LMFDB - Embedded newform 3630.2.a.bl.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$28.9856959337$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-0.618034$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -4.85410 q^{13} -1.38197 q^{14} -1.00000 q^{15} +1.00000 q^{16} +6.47214 q^{17} +1.00000 q^{18} -4.85410 q^{19} +1.00000 q^{20} +1.38197 q^{21} -8.61803 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.85410 q^{26} -1.00000 q^{27} -1.38197 q^{28} +7.23607 q^{29} -1.00000 q^{30} -7.23607 q^{31} +1.00000 q^{32} +6.47214 q^{34} -1.38197 q^{35} +1.00000 q^{36} -3.14590 q^{37} -4.85410 q^{38} +4.85410 q^{39} +1.00000 q^{40} -1.09017 q^{41} +1.38197 q^{42} +1.23607 q^{43} +1.00000 q^{45} -8.61803 q^{46} +11.7984 q^{47} -1.00000 q^{48} -5.09017 q^{49} +1.00000 q^{50} -6.47214 q^{51} -4.85410 q^{52} -13.0902 q^{53} -1.00000 q^{54} -1.38197 q^{56} +4.85410 q^{57} +7.23607 q^{58} -9.32624 q^{59} -1.00000 q^{60} -3.70820 q^{61} -7.23607 q^{62} -1.38197 q^{63} +1.00000 q^{64} -4.85410 q^{65} -15.7082 q^{67} +6.47214 q^{68} +8.61803 q^{69} -1.38197 q^{70} +8.18034 q^{71} +1.00000 q^{72} +2.00000 q^{73} -3.14590 q^{74} -1.00000 q^{75} -4.85410 q^{76} +4.85410 q^{78} -3.52786 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.09017 q^{82} -6.47214 q^{83} +1.38197 q^{84} +6.47214 q^{85} +1.23607 q^{86} -7.23607 q^{87} +11.5623 q^{89} +1.00000 q^{90} +6.70820 q^{91} -8.61803 q^{92} +7.23607 q^{93} +11.7984 q^{94} -4.85410 q^{95} -1.00000 q^{96} -2.00000 q^{97} -5.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - 3 q^{13} - 5 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + 2 q^{20} + 5 q^{21} - 15 q^{23} - 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - 5 q^{28} + 10 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} + 4 q^{34} - 5 q^{35} + 2 q^{36} - 13 q^{37} - 3 q^{38} + 3 q^{39} + 2 q^{40} + 9 q^{41} + 5 q^{42} - 2 q^{43} + 2 q^{45} - 15 q^{46} - q^{47} - 2 q^{48} + q^{49} + 2 q^{50} - 4 q^{51} - 3 q^{52} - 15 q^{53} - 2 q^{54} - 5 q^{56} + 3 q^{57} + 10 q^{58} - 3 q^{59} - 2 q^{60} + 6 q^{61} - 10 q^{62} - 5 q^{63} + 2 q^{64} - 3 q^{65} - 18 q^{67} + 4 q^{68} + 15 q^{69} - 5 q^{70} - 6 q^{71} + 2 q^{72} + 4 q^{73} - 13 q^{74} - 2 q^{75} - 3 q^{76} + 3 q^{78} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 9 q^{82} - 4 q^{83} + 5 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} + 3 q^{89} + 2 q^{90} - 15 q^{92} + 10 q^{93} - q^{94} - 3 q^{95} - 2 q^{96} - 4 q^{97} + q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - 3 * q^13 - 5 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 3 * q^19 + 2 * q^20 + 5 * q^21 - 15 * q^23 - 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - 5 * q^28 + 10 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 + 4 * q^34 - 5 * q^35 + 2 * q^36 - 13 * q^37 - 3 * q^38 + 3 * q^39 + 2 * q^40 + 9 * q^41 + 5 * q^42 - 2 * q^43 + 2 * q^45 - 15 * q^46 - q^47 - 2 * q^48 + q^49 + 2 * q^50 - 4 * q^51 - 3 * q^52 - 15 * q^53 - 2 * q^54 - 5 * q^56 + 3 * q^57 + 10 * q^58 - 3 * q^59 - 2 * q^60 + 6 * q^61 - 10 * q^62 - 5 * q^63 + 2 * q^64 - 3 * q^65 - 18 * q^67 + 4 * q^68 + 15 * q^69 - 5 * q^70 - 6 * q^71 + 2 * q^72 + 4 * q^73 - 13 * q^74 - 2 * q^75 - 3 * q^76 + 3 * q^78 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 9 * q^82 - 4 * q^83 + 5 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 + 3 * q^89 + 2 * q^90 - 15 * q^92 + 10 * q^93 - q^94 - 3 * q^95 - 2 * q^96 - 4 * q^97 + q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−1.38197	−0.522334	−0.261167	−	0.965294i	$-0.584107\pi$
$7$	−1.38197	−0.522334	−0.261167	+	0.965294i	$0.584107\pi$
$8$	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
$13$	−4.85410	−1.34629	−0.673143	−	0.739512i	$-0.735056\pi$
$13$	−4.85410	−1.34629	−0.673143	+	0.739512i	$0.735056\pi$
$14$	−1.38197	−0.369346
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	6.47214	1.56972	0.784862	−	0.619671i	$-0.212734\pi$
$17$	6.47214	1.56972	0.784862	+	0.619671i	$0.212734\pi$
$18$	1.00000	0.235702
$19$	−4.85410	−1.11361	−0.556804	−	0.830644i	$-0.687972\pi$
$19$	−4.85410	−1.11361	−0.556804	+	0.830644i	$0.687972\pi$
$20$	1.00000	0.223607
$21$	1.38197	0.301570
$22$	0	0
$23$	−8.61803	−1.79698	−0.898492	−	0.438990i	$-0.855336\pi$
$23$	−8.61803	−1.79698	−0.898492	+	0.438990i	$0.855336\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	−4.85410	−0.951968
$27$	−1.00000	−0.192450
$28$	−1.38197	−0.261167
$29$	7.23607	1.34370	0.671852	−	0.740685i	$-0.265499\pi$
$29$	7.23607	1.34370	0.671852	+	0.740685i	$0.265499\pi$
$30$	−1.00000	−0.182574
$31$	−7.23607	−1.29964	−0.649818	−	0.760090i	$-0.725155\pi$
$31$	−7.23607	−1.29964	−0.649818	+	0.760090i	$0.725155\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	6.47214	1.10996
$35$	−1.38197	−0.233595
$36$	1.00000	0.166667
$37$	−3.14590	−0.517182	−0.258591	−	0.965987i	$-0.583258\pi$
$37$	−3.14590	−0.517182	−0.258591	+	0.965987i	$0.583258\pi$
$38$	−4.85410	−0.787439
$39$	4.85410	0.777278
$40$	1.00000	0.158114
$41$	−1.09017	−0.170256	−0.0851280	−	0.996370i	$-0.527130\pi$
$41$	−1.09017	−0.170256	−0.0851280	+	0.996370i	$0.527130\pi$
$42$	1.38197	0.213242
$43$	1.23607	0.188499	0.0942493	−	0.995549i	$-0.469955\pi$
$43$	1.23607	0.188499	0.0942493	+	0.995549i	$0.469955\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−8.61803	−1.27066
$47$	11.7984	1.72097	0.860485	−	0.509476i	$-0.170161\pi$
$47$	11.7984	1.72097	0.860485	+	0.509476i	$0.170161\pi$
$48$	−1.00000	−0.144338
$49$	−5.09017	−0.727167
$50$	1.00000	0.141421
$51$	−6.47214	−0.906280
$52$	−4.85410	−0.673143
$53$	−13.0902	−1.79807	−0.899037	−	0.437874i	$-0.855732\pi$
$53$	−13.0902	−1.79807	−0.899037	+	0.437874i	$0.855732\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−1.38197	−0.184673
$57$	4.85410	0.642942
$58$	7.23607	0.950142
$59$	−9.32624	−1.21417	−0.607086	−	0.794636i	$-0.707662\pi$
$59$	−9.32624	−1.21417	−0.607086	+	0.794636i	$0.707662\pi$
$60$	−1.00000	−0.129099
$61$	−3.70820	−0.474787	−0.237393	−	0.971414i	$-0.576293\pi$
$61$	−3.70820	−0.474787	−0.237393	+	0.971414i	$0.576293\pi$
$62$	−7.23607	−0.918982
$63$	−1.38197	−0.174111
$64$	1.00000	0.125000
$65$	−4.85410	−0.602077
$66$	0	0
$67$	−15.7082	−1.91906	−0.959531	−	0.281602i	$-0.909134\pi$
$67$	−15.7082	−1.91906	−0.959531	+	0.281602i	$0.909134\pi$
$68$	6.47214	0.784862
$69$	8.61803	1.03749
$70$	−1.38197	−0.165177
$71$	8.18034	0.970828	0.485414	−	0.874284i	$-0.338669\pi$
$71$	8.18034	0.970828	0.485414	+	0.874284i	$0.338669\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−3.14590	−0.365703
$75$	−1.00000	−0.115470
$76$	−4.85410	−0.556804
$77$	0	0
$78$	4.85410	0.549619
$79$	−3.52786	−0.396916	−0.198458	−	0.980109i	$-0.563593\pi$
$79$	−3.52786	−0.396916	−0.198458	+	0.980109i	$0.563593\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−1.09017	−0.120389
$83$	−6.47214	−0.710409	−0.355205	−	0.934789i	$-0.615589\pi$
$83$	−6.47214	−0.710409	−0.355205	+	0.934789i	$0.615589\pi$
$84$	1.38197	0.150785
$85$	6.47214	0.702002
$86$	1.23607	0.133289
$87$	−7.23607	−0.775788
$88$	0	0
$89$	11.5623	1.22560	0.612801	−	0.790237i	$-0.290043\pi$
$89$	11.5623	1.22560	0.612801	+	0.790237i	$0.290043\pi$
$90$	1.00000	0.105409
$91$	6.70820	0.703211
$92$	−8.61803	−0.898492
$93$	7.23607	0.750345
$94$	11.7984	1.21691
$95$	−4.85410	−0.498020
$96$	−1.00000	−0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	−5.09017	−0.514185
$99$	0	0
$100$	1.00000	0.100000
$101$	7.41641	0.737960	0.368980	−	0.929437i	$-0.379707\pi$
$101$	7.41641	0.737960	0.368980	+	0.929437i	$0.379707\pi$
$102$	−6.47214	−0.640837
$103$	−4.85410	−0.478289	−0.239144	−	0.970984i	$-0.576867\pi$
$103$	−4.85410	−0.478289	−0.239144	+	0.970984i	$0.576867\pi$
$104$	−4.85410	−0.475984
$105$	1.38197	0.134866
$106$	−13.0902	−1.27143
$107$	1.52786	0.147704	0.0738521	−	0.997269i	$-0.476471\pi$
$107$	1.52786	0.147704	0.0738521	+	0.997269i	$0.476471\pi$
$108$	−1.00000	−0.0962250
$109$	7.41641	0.710363	0.355182	−	0.934797i	$-0.384419\pi$
$109$	7.41641	0.710363	0.355182	+	0.934797i	$0.384419\pi$
$110$	0	0
$111$	3.14590	0.298595
$112$	−1.38197	−0.130584
$113$	−3.52786	−0.331874	−0.165937	−	0.986136i	$-0.553065\pi$
$113$	−3.52786	−0.331874	−0.165937	+	0.986136i	$0.553065\pi$
$114$	4.85410	0.454628
$115$	−8.61803	−0.803636
$116$	7.23607	0.671852
$117$	−4.85410	−0.448762
$118$	−9.32624	−0.858550
$119$	−8.94427	−0.819920
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	−3.70820	−0.335725
$123$	1.09017	0.0982973
$124$	−7.23607	−0.649818
$125$	1.00000	0.0894427
$126$	−1.38197	−0.123115
$127$	10.5623	0.937253	0.468627	−	0.883396i	$-0.344749\pi$
$127$	10.5623	0.937253	0.468627	+	0.883396i	$0.344749\pi$
$128$	1.00000	0.0883883
$129$	−1.23607	−0.108830
$130$	−4.85410	−0.425733
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	6.70820	0.581675
$134$	−15.7082	−1.35698
$135$	−1.00000	−0.0860663
$136$	6.47214	0.554981
$137$	−19.4164	−1.65886	−0.829428	−	0.558614i	$-0.811333\pi$
$137$	−19.4164	−1.65886	−0.829428	+	0.558614i	$0.811333\pi$
$138$	8.61803	0.733616
$139$	−20.7984	−1.76410	−0.882048	−	0.471160i	$-0.843835\pi$
$139$	−20.7984	−1.76410	−0.882048	+	0.471160i	$0.843835\pi$
$140$	−1.38197	−0.116797
$141$	−11.7984	−0.993602
$142$	8.18034	0.686479
$143$	0	0
$144$	1.00000	0.0833333
$145$	7.23607	0.600923
$146$	2.00000	0.165521
$147$	5.09017	0.419830
$148$	−3.14590	−0.258591
$149$	−2.47214	−0.202525	−0.101263	−	0.994860i	$-0.532288\pi$
$149$	−2.47214	−0.202525	−0.101263	+	0.994860i	$0.532288\pi$
$150$	−1.00000	−0.0816497
$151$	−11.5279	−0.938124	−0.469062	−	0.883165i	$-0.655408\pi$
$151$	−11.5279	−0.938124	−0.469062	+	0.883165i	$0.655408\pi$
$152$	−4.85410	−0.393720
$153$	6.47214	0.523241
$154$	0	0
$155$	−7.23607	−0.581215
$156$	4.85410	0.388639
$157$	−2.14590	−0.171261	−0.0856307	−	0.996327i	$-0.527291\pi$
$157$	−2.14590	−0.171261	−0.0856307	+	0.996327i	$0.527291\pi$
$158$	−3.52786	−0.280662
$159$	13.0902	1.03812
$160$	1.00000	0.0790569
$161$	11.9098	0.938626
$162$	1.00000	0.0785674
$163$	−3.41641	−0.267594	−0.133797	−	0.991009i	$-0.542717\pi$
$163$	−3.41641	−0.267594	−0.133797	+	0.991009i	$0.542717\pi$
$164$	−1.09017	−0.0851280
$165$	0	0
$166$	−6.47214	−0.502335
$167$	−23.0344	−1.78246	−0.891229	−	0.453553i	$-0.850156\pi$
$167$	−23.0344	−1.78246	−0.891229	+	0.453553i	$0.850156\pi$
$168$	1.38197	0.106621
$169$	10.5623	0.812485
$170$	6.47214	0.496390
$171$	−4.85410	−0.371202
$172$	1.23607	0.0942493
$173$	−14.6180	−1.11139	−0.555694	−	0.831387i	$-0.687547\pi$
$173$	−14.6180	−1.11139	−0.555694	+	0.831387i	$0.687547\pi$
$174$	−7.23607	−0.548565
$175$	−1.38197	−0.104467
$176$	0	0
$177$	9.32624	0.701003
$178$	11.5623	0.866631
$179$	11.0902	0.828918	0.414459	−	0.910068i	$-0.363971\pi$
$179$	11.0902	0.828918	0.414459	+	0.910068i	$0.363971\pi$
$180$	1.00000	0.0745356
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	6.70820	0.497245
$183$	3.70820	0.274118
$184$	−8.61803	−0.635330
$185$	−3.14590	−0.231291
$186$	7.23607	0.530574
$187$	0	0
$188$	11.7984	0.860485
$189$	1.38197	0.100523
$190$	−4.85410	−0.352154
$191$	−6.18034	−0.447194	−0.223597	−	0.974682i	$-0.571780\pi$
$191$	−6.18034	−0.447194	−0.223597	+	0.974682i	$0.571780\pi$
$192$	−1.00000	−0.0721688
$193$	−1.70820	−0.122959	−0.0614796	−	0.998108i	$-0.519582\pi$
$193$	−1.70820	−0.122959	−0.0614796	+	0.998108i	$0.519582\pi$
$194$	−2.00000	−0.143592
$195$	4.85410	0.347609
$196$	−5.09017	−0.363584
$197$	14.6180	1.04149	0.520746	−	0.853712i	$-0.325654\pi$
$197$	14.6180	1.04149	0.520746	+	0.853712i	$0.325654\pi$
$198$	0	0
$199$	2.47214	0.175245	0.0876225	−	0.996154i	$-0.472073\pi$
$199$	2.47214	0.175245	0.0876225	+	0.996154i	$0.472073\pi$
$200$	1.00000	0.0707107
$201$	15.7082	1.10797
$202$	7.41641	0.521817
$203$	−10.0000	−0.701862
$204$	−6.47214	−0.453140
$205$	−1.09017	−0.0761408
$206$	−4.85410	−0.338201
$207$	−8.61803	−0.598995
$208$	−4.85410	−0.336571
$209$	0	0
$210$	1.38197	0.0953647
$211$	14.4721	0.996303	0.498151	−	0.867090i	$-0.334012\pi$
$211$	14.4721	0.996303	0.498151	+	0.867090i	$0.334012\pi$
$212$	−13.0902	−0.899037
$213$	−8.18034	−0.560508
$214$	1.52786	0.104443
$215$	1.23607	0.0842991
$216$	−1.00000	−0.0680414
$217$	10.0000	0.678844
$218$	7.41641	0.502303
$219$	−2.00000	−0.135147
$220$	0	0
$221$	−31.4164	−2.11330
$222$	3.14590	0.211139
$223$	−8.43769	−0.565030	−0.282515	−	0.959263i	$-0.591169\pi$
$223$	−8.43769	−0.565030	−0.282515	+	0.959263i	$0.591169\pi$
$224$	−1.38197	−0.0923365
$225$	1.00000	0.0666667
$226$	−3.52786	−0.234670
$227$	15.7082	1.04259	0.521295	−	0.853377i	$-0.325449\pi$
$227$	15.7082	1.04259	0.521295	+	0.853377i	$0.325449\pi$
$228$	4.85410	0.321471
$229$	5.05573	0.334092	0.167046	−	0.985949i	$-0.446577\pi$
$229$	5.05573	0.334092	0.167046	+	0.985949i	$0.446577\pi$
$230$	−8.61803	−0.568256
$231$	0	0
$232$	7.23607	0.475071
$233$	−3.23607	−0.212002	−0.106001	−	0.994366i	$-0.533805\pi$
$233$	−3.23607	−0.212002	−0.106001	+	0.994366i	$0.533805\pi$
$234$	−4.85410	−0.317323
$235$	11.7984	0.769641
$236$	−9.32624	−0.607086
$237$	3.52786	0.229159
$238$	−8.94427	−0.579771
$239$	12.1803	0.787881	0.393940	−	0.919136i	$-0.371112\pi$
$239$	12.1803	0.787881	0.393940	+	0.919136i	$0.371112\pi$
$240$	−1.00000	−0.0645497
$241$	5.56231	0.358300	0.179150	−	0.983822i	$-0.442665\pi$
$241$	5.56231	0.358300	0.179150	+	0.983822i	$0.442665\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	−3.70820	−0.237393
$245$	−5.09017	−0.325199
$246$	1.09017	0.0695067
$247$	23.5623	1.49923
$248$	−7.23607	−0.459491
$249$	6.47214	0.410155
$250$	1.00000	0.0632456
$251$	−3.67376	−0.231886	−0.115943	−	0.993256i	$-0.536989\pi$
$251$	−3.67376	−0.231886	−0.115943	+	0.993256i	$0.536989\pi$
$252$	−1.38197	−0.0870557
$253$	0	0
$254$	10.5623	0.662738
$255$	−6.47214	−0.405301
$256$	1.00000	0.0625000
$257$	−19.5279	−1.21811	−0.609057	−	0.793126i	$-0.708452\pi$
$257$	−19.5279	−1.21811	−0.609057	+	0.793126i	$0.708452\pi$
$258$	−1.23607	−0.0769542
$259$	4.34752	0.270142
$260$	−4.85410	−0.301039
$261$	7.23607	0.447901
$262$	0	0
$263$	0.381966	0.0235530	0.0117765	−	0.999931i	$-0.496251\pi$
$263$	0.381966	0.0235530	0.0117765	+	0.999931i	$0.496251\pi$
$264$	0	0
$265$	−13.0902	−0.804123
$266$	6.70820	0.411306
$267$	−11.5623	−0.707602
$268$	−15.7082	−0.959531
$269$	−21.5967	−1.31678	−0.658388	−	0.752678i	$-0.728762\pi$
$269$	−21.5967	−1.31678	−0.658388	+	0.752678i	$0.728762\pi$
$270$	−1.00000	−0.0608581
$271$	−6.29180	−0.382199	−0.191100	−	0.981571i	$-0.561205\pi$
$271$	−6.29180	−0.382199	−0.191100	+	0.981571i	$0.561205\pi$
$272$	6.47214	0.392431
$273$	−6.70820	−0.405999
$274$	−19.4164	−1.17299
$275$	0	0
$276$	8.61803	0.518745
$277$	−11.7426	−0.705547	−0.352774	−	0.935709i	$-0.614761\pi$
$277$	−11.7426	−0.705547	−0.352774	+	0.935709i	$0.614761\pi$
$278$	−20.7984	−1.24740
$279$	−7.23607	−0.433212
$280$	−1.38197	−0.0825883
$281$	26.9443	1.60736	0.803680	−	0.595061i	$-0.202872\pi$
$281$	26.9443	1.60736	0.803680	+	0.595061i	$0.202872\pi$
$282$	−11.7984	−0.702583
$283$	−17.1246	−1.01795	−0.508976	−	0.860781i	$-0.669976\pi$
$283$	−17.1246	−1.01795	−0.508976	+	0.860781i	$0.669976\pi$
$284$	8.18034	0.485414
$285$	4.85410	0.287532
$286$	0	0
$287$	1.50658	0.0889305
$288$	1.00000	0.0589256
$289$	24.8885	1.46403
$290$	7.23607	0.424917
$291$	2.00000	0.117242
$292$	2.00000	0.117041
$293$	−10.9098	−0.637359	−0.318680	−	0.947863i	$-0.603239\pi$
$293$	−10.9098	−0.637359	−0.318680	+	0.947863i	$0.603239\pi$
$294$	5.09017	0.296865
$295$	−9.32624	−0.542995
$296$	−3.14590	−0.182852
$297$	0	0
$298$	−2.47214	−0.143207
$299$	41.8328	2.41925
$300$	−1.00000	−0.0577350
$301$	−1.70820	−0.0984592
$302$	−11.5279	−0.663354
$303$	−7.41641	−0.426061
$304$	−4.85410	−0.278402
$305$	−3.70820	−0.212331
$306$	6.47214	0.369987
$307$	26.8328	1.53143	0.765715	−	0.643180i	$-0.222385\pi$
$307$	26.8328	1.53143	0.765715	+	0.643180i	$0.222385\pi$
$308$	0	0
$309$	4.85410	0.276140
$310$	−7.23607	−0.410981
$311$	11.8885	0.674137	0.337069	−	0.941480i	$-0.390565\pi$
$311$	11.8885	0.674137	0.337069	+	0.941480i	$0.390565\pi$
$312$	4.85410	0.274809
$313$	−7.70820	−0.435693	−0.217847	−	0.975983i	$-0.569903\pi$
$313$	−7.70820	−0.435693	−0.217847	+	0.975983i	$0.569903\pi$
$314$	−2.14590	−0.121100
$315$	−1.38197	−0.0778650
$316$	−3.52786	−0.198458
$317$	−22.0902	−1.24071	−0.620354	−	0.784322i	$-0.713011\pi$
$317$	−22.0902	−1.24071	−0.620354	+	0.784322i	$0.713011\pi$
$318$	13.0902	0.734060
$319$	0	0
$320$	1.00000	0.0559017
$321$	−1.52786	−0.0852771
$322$	11.9098	0.663709
$323$	−31.4164	−1.74806
$324$	1.00000	0.0555556
$325$	−4.85410	−0.269257
$326$	−3.41641	−0.189217
$327$	−7.41641	−0.410128
$328$	−1.09017	−0.0601946
$329$	−16.3050	−0.898921
$330$	0	0
$331$	16.8541	0.926385	0.463193	−	0.886258i	$-0.346704\pi$
$331$	16.8541	0.926385	0.463193	+	0.886258i	$0.346704\pi$
$332$	−6.47214	−0.355205
$333$	−3.14590	−0.172394
$334$	−23.0344	−1.26039
$335$	−15.7082	−0.858231
$336$	1.38197	0.0753924
$337$	−3.41641	−0.186104	−0.0930518	−	0.995661i	$-0.529662\pi$
$337$	−3.41641	−0.186104	−0.0930518	+	0.995661i	$0.529662\pi$
$338$	10.5623	0.574514
$339$	3.52786	0.191607
$340$	6.47214	0.351001
$341$	0	0
$342$	−4.85410	−0.262480
$343$	16.7082	0.902158
$344$	1.23607	0.0666443
$345$	8.61803	0.463979
$346$	−14.6180	−0.785870
$347$	3.70820	0.199067	0.0995334	−	0.995034i	$-0.468265\pi$
$347$	3.70820	0.199067	0.0995334	+	0.995034i	$0.468265\pi$
$348$	−7.23607	−0.387894
$349$	−13.4164	−0.718164	−0.359082	−	0.933306i	$-0.616910\pi$
$349$	−13.4164	−0.718164	−0.359082	+	0.933306i	$0.616910\pi$
$350$	−1.38197	−0.0738692
$351$	4.85410	0.259093
$352$	0	0
$353$	3.23607	0.172239	0.0861193	−	0.996285i	$-0.472553\pi$
$353$	3.23607	0.172239	0.0861193	+	0.996285i	$0.472553\pi$
$354$	9.32624	0.495684
$355$	8.18034	0.434167
$356$	11.5623	0.612801
$357$	8.94427	0.473381
$358$	11.0902	0.586134
$359$	24.7639	1.30699	0.653495	−	0.756931i	$-0.273302\pi$
$359$	24.7639	1.30699	0.653495	+	0.756931i	$0.273302\pi$
$360$	1.00000	0.0527046
$361$	4.56231	0.240121
$362$	0	0
$363$	0	0
$364$	6.70820	0.351605
$365$	2.00000	0.104685
$366$	3.70820	0.193831
$367$	8.58359	0.448060	0.224030	−	0.974582i	$-0.428079\pi$
$367$	8.58359	0.448060	0.224030	+	0.974582i	$0.428079\pi$
$368$	−8.61803	−0.449246
$369$	−1.09017	−0.0567520
$370$	−3.14590	−0.163547
$371$	18.0902	0.939195
$372$	7.23607	0.375173
$373$	34.5623	1.78957	0.894784	−	0.446499i	$-0.147329\pi$
$373$	34.5623	1.78957	0.894784	+	0.446499i	$0.147329\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	11.7984	0.608455
$377$	−35.1246	−1.80901
$378$	1.38197	0.0710807
$379$	−4.50658	−0.231487	−0.115744	−	0.993279i	$-0.536925\pi$
$379$	−4.50658	−0.231487	−0.115744	+	0.993279i	$0.536925\pi$
$380$	−4.85410	−0.249010
$381$	−10.5623	−0.541123
$382$	−6.18034	−0.316214
$383$	15.7426	0.804412	0.402206	−	0.915549i	$-0.368244\pi$
$383$	15.7426	0.804412	0.402206	+	0.915549i	$0.368244\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	−1.70820	−0.0869453
$387$	1.23607	0.0628329
$388$	−2.00000	−0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	4.85410	0.245797
$391$	−55.7771	−2.82077
$392$	−5.09017	−0.257092
$393$	0	0
$394$	14.6180	0.736446
$395$	−3.52786	−0.177506
$396$	0	0
$397$	−35.7426	−1.79387	−0.896936	−	0.442160i	$-0.854212\pi$
$397$	−35.7426	−1.79387	−0.896936	+	0.442160i	$0.854212\pi$
$398$	2.47214	0.123917
$399$	−6.70820	−0.335830
$400$	1.00000	0.0500000
$401$	10.0902	0.503879	0.251940	−	0.967743i	$-0.418932\pi$
$401$	10.0902	0.503879	0.251940	+	0.967743i	$0.418932\pi$
$402$	15.7082	0.783454
$403$	35.1246	1.74968
$404$	7.41641	0.368980
$405$	1.00000	0.0496904
$406$	−10.0000	−0.496292
$407$	0	0
$408$	−6.47214	−0.320418
$409$	22.5623	1.11563	0.557817	−	0.829964i	$-0.311639\pi$
$409$	22.5623	1.11563	0.557817	+	0.829964i	$0.311639\pi$
$410$	−1.09017	−0.0538397
$411$	19.4164	0.957741
$412$	−4.85410	−0.239144
$413$	12.8885	0.634204
$414$	−8.61803	−0.423553
$415$	−6.47214	−0.317705
$416$	−4.85410	−0.237992
$417$	20.7984	1.01850
$418$	0	0
$419$	−3.79837	−0.185563	−0.0927814	−	0.995687i	$-0.529576\pi$
$419$	−3.79837	−0.185563	−0.0927814	+	0.995687i	$0.529576\pi$
$420$	1.38197	0.0674330
$421$	−39.8885	−1.94405	−0.972024	−	0.234880i	$-0.924530\pi$
$421$	−39.8885	−1.94405	−0.972024	+	0.234880i	$0.924530\pi$
$422$	14.4721	0.704493
$423$	11.7984	0.573657
$424$	−13.0902	−0.635715
$425$	6.47214	0.313945
$426$	−8.18034	−0.396339
$427$	5.12461	0.247997
$428$	1.52786	0.0738521
$429$	0	0
$430$	1.23607	0.0596085
$431$	−34.6525	−1.66915	−0.834576	−	0.550894i	$-0.814287\pi$
$431$	−34.6525	−1.66915	−0.834576	+	0.550894i	$0.814287\pi$
$432$	−1.00000	−0.0481125
$433$	27.1246	1.30353	0.651763	−	0.758423i	$-0.274030\pi$
$433$	27.1246	1.30353	0.651763	+	0.758423i	$0.274030\pi$
$434$	10.0000	0.480015
$435$	−7.23607	−0.346943
$436$	7.41641	0.355182
$437$	41.8328	2.00113
$438$	−2.00000	−0.0955637
$439$	20.2918	0.968475	0.484237	−	0.874937i	$-0.339097\pi$
$439$	20.2918	0.968475	0.484237	+	0.874937i	$0.339097\pi$
$440$	0	0
$441$	−5.09017	−0.242389
$442$	−31.4164	−1.49433
$443$	8.47214	0.402523	0.201262	−	0.979538i	$-0.435496\pi$
$443$	8.47214	0.402523	0.201262	+	0.979538i	$0.435496\pi$
$444$	3.14590	0.149298
$445$	11.5623	0.548106
$446$	−8.43769	−0.399536
$447$	2.47214	0.116928
$448$	−1.38197	−0.0652918
$449$	38.0902	1.79759	0.898793	−	0.438373i	$-0.144445\pi$
$449$	38.0902	1.79759	0.898793	+	0.438373i	$0.144445\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−3.52786	−0.165937
$453$	11.5279	0.541626
$454$	15.7082	0.737223
$455$	6.70820	0.314485
$456$	4.85410	0.227314
$457$	34.8328	1.62941	0.814705	−	0.579875i	$-0.196899\pi$
$457$	34.8328	1.62941	0.814705	+	0.579875i	$0.196899\pi$
$458$	5.05573	0.236239
$459$	−6.47214	−0.302093
$460$	−8.61803	−0.401818
$461$	−15.7082	−0.731604	−0.365802	−	0.930693i	$-0.619205\pi$
$461$	−15.7082	−0.731604	−0.365802	+	0.930693i	$0.619205\pi$
$462$	0	0
$463$	−4.27051	−0.198467	−0.0992337	−	0.995064i	$-0.531639\pi$
$463$	−4.27051	−0.198467	−0.0992337	+	0.995064i	$0.531639\pi$
$464$	7.23607	0.335926
$465$	7.23607	0.335565
$466$	−3.23607	−0.149908
$467$	−9.52786	−0.440897	−0.220448	−	0.975399i	$-0.570752\pi$
$467$	−9.52786	−0.440897	−0.220448	+	0.975399i	$0.570752\pi$
$468$	−4.85410	−0.224381
$469$	21.7082	1.00239
$470$	11.7984	0.544218
$471$	2.14590	0.0988778
$472$	−9.32624	−0.429275
$473$	0	0
$474$	3.52786	0.162040
$475$	−4.85410	−0.222721
$476$	−8.94427	−0.409960
$477$	−13.0902	−0.599358
$478$	12.1803	0.557116
$479$	−2.76393	−0.126287	−0.0631436	−	0.998004i	$-0.520113\pi$
$479$	−2.76393	−0.126287	−0.0631436	+	0.998004i	$0.520113\pi$
$480$	−1.00000	−0.0456435
$481$	15.2705	0.696275
$482$	5.56231	0.253356
$483$	−11.9098	−0.541916
$484$	0	0
$485$	−2.00000	−0.0908153
$486$	−1.00000	−0.0453609
$487$	−23.4164	−1.06110	−0.530549	−	0.847654i	$-0.678014\pi$
$487$	−23.4164	−1.06110	−0.530549	+	0.847654i	$0.678014\pi$
$488$	−3.70820	−0.167863
$489$	3.41641	0.154495
$490$	−5.09017	−0.229950
$491$	−10.6738	−0.481700	−0.240850	−	0.970562i	$-0.577426\pi$
$491$	−10.6738	−0.481700	−0.240850	+	0.970562i	$0.577426\pi$
$492$	1.09017	0.0491487
$493$	46.8328	2.10924
$494$	23.5623	1.06012
$495$	0	0
$496$	−7.23607	−0.324909
$497$	−11.3050	−0.507096
$498$	6.47214	0.290023
$499$	12.4377	0.556788	0.278394	−	0.960467i	$-0.410198\pi$
$499$	12.4377	0.556788	0.278394	+	0.960467i	$0.410198\pi$
$500$	1.00000	0.0447214
$501$	23.0344	1.02910
$502$	−3.67376	−0.163968
$503$	14.4508	0.644332	0.322166	−	0.946683i	$-0.395589\pi$
$503$	14.4508	0.644332	0.322166	+	0.946683i	$0.395589\pi$
$504$	−1.38197	−0.0615577
$505$	7.41641	0.330026
$506$	0	0
$507$	−10.5623	−0.469088
$508$	10.5623	0.468627
$509$	26.3607	1.16842	0.584208	−	0.811604i	$-0.301405\pi$
$509$	26.3607	1.16842	0.584208	+	0.811604i	$0.301405\pi$
$510$	−6.47214	−0.286591
$511$	−2.76393	−0.122269
$512$	1.00000	0.0441942
$513$	4.85410	0.214314
$514$	−19.5279	−0.861337
$515$	−4.85410	−0.213897
$516$	−1.23607	−0.0544149
$517$	0	0
$518$	4.34752	0.191019
$519$	14.6180	0.641660
$520$	−4.85410	−0.212866
$521$	−12.7984	−0.560707	−0.280353	−	0.959897i	$-0.590452\pi$
$521$	−12.7984	−0.560707	−0.280353	+	0.959897i	$0.590452\pi$
$522$	7.23607	0.316714
$523$	−29.5967	−1.29418	−0.647088	−	0.762416i	$-0.724013\pi$
$523$	−29.5967	−1.29418	−0.647088	+	0.762416i	$0.724013\pi$
$524$	0	0
$525$	1.38197	0.0603139
$526$	0.381966	0.0166545
$527$	−46.8328	−2.04007
$528$	0	0
$529$	51.2705	2.22915
$530$	−13.0902	−0.568601
$531$	−9.32624	−0.404724
$532$	6.70820	0.290838
$533$	5.29180	0.229213
$534$	−11.5623	−0.500350
$535$	1.52786	0.0660553
$536$	−15.7082	−0.678491
$537$	−11.0902	−0.478576
$538$	−21.5967	−0.931102
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	−15.4164	−0.662803	−0.331402	−	0.943490i	$-0.607521\pi$
$541$	−15.4164	−0.662803	−0.331402	+	0.943490i	$0.607521\pi$
$542$	−6.29180	−0.270256
$543$	0	0
$544$	6.47214	0.277491
$545$	7.41641	0.317684
$546$	−6.70820	−0.287085
$547$	27.7082	1.18472	0.592359	−	0.805674i	$-0.298197\pi$
$547$	27.7082	1.18472	0.592359	+	0.805674i	$0.298197\pi$
$548$	−19.4164	−0.829428
$549$	−3.70820	−0.158262
$550$	0	0
$551$	−35.1246	−1.49636
$552$	8.61803	0.366808
$553$	4.87539	0.207323
$554$	−11.7426	−0.498897
$555$	3.14590	0.133536
$556$	−20.7984	−0.882048
$557$	41.5066	1.75869	0.879345	−	0.476185i	$-0.157981\pi$
$557$	41.5066	1.75869	0.879345	+	0.476185i	$0.157981\pi$
$558$	−7.23607	−0.306327
$559$	−6.00000	−0.253773
$560$	−1.38197	−0.0583987
$561$	0	0
$562$	26.9443	1.13658
$563$	−17.5279	−0.738711	−0.369356	−	0.929288i	$-0.620422\pi$
$563$	−17.5279	−0.738711	−0.369356	+	0.929288i	$0.620422\pi$
$564$	−11.7984	−0.496801
$565$	−3.52786	−0.148418
$566$	−17.1246	−0.719801
$567$	−1.38197	−0.0580371
$568$	8.18034	0.343239
$569$	−2.32624	−0.0975210	−0.0487605	−	0.998811i	$-0.515527\pi$
$569$	−2.32624	−0.0975210	−0.0487605	+	0.998811i	$0.515527\pi$
$570$	4.85410	0.203316
$571$	18.9787	0.794234	0.397117	−	0.917768i	$-0.370011\pi$
$571$	18.9787	0.794234	0.397117	+	0.917768i	$0.370011\pi$
$572$	0	0
$573$	6.18034	0.258187
$574$	1.50658	0.0628833
$575$	−8.61803	−0.359397
$576$	1.00000	0.0416667
$577$	−17.7082	−0.737202	−0.368601	−	0.929588i	$-0.620163\pi$
$577$	−17.7082	−0.737202	−0.368601	+	0.929588i	$0.620163\pi$
$578$	24.8885	1.03523
$579$	1.70820	0.0709905
$580$	7.23607	0.300461
$581$	8.94427	0.371071
$582$	2.00000	0.0829027
$583$	0	0
$584$	2.00000	0.0827606
$585$	−4.85410	−0.200692
$586$	−10.9098	−0.450681
$587$	−3.05573	−0.126123	−0.0630617	−	0.998010i	$-0.520086\pi$
$587$	−3.05573	−0.126123	−0.0630617	+	0.998010i	$0.520086\pi$
$588$	5.09017	0.209915
$589$	35.1246	1.44728
$590$	−9.32624	−0.383955
$591$	−14.6180	−0.601306
$592$	−3.14590	−0.129296
$593$	−23.8885	−0.980985	−0.490492	−	0.871445i	$-0.663183\pi$
$593$	−23.8885	−0.980985	−0.490492	+	0.871445i	$0.663183\pi$
$594$	0	0
$595$	−8.94427	−0.366679
$596$	−2.47214	−0.101263
$597$	−2.47214	−0.101178
$598$	41.8328	1.71067
$599$	0.180340	0.00736849	0.00368424	−	0.999993i	$-0.498827\pi$
$599$	0.180340	0.00736849	0.00368424	+	0.999993i	$0.498827\pi$
$600$	−1.00000	−0.0408248
$601$	−17.7984	−0.726011	−0.363005	−	0.931787i	$-0.618249\pi$
$601$	−17.7984	−0.726011	−0.363005	+	0.931787i	$0.618249\pi$
$602$	−1.70820	−0.0696212
$603$	−15.7082	−0.639688
$604$	−11.5279	−0.469062
$605$	0	0
$606$	−7.41641	−0.301271
$607$	−23.4164	−0.950443	−0.475221	−	0.879866i	$-0.657632\pi$
$607$	−23.4164	−0.950443	−0.475221	+	0.879866i	$0.657632\pi$
$608$	−4.85410	−0.196860
$609$	10.0000	0.405220
$610$	−3.70820	−0.150141
$611$	−57.2705	−2.31692
$612$	6.47214	0.261621
$613$	14.5836	0.589026	0.294513	−	0.955648i	$-0.404843\pi$
$613$	14.5836	0.589026	0.294513	+	0.955648i	$0.404843\pi$
$614$	26.8328	1.08288
$615$	1.09017	0.0439599
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	4.85410	0.195261
$619$	26.5623	1.06763	0.533815	−	0.845602i	$-0.320758\pi$
$619$	26.5623	1.06763	0.533815	+	0.845602i	$0.320758\pi$
$620$	−7.23607	−0.290607
$621$	8.61803	0.345830
$622$	11.8885	0.476687
$623$	−15.9787	−0.640174
$624$	4.85410	0.194320
$625$	1.00000	0.0400000
$626$	−7.70820	−0.308082
$627$	0	0
$628$	−2.14590	−0.0856307
$629$	−20.3607	−0.811833
$630$	−1.38197	−0.0550588
$631$	13.2361	0.526920	0.263460	−	0.964670i	$-0.415136\pi$
$631$	13.2361	0.526920	0.263460	+	0.964670i	$0.415136\pi$
$632$	−3.52786	−0.140331
$633$	−14.4721	−0.575216
$634$	−22.0902	−0.877313
$635$	10.5623	0.419152
$636$	13.0902	0.519059
$637$	24.7082	0.978975
$638$	0	0
$639$	8.18034	0.323609
$640$	1.00000	0.0395285
$641$	46.6312	1.84182	0.920911	−	0.389774i	$-0.127447\pi$
$641$	46.6312	1.84182	0.920911	+	0.389774i	$0.127447\pi$
$642$	−1.52786	−0.0603000
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	11.9098	0.469313
$645$	−1.23607	−0.0486701
$646$	−31.4164	−1.23606
$647$	−14.1115	−0.554779	−0.277389	−	0.960758i	$-0.589469\pi$
$647$	−14.1115	−0.554779	−0.277389	+	0.960758i	$0.589469\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	−4.85410	−0.190394
$651$	−10.0000	−0.391931
$652$	−3.41641	−0.133797
$653$	−13.6869	−0.535610	−0.267805	−	0.963473i	$-0.586298\pi$
$653$	−13.6869	−0.535610	−0.267805	+	0.963473i	$0.586298\pi$
$654$	−7.41641	−0.290004
$655$	0	0
$656$	−1.09017	−0.0425640
$657$	2.00000	0.0780274
$658$	−16.3050	−0.635633
$659$	−24.3262	−0.947616	−0.473808	−	0.880628i	$-0.657121\pi$
$659$	−24.3262	−0.947616	−0.473808	+	0.880628i	$0.657121\pi$
$660$	0	0
$661$	20.6525	0.803288	0.401644	−	0.915796i	$-0.368439\pi$
$661$	20.6525	0.803288	0.401644	+	0.915796i	$0.368439\pi$
$662$	16.8541	0.655053
$663$	31.4164	1.22011
$664$	−6.47214	−0.251168
$665$	6.70820	0.260133
$666$	−3.14590	−0.121901
$667$	−62.3607	−2.41462
$668$	−23.0344	−0.891229
$669$	8.43769	0.326220
$670$	−15.7082	−0.606861
$671$	0	0
$672$	1.38197	0.0533105
$673$	20.7639	0.800391	0.400195	−	0.916430i	$-0.368942\pi$
$673$	20.7639	0.800391	0.400195	+	0.916430i	$0.368942\pi$
$674$	−3.41641	−0.131595
$675$	−1.00000	−0.0384900
$676$	10.5623	0.406243
$677$	−10.3607	−0.398193	−0.199097	−	0.979980i	$-0.563801\pi$
$677$	−10.3607	−0.398193	−0.199097	+	0.979980i	$0.563801\pi$
$678$	3.52786	0.135487
$679$	2.76393	0.106070
$680$	6.47214	0.248195
$681$	−15.7082	−0.601940
$682$	0	0
$683$	43.0132	1.64585	0.822926	−	0.568148i	$-0.192340\pi$
$683$	43.0132	1.64585	0.822926	+	0.568148i	$0.192340\pi$
$684$	−4.85410	−0.185601
$685$	−19.4164	−0.741863
$686$	16.7082	0.637922
$687$	−5.05573	−0.192888
$688$	1.23607	0.0471246
$689$	63.5410	2.42072
$690$	8.61803	0.328083
$691$	11.2016	0.426130	0.213065	−	0.977038i	$-0.431655\pi$
$691$	11.2016	0.426130	0.213065	+	0.977038i	$0.431655\pi$
$692$	−14.6180	−0.555694
$693$	0	0
$694$	3.70820	0.140761
$695$	−20.7984	−0.788927
$696$	−7.23607	−0.274282
$697$	−7.05573	−0.267255
$698$	−13.4164	−0.507819
$699$	3.23607	0.122399
$700$	−1.38197	−0.0522334
$701$	−10.0689	−0.380296	−0.190148	−	0.981755i	$-0.560897\pi$
$701$	−10.0689	−0.380296	−0.190148	+	0.981755i	$0.560897\pi$
$702$	4.85410	0.183206
$703$	15.2705	0.575938
$704$	0	0
$705$	−11.7984	−0.444352
$706$	3.23607	0.121791
$707$	−10.2492	−0.385462
$708$	9.32624	0.350501
$709$	15.2361	0.572203	0.286101	−	0.958199i	$-0.407641\pi$
$709$	15.2361	0.572203	0.286101	+	0.958199i	$0.407641\pi$
$710$	8.18034	0.307003
$711$	−3.52786	−0.132305
$712$	11.5623	0.433316
$713$	62.3607	2.33543
$714$	8.94427	0.334731
$715$	0	0
$716$	11.0902	0.414459
$717$	−12.1803	−0.454883
$718$	24.7639	0.924182
$719$	32.4721	1.21101	0.605503	−	0.795843i	$-0.292972\pi$
$719$	32.4721	1.21101	0.605503	+	0.795843i	$0.292972\pi$
$720$	1.00000	0.0372678
$721$	6.70820	0.249827
$722$	4.56231	0.169791
$723$	−5.56231	−0.206864
$724$	0	0
$725$	7.23607	0.268741
$726$	0	0
$727$	−10.6869	−0.396356	−0.198178	−	0.980166i	$-0.563502\pi$
$727$	−10.6869	−0.396356	−0.198178	+	0.980166i	$0.563502\pi$
$728$	6.70820	0.248623
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	8.00000	0.295891
$732$	3.70820	0.137059
$733$	−10.5836	−0.390914	−0.195457	−	0.980712i	$-0.562619\pi$
$733$	−10.5836	−0.390914	−0.195457	+	0.980712i	$0.562619\pi$
$734$	8.58359	0.316826
$735$	5.09017	0.187754
$736$	−8.61803	−0.317665
$737$	0	0
$738$	−1.09017	−0.0401297
$739$	−4.14590	−0.152509	−0.0762547	−	0.997088i	$-0.524296\pi$
$739$	−4.14590	−0.152509	−0.0762547	+	0.997088i	$0.524296\pi$
$740$	−3.14590	−0.115646
$741$	−23.5623	−0.865583
$742$	18.0902	0.664111
$743$	−12.6180	−0.462911	−0.231455	−	0.972846i	$-0.574349\pi$
$743$	−12.6180	−0.462911	−0.231455	+	0.972846i	$0.574349\pi$
$744$	7.23607	0.265287
$745$	−2.47214	−0.0905721
$746$	34.5623	1.26542
$747$	−6.47214	−0.236803
$748$	0	0
$749$	−2.11146	−0.0771509
$750$	−1.00000	−0.0365148
$751$	8.58359	0.313220	0.156610	−	0.987661i	$-0.449943\pi$
$751$	8.58359	0.313220	0.156610	+	0.987661i	$0.449943\pi$
$752$	11.7984	0.430242
$753$	3.67376	0.133879
$754$	−35.1246	−1.27916
$755$	−11.5279	−0.419542
$756$	1.38197	0.0502616
$757$	50.1591	1.82306	0.911531	−	0.411232i	$-0.134901\pi$
$757$	50.1591	1.82306	0.911531	+	0.411232i	$0.134901\pi$
$758$	−4.50658	−0.163686
$759$	0	0
$760$	−4.85410	−0.176077
$761$	35.8885	1.30096	0.650479	−	0.759524i	$-0.274568\pi$
$761$	35.8885	1.30096	0.650479	+	0.759524i	$0.274568\pi$
$762$	−10.5623	−0.382632
$763$	−10.2492	−0.371047
$764$	−6.18034	−0.223597
$765$	6.47214	0.234001
$766$	15.7426	0.568805
$767$	45.2705	1.63462
$768$	−1.00000	−0.0360844
$769$	35.9098	1.29494	0.647471	−	0.762090i	$-0.275827\pi$
$769$	35.9098	1.29494	0.647471	+	0.762090i	$0.275827\pi$
$770$	0	0
$771$	19.5279	0.703279
$772$	−1.70820	−0.0614796
$773$	10.9098	0.392399	0.196200	−	0.980564i	$-0.437140\pi$
$773$	10.9098	0.392399	0.196200	+	0.980564i	$0.437140\pi$
$774$	1.23607	0.0444295
$775$	−7.23607	−0.259927
$776$	−2.00000	−0.0717958
$777$	−4.34752	−0.155967
$778$	6.00000	0.215110
$779$	5.29180	0.189598
$780$	4.85410	0.173805
$781$	0	0
$782$	−55.7771	−1.99458
$783$	−7.23607	−0.258596
$784$	−5.09017	−0.181792
$785$	−2.14590	−0.0765904
$786$	0	0
$787$	6.29180	0.224278	0.112139	−	0.993693i	$-0.464230\pi$
$787$	6.29180	0.224278	0.112139	+	0.993693i	$0.464230\pi$
$788$	14.6180	0.520746
$789$	−0.381966	−0.0135984
$790$	−3.52786	−0.125516
$791$	4.87539	0.173349
$792$	0	0
$793$	18.0000	0.639199
$794$	−35.7426	−1.26846
$795$	13.0902	0.464260
$796$	2.47214	0.0876225
$797$	21.9098	0.776086	0.388043	−	0.921641i	$-0.373151\pi$
$797$	21.9098	0.776086	0.388043	+	0.921641i	$0.373151\pi$
$798$	−6.70820	−0.237468
$799$	76.3607	2.70145
$800$	1.00000	0.0353553
$801$	11.5623	0.408534
$802$	10.0902	0.356296
$803$	0	0
$804$	15.7082	0.553986
$805$	11.9098	0.419766
$806$	35.1246	1.23721
$807$	21.5967	0.760242
$808$	7.41641	0.260908
$809$	16.7426	0.588640	0.294320	−	0.955707i	$-0.404907\pi$
$809$	16.7426	0.588640	0.294320	+	0.955707i	$0.404907\pi$
$810$	1.00000	0.0351364
$811$	35.9230	1.26143	0.630713	−	0.776016i	$-0.282762\pi$
$811$	35.9230	1.26143	0.630713	+	0.776016i	$0.282762\pi$
$812$	−10.0000	−0.350931
$813$	6.29180	0.220663
$814$	0	0
$815$	−3.41641	−0.119672
$816$	−6.47214	−0.226570
$817$	−6.00000	−0.209913
$818$	22.5623	0.788873
$819$	6.70820	0.234404
$820$	−1.09017	−0.0380704
$821$	45.0132	1.57097	0.785485	−	0.618881i	$-0.212414\pi$
$821$	45.0132	1.57097	0.785485	+	0.618881i	$0.212414\pi$
$822$	19.4164	0.677225
$823$	−7.14590	−0.249090	−0.124545	−	0.992214i	$-0.539747\pi$
$823$	−7.14590	−0.249090	−0.124545	+	0.992214i	$0.539747\pi$
$824$	−4.85410	−0.169101
$825$	0	0
$826$	12.8885	0.448450
$827$	3.34752	0.116405	0.0582024	−	0.998305i	$-0.481463\pi$
$827$	3.34752	0.116405	0.0582024	+	0.998305i	$0.481463\pi$
$828$	−8.61803	−0.299497
$829$	−30.9443	−1.07474	−0.537369	−	0.843347i	$-0.680582\pi$
$829$	−30.9443	−1.07474	−0.537369	+	0.843347i	$0.680582\pi$
$830$	−6.47214	−0.224651
$831$	11.7426	0.407348
$832$	−4.85410	−0.168286
$833$	−32.9443	−1.14145
$834$	20.7984	0.720189
$835$	−23.0344	−0.797140
$836$	0	0
$837$	7.23607	0.250115
$838$	−3.79837	−0.131213
$839$	−43.4853	−1.50128	−0.750639	−	0.660712i	$-0.770254\pi$
$839$	−43.4853	−1.50128	−0.750639	+	0.660712i	$0.770254\pi$
$840$	1.38197	0.0476824
$841$	23.3607	0.805541
$842$	−39.8885	−1.37465
$843$	−26.9443	−0.928010
$844$	14.4721	0.498151
$845$	10.5623	0.363354
$846$	11.7984	0.405636
$847$	0	0
$848$	−13.0902	−0.449518
$849$	17.1246	0.587715
$850$	6.47214	0.221992
$851$	27.1115	0.929369
$852$	−8.18034	−0.280254
$853$	−31.3820	−1.07450	−0.537249	−	0.843424i	$-0.680536\pi$
$853$	−31.3820	−1.07450	−0.537249	+	0.843424i	$0.680536\pi$
$854$	5.12461	0.175361
$855$	−4.85410	−0.166007
$856$	1.52786	0.0522213
$857$	37.5967	1.28428	0.642140	−	0.766587i	$-0.278047\pi$
$857$	37.5967	1.28428	0.642140	+	0.766587i	$0.278047\pi$
$858$	0	0
$859$	−12.5066	−0.426719	−0.213359	−	0.976974i	$-0.568441\pi$
$859$	−12.5066	−0.426719	−0.213359	+	0.976974i	$0.568441\pi$
$860$	1.23607	0.0421496
$861$	−1.50658	−0.0513440
$862$	−34.6525	−1.18027
$863$	−35.3951	−1.20486	−0.602432	−	0.798170i	$-0.705802\pi$
$863$	−35.3951	−1.20486	−0.602432	+	0.798170i	$0.705802\pi$
$864$	−1.00000	−0.0340207
$865$	−14.6180	−0.497028
$866$	27.1246	0.921732
$867$	−24.8885	−0.845259
$868$	10.0000	0.339422
$869$	0	0
$870$	−7.23607	−0.245326
$871$	76.2492	2.58361
$872$	7.41641	0.251151
$873$	−2.00000	−0.0676897
$874$	41.8328	1.41502
$875$	−1.38197	−0.0467190
$876$	−2.00000	−0.0675737
$877$	11.1459	0.376370	0.188185	−	0.982134i	$-0.439740\pi$
$877$	11.1459	0.376370	0.188185	+	0.982134i	$0.439740\pi$
$878$	20.2918	0.684815
$879$	10.9098	0.367979
$880$	0	0
$881$	8.50658	0.286594	0.143297	−	0.989680i	$-0.454230\pi$
$881$	8.50658	0.286594	0.143297	+	0.989680i	$0.454230\pi$
$882$	−5.09017	−0.171395
$883$	15.4164	0.518803	0.259402	−	0.965770i	$-0.416475\pi$
$883$	15.4164	0.518803	0.259402	+	0.965770i	$0.416475\pi$
$884$	−31.4164	−1.05665
$885$	9.32624	0.313498
$886$	8.47214	0.284627
$887$	−15.3820	−0.516476	−0.258238	−	0.966081i	$-0.583142\pi$
$887$	−15.3820	−0.516476	−0.258238	+	0.966081i	$0.583142\pi$
$888$	3.14590	0.105569
$889$	−14.5967	−0.489559
$890$	11.5623	0.387569
$891$	0	0
$892$	−8.43769	−0.282515
$893$	−57.2705	−1.91648
$894$	2.47214	0.0826806
$895$	11.0902	0.370703
$896$	−1.38197	−0.0461682
$897$	−41.8328	−1.39676
$898$	38.0902	1.27109
$899$	−52.3607	−1.74633
$900$	1.00000	0.0333333
$901$	−84.7214	−2.82248
$902$	0	0
$903$	1.70820	0.0568455
$904$	−3.52786	−0.117335
$905$	0	0
$906$	11.5279	0.382988
$907$	58.2492	1.93413	0.967067	−	0.254522i	$-0.0819183\pi$
$907$	58.2492	1.93413	0.967067	+	0.254522i	$0.0819183\pi$
$908$	15.7082	0.521295
$909$	7.41641	0.245987
$910$	6.70820	0.222375
$911$	−41.0132	−1.35883	−0.679413	−	0.733756i	$-0.737766\pi$
$911$	−41.0132	−1.35883	−0.679413	+	0.733756i	$0.737766\pi$
$912$	4.85410	0.160735
$913$	0	0
$914$	34.8328	1.15217
$915$	3.70820	0.122589
$916$	5.05573	0.167046
$917$	0	0
$918$	−6.47214	−0.213612
$919$	8.65248	0.285419	0.142709	−	0.989765i	$-0.454419\pi$
$919$	8.65248	0.285419	0.142709	+	0.989765i	$0.454419\pi$
$920$	−8.61803	−0.284128
$921$	−26.8328	−0.884171
$922$	−15.7082	−0.517322
$923$	−39.7082	−1.30701
$924$	0	0
$925$	−3.14590	−0.103436
$926$	−4.27051	−0.140338
$927$	−4.85410	−0.159430
$928$	7.23607	0.237536
$929$	−12.4377	−0.408068	−0.204034	−	0.978964i	$-0.565405\pi$
$929$	−12.4377	−0.408068	−0.204034	+	0.978964i	$0.565405\pi$
$930$	7.23607	0.237280
$931$	24.7082	0.809779
$932$	−3.23607	−0.106001
$933$	−11.8885	−0.389213
$934$	−9.52786	−0.311761
$935$	0	0
$936$	−4.85410	−0.158661
$937$	−14.8328	−0.484567	−0.242283	−	0.970206i	$-0.577896\pi$
$937$	−14.8328	−0.484567	−0.242283	+	0.970206i	$0.577896\pi$
$938$	21.7082	0.708798
$939$	7.70820	0.251548
$940$	11.7984	0.384821
$941$	−35.7771	−1.16630	−0.583150	−	0.812365i	$-0.698180\pi$
$941$	−35.7771	−1.16630	−0.583150	+	0.812365i	$0.698180\pi$
$942$	2.14590	0.0699171
$943$	9.39512	0.305947
$944$	−9.32624	−0.303543
$945$	1.38197	0.0449554
$946$	0	0
$947$	−26.9443	−0.875571	−0.437786	−	0.899079i	$-0.644237\pi$
$947$	−26.9443	−0.875571	−0.437786	+	0.899079i	$0.644237\pi$
$948$	3.52786	0.114580
$949$	−9.70820	−0.315142
$950$	−4.85410	−0.157488
$951$	22.0902	0.716323
$952$	−8.94427	−0.289886
$953$	37.0132	1.19897	0.599487	−	0.800385i	$-0.295371\pi$
$953$	37.0132	1.19897	0.599487	+	0.800385i	$0.295371\pi$
$954$	−13.0902	−0.423810
$955$	−6.18034	−0.199991
$956$	12.1803	0.393940
$957$	0	0
$958$	−2.76393	−0.0892986
$959$	26.8328	0.866477
$960$	−1.00000	−0.0322749
$961$	21.3607	0.689054
$962$	15.2705	0.492341
$963$	1.52786	0.0492347
$964$	5.56231	0.179150
$965$	−1.70820	−0.0549890
$966$	−11.9098	−0.383193
$967$	−57.9787	−1.86447	−0.932235	−	0.361854i	$-0.882144\pi$
$967$	−57.9787	−1.86447	−0.932235	+	0.361854i	$0.882144\pi$
$968$	0	0
$969$	31.4164	1.00924
$970$	−2.00000	−0.0642161
$971$	4.03444	0.129471	0.0647357	−	0.997902i	$-0.479380\pi$
$971$	4.03444	0.129471	0.0647357	+	0.997902i	$0.479380\pi$
$972$	−1.00000	−0.0320750
$973$	28.7426	0.921447
$974$	−23.4164	−0.750310
$975$	4.85410	0.155456
$976$	−3.70820	−0.118697
$977$	1.05573	0.0337757	0.0168879	−	0.999857i	$-0.494624\pi$
$977$	1.05573	0.0337757	0.0168879	+	0.999857i	$0.494624\pi$
$978$	3.41641	0.109245
$979$	0	0
$980$	−5.09017	−0.162600
$981$	7.41641	0.236788
$982$	−10.6738	−0.340613
$983$	21.2705	0.678424	0.339212	−	0.940710i	$-0.389840\pi$
$983$	21.2705	0.678424	0.339212	+	0.940710i	$0.389840\pi$
$984$	1.09017	0.0347533
$985$	14.6180	0.465769
$986$	46.8328	1.49146
$987$	16.3050	0.518992
$988$	23.5623	0.749617
$989$	−10.6525	−0.338729
$990$	0	0
$991$	−12.0000	−0.381193	−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000	−0.381193	−0.190596	+	0.981669i	$0.561042\pi$
$992$	−7.23607	−0.229745
$993$	−16.8541	−0.534849
$994$	−11.3050	−0.358571
$995$	2.47214	0.0783720
$996$	6.47214	0.205077
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	12.4377	0.393708
$999$	3.14590	0.0995318

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.a.91.1	✓	4	11.5	even	5
330.2.m.a.301.1	yes	4	11.9	even	5
990.2.n.h.91.1		4	33.5	odd	10
990.2.n.h.631.1		4	33.20	odd	10
3630.2.a.bf.1.1		2	11.10	odd	2
3630.2.a.bl.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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.38197 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} -4.85410 q^{13} -1.38197 q^{14} -1.00000 q^{15} +1.00000 q^{16} +6.47214 q^{17} +1.00000 q^{18} -4.85410 q^{19} +1.00000 q^{20} +1.38197 q^{21} -8.61803 q^{23} -1.00000 q^{24} +1.00000 q^{25} -4.85410 q^{26} -1.00000 q^{27} -1.38197 q^{28} +7.23607 q^{29} -1.00000 q^{30} -7.23607 q^{31} +1.00000 q^{32} +6.47214 q^{34} -1.38197 q^{35} +1.00000 q^{36} -3.14590 q^{37} -4.85410 q^{38} +4.85410 q^{39} +1.00000 q^{40} -1.09017 q^{41} +1.38197 q^{42} +1.23607 q^{43} +1.00000 q^{45} -8.61803 q^{46} +11.7984 q^{47} -1.00000 q^{48} -5.09017 q^{49} +1.00000 q^{50} -6.47214 q^{51} -4.85410 q^{52} -13.0902 q^{53} -1.00000 q^{54} -1.38197 q^{56} +4.85410 q^{57} +7.23607 q^{58} -9.32624 q^{59} -1.00000 q^{60} -3.70820 q^{61} -7.23607 q^{62} -1.38197 q^{63} +1.00000 q^{64} -4.85410 q^{65} -15.7082 q^{67} +6.47214 q^{68} +8.61803 q^{69} -1.38197 q^{70} +8.18034 q^{71} +1.00000 q^{72} +2.00000 q^{73} -3.14590 q^{74} -1.00000 q^{75} -4.85410 q^{76} +4.85410 q^{78} -3.52786 q^{79} +1.00000 q^{80} +1.00000 q^{81} -1.09017 q^{82} -6.47214 q^{83} +1.38197 q^{84} +6.47214 q^{85} +1.23607 q^{86} -7.23607 q^{87} +11.5623 q^{89} +1.00000 q^{90} +6.70820 q^{91} -8.61803 q^{92} +7.23607 q^{93} +11.7984 q^{94} -4.85410 q^{95} -1.00000 q^{96} -2.00000 q^{97} -5.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - 3 q^{13} - 5 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + 2 q^{20} + 5 q^{21} - 15 q^{23} - 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - 5 q^{28} + 10 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} + 4 q^{34} - 5 q^{35} + 2 q^{36} - 13 q^{37} - 3 q^{38} + 3 q^{39} + 2 q^{40} + 9 q^{41} + 5 q^{42} - 2 q^{43} + 2 q^{45} - 15 q^{46} - q^{47} - 2 q^{48} + q^{49} + 2 q^{50} - 4 q^{51} - 3 q^{52} - 15 q^{53} - 2 q^{54} - 5 q^{56} + 3 q^{57} + 10 q^{58} - 3 q^{59} - 2 q^{60} + 6 q^{61} - 10 q^{62} - 5 q^{63} + 2 q^{64} - 3 q^{65} - 18 q^{67} + 4 q^{68} + 15 q^{69} - 5 q^{70} - 6 q^{71} + 2 q^{72} + 4 q^{73} - 13 q^{74} - 2 q^{75} - 3 q^{76} + 3 q^{78} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 9 q^{82} - 4 q^{83} + 5 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} + 3 q^{89} + 2 q^{90} - 15 q^{92} + 10 q^{93} - q^{94} - 3 q^{95} - 2 q^{96} - 4 q^{97} + q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - 3 * q^13 - 5 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 3 * q^19 + 2 * q^20 + 5 * q^21 - 15 * q^23 - 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - 5 * q^28 + 10 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 + 4 * q^34 - 5 * q^35 + 2 * q^36 - 13 * q^37 - 3 * q^38 + 3 * q^39 + 2 * q^40 + 9 * q^41 + 5 * q^42 - 2 * q^43 + 2 * q^45 - 15 * q^46 - q^47 - 2 * q^48 + q^49 + 2 * q^50 - 4 * q^51 - 3 * q^52 - 15 * q^53 - 2 * q^54 - 5 * q^56 + 3 * q^57 + 10 * q^58 - 3 * q^59 - 2 * q^60 + 6 * q^61 - 10 * q^62 - 5 * q^63 + 2 * q^64 - 3 * q^65 - 18 * q^67 + 4 * q^68 + 15 * q^69 - 5 * q^70 - 6 * q^71 + 2 * q^72 + 4 * q^73 - 13 * q^74 - 2 * q^75 - 3 * q^76 + 3 * q^78 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 9 * q^82 - 4 * q^83 + 5 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 + 3 * q^89 + 2 * q^90 - 15 * q^92 + 10 * q^93 - q^94 - 3 * q^95 - 2 * q^96 - 4 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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