LMFDB - Embedded newform 6026.2.a.m.1.14

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:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
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)

$f(q)$	$=$	$q+1.00000 q^{2} -1.08669 q^{3} +1.00000 q^{4} -0.588357 q^{5} -1.08669 q^{6} -3.89024 q^{7} +1.00000 q^{8} -1.81911 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.08669 q^{3} +1.00000 q^{4} -0.588357 q^{5} -1.08669 q^{6} -3.89024 q^{7} +1.00000 q^{8} -1.81911 q^{9} -0.588357 q^{10} -1.57917 q^{11} -1.08669 q^{12} -2.79009 q^{13} -3.89024 q^{14} +0.639361 q^{15} +1.00000 q^{16} -4.34634 q^{17} -1.81911 q^{18} -8.24009 q^{19} -0.588357 q^{20} +4.22748 q^{21} -1.57917 q^{22} +1.00000 q^{23} -1.08669 q^{24} -4.65384 q^{25} -2.79009 q^{26} +5.23687 q^{27} -3.89024 q^{28} +2.87533 q^{29} +0.639361 q^{30} -4.33507 q^{31} +1.00000 q^{32} +1.71607 q^{33} -4.34634 q^{34} +2.28885 q^{35} -1.81911 q^{36} +0.877198 q^{37} -8.24009 q^{38} +3.03196 q^{39} -0.588357 q^{40} +0.656510 q^{41} +4.22748 q^{42} +8.44282 q^{43} -1.57917 q^{44} +1.07028 q^{45} +1.00000 q^{46} -7.04316 q^{47} -1.08669 q^{48} +8.13396 q^{49} -4.65384 q^{50} +4.72312 q^{51} -2.79009 q^{52} +11.4071 q^{53} +5.23687 q^{54} +0.929117 q^{55} -3.89024 q^{56} +8.95441 q^{57} +2.87533 q^{58} +3.46439 q^{59} +0.639361 q^{60} +1.74425 q^{61} -4.33507 q^{62} +7.07676 q^{63} +1.00000 q^{64} +1.64157 q^{65} +1.71607 q^{66} +2.58487 q^{67} -4.34634 q^{68} -1.08669 q^{69} +2.28885 q^{70} +12.9531 q^{71} -1.81911 q^{72} +11.3008 q^{73} +0.877198 q^{74} +5.05727 q^{75} -8.24009 q^{76} +6.14336 q^{77} +3.03196 q^{78} -9.17507 q^{79} -0.588357 q^{80} -0.233528 q^{81} +0.656510 q^{82} -17.2759 q^{83} +4.22748 q^{84} +2.55720 q^{85} +8.44282 q^{86} -3.12459 q^{87} -1.57917 q^{88} +1.26160 q^{89} +1.07028 q^{90} +10.8541 q^{91} +1.00000 q^{92} +4.71087 q^{93} -7.04316 q^{94} +4.84811 q^{95} -1.08669 q^{96} -1.72363 q^{97} +8.13396 q^{98} +2.87268 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) $ 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.08669	−0.627400	−0.313700	−	0.949522i	$-0.601569\pi$
$3$	−1.08669	−0.627400	−0.313700	+	0.949522i	$0.601569\pi$
$4$	1.00000	0.500000
$5$	−0.588357	−0.263121	−0.131561	−	0.991308i	$-0.541999\pi$
$5$	−0.588357	−0.263121	−0.131561	+	0.991308i	$0.541999\pi$
$6$	−1.08669	−0.443639
$7$	−3.89024	−1.47037	−0.735186	−	0.677865i	$-0.762905\pi$
$7$	−3.89024	−1.47037	−0.735186	+	0.677865i	$0.762905\pi$
$8$	1.00000	0.353553
$9$	−1.81911	−0.606369
$10$	−0.588357	−0.186055
$11$	−1.57917	−0.476139	−0.238069	−	0.971248i	$-0.576515\pi$
$11$	−1.57917	−0.476139	−0.238069	+	0.971248i	$0.576515\pi$
$12$	−1.08669	−0.313700
$13$	−2.79009	−0.773833	−0.386916	−	0.922115i	$-0.626460\pi$
$13$	−2.79009	−0.773833	−0.386916	+	0.922115i	$0.626460\pi$
$14$	−3.89024	−1.03971
$15$	0.639361	0.165082
$16$	1.00000	0.250000
$17$	−4.34634	−1.05414	−0.527071	−	0.849821i	$-0.676710\pi$
$17$	−4.34634	−1.05414	−0.527071	+	0.849821i	$0.676710\pi$
$18$	−1.81911	−0.428768
$19$	−8.24009	−1.89041	−0.945203	−	0.326483i	$-0.894136\pi$
$19$	−8.24009	−1.89041	−0.945203	+	0.326483i	$0.894136\pi$
$20$	−0.588357	−0.131561
$21$	4.22748	0.922512
$22$	−1.57917	−0.336681
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−1.08669	−0.221819
$25$	−4.65384	−0.930767
$26$	−2.79009	−0.547183
$27$	5.23687	1.00784
$28$	−3.89024	−0.735186
$29$	2.87533	0.533936	0.266968	−	0.963705i	$-0.413978\pi$
$29$	2.87533	0.533936	0.266968	+	0.963705i	$0.413978\pi$
$30$	0.639361	0.116731
$31$	−4.33507	−0.778602	−0.389301	−	0.921111i	$-0.627283\pi$
$31$	−4.33507	−0.778602	−0.389301	+	0.921111i	$0.627283\pi$
$32$	1.00000	0.176777
$33$	1.71607	0.298729
$34$	−4.34634	−0.745391
$35$	2.28885	0.386886
$36$	−1.81911	−0.303185
$37$	0.877198	0.144210	0.0721052	−	0.997397i	$-0.477028\pi$
$37$	0.877198	0.144210	0.0721052	+	0.997397i	$0.477028\pi$
$38$	−8.24009	−1.33672
$39$	3.03196	0.485503
$40$	−0.588357	−0.0930274
$41$	0.656510	0.102530	0.0512648	−	0.998685i	$-0.483675\pi$
$41$	0.656510	0.102530	0.0512648	+	0.998685i	$0.483675\pi$
$42$	4.22748	0.652314
$43$	8.44282	1.28752	0.643759	−	0.765228i	$-0.277374\pi$
$43$	8.44282	1.28752	0.643759	+	0.765228i	$0.277374\pi$
$44$	−1.57917	−0.238069
$45$	1.07028	0.159548
$46$	1.00000	0.147442
$47$	−7.04316	−1.02735	−0.513675	−	0.857985i	$-0.671716\pi$
$47$	−7.04316	−1.02735	−0.513675	+	0.857985i	$0.671716\pi$
$48$	−1.08669	−0.156850
$49$	8.13396	1.16199
$50$	−4.65384	−0.658152
$51$	4.72312	0.661369
$52$	−2.79009	−0.386916
$53$	11.4071	1.56689	0.783444	−	0.621462i	$-0.213461\pi$
$53$	11.4071	1.56689	0.783444	+	0.621462i	$0.213461\pi$
$54$	5.23687	0.712648
$55$	0.929117	0.125282
$56$	−3.89024	−0.519855
$57$	8.95441	1.18604
$58$	2.87533	0.377550
$59$	3.46439	0.451026	0.225513	−	0.974240i	$-0.427594\pi$
$59$	3.46439	0.451026	0.225513	+	0.974240i	$0.427594\pi$
$60$	0.639361	0.0825411
$61$	1.74425	0.223328	0.111664	−	0.993746i	$-0.464382\pi$
$61$	1.74425	0.223328	0.111664	+	0.993746i	$0.464382\pi$
$62$	−4.33507	−0.550554
$63$	7.07676	0.891588
$64$	1.00000	0.125000
$65$	1.64157	0.203612
$66$	1.71607	0.211234
$67$	2.58487	0.315792	0.157896	−	0.987456i	$-0.449529\pi$
$67$	2.58487	0.315792	0.157896	+	0.987456i	$0.449529\pi$
$68$	−4.34634	−0.527071
$69$	−1.08669	−0.130822
$70$	2.28885	0.273570
$71$	12.9531	1.53725	0.768627	−	0.639697i	$-0.220940\pi$
$71$	12.9531	1.53725	0.768627	+	0.639697i	$0.220940\pi$
$72$	−1.81911	−0.214384
$73$	11.3008	1.32266	0.661328	−	0.750097i	$-0.269993\pi$
$73$	11.3008	1.32266	0.661328	+	0.750097i	$0.269993\pi$
$74$	0.877198	0.101972
$75$	5.05727	0.583964
$76$	−8.24009	−0.945203
$77$	6.14336	0.700101
$78$	3.03196	0.343302
$79$	−9.17507	−1.03228	−0.516138	−	0.856506i	$-0.672631\pi$
$79$	−9.17507	−1.03228	−0.516138	+	0.856506i	$0.672631\pi$
$80$	−0.588357	−0.0657803
$81$	−0.233528	−0.0259476
$82$	0.656510	0.0724994
$83$	−17.2759	−1.89628	−0.948140	−	0.317853i	$-0.897038\pi$
$83$	−17.2759	−1.89628	−0.948140	+	0.317853i	$0.897038\pi$
$84$	4.22748	0.461256
$85$	2.55720	0.277367
$86$	8.44282	0.910413
$87$	−3.12459	−0.334992
$88$	−1.57917	−0.168340
$89$	1.26160	0.133729	0.0668645	−	0.997762i	$-0.478700\pi$
$89$	1.26160	0.133729	0.0668645	+	0.997762i	$0.478700\pi$
$90$	1.07028	0.112818
$91$	10.8541	1.13782
$92$	1.00000	0.104257
$93$	4.71087	0.488495
$94$	−7.04316	−0.726446
$95$	4.84811	0.497406
$96$	−1.08669	−0.110910
$97$	−1.72363	−0.175008	−0.0875040	−	0.996164i	$-0.527889\pi$
$97$	−1.72363	−0.175008	−0.0875040	+	0.996164i	$0.527889\pi$
$98$	8.13396	0.821654
$99$	2.87268	0.288716
$100$	−4.65384	−0.465384
$101$	−11.5643	−1.15069	−0.575345	−	0.817911i	$-0.695132\pi$
$101$	−11.5643	−1.15069	−0.575345	+	0.817911i	$0.695132\pi$
$102$	4.72312	0.467658
$103$	−9.48181	−0.934270	−0.467135	−	0.884186i	$-0.654714\pi$
$103$	−9.48181	−0.934270	−0.467135	+	0.884186i	$0.654714\pi$
$104$	−2.79009	−0.273591
$105$	−2.48727	−0.242732
$106$	11.4071	1.10796
$107$	−1.23688	−0.119574	−0.0597869	−	0.998211i	$-0.519042\pi$
$107$	−1.23688	−0.119574	−0.0597869	+	0.998211i	$0.519042\pi$
$108$	5.23687	0.503918
$109$	−12.6001	−1.20687	−0.603437	−	0.797411i	$-0.706202\pi$
$109$	−12.6001	−1.20687	−0.603437	+	0.797411i	$0.706202\pi$
$110$	0.929117	0.0885878
$111$	−0.953242	−0.0904777
$112$	−3.89024	−0.367593
$113$	7.28223	0.685055	0.342527	−	0.939508i	$-0.388717\pi$
$113$	7.28223	0.685055	0.342527	+	0.939508i	$0.388717\pi$
$114$	8.95441	0.838658
$115$	−0.588357	−0.0548645
$116$	2.87533	0.266968
$117$	5.07548	0.469228
$118$	3.46439	0.318923
$119$	16.9083	1.54998
$120$	0.639361	0.0583654
$121$	−8.50621	−0.773292
$122$	1.74425	0.157917
$123$	−0.713422	−0.0643271
$124$	−4.33507	−0.389301
$125$	5.67990	0.508026
$126$	7.07676	0.630448
$127$	−4.00351	−0.355254	−0.177627	−	0.984098i	$-0.556842\pi$
$127$	−4.00351	−0.355254	−0.177627	+	0.984098i	$0.556842\pi$
$128$	1.00000	0.0883883
$129$	−9.17472	−0.807789
$130$	1.64157	0.143975
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	1.71607	0.149365
$133$	32.0559	2.77960
$134$	2.58487	0.223299
$135$	−3.08115	−0.265183
$136$	−4.34634	−0.372695
$137$	−11.2225	−0.958799	−0.479399	−	0.877597i	$-0.659145\pi$
$137$	−11.2225	−0.958799	−0.479399	+	0.877597i	$0.659145\pi$
$138$	−1.08669	−0.0925051
$139$	20.5753	1.74518	0.872588	−	0.488456i	$-0.162440\pi$
$139$	20.5753	1.74518	0.872588	+	0.488456i	$0.162440\pi$
$140$	2.28885	0.193443
$141$	7.65372	0.644560
$142$	12.9531	1.08700
$143$	4.40604	0.368452
$144$	−1.81911	−0.151592
$145$	−1.69172	−0.140490
$146$	11.3008	0.935259
$147$	−8.83908	−0.729035
$148$	0.877198	0.0721052
$149$	21.0627	1.72552	0.862762	−	0.505610i	$-0.168732\pi$
$149$	21.0627	1.72552	0.862762	+	0.505610i	$0.168732\pi$
$150$	5.05727	0.412925
$151$	−17.9099	−1.45749	−0.728744	−	0.684787i	$-0.759895\pi$
$151$	−17.9099	−1.45749	−0.728744	+	0.684787i	$0.759895\pi$
$152$	−8.24009	−0.668360
$153$	7.90645	0.639199
$154$	6.14336	0.495046
$155$	2.55057	0.204866
$156$	3.03196	0.242751
$157$	−21.2391	−1.69506	−0.847532	−	0.530744i	$-0.821913\pi$
$157$	−21.2391	−1.69506	−0.847532	+	0.530744i	$0.821913\pi$
$158$	−9.17507	−0.729929
$159$	−12.3960	−0.983066
$160$	−0.588357	−0.0465137
$161$	−3.89024	−0.306594
$162$	−0.233528	−0.0183477
$163$	10.2300	0.801272	0.400636	−	0.916237i	$-0.368789\pi$
$163$	10.2300	0.801272	0.400636	+	0.916237i	$0.368789\pi$
$164$	0.656510	0.0512648
$165$	−1.00966	−0.0786020
$166$	−17.2759	−1.34087
$167$	−0.448762	−0.0347262	−0.0173631	−	0.999849i	$-0.505527\pi$
$167$	−0.448762	−0.0347262	−0.0173631	+	0.999849i	$0.505527\pi$
$168$	4.22748	0.326157
$169$	−5.21537	−0.401183
$170$	2.55720	0.196128
$171$	14.9896	1.14628
$172$	8.44282	0.643759
$173$	11.2599	0.856074	0.428037	−	0.903761i	$-0.359205\pi$
$173$	11.2599	0.856074	0.428037	+	0.903761i	$0.359205\pi$
$174$	−3.12459	−0.236875
$175$	18.1045	1.36857
$176$	−1.57917	−0.119035
$177$	−3.76472	−0.282974
$178$	1.26160	0.0945607
$179$	6.51325	0.486823	0.243411	−	0.969923i	$-0.421733\pi$
$179$	6.51325	0.486823	0.243411	+	0.969923i	$0.421733\pi$
$180$	1.07028	0.0797742
$181$	16.6155	1.23502	0.617512	−	0.786562i	$-0.288141\pi$
$181$	16.6155	1.23502	0.617512	+	0.786562i	$0.288141\pi$
$182$	10.8541	0.804562
$183$	−1.89546	−0.140116
$184$	1.00000	0.0737210
$185$	−0.516105	−0.0379448
$186$	4.71087	0.345418
$187$	6.86362	0.501918
$188$	−7.04316	−0.513675
$189$	−20.3727	−1.48189
$190$	4.84811	0.351719
$191$	4.70336	0.340323	0.170162	−	0.985416i	$-0.445571\pi$
$191$	4.70336	0.340323	0.170162	+	0.985416i	$0.445571\pi$
$192$	−1.08669	−0.0784250
$193$	−2.03533	−0.146506	−0.0732530	−	0.997313i	$-0.523338\pi$
$193$	−2.03533	−0.146506	−0.0732530	+	0.997313i	$0.523338\pi$
$194$	−1.72363	−0.123749
$195$	−1.78388	−0.127746
$196$	8.13396	0.580997
$197$	3.00086	0.213802	0.106901	−	0.994270i	$-0.465907\pi$
$197$	3.00086	0.213802	0.106901	+	0.994270i	$0.465907\pi$
$198$	2.87268	0.204153
$199$	1.59543	0.113097	0.0565486	−	0.998400i	$-0.481990\pi$
$199$	1.59543	0.113097	0.0565486	+	0.998400i	$0.481990\pi$
$200$	−4.65384	−0.329076
$201$	−2.80895	−0.198128
$202$	−11.5643	−0.813660
$203$	−11.1857	−0.785084
$204$	4.72312	0.330684
$205$	−0.386262	−0.0269777
$206$	−9.48181	−0.660629
$207$	−1.81911	−0.126437
$208$	−2.79009	−0.193458
$209$	13.0125	0.900095
$210$	−2.48727	−0.171638
$211$	−20.6423	−1.42107	−0.710536	−	0.703661i	$-0.751548\pi$
$211$	−20.6423	−1.42107	−0.710536	+	0.703661i	$0.751548\pi$
$212$	11.4071	0.783444
$213$	−14.0760	−0.964474
$214$	−1.23688	−0.0845514
$215$	−4.96739	−0.338773
$216$	5.23687	0.356324
$217$	16.8645	1.14483
$218$	−12.6001	−0.853389
$219$	−12.2804	−0.829835
$220$	0.929117	0.0626410
$221$	12.1267	0.815730
$222$	−0.953242	−0.0639774
$223$	−24.5177	−1.64183	−0.820913	−	0.571053i	$-0.806535\pi$
$223$	−24.5177	−1.64183	−0.820913	+	0.571053i	$0.806535\pi$
$224$	−3.89024	−0.259927
$225$	8.46583	0.564388
$226$	7.28223	0.484407
$227$	12.2943	0.816004	0.408002	−	0.912981i	$-0.366226\pi$
$227$	12.2943	0.816004	0.408002	+	0.912981i	$0.366226\pi$
$228$	8.95441	0.593021
$229$	−5.36121	−0.354278	−0.177139	−	0.984186i	$-0.556684\pi$
$229$	−5.36121	−0.354278	−0.177139	+	0.984186i	$0.556684\pi$
$230$	−0.588357	−0.0387951
$231$	−6.67592	−0.439243
$232$	2.87533	0.188775
$233$	14.0670	0.921562	0.460781	−	0.887514i	$-0.347569\pi$
$233$	14.0670	0.921562	0.460781	+	0.887514i	$0.347569\pi$
$234$	5.07548	0.331795
$235$	4.14389	0.270317
$236$	3.46439	0.225513
$237$	9.97044	0.647650
$238$	16.9083	1.09600
$239$	29.8440	1.93045	0.965224	−	0.261424i	$-0.0841921\pi$
$239$	29.8440	1.93045	0.965224	+	0.261424i	$0.0841921\pi$
$240$	0.639361	0.0412706
$241$	−9.16866	−0.590605	−0.295303	−	0.955404i	$-0.595420\pi$
$241$	−9.16866	−0.590605	−0.295303	+	0.955404i	$0.595420\pi$
$242$	−8.50621	−0.546800
$243$	−15.4568	−0.991557
$244$	1.74425	0.111664
$245$	−4.78567	−0.305745
$246$	−0.713422	−0.0454861
$247$	22.9906	1.46286
$248$	−4.33507	−0.275277
$249$	18.7736	1.18973
$250$	5.67990	0.359228
$251$	−12.3460	−0.779270	−0.389635	−	0.920969i	$-0.627399\pi$
$251$	−12.3460	−0.779270	−0.389635	+	0.920969i	$0.627399\pi$
$252$	7.07676	0.445794
$253$	−1.57917	−0.0992817
$254$	−4.00351	−0.251203
$255$	−2.77888	−0.174020
$256$	1.00000	0.0625000
$257$	−4.78659	−0.298579	−0.149290	−	0.988794i	$-0.547699\pi$
$257$	−4.78659	−0.298579	−0.149290	+	0.988794i	$0.547699\pi$
$258$	−9.17472	−0.571193
$259$	−3.41251	−0.212043
$260$	1.64157	0.101806
$261$	−5.23054	−0.323762
$262$	1.00000	0.0617802
$263$	7.51249	0.463240	0.231620	−	0.972806i	$-0.425597\pi$
$263$	7.51249	0.463240	0.231620	+	0.972806i	$0.425597\pi$
$264$	1.71607	0.105617
$265$	−6.71146	−0.412281
$266$	32.0559	1.96547
$267$	−1.37096	−0.0839016
$268$	2.58487	0.157896
$269$	3.34272	0.203809	0.101905	−	0.994794i	$-0.467506\pi$
$269$	3.34272	0.203809	0.101905	+	0.994794i	$0.467506\pi$
$270$	−3.08115	−0.187513
$271$	−21.4804	−1.30484	−0.652421	−	0.757857i	$-0.726246\pi$
$271$	−21.4804	−1.30484	−0.652421	+	0.757857i	$0.726246\pi$
$272$	−4.34634	−0.263535
$273$	−11.7951	−0.713870
$274$	−11.2225	−0.677973
$275$	7.34921	0.443174
$276$	−1.08669	−0.0654110
$277$	−26.5155	−1.59316	−0.796582	−	0.604530i	$-0.793361\pi$
$277$	−26.5155	−1.59316	−0.796582	+	0.604530i	$0.793361\pi$
$278$	20.5753	1.23403
$279$	7.88596	0.472120
$280$	2.28885	0.136785
$281$	−8.66393	−0.516847	−0.258423	−	0.966032i	$-0.583203\pi$
$281$	−8.66393	−0.516847	−0.258423	+	0.966032i	$0.583203\pi$
$282$	7.65372	0.455772
$283$	−0.838961	−0.0498711	−0.0249355	−	0.999689i	$-0.507938\pi$
$283$	−0.838961	−0.0498711	−0.0249355	+	0.999689i	$0.507938\pi$
$284$	12.9531	0.768627
$285$	−5.26839	−0.312072
$286$	4.40604	0.260535
$287$	−2.55398	−0.150757
$288$	−1.81911	−0.107192
$289$	1.89066	0.111215
$290$	−1.69172	−0.0993413
$291$	1.87305	0.109800
$292$	11.3008	0.661328
$293$	22.5950	1.32001	0.660007	−	0.751259i	$-0.270553\pi$
$293$	22.5950	1.32001	0.660007	+	0.751259i	$0.270553\pi$
$294$	−8.83908	−0.515506
$295$	−2.03830	−0.118674
$296$	0.877198	0.0509861
$297$	−8.26992	−0.479870
$298$	21.0627	1.22013
$299$	−2.79009	−0.161355
$300$	5.05727	0.291982
$301$	−32.8446	−1.89313
$302$	−17.9099	−1.03060
$303$	12.5668	0.721943
$304$	−8.24009	−0.472602
$305$	−1.02624	−0.0587624
$306$	7.90645	0.451982
$307$	−0.895550	−0.0511117	−0.0255559	−	0.999673i	$-0.508136\pi$
$307$	−0.895550	−0.0511117	−0.0255559	+	0.999673i	$0.508136\pi$
$308$	6.14336	0.350050
$309$	10.3038	0.586161
$310$	2.55057	0.144862
$311$	−13.7497	−0.779673	−0.389836	−	0.920884i	$-0.627468\pi$
$311$	−13.7497	−0.779673	−0.389836	+	0.920884i	$0.627468\pi$
$312$	3.03196	0.171651
$313$	−12.6875	−0.717137	−0.358569	−	0.933503i	$-0.616735\pi$
$313$	−12.6875	−0.717137	−0.358569	+	0.933503i	$0.616735\pi$
$314$	−21.2391	−1.19859
$315$	−4.16366	−0.234596
$316$	−9.17507	−0.516138
$317$	13.3106	0.747600	0.373800	−	0.927509i	$-0.378055\pi$
$317$	13.3106	0.747600	0.373800	+	0.927509i	$0.378055\pi$
$318$	−12.3960	−0.695133
$319$	−4.54065	−0.254227
$320$	−0.588357	−0.0328901
$321$	1.34410	0.0750206
$322$	−3.89024	−0.216795
$323$	35.8142	1.99276
$324$	−0.233528	−0.0129738
$325$	12.9846	0.720258
$326$	10.2300	0.566585
$327$	13.6924	0.757193
$328$	0.656510	0.0362497
$329$	27.3996	1.51059
$330$	−1.00966	−0.0555800
$331$	17.7781	0.977173	0.488586	−	0.872515i	$-0.337513\pi$
$331$	17.7781	0.977173	0.488586	+	0.872515i	$0.337513\pi$
$332$	−17.2759	−0.948140
$333$	−1.59572	−0.0874448
$334$	−0.448762	−0.0245552
$335$	−1.52082	−0.0830915
$336$	4.22748	0.230628
$337$	27.7065	1.50927	0.754635	−	0.656144i	$-0.227814\pi$
$337$	27.7065	1.50927	0.754635	+	0.656144i	$0.227814\pi$
$338$	−5.21537	−0.283679
$339$	−7.91352	−0.429803
$340$	2.55720	0.138683
$341$	6.84582	0.370722
$342$	14.9896	0.810545
$343$	−4.41136	−0.238191
$344$	8.44282	0.455206
$345$	0.639361	0.0344220
$346$	11.2599	0.605336
$347$	−25.3004	−1.35820	−0.679099	−	0.734047i	$-0.737629\pi$
$347$	−25.3004	−1.35820	−0.679099	+	0.734047i	$0.737629\pi$
$348$	−3.12459	−0.167496
$349$	31.9732	1.71149	0.855743	−	0.517402i	$-0.173101\pi$
$349$	31.9732	1.71149	0.855743	+	0.517402i	$0.173101\pi$
$350$	18.1045	0.967728
$351$	−14.6114	−0.779897
$352$	−1.57917	−0.0841702
$353$	−7.64120	−0.406700	−0.203350	−	0.979106i	$-0.565183\pi$
$353$	−7.64120	−0.406700	−0.203350	+	0.979106i	$0.565183\pi$
$354$	−3.76472	−0.200093
$355$	−7.62107	−0.404484
$356$	1.26160	0.0668645
$357$	−18.3741	−0.972458
$358$	6.51325	0.344236
$359$	1.20324	0.0635044	0.0317522	−	0.999496i	$-0.489891\pi$
$359$	1.20324	0.0635044	0.0317522	+	0.999496i	$0.489891\pi$
$360$	1.07028	0.0564089
$361$	48.8991	2.57364
$362$	16.6155	0.873293
$363$	9.24361	0.485164
$364$	10.8541	0.568911
$365$	−6.64889	−0.348019
$366$	−1.89546	−0.0990771
$367$	8.54953	0.446282	0.223141	−	0.974786i	$-0.428369\pi$
$367$	8.54953	0.446282	0.223141	+	0.974786i	$0.428369\pi$
$368$	1.00000	0.0521286
$369$	−1.19426	−0.0621708
$370$	−0.516105	−0.0268310
$371$	−44.3764	−2.30391
$372$	4.71087	0.244247
$373$	−28.0918	−1.45454	−0.727269	−	0.686353i	$-0.759211\pi$
$373$	−28.0918	−1.45454	−0.727269	+	0.686353i	$0.759211\pi$
$374$	6.86362	0.354909
$375$	−6.17228	−0.318735
$376$	−7.04316	−0.363223
$377$	−8.02245	−0.413177
$378$	−20.3727	−1.04786
$379$	−15.2126	−0.781420	−0.390710	−	0.920514i	$-0.627770\pi$
$379$	−15.2126	−0.781420	−0.390710	+	0.920514i	$0.627770\pi$
$380$	4.84811	0.248703
$381$	4.35058	0.222887
$382$	4.70336	0.240645
$383$	−26.8129	−1.37008	−0.685038	−	0.728507i	$-0.740215\pi$
$383$	−26.8129	−1.37008	−0.685038	+	0.728507i	$0.740215\pi$
$384$	−1.08669	−0.0554549
$385$	−3.61449	−0.184211
$386$	−2.03533	−0.103595
$387$	−15.3584	−0.780711
$388$	−1.72363	−0.0875040
$389$	33.0121	1.67378	0.836891	−	0.547370i	$-0.184371\pi$
$389$	33.0121	1.67378	0.836891	+	0.547370i	$0.184371\pi$
$390$	−1.78388	−0.0903301
$391$	−4.34634	−0.219804
$392$	8.13396	0.410827
$393$	−1.08669	−0.0548162
$394$	3.00086	0.151181
$395$	5.39821	0.271614
$396$	2.87268	0.144358
$397$	31.8489	1.59845	0.799225	−	0.601032i	$-0.205244\pi$
$397$	31.8489	1.59845	0.799225	+	0.601032i	$0.205244\pi$
$398$	1.59543	0.0799718
$399$	−34.8348	−1.74392
$400$	−4.65384	−0.232692
$401$	4.93046	0.246215	0.123108	−	0.992393i	$-0.460714\pi$
$401$	4.93046	0.246215	0.123108	+	0.992393i	$0.460714\pi$
$402$	−2.80895	−0.140098
$403$	12.0953	0.602508
$404$	−11.5643	−0.575345
$405$	0.137398	0.00682735
$406$	−11.1857	−0.555139
$407$	−1.38525	−0.0686642
$408$	4.72312	0.233829
$409$	29.8874	1.47784	0.738918	−	0.673795i	$-0.235337\pi$
$409$	29.8874	1.47784	0.738918	+	0.673795i	$0.235337\pi$
$410$	−0.386262	−0.0190761
$411$	12.1953	0.601551
$412$	−9.48181	−0.467135
$413$	−13.4773	−0.663176
$414$	−1.81911	−0.0894042
$415$	10.1644	0.498951
$416$	−2.79009	−0.136796
$417$	−22.3590	−1.09492
$418$	13.0125	0.636463
$419$	−35.9515	−1.75634	−0.878172	−	0.478345i	$-0.841237\pi$
$419$	−35.9515	−1.75634	−0.878172	+	0.478345i	$0.841237\pi$
$420$	−2.48727	−0.121366
$421$	−25.0691	−1.22179	−0.610896	−	0.791711i	$-0.709191\pi$
$421$	−25.0691	−1.22179	−0.610896	+	0.791711i	$0.709191\pi$
$422$	−20.6423	−1.00485
$423$	12.8123	0.622953
$424$	11.4071	0.553979
$425$	20.2271	0.981161
$426$	−14.0760	−0.681986
$427$	−6.78555	−0.328376
$428$	−1.23688	−0.0597869
$429$	−4.78800	−0.231167
$430$	−4.96739	−0.239549
$431$	13.2768	0.639519	0.319759	−	0.947499i	$-0.396398\pi$
$431$	13.2768	0.639519	0.319759	+	0.947499i	$0.396398\pi$
$432$	5.23687	0.251959
$433$	−5.55108	−0.266768	−0.133384	−	0.991064i	$-0.542584\pi$
$433$	−5.55108	−0.266768	−0.133384	+	0.991064i	$0.542584\pi$
$434$	16.8645	0.809520
$435$	1.83838	0.0881433
$436$	−12.6001	−0.603437
$437$	−8.24009	−0.394177
$438$	−12.2804	−0.586782
$439$	18.6070	0.888064	0.444032	−	0.896011i	$-0.353548\pi$
$439$	18.6070	0.888064	0.444032	+	0.896011i	$0.353548\pi$
$440$	0.929117	0.0442939
$441$	−14.7965	−0.704597
$442$	12.1267	0.576808
$443$	22.9657	1.09113	0.545566	−	0.838068i	$-0.316315\pi$
$443$	22.9657	1.09113	0.545566	+	0.838068i	$0.316315\pi$
$444$	−0.953242	−0.0452388
$445$	−0.742269	−0.0351869
$446$	−24.5177	−1.16095
$447$	−22.8886	−1.08259
$448$	−3.89024	−0.183796
$449$	28.5963	1.34954	0.674771	−	0.738028i	$-0.264243\pi$
$449$	28.5963	1.34954	0.674771	+	0.738028i	$0.264243\pi$
$450$	8.46583	0.399083
$451$	−1.03674	−0.0488183
$452$	7.28223	0.342527
$453$	19.4625	0.914428
$454$	12.2943	0.577002
$455$	−6.38610	−0.299385
$456$	8.95441	0.419329
$457$	−0.965163	−0.0451484	−0.0225742	−	0.999745i	$-0.507186\pi$
$457$	−0.965163	−0.0451484	−0.0225742	+	0.999745i	$0.507186\pi$
$458$	−5.36121	−0.250513
$459$	−22.7612	−1.06240
$460$	−0.588357	−0.0274323
$461$	31.7416	1.47836	0.739178	−	0.673510i	$-0.235214\pi$
$461$	31.7416	1.47836	0.739178	+	0.673510i	$0.235214\pi$
$462$	−6.67592	−0.310592
$463$	13.0727	0.607542	0.303771	−	0.952745i	$-0.401754\pi$
$463$	13.0727	0.607542	0.303771	+	0.952745i	$0.401754\pi$
$464$	2.87533	0.133484
$465$	−2.77167	−0.128533
$466$	14.0670	0.651643
$467$	−29.4148	−1.36115	−0.680577	−	0.732676i	$-0.738271\pi$
$467$	−29.4148	−1.36115	−0.680577	+	0.732676i	$0.738271\pi$
$468$	5.07548	0.234614
$469$	−10.0558	−0.464332
$470$	4.14389	0.191143
$471$	23.0803	1.06348
$472$	3.46439	0.159462
$473$	−13.3327	−0.613037
$474$	9.97044	0.457958
$475$	38.3480	1.75953
$476$	16.9083	0.774990
$477$	−20.7508	−0.950113
$478$	29.8440	1.36503
$479$	−34.8363	−1.59171	−0.795855	−	0.605488i	$-0.792978\pi$
$479$	−34.8363	−1.59171	−0.795855	+	0.605488i	$0.792978\pi$
$480$	0.639361	0.0291827
$481$	−2.44747	−0.111595
$482$	−9.16866	−0.417621
$483$	4.22748	0.192357
$484$	−8.50621	−0.386646
$485$	1.01411	0.0460483
$486$	−15.4568	−0.701136
$487$	36.0177	1.63212	0.816060	−	0.577968i	$-0.196154\pi$
$487$	36.0177	1.63212	0.816060	+	0.577968i	$0.196154\pi$
$488$	1.74425	0.0789585
$489$	−11.1168	−0.502718
$490$	−4.78567	−0.216194
$491$	19.6173	0.885318	0.442659	−	0.896690i	$-0.354035\pi$
$491$	19.6173	0.885318	0.442659	+	0.896690i	$0.354035\pi$
$492$	−0.713422	−0.0321636
$493$	−12.4972	−0.562844
$494$	22.9906	1.03440
$495$	−1.69016	−0.0759672
$496$	−4.33507	−0.194650
$497$	−50.3908	−2.26034
$498$	18.7736	0.841264
$499$	8.42152	0.376999	0.188500	−	0.982073i	$-0.439638\pi$
$499$	8.42152	0.376999	0.188500	+	0.982073i	$0.439638\pi$
$500$	5.67990	0.254013
$501$	0.487665	0.0217872
$502$	−12.3460	−0.551027
$503$	−12.8444	−0.572704	−0.286352	−	0.958125i	$-0.592443\pi$
$503$	−12.8444	−0.572704	−0.286352	+	0.958125i	$0.592443\pi$
$504$	7.07676	0.315224
$505$	6.80393	0.302771
$506$	−1.57917	−0.0702028
$507$	5.66749	0.251702
$508$	−4.00351	−0.177627
$509$	−40.4039	−1.79087	−0.895436	−	0.445190i	$-0.853136\pi$
$509$	−40.4039	−1.79087	−0.895436	+	0.445190i	$0.853136\pi$
$510$	−2.77888	−0.123051
$511$	−43.9627	−1.94480
$512$	1.00000	0.0441942
$513$	−43.1523	−1.90522
$514$	−4.78659	−0.211127
$515$	5.57869	0.245826
$516$	−9.17472	−0.403895
$517$	11.1224	0.489161
$518$	−3.41251	−0.149937
$519$	−12.2360	−0.537101
$520$	1.64157	0.0719876
$521$	−17.1408	−0.750950	−0.375475	−	0.926833i	$-0.622520\pi$
$521$	−17.1408	−0.750950	−0.375475	+	0.926833i	$0.622520\pi$
$522$	−5.23054	−0.228934
$523$	14.4886	0.633540	0.316770	−	0.948502i	$-0.397402\pi$
$523$	14.4886	0.633540	0.316770	+	0.948502i	$0.397402\pi$
$524$	1.00000	0.0436852
$525$	−19.6740	−0.858644
$526$	7.51249	0.327560
$527$	18.8417	0.820756
$528$	1.71607	0.0746823
$529$	1.00000	0.0434783
$530$	−6.71146	−0.291527
$531$	−6.30210	−0.273488
$532$	32.0559	1.38980
$533$	−1.83173	−0.0793408
$534$	−1.37096	−0.0593274
$535$	0.727727	0.0314624
$536$	2.58487	0.111649
$537$	−7.07787	−0.305433
$538$	3.34272	0.144115
$539$	−12.8449	−0.553270
$540$	−3.08115	−0.132591
$541$	−4.21350	−0.181153	−0.0905763	−	0.995890i	$-0.528871\pi$
$541$	−4.21350	−0.181153	−0.0905763	+	0.995890i	$0.528871\pi$
$542$	−21.4804	−0.922662
$543$	−18.0559	−0.774854
$544$	−4.34634	−0.186348
$545$	7.41337	0.317554
$546$	−11.7951	−0.504782
$547$	−23.6324	−1.01045	−0.505225	−	0.862988i	$-0.668590\pi$
$547$	−23.6324	−1.01045	−0.505225	+	0.862988i	$0.668590\pi$
$548$	−11.2225	−0.479399
$549$	−3.17298	−0.135419
$550$	7.34921	0.313371
$551$	−23.6930	−1.00936
$552$	−1.08669	−0.0462526
$553$	35.6932	1.51783
$554$	−26.5155	−1.12654
$555$	0.560846	0.0238066
$556$	20.5753	0.872588
$557$	26.9393	1.14146	0.570728	−	0.821139i	$-0.306661\pi$
$557$	26.9393	1.14146	0.570728	+	0.821139i	$0.306661\pi$
$558$	7.88596	0.333839
$559$	−23.5563	−0.996324
$560$	2.28885	0.0967215
$561$	−7.45862	−0.314903
$562$	−8.66393	−0.365466
$563$	23.1874	0.977234	0.488617	−	0.872498i	$-0.337502\pi$
$563$	23.1874	0.977234	0.488617	+	0.872498i	$0.337502\pi$
$564$	7.65372	0.322280
$565$	−4.28455	−0.180252
$566$	−0.838961	−0.0352642
$567$	0.908480	0.0381526
$568$	12.9531	0.543502
$569$	17.4931	0.733348	0.366674	−	0.930350i	$-0.380497\pi$
$569$	17.4931	0.733348	0.366674	+	0.930350i	$0.380497\pi$
$570$	−5.26839	−0.220669
$571$	−18.2044	−0.761832	−0.380916	−	0.924610i	$-0.624391\pi$
$571$	−18.2044	−0.761832	−0.380916	+	0.924610i	$0.624391\pi$
$572$	4.40604	0.184226
$573$	−5.11109	−0.213519
$574$	−2.55398	−0.106601
$575$	−4.65384	−0.194078
$576$	−1.81911	−0.0757961
$577$	−4.96962	−0.206888	−0.103444	−	0.994635i	$-0.532986\pi$
$577$	−4.96962	−0.206888	−0.103444	+	0.994635i	$0.532986\pi$
$578$	1.89066	0.0786410
$579$	2.21177	0.0919179
$580$	−1.69172	−0.0702449
$581$	67.2075	2.78824
$582$	1.87305	0.0776403
$583$	−18.0138	−0.746056
$584$	11.3008	0.467629
$585$	−2.98619	−0.123464
$586$	22.5950	0.933391
$587$	30.3404	1.25228	0.626142	−	0.779709i	$-0.284633\pi$
$587$	30.3404	1.25228	0.626142	+	0.779709i	$0.284633\pi$
$588$	−8.83908	−0.364518
$589$	35.7214	1.47187
$590$	−2.03830	−0.0839155
$591$	−3.26100	−0.134140
$592$	0.877198	0.0360526
$593$	30.5345	1.25390	0.626951	−	0.779058i	$-0.284302\pi$
$593$	30.5345	1.25390	0.626951	+	0.779058i	$0.284302\pi$
$594$	−8.26992	−0.339319
$595$	−9.94811	−0.407833
$596$	21.0627	0.862762
$597$	−1.73374	−0.0709572
$598$	−2.79009	−0.114095
$599$	−36.0176	−1.47164	−0.735819	−	0.677178i	$-0.763203\pi$
$599$	−36.0176	−1.47164	−0.735819	+	0.677178i	$0.763203\pi$
$600$	5.05727	0.206462
$601$	14.6886	0.599160	0.299580	−	0.954071i	$-0.403153\pi$
$601$	14.6886	0.599160	0.299580	+	0.954071i	$0.403153\pi$
$602$	−32.8446	−1.33865
$603$	−4.70215	−0.191487
$604$	−17.9099	−0.728744
$605$	5.00469	0.203469
$606$	12.5668	0.510491
$607$	−10.6152	−0.430856	−0.215428	−	0.976520i	$-0.569115\pi$
$607$	−10.6152	−0.430856	−0.215428	+	0.976520i	$0.569115\pi$
$608$	−8.24009	−0.334180
$609$	12.1554	0.492562
$610$	−1.02624	−0.0415513
$611$	19.6511	0.794997
$612$	7.90645	0.319599
$613$	−32.3984	−1.30856	−0.654279	−	0.756253i	$-0.727028\pi$
$613$	−32.3984	−1.30856	−0.654279	+	0.756253i	$0.727028\pi$
$614$	−0.895550	−0.0361415
$615$	0.419747	0.0169258
$616$	6.14336	0.247523
$617$	−20.8731	−0.840318	−0.420159	−	0.907450i	$-0.638026\pi$
$617$	−20.8731	−0.840318	−0.420159	+	0.907450i	$0.638026\pi$
$618$	10.3038	0.414479
$619$	3.15867	0.126958	0.0634788	−	0.997983i	$-0.479780\pi$
$619$	3.15867	0.126958	0.0634788	+	0.997983i	$0.479780\pi$
$620$	2.55057	0.102433
$621$	5.23687	0.210148
$622$	−13.7497	−0.551312
$623$	−4.90791	−0.196631
$624$	3.03196	0.121376
$625$	19.9274	0.797095
$626$	−12.6875	−0.507093
$627$	−14.1406	−0.564720
$628$	−21.2391	−0.847532
$629$	−3.81260	−0.152018
$630$	−4.16366	−0.165884
$631$	6.37549	0.253804	0.126902	−	0.991915i	$-0.459497\pi$
$631$	6.37549	0.253804	0.126902	+	0.991915i	$0.459497\pi$
$632$	−9.17507	−0.364965
$633$	22.4317	0.891581
$634$	13.3106	0.528633
$635$	2.35549	0.0934749
$636$	−12.3960	−0.491533
$637$	−22.6945	−0.899189
$638$	−4.54065	−0.179766
$639$	−23.5631	−0.932144
$640$	−0.588357	−0.0232568
$641$	−18.3514	−0.724836	−0.362418	−	0.932016i	$-0.618049\pi$
$641$	−18.3514	−0.724836	−0.362418	+	0.932016i	$0.618049\pi$
$642$	1.34410	0.0530475
$643$	−40.7585	−1.60736	−0.803680	−	0.595062i	$-0.797128\pi$
$643$	−40.7585	−1.60736	−0.803680	+	0.595062i	$0.797128\pi$
$644$	−3.89024	−0.153297
$645$	5.39801	0.212546
$646$	35.8142	1.40909
$647$	−13.8685	−0.545225	−0.272613	−	0.962124i	$-0.587888\pi$
$647$	−13.8685	−0.545225	−0.272613	+	0.962124i	$0.587888\pi$
$648$	−0.233528	−0.00917385
$649$	−5.47088	−0.214751
$650$	12.9846	0.509300
$651$	−18.3264	−0.718269
$652$	10.2300	0.400636
$653$	−32.3889	−1.26747	−0.633737	−	0.773549i	$-0.718480\pi$
$653$	−32.3889	−1.26747	−0.633737	+	0.773549i	$0.718480\pi$
$654$	13.6924	0.535416
$655$	−0.588357	−0.0229890
$656$	0.656510	0.0256324
$657$	−20.5573	−0.802018
$658$	27.3996	1.06815
$659$	17.9902	0.700799	0.350399	−	0.936600i	$-0.386046\pi$
$659$	17.9902	0.700799	0.350399	+	0.936600i	$0.386046\pi$
$660$	−1.00966	−0.0393010
$661$	30.7113	1.19453	0.597266	−	0.802043i	$-0.296254\pi$
$661$	30.7113	1.19453	0.597266	+	0.802043i	$0.296254\pi$
$662$	17.7781	0.690966
$663$	−13.1779	−0.511789
$664$	−17.2759	−0.670436
$665$	−18.8603	−0.731371
$666$	−1.59572	−0.0618328
$667$	2.87533	0.111333
$668$	−0.448762	−0.0173631
$669$	26.6431	1.03008
$670$	−1.52082	−0.0587546
$671$	−2.75447	−0.106335
$672$	4.22748	0.163079
$673$	40.6612	1.56737	0.783687	−	0.621156i	$-0.213337\pi$
$673$	40.6612	1.56737	0.783687	+	0.621156i	$0.213337\pi$
$674$	27.7065	1.06722
$675$	−24.3715	−0.938061
$676$	−5.21537	−0.200591
$677$	−12.7224	−0.488961	−0.244481	−	0.969654i	$-0.578617\pi$
$677$	−12.7224	−0.488961	−0.244481	+	0.969654i	$0.578617\pi$
$678$	−7.91352	−0.303917
$679$	6.70533	0.257327
$680$	2.55720	0.0980640
$681$	−13.3601	−0.511961
$682$	6.84582	0.262140
$683$	−8.21774	−0.314443	−0.157222	−	0.987563i	$-0.550254\pi$
$683$	−8.21774	−0.314443	−0.157222	+	0.987563i	$0.550254\pi$
$684$	14.9896	0.573142
$685$	6.60281	0.252280
$686$	−4.41136	−0.168427
$687$	5.82596	0.222274
$688$	8.44282	0.321880
$689$	−31.8269	−1.21251
$690$	0.639361	0.0243400
$691$	18.6433	0.709223	0.354612	−	0.935014i	$-0.384613\pi$
$691$	18.6433	0.709223	0.354612	+	0.935014i	$0.384613\pi$
$692$	11.2599	0.428037
$693$	−11.1754	−0.424519
$694$	−25.3004	−0.960390
$695$	−12.1056	−0.459193
$696$	−3.12459	−0.118437
$697$	−2.85342	−0.108081
$698$	31.9732	1.21020
$699$	−15.2865	−0.578188
$700$	18.1045	0.684287
$701$	21.2915	0.804168	0.402084	−	0.915603i	$-0.368286\pi$
$701$	21.2915	0.804168	0.402084	+	0.915603i	$0.368286\pi$
$702$	−14.6114	−0.551470
$703$	−7.22819	−0.272616
$704$	−1.57917	−0.0595173
$705$	−4.50312	−0.169597
$706$	−7.64120	−0.287580
$707$	44.9878	1.69194
$708$	−3.76472	−0.141487
$709$	−16.4265	−0.616910	−0.308455	−	0.951239i	$-0.599812\pi$
$709$	−16.4265	−0.616910	−0.308455	+	0.951239i	$0.599812\pi$
$710$	−7.62107	−0.286014
$711$	16.6904	0.625940
$712$	1.26160	0.0472804
$713$	−4.33507	−0.162350
$714$	−18.3741	−0.687632
$715$	−2.59232	−0.0969474
$716$	6.51325	0.243411
$717$	−32.4311	−1.21116
$718$	1.20324	0.0449044
$719$	28.1655	1.05039	0.525197	−	0.850981i	$-0.323992\pi$
$719$	28.1655	1.05039	0.525197	+	0.850981i	$0.323992\pi$
$720$	1.07028	0.0398871
$721$	36.8865	1.37372
$722$	48.8991	1.81984
$723$	9.96348	0.370546
$724$	16.6155	0.617512
$725$	−13.3813	−0.496970
$726$	9.24361	0.343062
$727$	−25.6156	−0.950032	−0.475016	−	0.879977i	$-0.657558\pi$
$727$	−25.6156	−0.950032	−0.475016	+	0.879977i	$0.657558\pi$
$728$	10.8541	0.402281
$729$	17.4974	0.648050
$730$	−6.64889	−0.246086
$731$	−36.6954	−1.35723
$732$	−1.89546	−0.0700581
$733$	0.941010	0.0347570	0.0173785	−	0.999849i	$-0.494468\pi$
$733$	0.941010	0.0347570	0.0173785	+	0.999849i	$0.494468\pi$
$734$	8.54953	0.315569
$735$	5.20053	0.191825
$736$	1.00000	0.0368605
$737$	−4.08196	−0.150361
$738$	−1.19426	−0.0439614
$739$	−3.11695	−0.114659	−0.0573294	−	0.998355i	$-0.518259\pi$
$739$	−3.11695	−0.114659	−0.0573294	+	0.998355i	$0.518259\pi$
$740$	−0.516105	−0.0189724
$741$	−24.9837	−0.917798
$742$	−44.3764	−1.62911
$743$	4.05979	0.148939	0.0744696	−	0.997223i	$-0.476274\pi$
$743$	4.05979	0.148939	0.0744696	+	0.997223i	$0.476274\pi$
$744$	4.71087	0.172709
$745$	−12.3924	−0.454022
$746$	−28.0918	−1.02851
$747$	31.4268	1.14985
$748$	6.86362	0.250959
$749$	4.81176	0.175818
$750$	−6.17228	−0.225380
$751$	−29.3158	−1.06975	−0.534874	−	0.844932i	$-0.679641\pi$
$751$	−29.3158	−1.06975	−0.534874	+	0.844932i	$0.679641\pi$
$752$	−7.04316	−0.256838
$753$	13.4162	0.488914
$754$	−8.02245	−0.292160
$755$	10.5374	0.383496
$756$	−20.3727	−0.740947
$757$	−1.44352	−0.0524655	−0.0262328	−	0.999656i	$-0.508351\pi$
$757$	−1.44352	−0.0524655	−0.0262328	+	0.999656i	$0.508351\pi$
$758$	−15.2126	−0.552547
$759$	1.71607	0.0622894
$760$	4.84811	0.175859
$761$	−9.03790	−0.327624	−0.163812	−	0.986492i	$-0.552379\pi$
$761$	−9.03790	−0.327624	−0.163812	+	0.986492i	$0.552379\pi$
$762$	4.35058	0.157605
$763$	49.0175	1.77455
$764$	4.70336	0.170162
$765$	−4.65182	−0.168187
$766$	−26.8129	−0.968790
$767$	−9.66599	−0.349019
$768$	−1.08669	−0.0392125
$769$	42.0729	1.51719	0.758593	−	0.651564i	$-0.225887\pi$
$769$	42.0729	1.51719	0.758593	+	0.651564i	$0.225887\pi$
$770$	−3.61449	−0.130257
$771$	5.20153	0.187329
$772$	−2.03533	−0.0732530
$773$	13.4253	0.482876	0.241438	−	0.970416i	$-0.422381\pi$
$773$	13.4253	0.482876	0.241438	+	0.970416i	$0.422381\pi$
$774$	−15.3584	−0.552046
$775$	20.1747	0.724697
$776$	−1.72363	−0.0618747
$777$	3.70834	0.133036
$778$	33.0121	1.18354
$779$	−5.40970	−0.193823
$780$	−1.78388	−0.0638730
$781$	−20.4552	−0.731946
$782$	−4.34634	−0.155425
$783$	15.0577	0.538120
$784$	8.13396	0.290498
$785$	12.4962	0.446007
$786$	−1.08669	−0.0387609
$787$	7.61443	0.271425	0.135713	−	0.990748i	$-0.456668\pi$
$787$	7.61443	0.271425	0.135713	+	0.990748i	$0.456668\pi$
$788$	3.00086	0.106901
$789$	−8.16374	−0.290637
$790$	5.39821	0.192060
$791$	−28.3296	−1.00728
$792$	2.87268	0.102076
$793$	−4.86662	−0.172819
$794$	31.8489	1.13027
$795$	7.29327	0.258665
$796$	1.59543	0.0565486
$797$	−27.9858	−0.991306	−0.495653	−	0.868521i	$-0.665071\pi$
$797$	−27.9858	−0.991306	−0.495653	+	0.868521i	$0.665071\pi$
$798$	−34.8348	−1.23314
$799$	30.6119	1.08297
$800$	−4.65384	−0.164538
$801$	−2.29498	−0.0810891
$802$	4.93046	0.174101
$803$	−17.8459	−0.629767
$804$	−2.80895	−0.0990640
$805$	2.28885	0.0806713
$806$	12.0953	0.426037
$807$	−3.63250	−0.127870
$808$	−11.5643	−0.406830
$809$	1.85063	0.0650646	0.0325323	−	0.999471i	$-0.489643\pi$
$809$	1.85063	0.0650646	0.0325323	+	0.999471i	$0.489643\pi$
$810$	0.137398	0.00482767
$811$	38.9754	1.36861	0.684306	−	0.729195i	$-0.260105\pi$
$811$	38.9754	1.36861	0.684306	+	0.729195i	$0.260105\pi$
$812$	−11.1857	−0.392542
$813$	23.3425	0.818658
$814$	−1.38525	−0.0485529
$815$	−6.01886	−0.210831
$816$	4.72312	0.165342
$817$	−69.5696	−2.43393
$818$	29.8874	1.04499
$819$	−19.7448	−0.689940
$820$	−0.386262	−0.0134889
$821$	17.5720	0.613266	0.306633	−	0.951828i	$-0.400798\pi$
$821$	17.5720	0.613266	0.306633	+	0.951828i	$0.400798\pi$
$822$	12.1953	0.425361
$823$	−47.1415	−1.64325	−0.821625	−	0.570029i	$-0.806932\pi$
$823$	−47.1415	−1.64325	−0.821625	+	0.570029i	$0.806932\pi$
$824$	−9.48181	−0.330314
$825$	−7.98631	−0.278048
$826$	−13.4773	−0.468936
$827$	−11.3426	−0.394422	−0.197211	−	0.980361i	$-0.563188\pi$
$827$	−11.3426	−0.394422	−0.197211	+	0.980361i	$0.563188\pi$
$828$	−1.81911	−0.0632183
$829$	3.42621	0.118997	0.0594986	−	0.998228i	$-0.481050\pi$
$829$	3.42621	0.118997	0.0594986	+	0.998228i	$0.481050\pi$
$830$	10.1644	0.352812
$831$	28.8141	0.999552
$832$	−2.79009	−0.0967291
$833$	−35.3529	−1.22491
$834$	−22.3590	−0.774228
$835$	0.264032	0.00913721
$836$	13.0125	0.450048
$837$	−22.7022	−0.784703
$838$	−35.9515	−1.24192
$839$	−17.4823	−0.603556	−0.301778	−	0.953378i	$-0.597580\pi$
$839$	−17.4823	−0.603556	−0.301778	+	0.953378i	$0.597580\pi$
$840$	−2.48727	−0.0858188
$841$	−20.7325	−0.714912
$842$	−25.0691	−0.863938
$843$	9.41500	0.324270
$844$	−20.6423	−0.710536
$845$	3.06850	0.105560
$846$	12.8123	0.440494
$847$	33.0912	1.13703
$848$	11.4071	0.391722
$849$	0.911690	0.0312891
$850$	20.2271	0.693785
$851$	0.877198	0.0300700
$852$	−14.0760	−0.482237
$853$	22.7541	0.779085	0.389542	−	0.921009i	$-0.372633\pi$
$853$	22.7541	0.779085	0.389542	+	0.921009i	$0.372633\pi$
$854$	−6.78555	−0.232197
$855$	−8.81923	−0.301611
$856$	−1.23688	−0.0422757
$857$	39.0648	1.33443	0.667214	−	0.744866i	$-0.267487\pi$
$857$	39.0648	1.33443	0.667214	+	0.744866i	$0.267487\pi$
$858$	−4.78800	−0.163460
$859$	15.4223	0.526201	0.263100	−	0.964768i	$-0.415255\pi$
$859$	15.4223	0.526201	0.263100	+	0.964768i	$0.415255\pi$
$860$	−4.96739	−0.169387
$861$	2.77538	0.0945848
$862$	13.2768	0.452208
$863$	−0.339808	−0.0115672	−0.00578360	−	0.999983i	$-0.501841\pi$
$863$	−0.339808	−0.0115672	−0.00578360	+	0.999983i	$0.501841\pi$
$864$	5.23687	0.178162
$865$	−6.62484	−0.225251
$866$	−5.55108	−0.188633
$867$	−2.05456	−0.0697764
$868$	16.8645	0.572417
$869$	14.4890	0.491506
$870$	1.83838	0.0623268
$871$	−7.21203	−0.244370
$872$	−12.6001	−0.426694
$873$	3.13546	0.106119
$874$	−8.24009	−0.278725
$875$	−22.0962	−0.746987
$876$	−12.2804	−0.414917
$877$	−11.3790	−0.384241	−0.192120	−	0.981371i	$-0.561536\pi$
$877$	−11.3790	−0.384241	−0.192120	+	0.981371i	$0.561536\pi$
$878$	18.6070	0.627956
$879$	−24.5538	−0.828178
$880$	0.929117	0.0313205
$881$	15.9542	0.537511	0.268755	−	0.963208i	$-0.413388\pi$
$881$	15.9542	0.537511	0.268755	+	0.963208i	$0.413388\pi$
$882$	−14.7965	−0.498225
$883$	−55.9767	−1.88377	−0.941883	−	0.335941i	$-0.890946\pi$
$883$	−55.9767	−1.88377	−0.941883	+	0.335941i	$0.890946\pi$
$884$	12.1267	0.407865
$885$	2.21500	0.0744563
$886$	22.9657	0.771547
$887$	−9.67437	−0.324834	−0.162417	−	0.986722i	$-0.551929\pi$
$887$	−9.67437	−0.324834	−0.162417	+	0.986722i	$0.551929\pi$
$888$	−0.953242	−0.0319887
$889$	15.5746	0.522356
$890$	−0.742269	−0.0248809
$891$	0.368781	0.0123546
$892$	−24.5177	−0.820913
$893$	58.0362	1.94211
$894$	−22.8886	−0.765510
$895$	−3.83211	−0.128093
$896$	−3.89024	−0.129964
$897$	3.03196	0.101234
$898$	28.5963	0.954270
$899$	−12.4648	−0.415723
$900$	8.46583	0.282194
$901$	−49.5792	−1.65172
$902$	−1.03674	−0.0345198
$903$	35.6919	1.18775
$904$	7.28223	0.242203
$905$	−9.77586	−0.324961
$906$	19.4625	0.646598
$907$	38.1787	1.26770	0.633852	−	0.773454i	$-0.281473\pi$
$907$	38.1787	1.26770	0.633852	+	0.773454i	$0.281473\pi$
$908$	12.2943	0.408002
$909$	21.0367	0.697742
$910$	−6.38610	−0.211697
$911$	−17.5064	−0.580013	−0.290006	−	0.957025i	$-0.593657\pi$
$911$	−17.5064	−0.580013	−0.290006	+	0.957025i	$0.593657\pi$
$912$	8.95441	0.296510
$913$	27.2817	0.902892
$914$	−0.965163	−0.0319248
$915$	1.11520	0.0368675
$916$	−5.36121	−0.177139
$917$	−3.89024	−0.128467
$918$	−22.7612	−0.751232
$919$	0.758434	0.0250184	0.0125092	−	0.999922i	$-0.496018\pi$
$919$	0.758434	0.0250184	0.0125092	+	0.999922i	$0.496018\pi$
$920$	−0.588357	−0.0193975
$921$	0.973184	0.0320675
$922$	31.7416	1.04536
$923$	−36.1405	−1.18958
$924$	−6.67592	−0.219622
$925$	−4.08234	−0.134226
$926$	13.0727	0.429597
$927$	17.2484	0.566513
$928$	2.87533	0.0943874
$929$	−5.47391	−0.179593	−0.0897965	−	0.995960i	$-0.528622\pi$
$929$	−5.47391	−0.179593	−0.0897965	+	0.995960i	$0.528622\pi$
$930$	−2.77167	−0.0908867
$931$	−67.0245	−2.19664
$932$	14.0670	0.460781
$933$	14.9416	0.489167
$934$	−29.4148	−0.962482
$935$	−4.03826	−0.132065
$936$	5.07548	0.165897
$937$	26.8043	0.875659	0.437830	−	0.899058i	$-0.355747\pi$
$937$	26.8043	0.875659	0.437830	+	0.899058i	$0.355747\pi$
$938$	−10.0558	−0.328332
$939$	13.7873	0.449932
$940$	4.14389	0.135159
$941$	4.20065	0.136937	0.0684686	−	0.997653i	$-0.478189\pi$
$941$	4.20065	0.136937	0.0684686	+	0.997653i	$0.478189\pi$
$942$	23.0803	0.751997
$943$	0.656510	0.0213789
$944$	3.46439	0.112756
$945$	11.9864	0.389918
$946$	−13.3327	−0.433483
$947$	−23.7450	−0.771607	−0.385804	−	0.922581i	$-0.626076\pi$
$947$	−23.7450	−0.771607	−0.385804	+	0.922581i	$0.626076\pi$
$948$	9.97044	0.323825
$949$	−31.5302	−1.02351
$950$	38.3480	1.24417
$951$	−14.4645	−0.469044
$952$	16.9083	0.548001
$953$	34.9518	1.13220	0.566099	−	0.824337i	$-0.308452\pi$
$953$	34.9518	1.13220	0.566099	+	0.824337i	$0.308452\pi$
$954$	−20.7508	−0.671831
$955$	−2.76725	−0.0895463
$956$	29.8440	0.965224
$957$	4.93427	0.159502
$958$	−34.8363	−1.12551
$959$	43.6580	1.40979
$960$	0.639361	0.0206353
$961$	−12.2072	−0.393780
$962$	−2.44747	−0.0789095
$963$	2.25002	0.0725058
$964$	−9.16866	−0.295303
$965$	1.19750	0.0385488
$966$	4.22748	0.136017
$967$	21.1159	0.679040	0.339520	−	0.940599i	$-0.389735\pi$
$967$	21.1159	0.679040	0.339520	+	0.940599i	$0.389735\pi$
$968$	−8.50621	−0.273400
$969$	−38.9189	−1.25026
$970$	1.01411	0.0325611
$971$	54.6042	1.75233	0.876166	−	0.482009i	$-0.160093\pi$
$971$	54.6042	1.75233	0.876166	+	0.482009i	$0.160093\pi$
$972$	−15.4568	−0.495778
$973$	−80.0429	−2.56606
$974$	36.0177	1.15408
$975$	−14.1103	−0.451890
$976$	1.74425	0.0558321
$977$	−10.8793	−0.348060	−0.174030	−	0.984740i	$-0.555679\pi$
$977$	−10.8793	−0.348060	−0.174030	+	0.984740i	$0.555679\pi$
$978$	−11.1168	−0.355475
$979$	−1.99228	−0.0636735
$980$	−4.78567	−0.152873
$981$	22.9210	0.731811
$982$	19.6173	0.626014
$983$	35.6412	1.13678	0.568388	−	0.822760i	$-0.307567\pi$
$983$	35.6412	1.13678	0.568388	+	0.822760i	$0.307567\pi$
$984$	−0.713422	−0.0227431
$985$	−1.76557	−0.0562559
$986$	−12.4972	−0.397991
$987$	−29.7748	−0.947742
$988$	22.9906	0.731429
$989$	8.44282	0.268466
$990$	−1.69016	−0.0537169
$991$	−22.9059	−0.727631	−0.363815	−	0.931471i	$-0.618526\pi$
$991$	−22.9059	−0.727631	−0.363815	+	0.931471i	$0.618526\pi$
$992$	−4.33507	−0.137639
$993$	−19.3193	−0.613078
$994$	−50.3908	−1.59830
$995$	−0.938684	−0.0297583
$996$	18.7736	0.594863
$997$	24.9386	0.789814	0.394907	−	0.918721i	$-0.370777\pi$
$997$	24.9386	0.789814	0.394907	+	0.918721i	$0.370777\pi$
$998$	8.42152	0.266579
$999$	4.59377	0.145341

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.m.1.14	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.m.1.14	✓	41	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.08669 q^{3} +1.00000 q^{4} -0.588357 q^{5} -1.08669 q^{6} -3.89024 q^{7} +1.00000 q^{8} -1.81911 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.08669 q^{3} +1.00000 q^{4} -0.588357 q^{5} -1.08669 q^{6} -3.89024 q^{7} +1.00000 q^{8} -1.81911 q^{9} -0.588357 q^{10} -1.57917 q^{11} -1.08669 q^{12} -2.79009 q^{13} -3.89024 q^{14} +0.639361 q^{15} +1.00000 q^{16} -4.34634 q^{17} -1.81911 q^{18} -8.24009 q^{19} -0.588357 q^{20} +4.22748 q^{21} -1.57917 q^{22} +1.00000 q^{23} -1.08669 q^{24} -4.65384 q^{25} -2.79009 q^{26} +5.23687 q^{27} -3.89024 q^{28} +2.87533 q^{29} +0.639361 q^{30} -4.33507 q^{31} +1.00000 q^{32} +1.71607 q^{33} -4.34634 q^{34} +2.28885 q^{35} -1.81911 q^{36} +0.877198 q^{37} -8.24009 q^{38} +3.03196 q^{39} -0.588357 q^{40} +0.656510 q^{41} +4.22748 q^{42} +8.44282 q^{43} -1.57917 q^{44} +1.07028 q^{45} +1.00000 q^{46} -7.04316 q^{47} -1.08669 q^{48} +8.13396 q^{49} -4.65384 q^{50} +4.72312 q^{51} -2.79009 q^{52} +11.4071 q^{53} +5.23687 q^{54} +0.929117 q^{55} -3.89024 q^{56} +8.95441 q^{57} +2.87533 q^{58} +3.46439 q^{59} +0.639361 q^{60} +1.74425 q^{61} -4.33507 q^{62} +7.07676 q^{63} +1.00000 q^{64} +1.64157 q^{65} +1.71607 q^{66} +2.58487 q^{67} -4.34634 q^{68} -1.08669 q^{69} +2.28885 q^{70} +12.9531 q^{71} -1.81911 q^{72} +11.3008 q^{73} +0.877198 q^{74} +5.05727 q^{75} -8.24009 q^{76} +6.14336 q^{77} +3.03196 q^{78} -9.17507 q^{79} -0.588357 q^{80} -0.233528 q^{81} +0.656510 q^{82} -17.2759 q^{83} +4.22748 q^{84} +2.55720 q^{85} +8.44282 q^{86} -3.12459 q^{87} -1.57917 q^{88} +1.26160 q^{89} +1.07028 q^{90} +10.8541 q^{91} +1.00000 q^{92} +4.71087 q^{93} -7.04316 q^{94} +4.84811 q^{95} -1.08669 q^{96} -1.72363 q^{97} +8.13396 q^{98} +2.87268 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9}+O(q^{10}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9	\( 41 q + 41 q^{2} + 4 q^{3} + 41 q^{4} + 9 q^{5} + 4 q^{6} + 12 q^{7} + 41 q^{8} + 63 q^{9} + 9 q^{10} + 4 q^{11} + 4 q^{12} + 16 q^{13} + 12 q^{14} + 10 q^{15} + 41 q^{16} + 10 q^{17} + 63 q^{18} + 16 q^{19} + 9 q^{20} + 16 q^{21} + 4 q^{22} + 41 q^{23} + 4 q^{24} + 76 q^{25} + 16 q^{26} + 7 q^{27} + 12 q^{28} + 28 q^{29} + 10 q^{30} + 25 q^{31} + 41 q^{32} + 5 q^{33} + 10 q^{34} + 4 q^{35} + 63 q^{36} + 26 q^{37} + 16 q^{38} + 50 q^{39} + 9 q^{40} + 27 q^{41} + 16 q^{42} + 12 q^{43} + 4 q^{44} + 44 q^{45} + 41 q^{46} + 18 q^{47} + 4 q^{48} + 87 q^{49} + 76 q^{50} + 24 q^{51} + 16 q^{52} + 63 q^{53} + 7 q^{54} + 18 q^{55} + 12 q^{56} - 12 q^{57} + 28 q^{58} + 33 q^{59} + 10 q^{60} + 24 q^{61} + 25 q^{62} + 48 q^{63} + 41 q^{64} + 21 q^{65} + 5 q^{66} - 9 q^{67} + 10 q^{68} + 4 q^{69} + 4 q^{70} + 36 q^{71} + 63 q^{72} + 36 q^{73} + 26 q^{74} + 6 q^{75} + 16 q^{76} + 48 q^{77} + 50 q^{78} + 51 q^{79} + 9 q^{80} + 149 q^{81} + 27 q^{82} - 27 q^{83} + 16 q^{84} + 52 q^{85} + 12 q^{86} - 3 q^{87} + 4 q^{88} + 68 q^{89} + 44 q^{90} + 22 q^{91} + 41 q^{92} + 45 q^{93} + 18 q^{94} + 46 q^{95} + 4 q^{96} + 16 q^{97} + 87 q^{98} - 10 q^{99}+O(q^{100}) \) 41 * q + 41 * q^2 + 4 * q^3 + 41 * q^4 + 9 * q^5 + 4 * q^6 + 12 * q^7 + 41 * q^8 + 63 * q^9 + 9 * q^10 + 4 * q^11 + 4 * q^12 + 16 * q^13 + 12 * q^14 + 10 * q^15 + 41 * q^16 + 10 * q^17 + 63 * q^18 + 16 * q^19 + 9 * q^20 + 16 * q^21 + 4 * q^22 + 41 * q^23 + 4 * q^24 + 76 * q^25 + 16 * q^26 + 7 * q^27 + 12 * q^28 + 28 * q^29 + 10 * q^30 + 25 * q^31 + 41 * q^32 + 5 * q^33 + 10 * q^34 + 4 * q^35 + 63 * q^36 + 26 * q^37 + 16 * q^38 + 50 * q^39 + 9 * q^40 + 27 * q^41 + 16 * q^42 + 12 * q^43 + 4 * q^44 + 44 * q^45 + 41 * q^46 + 18 * q^47 + 4 * q^48 + 87 * q^49 + 76 * q^50 + 24 * q^51 + 16 * q^52 + 63 * q^53 + 7 * q^54 + 18 * q^55 + 12 * q^56 - 12 * q^57 + 28 * q^58 + 33 * q^59 + 10 * q^60 + 24 * q^61 + 25 * q^62 + 48 * q^63 + 41 * q^64 + 21 * q^65 + 5 * q^66 - 9 * q^67 + 10 * q^68 + 4 * q^69 + 4 * q^70 + 36 * q^71 + 63 * q^72 + 36 * q^73 + 26 * q^74 + 6 * q^75 + 16 * q^76 + 48 * q^77 + 50 * q^78 + 51 * q^79 + 9 * q^80 + 149 * q^81 + 27 * q^82 - 27 * q^83 + 16 * q^84 + 52 * q^85 + 12 * q^86 - 3 * q^87 + 4 * q^88 + 68 * q^89 + 44 * q^90 + 22 * q^91 + 41 * q^92 + 45 * q^93 + 18 * q^94 + 46 * q^95 + 4 * q^96 + 16 * q^97 + 87 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more