LMFDB - Embedded newform 4011.2.a.m.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4011,2,Mod(1,4011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4011, 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("4011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4011 = 3 \cdot 7 \cdot 191 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4011.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:	$32.0279962507$
Analytic rank:	$0$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.08804 q^{2} +1.00000 q^{3} +2.35993 q^{4} -2.57813 q^{5} -2.08804 q^{6} -1.00000 q^{7} -0.751541 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.08804 q^{2} +1.00000 q^{3} +2.35993 q^{4} -2.57813 q^{5} -2.08804 q^{6} -1.00000 q^{7} -0.751541 q^{8} +1.00000 q^{9} +5.38324 q^{10} +2.22369 q^{11} +2.35993 q^{12} +3.69461 q^{13} +2.08804 q^{14} -2.57813 q^{15} -3.15060 q^{16} +7.02691 q^{17} -2.08804 q^{18} -7.75981 q^{19} -6.08419 q^{20} -1.00000 q^{21} -4.64316 q^{22} +5.23049 q^{23} -0.751541 q^{24} +1.64674 q^{25} -7.71450 q^{26} +1.00000 q^{27} -2.35993 q^{28} -7.88438 q^{29} +5.38324 q^{30} +5.46014 q^{31} +8.08168 q^{32} +2.22369 q^{33} -14.6725 q^{34} +2.57813 q^{35} +2.35993 q^{36} +3.57593 q^{37} +16.2028 q^{38} +3.69461 q^{39} +1.93757 q^{40} -9.26157 q^{41} +2.08804 q^{42} +6.03426 q^{43} +5.24775 q^{44} -2.57813 q^{45} -10.9215 q^{46} +12.2651 q^{47} -3.15060 q^{48} +1.00000 q^{49} -3.43847 q^{50} +7.02691 q^{51} +8.71899 q^{52} -2.08281 q^{53} -2.08804 q^{54} -5.73296 q^{55} +0.751541 q^{56} -7.75981 q^{57} +16.4629 q^{58} +9.76720 q^{59} -6.08419 q^{60} -7.73378 q^{61} -11.4010 q^{62} -1.00000 q^{63} -10.5737 q^{64} -9.52516 q^{65} -4.64316 q^{66} +1.90409 q^{67} +16.5830 q^{68} +5.23049 q^{69} -5.38324 q^{70} +11.3635 q^{71} -0.751541 q^{72} -5.81307 q^{73} -7.46669 q^{74} +1.64674 q^{75} -18.3126 q^{76} -2.22369 q^{77} -7.71450 q^{78} -11.8472 q^{79} +8.12265 q^{80} +1.00000 q^{81} +19.3386 q^{82} -7.41418 q^{83} -2.35993 q^{84} -18.1163 q^{85} -12.5998 q^{86} -7.88438 q^{87} -1.67119 q^{88} -8.25717 q^{89} +5.38324 q^{90} -3.69461 q^{91} +12.3436 q^{92} +5.46014 q^{93} -25.6101 q^{94} +20.0058 q^{95} +8.08168 q^{96} +0.695216 q^{97} -2.08804 q^{98} +2.22369 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.08804	−1.47647	−0.738235	−	0.674544i	$-0.764340\pi$
$2$	−2.08804	−1.47647	−0.738235	+	0.674544i	$0.764340\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.35993	1.17996
$5$	−2.57813	−1.15297	−0.576487	−	0.817106i	$-0.695577\pi$
$5$	−2.57813	−1.15297	−0.576487	+	0.817106i	$0.695577\pi$
$6$	−2.08804	−0.852440
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−0.751541	−0.265710
$9$	1.00000	0.333333
$10$	5.38324	1.70233
$11$	2.22369	0.670468	0.335234	−	0.942135i	$-0.391185\pi$
$11$	2.22369	0.670468	0.335234	+	0.942135i	$0.391185\pi$
$12$	2.35993	0.681252
$13$	3.69461	1.02470	0.512350	−	0.858777i	$-0.328775\pi$
$13$	3.69461	1.02470	0.512350	+	0.858777i	$0.328775\pi$
$14$	2.08804	0.558053
$15$	−2.57813	−0.665670
$16$	−3.15060	−0.787650
$17$	7.02691	1.70428	0.852138	−	0.523317i	$-0.175306\pi$
$17$	7.02691	1.70428	0.852138	+	0.523317i	$0.175306\pi$
$18$	−2.08804	−0.492157
$19$	−7.75981	−1.78022	−0.890112	−	0.455742i	$-0.849374\pi$
$19$	−7.75981	−1.78022	−0.890112	+	0.455742i	$0.849374\pi$
$20$	−6.08419	−1.36047
$21$	−1.00000	−0.218218
$22$	−4.64316	−0.989926
$23$	5.23049	1.09063	0.545317	−	0.838230i	$-0.316409\pi$
$23$	5.23049	1.09063	0.545317	+	0.838230i	$0.316409\pi$
$24$	−0.751541	−0.153408
$25$	1.64674	0.329348
$26$	−7.71450	−1.51294
$27$	1.00000	0.192450
$28$	−2.35993	−0.445984
$29$	−7.88438	−1.46409	−0.732047	−	0.681254i	$-0.761435\pi$
$29$	−7.88438	−1.46409	−0.732047	+	0.681254i	$0.761435\pi$
$30$	5.38324	0.982841
$31$	5.46014	0.980669	0.490335	−	0.871534i	$-0.336875\pi$
$31$	5.46014	0.980669	0.490335	+	0.871534i	$0.336875\pi$
$32$	8.08168	1.42865
$33$	2.22369	0.387095
$34$	−14.6725	−2.51631
$35$	2.57813	0.435783
$36$	2.35993	0.393321
$37$	3.57593	0.587879	0.293939	−	0.955824i	$-0.405034\pi$
$37$	3.57593	0.587879	0.293939	+	0.955824i	$0.405034\pi$
$38$	16.2028	2.62845
$39$	3.69461	0.591610
$40$	1.93757	0.306356
$41$	−9.26157	−1.44641	−0.723207	−	0.690631i	$-0.757333\pi$
$41$	−9.26157	−1.44641	−0.723207	+	0.690631i	$0.757333\pi$
$42$	2.08804	0.322192
$43$	6.03426	0.920215	0.460108	−	0.887863i	$-0.347811\pi$
$43$	6.03426	0.920215	0.460108	+	0.887863i	$0.347811\pi$
$44$	5.24775	0.791127
$45$	−2.57813	−0.384325
$46$	−10.9215	−1.61029
$47$	12.2651	1.78905	0.894524	−	0.447020i	$-0.147515\pi$
$47$	12.2651	1.78905	0.894524	+	0.447020i	$0.147515\pi$
$48$	−3.15060	−0.454750
$49$	1.00000	0.142857
$50$	−3.43847	−0.486273
$51$	7.02691	0.983964
$52$	8.71899	1.20911
$53$	−2.08281	−0.286095	−0.143048	−	0.989716i	$-0.545690\pi$
$53$	−2.08281	−0.286095	−0.143048	+	0.989716i	$0.545690\pi$
$54$	−2.08804	−0.284147
$55$	−5.73296	−0.773032
$56$	0.751541	0.100429
$57$	−7.75981	−1.02781
$58$	16.4629	2.16169
$59$	9.76720	1.27158	0.635790	−	0.771862i	$-0.280674\pi$
$59$	9.76720	1.27158	0.635790	+	0.771862i	$0.280674\pi$
$60$	−6.08419	−0.785466
$61$	−7.73378	−0.990209	−0.495104	−	0.868834i	$-0.664870\pi$
$61$	−7.73378	−0.990209	−0.495104	+	0.868834i	$0.664870\pi$
$62$	−11.4010	−1.44793
$63$	−1.00000	−0.125988
$64$	−10.5737	−1.32171
$65$	−9.52516	−1.18145
$66$	−4.64316	−0.571534
$67$	1.90409	0.232622	0.116311	−	0.993213i	$-0.462893\pi$
$67$	1.90409	0.232622	0.116311	+	0.993213i	$0.462893\pi$
$68$	16.5830	2.01098
$69$	5.23049	0.629677
$70$	−5.38324	−0.643421
$71$	11.3635	1.34860	0.674302	−	0.738455i	$-0.264444\pi$
$71$	11.3635	1.34860	0.674302	+	0.738455i	$0.264444\pi$
$72$	−0.751541	−0.0885699
$73$	−5.81307	−0.680369	−0.340184	−	0.940359i	$-0.610490\pi$
$73$	−5.81307	−0.680369	−0.340184	+	0.940359i	$0.610490\pi$
$74$	−7.46669	−0.867985
$75$	1.64674	0.190149
$76$	−18.3126	−2.10060
$77$	−2.22369	−0.253413
$78$	−7.71450	−0.873495
$79$	−11.8472	−1.33292	−0.666459	−	0.745542i	$-0.732191\pi$
$79$	−11.8472	−1.33292	−0.666459	+	0.745542i	$0.732191\pi$
$80$	8.12265	0.908140
$81$	1.00000	0.111111
$82$	19.3386	2.13559
$83$	−7.41418	−0.813812	−0.406906	−	0.913470i	$-0.633392\pi$
$83$	−7.41418	−0.813812	−0.406906	+	0.913470i	$0.633392\pi$
$84$	−2.35993	−0.257489
$85$	−18.1163	−1.96499
$86$	−12.5998	−1.35867
$87$	−7.88438	−0.845295
$88$	−1.67119	−0.178150
$89$	−8.25717	−0.875258	−0.437629	−	0.899156i	$-0.644182\pi$
$89$	−8.25717	−0.875258	−0.437629	+	0.899156i	$0.644182\pi$
$90$	5.38324	0.567444
$91$	−3.69461	−0.387300
$92$	12.3436	1.28691
$93$	5.46014	0.566190
$94$	−25.6101	−2.64148
$95$	20.0058	2.05255
$96$	8.08168	0.824833
$97$	0.695216	0.0705885	0.0352942	−	0.999377i	$-0.488763\pi$
$97$	0.695216	0.0705885	0.0352942	+	0.999377i	$0.488763\pi$
$98$	−2.08804	−0.210924
$99$	2.22369	0.223489
$100$	3.88619	0.388619
$101$	−7.17099	−0.713540	−0.356770	−	0.934192i	$-0.616122\pi$
$101$	−7.17099	−0.713540	−0.356770	+	0.934192i	$0.616122\pi$
$102$	−14.6725	−1.45279
$103$	−12.3142	−1.21335	−0.606675	−	0.794950i	$-0.707497\pi$
$103$	−12.3142	−1.21335	−0.606675	+	0.794950i	$0.707497\pi$
$104$	−2.77665	−0.272273
$105$	2.57813	0.251599
$106$	4.34899	0.422411
$107$	11.6302	1.12433	0.562166	−	0.827024i	$-0.309968\pi$
$107$	11.6302	1.12433	0.562166	+	0.827024i	$0.309968\pi$
$108$	2.35993	0.227084
$109$	−6.82042	−0.653277	−0.326639	−	0.945149i	$-0.605916\pi$
$109$	−6.82042	−0.653277	−0.326639	+	0.945149i	$0.605916\pi$
$110$	11.9707	1.14136
$111$	3.57593	0.339412
$112$	3.15060	0.297704
$113$	1.42912	0.134440	0.0672202	−	0.997738i	$-0.478587\pi$
$113$	1.42912	0.134440	0.0672202	+	0.997738i	$0.478587\pi$
$114$	16.2028	1.51753
$115$	−13.4849	−1.25747
$116$	−18.6066	−1.72758
$117$	3.69461	0.341566
$118$	−20.3943	−1.87745
$119$	−7.02691	−0.644156
$120$	1.93757	0.176875
$121$	−6.05520	−0.550473
$122$	16.1485	1.46201
$123$	−9.26157	−0.835088
$124$	12.8855	1.15715
$125$	8.64513	0.773244
$126$	2.08804	0.186018
$127$	−9.00870	−0.799393	−0.399697	−	0.916647i	$-0.630885\pi$
$127$	−9.00870	−0.799393	−0.399697	+	0.916647i	$0.630885\pi$
$128$	5.91497	0.522814
$129$	6.03426	0.531287
$130$	19.8890	1.74438
$131$	3.31739	0.289842	0.144921	−	0.989443i	$-0.453707\pi$
$131$	3.31739	0.289842	0.144921	+	0.989443i	$0.453707\pi$
$132$	5.24775	0.456758
$133$	7.75981	0.672861
$134$	−3.97582	−0.343459
$135$	−2.57813	−0.221890
$136$	−5.28101	−0.452843
$137$	20.9837	1.79276	0.896380	−	0.443287i	$-0.146188\pi$
$137$	20.9837	1.79276	0.896380	+	0.443287i	$0.146188\pi$
$138$	−10.9215	−0.929700
$139$	9.93023	0.842271	0.421136	−	0.906998i	$-0.361632\pi$
$139$	9.93023	0.842271	0.421136	+	0.906998i	$0.361632\pi$
$140$	6.08419	0.514208
$141$	12.2651	1.03291
$142$	−23.7276	−1.99117
$143$	8.21566	0.687028
$144$	−3.15060	−0.262550
$145$	20.3270	1.68806
$146$	12.1380	1.00454
$147$	1.00000	0.0824786
$148$	8.43892	0.693675
$149$	15.5497	1.27388	0.636941	−	0.770913i	$-0.280200\pi$
$149$	15.5497	1.27388	0.636941	+	0.770913i	$0.280200\pi$
$150$	−3.43847	−0.280750
$151$	−14.5418	−1.18339	−0.591696	−	0.806162i	$-0.701541\pi$
$151$	−14.5418	−1.18339	−0.591696	+	0.806162i	$0.701541\pi$
$152$	5.83182	0.473023
$153$	7.02691	0.568092
$154$	4.64316	0.374157
$155$	−14.0769	−1.13069
$156$	8.71899	0.698078
$157$	−15.8527	−1.26518	−0.632591	−	0.774486i	$-0.718009\pi$
$157$	−15.8527	−1.26518	−0.632591	+	0.774486i	$0.718009\pi$
$158$	24.7375	1.96801
$159$	−2.08281	−0.165177
$160$	−20.8356	−1.64720
$161$	−5.23049	−0.412221
$162$	−2.08804	−0.164052
$163$	14.1998	1.11222	0.556109	−	0.831110i	$-0.312294\pi$
$163$	14.1998	1.11222	0.556109	+	0.831110i	$0.312294\pi$
$164$	−21.8566	−1.70672
$165$	−5.73296	−0.446310
$166$	15.4811	1.20157
$167$	15.5731	1.20509	0.602543	−	0.798086i	$-0.294154\pi$
$167$	15.5731	1.20509	0.602543	+	0.798086i	$0.294154\pi$
$168$	0.751541	0.0579826
$169$	0.650107	0.0500083
$170$	37.8276	2.90124
$171$	−7.75981	−0.593408
$172$	14.2404	1.08582
$173$	18.0445	1.37190	0.685950	−	0.727649i	$-0.259387\pi$
$173$	18.0445	1.37190	0.685950	+	0.727649i	$0.259387\pi$
$174$	16.4629	1.24805
$175$	−1.64674	−0.124482
$176$	−7.00596	−0.528094
$177$	9.76720	0.734148
$178$	17.2413	1.29229
$179$	−6.09742	−0.455742	−0.227871	−	0.973691i	$-0.573177\pi$
$179$	−6.09742	−0.455742	−0.227871	+	0.973691i	$0.573177\pi$
$180$	−6.08419	−0.453489
$181$	17.9632	1.33519	0.667596	−	0.744524i	$-0.267323\pi$
$181$	17.9632	1.33519	0.667596	+	0.744524i	$0.267323\pi$
$182$	7.71450	0.571837
$183$	−7.73378	−0.571697
$184$	−3.93093	−0.289792
$185$	−9.21920	−0.677809
$186$	−11.4010	−0.835962
$187$	15.6257	1.14266
$188$	28.9447	2.11101
$189$	−1.00000	−0.0727393
$190$	−41.7730	−3.03053
$191$	−1.00000	−0.0723575
$191$	−1.00000	−0.0723575
$192$	−10.5737	−0.763090
$193$	11.1122	0.799872	0.399936	−	0.916543i	$-0.369032\pi$
$193$	11.1122	0.799872	0.399936	+	0.916543i	$0.369032\pi$
$194$	−1.45164	−0.104222
$195$	−9.52516	−0.682111
$196$	2.35993	0.168566
$197$	0.361930	0.0257865	0.0128932	−	0.999917i	$-0.495896\pi$
$197$	0.361930	0.0257865	0.0128932	+	0.999917i	$0.495896\pi$
$198$	−4.64316	−0.329975
$199$	10.6728	0.756578	0.378289	−	0.925688i	$-0.376513\pi$
$199$	10.6728	0.756578	0.378289	+	0.925688i	$0.376513\pi$
$200$	−1.23759	−0.0875111
$201$	1.90409	0.134304
$202$	14.9733	1.05352
$203$	7.88438	0.553375
$204$	16.5830	1.16104
$205$	23.8775	1.66768
$206$	25.7125	1.79148
$207$	5.23049	0.363544
$208$	−11.6402	−0.807105
$209$	−17.2554	−1.19358
$210$	−5.38324	−0.371479
$211$	−9.23131	−0.635510	−0.317755	−	0.948173i	$-0.602929\pi$
$211$	−9.23131	−0.635510	−0.317755	+	0.948173i	$0.602929\pi$
$212$	−4.91527	−0.337582
$213$	11.3635	0.778617
$214$	−24.2843	−1.66004
$215$	−15.5571	−1.06098
$216$	−0.751541	−0.0511359
$217$	−5.46014	−0.370658
$218$	14.2413	0.964544
$219$	−5.81307	−0.392811
$220$	−13.5294	−0.912149
$221$	25.9617	1.74637
$222$	−7.46669	−0.501131
$223$	11.2673	0.754515	0.377258	−	0.926108i	$-0.376867\pi$
$223$	11.2673	0.754515	0.377258	+	0.926108i	$0.376867\pi$
$224$	−8.08168	−0.539980
$225$	1.64674	0.109783
$226$	−2.98407	−0.198497
$227$	−7.17028	−0.475908	−0.237954	−	0.971276i	$-0.576477\pi$
$227$	−7.17028	−0.475908	−0.237954	+	0.971276i	$0.576477\pi$
$228$	−18.3126	−1.21278
$229$	22.5378	1.48934	0.744671	−	0.667432i	$-0.232606\pi$
$229$	22.5378	1.48934	0.744671	+	0.667432i	$0.232606\pi$
$230$	28.1570	1.85662
$231$	−2.22369	−0.146308
$232$	5.92544	0.389024
$233$	−21.9287	−1.43660	−0.718299	−	0.695734i	$-0.755079\pi$
$233$	−21.9287	−1.43660	−0.718299	+	0.695734i	$0.755079\pi$
$234$	−7.71450	−0.504312
$235$	−31.6210	−2.06273
$236$	23.0499	1.50042
$237$	−11.8472	−0.769560
$238$	14.6725	0.951076
$239$	11.2916	0.730393	0.365197	−	0.930930i	$-0.381002\pi$
$239$	11.2916	0.730393	0.365197	+	0.930930i	$0.381002\pi$
$240$	8.12265	0.524315
$241$	22.3383	1.43893	0.719467	−	0.694526i	$-0.244386\pi$
$241$	22.3383	1.43893	0.719467	+	0.694526i	$0.244386\pi$
$242$	12.6435	0.812756
$243$	1.00000	0.0641500
$244$	−18.2511	−1.16841
$245$	−2.57813	−0.164711
$246$	19.3386	1.23298
$247$	−28.6694	−1.82419
$248$	−4.10351	−0.260573
$249$	−7.41418	−0.469854
$250$	−18.0514	−1.14167
$251$	0.874439	0.0551941	0.0275971	−	0.999619i	$-0.491214\pi$
$251$	0.874439	0.0551941	0.0275971	+	0.999619i	$0.491214\pi$
$252$	−2.35993	−0.148661
$253$	11.6310	0.731235
$254$	18.8106	1.18028
$255$	−18.1163	−1.13448
$256$	8.79666	0.549792
$257$	−25.9365	−1.61787	−0.808937	−	0.587896i	$-0.799956\pi$
$257$	−25.9365	−1.61787	−0.808937	+	0.587896i	$0.799956\pi$
$258$	−12.5998	−0.784429
$259$	−3.57593	−0.222197
$260$	−22.4787	−1.39407
$261$	−7.88438	−0.488031
$262$	−6.92685	−0.427942
$263$	2.05703	0.126842	0.0634210	−	0.997987i	$-0.479799\pi$
$263$	2.05703	0.126842	0.0634210	+	0.997987i	$0.479799\pi$
$264$	−1.67119	−0.102855
$265$	5.36974	0.329860
$266$	−16.2028	−0.993459
$267$	−8.25717	−0.505330
$268$	4.49351	0.274485
$269$	0.800278	0.0487938	0.0243969	−	0.999702i	$-0.492233\pi$
$269$	0.800278	0.0487938	0.0243969	+	0.999702i	$0.492233\pi$
$270$	5.38324	0.327614
$271$	12.0616	0.732688	0.366344	−	0.930480i	$-0.380609\pi$
$271$	12.0616	0.732688	0.366344	+	0.930480i	$0.380609\pi$
$272$	−22.1390	−1.34237
$273$	−3.69461	−0.223608
$274$	−43.8149	−2.64695
$275$	3.66185	0.220818
$276$	12.3436	0.742996
$277$	32.0598	1.92629	0.963143	−	0.268989i	$-0.0866894\pi$
$277$	32.0598	1.92629	0.963143	+	0.268989i	$0.0866894\pi$
$278$	−20.7348	−1.24359
$279$	5.46014	0.326890
$280$	−1.93757	−0.115792
$281$	−13.1382	−0.783758	−0.391879	−	0.920017i	$-0.628175\pi$
$281$	−13.1382	−0.783758	−0.391879	+	0.920017i	$0.628175\pi$
$282$	−25.6101	−1.52506
$283$	18.4487	1.09666	0.548331	−	0.836262i	$-0.315264\pi$
$283$	18.4487	1.09666	0.548331	+	0.836262i	$0.315264\pi$
$284$	26.8171	1.59130
$285$	20.0058	1.18504
$286$	−17.1547	−1.01438
$287$	9.26157	0.546693
$288$	8.08168	0.476217
$289$	32.3774	1.90456
$290$	−42.4436	−2.49237
$291$	0.695216	0.0407543
$292$	−13.7184	−0.802810
$293$	14.3469	0.838156	0.419078	−	0.907950i	$-0.362353\pi$
$293$	14.3469	0.838156	0.419078	+	0.907950i	$0.362353\pi$
$294$	−2.08804	−0.121777
$295$	−25.1811	−1.46610
$296$	−2.68745	−0.156205
$297$	2.22369	0.129032
$298$	−32.4685	−1.88085
$299$	19.3246	1.11757
$300$	3.88619	0.224369
$301$	−6.03426	−0.347809
$302$	30.3638	1.74724
$303$	−7.17099	−0.411963
$304$	24.4481	1.40219
$305$	19.9387	1.14168
$306$	−14.6725	−0.838770
$307$	−26.2249	−1.49674	−0.748368	−	0.663283i	$-0.769162\pi$
$307$	−26.2249	−1.49674	−0.748368	+	0.663283i	$0.769162\pi$
$308$	−5.24775	−0.299018
$309$	−12.3142	−0.700528
$310$	29.3932	1.66942
$311$	−1.51916	−0.0861436	−0.0430718	−	0.999072i	$-0.513714\pi$
$311$	−1.51916	−0.0861436	−0.0430718	+	0.999072i	$0.513714\pi$
$312$	−2.77665	−0.157197
$313$	−28.8522	−1.63082	−0.815411	−	0.578883i	$-0.803489\pi$
$313$	−28.8522	−1.63082	−0.815411	+	0.578883i	$0.803489\pi$
$314$	33.1011	1.86800
$315$	2.57813	0.145261
$316$	−27.9586	−1.57279
$317$	22.4878	1.26304	0.631521	−	0.775359i	$-0.282431\pi$
$317$	22.4878	1.26304	0.631521	+	0.775359i	$0.282431\pi$
$318$	4.34899	0.243879
$319$	−17.5324	−0.981628
$320$	27.2603	1.52390
$321$	11.6302	0.649134
$322$	10.9215	0.608631
$323$	−54.5275	−3.03399
$324$	2.35993	0.131107
$325$	6.08406	0.337483
$326$	−29.6499	−1.64215
$327$	−6.82042	−0.377170
$328$	6.96045	0.384327
$329$	−12.2651	−0.676197
$330$	11.9707	0.658964
$331$	35.2455	1.93727	0.968635	−	0.248488i	$-0.0799337\pi$
$331$	35.2455	1.93727	0.968635	+	0.248488i	$0.0799337\pi$
$332$	−17.4969	−0.960268
$333$	3.57593	0.195960
$334$	−32.5174	−1.77927
$335$	−4.90899	−0.268207
$336$	3.15060	0.171879
$337$	30.6184	1.66789	0.833945	−	0.551848i	$-0.186077\pi$
$337$	30.6184	1.66789	0.833945	+	0.551848i	$0.186077\pi$
$338$	−1.35745	−0.0738357
$339$	1.42912	0.0776193
$340$	−42.7530	−2.31861
$341$	12.1417	0.657507
$342$	16.2028	0.876149
$343$	−1.00000	−0.0539949
$344$	−4.53499	−0.244510
$345$	−13.4849	−0.726001
$346$	−37.6778	−2.02557
$347$	27.4850	1.47547	0.737735	−	0.675090i	$-0.235895\pi$
$347$	27.4850	1.47547	0.737735	+	0.675090i	$0.235895\pi$
$348$	−18.6066	−0.997416
$349$	−19.4676	−1.04208	−0.521040	−	0.853533i	$-0.674456\pi$
$349$	−19.4676	−1.04208	−0.521040	+	0.853533i	$0.674456\pi$
$350$	3.43847	0.183794
$351$	3.69461	0.197203
$352$	17.9711	0.957865
$353$	15.4926	0.824588	0.412294	−	0.911051i	$-0.364728\pi$
$353$	15.4926	0.824588	0.412294	+	0.911051i	$0.364728\pi$
$354$	−20.3943	−1.08395
$355$	−29.2967	−1.55491
$356$	−19.4863	−1.03277
$357$	−7.02691	−0.371903
$358$	12.7317	0.672890
$359$	−9.43494	−0.497957	−0.248979	−	0.968509i	$-0.580095\pi$
$359$	−9.43494	−0.497957	−0.248979	+	0.968509i	$0.580095\pi$
$360$	1.93757	0.102119
$361$	41.2147	2.16920
$362$	−37.5079	−1.97137
$363$	−6.05520	−0.317816
$364$	−8.71899	−0.456999
$365$	14.9868	0.784447
$366$	16.1485	0.844094
$367$	−3.41891	−0.178466	−0.0892328	−	0.996011i	$-0.528442\pi$
$367$	−3.41891	−0.178466	−0.0892328	+	0.996011i	$0.528442\pi$
$368$	−16.4792	−0.859038
$369$	−9.26157	−0.482138
$370$	19.2501	1.00076
$371$	2.08281	0.108134
$372$	12.8855	0.668083
$373$	0.975047	0.0504860	0.0252430	−	0.999681i	$-0.491964\pi$
$373$	0.975047	0.0504860	0.0252430	+	0.999681i	$0.491964\pi$
$374$	−32.6271	−1.68711
$375$	8.64513	0.446432
$376$	−9.21772	−0.475368
$377$	−29.1297	−1.50026
$378$	2.08804	0.107397
$379$	−6.79171	−0.348867	−0.174433	−	0.984669i	$-0.555809\pi$
$379$	−6.79171	−0.348867	−0.174433	+	0.984669i	$0.555809\pi$
$380$	47.2122	2.42193
$381$	−9.00870	−0.461530
$382$	2.08804	0.106834
$383$	0.275042	0.0140540	0.00702698	−	0.999975i	$-0.497763\pi$
$383$	0.275042	0.0140540	0.00702698	+	0.999975i	$0.497763\pi$
$384$	5.91497	0.301847
$385$	5.73296	0.292179
$386$	−23.2027	−1.18099
$387$	6.03426	0.306738
$388$	1.64066	0.0832918
$389$	5.16870	0.262063	0.131032	−	0.991378i	$-0.458171\pi$
$389$	5.16870	0.262063	0.131032	+	0.991378i	$0.458171\pi$
$390$	19.8890	1.00712
$391$	36.7542	1.85874
$392$	−0.751541	−0.0379585
$393$	3.31739	0.167340
$394$	−0.755726	−0.0380729
$395$	30.5437	1.53682
$396$	5.24775	0.263709
$397$	21.2541	1.06671	0.533357	−	0.845890i	$-0.320930\pi$
$397$	21.2541	1.06671	0.533357	+	0.845890i	$0.320930\pi$
$398$	−22.2854	−1.11706
$399$	7.75981	0.388477
$400$	−5.18823	−0.259411
$401$	4.08639	0.204064	0.102032	−	0.994781i	$-0.467466\pi$
$401$	4.08639	0.204064	0.102032	+	0.994781i	$0.467466\pi$
$402$	−3.97582	−0.198296
$403$	20.1730	1.00489
$404$	−16.9230	−0.841951
$405$	−2.57813	−0.128108
$406$	−16.4629	−0.817042
$407$	7.95176	0.394154
$408$	−5.28101	−0.261449
$409$	−38.1975	−1.88874	−0.944371	−	0.328881i	$-0.893329\pi$
$409$	−38.1975	−1.88874	−0.944371	+	0.328881i	$0.893329\pi$
$410$	−49.8573	−2.46228
$411$	20.9837	1.03505
$412$	−29.0605	−1.43171
$413$	−9.76720	−0.480612
$414$	−10.9215	−0.536762
$415$	19.1147	0.938304
$416$	29.8586	1.46394
$417$	9.93023	0.486286
$418$	36.0301	1.76229
$419$	33.8683	1.65458	0.827288	−	0.561778i	$-0.189883\pi$
$419$	33.8683	1.65458	0.827288	+	0.561778i	$0.189883\pi$
$420$	6.08419	0.296878
$421$	22.2746	1.08560	0.542799	−	0.839863i	$-0.317365\pi$
$421$	22.2746	1.08560	0.542799	+	0.839863i	$0.317365\pi$
$422$	19.2754	0.938311
$423$	12.2651	0.596349
$424$	1.56531	0.0760183
$425$	11.5715	0.561301
$426$	−23.7276	−1.14961
$427$	7.73378	0.374264
$428$	27.4464	1.32667
$429$	8.21566	0.396656
$430$	32.4839	1.56651
$431$	−18.2279	−0.878008	−0.439004	−	0.898485i	$-0.644669\pi$
$431$	−18.2279	−0.878008	−0.439004	+	0.898485i	$0.644669\pi$
$432$	−3.15060	−0.151583
$433$	6.61223	0.317764	0.158882	−	0.987298i	$-0.449211\pi$
$433$	6.61223	0.317764	0.158882	+	0.987298i	$0.449211\pi$
$434$	11.4010	0.547266
$435$	20.3270	0.974603
$436$	−16.0957	−0.770843
$437$	−40.5877	−1.94157
$438$	12.1380	0.579974
$439$	10.3420	0.493598	0.246799	−	0.969067i	$-0.420621\pi$
$439$	10.3420	0.493598	0.246799	+	0.969067i	$0.420621\pi$
$440$	4.30855	0.205402
$441$	1.00000	0.0476190
$442$	−54.2091	−2.57846
$443$	−8.10817	−0.385231	−0.192615	−	0.981274i	$-0.561697\pi$
$443$	−8.10817	−0.385231	−0.192615	+	0.981274i	$0.561697\pi$
$444$	8.43892	0.400493
$445$	21.2880	1.00915
$446$	−23.5266	−1.11402
$447$	15.5497	0.735476
$448$	10.5737	0.499560
$449$	−20.8960	−0.986144	−0.493072	−	0.869988i	$-0.664126\pi$
$449$	−20.8960	−0.986144	−0.493072	+	0.869988i	$0.664126\pi$
$450$	−3.43847	−0.162091
$451$	−20.5949	−0.969775
$452$	3.37262	0.158635
$453$	−14.5418	−0.683231
$454$	14.9719	0.702664
$455$	9.52516	0.446547
$456$	5.83182	0.273100
$457$	16.9553	0.793137	0.396569	−	0.918005i	$-0.370201\pi$
$457$	16.9553	0.793137	0.396569	+	0.918005i	$0.370201\pi$
$458$	−47.0600	−2.19897
$459$	7.02691	0.327988
$460$	−31.8233	−1.48377
$461$	12.1599	0.566342	0.283171	−	0.959069i	$-0.408614\pi$
$461$	12.1599	0.566342	0.283171	+	0.959069i	$0.408614\pi$
$462$	4.64316	0.216020
$463$	5.31679	0.247092	0.123546	−	0.992339i	$-0.460573\pi$
$463$	5.31679	0.247092	0.123546	+	0.992339i	$0.460573\pi$
$464$	24.8406	1.15319
$465$	−14.0769	−0.652802
$466$	45.7881	2.12109
$467$	20.6794	0.956927	0.478463	−	0.878108i	$-0.341194\pi$
$467$	20.6794	0.956927	0.478463	+	0.878108i	$0.341194\pi$
$468$	8.71899	0.403036
$469$	−1.90409	−0.0879227
$470$	66.0260	3.04555
$471$	−15.8527	−0.730454
$472$	−7.34045	−0.337871
$473$	13.4183	0.616975
$474$	24.7375	1.13623
$475$	−12.7784	−0.586314
$476$	−16.5830	−0.760080
$477$	−2.08281	−0.0953651
$478$	−23.5774	−1.07840
$479$	24.2076	1.10607	0.553036	−	0.833157i	$-0.313469\pi$
$479$	24.2076	1.10607	0.553036	+	0.833157i	$0.313469\pi$
$480$	−20.8356	−0.951010
$481$	13.2116	0.602399
$482$	−46.6433	−2.12454
$483$	−5.23049	−0.237996
$484$	−14.2898	−0.649537
$485$	−1.79236	−0.0813867
$486$	−2.08804	−0.0947156
$487$	14.2758	0.646898	0.323449	−	0.946246i	$-0.395158\pi$
$487$	14.2758	0.646898	0.323449	+	0.946246i	$0.395158\pi$
$488$	5.81225	0.263108
$489$	14.1998	0.642139
$490$	5.38324	0.243190
$491$	−10.7427	−0.484810	−0.242405	−	0.970175i	$-0.577936\pi$
$491$	−10.7427	−0.484810	−0.242405	+	0.970175i	$0.577936\pi$
$492$	−21.8566	−0.985373
$493$	−55.4029	−2.49522
$494$	59.8631	2.69337
$495$	−5.73296	−0.257677
$496$	−17.2027	−0.772425
$497$	−11.3635	−0.509725
$498$	15.4811	0.693726
$499$	24.7211	1.10667	0.553334	−	0.832960i	$-0.313355\pi$
$499$	24.7211	1.10667	0.553334	+	0.832960i	$0.313355\pi$
$500$	20.4019	0.912399
$501$	15.5731	0.695757
$502$	−1.82587	−0.0814924
$503$	−41.1705	−1.83570	−0.917852	−	0.396924i	$-0.870078\pi$
$503$	−41.1705	−1.83570	−0.917852	+	0.396924i	$0.870078\pi$
$504$	0.751541	0.0334763
$505$	18.4877	0.822693
$506$	−24.2860	−1.07965
$507$	0.650107	0.0288723
$508$	−21.2599	−0.943254
$509$	28.7400	1.27388	0.636939	−	0.770914i	$-0.280200\pi$
$509$	28.7400	1.27388	0.636939	+	0.770914i	$0.280200\pi$
$510$	37.8276	1.67503
$511$	5.81307	0.257155
$512$	−30.1978	−1.33456
$513$	−7.75981	−0.342604
$514$	54.1565	2.38874
$515$	31.7475	1.39896
$516$	14.2404	0.626898
$517$	27.2738	1.19950
$518$	7.46669	0.328068
$519$	18.0445	0.792067
$520$	7.15855	0.313923
$521$	−2.38860	−0.104647	−0.0523233	−	0.998630i	$-0.516663\pi$
$521$	−2.38860	−0.104647	−0.0523233	+	0.998630i	$0.516663\pi$
$522$	16.4629	0.720563
$523$	−12.1159	−0.529793	−0.264896	−	0.964277i	$-0.585338\pi$
$523$	−12.1159	−0.529793	−0.264896	+	0.964277i	$0.585338\pi$
$524$	7.82879	0.342002
$525$	−1.64674	−0.0718697
$526$	−4.29517	−0.187278
$527$	38.3679	1.67133
$528$	−7.00596	−0.304895
$529$	4.35805	0.189481
$530$	−11.2123	−0.487029
$531$	9.76720	0.423860
$532$	18.3126	0.793951
$533$	−34.2179	−1.48214
$534$	17.2413	0.746105
$535$	−29.9841	−1.29633
$536$	−1.43100	−0.0618098
$537$	−6.09742	−0.263123
$538$	−1.67102	−0.0720426
$539$	2.22369	0.0957811
$540$	−6.08419	−0.261822
$541$	−13.3510	−0.574002	−0.287001	−	0.957930i	$-0.592658\pi$
$541$	−13.3510	−0.574002	−0.287001	+	0.957930i	$0.592658\pi$
$542$	−25.1851	−1.08179
$543$	17.9632	0.770874
$544$	56.7892	2.43482
$545$	17.5839	0.753212
$546$	7.71450	0.330150
$547$	20.7931	0.889051	0.444525	−	0.895766i	$-0.353372\pi$
$547$	20.7931	0.889051	0.444525	+	0.895766i	$0.353372\pi$
$548$	49.5200	2.11539
$549$	−7.73378	−0.330070
$550$	−7.64609	−0.326031
$551$	61.1814	2.60641
$552$	−3.93093	−0.167311
$553$	11.8472	0.503796
$554$	−66.9423	−2.84410
$555$	−9.21920	−0.391333
$556$	23.4346	0.993849
$557$	27.9654	1.18493	0.592466	−	0.805596i	$-0.298155\pi$
$557$	27.9654	1.18493	0.592466	+	0.805596i	$0.298155\pi$
$558$	−11.4010	−0.482643
$559$	22.2942	0.942944
$560$	−8.12265	−0.343245
$561$	15.6257	0.659716
$562$	27.4331	1.15720
$563$	−24.3316	−1.02545	−0.512727	−	0.858552i	$-0.671365\pi$
$563$	−24.3316	−1.02545	−0.512727	+	0.858552i	$0.671365\pi$
$564$	28.9447	1.21879
$565$	−3.68446	−0.155006
$566$	−38.5217	−1.61919
$567$	−1.00000	−0.0419961
$568$	−8.54017	−0.358338
$569$	39.0523	1.63716	0.818578	−	0.574395i	$-0.194763\pi$
$569$	39.0523	1.63716	0.818578	+	0.574395i	$0.194763\pi$
$570$	−41.7730	−1.74968
$571$	34.5397	1.44544	0.722720	−	0.691141i	$-0.242892\pi$
$571$	34.5397	1.44544	0.722720	+	0.691141i	$0.242892\pi$
$572$	19.3883	0.810668
$573$	−1.00000	−0.0417756
$574$	−19.3386	−0.807176
$575$	8.61327	0.359198
$576$	−10.5737	−0.440570
$577$	−13.1498	−0.547433	−0.273717	−	0.961810i	$-0.588253\pi$
$577$	−13.1498	−0.547433	−0.273717	+	0.961810i	$0.588253\pi$
$578$	−67.6055	−2.81202
$579$	11.1122	0.461807
$580$	47.9701	1.99185
$581$	7.41418	0.307592
$582$	−1.45164	−0.0601725
$583$	−4.63152	−0.191818
$584$	4.36876	0.180781
$585$	−9.52516	−0.393817
$586$	−29.9570	−1.23751
$587$	25.4229	1.04931	0.524657	−	0.851313i	$-0.324193\pi$
$587$	25.4229	1.04931	0.524657	+	0.851313i	$0.324193\pi$
$588$	2.35993	0.0973217
$589$	−42.3696	−1.74581
$590$	52.5792	2.16465
$591$	0.361930	0.0148878
$592$	−11.2663	−0.463043
$593$	−11.9933	−0.492506	−0.246253	−	0.969206i	$-0.579199\pi$
$593$	−11.9933	−0.492506	−0.246253	+	0.969206i	$0.579199\pi$
$594$	−4.64316	−0.190511
$595$	18.1163	0.742695
$596$	36.6961	1.50313
$597$	10.6728	0.436810
$598$	−40.3506	−1.65006
$599$	−33.9646	−1.38776	−0.693879	−	0.720092i	$-0.744100\pi$
$599$	−33.9646	−1.38776	−0.693879	+	0.720092i	$0.744100\pi$
$600$	−1.23759	−0.0505246
$601$	4.00283	0.163279	0.0816395	−	0.996662i	$-0.473984\pi$
$601$	4.00283	0.163279	0.0816395	+	0.996662i	$0.473984\pi$
$602$	12.5998	0.513529
$603$	1.90409	0.0775405
$604$	−34.3175	−1.39636
$605$	15.6111	0.634680
$606$	14.9733	0.608251
$607$	−39.8955	−1.61931	−0.809655	−	0.586906i	$-0.800346\pi$
$607$	−39.8955	−1.61931	−0.809655	+	0.586906i	$0.800346\pi$
$608$	−62.7123	−2.54332
$609$	7.88438	0.319491
$610$	−41.6328	−1.68566
$611$	45.3147	1.83324
$612$	16.5830	0.670327
$613$	9.26837	0.374346	0.187173	−	0.982327i	$-0.440068\pi$
$613$	9.26837	0.374346	0.187173	+	0.982327i	$0.440068\pi$
$614$	54.7588	2.20989
$615$	23.8775	0.962834
$616$	1.67119	0.0673343
$617$	26.8585	1.08128	0.540642	−	0.841253i	$-0.318181\pi$
$617$	26.8585	1.08128	0.540642	+	0.841253i	$0.318181\pi$
$618$	25.7125	1.03431
$619$	−24.0076	−0.964946	−0.482473	−	0.875911i	$-0.660261\pi$
$619$	−24.0076	−0.964946	−0.482473	+	0.875911i	$0.660261\pi$
$620$	−33.2205	−1.33417
$621$	5.23049	0.209892
$622$	3.17207	0.127188
$623$	8.25717	0.330816
$624$	−11.6402	−0.465982
$625$	−30.5220	−1.22088
$626$	60.2446	2.40786
$627$	−17.2554	−0.689115
$628$	−37.4112	−1.49287
$629$	25.1277	1.00191
$630$	−5.38324	−0.214474
$631$	10.0170	0.398771	0.199385	−	0.979921i	$-0.436105\pi$
$631$	10.0170	0.398771	0.199385	+	0.979921i	$0.436105\pi$
$632$	8.90368	0.354169
$633$	−9.23131	−0.366912
$634$	−46.9555	−1.86484
$635$	23.2256	0.921679
$636$	−4.91527	−0.194903
$637$	3.69461	0.146386
$638$	36.6085	1.44934
$639$	11.3635	0.449535
$640$	−15.2495	−0.602791
$641$	1.92284	0.0759476	0.0379738	−	0.999279i	$-0.487910\pi$
$641$	1.92284	0.0759476	0.0379738	+	0.999279i	$0.487910\pi$
$642$	−24.2843	−0.958426
$643$	16.0699	0.633736	0.316868	−	0.948470i	$-0.397369\pi$
$643$	16.0699	0.633736	0.316868	+	0.948470i	$0.397369\pi$
$644$	−12.3436	−0.486405
$645$	−15.5571	−0.612559
$646$	113.856	4.47960
$647$	−34.8868	−1.37154	−0.685772	−	0.727817i	$-0.740535\pi$
$647$	−34.8868	−1.37154	−0.685772	+	0.727817i	$0.740535\pi$
$648$	−0.751541	−0.0295233
$649$	21.7192	0.852554
$650$	−12.7038	−0.498284
$651$	−5.46014	−0.214000
$652$	33.5106	1.31237
$653$	−31.7894	−1.24402	−0.622008	−	0.783011i	$-0.713683\pi$
$653$	−31.7894	−1.24402	−0.622008	+	0.783011i	$0.713683\pi$
$654$	14.2413	0.556880
$655$	−8.55265	−0.334180
$656$	29.1795	1.13927
$657$	−5.81307	−0.226790
$658$	25.6101	0.998384
$659$	−9.51152	−0.370516	−0.185258	−	0.982690i	$-0.559312\pi$
$659$	−9.51152	−0.370516	−0.185258	+	0.982690i	$0.559312\pi$
$660$	−13.5294	−0.526630
$661$	13.6540	0.531080	0.265540	−	0.964100i	$-0.414450\pi$
$661$	13.6540	0.531080	0.265540	+	0.964100i	$0.414450\pi$
$662$	−73.5942	−2.86032
$663$	25.9617	1.00827
$664$	5.57206	0.216238
$665$	−20.0058	−0.775791
$666$	−7.46669	−0.289328
$667$	−41.2392	−1.59679
$668$	36.7515	1.42196
$669$	11.2673	0.435619
$670$	10.2502	0.395999
$671$	−17.1975	−0.663903
$672$	−8.08168	−0.311757
$673$	−21.6795	−0.835682	−0.417841	−	0.908520i	$-0.637213\pi$
$673$	−21.6795	−0.835682	−0.417841	+	0.908520i	$0.637213\pi$
$674$	−63.9325	−2.46259
$675$	1.64674	0.0633831
$676$	1.53421	0.0590079
$677$	10.4673	0.402292	0.201146	−	0.979561i	$-0.435533\pi$
$677$	10.4673	0.402292	0.201146	+	0.979561i	$0.435533\pi$
$678$	−2.98407	−0.114602
$679$	−0.695216	−0.0266799
$680$	13.6151	0.522116
$681$	−7.17028	−0.274766
$682$	−25.3523	−0.970790
$683$	−3.42076	−0.130892	−0.0654459	−	0.997856i	$-0.520847\pi$
$683$	−3.42076	−0.130892	−0.0654459	+	0.997856i	$0.520847\pi$
$684$	−18.3126	−0.700199
$685$	−54.0987	−2.06700
$686$	2.08804	0.0797219
$687$	22.5378	0.859872
$688$	−19.0115	−0.724808
$689$	−7.69515	−0.293162
$690$	28.1570	1.07192
$691$	−18.1802	−0.691607	−0.345803	−	0.938307i	$-0.612394\pi$
$691$	−18.1802	−0.691607	−0.345803	+	0.938307i	$0.612394\pi$
$692$	42.5838	1.61879
$693$	−2.22369	−0.0844710
$694$	−57.3898	−2.17849
$695$	−25.6014	−0.971117
$696$	5.92544	0.224603
$697$	−65.0802	−2.46509
$698$	40.6493	1.53860
$699$	−21.9287	−0.829421
$700$	−3.88619	−0.146884
$701$	29.8654	1.12800	0.564001	−	0.825774i	$-0.309261\pi$
$701$	29.8654	1.12800	0.564001	+	0.825774i	$0.309261\pi$
$702$	−7.71450	−0.291165
$703$	−27.7485	−1.04656
$704$	−23.5126	−0.886165
$705$	−31.6210	−1.19091
$706$	−32.3492	−1.21748
$707$	7.17099	0.269693
$708$	23.0499	0.866267
$709$	−17.7220	−0.665564	−0.332782	−	0.943004i	$-0.607987\pi$
$709$	−17.7220	−0.665564	−0.332782	+	0.943004i	$0.607987\pi$
$710$	61.1727	2.29577
$711$	−11.8472	−0.444306
$712$	6.20560	0.232565
$713$	28.5592	1.06955
$714$	14.6725	0.549104
$715$	−21.1810	−0.792125
$716$	−14.3895	−0.537759
$717$	11.2916	0.421693
$718$	19.7006	0.735219
$719$	−34.1172	−1.27236	−0.636178	−	0.771543i	$-0.719485\pi$
$719$	−34.1172	−1.27236	−0.636178	+	0.771543i	$0.719485\pi$
$720$	8.12265	0.302713
$721$	12.3142	0.458604
$722$	−86.0581	−3.20275
$723$	22.3383	0.830769
$724$	42.3918	1.57548
$725$	−12.9836	−0.482197
$726$	12.6435	0.469245
$727$	−19.8931	−0.737793	−0.368897	−	0.929470i	$-0.620264\pi$
$727$	−19.8931	−0.737793	−0.368897	+	0.929470i	$0.620264\pi$
$728$	2.77665	0.102909
$729$	1.00000	0.0370370
$730$	−31.2932	−1.15821
$731$	42.4022	1.56830
$732$	−18.2511	−0.674582
$733$	18.5941	0.686790	0.343395	−	0.939191i	$-0.388423\pi$
$733$	18.5941	0.686790	0.343395	+	0.939191i	$0.388423\pi$
$734$	7.13883	0.263499
$735$	−2.57813	−0.0950957
$736$	42.2711	1.55813
$737$	4.23411	0.155965
$738$	19.3386	0.711863
$739$	19.2882	0.709526	0.354763	−	0.934956i	$-0.384562\pi$
$739$	19.2882	0.709526	0.354763	+	0.934956i	$0.384562\pi$
$740$	−21.7566	−0.799789
$741$	−28.6694	−1.05320
$742$	−4.34899	−0.159656
$743$	42.1568	1.54658	0.773291	−	0.634051i	$-0.218609\pi$
$743$	42.1568	1.54658	0.773291	+	0.634051i	$0.218609\pi$
$744$	−4.10351	−0.150442
$745$	−40.0891	−1.46875
$746$	−2.03594	−0.0745411
$747$	−7.41418	−0.271271
$748$	36.8754	1.34830
$749$	−11.6302	−0.424958
$750$	−18.0514	−0.659144
$751$	−3.21171	−0.117197	−0.0585984	−	0.998282i	$-0.518663\pi$
$751$	−3.21171	−0.117197	−0.0585984	+	0.998282i	$0.518663\pi$
$752$	−38.6424	−1.40914
$753$	0.874439	0.0318663
$754$	60.8241	2.21508
$755$	37.4905	1.36442
$756$	−2.35993	−0.0858297
$757$	43.3091	1.57410	0.787048	−	0.616891i	$-0.211608\pi$
$757$	43.3091	1.57410	0.787048	+	0.616891i	$0.211608\pi$
$758$	14.1814	0.515091
$759$	11.6310	0.422179
$760$	−15.0352	−0.545383
$761$	−35.9225	−1.30219	−0.651094	−	0.758997i	$-0.725690\pi$
$761$	−35.9225	−1.30219	−0.651094	+	0.758997i	$0.725690\pi$
$762$	18.8106	0.681435
$763$	6.82042	0.246916
$764$	−2.35993	−0.0853791
$765$	−18.1163	−0.654995
$766$	−0.574299	−0.0207503
$767$	36.0859	1.30299
$768$	8.79666	0.317422
$769$	−42.0203	−1.51529	−0.757646	−	0.652666i	$-0.773651\pi$
$769$	−42.0203	−1.51529	−0.757646	+	0.652666i	$0.773651\pi$
$770$	−11.9707	−0.431393
$771$	−25.9365	−0.934080
$772$	26.2239	0.943820
$773$	20.2243	0.727416	0.363708	−	0.931513i	$-0.381511\pi$
$773$	20.2243	0.727416	0.363708	+	0.931513i	$0.381511\pi$
$774$	−12.5998	−0.452890
$775$	8.99144	0.322982
$776$	−0.522483	−0.0187561
$777$	−3.57593	−0.128286
$778$	−10.7925	−0.386928
$779$	71.8681	2.57494
$780$	−22.4787	−0.804866
$781$	25.2690	0.904196
$782$	−76.7444	−2.74437
$783$	−7.88438	−0.281765
$784$	−3.15060	−0.112521
$785$	40.8703	1.45872
$786$	−6.92685	−0.247073
$787$	17.6413	0.628846	0.314423	−	0.949283i	$-0.398189\pi$
$787$	17.6413	0.628846	0.314423	+	0.949283i	$0.398189\pi$
$788$	0.854129	0.0304271
$789$	2.05703	0.0732323
$790$	−63.7765	−2.26907
$791$	−1.42912	−0.0508137
$792$	−1.67119	−0.0593833
$793$	−28.5733	−1.01467
$794$	−44.3795	−1.57497
$795$	5.36974	0.190445
$796$	25.1871	0.892733
$797$	40.4692	1.43349	0.716746	−	0.697334i	$-0.245631\pi$
$797$	40.4692	1.43349	0.716746	+	0.697334i	$0.245631\pi$
$798$	−16.2028	−0.573574
$799$	86.1857	3.04903
$800$	13.3084	0.470524
$801$	−8.25717	−0.291753
$802$	−8.53255	−0.301295
$803$	−12.9265	−0.456166
$804$	4.49351	0.158474
$805$	13.4849	0.475279
$806$	−42.1222	−1.48369
$807$	0.800278	0.0281711
$808$	5.38929	0.189595
$809$	−50.2230	−1.76575	−0.882874	−	0.469610i	$-0.844395\pi$
$809$	−50.2230	−1.76575	−0.882874	+	0.469610i	$0.844395\pi$
$810$	5.38324	0.189148
$811$	6.75608	0.237238	0.118619	−	0.992940i	$-0.462153\pi$
$811$	6.75608	0.237238	0.118619	+	0.992940i	$0.462153\pi$
$812$	18.6066	0.652962
$813$	12.0616	0.423017
$814$	−16.6036	−0.581956
$815$	−36.6090	−1.28236
$816$	−22.1390	−0.775020
$817$	−46.8247	−1.63819
$818$	79.7580	2.78867
$819$	−3.69461	−0.129100
$820$	56.3492	1.96780
$821$	17.0642	0.595546	0.297773	−	0.954637i	$-0.403756\pi$
$821$	17.0642	0.595546	0.297773	+	0.954637i	$0.403756\pi$
$822$	−43.8149	−1.52822
$823$	6.88606	0.240033	0.120016	−	0.992772i	$-0.461705\pi$
$823$	6.88606	0.240033	0.120016	+	0.992772i	$0.461705\pi$
$824$	9.25460	0.322399
$825$	3.66185	0.127489
$826$	20.3943	0.709610
$827$	−36.6279	−1.27368	−0.636838	−	0.770998i	$-0.719758\pi$
$827$	−36.6279	−1.27368	−0.636838	+	0.770998i	$0.719758\pi$
$828$	12.3436	0.428969
$829$	−24.7422	−0.859334	−0.429667	−	0.902987i	$-0.641369\pi$
$829$	−24.7422	−0.859334	−0.429667	+	0.902987i	$0.641369\pi$
$830$	−39.9123	−1.38538
$831$	32.0598	1.11214
$832$	−39.0656	−1.35436
$833$	7.02691	0.243468
$834$	−20.7348	−0.717986
$835$	−40.1496	−1.38943
$836$	−40.7215	−1.40838
$837$	5.46014	0.188730
$838$	−70.7185	−2.44293
$839$	−21.3352	−0.736572	−0.368286	−	0.929713i	$-0.620055\pi$
$839$	−21.3352	−0.736572	−0.368286	+	0.929713i	$0.620055\pi$
$840$	−1.93757	−0.0668525
$841$	33.1635	1.14357
$842$	−46.5103	−1.60285
$843$	−13.1382	−0.452503
$844$	−21.7852	−0.749878
$845$	−1.67606	−0.0576582
$846$	−25.6101	−0.880492
$847$	6.05520	0.208059
$848$	6.56209	0.225343
$849$	18.4487	0.633158
$850$	−24.1618	−0.828743
$851$	18.7039	0.641160
$852$	26.8171	0.918740
$853$	12.8311	0.439327	0.219664	−	0.975576i	$-0.429504\pi$
$853$	12.8311	0.439327	0.219664	+	0.975576i	$0.429504\pi$
$854$	−16.1485	−0.552589
$855$	20.0058	0.684184
$856$	−8.74056	−0.298746
$857$	12.0677	0.412224	0.206112	−	0.978528i	$-0.433919\pi$
$857$	12.0677	0.412224	0.206112	+	0.978528i	$0.433919\pi$
$858$	−17.1547	−0.585650
$859$	−25.9688	−0.886043	−0.443021	−	0.896511i	$-0.646093\pi$
$859$	−25.9688	−0.886043	−0.443021	+	0.896511i	$0.646093\pi$
$860$	−36.7136	−1.25192
$861$	9.26157	0.315634
$862$	38.0607	1.29635
$863$	−37.8396	−1.28808	−0.644038	−	0.764994i	$-0.722742\pi$
$863$	−37.8396	−1.28808	−0.644038	+	0.764994i	$0.722742\pi$
$864$	8.08168	0.274944
$865$	−46.5211	−1.58176
$866$	−13.8066	−0.469169
$867$	32.3774	1.09960
$868$	−12.8855	−0.437363
$869$	−26.3446	−0.893679
$870$	−42.4436	−1.43897
$871$	7.03486	0.238367
$872$	5.12582	0.173582
$873$	0.695216	0.0235295
$874$	84.7488	2.86667
$875$	−8.64513	−0.292259
$876$	−13.7184	−0.463503
$877$	50.4345	1.70305	0.851525	−	0.524314i	$-0.175678\pi$
$877$	50.4345	1.70305	0.851525	+	0.524314i	$0.175678\pi$
$878$	−21.5946	−0.728783
$879$	14.3469	0.483910
$880$	18.0623	0.608879
$881$	−23.9595	−0.807216	−0.403608	−	0.914932i	$-0.632244\pi$
$881$	−23.9595	−0.807216	−0.403608	+	0.914932i	$0.632244\pi$
$882$	−2.08804	−0.0703081
$883$	−8.05681	−0.271133	−0.135567	−	0.990768i	$-0.543285\pi$
$883$	−8.05681	−0.271133	−0.135567	+	0.990768i	$0.543285\pi$
$884$	61.2676	2.06065
$885$	−25.1811	−0.846453
$886$	16.9302	0.568781
$887$	20.1184	0.675509	0.337755	−	0.941234i	$-0.390333\pi$
$887$	20.1184	0.675509	0.337755	+	0.941234i	$0.390333\pi$
$888$	−2.68745	−0.0901851
$889$	9.00870	0.302142
$890$	−44.4503	−1.48998
$891$	2.22369	0.0744964
$892$	26.5900	0.890300
$893$	−95.1749	−3.18491
$894$	−32.4685	−1.08591
$895$	15.7199	0.525459
$896$	−5.91497	−0.197605
$897$	19.3246	0.645230
$898$	43.6318	1.45601
$899$	−43.0498	−1.43579
$900$	3.88619	0.129540
$901$	−14.6357	−0.487585
$902$	43.0030	1.43184
$903$	−6.03426	−0.200807
$904$	−1.07404	−0.0357222
$905$	−46.3114	−1.53944
$906$	30.3638	1.00877
$907$	12.8319	0.426077	0.213038	−	0.977044i	$-0.431664\pi$
$907$	12.8319	0.426077	0.213038	+	0.977044i	$0.431664\pi$
$908$	−16.9213	−0.561554
$909$	−7.17099	−0.237847
$910$	−19.8890	−0.659313
$911$	−32.1742	−1.06598	−0.532989	−	0.846122i	$-0.678931\pi$
$911$	−32.1742	−1.06598	−0.532989	+	0.846122i	$0.678931\pi$
$912$	24.4481	0.809557
$913$	−16.4868	−0.545635
$914$	−35.4035	−1.17104
$915$	19.9387	0.659152
$916$	53.1876	1.75737
$917$	−3.31739	−0.109550
$918$	−14.6725	−0.484264
$919$	−12.8101	−0.422567	−0.211284	−	0.977425i	$-0.567764\pi$
$919$	−12.8101	−0.422567	−0.211284	+	0.977425i	$0.567764\pi$
$920$	10.1344	0.334122
$921$	−26.2249	−0.864141
$922$	−25.3904	−0.836187
$923$	41.9838	1.38191
$924$	−5.24775	−0.172638
$925$	5.88863	0.193617
$926$	−11.1017	−0.364824
$927$	−12.3142	−0.404450
$928$	−63.7190	−2.09168
$929$	−33.2971	−1.09244	−0.546221	−	0.837641i	$-0.683934\pi$
$929$	−33.2971	−1.09244	−0.546221	+	0.837641i	$0.683934\pi$
$930$	29.3932	0.963842
$931$	−7.75981	−0.254318
$932$	−51.7502	−1.69513
$933$	−1.51916	−0.0497351
$934$	−43.1794	−1.41287
$935$	−40.2850	−1.31746
$936$	−2.77665	−0.0907575
$937$	28.8912	0.943834	0.471917	−	0.881643i	$-0.343562\pi$
$937$	28.8912	0.943834	0.471917	+	0.881643i	$0.343562\pi$
$938$	3.97582	0.129815
$939$	−28.8522	−0.941555
$940$	−74.6232	−2.43394
$941$	18.1302	0.591027	0.295514	−	0.955338i	$-0.404509\pi$
$941$	18.1302	0.591027	0.295514	+	0.955338i	$0.404509\pi$
$942$	33.1011	1.07849
$943$	−48.4426	−1.57751
$944$	−30.7726	−1.00156
$945$	2.57813	0.0838665
$946$	−28.0180	−0.910945
$947$	−33.7022	−1.09518	−0.547588	−	0.836748i	$-0.684454\pi$
$947$	−33.7022	−1.09518	−0.547588	+	0.836748i	$0.684454\pi$
$948$	−27.9586	−0.908053
$949$	−21.4770	−0.697173
$950$	26.6819	0.865675
$951$	22.4878	0.729217
$952$	5.28101	0.171158
$953$	−53.9821	−1.74865	−0.874326	−	0.485338i	$-0.838696\pi$
$953$	−53.9821	−1.74865	−0.874326	+	0.485338i	$0.838696\pi$
$954$	4.34899	0.140804
$955$	2.57813	0.0834263
$956$	26.6474	0.861837
$957$	−17.5324	−0.566743
$958$	−50.5465	−1.63308
$959$	−20.9837	−0.677599
$960$	27.2603	0.879823
$961$	−1.18692	−0.0382877
$962$	−27.5865	−0.889424
$963$	11.6302	0.374778
$964$	52.7167	1.69789
$965$	−28.6486	−0.922232
$966$	10.9215	0.351393
$967$	−6.67633	−0.214696	−0.107348	−	0.994221i	$-0.534236\pi$
$967$	−6.67633	−0.214696	−0.107348	+	0.994221i	$0.534236\pi$
$968$	4.55073	0.146266
$969$	−54.5275	−1.75168
$970$	3.74252	0.120165
$971$	−9.56667	−0.307009	−0.153505	−	0.988148i	$-0.549056\pi$
$971$	−9.56667	−0.307009	−0.153505	+	0.988148i	$0.549056\pi$
$972$	2.35993	0.0756947
$973$	−9.93023	−0.318349
$974$	−29.8085	−0.955125
$975$	6.08406	0.194846
$976$	24.3661	0.779938
$977$	25.4704	0.814870	0.407435	−	0.913234i	$-0.366423\pi$
$977$	25.4704	0.814870	0.407435	+	0.913234i	$0.366423\pi$
$978$	−29.6499	−0.948099
$979$	−18.3614	−0.586833
$980$	−6.08419	−0.194352
$981$	−6.82042	−0.217759
$982$	22.4311	0.715807
$983$	5.99386	0.191174	0.0955872	−	0.995421i	$-0.469527\pi$
$983$	5.99386	0.191174	0.0955872	+	0.995421i	$0.469527\pi$
$984$	6.96045	0.221891
$985$	−0.933103	−0.0297311
$986$	115.684	3.68412
$987$	−12.2651	−0.390402
$988$	−67.6578	−2.15248
$989$	31.5621	1.00362
$990$	11.9707	0.380453
$991$	−14.8545	−0.471868	−0.235934	−	0.971769i	$-0.575815\pi$
$991$	−14.8545	−0.471868	−0.235934	+	0.971769i	$0.575815\pi$
$992$	44.1270	1.40104
$993$	35.2455	1.11848
$994$	23.7276	0.752593
$995$	−27.5159	−0.872314
$996$	−17.4969	−0.554411
$997$	3.43580	0.108813	0.0544065	−	0.998519i	$-0.482673\pi$
$997$	3.43580	0.108813	0.0544065	+	0.998519i	$0.482673\pi$
$998$	−51.6187	−1.63396
$999$	3.57593	0.113137

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4011.2.a.m.1.5	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4011.2.a.m.1.5	✓	29	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:	\( N \)	\(=\)	\( 4011 = 3 \cdot 7 \cdot 191 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4011.a (trivial)

\(f(q)\)	\(=\)	\(q-2.08804 q^{2} +1.00000 q^{3} +2.35993 q^{4} -2.57813 q^{5} -2.08804 q^{6} -1.00000 q^{7} -0.751541 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.08804 q^{2} +1.00000 q^{3} +2.35993 q^{4} -2.57813 q^{5} -2.08804 q^{6} -1.00000 q^{7} -0.751541 q^{8} +1.00000 q^{9} +5.38324 q^{10} +2.22369 q^{11} +2.35993 q^{12} +3.69461 q^{13} +2.08804 q^{14} -2.57813 q^{15} -3.15060 q^{16} +7.02691 q^{17} -2.08804 q^{18} -7.75981 q^{19} -6.08419 q^{20} -1.00000 q^{21} -4.64316 q^{22} +5.23049 q^{23} -0.751541 q^{24} +1.64674 q^{25} -7.71450 q^{26} +1.00000 q^{27} -2.35993 q^{28} -7.88438 q^{29} +5.38324 q^{30} +5.46014 q^{31} +8.08168 q^{32} +2.22369 q^{33} -14.6725 q^{34} +2.57813 q^{35} +2.35993 q^{36} +3.57593 q^{37} +16.2028 q^{38} +3.69461 q^{39} +1.93757 q^{40} -9.26157 q^{41} +2.08804 q^{42} +6.03426 q^{43} +5.24775 q^{44} -2.57813 q^{45} -10.9215 q^{46} +12.2651 q^{47} -3.15060 q^{48} +1.00000 q^{49} -3.43847 q^{50} +7.02691 q^{51} +8.71899 q^{52} -2.08281 q^{53} -2.08804 q^{54} -5.73296 q^{55} +0.751541 q^{56} -7.75981 q^{57} +16.4629 q^{58} +9.76720 q^{59} -6.08419 q^{60} -7.73378 q^{61} -11.4010 q^{62} -1.00000 q^{63} -10.5737 q^{64} -9.52516 q^{65} -4.64316 q^{66} +1.90409 q^{67} +16.5830 q^{68} +5.23049 q^{69} -5.38324 q^{70} +11.3635 q^{71} -0.751541 q^{72} -5.81307 q^{73} -7.46669 q^{74} +1.64674 q^{75} -18.3126 q^{76} -2.22369 q^{77} -7.71450 q^{78} -11.8472 q^{79} +8.12265 q^{80} +1.00000 q^{81} +19.3386 q^{82} -7.41418 q^{83} -2.35993 q^{84} -18.1163 q^{85} -12.5998 q^{86} -7.88438 q^{87} -1.67119 q^{88} -8.25717 q^{89} +5.38324 q^{90} -3.69461 q^{91} +12.3436 q^{92} +5.46014 q^{93} -25.6101 q^{94} +20.0058 q^{95} +8.08168 q^{96} +0.695216 q^{97} -2.08804 q^{98} +2.22369 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9	\( 29 q + 6 q^{2} + 29 q^{3} + 40 q^{4} + 22 q^{5} + 6 q^{6} - 29 q^{7} + 15 q^{8} + 29 q^{9} + 11 q^{11} + 40 q^{12} + 13 q^{13} - 6 q^{14} + 22 q^{15} + 58 q^{16} + 17 q^{17} + 6 q^{18} + 3 q^{19} + 52 q^{20} - 29 q^{21} + 17 q^{22} + 36 q^{23} + 15 q^{24} + 57 q^{25} + 25 q^{26} + 29 q^{27} - 40 q^{28} + 20 q^{29} + 6 q^{31} + 46 q^{32} + 11 q^{33} + 18 q^{34} - 22 q^{35} + 40 q^{36} + 22 q^{37} + 8 q^{38} + 13 q^{39} + 6 q^{40} + 26 q^{41} - 6 q^{42} + 21 q^{43} + 22 q^{44} + 22 q^{45} + 28 q^{46} + 41 q^{47} + 58 q^{48} + 29 q^{49} + 18 q^{50} + 17 q^{51} + 2 q^{52} + 37 q^{53} + 6 q^{54} + 7 q^{55} - 15 q^{56} + 3 q^{57} + 9 q^{58} + 27 q^{59} + 52 q^{60} + 20 q^{61} - 12 q^{62} - 29 q^{63} + 59 q^{64} + 3 q^{65} + 17 q^{66} + 30 q^{67} + 33 q^{68} + 36 q^{69} + 68 q^{71} + 15 q^{72} + q^{73} + 21 q^{74} + 57 q^{75} + 11 q^{76} - 11 q^{77} + 25 q^{78} + 34 q^{79} + 110 q^{80} + 29 q^{81} - 49 q^{82} + 13 q^{83} - 40 q^{84} + 27 q^{85} + 35 q^{86} + 20 q^{87} + 17 q^{88} + 61 q^{89} - 13 q^{91} + 86 q^{92} + 6 q^{93} - 19 q^{94} + 25 q^{95} + 46 q^{96} - 3 q^{97} + 6 q^{98} + 11 q^{99}+O(q^{100}) \) 29 * q + 6 * q^2 + 29 * q^3 + 40 * q^4 + 22 * q^5 + 6 * q^6 - 29 * q^7 + 15 * q^8 + 29 * q^9 + 11 * q^11 + 40 * q^12 + 13 * q^13 - 6 * q^14 + 22 * q^15 + 58 * q^16 + 17 * q^17 + 6 * q^18 + 3 * q^19 + 52 * q^20 - 29 * q^21 + 17 * q^22 + 36 * q^23 + 15 * q^24 + 57 * q^25 + 25 * q^26 + 29 * q^27 - 40 * q^28 + 20 * q^29 + 6 * q^31 + 46 * q^32 + 11 * q^33 + 18 * q^34 - 22 * q^35 + 40 * q^36 + 22 * q^37 + 8 * q^38 + 13 * q^39 + 6 * q^40 + 26 * q^41 - 6 * q^42 + 21 * q^43 + 22 * q^44 + 22 * q^45 + 28 * q^46 + 41 * q^47 + 58 * q^48 + 29 * q^49 + 18 * q^50 + 17 * q^51 + 2 * q^52 + 37 * q^53 + 6 * q^54 + 7 * q^55 - 15 * q^56 + 3 * q^57 + 9 * q^58 + 27 * q^59 + 52 * q^60 + 20 * q^61 - 12 * q^62 - 29 * q^63 + 59 * q^64 + 3 * q^65 + 17 * q^66 + 30 * q^67 + 33 * q^68 + 36 * q^69 + 68 * q^71 + 15 * q^72 + q^73 + 21 * q^74 + 57 * q^75 + 11 * q^76 - 11 * q^77 + 25 * q^78 + 34 * q^79 + 110 * q^80 + 29 * q^81 - 49 * q^82 + 13 * q^83 - 40 * q^84 + 27 * q^85 + 35 * q^86 + 20 * q^87 + 17 * q^88 + 61 * q^89 - 13 * q^91 + 86 * q^92 + 6 * q^93 - 19 * q^94 + 25 * q^95 + 46 * q^96 - 3 * q^97 + 6 * q^98 + 11 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more