LMFDB - Embedded newform 4830.2.a.ca.1.2

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:	$1$
Dimension:	$3$
Coefficient field:	3.3.316.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 4x + 2 $ x^3 - x^2 - 4*x + 2
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			1.2
Root			$-1.81361$ 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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.578337 q^{11} -1.00000 q^{12} +4.20555 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.62721 q^{17} +1.00000 q^{18} -5.62721 q^{19} +1.00000 q^{20} +1.00000 q^{21} -0.578337 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.20555 q^{26} -1.00000 q^{27} -1.00000 q^{28} +5.83276 q^{29} -1.00000 q^{30} -9.62721 q^{31} +1.00000 q^{32} +0.578337 q^{33} -7.62721 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -5.62721 q^{38} -4.20555 q^{39} +1.00000 q^{40} +3.15667 q^{41} +1.00000 q^{42} -0.578337 q^{43} -0.578337 q^{44} +1.00000 q^{45} -1.00000 q^{46} -9.62721 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +7.62721 q^{51} +4.20555 q^{52} -2.00000 q^{53} -1.00000 q^{54} -0.578337 q^{55} -1.00000 q^{56} +5.62721 q^{57} +5.83276 q^{58} -8.41110 q^{59} -1.00000 q^{60} +1.25443 q^{61} -9.62721 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.20555 q^{65} +0.578337 q^{66} -8.57834 q^{67} -7.62721 q^{68} +1.00000 q^{69} -1.00000 q^{70} -6.67609 q^{71} +1.00000 q^{72} +0.843326 q^{73} -2.00000 q^{74} -1.00000 q^{75} -5.62721 q^{76} +0.578337 q^{77} -4.20555 q^{78} +10.0978 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.15667 q^{82} +10.0383 q^{83} +1.00000 q^{84} -7.62721 q^{85} -0.578337 q^{86} -5.83276 q^{87} -0.578337 q^{88} -0.951124 q^{89} +1.00000 q^{90} -4.20555 q^{91} -1.00000 q^{92} +9.62721 q^{93} -9.62721 q^{94} -5.62721 q^{95} -1.00000 q^{96} -3.04888 q^{97} +1.00000 q^{98} -0.578337 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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} - 3 q^{12} - 2 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 10 q^{17} + 3 q^{18} - 4 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} - 10 q^{29} - 3 q^{30} - 16 q^{31} + 3 q^{32} - 10 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} + 6 q^{41} + 3 q^{42} + 3 q^{45} - 3 q^{46} - 16 q^{47} - 3 q^{48} + 3 q^{49} + 3 q^{50} + 10 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{54} - 3 q^{56} + 4 q^{57} - 10 q^{58} + 4 q^{59} - 3 q^{60} - 22 q^{61} - 16 q^{62} - 3 q^{63} + 3 q^{64} - 2 q^{65} - 24 q^{67} - 10 q^{68} + 3 q^{69} - 3 q^{70} + 4 q^{71} + 3 q^{72} + 6 q^{73} - 6 q^{74} - 3 q^{75} - 4 q^{76} + 2 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} + 6 q^{82} - 12 q^{83} + 3 q^{84} - 10 q^{85} + 10 q^{87} - 14 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} + 16 q^{93} - 16 q^{94} - 4 q^{95} - 3 q^{96} + 2 q^{97} + 3 q^{98}+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 - 3 * q^12 - 2 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 10 * q^17 + 3 * q^18 - 4 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 - 10 * q^29 - 3 * q^30 - 16 * q^31 + 3 * q^32 - 10 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 6 * q^41 + 3 * q^42 + 3 * q^45 - 3 * q^46 - 16 * q^47 - 3 * q^48 + 3 * q^49 + 3 * q^50 + 10 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^54 - 3 * q^56 + 4 * q^57 - 10 * q^58 + 4 * q^59 - 3 * q^60 - 22 * q^61 - 16 * q^62 - 3 * q^63 + 3 * q^64 - 2 * q^65 - 24 * q^67 - 10 * q^68 + 3 * q^69 - 3 * q^70 + 4 * q^71 + 3 * q^72 + 6 * q^73 - 6 * q^74 - 3 * q^75 - 4 * q^76 + 2 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 + 6 * q^82 - 12 * q^83 + 3 * q^84 - 10 * q^85 + 10 * q^87 - 14 * q^89 + 3 * q^90 + 2 * q^91 - 3 * q^92 + 16 * q^93 - 16 * q^94 - 4 * q^95 - 3 * q^96 + 2 * q^97 + 3 * 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
$11$	−0.578337	−0.174375	−0.0871876	−	0.996192i	$-0.527788\pi$
$11$	−0.578337	−0.174375	−0.0871876	+	0.996192i	$0.527788\pi$
$12$	−1.00000	−0.288675
$13$	4.20555	1.16641	0.583205	−	0.812325i	$-0.301798\pi$
$13$	4.20555	1.16641	0.583205	+	0.812325i	$0.301798\pi$
$14$	−1.00000	−0.267261
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−7.62721	−1.84987	−0.924935	−	0.380124i	$-0.875881\pi$
$17$	−7.62721	−1.84987	−0.924935	+	0.380124i	$0.875881\pi$
$18$	1.00000	0.235702
$19$	−5.62721	−1.29097	−0.645486	−	0.763772i	$-0.723345\pi$
$19$	−5.62721	−1.29097	−0.645486	+	0.763772i	$0.723345\pi$
$20$	1.00000	0.223607
$21$	1.00000	0.218218
$22$	−0.578337	−0.123302
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	4.20555	0.824776
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	5.83276	1.08312	0.541558	−	0.840663i	$-0.317834\pi$
$29$	5.83276	1.08312	0.541558	+	0.840663i	$0.317834\pi$
$30$	−1.00000	−0.182574
$31$	−9.62721	−1.72910	−0.864549	−	0.502548i	$-0.832396\pi$
$31$	−9.62721	−1.72910	−0.864549	+	0.502548i	$0.832396\pi$
$32$	1.00000	0.176777
$33$	0.578337	0.100676
$34$	−7.62721	−1.30806
$35$	−1.00000	−0.169031
$36$	1.00000	0.166667
$37$	−2.00000	−0.328798	−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000	−0.328798	−0.164399	+	0.986394i	$0.552568\pi$
$38$	−5.62721	−0.912854
$39$	−4.20555	−0.673427
$40$	1.00000	0.158114
$41$	3.15667	0.492990	0.246495	−	0.969144i	$-0.420721\pi$
$41$	3.15667	0.492990	0.246495	+	0.969144i	$0.420721\pi$
$42$	1.00000	0.154303
$43$	−0.578337	−0.0881956	−0.0440978	−	0.999027i	$-0.514041\pi$
$43$	−0.578337	−0.0881956	−0.0440978	+	0.999027i	$0.514041\pi$
$44$	−0.578337	−0.0871876
$45$	1.00000	0.149071
$46$	−1.00000	−0.147442
$47$	−9.62721	−1.40427	−0.702137	−	0.712042i	$-0.747770\pi$
$47$	−9.62721	−1.40427	−0.702137	+	0.712042i	$0.747770\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	1.00000	0.141421
$51$	7.62721	1.06802
$52$	4.20555	0.583205
$53$	−2.00000	−0.274721	−0.137361	−	0.990521i	$-0.543862\pi$
$53$	−2.00000	−0.274721	−0.137361	+	0.990521i	$0.543862\pi$
$54$	−1.00000	−0.136083
$55$	−0.578337	−0.0779830
$56$	−1.00000	−0.133631
$57$	5.62721	0.745343
$58$	5.83276	0.765879
$59$	−8.41110	−1.09503	−0.547516	−	0.836795i	$-0.684426\pi$
$59$	−8.41110	−1.09503	−0.547516	+	0.836795i	$0.684426\pi$
$60$	−1.00000	−0.129099
$61$	1.25443	0.160613	0.0803064	−	0.996770i	$-0.474410\pi$
$61$	1.25443	0.160613	0.0803064	+	0.996770i	$0.474410\pi$
$62$	−9.62721	−1.22266
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	4.20555	0.521634
$66$	0.578337	0.0711884
$67$	−8.57834	−1.04801	−0.524005	−	0.851715i	$-0.675563\pi$
$67$	−8.57834	−1.04801	−0.524005	+	0.851715i	$0.675563\pi$
$68$	−7.62721	−0.924935
$69$	1.00000	0.120386
$70$	−1.00000	−0.119523
$71$	−6.67609	−0.792306	−0.396153	−	0.918185i	$-0.629655\pi$
$71$	−6.67609	−0.792306	−0.396153	+	0.918185i	$0.629655\pi$
$72$	1.00000	0.117851
$73$	0.843326	0.0987038	0.0493519	−	0.998781i	$-0.484284\pi$
$73$	0.843326	0.0987038	0.0493519	+	0.998781i	$0.484284\pi$
$74$	−2.00000	−0.232495
$75$	−1.00000	−0.115470
$76$	−5.62721	−0.645486
$77$	0.578337	0.0659076
$78$	−4.20555	−0.476185
$79$	10.0978	1.13609	0.568043	−	0.822999i	$-0.307701\pi$
$79$	10.0978	1.13609	0.568043	+	0.822999i	$0.307701\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	3.15667	0.348596
$83$	10.0383	1.10185	0.550924	−	0.834555i	$-0.314275\pi$
$83$	10.0383	1.10185	0.550924	+	0.834555i	$0.314275\pi$
$84$	1.00000	0.109109
$85$	−7.62721	−0.827287
$86$	−0.578337	−0.0623637
$87$	−5.83276	−0.625338
$88$	−0.578337	−0.0616509
$89$	−0.951124	−0.100819	−0.0504095	−	0.998729i	$-0.516053\pi$
$89$	−0.951124	−0.100819	−0.0504095	+	0.998729i	$0.516053\pi$
$90$	1.00000	0.105409
$91$	−4.20555	−0.440861
$92$	−1.00000	−0.104257
$93$	9.62721	0.998295
$94$	−9.62721	−0.992971
$95$	−5.62721	−0.577340
$96$	−1.00000	−0.102062
$97$	−3.04888	−0.309566	−0.154783	−	0.987948i	$-0.549468\pi$
$97$	−3.04888	−0.309566	−0.154783	+	0.987948i	$0.549468\pi$
$98$	1.00000	0.101015
$99$	−0.578337	−0.0581251
$100$	1.00000	0.100000
$101$	18.7144	1.86215	0.931076	−	0.364824i	$-0.118871\pi$
$101$	18.7144	1.86215	0.931076	+	0.364824i	$0.118871\pi$
$102$	7.62721	0.755207
$103$	−8.00000	−0.788263	−0.394132	−	0.919054i	$-0.628955\pi$
$103$	−8.00000	−0.788263	−0.394132	+	0.919054i	$0.628955\pi$
$104$	4.20555	0.412388
$105$	1.00000	0.0975900
$106$	−2.00000	−0.194257
$107$	7.25443	0.701312	0.350656	−	0.936504i	$-0.385959\pi$
$107$	7.25443	0.701312	0.350656	+	0.936504i	$0.385959\pi$
$108$	−1.00000	−0.0962250
$109$	−16.5089	−1.58126	−0.790631	−	0.612293i	$-0.790247\pi$
$109$	−16.5089	−1.58126	−0.790631	+	0.612293i	$0.790247\pi$
$110$	−0.578337	−0.0551423
$111$	2.00000	0.189832
$112$	−1.00000	−0.0944911
$113$	−1.25443	−0.118006	−0.0590032	−	0.998258i	$-0.518792\pi$
$113$	−1.25443	−0.118006	−0.0590032	+	0.998258i	$0.518792\pi$
$114$	5.62721	0.527037
$115$	−1.00000	−0.0932505
$116$	5.83276	0.541558
$117$	4.20555	0.388803
$118$	−8.41110	−0.774305
$119$	7.62721	0.699185
$120$	−1.00000	−0.0912871
$121$	−10.6655	−0.969593
$122$	1.25443	0.113570
$123$	−3.15667	−0.284628
$124$	−9.62721	−0.864549
$125$	1.00000	0.0894427
$126$	−1.00000	−0.0890871
$127$	−2.26499	−0.200985	−0.100493	−	0.994938i	$-0.532042\pi$
$127$	−2.26499	−0.200985	−0.100493	+	0.994938i	$0.532042\pi$
$128$	1.00000	0.0883883
$129$	0.578337	0.0509197
$130$	4.20555	0.368851
$131$	−4.00000	−0.349482	−0.174741	−	0.984614i	$-0.555909\pi$
$131$	−4.00000	−0.349482	−0.174741	+	0.984614i	$0.555909\pi$
$132$	0.578337	0.0503378
$133$	5.62721	0.487941
$134$	−8.57834	−0.741055
$135$	−1.00000	−0.0860663
$136$	−7.62721	−0.654028
$137$	−12.5089	−1.06870	−0.534352	−	0.845262i	$-0.679444\pi$
$137$	−12.5089	−1.06870	−0.534352	+	0.845262i	$0.679444\pi$
$138$	1.00000	0.0851257
$139$	−8.41110	−0.713420	−0.356710	−	0.934215i	$-0.616102\pi$
$139$	−8.41110	−0.713420	−0.356710	+	0.934215i	$0.616102\pi$
$140$	−1.00000	−0.0845154
$141$	9.62721	0.810758
$142$	−6.67609	−0.560245
$143$	−2.43223	−0.203393
$144$	1.00000	0.0833333
$145$	5.83276	0.484385
$146$	0.843326	0.0697941
$147$	−1.00000	−0.0824786
$148$	−2.00000	−0.164399
$149$	−2.00000	−0.163846	−0.0819232	−	0.996639i	$-0.526106\pi$
$149$	−2.00000	−0.163846	−0.0819232	+	0.996639i	$0.526106\pi$
$150$	−1.00000	−0.0816497
$151$	4.41110	0.358970	0.179485	−	0.983761i	$-0.442557\pi$
$151$	4.41110	0.358970	0.179485	+	0.983761i	$0.442557\pi$
$152$	−5.62721	−0.456427
$153$	−7.62721	−0.616624
$154$	0.578337	0.0466037
$155$	−9.62721	−0.773276
$156$	−4.20555	−0.336713
$157$	−4.31335	−0.344243	−0.172121	−	0.985076i	$-0.555062\pi$
$157$	−4.31335	−0.344243	−0.172121	+	0.985076i	$0.555062\pi$
$158$	10.0978	0.803334
$159$	2.00000	0.158610
$160$	1.00000	0.0790569
$161$	1.00000	0.0788110
$162$	1.00000	0.0785674
$163$	0.411100	0.0321999	0.0160999	−	0.999870i	$-0.494875\pi$
$163$	0.411100	0.0321999	0.0160999	+	0.999870i	$0.494875\pi$
$164$	3.15667	0.246495
$165$	0.578337	0.0450235
$166$	10.0383	0.779124
$167$	17.2927	1.33815	0.669076	−	0.743194i	$-0.266690\pi$
$167$	17.2927	1.33815	0.669076	+	0.743194i	$0.266690\pi$
$168$	1.00000	0.0771517
$169$	4.68665	0.360512
$170$	−7.62721	−0.584981
$171$	−5.62721	−0.430324
$172$	−0.578337	−0.0440978
$173$	−19.6272	−1.49223	−0.746115	−	0.665817i	$-0.768083\pi$
$173$	−19.6272	−1.49223	−0.746115	+	0.665817i	$0.768083\pi$
$174$	−5.83276	−0.442181
$175$	−1.00000	−0.0755929
$176$	−0.578337	−0.0435938
$177$	8.41110	0.632217
$178$	−0.951124	−0.0712898
$179$	19.6655	1.46987	0.734935	−	0.678137i	$-0.237213\pi$
$179$	19.6655	1.46987	0.734935	+	0.678137i	$0.237213\pi$
$180$	1.00000	0.0745356
$181$	9.25443	0.687876	0.343938	−	0.938992i	$-0.388239\pi$
$181$	9.25443	0.687876	0.343938	+	0.938992i	$0.388239\pi$
$182$	−4.20555	−0.311736
$183$	−1.25443	−0.0927298
$184$	−1.00000	−0.0737210
$185$	−2.00000	−0.147043
$186$	9.62721	0.705902
$187$	4.41110	0.322572
$188$	−9.62721	−0.702137
$189$	1.00000	0.0727393
$190$	−5.62721	−0.408241
$191$	−21.5678	−1.56059	−0.780295	−	0.625412i	$-0.784931\pi$
$191$	−21.5678	−1.56059	−0.780295	+	0.625412i	$0.784931\pi$
$192$	−1.00000	−0.0721688
$193$	−1.58890	−0.114372	−0.0571858	−	0.998364i	$-0.518213\pi$
$193$	−1.58890	−0.114372	−0.0571858	+	0.998364i	$0.518213\pi$
$194$	−3.04888	−0.218897
$195$	−4.20555	−0.301166
$196$	1.00000	0.0714286
$197$	2.74557	0.195614	0.0978070	−	0.995205i	$-0.468817\pi$
$197$	2.74557	0.195614	0.0978070	+	0.995205i	$0.468817\pi$
$198$	−0.578337	−0.0411006
$199$	−16.8222	−1.19249	−0.596247	−	0.802801i	$-0.703342\pi$
$199$	−16.8222	−1.19249	−0.596247	+	0.802801i	$0.703342\pi$
$200$	1.00000	0.0707107
$201$	8.57834	0.605069
$202$	18.7144	1.31674
$203$	−5.83276	−0.409380
$204$	7.62721	0.534012
$205$	3.15667	0.220472
$206$	−8.00000	−0.557386
$207$	−1.00000	−0.0695048
$208$	4.20555	0.291602
$209$	3.25443	0.225113
$210$	1.00000	0.0690066
$211$	16.4111	1.12979	0.564893	−	0.825164i	$-0.308917\pi$
$211$	16.4111	1.12979	0.564893	+	0.825164i	$0.308917\pi$
$212$	−2.00000	−0.137361
$213$	6.67609	0.457438
$214$	7.25443	0.495902
$215$	−0.578337	−0.0394423
$216$	−1.00000	−0.0680414
$217$	9.62721	0.653538
$218$	−16.5089	−1.11812
$219$	−0.843326	−0.0569867
$220$	−0.578337	−0.0389915
$221$	−32.0766	−2.15771
$222$	2.00000	0.134231
$223$	1.45998	0.0977672	0.0488836	−	0.998804i	$-0.484434\pi$
$223$	1.45998	0.0977672	0.0488836	+	0.998804i	$0.484434\pi$
$224$	−1.00000	−0.0668153
$225$	1.00000	0.0666667
$226$	−1.25443	−0.0834432
$227$	−11.1950	−0.743037	−0.371519	−	0.928425i	$-0.621163\pi$
$227$	−11.1950	−0.743037	−0.371519	+	0.928425i	$0.621163\pi$
$228$	5.62721	0.372671
$229$	15.1567	1.00158	0.500791	−	0.865568i	$-0.333043\pi$
$229$	15.1567	1.00158	0.500791	+	0.865568i	$0.333043\pi$
$230$	−1.00000	−0.0659380
$231$	−0.578337	−0.0380518
$232$	5.83276	0.382940
$233$	−19.3522	−1.26780	−0.633902	−	0.773414i	$-0.718548\pi$
$233$	−19.3522	−1.26780	−0.633902	+	0.773414i	$0.718548\pi$
$234$	4.20555	0.274925
$235$	−9.62721	−0.628010
$236$	−8.41110	−0.547516
$237$	−10.0978	−0.655919
$238$	7.62721	0.494399
$239$	1.32391	0.0856367	0.0428183	−	0.999083i	$-0.486366\pi$
$239$	1.32391	0.0856367	0.0428183	+	0.999083i	$0.486366\pi$
$240$	−1.00000	−0.0645497
$241$	−14.1361	−0.910584	−0.455292	−	0.890342i	$-0.650465\pi$
$241$	−14.1361	−0.910584	−0.455292	+	0.890342i	$0.650465\pi$
$242$	−10.6655	−0.685606
$243$	−1.00000	−0.0641500
$244$	1.25443	0.0803064
$245$	1.00000	0.0638877
$246$	−3.15667	−0.201262
$247$	−23.6655	−1.50580
$248$	−9.62721	−0.611329
$249$	−10.0383	−0.636152
$250$	1.00000	0.0632456
$251$	7.89220	0.498151	0.249076	−	0.968484i	$-0.419873\pi$
$251$	7.89220	0.498151	0.249076	+	0.968484i	$0.419873\pi$
$252$	−1.00000	−0.0629941
$253$	0.578337	0.0363597
$254$	−2.26499	−0.142118
$255$	7.62721	0.477635
$256$	1.00000	0.0625000
$257$	−22.8222	−1.42361	−0.711805	−	0.702377i	$-0.752122\pi$
$257$	−22.8222	−1.42361	−0.711805	+	0.702377i	$0.752122\pi$
$258$	0.578337	0.0360057
$259$	2.00000	0.124274
$260$	4.20555	0.260817
$261$	5.83276	0.361039
$262$	−4.00000	−0.247121
$263$	14.5089	0.894654	0.447327	−	0.894370i	$-0.352376\pi$
$263$	14.5089	0.894654	0.447327	+	0.894370i	$0.352376\pi$
$264$	0.578337	0.0355942
$265$	−2.00000	−0.122859
$266$	5.62721	0.345027
$267$	0.951124	0.0582078
$268$	−8.57834	−0.524005
$269$	11.0489	0.673662	0.336831	−	0.941565i	$-0.390645\pi$
$269$	11.0489	0.673662	0.336831	+	0.941565i	$0.390645\pi$
$270$	−1.00000	−0.0608581
$271$	−7.31386	−0.444286	−0.222143	−	0.975014i	$-0.571305\pi$
$271$	−7.31386	−0.444286	−0.222143	+	0.975014i	$0.571305\pi$
$272$	−7.62721	−0.462468
$273$	4.20555	0.254531
$274$	−12.5089	−0.755687
$275$	−0.578337	−0.0348750
$276$	1.00000	0.0601929
$277$	10.2439	0.615494	0.307747	−	0.951468i	$-0.400425\pi$
$277$	10.2439	0.615494	0.307747	+	0.951468i	$0.400425\pi$
$278$	−8.41110	−0.504464
$279$	−9.62721	−0.576366
$280$	−1.00000	−0.0597614
$281$	−23.9305	−1.42757	−0.713787	−	0.700362i	$-0.753022\pi$
$281$	−23.9305	−1.42757	−0.713787	+	0.700362i	$0.753022\pi$
$282$	9.62721	0.573292
$283$	−15.8922	−0.944693	−0.472347	−	0.881413i	$-0.656593\pi$
$283$	−15.8922	−0.944693	−0.472347	+	0.881413i	$0.656593\pi$
$284$	−6.67609	−0.396153
$285$	5.62721	0.333327
$286$	−2.43223	−0.143821
$287$	−3.15667	−0.186333
$288$	1.00000	0.0589256
$289$	41.1744	2.42202
$290$	5.83276	0.342512
$291$	3.04888	0.178728
$292$	0.843326	0.0493519
$293$	−22.4111	−1.30927	−0.654635	−	0.755945i	$-0.727178\pi$
$293$	−22.4111	−1.30927	−0.654635	+	0.755945i	$0.727178\pi$
$294$	−1.00000	−0.0583212
$295$	−8.41110	−0.489713
$296$	−2.00000	−0.116248
$297$	0.578337	0.0335585
$298$	−2.00000	−0.115857
$299$	−4.20555	−0.243213
$300$	−1.00000	−0.0577350
$301$	0.578337	0.0333348
$302$	4.41110	0.253830
$303$	−18.7144	−1.07511
$304$	−5.62721	−0.322743
$305$	1.25443	0.0718282
$306$	−7.62721	−0.436019
$307$	−24.1955	−1.38091	−0.690455	−	0.723375i	$-0.742590\pi$
$307$	−24.1955	−1.38091	−0.690455	+	0.723375i	$0.742590\pi$
$308$	0.578337	0.0329538
$309$	8.00000	0.455104
$310$	−9.62721	−0.546789
$311$	−22.2056	−1.25916	−0.629581	−	0.776935i	$-0.716773\pi$
$311$	−22.2056	−1.25916	−0.629581	+	0.776935i	$0.716773\pi$
$312$	−4.20555	−0.238092
$313$	−32.2822	−1.82470	−0.912348	−	0.409415i	$-0.865733\pi$
$313$	−32.2822	−1.82470	−0.912348	+	0.409415i	$0.865733\pi$
$314$	−4.31335	−0.243416
$315$	−1.00000	−0.0563436
$316$	10.0978	0.568043
$317$	10.4111	0.584746	0.292373	−	0.956304i	$-0.405555\pi$
$317$	10.4111	0.584746	0.292373	+	0.956304i	$0.405555\pi$
$318$	2.00000	0.112154
$319$	−3.37330	−0.188869
$320$	1.00000	0.0559017
$321$	−7.25443	−0.404903
$322$	1.00000	0.0557278
$323$	42.9200	2.38813
$324$	1.00000	0.0555556
$325$	4.20555	0.233282
$326$	0.411100	0.0227687
$327$	16.5089	0.912942
$328$	3.15667	0.174298
$329$	9.62721	0.530765
$330$	0.578337	0.0318364
$331$	−28.8222	−1.58421	−0.792106	−	0.610384i	$-0.791015\pi$
$331$	−28.8222	−1.58421	−0.792106	+	0.610384i	$0.791015\pi$
$332$	10.0383	0.550924
$333$	−2.00000	−0.109599
$334$	17.2927	0.946217
$335$	−8.57834	−0.468685
$336$	1.00000	0.0545545
$337$	3.93051	0.214109	0.107054	−	0.994253i	$-0.465858\pi$
$337$	3.93051	0.214109	0.107054	+	0.994253i	$0.465858\pi$
$338$	4.68665	0.254920
$339$	1.25443	0.0681311
$340$	−7.62721	−0.413644
$341$	5.56777	0.301512
$342$	−5.62721	−0.304285
$343$	−1.00000	−0.0539949
$344$	−0.578337	−0.0311818
$345$	1.00000	0.0538382
$346$	−19.6272	−1.05517
$347$	24.4111	1.31046	0.655228	−	0.755431i	$-0.272572\pi$
$347$	24.4111	1.31046	0.655228	+	0.755431i	$0.272572\pi$
$348$	−5.83276	−0.312669
$349$	16.5683	0.886880	0.443440	−	0.896304i	$-0.353758\pi$
$349$	16.5683	0.886880	0.443440	+	0.896304i	$0.353758\pi$
$350$	−1.00000	−0.0534522
$351$	−4.20555	−0.224476
$352$	−0.578337	−0.0308255
$353$	11.1567	0.593810	0.296905	−	0.954907i	$-0.404046\pi$
$353$	11.1567	0.593810	0.296905	+	0.954907i	$0.404046\pi$
$354$	8.41110	0.447045
$355$	−6.67609	−0.354330
$356$	−0.951124	−0.0504095
$357$	−7.62721	−0.403675
$358$	19.6655	1.03936
$359$	13.5678	0.716080	0.358040	−	0.933706i	$-0.383445\pi$
$359$	13.5678	0.716080	0.358040	+	0.933706i	$0.383445\pi$
$360$	1.00000	0.0527046
$361$	12.6655	0.666607
$362$	9.25443	0.486402
$363$	10.6655	0.559795
$364$	−4.20555	−0.220431
$365$	0.843326	0.0441417
$366$	−1.25443	−0.0655699
$367$	20.1955	1.05420	0.527098	−	0.849804i	$-0.323280\pi$
$367$	20.1955	1.05420	0.527098	+	0.849804i	$0.323280\pi$
$368$	−1.00000	−0.0521286
$369$	3.15667	0.164330
$370$	−2.00000	−0.103975
$371$	2.00000	0.103835
$372$	9.62721	0.499148
$373$	−2.00000	−0.103556	−0.0517780	−	0.998659i	$-0.516489\pi$
$373$	−2.00000	−0.103556	−0.0517780	+	0.998659i	$0.516489\pi$
$374$	4.41110	0.228093
$375$	−1.00000	−0.0516398
$376$	−9.62721	−0.496486
$377$	24.5300	1.26336
$378$	1.00000	0.0514344
$379$	32.0766	1.64767	0.823833	−	0.566833i	$-0.191831\pi$
$379$	32.0766	1.64767	0.823833	+	0.566833i	$0.191831\pi$
$380$	−5.62721	−0.288670
$381$	2.26499	0.116039
$382$	−21.5678	−1.10350
$383$	−6.84333	−0.349678	−0.174839	−	0.984597i	$-0.555940\pi$
$383$	−6.84333	−0.349678	−0.174839	+	0.984597i	$0.555940\pi$
$384$	−1.00000	−0.0510310
$385$	0.578337	0.0294748
$386$	−1.58890	−0.0808729
$387$	−0.578337	−0.0293985
$388$	−3.04888	−0.154783
$389$	33.2544	1.68607	0.843033	−	0.537862i	$-0.180768\pi$
$389$	33.2544	1.68607	0.843033	+	0.537862i	$0.180768\pi$
$390$	−4.20555	−0.212956
$391$	7.62721	0.385725
$392$	1.00000	0.0505076
$393$	4.00000	0.201773
$394$	2.74557	0.138320
$395$	10.0978	0.508073
$396$	−0.578337	−0.0290625
$397$	4.20555	0.211071	0.105535	−	0.994416i	$-0.466344\pi$
$397$	4.20555	0.211071	0.105535	+	0.994416i	$0.466344\pi$
$398$	−16.8222	−0.843221
$399$	−5.62721	−0.281713
$400$	1.00000	0.0500000
$401$	−25.0872	−1.25279	−0.626397	−	0.779504i	$-0.715471\pi$
$401$	−25.0872	−1.25279	−0.626397	+	0.779504i	$0.715471\pi$
$402$	8.57834	0.427849
$403$	−40.4877	−2.01684
$404$	18.7144	0.931076
$405$	1.00000	0.0496904
$406$	−5.83276	−0.289475
$407$	1.15667	0.0573342
$408$	7.62721	0.377603
$409$	6.41110	0.317009	0.158504	−	0.987358i	$-0.449333\pi$
$409$	6.41110	0.317009	0.158504	+	0.987358i	$0.449333\pi$
$410$	3.15667	0.155897
$411$	12.5089	0.617016
$412$	−8.00000	−0.394132
$413$	8.41110	0.413883
$414$	−1.00000	−0.0491473
$415$	10.0383	0.492761
$416$	4.20555	0.206194
$417$	8.41110	0.411893
$418$	3.25443	0.159179
$419$	−33.6555	−1.64418	−0.822089	−	0.569359i	$-0.807191\pi$
$419$	−33.6555	−1.64418	−0.822089	+	0.569359i	$0.807191\pi$
$420$	1.00000	0.0487950
$421$	23.1567	1.12859	0.564294	−	0.825574i	$-0.309149\pi$
$421$	23.1567	1.12859	0.564294	+	0.825574i	$0.309149\pi$
$422$	16.4111	0.798880
$423$	−9.62721	−0.468091
$424$	−2.00000	−0.0971286
$425$	−7.62721	−0.369974
$426$	6.67609	0.323458
$427$	−1.25443	−0.0607059
$428$	7.25443	0.350656
$429$	2.43223	0.117429
$430$	−0.578337	−0.0278899
$431$	−5.90225	−0.284301	−0.142151	−	0.989845i	$-0.545402\pi$
$431$	−5.90225	−0.284301	−0.142151	+	0.989845i	$0.545402\pi$
$432$	−1.00000	−0.0481125
$433$	−25.5577	−1.22823	−0.614113	−	0.789218i	$-0.710486\pi$
$433$	−25.5577	−1.22823	−0.614113	+	0.789218i	$0.710486\pi$
$434$	9.62721	0.462121
$435$	−5.83276	−0.279660
$436$	−16.5089	−0.790631
$437$	5.62721	0.269186
$438$	−0.843326	−0.0402957
$439$	30.9794	1.47857	0.739283	−	0.673395i	$-0.235165\pi$
$439$	30.9794	1.47857	0.739283	+	0.673395i	$0.235165\pi$
$440$	−0.578337	−0.0275711
$441$	1.00000	0.0476190
$442$	−32.0766	−1.52573
$443$	22.0978	1.04990	0.524948	−	0.851134i	$-0.324085\pi$
$443$	22.0978	1.04990	0.524948	+	0.851134i	$0.324085\pi$
$444$	2.00000	0.0949158
$445$	−0.951124	−0.0450876
$446$	1.45998	0.0691319
$447$	2.00000	0.0945968
$448$	−1.00000	−0.0472456
$449$	14.7456	0.695887	0.347943	−	0.937516i	$-0.386880\pi$
$449$	14.7456	0.695887	0.347943	+	0.937516i	$0.386880\pi$
$450$	1.00000	0.0471405
$451$	−1.82562	−0.0859652
$452$	−1.25443	−0.0590032
$453$	−4.41110	−0.207252
$454$	−11.1950	−0.525407
$455$	−4.20555	−0.197159
$456$	5.62721	0.263518
$457$	22.0283	1.03044	0.515219	−	0.857058i	$-0.327710\pi$
$457$	22.0283	1.03044	0.515219	+	0.857058i	$0.327710\pi$
$458$	15.1567	0.708225
$459$	7.62721	0.356008
$460$	−1.00000	−0.0466252
$461$	26.7144	1.24421	0.622107	−	0.782932i	$-0.286277\pi$
$461$	26.7144	1.24421	0.622107	+	0.782932i	$0.286277\pi$
$462$	−0.578337	−0.0269067
$463$	14.3416	0.666511	0.333256	−	0.942836i	$-0.391853\pi$
$463$	14.3416	0.666511	0.333256	+	0.942836i	$0.391853\pi$
$464$	5.83276	0.270779
$465$	9.62721	0.446451
$466$	−19.3522	−0.896472
$467$	−20.3517	−0.941763	−0.470881	−	0.882197i	$-0.656064\pi$
$467$	−20.3517	−0.941763	−0.470881	+	0.882197i	$0.656064\pi$
$468$	4.20555	0.194402
$469$	8.57834	0.396111
$470$	−9.62721	−0.444070
$471$	4.31335	0.198749
$472$	−8.41110	−0.387152
$473$	0.334474	0.0153791
$474$	−10.0978	−0.463805
$475$	−5.62721	−0.258194
$476$	7.62721	0.349593
$477$	−2.00000	−0.0915737
$478$	1.32391	0.0605543
$479$	16.0000	0.731059	0.365529	−	0.930800i	$-0.380888\pi$
$479$	16.0000	0.731059	0.365529	+	0.930800i	$0.380888\pi$
$480$	−1.00000	−0.0456435
$481$	−8.41110	−0.383513
$482$	−14.1361	−0.643880
$483$	−1.00000	−0.0455016
$484$	−10.6655	−0.484797
$485$	−3.04888	−0.138442
$486$	−1.00000	−0.0453609
$487$	−27.3028	−1.23721	−0.618604	−	0.785703i	$-0.712301\pi$
$487$	−27.3028	−1.23721	−0.618604	+	0.785703i	$0.712301\pi$
$488$	1.25443	0.0567852
$489$	−0.411100	−0.0185906
$490$	1.00000	0.0451754
$491$	25.3522	1.14413	0.572064	−	0.820209i	$-0.306143\pi$
$491$	25.3522	1.14413	0.572064	+	0.820209i	$0.306143\pi$
$492$	−3.15667	−0.142314
$493$	−44.4877	−2.00363
$494$	−23.6655	−1.06476
$495$	−0.578337	−0.0259943
$496$	−9.62721	−0.432275
$497$	6.67609	0.299464
$498$	−10.0383	−0.449828
$499$	−37.4288	−1.67554	−0.837772	−	0.546021i	$-0.816142\pi$
$499$	−37.4288	−1.67554	−0.837772	+	0.546021i	$0.816142\pi$
$500$	1.00000	0.0447214
$501$	−17.2927	−0.772583
$502$	7.89220	0.352246
$503$	18.0978	0.806939	0.403469	−	0.914993i	$-0.367804\pi$
$503$	18.0978	0.806939	0.403469	+	0.914993i	$0.367804\pi$
$504$	−1.00000	−0.0445435
$505$	18.7144	0.832780
$506$	0.578337	0.0257102
$507$	−4.68665	−0.208142
$508$	−2.26499	−0.100493
$509$	22.5189	0.998133	0.499066	−	0.866564i	$-0.333676\pi$
$509$	22.5189	0.998133	0.499066	+	0.866564i	$0.333676\pi$
$510$	7.62721	0.337739
$511$	−0.843326	−0.0373065
$512$	1.00000	0.0441942
$513$	5.62721	0.248448
$514$	−22.8222	−1.00664
$515$	−8.00000	−0.352522
$516$	0.578337	0.0254599
$517$	5.56777	0.244870
$518$	2.00000	0.0878750
$519$	19.6272	0.861539
$520$	4.20555	0.184426
$521$	19.6756	0.862002	0.431001	−	0.902351i	$-0.358160\pi$
$521$	19.6756	0.862002	0.431001	+	0.902351i	$0.358160\pi$
$522$	5.83276	0.255293
$523$	−20.5189	−0.897229	−0.448614	−	0.893725i	$-0.648082\pi$
$523$	−20.5189	−0.897229	−0.448614	+	0.893725i	$0.648082\pi$
$524$	−4.00000	−0.174741
$525$	1.00000	0.0436436
$526$	14.5089	0.632616
$527$	73.4288	3.19861
$528$	0.578337	0.0251689
$529$	1.00000	0.0434783
$530$	−2.00000	−0.0868744
$531$	−8.41110	−0.365011
$532$	5.62721	0.243971
$533$	13.2756	0.575028
$534$	0.951124	0.0411592
$535$	7.25443	0.313636
$536$	−8.57834	−0.370528
$537$	−19.6655	−0.848630
$538$	11.0489	0.476351
$539$	−0.578337	−0.0249107
$540$	−1.00000	−0.0430331
$541$	23.1567	0.995583	0.497792	−	0.867297i	$-0.334144\pi$
$541$	23.1567	0.995583	0.497792	+	0.867297i	$0.334144\pi$
$542$	−7.31386	−0.314157
$543$	−9.25443	−0.397145
$544$	−7.62721	−0.327014
$545$	−16.5089	−0.707162
$546$	4.20555	0.179981
$547$	−39.7422	−1.69925	−0.849626	−	0.527386i	$-0.823172\pi$
$547$	−39.7422	−1.69925	−0.849626	+	0.527386i	$0.823172\pi$
$548$	−12.5089	−0.534352
$549$	1.25443	0.0535376
$550$	−0.578337	−0.0246604
$551$	−32.8222	−1.39827
$552$	1.00000	0.0425628
$553$	−10.0978	−0.429400
$554$	10.2439	0.435220
$555$	2.00000	0.0848953
$556$	−8.41110	−0.356710
$557$	12.5089	0.530017	0.265009	−	0.964246i	$-0.414625\pi$
$557$	12.5089	0.530017	0.265009	+	0.964246i	$0.414625\pi$
$558$	−9.62721	−0.407552
$559$	−2.43223	−0.102872
$560$	−1.00000	−0.0422577
$561$	−4.41110	−0.186237
$562$	−23.9305	−1.00945
$563$	28.3517	1.19488	0.597440	−	0.801914i	$-0.296185\pi$
$563$	28.3517	1.19488	0.597440	+	0.801914i	$0.296185\pi$
$564$	9.62721	0.405379
$565$	−1.25443	−0.0527741
$566$	−15.8922	−0.667999
$567$	−1.00000	−0.0419961
$568$	−6.67609	−0.280122
$569$	−17.0872	−0.716332	−0.358166	−	0.933658i	$-0.616598\pi$
$569$	−17.0872	−0.716332	−0.358166	+	0.933658i	$0.616598\pi$
$570$	5.62721	0.235698
$571$	26.5089	1.10936	0.554680	−	0.832063i	$-0.312841\pi$
$571$	26.5089	1.10936	0.554680	+	0.832063i	$0.312841\pi$
$572$	−2.43223	−0.101696
$573$	21.5678	0.901007
$574$	−3.15667	−0.131757
$575$	−1.00000	−0.0417029
$576$	1.00000	0.0416667
$577$	−8.09775	−0.337114	−0.168557	−	0.985692i	$-0.553911\pi$
$577$	−8.09775	−0.337114	−0.168557	+	0.985692i	$0.553911\pi$
$578$	41.1744	1.71263
$579$	1.58890	0.0660324
$580$	5.83276	0.242192
$581$	−10.0383	−0.416459
$582$	3.04888	0.126380
$583$	1.15667	0.0479046
$584$	0.843326	0.0348971
$585$	4.20555	0.173878
$586$	−22.4111	−0.925794
$587$	−36.8222	−1.51981	−0.759907	−	0.650031i	$-0.774756\pi$
$587$	−36.8222	−1.51981	−0.759907	+	0.650031i	$0.774756\pi$
$588$	−1.00000	−0.0412393
$589$	54.1744	2.23222
$590$	−8.41110	−0.346280
$591$	−2.74557	−0.112938
$592$	−2.00000	−0.0821995
$593$	−0.313348	−0.0128677	−0.00643384	−	0.999979i	$-0.502048\pi$
$593$	−0.313348	−0.0128677	−0.00643384	+	0.999979i	$0.502048\pi$
$594$	0.578337	0.0237295
$595$	7.62721	0.312685
$596$	−2.00000	−0.0819232
$597$	16.8222	0.688487
$598$	−4.20555	−0.171978
$599$	21.7350	0.888068	0.444034	−	0.896010i	$-0.353547\pi$
$599$	21.7350	0.888068	0.444034	+	0.896010i	$0.353547\pi$
$600$	−1.00000	−0.0408248
$601$	41.6655	1.69957	0.849786	−	0.527128i	$-0.176731\pi$
$601$	41.6655	1.69957	0.849786	+	0.527128i	$0.176731\pi$
$602$	0.578337	0.0235713
$603$	−8.57834	−0.349337
$604$	4.41110	0.179485
$605$	−10.6655	−0.433615
$606$	−18.7144	−0.760221
$607$	−30.8122	−1.25063	−0.625313	−	0.780374i	$-0.715029\pi$
$607$	−30.8122	−1.25063	−0.625313	+	0.780374i	$0.715029\pi$
$608$	−5.62721	−0.228214
$609$	5.83276	0.236355
$610$	1.25443	0.0507902
$611$	−40.4877	−1.63796
$612$	−7.62721	−0.308312
$613$	−37.2544	−1.50469	−0.752346	−	0.658768i	$-0.771078\pi$
$613$	−37.2544	−1.50469	−0.752346	+	0.658768i	$0.771078\pi$
$614$	−24.1955	−0.976451
$615$	−3.15667	−0.127289
$616$	0.578337	0.0233019
$617$	0.843326	0.0339510	0.0169755	−	0.999856i	$-0.494596\pi$
$617$	0.843326	0.0339510	0.0169755	+	0.999856i	$0.494596\pi$
$618$	8.00000	0.321807
$619$	32.7628	1.31685	0.658423	−	0.752648i	$-0.271224\pi$
$619$	32.7628	1.31685	0.658423	+	0.752648i	$0.271224\pi$
$620$	−9.62721	−0.386638
$621$	1.00000	0.0401286
$622$	−22.2056	−0.890361
$623$	0.951124	0.0381060
$624$	−4.20555	−0.168357
$625$	1.00000	0.0400000
$626$	−32.2822	−1.29026
$627$	−3.25443	−0.129969
$628$	−4.31335	−0.172121
$629$	15.2544	0.608234
$630$	−1.00000	−0.0398410
$631$	−38.2933	−1.52443	−0.762215	−	0.647324i	$-0.775888\pi$
$631$	−38.2933	−1.52443	−0.762215	+	0.647324i	$0.775888\pi$
$632$	10.0978	0.401667
$633$	−16.4111	−0.652283
$634$	10.4111	0.413478
$635$	−2.26499	−0.0898833
$636$	2.00000	0.0793052
$637$	4.20555	0.166630
$638$	−3.37330	−0.133550
$639$	−6.67609	−0.264102
$640$	1.00000	0.0395285
$641$	−31.9305	−1.26118	−0.630590	−	0.776116i	$-0.717187\pi$
$641$	−31.9305	−1.26118	−0.630590	+	0.776116i	$0.717187\pi$
$642$	−7.25443	−0.286309
$643$	−15.7733	−0.622039	−0.311020	−	0.950403i	$-0.600670\pi$
$643$	−15.7733	−0.622039	−0.311020	+	0.950403i	$0.600670\pi$
$644$	1.00000	0.0394055
$645$	0.578337	0.0227720
$646$	42.9200	1.68866
$647$	3.94056	0.154919	0.0774597	−	0.996995i	$-0.475319\pi$
$647$	3.94056	0.154919	0.0774597	+	0.996995i	$0.475319\pi$
$648$	1.00000	0.0392837
$649$	4.86445	0.190946
$650$	4.20555	0.164955
$651$	−9.62721	−0.377320
$652$	0.411100	0.0160999
$653$	33.8610	1.32508	0.662542	−	0.749025i	$-0.269478\pi$
$653$	33.8610	1.32508	0.662542	+	0.749025i	$0.269478\pi$
$654$	16.5089	0.645547
$655$	−4.00000	−0.156293
$656$	3.15667	0.123247
$657$	0.843326	0.0329013
$658$	9.62721	0.375308
$659$	28.9894	1.12927	0.564634	−	0.825341i	$-0.309017\pi$
$659$	28.9894	1.12927	0.564634	+	0.825341i	$0.309017\pi$
$660$	0.578337	0.0225117
$661$	−3.15667	−0.122780	−0.0613902	−	0.998114i	$-0.519553\pi$
$661$	−3.15667	−0.122780	−0.0613902	+	0.998114i	$0.519553\pi$
$662$	−28.8222	−1.12021
$663$	32.0766	1.24575
$664$	10.0383	0.389562
$665$	5.62721	0.218214
$666$	−2.00000	−0.0774984
$667$	−5.83276	−0.225845
$668$	17.2927	0.669076
$669$	−1.45998	−0.0564459
$670$	−8.57834	−0.331410
$671$	−0.725481	−0.0280069
$672$	1.00000	0.0385758
$673$	−3.56777	−0.137528	−0.0687638	−	0.997633i	$-0.521905\pi$
$673$	−3.56777	−0.137528	−0.0687638	+	0.997633i	$0.521905\pi$
$674$	3.93051	0.151398
$675$	−1.00000	−0.0384900
$676$	4.68665	0.180256
$677$	−3.49115	−0.134176	−0.0670879	−	0.997747i	$-0.521371\pi$
$677$	−3.49115	−0.134176	−0.0670879	+	0.997747i	$0.521371\pi$
$678$	1.25443	0.0481759
$679$	3.04888	0.117005
$680$	−7.62721	−0.292490
$681$	11.1950	0.428993
$682$	5.56777	0.213201
$683$	33.2333	1.27164	0.635818	−	0.771839i	$-0.280663\pi$
$683$	33.2333	1.27164	0.635818	+	0.771839i	$0.280663\pi$
$684$	−5.62721	−0.215162
$685$	−12.5089	−0.477939
$686$	−1.00000	−0.0381802
$687$	−15.1567	−0.578263
$688$	−0.578337	−0.0220489
$689$	−8.41110	−0.320437
$690$	1.00000	0.0380693
$691$	−29.1567	−1.10917	−0.554586	−	0.832126i	$-0.687123\pi$
$691$	−29.1567	−1.10917	−0.554586	+	0.832126i	$0.687123\pi$
$692$	−19.6272	−0.746115
$693$	0.578337	0.0219692
$694$	24.4111	0.926633
$695$	−8.41110	−0.319051
$696$	−5.83276	−0.221090
$697$	−24.0766	−0.911967
$698$	16.5683	0.627119
$699$	19.3522	0.731967
$700$	−1.00000	−0.0377964
$701$	39.9789	1.50998	0.754991	−	0.655736i	$-0.227641\pi$
$701$	39.9789	1.50998	0.754991	+	0.655736i	$0.227641\pi$
$702$	−4.20555	−0.158728
$703$	11.2544	0.424469
$704$	−0.578337	−0.0217969
$705$	9.62721	0.362582
$706$	11.1567	0.419887
$707$	−18.7144	−0.703828
$708$	8.41110	0.316109
$709$	7.15667	0.268775	0.134387	−	0.990929i	$-0.457093\pi$
$709$	7.15667	0.268775	0.134387	+	0.990929i	$0.457093\pi$
$710$	−6.67609	−0.250549
$711$	10.0978	0.378695
$712$	−0.951124	−0.0356449
$713$	9.62721	0.360542
$714$	−7.62721	−0.285441
$715$	−2.43223	−0.0909601
$716$	19.6655	0.734935
$717$	−1.32391	−0.0494424
$718$	13.5678	0.506345
$719$	7.69670	0.287038	0.143519	−	0.989648i	$-0.454158\pi$
$719$	7.69670	0.287038	0.143519	+	0.989648i	$0.454158\pi$
$720$	1.00000	0.0372678
$721$	8.00000	0.297936
$722$	12.6655	0.471362
$723$	14.1361	0.525726
$724$	9.25443	0.343938
$725$	5.83276	0.216623
$726$	10.6655	0.395835
$727$	−10.9200	−0.404999	−0.202499	−	0.979282i	$-0.564906\pi$
$727$	−10.9200	−0.404999	−0.202499	+	0.979282i	$0.564906\pi$
$728$	−4.20555	−0.155868
$729$	1.00000	0.0370370
$730$	0.843326	0.0312129
$731$	4.41110	0.163150
$732$	−1.25443	−0.0463649
$733$	23.7633	0.877717	0.438858	−	0.898556i	$-0.355383\pi$
$733$	23.7633	0.877717	0.438858	+	0.898556i	$0.355383\pi$
$734$	20.1955	0.745430
$735$	−1.00000	−0.0368856
$736$	−1.00000	−0.0368605
$737$	4.96117	0.182747
$738$	3.15667	0.116199
$739$	−6.09775	−0.224309	−0.112155	−	0.993691i	$-0.535775\pi$
$739$	−6.09775	−0.224309	−0.112155	+	0.993691i	$0.535775\pi$
$740$	−2.00000	−0.0735215
$741$	23.6655	0.869375
$742$	2.00000	0.0734223
$743$	0.215597	0.00790947	0.00395474	−	0.999992i	$-0.498741\pi$
$743$	0.215597	0.00790947	0.00395474	+	0.999992i	$0.498741\pi$
$744$	9.62721	0.352951
$745$	−2.00000	−0.0732743
$746$	−2.00000	−0.0732252
$747$	10.0383	0.367283
$748$	4.41110	0.161286
$749$	−7.25443	−0.265071
$750$	−1.00000	−0.0365148
$751$	13.6867	0.499433	0.249717	−	0.968319i	$-0.419663\pi$
$751$	13.6867	0.499433	0.249717	+	0.968319i	$0.419663\pi$
$752$	−9.62721	−0.351068
$753$	−7.89220	−0.287608
$754$	24.5300	0.893329
$755$	4.41110	0.160536
$756$	1.00000	0.0363696
$757$	35.5678	1.29273	0.646366	−	0.763027i	$-0.276288\pi$
$757$	35.5678	1.29273	0.646366	+	0.763027i	$0.276288\pi$
$758$	32.0766	1.16508
$759$	−0.578337	−0.0209923
$760$	−5.62721	−0.204120
$761$	36.7044	1.33053	0.665266	−	0.746606i	$-0.268318\pi$
$761$	36.7044	1.33053	0.665266	+	0.746606i	$0.268318\pi$
$762$	2.26499	0.0820519
$763$	16.5089	0.597661
$764$	−21.5678	−0.780295
$765$	−7.62721	−0.275762
$766$	−6.84333	−0.247259
$767$	−35.3733	−1.27726
$768$	−1.00000	−0.0360844
$769$	−50.4283	−1.81849	−0.909245	−	0.416261i	$-0.863340\pi$
$769$	−50.4283	−1.81849	−0.909245	+	0.416261i	$0.863340\pi$
$770$	0.578337	0.0208418
$771$	22.8222	0.821921
$772$	−1.58890	−0.0571858
$773$	6.33447	0.227835	0.113918	−	0.993490i	$-0.463660\pi$
$773$	6.33447	0.227835	0.113918	+	0.993490i	$0.463660\pi$
$774$	−0.578337	−0.0207879
$775$	−9.62721	−0.345820
$776$	−3.04888	−0.109448
$777$	−2.00000	−0.0717496
$778$	33.2544	1.19223
$779$	−17.7633	−0.636435
$780$	−4.20555	−0.150583
$781$	3.86103	0.138159
$782$	7.62721	0.272749
$783$	−5.83276	−0.208446
$784$	1.00000	0.0357143
$785$	−4.31335	−0.153950
$786$	4.00000	0.142675
$787$	−22.9511	−0.818119	−0.409060	−	0.912508i	$-0.634143\pi$
$787$	−22.9511	−0.818119	−0.409060	+	0.912508i	$0.634143\pi$
$788$	2.74557	0.0978070
$789$	−14.5089	−0.516529
$790$	10.0978	0.359262
$791$	1.25443	0.0446023
$792$	−0.578337	−0.0205503
$793$	5.27555	0.187340
$794$	4.20555	0.149249
$795$	2.00000	0.0709327
$796$	−16.8222	−0.596247
$797$	−7.56777	−0.268064	−0.134032	−	0.990977i	$-0.542793\pi$
$797$	−7.56777	−0.268064	−0.134032	+	0.990977i	$0.542793\pi$
$798$	−5.62721	−0.199201
$799$	73.4288	2.59772
$800$	1.00000	0.0353553
$801$	−0.951124	−0.0336063
$802$	−25.0872	−0.885859
$803$	−0.487727	−0.0172115
$804$	8.57834	0.302535
$805$	1.00000	0.0352454
$806$	−40.4877	−1.42612
$807$	−11.0489	−0.388939
$808$	18.7144	0.658370
$809$	7.08005	0.248921	0.124461	−	0.992225i	$-0.460280\pi$
$809$	7.08005	0.248921	0.124461	+	0.992225i	$0.460280\pi$
$810$	1.00000	0.0351364
$811$	−4.21560	−0.148030	−0.0740148	−	0.997257i	$-0.523581\pi$
$811$	−4.21560	−0.148030	−0.0740148	+	0.997257i	$0.523581\pi$
$812$	−5.83276	−0.204690
$813$	7.31386	0.256508
$814$	1.15667	0.0405414
$815$	0.411100	0.0144002
$816$	7.62721	0.267006
$817$	3.25443	0.113858
$818$	6.41110	0.224159
$819$	−4.20555	−0.146954
$820$	3.15667	0.110236
$821$	26.2439	0.915917	0.457959	−	0.888974i	$-0.348581\pi$
$821$	26.2439	0.915917	0.457959	+	0.888974i	$0.348581\pi$
$822$	12.5089	0.436296
$823$	53.0661	1.84977	0.924883	−	0.380251i	$-0.124162\pi$
$823$	53.0661	1.84977	0.924883	+	0.380251i	$0.124162\pi$
$824$	−8.00000	−0.278693
$825$	0.578337	0.0201351
$826$	8.41110	0.292660
$827$	27.8811	0.969522	0.484761	−	0.874647i	$-0.338907\pi$
$827$	27.8811	0.969522	0.484761	+	0.874647i	$0.338907\pi$
$828$	−1.00000	−0.0347524
$829$	−20.5683	−0.714366	−0.357183	−	0.934034i	$-0.616263\pi$
$829$	−20.5683	−0.714366	−0.357183	+	0.934034i	$0.616263\pi$
$830$	10.0383	0.348435
$831$	−10.2439	−0.355356
$832$	4.20555	0.145801
$833$	−7.62721	−0.264267
$834$	8.41110	0.291253
$835$	17.2927	0.598440
$836$	3.25443	0.112557
$837$	9.62721	0.332765
$838$	−33.6555	−1.16261
$839$	20.4111	0.704669	0.352335	−	0.935874i	$-0.385388\pi$
$839$	20.4111	0.704669	0.352335	+	0.935874i	$0.385388\pi$
$840$	1.00000	0.0345033
$841$	5.02113	0.173142
$842$	23.1567	0.798032
$843$	23.9305	0.824211
$844$	16.4111	0.564893
$845$	4.68665	0.161226
$846$	−9.62721	−0.330990
$847$	10.6655	0.366472
$848$	−2.00000	−0.0686803
$849$	15.8922	0.545419
$850$	−7.62721	−0.261611
$851$	2.00000	0.0685591
$852$	6.67609	0.228719
$853$	−46.4988	−1.59209	−0.796044	−	0.605238i	$-0.793078\pi$
$853$	−46.4988	−1.59209	−0.796044	+	0.605238i	$0.793078\pi$
$854$	−1.25443	−0.0429256
$855$	−5.62721	−0.192447
$856$	7.25443	0.247951
$857$	−37.6655	−1.28663	−0.643315	−	0.765602i	$-0.722441\pi$
$857$	−37.6655	−1.28663	−0.643315	+	0.765602i	$0.722441\pi$
$858$	2.43223	0.0830348
$859$	−23.0388	−0.786075	−0.393037	−	0.919523i	$-0.628576\pi$
$859$	−23.0388	−0.786075	−0.393037	+	0.919523i	$0.628576\pi$
$860$	−0.578337	−0.0197211
$861$	3.15667	0.107579
$862$	−5.90225	−0.201031
$863$	−16.6066	−0.565295	−0.282648	−	0.959224i	$-0.591213\pi$
$863$	−16.6066	−0.565295	−0.282648	+	0.959224i	$0.591213\pi$
$864$	−1.00000	−0.0340207
$865$	−19.6272	−0.667345
$866$	−25.5577	−0.868487
$867$	−41.1744	−1.39836
$868$	9.62721	0.326769
$869$	−5.83990	−0.198105
$870$	−5.83276	−0.197749
$871$	−36.0766	−1.22241
$872$	−16.5089	−0.559060
$873$	−3.04888	−0.103189
$874$	5.62721	0.190343
$875$	−1.00000	−0.0338062
$876$	−0.843326	−0.0284933
$877$	−25.1638	−0.849722	−0.424861	−	0.905259i	$-0.639677\pi$
$877$	−25.1638	−0.849722	−0.424861	+	0.905259i	$0.639677\pi$
$878$	30.9794	1.04550
$879$	22.4111	0.755908
$880$	−0.578337	−0.0194957
$881$	−8.01005	−0.269865	−0.134933	−	0.990855i	$-0.543082\pi$
$881$	−8.01005	−0.269865	−0.134933	+	0.990855i	$0.543082\pi$
$882$	1.00000	0.0336718
$883$	−46.9200	−1.57898	−0.789491	−	0.613762i	$-0.789655\pi$
$883$	−46.9200	−1.57898	−0.789491	+	0.613762i	$0.789655\pi$
$884$	−32.0766	−1.07885
$885$	8.41110	0.282736
$886$	22.0978	0.742388
$887$	56.1361	1.88486	0.942432	−	0.334397i	$-0.108533\pi$
$887$	56.1361	1.88486	0.942432	+	0.334397i	$0.108533\pi$
$888$	2.00000	0.0671156
$889$	2.26499	0.0759653
$890$	−0.951124	−0.0318818
$891$	−0.578337	−0.0193750
$892$	1.45998	0.0488836
$893$	54.1744	1.81288
$894$	2.00000	0.0668900
$895$	19.6655	0.657346
$896$	−1.00000	−0.0334077
$897$	4.20555	0.140419
$898$	14.7456	0.492066
$899$	−56.1533	−1.87282
$900$	1.00000	0.0333333
$901$	15.2544	0.508199
$902$	−1.82562	−0.0607866
$903$	−0.578337	−0.0192459
$904$	−1.25443	−0.0417216
$905$	9.25443	0.307628
$906$	−4.41110	−0.146549
$907$	−11.0106	−0.365600	−0.182800	−	0.983150i	$-0.558516\pi$
$907$	−11.0106	−0.365600	−0.182800	+	0.983150i	$0.558516\pi$
$908$	−11.1950	−0.371519
$909$	18.7144	0.620718
$910$	−4.20555	−0.139413
$911$	−13.0800	−0.433361	−0.216681	−	0.976243i	$-0.569523\pi$
$911$	−13.0800	−0.433361	−0.216681	+	0.976243i	$0.569523\pi$
$912$	5.62721	0.186336
$913$	−5.80553	−0.192135
$914$	22.0283	0.728630
$915$	−1.25443	−0.0414700
$916$	15.1567	0.500791
$917$	4.00000	0.132092
$918$	7.62721	0.251736
$919$	−26.9200	−0.888007	−0.444004	−	0.896025i	$-0.646442\pi$
$919$	−26.9200	−0.888007	−0.444004	+	0.896025i	$0.646442\pi$
$920$	−1.00000	−0.0329690
$921$	24.1955	0.797269
$922$	26.7144	0.879792
$923$	−28.0766	−0.924153
$924$	−0.578337	−0.0190259
$925$	−2.00000	−0.0657596
$926$	14.3416	0.471295
$927$	−8.00000	−0.262754
$928$	5.83276	0.191470
$929$	52.9200	1.73625	0.868124	−	0.496348i	$-0.165326\pi$
$929$	52.9200	1.73625	0.868124	+	0.496348i	$0.165326\pi$
$930$	9.62721	0.315689
$931$	−5.62721	−0.184424
$932$	−19.3522	−0.633902
$933$	22.2056	0.726977
$934$	−20.3517	−0.665927
$935$	4.41110	0.144258
$936$	4.20555	0.137463
$937$	23.5366	0.768907	0.384454	−	0.923144i	$-0.374390\pi$
$937$	23.5366	0.768907	0.384454	+	0.923144i	$0.374390\pi$
$938$	8.57834	0.280093
$939$	32.2822	1.05349
$940$	−9.62721	−0.314005
$941$	−6.19550	−0.201968	−0.100984	−	0.994888i	$-0.532199\pi$
$941$	−6.19550	−0.201968	−0.100984	+	0.994888i	$0.532199\pi$
$942$	4.31335	0.140536
$943$	−3.15667	−0.102795
$944$	−8.41110	−0.273758
$945$	1.00000	0.0325300
$946$	0.334474	0.0108747
$947$	−33.2333	−1.07994	−0.539969	−	0.841685i	$-0.681564\pi$
$947$	−33.2333	−1.07994	−0.539969	+	0.841685i	$0.681564\pi$
$948$	−10.0978	−0.327960
$949$	3.54665	0.115129
$950$	−5.62721	−0.182571
$951$	−10.4111	−0.337603
$952$	7.62721	0.247199
$953$	42.2721	1.36933	0.684664	−	0.728859i	$-0.259949\pi$
$953$	42.2721	1.36933	0.684664	+	0.728859i	$0.259949\pi$
$954$	−2.00000	−0.0647524
$955$	−21.5678	−0.697917
$956$	1.32391	0.0428183
$957$	3.37330	0.109043
$958$	16.0000	0.516937
$959$	12.5089	0.403932
$960$	−1.00000	−0.0322749
$961$	61.6832	1.98978
$962$	−8.41110	−0.271185
$963$	7.25443	0.233771
$964$	−14.1361	−0.455292
$965$	−1.58890	−0.0511485
$966$	−1.00000	−0.0321745
$967$	6.34162	0.203933	0.101966	−	0.994788i	$-0.467487\pi$
$967$	6.34162	0.203933	0.101966	+	0.994788i	$0.467487\pi$
$968$	−10.6655	−0.342803
$969$	−42.9200	−1.37879
$970$	−3.04888	−0.0978935
$971$	61.7321	1.98108	0.990539	−	0.137233i	$-0.0438209\pi$
$971$	61.7321	1.98108	0.990539	+	0.137233i	$0.0438209\pi$
$972$	−1.00000	−0.0320750
$973$	8.41110	0.269647
$974$	−27.3028	−0.874838
$975$	−4.20555	−0.134685
$976$	1.25443	0.0401532
$977$	18.3345	0.586572	0.293286	−	0.956025i	$-0.405251\pi$
$977$	18.3345	0.586572	0.293286	+	0.956025i	$0.405251\pi$
$978$	−0.411100	−0.0131455
$979$	0.550070	0.0175803
$980$	1.00000	0.0319438
$981$	−16.5089	−0.527087
$982$	25.3522	0.809021
$983$	8.33447	0.265828	0.132914	−	0.991128i	$-0.457567\pi$
$983$	8.33447	0.265828	0.132914	+	0.991128i	$0.457567\pi$
$984$	−3.15667	−0.100631
$985$	2.74557	0.0874813
$986$	−44.4877	−1.41678
$987$	−9.62721	−0.306438
$988$	−23.6655	−0.752901
$989$	0.578337	0.0183900
$990$	−0.578337	−0.0183808
$991$	−2.91995	−0.0927553	−0.0463777	−	0.998924i	$-0.514768\pi$
$991$	−2.91995	−0.0927553	−0.0463777	+	0.998924i	$0.514768\pi$
$992$	−9.62721	−0.305664
$993$	28.8222	0.914645
$994$	6.67609	0.211753
$995$	−16.8222	−0.533300
$996$	−10.0383	−0.318076
$997$	27.5366	0.872093	0.436046	−	0.899924i	$-0.356378\pi$
$997$	27.5366	0.872093	0.436046	+	0.899924i	$0.356378\pi$
$998$	−37.4288	−1.18479
$999$	2.00000	0.0632772

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4830.2.a.ca.1.2	✓	3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4830.2.a.ca.1.2	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -1.00000 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -0.578337 q^{11} -1.00000 q^{12} +4.20555 q^{13} -1.00000 q^{14} -1.00000 q^{15} +1.00000 q^{16} -7.62721 q^{17} +1.00000 q^{18} -5.62721 q^{19} +1.00000 q^{20} +1.00000 q^{21} -0.578337 q^{22} -1.00000 q^{23} -1.00000 q^{24} +1.00000 q^{25} +4.20555 q^{26} -1.00000 q^{27} -1.00000 q^{28} +5.83276 q^{29} -1.00000 q^{30} -9.62721 q^{31} +1.00000 q^{32} +0.578337 q^{33} -7.62721 q^{34} -1.00000 q^{35} +1.00000 q^{36} -2.00000 q^{37} -5.62721 q^{38} -4.20555 q^{39} +1.00000 q^{40} +3.15667 q^{41} +1.00000 q^{42} -0.578337 q^{43} -0.578337 q^{44} +1.00000 q^{45} -1.00000 q^{46} -9.62721 q^{47} -1.00000 q^{48} +1.00000 q^{49} +1.00000 q^{50} +7.62721 q^{51} +4.20555 q^{52} -2.00000 q^{53} -1.00000 q^{54} -0.578337 q^{55} -1.00000 q^{56} +5.62721 q^{57} +5.83276 q^{58} -8.41110 q^{59} -1.00000 q^{60} +1.25443 q^{61} -9.62721 q^{62} -1.00000 q^{63} +1.00000 q^{64} +4.20555 q^{65} +0.578337 q^{66} -8.57834 q^{67} -7.62721 q^{68} +1.00000 q^{69} -1.00000 q^{70} -6.67609 q^{71} +1.00000 q^{72} +0.843326 q^{73} -2.00000 q^{74} -1.00000 q^{75} -5.62721 q^{76} +0.578337 q^{77} -4.20555 q^{78} +10.0978 q^{79} +1.00000 q^{80} +1.00000 q^{81} +3.15667 q^{82} +10.0383 q^{83} +1.00000 q^{84} -7.62721 q^{85} -0.578337 q^{86} -5.83276 q^{87} -0.578337 q^{88} -0.951124 q^{89} +1.00000 q^{90} -4.20555 q^{91} -1.00000 q^{92} +9.62721 q^{93} -9.62721 q^{94} -5.62721 q^{95} -1.00000 q^{96} -3.04888 q^{97} +1.00000 q^{98} -0.578337 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 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	\( 3 q + 3 q^{2} - 3 q^{3} + 3 q^{4} + 3 q^{5} - 3 q^{6} - 3 q^{7} + 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{12} - 2 q^{13} - 3 q^{14} - 3 q^{15} + 3 q^{16} - 10 q^{17} + 3 q^{18} - 4 q^{19} + 3 q^{20} + 3 q^{21} - 3 q^{23} - 3 q^{24} + 3 q^{25} - 2 q^{26} - 3 q^{27} - 3 q^{28} - 10 q^{29} - 3 q^{30} - 16 q^{31} + 3 q^{32} - 10 q^{34} - 3 q^{35} + 3 q^{36} - 6 q^{37} - 4 q^{38} + 2 q^{39} + 3 q^{40} + 6 q^{41} + 3 q^{42} + 3 q^{45} - 3 q^{46} - 16 q^{47} - 3 q^{48} + 3 q^{49} + 3 q^{50} + 10 q^{51} - 2 q^{52} - 6 q^{53} - 3 q^{54} - 3 q^{56} + 4 q^{57} - 10 q^{58} + 4 q^{59} - 3 q^{60} - 22 q^{61} - 16 q^{62} - 3 q^{63} + 3 q^{64} - 2 q^{65} - 24 q^{67} - 10 q^{68} + 3 q^{69} - 3 q^{70} + 4 q^{71} + 3 q^{72} + 6 q^{73} - 6 q^{74} - 3 q^{75} - 4 q^{76} + 2 q^{78} + 8 q^{79} + 3 q^{80} + 3 q^{81} + 6 q^{82} - 12 q^{83} + 3 q^{84} - 10 q^{85} + 10 q^{87} - 14 q^{89} + 3 q^{90} + 2 q^{91} - 3 q^{92} + 16 q^{93} - 16 q^{94} - 4 q^{95} - 3 q^{96} + 2 q^{97} + 3 q^{98}+O(q^{100}) \) 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 - 3 * q^12 - 2 * q^13 - 3 * q^14 - 3 * q^15 + 3 * q^16 - 10 * q^17 + 3 * q^18 - 4 * q^19 + 3 * q^20 + 3 * q^21 - 3 * q^23 - 3 * q^24 + 3 * q^25 - 2 * q^26 - 3 * q^27 - 3 * q^28 - 10 * q^29 - 3 * q^30 - 16 * q^31 + 3 * q^32 - 10 * q^34 - 3 * q^35 + 3 * q^36 - 6 * q^37 - 4 * q^38 + 2 * q^39 + 3 * q^40 + 6 * q^41 + 3 * q^42 + 3 * q^45 - 3 * q^46 - 16 * q^47 - 3 * q^48 + 3 * q^49 + 3 * q^50 + 10 * q^51 - 2 * q^52 - 6 * q^53 - 3 * q^54 - 3 * q^56 + 4 * q^57 - 10 * q^58 + 4 * q^59 - 3 * q^60 - 22 * q^61 - 16 * q^62 - 3 * q^63 + 3 * q^64 - 2 * q^65 - 24 * q^67 - 10 * q^68 + 3 * q^69 - 3 * q^70 + 4 * q^71 + 3 * q^72 + 6 * q^73 - 6 * q^74 - 3 * q^75 - 4 * q^76 + 2 * q^78 + 8 * q^79 + 3 * q^80 + 3 * q^81 + 6 * q^82 - 12 * q^83 + 3 * q^84 - 10 * q^85 + 10 * q^87 - 14 * q^89 + 3 * q^90 + 2 * q^91 - 3 * q^92 + 16 * q^93 - 16 * q^94 - 4 * q^95 - 3 * q^96 + 2 * q^97 + 3 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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