LMFDB - Embedded newform 7942.2.a.bi.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7942,2,Mod(1,7942)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7942, 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("7942.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7942 = 2 \cdot 11 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7942.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:	$63.4171892853$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.621.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 6x - 3 $ x^3 - 6*x - 3
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 418)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-2.14510$ of defining polynomial
Character	$\chi$	$=$	7942.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} +2.14510 q^{6} +2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} +2.14510 q^{6} +2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} -1.60147 q^{10} -1.00000 q^{11} +2.14510 q^{12} -4.89167 q^{13} +2.89167 q^{14} -3.43531 q^{15} +1.00000 q^{16} -5.74657 q^{17} +1.60147 q^{18} -1.60147 q^{20} +6.20293 q^{21} -1.00000 q^{22} -7.74657 q^{23} +2.14510 q^{24} -2.43531 q^{25} -4.89167 q^{26} -3.00000 q^{27} +2.89167 q^{28} -5.34803 q^{29} -3.43531 q^{30} +7.43531 q^{31} +1.00000 q^{32} -2.14510 q^{33} -5.74657 q^{34} -4.63091 q^{35} +1.60147 q^{36} +7.49314 q^{37} -10.4931 q^{39} -1.60147 q^{40} +2.05783 q^{41} +6.20293 q^{42} -10.6887 q^{43} -1.00000 q^{44} -2.56469 q^{45} -7.74657 q^{46} -7.08727 q^{47} +2.14510 q^{48} +1.36176 q^{49} -2.43531 q^{50} -12.3270 q^{51} -4.89167 q^{52} -8.32698 q^{53} -3.00000 q^{54} +1.60147 q^{55} +2.89167 q^{56} -5.34803 q^{58} +2.54364 q^{59} -3.43531 q^{60} +13.4931 q^{61} +7.43531 q^{62} +4.63091 q^{63} +1.00000 q^{64} +7.83384 q^{65} -2.14510 q^{66} +10.3848 q^{67} -5.74657 q^{68} -16.6172 q^{69} -4.63091 q^{70} -14.9789 q^{71} +1.60147 q^{72} -3.74657 q^{73} +7.49314 q^{74} -5.22399 q^{75} -2.89167 q^{77} -10.4931 q^{78} +8.69607 q^{79} -1.60147 q^{80} -11.2397 q^{81} +2.05783 q^{82} -6.10833 q^{83} +6.20293 q^{84} +9.20293 q^{85} -10.6887 q^{86} -11.4721 q^{87} -1.00000 q^{88} -3.20293 q^{89} -2.56469 q^{90} -14.1451 q^{91} -7.74657 q^{92} +15.9495 q^{93} -7.08727 q^{94} +2.14510 q^{96} +6.98627 q^{97} +1.36176 q^{98} -1.60147 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9	$ 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 6 q^{14} + 9 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} + 15 q^{21} - 3 q^{22} - 15 q^{23} + 12 q^{25} - 9 q^{27} - 6 q^{28} - 6 q^{29} + 9 q^{30} + 3 q^{31} + 3 q^{32} - 9 q^{34} + 3 q^{36} + 6 q^{37} - 15 q^{39} - 3 q^{40} + 9 q^{41} + 15 q^{42} - 21 q^{43} - 3 q^{44} - 27 q^{45} - 15 q^{46} - 12 q^{47} + 27 q^{49} + 12 q^{50} - 3 q^{51} + 9 q^{53} - 9 q^{54} + 3 q^{55} - 6 q^{56} - 6 q^{58} + 3 q^{59} + 9 q^{60} + 24 q^{61} + 3 q^{62} + 3 q^{64} + 6 q^{65} - 9 q^{68} - 3 q^{69} - 21 q^{71} + 3 q^{72} - 3 q^{73} + 6 q^{74} - 36 q^{75} + 6 q^{77} - 15 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} - 33 q^{83} + 15 q^{84} + 24 q^{85} - 21 q^{86} + 6 q^{87} - 3 q^{88} - 6 q^{89} - 27 q^{90} - 36 q^{91} - 15 q^{92} + 36 q^{93} - 12 q^{94} - 12 q^{97} + 27 q^{98} - 3 q^{99}+O(q^{100}) $ 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 6 * q^14 + 9 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 + 15 * q^21 - 3 * q^22 - 15 * q^23 + 12 * q^25 - 9 * q^27 - 6 * q^28 - 6 * q^29 + 9 * q^30 + 3 * q^31 + 3 * q^32 - 9 * q^34 + 3 * q^36 + 6 * q^37 - 15 * q^39 - 3 * q^40 + 9 * q^41 + 15 * q^42 - 21 * q^43 - 3 * q^44 - 27 * q^45 - 15 * q^46 - 12 * q^47 + 27 * q^49 + 12 * q^50 - 3 * q^51 + 9 * q^53 - 9 * q^54 + 3 * q^55 - 6 * q^56 - 6 * q^58 + 3 * q^59 + 9 * q^60 + 24 * q^61 + 3 * q^62 + 3 * q^64 + 6 * q^65 - 9 * q^68 - 3 * q^69 - 21 * q^71 + 3 * q^72 - 3 * q^73 + 6 * q^74 - 36 * q^75 + 6 * q^77 - 15 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 - 33 * q^83 + 15 * q^84 + 24 * q^85 - 21 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 27 * q^90 - 36 * q^91 - 15 * q^92 + 36 * q^93 - 12 * q^94 - 12 * q^97 + 27 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	2.14510	1.23848	0.619238	−	0.785204i	$-0.287442\pi$
$3$	2.14510	1.23848	0.619238	+	0.785204i	$0.287442\pi$
$4$	1.00000	0.500000
$5$	−1.60147	−0.716197	−0.358099	−	0.933684i	$-0.616575\pi$
$5$	−1.60147	−0.716197	−0.358099	+	0.933684i	$0.616575\pi$
$6$	2.14510	0.875735
$7$	2.89167	1.09295	0.546474	−	0.837476i	$-0.315970\pi$
$7$	2.89167	1.09295	0.546474	+	0.837476i	$0.315970\pi$
$8$	1.00000	0.353553
$9$	1.60147	0.533822
$10$	−1.60147	−0.506428
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	2.14510	0.619238
$13$	−4.89167	−1.35671	−0.678353	−	0.734736i	$-0.737306\pi$
$13$	−4.89167	−1.35671	−0.678353	+	0.734736i	$0.737306\pi$
$14$	2.89167	0.772832
$15$	−3.43531	−0.886993
$16$	1.00000	0.250000
$17$	−5.74657	−1.39375	−0.696874	−	0.717194i	$-0.745426\pi$
$17$	−5.74657	−1.39375	−0.696874	+	0.717194i	$0.745426\pi$
$18$	1.60147	0.377469
$19$	0	0
$19$	0	0
$20$	−1.60147	−0.358099
$21$	6.20293	1.35359
$22$	−1.00000	−0.213201
$23$	−7.74657	−1.61527	−0.807636	−	0.589682i	$-0.799253\pi$
$23$	−7.74657	−1.61527	−0.807636	+	0.589682i	$0.799253\pi$
$24$	2.14510	0.437867
$25$	−2.43531	−0.487062
$26$	−4.89167	−0.959336
$27$	−3.00000	−0.577350
$28$	2.89167	0.546474
$29$	−5.34803	−0.993105	−0.496552	−	0.868007i	$-0.665401\pi$
$29$	−5.34803	−0.993105	−0.496552	+	0.868007i	$0.665401\pi$
$30$	−3.43531	−0.627199
$31$	7.43531	1.33542	0.667710	−	0.744421i	$-0.267274\pi$
$31$	7.43531	1.33542	0.667710	+	0.744421i	$0.267274\pi$
$32$	1.00000	0.176777
$33$	−2.14510	−0.373414
$34$	−5.74657	−0.985528
$35$	−4.63091	−0.782767
$36$	1.60147	0.266911
$37$	7.49314	1.23186	0.615932	−	0.787799i	$-0.288780\pi$
$37$	7.49314	1.23186	0.615932	+	0.787799i	$0.288780\pi$
$38$	0	0
$39$	−10.4931	−1.68025
$40$	−1.60147	−0.253214
$41$	2.05783	0.321379	0.160689	−	0.987005i	$-0.448628\pi$
$41$	2.05783	0.321379	0.160689	+	0.987005i	$0.448628\pi$
$42$	6.20293	0.957133
$43$	−10.6887	−1.63002	−0.815009	−	0.579449i	$-0.803268\pi$
$43$	−10.6887	−1.63002	−0.815009	+	0.579449i	$0.803268\pi$
$44$	−1.00000	−0.150756
$45$	−2.56469	−0.382322
$46$	−7.74657	−1.14217
$47$	−7.08727	−1.03379	−0.516893	−	0.856050i	$-0.672911\pi$
$47$	−7.08727	−1.03379	−0.516893	+	0.856050i	$0.672911\pi$
$48$	2.14510	0.309619
$49$	1.36176	0.194537
$50$	−2.43531	−0.344405
$51$	−12.3270	−1.72612
$52$	−4.89167	−0.678353
$53$	−8.32698	−1.14380	−0.571899	−	0.820324i	$-0.693793\pi$
$53$	−8.32698	−1.14380	−0.571899	+	0.820324i	$0.693793\pi$
$54$	−3.00000	−0.408248
$55$	1.60147	0.215942
$56$	2.89167	0.386416
$57$	0	0
$58$	−5.34803	−0.702231
$59$	2.54364	0.331153	0.165577	−	0.986197i	$-0.447051\pi$
$59$	2.54364	0.331153	0.165577	+	0.986197i	$0.447051\pi$
$60$	−3.43531	−0.443496
$61$	13.4931	1.72762	0.863810	−	0.503818i	$-0.168072\pi$
$61$	13.4931	1.72762	0.863810	+	0.503818i	$0.168072\pi$
$62$	7.43531	0.944285
$63$	4.63091	0.583440
$64$	1.00000	0.125000
$65$	7.83384	0.971669
$66$	−2.14510	−0.264044
$67$	10.3848	1.26871	0.634353	−	0.773043i	$-0.281267\pi$
$67$	10.3848	1.26871	0.634353	+	0.773043i	$0.281267\pi$
$68$	−5.74657	−0.696874
$69$	−16.6172	−2.00047
$70$	−4.63091	−0.553500
$71$	−14.9789	−1.77767	−0.888837	−	0.458224i	$-0.848486\pi$
$71$	−14.9789	−1.77767	−0.888837	+	0.458224i	$0.848486\pi$
$72$	1.60147	0.188735
$73$	−3.74657	−0.438503	−0.219251	−	0.975668i	$-0.570361\pi$
$73$	−3.74657	−0.438503	−0.219251	+	0.975668i	$0.570361\pi$
$74$	7.49314	0.871059
$75$	−5.22399	−0.603214
$76$	0	0
$77$	−2.89167	−0.329536
$78$	−10.4931	−1.18811
$79$	8.69607	0.978384	0.489192	−	0.872176i	$-0.337292\pi$
$79$	8.69607	0.978384	0.489192	+	0.872176i	$0.337292\pi$
$80$	−1.60147	−0.179049
$81$	−11.2397	−1.24886
$82$	2.05783	0.227249
$83$	−6.10833	−0.670476	−0.335238	−	0.942133i	$-0.608817\pi$
$83$	−6.10833	−0.670476	−0.335238	+	0.942133i	$0.608817\pi$
$84$	6.20293	0.676795
$85$	9.20293	0.998198
$86$	−10.6887	−1.15260
$87$	−11.4721	−1.22994
$88$	−1.00000	−0.106600
$89$	−3.20293	−0.339510	−0.169755	−	0.985486i	$-0.554298\pi$
$89$	−3.20293	−0.339510	−0.169755	+	0.985486i	$0.554298\pi$
$90$	−2.56469	−0.270342
$91$	−14.1451	−1.48281
$92$	−7.74657	−0.807636
$93$	15.9495	1.65389
$94$	−7.08727	−0.730997
$95$	0	0
$96$	2.14510	0.218934
$97$	6.98627	0.709349	0.354674	−	0.934990i	$-0.384592\pi$
$97$	6.98627	0.709349	0.354674	+	0.934990i	$0.384592\pi$
$98$	1.36176	0.137559
$99$	−1.60147	−0.160953
$100$	−2.43531	−0.243531
$101$	−1.20293	−0.119696	−0.0598481	−	0.998207i	$-0.519062\pi$
$101$	−1.20293	−0.119696	−0.0598481	+	0.998207i	$0.519062\pi$
$102$	−12.3270	−1.22055
$103$	−16.8779	−1.66303	−0.831517	−	0.555500i	$-0.812527\pi$
$103$	−16.8779	−1.66303	−0.831517	+	0.555500i	$0.812527\pi$
$104$	−4.89167	−0.479668
$105$	−9.93378	−0.969438
$106$	−8.32698	−0.808788
$107$	8.03677	0.776944	0.388472	−	0.921460i	$-0.373003\pi$
$107$	8.03677	0.776944	0.388472	+	0.921460i	$0.373003\pi$
$108$	−3.00000	−0.288675
$109$	−11.5299	−1.10437	−0.552183	−	0.833723i	$-0.686205\pi$
$109$	−11.5299	−1.10437	−0.552183	+	0.833723i	$0.686205\pi$
$110$	1.60147	0.152694
$111$	16.0735	1.52563
$112$	2.89167	0.273237
$113$	8.00000	0.752577	0.376288	−	0.926503i	$-0.377200\pi$
$113$	8.00000	0.752577	0.376288	+	0.926503i	$0.377200\pi$
$114$	0	0
$115$	12.4059	1.15685
$116$	−5.34803	−0.496552
$117$	−7.83384	−0.724239
$118$	2.54364	0.234161
$119$	−16.6172	−1.52329
$120$	−3.43531	−0.313599
$121$	1.00000	0.0909091
$122$	13.4931	1.22161
$123$	4.41425	0.398020
$124$	7.43531	0.667710
$125$	11.9074	1.06503
$126$	4.63091	0.412554
$127$	21.2765	1.88798	0.943991	−	0.329971i	$-0.107039\pi$
$127$	21.2765	1.88798	0.943991	+	0.329971i	$0.107039\pi$
$128$	1.00000	0.0883883
$129$	−22.9284	−2.01874
$130$	7.83384	0.687073
$131$	−3.43531	−0.300144	−0.150072	−	0.988675i	$-0.547951\pi$
$131$	−3.43531	−0.300144	−0.150072	+	0.988675i	$0.547951\pi$
$132$	−2.14510	−0.186707
$133$	0	0
$134$	10.3848	0.897111
$135$	4.80440	0.413497
$136$	−5.74657	−0.492764
$137$	13.5877	1.16088	0.580439	−	0.814303i	$-0.302881\pi$
$137$	13.5877	1.16088	0.580439	+	0.814303i	$0.302881\pi$
$138$	−16.6172	−1.41455
$139$	3.19560	0.271048	0.135524	−	0.990774i	$-0.456728\pi$
$139$	3.19560	0.271048	0.135524	+	0.990774i	$0.456728\pi$
$140$	−4.63091	−0.391383
$141$	−15.2029	−1.28032
$142$	−14.9789	−1.25701
$143$	4.89167	0.409062
$144$	1.60147	0.133455
$145$	8.56469	0.711259
$146$	−3.74657	−0.310068
$147$	2.92112	0.240930
$148$	7.49314	0.615932
$149$	−12.0735	−0.989104	−0.494552	−	0.869148i	$-0.664668\pi$
$149$	−12.0735	−0.989104	−0.494552	+	0.869148i	$0.664668\pi$
$150$	−5.22399	−0.426537
$151$	4.91273	0.399792	0.199896	−	0.979817i	$-0.435940\pi$
$151$	4.91273	0.399792	0.199896	+	0.979817i	$0.435940\pi$
$152$	0	0
$153$	−9.20293	−0.744013
$154$	−2.89167	−0.233017
$155$	−11.9074	−0.956425
$156$	−10.4931	−0.840123
$157$	8.00733	0.639054	0.319527	−	0.947577i	$-0.396476\pi$
$157$	8.00733	0.639054	0.319527	+	0.947577i	$0.396476\pi$
$158$	8.69607	0.691822
$159$	−17.8622	−1.41657
$160$	−1.60147	−0.126607
$161$	−22.4005	−1.76541
$162$	−11.2397	−0.883075
$163$	1.88434	0.147593	0.0737966	−	0.997273i	$-0.476488\pi$
$163$	1.88434	0.147593	0.0737966	+	0.997273i	$0.476488\pi$
$164$	2.05783	0.160689
$165$	3.43531	0.267438
$166$	−6.10833	−0.474098
$167$	4.98627	0.385849	0.192925	−	0.981214i	$-0.438203\pi$
$167$	4.98627	0.385849	0.192925	+	0.981214i	$0.438203\pi$
$168$	6.20293	0.478567
$169$	10.9284	0.840650
$170$	9.20293	0.705833
$171$	0	0
$172$	−10.6887	−0.815009
$173$	−6.51419	−0.495265	−0.247632	−	0.968854i	$-0.579653\pi$
$173$	−6.51419	−0.495265	−0.247632	+	0.968854i	$0.579653\pi$
$174$	−11.4721	−0.869696
$175$	−7.04211	−0.532333
$176$	−1.00000	−0.0753778
$177$	5.45636	0.410125
$178$	−3.20293	−0.240070
$179$	5.55096	0.414899	0.207449	−	0.978246i	$-0.433484\pi$
$179$	5.55096	0.414899	0.207449	+	0.978246i	$0.433484\pi$
$180$	−2.56469	−0.191161
$181$	−1.88434	−0.140062	−0.0700311	−	0.997545i	$-0.522310\pi$
$181$	−1.88434	−0.140062	−0.0700311	+	0.997545i	$0.522310\pi$
$182$	−14.1451	−1.04850
$183$	28.9442	2.13961
$184$	−7.74657	−0.571085
$185$	−12.0000	−0.882258
$186$	15.9495	1.16947
$187$	5.74657	0.420231
$188$	−7.08727	−0.516893
$189$	−8.67501	−0.631014
$190$	0	0
$191$	2.44264	0.176743	0.0883715	−	0.996088i	$-0.471834\pi$
$191$	2.44264	0.176743	0.0883715	+	0.996088i	$0.471834\pi$
$192$	2.14510	0.154809
$193$	9.67501	0.696423	0.348211	−	0.937416i	$-0.386789\pi$
$193$	9.67501	0.696423	0.348211	+	0.937416i	$0.386789\pi$
$194$	6.98627	0.501585
$195$	16.8044	1.20339
$196$	1.36176	0.0972686
$197$	−17.4931	−1.24633	−0.623167	−	0.782089i	$-0.714154\pi$
$197$	−17.4931	−1.24633	−0.623167	+	0.782089i	$0.714154\pi$
$198$	−1.60147	−0.113811
$199$	−25.2397	−1.78920	−0.894598	−	0.446873i	$-0.852538\pi$
$199$	−25.2397	−1.78920	−0.894598	+	0.446873i	$0.852538\pi$
$200$	−2.43531	−0.172202
$201$	22.2765	1.57126
$202$	−1.20293	−0.0846379
$203$	−15.4648	−1.08541
$204$	−12.3270	−0.863061
$205$	−3.29554	−0.230171
$206$	−16.8779	−1.17594
$207$	−12.4059	−0.862267
$208$	−4.89167	−0.339176
$209$	0	0
$210$	−9.93378	−0.685496
$211$	14.8338	1.02120	0.510602	−	0.859817i	$-0.329423\pi$
$211$	14.8338	1.02120	0.510602	+	0.859817i	$0.329423\pi$
$212$	−8.32698	−0.571899
$213$	−32.1314	−2.20161
$214$	8.03677	0.549383
$215$	17.1176	1.16741
$216$	−3.00000	−0.204124
$217$	21.5005	1.45955
$218$	−11.5299	−0.780904
$219$	−8.03677	−0.543075
$220$	1.60147	0.107971
$221$	28.1103	1.89090
$222$	16.0735	1.07879
$223$	−11.4931	−0.769637	−0.384819	−	0.922992i	$-0.625736\pi$
$223$	−11.4931	−0.769637	−0.384819	+	0.922992i	$0.625736\pi$
$224$	2.89167	0.193208
$225$	−3.90006	−0.260004
$226$	8.00000	0.532152
$227$	−8.73284	−0.579619	−0.289810	−	0.957084i	$-0.593592\pi$
$227$	−8.73284	−0.579619	−0.289810	+	0.957084i	$0.593592\pi$
$228$	0	0
$229$	7.84117	0.518159	0.259080	−	0.965856i	$-0.416581\pi$
$229$	7.84117	0.518159	0.259080	+	0.965856i	$0.416581\pi$
$230$	12.4059	0.818018
$231$	−6.20293	−0.408123
$232$	−5.34803	−0.351116
$233$	−12.5069	−0.819352	−0.409676	−	0.912231i	$-0.634358\pi$
$233$	−12.5069	−0.819352	−0.409676	+	0.912231i	$0.634358\pi$
$234$	−7.83384	−0.512114
$235$	11.3500	0.740394
$236$	2.54364	0.165577
$237$	18.6540	1.21170
$238$	−16.6172	−1.07713
$239$	24.6245	1.59283	0.796414	−	0.604752i	$-0.206728\pi$
$239$	24.6245	1.59283	0.796414	+	0.604752i	$0.206728\pi$
$240$	−3.43531	−0.221748
$241$	−16.0809	−1.03586	−0.517930	−	0.855423i	$-0.673297\pi$
$241$	−16.0809	−1.03586	−0.517930	+	0.855423i	$0.673297\pi$
$242$	1.00000	0.0642824
$243$	−15.1103	−0.969328
$244$	13.4931	0.863810
$245$	−2.18081	−0.139327
$246$	4.41425	0.281443
$247$	0	0
$248$	7.43531	0.472143
$249$	−13.1030	−0.830368
$250$	11.9074	0.753089
$251$	13.0873	0.826061	0.413031	−	0.910717i	$-0.364470\pi$
$251$	13.0873	0.826061	0.413031	+	0.910717i	$0.364470\pi$
$252$	4.63091	0.291720
$253$	7.74657	0.487023
$254$	21.2765	1.33500
$255$	19.7412	1.23624
$256$	1.00000	0.0625000
$257$	−0.723522	−0.0451320	−0.0225660	−	0.999745i	$-0.507184\pi$
$257$	−0.723522	−0.0451320	−0.0225660	+	0.999745i	$0.507184\pi$
$258$	−22.9284	−1.42746
$259$	21.6677	1.34636
$260$	7.83384	0.485834
$261$	−8.56469	−0.530141
$262$	−3.43531	−0.212234
$263$	13.7760	0.849465	0.424733	−	0.905319i	$-0.360368\pi$
$263$	13.7760	0.849465	0.424733	+	0.905319i	$0.360368\pi$
$264$	−2.14510	−0.132022
$265$	13.3354	0.819185
$266$	0	0
$267$	−6.87062	−0.420475
$268$	10.3848	0.634353
$269$	19.9579	1.21685	0.608427	−	0.793610i	$-0.291801\pi$
$269$	19.9579	1.21685	0.608427	+	0.793610i	$0.291801\pi$
$270$	4.80440	0.292386
$271$	28.7486	1.74635	0.873175	−	0.487406i	$-0.162057\pi$
$271$	28.7486	1.74635	0.873175	+	0.487406i	$0.162057\pi$
$272$	−5.74657	−0.348437
$273$	−30.3427	−1.83642
$274$	13.5877	0.820865
$275$	2.43531	0.146855
$276$	−16.6172	−1.00024
$277$	3.08727	0.185496	0.0927482	−	0.995690i	$-0.470435\pi$
$277$	3.08727	0.185496	0.0927482	+	0.995690i	$0.470435\pi$
$278$	3.19560	0.191660
$279$	11.9074	0.712877
$280$	−4.63091	−0.276750
$281$	−9.09460	−0.542538	−0.271269	−	0.962504i	$-0.587443\pi$
$281$	−9.09460	−0.542538	−0.271269	+	0.962504i	$0.587443\pi$
$282$	−15.2029	−0.905321
$283$	13.1451	0.781395	0.390698	−	0.920519i	$-0.372234\pi$
$283$	13.1451	0.781395	0.390698	+	0.920519i	$0.372234\pi$
$284$	−14.9789	−0.888837
$285$	0	0
$286$	4.89167	0.289251
$287$	5.95056	0.351251
$288$	1.60147	0.0943673
$289$	16.0230	0.942532
$290$	8.56469	0.502936
$291$	14.9863	0.878511
$292$	−3.74657	−0.219251
$293$	−3.10833	−0.181591	−0.0907953	−	0.995870i	$-0.528941\pi$
$293$	−3.10833	−0.181591	−0.0907953	+	0.995870i	$0.528941\pi$
$294$	2.92112	0.170363
$295$	−4.07355	−0.237171
$296$	7.49314	0.435530
$297$	3.00000	0.174078
$298$	−12.0735	−0.699402
$299$	37.8937	2.19145
$300$	−5.22399	−0.301607
$301$	−30.9083	−1.78153
$302$	4.91273	0.282696
$303$	−2.58041	−0.148241
$304$	0	0
$305$	−21.6088	−1.23732
$306$	−9.20293	−0.526097
$307$	−2.18920	−0.124944	−0.0624722	−	0.998047i	$-0.519898\pi$
$307$	−2.18920	−0.124944	−0.0624722	+	0.998047i	$0.519898\pi$
$308$	−2.89167	−0.164768
$309$	−36.2049	−2.05963
$310$	−11.9074	−0.676294
$311$	3.92112	0.222346	0.111173	−	0.993801i	$-0.464539\pi$
$311$	3.92112	0.222346	0.111173	+	0.993801i	$0.464539\pi$
$312$	−10.4931	−0.594057
$313$	−21.7118	−1.22722	−0.613611	−	0.789608i	$-0.710284\pi$
$313$	−21.7118	−1.22722	−0.613611	+	0.789608i	$0.710284\pi$
$314$	8.00733	0.451880
$315$	−7.41625	−0.417858
$316$	8.69607	0.489192
$317$	−6.90739	−0.387958	−0.193979	−	0.981006i	$-0.562139\pi$
$317$	−6.90739	−0.387958	−0.193979	+	0.981006i	$0.562139\pi$
$318$	−17.8622	−1.00166
$319$	5.34803	0.299432
$320$	−1.60147	−0.0895246
$321$	17.2397	0.962226
$322$	−22.4005	−1.24833
$323$	0	0
$324$	−11.2397	−0.624428
$325$	11.9127	0.660799
$326$	1.88434	0.104364
$327$	−24.7328	−1.36773
$328$	2.05783	0.113625
$329$	−20.4941	−1.12987
$330$	3.43531	0.189107
$331$	−32.1030	−1.76454	−0.882270	−	0.470744i	$-0.843986\pi$
$331$	−32.1030	−1.76454	−0.882270	+	0.470744i	$0.843986\pi$
$332$	−6.10833	−0.335238
$333$	12.0000	0.657596
$334$	4.98627	0.272837
$335$	−16.6309	−0.908644
$336$	6.20293	0.338398
$337$	1.55096	0.0844864	0.0422432	−	0.999107i	$-0.486550\pi$
$337$	1.55096	0.0844864	0.0422432	+	0.999107i	$0.486550\pi$
$338$	10.9284	0.594429
$339$	17.1608	0.932048
$340$	9.20293	0.499099
$341$	−7.43531	−0.402645
$342$	0	0
$343$	−16.3039	−0.880330
$344$	−10.6887	−0.576298
$345$	26.6118	1.43273
$346$	−6.51419	−0.350205
$347$	−0.506864	−0.0272099	−0.0136049	−	0.999907i	$-0.504331\pi$
$347$	−0.506864	−0.0272099	−0.0136049	+	0.999907i	$0.504331\pi$
$348$	−11.4721	−0.614968
$349$	10.8117	0.578738	0.289369	−	0.957218i	$-0.406554\pi$
$349$	10.8117	0.578738	0.289369	+	0.957218i	$0.406554\pi$
$350$	−7.04211	−0.376417
$351$	14.6750	0.783294
$352$	−1.00000	−0.0533002
$353$	27.0966	1.44221	0.721103	−	0.692828i	$-0.243635\pi$
$353$	27.0966	1.44221	0.721103	+	0.692828i	$0.243635\pi$
$354$	5.45636	0.290002
$355$	23.9883	1.27316
$356$	−3.20293	−0.169755
$357$	−35.6456	−1.88656
$358$	5.55096	0.293378
$359$	−20.7486	−1.09507	−0.547534	−	0.836784i	$-0.684433\pi$
$359$	−20.7486	−1.09507	−0.547534	+	0.836784i	$0.684433\pi$
$360$	−2.56469	−0.135171
$361$	0	0
$362$	−1.88434	−0.0990389
$363$	2.14510	0.112589
$364$	−14.1451	−0.741405
$365$	6.00000	0.314054
$366$	28.9442	1.51294
$367$	25.6402	1.33841	0.669205	−	0.743078i	$-0.266635\pi$
$367$	25.6402	1.33841	0.669205	+	0.743078i	$0.266635\pi$
$368$	−7.74657	−0.403818
$369$	3.29554	0.171559
$370$	−12.0000	−0.623850
$371$	−24.0789	−1.25011
$372$	15.9495	0.826943
$373$	−25.2049	−1.30506	−0.652531	−	0.757762i	$-0.726293\pi$
$373$	−25.2049	−1.30506	−0.652531	+	0.757762i	$0.726293\pi$
$374$	5.74657	0.297148
$375$	25.5426	1.31901
$376$	−7.08727	−0.365498
$377$	26.1608	1.34735
$378$	−8.67501	−0.446195
$379$	−3.47208	−0.178349	−0.0891744	−	0.996016i	$-0.528423\pi$
$379$	−3.47208	−0.178349	−0.0891744	+	0.996016i	$0.528423\pi$
$380$	0	0
$381$	45.6402	2.33822
$382$	2.44264	0.124976
$383$	−23.1176	−1.18126	−0.590628	−	0.806944i	$-0.701120\pi$
$383$	−23.1176	−1.18126	−0.590628	+	0.806944i	$0.701120\pi$
$384$	2.14510	0.109467
$385$	4.63091	0.236013
$386$	9.67501	0.492445
$387$	−17.1176	−0.870139
$388$	6.98627	0.354674
$389$	−26.7623	−1.35690	−0.678451	−	0.734646i	$-0.737348\pi$
$389$	−26.7623	−1.35690	−0.678451	+	0.734646i	$0.737348\pi$
$390$	16.8044	0.850924
$391$	44.5162	2.25128
$392$	1.36176	0.0687793
$393$	−7.36909	−0.371721
$394$	−17.4931	−0.881291
$395$	−13.9265	−0.700716
$396$	−1.60147	−0.0804767
$397$	−31.1030	−1.56101	−0.780507	−	0.625147i	$-0.785039\pi$
$397$	−31.1030	−1.56101	−0.780507	+	0.625147i	$0.785039\pi$
$398$	−25.2397	−1.26515
$399$	0	0
$400$	−2.43531	−0.121765
$401$	−29.3500	−1.46567	−0.732835	−	0.680406i	$-0.761803\pi$
$401$	−29.3500	−1.46567	−0.732835	+	0.680406i	$0.761803\pi$
$402$	22.2765	1.11105
$403$	−36.3711	−1.81177
$404$	−1.20293	−0.0598481
$405$	18.0000	0.894427
$406$	−15.4648	−0.767503
$407$	−7.49314	−0.371421
$408$	−12.3270	−0.610276
$409$	−8.58774	−0.424636	−0.212318	−	0.977201i	$-0.568101\pi$
$409$	−8.58774	−0.424636	−0.212318	+	0.977201i	$0.568101\pi$
$410$	−3.29554	−0.162755
$411$	29.1471	1.43772
$412$	−16.8779	−0.831517
$413$	7.35536	0.361934
$414$	−12.4059	−0.609715
$415$	9.78228	0.480193
$416$	−4.89167	−0.239834
$417$	6.85490	0.335686
$418$	0	0
$419$	7.59414	0.370998	0.185499	−	0.982644i	$-0.440610\pi$
$419$	7.59414	0.370998	0.185499	+	0.982644i	$0.440610\pi$
$420$	−9.93378	−0.484719
$421$	−8.76030	−0.426951	−0.213475	−	0.976948i	$-0.568478\pi$
$421$	−8.76030	−0.426951	−0.213475	+	0.976948i	$0.568478\pi$
$422$	14.8338	0.722100
$423$	−11.3500	−0.551857
$424$	−8.32698	−0.404394
$425$	13.9947	0.678841
$426$	−32.1314	−1.55677
$427$	39.0177	1.88820
$428$	8.03677	0.388472
$429$	10.4931	0.506613
$430$	17.1176	0.825486
$431$	33.6677	1.62172	0.810858	−	0.585243i	$-0.199001\pi$
$431$	33.6677	1.62172	0.810858	+	0.585243i	$0.199001\pi$
$432$	−3.00000	−0.144338
$433$	−30.5383	−1.46758	−0.733789	−	0.679378i	$-0.762250\pi$
$433$	−30.5383	−1.46758	−0.733789	+	0.679378i	$0.762250\pi$
$434$	21.5005	1.03206
$435$	18.3721	0.880877
$436$	−11.5299	−0.552183
$437$	0	0
$438$	−8.03677	−0.384012
$439$	12.5069	0.596920	0.298460	−	0.954422i	$-0.403527\pi$
$439$	12.5069	0.596920	0.298460	+	0.954422i	$0.403527\pi$
$440$	1.60147	0.0763469
$441$	2.18081	0.103848
$442$	28.1103	1.33707
$443$	−17.6677	−0.839417	−0.419709	−	0.907659i	$-0.637868\pi$
$443$	−17.6677	−0.839417	−0.419709	+	0.907659i	$0.637868\pi$
$444$	16.0735	0.762817
$445$	5.12938	0.243156
$446$	−11.4931	−0.544216
$447$	−25.8990	−1.22498
$448$	2.89167	0.136619
$449$	17.7098	0.835777	0.417888	−	0.908498i	$-0.362770\pi$
$449$	17.7098	0.835777	0.417888	+	0.908498i	$0.362770\pi$
$450$	−3.90006	−0.183851
$451$	−2.05783	−0.0968994
$452$	8.00000	0.376288
$453$	10.5383	0.495133
$454$	−8.73284	−0.409853
$455$	22.6529	1.06198
$456$	0	0
$457$	−24.8064	−1.16039	−0.580197	−	0.814476i	$-0.697024\pi$
$457$	−24.8064	−1.16039	−0.580197	+	0.814476i	$0.697024\pi$
$458$	7.84117	0.366394
$459$	17.2397	0.804681
$460$	12.4059	0.578426
$461$	−2.98627	−0.139085	−0.0695423	−	0.997579i	$-0.522154\pi$
$461$	−2.98627	−0.139085	−0.0695423	+	0.997579i	$0.522154\pi$
$462$	−6.20293	−0.288586
$463$	−39.5667	−1.83882	−0.919410	−	0.393301i	$-0.871333\pi$
$463$	−39.5667	−1.83882	−0.919410	+	0.393301i	$0.871333\pi$
$464$	−5.34803	−0.248276
$465$	−25.5426	−1.18451
$466$	−12.5069	−0.579369
$467$	4.46475	0.206604	0.103302	−	0.994650i	$-0.467059\pi$
$467$	4.46475	0.206604	0.103302	+	0.994650i	$0.467059\pi$
$468$	−7.83384	−0.362119
$469$	30.0294	1.38663
$470$	11.3500	0.523538
$471$	17.1765	0.791453
$472$	2.54364	0.117080
$473$	10.6887	0.491469
$474$	18.6540	0.856805
$475$	0	0
$476$	−16.6172	−0.761647
$477$	−13.3354	−0.610585
$478$	24.6245	1.12630
$479$	−20.8863	−0.954321	−0.477161	−	0.878816i	$-0.658334\pi$
$479$	−20.8863	−0.954321	−0.477161	+	0.878816i	$0.658334\pi$
$480$	−3.43531	−0.156800
$481$	−36.6540	−1.67128
$482$	−16.0809	−0.732464
$483$	−48.0514	−2.18642
$484$	1.00000	0.0454545
$485$	−11.1883	−0.508033
$486$	−15.1103	−0.685418
$487$	−15.2838	−0.692575	−0.346288	−	0.938128i	$-0.612558\pi$
$487$	−15.2838	−0.692575	−0.346288	+	0.938128i	$0.612558\pi$
$488$	13.4931	0.610806
$489$	4.04211	0.182791
$490$	−2.18081	−0.0985191
$491$	3.31965	0.149814	0.0749069	−	0.997191i	$-0.476134\pi$
$491$	3.31965	0.149814	0.0749069	+	0.997191i	$0.476134\pi$
$492$	4.41425	0.199010
$493$	30.7328	1.38414
$494$	0	0
$495$	2.56469	0.115274
$496$	7.43531	0.333855
$497$	−43.3142	−1.94291
$498$	−13.1030	−0.587159
$499$	−2.07355	−0.0928247	−0.0464124	−	0.998922i	$-0.514779\pi$
$499$	−2.07355	−0.0928247	−0.0464124	+	0.998922i	$0.514779\pi$
$500$	11.9074	0.532515
$501$	10.6961	0.477865
$502$	13.0873	0.584114
$503$	−1.11672	−0.0497921	−0.0248960	−	0.999690i	$-0.507925\pi$
$503$	−1.11672	−0.0497921	−0.0248960	+	0.999690i	$0.507925\pi$
$504$	4.63091	0.206277
$505$	1.92645	0.0857260
$506$	7.74657	0.344377
$507$	23.4426	1.04112
$508$	21.2765	0.943991
$509$	38.2481	1.69532	0.847659	−	0.530542i	$-0.178012\pi$
$509$	38.2481	1.69532	0.847659	+	0.530542i	$0.178012\pi$
$510$	19.7412	0.874156
$511$	−10.8338	−0.479261
$512$	1.00000	0.0441942
$513$	0	0
$514$	−0.723522	−0.0319132
$515$	27.0294	1.19106
$516$	−22.9284	−1.00937
$517$	7.08727	0.311698
$518$	21.6677	0.952023
$519$	−13.9736	−0.613373
$520$	7.83384	0.343537
$521$	−10.8853	−0.476892	−0.238446	−	0.971156i	$-0.576638\pi$
$521$	−10.8853	−0.476892	−0.238446	+	0.971156i	$0.576638\pi$
$522$	−8.56469	−0.374866
$523$	15.7191	0.687349	0.343674	−	0.939089i	$-0.388328\pi$
$523$	15.7191	0.687349	0.343674	+	0.939089i	$0.388328\pi$
$524$	−3.43531	−0.150072
$525$	−15.1060	−0.659282
$526$	13.7760	0.600663
$527$	−42.7275	−1.86124
$528$	−2.14510	−0.0933536
$529$	37.0093	1.60910
$530$	13.3354	0.579251
$531$	4.07355	0.176777
$532$	0	0
$533$	−10.0662	−0.436016
$534$	−6.87062	−0.297321
$535$	−12.8706	−0.556445
$536$	10.3848	0.448555
$537$	11.9074	0.513842
$538$	19.9579	0.860446
$539$	−1.36176	−0.0586552
$540$	4.80440	0.206748
$541$	−26.4373	−1.13663	−0.568314	−	0.822812i	$-0.692404\pi$
$541$	−26.4373	−1.13663	−0.568314	+	0.822812i	$0.692404\pi$
$542$	28.7486	1.23486
$543$	−4.04211	−0.173464
$544$	−5.74657	−0.246382
$545$	18.4648	0.790943
$546$	−30.3427	−1.29855
$547$	24.9588	1.06716	0.533581	−	0.845749i	$-0.320846\pi$
$547$	24.9588	1.06716	0.533581	+	0.845749i	$0.320846\pi$
$548$	13.5877	0.580439
$549$	21.6088	0.922241
$550$	2.43531	0.103842
$551$	0	0
$552$	−16.6172	−0.707274
$553$	25.1462	1.06932
$554$	3.08727	0.131166
$555$	−25.7412	−1.09265
$556$	3.19560	0.135524
$557$	8.30486	0.351888	0.175944	−	0.984400i	$-0.443702\pi$
$557$	8.30486	0.351888	0.175944	+	0.984400i	$0.443702\pi$
$558$	11.9074	0.504080
$559$	52.2858	2.21145
$560$	−4.63091	−0.195692
$561$	12.3270	0.520445
$562$	−9.09460	−0.383633
$563$	−41.6402	−1.75493	−0.877463	−	0.479644i	$-0.840766\pi$
$563$	−41.6402	−1.75493	−0.877463	+	0.479644i	$0.840766\pi$
$564$	−15.2029	−0.640159
$565$	−12.8117	−0.538993
$566$	13.1451	0.552530
$567$	−32.5015	−1.36494
$568$	−14.9789	−0.628503
$569$	14.9138	0.625219	0.312609	−	0.949882i	$-0.398797\pi$
$569$	14.9138	0.625219	0.312609	+	0.949882i	$0.398797\pi$
$570$	0	0
$571$	−23.0020	−0.962603	−0.481302	−	0.876555i	$-0.659836\pi$
$571$	−23.0020	−0.962603	−0.481302	+	0.876555i	$0.659836\pi$
$572$	4.89167	0.204531
$573$	5.23970	0.218892
$574$	5.95056	0.248372
$575$	18.8653	0.786737
$576$	1.60147	0.0667277
$577$	−33.6613	−1.40134	−0.700669	−	0.713487i	$-0.747115\pi$
$577$	−33.6613	−1.40134	−0.700669	+	0.713487i	$0.747115\pi$
$578$	16.0230	0.666471
$579$	20.7539	0.862502
$580$	8.56469	0.355629
$581$	−17.6633	−0.732796
$582$	14.9863	0.621201
$583$	8.32698	0.344868
$584$	−3.74657	−0.155034
$585$	12.5456	0.518698
$586$	−3.10833	−0.128404
$587$	4.00000	0.165098	0.0825488	−	0.996587i	$-0.473694\pi$
$587$	4.00000	0.165098	0.0825488	+	0.996587i	$0.473694\pi$
$588$	2.92112	0.120465
$589$	0	0
$590$	−4.07355	−0.167705
$591$	−37.5246	−1.54355
$592$	7.49314	0.307966
$593$	−30.9588	−1.27133	−0.635663	−	0.771967i	$-0.719273\pi$
$593$	−30.9588	−1.27133	−0.635663	+	0.771967i	$0.719273\pi$
$594$	3.00000	0.123091
$595$	26.6118	1.09098
$596$	−12.0735	−0.494552
$597$	−54.1418	−2.21587
$598$	37.8937	1.54959
$599$	−3.93378	−0.160730	−0.0803650	−	0.996766i	$-0.525609\pi$
$599$	−3.93378	−0.160730	−0.0803650	+	0.996766i	$0.525609\pi$
$600$	−5.22399	−0.213268
$601$	−23.1451	−0.944108	−0.472054	−	0.881570i	$-0.656487\pi$
$601$	−23.1451	−0.944108	−0.472054	+	0.881570i	$0.656487\pi$
$602$	−30.9083	−1.25973
$603$	16.6309	0.677263
$604$	4.91273	0.199896
$605$	−1.60147	−0.0651088
$606$	−2.58041	−0.104822
$607$	1.78334	0.0723836	0.0361918	−	0.999345i	$-0.488477\pi$
$607$	1.78334	0.0723836	0.0361918	+	0.999345i	$0.488477\pi$
$608$	0	0
$609$	−33.1735	−1.34426
$610$	−21.6088	−0.874914
$611$	34.6686	1.40254
$612$	−9.20293	−0.372006
$613$	−33.0598	−1.33527	−0.667637	−	0.744487i	$-0.732694\pi$
$613$	−33.0598	−1.33527	−0.667637	+	0.744487i	$0.732694\pi$
$614$	−2.18920	−0.0883491
$615$	−7.06927	−0.285061
$616$	−2.89167	−0.116509
$617$	−21.8412	−0.879292	−0.439646	−	0.898171i	$-0.644896\pi$
$617$	−21.8412	−0.879292	−0.439646	+	0.898171i	$0.644896\pi$
$618$	−36.2049	−1.45638
$619$	−46.2206	−1.85776	−0.928882	−	0.370375i	$-0.879229\pi$
$619$	−46.2206	−1.85776	−0.928882	+	0.370375i	$0.879229\pi$
$620$	−11.9074	−0.478212
$621$	23.2397	0.932577
$622$	3.92112	0.157222
$623$	−9.26182	−0.371067
$624$	−10.4931	−0.420062
$625$	−6.89273	−0.275709
$626$	−21.7118	−0.867778
$627$	0	0
$628$	8.00733	0.319527
$629$	−43.0598	−1.71691
$630$	−7.41625	−0.295470
$631$	0.317659	0.0126458	0.00632291	−	0.999980i	$-0.497987\pi$
$631$	0.317659	0.0126458	0.00632291	+	0.999980i	$0.497987\pi$
$632$	8.69607	0.345911
$633$	31.8201	1.26474
$634$	−6.90739	−0.274327
$635$	−34.0735	−1.35217
$636$	−17.8622	−0.708283
$637$	−6.66129	−0.263930
$638$	5.34803	0.211731
$639$	−23.9883	−0.948961
$640$	−1.60147	−0.0633035
$641$	41.5246	1.64012	0.820061	−	0.572276i	$-0.193939\pi$
$641$	41.5246	1.64012	0.820061	+	0.572276i	$0.193939\pi$
$642$	17.2397	0.680397
$643$	7.26182	0.286378	0.143189	−	0.989695i	$-0.454264\pi$
$643$	7.26182	0.286378	0.143189	+	0.989695i	$0.454264\pi$
$644$	−22.4005	−0.882704
$645$	36.7191	1.44581
$646$	0	0
$647$	29.0819	1.14333	0.571664	−	0.820487i	$-0.306298\pi$
$647$	29.0819	1.14333	0.571664	+	0.820487i	$0.306298\pi$
$648$	−11.2397	−0.441537
$649$	−2.54364	−0.0998465
$650$	11.9127	0.467256
$651$	46.1207	1.80761
$652$	1.88434	0.0737966
$653$	12.6529	0.495146	0.247573	−	0.968869i	$-0.420367\pi$
$653$	12.6529	0.495146	0.247573	+	0.968869i	$0.420367\pi$
$654$	−24.7328	−0.967131
$655$	5.50153	0.214962
$656$	2.05783	0.0803447
$657$	−6.00000	−0.234082
$658$	−20.4941	−0.798942
$659$	−49.4878	−1.92777	−0.963886	−	0.266317i	$-0.914193\pi$
$659$	−49.4878	−1.92777	−0.963886	+	0.266317i	$0.914193\pi$
$660$	3.43531	0.133719
$661$	−4.94950	−0.192513	−0.0962566	−	0.995357i	$-0.530687\pi$
$661$	−4.94950	−0.192513	−0.0962566	+	0.995357i	$0.530687\pi$
$662$	−32.1030	−1.24772
$663$	60.2995	2.34184
$664$	−6.10833	−0.237049
$665$	0	0
$666$	12.0000	0.464991
$667$	41.4289	1.60413
$668$	4.98627	0.192925
$669$	−24.6540	−0.953177
$670$	−16.6309	−0.642508
$671$	−13.4931	−0.520897
$672$	6.20293	0.239283
$673$	−21.9001	−0.844185	−0.422093	−	0.906553i	$-0.638704\pi$
$673$	−21.9001	−0.844185	−0.422093	+	0.906553i	$0.638704\pi$
$674$	1.55096	0.0597409
$675$	7.30592	0.281205
$676$	10.9284	0.420325
$677$	−26.4353	−1.01599	−0.507996	−	0.861360i	$-0.669613\pi$
$677$	−26.4353	−1.01599	−0.507996	+	0.861360i	$0.669613\pi$
$678$	17.1608	0.659057
$679$	20.2020	0.775282
$680$	9.20293	0.352916
$681$	−18.7328	−0.717844
$682$	−7.43531	−0.284713
$683$	−9.82545	−0.375960	−0.187980	−	0.982173i	$-0.560194\pi$
$683$	−9.82545	−0.375960	−0.187980	+	0.982173i	$0.560194\pi$
$684$	0	0
$685$	−21.7603	−0.831418
$686$	−16.3039	−0.622487
$687$	16.8201	0.641727
$688$	−10.6887	−0.407504
$689$	40.7328	1.55180
$690$	26.6118	1.01310
$691$	−19.8255	−0.754196	−0.377098	−	0.926173i	$-0.623078\pi$
$691$	−19.8255	−0.754196	−0.377098	+	0.926173i	$0.623078\pi$
$692$	−6.51419	−0.247632
$693$	−4.63091	−0.175914
$694$	−0.506864	−0.0192403
$695$	−5.11765	−0.194123
$696$	−11.4721	−0.434848
$697$	−11.8255	−0.447921
$698$	10.8117	0.409230
$699$	−26.8285	−1.01475
$700$	−7.04211	−0.266167
$701$	−10.7550	−0.406209	−0.203105	−	0.979157i	$-0.565103\pi$
$701$	−10.7550	−0.406209	−0.203105	+	0.979157i	$0.565103\pi$
$702$	14.6750	0.553873
$703$	0	0
$704$	−1.00000	−0.0376889
$705$	24.3470	0.916960
$706$	27.0966	1.01979
$707$	−3.47848	−0.130822
$708$	5.45636	0.205063
$709$	−1.82651	−0.0685962	−0.0342981	−	0.999412i	$-0.510920\pi$
$709$	−1.82651	−0.0685962	−0.0342981	+	0.999412i	$0.510920\pi$
$710$	23.9883	0.900264
$711$	13.9265	0.522283
$712$	−3.20293	−0.120035
$713$	−57.5981	−2.15707
$714$	−35.6456	−1.33400
$715$	−7.83384	−0.292969
$716$	5.55096	0.207449
$717$	52.8221	1.97268
$718$	−20.7486	−0.774329
$719$	−4.65929	−0.173762	−0.0868812	−	0.996219i	$-0.527690\pi$
$719$	−4.65929	−0.173762	−0.0868812	+	0.996219i	$0.527690\pi$
$720$	−2.56469	−0.0955804
$721$	−48.8055	−1.81761
$722$	0	0
$723$	−34.4951	−1.28289
$724$	−1.88434	−0.0700311
$725$	13.0241	0.483703
$726$	2.14510	0.0796122
$727$	19.9358	0.739377	0.369688	−	0.929156i	$-0.379464\pi$
$727$	19.9358	0.739377	0.369688	+	0.929156i	$0.379464\pi$
$728$	−14.1451	−0.524252
$729$	1.30592	0.0483676
$730$	6.00000	0.222070
$731$	61.4236	2.27183
$732$	28.9442	1.06981
$733$	13.7687	0.508558	0.254279	−	0.967131i	$-0.418162\pi$
$733$	13.7687	0.508558	0.254279	+	0.967131i	$0.418162\pi$
$734$	25.6402	0.946398
$735$	−4.67807	−0.172553
$736$	−7.74657	−0.285542
$737$	−10.3848	−0.382529
$738$	3.29554	0.121311
$739$	22.4867	0.827188	0.413594	−	0.910461i	$-0.364273\pi$
$739$	22.4867	0.827188	0.413594	+	0.910461i	$0.364273\pi$
$740$	−12.0000	−0.441129
$741$	0	0
$742$	−24.0789	−0.883964
$743$	50.6540	1.85831	0.929157	−	0.369686i	$-0.120535\pi$
$743$	50.6540	1.85831	0.929157	+	0.369686i	$0.120535\pi$
$744$	15.9495	0.584737
$745$	19.3354	0.708393
$746$	−25.2049	−0.922818
$747$	−9.78228	−0.357915
$748$	5.74657	0.210115
$749$	23.2397	0.849160
$750$	25.5426	0.932683
$751$	38.9127	1.41995	0.709973	−	0.704229i	$-0.248707\pi$
$751$	38.9127	1.41995	0.709973	+	0.704229i	$0.248707\pi$
$752$	−7.08727	−0.258446
$753$	28.0735	1.02306
$754$	26.1608	0.952721
$755$	−7.86756	−0.286330
$756$	−8.67501	−0.315507
$757$	−20.5877	−0.748274	−0.374137	−	0.927373i	$-0.622061\pi$
$757$	−20.5877	−0.748274	−0.374137	+	0.927373i	$0.622061\pi$
$758$	−3.47208	−0.126112
$759$	16.6172	0.603166
$760$	0	0
$761$	10.6025	0.384341	0.192171	−	0.981362i	$-0.438447\pi$
$761$	10.6025	0.384341	0.192171	+	0.981362i	$0.438447\pi$
$762$	45.6402	1.65337
$763$	−33.3407	−1.20701
$764$	2.44264	0.0883715
$765$	14.7382	0.532860
$766$	−23.1176	−0.835275
$767$	−12.4426	−0.449278
$768$	2.14510	0.0774047
$769$	−8.77495	−0.316433	−0.158216	−	0.987404i	$-0.550574\pi$
$769$	−8.77495	−0.316433	−0.158216	+	0.987404i	$0.550574\pi$
$770$	4.63091	0.166886
$771$	−1.55203	−0.0558949
$772$	9.67501	0.348211
$773$	46.8653	1.68563	0.842813	−	0.538206i	$-0.180898\pi$
$773$	46.8653	1.68563	0.842813	+	0.538206i	$0.180898\pi$
$774$	−17.1176	−0.615281
$775$	−18.1073	−0.650432
$776$	6.98627	0.250793
$777$	46.4794	1.66744
$778$	−26.7623	−0.959474
$779$	0	0
$780$	16.8044	0.601694
$781$	14.9789	0.535989
$782$	44.5162	1.59190
$783$	16.0441	0.573369
$784$	1.36176	0.0486343
$785$	−12.8235	−0.457689
$786$	−7.36909	−0.262847
$787$	27.4143	0.977213	0.488606	−	0.872504i	$-0.337505\pi$
$787$	27.4143	0.977213	0.488606	+	0.872504i	$0.337505\pi$
$788$	−17.4931	−0.623167
$789$	29.5510	1.05204
$790$	−13.9265	−0.495481
$791$	23.1334	0.822528
$792$	−1.60147	−0.0569056
$793$	−66.0040	−2.34387
$794$	−31.1030	−1.10380
$795$	28.6057	1.01454
$796$	−25.2397	−0.894598
$797$	9.16616	0.324682	0.162341	−	0.986735i	$-0.448096\pi$
$797$	9.16616	0.324682	0.162341	+	0.986735i	$0.448096\pi$
$798$	0	0
$799$	40.7275	1.44084
$800$	−2.43531	−0.0861011
$801$	−5.12938	−0.181238
$802$	−29.3500	−1.03639
$803$	3.74657	0.132214
$804$	22.2765	0.785631
$805$	35.8737	1.26438
$806$	−36.3711	−1.28112
$807$	42.8117	1.50704
$808$	−1.20293	−0.0423190
$809$	48.0829	1.69050	0.845252	−	0.534368i	$-0.179450\pi$
$809$	48.0829	1.69050	0.845252	+	0.534368i	$0.179450\pi$
$810$	18.0000	0.632456
$811$	2.67395	0.0938951	0.0469475	−	0.998897i	$-0.485051\pi$
$811$	2.67395	0.0938951	0.0469475	+	0.998897i	$0.485051\pi$
$812$	−15.4648	−0.542706
$813$	61.6686	2.16281
$814$	−7.49314	−0.262634
$815$	−3.01771	−0.105706
$816$	−12.3270	−0.431531
$817$	0	0
$818$	−8.58774	−0.300263
$819$	−22.6529	−0.791556
$820$	−3.29554	−0.115085
$821$	29.5078	1.02983	0.514915	−	0.857242i	$-0.327824\pi$
$821$	29.5078	1.02983	0.514915	+	0.857242i	$0.327824\pi$
$822$	29.1471	1.01662
$823$	−2.39654	−0.0835382	−0.0417691	−	0.999127i	$-0.513299\pi$
$823$	−2.39654	−0.0835382	−0.0417691	+	0.999127i	$0.513299\pi$
$824$	−16.8779	−0.587971
$825$	5.22399	0.181876
$826$	7.35536	0.255926
$827$	−7.78868	−0.270839	−0.135419	−	0.990788i	$-0.543238\pi$
$827$	−7.78868	−0.270839	−0.135419	+	0.990788i	$0.543238\pi$
$828$	−12.4059	−0.431134
$829$	−13.2818	−0.461296	−0.230648	−	0.973037i	$-0.574085\pi$
$829$	−13.2818	−0.461296	−0.230648	+	0.973037i	$0.574085\pi$
$830$	9.78228	0.339548
$831$	6.62252	0.229733
$832$	−4.89167	−0.169588
$833$	−7.82545	−0.271136
$834$	6.85490	0.237366
$835$	−7.98534	−0.276344
$836$	0	0
$837$	−22.3059	−0.771006
$838$	7.59414	0.262335
$839$	33.9063	1.17058	0.585288	−	0.810825i	$-0.300981\pi$
$839$	33.9063	1.17058	0.585288	+	0.810825i	$0.300981\pi$
$840$	−9.93378	−0.342748
$841$	−0.398534	−0.0137426
$842$	−8.76030	−0.301900
$843$	−19.5089	−0.671921
$844$	14.8338	0.510602
$845$	−17.5015	−0.602071
$846$	−11.3500	−0.390222
$847$	2.89167	0.0993590
$848$	−8.32698	−0.285950
$849$	28.1976	0.967739
$850$	13.9947	0.480013
$851$	−58.0461	−1.98979
$852$	−32.1314	−1.10080
$853$	40.0735	1.37209	0.686046	−	0.727558i	$-0.259345\pi$
$853$	40.0735	1.37209	0.686046	+	0.727558i	$0.259345\pi$
$854$	39.0177	1.33516
$855$	0	0
$856$	8.03677	0.274691
$857$	−0.665693	−0.0227396	−0.0113698	−	0.999935i	$-0.503619\pi$
$857$	−0.665693	−0.0227396	−0.0113698	+	0.999935i	$0.503619\pi$
$858$	10.4931	0.358230
$859$	13.8990	0.474228	0.237114	−	0.971482i	$-0.423799\pi$
$859$	13.8990	0.474228	0.237114	+	0.971482i	$0.423799\pi$
$860$	17.1176	0.583707
$861$	12.7646	0.435015
$862$	33.6677	1.14673
$863$	40.3941	1.37503	0.687516	−	0.726169i	$-0.258701\pi$
$863$	40.3941	1.37503	0.687516	+	0.726169i	$0.258701\pi$
$864$	−3.00000	−0.102062
$865$	10.4323	0.354707
$866$	−30.5383	−1.03773
$867$	34.3711	1.16730
$868$	21.5005	0.729773
$869$	−8.69607	−0.294994
$870$	18.3721	0.622874
$871$	−50.7991	−1.72126
$872$	−11.5299	−0.390452
$873$	11.1883	0.378666
$874$	0	0
$875$	34.4323	1.16402
$876$	−8.03677	−0.271537
$877$	−15.6108	−0.527139	−0.263569	−	0.964640i	$-0.584900\pi$
$877$	−15.6108	−0.527139	−0.263569	+	0.964640i	$0.584900\pi$
$878$	12.5069	0.422086
$879$	−6.66769	−0.224895
$880$	1.60147	0.0539854
$881$	19.9843	0.673288	0.336644	−	0.941632i	$-0.390708\pi$
$881$	19.9843	0.673288	0.336644	+	0.941632i	$0.390708\pi$
$882$	2.18081	0.0734318
$883$	20.2167	0.680345	0.340172	−	0.940363i	$-0.389515\pi$
$883$	20.2167	0.680345	0.340172	+	0.940363i	$0.389515\pi$
$884$	28.1103	0.945452
$885$	−8.73818	−0.293731
$886$	−17.6677	−0.593557
$887$	−20.1471	−0.676473	−0.338237	−	0.941061i	$-0.609830\pi$
$887$	−20.1471	−0.676473	−0.338237	+	0.941061i	$0.609830\pi$
$888$	16.0735	0.539393
$889$	61.5246	2.06347
$890$	5.12938	0.171937
$891$	11.2397	0.376544
$892$	−11.4931	−0.384819
$893$	0	0
$894$	−25.8990	−0.866192
$895$	−8.88968	−0.297149
$896$	2.89167	0.0966039
$897$	81.2858	2.71405
$898$	17.7098	0.590984
$899$	−39.7643	−1.32621
$900$	−3.90006	−0.130002
$901$	47.8516	1.59417
$902$	−2.05783	−0.0685182
$903$	−66.3015	−2.20638
$904$	8.00000	0.266076
$905$	3.01771	0.100312
$906$	10.5383	0.350112
$907$	−4.57109	−0.151781	−0.0758903	−	0.997116i	$-0.524180\pi$
$907$	−4.57109	−0.151781	−0.0758903	+	0.997116i	$0.524180\pi$
$908$	−8.73284	−0.289810
$909$	−1.92645	−0.0638964
$910$	22.6529	0.750936
$911$	−51.6402	−1.71092	−0.855459	−	0.517871i	$-0.826725\pi$
$911$	−51.6402	−1.71092	−0.855459	+	0.517871i	$0.826725\pi$
$912$	0	0
$913$	6.10833	0.202156
$914$	−24.8064	−0.820522
$915$	−46.3531	−1.53239
$916$	7.84117	0.259080
$917$	−9.93378	−0.328042
$918$	17.2397	0.568995
$919$	−48.8412	−1.61112	−0.805561	−	0.592513i	$-0.798136\pi$
$919$	−48.8412	−1.61112	−0.805561	+	0.592513i	$0.798136\pi$
$920$	12.4059	0.409009
$921$	−4.69607	−0.154741
$922$	−2.98627	−0.0983477
$923$	73.2721	2.41178
$924$	−6.20293	−0.204061
$925$	−18.2481	−0.599994
$926$	−39.5667	−1.30024
$927$	−27.0294	−0.887763
$928$	−5.34803	−0.175558
$929$	−57.8819	−1.89904	−0.949522	−	0.313700i	$-0.898431\pi$
$929$	−57.8819	−1.89904	−0.949522	+	0.313700i	$0.898431\pi$
$930$	−25.5426	−0.837574
$931$	0	0
$932$	−12.5069	−0.409676
$933$	8.41120	0.275370
$934$	4.46475	0.146091
$935$	−9.20293	−0.300968
$936$	−7.83384	−0.256057
$937$	−57.6496	−1.88333	−0.941664	−	0.336553i	$-0.890739\pi$
$937$	−57.6496	−1.88333	−0.941664	+	0.336553i	$0.890739\pi$
$938$	30.0294	0.980496
$939$	−46.5740	−1.51989
$940$	11.3500	0.370197
$941$	15.0966	0.492135	0.246067	−	0.969253i	$-0.420862\pi$
$941$	15.0966	0.492135	0.246067	+	0.969253i	$0.420862\pi$
$942$	17.1765	0.559642
$943$	−15.9411	−0.519114
$944$	2.54364	0.0827883
$945$	13.8927	0.451931
$946$	10.6887	0.347521
$947$	33.3775	1.08462	0.542311	−	0.840178i	$-0.317549\pi$
$947$	33.3775	1.08462	0.542311	+	0.840178i	$0.317549\pi$
$948$	18.6540	0.605852
$949$	18.3270	0.594919
$950$	0	0
$951$	−14.8171	−0.480476
$952$	−16.6172	−0.538566
$953$	12.4794	0.404248	0.202124	−	0.979360i	$-0.435216\pi$
$953$	12.4794	0.404248	0.202124	+	0.979360i	$0.435216\pi$
$954$	−13.3354	−0.431749
$955$	−3.91180	−0.126583
$956$	24.6245	0.796414
$957$	11.4721	0.370840
$958$	−20.8863	−0.674807
$959$	39.2913	1.26878
$960$	−3.43531	−0.110874
$961$	24.2838	0.783349
$962$	−36.6540	−1.18177
$963$	12.8706	0.414750
$964$	−16.0809	−0.517930
$965$	−15.4942	−0.498776
$966$	−48.0514	−1.54603
$967$	−12.5804	−0.404559	−0.202279	−	0.979328i	$-0.564835\pi$
$967$	−12.5804	−0.404559	−0.202279	+	0.979328i	$0.564835\pi$
$968$	1.00000	0.0321412
$969$	0	0
$970$	−11.1883	−0.359234
$971$	1.79067	0.0574653	0.0287327	−	0.999587i	$-0.490853\pi$
$971$	1.79067	0.0574653	0.0287327	+	0.999587i	$0.490853\pi$
$972$	−15.1103	−0.484664
$973$	9.24063	0.296241
$974$	−15.2838	−0.489725
$975$	25.5540	0.818384
$976$	13.4931	0.431905
$977$	−6.40586	−0.204942	−0.102471	−	0.994736i	$-0.532675\pi$
$977$	−6.40586	−0.204942	−0.102471	+	0.994736i	$0.532675\pi$
$978$	4.04211	0.129252
$979$	3.20293	0.102366
$980$	−2.18081	−0.0696635
$981$	−18.4648	−0.589534
$982$	3.31965	0.105934
$983$	20.5647	0.655912	0.327956	−	0.944693i	$-0.393640\pi$
$983$	20.5647	0.655912	0.327956	+	0.944693i	$0.393640\pi$
$984$	4.41425	0.140721
$985$	28.0147	0.892621
$986$	30.7328	0.978733
$987$	−43.9619	−1.39932
$988$	0	0
$989$	82.8011	2.63292
$990$	2.56469	0.0815113
$991$	29.0166	0.921744	0.460872	−	0.887467i	$-0.347537\pi$
$991$	29.0166	0.921744	0.460872	+	0.887467i	$0.347537\pi$
$992$	7.43531	0.236071
$993$	−68.8642	−2.18534
$994$	−43.3142	−1.37384
$995$	40.4205	1.28142
$996$	−13.1030	−0.415184
$997$	42.3638	1.34167	0.670837	−	0.741605i	$-0.265935\pi$
$997$	42.3638	1.34167	0.670837	+	0.741605i	$0.265935\pi$
$998$	−2.07355	−0.0656370
$999$	−22.4794	−0.711217

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7942.2.a.bi.1.3		3
19.18	odd	2		418.2.a.g.1.1	✓	3
57.56	even	2		3762.2.a.bg.1.2		3
76.75	even	2		3344.2.a.q.1.3		3
209.208	even	2		4598.2.a.bo.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
418.2.a.g.1.1	✓	3	19.18	odd	2
3344.2.a.q.1.3		3	76.75	even	2
3762.2.a.bg.1.2		3	57.56	even	2
4598.2.a.bo.1.1		3	209.208	even	2
7942.2.a.bi.1.3		3	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:	\( N \)	\(=\)	\( 7942 = 2 \cdot 11 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7942.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} +2.14510 q^{6} +2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.14510 q^{3} +1.00000 q^{4} -1.60147 q^{5} +2.14510 q^{6} +2.89167 q^{7} +1.00000 q^{8} +1.60147 q^{9} -1.60147 q^{10} -1.00000 q^{11} +2.14510 q^{12} -4.89167 q^{13} +2.89167 q^{14} -3.43531 q^{15} +1.00000 q^{16} -5.74657 q^{17} +1.60147 q^{18} -1.60147 q^{20} +6.20293 q^{21} -1.00000 q^{22} -7.74657 q^{23} +2.14510 q^{24} -2.43531 q^{25} -4.89167 q^{26} -3.00000 q^{27} +2.89167 q^{28} -5.34803 q^{29} -3.43531 q^{30} +7.43531 q^{31} +1.00000 q^{32} -2.14510 q^{33} -5.74657 q^{34} -4.63091 q^{35} +1.60147 q^{36} +7.49314 q^{37} -10.4931 q^{39} -1.60147 q^{40} +2.05783 q^{41} +6.20293 q^{42} -10.6887 q^{43} -1.00000 q^{44} -2.56469 q^{45} -7.74657 q^{46} -7.08727 q^{47} +2.14510 q^{48} +1.36176 q^{49} -2.43531 q^{50} -12.3270 q^{51} -4.89167 q^{52} -8.32698 q^{53} -3.00000 q^{54} +1.60147 q^{55} +2.89167 q^{56} -5.34803 q^{58} +2.54364 q^{59} -3.43531 q^{60} +13.4931 q^{61} +7.43531 q^{62} +4.63091 q^{63} +1.00000 q^{64} +7.83384 q^{65} -2.14510 q^{66} +10.3848 q^{67} -5.74657 q^{68} -16.6172 q^{69} -4.63091 q^{70} -14.9789 q^{71} +1.60147 q^{72} -3.74657 q^{73} +7.49314 q^{74} -5.22399 q^{75} -2.89167 q^{77} -10.4931 q^{78} +8.69607 q^{79} -1.60147 q^{80} -11.2397 q^{81} +2.05783 q^{82} -6.10833 q^{83} +6.20293 q^{84} +9.20293 q^{85} -10.6887 q^{86} -11.4721 q^{87} -1.00000 q^{88} -3.20293 q^{89} -2.56469 q^{90} -14.1451 q^{91} -7.74657 q^{92} +15.9495 q^{93} -7.08727 q^{94} +2.14510 q^{96} +6.98627 q^{97} +1.36176 q^{98} -1.60147 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9}+O(q^{10}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9	\( 3 q + 3 q^{2} + 3 q^{4} - 3 q^{5} - 6 q^{7} + 3 q^{8} + 3 q^{9} - 3 q^{10} - 3 q^{11} - 6 q^{14} + 9 q^{15} + 3 q^{16} - 9 q^{17} + 3 q^{18} - 3 q^{20} + 15 q^{21} - 3 q^{22} - 15 q^{23} + 12 q^{25} - 9 q^{27} - 6 q^{28} - 6 q^{29} + 9 q^{30} + 3 q^{31} + 3 q^{32} - 9 q^{34} + 3 q^{36} + 6 q^{37} - 15 q^{39} - 3 q^{40} + 9 q^{41} + 15 q^{42} - 21 q^{43} - 3 q^{44} - 27 q^{45} - 15 q^{46} - 12 q^{47} + 27 q^{49} + 12 q^{50} - 3 q^{51} + 9 q^{53} - 9 q^{54} + 3 q^{55} - 6 q^{56} - 6 q^{58} + 3 q^{59} + 9 q^{60} + 24 q^{61} + 3 q^{62} + 3 q^{64} + 6 q^{65} - 9 q^{68} - 3 q^{69} - 21 q^{71} + 3 q^{72} - 3 q^{73} + 6 q^{74} - 36 q^{75} + 6 q^{77} - 15 q^{78} + 6 q^{79} - 3 q^{80} - 9 q^{81} + 9 q^{82} - 33 q^{83} + 15 q^{84} + 24 q^{85} - 21 q^{86} + 6 q^{87} - 3 q^{88} - 6 q^{89} - 27 q^{90} - 36 q^{91} - 15 q^{92} + 36 q^{93} - 12 q^{94} - 12 q^{97} + 27 q^{98} - 3 q^{99}+O(q^{100}) \) 3 * q + 3 * q^2 + 3 * q^4 - 3 * q^5 - 6 * q^7 + 3 * q^8 + 3 * q^9 - 3 * q^10 - 3 * q^11 - 6 * q^14 + 9 * q^15 + 3 * q^16 - 9 * q^17 + 3 * q^18 - 3 * q^20 + 15 * q^21 - 3 * q^22 - 15 * q^23 + 12 * q^25 - 9 * q^27 - 6 * q^28 - 6 * q^29 + 9 * q^30 + 3 * q^31 + 3 * q^32 - 9 * q^34 + 3 * q^36 + 6 * q^37 - 15 * q^39 - 3 * q^40 + 9 * q^41 + 15 * q^42 - 21 * q^43 - 3 * q^44 - 27 * q^45 - 15 * q^46 - 12 * q^47 + 27 * q^49 + 12 * q^50 - 3 * q^51 + 9 * q^53 - 9 * q^54 + 3 * q^55 - 6 * q^56 - 6 * q^58 + 3 * q^59 + 9 * q^60 + 24 * q^61 + 3 * q^62 + 3 * q^64 + 6 * q^65 - 9 * q^68 - 3 * q^69 - 21 * q^71 + 3 * q^72 - 3 * q^73 + 6 * q^74 - 36 * q^75 + 6 * q^77 - 15 * q^78 + 6 * q^79 - 3 * q^80 - 9 * q^81 + 9 * q^82 - 33 * q^83 + 15 * q^84 + 24 * q^85 - 21 * q^86 + 6 * q^87 - 3 * q^88 - 6 * q^89 - 27 * q^90 - 36 * q^91 - 15 * q^92 + 36 * q^93 - 12 * q^94 - 12 * q^97 + 27 * q^98 - 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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