LMFDB - Embedded newform 7935.2.a.bu.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7935,2,Mod(1,7935)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7935, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.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:	$63.3612940039$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	no (minimal twist has level 345)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.59695 q^{2} -1.00000 q^{3} +0.550248 q^{4} +1.00000 q^{5} -1.59695 q^{6} +3.15385 q^{7} -2.31518 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.59695 q^{2} -1.00000 q^{3} +0.550248 q^{4} +1.00000 q^{5} -1.59695 q^{6} +3.15385 q^{7} -2.31518 q^{8} +1.00000 q^{9} +1.59695 q^{10} +3.93622 q^{11} -0.550248 q^{12} +5.83236 q^{13} +5.03655 q^{14} -1.00000 q^{15} -4.79772 q^{16} +3.95982 q^{17} +1.59695 q^{18} +5.47856 q^{19} +0.550248 q^{20} -3.15385 q^{21} +6.28595 q^{22} +2.31518 q^{24} +1.00000 q^{25} +9.31399 q^{26} -1.00000 q^{27} +1.73540 q^{28} -6.54323 q^{29} -1.59695 q^{30} +5.79234 q^{31} -3.03136 q^{32} -3.93622 q^{33} +6.32363 q^{34} +3.15385 q^{35} +0.550248 q^{36} +4.28799 q^{37} +8.74899 q^{38} -5.83236 q^{39} -2.31518 q^{40} +4.15262 q^{41} -5.03655 q^{42} +3.97479 q^{43} +2.16590 q^{44} +1.00000 q^{45} -11.4438 q^{47} +4.79772 q^{48} +2.94680 q^{49} +1.59695 q^{50} -3.95982 q^{51} +3.20924 q^{52} -4.29277 q^{53} -1.59695 q^{54} +3.93622 q^{55} -7.30174 q^{56} -5.47856 q^{57} -10.4492 q^{58} -13.8795 q^{59} -0.550248 q^{60} +2.38454 q^{61} +9.25007 q^{62} +3.15385 q^{63} +4.75452 q^{64} +5.83236 q^{65} -6.28595 q^{66} +10.2832 q^{67} +2.17888 q^{68} +5.03655 q^{70} -7.43010 q^{71} -2.31518 q^{72} +4.84630 q^{73} +6.84770 q^{74} -1.00000 q^{75} +3.01457 q^{76} +12.4143 q^{77} -9.31399 q^{78} -9.59938 q^{79} -4.79772 q^{80} +1.00000 q^{81} +6.63153 q^{82} +8.40615 q^{83} -1.73540 q^{84} +3.95982 q^{85} +6.34754 q^{86} +6.54323 q^{87} -9.11307 q^{88} -9.86016 q^{89} +1.59695 q^{90} +18.3944 q^{91} -5.79234 q^{93} -18.2752 q^{94} +5.47856 q^{95} +3.03136 q^{96} -15.3346 q^{97} +4.70588 q^{98} +3.93622 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * 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 $

$2$	1.59695	1.12921	0.564607	−	0.825360i	$-0.309028\pi$
$2$	1.59695	1.12921	0.564607	+	0.825360i	$0.309028\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	0.550248	0.275124
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.59695	−0.651952
$7$	3.15385	1.19204	0.596022	−	0.802968i	$-0.296747\pi$
$7$	3.15385	1.19204	0.596022	+	0.802968i	$0.296747\pi$
$8$	−2.31518	−0.818540
$9$	1.00000	0.333333
$10$	1.59695	0.505000
$11$	3.93622	1.18682	0.593408	−	0.804902i	$-0.297782\pi$
$11$	3.93622	1.18682	0.593408	+	0.804902i	$0.297782\pi$
$12$	−0.550248	−0.158843
$13$	5.83236	1.61761	0.808803	−	0.588080i	$-0.200116\pi$
$13$	5.83236	1.61761	0.808803	+	0.588080i	$0.200116\pi$
$14$	5.03655	1.34607
$15$	−1.00000	−0.258199
$16$	−4.79772	−1.19943
$17$	3.95982	0.960397	0.480199	−	0.877160i	$-0.340565\pi$
$17$	3.95982	0.960397	0.480199	+	0.877160i	$0.340565\pi$
$18$	1.59695	0.376405
$19$	5.47856	1.25687	0.628434	−	0.777863i	$-0.283696\pi$
$19$	5.47856	1.25687	0.628434	+	0.777863i	$0.283696\pi$
$20$	0.550248	0.123039
$21$	−3.15385	−0.688227
$22$	6.28595	1.34017
$23$	0	0
$23$	0	0
$24$	2.31518	0.472584
$25$	1.00000	0.200000
$26$	9.31399	1.82662
$27$	−1.00000	−0.192450
$28$	1.73540	0.327960
$29$	−6.54323	−1.21505	−0.607524	−	0.794301i	$-0.707837\pi$
$29$	−6.54323	−1.21505	−0.607524	+	0.794301i	$0.707837\pi$
$30$	−1.59695	−0.291562
$31$	5.79234	1.04033	0.520167	−	0.854064i	$-0.325870\pi$
$31$	5.79234	1.04033	0.520167	+	0.854064i	$0.325870\pi$
$32$	−3.03136	−0.535874
$33$	−3.93622	−0.685208
$34$	6.32363	1.08449
$35$	3.15385	0.533099
$36$	0.550248	0.0917080
$37$	4.28799	0.704941	0.352470	−	0.935823i	$-0.385342\pi$
$37$	4.28799	0.704941	0.352470	+	0.935823i	$0.385342\pi$
$38$	8.74899	1.41927
$39$	−5.83236	−0.933925
$40$	−2.31518	−0.366062
$41$	4.15262	0.648530	0.324265	−	0.945966i	$-0.394883\pi$
$41$	4.15262	0.648530	0.324265	+	0.945966i	$0.394883\pi$
$42$	−5.03655	−0.777156
$43$	3.97479	0.606150	0.303075	−	0.952967i	$-0.401987\pi$
$43$	3.97479	0.606150	0.303075	+	0.952967i	$0.401987\pi$
$44$	2.16590	0.326521
$45$	1.00000	0.149071
$46$	0	0
$47$	−11.4438	−1.66925	−0.834625	−	0.550818i	$-0.814316\pi$
$47$	−11.4438	−1.66925	−0.834625	+	0.550818i	$0.814316\pi$
$48$	4.79772	0.692492
$49$	2.94680	0.420971
$50$	1.59695	0.225843
$51$	−3.95982	−0.554486
$52$	3.20924	0.445042
$53$	−4.29277	−0.589657	−0.294829	−	0.955550i	$-0.595263\pi$
$53$	−4.29277	−0.589657	−0.294829	+	0.955550i	$0.595263\pi$
$54$	−1.59695	−0.217317
$55$	3.93622	0.530760
$56$	−7.30174	−0.975736
$57$	−5.47856	−0.725653
$58$	−10.4492	−1.37205
$59$	−13.8795	−1.80696	−0.903478	−	0.428635i	$-0.858995\pi$
$59$	−13.8795	−1.80696	−0.903478	+	0.428635i	$0.858995\pi$
$60$	−0.550248	−0.0710367
$61$	2.38454	0.305310	0.152655	−	0.988280i	$-0.451218\pi$
$61$	2.38454	0.305310	0.152655	+	0.988280i	$0.451218\pi$
$62$	9.25007	1.17476
$63$	3.15385	0.397348
$64$	4.75452	0.594315
$65$	5.83236	0.723415
$66$	−6.28595	−0.773747
$67$	10.2832	1.25630	0.628148	−	0.778094i	$-0.283813\pi$
$67$	10.2832	1.25630	0.628148	+	0.778094i	$0.283813\pi$
$68$	2.17888	0.264228
$69$	0	0
$70$	5.03655	0.601982
$71$	−7.43010	−0.881791	−0.440896	−	0.897558i	$-0.645339\pi$
$71$	−7.43010	−0.881791	−0.440896	+	0.897558i	$0.645339\pi$
$72$	−2.31518	−0.272847
$73$	4.84630	0.567216	0.283608	−	0.958940i	$-0.408468\pi$
$73$	4.84630	0.567216	0.283608	+	0.958940i	$0.408468\pi$
$74$	6.84770	0.796029
$75$	−1.00000	−0.115470
$76$	3.01457	0.345795
$77$	12.4143	1.41474
$78$	−9.31399	−1.05460
$79$	−9.59938	−1.08001	−0.540007	−	0.841660i	$-0.681579\pi$
$79$	−9.59938	−1.08001	−0.540007	+	0.841660i	$0.681579\pi$
$80$	−4.79772	−0.536402
$81$	1.00000	0.111111
$82$	6.63153	0.732329
$83$	8.40615	0.922695	0.461348	−	0.887220i	$-0.347366\pi$
$83$	8.40615	0.922695	0.461348	+	0.887220i	$0.347366\pi$
$84$	−1.73540	−0.189348
$85$	3.95982	0.429503
$86$	6.34754	0.684473
$87$	6.54323	0.701508
$88$	−9.11307	−0.971456
$89$	−9.86016	−1.04518	−0.522588	−	0.852586i	$-0.675033\pi$
$89$	−9.86016	−1.04518	−0.522588	+	0.852586i	$0.675033\pi$
$90$	1.59695	0.168333
$91$	18.3944	1.92826
$92$	0	0
$93$	−5.79234	−0.600638
$94$	−18.2752	−1.88494
$95$	5.47856	0.562089
$96$	3.03136	0.309387
$97$	−15.3346	−1.55699	−0.778495	−	0.627650i	$-0.784017\pi$
$97$	−15.3346	−1.55699	−0.778495	+	0.627650i	$0.784017\pi$
$98$	4.70588	0.475366
$99$	3.93622	0.395605
$100$	0.550248	0.0550248
$101$	10.0637	1.00137	0.500686	−	0.865629i	$-0.333081\pi$
$101$	10.0637	1.00137	0.500686	+	0.865629i	$0.333081\pi$
$102$	−6.32363	−0.626133
$103$	−9.97456	−0.982823	−0.491411	−	0.870928i	$-0.663519\pi$
$103$	−9.97456	−0.982823	−0.491411	+	0.870928i	$0.663519\pi$
$104$	−13.5030	−1.32408
$105$	−3.15385	−0.307785
$106$	−6.85533	−0.665849
$107$	−9.62522	−0.930505	−0.465253	−	0.885178i	$-0.654037\pi$
$107$	−9.62522	−0.930505	−0.465253	+	0.885178i	$0.654037\pi$
$108$	−0.550248	−0.0529476
$109$	−6.33427	−0.606713	−0.303357	−	0.952877i	$-0.598107\pi$
$109$	−6.33427	−0.606713	−0.303357	+	0.952877i	$0.598107\pi$
$110$	6.28595	0.599342
$111$	−4.28799	−0.406998
$112$	−15.1313	−1.42978
$113$	−1.40316	−0.131998	−0.0659992	−	0.997820i	$-0.521023\pi$
$113$	−1.40316	−0.131998	−0.0659992	+	0.997820i	$0.521023\pi$
$114$	−8.74899	−0.819418
$115$	0	0
$116$	−3.60040	−0.334289
$117$	5.83236	0.539202
$118$	−22.1648	−2.04044
$119$	12.4887	1.14484
$120$	2.31518	0.211346
$121$	4.49385	0.408532
$122$	3.80800	0.344760
$123$	−4.15262	−0.374429
$124$	3.18722	0.286221
$125$	1.00000	0.0894427
$126$	5.03655	0.448691
$127$	9.47983	0.841199	0.420599	−	0.907246i	$-0.361820\pi$
$127$	9.47983	0.841199	0.420599	+	0.907246i	$0.361820\pi$
$128$	13.6554	1.20698
$129$	−3.97479	−0.349961
$130$	9.31399	0.816891
$131$	10.5647	0.923038	0.461519	−	0.887130i	$-0.347305\pi$
$131$	10.5647	0.923038	0.461519	+	0.887130i	$0.347305\pi$
$132$	−2.16590	−0.188517
$133$	17.2786	1.49824
$134$	16.4218	1.41863
$135$	−1.00000	−0.0860663
$136$	−9.16770	−0.786124
$137$	−15.2769	−1.30519	−0.652596	−	0.757706i	$-0.726320\pi$
$137$	−15.2769	−1.30519	−0.652596	+	0.757706i	$0.726320\pi$
$138$	0	0
$139$	−14.5570	−1.23471	−0.617356	−	0.786684i	$-0.711796\pi$
$139$	−14.5570	−1.23471	−0.617356	+	0.786684i	$0.711796\pi$
$140$	1.73540	0.146668
$141$	11.4438	0.963742
$142$	−11.8655	−0.995731
$143$	22.9575	1.91980
$144$	−4.79772	−0.399810
$145$	−6.54323	−0.543386
$146$	7.73930	0.640509
$147$	−2.94680	−0.243048
$148$	2.35946	0.193946
$149$	5.81663	0.476517	0.238259	−	0.971202i	$-0.423423\pi$
$149$	5.81663	0.476517	0.238259	+	0.971202i	$0.423423\pi$
$150$	−1.59695	−0.130390
$151$	21.0786	1.71535	0.857677	−	0.514190i	$-0.171907\pi$
$151$	21.0786	1.71535	0.857677	+	0.514190i	$0.171907\pi$
$152$	−12.6839	−1.02880
$153$	3.95982	0.320132
$154$	19.8250	1.59754
$155$	5.79234	0.465252
$156$	−3.20924	−0.256945
$157$	19.1849	1.53112	0.765561	−	0.643364i	$-0.222462\pi$
$157$	19.1849	1.53112	0.765561	+	0.643364i	$0.222462\pi$
$158$	−15.3297	−1.21957
$159$	4.29277	0.340439
$160$	−3.03136	−0.239650
$161$	0	0
$162$	1.59695	0.125468
$163$	12.5719	0.984710	0.492355	−	0.870395i	$-0.336136\pi$
$163$	12.5719	0.984710	0.492355	+	0.870395i	$0.336136\pi$
$164$	2.28497	0.178426
$165$	−3.93622	−0.306435
$166$	13.4242	1.04192
$167$	−14.1477	−1.09479	−0.547393	−	0.836876i	$-0.684380\pi$
$167$	−14.1477	−1.09479	−0.547393	+	0.836876i	$0.684380\pi$
$168$	7.30174	0.563342
$169$	21.0164	1.61665
$170$	6.32363	0.485000
$171$	5.47856	0.418956
$172$	2.18712	0.166766
$173$	−14.0316	−1.06680	−0.533402	−	0.845862i	$-0.679087\pi$
$173$	−14.0316	−1.06680	−0.533402	+	0.845862i	$0.679087\pi$
$174$	10.4492	0.792153
$175$	3.15385	0.238409
$176$	−18.8849	−1.42350
$177$	13.8795	1.04325
$178$	−15.7462	−1.18023
$179$	5.83338	0.436007	0.218004	−	0.975948i	$-0.430046\pi$
$179$	5.83338	0.436007	0.218004	+	0.975948i	$0.430046\pi$
$180$	0.550248	0.0410131
$181$	−6.81237	−0.506359	−0.253180	−	0.967419i	$-0.581476\pi$
$181$	−6.81237	−0.506359	−0.253180	+	0.967419i	$0.581476\pi$
$182$	29.3750	2.17742
$183$	−2.38454	−0.176271
$184$	0	0
$185$	4.28799	0.315259
$186$	−9.25007	−0.678248
$187$	15.5867	1.13981
$188$	−6.29693	−0.459251
$189$	−3.15385	−0.229409
$190$	8.74899	0.634718
$191$	7.50481	0.543029	0.271514	−	0.962434i	$-0.412476\pi$
$191$	7.50481	0.543029	0.271514	+	0.962434i	$0.412476\pi$
$192$	−4.75452	−0.343128
$193$	11.0495	0.795357	0.397679	−	0.917525i	$-0.369816\pi$
$193$	11.0495	0.795357	0.397679	+	0.917525i	$0.369816\pi$
$194$	−24.4886	−1.75818
$195$	−5.83236	−0.417664
$196$	1.62147	0.115819
$197$	−11.5639	−0.823896	−0.411948	−	0.911207i	$-0.635152\pi$
$197$	−11.5639	−0.823896	−0.411948	+	0.911207i	$0.635152\pi$
$198$	6.28595	0.446723
$199$	−21.8556	−1.54931	−0.774653	−	0.632387i	$-0.782075\pi$
$199$	−21.8556	−1.54931	−0.774653	+	0.632387i	$0.782075\pi$
$200$	−2.31518	−0.163708
$201$	−10.2832	−0.725323
$202$	16.0712	1.13076
$203$	−20.6364	−1.44839
$204$	−2.17888	−0.152552
$205$	4.15262	0.290032
$206$	−15.9289	−1.10982
$207$	0	0
$208$	−27.9821	−1.94021
$209$	21.5648	1.49167
$210$	−5.03655	−0.347555
$211$	−14.5644	−1.00265	−0.501326	−	0.865258i	$-0.667154\pi$
$211$	−14.5644	−1.00265	−0.501326	+	0.865258i	$0.667154\pi$
$212$	−2.36209	−0.162229
$213$	7.43010	0.509102
$214$	−15.3710	−1.05074
$215$	3.97479	0.271078
$216$	2.31518	0.157528
$217$	18.2682	1.24013
$218$	−10.1155	−0.685109
$219$	−4.84630	−0.327483
$220$	2.16590	0.146025
$221$	23.0951	1.55354
$222$	−6.84770	−0.459587
$223$	−1.77197	−0.118660	−0.0593301	−	0.998238i	$-0.518896\pi$
$223$	−1.77197	−0.118660	−0.0593301	+	0.998238i	$0.518896\pi$
$224$	−9.56047	−0.638786
$225$	1.00000	0.0666667
$226$	−2.24078	−0.149054
$227$	−1.00635	−0.0667938	−0.0333969	−	0.999442i	$-0.510633\pi$
$227$	−1.00635	−0.0667938	−0.0333969	+	0.999442i	$0.510633\pi$
$228$	−3.01457	−0.199645
$229$	−19.6059	−1.29559	−0.647797	−	0.761813i	$-0.724309\pi$
$229$	−19.6059	−1.29559	−0.647797	+	0.761813i	$0.724309\pi$
$230$	0	0
$231$	−12.4143	−0.816799
$232$	15.1488	0.994565
$233$	5.02512	0.329206	0.164603	−	0.986360i	$-0.447366\pi$
$233$	5.02512	0.329206	0.164603	+	0.986360i	$0.447366\pi$
$234$	9.31399	0.608874
$235$	−11.4438	−0.746512
$236$	−7.63716	−0.497137
$237$	9.59938	0.623547
$238$	19.9438	1.29277
$239$	19.4577	1.25862	0.629308	−	0.777156i	$-0.283338\pi$
$239$	19.4577	1.25862	0.629308	+	0.777156i	$0.283338\pi$
$240$	4.79772	0.309692
$241$	17.6543	1.13721	0.568606	−	0.822610i	$-0.307483\pi$
$241$	17.6543	1.13721	0.568606	+	0.822610i	$0.307483\pi$
$242$	7.17646	0.461320
$243$	−1.00000	−0.0641500
$244$	1.31209	0.0839980
$245$	2.94680	0.188264
$246$	−6.63153	−0.422811
$247$	31.9530	2.03312
$248$	−13.4103	−0.851556
$249$	−8.40615	−0.532718
$250$	1.59695	0.101000
$251$	13.8869	0.876534	0.438267	−	0.898845i	$-0.355592\pi$
$251$	13.8869	0.876534	0.438267	+	0.898845i	$0.355592\pi$
$252$	1.73540	0.109320
$253$	0	0
$254$	15.1388	0.949893
$255$	−3.95982	−0.247974
$256$	12.2980	0.768626
$257$	−16.6861	−1.04085	−0.520424	−	0.853908i	$-0.674226\pi$
$257$	−16.6861	−1.04085	−0.520424	+	0.853908i	$0.674226\pi$
$258$	−6.34754	−0.395181
$259$	13.5237	0.840321
$260$	3.20924	0.199029
$261$	−6.54323	−0.405016
$262$	16.8712	1.04231
$263$	−4.26366	−0.262909	−0.131454	−	0.991322i	$-0.541965\pi$
$263$	−4.26366	−0.262909	−0.131454	+	0.991322i	$0.541965\pi$
$264$	9.11307	0.560871
$265$	−4.29277	−0.263703
$266$	27.5930	1.69184
$267$	9.86016	0.603432
$268$	5.65832	0.345637
$269$	−21.2982	−1.29858	−0.649288	−	0.760543i	$-0.724933\pi$
$269$	−21.2982	−1.29858	−0.649288	+	0.760543i	$0.724933\pi$
$270$	−1.59695	−0.0971873
$271$	7.03244	0.427190	0.213595	−	0.976922i	$-0.431483\pi$
$271$	7.03244	0.427190	0.213595	+	0.976922i	$0.431483\pi$
$272$	−18.9981	−1.15193
$273$	−18.3944	−1.11328
$274$	−24.3964	−1.47384
$275$	3.93622	0.237363
$276$	0	0
$277$	22.4016	1.34598	0.672991	−	0.739650i	$-0.265009\pi$
$277$	22.4016	1.34598	0.672991	+	0.739650i	$0.265009\pi$
$278$	−23.2468	−1.39425
$279$	5.79234	0.346778
$280$	−7.30174	−0.436363
$281$	−0.667600	−0.0398257	−0.0199128	−	0.999802i	$-0.506339\pi$
$281$	−0.667600	−0.0398257	−0.0199128	+	0.999802i	$0.506339\pi$
$282$	18.2752	1.08827
$283$	8.38815	0.498624	0.249312	−	0.968423i	$-0.419796\pi$
$283$	8.38815	0.498624	0.249312	+	0.968423i	$0.419796\pi$
$284$	−4.08840	−0.242602
$285$	−5.47856	−0.324522
$286$	36.6619	2.16787
$287$	13.0968	0.773077
$288$	−3.03136	−0.178625
$289$	−1.31983	−0.0776370
$290$	−10.4492	−0.613599
$291$	15.3346	0.898929
$292$	2.66667	0.156055
$293$	10.5955	0.618998	0.309499	−	0.950900i	$-0.399839\pi$
$293$	10.5955	0.618998	0.309499	+	0.950900i	$0.399839\pi$
$294$	−4.70588	−0.274453
$295$	−13.8795	−0.808095
$296$	−9.92747	−0.577022
$297$	−3.93622	−0.228403
$298$	9.28887	0.538090
$299$	0	0
$300$	−0.550248	−0.0317686
$301$	12.5359	0.722558
$302$	33.6615	1.93700
$303$	−10.0637	−0.578142
$304$	−26.2846	−1.50753
$305$	2.38454	0.136539
$306$	6.32363	0.361498
$307$	−4.28290	−0.244438	−0.122219	−	0.992503i	$-0.539001\pi$
$307$	−4.28290	−0.244438	−0.122219	+	0.992503i	$0.539001\pi$
$308$	6.83093	0.389228
$309$	9.97456	0.567433
$310$	9.25007	0.525369
$311$	−2.25106	−0.127646	−0.0638230	−	0.997961i	$-0.520329\pi$
$311$	−2.25106	−0.127646	−0.0638230	+	0.997961i	$0.520329\pi$
$312$	13.5030	0.764455
$313$	25.0880	1.41806	0.709028	−	0.705180i	$-0.249134\pi$
$313$	25.0880	1.41806	0.709028	+	0.705180i	$0.249134\pi$
$314$	30.6373	1.72896
$315$	3.15385	0.177700
$316$	−5.28204	−0.297138
$317$	28.8505	1.62040	0.810202	−	0.586150i	$-0.199357\pi$
$317$	28.8505	1.62040	0.810202	+	0.586150i	$0.199357\pi$
$318$	6.85533	0.384428
$319$	−25.7556	−1.44204
$320$	4.75452	0.265786
$321$	9.62522	0.537227
$322$	0	0
$323$	21.6941	1.20709
$324$	0.550248	0.0305693
$325$	5.83236	0.323521
$326$	20.0767	1.11195
$327$	6.33427	0.350286
$328$	−9.61407	−0.530848
$329$	−36.0921	−1.98982
$330$	−6.28595	−0.346030
$331$	−29.9214	−1.64463	−0.822315	−	0.569032i	$-0.807318\pi$
$331$	−29.9214	−1.64463	−0.822315	+	0.569032i	$0.807318\pi$
$332$	4.62547	0.253855
$333$	4.28799	0.234980
$334$	−22.5932	−1.23625
$335$	10.2832	0.561833
$336$	15.1313	0.825481
$337$	25.4551	1.38663	0.693313	−	0.720637i	$-0.256151\pi$
$337$	25.4551	1.38663	0.693313	+	0.720637i	$0.256151\pi$
$338$	33.5622	1.82554
$339$	1.40316	0.0762093
$340$	2.17888	0.118166
$341$	22.7999	1.23469
$342$	8.74899	0.473091
$343$	−12.7832	−0.690229
$344$	−9.20236	−0.496158
$345$	0	0
$346$	−22.4078	−1.20465
$347$	−12.9541	−0.695414	−0.347707	−	0.937603i	$-0.613040\pi$
$347$	−12.9541	−0.695414	−0.347707	+	0.937603i	$0.613040\pi$
$348$	3.60040	0.193002
$349$	2.48764	0.133160	0.0665802	−	0.997781i	$-0.478791\pi$
$349$	2.48764	0.133160	0.0665802	+	0.997781i	$0.478791\pi$
$350$	5.03655	0.269215
$351$	−5.83236	−0.311308
$352$	−11.9321	−0.635983
$353$	25.5808	1.36153	0.680763	−	0.732504i	$-0.261648\pi$
$353$	25.5808	1.36153	0.680763	+	0.732504i	$0.261648\pi$
$354$	22.1648	1.17805
$355$	−7.43010	−0.394349
$356$	−5.42553	−0.287553
$357$	−12.4887	−0.660972
$358$	9.31561	0.492345
$359$	8.80926	0.464935	0.232468	−	0.972604i	$-0.425320\pi$
$359$	8.80926	0.464935	0.232468	+	0.972604i	$0.425320\pi$
$360$	−2.31518	−0.122021
$361$	11.0147	0.579719
$362$	−10.8790	−0.571788
$363$	−4.49385	−0.235866
$364$	10.1215	0.530510
$365$	4.84630	0.253667
$366$	−3.80800	−0.199047
$367$	−21.5533	−1.12507	−0.562537	−	0.826772i	$-0.690175\pi$
$367$	−21.5533	−1.12507	−0.562537	+	0.826772i	$0.690175\pi$
$368$	0	0
$369$	4.15262	0.216177
$370$	6.84770	0.355995
$371$	−13.5388	−0.702898
$372$	−3.18722	−0.165250
$373$	−21.1805	−1.09668	−0.548342	−	0.836254i	$-0.684741\pi$
$373$	−21.1805	−1.09668	−0.548342	+	0.836254i	$0.684741\pi$
$374$	24.8912	1.28709
$375$	−1.00000	−0.0516398
$376$	26.4945	1.36635
$377$	−38.1625	−1.96547
$378$	−5.03655	−0.259052
$379$	18.0363	0.926465	0.463232	−	0.886237i	$-0.346690\pi$
$379$	18.0363	0.926465	0.463232	+	0.886237i	$0.346690\pi$
$380$	3.01457	0.154644
$381$	−9.47983	−0.485666
$382$	11.9848	0.613196
$383$	−6.92259	−0.353728	−0.176864	−	0.984235i	$-0.556595\pi$
$383$	−6.92259	−0.353728	−0.176864	+	0.984235i	$0.556595\pi$
$384$	−13.6554	−0.696851
$385$	12.4143	0.632690
$386$	17.6454	0.898129
$387$	3.97479	0.202050
$388$	−8.43782	−0.428365
$389$	0.342102	0.0173453	0.00867264	−	0.999962i	$-0.497239\pi$
$389$	0.342102	0.0173453	0.00867264	+	0.999962i	$0.497239\pi$
$390$	−9.31399	−0.471632
$391$	0	0
$392$	−6.82237	−0.344582
$393$	−10.5647	−0.532916
$394$	−18.4670	−0.930355
$395$	−9.59938	−0.482997
$396$	2.16590	0.108840
$397$	0.413811	0.0207686	0.0103843	−	0.999946i	$-0.496695\pi$
$397$	0.413811	0.0207686	0.0103843	+	0.999946i	$0.496695\pi$
$398$	−34.9024	−1.74950
$399$	−17.2786	−0.865011
$400$	−4.79772	−0.239886
$401$	−26.3310	−1.31491	−0.657453	−	0.753496i	$-0.728366\pi$
$401$	−26.3310	−1.31491	−0.657453	+	0.753496i	$0.728366\pi$
$402$	−16.4218	−0.819045
$403$	33.7830	1.68285
$404$	5.53751	0.275501
$405$	1.00000	0.0496904
$406$	−32.9553	−1.63554
$407$	16.8785	0.836635
$408$	9.16770	0.453869
$409$	−15.2266	−0.752907	−0.376453	−	0.926436i	$-0.622857\pi$
$409$	−15.2266	−0.752907	−0.376453	+	0.926436i	$0.622857\pi$
$410$	6.63153	0.327508
$411$	15.2769	0.753553
$412$	−5.48848	−0.270398
$413$	−43.7739	−2.15397
$414$	0	0
$415$	8.40615	0.412642
$416$	−17.6800	−0.866833
$417$	14.5570	0.712861
$418$	34.4380	1.68442
$419$	25.2312	1.23263	0.616313	−	0.787501i	$-0.288626\pi$
$419$	25.2312	1.23263	0.616313	+	0.787501i	$0.288626\pi$
$420$	−1.73540	−0.0846789
$421$	2.32484	0.113306	0.0566530	−	0.998394i	$-0.481957\pi$
$421$	2.32484	0.113306	0.0566530	+	0.998394i	$0.481957\pi$
$422$	−23.2586	−1.13221
$423$	−11.4438	−0.556417
$424$	9.93854	0.482658
$425$	3.95982	0.192079
$426$	11.8655	0.574885
$427$	7.52051	0.363943
$428$	−5.29626	−0.256004
$429$	−22.9575	−1.10840
$430$	6.34754	0.306106
$431$	−11.1893	−0.538969	−0.269485	−	0.963005i	$-0.586853\pi$
$431$	−11.1893	−0.538969	−0.269485	+	0.963005i	$0.586853\pi$
$432$	4.79772	0.230831
$433$	6.64192	0.319190	0.159595	−	0.987183i	$-0.448981\pi$
$433$	6.64192	0.319190	0.159595	+	0.987183i	$0.448981\pi$
$434$	29.1734	1.40037
$435$	6.54323	0.313724
$436$	−3.48542	−0.166921
$437$	0	0
$438$	−7.73930	−0.369798
$439$	34.9295	1.66709	0.833546	−	0.552450i	$-0.186307\pi$
$439$	34.9295	1.66709	0.833546	+	0.552450i	$0.186307\pi$
$440$	−9.11307	−0.434449
$441$	2.94680	0.140324
$442$	36.8817	1.75428
$443$	15.9216	0.756460	0.378230	−	0.925712i	$-0.376533\pi$
$443$	15.9216	0.756460	0.378230	+	0.925712i	$0.376533\pi$
$444$	−2.35946	−0.111975
$445$	−9.86016	−0.467417
$446$	−2.82975	−0.133993
$447$	−5.81663	−0.275117
$448$	14.9951	0.708450
$449$	−5.41536	−0.255567	−0.127783	−	0.991802i	$-0.540786\pi$
$449$	−5.41536	−0.255567	−0.127783	+	0.991802i	$0.540786\pi$
$450$	1.59695	0.0752809
$451$	16.3456	0.769686
$452$	−0.772087	−0.0363159
$453$	−21.0786	−0.990360
$454$	−1.60709	−0.0754245
$455$	18.3944	0.862344
$456$	12.6839	0.593976
$457$	−20.5929	−0.963294	−0.481647	−	0.876365i	$-0.659961\pi$
$457$	−20.5929	−0.963294	−0.481647	+	0.876365i	$0.659961\pi$
$458$	−31.3096	−1.46300
$459$	−3.95982	−0.184829
$460$	0	0
$461$	4.56278	0.212510	0.106255	−	0.994339i	$-0.466114\pi$
$461$	4.56278	0.212510	0.106255	+	0.994339i	$0.466114\pi$
$462$	−19.8250	−0.922341
$463$	−17.8233	−0.828320	−0.414160	−	0.910204i	$-0.635925\pi$
$463$	−17.8233	−0.828320	−0.414160	+	0.910204i	$0.635925\pi$
$464$	31.3926	1.45737
$465$	−5.79234	−0.268613
$466$	8.02486	0.371744
$467$	−4.29164	−0.198593	−0.0992967	−	0.995058i	$-0.531659\pi$
$467$	−4.29164	−0.198593	−0.0992967	+	0.995058i	$0.531659\pi$
$468$	3.20924	0.148347
$469$	32.4318	1.49756
$470$	−18.2752	−0.842971
$471$	−19.1849	−0.883993
$472$	32.1335	1.47907
$473$	15.6457	0.719388
$474$	15.3297	0.704118
$475$	5.47856	0.251374
$476$	6.87188	0.314972
$477$	−4.29277	−0.196552
$478$	31.0730	1.42125
$479$	−7.66217	−0.350093	−0.175047	−	0.984560i	$-0.556008\pi$
$479$	−7.66217	−0.350093	−0.175047	+	0.984560i	$0.556008\pi$
$480$	3.03136	0.138362
$481$	25.0091	1.14032
$482$	28.1930	1.28416
$483$	0	0
$484$	2.47273	0.112397
$485$	−15.3346	−0.696307
$486$	−1.59695	−0.0724391
$487$	−32.0485	−1.45226	−0.726129	−	0.687559i	$-0.758682\pi$
$487$	−32.0485	−1.45226	−0.726129	+	0.687559i	$0.758682\pi$
$488$	−5.52065	−0.249908
$489$	−12.5719	−0.568522
$490$	4.70588	0.212590
$491$	27.7507	1.25237	0.626186	−	0.779674i	$-0.284615\pi$
$491$	27.7507	1.25237	0.626186	+	0.779674i	$0.284615\pi$
$492$	−2.28497	−0.103014
$493$	−25.9100	−1.16693
$494$	51.0273	2.29583
$495$	3.93622	0.176920
$496$	−27.7900	−1.24781
$497$	−23.4335	−1.05113
$498$	−13.4242	−0.601553
$499$	−7.33728	−0.328462	−0.164231	−	0.986422i	$-0.552514\pi$
$499$	−7.33728	−0.328462	−0.164231	+	0.986422i	$0.552514\pi$
$500$	0.550248	0.0246078
$501$	14.1477	0.632075
$502$	22.1767	0.989794
$503$	−0.327014	−0.0145808	−0.00729042	−	0.999973i	$-0.502321\pi$
$503$	−0.327014	−0.0145808	−0.00729042	+	0.999973i	$0.502321\pi$
$504$	−7.30174	−0.325245
$505$	10.0637	0.447827
$506$	0	0
$507$	−21.0164	−0.933373
$508$	5.21626	0.231434
$509$	5.93584	0.263102	0.131551	−	0.991309i	$-0.458004\pi$
$509$	5.93584	0.263102	0.131551	+	0.991309i	$0.458004\pi$
$510$	−6.32363	−0.280015
$511$	15.2845	0.676147
$512$	−7.67157	−0.339039
$513$	−5.47856	−0.241884
$514$	−26.6468	−1.17534
$515$	−9.97456	−0.439532
$516$	−2.18712	−0.0962826
$517$	−45.0454	−1.98109
$518$	21.5966	0.948902
$519$	14.0316	0.615919
$520$	−13.5030	−0.592145
$521$	3.04676	0.133481	0.0667404	−	0.997770i	$-0.478740\pi$
$521$	3.04676	0.133481	0.0667404	+	0.997770i	$0.478740\pi$
$522$	−10.4492	−0.457350
$523$	−13.1323	−0.574236	−0.287118	−	0.957895i	$-0.592697\pi$
$523$	−13.1323	−0.574236	−0.287118	+	0.957895i	$0.592697\pi$
$524$	5.81318	0.253950
$525$	−3.15385	−0.137645
$526$	−6.80885	−0.296880
$527$	22.9366	0.999135
$528$	18.8849	0.821860
$529$	0	0
$530$	−6.85533	−0.297777
$531$	−13.8795	−0.602318
$532$	9.50751	0.412203
$533$	24.2196	1.04907
$534$	15.7462	0.681404
$535$	−9.62522	−0.416135
$536$	−23.8075	−1.02833
$537$	−5.83338	−0.251729
$538$	−34.0122	−1.46637
$539$	11.5992	0.499615
$540$	−0.550248	−0.0236789
$541$	−11.9281	−0.512830	−0.256415	−	0.966567i	$-0.582541\pi$
$541$	−11.9281	−0.512830	−0.256415	+	0.966567i	$0.582541\pi$
$542$	11.2305	0.482389
$543$	6.81237	0.292347
$544$	−12.0036	−0.514652
$545$	−6.33427	−0.271330
$546$	−29.3750	−1.25713
$547$	6.09851	0.260754	0.130377	−	0.991465i	$-0.458381\pi$
$547$	6.09851	0.260754	0.130377	+	0.991465i	$0.458381\pi$
$548$	−8.40607	−0.359089
$549$	2.38454	0.101770
$550$	6.28595	0.268034
$551$	−35.8475	−1.52716
$552$	0	0
$553$	−30.2751	−1.28743
$554$	35.7743	1.51990
$555$	−4.28799	−0.182015
$556$	−8.00998	−0.339699
$557$	37.4088	1.58506	0.792530	−	0.609832i	$-0.208763\pi$
$557$	37.4088	1.58506	0.792530	+	0.609832i	$0.208763\pi$
$558$	9.25007	0.391587
$559$	23.1824	0.980512
$560$	−15.1313	−0.639415
$561$	−15.5867	−0.658072
$562$	−1.06612	−0.0449717
$563$	−8.97422	−0.378218	−0.189109	−	0.981956i	$-0.560560\pi$
$563$	−8.97422	−0.378218	−0.189109	+	0.981956i	$0.560560\pi$
$564$	6.29693	0.265149
$565$	−1.40316	−0.0590315
$566$	13.3955	0.563053
$567$	3.15385	0.132449
$568$	17.2020	0.721781
$569$	−19.3436	−0.810925	−0.405463	−	0.914112i	$-0.632890\pi$
$569$	−19.3436	−0.810925	−0.405463	+	0.914112i	$0.632890\pi$
$570$	−8.74899	−0.366455
$571$	17.6474	0.738521	0.369260	−	0.929326i	$-0.379611\pi$
$571$	17.6474	0.738521	0.369260	+	0.929326i	$0.379611\pi$
$572$	12.6323	0.528183
$573$	−7.50481	−0.313518
$574$	20.9149	0.872970
$575$	0	0
$576$	4.75452	0.198105
$577$	2.27364	0.0946531	0.0473265	−	0.998879i	$-0.484930\pi$
$577$	2.27364	0.0946531	0.0473265	+	0.998879i	$0.484930\pi$
$578$	−2.10770	−0.0876687
$579$	−11.0495	−0.459200
$580$	−3.60040	−0.149498
$581$	26.5118	1.09989
$582$	24.4886	1.01508
$583$	−16.8973	−0.699814
$584$	−11.2201	−0.464289
$585$	5.83236	0.241138
$586$	16.9205	0.698981
$587$	43.4015	1.79137	0.895686	−	0.444687i	$-0.146685\pi$
$587$	43.4015	1.79137	0.895686	+	0.444687i	$0.146685\pi$
$588$	−1.62147	−0.0668682
$589$	31.7337	1.30756
$590$	−22.1648	−0.912512
$591$	11.5639	0.475677
$592$	−20.5726	−0.845528
$593$	5.96063	0.244774	0.122387	−	0.992482i	$-0.460945\pi$
$593$	5.96063	0.244774	0.122387	+	0.992482i	$0.460945\pi$
$594$	−6.28595	−0.257916
$595$	12.4887	0.511987
$596$	3.20059	0.131101
$597$	21.8556	0.894492
$598$	0	0
$599$	−42.4563	−1.73472	−0.867359	−	0.497683i	$-0.834184\pi$
$599$	−42.4563	−1.73472	−0.867359	+	0.497683i	$0.834184\pi$
$600$	2.31518	0.0945169
$601$	−48.4578	−1.97664	−0.988318	−	0.152406i	$-0.951298\pi$
$601$	−48.4578	−1.97664	−0.988318	+	0.152406i	$0.951298\pi$
$602$	20.0192	0.815922
$603$	10.2832	0.418765
$604$	11.5985	0.471935
$605$	4.49385	0.182701
$606$	−16.0712	−0.652846
$607$	−26.6289	−1.08084	−0.540418	−	0.841397i	$-0.681734\pi$
$607$	−26.6289	−1.08084	−0.540418	+	0.841397i	$0.681734\pi$
$608$	−16.6075	−0.673523
$609$	20.6364	0.836229
$610$	3.80800	0.154181
$611$	−66.7444	−2.70019
$612$	2.17888	0.0880761
$613$	11.8440	0.478374	0.239187	−	0.970974i	$-0.423119\pi$
$613$	11.8440	0.478374	0.239187	+	0.970974i	$0.423119\pi$
$614$	−6.83958	−0.276023
$615$	−4.15262	−0.167450
$616$	−28.7413	−1.15802
$617$	12.1685	0.489884	0.244942	−	0.969538i	$-0.421231\pi$
$617$	12.1685	0.489884	0.244942	+	0.969538i	$0.421231\pi$
$618$	15.9289	0.640753
$619$	10.4945	0.421809	0.210905	−	0.977507i	$-0.432359\pi$
$619$	10.4945	0.421809	0.210905	+	0.977507i	$0.432359\pi$
$620$	3.18722	0.128002
$621$	0	0
$622$	−3.59483	−0.144140
$623$	−31.0975	−1.24590
$624$	27.9821	1.12018
$625$	1.00000	0.0400000
$626$	40.0642	1.60129
$627$	−21.5648	−0.861217
$628$	10.5564	0.421248
$629$	16.9797	0.677023
$630$	5.03655	0.200661
$631$	19.0188	0.757127	0.378563	−	0.925575i	$-0.376418\pi$
$631$	19.0188	0.757127	0.378563	+	0.925575i	$0.376418\pi$
$632$	22.2243	0.884035
$633$	14.5644	0.578882
$634$	46.0728	1.82978
$635$	9.47983	0.376195
$636$	2.36209	0.0936628
$637$	17.1868	0.680965
$638$	−41.1304	−1.62837
$639$	−7.43010	−0.293930
$640$	13.6554	0.539779
$641$	7.40097	0.292321	0.146160	−	0.989261i	$-0.453308\pi$
$641$	7.40097	0.292321	0.146160	+	0.989261i	$0.453308\pi$
$642$	15.3710	0.606645
$643$	−32.3734	−1.27668	−0.638341	−	0.769754i	$-0.720379\pi$
$643$	−32.3734	−1.27668	−0.638341	+	0.769754i	$0.720379\pi$
$644$	0	0
$645$	−3.97479	−0.156507
$646$	34.6444	1.36307
$647$	12.6224	0.496238	0.248119	−	0.968730i	$-0.420188\pi$
$647$	12.6224	0.496238	0.248119	+	0.968730i	$0.420188\pi$
$648$	−2.31518	−0.0909489
$649$	−54.6328	−2.14452
$650$	9.31399	0.365325
$651$	−18.2682	−0.715987
$652$	6.91768	0.270917
$653$	−44.9565	−1.75928	−0.879641	−	0.475638i	$-0.842217\pi$
$653$	−44.9565	−1.75928	−0.879641	+	0.475638i	$0.842217\pi$
$654$	10.1155	0.395548
$655$	10.5647	0.412795
$656$	−19.9231	−0.777867
$657$	4.84630	0.189072
$658$	−57.6373	−2.24693
$659$	42.1042	1.64015	0.820073	−	0.572259i	$-0.193933\pi$
$659$	42.1042	1.64015	0.820073	+	0.572259i	$0.193933\pi$
$660$	−2.16590	−0.0843075
$661$	−3.69643	−0.143775	−0.0718873	−	0.997413i	$-0.522902\pi$
$661$	−3.69643	−0.143775	−0.0718873	+	0.997413i	$0.522902\pi$
$662$	−47.7830	−1.85714
$663$	−23.0951	−0.896939
$664$	−19.4618	−0.755263
$665$	17.2786	0.670035
$666$	6.84770	0.265343
$667$	0	0
$668$	−7.78477	−0.301202
$669$	1.77197	0.0685084
$670$	16.4218	0.634429
$671$	9.38610	0.362346
$672$	9.56047	0.368803
$673$	−9.13570	−0.352155	−0.176078	−	0.984376i	$-0.556341\pi$
$673$	−9.13570	−0.352155	−0.176078	+	0.984376i	$0.556341\pi$
$674$	40.6504	1.56580
$675$	−1.00000	−0.0384900
$676$	11.5643	0.444779
$677$	−8.76436	−0.336842	−0.168421	−	0.985715i	$-0.553867\pi$
$677$	−8.76436	−0.336842	−0.168421	+	0.985715i	$0.553867\pi$
$678$	2.24078	0.0860566
$679$	−48.3630	−1.85600
$680$	−9.16770	−0.351565
$681$	1.00635	0.0385634
$682$	36.4104	1.39422
$683$	−21.2139	−0.811729	−0.405865	−	0.913933i	$-0.633030\pi$
$683$	−21.2139	−0.811729	−0.405865	+	0.913933i	$0.633030\pi$
$684$	3.01457	0.115265
$685$	−15.2769	−0.583699
$686$	−20.4141	−0.779416
$687$	19.6059	0.748011
$688$	−19.0699	−0.727035
$689$	−25.0370	−0.953833
$690$	0	0
$691$	−37.0421	−1.40915	−0.704575	−	0.709630i	$-0.748862\pi$
$691$	−37.0421	−1.40915	−0.704575	+	0.709630i	$0.748862\pi$
$692$	−7.72086	−0.293503
$693$	12.4143	0.471579
$694$	−20.6871	−0.785271
$695$	−14.5570	−0.552180
$696$	−15.1488	−0.574213
$697$	16.4436	0.622847
$698$	3.97264	0.150367
$699$	−5.02512	−0.190067
$700$	1.73540	0.0655920
$701$	−20.7680	−0.784398	−0.392199	−	0.919880i	$-0.628286\pi$
$701$	−20.7680	−0.784398	−0.392199	+	0.919880i	$0.628286\pi$
$702$	−9.31399	−0.351534
$703$	23.4920	0.886018
$704$	18.7148	0.705342
$705$	11.4438	0.430999
$706$	40.8512	1.53745
$707$	31.7393	1.19368
$708$	7.63716	0.287022
$709$	27.2373	1.02292	0.511459	−	0.859308i	$-0.329105\pi$
$709$	27.2373	1.02292	0.511459	+	0.859308i	$0.329105\pi$
$710$	−11.8655	−0.445304
$711$	−9.59938	−0.360005
$712$	22.8281	0.855518
$713$	0	0
$714$	−19.9438	−0.746378
$715$	22.9575	0.858561
$716$	3.20980	0.119956
$717$	−19.4577	−0.726663
$718$	14.0680	0.525011
$719$	7.61232	0.283892	0.141946	−	0.989874i	$-0.454664\pi$
$719$	7.61232	0.283892	0.141946	+	0.989874i	$0.454664\pi$
$720$	−4.79772	−0.178801
$721$	−31.4583	−1.17157
$722$	17.5899	0.654626
$723$	−17.6543	−0.656570
$724$	−3.74849	−0.139312
$725$	−6.54323	−0.243010
$726$	−7.17646	−0.266343
$727$	−34.4174	−1.27647	−0.638236	−	0.769841i	$-0.720336\pi$
$727$	−34.4174	−1.27647	−0.638236	+	0.769841i	$0.720336\pi$
$728$	−42.5864	−1.57836
$729$	1.00000	0.0370370
$730$	7.73930	0.286444
$731$	15.7395	0.582145
$732$	−1.31209	−0.0484963
$733$	−35.7553	−1.32065	−0.660327	−	0.750978i	$-0.729582\pi$
$733$	−35.7553	−1.32065	−0.660327	+	0.750978i	$0.729582\pi$
$734$	−34.4196	−1.27045
$735$	−2.94680	−0.108694
$736$	0	0
$737$	40.4771	1.49099
$738$	6.63153	0.244110
$739$	10.4981	0.386178	0.193089	−	0.981181i	$-0.438149\pi$
$739$	10.4981	0.386178	0.193089	+	0.981181i	$0.438149\pi$
$740$	2.35946	0.0867353
$741$	−31.9530	−1.17382
$742$	−21.6207	−0.793722
$743$	−41.5766	−1.52530	−0.762649	−	0.646813i	$-0.776102\pi$
$743$	−41.5766	−1.52530	−0.762649	+	0.646813i	$0.776102\pi$
$744$	13.4103	0.491646
$745$	5.81663	0.213105
$746$	−33.8242	−1.23839
$747$	8.40615	0.307565
$748$	8.57657	0.313590
$749$	−30.3565	−1.10920
$750$	−1.59695	−0.0583124
$751$	41.5376	1.51573	0.757864	−	0.652413i	$-0.226243\pi$
$751$	41.5376	1.51573	0.757864	+	0.652413i	$0.226243\pi$
$752$	54.9042	2.00215
$753$	−13.8869	−0.506067
$754$	−60.9436	−2.21943
$755$	21.0786	0.767129
$756$	−1.73540	−0.0631159
$757$	−40.1294	−1.45853	−0.729263	−	0.684233i	$-0.760137\pi$
$757$	−40.1294	−1.45853	−0.729263	+	0.684233i	$0.760137\pi$
$758$	28.8031	1.04618
$759$	0	0
$760$	−12.6839	−0.460092
$761$	20.1074	0.728894	0.364447	−	0.931224i	$-0.381258\pi$
$761$	20.1074	0.728894	0.364447	+	0.931224i	$0.381258\pi$
$762$	−15.1388	−0.548421
$763$	−19.9774	−0.723229
$764$	4.12950	0.149400
$765$	3.95982	0.143168
$766$	−11.0550	−0.399434
$767$	−80.9502	−2.92294
$768$	−12.2980	−0.443767
$769$	28.1820	1.01627	0.508134	−	0.861278i	$-0.330335\pi$
$769$	28.1820	1.01627	0.508134	+	0.861278i	$0.330335\pi$
$770$	19.8250	0.714442
$771$	16.6861	0.600934
$772$	6.07994	0.218822
$773$	−39.5086	−1.42102	−0.710512	−	0.703685i	$-0.751537\pi$
$773$	−39.5086	−1.42102	−0.710512	+	0.703685i	$0.751537\pi$
$774$	6.34754	0.228158
$775$	5.79234	0.208067
$776$	35.5023	1.27446
$777$	−13.5237	−0.485160
$778$	0.546320	0.0195865
$779$	22.7504	0.815117
$780$	−3.20924	−0.114909
$781$	−29.2465	−1.04652
$782$	0	0
$783$	6.54323	0.233836
$784$	−14.1379	−0.504925
$785$	19.1849	0.684738
$786$	−16.8712	−0.601777
$787$	−47.5964	−1.69663	−0.848315	−	0.529492i	$-0.822383\pi$
$787$	−47.5964	−1.69663	−0.848315	+	0.529492i	$0.822383\pi$
$788$	−6.36303	−0.226674
$789$	4.26366	0.151790
$790$	−15.3297	−0.545407
$791$	−4.42537	−0.157348
$792$	−9.11307	−0.323819
$793$	13.9075	0.493871
$794$	0.660835	0.0234521
$795$	4.29277	0.152249
$796$	−12.0260	−0.426251
$797$	−8.72578	−0.309083	−0.154542	−	0.987986i	$-0.549390\pi$
$797$	−8.72578	−0.309083	−0.154542	+	0.987986i	$0.549390\pi$
$798$	−27.5930	−0.976783
$799$	−45.3154	−1.60314
$800$	−3.03136	−0.107175
$801$	−9.86016	−0.348392
$802$	−42.0492	−1.48481
$803$	19.0761	0.673182
$804$	−5.65832	−0.199554
$805$	0	0
$806$	53.9498	1.90030
$807$	21.2982	0.749733
$808$	−23.2992	−0.819663
$809$	−26.6379	−0.936539	−0.468270	−	0.883586i	$-0.655122\pi$
$809$	−26.6379	−0.936539	−0.468270	+	0.883586i	$0.655122\pi$
$810$	1.59695	0.0561111
$811$	1.27595	0.0448047	0.0224023	−	0.999749i	$-0.492869\pi$
$811$	1.27595	0.0448047	0.0224023	+	0.999749i	$0.492869\pi$
$812$	−11.3551	−0.398487
$813$	−7.03244	−0.246639
$814$	26.9541	0.944740
$815$	12.5719	0.440376
$816$	18.9981	0.665067
$817$	21.7761	0.761851
$818$	−24.3161	−0.850193
$819$	18.3944	0.642753
$820$	2.28497	0.0797946
$821$	−2.15620	−0.0752520	−0.0376260	−	0.999292i	$-0.511980\pi$
$821$	−2.15620	−0.0752520	−0.0376260	+	0.999292i	$0.511980\pi$
$822$	24.3964	0.850922
$823$	26.6507	0.928984	0.464492	−	0.885577i	$-0.346237\pi$
$823$	26.6507	0.928984	0.464492	+	0.885577i	$0.346237\pi$
$824$	23.0929	0.804480
$825$	−3.93622	−0.137042
$826$	−69.9047	−2.43229
$827$	33.2235	1.15529	0.577647	−	0.816287i	$-0.303971\pi$
$827$	33.2235	1.15529	0.577647	+	0.816287i	$0.303971\pi$
$828$	0	0
$829$	11.5696	0.401828	0.200914	−	0.979609i	$-0.435609\pi$
$829$	11.5696	0.401828	0.200914	+	0.979609i	$0.435609\pi$
$830$	13.4242	0.465961
$831$	−22.4016	−0.777104
$832$	27.7301	0.961367
$833$	11.6688	0.404299
$834$	23.2468	0.804973
$835$	−14.1477	−0.489603
$836$	11.8660	0.410395
$837$	−5.79234	−0.200213
$838$	40.2930	1.39190
$839$	6.76579	0.233581	0.116791	−	0.993157i	$-0.462739\pi$
$839$	6.76579	0.233581	0.116791	+	0.993157i	$0.462739\pi$
$840$	7.30174	0.251934
$841$	13.8139	0.476341
$842$	3.71266	0.127947
$843$	0.667600	0.0229934
$844$	−8.01401	−0.275854
$845$	21.0164	0.722988
$846$	−18.2752	−0.628314
$847$	14.1730	0.486988
$848$	20.5955	0.707253
$849$	−8.38815	−0.287881
$850$	6.32363	0.216899
$851$	0	0
$852$	4.08840	0.140066
$853$	11.5961	0.397044	0.198522	−	0.980096i	$-0.436386\pi$
$853$	11.5961	0.397044	0.198522	+	0.980096i	$0.436386\pi$
$854$	12.0099	0.410969
$855$	5.47856	0.187363
$856$	22.2841	0.761656
$857$	23.3136	0.796376	0.398188	−	0.917304i	$-0.369639\pi$
$857$	23.3136	0.796376	0.398188	+	0.917304i	$0.369639\pi$
$858$	−36.6619	−1.25162
$859$	−39.6318	−1.35222	−0.676110	−	0.736800i	$-0.736336\pi$
$859$	−39.6318	−1.35222	−0.676110	+	0.736800i	$0.736336\pi$
$860$	2.18712	0.0745802
$861$	−13.0968	−0.446336
$862$	−17.8687	−0.608611
$863$	8.89344	0.302736	0.151368	−	0.988477i	$-0.451632\pi$
$863$	8.89344	0.302736	0.151368	+	0.988477i	$0.451632\pi$
$864$	3.03136	0.103129
$865$	−14.0316	−0.477089
$866$	10.6068	0.360434
$867$	1.31983	0.0448237
$868$	10.0520	0.341188
$869$	−37.7853	−1.28178
$870$	10.4492	0.354262
$871$	59.9755	2.03219
$872$	14.6650	0.496619
$873$	−15.3346	−0.518997
$874$	0	0
$875$	3.15385	0.106620
$876$	−2.66667	−0.0900983
$877$	−22.5934	−0.762926	−0.381463	−	0.924384i	$-0.624580\pi$
$877$	−22.5934	−0.762926	−0.381463	+	0.924384i	$0.624580\pi$
$878$	55.7806	1.88250
$879$	−10.5955	−0.357379
$880$	−18.8849	−0.636610
$881$	−13.4061	−0.451664	−0.225832	−	0.974166i	$-0.572510\pi$
$881$	−13.4061	−0.451664	−0.225832	+	0.974166i	$0.572510\pi$
$882$	4.70588	0.158455
$883$	46.7697	1.57392	0.786962	−	0.617001i	$-0.211653\pi$
$883$	46.7697	1.57392	0.786962	+	0.617001i	$0.211653\pi$
$884$	12.7080	0.427417
$885$	13.8795	0.466554
$886$	25.4260	0.854205
$887$	−12.0307	−0.403952	−0.201976	−	0.979390i	$-0.564736\pi$
$887$	−12.0307	−0.403952	−0.201976	+	0.979390i	$0.564736\pi$
$888$	9.92747	0.333144
$889$	29.8980	1.00275
$890$	−15.7462	−0.527813
$891$	3.93622	0.131868
$892$	−0.975025	−0.0326462
$893$	−62.6956	−2.09803
$894$	−9.28887	−0.310666
$895$	5.83338	0.194988
$896$	43.0673	1.43878
$897$	0	0
$898$	−8.64806	−0.288590
$899$	−37.9006	−1.26406
$900$	0.550248	0.0183416
$901$	−16.9986	−0.566305
$902$	26.1032	0.869140
$903$	−12.5359	−0.417169
$904$	3.24858	0.108046
$905$	−6.81237	−0.226451
$906$	−33.6615	−1.11833
$907$	8.13587	0.270147	0.135074	−	0.990836i	$-0.456873\pi$
$907$	8.13587	0.270147	0.135074	+	0.990836i	$0.456873\pi$
$908$	−0.553742	−0.0183766
$909$	10.0637	0.333790
$910$	29.3750	0.973770
$911$	−22.6745	−0.751241	−0.375620	−	0.926774i	$-0.622570\pi$
$911$	−22.6745	−0.751241	−0.375620	+	0.926774i	$0.622570\pi$
$912$	26.2846	0.870371
$913$	33.0885	1.09507
$914$	−32.8858	−1.08777
$915$	−2.38454	−0.0788306
$916$	−10.7881	−0.356449
$917$	33.3194	1.10030
$918$	−6.32363	−0.208711
$919$	−45.8160	−1.51133	−0.755665	−	0.654959i	$-0.772686\pi$
$919$	−45.8160	−1.51133	−0.755665	+	0.654959i	$0.772686\pi$
$920$	0	0
$921$	4.28290	0.141126
$922$	7.28653	0.239969
$923$	−43.3350	−1.42639
$924$	−6.83093	−0.224721
$925$	4.28799	0.140988
$926$	−28.4630	−0.935351
$927$	−9.97456	−0.327608
$928$	19.8349	0.651112
$929$	17.4908	0.573853	0.286927	−	0.957953i	$-0.407366\pi$
$929$	17.4908	0.573853	0.286927	+	0.957953i	$0.407366\pi$
$930$	−9.25007	−0.303322
$931$	16.1442	0.529105
$932$	2.76506	0.0905726
$933$	2.25106	0.0736964
$934$	−6.85353	−0.224254
$935$	15.5867	0.509741
$936$	−13.5030	−0.441358
$937$	7.07166	0.231021	0.115511	−	0.993306i	$-0.463150\pi$
$937$	7.07166	0.231021	0.115511	+	0.993306i	$0.463150\pi$
$938$	51.7920	1.69107
$939$	−25.0880	−0.818715
$940$	−6.29693	−0.205383
$941$	30.7731	1.00317	0.501587	−	0.865107i	$-0.332750\pi$
$941$	30.7731	1.00317	0.501587	+	0.865107i	$0.332750\pi$
$942$	−30.6373	−0.998217
$943$	0	0
$944$	66.5899	2.16732
$945$	−3.15385	−0.102595
$946$	24.9853	0.812343
$947$	7.09429	0.230533	0.115267	−	0.993335i	$-0.463228\pi$
$947$	7.09429	0.230533	0.115267	+	0.993335i	$0.463228\pi$
$948$	5.28204	0.171553
$949$	28.2654	0.917533
$950$	8.74899	0.283855
$951$	−28.8505	−0.935541
$952$	−28.9136	−0.937095
$953$	54.9854	1.78115	0.890576	−	0.454834i	$-0.150302\pi$
$953$	54.9854	1.78115	0.890576	+	0.454834i	$0.150302\pi$
$954$	−6.85533	−0.221950
$955$	7.50481	0.242850
$956$	10.7066	0.346276
$957$	25.7556	0.832561
$958$	−12.2361	−0.395330
$959$	−48.1810	−1.55585
$960$	−4.75452	−0.153451
$961$	2.55119	0.0822965
$962$	39.9383	1.28766
$963$	−9.62522	−0.310168
$964$	9.71423	0.312874
$965$	11.0495	0.355695
$966$	0	0
$967$	25.6631	0.825268	0.412634	−	0.910897i	$-0.364609\pi$
$967$	25.6631	0.825268	0.412634	+	0.910897i	$0.364609\pi$
$968$	−10.4041	−0.334400
$969$	−21.6941	−0.696916
$970$	−24.4886	−0.786280
$971$	−25.2325	−0.809751	−0.404875	−	0.914372i	$-0.632685\pi$
$971$	−25.2325	−0.809751	−0.404875	+	0.914372i	$0.632685\pi$
$972$	−0.550248	−0.0176492
$973$	−45.9108	−1.47183
$974$	−51.1799	−1.63991
$975$	−5.83236	−0.186785
$976$	−11.4404	−0.366198
$977$	30.7209	0.982848	0.491424	−	0.870921i	$-0.336477\pi$
$977$	30.7209	0.982848	0.491424	+	0.870921i	$0.336477\pi$
$978$	−20.0767	−0.641983
$979$	−38.8118	−1.24043
$980$	1.62147	0.0517959
$981$	−6.33427	−0.202238
$982$	44.3165	1.41420
$983$	24.5765	0.783868	0.391934	−	0.919993i	$-0.371806\pi$
$983$	24.5765	0.783868	0.391934	+	0.919993i	$0.371806\pi$
$984$	9.61407	0.306485
$985$	−11.5639	−0.368458
$986$	−41.3770	−1.31771
$987$	36.0921	1.14882
$988$	17.5821	0.559360
$989$	0	0
$990$	6.28595	0.199781
$991$	32.8497	1.04351	0.521753	−	0.853096i	$-0.325278\pi$
$991$	32.8497	1.04351	0.521753	+	0.853096i	$0.325278\pi$
$992$	−17.5587	−0.557488
$993$	29.9214	0.949528
$994$	−37.4221	−1.18696
$995$	−21.8556	−0.692871
$996$	−4.62547	−0.146564
$997$	29.1053	0.921774	0.460887	−	0.887459i	$-0.347531\pi$
$997$	29.1053	0.921774	0.460887	+	0.887459i	$0.347531\pi$
$998$	−11.7173	−0.370903
$999$	−4.28799	−0.135666

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bu.1.19		25
23.2	even	11		345.2.m.d.211.4	yes	50
23.12	even	11		345.2.m.d.121.4	✓	50
23.22	odd	2		7935.2.a.bt.1.19		25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.m.d.121.4	✓	50	23.12	even	11
345.2.m.d.211.4	yes	50	23.2	even	11
7935.2.a.bt.1.19		25	23.22	odd	2
7935.2.a.bu.1.19		25	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:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+1.59695 q^{2} -1.00000 q^{3} +0.550248 q^{4} +1.00000 q^{5} -1.59695 q^{6} +3.15385 q^{7} -2.31518 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.59695 q^{2} -1.00000 q^{3} +0.550248 q^{4} +1.00000 q^{5} -1.59695 q^{6} +3.15385 q^{7} -2.31518 q^{8} +1.00000 q^{9} +1.59695 q^{10} +3.93622 q^{11} -0.550248 q^{12} +5.83236 q^{13} +5.03655 q^{14} -1.00000 q^{15} -4.79772 q^{16} +3.95982 q^{17} +1.59695 q^{18} +5.47856 q^{19} +0.550248 q^{20} -3.15385 q^{21} +6.28595 q^{22} +2.31518 q^{24} +1.00000 q^{25} +9.31399 q^{26} -1.00000 q^{27} +1.73540 q^{28} -6.54323 q^{29} -1.59695 q^{30} +5.79234 q^{31} -3.03136 q^{32} -3.93622 q^{33} +6.32363 q^{34} +3.15385 q^{35} +0.550248 q^{36} +4.28799 q^{37} +8.74899 q^{38} -5.83236 q^{39} -2.31518 q^{40} +4.15262 q^{41} -5.03655 q^{42} +3.97479 q^{43} +2.16590 q^{44} +1.00000 q^{45} -11.4438 q^{47} +4.79772 q^{48} +2.94680 q^{49} +1.59695 q^{50} -3.95982 q^{51} +3.20924 q^{52} -4.29277 q^{53} -1.59695 q^{54} +3.93622 q^{55} -7.30174 q^{56} -5.47856 q^{57} -10.4492 q^{58} -13.8795 q^{59} -0.550248 q^{60} +2.38454 q^{61} +9.25007 q^{62} +3.15385 q^{63} +4.75452 q^{64} +5.83236 q^{65} -6.28595 q^{66} +10.2832 q^{67} +2.17888 q^{68} +5.03655 q^{70} -7.43010 q^{71} -2.31518 q^{72} +4.84630 q^{73} +6.84770 q^{74} -1.00000 q^{75} +3.01457 q^{76} +12.4143 q^{77} -9.31399 q^{78} -9.59938 q^{79} -4.79772 q^{80} +1.00000 q^{81} +6.63153 q^{82} +8.40615 q^{83} -1.73540 q^{84} +3.95982 q^{85} +6.34754 q^{86} +6.54323 q^{87} -9.11307 q^{88} -9.86016 q^{89} +1.59695 q^{90} +18.3944 q^{91} -5.79234 q^{93} -18.2752 q^{94} +5.47856 q^{95} +3.03136 q^{96} -15.3346 q^{97} +4.70588 q^{98} +3.93622 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9	\( 25 q + q^{2} - 25 q^{3} + 31 q^{4} + 25 q^{5} - q^{6} - 15 q^{7} + 3 q^{8} + 25 q^{9} + q^{10} + 15 q^{11} - 31 q^{12} + 24 q^{13} + 5 q^{14} - 25 q^{15} + 39 q^{16} - 6 q^{17} + q^{18} + 13 q^{19} + 31 q^{20} + 15 q^{21} - 21 q^{22} - 3 q^{24} + 25 q^{25} + 21 q^{26} - 25 q^{27} - 41 q^{28} + q^{29} - q^{30} + 18 q^{31} + 17 q^{32} - 15 q^{33} + 7 q^{34} - 15 q^{35} + 31 q^{36} - 8 q^{37} + 15 q^{38} - 24 q^{39} + 3 q^{40} + 36 q^{41} - 5 q^{42} - 36 q^{43} + 90 q^{44} + 25 q^{45} + 11 q^{47} - 39 q^{48} + 92 q^{49} + q^{50} + 6 q^{51} + 35 q^{52} + 6 q^{53} - q^{54} + 15 q^{55} + 15 q^{56} - 13 q^{57} + 42 q^{58} - 3 q^{59} - 31 q^{60} + 71 q^{61} - 7 q^{62} - 15 q^{63} + 47 q^{64} + 24 q^{65} + 21 q^{66} - 10 q^{67} - 23 q^{68} + 5 q^{70} - 18 q^{71} + 3 q^{72} + 83 q^{73} + 67 q^{74} - 25 q^{75} - 12 q^{76} + 27 q^{77} - 21 q^{78} + 33 q^{79} + 39 q^{80} + 25 q^{81} + 49 q^{82} - 2 q^{83} + 41 q^{84} - 6 q^{85} - 35 q^{86} - q^{87} - 33 q^{88} + 11 q^{89} + q^{90} + 28 q^{91} - 18 q^{93} + 80 q^{94} + 13 q^{95} - 17 q^{96} - 48 q^{97} + 4 q^{98} + 15 q^{99}+O(q^{100}) \) 25 * q + q^2 - 25 * q^3 + 31 * q^4 + 25 * q^5 - q^6 - 15 * q^7 + 3 * q^8 + 25 * q^9 + q^10 + 15 * q^11 - 31 * q^12 + 24 * q^13 + 5 * q^14 - 25 * q^15 + 39 * q^16 - 6 * q^17 + q^18 + 13 * q^19 + 31 * q^20 + 15 * q^21 - 21 * q^22 - 3 * q^24 + 25 * q^25 + 21 * q^26 - 25 * q^27 - 41 * q^28 + q^29 - q^30 + 18 * q^31 + 17 * q^32 - 15 * q^33 + 7 * q^34 - 15 * q^35 + 31 * q^36 - 8 * q^37 + 15 * q^38 - 24 * q^39 + 3 * q^40 + 36 * q^41 - 5 * q^42 - 36 * q^43 + 90 * q^44 + 25 * q^45 + 11 * q^47 - 39 * q^48 + 92 * q^49 + q^50 + 6 * q^51 + 35 * q^52 + 6 * q^53 - q^54 + 15 * q^55 + 15 * q^56 - 13 * q^57 + 42 * q^58 - 3 * q^59 - 31 * q^60 + 71 * q^61 - 7 * q^62 - 15 * q^63 + 47 * q^64 + 24 * q^65 + 21 * q^66 - 10 * q^67 - 23 * q^68 + 5 * q^70 - 18 * q^71 + 3 * q^72 + 83 * q^73 + 67 * q^74 - 25 * q^75 - 12 * q^76 + 27 * q^77 - 21 * q^78 + 33 * q^79 + 39 * q^80 + 25 * q^81 + 49 * q^82 - 2 * q^83 + 41 * q^84 - 6 * q^85 - 35 * q^86 - q^87 - 33 * q^88 + 11 * q^89 + q^90 + 28 * q^91 - 18 * q^93 + 80 * q^94 + 13 * q^95 - 17 * q^96 - 48 * q^97 + 4 * q^98 + 15 * q^99

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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