LMFDB - Embedded newform 3179.2.a.bi.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3179,2,Mod(1,3179)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3179, 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("3179.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3179 = 11 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3179.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:	$25.3844428026$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 187)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	3179.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.05589 q^{2} -0.418655 q^{3} -0.885097 q^{4} +1.19765 q^{5} -0.442053 q^{6} -3.31423 q^{7} -3.04634 q^{8} -2.82473 q^{9} +O(q^{10})$	\(q+1.05589 q^{2} -0.418655 q^{3} -0.885097 q^{4} +1.19765 q^{5} -0.442053 q^{6} -3.31423 q^{7} -3.04634 q^{8} -2.82473 q^{9} +1.26458 q^{10} -1.00000 q^{11} +0.370550 q^{12} +0.322834 q^{13} -3.49946 q^{14} -0.501400 q^{15} -1.44641 q^{16} -2.98260 q^{18} +3.31832 q^{19} -1.06003 q^{20} +1.38752 q^{21} -1.05589 q^{22} +8.91769 q^{23} +1.27537 q^{24} -3.56565 q^{25} +0.340877 q^{26} +2.43855 q^{27} +2.93342 q^{28} -10.4961 q^{29} -0.529423 q^{30} -4.92167 q^{31} +4.56544 q^{32} +0.418655 q^{33} -3.96927 q^{35} +2.50016 q^{36} +8.19938 q^{37} +3.50378 q^{38} -0.135156 q^{39} -3.64844 q^{40} +11.0398 q^{41} +1.46507 q^{42} -7.49008 q^{43} +0.885097 q^{44} -3.38302 q^{45} +9.41610 q^{46} +0.500901 q^{47} +0.605545 q^{48} +3.98412 q^{49} -3.76493 q^{50} -0.285739 q^{52} -3.37036 q^{53} +2.57484 q^{54} -1.19765 q^{55} +10.0963 q^{56} -1.38923 q^{57} -11.0827 q^{58} +4.59427 q^{59} +0.443788 q^{60} +11.3401 q^{61} -5.19674 q^{62} +9.36180 q^{63} +7.71342 q^{64} +0.386640 q^{65} +0.442053 q^{66} +3.61201 q^{67} -3.73343 q^{69} -4.19111 q^{70} +8.25890 q^{71} +8.60509 q^{72} +7.88324 q^{73} +8.65764 q^{74} +1.49277 q^{75} -2.93703 q^{76} +3.31423 q^{77} -0.142710 q^{78} +8.70022 q^{79} -1.73228 q^{80} +7.45327 q^{81} +11.6568 q^{82} +4.18587 q^{83} -1.22809 q^{84} -7.90870 q^{86} +4.39423 q^{87} +3.04634 q^{88} -13.1996 q^{89} -3.57210 q^{90} -1.06995 q^{91} -7.89302 q^{92} +2.06048 q^{93} +0.528896 q^{94} +3.97417 q^{95} -1.91134 q^{96} -4.82843 q^{97} +4.20679 q^{98} +2.82473 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) $ 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9	$ 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) $ 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9 + 24 * q^10 - 28 * q^11 + 24 * q^12 + 16 * q^14 - 16 * q^15 + 16 * q^16 + 32 * q^20 + 8 * q^23 - 8 * q^24 + 20 * q^25 - 24 * q^26 + 32 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 + 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 + 64 * q^37 - 8 * q^38 + 32 * q^39 + 72 * q^40 + 28 * q^41 + 24 * q^42 + 16 * q^43 - 24 * q^44 + 24 * q^45 - 36 * q^47 + 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 + 64 * q^54 - 16 * q^55 + 48 * q^56 + 32 * q^57 - 16 * q^58 - 28 * q^59 + 8 * q^60 + 104 * q^61 - 8 * q^62 + 28 * q^63 + 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 + 40 * q^71 + 40 * q^72 + 76 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 12 * q^77 - 24 * q^78 + 24 * q^79 + 8 * q^80 + 12 * q^81 + 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 + 16 * q^90 + 80 * q^91 - 56 * q^92 + 24 * q^97 - 24 * q^98 - 20 * 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 $

$2$	1.05589	0.746627	0.373313	−	0.927705i	$-0.378222\pi$
$2$	1.05589	0.746627	0.373313	+	0.927705i	$0.378222\pi$
$3$	−0.418655	−0.241710	−0.120855	−	0.992670i	$-0.538564\pi$
$3$	−0.418655	−0.241710	−0.120855	+	0.992670i	$0.538564\pi$
$4$	−0.885097	−0.442549
$5$	1.19765	0.535603	0.267802	−	0.963474i	$-0.413703\pi$
$5$	1.19765	0.535603	0.267802	+	0.963474i	$0.413703\pi$
$6$	−0.442053	−0.180467
$7$	−3.31423	−1.25266	−0.626331	−	0.779557i	$-0.715444\pi$
$7$	−3.31423	−1.25266	−0.626331	+	0.779557i	$0.715444\pi$
$8$	−3.04634	−1.07705
$9$	−2.82473	−0.941576
$10$	1.26458	0.399896
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	0.370550	0.106969
$13$	0.322834	0.0895380	0.0447690	−	0.998997i	$-0.485745\pi$
$13$	0.322834	0.0895380	0.0447690	+	0.998997i	$0.485745\pi$
$14$	−3.49946	−0.935270
$15$	−0.501400	−0.129461
$16$	−1.44641	−0.361602
$17$	0	0
$17$	0	0
$18$	−2.98260	−0.703006
$19$	3.31832	0.761274	0.380637	−	0.924724i	$-0.375705\pi$
$19$	3.31832	0.761274	0.380637	+	0.924724i	$0.375705\pi$
$20$	−1.06003	−0.237031
$21$	1.38752	0.302781
$22$	−1.05589	−0.225116
$23$	8.91769	1.85947	0.929733	−	0.368233i	$-0.120037\pi$
$23$	8.91769	1.85947	0.929733	+	0.368233i	$0.120037\pi$
$24$	1.27537	0.260333
$25$	−3.56565	−0.713129
$26$	0.340877	0.0668514
$27$	2.43855	0.469299
$28$	2.93342	0.554364
$29$	−10.4961	−1.94907	−0.974536	−	0.224231i	$-0.928013\pi$
$29$	−10.4961	−1.94907	−0.974536	+	0.224231i	$0.928013\pi$
$30$	−0.529423	−0.0966589
$31$	−4.92167	−0.883958	−0.441979	−	0.897025i	$-0.645723\pi$
$31$	−4.92167	−0.883958	−0.441979	+	0.897025i	$0.645723\pi$
$32$	4.56544	0.807064
$33$	0.418655	0.0728784
$34$	0	0
$35$	−3.96927	−0.670930
$36$	2.50016	0.416693
$37$	8.19938	1.34797	0.673985	−	0.738745i	$-0.264581\pi$
$37$	8.19938	1.34797	0.673985	+	0.738745i	$0.264581\pi$
$38$	3.50378	0.568388
$39$	−0.135156	−0.0216423
$40$	−3.64844	−0.576869
$41$	11.0398	1.72413	0.862065	−	0.506799i	$-0.169171\pi$
$41$	11.0398	1.72413	0.862065	+	0.506799i	$0.169171\pi$
$42$	1.46507	0.226065
$43$	−7.49008	−1.14223	−0.571113	−	0.820871i	$-0.693488\pi$
$43$	−7.49008	−1.14223	−0.571113	+	0.820871i	$0.693488\pi$
$44$	0.885097	0.133433
$45$	−3.38302	−0.504311
$46$	9.41610	1.38833
$47$	0.500901	0.0730640	0.0365320	−	0.999332i	$-0.488369\pi$
$47$	0.500901	0.0730640	0.0365320	+	0.999332i	$0.488369\pi$
$48$	0.605545	0.0874030
$49$	3.98412	0.569161
$50$	−3.76493	−0.532441
$51$	0	0
$52$	−0.285739	−0.0396249
$53$	−3.37036	−0.462955	−0.231477	−	0.972840i	$-0.574356\pi$
$53$	−3.37036	−0.462955	−0.231477	+	0.972840i	$0.574356\pi$
$54$	2.57484	0.350391
$55$	−1.19765	−0.161490
$56$	10.0963	1.34917
$57$	−1.38923	−0.184008
$58$	−11.0827	−1.45523
$59$	4.59427	0.598123	0.299062	−	0.954234i	$-0.403326\pi$
$59$	4.59427	0.598123	0.299062	+	0.954234i	$0.403326\pi$
$60$	0.443788	0.0572927
$61$	11.3401	1.45195	0.725976	−	0.687720i	$-0.241388\pi$
$61$	11.3401	1.45195	0.725976	+	0.687720i	$0.241388\pi$
$62$	−5.19674	−0.659987
$63$	9.36180	1.17948
$64$	7.71342	0.964177
$65$	0.386640	0.0479568
$66$	0.442053	0.0544130
$67$	3.61201	0.441278	0.220639	−	0.975356i	$-0.429186\pi$
$67$	3.61201	0.441278	0.220639	+	0.975356i	$0.429186\pi$
$68$	0	0
$69$	−3.73343	−0.449452
$70$	−4.19111	−0.500934
$71$	8.25890	0.980152	0.490076	−	0.871680i	$-0.336969\pi$
$71$	8.25890	0.980152	0.490076	+	0.871680i	$0.336969\pi$
$72$	8.60509	1.01412
$73$	7.88324	0.922664	0.461332	−	0.887228i	$-0.347372\pi$
$73$	7.88324	0.922664	0.461332	+	0.887228i	$0.347372\pi$
$74$	8.65764	1.00643
$75$	1.49277	0.172371
$76$	−2.93703	−0.336901
$77$	3.31423	0.377692
$78$	−0.142710	−0.0161587
$79$	8.70022	0.978851	0.489425	−	0.872045i	$-0.337207\pi$
$79$	8.70022	0.978851	0.489425	+	0.872045i	$0.337207\pi$
$80$	−1.73228	−0.193675
$81$	7.45327	0.828142
$82$	11.6568	1.28728
$83$	4.18587	0.459459	0.229729	−	0.973255i	$-0.426216\pi$
$83$	4.18587	0.459459	0.229729	+	0.973255i	$0.426216\pi$
$84$	−1.22809	−0.133995
$85$	0	0
$86$	−7.90870	−0.852817
$87$	4.39423	0.471111
$88$	3.04634	0.324741
$89$	−13.1996	−1.39916	−0.699580	−	0.714554i	$-0.746630\pi$
$89$	−13.1996	−1.39916	−0.699580	+	0.714554i	$0.746630\pi$
$90$	−3.57210	−0.376532
$91$	−1.06995	−0.112161
$92$	−7.89302	−0.822905
$93$	2.06048	0.213662
$94$	0.528896	0.0545515
$95$	3.97417	0.407741
$96$	−1.91134	−0.195076
$97$	−4.82843	−0.490253	−0.245126	−	0.969491i	$-0.578829\pi$
$97$	−4.82843	−0.490253	−0.245126	+	0.969491i	$0.578829\pi$
$98$	4.20679	0.424950
$99$	2.82473	0.283896
$100$	3.15594	0.315594
$101$	18.2550	1.81644	0.908221	−	0.418492i	$-0.137441\pi$
$101$	18.2550	1.81644	0.908221	+	0.418492i	$0.137441\pi$
$102$	0	0
$103$	−18.5779	−1.83053	−0.915265	−	0.402852i	$-0.868019\pi$
$103$	−18.5779	−1.83053	−0.915265	+	0.402852i	$0.868019\pi$
$104$	−0.983463	−0.0964365
$105$	1.66175	0.162171
$106$	−3.55873	−0.345654
$107$	3.15658	0.305158	0.152579	−	0.988291i	$-0.451242\pi$
$107$	3.15658	0.305158	0.152579	+	0.988291i	$0.451242\pi$
$108$	−2.15835	−0.207688
$109$	9.43198	0.903420	0.451710	−	0.892165i	$-0.350814\pi$
$109$	9.43198	0.903420	0.451710	+	0.892165i	$0.350814\pi$
$110$	−1.26458	−0.120573
$111$	−3.43271	−0.325818
$112$	4.79373	0.452965
$113$	8.35020	0.785521	0.392760	−	0.919641i	$-0.371520\pi$
$113$	8.35020	0.785521	0.392760	+	0.919641i	$0.371520\pi$
$114$	−1.46687	−0.137385
$115$	10.6802	0.995937
$116$	9.29005	0.862559
$117$	−0.911918	−0.0843068
$118$	4.85104	0.446575
$119$	0	0
$120$	1.52744	0.139435
$121$	1.00000	0.0909091
$122$	11.9739	1.08407
$123$	−4.62187	−0.416740
$124$	4.35616	0.391194
$125$	−10.2586	−0.917558
$126$	9.88503	0.880628
$127$	−6.88920	−0.611317	−0.305659	−	0.952141i	$-0.598877\pi$
$127$	−6.88920	−0.611317	−0.305659	+	0.952141i	$0.598877\pi$
$128$	−0.986366	−0.0871833
$129$	3.13576	0.276088
$130$	0.408250	0.0358059
$131$	−4.87090	−0.425573	−0.212786	−	0.977099i	$-0.568254\pi$
$131$	−4.87090	−0.425573	−0.212786	+	0.977099i	$0.568254\pi$
$132$	−0.370550	−0.0322523
$133$	−10.9977	−0.953619
$134$	3.81389	0.329470
$135$	2.92052	0.251358
$136$	0	0
$137$	12.3123	1.05191	0.525954	−	0.850513i	$-0.323708\pi$
$137$	12.3123	1.05191	0.525954	+	0.850513i	$0.323708\pi$
$138$	−3.94209	−0.335573
$139$	8.72929	0.740408	0.370204	−	0.928950i	$-0.379288\pi$
$139$	8.72929	0.740408	0.370204	+	0.928950i	$0.379288\pi$
$140$	3.51319	0.296919
$141$	−0.209705	−0.0176603
$142$	8.72049	0.731807
$143$	−0.322834	−0.0269967
$144$	4.08571	0.340476
$145$	−12.5706	−1.04393
$146$	8.32383	0.688885
$147$	−1.66797	−0.137572
$148$	−7.25725	−0.596542
$149$	−6.42254	−0.526155	−0.263078	−	0.964775i	$-0.584738\pi$
$149$	−6.42254	−0.526155	−0.263078	+	0.964775i	$0.584738\pi$
$150$	1.57620	0.128697
$151$	−15.9346	−1.29674	−0.648370	−	0.761325i	$-0.724549\pi$
$151$	−15.9346	−1.29674	−0.648370	+	0.761325i	$0.724549\pi$
$152$	−10.1087	−0.819927
$153$	0	0
$154$	3.49946	0.281995
$155$	−5.89442	−0.473451
$156$	0.119626	0.00957775
$157$	19.7763	1.57832	0.789159	−	0.614190i	$-0.210517\pi$
$157$	19.7763	1.57832	0.789159	+	0.614190i	$0.210517\pi$
$158$	9.18647	0.730836
$159$	1.41102	0.111901
$160$	5.46778	0.432266
$161$	−29.5553	−2.32928
$162$	7.86983	0.618313
$163$	3.27472	0.256496	0.128248	−	0.991742i	$-0.459065\pi$
$163$	3.27472	0.256496	0.128248	+	0.991742i	$0.459065\pi$
$164$	−9.77131	−0.763011
$165$	0.501400	0.0390339
$166$	4.41981	0.343044
$167$	−2.41144	−0.186603	−0.0933016	−	0.995638i	$-0.529742\pi$
$167$	−2.41144	−0.186603	−0.0933016	+	0.995638i	$0.529742\pi$
$168$	−4.22686	−0.326109
$169$	−12.8958	−0.991983
$170$	0	0
$171$	−9.37335	−0.716798
$172$	6.62945	0.505491
$173$	−5.85254	−0.444961	−0.222480	−	0.974937i	$-0.571415\pi$
$173$	−5.85254	−0.444961	−0.222480	+	0.974937i	$0.571415\pi$
$174$	4.63982	0.351744
$175$	11.8174	0.893309
$176$	1.44641	0.109027
$177$	−1.92341	−0.144573
$178$	−13.9374	−1.04465
$179$	−0.341973	−0.0255603	−0.0127801	−	0.999918i	$-0.504068\pi$
$179$	−0.341973	−0.0255603	−0.0127801	+	0.999918i	$0.504068\pi$
$180$	2.99430	0.223182
$181$	−14.8580	−1.10438	−0.552191	−	0.833717i	$-0.686208\pi$
$181$	−14.8580	−1.10438	−0.552191	+	0.833717i	$0.686208\pi$
$182$	−1.12974	−0.0837422
$183$	−4.74759	−0.350952
$184$	−27.1664	−2.00273
$185$	9.81995	0.721977
$186$	2.17564	0.159526
$187$	0	0
$188$	−0.443346	−0.0323344
$189$	−8.08192	−0.587873
$190$	4.19628	0.304430
$191$	13.9561	1.00983	0.504913	−	0.863170i	$-0.331524\pi$
$191$	13.9561	1.00983	0.504913	+	0.863170i	$0.331524\pi$
$192$	−3.22926	−0.233052
$193$	13.5452	0.975005	0.487503	−	0.873122i	$-0.337908\pi$
$193$	13.5452	0.975005	0.487503	+	0.873122i	$0.337908\pi$
$194$	−5.09829	−0.366036
$195$	−0.161869	−0.0115917
$196$	−3.52634	−0.251881
$197$	6.73224	0.479653	0.239826	−	0.970816i	$-0.422910\pi$
$197$	6.73224	0.479653	0.239826	+	0.970816i	$0.422910\pi$
$198$	2.98260	0.211964
$199$	4.34235	0.307821	0.153911	−	0.988085i	$-0.450813\pi$
$199$	4.34235	0.307821	0.153911	+	0.988085i	$0.450813\pi$
$200$	10.8622	0.768072
$201$	−1.51219	−0.106661
$202$	19.2753	1.35620
$203$	34.7864	2.44153
$204$	0	0
$205$	13.2218	0.923449
$206$	−19.6162	−1.36672
$207$	−25.1901	−1.75083
$208$	−0.466949	−0.0323771
$209$	−3.31832	−0.229533
$210$	1.75463	0.121081
$211$	8.03042	0.552837	0.276419	−	0.961037i	$-0.410852\pi$
$211$	8.03042	0.552837	0.276419	+	0.961037i	$0.410852\pi$
$212$	2.98310	0.204880
$213$	−3.45763	−0.236913
$214$	3.33300	0.227839
$215$	−8.97046	−0.611780
$216$	−7.42866	−0.505456
$217$	16.3116	1.10730
$218$	9.95913	0.674517
$219$	−3.30036	−0.223017
$220$	1.06003	0.0714674
$221$	0	0
$222$	−3.62456	−0.243265
$223$	9.51078	0.636889	0.318445	−	0.947941i	$-0.396840\pi$
$223$	9.51078	0.636889	0.318445	+	0.947941i	$0.396840\pi$
$224$	−15.1309	−1.01098
$225$	10.0720	0.671465
$226$	8.81689	0.586491
$227$	−2.99260	−0.198626	−0.0993130	−	0.995056i	$-0.531664\pi$
$227$	−2.99260	−0.198626	−0.0993130	+	0.995056i	$0.531664\pi$
$228$	1.22960	0.0814325
$229$	−11.3482	−0.749912	−0.374956	−	0.927043i	$-0.622342\pi$
$229$	−11.3482	−0.749912	−0.374956	+	0.927043i	$0.622342\pi$
$230$	11.2771	0.743593
$231$	−1.38752	−0.0912920
$232$	31.9747	2.09924
$233$	−5.81951	−0.381249	−0.190624	−	0.981663i	$-0.561051\pi$
$233$	−5.81951	−0.381249	−0.190624	+	0.981663i	$0.561051\pi$
$234$	−0.962884	−0.0629457
$235$	0.599902	0.0391333
$236$	−4.06638	−0.264699
$237$	−3.64239	−0.236598
$238$	0	0
$239$	5.68959	0.368029	0.184015	−	0.982924i	$-0.441091\pi$
$239$	5.68959	0.368029	0.184015	+	0.982924i	$0.441091\pi$
$240$	0.725229	0.0468133
$241$	5.17597	0.333414	0.166707	−	0.986006i	$-0.446687\pi$
$241$	5.17597	0.333414	0.166707	+	0.986006i	$0.446687\pi$
$242$	1.05589	0.0678751
$243$	−10.4360	−0.669470
$244$	−10.0371	−0.642559
$245$	4.77157	0.304844
$246$	−4.88018	−0.311149
$247$	1.07127	0.0681630
$248$	14.9931	0.952063
$249$	−1.75243	−0.111056
$250$	−10.8320	−0.685073
$251$	−15.0997	−0.953082	−0.476541	−	0.879152i	$-0.658110\pi$
$251$	−15.0997	−0.953082	−0.476541	+	0.879152i	$0.658110\pi$
$252$	−8.28611	−0.521976
$253$	−8.91769	−0.560650
$254$	−7.27423	−0.456426
$255$	0	0
$256$	−16.4683	−1.02927
$257$	6.24221	0.389379	0.194689	−	0.980865i	$-0.437630\pi$
$257$	6.24221	0.389379	0.194689	+	0.980865i	$0.437630\pi$
$258$	3.31101	0.206135
$259$	−27.1746	−1.68855
$260$	−0.342214	−0.0212232
$261$	29.6486	1.83520
$262$	−5.14313	−0.317744
$263$	14.7194	0.907634	0.453817	−	0.891095i	$-0.350062\pi$
$263$	14.7194	0.907634	0.453817	+	0.891095i	$0.350062\pi$
$264$	−1.27537	−0.0784934
$265$	−4.03650	−0.247960
$266$	−11.6123	−0.711997
$267$	5.52609	0.338191
$268$	−3.19698	−0.195287
$269$	−11.5718	−0.705544	−0.352772	−	0.935709i	$-0.614761\pi$
$269$	−11.5718	−0.705544	−0.352772	+	0.935709i	$0.614761\pi$
$270$	3.08374	0.187671
$271$	−17.1350	−1.04088	−0.520439	−	0.853899i	$-0.674232\pi$
$271$	−17.1350	−1.04088	−0.520439	+	0.853899i	$0.674232\pi$
$272$	0	0
$273$	0.447938	0.0271104
$274$	13.0004	0.785382
$275$	3.56565	0.215017
$276$	3.30445	0.198905
$277$	−3.58237	−0.215244	−0.107622	−	0.994192i	$-0.534324\pi$
$277$	−3.58237	−0.215244	−0.107622	+	0.994192i	$0.534324\pi$
$278$	9.21716	0.552809
$279$	13.9024	0.832314
$280$	12.0918	0.722622
$281$	13.0595	0.779064	0.389532	−	0.921013i	$-0.372637\pi$
$281$	13.0595	0.779064	0.389532	+	0.921013i	$0.372637\pi$
$282$	−0.221425	−0.0131857
$283$	−8.12096	−0.482741	−0.241370	−	0.970433i	$-0.577597\pi$
$283$	−8.12096	−0.482741	−0.241370	+	0.970433i	$0.577597\pi$
$284$	−7.30993	−0.433765
$285$	−1.66380	−0.0985553
$286$	−0.340877	−0.0201565
$287$	−36.5885	−2.15975
$288$	−12.8961	−0.759912
$289$	0	0
$290$	−13.2731	−0.779425
$291$	2.02144	0.118499
$292$	−6.97744	−0.408324
$293$	21.9369	1.28157	0.640785	−	0.767721i	$-0.278609\pi$
$293$	21.9369	1.28157	0.640785	+	0.767721i	$0.278609\pi$
$294$	−1.76119	−0.102715
$295$	5.50231	0.320357
$296$	−24.9781	−1.45182
$297$	−2.43855	−0.141499
$298$	−6.78150	−0.392842
$299$	2.87893	0.166493
$300$	−1.32125	−0.0762824
$301$	24.8239	1.43082
$302$	−16.8252	−0.968181
$303$	−7.64254	−0.439053
$304$	−4.79964	−0.275278
$305$	13.5814	0.777670
$306$	0	0
$307$	3.17581	0.181253	0.0906266	−	0.995885i	$-0.471113\pi$
$307$	3.17581	0.181253	0.0906266	+	0.995885i	$0.471113\pi$
$308$	−2.93342	−0.167147
$309$	7.77770	0.442458
$310$	−6.22385	−0.353491
$311$	4.83349	0.274082	0.137041	−	0.990565i	$-0.456241\pi$
$311$	4.83349	0.274082	0.137041	+	0.990565i	$0.456241\pi$
$312$	0.411731	0.0233097
$313$	−11.4423	−0.646755	−0.323378	−	0.946270i	$-0.604818\pi$
$313$	−11.4423	−0.646755	−0.323378	+	0.946270i	$0.604818\pi$
$314$	20.8815	1.17841
$315$	11.2121	0.631731
$316$	−7.70054	−0.433189
$317$	7.08543	0.397957	0.198979	−	0.980004i	$-0.436238\pi$
$317$	7.08543	0.397957	0.198979	+	0.980004i	$0.436238\pi$
$318$	1.48988	0.0835482
$319$	10.4961	0.587667
$320$	9.23794	0.516416
$321$	−1.32152	−0.0737599
$322$	−31.2071	−1.73910
$323$	0	0
$324$	−6.59687	−0.366493
$325$	−1.15111	−0.0638521
$326$	3.45774	0.191507
$327$	−3.94874	−0.218366
$328$	−33.6311	−1.85696
$329$	−1.66010	−0.0915244
$330$	0.529423	0.0291438
$331$	−28.3500	−1.55826	−0.779128	−	0.626865i	$-0.784338\pi$
$331$	−28.3500	−1.55826	−0.779128	+	0.626865i	$0.784338\pi$
$332$	−3.70490	−0.203333
$333$	−23.1610	−1.26922
$334$	−2.54622	−0.139323
$335$	4.32591	0.236350
$336$	−2.00692	−0.109486
$337$	21.7250	1.18343	0.591717	−	0.806146i	$-0.298450\pi$
$337$	21.7250	1.18343	0.591717	+	0.806146i	$0.298450\pi$
$338$	−13.6165	−0.740641
$339$	−3.49585	−0.189868
$340$	0	0
$341$	4.92167	0.266523
$342$	−9.89722	−0.535180
$343$	9.99531	0.539696
$344$	22.8174	1.23023
$345$	−4.47133	−0.240728
$346$	−6.17964	−0.332219
$347$	12.2844	0.659459	0.329730	−	0.944075i	$-0.393042\pi$
$347$	12.2844	0.659459	0.329730	+	0.944075i	$0.393042\pi$
$348$	−3.88932	−0.208490
$349$	10.4949	0.561781	0.280890	−	0.959740i	$-0.409370\pi$
$349$	10.4949	0.561781	0.280890	+	0.959740i	$0.409370\pi$
$350$	12.4778	0.666968
$351$	0.787246	0.0420201
$352$	−4.56544	−0.243339
$353$	18.0064	0.958382	0.479191	−	0.877711i	$-0.340930\pi$
$353$	18.0064	0.958382	0.479191	+	0.877711i	$0.340930\pi$
$354$	−2.03091	−0.107942
$355$	9.89124	0.524972
$356$	11.6830	0.619196
$357$	0	0
$358$	−0.361086	−0.0190840
$359$	−6.90470	−0.364416	−0.182208	−	0.983260i	$-0.558324\pi$
$359$	−6.90470	−0.364416	−0.182208	+	0.983260i	$0.558324\pi$
$360$	10.3059	0.543166
$361$	−7.98876	−0.420461
$362$	−15.6884	−0.824562
$363$	−0.418655	−0.0219737
$364$	0.947006	0.0496366
$365$	9.44133	0.494182
$366$	−5.01293	−0.262030
$367$	−17.8672	−0.932661	−0.466331	−	0.884611i	$-0.654424\pi$
$367$	−17.8672	−0.932661	−0.466331	+	0.884611i	$0.654424\pi$
$368$	−12.8986	−0.672387
$369$	−31.1845	−1.62340
$370$	10.3688	0.539047
$371$	11.1702	0.579926
$372$	−1.82373	−0.0945558
$373$	18.7990	0.973376	0.486688	−	0.873576i	$-0.338205\pi$
$373$	18.7990	0.973376	0.486688	+	0.873576i	$0.338205\pi$
$374$	0	0
$375$	4.29481	0.221783
$376$	−1.52592	−0.0786932
$377$	−3.38849	−0.174516
$378$	−8.53361	−0.438922
$379$	8.31378	0.427050	0.213525	−	0.976938i	$-0.431505\pi$
$379$	8.31378	0.427050	0.213525	+	0.976938i	$0.431505\pi$
$380$	−3.51753	−0.180445
$381$	2.88420	0.147762
$382$	14.7361	0.753964
$383$	25.9928	1.32817	0.664085	−	0.747657i	$-0.268821\pi$
$383$	25.9928	1.32817	0.664085	+	0.747657i	$0.268821\pi$
$384$	0.412947	0.0210731
$385$	3.96927	0.202293
$386$	14.3022	0.727965
$387$	21.1574	1.07549
$388$	4.27363	0.216961
$389$	−11.2323	−0.569499	−0.284750	−	0.958602i	$-0.591910\pi$
$389$	−11.2323	−0.569499	−0.284750	+	0.958602i	$0.591910\pi$
$390$	−0.170916	−0.00865465
$391$	0	0
$392$	−12.1370	−0.613012
$393$	2.03923	0.102865
$394$	7.10851	0.358121
$395$	10.4198	0.524276
$396$	−2.50016	−0.125638
$397$	−6.20235	−0.311287	−0.155644	−	0.987813i	$-0.549745\pi$
$397$	−6.20235	−0.311287	−0.155644	+	0.987813i	$0.549745\pi$
$398$	4.58504	0.229828
$399$	4.60423	0.230500
$400$	5.15738	0.257869
$401$	−22.1800	−1.10762	−0.553808	−	0.832644i	$-0.686826\pi$
$401$	−22.1800	−1.10762	−0.553808	+	0.832644i	$0.686826\pi$
$402$	−1.59670	−0.0796363
$403$	−1.58888	−0.0791478
$404$	−16.1575	−0.803864
$405$	8.92638	0.443555
$406$	36.7306	1.82291
$407$	−8.19938	−0.406428
$408$	0	0
$409$	30.4544	1.50587	0.752936	−	0.658094i	$-0.228637\pi$
$409$	30.4544	1.50587	0.752936	+	0.658094i	$0.228637\pi$
$410$	13.9607	0.689472
$411$	−5.15459	−0.254257
$412$	16.4432	0.810099
$413$	−15.2265	−0.749246
$414$	−26.5979	−1.30722
$415$	5.01319	0.246088
$416$	1.47388	0.0722628
$417$	−3.65456	−0.178964
$418$	−3.50378	−0.171375
$419$	23.7681	1.16115	0.580573	−	0.814208i	$-0.302829\pi$
$419$	23.7681	1.16115	0.580573	+	0.814208i	$0.302829\pi$
$420$	−1.47081	−0.0717684
$421$	4.48385	0.218529	0.109265	−	0.994013i	$-0.465150\pi$
$421$	4.48385	0.218529	0.109265	+	0.994013i	$0.465150\pi$
$422$	8.47924	0.412763
$423$	−1.41491	−0.0687953
$424$	10.2673	0.498623
$425$	0	0
$426$	−3.65087	−0.176885
$427$	−37.5837	−1.81880
$428$	−2.79388	−0.135047
$429$	0.135156	0.00652539
$430$	−9.47182	−0.456772
$431$	23.7677	1.14485	0.572425	−	0.819957i	$-0.306003\pi$
$431$	23.7677	1.14485	0.572425	+	0.819957i	$0.306003\pi$
$432$	−3.52714	−0.169699
$433$	14.7818	0.710368	0.355184	−	0.934796i	$-0.384418\pi$
$433$	14.7818	0.710368	0.355184	+	0.934796i	$0.384418\pi$
$434$	17.2232	0.826740
$435$	5.26273	0.252329
$436$	−8.34822	−0.399807
$437$	29.5917	1.41556
$438$	−3.48481	−0.166511
$439$	−7.75531	−0.370141	−0.185070	−	0.982725i	$-0.559251\pi$
$439$	−7.75531	−0.370141	−0.185070	+	0.982725i	$0.559251\pi$
$440$	3.64844	0.173933
$441$	−11.2541	−0.535908
$442$	0	0
$443$	33.6384	1.59821	0.799105	−	0.601191i	$-0.205307\pi$
$443$	33.6384	1.59821	0.799105	+	0.601191i	$0.205307\pi$
$444$	3.03828	0.144190
$445$	−15.8085	−0.749395
$446$	10.0423	0.475518
$447$	2.68883	0.127177
$448$	−25.5640	−1.20779
$449$	1.01869	0.0480749	0.0240374	−	0.999711i	$-0.492348\pi$
$449$	1.01869	0.0480749	0.0240374	+	0.999711i	$0.492348\pi$
$450$	10.6349	0.501334
$451$	−11.0398	−0.519844
$452$	−7.39074	−0.347631
$453$	6.67110	0.313436
$454$	−3.15986	−0.148299
$455$	−1.28142	−0.0600737
$456$	4.23207	0.198185
$457$	16.6066	0.776825	0.388413	−	0.921486i	$-0.373024\pi$
$457$	16.6066	0.776825	0.388413	+	0.921486i	$0.373024\pi$
$458$	−11.9825	−0.559905
$459$	0	0
$460$	−9.45304	−0.440750
$461$	9.02233	0.420212	0.210106	−	0.977679i	$-0.432619\pi$
$461$	9.02233	0.420212	0.210106	+	0.977679i	$0.432619\pi$
$462$	−1.46507	−0.0681610
$463$	−32.4882	−1.50986	−0.754928	−	0.655808i	$-0.772328\pi$
$463$	−32.4882	−1.50986	−0.754928	+	0.655808i	$0.772328\pi$
$464$	15.1816	0.704788
$465$	2.46772	0.114438
$466$	−6.14476	−0.284650
$467$	4.31254	0.199560	0.0997802	−	0.995010i	$-0.468186\pi$
$467$	4.31254	0.199560	0.0997802	+	0.995010i	$0.468186\pi$
$468$	0.807136	0.0373099
$469$	−11.9710	−0.552772
$470$	0.633430	0.0292180
$471$	−8.27942	−0.381496
$472$	−13.9957	−0.644206
$473$	7.49008	0.344394
$474$	−3.84596	−0.176651
$475$	−11.8319	−0.542887
$476$	0	0
$477$	9.52035	0.435907
$478$	6.00758	0.274780
$479$	−34.7137	−1.58611	−0.793055	−	0.609151i	$-0.791511\pi$
$479$	−34.7137	−1.58611	−0.793055	+	0.609151i	$0.791511\pi$
$480$	−2.28911	−0.104483
$481$	2.64704	0.120694
$482$	5.46526	0.248936
$483$	12.3735	0.563012
$484$	−0.885097	−0.0402317
$485$	−5.78275	−0.262581
$486$	−11.0193	−0.499844
$487$	−13.3358	−0.604305	−0.302152	−	0.953260i	$-0.597705\pi$
$487$	−13.3358	−0.604305	−0.302152	+	0.953260i	$0.597705\pi$
$488$	−34.5459	−1.56382
$489$	−1.37098	−0.0619977
$490$	5.03825	0.227605
$491$	−6.76653	−0.305369	−0.152685	−	0.988275i	$-0.548792\pi$
$491$	−6.76653	−0.305369	−0.152685	+	0.988275i	$0.548792\pi$
$492$	4.09080	0.184428
$493$	0	0
$494$	1.13114	0.0508923
$495$	3.38302	0.152056
$496$	7.11874	0.319641
$497$	−27.3719	−1.22780
$498$	−1.85038	−0.0829173
$499$	−26.1867	−1.17228	−0.586138	−	0.810211i	$-0.699352\pi$
$499$	−26.1867	−1.17228	−0.586138	+	0.810211i	$0.699352\pi$
$500$	9.07987	0.406064
$501$	1.00956	0.0451039
$502$	−15.9436	−0.711597
$503$	−31.4686	−1.40312	−0.701558	−	0.712612i	$-0.747512\pi$
$503$	−31.4686	−1.40312	−0.701558	+	0.712612i	$0.747512\pi$
$504$	−28.5193	−1.27035
$505$	21.8630	0.972892
$506$	−9.41610	−0.418596
$507$	5.39888	0.239773
$508$	6.09761	0.270538
$509$	26.5254	1.17572	0.587859	−	0.808964i	$-0.299971\pi$
$509$	26.5254	1.17572	0.587859	+	0.808964i	$0.299971\pi$
$510$	0	0
$511$	−26.1269	−1.15579
$512$	−15.4160	−0.681297
$513$	8.09188	0.357265
$514$	6.59109	0.290720
$515$	−22.2497	−0.980438
$516$	−2.77545	−0.122182
$517$	−0.500901	−0.0220296
$518$	−28.6934	−1.26072
$519$	2.45019	0.107552
$520$	−1.17784	−0.0516517
$521$	11.5828	0.507450	0.253725	−	0.967276i	$-0.418344\pi$
$521$	11.5828	0.507450	0.253725	+	0.967276i	$0.418344\pi$
$522$	31.3056	1.37021
$523$	−29.7080	−1.29904	−0.649520	−	0.760344i	$-0.725030\pi$
$523$	−29.7080	−1.29904	−0.649520	+	0.760344i	$0.725030\pi$
$524$	4.31122	0.188337
$525$	−4.94740	−0.215922
$526$	15.5420	0.677664
$527$	0	0
$528$	−0.605545	−0.0263530
$529$	56.5252	2.45762
$530$	−4.26210	−0.185134
$531$	−12.9776	−0.563178
$532$	9.73401	0.422023
$533$	3.56402	0.154375
$534$	5.83494	0.252503
$535$	3.78047	0.163444
$536$	−11.0034	−0.475276
$537$	0.143169	0.00617819
$538$	−12.2185	−0.526778
$539$	−3.98412	−0.171608
$540$	−2.58494	−0.111238
$541$	5.95212	0.255902	0.127951	−	0.991781i	$-0.459160\pi$
$541$	5.95212	0.255902	0.127951	+	0.991781i	$0.459160\pi$
$542$	−18.0927	−0.777148
$543$	6.22035	0.266941
$544$	0	0
$545$	11.2962	0.483875
$546$	0.472973	0.0202414
$547$	−18.0101	−0.770054	−0.385027	−	0.922905i	$-0.625808\pi$
$547$	−18.0101	−0.770054	−0.385027	+	0.922905i	$0.625808\pi$
$548$	−10.8976	−0.465520
$549$	−32.0327	−1.36712
$550$	3.76493	0.160537
$551$	−34.8293	−1.48378
$552$	11.3733	0.484081
$553$	−28.8345	−1.22617
$554$	−3.78259	−0.160707
$555$	−4.11117	−0.174509
$556$	−7.72627	−0.327667
$557$	4.05936	0.172001	0.0860003	−	0.996295i	$-0.472591\pi$
$557$	4.05936	0.172001	0.0860003	+	0.996295i	$0.472591\pi$
$558$	14.6794	0.621428
$559$	−2.41805	−0.102273
$560$	5.74119	0.242609
$561$	0	0
$562$	13.7894	0.581670
$563$	−19.0419	−0.802520	−0.401260	−	0.915964i	$-0.631428\pi$
$563$	−19.0419	−0.802520	−0.401260	+	0.915964i	$0.631428\pi$
$564$	0.185609	0.00781555
$565$	10.0006	0.420727
$566$	−8.57483	−0.360427
$567$	−24.7019	−1.03738
$568$	−25.1595	−1.05567
$569$	−3.47073	−0.145501	−0.0727503	−	0.997350i	$-0.523178\pi$
$569$	−3.47073	−0.145501	−0.0727503	+	0.997350i	$0.523178\pi$
$570$	−1.75679	−0.0735840
$571$	24.1149	1.00918	0.504589	−	0.863360i	$-0.331644\pi$
$571$	24.1149	1.00918	0.504589	+	0.863360i	$0.331644\pi$
$572$	0.285739	0.0119474
$573$	−5.84278	−0.244086
$574$	−38.6334	−1.61253
$575$	−31.7973	−1.32604
$576$	−21.7883	−0.907846
$577$	−3.31891	−0.138168	−0.0690840	−	0.997611i	$-0.522008\pi$
$577$	−3.31891	−0.138168	−0.0690840	+	0.997611i	$0.522008\pi$
$578$	0	0
$579$	−5.67076	−0.235669
$580$	11.1262	0.461990
$581$	−13.8729	−0.575546
$582$	2.13442	0.0884747
$583$	3.37036	0.139586
$584$	−24.0151	−0.993751
$585$	−1.09215	−0.0451550
$586$	23.1630	0.956854
$587$	−20.7528	−0.856559	−0.428280	−	0.903646i	$-0.640880\pi$
$587$	−20.7528	−0.856559	−0.428280	+	0.903646i	$0.640880\pi$
$588$	1.47632	0.0608823
$589$	−16.3317	−0.672935
$590$	5.80983	0.239187
$591$	−2.81849	−0.115937
$592$	−11.8596	−0.487429
$593$	−19.9195	−0.817996	−0.408998	−	0.912535i	$-0.634122\pi$
$593$	−19.9195	−0.817996	−0.408998	+	0.912535i	$0.634122\pi$
$594$	−2.57484	−0.105647
$595$	0	0
$596$	5.68458	0.232849
$597$	−1.81795	−0.0744036
$598$	3.03983	0.124308
$599$	10.9441	0.447162	0.223581	−	0.974685i	$-0.428225\pi$
$599$	10.9441	0.447162	0.223581	+	0.974685i	$0.428225\pi$
$600$	−4.54750	−0.185651
$601$	10.9956	0.448520	0.224260	−	0.974529i	$-0.428003\pi$
$601$	10.9956	0.448520	0.224260	+	0.974529i	$0.428003\pi$
$602$	26.2113	1.06829
$603$	−10.2030	−0.415497
$604$	14.1037	0.573871
$605$	1.19765	0.0486912
$606$	−8.06968	−0.327808
$607$	14.5116	0.589009	0.294504	−	0.955650i	$-0.404845\pi$
$607$	14.5116	0.589009	0.294504	+	0.955650i	$0.404845\pi$
$608$	15.1496	0.614397
$609$	−14.5635	−0.590142
$610$	14.3405	0.580629
$611$	0.161708	0.00654200
$612$	0	0
$613$	6.79186	0.274321	0.137160	−	0.990549i	$-0.456202\pi$
$613$	6.79186	0.274321	0.137160	+	0.990549i	$0.456202\pi$
$614$	3.35331	0.135328
$615$	−5.53536	−0.223207
$616$	−10.0963	−0.406791
$617$	30.5490	1.22986	0.614928	−	0.788583i	$-0.289185\pi$
$617$	30.5490	1.22986	0.614928	+	0.788583i	$0.289185\pi$
$618$	8.21240	0.330351
$619$	−42.9928	−1.72803	−0.864014	−	0.503468i	$-0.832057\pi$
$619$	−42.9928	−1.72803	−0.864014	+	0.503468i	$0.832057\pi$
$620$	5.21713	0.209525
$621$	21.7462	0.872646
$622$	5.10363	0.204637
$623$	43.7467	1.75267
$624$	0.195491	0.00782588
$625$	5.54205	0.221682
$626$	−12.0818	−0.482885
$627$	1.38923	0.0554805
$628$	−17.5039	−0.698482
$629$	0	0
$630$	11.8388	0.471667
$631$	−8.83707	−0.351798	−0.175899	−	0.984408i	$-0.556283\pi$
$631$	−8.83707	−0.351798	−0.175899	+	0.984408i	$0.556283\pi$
$632$	−26.5038	−1.05427
$633$	−3.36197	−0.133626
$634$	7.48143	0.297126
$635$	−8.25082	−0.327424
$636$	−1.24889	−0.0495216
$637$	1.28621	0.0509615
$638$	11.0827	0.438768
$639$	−23.3292	−0.922887
$640$	−1.18132	−0.0466957
$641$	12.8762	0.508577	0.254289	−	0.967128i	$-0.418159\pi$
$641$	12.8762	0.508577	0.254289	+	0.967128i	$0.418159\pi$
$642$	−1.39538	−0.0550711
$643$	−41.9366	−1.65382	−0.826910	−	0.562335i	$-0.809903\pi$
$643$	−41.9366	−1.65382	−0.826910	+	0.562335i	$0.809903\pi$
$644$	26.1593	1.03082
$645$	3.75553	0.147874
$646$	0	0
$647$	37.1096	1.45893	0.729465	−	0.684018i	$-0.239769\pi$
$647$	37.1096	1.45893	0.729465	+	0.684018i	$0.239769\pi$
$648$	−22.7052	−0.891946
$649$	−4.59427	−0.180341
$650$	−1.21545	−0.0476737
$651$	−6.82891	−0.267646
$652$	−2.89845	−0.113512
$653$	−4.47444	−0.175098	−0.0875491	−	0.996160i	$-0.527903\pi$
$653$	−4.47444	−0.175098	−0.0875491	+	0.996160i	$0.527903\pi$
$654$	−4.16944	−0.163038
$655$	−5.83361	−0.227938
$656$	−15.9681	−0.623448
$657$	−22.2680	−0.868758
$658$	−1.75288	−0.0683346
$659$	−20.8419	−0.811887	−0.405943	−	0.913898i	$-0.633057\pi$
$659$	−20.8419	−0.811887	−0.405943	+	0.913898i	$0.633057\pi$
$660$	−0.443788	−0.0172744
$661$	9.42390	0.366547	0.183274	−	0.983062i	$-0.441331\pi$
$661$	9.42390	0.366547	0.183274	+	0.983062i	$0.441331\pi$
$662$	−29.9345	−1.16344
$663$	0	0
$664$	−12.7516	−0.494858
$665$	−13.1713	−0.510762
$666$	−24.4555	−0.947630
$667$	−93.6007	−3.62423
$668$	2.13436	0.0825810
$669$	−3.98173	−0.153943
$670$	4.56769	0.176465
$671$	−11.3401	−0.437780
$672$	6.33463	0.244364
$673$	4.36540	0.168274	0.0841368	−	0.996454i	$-0.473187\pi$
$673$	4.36540	0.168274	0.0841368	+	0.996454i	$0.473187\pi$
$674$	22.9391	0.883583
$675$	−8.69500	−0.334671
$676$	11.4140	0.439001
$677$	41.2517	1.58543	0.792715	−	0.609593i	$-0.208667\pi$
$677$	41.2517	1.58543	0.792715	+	0.609593i	$0.208667\pi$
$678$	−3.69123	−0.141761
$679$	16.0025	0.614121
$680$	0	0
$681$	1.25287	0.0480100
$682$	5.19674	0.198993
$683$	24.3752	0.932692	0.466346	−	0.884602i	$-0.345570\pi$
$683$	24.3752	0.932692	0.466346	+	0.884602i	$0.345570\pi$
$684$	8.29633	0.317218
$685$	14.7457	0.563405
$686$	10.5539	0.402951
$687$	4.75099	0.181262
$688$	10.8337	0.413031
$689$	−1.08807	−0.0414520
$690$	−4.72123	−0.179734
$691$	23.3621	0.888738	0.444369	−	0.895844i	$-0.353428\pi$
$691$	23.3621	0.888738	0.444369	+	0.895844i	$0.353428\pi$
$692$	5.18007	0.196917
$693$	−9.36180	−0.355625
$694$	12.9709	0.492370
$695$	10.4546	0.396565
$696$	−13.3863	−0.507408
$697$	0	0
$698$	11.0815	0.419441
$699$	2.43636	0.0921518
$700$	−10.4595	−0.395333
$701$	33.2360	1.25531	0.627654	−	0.778492i	$-0.284015\pi$
$701$	33.2360	1.25531	0.627654	+	0.778492i	$0.284015\pi$
$702$	0.831245	0.0313733
$703$	27.2082	1.02617
$704$	−7.71342	−0.290710
$705$	−0.251152	−0.00945893
$706$	19.0127	0.715553
$707$	−60.5013	−2.27539
$708$	1.70241	0.0639804
$709$	6.03926	0.226809	0.113405	−	0.993549i	$-0.463824\pi$
$709$	6.03926	0.226809	0.113405	+	0.993549i	$0.463824\pi$
$710$	10.4441	0.391958
$711$	−24.5757	−0.921662
$712$	40.2107	1.50696
$713$	−43.8899	−1.64369
$714$	0	0
$715$	−0.386640	−0.0144595
$716$	0.302680	0.0113117
$717$	−2.38197	−0.0889565
$718$	−7.29060	−0.272083
$719$	31.7821	1.18527	0.592636	−	0.805470i	$-0.298087\pi$
$719$	31.7821	1.18527	0.592636	+	0.805470i	$0.298087\pi$
$720$	4.89323	0.182360
$721$	61.5713	2.29303
$722$	−8.43525	−0.313928
$723$	−2.16695	−0.0805896
$724$	13.1507	0.488743
$725$	37.4253	1.38994
$726$	−0.442053	−0.0164061
$727$	−42.9172	−1.59171	−0.795855	−	0.605488i	$-0.792978\pi$
$727$	−42.9172	−1.59171	−0.795855	+	0.605488i	$0.792978\pi$
$728$	3.25942	0.120802
$729$	−17.9907	−0.666324
$730$	9.96900	0.368969
$731$	0	0
$732$	4.20208	0.155313
$733$	−25.6381	−0.946966	−0.473483	−	0.880803i	$-0.657003\pi$
$733$	−25.6381	−0.946966	−0.473483	+	0.880803i	$0.657003\pi$
$734$	−18.8658	−0.696350
$735$	−1.99764	−0.0736840
$736$	40.7132	1.50071
$737$	−3.61201	−0.133050
$738$	−32.9274	−1.21207
$739$	−3.95129	−0.145350	−0.0726752	−	0.997356i	$-0.523154\pi$
$739$	−3.95129	−0.145350	−0.0726752	+	0.997356i	$0.523154\pi$
$740$	−8.69161	−0.319510
$741$	−0.448490	−0.0164757
$742$	11.7944	0.432988
$743$	7.01578	0.257384	0.128692	−	0.991685i	$-0.458922\pi$
$743$	7.01578	0.257384	0.128692	+	0.991685i	$0.458922\pi$
$744$	−6.27693	−0.230123
$745$	−7.69193	−0.281811
$746$	19.8497	0.726748
$747$	−11.8239	−0.432615
$748$	0	0
$749$	−10.4616	−0.382260
$750$	4.53485	0.165589
$751$	53.7300	1.96064	0.980318	−	0.197427i	$-0.0632585\pi$
$751$	53.7300	1.96064	0.980318	+	0.197427i	$0.0632585\pi$
$752$	−0.724508	−0.0264201
$753$	6.32155	0.230370
$754$	−3.57787	−0.130298
$755$	−19.0840	−0.694538
$756$	7.15328	0.260162
$757$	1.14437	0.0415930	0.0207965	−	0.999784i	$-0.493380\pi$
$757$	1.14437	0.0415930	0.0207965	+	0.999784i	$0.493380\pi$
$758$	8.77843	0.318847
$759$	3.73343	0.135515
$760$	−12.1067	−0.439156
$761$	−21.3830	−0.775134	−0.387567	−	0.921841i	$-0.626684\pi$
$761$	−21.3830	−0.775134	−0.387567	+	0.921841i	$0.626684\pi$
$762$	3.04539	0.110323
$763$	−31.2598	−1.13168
$764$	−12.3525	−0.446898
$765$	0	0
$766$	27.4455	0.991647
$767$	1.48319	0.0535547
$768$	6.89454	0.248785
$769$	5.48589	0.197826	0.0989131	−	0.995096i	$-0.468463\pi$
$769$	5.48589	0.197826	0.0989131	+	0.995096i	$0.468463\pi$
$770$	4.19111	0.151037
$771$	−2.61333	−0.0941169
$772$	−11.9888	−0.431487
$773$	11.6678	0.419663	0.209831	−	0.977738i	$-0.432708\pi$
$773$	11.6678	0.419663	0.209831	+	0.977738i	$0.432708\pi$
$774$	22.3399	0.802992
$775$	17.5489	0.630376
$776$	14.7091	0.528024
$777$	11.3768	0.408140
$778$	−11.8601	−0.425203
$779$	36.6336	1.31254
$780$	0.143270	0.00512988
$781$	−8.25890	−0.295527
$782$	0	0
$783$	−25.5952	−0.914698
$784$	−5.76267	−0.205810
$785$	23.6849	0.845352
$786$	2.15320	0.0768020
$787$	−38.5467	−1.37404	−0.687021	−	0.726638i	$-0.741082\pi$
$787$	−38.5467	−1.37404	−0.687021	+	0.726638i	$0.741082\pi$
$788$	−5.95869	−0.212270
$789$	−6.16233	−0.219385
$790$	11.0021	0.391438
$791$	−27.6745	−0.983991
$792$	−8.60509	−0.305769
$793$	3.66097	0.130005
$794$	−6.54900	−0.232415
$795$	1.68990	0.0599345
$796$	−3.84340	−0.136226
$797$	−24.3706	−0.863251	−0.431625	−	0.902053i	$-0.642060\pi$
$797$	−24.3706	−0.863251	−0.431625	+	0.902053i	$0.642060\pi$
$798$	4.86155	0.172097
$799$	0	0
$800$	−16.2787	−0.575541
$801$	37.2854	1.31742
$802$	−23.4196	−0.826976
$803$	−7.88324	−0.278194
$804$	1.33843	0.0472029
$805$	−35.3967	−1.24757
$806$	−1.67768	−0.0590939
$807$	4.84458	0.170537
$808$	−55.6110	−1.95639
$809$	41.9832	1.47605	0.738025	−	0.674774i	$-0.235759\pi$
$809$	41.9832	1.47605	0.738025	+	0.674774i	$0.235759\pi$
$810$	9.42527	0.331170
$811$	20.1487	0.707518	0.353759	−	0.935337i	$-0.384903\pi$
$811$	20.1487	0.707518	0.353759	+	0.935337i	$0.384903\pi$
$812$	−30.7894	−1.08049
$813$	7.17366	0.251591
$814$	−8.65764	−0.303450
$815$	3.92195	0.137380
$816$	0	0
$817$	−24.8545	−0.869548
$818$	32.1565	1.12432
$819$	3.02231	0.105608
$820$	−11.7026	−0.408671
$821$	−42.3070	−1.47652	−0.738262	−	0.674515i	$-0.764353\pi$
$821$	−42.3070	−1.47652	−0.738262	+	0.674515i	$0.764353\pi$
$822$	−5.44267	−0.189835
$823$	−9.30475	−0.324343	−0.162172	−	0.986763i	$-0.551850\pi$
$823$	−9.30475	−0.324343	−0.162172	+	0.986763i	$0.551850\pi$
$824$	56.5945	1.97156
$825$	−1.49277	−0.0519717
$826$	−16.0775	−0.559407
$827$	−25.5305	−0.887783	−0.443892	−	0.896080i	$-0.646403\pi$
$827$	−25.5305	−0.887783	−0.443892	+	0.896080i	$0.646403\pi$
$828$	22.2956	0.774827
$829$	−24.3880	−0.847031	−0.423516	−	0.905889i	$-0.639204\pi$
$829$	−24.3880	−0.847031	−0.423516	+	0.905889i	$0.639204\pi$
$830$	5.29337	0.183736
$831$	1.49978	0.0520267
$832$	2.49015	0.0863305
$833$	0	0
$834$	−3.85881	−0.133620
$835$	−2.88806	−0.0999453
$836$	2.93703	0.101579
$837$	−12.0017	−0.414841
$838$	25.0964	0.866942
$839$	−28.5417	−0.985370	−0.492685	−	0.870208i	$-0.663984\pi$
$839$	−28.5417	−0.985370	−0.492685	+	0.870208i	$0.663984\pi$
$840$	−5.06228	−0.174665
$841$	81.1676	2.79888
$842$	4.73445	0.163160
$843$	−5.46742	−0.188308
$844$	−7.10771	−0.244657
$845$	−15.4446	−0.531309
$846$	−1.49399	−0.0513644
$847$	−3.31423	−0.113878
$848$	4.87492	0.167405
$849$	3.39988	0.116683
$850$	0	0
$851$	73.1195	2.50651
$852$	3.06034	0.104845
$853$	1.76259	0.0603500	0.0301750	−	0.999545i	$-0.490394\pi$
$853$	1.76259	0.0603500	0.0301750	+	0.999545i	$0.490394\pi$
$854$	−39.6843	−1.35797
$855$	−11.2259	−0.383919
$856$	−9.61604	−0.328669
$857$	53.1840	1.81673	0.908365	−	0.418177i	$-0.137331\pi$
$857$	53.1840	1.81673	0.908365	+	0.418177i	$0.137331\pi$
$858$	0.142710	0.00487203
$859$	19.8292	0.676564	0.338282	−	0.941045i	$-0.390154\pi$
$859$	19.8292	0.676564	0.338282	+	0.941045i	$0.390154\pi$
$860$	7.93973	0.270743
$861$	15.3179	0.522034
$862$	25.0961	0.854776
$863$	−15.4595	−0.526246	−0.263123	−	0.964762i	$-0.584752\pi$
$863$	−15.4595	−0.526246	−0.263123	+	0.964762i	$0.584752\pi$
$864$	11.1331	0.378754
$865$	−7.00927	−0.238322
$866$	15.6080	0.530380
$867$	0	0
$868$	−14.4373	−0.490034
$869$	−8.70022	−0.295135
$870$	5.55686	0.188395
$871$	1.16608	0.0395111
$872$	−28.7331	−0.973024
$873$	13.6390	0.461610
$874$	31.2456	1.05690
$875$	33.9994	1.14939
$876$	2.92114	0.0986961
$877$	45.9266	1.55083	0.775415	−	0.631452i	$-0.217541\pi$
$877$	45.9266	1.55083	0.775415	+	0.631452i	$0.217541\pi$
$878$	−8.18875	−0.276357
$879$	−9.18400	−0.309769
$880$	1.73228	0.0583953
$881$	11.5494	0.389109	0.194554	−	0.980892i	$-0.437674\pi$
$881$	11.5494	0.389109	0.194554	+	0.980892i	$0.437674\pi$
$882$	−11.8831	−0.400123
$883$	45.0933	1.51751	0.758755	−	0.651376i	$-0.225808\pi$
$883$	45.0933	1.51751	0.758755	+	0.651376i	$0.225808\pi$
$884$	0	0
$885$	−2.30357	−0.0774336
$886$	35.5185	1.19327
$887$	36.5525	1.22731	0.613656	−	0.789573i	$-0.289698\pi$
$887$	36.5525	1.22731	0.613656	+	0.789573i	$0.289698\pi$
$888$	10.4572	0.350921
$889$	22.8324	0.765774
$890$	−16.6920	−0.559518
$891$	−7.45327	−0.249694
$892$	−8.41797	−0.281854
$893$	1.66215	0.0556217
$894$	2.83911	0.0949539
$895$	−0.409563	−0.0136902
$896$	3.26905	0.109211
$897$	−1.20528	−0.0402431
$898$	1.07562	0.0358940
$899$	51.6582	1.72290
$900$	−8.91468	−0.297156
$901$	0	0
$902$	−11.6568	−0.388130
$903$	−10.3926	−0.345845
$904$	−25.4376	−0.846041
$905$	−17.7946	−0.591511
$906$	7.04394	0.234019
$907$	40.4685	1.34373	0.671866	−	0.740672i	$-0.265493\pi$
$907$	40.4685	1.34373	0.671866	+	0.740672i	$0.265493\pi$
$908$	2.64874	0.0879017
$909$	−51.5654	−1.71032
$910$	−1.35303	−0.0448526
$911$	19.9615	0.661355	0.330677	−	0.943744i	$-0.392723\pi$
$911$	19.9615	0.661355	0.330677	+	0.943744i	$0.392723\pi$
$912$	2.00939	0.0665376
$913$	−4.18587	−0.138532
$914$	17.5348	0.579999
$915$	−5.68593	−0.187971
$916$	10.0443	0.331873
$917$	16.1433	0.533098
$918$	0	0
$919$	12.2595	0.404403	0.202201	−	0.979344i	$-0.435190\pi$
$919$	12.2595	0.404403	0.202201	+	0.979344i	$0.435190\pi$
$920$	−32.5357	−1.07267
$921$	−1.32957	−0.0438108
$922$	9.52658	0.313741
$923$	2.66625	0.0877608
$924$	1.22809	0.0404012
$925$	−29.2361	−0.961276
$926$	−34.3040	−1.12730
$927$	52.4774	1.72358
$928$	−47.9192	−1.57302
$929$	5.64000	0.185043	0.0925213	−	0.995711i	$-0.470507\pi$
$929$	5.64000	0.185043	0.0925213	+	0.995711i	$0.470507\pi$
$930$	2.60564	0.0854425
$931$	13.2206	0.433287
$932$	5.15083	0.168721
$933$	−2.02356	−0.0662485
$934$	4.55356	0.148997
$935$	0	0
$936$	2.77801	0.0908023
$937$	56.3502	1.84088	0.920441	−	0.390883i	$-0.127830\pi$
$937$	56.3502	1.84088	0.920441	+	0.390883i	$0.127830\pi$
$938$	−12.6401	−0.412714
$939$	4.79036	0.156327
$940$	−0.530972	−0.0173184
$941$	20.9042	0.681458	0.340729	−	0.940162i	$-0.389326\pi$
$941$	20.9042	0.681458	0.340729	+	0.940162i	$0.389326\pi$
$942$	−8.74215	−0.284835
$943$	98.4496	3.20596
$944$	−6.64519	−0.216283
$945$	−9.67927	−0.314867
$946$	7.90870	0.257134
$947$	−41.9759	−1.36403	−0.682016	−	0.731337i	$-0.738897\pi$
$947$	−41.9759	−1.36403	−0.682016	+	0.731337i	$0.738897\pi$
$948$	3.22387	0.104706
$949$	2.54498	0.0826135
$950$	−12.4932	−0.405334
$951$	−2.96635	−0.0961904
$952$	0	0
$953$	10.0818	0.326582	0.163291	−	0.986578i	$-0.447789\pi$
$953$	10.0818	0.326582	0.163291	+	0.986578i	$0.447789\pi$
$954$	10.0524	0.325460
$955$	16.7144	0.540867
$956$	−5.03584	−0.162871
$957$	−4.39423	−0.142045
$958$	−36.6538	−1.18423
$959$	−40.8057	−1.31768
$960$	−3.86751	−0.124823
$961$	−6.77716	−0.218618
$962$	2.79498	0.0901137
$963$	−8.91649	−0.287330
$964$	−4.58124	−0.147552
$965$	16.2224	0.522216
$966$	13.0650	0.420360
$967$	42.1344	1.35495	0.677476	−	0.735545i	$-0.263074\pi$
$967$	42.1344	1.35495	0.677476	+	0.735545i	$0.263074\pi$
$968$	−3.04634	−0.0979132
$969$	0	0
$970$	−6.10594	−0.196050
$971$	54.9954	1.76489	0.882443	−	0.470419i	$-0.155897\pi$
$971$	54.9954	1.76489	0.882443	+	0.470419i	$0.155897\pi$
$972$	9.23687	0.296273
$973$	−28.9309	−0.927481
$974$	−14.0812	−0.451190
$975$	0.481918	0.0154337
$976$	−16.4024	−0.525029
$977$	−3.70677	−0.118590	−0.0592950	−	0.998241i	$-0.518885\pi$
$977$	−3.70677	−0.118590	−0.0592950	+	0.998241i	$0.518885\pi$
$978$	−1.44760	−0.0462891
$979$	13.1996	0.421863
$980$	−4.22330	−0.134908
$981$	−26.6428	−0.850638
$982$	−7.14470	−0.227997
$983$	−9.61598	−0.306702	−0.153351	−	0.988172i	$-0.549007\pi$
$983$	−9.61598	−0.306702	−0.153351	+	0.988172i	$0.549007\pi$
$984$	14.0798	0.448848
$985$	8.06284	0.256904
$986$	0	0
$987$	0.695010	0.0221224
$988$	−0.948174	−0.0301654
$989$	−66.7942	−2.12393
$990$	3.57210	0.113529
$991$	15.4309	0.490178	0.245089	−	0.969501i	$-0.421183\pi$
$991$	15.4309	0.490178	0.245089	+	0.969501i	$0.421183\pi$
$992$	−22.4696	−0.713410
$993$	11.8689	0.376647
$994$	−28.9017	−0.916707
$995$	5.20060	0.164870
$996$	1.55107	0.0491477
$997$	40.3670	1.27844	0.639218	−	0.769026i	$-0.279258\pi$
$997$	40.3670	1.27844	0.639218	+	0.769026i	$0.279258\pi$
$998$	−27.6502	−0.875252
$999$	19.9946	0.632601

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3179.2.a.bi.1.20		28
17.10	odd	16		187.2.h.a.100.5	✓	56
17.12	odd	16		187.2.h.a.144.5	yes	56
17.16	even	2		3179.2.a.bh.1.20		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
187.2.h.a.100.5	✓	56	17.10	odd	16
187.2.h.a.144.5	yes	56	17.12	odd	16
3179.2.a.bh.1.20		28	17.16	even	2
3179.2.a.bi.1.20		28	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:	\( N \)	\(=\)	\( 3179 = 11 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3179.a (trivial)

\(f(q)\)	\(=\)	\(q+1.05589 q^{2} -0.418655 q^{3} -0.885097 q^{4} +1.19765 q^{5} -0.442053 q^{6} -3.31423 q^{7} -3.04634 q^{8} -2.82473 q^{9} +O(q^{10})\)	\(q+1.05589 q^{2} -0.418655 q^{3} -0.885097 q^{4} +1.19765 q^{5} -0.442053 q^{6} -3.31423 q^{7} -3.04634 q^{8} -2.82473 q^{9} +1.26458 q^{10} -1.00000 q^{11} +0.370550 q^{12} +0.322834 q^{13} -3.49946 q^{14} -0.501400 q^{15} -1.44641 q^{16} -2.98260 q^{18} +3.31832 q^{19} -1.06003 q^{20} +1.38752 q^{21} -1.05589 q^{22} +8.91769 q^{23} +1.27537 q^{24} -3.56565 q^{25} +0.340877 q^{26} +2.43855 q^{27} +2.93342 q^{28} -10.4961 q^{29} -0.529423 q^{30} -4.92167 q^{31} +4.56544 q^{32} +0.418655 q^{33} -3.96927 q^{35} +2.50016 q^{36} +8.19938 q^{37} +3.50378 q^{38} -0.135156 q^{39} -3.64844 q^{40} +11.0398 q^{41} +1.46507 q^{42} -7.49008 q^{43} +0.885097 q^{44} -3.38302 q^{45} +9.41610 q^{46} +0.500901 q^{47} +0.605545 q^{48} +3.98412 q^{49} -3.76493 q^{50} -0.285739 q^{52} -3.37036 q^{53} +2.57484 q^{54} -1.19765 q^{55} +10.0963 q^{56} -1.38923 q^{57} -11.0827 q^{58} +4.59427 q^{59} +0.443788 q^{60} +11.3401 q^{61} -5.19674 q^{62} +9.36180 q^{63} +7.71342 q^{64} +0.386640 q^{65} +0.442053 q^{66} +3.61201 q^{67} -3.73343 q^{69} -4.19111 q^{70} +8.25890 q^{71} +8.60509 q^{72} +7.88324 q^{73} +8.65764 q^{74} +1.49277 q^{75} -2.93703 q^{76} +3.31423 q^{77} -0.142710 q^{78} +8.70022 q^{79} -1.73228 q^{80} +7.45327 q^{81} +11.6568 q^{82} +4.18587 q^{83} -1.22809 q^{84} -7.90870 q^{86} +4.39423 q^{87} +3.04634 q^{88} -13.1996 q^{89} -3.57210 q^{90} -1.06995 q^{91} -7.89302 q^{92} +2.06048 q^{93} +0.528896 q^{94} +3.97417 q^{95} -1.91134 q^{96} -4.82843 q^{97} +4.20679 q^{98} +2.82473 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9}+O(q^{10}) \) 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9	\( 28 q + 8 q^{3} + 24 q^{4} + 16 q^{5} + 16 q^{6} + 12 q^{7} + 20 q^{9} + 24 q^{10} - 28 q^{11} + 24 q^{12} + 16 q^{14} - 16 q^{15} + 16 q^{16} + 32 q^{20} + 8 q^{23} - 8 q^{24} + 20 q^{25} - 24 q^{26} + 32 q^{27} + 32 q^{28} + 36 q^{29} + 40 q^{30} + 56 q^{31} + 40 q^{32} - 8 q^{33} + 16 q^{35} + 40 q^{36} + 64 q^{37} - 8 q^{38} + 32 q^{39} + 72 q^{40} + 28 q^{41} + 24 q^{42} + 16 q^{43} - 24 q^{44} + 24 q^{45} - 36 q^{47} + 56 q^{48} + 16 q^{49} + 56 q^{50} - 20 q^{53} + 64 q^{54} - 16 q^{55} + 48 q^{56} + 32 q^{57} - 16 q^{58} - 28 q^{59} + 8 q^{60} + 104 q^{61} - 8 q^{62} + 28 q^{63} + 32 q^{65} - 16 q^{66} - 12 q^{67} - 32 q^{69} + 40 q^{71} + 40 q^{72} + 76 q^{73} + 24 q^{74} - 16 q^{75} - 16 q^{76} - 12 q^{77} - 24 q^{78} + 24 q^{79} + 8 q^{80} + 12 q^{81} + 56 q^{82} + 32 q^{83} - 40 q^{84} - 16 q^{86} - 8 q^{87} - 52 q^{89} + 16 q^{90} + 80 q^{91} - 56 q^{92} + 24 q^{97} - 24 q^{98} - 20 q^{99}+O(q^{100}) \) 28 * q + 8 * q^3 + 24 * q^4 + 16 * q^5 + 16 * q^6 + 12 * q^7 + 20 * q^9 + 24 * q^10 - 28 * q^11 + 24 * q^12 + 16 * q^14 - 16 * q^15 + 16 * q^16 + 32 * q^20 + 8 * q^23 - 8 * q^24 + 20 * q^25 - 24 * q^26 + 32 * q^27 + 32 * q^28 + 36 * q^29 + 40 * q^30 + 56 * q^31 + 40 * q^32 - 8 * q^33 + 16 * q^35 + 40 * q^36 + 64 * q^37 - 8 * q^38 + 32 * q^39 + 72 * q^40 + 28 * q^41 + 24 * q^42 + 16 * q^43 - 24 * q^44 + 24 * q^45 - 36 * q^47 + 56 * q^48 + 16 * q^49 + 56 * q^50 - 20 * q^53 + 64 * q^54 - 16 * q^55 + 48 * q^56 + 32 * q^57 - 16 * q^58 - 28 * q^59 + 8 * q^60 + 104 * q^61 - 8 * q^62 + 28 * q^63 + 32 * q^65 - 16 * q^66 - 12 * q^67 - 32 * q^69 + 40 * q^71 + 40 * q^72 + 76 * q^73 + 24 * q^74 - 16 * q^75 - 16 * q^76 - 12 * q^77 - 24 * q^78 + 24 * q^79 + 8 * q^80 + 12 * q^81 + 56 * q^82 + 32 * q^83 - 40 * q^84 - 16 * q^86 - 8 * q^87 - 52 * q^89 + 16 * q^90 + 80 * q^91 - 56 * q^92 + 24 * q^97 - 24 * q^98 - 20 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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