LMFDB - Embedded newform 7935.2.a.bm.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("7935.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7935 = 3 \cdot 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7935.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.3612940039$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{10} + 92x^{8} - 4x^{7} - 234x^{6} + 32x^{5} + 252x^{4} - 68x^{3} - 76x^{2} + 32x - 2 $ x^12 - 16x^10 + 92x^8 - 4x^7 - 234x^6 + 32x^5 + 252x^4 - 68x^3 - 76x^2 + 32*x - 2
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$0.430223$ of defining polynomial
Character	$\chi$	$=$	7935.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.430223 q^{2} +1.00000 q^{3} -1.81491 q^{4} +1.00000 q^{5} +0.430223 q^{6} -1.05251 q^{7} -1.64126 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.430223 q^{2} +1.00000 q^{3} -1.81491 q^{4} +1.00000 q^{5} +0.430223 q^{6} -1.05251 q^{7} -1.64126 q^{8} +1.00000 q^{9} +0.430223 q^{10} -5.03988 q^{11} -1.81491 q^{12} +6.13139 q^{13} -0.452812 q^{14} +1.00000 q^{15} +2.92371 q^{16} -0.665095 q^{17} +0.430223 q^{18} -6.94180 q^{19} -1.81491 q^{20} -1.05251 q^{21} -2.16827 q^{22} -1.64126 q^{24} +1.00000 q^{25} +2.63786 q^{26} +1.00000 q^{27} +1.91020 q^{28} -5.59198 q^{29} +0.430223 q^{30} +10.4423 q^{31} +4.54037 q^{32} -5.03988 q^{33} -0.286139 q^{34} -1.05251 q^{35} -1.81491 q^{36} +2.93153 q^{37} -2.98652 q^{38} +6.13139 q^{39} -1.64126 q^{40} +5.78688 q^{41} -0.452812 q^{42} +11.2423 q^{43} +9.14691 q^{44} +1.00000 q^{45} +1.07689 q^{47} +2.92371 q^{48} -5.89223 q^{49} +0.430223 q^{50} -0.665095 q^{51} -11.1279 q^{52} -12.4542 q^{53} +0.430223 q^{54} -5.03988 q^{55} +1.72744 q^{56} -6.94180 q^{57} -2.40580 q^{58} -5.52369 q^{59} -1.81491 q^{60} +0.649215 q^{61} +4.49250 q^{62} -1.05251 q^{63} -3.89404 q^{64} +6.13139 q^{65} -2.16827 q^{66} +9.01569 q^{67} +1.20709 q^{68} -0.452812 q^{70} -3.99712 q^{71} -1.64126 q^{72} -11.6288 q^{73} +1.26121 q^{74} +1.00000 q^{75} +12.5987 q^{76} +5.30450 q^{77} +2.63786 q^{78} +11.1004 q^{79} +2.92371 q^{80} +1.00000 q^{81} +2.48965 q^{82} -14.6802 q^{83} +1.91020 q^{84} -0.665095 q^{85} +4.83671 q^{86} -5.59198 q^{87} +8.27175 q^{88} -11.9158 q^{89} +0.430223 q^{90} -6.45332 q^{91} +10.4423 q^{93} +0.463301 q^{94} -6.94180 q^{95} +4.54037 q^{96} -1.28176 q^{97} -2.53497 q^{98} -5.03988 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9	$ 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 16 q^{14} + 12 q^{15} - 28 q^{17} - 16 q^{19} + 8 q^{20} - 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} - 8 q^{28} - 16 q^{29} + 20 q^{32} - 24 q^{33} - 16 q^{34} - 4 q^{35} + 8 q^{36} - 20 q^{37} - 16 q^{38} - 8 q^{39} - 4 q^{41} - 16 q^{42} + 12 q^{43} - 16 q^{44} + 12 q^{45} + 4 q^{47} + 24 q^{49} - 28 q^{51} - 36 q^{52} - 28 q^{53} - 24 q^{55} - 56 q^{56} - 16 q^{57} + 20 q^{59} + 8 q^{60} - 32 q^{61} + 12 q^{62} - 4 q^{63} - 4 q^{64} - 8 q^{65} + 4 q^{67} - 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} + 36 q^{74} + 12 q^{75} - 8 q^{76} - 28 q^{77} - 36 q^{78} - 40 q^{79} + 12 q^{81} - 28 q^{82} - 100 q^{83} - 8 q^{84} - 28 q^{85} + 20 q^{86} - 16 q^{87} - 80 q^{89} + 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} + 8 q^{97} + 28 q^{98} - 24 q^{99}+O(q^{100}) $ 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 16 * q^14 + 12 * q^15 - 28 * q^17 - 16 * q^19 + 8 * q^20 - 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 - 8 * q^28 - 16 * q^29 + 20 * q^32 - 24 * q^33 - 16 * q^34 - 4 * q^35 + 8 * q^36 - 20 * q^37 - 16 * q^38 - 8 * q^39 - 4 * q^41 - 16 * q^42 + 12 * q^43 - 16 * q^44 + 12 * q^45 + 4 * q^47 + 24 * q^49 - 28 * q^51 - 36 * q^52 - 28 * q^53 - 24 * q^55 - 56 * q^56 - 16 * q^57 + 20 * q^59 + 8 * q^60 - 32 * q^61 + 12 * q^62 - 4 * q^63 - 4 * q^64 - 8 * q^65 + 4 * q^67 - 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 + 36 * q^74 + 12 * q^75 - 8 * q^76 - 28 * q^77 - 36 * q^78 - 40 * q^79 + 12 * q^81 - 28 * q^82 - 100 * q^83 - 8 * q^84 - 28 * q^85 + 20 * q^86 - 16 * q^87 - 80 * q^89 + 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 + 8 * q^97 + 28 * q^98 - 24 * 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 $

$2$	0.430223	0.304214	0.152107	−	0.988364i	$-0.451394\pi$
$2$	0.430223	0.304214	0.152107	+	0.988364i	$0.451394\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.81491	−0.907454
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.430223	0.175638
$7$	−1.05251	−0.397810	−0.198905	−	0.980019i	$-0.563738\pi$
$7$	−1.05251	−0.397810	−0.198905	+	0.980019i	$0.563738\pi$
$8$	−1.64126	−0.580274
$9$	1.00000	0.333333
$10$	0.430223	0.136048
$11$	−5.03988	−1.51958	−0.759790	−	0.650169i	$-0.774698\pi$
$11$	−5.03988	−1.51958	−0.759790	+	0.650169i	$0.774698\pi$
$12$	−1.81491	−0.523919
$13$	6.13139	1.70054	0.850270	−	0.526347i	$-0.176439\pi$
$13$	6.13139	1.70054	0.850270	+	0.526347i	$0.176439\pi$
$14$	−0.452812	−0.121019
$15$	1.00000	0.258199
$16$	2.92371	0.730927
$17$	−0.665095	−0.161309	−0.0806546	−	0.996742i	$-0.525701\pi$
$17$	−0.665095	−0.161309	−0.0806546	+	0.996742i	$0.525701\pi$
$18$	0.430223	0.101405
$19$	−6.94180	−1.59256	−0.796279	−	0.604929i	$-0.793201\pi$
$19$	−6.94180	−1.59256	−0.796279	+	0.604929i	$0.793201\pi$
$20$	−1.81491	−0.405826
$21$	−1.05251	−0.229675
$22$	−2.16827	−0.462277
$23$	0	0
$23$	0	0
$24$	−1.64126	−0.335021
$25$	1.00000	0.200000
$26$	2.63786	0.517328
$27$	1.00000	0.192450
$28$	1.91020	0.360994
$29$	−5.59198	−1.03840	−0.519202	−	0.854652i	$-0.673771\pi$
$29$	−5.59198	−1.03840	−0.519202	+	0.854652i	$0.673771\pi$
$30$	0.430223	0.0785476
$31$	10.4423	1.87548	0.937742	−	0.347332i	$-0.112912\pi$
$31$	10.4423	1.87548	0.937742	+	0.347332i	$0.112912\pi$
$32$	4.54037	0.802632
$33$	−5.03988	−0.877330
$34$	−0.286139	−0.0490724
$35$	−1.05251	−0.177906
$36$	−1.81491	−0.302485
$37$	2.93153	0.481940	0.240970	−	0.970533i	$-0.422534\pi$
$37$	2.93153	0.481940	0.240970	+	0.970533i	$0.422534\pi$
$38$	−2.98652	−0.484478
$39$	6.13139	0.981807
$40$	−1.64126	−0.259506
$41$	5.78688	0.903760	0.451880	−	0.892079i	$-0.350754\pi$
$41$	5.78688	0.903760	0.451880	+	0.892079i	$0.350754\pi$
$42$	−0.452812	−0.0698704
$43$	11.2423	1.71444	0.857219	−	0.514951i	$-0.172190\pi$
$43$	11.2423	1.71444	0.857219	+	0.514951i	$0.172190\pi$
$44$	9.14691	1.37895
$45$	1.00000	0.149071
$46$	0	0
$47$	1.07689	0.157080	0.0785400	−	0.996911i	$-0.474974\pi$
$47$	1.07689	0.157080	0.0785400	+	0.996911i	$0.474974\pi$
$48$	2.92371	0.422001
$49$	−5.89223	−0.841748
$50$	0.430223	0.0608427
$51$	−0.665095	−0.0931319
$52$	−11.1279	−1.54316
$53$	−12.4542	−1.71071	−0.855356	−	0.518041i	$-0.826662\pi$
$53$	−12.4542	−1.71071	−0.855356	+	0.518041i	$0.826662\pi$
$54$	0.430223	0.0585459
$55$	−5.03988	−0.679577
$56$	1.72744	0.230838
$57$	−6.94180	−0.919464
$58$	−2.40580	−0.315897
$59$	−5.52369	−0.719123	−0.359562	−	0.933121i	$-0.617074\pi$
$59$	−5.52369	−0.719123	−0.359562	+	0.933121i	$0.617074\pi$
$60$	−1.81491	−0.234304
$61$	0.649215	0.0831234	0.0415617	−	0.999136i	$-0.486767\pi$
$61$	0.649215	0.0831234	0.0415617	+	0.999136i	$0.486767\pi$
$62$	4.49250	0.570548
$63$	−1.05251	−0.132603
$64$	−3.89404	−0.486755
$65$	6.13139	0.760505
$66$	−2.16827	−0.266896
$67$	9.01569	1.10144	0.550721	−	0.834689i	$-0.314353\pi$
$67$	9.01569	1.10144	0.550721	+	0.834689i	$0.314353\pi$
$68$	1.20709	0.146381
$69$	0	0
$70$	−0.452812	−0.0541214
$71$	−3.99712	−0.474371	−0.237185	−	0.971464i	$-0.576225\pi$
$71$	−3.99712	−0.474371	−0.237185	+	0.971464i	$0.576225\pi$
$72$	−1.64126	−0.193425
$73$	−11.6288	−1.36104	−0.680521	−	0.732728i	$-0.738247\pi$
$73$	−11.6288	−1.36104	−0.680521	+	0.732728i	$0.738247\pi$
$74$	1.26121	0.146613
$75$	1.00000	0.115470
$76$	12.5987	1.44517
$77$	5.30450	0.604503
$78$	2.63786	0.298679
$79$	11.1004	1.24889	0.624445	−	0.781069i	$-0.285325\pi$
$79$	11.1004	1.24889	0.624445	+	0.781069i	$0.285325\pi$
$80$	2.92371	0.326880
$81$	1.00000	0.111111
$82$	2.48965	0.274936
$83$	−14.6802	−1.61136	−0.805682	−	0.592349i	$-0.798201\pi$
$83$	−14.6802	−1.61136	−0.805682	+	0.592349i	$0.798201\pi$
$84$	1.91020	0.208420
$85$	−0.665095	−0.0721396
$86$	4.83671	0.521556
$87$	−5.59198	−0.599523
$88$	8.27175	0.881772
$89$	−11.9158	−1.26307	−0.631534	−	0.775348i	$-0.717574\pi$
$89$	−11.9158	−1.26307	−0.631534	+	0.775348i	$0.717574\pi$
$90$	0.430223	0.0453495
$91$	−6.45332	−0.676491
$92$	0	0
$93$	10.4423	1.08281
$94$	0.463301	0.0477859
$95$	−6.94180	−0.712214
$96$	4.54037	0.463400
$97$	−1.28176	−0.130143	−0.0650714	−	0.997881i	$-0.520728\pi$
$97$	−1.28176	−0.130143	−0.0650714	+	0.997881i	$0.520728\pi$
$98$	−2.53497	−0.256071
$99$	−5.03988	−0.506527
$100$	−1.81491	−0.181491
$101$	−19.7989	−1.97006	−0.985032	−	0.172372i	$-0.944857\pi$
$101$	−19.7989	−1.97006	−0.985032	+	0.172372i	$0.944857\pi$
$102$	−0.286139	−0.0283320
$103$	−6.16619	−0.607573	−0.303787	−	0.952740i	$-0.598251\pi$
$103$	−6.16619	−0.607573	−0.303787	+	0.952740i	$0.598251\pi$
$104$	−10.0632	−0.986779
$105$	−1.05251	−0.102714
$106$	−5.35807	−0.520422
$107$	−15.7970	−1.52715	−0.763575	−	0.645719i	$-0.776558\pi$
$107$	−15.7970	−1.52715	−0.763575	+	0.645719i	$0.776558\pi$
$108$	−1.81491	−0.174640
$109$	−5.49351	−0.526183	−0.263092	−	0.964771i	$-0.584742\pi$
$109$	−5.49351	−0.526183	−0.263092	+	0.964771i	$0.584742\pi$
$110$	−2.16827	−0.206737
$111$	2.93153	0.278248
$112$	−3.07722	−0.290770
$113$	−4.77647	−0.449333	−0.224666	−	0.974436i	$-0.572129\pi$
$113$	−4.77647	−0.449333	−0.224666	+	0.974436i	$0.572129\pi$
$114$	−2.98652	−0.279713
$115$	0	0
$116$	10.1489	0.942304
$117$	6.13139	0.566847
$118$	−2.37642	−0.218767
$119$	0.700016	0.0641703
$120$	−1.64126	−0.149826
$121$	14.4003	1.30912
$122$	0.279307	0.0252873
$123$	5.78688	0.521786
$124$	−18.9517	−1.70192
$125$	1.00000	0.0894427
$126$	−0.452812	−0.0403397
$127$	−4.35926	−0.386822	−0.193411	−	0.981118i	$-0.561955\pi$
$127$	−4.35926	−0.386822	−0.193411	+	0.981118i	$0.561955\pi$
$128$	−10.7560	−0.950709
$129$	11.2423	0.989832
$130$	2.63786	0.231356
$131$	15.2516	1.33254	0.666271	−	0.745710i	$-0.267889\pi$
$131$	15.2516	1.33254	0.666271	+	0.745710i	$0.267889\pi$
$132$	9.14691	0.796136
$133$	7.30628	0.633535
$134$	3.87876	0.335074
$135$	1.00000	0.0860663
$136$	1.09159	0.0936034
$137$	−11.4851	−0.981242	−0.490621	−	0.871373i	$-0.663230\pi$
$137$	−11.4851	−0.981242	−0.490621	+	0.871373i	$0.663230\pi$
$138$	0	0
$139$	−14.7765	−1.25332	−0.626662	−	0.779291i	$-0.715579\pi$
$139$	−14.7765	−1.25332	−0.626662	+	0.779291i	$0.715579\pi$
$140$	1.91020	0.161441
$141$	1.07689	0.0906902
$142$	−1.71965	−0.144310
$143$	−30.9014	−2.58411
$144$	2.92371	0.243642
$145$	−5.59198	−0.464388
$146$	−5.00296	−0.414048
$147$	−5.89223	−0.485983
$148$	−5.32045	−0.437338
$149$	9.94866	0.815026	0.407513	−	0.913199i	$-0.366396\pi$
$149$	9.94866	0.815026	0.407513	+	0.913199i	$0.366396\pi$
$150$	0.430223	0.0351276
$151$	3.55159	0.289025	0.144512	−	0.989503i	$-0.453839\pi$
$151$	3.55159	0.289025	0.144512	+	0.989503i	$0.453839\pi$
$152$	11.3933	0.924119
$153$	−0.665095	−0.0537697
$154$	2.28212	0.183898
$155$	10.4423	0.838742
$156$	−11.1279	−0.890945
$157$	−0.509942	−0.0406978	−0.0203489	−	0.999793i	$-0.506478\pi$
$157$	−0.509942	−0.0406978	−0.0203489	+	0.999793i	$0.506478\pi$
$158$	4.77564	0.379929
$159$	−12.4542	−0.987680
$160$	4.54037	0.358948
$161$	0	0
$162$	0.430223	0.0338015
$163$	−7.02685	−0.550385	−0.275193	−	0.961389i	$-0.588742\pi$
$163$	−7.02685	−0.550385	−0.275193	+	0.961389i	$0.588742\pi$
$164$	−10.5027	−0.820120
$165$	−5.03988	−0.392354
$166$	−6.31577	−0.490199
$167$	11.2380	0.869620	0.434810	−	0.900522i	$-0.356816\pi$
$167$	11.2380	0.869620	0.434810	+	0.900522i	$0.356816\pi$
$168$	1.72744	0.133275
$169$	24.5939	1.89184
$170$	−0.286139	−0.0219459
$171$	−6.94180	−0.530853
$172$	−20.4038	−1.55577
$173$	−14.7950	−1.12484	−0.562420	−	0.826852i	$-0.690130\pi$
$173$	−14.7950	−1.12484	−0.562420	+	0.826852i	$0.690130\pi$
$174$	−2.40580	−0.182383
$175$	−1.05251	−0.0795619
$176$	−14.7351	−1.11070
$177$	−5.52369	−0.415186
$178$	−5.12644	−0.384243
$179$	−4.25705	−0.318187	−0.159094	−	0.987264i	$-0.550857\pi$
$179$	−4.25705	−0.318187	−0.159094	+	0.987264i	$0.550857\pi$
$180$	−1.81491	−0.135275
$181$	2.86681	0.213088	0.106544	−	0.994308i	$-0.466021\pi$
$181$	2.86681	0.213088	0.106544	+	0.994308i	$0.466021\pi$
$182$	−2.77637	−0.205798
$183$	0.649215	0.0479913
$184$	0	0
$185$	2.93153	0.215530
$186$	4.49250	0.329406
$187$	3.35199	0.245122
$188$	−1.95445	−0.142543
$189$	−1.05251	−0.0765585
$190$	−2.98652	−0.216665
$191$	8.97843	0.649656	0.324828	−	0.945773i	$-0.394694\pi$
$191$	8.97843	0.649656	0.324828	+	0.945773i	$0.394694\pi$
$192$	−3.89404	−0.281028
$193$	−10.3399	−0.744279	−0.372140	−	0.928177i	$-0.621376\pi$
$193$	−10.3399	−0.744279	−0.372140	+	0.928177i	$0.621376\pi$
$194$	−0.551442	−0.0395912
$195$	6.13139	0.439078
$196$	10.6939	0.763847
$197$	−3.80594	−0.271162	−0.135581	−	0.990766i	$-0.543290\pi$
$197$	−3.80594	−0.271162	−0.135581	+	0.990766i	$0.543290\pi$
$198$	−2.16827	−0.154092
$199$	−8.97746	−0.636395	−0.318198	−	0.948024i	$-0.603078\pi$
$199$	−8.97746	−0.636395	−0.318198	+	0.948024i	$0.603078\pi$
$200$	−1.64126	−0.116055
$201$	9.01569	0.635918
$202$	−8.51794	−0.599320
$203$	5.88559	0.413087
$204$	1.20709	0.0845129
$205$	5.78688	0.404174
$206$	−2.65284	−0.184832
$207$	0	0
$208$	17.9264	1.24297
$209$	34.9858	2.42002
$210$	−0.452812	−0.0312470
$211$	17.3964	1.19762	0.598808	−	0.800892i	$-0.295641\pi$
$211$	17.3964	1.19762	0.598808	+	0.800892i	$0.295641\pi$
$212$	22.6032	1.55239
$213$	−3.99712	−0.273878
$214$	−6.79622	−0.464580
$215$	11.2423	0.766720
$216$	−1.64126	−0.111674
$217$	−10.9905	−0.746086
$218$	−2.36344	−0.160072
$219$	−11.6288	−0.785798
$220$	9.14691	0.616685
$221$	−4.07795	−0.274313
$222$	1.26121	0.0846469
$223$	5.03214	0.336977	0.168488	−	0.985704i	$-0.446111\pi$
$223$	5.03214	0.336977	0.168488	+	0.985704i	$0.446111\pi$
$224$	−4.77876	−0.319295
$225$	1.00000	0.0666667
$226$	−2.05495	−0.136693
$227$	10.4864	0.696007	0.348004	−	0.937493i	$-0.386860\pi$
$227$	10.4864	0.696007	0.348004	+	0.937493i	$0.386860\pi$
$228$	12.5987	0.834371
$229$	−2.87840	−0.190210	−0.0951050	−	0.995467i	$-0.530319\pi$
$229$	−2.87840	−0.190210	−0.0951050	+	0.995467i	$0.530319\pi$
$230$	0	0
$231$	5.30450	0.349010
$232$	9.17790	0.602558
$233$	11.3871	0.745992	0.372996	−	0.927833i	$-0.378331\pi$
$233$	11.3871	0.745992	0.372996	+	0.927833i	$0.378331\pi$
$234$	2.63786	0.172443
$235$	1.07689	0.0702483
$236$	10.0250	0.652571
$237$	11.1004	0.721047
$238$	0.301163	0.0195215
$239$	13.5634	0.877341	0.438670	−	0.898648i	$-0.355450\pi$
$239$	13.5634	0.877341	0.438670	+	0.898648i	$0.355450\pi$
$240$	2.92371	0.188725
$241$	−8.71227	−0.561207	−0.280603	−	0.959824i	$-0.590535\pi$
$241$	−8.71227	−0.561207	−0.280603	+	0.959824i	$0.590535\pi$
$242$	6.19536	0.398253
$243$	1.00000	0.0641500
$244$	−1.17827	−0.0754307
$245$	−5.89223	−0.376441
$246$	2.48965	0.158734
$247$	−42.5629	−2.70821
$248$	−17.1385	−1.08829
$249$	−14.6802	−0.930321
$250$	0.430223	0.0272097
$251$	14.1864	0.895436	0.447718	−	0.894175i	$-0.352237\pi$
$251$	14.1864	0.895436	0.447718	+	0.894175i	$0.352237\pi$
$252$	1.91020	0.120331
$253$	0	0
$254$	−1.87545	−0.117676
$255$	−0.665095	−0.0416498
$256$	3.16059	0.197537
$257$	−6.78141	−0.423012	−0.211506	−	0.977377i	$-0.567837\pi$
$257$	−6.78141	−0.423012	−0.211506	+	0.977377i	$0.567837\pi$
$258$	4.83671	0.301120
$259$	−3.08545	−0.191720
$260$	−11.1279	−0.690123
$261$	−5.59198	−0.346135
$262$	6.56161	0.405377
$263$	−13.1403	−0.810267	−0.405134	−	0.914257i	$-0.632775\pi$
$263$	−13.1403	−0.810267	−0.405134	+	0.914257i	$0.632775\pi$
$264$	8.27175	0.509091
$265$	−12.4542	−0.765054
$266$	3.14333	0.192730
$267$	−11.9158	−0.729233
$268$	−16.3626	−0.999508
$269$	−15.2698	−0.931017	−0.465508	−	0.885043i	$-0.654129\pi$
$269$	−15.2698	−0.931017	−0.465508	+	0.885043i	$0.654129\pi$
$270$	0.430223	0.0261825
$271$	−24.3668	−1.48018	−0.740088	−	0.672511i	$-0.765216\pi$
$271$	−24.3668	−1.48018	−0.740088	+	0.672511i	$0.765216\pi$
$272$	−1.94454	−0.117905
$273$	−6.45332	−0.390572
$274$	−4.94117	−0.298507
$275$	−5.03988	−0.303916
$276$	0	0
$277$	−7.19461	−0.432282	−0.216141	−	0.976362i	$-0.569347\pi$
$277$	−7.19461	−0.432282	−0.216141	+	0.976362i	$0.569347\pi$
$278$	−6.35718	−0.381278
$279$	10.4423	0.625162
$280$	1.72744	0.103234
$281$	8.63378	0.515048	0.257524	−	0.966272i	$-0.417093\pi$
$281$	8.63378	0.515048	0.257524	+	0.966272i	$0.417093\pi$
$282$	0.463301	0.0275892
$283$	−18.2756	−1.08637	−0.543186	−	0.839613i	$-0.682782\pi$
$283$	−18.2756	−1.08637	−0.543186	+	0.839613i	$0.682782\pi$
$284$	7.25440	0.430469
$285$	−6.94180	−0.411197
$286$	−13.2945	−0.786120
$287$	−6.09073	−0.359524
$288$	4.54037	0.267544
$289$	−16.5576	−0.973979
$290$	−2.40580	−0.141273
$291$	−1.28176	−0.0751380
$292$	21.1051	1.23508
$293$	−13.8808	−0.810927	−0.405464	−	0.914111i	$-0.632890\pi$
$293$	−13.8808	−0.810927	−0.405464	+	0.914111i	$0.632890\pi$
$294$	−2.53497	−0.147843
$295$	−5.52369	−0.321602
$296$	−4.81140	−0.279657
$297$	−5.03988	−0.292443
$298$	4.28014	0.247942
$299$	0	0
$300$	−1.81491	−0.104784
$301$	−11.8326	−0.682020
$302$	1.52798	0.0879252
$303$	−19.7989	−1.13742
$304$	−20.2958	−1.16404
$305$	0.649215	0.0371739
$306$	−0.286139	−0.0163575
$307$	−10.7904	−0.615841	−0.307921	−	0.951412i	$-0.599633\pi$
$307$	−10.7904	−0.615841	−0.307921	+	0.951412i	$0.599633\pi$
$308$	−9.62717	−0.548559
$309$	−6.16619	−0.350782
$310$	4.49250	0.255157
$311$	−25.8055	−1.46330	−0.731648	−	0.681683i	$-0.761248\pi$
$311$	−25.8055	−1.46330	−0.731648	+	0.681683i	$0.761248\pi$
$312$	−10.0632	−0.569717
$313$	−13.6894	−0.773768	−0.386884	−	0.922128i	$-0.626449\pi$
$313$	−13.6894	−0.773768	−0.386884	+	0.922128i	$0.626449\pi$
$314$	−0.219389	−0.0123808
$315$	−1.05251	−0.0593020
$316$	−20.1462	−1.13331
$317$	14.2255	0.798982	0.399491	−	0.916737i	$-0.369187\pi$
$317$	14.2255	0.798982	0.399491	+	0.916737i	$0.369187\pi$
$318$	−5.35807	−0.300466
$319$	28.1829	1.57794
$320$	−3.89404	−0.217684
$321$	−15.7970	−0.881701
$322$	0	0
$323$	4.61695	0.256894
$324$	−1.81491	−0.100828
$325$	6.13139	0.340108
$326$	−3.02311	−0.167435
$327$	−5.49351	−0.303792
$328$	−9.49779	−0.524428
$329$	−1.13343	−0.0624879
$330$	−2.16827	−0.119359
$331$	4.82711	0.265322	0.132661	−	0.991161i	$-0.457648\pi$
$331$	4.82711	0.265322	0.132661	+	0.991161i	$0.457648\pi$
$332$	26.6432	1.46224
$333$	2.93153	0.160647
$334$	4.83483	0.264550
$335$	9.01569	0.492580
$336$	−3.07722	−0.167876
$337$	−3.71616	−0.202432	−0.101216	−	0.994864i	$-0.532273\pi$
$337$	−3.71616	−0.202432	−0.101216	+	0.994864i	$0.532273\pi$
$338$	10.5809	0.575523
$339$	−4.77647	−0.259422
$340$	1.20709	0.0654634
$341$	−52.6277	−2.84995
$342$	−2.98652	−0.161493
$343$	13.5691	0.732665
$344$	−18.4516	−0.994844
$345$	0	0
$346$	−6.36513	−0.342192
$347$	35.3241	1.89630	0.948149	−	0.317825i	$-0.102952\pi$
$347$	35.3241	1.89630	0.948149	+	0.317825i	$0.102952\pi$
$348$	10.1489	0.544039
$349$	−3.98562	−0.213345	−0.106673	−	0.994294i	$-0.534020\pi$
$349$	−3.98562	−0.213345	−0.106673	+	0.994294i	$0.534020\pi$
$350$	−0.452812	−0.0242038
$351$	6.13139	0.327269
$352$	−22.8829	−1.21966
$353$	−27.3174	−1.45396	−0.726980	−	0.686658i	$-0.759077\pi$
$353$	−27.3174	−1.45396	−0.726980	+	0.686658i	$0.759077\pi$
$354$	−2.37642	−0.126305
$355$	−3.99712	−0.212145
$356$	21.6260	1.14618
$357$	0.700016	0.0370488
$358$	−1.83148	−0.0967968
$359$	−22.3003	−1.17697	−0.588483	−	0.808510i	$-0.700274\pi$
$359$	−22.3003	−1.17697	−0.588483	+	0.808510i	$0.700274\pi$
$360$	−1.64126	−0.0865021
$361$	29.1886	1.53624
$362$	1.23337	0.0648244
$363$	14.4003	0.755822
$364$	11.7122	0.613885
$365$	−11.6288	−0.608677
$366$	0.279307	0.0145996
$367$	−7.00676	−0.365750	−0.182875	−	0.983136i	$-0.558540\pi$
$367$	−7.00676	−0.365750	−0.182875	+	0.983136i	$0.558540\pi$
$368$	0	0
$369$	5.78688	0.301253
$370$	1.26121	0.0655672
$371$	13.1081	0.680538
$372$	−18.9517	−0.982602
$373$	23.0680	1.19442	0.597209	−	0.802086i	$-0.296276\pi$
$373$	23.0680	1.19442	0.597209	+	0.802086i	$0.296276\pi$
$374$	1.44211	0.0745695
$375$	1.00000	0.0516398
$376$	−1.76745	−0.0911494
$377$	−34.2866	−1.76585
$378$	−0.452812	−0.0232901
$379$	14.7444	0.757371	0.378685	−	0.925526i	$-0.376376\pi$
$379$	14.7444	0.757371	0.378685	+	0.925526i	$0.376376\pi$
$380$	12.5987	0.646301
$381$	−4.35926	−0.223332
$382$	3.86273	0.197634
$383$	−21.5209	−1.09967	−0.549833	−	0.835274i	$-0.685309\pi$
$383$	−21.5209	−1.09967	−0.549833	+	0.835274i	$0.685309\pi$
$384$	−10.7560	−0.548892
$385$	5.30450	0.270342
$386$	−4.44845	−0.226420
$387$	11.2423	0.571480
$388$	2.32627	0.118099
$389$	13.9433	0.706956	0.353478	−	0.935443i	$-0.384999\pi$
$389$	13.9433	0.706956	0.353478	+	0.935443i	$0.384999\pi$
$390$	2.63786	0.133573
$391$	0	0
$392$	9.67069	0.488444
$393$	15.2516	0.769343
$394$	−1.63740	−0.0824911
$395$	11.1004	0.558520
$396$	9.14691	0.459650
$397$	−19.0575	−0.956467	−0.478233	−	0.878233i	$-0.658723\pi$
$397$	−19.0575	−0.956467	−0.478233	+	0.878233i	$0.658723\pi$
$398$	−3.86231	−0.193600
$399$	7.30628	0.365772
$400$	2.92371	0.146185
$401$	−21.3123	−1.06428	−0.532142	−	0.846655i	$-0.678613\pi$
$401$	−21.3123	−1.06428	−0.532142	+	0.846655i	$0.678613\pi$
$402$	3.87876	0.193455
$403$	64.0255	3.18934
$404$	35.9332	1.78774
$405$	1.00000	0.0496904
$406$	2.53211	0.125667
$407$	−14.7745	−0.732346
$408$	1.09159	0.0540420
$409$	−22.5163	−1.11336	−0.556680	−	0.830727i	$-0.687925\pi$
$409$	−22.5163	−1.11336	−0.556680	+	0.830727i	$0.687925\pi$
$410$	2.48965	0.122955
$411$	−11.4851	−0.566520
$412$	11.1911	0.551345
$413$	5.81371	0.286074
$414$	0	0
$415$	−14.6802	−0.720624
$416$	27.8388	1.36491
$417$	−14.7765	−0.723607
$418$	15.0517	0.736203
$419$	23.4394	1.14509	0.572545	−	0.819874i	$-0.305956\pi$
$419$	23.4394	1.14509	0.572545	+	0.819874i	$0.305956\pi$
$420$	1.91020	0.0932082
$421$	−31.0102	−1.51135	−0.755673	−	0.654949i	$-0.772690\pi$
$421$	−31.0102	−1.51135	−0.755673	+	0.654949i	$0.772690\pi$
$422$	7.48433	0.364331
$423$	1.07689	0.0523600
$424$	20.4406	0.992681
$425$	−0.665095	−0.0322618
$426$	−1.71965	−0.0833174
$427$	−0.683302	−0.0330673
$428$	28.6700	1.38582
$429$	−30.9014	−1.49193
$430$	4.83671	0.233247
$431$	−20.2818	−0.976938	−0.488469	−	0.872581i	$-0.662444\pi$
$431$	−20.2818	−0.976938	−0.488469	+	0.872581i	$0.662444\pi$
$432$	2.92371	0.140667
$433$	10.2075	0.490543	0.245272	−	0.969454i	$-0.421123\pi$
$433$	10.2075	0.490543	0.245272	+	0.969454i	$0.421123\pi$
$434$	−4.72838	−0.226970
$435$	−5.59198	−0.268115
$436$	9.97022	0.477487
$437$	0	0
$438$	−5.00296	−0.239051
$439$	9.38450	0.447898	0.223949	−	0.974601i	$-0.428105\pi$
$439$	9.38450	0.447898	0.223949	+	0.974601i	$0.428105\pi$
$440$	8.27175	0.394340
$441$	−5.89223	−0.280583
$442$	−1.75443	−0.0834497
$443$	25.0346	1.18943	0.594715	−	0.803937i	$-0.297265\pi$
$443$	25.0346	1.18943	0.594715	+	0.803937i	$0.297265\pi$
$444$	−5.32045	−0.252497
$445$	−11.9158	−0.564861
$446$	2.16494	0.102513
$447$	9.94866	0.470555
$448$	4.09850	0.193636
$449$	4.02584	0.189991	0.0949957	−	0.995478i	$-0.469716\pi$
$449$	4.02584	0.189991	0.0949957	+	0.995478i	$0.469716\pi$
$450$	0.430223	0.0202809
$451$	−29.1652	−1.37333
$452$	8.66886	0.407749
$453$	3.55159	0.166868
$454$	4.51149	0.211735
$455$	−6.45332	−0.302536
$456$	11.3933	0.533541
$457$	20.3152	0.950306	0.475153	−	0.879903i	$-0.342393\pi$
$457$	20.3152	0.950306	0.475153	+	0.879903i	$0.342393\pi$
$458$	−1.23835	−0.0578645
$459$	−0.665095	−0.0310440
$460$	0	0
$461$	7.10105	0.330729	0.165364	−	0.986233i	$-0.447120\pi$
$461$	7.10105	0.330729	0.165364	+	0.986233i	$0.447120\pi$
$462$	2.28212	0.106174
$463$	−22.3141	−1.03703	−0.518513	−	0.855070i	$-0.673514\pi$
$463$	−22.3141	−1.03703	−0.518513	+	0.855070i	$0.673514\pi$
$464$	−16.3493	−0.758997
$465$	10.4423	0.484248
$466$	4.89898	0.226941
$467$	13.2032	0.610970	0.305485	−	0.952197i	$-0.401181\pi$
$467$	13.2032	0.610970	0.305485	+	0.952197i	$0.401181\pi$
$468$	−11.1279	−0.514387
$469$	−9.48906	−0.438164
$470$	0.463301	0.0213705
$471$	−0.509942	−0.0234969
$472$	9.06582	0.417288
$473$	−56.6599	−2.60523
$474$	4.77564	0.219352
$475$	−6.94180	−0.318512
$476$	−1.27046	−0.0582316
$477$	−12.4542	−0.570237
$478$	5.83527	0.266899
$479$	−18.2982	−0.836064	−0.418032	−	0.908432i	$-0.637280\pi$
$479$	−18.2982	−0.836064	−0.418032	+	0.908432i	$0.637280\pi$
$480$	4.54037	0.207239
$481$	17.9743	0.819558
$482$	−3.74822	−0.170727
$483$	0	0
$484$	−26.1353	−1.18797
$485$	−1.28176	−0.0582017
$486$	0.430223	0.0195153
$487$	21.7823	0.987052	0.493526	−	0.869731i	$-0.335708\pi$
$487$	21.7823	0.987052	0.493526	+	0.869731i	$0.335708\pi$
$488$	−1.06553	−0.0482343
$489$	−7.02685	−0.317765
$490$	−2.53497	−0.114518
$491$	31.8272	1.43634	0.718171	−	0.695867i	$-0.244980\pi$
$491$	31.8272	1.43634	0.718171	+	0.695867i	$0.244980\pi$
$492$	−10.5027	−0.473497
$493$	3.71919	0.167504
$494$	−18.3115	−0.823874
$495$	−5.03988	−0.226526
$496$	30.5301	1.37084
$497$	4.20699	0.188709
$498$	−6.31577	−0.283016
$499$	−13.2141	−0.591543	−0.295772	−	0.955259i	$-0.595577\pi$
$499$	−13.2141	−0.591543	−0.295772	+	0.955259i	$0.595577\pi$
$500$	−1.81491	−0.0811652
$501$	11.2380	0.502075
$502$	6.10331	0.272404
$503$	8.09588	0.360977	0.180489	−	0.983577i	$-0.442232\pi$
$503$	8.09588	0.360977	0.180489	+	0.983577i	$0.442232\pi$
$504$	1.72744	0.0769461
$505$	−19.7989	−0.881039
$506$	0	0
$507$	24.5939	1.09225
$508$	7.91165	0.351023
$509$	−16.1568	−0.716139	−0.358070	−	0.933695i	$-0.616565\pi$
$509$	−16.1568	−0.716139	−0.358070	+	0.933695i	$0.616565\pi$
$510$	−0.286139	−0.0126704
$511$	12.2393	0.541436
$512$	22.8719	1.01080
$513$	−6.94180	−0.306488
$514$	−2.91752	−0.128686
$515$	−6.16619	−0.271715
$516$	−20.4038	−0.898227
$517$	−5.42737	−0.238696
$518$	−1.32743	−0.0583239
$519$	−14.7950	−0.649427
$520$	−10.0632	−0.441301
$521$	42.1479	1.84653	0.923266	−	0.384162i	$-0.125510\pi$
$521$	42.1479	1.84653	0.923266	+	0.384162i	$0.125510\pi$
$522$	−2.40580	−0.105299
$523$	−37.7850	−1.65222	−0.826111	−	0.563507i	$-0.809452\pi$
$523$	−37.7850	−1.65222	−0.826111	+	0.563507i	$0.809452\pi$
$524$	−27.6803	−1.20922
$525$	−1.05251	−0.0459351
$526$	−5.65327	−0.246494
$527$	−6.94509	−0.302533
$528$	−14.7351	−0.641264
$529$	0	0
$530$	−5.35807	−0.232740
$531$	−5.52369	−0.239708
$532$	−13.2602	−0.574904
$533$	35.4816	1.53688
$534$	−5.12644	−0.221843
$535$	−15.7970	−0.682963
$536$	−14.7971	−0.639138
$537$	−4.25705	−0.183705
$538$	−6.56943	−0.283228
$539$	29.6961	1.27910
$540$	−1.81491	−0.0781012
$541$	−34.0198	−1.46262	−0.731312	−	0.682043i	$-0.761091\pi$
$541$	−34.0198	−1.46262	−0.731312	+	0.682043i	$0.761091\pi$
$542$	−10.4831	−0.450289
$543$	2.86681	0.123027
$544$	−3.01978	−0.129472
$545$	−5.49351	−0.235316
$546$	−2.77637	−0.118817
$547$	−33.1647	−1.41802	−0.709011	−	0.705197i	$-0.750858\pi$
$547$	−33.1647	−1.41802	−0.709011	+	0.705197i	$0.750858\pi$
$548$	20.8445	0.890432
$549$	0.649215	0.0277078
$550$	−2.16827	−0.0924554
$551$	38.8184	1.65372
$552$	0	0
$553$	−11.6832	−0.496820
$554$	−3.09529	−0.131506
$555$	2.93153	0.124436
$556$	26.8179	1.13733
$557$	−21.9520	−0.930137	−0.465069	−	0.885275i	$-0.653970\pi$
$557$	−21.9520	−0.930137	−0.465069	+	0.885275i	$0.653970\pi$
$558$	4.49250	0.190183
$559$	68.9310	2.91547
$560$	−3.07722	−0.130036
$561$	3.35199	0.141521
$562$	3.71445	0.156685
$563$	29.4256	1.24014	0.620070	−	0.784546i	$-0.287104\pi$
$563$	29.4256	1.24014	0.620070	+	0.784546i	$0.287104\pi$
$564$	−1.95445	−0.0822972
$565$	−4.77647	−0.200948
$566$	−7.86258	−0.330489
$567$	−1.05251	−0.0442011
$568$	6.56032	0.275265
$569$	−18.6976	−0.783845	−0.391923	−	0.919998i	$-0.628190\pi$
$569$	−18.6976	−0.783845	−0.391923	+	0.919998i	$0.628190\pi$
$570$	−2.98652	−0.125092
$571$	41.8617	1.75186	0.875928	−	0.482442i	$-0.160250\pi$
$571$	41.8617	1.75186	0.875928	+	0.482442i	$0.160250\pi$
$572$	56.0832	2.34496
$573$	8.97843	0.375079
$574$	−2.62037	−0.109372
$575$	0	0
$576$	−3.89404	−0.162252
$577$	−36.8034	−1.53214	−0.766072	−	0.642755i	$-0.777791\pi$
$577$	−36.8034	−1.53214	−0.766072	+	0.642755i	$0.777791\pi$
$578$	−7.12348	−0.296298
$579$	−10.3399	−0.429710
$580$	10.1489	0.421411
$581$	15.4510	0.641016
$582$	−0.551442	−0.0228580
$583$	62.7675	2.59956
$584$	19.0858	0.789777
$585$	6.13139	0.253502
$586$	−5.97186	−0.246695
$587$	−6.34621	−0.261936	−0.130968	−	0.991387i	$-0.541809\pi$
$587$	−6.34621	−0.261936	−0.130968	+	0.991387i	$0.541809\pi$
$588$	10.6939	0.441007
$589$	−72.4881	−2.98682
$590$	−2.37642	−0.0978356
$591$	−3.80594	−0.156555
$592$	8.57092	0.352263
$593$	18.4270	0.756704	0.378352	−	0.925662i	$-0.376491\pi$
$593$	18.4270	0.756704	0.378352	+	0.925662i	$0.376491\pi$
$594$	−2.16827	−0.0889652
$595$	0.700016	0.0286978
$596$	−18.0559	−0.739599
$597$	−8.97746	−0.367423
$598$	0	0
$599$	34.5836	1.41305	0.706524	−	0.707689i	$-0.250262\pi$
$599$	34.5836	1.41305	0.706524	+	0.707689i	$0.250262\pi$
$600$	−1.64126	−0.0670042
$601$	−4.20712	−0.171612	−0.0858061	−	0.996312i	$-0.527347\pi$
$601$	−4.20712	−0.171612	−0.0858061	+	0.996312i	$0.527347\pi$
$602$	−5.09066	−0.207480
$603$	9.01569	0.367147
$604$	−6.44581	−0.262276
$605$	14.4003	0.585457
$606$	−8.51794	−0.346018
$607$	4.21636	0.171137	0.0855683	−	0.996332i	$-0.472729\pi$
$607$	4.21636	0.171137	0.0855683	+	0.996332i	$0.472729\pi$
$608$	−31.5183	−1.27824
$609$	5.88559	0.238496
$610$	0.279307	0.0113088
$611$	6.60280	0.267121
$612$	1.20709	0.0487935
$613$	−1.70603	−0.0689059	−0.0344530	−	0.999406i	$-0.510969\pi$
$613$	−1.70603	−0.0689059	−0.0344530	+	0.999406i	$0.510969\pi$
$614$	−4.64229	−0.187347
$615$	5.78688	0.233350
$616$	−8.70606	−0.350777
$617$	4.08198	0.164335	0.0821673	−	0.996619i	$-0.473816\pi$
$617$	4.08198	0.164335	0.0821673	+	0.996619i	$0.473816\pi$
$618$	−2.65284	−0.106713
$619$	−24.7700	−0.995591	−0.497795	−	0.867295i	$-0.665857\pi$
$619$	−24.7700	−0.995591	−0.497795	+	0.867295i	$0.665857\pi$
$620$	−18.9517	−0.761120
$621$	0	0
$622$	−11.1021	−0.445154
$623$	12.5414	0.502461
$624$	17.9264	0.717629
$625$	1.00000	0.0400000
$626$	−5.88948	−0.235391
$627$	34.9858	1.39720
$628$	0.925498	0.0369314
$629$	−1.94974	−0.0777413
$630$	−0.452812	−0.0180405
$631$	−5.72074	−0.227739	−0.113869	−	0.993496i	$-0.536325\pi$
$631$	−5.72074	−0.227739	−0.113869	+	0.993496i	$0.536325\pi$
$632$	−18.2186	−0.724698
$633$	17.3964	0.691444
$634$	6.12012	0.243061
$635$	−4.35926	−0.172992
$636$	22.6032	0.896274
$637$	−36.1275	−1.43143
$638$	12.1249	0.480030
$639$	−3.99712	−0.158124
$640$	−10.7560	−0.425170
$641$	−1.80090	−0.0711314	−0.0355657	−	0.999367i	$-0.511323\pi$
$641$	−1.80090	−0.0711314	−0.0355657	+	0.999367i	$0.511323\pi$
$642$	−6.79622	−0.268225
$643$	−20.1467	−0.794509	−0.397254	−	0.917709i	$-0.630037\pi$
$643$	−20.1467	−0.794509	−0.397254	+	0.917709i	$0.630037\pi$
$644$	0	0
$645$	11.2423	0.442666
$646$	1.98632	0.0781507
$647$	−27.1468	−1.06725	−0.533626	−	0.845721i	$-0.679171\pi$
$647$	−27.1468	−1.06725	−0.533626	+	0.845721i	$0.679171\pi$
$648$	−1.64126	−0.0644748
$649$	27.8387	1.09276
$650$	2.63786	0.103466
$651$	−10.9905	−0.430753
$652$	12.7531	0.499449
$653$	−18.5301	−0.725140	−0.362570	−	0.931957i	$-0.618101\pi$
$653$	−18.5301	−0.725140	−0.362570	+	0.931957i	$0.618101\pi$
$654$	−2.36344	−0.0924177
$655$	15.2516	0.595931
$656$	16.9192	0.660582
$657$	−11.6288	−0.453681
$658$	−0.487627	−0.0190097
$659$	5.05789	0.197027	0.0985137	−	0.995136i	$-0.468591\pi$
$659$	5.05789	0.197027	0.0985137	+	0.995136i	$0.468591\pi$
$660$	9.14691	0.356043
$661$	15.3833	0.598339	0.299170	−	0.954200i	$-0.403290\pi$
$661$	15.3833	0.598339	0.299170	+	0.954200i	$0.403290\pi$
$662$	2.07673	0.0807146
$663$	−4.07795	−0.158374
$664$	24.0941	0.935032
$665$	7.30628	0.283325
$666$	1.26121	0.0488709
$667$	0	0
$668$	−20.3959	−0.789140
$669$	5.03214	0.194554
$670$	3.87876	0.149849
$671$	−3.27196	−0.126313
$672$	−4.77876	−0.184345
$673$	24.7720	0.954890	0.477445	−	0.878662i	$-0.341563\pi$
$673$	24.7720	0.954890	0.477445	+	0.878662i	$0.341563\pi$
$674$	−1.59878	−0.0615826
$675$	1.00000	0.0384900
$676$	−44.6356	−1.71676
$677$	−40.6032	−1.56051	−0.780253	−	0.625464i	$-0.784910\pi$
$677$	−40.6032	−1.56051	−0.780253	+	0.625464i	$0.784910\pi$
$678$	−2.05495	−0.0789198
$679$	1.34906	0.0517721
$680$	1.09159	0.0418607
$681$	10.4864	0.401840
$682$	−22.6416	−0.866993
$683$	16.5581	0.633576	0.316788	−	0.948496i	$-0.397396\pi$
$683$	16.5581	0.633576	0.316788	+	0.948496i	$0.397396\pi$
$684$	12.5987	0.481724
$685$	−11.4851	−0.438825
$686$	5.83776	0.222887
$687$	−2.87840	−0.109818
$688$	32.8693	1.25313
$689$	−76.3613	−2.90913
$690$	0	0
$691$	22.7450	0.865260	0.432630	−	0.901572i	$-0.357586\pi$
$691$	22.7450	0.865260	0.432630	+	0.901572i	$0.357586\pi$
$692$	26.8515	1.02074
$693$	5.30450	0.201501
$694$	15.1973	0.576880
$695$	−14.7765	−0.560503
$696$	9.17790	0.347887
$697$	−3.84883	−0.145785
$698$	−1.71471	−0.0649026
$699$	11.3871	0.430699
$700$	1.91020	0.0721988
$701$	−15.9414	−0.602098	−0.301049	−	0.953609i	$-0.597337\pi$
$701$	−15.9414	−0.602098	−0.301049	+	0.953609i	$0.597337\pi$
$702$	2.63786	0.0995597
$703$	−20.3501	−0.767517
$704$	19.6255	0.739664
$705$	1.07689	0.0405579
$706$	−11.7526	−0.442315
$707$	20.8384	0.783710
$708$	10.0250	0.376762
$709$	20.9444	0.786585	0.393292	−	0.919413i	$-0.371336\pi$
$709$	20.9444	0.786585	0.393292	+	0.919413i	$0.371336\pi$
$710$	−1.71965	−0.0645374
$711$	11.1004	0.416296
$712$	19.5569	0.732925
$713$	0	0
$714$	0.301163	0.0112707
$715$	−30.9014	−1.15565
$716$	7.72616	0.288740
$717$	13.5634	0.506533
$718$	−9.59411	−0.358049
$719$	0.867000	0.0323336	0.0161668	−	0.999869i	$-0.494854\pi$
$719$	0.867000	0.0323336	0.0161668	+	0.999869i	$0.494854\pi$
$720$	2.92371	0.108960
$721$	6.48995	0.241698
$722$	12.5576	0.467346
$723$	−8.71227	−0.324013
$724$	−5.20300	−0.193368
$725$	−5.59198	−0.207681
$726$	6.19536	0.229931
$727$	17.5782	0.651939	0.325969	−	0.945380i	$-0.394309\pi$
$727$	17.5782	0.651939	0.325969	+	0.945380i	$0.394309\pi$
$728$	10.5916	0.392550
$729$	1.00000	0.0370370
$730$	−5.00296	−0.185168
$731$	−7.47721	−0.276555
$732$	−1.17827	−0.0435499
$733$	1.28111	0.0473189	0.0236594	−	0.999720i	$-0.492468\pi$
$733$	1.28111	0.0473189	0.0236594	+	0.999720i	$0.492468\pi$
$734$	−3.01447	−0.111266
$735$	−5.89223	−0.217338
$736$	0	0
$737$	−45.4379	−1.67373
$738$	2.48965	0.0916453
$739$	22.3029	0.820425	0.410213	−	0.911990i	$-0.365454\pi$
$739$	22.3029	0.820425	0.410213	+	0.911990i	$0.365454\pi$
$740$	−5.32045	−0.195584
$741$	−42.5629	−1.56359
$742$	5.63940	0.207029
$743$	3.25485	0.119409	0.0597044	−	0.998216i	$-0.480984\pi$
$743$	3.25485	0.119409	0.0597044	+	0.998216i	$0.480984\pi$
$744$	−17.1385	−0.628327
$745$	9.94866	0.364491
$746$	9.92440	0.363358
$747$	−14.6802	−0.537121
$748$	−6.08356	−0.222437
$749$	16.6264	0.607515
$750$	0.430223	0.0157095
$751$	0.861203	0.0314257	0.0157129	−	0.999877i	$-0.494998\pi$
$751$	0.861203	0.0314257	0.0157129	+	0.999877i	$0.494998\pi$
$752$	3.14850	0.114814
$753$	14.1864	0.516980
$754$	−14.7509	−0.537195
$755$	3.55159	0.129256
$756$	1.91020	0.0694733
$757$	−2.92413	−0.106279	−0.0531397	−	0.998587i	$-0.516923\pi$
$757$	−2.92413	−0.106279	−0.0531397	+	0.998587i	$0.516923\pi$
$758$	6.34339	0.230402
$759$	0	0
$760$	11.3933	0.413279
$761$	35.9844	1.30443	0.652216	−	0.758033i	$-0.273839\pi$
$761$	35.9844	1.30443	0.652216	+	0.758033i	$0.273839\pi$
$762$	−1.87545	−0.0679405
$763$	5.78195	0.209321
$764$	−16.2950	−0.589533
$765$	−0.665095	−0.0240465
$766$	−9.25879	−0.334534
$767$	−33.8679	−1.22290
$768$	3.16059	0.114048
$769$	3.38484	0.122060	0.0610302	−	0.998136i	$-0.480561\pi$
$769$	3.38484	0.122060	0.0610302	+	0.998136i	$0.480561\pi$
$770$	2.28212	0.0822418
$771$	−6.78141	−0.244226
$772$	18.7659	0.675399
$773$	47.4116	1.70528	0.852639	−	0.522501i	$-0.175001\pi$
$773$	47.4116	1.70528	0.852639	+	0.522501i	$0.175001\pi$
$774$	4.83671	0.173852
$775$	10.4423	0.375097
$776$	2.10370	0.0755185
$777$	−3.08545	−0.110690
$778$	5.99875	0.215066
$779$	−40.1714	−1.43929
$780$	−11.1279	−0.398443
$781$	20.1450	0.720844
$782$	0	0
$783$	−5.59198	−0.199841
$784$	−17.2272	−0.615256
$785$	−0.509942	−0.0182006
$786$	6.56161	0.234045
$787$	52.3673	1.86669	0.933346	−	0.358978i	$-0.116875\pi$
$787$	52.3673	1.86669	0.933346	+	0.358978i	$0.116875\pi$
$788$	6.90743	0.246067
$789$	−13.1403	−0.467808
$790$	4.77564	0.169910
$791$	5.02726	0.178749
$792$	8.27175	0.293924
$793$	3.98059	0.141355
$794$	−8.19896	−0.290970
$795$	−12.4542	−0.441704
$796$	16.2933	0.577499
$797$	15.8129	0.560120	0.280060	−	0.959982i	$-0.409646\pi$
$797$	15.8129	0.560120	0.280060	+	0.959982i	$0.409646\pi$
$798$	3.14333	0.111273
$799$	−0.716231	−0.0253384
$800$	4.54037	0.160526
$801$	−11.9158	−0.421023
$802$	−9.16903	−0.323770
$803$	58.6075	2.06821
$804$	−16.3626	−0.577066
$805$	0	0
$806$	27.5452	0.970240
$807$	−15.2698	−0.537523
$808$	32.4952	1.14318
$809$	−52.9234	−1.86069	−0.930344	−	0.366688i	$-0.880492\pi$
$809$	−52.9234	−1.86069	−0.930344	+	0.366688i	$0.880492\pi$
$810$	0.430223	0.0151165
$811$	4.39182	0.154218	0.0771088	−	0.997023i	$-0.475431\pi$
$811$	4.39182	0.154218	0.0771088	+	0.997023i	$0.475431\pi$
$812$	−10.6818	−0.374858
$813$	−24.3668	−0.854579
$814$	−6.35634	−0.222790
$815$	−7.02685	−0.246140
$816$	−1.94454	−0.0680726
$817$	−78.0420	−2.73034
$818$	−9.68703	−0.338699
$819$	−6.45332	−0.225497
$820$	−10.5027	−0.366769
$821$	20.8317	0.727030	0.363515	−	0.931588i	$-0.381577\pi$
$821$	20.8317	0.727030	0.363515	+	0.931588i	$0.381577\pi$
$822$	−4.94117	−0.172343
$823$	50.3419	1.75481	0.877404	−	0.479752i	$-0.159273\pi$
$823$	50.3419	1.75481	0.877404	+	0.479752i	$0.159273\pi$
$824$	10.1203	0.352559
$825$	−5.03988	−0.175466
$826$	2.50119	0.0870277
$827$	−12.1703	−0.423202	−0.211601	−	0.977356i	$-0.567868\pi$
$827$	−12.1703	−0.423202	−0.211601	+	0.977356i	$0.567868\pi$
$828$	0	0
$829$	−1.95268	−0.0678194	−0.0339097	−	0.999425i	$-0.510796\pi$
$829$	−1.95268	−0.0678194	−0.0339097	+	0.999425i	$0.510796\pi$
$830$	−6.31577	−0.219224
$831$	−7.19461	−0.249578
$832$	−23.8759	−0.827747
$833$	3.91889	0.135782
$834$	−6.35718	−0.220131
$835$	11.2380	0.388906
$836$	−63.4960	−2.19606
$837$	10.4423	0.360937
$838$	10.0842	0.348352
$839$	34.2928	1.18392	0.591959	−	0.805968i	$-0.298355\pi$
$839$	34.2928	1.18392	0.591959	+	0.805968i	$0.298355\pi$
$840$	1.72744	0.0596022
$841$	2.27021	0.0782831
$842$	−13.3413	−0.459772
$843$	8.63378	0.297363
$844$	−31.5729	−1.08678
$845$	24.5939	0.846055
$846$	0.463301	0.0159286
$847$	−15.1564	−0.520781
$848$	−36.4124	−1.25041
$849$	−18.2756	−0.627217
$850$	−0.286139	−0.00981449
$851$	0	0
$852$	7.25440	0.248532
$853$	−16.9120	−0.579055	−0.289528	−	0.957170i	$-0.593498\pi$
$853$	−16.9120	−0.579055	−0.289528	+	0.957170i	$0.593498\pi$
$854$	−0.293972	−0.0100595
$855$	−6.94180	−0.237405
$856$	25.9270	0.886165
$857$	−40.0156	−1.36691	−0.683454	−	0.729994i	$-0.739523\pi$
$857$	−40.0156	−1.36691	−0.683454	+	0.729994i	$0.739523\pi$
$858$	−13.2945	−0.453867
$859$	23.0530	0.786559	0.393280	−	0.919419i	$-0.371340\pi$
$859$	23.0530	0.786559	0.393280	+	0.919419i	$0.371340\pi$
$860$	−20.4038	−0.695763
$861$	−6.09073	−0.207571
$862$	−8.72568	−0.297198
$863$	−10.8136	−0.368099	−0.184050	−	0.982917i	$-0.558921\pi$
$863$	−10.8136	−0.368099	−0.184050	+	0.982917i	$0.558921\pi$
$864$	4.54037	0.154467
$865$	−14.7950	−0.503044
$866$	4.39152	0.149230
$867$	−16.5576	−0.562327
$868$	19.9468	0.677039
$869$	−55.9445	−1.89779
$870$	−2.40580	−0.0815642
$871$	55.2787	1.87305
$872$	9.01629	0.305330
$873$	−1.28176	−0.0433810
$874$	0	0
$875$	−1.05251	−0.0355812
$876$	21.1051	0.713076
$877$	−11.4088	−0.385249	−0.192624	−	0.981273i	$-0.561700\pi$
$877$	−11.4088	−0.385249	−0.192624	+	0.981273i	$0.561700\pi$
$878$	4.03743	0.136257
$879$	−13.8808	−0.468189
$880$	−14.7351	−0.496721
$881$	−48.8915	−1.64720	−0.823598	−	0.567174i	$-0.808037\pi$
$881$	−48.8915	−1.64720	−0.823598	+	0.567174i	$0.808037\pi$
$882$	−2.53497	−0.0853570
$883$	23.5664	0.793073	0.396536	−	0.918019i	$-0.370212\pi$
$883$	23.5664	0.793073	0.396536	+	0.918019i	$0.370212\pi$
$884$	7.40111	0.248926
$885$	−5.52369	−0.185677
$886$	10.7705	0.361841
$887$	−31.5247	−1.05850	−0.529248	−	0.848467i	$-0.677526\pi$
$887$	−31.5247	−1.05850	−0.529248	+	0.848467i	$0.677526\pi$
$888$	−4.81140	−0.161460
$889$	4.58814	0.153881
$890$	−5.12644	−0.171839
$891$	−5.03988	−0.168842
$892$	−9.13287	−0.305791
$893$	−7.47553	−0.250159
$894$	4.28014	0.143149
$895$	−4.25705	−0.142298
$896$	11.3208	0.378201
$897$	0	0
$898$	1.73201	0.0577980
$899$	−58.3929	−1.94751
$900$	−1.81491	−0.0604969
$901$	8.28320	0.275953
$902$	−12.5475	−0.417787
$903$	−11.8326	−0.393765
$904$	7.83944	0.260736
$905$	2.86681	0.0952960
$906$	1.52798	0.0507636
$907$	−45.9191	−1.52472	−0.762360	−	0.647153i	$-0.775959\pi$
$907$	−45.9191	−1.52472	−0.762360	+	0.647153i	$0.775959\pi$
$908$	−19.0319	−0.631595
$909$	−19.7989	−0.656688
$910$	−2.77637	−0.0920356
$911$	−12.9938	−0.430504	−0.215252	−	0.976559i	$-0.569057\pi$
$911$	−12.9938	−0.430504	−0.215252	+	0.976559i	$0.569057\pi$
$912$	−20.2958	−0.672061
$913$	73.9865	2.44859
$914$	8.74008	0.289096
$915$	0.649215	0.0214624
$916$	5.22403	0.172607
$917$	−16.0524	−0.530098
$918$	−0.286139	−0.00944400
$919$	1.95087	0.0643533	0.0321767	−	0.999482i	$-0.489756\pi$
$919$	1.95087	0.0643533	0.0321767	+	0.999482i	$0.489756\pi$
$920$	0	0
$921$	−10.7904	−0.355556
$922$	3.05503	0.100612
$923$	−24.5079	−0.806686
$924$	−9.62717	−0.316711
$925$	2.93153	0.0963880
$926$	−9.60006	−0.315478
$927$	−6.16619	−0.202524
$928$	−25.3896	−0.833456
$929$	28.7257	0.942461	0.471230	−	0.882010i	$-0.343810\pi$
$929$	28.7257	0.942461	0.471230	+	0.882010i	$0.343810\pi$
$930$	4.49250	0.147315
$931$	40.9027	1.34053
$932$	−20.6665	−0.676954
$933$	−25.8055	−0.844834
$934$	5.68031	0.185866
$935$	3.35199	0.109622
$936$	−10.0632	−0.328926
$937$	−40.4347	−1.32094	−0.660472	−	0.750851i	$-0.729644\pi$
$937$	−40.4347	−1.32094	−0.660472	+	0.750851i	$0.729644\pi$
$938$	−4.08241	−0.133296
$939$	−13.6894	−0.446735
$940$	−1.95445	−0.0637471
$941$	−6.03314	−0.196675	−0.0983374	−	0.995153i	$-0.531352\pi$
$941$	−6.03314	−0.196675	−0.0983374	+	0.995153i	$0.531352\pi$
$942$	−0.219389	−0.00714808
$943$	0	0
$944$	−16.1497	−0.525626
$945$	−1.05251	−0.0342380
$946$	−24.3764	−0.792545
$947$	−16.0111	−0.520289	−0.260145	−	0.965570i	$-0.583770\pi$
$947$	−16.0111	−0.520289	−0.260145	+	0.965570i	$0.583770\pi$
$948$	−20.1462	−0.654317
$949$	−71.3004	−2.31451
$950$	−2.98652	−0.0968956
$951$	14.2255	0.461292
$952$	−1.14891	−0.0372363
$953$	20.5857	0.666838	0.333419	−	0.942779i	$-0.391798\pi$
$953$	20.5857	0.666838	0.333419	+	0.942779i	$0.391798\pi$
$954$	−5.35807	−0.173474
$955$	8.97843	0.290535
$956$	−24.6163	−0.796147
$957$	28.1829	0.911023
$958$	−7.87229	−0.254342
$959$	12.0882	0.390348
$960$	−3.89404	−0.125680
$961$	78.0407	2.51744
$962$	7.73297	0.249321
$963$	−15.7970	−0.509050
$964$	15.8120	0.509269
$965$	−10.3399	−0.332852
$966$	0	0
$967$	10.9518	0.352185	0.176093	−	0.984374i	$-0.443654\pi$
$967$	10.9518	0.352185	0.176093	+	0.984374i	$0.443654\pi$
$968$	−23.6347	−0.759649
$969$	4.61695	0.148318
$970$	−0.551442	−0.0177057
$971$	19.9822	0.641258	0.320629	−	0.947205i	$-0.396106\pi$
$971$	19.9822	0.641258	0.320629	+	0.947205i	$0.396106\pi$
$972$	−1.81491	−0.0582132
$973$	15.5523	0.498584
$974$	9.37126	0.300275
$975$	6.13139	0.196361
$976$	1.89811	0.0607572
$977$	26.7443	0.855625	0.427812	−	0.903868i	$-0.359284\pi$
$977$	26.7443	0.855625	0.427812	+	0.903868i	$0.359284\pi$
$978$	−3.02311	−0.0966684
$979$	60.0540	1.91933
$980$	10.6939	0.341603
$981$	−5.49351	−0.175394
$982$	13.6928	0.436955
$983$	−21.0639	−0.671835	−0.335917	−	0.941891i	$-0.609046\pi$
$983$	−21.0639	−0.671835	−0.335917	+	0.941891i	$0.609046\pi$
$984$	−9.49779	−0.302779
$985$	−3.80594	−0.121267
$986$	1.60008	0.0509570
$987$	−1.13343	−0.0360774
$988$	77.2477	2.45758
$989$	0	0
$990$	−2.16827	−0.0689122
$991$	−13.7689	−0.437385	−0.218692	−	0.975794i	$-0.570179\pi$
$991$	−13.7689	−0.437385	−0.218692	+	0.975794i	$0.570179\pi$
$992$	47.4117	1.50532
$993$	4.82711	0.153184
$994$	1.80994	0.0574079
$995$	−8.97746	−0.284605
$996$	26.6432	0.844224
$997$	18.1968	0.576297	0.288148	−	0.957586i	$-0.406960\pi$
$997$	18.1968	0.576297	0.288148	+	0.957586i	$0.406960\pi$
$998$	−5.68500	−0.179955
$999$	2.93153	0.0927494

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7935.2.a.bm.1.7	yes	12
23.22	odd	2		7935.2.a.bl.1.7	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
7935.2.a.bl.1.7	✓	12	23.22	odd	2
7935.2.a.bm.1.7	yes	12	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 7935 = 3 \cdot 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7935.a (trivial)

\(f(q)\)	\(=\)	\(q+0.430223 q^{2} +1.00000 q^{3} -1.81491 q^{4} +1.00000 q^{5} +0.430223 q^{6} -1.05251 q^{7} -1.64126 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.430223 q^{2} +1.00000 q^{3} -1.81491 q^{4} +1.00000 q^{5} +0.430223 q^{6} -1.05251 q^{7} -1.64126 q^{8} +1.00000 q^{9} +0.430223 q^{10} -5.03988 q^{11} -1.81491 q^{12} +6.13139 q^{13} -0.452812 q^{14} +1.00000 q^{15} +2.92371 q^{16} -0.665095 q^{17} +0.430223 q^{18} -6.94180 q^{19} -1.81491 q^{20} -1.05251 q^{21} -2.16827 q^{22} -1.64126 q^{24} +1.00000 q^{25} +2.63786 q^{26} +1.00000 q^{27} +1.91020 q^{28} -5.59198 q^{29} +0.430223 q^{30} +10.4423 q^{31} +4.54037 q^{32} -5.03988 q^{33} -0.286139 q^{34} -1.05251 q^{35} -1.81491 q^{36} +2.93153 q^{37} -2.98652 q^{38} +6.13139 q^{39} -1.64126 q^{40} +5.78688 q^{41} -0.452812 q^{42} +11.2423 q^{43} +9.14691 q^{44} +1.00000 q^{45} +1.07689 q^{47} +2.92371 q^{48} -5.89223 q^{49} +0.430223 q^{50} -0.665095 q^{51} -11.1279 q^{52} -12.4542 q^{53} +0.430223 q^{54} -5.03988 q^{55} +1.72744 q^{56} -6.94180 q^{57} -2.40580 q^{58} -5.52369 q^{59} -1.81491 q^{60} +0.649215 q^{61} +4.49250 q^{62} -1.05251 q^{63} -3.89404 q^{64} +6.13139 q^{65} -2.16827 q^{66} +9.01569 q^{67} +1.20709 q^{68} -0.452812 q^{70} -3.99712 q^{71} -1.64126 q^{72} -11.6288 q^{73} +1.26121 q^{74} +1.00000 q^{75} +12.5987 q^{76} +5.30450 q^{77} +2.63786 q^{78} +11.1004 q^{79} +2.92371 q^{80} +1.00000 q^{81} +2.48965 q^{82} -14.6802 q^{83} +1.91020 q^{84} -0.665095 q^{85} +4.83671 q^{86} -5.59198 q^{87} +8.27175 q^{88} -11.9158 q^{89} +0.430223 q^{90} -6.45332 q^{91} +10.4423 q^{93} +0.463301 q^{94} -6.94180 q^{95} +4.54037 q^{96} -1.28176 q^{97} -2.53497 q^{98} -5.03988 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9	\( 12 q + 12 q^{3} + 8 q^{4} + 12 q^{5} - 4 q^{7} + 12 q^{9} - 24 q^{11} + 8 q^{12} - 8 q^{13} - 16 q^{14} + 12 q^{15} - 28 q^{17} - 16 q^{19} + 8 q^{20} - 4 q^{21} + 12 q^{25} - 36 q^{26} + 12 q^{27} - 8 q^{28} - 16 q^{29} + 20 q^{32} - 24 q^{33} - 16 q^{34} - 4 q^{35} + 8 q^{36} - 20 q^{37} - 16 q^{38} - 8 q^{39} - 4 q^{41} - 16 q^{42} + 12 q^{43} - 16 q^{44} + 12 q^{45} + 4 q^{47} + 24 q^{49} - 28 q^{51} - 36 q^{52} - 28 q^{53} - 24 q^{55} - 56 q^{56} - 16 q^{57} + 20 q^{59} + 8 q^{60} - 32 q^{61} + 12 q^{62} - 4 q^{63} - 4 q^{64} - 8 q^{65} + 4 q^{67} - 64 q^{68} - 16 q^{70} - 8 q^{71} + 4 q^{73} + 36 q^{74} + 12 q^{75} - 8 q^{76} - 28 q^{77} - 36 q^{78} - 40 q^{79} + 12 q^{81} - 28 q^{82} - 100 q^{83} - 8 q^{84} - 28 q^{85} + 20 q^{86} - 16 q^{87} - 80 q^{89} + 24 q^{91} + 44 q^{94} - 16 q^{95} + 20 q^{96} + 8 q^{97} + 28 q^{98} - 24 q^{99}+O(q^{100}) \) 12 * q + 12 * q^3 + 8 * q^4 + 12 * q^5 - 4 * q^7 + 12 * q^9 - 24 * q^11 + 8 * q^12 - 8 * q^13 - 16 * q^14 + 12 * q^15 - 28 * q^17 - 16 * q^19 + 8 * q^20 - 4 * q^21 + 12 * q^25 - 36 * q^26 + 12 * q^27 - 8 * q^28 - 16 * q^29 + 20 * q^32 - 24 * q^33 - 16 * q^34 - 4 * q^35 + 8 * q^36 - 20 * q^37 - 16 * q^38 - 8 * q^39 - 4 * q^41 - 16 * q^42 + 12 * q^43 - 16 * q^44 + 12 * q^45 + 4 * q^47 + 24 * q^49 - 28 * q^51 - 36 * q^52 - 28 * q^53 - 24 * q^55 - 56 * q^56 - 16 * q^57 + 20 * q^59 + 8 * q^60 - 32 * q^61 + 12 * q^62 - 4 * q^63 - 4 * q^64 - 8 * q^65 + 4 * q^67 - 64 * q^68 - 16 * q^70 - 8 * q^71 + 4 * q^73 + 36 * q^74 + 12 * q^75 - 8 * q^76 - 28 * q^77 - 36 * q^78 - 40 * q^79 + 12 * q^81 - 28 * q^82 - 100 * q^83 - 8 * q^84 - 28 * q^85 + 20 * q^86 - 16 * q^87 - 80 * q^89 + 24 * q^91 + 44 * q^94 - 16 * q^95 + 20 * q^96 + 8 * q^97 + 28 * q^98 - 24 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more