0.538538	−	0.842601i	$-0.318977\pi$
$431$	22.3607	1.07708	0.538538	+	0.842601i	$0.318977\pi$
$432$	−1.00000	−0.0481125
$433$	−22.8328	−1.09728	−0.548638	−	0.836060i	$-0.684853\pi$
$433$	−22.8328	−1.09728	−0.548638	+	0.836060i	$0.684853\pi$
$434$	4.47214	0.214669
$435$	−2.61803	−0.125525
$436$	−2.47214	−0.118394
$437$	8.47214	0.405277
$438$	−13.4164	−0.641061
$439$	1.67376	0.0798843	0.0399422	−	0.999202i	$-0.487283\pi$
$439$	1.67376	0.0798843	0.0399422	+	0.999202i	$0.487283\pi$
$440$	0	0
$441$	3.47214	0.165340
$442$	−20.5967	−0.979687
$443$	−18.6525	−0.886206	−0.443103	−	0.896471i	$-0.646122\pi$
$443$	−18.6525	−0.886206	−0.443103	+	0.896471i	$0.646122\pi$
$444$	6.38197	0.302875
$445$	−17.2361	−0.817068
$446$	7.23607	0.342638
$447$	7.61803	0.360321
$448$	−3.23607	−0.152890
$449$	−11.1246	−0.525003	−0.262501	−	0.964932i	$-0.584547\pi$
$449$	−11.1246	−0.525003	−0.262501	+	0.964932i	$0.584547\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−19.5623	−0.920133
$453$	−20.9443	−0.984048
$454$	20.3607	0.955574
$455$	10.9443	0.513075
$456$	−1.23607	−0.0578842
$457$	4.65248	0.217634	0.108817	−	0.994062i	$-0.465294\pi$
$457$	4.65248	0.217634	0.108817	+	0.994062i	$0.465294\pi$
$458$	0.763932	0.0356962
$459$	6.09017	0.284265
$460$	−6.85410	−0.319574
$461$	23.2148	1.08122	0.540610	−	0.841273i	$-0.318193\pi$
$461$	23.2148	1.08122	0.540610	+	0.841273i	$0.318193\pi$
$462$	0	0
$463$	11.8885	0.552507	0.276254	−	0.961085i	$-0.410907\pi$
$463$	11.8885	0.552507	0.276254	+	0.961085i	$0.410907\pi$
$464$	−2.61803	−0.121539
$465$	−1.38197	−0.0640871
$466$	−4.43769	−0.205572
$467$	28.5410	1.32072	0.660360	−	0.750949i	$-0.270404\pi$
$467$	28.5410	1.32072	0.660360	+	0.750949i	$0.270404\pi$
$468$	3.38197	0.156331
$469$	16.4721	0.760613
$470$	4.32624	0.199554
$471$	9.27051	0.427163
$472$	14.0902	0.648553
$473$	0	0
$474$	4.09017	0.187868
$475$	1.23607	0.0567147
$476$	19.7082	0.903324
$477$	8.47214	0.387912
$478$	−3.23607	−0.148014
$479$	12.7639	0.583199	0.291599	−	0.956541i	$-0.405813\pi$
$479$	12.7639	0.583199	0.291599	+	0.956541i	$0.405813\pi$
$480$	1.00000	0.0456435
$481$	−21.5836	−0.984127
$482$	−23.8885	−1.08809
$483$	22.1803	1.00924
$484$	0	0
$485$	−18.6525	−0.846965
$486$	−1.00000	−0.0453609
$487$	11.4164	0.517327	0.258663	−	0.965968i	$-0.416718\pi$
$487$	11.4164	0.517327	0.258663	+	0.965968i	$0.416718\pi$
$488$	0	0
$489$	−0.854102	−0.0386238
$490$	−3.47214	−0.156855
$491$	28.0344	1.26518	0.632588	−	0.774488i	$-0.281993\pi$
$491$	28.0344	1.26518	0.632588	+	0.774488i	$0.281993\pi$
$492$	−1.23607	−0.0557262
$493$	15.9443	0.718094
$494$	4.18034	0.188082
$495$	0	0
$496$	−1.38197	−0.0620521
$497$	−33.8885	−1.52011
$498$	−4.00000	−0.179244
$499$	−32.4721	−1.45365	−0.726826	−	0.686821i	$-0.759005\pi$
$499$	−32.4721	−1.45365	−0.726826	+	0.686821i	$0.759005\pi$
$500$	−1.00000	−0.0447214
$501$	13.2705	0.592883
$502$	8.38197	0.374105
$503$	−24.3262	−1.08465	−0.542327	−	0.840168i	$-0.682456\pi$
$503$	−24.3262	−1.08465	−0.542327	+	0.840168i	$0.682456\pi$
$504$	−3.23607	−0.144146
$505$	−15.6180	−0.694993
$506$	0	0
$507$	1.56231	0.0693844
$508$	14.6525	0.650098
$509$	8.79837	0.389981	0.194991	−	0.980805i	$-0.437532\pi$
$509$	8.79837	0.389981	0.194991	+	0.980805i	$0.437532\pi$
$510$	−6.09017	−0.269677
$511$	−43.4164	−1.92063
$512$	1.00000	0.0441942
$513$	−1.23607	−0.0545737
$514$	30.3607	1.33915
$515$	−6.76393	−0.298054
$516$	0.0901699	0.00396951
$517$	0	0
$518$	20.6525	0.907418
$519$	9.52786	0.418227
$520$	−3.38197	−0.148309
$521$	−2.36068	−0.103423	−0.0517116	−	0.998662i	$-0.516468\pi$
$521$	−2.36068	−0.103423	−0.0517116	+	0.998662i	$0.516468\pi$
$522$	−2.61803	−0.114588
$523$	38.8328	1.69804	0.849020	−	0.528360i	$-0.177193\pi$
$523$	38.8328	1.69804	0.849020	+	0.528360i	$0.177193\pi$
$524$	−3.38197	−0.147742
$525$	3.23607	0.141234
$526$	6.85410	0.298853
$527$	8.41641	0.366624
$528$	0	0
$529$	23.9787	1.04255
$530$	−8.47214	−0.368006
$531$	14.0902	0.611461
$532$	−4.00000	−0.173422
$533$	4.18034	0.181071
$534$	−17.2361	−0.745878
$535$	−6.29180	−0.272018
$536$	−5.09017	−0.219862
$537$	−18.1459	−0.783053
$538$	3.20163	0.138032
$539$	0	0
$540$	1.00000	0.0430331
$541$	26.0689	1.12079	0.560394	−	0.828226i	$-0.310650\pi$
$541$	26.0689	1.12079	0.560394	+	0.828226i	$0.310650\pi$
$542$	−6.38197	−0.274129
$543$	−21.8885	−0.939327
$544$	−6.09017	−0.261114
$545$	2.47214	0.105895
$546$	10.9443	0.468372
$547$	34.3262	1.46768	0.733842	−	0.679320i	$-0.237725\pi$
$547$	34.3262	1.46768	0.733842	+	0.679320i	$0.237725\pi$
$548$	−12.7984	−0.546719
$549$	0	0
$550$	0	0
$551$	−3.23607	−0.137861
$552$	−6.85410	−0.291730
$553$	13.2361	0.562855
$554$	−23.5066	−0.998699
$555$	−6.38197	−0.270899
$556$	8.76393	0.371674
$557$	−35.1246	−1.48828	−0.744139	−	0.668025i	$-0.767140\pi$
$557$	−35.1246	−1.48828	−0.744139	+	0.668025i	$0.767140\pi$
$558$	−1.38197	−0.0585033
$559$	−0.304952	−0.0128981
$560$	3.23607	0.136749
$561$	0	0
$562$	−7.52786	−0.317544
$563$	17.0557	0.718813	0.359407	−	0.933181i	$-0.382979\pi$
$563$	17.0557	0.718813	0.359407	+	0.933181i	$0.382979\pi$
$564$	4.32624	0.182167
$565$	19.5623	0.822992
$566$	−22.3262	−0.938442
$567$	−3.23607	−0.135902
$568$	10.4721	0.439401
$569$	−25.4164	−1.06551	−0.532756	−	0.846269i	$-0.678844\pi$
$569$	−25.4164	−1.06551	−0.532756	+	0.846269i	$0.678844\pi$
$570$	1.23607	0.0517732
$571$	−28.3607	−1.18686	−0.593429	−	0.804887i	$-0.702226\pi$
$571$	−28.3607	−1.18686	−0.593429	+	0.804887i	$0.702226\pi$
$572$	0	0
$573$	−9.23607	−0.385842
$574$	−4.00000	−0.166957
$575$	6.85410	0.285836
$576$	1.00000	0.0416667
$577$	17.0557	0.710039	0.355020	−	0.934859i	$-0.384474\pi$
$577$	17.0557	0.710039	0.355020	+	0.934859i	$0.384474\pi$
$578$	20.0902	0.835641
$579$	20.9443	0.870414
$580$	2.61803	0.108708
$581$	−12.9443	−0.537019
$582$	−18.6525	−0.773170
$583$	0	0
$584$	13.4164	0.555175
$585$	−3.38197	−0.139827
$586$	−20.0000	−0.826192
$587$	−26.2918	−1.08518	−0.542589	−	0.839998i	$-0.682556\pi$
$587$	−26.2918	−1.08518	−0.542589	+	0.839998i	$0.682556\pi$
$588$	−3.47214	−0.143188
$589$	−1.70820	−0.0703853
$590$	−14.0902	−0.580083
$591$	−10.9443	−0.450187
$592$	−6.38197	−0.262297
$593$	−17.6738	−0.725774	−0.362887	−	0.931833i	$-0.618209\pi$
$593$	−17.6738	−0.725774	−0.362887	+	0.931833i	$0.618209\pi$
$594$	0	0
$595$	−19.7082	−0.807958
$596$	−7.61803	−0.312047
$597$	−25.9787	−1.06324
$598$	23.1803	0.947915
$599$	18.1803	0.742829	0.371414	−	0.928467i	$-0.378873\pi$
$599$	18.1803	0.742829	0.371414	+	0.928467i	$0.378873\pi$
$600$	−1.00000	−0.0408248
$601$	−18.9443	−0.772753	−0.386376	−	0.922341i	$-0.626273\pi$
$601$	−18.9443	−0.772753	−0.386376	+	0.922341i	$0.626273\pi$
$602$	0.291796	0.0118927
$603$	−5.09017	−0.207288
$604$	20.9443	0.852210
$605$	0	0
$606$	−15.6180	−0.634439
$607$	−4.47214	−0.181518	−0.0907592	−	0.995873i	$-0.528929\pi$
$607$	−4.47214	−0.181518	−0.0907592	+	0.995873i	$0.528929\pi$
$608$	1.23607	0.0501292
$609$	−8.47214	−0.343308
$610$	0	0
$611$	−14.6312	−0.591915
$612$	−6.09017	−0.246181
$613$	6.00000	0.242338	0.121169	−	0.992632i	$-0.461336\pi$
$613$	6.00000	0.242338	0.121169	+	0.992632i	$0.461336\pi$
$614$	−33.4508	−1.34997
$615$	1.23607	0.0498431
$616$	0	0
$617$	26.3607	1.06124	0.530621	−	0.847610i	$-0.321959\pi$
$617$	26.3607	1.06124	0.530621	+	0.847610i	$0.321959\pi$
$618$	−6.76393	−0.272085
$619$	9.52786	0.382957	0.191479	−	0.981497i	$-0.438672\pi$
$619$	9.52786	0.382957	0.191479	+	0.981497i	$0.438672\pi$
$620$	1.38197	0.0555011
$621$	−6.85410	−0.275046
$622$	9.23607	0.370333
$623$	−55.7771	−2.23466
$624$	−3.38197	−0.135387
$625$	1.00000	0.0400000
$626$	8.47214	0.338615
$627$	0	0
$628$	−9.27051	−0.369934
$629$	38.8673	1.54974
$630$	3.23607	0.128928
$631$	−5.67376	−0.225869	−0.112934	−	0.993602i	$-0.536025\pi$
$631$	−5.67376	−0.225869	−0.112934	+	0.993602i	$0.536025\pi$
$632$	−4.09017	−0.162698
$633$	25.2361	1.00304
$634$	−27.4164	−1.08884
$635$	−14.6525	−0.581466
$636$	−8.47214	−0.335942
$637$	11.7426	0.465261
$638$	0	0
$639$	10.4721	0.414271
$640$	−1.00000	−0.0395285
$641$	12.1803	0.481095	0.240547	−	0.970637i	$-0.422673\pi$
$641$	12.1803	0.481095	0.240547	+	0.970637i	$0.422673\pi$
$642$	−6.29180	−0.248317
$643$	−4.79837	−0.189229	−0.0946147	−	0.995514i	$-0.530162\pi$
$643$	−4.79837	−0.189229	−0.0946147	+	0.995514i	$0.530162\pi$
$644$	−22.1803	−0.874028
$645$	−0.0901699	−0.00355044
$646$	−7.52786	−0.296180
$647$	−12.3820	−0.486785	−0.243393	−	0.969928i	$-0.578260\pi$
$647$	−12.3820	−0.486785	−0.243393	+	0.969928i	$0.578260\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	3.38197	0.132652
$651$	−4.47214	−0.175277
$652$	0.854102	0.0334492
$653$	24.5410	0.960364	0.480182	−	0.877169i	$-0.340571\pi$
$653$	24.5410	0.960364	0.480182	+	0.877169i	$0.340571\pi$
$654$	2.47214	0.0966682
$655$	3.38197	0.132144
$656$	1.23607	0.0482603
$657$	13.4164	0.523424
$658$	14.0000	0.545777
$659$	−15.4164	−0.600538	−0.300269	−	0.953855i	$-0.597076\pi$
$659$	−15.4164	−0.600538	−0.300269	+	0.953855i	$0.597076\pi$
$660$	0	0
$661$	8.36068	0.325193	0.162596	−	0.986693i	$-0.448013\pi$
$661$	8.36068	0.325193	0.162596	+	0.986693i	$0.448013\pi$
$662$	9.23607	0.358970
$663$	20.5967	0.799911
$664$	4.00000	0.155230
$665$	4.00000	0.155113
$666$	−6.38197	−0.247296
$667$	−17.9443	−0.694805
$668$	−13.2705	−0.513451
$669$	−7.23607	−0.279763
$670$	5.09017	0.196650
$671$	0	0
$672$	3.23607	0.124834
$673$	−15.7082	−0.605507	−0.302753	−	0.953069i	$-0.597906\pi$
$673$	−15.7082	−0.605507	−0.302753	+	0.953069i	$0.597906\pi$
$674$	−15.2361	−0.586871
$675$	−1.00000	−0.0384900
$676$	−1.56231	−0.0600887
$677$	27.2361	1.04677	0.523384	−	0.852097i	$-0.324670\pi$
$677$	27.2361	1.04677	0.523384	+	0.852097i	$0.324670\pi$
$678$	19.5623	0.751286
$679$	−60.3607	−2.31643
$680$	6.09017	0.233547
$681$	−20.3607	−0.780223
$682$	0	0
$683$	21.1246	0.808311	0.404155	−	0.914690i	$-0.367565\pi$
$683$	21.1246	0.808311	0.404155	+	0.914690i	$0.367565\pi$
$684$	1.23607	0.0472622
$685$	12.7984	0.489001
$686$	11.4164	0.435880
$687$	−0.763932	−0.0291458
$688$	−0.0901699	−0.00343770
$689$	28.6525	1.09157
$690$	6.85410	0.260931
$691$	−20.6525	−0.785657	−0.392829	−	0.919612i	$-0.628503\pi$
$691$	−20.6525	−0.785657	−0.392829	+	0.919612i	$0.628503\pi$
$692$	−9.52786	−0.362195
$693$	0	0
$694$	35.8885	1.36231
$695$	−8.76393	−0.332435
$696$	2.61803	0.0992363
$697$	−7.52786	−0.285138
$698$	−11.4164	−0.432117
$699$	4.43769	0.167849
$700$	−3.23607	−0.122312
$701$	−3.52786	−0.133246	−0.0666228	−	0.997778i	$-0.521222\pi$
$701$	−3.52786	−0.133246	−0.0666228	+	0.997778i	$0.521222\pi$
$702$	−3.38197	−0.127644
$703$	−7.88854	−0.297522
$704$	0	0
$705$	−4.32624	−0.162936
$706$	23.6180	0.888876
$707$	−50.5410	−1.90079
$708$	−14.0902	−0.529541
$709$	−10.5836	−0.397475	−0.198738	−	0.980053i	$-0.563684\pi$
$709$	−10.5836	−0.397475	−0.198738	+	0.980053i	$0.563684\pi$
$710$	−10.4721	−0.393012
$711$	−4.09017	−0.153393
$712$	17.2361	0.645949
$713$	−9.47214	−0.354734
$714$	−19.7082	−0.737561
$715$	0	0
$716$	18.1459	0.678144
$717$	3.23607	0.120853
$718$	−12.1803	−0.454566
$719$	40.6525	1.51608	0.758041	−	0.652207i	$-0.226157\pi$
$719$	40.6525	1.51608	0.758041	+	0.652207i	$0.226157\pi$
$720$	−1.00000	−0.0372678
$721$	−21.8885	−0.815172
$722$	−17.4721	−0.650246
$723$	23.8885	0.888425
$724$	21.8885	0.813481
$725$	−2.61803	−0.0972313
$726$	0	0
$727$	−50.1803	−1.86109	−0.930543	−	0.366183i	$-0.880664\pi$
$727$	−50.1803	−1.86109	−0.930543	+	0.366183i	$0.880664\pi$
$728$	−10.9443	−0.405622
$729$	1.00000	0.0370370
$730$	−13.4164	−0.496564
$731$	0.549150	0.0203111
$732$	0	0
$733$	51.3262	1.89578	0.947889	−	0.318601i	$-0.103213\pi$
$733$	51.3262	1.89578	0.947889	+	0.318601i	$0.103213\pi$
$734$	−26.7639	−0.987875
$735$	3.47214	0.128072
$736$	6.85410	0.252646
$737$	0	0
$738$	1.23607	0.0455003
$739$	27.0132	0.993695	0.496847	−	0.867838i	$-0.334491\pi$
$739$	27.0132	0.993695	0.496847	+	0.867838i	$0.334491\pi$
$740$	6.38197	0.234606
$741$	−4.18034	−0.153569
$742$	−27.4164	−1.00649
$743$	10.7984	0.396154	0.198077	−	0.980186i	$-0.436530\pi$
$743$	10.7984	0.396154	0.198077	+	0.980186i	$0.436530\pi$
$744$	1.38197	0.0506653
$745$	7.61803	0.279103
$746$	−11.5279	−0.422065
$747$	4.00000	0.146352
$748$	0	0
$749$	−20.3607	−0.743963
$750$	1.00000	0.0365148
$751$	−29.0344	−1.05948	−0.529741	−	0.848160i	$-0.677711\pi$
$751$	−29.0344	−1.05948	−0.529741	+	0.848160i	$0.677711\pi$
$752$	−4.32624	−0.157762
$753$	−8.38197	−0.305456
$754$	−8.85410	−0.322447
$755$	−20.9443	−0.762240
$756$	3.23607	0.117695
$757$	−53.8541	−1.95736	−0.978680	−	0.205389i	$-0.934154\pi$
$757$	−53.8541	−1.95736	−0.978680	+	0.205389i	$0.934154\pi$
$758$	−12.3607	−0.448960
$759$	0	0
$760$	−1.23607	−0.0448369
$761$	−10.0000	−0.362500	−0.181250	−	0.983437i	$-0.558014\pi$
$761$	−10.0000	−0.362500	−0.181250	+	0.983437i	$0.558014\pi$
$762$	−14.6525	−0.530803
$763$	8.00000	0.289619
$764$	9.23607	0.334149
$765$	6.09017	0.220191
$766$	−0.326238	−0.0117875
$767$	47.6525	1.72063
$768$	−1.00000	−0.0360844
$769$	−24.4508	−0.881720	−0.440860	−	0.897576i	$-0.645327\pi$
$769$	−24.4508	−0.881720	−0.440860	+	0.897576i	$0.645327\pi$
$770$	0	0
$771$	−30.3607	−1.09341
$772$	−20.9443	−0.753801
$773$	19.5967	0.704846	0.352423	−	0.935841i	$-0.385358\pi$
$773$	19.5967	0.704846	0.352423	+	0.935841i	$0.385358\pi$
$774$	−0.0901699	−0.00324109
$775$	−1.38197	−0.0496417
$776$	18.6525	0.669585
$777$	−20.6525	−0.740903
$778$	6.85410	0.245731
$779$	1.52786	0.0547414
$780$	3.38197	0.121094
$781$	0	0
$782$	−41.7426	−1.49271
$783$	2.61803	0.0935609
$784$	3.47214	0.124005
$785$	9.27051	0.330879
$786$	3.38197	0.120631
$787$	21.0344	0.749797	0.374898	−	0.927066i	$-0.377678\pi$
$787$	21.0344	0.749797	0.374898	+	0.927066i	$0.377678\pi$
$788$	10.9443	0.389874
$789$	−6.85410	−0.244012
$790$	4.09017	0.145522
$791$	63.3050	2.25086
$792$	0	0
$793$	0	0
$794$	2.20163	0.0781328
$795$	8.47214	0.300476
$796$	25.9787	0.920791
$797$	−21.7082	−0.768944	−0.384472	−	0.923137i	$-0.625616\pi$
$797$	−21.7082	−0.768944	−0.384472	+	0.923137i	$0.625616\pi$
$798$	4.00000	0.141598
$799$	26.3475	0.932108
$800$	1.00000	0.0353553
$801$	17.2361	0.609007
$802$	22.0689	0.779279
$803$	0	0
$804$	5.09017	0.179516
$805$	22.1803	0.781754
$806$	−4.67376	−0.164626
$807$	−3.20163	−0.112703
$808$	15.6180	0.549441
$809$	−2.65248	−0.0932561	−0.0466280	−	0.998912i	$-0.514848\pi$
$809$	−2.65248	−0.0932561	−0.0466280	+	0.998912i	$0.514848\pi$
$810$	−1.00000	−0.0351364
$811$	−4.58359	−0.160952	−0.0804758	−	0.996757i	$-0.525644\pi$
$811$	−4.58359	−0.160952	−0.0804758	+	0.996757i	$0.525644\pi$
$812$	8.47214	0.297314
$813$	6.38197	0.223825
$814$	0	0
$815$	−0.854102	−0.0299179
$816$	6.09017	0.213199
$817$	−0.111456	−0.00389936
$818$	12.9787	0.453790
$819$	−10.9443	−0.382424
$820$	−1.23607	−0.0431654
$821$	−43.3050	−1.51135	−0.755677	−	0.654945i	$-0.772692\pi$
$821$	−43.3050	−1.51135	−0.755677	+	0.654945i	$0.772692\pi$
$822$	12.7984	0.446395
$823$	−12.7639	−0.444923	−0.222461	−	0.974942i	$-0.571409\pi$
$823$	−12.7639	−0.444923	−0.222461	+	0.974942i	$0.571409\pi$
$824$	6.76393	0.235633
$825$	0	0
$826$	−45.5967	−1.58651
$827$	30.2918	1.05335	0.526674	−	0.850067i	$-0.323439\pi$
$827$	30.2918	1.05335	0.526674	+	0.850067i	$0.323439\pi$
$828$	6.85410	0.238197
$829$	35.5967	1.23633	0.618163	−	0.786050i	$-0.287877\pi$
$829$	35.5967	1.23633	0.618163	+	0.786050i	$0.287877\pi$
$830$	−4.00000	−0.138842
$831$	23.5066	0.815434
$832$	3.38197	0.117249
$833$	−21.1459	−0.732662
$834$	−8.76393	−0.303470
$835$	13.2705	0.459245
$836$	0	0
$837$	1.38197	0.0477677
$838$	22.8541	0.789482
$839$	−23.3475	−0.806046	−0.403023	−	0.915190i	$-0.632041\pi$
$839$	−23.3475	−0.806046	−0.403023	+	0.915190i	$0.632041\pi$
$840$	−3.23607	−0.111655
$841$	−22.1459	−0.763652
$842$	−2.47214	−0.0851954
$843$	7.52786	0.259273
$844$	−25.2361	−0.868661
$845$	1.56231	0.0537450
$846$	−4.32624	−0.148739
$847$	0	0
$848$	8.47214	0.290934
$849$	22.3262	0.766235
$850$	−6.09017	−0.208891
$851$	−43.7426	−1.49948
$852$	−10.4721	−0.358769
$853$	−27.5279	−0.942536	−0.471268	−	0.881990i	$-0.656204\pi$
$853$	−27.5279	−0.942536	−0.471268	+	0.881990i	$0.656204\pi$
$854$	0	0
$855$	−1.23607	−0.0422726
$856$	6.29180	0.215049
$857$	24.1591	0.825258	0.412629	−	0.910899i	$-0.364611\pi$
$857$	24.1591	0.825258	0.412629	+	0.910899i	$0.364611\pi$
$858$	0	0
$859$	−19.1246	−0.652523	−0.326262	−	0.945279i	$-0.605789\pi$
$859$	−19.1246	−0.652523	−0.326262	+	0.945279i	$0.605789\pi$
$860$	0.0901699	0.00307477
$861$	4.00000	0.136320
$862$	22.3607	0.761608
$863$	−44.3394	−1.50933	−0.754665	−	0.656110i	$-0.772201\pi$
$863$	−44.3394	−1.50933	−0.754665	+	0.656110i	$0.772201\pi$
$864$	−1.00000	−0.0340207
$865$	9.52786	0.323957
$866$	−22.8328	−0.775891
$867$	−20.0902	−0.682298
$868$	4.47214	0.151794
$869$	0	0
$870$	−2.61803	−0.0887597
$871$	−17.2148	−0.583301
$872$	−2.47214	−0.0837171
$873$	18.6525	0.631291
$874$	8.47214	0.286574
$875$	3.23607	0.109399
$876$	−13.4164	−0.453298
$877$	18.9656	0.640421	0.320211	−	0.947346i	$-0.396246\pi$
$877$	18.9656	0.640421	0.320211	+	0.947346i	$0.396246\pi$
$878$	1.67376	0.0564867
$879$	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	$0.456973\pi$
$882$	3.47214	0.116913
$883$	−4.67376	−0.157285	−0.0786423	−	0.996903i	$-0.525058\pi$
$883$	−4.67376	−0.157285	−0.0786423	+	0.996903i	$0.525058\pi$
$884$	−20.5967	−0.692744
$885$	14.0902	0.473636
$886$	−18.6525	−0.626642
$887$	−42.4508	−1.42536	−0.712680	−	0.701489i	$-0.752519\pi$
$887$	−42.4508	−1.42536	−0.712680	+	0.701489i	$0.752519\pi$
$888$	6.38197	0.214165
$889$	−47.4164	−1.59030
$890$	−17.2361	−0.577754
$891$	0	0
$892$	7.23607	0.242281
$893$	−5.34752	−0.178948
$894$	7.61803	0.254785
$895$	−18.1459	−0.606550
$896$	−3.23607	−0.108109
$897$	−23.1803	−0.773969
$898$	−11.1246	−0.371233
$899$	3.61803	0.120668
$900$	1.00000	0.0333333
$901$	−51.5967	−1.71894
$902$	0	0
$903$	−0.291796	−0.00971037
$904$	−19.5623	−0.650633
$905$	−21.8885	−0.727600
$906$	−20.9443	−0.695827
$907$	−23.5066	−0.780523	−0.390262	−	0.920704i	$-0.627615\pi$
$907$	−23.5066	−0.780523	−0.390262	+	0.920704i	$0.627615\pi$
$908$	20.3607	0.675693
$909$	15.6180	0.518017
$910$	10.9443	0.362799
$911$	3.52786	0.116883	0.0584417	−	0.998291i	$-0.481387\pi$
$911$	3.52786	0.116883	0.0584417	+	0.998291i	$0.481387\pi$
$912$	−1.23607	−0.0409303
$913$	0	0
$914$	4.65248	0.153890
$915$	0	0
$916$	0.763932	0.0252410
$917$	10.9443	0.361412
$918$	6.09017	0.201006
$919$	46.3394	1.52860	0.764298	−	0.644863i	$-0.223086\pi$
$919$	46.3394	1.52860	0.764298	+	0.644863i	$0.223086\pi$
$920$	−6.85410	−0.225973
$921$	33.4508	1.10224
$922$	23.2148	0.764538
$923$	35.4164	1.16575
$924$	0	0
$925$	−6.38197	−0.209838
$926$	11.8885	0.390682
$927$	6.76393	0.222157
$928$	−2.61803	−0.0859412
$929$	−30.4721	−0.999758	−0.499879	−	0.866095i	$-0.666622\pi$
$929$	−30.4721	−0.999758	−0.499879	+	0.866095i	$0.666622\pi$
$930$	−1.38197	−0.0453165
$931$	4.29180	0.140658
$932$	−4.43769	−0.145362
$933$	−9.23607	−0.302375
$934$	28.5410	0.933891
$935$	0	0
$936$	3.38197	0.110543
$937$	−42.6525	−1.39340	−0.696698	−	0.717365i	$-0.745348\pi$
$937$	−42.6525	−1.39340	−0.696698	+	0.717365i	$0.745348\pi$
$938$	16.4721	0.537834
$939$	−8.47214	−0.276478
$940$	4.32624	0.141106
$941$	1.02129	0.0332930	0.0166465	−	0.999861i	$-0.494701\pi$
$941$	1.02129	0.0332930	0.0166465	+	0.999861i	$0.494701\pi$
$942$	9.27051	0.302050
$943$	8.47214	0.275891
$944$	14.0902	0.458596
$945$	−3.23607	−0.105269
$946$	0	0
$947$	−12.0000	−0.389948	−0.194974	−	0.980808i	$-0.562462\pi$
$947$	−12.0000	−0.389948	−0.194974	+	0.980808i	$0.562462\pi$
$948$	4.09017	0.132843
$949$	45.3738	1.47290
$950$	1.23607	0.0401033
$951$	27.4164	0.889038
$952$	19.7082	0.638747
$953$	−59.2148	−1.91815	−0.959077	−	0.283144i	$-0.908623\pi$
$953$	−59.2148	−1.91815	−0.959077	+	0.283144i	$0.908623\pi$
$954$	8.47214	0.274296
$955$	−9.23607	−0.298872
$956$	−3.23607	−0.104662
$957$	0	0
$958$	12.7639	0.412384
$959$	41.4164	1.33741
$960$	1.00000	0.0322749
$961$	−29.0902	−0.938393
$962$	−21.5836	−0.695883
$963$	6.29180	0.202750
$964$	−23.8885	−0.769398
$965$	20.9443	0.674220
$966$	22.1803	0.713641
$967$	53.3050	1.71417	0.857086	−	0.515174i	$-0.172273\pi$
$967$	53.3050	1.71417	0.857086	+	0.515174i	$0.172273\pi$
$968$	0	0
$969$	7.52786	0.241830
$970$	−18.6525	−0.598895
$971$	8.36068	0.268307	0.134153	−	0.990961i	$-0.457168\pi$
$971$	8.36068	0.268307	0.134153	+	0.990961i	$0.457168\pi$
$972$	−1.00000	−0.0320750
$973$	−28.3607	−0.909202
$974$	11.4164	0.365805
$975$	−3.38197	−0.108310
$976$	0	0
$977$	28.8328	0.922443	0.461222	−	0.887285i	$-0.347411\pi$
$977$	28.8328	0.922443	0.461222	+	0.887285i	$0.347411\pi$
$978$	−0.854102	−0.0273112
$979$	0	0
$980$	−3.47214	−0.110913
$981$	−2.47214	−0.0789292
$982$	28.0344	0.894615
$983$	−51.1935	−1.63282	−0.816409	−	0.577473i	$-0.804039\pi$
$983$	−51.1935	−1.63282	−0.816409	+	0.577473i	$0.804039\pi$
$984$	−1.23607	−0.0394044
$985$	−10.9443	−0.348713
$986$	15.9443	0.507769
$987$	−14.0000	−0.445625
$988$	4.18034	0.132994
$989$	−0.618034	−0.0196523
$990$	0	0
$991$	54.5197	1.73188	0.865938	−	0.500151i	$-0.166722\pi$
$991$	54.5197	1.73188	0.865938	+	0.500151i	$0.166722\pi$
$992$	−1.38197	−0.0438775
$993$	−9.23607	−0.293098
$994$	−33.8885	−1.07488
$995$	−25.9787	−0.823581
$996$	−4.00000	−0.126745
$997$	−25.0344	−0.792849	−0.396424	−	0.918067i	$-0.629749\pi$
$997$	−25.0344	−0.792849	−0.396424	+	0.918067i	$0.629749\pi$
$998$	−32.4721	−1.02789
$999$	6.38197	0.201916

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bj.1.1		2
11.5	even	5		330.2.m.b.91.1	✓	4
11.9	even	5		330.2.m.b.301.1	yes	4
11.10	odd	2		3630.2.a.bb.1.2		2
33.5	odd	10		990.2.n.e.91.1		4
33.20	odd	10		990.2.n.e.631.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.b.91.1	✓	4	11.5	even	5
330.2.m.b.301.1	yes	4	11.9	even	5
990.2.n.e.91.1		4	33.5	odd	10
990.2.n.e.631.1		4	33.20	odd	10
3630.2.a.bb.1.2		2	11.10	odd	2
3630.2.a.bj.1.1		2	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} -3.23607 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -1.00000 q^{12} +3.38197 q^{13} -3.23607 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.09017 q^{17} +1.00000 q^{18} +1.23607 q^{19} -1.00000 q^{20} +3.23607 q^{21} +6.85410 q^{23} -1.00000 q^{24} +1.00000 q^{25} +3.38197 q^{26} -1.00000 q^{27} -3.23607 q^{28} -2.61803 q^{29} +1.00000 q^{30} -1.38197 q^{31} +1.00000 q^{32} -6.09017 q^{34} +3.23607 q^{35} +1.00000 q^{36} -6.38197 q^{37} +1.23607 q^{38} -3.38197 q^{39} -1.00000 q^{40} +1.23607 q^{41} +3.23607 q^{42} -0.0901699 q^{43} -1.00000 q^{45} +6.85410 q^{46} -4.32624 q^{47} -1.00000 q^{48} +3.47214 q^{49} +1.00000 q^{50} +6.09017 q^{51} +3.38197 q^{52} +8.47214 q^{53} -1.00000 q^{54} -3.23607 q^{56} -1.23607 q^{57} -2.61803 q^{58} +14.0902 q^{59} +1.00000 q^{60} -1.38197 q^{62} -3.23607 q^{63} +1.00000 q^{64} -3.38197 q^{65} -5.09017 q^{67} -6.09017 q^{68} -6.85410 q^{69} +3.23607 q^{70} +10.4721 q^{71} +1.00000 q^{72} +13.4164 q^{73} -6.38197 q^{74} -1.00000 q^{75} +1.23607 q^{76} -3.38197 q^{78} -4.09017 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.23607 q^{82} +4.00000 q^{83} +3.23607 q^{84} +6.09017 q^{85} -0.0901699 q^{86} +2.61803 q^{87} +17.2361 q^{89} -1.00000 q^{90} -10.9443 q^{91} +6.85410 q^{92} +1.38197 q^{93} -4.32624 q^{94} -1.23607 q^{95} -1.00000 q^{96} +18.6525 q^{97} +3.47214 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 - 2 * q^5 - 2 * q^6 - 2 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} - 2 q^{5} - 2 q^{6} - 2 q^{7} + 2 q^{8} + 2 q^{9} - 2 q^{10} - 2 q^{12} + 9 q^{13} - 2 q^{14} + 2 q^{15} + 2 q^{16} - q^{17} + 2 q^{18} - 2 q^{19} - 2 q^{20} + 2 q^{21} + 7 q^{23} - 2 q^{24} + 2 q^{25} + 9 q^{26} - 2 q^{27} - 2 q^{28} - 3 q^{29} + 2 q^{30} - 5 q^{31} + 2 q^{32} - q^{34} + 2 q^{35} + 2 q^{36} - 15 q^{37} - 2 q^{38} - 9 q^{39} - 2 q^{40} - 2 q^{41} + 2 q^{42} + 11 q^{43} - 2 q^{45} + 7 q^{46} + 7 q^{47} - 2 q^{48} - 2 q^{49} + 2 q^{50} + q^{51} + 9 q^{52} + 8 q^{53} - 2 q^{54} - 2 q^{56} + 2 q^{57} - 3 q^{58} + 17 q^{59} + 2 q^{60} - 5 q^{62} - 2 q^{63} + 2 q^{64} - 9 q^{65} + q^{67} - q^{68} - 7 q^{69} + 2 q^{70} + 12 q^{71} + 2 q^{72} - 15 q^{74} - 2 q^{75} - 2 q^{76} - 9 q^{78} + 3 q^{79} - 2 q^{80} + 2 q^{81} - 2 q^{82} + 8 q^{83} + 2 q^{84} + q^{85} + 11 q^{86} + 3 q^{87} + 30 q^{89} - 2 q^{90} - 4 q^{91} + 7 q^{92} + 5 q^{93} + 7 q^{94} + 2 q^{95} - 2 q^{96} + 6 q^{97} - 2 q^{98}+O(q^{100}) \) 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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Database

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