LMFDB - Embedded newform 4730.2.a.o.1.2

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			1.2
Root			$2.30278$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} -2.30278 q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} -2.30278 q^{7} -1.00000 q^{8} +2.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.30278 q^{12} +2.00000 q^{13} +2.30278 q^{14} -2.30278 q^{15} +1.00000 q^{16} +1.30278 q^{17} -2.30278 q^{18} -5.30278 q^{19} -1.00000 q^{20} -5.30278 q^{21} -1.00000 q^{22} -2.30278 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.60555 q^{27} -2.30278 q^{28} +6.00000 q^{29} +2.30278 q^{30} -4.00000 q^{31} -1.00000 q^{32} +2.30278 q^{33} -1.30278 q^{34} +2.30278 q^{35} +2.30278 q^{36} -1.39445 q^{37} +5.30278 q^{38} +4.60555 q^{39} +1.00000 q^{40} -6.00000 q^{41} +5.30278 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.30278 q^{45} -9.51388 q^{47} +2.30278 q^{48} -1.69722 q^{49} -1.00000 q^{50} +3.00000 q^{51} +2.00000 q^{52} -3.90833 q^{53} +1.60555 q^{54} -1.00000 q^{55} +2.30278 q^{56} -12.2111 q^{57} -6.00000 q^{58} -6.90833 q^{59} -2.30278 q^{60} +8.00000 q^{61} +4.00000 q^{62} -5.30278 q^{63} +1.00000 q^{64} -2.00000 q^{65} -2.30278 q^{66} -4.00000 q^{67} +1.30278 q^{68} -2.30278 q^{70} -12.9083 q^{71} -2.30278 q^{72} +7.21110 q^{73} +1.39445 q^{74} +2.30278 q^{75} -5.30278 q^{76} -2.30278 q^{77} -4.60555 q^{78} +6.30278 q^{79} -1.00000 q^{80} -10.6056 q^{81} +6.00000 q^{82} -4.30278 q^{83} -5.30278 q^{84} -1.30278 q^{85} -1.00000 q^{86} +13.8167 q^{87} -1.00000 q^{88} +6.00000 q^{89} +2.30278 q^{90} -4.60555 q^{91} -9.21110 q^{93} +9.51388 q^{94} +5.30278 q^{95} -2.30278 q^{96} +5.39445 q^{97} +1.69722 q^{98} +2.30278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.30278	1.32951	0.664754	−	0.747062i	$-0.268536\pi$
$3$	2.30278	1.32951	0.664754	+	0.747062i	$0.268536\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−2.30278	−0.940104
$7$	−2.30278	−0.870367	−0.435184	−	0.900342i	$-0.643317\pi$
$7$	−2.30278	−0.870367	−0.435184	+	0.900342i	$0.643317\pi$
$8$	−1.00000	−0.353553
$9$	2.30278	0.767592
$10$	1.00000	0.316228
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.30278	0.664754
$13$	2.00000	0.554700	0.277350	−	0.960769i	$-0.410544\pi$
$13$	2.00000	0.554700	0.277350	+	0.960769i	$0.410544\pi$
$14$	2.30278	0.615443
$15$	−2.30278	−0.594574
$16$	1.00000	0.250000
$17$	1.30278	0.315970	0.157985	−	0.987442i	$-0.449500\pi$
$17$	1.30278	0.315970	0.157985	+	0.987442i	$0.449500\pi$
$18$	−2.30278	−0.542769
$19$	−5.30278	−1.21654	−0.608270	−	0.793730i	$-0.708136\pi$
$19$	−5.30278	−1.21654	−0.608270	+	0.793730i	$0.708136\pi$
$20$	−1.00000	−0.223607
$21$	−5.30278	−1.15716
$22$	−1.00000	−0.213201
$23$	0	0		−	1.00000i	$-0.5\pi$
$23$	0	0			1.00000i	$0.5\pi$
$24$	−2.30278	−0.470052
$25$	1.00000	0.200000
$26$	−2.00000	−0.392232
$27$	−1.60555	−0.308988
$28$	−2.30278	−0.435184
$29$	6.00000	1.11417	0.557086	−	0.830455i	$-0.311919\pi$
$29$	6.00000	1.11417	0.557086	+	0.830455i	$0.311919\pi$
$30$	2.30278	0.420427
$31$	−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
$33$	2.30278	0.400862
$34$	−1.30278	−0.223424
$35$	2.30278	0.389240
$36$	2.30278	0.383796
$37$	−1.39445	−0.229246	−0.114623	−	0.993409i	$-0.536566\pi$
$37$	−1.39445	−0.229246	−0.114623	+	0.993409i	$0.536566\pi$
$38$	5.30278	0.860224
$39$	4.60555	0.737478
$40$	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	$0.655213\pi$
$42$	5.30278	0.818236
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.00000	0.150756
$45$	−2.30278	−0.343278
$46$	0	0
$47$	−9.51388	−1.38774	−0.693871	−	0.720099i	$-0.744096\pi$
$47$	−9.51388	−1.38774	−0.693871	+	0.720099i	$0.744096\pi$
$48$	2.30278	0.332377
$49$	−1.69722	−0.242461
$50$	−1.00000	−0.141421
$51$	3.00000	0.420084
$52$	2.00000	0.277350
$53$	−3.90833	−0.536850	−0.268425	−	0.963301i	$-0.586503\pi$
$53$	−3.90833	−0.536850	−0.268425	+	0.963301i	$0.586503\pi$
$54$	1.60555	0.218488
$55$	−1.00000	−0.134840
$56$	2.30278	0.307721
$57$	−12.2111	−1.61740
$58$	−6.00000	−0.787839
$59$	−6.90833	−0.899388	−0.449694	−	0.893183i	$-0.648467\pi$
$59$	−6.90833	−0.899388	−0.449694	+	0.893183i	$0.648467\pi$
$60$	−2.30278	−0.297287
$61$	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
$63$	−5.30278	−0.668087
$64$	1.00000	0.125000
$65$	−2.00000	−0.248069
$66$	−2.30278	−0.283452
$67$	−4.00000	−0.488678	−0.244339	−	0.969690i	$-0.578571\pi$
$67$	−4.00000	−0.488678	−0.244339	+	0.969690i	$0.578571\pi$
$68$	1.30278	0.157985
$69$	0	0
$70$	−2.30278	−0.275234
$71$	−12.9083	−1.53194	−0.765968	−	0.642878i	$-0.777740\pi$
$71$	−12.9083	−1.53194	−0.765968	+	0.642878i	$0.777740\pi$
$72$	−2.30278	−0.271385
$73$	7.21110	0.843996	0.421998	−	0.906597i	$-0.361329\pi$
$73$	7.21110	0.843996	0.421998	+	0.906597i	$0.361329\pi$
$74$	1.39445	0.162101
$75$	2.30278	0.265902
$76$	−5.30278	−0.608270
$77$	−2.30278	−0.262426
$78$	−4.60555	−0.521476
$79$	6.30278	0.709118	0.354559	−	0.935034i	$-0.384631\pi$
$79$	6.30278	0.709118	0.354559	+	0.935034i	$0.384631\pi$
$80$	−1.00000	−0.111803
$81$	−10.6056	−1.17839
$82$	6.00000	0.662589
$83$	−4.30278	−0.472291	−0.236145	−	0.971718i	$-0.575884\pi$
$83$	−4.30278	−0.472291	−0.236145	+	0.971718i	$0.575884\pi$
$84$	−5.30278	−0.578580
$85$	−1.30278	−0.141306
$86$	−1.00000	−0.107833
$87$	13.8167	1.48130
$88$	−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	$0.396989\pi$
$90$	2.30278	0.242734
$91$	−4.60555	−0.482793
$92$	0	0
$93$	−9.21110	−0.955147
$94$	9.51388	0.981282
$95$	5.30278	0.544053
$96$	−2.30278	−0.235026
$97$	5.39445	0.547723	0.273862	−	0.961769i	$-0.411699\pi$
$97$	5.39445	0.547723	0.273862	+	0.961769i	$0.411699\pi$
$98$	1.69722	0.171446
$99$	2.30278	0.231438
$100$	1.00000	0.100000
$101$	18.1194	1.80295	0.901475	−	0.432831i	$-0.142485\pi$
$101$	18.1194	1.80295	0.901475	+	0.432831i	$0.142485\pi$
$102$	−3.00000	−0.297044
$103$	−0.0916731	−0.00903282	−0.00451641	−	0.999990i	$-0.501438\pi$
$103$	−0.0916731	−0.00903282	−0.00451641	+	0.999990i	$0.501438\pi$
$104$	−2.00000	−0.196116
$105$	5.30278	0.517498
$106$	3.90833	0.379610
$107$	1.30278	0.125944	0.0629720	−	0.998015i	$-0.479942\pi$
$107$	1.30278	0.125944	0.0629720	+	0.998015i	$0.479942\pi$
$108$	−1.60555	−0.154494
$109$	−6.09167	−0.583476	−0.291738	−	0.956498i	$-0.594234\pi$
$109$	−6.09167	−0.583476	−0.291738	+	0.956498i	$0.594234\pi$
$110$	1.00000	0.0953463
$111$	−3.21110	−0.304784
$112$	−2.30278	−0.217592
$113$	12.5139	1.17721	0.588603	−	0.808422i	$-0.299678\pi$
$113$	12.5139	1.17721	0.588603	+	0.808422i	$0.299678\pi$
$114$	12.2111	1.14367
$115$	0	0
$116$	6.00000	0.557086
$117$	4.60555	0.425783
$118$	6.90833	0.635963
$119$	−3.00000	−0.275010
$120$	2.30278	0.210214
$121$	1.00000	0.0909091
$122$	−8.00000	−0.724286
$123$	−13.8167	−1.24581
$124$	−4.00000	−0.359211
$125$	−1.00000	−0.0894427
$126$	5.30278	0.472409
$127$	−8.42221	−0.747350	−0.373675	−	0.927560i	$-0.621902\pi$
$127$	−8.42221	−0.747350	−0.373675	+	0.927560i	$0.621902\pi$
$128$	−1.00000	−0.0883883
$129$	2.30278	0.202748
$130$	2.00000	0.175412
$131$	−17.2111	−1.50374	−0.751871	−	0.659311i	$-0.770848\pi$
$131$	−17.2111	−1.50374	−0.751871	+	0.659311i	$0.770848\pi$
$132$	2.30278	0.200431
$133$	12.2111	1.05884
$134$	4.00000	0.345547
$135$	1.60555	0.138184
$136$	−1.30278	−0.111712
$137$	−21.6333	−1.84826	−0.924129	−	0.382080i	$-0.875208\pi$
$137$	−21.6333	−1.84826	−0.924129	+	0.382080i	$0.875208\pi$
$138$	0	0
$139$	−15.2111	−1.29019	−0.645094	−	0.764103i	$-0.723182\pi$
$139$	−15.2111	−1.29019	−0.645094	+	0.764103i	$0.723182\pi$
$140$	2.30278	0.194620
$141$	−21.9083	−1.84501
$142$	12.9083	1.08324
$143$	2.00000	0.167248
$144$	2.30278	0.191898
$145$	−6.00000	−0.498273
$146$	−7.21110	−0.596795
$147$	−3.90833	−0.322353
$148$	−1.39445	−0.114623
$149$	−14.6056	−1.19653	−0.598267	−	0.801297i	$-0.704144\pi$
$149$	−14.6056	−1.19653	−0.598267	+	0.801297i	$0.704144\pi$
$150$	−2.30278	−0.188021
$151$	12.4222	1.01090	0.505452	−	0.862855i	$-0.331326\pi$
$151$	12.4222	1.01090	0.505452	+	0.862855i	$0.331326\pi$
$152$	5.30278	0.430112
$153$	3.00000	0.242536
$154$	2.30278	0.185563
$155$	4.00000	0.321288
$156$	4.60555	0.368739
$157$	−4.00000	−0.319235	−0.159617	−	0.987179i	$-0.551026\pi$
$157$	−4.00000	−0.319235	−0.159617	+	0.987179i	$0.551026\pi$
$158$	−6.30278	−0.501422
$159$	−9.00000	−0.713746
$160$	1.00000	0.0790569
$161$	0	0
$162$	10.6056	0.833251
$163$	−4.51388	−0.353554	−0.176777	−	0.984251i	$-0.556567\pi$
$163$	−4.51388	−0.353554	−0.176777	+	0.984251i	$0.556567\pi$
$164$	−6.00000	−0.468521
$165$	−2.30278	−0.179271
$166$	4.30278	0.333960
$167$	−16.4222	−1.27079	−0.635394	−	0.772188i	$-0.719162\pi$
$167$	−16.4222	−1.27079	−0.635394	+	0.772188i	$0.719162\pi$
$168$	5.30278	0.409118
$169$	−9.00000	−0.692308
$170$	1.30278	0.0999183
$171$	−12.2111	−0.933806
$172$	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	$0.349220\pi$
$174$	−13.8167	−1.04744
$175$	−2.30278	−0.174073
$176$	1.00000	0.0753778
$177$	−15.9083	−1.19574
$178$	−6.00000	−0.449719
$179$	19.8167	1.48117	0.740583	−	0.671965i	$-0.234549\pi$
$179$	19.8167	1.48117	0.740583	+	0.671965i	$0.234549\pi$
$180$	−2.30278	−0.171639
$181$	−26.4222	−1.96395	−0.981974	−	0.189019i	$-0.939469\pi$
$181$	−26.4222	−1.96395	−0.981974	+	0.189019i	$0.939469\pi$
$182$	4.60555	0.341386
$183$	18.4222	1.36181
$184$	0	0
$185$	1.39445	0.102522
$186$	9.21110	0.675391
$187$	1.30278	0.0952684
$188$	−9.51388	−0.693871
$189$	3.69722	0.268934
$190$	−5.30278	−0.384704
$191$	−23.7250	−1.71668	−0.858340	−	0.513082i	$-0.828504\pi$
$191$	−23.7250	−1.71668	−0.858340	+	0.513082i	$0.828504\pi$
$192$	2.30278	0.166189
$193$	−9.09167	−0.654433	−0.327216	−	0.944949i	$-0.606111\pi$
$193$	−9.09167	−0.654433	−0.327216	+	0.944949i	$0.606111\pi$
$194$	−5.39445	−0.387299
$195$	−4.60555	−0.329810
$196$	−1.69722	−0.121230
$197$	23.2111	1.65372	0.826861	−	0.562406i	$-0.190124\pi$
$197$	23.2111	1.65372	0.826861	+	0.562406i	$0.190124\pi$
$198$	−2.30278	−0.163651
$199$	−12.0917	−0.857156	−0.428578	−	0.903505i	$-0.640985\pi$
$199$	−12.0917	−0.857156	−0.428578	+	0.903505i	$0.640985\pi$
$200$	−1.00000	−0.0707107
$201$	−9.21110	−0.649701
$202$	−18.1194	−1.27488
$203$	−13.8167	−0.969739
$204$	3.00000	0.210042
$205$	6.00000	0.419058
$206$	0.0916731	0.00638717
$207$	0	0
$208$	2.00000	0.138675
$209$	−5.30278	−0.366801
$210$	−5.30278	−0.365926
$211$	−20.3028	−1.39770	−0.698850	−	0.715268i	$-0.746305\pi$
$211$	−20.3028	−1.39770	−0.698850	+	0.715268i	$0.746305\pi$
$212$	−3.90833	−0.268425
$213$	−29.7250	−2.03672
$214$	−1.30278	−0.0890559
$215$	−1.00000	−0.0681994
$216$	1.60555	0.109244
$217$	9.21110	0.625290
$218$	6.09167	0.412580
$219$	16.6056	1.12210
$220$	−1.00000	−0.0674200
$221$	2.60555	0.175268
$222$	3.21110	0.215515
$223$	−28.0000	−1.87502	−0.937509	−	0.347960i	$-0.886874\pi$
$223$	−28.0000	−1.87502	−0.937509	+	0.347960i	$0.886874\pi$
$224$	2.30278	0.153861
$225$	2.30278	0.153518
$226$	−12.5139	−0.832411
$227$	−2.60555	−0.172937	−0.0864683	−	0.996255i	$-0.527558\pi$
$227$	−2.60555	−0.172937	−0.0864683	+	0.996255i	$0.527558\pi$
$228$	−12.2111	−0.808700
$229$	15.0278	0.993062	0.496531	−	0.868019i	$-0.334607\pi$
$229$	15.0278	0.993062	0.496531	+	0.868019i	$0.334607\pi$
$230$	0	0
$231$	−5.30278	−0.348897
$232$	−6.00000	−0.393919
$233$	4.18335	0.274060	0.137030	−	0.990567i	$-0.456244\pi$
$233$	4.18335	0.274060	0.137030	+	0.990567i	$0.456244\pi$
$234$	−4.60555	−0.301074
$235$	9.51388	0.620617
$236$	−6.90833	−0.449694
$237$	14.5139	0.942778
$238$	3.00000	0.194461
$239$	20.3305	1.31507	0.657536	−	0.753423i	$-0.271599\pi$
$239$	20.3305	1.31507	0.657536	+	0.753423i	$0.271599\pi$
$240$	−2.30278	−0.148644
$241$	−16.1194	−1.03834	−0.519172	−	0.854670i	$-0.673760\pi$
$241$	−16.1194	−1.03834	−0.519172	+	0.854670i	$0.673760\pi$
$242$	−1.00000	−0.0642824
$243$	−19.6056	−1.25770
$244$	8.00000	0.512148
$245$	1.69722	0.108432
$246$	13.8167	0.880918
$247$	−10.6056	−0.674815
$248$	4.00000	0.254000
$249$	−9.90833	−0.627915
$250$	1.00000	0.0632456
$251$	−0.513878	−0.0324357	−0.0162179	−	0.999868i	$-0.505163\pi$
$251$	−0.513878	−0.0324357	−0.0162179	+	0.999868i	$0.505163\pi$
$252$	−5.30278	−0.334043
$253$	0	0
$254$	8.42221	0.528456
$255$	−3.00000	−0.187867
$256$	1.00000	0.0625000
$257$	15.1194	0.943124	0.471562	−	0.881833i	$-0.343690\pi$
$257$	15.1194	0.943124	0.471562	+	0.881833i	$0.343690\pi$
$258$	−2.30278	−0.143365
$259$	3.21110	0.199528
$260$	−2.00000	−0.124035
$261$	13.8167	0.855229
$262$	17.2111	1.06331
$263$	8.33053	0.513683	0.256841	−	0.966454i	$-0.417318\pi$
$263$	8.33053	0.513683	0.256841	+	0.966454i	$0.417318\pi$
$264$	−2.30278	−0.141726
$265$	3.90833	0.240087
$266$	−12.2111	−0.748711
$267$	13.8167	0.845565
$268$	−4.00000	−0.244339
$269$	0	0		−	1.00000i	$-0.5\pi$
$269$	0	0			1.00000i	$0.5\pi$
$270$	−1.60555	−0.0977107
$271$	−26.4222	−1.60503	−0.802517	−	0.596629i	$-0.796506\pi$
$271$	−26.4222	−1.60503	−0.802517	+	0.596629i	$0.796506\pi$
$272$	1.30278	0.0789924
$273$	−10.6056	−0.641877
$274$	21.6333	1.30692
$275$	1.00000	0.0603023
$276$	0	0
$277$	17.9083	1.07601	0.538004	−	0.842943i	$-0.319179\pi$
$277$	17.9083	1.07601	0.538004	+	0.842943i	$0.319179\pi$
$278$	15.2111	0.912301
$279$	−9.21110	−0.551454
$280$	−2.30278	−0.137617
$281$	−18.0000	−1.07379	−0.536895	−	0.843649i	$-0.680403\pi$
$281$	−18.0000	−1.07379	−0.536895	+	0.843649i	$0.680403\pi$
$282$	21.9083	1.30462
$283$	−9.48612	−0.563891	−0.281946	−	0.959430i	$-0.590980\pi$
$283$	−9.48612	−0.563891	−0.281946	+	0.959430i	$0.590980\pi$
$284$	−12.9083	−0.765968
$285$	12.2111	0.723323
$286$	−2.00000	−0.118262
$287$	13.8167	0.815571
$288$	−2.30278	−0.135692
$289$	−15.3028	−0.900163
$290$	6.00000	0.352332
$291$	12.4222	0.728203
$292$	7.21110	0.421998
$293$	7.81665	0.456654	0.228327	−	0.973585i	$-0.426675\pi$
$293$	7.81665	0.456654	0.228327	+	0.973585i	$0.426675\pi$
$294$	3.90833	0.227938
$295$	6.90833	0.402218
$296$	1.39445	0.0810507
$297$	−1.60555	−0.0931635
$298$	14.6056	0.846077
$299$	0	0
$300$	2.30278	0.132951
$301$	−2.30278	−0.132730
$302$	−12.4222	−0.714818
$303$	41.7250	2.39704
$304$	−5.30278	−0.304135
$305$	−8.00000	−0.458079
$306$	−3.00000	−0.171499
$307$	24.3028	1.38703	0.693516	−	0.720441i	$-0.256061\pi$
$307$	24.3028	1.38703	0.693516	+	0.720441i	$0.256061\pi$
$308$	−2.30278	−0.131213
$309$	−0.211103	−0.0120092
$310$	−4.00000	−0.227185
$311$	2.60555	0.147747	0.0738736	−	0.997268i	$-0.476464\pi$
$311$	2.60555	0.147747	0.0738736	+	0.997268i	$0.476464\pi$
$312$	−4.60555	−0.260738
$313$	−9.72498	−0.549688	−0.274844	−	0.961489i	$-0.588626\pi$
$313$	−9.72498	−0.549688	−0.274844	+	0.961489i	$0.588626\pi$
$314$	4.00000	0.225733
$315$	5.30278	0.298778
$316$	6.30278	0.354559
$317$	−8.48612	−0.476628	−0.238314	−	0.971188i	$-0.576595\pi$
$317$	−8.48612	−0.476628	−0.238314	+	0.971188i	$0.576595\pi$
$318$	9.00000	0.504695
$319$	6.00000	0.335936
$320$	−1.00000	−0.0559017
$321$	3.00000	0.167444
$322$	0	0
$323$	−6.90833	−0.384390
$324$	−10.6056	−0.589197
$325$	2.00000	0.110940
$326$	4.51388	0.250001
$327$	−14.0278	−0.775737
$328$	6.00000	0.331295
$329$	21.9083	1.20785
$330$	2.30278	0.126764
$331$	−10.0000	−0.549650	−0.274825	−	0.961494i	$-0.588620\pi$
$331$	−10.0000	−0.549650	−0.274825	+	0.961494i	$0.588620\pi$
$332$	−4.30278	−0.236145
$333$	−3.21110	−0.175967
$334$	16.4222	0.898583
$335$	4.00000	0.218543
$336$	−5.30278	−0.289290
$337$	−22.5139	−1.22641	−0.613205	−	0.789924i	$-0.710120\pi$
$337$	−22.5139	−1.22641	−0.613205	+	0.789924i	$0.710120\pi$
$338$	9.00000	0.489535
$339$	28.8167	1.56511
$340$	−1.30278	−0.0706529
$341$	−4.00000	−0.216612
$342$	12.2111	0.660301
$343$	20.0278	1.08140
$344$	−1.00000	−0.0539164
$345$	0	0
$346$	−12.0000	−0.645124
$347$	7.81665	0.419620	0.209810	−	0.977742i	$-0.432715\pi$
$347$	7.81665	0.419620	0.209810	+	0.977742i	$0.432715\pi$
$348$	13.8167	0.740650
$349$	−10.0000	−0.535288	−0.267644	−	0.963518i	$-0.586245\pi$
$349$	−10.0000	−0.535288	−0.267644	+	0.963518i	$0.586245\pi$
$350$	2.30278	0.123089
$351$	−3.21110	−0.171396
$352$	−1.00000	−0.0533002
$353$	16.4222	0.874066	0.437033	−	0.899446i	$-0.356029\pi$
$353$	16.4222	0.874066	0.437033	+	0.899446i	$0.356029\pi$
$354$	15.9083	0.845518
$355$	12.9083	0.685103
$356$	6.00000	0.317999
$357$	−6.90833	−0.365627
$358$	−19.8167	−1.04734
$359$	32.8444	1.73346	0.866731	−	0.498776i	$-0.166217\pi$
$359$	32.8444	1.73346	0.866731	+	0.498776i	$0.166217\pi$
$360$	2.30278	0.121367
$361$	9.11943	0.479970
$362$	26.4222	1.38872
$363$	2.30278	0.120864
$364$	−4.60555	−0.241396
$365$	−7.21110	−0.377446
$366$	−18.4222	−0.962944
$367$	−7.90833	−0.412811	−0.206406	−	0.978467i	$-0.566177\pi$
$367$	−7.90833	−0.412811	−0.206406	+	0.978467i	$0.566177\pi$
$368$	0	0
$369$	−13.8167	−0.719266
$370$	−1.39445	−0.0724939
$371$	9.00000	0.467257
$372$	−9.21110	−0.477573
$373$	−32.5416	−1.68494	−0.842471	−	0.538742i	$-0.818900\pi$
$373$	−32.5416	−1.68494	−0.842471	+	0.538742i	$0.818900\pi$
$374$	−1.30278	−0.0673649
$375$	−2.30278	−0.118915
$376$	9.51388	0.490641
$377$	12.0000	0.618031
$378$	−3.69722	−0.190165
$379$	−9.33053	−0.479277	−0.239639	−	0.970862i	$-0.577029\pi$
$379$	−9.33053	−0.479277	−0.239639	+	0.970862i	$0.577029\pi$
$380$	5.30278	0.272027
$381$	−19.3944	−0.993608
$382$	23.7250	1.21388
$383$	23.2111	1.18603	0.593016	−	0.805191i	$-0.297937\pi$
$383$	23.2111	1.18603	0.593016	+	0.805191i	$0.297937\pi$
$384$	−2.30278	−0.117513
$385$	2.30278	0.117360
$386$	9.09167	0.462754
$387$	2.30278	0.117057
$388$	5.39445	0.273862
$389$	30.9083	1.56711	0.783557	−	0.621320i	$-0.213403\pi$
$389$	30.9083	1.56711	0.783557	+	0.621320i	$0.213403\pi$
$390$	4.60555	0.233211
$391$	0	0
$392$	1.69722	0.0857228
$393$	−39.6333	−1.99924
$394$	−23.2111	−1.16936
$395$	−6.30278	−0.317127
$396$	2.30278	0.115719
$397$	18.5416	0.930578	0.465289	−	0.885159i	$-0.345950\pi$
$397$	18.5416	0.930578	0.465289	+	0.885159i	$0.345950\pi$
$398$	12.0917	0.606101
$399$	28.1194	1.40773
$400$	1.00000	0.0500000
$401$	25.5416	1.27549	0.637744	−	0.770248i	$-0.279868\pi$
$401$	25.5416	1.27549	0.637744	+	0.770248i	$0.279868\pi$
$402$	9.21110	0.459408
$403$	−8.00000	−0.398508
$404$	18.1194	0.901475
$405$	10.6056	0.526994
$406$	13.8167	0.685709
$407$	−1.39445	−0.0691203
$408$	−3.00000	−0.148522
$409$	−6.88057	−0.340222	−0.170111	−	0.985425i	$-0.554413\pi$
$409$	−6.88057	−0.340222	−0.170111	+	0.985425i	$0.554413\pi$
$410$	−6.00000	−0.296319
$411$	−49.8167	−2.45727
$412$	−0.0916731	−0.00451641
$413$	15.9083	0.782798
$414$	0	0
$415$	4.30278	0.211215
$416$	−2.00000	−0.0980581
$417$	−35.0278	−1.71532
$418$	5.30278	0.259367
$419$	9.63331	0.470618	0.235309	−	0.971921i	$-0.424390\pi$
$419$	9.63331	0.470618	0.235309	+	0.971921i	$0.424390\pi$
$420$	5.30278	0.258749
$421$	26.5139	1.29221	0.646104	−	0.763250i	$-0.276397\pi$
$421$	26.5139	1.29221	0.646104	+	0.763250i	$0.276397\pi$
$422$	20.3028	0.988324
$423$	−21.9083	−1.06522
$424$	3.90833	0.189805
$425$	1.30278	0.0631939
$426$	29.7250	1.44018
$427$	−18.4222	−0.891513
$428$	1.30278	0.0629720
$429$	4.60555	0.222358
$430$	1.00000	0.0482243
$431$	−3.51388	−0.169258	−0.0846288	−	0.996413i	$-0.526970\pi$
$431$	−3.51388	−0.169258	−0.0846288	+	0.996413i	$0.526970\pi$
$432$	−1.60555	−0.0772471
$433$	−8.42221	−0.404745	−0.202373	−	0.979309i	$-0.564865\pi$
$433$	−8.42221	−0.404745	−0.202373	+	0.979309i	$0.564865\pi$
$434$	−9.21110	−0.442147
$435$	−13.8167	−0.662458
$436$	−6.09167	−0.291738
$437$	0	0
$438$	−16.6056	−0.793444
$439$	7.48612	0.357293	0.178647	−	0.983913i	$-0.442828\pi$
$439$	7.48612	0.357293	0.178647	+	0.983913i	$0.442828\pi$
$440$	1.00000	0.0476731
$441$	−3.90833	−0.186111
$442$	−2.60555	−0.123933
$443$	4.18335	0.198757	0.0993784	−	0.995050i	$-0.468315\pi$
$443$	4.18335	0.198757	0.0993784	+	0.995050i	$0.468315\pi$
$444$	−3.21110	−0.152392
$445$	−6.00000	−0.284427
$446$	28.0000	1.32584
$447$	−33.6333	−1.59080
$448$	−2.30278	−0.108796
$449$	−17.2111	−0.812242	−0.406121	−	0.913819i	$-0.633119\pi$
$449$	−17.2111	−0.812242	−0.406121	+	0.913819i	$0.633119\pi$
$450$	−2.30278	−0.108554
$451$	−6.00000	−0.282529
$452$	12.5139	0.588603
$453$	28.6056	1.34401
$454$	2.60555	0.122285
$455$	4.60555	0.215912
$456$	12.2111	0.571837
$457$	−32.4222	−1.51665	−0.758323	−	0.651879i	$-0.773981\pi$
$457$	−32.4222	−1.51665	−0.758323	+	0.651879i	$0.773981\pi$
$458$	−15.0278	−0.702201
$459$	−2.09167	−0.0976309
$460$	0	0
$461$	20.3305	0.946887	0.473444	−	0.880824i	$-0.343011\pi$
$461$	20.3305	0.946887	0.473444	+	0.880824i	$0.343011\pi$
$462$	5.30278	0.246707
$463$	9.02776	0.419555	0.209778	−	0.977749i	$-0.432726\pi$
$463$	9.02776	0.419555	0.209778	+	0.977749i	$0.432726\pi$
$464$	6.00000	0.278543
$465$	9.21110	0.427155
$466$	−4.18335	−0.193790
$467$	−4.69722	−0.217362	−0.108681	−	0.994077i	$-0.534663\pi$
$467$	−4.69722	−0.217362	−0.108681	+	0.994077i	$0.534663\pi$
$468$	4.60555	0.212892
$469$	9.21110	0.425329
$470$	−9.51388	−0.438842
$471$	−9.21110	−0.424425
$472$	6.90833	0.317982
$473$	1.00000	0.0459800
$474$	−14.5139	−0.666645
$475$	−5.30278	−0.243308
$476$	−3.00000	−0.137505
$477$	−9.00000	−0.412082
$478$	−20.3305	−0.929897
$479$	20.8444	0.952405	0.476203	−	0.879336i	$-0.342013\pi$
$479$	20.8444	0.952405	0.476203	+	0.879336i	$0.342013\pi$
$480$	2.30278	0.105107
$481$	−2.78890	−0.127163
$482$	16.1194	0.734220
$483$	0	0
$484$	1.00000	0.0454545
$485$	−5.39445	−0.244949
$486$	19.6056	0.889326
$487$	19.3305	0.875950	0.437975	−	0.898987i	$-0.355696\pi$
$487$	19.3305	0.875950	0.437975	+	0.898987i	$0.355696\pi$
$488$	−8.00000	−0.362143
$489$	−10.3944	−0.470053
$490$	−1.69722	−0.0766728
$491$	−9.27502	−0.418576	−0.209288	−	0.977854i	$-0.567115\pi$
$491$	−9.27502	−0.418576	−0.209288	+	0.977854i	$0.567115\pi$
$492$	−13.8167	−0.622903
$493$	7.81665	0.352044
$494$	10.6056	0.477166
$495$	−2.30278	−0.103502
$496$	−4.00000	−0.179605
$497$	29.7250	1.33335
$498$	9.90833	0.444003
$499$	12.4222	0.556094	0.278047	−	0.960567i	$-0.410313\pi$
$499$	12.4222	0.556094	0.278047	+	0.960567i	$0.410313\pi$
$500$	−1.00000	−0.0447214
$501$	−37.8167	−1.68952
$502$	0.513878	0.0229355
$503$	20.3305	0.906494	0.453247	−	0.891385i	$-0.350266\pi$
$503$	20.3305	0.906494	0.453247	+	0.891385i	$0.350266\pi$
$504$	5.30278	0.236204
$505$	−18.1194	−0.806304
$506$	0	0
$507$	−20.7250	−0.920429
$508$	−8.42221	−0.373675
$509$	−7.81665	−0.346467	−0.173234	−	0.984881i	$-0.555422\pi$
$509$	−7.81665	−0.346467	−0.173234	+	0.984881i	$0.555422\pi$
$510$	3.00000	0.132842
$511$	−16.6056	−0.734586
$512$	−1.00000	−0.0441942
$513$	8.51388	0.375897
$514$	−15.1194	−0.666889
$515$	0.0916731	0.00403960
$516$	2.30278	0.101374
$517$	−9.51388	−0.418420
$518$	−3.21110	−0.141088
$519$	27.6333	1.21297
$520$	2.00000	0.0877058
$521$	1.81665	0.0795890	0.0397945	−	0.999208i	$-0.487330\pi$
$521$	1.81665	0.0795890	0.0397945	+	0.999208i	$0.487330\pi$
$522$	−13.8167	−0.604739
$523$	2.00000	0.0874539	0.0437269	−	0.999044i	$-0.486077\pi$
$523$	2.00000	0.0874539	0.0437269	+	0.999044i	$0.486077\pi$
$524$	−17.2111	−0.751871
$525$	−5.30278	−0.231432
$526$	−8.33053	−0.363228
$527$	−5.21110	−0.226999
$528$	2.30278	0.100215
$529$	−23.0000	−1.00000
$530$	−3.90833	−0.169767
$531$	−15.9083	−0.690363
$532$	12.2111	0.529418
$533$	−12.0000	−0.519778
$534$	−13.8167	−0.597905
$535$	−1.30278	−0.0563239
$536$	4.00000	0.172774
$537$	45.6333	1.96922
$538$	0	0
$539$	−1.69722	−0.0731046
$540$	1.60555	0.0690919
$541$	−37.5139	−1.61285	−0.806424	−	0.591338i	$-0.798600\pi$
$541$	−37.5139	−1.61285	−0.806424	+	0.591338i	$0.798600\pi$
$542$	26.4222	1.13493
$543$	−60.8444	−2.61108
$544$	−1.30278	−0.0558560
$545$	6.09167	0.260939
$546$	10.6056	0.453876
$547$	29.7527	1.27214	0.636068	−	0.771633i	$-0.280560\pi$
$547$	29.7527	1.27214	0.636068	+	0.771633i	$0.280560\pi$
$548$	−21.6333	−0.924129
$549$	18.4222	0.786241
$550$	−1.00000	−0.0426401
$551$	−31.8167	−1.35544
$552$	0	0
$553$	−14.5139	−0.617193
$554$	−17.9083	−0.760852
$555$	3.21110	0.136304
$556$	−15.2111	−0.645094
$557$	−42.2389	−1.78972	−0.894859	−	0.446349i	$-0.852724\pi$
$557$	−42.2389	−1.78972	−0.894859	+	0.446349i	$0.852724\pi$
$558$	9.21110	0.389937
$559$	2.00000	0.0845910
$560$	2.30278	0.0973100
$561$	3.00000	0.126660
$562$	18.0000	0.759284
$563$	3.63331	0.153126	0.0765628	−	0.997065i	$-0.475605\pi$
$563$	3.63331	0.153126	0.0765628	+	0.997065i	$0.475605\pi$
$564$	−21.9083	−0.922507
$565$	−12.5139	−0.526463
$566$	9.48612	0.398731
$567$	24.4222	1.02564
$568$	12.9083	0.541621
$569$	24.2389	1.01615	0.508073	−	0.861314i	$-0.330358\pi$
$569$	24.2389	1.01615	0.508073	+	0.861314i	$0.330358\pi$
$570$	−12.2111	−0.511467
$571$	−7.90833	−0.330953	−0.165477	−	0.986214i	$-0.552916\pi$
$571$	−7.90833	−0.330953	−0.165477	+	0.986214i	$0.552916\pi$
$572$	2.00000	0.0836242
$573$	−54.6333	−2.28234
$574$	−13.8167	−0.576696
$575$	0	0
$576$	2.30278	0.0959490
$577$	32.9083	1.36999	0.684996	−	0.728547i	$-0.259804\pi$
$577$	32.9083	1.36999	0.684996	+	0.728547i	$0.259804\pi$
$578$	15.3028	0.636512
$579$	−20.9361	−0.870074
$580$	−6.00000	−0.249136
$581$	9.90833	0.411067
$582$	−12.4222	−0.514917
$583$	−3.90833	−0.161866
$584$	−7.21110	−0.298398
$585$	−4.60555	−0.190416
$586$	−7.81665	−0.322903
$587$	6.90833	0.285137	0.142569	−	0.989785i	$-0.454464\pi$
$587$	6.90833	0.285137	0.142569	+	0.989785i	$0.454464\pi$
$588$	−3.90833	−0.161177
$589$	21.2111	0.873988
$590$	−6.90833	−0.284411
$591$	53.4500	2.19864
$592$	−1.39445	−0.0573115
$593$	−16.4222	−0.674379	−0.337190	−	0.941437i	$-0.609476\pi$
$593$	−16.4222	−0.674379	−0.337190	+	0.941437i	$0.609476\pi$
$594$	1.60555	0.0658766
$595$	3.00000	0.122988
$596$	−14.6056	−0.598267
$597$	−27.8444	−1.13960
$598$	0	0
$599$	−33.6333	−1.37422	−0.687110	−	0.726554i	$-0.741121\pi$
$599$	−33.6333	−1.37422	−0.687110	+	0.726554i	$0.741121\pi$
$600$	−2.30278	−0.0940104
$601$	38.9083	1.58710	0.793552	−	0.608503i	$-0.208229\pi$
$601$	38.9083	1.58710	0.793552	+	0.608503i	$0.208229\pi$
$602$	2.30278	0.0938541
$603$	−9.21110	−0.375105
$604$	12.4222	0.505452
$605$	−1.00000	−0.0406558
$606$	−41.7250	−1.69496
$607$	24.6972	1.00243	0.501215	−	0.865323i	$-0.332887\pi$
$607$	24.6972	1.00243	0.501215	+	0.865323i	$0.332887\pi$
$608$	5.30278	0.215056
$609$	−31.8167	−1.28928
$610$	8.00000	0.323911
$611$	−19.0278	−0.769781
$612$	3.00000	0.121268
$613$	−10.7889	−0.435759	−0.217880	−	0.975976i	$-0.569914\pi$
$613$	−10.7889	−0.435759	−0.217880	+	0.975976i	$0.569914\pi$
$614$	−24.3028	−0.980780
$615$	13.8167	0.557141
$616$	2.30278	0.0927815
$617$	−21.6333	−0.870924	−0.435462	−	0.900207i	$-0.643415\pi$
$617$	−21.6333	−0.870924	−0.435462	+	0.900207i	$0.643415\pi$
$618$	0.211103	0.00849179
$619$	21.5416	0.865831	0.432916	−	0.901434i	$-0.357485\pi$
$619$	21.5416	0.865831	0.432916	+	0.901434i	$0.357485\pi$
$620$	4.00000	0.160644
$621$	0	0
$622$	−2.60555	−0.104473
$623$	−13.8167	−0.553553
$624$	4.60555	0.184370
$625$	1.00000	0.0400000
$626$	9.72498	0.388688
$627$	−12.2111	−0.487664
$628$	−4.00000	−0.159617
$629$	−1.81665	−0.0724347
$630$	−5.30278	−0.211268
$631$	29.5139	1.17493	0.587464	−	0.809250i	$-0.300126\pi$
$631$	29.5139	1.17493	0.587464	+	0.809250i	$0.300126\pi$
$632$	−6.30278	−0.250711
$633$	−46.7527	−1.85825
$634$	8.48612	0.337027
$635$	8.42221	0.334225
$636$	−9.00000	−0.356873
$637$	−3.39445	−0.134493
$638$	−6.00000	−0.237542
$639$	−29.7250	−1.17590
$640$	1.00000	0.0395285
$641$	19.5778	0.773276	0.386638	−	0.922231i	$-0.373636\pi$
$641$	19.5778	0.773276	0.386638	+	0.922231i	$0.373636\pi$
$642$	−3.00000	−0.118401
$643$	11.6333	0.458773	0.229386	−	0.973335i	$-0.426328\pi$
$643$	11.6333	0.458773	0.229386	+	0.973335i	$0.426328\pi$
$644$	0	0
$645$	−2.30278	−0.0906717
$646$	6.90833	0.271804
$647$	33.3944	1.31287	0.656436	−	0.754382i	$-0.272063\pi$
$647$	33.3944	1.31287	0.656436	+	0.754382i	$0.272063\pi$
$648$	10.6056	0.416625
$649$	−6.90833	−0.271176
$650$	−2.00000	−0.0784465
$651$	21.2111	0.831329
$652$	−4.51388	−0.176777
$653$	32.8444	1.28530	0.642651	−	0.766159i	$-0.277835\pi$
$653$	32.8444	1.28530	0.642651	+	0.766159i	$0.277835\pi$
$654$	14.0278	0.548529
$655$	17.2111	0.672493
$656$	−6.00000	−0.234261
$657$	16.6056	0.647844
$658$	−21.9083	−0.854076
$659$	−19.8167	−0.771947	−0.385974	−	0.922510i	$-0.626134\pi$
$659$	−19.8167	−0.771947	−0.385974	+	0.922510i	$0.626134\pi$
$660$	−2.30278	−0.0896354
$661$	9.81665	0.381824	0.190912	−	0.981607i	$-0.438856\pi$
$661$	9.81665	0.381824	0.190912	+	0.981607i	$0.438856\pi$
$662$	10.0000	0.388661
$663$	6.00000	0.233021
$664$	4.30278	0.166980
$665$	−12.2111	−0.473526
$666$	3.21110	0.124428
$667$	0	0
$668$	−16.4222	−0.635394
$669$	−64.4777	−2.49285
$670$	−4.00000	−0.154533
$671$	8.00000	0.308837
$672$	5.30278	0.204559
$673$	−38.6611	−1.49027	−0.745137	−	0.666911i	$-0.767616\pi$
$673$	−38.6611	−1.49027	−0.745137	+	0.666911i	$0.767616\pi$
$674$	22.5139	0.867202
$675$	−1.60555	−0.0617977
$676$	−9.00000	−0.346154
$677$	43.6972	1.67942	0.839710	−	0.543035i	$-0.182725\pi$
$677$	43.6972	1.67942	0.839710	+	0.543035i	$0.182725\pi$
$678$	−28.8167	−1.10670
$679$	−12.4222	−0.476720
$680$	1.30278	0.0499592
$681$	−6.00000	−0.229920
$682$	4.00000	0.153168
$683$	−28.1833	−1.07841	−0.539203	−	0.842176i	$-0.681274\pi$
$683$	−28.1833	−1.07841	−0.539203	+	0.842176i	$0.681274\pi$
$684$	−12.2111	−0.466903
$685$	21.6333	0.826566
$686$	−20.0278	−0.764663
$687$	34.6056	1.32028
$688$	1.00000	0.0381246
$689$	−7.81665	−0.297791
$690$	0	0
$691$	−45.4500	−1.72900	−0.864499	−	0.502635i	$-0.832364\pi$
$691$	−45.4500	−1.72900	−0.864499	+	0.502635i	$0.832364\pi$
$692$	12.0000	0.456172
$693$	−5.30278	−0.201436
$694$	−7.81665	−0.296716
$695$	15.2111	0.576990
$696$	−13.8167	−0.523719
$697$	−7.81665	−0.296077
$698$	10.0000	0.378506
$699$	9.63331	0.364365
$700$	−2.30278	−0.0870367
$701$	−25.5416	−0.964694	−0.482347	−	0.875980i	$-0.660216\pi$
$701$	−25.5416	−0.964694	−0.482347	+	0.875980i	$0.660216\pi$
$702$	3.21110	0.121195
$703$	7.39445	0.278887
$704$	1.00000	0.0376889
$705$	21.9083	0.825115
$706$	−16.4222	−0.618058
$707$	−41.7250	−1.56923
$708$	−15.9083	−0.597872
$709$	−10.7889	−0.405186	−0.202593	−	0.979263i	$-0.564937\pi$
$709$	−10.7889	−0.405186	−0.202593	+	0.979263i	$0.564937\pi$
$710$	−12.9083	−0.484441
$711$	14.5139	0.544313
$712$	−6.00000	−0.224860
$713$	0	0
$714$	6.90833	0.258538
$715$	−2.00000	−0.0747958
$716$	19.8167	0.740583
$717$	46.8167	1.74840
$718$	−32.8444	−1.22574
$719$	0.788897	0.0294209	0.0147105	−	0.999892i	$-0.495317\pi$
$719$	0.788897	0.0294209	0.0147105	+	0.999892i	$0.495317\pi$
$720$	−2.30278	−0.0858194
$721$	0.211103	0.00786187
$722$	−9.11943	−0.339390
$723$	−37.1194	−1.38049
$724$	−26.4222	−0.981974
$725$	6.00000	0.222834
$726$	−2.30278	−0.0854640
$727$	26.0000	0.964287	0.482143	−	0.876092i	$-0.339858\pi$
$727$	26.0000	0.964287	0.482143	+	0.876092i	$0.339858\pi$
$728$	4.60555	0.170693
$729$	−13.3305	−0.493723
$730$	7.21110	0.266895
$731$	1.30278	0.0481849
$732$	18.4222	0.680904
$733$	25.7250	0.950174	0.475087	−	0.879939i	$-0.342417\pi$
$733$	25.7250	0.950174	0.475087	+	0.879939i	$0.342417\pi$
$734$	7.90833	0.291902
$735$	3.90833	0.144161
$736$	0	0
$737$	−4.00000	−0.147342
$738$	13.8167	0.508598
$739$	−17.1472	−0.630769	−0.315385	−	0.948964i	$-0.602134\pi$
$739$	−17.1472	−0.630769	−0.315385	+	0.948964i	$0.602134\pi$
$740$	1.39445	0.0512610
$741$	−24.4222	−0.897172
$742$	−9.00000	−0.330400
$743$	27.7527	1.01815	0.509075	−	0.860722i	$-0.329988\pi$
$743$	27.7527	1.01815	0.509075	+	0.860722i	$0.329988\pi$
$744$	9.21110	0.337695
$745$	14.6056	0.535106
$746$	32.5416	1.19143
$747$	−9.90833	−0.362527
$748$	1.30278	0.0476342
$749$	−3.00000	−0.109618
$750$	2.30278	0.0840855
$751$	−15.0917	−0.550703	−0.275351	−	0.961344i	$-0.588794\pi$
$751$	−15.0917	−0.550703	−0.275351	+	0.961344i	$0.588794\pi$
$752$	−9.51388	−0.346935
$753$	−1.18335	−0.0431235
$754$	−12.0000	−0.437014
$755$	−12.4222	−0.452090
$756$	3.69722	0.134467
$757$	33.0278	1.20041	0.600207	−	0.799845i	$-0.295085\pi$
$757$	33.0278	1.20041	0.600207	+	0.799845i	$0.295085\pi$
$758$	9.33053	0.338900
$759$	0	0
$760$	−5.30278	−0.192352
$761$	42.0000	1.52250	0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000	1.52250	0.761249	+	0.648459i	$0.224586\pi$
$762$	19.3944	0.702587
$763$	14.0278	0.507839
$764$	−23.7250	−0.858340
$765$	−3.00000	−0.108465
$766$	−23.2111	−0.838651
$767$	−13.8167	−0.498890
$768$	2.30278	0.0830943
$769$	−16.2389	−0.585588	−0.292794	−	0.956176i	$-0.594585\pi$
$769$	−16.2389	−0.585588	−0.292794	+	0.956176i	$0.594585\pi$
$770$	−2.30278	−0.0829863
$771$	34.8167	1.25389
$772$	−9.09167	−0.327216
$773$	35.4500	1.27505	0.637523	−	0.770431i	$-0.279959\pi$
$773$	35.4500	1.27505	0.637523	+	0.770431i	$0.279959\pi$
$774$	−2.30278	−0.0827716
$775$	−4.00000	−0.143684
$776$	−5.39445	−0.193649
$777$	7.39445	0.265274
$778$	−30.9083	−1.10812
$779$	31.8167	1.13995
$780$	−4.60555	−0.164905
$781$	−12.9083	−0.461896
$782$	0	0
$783$	−9.63331	−0.344266
$784$	−1.69722	−0.0606152
$785$	4.00000	0.142766
$786$	39.6333	1.41367
$787$	35.3583	1.26039	0.630193	−	0.776438i	$-0.282976\pi$
$787$	35.3583	1.26039	0.630193	+	0.776438i	$0.282976\pi$
$788$	23.2111	0.826861
$789$	19.1833	0.682945
$790$	6.30278	0.224243
$791$	−28.8167	−1.02460
$792$	−2.30278	−0.0818256
$793$	16.0000	0.568177
$794$	−18.5416	−0.658018
$795$	9.00000	0.319197
$796$	−12.0917	−0.428578
$797$	−18.9083	−0.669767	−0.334884	−	0.942259i	$-0.608697\pi$
$797$	−18.9083	−0.669767	−0.334884	+	0.942259i	$0.608697\pi$
$798$	−28.1194	−0.995417
$799$	−12.3944	−0.438484
$800$	−1.00000	−0.0353553
$801$	13.8167	0.488187
$802$	−25.5416	−0.901906
$803$	7.21110	0.254474
$804$	−9.21110	−0.324851
$805$	0	0
$806$	8.00000	0.281788
$807$	0	0
$808$	−18.1194	−0.637439
$809$	−7.81665	−0.274819	−0.137409	−	0.990514i	$-0.543878\pi$
$809$	−7.81665	−0.274819	−0.137409	+	0.990514i	$0.543878\pi$
$810$	−10.6056	−0.372641
$811$	26.1194	0.917177	0.458589	−	0.888649i	$-0.348355\pi$
$811$	26.1194	0.917177	0.458589	+	0.888649i	$0.348355\pi$
$812$	−13.8167	−0.484869
$813$	−60.8444	−2.13391
$814$	1.39445	0.0488754
$815$	4.51388	0.158114
$816$	3.00000	0.105021
$817$	−5.30278	−0.185521
$818$	6.88057	0.240574
$819$	−10.6056	−0.370588
$820$	6.00000	0.209529
$821$	−14.7250	−0.513905	−0.256953	−	0.966424i	$-0.582718\pi$
$821$	−14.7250	−0.513905	−0.256953	+	0.966424i	$0.582718\pi$
$822$	49.8167	1.73756
$823$	34.0555	1.18710	0.593550	−	0.804797i	$-0.297726\pi$
$823$	34.0555	1.18710	0.593550	+	0.804797i	$0.297726\pi$
$824$	0.0916731	0.00319358
$825$	2.30278	0.0801724
$826$	−15.9083	−0.553521
$827$	−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	$0.701044\pi$
$830$	−4.30278	−0.149352
$831$	41.2389	1.43056
$832$	2.00000	0.0693375
$833$	−2.21110	−0.0766102
$834$	35.0278	1.21291
$835$	16.4222	0.568314
$836$	−5.30278	−0.183400
$837$	6.42221	0.221984
$838$	−9.63331	−0.332777
$839$	12.0000	0.414286	0.207143	−	0.978311i	$-0.433583\pi$
$839$	12.0000	0.414286	0.207143	+	0.978311i	$0.433583\pi$
$840$	−5.30278	−0.182963
$841$	7.00000	0.241379
$842$	−26.5139	−0.913729
$843$	−41.4500	−1.42761
$844$	−20.3028	−0.698850
$845$	9.00000	0.309609
$846$	21.9083	0.753224
$847$	−2.30278	−0.0791243
$848$	−3.90833	−0.134212
$849$	−21.8444	−0.749698
$850$	−1.30278	−0.0446848
$851$	0	0
$852$	−29.7250	−1.01836
$853$	17.3944	0.595575	0.297787	−	0.954632i	$-0.403751\pi$
$853$	17.3944	0.595575	0.297787	+	0.954632i	$0.403751\pi$
$854$	18.4222	0.630395
$855$	12.2111	0.417611
$856$	−1.30278	−0.0445280
$857$	−17.0917	−0.583840	−0.291920	−	0.956443i	$-0.594294\pi$
$857$	−17.0917	−0.583840	−0.291920	+	0.956443i	$0.594294\pi$
$858$	−4.60555	−0.157231
$859$	22.8444	0.779441	0.389721	−	0.920933i	$-0.372572\pi$
$859$	22.8444	0.779441	0.389721	+	0.920933i	$0.372572\pi$
$860$	−1.00000	−0.0340997
$861$	31.8167	1.08431
$862$	3.51388	0.119683
$863$	−11.2111	−0.381630	−0.190815	−	0.981626i	$-0.561113\pi$
$863$	−11.2111	−0.381630	−0.190815	+	0.981626i	$0.561113\pi$
$864$	1.60555	0.0546220
$865$	−12.0000	−0.408012
$866$	8.42221	0.286198
$867$	−35.2389	−1.19677
$868$	9.21110	0.312645
$869$	6.30278	0.213807
$870$	13.8167	0.468428
$871$	−8.00000	−0.271070
$872$	6.09167	0.206290
$873$	12.4222	0.420428
$874$	0	0
$875$	2.30278	0.0778480
$876$	16.6056	0.561050
$877$	27.5778	0.931236	0.465618	−	0.884986i	$-0.345832\pi$
$877$	27.5778	0.931236	0.465618	+	0.884986i	$0.345832\pi$
$878$	−7.48612	−0.252644
$879$	18.0000	0.607125
$880$	−1.00000	−0.0337100
$881$	−21.7527	−0.732868	−0.366434	−	0.930444i	$-0.619422\pi$
$881$	−21.7527	−0.732868	−0.366434	+	0.930444i	$0.619422\pi$
$882$	3.90833	0.131600
$883$	−10.2389	−0.344565	−0.172283	−	0.985048i	$-0.555114\pi$
$883$	−10.2389	−0.344565	−0.172283	+	0.985048i	$0.555114\pi$
$884$	2.60555	0.0876342
$885$	15.9083	0.534753
$886$	−4.18335	−0.140542
$887$	11.4861	0.385666	0.192833	−	0.981232i	$-0.438232\pi$
$887$	11.4861	0.385666	0.192833	+	0.981232i	$0.438232\pi$
$888$	3.21110	0.107758
$889$	19.3944	0.650469
$890$	6.00000	0.201120
$891$	−10.6056	−0.355299
$892$	−28.0000	−0.937509
$893$	50.4500	1.68824
$894$	33.6333	1.12487
$895$	−19.8167	−0.662398
$896$	2.30278	0.0769303
$897$	0	0
$898$	17.2111	0.574342
$899$	−24.0000	−0.800445
$900$	2.30278	0.0767592
$901$	−5.09167	−0.169628
$902$	6.00000	0.199778
$903$	−5.30278	−0.176465
$904$	−12.5139	−0.416205
$905$	26.4222	0.878304
$906$	−28.6056	−0.950356
$907$	−33.4500	−1.11069	−0.555344	−	0.831621i	$-0.687413\pi$
$907$	−33.4500	−1.11069	−0.555344	+	0.831621i	$0.687413\pi$
$908$	−2.60555	−0.0864683
$909$	41.7250	1.38393
$910$	−4.60555	−0.152673
$911$	−35.7250	−1.18362	−0.591811	−	0.806077i	$-0.701587\pi$
$911$	−35.7250	−1.18362	−0.591811	+	0.806077i	$0.701587\pi$
$912$	−12.2111	−0.404350
$913$	−4.30278	−0.142401
$914$	32.4222	1.07243
$915$	−18.4222	−0.609019
$916$	15.0278	0.496531
$917$	39.6333	1.30881
$918$	2.09167	0.0690355
$919$	−53.9361	−1.77919	−0.889594	−	0.456753i	$-0.849012\pi$
$919$	−53.9361	−1.77919	−0.889594	+	0.456753i	$0.849012\pi$
$920$	0	0
$921$	55.9638	1.84407
$922$	−20.3305	−0.669550
$923$	−25.8167	−0.849766
$924$	−5.30278	−0.174449
$925$	−1.39445	−0.0458492
$926$	−9.02776	−0.296670
$927$	−0.211103	−0.00693352
$928$	−6.00000	−0.196960
$929$	−6.78890	−0.222737	−0.111368	−	0.993779i	$-0.535523\pi$
$929$	−6.78890	−0.222737	−0.111368	+	0.993779i	$0.535523\pi$
$930$	−9.21110	−0.302044
$931$	9.00000	0.294963
$932$	4.18335	0.137030
$933$	6.00000	0.196431
$934$	4.69722	0.153698
$935$	−1.30278	−0.0426053
$936$	−4.60555	−0.150537
$937$	−42.0555	−1.37389	−0.686947	−	0.726708i	$-0.741049\pi$
$937$	−42.0555	−1.37389	−0.686947	+	0.726708i	$0.741049\pi$
$938$	−9.21110	−0.300753
$939$	−22.3944	−0.730815
$940$	9.51388	0.310308
$941$	−3.11943	−0.101690	−0.0508452	−	0.998707i	$-0.516192\pi$
$941$	−3.11943	−0.101690	−0.0508452	+	0.998707i	$0.516192\pi$
$942$	9.21110	0.300114
$943$	0	0
$944$	−6.90833	−0.224847
$945$	−3.69722	−0.120271
$946$	−1.00000	−0.0325128
$947$	0	0		−	1.00000i	$-0.5\pi$
$947$	0	0			1.00000i	$0.5\pi$
$948$	14.5139	0.471389
$949$	14.4222	0.468165
$950$	5.30278	0.172045
$951$	−19.5416	−0.633681
$952$	3.00000	0.0972306
$953$	36.2389	1.17389	0.586946	−	0.809626i	$-0.300330\pi$
$953$	36.2389	1.17389	0.586946	+	0.809626i	$0.300330\pi$
$954$	9.00000	0.291386
$955$	23.7250	0.767722
$956$	20.3305	0.657536
$957$	13.8167	0.446629
$958$	−20.8444	−0.673452
$959$	49.8167	1.60866
$960$	−2.30278	−0.0743218
$961$	−15.0000	−0.483871
$962$	2.78890	0.0899177
$963$	3.00000	0.0966736
$964$	−16.1194	−0.519172
$965$	9.09167	0.292671
$966$	0	0
$967$	6.18335	0.198843	0.0994215	−	0.995045i	$-0.468301\pi$
$967$	6.18335	0.198843	0.0994215	+	0.995045i	$0.468301\pi$
$968$	−1.00000	−0.0321412
$969$	−15.9083	−0.511049
$970$	5.39445	0.173205
$971$	41.1749	1.32137	0.660683	−	0.750665i	$-0.270267\pi$
$971$	41.1749	1.32137	0.660683	+	0.750665i	$0.270267\pi$
$972$	−19.6056	−0.628848
$973$	35.0278	1.12294
$974$	−19.3305	−0.619390
$975$	4.60555	0.147496
$976$	8.00000	0.256074
$977$	−3.63331	−0.116240	−0.0581199	−	0.998310i	$-0.518511\pi$
$977$	−3.63331	−0.116240	−0.0581199	+	0.998310i	$0.518511\pi$
$978$	10.3944	0.332378
$979$	6.00000	0.191761
$980$	1.69722	0.0542158
$981$	−14.0278	−0.447872
$982$	9.27502	0.295978
$983$	−15.6333	−0.498625	−0.249313	−	0.968423i	$-0.580205\pi$
$983$	−15.6333	−0.498625	−0.249313	+	0.968423i	$0.580205\pi$
$984$	13.8167	0.440459
$985$	−23.2111	−0.739567
$986$	−7.81665	−0.248933
$987$	50.4500	1.60584
$988$	−10.6056	−0.337408
$989$	0	0
$990$	2.30278	0.0731870
$991$	−45.2111	−1.43618	−0.718089	−	0.695951i	$-0.754983\pi$
$991$	−45.2111	−1.43618	−0.718089	+	0.695951i	$0.754983\pi$
$992$	4.00000	0.127000
$993$	−23.0278	−0.730764
$994$	−29.7250	−0.942819
$995$	12.0917	0.383332
$996$	−9.90833	−0.313957
$997$	39.6972	1.25722	0.628612	−	0.777719i	$-0.283623\pi$
$997$	39.6972	1.25722	0.628612	+	0.777719i	$0.283623\pi$
$998$	−12.4222	−0.393218
$999$	2.23886	0.0708344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4730.2.a.o.1.2	✓	2

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} -2.30278 q^{7} -1.00000 q^{8} +2.30278 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.30278 q^{3} +1.00000 q^{4} -1.00000 q^{5} -2.30278 q^{6} -2.30278 q^{7} -1.00000 q^{8} +2.30278 q^{9} +1.00000 q^{10} +1.00000 q^{11} +2.30278 q^{12} +2.00000 q^{13} +2.30278 q^{14} -2.30278 q^{15} +1.00000 q^{16} +1.30278 q^{17} -2.30278 q^{18} -5.30278 q^{19} -1.00000 q^{20} -5.30278 q^{21} -1.00000 q^{22} -2.30278 q^{24} +1.00000 q^{25} -2.00000 q^{26} -1.60555 q^{27} -2.30278 q^{28} +6.00000 q^{29} +2.30278 q^{30} -4.00000 q^{31} -1.00000 q^{32} +2.30278 q^{33} -1.30278 q^{34} +2.30278 q^{35} +2.30278 q^{36} -1.39445 q^{37} +5.30278 q^{38} +4.60555 q^{39} +1.00000 q^{40} -6.00000 q^{41} +5.30278 q^{42} +1.00000 q^{43} +1.00000 q^{44} -2.30278 q^{45} -9.51388 q^{47} +2.30278 q^{48} -1.69722 q^{49} -1.00000 q^{50} +3.00000 q^{51} +2.00000 q^{52} -3.90833 q^{53} +1.60555 q^{54} -1.00000 q^{55} +2.30278 q^{56} -12.2111 q^{57} -6.00000 q^{58} -6.90833 q^{59} -2.30278 q^{60} +8.00000 q^{61} +4.00000 q^{62} -5.30278 q^{63} +1.00000 q^{64} -2.00000 q^{65} -2.30278 q^{66} -4.00000 q^{67} +1.30278 q^{68} -2.30278 q^{70} -12.9083 q^{71} -2.30278 q^{72} +7.21110 q^{73} +1.39445 q^{74} +2.30278 q^{75} -5.30278 q^{76} -2.30278 q^{77} -4.60555 q^{78} +6.30278 q^{79} -1.00000 q^{80} -10.6056 q^{81} +6.00000 q^{82} -4.30278 q^{83} -5.30278 q^{84} -1.30278 q^{85} -1.00000 q^{86} +13.8167 q^{87} -1.00000 q^{88} +6.00000 q^{89} +2.30278 q^{90} -4.60555 q^{91} -9.21110 q^{93} +9.51388 q^{94} +5.30278 q^{95} -2.30278 q^{96} +5.39445 q^{97} +1.69722 q^{98} +2.30278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + q^{3} + 2 q^{4} - 2 q^{5} - q^{6} - q^{7} - 2 q^{8} + q^{9}+O(q^{10}) \) 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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Representations

Groups

Database

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