LMFDB - Embedded newform 8018.2.a.f.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, 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("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$1$
Dimension:	$34$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.91986 q^{3} +1.00000 q^{4} +0.472260 q^{5} +1.91986 q^{6} +4.62137 q^{7} -1.00000 q^{8} +0.685870 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.91986 q^{3} +1.00000 q^{4} +0.472260 q^{5} +1.91986 q^{6} +4.62137 q^{7} -1.00000 q^{8} +0.685870 q^{9} -0.472260 q^{10} -0.111615 q^{11} -1.91986 q^{12} +0.272381 q^{13} -4.62137 q^{14} -0.906673 q^{15} +1.00000 q^{16} +2.02660 q^{17} -0.685870 q^{18} -1.00000 q^{19} +0.472260 q^{20} -8.87239 q^{21} +0.111615 q^{22} +5.62701 q^{23} +1.91986 q^{24} -4.77697 q^{25} -0.272381 q^{26} +4.44281 q^{27} +4.62137 q^{28} -4.88771 q^{29} +0.906673 q^{30} -8.39165 q^{31} -1.00000 q^{32} +0.214285 q^{33} -2.02660 q^{34} +2.18249 q^{35} +0.685870 q^{36} +7.54400 q^{37} +1.00000 q^{38} -0.522934 q^{39} -0.472260 q^{40} -5.51603 q^{41} +8.87239 q^{42} +0.252608 q^{43} -0.111615 q^{44} +0.323909 q^{45} -5.62701 q^{46} +3.79423 q^{47} -1.91986 q^{48} +14.3571 q^{49} +4.77697 q^{50} -3.89079 q^{51} +0.272381 q^{52} -2.47409 q^{53} -4.44281 q^{54} -0.0527112 q^{55} -4.62137 q^{56} +1.91986 q^{57} +4.88771 q^{58} -10.5518 q^{59} -0.906673 q^{60} -7.76848 q^{61} +8.39165 q^{62} +3.16966 q^{63} +1.00000 q^{64} +0.128634 q^{65} -0.214285 q^{66} -13.7548 q^{67} +2.02660 q^{68} -10.8031 q^{69} -2.18249 q^{70} +7.29402 q^{71} -0.685870 q^{72} -9.98277 q^{73} -7.54400 q^{74} +9.17112 q^{75} -1.00000 q^{76} -0.515814 q^{77} +0.522934 q^{78} -8.19692 q^{79} +0.472260 q^{80} -10.5872 q^{81} +5.51603 q^{82} +4.34992 q^{83} -8.87239 q^{84} +0.957080 q^{85} -0.252608 q^{86} +9.38373 q^{87} +0.111615 q^{88} +1.85112 q^{89} -0.323909 q^{90} +1.25877 q^{91} +5.62701 q^{92} +16.1108 q^{93} -3.79423 q^{94} -0.472260 q^{95} +1.91986 q^{96} -4.37494 q^{97} -14.3571 q^{98} -0.0765533 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) $ 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * 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
$3$	−1.91986	−1.10843	−0.554216	−	0.832373i	$-0.686982\pi$
$3$	−1.91986	−1.10843	−0.554216	+	0.832373i	$0.686982\pi$
$4$	1.00000	0.500000
$5$	0.472260	0.211201	0.105600	−	0.994409i	$-0.466324\pi$
$5$	0.472260	0.211201	0.105600	+	0.994409i	$0.466324\pi$
$6$	1.91986	0.783780
$7$	4.62137	1.74671	0.873357	−	0.487081i	$-0.161938\pi$
$7$	4.62137	1.74671	0.873357	+	0.487081i	$0.161938\pi$
$8$	−1.00000	−0.353553
$9$	0.685870	0.228623
$10$	−0.472260	−0.149342
$11$	−0.111615	−0.0336531	−0.0168266	−	0.999858i	$-0.505356\pi$
$11$	−0.111615	−0.0336531	−0.0168266	+	0.999858i	$0.505356\pi$
$12$	−1.91986	−0.554216
$13$	0.272381	0.0755449	0.0377724	−	0.999286i	$-0.487974\pi$
$13$	0.272381	0.0755449	0.0377724	+	0.999286i	$0.487974\pi$
$14$	−4.62137	−1.23511
$15$	−0.906673	−0.234102
$16$	1.00000	0.250000
$17$	2.02660	0.491522	0.245761	−	0.969330i	$-0.420962\pi$
$17$	2.02660	0.491522	0.245761	+	0.969330i	$0.420962\pi$
$18$	−0.685870	−0.161661
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.472260	0.105600
$21$	−8.87239	−1.93612
$22$	0.111615	0.0237964
$23$	5.62701	1.17331	0.586657	−	0.809836i	$-0.300444\pi$
$23$	5.62701	1.17331	0.586657	+	0.809836i	$0.300444\pi$
$24$	1.91986	0.391890
$25$	−4.77697	−0.955394
$26$	−0.272381	−0.0534183
$27$	4.44281	0.855019
$28$	4.62137	0.873357
$29$	−4.88771	−0.907625	−0.453812	−	0.891097i	$-0.649936\pi$
$29$	−4.88771	−0.907625	−0.453812	+	0.891097i	$0.649936\pi$
$30$	0.906673	0.165535
$31$	−8.39165	−1.50719	−0.753593	−	0.657342i	$-0.771681\pi$
$31$	−8.39165	−1.50719	−0.753593	+	0.657342i	$0.771681\pi$
$32$	−1.00000	−0.176777
$33$	0.214285	0.0373022
$34$	−2.02660	−0.347559
$35$	2.18249	0.368908
$36$	0.685870	0.114312
$37$	7.54400	1.24023	0.620113	−	0.784513i	$-0.287087\pi$
$37$	7.54400	1.24023	0.620113	+	0.784513i	$0.287087\pi$
$38$	1.00000	0.162221
$39$	−0.522934	−0.0837364
$40$	−0.472260	−0.0746708
$41$	−5.51603	−0.861460	−0.430730	−	0.902481i	$-0.641744\pi$
$41$	−5.51603	−0.861460	−0.430730	+	0.902481i	$0.641744\pi$
$42$	8.87239	1.36904
$43$	0.252608	0.0385224	0.0192612	−	0.999814i	$-0.493869\pi$
$43$	0.252608	0.0385224	0.0192612	+	0.999814i	$0.493869\pi$
$44$	−0.111615	−0.0168266
$45$	0.323909	0.0482855
$46$	−5.62701	−0.829658
$47$	3.79423	0.553445	0.276722	−	0.960950i	$-0.410752\pi$
$47$	3.79423	0.553445	0.276722	+	0.960950i	$0.410752\pi$
$48$	−1.91986	−0.277108
$49$	14.3571	2.05101
$50$	4.77697	0.675566
$51$	−3.89079	−0.544819
$52$	0.272381	0.0377724
$53$	−2.47409	−0.339842	−0.169921	−	0.985458i	$-0.554351\pi$
$53$	−2.47409	−0.339842	−0.169921	+	0.985458i	$0.554351\pi$
$54$	−4.44281	−0.604590
$55$	−0.0527112	−0.00710757
$56$	−4.62137	−0.617557
$57$	1.91986	0.254292
$58$	4.88771	0.641788
$59$	−10.5518	−1.37373	−0.686865	−	0.726785i	$-0.741014\pi$
$59$	−10.5518	−1.37373	−0.686865	+	0.726785i	$0.741014\pi$
$60$	−0.906673	−0.117051
$61$	−7.76848	−0.994652	−0.497326	−	0.867564i	$-0.665685\pi$
$61$	−7.76848	−0.994652	−0.497326	+	0.867564i	$0.665685\pi$
$62$	8.39165	1.06574
$63$	3.16966	0.399340
$64$	1.00000	0.125000
$65$	0.128634	0.0159551
$66$	−0.214285	−0.0263767
$67$	−13.7548	−1.68042	−0.840209	−	0.542263i	$-0.817567\pi$
$67$	−13.7548	−1.68042	−0.840209	+	0.542263i	$0.817567\pi$
$68$	2.02660	0.245761
$69$	−10.8031	−1.30054
$70$	−2.18249	−0.260857
$71$	7.29402	0.865641	0.432820	−	0.901480i	$-0.357518\pi$
$71$	7.29402	0.865641	0.432820	+	0.901480i	$0.357518\pi$
$72$	−0.685870	−0.0808306
$73$	−9.98277	−1.16839	−0.584197	−	0.811612i	$-0.698591\pi$
$73$	−9.98277	−1.16839	−0.584197	+	0.811612i	$0.698591\pi$
$74$	−7.54400	−0.876972
$75$	9.17112	1.05899
$76$	−1.00000	−0.114708
$77$	−0.515814	−0.0587824
$78$	0.522934	0.0592106
$79$	−8.19692	−0.922225	−0.461113	−	0.887342i	$-0.652550\pi$
$79$	−8.19692	−0.922225	−0.461113	+	0.887342i	$0.652550\pi$
$80$	0.472260	0.0528002
$81$	−10.5872	−1.17635
$82$	5.51603	0.609144
$83$	4.34992	0.477465	0.238733	−	0.971085i	$-0.423268\pi$
$83$	4.34992	0.477465	0.238733	+	0.971085i	$0.423268\pi$
$84$	−8.87239	−0.968058
$85$	0.957080	0.103810
$86$	−0.252608	−0.0272394
$87$	9.38373	1.00604
$88$	0.111615	0.0118982
$89$	1.85112	0.196219	0.0981093	−	0.995176i	$-0.468721\pi$
$89$	1.85112	0.196219	0.0981093	+	0.995176i	$0.468721\pi$
$90$	−0.323909	−0.0341430
$91$	1.25877	0.131955
$92$	5.62701	0.586657
$93$	16.1108	1.67061
$94$	−3.79423	−0.391345
$95$	−0.472260	−0.0484528
$96$	1.91986	0.195945
$97$	−4.37494	−0.444208	−0.222104	−	0.975023i	$-0.571292\pi$
$97$	−4.37494	−0.444208	−0.222104	+	0.975023i	$0.571292\pi$
$98$	−14.3571	−1.45028
$99$	−0.0765533	−0.00769389
$100$	−4.77697	−0.477697
$101$	−9.21439	−0.916866	−0.458433	−	0.888729i	$-0.651589\pi$
$101$	−9.21439	−0.916866	−0.458433	+	0.888729i	$0.651589\pi$
$102$	3.89079	0.385245
$103$	−4.24953	−0.418719	−0.209360	−	0.977839i	$-0.567138\pi$
$103$	−4.24953	−0.418719	−0.209360	+	0.977839i	$0.567138\pi$
$104$	−0.272381	−0.0267091
$105$	−4.19007	−0.408909
$106$	2.47409	0.240305
$107$	4.84308	0.468198	0.234099	−	0.972213i	$-0.424786\pi$
$107$	4.84308	0.468198	0.234099	+	0.972213i	$0.424786\pi$
$108$	4.44281	0.427510
$109$	−8.35783	−0.800535	−0.400268	−	0.916398i	$-0.631083\pi$
$109$	−8.35783	−0.800535	−0.400268	+	0.916398i	$0.631083\pi$
$110$	0.0527112	0.00502581
$111$	−14.4834	−1.37471
$112$	4.62137	0.436678
$113$	−1.90512	−0.179219	−0.0896095	−	0.995977i	$-0.528562\pi$
$113$	−1.90512	−0.179219	−0.0896095	+	0.995977i	$0.528562\pi$
$114$	−1.91986	−0.179812
$115$	2.65741	0.247805
$116$	−4.88771	−0.453812
$117$	0.186818	0.0172713
$118$	10.5518	0.971374
$119$	9.36566	0.858548
$120$	0.906673	0.0827676
$121$	−10.9875	−0.998867
$122$	7.76848	0.703325
$123$	10.5900	0.954870
$124$	−8.39165	−0.753593
$125$	−4.61727	−0.412981
$126$	−3.16966	−0.282376
$127$	−13.6337	−1.20980	−0.604899	−	0.796302i	$-0.706787\pi$
$127$	−13.6337	−1.20980	−0.604899	+	0.796302i	$0.706787\pi$
$128$	−1.00000	−0.0883883
$129$	−0.484973	−0.0426995
$130$	−0.128634	−0.0112820
$131$	−9.39429	−0.820783	−0.410391	−	0.911909i	$-0.634608\pi$
$131$	−9.39429	−0.820783	−0.410391	+	0.911909i	$0.634608\pi$
$132$	0.214285	0.0186511
$133$	−4.62137	−0.400724
$134$	13.7548	1.18823
$135$	2.09816	0.180581
$136$	−2.02660	−0.173779
$137$	−16.8861	−1.44268	−0.721339	−	0.692582i	$-0.756473\pi$
$137$	−16.8861	−1.44268	−0.721339	+	0.692582i	$0.756473\pi$
$138$	10.8031	0.919620
$139$	16.6058	1.40849	0.704243	−	0.709959i	$-0.251286\pi$
$139$	16.6058	1.40849	0.704243	+	0.709959i	$0.251286\pi$
$140$	2.18249	0.184454
$141$	−7.28439	−0.613456
$142$	−7.29402	−0.612100
$143$	−0.0304018	−0.00254232
$144$	0.685870	0.0571558
$145$	−2.30827	−0.191691
$146$	9.98277	0.826180
$147$	−27.5636	−2.27341
$148$	7.54400	0.620113
$149$	2.75899	0.226026	0.113013	−	0.993594i	$-0.463950\pi$
$149$	2.75899	0.226026	0.113013	+	0.993594i	$0.463950\pi$
$150$	−9.17112	−0.748819
$151$	−16.5692	−1.34838	−0.674192	−	0.738556i	$-0.735508\pi$
$151$	−16.5692	−1.34838	−0.674192	+	0.738556i	$0.735508\pi$
$152$	1.00000	0.0811107
$153$	1.38998	0.112373
$154$	0.515814	0.0415654
$155$	−3.96304	−0.318319
$156$	−0.522934	−0.0418682
$157$	22.1872	1.77073	0.885367	−	0.464893i	$-0.153907\pi$
$157$	22.1872	1.77073	0.885367	+	0.464893i	$0.153907\pi$
$158$	8.19692	0.652112
$159$	4.74991	0.376692
$160$	−0.472260	−0.0373354
$161$	26.0045	2.04944
$162$	10.5872	0.831808
$163$	18.7445	1.46818	0.734090	−	0.679052i	$-0.237609\pi$
$163$	18.7445	1.46818	0.734090	+	0.679052i	$0.237609\pi$
$164$	−5.51603	−0.430730
$165$	0.101198	0.00787827
$166$	−4.34992	−0.337619
$167$	11.2702	0.872115	0.436057	−	0.899919i	$-0.356375\pi$
$167$	11.2702	0.872115	0.436057	+	0.899919i	$0.356375\pi$
$168$	8.87239	0.684520
$169$	−12.9258	−0.994293
$170$	−0.957080	−0.0734047
$171$	−0.685870	−0.0524498
$172$	0.252608	0.0192612
$173$	16.3680	1.24444	0.622218	−	0.782844i	$-0.286232\pi$
$173$	16.3680	1.24444	0.622218	+	0.782844i	$0.286232\pi$
$174$	−9.38373	−0.711378
$175$	−22.0762	−1.66880
$176$	−0.111615	−0.00841329
$177$	20.2580	1.52269
$178$	−1.85112	−0.138747
$179$	6.99012	0.522466	0.261233	−	0.965276i	$-0.415871\pi$
$179$	6.99012	0.522466	0.261233	+	0.965276i	$0.415871\pi$
$180$	0.323909	0.0241427
$181$	10.2038	0.758439	0.379219	−	0.925307i	$-0.376193\pi$
$181$	10.2038	0.758439	0.379219	+	0.925307i	$0.376193\pi$
$182$	−1.25877	−0.0933065
$183$	14.9144	1.10251
$184$	−5.62701	−0.414829
$185$	3.56272	0.261937
$186$	−16.1108	−1.18130
$187$	−0.226198	−0.0165413
$188$	3.79423	0.276722
$189$	20.5319	1.49347
$190$	0.472260	0.0342613
$191$	−11.5053	−0.832494	−0.416247	−	0.909252i	$-0.636655\pi$
$191$	−11.5053	−0.832494	−0.416247	+	0.909252i	$0.636655\pi$
$192$	−1.91986	−0.138554
$193$	6.94976	0.500254	0.250127	−	0.968213i	$-0.419528\pi$
$193$	6.94976	0.500254	0.250127	+	0.968213i	$0.419528\pi$
$194$	4.37494	0.314102
$195$	−0.246960	−0.0176852
$196$	14.3571	1.02550
$197$	−0.472969	−0.0336977	−0.0168488	−	0.999858i	$-0.505363\pi$
$197$	−0.472969	−0.0336977	−0.0168488	+	0.999858i	$0.505363\pi$
$198$	0.0765533	0.00544041
$199$	−2.12016	−0.150294	−0.0751472	−	0.997172i	$-0.523943\pi$
$199$	−2.12016	−0.150294	−0.0751472	+	0.997172i	$0.523943\pi$
$200$	4.77697	0.337783
$201$	26.4073	1.86263
$202$	9.21439	0.648322
$203$	−22.5879	−1.58536
$204$	−3.89079	−0.272410
$205$	−2.60500	−0.181941
$206$	4.24953	0.296079
$207$	3.85940	0.268247
$208$	0.272381	0.0188862
$209$	0.111615	0.00772056
$210$	4.19007	0.289142
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−2.47409	−0.169921
$213$	−14.0035	−0.959505
$214$	−4.84308	−0.331066
$215$	0.119297	0.00813596
$216$	−4.44281	−0.302295
$217$	−38.7809	−2.63262
$218$	8.35783	0.566064
$219$	19.1655	1.29509
$220$	−0.0527112	−0.00355379
$221$	0.552006	0.0371320
$222$	14.4834	0.972064
$223$	23.2965	1.56005	0.780025	−	0.625748i	$-0.215206\pi$
$223$	23.2965	1.56005	0.780025	+	0.625748i	$0.215206\pi$
$224$	−4.62137	−0.308778
$225$	−3.27638	−0.218425
$226$	1.90512	0.126727
$227$	−11.2543	−0.746972	−0.373486	−	0.927636i	$-0.621838\pi$
$227$	−11.2543	−0.746972	−0.373486	+	0.927636i	$0.621838\pi$
$228$	1.91986	0.127146
$229$	−18.2204	−1.20404	−0.602018	−	0.798483i	$-0.705636\pi$
$229$	−18.2204	−1.20404	−0.602018	+	0.798483i	$0.705636\pi$
$230$	−2.65741	−0.175224
$231$	0.990291	0.0651564
$232$	4.88771	0.320894
$233$	20.8797	1.36788	0.683938	−	0.729540i	$-0.260266\pi$
$233$	20.8797	1.36788	0.683938	+	0.729540i	$0.260266\pi$
$234$	−0.186818	−0.0122127
$235$	1.79186	0.116888
$236$	−10.5518	−0.686865
$237$	15.7370	1.02222
$238$	−9.36566	−0.607085
$239$	−6.35982	−0.411383	−0.205691	−	0.978617i	$-0.565944\pi$
$239$	−6.35982	−0.411383	−0.205691	+	0.978617i	$0.565944\pi$
$240$	−0.906673	−0.0585255
$241$	−27.5421	−1.77414	−0.887072	−	0.461631i	$-0.847265\pi$
$241$	−27.5421	−1.77414	−0.887072	+	0.461631i	$0.847265\pi$
$242$	10.9875	0.706306
$243$	6.99752	0.448891
$244$	−7.76848	−0.497326
$245$	6.78026	0.433175
$246$	−10.5900	−0.675195
$247$	−0.272381	−0.0173312
$248$	8.39165	0.532870
$249$	−8.35124	−0.529238
$250$	4.61727	0.292022
$251$	25.8059	1.62886	0.814428	−	0.580265i	$-0.197051\pi$
$251$	25.8059	1.62886	0.814428	+	0.580265i	$0.197051\pi$
$252$	3.16966	0.199670
$253$	−0.628058	−0.0394857
$254$	13.6337	0.855457
$255$	−1.83746	−0.115066
$256$	1.00000	0.0625000
$257$	−27.3503	−1.70606	−0.853032	−	0.521859i	$-0.825239\pi$
$257$	−27.3503	−1.70606	−0.853032	+	0.521859i	$0.825239\pi$
$258$	0.484973	0.0301931
$259$	34.8636	2.16632
$260$	0.128634	0.00797757
$261$	−3.35233	−0.207504
$262$	9.39429	0.580381
$263$	−20.0329	−1.23528	−0.617642	−	0.786459i	$-0.711912\pi$
$263$	−20.0329	−1.23528	−0.617642	+	0.786459i	$0.711912\pi$
$264$	−0.214285	−0.0131883
$265$	−1.16841	−0.0717750
$266$	4.62137	0.283354
$267$	−3.55390	−0.217495
$268$	−13.7548	−0.840209
$269$	−17.9291	−1.09316	−0.546579	−	0.837408i	$-0.684070\pi$
$269$	−17.9291	−1.09316	−0.546579	+	0.837408i	$0.684070\pi$
$270$	−2.09816	−0.127690
$271$	−29.8009	−1.81028	−0.905139	−	0.425116i	$-0.860233\pi$
$271$	−29.8009	−1.81028	−0.905139	+	0.425116i	$0.860233\pi$
$272$	2.02660	0.122880
$273$	−2.41667	−0.146264
$274$	16.8861	1.02013
$275$	0.533181	0.0321520
$276$	−10.8031	−0.650269
$277$	30.3358	1.82270	0.911351	−	0.411631i	$-0.135041\pi$
$277$	30.3358	1.82270	0.911351	+	0.411631i	$0.135041\pi$
$278$	−16.6058	−0.995950
$279$	−5.75558	−0.344578
$280$	−2.18249	−0.130429
$281$	8.78673	0.524173	0.262086	−	0.965044i	$-0.415589\pi$
$281$	8.78673	0.524173	0.262086	+	0.965044i	$0.415589\pi$
$282$	7.28439	0.433779
$283$	−1.62138	−0.0963808	−0.0481904	−	0.998838i	$-0.515345\pi$
$283$	−1.62138	−0.0963808	−0.0481904	+	0.998838i	$0.515345\pi$
$284$	7.29402	0.432820
$285$	0.906673	0.0537067
$286$	0.0304018	0.00179769
$287$	−25.4916	−1.50472
$288$	−0.685870	−0.0404153
$289$	−12.8929	−0.758406
$290$	2.30827	0.135546
$291$	8.39928	0.492375
$292$	−9.98277	−0.584197
$293$	32.3187	1.88808	0.944041	−	0.329829i	$-0.106991\pi$
$293$	32.3187	1.88808	0.944041	+	0.329829i	$0.106991\pi$
$294$	27.5636	1.60754
$295$	−4.98320	−0.290133
$296$	−7.54400	−0.438486
$297$	−0.495884	−0.0287741
$298$	−2.75899	−0.159824
$299$	1.53269	0.0886378
$300$	9.17112	0.529495
$301$	1.16740	0.0672876
$302$	16.5692	0.953452
$303$	17.6904	1.01628
$304$	−1.00000	−0.0573539
$305$	−3.66874	−0.210071
$306$	−1.38998	−0.0794600
$307$	26.3266	1.50254	0.751268	−	0.659997i	$-0.229443\pi$
$307$	26.3266	1.50254	0.751268	+	0.659997i	$0.229443\pi$
$308$	−0.515814	−0.0293912
$309$	8.15852	0.464122
$310$	3.96304	0.225085
$311$	22.1733	1.25733	0.628666	−	0.777676i	$-0.283601\pi$
$311$	22.1733	1.25733	0.628666	+	0.777676i	$0.283601\pi$
$312$	0.522934	0.0296053
$313$	−10.6795	−0.603640	−0.301820	−	0.953365i	$-0.597594\pi$
$313$	−10.6795	−0.603640	−0.301820	+	0.953365i	$0.597594\pi$
$314$	−22.1872	−1.25210
$315$	1.49690	0.0843409
$316$	−8.19692	−0.461113
$317$	9.60508	0.539475	0.269737	−	0.962934i	$-0.413063\pi$
$317$	9.60508	0.539475	0.269737	+	0.962934i	$0.413063\pi$
$318$	−4.74991	−0.266362
$319$	0.545541	0.0305444
$320$	0.472260	0.0264001
$321$	−9.29805	−0.518966
$322$	−26.0045	−1.44917
$323$	−2.02660	−0.112763
$324$	−10.5872	−0.588177
$325$	−1.30116	−0.0721751
$326$	−18.7445	−1.03816
$327$	16.0459	0.887339
$328$	5.51603	0.304572
$329$	17.5345	0.966710
$330$	−0.101198	−0.00557078
$331$	−2.66520	−0.146492	−0.0732462	−	0.997314i	$-0.523336\pi$
$331$	−2.66520	−0.146492	−0.0732462	+	0.997314i	$0.523336\pi$
$332$	4.34992	0.238733
$333$	5.17420	0.283544
$334$	−11.2702	−0.616678
$335$	−6.49584	−0.354906
$336$	−8.87239	−0.484029
$337$	−0.227011	−0.0123661	−0.00618304	−	0.999981i	$-0.501968\pi$
$337$	−0.227011	−0.0123661	−0.00618304	+	0.999981i	$0.501968\pi$
$338$	12.9258	0.703071
$339$	3.65757	0.198652
$340$	0.957080	0.0519049
$341$	0.936633	0.0507215
$342$	0.685870	0.0370876
$343$	33.9997	1.83581
$344$	−0.252608	−0.0136197
$345$	−5.10186	−0.274675
$346$	−16.3680	−0.879949
$347$	13.8514	0.743584	0.371792	−	0.928316i	$-0.378743\pi$
$347$	13.8514	0.743584	0.371792	+	0.928316i	$0.378743\pi$
$348$	9.38373	0.503020
$349$	−31.8668	−1.70579	−0.852896	−	0.522081i	$-0.825156\pi$
$349$	−31.8668	−1.70579	−0.852896	+	0.522081i	$0.825156\pi$
$350$	22.0762	1.18002
$351$	1.21014	0.0645923
$352$	0.111615	0.00594909
$353$	16.6465	0.886002	0.443001	−	0.896521i	$-0.353914\pi$
$353$	16.6465	0.886002	0.443001	+	0.896521i	$0.353914\pi$
$354$	−20.2580	−1.07670
$355$	3.44467	0.182824
$356$	1.85112	0.0981093
$357$	−17.9808	−0.951643
$358$	−6.99012	−0.369439
$359$	26.3584	1.39114	0.695571	−	0.718457i	$-0.255152\pi$
$359$	26.3584	1.39114	0.695571	+	0.718457i	$0.255152\pi$
$360$	−0.323909	−0.0170715
$361$	1.00000	0.0526316
$362$	−10.2038	−0.536297
$363$	21.0946	1.10718
$364$	1.25877	0.0659776
$365$	−4.71446	−0.246766
$366$	−14.9144	−0.779589
$367$	−25.7657	−1.34496	−0.672480	−	0.740116i	$-0.734771\pi$
$367$	−25.7657	−1.34496	−0.672480	+	0.740116i	$0.734771\pi$
$368$	5.62701	0.293328
$369$	−3.78328	−0.196950
$370$	−3.56272	−0.185217
$371$	−11.4337	−0.593607
$372$	16.1108	0.835307
$373$	28.1372	1.45689	0.728444	−	0.685105i	$-0.240244\pi$
$373$	28.1372	1.45689	0.728444	+	0.685105i	$0.240244\pi$
$374$	0.226198	0.0116964
$375$	8.86452	0.457762
$376$	−3.79423	−0.195672
$377$	−1.33132	−0.0685664
$378$	−20.5319	−1.05605
$379$	−13.5334	−0.695163	−0.347581	−	0.937650i	$-0.612997\pi$
$379$	−13.5334	−0.695163	−0.347581	+	0.937650i	$0.612997\pi$
$380$	−0.472260	−0.0242264
$381$	26.1749	1.34098
$382$	11.5053	0.588662
$383$	−24.5134	−1.25257	−0.626287	−	0.779592i	$-0.715426\pi$
$383$	−24.5134	−1.25257	−0.626287	+	0.779592i	$0.715426\pi$
$384$	1.91986	0.0979725
$385$	−0.243598	−0.0124149
$386$	−6.94976	−0.353733
$387$	0.173256	0.00880712
$388$	−4.37494	−0.222104
$389$	16.4578	0.834444	0.417222	−	0.908804i	$-0.363004\pi$
$389$	16.4578	0.834444	0.417222	+	0.908804i	$0.363004\pi$
$390$	0.246960	0.0125053
$391$	11.4037	0.576709
$392$	−14.3571	−0.725141
$393$	18.0357	0.909783
$394$	0.472969	0.0238278
$395$	−3.87107	−0.194775
$396$	−0.0765533	−0.00384695
$397$	5.94014	0.298127	0.149063	−	0.988828i	$-0.452374\pi$
$397$	5.94014	0.298127	0.149063	+	0.988828i	$0.452374\pi$
$398$	2.12016	0.106274
$399$	8.87239	0.444175
$400$	−4.77697	−0.238849
$401$	28.2705	1.41176	0.705880	−	0.708332i	$-0.250552\pi$
$401$	28.2705	1.41176	0.705880	+	0.708332i	$0.250552\pi$
$402$	−26.4073	−1.31708
$403$	−2.28573	−0.113860
$404$	−9.21439	−0.458433
$405$	−4.99990	−0.248447
$406$	22.5879	1.12102
$407$	−0.842022	−0.0417375
$408$	3.89079	0.192623
$409$	−8.18671	−0.404807	−0.202403	−	0.979302i	$-0.564875\pi$
$409$	−8.18671	−0.404807	−0.202403	+	0.979302i	$0.564875\pi$
$410$	2.60500	0.128652
$411$	32.4190	1.59911
$412$	−4.24953	−0.209360
$413$	−48.7639	−2.39951
$414$	−3.85940	−0.189679
$415$	2.05429	0.100841
$416$	−0.272381	−0.0133546
$417$	−31.8809	−1.56121
$418$	−0.111615	−0.00545926
$419$	21.3479	1.04291	0.521456	−	0.853278i	$-0.325389\pi$
$419$	21.3479	1.04291	0.521456	+	0.853278i	$0.325389\pi$
$420$	−4.19007	−0.204455
$421$	12.7248	0.620167	0.310084	−	0.950709i	$-0.399643\pi$
$421$	12.7248	0.620167	0.310084	+	0.950709i	$0.399643\pi$
$422$	1.00000	0.0486792
$423$	2.60235	0.126530
$424$	2.47409	0.120152
$425$	−9.68099	−0.469597
$426$	14.0035	0.678472
$427$	−35.9010	−1.73737
$428$	4.84308	0.234099
$429$	0.0583672	0.00281799
$430$	−0.119297	−0.00575300
$431$	−29.0466	−1.39913	−0.699564	−	0.714570i	$-0.746622\pi$
$431$	−29.0466	−1.39913	−0.699564	+	0.714570i	$0.746622\pi$
$432$	4.44281	0.213755
$433$	−26.0853	−1.25358	−0.626791	−	0.779188i	$-0.715632\pi$
$433$	−26.0853	−1.25358	−0.626791	+	0.779188i	$0.715632\pi$
$434$	38.7809	1.86154
$435$	4.43155	0.212477
$436$	−8.35783	−0.400268
$437$	−5.62701	−0.269177
$438$	−19.1655	−0.915765
$439$	9.67726	0.461870	0.230935	−	0.972969i	$-0.425821\pi$
$439$	9.67726	0.461870	0.230935	+	0.972969i	$0.425821\pi$
$440$	0.0527112	0.00251291
$441$	9.84708	0.468909
$442$	−0.552006	−0.0262563
$443$	−36.4375	−1.73120	−0.865599	−	0.500738i	$-0.833062\pi$
$443$	−36.4375	−1.73120	−0.865599	+	0.500738i	$0.833062\pi$
$444$	−14.4834	−0.687353
$445$	0.874210	0.0414415
$446$	−23.2965	−1.10312
$447$	−5.29689	−0.250534
$448$	4.62137	0.218339
$449$	41.2136	1.94499	0.972496	−	0.232920i	$-0.0748282\pi$
$449$	41.2136	1.94499	0.972496	+	0.232920i	$0.0748282\pi$
$450$	3.27638	0.154450
$451$	0.615671	0.0289908
$452$	−1.90512	−0.0896095
$453$	31.8106	1.49459
$454$	11.2543	0.528189
$455$	0.594468	0.0278691
$456$	−1.91986	−0.0899058
$457$	−25.3327	−1.18501	−0.592507	−	0.805565i	$-0.701862\pi$
$457$	−25.3327	−1.18501	−0.592507	+	0.805565i	$0.701862\pi$
$458$	18.2204	0.851382
$459$	9.00379	0.420261
$460$	2.65741	0.123902
$461$	−24.6118	−1.14629	−0.573143	−	0.819456i	$-0.694276\pi$
$461$	−24.6118	−1.14629	−0.573143	+	0.819456i	$0.694276\pi$
$462$	−0.990291	−0.0460725
$463$	14.9610	0.695295	0.347648	−	0.937625i	$-0.386981\pi$
$463$	14.9610	0.695295	0.347648	+	0.937625i	$0.386981\pi$
$464$	−4.88771	−0.226906
$465$	7.60849	0.352835
$466$	−20.8797	−0.967235
$467$	−12.6145	−0.583730	−0.291865	−	0.956460i	$-0.594276\pi$
$467$	−12.6145	−0.583730	−0.291865	+	0.956460i	$0.594276\pi$
$468$	0.186818	0.00863566
$469$	−63.5661	−2.93521
$470$	−1.79186	−0.0826523
$471$	−42.5964	−1.96274
$472$	10.5518	0.485687
$473$	−0.0281948	−0.00129640
$474$	−15.7370	−0.722822
$475$	4.77697	0.219182
$476$	9.36566	0.429274
$477$	−1.69690	−0.0776959
$478$	6.35982	0.290891
$479$	−6.67518	−0.304997	−0.152498	−	0.988304i	$-0.548732\pi$
$479$	−6.67518	−0.304997	−0.152498	+	0.988304i	$0.548732\pi$
$480$	0.906673	0.0413838
$481$	2.05484	0.0936927
$482$	27.5421	1.25451
$483$	−49.9251	−2.27167
$484$	−10.9875	−0.499434
$485$	−2.06611	−0.0938171
$486$	−6.99752	−0.317414
$487$	−26.2374	−1.18893	−0.594465	−	0.804121i	$-0.702636\pi$
$487$	−26.2374	−1.18893	−0.594465	+	0.804121i	$0.702636\pi$
$488$	7.76848	0.351663
$489$	−35.9868	−1.62738
$490$	−6.78026	−0.306301
$491$	−22.9290	−1.03477	−0.517385	−	0.855753i	$-0.673095\pi$
$491$	−22.9290	−1.03477	−0.517385	+	0.855753i	$0.673095\pi$
$492$	10.5900	0.477435
$493$	−9.90541	−0.446117
$494$	0.272381	0.0122550
$495$	−0.0361530	−0.00162496
$496$	−8.39165	−0.376796
$497$	33.7084	1.51203
$498$	8.35124	0.374228
$499$	−16.2548	−0.727666	−0.363833	−	0.931464i	$-0.618532\pi$
$499$	−16.2548	−0.727666	−0.363833	+	0.931464i	$0.618532\pi$
$500$	−4.61727	−0.206490
$501$	−21.6372	−0.966680
$502$	−25.8059	−1.15177
$503$	24.5006	1.09243	0.546214	−	0.837646i	$-0.316069\pi$
$503$	24.5006	1.09243	0.546214	+	0.837646i	$0.316069\pi$
$504$	−3.16966	−0.141188
$505$	−4.35158	−0.193643
$506$	0.628058	0.0279206
$507$	24.8158	1.10211
$508$	−13.6337	−0.604899
$509$	19.8209	0.878546	0.439273	−	0.898354i	$-0.355236\pi$
$509$	19.8209	0.878546	0.439273	+	0.898354i	$0.355236\pi$
$510$	1.83746	0.0813641
$511$	−46.1341	−2.04085
$512$	−1.00000	−0.0441942
$513$	−4.44281	−0.196155
$514$	27.3503	1.20637
$515$	−2.00688	−0.0884338
$516$	−0.484973	−0.0213497
$517$	−0.423492	−0.0186252
$518$	−34.8636	−1.53182
$519$	−31.4243	−1.37937
$520$	−0.128634	−0.00564100
$521$	−2.52355	−0.110559	−0.0552794	−	0.998471i	$-0.517605\pi$
$521$	−2.52355	−0.110559	−0.0552794	+	0.998471i	$0.517605\pi$
$522$	3.35233	0.146728
$523$	17.4823	0.764449	0.382224	−	0.924070i	$-0.375158\pi$
$523$	17.4823	0.764449	0.382224	+	0.924070i	$0.375158\pi$
$524$	−9.39429	−0.410391
$525$	42.3832	1.84975
$526$	20.0329	0.873478
$527$	−17.0065	−0.740815
$528$	0.214285	0.00932556
$529$	8.66327	0.376664
$530$	1.16841	0.0507526
$531$	−7.23718	−0.314067
$532$	−4.62137	−0.200362
$533$	−1.50246	−0.0650789
$534$	3.55390	0.153792
$535$	2.28719	0.0988839
$536$	13.7548	0.594117
$537$	−13.4201	−0.579118
$538$	17.9291	0.772979
$539$	−1.60246	−0.0690229
$540$	2.09816	0.0902904
$541$	8.02592	0.345061	0.172531	−	0.985004i	$-0.444806\pi$
$541$	8.02592	0.345061	0.172531	+	0.985004i	$0.444806\pi$
$542$	29.8009	1.28006
$543$	−19.5898	−0.840679
$544$	−2.02660	−0.0868896
$545$	−3.94707	−0.169074
$546$	2.41667	0.103424
$547$	−40.5232	−1.73265	−0.866324	−	0.499483i	$-0.833523\pi$
$547$	−40.5232	−1.73265	−0.866324	+	0.499483i	$0.833523\pi$
$548$	−16.8861	−0.721339
$549$	−5.32817	−0.227401
$550$	−0.533181	−0.0227349
$551$	4.88771	0.208223
$552$	10.8031	0.459810
$553$	−37.8810	−1.61086
$554$	−30.3358	−1.28884
$555$	−6.83994	−0.290339
$556$	16.6058	0.704243
$557$	30.5384	1.29395	0.646977	−	0.762510i	$-0.276033\pi$
$557$	30.5384	1.29395	0.646977	+	0.762510i	$0.276033\pi$
$558$	5.75558	0.243653
$559$	0.0688057	0.00291017
$560$	2.18249	0.0922269
$561$	0.434270	0.0183349
$562$	−8.78673	−0.370646
$563$	−31.7971	−1.34009	−0.670044	−	0.742321i	$-0.733725\pi$
$563$	−31.7971	−1.34009	−0.670044	+	0.742321i	$0.733725\pi$
$564$	−7.28439	−0.306728
$565$	−0.899713	−0.0378512
$566$	1.62138	0.0681515
$567$	−48.9273	−2.05476
$568$	−7.29402	−0.306050
$569$	−8.51692	−0.357048	−0.178524	−	0.983936i	$-0.557132\pi$
$569$	−8.51692	−0.357048	−0.178524	+	0.983936i	$0.557132\pi$
$570$	−0.906673	−0.0379764
$571$	24.6385	1.03109	0.515544	−	0.856863i	$-0.327590\pi$
$571$	24.6385	1.03109	0.515544	+	0.856863i	$0.327590\pi$
$572$	−0.0304018	−0.00127116
$573$	22.0886	0.922764
$574$	25.4916	1.06400
$575$	−26.8801	−1.12098
$576$	0.685870	0.0285779
$577$	13.6248	0.567208	0.283604	−	0.958942i	$-0.408470\pi$
$577$	13.6248	0.567208	0.283604	+	0.958942i	$0.408470\pi$
$578$	12.8929	0.536274
$579$	−13.3426	−0.554498
$580$	−2.30827	−0.0958456
$581$	20.1026	0.833995
$582$	−8.39928	−0.348161
$583$	0.276145	0.0114368
$584$	9.98277	0.413090
$585$	0.0882266	0.00364772
$586$	−32.3187	−1.33508
$587$	−31.3795	−1.29517	−0.647586	−	0.761992i	$-0.724221\pi$
$587$	−31.3795	−1.29517	−0.647586	+	0.761992i	$0.724221\pi$
$588$	−27.5636	−1.13670
$589$	8.39165	0.345772
$590$	4.98320	0.205155
$591$	0.908035	0.0373516
$592$	7.54400	0.310056
$593$	36.9806	1.51861	0.759305	−	0.650735i	$-0.225539\pi$
$593$	36.9806	1.51861	0.759305	+	0.650735i	$0.225539\pi$
$594$	0.495884	0.0203463
$595$	4.42302	0.181326
$596$	2.75899	0.113013
$597$	4.07042	0.166591
$598$	−1.53269	−0.0626764
$599$	−32.6016	−1.33207	−0.666034	−	0.745922i	$-0.732009\pi$
$599$	−32.6016	−1.33207	−0.666034	+	0.745922i	$0.732009\pi$
$600$	−9.17112	−0.374410
$601$	−22.7501	−0.927997	−0.463999	−	0.885836i	$-0.653586\pi$
$601$	−22.7501	−0.927997	−0.463999	+	0.885836i	$0.653586\pi$
$602$	−1.16740	−0.0475795
$603$	−9.43401	−0.384183
$604$	−16.5692	−0.674192
$605$	−5.18897	−0.210962
$606$	−17.6904	−0.718622
$607$	−25.7053	−1.04335	−0.521673	−	0.853145i	$-0.674692\pi$
$607$	−25.7053	−1.04335	−0.521673	+	0.853145i	$0.674692\pi$
$608$	1.00000	0.0405554
$609$	43.3657	1.75727
$610$	3.66874	0.148543
$611$	1.03348	0.0418099
$612$	1.38998	0.0561867
$613$	−30.0177	−1.21240	−0.606202	−	0.795311i	$-0.707308\pi$
$613$	−30.0177	−1.21240	−0.606202	+	0.795311i	$0.707308\pi$
$614$	−26.3266	−1.06245
$615$	5.00124	0.201669
$616$	0.515814	0.0207827
$617$	−28.4706	−1.14618	−0.573092	−	0.819491i	$-0.694256\pi$
$617$	−28.4706	−1.14618	−0.573092	+	0.819491i	$0.694256\pi$
$618$	−8.15852	−0.328184
$619$	−9.44005	−0.379428	−0.189714	−	0.981839i	$-0.560756\pi$
$619$	−9.44005	−0.379428	−0.189714	+	0.981839i	$0.560756\pi$
$620$	−3.96304	−0.159159
$621$	24.9997	1.00321
$622$	−22.1733	−0.889068
$623$	8.55472	0.342738
$624$	−0.522934	−0.0209341
$625$	21.7043	0.868172
$626$	10.6795	0.426838
$627$	−0.214285	−0.00855772
$628$	22.1872	0.885367
$629$	15.2886	0.609598
$630$	−1.49690	−0.0596380
$631$	−19.1209	−0.761189	−0.380595	−	0.924742i	$-0.624281\pi$
$631$	−19.1209	−0.761189	−0.380595	+	0.924742i	$0.624281\pi$
$632$	8.19692	0.326056
$633$	1.91986	0.0763077
$634$	−9.60508	−0.381466
$635$	−6.43866	−0.255511
$636$	4.74991	0.188346
$637$	3.91059	0.154943
$638$	−0.545541	−0.0215982
$639$	5.00275	0.197906
$640$	−0.472260	−0.0186677
$641$	−5.39138	−0.212947	−0.106473	−	0.994316i	$-0.533956\pi$
$641$	−5.39138	−0.212947	−0.106473	+	0.994316i	$0.533956\pi$
$642$	9.29805	0.366965
$643$	−36.3332	−1.43284	−0.716421	−	0.697668i	$-0.754221\pi$
$643$	−36.3332	−1.43284	−0.716421	+	0.697668i	$0.754221\pi$
$644$	26.0045	1.02472
$645$	−0.229033	−0.00901817
$646$	2.02660	0.0797354
$647$	0.622710	0.0244813	0.0122406	−	0.999925i	$-0.496104\pi$
$647$	0.622710	0.0244813	0.0122406	+	0.999925i	$0.496104\pi$
$648$	10.5872	0.415904
$649$	1.17774	0.0462303
$650$	1.30116	0.0510355
$651$	74.4540	2.91808
$652$	18.7445	0.734090
$653$	−37.2732	−1.45861	−0.729306	−	0.684188i	$-0.760157\pi$
$653$	−37.2732	−1.45861	−0.729306	+	0.684188i	$0.760157\pi$
$654$	−16.0459	−0.627444
$655$	−4.43654	−0.173350
$656$	−5.51603	−0.215365
$657$	−6.84688	−0.267122
$658$	−17.5345	−0.683567
$659$	−38.7745	−1.51044	−0.755221	−	0.655470i	$-0.772470\pi$
$659$	−38.7745	−1.51044	−0.755221	+	0.655470i	$0.772470\pi$
$660$	0.101198	0.00393913
$661$	−12.6203	−0.490872	−0.245436	−	0.969413i	$-0.578931\pi$
$661$	−12.6203	−0.490872	−0.245436	+	0.969413i	$0.578931\pi$
$662$	2.66520	0.103586
$663$	−1.05978	−0.0411583
$664$	−4.34992	−0.168809
$665$	−2.18249	−0.0846332
$666$	−5.17420	−0.200496
$667$	−27.5032	−1.06493
$668$	11.2702	0.436057
$669$	−44.7261	−1.72921
$670$	6.49584	0.250956
$671$	0.867078	0.0334732
$672$	8.87239	0.342260
$673$	0.576782	0.0222333	0.0111166	−	0.999938i	$-0.496461\pi$
$673$	0.576782	0.0222333	0.0111166	+	0.999938i	$0.496461\pi$
$674$	0.227011	0.00874414
$675$	−21.2232	−0.816880
$676$	−12.9258	−0.497146
$677$	1.72191	0.0661782	0.0330891	−	0.999452i	$-0.489465\pi$
$677$	1.72191	0.0661782	0.0330891	+	0.999452i	$0.489465\pi$
$678$	−3.65757	−0.140468
$679$	−20.2182	−0.775904
$680$	−0.957080	−0.0367023
$681$	21.6066	0.827968
$682$	−0.936633	−0.0358655
$683$	−25.2785	−0.967254	−0.483627	−	0.875274i	$-0.660681\pi$
$683$	−25.2785	−0.967254	−0.483627	+	0.875274i	$0.660681\pi$
$684$	−0.685870	−0.0262249
$685$	−7.97463	−0.304695
$686$	−33.9997	−1.29812
$687$	34.9806	1.33459
$688$	0.252608	0.00963060
$689$	−0.673895	−0.0256734
$690$	5.10186	0.194225
$691$	−6.74199	−0.256477	−0.128239	−	0.991743i	$-0.540932\pi$
$691$	−6.74199	−0.256477	−0.128239	+	0.991743i	$0.540932\pi$
$692$	16.3680	0.622218
$693$	−0.353781	−0.0134390
$694$	−13.8514	−0.525794
$695$	7.84225	0.297474
$696$	−9.38373	−0.355689
$697$	−11.1788	−0.423426
$698$	31.8668	1.20618
$699$	−40.0862	−1.51620
$700$	−22.0762	−0.834400
$701$	−1.00611	−0.0380003	−0.0190001	−	0.999819i	$-0.506048\pi$
$701$	−1.00611	−0.0380003	−0.0190001	+	0.999819i	$0.506048\pi$
$702$	−1.21014	−0.0456737
$703$	−7.54400	−0.284527
$704$	−0.111615	−0.00420664
$705$	−3.44012	−0.129563
$706$	−16.6465	−0.626498
$707$	−42.5831	−1.60150
$708$	20.2580	0.761344
$709$	9.38550	0.352480	0.176240	−	0.984347i	$-0.443607\pi$
$709$	9.38550	0.352480	0.176240	+	0.984347i	$0.443607\pi$
$710$	−3.44467	−0.129276
$711$	−5.62202	−0.210842
$712$	−1.85112	−0.0693737
$713$	−47.2199	−1.76840
$714$	17.9808	0.672913
$715$	−0.0143575	−0.000536941 0
$716$	6.99012	0.261233
$717$	12.2100	0.455990
$718$	−26.3584	−0.983686
$719$	33.4334	1.24685	0.623427	−	0.781881i	$-0.285740\pi$
$719$	33.4334	1.24685	0.623427	+	0.781881i	$0.285740\pi$
$720$	0.323909	0.0120714
$721$	−19.6387	−0.731382
$722$	−1.00000	−0.0372161
$723$	52.8771	1.96652
$724$	10.2038	0.379219
$725$	23.3484	0.867139
$726$	−21.0946	−0.782893
$727$	−11.8978	−0.441264	−0.220632	−	0.975357i	$-0.570812\pi$
$727$	−11.8978	−0.441264	−0.220632	+	0.975357i	$0.570812\pi$
$728$	−1.25877	−0.0466532
$729$	18.3273	0.678789
$730$	4.71446	0.174490
$731$	0.511935	0.0189346
$732$	14.9144	0.551253
$733$	−17.3766	−0.641818	−0.320909	−	0.947110i	$-0.603988\pi$
$733$	−17.3766	−0.641818	−0.320909	+	0.947110i	$0.603988\pi$
$734$	25.7657	0.951030
$735$	−13.0172	−0.480145
$736$	−5.62701	−0.207414
$737$	1.53524	0.0565513
$738$	3.78328	0.139265
$739$	−23.7805	−0.874780	−0.437390	−	0.899272i	$-0.644097\pi$
$739$	−23.7805	−0.874780	−0.437390	+	0.899272i	$0.644097\pi$
$740$	3.56272	0.130968
$741$	0.522934	0.0192105
$742$	11.4337	0.419744
$743$	−21.9105	−0.803817	−0.401909	−	0.915680i	$-0.631653\pi$
$743$	−21.9105	−0.803817	−0.401909	+	0.915680i	$0.631653\pi$
$744$	−16.1108	−0.590651
$745$	1.30296	0.0477368
$746$	−28.1372	−1.03018
$747$	2.98348	0.109160
$748$	−0.226198	−0.00827063
$749$	22.3817	0.817808
$750$	−8.86452	−0.323686
$751$	−21.3312	−0.778387	−0.389194	−	0.921156i	$-0.627246\pi$
$751$	−21.3312	−0.778387	−0.389194	+	0.921156i	$0.627246\pi$
$752$	3.79423	0.138361
$753$	−49.5438	−1.80548
$754$	1.33132	0.0484838
$755$	−7.82497	−0.284780
$756$	20.5319	0.746737
$757$	−9.54262	−0.346832	−0.173416	−	0.984849i	$-0.555481\pi$
$757$	−9.54262	−0.346832	−0.173416	+	0.984849i	$0.555481\pi$
$758$	13.5334	0.491554
$759$	1.20578	0.0437672
$760$	0.472260	0.0171307
$761$	49.9803	1.81178	0.905892	−	0.423508i	$-0.139201\pi$
$761$	49.9803	1.81178	0.905892	+	0.423508i	$0.139201\pi$
$762$	−26.1749	−0.948216
$763$	−38.6246	−1.39831
$764$	−11.5053	−0.416247
$765$	0.656432	0.0237334
$766$	24.5134	0.885704
$767$	−2.87412	−0.103778
$768$	−1.91986	−0.0692771
$769$	27.8025	1.00258	0.501291	−	0.865279i	$-0.332859\pi$
$769$	27.8025	1.00258	0.501291	+	0.865279i	$0.332859\pi$
$770$	0.243598	0.00877866
$771$	52.5088	1.89106
$772$	6.94976	0.250127
$773$	−26.8412	−0.965409	−0.482705	−	0.875783i	$-0.660346\pi$
$773$	−26.8412	−0.965409	−0.482705	+	0.875783i	$0.660346\pi$
$774$	−0.173256	−0.00622757
$775$	40.0867	1.43996
$776$	4.37494	0.157051
$777$	−66.9333	−2.40122
$778$	−16.4578	−0.590041
$779$	5.51603	0.197632
$780$	−0.246960	−0.00884260
$781$	−0.814121	−0.0291315
$782$	−11.4037	−0.407795
$783$	−21.7152	−0.776036
$784$	14.3571	0.512752
$785$	10.4781	0.373981
$786$	−18.0357	−0.643313
$787$	50.9265	1.81533	0.907667	−	0.419692i	$-0.137862\pi$
$787$	50.9265	1.81533	0.907667	+	0.419692i	$0.137862\pi$
$788$	−0.472969	−0.0168488
$789$	38.4605	1.36923
$790$	3.87107	0.137727
$791$	−8.80428	−0.313044
$792$	0.0765533	0.00272020
$793$	−2.11599	−0.0751409
$794$	−5.94014	−0.210808
$795$	2.24319	0.0795578
$796$	−2.12016	−0.0751472
$797$	39.2707	1.39104	0.695519	−	0.718507i	$-0.255174\pi$
$797$	39.2707	1.39104	0.695519	+	0.718507i	$0.255174\pi$
$798$	−8.87239	−0.314079
$799$	7.68937	0.272030
$800$	4.77697	0.168891
$801$	1.26963	0.0448601
$802$	−28.2705	−0.998265
$803$	1.11423	0.0393201
$804$	26.4073	0.931315
$805$	12.2809	0.432844
$806$	2.28573	0.0805113
$807$	34.4214	1.21169
$808$	9.21439	0.324161
$809$	23.1539	0.814049	0.407025	−	0.913417i	$-0.366566\pi$
$809$	23.1539	0.814049	0.407025	+	0.913417i	$0.366566\pi$
$810$	4.99990	0.175679
$811$	27.1373	0.952918	0.476459	−	0.879197i	$-0.341920\pi$
$811$	27.1373	0.952918	0.476459	+	0.879197i	$0.341920\pi$
$812$	−22.5879	−0.792680
$813$	57.2137	2.00657
$814$	0.842022	0.0295129
$815$	8.85226	0.310081
$816$	−3.89079	−0.136205
$817$	−0.252608	−0.00883764
$818$	8.18671	0.286242
$819$	0.863355	0.0301681
$820$	−2.60500	−0.0909705
$821$	−17.1421	−0.598265	−0.299132	−	0.954212i	$-0.596697\pi$
$821$	−17.1421	−0.598265	−0.299132	+	0.954212i	$0.596697\pi$
$822$	−32.4190	−1.13074
$823$	−45.7326	−1.59414	−0.797069	−	0.603888i	$-0.793617\pi$
$823$	−45.7326	−1.59414	−0.797069	+	0.603888i	$0.793617\pi$
$824$	4.24953	0.148040
$825$	−1.02363	−0.0356384
$826$	48.7639	1.69671
$827$	16.0868	0.559393	0.279697	−	0.960088i	$-0.409766\pi$
$827$	16.0868	0.559393	0.279697	+	0.960088i	$0.409766\pi$
$828$	3.85940	0.134123
$829$	−31.4246	−1.09142	−0.545711	−	0.837973i	$-0.683740\pi$
$829$	−31.4246	−1.09142	−0.545711	+	0.837973i	$0.683740\pi$
$830$	−2.05429	−0.0713054
$831$	−58.2405	−2.02034
$832$	0.272381	0.00944311
$833$	29.0960	1.00812
$834$	31.8809	1.10394
$835$	5.32246	0.184191
$836$	0.111615	0.00386028
$837$	−37.2825	−1.28867
$838$	−21.3479	−0.737450
$839$	−8.18920	−0.282722	−0.141361	−	0.989958i	$-0.545148\pi$
$839$	−8.18920	−0.282722	−0.141361	+	0.989958i	$0.545148\pi$
$840$	4.19007	0.144571
$841$	−5.11031	−0.176218
$842$	−12.7248	−0.438525
$843$	−16.8693	−0.581010
$844$	−1.00000	−0.0344214
$845$	−6.10434	−0.209996
$846$	−2.60235	−0.0894705
$847$	−50.7775	−1.74474
$848$	−2.47409	−0.0849606
$849$	3.11282	0.106832
$850$	9.68099	0.332055
$851$	42.4502	1.45517
$852$	−14.0035	−0.479752
$853$	6.06450	0.207645	0.103822	−	0.994596i	$-0.466893\pi$
$853$	6.06450	0.207645	0.103822	+	0.994596i	$0.466893\pi$
$854$	35.9010	1.22851
$855$	−0.323909	−0.0110774
$856$	−4.84308	−0.165533
$857$	0.554792	0.0189513	0.00947567	−	0.999955i	$-0.496984\pi$
$857$	0.554792	0.0189513	0.00947567	+	0.999955i	$0.496984\pi$
$858$	−0.0583672	−0.00199262
$859$	−51.2323	−1.74803	−0.874013	−	0.485903i	$-0.838491\pi$
$859$	−51.2323	−1.74803	−0.874013	+	0.485903i	$0.838491\pi$
$860$	0.119297	0.00406798
$861$	48.9404	1.66788
$862$	29.0466	0.989332
$863$	−12.4317	−0.423179	−0.211590	−	0.977359i	$-0.567864\pi$
$863$	−12.4317	−0.423179	−0.211590	+	0.977359i	$0.567864\pi$
$864$	−4.44281	−0.151147
$865$	7.72994	0.262826
$866$	26.0853	0.886416
$867$	24.7526	0.840642
$868$	−38.7809	−1.31631
$869$	0.914898	0.0310358
$870$	−4.43155	−0.150244
$871$	−3.74655	−0.126947
$872$	8.35783	0.283032
$873$	−3.00064	−0.101556
$874$	5.62701	0.190337
$875$	−21.3381	−0.721360
$876$	19.1655	0.647543
$877$	−45.6458	−1.54135	−0.770675	−	0.637229i	$-0.780081\pi$
$877$	−45.6458	−1.54135	−0.770675	+	0.637229i	$0.780081\pi$
$878$	−9.67726	−0.326592
$879$	−62.0475	−2.09281
$880$	−0.0527112	−0.00177689
$881$	−35.1750	−1.18507	−0.592537	−	0.805543i	$-0.701874\pi$
$881$	−35.1750	−1.18507	−0.592537	+	0.805543i	$0.701874\pi$
$882$	−9.84708	−0.331569
$883$	24.5711	0.826884	0.413442	−	0.910530i	$-0.364326\pi$
$883$	24.5711	0.826884	0.413442	+	0.910530i	$0.364326\pi$
$884$	0.552006	0.0185660
$885$	9.56705	0.321593
$886$	36.4375	1.22414
$887$	21.0111	0.705485	0.352743	−	0.935720i	$-0.385249\pi$
$887$	21.0111	0.705485	0.352743	+	0.935720i	$0.385249\pi$
$888$	14.4834	0.486032
$889$	−63.0066	−2.11317
$890$	−0.874210	−0.0293036
$891$	1.18169	0.0395880
$892$	23.2965	0.780025
$893$	−3.79423	−0.126969
$894$	5.29689	0.177154
$895$	3.30115	0.110345
$896$	−4.62137	−0.154389
$897$	−2.94256	−0.0982491
$898$	−41.2136	−1.37532
$899$	41.0159	1.36796
$900$	−3.27638	−0.109213
$901$	−5.01398	−0.167040
$902$	−0.615671	−0.0204996
$903$	−2.24124	−0.0745838
$904$	1.90512	0.0633635
$905$	4.81882	0.160183
$906$	−31.8106	−1.05684
$907$	−29.0385	−0.964209	−0.482104	−	0.876114i	$-0.660127\pi$
$907$	−29.0385	−0.964209	−0.482104	+	0.876114i	$0.660127\pi$
$908$	−11.2543	−0.373486
$909$	−6.31988	−0.209617
$910$	−0.594468	−0.0197064
$911$	49.5077	1.64026	0.820132	−	0.572175i	$-0.193900\pi$
$911$	49.5077	1.64026	0.820132	+	0.572175i	$0.193900\pi$
$912$	1.91986	0.0635730
$913$	−0.485515	−0.0160682
$914$	25.3327	0.837932
$915$	7.04348	0.232850
$916$	−18.2204	−0.602018
$917$	−43.4145	−1.43367
$918$	−9.00379	−0.297169
$919$	−31.6305	−1.04339	−0.521697	−	0.853131i	$-0.674701\pi$
$919$	−31.6305	−1.04339	−0.521697	+	0.853131i	$0.674701\pi$
$920$	−2.65741	−0.0876122
$921$	−50.5434	−1.66546
$922$	24.6118	0.810546
$923$	1.98675	0.0653947
$924$	0.990291	0.0325782
$925$	−36.0374	−1.18490
$926$	−14.9610	−0.491648
$927$	−2.91463	−0.0957290
$928$	4.88771	0.160447
$929$	22.1704	0.727386	0.363693	−	0.931519i	$-0.381516\pi$
$929$	22.1704	0.727386	0.363693	+	0.931519i	$0.381516\pi$
$930$	−7.60849	−0.249492
$931$	−14.3571	−0.470534
$932$	20.8797	0.683938
$933$	−42.5696	−1.39367
$934$	12.6145	0.412759
$935$	−0.106824	−0.00349353
$936$	−0.186818	−0.00610634
$937$	−41.9507	−1.37047	−0.685234	−	0.728323i	$-0.740300\pi$
$937$	−41.9507	−1.37047	−0.685234	+	0.728323i	$0.740300\pi$
$938$	63.5661	2.07551
$939$	20.5031	0.669094
$940$	1.79186	0.0584440
$941$	16.3507	0.533017	0.266509	−	0.963833i	$-0.414130\pi$
$941$	16.3507	0.533017	0.266509	+	0.963833i	$0.414130\pi$
$942$	42.5964	1.38787
$943$	−31.0388	−1.01076
$944$	−10.5518	−0.343433
$945$	9.69637	0.315423
$946$	0.0281948	0.000916693 0
$947$	−8.77637	−0.285194	−0.142597	−	0.989781i	$-0.545545\pi$
$947$	−8.77637	−0.285194	−0.142597	+	0.989781i	$0.545545\pi$
$948$	15.7370	0.511112
$949$	−2.71912	−0.0882662
$950$	−4.77697	−0.154985
$951$	−18.4404	−0.597972
$952$	−9.36566	−0.303543
$953$	38.8286	1.25778	0.628890	−	0.777494i	$-0.283509\pi$
$953$	38.8286	1.25778	0.628890	+	0.777494i	$0.283509\pi$
$954$	1.69690	0.0549393
$955$	−5.43349	−0.175824
$956$	−6.35982	−0.205691
$957$	−1.04736	−0.0338564
$958$	6.67518	0.215665
$959$	−78.0370	−2.51995
$960$	−0.906673	−0.0292628
$961$	39.4198	1.27161
$962$	−2.05484	−0.0662507
$963$	3.32172	0.107041
$964$	−27.5421	−0.887072
$965$	3.28209	0.105654
$966$	49.9251	1.60631
$967$	16.0077	0.514772	0.257386	−	0.966309i	$-0.417139\pi$
$967$	16.0077	0.514772	0.257386	+	0.966309i	$0.417139\pi$
$968$	10.9875	0.353153
$969$	3.89079	0.124990
$970$	2.06611	0.0663387
$971$	−50.8387	−1.63149	−0.815745	−	0.578411i	$-0.803673\pi$
$971$	−50.8387	−1.63149	−0.815745	+	0.578411i	$0.803673\pi$
$972$	6.99752	0.224446
$973$	76.7416	2.46022
$974$	26.2374	0.840700
$975$	2.49804	0.0800013
$976$	−7.76848	−0.248663
$977$	−17.2482	−0.551818	−0.275909	−	0.961184i	$-0.588979\pi$
$977$	−17.2482	−0.551818	−0.275909	+	0.961184i	$0.588979\pi$
$978$	35.9868	1.15073
$979$	−0.206613	−0.00660337
$980$	6.78026	0.216588
$981$	−5.73239	−0.183021
$982$	22.9290	0.731693
$983$	42.2447	1.34740	0.673698	−	0.739007i	$-0.264705\pi$
$983$	42.2447	1.34740	0.673698	+	0.739007i	$0.264705\pi$
$984$	−10.5900	−0.337598
$985$	−0.223364	−0.00711697
$986$	9.90541	0.315453
$987$	−33.6639	−1.07153
$988$	−0.272381	−0.00866559
$989$	1.42143	0.0451988
$990$	0.0361530	0.00114902
$991$	48.6224	1.54454	0.772271	−	0.635293i	$-0.219121\pi$
$991$	48.6224	1.54454	0.772271	+	0.635293i	$0.219121\pi$
$992$	8.39165	0.266435
$993$	5.11681	0.162377
$994$	−33.7084	−1.06916
$995$	−1.00127	−0.0317423
$996$	−8.35124	−0.264619
$997$	21.0111	0.665427	0.332713	−	0.943028i	$-0.392036\pi$
$997$	21.0111	0.665427	0.332713	+	0.943028i	$0.392036\pi$
$998$	16.2548	0.514538
$999$	33.5165	1.06042

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.f.1.11	✓	34

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.f.1.11	✓	34	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.91986 q^{3} +1.00000 q^{4} +0.472260 q^{5} +1.91986 q^{6} +4.62137 q^{7} -1.00000 q^{8} +0.685870 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.91986 q^{3} +1.00000 q^{4} +0.472260 q^{5} +1.91986 q^{6} +4.62137 q^{7} -1.00000 q^{8} +0.685870 q^{9} -0.472260 q^{10} -0.111615 q^{11} -1.91986 q^{12} +0.272381 q^{13} -4.62137 q^{14} -0.906673 q^{15} +1.00000 q^{16} +2.02660 q^{17} -0.685870 q^{18} -1.00000 q^{19} +0.472260 q^{20} -8.87239 q^{21} +0.111615 q^{22} +5.62701 q^{23} +1.91986 q^{24} -4.77697 q^{25} -0.272381 q^{26} +4.44281 q^{27} +4.62137 q^{28} -4.88771 q^{29} +0.906673 q^{30} -8.39165 q^{31} -1.00000 q^{32} +0.214285 q^{33} -2.02660 q^{34} +2.18249 q^{35} +0.685870 q^{36} +7.54400 q^{37} +1.00000 q^{38} -0.522934 q^{39} -0.472260 q^{40} -5.51603 q^{41} +8.87239 q^{42} +0.252608 q^{43} -0.111615 q^{44} +0.323909 q^{45} -5.62701 q^{46} +3.79423 q^{47} -1.91986 q^{48} +14.3571 q^{49} +4.77697 q^{50} -3.89079 q^{51} +0.272381 q^{52} -2.47409 q^{53} -4.44281 q^{54} -0.0527112 q^{55} -4.62137 q^{56} +1.91986 q^{57} +4.88771 q^{58} -10.5518 q^{59} -0.906673 q^{60} -7.76848 q^{61} +8.39165 q^{62} +3.16966 q^{63} +1.00000 q^{64} +0.128634 q^{65} -0.214285 q^{66} -13.7548 q^{67} +2.02660 q^{68} -10.8031 q^{69} -2.18249 q^{70} +7.29402 q^{71} -0.685870 q^{72} -9.98277 q^{73} -7.54400 q^{74} +9.17112 q^{75} -1.00000 q^{76} -0.515814 q^{77} +0.522934 q^{78} -8.19692 q^{79} +0.472260 q^{80} -10.5872 q^{81} +5.51603 q^{82} +4.34992 q^{83} -8.87239 q^{84} +0.957080 q^{85} -0.252608 q^{86} +9.38373 q^{87} +0.111615 q^{88} +1.85112 q^{89} -0.323909 q^{90} +1.25877 q^{91} +5.62701 q^{92} +16.1108 q^{93} -3.79423 q^{94} -0.472260 q^{95} +1.91986 q^{96} -4.37494 q^{97} -14.3571 q^{98} -0.0765533 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9}+O(q^{10}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9	\( 34 q - 34 q^{2} - 10 q^{3} + 34 q^{4} + 7 q^{5} + 10 q^{6} - 6 q^{7} - 34 q^{8} + 38 q^{9} - 7 q^{10} + 4 q^{11} - 10 q^{12} - 5 q^{13} + 6 q^{14} - 17 q^{15} + 34 q^{16} + 8 q^{17} - 38 q^{18} - 34 q^{19} + 7 q^{20} - 4 q^{22} - 24 q^{23} + 10 q^{24} + 5 q^{25} + 5 q^{26} - 31 q^{27} - 6 q^{28} + 24 q^{29} + 17 q^{30} - 28 q^{31} - 34 q^{32} - 16 q^{33} - 8 q^{34} + 2 q^{35} + 38 q^{36} - 36 q^{37} + 34 q^{38} - 9 q^{39} - 7 q^{40} + 9 q^{41} - 24 q^{43} + 4 q^{44} + 22 q^{45} + 24 q^{46} - 29 q^{47} - 10 q^{48} + 22 q^{49} - 5 q^{50} - 21 q^{51} - 5 q^{52} - 9 q^{53} + 31 q^{54} - 28 q^{55} + 6 q^{56} + 10 q^{57} - 24 q^{58} - 28 q^{59} - 17 q^{60} + 23 q^{61} + 28 q^{62} - 27 q^{63} + 34 q^{64} - 6 q^{65} + 16 q^{66} - 51 q^{67} + 8 q^{68} - 17 q^{69} - 2 q^{70} - 31 q^{71} - 38 q^{72} - 26 q^{73} + 36 q^{74} - 109 q^{75} - 34 q^{76} - 28 q^{77} + 9 q^{78} - 36 q^{79} + 7 q^{80} + 6 q^{81} - 9 q^{82} - 10 q^{83} - 32 q^{85} + 24 q^{86} - 8 q^{87} - 4 q^{88} - 34 q^{89} - 22 q^{90} - 41 q^{91} - 24 q^{92} - 33 q^{93} + 29 q^{94} - 7 q^{95} + 10 q^{96} - 56 q^{97} - 22 q^{98} - 28 q^{99}+O(q^{100}) \) 34 * q - 34 * q^2 - 10 * q^3 + 34 * q^4 + 7 * q^5 + 10 * q^6 - 6 * q^7 - 34 * q^8 + 38 * q^9 - 7 * q^10 + 4 * q^11 - 10 * q^12 - 5 * q^13 + 6 * q^14 - 17 * q^15 + 34 * q^16 + 8 * q^17 - 38 * q^18 - 34 * q^19 + 7 * q^20 - 4 * q^22 - 24 * q^23 + 10 * q^24 + 5 * q^25 + 5 * q^26 - 31 * q^27 - 6 * q^28 + 24 * q^29 + 17 * q^30 - 28 * q^31 - 34 * q^32 - 16 * q^33 - 8 * q^34 + 2 * q^35 + 38 * q^36 - 36 * q^37 + 34 * q^38 - 9 * q^39 - 7 * q^40 + 9 * q^41 - 24 * q^43 + 4 * q^44 + 22 * q^45 + 24 * q^46 - 29 * q^47 - 10 * q^48 + 22 * q^49 - 5 * q^50 - 21 * q^51 - 5 * q^52 - 9 * q^53 + 31 * q^54 - 28 * q^55 + 6 * q^56 + 10 * q^57 - 24 * q^58 - 28 * q^59 - 17 * q^60 + 23 * q^61 + 28 * q^62 - 27 * q^63 + 34 * q^64 - 6 * q^65 + 16 * q^66 - 51 * q^67 + 8 * q^68 - 17 * q^69 - 2 * q^70 - 31 * q^71 - 38 * q^72 - 26 * q^73 + 36 * q^74 - 109 * q^75 - 34 * q^76 - 28 * q^77 + 9 * q^78 - 36 * q^79 + 7 * q^80 + 6 * q^81 - 9 * q^82 - 10 * q^83 - 32 * q^85 + 24 * q^86 - 8 * q^87 - 4 * q^88 - 34 * q^89 - 22 * q^90 - 41 * q^91 - 24 * q^92 - 33 * q^93 + 29 * q^94 - 7 * q^95 + 10 * q^96 - 56 * q^97 - 22 * q^98 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more