LMFDB - Embedded newform 4830.2.a.bz.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4830,2,Mod(1,4830)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4830, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("4830.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4830.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:	$38.5677441763$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.148.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 3x + 1 $ x^3 - x^2 - 3*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.48119$ of defining polynomial
Character	$\chi$	$=$	4830.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -6.31265 q^{11} -1.00000 q^{12} +2.96239 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.57452 q^{17} +1.00000 q^{18} -5.35026 q^{19} -1.00000 q^{20} -1.00000 q^{21} -6.31265 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.96239 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.61213 q^{29} +1.00000 q^{30} +5.35026 q^{31} +1.00000 q^{32} +6.31265 q^{33} -6.57452 q^{34} -1.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -5.35026 q^{38} -2.96239 q^{39} -1.00000 q^{40} +1.22425 q^{41} -1.00000 q^{42} +10.3127 q^{43} -6.31265 q^{44} -1.00000 q^{45} +1.00000 q^{46} +5.35026 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +6.57452 q^{51} +2.96239 q^{52} -1.22425 q^{53} -1.00000 q^{54} +6.31265 q^{55} +1.00000 q^{56} +5.35026 q^{57} +5.61213 q^{58} +10.7005 q^{59} +1.00000 q^{60} +12.7005 q^{61} +5.35026 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.96239 q^{65} +6.31265 q^{66} +10.3127 q^{67} -6.57452 q^{68} -1.00000 q^{69} -1.00000 q^{70} -0.387873 q^{71} +1.00000 q^{72} -15.4010 q^{73} +2.00000 q^{74} -1.00000 q^{75} -5.35026 q^{76} -6.31265 q^{77} -2.96239 q^{78} -6.70052 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.22425 q^{82} +7.27504 q^{83} -1.00000 q^{84} +6.57452 q^{85} +10.3127 q^{86} -5.61213 q^{87} -6.31265 q^{88} -15.5877 q^{89} -1.00000 q^{90} +2.96239 q^{91} +1.00000 q^{92} -5.35026 q^{93} +5.35026 q^{94} +5.35026 q^{95} -1.00000 q^{96} +2.96239 q^{97} +1.00000 q^{98} -6.31265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 2 q^{11} - 3 q^{12} - 2 q^{13} + 3 q^{14} + 3 q^{15} + 3 q^{16} - 8 q^{17} + 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{21} + 2 q^{22} + 3 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} + 3 q^{28} + 16 q^{29} + 3 q^{30} + 6 q^{31} + 3 q^{32} - 2 q^{33} - 8 q^{34} - 3 q^{35} + 3 q^{36} + 6 q^{37} - 6 q^{38} + 2 q^{39} - 3 q^{40} + 2 q^{41} - 3 q^{42} + 10 q^{43} + 2 q^{44} - 3 q^{45} + 3 q^{46} + 6 q^{47} - 3 q^{48} + 3 q^{49} + 3 q^{50} + 8 q^{51} - 2 q^{52} - 2 q^{53} - 3 q^{54} - 2 q^{55} + 3 q^{56} + 6 q^{57} + 16 q^{58} + 12 q^{59} + 3 q^{60} + 18 q^{61} + 6 q^{62} + 3 q^{63} + 3 q^{64} + 2 q^{65} - 2 q^{66} + 10 q^{67} - 8 q^{68} - 3 q^{69} - 3 q^{70} - 2 q^{71} + 3 q^{72} - 6 q^{73} + 6 q^{74} - 3 q^{75} - 6 q^{76} + 2 q^{77} + 2 q^{78} - 3 q^{80} + 3 q^{81} + 2 q^{82} - 10 q^{83} - 3 q^{84} + 8 q^{85} + 10 q^{86} - 16 q^{87} + 2 q^{88} + 6 q^{89} - 3 q^{90} - 2 q^{91} + 3 q^{92} - 6 q^{93} + 6 q^{94} + 6 q^{95} - 3 q^{96} - 2 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 2 * q^11 - 3 * q^12 - 2 * q^13 + 3 * q^14 + 3 * q^15 + 3 * q^16 - 8 * q^17 + 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^21 + 2 * q^22 + 3 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 + 3 * q^28 + 16 * q^29 + 3 * q^30 + 6 * q^31 + 3 * q^32 - 2 * q^33 - 8 * q^34 - 3 * q^35 + 3 * q^36 + 6 * q^37 - 6 * q^38 + 2 * q^39 - 3 * q^40 + 2 * q^41 - 3 * q^42 + 10 * q^43 + 2 * q^44 - 3 * q^45 + 3 * q^46 + 6 * q^47 - 3 * q^48 + 3 * q^49 + 3 * q^50 + 8 * q^51 - 2 * q^52 - 2 * q^53 - 3 * q^54 - 2 * q^55 + 3 * q^56 + 6 * q^57 + 16 * q^58 + 12 * q^59 + 3 * q^60 + 18 * q^61 + 6 * q^62 + 3 * q^63 + 3 * q^64 + 2 * q^65 - 2 * q^66 + 10 * q^67 - 8 * q^68 - 3 * q^69 - 3 * q^70 - 2 * q^71 + 3 * q^72 - 6 * q^73 + 6 * q^74 - 3 * q^75 - 6 * q^76 + 2 * q^77 + 2 * q^78 - 3 * q^80 + 3 * q^81 + 2 * q^82 - 10 * q^83 - 3 * q^84 + 8 * q^85 + 10 * q^86 - 16 * q^87 + 2 * q^88 + 6 * q^89 - 3 * q^90 - 2 * q^91 + 3 * q^92 - 6 * q^93 + 6 * q^94 + 6 * q^95 - 3 * q^96 - 2 * q^97 + 3 * q^98 + 2 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−1.00000	−0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	−1.00000	−0.316228
$11$	−6.31265	−1.90334	−0.951668	−	0.307129i	$-0.900632\pi$
$11$	−6.31265	−1.90334	−0.951668	+	0.307129i	$0.900632\pi$
$12$	−1.00000	−0.288675
$13$	2.96239	0.821619	0.410809	−	0.911721i	$-0.365246\pi$
$13$	2.96239	0.821619	0.410809	+	0.911721i	$0.365246\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	−6.57452	−1.59455	−0.797277	−	0.603613i	$-0.793727\pi$
$17$	−6.57452	−1.59455	−0.797277	+	0.603613i	$0.793727\pi$
$18$	1.00000	0.235702
$19$	−5.35026	−1.22743	−0.613717	−	0.789526i	$-0.710326\pi$
$19$	−5.35026	−1.22743	−0.613717	+	0.789526i	$0.710326\pi$
$20$	−1.00000	−0.223607
$21$	−1.00000	−0.218218
$22$	−6.31265	−1.34586
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	2.96239	0.580972
$27$	−1.00000	−0.192450
$28$	1.00000	0.188982
$29$	5.61213	1.04215	0.521073	−	0.853512i	$-0.325532\pi$
$29$	5.61213	1.04215	0.521073	+	0.853512i	$0.325532\pi$
$30$	1.00000	0.182574
$31$	5.35026	0.960935	0.480468	−	0.877012i	$-0.340467\pi$
$31$	5.35026	0.960935	0.480468	+	0.877012i	$0.340467\pi$
$32$	1.00000	0.176777
$33$	6.31265	1.09889
$34$	−6.57452	−1.12752
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	2.00000	0.328798	0.164399	−	0.986394i	$-0.447432\pi$
$37$	2.00000	0.328798	0.164399	+	0.986394i	$0.447432\pi$
$38$	−5.35026	−0.867927
$39$	−2.96239	−0.474362
$40$	−1.00000	−0.158114
$41$	1.22425	0.191196	0.0955982	−	0.995420i	$-0.469524\pi$
$41$	1.22425	0.191196	0.0955982	+	0.995420i	$0.469524\pi$
$42$	−1.00000	−0.154303
$43$	10.3127	1.57266	0.786332	−	0.617804i	$-0.211977\pi$
$43$	10.3127	1.57266	0.786332	+	0.617804i	$0.211977\pi$
$44$	−6.31265	−0.951668
$45$	−1.00000	−0.149071
$46$	1.00000	0.147442
$47$	5.35026	0.780416	0.390208	−	0.920727i	$-0.372403\pi$
$47$	5.35026	0.780416	0.390208	+	0.920727i	$0.372403\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	6.57452	0.920616
$52$	2.96239	0.410809
$53$	−1.22425	−0.168164	−0.0840821	−	0.996459i	$-0.526796\pi$
$53$	−1.22425	−0.168164	−0.0840821	+	0.996459i	$0.526796\pi$
$54$	−1.00000	−0.136083
$55$	6.31265	0.851198
$56$	1.00000	0.133631
$57$	5.35026	0.708659
$58$	5.61213	0.736908
$59$	10.7005	1.39309	0.696545	−	0.717513i	$-0.254720\pi$
$59$	10.7005	1.39309	0.696545	+	0.717513i	$0.254720\pi$
$60$	1.00000	0.129099
$61$	12.7005	1.62614	0.813068	−	0.582169i	$-0.197796\pi$
$61$	12.7005	1.62614	0.813068	+	0.582169i	$0.197796\pi$
$62$	5.35026	0.679484
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	−2.96239	−0.367439
$66$	6.31265	0.777034
$67$	10.3127	1.25989	0.629945	−	0.776639i	$-0.283077\pi$
$67$	10.3127	1.25989	0.629945	+	0.776639i	$0.283077\pi$
$68$	−6.57452	−0.797277
$69$	−1.00000	−0.120386
$70$	−1.00000	−0.119523
$71$	−0.387873	−0.0460321	−0.0230160	−	0.999735i	$-0.507327\pi$
$71$	−0.387873	−0.0460321	−0.0230160	+	0.999735i	$0.507327\pi$
$72$	1.00000	0.117851
$73$	−15.4010	−1.80256	−0.901278	−	0.433241i	$-0.857370\pi$
$73$	−15.4010	−1.80256	−0.901278	+	0.433241i	$0.857370\pi$
$74$	2.00000	0.232495
$75$	−1.00000	−0.115470
$76$	−5.35026	−0.613717
$77$	−6.31265	−0.719393
$78$	−2.96239	−0.335424
$79$	−6.70052	−0.753868	−0.376934	−	0.926240i	$-0.623022\pi$
$79$	−6.70052	−0.753868	−0.376934	+	0.926240i	$0.623022\pi$
$80$	−1.00000	−0.111803
$81$	1.00000	0.111111
$82$	1.22425	0.135196
$83$	7.27504	0.798539	0.399270	−	0.916834i	$-0.369264\pi$
$83$	7.27504	0.798539	0.399270	+	0.916834i	$0.369264\pi$
$84$	−1.00000	−0.109109
$85$	6.57452	0.713106
$86$	10.3127	1.11204
$87$	−5.61213	−0.601683
$88$	−6.31265	−0.672931
$89$	−15.5877	−1.65229	−0.826146	−	0.563456i	$-0.809471\pi$
$89$	−15.5877	−1.65229	−0.826146	+	0.563456i	$0.809471\pi$
$90$	−1.00000	−0.105409
$91$	2.96239	0.310543
$92$	1.00000	0.104257
$93$	−5.35026	−0.554796
$94$	5.35026	0.551837
$95$	5.35026	0.548925
$96$	−1.00000	−0.102062
$97$	2.96239	0.300785	0.150392	−	0.988626i	$-0.451946\pi$
$97$	2.96239	0.300785	0.150392	+	0.988626i	$0.451946\pi$
$98$	1.00000	0.101015
$99$	−6.31265	−0.634445
$100$	1.00000	0.100000
$101$	−13.6629	−1.35951	−0.679755	−	0.733439i	$-0.737914\pi$
$101$	−13.6629	−1.35951	−0.679755	+	0.733439i	$0.737914\pi$
$102$	6.57452	0.650974
$103$	16.6253	1.63814	0.819070	−	0.573694i	$-0.194490\pi$
$103$	16.6253	1.63814	0.819070	+	0.573694i	$0.194490\pi$
$104$	2.96239	0.290486
$105$	1.00000	0.0975900
$106$	−1.22425	−0.118910
$107$	−5.92478	−0.572770	−0.286385	−	0.958115i	$-0.592454\pi$
$107$	−5.92478	−0.572770	−0.286385	+	0.958115i	$0.592454\pi$
$108$	−1.00000	−0.0962250
$109$	−9.84955	−0.943416	−0.471708	−	0.881755i	$-0.656362\pi$
$109$	−9.84955	−0.943416	−0.471708	+	0.881755i	$0.656362\pi$
$110$	6.31265	0.601888
$111$	−2.00000	−0.189832
$112$	1.00000	0.0944911
$113$	12.7005	1.19476	0.597382	−	0.801957i	$-0.296207\pi$
$113$	12.7005	1.19476	0.597382	+	0.801957i	$0.296207\pi$
$114$	5.35026	0.501098
$115$	−1.00000	−0.0932505
$116$	5.61213	0.521073
$117$	2.96239	0.273873
$118$	10.7005	0.985063
$119$	−6.57452	−0.602685
$120$	1.00000	0.0912871
$121$	28.8496	2.62269
$122$	12.7005	1.14985
$123$	−1.22425	−0.110387
$124$	5.35026	0.480468
$125$	−1.00000	−0.0894427
$126$	1.00000	0.0890871
$127$	14.3127	1.27004	0.635021	−	0.772495i	$-0.280991\pi$
$127$	14.3127	1.27004	0.635021	+	0.772495i	$0.280991\pi$
$128$	1.00000	0.0883883
$129$	−10.3127	−0.907978
$130$	−2.96239	−0.259819
$131$	−2.44851	−0.213927	−0.106964	−	0.994263i	$-0.534113\pi$
$131$	−2.44851	−0.213927	−0.106964	+	0.994263i	$0.534113\pi$
$132$	6.31265	0.549446
$133$	−5.35026	−0.463927
$134$	10.3127	0.890877
$135$	1.00000	0.0860663
$136$	−6.57452	−0.563760
$137$	2.00000	0.170872	0.0854358	−	0.996344i	$-0.472772\pi$
$137$	2.00000	0.170872	0.0854358	+	0.996344i	$0.472772\pi$
$138$	−1.00000	−0.0851257
$139$	13.9248	1.18108	0.590542	−	0.807007i	$-0.298914\pi$
$139$	13.9248	1.18108	0.590542	+	0.807007i	$0.298914\pi$
$140$	−1.00000	−0.0845154
$141$	−5.35026	−0.450573
$142$	−0.387873	−0.0325496
$143$	−18.7005	−1.56382
$144$	1.00000	0.0833333
$145$	−5.61213	−0.466062
$146$	−15.4010	−1.27460
$147$	−1.00000	−0.0824786
$148$	2.00000	0.164399
$149$	10.0000	0.819232	0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000	0.819232	0.409616	+	0.912258i	$0.365663\pi$
$150$	−1.00000	−0.0816497
$151$	9.92478	0.807667	0.403833	−	0.914833i	$-0.367678\pi$
$151$	9.92478	0.807667	0.403833	+	0.914833i	$0.367678\pi$
$152$	−5.35026	−0.433964
$153$	−6.57452	−0.531518
$154$	−6.31265	−0.508688
$155$	−5.35026	−0.429743
$156$	−2.96239	−0.237181
$157$	−14.6253	−1.16723	−0.583613	−	0.812032i	$-0.698361\pi$
$157$	−14.6253	−1.16723	−0.583613	+	0.812032i	$0.698361\pi$
$158$	−6.70052	−0.533065
$159$	1.22425	0.0970896
$160$	−1.00000	−0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	5.29948	0.415087	0.207544	−	0.978226i	$-0.433453\pi$
$163$	5.29948	0.415087	0.207544	+	0.978226i	$0.433453\pi$
$164$	1.22425	0.0955982
$165$	−6.31265	−0.491439
$166$	7.27504	0.564653
$167$	1.87399	0.145014	0.0725069	−	0.997368i	$-0.476900\pi$
$167$	1.87399	0.145014	0.0725069	+	0.997368i	$0.476900\pi$
$168$	−1.00000	−0.0771517
$169$	−4.22425	−0.324943
$170$	6.57452	0.504242
$171$	−5.35026	−0.409145
$172$	10.3127	0.786332
$173$	−18.0508	−1.37238	−0.686188	−	0.727424i	$-0.740717\pi$
$173$	−18.0508	−1.37238	−0.686188	+	0.727424i	$0.740717\pi$
$174$	−5.61213	−0.425454
$175$	1.00000	0.0755929
$176$	−6.31265	−0.475834
$177$	−10.7005	−0.804301
$178$	−15.5877	−1.16835
$179$	21.4010	1.59959	0.799795	−	0.600274i	$-0.204942\pi$
$179$	21.4010	1.59959	0.799795	+	0.600274i	$0.204942\pi$
$180$	−1.00000	−0.0745356
$181$	−7.14903	−0.531383	−0.265692	−	0.964058i	$-0.585600\pi$
$181$	−7.14903	−0.531383	−0.265692	+	0.964058i	$0.585600\pi$
$182$	2.96239	0.219587
$183$	−12.7005	−0.938850
$184$	1.00000	0.0737210
$185$	−2.00000	−0.147043
$186$	−5.35026	−0.392300
$187$	41.5026	3.03497
$188$	5.35026	0.390208
$189$	−1.00000	−0.0727393
$190$	5.35026	0.388149
$191$	−10.7005	−0.774263	−0.387131	−	0.922025i	$-0.626534\pi$
$191$	−10.7005	−0.774263	−0.387131	+	0.922025i	$0.626534\pi$
$192$	−1.00000	−0.0721688
$193$	8.70052	0.626277	0.313139	−	0.949707i	$-0.398620\pi$
$193$	8.70052	0.626277	0.313139	+	0.949707i	$0.398620\pi$
$194$	2.96239	0.212687
$195$	2.96239	0.212141
$196$	1.00000	0.0714286
$197$	16.7005	1.18986	0.594932	−	0.803776i	$-0.297179\pi$
$197$	16.7005	1.18986	0.594932	+	0.803776i	$0.297179\pi$
$198$	−6.31265	−0.448621
$199$	−0.625301	−0.0443264	−0.0221632	−	0.999754i	$-0.507055\pi$
$199$	−0.625301	−0.0443264	−0.0221632	+	0.999754i	$0.507055\pi$
$200$	1.00000	0.0707107
$201$	−10.3127	−0.727398
$202$	−13.6629	−0.961319
$203$	5.61213	0.393894
$204$	6.57452	0.460308
$205$	−1.22425	−0.0855056
$206$	16.6253	1.15834
$207$	1.00000	0.0695048
$208$	2.96239	0.205405
$209$	33.7743	2.33622
$210$	1.00000	0.0690066
$211$	−6.55008	−0.450926	−0.225463	−	0.974252i	$-0.572389\pi$
$211$	−6.55008	−0.450926	−0.225463	+	0.974252i	$0.572389\pi$
$212$	−1.22425	−0.0840821
$213$	0.387873	0.0265766
$214$	−5.92478	−0.405009
$215$	−10.3127	−0.703317
$216$	−1.00000	−0.0680414
$217$	5.35026	0.363199
$218$	−9.84955	−0.667096
$219$	15.4010	1.04071
$220$	6.31265	0.425599
$221$	−19.4763	−1.31012
$222$	−2.00000	−0.134231
$223$	2.26187	0.151466	0.0757328	−	0.997128i	$-0.475870\pi$
$223$	2.26187	0.151466	0.0757328	+	0.997128i	$0.475870\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	12.7005	0.844826
$227$	11.7988	0.783112	0.391556	−	0.920154i	$-0.371937\pi$
$227$	11.7988	0.783112	0.391556	+	0.920154i	$0.371937\pi$
$228$	5.35026	0.354330
$229$	17.2243	1.13821	0.569105	−	0.822265i	$-0.307290\pi$
$229$	17.2243	1.13821	0.569105	+	0.822265i	$0.307290\pi$
$230$	−1.00000	−0.0659380
$231$	6.31265	0.415342
$232$	5.61213	0.368454
$233$	9.84955	0.645266	0.322633	−	0.946524i	$-0.395432\pi$
$233$	9.84955	0.645266	0.322633	+	0.946524i	$0.395432\pi$
$234$	2.96239	0.193657
$235$	−5.35026	−0.349013
$236$	10.7005	0.696545
$237$	6.70052	0.435246
$238$	−6.57452	−0.426163
$239$	−0.387873	−0.0250894	−0.0125447	−	0.999921i	$-0.503993\pi$
$239$	−0.387873	−0.0250894	−0.0125447	+	0.999921i	$0.503993\pi$
$240$	1.00000	0.0645497
$241$	−6.57452	−0.423502	−0.211751	−	0.977324i	$-0.567917\pi$
$241$	−6.57452	−0.423502	−0.211751	+	0.977324i	$0.567917\pi$
$242$	28.8496	1.85452
$243$	−1.00000	−0.0641500
$244$	12.7005	0.813068
$245$	−1.00000	−0.0638877
$246$	−1.22425	−0.0780556
$247$	−15.8496	−1.00848
$248$	5.35026	0.339742
$249$	−7.27504	−0.461037
$250$	−1.00000	−0.0632456
$251$	−0.186642	−0.0117808	−0.00589038	−	0.999983i	$-0.501875\pi$
$251$	−0.186642	−0.0117808	−0.00589038	+	0.999983i	$0.501875\pi$
$252$	1.00000	0.0629941
$253$	−6.31265	−0.396873
$254$	14.3127	0.898056
$255$	−6.57452	−0.411712
$256$	1.00000	0.0625000
$257$	8.44851	0.527003	0.263502	−	0.964659i	$-0.415123\pi$
$257$	8.44851	0.527003	0.263502	+	0.964659i	$0.415123\pi$
$258$	−10.3127	−0.642038
$259$	2.00000	0.124274
$260$	−2.96239	−0.183720
$261$	5.61213	0.347382
$262$	−2.44851	−0.151269
$263$	28.4749	1.75583	0.877917	−	0.478812i	$-0.158932\pi$
$263$	28.4749	1.75583	0.877917	+	0.478812i	$0.158932\pi$
$264$	6.31265	0.388517
$265$	1.22425	0.0752053
$266$	−5.35026	−0.328046
$267$	15.5877	0.953951
$268$	10.3127	0.629945
$269$	26.8119	1.63475	0.817377	−	0.576104i	$-0.195428\pi$
$269$	26.8119	1.63475	0.817377	+	0.576104i	$0.195428\pi$
$270$	1.00000	0.0608581
$271$	5.35026	0.325005	0.162503	−	0.986708i	$-0.448043\pi$
$271$	5.35026	0.325005	0.162503	+	0.986708i	$0.448043\pi$
$272$	−6.57452	−0.398639
$273$	−2.96239	−0.179292
$274$	2.00000	0.120824
$275$	−6.31265	−0.380667
$276$	−1.00000	−0.0601929
$277$	4.31265	0.259122	0.129561	−	0.991571i	$-0.458643\pi$
$277$	4.31265	0.259122	0.129561	+	0.991571i	$0.458643\pi$
$278$	13.9248	0.835153
$279$	5.35026	0.320312
$280$	−1.00000	−0.0597614
$281$	5.08840	0.303548	0.151774	−	0.988415i	$-0.451501\pi$
$281$	5.08840	0.303548	0.151774	+	0.988415i	$0.451501\pi$
$282$	−5.35026	−0.318603
$283$	−8.43866	−0.501626	−0.250813	−	0.968036i	$-0.580698\pi$
$283$	−8.43866	−0.501626	−0.250813	+	0.968036i	$0.580698\pi$
$284$	−0.387873	−0.0230160
$285$	−5.35026	−0.316922
$286$	−18.7005	−1.10579
$287$	1.22425	0.0722654
$288$	1.00000	0.0589256
$289$	26.2243	1.54260
$290$	−5.61213	−0.329555
$291$	−2.96239	−0.173658
$292$	−15.4010	−0.901278
$293$	−7.92478	−0.462970	−0.231485	−	0.972838i	$-0.574358\pi$
$293$	−7.92478	−0.462970	−0.231485	+	0.972838i	$0.574358\pi$
$294$	−1.00000	−0.0583212
$295$	−10.7005	−0.623009
$296$	2.00000	0.116248
$297$	6.31265	0.366297
$298$	10.0000	0.579284
$299$	2.96239	0.171319
$300$	−1.00000	−0.0577350
$301$	10.3127	0.594411
$302$	9.92478	0.571107
$303$	13.6629	0.784914
$304$	−5.35026	−0.306859
$305$	−12.7005	−0.727230
$306$	−6.57452	−0.375840
$307$	−16.4749	−0.940270	−0.470135	−	0.882595i	$-0.655795\pi$
$307$	−16.4749	−0.940270	−0.470135	+	0.882595i	$0.655795\pi$
$308$	−6.31265	−0.359697
$309$	−16.6253	−0.945780
$310$	−5.35026	−0.303874
$311$	−8.18664	−0.464222	−0.232111	−	0.972689i	$-0.574563\pi$
$311$	−8.18664	−0.464222	−0.232111	+	0.972689i	$0.574563\pi$
$312$	−2.96239	−0.167712
$313$	−8.51388	−0.481233	−0.240617	−	0.970620i	$-0.577350\pi$
$313$	−8.51388	−0.481233	−0.240617	+	0.970620i	$0.577350\pi$
$314$	−14.6253	−0.825353
$315$	−1.00000	−0.0563436
$316$	−6.70052	−0.376934
$317$	1.47627	0.0829156	0.0414578	−	0.999140i	$-0.486800\pi$
$317$	1.47627	0.0829156	0.0414578	+	0.999140i	$0.486800\pi$
$318$	1.22425	0.0686527
$319$	−35.4274	−1.98355
$320$	−1.00000	−0.0559017
$321$	5.92478	0.330689
$322$	1.00000	0.0557278
$323$	35.1754	1.95721
$324$	1.00000	0.0555556
$325$	2.96239	0.164324
$326$	5.29948	0.293511
$327$	9.84955	0.544682
$328$	1.22425	0.0675981
$329$	5.35026	0.294969
$330$	−6.31265	−0.347500
$331$	−7.22425	−0.397081	−0.198540	−	0.980093i	$-0.563620\pi$
$331$	−7.22425	−0.397081	−0.198540	+	0.980093i	$0.563620\pi$
$332$	7.27504	0.399270
$333$	2.00000	0.109599
$334$	1.87399	0.102540
$335$	−10.3127	−0.563440
$336$	−1.00000	−0.0545545
$337$	−9.71370	−0.529139	−0.264569	−	0.964367i	$-0.585230\pi$
$337$	−9.71370	−0.529139	−0.264569	+	0.964367i	$0.585230\pi$
$338$	−4.22425	−0.229769
$339$	−12.7005	−0.689798
$340$	6.57452	0.356553
$341$	−33.7743	−1.82898
$342$	−5.35026	−0.289309
$343$	1.00000	0.0539949
$344$	10.3127	0.556021
$345$	1.00000	0.0538382
$346$	−18.0508	−0.970416
$347$	−5.92478	−0.318059	−0.159029	−	0.987274i	$-0.550836\pi$
$347$	−5.92478	−0.318059	−0.159029	+	0.987274i	$0.550836\pi$
$348$	−5.61213	−0.300842
$349$	19.3503	1.03580	0.517898	−	0.855442i	$-0.326715\pi$
$349$	19.3503	1.03580	0.517898	+	0.855442i	$0.326715\pi$
$350$	1.00000	0.0534522
$351$	−2.96239	−0.158121
$352$	−6.31265	−0.336465
$353$	−21.2243	−1.12965	−0.564827	−	0.825210i	$-0.691057\pi$
$353$	−21.2243	−1.12965	−0.564827	+	0.825210i	$0.691057\pi$
$354$	−10.7005	−0.568726
$355$	0.387873	0.0205862
$356$	−15.5877	−0.826146
$357$	6.57452	0.347960
$358$	21.4010	1.13108
$359$	−36.9986	−1.95271	−0.976355	−	0.216172i	$-0.930643\pi$
$359$	−36.9986	−1.95271	−0.976355	+	0.216172i	$0.930643\pi$
$360$	−1.00000	−0.0527046
$361$	9.62530	0.506595
$362$	−7.14903	−0.375745
$363$	−28.8496	−1.51421
$364$	2.96239	0.155271
$365$	15.4010	0.806128
$366$	−12.7005	−0.663867
$367$	−23.0738	−1.20444	−0.602221	−	0.798329i	$-0.705718\pi$
$367$	−23.0738	−1.20444	−0.602221	+	0.798329i	$0.705718\pi$
$368$	1.00000	0.0521286
$369$	1.22425	0.0637321
$370$	−2.00000	−0.103975
$371$	−1.22425	−0.0635601
$372$	−5.35026	−0.277398
$373$	−12.4485	−0.644559	−0.322280	−	0.946645i	$-0.604449\pi$
$373$	−12.4485	−0.644559	−0.322280	+	0.946645i	$0.604449\pi$
$374$	41.5026	2.14605
$375$	1.00000	0.0516398
$376$	5.35026	0.275919
$377$	16.6253	0.856247
$378$	−1.00000	−0.0514344
$379$	35.3258	1.81457	0.907283	−	0.420521i	$-0.138153\pi$
$379$	35.3258	1.81457	0.907283	+	0.420521i	$0.138153\pi$
$380$	5.35026	0.274463
$381$	−14.3127	−0.733259
$382$	−10.7005	−0.547486
$383$	23.8496	1.21866	0.609328	−	0.792919i	$-0.291439\pi$
$383$	23.8496	1.21866	0.609328	+	0.792919i	$0.291439\pi$
$384$	−1.00000	−0.0510310
$385$	6.31265	0.321722
$386$	8.70052	0.442845
$387$	10.3127	0.524221
$388$	2.96239	0.150392
$389$	−13.4763	−0.683274	−0.341637	−	0.939832i	$-0.610981\pi$
$389$	−13.4763	−0.683274	−0.341637	+	0.939832i	$0.610981\pi$
$390$	2.96239	0.150006
$391$	−6.57452	−0.332488
$392$	1.00000	0.0505076
$393$	2.44851	0.123511
$394$	16.7005	0.841360
$395$	6.70052	0.337140
$396$	−6.31265	−0.317223
$397$	−30.2882	−1.52012	−0.760061	−	0.649852i	$-0.774831\pi$
$397$	−30.2882	−1.52012	−0.760061	+	0.649852i	$0.774831\pi$
$398$	−0.625301	−0.0313435
$399$	5.35026	0.267848
$400$	1.00000	0.0500000
$401$	16.1622	0.807102	0.403551	−	0.914957i	$-0.367776\pi$
$401$	16.1622	0.807102	0.403551	+	0.914957i	$0.367776\pi$
$402$	−10.3127	−0.514348
$403$	15.8496	0.789523
$404$	−13.6629	−0.679755
$405$	−1.00000	−0.0496904
$406$	5.61213	0.278525
$407$	−12.6253	−0.625813
$408$	6.57452	0.325487
$409$	17.3258	0.856707	0.428353	−	0.903611i	$-0.359094\pi$
$409$	17.3258	0.856707	0.428353	+	0.903611i	$0.359094\pi$
$410$	−1.22425	−0.0604616
$411$	−2.00000	−0.0986527
$412$	16.6253	0.819070
$413$	10.7005	0.526538
$414$	1.00000	0.0491473
$415$	−7.27504	−0.357118
$416$	2.96239	0.145243
$417$	−13.9248	−0.681899
$418$	33.7743	1.65196
$419$	2.88717	0.141047	0.0705236	−	0.997510i	$-0.477533\pi$
$419$	2.88717	0.141047	0.0705236	+	0.997510i	$0.477533\pi$
$420$	1.00000	0.0487950
$421$	32.8021	1.59868	0.799338	−	0.600881i	$-0.205184\pi$
$421$	32.8021	1.59868	0.799338	+	0.600881i	$0.205184\pi$
$422$	−6.55008	−0.318853
$423$	5.35026	0.260139
$424$	−1.22425	−0.0594550
$425$	−6.57452	−0.318911
$426$	0.387873	0.0187925
$427$	12.7005	0.614621
$428$	−5.92478	−0.286385
$429$	18.7005	0.902870
$430$	−10.3127	−0.497320
$431$	0.252016	0.0121392	0.00606959	−	0.999982i	$-0.498068\pi$
$431$	0.252016	0.0121392	0.00606959	+	0.999982i	$0.498068\pi$
$432$	−1.00000	−0.0481125
$433$	−31.3357	−1.50590	−0.752948	−	0.658080i	$-0.771369\pi$
$433$	−31.3357	−1.50590	−0.752948	+	0.658080i	$0.771369\pi$
$434$	5.35026	0.256821
$435$	5.61213	0.269081
$436$	−9.84955	−0.471708
$437$	−5.35026	−0.255938
$438$	15.4010	0.735890
$439$	22.2276	1.06086	0.530432	−	0.847727i	$-0.322030\pi$
$439$	22.2276	1.06086	0.530432	+	0.847727i	$0.322030\pi$
$440$	6.31265	0.300944
$441$	1.00000	0.0476190
$442$	−19.4763	−0.926392
$443$	−13.9248	−0.661586	−0.330793	−	0.943703i	$-0.607316\pi$
$443$	−13.9248	−0.661586	−0.330793	+	0.943703i	$0.607316\pi$
$444$	−2.00000	−0.0949158
$445$	15.5877	0.738927
$446$	2.26187	0.107102
$447$	−10.0000	−0.472984
$448$	1.00000	0.0472456
$449$	−30.2228	−1.42630	−0.713152	−	0.701009i	$-0.752733\pi$
$449$	−30.2228	−1.42630	−0.713152	+	0.701009i	$0.752733\pi$
$450$	1.00000	0.0471405
$451$	−7.72829	−0.363911
$452$	12.7005	0.597382
$453$	−9.92478	−0.466307
$454$	11.7988	0.553744
$455$	−2.96239	−0.138879
$456$	5.35026	0.250549
$457$	−3.93937	−0.184276	−0.0921379	−	0.995746i	$-0.529370\pi$
$457$	−3.93937	−0.184276	−0.0921379	+	0.995746i	$0.529370\pi$
$458$	17.2243	0.804837
$459$	6.57452	0.306872
$460$	−1.00000	−0.0466252
$461$	−12.4123	−0.578099	−0.289049	−	0.957314i	$-0.593339\pi$
$461$	−12.4123	−0.578099	−0.289049	+	0.957314i	$0.593339\pi$
$462$	6.31265	0.293691
$463$	−5.16362	−0.239974	−0.119987	−	0.992775i	$-0.538285\pi$
$463$	−5.16362	−0.239974	−0.119987	+	0.992775i	$0.538285\pi$
$464$	5.61213	0.260536
$465$	5.35026	0.248112
$466$	9.84955	0.456272
$467$	−8.82653	−0.408443	−0.204222	−	0.978925i	$-0.565466\pi$
$467$	−8.82653	−0.408443	−0.204222	+	0.978925i	$0.565466\pi$
$468$	2.96239	0.136936
$469$	10.3127	0.476194
$470$	−5.35026	−0.246789
$471$	14.6253	0.673898
$472$	10.7005	0.492532
$473$	−65.1002	−2.99331
$474$	6.70052	0.307765
$475$	−5.35026	−0.245487
$476$	−6.57452	−0.301342
$477$	−1.22425	−0.0560547
$478$	−0.387873	−0.0177409
$479$	26.9234	1.23016	0.615080	−	0.788465i	$-0.289124\pi$
$479$	26.9234	1.23016	0.615080	+	0.788465i	$0.289124\pi$
$480$	1.00000	0.0456435
$481$	5.92478	0.270147
$482$	−6.57452	−0.299461
$483$	−1.00000	−0.0455016
$484$	28.8496	1.31134
$485$	−2.96239	−0.134515
$486$	−1.00000	−0.0453609
$487$	−39.9657	−1.81102	−0.905510	−	0.424326i	$-0.860511\pi$
$487$	−39.9657	−1.81102	−0.905510	+	0.424326i	$0.860511\pi$
$488$	12.7005	0.574926
$489$	−5.29948	−0.239651
$490$	−1.00000	−0.0451754
$491$	33.8759	1.52880	0.764399	−	0.644743i	$-0.223036\pi$
$491$	33.8759	1.52880	0.764399	+	0.644743i	$0.223036\pi$
$492$	−1.22425	−0.0551936
$493$	−36.8970	−1.66176
$494$	−15.8496	−0.713105
$495$	6.31265	0.283733
$496$	5.35026	0.240234
$497$	−0.387873	−0.0173985
$498$	−7.27504	−0.326002
$499$	38.5501	1.72574	0.862869	−	0.505427i	$-0.168665\pi$
$499$	38.5501	1.72574	0.862869	+	0.505427i	$0.168665\pi$
$500$	−1.00000	−0.0447214
$501$	−1.87399	−0.0837238
$502$	−0.186642	−0.00833026
$503$	−28.1016	−1.25299	−0.626494	−	0.779427i	$-0.715511\pi$
$503$	−28.1016	−1.25299	−0.626494	+	0.779427i	$0.715511\pi$
$504$	1.00000	0.0445435
$505$	13.6629	0.607992
$506$	−6.31265	−0.280632
$507$	4.22425	0.187606
$508$	14.3127	0.635021
$509$	22.1866	0.983406	0.491703	−	0.870763i	$-0.336375\pi$
$509$	22.1866	0.983406	0.491703	+	0.870763i	$0.336375\pi$
$510$	−6.57452	−0.291124
$511$	−15.4010	−0.681302
$512$	1.00000	0.0441942
$513$	5.35026	0.236220
$514$	8.44851	0.372648
$515$	−16.6253	−0.732598
$516$	−10.3127	−0.453989
$517$	−33.7743	−1.48539
$518$	2.00000	0.0878750
$519$	18.0508	0.792342
$520$	−2.96239	−0.129909
$521$	0.111420	0.00488138	0.00244069	−	0.999997i	$-0.499223\pi$
$521$	0.111420	0.00488138	0.00244069	+	0.999997i	$0.499223\pi$
$522$	5.61213	0.245636
$523$	−22.8872	−1.00079	−0.500393	−	0.865798i	$-0.666811\pi$
$523$	−22.8872	−1.00079	−0.500393	+	0.865798i	$0.666811\pi$
$524$	−2.44851	−0.106964
$525$	−1.00000	−0.0436436
$526$	28.4749	1.24156
$527$	−35.1754	−1.53226
$528$	6.31265	0.274723
$529$	1.00000	0.0434783
$530$	1.22425	0.0531782
$531$	10.7005	0.464363
$532$	−5.35026	−0.231963
$533$	3.62672	0.157090
$534$	15.5877	0.674545
$535$	5.92478	0.256150
$536$	10.3127	0.445439
$537$	−21.4010	−0.923523
$538$	26.8119	1.15594
$539$	−6.31265	−0.271905
$540$	1.00000	0.0430331
$541$	−22.6253	−0.972738	−0.486369	−	0.873754i	$-0.661679\pi$
$541$	−22.6253	−0.972738	−0.486369	+	0.873754i	$0.661679\pi$
$542$	5.35026	0.229813
$543$	7.14903	0.306794
$544$	−6.57452	−0.281880
$545$	9.84955	0.421909
$546$	−2.96239	−0.126779
$547$	18.8218	0.804762	0.402381	−	0.915472i	$-0.368183\pi$
$547$	18.8218	0.804762	0.402381	+	0.915472i	$0.368183\pi$
$548$	2.00000	0.0854358
$549$	12.7005	0.542045
$550$	−6.31265	−0.269172
$551$	−30.0263	−1.27917
$552$	−1.00000	−0.0425628
$553$	−6.70052	−0.284935
$554$	4.31265	0.183227
$555$	2.00000	0.0848953
$556$	13.9248	0.590542
$557$	20.8021	0.881413	0.440707	−	0.897651i	$-0.354728\pi$
$557$	20.8021	0.881413	0.440707	+	0.897651i	$0.354728\pi$
$558$	5.35026	0.226495
$559$	30.5501	1.29213
$560$	−1.00000	−0.0422577
$561$	−41.5026	−1.75224
$562$	5.08840	0.214641
$563$	23.2750	0.980926	0.490463	−	0.871462i	$-0.336828\pi$
$563$	23.2750	0.980926	0.490463	+	0.871462i	$0.336828\pi$
$564$	−5.35026	−0.225287
$565$	−12.7005	−0.534315
$566$	−8.43866	−0.354703
$567$	1.00000	0.0419961
$568$	−0.387873	−0.0162748
$569$	24.1622	1.01293	0.506466	−	0.862260i	$-0.330952\pi$
$569$	24.1622	1.01293	0.506466	+	0.862260i	$0.330952\pi$
$570$	−5.35026	−0.224098
$571$	43.4274	1.81738	0.908690	−	0.417472i	$-0.137084\pi$
$571$	43.4274	1.81738	0.908690	+	0.417472i	$0.137084\pi$
$572$	−18.7005	−0.781908
$573$	10.7005	0.447021
$574$	1.22425	0.0510994
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	37.1754	1.54763	0.773816	−	0.633411i	$-0.218346\pi$
$577$	37.1754	1.54763	0.773816	+	0.633411i	$0.218346\pi$
$578$	26.2243	1.09079
$579$	−8.70052	−0.361581
$580$	−5.61213	−0.233031
$581$	7.27504	0.301819
$582$	−2.96239	−0.122795
$583$	7.72829	0.320073
$584$	−15.4010	−0.637300
$585$	−2.96239	−0.122480
$586$	−7.92478	−0.327370
$587$	−26.4485	−1.09165	−0.545823	−	0.837900i	$-0.683783\pi$
$587$	−26.4485	−1.09165	−0.545823	+	0.837900i	$0.683783\pi$
$588$	−1.00000	−0.0412393
$589$	−28.6253	−1.17948
$590$	−10.7005	−0.440534
$591$	−16.7005	−0.686968
$592$	2.00000	0.0821995
$593$	−25.8496	−1.06151	−0.530757	−	0.847524i	$-0.678092\pi$
$593$	−25.8496	−1.06151	−0.530757	+	0.847524i	$0.678092\pi$
$594$	6.31265	0.259011
$595$	6.57452	0.269529
$596$	10.0000	0.409616
$597$	0.625301	0.0255919
$598$	2.96239	0.121141
$599$	17.5369	0.716538	0.358269	−	0.933618i	$-0.383367\pi$
$599$	17.5369	0.716538	0.358269	+	0.933618i	$0.383367\pi$
$600$	−1.00000	−0.0408248
$601$	−14.7757	−0.602715	−0.301358	−	0.953511i	$-0.597440\pi$
$601$	−14.7757	−0.602715	−0.301358	+	0.953511i	$0.597440\pi$
$602$	10.3127	0.420312
$603$	10.3127	0.419964
$604$	9.92478	0.403833
$605$	−28.8496	−1.17290
$606$	13.6629	0.555018
$607$	−42.7367	−1.73463	−0.867315	−	0.497760i	$-0.834156\pi$
$607$	−42.7367	−1.73463	−0.867315	+	0.497760i	$0.834156\pi$
$608$	−5.35026	−0.216982
$609$	−5.61213	−0.227415
$610$	−12.7005	−0.514229
$611$	15.8496	0.641204
$612$	−6.57452	−0.265759
$613$	9.47627	0.382743	0.191371	−	0.981518i	$-0.438706\pi$
$613$	9.47627	0.382743	0.191371	+	0.981518i	$0.438706\pi$
$614$	−16.4749	−0.664871
$615$	1.22425	0.0493667
$616$	−6.31265	−0.254344
$617$	−0.327239	−0.0131741	−0.00658707	−	0.999978i	$-0.502097\pi$
$617$	−0.327239	−0.0131741	−0.00658707	+	0.999978i	$0.502097\pi$
$618$	−16.6253	−0.668768
$619$	−16.0508	−0.645136	−0.322568	−	0.946546i	$-0.604546\pi$
$619$	−16.0508	−0.645136	−0.322568	+	0.946546i	$0.604546\pi$
$620$	−5.35026	−0.214872
$621$	−1.00000	−0.0401286
$622$	−8.18664	−0.328254
$623$	−15.5877	−0.624508
$624$	−2.96239	−0.118590
$625$	1.00000	0.0400000
$626$	−8.51388	−0.340283
$627$	−33.7743	−1.34882
$628$	−14.6253	−0.583613
$629$	−13.1490	−0.524286
$630$	−1.00000	−0.0398410
$631$	−39.9511	−1.59043	−0.795215	−	0.606328i	$-0.792642\pi$
$631$	−39.9511	−1.59043	−0.795215	+	0.606328i	$0.792642\pi$
$632$	−6.70052	−0.266533
$633$	6.55008	0.260342
$634$	1.47627	0.0586302
$635$	−14.3127	−0.567980
$636$	1.22425	0.0485448
$637$	2.96239	0.117374
$638$	−35.4274	−1.40258
$639$	−0.387873	−0.0153440
$640$	−1.00000	−0.0395285
$641$	1.98541	0.0784190	0.0392095	−	0.999231i	$-0.487516\pi$
$641$	1.98541	0.0784190	0.0392095	+	0.999231i	$0.487516\pi$
$642$	5.92478	0.233832
$643$	14.4123	0.568366	0.284183	−	0.958770i	$-0.408278\pi$
$643$	14.4123	0.568366	0.284183	+	0.958770i	$0.408278\pi$
$644$	1.00000	0.0394055
$645$	10.3127	0.406060
$646$	35.1754	1.38396
$647$	−46.6009	−1.83207	−0.916034	−	0.401100i	$-0.868628\pi$
$647$	−46.6009	−1.83207	−0.916034	+	0.401100i	$0.868628\pi$
$648$	1.00000	0.0392837
$649$	−67.5487	−2.65152
$650$	2.96239	0.116194
$651$	−5.35026	−0.209693
$652$	5.29948	0.207544
$653$	−17.7283	−0.693761	−0.346881	−	0.937909i	$-0.612759\pi$
$653$	−17.7283	−0.693761	−0.346881	+	0.937909i	$0.612759\pi$
$654$	9.84955	0.385148
$655$	2.44851	0.0956711
$656$	1.22425	0.0477991
$657$	−15.4010	−0.600852
$658$	5.35026	0.208575
$659$	29.6385	1.15455	0.577276	−	0.816549i	$-0.304116\pi$
$659$	29.6385	1.15455	0.577276	+	0.816549i	$0.304116\pi$
$660$	−6.31265	−0.245720
$661$	41.4274	1.61134	0.805669	−	0.592365i	$-0.201806\pi$
$661$	41.4274	1.61134	0.805669	+	0.592365i	$0.201806\pi$
$662$	−7.22425	−0.280779
$663$	19.4763	0.756396
$664$	7.27504	0.282326
$665$	5.35026	0.207474
$666$	2.00000	0.0774984
$667$	5.61213	0.217302
$668$	1.87399	0.0725069
$669$	−2.26187	−0.0874488
$670$	−10.3127	−0.398412
$671$	−80.1740	−3.09508
$672$	−1.00000	−0.0385758
$673$	−14.5237	−0.559849	−0.279924	−	0.960022i	$-0.590309\pi$
$673$	−14.5237	−0.559849	−0.279924	+	0.960022i	$0.590309\pi$
$674$	−9.71370	−0.374158
$675$	−1.00000	−0.0384900
$676$	−4.22425	−0.162471
$677$	30.3536	1.16658	0.583292	−	0.812263i	$-0.301765\pi$
$677$	30.3536	1.16658	0.583292	+	0.812263i	$0.301765\pi$
$678$	−12.7005	−0.487761
$679$	2.96239	0.113686
$680$	6.57452	0.252121
$681$	−11.7988	−0.452130
$682$	−33.7743	−1.29329
$683$	23.1754	0.886781	0.443391	−	0.896328i	$-0.353775\pi$
$683$	23.1754	0.886781	0.443391	+	0.896328i	$0.353775\pi$
$684$	−5.35026	−0.204572
$685$	−2.00000	−0.0764161
$686$	1.00000	0.0381802
$687$	−17.2243	−0.657146
$688$	10.3127	0.393166
$689$	−3.62672	−0.138167
$690$	1.00000	0.0380693
$691$	9.67276	0.367969	0.183985	−	0.982929i	$-0.441100\pi$
$691$	9.67276	0.367969	0.183985	+	0.982929i	$0.441100\pi$
$692$	−18.0508	−0.686188
$693$	−6.31265	−0.239798
$694$	−5.92478	−0.224901
$695$	−13.9248	−0.528197
$696$	−5.61213	−0.212727
$697$	−8.04888	−0.304873
$698$	19.3503	0.732418
$699$	−9.84955	−0.372544
$700$	1.00000	0.0377964
$701$	17.2243	0.650551	0.325276	−	0.945619i	$-0.394543\pi$
$701$	17.2243	0.650551	0.325276	+	0.945619i	$0.394543\pi$
$702$	−2.96239	−0.111808
$703$	−10.7005	−0.403578
$704$	−6.31265	−0.237917
$705$	5.35026	0.201503
$706$	−21.2243	−0.798785
$707$	−13.6629	−0.513847
$708$	−10.7005	−0.402150
$709$	11.8232	0.444030	0.222015	−	0.975043i	$-0.428737\pi$
$709$	11.8232	0.444030	0.222015	+	0.975043i	$0.428737\pi$
$710$	0.387873	0.0145566
$711$	−6.70052	−0.251289
$712$	−15.5877	−0.584173
$713$	5.35026	0.200369
$714$	6.57452	0.246045
$715$	18.7005	0.699360
$716$	21.4010	0.799795
$717$	0.387873	0.0144854
$718$	−36.9986	−1.38077
$719$	−38.4650	−1.43450	−0.717251	−	0.696815i	$-0.754600\pi$
$719$	−38.4650	−1.43450	−0.717251	+	0.696815i	$0.754600\pi$
$720$	−1.00000	−0.0372678
$721$	16.6253	0.619159
$722$	9.62530	0.358217
$723$	6.57452	0.244509
$724$	−7.14903	−0.265692
$725$	5.61213	0.208429
$726$	−28.8496	−1.07071
$727$	43.1754	1.60129	0.800643	−	0.599142i	$-0.204491\pi$
$727$	43.1754	1.60129	0.800643	+	0.599142i	$0.204491\pi$
$728$	2.96239	0.109793
$729$	1.00000	0.0370370
$730$	15.4010	0.570018
$731$	−67.8007	−2.50770
$732$	−12.7005	−0.469425
$733$	−39.1490	−1.44600	−0.723001	−	0.690847i	$-0.757238\pi$
$733$	−39.1490	−1.44600	−0.723001	+	0.690847i	$0.757238\pi$
$734$	−23.0738	−0.851670
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	−65.1002	−2.39800
$738$	1.22425	0.0450654
$739$	29.9248	1.10080	0.550400	−	0.834901i	$-0.314475\pi$
$739$	29.9248	1.10080	0.550400	+	0.834901i	$0.314475\pi$
$740$	−2.00000	−0.0735215
$741$	15.8496	0.582248
$742$	−1.22425	−0.0449438
$743$	4.40246	0.161511	0.0807553	−	0.996734i	$-0.474267\pi$
$743$	4.40246	0.161511	0.0807553	+	0.996734i	$0.474267\pi$
$744$	−5.35026	−0.196150
$745$	−10.0000	−0.366372
$746$	−12.4485	−0.455772
$747$	7.27504	0.266180
$748$	41.5026	1.51749
$749$	−5.92478	−0.216487
$750$	1.00000	0.0365148
$751$	−38.6516	−1.41042	−0.705209	−	0.708999i	$-0.749147\pi$
$751$	−38.6516	−1.41042	−0.705209	+	0.708999i	$0.749147\pi$
$752$	5.35026	0.195104
$753$	0.186642	0.00680163
$754$	16.6253	0.605458
$755$	−9.92478	−0.361200
$756$	−1.00000	−0.0363696
$757$	−45.1754	−1.64193	−0.820964	−	0.570981i	$-0.806563\pi$
$757$	−45.1754	−1.64193	−0.820964	+	0.570981i	$0.806563\pi$
$758$	35.3258	1.28309
$759$	6.31265	0.229135
$760$	5.35026	0.194074
$761$	40.0263	1.45095	0.725477	−	0.688246i	$-0.241619\pi$
$761$	40.0263	1.45095	0.725477	+	0.688246i	$0.241619\pi$
$762$	−14.3127	−0.518493
$763$	−9.84955	−0.356578
$764$	−10.7005	−0.387131
$765$	6.57452	0.237702
$766$	23.8496	0.861719
$767$	31.6991	1.14459
$768$	−1.00000	−0.0360844
$769$	3.45183	0.124476	0.0622381	−	0.998061i	$-0.480176\pi$
$769$	3.45183	0.124476	0.0622381	+	0.998061i	$0.480176\pi$
$770$	6.31265	0.227492
$771$	−8.44851	−0.304266
$772$	8.70052	0.313139
$773$	−5.22425	−0.187903	−0.0939517	−	0.995577i	$-0.529950\pi$
$773$	−5.22425	−0.187903	−0.0939517	+	0.995577i	$0.529950\pi$
$774$	10.3127	0.370681
$775$	5.35026	0.192187
$776$	2.96239	0.106344
$777$	−2.00000	−0.0717496
$778$	−13.4763	−0.483148
$779$	−6.55008	−0.234681
$780$	2.96239	0.106071
$781$	2.44851	0.0876145
$782$	−6.57452	−0.235104
$783$	−5.61213	−0.200561
$784$	1.00000	0.0357143
$785$	14.6253	0.521999
$786$	2.44851	0.0873354
$787$	22.6155	0.806154	0.403077	−	0.915166i	$-0.367941\pi$
$787$	22.6155	0.806154	0.403077	+	0.915166i	$0.367941\pi$
$788$	16.7005	0.594932
$789$	−28.4749	−1.01373
$790$	6.70052	0.238394
$791$	12.7005	0.451579
$792$	−6.31265	−0.224310
$793$	37.6239	1.33606
$794$	−30.2882	−1.07489
$795$	−1.22425	−0.0434198
$796$	−0.625301	−0.0221632
$797$	−6.40246	−0.226787	−0.113393	−	0.993550i	$-0.536172\pi$
$797$	−6.40246	−0.226787	−0.113393	+	0.993550i	$0.536172\pi$
$798$	5.35026	0.189397
$799$	−35.1754	−1.24442
$800$	1.00000	0.0353553
$801$	−15.5877	−0.550764
$802$	16.1622	0.570707
$803$	97.2214	3.43087
$804$	−10.3127	−0.363699
$805$	−1.00000	−0.0352454
$806$	15.8496	0.558277
$807$	−26.8119	−0.943825
$808$	−13.6629	−0.480660
$809$	18.2520	0.641707	0.320853	−	0.947129i	$-0.396030\pi$
$809$	18.2520	0.641707	0.320853	+	0.947129i	$0.396030\pi$
$810$	−1.00000	−0.0351364
$811$	35.3258	1.24046	0.620229	−	0.784421i	$-0.287040\pi$
$811$	35.3258	1.24046	0.620229	+	0.784421i	$0.287040\pi$
$812$	5.61213	0.196947
$813$	−5.35026	−0.187642
$814$	−12.6253	−0.442517
$815$	−5.29948	−0.185633
$816$	6.57452	0.230154
$817$	−55.1754	−1.93034
$818$	17.3258	0.605783
$819$	2.96239	0.103514
$820$	−1.22425	−0.0427528
$821$	−22.9116	−0.799620	−0.399810	−	0.916598i	$-0.630924\pi$
$821$	−22.9116	−0.799620	−0.399810	+	0.916598i	$0.630924\pi$
$822$	−2.00000	−0.0697580
$823$	−9.68735	−0.337680	−0.168840	−	0.985643i	$-0.554002\pi$
$823$	−9.68735	−0.337680	−0.168840	+	0.985643i	$0.554002\pi$
$824$	16.6253	0.579170
$825$	6.31265	0.219778
$826$	10.7005	0.372319
$827$	10.0752	0.350350	0.175175	−	0.984537i	$-0.443951\pi$
$827$	10.0752	0.350350	0.175175	+	0.984537i	$0.443951\pi$
$828$	1.00000	0.0347524
$829$	2.20123	0.0764519	0.0382260	−	0.999269i	$-0.487829\pi$
$829$	2.20123	0.0764519	0.0382260	+	0.999269i	$0.487829\pi$
$830$	−7.27504	−0.252520
$831$	−4.31265	−0.149604
$832$	2.96239	0.102702
$833$	−6.57452	−0.227793
$834$	−13.9248	−0.482176
$835$	−1.87399	−0.0648522
$836$	33.7743	1.16811
$837$	−5.35026	−0.184932
$838$	2.88717	0.0997355
$839$	30.7005	1.05990	0.529950	−	0.848029i	$-0.322211\pi$
$839$	30.7005	1.05990	0.529950	+	0.848029i	$0.322211\pi$
$840$	1.00000	0.0345033
$841$	2.49597	0.0860679
$842$	32.8021	1.13043
$843$	−5.08840	−0.175254
$844$	−6.55008	−0.225463
$845$	4.22425	0.145319
$846$	5.35026	0.183946
$847$	28.8496	0.991282
$848$	−1.22425	−0.0420410
$849$	8.43866	0.289614
$850$	−6.57452	−0.225504
$851$	2.00000	0.0685591
$852$	0.387873	0.0132883
$853$	−7.83971	−0.268426	−0.134213	−	0.990952i	$-0.542851\pi$
$853$	−7.83971	−0.268426	−0.134213	+	0.990952i	$0.542851\pi$
$854$	12.7005	0.434603
$855$	5.35026	0.182975
$856$	−5.92478	−0.202505
$857$	−37.2243	−1.27156	−0.635778	−	0.771872i	$-0.719321\pi$
$857$	−37.2243	−1.27156	−0.635778	+	0.771872i	$0.719321\pi$
$858$	18.7005	0.638425
$859$	9.67276	0.330030	0.165015	−	0.986291i	$-0.447233\pi$
$859$	9.67276	0.330030	0.165015	+	0.986291i	$0.447233\pi$
$860$	−10.3127	−0.351658
$861$	−1.22425	−0.0417225
$862$	0.252016	0.00858370
$863$	−29.7743	−1.01353	−0.506765	−	0.862084i	$-0.669159\pi$
$863$	−29.7743	−1.01353	−0.506765	+	0.862084i	$0.669159\pi$
$864$	−1.00000	−0.0340207
$865$	18.0508	0.613745
$866$	−31.3357	−1.06483
$867$	−26.2243	−0.890622
$868$	5.35026	0.181600
$869$	42.2981	1.43486
$870$	5.61213	0.190269
$871$	30.5501	1.03515
$872$	−9.84955	−0.333548
$873$	2.96239	0.100262
$874$	−5.35026	−0.180975
$875$	−1.00000	−0.0338062
$876$	15.4010	0.520353
$877$	47.7597	1.61273	0.806366	−	0.591417i	$-0.201431\pi$
$877$	47.7597	1.61273	0.806366	+	0.591417i	$0.201431\pi$
$878$	22.2276	0.750144
$879$	7.92478	0.267296
$880$	6.31265	0.212799
$881$	−23.9902	−0.808249	−0.404124	−	0.914704i	$-0.632424\pi$
$881$	−23.9902	−0.808249	−0.404124	+	0.914704i	$0.632424\pi$
$882$	1.00000	0.0336718
$883$	−29.5026	−0.992842	−0.496421	−	0.868082i	$-0.665353\pi$
$883$	−29.5026	−0.992842	−0.496421	+	0.868082i	$0.665353\pi$
$884$	−19.4763	−0.655058
$885$	10.7005	0.359694
$886$	−13.9248	−0.467812
$887$	−22.0968	−0.741939	−0.370969	−	0.928645i	$-0.620975\pi$
$887$	−22.0968	−0.741939	−0.370969	+	0.928645i	$0.620975\pi$
$888$	−2.00000	−0.0671156
$889$	14.3127	0.480031
$890$	15.5877	0.522501
$891$	−6.31265	−0.211482
$892$	2.26187	0.0757328
$893$	−28.6253	−0.957909
$894$	−10.0000	−0.334450
$895$	−21.4010	−0.715358
$896$	1.00000	0.0334077
$897$	−2.96239	−0.0989113
$898$	−30.2228	−1.00855
$899$	30.0263	1.00143
$900$	1.00000	0.0333333
$901$	8.04888	0.268147
$902$	−7.72829	−0.257324
$903$	−10.3127	−0.343184
$904$	12.7005	0.422413
$905$	7.14903	0.237642
$906$	−9.92478	−0.329729
$907$	−18.9868	−0.630447	−0.315224	−	0.949017i	$-0.602080\pi$
$907$	−18.9868	−0.630447	−0.315224	+	0.949017i	$0.602080\pi$
$908$	11.7988	0.391556
$909$	−13.6629	−0.453170
$910$	−2.96239	−0.0982022
$911$	8.37328	0.277419	0.138710	−	0.990333i	$-0.455705\pi$
$911$	8.37328	0.277419	0.138710	+	0.990333i	$0.455705\pi$
$912$	5.35026	0.177165
$913$	−45.9248	−1.51989
$914$	−3.93937	−0.130303
$915$	12.7005	0.419866
$916$	17.2243	0.569105
$917$	−2.44851	−0.0808568
$918$	6.57452	0.216991
$919$	8.67418	0.286135	0.143067	−	0.989713i	$-0.454303\pi$
$919$	8.67418	0.286135	0.143067	+	0.989713i	$0.454303\pi$
$920$	−1.00000	−0.0329690
$921$	16.4749	0.542865
$922$	−12.4123	−0.408778
$923$	−1.14903	−0.0378208
$924$	6.31265	0.207671
$925$	2.00000	0.0657596
$926$	−5.16362	−0.169687
$927$	16.6253	0.546047
$928$	5.61213	0.184227
$929$	−1.59754	−0.0524135	−0.0262068	−	0.999657i	$-0.508343\pi$
$929$	−1.59754	−0.0524135	−0.0262068	+	0.999657i	$0.508343\pi$
$930$	5.35026	0.175442
$931$	−5.35026	−0.175348
$932$	9.84955	0.322633
$933$	8.18664	0.268019
$934$	−8.82653	−0.288813
$935$	−41.5026	−1.35728
$936$	2.96239	0.0968287
$937$	−3.88858	−0.127034	−0.0635172	−	0.997981i	$-0.520232\pi$
$937$	−3.88858	−0.127034	−0.0635172	+	0.997981i	$0.520232\pi$
$938$	10.3127	0.336720
$939$	8.51388	0.277840
$940$	−5.35026	−0.174506
$941$	−17.8496	−0.581879	−0.290939	−	0.956741i	$-0.593968\pi$
$941$	−17.8496	−0.581879	−0.290939	+	0.956741i	$0.593968\pi$
$942$	14.6253	0.476518
$943$	1.22425	0.0398672
$944$	10.7005	0.348272
$945$	1.00000	0.0325300
$946$	−65.1002	−2.11659
$947$	53.2017	1.72882	0.864412	−	0.502784i	$-0.167691\pi$
$947$	53.2017	1.72882	0.864412	+	0.502784i	$0.167691\pi$
$948$	6.70052	0.217623
$949$	−45.6239	−1.48101
$950$	−5.35026	−0.173585
$951$	−1.47627	−0.0478713
$952$	−6.57452	−0.213081
$953$	14.9986	0.485852	0.242926	−	0.970045i	$-0.421893\pi$
$953$	14.9986	0.485852	0.242926	+	0.970045i	$0.421893\pi$
$954$	−1.22425	−0.0396367
$955$	10.7005	0.346261
$956$	−0.387873	−0.0125447
$957$	35.4274	1.14521
$958$	26.9234	0.869854
$959$	2.00000	0.0645834
$960$	1.00000	0.0322749
$961$	−2.37470	−0.0766032
$962$	5.92478	0.191022
$963$	−5.92478	−0.190923
$964$	−6.57452	−0.211751
$965$	−8.70052	−0.280080
$966$	−1.00000	−0.0321745
$967$	13.9394	0.448260	0.224130	−	0.974559i	$-0.428046\pi$
$967$	13.9394	0.448260	0.224130	+	0.974559i	$0.428046\pi$
$968$	28.8496	0.927260
$969$	−35.1754	−1.13000
$970$	−2.96239	−0.0951166
$971$	−10.7856	−0.346126	−0.173063	−	0.984911i	$-0.555366\pi$
$971$	−10.7856	−0.346126	−0.173063	+	0.984911i	$0.555366\pi$
$972$	−1.00000	−0.0320750
$973$	13.9248	0.446408
$974$	−39.9657	−1.28058
$975$	−2.96239	−0.0948724
$976$	12.7005	0.406534
$977$	11.5223	0.368632	0.184316	−	0.982867i	$-0.440993\pi$
$977$	11.5223	0.368632	0.184316	+	0.982867i	$0.440993\pi$
$978$	−5.29948	−0.169459
$979$	98.3996	3.14487
$980$	−1.00000	−0.0319438
$981$	−9.84955	−0.314472
$982$	33.8759	1.08102
$983$	9.40105	0.299847	0.149923	−	0.988698i	$-0.452097\pi$
$983$	9.40105	0.299847	0.149923	+	0.988698i	$0.452097\pi$
$984$	−1.22425	−0.0390278
$985$	−16.7005	−0.532123
$986$	−36.8970	−1.17504
$987$	−5.35026	−0.170301
$988$	−15.8496	−0.504241
$989$	10.3127	0.327923
$990$	6.31265	0.200629
$991$	−20.2228	−0.642400	−0.321200	−	0.947011i	$-0.604086\pi$
$991$	−20.2228	−0.642400	−0.321200	+	0.947011i	$0.604086\pi$
$992$	5.35026	0.169871
$993$	7.22425	0.229255
$994$	−0.387873	−0.0123026
$995$	0.625301	0.0198234
$996$	−7.27504	−0.230518
$997$	−44.7367	−1.41683	−0.708413	−	0.705798i	$-0.750589\pi$
$997$	−44.7367	−1.41683	−0.708413	+	0.705798i	$0.750589\pi$
$998$	38.5501	1.22028
$999$	−2.00000	−0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.bz.1.1	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.bz.1.1	✓	3	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:	\( N \)	\(=\)	\( 4830 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4830.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -1.00000 q^{5} -1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} -1.00000 q^{10} -6.31265 q^{11} -1.00000 q^{12} +2.96239 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} -6.57452 q^{17} +1.00000 q^{18} -5.35026 q^{19} -1.00000 q^{20} -1.00000 q^{21} -6.31265 q^{22} +1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +2.96239 q^{26} -1.00000 q^{27} +1.00000 q^{28} +5.61213 q^{29} +1.00000 q^{30} +5.35026 q^{31} +1.00000 q^{32} +6.31265 q^{33} -6.57452 q^{34} -1.00000 q^{35} +1.00000 q^{36} +2.00000 q^{37} -5.35026 q^{38} -2.96239 q^{39} -1.00000 q^{40} +1.22425 q^{41} -1.00000 q^{42} +10.3127 q^{43} -6.31265 q^{44} -1.00000 q^{45} +1.00000 q^{46} +5.35026 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +6.57452 q^{51} +2.96239 q^{52} -1.22425 q^{53} -1.00000 q^{54} +6.31265 q^{55} +1.00000 q^{56} +5.35026 q^{57} +5.61213 q^{58} +10.7005 q^{59} +1.00000 q^{60} +12.7005 q^{61} +5.35026 q^{62} +1.00000 q^{63} +1.00000 q^{64} -2.96239 q^{65} +6.31265 q^{66} +10.3127 q^{67} -6.57452 q^{68} -1.00000 q^{69} -1.00000 q^{70} -0.387873 q^{71} +1.00000 q^{72} -15.4010 q^{73} +2.00000 q^{74} -1.00000 q^{75} -5.35026 q^{76} -6.31265 q^{77} -2.96239 q^{78} -6.70052 q^{79} -1.00000 q^{80} +1.00000 q^{81} +1.22425 q^{82} +7.27504 q^{83} -1.00000 q^{84} +6.57452 q^{85} +10.3127 q^{86} -5.61213 q^{87} -6.31265 q^{88} -15.5877 q^{89} -1.00000 q^{90} +2.96239 q^{91} +1.00000 q^{92} -5.35026 q^{93} +5.35026 q^{94} +5.35026 q^{95} -1.00000 q^{96} +2.96239 q^{97} +1.00000 q^{98} -6.31265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} - 3 q^{6} + 3 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} + 2 q^{11} - 3 q^{12} - 2 q^{13} + 3 q^{14} + 3 q^{15} + 3 q^{16} - 8 q^{17} + 3 q^{18} - 6 q^{19} - 3 q^{20} - 3 q^{21} + 2 q^{22} + 3 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} + 3 q^{28} + 16 q^{29} + 3 q^{30} + 6 q^{31} + 3 q^{32} - 2 q^{33} - 8 q^{34} - 3 q^{35} + 3 q^{36} + 6 q^{37} - 6 q^{38} + 2 q^{39} - 3 q^{40} + 2 q^{41} - 3 q^{42} + 10 q^{43} + 2 q^{44} - 3 q^{45} + 3 q^{46} + 6 q^{47} - 3 q^{48} + 3 q^{49} + 3 q^{50} + 8 q^{51} - 2 q^{52} - 2 q^{53} - 3 q^{54} - 2 q^{55} + 3 q^{56} + 6 q^{57} + 16 q^{58} + 12 q^{59} + 3 q^{60} + 18 q^{61} + 6 q^{62} + 3 q^{63} + 3 q^{64} + 2 q^{65} - 2 q^{66} + 10 q^{67} - 8 q^{68} - 3 q^{69} - 3 q^{70} - 2 q^{71} + 3 q^{72} - 6 q^{73} + 6 q^{74} - 3 q^{75} - 6 q^{76} + 2 q^{77} + 2 q^{78} - 3 q^{80} + 3 q^{81} + 2 q^{82} - 10 q^{83} - 3 q^{84} + 8 q^{85} + 10 q^{86} - 16 q^{87} + 2 q^{88} + 6 q^{89} - 3 q^{90} - 2 q^{91} + 3 q^{92} - 6 q^{93} + 6 q^{94} + 6 q^{95} - 3 q^{96} - 2 q^{97} + 3 q^{98} + 2 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 - 3 * q^3 + 3 * q^4 - 3 * q^5 - 3 * q^6 + 3 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 + 2 * q^11 - 3 * q^12 - 2 * q^13 + 3 * q^14 + 3 * q^15 + 3 * q^16 - 8 * q^17 + 3 * q^18 - 6 * q^19 - 3 * q^20 - 3 * q^21 + 2 * q^22 + 3 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 + 3 * q^28 + 16 * q^29 + 3 * q^30 + 6 * q^31 + 3 * q^32 - 2 * q^33 - 8 * q^34 - 3 * q^35 + 3 * q^36 + 6 * q^37 - 6 * q^38 + 2 * q^39 - 3 * q^40 + 2 * q^41 - 3 * q^42 + 10 * q^43 + 2 * q^44 - 3 * q^45 + 3 * q^46 + 6 * q^47 - 3 * q^48 + 3 * q^49 + 3 * q^50 + 8 * q^51 - 2 * q^52 - 2 * q^53 - 3 * q^54 - 2 * q^55 + 3 * q^56 + 6 * q^57 + 16 * q^58 + 12 * q^59 + 3 * q^60 + 18 * q^61 + 6 * q^62 + 3 * q^63 + 3 * q^64 + 2 * q^65 - 2 * q^66 + 10 * q^67 - 8 * q^68 - 3 * q^69 - 3 * q^70 - 2 * q^71 + 3 * q^72 - 6 * q^73 + 6 * q^74 - 3 * q^75 - 6 * q^76 + 2 * q^77 + 2 * q^78 - 3 * q^80 + 3 * q^81 + 2 * q^82 - 10 * q^83 - 3 * q^84 + 8 * q^85 + 10 * q^86 - 16 * q^87 + 2 * q^88 + 6 * q^89 - 3 * q^90 - 2 * q^91 + 3 * q^92 - 6 * q^93 + 6 * q^94 + 6 * q^95 - 3 * q^96 - 2 * q^97 + 3 * q^98 + 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more