LMFDB - Embedded newform 6026.2.a.h.1.22

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.22
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +2.61321 q^{3} +1.00000 q^{4} -2.46460 q^{5} -2.61321 q^{6} +4.06006 q^{7} -1.00000 q^{8} +3.82884 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.61321 q^{3} +1.00000 q^{4} -2.46460 q^{5} -2.61321 q^{6} +4.06006 q^{7} -1.00000 q^{8} +3.82884 q^{9} +2.46460 q^{10} +1.03029 q^{11} +2.61321 q^{12} -4.93570 q^{13} -4.06006 q^{14} -6.44050 q^{15} +1.00000 q^{16} +0.256949 q^{17} -3.82884 q^{18} -5.12733 q^{19} -2.46460 q^{20} +10.6098 q^{21} -1.03029 q^{22} -1.00000 q^{23} -2.61321 q^{24} +1.07424 q^{25} +4.93570 q^{26} +2.16593 q^{27} +4.06006 q^{28} -3.96125 q^{29} +6.44050 q^{30} -0.0806486 q^{31} -1.00000 q^{32} +2.69237 q^{33} -0.256949 q^{34} -10.0064 q^{35} +3.82884 q^{36} -4.61356 q^{37} +5.12733 q^{38} -12.8980 q^{39} +2.46460 q^{40} -4.16327 q^{41} -10.6098 q^{42} -5.83536 q^{43} +1.03029 q^{44} -9.43655 q^{45} +1.00000 q^{46} +2.83318 q^{47} +2.61321 q^{48} +9.48405 q^{49} -1.07424 q^{50} +0.671460 q^{51} -4.93570 q^{52} +5.76430 q^{53} -2.16593 q^{54} -2.53926 q^{55} -4.06006 q^{56} -13.3988 q^{57} +3.96125 q^{58} +1.27609 q^{59} -6.44050 q^{60} -7.85246 q^{61} +0.0806486 q^{62} +15.5453 q^{63} +1.00000 q^{64} +12.1645 q^{65} -2.69237 q^{66} -5.27565 q^{67} +0.256949 q^{68} -2.61321 q^{69} +10.0064 q^{70} +1.38217 q^{71} -3.82884 q^{72} -2.78391 q^{73} +4.61356 q^{74} +2.80720 q^{75} -5.12733 q^{76} +4.18305 q^{77} +12.8980 q^{78} -5.36636 q^{79} -2.46460 q^{80} -5.82650 q^{81} +4.16327 q^{82} -14.1754 q^{83} +10.6098 q^{84} -0.633276 q^{85} +5.83536 q^{86} -10.3516 q^{87} -1.03029 q^{88} +6.38009 q^{89} +9.43655 q^{90} -20.0392 q^{91} -1.00000 q^{92} -0.210751 q^{93} -2.83318 q^{94} +12.6368 q^{95} -2.61321 q^{96} -7.88326 q^{97} -9.48405 q^{98} +3.94483 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	2.61321	1.50873	0.754367	−	0.656452i	$-0.227944\pi$
$3$	2.61321	1.50873	0.754367	+	0.656452i	$0.227944\pi$
$4$	1.00000	0.500000
$5$	−2.46460	−1.10220	−0.551101	−	0.834439i	$-0.685792\pi$
$5$	−2.46460	−1.10220	−0.551101	+	0.834439i	$0.685792\pi$
$6$	−2.61321	−1.06684
$7$	4.06006	1.53456	0.767278	−	0.641314i	$-0.221610\pi$
$7$	4.06006	1.53456	0.767278	+	0.641314i	$0.221610\pi$
$8$	−1.00000	−0.353553
$9$	3.82884	1.27628
$10$	2.46460	0.779374
$11$	1.03029	0.310645	0.155322	−	0.987864i	$-0.450358\pi$
$11$	1.03029	0.310645	0.155322	+	0.987864i	$0.450358\pi$
$12$	2.61321	0.754367
$13$	−4.93570	−1.36892	−0.684458	−	0.729052i	$-0.739961\pi$
$13$	−4.93570	−1.36892	−0.684458	+	0.729052i	$0.739961\pi$
$14$	−4.06006	−1.08510
$15$	−6.44050	−1.66293
$16$	1.00000	0.250000
$17$	0.256949	0.0623193	0.0311596	−	0.999514i	$-0.490080\pi$
$17$	0.256949	0.0623193	0.0311596	+	0.999514i	$0.490080\pi$
$18$	−3.82884	−0.902467
$19$	−5.12733	−1.17629	−0.588145	−	0.808756i	$-0.700142\pi$
$19$	−5.12733	−1.17629	−0.588145	+	0.808756i	$0.700142\pi$
$20$	−2.46460	−0.551101
$21$	10.6098	2.31524
$22$	−1.03029	−0.219659
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	−2.61321	−0.533418
$25$	1.07424	0.214847
$26$	4.93570	0.967970
$27$	2.16593	0.416834
$28$	4.06006	0.767278
$29$	−3.96125	−0.735586	−0.367793	−	0.929908i	$-0.619886\pi$
$29$	−3.96125	−0.735586	−0.367793	+	0.929908i	$0.619886\pi$
$30$	6.44050	1.17587
$31$	−0.0806486	−0.0144849	−0.00724246	−	0.999974i	$-0.502305\pi$
$31$	−0.0806486	−0.0144849	−0.00724246	+	0.999974i	$0.502305\pi$
$32$	−1.00000	−0.176777
$33$	2.69237	0.468681
$34$	−0.256949	−0.0440664
$35$	−10.0064	−1.69139
$36$	3.82884	0.638140
$37$	−4.61356	−0.758464	−0.379232	−	0.925302i	$-0.623812\pi$
$37$	−4.61356	−0.758464	−0.379232	+	0.925302i	$0.623812\pi$
$38$	5.12733	0.831762
$39$	−12.8980	−2.06533
$40$	2.46460	0.389687
$41$	−4.16327	−0.650193	−0.325097	−	0.945681i	$-0.605397\pi$
$41$	−4.16327	−0.650193	−0.325097	+	0.945681i	$0.605397\pi$
$42$	−10.6098	−1.63712
$43$	−5.83536	−0.889884	−0.444942	−	0.895559i	$-0.646776\pi$
$43$	−5.83536	−0.889884	−0.444942	+	0.895559i	$0.646776\pi$
$44$	1.03029	0.155322
$45$	−9.43655	−1.40672
$46$	1.00000	0.147442
$47$	2.83318	0.413262	0.206631	−	0.978419i	$-0.433750\pi$
$47$	2.83318	0.413262	0.206631	+	0.978419i	$0.433750\pi$
$48$	2.61321	0.377184
$49$	9.48405	1.35486
$50$	−1.07424	−0.151920
$51$	0.671460	0.0940233
$52$	−4.93570	−0.684458
$53$	5.76430	0.791787	0.395894	−	0.918296i	$-0.370435\pi$
$53$	5.76430	0.791787	0.395894	+	0.918296i	$0.370435\pi$
$54$	−2.16593	−0.294746
$55$	−2.53926	−0.342393
$56$	−4.06006	−0.542548
$57$	−13.3988	−1.77471
$58$	3.96125	0.520138
$59$	1.27609	0.166133	0.0830667	−	0.996544i	$-0.473529\pi$
$59$	1.27609	0.166133	0.0830667	+	0.996544i	$0.473529\pi$
$60$	−6.44050	−0.831465
$61$	−7.85246	−1.00540	−0.502702	−	0.864460i	$-0.667661\pi$
$61$	−7.85246	−1.00540	−0.502702	+	0.864460i	$0.667661\pi$
$62$	0.0806486	0.0102424
$63$	15.5453	1.95852
$64$	1.00000	0.125000
$65$	12.1645	1.50882
$66$	−2.69237	−0.331407
$67$	−5.27565	−0.644524	−0.322262	−	0.946651i	$-0.604443\pi$
$67$	−5.27565	−0.644524	−0.322262	+	0.946651i	$0.604443\pi$
$68$	0.256949	0.0311596
$69$	−2.61321	−0.314593
$70$	10.0064	1.19599
$71$	1.38217	0.164034	0.0820170	−	0.996631i	$-0.473864\pi$
$71$	1.38217	0.164034	0.0820170	+	0.996631i	$0.473864\pi$
$72$	−3.82884	−0.451233
$73$	−2.78391	−0.325831	−0.162916	−	0.986640i	$-0.552090\pi$
$73$	−2.78391	−0.325831	−0.162916	+	0.986640i	$0.552090\pi$
$74$	4.61356	0.536315
$75$	2.80720	0.324148
$76$	−5.12733	−0.588145
$77$	4.18305	0.476702
$78$	12.8980	1.46041
$79$	−5.36636	−0.603762	−0.301881	−	0.953346i	$-0.597615\pi$
$79$	−5.36636	−0.603762	−0.301881	+	0.953346i	$0.597615\pi$
$80$	−2.46460	−0.275550
$81$	−5.82650	−0.647389
$82$	4.16327	0.459756
$83$	−14.1754	−1.55596	−0.777978	−	0.628292i	$-0.783754\pi$
$83$	−14.1754	−1.55596	−0.777978	+	0.628292i	$0.783754\pi$
$84$	10.6098	1.15762
$85$	−0.633276	−0.0686884
$86$	5.83536	0.629243
$87$	−10.3516	−1.10980
$88$	−1.03029	−0.109830
$89$	6.38009	0.676288	0.338144	−	0.941094i	$-0.390201\pi$
$89$	6.38009	0.676288	0.338144	+	0.941094i	$0.390201\pi$
$90$	9.43655	0.994700
$91$	−20.0392	−2.10068
$92$	−1.00000	−0.104257
$93$	−0.210751	−0.0218539
$94$	−2.83318	−0.292220
$95$	12.6368	1.29651
$96$	−2.61321	−0.266709
$97$	−7.88326	−0.800424	−0.400212	−	0.916423i	$-0.631063\pi$
$97$	−7.88326	−0.800424	−0.400212	+	0.916423i	$0.631063\pi$
$98$	−9.48405	−0.958034
$99$	3.94483	0.396470
$100$	1.07424	0.107424
$101$	−3.95704	−0.393740	−0.196870	−	0.980430i	$-0.563078\pi$
$101$	−3.95704	−0.393740	−0.196870	+	0.980430i	$0.563078\pi$
$102$	−0.671460	−0.0664845
$103$	−12.7368	−1.25499	−0.627496	−	0.778620i	$-0.715920\pi$
$103$	−12.7368	−1.25499	−0.627496	+	0.778620i	$0.715920\pi$
$104$	4.93570	0.483985
$105$	−26.1488	−2.55186
$106$	−5.76430	−0.559878
$107$	7.94224	0.767805	0.383903	−	0.923374i	$-0.374580\pi$
$107$	7.94224	0.767805	0.383903	+	0.923374i	$0.374580\pi$
$108$	2.16593	0.208417
$109$	5.74434	0.550208	0.275104	−	0.961414i	$-0.411288\pi$
$109$	5.74434	0.550208	0.275104	+	0.961414i	$0.411288\pi$
$110$	2.53926	0.242109
$111$	−12.0562	−1.14432
$112$	4.06006	0.383639
$113$	5.65112	0.531612	0.265806	−	0.964026i	$-0.414362\pi$
$113$	5.65112	0.531612	0.265806	+	0.964026i	$0.414362\pi$
$114$	13.3988	1.25491
$115$	2.46460	0.229825
$116$	−3.96125	−0.367793
$117$	−18.8980	−1.74712
$118$	−1.27609	−0.117474
$119$	1.04323	0.0956325
$120$	6.44050	0.587934
$121$	−9.93850	−0.903500
$122$	7.85246	0.710928
$123$	−10.8795	−0.980969
$124$	−0.0806486	−0.00724246
$125$	9.67542	0.865396
$126$	−15.5453	−1.38489
$127$	−7.54177	−0.669223	−0.334612	−	0.942356i	$-0.608605\pi$
$127$	−7.54177	−0.669223	−0.334612	+	0.942356i	$0.608605\pi$
$128$	−1.00000	−0.0883883
$129$	−15.2490	−1.34260
$130$	−12.1645	−1.06690
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	2.69237	0.234340
$133$	−20.8172	−1.80508
$134$	5.27565	0.455747
$135$	−5.33815	−0.459435
$136$	−0.256949	−0.0220332
$137$	20.8042	1.77742	0.888710	−	0.458470i	$-0.151602\pi$
$137$	20.8042	1.77742	0.888710	+	0.458470i	$0.151602\pi$
$138$	2.61321	0.222451
$139$	−8.73639	−0.741011	−0.370505	−	0.928830i	$-0.620815\pi$
$139$	−8.73639	−0.741011	−0.370505	+	0.928830i	$0.620815\pi$
$140$	−10.0064	−0.845695
$141$	7.40369	0.623503
$142$	−1.38217	−0.115990
$143$	−5.08522	−0.425247
$144$	3.82884	0.319070
$145$	9.76288	0.810763
$146$	2.78391	0.230398
$147$	24.7838	2.04413
$148$	−4.61356	−0.379232
$149$	−7.50344	−0.614705	−0.307353	−	0.951596i	$-0.599443\pi$
$149$	−7.50344	−0.614705	−0.307353	+	0.951596i	$0.599443\pi$
$150$	−2.80720	−0.229207
$151$	9.87969	0.803998	0.401999	−	0.915640i	$-0.368316\pi$
$151$	9.87969	0.803998	0.401999	+	0.915640i	$0.368316\pi$
$152$	5.12733	0.415881
$153$	0.983817	0.0795369
$154$	−4.18305	−0.337079
$155$	0.198766	0.0159653
$156$	−12.8980	−1.03267
$157$	17.5891	1.40376	0.701880	−	0.712296i	$-0.252344\pi$
$157$	17.5891	1.40376	0.701880	+	0.712296i	$0.252344\pi$
$158$	5.36636	0.426924
$159$	15.0633	1.19460
$160$	2.46460	0.194843
$161$	−4.06006	−0.319977
$162$	5.82650	0.457773
$163$	−13.1203	−1.02766	−0.513830	−	0.857892i	$-0.671774\pi$
$163$	−13.1203	−1.02766	−0.513830	+	0.857892i	$0.671774\pi$
$164$	−4.16327	−0.325097
$165$	−6.63560	−0.516581
$166$	14.1754	1.10023
$167$	8.33628	0.645080	0.322540	−	0.946556i	$-0.395463\pi$
$167$	8.33628	0.645080	0.322540	+	0.946556i	$0.395463\pi$
$168$	−10.6098	−0.818561
$169$	11.3611	0.873933
$170$	0.633276	0.0485700
$171$	−19.6317	−1.50128
$172$	−5.83536	−0.444942
$173$	11.0881	0.843016	0.421508	−	0.906825i	$-0.361501\pi$
$173$	11.0881	0.843016	0.421508	+	0.906825i	$0.361501\pi$
$174$	10.3516	0.784750
$175$	4.36146	0.329696
$176$	1.03029	0.0776612
$177$	3.33470	0.250651
$178$	−6.38009	−0.478208
$179$	2.40207	0.179539	0.0897695	−	0.995963i	$-0.471387\pi$
$179$	2.40207	0.179539	0.0897695	+	0.995963i	$0.471387\pi$
$180$	−9.43655	−0.703359
$181$	11.4238	0.849122	0.424561	−	0.905399i	$-0.360429\pi$
$181$	11.4238	0.849122	0.424561	+	0.905399i	$0.360429\pi$
$182$	20.0392	1.48541
$183$	−20.5201	−1.51689
$184$	1.00000	0.0737210
$185$	11.3706	0.835980
$186$	0.210751	0.0154530
$187$	0.264733	0.0193592
$188$	2.83318	0.206631
$189$	8.79381	0.639655
$190$	−12.6368	−0.916770
$191$	10.4539	0.756414	0.378207	−	0.925721i	$-0.376541\pi$
$191$	10.4539	0.756414	0.378207	+	0.925721i	$0.376541\pi$
$192$	2.61321	0.188592
$193$	−6.97261	−0.501900	−0.250950	−	0.968000i	$-0.580743\pi$
$193$	−6.97261	−0.501900	−0.250950	+	0.968000i	$0.580743\pi$
$194$	7.88326	0.565985
$195$	31.7884	2.27641
$196$	9.48405	0.677432
$197$	−17.9457	−1.27858	−0.639289	−	0.768966i	$-0.720771\pi$
$197$	−17.9457	−1.27858	−0.639289	+	0.768966i	$0.720771\pi$
$198$	−3.94483	−0.280347
$199$	−0.362664	−0.0257086	−0.0128543	−	0.999917i	$-0.504092\pi$
$199$	−0.362664	−0.0257086	−0.0128543	+	0.999917i	$0.504092\pi$
$200$	−1.07424	−0.0759601
$201$	−13.7864	−0.972415
$202$	3.95704	0.278417
$203$	−16.0829	−1.12880
$204$	0.671460	0.0470116
$205$	10.2608	0.716644
$206$	12.7368	0.887413
$207$	−3.82884	−0.266123
$208$	−4.93570	−0.342229
$209$	−5.28265	−0.365408
$210$	26.1488	1.80444
$211$	8.52240	0.586706	0.293353	−	0.956004i	$-0.405229\pi$
$211$	8.52240	0.586706	0.293353	+	0.956004i	$0.405229\pi$
$212$	5.76430	0.395894
$213$	3.61191	0.247484
$214$	−7.94224	−0.542920
$215$	14.3818	0.980831
$216$	−2.16593	−0.147373
$217$	−0.327438	−0.0222279
$218$	−5.74434	−0.389056
$219$	−7.27492	−0.491593
$220$	−2.53926	−0.171197
$221$	−1.26822	−0.0853099
$222$	12.0562	0.809157
$223$	20.1779	1.35121	0.675606	−	0.737263i	$-0.263882\pi$
$223$	20.1779	1.35121	0.675606	+	0.737263i	$0.263882\pi$
$224$	−4.06006	−0.271274
$225$	4.11308	0.274206
$226$	−5.65112	−0.375907
$227$	5.34182	0.354549	0.177274	−	0.984161i	$-0.443272\pi$
$227$	5.34182	0.354549	0.177274	+	0.984161i	$0.443272\pi$
$228$	−13.3988	−0.887355
$229$	10.2046	0.674337	0.337169	−	0.941444i	$-0.390531\pi$
$229$	10.2046	0.674337	0.337169	+	0.941444i	$0.390531\pi$
$230$	−2.46460	−0.162511
$231$	10.9312	0.719217
$232$	3.96125	0.260069
$233$	16.2997	1.06783	0.533916	−	0.845538i	$-0.320720\pi$
$233$	16.2997	1.06783	0.533916	+	0.845538i	$0.320720\pi$
$234$	18.8980	1.23540
$235$	−6.98265	−0.455498
$236$	1.27609	0.0830667
$237$	−14.0234	−0.910917
$238$	−1.04323	−0.0676224
$239$	−1.15965	−0.0750118	−0.0375059	−	0.999296i	$-0.511941\pi$
$239$	−1.15965	−0.0750118	−0.0375059	+	0.999296i	$0.511941\pi$
$240$	−6.44050	−0.415732
$241$	−12.4628	−0.802797	−0.401399	−	0.915903i	$-0.631476\pi$
$241$	−12.4628	−0.802797	−0.401399	+	0.915903i	$0.631476\pi$
$242$	9.93850	0.638871
$243$	−21.7236	−1.39357
$244$	−7.85246	−0.502702
$245$	−23.3744	−1.49333
$246$	10.8795	0.693650
$247$	25.3070	1.61024
$248$	0.0806486	0.00512119
$249$	−37.0433	−2.34752
$250$	−9.67542	−0.611927
$251$	−3.15632	−0.199225	−0.0996125	−	0.995026i	$-0.531760\pi$
$251$	−3.15632	−0.199225	−0.0996125	+	0.995026i	$0.531760\pi$
$252$	15.5453	0.979262
$253$	−1.03029	−0.0647740
$254$	7.54177	0.473212
$255$	−1.65488	−0.103633
$256$	1.00000	0.0625000
$257$	24.2604	1.51332	0.756661	−	0.653808i	$-0.226830\pi$
$257$	24.2604	1.51332	0.756661	+	0.653808i	$0.226830\pi$
$258$	15.2490	0.949361
$259$	−18.7313	−1.16391
$260$	12.1645	0.754411
$261$	−15.1670	−0.938814
$262$	1.00000	0.0617802
$263$	−14.6955	−0.906161	−0.453081	−	0.891470i	$-0.649675\pi$
$263$	−14.6955	−0.906161	−0.453081	+	0.891470i	$0.649675\pi$
$264$	−2.69237	−0.165704
$265$	−14.2067	−0.872709
$266$	20.8172	1.27639
$267$	16.6725	1.02034
$268$	−5.27565	−0.322262
$269$	−3.46930	−0.211527	−0.105764	−	0.994391i	$-0.533729\pi$
$269$	−3.46930	−0.211527	−0.105764	+	0.994391i	$0.533729\pi$
$270$	5.33815	0.324870
$271$	23.9808	1.45673	0.728364	−	0.685191i	$-0.240281\pi$
$271$	23.9808	1.45673	0.728364	+	0.685191i	$0.240281\pi$
$272$	0.256949	0.0155798
$273$	−52.3666	−3.16937
$274$	−20.8042	−1.25683
$275$	1.10678	0.0667413
$276$	−2.61321	−0.157296
$277$	−5.96668	−0.358503	−0.179252	−	0.983803i	$-0.557368\pi$
$277$	−5.96668	−0.358503	−0.179252	+	0.983803i	$0.557368\pi$
$278$	8.73639	0.523974
$279$	−0.308791	−0.0184868
$280$	10.0064	0.597997
$281$	−25.3593	−1.51281	−0.756406	−	0.654103i	$-0.773046\pi$
$281$	−25.3593	−1.51281	−0.756406	+	0.654103i	$0.773046\pi$
$282$	−7.40369	−0.440883
$283$	−0.748329	−0.0444836	−0.0222418	−	0.999753i	$-0.507080\pi$
$283$	−0.748329	−0.0444836	−0.0222418	+	0.999753i	$0.507080\pi$
$284$	1.38217	0.0820170
$285$	33.0225	1.95609
$286$	5.08522	0.300695
$287$	−16.9031	−0.997758
$288$	−3.82884	−0.225617
$289$	−16.9340	−0.996116
$290$	−9.76288	−0.573296
$291$	−20.6006	−1.20763
$292$	−2.78391	−0.162916
$293$	−15.8128	−0.923794	−0.461897	−	0.886934i	$-0.652831\pi$
$293$	−15.8128	−0.923794	−0.461897	+	0.886934i	$0.652831\pi$
$294$	−24.7838	−1.44542
$295$	−3.14506	−0.183112
$296$	4.61356	0.268157
$297$	2.23155	0.129487
$298$	7.50344	0.434662
$299$	4.93570	0.285439
$300$	2.80720	0.162074
$301$	−23.6919	−1.36558
$302$	−9.87969	−0.568512
$303$	−10.3406	−0.594050
$304$	−5.12733	−0.294072
$305$	19.3531	1.10816
$306$	−0.983817	−0.0562411
$307$	25.3520	1.44691	0.723457	−	0.690370i	$-0.242552\pi$
$307$	25.3520	1.44691	0.723457	+	0.690370i	$0.242552\pi$
$308$	4.18305	0.238351
$309$	−33.2838	−1.89345
$310$	−0.198766	−0.0112892
$311$	8.95383	0.507725	0.253863	−	0.967240i	$-0.418299\pi$
$311$	8.95383	0.507725	0.253863	+	0.967240i	$0.418299\pi$
$312$	12.8980	0.730205
$313$	3.48114	0.196766	0.0983828	−	0.995149i	$-0.468633\pi$
$313$	3.48114	0.196766	0.0983828	+	0.995149i	$0.468633\pi$
$314$	−17.5891	−0.992608
$315$	−38.3129	−2.15869
$316$	−5.36636	−0.301881
$317$	−26.3779	−1.48153	−0.740765	−	0.671764i	$-0.765537\pi$
$317$	−26.3779	−1.48153	−0.740765	+	0.671764i	$0.765537\pi$
$318$	−15.0633	−0.844707
$319$	−4.08125	−0.228506
$320$	−2.46460	−0.137775
$321$	20.7547	1.15841
$322$	4.06006	0.226258
$323$	−1.31746	−0.0733055
$324$	−5.82650	−0.323694
$325$	−5.30211	−0.294108
$326$	13.1203	0.726665
$327$	15.0112	0.830119
$328$	4.16327	0.229878
$329$	11.5029	0.634174
$330$	6.63560	0.365278
$331$	−19.0214	−1.04551	−0.522754	−	0.852483i	$-0.675095\pi$
$331$	−19.0214	−1.04551	−0.522754	+	0.852483i	$0.675095\pi$
$332$	−14.1754	−0.777978
$333$	−17.6646	−0.968013
$334$	−8.33628	−0.456141
$335$	13.0024	0.710395
$336$	10.6098	0.578810
$337$	−26.8355	−1.46182	−0.730912	−	0.682472i	$-0.760905\pi$
$337$	−26.8355	−1.46182	−0.730912	+	0.682472i	$0.760905\pi$
$338$	−11.3611	−0.617964
$339$	14.7675	0.802062
$340$	−0.633276	−0.0343442
$341$	−0.0830917	−0.00449967
$342$	19.6317	1.06156
$343$	10.0854	0.544559
$344$	5.83536	0.314621
$345$	6.44050	0.346745
$346$	−11.0881	−0.596103
$347$	−22.6425	−1.21551	−0.607757	−	0.794123i	$-0.707931\pi$
$347$	−22.6425	−1.21551	−0.607757	+	0.794123i	$0.707931\pi$
$348$	−10.3516	−0.554902
$349$	−0.350620	−0.0187683	−0.00938413	−	0.999956i	$-0.502987\pi$
$349$	−0.350620	−0.0187683	−0.00938413	+	0.999956i	$0.502987\pi$
$350$	−4.36146	−0.233130
$351$	−10.6904	−0.570611
$352$	−1.03029	−0.0549148
$353$	−32.9679	−1.75470	−0.877352	−	0.479848i	$-0.840692\pi$
$353$	−32.9679	−1.75470	−0.877352	+	0.479848i	$0.840692\pi$
$354$	−3.33470	−0.177237
$355$	−3.40650	−0.180798
$356$	6.38009	0.338144
$357$	2.72617	0.144284
$358$	−2.40207	−0.126953
$359$	3.91067	0.206397	0.103199	−	0.994661i	$-0.467092\pi$
$359$	3.91067	0.206397	0.103199	+	0.994661i	$0.467092\pi$
$360$	9.43655	0.497350
$361$	7.28950	0.383658
$362$	−11.4238	−0.600420
$363$	−25.9713	−1.36314
$364$	−20.0392	−1.05034
$365$	6.86120	0.359132
$366$	20.5201	1.07260
$367$	−14.9048	−0.778025	−0.389013	−	0.921232i	$-0.627184\pi$
$367$	−14.9048	−0.778025	−0.389013	+	0.921232i	$0.627184\pi$
$368$	−1.00000	−0.0521286
$369$	−15.9405	−0.829829
$370$	−11.3706	−0.591127
$371$	23.4034	1.21504
$372$	−0.210751	−0.0109270
$373$	12.1823	0.630778	0.315389	−	0.948962i	$-0.397865\pi$
$373$	12.1823	0.630778	0.315389	+	0.948962i	$0.397865\pi$
$374$	−0.264733	−0.0136890
$375$	25.2839	1.30565
$376$	−2.83318	−0.146110
$377$	19.5515	1.00696
$378$	−8.79381	−0.452305
$379$	−4.35114	−0.223503	−0.111752	−	0.993736i	$-0.535646\pi$
$379$	−4.35114	−0.223503	−0.111752	+	0.993736i	$0.535646\pi$
$380$	12.6368	0.648254
$381$	−19.7082	−1.00968
$382$	−10.4539	−0.534866
$383$	5.18766	0.265077	0.132538	−	0.991178i	$-0.457687\pi$
$383$	5.18766	0.265077	0.132538	+	0.991178i	$0.457687\pi$
$384$	−2.61321	−0.133355
$385$	−10.3095	−0.525422
$386$	6.97261	0.354897
$387$	−22.3427	−1.13574
$388$	−7.88326	−0.400212
$389$	−16.1391	−0.818284	−0.409142	−	0.912471i	$-0.634172\pi$
$389$	−16.1391	−0.818284	−0.409142	+	0.912471i	$0.634172\pi$
$390$	−31.7884	−1.60967
$391$	−0.256949	−0.0129945
$392$	−9.48405	−0.479017
$393$	−2.61321	−0.131819
$394$	17.9457	0.904092
$395$	13.2259	0.665467
$396$	3.94483	0.198235
$397$	−23.2019	−1.16447	−0.582234	−	0.813021i	$-0.697821\pi$
$397$	−23.2019	−1.16447	−0.582234	+	0.813021i	$0.697821\pi$
$398$	0.362664	0.0181787
$399$	−54.3997	−2.72339
$400$	1.07424	0.0537119
$401$	5.76006	0.287644	0.143822	−	0.989604i	$-0.454061\pi$
$401$	5.76006	0.287644	0.143822	+	0.989604i	$0.454061\pi$
$402$	13.7864	0.687602
$403$	0.398057	0.0198287
$404$	−3.95704	−0.196870
$405$	14.3600	0.713552
$406$	16.0829	0.798181
$407$	−4.75331	−0.235613
$408$	−0.671460	−0.0332422
$409$	−30.9244	−1.52912	−0.764558	−	0.644555i	$-0.777042\pi$
$409$	−30.9244	−1.52912	−0.764558	+	0.644555i	$0.777042\pi$
$410$	−10.2608	−0.506744
$411$	54.3656	2.68166
$412$	−12.7368	−0.627496
$413$	5.18101	0.254941
$414$	3.82884	0.188177
$415$	34.9367	1.71498
$416$	4.93570	0.241993
$417$	−22.8300	−1.11799
$418$	5.28265	0.258383
$419$	2.16367	0.105702	0.0528512	−	0.998602i	$-0.483169\pi$
$419$	2.16367	0.105702	0.0528512	+	0.998602i	$0.483169\pi$
$420$	−26.1488	−1.27593
$421$	−3.93612	−0.191835	−0.0959173	−	0.995389i	$-0.530578\pi$
$421$	−3.93612	−0.191835	−0.0959173	+	0.995389i	$0.530578\pi$
$422$	−8.52240	−0.414864
$423$	10.8478	0.527438
$424$	−5.76430	−0.279939
$425$	0.276024	0.0133891
$426$	−3.61191	−0.174997
$427$	−31.8814	−1.54285
$428$	7.94224	0.383903
$429$	−13.2887	−0.641585
$430$	−14.3818	−0.693552
$431$	−8.62291	−0.415351	−0.207675	−	0.978198i	$-0.566590\pi$
$431$	−8.62291	−0.415351	−0.207675	+	0.978198i	$0.566590\pi$
$432$	2.16593	0.104209
$433$	7.61305	0.365860	0.182930	−	0.983126i	$-0.441442\pi$
$433$	7.61305	0.365860	0.182930	+	0.983126i	$0.441442\pi$
$434$	0.327438	0.0157175
$435$	25.5124	1.22323
$436$	5.74434	0.275104
$437$	5.12733	0.245273
$438$	7.27492	0.347609
$439$	27.4241	1.30888	0.654441	−	0.756113i	$-0.272904\pi$
$439$	27.4241	1.30888	0.654441	+	0.756113i	$0.272904\pi$
$440$	2.53926	0.121054
$441$	36.3129	1.72919
$442$	1.26822	0.0603232
$443$	32.2311	1.53135	0.765674	−	0.643229i	$-0.222406\pi$
$443$	32.2311	1.53135	0.765674	+	0.643229i	$0.222406\pi$
$444$	−12.0562	−0.572160
$445$	−15.7243	−0.745405
$446$	−20.1779	−0.955451
$447$	−19.6080	−0.927427
$448$	4.06006	0.191820
$449$	8.58229	0.405023	0.202512	−	0.979280i	$-0.435090\pi$
$449$	8.58229	0.405023	0.202512	+	0.979280i	$0.435090\pi$
$450$	−4.11308	−0.193893
$451$	−4.28938	−0.201979
$452$	5.65112	0.265806
$453$	25.8177	1.21302
$454$	−5.34182	−0.250704
$455$	49.3886	2.31537
$456$	13.3988	0.627454
$457$	35.1028	1.64204	0.821020	−	0.570899i	$-0.193405\pi$
$457$	35.1028	1.64204	0.821020	+	0.570899i	$0.193405\pi$
$458$	−10.2046	−0.476829
$459$	0.556534	0.0259768
$460$	2.46460	0.114912
$461$	7.19294	0.335009	0.167504	−	0.985871i	$-0.446429\pi$
$461$	7.19294	0.335009	0.167504	+	0.985871i	$0.446429\pi$
$462$	−10.9312	−0.508563
$463$	−13.5194	−0.628298	−0.314149	−	0.949374i	$-0.601719\pi$
$463$	−13.5194	−0.628298	−0.314149	+	0.949374i	$0.601719\pi$
$464$	−3.96125	−0.183896
$465$	0.519417	0.0240874
$466$	−16.2997	−0.755071
$467$	24.6912	1.14257	0.571287	−	0.820751i	$-0.306445\pi$
$467$	24.6912	1.14257	0.571287	+	0.820751i	$0.306445\pi$
$468$	−18.8980	−0.873561
$469$	−21.4194	−0.989058
$470$	6.98265	0.322086
$471$	45.9638	2.11790
$472$	−1.27609	−0.0587370
$473$	−6.01213	−0.276438
$474$	14.0234	0.644116
$475$	−5.50797	−0.252723
$476$	1.04323	0.0478162
$477$	22.0706	1.01054
$478$	1.15965	0.0530414
$479$	6.43722	0.294124	0.147062	−	0.989127i	$-0.453018\pi$
$479$	6.43722	0.294124	0.147062	+	0.989127i	$0.453018\pi$
$480$	6.44050	0.293967
$481$	22.7711	1.03827
$482$	12.4628	0.567663
$483$	−10.6098	−0.482761
$484$	−9.93850	−0.451750
$485$	19.4291	0.882228
$486$	21.7236	0.985404
$487$	33.9194	1.53704	0.768518	−	0.639828i	$-0.220994\pi$
$487$	33.9194	1.53704	0.768518	+	0.639828i	$0.220994\pi$
$488$	7.85246	0.355464
$489$	−34.2860	−1.55047
$490$	23.3744	1.05595
$491$	7.46978	0.337107	0.168553	−	0.985693i	$-0.446090\pi$
$491$	7.46978	0.337107	0.168553	+	0.985693i	$0.446090\pi$
$492$	−10.8795	−0.490485
$493$	−1.01784	−0.0458412
$494$	−25.3070	−1.13861
$495$	−9.72241	−0.436990
$496$	−0.0806486	−0.00362123
$497$	5.61171	0.251719
$498$	37.0433	1.65995
$499$	−20.1995	−0.904255	−0.452128	−	0.891953i	$-0.649335\pi$
$499$	−20.1995	−0.904255	−0.452128	+	0.891953i	$0.649335\pi$
$500$	9.67542	0.432698
$501$	21.7844	0.973255
$502$	3.15632	0.140873
$503$	8.94229	0.398717	0.199358	−	0.979927i	$-0.436114\pi$
$503$	8.94229	0.398717	0.199358	+	0.979927i	$0.436114\pi$
$504$	−15.5453	−0.692443
$505$	9.75251	0.433981
$506$	1.03029	0.0458021
$507$	29.6890	1.31853
$508$	−7.54177	−0.334612
$509$	32.0355	1.41995	0.709975	−	0.704227i	$-0.248706\pi$
$509$	32.0355	1.41995	0.709975	+	0.704227i	$0.248706\pi$
$510$	1.65488	0.0732793
$511$	−11.3028	−0.500007
$512$	−1.00000	−0.0441942
$513$	−11.1055	−0.490318
$514$	−24.2604	−1.07008
$515$	31.3910	1.38325
$516$	−15.2490	−0.671299
$517$	2.91901	0.128378
$518$	18.7313	0.823006
$519$	28.9756	1.27189
$520$	−12.1645	−0.533449
$521$	−23.9646	−1.04991	−0.524954	−	0.851131i	$-0.675917\pi$
$521$	−23.9646	−1.04991	−0.524954	+	0.851131i	$0.675917\pi$
$522$	15.1670	0.663841
$523$	−42.2103	−1.84573	−0.922863	−	0.385129i	$-0.874157\pi$
$523$	−42.2103	−1.84573	−0.922863	+	0.385129i	$0.874157\pi$
$524$	−1.00000	−0.0436852
$525$	11.3974	0.497423
$526$	14.6955	0.640753
$527$	−0.0207226	−0.000902690 0
$528$	2.69237	0.117170
$529$	1.00000	0.0434783
$530$	14.2067	0.617098
$531$	4.88596	0.212033
$532$	−20.8172	−0.902542
$533$	20.5486	0.890060
$534$	−16.6725	−0.721489
$535$	−19.5744	−0.846276
$536$	5.27565	0.227874
$537$	6.27709	0.270877
$538$	3.46930	0.149572
$539$	9.77135	0.420882
$540$	−5.33815	−0.229717
$541$	−13.2569	−0.569960	−0.284980	−	0.958533i	$-0.591987\pi$
$541$	−13.2569	−0.569960	−0.284980	+	0.958533i	$0.591987\pi$
$542$	−23.9808	−1.03006
$543$	29.8526	1.28110
$544$	−0.256949	−0.0110166
$545$	−14.1575	−0.606440
$546$	52.3666	2.24108
$547$	34.7110	1.48414	0.742068	−	0.670325i	$-0.233845\pi$
$547$	34.7110	1.48414	0.742068	+	0.670325i	$0.233845\pi$
$548$	20.8042	0.888710
$549$	−30.0658	−1.28318
$550$	−1.10678	−0.0471932
$551$	20.3106	0.865262
$552$	2.61321	0.111225
$553$	−21.7877	−0.926507
$554$	5.96668	0.253500
$555$	29.7136	1.26127
$556$	−8.73639	−0.370505
$557$	−23.4771	−0.994757	−0.497378	−	0.867534i	$-0.665704\pi$
$557$	−23.4771	−0.994757	−0.497378	+	0.867534i	$0.665704\pi$
$558$	0.308791	0.0130722
$559$	28.8016	1.21818
$560$	−10.0064	−0.422848
$561$	0.691801	0.0292079
$562$	25.3593	1.06972
$563$	−7.95544	−0.335282	−0.167641	−	0.985848i	$-0.553615\pi$
$563$	−7.95544	−0.335282	−0.167641	+	0.985848i	$0.553615\pi$
$564$	7.40369	0.311751
$565$	−13.9277	−0.585944
$566$	0.748329	0.0314546
$567$	−23.6559	−0.993454
$568$	−1.38217	−0.0579948
$569$	−6.93554	−0.290753	−0.145376	−	0.989376i	$-0.546439\pi$
$569$	−6.93554	−0.290753	−0.145376	+	0.989376i	$0.546439\pi$
$570$	−33.0225	−1.38316
$571$	0.766036	0.0320576	0.0160288	−	0.999872i	$-0.494898\pi$
$571$	0.766036	0.0320576	0.0160288	+	0.999872i	$0.494898\pi$
$572$	−5.08522	−0.212624
$573$	27.3181	1.14123
$574$	16.9031	0.705522
$575$	−1.07424	−0.0447988
$576$	3.82884	0.159535
$577$	−45.6228	−1.89930	−0.949651	−	0.313309i	$-0.898562\pi$
$577$	−45.6228	−1.89930	−0.949651	+	0.313309i	$0.898562\pi$
$578$	16.9340	0.704361
$579$	−18.2209	−0.757234
$580$	9.76288	0.405382
$581$	−57.5530	−2.38770
$582$	20.6006	0.853921
$583$	5.93891	0.245965
$584$	2.78391	0.115199
$585$	46.5760	1.92568
$586$	15.8128	0.653221
$587$	33.4332	1.37994	0.689968	−	0.723840i	$-0.257625\pi$
$587$	33.4332	1.37994	0.689968	+	0.723840i	$0.257625\pi$
$588$	24.7838	1.02207
$589$	0.413512	0.0170385
$590$	3.14506	0.129480
$591$	−46.8958	−1.92904
$592$	−4.61356	−0.189616
$593$	−31.2735	−1.28425	−0.642124	−	0.766601i	$-0.721946\pi$
$593$	−31.2735	−1.28425	−0.642124	+	0.766601i	$0.721946\pi$
$594$	−2.23155	−0.0915614
$595$	−2.57113	−0.105406
$596$	−7.50344	−0.307353
$597$	−0.947716	−0.0387874
$598$	−4.93570	−0.201836
$599$	7.76407	0.317231	0.158616	−	0.987340i	$-0.449297\pi$
$599$	7.76407	0.317231	0.158616	+	0.987340i	$0.449297\pi$
$600$	−2.80720	−0.114604
$601$	7.73333	0.315449	0.157725	−	0.987483i	$-0.449584\pi$
$601$	7.73333	0.315449	0.157725	+	0.987483i	$0.449584\pi$
$602$	23.6919	0.965609
$603$	−20.1996	−0.822593
$604$	9.87969	0.401999
$605$	24.4944	0.995838
$606$	10.3406	0.420057
$607$	30.0363	1.21914	0.609569	−	0.792733i	$-0.291343\pi$
$607$	30.0363	1.21914	0.609569	+	0.792733i	$0.291343\pi$
$608$	5.12733	0.207941
$609$	−42.0279	−1.70306
$610$	−19.3531	−0.783586
$611$	−13.9837	−0.565721
$612$	0.983817	0.0397684
$613$	11.3280	0.457533	0.228767	−	0.973481i	$-0.426531\pi$
$613$	11.3280	0.457533	0.228767	+	0.973481i	$0.426531\pi$
$614$	−25.3520	−1.02312
$615$	26.8135	1.08123
$616$	−4.18305	−0.168540
$617$	−39.2950	−1.58196	−0.790978	−	0.611845i	$-0.790428\pi$
$617$	−39.2950	−1.58196	−0.790978	+	0.611845i	$0.790428\pi$
$618$	33.2838	1.33887
$619$	−3.37719	−0.135741	−0.0678704	−	0.997694i	$-0.521620\pi$
$619$	−3.37719	−0.135741	−0.0678704	+	0.997694i	$0.521620\pi$
$620$	0.198766	0.00798265
$621$	−2.16593	−0.0869159
$622$	−8.95383	−0.359016
$623$	25.9035	1.03780
$624$	−12.8980	−0.516333
$625$	−29.2172	−1.16869
$626$	−3.48114	−0.139134
$627$	−13.8046	−0.551304
$628$	17.5891	0.701880
$629$	−1.18545	−0.0472669
$630$	38.3129	1.52642
$631$	8.51606	0.339019	0.169510	−	0.985529i	$-0.445782\pi$
$631$	8.51606	0.339019	0.169510	+	0.985529i	$0.445782\pi$
$632$	5.36636	0.213462
$633$	22.2708	0.885184
$634$	26.3779	1.04760
$635$	18.5874	0.737619
$636$	15.0633	0.597298
$637$	−46.8104	−1.85470
$638$	4.08125	0.161578
$639$	5.29213	0.209353
$640$	2.46460	0.0974217
$641$	32.4585	1.28203	0.641017	−	0.767527i	$-0.278513\pi$
$641$	32.4585	1.28203	0.641017	+	0.767527i	$0.278513\pi$
$642$	−20.7547	−0.819123
$643$	2.53854	0.100110	0.0500552	−	0.998746i	$-0.484060\pi$
$643$	2.53854	0.100110	0.0500552	+	0.998746i	$0.484060\pi$
$644$	−4.06006	−0.159989
$645$	37.5826	1.47981
$646$	1.31746	0.0518348
$647$	−12.9860	−0.510532	−0.255266	−	0.966871i	$-0.582163\pi$
$647$	−12.9860	−0.510532	−0.255266	+	0.966871i	$0.582163\pi$
$648$	5.82650	0.228886
$649$	1.31475	0.0516085
$650$	5.30211	0.207966
$651$	−0.855663	−0.0335361
$652$	−13.1203	−0.513830
$653$	22.0163	0.861564	0.430782	−	0.902456i	$-0.358238\pi$
$653$	22.0163	0.861564	0.430782	+	0.902456i	$0.358238\pi$
$654$	−15.0112	−0.586982
$655$	2.46460	0.0962998
$656$	−4.16327	−0.162548
$657$	−10.6591	−0.415852
$658$	−11.5029	−0.448429
$659$	−42.7893	−1.66684	−0.833418	−	0.552643i	$-0.813619\pi$
$659$	−42.7893	−1.66684	−0.833418	+	0.552643i	$0.813619\pi$
$660$	−6.63560	−0.258290
$661$	−37.0865	−1.44250	−0.721249	−	0.692675i	$-0.756432\pi$
$661$	−37.0865	−1.44250	−0.721249	+	0.692675i	$0.756432\pi$
$662$	19.0214	0.739286
$663$	−3.31413	−0.128710
$664$	14.1754	0.550113
$665$	51.3061	1.98957
$666$	17.6646	0.684488
$667$	3.96125	0.153380
$668$	8.33628	0.322540
$669$	52.7290	2.03862
$670$	−13.0024	−0.502325
$671$	−8.09033	−0.312324
$672$	−10.6098	−0.409280
$673$	12.2864	0.473606	0.236803	−	0.971558i	$-0.423900\pi$
$673$	12.2864	0.473606	0.236803	+	0.971558i	$0.423900\pi$
$674$	26.8355	1.03367
$675$	2.32673	0.0895557
$676$	11.3611	0.436967
$677$	6.20632	0.238528	0.119264	−	0.992863i	$-0.461946\pi$
$677$	6.20632	0.238528	0.119264	+	0.992863i	$0.461946\pi$
$678$	−14.7675	−0.567144
$679$	−32.0065	−1.22830
$680$	0.633276	0.0242850
$681$	13.9593	0.534920
$682$	0.0830917	0.00318175
$683$	−10.4369	−0.399356	−0.199678	−	0.979862i	$-0.563990\pi$
$683$	−10.4369	−0.399356	−0.199678	+	0.979862i	$0.563990\pi$
$684$	−19.6317	−0.750638
$685$	−51.2739	−1.95907
$686$	−10.0854	−0.385062
$687$	26.6667	1.01740
$688$	−5.83536	−0.222471
$689$	−28.4508	−1.08389
$690$	−6.44050	−0.245186
$691$	−3.34748	−0.127344	−0.0636721	−	0.997971i	$-0.520281\pi$
$691$	−3.34748	−0.127344	−0.0636721	+	0.997971i	$0.520281\pi$
$692$	11.0881	0.421508
$693$	16.0162	0.608406
$694$	22.6425	0.859499
$695$	21.5317	0.816743
$696$	10.3516	0.392375
$697$	−1.06975	−0.0405196
$698$	0.350620	0.0132712
$699$	42.5946	1.61108
$700$	4.36146	0.164848
$701$	2.22995	0.0842241	0.0421120	−	0.999113i	$-0.486591\pi$
$701$	2.22995	0.0842241	0.0421120	+	0.999113i	$0.486591\pi$
$702$	10.6904	0.403483
$703$	23.6552	0.892173
$704$	1.03029	0.0388306
$705$	−18.2471	−0.687226
$706$	32.9679	1.24076
$707$	−16.0658	−0.604217
$708$	3.33470	0.125326
$709$	−4.05495	−0.152287	−0.0761435	−	0.997097i	$-0.524261\pi$
$709$	−4.05495	−0.152287	−0.0761435	+	0.997097i	$0.524261\pi$
$710$	3.40650	0.127844
$711$	−20.5469	−0.770570
$712$	−6.38009	−0.239104
$713$	0.0806486	0.00302032
$714$	−2.72617	−0.102024
$715$	12.5330	0.468708
$716$	2.40207	0.0897695
$717$	−3.03041	−0.113173
$718$	−3.91067	−0.145945
$719$	12.6092	0.470244	0.235122	−	0.971966i	$-0.424451\pi$
$719$	12.6092	0.470244	0.235122	+	0.971966i	$0.424451\pi$
$720$	−9.43655	−0.351679
$721$	−51.7120	−1.92586
$722$	−7.28950	−0.271287
$723$	−32.5678	−1.21121
$724$	11.4238	0.424561
$725$	−4.25532	−0.158039
$726$	25.9713	0.963887
$727$	−21.3490	−0.791792	−0.395896	−	0.918295i	$-0.629566\pi$
$727$	−21.3490	−0.791792	−0.395896	+	0.918295i	$0.629566\pi$
$728$	20.0392	0.742703
$729$	−39.2888	−1.45514
$730$	−6.86120	−0.253945
$731$	−1.49939	−0.0554569
$732$	−20.5201	−0.758444
$733$	−23.9044	−0.882929	−0.441465	−	0.897279i	$-0.645541\pi$
$733$	−23.9044	−0.882929	−0.441465	+	0.897279i	$0.645541\pi$
$734$	14.9048	0.550147
$735$	−61.0820	−2.25304
$736$	1.00000	0.0368605
$737$	−5.43547	−0.200218
$738$	15.9405	0.586778
$739$	−29.1792	−1.07338	−0.536688	−	0.843781i	$-0.680325\pi$
$739$	−29.1792	−1.07338	−0.536688	+	0.843781i	$0.680325\pi$
$740$	11.3706	0.417990
$741$	66.1323	2.42943
$742$	−23.4034	−0.859165
$743$	−30.5862	−1.12210	−0.561049	−	0.827783i	$-0.689602\pi$
$743$	−30.5862	−1.12210	−0.561049	+	0.827783i	$0.689602\pi$
$744$	0.210751	0.00772652
$745$	18.4929	0.677529
$746$	−12.1823	−0.446027
$747$	−54.2755	−1.98584
$748$	0.264733	0.00967958
$749$	32.2459	1.17824
$750$	−25.2839	−0.923236
$751$	14.1003	0.514527	0.257264	−	0.966341i	$-0.417179\pi$
$751$	14.1003	0.514527	0.257264	+	0.966341i	$0.417179\pi$
$752$	2.83318	0.103316
$753$	−8.24811	−0.300578
$754$	−19.5515	−0.712025
$755$	−24.3495	−0.886168
$756$	8.79381	0.319828
$757$	39.4538	1.43397	0.716986	−	0.697088i	$-0.245521\pi$
$757$	39.4538	1.43397	0.716986	+	0.697088i	$0.245521\pi$
$758$	4.35114	0.158041
$759$	−2.69237	−0.0977267
$760$	−12.6368	−0.458385
$761$	17.2775	0.626308	0.313154	−	0.949702i	$-0.398614\pi$
$761$	17.2775	0.626308	0.313154	+	0.949702i	$0.398614\pi$
$762$	19.7082	0.713952
$763$	23.3224	0.844326
$764$	10.4539	0.378207
$765$	−2.42471	−0.0876656
$766$	−5.18766	−0.187438
$767$	−6.29842	−0.227423
$768$	2.61321	0.0942959
$769$	−6.95411	−0.250771	−0.125386	−	0.992108i	$-0.540017\pi$
$769$	−6.95411	−0.250771	−0.125386	+	0.992108i	$0.540017\pi$
$770$	10.3095	0.371529
$771$	63.3974	2.28320
$772$	−6.97261	−0.250950
$773$	21.2462	0.764174	0.382087	−	0.924126i	$-0.375205\pi$
$773$	21.2462	0.764174	0.382087	+	0.924126i	$0.375205\pi$
$774$	22.3427	0.803090
$775$	−0.0866358	−0.00311205
$776$	7.88326	0.282993
$777$	−48.9487	−1.75603
$778$	16.1391	0.578614
$779$	21.3464	0.764816
$780$	31.7884	1.13821
$781$	1.42404	0.0509563
$782$	0.256949	0.00918848
$783$	−8.57980	−0.306617
$784$	9.48405	0.338716
$785$	−43.3499	−1.54723
$786$	2.61321	0.0932099
$787$	7.84936	0.279800	0.139900	−	0.990166i	$-0.455322\pi$
$787$	7.84936	0.279800	0.139900	+	0.990166i	$0.455322\pi$
$788$	−17.9457	−0.639289
$789$	−38.4023	−1.36716
$790$	−13.2259	−0.470556
$791$	22.9439	0.815789
$792$	−3.94483	−0.140173
$793$	38.7574	1.37631
$794$	23.2019	0.823404
$795$	−37.1249	−1.31669
$796$	−0.362664	−0.0128543
$797$	−33.5609	−1.18879	−0.594394	−	0.804174i	$-0.702608\pi$
$797$	−33.5609	−1.18879	−0.594394	+	0.804174i	$0.702608\pi$
$798$	54.3997	1.92573
$799$	0.727983	0.0257542
$800$	−1.07424	−0.0379800
$801$	24.4283	0.863133
$802$	−5.76006	−0.203395
$803$	−2.86824	−0.101218
$804$	−13.7864	−0.486208
$805$	10.0064	0.352679
$806$	−0.398057	−0.0140210
$807$	−9.06600	−0.319138
$808$	3.95704	0.139208
$809$	6.12572	0.215369	0.107684	−	0.994185i	$-0.465656\pi$
$809$	6.12572	0.215369	0.107684	+	0.994185i	$0.465656\pi$
$810$	−14.3600	−0.504558
$811$	−17.7222	−0.622311	−0.311156	−	0.950359i	$-0.600716\pi$
$811$	−17.7222	−0.622311	−0.311156	+	0.950359i	$0.600716\pi$
$812$	−16.0829	−0.564399
$813$	62.6666	2.19782
$814$	4.75331	0.166604
$815$	32.3362	1.13269
$816$	0.671460	0.0235058
$817$	29.9198	1.04676
$818$	30.9244	1.08125
$819$	−76.7270	−2.68106
$820$	10.2608	0.358322
$821$	−14.1704	−0.494552	−0.247276	−	0.968945i	$-0.579535\pi$
$821$	−14.1704	−0.494552	−0.247276	+	0.968945i	$0.579535\pi$
$822$	−54.3656	−1.89622
$823$	10.3359	0.360288	0.180144	−	0.983640i	$-0.442344\pi$
$823$	10.3359	0.360288	0.180144	+	0.983640i	$0.442344\pi$
$824$	12.7368	0.443707
$825$	2.89224	0.100695
$826$	−5.18101	−0.180270
$827$	−36.9315	−1.28424	−0.642118	−	0.766606i	$-0.721944\pi$
$827$	−36.9315	−1.28424	−0.642118	+	0.766606i	$0.721944\pi$
$828$	−3.82884	−0.133061
$829$	21.8418	0.758598	0.379299	−	0.925274i	$-0.376165\pi$
$829$	21.8418	0.758598	0.379299	+	0.925274i	$0.376165\pi$
$830$	−34.9367	−1.21267
$831$	−15.5922	−0.540886
$832$	−4.93570	−0.171115
$833$	2.43692	0.0844342
$834$	22.8300	0.790537
$835$	−20.5456	−0.711008
$836$	−5.28265	−0.182704
$837$	−0.174680	−0.00603781
$838$	−2.16367	−0.0747429
$839$	53.1887	1.83628	0.918139	−	0.396259i	$-0.129692\pi$
$839$	53.1887	1.83628	0.918139	+	0.396259i	$0.129692\pi$
$840$	26.1488	0.902218
$841$	−13.3085	−0.458914
$842$	3.93612	0.135648
$843$	−66.2692	−2.28243
$844$	8.52240	0.293353
$845$	−28.0006	−0.963250
$846$	−10.8478	−0.372955
$847$	−40.3508	−1.38647
$848$	5.76430	0.197947
$849$	−1.95554	−0.0671139
$850$	−0.276024	−0.00946755
$851$	4.61356	0.158151
$852$	3.61191	0.123742
$853$	9.64123	0.330109	0.165055	−	0.986284i	$-0.447220\pi$
$853$	9.64123	0.330109	0.165055	+	0.986284i	$0.447220\pi$
$854$	31.8814	1.09096
$855$	48.3843	1.65471
$856$	−7.94224	−0.271460
$857$	24.7885	0.846757	0.423379	−	0.905953i	$-0.360844\pi$
$857$	24.7885	0.846757	0.423379	+	0.905953i	$0.360844\pi$
$858$	13.2887	0.453669
$859$	28.7547	0.981096	0.490548	−	0.871414i	$-0.336797\pi$
$859$	28.7547	0.981096	0.490548	+	0.871414i	$0.336797\pi$
$860$	14.3818	0.490415
$861$	−44.1713	−1.50535
$862$	8.62291	0.293697
$863$	3.87015	0.131742	0.0658708	−	0.997828i	$-0.479017\pi$
$863$	3.87015	0.131742	0.0658708	+	0.997828i	$0.479017\pi$
$864$	−2.16593	−0.0736865
$865$	−27.3278	−0.929174
$866$	−7.61305	−0.258702
$867$	−44.2520	−1.50288
$868$	−0.327438	−0.0111140
$869$	−5.52892	−0.187556
$870$	−25.5124	−0.864952
$871$	26.0390	0.882299
$872$	−5.74434	−0.194528
$873$	−30.1838	−1.02157
$874$	−5.12733	−0.173434
$875$	39.2827	1.32800
$876$	−7.27492	−0.245797
$877$	−46.6413	−1.57497	−0.787483	−	0.616336i	$-0.788616\pi$
$877$	−46.6413	−1.57497	−0.787483	+	0.616336i	$0.788616\pi$
$878$	−27.4241	−0.925519
$879$	−41.3221	−1.39376
$880$	−2.53926	−0.0855983
$881$	−28.0863	−0.946252	−0.473126	−	0.880995i	$-0.656874\pi$
$881$	−28.0863	−0.946252	−0.473126	+	0.880995i	$0.656874\pi$
$882$	−36.3129	−1.22272
$883$	−40.3865	−1.35911	−0.679557	−	0.733622i	$-0.737828\pi$
$883$	−40.3865	−1.35911	−0.679557	+	0.733622i	$0.737828\pi$
$884$	−1.26822	−0.0426550
$885$	−8.21868	−0.276268
$886$	−32.2311	−1.08283
$887$	17.8512	0.599383	0.299692	−	0.954036i	$-0.403116\pi$
$887$	17.8512	0.599383	0.299692	+	0.954036i	$0.403116\pi$
$888$	12.0562	0.404578
$889$	−30.6200	−1.02696
$890$	15.7243	0.527081
$891$	−6.00300	−0.201108
$892$	20.1779	0.675606
$893$	−14.5267	−0.486116
$894$	19.6080	0.655790
$895$	−5.92013	−0.197888
$896$	−4.06006	−0.135637
$897$	12.8980	0.430652
$898$	−8.58229	−0.286395
$899$	0.319469	0.0106549
$900$	4.11308	0.137103
$901$	1.48113	0.0493436
$902$	4.28938	0.142821
$903$	−61.9117	−2.06029
$904$	−5.65112	−0.187953
$905$	−28.1550	−0.935903
$906$	−25.8177	−0.857734
$907$	−34.3843	−1.14171	−0.570856	−	0.821050i	$-0.693389\pi$
$907$	−34.3843	−1.14171	−0.570856	+	0.821050i	$0.693389\pi$
$908$	5.34182	0.177274
$909$	−15.1509	−0.502523
$910$	−49.3886	−1.63722
$911$	−27.3875	−0.907388	−0.453694	−	0.891158i	$-0.649894\pi$
$911$	−27.3875	−0.907388	−0.453694	+	0.891158i	$0.649894\pi$
$912$	−13.3988	−0.443677
$913$	−14.6048	−0.483350
$914$	−35.1028	−1.16110
$915$	50.5737	1.67192
$916$	10.2046	0.337169
$917$	−4.06006	−0.134075
$918$	−0.556534	−0.0183684
$919$	−38.4676	−1.26893	−0.634465	−	0.772952i	$-0.718780\pi$
$919$	−38.4676	−1.26893	−0.634465	+	0.772952i	$0.718780\pi$
$920$	−2.46460	−0.0812553
$921$	66.2499	2.18301
$922$	−7.19294	−0.236887
$923$	−6.82200	−0.224549
$924$	10.9312	0.359609
$925$	−4.95605	−0.162954
$926$	13.5194	0.444274
$927$	−48.7671	−1.60172
$928$	3.96125	0.130034
$929$	2.52996	0.0830055	0.0415027	−	0.999138i	$-0.486785\pi$
$929$	2.52996	0.0830055	0.0415027	+	0.999138i	$0.486785\pi$
$930$	−0.519417	−0.0170324
$931$	−48.6278	−1.59371
$932$	16.2997	0.533916
$933$	23.3982	0.766023
$934$	−24.6912	−0.807921
$935$	−0.652459	−0.0213377
$936$	18.8980	0.617701
$937$	23.7517	0.775934	0.387967	−	0.921673i	$-0.373178\pi$
$937$	23.7517	0.775934	0.387967	+	0.921673i	$0.373178\pi$
$938$	21.4194	0.699370
$939$	9.09693	0.296867
$940$	−6.98265	−0.227749
$941$	−49.9042	−1.62683	−0.813415	−	0.581683i	$-0.802394\pi$
$941$	−49.9042	−1.62683	−0.813415	+	0.581683i	$0.802394\pi$
$942$	−45.9638	−1.49758
$943$	4.16327	0.135575
$944$	1.27609	0.0415333
$945$	−21.6732	−0.705029
$946$	6.01213	0.195471
$947$	17.6480	0.573484	0.286742	−	0.958008i	$-0.407428\pi$
$947$	17.6480	0.573484	0.286742	+	0.958008i	$0.407428\pi$
$948$	−14.0234	−0.455458
$949$	13.7405	0.446036
$950$	5.50797	0.178702
$951$	−68.9309	−2.23524
$952$	−1.04323	−0.0338112
$953$	−6.30174	−0.204133	−0.102067	−	0.994778i	$-0.532546\pi$
$953$	−6.30174	−0.204133	−0.102067	+	0.994778i	$0.532546\pi$
$954$	−22.0706	−0.714561
$955$	−25.7645	−0.833721
$956$	−1.15965	−0.0375059
$957$	−10.6651	−0.344755
$958$	−6.43722	−0.207977
$959$	84.4661	2.72755
$960$	−6.44050	−0.207866
$961$	−30.9935	−0.999790
$962$	−22.7711	−0.734171
$963$	30.4096	0.979935
$964$	−12.4628	−0.401399
$965$	17.1847	0.553195
$966$	10.6098	0.341363
$967$	−1.51728	−0.0487923	−0.0243962	−	0.999702i	$-0.507766\pi$
$967$	−1.51728	−0.0487923	−0.0243962	+	0.999702i	$0.507766\pi$
$968$	9.93850	0.319435
$969$	−3.44280	−0.110599
$970$	−19.4291	−0.623829
$971$	12.8418	0.412113	0.206057	−	0.978540i	$-0.433937\pi$
$971$	12.8418	0.412113	0.206057	+	0.978540i	$0.433937\pi$
$972$	−21.7236	−0.696786
$973$	−35.4702	−1.13712
$974$	−33.9194	−1.08685
$975$	−13.8555	−0.443731
$976$	−7.85246	−0.251351
$977$	−7.00710	−0.224177	−0.112089	−	0.993698i	$-0.535754\pi$
$977$	−7.00710	−0.224177	−0.112089	+	0.993698i	$0.535754\pi$
$978$	34.2860	1.09635
$979$	6.57336	0.210085
$980$	−23.3744	−0.746666
$981$	21.9942	0.702220
$982$	−7.46978	−0.238370
$983$	−38.9250	−1.24151	−0.620757	−	0.784003i	$-0.713175\pi$
$983$	−38.9250	−1.24151	−0.620757	+	0.784003i	$0.713175\pi$
$984$	10.8795	0.346825
$985$	44.2289	1.40925
$986$	1.01784	0.0324146
$987$	30.0594	0.956800
$988$	25.3070	0.805121
$989$	5.83536	0.185554
$990$	9.72241	0.308998
$991$	3.80495	0.120868	0.0604341	−	0.998172i	$-0.480752\pi$
$991$	3.80495	0.120868	0.0604341	+	0.998172i	$0.480752\pi$
$992$	0.0806486	0.00256060
$993$	−49.7067	−1.57739
$994$	−5.61171	−0.177992
$995$	0.893821	0.0283360
$996$	−37.0433	−1.17376
$997$	52.0815	1.64944	0.824718	−	0.565544i	$-0.191334\pi$
$997$	52.0815	1.64944	0.824718	+	0.565544i	$0.191334\pi$
$998$	20.1995	0.639405
$999$	−9.99265	−0.316154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.22	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.22	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.61321 q^{3} +1.00000 q^{4} -2.46460 q^{5} -2.61321 q^{6} +4.06006 q^{7} -1.00000 q^{8} +3.82884 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.61321 q^{3} +1.00000 q^{4} -2.46460 q^{5} -2.61321 q^{6} +4.06006 q^{7} -1.00000 q^{8} +3.82884 q^{9} +2.46460 q^{10} +1.03029 q^{11} +2.61321 q^{12} -4.93570 q^{13} -4.06006 q^{14} -6.44050 q^{15} +1.00000 q^{16} +0.256949 q^{17} -3.82884 q^{18} -5.12733 q^{19} -2.46460 q^{20} +10.6098 q^{21} -1.03029 q^{22} -1.00000 q^{23} -2.61321 q^{24} +1.07424 q^{25} +4.93570 q^{26} +2.16593 q^{27} +4.06006 q^{28} -3.96125 q^{29} +6.44050 q^{30} -0.0806486 q^{31} -1.00000 q^{32} +2.69237 q^{33} -0.256949 q^{34} -10.0064 q^{35} +3.82884 q^{36} -4.61356 q^{37} +5.12733 q^{38} -12.8980 q^{39} +2.46460 q^{40} -4.16327 q^{41} -10.6098 q^{42} -5.83536 q^{43} +1.03029 q^{44} -9.43655 q^{45} +1.00000 q^{46} +2.83318 q^{47} +2.61321 q^{48} +9.48405 q^{49} -1.07424 q^{50} +0.671460 q^{51} -4.93570 q^{52} +5.76430 q^{53} -2.16593 q^{54} -2.53926 q^{55} -4.06006 q^{56} -13.3988 q^{57} +3.96125 q^{58} +1.27609 q^{59} -6.44050 q^{60} -7.85246 q^{61} +0.0806486 q^{62} +15.5453 q^{63} +1.00000 q^{64} +12.1645 q^{65} -2.69237 q^{66} -5.27565 q^{67} +0.256949 q^{68} -2.61321 q^{69} +10.0064 q^{70} +1.38217 q^{71} -3.82884 q^{72} -2.78391 q^{73} +4.61356 q^{74} +2.80720 q^{75} -5.12733 q^{76} +4.18305 q^{77} +12.8980 q^{78} -5.36636 q^{79} -2.46460 q^{80} -5.82650 q^{81} +4.16327 q^{82} -14.1754 q^{83} +10.6098 q^{84} -0.633276 q^{85} +5.83536 q^{86} -10.3516 q^{87} -1.03029 q^{88} +6.38009 q^{89} +9.43655 q^{90} -20.0392 q^{91} -1.00000 q^{92} -0.210751 q^{93} -2.83318 q^{94} +12.6368 q^{95} -2.61321 q^{96} -7.88326 q^{97} -9.48405 q^{98} +3.94483 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more