LMFDB - Embedded newform 4029.2.a.f.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, 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("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$1$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.821645 q^{2} -1.00000 q^{3} -1.32490 q^{4} +1.58661 q^{5} +0.821645 q^{6} +1.25319 q^{7} +2.73189 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.821645 q^{2} -1.00000 q^{3} -1.32490 q^{4} +1.58661 q^{5} +0.821645 q^{6} +1.25319 q^{7} +2.73189 q^{8} +1.00000 q^{9} -1.30363 q^{10} -1.54012 q^{11} +1.32490 q^{12} +0.937074 q^{13} -1.02968 q^{14} -1.58661 q^{15} +0.405155 q^{16} +1.00000 q^{17} -0.821645 q^{18} -3.77792 q^{19} -2.10210 q^{20} -1.25319 q^{21} +1.26543 q^{22} -2.63234 q^{23} -2.73189 q^{24} -2.48267 q^{25} -0.769942 q^{26} -1.00000 q^{27} -1.66035 q^{28} +5.33373 q^{29} +1.30363 q^{30} +3.12973 q^{31} -5.79667 q^{32} +1.54012 q^{33} -0.821645 q^{34} +1.98833 q^{35} -1.32490 q^{36} +5.59640 q^{37} +3.10411 q^{38} -0.937074 q^{39} +4.33444 q^{40} -8.59699 q^{41} +1.02968 q^{42} -3.34419 q^{43} +2.04050 q^{44} +1.58661 q^{45} +2.16285 q^{46} -4.27835 q^{47} -0.405155 q^{48} -5.42951 q^{49} +2.03987 q^{50} -1.00000 q^{51} -1.24153 q^{52} -0.964407 q^{53} +0.821645 q^{54} -2.44357 q^{55} +3.42358 q^{56} +3.77792 q^{57} -4.38243 q^{58} -8.70732 q^{59} +2.10210 q^{60} -6.92887 q^{61} -2.57153 q^{62} +1.25319 q^{63} +3.95250 q^{64} +1.48677 q^{65} -1.26543 q^{66} -13.4955 q^{67} -1.32490 q^{68} +2.63234 q^{69} -1.63370 q^{70} +7.62314 q^{71} +2.73189 q^{72} +9.85250 q^{73} -4.59826 q^{74} +2.48267 q^{75} +5.00537 q^{76} -1.93007 q^{77} +0.769942 q^{78} +1.00000 q^{79} +0.642823 q^{80} +1.00000 q^{81} +7.06367 q^{82} -9.17319 q^{83} +1.66035 q^{84} +1.58661 q^{85} +2.74774 q^{86} -5.33373 q^{87} -4.20744 q^{88} +16.3346 q^{89} -1.30363 q^{90} +1.17433 q^{91} +3.48759 q^{92} -3.12973 q^{93} +3.51528 q^{94} -5.99409 q^{95} +5.79667 q^{96} +16.6297 q^{97} +4.46113 q^{98} -1.54012 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) $ 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * 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 $

$2$	−0.821645	−0.580991	−0.290495	−	0.956876i	$-0.593820\pi$
$2$	−0.821645	−0.580991	−0.290495	+	0.956876i	$0.593820\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.32490	−0.662449
$5$	1.58661	0.709554	0.354777	−	0.934951i	$-0.384557\pi$
$5$	1.58661	0.709554	0.354777	+	0.934951i	$0.384557\pi$
$6$	0.821645	0.335435
$7$	1.25319	0.473662	0.236831	−	0.971551i	$-0.423891\pi$
$7$	1.25319	0.473662	0.236831	+	0.971551i	$0.423891\pi$
$8$	2.73189	0.965868
$9$	1.00000	0.333333
$10$	−1.30363	−0.412244
$11$	−1.54012	−0.464364	−0.232182	−	0.972672i	$-0.574586\pi$
$11$	−1.54012	−0.464364	−0.232182	+	0.972672i	$0.574586\pi$
$12$	1.32490	0.382465
$13$	0.937074	0.259898	0.129949	−	0.991521i	$-0.458519\pi$
$13$	0.937074	0.259898	0.129949	+	0.991521i	$0.458519\pi$
$14$	−1.02968	−0.275193
$15$	−1.58661	−0.409661
$16$	0.405155	0.101289
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−0.821645	−0.193664
$19$	−3.77792	−0.866715	−0.433357	−	0.901222i	$-0.642671\pi$
$19$	−3.77792	−0.866715	−0.433357	+	0.901222i	$0.642671\pi$
$20$	−2.10210	−0.470044
$21$	−1.25319	−0.273469
$22$	1.26543	0.269791
$23$	−2.63234	−0.548881	−0.274441	−	0.961604i	$-0.588493\pi$
$23$	−2.63234	−0.548881	−0.274441	+	0.961604i	$0.588493\pi$
$24$	−2.73189	−0.557644
$25$	−2.48267	−0.496533
$26$	−0.769942	−0.150998
$27$	−1.00000	−0.192450
$28$	−1.66035	−0.313777
$29$	5.33373	0.990448	0.495224	−	0.868765i	$-0.335086\pi$
$29$	5.33373	0.990448	0.495224	+	0.868765i	$0.335086\pi$
$30$	1.30363	0.238009
$31$	3.12973	0.562117	0.281058	−	0.959691i	$-0.409315\pi$
$31$	3.12973	0.562117	0.281058	+	0.959691i	$0.409315\pi$
$32$	−5.79667	−1.02472
$33$	1.54012	0.268101
$34$	−0.821645	−0.140911
$35$	1.98833	0.336089
$36$	−1.32490	−0.220816
$37$	5.59640	0.920042	0.460021	−	0.887908i	$-0.347842\pi$
$37$	5.59640	0.920042	0.460021	+	0.887908i	$0.347842\pi$
$38$	3.10411	0.503554
$39$	−0.937074	−0.150052
$40$	4.33444	0.685336
$41$	−8.59699	−1.34262	−0.671312	−	0.741175i	$-0.734269\pi$
$41$	−8.59699	−1.34262	−0.671312	+	0.741175i	$0.734269\pi$
$42$	1.02968	0.158883
$43$	−3.34419	−0.509984	−0.254992	−	0.966943i	$-0.582073\pi$
$43$	−3.34419	−0.509984	−0.254992	+	0.966943i	$0.582073\pi$
$44$	2.04050	0.307618
$45$	1.58661	0.236518
$46$	2.16285	0.318895
$47$	−4.27835	−0.624061	−0.312031	−	0.950072i	$-0.601009\pi$
$47$	−4.27835	−0.624061	−0.312031	+	0.950072i	$0.601009\pi$
$48$	−0.405155	−0.0584791
$49$	−5.42951	−0.775644
$50$	2.03987	0.288481
$51$	−1.00000	−0.140028
$52$	−1.24153	−0.172169
$53$	−0.964407	−0.132471	−0.0662357	−	0.997804i	$-0.521099\pi$
$53$	−0.964407	−0.132471	−0.0662357	+	0.997804i	$0.521099\pi$
$54$	0.821645	0.111812
$55$	−2.44357	−0.329491
$56$	3.42358	0.457495
$57$	3.77792	0.500398
$58$	−4.38243	−0.575441
$59$	−8.70732	−1.13360	−0.566798	−	0.823857i	$-0.691818\pi$
$59$	−8.70732	−1.13360	−0.566798	+	0.823857i	$0.691818\pi$
$60$	2.10210	0.271380
$61$	−6.92887	−0.887151	−0.443576	−	0.896237i	$-0.646290\pi$
$61$	−6.92887	−0.887151	−0.443576	+	0.896237i	$0.646290\pi$
$62$	−2.57153	−0.326585
$63$	1.25319	0.157887
$64$	3.95250	0.494062
$65$	1.48677	0.184411
$66$	−1.26543	−0.155764
$67$	−13.4955	−1.64874	−0.824371	−	0.566051i	$-0.808471\pi$
$67$	−13.4955	−1.64874	−0.824371	+	0.566051i	$0.808471\pi$
$68$	−1.32490	−0.160668
$69$	2.63234	0.316897
$70$	−1.63370	−0.195265
$71$	7.62314	0.904700	0.452350	−	0.891840i	$-0.350586\pi$
$71$	7.62314	0.904700	0.452350	+	0.891840i	$0.350586\pi$
$72$	2.73189	0.321956
$73$	9.85250	1.15315	0.576574	−	0.817045i	$-0.304389\pi$
$73$	9.85250	1.15315	0.576574	+	0.817045i	$0.304389\pi$
$74$	−4.59826	−0.534536
$75$	2.48267	0.286674
$76$	5.00537	0.574155
$77$	−1.93007	−0.219952
$78$	0.769942	0.0871788
$79$	1.00000	0.112509
$79$	1.00000	0.112509
$80$	0.642823	0.0718698
$81$	1.00000	0.111111
$82$	7.06367	0.780052
$83$	−9.17319	−1.00689	−0.503444	−	0.864028i	$-0.667934\pi$
$83$	−9.17319	−1.00689	−0.503444	+	0.864028i	$0.667934\pi$
$84$	1.66035	0.181159
$85$	1.58661	0.172092
$86$	2.74774	0.296296
$87$	−5.33373	−0.571835
$88$	−4.20744	−0.448514
$89$	16.3346	1.73147	0.865735	−	0.500503i	$-0.166852\pi$
$89$	16.3346	1.73147	0.865735	+	0.500503i	$0.166852\pi$
$90$	−1.30363	−0.137415
$91$	1.17433	0.123104
$92$	3.48759	0.363606
$93$	−3.12973	−0.324538
$94$	3.51528	0.362574
$95$	−5.99409	−0.614981
$96$	5.79667	0.591620
$97$	16.6297	1.68849	0.844247	−	0.535955i	$-0.180048\pi$
$97$	16.6297	1.68849	0.844247	+	0.535955i	$0.180048\pi$
$98$	4.46113	0.450642
$99$	−1.54012	−0.154788
$100$	3.28928	0.328928
$101$	6.29138	0.626016	0.313008	−	0.949750i	$-0.398663\pi$
$101$	6.29138	0.626016	0.313008	+	0.949750i	$0.398663\pi$
$102$	0.821645	0.0813550
$103$	3.62300	0.356985	0.178493	−	0.983941i	$-0.442878\pi$
$103$	3.62300	0.356985	0.178493	+	0.983941i	$0.442878\pi$
$104$	2.55998	0.251027
$105$	−1.98833	−0.194041
$106$	0.792400	0.0769647
$107$	−7.99972	−0.773362	−0.386681	−	0.922213i	$-0.626379\pi$
$107$	−7.99972	−0.773362	−0.386681	+	0.922213i	$0.626379\pi$
$108$	1.32490	0.127488
$109$	6.73145	0.644756	0.322378	−	0.946611i	$-0.395518\pi$
$109$	6.73145	0.644756	0.322378	+	0.946611i	$0.395518\pi$
$110$	2.00775	0.191431
$111$	−5.59640	−0.531187
$112$	0.507737	0.0479767
$113$	12.4669	1.17279	0.586393	−	0.810027i	$-0.300548\pi$
$113$	12.4669	1.17279	0.586393	+	0.810027i	$0.300548\pi$
$114$	−3.10411	−0.290727
$115$	−4.17650	−0.389461
$116$	−7.06665	−0.656122
$117$	0.937074	0.0866325
$118$	7.15433	0.658609
$119$	1.25319	0.114880
$120$	−4.33444	−0.395679
$121$	−8.62803	−0.784366
$122$	5.69308	0.515427
$123$	8.59699	0.775164
$124$	−4.14658	−0.372374
$125$	−11.8721	−1.06187
$126$	−1.02968	−0.0917312
$127$	8.65306	0.767834	0.383917	−	0.923368i	$-0.374575\pi$
$127$	8.65306	0.767834	0.383917	+	0.923368i	$0.374575\pi$
$128$	8.34579	0.737670
$129$	3.34419	0.294439
$130$	−1.22160	−0.107141
$131$	9.26668	0.809634	0.404817	−	0.914398i	$-0.367335\pi$
$131$	9.26668	0.809634	0.404817	+	0.914398i	$0.367335\pi$
$132$	−2.04050	−0.177603
$133$	−4.73446	−0.410530
$134$	11.0885	0.957904
$135$	−1.58661	−0.136554
$136$	2.73189	0.234257
$137$	−16.2353	−1.38707	−0.693537	−	0.720421i	$-0.743949\pi$
$137$	−16.2353	−1.38707	−0.693537	+	0.720421i	$0.743949\pi$
$138$	−2.16285	−0.184114
$139$	3.49498	0.296440	0.148220	−	0.988954i	$-0.452646\pi$
$139$	3.49498	0.296440	0.148220	+	0.988954i	$0.452646\pi$
$140$	−2.63433	−0.222642
$141$	4.27835	0.360302
$142$	−6.26352	−0.525623
$143$	−1.44321	−0.120687
$144$	0.405155	0.0337629
$145$	8.46255	0.702776
$146$	−8.09526	−0.669968
$147$	5.42951	0.447818
$148$	−7.41466	−0.609482
$149$	−4.86385	−0.398462	−0.199231	−	0.979953i	$-0.563844\pi$
$149$	−4.86385	−0.398462	−0.199231	+	0.979953i	$0.563844\pi$
$150$	−2.03987	−0.166555
$151$	−5.82205	−0.473791	−0.236896	−	0.971535i	$-0.576130\pi$
$151$	−5.82205	−0.473791	−0.236896	+	0.971535i	$0.576130\pi$
$152$	−10.3209	−0.837132
$153$	1.00000	0.0808452
$154$	1.58583	0.127790
$155$	4.96567	0.398852
$156$	1.24153	0.0994018
$157$	−17.4260	−1.39075	−0.695373	−	0.718649i	$-0.744761\pi$
$157$	−17.4260	−1.39075	−0.695373	+	0.718649i	$0.744761\pi$
$158$	−0.821645	−0.0653666
$159$	0.964407	0.0764824
$160$	−9.19706	−0.727091
$161$	−3.29883	−0.259984
$162$	−0.821645	−0.0645546
$163$	−11.4159	−0.894161	−0.447081	−	0.894494i	$-0.647536\pi$
$163$	−11.4159	−0.894161	−0.447081	+	0.894494i	$0.647536\pi$
$164$	11.3901	0.889420
$165$	2.44357	0.190232
$166$	7.53711	0.584993
$167$	3.06392	0.237093	0.118547	−	0.992948i	$-0.462177\pi$
$167$	3.06392	0.237093	0.118547	+	0.992948i	$0.462177\pi$
$168$	−3.42358	−0.264135
$169$	−12.1219	−0.932453
$170$	−1.30363	−0.0999840
$171$	−3.77792	−0.288905
$172$	4.43071	0.337839
$173$	−3.21906	−0.244741	−0.122370	−	0.992484i	$-0.539050\pi$
$173$	−3.21906	−0.244741	−0.122370	+	0.992484i	$0.539050\pi$
$174$	4.38243	0.332231
$175$	−3.11126	−0.235189
$176$	−0.623988	−0.0470348
$177$	8.70732	0.654482
$178$	−13.4213	−1.00597
$179$	−2.50817	−0.187470	−0.0937348	−	0.995597i	$-0.529881\pi$
$179$	−2.50817	−0.187470	−0.0937348	+	0.995597i	$0.529881\pi$
$180$	−2.10210	−0.156681
$181$	−15.6232	−1.16126	−0.580632	−	0.814166i	$-0.697195\pi$
$181$	−15.6232	−1.16126	−0.580632	+	0.814166i	$0.697195\pi$
$182$	−0.964886	−0.0715221
$183$	6.92887	0.512197
$184$	−7.19126	−0.530147
$185$	8.87931	0.652820
$186$	2.57153	0.188554
$187$	−1.54012	−0.112625
$188$	5.66838	0.413409
$189$	−1.25319	−0.0911563
$190$	4.92502	0.357298
$191$	7.84911	0.567942	0.283971	−	0.958833i	$-0.408348\pi$
$191$	7.84911	0.567942	0.283971	+	0.958833i	$0.408348\pi$
$192$	−3.95250	−0.285247
$193$	2.87009	0.206594	0.103297	−	0.994651i	$-0.467061\pi$
$193$	2.87009	0.206594	0.103297	+	0.994651i	$0.467061\pi$
$194$	−13.6637	−0.980999
$195$	−1.48677	−0.106470
$196$	7.19355	0.513825
$197$	−21.9591	−1.56452	−0.782260	−	0.622952i	$-0.785933\pi$
$197$	−21.9591	−1.56452	−0.782260	+	0.622952i	$0.785933\pi$
$198$	1.26543	0.0899304
$199$	−10.3106	−0.730896	−0.365448	−	0.930832i	$-0.619084\pi$
$199$	−10.3106	−0.730896	−0.365448	+	0.930832i	$0.619084\pi$
$200$	−6.78237	−0.479586
$201$	13.4955	0.951901
$202$	−5.16929	−0.363710
$203$	6.68418	0.469138
$204$	1.32490	0.0927615
$205$	−13.6401	−0.952664
$206$	−2.97682	−0.207405
$207$	−2.63234	−0.182960
$208$	0.379660	0.0263247
$209$	5.81846	0.402471
$210$	1.63370	0.112736
$211$	8.19801	0.564374	0.282187	−	0.959359i	$-0.408940\pi$
$211$	8.19801	0.564374	0.282187	+	0.959359i	$0.408940\pi$
$212$	1.27774	0.0877556
$213$	−7.62314	−0.522329
$214$	6.57294	0.449317
$215$	−5.30593	−0.361861
$216$	−2.73189	−0.185881
$217$	3.92216	0.266253
$218$	−5.53087	−0.374598
$219$	−9.85250	−0.665770
$220$	3.23749	0.218271
$221$	0.937074	0.0630344
$222$	4.59826	0.308615
$223$	−26.5732	−1.77947	−0.889736	−	0.456476i	$-0.849111\pi$
$223$	−26.5732	−1.77947	−0.889736	+	0.456476i	$0.849111\pi$
$224$	−7.26434	−0.485369
$225$	−2.48267	−0.165511
$226$	−10.2434	−0.681378
$227$	3.67059	0.243625	0.121813	−	0.992553i	$-0.461129\pi$
$227$	3.67059	0.243625	0.121813	+	0.992553i	$0.461129\pi$
$228$	−5.00537	−0.331488
$229$	−4.03971	−0.266952	−0.133476	−	0.991052i	$-0.542614\pi$
$229$	−4.03971	−0.266952	−0.133476	+	0.991052i	$0.542614\pi$
$230$	3.43160	0.226273
$231$	1.93007	0.126989
$232$	14.5711	0.956642
$233$	−17.3679	−1.13781	−0.568903	−	0.822405i	$-0.692632\pi$
$233$	−17.3679	−1.13781	−0.568903	+	0.822405i	$0.692632\pi$
$234$	−0.769942	−0.0503327
$235$	−6.78807	−0.442805
$236$	11.5363	0.750950
$237$	−1.00000	−0.0649570
$238$	−1.02968	−0.0667442
$239$	20.2061	1.30702	0.653511	−	0.756917i	$-0.273295\pi$
$239$	20.2061	1.30702	0.653511	+	0.756917i	$0.273295\pi$
$240$	−0.642823	−0.0414941
$241$	−28.9768	−1.86656	−0.933280	−	0.359150i	$-0.883067\pi$
$241$	−28.9768	−1.86656	−0.933280	+	0.359150i	$0.883067\pi$
$242$	7.08918	0.455710
$243$	−1.00000	−0.0641500
$244$	9.18006	0.587693
$245$	−8.61452	−0.550361
$246$	−7.06367	−0.450363
$247$	−3.54019	−0.225257
$248$	8.55008	0.542930
$249$	9.17319	0.581327
$250$	9.75464	0.616938
$251$	1.47633	0.0931852	0.0465926	−	0.998914i	$-0.485164\pi$
$251$	1.47633	0.0931852	0.0465926	+	0.998914i	$0.485164\pi$
$252$	−1.66035	−0.104592
$253$	4.05412	0.254881
$254$	−7.10974	−0.446105
$255$	−1.58661	−0.0993574
$256$	−14.7623	−0.922642
$257$	−13.5010	−0.842167	−0.421083	−	0.907022i	$-0.638350\pi$
$257$	−13.5010	−0.842167	−0.421083	+	0.907022i	$0.638350\pi$
$258$	−2.74774	−0.171067
$259$	7.01337	0.435789
$260$	−1.96982	−0.122163
$261$	5.33373	0.330149
$262$	−7.61393	−0.470390
$263$	−4.19437	−0.258636	−0.129318	−	0.991603i	$-0.541279\pi$
$263$	−4.19437	−0.258636	−0.129318	+	0.991603i	$0.541279\pi$
$264$	4.20744	0.258950
$265$	−1.53014	−0.0939956
$266$	3.89005	0.238514
$267$	−16.3346	−0.999664
$268$	17.8802	1.09221
$269$	2.20237	0.134281	0.0671403	−	0.997744i	$-0.478612\pi$
$269$	2.20237	0.134281	0.0671403	+	0.997744i	$0.478612\pi$
$270$	1.30363	0.0793365
$271$	−26.2951	−1.59731	−0.798657	−	0.601786i	$-0.794456\pi$
$271$	−26.2951	−1.59731	−0.798657	+	0.601786i	$0.794456\pi$
$272$	0.405155	0.0245661
$273$	−1.17433	−0.0710739
$274$	13.3396	0.805877
$275$	3.82361	0.230572
$276$	−3.48759	−0.209928
$277$	11.1233	0.668335	0.334168	−	0.942514i	$-0.391545\pi$
$277$	11.1233	0.668335	0.334168	+	0.942514i	$0.391545\pi$
$278$	−2.87163	−0.172229
$279$	3.12973	0.187372
$280$	5.43189	0.324618
$281$	9.38241	0.559707	0.279854	−	0.960043i	$-0.409714\pi$
$281$	9.38241	0.559707	0.279854	+	0.960043i	$0.409714\pi$
$282$	−3.51528	−0.209332
$283$	−14.7630	−0.877569	−0.438784	−	0.898592i	$-0.644591\pi$
$283$	−14.7630	−0.877569	−0.438784	+	0.898592i	$0.644591\pi$
$284$	−10.0999	−0.599318
$285$	5.99409	0.355059
$286$	1.18580	0.0701181
$287$	−10.7737	−0.635950
$288$	−5.79667	−0.341572
$289$	1.00000	0.0588235
$290$	−6.95321	−0.408307
$291$	−16.6297	−0.974852
$292$	−13.0536	−0.763902
$293$	1.22718	0.0716924	0.0358462	−	0.999357i	$-0.488587\pi$
$293$	1.22718	0.0716924	0.0358462	+	0.999357i	$0.488587\pi$
$294$	−4.46113	−0.260178
$295$	−13.8151	−0.804348
$296$	15.2887	0.888640
$297$	1.54012	0.0893669
$298$	3.99636	0.231503
$299$	−2.46670	−0.142653
$300$	−3.28928	−0.189907
$301$	−4.19091	−0.241560
$302$	4.78366	0.275268
$303$	−6.29138	−0.361431
$304$	−1.53064	−0.0877885
$305$	−10.9934	−0.629482
$306$	−0.821645	−0.0469703
$307$	−10.4425	−0.595984	−0.297992	−	0.954568i	$-0.596317\pi$
$307$	−10.4425	−0.595984	−0.297992	+	0.954568i	$0.596317\pi$
$308$	2.55715	0.145707
$309$	−3.62300	−0.206105
$310$	−4.08002	−0.231729
$311$	−22.6925	−1.28678	−0.643388	−	0.765540i	$-0.722472\pi$
$311$	−22.6925	−1.28678	−0.643388	+	0.765540i	$0.722472\pi$
$312$	−2.55998	−0.144930
$313$	17.3360	0.979889	0.489945	−	0.871754i	$-0.337017\pi$
$313$	17.3360	0.979889	0.489945	+	0.871754i	$0.337017\pi$
$314$	14.3180	0.808011
$315$	1.98833	0.112030
$316$	−1.32490	−0.0745314
$317$	1.44352	0.0810761	0.0405381	−	0.999178i	$-0.487093\pi$
$317$	1.44352	0.0810761	0.0405381	+	0.999178i	$0.487093\pi$
$318$	−0.792400	−0.0444356
$319$	−8.21458	−0.459928
$320$	6.27107	0.350564
$321$	7.99972	0.446501
$322$	2.71047	0.151048
$323$	−3.77792	−0.210209
$324$	−1.32490	−0.0736055
$325$	−2.32644	−0.129048
$326$	9.37981	0.519500
$327$	−6.73145	−0.372250
$328$	−23.4860	−1.29680
$329$	−5.36159	−0.295594
$330$	−2.00775	−0.110523
$331$	−2.03774	−0.112004	−0.0560022	−	0.998431i	$-0.517835\pi$
$331$	−2.03774	−0.112004	−0.0560022	+	0.998431i	$0.517835\pi$
$332$	12.1535	0.667012
$333$	5.59640	0.306681
$334$	−2.51745	−0.137749
$335$	−21.4122	−1.16987
$336$	−0.507737	−0.0276993
$337$	−2.05951	−0.112189	−0.0560943	−	0.998425i	$-0.517865\pi$
$337$	−2.05951	−0.112189	−0.0560943	+	0.998425i	$0.517865\pi$
$338$	9.95990	0.541747
$339$	−12.4669	−0.677108
$340$	−2.10210	−0.114002
$341$	−4.82017	−0.261027
$342$	3.10411	0.167851
$343$	−15.5766	−0.841056
$344$	−9.13595	−0.492577
$345$	4.17650	0.224855
$346$	2.64493	0.142192
$347$	−20.0902	−1.07850	−0.539249	−	0.842147i	$-0.681292\pi$
$347$	−20.0902	−1.07850	−0.539249	+	0.842147i	$0.681292\pi$
$348$	7.06665	0.378812
$349$	6.03108	0.322836	0.161418	−	0.986886i	$-0.448393\pi$
$349$	6.03108	0.322836	0.161418	+	0.986886i	$0.448393\pi$
$350$	2.55635	0.136643
$351$	−0.937074	−0.0500173
$352$	8.92757	0.475841
$353$	35.5079	1.88989	0.944947	−	0.327223i	$-0.106113\pi$
$353$	35.5079	1.88989	0.944947	+	0.327223i	$0.106113\pi$
$354$	−7.15433	−0.380248
$355$	12.0950	0.641934
$356$	−21.6418	−1.14701
$357$	−1.25319	−0.0663260
$358$	2.06083	0.108918
$359$	−35.3289	−1.86459	−0.932294	−	0.361702i	$-0.882196\pi$
$359$	−35.3289	−1.86459	−0.932294	+	0.361702i	$0.882196\pi$
$360$	4.33444	0.228445
$361$	−4.72730	−0.248805
$362$	12.8367	0.674684
$363$	8.62803	0.452854
$364$	−1.55587	−0.0815499
$365$	15.6321	0.818220
$366$	−5.69308	−0.297582
$367$	−22.4179	−1.17020	−0.585102	−	0.810960i	$-0.698946\pi$
$367$	−22.4179	−1.17020	−0.585102	+	0.810960i	$0.698946\pi$
$368$	−1.06651	−0.0555955
$369$	−8.59699	−0.447541
$370$	−7.29564	−0.379282
$371$	−1.20859	−0.0627467
$372$	4.14658	0.214990
$373$	3.79555	0.196526	0.0982631	−	0.995160i	$-0.468671\pi$
$373$	3.79555	0.196526	0.0982631	+	0.995160i	$0.468671\pi$
$374$	1.26543	0.0654340
$375$	11.8721	0.613072
$376$	−11.6880	−0.602761
$377$	4.99810	0.257415
$378$	1.02968	0.0529610
$379$	14.2215	0.730507	0.365254	−	0.930908i	$-0.380982\pi$
$379$	14.2215	0.730507	0.365254	+	0.930908i	$0.380982\pi$
$380$	7.94157	0.407394
$381$	−8.65306	−0.443309
$382$	−6.44919	−0.329969
$383$	11.3539	0.580159	0.290080	−	0.957003i	$-0.406318\pi$
$383$	11.3539	0.580159	0.290080	+	0.957003i	$0.406318\pi$
$384$	−8.34579	−0.425894
$385$	−3.06227	−0.156068
$386$	−2.35820	−0.120029
$387$	−3.34419	−0.169995
$388$	−22.0327	−1.11854
$389$	18.8907	0.957796	0.478898	−	0.877871i	$-0.341036\pi$
$389$	18.8907	0.957796	0.478898	+	0.877871i	$0.341036\pi$
$390$	1.22160	0.0618581
$391$	−2.63234	−0.133123
$392$	−14.8328	−0.749170
$393$	−9.26668	−0.467442
$394$	18.0426	0.908972
$395$	1.58661	0.0798311
$396$	2.04050	0.102539
$397$	−32.1738	−1.61476	−0.807379	−	0.590033i	$-0.799115\pi$
$397$	−32.1738	−1.61476	−0.807379	+	0.590033i	$0.799115\pi$
$398$	8.47162	0.424644
$399$	4.73446	0.237020
$400$	−1.00586	−0.0502932
$401$	10.8908	0.543863	0.271931	−	0.962317i	$-0.412338\pi$
$401$	10.8908	0.543863	0.271931	+	0.962317i	$0.412338\pi$
$402$	−11.0885	−0.553046
$403$	2.93279	0.146093
$404$	−8.33545	−0.414704
$405$	1.58661	0.0788393
$406$	−5.49203	−0.272565
$407$	−8.61913	−0.427235
$408$	−2.73189	−0.135249
$409$	−23.4058	−1.15734	−0.578671	−	0.815561i	$-0.696429\pi$
$409$	−23.4058	−1.15734	−0.578671	+	0.815561i	$0.696429\pi$
$410$	11.2073	0.553489
$411$	16.2353	0.800827
$412$	−4.80011	−0.236485
$413$	−10.9119	−0.536942
$414$	2.16285	0.106298
$415$	−14.5543	−0.714441
$416$	−5.43191	−0.266321
$417$	−3.49498	−0.171150
$418$	−4.78071	−0.233832
$419$	19.2775	0.941765	0.470883	−	0.882196i	$-0.343936\pi$
$419$	19.2775	0.941765	0.470883	+	0.882196i	$0.343936\pi$
$420$	2.63433	0.128542
$421$	5.04976	0.246110	0.123055	−	0.992400i	$-0.460731\pi$
$421$	5.04976	0.246110	0.123055	+	0.992400i	$0.460731\pi$
$422$	−6.73586	−0.327896
$423$	−4.27835	−0.208020
$424$	−2.63465	−0.127950
$425$	−2.48267	−0.120427
$426$	6.26352	0.303468
$427$	−8.68321	−0.420210
$428$	10.5988	0.512314
$429$	1.44321	0.0696787
$430$	4.35959	0.210238
$431$	12.5735	0.605645	0.302823	−	0.953047i	$-0.402071\pi$
$431$	12.5735	0.605645	0.302823	+	0.953047i	$0.402071\pi$
$432$	−0.405155	−0.0194930
$433$	−17.2920	−0.831002	−0.415501	−	0.909593i	$-0.636394\pi$
$433$	−17.2920	−0.831002	−0.415501	+	0.909593i	$0.636394\pi$
$434$	−3.22262	−0.154691
$435$	−8.46255	−0.405748
$436$	−8.91849	−0.427118
$437$	9.94478	0.475723
$438$	8.09526	0.386806
$439$	−33.5960	−1.60345	−0.801724	−	0.597694i	$-0.796084\pi$
$439$	−33.5960	−1.60345	−0.801724	+	0.597694i	$0.796084\pi$
$440$	−6.67557	−0.318245
$441$	−5.42951	−0.258548
$442$	−0.769942	−0.0366224
$443$	−6.80354	−0.323246	−0.161623	−	0.986853i	$-0.551673\pi$
$443$	−6.80354	−0.323246	−0.161623	+	0.986853i	$0.551673\pi$
$444$	7.41466	0.351884
$445$	25.9167	1.22857
$446$	21.8337	1.03386
$447$	4.86385	0.230052
$448$	4.95324	0.234019
$449$	16.9132	0.798182	0.399091	−	0.916911i	$-0.369326\pi$
$449$	16.9132	0.798182	0.399091	+	0.916911i	$0.369326\pi$
$450$	2.03987	0.0961604
$451$	13.2404	0.623466
$452$	−16.5174	−0.776911
$453$	5.82205	0.273544
$454$	−3.01592	−0.141544
$455$	1.86321	0.0873487
$456$	10.3209	0.483319
$457$	1.50288	0.0703018	0.0351509	−	0.999382i	$-0.488809\pi$
$457$	1.50288	0.0703018	0.0351509	+	0.999382i	$0.488809\pi$
$458$	3.31921	0.155097
$459$	−1.00000	−0.0466760
$460$	5.53344	0.257998
$461$	20.2534	0.943296	0.471648	−	0.881787i	$-0.343659\pi$
$461$	20.2534	0.943296	0.471648	+	0.881787i	$0.343659\pi$
$462$	−1.58583	−0.0737796
$463$	−33.0375	−1.53538	−0.767692	−	0.640819i	$-0.778595\pi$
$463$	−33.0375	−1.53538	−0.767692	+	0.640819i	$0.778595\pi$
$464$	2.16099	0.100321
$465$	−4.96567	−0.230277
$466$	14.2702	0.661055
$467$	38.8110	1.79596	0.897978	−	0.440040i	$-0.145036\pi$
$467$	38.8110	1.79596	0.897978	+	0.440040i	$0.145036\pi$
$468$	−1.24153	−0.0573897
$469$	−16.9125	−0.780946
$470$	5.57739	0.257266
$471$	17.4260	0.802948
$472$	−23.7874	−1.09490
$473$	5.15046	0.236818
$474$	0.821645	0.0377394
$475$	9.37932	0.430353
$476$	−1.66035	−0.0761022
$477$	−0.964407	−0.0441572
$478$	−16.6022	−0.759368
$479$	−7.67535	−0.350696	−0.175348	−	0.984507i	$-0.556105\pi$
$479$	−7.67535	−0.350696	−0.175348	+	0.984507i	$0.556105\pi$
$480$	9.19706	0.419786
$481$	5.24424	0.239117
$482$	23.8087	1.08445
$483$	3.29883	0.150102
$484$	11.4313	0.519603
$485$	26.3849	1.19808
$486$	0.821645	0.0372706
$487$	2.71177	0.122882	0.0614410	−	0.998111i	$-0.480430\pi$
$487$	2.71177	0.122882	0.0614410	+	0.998111i	$0.480430\pi$
$488$	−18.9289	−0.856871
$489$	11.4159	0.516244
$490$	7.07808	0.319755
$491$	14.3920	0.649500	0.324750	−	0.945800i	$-0.394720\pi$
$491$	14.3920	0.649500	0.324750	+	0.945800i	$0.394720\pi$
$492$	−11.3901	−0.513507
$493$	5.33373	0.240219
$494$	2.90878	0.130872
$495$	−2.44357	−0.109830
$496$	1.26803	0.0569361
$497$	9.55326	0.428522
$498$	−7.53711	−0.337746
$499$	15.4731	0.692669	0.346335	−	0.938111i	$-0.387426\pi$
$499$	15.4731	0.692669	0.346335	+	0.938111i	$0.387426\pi$
$500$	15.7293	0.703436
$501$	−3.06392	−0.136886
$502$	−1.21302	−0.0541398
$503$	−6.08201	−0.271184	−0.135592	−	0.990765i	$-0.543294\pi$
$503$	−6.08201	−0.271184	−0.135592	+	0.990765i	$0.543294\pi$
$504$	3.42358	0.152498
$505$	9.98198	0.444192
$506$	−3.33105	−0.148083
$507$	12.1219	0.538352
$508$	−11.4644	−0.508652
$509$	−3.32346	−0.147310	−0.0736548	−	0.997284i	$-0.523466\pi$
$509$	−3.32346	−0.147310	−0.0736548	+	0.997284i	$0.523466\pi$
$510$	1.30363	0.0577258
$511$	12.3471	0.546202
$512$	−4.56223	−0.201624
$513$	3.77792	0.166799
$514$	11.0930	0.489291
$515$	5.74830	0.253300
$516$	−4.43071	−0.195051
$517$	6.58917	0.289792
$518$	−5.76250	−0.253190
$519$	3.21906	0.141301
$520$	4.06169	0.178117
$521$	30.2789	1.32654	0.663271	−	0.748380i	$-0.269168\pi$
$521$	30.2789	1.32654	0.663271	+	0.748380i	$0.269168\pi$
$522$	−4.38243	−0.191814
$523$	−4.32684	−0.189200	−0.0945998	−	0.995515i	$-0.530157\pi$
$523$	−4.32684	−0.189200	−0.0945998	+	0.995515i	$0.530157\pi$
$524$	−12.2774	−0.536341
$525$	3.11126	0.135786
$526$	3.44629	0.150265
$527$	3.12973	0.136333
$528$	0.623988	0.0271556
$529$	−16.0708	−0.698730
$530$	1.25723	0.0546106
$531$	−8.70732	−0.377865
$532$	6.27269	0.271955
$533$	−8.05601	−0.348945
$534$	13.4213	0.580796
$535$	−12.6924	−0.548742
$536$	−36.8683	−1.59247
$537$	2.50817	0.108236
$538$	−1.80956	−0.0780159
$539$	8.36210	0.360181
$540$	2.10210	0.0904599
$541$	10.4189	0.447944	0.223972	−	0.974596i	$-0.428098\pi$
$541$	10.4189	0.447944	0.223972	+	0.974596i	$0.428098\pi$
$542$	21.6053	0.928025
$543$	15.6232	0.670456
$544$	−5.79667	−0.248530
$545$	10.6802	0.457489
$546$	0.964886	0.0412933
$547$	22.2263	0.950328	0.475164	−	0.879897i	$-0.342389\pi$
$547$	22.2263	0.950328	0.475164	+	0.879897i	$0.342389\pi$
$548$	21.5101	0.918866
$549$	−6.92887	−0.295717
$550$	−3.14165	−0.133960
$551$	−20.1504	−0.858436
$552$	7.19126	0.306080
$553$	1.25319	0.0532912
$554$	−9.13942	−0.388297
$555$	−8.87931	−0.376906
$556$	−4.63049	−0.196377
$557$	−33.2486	−1.40879	−0.704393	−	0.709810i	$-0.748781\pi$
$557$	−33.2486	−1.40879	−0.704393	+	0.709810i	$0.748781\pi$
$558$	−2.57153	−0.108862
$559$	−3.13375	−0.132544
$560$	0.805581	0.0340420
$561$	1.54012	0.0650240
$562$	−7.70901	−0.325185
$563$	7.25191	0.305632	0.152816	−	0.988255i	$-0.451166\pi$
$563$	7.25191	0.305632	0.152816	+	0.988255i	$0.451166\pi$
$564$	−5.66838	−0.238682
$565$	19.7801	0.832154
$566$	12.1299	0.509860
$567$	1.25319	0.0526291
$568$	20.8256	0.873821
$569$	4.57829	0.191932	0.0959659	−	0.995385i	$-0.469406\pi$
$569$	4.57829	0.191932	0.0959659	+	0.995385i	$0.469406\pi$
$570$	−4.92502	−0.206286
$571$	−47.6484	−1.99403	−0.997013	−	0.0772382i	$-0.975390\pi$
$571$	−47.6484	−1.99403	−0.997013	+	0.0772382i	$0.975390\pi$
$572$	1.91210	0.0799491
$573$	−7.84911	−0.327901
$574$	8.85214	0.369481
$575$	6.53522	0.272538
$576$	3.95250	0.164687
$577$	5.97643	0.248802	0.124401	−	0.992232i	$-0.460299\pi$
$577$	5.97643	0.248802	0.124401	+	0.992232i	$0.460299\pi$
$578$	−0.821645	−0.0341759
$579$	−2.87009	−0.119277
$580$	−11.2120	−0.465554
$581$	−11.4958	−0.476925
$582$	13.6637	0.566380
$583$	1.48530	0.0615150
$584$	26.9159	1.11379
$585$	1.48677	0.0614704
$586$	−1.00830	−0.0416526
$587$	−28.9925	−1.19665	−0.598324	−	0.801254i	$-0.704166\pi$
$587$	−28.9925	−1.19665	−0.598324	+	0.801254i	$0.704166\pi$
$588$	−7.19355	−0.296657
$589$	−11.8239	−0.487195
$590$	11.3511	0.467319
$591$	21.9591	0.903276
$592$	2.26741	0.0931900
$593$	26.5416	1.08993	0.544966	−	0.838458i	$-0.316542\pi$
$593$	26.5416	1.08993	0.544966	+	0.838458i	$0.316542\pi$
$594$	−1.26543	−0.0519214
$595$	1.98833	0.0815135
$596$	6.44411	0.263961
$597$	10.3106	0.421983
$598$	2.02675	0.0828800
$599$	31.8408	1.30098	0.650490	−	0.759515i	$-0.274564\pi$
$599$	31.8408	1.30098	0.650490	+	0.759515i	$0.274564\pi$
$600$	6.78237	0.276889
$601$	−25.4810	−1.03939	−0.519695	−	0.854352i	$-0.673954\pi$
$601$	−25.4810	−1.03939	−0.519695	+	0.854352i	$0.673954\pi$
$602$	3.44344	0.140344
$603$	−13.4955	−0.549580
$604$	7.71362	0.313863
$605$	−13.6893	−0.556550
$606$	5.16929	0.209988
$607$	3.79662	0.154100	0.0770500	−	0.997027i	$-0.475450\pi$
$607$	3.79662	0.154100	0.0770500	+	0.997027i	$0.475450\pi$
$608$	21.8994	0.888137
$609$	−6.68418	−0.270857
$610$	9.03270	0.365723
$611$	−4.00913	−0.162192
$612$	−1.32490	−0.0535559
$613$	29.4649	1.19008	0.595039	−	0.803697i	$-0.297137\pi$
$613$	29.4649	1.19008	0.595039	+	0.803697i	$0.297137\pi$
$614$	8.58002	0.346261
$615$	13.6401	0.550021
$616$	−5.27273	−0.212444
$617$	−2.56798	−0.103383	−0.0516915	−	0.998663i	$-0.516461\pi$
$617$	−2.56798	−0.103383	−0.0516915	+	0.998663i	$0.516461\pi$
$618$	2.97682	0.119745
$619$	12.0453	0.484143	0.242071	−	0.970258i	$-0.422173\pi$
$619$	12.0453	0.484143	0.242071	+	0.970258i	$0.422173\pi$
$620$	−6.57901	−0.264219
$621$	2.63234	0.105632
$622$	18.6452	0.747605
$623$	20.4705	0.820132
$624$	−0.379660	−0.0151986
$625$	−6.42304	−0.256922
$626$	−14.2441	−0.569307
$627$	−5.81846	−0.232367
$628$	23.0877	0.921299
$629$	5.59640	0.223143
$630$	−1.63370	−0.0650882
$631$	−43.3142	−1.72431	−0.862156	−	0.506642i	$-0.830887\pi$
$631$	−43.3142	−1.72431	−0.862156	+	0.506642i	$0.830887\pi$
$632$	2.73189	0.108669
$633$	−8.19801	−0.325842
$634$	−1.18606	−0.0471045
$635$	13.7290	0.544820
$636$	−1.27774	−0.0506657
$637$	−5.08785	−0.201588
$638$	6.74947	0.267214
$639$	7.62314	0.301567
$640$	13.2415	0.523417
$641$	23.3167	0.920956	0.460478	−	0.887671i	$-0.347678\pi$
$641$	23.3167	0.920956	0.460478	+	0.887671i	$0.347678\pi$
$642$	−6.57294	−0.259413
$643$	−28.3165	−1.11670	−0.558348	−	0.829607i	$-0.688564\pi$
$643$	−28.3165	−1.11670	−0.558348	+	0.829607i	$0.688564\pi$
$644$	4.37062	0.172226
$645$	5.30593	0.208921
$646$	3.10411	0.122130
$647$	18.2716	0.718331	0.359165	−	0.933274i	$-0.383061\pi$
$647$	18.2716	0.718331	0.359165	+	0.933274i	$0.383061\pi$
$648$	2.73189	0.107319
$649$	13.4103	0.526401
$650$	1.91151	0.0749756
$651$	−3.92216	−0.153721
$652$	15.1249	0.592337
$653$	30.5520	1.19559	0.597796	−	0.801649i	$-0.296043\pi$
$653$	30.5520	1.19559	0.597796	+	0.801649i	$0.296043\pi$
$654$	5.53087	0.216274
$655$	14.7026	0.574479
$656$	−3.48311	−0.135993
$657$	9.85250	0.384382
$658$	4.40533	0.171738
$659$	−29.6196	−1.15382	−0.576909	−	0.816809i	$-0.695741\pi$
$659$	−29.6196	−1.15382	−0.576909	+	0.816809i	$0.695741\pi$
$660$	−3.23749	−0.126019
$661$	−34.3888	−1.33757	−0.668785	−	0.743456i	$-0.733185\pi$
$661$	−34.3888	−1.33757	−0.668785	+	0.743456i	$0.733185\pi$
$662$	1.67430	0.0650736
$663$	−0.937074	−0.0363929
$664$	−25.0601	−0.972521
$665$	−7.51175	−0.291293
$666$	−4.59826	−0.178179
$667$	−14.0402	−0.543638
$668$	−4.05938	−0.157062
$669$	26.5732	1.02738
$670$	17.5932	0.679684
$671$	10.6713	0.411961
$672$	7.26434	0.280228
$673$	38.4164	1.48084	0.740422	−	0.672143i	$-0.234626\pi$
$673$	38.4164	1.48084	0.740422	+	0.672143i	$0.234626\pi$
$674$	1.69219	0.0651806
$675$	2.48267	0.0955579
$676$	16.0603	0.617703
$677$	−40.6025	−1.56048	−0.780241	−	0.625479i	$-0.784904\pi$
$677$	−40.6025	−1.56048	−0.780241	+	0.625479i	$0.784904\pi$
$678$	10.2434	0.393394
$679$	20.8403	0.799776
$680$	4.33444	0.166218
$681$	−3.67059	−0.140657
$682$	3.96047	0.151654
$683$	−5.05943	−0.193594	−0.0967969	−	0.995304i	$-0.530860\pi$
$683$	−5.05943	−0.193594	−0.0967969	+	0.995304i	$0.530860\pi$
$684$	5.00537	0.191385
$685$	−25.7591	−0.984204
$686$	12.7984	0.488646
$687$	4.03971	0.154125
$688$	−1.35491	−0.0516556
$689$	−0.903720	−0.0344290
$690$	−3.43160	−0.130639
$691$	40.8268	1.55313	0.776563	−	0.630039i	$-0.216961\pi$
$691$	40.8268	1.55313	0.776563	+	0.630039i	$0.216961\pi$
$692$	4.26493	0.162128
$693$	−1.93007	−0.0733172
$694$	16.5070	0.626597
$695$	5.54517	0.210340
$696$	−14.5711	−0.552318
$697$	−8.59699	−0.325634
$698$	−4.95541	−0.187565
$699$	17.3679	0.656913
$700$	4.12210	0.155801
$701$	−14.4940	−0.547431	−0.273715	−	0.961811i	$-0.588253\pi$
$701$	−14.4940	−0.547431	−0.273715	+	0.961811i	$0.588253\pi$
$702$	0.769942	0.0290596
$703$	−21.1428	−0.797414
$704$	−6.08732	−0.229425
$705$	6.78807	0.255654
$706$	−29.1749	−1.09801
$707$	7.88431	0.296520
$708$	−11.5363	−0.433561
$709$	−28.1480	−1.05712	−0.528560	−	0.848896i	$-0.677268\pi$
$709$	−28.1480	−1.05712	−0.528560	+	0.848896i	$0.677268\pi$
$710$	−9.93776	−0.372958
$711$	1.00000	0.0375029
$712$	44.6244	1.67237
$713$	−8.23852	−0.308535
$714$	1.02968	0.0385348
$715$	−2.28981	−0.0856340
$716$	3.32307	0.124189
$717$	−20.2061	−0.754609
$718$	29.0278	1.08331
$719$	−15.5419	−0.579614	−0.289807	−	0.957085i	$-0.593591\pi$
$719$	−15.5419	−0.579614	−0.289807	+	0.957085i	$0.593591\pi$
$720$	0.642823	0.0239566
$721$	4.54032	0.169090
$722$	3.88416	0.144554
$723$	28.9768	1.07766
$724$	20.6992	0.769279
$725$	−13.2419	−0.491790
$726$	−7.08918	−0.263104
$727$	29.9181	1.10960	0.554800	−	0.831983i	$-0.312795\pi$
$727$	29.9181	1.10960	0.554800	+	0.831983i	$0.312795\pi$
$728$	3.20815	0.118902
$729$	1.00000	0.0370370
$730$	−12.8440	−0.475379
$731$	−3.34419	−0.123689
$732$	−9.18006	−0.339305
$733$	22.1540	0.818277	0.409139	−	0.912472i	$-0.365829\pi$
$733$	22.1540	0.818277	0.409139	+	0.912472i	$0.365829\pi$
$734$	18.4196	0.679878
$735$	8.61452	0.317751
$736$	15.2588	0.562447
$737$	20.7847	0.765616
$738$	7.06367	0.260017
$739$	−20.5248	−0.755017	−0.377509	−	0.926006i	$-0.623219\pi$
$739$	−20.5248	−0.755017	−0.377509	+	0.926006i	$0.623219\pi$
$740$	−11.7642	−0.432460
$741$	3.54019	0.130052
$742$	0.993030	0.0364553
$743$	2.93466	0.107662	0.0538312	−	0.998550i	$-0.482857\pi$
$743$	2.93466	0.107662	0.0538312	+	0.998550i	$0.482857\pi$
$744$	−8.55008	−0.313461
$745$	−7.71704	−0.282730
$746$	−3.11860	−0.114180
$747$	−9.17319	−0.335629
$748$	2.04050	0.0746082
$749$	−10.0252	−0.366313
$750$	−9.75464	−0.356189
$751$	−33.2694	−1.21402	−0.607009	−	0.794695i	$-0.707631\pi$
$751$	−33.2694	−1.21402	−0.607009	+	0.794695i	$0.707631\pi$
$752$	−1.73339	−0.0632104
$753$	−1.47633	−0.0538005
$754$	−4.10666	−0.149556
$755$	−9.23732	−0.336180
$756$	1.66035	0.0603865
$757$	−50.9753	−1.85273	−0.926365	−	0.376627i	$-0.877084\pi$
$757$	−50.9753	−1.85273	−0.926365	+	0.376627i	$0.877084\pi$
$758$	−11.6850	−0.424418
$759$	−4.05412	−0.147155
$760$	−16.3752	−0.593991
$761$	−47.8652	−1.73511	−0.867556	−	0.497340i	$-0.834310\pi$
$761$	−47.8652	−1.73511	−0.867556	+	0.497340i	$0.834310\pi$
$762$	7.10974	0.257559
$763$	8.43581	0.305397
$764$	−10.3993	−0.376233
$765$	1.58661	0.0573640
$766$	−9.32891	−0.337067
$767$	−8.15940	−0.294619
$768$	14.7623	0.532688
$769$	15.7074	0.566422	0.283211	−	0.959058i	$-0.408600\pi$
$769$	15.7074	0.566422	0.283211	+	0.959058i	$0.408600\pi$
$770$	2.51610	0.0906739
$771$	13.5010	0.486225
$772$	−3.80258	−0.136858
$773$	48.3542	1.73918	0.869589	−	0.493775i	$-0.164384\pi$
$773$	48.3542	1.73918	0.869589	+	0.493775i	$0.164384\pi$
$774$	2.74774	0.0987654
$775$	−7.77008	−0.279110
$776$	45.4306	1.63086
$777$	−7.01337	−0.251603
$778$	−15.5214	−0.556471
$779$	32.4788	1.16367
$780$	1.96982	0.0705309
$781$	−11.7406	−0.420110
$782$	2.16285	0.0773434
$783$	−5.33373	−0.190612
$784$	−2.19979	−0.0785640
$785$	−27.6483	−0.986809
$786$	7.61393	0.271580
$787$	2.80945	0.100146	0.0500731	−	0.998746i	$-0.484055\pi$
$787$	2.80945	0.100146	0.0500731	+	0.998746i	$0.484055\pi$
$788$	29.0936	1.03642
$789$	4.19437	0.149324
$790$	−1.30363	−0.0463811
$791$	15.6234	0.555504
$792$	−4.20744	−0.149505
$793$	−6.49287	−0.230568
$794$	26.4355	0.938160
$795$	1.53014	0.0542684
$796$	13.6604	0.484181
$797$	−33.6702	−1.19266	−0.596330	−	0.802739i	$-0.703375\pi$
$797$	−33.6702	−1.19266	−0.596330	+	0.802739i	$0.703375\pi$
$798$	−3.89005	−0.137706
$799$	−4.27835	−0.151357
$800$	14.3912	0.508806
$801$	16.3346	0.577156
$802$	−8.94841	−0.315979
$803$	−15.1740	−0.535480
$804$	−17.8802	−0.630586
$805$	−5.23396	−0.184473
$806$	−2.40971	−0.0848785
$807$	−2.20237	−0.0775270
$808$	17.1874	0.604649
$809$	−51.0675	−1.79544	−0.897720	−	0.440567i	$-0.854777\pi$
$809$	−51.0675	−1.79544	−0.897720	+	0.440567i	$0.854777\pi$
$810$	−1.30363	−0.0458049
$811$	36.8319	1.29334	0.646671	−	0.762769i	$-0.276161\pi$
$811$	36.8319	1.29334	0.646671	+	0.762769i	$0.276161\pi$
$812$	−8.85587	−0.310780
$813$	26.2951	0.922210
$814$	7.08187	0.248219
$815$	−18.1126	−0.634456
$816$	−0.405155	−0.0141833
$817$	12.6341	0.442011
$818$	19.2313	0.672406
$819$	1.17433	0.0410346
$820$	18.0717	0.631092
$821$	48.8454	1.70472	0.852358	−	0.522958i	$-0.175172\pi$
$821$	48.8454	1.70472	0.852358	+	0.522958i	$0.175172\pi$
$822$	−13.3396	−0.465274
$823$	−43.5986	−1.51975	−0.759876	−	0.650068i	$-0.774740\pi$
$823$	−43.5986	−1.51975	−0.759876	+	0.650068i	$0.774740\pi$
$824$	9.89764	0.344801
$825$	−3.82361	−0.133121
$826$	8.96575	0.311958
$827$	44.6453	1.55247	0.776234	−	0.630445i	$-0.217127\pi$
$827$	44.6453	1.55247	0.776234	+	0.630445i	$0.217127\pi$
$828$	3.48759	0.121202
$829$	21.1612	0.734960	0.367480	−	0.930031i	$-0.380221\pi$
$829$	21.1612	0.734960	0.367480	+	0.930031i	$0.380221\pi$
$830$	11.9585	0.415084
$831$	−11.1233	−0.385863
$832$	3.70378	0.128406
$833$	−5.42951	−0.188121
$834$	2.87163	0.0994365
$835$	4.86125	0.168230
$836$	−7.70887	−0.266617
$837$	−3.12973	−0.108179
$838$	−15.8392	−0.547157
$839$	13.5433	0.467567	0.233783	−	0.972289i	$-0.424889\pi$
$839$	13.5433	0.467567	0.233783	+	0.972289i	$0.424889\pi$
$840$	−5.43189	−0.187418
$841$	−0.551372	−0.0190128
$842$	−4.14911	−0.142988
$843$	−9.38241	−0.323147
$844$	−10.8615	−0.373870
$845$	−19.2327	−0.661626
$846$	3.51528	0.120858
$847$	−10.8126	−0.371525
$848$	−0.390734	−0.0134179
$849$	14.7630	0.506665
$850$	2.03987	0.0699670
$851$	−14.7316	−0.504994
$852$	10.0999	0.346017
$853$	21.9946	0.753082	0.376541	−	0.926400i	$-0.377113\pi$
$853$	21.9946	0.753082	0.376541	+	0.926400i	$0.377113\pi$
$854$	7.13452	0.244138
$855$	−5.99409	−0.204994
$856$	−21.8543	−0.746966
$857$	−38.9264	−1.32970	−0.664850	−	0.746977i	$-0.731504\pi$
$857$	−38.9264	−1.32970	−0.664850	+	0.746977i	$0.731504\pi$
$858$	−1.18580	−0.0404827
$859$	−27.7549	−0.946986	−0.473493	−	0.880798i	$-0.657007\pi$
$859$	−27.7549	−0.946986	−0.473493	+	0.880798i	$0.657007\pi$
$860$	7.02982	0.239715
$861$	10.7737	0.367166
$862$	−10.3310	−0.351874
$863$	38.1633	1.29909	0.649546	−	0.760322i	$-0.274959\pi$
$863$	38.1633	1.29909	0.649546	+	0.760322i	$0.274959\pi$
$864$	5.79667	0.197207
$865$	−5.10740	−0.173657
$866$	14.2079	0.482805
$867$	−1.00000	−0.0339618
$868$	−5.19646	−0.176379
$869$	−1.54012	−0.0522450
$870$	6.95321	0.235736
$871$	−12.6463	−0.428504
$872$	18.3896	0.622749
$873$	16.6297	0.562831
$874$	−8.17108	−0.276391
$875$	−14.8780	−0.502968
$876$	13.0536	0.441039
$877$	17.4944	0.590746	0.295373	−	0.955382i	$-0.404556\pi$
$877$	17.4944	0.590746	0.295373	+	0.955382i	$0.404556\pi$
$878$	27.6040	0.931589
$879$	−1.22718	−0.0413916
$880$	−0.990026	−0.0333738
$881$	−21.6378	−0.728996	−0.364498	−	0.931204i	$-0.618759\pi$
$881$	−21.6378	−0.728996	−0.364498	+	0.931204i	$0.618759\pi$
$882$	4.46113	0.150214
$883$	4.27075	0.143722	0.0718611	−	0.997415i	$-0.477106\pi$
$883$	4.27075	0.143722	0.0718611	+	0.997415i	$0.477106\pi$
$884$	−1.24153	−0.0417571
$885$	13.8151	0.464390
$886$	5.59009	0.187803
$887$	−5.67559	−0.190568	−0.0952838	−	0.995450i	$-0.530376\pi$
$887$	−5.67559	−0.190568	−0.0952838	+	0.995450i	$0.530376\pi$
$888$	−15.2887	−0.513056
$889$	10.8439	0.363694
$890$	−21.2944	−0.713789
$891$	−1.54012	−0.0515960
$892$	35.2068	1.17881
$893$	16.1633	0.540883
$894$	−3.99636	−0.133658
$895$	−3.97949	−0.133020
$896$	10.4589	0.349407
$897$	2.46670	0.0823606
$898$	−13.8966	−0.463737
$899$	16.6931	0.556747
$900$	3.28928	0.109643
$901$	−0.964407	−0.0321290
$902$	−10.8789	−0.362228
$903$	4.19091	0.139465
$904$	34.0581	1.13276
$905$	−24.7880	−0.823980
$906$	−4.78366	−0.158926
$907$	−35.1186	−1.16609	−0.583047	−	0.812438i	$-0.698140\pi$
$907$	−35.1186	−1.16609	−0.583047	+	0.812438i	$0.698140\pi$
$908$	−4.86315	−0.161389
$909$	6.29138	0.208672
$910$	−1.53090	−0.0507488
$911$	−2.08659	−0.0691317	−0.0345658	−	0.999402i	$-0.511005\pi$
$911$	−2.08659	−0.0691317	−0.0345658	+	0.999402i	$0.511005\pi$
$912$	1.53064	0.0506847
$913$	14.1278	0.467562
$914$	−1.23484	−0.0408447
$915$	10.9934	0.363431
$916$	5.35221	0.176842
$917$	11.6129	0.383493
$918$	0.821645	0.0271183
$919$	12.5099	0.412663	0.206331	−	0.978482i	$-0.433847\pi$
$919$	12.5099	0.412663	0.206331	+	0.978482i	$0.433847\pi$
$920$	−11.4097	−0.376168
$921$	10.4425	0.344092
$922$	−16.6411	−0.548046
$923$	7.14345	0.235129
$924$	−2.55715	−0.0841239
$925$	−13.8940	−0.456832
$926$	27.1451	0.892045
$927$	3.62300	0.118995
$928$	−30.9178	−1.01493
$929$	8.87243	0.291095	0.145547	−	0.989351i	$-0.453506\pi$
$929$	8.87243	0.291095	0.145547	+	0.989351i	$0.453506\pi$
$930$	4.08002	0.133789
$931$	20.5123	0.672262
$932$	23.0107	0.753739
$933$	22.6925	0.742921
$934$	−31.8888	−1.04343
$935$	−2.44357	−0.0799134
$936$	2.55998	0.0836756
$937$	37.9440	1.23957	0.619787	−	0.784770i	$-0.287219\pi$
$937$	37.9440	1.23957	0.619787	+	0.784770i	$0.287219\pi$
$938$	13.8961	0.453723
$939$	−17.3360	−0.565739
$940$	8.99351	0.293336
$941$	−14.8526	−0.484181	−0.242091	−	0.970254i	$-0.577833\pi$
$941$	−14.8526	−0.484181	−0.242091	+	0.970254i	$0.577833\pi$
$942$	−14.3180	−0.466505
$943$	22.6302	0.736941
$944$	−3.52781	−0.114821
$945$	−1.98833	−0.0646803
$946$	−4.23185	−0.137589
$947$	−28.2808	−0.919003	−0.459502	−	0.888177i	$-0.651972\pi$
$947$	−28.2808	−0.919003	−0.459502	+	0.888177i	$0.651972\pi$
$948$	1.32490	0.0430307
$949$	9.23252	0.299700
$950$	−7.70647	−0.250031
$951$	−1.44352	−0.0468093
$952$	3.42358	0.110959
$953$	33.0037	1.06909	0.534547	−	0.845139i	$-0.320482\pi$
$953$	33.0037	1.06909	0.534547	+	0.845139i	$0.320482\pi$
$954$	0.792400	0.0256549
$955$	12.4535	0.402985
$956$	−26.7710	−0.865836
$957$	8.21458	0.265540
$958$	6.30641	0.203751
$959$	−20.3459	−0.657004
$960$	−6.27107	−0.202398
$961$	−21.2048	−0.684025
$962$	−4.30891	−0.138925
$963$	−7.99972	−0.257787
$964$	38.3913	1.23650
$965$	4.55372	0.146589
$966$	−2.71047	−0.0872079
$967$	19.2362	0.618595	0.309297	−	0.950965i	$-0.399906\pi$
$967$	19.2362	0.618595	0.309297	+	0.950965i	$0.399906\pi$
$968$	−23.5708	−0.757594
$969$	3.77792	0.121364
$970$	−21.6790	−0.696072
$971$	35.4762	1.13849	0.569243	−	0.822170i	$-0.307237\pi$
$971$	35.4762	1.13849	0.569243	+	0.822170i	$0.307237\pi$
$972$	1.32490	0.0424962
$973$	4.37988	0.140412
$974$	−2.22811	−0.0713933
$975$	2.32644	0.0745058
$976$	−2.80727	−0.0898585
$977$	−60.2770	−1.92843	−0.964215	−	0.265120i	$-0.914588\pi$
$977$	−60.2770	−1.92843	−0.964215	+	0.265120i	$0.914588\pi$
$978$	−9.37981	−0.299933
$979$	−25.1573	−0.804032
$980$	11.4134	0.364587
$981$	6.73145	0.214919
$982$	−11.8251	−0.377354
$983$	−27.0223	−0.861878	−0.430939	−	0.902381i	$-0.641818\pi$
$983$	−27.0223	−0.861878	−0.430939	+	0.902381i	$0.641818\pi$
$984$	23.4860	0.748707
$985$	−34.8405	−1.11011
$986$	−4.38243	−0.139565
$987$	5.36159	0.170661
$988$	4.69040	0.149221
$989$	8.80304	0.279921
$990$	2.00775	0.0638105
$991$	18.1027	0.575052	0.287526	−	0.957773i	$-0.407167\pi$
$991$	18.1027	0.575052	0.287526	+	0.957773i	$0.407167\pi$
$992$	−18.1420	−0.576010
$993$	2.03774	0.0646658
$994$	−7.84939	−0.248968
$995$	−16.3588	−0.518610
$996$	−12.1535	−0.385100
$997$	51.0517	1.61682	0.808412	−	0.588617i	$-0.200328\pi$
$997$	51.0517	1.61682	0.808412	+	0.588617i	$0.200328\pi$
$998$	−12.7134	−0.402435
$999$	−5.59640	−0.177062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.f.1.10	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.f.1.10	✓	22	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q-0.821645 q^{2} -1.00000 q^{3} -1.32490 q^{4} +1.58661 q^{5} +0.821645 q^{6} +1.25319 q^{7} +2.73189 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.821645 q^{2} -1.00000 q^{3} -1.32490 q^{4} +1.58661 q^{5} +0.821645 q^{6} +1.25319 q^{7} +2.73189 q^{8} +1.00000 q^{9} -1.30363 q^{10} -1.54012 q^{11} +1.32490 q^{12} +0.937074 q^{13} -1.02968 q^{14} -1.58661 q^{15} +0.405155 q^{16} +1.00000 q^{17} -0.821645 q^{18} -3.77792 q^{19} -2.10210 q^{20} -1.25319 q^{21} +1.26543 q^{22} -2.63234 q^{23} -2.73189 q^{24} -2.48267 q^{25} -0.769942 q^{26} -1.00000 q^{27} -1.66035 q^{28} +5.33373 q^{29} +1.30363 q^{30} +3.12973 q^{31} -5.79667 q^{32} +1.54012 q^{33} -0.821645 q^{34} +1.98833 q^{35} -1.32490 q^{36} +5.59640 q^{37} +3.10411 q^{38} -0.937074 q^{39} +4.33444 q^{40} -8.59699 q^{41} +1.02968 q^{42} -3.34419 q^{43} +2.04050 q^{44} +1.58661 q^{45} +2.16285 q^{46} -4.27835 q^{47} -0.405155 q^{48} -5.42951 q^{49} +2.03987 q^{50} -1.00000 q^{51} -1.24153 q^{52} -0.964407 q^{53} +0.821645 q^{54} -2.44357 q^{55} +3.42358 q^{56} +3.77792 q^{57} -4.38243 q^{58} -8.70732 q^{59} +2.10210 q^{60} -6.92887 q^{61} -2.57153 q^{62} +1.25319 q^{63} +3.95250 q^{64} +1.48677 q^{65} -1.26543 q^{66} -13.4955 q^{67} -1.32490 q^{68} +2.63234 q^{69} -1.63370 q^{70} +7.62314 q^{71} +2.73189 q^{72} +9.85250 q^{73} -4.59826 q^{74} +2.48267 q^{75} +5.00537 q^{76} -1.93007 q^{77} +0.769942 q^{78} +1.00000 q^{79} +0.642823 q^{80} +1.00000 q^{81} +7.06367 q^{82} -9.17319 q^{83} +1.66035 q^{84} +1.58661 q^{85} +2.74774 q^{86} -5.33373 q^{87} -4.20744 q^{88} +16.3346 q^{89} -1.30363 q^{90} +1.17433 q^{91} +3.48759 q^{92} -3.12973 q^{93} +3.51528 q^{94} -5.99409 q^{95} +5.79667 q^{96} +16.6297 q^{97} +4.46113 q^{98} -1.54012 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9}+O(q^{10}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9	\( 22 q + q^{2} - 22 q^{3} + 19 q^{4} + q^{5} - q^{6} - 15 q^{7} + 15 q^{8} + 22 q^{9} - 13 q^{10} - 23 q^{11} - 19 q^{12} - 18 q^{13} - 9 q^{14} - q^{15} + 21 q^{16} + 22 q^{17} + q^{18} - 30 q^{19} - 7 q^{20} + 15 q^{21} + 4 q^{22} - 3 q^{23} - 15 q^{24} + 19 q^{25} - 7 q^{26} - 22 q^{27} - 25 q^{28} - 7 q^{29} + 13 q^{30} - 10 q^{31} + 31 q^{32} + 23 q^{33} + q^{34} - 11 q^{35} + 19 q^{36} - q^{37} - 29 q^{38} + 18 q^{39} - 59 q^{40} + 9 q^{42} - 43 q^{43} - 80 q^{44} + q^{45} - 43 q^{46} + 2 q^{47} - 21 q^{48} + 43 q^{49} + 25 q^{50} - 22 q^{51} - 5 q^{52} - q^{53} - q^{54} - 19 q^{55} - 8 q^{56} + 30 q^{57} - 43 q^{58} - 28 q^{59} + 7 q^{60} - 29 q^{61} - 3 q^{62} - 15 q^{63} + 23 q^{64} + 19 q^{65} - 4 q^{66} - 16 q^{67} + 19 q^{68} + 3 q^{69} - 5 q^{70} - q^{71} + 15 q^{72} - 19 q^{73} - 24 q^{74} - 19 q^{75} - 72 q^{76} + 24 q^{77} + 7 q^{78} + 22 q^{79} - 82 q^{80} + 22 q^{81} - 81 q^{82} - 29 q^{83} + 25 q^{84} + q^{85} - 42 q^{86} + 7 q^{87} - 43 q^{88} - 28 q^{89} - 13 q^{90} - 96 q^{91} - 11 q^{92} + 10 q^{93} - 63 q^{94} - 23 q^{95} - 31 q^{96} - 51 q^{97} + 12 q^{98} - 23 q^{99}+O(q^{100}) \) 22 * q + q^2 - 22 * q^3 + 19 * q^4 + q^5 - q^6 - 15 * q^7 + 15 * q^8 + 22 * q^9 - 13 * q^10 - 23 * q^11 - 19 * q^12 - 18 * q^13 - 9 * q^14 - q^15 + 21 * q^16 + 22 * q^17 + q^18 - 30 * q^19 - 7 * q^20 + 15 * q^21 + 4 * q^22 - 3 * q^23 - 15 * q^24 + 19 * q^25 - 7 * q^26 - 22 * q^27 - 25 * q^28 - 7 * q^29 + 13 * q^30 - 10 * q^31 + 31 * q^32 + 23 * q^33 + q^34 - 11 * q^35 + 19 * q^36 - q^37 - 29 * q^38 + 18 * q^39 - 59 * q^40 + 9 * q^42 - 43 * q^43 - 80 * q^44 + q^45 - 43 * q^46 + 2 * q^47 - 21 * q^48 + 43 * q^49 + 25 * q^50 - 22 * q^51 - 5 * q^52 - q^53 - q^54 - 19 * q^55 - 8 * q^56 + 30 * q^57 - 43 * q^58 - 28 * q^59 + 7 * q^60 - 29 * q^61 - 3 * q^62 - 15 * q^63 + 23 * q^64 + 19 * q^65 - 4 * q^66 - 16 * q^67 + 19 * q^68 + 3 * q^69 - 5 * q^70 - q^71 + 15 * q^72 - 19 * q^73 - 24 * q^74 - 19 * q^75 - 72 * q^76 + 24 * q^77 + 7 * q^78 + 22 * q^79 - 82 * q^80 + 22 * q^81 - 81 * q^82 - 29 * q^83 + 25 * q^84 + q^85 - 42 * q^86 + 7 * q^87 - 43 * q^88 - 28 * q^89 - 13 * q^90 - 96 * q^91 - 11 * q^92 + 10 * q^93 - 63 * q^94 - 23 * q^95 - 31 * q^96 - 51 * q^97 + 12 * q^98 - 23 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more