LMFDB - Embedded newform 4730.2.a.o.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4730,2,Mod(1,4730)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4730, 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("4730.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4730 = 2 \cdot 5 \cdot 11 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4730.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:	$37.7692401561$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.30278$ of defining polynomial
Character	$\chi$	$=$	4730.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} +1.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} +1.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.30278 q^{12} +2.00000 q^{13} -1.30278 q^{14} +1.30278 q^{15} +1.00000 q^{16} -2.30278 q^{17} +1.30278 q^{18} -1.69722 q^{19} -1.00000 q^{20} -1.69722 q^{21} -1.00000 q^{22} +1.30278 q^{24} +1.00000 q^{25} -2.00000 q^{26} +5.60555 q^{27} +1.30278 q^{28} +6.00000 q^{29} -1.30278 q^{30} -4.00000 q^{31} -1.00000 q^{32} -1.30278 q^{33} +2.30278 q^{34} -1.30278 q^{35} -1.30278 q^{36} -8.60555 q^{37} +1.69722 q^{38} -2.60555 q^{39} +1.00000 q^{40} -6.00000 q^{41} +1.69722 q^{42} +1.00000 q^{43} +1.00000 q^{44} +1.30278 q^{45} +8.51388 q^{47} -1.30278 q^{48} -5.30278 q^{49} -1.00000 q^{50} +3.00000 q^{51} +2.00000 q^{52} +6.90833 q^{53} -5.60555 q^{54} -1.00000 q^{55} -1.30278 q^{56} +2.21110 q^{57} -6.00000 q^{58} +3.90833 q^{59} +1.30278 q^{60} +8.00000 q^{61} +4.00000 q^{62} -1.69722 q^{63} +1.00000 q^{64} -2.00000 q^{65} +1.30278 q^{66} -4.00000 q^{67} -2.30278 q^{68} +1.30278 q^{70} -2.09167 q^{71} +1.30278 q^{72} -7.21110 q^{73} +8.60555 q^{74} -1.30278 q^{75} -1.69722 q^{76} +1.30278 q^{77} +2.60555 q^{78} +2.69722 q^{79} -1.00000 q^{80} -3.39445 q^{81} +6.00000 q^{82} -0.697224 q^{83} -1.69722 q^{84} +2.30278 q^{85} -1.00000 q^{86} -7.81665 q^{87} -1.00000 q^{88} +6.00000 q^{89} -1.30278 q^{90} +2.60555 q^{91} +5.21110 q^{93} -8.51388 q^{94} +1.69722 q^{95} +1.30278 q^{96} +12.6056 q^{97} +5.30278 q^{98} -1.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8 + q^9	$ 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} + q^{14} - q^{15} + 2 q^{16} - q^{17} - q^{18} - 7 q^{19} - 2 q^{20} - 7 q^{21} - 2 q^{22} - q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{27} - q^{28} + 12 q^{29} + q^{30} - 8 q^{31} - 2 q^{32} + q^{33} + q^{34} + q^{35} + q^{36} - 10 q^{37} + 7 q^{38} + 2 q^{39} + 2 q^{40} - 12 q^{41} + 7 q^{42} + 2 q^{43} + 2 q^{44} - q^{45} - q^{47} + q^{48} - 7 q^{49} - 2 q^{50} + 6 q^{51} + 4 q^{52} + 3 q^{53} - 4 q^{54} - 2 q^{55} + q^{56} - 10 q^{57} - 12 q^{58} - 3 q^{59} - q^{60} + 16 q^{61} + 8 q^{62} - 7 q^{63} + 2 q^{64} - 4 q^{65} - q^{66} - 8 q^{67} - q^{68} - q^{70} - 15 q^{71} - q^{72} + 10 q^{74} + q^{75} - 7 q^{76} - q^{77} - 2 q^{78} + 9 q^{79} - 2 q^{80} - 14 q^{81} + 12 q^{82} - 5 q^{83} - 7 q^{84} + q^{85} - 2 q^{86} + 6 q^{87} - 2 q^{88} + 12 q^{89} + q^{90} - 2 q^{91} - 4 q^{93} + q^{94} + 7 q^{95} - q^{96} + 18 q^{97} + 7 q^{98} + q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8 + q^9 + 2 * q^10 + 2 * q^11 + q^12 + 4 * q^13 + q^14 - q^15 + 2 * q^16 - q^17 - q^18 - 7 * q^19 - 2 * q^20 - 7 * q^21 - 2 * q^22 - q^24 + 2 * q^25 - 4 * q^26 + 4 * q^27 - q^28 + 12 * q^29 + q^30 - 8 * q^31 - 2 * q^32 + q^33 + q^34 + q^35 + q^36 - 10 * q^37 + 7 * q^38 + 2 * q^39 + 2 * q^40 - 12 * q^41 + 7 * q^42 + 2 * q^43 + 2 * q^44 - q^45 - q^47 + q^48 - 7 * q^49 - 2 * q^50 + 6 * q^51 + 4 * q^52 + 3 * q^53 - 4 * q^54 - 2 * q^55 + q^56 - 10 * q^57 - 12 * q^58 - 3 * q^59 - q^60 + 16 * q^61 + 8 * q^62 - 7 * q^63 + 2 * q^64 - 4 * q^65 - q^66 - 8 * q^67 - q^68 - q^70 - 15 * q^71 - q^72 + 10 * q^74 + q^75 - 7 * q^76 - q^77 - 2 * q^78 + 9 * q^79 - 2 * q^80 - 14 * q^81 + 12 * q^82 - 5 * q^83 - 7 * q^84 + q^85 - 2 * q^86 + 6 * q^87 - 2 * q^88 + 12 * q^89 + q^90 - 2 * q^91 - 4 * q^93 + q^94 + 7 * q^95 - q^96 + 18 * q^97 + 7 * q^98 + q^99

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
$3$	−1.30278	−0.752158	−0.376079	−	0.926588i	$-0.622728\pi$
$3$	−1.30278	−0.752158	−0.376079	+	0.926588i	$0.622728\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.30278	0.531856
$7$	1.30278	0.492403	0.246201	−	0.969219i	$-0.420818\pi$
$7$	1.30278	0.492403	0.246201	+	0.969219i	$0.420818\pi$
$8$	−1.00000	−0.353553
$9$	−1.30278	−0.434259
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	−1.30278	−0.376079
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	−1.30278	−0.348181
$15$	1.30278	0.336375
$16$	1.00000	0.250000
$17$	−2.30278	−0.558505	−0.279253	−	0.960218i	$-0.590087\pi$
$17$	−2.30278	−0.558505	−0.279253	+	0.960218i	$0.590087\pi$
$18$	1.30278	0.307067
$19$	−1.69722	−0.389370	−0.194685	−	0.980866i	$-0.562368\pi$
$19$	−1.69722	−0.389370	−0.194685	+	0.980866i	$0.562368\pi$
$20$	−1.00000	−0.223607
$21$	−1.69722	−0.370365
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	1.30278	0.265928
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	5.60555	1.07879
$28$	1.30278	0.246201
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	−1.30278	−0.237853
$31$	−4.00000	−0.718421	−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000	−0.718421	−0.359211	+	0.933257i	$0.616954\pi$
$32$	−1.00000	−0.176777
$33$	−1.30278	−0.226784
$34$	2.30278	0.394923
$35$	−1.30278	−0.220209
$36$	−1.30278	−0.217129
$37$	−8.60555	−1.41474	−0.707372	−	0.706842i	$-0.750119\pi$
$37$	−8.60555	−1.41474	−0.707372	+	0.706842i	$0.750119\pi$
$38$	1.69722	0.275326
$39$	−2.60555	−0.417222
$40$	1.00000	0.158114
$41$	−6.00000	−0.937043	−0.468521	−	0.883452i	$-0.655213\pi$
$41$	−6.00000	−0.937043	−0.468521	+	0.883452i	$0.655213\pi$
$42$	1.69722	0.261887
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	1.30278	0.194206
$46$	0	0
$47$	8.51388	1.24188	0.620938	−	0.783859i	$-0.286752\pi$
$47$	8.51388	1.24188	0.620938	+	0.783859i	$0.286752\pi$
$48$	−1.30278	−0.188039
$49$	−5.30278	−0.757539
$50$	−1.00000	−0.141421
$51$	3.00000	0.420084
$52$	2.00000	0.277350
$53$	6.90833	0.948932	0.474466	−	0.880274i	$-0.342641\pi$
$53$	6.90833	0.948932	0.474466	+	0.880274i	$0.342641\pi$
$54$	−5.60555	−0.762819
$55$	−1.00000	−0.134840
$56$	−1.30278	−0.174091
$57$	2.21110	0.292868
$58$	−6.00000	−0.787839
$59$	3.90833	0.508821	0.254410	−	0.967096i	$-0.418119\pi$
$59$	3.90833	0.508821	0.254410	+	0.967096i	$0.418119\pi$
$60$	1.30278	0.168188
$61$	8.00000	1.02430	0.512148	−	0.858898i	$-0.328850\pi$
$61$	8.00000	1.02430	0.512148	+	0.858898i	$0.328850\pi$
$62$	4.00000	0.508001
$63$	−1.69722	−0.213830
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	1.30278	0.160361
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	−2.30278	−0.279253
$69$	0	0
$70$	1.30278	0.155711
$71$	−2.09167	−0.248236	−0.124118	−	0.992267i	$-0.539610\pi$
$71$	−2.09167	−0.248236	−0.124118	+	0.992267i	$0.539610\pi$
$72$	1.30278	0.153534
$73$	−7.21110	−0.843996	−0.421998	−	0.906597i	$-0.638671\pi$
$73$	−7.21110	−0.843996	−0.421998	+	0.906597i	$0.638671\pi$
$74$	8.60555	1.00038
$75$	−1.30278	−0.150432
$76$	−1.69722	−0.194685
$77$	1.30278	0.148465
$78$	2.60555	0.295021
$79$	2.69722	0.303461	0.151731	−	0.988422i	$-0.451515\pi$
$79$	2.69722	0.303461	0.151731	+	0.988422i	$0.451515\pi$
$80$	−1.00000	−0.111803
$81$	−3.39445	−0.377161
$82$	6.00000	0.662589
$83$	−0.697224	−0.0765303	−0.0382652	−	0.999268i	$-0.512183\pi$
$83$	−0.697224	−0.0765303	−0.0382652	+	0.999268i	$0.512183\pi$
$84$	−1.69722	−0.185182
$85$	2.30278	0.249771
$86$	−1.00000	−0.107833
$87$	−7.81665	−0.838033
$88$	−1.00000	−0.106600
$89$	6.00000	0.635999	0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000	0.635999	0.317999	+	0.948091i	$0.396989\pi$
$90$	−1.30278	−0.137325
$91$	2.60555	0.273136
$92$	0	0
$93$	5.21110	0.540366
$94$	−8.51388	−0.878139
$95$	1.69722	0.174132
$96$	1.30278	0.132964
$97$	12.6056	1.27990	0.639950	−	0.768417i	$-0.278955\pi$
$97$	12.6056	1.27990	0.639950	+	0.768417i	$0.278955\pi$
$98$	5.30278	0.535661
$99$	−1.30278	−0.130934
$100$	1.00000	0.100000
$101$	−7.11943	−0.708410	−0.354205	−	0.935168i	$-0.615248\pi$
$101$	−7.11943	−0.708410	−0.354205	+	0.935168i	$0.615248\pi$
$102$	−3.00000	−0.297044
$103$	−10.9083	−1.07483	−0.537415	−	0.843318i	$-0.680599\pi$
$103$	−10.9083	−1.07483	−0.537415	+	0.843318i	$0.680599\pi$
$104$	−2.00000	−0.196116
$105$	1.69722	0.165632
$106$	−6.90833	−0.670996
$107$	−2.30278	−0.222618	−0.111309	−	0.993786i	$-0.535504\pi$
$107$	−2.30278	−0.222618	−0.111309	+	0.993786i	$0.535504\pi$
$108$	5.60555	0.539394
$109$	−16.9083	−1.61952	−0.809762	−	0.586758i	$-0.800404\pi$
$109$	−16.9083	−1.61952	−0.809762	+	0.586758i	$0.800404\pi$
$110$	1.00000	0.0953463
$111$	11.2111	1.06411
$112$	1.30278	0.123101
$113$	−5.51388	−0.518702	−0.259351	−	0.965783i	$-0.583509\pi$
$113$	−5.51388	−0.518702	−0.259351	+	0.965783i	$0.583509\pi$
$114$	−2.21110	−0.207089
$115$	0	0
$116$	6.00000	0.557086
$117$	−2.60555	−0.240883
$118$	−3.90833	−0.359791
$119$	−3.00000	−0.275010
$120$	−1.30278	−0.118927
$121$	1.00000	0.0909091
$122$	−8.00000	−0.724286
$123$	7.81665	0.704804
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	1.69722	0.151201
$127$	20.4222	1.81218	0.906089	−	0.423087i	$-0.139054\pi$
$127$	20.4222	1.81218	0.906089	+	0.423087i	$0.139054\pi$
$128$	−1.00000	−0.0883883
$129$	−1.30278	−0.114703
$130$	2.00000	0.175412
$131$	−2.78890	−0.243667	−0.121834	−	0.992551i	$-0.538877\pi$
$131$	−2.78890	−0.243667	−0.121834	+	0.992551i	$0.538877\pi$
$132$	−1.30278	−0.113392
$133$	−2.21110	−0.191727
$134$	4.00000	0.345547
$135$	−5.60555	−0.482449
$136$	2.30278	0.197461
$137$	21.6333	1.84826	0.924129	−	0.382080i	$-0.124792\pi$
$137$	21.6333	1.84826	0.924129	+	0.382080i	$0.124792\pi$
$138$	0	0
$139$	−0.788897	−0.0669134	−0.0334567	−	0.999440i	$-0.510652\pi$
$139$	−0.788897	−0.0669134	−0.0334567	+	0.999440i	$0.510652\pi$
$140$	−1.30278	−0.110105
$141$	−11.0917	−0.934087
$142$	2.09167	0.175529
$143$	2.00000	0.167248
$144$	−1.30278	−0.108565
$145$	−6.00000	−0.498273
$146$	7.21110	0.596795
$147$	6.90833	0.569789
$148$	−8.60555	−0.707372
$149$	−7.39445	−0.605777	−0.302888	−	0.953026i	$-0.597951\pi$
$149$	−7.39445	−0.605777	−0.302888	+	0.953026i	$0.597951\pi$
$150$	1.30278	0.106371
$151$	−16.4222	−1.33642	−0.668210	−	0.743973i	$-0.732939\pi$
$151$	−16.4222	−1.33642	−0.668210	+	0.743973i	$0.732939\pi$
$152$	1.69722	0.137663
$153$	3.00000	0.242536
$154$	−1.30278	−0.104981
$155$	4.00000	0.321288
$156$	−2.60555	−0.208611
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−2.69722	−0.214580
$159$	−9.00000	−0.713746
$160$	1.00000	0.0790569
$161$	0	0
$162$	3.39445	0.266693
$163$	13.5139	1.05849	0.529244	−	0.848469i	$-0.322475\pi$
$163$	13.5139	1.05849	0.529244	+	0.848469i	$0.322475\pi$
$164$	−6.00000	−0.468521
$165$	1.30278	0.101421
$166$	0.697224	0.0541151
$167$	12.4222	0.961259	0.480630	−	0.876924i	$-0.340408\pi$
$167$	12.4222	0.961259	0.480630	+	0.876924i	$0.340408\pi$
$168$	1.69722	0.130944
$169$	−9.00000	−0.692308
$170$	−2.30278	−0.176615
$171$	2.21110	0.169087
$172$	1.00000	0.0762493
$173$	12.0000	0.912343	0.456172	−	0.889892i	$-0.349220\pi$
$173$	12.0000	0.912343	0.456172	+	0.889892i	$0.349220\pi$
$174$	7.81665	0.592579
$175$	1.30278	0.0984806
$176$	1.00000	0.0753778
$177$	−5.09167	−0.382714
$178$	−6.00000	−0.449719
$179$	−1.81665	−0.135783	−0.0678915	−	0.997693i	$-0.521627\pi$
$179$	−1.81665	−0.135783	−0.0678915	+	0.997693i	$0.521627\pi$
$180$	1.30278	0.0971032
$181$	2.42221	0.180041	0.0900205	−	0.995940i	$-0.471307\pi$
$181$	2.42221	0.180041	0.0900205	+	0.995940i	$0.471307\pi$
$182$	−2.60555	−0.193136
$183$	−10.4222	−0.770432
$184$	0	0
$185$	8.60555	0.632693
$186$	−5.21110	−0.382097
$187$	−2.30278	−0.168396
$188$	8.51388	0.620938
$189$	7.30278	0.531199
$190$	−1.69722	−0.123130
$191$	8.72498	0.631317	0.315659	−	0.948873i	$-0.397775\pi$
$191$	8.72498	0.631317	0.315659	+	0.948873i	$0.397775\pi$
$192$	−1.30278	−0.0940197
$193$	−19.9083	−1.43303	−0.716516	−	0.697570i	$-0.754264\pi$
$193$	−19.9083	−1.43303	−0.716516	+	0.697570i	$0.754264\pi$
$194$	−12.6056	−0.905026
$195$	2.60555	0.186587
$196$	−5.30278	−0.378770
$197$	8.78890	0.626183	0.313092	−	0.949723i	$-0.398635\pi$
$197$	8.78890	0.626183	0.313092	+	0.949723i	$0.398635\pi$
$198$	1.30278	0.0925842
$199$	−22.9083	−1.62393	−0.811964	−	0.583707i	$-0.801602\pi$
$199$	−22.9083	−1.62393	−0.811964	+	0.583707i	$0.801602\pi$
$200$	−1.00000	−0.0707107
$201$	5.21110	0.367563
$202$	7.11943	0.500921
$203$	7.81665	0.548622
$204$	3.00000	0.210042
$205$	6.00000	0.419058
$206$	10.9083	0.760019
$207$	0	0
$208$	2.00000	0.138675
$209$	−1.69722	−0.117399
$210$	−1.69722	−0.117120
$211$	−16.6972	−1.14948	−0.574742	−	0.818335i	$-0.694898\pi$
$211$	−16.6972	−1.14948	−0.574742	+	0.818335i	$0.694898\pi$
$212$	6.90833	0.474466
$213$	2.72498	0.186713
$214$	2.30278	0.157415
$215$	−1.00000	−0.0681994
$216$	−5.60555	−0.381409
$217$	−5.21110	−0.353753
$218$	16.9083	1.14518
$219$	9.39445	0.634818
$220$	−1.00000	−0.0674200
$221$	−4.60555	−0.309803
$222$	−11.2111	−0.752440
$223$	−28.0000	−1.87502	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000	−1.87502	−0.937509	+	0.347960i	$0.886874\pi$
$224$	−1.30278	−0.0870454
$225$	−1.30278	−0.0868517
$226$	5.51388	0.366778
$227$	4.60555	0.305681	0.152841	−	0.988251i	$-0.451158\pi$
$227$	4.60555	0.305681	0.152841	+	0.988251i	$0.451158\pi$
$228$	2.21110	0.146434
$229$	−21.0278	−1.38955	−0.694777	−	0.719226i	$-0.744497\pi$
$229$	−21.0278	−1.38955	−0.694777	+	0.719226i	$0.744497\pi$
$230$	0	0
$231$	−1.69722	−0.111669
$232$	−6.00000	−0.393919
$233$	25.8167	1.69131	0.845653	−	0.533734i	$-0.179212\pi$
$233$	25.8167	1.69131	0.845653	+	0.533734i	$0.179212\pi$
$234$	2.60555	0.170330
$235$	−8.51388	−0.555384
$236$	3.90833	0.254410
$237$	−3.51388	−0.228251
$238$	3.00000	0.194461
$239$	−19.3305	−1.25039	−0.625194	−	0.780469i	$-0.714980\pi$
$239$	−19.3305	−1.25039	−0.625194	+	0.780469i	$0.714980\pi$
$240$	1.30278	0.0840938
$241$	9.11943	0.587434	0.293717	−	0.955892i	$-0.405108\pi$
$241$	9.11943	0.587434	0.293717	+	0.955892i	$0.405108\pi$
$242$	−1.00000	−0.0642824
$243$	−12.3944	−0.795104
$244$	8.00000	0.512148
$245$	5.30278	0.338782
$246$	−7.81665	−0.498372
$247$	−3.39445	−0.215984
$248$	4.00000	0.254000
$249$	0.908327	0.0575629
$250$	1.00000	0.0632456
$251$	17.5139	1.10547	0.552733	−	0.833358i	$-0.313585\pi$
$251$	17.5139	1.10547	0.552733	+	0.833358i	$0.313585\pi$
$252$	−1.69722	−0.106915
$253$	0	0
$254$	−20.4222	−1.28140
$255$	−3.00000	−0.187867
$256$	1.00000	0.0625000
$257$	−10.1194	−0.631233	−0.315616	−	0.948887i	$-0.602211\pi$
$257$	−10.1194	−0.631233	−0.315616	+	0.948887i	$0.602211\pi$
$258$	1.30278	0.0811073
$259$	−11.2111	−0.696624
$260$	−2.00000	−0.124035
$261$	−7.81665	−0.483839
$262$	2.78890	0.172299
$263$	−31.3305	−1.93192	−0.965962	−	0.258685i	$-0.916711\pi$
$263$	−31.3305	−1.93192	−0.965962	+	0.258685i	$0.916711\pi$
$264$	1.30278	0.0801803
$265$	−6.90833	−0.424375
$266$	2.21110	0.135571
$267$	−7.81665	−0.478371
$268$	−4.00000	−0.244339
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	5.60555	0.341143
$271$	2.42221	0.147138	0.0735692	−	0.997290i	$-0.476561\pi$
$271$	2.42221	0.147138	0.0735692	+	0.997290i	$0.476561\pi$
$272$	−2.30278	−0.139626
$273$	−3.39445	−0.205441
$274$	−21.6333	−1.30692
$275$	1.00000	0.0603023
$276$	0	0
$277$	7.09167	0.426097	0.213049	−	0.977042i	$-0.431661\pi$
$277$	7.09167	0.426097	0.213049	+	0.977042i	$0.431661\pi$
$278$	0.788897	0.0473149
$279$	5.21110	0.311981
$280$	1.30278	0.0778557
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	11.0917	0.660500
$283$	−27.5139	−1.63553	−0.817765	−	0.575552i	$-0.804787\pi$
$283$	−27.5139	−1.63553	−0.817765	+	0.575552i	$0.804787\pi$
$284$	−2.09167	−0.124118
$285$	−2.21110	−0.130974
$286$	−2.00000	−0.118262
$287$	−7.81665	−0.461402
$288$	1.30278	0.0767668
$289$	−11.6972	−0.688072
$290$	6.00000	0.352332
$291$	−16.4222	−0.962687
$292$	−7.21110	−0.421998
$293$	−13.8167	−0.807178	−0.403589	−	0.914940i	$-0.632237\pi$
$293$	−13.8167	−0.807178	−0.403589	+	0.914940i	$0.632237\pi$
$294$	−6.90833	−0.402902
$295$	−3.90833	−0.227552
$296$	8.60555	0.500188
$297$	5.60555	0.325267
$298$	7.39445	0.428349
$299$	0	0
$300$	−1.30278	−0.0752158
$301$	1.30278	0.0750907
$302$	16.4222	0.944992
$303$	9.27502	0.532836
$304$	−1.69722	−0.0973425
$305$	−8.00000	−0.458079
$306$	−3.00000	−0.171499
$307$	20.6972	1.18125	0.590626	−	0.806945i	$-0.298881\pi$
$307$	20.6972	1.18125	0.590626	+	0.806945i	$0.298881\pi$
$308$	1.30278	0.0742325
$309$	14.2111	0.808441
$310$	−4.00000	−0.227185
$311$	−4.60555	−0.261157	−0.130578	−	0.991438i	$-0.541683\pi$
$311$	−4.60555	−0.261157	−0.130578	+	0.991438i	$0.541683\pi$
$312$	2.60555	0.147510
$313$	22.7250	1.28449	0.642246	−	0.766499i	$-0.278003\pi$
$313$	22.7250	1.28449	0.642246	+	0.766499i	$0.278003\pi$
$314$	4.00000	0.225733
$315$	1.69722	0.0956278
$316$	2.69722	0.151731
$317$	−26.5139	−1.48917	−0.744584	−	0.667529i	$-0.767352\pi$
$317$	−26.5139	−1.48917	−0.744584	+	0.667529i	$0.767352\pi$
$318$	9.00000	0.504695
$319$	6.00000	0.335936
$320$	−1.00000	−0.0559017
$321$	3.00000	0.167444
$322$	0	0
$323$	3.90833	0.217465
$324$	−3.39445	−0.188580
$325$	2.00000	0.110940
$326$	−13.5139	−0.748464
$327$	22.0278	1.21814
$328$	6.00000	0.331295
$329$	11.0917	0.611504
$330$	−1.30278	−0.0717154
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	−0.697224	−0.0382652
$333$	11.2111	0.614365
$334$	−12.4222	−0.679713
$335$	4.00000	0.218543
$336$	−1.69722	−0.0925912
$337$	−4.48612	−0.244375	−0.122187	−	0.992507i	$-0.538991\pi$
$337$	−4.48612	−0.244375	−0.122187	+	0.992507i	$0.538991\pi$
$338$	9.00000	0.489535
$339$	7.18335	0.390146
$340$	2.30278	0.124886
$341$	−4.00000	−0.216612
$342$	−2.21110	−0.119563
$343$	−16.0278	−0.865417
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−12.0000	−0.645124
$347$	−13.8167	−0.741717	−0.370858	−	0.928689i	$-0.620936\pi$
$347$	−13.8167	−0.741717	−0.370858	+	0.928689i	$0.620936\pi$
$348$	−7.81665	−0.419017
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	−1.30278	−0.0696363
$351$	11.2111	0.598404
$352$	−1.00000	−0.0533002
$353$	−12.4222	−0.661167	−0.330584	−	0.943777i	$-0.607246\pi$
$353$	−12.4222	−0.661167	−0.330584	+	0.943777i	$0.607246\pi$
$354$	5.09167	0.270619
$355$	2.09167	0.111014
$356$	6.00000	0.317999
$357$	3.90833	0.206851
$358$	1.81665	0.0960131
$359$	−24.8444	−1.31124	−0.655619	−	0.755092i	$-0.727592\pi$
$359$	−24.8444	−1.31124	−0.655619	+	0.755092i	$0.727592\pi$
$360$	−1.30278	−0.0686623
$361$	−16.1194	−0.848391
$362$	−2.42221	−0.127308
$363$	−1.30278	−0.0683780
$364$	2.60555	0.136568
$365$	7.21110	0.377446
$366$	10.4222	0.544777
$367$	2.90833	0.151813	0.0759067	−	0.997115i	$-0.475815\pi$
$367$	2.90833	0.151813	0.0759067	+	0.997115i	$0.475815\pi$
$368$	0	0
$369$	7.81665	0.406919
$370$	−8.60555	−0.447381
$371$	9.00000	0.467257
$372$	5.21110	0.270183
$373$	21.5416	1.11538	0.557692	−	0.830048i	$-0.311687\pi$
$373$	21.5416	1.11538	0.557692	+	0.830048i	$0.311687\pi$
$374$	2.30278	0.119074
$375$	1.30278	0.0672750
$376$	−8.51388	−0.439070
$377$	12.0000	0.618031
$378$	−7.30278	−0.375614
$379$	30.3305	1.55797	0.778987	−	0.627040i	$-0.215734\pi$
$379$	30.3305	1.55797	0.778987	+	0.627040i	$0.215734\pi$
$380$	1.69722	0.0870658
$381$	−26.6056	−1.36304
$382$	−8.72498	−0.446409
$383$	8.78890	0.449092	0.224546	−	0.974464i	$-0.427910\pi$
$383$	8.78890	0.449092	0.224546	+	0.974464i	$0.427910\pi$
$384$	1.30278	0.0664820
$385$	−1.30278	−0.0663956
$386$	19.9083	1.01331
$387$	−1.30278	−0.0662238
$388$	12.6056	0.639950
$389$	20.0917	1.01869	0.509344	−	0.860563i	$-0.329888\pi$
$389$	20.0917	1.01869	0.509344	+	0.860563i	$0.329888\pi$
$390$	−2.60555	−0.131937
$391$	0	0
$392$	5.30278	0.267831
$393$	3.63331	0.183276
$394$	−8.78890	−0.442778
$395$	−2.69722	−0.135712
$396$	−1.30278	−0.0654669
$397$	−35.5416	−1.78378	−0.891892	−	0.452249i	$-0.850622\pi$
$397$	−35.5416	−1.78378	−0.891892	+	0.452249i	$0.850622\pi$
$398$	22.9083	1.14829
$399$	2.88057	0.144209
$400$	1.00000	0.0500000
$401$	−28.5416	−1.42530	−0.712651	−	0.701519i	$-0.752505\pi$
$401$	−28.5416	−1.42530	−0.712651	+	0.701519i	$0.752505\pi$
$402$	−5.21110	−0.259906
$403$	−8.00000	−0.398508
$404$	−7.11943	−0.354205
$405$	3.39445	0.168672
$406$	−7.81665	−0.387934
$407$	−8.60555	−0.426561
$408$	−3.00000	−0.148522
$409$	−32.1194	−1.58820	−0.794102	−	0.607785i	$-0.792058\pi$
$409$	−32.1194	−1.58820	−0.794102	+	0.607785i	$0.792058\pi$
$410$	−6.00000	−0.296319
$411$	−28.1833	−1.39018
$412$	−10.9083	−0.537415
$413$	5.09167	0.250545
$414$	0	0
$415$	0.697224	0.0342254
$416$	−2.00000	−0.0980581
$417$	1.02776	0.0503294
$418$	1.69722	0.0830140
$419$	−33.6333	−1.64309	−0.821547	−	0.570140i	$-0.806889\pi$
$419$	−33.6333	−1.64309	−0.821547	+	0.570140i	$0.806889\pi$
$420$	1.69722	0.0828161
$421$	8.48612	0.413588	0.206794	−	0.978384i	$-0.433697\pi$
$421$	8.48612	0.413588	0.206794	+	0.978384i	$0.433697\pi$
$422$	16.6972	0.812808
$423$	−11.0917	−0.539296
$424$	−6.90833	−0.335498
$425$	−2.30278	−0.111701
$426$	−2.72498	−0.132026
$427$	10.4222	0.504366
$428$	−2.30278	−0.111309
$429$	−2.60555	−0.125797
$430$	1.00000	0.0482243
$431$	14.5139	0.699109	0.349554	−	0.936916i	$-0.386333\pi$
$431$	14.5139	0.699109	0.349554	+	0.936916i	$0.386333\pi$
$432$	5.60555	0.269697
$433$	20.4222	0.981429	0.490714	−	0.871321i	$-0.336736\pi$
$433$	20.4222	0.981429	0.490714	+	0.871321i	$0.336736\pi$
$434$	5.21110	0.250141
$435$	7.81665	0.374780
$436$	−16.9083	−0.809762
$437$	0	0
$438$	−9.39445	−0.448884
$439$	25.5139	1.21771	0.608855	−	0.793281i	$-0.291629\pi$
$439$	25.5139	1.21771	0.608855	+	0.793281i	$0.291629\pi$
$440$	1.00000	0.0476731
$441$	6.90833	0.328968
$442$	4.60555	0.219064
$443$	25.8167	1.22659	0.613293	−	0.789855i	$-0.289844\pi$
$443$	25.8167	1.22659	0.613293	+	0.789855i	$0.289844\pi$
$444$	11.2111	0.532055
$445$	−6.00000	−0.284427
$446$	28.0000	1.32584
$447$	9.63331	0.455640
$448$	1.30278	0.0615504
$449$	−2.78890	−0.131616	−0.0658081	−	0.997832i	$-0.520963\pi$
$449$	−2.78890	−0.131616	−0.0658081	+	0.997832i	$0.520963\pi$
$450$	1.30278	0.0614134
$451$	−6.00000	−0.282529
$452$	−5.51388	−0.259351
$453$	21.3944	1.00520
$454$	−4.60555	−0.216149
$455$	−2.60555	−0.122150
$456$	−2.21110	−0.103544
$457$	−3.57779	−0.167362	−0.0836811	−	0.996493i	$-0.526668\pi$
$457$	−3.57779	−0.167362	−0.0836811	+	0.996493i	$0.526668\pi$
$458$	21.0278	0.982563
$459$	−12.9083	−0.602509
$460$	0	0
$461$	−19.3305	−0.900313	−0.450156	−	0.892950i	$-0.648632\pi$
$461$	−19.3305	−0.900313	−0.450156	+	0.892950i	$0.648632\pi$
$462$	1.69722	0.0789620
$463$	−27.0278	−1.25609	−0.628043	−	0.778178i	$-0.716144\pi$
$463$	−27.0278	−1.25609	−0.628043	+	0.778178i	$0.716144\pi$
$464$	6.00000	0.278543
$465$	−5.21110	−0.241659
$466$	−25.8167	−1.19593
$467$	−8.30278	−0.384207	−0.192103	−	0.981375i	$-0.561531\pi$
$467$	−8.30278	−0.384207	−0.192103	+	0.981375i	$0.561531\pi$
$468$	−2.60555	−0.120442
$469$	−5.21110	−0.240626
$470$	8.51388	0.392716
$471$	5.21110	0.240115
$472$	−3.90833	−0.179895
$473$	1.00000	0.0459800
$474$	3.51388	0.161398
$475$	−1.69722	−0.0778740
$476$	−3.00000	−0.137505
$477$	−9.00000	−0.412082
$478$	19.3305	0.884158
$479$	−36.8444	−1.68346	−0.841732	−	0.539896i	$-0.818464\pi$
$479$	−36.8444	−1.68346	−0.841732	+	0.539896i	$0.818464\pi$
$480$	−1.30278	−0.0594633
$481$	−17.2111	−0.784759
$482$	−9.11943	−0.415379
$483$	0	0
$484$	1.00000	0.0454545
$485$	−12.6056	−0.572389
$486$	12.3944	0.562224
$487$	−20.3305	−0.921264	−0.460632	−	0.887591i	$-0.652377\pi$
$487$	−20.3305	−0.921264	−0.460632	+	0.887591i	$0.652377\pi$
$488$	−8.00000	−0.362143
$489$	−17.6056	−0.796151
$490$	−5.30278	−0.239555
$491$	−41.7250	−1.88302	−0.941511	−	0.336982i	$-0.890594\pi$
$491$	−41.7250	−1.88302	−0.941511	+	0.336982i	$0.890594\pi$
$492$	7.81665	0.352402
$493$	−13.8167	−0.622271
$494$	3.39445	0.152723
$495$	1.30278	0.0585554
$496$	−4.00000	−0.179605
$497$	−2.72498	−0.122232
$498$	−0.908327	−0.0407031
$499$	−16.4222	−0.735159	−0.367579	−	0.929992i	$-0.619813\pi$
$499$	−16.4222	−0.735159	−0.367579	+	0.929992i	$0.619813\pi$
$500$	−1.00000	−0.0447214
$501$	−16.1833	−0.723019
$502$	−17.5139	−0.781683
$503$	−19.3305	−0.861906	−0.430953	−	0.902374i	$-0.641822\pi$
$503$	−19.3305	−0.861906	−0.430953	+	0.902374i	$0.641822\pi$
$504$	1.69722	0.0756004
$505$	7.11943	0.316810
$506$	0	0
$507$	11.7250	0.520725
$508$	20.4222	0.906089
$509$	13.8167	0.612412	0.306206	−	0.951965i	$-0.400940\pi$
$509$	13.8167	0.612412	0.306206	+	0.951965i	$0.400940\pi$
$510$	3.00000	0.132842
$511$	−9.39445	−0.415586
$512$	−1.00000	−0.0441942
$513$	−9.51388	−0.420048
$514$	10.1194	0.446349
$515$	10.9083	0.480678
$516$	−1.30278	−0.0573515
$517$	8.51388	0.374440
$518$	11.2111	0.492588
$519$	−15.6333	−0.686226
$520$	2.00000	0.0877058
$521$	−19.8167	−0.868183	−0.434092	−	0.900869i	$-0.642931\pi$
$521$	−19.8167	−0.868183	−0.434092	+	0.900869i	$0.642931\pi$
$522$	7.81665	0.342126
$523$	2.00000	0.0874539	0.0437269	−	0.999044i	$-0.486077\pi$
$523$	2.00000	0.0874539	0.0437269	+	0.999044i	$0.486077\pi$
$524$	−2.78890	−0.121834
$525$	−1.69722	−0.0740729
$526$	31.3305	1.36608
$527$	9.21110	0.401242
$528$	−1.30278	−0.0566960
$529$	−23.0000	−1.00000
$530$	6.90833	0.300079
$531$	−5.09167	−0.220960
$532$	−2.21110	−0.0958635
$533$	−12.0000	−0.519778
$534$	7.81665	0.338260
$535$	2.30278	0.0995577
$536$	4.00000	0.172774
$537$	2.36669	0.102130
$538$	0	0
$539$	−5.30278	−0.228407
$540$	−5.60555	−0.241225
$541$	−19.4861	−0.837774	−0.418887	−	0.908038i	$-0.637580\pi$
$541$	−19.4861	−0.837774	−0.418887	+	0.908038i	$0.637580\pi$
$542$	−2.42221	−0.104043
$543$	−3.15559	−0.135419
$544$	2.30278	0.0987307
$545$	16.9083	0.724273
$546$	3.39445	0.145269
$547$	−38.7527	−1.65695	−0.828474	−	0.560028i	$-0.810790\pi$
$547$	−38.7527	−1.65695	−0.828474	+	0.560028i	$0.810790\pi$
$548$	21.6333	0.924129
$549$	−10.4222	−0.444809
$550$	−1.00000	−0.0426401
$551$	−10.1833	−0.433825
$552$	0	0
$553$	3.51388	0.149425
$554$	−7.09167	−0.301296
$555$	−11.2111	−0.475885
$556$	−0.788897	−0.0334567
$557$	8.23886	0.349092	0.174546	−	0.984649i	$-0.444154\pi$
$557$	8.23886	0.349092	0.174546	+	0.984649i	$0.444154\pi$
$558$	−5.21110	−0.220604
$559$	2.00000	0.0845910
$560$	−1.30278	−0.0550523
$561$	3.00000	0.126660
$562$	18.0000	0.759284
$563$	−39.6333	−1.67034	−0.835172	−	0.549988i	$-0.814632\pi$
$563$	−39.6333	−1.67034	−0.835172	+	0.549988i	$0.814632\pi$
$564$	−11.0917	−0.467044
$565$	5.51388	0.231971
$566$	27.5139	1.15649
$567$	−4.42221	−0.185715
$568$	2.09167	0.0877647
$569$	−26.2389	−1.09999	−0.549995	−	0.835168i	$-0.685370\pi$
$569$	−26.2389	−1.09999	−0.549995	+	0.835168i	$0.685370\pi$
$570$	2.21110	0.0926129
$571$	2.90833	0.121710	0.0608548	−	0.998147i	$-0.480617\pi$
$571$	2.90833	0.121710	0.0608548	+	0.998147i	$0.480617\pi$
$572$	2.00000	0.0836242
$573$	−11.3667	−0.474850
$574$	7.81665	0.326261
$575$	0	0
$576$	−1.30278	−0.0542823
$577$	22.0917	0.919688	0.459844	−	0.888000i	$-0.347905\pi$
$577$	22.0917	0.919688	0.459844	+	0.888000i	$0.347905\pi$
$578$	11.6972	0.486540
$579$	25.9361	1.07787
$580$	−6.00000	−0.249136
$581$	−0.908327	−0.0376838
$582$	16.4222	0.680722
$583$	6.90833	0.286114
$584$	7.21110	0.298398
$585$	2.60555	0.107726
$586$	13.8167	0.570761
$587$	−3.90833	−0.161314	−0.0806570	−	0.996742i	$-0.525702\pi$
$587$	−3.90833	−0.161314	−0.0806570	+	0.996742i	$0.525702\pi$
$588$	6.90833	0.284895
$589$	6.78890	0.279732
$590$	3.90833	0.160903
$591$	−11.4500	−0.470988
$592$	−8.60555	−0.353686
$593$	12.4222	0.510119	0.255059	−	0.966925i	$-0.417905\pi$
$593$	12.4222	0.510119	0.255059	+	0.966925i	$0.417905\pi$
$594$	−5.60555	−0.229999
$595$	3.00000	0.122988
$596$	−7.39445	−0.302888
$597$	29.8444	1.22145
$598$	0	0
$599$	9.63331	0.393606	0.196803	−	0.980443i	$-0.436944\pi$
$599$	9.63331	0.393606	0.196803	+	0.980443i	$0.436944\pi$
$600$	1.30278	0.0531856
$601$	28.0917	1.14588	0.572942	−	0.819596i	$-0.305802\pi$
$601$	28.0917	1.14588	0.572942	+	0.819596i	$0.305802\pi$
$602$	−1.30278	−0.0530972
$603$	5.21110	0.212213
$604$	−16.4222	−0.668210
$605$	−1.00000	−0.0406558
$606$	−9.27502	−0.376772
$607$	28.3028	1.14877	0.574387	−	0.818584i	$-0.305240\pi$
$607$	28.3028	1.14877	0.574387	+	0.818584i	$0.305240\pi$
$608$	1.69722	0.0688315
$609$	−10.1833	−0.412650
$610$	8.00000	0.323911
$611$	17.0278	0.688869
$612$	3.00000	0.121268
$613$	−25.2111	−1.01827	−0.509133	−	0.860688i	$-0.670034\pi$
$613$	−25.2111	−1.01827	−0.509133	+	0.860688i	$0.670034\pi$
$614$	−20.6972	−0.835272
$615$	−7.81665	−0.315198
$616$	−1.30278	−0.0524903
$617$	21.6333	0.870924	0.435462	−	0.900207i	$-0.356585\pi$
$617$	21.6333	0.870924	0.435462	+	0.900207i	$0.356585\pi$
$618$	−14.2111	−0.571654
$619$	−32.5416	−1.30796	−0.653979	−	0.756512i	$-0.726902\pi$
$619$	−32.5416	−1.30796	−0.653979	+	0.756512i	$0.726902\pi$
$620$	4.00000	0.160644
$621$	0	0
$622$	4.60555	0.184666
$623$	7.81665	0.313168
$624$	−2.60555	−0.104306
$625$	1.00000	0.0400000
$626$	−22.7250	−0.908273
$627$	2.21110	0.0883029
$628$	−4.00000	−0.159617
$629$	19.8167	0.790142
$630$	−1.69722	−0.0676190
$631$	11.4861	0.457255	0.228628	−	0.973514i	$-0.426576\pi$
$631$	11.4861	0.457255	0.228628	+	0.973514i	$0.426576\pi$
$632$	−2.69722	−0.107290
$633$	21.7527	0.864594
$634$	26.5139	1.05300
$635$	−20.4222	−0.810430
$636$	−9.00000	−0.356873
$637$	−10.6056	−0.420207
$638$	−6.00000	−0.237542
$639$	2.72498	0.107799
$640$	1.00000	0.0395285
$641$	48.4222	1.91256	0.956281	−	0.292449i	$-0.0944702\pi$
$641$	48.4222	1.91256	0.956281	+	0.292449i	$0.0944702\pi$
$642$	−3.00000	−0.118401
$643$	−31.6333	−1.24750	−0.623748	−	0.781626i	$-0.714391\pi$
$643$	−31.6333	−1.24750	−0.623748	+	0.781626i	$0.714391\pi$
$644$	0	0
$645$	1.30278	0.0512967
$646$	−3.90833	−0.153771
$647$	40.6056	1.59637	0.798184	−	0.602413i	$-0.205794\pi$
$647$	40.6056	1.59637	0.798184	+	0.602413i	$0.205794\pi$
$648$	3.39445	0.133347
$649$	3.90833	0.153415
$650$	−2.00000	−0.0784465
$651$	6.78890	0.266078
$652$	13.5139	0.529244
$653$	−24.8444	−0.972237	−0.486118	−	0.873893i	$-0.661588\pi$
$653$	−24.8444	−0.972237	−0.486118	+	0.873893i	$0.661588\pi$
$654$	−22.0278	−0.861353
$655$	2.78890	0.108971
$656$	−6.00000	−0.234261
$657$	9.39445	0.366512
$658$	−11.0917	−0.432398
$659$	1.81665	0.0707668	0.0353834	−	0.999374i	$-0.488735\pi$
$659$	1.81665	0.0707668	0.0353834	+	0.999374i	$0.488735\pi$
$660$	1.30278	0.0507105
$661$	−11.8167	−0.459615	−0.229807	−	0.973236i	$-0.573810\pi$
$661$	−11.8167	−0.459615	−0.229807	+	0.973236i	$0.573810\pi$
$662$	10.0000	0.388661
$663$	6.00000	0.233021
$664$	0.697224	0.0270576
$665$	2.21110	0.0857429
$666$	−11.2111	−0.434421
$667$	0	0
$668$	12.4222	0.480630
$669$	36.4777	1.41031
$670$	−4.00000	−0.154533
$671$	8.00000	0.308837
$672$	1.69722	0.0654719
$673$	40.6611	1.56737	0.783684	−	0.621159i	$-0.213338\pi$
$673$	40.6611	1.56737	0.783684	+	0.621159i	$0.213338\pi$
$674$	4.48612	0.172799
$675$	5.60555	0.215758
$676$	−9.00000	−0.346154
$677$	47.3028	1.81799	0.908997	−	0.416803i	$-0.136850\pi$
$677$	47.3028	1.81799	0.908997	+	0.416803i	$0.136850\pi$
$678$	−7.18335	−0.275875
$679$	16.4222	0.630226
$680$	−2.30278	−0.0883074
$681$	−6.00000	−0.229920
$682$	4.00000	0.153168
$683$	−49.8167	−1.90618	−0.953091	−	0.302685i	$-0.902117\pi$
$683$	−49.8167	−1.90618	−0.953091	+	0.302685i	$0.902117\pi$
$684$	2.21110	0.0845436
$685$	−21.6333	−0.826566
$686$	16.0278	0.611943
$687$	27.3944	1.04516
$688$	1.00000	0.0381246
$689$	13.8167	0.526373
$690$	0	0
$691$	19.4500	0.739911	0.369956	−	0.929049i	$-0.379373\pi$
$691$	19.4500	0.739911	0.369956	+	0.929049i	$0.379373\pi$
$692$	12.0000	0.456172
$693$	−1.69722	−0.0644722
$694$	13.8167	0.524473
$695$	0.788897	0.0299246
$696$	7.81665	0.296289
$697$	13.8167	0.523343
$698$	10.0000	0.378506
$699$	−33.6333	−1.27213
$700$	1.30278	0.0492403
$701$	28.5416	1.07800	0.539001	−	0.842305i	$-0.318802\pi$
$701$	28.5416	1.07800	0.539001	+	0.842305i	$0.318802\pi$
$702$	−11.2111	−0.423136
$703$	14.6056	0.550859
$704$	1.00000	0.0376889
$705$	11.0917	0.417737
$706$	12.4222	0.467516
$707$	−9.27502	−0.348823
$708$	−5.09167	−0.191357
$709$	−25.2111	−0.946823	−0.473411	−	0.880841i	$-0.656978\pi$
$709$	−25.2111	−0.946823	−0.473411	+	0.880841i	$0.656978\pi$
$710$	−2.09167	−0.0784991
$711$	−3.51388	−0.131781
$712$	−6.00000	−0.224860
$713$	0	0
$714$	−3.90833	−0.146265
$715$	−2.00000	−0.0747958
$716$	−1.81665	−0.0678915
$717$	25.1833	0.940489
$718$	24.8444	0.927185
$719$	15.2111	0.567278	0.283639	−	0.958931i	$-0.408458\pi$
$719$	15.2111	0.567278	0.283639	+	0.958931i	$0.408458\pi$
$720$	1.30278	0.0485516
$721$	−14.2111	−0.529249
$722$	16.1194	0.599903
$723$	−11.8806	−0.441843
$724$	2.42221	0.0900205
$725$	6.00000	0.222834
$726$	1.30278	0.0483505
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	−2.60555	−0.0965682
$729$	26.3305	0.975205
$730$	−7.21110	−0.266895
$731$	−2.30278	−0.0851712
$732$	−10.4222	−0.385216
$733$	−6.72498	−0.248393	−0.124196	−	0.992258i	$-0.539635\pi$
$733$	−6.72498	−0.248393	−0.124196	+	0.992258i	$0.539635\pi$
$734$	−2.90833	−0.107348
$735$	−6.90833	−0.254817
$736$	0	0
$737$	−4.00000	−0.147342
$738$	−7.81665	−0.287735
$739$	44.1472	1.62398	0.811990	−	0.583671i	$-0.198384\pi$
$739$	44.1472	1.62398	0.811990	+	0.583671i	$0.198384\pi$
$740$	8.60555	0.316346
$741$	4.42221	0.162454
$742$	−9.00000	−0.330400
$743$	−40.7527	−1.49507	−0.747536	−	0.664221i	$-0.768763\pi$
$743$	−40.7527	−1.49507	−0.747536	+	0.664221i	$0.768763\pi$
$744$	−5.21110	−0.191048
$745$	7.39445	0.270912
$746$	−21.5416	−0.788695
$747$	0.908327	0.0332339
$748$	−2.30278	−0.0841978
$749$	−3.00000	−0.109618
$750$	−1.30278	−0.0475706
$751$	−25.9083	−0.945408	−0.472704	−	0.881221i	$-0.656722\pi$
$751$	−25.9083	−0.945408	−0.472704	+	0.881221i	$0.656722\pi$
$752$	8.51388	0.310469
$753$	−22.8167	−0.831485
$754$	−12.0000	−0.437014
$755$	16.4222	0.597665
$756$	7.30278	0.265599
$757$	−3.02776	−0.110046	−0.0550228	−	0.998485i	$-0.517523\pi$
$757$	−3.02776	−0.110046	−0.0550228	+	0.998485i	$0.517523\pi$
$758$	−30.3305	−1.10165
$759$	0	0
$760$	−1.69722	−0.0615648
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	26.6056	0.963817
$763$	−22.0278	−0.797458
$764$	8.72498	0.315659
$765$	−3.00000	−0.108465
$766$	−8.78890	−0.317556
$767$	7.81665	0.282243
$768$	−1.30278	−0.0470099
$769$	34.2389	1.23468	0.617342	−	0.786695i	$-0.288209\pi$
$769$	34.2389	1.23468	0.617342	+	0.786695i	$0.288209\pi$
$770$	1.30278	0.0469488
$771$	13.1833	0.474787
$772$	−19.9083	−0.716516
$773$	−29.4500	−1.05924	−0.529621	−	0.848235i	$-0.677666\pi$
$773$	−29.4500	−1.05924	−0.529621	+	0.848235i	$0.677666\pi$
$774$	1.30278	0.0468273
$775$	−4.00000	−0.143684
$776$	−12.6056	−0.452513
$777$	14.6056	0.523971
$778$	−20.0917	−0.720321
$779$	10.1833	0.364856
$780$	2.60555	0.0932937
$781$	−2.09167	−0.0748459
$782$	0	0
$783$	33.6333	1.20196
$784$	−5.30278	−0.189385
$785$	4.00000	0.142766
$786$	−3.63331	−0.129596
$787$	−40.3583	−1.43862	−0.719309	−	0.694690i	$-0.755541\pi$
$787$	−40.3583	−1.43862	−0.719309	+	0.694690i	$0.755541\pi$
$788$	8.78890	0.313092
$789$	40.8167	1.45311
$790$	2.69722	0.0959629
$791$	−7.18335	−0.255410
$792$	1.30278	0.0462921
$793$	16.0000	0.568177
$794$	35.5416	1.26133
$795$	9.00000	0.319197
$796$	−22.9083	−0.811964
$797$	−8.09167	−0.286622	−0.143311	−	0.989678i	$-0.545775\pi$
$797$	−8.09167	−0.286622	−0.143311	+	0.989678i	$0.545775\pi$
$798$	−2.88057	−0.101971
$799$	−19.6056	−0.693595
$800$	−1.00000	−0.0353553
$801$	−7.81665	−0.276188
$802$	28.5416	1.00784
$803$	−7.21110	−0.254474
$804$	5.21110	0.183781
$805$	0	0
$806$	8.00000	0.281788
$807$	0	0
$808$	7.11943	0.250461
$809$	13.8167	0.485768	0.242884	−	0.970055i	$-0.421907\pi$
$809$	13.8167	0.485768	0.242884	+	0.970055i	$0.421907\pi$
$810$	−3.39445	−0.119269
$811$	0.880571	0.0309210	0.0154605	−	0.999880i	$-0.495079\pi$
$811$	0.880571	0.0309210	0.0154605	+	0.999880i	$0.495079\pi$
$812$	7.81665	0.274311
$813$	−3.15559	−0.110671
$814$	8.60555	0.301624
$815$	−13.5139	−0.473371
$816$	3.00000	0.105021
$817$	−1.69722	−0.0593784
$818$	32.1194	1.12303
$819$	−3.39445	−0.118612
$820$	6.00000	0.209529
$821$	17.7250	0.618606	0.309303	−	0.950964i	$-0.399904\pi$
$821$	17.7250	0.618606	0.309303	+	0.950964i	$0.399904\pi$
$822$	28.1833	0.983007
$823$	−38.0555	−1.32653	−0.663266	−	0.748384i	$-0.730830\pi$
$823$	−38.0555	−1.32653	−0.663266	+	0.748384i	$0.730830\pi$
$824$	10.9083	0.380010
$825$	−1.30278	−0.0453568
$826$	−5.09167	−0.177162
$827$	−36.0000	−1.25184	−0.625921	−	0.779886i	$-0.715277\pi$
$827$	−36.0000	−1.25184	−0.625921	+	0.779886i	$0.715277\pi$
$828$	0	0
$829$	−34.0000	−1.18087	−0.590434	−	0.807086i	$-0.701044\pi$
$829$	−34.0000	−1.18087	−0.590434	+	0.807086i	$0.701044\pi$
$830$	−0.697224	−0.0242010
$831$	−9.23886	−0.320492
$832$	2.00000	0.0693375
$833$	12.2111	0.423090
$834$	−1.02776	−0.0355883
$835$	−12.4222	−0.429888
$836$	−1.69722	−0.0586997
$837$	−22.4222	−0.775025
$838$	33.6333	1.16184
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	−1.69722	−0.0585598
$841$	7.00000	0.241379
$842$	−8.48612	−0.292451
$843$	23.4500	0.807660
$844$	−16.6972	−0.574742
$845$	9.00000	0.309609
$846$	11.0917	0.381340
$847$	1.30278	0.0447639
$848$	6.90833	0.237233
$849$	35.8444	1.23018
$850$	2.30278	0.0789846
$851$	0	0
$852$	2.72498	0.0933563
$853$	24.6056	0.842478	0.421239	−	0.906950i	$-0.361595\pi$
$853$	24.6056	0.842478	0.421239	+	0.906950i	$0.361595\pi$
$854$	−10.4222	−0.356641
$855$	−2.21110	−0.0756181
$856$	2.30278	0.0787073
$857$	−27.9083	−0.953330	−0.476665	−	0.879085i	$-0.658155\pi$
$857$	−27.9083	−0.953330	−0.476665	+	0.879085i	$0.658155\pi$
$858$	2.60555	0.0889521
$859$	−34.8444	−1.18888	−0.594438	−	0.804141i	$-0.702625\pi$
$859$	−34.8444	−1.18888	−0.594438	+	0.804141i	$0.702625\pi$
$860$	−1.00000	−0.0340997
$861$	10.1833	0.347048
$862$	−14.5139	−0.494345
$863$	3.21110	0.109307	0.0546536	−	0.998505i	$-0.482595\pi$
$863$	3.21110	0.109307	0.0546536	+	0.998505i	$0.482595\pi$
$864$	−5.60555	−0.190705
$865$	−12.0000	−0.408012
$866$	−20.4222	−0.693975
$867$	15.2389	0.517539
$868$	−5.21110	−0.176876
$869$	2.69722	0.0914971
$870$	−7.81665	−0.265009
$871$	−8.00000	−0.271070
$872$	16.9083	0.572588
$873$	−16.4222	−0.555807
$874$	0	0
$875$	−1.30278	−0.0440419
$876$	9.39445	0.317409
$877$	56.4222	1.90524	0.952621	−	0.304159i	$-0.0983754\pi$
$877$	56.4222	1.90524	0.952621	+	0.304159i	$0.0983754\pi$
$878$	−25.5139	−0.861052
$879$	18.0000	0.607125
$880$	−1.00000	−0.0337100
$881$	46.7527	1.57514	0.787570	−	0.616225i	$-0.211339\pi$
$881$	46.7527	1.57514	0.787570	+	0.616225i	$0.211339\pi$
$882$	−6.90833	−0.232615
$883$	40.2389	1.35415	0.677073	−	0.735916i	$-0.263248\pi$
$883$	40.2389	1.35415	0.677073	+	0.735916i	$0.263248\pi$
$884$	−4.60555	−0.154901
$885$	5.09167	0.171155
$886$	−25.8167	−0.867327
$887$	29.5139	0.990979	0.495490	−	0.868614i	$-0.334989\pi$
$887$	29.5139	0.990979	0.495490	+	0.868614i	$0.334989\pi$
$888$	−11.2111	−0.376220
$889$	26.6056	0.892322
$890$	6.00000	0.201120
$891$	−3.39445	−0.113718
$892$	−28.0000	−0.937509
$893$	−14.4500	−0.483550
$894$	−9.63331	−0.322186
$895$	1.81665	0.0607240
$896$	−1.30278	−0.0435227
$897$	0	0
$898$	2.78890	0.0930667
$899$	−24.0000	−0.800445
$900$	−1.30278	−0.0434259
$901$	−15.9083	−0.529983
$902$	6.00000	0.199778
$903$	−1.69722	−0.0564801
$904$	5.51388	0.183389
$905$	−2.42221	−0.0805168
$906$	−21.3944	−0.710783
$907$	31.4500	1.04428	0.522139	−	0.852860i	$-0.325134\pi$
$907$	31.4500	1.04428	0.522139	+	0.852860i	$0.325134\pi$
$908$	4.60555	0.152841
$909$	9.27502	0.307633
$910$	2.60555	0.0863732
$911$	−3.27502	−0.108506	−0.0542531	−	0.998527i	$-0.517278\pi$
$911$	−3.27502	−0.108506	−0.0542531	+	0.998527i	$0.517278\pi$
$912$	2.21110	0.0732169
$913$	−0.697224	−0.0230748
$914$	3.57779	0.118343
$915$	10.4222	0.344547
$916$	−21.0278	−0.694777
$917$	−3.63331	−0.119982
$918$	12.9083	0.426038
$919$	−7.06392	−0.233017	−0.116509	−	0.993190i	$-0.537170\pi$
$919$	−7.06392	−0.233017	−0.116509	+	0.993190i	$0.537170\pi$
$920$	0	0
$921$	−26.9638	−0.888489
$922$	19.3305	0.636617
$923$	−4.18335	−0.137697
$924$	−1.69722	−0.0558346
$925$	−8.60555	−0.282949
$926$	27.0278	0.888187
$927$	14.2111	0.466754
$928$	−6.00000	−0.196960
$929$	−21.2111	−0.695914	−0.347957	−	0.937511i	$-0.613124\pi$
$929$	−21.2111	−0.695914	−0.347957	+	0.937511i	$0.613124\pi$
$930$	5.21110	0.170879
$931$	9.00000	0.294963
$932$	25.8167	0.845653
$933$	6.00000	0.196431
$934$	8.30278	0.271675
$935$	2.30278	0.0753088
$936$	2.60555	0.0851651
$937$	30.0555	0.981871	0.490935	−	0.871196i	$-0.336655\pi$
$937$	30.0555	0.981871	0.490935	+	0.871196i	$0.336655\pi$
$938$	5.21110	0.170149
$939$	−29.6056	−0.966141
$940$	−8.51388	−0.277692
$941$	22.1194	0.721073	0.360536	−	0.932745i	$-0.382594\pi$
$941$	22.1194	0.721073	0.360536	+	0.932745i	$0.382594\pi$
$942$	−5.21110	−0.169787
$943$	0	0
$944$	3.90833	0.127205
$945$	−7.30278	−0.237559
$946$	−1.00000	−0.0325128
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	−3.51388	−0.114125
$949$	−14.4222	−0.468165
$950$	1.69722	0.0550652
$951$	34.5416	1.12009
$952$	3.00000	0.0972306
$953$	−14.2389	−0.461242	−0.230621	−	0.973044i	$-0.574076\pi$
$953$	−14.2389	−0.461242	−0.230621	+	0.973044i	$0.574076\pi$
$954$	9.00000	0.291386
$955$	−8.72498	−0.282334
$956$	−19.3305	−0.625194
$957$	−7.81665	−0.252677
$958$	36.8444	1.19039
$959$	28.1833	0.910088
$960$	1.30278	0.0420469
$961$	−15.0000	−0.483871
$962$	17.2111	0.554908
$963$	3.00000	0.0966736
$964$	9.11943	0.293717
$965$	19.9083	0.640872
$966$	0	0
$967$	27.8167	0.894523	0.447262	−	0.894403i	$-0.352399\pi$
$967$	27.8167	0.894523	0.447262	+	0.894403i	$0.352399\pi$
$968$	−1.00000	−0.0321412
$969$	−5.09167	−0.163568
$970$	12.6056	0.404740
$971$	−56.1749	−1.80274	−0.901370	−	0.433050i	$-0.857437\pi$
$971$	−56.1749	−1.80274	−0.901370	+	0.433050i	$0.857437\pi$
$972$	−12.3944	−0.397552
$973$	−1.02776	−0.0329484
$974$	20.3305	0.651432
$975$	−2.60555	−0.0834444
$976$	8.00000	0.256074
$977$	39.6333	1.26798	0.633991	−	0.773340i	$-0.281416\pi$
$977$	39.6333	1.26798	0.633991	+	0.773340i	$0.281416\pi$
$978$	17.6056	0.562963
$979$	6.00000	0.191761
$980$	5.30278	0.169391
$981$	22.0278	0.703292
$982$	41.7250	1.33150
$983$	27.6333	0.881366	0.440683	−	0.897663i	$-0.354736\pi$
$983$	27.6333	0.881366	0.440683	+	0.897663i	$0.354736\pi$
$984$	−7.81665	−0.249186
$985$	−8.78890	−0.280038
$986$	13.8167	0.440012
$987$	−14.4500	−0.459947
$988$	−3.39445	−0.107992
$989$	0	0
$990$	−1.30278	−0.0414049
$991$	−30.7889	−0.978042	−0.489021	−	0.872272i	$-0.662646\pi$
$991$	−30.7889	−0.978042	−0.489021	+	0.872272i	$0.662646\pi$
$992$	4.00000	0.127000
$993$	13.0278	0.413423
$994$	2.72498	0.0864311
$995$	22.9083	0.726243
$996$	0.908327	0.0287814
$997$	43.3028	1.37141	0.685706	−	0.727878i	$-0.259493\pi$
$997$	43.3028	1.37141	0.685706	+	0.727878i	$0.259493\pi$
$998$	16.4222	0.519836
$999$	−48.2389	−1.52621

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.o.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4730.2.a.o.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:	\( N \)	\(=\)	\( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4730.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} +1.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +1.30278 q^{6} +1.30278 q^{7} -1.00000 q^{8} -1.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} -1.30278 q^{12} +2.00000 q^{13} -1.30278 q^{14} +1.30278 q^{15} +1.00000 q^{16} -2.30278 q^{17} +1.30278 q^{18} -1.69722 q^{19} -1.00000 q^{20} -1.69722 q^{21} -1.00000 q^{22} +1.30278 q^{24} +1.00000 q^{25} -2.00000 q^{26} +5.60555 q^{27} +1.30278 q^{28} +6.00000 q^{29} -1.30278 q^{30} -4.00000 q^{31} -1.00000 q^{32} -1.30278 q^{33} +2.30278 q^{34} -1.30278 q^{35} -1.30278 q^{36} -8.60555 q^{37} +1.69722 q^{38} -2.60555 q^{39} +1.00000 q^{40} -6.00000 q^{41} +1.69722 q^{42} +1.00000 q^{43} +1.00000 q^{44} +1.30278 q^{45} +8.51388 q^{47} -1.30278 q^{48} -5.30278 q^{49} -1.00000 q^{50} +3.00000 q^{51} +2.00000 q^{52} +6.90833 q^{53} -5.60555 q^{54} -1.00000 q^{55} -1.30278 q^{56} +2.21110 q^{57} -6.00000 q^{58} +3.90833 q^{59} +1.30278 q^{60} +8.00000 q^{61} +4.00000 q^{62} -1.69722 q^{63} +1.00000 q^{64} -2.00000 q^{65} +1.30278 q^{66} -4.00000 q^{67} -2.30278 q^{68} +1.30278 q^{70} -2.09167 q^{71} +1.30278 q^{72} -7.21110 q^{73} +8.60555 q^{74} -1.30278 q^{75} -1.69722 q^{76} +1.30278 q^{77} +2.60555 q^{78} +2.69722 q^{79} -1.00000 q^{80} -3.39445 q^{81} +6.00000 q^{82} -0.697224 q^{83} -1.69722 q^{84} +2.30278 q^{85} -1.00000 q^{86} -7.81665 q^{87} -1.00000 q^{88} +6.00000 q^{89} -1.30278 q^{90} +2.60555 q^{91} +5.21110 q^{93} -8.51388 q^{94} +1.69722 q^{95} +1.30278 q^{96} +12.6056 q^{97} +5.30278 q^{98} -1.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8 + q^9	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{9} + 2 q^{10} + 2 q^{11} + q^{12} + 4 q^{13} + q^{14} - q^{15} + 2 q^{16} - q^{17} - q^{18} - 7 q^{19} - 2 q^{20} - 7 q^{21} - 2 q^{22} - q^{24} + 2 q^{25} - 4 q^{26} + 4 q^{27} - q^{28} + 12 q^{29} + q^{30} - 8 q^{31} - 2 q^{32} + q^{33} + q^{34} + q^{35} + q^{36} - 10 q^{37} + 7 q^{38} + 2 q^{39} + 2 q^{40} - 12 q^{41} + 7 q^{42} + 2 q^{43} + 2 q^{44} - q^{45} - q^{47} + q^{48} - 7 q^{49} - 2 q^{50} + 6 q^{51} + 4 q^{52} + 3 q^{53} - 4 q^{54} - 2 q^{55} + q^{56} - 10 q^{57} - 12 q^{58} - 3 q^{59} - q^{60} + 16 q^{61} + 8 q^{62} - 7 q^{63} + 2 q^{64} - 4 q^{65} - q^{66} - 8 q^{67} - q^{68} - q^{70} - 15 q^{71} - q^{72} + 10 q^{74} + q^{75} - 7 q^{76} - q^{77} - 2 q^{78} + 9 q^{79} - 2 q^{80} - 14 q^{81} + 12 q^{82} - 5 q^{83} - 7 q^{84} + q^{85} - 2 q^{86} + 6 q^{87} - 2 q^{88} + 12 q^{89} + q^{90} - 2 q^{91} - 4 q^{93} + q^{94} + 7 q^{95} - q^{96} + 18 q^{97} + 7 q^{98} + q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 + q^3 + 2 * q^4 - 2 * q^5 - q^6 - q^7 - 2 * q^8 + q^9 + 2 * q^10 + 2 * q^11 + q^12 + 4 * q^13 + q^14 - q^15 + 2 * q^16 - q^17 - q^18 - 7 * q^19 - 2 * q^20 - 7 * q^21 - 2 * q^22 - q^24 + 2 * q^25 - 4 * q^26 + 4 * q^27 - q^28 + 12 * q^29 + q^30 - 8 * q^31 - 2 * q^32 + q^33 + q^34 + q^35 + q^36 - 10 * q^37 + 7 * q^38 + 2 * q^39 + 2 * q^40 - 12 * q^41 + 7 * q^42 + 2 * q^43 + 2 * q^44 - q^45 - q^47 + q^48 - 7 * q^49 - 2 * q^50 + 6 * q^51 + 4 * q^52 + 3 * q^53 - 4 * q^54 - 2 * q^55 + q^56 - 10 * q^57 - 12 * q^58 - 3 * q^59 - q^60 + 16 * q^61 + 8 * q^62 - 7 * q^63 + 2 * q^64 - 4 * q^65 - q^66 - 8 * q^67 - q^68 - q^70 - 15 * q^71 - q^72 + 10 * q^74 + q^75 - 7 * q^76 - q^77 - 2 * q^78 + 9 * q^79 - 2 * q^80 - 14 * q^81 + 12 * q^82 - 5 * q^83 - 7 * q^84 + q^85 - 2 * q^86 + 6 * q^87 - 2 * q^88 + 12 * q^89 + q^90 - 2 * q^91 - 4 * q^93 + q^94 + 7 * q^95 - q^96 + 18 * q^97 + 7 * q^98 + q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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