LMFDB - Embedded newform 4830.2.a.ce.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:	$4$
Coefficient field:	4.4.6809.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} - x + 1 $ x^4 - 5*x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{29}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-2.06963$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.13926 q^{11} +1.00000 q^{12} +3.17290 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.966357 q^{17} +1.00000 q^{18} +2.96636 q^{19} +1.00000 q^{20} +1.00000 q^{21} -4.13926 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.17290 q^{26} +1.00000 q^{27} +1.00000 q^{28} +5.60036 q^{29} +1.00000 q^{30} +6.70598 q^{31} +1.00000 q^{32} -4.13926 q^{33} +0.966357 q^{34} +1.00000 q^{35} +1.00000 q^{36} -7.67233 q^{37} +2.96636 q^{38} +3.17290 q^{39} +1.00000 q^{40} -7.13344 q^{41} +1.00000 q^{42} -7.87887 q^{43} -4.13926 q^{44} +1.00000 q^{45} +1.00000 q^{46} +9.31215 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +0.966357 q^{51} +3.17290 q^{52} +11.6723 q^{53} +1.00000 q^{54} -4.13926 q^{55} +1.00000 q^{56} +2.96636 q^{57} +5.60036 q^{58} +2.60618 q^{59} +1.00000 q^{60} -4.34580 q^{61} +6.70598 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.17290 q^{65} -4.13926 q^{66} -0.399638 q^{67} +0.966357 q^{68} +1.00000 q^{69} +1.00000 q^{70} -1.53308 q^{71} +1.00000 q^{72} -0.606179 q^{73} -7.67233 q^{74} +1.00000 q^{75} +2.96636 q^{76} -4.13926 q^{77} +3.17290 q^{78} -9.67233 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.13344 q^{82} +11.2449 q^{83} +1.00000 q^{84} +0.966357 q^{85} -7.87887 q^{86} +5.60036 q^{87} -4.13926 q^{88} +15.1910 q^{89} +1.00000 q^{90} +3.17290 q^{91} +1.00000 q^{92} +6.70598 q^{93} +9.31215 q^{94} +2.96636 q^{95} +1.00000 q^{96} +2.63400 q^{97} +1.00000 q^{98} -4.13926 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	$ 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} + 14 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 2 q^{34} + 4 q^{35} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{42} + 10 q^{43} + 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} + 4 q^{54} + 4 q^{56} + 6 q^{57} + 14 q^{58} + 14 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} + 14 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} + 2 q^{78} - 2 q^{79} + 4 q^{80} + 4 q^{81} + 6 q^{83} + 4 q^{84} - 2 q^{85} + 10 q^{86} + 14 q^{87} - 8 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} + 10 q^{94} + 6 q^{95} + 4 q^{96} + 8 q^{97} + 4 q^{98}+O(q^{100}) $ 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^12 + 2 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 + 14 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 2 * q^34 + 4 * q^35 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^42 + 10 * q^43 + 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 + 4 * q^54 + 4 * q^56 + 6 * q^57 + 14 * q^58 + 14 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 14 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 + 2 * q^78 - 2 * q^79 + 4 * q^80 + 4 * q^81 + 6 * q^83 + 4 * q^84 - 2 * q^85 + 10 * q^86 + 14 * q^87 - 8 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 + 10 * q^94 + 6 * q^95 + 4 * q^96 + 8 * q^97 + 4 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.00000	0.408248
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	−4.13926	−1.24803	−0.624016	−	0.781411i	$-0.714500\pi$
$11$	−4.13926	−1.24803	−0.624016	+	0.781411i	$0.714500\pi$
$12$	1.00000	0.288675
$13$	3.17290	0.880004	0.440002	−	0.897997i	$-0.354978\pi$
$13$	3.17290	0.880004	0.440002	+	0.897997i	$0.354978\pi$
$14$	1.00000	0.267261
$15$	1.00000	0.258199
$16$	1.00000	0.250000
$17$	0.966357	0.234376	0.117188	−	0.993110i	$-0.462612\pi$
$17$	0.966357	0.234376	0.117188	+	0.993110i	$0.462612\pi$
$18$	1.00000	0.235702
$19$	2.96636	0.680529	0.340265	−	0.940330i	$-0.389483\pi$
$19$	2.96636	0.680529	0.340265	+	0.940330i	$0.389483\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	−4.13926	−0.882492
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	1.00000	0.204124
$25$	1.00000	0.200000
$26$	3.17290	0.622257
$27$	1.00000	0.192450
$28$	1.00000	0.188982
$29$	5.60036	1.03996	0.519981	−	0.854178i	$-0.325939\pi$
$29$	5.60036	1.03996	0.519981	+	0.854178i	$0.325939\pi$
$30$	1.00000	0.182574
$31$	6.70598	1.20443	0.602214	−	0.798334i	$-0.294285\pi$
$31$	6.70598	1.20443	0.602214	+	0.798334i	$0.294285\pi$
$32$	1.00000	0.176777
$33$	−4.13926	−0.720552
$34$	0.966357	0.165729
$35$	1.00000	0.169031
$36$	1.00000	0.166667
$37$	−7.67233	−1.26132	−0.630662	−	0.776058i	$-0.717217\pi$
$37$	−7.67233	−1.26132	−0.630662	+	0.776058i	$0.717217\pi$
$38$	2.96636	0.481207
$39$	3.17290	0.508070
$40$	1.00000	0.158114
$41$	−7.13344	−1.11406	−0.557028	−	0.830494i	$-0.688058\pi$
$41$	−7.13344	−1.11406	−0.557028	+	0.830494i	$0.688058\pi$
$42$	1.00000	0.154303
$43$	−7.87887	−1.20152	−0.600759	−	0.799431i	$-0.705135\pi$
$43$	−7.87887	−1.20152	−0.600759	+	0.799431i	$0.705135\pi$
$44$	−4.13926	−0.624016
$45$	1.00000	0.149071
$46$	1.00000	0.147442
$47$	9.31215	1.35832	0.679159	−	0.733991i	$-0.262345\pi$
$47$	9.31215	1.35832	0.679159	+	0.733991i	$0.262345\pi$
$48$	1.00000	0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	0.966357	0.135317
$52$	3.17290	0.440002
$53$	11.6723	1.60332	0.801659	−	0.597781i	$-0.203951\pi$
$53$	11.6723	1.60332	0.801659	+	0.597781i	$0.203951\pi$
$54$	1.00000	0.136083
$55$	−4.13926	−0.558137
$56$	1.00000	0.133631
$57$	2.96636	0.392904
$58$	5.60036	0.735364
$59$	2.60618	0.339296	0.169648	−	0.985505i	$-0.445737\pi$
$59$	2.60618	0.339296	0.169648	+	0.985505i	$0.445737\pi$
$60$	1.00000	0.129099
$61$	−4.34580	−0.556422	−0.278211	−	0.960520i	$-0.589741\pi$
$61$	−4.34580	−0.556422	−0.278211	+	0.960520i	$0.589741\pi$
$62$	6.70598	0.851660
$63$	1.00000	0.125988
$64$	1.00000	0.125000
$65$	3.17290	0.393550
$66$	−4.13926	−0.509507
$67$	−0.399638	−0.0488235	−0.0244118	−	0.999702i	$-0.507771\pi$
$67$	−0.399638	−0.0488235	−0.0244118	+	0.999702i	$0.507771\pi$
$68$	0.966357	0.117188
$69$	1.00000	0.120386
$70$	1.00000	0.119523
$71$	−1.53308	−0.181943	−0.0909714	−	0.995854i	$-0.528997\pi$
$71$	−1.53308	−0.181943	−0.0909714	+	0.995854i	$0.528997\pi$
$72$	1.00000	0.117851
$73$	−0.606179	−0.0709479	−0.0354739	−	0.999371i	$-0.511294\pi$
$73$	−0.606179	−0.0709479	−0.0354739	+	0.999371i	$0.511294\pi$
$74$	−7.67233	−0.891891
$75$	1.00000	0.115470
$76$	2.96636	0.340265
$77$	−4.13926	−0.471712
$78$	3.17290	0.359260
$79$	−9.67233	−1.08822	−0.544111	−	0.839013i	$-0.683133\pi$
$79$	−9.67233	−1.08822	−0.544111	+	0.839013i	$0.683133\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	−7.13344	−0.787757
$83$	11.2449	1.23428	0.617142	−	0.786852i	$-0.288290\pi$
$83$	11.2449	1.23428	0.617142	+	0.786852i	$0.288290\pi$
$84$	1.00000	0.109109
$85$	0.966357	0.104816
$86$	−7.87887	−0.849601
$87$	5.60036	0.600422
$88$	−4.13926	−0.441246
$89$	15.1910	1.61025	0.805123	−	0.593108i	$-0.202099\pi$
$89$	15.1910	1.61025	0.805123	+	0.593108i	$0.202099\pi$
$90$	1.00000	0.105409
$91$	3.17290	0.332610
$92$	1.00000	0.104257
$93$	6.70598	0.695377
$94$	9.31215	0.960475
$95$	2.96636	0.304342
$96$	1.00000	0.102062
$97$	2.63400	0.267443	0.133721	−	0.991019i	$-0.457307\pi$
$97$	2.63400	0.267443	0.133721	+	0.991019i	$0.457307\pi$
$98$	1.00000	0.101015
$99$	−4.13926	−0.416011
$100$	1.00000	0.100000
$101$	−5.77908	−0.575040	−0.287520	−	0.957775i	$-0.592831\pi$
$101$	−5.77908	−0.575040	−0.287520	+	0.957775i	$0.592831\pi$
$102$	0.966357	0.0956836
$103$	−6.34580	−0.625270	−0.312635	−	0.949873i	$-0.601212\pi$
$103$	−6.34580	−0.625270	−0.312635	+	0.949873i	$0.601212\pi$
$104$	3.17290	0.311128
$105$	1.00000	0.0975900
$106$	11.6723	1.13372
$107$	5.26801	0.509278	0.254639	−	0.967036i	$-0.418043\pi$
$107$	5.26801	0.509278	0.254639	+	0.967036i	$0.418043\pi$
$108$	1.00000	0.0962250
$109$	−7.26801	−0.696149	−0.348075	−	0.937467i	$-0.613164\pi$
$109$	−7.26801	−0.696149	−0.348075	+	0.937467i	$0.613164\pi$
$110$	−4.13926	−0.394663
$111$	−7.67233	−0.728226
$112$	1.00000	0.0944911
$113$	5.32654	0.501078	0.250539	−	0.968106i	$-0.419392\pi$
$113$	5.32654	0.501078	0.250539	+	0.968106i	$0.419392\pi$
$114$	2.96636	0.277825
$115$	1.00000	0.0932505
$116$	5.60036	0.519981
$117$	3.17290	0.293335
$118$	2.60618	0.239918
$119$	0.966357	0.0885858
$120$	1.00000	0.0912871
$121$	6.13344	0.557585
$122$	−4.34580	−0.393450
$123$	−7.13344	−0.643201
$124$	6.70598	0.602214
$125$	1.00000	0.0894427
$126$	1.00000	0.0890871
$127$	13.8116	1.22558	0.612790	−	0.790246i	$-0.290047\pi$
$127$	13.8116	1.22558	0.612790	+	0.790246i	$0.290047\pi$
$128$	1.00000	0.0883883
$129$	−7.87887	−0.693696
$130$	3.17290	0.278282
$131$	14.0854	1.23065	0.615324	−	0.788274i	$-0.289025\pi$
$131$	14.0854	1.23065	0.615324	+	0.788274i	$0.289025\pi$
$132$	−4.13926	−0.360276
$133$	2.96636	0.257216
$134$	−0.399638	−0.0345234
$135$	1.00000	0.0860663
$136$	0.966357	0.0828645
$137$	−8.08542	−0.690784	−0.345392	−	0.938459i	$-0.612254\pi$
$137$	−8.08542	−0.690784	−0.345392	+	0.938459i	$0.612254\pi$
$138$	1.00000	0.0851257
$139$	20.2966	1.72154	0.860769	−	0.508995i	$-0.169983\pi$
$139$	20.2966	1.72154	0.860769	+	0.508995i	$0.169983\pi$
$140$	1.00000	0.0845154
$141$	9.31215	0.784225
$142$	−1.53308	−0.128653
$143$	−13.1334	−1.09827
$144$	1.00000	0.0833333
$145$	5.60036	0.465085
$146$	−0.606179	−0.0501677
$147$	1.00000	0.0824786
$148$	−7.67233	−0.630662
$149$	6.27851	0.514356	0.257178	−	0.966364i	$-0.417207\pi$
$149$	6.27851	0.514356	0.257178	+	0.966364i	$0.417207\pi$
$150$	1.00000	0.0816497
$151$	−2.34580	−0.190898	−0.0954491	−	0.995434i	$-0.530429\pi$
$151$	−2.34580	−0.190898	−0.0954491	+	0.995434i	$0.530429\pi$
$152$	2.96636	0.240603
$153$	0.966357	0.0781254
$154$	−4.13926	−0.333551
$155$	6.70598	0.538637
$156$	3.17290	0.254035
$157$	−23.8250	−1.90144	−0.950722	−	0.310044i	$-0.899656\pi$
$157$	−23.8250	−1.90144	−0.950722	+	0.310044i	$0.899656\pi$
$158$	−9.67233	−0.769489
$159$	11.6723	0.925676
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	−17.1334	−1.34199	−0.670997	−	0.741460i	$-0.734134\pi$
$163$	−17.1334	−1.34199	−0.670997	+	0.741460i	$0.734134\pi$
$164$	−7.13344	−0.557028
$165$	−4.13926	−0.322241
$166$	11.2449	0.872771
$167$	−8.51288	−0.658746	−0.329373	−	0.944200i	$-0.606837\pi$
$167$	−8.51288	−0.658746	−0.329373	+	0.944200i	$0.606837\pi$
$168$	1.00000	0.0771517
$169$	−2.93271	−0.225593
$170$	0.966357	0.0741162
$171$	2.96636	0.226843
$172$	−7.87887	−0.600759
$173$	1.63982	0.124673	0.0623367	−	0.998055i	$-0.480145\pi$
$173$	1.63982	0.124673	0.0623367	+	0.998055i	$0.480145\pi$
$174$	5.60036	0.424562
$175$	1.00000	0.0755929
$176$	−4.13926	−0.312008
$177$	2.60618	0.195892
$178$	15.1910	1.13862
$179$	19.7577	1.47676	0.738382	−	0.674383i	$-0.235590\pi$
$179$	19.7577	1.47676	0.738382	+	0.674383i	$0.235590\pi$
$180$	1.00000	0.0745356
$181$	−18.9989	−1.41217	−0.706087	−	0.708125i	$-0.749541\pi$
$181$	−18.9989	−1.41217	−0.706087	+	0.708125i	$0.749541\pi$
$182$	3.17290	0.235191
$183$	−4.34580	−0.321251
$184$	1.00000	0.0737210
$185$	−7.67233	−0.564081
$186$	6.70598	0.491706
$187$	−4.00000	−0.292509
$188$	9.31215	0.679159
$189$	1.00000	0.0727393
$190$	2.96636	0.215202
$191$	−14.9403	−1.08105	−0.540523	−	0.841329i	$-0.681773\pi$
$191$	−14.9403	−1.08105	−0.540523	+	0.841329i	$0.681773\pi$
$192$	1.00000	0.0721688
$193$	−22.4225	−1.61400	−0.807002	−	0.590549i	$-0.798911\pi$
$193$	−22.4225	−1.61400	−0.807002	+	0.590549i	$0.798911\pi$
$194$	2.63400	0.189111
$195$	3.17290	0.227216
$196$	1.00000	0.0714286
$197$	−15.4120	−1.09806	−0.549028	−	0.835804i	$-0.685002\pi$
$197$	−15.4120	−1.09806	−0.549028	+	0.835804i	$0.685002\pi$
$198$	−4.13926	−0.294164
$199$	−8.27851	−0.586848	−0.293424	−	0.955982i	$-0.594795\pi$
$199$	−8.27851	−0.586848	−0.293424	+	0.955982i	$0.594795\pi$
$200$	1.00000	0.0707107
$201$	−0.399638	−0.0281883
$202$	−5.77908	−0.406614
$203$	5.60036	0.393068
$204$	0.966357	0.0676585
$205$	−7.13344	−0.498221
$206$	−6.34580	−0.442133
$207$	1.00000	0.0695048
$208$	3.17290	0.220001
$209$	−12.2785	−0.849322
$210$	1.00000	0.0690066
$211$	17.3563	1.19486	0.597428	−	0.801922i	$-0.296189\pi$
$211$	17.3563	1.19486	0.597428	+	0.801922i	$0.296189\pi$
$212$	11.6723	0.801659
$213$	−1.53308	−0.105045
$214$	5.26801	0.360114
$215$	−7.87887	−0.537335
$216$	1.00000	0.0680414
$217$	6.70598	0.455231
$218$	−7.26801	−0.492252
$219$	−0.606179	−0.0409618
$220$	−4.13926	−0.279069
$221$	3.06615	0.206252
$222$	−7.67233	−0.514933
$223$	16.8336	1.12726	0.563631	−	0.826027i	$-0.309404\pi$
$223$	16.8336	1.12726	0.563631	+	0.826027i	$0.309404\pi$
$224$	1.00000	0.0668153
$225$	1.00000	0.0666667
$226$	5.32654	0.354316
$227$	−12.0441	−0.799398	−0.399699	−	0.916646i	$-0.630885\pi$
$227$	−12.0441	−0.799398	−0.399699	+	0.916646i	$0.630885\pi$
$228$	2.96636	0.196452
$229$	−1.72149	−0.113759	−0.0568796	−	0.998381i	$-0.518115\pi$
$229$	−1.72149	−0.113759	−0.0568796	+	0.998381i	$0.518115\pi$
$230$	1.00000	0.0659380
$231$	−4.13926	−0.272343
$232$	5.60036	0.367682
$233$	−0.731990	−0.0479543	−0.0239771	−	0.999713i	$-0.507633\pi$
$233$	−0.731990	−0.0479543	−0.0239771	+	0.999713i	$0.507633\pi$
$234$	3.17290	0.207419
$235$	9.31215	0.607458
$236$	2.60618	0.169648
$237$	−9.67233	−0.628286
$238$	0.966357	0.0626396
$239$	−9.53308	−0.616643	−0.308322	−	0.951282i	$-0.599767\pi$
$239$	−9.53308	−0.616643	−0.308322	+	0.951282i	$0.599767\pi$
$240$	1.00000	0.0645497
$241$	12.5802	0.810360	0.405180	−	0.914237i	$-0.367209\pi$
$241$	12.5802	0.810360	0.405180	+	0.914237i	$0.367209\pi$
$242$	6.13344	0.394272
$243$	1.00000	0.0641500
$244$	−4.34580	−0.278211
$245$	1.00000	0.0638877
$246$	−7.13344	−0.454811
$247$	9.41195	0.598868
$248$	6.70598	0.425830
$249$	11.2449	0.712615
$250$	1.00000	0.0632456
$251$	18.0460	1.13905	0.569525	−	0.821974i	$-0.307127\pi$
$251$	18.0460	1.13905	0.569525	+	0.821974i	$0.307127\pi$
$252$	1.00000	0.0629941
$253$	−4.13926	−0.260233
$254$	13.8116	0.866616
$255$	0.966357	0.0605156
$256$	1.00000	0.0625000
$257$	−8.36393	−0.521727	−0.260864	−	0.965376i	$-0.584007\pi$
$257$	−8.36393	−0.521727	−0.260864	+	0.965376i	$0.584007\pi$
$258$	−7.87887	−0.490517
$259$	−7.67233	−0.476736
$260$	3.17290	0.196775
$261$	5.60036	0.346654
$262$	14.0854	0.870200
$263$	−9.93271	−0.612477	−0.306239	−	0.951955i	$-0.599071\pi$
$263$	−9.93271	−0.612477	−0.306239	+	0.951955i	$0.599071\pi$
$264$	−4.13926	−0.254754
$265$	11.6723	0.717026
$266$	2.96636	0.181879
$267$	15.1910	0.929676
$268$	−0.399638	−0.0244118
$269$	−29.5368	−1.80089	−0.900446	−	0.434968i	$-0.856760\pi$
$269$	−29.5368	−1.80089	−0.900446	+	0.434968i	$0.856760\pi$
$270$	1.00000	0.0608581
$271$	27.3976	1.66428	0.832142	−	0.554563i	$-0.187114\pi$
$271$	27.3976	1.66428	0.832142	+	0.554563i	$0.187114\pi$
$272$	0.966357	0.0585940
$273$	3.17290	0.192033
$274$	−8.08542	−0.488458
$275$	−4.13926	−0.249607
$276$	1.00000	0.0601929
$277$	6.81272	0.409337	0.204668	−	0.978831i	$-0.434388\pi$
$277$	6.81272	0.409337	0.204668	+	0.978831i	$0.434388\pi$
$278$	20.2966	1.21731
$279$	6.70598	0.401476
$280$	1.00000	0.0597614
$281$	21.0796	1.25750	0.628752	−	0.777606i	$-0.283566\pi$
$281$	21.0796	1.25750	0.628752	+	0.777606i	$0.283566\pi$
$282$	9.31215	0.554531
$283$	−4.22092	−0.250908	−0.125454	−	0.992099i	$-0.540039\pi$
$283$	−4.22092	−0.250908	−0.125454	+	0.992099i	$0.540039\pi$
$284$	−1.53308	−0.0909714
$285$	2.96636	0.175712
$286$	−13.1334	−0.776597
$287$	−7.13344	−0.421074
$288$	1.00000	0.0589256
$289$	−16.0662	−0.945068
$290$	5.60036	0.328865
$291$	2.63400	0.154408
$292$	−0.606179	−0.0354739
$293$	−4.06729	−0.237613	−0.118807	−	0.992917i	$-0.537907\pi$
$293$	−4.06729	−0.237613	−0.118807	+	0.992917i	$0.537907\pi$
$294$	1.00000	0.0583212
$295$	2.60618	0.151738
$296$	−7.67233	−0.445945
$297$	−4.13926	−0.240184
$298$	6.27851	0.363704
$299$	3.17290	0.183493
$300$	1.00000	0.0577350
$301$	−7.87887	−0.454131
$302$	−2.34580	−0.134985
$303$	−5.77908	−0.331999
$304$	2.96636	0.170132
$305$	−4.34580	−0.248840
$306$	0.966357	0.0552430
$307$	−1.78877	−0.102091	−0.0510454	−	0.998696i	$-0.516255\pi$
$307$	−1.78877	−0.102091	−0.0510454	+	0.998696i	$0.516255\pi$
$308$	−4.13926	−0.235856
$309$	−6.34580	−0.361000
$310$	6.70598	0.380874
$311$	−0.239052	−0.0135554	−0.00677770	−	0.999977i	$-0.502157\pi$
$311$	−0.239052	−0.0135554	−0.00677770	+	0.999977i	$0.502157\pi$
$312$	3.17290	0.179630
$313$	−33.9787	−1.92059	−0.960294	−	0.278990i	$-0.910000\pi$
$313$	−33.9787	−1.92059	−0.960294	+	0.278990i	$0.910000\pi$
$314$	−23.8250	−1.34452
$315$	1.00000	0.0563436
$316$	−9.67233	−0.544111
$317$	7.51963	0.422345	0.211172	−	0.977449i	$-0.432272\pi$
$317$	7.51963	0.422345	0.211172	+	0.977449i	$0.432272\pi$
$318$	11.6723	0.654552
$319$	−23.1813	−1.29791
$320$	1.00000	0.0559017
$321$	5.26801	0.294032
$322$	1.00000	0.0557278
$323$	2.86656	0.159500
$324$	1.00000	0.0555556
$325$	3.17290	0.176001
$326$	−17.1334	−0.948933
$327$	−7.26801	−0.401922
$328$	−7.13344	−0.393878
$329$	9.31215	0.513396
$330$	−4.13926	−0.227859
$331$	−13.4120	−0.737187	−0.368594	−	0.929591i	$-0.620161\pi$
$331$	−13.4120	−0.737187	−0.368594	+	0.929591i	$0.620161\pi$
$332$	11.2449	0.617142
$333$	−7.67233	−0.420441
$334$	−8.51288	−0.465804
$335$	−0.399638	−0.0218345
$336$	1.00000	0.0545545
$337$	2.13926	0.116533	0.0582663	−	0.998301i	$-0.481443\pi$
$337$	2.13926	0.116533	0.0582663	+	0.998301i	$0.481443\pi$
$338$	−2.93271	−0.159519
$339$	5.32654	0.289298
$340$	0.966357	0.0524081
$341$	−27.7577	−1.50317
$342$	2.96636	0.160402
$343$	1.00000	0.0539949
$344$	−7.87887	−0.424800
$345$	1.00000	0.0538382
$346$	1.63982	0.0881574
$347$	1.13344	0.0608462	0.0304231	−	0.999537i	$-0.490315\pi$
$347$	1.13344	0.0608462	0.0304231	+	0.999537i	$0.490315\pi$
$348$	5.60036	0.300211
$349$	−22.7357	−1.21702	−0.608508	−	0.793548i	$-0.708232\pi$
$349$	−22.7357	−1.21702	−0.608508	+	0.793548i	$0.708232\pi$
$350$	1.00000	0.0534522
$351$	3.17290	0.169357
$352$	−4.13926	−0.220623
$353$	−16.8847	−0.898681	−0.449341	−	0.893360i	$-0.648341\pi$
$353$	−16.8847	−0.898681	−0.449341	+	0.893360i	$0.648341\pi$
$354$	2.60618	0.138517
$355$	−1.53308	−0.0813673
$356$	15.1910	0.805123
$357$	0.966357	0.0511451
$358$	19.7577	1.04423
$359$	−5.75125	−0.303539	−0.151770	−	0.988416i	$-0.548497\pi$
$359$	−5.75125	−0.303539	−0.151770	+	0.988416i	$0.548497\pi$
$360$	1.00000	0.0527046
$361$	−10.2007	−0.536880
$362$	−18.9989	−0.998558
$363$	6.13344	0.321922
$364$	3.17290	0.166305
$365$	−0.606179	−0.0317289
$366$	−4.34580	−0.227158
$367$	−16.6127	−0.867175	−0.433587	−	0.901112i	$-0.642752\pi$
$367$	−16.6127	−0.867175	−0.433587	+	0.901112i	$0.642752\pi$
$368$	1.00000	0.0521286
$369$	−7.13344	−0.371352
$370$	−7.67233	−0.398866
$371$	11.6723	0.605997
$372$	6.70598	0.347689
$373$	27.7086	1.43470	0.717348	−	0.696715i	$-0.245356\pi$
$373$	27.7086	1.43470	0.717348	+	0.696715i	$0.245356\pi$
$374$	−4.00000	−0.206835
$375$	1.00000	0.0516398
$376$	9.31215	0.480238
$377$	17.7694	0.915170
$378$	1.00000	0.0514344
$379$	23.0843	1.18576	0.592880	−	0.805291i	$-0.297991\pi$
$379$	23.0843	1.18576	0.592880	+	0.805291i	$0.297991\pi$
$380$	2.96636	0.152171
$381$	13.8116	0.707589
$382$	−14.9403	−0.764414
$383$	−28.4493	−1.45369	−0.726847	−	0.686800i	$-0.759015\pi$
$383$	−28.4493	−1.45369	−0.726847	+	0.686800i	$0.759015\pi$
$384$	1.00000	0.0510310
$385$	−4.13926	−0.210956
$386$	−22.4225	−1.14127
$387$	−7.87887	−0.400506
$388$	2.63400	0.133721
$389$	35.1140	1.78035	0.890176	−	0.455616i	$-0.150581\pi$
$389$	35.1140	1.78035	0.890176	+	0.455616i	$0.150581\pi$
$390$	3.17290	0.160666
$391$	0.966357	0.0488708
$392$	1.00000	0.0505076
$393$	14.0854	0.710515
$394$	−15.4120	−0.776443
$395$	−9.67233	−0.486668
$396$	−4.13926	−0.208005
$397$	28.9190	1.45140	0.725702	−	0.688009i	$-0.241515\pi$
$397$	28.9190	1.45140	0.725702	+	0.688009i	$0.241515\pi$
$398$	−8.27851	−0.414964
$399$	2.96636	0.148504
$400$	1.00000	0.0500000
$401$	26.8221	1.33943	0.669716	−	0.742618i	$-0.266416\pi$
$401$	26.8221	1.33943	0.669716	+	0.742618i	$0.266416\pi$
$402$	−0.399638	−0.0199321
$403$	21.2774	1.05990
$404$	−5.77908	−0.287520
$405$	1.00000	0.0496904
$406$	5.60036	0.277941
$407$	31.7577	1.57417
$408$	0.966357	0.0478418
$409$	0.489738	0.0242160	0.0121080	−	0.999927i	$-0.496146\pi$
$409$	0.489738	0.0242160	0.0121080	+	0.999927i	$0.496146\pi$
$410$	−7.13344	−0.352295
$411$	−8.08542	−0.398824
$412$	−6.34580	−0.312635
$413$	2.60618	0.128242
$414$	1.00000	0.0491473
$415$	11.2449	0.551989
$416$	3.17290	0.155564
$417$	20.2966	0.993931
$418$	−12.2785	−0.600562
$419$	−33.8826	−1.65527	−0.827637	−	0.561263i	$-0.810315\pi$
$419$	−33.8826	−1.65527	−0.827637	+	0.561263i	$0.810315\pi$
$420$	1.00000	0.0487950
$421$	−19.3832	−0.944679	−0.472339	−	0.881417i	$-0.656590\pi$
$421$	−19.3832	−0.944679	−0.472339	+	0.881417i	$0.656590\pi$
$422$	17.3563	0.844891
$423$	9.31215	0.452772
$424$	11.6723	0.566859
$425$	0.966357	0.0468752
$426$	−1.53308	−0.0742778
$427$	−4.34580	−0.210308
$428$	5.26801	0.254639
$429$	−13.1334	−0.634088
$430$	−7.87887	−0.379953
$431$	−25.4301	−1.22492	−0.612462	−	0.790500i	$-0.709821\pi$
$431$	−25.4301	−1.22492	−0.612462	+	0.790500i	$0.709821\pi$
$432$	1.00000	0.0481125
$433$	−23.6329	−1.13572	−0.567862	−	0.823124i	$-0.692229\pi$
$433$	−23.6329	−1.13572	−0.567862	+	0.823124i	$0.692229\pi$
$434$	6.70598	0.321897
$435$	5.60036	0.268517
$436$	−7.26801	−0.348075
$437$	2.96636	0.141900
$438$	−0.606179	−0.0289644
$439$	−3.63982	−0.173719	−0.0868596	−	0.996221i	$-0.527683\pi$
$439$	−3.63982	−0.173719	−0.0868596	+	0.996221i	$0.527683\pi$
$440$	−4.13926	−0.197331
$441$	1.00000	0.0476190
$442$	3.06615	0.145842
$443$	−1.13344	−0.0538513	−0.0269257	−	0.999637i	$-0.508572\pi$
$443$	−1.13344	−0.0538513	−0.0269257	+	0.999637i	$0.508572\pi$
$444$	−7.67233	−0.364113
$445$	15.1910	0.720124
$446$	16.8336	0.797094
$447$	6.27851	0.296963
$448$	1.00000	0.0472456
$449$	−24.9316	−1.17659	−0.588297	−	0.808645i	$-0.700201\pi$
$449$	−24.9316	−1.17659	−0.588297	+	0.808645i	$0.700201\pi$
$450$	1.00000	0.0471405
$451$	29.5271	1.39038
$452$	5.32654	0.250539
$453$	−2.34580	−0.110215
$454$	−12.0441	−0.565260
$455$	3.17290	0.148748
$456$	2.96636	0.138912
$457$	22.7519	1.06429	0.532145	−	0.846653i	$-0.321386\pi$
$457$	22.7519	1.06429	0.532145	+	0.846653i	$0.321386\pi$
$458$	−1.72149	−0.0804399
$459$	0.966357	0.0451057
$460$	1.00000	0.0466252
$461$	−17.6445	−0.821787	−0.410893	−	0.911683i	$-0.634783\pi$
$461$	−17.6445	−0.821787	−0.410893	+	0.911683i	$0.634783\pi$
$462$	−4.13926	−0.192576
$463$	12.5436	0.582950	0.291475	−	0.956579i	$-0.405854\pi$
$463$	12.5436	0.582950	0.291475	+	0.956579i	$0.405854\pi$
$464$	5.60036	0.259990
$465$	6.70598	0.310982
$466$	−0.731990	−0.0339088
$467$	34.0037	1.57351	0.786753	−	0.617268i	$-0.211761\pi$
$467$	34.0037	1.57351	0.786753	+	0.617268i	$0.211761\pi$
$468$	3.17290	0.146667
$469$	−0.399638	−0.0184536
$470$	9.31215	0.429538
$471$	−23.8250	−1.09780
$472$	2.60618	0.119959
$473$	32.6127	1.49953
$474$	−9.67233	−0.444265
$475$	2.96636	0.136106
$476$	0.966357	0.0442929
$477$	11.6723	0.534439
$478$	−9.53308	−0.436033
$479$	1.13344	0.0517882	0.0258941	−	0.999665i	$-0.491757\pi$
$479$	1.13344	0.0517882	0.0258941	+	0.999665i	$0.491757\pi$
$480$	1.00000	0.0456435
$481$	−24.3435	−1.10997
$482$	12.5802	0.573011
$483$	1.00000	0.0455016
$484$	6.13344	0.278793
$485$	2.63400	0.119604
$486$	1.00000	0.0453609
$487$	26.9450	1.22100	0.610498	−	0.792018i	$-0.290969\pi$
$487$	26.9450	1.22100	0.610498	+	0.792018i	$0.290969\pi$
$488$	−4.34580	−0.196725
$489$	−17.1334	−0.774801
$490$	1.00000	0.0451754
$491$	−9.54652	−0.430828	−0.215414	−	0.976523i	$-0.569110\pi$
$491$	−9.54652	−0.430828	−0.215414	+	0.976523i	$0.569110\pi$
$492$	−7.13344	−0.321600
$493$	5.41195	0.243742
$494$	9.41195	0.423464
$495$	−4.13926	−0.186046
$496$	6.70598	0.301107
$497$	−1.53308	−0.0687679
$498$	11.2449	0.503895
$499$	−23.2007	−1.03861	−0.519304	−	0.854590i	$-0.673809\pi$
$499$	−23.2007	−1.03861	−0.519304	+	0.854590i	$0.673809\pi$
$500$	1.00000	0.0447214
$501$	−8.51288	−0.380327
$502$	18.0460	0.805430
$503$	11.4505	0.510551	0.255276	−	0.966868i	$-0.417834\pi$
$503$	11.4505	0.510551	0.255276	+	0.966868i	$0.417834\pi$
$504$	1.00000	0.0445435
$505$	−5.77908	−0.257166
$506$	−4.13926	−0.184012
$507$	−2.93271	−0.130246
$508$	13.8116	0.612790
$509$	19.8557	0.880090	0.440045	−	0.897976i	$-0.354963\pi$
$509$	19.8557	0.880090	0.440045	+	0.897976i	$0.354963\pi$
$510$	0.966357	0.0427910
$511$	−0.606179	−0.0268158
$512$	1.00000	0.0441942
$513$	2.96636	0.130968
$514$	−8.36393	−0.368917
$515$	−6.34580	−0.279629
$516$	−7.87887	−0.346848
$517$	−38.5454	−1.69522
$518$	−7.67233	−0.337103
$519$	1.63982	0.0719802
$520$	3.17290	0.139141
$521$	17.4579	0.764845	0.382422	−	0.923988i	$-0.375090\pi$
$521$	17.4579	0.764845	0.382422	+	0.923988i	$0.375090\pi$
$522$	5.60036	0.245121
$523$	−29.6041	−1.29450	−0.647249	−	0.762279i	$-0.724080\pi$
$523$	−29.6041	−1.29450	−0.647249	+	0.762279i	$0.724080\pi$
$524$	14.0854	0.615324
$525$	1.00000	0.0436436
$526$	−9.93271	−0.433087
$527$	6.48037	0.282289
$528$	−4.13926	−0.180138
$529$	1.00000	0.0434783
$530$	11.6723	0.507014
$531$	2.60618	0.113099
$532$	2.96636	0.128608
$533$	−22.6337	−0.980373
$534$	15.1910	0.657380
$535$	5.26801	0.227756
$536$	−0.399638	−0.0172617
$537$	19.7577	0.852610
$538$	−29.5368	−1.27342
$539$	−4.13926	−0.178290
$540$	1.00000	0.0430331
$541$	11.8538	0.509634	0.254817	−	0.966989i	$-0.417985\pi$
$541$	11.8538	0.509634	0.254817	+	0.966989i	$0.417985\pi$
$542$	27.3976	1.17683
$543$	−18.9989	−0.815319
$544$	0.966357	0.0414322
$545$	−7.26801	−0.311327
$546$	3.17290	0.135788
$547$	−37.6115	−1.60815	−0.804077	−	0.594526i	$-0.797340\pi$
$547$	−37.6115	−1.60815	−0.804077	+	0.594526i	$0.797340\pi$
$548$	−8.08542	−0.345392
$549$	−4.34580	−0.185474
$550$	−4.13926	−0.176498
$551$	16.6127	0.707724
$552$	1.00000	0.0425628
$553$	−9.67233	−0.411309
$554$	6.81272	0.289445
$555$	−7.67233	−0.325672
$556$	20.2966	0.860769
$557$	−16.0065	−0.678217	−0.339109	−	0.940747i	$-0.610125\pi$
$557$	−16.0065	−0.678217	−0.339109	+	0.940747i	$0.610125\pi$
$558$	6.70598	0.283887
$559$	−24.9989	−1.05734
$560$	1.00000	0.0422577
$561$	−4.00000	−0.168880
$562$	21.0796	0.889189
$563$	18.2033	0.767179	0.383590	−	0.923504i	$-0.374688\pi$
$563$	18.2033	0.767179	0.383590	+	0.923504i	$0.374688\pi$
$564$	9.31215	0.392112
$565$	5.32654	0.224089
$566$	−4.22092	−0.177419
$567$	1.00000	0.0419961
$568$	−1.53308	−0.0643265
$569$	−17.3312	−0.726563	−0.363281	−	0.931680i	$-0.618344\pi$
$569$	−17.3312	−0.726563	−0.363281	+	0.931680i	$0.618344\pi$
$570$	2.96636	0.124247
$571$	−1.67233	−0.0699849	−0.0349925	−	0.999388i	$-0.511141\pi$
$571$	−1.67233	−0.0699849	−0.0349925	+	0.999388i	$0.511141\pi$
$572$	−13.1334	−0.549137
$573$	−14.9403	−0.624142
$574$	−7.13344	−0.297744
$575$	1.00000	0.0417029
$576$	1.00000	0.0416667
$577$	8.36393	0.348195	0.174097	−	0.984728i	$-0.444299\pi$
$577$	8.36393	0.348195	0.174097	+	0.984728i	$0.444299\pi$
$578$	−16.0662	−0.668264
$579$	−22.4225	−0.931845
$580$	5.60036	0.232542
$581$	11.2449	0.466516
$582$	2.63400	0.109183
$583$	−48.3148	−2.00099
$584$	−0.606179	−0.0250839
$585$	3.17290	0.131183
$586$	−4.06729	−0.168018
$587$	−4.02689	−0.166208	−0.0831038	−	0.996541i	$-0.526483\pi$
$587$	−4.02689	−0.166208	−0.0831038	+	0.996541i	$0.526483\pi$
$588$	1.00000	0.0412393
$589$	19.8923	0.819649
$590$	2.60618	0.107295
$591$	−15.4120	−0.633963
$592$	−7.67233	−0.315331
$593$	23.6723	0.972106	0.486053	−	0.873929i	$-0.338436\pi$
$593$	23.6723	0.972106	0.486053	+	0.873929i	$0.338436\pi$
$594$	−4.13926	−0.169836
$595$	0.966357	0.0396168
$596$	6.27851	0.257178
$597$	−8.27851	−0.338817
$598$	3.17290	0.129749
$599$	−13.5887	−0.555220	−0.277610	−	0.960694i	$-0.589542\pi$
$599$	−13.5887	−0.555220	−0.277610	+	0.960694i	$0.589542\pi$
$600$	1.00000	0.0408248
$601$	−1.05678	−0.0431071	−0.0215536	−	0.999768i	$-0.506861\pi$
$601$	−1.05678	−0.0431071	−0.0215536	+	0.999768i	$0.506861\pi$
$602$	−7.87887	−0.321119
$603$	−0.399638	−0.0162745
$604$	−2.34580	−0.0954491
$605$	6.13344	0.249360
$606$	−5.77908	−0.234759
$607$	−39.9593	−1.62190	−0.810949	−	0.585117i	$-0.801048\pi$
$607$	−39.9593	−1.62190	−0.810949	+	0.585117i	$0.801048\pi$
$608$	2.96636	0.120302
$609$	5.60036	0.226938
$610$	−4.34580	−0.175956
$611$	29.5465	1.19532
$612$	0.966357	0.0390627
$613$	1.81854	0.0734500	0.0367250	−	0.999325i	$-0.488307\pi$
$613$	1.81854	0.0734500	0.0367250	+	0.999325i	$0.488307\pi$
$614$	−1.78877	−0.0721890
$615$	−7.13344	−0.287648
$616$	−4.13926	−0.166775
$617$	31.1516	1.25411	0.627057	−	0.778973i	$-0.284259\pi$
$617$	31.1516	1.25411	0.627057	+	0.778973i	$0.284259\pi$
$618$	−6.34580	−0.255265
$619$	−39.9458	−1.60556	−0.802779	−	0.596276i	$-0.796646\pi$
$619$	−39.9458	−1.60556	−0.802779	+	0.596276i	$0.796646\pi$
$620$	6.70598	0.269318
$621$	1.00000	0.0401286
$622$	−0.239052	−0.00958512
$623$	15.1910	0.608616
$624$	3.17290	0.127018
$625$	1.00000	0.0400000
$626$	−33.9787	−1.35806
$627$	−12.2785	−0.490357
$628$	−23.8250	−0.950722
$629$	−7.41421	−0.295624
$630$	1.00000	0.0398410
$631$	25.9777	1.03416	0.517079	−	0.855938i	$-0.327019\pi$
$631$	25.9777	1.03416	0.517079	+	0.855938i	$0.327019\pi$
$632$	−9.67233	−0.384745
$633$	17.3563	0.689851
$634$	7.51963	0.298643
$635$	13.8116	0.548096
$636$	11.6723	0.462838
$637$	3.17290	0.125715
$638$	−23.1813	−0.917758
$639$	−1.53308	−0.0606476
$640$	1.00000	0.0395285
$641$	−45.7443	−1.80679	−0.903396	−	0.428808i	$-0.858934\pi$
$641$	−45.7443	−1.80679	−0.903396	+	0.428808i	$0.858934\pi$
$642$	5.26801	0.207912
$643$	−10.4228	−0.411034	−0.205517	−	0.978654i	$-0.565888\pi$
$643$	−10.4228	−0.411034	−0.205517	+	0.978654i	$0.565888\pi$
$644$	1.00000	0.0394055
$645$	−7.87887	−0.310230
$646$	2.86656	0.112783
$647$	−10.3899	−0.408471	−0.204235	−	0.978922i	$-0.565471\pi$
$647$	−10.3899	−0.408471	−0.204235	+	0.978922i	$0.565471\pi$
$648$	1.00000	0.0392837
$649$	−10.7876	−0.423452
$650$	3.17290	0.124451
$651$	6.70598	0.262828
$652$	−17.1334	−0.670997
$653$	−8.12294	−0.317875	−0.158938	−	0.987289i	$-0.550807\pi$
$653$	−8.12294	−0.317875	−0.158938	+	0.987289i	$0.550807\pi$
$654$	−7.26801	−0.284202
$655$	14.0854	0.550363
$656$	−7.13344	−0.278514
$657$	−0.606179	−0.0236493
$658$	9.31215	0.363026
$659$	−39.6835	−1.54585	−0.772925	−	0.634497i	$-0.781207\pi$
$659$	−39.6835	−1.54585	−0.772925	+	0.634497i	$0.781207\pi$
$660$	−4.13926	−0.161120
$661$	−34.3148	−1.33469	−0.667345	−	0.744749i	$-0.732569\pi$
$661$	−34.3148	−1.33469	−0.667345	+	0.744749i	$0.732569\pi$
$662$	−13.4120	−0.521270
$663$	3.06615	0.119080
$664$	11.2449	0.436386
$665$	2.96636	0.115030
$666$	−7.67233	−0.297297
$667$	5.60036	0.216847
$668$	−8.51288	−0.329373
$669$	16.8336	0.650824
$670$	−0.399638	−0.0154394
$671$	17.9884	0.694433
$672$	1.00000	0.0385758
$673$	−41.4886	−1.59927	−0.799634	−	0.600488i	$-0.794973\pi$
$673$	−41.4886	−1.59927	−0.799634	+	0.600488i	$0.794973\pi$
$674$	2.13926	0.0824011
$675$	1.00000	0.0384900
$676$	−2.93271	−0.112797
$677$	0.787642	0.0302715	0.0151358	−	0.999885i	$-0.495182\pi$
$677$	0.787642	0.0302715	0.0151358	+	0.999885i	$0.495182\pi$
$678$	5.32654	0.204564
$679$	2.63400	0.101084
$680$	0.966357	0.0370581
$681$	−12.0441	−0.461533
$682$	−27.7577	−1.06290
$683$	−5.26801	−0.201575	−0.100787	−	0.994908i	$-0.532136\pi$
$683$	−5.26801	−0.201575	−0.100787	+	0.994908i	$0.532136\pi$
$684$	2.96636	0.113422
$685$	−8.08542	−0.308928
$686$	1.00000	0.0381802
$687$	−1.72149	−0.0656789
$688$	−7.87887	−0.300379
$689$	37.0351	1.41093
$690$	1.00000	0.0380693
$691$	8.31603	0.316357	0.158178	−	0.987411i	$-0.449438\pi$
$691$	8.31603	0.316357	0.158178	+	0.987411i	$0.449438\pi$
$692$	1.63982	0.0623367
$693$	−4.13926	−0.157237
$694$	1.13344	0.0430248
$695$	20.2966	0.769895
$696$	5.60036	0.212281
$697$	−6.89345	−0.261108
$698$	−22.7357	−0.860560
$699$	−0.731990	−0.0276864
$700$	1.00000	0.0377964
$701$	39.1140	1.47732	0.738659	−	0.674080i	$-0.235460\pi$
$701$	39.1140	1.47732	0.738659	+	0.674080i	$0.235460\pi$
$702$	3.17290	0.119753
$703$	−22.7589	−0.858367
$704$	−4.13926	−0.156004
$705$	9.31215	0.350716
$706$	−16.8847	−0.635464
$707$	−5.77908	−0.217345
$708$	2.60618	0.0979462
$709$	9.67883	0.363496	0.181748	−	0.983345i	$-0.441824\pi$
$709$	9.67883	0.363496	0.181748	+	0.983345i	$0.441824\pi$
$710$	−1.53308	−0.0575353
$711$	−9.67233	−0.362741
$712$	15.1910	0.569308
$713$	6.70598	0.251141
$714$	0.966357	0.0361650
$715$	−13.1334	−0.491163
$716$	19.7577	0.738382
$717$	−9.53308	−0.356019
$718$	−5.75125	−0.214635
$719$	−0.317971	−0.0118583	−0.00592916	−	0.999982i	$-0.501887\pi$
$719$	−0.317971	−0.0118583	−0.00592916	+	0.999982i	$0.501887\pi$
$720$	1.00000	0.0372678
$721$	−6.34580	−0.236330
$722$	−10.2007	−0.379632
$723$	12.5802	0.467861
$724$	−18.9989	−0.706087
$725$	5.60036	0.207992
$726$	6.13344	0.227633
$727$	−15.5582	−0.577020	−0.288510	−	0.957477i	$-0.593160\pi$
$727$	−15.5582	−0.577020	−0.288510	+	0.957477i	$0.593160\pi$
$728$	3.17290	0.117595
$729$	1.00000	0.0370370
$730$	−0.606179	−0.0224357
$731$	−7.61381	−0.281607
$732$	−4.34580	−0.160625
$733$	27.4482	1.01382	0.506911	−	0.861998i	$-0.330787\pi$
$733$	27.4482	1.01382	0.506911	+	0.861998i	$0.330787\pi$
$734$	−16.6127	−0.613185
$735$	1.00000	0.0368856
$736$	1.00000	0.0368605
$737$	1.65420	0.0609333
$738$	−7.13344	−0.262586
$739$	24.6127	0.905392	0.452696	−	0.891665i	$-0.350462\pi$
$739$	24.6127	0.905392	0.452696	+	0.891665i	$0.350462\pi$
$740$	−7.67233	−0.282041
$741$	9.41195	0.345757
$742$	11.6723	0.428505
$743$	38.5454	1.41409	0.707047	−	0.707167i	$-0.250027\pi$
$743$	38.5454	1.41409	0.707047	+	0.707167i	$0.250027\pi$
$744$	6.70598	0.245853
$745$	6.27851	0.230027
$746$	27.7086	1.01448
$747$	11.2449	0.411428
$748$	−4.00000	−0.146254
$749$	5.26801	0.192489
$750$	1.00000	0.0365148
$751$	31.0286	1.13225	0.566125	−	0.824319i	$-0.308442\pi$
$751$	31.0286	1.13225	0.566125	+	0.824319i	$0.308442\pi$
$752$	9.31215	0.339579
$753$	18.0460	0.657631
$754$	17.7694	0.647123
$755$	−2.34580	−0.0853723
$756$	1.00000	0.0363696
$757$	13.1269	0.477107	0.238553	−	0.971129i	$-0.423327\pi$
$757$	13.1269	0.477107	0.238553	+	0.971129i	$0.423327\pi$
$758$	23.0843	0.838459
$759$	−4.13926	−0.150245
$760$	2.96636	0.107601
$761$	−36.1592	−1.31077	−0.655385	−	0.755295i	$-0.727494\pi$
$761$	−36.1592	−1.31077	−0.655385	+	0.755295i	$0.727494\pi$
$762$	13.8116	0.500341
$763$	−7.26801	−0.263120
$764$	−14.9403	−0.540523
$765$	0.966357	0.0349387
$766$	−28.4493	−1.02792
$767$	8.26914	0.298581
$768$	1.00000	0.0360844
$769$	−26.6206	−0.959962	−0.479981	−	0.877279i	$-0.659356\pi$
$769$	−26.6206	−0.959962	−0.479981	+	0.877279i	$0.659356\pi$
$770$	−4.13926	−0.149168
$771$	−8.36393	−0.301219
$772$	−22.4225	−0.807002
$773$	−51.4770	−1.85150	−0.925749	−	0.378139i	$-0.876564\pi$
$773$	−51.4770	−1.85150	−0.925749	+	0.378139i	$0.876564\pi$
$774$	−7.87887	−0.283200
$775$	6.70598	0.240886
$776$	2.63400	0.0945553
$777$	−7.67233	−0.275243
$778$	35.1140	1.25890
$779$	−21.1603	−0.758147
$780$	3.17290	0.113608
$781$	6.34580	0.227070
$782$	0.966357	0.0345569
$783$	5.60036	0.200141
$784$	1.00000	0.0357143
$785$	−23.8250	−0.850352
$786$	14.0854	0.502410
$787$	−14.0191	−0.499726	−0.249863	−	0.968281i	$-0.580386\pi$
$787$	−14.0191	−0.499726	−0.249863	+	0.968281i	$0.580386\pi$
$788$	−15.4120	−0.549028
$789$	−9.93271	−0.353614
$790$	−9.67233	−0.344126
$791$	5.32654	0.189390
$792$	−4.13926	−0.147082
$793$	−13.7888	−0.489654
$794$	28.9190	1.02630
$795$	11.6723	0.413975
$796$	−8.27851	−0.293424
$797$	37.1581	1.31621	0.658103	−	0.752928i	$-0.271359\pi$
$797$	37.1581	1.31621	0.658103	+	0.752928i	$0.271359\pi$
$798$	2.96636	0.105008
$799$	8.99887	0.318357
$800$	1.00000	0.0353553
$801$	15.1910	0.536749
$802$	26.8221	0.947121
$803$	2.50913	0.0885453
$804$	−0.399638	−0.0140941
$805$	1.00000	0.0352454
$806$	21.2774	0.749464
$807$	−29.5368	−1.03975
$808$	−5.77908	−0.203307
$809$	−39.6115	−1.39267	−0.696334	−	0.717718i	$-0.745187\pi$
$809$	−39.6115	−1.39267	−0.696334	+	0.717718i	$0.745187\pi$
$810$	1.00000	0.0351364
$811$	−28.8443	−1.01286	−0.506430	−	0.862281i	$-0.669035\pi$
$811$	−28.8443	−1.01286	−0.506430	+	0.862281i	$0.669035\pi$
$812$	5.60036	0.196534
$813$	27.3976	0.960875
$814$	31.7577	1.11311
$815$	−17.1334	−0.600158
$816$	0.966357	0.0338293
$817$	−23.3716	−0.817667
$818$	0.489738	0.0171233
$819$	3.17290	0.110870
$820$	−7.13344	−0.249110
$821$	−12.4763	−0.435426	−0.217713	−	0.976013i	$-0.569860\pi$
$821$	−12.4763	−0.435426	−0.217713	+	0.976013i	$0.569860\pi$
$822$	−8.08542	−0.282011
$823$	−10.4763	−0.365181	−0.182590	−	0.983189i	$-0.558448\pi$
$823$	−10.4763	−0.365181	−0.182590	+	0.983189i	$0.558448\pi$
$824$	−6.34580	−0.221066
$825$	−4.13926	−0.144110
$826$	2.60618	0.0906806
$827$	−3.55816	−0.123729	−0.0618646	−	0.998085i	$-0.519705\pi$
$827$	−3.55816	−0.123729	−0.0618646	+	0.998085i	$0.519705\pi$
$828$	1.00000	0.0347524
$829$	−23.7252	−0.824012	−0.412006	−	0.911181i	$-0.635172\pi$
$829$	−23.7252	−0.824012	−0.412006	+	0.911181i	$0.635172\pi$
$830$	11.2449	0.390315
$831$	6.81272	0.236331
$832$	3.17290	0.110000
$833$	0.966357	0.0334823
$834$	20.2966	0.702815
$835$	−8.51288	−0.294600
$836$	−12.2785	−0.424661
$837$	6.70598	0.231792
$838$	−33.8826	−1.17046
$839$	−56.9795	−1.96715	−0.983575	−	0.180500i	$-0.942228\pi$
$839$	−56.9795	−1.96715	−0.983575	+	0.180500i	$0.942228\pi$
$840$	1.00000	0.0345033
$841$	2.36406	0.0815192
$842$	−19.3832	−0.667989
$843$	21.0796	0.726020
$844$	17.3563	0.597428
$845$	−2.93271	−0.100888
$846$	9.31215	0.320158
$847$	6.13344	0.210747
$848$	11.6723	0.400830
$849$	−4.22092	−0.144862
$850$	0.966357	0.0331458
$851$	−7.67233	−0.263004
$852$	−1.53308	−0.0525223
$853$	−10.0395	−0.343745	−0.171872	−	0.985119i	$-0.554982\pi$
$853$	−10.0395	−0.343745	−0.171872	+	0.985119i	$0.554982\pi$
$854$	−4.34580	−0.148710
$855$	2.96636	0.101447
$856$	5.26801	0.180057
$857$	9.82791	0.335715	0.167857	−	0.985811i	$-0.446315\pi$
$857$	9.82791	0.335715	0.167857	+	0.985811i	$0.446315\pi$
$858$	−13.1334	−0.448368
$859$	−8.56766	−0.292325	−0.146162	−	0.989261i	$-0.546692\pi$
$859$	−8.56766	−0.292325	−0.146162	+	0.989261i	$0.546692\pi$
$860$	−7.87887	−0.268667
$861$	−7.13344	−0.243107
$862$	−25.4301	−0.866152
$863$	−1.26801	−0.0431636	−0.0215818	−	0.999767i	$-0.506870\pi$
$863$	−1.26801	−0.0431636	−0.0215818	+	0.999767i	$0.506870\pi$
$864$	1.00000	0.0340207
$865$	1.63982	0.0557556
$866$	−23.6329	−0.803078
$867$	−16.0662	−0.545635
$868$	6.70598	0.227616
$869$	40.0363	1.35814
$870$	5.60036	0.189870
$871$	−1.26801	−0.0429649
$872$	−7.26801	−0.246126
$873$	2.63400	0.0891476
$874$	2.96636	0.100339
$875$	1.00000	0.0338062
$876$	−0.606179	−0.0204809
$877$	17.9578	0.606392	0.303196	−	0.952928i	$-0.401946\pi$
$877$	17.9578	0.606392	0.303196	+	0.952928i	$0.401946\pi$
$878$	−3.63982	−0.122838
$879$	−4.06729	−0.137186
$880$	−4.13926	−0.139534
$881$	32.0692	1.08044	0.540220	−	0.841524i	$-0.318341\pi$
$881$	32.0692	1.08044	0.540220	+	0.841524i	$0.318341\pi$
$882$	1.00000	0.0336718
$883$	19.4003	0.652873	0.326436	−	0.945219i	$-0.394152\pi$
$883$	19.4003	0.652873	0.326436	+	0.945219i	$0.394152\pi$
$884$	3.06615	0.103126
$885$	2.60618	0.0876058
$886$	−1.13344	−0.0380786
$887$	19.9002	0.668183	0.334092	−	0.942541i	$-0.391570\pi$
$887$	19.9002	0.668183	0.334092	+	0.942541i	$0.391570\pi$
$888$	−7.67233	−0.257467
$889$	13.8116	0.463226
$890$	15.1910	0.509204
$891$	−4.13926	−0.138670
$892$	16.8336	0.563631
$893$	27.6232	0.924374
$894$	6.27851	0.209985
$895$	19.7577	0.660429
$896$	1.00000	0.0334077
$897$	3.17290	0.105940
$898$	−24.9316	−0.831978
$899$	37.5559	1.25256
$900$	1.00000	0.0333333
$901$	11.2796	0.375779
$902$	29.5271	0.983146
$903$	−7.87887	−0.262193
$904$	5.32654	0.177158
$905$	−18.9989	−0.631544
$906$	−2.34580	−0.0779339
$907$	11.5716	0.384229	0.192114	−	0.981373i	$-0.438466\pi$
$907$	11.5716	0.384229	0.192114	+	0.981373i	$0.438466\pi$
$908$	−12.0441	−0.399699
$909$	−5.77908	−0.191680
$910$	3.17290	0.105181
$911$	−11.3534	−0.376156	−0.188078	−	0.982154i	$-0.560226\pi$
$911$	−11.3534	−0.376156	−0.188078	+	0.982154i	$0.560226\pi$
$912$	2.96636	0.0982259
$913$	−46.5454	−1.54043
$914$	22.7519	0.752567
$915$	−4.34580	−0.143668
$916$	−1.72149	−0.0568796
$917$	14.0854	0.465141
$918$	0.966357	0.0318945
$919$	−4.64657	−0.153276	−0.0766382	−	0.997059i	$-0.524419\pi$
$919$	−4.64657	−0.153276	−0.0766382	+	0.997059i	$0.524419\pi$
$920$	1.00000	0.0329690
$921$	−1.78877	−0.0589421
$922$	−17.6445	−0.581091
$923$	−4.86430	−0.160110
$924$	−4.13926	−0.136172
$925$	−7.67233	−0.252265
$926$	12.5436	0.412208
$927$	−6.34580	−0.208423
$928$	5.60036	0.183841
$929$	−55.3136	−1.81478	−0.907391	−	0.420288i	$-0.861929\pi$
$929$	−55.3136	−1.81478	−0.907391	+	0.420288i	$0.861929\pi$
$930$	6.70598	0.219898
$931$	2.96636	0.0972184
$932$	−0.731990	−0.0239771
$933$	−0.239052	−0.00782622
$934$	34.0037	1.11264
$935$	−4.00000	−0.130814
$936$	3.17290	0.103709
$937$	28.2168	0.921802	0.460901	−	0.887451i	$-0.347526\pi$
$937$	28.2168	0.921802	0.460901	+	0.887451i	$0.347526\pi$
$938$	−0.399638	−0.0130486
$939$	−33.9787	−1.10885
$940$	9.31215	0.303729
$941$	−39.6115	−1.29130	−0.645650	−	0.763634i	$-0.723413\pi$
$941$	−39.6115	−1.29130	−0.645650	+	0.763634i	$0.723413\pi$
$942$	−23.8250	−0.776262
$943$	−7.13344	−0.232297
$944$	2.60618	0.0848239
$945$	1.00000	0.0325300
$946$	32.6127	1.06033
$947$	21.8538	0.710153	0.355076	−	0.934837i	$-0.384455\pi$
$947$	21.8538	0.710153	0.355076	+	0.934837i	$0.384455\pi$
$948$	−9.67233	−0.314143
$949$	−1.92334	−0.0624344
$950$	2.96636	0.0962413
$951$	7.51963	0.243841
$952$	0.966357	0.0313198
$953$	−19.5359	−0.632830	−0.316415	−	0.948621i	$-0.602479\pi$
$953$	−19.5359	−0.632830	−0.316415	+	0.948621i	$0.602479\pi$
$954$	11.6723	0.377906
$955$	−14.9403	−0.483458
$956$	−9.53308	−0.308322
$957$	−23.1813	−0.749346
$958$	1.13344	0.0366198
$959$	−8.08542	−0.261092
$960$	1.00000	0.0322749
$961$	13.9701	0.450649
$962$	−24.3435	−0.784867
$963$	5.26801	0.169759
$964$	12.5802	0.405180
$965$	−22.4225	−0.721804
$966$	1.00000	0.0321745
$967$	33.2352	1.06877	0.534386	−	0.845241i	$-0.320543\pi$
$967$	33.2352	1.06877	0.534386	+	0.845241i	$0.320543\pi$
$968$	6.13344	0.197136
$969$	2.86656	0.0920872
$970$	2.63400	0.0845728
$971$	30.4684	0.977778	0.488889	−	0.872346i	$-0.337402\pi$
$971$	30.4684	0.977778	0.488889	+	0.872346i	$0.337402\pi$
$972$	1.00000	0.0320750
$973$	20.2966	0.650680
$974$	26.9450	0.863374
$975$	3.17290	0.101614
$976$	−4.34580	−0.139106
$977$	−0.579289	−0.0185331	−0.00926655	−	0.999957i	$-0.502950\pi$
$977$	−0.579289	−0.0185331	−0.00926655	+	0.999957i	$0.502950\pi$
$978$	−17.1334	−0.547867
$979$	−62.8796	−2.00964
$980$	1.00000	0.0319438
$981$	−7.26801	−0.232050
$982$	−9.54652	−0.304642
$983$	28.1802	0.898809	0.449404	−	0.893328i	$-0.351636\pi$
$983$	28.1802	0.898809	0.449404	+	0.893328i	$0.351636\pi$
$984$	−7.13344	−0.227406
$985$	−15.4120	−0.491066
$986$	5.41195	0.172352
$987$	9.31215	0.296409
$988$	9.41195	0.299434
$989$	−7.87887	−0.250534
$990$	−4.13926	−0.131554
$991$	12.6127	0.400655	0.200327	−	0.979729i	$-0.435799\pi$
$991$	12.6127	0.400655	0.200327	+	0.979729i	$0.435799\pi$
$992$	6.70598	0.212915
$993$	−13.4120	−0.425615
$994$	−1.53308	−0.0486262
$995$	−8.27851	−0.262446
$996$	11.2449	0.356307
$997$	−4.27008	−0.135235	−0.0676174	−	0.997711i	$-0.521540\pi$
$997$	−4.27008	−0.135235	−0.0676174	+	0.997711i	$0.521540\pi$
$998$	−23.2007	−0.734406
$999$	−7.67233	−0.242742

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.ce.1.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.ce.1.1	✓	4	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} +1.00000 q^{6} +1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -4.13926 q^{11} +1.00000 q^{12} +3.17290 q^{13} +1.00000 q^{14} +1.00000 q^{15} +1.00000 q^{16} +0.966357 q^{17} +1.00000 q^{18} +2.96636 q^{19} +1.00000 q^{20} +1.00000 q^{21} -4.13926 q^{22} +1.00000 q^{23} +1.00000 q^{24} +1.00000 q^{25} +3.17290 q^{26} +1.00000 q^{27} +1.00000 q^{28} +5.60036 q^{29} +1.00000 q^{30} +6.70598 q^{31} +1.00000 q^{32} -4.13926 q^{33} +0.966357 q^{34} +1.00000 q^{35} +1.00000 q^{36} -7.67233 q^{37} +2.96636 q^{38} +3.17290 q^{39} +1.00000 q^{40} -7.13344 q^{41} +1.00000 q^{42} -7.87887 q^{43} -4.13926 q^{44} +1.00000 q^{45} +1.00000 q^{46} +9.31215 q^{47} +1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +0.966357 q^{51} +3.17290 q^{52} +11.6723 q^{53} +1.00000 q^{54} -4.13926 q^{55} +1.00000 q^{56} +2.96636 q^{57} +5.60036 q^{58} +2.60618 q^{59} +1.00000 q^{60} -4.34580 q^{61} +6.70598 q^{62} +1.00000 q^{63} +1.00000 q^{64} +3.17290 q^{65} -4.13926 q^{66} -0.399638 q^{67} +0.966357 q^{68} +1.00000 q^{69} +1.00000 q^{70} -1.53308 q^{71} +1.00000 q^{72} -0.606179 q^{73} -7.67233 q^{74} +1.00000 q^{75} +2.96636 q^{76} -4.13926 q^{77} +3.17290 q^{78} -9.67233 q^{79} +1.00000 q^{80} +1.00000 q^{81} -7.13344 q^{82} +11.2449 q^{83} +1.00000 q^{84} +0.966357 q^{85} -7.87887 q^{86} +5.60036 q^{87} -4.13926 q^{88} +15.1910 q^{89} +1.00000 q^{90} +3.17290 q^{91} +1.00000 q^{92} +6.70598 q^{93} +9.31215 q^{94} +2.96636 q^{95} +1.00000 q^{96} +2.63400 q^{97} +1.00000 q^{98} -4.13926 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9	\( 4 q + 4 q^{2} + 4 q^{3} + 4 q^{4} + 4 q^{5} + 4 q^{6} + 4 q^{7} + 4 q^{8} + 4 q^{9} + 4 q^{10} + 4 q^{12} + 2 q^{13} + 4 q^{14} + 4 q^{15} + 4 q^{16} - 2 q^{17} + 4 q^{18} + 6 q^{19} + 4 q^{20} + 4 q^{21} + 4 q^{23} + 4 q^{24} + 4 q^{25} + 2 q^{26} + 4 q^{27} + 4 q^{28} + 14 q^{29} + 4 q^{30} - 4 q^{31} + 4 q^{32} - 2 q^{34} + 4 q^{35} + 4 q^{36} + 6 q^{37} + 6 q^{38} + 2 q^{39} + 4 q^{40} + 4 q^{42} + 10 q^{43} + 4 q^{45} + 4 q^{46} + 10 q^{47} + 4 q^{48} + 4 q^{49} + 4 q^{50} - 2 q^{51} + 2 q^{52} + 10 q^{53} + 4 q^{54} + 4 q^{56} + 6 q^{57} + 14 q^{58} + 14 q^{59} + 4 q^{60} + 4 q^{61} - 4 q^{62} + 4 q^{63} + 4 q^{64} + 2 q^{65} - 10 q^{67} - 2 q^{68} + 4 q^{69} + 4 q^{70} + 14 q^{71} + 4 q^{72} - 6 q^{73} + 6 q^{74} + 4 q^{75} + 6 q^{76} + 2 q^{78} - 2 q^{79} + 4 q^{80} + 4 q^{81} + 6 q^{83} + 4 q^{84} - 2 q^{85} + 10 q^{86} + 14 q^{87} - 8 q^{89} + 4 q^{90} + 2 q^{91} + 4 q^{92} - 4 q^{93} + 10 q^{94} + 6 q^{95} + 4 q^{96} + 8 q^{97} + 4 q^{98}+O(q^{100}) \) 4 * q + 4 * q^2 + 4 * q^3 + 4 * q^4 + 4 * q^5 + 4 * q^6 + 4 * q^7 + 4 * q^8 + 4 * q^9 + 4 * q^10 + 4 * q^12 + 2 * q^13 + 4 * q^14 + 4 * q^15 + 4 * q^16 - 2 * q^17 + 4 * q^18 + 6 * q^19 + 4 * q^20 + 4 * q^21 + 4 * q^23 + 4 * q^24 + 4 * q^25 + 2 * q^26 + 4 * q^27 + 4 * q^28 + 14 * q^29 + 4 * q^30 - 4 * q^31 + 4 * q^32 - 2 * q^34 + 4 * q^35 + 4 * q^36 + 6 * q^37 + 6 * q^38 + 2 * q^39 + 4 * q^40 + 4 * q^42 + 10 * q^43 + 4 * q^45 + 4 * q^46 + 10 * q^47 + 4 * q^48 + 4 * q^49 + 4 * q^50 - 2 * q^51 + 2 * q^52 + 10 * q^53 + 4 * q^54 + 4 * q^56 + 6 * q^57 + 14 * q^58 + 14 * q^59 + 4 * q^60 + 4 * q^61 - 4 * q^62 + 4 * q^63 + 4 * q^64 + 2 * q^65 - 10 * q^67 - 2 * q^68 + 4 * q^69 + 4 * q^70 + 14 * q^71 + 4 * q^72 - 6 * q^73 + 6 * q^74 + 4 * q^75 + 6 * q^76 + 2 * q^78 - 2 * q^79 + 4 * q^80 + 4 * q^81 + 6 * q^83 + 4 * q^84 - 2 * q^85 + 10 * q^86 + 14 * q^87 - 8 * q^89 + 4 * q^90 + 2 * q^91 + 4 * q^92 - 4 * q^93 + 10 * q^94 + 6 * q^95 + 4 * q^96 + 8 * q^97 + 4 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

Properties

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