LMFDB - Embedded newform 6026.2.a.f.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 5 x^{19} - 17 x^{18} + 115 x^{17} + 78 x^{16} - 1083 x^{15} + 248 x^{14} + 5359 x^{13} + \cdots - 18 $ x^20 - 5x^19 - 17x^18 + 115x^17 + 78x^16 - 1083x^15 + 248x^14 + 5359x^13 - 3723x^12 - 14776x^11 + 14837x^10 + 21886x^9 - 28084x^8 - 14682x^7 + 25315x^6 + 2042x^5 - 9137x^4 + 576x^3 + 1159x^2 - 78*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Root			$-2.44709$ of defining polynomial
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.44709 q^{3} +1.00000 q^{4} -0.0770010 q^{5} +2.44709 q^{6} -0.359767 q^{7} +1.00000 q^{8} +2.98826 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.44709 q^{3} +1.00000 q^{4} -0.0770010 q^{5} +2.44709 q^{6} -0.359767 q^{7} +1.00000 q^{8} +2.98826 q^{9} -0.0770010 q^{10} -3.66611 q^{11} +2.44709 q^{12} -6.69821 q^{13} -0.359767 q^{14} -0.188428 q^{15} +1.00000 q^{16} -5.64189 q^{17} +2.98826 q^{18} -1.41138 q^{19} -0.0770010 q^{20} -0.880384 q^{21} -3.66611 q^{22} +1.00000 q^{23} +2.44709 q^{24} -4.99407 q^{25} -6.69821 q^{26} -0.0287380 q^{27} -0.359767 q^{28} -1.62449 q^{29} -0.188428 q^{30} +1.09078 q^{31} +1.00000 q^{32} -8.97130 q^{33} -5.64189 q^{34} +0.0277024 q^{35} +2.98826 q^{36} +4.97797 q^{37} -1.41138 q^{38} -16.3911 q^{39} -0.0770010 q^{40} +3.81225 q^{41} -0.880384 q^{42} +0.152554 q^{43} -3.66611 q^{44} -0.230099 q^{45} +1.00000 q^{46} +4.46930 q^{47} +2.44709 q^{48} -6.87057 q^{49} -4.99407 q^{50} -13.8062 q^{51} -6.69821 q^{52} -4.22938 q^{53} -0.0287380 q^{54} +0.282294 q^{55} -0.359767 q^{56} -3.45377 q^{57} -1.62449 q^{58} -9.97915 q^{59} -0.188428 q^{60} +0.235526 q^{61} +1.09078 q^{62} -1.07508 q^{63} +1.00000 q^{64} +0.515769 q^{65} -8.97130 q^{66} +11.9904 q^{67} -5.64189 q^{68} +2.44709 q^{69} +0.0277024 q^{70} -4.13915 q^{71} +2.98826 q^{72} +4.60000 q^{73} +4.97797 q^{74} -12.2209 q^{75} -1.41138 q^{76} +1.31895 q^{77} -16.3911 q^{78} -4.91366 q^{79} -0.0770010 q^{80} -9.03509 q^{81} +3.81225 q^{82} +10.6940 q^{83} -0.880384 q^{84} +0.434431 q^{85} +0.152554 q^{86} -3.97528 q^{87} -3.66611 q^{88} +9.61342 q^{89} -0.230099 q^{90} +2.40980 q^{91} +1.00000 q^{92} +2.66925 q^{93} +4.46930 q^{94} +0.108678 q^{95} +2.44709 q^{96} +1.04618 q^{97} -6.87057 q^{98} -10.9553 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) $ 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.44709	1.41283	0.706414	−	0.707798i	$-0.250312\pi$
$3$	2.44709	1.41283	0.706414	+	0.707798i	$0.250312\pi$
$4$	1.00000	0.500000
$5$	−0.0770010	−0.0344359	−0.0172179	−	0.999852i	$-0.505481\pi$
$5$	−0.0770010	−0.0344359	−0.0172179	+	0.999852i	$0.505481\pi$
$6$	2.44709	0.999021
$7$	−0.359767	−0.135979	−0.0679896	−	0.997686i	$-0.521658\pi$
$7$	−0.359767	−0.135979	−0.0679896	+	0.997686i	$0.521658\pi$
$8$	1.00000	0.353553
$9$	2.98826	0.996085
$10$	−0.0770010	−0.0243498
$11$	−3.66611	−1.10537	−0.552687	−	0.833389i	$-0.686397\pi$
$11$	−3.66611	−1.10537	−0.552687	+	0.833389i	$0.686397\pi$
$12$	2.44709	0.706414
$13$	−6.69821	−1.85775	−0.928874	−	0.370395i	$-0.879222\pi$
$13$	−6.69821	−1.85775	−0.928874	+	0.370395i	$0.879222\pi$
$14$	−0.359767	−0.0961519
$15$	−0.188428	−0.0486520
$16$	1.00000	0.250000
$17$	−5.64189	−1.36836	−0.684180	−	0.729313i	$-0.739840\pi$
$17$	−5.64189	−1.36836	−0.684180	+	0.729313i	$0.739840\pi$
$18$	2.98826	0.704339
$19$	−1.41138	−0.323792	−0.161896	−	0.986808i	$-0.551761\pi$
$19$	−1.41138	−0.323792	−0.161896	+	0.986808i	$0.551761\pi$
$20$	−0.0770010	−0.0172179
$21$	−0.880384	−0.192115
$22$	−3.66611	−0.781617
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	2.44709	0.499510
$25$	−4.99407	−0.998814
$26$	−6.69821	−1.31363
$27$	−0.0287380	−0.00553062
$28$	−0.359767	−0.0679896
$29$	−1.62449	−0.301660	−0.150830	−	0.988560i	$-0.548195\pi$
$29$	−1.62449	−0.301660	−0.150830	+	0.988560i	$0.548195\pi$
$30$	−0.188428	−0.0344022
$31$	1.09078	0.195911	0.0979554	−	0.995191i	$-0.468770\pi$
$31$	1.09078	0.195911	0.0979554	+	0.995191i	$0.468770\pi$
$32$	1.00000	0.176777
$33$	−8.97130	−1.56170
$34$	−5.64189	−0.967577
$35$	0.0277024	0.00468257
$36$	2.98826	0.498043
$37$	4.97797	0.818373	0.409187	−	0.912451i	$-0.365813\pi$
$37$	4.97797	0.818373	0.409187	+	0.912451i	$0.365813\pi$
$38$	−1.41138	−0.228956
$39$	−16.3911	−2.62468
$40$	−0.0770010	−0.0121749
$41$	3.81225	0.595374	0.297687	−	0.954664i	$-0.403785\pi$
$41$	3.81225	0.595374	0.297687	+	0.954664i	$0.403785\pi$
$42$	−0.880384	−0.135846
$43$	0.152554	0.0232642	0.0116321	−	0.999932i	$-0.496297\pi$
$43$	0.152554	0.0232642	0.0116321	+	0.999932i	$0.496297\pi$
$44$	−3.66611	−0.552687
$45$	−0.230099	−0.0343011
$46$	1.00000	0.147442
$47$	4.46930	0.651915	0.325957	−	0.945384i	$-0.394313\pi$
$47$	4.46930	0.651915	0.325957	+	0.945384i	$0.394313\pi$
$48$	2.44709	0.353207
$49$	−6.87057	−0.981510
$50$	−4.99407	−0.706268
$51$	−13.8062	−1.93326
$52$	−6.69821	−0.928874
$53$	−4.22938	−0.580949	−0.290475	−	0.956883i	$-0.593813\pi$
$53$	−4.22938	−0.580949	−0.290475	+	0.956883i	$0.593813\pi$
$54$	−0.0287380	−0.00391074
$55$	0.282294	0.0380645
$56$	−0.359767	−0.0480759
$57$	−3.45377	−0.457463
$58$	−1.62449	−0.213306
$59$	−9.97915	−1.29918	−0.649588	−	0.760287i	$-0.725058\pi$
$59$	−9.97915	−1.29918	−0.649588	+	0.760287i	$0.725058\pi$
$60$	−0.188428	−0.0243260
$61$	0.235526	0.0301561	0.0150780	−	0.999886i	$-0.495200\pi$
$61$	0.235526	0.0301561	0.0150780	+	0.999886i	$0.495200\pi$
$62$	1.09078	0.138530
$63$	−1.07508	−0.135447
$64$	1.00000	0.125000
$65$	0.515769	0.0639732
$66$	−8.97130	−1.10429
$67$	11.9904	1.46486	0.732432	−	0.680840i	$-0.238385\pi$
$67$	11.9904	1.46486	0.732432	+	0.680840i	$0.238385\pi$
$68$	−5.64189	−0.684180
$69$	2.44709	0.294595
$70$	0.0277024	0.00331108
$71$	−4.13915	−0.491226	−0.245613	−	0.969368i	$-0.578989\pi$
$71$	−4.13915	−0.491226	−0.245613	+	0.969368i	$0.578989\pi$
$72$	2.98826	0.352169
$73$	4.60000	0.538389	0.269194	−	0.963086i	$-0.413243\pi$
$73$	4.60000	0.538389	0.269194	+	0.963086i	$0.413243\pi$
$74$	4.97797	0.578677
$75$	−12.2209	−1.41115
$76$	−1.41138	−0.161896
$77$	1.31895	0.150308
$78$	−16.3911	−1.85593
$79$	−4.91366	−0.552830	−0.276415	−	0.961038i	$-0.589146\pi$
$79$	−4.91366	−0.552830	−0.276415	+	0.961038i	$0.589146\pi$
$80$	−0.0770010	−0.00860897
$81$	−9.03509	−1.00390
$82$	3.81225	0.420993
$83$	10.6940	1.17382	0.586910	−	0.809652i	$-0.300344\pi$
$83$	10.6940	1.17382	0.586910	+	0.809652i	$0.300344\pi$
$84$	−0.880384	−0.0960577
$85$	0.434431	0.0471207
$86$	0.152554	0.0164503
$87$	−3.97528	−0.426195
$88$	−3.66611	−0.390808
$89$	9.61342	1.01902	0.509510	−	0.860465i	$-0.329827\pi$
$89$	9.61342	1.01902	0.509510	+	0.860465i	$0.329827\pi$
$90$	−0.230099	−0.0242545
$91$	2.40980	0.252615
$92$	1.00000	0.104257
$93$	2.66925	0.276788
$94$	4.46930	0.460973
$95$	0.108678	0.0111501
$96$	2.44709	0.249755
$97$	1.04618	0.106223	0.0531116	−	0.998589i	$-0.483086\pi$
$97$	1.04618	0.106223	0.0531116	+	0.998589i	$0.483086\pi$
$98$	−6.87057	−0.694032
$99$	−10.9553	−1.10105
$100$	−4.99407	−0.499407
$101$	−3.48203	−0.346475	−0.173238	−	0.984880i	$-0.555423\pi$
$101$	−3.48203	−0.346475	−0.173238	+	0.984880i	$0.555423\pi$
$102$	−13.8062	−1.36702
$103$	−15.8847	−1.56517	−0.782583	−	0.622546i	$-0.786098\pi$
$103$	−15.8847	−1.56517	−0.782583	+	0.622546i	$0.786098\pi$
$104$	−6.69821	−0.656813
$105$	0.0677904	0.00661567
$106$	−4.22938	−0.410793
$107$	−7.75879	−0.750071	−0.375035	−	0.927011i	$-0.622369\pi$
$107$	−7.75879	−0.750071	−0.375035	+	0.927011i	$0.622369\pi$
$108$	−0.0287380	−0.00276531
$109$	2.11790	0.202858	0.101429	−	0.994843i	$-0.467659\pi$
$109$	2.11790	0.202858	0.101429	+	0.994843i	$0.467659\pi$
$110$	0.282294	0.0269157
$111$	12.1815	1.15622
$112$	−0.359767	−0.0339948
$113$	−3.52831	−0.331916	−0.165958	−	0.986133i	$-0.553072\pi$
$113$	−3.52831	−0.331916	−0.165958	+	0.986133i	$0.553072\pi$
$114$	−3.45377	−0.323475
$115$	−0.0770010	−0.00718038
$116$	−1.62449	−0.150830
$117$	−20.0160	−1.85048
$118$	−9.97915	−0.918656
$119$	2.02977	0.186069
$120$	−0.188428	−0.0172011
$121$	2.44035	0.221850
$122$	0.235526	0.0213236
$123$	9.32893	0.841161
$124$	1.09078	0.0979554
$125$	0.769553	0.0688309
$126$	−1.07508	−0.0957755
$127$	−15.5820	−1.38268	−0.691341	−	0.722529i	$-0.742980\pi$
$127$	−15.5820	−1.38268	−0.691341	+	0.722529i	$0.742980\pi$
$128$	1.00000	0.0883883
$129$	0.373313	0.0328683
$130$	0.515769	0.0452359
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−8.97130	−0.780852
$133$	0.507768	0.0440291
$134$	11.9904	1.03581
$135$	0.00221285	0.000190452 0
$136$	−5.64189	−0.483788
$137$	14.1702	1.21064	0.605320	−	0.795983i	$-0.293045\pi$
$137$	14.1702	1.21064	0.605320	+	0.795983i	$0.293045\pi$
$138$	2.44709	0.208310
$139$	−7.60023	−0.644643	−0.322321	−	0.946630i	$-0.604463\pi$
$139$	−7.60023	−0.644643	−0.322321	+	0.946630i	$0.604463\pi$
$140$	0.0277024	0.00234128
$141$	10.9368	0.921044
$142$	−4.13915	−0.347349
$143$	24.5564	2.05351
$144$	2.98826	0.249021
$145$	0.125087	0.0103879
$146$	4.60000	0.380698
$147$	−16.8129	−1.38671
$148$	4.97797	0.409187
$149$	12.5150	1.02527	0.512636	−	0.858606i	$-0.328669\pi$
$149$	12.5150	1.02527	0.512636	+	0.858606i	$0.328669\pi$
$150$	−12.2209	−0.997836
$151$	−1.22805	−0.0999372	−0.0499686	−	0.998751i	$-0.515912\pi$
$151$	−1.22805	−0.0999372	−0.0499686	+	0.998751i	$0.515912\pi$
$152$	−1.41138	−0.114478
$153$	−16.8594	−1.36300
$154$	1.31895	0.106284
$155$	−0.0839915	−0.00674636
$156$	−16.3911	−1.31234
$157$	0.609530	0.0486458	0.0243229	−	0.999704i	$-0.492257\pi$
$157$	0.609530	0.0486458	0.0243229	+	0.999704i	$0.492257\pi$
$158$	−4.91366	−0.390910
$159$	−10.3497	−0.820782
$160$	−0.0770010	−0.00608746
$161$	−0.359767	−0.0283536
$162$	−9.03509	−0.709864
$163$	19.7088	1.54371	0.771855	−	0.635798i	$-0.219329\pi$
$163$	19.7088	1.54371	0.771855	+	0.635798i	$0.219329\pi$
$164$	3.81225	0.297687
$165$	0.690799	0.0537786
$166$	10.6940	0.830016
$167$	−6.46208	−0.500051	−0.250025	−	0.968239i	$-0.580439\pi$
$167$	−6.46208	−0.500051	−0.250025	+	0.968239i	$0.580439\pi$
$168$	−0.880384	−0.0679231
$169$	31.8660	2.45123
$170$	0.434431	0.0333194
$171$	−4.21756	−0.322525
$172$	0.152554	0.0116321
$173$	−7.71728	−0.586734	−0.293367	−	0.956000i	$-0.594776\pi$
$173$	−7.71728	−0.586734	−0.293367	+	0.956000i	$0.594776\pi$
$174$	−3.97528	−0.301365
$175$	1.79670	0.135818
$176$	−3.66611	−0.276343
$177$	−24.4199	−1.83551
$178$	9.61342	0.720556
$179$	−22.1531	−1.65580	−0.827899	−	0.560877i	$-0.810464\pi$
$179$	−22.1531	−1.65580	−0.827899	+	0.560877i	$0.810464\pi$
$180$	−0.230099	−0.0171505
$181$	25.2402	1.87609	0.938045	−	0.346514i	$-0.112635\pi$
$181$	25.2402	1.87609	0.938045	+	0.346514i	$0.112635\pi$
$182$	2.40980	0.178626
$183$	0.576354	0.0426053
$184$	1.00000	0.0737210
$185$	−0.383309	−0.0281814
$186$	2.66925	0.195719
$187$	20.6838	1.51255
$188$	4.46930	0.325957
$189$	0.0103390	0.000752050 0
$190$	0.108678	0.00788430
$191$	26.1532	1.89238	0.946190	−	0.323612i	$-0.104897\pi$
$191$	26.1532	1.89238	0.946190	+	0.323612i	$0.104897\pi$
$192$	2.44709	0.176604
$193$	−0.125083	−0.00900365	−0.00450183	−	0.999990i	$-0.501433\pi$
$193$	−0.125083	−0.00900365	−0.00450183	+	0.999990i	$0.501433\pi$
$194$	1.04618	0.0751111
$195$	1.26213	0.0903832
$196$	−6.87057	−0.490755
$197$	−9.82984	−0.700347	−0.350174	−	0.936685i	$-0.613877\pi$
$197$	−9.82984	−0.700347	−0.350174	+	0.936685i	$0.613877\pi$
$198$	−10.9553	−0.778557
$199$	15.8715	1.12510	0.562550	−	0.826763i	$-0.309820\pi$
$199$	15.8715	1.12510	0.562550	+	0.826763i	$0.309820\pi$
$200$	−4.99407	−0.353134
$201$	29.3417	2.06960
$202$	−3.48203	−0.244995
$203$	0.584439	0.0410196
$204$	−13.8062	−0.966629
$205$	−0.293547	−0.0205022
$206$	−15.8847	−1.10674
$207$	2.98826	0.207698
$208$	−6.69821	−0.464437
$209$	5.17427	0.357911
$210$	0.0677904	0.00467798
$211$	−14.6594	−1.00920	−0.504598	−	0.863354i	$-0.668359\pi$
$211$	−14.6594	−1.00920	−0.504598	+	0.863354i	$0.668359\pi$
$212$	−4.22938	−0.290475
$213$	−10.1289	−0.694019
$214$	−7.75879	−0.530380
$215$	−0.0117468	−0.000801123 0
$216$	−0.0287380	−0.00195537
$217$	−0.392429	−0.0266398
$218$	2.11790	0.143442
$219$	11.2566	0.760651
$220$	0.282294	0.0190323
$221$	37.7906	2.54207
$222$	12.1815	0.817572
$223$	−14.1861	−0.949969	−0.474984	−	0.879994i	$-0.657546\pi$
$223$	−14.1861	−0.949969	−0.474984	+	0.879994i	$0.657546\pi$
$224$	−0.359767	−0.0240380
$225$	−14.9236	−0.994904
$226$	−3.52831	−0.234700
$227$	−13.0888	−0.868737	−0.434369	−	0.900735i	$-0.643028\pi$
$227$	−13.0888	−0.868737	−0.434369	+	0.900735i	$0.643028\pi$
$228$	−3.45377	−0.228732
$229$	−16.8216	−1.11161	−0.555803	−	0.831314i	$-0.687589\pi$
$229$	−16.8216	−1.11161	−0.555803	+	0.831314i	$0.687589\pi$
$230$	−0.0770010	−0.00507729
$231$	3.22758	0.212359
$232$	−1.62449	−0.106653
$233$	−10.3164	−0.675848	−0.337924	−	0.941173i	$-0.609725\pi$
$233$	−10.3164	−0.675848	−0.337924	+	0.941173i	$0.609725\pi$
$234$	−20.0160	−1.30848
$235$	−0.344141	−0.0224493
$236$	−9.97915	−0.649588
$237$	−12.0242	−0.781054
$238$	2.02977	0.131570
$239$	−10.4585	−0.676502	−0.338251	−	0.941056i	$-0.609835\pi$
$239$	−10.4585	−0.676502	−0.338251	+	0.941056i	$0.609835\pi$
$240$	−0.188428	−0.0121630
$241$	4.76050	0.306651	0.153325	−	0.988176i	$-0.451002\pi$
$241$	4.76050	0.306651	0.153325	+	0.988176i	$0.451002\pi$
$242$	2.44035	0.156872
$243$	−22.0235	−1.41281
$244$	0.235526	0.0150780
$245$	0.529040	0.0337992
$246$	9.32893	0.594791
$247$	9.45371	0.601525
$248$	1.09078	0.0692649
$249$	26.1692	1.65841
$250$	0.769553	0.0486708
$251$	7.83866	0.494772	0.247386	−	0.968917i	$-0.420428\pi$
$251$	7.83866	0.494772	0.247386	+	0.968917i	$0.420428\pi$
$252$	−1.07508	−0.0677235
$253$	−3.66611	−0.230486
$254$	−15.5820	−0.977704
$255$	1.06309	0.0665735
$256$	1.00000	0.0625000
$257$	9.25723	0.577450	0.288725	−	0.957412i	$-0.406769\pi$
$257$	9.25723	0.577450	0.288725	+	0.957412i	$0.406769\pi$
$258$	0.373313	0.0232414
$259$	−1.79091	−0.111282
$260$	0.515769	0.0319866
$261$	−4.85440	−0.300480
$262$	−1.00000	−0.0617802
$263$	4.35897	0.268786	0.134393	−	0.990928i	$-0.457092\pi$
$263$	4.35897	0.268786	0.134393	+	0.990928i	$0.457092\pi$
$264$	−8.97130	−0.552145
$265$	0.325666	0.0200055
$266$	0.507768	0.0311332
$267$	23.5249	1.43970
$268$	11.9904	0.732432
$269$	20.6935	1.26170	0.630852	−	0.775903i	$-0.282706\pi$
$269$	20.6935	1.26170	0.630852	+	0.775903i	$0.282706\pi$
$270$	0.00221285	0.000134670 0
$271$	16.2583	0.987620	0.493810	−	0.869570i	$-0.335604\pi$
$271$	16.2583	0.987620	0.493810	+	0.869570i	$0.335604\pi$
$272$	−5.64189	−0.342090
$273$	5.89699	0.356902
$274$	14.1702	0.856051
$275$	18.3088	1.10406
$276$	2.44709	0.147298
$277$	2.51096	0.150869	0.0754345	−	0.997151i	$-0.475966\pi$
$277$	2.51096	0.150869	0.0754345	+	0.997151i	$0.475966\pi$
$278$	−7.60023	−0.455831
$279$	3.25954	0.195144
$280$	0.0277024	0.00165554
$281$	11.6681	0.696059	0.348030	−	0.937484i	$-0.386851\pi$
$281$	11.6681	0.696059	0.348030	+	0.937484i	$0.386851\pi$
$282$	10.9368	0.651276
$283$	−8.17312	−0.485842	−0.242921	−	0.970046i	$-0.578106\pi$
$283$	−8.17312	−0.485842	−0.242921	+	0.970046i	$0.578106\pi$
$284$	−4.13915	−0.245613
$285$	0.265944	0.0157532
$286$	24.5564	1.45205
$287$	−1.37152	−0.0809585
$288$	2.98826	0.176085
$289$	14.8310	0.872409
$290$	0.125087	0.00734539
$291$	2.56009	0.150075
$292$	4.60000	0.269194
$293$	−23.6983	−1.38447	−0.692235	−	0.721672i	$-0.743374\pi$
$293$	−23.6983	−1.38447	−0.692235	+	0.721672i	$0.743374\pi$
$294$	−16.8129	−0.980549
$295$	0.768405	0.0447383
$296$	4.97797	0.289339
$297$	0.105356	0.00611340
$298$	12.5150	0.724976
$299$	−6.69821	−0.387367
$300$	−12.2209	−0.705577
$301$	−0.0548838	−0.00316345
$302$	−1.22805	−0.0706662
$303$	−8.52085	−0.489510
$304$	−1.41138	−0.0809481
$305$	−0.0181358	−0.00103845
$306$	−16.8594	−0.963789
$307$	17.4742	0.997307	0.498654	−	0.866801i	$-0.333828\pi$
$307$	17.4742	0.997307	0.498654	+	0.866801i	$0.333828\pi$
$308$	1.31895	0.0751539
$309$	−38.8713	−2.21131
$310$	−0.0839915	−0.00477040
$311$	−9.99314	−0.566659	−0.283330	−	0.959023i	$-0.591439\pi$
$311$	−9.99314	−0.566659	−0.283330	+	0.959023i	$0.591439\pi$
$312$	−16.3911	−0.927965
$313$	−5.30333	−0.299762	−0.149881	−	0.988704i	$-0.547889\pi$
$313$	−5.30333	−0.299762	−0.149881	+	0.988704i	$0.547889\pi$
$314$	0.609530	0.0343978
$315$	0.0827820	0.00466424
$316$	−4.91366	−0.276415
$317$	−7.84050	−0.440367	−0.220183	−	0.975459i	$-0.570666\pi$
$317$	−7.84050	−0.440367	−0.220183	+	0.975459i	$0.570666\pi$
$318$	−10.3497	−0.580381
$319$	5.95556	0.333447
$320$	−0.0770010	−0.00430449
$321$	−18.9865	−1.05972
$322$	−0.359767	−0.0200491
$323$	7.96285	0.443065
$324$	−9.03509	−0.501950
$325$	33.4513	1.85555
$326$	19.7088	1.09157
$327$	5.18268	0.286603
$328$	3.81225	0.210496
$329$	−1.60791	−0.0886469
$330$	0.690799	0.0380272
$331$	−15.0327	−0.826271	−0.413136	−	0.910670i	$-0.635566\pi$
$331$	−15.0327	−0.826271	−0.413136	+	0.910670i	$0.635566\pi$
$332$	10.6940	0.586910
$333$	14.8755	0.815170
$334$	−6.46208	−0.353589
$335$	−0.923275	−0.0504439
$336$	−0.880384	−0.0480289
$337$	−24.4658	−1.33274	−0.666368	−	0.745623i	$-0.732152\pi$
$337$	−24.4658	−1.33274	−0.666368	+	0.745623i	$0.732152\pi$
$338$	31.8660	1.73328
$339$	−8.63410	−0.468940
$340$	0.434431	0.0235603
$341$	−3.99893	−0.216554
$342$	−4.21756	−0.228060
$343$	4.99018	0.269444
$344$	0.152554	0.00822514
$345$	−0.188428	−0.0101446
$346$	−7.71728	−0.414884
$347$	23.5285	1.26308	0.631538	−	0.775345i	$-0.282424\pi$
$347$	23.5285	1.26308	0.631538	+	0.775345i	$0.282424\pi$
$348$	−3.97528	−0.213097
$349$	10.5376	0.564066	0.282033	−	0.959405i	$-0.408991\pi$
$349$	10.5376	0.564066	0.282033	+	0.959405i	$0.408991\pi$
$350$	1.79670	0.0960379
$351$	0.192493	0.0102745
$352$	−3.66611	−0.195404
$353$	4.74889	0.252758	0.126379	−	0.991982i	$-0.459664\pi$
$353$	4.74889	0.252758	0.126379	+	0.991982i	$0.459664\pi$
$354$	−24.4199	−1.29790
$355$	0.318718	0.0169158
$356$	9.61342	0.509510
$357$	4.96703	0.262883
$358$	−22.1531	−1.17083
$359$	6.76797	0.357200	0.178600	−	0.983922i	$-0.442843\pi$
$359$	6.76797	0.357200	0.178600	+	0.983922i	$0.442843\pi$
$360$	−0.230099	−0.0121273
$361$	−17.0080	−0.895159
$362$	25.2402	1.32660
$363$	5.97176	0.313436
$364$	2.40980	0.126308
$365$	−0.354204	−0.0185399
$366$	0.576354	0.0301265
$367$	−14.6176	−0.763033	−0.381516	−	0.924362i	$-0.624598\pi$
$367$	−14.6176	−0.763033	−0.381516	+	0.924362i	$0.624598\pi$
$368$	1.00000	0.0521286
$369$	11.3920	0.593043
$370$	−0.383309	−0.0199273
$371$	1.52159	0.0789971
$372$	2.66925	0.138394
$373$	7.19317	0.372448	0.186224	−	0.982507i	$-0.440375\pi$
$373$	7.19317	0.372448	0.186224	+	0.982507i	$0.440375\pi$
$374$	20.6838	1.06953
$375$	1.88317	0.0972463
$376$	4.46930	0.230487
$377$	10.8812	0.560409
$378$	0.0103390	0.000531780 0
$379$	−8.63295	−0.443445	−0.221722	−	0.975110i	$-0.571168\pi$
$379$	−8.63295	−0.443445	−0.221722	+	0.975110i	$0.571168\pi$
$380$	0.108678	0.00557504
$381$	−38.1307	−1.95349
$382$	26.1532	1.33811
$383$	−12.4310	−0.635193	−0.317596	−	0.948226i	$-0.602876\pi$
$383$	−12.4310	−0.635193	−0.317596	+	0.948226i	$0.602876\pi$
$384$	2.44709	0.124878
$385$	−0.101560	−0.00517598
$386$	−0.125083	−0.00636655
$387$	0.455869	0.0231731
$388$	1.04618	0.0531116
$389$	−17.2456	−0.874387	−0.437193	−	0.899367i	$-0.644028\pi$
$389$	−17.2456	−0.874387	−0.437193	+	0.899367i	$0.644028\pi$
$390$	1.26213	0.0639106
$391$	−5.64189	−0.285323
$392$	−6.87057	−0.347016
$393$	−2.44709	−0.123439
$394$	−9.82984	−0.495220
$395$	0.378357	0.0190372
$396$	−10.9553	−0.550523
$397$	20.9626	1.05209	0.526043	−	0.850458i	$-0.323675\pi$
$397$	20.9626	1.05209	0.526043	+	0.850458i	$0.323675\pi$
$398$	15.8715	0.795566
$399$	1.24255	0.0622055
$400$	−4.99407	−0.249704
$401$	−1.66076	−0.0829345	−0.0414673	−	0.999140i	$-0.513203\pi$
$401$	−1.66076	−0.0829345	−0.0414673	+	0.999140i	$0.513203\pi$
$402$	29.3417	1.46343
$403$	−7.30630	−0.363953
$404$	−3.48203	−0.173238
$405$	0.695711	0.0345702
$406$	0.584439	0.0290052
$407$	−18.2498	−0.904608
$408$	−13.8062	−0.683510
$409$	−27.7587	−1.37258	−0.686290	−	0.727328i	$-0.740762\pi$
$409$	−27.7587	−1.37258	−0.686290	+	0.727328i	$0.740762\pi$
$410$	−0.293547	−0.0144973
$411$	34.6757	1.71043
$412$	−15.8847	−0.782583
$413$	3.59017	0.176661
$414$	2.98826	0.146865
$415$	−0.823449	−0.0404215
$416$	−6.69821	−0.328407
$417$	−18.5985	−0.910770
$418$	5.17427	0.253082
$419$	−8.53855	−0.417135	−0.208568	−	0.978008i	$-0.566880\pi$
$419$	−8.53855	−0.417135	−0.208568	+	0.978008i	$0.566880\pi$
$420$	0.0677904	0.00330783
$421$	−35.8694	−1.74817	−0.874084	−	0.485775i	$-0.838537\pi$
$421$	−35.8694	−1.74817	−0.874084	+	0.485775i	$0.838537\pi$
$422$	−14.6594	−0.713610
$423$	13.3554	0.649363
$424$	−4.22938	−0.205397
$425$	28.1760	1.36674
$426$	−10.1289	−0.490745
$427$	−0.0847347	−0.00410060
$428$	−7.75879	−0.375035
$429$	60.0917	2.90125
$430$	−0.0117468	−0.000566480 0
$431$	−0.852484	−0.0410627	−0.0205314	−	0.999789i	$-0.506536\pi$
$431$	−0.852484	−0.0410627	−0.0205314	+	0.999789i	$0.506536\pi$
$432$	−0.0287380	−0.00138266
$433$	4.03570	0.193944	0.0969718	−	0.995287i	$-0.469084\pi$
$433$	4.03570	0.193944	0.0969718	+	0.995287i	$0.469084\pi$
$434$	−0.392429	−0.0188372
$435$	0.306100	0.0146764
$436$	2.11790	0.101429
$437$	−1.41138	−0.0675154
$438$	11.2566	0.537862
$439$	−0.117931	−0.00562852	−0.00281426	−	0.999996i	$-0.500896\pi$
$439$	−0.117931	−0.00562852	−0.00281426	+	0.999996i	$0.500896\pi$
$440$	0.282294	0.0134578
$441$	−20.5310	−0.977667
$442$	37.7906	1.79751
$443$	12.4194	0.590064	0.295032	−	0.955487i	$-0.404670\pi$
$443$	12.4194	0.590064	0.295032	+	0.955487i	$0.404670\pi$
$444$	12.1815	0.578111
$445$	−0.740243	−0.0350909
$446$	−14.1861	−0.671729
$447$	30.6254	1.44853
$448$	−0.359767	−0.0169974
$449$	−14.0148	−0.661397	−0.330699	−	0.943736i	$-0.607284\pi$
$449$	−14.0148	−0.661397	−0.330699	+	0.943736i	$0.607284\pi$
$450$	−14.9236	−0.703504
$451$	−13.9761	−0.658110
$452$	−3.52831	−0.165958
$453$	−3.00515	−0.141194
$454$	−13.0888	−0.614290
$455$	−0.185557	−0.00869903
$456$	−3.45377	−0.161738
$457$	−27.9108	−1.30561	−0.652806	−	0.757525i	$-0.726408\pi$
$457$	−27.9108	−1.30561	−0.652806	+	0.757525i	$0.726408\pi$
$458$	−16.8216	−0.786024
$459$	0.162137	0.00756789
$460$	−0.0770010	−0.00359019
$461$	−2.20349	−0.102627	−0.0513135	−	0.998683i	$-0.516341\pi$
$461$	−2.20349	−0.102627	−0.0513135	+	0.998683i	$0.516341\pi$
$462$	3.22758	0.150161
$463$	3.56364	0.165616	0.0828082	−	0.996566i	$-0.473611\pi$
$463$	3.56364	0.165616	0.0828082	+	0.996566i	$0.473611\pi$
$464$	−1.62449	−0.0754151
$465$	−0.205535	−0.00953145
$466$	−10.3164	−0.477897
$467$	−9.87851	−0.457123	−0.228561	−	0.973529i	$-0.573402\pi$
$467$	−9.87851	−0.457123	−0.228561	+	0.973529i	$0.573402\pi$
$468$	−20.0160	−0.925238
$469$	−4.31376	−0.199191
$470$	−0.344141	−0.0158740
$471$	1.49158	0.0687282
$472$	−9.97915	−0.459328
$473$	−0.559278	−0.0257156
$474$	−12.0242	−0.552289
$475$	7.04852	0.323408
$476$	2.02977	0.0930343
$477$	−12.6385	−0.578675
$478$	−10.4585	−0.478359
$479$	−24.7259	−1.12976	−0.564879	−	0.825174i	$-0.691077\pi$
$479$	−24.7259	−1.12976	−0.564879	+	0.825174i	$0.691077\pi$
$480$	−0.188428	−0.00860054
$481$	−33.3435	−1.52033
$482$	4.76050	0.216835
$483$	−0.880384	−0.0400588
$484$	2.44035	0.110925
$485$	−0.0805567	−0.00365789
$486$	−22.0235	−0.999006
$487$	−9.51411	−0.431125	−0.215563	−	0.976490i	$-0.569159\pi$
$487$	−9.51411	−0.431125	−0.215563	+	0.976490i	$0.569159\pi$
$488$	0.235526	0.0106618
$489$	48.2292	2.18100
$490$	0.529040	0.0238996
$491$	−13.0888	−0.590689	−0.295344	−	0.955391i	$-0.595434\pi$
$491$	−13.0888	−0.590689	−0.295344	+	0.955391i	$0.595434\pi$
$492$	9.32893	0.420581
$493$	9.16521	0.412780
$494$	9.45371	0.425342
$495$	0.843567	0.0379155
$496$	1.09078	0.0489777
$497$	1.48913	0.0667966
$498$	26.1692	1.17267
$499$	−2.47640	−0.110859	−0.0554294	−	0.998463i	$-0.517653\pi$
$499$	−2.47640	−0.110859	−0.0554294	+	0.998463i	$0.517653\pi$
$500$	0.769553	0.0344155
$501$	−15.8133	−0.706486
$502$	7.83866	0.349856
$503$	−12.7834	−0.569985	−0.284992	−	0.958530i	$-0.591991\pi$
$503$	−12.7834	−0.569985	−0.284992	+	0.958530i	$0.591991\pi$
$504$	−1.07508	−0.0478877
$505$	0.268120	0.0119312
$506$	−3.66611	−0.162978
$507$	77.9790	3.46317
$508$	−15.5820	−0.691341
$509$	38.2276	1.69441	0.847205	−	0.531266i	$-0.178284\pi$
$509$	38.2276	1.69441	0.847205	+	0.531266i	$0.178284\pi$
$510$	1.06309	0.0470746
$511$	−1.65493	−0.0732097
$512$	1.00000	0.0441942
$513$	0.0405601	0.00179077
$514$	9.25723	0.408319
$515$	1.22314	0.0538979
$516$	0.373313	0.0164342
$517$	−16.3849	−0.720609
$518$	−1.79091	−0.0786881
$519$	−18.8849	−0.828955
$520$	0.515769	0.0226180
$521$	13.5792	0.594915	0.297458	−	0.954735i	$-0.403861\pi$
$521$	13.5792	0.594915	0.297458	+	0.954735i	$0.403861\pi$
$522$	−4.85440	−0.212471
$523$	−3.15721	−0.138055	−0.0690276	−	0.997615i	$-0.521990\pi$
$523$	−3.15721	−0.138055	−0.0690276	+	0.997615i	$0.521990\pi$
$524$	−1.00000	−0.0436852
$525$	4.39670	0.191888
$526$	4.35897	0.190060
$527$	−6.15409	−0.268076
$528$	−8.97130	−0.390426
$529$	1.00000	0.0434783
$530$	0.325666	0.0141460
$531$	−29.8203	−1.29409
$532$	0.507768	0.0220145
$533$	−25.5353	−1.10605
$534$	23.5249	1.01802
$535$	0.597434	0.0258293
$536$	11.9904	0.517907
$537$	−54.2106	−2.33936
$538$	20.6935	0.892159
$539$	25.1882	1.08493
$540$	0.00221285	9.52260e−5 0
$541$	−4.52635	−0.194603	−0.0973016	−	0.995255i	$-0.531021\pi$
$541$	−4.52635	−0.194603	−0.0973016	+	0.995255i	$0.531021\pi$
$542$	16.2583	0.698353
$543$	61.7651	2.65059
$544$	−5.64189	−0.241894
$545$	−0.163080	−0.00698558
$546$	5.89699	0.252368
$547$	−21.3026	−0.910832	−0.455416	−	0.890279i	$-0.650510\pi$
$547$	−21.3026	−0.910832	−0.455416	+	0.890279i	$0.650510\pi$
$548$	14.1702	0.605320
$549$	0.703813	0.0300380
$550$	18.3088	0.780690
$551$	2.29277	0.0976754
$552$	2.44709	0.104155
$553$	1.76778	0.0751735
$554$	2.51096	0.106681
$555$	−0.937991	−0.0398155
$556$	−7.60023	−0.322321
$557$	−35.7471	−1.51465	−0.757327	−	0.653035i	$-0.773495\pi$
$557$	−35.7471	−1.51465	−0.757327	+	0.653035i	$0.773495\pi$
$558$	3.25954	0.137988
$559$	−1.02184	−0.0432190
$560$	0.0277024	0.00117064
$561$	50.6151	2.13697
$562$	11.6681	0.492188
$563$	−10.9265	−0.460497	−0.230249	−	0.973132i	$-0.573954\pi$
$563$	−10.9265	−0.460497	−0.230249	+	0.973132i	$0.573954\pi$
$564$	10.9368	0.460522
$565$	0.271684	0.0114298
$566$	−8.17312	−0.343542
$567$	3.25053	0.136510
$568$	−4.13915	−0.173675
$569$	8.47720	0.355383	0.177691	−	0.984086i	$-0.443137\pi$
$569$	8.47720	0.355383	0.177691	+	0.984086i	$0.443137\pi$
$570$	0.265944	0.0111392
$571$	10.7559	0.450119	0.225060	−	0.974345i	$-0.427742\pi$
$571$	10.7559	0.450119	0.225060	+	0.974345i	$0.427742\pi$
$572$	24.5564	1.02675
$573$	63.9993	2.67361
$574$	−1.37152	−0.0572463
$575$	−4.99407	−0.208267
$576$	2.98826	0.124511
$577$	−25.1957	−1.04891	−0.524455	−	0.851438i	$-0.675731\pi$
$577$	−25.1957	−1.04891	−0.524455	+	0.851438i	$0.675731\pi$
$578$	14.8310	0.616887
$579$	−0.306089	−0.0127206
$580$	0.125087	0.00519397
$581$	−3.84735	−0.159615
$582$	2.56009	0.106119
$583$	15.5054	0.642166
$584$	4.60000	0.190349
$585$	1.54125	0.0637228
$586$	−23.6983	−0.978968
$587$	22.2960	0.920254	0.460127	−	0.887853i	$-0.347804\pi$
$587$	22.2960	0.920254	0.460127	+	0.887853i	$0.347804\pi$
$588$	−16.8129	−0.693353
$589$	−1.53951	−0.0634344
$590$	0.768405	0.0316347
$591$	−24.0545	−0.989471
$592$	4.97797	0.204593
$593$	21.5094	0.883284	0.441642	−	0.897191i	$-0.354396\pi$
$593$	21.5094	0.883284	0.441642	+	0.897191i	$0.354396\pi$
$594$	0.105356	0.00432283
$595$	−0.156294	−0.00640744
$596$	12.5150	0.512636
$597$	38.8390	1.58957
$598$	−6.69821	−0.273910
$599$	6.43703	0.263010	0.131505	−	0.991316i	$-0.458019\pi$
$599$	6.43703	0.263010	0.131505	+	0.991316i	$0.458019\pi$
$600$	−12.2209	−0.498918
$601$	−43.1099	−1.75849	−0.879246	−	0.476368i	$-0.841953\pi$
$601$	−43.1099	−1.75849	−0.879246	+	0.476368i	$0.841953\pi$
$602$	−0.0548838	−0.00223690
$603$	35.8305	1.45913
$604$	−1.22805	−0.0499686
$605$	−0.187909	−0.00763960
$606$	−8.52085	−0.346136
$607$	36.6478	1.48749	0.743744	−	0.668465i	$-0.233048\pi$
$607$	36.6478	1.48749	0.743744	+	0.668465i	$0.233048\pi$
$608$	−1.41138	−0.0572389
$609$	1.43018	0.0579536
$610$	−0.0181358	−0.000734295 0
$611$	−29.9363	−1.21109
$612$	−16.8594	−0.681502
$613$	−34.6253	−1.39850	−0.699252	−	0.714875i	$-0.746483\pi$
$613$	−34.6253	−1.39850	−0.699252	+	0.714875i	$0.746483\pi$
$614$	17.4742	0.705203
$615$	−0.718337	−0.0289661
$616$	1.31895	0.0531419
$617$	21.3037	0.857655	0.428828	−	0.903386i	$-0.358927\pi$
$617$	21.3037	0.857655	0.428828	+	0.903386i	$0.358927\pi$
$618$	−38.8713	−1.56363
$619$	32.7921	1.31803	0.659013	−	0.752131i	$-0.270974\pi$
$619$	32.7921	1.31803	0.659013	+	0.752131i	$0.270974\pi$
$620$	−0.0839915	−0.00337318
$621$	−0.0287380	−0.00115321
$622$	−9.99314	−0.400689
$623$	−3.45860	−0.138566
$624$	−16.3911	−0.656170
$625$	24.9111	0.996444
$626$	−5.30333	−0.211964
$627$	12.6619	0.505668
$628$	0.609530	0.0243229
$629$	−28.0852	−1.11983
$630$	0.0827820	0.00329811
$631$	−7.51795	−0.299285	−0.149642	−	0.988740i	$-0.547812\pi$
$631$	−7.51795	−0.299285	−0.149642	+	0.988740i	$0.547812\pi$
$632$	−4.91366	−0.195455
$633$	−35.8730	−1.42582
$634$	−7.84050	−0.311386
$635$	1.19983	0.0476139
$636$	−10.3497	−0.410391
$637$	46.0205	1.82340
$638$	5.95556	0.235783
$639$	−12.3688	−0.489303
$640$	−0.0770010	−0.00304373
$641$	−10.3038	−0.406975	−0.203488	−	0.979078i	$-0.565228\pi$
$641$	−10.3038	−0.406975	−0.203488	+	0.979078i	$0.565228\pi$
$642$	−18.9865	−0.749336
$643$	26.3453	1.03896	0.519479	−	0.854483i	$-0.326126\pi$
$643$	26.3453	1.03896	0.519479	+	0.854483i	$0.326126\pi$
$644$	−0.359767	−0.0141768
$645$	−0.0287454	−0.00113185
$646$	7.96285	0.313294
$647$	−33.2186	−1.30596	−0.652980	−	0.757375i	$-0.726481\pi$
$647$	−33.2186	−1.30596	−0.652980	+	0.757375i	$0.726481\pi$
$648$	−9.03509	−0.354932
$649$	36.5847	1.43607
$650$	33.4513	1.31207
$651$	−0.960309	−0.0376375
$652$	19.7088	0.771855
$653$	−23.4687	−0.918401	−0.459200	−	0.888333i	$-0.651864\pi$
$653$	−23.4687	−0.918401	−0.459200	+	0.888333i	$0.651864\pi$
$654$	5.18268	0.202659
$655$	0.0770010	0.00300868
$656$	3.81225	0.148843
$657$	13.7460	0.536281
$658$	−1.60791	−0.0626828
$659$	26.9258	1.04888	0.524440	−	0.851448i	$-0.324275\pi$
$659$	26.9258	1.04888	0.524440	+	0.851448i	$0.324275\pi$
$660$	0.690799	0.0268893
$661$	28.1550	1.09510	0.547552	−	0.836772i	$-0.315560\pi$
$661$	28.1550	1.09510	0.547552	+	0.836772i	$0.315560\pi$
$662$	−15.0327	−0.584262
$663$	92.4770	3.59151
$664$	10.6940	0.415008
$665$	−0.0390986	−0.00151618
$666$	14.8755	0.576412
$667$	−1.62449	−0.0629006
$668$	−6.46208	−0.250025
$669$	−34.7146	−1.34214
$670$	−0.923275	−0.0356692
$671$	−0.863465	−0.0333337
$672$	−0.880384	−0.0339615
$673$	24.1081	0.929299	0.464650	−	0.885495i	$-0.346180\pi$
$673$	24.1081	0.929299	0.464650	+	0.885495i	$0.346180\pi$
$674$	−24.4658	−0.942386
$675$	0.143519	0.00552407
$676$	31.8660	1.22562
$677$	40.3610	1.55120	0.775600	−	0.631224i	$-0.217447\pi$
$677$	40.3610	1.55120	0.775600	+	0.631224i	$0.217447\pi$
$678$	−8.63410	−0.331591
$679$	−0.376380	−0.0144442
$680$	0.434431	0.0166597
$681$	−32.0296	−1.22738
$682$	−3.99893	−0.153127
$683$	−29.5682	−1.13139	−0.565697	−	0.824613i	$-0.691393\pi$
$683$	−29.5682	−1.13139	−0.565697	+	0.824613i	$0.691393\pi$
$684$	−4.21756	−0.161262
$685$	−1.09112	−0.0416894
$686$	4.99018	0.190526
$687$	−41.1641	−1.57051
$688$	0.152554	0.00581605
$689$	28.3292	1.07926
$690$	−0.188428	−0.00717335
$691$	−39.2753	−1.49410	−0.747051	−	0.664767i	$-0.768531\pi$
$691$	−39.2753	−1.49410	−0.747051	+	0.664767i	$0.768531\pi$
$692$	−7.71728	−0.293367
$693$	3.94135	0.149719
$694$	23.5285	0.893130
$695$	0.585225	0.0221988
$696$	−3.97528	−0.150683
$697$	−21.5083	−0.814686
$698$	10.5376	0.398855
$699$	−25.2451	−0.954858
$700$	1.79670	0.0679090
$701$	−41.0717	−1.55126	−0.775628	−	0.631190i	$-0.782567\pi$
$701$	−41.0717	−1.55126	−0.775628	+	0.631190i	$0.782567\pi$
$702$	0.192493	0.00726518
$703$	−7.02580	−0.264983
$704$	−3.66611	−0.138172
$705$	−0.842144	−0.0317170
$706$	4.74889	0.178727
$707$	1.25272	0.0471134
$708$	−24.4199	−0.917756
$709$	2.40746	0.0904142	0.0452071	−	0.998978i	$-0.485605\pi$
$709$	2.40746	0.0904142	0.0452071	+	0.998978i	$0.485605\pi$
$710$	0.318718	0.0119613
$711$	−14.6833	−0.550666
$712$	9.61342	0.360278
$713$	1.09078	0.0408502
$714$	4.96703	0.185886
$715$	−1.89086	−0.0707143
$716$	−22.1531	−0.827899
$717$	−25.5928	−0.955782
$718$	6.76797	0.252578
$719$	−12.1898	−0.454603	−0.227301	−	0.973824i	$-0.572990\pi$
$719$	−12.1898	−0.454603	−0.227301	+	0.973824i	$0.572990\pi$
$720$	−0.230099	−0.00857527
$721$	5.71480	0.212830
$722$	−17.0080	−0.632973
$723$	11.6494	0.433245
$724$	25.2402	0.938045
$725$	8.11283	0.301303
$726$	5.97176	0.221633
$727$	5.31175	0.197002	0.0985010	−	0.995137i	$-0.468595\pi$
$727$	5.31175	0.197002	0.0985010	+	0.995137i	$0.468595\pi$
$728$	2.40980	0.0893130
$729$	−26.7882	−0.992156
$730$	−0.354204	−0.0131097
$731$	−0.860691	−0.0318338
$732$	0.576354	0.0213027
$733$	29.0419	1.07269	0.536343	−	0.844000i	$-0.319805\pi$
$733$	29.0419	1.07269	0.536343	+	0.844000i	$0.319805\pi$
$734$	−14.6176	−0.539546
$735$	1.29461	0.0477524
$736$	1.00000	0.0368605
$737$	−43.9582	−1.61922
$738$	11.3920	0.419345
$739$	29.7560	1.09459	0.547296	−	0.836939i	$-0.315657\pi$
$739$	29.7560	1.09459	0.547296	+	0.836939i	$0.315657\pi$
$740$	−0.383309	−0.0140907
$741$	23.1341	0.849852
$742$	1.52159	0.0558594
$743$	−36.7148	−1.34694	−0.673468	−	0.739216i	$-0.735196\pi$
$743$	−36.7148	−1.34694	−0.673468	+	0.739216i	$0.735196\pi$
$744$	2.66925	0.0978594
$745$	−0.963670	−0.0353061
$746$	7.19317	0.263361
$747$	31.9564	1.16922
$748$	20.6838	0.756274
$749$	2.79136	0.101994
$750$	1.88317	0.0687635
$751$	−9.87869	−0.360479	−0.180239	−	0.983623i	$-0.557687\pi$
$751$	−9.87869	−0.360479	−0.180239	+	0.983623i	$0.557687\pi$
$752$	4.46930	0.162979
$753$	19.1819	0.699028
$754$	10.8812	0.396269
$755$	0.0945609	0.00344142
$756$	0.0103390	0.000376025 0
$757$	−19.9538	−0.725235	−0.362617	−	0.931938i	$-0.618117\pi$
$757$	−19.9538	−0.725235	−0.362617	+	0.931938i	$0.618117\pi$
$758$	−8.63295	−0.313563
$759$	−8.97130	−0.325638
$760$	0.108678	0.00394215
$761$	26.9749	0.977838	0.488919	−	0.872329i	$-0.337391\pi$
$761$	26.9749	0.977838	0.488919	+	0.872329i	$0.337391\pi$
$762$	−38.1307	−1.38133
$763$	−0.761950	−0.0275844
$764$	26.1532	0.946190
$765$	1.29819	0.0469362
$766$	−12.4310	−0.449149
$767$	66.8425	2.41354
$768$	2.44709	0.0883018
$769$	31.9416	1.15184	0.575921	−	0.817505i	$-0.304643\pi$
$769$	31.9416	1.15184	0.575921	+	0.817505i	$0.304643\pi$
$770$	−0.101560	−0.00365997
$771$	22.6533	0.815838
$772$	−0.125083	−0.00450183
$773$	25.8955	0.931398	0.465699	−	0.884943i	$-0.345803\pi$
$773$	25.8955	0.931398	0.465699	+	0.884943i	$0.345803\pi$
$774$	0.455869	0.0163859
$775$	−5.44746	−0.195678
$776$	1.04618	0.0375556
$777$	−4.38252	−0.157222
$778$	−17.2456	−0.618285
$779$	−5.38053	−0.192777
$780$	1.26213	0.0451916
$781$	15.1746	0.542988
$782$	−5.64189	−0.201754
$783$	0.0466846	0.00166837
$784$	−6.87057	−0.245377
$785$	−0.0469344	−0.00167516
$786$	−2.44709	−0.0872849
$787$	17.9303	0.639145	0.319573	−	0.947562i	$-0.396461\pi$
$787$	17.9303	0.639145	0.319573	+	0.947562i	$0.396461\pi$
$788$	−9.82984	−0.350174
$789$	10.6668	0.379748
$790$	0.378357	0.0134613
$791$	1.26937	0.0451337
$792$	−10.9553	−0.389279
$793$	−1.57760	−0.0560224
$794$	20.9626	0.743937
$795$	0.796935	0.0282644
$796$	15.8715	0.562550
$797$	−11.9637	−0.423776	−0.211888	−	0.977294i	$-0.567961\pi$
$797$	−11.9637	−0.423776	−0.211888	+	0.977294i	$0.567961\pi$
$798$	1.24255	0.0439859
$799$	−25.2153	−0.892054
$800$	−4.99407	−0.176567
$801$	28.7274	1.01503
$802$	−1.66076	−0.0586436
$803$	−16.8641	−0.595121
$804$	29.3417	1.03480
$805$	0.0277024	0.000976383 0
$806$	−7.30630	−0.257354
$807$	50.6388	1.78257
$808$	−3.48203	−0.122497
$809$	10.3940	0.365434	0.182717	−	0.983166i	$-0.441511\pi$
$809$	10.3940	0.365434	0.182717	+	0.983166i	$0.441511\pi$
$810$	0.695711	0.0244448
$811$	−40.9662	−1.43852	−0.719259	−	0.694742i	$-0.755519\pi$
$811$	−40.9662	−1.43852	−0.719259	+	0.694742i	$0.755519\pi$
$812$	0.584439	0.0205098
$813$	39.7855	1.39534
$814$	−18.2498	−0.639654
$815$	−1.51760	−0.0531590
$816$	−13.8062	−0.483315
$817$	−0.215311	−0.00753277
$818$	−27.7587	−0.970561
$819$	7.20109	0.251626
$820$	−0.293547	−0.0102511
$821$	−2.81994	−0.0984166	−0.0492083	−	0.998789i	$-0.515670\pi$
$821$	−2.81994	−0.0984166	−0.0492083	+	0.998789i	$0.515670\pi$
$822$	34.6757	1.20945
$823$	34.4573	1.20110	0.600552	−	0.799585i	$-0.294947\pi$
$823$	34.4573	1.20110	0.600552	+	0.799585i	$0.294947\pi$
$824$	−15.8847	−0.553370
$825$	44.8033	1.55985
$826$	3.59017	0.124918
$827$	28.4282	0.988544	0.494272	−	0.869307i	$-0.335435\pi$
$827$	28.4282	0.988544	0.494272	+	0.869307i	$0.335435\pi$
$828$	2.98826	0.103849
$829$	−34.0395	−1.18224	−0.591121	−	0.806583i	$-0.701314\pi$
$829$	−34.0395	−1.18224	−0.591121	+	0.806583i	$0.701314\pi$
$830$	−0.823449	−0.0285823
$831$	6.14455	0.213152
$832$	−6.69821	−0.232219
$833$	38.7630	1.34306
$834$	−18.5985	−0.644012
$835$	0.497586	0.0172197
$836$	5.17427	0.178956
$837$	−0.0313469	−0.00108351
$838$	−8.53855	−0.294959
$839$	−7.69157	−0.265543	−0.132771	−	0.991147i	$-0.542388\pi$
$839$	−7.69157	−0.265543	−0.132771	+	0.991147i	$0.542388\pi$
$840$	0.0677904	0.00233899
$841$	−26.3610	−0.909001
$842$	−35.8694	−1.23614
$843$	28.5529	0.983413
$844$	−14.6594	−0.504598
$845$	−2.45371	−0.0844103
$846$	13.3554	0.459169
$847$	−0.877958	−0.0301670
$848$	−4.22938	−0.145237
$849$	−20.0004	−0.686411
$850$	28.1760	0.966429
$851$	4.97797	0.170643
$852$	−10.1289	−0.347009
$853$	−13.7007	−0.469102	−0.234551	−	0.972104i	$-0.575362\pi$
$853$	−13.7007	−0.469102	−0.234551	+	0.972104i	$0.575362\pi$
$854$	−0.0847347	−0.00289956
$855$	0.324756	0.0111064
$856$	−7.75879	−0.265190
$857$	32.6147	1.11410	0.557048	−	0.830480i	$-0.311934\pi$
$857$	32.6147	1.11410	0.557048	+	0.830480i	$0.311934\pi$
$858$	60.0917	2.05150
$859$	−21.8853	−0.746716	−0.373358	−	0.927687i	$-0.621794\pi$
$859$	−21.8853	−0.746716	−0.373358	+	0.927687i	$0.621794\pi$
$860$	−0.0117468	−0.000400562 0
$861$	−3.35624	−0.114381
$862$	−0.852484	−0.0290357
$863$	1.40136	0.0477028	0.0238514	−	0.999716i	$-0.492407\pi$
$863$	1.40136	0.0477028	0.0238514	+	0.999716i	$0.492407\pi$
$864$	−0.0287380	−0.000977685 0
$865$	0.594238	0.0202047
$866$	4.03570	0.137139
$867$	36.2927	1.23257
$868$	−0.392429	−0.0133199
$869$	18.0140	0.611084
$870$	0.306100	0.0103778
$871$	−80.3144	−2.72135
$872$	2.11790	0.0717210
$873$	3.12625	0.105807
$874$	−1.41138	−0.0477406
$875$	−0.276860	−0.00935958
$876$	11.2566	0.380326
$877$	13.0390	0.440295	0.220148	−	0.975467i	$-0.429346\pi$
$877$	13.0390	0.440295	0.220148	+	0.975467i	$0.429346\pi$
$878$	−0.117931	−0.00397997
$879$	−57.9919	−1.95602
$880$	0.282294	0.00951613
$881$	17.3658	0.585070	0.292535	−	0.956255i	$-0.405501\pi$
$881$	17.3658	0.585070	0.292535	+	0.956255i	$0.405501\pi$
$882$	−20.5310	−0.691315
$883$	15.4101	0.518590	0.259295	−	0.965798i	$-0.416510\pi$
$883$	15.4101	0.518590	0.259295	+	0.965798i	$0.416510\pi$
$884$	37.7906	1.27103
$885$	1.88036	0.0632075
$886$	12.4194	0.417238
$887$	28.1172	0.944084	0.472042	−	0.881576i	$-0.343517\pi$
$887$	28.1172	0.944084	0.472042	+	0.881576i	$0.343517\pi$
$888$	12.1815	0.408786
$889$	5.60591	0.188016
$890$	−0.740243	−0.0248130
$891$	33.1236	1.10968
$892$	−14.1861	−0.474984
$893$	−6.30788	−0.211085
$894$	30.6254	1.02427
$895$	1.70581	0.0570189
$896$	−0.359767	−0.0120190
$897$	−16.3911	−0.547284
$898$	−14.0148	−0.467679
$899$	−1.77197	−0.0590985
$900$	−14.9236	−0.497452
$901$	23.8617	0.794948
$902$	−13.9761	−0.465354
$903$	−0.134306	−0.00446941
$904$	−3.52831	−0.117350
$905$	−1.94352	−0.0646048
$906$	−3.00515	−0.0998393
$907$	−27.7403	−0.921101	−0.460550	−	0.887634i	$-0.652348\pi$
$907$	−27.7403	−0.921101	−0.460550	+	0.887634i	$0.652348\pi$
$908$	−13.0888	−0.434369
$909$	−10.4052	−0.345119
$910$	−0.185557	−0.00615115
$911$	5.88585	0.195007	0.0975035	−	0.995235i	$-0.468914\pi$
$911$	5.88585	0.195007	0.0975035	+	0.995235i	$0.468914\pi$
$912$	−3.45377	−0.114366
$913$	−39.2054	−1.29751
$914$	−27.9108	−0.923207
$915$	−0.0443799	−0.00146715
$916$	−16.8216	−0.555803
$917$	0.359767	0.0118806
$918$	0.162137	0.00535130
$919$	−42.9258	−1.41599	−0.707996	−	0.706216i	$-0.750401\pi$
$919$	−42.9258	−1.41599	−0.707996	+	0.706216i	$0.750401\pi$
$920$	−0.0770010	−0.00253865
$921$	42.7611	1.40902
$922$	−2.20349	−0.0725682
$923$	27.7249	0.912575
$924$	3.22758	0.106180
$925$	−24.8603	−0.817403
$926$	3.56364	0.117109
$927$	−47.4676	−1.55904
$928$	−1.62449	−0.0533265
$929$	−20.4061	−0.669504	−0.334752	−	0.942306i	$-0.608653\pi$
$929$	−20.4061	−0.669504	−0.334752	+	0.942306i	$0.608653\pi$
$930$	−0.205535	−0.00673975
$931$	9.69697	0.317805
$932$	−10.3164	−0.337924
$933$	−24.4541	−0.800592
$934$	−9.87851	−0.323235
$935$	−1.59267	−0.0520860
$936$	−20.0160	−0.654242
$937$	−39.4530	−1.28887	−0.644437	−	0.764658i	$-0.722908\pi$
$937$	−39.4530	−1.28887	−0.644437	+	0.764658i	$0.722908\pi$
$938$	−4.31376	−0.140849
$939$	−12.9777	−0.423512
$940$	−0.344141	−0.0112246
$941$	−41.3227	−1.34708	−0.673540	−	0.739150i	$-0.735227\pi$
$941$	−41.3227	−1.34708	−0.673540	+	0.739150i	$0.735227\pi$
$942$	1.49158	0.0485982
$943$	3.81225	0.124144
$944$	−9.97915	−0.324794
$945$	−0.000796112 0	−2.58975e−5 0
$946$	−0.559278	−0.0181837
$947$	6.77208	0.220063	0.110031	−	0.993928i	$-0.464905\pi$
$947$	6.77208	0.220063	0.110031	+	0.993928i	$0.464905\pi$
$948$	−12.0242	−0.390527
$949$	−30.8117	−1.00019
$950$	7.04852	0.228684
$951$	−19.1864	−0.622163
$952$	2.02977	0.0657852
$953$	39.9960	1.29560	0.647798	−	0.761812i	$-0.275690\pi$
$953$	39.9960	1.29560	0.647798	+	0.761812i	$0.275690\pi$
$954$	−12.6385	−0.409185
$955$	−2.01382	−0.0651658
$956$	−10.4585	−0.338251
$957$	14.5738	0.471104
$958$	−24.7259	−0.798859
$959$	−5.09796	−0.164622
$960$	−0.188428	−0.00608150
$961$	−29.8102	−0.961619
$962$	−33.3435	−1.07504
$963$	−23.1853	−0.747134
$964$	4.76050	0.153325
$965$	0.00963150	0.000310049 0
$966$	−0.880384	−0.0283259
$967$	−50.7143	−1.63086	−0.815430	−	0.578855i	$-0.803500\pi$
$967$	−50.7143	−1.63086	−0.815430	+	0.578855i	$0.803500\pi$
$968$	2.44035	0.0784358
$969$	19.4858	0.625974
$970$	−0.0805567	−0.00258652
$971$	48.4411	1.55455	0.777275	−	0.629161i	$-0.216601\pi$
$971$	48.4411	1.55455	0.777275	+	0.629161i	$0.216601\pi$
$972$	−22.0235	−0.706404
$973$	2.73431	0.0876581
$974$	−9.51411	−0.304852
$975$	81.8585	2.62157
$976$	0.235526	0.00753901
$977$	27.7816	0.888811	0.444406	−	0.895826i	$-0.353415\pi$
$977$	27.7816	0.888811	0.444406	+	0.895826i	$0.353415\pi$
$978$	48.2292	1.54220
$979$	−35.2438	−1.12640
$980$	0.529040	0.0168996
$981$	6.32881	0.202063
$982$	−13.0888	−0.417680
$983$	−31.7998	−1.01425	−0.507127	−	0.861871i	$-0.669293\pi$
$983$	−31.7998	−1.01425	−0.507127	+	0.861871i	$0.669293\pi$
$984$	9.32893	0.297395
$985$	0.756907	0.0241171
$986$	9.16521	0.291880
$987$	−3.93470	−0.125243
$988$	9.45371	0.300762
$989$	0.152554	0.00485092
$990$	0.843567	0.0268103
$991$	−14.7222	−0.467666	−0.233833	−	0.972277i	$-0.575127\pi$
$991$	−14.7222	−0.467666	−0.233833	+	0.972277i	$0.575127\pi$
$992$	1.09078	0.0346324
$993$	−36.7864	−1.16738
$994$	1.48913	0.0472323
$995$	−1.22212	−0.0387438
$996$	26.1692	0.829203
$997$	−15.5457	−0.492336	−0.246168	−	0.969227i	$-0.579171\pi$
$997$	−15.5457	−0.492336	−0.246168	+	0.969227i	$0.579171\pi$
$998$	−2.47640	−0.0783890
$999$	−0.143057	−0.00452611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.f.1.20	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.f.1.20	✓	20	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.44709 q^{3} +1.00000 q^{4} -0.0770010 q^{5} +2.44709 q^{6} -0.359767 q^{7} +1.00000 q^{8} +2.98826 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.44709 q^{3} +1.00000 q^{4} -0.0770010 q^{5} +2.44709 q^{6} -0.359767 q^{7} +1.00000 q^{8} +2.98826 q^{9} -0.0770010 q^{10} -3.66611 q^{11} +2.44709 q^{12} -6.69821 q^{13} -0.359767 q^{14} -0.188428 q^{15} +1.00000 q^{16} -5.64189 q^{17} +2.98826 q^{18} -1.41138 q^{19} -0.0770010 q^{20} -0.880384 q^{21} -3.66611 q^{22} +1.00000 q^{23} +2.44709 q^{24} -4.99407 q^{25} -6.69821 q^{26} -0.0287380 q^{27} -0.359767 q^{28} -1.62449 q^{29} -0.188428 q^{30} +1.09078 q^{31} +1.00000 q^{32} -8.97130 q^{33} -5.64189 q^{34} +0.0277024 q^{35} +2.98826 q^{36} +4.97797 q^{37} -1.41138 q^{38} -16.3911 q^{39} -0.0770010 q^{40} +3.81225 q^{41} -0.880384 q^{42} +0.152554 q^{43} -3.66611 q^{44} -0.230099 q^{45} +1.00000 q^{46} +4.46930 q^{47} +2.44709 q^{48} -6.87057 q^{49} -4.99407 q^{50} -13.8062 q^{51} -6.69821 q^{52} -4.22938 q^{53} -0.0287380 q^{54} +0.282294 q^{55} -0.359767 q^{56} -3.45377 q^{57} -1.62449 q^{58} -9.97915 q^{59} -0.188428 q^{60} +0.235526 q^{61} +1.09078 q^{62} -1.07508 q^{63} +1.00000 q^{64} +0.515769 q^{65} -8.97130 q^{66} +11.9904 q^{67} -5.64189 q^{68} +2.44709 q^{69} +0.0277024 q^{70} -4.13915 q^{71} +2.98826 q^{72} +4.60000 q^{73} +4.97797 q^{74} -12.2209 q^{75} -1.41138 q^{76} +1.31895 q^{77} -16.3911 q^{78} -4.91366 q^{79} -0.0770010 q^{80} -9.03509 q^{81} +3.81225 q^{82} +10.6940 q^{83} -0.880384 q^{84} +0.434431 q^{85} +0.152554 q^{86} -3.97528 q^{87} -3.66611 q^{88} +9.61342 q^{89} -0.230099 q^{90} +2.40980 q^{91} +1.00000 q^{92} +2.66925 q^{93} +4.46930 q^{94} +0.108678 q^{95} +2.44709 q^{96} +1.04618 q^{97} -6.87057 q^{98} -10.9553 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9}+O(q^{10}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9	\( 20 q + 20 q^{2} - 5 q^{3} + 20 q^{4} - 6 q^{5} - 5 q^{6} - 12 q^{7} + 20 q^{8} - q^{9} - 6 q^{10} - 3 q^{11} - 5 q^{12} - 13 q^{13} - 12 q^{14} - 10 q^{15} + 20 q^{16} - 14 q^{17} - q^{18} - 21 q^{19} - 6 q^{20} - 8 q^{21} - 3 q^{22} + 20 q^{23} - 5 q^{24} - 14 q^{25} - 13 q^{26} - 5 q^{27} - 12 q^{28} - 27 q^{29} - 10 q^{30} - 27 q^{31} + 20 q^{32} - 12 q^{33} - 14 q^{34} - 23 q^{35} - q^{36} - 19 q^{37} - 21 q^{38} - 35 q^{39} - 6 q^{40} - 17 q^{41} - 8 q^{42} - 27 q^{43} - 3 q^{44} + 4 q^{45} + 20 q^{46} - 28 q^{47} - 5 q^{48} - 10 q^{49} - 14 q^{50} + 6 q^{51} - 13 q^{52} - 47 q^{53} - 5 q^{54} - 4 q^{55} - 12 q^{56} - 16 q^{57} - 27 q^{58} - 16 q^{59} - 10 q^{60} - 9 q^{61} - 27 q^{62} - 9 q^{63} + 20 q^{64} + 9 q^{65} - 12 q^{66} - 8 q^{67} - 14 q^{68} - 5 q^{69} - 23 q^{70} - 30 q^{71} - q^{72} - 26 q^{73} - 19 q^{74} - 18 q^{75} - 21 q^{76} - 50 q^{77} - 35 q^{78} - 35 q^{79} - 6 q^{80} - 60 q^{81} - 17 q^{82} + 2 q^{83} - 8 q^{84} - 62 q^{85} - 27 q^{86} + q^{87} - 3 q^{88} - 25 q^{89} + 4 q^{90} + 22 q^{91} + 20 q^{92} - 21 q^{93} - 28 q^{94} - 14 q^{95} - 5 q^{96} + 2 q^{97} - 10 q^{98} - 5 q^{99}+O(q^{100}) \) 20 * q + 20 * q^2 - 5 * q^3 + 20 * q^4 - 6 * q^5 - 5 * q^6 - 12 * q^7 + 20 * q^8 - q^9 - 6 * q^10 - 3 * q^11 - 5 * q^12 - 13 * q^13 - 12 * q^14 - 10 * q^15 + 20 * q^16 - 14 * q^17 - q^18 - 21 * q^19 - 6 * q^20 - 8 * q^21 - 3 * q^22 + 20 * q^23 - 5 * q^24 - 14 * q^25 - 13 * q^26 - 5 * q^27 - 12 * q^28 - 27 * q^29 - 10 * q^30 - 27 * q^31 + 20 * q^32 - 12 * q^33 - 14 * q^34 - 23 * q^35 - q^36 - 19 * q^37 - 21 * q^38 - 35 * q^39 - 6 * q^40 - 17 * q^41 - 8 * q^42 - 27 * q^43 - 3 * q^44 + 4 * q^45 + 20 * q^46 - 28 * q^47 - 5 * q^48 - 10 * q^49 - 14 * q^50 + 6 * q^51 - 13 * q^52 - 47 * q^53 - 5 * q^54 - 4 * q^55 - 12 * q^56 - 16 * q^57 - 27 * q^58 - 16 * q^59 - 10 * q^60 - 9 * q^61 - 27 * q^62 - 9 * q^63 + 20 * q^64 + 9 * q^65 - 12 * q^66 - 8 * q^67 - 14 * q^68 - 5 * q^69 - 23 * q^70 - 30 * q^71 - q^72 - 26 * q^73 - 19 * q^74 - 18 * q^75 - 21 * q^76 - 50 * q^77 - 35 * q^78 - 35 * q^79 - 6 * q^80 - 60 * q^81 - 17 * q^82 + 2 * q^83 - 8 * q^84 - 62 * q^85 - 27 * q^86 + q^87 - 3 * q^88 - 25 * q^89 + 4 * q^90 + 22 * q^91 + 20 * q^92 - 21 * q^93 - 28 * q^94 - 14 * q^95 - 5 * q^96 + 2 * q^97 - 10 * q^98 - 5 * q^99

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