LMFDB - Embedded newform 8026.2.a.d.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$96$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.34006 q^{3} +1.00000 q^{4} +0.570499 q^{5} -3.34006 q^{6} -3.09347 q^{7} +1.00000 q^{8} +8.15597 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.34006 q^{3} +1.00000 q^{4} +0.570499 q^{5} -3.34006 q^{6} -3.09347 q^{7} +1.00000 q^{8} +8.15597 q^{9} +0.570499 q^{10} -6.56501 q^{11} -3.34006 q^{12} -3.19778 q^{13} -3.09347 q^{14} -1.90550 q^{15} +1.00000 q^{16} +0.401095 q^{17} +8.15597 q^{18} -8.39596 q^{19} +0.570499 q^{20} +10.3324 q^{21} -6.56501 q^{22} -4.63679 q^{23} -3.34006 q^{24} -4.67453 q^{25} -3.19778 q^{26} -17.2212 q^{27} -3.09347 q^{28} -0.863431 q^{29} -1.90550 q^{30} +7.31717 q^{31} +1.00000 q^{32} +21.9275 q^{33} +0.401095 q^{34} -1.76482 q^{35} +8.15597 q^{36} -3.96004 q^{37} -8.39596 q^{38} +10.6808 q^{39} +0.570499 q^{40} -2.36465 q^{41} +10.3324 q^{42} -2.12462 q^{43} -6.56501 q^{44} +4.65297 q^{45} -4.63679 q^{46} -11.0545 q^{47} -3.34006 q^{48} +2.56957 q^{49} -4.67453 q^{50} -1.33968 q^{51} -3.19778 q^{52} -4.61550 q^{53} -17.2212 q^{54} -3.74533 q^{55} -3.09347 q^{56} +28.0430 q^{57} -0.863431 q^{58} +10.3940 q^{59} -1.90550 q^{60} -12.1206 q^{61} +7.31717 q^{62} -25.2303 q^{63} +1.00000 q^{64} -1.82433 q^{65} +21.9275 q^{66} -11.4091 q^{67} +0.401095 q^{68} +15.4871 q^{69} -1.76482 q^{70} -1.06283 q^{71} +8.15597 q^{72} +8.12524 q^{73} -3.96004 q^{74} +15.6132 q^{75} -8.39596 q^{76} +20.3087 q^{77} +10.6808 q^{78} -2.40855 q^{79} +0.570499 q^{80} +33.0520 q^{81} -2.36465 q^{82} +6.11502 q^{83} +10.3324 q^{84} +0.228824 q^{85} -2.12462 q^{86} +2.88391 q^{87} -6.56501 q^{88} +9.22117 q^{89} +4.65297 q^{90} +9.89225 q^{91} -4.63679 q^{92} -24.4397 q^{93} -11.0545 q^{94} -4.78989 q^{95} -3.34006 q^{96} -1.44651 q^{97} +2.56957 q^{98} -53.5441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) $ 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.34006	−1.92838	−0.964191	−	0.265209i	$-0.914559\pi$
$3$	−3.34006	−1.92838	−0.964191	+	0.265209i	$0.914559\pi$
$4$	1.00000	0.500000
$5$	0.570499	0.255135	0.127567	−	0.991830i	$-0.459283\pi$
$5$	0.570499	0.255135	0.127567	+	0.991830i	$0.459283\pi$
$6$	−3.34006	−1.36357
$7$	−3.09347	−1.16922	−0.584611	−	0.811314i	$-0.698753\pi$
$7$	−3.09347	−1.16922	−0.584611	+	0.811314i	$0.698753\pi$
$8$	1.00000	0.353553
$9$	8.15597	2.71866
$10$	0.570499	0.180408
$11$	−6.56501	−1.97943	−0.989713	−	0.143067i	$-0.954304\pi$
$11$	−6.56501	−1.97943	−0.989713	+	0.143067i	$0.954304\pi$
$12$	−3.34006	−0.964191
$13$	−3.19778	−0.886905	−0.443452	−	0.896298i	$-0.646247\pi$
$13$	−3.19778	−0.886905	−0.443452	+	0.896298i	$0.646247\pi$
$14$	−3.09347	−0.826765
$15$	−1.90550	−0.491998
$16$	1.00000	0.250000
$17$	0.401095	0.0972797	0.0486399	−	0.998816i	$-0.484511\pi$
$17$	0.401095	0.0972797	0.0486399	+	0.998816i	$0.484511\pi$
$18$	8.15597	1.92238
$19$	−8.39596	−1.92617	−0.963083	−	0.269205i	$-0.913239\pi$
$19$	−8.39596	−1.92617	−0.963083	+	0.269205i	$0.913239\pi$
$20$	0.570499	0.127567
$21$	10.3324	2.25471
$22$	−6.56501	−1.39967
$23$	−4.63679	−0.966838	−0.483419	−	0.875389i	$-0.660605\pi$
$23$	−4.63679	−0.966838	−0.483419	+	0.875389i	$0.660605\pi$
$24$	−3.34006	−0.681786
$25$	−4.67453	−0.934906
$26$	−3.19778	−0.627137
$27$	−17.2212	−3.31423
$28$	−3.09347	−0.584611
$29$	−0.863431	−0.160335	−0.0801676	−	0.996781i	$-0.525546\pi$
$29$	−0.863431	−0.160335	−0.0801676	+	0.996781i	$0.525546\pi$
$30$	−1.90550	−0.347895
$31$	7.31717	1.31420	0.657101	−	0.753803i	$-0.271783\pi$
$31$	7.31717	1.31420	0.657101	+	0.753803i	$0.271783\pi$
$32$	1.00000	0.176777
$33$	21.9275	3.81709
$34$	0.401095	0.0687872
$35$	−1.76482	−0.298310
$36$	8.15597	1.35933
$37$	−3.96004	−0.651027	−0.325514	−	0.945537i	$-0.605537\pi$
$37$	−3.96004	−0.651027	−0.325514	+	0.945537i	$0.605537\pi$
$38$	−8.39596	−1.36200
$39$	10.6808	1.71029
$40$	0.570499	0.0902038
$41$	−2.36465	−0.369296	−0.184648	−	0.982805i	$-0.559115\pi$
$41$	−2.36465	−0.369296	−0.184648	+	0.982805i	$0.559115\pi$
$42$	10.3324	1.59432
$43$	−2.12462	−0.324002	−0.162001	−	0.986791i	$-0.551795\pi$
$43$	−2.12462	−0.324002	−0.162001	+	0.986791i	$0.551795\pi$
$44$	−6.56501	−0.989713
$45$	4.65297	0.693625
$46$	−4.63679	−0.683657
$47$	−11.0545	−1.61247	−0.806234	−	0.591597i	$-0.798498\pi$
$47$	−11.0545	−1.61247	−0.806234	+	0.591597i	$0.798498\pi$
$48$	−3.34006	−0.482096
$49$	2.56957	0.367081
$50$	−4.67453	−0.661078
$51$	−1.33968	−0.187592
$52$	−3.19778	−0.443452
$53$	−4.61550	−0.633987	−0.316994	−	0.948428i	$-0.602673\pi$
$53$	−4.61550	−0.633987	−0.316994	+	0.948428i	$0.602673\pi$
$54$	−17.2212	−2.34351
$55$	−3.74533	−0.505021
$56$	−3.09347	−0.413383
$57$	28.0430	3.71438
$58$	−0.863431	−0.113374
$59$	10.3940	1.35318	0.676590	−	0.736360i	$-0.263457\pi$
$59$	10.3940	1.35318	0.676590	+	0.736360i	$0.263457\pi$
$60$	−1.90550	−0.245999
$61$	−12.1206	−1.55189	−0.775944	−	0.630802i	$-0.782726\pi$
$61$	−12.1206	−1.55189	−0.775944	+	0.630802i	$0.782726\pi$
$62$	7.31717	0.929281
$63$	−25.2303	−3.17872
$64$	1.00000	0.125000
$65$	−1.82433	−0.226280
$66$	21.9275	2.69909
$67$	−11.4091	−1.39385	−0.696924	−	0.717145i	$-0.745449\pi$
$67$	−11.4091	−1.39385	−0.696924	+	0.717145i	$0.745449\pi$
$68$	0.401095	0.0486399
$69$	15.4871	1.86443
$70$	−1.76482	−0.210937
$71$	−1.06283	−0.126134	−0.0630672	−	0.998009i	$-0.520088\pi$
$71$	−1.06283	−0.126134	−0.0630672	+	0.998009i	$0.520088\pi$
$72$	8.15597	0.961191
$73$	8.12524	0.950988	0.475494	−	0.879719i	$-0.342269\pi$
$73$	8.12524	0.950988	0.475494	+	0.879719i	$0.342269\pi$
$74$	−3.96004	−0.460346
$75$	15.6132	1.80286
$76$	−8.39596	−0.963083
$77$	20.3087	2.31439
$78$	10.6808	1.20936
$79$	−2.40855	−0.270983	−0.135491	−	0.990779i	$-0.543261\pi$
$79$	−2.40855	−0.270983	−0.135491	+	0.990779i	$0.543261\pi$
$80$	0.570499	0.0637837
$81$	33.0520	3.67244
$82$	−2.36465	−0.261132
$83$	6.11502	0.671211	0.335605	−	0.942003i	$-0.391059\pi$
$83$	6.11502	0.671211	0.335605	+	0.942003i	$0.391059\pi$
$84$	10.3324	1.12735
$85$	0.228824	0.0248195
$86$	−2.12462	−0.229104
$87$	2.88391	0.309187
$88$	−6.56501	−0.699833
$89$	9.22117	0.977442	0.488721	−	0.872440i	$-0.337464\pi$
$89$	9.22117	0.977442	0.488721	+	0.872440i	$0.337464\pi$
$90$	4.65297	0.490467
$91$	9.89225	1.03699
$92$	−4.63679	−0.483419
$93$	−24.4397	−2.53428
$94$	−11.0545	−1.14019
$95$	−4.78989	−0.491432
$96$	−3.34006	−0.340893
$97$	−1.44651	−0.146870	−0.0734352	−	0.997300i	$-0.523396\pi$
$97$	−1.44651	−0.146870	−0.0734352	+	0.997300i	$0.523396\pi$
$98$	2.56957	0.259566
$99$	−53.5441	−5.38138
$100$	−4.67453	−0.467453
$101$	−7.47798	−0.744087	−0.372043	−	0.928215i	$-0.621343\pi$
$101$	−7.47798	−0.744087	−0.372043	+	0.928215i	$0.621343\pi$
$102$	−1.33968	−0.132648
$103$	−2.04885	−0.201880	−0.100940	−	0.994893i	$-0.532185\pi$
$103$	−2.04885	−0.201880	−0.100940	+	0.994893i	$0.532185\pi$
$104$	−3.19778	−0.313568
$105$	5.89461	0.575255
$106$	−4.61550	−0.448297
$107$	−5.02379	−0.485668	−0.242834	−	0.970068i	$-0.578077\pi$
$107$	−5.02379	−0.485668	−0.242834	+	0.970068i	$0.578077\pi$
$108$	−17.2212	−1.65711
$109$	12.3628	1.18414	0.592070	−	0.805887i	$-0.298311\pi$
$109$	12.3628	1.18414	0.592070	+	0.805887i	$0.298311\pi$
$110$	−3.74533	−0.357104
$111$	13.2268	1.25543
$112$	−3.09347	−0.292306
$113$	−20.7274	−1.94987	−0.974935	−	0.222490i	$-0.928582\pi$
$113$	−20.7274	−1.94987	−0.974935	+	0.222490i	$0.928582\pi$
$114$	28.0430	2.62647
$115$	−2.64528	−0.246674
$116$	−0.863431	−0.0801676
$117$	−26.0810	−2.41119
$118$	10.3940	0.956843
$119$	−1.24078	−0.113742
$120$	−1.90550	−0.173947
$121$	32.0994	2.91813
$122$	−12.1206	−1.09735
$123$	7.89806	0.712144
$124$	7.31717	0.657101
$125$	−5.51931	−0.493662
$126$	−25.2303	−2.24769
$127$	7.05401	0.625942	0.312971	−	0.949763i	$-0.398676\pi$
$127$	7.05401	0.625942	0.312971	+	0.949763i	$0.398676\pi$
$128$	1.00000	0.0883883
$129$	7.09637	0.624800
$130$	−1.82433	−0.160004
$131$	−14.3868	−1.25698	−0.628492	−	0.777816i	$-0.716328\pi$
$131$	−14.3868	−1.25698	−0.628492	+	0.777816i	$0.716328\pi$
$132$	21.9275	1.90854
$133$	25.9727	2.25212
$134$	−11.4091	−0.985600
$135$	−9.82470	−0.845575
$136$	0.401095	0.0343936
$137$	−3.54921	−0.303229	−0.151615	−	0.988440i	$-0.548447\pi$
$137$	−3.54921	−0.303229	−0.151615	+	0.988440i	$0.548447\pi$
$138$	15.4871	1.31835
$139$	−2.93960	−0.249334	−0.124667	−	0.992199i	$-0.539786\pi$
$139$	−2.93960	−0.249334	−0.124667	+	0.992199i	$0.539786\pi$
$140$	−1.76482	−0.149155
$141$	36.9227	3.10945
$142$	−1.06283	−0.0891905
$143$	20.9935	1.75556
$144$	8.15597	0.679664
$145$	−0.492587	−0.0409071
$146$	8.12524	0.672450
$147$	−8.58251	−0.707873
$148$	−3.96004	−0.325514
$149$	−4.78829	−0.392272	−0.196136	−	0.980577i	$-0.562839\pi$
$149$	−4.78829	−0.392272	−0.196136	+	0.980577i	$0.562839\pi$
$150$	15.6132	1.27481
$151$	−0.567993	−0.0462226	−0.0231113	−	0.999733i	$-0.507357\pi$
$151$	−0.567993	−0.0462226	−0.0231113	+	0.999733i	$0.507357\pi$
$152$	−8.39596	−0.681002
$153$	3.27132	0.264470
$154$	20.3087	1.63652
$155$	4.17444	0.335299
$156$	10.6808	0.855146
$157$	−19.4572	−1.55286	−0.776429	−	0.630205i	$-0.782971\pi$
$157$	−19.4572	−1.55286	−0.776429	+	0.630205i	$0.782971\pi$
$158$	−2.40855	−0.191614
$159$	15.4160	1.22257
$160$	0.570499	0.0451019
$161$	14.3438	1.13045
$162$	33.0520	2.59681
$163$	10.4094	0.815327	0.407663	−	0.913132i	$-0.366344\pi$
$163$	10.4094	0.815327	0.407663	+	0.913132i	$0.366344\pi$
$164$	−2.36465	−0.184648
$165$	12.5096	0.973873
$166$	6.11502	0.474618
$167$	−11.2021	−0.866847	−0.433424	−	0.901190i	$-0.642695\pi$
$167$	−11.2021	−0.866847	−0.433424	+	0.901190i	$0.642695\pi$
$168$	10.3324	0.797160
$169$	−2.77419	−0.213400
$170$	0.228824	0.0175500
$171$	−68.4772	−5.23659
$172$	−2.12462	−0.162001
$173$	11.1371	0.846740	0.423370	−	0.905957i	$-0.360847\pi$
$173$	11.1371	0.846740	0.423370	+	0.905957i	$0.360847\pi$
$174$	2.88391	0.218629
$175$	14.4605	1.09311
$176$	−6.56501	−0.494857
$177$	−34.7165	−2.60945
$178$	9.22117	0.691156
$179$	−1.13314	−0.0846952	−0.0423476	−	0.999103i	$-0.513484\pi$
$179$	−1.13314	−0.0846952	−0.0423476	+	0.999103i	$0.513484\pi$
$180$	4.65297	0.346812
$181$	−13.5849	−1.00976	−0.504880	−	0.863189i	$-0.668463\pi$
$181$	−13.5849	−1.00976	−0.504880	+	0.863189i	$0.668463\pi$
$182$	9.89225	0.733262
$183$	40.4836	2.99263
$184$	−4.63679	−0.341829
$185$	−2.25920	−0.166100
$186$	−24.4397	−1.79201
$187$	−2.63319	−0.192558
$188$	−11.0545	−0.806234
$189$	53.2734	3.87507
$190$	−4.78989	−0.347495
$191$	−4.80582	−0.347737	−0.173869	−	0.984769i	$-0.555627\pi$
$191$	−4.80582	−0.347737	−0.173869	+	0.984769i	$0.555627\pi$
$192$	−3.34006	−0.241048
$193$	−17.4574	−1.25661	−0.628304	−	0.777968i	$-0.716251\pi$
$193$	−17.4574	−1.25661	−0.628304	+	0.777968i	$0.716251\pi$
$194$	−1.44651	−0.103853
$195$	6.09337	0.436355
$196$	2.56957	0.183541
$197$	−9.53216	−0.679139	−0.339569	−	0.940581i	$-0.610281\pi$
$197$	−9.53216	−0.679139	−0.339569	+	0.940581i	$0.610281\pi$
$198$	−53.5441	−3.80521
$199$	−6.12553	−0.434228	−0.217114	−	0.976146i	$-0.569664\pi$
$199$	−6.12553	−0.434228	−0.217114	+	0.976146i	$0.569664\pi$
$200$	−4.67453	−0.330539
$201$	38.1072	2.68787
$202$	−7.47798	−0.526149
$203$	2.67100	0.187467
$204$	−1.33968	−0.0937962
$205$	−1.34903	−0.0942204
$206$	−2.04885	−0.142750
$207$	−37.8175	−2.62850
$208$	−3.19778	−0.221726
$209$	55.1196	3.81270
$210$	5.89461	0.406767
$211$	22.9526	1.58012	0.790062	−	0.613027i	$-0.210048\pi$
$211$	22.9526	1.58012	0.790062	+	0.613027i	$0.210048\pi$
$212$	−4.61550	−0.316994
$213$	3.54990	0.243235
$214$	−5.02379	−0.343419
$215$	−1.21210	−0.0826643
$216$	−17.2212	−1.17176
$217$	−22.6354	−1.53659
$218$	12.3628	0.837313
$219$	−27.1388	−1.83387
$220$	−3.74533	−0.252510
$221$	−1.28261	−0.0862779
$222$	13.2268	0.887723
$223$	12.4547	0.834032	0.417016	−	0.908899i	$-0.363076\pi$
$223$	12.4547	0.834032	0.417016	+	0.908899i	$0.363076\pi$
$224$	−3.09347	−0.206691
$225$	−38.1253	−2.54169
$226$	−20.7274	−1.37877
$227$	−25.2511	−1.67598	−0.837988	−	0.545689i	$-0.816268\pi$
$227$	−25.2511	−1.67598	−0.837988	+	0.545689i	$0.816268\pi$
$228$	28.0430	1.85719
$229$	−5.46815	−0.361346	−0.180673	−	0.983543i	$-0.557828\pi$
$229$	−5.46815	−0.361346	−0.180673	+	0.983543i	$0.557828\pi$
$230$	−2.64528	−0.174425
$231$	−67.8321	−4.46303
$232$	−0.863431	−0.0566870
$233$	−8.07674	−0.529125	−0.264562	−	0.964369i	$-0.585228\pi$
$233$	−8.07674	−0.529125	−0.264562	+	0.964369i	$0.585228\pi$
$234$	−26.0810	−1.70497
$235$	−6.30659	−0.411397
$236$	10.3940	0.676590
$237$	8.04469	0.522559
$238$	−1.24078	−0.0804275
$239$	−1.97285	−0.127613	−0.0638067	−	0.997962i	$-0.520324\pi$
$239$	−1.97285	−0.127613	−0.0638067	+	0.997962i	$0.520324\pi$
$240$	−1.90550	−0.122999
$241$	−11.5518	−0.744114	−0.372057	−	0.928210i	$-0.621347\pi$
$241$	−11.5518	−0.744114	−0.372057	+	0.928210i	$0.621347\pi$
$242$	32.0994	2.06343
$243$	−58.7317	−3.76764
$244$	−12.1206	−0.775944
$245$	1.46594	0.0936553
$246$	7.89806	0.503562
$247$	26.8485	1.70833
$248$	7.31717	0.464640
$249$	−20.4245	−1.29435
$250$	−5.51931	−0.349072
$251$	1.93345	0.122039	0.0610193	−	0.998137i	$-0.480565\pi$
$251$	1.93345	0.122039	0.0610193	+	0.998137i	$0.480565\pi$
$252$	−25.2303	−1.58936
$253$	30.4406	1.91378
$254$	7.05401	0.442608
$255$	−0.764285	−0.0478614
$256$	1.00000	0.0625000
$257$	29.1217	1.81656	0.908281	−	0.418360i	$-0.137395\pi$
$257$	29.1217	1.81656	0.908281	+	0.418360i	$0.137395\pi$
$258$	7.09637	0.441800
$259$	12.2503	0.761196
$260$	−1.82433	−0.113140
$261$	−7.04212	−0.435896
$262$	−14.3868	−0.888822
$263$	24.7267	1.52472	0.762358	−	0.647155i	$-0.224042\pi$
$263$	24.7267	1.52472	0.762358	+	0.647155i	$0.224042\pi$
$264$	21.9275	1.34954
$265$	−2.63314	−0.161752
$266$	25.9727	1.59249
$267$	−30.7992	−1.88488
$268$	−11.4091	−0.696924
$269$	18.7619	1.14394	0.571968	−	0.820276i	$-0.306180\pi$
$269$	18.7619	1.14394	0.571968	+	0.820276i	$0.306180\pi$
$270$	−9.82470	−0.597912
$271$	−1.18924	−0.0722412	−0.0361206	−	0.999347i	$-0.511500\pi$
$271$	−1.18924	−0.0722412	−0.0361206	+	0.999347i	$0.511500\pi$
$272$	0.401095	0.0243199
$273$	−33.0407	−1.99971
$274$	−3.54921	−0.214416
$275$	30.6884	1.85058
$276$	15.4871	0.932216
$277$	−18.1572	−1.09096	−0.545480	−	0.838124i	$-0.683653\pi$
$277$	−18.1572	−1.09096	−0.545480	+	0.838124i	$0.683653\pi$
$278$	−2.93960	−0.176305
$279$	59.6786	3.57286
$280$	−1.76482	−0.105468
$281$	−16.5293	−0.986052	−0.493026	−	0.870014i	$-0.664109\pi$
$281$	−16.5293	−0.986052	−0.493026	+	0.870014i	$0.664109\pi$
$282$	36.9227	2.19872
$283$	10.0329	0.596396	0.298198	−	0.954504i	$-0.403614\pi$
$283$	10.0329	0.596396	0.298198	+	0.954504i	$0.403614\pi$
$284$	−1.06283	−0.0630672
$285$	15.9985	0.947669
$286$	20.9935	1.24137
$287$	7.31498	0.431789
$288$	8.15597	0.480595
$289$	−16.8391	−0.990537
$290$	−0.492587	−0.0289257
$291$	4.83141	0.283222
$292$	8.12524	0.475494
$293$	12.7121	0.742650	0.371325	−	0.928503i	$-0.378904\pi$
$293$	12.7121	0.742650	0.371325	+	0.928503i	$0.378904\pi$
$294$	−8.58251	−0.500542
$295$	5.92976	0.345244
$296$	−3.96004	−0.230173
$297$	113.058	6.56027
$298$	−4.78829	−0.277378
$299$	14.8274	0.857493
$300$	15.6132	0.901428
$301$	6.57247	0.378831
$302$	−0.567993	−0.0326843
$303$	24.9769	1.43488
$304$	−8.39596	−0.481541
$305$	−6.91481	−0.395941
$306$	3.27132	0.187009
$307$	−18.6932	−1.06688	−0.533440	−	0.845838i	$-0.679101\pi$
$307$	−18.6932	−1.06688	−0.533440	+	0.845838i	$0.679101\pi$
$308$	20.3087	1.15719
$309$	6.84329	0.389301
$310$	4.17444	0.237092
$311$	4.77816	0.270945	0.135472	−	0.990781i	$-0.456745\pi$
$311$	4.77816	0.270945	0.135472	+	0.990781i	$0.456745\pi$
$312$	10.6808	0.604679
$313$	16.6751	0.942531	0.471266	−	0.881991i	$-0.343797\pi$
$313$	16.6751	0.942531	0.471266	+	0.881991i	$0.343797\pi$
$314$	−19.4572	−1.09804
$315$	−14.3938	−0.811002
$316$	−2.40855	−0.135491
$317$	27.7591	1.55911	0.779553	−	0.626336i	$-0.215446\pi$
$317$	27.7591	1.55911	0.779553	+	0.626336i	$0.215446\pi$
$318$	15.4160	0.864487
$319$	5.66844	0.317372
$320$	0.570499	0.0318919
$321$	16.7797	0.936553
$322$	14.3438	0.799348
$323$	−3.36758	−0.187377
$324$	33.0520	1.83622
$325$	14.9481	0.829173
$326$	10.4094	0.576523
$327$	−41.2924	−2.28347
$328$	−2.36465	−0.130566
$329$	34.1969	1.88533
$330$	12.5096	0.688632
$331$	−3.99767	−0.219732	−0.109866	−	0.993946i	$-0.535042\pi$
$331$	−3.99767	−0.219732	−0.109866	+	0.993946i	$0.535042\pi$
$332$	6.11502	0.335605
$333$	−32.2980	−1.76992
$334$	−11.2021	−0.612953
$335$	−6.50890	−0.355619
$336$	10.3324	0.563677
$337$	−4.08641	−0.222601	−0.111301	−	0.993787i	$-0.535502\pi$
$337$	−4.08641	−0.222601	−0.111301	+	0.993787i	$0.535502\pi$
$338$	−2.77419	−0.150896
$339$	69.2307	3.76009
$340$	0.228824	0.0124097
$341$	−48.0373	−2.60137
$342$	−68.4772	−3.70282
$343$	13.7054	0.740023
$344$	−2.12462	−0.114552
$345$	8.83540	0.475682
$346$	11.1371	0.598736
$347$	−17.6609	−0.948088	−0.474044	−	0.880501i	$-0.657206\pi$
$347$	−17.6609	−0.948088	−0.474044	+	0.880501i	$0.657206\pi$
$348$	2.88391	0.154594
$349$	17.1942	0.920385	0.460193	−	0.887819i	$-0.347780\pi$
$349$	17.1942	0.920385	0.460193	+	0.887819i	$0.347780\pi$
$350$	14.4605	0.772948
$351$	55.0697	2.93941
$352$	−6.56501	−0.349916
$353$	−35.5919	−1.89437	−0.947183	−	0.320694i	$-0.896084\pi$
$353$	−35.5919	−1.89437	−0.947183	+	0.320694i	$0.896084\pi$
$354$	−34.7165	−1.84516
$355$	−0.606342	−0.0321813
$356$	9.22117	0.488721
$357$	4.14426	0.219337
$358$	−1.13314	−0.0598885
$359$	11.3938	0.601342	0.300671	−	0.953728i	$-0.402789\pi$
$359$	11.3938	0.601342	0.300671	+	0.953728i	$0.402789\pi$
$360$	4.65297	0.245233
$361$	51.4922	2.71012
$362$	−13.5849	−0.714008
$363$	−107.214	−5.62726
$364$	9.89225	0.518495
$365$	4.63544	0.242630
$366$	40.4836	2.11611
$367$	28.9954	1.51355	0.756773	−	0.653678i	$-0.226775\pi$
$367$	28.9954	1.51355	0.756773	+	0.653678i	$0.226775\pi$
$368$	−4.63679	−0.241709
$369$	−19.2860	−1.00399
$370$	−2.25920	−0.117450
$371$	14.2779	0.741272
$372$	−24.4397	−1.26714
$373$	14.0693	0.728480	0.364240	−	0.931305i	$-0.381329\pi$
$373$	14.0693	0.728480	0.364240	+	0.931305i	$0.381329\pi$
$374$	−2.63319	−0.136159
$375$	18.4348	0.951969
$376$	−11.0545	−0.570093
$377$	2.76106	0.142202
$378$	53.2734	2.74009
$379$	−35.9360	−1.84591	−0.922954	−	0.384910i	$-0.874232\pi$
$379$	−35.9360	−1.84591	−0.922954	+	0.384910i	$0.874232\pi$
$380$	−4.78989	−0.245716
$381$	−23.5608	−1.20706
$382$	−4.80582	−0.245887
$383$	35.8884	1.83381	0.916906	−	0.399104i	$-0.130679\pi$
$383$	35.8884	1.83381	0.916906	+	0.399104i	$0.130679\pi$
$384$	−3.34006	−0.170447
$385$	11.5861	0.590482
$386$	−17.4574	−0.888556
$387$	−17.3284	−0.880851
$388$	−1.44651	−0.0734352
$389$	9.14107	0.463471	0.231735	−	0.972779i	$-0.425560\pi$
$389$	9.14107	0.463471	0.231735	+	0.972779i	$0.425560\pi$
$390$	6.09337	0.308550
$391$	−1.85979	−0.0940537
$392$	2.56957	0.129783
$393$	48.0528	2.42395
$394$	−9.53216	−0.480224
$395$	−1.37407	−0.0691372
$396$	−53.5441	−2.69069
$397$	−1.37077	−0.0687971	−0.0343985	−	0.999408i	$-0.510952\pi$
$397$	−1.37077	−0.0687971	−0.0343985	+	0.999408i	$0.510952\pi$
$398$	−6.12553	−0.307045
$399$	−86.7502	−4.34294
$400$	−4.67453	−0.233727
$401$	9.82189	0.490482	0.245241	−	0.969462i	$-0.421133\pi$
$401$	9.82189	0.490482	0.245241	+	0.969462i	$0.421133\pi$
$402$	38.1072	1.90061
$403$	−23.3987	−1.16557
$404$	−7.47798	−0.372043
$405$	18.8561	0.936968
$406$	2.67100	0.132560
$407$	25.9977	1.28866
$408$	−1.33968	−0.0663240
$409$	−10.1018	−0.499500	−0.249750	−	0.968310i	$-0.580348\pi$
$409$	−10.1018	−0.499500	−0.249750	+	0.968310i	$0.580348\pi$
$410$	−1.34903	−0.0666239
$411$	11.8546	0.584742
$412$	−2.04885	−0.100940
$413$	−32.1535	−1.58217
$414$	−37.8175	−1.85863
$415$	3.48861	0.171249
$416$	−3.19778	−0.156784
$417$	9.81843	0.480810
$418$	55.1196	2.69599
$419$	−5.36924	−0.262305	−0.131152	−	0.991362i	$-0.541868\pi$
$419$	−5.36924	−0.262305	−0.131152	+	0.991362i	$0.541868\pi$
$420$	5.89461	0.287627
$421$	8.52761	0.415611	0.207805	−	0.978170i	$-0.433368\pi$
$421$	8.52761	0.415611	0.207805	+	0.978170i	$0.433368\pi$
$422$	22.9526	1.11732
$423$	−90.1604	−4.38375
$424$	−4.61550	−0.224148
$425$	−1.87493	−0.0909474
$426$	3.54990	0.171993
$427$	37.4948	1.81450
$428$	−5.02379	−0.242834
$429$	−70.1194	−3.38540
$430$	−1.21210	−0.0584525
$431$	−19.1358	−0.921739	−0.460869	−	0.887468i	$-0.652462\pi$
$431$	−19.1358	−0.921739	−0.460869	+	0.887468i	$0.652462\pi$
$432$	−17.2212	−0.828557
$433$	32.9580	1.58386	0.791930	−	0.610612i	$-0.209076\pi$
$433$	32.9580	1.58386	0.791930	+	0.610612i	$0.209076\pi$
$434$	−22.6354	−1.08654
$435$	1.64527	0.0788845
$436$	12.3628	0.592070
$437$	38.9303	1.86229
$438$	−27.1388	−1.29674
$439$	21.0136	1.00292	0.501462	−	0.865179i	$-0.332796\pi$
$439$	21.0136	1.00292	0.501462	+	0.865179i	$0.332796\pi$
$440$	−3.74533	−0.178552
$441$	20.9573	0.997969
$442$	−1.28261	−0.0610077
$443$	−34.1129	−1.62075	−0.810375	−	0.585911i	$-0.800737\pi$
$443$	−34.1129	−1.62075	−0.810375	+	0.585911i	$0.800737\pi$
$444$	13.2268	0.627715
$445$	5.26067	0.249380
$446$	12.4547	0.589749
$447$	15.9932	0.756451
$448$	−3.09347	−0.146153
$449$	−8.87757	−0.418958	−0.209479	−	0.977813i	$-0.567177\pi$
$449$	−8.87757	−0.418958	−0.209479	+	0.977813i	$0.567177\pi$
$450$	−38.1253	−1.79725
$451$	15.5240	0.730995
$452$	−20.7274	−0.974935
$453$	1.89713	0.0891348
$454$	−25.2511	−1.18509
$455$	5.64352	0.264572
$456$	28.0430	1.31323
$457$	37.7291	1.76489	0.882446	−	0.470413i	$-0.155895\pi$
$457$	37.7291	1.76489	0.882446	+	0.470413i	$0.155895\pi$
$458$	−5.46815	−0.255510
$459$	−6.90734	−0.322407
$460$	−2.64528	−0.123337
$461$	40.0866	1.86702	0.933509	−	0.358555i	$-0.116730\pi$
$461$	40.0866	1.86702	0.933509	+	0.358555i	$0.116730\pi$
$462$	−67.8321	−3.15584
$463$	−39.3704	−1.82970	−0.914849	−	0.403796i	$-0.867690\pi$
$463$	−39.3704	−1.82970	−0.914849	+	0.403796i	$0.867690\pi$
$464$	−0.863431	−0.0400838
$465$	−13.9429	−0.646584
$466$	−8.07674	−0.374148
$467$	30.5105	1.41186	0.705929	−	0.708283i	$-0.250530\pi$
$467$	30.5105	1.41186	0.705929	+	0.708283i	$0.250530\pi$
$468$	−26.0810	−1.20560
$469$	35.2939	1.62972
$470$	−6.30659	−0.290902
$471$	64.9883	2.99450
$472$	10.3940	0.478422
$473$	13.9482	0.641338
$474$	8.04469	0.369505
$475$	39.2472	1.80078
$476$	−1.24078	−0.0568708
$477$	−37.6439	−1.72359
$478$	−1.97285	−0.0902363
$479$	−27.4870	−1.25591	−0.627957	−	0.778248i	$-0.716108\pi$
$479$	−27.4870	−1.25591	−0.627957	+	0.778248i	$0.716108\pi$
$480$	−1.90550	−0.0869737
$481$	12.6634	0.577399
$482$	−11.5518	−0.526168
$483$	−47.9090	−2.17994
$484$	32.0994	1.45906
$485$	−0.825231	−0.0374718
$486$	−58.7317	−2.66412
$487$	−26.5919	−1.20499	−0.602497	−	0.798121i	$-0.705828\pi$
$487$	−26.5919	−1.20499	−0.602497	+	0.798121i	$0.705828\pi$
$488$	−12.1206	−0.548675
$489$	−34.7680	−1.57226
$490$	1.46594	0.0662243
$491$	7.61432	0.343629	0.171815	−	0.985129i	$-0.445037\pi$
$491$	7.61432	0.343629	0.171815	+	0.985129i	$0.445037\pi$
$492$	7.89806	0.356072
$493$	−0.346318	−0.0155974
$494$	26.8485	1.20797
$495$	−30.5468	−1.37298
$496$	7.31717	0.328550
$497$	3.28783	0.147479
$498$	−20.4245	−0.915244
$499$	26.0346	1.16547	0.582735	−	0.812662i	$-0.301983\pi$
$499$	26.0346	1.16547	0.582735	+	0.812662i	$0.301983\pi$
$500$	−5.51931	−0.246831
$501$	37.4157	1.67161
$502$	1.93345	0.0862943
$503$	−18.9978	−0.847070	−0.423535	−	0.905880i	$-0.639211\pi$
$503$	−18.9978	−0.847070	−0.423535	+	0.905880i	$0.639211\pi$
$504$	−25.2303	−1.12385
$505$	−4.26618	−0.189843
$506$	30.4406	1.35325
$507$	9.26597	0.411516
$508$	7.05401	0.312971
$509$	26.0097	1.15286	0.576429	−	0.817147i	$-0.304446\pi$
$509$	26.0097	1.15286	0.576429	+	0.817147i	$0.304446\pi$
$510$	−0.764285	−0.0338431
$511$	−25.1352	−1.11192
$512$	1.00000	0.0441942
$513$	144.589	6.38375
$514$	29.1217	1.28450
$515$	−1.16887	−0.0515066
$516$	7.09637	0.312400
$517$	72.5731	3.19176
$518$	12.2503	0.538247
$519$	−37.1986	−1.63284
$520$	−1.82433	−0.0800022
$521$	−12.1304	−0.531442	−0.265721	−	0.964050i	$-0.585610\pi$
$521$	−12.1304	−0.531442	−0.265721	+	0.964050i	$0.585610\pi$
$522$	−7.04212	−0.308225
$523$	24.0433	1.05134	0.525670	−	0.850689i	$-0.323815\pi$
$523$	24.0433	1.05134	0.525670	+	0.850689i	$0.323815\pi$
$524$	−14.3868	−0.628492
$525$	−48.2990	−2.10794
$526$	24.7267	1.07814
$527$	2.93488	0.127845
$528$	21.9275	0.954272
$529$	−1.50018	−0.0652251
$530$	−2.63314	−0.114376
$531$	84.7730	3.67884
$532$	25.9727	1.12606
$533$	7.56163	0.327531
$534$	−30.7992	−1.33281
$535$	−2.86607	−0.123911
$536$	−11.4091	−0.492800
$537$	3.78476	0.163325
$538$	18.7619	0.808884
$539$	−16.8693	−0.726611
$540$	−9.82470	−0.422788
$541$	−37.4029	−1.60808	−0.804039	−	0.594577i	$-0.797320\pi$
$541$	−37.4029	−1.60808	−0.804039	+	0.594577i	$0.797320\pi$
$542$	−1.18924	−0.0510822
$543$	45.3744	1.94720
$544$	0.401095	0.0171968
$545$	7.05296	0.302116
$546$	−33.0407	−1.41401
$547$	−29.3939	−1.25679	−0.628395	−	0.777894i	$-0.716288\pi$
$547$	−29.3939	−1.25679	−0.628395	+	0.777894i	$0.716288\pi$
$548$	−3.54921	−0.151615
$549$	−98.8555	−4.21905
$550$	30.6884	1.30856
$551$	7.24934	0.308832
$552$	15.4871	0.659176
$553$	7.45078	0.316839
$554$	−18.1572	−0.771425
$555$	7.54586	0.320304
$556$	−2.93960	−0.124667
$557$	−18.9067	−0.801102	−0.400551	−	0.916274i	$-0.631181\pi$
$557$	−18.9067	−0.801102	−0.400551	+	0.916274i	$0.631181\pi$
$558$	59.6786	2.52640
$559$	6.79409	0.287359
$560$	−1.76482	−0.0745774
$561$	8.79501	0.371325
$562$	−16.5293	−0.697244
$563$	−0.233341	−0.00983415	−0.00491707	−	0.999988i	$-0.501565\pi$
$563$	−0.233341	−0.00983415	−0.00491707	+	0.999988i	$0.501565\pi$
$564$	36.9227	1.55473
$565$	−11.8250	−0.497480
$566$	10.0329	0.421716
$567$	−102.245	−4.29390
$568$	−1.06283	−0.0445952
$569$	−33.4268	−1.40132	−0.700661	−	0.713494i	$-0.747112\pi$
$569$	−33.4268	−1.40132	−0.700661	+	0.713494i	$0.747112\pi$
$570$	15.9985	0.670103
$571$	17.6597	0.739037	0.369518	−	0.929223i	$-0.379523\pi$
$571$	17.6597	0.739037	0.369518	+	0.929223i	$0.379523\pi$
$572$	20.9935	0.877781
$573$	16.0517	0.670570
$574$	7.31498	0.305321
$575$	21.6748	0.903902
$576$	8.15597	0.339832
$577$	21.1607	0.880932	0.440466	−	0.897769i	$-0.354813\pi$
$577$	21.1607	0.880932	0.440466	+	0.897769i	$0.354813\pi$
$578$	−16.8391	−0.700415
$579$	58.3085	2.42322
$580$	−0.492587	−0.0204536
$581$	−18.9166	−0.784795
$582$	4.83141	0.200268
$583$	30.3008	1.25493
$584$	8.12524	0.336225
$585$	−14.8792	−0.615179
$586$	12.7121	0.525133
$587$	−5.26346	−0.217246	−0.108623	−	0.994083i	$-0.534644\pi$
$587$	−5.26346	−0.217246	−0.108623	+	0.994083i	$0.534644\pi$
$588$	−8.58251	−0.353937
$589$	−61.4346	−2.53137
$590$	5.92976	0.244124
$591$	31.8380	1.30964
$592$	−3.96004	−0.162757
$593$	−25.8206	−1.06033	−0.530163	−	0.847896i	$-0.677869\pi$
$593$	−25.8206	−1.06033	−0.530163	+	0.847896i	$0.677869\pi$
$594$	113.058	4.63881
$595$	−0.707861	−0.0290195
$596$	−4.78829	−0.196136
$597$	20.4596	0.837357
$598$	14.8274	0.606339
$599$	10.1345	0.414083	0.207042	−	0.978332i	$-0.433616\pi$
$599$	10.1345	0.414083	0.207042	+	0.978332i	$0.433616\pi$
$600$	15.6132	0.637406
$601$	19.6608	0.801982	0.400991	−	0.916082i	$-0.368666\pi$
$601$	19.6608	0.801982	0.400991	+	0.916082i	$0.368666\pi$
$602$	6.57247	0.267874
$603$	−93.0526	−3.78940
$604$	−0.567993	−0.0231113
$605$	18.3127	0.744516
$606$	24.9769	1.01462
$607$	6.82396	0.276976	0.138488	−	0.990364i	$-0.455776\pi$
$607$	6.82396	0.276976	0.138488	+	0.990364i	$0.455776\pi$
$608$	−8.39596	−0.340501
$609$	−8.92129	−0.361509
$610$	−6.91481	−0.279972
$611$	35.3499	1.43011
$612$	3.27132	0.132235
$613$	−24.0408	−0.971001	−0.485500	−	0.874236i	$-0.661363\pi$
$613$	−24.0408	−0.971001	−0.485500	+	0.874236i	$0.661363\pi$
$614$	−18.6932	−0.754398
$615$	4.50584	0.181693
$616$	20.3087	0.818260
$617$	3.98845	0.160569	0.0802844	−	0.996772i	$-0.474417\pi$
$617$	3.98845	0.160569	0.0802844	+	0.996772i	$0.474417\pi$
$618$	6.84329	0.275277
$619$	−11.7193	−0.471040	−0.235520	−	0.971870i	$-0.575679\pi$
$619$	−11.7193	−0.471040	−0.235520	+	0.971870i	$0.575679\pi$
$620$	4.17444	0.167649
$621$	79.8512	3.20432
$622$	4.77816	0.191587
$623$	−28.5254	−1.14285
$624$	10.6808	0.427573
$625$	20.2239	0.808956
$626$	16.6751	0.666470
$627$	−184.103	−7.35235
$628$	−19.4572	−0.776429
$629$	−1.58835	−0.0633318
$630$	−14.3938	−0.573465
$631$	−19.6610	−0.782694	−0.391347	−	0.920243i	$-0.627991\pi$
$631$	−19.6610	−0.782694	−0.391347	+	0.920243i	$0.627991\pi$
$632$	−2.40855	−0.0958069
$633$	−76.6631	−3.04708
$634$	27.7591	1.10245
$635$	4.02431	0.159700
$636$	15.4160	0.611285
$637$	−8.21692	−0.325566
$638$	5.66844	0.224416
$639$	−8.66839	−0.342916
$640$	0.570499	0.0225510
$641$	7.96758	0.314700	0.157350	−	0.987543i	$-0.449705\pi$
$641$	7.96758	0.314700	0.157350	+	0.987543i	$0.449705\pi$
$642$	16.7797	0.662243
$643$	27.2471	1.07452	0.537260	−	0.843417i	$-0.319459\pi$
$643$	27.2471	1.07452	0.537260	+	0.843417i	$0.319459\pi$
$644$	14.3438	0.565224
$645$	4.04847	0.159408
$646$	−3.36758	−0.132495
$647$	−25.7058	−1.01060	−0.505300	−	0.862944i	$-0.668618\pi$
$647$	−25.7058	−1.01060	−0.505300	+	0.862944i	$0.668618\pi$
$648$	33.0520	1.29840
$649$	−68.2366	−2.67852
$650$	14.9481	0.586314
$651$	75.6037	2.96314
$652$	10.4094	0.407663
$653$	−32.1579	−1.25844	−0.629218	−	0.777229i	$-0.716625\pi$
$653$	−32.1579	−1.25844	−0.629218	+	0.777229i	$0.716625\pi$
$654$	−41.2924	−1.61466
$655$	−8.20768	−0.320701
$656$	−2.36465	−0.0923241
$657$	66.2692	2.58541
$658$	34.1969	1.33313
$659$	13.2948	0.517891	0.258945	−	0.965892i	$-0.416625\pi$
$659$	13.2948	0.517891	0.258945	+	0.965892i	$0.416625\pi$
$660$	12.5096	0.486937
$661$	−28.7987	−1.12014	−0.560070	−	0.828445i	$-0.689226\pi$
$661$	−28.7987	−1.12014	−0.560070	+	0.828445i	$0.689226\pi$
$662$	−3.99767	−0.155374
$663$	4.28400	0.166377
$664$	6.11502	0.237309
$665$	14.8174	0.574594
$666$	−32.2980	−1.25152
$667$	4.00355	0.155018
$668$	−11.2021	−0.433424
$669$	−41.5996	−1.60833
$670$	−6.50890	−0.251461
$671$	79.5721	3.07185
$672$	10.3324	0.398580
$673$	−24.4023	−0.940640	−0.470320	−	0.882496i	$-0.655861\pi$
$673$	−24.4023	−0.940640	−0.470320	+	0.882496i	$0.655861\pi$
$674$	−4.08641	−0.157403
$675$	80.5012	3.09849
$676$	−2.77419	−0.106700
$677$	−29.5426	−1.13541	−0.567707	−	0.823230i	$-0.692170\pi$
$677$	−29.5426	−1.13541	−0.567707	+	0.823230i	$0.692170\pi$
$678$	69.2307	2.65879
$679$	4.47473	0.171724
$680$	0.228824	0.00877500
$681$	84.3402	3.23192
$682$	−48.0373	−1.83944
$683$	15.7194	0.601486	0.300743	−	0.953705i	$-0.402765\pi$
$683$	15.7194	0.601486	0.300743	+	0.953705i	$0.402765\pi$
$684$	−68.4772	−2.61829
$685$	−2.02482	−0.0773644
$686$	13.7054	0.523275
$687$	18.2639	0.696813
$688$	−2.12462	−0.0810006
$689$	14.7593	0.562286
$690$	8.83540	0.336358
$691$	−29.9414	−1.13902	−0.569512	−	0.821983i	$-0.692868\pi$
$691$	−29.9414	−1.13902	−0.569512	+	0.821983i	$0.692868\pi$
$692$	11.1371	0.423370
$693$	165.637	6.29203
$694$	−17.6609	−0.670399
$695$	−1.67704	−0.0636137
$696$	2.88391	0.109314
$697$	−0.948448	−0.0359250
$698$	17.1942	0.650811
$699$	26.9768	1.02035
$700$	14.4605	0.546557
$701$	20.6465	0.779806	0.389903	−	0.920856i	$-0.372509\pi$
$701$	20.6465	0.779806	0.389903	+	0.920856i	$0.372509\pi$
$702$	55.0697	2.07847
$703$	33.2484	1.25399
$704$	−6.56501	−0.247428
$705$	21.0644	0.793330
$706$	−35.5919	−1.33952
$707$	23.1329	0.870003
$708$	−34.7165	−1.30472
$709$	26.1889	0.983543	0.491772	−	0.870724i	$-0.336350\pi$
$709$	26.1889	0.983543	0.491772	+	0.870724i	$0.336350\pi$
$710$	−0.606342	−0.0227556
$711$	−19.6441	−0.736710
$712$	9.22117	0.345578
$713$	−33.9282	−1.27062
$714$	4.14426	0.155095
$715$	11.9768	0.447905
$716$	−1.13314	−0.0423476
$717$	6.58944	0.246087
$718$	11.3938	0.425213
$719$	32.7086	1.21983	0.609913	−	0.792468i	$-0.291204\pi$
$719$	32.7086	1.21983	0.609913	+	0.792468i	$0.291204\pi$
$720$	4.65297	0.173406
$721$	6.33807	0.236042
$722$	51.4922	1.91634
$723$	38.5835	1.43494
$724$	−13.5849	−0.504880
$725$	4.03614	0.149898
$726$	−107.214	−3.97908
$727$	6.70580	0.248704	0.124352	−	0.992238i	$-0.460315\pi$
$727$	6.70580	0.248704	0.124352	+	0.992238i	$0.460315\pi$
$728$	9.89225	0.366631
$729$	97.0113	3.59301
$730$	4.63544	0.171565
$731$	−0.852176	−0.0315189
$732$	40.4836	1.49632
$733$	−33.0287	−1.21994	−0.609972	−	0.792423i	$-0.708819\pi$
$733$	−33.0287	−1.21994	−0.609972	+	0.792423i	$0.708819\pi$
$734$	28.9954	1.07024
$735$	−4.89631	−0.180603
$736$	−4.63679	−0.170914
$737$	74.9012	2.75902
$738$	−19.2860	−0.709928
$739$	−8.13782	−0.299354	−0.149677	−	0.988735i	$-0.547823\pi$
$739$	−8.13782	−0.299354	−0.149677	+	0.988735i	$0.547823\pi$
$740$	−2.25920	−0.0830499
$741$	−89.6753	−3.29431
$742$	14.2779	0.524158
$743$	−19.9742	−0.732784	−0.366392	−	0.930461i	$-0.619407\pi$
$743$	−19.9742	−0.732784	−0.366392	+	0.930461i	$0.619407\pi$
$744$	−24.4397	−0.896004
$745$	−2.73172	−0.100082
$746$	14.0693	0.515113
$747$	49.8739	1.82479
$748$	−2.63319	−0.0962790
$749$	15.5410	0.567854
$750$	18.4348	0.673144
$751$	1.41724	0.0517160	0.0258580	−	0.999666i	$-0.491768\pi$
$751$	1.41724	0.0517160	0.0258580	+	0.999666i	$0.491768\pi$
$752$	−11.0545	−0.403117
$753$	−6.45785	−0.235337
$754$	2.76106	0.100552
$755$	−0.324039	−0.0117930
$756$	53.2734	1.93754
$757$	3.05127	0.110900	0.0554502	−	0.998461i	$-0.482341\pi$
$757$	3.05127	0.110900	0.0554502	+	0.998461i	$0.482341\pi$
$758$	−35.9360	−1.30525
$759$	−101.673	−3.69051
$760$	−4.78989	−0.173748
$761$	−5.92196	−0.214671	−0.107335	−	0.994223i	$-0.534232\pi$
$761$	−5.92196	−0.214671	−0.107335	+	0.994223i	$0.534232\pi$
$762$	−23.5608	−0.853517
$763$	−38.2439	−1.38452
$764$	−4.80582	−0.173869
$765$	1.86628	0.0674756
$766$	35.8884	1.29670
$767$	−33.2377	−1.20014
$768$	−3.34006	−0.120524
$769$	17.6940	0.638062	0.319031	−	0.947744i	$-0.396643\pi$
$769$	17.6940	0.638062	0.319031	+	0.947744i	$0.396643\pi$
$770$	11.5861	0.417534
$771$	−97.2681	−3.50303
$772$	−17.4574	−0.628304
$773$	−22.2158	−0.799046	−0.399523	−	0.916723i	$-0.630824\pi$
$773$	−22.2158	−0.799046	−0.399523	+	0.916723i	$0.630824\pi$
$774$	−17.3284	−0.622856
$775$	−34.2043	−1.22866
$776$	−1.44651	−0.0519266
$777$	−40.9166	−1.46788
$778$	9.14107	0.327723
$779$	19.8535	0.711326
$780$	6.09337	0.218178
$781$	6.97747	0.249674
$782$	−1.85979	−0.0665060
$783$	14.8694	0.531387
$784$	2.56957	0.0917704
$785$	−11.1003	−0.396188
$786$	48.0528	1.71399
$787$	52.7132	1.87902	0.939511	−	0.342517i	$-0.111280\pi$
$787$	52.7132	1.87902	0.939511	+	0.342517i	$0.111280\pi$
$788$	−9.53216	−0.339569
$789$	−82.5887	−2.94024
$790$	−1.37407	−0.0488874
$791$	64.1196	2.27983
$792$	−53.5441	−1.90261
$793$	38.7591	1.37638
$794$	−1.37077	−0.0486469
$795$	8.79482	0.311920
$796$	−6.12553	−0.217114
$797$	−12.7297	−0.450908	−0.225454	−	0.974254i	$-0.572387\pi$
$797$	−12.7297	−0.450908	−0.225454	+	0.974254i	$0.572387\pi$
$798$	−86.7502	−3.07092
$799$	−4.43391	−0.156860
$800$	−4.67453	−0.165270
$801$	75.2076	2.65733
$802$	9.82189	0.346823
$803$	−53.3423	−1.88241
$804$	38.1072	1.34394
$805$	8.18311	0.288417
$806$	−23.3987	−0.824184
$807$	−62.6659	−2.20594
$808$	−7.47798	−0.263074
$809$	−37.0206	−1.30157	−0.650787	−	0.759260i	$-0.725561\pi$
$809$	−37.0206	−1.30157	−0.650787	+	0.759260i	$0.725561\pi$
$810$	18.8561	0.662536
$811$	−4.49232	−0.157747	−0.0788733	−	0.996885i	$-0.525132\pi$
$811$	−4.49232	−0.157747	−0.0788733	+	0.996885i	$0.525132\pi$
$812$	2.67100	0.0937337
$813$	3.97213	0.139309
$814$	25.9977	0.911220
$815$	5.93855	0.208018
$816$	−1.33968	−0.0468981
$817$	17.8383	0.624082
$818$	−10.1018	−0.353200
$819$	80.6809	2.81922
$820$	−1.34903	−0.0471102
$821$	−47.0747	−1.64292	−0.821460	−	0.570266i	$-0.806840\pi$
$821$	−47.0747	−1.64292	−0.821460	+	0.570266i	$0.806840\pi$
$822$	11.8546	0.413475
$823$	8.01977	0.279551	0.139776	−	0.990183i	$-0.455362\pi$
$823$	8.01977	0.279551	0.139776	+	0.990183i	$0.455362\pi$
$824$	−2.04885	−0.0713752
$825$	−102.501	−3.56862
$826$	−32.1535	−1.11876
$827$	−20.6720	−0.718834	−0.359417	−	0.933177i	$-0.617024\pi$
$827$	−20.6720	−0.718834	−0.359417	+	0.933177i	$0.617024\pi$
$828$	−37.8175	−1.31425
$829$	−46.6973	−1.62187	−0.810933	−	0.585139i	$-0.801040\pi$
$829$	−46.6973	−1.62187	−0.810933	+	0.585139i	$0.801040\pi$
$830$	3.48861	0.121092
$831$	60.6461	2.10379
$832$	−3.19778	−0.110863
$833$	1.03064	0.0357096
$834$	9.81843	0.339984
$835$	−6.39081	−0.221163
$836$	55.1196	1.90635
$837$	−126.011	−4.35556
$838$	−5.36924	−0.185477
$839$	6.13359	0.211755	0.105878	−	0.994379i	$-0.466235\pi$
$839$	6.13359	0.211755	0.105878	+	0.994379i	$0.466235\pi$
$840$	5.89461	0.203383
$841$	−28.2545	−0.974293
$842$	8.52761	0.293881
$843$	55.2086	1.90149
$844$	22.9526	0.790062
$845$	−1.58268	−0.0544457
$846$	−90.1604	−3.09978
$847$	−99.2986	−3.41194
$848$	−4.61550	−0.158497
$849$	−33.5106	−1.15008
$850$	−1.87493	−0.0643095
$851$	18.3619	0.629438
$852$	3.54990	0.121618
$853$	−39.5780	−1.35512	−0.677562	−	0.735466i	$-0.736963\pi$
$853$	−39.5780	−1.35512	−0.677562	+	0.735466i	$0.736963\pi$
$854$	37.4948	1.28305
$855$	−39.0662	−1.33604
$856$	−5.02379	−0.171710
$857$	−26.1864	−0.894511	−0.447256	−	0.894406i	$-0.647599\pi$
$857$	−26.1864	−0.894511	−0.447256	+	0.894406i	$0.647599\pi$
$858$	−70.1194	−2.39384
$859$	−36.5382	−1.24667	−0.623334	−	0.781956i	$-0.714222\pi$
$859$	−36.5382	−1.24667	−0.623334	+	0.781956i	$0.714222\pi$
$860$	−1.21210	−0.0413322
$861$	−24.4324	−0.832655
$862$	−19.1358	−0.651768
$863$	−31.5059	−1.07247	−0.536237	−	0.844068i	$-0.680155\pi$
$863$	−31.5059	−1.07247	−0.536237	+	0.844068i	$0.680155\pi$
$864$	−17.2212	−0.585878
$865$	6.35372	0.216033
$866$	32.9580	1.11996
$867$	56.2436	1.91013
$868$	−22.6354	−0.768297
$869$	15.8122	0.536391
$870$	1.64527	0.0557798
$871$	36.4839	1.23621
$872$	12.3628	0.418657
$873$	−11.7977	−0.399291
$874$	38.9303	1.31684
$875$	17.0738	0.577201
$876$	−27.1388	−0.916934
$877$	−54.0178	−1.82405	−0.912025	−	0.410134i	$-0.865482\pi$
$877$	−54.0178	−1.82405	−0.912025	+	0.410134i	$0.865482\pi$
$878$	21.0136	0.709175
$879$	−42.4592	−1.43211
$880$	−3.74533	−0.126255
$881$	−8.54493	−0.287886	−0.143943	−	0.989586i	$-0.545978\pi$
$881$	−8.54493	−0.287886	−0.143943	+	0.989586i	$0.545978\pi$
$882$	20.9573	0.705670
$883$	−32.6213	−1.09779	−0.548897	−	0.835890i	$-0.684952\pi$
$883$	−32.6213	−1.09779	−0.548897	+	0.835890i	$0.684952\pi$
$884$	−1.28261	−0.0431389
$885$	−19.8057	−0.665762
$886$	−34.1129	−1.14604
$887$	−40.9160	−1.37382	−0.686912	−	0.726740i	$-0.741034\pi$
$887$	−40.9160	−1.37382	−0.686912	+	0.726740i	$0.741034\pi$
$888$	13.2268	0.443861
$889$	−21.8214	−0.731866
$890$	5.26067	0.176338
$891$	−216.987	−7.26932
$892$	12.4547	0.417016
$893$	92.8133	3.10588
$894$	15.9932	0.534891
$895$	−0.646458	−0.0216087
$896$	−3.09347	−0.103346
$897$	−49.5245	−1.65357
$898$	−8.87757	−0.296248
$899$	−6.31787	−0.210713
$900$	−38.1253	−1.27084
$901$	−1.85125	−0.0616741
$902$	15.5240	0.516891
$903$	−21.9524	−0.730530
$904$	−20.7274	−0.689383
$905$	−7.75019	−0.257625
$906$	1.89713	0.0630278
$907$	20.9934	0.697073	0.348536	−	0.937295i	$-0.386679\pi$
$907$	20.9934	0.697073	0.348536	+	0.937295i	$0.386679\pi$
$908$	−25.2511	−0.837988
$909$	−60.9902	−2.02292
$910$	5.64352	0.187081
$911$	−21.7201	−0.719620	−0.359810	−	0.933026i	$-0.617158\pi$
$911$	−21.7201	−0.719620	−0.359810	+	0.933026i	$0.617158\pi$
$912$	28.0430	0.928596
$913$	−40.1452	−1.32861
$914$	37.7291	1.24797
$915$	23.0958	0.763525
$916$	−5.46815	−0.180673
$917$	44.5053	1.46969
$918$	−6.90734	−0.227976
$919$	6.21279	0.204941	0.102471	−	0.994736i	$-0.467325\pi$
$919$	6.21279	0.204941	0.102471	+	0.994736i	$0.467325\pi$
$920$	−2.64528	−0.0872125
$921$	62.4364	2.05735
$922$	40.0866	1.32018
$923$	3.39869	0.111869
$924$	−67.8321	−2.23151
$925$	18.5113	0.608649
$926$	−39.3704	−1.29379
$927$	−16.7104	−0.548842
$928$	−0.863431	−0.0283435
$929$	26.6588	0.874646	0.437323	−	0.899305i	$-0.355927\pi$
$929$	26.6588	0.874646	0.437323	+	0.899305i	$0.355927\pi$
$930$	−13.9429	−0.457204
$931$	−21.5740	−0.707060
$932$	−8.07674	−0.264562
$933$	−15.9593	−0.522485
$934$	30.5105	0.998334
$935$	−1.50223	−0.0491283
$936$	−26.0810	−0.852485
$937$	−42.5063	−1.38862	−0.694309	−	0.719677i	$-0.744290\pi$
$937$	−42.5063	−1.38862	−0.694309	+	0.719677i	$0.744290\pi$
$938$	35.2939	1.15239
$939$	−55.6957	−1.81756
$940$	−6.30659	−0.205698
$941$	31.5302	1.02785	0.513927	−	0.857834i	$-0.328190\pi$
$941$	31.5302	1.02785	0.513927	+	0.857834i	$0.328190\pi$
$942$	64.9883	2.11743
$943$	10.9644	0.357049
$944$	10.3940	0.338295
$945$	30.3924	0.988666
$946$	13.9482	0.453495
$947$	−13.1272	−0.426577	−0.213289	−	0.976989i	$-0.568417\pi$
$947$	−13.1272	−0.426577	−0.213289	+	0.976989i	$0.568417\pi$
$948$	8.04469	0.261279
$949$	−25.9827	−0.843436
$950$	39.2472	1.27335
$951$	−92.7170	−3.00655
$952$	−1.24078	−0.0402138
$953$	−22.0680	−0.714852	−0.357426	−	0.933941i	$-0.616346\pi$
$953$	−22.0680	−0.714852	−0.357426	+	0.933941i	$0.616346\pi$
$954$	−37.6439	−1.21876
$955$	−2.74172	−0.0887199
$956$	−1.97285	−0.0638067
$957$	−18.9329	−0.612014
$958$	−27.4870	−0.888065
$959$	10.9794	0.354543
$960$	−1.90550	−0.0614997
$961$	22.5409	0.727126
$962$	12.6634	0.408283
$963$	−40.9739	−1.32036
$964$	−11.5518	−0.372057
$965$	−9.95940	−0.320605
$966$	−47.9090	−1.54145
$967$	−52.7671	−1.69687	−0.848437	−	0.529296i	$-0.822456\pi$
$967$	−52.7671	−1.69687	−0.848437	+	0.529296i	$0.822456\pi$
$968$	32.0994	1.03171
$969$	11.2479	0.361334
$970$	−0.825231	−0.0264966
$971$	36.7630	1.17978	0.589891	−	0.807483i	$-0.299171\pi$
$971$	36.7630	1.17978	0.589891	+	0.807483i	$0.299171\pi$
$972$	−58.7317	−1.88382
$973$	9.09357	0.291526
$974$	−26.5919	−0.852060
$975$	−49.9276	−1.59896
$976$	−12.1206	−0.387972
$977$	22.7895	0.729100	0.364550	−	0.931184i	$-0.381223\pi$
$977$	22.7895	0.729100	0.364550	+	0.931184i	$0.381223\pi$
$978$	−34.7680	−1.11176
$979$	−60.5371	−1.93477
$980$	1.46594	0.0468277
$981$	100.831	3.21927
$982$	7.61432	0.242983
$983$	11.7849	0.375880	0.187940	−	0.982181i	$-0.439819\pi$
$983$	11.7849	0.375880	0.187940	+	0.982181i	$0.439819\pi$
$984$	7.89806	0.251781
$985$	−5.43809	−0.173272
$986$	−0.346318	−0.0110290
$987$	−114.219	−3.63564
$988$	26.8485	0.854163
$989$	9.85144	0.313258
$990$	−30.5468	−0.970842
$991$	53.1225	1.68749	0.843746	−	0.536743i	$-0.180346\pi$
$991$	53.1225	1.68749	0.843746	+	0.536743i	$0.180346\pi$
$992$	7.31717	0.232320
$993$	13.3525	0.423727
$994$	3.28783	0.104283
$995$	−3.49461	−0.110787
$996$	−20.4245	−0.647175
$997$	−2.71608	−0.0860192	−0.0430096	−	0.999075i	$-0.513695\pi$
$997$	−2.71608	−0.0860192	−0.0430096	+	0.999075i	$0.513695\pi$
$998$	26.0346	0.824112
$999$	68.1969	2.15765

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.d.1.2	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.d.1.2	✓	96	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.34006 q^{3} +1.00000 q^{4} +0.570499 q^{5} -3.34006 q^{6} -3.09347 q^{7} +1.00000 q^{8} +8.15597 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.34006 q^{3} +1.00000 q^{4} +0.570499 q^{5} -3.34006 q^{6} -3.09347 q^{7} +1.00000 q^{8} +8.15597 q^{9} +0.570499 q^{10} -6.56501 q^{11} -3.34006 q^{12} -3.19778 q^{13} -3.09347 q^{14} -1.90550 q^{15} +1.00000 q^{16} +0.401095 q^{17} +8.15597 q^{18} -8.39596 q^{19} +0.570499 q^{20} +10.3324 q^{21} -6.56501 q^{22} -4.63679 q^{23} -3.34006 q^{24} -4.67453 q^{25} -3.19778 q^{26} -17.2212 q^{27} -3.09347 q^{28} -0.863431 q^{29} -1.90550 q^{30} +7.31717 q^{31} +1.00000 q^{32} +21.9275 q^{33} +0.401095 q^{34} -1.76482 q^{35} +8.15597 q^{36} -3.96004 q^{37} -8.39596 q^{38} +10.6808 q^{39} +0.570499 q^{40} -2.36465 q^{41} +10.3324 q^{42} -2.12462 q^{43} -6.56501 q^{44} +4.65297 q^{45} -4.63679 q^{46} -11.0545 q^{47} -3.34006 q^{48} +2.56957 q^{49} -4.67453 q^{50} -1.33968 q^{51} -3.19778 q^{52} -4.61550 q^{53} -17.2212 q^{54} -3.74533 q^{55} -3.09347 q^{56} +28.0430 q^{57} -0.863431 q^{58} +10.3940 q^{59} -1.90550 q^{60} -12.1206 q^{61} +7.31717 q^{62} -25.2303 q^{63} +1.00000 q^{64} -1.82433 q^{65} +21.9275 q^{66} -11.4091 q^{67} +0.401095 q^{68} +15.4871 q^{69} -1.76482 q^{70} -1.06283 q^{71} +8.15597 q^{72} +8.12524 q^{73} -3.96004 q^{74} +15.6132 q^{75} -8.39596 q^{76} +20.3087 q^{77} +10.6808 q^{78} -2.40855 q^{79} +0.570499 q^{80} +33.0520 q^{81} -2.36465 q^{82} +6.11502 q^{83} +10.3324 q^{84} +0.228824 q^{85} -2.12462 q^{86} +2.88391 q^{87} -6.56501 q^{88} +9.22117 q^{89} +4.65297 q^{90} +9.89225 q^{91} -4.63679 q^{92} -24.4397 q^{93} -11.0545 q^{94} -4.78989 q^{95} -3.34006 q^{96} -1.44651 q^{97} +2.56957 q^{98} -53.5441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9}+O(q^{10}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9	\( 96 q + 96 q^{2} + 8 q^{3} + 96 q^{4} + 39 q^{5} + 8 q^{6} + 19 q^{7} + 96 q^{8} + 130 q^{9} + 39 q^{10} + 36 q^{11} + 8 q^{12} + 63 q^{13} + 19 q^{14} + 17 q^{15} + 96 q^{16} + 56 q^{17} + 130 q^{18} + 17 q^{19} + 39 q^{20} + 51 q^{21} + 36 q^{22} + 47 q^{23} + 8 q^{24} + 147 q^{25} + 63 q^{26} + 17 q^{27} + 19 q^{28} + 60 q^{29} + 17 q^{30} + 63 q^{31} + 96 q^{32} + 55 q^{33} + 56 q^{34} + 45 q^{35} + 130 q^{36} + 46 q^{37} + 17 q^{38} + 22 q^{39} + 39 q^{40} + 101 q^{41} + 51 q^{42} - 3 q^{43} + 36 q^{44} + 106 q^{45} + 47 q^{46} + 99 q^{47} + 8 q^{48} + 175 q^{49} + 147 q^{50} - q^{51} + 63 q^{52} + 75 q^{53} + 17 q^{54} + 80 q^{55} + 19 q^{56} + 35 q^{57} + 60 q^{58} + 129 q^{59} + 17 q^{60} + 75 q^{61} + 63 q^{62} + 20 q^{63} + 96 q^{64} + 55 q^{65} + 55 q^{66} + 2 q^{67} + 56 q^{68} + 57 q^{69} + 45 q^{70} + 87 q^{71} + 130 q^{72} + 120 q^{73} + 46 q^{74} - 15 q^{75} + 17 q^{76} + 95 q^{77} + 22 q^{78} + 21 q^{79} + 39 q^{80} + 180 q^{81} + 101 q^{82} + 69 q^{83} + 51 q^{84} + 59 q^{85} - 3 q^{86} + 63 q^{87} + 36 q^{88} + 144 q^{89} + 106 q^{90} - 5 q^{91} + 47 q^{92} + 59 q^{93} + 99 q^{94} + 23 q^{95} + 8 q^{96} + 99 q^{97} + 175 q^{98} + 42 q^{99}+O(q^{100}) \) 96 * q + 96 * q^2 + 8 * q^3 + 96 * q^4 + 39 * q^5 + 8 * q^6 + 19 * q^7 + 96 * q^8 + 130 * q^9 + 39 * q^10 + 36 * q^11 + 8 * q^12 + 63 * q^13 + 19 * q^14 + 17 * q^15 + 96 * q^16 + 56 * q^17 + 130 * q^18 + 17 * q^19 + 39 * q^20 + 51 * q^21 + 36 * q^22 + 47 * q^23 + 8 * q^24 + 147 * q^25 + 63 * q^26 + 17 * q^27 + 19 * q^28 + 60 * q^29 + 17 * q^30 + 63 * q^31 + 96 * q^32 + 55 * q^33 + 56 * q^34 + 45 * q^35 + 130 * q^36 + 46 * q^37 + 17 * q^38 + 22 * q^39 + 39 * q^40 + 101 * q^41 + 51 * q^42 - 3 * q^43 + 36 * q^44 + 106 * q^45 + 47 * q^46 + 99 * q^47 + 8 * q^48 + 175 * q^49 + 147 * q^50 - q^51 + 63 * q^52 + 75 * q^53 + 17 * q^54 + 80 * q^55 + 19 * q^56 + 35 * q^57 + 60 * q^58 + 129 * q^59 + 17 * q^60 + 75 * q^61 + 63 * q^62 + 20 * q^63 + 96 * q^64 + 55 * q^65 + 55 * q^66 + 2 * q^67 + 56 * q^68 + 57 * q^69 + 45 * q^70 + 87 * q^71 + 130 * q^72 + 120 * q^73 + 46 * q^74 - 15 * q^75 + 17 * q^76 + 95 * q^77 + 22 * q^78 + 21 * q^79 + 39 * q^80 + 180 * q^81 + 101 * q^82 + 69 * q^83 + 51 * q^84 + 59 * q^85 - 3 * q^86 + 63 * q^87 + 36 * q^88 + 144 * q^89 + 106 * q^90 - 5 * q^91 + 47 * q^92 + 59 * q^93 + 99 * q^94 + 23 * q^95 + 8 * q^96 + 99 * q^97 + 175 * q^98 + 42 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more