LMFDB - Embedded newform 430.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [430,2,Mod(1,430)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(430, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("430.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 430 = 2 \cdot 5 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	430.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:	$3.43356728692$
Analytic rank:	$0$
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:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.81361$ of defining polynomial
Character	$\chi$	$=$	430.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.10278 q^{6} -2.28917 q^{7} -1.00000 q^{8} +6.62721 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.10278 q^{6} -2.28917 q^{7} -1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{10} -4.72999 q^{11} -3.10278 q^{12} -5.33804 q^{13} +2.28917 q^{14} +3.10278 q^{15} +1.00000 q^{16} +4.52444 q^{17} -6.62721 q^{18} -3.91638 q^{19} -1.00000 q^{20} +7.10278 q^{21} +4.72999 q^{22} +6.52444 q^{23} +3.10278 q^{24} +1.00000 q^{25} +5.33804 q^{26} -11.2544 q^{27} -2.28917 q^{28} +9.59749 q^{29} -3.10278 q^{30} +6.44082 q^{31} -1.00000 q^{32} +14.6761 q^{33} -4.52444 q^{34} +2.28917 q^{35} +6.62721 q^{36} -3.94610 q^{37} +3.91638 q^{38} +16.5628 q^{39} +1.00000 q^{40} -3.54359 q^{41} -7.10278 q^{42} +1.00000 q^{43} -4.72999 q^{44} -6.62721 q^{45} -6.52444 q^{46} -3.10278 q^{47} -3.10278 q^{48} -1.75971 q^{49} -1.00000 q^{50} -14.0383 q^{51} -5.33804 q^{52} +12.7839 q^{53} +11.2544 q^{54} +4.72999 q^{55} +2.28917 q^{56} +12.1517 q^{57} -9.59749 q^{58} +9.04888 q^{59} +3.10278 q^{60} -3.97028 q^{61} -6.44082 q^{62} -15.1708 q^{63} +1.00000 q^{64} +5.33804 q^{65} -14.6761 q^{66} -0.980843 q^{67} +4.52444 q^{68} -20.2439 q^{69} -2.28917 q^{70} -8.72999 q^{71} -6.62721 q^{72} +12.2736 q^{73} +3.94610 q^{74} -3.10278 q^{75} -3.91638 q^{76} +10.8277 q^{77} -16.5628 q^{78} +0.235269 q^{79} -1.00000 q^{80} +15.0383 q^{81} +3.54359 q^{82} +6.78389 q^{83} +7.10278 q^{84} -4.52444 q^{85} -1.00000 q^{86} -29.7789 q^{87} +4.72999 q^{88} -15.2005 q^{89} +6.62721 q^{90} +12.2197 q^{91} +6.52444 q^{92} -19.9844 q^{93} +3.10278 q^{94} +3.91638 q^{95} +3.10278 q^{96} -3.94610 q^{97} +1.75971 q^{98} -31.3466 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) $ 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} + 2 q^{15} + 3 q^{16} + 8 q^{17} - 7 q^{18} + 2 q^{19} - 3 q^{20} + 14 q^{21} - 6 q^{22} + 14 q^{23} + 2 q^{24} + 3 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{32} + 20 q^{33} - 8 q^{34} + 6 q^{35} + 7 q^{36} - 8 q^{37} - 2 q^{38} + 2 q^{39} + 3 q^{40} + 16 q^{41} - 14 q^{42} + 3 q^{43} + 6 q^{44} - 7 q^{45} - 14 q^{46} - 2 q^{47} - 2 q^{48} + 5 q^{49} - 3 q^{50} - 4 q^{52} + 22 q^{53} + 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} - 6 q^{58} + 16 q^{59} + 2 q^{60} - 2 q^{61} - 6 q^{63} + 3 q^{64} + 4 q^{65} - 20 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{70} - 6 q^{71} - 7 q^{72} - 10 q^{73} + 8 q^{74} - 2 q^{75} + 2 q^{76} - 10 q^{77} - 2 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 16 q^{82} + 4 q^{83} + 14 q^{84} - 8 q^{85} - 3 q^{86} - 58 q^{87} - 6 q^{88} - 16 q^{89} + 7 q^{90} - 14 q^{91} + 14 q^{92} - 14 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 5 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9 + 3 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^14 + 2 * q^15 + 3 * q^16 + 8 * q^17 - 7 * q^18 + 2 * q^19 - 3 * q^20 + 14 * q^21 - 6 * q^22 + 14 * q^23 + 2 * q^24 + 3 * q^25 + 4 * q^26 - 8 * q^27 - 6 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^32 + 20 * q^33 - 8 * q^34 + 6 * q^35 + 7 * q^36 - 8 * q^37 - 2 * q^38 + 2 * q^39 + 3 * q^40 + 16 * q^41 - 14 * q^42 + 3 * q^43 + 6 * q^44 - 7 * q^45 - 14 * q^46 - 2 * q^47 - 2 * q^48 + 5 * q^49 - 3 * q^50 - 4 * q^52 + 22 * q^53 + 8 * q^54 - 6 * q^55 + 6 * q^56 + 18 * q^57 - 6 * q^58 + 16 * q^59 + 2 * q^60 - 2 * q^61 - 6 * q^63 + 3 * q^64 + 4 * q^65 - 20 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 6 * q^70 - 6 * q^71 - 7 * q^72 - 10 * q^73 + 8 * q^74 - 2 * q^75 + 2 * q^76 - 10 * q^77 - 2 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 16 * q^82 + 4 * q^83 + 14 * q^84 - 8 * q^85 - 3 * q^86 - 58 * q^87 - 6 * q^88 - 16 * q^89 + 7 * q^90 - 14 * q^91 + 14 * q^92 - 14 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 - 8 * q^97 - 5 * q^98 - 30 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.10278	−1.79139	−0.895694	−	0.444671i	$-0.853321\pi$
$3$	−3.10278	−1.79139	−0.895694	+	0.444671i	$0.853321\pi$
$4$	1.00000	0.500000
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	3.10278	1.26670
$7$	−2.28917	−0.865224	−0.432612	−	0.901580i	$-0.642408\pi$
$7$	−2.28917	−0.865224	−0.432612	+	0.901580i	$0.642408\pi$
$8$	−1.00000	−0.353553
$9$	6.62721	2.20907
$10$	1.00000	0.316228
$11$	−4.72999	−1.42615	−0.713073	−	0.701090i	$-0.752697\pi$
$11$	−4.72999	−1.42615	−0.713073	+	0.701090i	$0.752697\pi$
$12$	−3.10278	−0.895694
$13$	−5.33804	−1.48051	−0.740254	−	0.672328i	$-0.765295\pi$
$13$	−5.33804	−1.48051	−0.740254	+	0.672328i	$0.765295\pi$
$14$	2.28917	0.611806
$15$	3.10278	0.801133
$16$	1.00000	0.250000
$17$	4.52444	1.09734	0.548669	−	0.836040i	$-0.315135\pi$
$17$	4.52444	1.09734	0.548669	+	0.836040i	$0.315135\pi$
$18$	−6.62721	−1.56205
$19$	−3.91638	−0.898480	−0.449240	−	0.893411i	$-0.648305\pi$
$19$	−3.91638	−0.898480	−0.449240	+	0.893411i	$0.648305\pi$
$20$	−1.00000	−0.223607
$21$	7.10278	1.54995
$22$	4.72999	1.00844
$23$	6.52444	1.36044	0.680220	−	0.733008i	$-0.261884\pi$
$23$	6.52444	1.36044	0.680220	+	0.733008i	$0.261884\pi$
$24$	3.10278	0.633351
$25$	1.00000	0.200000
$26$	5.33804	1.04688
$27$	−11.2544	−2.16592
$28$	−2.28917	−0.432612
$29$	9.59749	1.78221	0.891105	−	0.453797i	$-0.149931\pi$
$29$	9.59749	1.78221	0.891105	+	0.453797i	$0.149931\pi$
$30$	−3.10278	−0.566487
$31$	6.44082	1.15681	0.578403	−	0.815751i	$-0.303676\pi$
$31$	6.44082	1.15681	0.578403	+	0.815751i	$0.303676\pi$
$32$	−1.00000	−0.176777
$33$	14.6761	2.55478
$34$	−4.52444	−0.775935
$35$	2.28917	0.386940
$36$	6.62721	1.10454
$37$	−3.94610	−0.648735	−0.324367	−	0.945931i	$-0.605151\pi$
$37$	−3.94610	−0.648735	−0.324367	+	0.945931i	$0.605151\pi$
$38$	3.91638	0.635321
$39$	16.5628	2.65216
$40$	1.00000	0.158114
$41$	−3.54359	−0.553416	−0.276708	−	0.960954i	$-0.589244\pi$
$41$	−3.54359	−0.553416	−0.276708	+	0.960954i	$0.589244\pi$
$42$	−7.10278	−1.09598
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	−4.72999	−0.713073
$45$	−6.62721	−0.987927
$46$	−6.52444	−0.961976
$47$	−3.10278	−0.452586	−0.226293	−	0.974059i	$-0.572661\pi$
$47$	−3.10278	−0.452586	−0.226293	+	0.974059i	$0.572661\pi$
$48$	−3.10278	−0.447847
$49$	−1.75971	−0.251387
$50$	−1.00000	−0.141421
$51$	−14.0383	−1.96576
$52$	−5.33804	−0.740254
$53$	12.7839	1.75600	0.878001	−	0.478659i	$-0.158877\pi$
$53$	12.7839	1.75600	0.878001	+	0.478659i	$0.158877\pi$
$54$	11.2544	1.53153
$55$	4.72999	0.637791
$56$	2.28917	0.305903
$57$	12.1517	1.60953
$58$	−9.59749	−1.26021
$59$	9.04888	1.17806	0.589032	−	0.808110i	$-0.299509\pi$
$59$	9.04888	1.17806	0.589032	+	0.808110i	$0.299509\pi$
$60$	3.10278	0.400567
$61$	−3.97028	−0.508342	−0.254171	−	0.967159i	$-0.581803\pi$
$61$	−3.97028	−0.508342	−0.254171	+	0.967159i	$0.581803\pi$
$62$	−6.44082	−0.817985
$63$	−15.1708	−1.91134
$64$	1.00000	0.125000
$65$	5.33804	0.662103
$66$	−14.6761	−1.80650
$67$	−0.980843	−0.119829	−0.0599145	−	0.998204i	$-0.519083\pi$
$67$	−0.980843	−0.119829	−0.0599145	+	0.998204i	$0.519083\pi$
$68$	4.52444	0.548669
$69$	−20.2439	−2.43707
$70$	−2.28917	−0.273608
$71$	−8.72999	−1.03606	−0.518029	−	0.855363i	$-0.673334\pi$
$71$	−8.72999	−1.03606	−0.518029	+	0.855363i	$0.673334\pi$
$72$	−6.62721	−0.781025
$73$	12.2736	1.43651	0.718257	−	0.695778i	$-0.244940\pi$
$73$	12.2736	1.43651	0.718257	+	0.695778i	$0.244940\pi$
$74$	3.94610	0.458725
$75$	−3.10278	−0.358278
$76$	−3.91638	−0.449240
$77$	10.8277	1.23394
$78$	−16.5628	−1.87536
$79$	0.235269	0.0264699	0.0132349	−	0.999912i	$-0.495787\pi$
$79$	0.235269	0.0264699	0.0132349	+	0.999912i	$0.495787\pi$
$80$	−1.00000	−0.111803
$81$	15.0383	1.67092
$82$	3.54359	0.391325
$83$	6.78389	0.744628	0.372314	−	0.928107i	$-0.378564\pi$
$83$	6.78389	0.744628	0.372314	+	0.928107i	$0.378564\pi$
$84$	7.10278	0.774976
$85$	−4.52444	−0.490744
$86$	−1.00000	−0.107833
$87$	−29.7789	−3.19263
$88$	4.72999	0.504218
$89$	−15.2005	−1.61125	−0.805626	−	0.592424i	$-0.798171\pi$
$89$	−15.2005	−1.61125	−0.805626	+	0.592424i	$0.798171\pi$
$90$	6.62721	0.698570
$91$	12.2197	1.28097
$92$	6.52444	0.680220
$93$	−19.9844	−2.07229
$94$	3.10278	0.320027
$95$	3.91638	0.401812
$96$	3.10278	0.316676
$97$	−3.94610	−0.400666	−0.200333	−	0.979728i	$-0.564202\pi$
$97$	−3.94610	−0.400666	−0.200333	+	0.979728i	$0.564202\pi$
$98$	1.75971	0.177757
$99$	−31.3466	−3.15046
$100$	1.00000	0.100000
$101$	−10.7300	−1.06767	−0.533837	−	0.845587i	$-0.679250\pi$
$101$	−10.7300	−1.06767	−0.533837	+	0.845587i	$0.679250\pi$
$102$	14.0383	1.39000
$103$	−5.62721	−0.554466	−0.277233	−	0.960803i	$-0.589417\pi$
$103$	−5.62721	−0.554466	−0.277233	+	0.960803i	$0.589417\pi$
$104$	5.33804	0.523438
$105$	−7.10278	−0.693160
$106$	−12.7839	−1.24168
$107$	0.343068	0.0331656	0.0165828	−	0.999862i	$-0.494721\pi$
$107$	0.343068	0.0331656	0.0165828	+	0.999862i	$0.494721\pi$
$108$	−11.2544	−1.08296
$109$	7.62721	0.730555	0.365277	−	0.930899i	$-0.380974\pi$
$109$	7.62721	0.730555	0.365277	+	0.930899i	$0.380974\pi$
$110$	−4.72999	−0.450987
$111$	12.2439	1.16214
$112$	−2.28917	−0.216306
$113$	5.76473	0.542300	0.271150	−	0.962537i	$-0.412596\pi$
$113$	5.76473	0.542300	0.271150	+	0.962537i	$0.412596\pi$
$114$	−12.1517	−1.13811
$115$	−6.52444	−0.608407
$116$	9.59749	0.891105
$117$	−35.3764	−3.27055
$118$	−9.04888	−0.833017
$119$	−10.3572	−0.949443
$120$	−3.10278	−0.283243
$121$	11.3728	1.03389
$122$	3.97028	0.359452
$123$	10.9950	0.991384
$124$	6.44082	0.578403
$125$	−1.00000	−0.0894427
$126$	15.1708	1.35152
$127$	1.04888	0.0930727	0.0465363	−	0.998917i	$-0.485182\pi$
$127$	1.04888	0.0930727	0.0465363	+	0.998917i	$0.485182\pi$
$128$	−1.00000	−0.0883883
$129$	−3.10278	−0.273184
$130$	−5.33804	−0.468177
$131$	22.0383	1.92550	0.962748	−	0.270400i	$-0.0871558\pi$
$131$	22.0383	1.92550	0.962748	+	0.270400i	$0.0871558\pi$
$132$	14.6761	1.27739
$133$	8.96526	0.777386
$134$	0.980843	0.0847320
$135$	11.2544	0.968627
$136$	−4.52444	−0.387967
$137$	−0.137518	−0.0117489	−0.00587446	−	0.999983i	$-0.501870\pi$
$137$	−0.137518	−0.0117489	−0.00587446	+	0.999983i	$0.501870\pi$
$138$	20.2439	1.72327
$139$	12.7300	1.07974	0.539872	−	0.841747i	$-0.318473\pi$
$139$	12.7300	1.07974	0.539872	+	0.841747i	$0.318473\pi$
$140$	2.28917	0.193470
$141$	9.62721	0.810758
$142$	8.72999	0.732604
$143$	25.2489	2.11142
$144$	6.62721	0.552268
$145$	−9.59749	−0.797028
$146$	−12.2736	−1.01577
$147$	5.45998	0.450331
$148$	−3.94610	−0.324367
$149$	24.1063	1.97487	0.987434	−	0.158029i	$-0.0505141\pi$
$149$	24.1063	1.97487	0.987434	+	0.158029i	$0.0505141\pi$
$150$	3.10278	0.253341
$151$	−9.62721	−0.783451	−0.391726	−	0.920082i	$-0.628122\pi$
$151$	−9.62721	−0.783451	−0.391726	+	0.920082i	$0.628122\pi$
$152$	3.91638	0.317660
$153$	29.9844	2.42410
$154$	−10.8277	−0.872524
$155$	−6.44082	−0.517339
$156$	16.5628	1.32608
$157$	1.74055	0.138911	0.0694555	−	0.997585i	$-0.477874\pi$
$157$	1.74055	0.138911	0.0694555	+	0.997585i	$0.477874\pi$
$158$	−0.235269	−0.0187170
$159$	−39.6655	−3.14568
$160$	1.00000	0.0790569
$161$	−14.9355	−1.17709
$162$	−15.0383	−1.18152
$163$	−14.0978	−1.10422	−0.552111	−	0.833771i	$-0.686177\pi$
$163$	−14.0978	−1.10422	−0.552111	+	0.833771i	$0.686177\pi$
$164$	−3.54359	−0.276708
$165$	−14.6761	−1.14253
$166$	−6.78389	−0.526532
$167$	−0.318888	−0.0246763	−0.0123381	−	0.999924i	$-0.503927\pi$
$167$	−0.318888	−0.0246763	−0.0123381	+	0.999924i	$0.503927\pi$
$168$	−7.10278	−0.547991
$169$	15.4947	1.19190
$170$	4.52444	0.347009
$171$	−25.9547	−1.98481
$172$	1.00000	0.0762493
$173$	−3.24029	−0.246355	−0.123177	−	0.992385i	$-0.539308\pi$
$173$	−3.24029	−0.246355	−0.123177	+	0.992385i	$0.539308\pi$
$174$	29.7789	2.25753
$175$	−2.28917	−0.173045
$176$	−4.72999	−0.356536
$177$	−28.0766	−2.11037
$178$	15.2005	1.13933
$179$	−6.70027	−0.500802	−0.250401	−	0.968142i	$-0.580562\pi$
$179$	−6.70027	−0.500802	−0.250401	+	0.968142i	$0.580562\pi$
$180$	−6.62721	−0.493963
$181$	−14.6222	−1.08686	−0.543429	−	0.839455i	$-0.682874\pi$
$181$	−14.6222	−1.08686	−0.543429	+	0.839455i	$0.682874\pi$
$182$	−12.2197	−0.905783
$183$	12.3189	0.910638
$184$	−6.52444	−0.480988
$185$	3.94610	0.290123
$186$	19.9844	1.46533
$187$	−21.4005	−1.56496
$188$	−3.10278	−0.226293
$189$	25.7633	1.87400
$190$	−3.91638	−0.284124
$191$	1.36776	0.0989679	0.0494840	−	0.998775i	$-0.484242\pi$
$191$	1.36776	0.0989679	0.0494840	+	0.998775i	$0.484242\pi$
$192$	−3.10278	−0.223924
$193$	16.3728	1.17854	0.589269	−	0.807937i	$-0.299416\pi$
$193$	16.3728	1.17854	0.589269	+	0.807937i	$0.299416\pi$
$194$	3.94610	0.283314
$195$	−16.5628	−1.18608
$196$	−1.75971	−0.125693
$197$	12.2892	0.875567	0.437784	−	0.899080i	$-0.355764\pi$
$197$	12.2892	0.875567	0.437784	+	0.899080i	$0.355764\pi$
$198$	31.3466	2.22771
$199$	6.93554	0.491647	0.245824	−	0.969315i	$-0.420942\pi$
$199$	6.93554	0.491647	0.245824	+	0.969315i	$0.420942\pi$
$200$	−1.00000	−0.0707107
$201$	3.04334	0.214660
$202$	10.7300	0.754959
$203$	−21.9703	−1.54201
$204$	−14.0383	−0.982879
$205$	3.54359	0.247495
$206$	5.62721	0.392067
$207$	43.2388	3.00531
$208$	−5.33804	−0.370127
$209$	18.5244	1.28136
$210$	7.10278	0.490138
$211$	17.1567	1.18111	0.590557	−	0.806996i	$-0.298908\pi$
$211$	17.1567	1.18111	0.590557	+	0.806996i	$0.298908\pi$
$212$	12.7839	0.878001
$213$	27.0872	1.85598
$214$	−0.343068	−0.0234516
$215$	−1.00000	−0.0681994
$216$	11.2544	0.765767
$217$	−14.7441	−1.00090
$218$	−7.62721	−0.516580
$219$	−38.0822	−2.57335
$220$	4.72999	0.318896
$221$	−24.1517	−1.62462
$222$	−12.2439	−0.821754
$223$	−11.4217	−0.764851	−0.382426	−	0.923986i	$-0.624911\pi$
$223$	−11.4217	−0.764851	−0.382426	+	0.923986i	$0.624911\pi$
$224$	2.28917	0.152952
$225$	6.62721	0.441814
$226$	−5.76473	−0.383464
$227$	19.3622	1.28512	0.642558	−	0.766237i	$-0.277873\pi$
$227$	19.3622	1.28512	0.642558	+	0.766237i	$0.277873\pi$
$228$	12.1517	0.804763
$229$	−2.30330	−0.152206	−0.0761032	−	0.997100i	$-0.524248\pi$
$229$	−2.30330	−0.152206	−0.0761032	+	0.997100i	$0.524248\pi$
$230$	6.52444	0.430209
$231$	−33.5960	−2.21046
$232$	−9.59749	−0.630106
$233$	8.26499	0.541457	0.270729	−	0.962656i	$-0.412735\pi$
$233$	8.26499	0.541457	0.270729	+	0.962656i	$0.412735\pi$
$234$	35.3764	2.31262
$235$	3.10278	0.202403
$236$	9.04888	0.589032
$237$	−0.729988	−0.0474178
$238$	10.3572	0.671358
$239$	11.4897	0.743207	0.371603	−	0.928392i	$-0.378808\pi$
$239$	11.4897	0.743207	0.371603	+	0.928392i	$0.378808\pi$
$240$	3.10278	0.200283
$241$	9.57331	0.616671	0.308336	−	0.951278i	$-0.400228\pi$
$241$	9.57331	0.616671	0.308336	+	0.951278i	$0.400228\pi$
$242$	−11.3728	−0.731070
$243$	−12.8972	−0.827357
$244$	−3.97028	−0.254171
$245$	1.75971	0.112424
$246$	−10.9950	−0.701014
$247$	20.9058	1.33021
$248$	−6.44082	−0.408992
$249$	−21.0489	−1.33392
$250$	1.00000	0.0632456
$251$	26.3416	1.66267	0.831334	−	0.555773i	$-0.187578\pi$
$251$	26.3416	1.66267	0.831334	+	0.555773i	$0.187578\pi$
$252$	−15.1708	−0.955671
$253$	−30.8605	−1.94018
$254$	−1.04888	−0.0658123
$255$	14.0383	0.879113
$256$	1.00000	0.0625000
$257$	−13.4897	−0.841464	−0.420732	−	0.907185i	$-0.638227\pi$
$257$	−13.4897	−0.841464	−0.420732	+	0.907185i	$0.638227\pi$
$258$	3.10278	0.193170
$259$	9.03329	0.561301
$260$	5.33804	0.331051
$261$	63.6046	3.93703
$262$	−22.0383	−1.36153
$263$	−7.64135	−0.471186	−0.235593	−	0.971852i	$-0.575703\pi$
$263$	−7.64135	−0.471186	−0.235593	+	0.971852i	$0.575703\pi$
$264$	−14.6761	−0.903251
$265$	−12.7839	−0.785308
$266$	−8.96526	−0.549695
$267$	47.1638	2.88638
$268$	−0.980843	−0.0599145
$269$	−17.1950	−1.04840	−0.524198	−	0.851596i	$-0.675635\pi$
$269$	−17.1950	−1.04840	−0.524198	+	0.851596i	$0.675635\pi$
$270$	−11.2544	−0.684923
$271$	−17.0575	−1.03617	−0.518084	−	0.855330i	$-0.673354\pi$
$271$	−17.0575	−1.03617	−0.518084	+	0.855330i	$0.673354\pi$
$272$	4.52444	0.274334
$273$	−37.9149	−2.29472
$274$	0.137518	0.00830774
$275$	−4.72999	−0.285229
$276$	−20.2439	−1.21854
$277$	16.3728	0.983745	0.491873	−	0.870667i	$-0.336313\pi$
$277$	16.3728	0.983745	0.491873	+	0.870667i	$0.336313\pi$
$278$	−12.7300	−0.763494
$279$	42.6847	2.55547
$280$	−2.28917	−0.136804
$281$	−20.0625	−1.19683	−0.598414	−	0.801187i	$-0.704202\pi$
$281$	−20.0625	−1.19683	−0.598414	+	0.801187i	$0.704202\pi$
$282$	−9.62721	−0.573292
$283$	−0.343068	−0.0203933	−0.0101966	−	0.999948i	$-0.503246\pi$
$283$	−0.343068	−0.0203933	−0.0101966	+	0.999948i	$0.503246\pi$
$284$	−8.72999	−0.518029
$285$	−12.1517	−0.719802
$286$	−25.2489	−1.49300
$287$	8.11189	0.478829
$288$	−6.62721	−0.390512
$289$	3.47054	0.204149
$290$	9.59749	0.563584
$291$	12.2439	0.717748
$292$	12.2736	0.718257
$293$	14.4111	0.841905	0.420953	−	0.907083i	$-0.361696\pi$
$293$	14.4111	0.841905	0.420953	+	0.907083i	$0.361696\pi$
$294$	−5.45998	−0.318432
$295$	−9.04888	−0.526846
$296$	3.94610	0.229362
$297$	53.2333	3.08891
$298$	−24.1063	−1.39644
$299$	−34.8277	−2.01414
$300$	−3.10278	−0.179139
$301$	−2.28917	−0.131945
$302$	9.62721	0.553984
$303$	33.2927	1.91262
$304$	−3.91638	−0.224620
$305$	3.97028	0.227338
$306$	−29.9844	−1.71409
$307$	17.6358	1.00653	0.503264	−	0.864133i	$-0.332132\pi$
$307$	17.6358	1.00653	0.503264	+	0.864133i	$0.332132\pi$
$308$	10.8277	0.616968
$309$	17.4600	0.993263
$310$	6.44082	0.365814
$311$	−9.69525	−0.549767	−0.274883	−	0.961478i	$-0.588639\pi$
$311$	−9.69525	−0.549767	−0.274883	+	0.961478i	$0.588639\pi$
$312$	−16.5628	−0.937681
$313$	10.4111	0.588470	0.294235	−	0.955733i	$-0.404935\pi$
$313$	10.4111	0.588470	0.294235	+	0.955733i	$0.404935\pi$
$314$	−1.74055	−0.0982250
$315$	15.1708	0.854778
$316$	0.235269	0.0132349
$317$	−19.3764	−1.08828	−0.544142	−	0.838993i	$-0.683145\pi$
$317$	−19.3764	−1.08828	−0.544142	+	0.838993i	$0.683145\pi$
$318$	39.6655	2.22433
$319$	−45.3960	−2.54169
$320$	−1.00000	−0.0559017
$321$	−1.06446	−0.0594125
$322$	14.9355	0.832325
$323$	−17.7194	−0.985935
$324$	15.0383	0.835462
$325$	−5.33804	−0.296101
$326$	14.0978	0.780802
$327$	−23.6655	−1.30871
$328$	3.54359	0.195662
$329$	7.10278	0.391589
$330$	14.6761	0.807892
$331$	−3.72496	−0.204743	−0.102371	−	0.994746i	$-0.532643\pi$
$331$	−3.72496	−0.204743	−0.102371	+	0.994746i	$0.532643\pi$
$332$	6.78389	0.372314
$333$	−26.1517	−1.43310
$334$	0.318888	0.0174488
$335$	0.980843	0.0535892
$336$	7.10278	0.387488
$337$	6.74557	0.367455	0.183727	−	0.982977i	$-0.441184\pi$
$337$	6.74557	0.367455	0.183727	+	0.982977i	$0.441184\pi$
$338$	−15.4947	−0.842802
$339$	−17.8867	−0.971470
$340$	−4.52444	−0.245372
$341$	−30.4650	−1.64977
$342$	25.9547	1.40347
$343$	20.0524	1.08273
$344$	−1.00000	−0.0539164
$345$	20.2439	1.08989
$346$	3.24029	0.174199
$347$	17.4756	0.938137	0.469069	−	0.883162i	$-0.344590\pi$
$347$	17.4756	0.938137	0.469069	+	0.883162i	$0.344590\pi$
$348$	−29.7789	−1.59631
$349$	27.1255	1.45199	0.725997	−	0.687697i	$-0.241378\pi$
$349$	27.1255	1.45199	0.725997	+	0.687697i	$0.241378\pi$
$350$	2.28917	0.122361
$351$	60.0766	3.20665
$352$	4.72999	0.252109
$353$	−32.3572	−1.72220	−0.861100	−	0.508436i	$-0.830224\pi$
$353$	−32.3572	−1.72220	−0.861100	+	0.508436i	$0.830224\pi$
$354$	28.0766	1.49226
$355$	8.72999	0.463340
$356$	−15.2005	−0.805626
$357$	32.1361	1.70082
$358$	6.70027	0.354120
$359$	25.2247	1.33131	0.665655	−	0.746260i	$-0.268152\pi$
$359$	25.2247	1.33131	0.665655	+	0.746260i	$0.268152\pi$
$360$	6.62721	0.349285
$361$	−3.66196	−0.192735
$362$	14.6222	0.768525
$363$	−35.2872	−1.85210
$364$	12.2197	0.640485
$365$	−12.2736	−0.642429
$366$	−12.3189	−0.643919
$367$	18.5089	0.966154	0.483077	−	0.875578i	$-0.339519\pi$
$367$	18.5089	0.966154	0.483077	+	0.875578i	$0.339519\pi$
$368$	6.52444	0.340110
$369$	−23.4842	−1.22254
$370$	−3.94610	−0.205148
$371$	−29.2645	−1.51934
$372$	−19.9844	−1.03614
$373$	−11.3083	−0.585523	−0.292761	−	0.956186i	$-0.594574\pi$
$373$	−11.3083	−0.585523	−0.292761	+	0.956186i	$0.594574\pi$
$374$	21.4005	1.10660
$375$	3.10278	0.160227
$376$	3.10278	0.160013
$377$	−51.2318	−2.63857
$378$	−25.7633	−1.32512
$379$	15.7250	0.807737	0.403869	−	0.914817i	$-0.367665\pi$
$379$	15.7250	0.807737	0.403869	+	0.914817i	$0.367665\pi$
$380$	3.91638	0.200906
$381$	−3.25443	−0.166729
$382$	−1.36776	−0.0699809
$383$	−3.91638	−0.200118	−0.100059	−	0.994982i	$-0.531903\pi$
$383$	−3.91638	−0.200118	−0.100059	+	0.994982i	$0.531903\pi$
$384$	3.10278	0.158338
$385$	−10.8277	−0.551833
$386$	−16.3728	−0.833353
$387$	6.62721	0.336880
$388$	−3.94610	−0.200333
$389$	21.7733	1.10395	0.551976	−	0.833860i	$-0.313874\pi$
$389$	21.7733	1.10395	0.551976	+	0.833860i	$0.313874\pi$
$390$	16.5628	0.838688
$391$	29.5194	1.49286
$392$	1.75971	0.0888786
$393$	−68.3799	−3.44931
$394$	−12.2892	−0.619119
$395$	−0.235269	−0.0118377
$396$	−31.3466	−1.57523
$397$	3.93051	0.197267	0.0986334	−	0.995124i	$-0.468553\pi$
$397$	3.93051	0.197267	0.0986334	+	0.995124i	$0.468553\pi$
$398$	−6.93554	−0.347647
$399$	−27.8172	−1.39260
$400$	1.00000	0.0500000
$401$	27.6202	1.37929	0.689644	−	0.724149i	$-0.257767\pi$
$401$	27.6202	1.37929	0.689644	+	0.724149i	$0.257767\pi$
$402$	−3.04334	−0.151788
$403$	−34.3814	−1.71266
$404$	−10.7300	−0.533837
$405$	−15.0383	−0.747260
$406$	21.9703	1.09037
$407$	18.6650	0.925190
$408$	14.0383	0.695000
$409$	9.43725	0.466642	0.233321	−	0.972400i	$-0.425041\pi$
$409$	9.43725	0.466642	0.233321	+	0.972400i	$0.425041\pi$
$410$	−3.54359	−0.175006
$411$	0.426686	0.0210469
$412$	−5.62721	−0.277233
$413$	−20.7144	−1.01929
$414$	−43.2388	−2.12507
$415$	−6.78389	−0.333008
$416$	5.33804	0.261719
$417$	−39.4983	−1.93424
$418$	−18.5244	−0.906060
$419$	10.0736	0.492126	0.246063	−	0.969254i	$-0.420863\pi$
$419$	10.0736	0.492126	0.246063	+	0.969254i	$0.420863\pi$
$420$	−7.10278	−0.346580
$421$	−35.6358	−1.73678	−0.868391	−	0.495879i	$-0.834846\pi$
$421$	−35.6358	−1.73678	−0.868391	+	0.495879i	$0.834846\pi$
$422$	−17.1567	−0.835174
$423$	−20.5628	−0.999795
$424$	−12.7839	−0.620840
$425$	4.52444	0.219467
$426$	−27.0872	−1.31238
$427$	9.08864	0.439830
$428$	0.343068	0.0165828
$429$	−78.3416	−3.78237
$430$	1.00000	0.0482243
$431$	37.7038	1.81613	0.908065	−	0.418829i	$-0.137559\pi$
$431$	37.7038	1.81613	0.908065	+	0.418829i	$0.137559\pi$
$432$	−11.2544	−0.541479
$433$	20.5769	0.988862	0.494431	−	0.869217i	$-0.335376\pi$
$433$	20.5769	0.988862	0.494431	+	0.869217i	$0.335376\pi$
$434$	14.7441	0.707740
$435$	29.7789	1.42779
$436$	7.62721	0.365277
$437$	−25.5522	−1.22233
$438$	38.0822	1.81964
$439$	−12.7456	−0.608313	−0.304157	−	0.952622i	$-0.598375\pi$
$439$	−12.7456	−0.608313	−0.304157	+	0.952622i	$0.598375\pi$
$440$	−4.72999	−0.225493
$441$	−11.6620	−0.555331
$442$	24.1517	1.14878
$443$	3.24583	0.154214	0.0771071	−	0.997023i	$-0.475432\pi$
$443$	3.24583	0.154214	0.0771071	+	0.997023i	$0.475432\pi$
$444$	12.2439	0.581068
$445$	15.2005	0.720574
$446$	11.4217	0.540831
$447$	−74.7966	−3.53776
$448$	−2.28917	−0.108153
$449$	24.1305	1.13879	0.569395	−	0.822064i	$-0.307178\pi$
$449$	24.1305	1.13879	0.569395	+	0.822064i	$0.307178\pi$
$450$	−6.62721	−0.312410
$451$	16.7612	0.789252
$452$	5.76473	0.271150
$453$	29.8711	1.40347
$454$	−19.3622	−0.908714
$455$	−12.2197	−0.572868
$456$	−12.1517	−0.569053
$457$	−25.0278	−1.17075	−0.585374	−	0.810763i	$-0.699052\pi$
$457$	−25.0278	−1.17075	−0.585374	+	0.810763i	$0.699052\pi$
$458$	2.30330	0.107626
$459$	−50.9200	−2.37674
$460$	−6.52444	−0.304203
$461$	−40.9355	−1.90656	−0.953279	−	0.302091i	$-0.902315\pi$
$461$	−40.9355	−1.90656	−0.953279	+	0.302091i	$0.902315\pi$
$462$	33.5960	1.56303
$463$	27.2302	1.26550	0.632748	−	0.774357i	$-0.281927\pi$
$463$	27.2302	1.26550	0.632748	+	0.774357i	$0.281927\pi$
$464$	9.59749	0.445552
$465$	19.9844	0.926755
$466$	−8.26499	−0.382868
$467$	−1.00502	−0.0465069	−0.0232535	−	0.999730i	$-0.507402\pi$
$467$	−1.00502	−0.0465069	−0.0232535	+	0.999730i	$0.507402\pi$
$468$	−35.3764	−1.63527
$469$	2.24532	0.103679
$470$	−3.10278	−0.143120
$471$	−5.40054	−0.248844
$472$	−9.04888	−0.416508
$473$	−4.72999	−0.217485
$474$	0.729988	0.0335295
$475$	−3.91638	−0.179696
$476$	−10.3572	−0.474722
$477$	84.7215	3.87913
$478$	−11.4897	−0.525526
$479$	31.9688	1.46069	0.730347	−	0.683077i	$-0.239359\pi$
$479$	31.9688	1.46069	0.730347	+	0.683077i	$0.239359\pi$
$480$	−3.10278	−0.141622
$481$	21.0645	0.960457
$482$	−9.57331	−0.436052
$483$	46.3416	2.10862
$484$	11.3728	0.516945
$485$	3.94610	0.179183
$486$	12.8972	0.585030
$487$	−21.0816	−0.955301	−0.477650	−	0.878550i	$-0.658511\pi$
$487$	−21.0816	−0.955301	−0.477650	+	0.878550i	$0.658511\pi$
$488$	3.97028	0.179726
$489$	43.7422	1.97809
$490$	−1.75971	−0.0794955
$491$	−24.1361	−1.08925	−0.544623	−	0.838681i	$-0.683327\pi$
$491$	−24.1361	−1.08925	−0.544623	+	0.838681i	$0.683327\pi$
$492$	10.9950	0.495692
$493$	43.4233	1.95569
$494$	−20.9058	−0.940597
$495$	31.3466	1.40893
$496$	6.44082	0.289201
$497$	19.9844	0.896423
$498$	21.0489	0.943223
$499$	−1.29973	−0.0581840	−0.0290920	−	0.999577i	$-0.509262\pi$
$499$	−1.29973	−0.0581840	−0.0290920	+	0.999577i	$0.509262\pi$
$500$	−1.00000	−0.0447214
$501$	0.989437	0.0442048
$502$	−26.3416	−1.17568
$503$	−15.1950	−0.677511	−0.338756	−	0.940874i	$-0.610006\pi$
$503$	−15.1950	−0.677511	−0.338756	+	0.940874i	$0.610006\pi$
$504$	15.1708	0.675761
$505$	10.7300	0.477478
$506$	30.8605	1.37192
$507$	−48.0766	−2.13516
$508$	1.04888	0.0465363
$509$	−13.9406	−0.617905	−0.308952	−	0.951078i	$-0.599978\pi$
$509$	−13.9406	−0.617905	−0.308952	+	0.951078i	$0.599978\pi$
$510$	−14.0383	−0.621627
$511$	−28.0963	−1.24291
$512$	−1.00000	−0.0441942
$513$	44.0766	1.94603
$514$	13.4897	0.595005
$515$	5.62721	0.247965
$516$	−3.10278	−0.136592
$517$	14.6761	0.645454
$518$	−9.03329	−0.396900
$519$	10.0539	0.441317
$520$	−5.33804	−0.234089
$521$	−8.30884	−0.364017	−0.182008	−	0.983297i	$-0.558260\pi$
$521$	−8.30884	−0.364017	−0.182008	+	0.983297i	$0.558260\pi$
$522$	−63.6046	−2.78390
$523$	−20.0922	−0.878571	−0.439286	−	0.898347i	$-0.644768\pi$
$523$	−20.0922	−0.878571	−0.439286	+	0.898347i	$0.644768\pi$
$524$	22.0383	0.962748
$525$	7.10278	0.309991
$526$	7.64135	0.333179
$527$	29.1411	1.26941
$528$	14.6761	0.638695
$529$	19.5683	0.850795
$530$	12.7839	0.555297
$531$	59.9688	2.60243
$532$	8.96526	0.388693
$533$	18.9159	0.819337
$534$	−47.1638	−2.04098
$535$	−0.343068	−0.0148321
$536$	0.980843	0.0423660
$537$	20.7894	0.897130
$538$	17.1950	0.741329
$539$	8.32339	0.358514
$540$	11.2544	0.484313
$541$	−18.3033	−0.786920	−0.393460	−	0.919342i	$-0.628722\pi$
$541$	−18.3033	−0.786920	−0.393460	+	0.919342i	$0.628722\pi$
$542$	17.0575	0.732681
$543$	45.3694	1.94699
$544$	−4.52444	−0.193984
$545$	−7.62721	−0.326714
$546$	37.9149	1.62261
$547$	−10.5089	−0.449326	−0.224663	−	0.974437i	$-0.572128\pi$
$547$	−10.5089	−0.449326	−0.224663	+	0.974437i	$0.572128\pi$
$548$	−0.137518	−0.00587446
$549$	−26.3119	−1.12296
$550$	4.72999	0.201687
$551$	−37.5874	−1.60128
$552$	20.2439	0.861636
$553$	−0.538571	−0.0229024
$554$	−16.3728	−0.695613
$555$	−12.2439	−0.519723
$556$	12.7300	0.539872
$557$	21.4147	0.907369	0.453684	−	0.891162i	$-0.350109\pi$
$557$	21.4147	0.907369	0.453684	+	0.891162i	$0.350109\pi$
$558$	−42.6847	−1.80699
$559$	−5.33804	−0.225775
$560$	2.28917	0.0967350
$561$	66.4011	2.80345
$562$	20.0625	0.846285
$563$	1.66698	0.0702548	0.0351274	−	0.999383i	$-0.488816\pi$
$563$	1.66698	0.0702548	0.0351274	+	0.999383i	$0.488816\pi$
$564$	9.62721	0.405379
$565$	−5.76473	−0.242524
$566$	0.343068	0.0144202
$567$	−34.4252	−1.44572
$568$	8.72999	0.366302
$569$	41.0036	1.71896	0.859480	−	0.511170i	$-0.170788\pi$
$569$	41.0036	1.71896	0.859480	+	0.511170i	$0.170788\pi$
$570$	12.1517	0.508977
$571$	44.1008	1.84556	0.922781	−	0.385326i	$-0.125911\pi$
$571$	44.1008	1.84556	0.922781	+	0.385326i	$0.125911\pi$
$572$	25.2489	1.05571
$573$	−4.24386	−0.177290
$574$	−8.11189	−0.338584
$575$	6.52444	0.272088
$576$	6.62721	0.276134
$577$	35.7719	1.48920	0.744601	−	0.667510i	$-0.232640\pi$
$577$	35.7719	1.48920	0.744601	+	0.667510i	$0.232640\pi$
$578$	−3.47054	−0.144355
$579$	−50.8011	−2.11122
$580$	−9.59749	−0.398514
$581$	−15.5295	−0.644271
$582$	−12.2439	−0.507524
$583$	−60.4676	−2.50431
$584$	−12.2736	−0.507884
$585$	35.3764	1.46263
$586$	−14.4111	−0.595317
$587$	−8.78943	−0.362778	−0.181389	−	0.983411i	$-0.558059\pi$
$587$	−8.78943	−0.362778	−0.181389	+	0.983411i	$0.558059\pi$
$588$	5.45998	0.225166
$589$	−25.2247	−1.03937
$590$	9.04888	0.372536
$591$	−38.1305	−1.56848
$592$	−3.94610	−0.162184
$593$	30.2041	1.24033	0.620167	−	0.784470i	$-0.287065\pi$
$593$	30.2041	1.24033	0.620167	+	0.784470i	$0.287065\pi$
$594$	−53.2333	−2.18419
$595$	10.3572	0.424604
$596$	24.1063	0.987434
$597$	−21.5194	−0.880731
$598$	34.8277	1.42421
$599$	34.4011	1.40559	0.702794	−	0.711393i	$-0.251935\pi$
$599$	34.4011	1.40559	0.702794	+	0.711393i	$0.251935\pi$
$600$	3.10278	0.126670
$601$	38.8505	1.58474	0.792372	−	0.610038i	$-0.208846\pi$
$601$	38.8505	1.58474	0.792372	+	0.610038i	$0.208846\pi$
$602$	2.28917	0.0932995
$603$	−6.50026	−0.264711
$604$	−9.62721	−0.391726
$605$	−11.3728	−0.462370
$606$	−33.2927	−1.35243
$607$	−23.1950	−0.941455	−0.470728	−	0.882279i	$-0.656009\pi$
$607$	−23.1950	−0.941455	−0.470728	+	0.882279i	$0.656009\pi$
$608$	3.91638	0.158830
$609$	68.1688	2.76234
$610$	−3.97028	−0.160752
$611$	16.5628	0.670057
$612$	29.9844	1.21205
$613$	−15.4358	−0.623446	−0.311723	−	0.950173i	$-0.600906\pi$
$613$	−15.4358	−0.623446	−0.311723	+	0.950173i	$0.600906\pi$
$614$	−17.6358	−0.711723
$615$	−10.9950	−0.443360
$616$	−10.8277	−0.436262
$617$	−12.5572	−0.505534	−0.252767	−	0.967527i	$-0.581341\pi$
$617$	−12.5572	−0.505534	−0.252767	+	0.967527i	$0.581341\pi$
$618$	−17.4600	−0.702343
$619$	−6.22114	−0.250049	−0.125024	−	0.992154i	$-0.539901\pi$
$619$	−6.22114	−0.250049	−0.125024	+	0.992154i	$0.539901\pi$
$620$	−6.44082	−0.258670
$621$	−73.4288	−2.94660
$622$	9.69525	0.388744
$623$	34.7966	1.39410
$624$	16.5628	0.663041
$625$	1.00000	0.0400000
$626$	−10.4111	−0.416111
$627$	−57.4772	−2.29542
$628$	1.74055	0.0694555
$629$	−17.8539	−0.711881
$630$	−15.1708	−0.604419
$631$	20.4550	0.814299	0.407149	−	0.913362i	$-0.366523\pi$
$631$	20.4550	0.814299	0.407149	+	0.913362i	$0.366523\pi$
$632$	−0.235269	−0.00935851
$633$	−53.2333	−2.11583
$634$	19.3764	0.769533
$635$	−1.04888	−0.0416234
$636$	−39.6655	−1.57284
$637$	9.39340	0.372180
$638$	45.3960	1.79725
$639$	−57.8555	−2.28873
$640$	1.00000	0.0395285
$641$	−8.95112	−0.353548	−0.176774	−	0.984251i	$-0.556566\pi$
$641$	−8.95112	−0.353548	−0.176774	+	0.984251i	$0.556566\pi$
$642$	1.06446	0.0420110
$643$	0.813607	0.0320855	0.0160428	−	0.999871i	$-0.494893\pi$
$643$	0.813607	0.0320855	0.0160428	+	0.999871i	$0.494893\pi$
$644$	−14.9355	−0.588543
$645$	3.10278	0.122172
$646$	17.7194	0.697161
$647$	30.6519	1.20505	0.602525	−	0.798100i	$-0.294161\pi$
$647$	30.6519	1.20505	0.602525	+	0.798100i	$0.294161\pi$
$648$	−15.0383	−0.590761
$649$	−42.8011	−1.68009
$650$	5.33804	0.209375
$651$	45.7477	1.79299
$652$	−14.0978	−0.552111
$653$	−36.2978	−1.42044	−0.710221	−	0.703979i	$-0.751405\pi$
$653$	−36.2978	−1.42044	−0.710221	+	0.703979i	$0.751405\pi$
$654$	23.6655	0.925395
$655$	−22.0383	−0.861108
$656$	−3.54359	−0.138354
$657$	81.3396	3.17336
$658$	−7.10278	−0.276895
$659$	−28.6988	−1.11795	−0.558974	−	0.829185i	$-0.688805\pi$
$659$	−28.6988	−1.11795	−0.558974	+	0.829185i	$0.688805\pi$
$660$	−14.6761	−0.571266
$661$	7.83830	0.304875	0.152437	−	0.988313i	$-0.451288\pi$
$661$	7.83830	0.304875	0.152437	+	0.988313i	$0.451288\pi$
$662$	3.72496	0.144775
$663$	74.9371	2.91032
$664$	−6.78389	−0.263266
$665$	−8.96526	−0.347658
$666$	26.1517	1.01336
$667$	62.6183	2.42459
$668$	−0.318888	−0.0123381
$669$	35.4389	1.37015
$670$	−0.980843	−0.0378933
$671$	18.7794	0.724970
$672$	−7.10278	−0.273995
$673$	18.1758	0.700627	0.350313	−	0.936633i	$-0.386075\pi$
$673$	18.1758	0.700627	0.350313	+	0.936633i	$0.386075\pi$
$674$	−6.74557	−0.259830
$675$	−11.2544	−0.433183
$676$	15.4947	0.595951
$677$	−11.0489	−0.424643	−0.212321	−	0.977200i	$-0.568102\pi$
$677$	−11.0489	−0.424643	−0.212321	+	0.977200i	$0.568102\pi$
$678$	17.8867	0.686933
$679$	9.03329	0.346666
$680$	4.52444	0.173504
$681$	−60.0766	−2.30214
$682$	30.4650	1.16657
$683$	26.8122	1.02594	0.512969	−	0.858407i	$-0.328545\pi$
$683$	26.8122	1.02594	0.512969	+	0.858407i	$0.328545\pi$
$684$	−25.9547	−0.992403
$685$	0.137518	0.00525428
$686$	−20.0524	−0.765606
$687$	7.14663	0.272661
$688$	1.00000	0.0381246
$689$	−68.2410	−2.59977
$690$	−20.2439	−0.770671
$691$	10.4806	0.398700	0.199350	−	0.979928i	$-0.436117\pi$
$691$	10.4806	0.398700	0.199350	+	0.979928i	$0.436117\pi$
$692$	−3.24029	−0.123177
$693$	71.7577	2.72585
$694$	−17.4756	−0.663363
$695$	−12.7300	−0.482876
$696$	29.7789	1.12876
$697$	−16.0328	−0.607285
$698$	−27.1255	−1.02672
$699$	−25.6444	−0.969960
$700$	−2.28917	−0.0865224
$701$	−31.1099	−1.17501	−0.587503	−	0.809222i	$-0.699889\pi$
$701$	−31.1099	−1.17501	−0.587503	+	0.809222i	$0.699889\pi$
$702$	−60.0766	−2.26745
$703$	15.4544	0.582875
$704$	−4.72999	−0.178268
$705$	−9.62721	−0.362582
$706$	32.3572	1.21778
$707$	24.5628	0.923777
$708$	−28.0766	−1.05518
$709$	11.9461	0.448645	0.224323	−	0.974515i	$-0.427983\pi$
$709$	11.9461	0.448645	0.224323	+	0.974515i	$0.427983\pi$
$710$	−8.72999	−0.327631
$711$	1.55918	0.0584738
$712$	15.2005	0.569664
$713$	42.0227	1.57376
$714$	−32.1361	−1.20266
$715$	−25.2489	−0.944255
$716$	−6.70027	−0.250401
$717$	−35.6499	−1.33137
$718$	−25.2247	−0.941378
$719$	−23.3139	−0.869460	−0.434730	−	0.900561i	$-0.643156\pi$
$719$	−23.3139	−0.869460	−0.434730	+	0.900561i	$0.643156\pi$
$720$	−6.62721	−0.246982
$721$	12.8816	0.479737
$722$	3.66196	0.136284
$723$	−29.7038	−1.10470
$724$	−14.6222	−0.543429
$725$	9.59749	0.356442
$726$	35.2872	1.30963
$727$	9.96169	0.369459	0.184729	−	0.982789i	$-0.440859\pi$
$727$	9.96169	0.369459	0.184729	+	0.982789i	$0.440859\pi$
$728$	−12.2197	−0.452892
$729$	−5.09775	−0.188806
$730$	12.2736	0.454266
$731$	4.52444	0.167342
$732$	12.3189	0.455319
$733$	−11.4756	−0.423860	−0.211930	−	0.977285i	$-0.567975\pi$
$733$	−11.4756	−0.423860	−0.211930	+	0.977285i	$0.567975\pi$
$734$	−18.5089	−0.683174
$735$	−5.45998	−0.201394
$736$	−6.52444	−0.240494
$737$	4.63938	0.170894
$738$	23.4842	0.864464
$739$	21.3764	0.786342	0.393171	−	0.919465i	$-0.371378\pi$
$739$	21.3764	0.786342	0.393171	+	0.919465i	$0.371378\pi$
$740$	3.94610	0.145062
$741$	−64.8661	−2.38291
$742$	29.2645	1.07433
$743$	−21.7108	−0.796493	−0.398247	−	0.917278i	$-0.630381\pi$
$743$	−21.7108	−0.796493	−0.398247	+	0.917278i	$0.630381\pi$
$744$	19.9844	0.732664
$745$	−24.1063	−0.883188
$746$	11.3083	0.414027
$747$	44.9583	1.64494
$748$	−21.4005	−0.782481
$749$	−0.785340	−0.0286957
$750$	−3.10278	−0.113297
$751$	−2.66050	−0.0970831	−0.0485416	−	0.998821i	$-0.515457\pi$
$751$	−2.66050	−0.0970831	−0.0485416	+	0.998821i	$0.515457\pi$
$752$	−3.10278	−0.113147
$753$	−81.7321	−2.97848
$754$	51.2318	1.86575
$755$	9.62721	0.350370
$756$	25.7633	0.937001
$757$	35.3411	1.28449	0.642247	−	0.766498i	$-0.278002\pi$
$757$	35.3411	1.28449	0.642247	+	0.766498i	$0.278002\pi$
$758$	−15.7250	−0.571156
$759$	95.7532	3.47562
$760$	−3.91638	−0.142062
$761$	43.3411	1.57111	0.785557	−	0.618790i	$-0.212377\pi$
$761$	43.3411	1.57111	0.785557	+	0.618790i	$0.212377\pi$
$762$	3.25443	0.117895
$763$	−17.4600	−0.632094
$764$	1.36776	0.0494840
$765$	−29.9844	−1.08409
$766$	3.91638	0.141505
$767$	−48.3033	−1.74413
$768$	−3.10278	−0.111962
$769$	24.6519	0.888971	0.444485	−	0.895786i	$-0.353387\pi$
$769$	24.6519	0.888971	0.444485	+	0.895786i	$0.353387\pi$
$770$	10.8277	0.390205
$771$	41.8555	1.50739
$772$	16.3728	0.589269
$773$	15.3083	0.550602	0.275301	−	0.961358i	$-0.411222\pi$
$773$	15.3083	0.550602	0.275301	+	0.961358i	$0.411222\pi$
$774$	−6.62721	−0.238210
$775$	6.44082	0.231361
$776$	3.94610	0.141657
$777$	−28.0283	−1.00551
$778$	−21.7733	−0.780612
$779$	13.8781	0.497233
$780$	−16.5628	−0.593042
$781$	41.2927	1.47757
$782$	−29.5194	−1.05561
$783$	−108.014	−3.86012
$784$	−1.75971	−0.0628467
$785$	−1.74055	−0.0621229
$786$	68.3799	2.43903
$787$	13.4403	0.479095	0.239548	−	0.970885i	$-0.423001\pi$
$787$	13.4403	0.479095	0.239548	+	0.970885i	$0.423001\pi$
$788$	12.2892	0.437784
$789$	23.7094	0.844076
$790$	0.235269	0.00837051
$791$	−13.1964	−0.469211
$792$	31.3466	1.11385
$793$	21.1935	0.752604
$794$	−3.93051	−0.139489
$795$	39.6655	1.40679
$796$	6.93554	0.245824
$797$	−43.6797	−1.54721	−0.773606	−	0.633666i	$-0.781549\pi$
$797$	−43.6797	−1.54721	−0.773606	+	0.633666i	$0.781549\pi$
$798$	27.8172	0.984717
$799$	−14.0383	−0.496640
$800$	−1.00000	−0.0353553
$801$	−100.737	−3.55937
$802$	−27.6202	−0.975304
$803$	−58.0539	−2.04868
$804$	3.04334	0.107330
$805$	14.9355	0.526409
$806$	34.3814	1.21103
$807$	53.3522	1.87809
$808$	10.7300	0.377480
$809$	−28.5019	−1.00207	−0.501036	−	0.865426i	$-0.667048\pi$
$809$	−28.5019	−1.00207	−0.501036	+	0.865426i	$0.667048\pi$
$810$	15.0383	0.528392
$811$	−11.5819	−0.406696	−0.203348	−	0.979107i	$-0.565182\pi$
$811$	−11.5819	−0.406696	−0.203348	+	0.979107i	$0.565182\pi$
$812$	−21.9703	−0.771006
$813$	52.9255	1.85618
$814$	−18.6650	−0.654208
$815$	14.0978	0.493823
$816$	−14.0383	−0.491439
$817$	−3.91638	−0.137017
$818$	−9.43725	−0.329966
$819$	80.9824	2.82976
$820$	3.54359	0.123748
$821$	−6.22668	−0.217312	−0.108656	−	0.994079i	$-0.534655\pi$
$821$	−6.22668	−0.217312	−0.108656	+	0.994079i	$0.534655\pi$
$822$	−0.426686	−0.0148824
$823$	50.5260	1.76123	0.880614	−	0.473835i	$-0.157131\pi$
$823$	50.5260	1.76123	0.880614	+	0.473835i	$0.157131\pi$
$824$	5.62721	0.196033
$825$	14.6761	0.510956
$826$	20.7144	0.720746
$827$	−16.1447	−0.561405	−0.280702	−	0.959795i	$-0.590567\pi$
$827$	−16.1447	−0.561405	−0.280702	+	0.959795i	$0.590567\pi$
$828$	43.2388	1.50265
$829$	−52.4096	−1.82026	−0.910131	−	0.414320i	$-0.864019\pi$
$829$	−52.4096	−1.82026	−0.910131	+	0.414320i	$0.864019\pi$
$830$	6.78389	0.235472
$831$	−50.8011	−1.76227
$832$	−5.33804	−0.185063
$833$	−7.96169	−0.275856
$834$	39.4983	1.36771
$835$	0.318888	0.0110356
$836$	18.5244	0.640681
$837$	−72.4877	−2.50554
$838$	−10.0736	−0.347986
$839$	12.6222	0.435766	0.217883	−	0.975975i	$-0.430085\pi$
$839$	12.6222	0.435766	0.217883	+	0.975975i	$0.430085\pi$
$840$	7.10278	0.245069
$841$	63.1119	2.17627
$842$	35.6358	1.22809
$843$	62.2494	2.14398
$844$	17.1567	0.590557
$845$	−15.4947	−0.533035
$846$	20.5628	0.706962
$847$	−26.0342	−0.894547
$848$	12.7839	0.439000
$849$	1.06446	0.0365322
$850$	−4.52444	−0.155187
$851$	−25.7461	−0.882565
$852$	27.0872	0.927992
$853$	−47.1567	−1.61461	−0.807307	−	0.590132i	$-0.799076\pi$
$853$	−47.1567	−1.61461	−0.807307	+	0.590132i	$0.799076\pi$
$854$	−9.08864	−0.311007
$855$	25.9547	0.887632
$856$	−0.343068	−0.0117258
$857$	−30.3955	−1.03829	−0.519145	−	0.854686i	$-0.673750\pi$
$857$	−30.3955	−1.03829	−0.519145	+	0.854686i	$0.673750\pi$
$858$	78.3416	2.67454
$859$	8.16024	0.278424	0.139212	−	0.990263i	$-0.455543\pi$
$859$	8.16024	0.278424	0.139212	+	0.990263i	$0.455543\pi$
$860$	−1.00000	−0.0340997
$861$	−25.1694	−0.857769
$862$	−37.7038	−1.28420
$863$	7.49829	0.255245	0.127622	−	0.991823i	$-0.459265\pi$
$863$	7.49829	0.255245	0.127622	+	0.991823i	$0.459265\pi$
$864$	11.2544	0.382883
$865$	3.24029	0.110173
$866$	−20.5769	−0.699231
$867$	−10.7683	−0.365711
$868$	−14.7441	−0.500448
$869$	−1.11282	−0.0377499
$870$	−29.7789	−1.00960
$871$	5.23579	0.177408
$872$	−7.62721	−0.258290
$873$	−26.1517	−0.885099
$874$	25.5522	0.864316
$875$	2.28917	0.0773880
$876$	−38.0822	−1.28668
$877$	11.4116	0.385343	0.192671	−	0.981263i	$-0.438285\pi$
$877$	11.4116	0.385343	0.192671	+	0.981263i	$0.438285\pi$
$878$	12.7456	0.430142
$879$	−44.7144	−1.50818
$880$	4.72999	0.159448
$881$	−45.4741	−1.53206	−0.766031	−	0.642804i	$-0.777771\pi$
$881$	−45.4741	−1.53206	−0.766031	+	0.642804i	$0.777771\pi$
$882$	11.6620	0.392678
$883$	−45.8313	−1.54235	−0.771173	−	0.636625i	$-0.780330\pi$
$883$	−45.8313	−1.54235	−0.771173	+	0.636625i	$0.780330\pi$
$884$	−24.1517	−0.812308
$885$	28.0766	0.943785
$886$	−3.24583	−0.109046
$887$	−56.5119	−1.89748	−0.948742	−	0.316051i	$-0.897643\pi$
$887$	−56.5119	−1.89748	−0.948742	+	0.316051i	$0.897643\pi$
$888$	−12.2439	−0.410877
$889$	−2.40105	−0.0805288
$890$	−15.2005	−0.509523
$891$	−71.1310	−2.38298
$892$	−11.4217	−0.382426
$893$	12.1517	0.406639
$894$	74.7966	2.50157
$895$	6.70027	0.223965
$896$	2.28917	0.0764758
$897$	108.063	3.60811
$898$	−24.1305	−0.805246
$899$	61.8157	2.06167
$900$	6.62721	0.220907
$901$	57.8399	1.92693
$902$	−16.7612	−0.558086
$903$	7.10278	0.236366
$904$	−5.76473	−0.191732
$905$	14.6222	0.486058
$906$	−29.8711	−0.992400
$907$	2.01864	0.0670279	0.0335139	−	0.999438i	$-0.489330\pi$
$907$	2.01864	0.0670279	0.0335139	+	0.999438i	$0.489330\pi$
$908$	19.3622	0.642558
$909$	−71.1099	−2.35857
$910$	12.2197	0.405079
$911$	−28.9255	−0.958344	−0.479172	−	0.877721i	$-0.659063\pi$
$911$	−28.9255	−0.958344	−0.479172	+	0.877721i	$0.659063\pi$
$912$	12.1517	0.402381
$913$	−32.0877	−1.06195
$914$	25.0278	0.827844
$915$	−12.3189	−0.407250
$916$	−2.30330	−0.0761032
$917$	−50.4494	−1.66599
$918$	50.9200	1.68061
$919$	−25.3608	−0.836575	−0.418287	−	0.908315i	$-0.637369\pi$
$919$	−25.3608	−0.836575	−0.418287	+	0.908315i	$0.637369\pi$
$920$	6.52444	0.215104
$921$	−54.7199	−1.80308
$922$	40.9355	1.34814
$923$	46.6011	1.53389
$924$	−33.5960	−1.10523
$925$	−3.94610	−0.129747
$926$	−27.2302	−0.894841
$927$	−37.2927	−1.22485
$928$	−9.59749	−0.315053
$929$	4.61665	0.151467	0.0757337	−	0.997128i	$-0.475870\pi$
$929$	4.61665	0.151467	0.0757337	+	0.997128i	$0.475870\pi$
$930$	−19.9844	−0.655315
$931$	6.89169	0.225866
$932$	8.26499	0.270729
$933$	30.0822	0.984846
$934$	1.00502	0.0328854
$935$	21.4005	0.699872
$936$	35.3764	1.15631
$937$	−51.9305	−1.69650	−0.848248	−	0.529599i	$-0.822342\pi$
$937$	−51.9305	−1.69650	−0.848248	+	0.529599i	$0.822342\pi$
$938$	−2.24532	−0.0733122
$939$	−32.3033	−1.05418
$940$	3.10278	0.101201
$941$	−9.31837	−0.303770	−0.151885	−	0.988398i	$-0.548534\pi$
$941$	−9.31837	−0.303770	−0.151885	+	0.988398i	$0.548534\pi$
$942$	5.40054	0.175959
$943$	−23.1200	−0.752890
$944$	9.04888	0.294516
$945$	−25.7633	−0.838079
$946$	4.72999	0.153785
$947$	−45.7436	−1.48647	−0.743234	−	0.669032i	$-0.766709\pi$
$947$	−45.7436	−1.48647	−0.743234	+	0.669032i	$0.766709\pi$
$948$	−0.729988	−0.0237089
$949$	−65.5169	−2.12677
$950$	3.91638	0.127064
$951$	60.1205	1.94954
$952$	10.3572	0.335679
$953$	−21.5381	−0.697686	−0.348843	−	0.937181i	$-0.613425\pi$
$953$	−21.5381	−0.697686	−0.348843	+	0.937181i	$0.613425\pi$
$954$	−84.7215	−2.74296
$955$	−1.36776	−0.0442598
$956$	11.4897	0.371603
$957$	140.854	4.55315
$958$	−31.9688	−1.03287
$959$	0.314801	0.0101655
$960$	3.10278	0.100142
$961$	10.4842	0.338199
$962$	−21.0645	−0.679146
$963$	2.27358	0.0732652
$964$	9.57331	0.308336
$965$	−16.3728	−0.527059
$966$	−46.3416	−1.49102
$967$	−53.3850	−1.71674	−0.858372	−	0.513028i	$-0.828524\pi$
$967$	−53.3850	−1.71674	−0.858372	+	0.513028i	$0.828524\pi$
$968$	−11.3728	−0.365535
$969$	54.9794	1.76619
$970$	−3.94610	−0.126702
$971$	37.5522	1.20511	0.602554	−	0.798078i	$-0.294150\pi$
$971$	37.5522	1.20511	0.602554	+	0.798078i	$0.294150\pi$
$972$	−12.8972	−0.413679
$973$	−29.1411	−0.934220
$974$	21.0816	0.675500
$975$	16.5628	0.530433
$976$	−3.97028	−0.127086
$977$	44.3260	1.41812	0.709058	−	0.705151i	$-0.249121\pi$
$977$	44.3260	1.41812	0.709058	+	0.705151i	$0.249121\pi$
$978$	−43.7422	−1.39872
$979$	71.8983	2.29788
$980$	1.75971	0.0562118
$981$	50.5472	1.61385
$982$	24.1361	0.770213
$983$	10.0736	0.321297	0.160649	−	0.987012i	$-0.448641\pi$
$983$	10.0736	0.321297	0.160649	+	0.987012i	$0.448641\pi$
$984$	−10.9950	−0.350507
$985$	−12.2892	−0.391565
$986$	−43.4233	−1.38288
$987$	−22.0383	−0.701487
$988$	20.9058	0.665103
$989$	6.52444	0.207465
$990$	−31.3466	−0.996262
$991$	−42.7044	−1.35655	−0.678274	−	0.734809i	$-0.737272\pi$
$991$	−42.7044	−1.35655	−0.678274	+	0.734809i	$0.737272\pi$
$992$	−6.44082	−0.204496
$993$	11.5577	0.366773
$994$	−19.9844	−0.633867
$995$	−6.93554	−0.219871
$996$	−21.0489	−0.666959
$997$	1.64834	0.0522034	0.0261017	−	0.999659i	$-0.491691\pi$
$997$	1.64834	0.0522034	0.0261017	+	0.999659i	$0.491691\pi$
$998$	1.29973	0.0411423
$999$	44.4111	1.40511

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	430.2.a.h.1.1	✓	3
3.2	odd	2		3870.2.a.bn.1.2		3
4.3	odd	2		3440.2.a.n.1.3		3
5.2	odd	4		2150.2.b.t.1549.3		6
5.3	odd	4		2150.2.b.t.1549.4		6
5.4	even	2		2150.2.a.bf.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
430.2.a.h.1.1	✓	3	1.1	even	1	trivial
2150.2.a.bf.1.3		3	5.4	even	2
2150.2.b.t.1549.3		6	5.2	odd	4
2150.2.b.t.1549.4		6	5.3	odd	4
3440.2.a.n.1.3		3	4.3	odd	2
3870.2.a.bn.1.2		3	3.2	odd	2

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:	\( N \)	\(=\)	\( 430 = 2 \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	430.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.10278 q^{6} -2.28917 q^{7} -1.00000 q^{8} +6.62721 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.10278 q^{3} +1.00000 q^{4} -1.00000 q^{5} +3.10278 q^{6} -2.28917 q^{7} -1.00000 q^{8} +6.62721 q^{9} +1.00000 q^{10} -4.72999 q^{11} -3.10278 q^{12} -5.33804 q^{13} +2.28917 q^{14} +3.10278 q^{15} +1.00000 q^{16} +4.52444 q^{17} -6.62721 q^{18} -3.91638 q^{19} -1.00000 q^{20} +7.10278 q^{21} +4.72999 q^{22} +6.52444 q^{23} +3.10278 q^{24} +1.00000 q^{25} +5.33804 q^{26} -11.2544 q^{27} -2.28917 q^{28} +9.59749 q^{29} -3.10278 q^{30} +6.44082 q^{31} -1.00000 q^{32} +14.6761 q^{33} -4.52444 q^{34} +2.28917 q^{35} +6.62721 q^{36} -3.94610 q^{37} +3.91638 q^{38} +16.5628 q^{39} +1.00000 q^{40} -3.54359 q^{41} -7.10278 q^{42} +1.00000 q^{43} -4.72999 q^{44} -6.62721 q^{45} -6.52444 q^{46} -3.10278 q^{47} -3.10278 q^{48} -1.75971 q^{49} -1.00000 q^{50} -14.0383 q^{51} -5.33804 q^{52} +12.7839 q^{53} +11.2544 q^{54} +4.72999 q^{55} +2.28917 q^{56} +12.1517 q^{57} -9.59749 q^{58} +9.04888 q^{59} +3.10278 q^{60} -3.97028 q^{61} -6.44082 q^{62} -15.1708 q^{63} +1.00000 q^{64} +5.33804 q^{65} -14.6761 q^{66} -0.980843 q^{67} +4.52444 q^{68} -20.2439 q^{69} -2.28917 q^{70} -8.72999 q^{71} -6.62721 q^{72} +12.2736 q^{73} +3.94610 q^{74} -3.10278 q^{75} -3.91638 q^{76} +10.8277 q^{77} -16.5628 q^{78} +0.235269 q^{79} -1.00000 q^{80} +15.0383 q^{81} +3.54359 q^{82} +6.78389 q^{83} +7.10278 q^{84} -4.52444 q^{85} -1.00000 q^{86} -29.7789 q^{87} +4.72999 q^{88} -15.2005 q^{89} +6.62721 q^{90} +12.2197 q^{91} +6.52444 q^{92} -19.9844 q^{93} +3.10278 q^{94} +3.91638 q^{95} +3.10278 q^{96} -3.94610 q^{97} +1.75971 q^{98} -31.3466 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9}+O(q^{10}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9	\( 3 q - 3 q^{2} - 2 q^{3} + 3 q^{4} - 3 q^{5} + 2 q^{6} - 6 q^{7} - 3 q^{8} + 7 q^{9} + 3 q^{10} + 6 q^{11} - 2 q^{12} - 4 q^{13} + 6 q^{14} + 2 q^{15} + 3 q^{16} + 8 q^{17} - 7 q^{18} + 2 q^{19} - 3 q^{20} + 14 q^{21} - 6 q^{22} + 14 q^{23} + 2 q^{24} + 3 q^{25} + 4 q^{26} - 8 q^{27} - 6 q^{28} + 6 q^{29} - 2 q^{30} - 3 q^{32} + 20 q^{33} - 8 q^{34} + 6 q^{35} + 7 q^{36} - 8 q^{37} - 2 q^{38} + 2 q^{39} + 3 q^{40} + 16 q^{41} - 14 q^{42} + 3 q^{43} + 6 q^{44} - 7 q^{45} - 14 q^{46} - 2 q^{47} - 2 q^{48} + 5 q^{49} - 3 q^{50} - 4 q^{52} + 22 q^{53} + 8 q^{54} - 6 q^{55} + 6 q^{56} + 18 q^{57} - 6 q^{58} + 16 q^{59} + 2 q^{60} - 2 q^{61} - 6 q^{63} + 3 q^{64} + 4 q^{65} - 20 q^{66} - 24 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{70} - 6 q^{71} - 7 q^{72} - 10 q^{73} + 8 q^{74} - 2 q^{75} + 2 q^{76} - 10 q^{77} - 2 q^{78} - 4 q^{79} - 3 q^{80} + 3 q^{81} - 16 q^{82} + 4 q^{83} + 14 q^{84} - 8 q^{85} - 3 q^{86} - 58 q^{87} - 6 q^{88} - 16 q^{89} + 7 q^{90} - 14 q^{91} + 14 q^{92} - 14 q^{93} + 2 q^{94} - 2 q^{95} + 2 q^{96} - 8 q^{97} - 5 q^{98} - 30 q^{99}+O(q^{100}) \) 3 * q - 3 * q^2 - 2 * q^3 + 3 * q^4 - 3 * q^5 + 2 * q^6 - 6 * q^7 - 3 * q^8 + 7 * q^9 + 3 * q^10 + 6 * q^11 - 2 * q^12 - 4 * q^13 + 6 * q^14 + 2 * q^15 + 3 * q^16 + 8 * q^17 - 7 * q^18 + 2 * q^19 - 3 * q^20 + 14 * q^21 - 6 * q^22 + 14 * q^23 + 2 * q^24 + 3 * q^25 + 4 * q^26 - 8 * q^27 - 6 * q^28 + 6 * q^29 - 2 * q^30 - 3 * q^32 + 20 * q^33 - 8 * q^34 + 6 * q^35 + 7 * q^36 - 8 * q^37 - 2 * q^38 + 2 * q^39 + 3 * q^40 + 16 * q^41 - 14 * q^42 + 3 * q^43 + 6 * q^44 - 7 * q^45 - 14 * q^46 - 2 * q^47 - 2 * q^48 + 5 * q^49 - 3 * q^50 - 4 * q^52 + 22 * q^53 + 8 * q^54 - 6 * q^55 + 6 * q^56 + 18 * q^57 - 6 * q^58 + 16 * q^59 + 2 * q^60 - 2 * q^61 - 6 * q^63 + 3 * q^64 + 4 * q^65 - 20 * q^66 - 24 * q^67 + 8 * q^68 - 4 * q^69 - 6 * q^70 - 6 * q^71 - 7 * q^72 - 10 * q^73 + 8 * q^74 - 2 * q^75 + 2 * q^76 - 10 * q^77 - 2 * q^78 - 4 * q^79 - 3 * q^80 + 3 * q^81 - 16 * q^82 + 4 * q^83 + 14 * q^84 - 8 * q^85 - 3 * q^86 - 58 * q^87 - 6 * q^88 - 16 * q^89 + 7 * q^90 - 14 * q^91 + 14 * q^92 - 14 * q^93 + 2 * q^94 - 2 * q^95 + 2 * q^96 - 8 * q^97 - 5 * q^98 - 30 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more