LMFDB - Embedded newform 8035.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.80100 q^{2} +2.46905 q^{3} +5.84558 q^{4} +1.00000 q^{5} -6.91579 q^{6} +0.471155 q^{7} -10.7715 q^{8} +3.09620 q^{9} +O(q^{10})$	\(q-2.80100 q^{2} +2.46905 q^{3} +5.84558 q^{4} +1.00000 q^{5} -6.91579 q^{6} +0.471155 q^{7} -10.7715 q^{8} +3.09620 q^{9} -2.80100 q^{10} -4.30458 q^{11} +14.4330 q^{12} +1.85656 q^{13} -1.31970 q^{14} +2.46905 q^{15} +18.4797 q^{16} -0.178455 q^{17} -8.67243 q^{18} -2.89409 q^{19} +5.84558 q^{20} +1.16331 q^{21} +12.0571 q^{22} -2.43251 q^{23} -26.5952 q^{24} +1.00000 q^{25} -5.20021 q^{26} +0.237513 q^{27} +2.75418 q^{28} -2.73096 q^{29} -6.91579 q^{30} +8.72046 q^{31} -30.2185 q^{32} -10.6282 q^{33} +0.499851 q^{34} +0.471155 q^{35} +18.0991 q^{36} +3.28650 q^{37} +8.10633 q^{38} +4.58392 q^{39} -10.7715 q^{40} +2.38482 q^{41} -3.25841 q^{42} -1.86980 q^{43} -25.1628 q^{44} +3.09620 q^{45} +6.81345 q^{46} +5.73021 q^{47} +45.6271 q^{48} -6.77801 q^{49} -2.80100 q^{50} -0.440613 q^{51} +10.8526 q^{52} -8.48752 q^{53} -0.665274 q^{54} -4.30458 q^{55} -5.07503 q^{56} -7.14564 q^{57} +7.64940 q^{58} -11.1845 q^{59} +14.4330 q^{60} -14.6674 q^{61} -24.4260 q^{62} +1.45879 q^{63} +47.6827 q^{64} +1.85656 q^{65} +29.7696 q^{66} -5.65361 q^{67} -1.04317 q^{68} -6.00598 q^{69} -1.31970 q^{70} +5.16683 q^{71} -33.3505 q^{72} -12.3727 q^{73} -9.20547 q^{74} +2.46905 q^{75} -16.9176 q^{76} -2.02813 q^{77} -12.8396 q^{78} -15.9687 q^{79} +18.4797 q^{80} -8.70216 q^{81} -6.67987 q^{82} -6.51059 q^{83} +6.80019 q^{84} -0.178455 q^{85} +5.23731 q^{86} -6.74287 q^{87} +46.3666 q^{88} -2.19459 q^{89} -8.67243 q^{90} +0.874726 q^{91} -14.2194 q^{92} +21.5312 q^{93} -16.0503 q^{94} -2.89409 q^{95} -74.6110 q^{96} +12.1592 q^{97} +18.9852 q^{98} -13.3278 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) $ 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * 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 $

$2$	−2.80100	−1.98060	−0.990302	−	0.138933i	$-0.955633\pi$
$2$	−2.80100	−1.98060	−0.990302	+	0.138933i	$0.955633\pi$
$3$	2.46905	1.42551	0.712753	−	0.701415i	$-0.247448\pi$
$3$	2.46905	1.42551	0.712753	+	0.701415i	$0.247448\pi$
$4$	5.84558	2.92279
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−6.91579	−2.82336
$7$	0.471155	0.178080	0.0890400	−	0.996028i	$-0.471620\pi$
$7$	0.471155	0.178080	0.0890400	+	0.996028i	$0.471620\pi$
$8$	−10.7715	−3.80829
$9$	3.09620	1.03207
$10$	−2.80100	−0.885753
$11$	−4.30458	−1.29788	−0.648940	−	0.760840i	$-0.724787\pi$
$11$	−4.30458	−1.29788	−0.648940	+	0.760840i	$0.724787\pi$
$12$	14.4330	4.16645
$13$	1.85656	0.514916	0.257458	−	0.966290i	$-0.417115\pi$
$13$	1.85656	0.514916	0.257458	+	0.966290i	$0.417115\pi$
$14$	−1.31970	−0.352706
$15$	2.46905	0.637505
$16$	18.4797	4.61991
$17$	−0.178455	−0.0432816	−0.0216408	−	0.999766i	$-0.506889\pi$
$17$	−0.178455	−0.0432816	−0.0216408	+	0.999766i	$0.506889\pi$
$18$	−8.67243	−2.04411
$19$	−2.89409	−0.663949	−0.331975	−	0.943288i	$-0.607715\pi$
$19$	−2.89409	−0.663949	−0.331975	+	0.943288i	$0.607715\pi$
$20$	5.84558	1.30711
$21$	1.16331	0.253854
$22$	12.0571	2.57059
$23$	−2.43251	−0.507213	−0.253607	−	0.967307i	$-0.581617\pi$
$23$	−2.43251	−0.507213	−0.253607	+	0.967307i	$0.581617\pi$
$24$	−26.5952	−5.42873
$25$	1.00000	0.200000
$26$	−5.20021	−1.01984
$27$	0.237513	0.0457095
$28$	2.75418	0.520490
$29$	−2.73096	−0.507126	−0.253563	−	0.967319i	$-0.581603\pi$
$29$	−2.73096	−0.507126	−0.253563	+	0.967319i	$0.581603\pi$
$30$	−6.91579	−1.26265
$31$	8.72046	1.56624	0.783121	−	0.621870i	$-0.213627\pi$
$31$	8.72046	1.56624	0.783121	+	0.621870i	$0.213627\pi$
$32$	−30.2185	−5.34193
$33$	−10.6282	−1.85014
$34$	0.499851	0.0857237
$35$	0.471155	0.0796398
$36$	18.0991	3.01651
$37$	3.28650	0.540297	0.270148	−	0.962819i	$-0.412927\pi$
$37$	3.28650	0.540297	0.270148	+	0.962819i	$0.412927\pi$
$38$	8.10633	1.31502
$39$	4.58392	0.734015
$40$	−10.7715	−1.70312
$41$	2.38482	0.372446	0.186223	−	0.982507i	$-0.440375\pi$
$41$	2.38482	0.372446	0.186223	+	0.982507i	$0.440375\pi$
$42$	−3.25841	−0.502784
$43$	−1.86980	−0.285142	−0.142571	−	0.989785i	$-0.545537\pi$
$43$	−1.86980	−0.285142	−0.142571	+	0.989785i	$0.545537\pi$
$44$	−25.1628	−3.79343
$45$	3.09620	0.461554
$46$	6.81345	1.00459
$47$	5.73021	0.835837	0.417919	−	0.908484i	$-0.362760\pi$
$47$	5.73021	0.835837	0.417919	+	0.908484i	$0.362760\pi$
$48$	45.6271	6.58571
$49$	−6.77801	−0.968288
$50$	−2.80100	−0.396121
$51$	−0.440613	−0.0616982
$52$	10.8526	1.50499
$53$	−8.48752	−1.16585	−0.582925	−	0.812526i	$-0.698092\pi$
$53$	−8.48752	−1.16585	−0.582925	+	0.812526i	$0.698092\pi$
$54$	−0.665274	−0.0905323
$55$	−4.30458	−0.580430
$56$	−5.07503	−0.678179
$57$	−7.14564	−0.946463
$58$	7.64940	1.00442
$59$	−11.1845	−1.45609	−0.728046	−	0.685528i	$-0.759571\pi$
$59$	−11.1845	−1.45609	−0.728046	+	0.685528i	$0.759571\pi$
$60$	14.4330	1.86329
$61$	−14.6674	−1.87797	−0.938985	−	0.343959i	$-0.888232\pi$
$61$	−14.6674	−1.87797	−0.938985	+	0.343959i	$0.888232\pi$
$62$	−24.4260	−3.10210
$63$	1.45879	0.183790
$64$	47.6827	5.96033
$65$	1.85656	0.230277
$66$	29.7696	3.66438
$67$	−5.65361	−0.690698	−0.345349	−	0.938474i	$-0.612240\pi$
$67$	−5.65361	−0.690698	−0.345349	+	0.938474i	$0.612240\pi$
$68$	−1.04317	−0.126503
$69$	−6.00598	−0.723035
$70$	−1.31970	−0.157735
$71$	5.16683	0.613190	0.306595	−	0.951840i	$-0.400810\pi$
$71$	5.16683	0.613190	0.306595	+	0.951840i	$0.400810\pi$
$72$	−33.3505	−3.93040
$73$	−12.3727	−1.44812	−0.724059	−	0.689738i	$-0.757726\pi$
$73$	−12.3727	−1.44812	−0.724059	+	0.689738i	$0.757726\pi$
$74$	−9.20547	−1.07011
$75$	2.46905	0.285101
$76$	−16.9176	−1.94058
$77$	−2.02813	−0.231126
$78$	−12.8396	−1.45379
$79$	−15.9687	−1.79662	−0.898312	−	0.439358i	$-0.855206\pi$
$79$	−15.9687	−1.79662	−0.898312	+	0.439358i	$0.855206\pi$
$80$	18.4797	2.06609
$81$	−8.70216	−0.966906
$82$	−6.67987	−0.737668
$83$	−6.51059	−0.714631	−0.357315	−	0.933984i	$-0.616308\pi$
$83$	−6.51059	−0.714631	−0.357315	+	0.933984i	$0.616308\pi$
$84$	6.80019	0.741962
$85$	−0.178455	−0.0193561
$86$	5.23731	0.564753
$87$	−6.74287	−0.722911
$88$	46.3666	4.94270
$89$	−2.19459	−0.232626	−0.116313	−	0.993213i	$-0.537108\pi$
$89$	−2.19459	−0.232626	−0.116313	+	0.993213i	$0.537108\pi$
$90$	−8.67243	−0.914155
$91$	0.874726	0.0916962
$92$	−14.2194	−1.48248
$93$	21.5312	2.23269
$94$	−16.0503	−1.65546
$95$	−2.89409	−0.296927
$96$	−74.6110	−7.61495
$97$	12.1592	1.23458	0.617288	−	0.786737i	$-0.288231\pi$
$97$	12.1592	1.23458	0.617288	+	0.786737i	$0.288231\pi$
$98$	18.9852	1.91779
$99$	−13.3278	−1.33950
$100$	5.84558	0.584558
$101$	1.86628	0.185702	0.0928511	−	0.995680i	$-0.470402\pi$
$101$	1.86628	0.185702	0.0928511	+	0.995680i	$0.470402\pi$
$102$	1.23416	0.122200
$103$	17.2973	1.70436	0.852178	−	0.523252i	$-0.175281\pi$
$103$	17.2973	1.70436	0.852178	+	0.523252i	$0.175281\pi$
$104$	−19.9978	−1.96095
$105$	1.16331	0.113527
$106$	23.7735	2.30909
$107$	−4.07146	−0.393603	−0.196801	−	0.980443i	$-0.563055\pi$
$107$	−4.07146	−0.393603	−0.196801	+	0.980443i	$0.563055\pi$
$108$	1.38840	0.133599
$109$	19.5491	1.87246	0.936232	−	0.351383i	$-0.114288\pi$
$109$	19.5491	1.87246	0.936232	+	0.351383i	$0.114288\pi$
$110$	12.0571	1.14960
$111$	8.11452	0.770196
$112$	8.70679	0.822714
$113$	1.81511	0.170751	0.0853756	−	0.996349i	$-0.472791\pi$
$113$	1.81511	0.170751	0.0853756	+	0.996349i	$0.472791\pi$
$114$	20.0149	1.87457
$115$	−2.43251	−0.226833
$116$	−15.9640	−1.48222
$117$	5.74826	0.531427
$118$	31.3276	2.88394
$119$	−0.0840798	−0.00770759
$120$	−26.5952	−2.42780
$121$	7.52942	0.684493
$122$	41.0834	3.71951
$123$	5.88823	0.530924
$124$	50.9762	4.57780
$125$	1.00000	0.0894427
$126$	−4.08606	−0.364016
$127$	9.78525	0.868301	0.434150	−	0.900840i	$-0.357049\pi$
$127$	9.78525	0.868301	0.434150	+	0.900840i	$0.357049\pi$
$128$	−73.1219	−6.46313
$129$	−4.61663	−0.406472
$130$	−5.20021	−0.456088
$131$	−20.3140	−1.77484	−0.887420	−	0.460963i	$-0.847504\pi$
$131$	−20.3140	−1.77484	−0.887420	+	0.460963i	$0.847504\pi$
$132$	−62.1281	−5.40756
$133$	−1.36357	−0.118236
$134$	15.8357	1.36800
$135$	0.237513	0.0204419
$136$	1.92222	0.164829
$137$	−5.55181	−0.474323	−0.237161	−	0.971470i	$-0.576217\pi$
$137$	−5.55181	−0.474323	−0.237161	+	0.971470i	$0.576217\pi$
$138$	16.8227	1.43205
$139$	16.0976	1.36538	0.682691	−	0.730707i	$-0.260809\pi$
$139$	16.0976	1.36538	0.682691	+	0.730707i	$0.260809\pi$
$140$	2.75418	0.232770
$141$	14.1482	1.19149
$142$	−14.4723	−1.21449
$143$	−7.99170	−0.668299
$144$	57.2166	4.76805
$145$	−2.73096	−0.226794
$146$	34.6560	2.86815
$147$	−16.7352	−1.38030
$148$	19.2115	1.57917
$149$	4.75861	0.389840	0.194920	−	0.980819i	$-0.437555\pi$
$149$	4.75861	0.389840	0.194920	+	0.980819i	$0.437555\pi$
$150$	−6.91579	−0.564672
$151$	1.22122	0.0993811	0.0496906	−	0.998765i	$-0.484176\pi$
$151$	1.22122	0.0993811	0.0496906	+	0.998765i	$0.484176\pi$
$152$	31.1735	2.52851
$153$	−0.552531	−0.0446694
$154$	5.68078	0.457770
$155$	8.72046	0.700445
$156$	26.7957	2.14537
$157$	−20.1360	−1.60703	−0.803513	−	0.595288i	$-0.797038\pi$
$157$	−20.1360	−1.60703	−0.803513	+	0.595288i	$0.797038\pi$
$158$	44.7284	3.55840
$159$	−20.9561	−1.66193
$160$	−30.2185	−2.38898
$161$	−1.14609	−0.0903245
$162$	24.3747	1.91506
$163$	2.32163	0.181844	0.0909221	−	0.995858i	$-0.471019\pi$
$163$	2.32163	0.181844	0.0909221	+	0.995858i	$0.471019\pi$
$164$	13.9407	1.08858
$165$	−10.6282	−0.827406
$166$	18.2361	1.41540
$167$	−14.1819	−1.09743	−0.548714	−	0.836010i	$-0.684882\pi$
$167$	−14.1819	−1.09743	−0.548714	+	0.836010i	$0.684882\pi$
$168$	−12.5305	−0.966748
$169$	−9.55320	−0.734862
$170$	0.499851	0.0383368
$171$	−8.96067	−0.685239
$172$	−10.9301	−0.833410
$173$	5.95304	0.452601	0.226301	−	0.974057i	$-0.427337\pi$
$173$	5.95304	0.452601	0.226301	+	0.974057i	$0.427337\pi$
$174$	18.8867	1.43180
$175$	0.471155	0.0356160
$176$	−79.5472	−5.99609
$177$	−27.6150	−2.07567
$178$	6.14705	0.460741
$179$	7.24950	0.541853	0.270926	−	0.962600i	$-0.412670\pi$
$179$	7.24950	0.541853	0.270926	+	0.962600i	$0.412670\pi$
$180$	18.0991	1.34902
$181$	−14.0549	−1.04469	−0.522347	−	0.852733i	$-0.674944\pi$
$181$	−14.0549	−1.04469	−0.522347	+	0.852733i	$0.674944\pi$
$182$	−2.45010	−0.181614
$183$	−36.2145	−2.67706
$184$	26.2017	1.93161
$185$	3.28650	0.241628
$186$	−60.3089	−4.42207
$187$	0.768172	0.0561743
$188$	33.4964	2.44298
$189$	0.111906	0.00813994
$190$	8.10633	0.588095
$191$	−16.5296	−1.19604	−0.598021	−	0.801480i	$-0.704046\pi$
$191$	−16.5296	−1.19604	−0.598021	+	0.801480i	$0.704046\pi$
$192$	117.731	8.49649
$193$	−8.96542	−0.645345	−0.322672	−	0.946511i	$-0.604581\pi$
$193$	−8.96542	−0.645345	−0.322672	+	0.946511i	$0.604581\pi$
$194$	−34.0578	−2.44521
$195$	4.58392	0.328262
$196$	−39.6214	−2.83010
$197$	21.4981	1.53168	0.765840	−	0.643031i	$-0.222324\pi$
$197$	21.4981	1.53168	0.765840	+	0.643031i	$0.222324\pi$
$198$	37.3312	2.65301
$199$	−1.79501	−0.127245	−0.0636226	−	0.997974i	$-0.520265\pi$
$199$	−1.79501	−0.127245	−0.0636226	+	0.997974i	$0.520265\pi$
$200$	−10.7715	−0.761657
$201$	−13.9590	−0.984594
$202$	−5.22746	−0.367802
$203$	−1.28671	−0.0903090
$204$	−2.57564	−0.180331
$205$	2.38482	0.166563
$206$	−48.4497	−3.37565
$207$	−7.53153	−0.523477
$208$	34.3085	2.37887
$209$	12.4578	0.861727
$210$	−3.25841	−0.224852
$211$	−0.473769	−0.0326156	−0.0163078	−	0.999867i	$-0.505191\pi$
$211$	−0.473769	−0.0326156	−0.0163078	+	0.999867i	$0.505191\pi$
$212$	−49.6145	−3.40754
$213$	12.7572	0.874106
$214$	11.4041	0.779571
$215$	−1.86980	−0.127519
$216$	−2.55837	−0.174075
$217$	4.10869	0.278916
$218$	−54.7569	−3.70861
$219$	−30.5489	−2.06430
$220$	−25.1628	−1.69647
$221$	−0.331311	−0.0222864
$222$	−22.7287	−1.52545
$223$	13.6652	0.915093	0.457546	−	0.889186i	$-0.348728\pi$
$223$	13.6652	0.915093	0.457546	+	0.889186i	$0.348728\pi$
$224$	−14.2376	−0.951291
$225$	3.09620	0.206413
$226$	−5.08412	−0.338190
$227$	−13.6670	−0.907107	−0.453554	−	0.891229i	$-0.649844\pi$
$227$	−13.6670	−0.907107	−0.453554	+	0.891229i	$0.649844\pi$
$228$	−41.7704	−2.76631
$229$	0.606362	0.0400696	0.0200348	−	0.999799i	$-0.493622\pi$
$229$	0.606362	0.0400696	0.0200348	+	0.999799i	$0.493622\pi$
$230$	6.81345	0.449266
$231$	−5.00754	−0.329472
$232$	29.4164	1.93128
$233$	−5.03739	−0.330010	−0.165005	−	0.986293i	$-0.552764\pi$
$233$	−5.03739	−0.330010	−0.165005	+	0.986293i	$0.552764\pi$
$234$	−16.1009	−1.05255
$235$	5.73021	0.373798
$236$	−65.3797	−4.25585
$237$	−39.4276	−2.56110
$238$	0.235507	0.0152657
$239$	12.8609	0.831903	0.415951	−	0.909387i	$-0.363449\pi$
$239$	12.8609	0.831903	0.415951	+	0.909387i	$0.363449\pi$
$240$	45.6271	2.94522
$241$	−27.9680	−1.80158	−0.900788	−	0.434258i	$-0.857011\pi$
$241$	−27.9680	−1.80158	−0.900788	+	0.434258i	$0.857011\pi$
$242$	−21.0899	−1.35571
$243$	−22.1986	−1.42404
$244$	−85.7395	−5.48891
$245$	−6.77801	−0.433031
$246$	−16.4929	−1.05155
$247$	−5.37304	−0.341878
$248$	−93.9321	−5.96470
$249$	−16.0750	−1.01871
$250$	−2.80100	−0.177151
$251$	−13.4787	−0.850766	−0.425383	−	0.905013i	$-0.639861\pi$
$251$	−13.4787	−0.850766	−0.425383	+	0.905013i	$0.639861\pi$
$252$	8.52747	0.537180
$253$	10.4709	0.658302
$254$	−27.4085	−1.71976
$255$	−0.440613	−0.0275923
$256$	109.449	6.84056
$257$	28.2576	1.76266	0.881330	−	0.472501i	$-0.156649\pi$
$257$	28.2576	1.76266	0.881330	+	0.472501i	$0.156649\pi$
$258$	12.9312	0.805059
$259$	1.54845	0.0962161
$260$	10.8526	0.673053
$261$	−8.45558	−0.523387
$262$	56.8993	3.51525
$263$	0.0401333	0.00247472	0.00123736	−	0.999999i	$-0.499606\pi$
$263$	0.0401333	0.00247472	0.00123736	+	0.999999i	$0.499606\pi$
$264$	114.481	7.04584
$265$	−8.48752	−0.521384
$266$	3.81934	0.234179
$267$	−5.41856	−0.331610
$268$	−33.0486	−2.01877
$269$	21.2976	1.29854	0.649269	−	0.760559i	$-0.275075\pi$
$269$	21.2976	1.29854	0.649269	+	0.760559i	$0.275075\pi$
$270$	−0.665274	−0.0404873
$271$	11.4428	0.695098	0.347549	−	0.937662i	$-0.387014\pi$
$271$	11.4428	0.695098	0.347549	+	0.937662i	$0.387014\pi$
$272$	−3.29778	−0.199957
$273$	2.15974	0.130713
$274$	15.5506	0.939445
$275$	−4.30458	−0.259576
$276$	−35.1084	−2.11328
$277$	20.5208	1.23298	0.616489	−	0.787364i	$-0.288555\pi$
$277$	20.5208	1.23298	0.616489	+	0.787364i	$0.288555\pi$
$278$	−45.0894	−2.70428
$279$	27.0003	1.61646
$280$	−5.07503	−0.303291
$281$	−17.1804	−1.02490	−0.512448	−	0.858718i	$-0.671261\pi$
$281$	−17.1804	−1.02490	−0.512448	+	0.858718i	$0.671261\pi$
$282$	−39.6290	−2.35987
$283$	−14.6406	−0.870294	−0.435147	−	0.900359i	$-0.643304\pi$
$283$	−14.6406	−0.870294	−0.435147	+	0.900359i	$0.643304\pi$
$284$	30.2031	1.79223
$285$	−7.14564	−0.423271
$286$	22.3847	1.32364
$287$	1.12362	0.0663252
$288$	−93.5625	−5.51322
$289$	−16.9682	−0.998127
$290$	7.64940	0.449188
$291$	30.0216	1.75989
$292$	−72.3258	−4.23255
$293$	24.8858	1.45384	0.726921	−	0.686722i	$-0.240951\pi$
$293$	24.8858	1.45384	0.726921	+	0.686722i	$0.240951\pi$
$294$	46.8753	2.73383
$295$	−11.1845	−0.651184
$296$	−35.4004	−2.05761
$297$	−1.02240	−0.0593254
$298$	−13.3288	−0.772119
$299$	−4.51609	−0.261172
$300$	14.4330	0.833291
$301$	−0.880967	−0.0507781
$302$	−3.42062	−0.196835
$303$	4.60794	0.264719
$304$	−53.4817	−3.06739
$305$	−14.6674	−0.839854
$306$	1.54764	0.0884725
$307$	−5.19630	−0.296568	−0.148284	−	0.988945i	$-0.547375\pi$
$307$	−5.19630	−0.296568	−0.148284	+	0.988945i	$0.547375\pi$
$308$	−11.8556	−0.675534
$309$	42.7079	2.42957
$310$	−24.4260	−1.38730
$311$	−6.04263	−0.342646	−0.171323	−	0.985215i	$-0.554804\pi$
$311$	−6.04263	−0.342646	−0.171323	+	0.985215i	$0.554804\pi$
$312$	−49.3755	−2.79534
$313$	−17.1317	−0.968343	−0.484172	−	0.874973i	$-0.660879\pi$
$313$	−17.1317	−0.968343	−0.484172	+	0.874973i	$0.660879\pi$
$314$	56.4008	3.18288
$315$	1.45879	0.0821935
$316$	−93.3466	−5.25115
$317$	−2.06053	−0.115731	−0.0578655	−	0.998324i	$-0.518429\pi$
$317$	−2.06053	−0.115731	−0.0578655	+	0.998324i	$0.518429\pi$
$318$	58.6979	3.29162
$319$	11.7556	0.658189
$320$	47.6827	2.66554
$321$	−10.0526	−0.561083
$322$	3.21019	0.178897
$323$	0.516463	0.0287368
$324$	−50.8692	−2.82606
$325$	1.85656	0.102983
$326$	−6.50288	−0.360161
$327$	48.2676	2.66921
$328$	−25.6880	−1.41838
$329$	2.69982	0.148846
$330$	29.7696	1.63876
$331$	−13.4591	−0.739781	−0.369891	−	0.929075i	$-0.620605\pi$
$331$	−13.4591	−0.739781	−0.369891	+	0.929075i	$0.620605\pi$
$332$	−38.0582	−2.08872
$333$	10.1756	0.557622
$334$	39.7234	2.17357
$335$	−5.65361	−0.308890
$336$	21.4975	1.17278
$337$	5.13973	0.279979	0.139990	−	0.990153i	$-0.455293\pi$
$337$	5.13973	0.279979	0.139990	+	0.990153i	$0.455293\pi$
$338$	26.7585	1.45547
$339$	4.48159	0.243407
$340$	−1.04317	−0.0565739
$341$	−37.5380	−2.03279
$342$	25.0988	1.35719
$343$	−6.49158	−0.350513
$344$	20.1405	1.08590
$345$	−6.00598	−0.323351
$346$	−16.6745	−0.896424
$347$	−17.3242	−0.930010	−0.465005	−	0.885308i	$-0.653948\pi$
$347$	−17.3242	−0.930010	−0.465005	+	0.885308i	$0.653948\pi$
$348$	−39.4160	−2.11292
$349$	−24.3399	−1.30289	−0.651443	−	0.758698i	$-0.725836\pi$
$349$	−24.3399	−1.30289	−0.651443	+	0.758698i	$0.725836\pi$
$350$	−1.31970	−0.0705412
$351$	0.440957	0.0235365
$352$	130.078	6.93319
$353$	16.3263	0.868963	0.434482	−	0.900681i	$-0.356932\pi$
$353$	16.3263	0.868963	0.434482	+	0.900681i	$0.356932\pi$
$354$	77.3494	4.11108
$355$	5.16683	0.274227
$356$	−12.8287	−0.679918
$357$	−0.207597	−0.0109872
$358$	−20.3058	−1.07320
$359$	−8.78011	−0.463397	−0.231698	−	0.972788i	$-0.574428\pi$
$359$	−8.78011	−0.463397	−0.231698	+	0.972788i	$0.574428\pi$
$360$	−33.3505	−1.75773
$361$	−10.6243	−0.559171
$362$	39.3678	2.06913
$363$	18.5905	0.975748
$364$	5.11328	0.268009
$365$	−12.3727	−0.647618
$366$	101.437	5.30219
$367$	16.5931	0.866152	0.433076	−	0.901357i	$-0.357428\pi$
$367$	16.5931	0.866152	0.433076	+	0.901357i	$0.357428\pi$
$368$	−44.9519	−2.34328
$369$	7.38387	0.384389
$370$	−9.20547	−0.478570
$371$	−3.99894	−0.207615
$372$	125.863	6.52567
$373$	−12.0711	−0.625018	−0.312509	−	0.949915i	$-0.601169\pi$
$373$	−12.0711	−0.625018	−0.312509	+	0.949915i	$0.601169\pi$
$374$	−2.15165	−0.111259
$375$	2.46905	0.127501
$376$	−61.7227	−3.18311
$377$	−5.07018	−0.261127
$378$	−0.313447	−0.0161220
$379$	−5.99096	−0.307735	−0.153867	−	0.988091i	$-0.549173\pi$
$379$	−5.99096	−0.307735	−0.153867	+	0.988091i	$0.549173\pi$
$380$	−16.9176	−0.867856
$381$	24.1603	1.23777
$382$	46.2995	2.36889
$383$	19.6761	1.00540	0.502702	−	0.864460i	$-0.332339\pi$
$383$	19.6761	1.00540	0.502702	+	0.864460i	$0.332339\pi$
$384$	−180.542	−9.21322
$385$	−2.02813	−0.103363
$386$	25.1121	1.27817
$387$	−5.78927	−0.294285
$388$	71.0774	3.60841
$389$	−25.9260	−1.31450	−0.657249	−	0.753673i	$-0.728280\pi$
$389$	−25.9260	−1.31450	−0.657249	+	0.753673i	$0.728280\pi$
$390$	−12.8396	−0.650156
$391$	0.434092	0.0219530
$392$	73.0091	3.68752
$393$	−50.1561	−2.53004
$394$	−60.2162	−3.03365
$395$	−15.9687	−0.803475
$396$	−77.9089	−3.91507
$397$	−11.4155	−0.572928	−0.286464	−	0.958091i	$-0.592480\pi$
$397$	−11.4155	−0.572928	−0.286464	+	0.958091i	$0.592480\pi$
$398$	5.02783	0.252022
$399$	−3.36671	−0.168546
$400$	18.4797	0.923983
$401$	−3.42592	−0.171082	−0.0855411	−	0.996335i	$-0.527262\pi$
$401$	−3.42592	−0.171082	−0.0855411	+	0.996335i	$0.527262\pi$
$402$	39.0992	1.95009
$403$	16.1900	0.806483
$404$	10.9095	0.542769
$405$	−8.70216	−0.432414
$406$	3.60406	0.178866
$407$	−14.1470	−0.701241
$408$	4.74604	0.234964
$409$	27.0628	1.33817	0.669084	−	0.743186i	$-0.266686\pi$
$409$	27.0628	1.33817	0.669084	+	0.743186i	$0.266686\pi$
$410$	−6.67987	−0.329895
$411$	−13.7077	−0.676150
$412$	101.113	4.98147
$413$	−5.26962	−0.259301
$414$	21.0958	1.03680
$415$	−6.51059	−0.319592
$416$	−56.1024	−2.75065
$417$	39.7458	1.94636
$418$	−34.8944	−1.70674
$419$	−26.0108	−1.27071	−0.635355	−	0.772220i	$-0.719146\pi$
$419$	−26.0108	−1.27071	−0.635355	+	0.772220i	$0.719146\pi$
$420$	6.80019	0.331815
$421$	−19.3266	−0.941921	−0.470961	−	0.882154i	$-0.656093\pi$
$421$	−19.3266	−0.941921	−0.470961	+	0.882154i	$0.656093\pi$
$422$	1.32702	0.0645985
$423$	17.7419	0.862639
$424$	91.4230	4.43989
$425$	−0.178455	−0.00865632
$426$	−35.7327	−1.73126
$427$	−6.91063	−0.334429
$428$	−23.8000	−1.15042
$429$	−19.7319	−0.952664
$430$	5.23731	0.252565
$431$	−10.9231	−0.526146	−0.263073	−	0.964776i	$-0.584736\pi$
$431$	−10.9231	−0.526146	−0.263073	+	0.964776i	$0.584736\pi$
$432$	4.38916	0.211174
$433$	−3.54477	−0.170351	−0.0851754	−	0.996366i	$-0.527145\pi$
$433$	−3.54477	−0.170351	−0.0851754	+	0.996366i	$0.527145\pi$
$434$	−11.5084	−0.552423
$435$	−6.74287	−0.323296
$436$	114.276	5.47282
$437$	7.03990	0.336764
$438$	85.5672	4.08856
$439$	−4.19869	−0.200393	−0.100196	−	0.994968i	$-0.531947\pi$
$439$	−4.19869	−0.200393	−0.100196	+	0.994968i	$0.531947\pi$
$440$	46.3666	2.21044
$441$	−20.9861	−0.999336
$442$	0.928001	0.0441405
$443$	16.5389	0.785786	0.392893	−	0.919584i	$-0.371474\pi$
$443$	16.5389	0.785786	0.392893	+	0.919584i	$0.371474\pi$
$444$	47.4341	2.25112
$445$	−2.19459	−0.104034
$446$	−38.2763	−1.81244
$447$	11.7492	0.555719
$448$	22.4659	1.06142
$449$	−20.4183	−0.963598	−0.481799	−	0.876282i	$-0.660017\pi$
$449$	−20.4183	−0.963598	−0.481799	+	0.876282i	$0.660017\pi$
$450$	−8.67243	−0.408822
$451$	−10.2657	−0.483391
$452$	10.6104	0.499070
$453$	3.01524	0.141668
$454$	38.2811	1.79662
$455$	0.874726	0.0410078
$456$	76.9690	3.60440
$457$	−17.0583	−0.797953	−0.398976	−	0.916961i	$-0.630634\pi$
$457$	−17.0583	−0.797953	−0.398976	+	0.916961i	$0.630634\pi$
$458$	−1.69842	−0.0793619
$459$	−0.0423854	−0.00197838
$460$	−14.2194	−0.662984
$461$	−32.6958	−1.52280	−0.761398	−	0.648285i	$-0.775486\pi$
$461$	−32.6958	−1.52280	−0.761398	+	0.648285i	$0.775486\pi$
$462$	14.0261	0.652553
$463$	1.70924	0.0794350	0.0397175	−	0.999211i	$-0.487354\pi$
$463$	1.70924	0.0794350	0.0397175	+	0.999211i	$0.487354\pi$
$464$	−50.4672	−2.34288
$465$	21.5312	0.998488
$466$	14.1097	0.653620
$467$	25.4805	1.17910	0.589549	−	0.807732i	$-0.299305\pi$
$467$	25.4805	1.17910	0.589549	+	0.807732i	$0.299305\pi$
$468$	33.6019	1.55325
$469$	−2.66373	−0.123000
$470$	−16.0503	−0.740345
$471$	−49.7167	−2.29082
$472$	120.473	5.54522
$473$	8.04871	0.370080
$474$	110.437	5.07252
$475$	−2.89409	−0.132790
$476$	−0.491496	−0.0225277
$477$	−26.2790	−1.20323
$478$	−36.0233	−1.64767
$479$	18.9463	0.865678	0.432839	−	0.901471i	$-0.357512\pi$
$479$	18.9463	0.865678	0.432839	+	0.901471i	$0.357512\pi$
$480$	−74.6110	−3.40551
$481$	6.10157	0.278208
$482$	78.3382	3.56821
$483$	−2.82975	−0.128758
$484$	44.0138	2.00063
$485$	12.1592	0.552119
$486$	62.1781	2.82046
$487$	19.6536	0.890587	0.445294	−	0.895385i	$-0.353099\pi$
$487$	19.6536	0.890587	0.445294	+	0.895385i	$0.353099\pi$
$488$	157.989	7.15184
$489$	5.73222	0.259220
$490$	18.9852	0.857663
$491$	6.24630	0.281891	0.140946	−	0.990017i	$-0.454986\pi$
$491$	6.24630	0.281891	0.140946	+	0.990017i	$0.454986\pi$
$492$	34.4201	1.55178
$493$	0.487352	0.0219492
$494$	15.0499	0.677125
$495$	−13.3278	−0.599041
$496$	161.151	7.23590
$497$	2.43438	0.109197
$498$	45.0259	2.01766
$499$	24.8823	1.11388	0.556942	−	0.830552i	$-0.311975\pi$
$499$	24.8823	1.11388	0.556942	+	0.830552i	$0.311975\pi$
$500$	5.84558	0.261422
$501$	−35.0157	−1.56439
$502$	37.7537	1.68503
$503$	7.55237	0.336743	0.168372	−	0.985724i	$-0.446149\pi$
$503$	7.55237	0.336743	0.168372	+	0.985724i	$0.446149\pi$
$504$	−15.7133	−0.699926
$505$	1.86628	0.0830486
$506$	−29.3290	−1.30384
$507$	−23.5873	−1.04755
$508$	57.2005	2.53786
$509$	17.2231	0.763400	0.381700	−	0.924286i	$-0.375339\pi$
$509$	17.2231	0.763400	0.381700	+	0.924286i	$0.375339\pi$
$510$	1.23416	0.0546493
$511$	−5.82948	−0.257881
$512$	−160.322	−7.08531
$513$	−0.687385	−0.0303488
$514$	−79.1494	−3.49113
$515$	17.2973	0.762211
$516$	−26.9869	−1.18803
$517$	−24.6662	−1.08482
$518$	−4.33721	−0.190566
$519$	14.6983	0.645186
$520$	−19.9978	−0.876962
$521$	14.6804	0.643162	0.321581	−	0.946882i	$-0.395786\pi$
$521$	14.6804	0.643162	0.321581	+	0.946882i	$0.395786\pi$
$522$	23.6841	1.03662
$523$	34.3761	1.50316	0.751580	−	0.659642i	$-0.229292\pi$
$523$	34.3761	1.50316	0.751580	+	0.659642i	$0.229292\pi$
$524$	−118.747	−5.18748
$525$	1.16331	0.0507708
$526$	−0.112413	−0.00490145
$527$	−1.55621	−0.0677894
$528$	−196.406	−8.54746
$529$	−17.0829	−0.742735
$530$	23.7735	1.03266
$531$	−34.6293	−1.50278
$532$	−7.97083	−0.345579
$533$	4.42755	0.191779
$534$	15.1774	0.656788
$535$	−4.07146	−0.176025
$536$	60.8976	2.63038
$537$	17.8994	0.772414
$538$	−59.6546	−2.57189
$539$	29.1765	1.25672
$540$	1.38840	0.0597474
$541$	−5.86953	−0.252351	−0.126175	−	0.992008i	$-0.540270\pi$
$541$	−5.86953	−0.252351	−0.126175	+	0.992008i	$0.540270\pi$
$542$	−32.0511	−1.37671
$543$	−34.7023	−1.48922
$544$	5.39264	0.231207
$545$	19.5491	0.837391
$546$	−6.04943	−0.258892
$547$	−34.3502	−1.46871	−0.734354	−	0.678767i	$-0.762515\pi$
$547$	−34.3502	−1.46871	−0.734354	+	0.678767i	$0.762515\pi$
$548$	−32.4535	−1.38635
$549$	−45.4132	−1.93819
$550$	12.0571	0.514117
$551$	7.90363	0.336706
$552$	64.6932	2.75352
$553$	−7.52376	−0.319943
$554$	−57.4788	−2.44204
$555$	8.11452	0.344442
$556$	94.1000	3.99073
$557$	−41.8420	−1.77290	−0.886452	−	0.462821i	$-0.846837\pi$
$557$	−41.8420	−1.77290	−0.886452	+	0.462821i	$0.846837\pi$
$558$	−75.6277	−3.20157
$559$	−3.47139	−0.146824
$560$	8.70679	0.367929
$561$	1.89665	0.0800768
$562$	48.1222	2.02991
$563$	−14.0276	−0.591191	−0.295596	−	0.955313i	$-0.595518\pi$
$563$	−14.0276	−0.591191	−0.295596	+	0.955313i	$0.595518\pi$
$564$	82.7042	3.48248
$565$	1.81511	0.0763622
$566$	41.0083	1.72371
$567$	−4.10007	−0.172187
$568$	−55.6543	−2.33520
$569$	20.1169	0.843345	0.421673	−	0.906748i	$-0.361443\pi$
$569$	20.1169	0.843345	0.421673	+	0.906748i	$0.361443\pi$
$570$	20.0149	0.838333
$571$	−1.47091	−0.0615558	−0.0307779	−	0.999526i	$-0.509798\pi$
$571$	−1.47091	−0.0615558	−0.0307779	+	0.999526i	$0.509798\pi$
$572$	−46.7161	−1.95330
$573$	−40.8125	−1.70497
$574$	−3.14726	−0.131364
$575$	−2.43251	−0.101443
$576$	147.635	6.15146
$577$	5.97992	0.248947	0.124474	−	0.992223i	$-0.460276\pi$
$577$	5.97992	0.248947	0.124474	+	0.992223i	$0.460276\pi$
$578$	47.5277	1.97689
$579$	−22.1360	−0.919943
$580$	−15.9640	−0.662871
$581$	−3.06750	−0.127261
$582$	−84.0903	−3.48565
$583$	36.5352	1.51313
$584$	133.272	5.51485
$585$	5.74826	0.237661
$586$	−69.7049	−2.87948
$587$	34.0305	1.40459	0.702295	−	0.711886i	$-0.252159\pi$
$587$	34.0305	1.40459	0.702295	+	0.711886i	$0.252159\pi$
$588$	−97.8272	−4.03432
$589$	−25.2378	−1.03991
$590$	31.3276	1.28974
$591$	53.0799	2.18342
$592$	60.7333	2.49613
$593$	28.3672	1.16490	0.582450	−	0.812866i	$-0.302094\pi$
$593$	28.3672	1.16490	0.582450	+	0.812866i	$0.302094\pi$
$594$	2.86373	0.117500
$595$	−0.0840798	−0.00344694
$596$	27.8168	1.13942
$597$	−4.43197	−0.181389
$598$	12.6495	0.517279
$599$	−2.14990	−0.0878427	−0.0439213	−	0.999035i	$-0.513985\pi$
$599$	−2.14990	−0.0878427	−0.0439213	+	0.999035i	$0.513985\pi$
$600$	−26.5952	−1.08575
$601$	−33.0382	−1.34765	−0.673827	−	0.738889i	$-0.735351\pi$
$601$	−33.0382	−1.34765	−0.673827	+	0.738889i	$0.735351\pi$
$602$	2.46759	0.100571
$603$	−17.5047	−0.712846
$604$	7.13871	0.290470
$605$	7.52942	0.306114
$606$	−12.9068	−0.524304
$607$	21.1533	0.858584	0.429292	−	0.903166i	$-0.358763\pi$
$607$	21.1533	0.858584	0.429292	+	0.903166i	$0.358763\pi$
$608$	87.4551	3.54677
$609$	−3.17694	−0.128736
$610$	41.0834	1.66342
$611$	10.6385	0.430386
$612$	−3.22986	−0.130559
$613$	−31.2626	−1.26268	−0.631342	−	0.775505i	$-0.717495\pi$
$613$	−31.2626	−1.26268	−0.631342	+	0.775505i	$0.717495\pi$
$614$	14.5548	0.587384
$615$	5.88823	0.237437
$616$	21.8459	0.880196
$617$	31.0270	1.24910	0.624551	−	0.780984i	$-0.285282\pi$
$617$	31.0270	1.24910	0.624551	+	0.780984i	$0.285282\pi$
$618$	−119.625	−4.81201
$619$	−6.66466	−0.267875	−0.133938	−	0.990990i	$-0.542762\pi$
$619$	−6.66466	−0.267875	−0.133938	+	0.990990i	$0.542762\pi$
$620$	50.9762	2.04725
$621$	−0.577754	−0.0231844
$622$	16.9254	0.678646
$623$	−1.03399	−0.0414261
$624$	84.7093	3.39109
$625$	1.00000	0.0400000
$626$	47.9859	1.91790
$627$	30.7590	1.22840
$628$	−117.706	−4.69700
$629$	−0.586491	−0.0233849
$630$	−4.08606	−0.162793
$631$	36.9225	1.46986	0.734931	−	0.678142i	$-0.237214\pi$
$631$	36.9225	1.46986	0.734931	+	0.678142i	$0.237214\pi$
$632$	172.007	6.84206
$633$	−1.16976	−0.0464937
$634$	5.77154	0.229217
$635$	9.78525	0.388316
$636$	−122.501	−4.85746
$637$	−12.5838	−0.498587
$638$	−32.9275	−1.30361
$639$	15.9975	0.632852
$640$	−73.1219	−2.89040
$641$	−21.9618	−0.867439	−0.433719	−	0.901048i	$-0.642799\pi$
$641$	−21.9618	−0.867439	−0.433719	+	0.901048i	$0.642799\pi$
$642$	28.1574	1.11128
$643$	−37.3526	−1.47304	−0.736522	−	0.676414i	$-0.763533\pi$
$643$	−37.3526	−1.47304	−0.736522	+	0.676414i	$0.763533\pi$
$644$	−6.69956	−0.264000
$645$	−4.61663	−0.181780
$646$	−1.44661	−0.0569162
$647$	11.7911	0.463557	0.231779	−	0.972769i	$-0.425545\pi$
$647$	11.7911	0.463557	0.231779	+	0.972769i	$0.425545\pi$
$648$	93.7349	3.68226
$649$	48.1444	1.88983
$650$	−5.20021	−0.203969
$651$	10.1446	0.397597
$652$	13.5713	0.531493
$653$	33.0310	1.29260	0.646301	−	0.763082i	$-0.276315\pi$
$653$	33.0310	1.29260	0.646301	+	0.763082i	$0.276315\pi$
$654$	−135.197	−5.28664
$655$	−20.3140	−0.793732
$656$	44.0706	1.72067
$657$	−38.3084	−1.49455
$658$	−7.56218	−0.294805
$659$	22.6605	0.882728	0.441364	−	0.897328i	$-0.354495\pi$
$659$	22.6605	0.882728	0.441364	+	0.897328i	$0.354495\pi$
$660$	−62.1281	−2.41833
$661$	−1.75086	−0.0681006	−0.0340503	−	0.999420i	$-0.510841\pi$
$661$	−1.75086	−0.0681006	−0.0340503	+	0.999420i	$0.510841\pi$
$662$	37.6990	1.46521
$663$	−0.818022	−0.0317694
$664$	70.1286	2.72152
$665$	−1.36357	−0.0528768
$666$	−28.5019	−1.10443
$667$	6.64308	0.257221
$668$	−82.9013	−3.20755
$669$	33.7402	1.30447
$670$	15.8357	0.611788
$671$	63.1371	2.43738
$672$	−35.1534	−1.35607
$673$	27.3625	1.05475	0.527374	−	0.849633i	$-0.323177\pi$
$673$	27.3625	1.05475	0.527374	+	0.849633i	$0.323177\pi$
$674$	−14.3964	−0.554528
$675$	0.237513	0.00914189
$676$	−55.8440	−2.14785
$677$	−28.9301	−1.11187	−0.555936	−	0.831225i	$-0.687640\pi$
$677$	−28.9301	−1.11187	−0.555936	+	0.831225i	$0.687640\pi$
$678$	−12.5529	−0.482092
$679$	5.72885	0.219853
$680$	1.92222	0.0737136
$681$	−33.7444	−1.29309
$682$	105.144	4.02616
$683$	−13.8383	−0.529510	−0.264755	−	0.964316i	$-0.585291\pi$
$683$	−13.8383	−0.529510	−0.264755	+	0.964316i	$0.585291\pi$
$684$	−52.3803	−2.00281
$685$	−5.55181	−0.212124
$686$	18.1829	0.694227
$687$	1.49714	0.0571194
$688$	−34.5533	−1.31733
$689$	−15.7576	−0.600315
$690$	16.8227	0.640430
$691$	−26.0162	−0.989703	−0.494851	−	0.868978i	$-0.664778\pi$
$691$	−26.0162	−0.989703	−0.494851	+	0.868978i	$0.664778\pi$
$692$	34.7990	1.32286
$693$	−6.27948	−0.238538
$694$	48.5249	1.84198
$695$	16.0976	0.610618
$696$	72.6305	2.75305
$697$	−0.425582	−0.0161201
$698$	68.1760	2.58050
$699$	−12.4376	−0.470432
$700$	2.75418	0.104098
$701$	−28.2915	−1.06856	−0.534278	−	0.845309i	$-0.679416\pi$
$701$	−28.2915	−1.06856	−0.534278	+	0.845309i	$0.679416\pi$
$702$	−1.23512	−0.0466165
$703$	−9.51142	−0.358730
$704$	−205.254	−7.73580
$705$	14.1482	0.532851
$706$	−45.7300	−1.72107
$707$	0.879310	0.0330698
$708$	−161.426	−6.06674
$709$	25.0060	0.939119	0.469560	−	0.882901i	$-0.344413\pi$
$709$	25.0060	0.939119	0.469560	+	0.882901i	$0.344413\pi$
$710$	−14.4723	−0.543135
$711$	−49.4424	−1.85423
$712$	23.6390	0.885908
$713$	−21.2126	−0.794419
$714$	0.581479	0.0217613
$715$	−7.99170	−0.298872
$716$	42.3775	1.58372
$717$	31.7542	1.18588
$718$	24.5931	0.917805
$719$	−23.2394	−0.866683	−0.433341	−	0.901230i	$-0.642666\pi$
$719$	−23.2394	−0.866683	−0.433341	+	0.901230i	$0.642666\pi$
$720$	57.2166	2.13234
$721$	8.14972	0.303512
$722$	29.7585	1.10750
$723$	−69.0543	−2.56816
$724$	−82.1592	−3.05342
$725$	−2.73096	−0.101425
$726$	−52.0719	−1.93257
$727$	−6.69094	−0.248153	−0.124077	−	0.992273i	$-0.539597\pi$
$727$	−6.69094	−0.248153	−0.124077	+	0.992273i	$0.539597\pi$
$728$	−9.42208	−0.349205
$729$	−28.7029	−1.06307
$730$	34.6560	1.28267
$731$	0.333675	0.0123414
$732$	−211.695	−7.82447
$733$	35.5123	1.31168	0.655838	−	0.754902i	$-0.272316\pi$
$733$	35.5123	1.31168	0.655838	+	0.754902i	$0.272316\pi$
$734$	−46.4772	−1.71550
$735$	−16.7352	−0.617288
$736$	73.5068	2.70950
$737$	24.3364	0.896444
$738$	−20.6822	−0.761322
$739$	50.8321	1.86989	0.934945	−	0.354794i	$-0.115449\pi$
$739$	50.8321	1.86989	0.934945	+	0.354794i	$0.115449\pi$
$740$	19.2115	0.706228
$741$	−13.2663	−0.487349
$742$	11.2010	0.411202
$743$	−21.5989	−0.792386	−0.396193	−	0.918167i	$-0.629669\pi$
$743$	−21.5989	−0.792386	−0.396193	+	0.918167i	$0.629669\pi$
$744$	−231.923	−8.50271
$745$	4.75861	0.174342
$746$	33.8111	1.23791
$747$	−20.1581	−0.737545
$748$	4.49041	0.164186
$749$	−1.91829	−0.0700928
$750$	−6.91579	−0.252529
$751$	−10.7312	−0.391588	−0.195794	−	0.980645i	$-0.562728\pi$
$751$	−10.7312	−0.391588	−0.195794	+	0.980645i	$0.562728\pi$
$752$	105.892	3.86150
$753$	−33.2795	−1.21277
$754$	14.2015	0.517190
$755$	1.22122	0.0444446
$756$	0.654154	0.0237913
$757$	−14.0876	−0.512022	−0.256011	−	0.966674i	$-0.582408\pi$
$757$	−14.0876	−0.512022	−0.256011	+	0.966674i	$0.582408\pi$
$758$	16.7807	0.609501
$759$	25.8532	0.938413
$760$	31.1735	1.13078
$761$	−15.0047	−0.543919	−0.271960	−	0.962309i	$-0.587672\pi$
$761$	−15.0047	−0.543919	−0.271960	+	0.962309i	$0.587672\pi$
$762$	−67.6728	−2.45153
$763$	9.21066	0.333448
$764$	−96.6254	−3.49578
$765$	−0.552531	−0.0199768
$766$	−55.1128	−1.99131
$767$	−20.7646	−0.749765
$768$	270.235	9.75126
$769$	−29.3632	−1.05886	−0.529432	−	0.848353i	$-0.677595\pi$
$769$	−29.3632	−1.05886	−0.529432	+	0.848353i	$0.677595\pi$
$770$	5.68078	0.204721
$771$	69.7694	2.51268
$772$	−52.4081	−1.88621
$773$	35.0406	1.26032	0.630161	−	0.776465i	$-0.282989\pi$
$773$	35.0406	1.26032	0.630161	+	0.776465i	$0.282989\pi$
$774$	16.2157	0.582862
$775$	8.72046	0.313248
$776$	−130.972	−4.70162
$777$	3.82320	0.137157
$778$	72.6185	2.60350
$779$	−6.90188	−0.247285
$780$	26.7957	0.959440
$781$	−22.2410	−0.795847
$782$	−1.21589	−0.0434802
$783$	−0.648639	−0.0231805
$784$	−125.255	−4.47340
$785$	−20.1360	−0.718684
$786$	140.487	5.01101
$787$	−39.0907	−1.39343	−0.696717	−	0.717346i	$-0.745357\pi$
$787$	−39.0907	−1.39343	−0.696717	+	0.717346i	$0.745357\pi$
$788$	125.669	4.47678
$789$	0.0990910	0.00352773
$790$	44.7284	1.59136
$791$	0.855199	0.0304074
$792$	143.560	5.10119
$793$	−27.2309	−0.966996
$794$	31.9748	1.13474
$795$	−20.9561	−0.743236
$796$	−10.4929	−0.371911
$797$	−32.8057	−1.16204	−0.581018	−	0.813890i	$-0.697346\pi$
$797$	−32.8057	−1.16204	−0.581018	+	0.813890i	$0.697346\pi$
$798$	9.43014	0.333823
$799$	−1.02258	−0.0361764
$800$	−30.2185	−1.06839
$801$	−6.79489	−0.240086
$802$	9.59598	0.338846
$803$	53.2594	1.87948
$804$	−81.5986	−2.87776
$805$	−1.14609	−0.0403944
$806$	−45.3482	−1.59732
$807$	52.5848	1.85107
$808$	−20.1026	−0.707207
$809$	−16.6601	−0.585737	−0.292868	−	0.956153i	$-0.594610\pi$
$809$	−16.6601	−0.585737	−0.292868	+	0.956153i	$0.594610\pi$
$810$	24.3747	0.856440
$811$	2.73464	0.0960262	0.0480131	−	0.998847i	$-0.484711\pi$
$811$	2.73464	0.0960262	0.0480131	+	0.998847i	$0.484711\pi$
$812$	−7.52154	−0.263954
$813$	28.2527	0.990866
$814$	39.6257	1.38888
$815$	2.32163	0.0813232
$816$	−8.14237	−0.285040
$817$	5.41137	0.189320
$818$	−75.8028	−2.65038
$819$	2.70832	0.0946365
$820$	13.9407	0.486829
$821$	0.518890	0.0181094	0.00905469	−	0.999959i	$-0.497118\pi$
$821$	0.518890	0.0181094	0.00905469	+	0.999959i	$0.497118\pi$
$822$	38.3951	1.33918
$823$	−22.3238	−0.778158	−0.389079	−	0.921204i	$-0.627207\pi$
$823$	−22.3238	−0.778158	−0.389079	+	0.921204i	$0.627207\pi$
$824$	−186.317	−6.49067
$825$	−10.6282	−0.370027
$826$	14.7602	0.513572
$827$	−9.84058	−0.342191	−0.171095	−	0.985254i	$-0.554731\pi$
$827$	−9.84058	−0.342191	−0.171095	+	0.985254i	$0.554731\pi$
$828$	−44.0261	−1.53001
$829$	11.3364	0.393730	0.196865	−	0.980431i	$-0.436924\pi$
$829$	11.3364	0.393730	0.196865	+	0.980431i	$0.436924\pi$
$830$	18.2361	0.632986
$831$	50.6669	1.75762
$832$	88.5255	3.06907
$833$	1.20957	0.0419090
$834$	−111.328	−3.85497
$835$	−14.1819	−0.490784
$836$	72.8233	2.51865
$837$	2.07123	0.0715921
$838$	72.8561	2.51677
$839$	32.7605	1.13102	0.565509	−	0.824742i	$-0.308680\pi$
$839$	32.7605	1.13102	0.565509	+	0.824742i	$0.308680\pi$
$840$	−12.5305	−0.432343
$841$	−21.5419	−0.742823
$842$	54.1338	1.86557
$843$	−42.4192	−1.46099
$844$	−2.76945	−0.0953285
$845$	−9.55320	−0.328640
$846$	−49.6949	−1.70855
$847$	3.54753	0.121894
$848$	−156.846	−5.38613
$849$	−36.1484	−1.24061
$850$	0.499851	0.0171447
$851$	−7.99444	−0.274046
$852$	74.5730	2.55483
$853$	3.56132	0.121937	0.0609687	−	0.998140i	$-0.480581\pi$
$853$	3.56132	0.121937	0.0609687	+	0.998140i	$0.480581\pi$
$854$	19.3566	0.662371
$855$	−8.96067	−0.306448
$856$	43.8556	1.49895
$857$	−56.8535	−1.94208	−0.971039	−	0.238922i	$-0.923206\pi$
$857$	−56.8535	−1.94208	−0.971039	+	0.238922i	$0.923206\pi$
$858$	55.2689	1.88685
$859$	−12.2079	−0.416527	−0.208263	−	0.978073i	$-0.566781\pi$
$859$	−12.2079	−0.416527	−0.208263	+	0.978073i	$0.566781\pi$
$860$	−10.9301	−0.372712
$861$	2.77427	0.0945470
$862$	30.5955	1.04209
$863$	49.1488	1.67304	0.836522	−	0.547933i	$-0.184585\pi$
$863$	49.1488	1.67304	0.836522	+	0.547933i	$0.184585\pi$
$864$	−7.17730	−0.244177
$865$	5.95304	0.202410
$866$	9.92889	0.337397
$867$	−41.8952	−1.42283
$868$	24.0177	0.815214
$869$	68.7387	2.33180
$870$	18.8867	0.640321
$871$	−10.4962	−0.355652
$872$	−210.572	−7.13088
$873$	37.6472	1.27416
$874$	−19.7187	−0.666996
$875$	0.471155	0.0159280
$876$	−178.576	−6.03352
$877$	−0.632477	−0.0213572	−0.0106786	−	0.999943i	$-0.503399\pi$
$877$	−0.632477	−0.0213572	−0.0106786	+	0.999943i	$0.503399\pi$
$878$	11.7605	0.396898
$879$	61.4441	2.07246
$880$	−79.5472	−2.68153
$881$	−26.4229	−0.890209	−0.445104	−	0.895479i	$-0.646833\pi$
$881$	−26.4229	−0.890209	−0.445104	+	0.895479i	$0.646833\pi$
$882$	58.7819	1.97929
$883$	33.7148	1.13459	0.567297	−	0.823513i	$-0.307989\pi$
$883$	33.7148	1.13459	0.567297	+	0.823513i	$0.307989\pi$
$884$	−1.93670	−0.0651384
$885$	−27.6150	−0.928267
$886$	−46.3253	−1.55633
$887$	2.06441	0.0693162	0.0346581	−	0.999399i	$-0.488966\pi$
$887$	2.06441	0.0693162	0.0346581	+	0.999399i	$0.488966\pi$
$888$	−87.4052	−2.93313
$889$	4.61037	0.154627
$890$	6.14705	0.206050
$891$	37.4591	1.25493
$892$	79.8813	2.67462
$893$	−16.5837	−0.554954
$894$	−32.9095	−1.10066
$895$	7.24950	0.242324
$896$	−34.4518	−1.15095
$897$	−11.1504	−0.372302
$898$	57.1915	1.90851
$899$	−23.8152	−0.794282
$900$	18.0991	0.603302
$901$	1.51464	0.0504599
$902$	28.7541	0.957405
$903$	−2.17515	−0.0723844
$904$	−19.5514	−0.650269
$905$	−14.0549	−0.467202
$906$	−8.44567	−0.280589
$907$	51.0746	1.69590	0.847952	−	0.530073i	$-0.177835\pi$
$907$	51.0746	1.69590	0.847952	+	0.530073i	$0.177835\pi$
$908$	−79.8913	−2.65129
$909$	5.77838	0.191657
$910$	−2.45010	−0.0812202
$911$	−33.3385	−1.10455	−0.552277	−	0.833661i	$-0.686241\pi$
$911$	−33.3385	−1.10455	−0.552277	+	0.833661i	$0.686241\pi$
$912$	−132.049	−4.37258
$913$	28.0254	0.927505
$914$	47.7802	1.58043
$915$	−36.2145	−1.19722
$916$	3.54454	0.117115
$917$	−9.57103	−0.316063
$918$	0.118721	0.00391838
$919$	48.9532	1.61482	0.807409	−	0.589992i	$-0.200869\pi$
$919$	48.9532	1.61482	0.807409	+	0.589992i	$0.200869\pi$
$920$	26.2017	0.863843
$921$	−12.8299	−0.422760
$922$	91.5808	3.01605
$923$	9.59251	0.315741
$924$	−29.2720	−0.962978
$925$	3.28650	0.108059
$926$	−4.78757	−0.157329
$927$	53.5559	1.75901
$928$	82.5255	2.70903
$929$	−36.2445	−1.18914	−0.594571	−	0.804043i	$-0.702678\pi$
$929$	−36.2445	−1.18914	−0.594571	+	0.804043i	$0.702678\pi$
$930$	−60.3089	−1.97761
$931$	19.6162	0.642894
$932$	−29.4465	−0.964551
$933$	−14.9195	−0.488444
$934$	−71.3709	−2.33533
$935$	0.768172	0.0251219
$936$	−61.9172	−2.02383
$937$	34.9749	1.14258	0.571291	−	0.820748i	$-0.306443\pi$
$937$	34.9749	1.14258	0.571291	+	0.820748i	$0.306443\pi$
$938$	7.46109	0.243613
$939$	−42.2991	−1.38038
$940$	33.4964	1.09253
$941$	47.9901	1.56443	0.782217	−	0.623007i	$-0.214089\pi$
$941$	47.9901	1.56443	0.782217	+	0.623007i	$0.214089\pi$
$942$	139.256	4.53721
$943$	−5.80110	−0.188910
$944$	−206.685	−6.72702
$945$	0.111906	0.00364029
$946$	−22.5444	−0.732982
$947$	−20.9490	−0.680752	−0.340376	−	0.940289i	$-0.610554\pi$
$947$	−20.9490	−0.680752	−0.340376	+	0.940289i	$0.610554\pi$
$948$	−230.477	−7.48555
$949$	−22.9707	−0.745659
$950$	8.10633	0.263004
$951$	−5.08755	−0.164975
$952$	0.905663	0.0293527
$953$	−47.9110	−1.55199	−0.775995	−	0.630739i	$-0.782752\pi$
$953$	−47.9110	−1.55199	−0.775995	+	0.630739i	$0.782752\pi$
$954$	73.6075	2.38313
$955$	−16.5296	−0.534887
$956$	75.1794	2.43148
$957$	29.0252	0.938252
$958$	−53.0685	−1.71456
$959$	−2.61576	−0.0844674
$960$	117.731	3.79975
$961$	45.0465	1.45311
$962$	−17.0905	−0.551019
$963$	−12.6060	−0.406224
$964$	−163.489	−5.26563
$965$	−8.96542	−0.288607
$966$	7.92612	0.255019
$967$	−7.44111	−0.239290	−0.119645	−	0.992817i	$-0.538176\pi$
$967$	−7.44111	−0.239290	−0.119645	+	0.992817i	$0.538176\pi$
$968$	−81.1028	−2.60674
$969$	1.27517	0.0409644
$970$	−34.0578	−1.09353
$971$	−60.5808	−1.94413	−0.972065	−	0.234714i	$-0.924585\pi$
$971$	−60.5808	−1.94413	−0.972065	+	0.234714i	$0.924585\pi$
$972$	−129.764	−4.16217
$973$	7.58448	0.243147
$974$	−55.0495	−1.76390
$975$	4.58392	0.146803
$976$	−271.049	−8.67606
$977$	−52.1726	−1.66915	−0.834575	−	0.550894i	$-0.814287\pi$
$977$	−52.1726	−1.66915	−0.834575	+	0.550894i	$0.814287\pi$
$978$	−16.0559	−0.513412
$979$	9.44680	0.301921
$980$	−39.6214	−1.26566
$981$	60.5278	1.93250
$982$	−17.4958	−0.558315
$983$	48.5731	1.54924	0.774620	−	0.632427i	$-0.217941\pi$
$983$	48.5731	1.54924	0.774620	+	0.632427i	$0.217941\pi$
$984$	−63.4249	−2.02191
$985$	21.4981	0.684988
$986$	−1.36507	−0.0434727
$987$	6.66598	0.212181
$988$	−31.4085	−0.999238
$989$	4.54831	0.144628
$990$	37.3312	1.18646
$991$	−56.7095	−1.80144	−0.900718	−	0.434405i	$-0.856959\pi$
$991$	−56.7095	−1.80144	−0.900718	+	0.434405i	$0.856959\pi$
$992$	−263.520	−8.36676
$993$	−33.2313	−1.05456
$994$	−6.81869	−0.216276
$995$	−1.79501	−0.0569058
$996$	−93.9675	−2.97747
$997$	−24.6817	−0.781678	−0.390839	−	0.920459i	$-0.627815\pi$
$997$	−24.6817	−0.781678	−0.390839	+	0.920459i	$0.627815\pi$
$998$	−69.6951	−2.20616
$999$	0.780587	0.0246967

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.b.1.1	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.b.1.1	✓	114	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.80100 q^{2} +2.46905 q^{3} +5.84558 q^{4} +1.00000 q^{5} -6.91579 q^{6} +0.471155 q^{7} -10.7715 q^{8} +3.09620 q^{9} +O(q^{10})\)	\(q-2.80100 q^{2} +2.46905 q^{3} +5.84558 q^{4} +1.00000 q^{5} -6.91579 q^{6} +0.471155 q^{7} -10.7715 q^{8} +3.09620 q^{9} -2.80100 q^{10} -4.30458 q^{11} +14.4330 q^{12} +1.85656 q^{13} -1.31970 q^{14} +2.46905 q^{15} +18.4797 q^{16} -0.178455 q^{17} -8.67243 q^{18} -2.89409 q^{19} +5.84558 q^{20} +1.16331 q^{21} +12.0571 q^{22} -2.43251 q^{23} -26.5952 q^{24} +1.00000 q^{25} -5.20021 q^{26} +0.237513 q^{27} +2.75418 q^{28} -2.73096 q^{29} -6.91579 q^{30} +8.72046 q^{31} -30.2185 q^{32} -10.6282 q^{33} +0.499851 q^{34} +0.471155 q^{35} +18.0991 q^{36} +3.28650 q^{37} +8.10633 q^{38} +4.58392 q^{39} -10.7715 q^{40} +2.38482 q^{41} -3.25841 q^{42} -1.86980 q^{43} -25.1628 q^{44} +3.09620 q^{45} +6.81345 q^{46} +5.73021 q^{47} +45.6271 q^{48} -6.77801 q^{49} -2.80100 q^{50} -0.440613 q^{51} +10.8526 q^{52} -8.48752 q^{53} -0.665274 q^{54} -4.30458 q^{55} -5.07503 q^{56} -7.14564 q^{57} +7.64940 q^{58} -11.1845 q^{59} +14.4330 q^{60} -14.6674 q^{61} -24.4260 q^{62} +1.45879 q^{63} +47.6827 q^{64} +1.85656 q^{65} +29.7696 q^{66} -5.65361 q^{67} -1.04317 q^{68} -6.00598 q^{69} -1.31970 q^{70} +5.16683 q^{71} -33.3505 q^{72} -12.3727 q^{73} -9.20547 q^{74} +2.46905 q^{75} -16.9176 q^{76} -2.02813 q^{77} -12.8396 q^{78} -15.9687 q^{79} +18.4797 q^{80} -8.70216 q^{81} -6.67987 q^{82} -6.51059 q^{83} +6.80019 q^{84} -0.178455 q^{85} +5.23731 q^{86} -6.74287 q^{87} +46.3666 q^{88} -2.19459 q^{89} -8.67243 q^{90} +0.874726 q^{91} -14.2194 q^{92} +21.5312 q^{93} -16.0503 q^{94} -2.89409 q^{95} -74.6110 q^{96} +12.1592 q^{97} +18.9852 q^{98} -13.3278 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9}+O(q^{10}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9	\( 114 q - 17 q^{2} - 10 q^{3} + 93 q^{4} + 114 q^{5} - 24 q^{6} - 11 q^{7} - 48 q^{8} + 66 q^{9} - 17 q^{10} - 44 q^{11} - 25 q^{12} - 26 q^{13} - 43 q^{14} - 10 q^{15} + 59 q^{16} - 57 q^{17} - 33 q^{18} - 69 q^{19} + 93 q^{20} - 107 q^{21} - 19 q^{22} - 45 q^{23} - 45 q^{24} + 114 q^{25} - 54 q^{26} - 34 q^{27} - 6 q^{28} - 166 q^{29} - 24 q^{30} - 67 q^{31} - 98 q^{32} - 38 q^{33} - 41 q^{34} - 11 q^{35} - 3 q^{36} - 44 q^{37} - 19 q^{38} - 66 q^{39} - 48 q^{40} - 141 q^{41} + q^{42} - 30 q^{43} - 125 q^{44} + 66 q^{45} - 59 q^{46} - 17 q^{47} - 35 q^{48} - 15 q^{49} - 17 q^{50} - 67 q^{51} - 26 q^{52} - 154 q^{53} - 45 q^{54} - 44 q^{55} - 118 q^{56} - 70 q^{57} + 11 q^{58} - 75 q^{59} - 25 q^{60} - 144 q^{61} - 35 q^{62} - 25 q^{63} + 16 q^{64} - 26 q^{65} - 68 q^{66} - 2 q^{67} - 99 q^{68} - 118 q^{69} - 43 q^{70} - 104 q^{71} - 73 q^{72} - 22 q^{73} - 107 q^{74} - 10 q^{75} - 172 q^{76} - 100 q^{77} - 2 q^{78} - 91 q^{79} + 59 q^{80} - 54 q^{81} + 20 q^{82} - 44 q^{83} - 156 q^{84} - 57 q^{85} - 50 q^{86} + 5 q^{87} - 13 q^{88} - 150 q^{89} - 33 q^{90} - 54 q^{91} - 77 q^{92} - 50 q^{93} - 105 q^{94} - 69 q^{95} - 78 q^{96} - 31 q^{97} - 64 q^{98} - 101 q^{99}+O(q^{100}) \) 114 * q - 17 * q^2 - 10 * q^3 + 93 * q^4 + 114 * q^5 - 24 * q^6 - 11 * q^7 - 48 * q^8 + 66 * q^9 - 17 * q^10 - 44 * q^11 - 25 * q^12 - 26 * q^13 - 43 * q^14 - 10 * q^15 + 59 * q^16 - 57 * q^17 - 33 * q^18 - 69 * q^19 + 93 * q^20 - 107 * q^21 - 19 * q^22 - 45 * q^23 - 45 * q^24 + 114 * q^25 - 54 * q^26 - 34 * q^27 - 6 * q^28 - 166 * q^29 - 24 * q^30 - 67 * q^31 - 98 * q^32 - 38 * q^33 - 41 * q^34 - 11 * q^35 - 3 * q^36 - 44 * q^37 - 19 * q^38 - 66 * q^39 - 48 * q^40 - 141 * q^41 + q^42 - 30 * q^43 - 125 * q^44 + 66 * q^45 - 59 * q^46 - 17 * q^47 - 35 * q^48 - 15 * q^49 - 17 * q^50 - 67 * q^51 - 26 * q^52 - 154 * q^53 - 45 * q^54 - 44 * q^55 - 118 * q^56 - 70 * q^57 + 11 * q^58 - 75 * q^59 - 25 * q^60 - 144 * q^61 - 35 * q^62 - 25 * q^63 + 16 * q^64 - 26 * q^65 - 68 * q^66 - 2 * q^67 - 99 * q^68 - 118 * q^69 - 43 * q^70 - 104 * q^71 - 73 * q^72 - 22 * q^73 - 107 * q^74 - 10 * q^75 - 172 * q^76 - 100 * q^77 - 2 * q^78 - 91 * q^79 + 59 * q^80 - 54 * q^81 + 20 * q^82 - 44 * q^83 - 156 * q^84 - 57 * q^85 - 50 * q^86 + 5 * q^87 - 13 * q^88 - 150 * q^89 - 33 * q^90 - 54 * q^91 - 77 * q^92 - 50 * q^93 - 105 * q^94 - 69 * q^95 - 78 * q^96 - 31 * q^97 - 64 * q^98 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more