LMFDB - Embedded newform 7595.2.a.bf.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [7595,2,Mod(1,7595)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(7595, 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("7595.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 7595 = 5 \cdot 7^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	7595.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:	$60.6463803352$
Analytic rank:	$1$
Dimension:	$21$
Twist minimal:	no (minimal twist has level 1085)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	7595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.42068 q^{2} -0.0109751 q^{3} +0.0183294 q^{4} +1.00000 q^{5} -0.0155920 q^{6} -2.81532 q^{8} -2.99988 q^{9} +O(q^{10})$	\(q+1.42068 q^{2} -0.0109751 q^{3} +0.0183294 q^{4} +1.00000 q^{5} -0.0155920 q^{6} -2.81532 q^{8} -2.99988 q^{9} +1.42068 q^{10} -3.56878 q^{11} -0.000201166 q^{12} +4.94419 q^{13} -0.0109751 q^{15} -4.03632 q^{16} +2.17389 q^{17} -4.26187 q^{18} +4.36779 q^{19} +0.0183294 q^{20} -5.07009 q^{22} -0.118049 q^{23} +0.0308983 q^{24} +1.00000 q^{25} +7.02411 q^{26} +0.0658490 q^{27} +5.24777 q^{29} -0.0155920 q^{30} -1.00000 q^{31} -0.103684 q^{32} +0.0391675 q^{33} +3.08840 q^{34} -0.0549860 q^{36} -10.1451 q^{37} +6.20523 q^{38} -0.0542627 q^{39} -2.81532 q^{40} -10.0302 q^{41} +1.90768 q^{43} -0.0654136 q^{44} -2.99988 q^{45} -0.167710 q^{46} +7.49475 q^{47} +0.0442989 q^{48} +1.42068 q^{50} -0.0238586 q^{51} +0.0906241 q^{52} -4.74215 q^{53} +0.0935503 q^{54} -3.56878 q^{55} -0.0479367 q^{57} +7.45540 q^{58} -11.0134 q^{59} -0.000201166 q^{60} -14.5853 q^{61} -1.42068 q^{62} +7.92534 q^{64} +4.94419 q^{65} +0.0556445 q^{66} -4.07482 q^{67} +0.0398462 q^{68} +0.00129559 q^{69} +6.59972 q^{71} +8.44562 q^{72} +5.32426 q^{73} -14.4129 q^{74} -0.0109751 q^{75} +0.0800590 q^{76} -0.0770899 q^{78} +1.27805 q^{79} -4.03632 q^{80} +8.99892 q^{81} -14.2497 q^{82} -7.22714 q^{83} +2.17389 q^{85} +2.71020 q^{86} -0.0575945 q^{87} +10.0472 q^{88} +1.08967 q^{89} -4.26187 q^{90} -0.00216377 q^{92} +0.0109751 q^{93} +10.6476 q^{94} +4.36779 q^{95} +0.00113793 q^{96} +17.0837 q^{97} +10.7059 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	$ 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) $ 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * 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 $

$2$	1.42068	1.00457	0.502286	−	0.864702i	$-0.332492\pi$
$2$	1.42068	1.00457	0.502286	+	0.864702i	$0.332492\pi$
$3$	−0.0109751	−0.00633645	−0.00316822	−	0.999995i	$-0.501008\pi$
$3$	−0.0109751	−0.00633645	−0.00316822	+	0.999995i	$0.501008\pi$
$4$	0.0183294	0.00916471
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.0155920	−0.00636542
$7$	0	0
$7$	0	0
$8$	−2.81532	−0.995365
$9$	−2.99988	−0.999960
$10$	1.42068	0.449258
$11$	−3.56878	−1.07603	−0.538014	−	0.842936i	$-0.680825\pi$
$11$	−3.56878	−1.07603	−0.538014	+	0.842936i	$0.680825\pi$
$12$	−0.000201166 0	−5.80717e−5 0
$13$	4.94419	1.37127	0.685636	−	0.727945i	$-0.259524\pi$
$13$	4.94419	1.37127	0.685636	+	0.727945i	$0.259524\pi$
$14$	0	0
$15$	−0.0109751	−0.00283375
$16$	−4.03632	−1.00908
$17$	2.17389	0.527246	0.263623	−	0.964626i	$-0.415082\pi$
$17$	2.17389	0.527246	0.263623	+	0.964626i	$0.415082\pi$
$18$	−4.26187	−1.00453
$19$	4.36779	1.00204	0.501020	−	0.865436i	$-0.332958\pi$
$19$	4.36779	1.00204	0.501020	+	0.865436i	$0.332958\pi$
$20$	0.0183294	0.00409858
$21$	0	0
$22$	−5.07009	−1.08095
$23$	−0.118049	−0.0246149	−0.0123075	−	0.999924i	$-0.503918\pi$
$23$	−0.118049	−0.0246149	−0.0123075	+	0.999924i	$0.503918\pi$
$24$	0.0308983	0.00630708
$25$	1.00000	0.200000
$26$	7.02411	1.37754
$27$	0.0658490	0.0126726
$28$	0	0
$29$	5.24777	0.974486	0.487243	−	0.873266i	$-0.338003\pi$
$29$	5.24777	0.974486	0.487243	+	0.873266i	$0.338003\pi$
$30$	−0.0155920	−0.00284670
$31$	−1.00000	−0.179605
$31$	−1.00000	−0.179605
$32$	−0.103684	−0.0183288
$33$	0.0391675	0.00681819
$34$	3.08840	0.529657
$35$	0	0
$36$	−0.0549860	−0.00916434
$37$	−10.1451	−1.66785	−0.833923	−	0.551881i	$-0.813910\pi$
$37$	−10.1451	−1.66785	−0.833923	+	0.551881i	$0.813910\pi$
$38$	6.20523	1.00662
$39$	−0.0542627	−0.00868899
$40$	−2.81532	−0.445141
$41$	−10.0302	−1.56645	−0.783227	−	0.621736i	$-0.786428\pi$
$41$	−10.0302	−1.56645	−0.783227	+	0.621736i	$0.786428\pi$
$42$	0	0
$43$	1.90768	0.290918	0.145459	−	0.989364i	$-0.453534\pi$
$43$	1.90768	0.290918	0.145459	+	0.989364i	$0.453534\pi$
$44$	−0.0654136	−0.00986147
$45$	−2.99988	−0.447196
$46$	−0.167710	−0.0247274
$47$	7.49475	1.09322	0.546611	−	0.837387i	$-0.315918\pi$
$47$	7.49475	1.09322	0.546611	+	0.837387i	$0.315918\pi$
$48$	0.0442989	0.00639399
$49$	0	0
$50$	1.42068	0.200914
$51$	−0.0238586	−0.00334087
$52$	0.0906241	0.0125673
$53$	−4.74215	−0.651384	−0.325692	−	0.945476i	$-0.605597\pi$
$53$	−4.74215	−0.651384	−0.325692	+	0.945476i	$0.605597\pi$
$54$	0.0935503	0.0127306
$55$	−3.56878	−0.481214
$56$	0	0
$57$	−0.0479367	−0.00634937
$58$	7.45540	0.978941
$59$	−11.0134	−1.43382	−0.716908	−	0.697168i	$-0.754443\pi$
$59$	−11.0134	−1.43382	−0.716908	+	0.697168i	$0.754443\pi$
$60$	−0.000201166 0	−2.59705e−5 0
$61$	−14.5853	−1.86745	−0.933727	−	0.357986i	$-0.883464\pi$
$61$	−14.5853	−1.86745	−0.933727	+	0.357986i	$0.883464\pi$
$62$	−1.42068	−0.180426
$63$	0	0
$64$	7.92534	0.990668
$65$	4.94419	0.613251
$66$	0.0556445	0.00684936
$67$	−4.07482	−0.497818	−0.248909	−	0.968527i	$-0.580072\pi$
$67$	−4.07482	−0.497818	−0.248909	+	0.968527i	$0.580072\pi$
$68$	0.0398462	0.00483206
$69$	0.00129559	0.000155971 0
$70$	0	0
$71$	6.59972	0.783243	0.391621	−	0.920126i	$-0.371914\pi$
$71$	6.59972	0.783243	0.391621	+	0.920126i	$0.371914\pi$
$72$	8.44562	0.995325
$73$	5.32426	0.623158	0.311579	−	0.950220i	$-0.399142\pi$
$73$	5.32426	0.623158	0.311579	+	0.950220i	$0.399142\pi$
$74$	−14.4129	−1.67547
$75$	−0.0109751	−0.00126729
$76$	0.0800590	0.00918340
$77$	0	0
$78$	−0.0770899	−0.00872871
$79$	1.27805	0.143791	0.0718957	−	0.997412i	$-0.477095\pi$
$79$	1.27805	0.143791	0.0718957	+	0.997412i	$0.477095\pi$
$80$	−4.03632	−0.451275
$81$	8.99892	0.999880
$82$	−14.2497	−1.57362
$83$	−7.22714	−0.793281	−0.396641	−	0.917974i	$-0.629824\pi$
$83$	−7.22714	−0.793281	−0.396641	+	0.917974i	$0.629824\pi$
$84$	0	0
$85$	2.17389	0.235792
$86$	2.71020	0.292248
$87$	−0.0575945	−0.00617478
$88$	10.0472	1.07104
$89$	1.08967	0.115505	0.0577525	−	0.998331i	$-0.481607\pi$
$89$	1.08967	0.115505	0.0577525	+	0.998331i	$0.481607\pi$
$90$	−4.26187	−0.449240
$91$	0	0
$92$	−0.00216377	−0.000225588 0
$93$	0.0109751	0.00113806
$94$	10.6476	1.09822
$95$	4.36779	0.448126
$96$	0.00113793	0.000116140 0
$97$	17.0837	1.73459	0.867294	−	0.497797i	$-0.165857\pi$
$97$	17.0837	1.73459	0.867294	+	0.497797i	$0.165857\pi$
$98$	0	0
$99$	10.7059	1.07598
$100$	0.0183294	0.00183294
$101$	−2.35987	−0.234816	−0.117408	−	0.993084i	$-0.537459\pi$
$101$	−2.35987	−0.234816	−0.117408	+	0.993084i	$0.537459\pi$
$102$	−0.0338954	−0.00335614
$103$	−9.78944	−0.964582	−0.482291	−	0.876011i	$-0.660195\pi$
$103$	−9.78944	−0.964582	−0.482291	+	0.876011i	$0.660195\pi$
$104$	−13.9195	−1.36492
$105$	0	0
$106$	−6.73707	−0.654362
$107$	−8.63611	−0.834884	−0.417442	−	0.908703i	$-0.637073\pi$
$107$	−8.63611	−0.834884	−0.417442	+	0.908703i	$0.637073\pi$
$108$	0.00120697	0.000116141 0
$109$	−15.4748	−1.48221	−0.741107	−	0.671387i	$-0.765699\pi$
$109$	−15.4748	−1.48221	−0.741107	+	0.671387i	$0.765699\pi$
$110$	−5.07009	−0.483414
$111$	0.111343	0.0105682
$112$	0	0
$113$	1.08520	0.102087	0.0510437	−	0.998696i	$-0.483745\pi$
$113$	1.08520	0.102087	0.0510437	+	0.998696i	$0.483745\pi$
$114$	−0.0681027	−0.00637840
$115$	−0.118049	−0.0110081
$116$	0.0961885	0.00893088
$117$	−14.8320	−1.37122
$118$	−15.6464	−1.44037
$119$	0	0
$120$	0.0308983	0.00282061
$121$	1.73618	0.157834
$122$	−20.7210	−1.87599
$123$	0.110082	0.00992575
$124$	−0.0183294	−0.00164603
$125$	1.00000	0.0894427
$126$	0	0
$127$	−12.7231	−1.12899	−0.564495	−	0.825437i	$-0.690929\pi$
$127$	−12.7231	−1.12899	−0.564495	+	0.825437i	$0.690929\pi$
$128$	11.4667	1.01353
$129$	−0.0209368	−0.00184339
$130$	7.02411	0.616055
$131$	−5.83883	−0.510141	−0.255070	−	0.966922i	$-0.582099\pi$
$131$	−5.83883	−0.510141	−0.255070	+	0.966922i	$0.582099\pi$
$132$	0.000717918 0	6.24867e−5 0
$133$	0	0
$134$	−5.78901	−0.500094
$135$	0.0658490	0.00566738
$136$	−6.12020	−0.524803
$137$	−7.25543	−0.619873	−0.309936	−	0.950757i	$-0.600308\pi$
$137$	−7.25543	−0.619873	−0.309936	+	0.950757i	$0.600308\pi$
$138$	0.00184062	0.000156684 0
$139$	−17.1639	−1.45582	−0.727911	−	0.685672i	$-0.759509\pi$
$139$	−17.1639	−1.45582	−0.727911	+	0.685672i	$0.759509\pi$
$140$	0	0
$141$	−0.0822553	−0.00692715
$142$	9.37609	0.786824
$143$	−17.6447	−1.47552
$144$	12.1085	1.00904
$145$	5.24777	0.435803
$146$	7.56407	0.626007
$147$	0	0
$148$	−0.185954	−0.0152853
$149$	−22.5381	−1.84640	−0.923198	−	0.384325i	$-0.874434\pi$
$149$	−22.5381	−1.84640	−0.923198	+	0.384325i	$0.874434\pi$
$150$	−0.0155920	−0.00127308
$151$	−10.1824	−0.828634	−0.414317	−	0.910133i	$-0.635979\pi$
$151$	−10.1824	−0.828634	−0.414317	+	0.910133i	$0.635979\pi$
$152$	−12.2967	−0.997395
$153$	−6.52142	−0.527225
$154$	0	0
$155$	−1.00000	−0.0803219
$156$	−0.000994604 0	−7.96320e−5 0
$157$	−12.8484	−1.02541	−0.512707	−	0.858564i	$-0.671357\pi$
$157$	−12.8484	−1.02541	−0.512707	+	0.858564i	$0.671357\pi$
$158$	1.81569	0.144449
$159$	0.0520453	0.00412746
$160$	−0.103684	−0.00819691
$161$	0	0
$162$	12.7846	1.00445
$163$	−3.77507	−0.295686	−0.147843	−	0.989011i	$-0.547233\pi$
$163$	−3.77507	−0.295686	−0.147843	+	0.989011i	$0.547233\pi$
$164$	−0.183848	−0.0143561
$165$	0.0391675	0.00304919
$166$	−10.2674	−0.796908
$167$	14.4282	1.11649	0.558245	−	0.829676i	$-0.311475\pi$
$167$	14.4282	1.11649	0.558245	+	0.829676i	$0.311475\pi$
$168$	0	0
$169$	11.4450	0.880384
$170$	3.08840	0.236870
$171$	−13.1028	−1.00200
$172$	0.0349666	0.00266618
$173$	−22.5083	−1.71127	−0.855637	−	0.517576i	$-0.826834\pi$
$173$	−22.5083	−1.71127	−0.855637	+	0.517576i	$0.826834\pi$
$174$	−0.0818233	−0.00620301
$175$	0	0
$176$	14.4047	1.08580
$177$	0.120872	0.00908530
$178$	1.54807	0.116033
$179$	−21.3147	−1.59314	−0.796569	−	0.604548i	$-0.793354\pi$
$179$	−21.3147	−1.59314	−0.796569	+	0.604548i	$0.793354\pi$
$180$	−0.0549860	−0.00409842
$181$	8.71569	0.647832	0.323916	−	0.946086i	$-0.395000\pi$
$181$	8.71569	0.647832	0.323916	+	0.946086i	$0.395000\pi$
$182$	0	0
$183$	0.160074	0.0118330
$184$	0.332345	0.0245008
$185$	−10.1451	−0.745883
$186$	0.0155920	0.00114326
$187$	−7.75814	−0.567331
$188$	0.137374	0.0100191
$189$	0	0
$190$	6.20523	0.450175
$191$	19.2247	1.39105	0.695525	−	0.718502i	$-0.255172\pi$
$191$	19.2247	1.39105	0.695525	+	0.718502i	$0.255172\pi$
$192$	−0.0869811	−0.00627732
$193$	1.36025	0.0979133	0.0489566	−	0.998801i	$-0.484410\pi$
$193$	1.36025	0.0979133	0.0489566	+	0.998801i	$0.484410\pi$
$194$	24.2705	1.74252
$195$	−0.0542627	−0.00388583
$196$	0	0
$197$	10.5955	0.754897	0.377448	−	0.926031i	$-0.376802\pi$
$197$	10.5955	0.754897	0.377448	+	0.926031i	$0.376802\pi$
$198$	15.2097	1.08090
$199$	−11.4272	−0.810055	−0.405027	−	0.914305i	$-0.632738\pi$
$199$	−11.4272	−0.810055	−0.405027	+	0.914305i	$0.632738\pi$
$200$	−2.81532	−0.199073
$201$	0.0447213	0.00315440
$202$	−3.35262	−0.235890
$203$	0	0
$204$	−0.000437314 0	−3.06181e−5 0
$205$	−10.0302	−0.700539
$206$	−13.9077	−0.968992
$207$	0.354133	0.0246139
$208$	−19.9563	−1.38372
$209$	−15.5877	−1.07822
$210$	0	0
$211$	−15.1320	−1.04173	−0.520865	−	0.853639i	$-0.674390\pi$
$211$	−15.1320	−1.04173	−0.520865	+	0.853639i	$0.674390\pi$
$212$	−0.0869207	−0.00596974
$213$	−0.0724323	−0.00496298
$214$	−12.2691	−0.838701
$215$	1.90768	0.130102
$216$	−0.185386	−0.0126139
$217$	0	0
$218$	−21.9847	−1.48899
$219$	−0.0584340	−0.00394861
$220$	−0.0654136	−0.00441018
$221$	10.7481	0.722998
$222$	0.158183	0.0106165
$223$	22.6048	1.51373	0.756865	−	0.653571i	$-0.226730\pi$
$223$	22.6048	1.51373	0.756865	+	0.653571i	$0.226730\pi$
$224$	0	0
$225$	−2.99988	−0.199992
$226$	1.54173	0.102554
$227$	2.17362	0.144268	0.0721340	−	0.997395i	$-0.477019\pi$
$227$	2.17362	0.144268	0.0721340	+	0.997395i	$0.477019\pi$
$228$	−0.000878652 0	−5.81901e−5 0
$229$	0.710082	0.0469236	0.0234618	−	0.999725i	$-0.492531\pi$
$229$	0.710082	0.0469236	0.0234618	+	0.999725i	$0.492531\pi$
$230$	−0.167710	−0.0110584
$231$	0	0
$232$	−14.7741	−0.969970
$233$	3.54142	0.232006	0.116003	−	0.993249i	$-0.462992\pi$
$233$	3.54142	0.232006	0.116003	+	0.993249i	$0.462992\pi$
$234$	−21.0715	−1.37749
$235$	7.49475	0.488904
$236$	−0.201868	−0.0131405
$237$	−0.0140266	−0.000911127 0
$238$	0	0
$239$	−25.7774	−1.66740	−0.833701	−	0.552217i	$-0.813782\pi$
$239$	−25.7774	−1.66740	−0.833701	+	0.552217i	$0.813782\pi$
$240$	0.0442989	0.00285948
$241$	−20.1651	−1.29895	−0.649473	−	0.760385i	$-0.725010\pi$
$241$	−20.1651	−1.29895	−0.649473	+	0.760385i	$0.725010\pi$
$242$	2.46655	0.158556
$243$	−0.296311	−0.0190083
$244$	−0.267340	−0.0171147
$245$	0	0
$246$	0.156391	0.00997113
$247$	21.5952	1.37407
$248$	2.81532	0.178773
$249$	0.0793182	0.00502659
$250$	1.42068	0.0898516
$251$	13.8356	0.873298	0.436649	−	0.899632i	$-0.356165\pi$
$251$	13.8356	0.873298	0.436649	+	0.899632i	$0.356165\pi$
$252$	0	0
$253$	0.421290	0.0264863
$254$	−18.0754	−1.13415
$255$	−0.0238586	−0.00149408
$256$	0.439869	0.0274918
$257$	20.4578	1.27612	0.638060	−	0.769987i	$-0.279737\pi$
$257$	20.4578	1.27612	0.638060	+	0.769987i	$0.279737\pi$
$258$	−0.0297445	−0.00185181
$259$	0	0
$260$	0.0906241	0.00562027
$261$	−15.7427	−0.974447
$262$	−8.29510	−0.512473
$263$	19.9769	1.23183	0.615916	−	0.787812i	$-0.288786\pi$
$263$	19.9769	1.23183	0.615916	+	0.787812i	$0.288786\pi$
$264$	−0.110269	−0.00678659
$265$	−4.74215	−0.291308
$266$	0	0
$267$	−0.0119592	−0.000731891 0
$268$	−0.0746890	−0.00456236
$269$	3.93970	0.240208	0.120104	−	0.992761i	$-0.461677\pi$
$269$	3.93970	0.240208	0.120104	+	0.992761i	$0.461677\pi$
$270$	0.0935503	0.00569329
$271$	21.8750	1.32881	0.664407	−	0.747371i	$-0.268684\pi$
$271$	21.8750	1.32881	0.664407	+	0.747371i	$0.268684\pi$
$272$	−8.77453	−0.532034
$273$	0	0
$274$	−10.3076	−0.622707
$275$	−3.56878	−0.215205
$276$	2.37475e−5 0	1.42943e−6 0
$277$	18.5792	1.11632	0.558158	−	0.829734i	$-0.311508\pi$
$277$	18.5792	1.11632	0.558158	+	0.829734i	$0.311508\pi$
$278$	−24.3844	−1.46248
$279$	2.99988	0.179598
$280$	0	0
$281$	25.1167	1.49834	0.749168	−	0.662381i	$-0.230454\pi$
$281$	25.1167	1.49834	0.749168	+	0.662381i	$0.230454\pi$
$282$	−0.116858	−0.00695882
$283$	10.6326	0.632043	0.316021	−	0.948752i	$-0.397653\pi$
$283$	10.6326	0.632043	0.316021	+	0.948752i	$0.397653\pi$
$284$	0.120969	0.00717819
$285$	−0.0479367	−0.00283953
$286$	−25.0675	−1.48227
$287$	0	0
$288$	0.311038	0.0183281
$289$	−12.2742	−0.722011
$290$	7.45540	0.437796
$291$	−0.187495	−0.0109911
$292$	0.0975906	0.00571106
$293$	−13.3050	−0.777285	−0.388643	−	0.921389i	$-0.627056\pi$
$293$	−13.3050	−0.777285	−0.388643	+	0.921389i	$0.627056\pi$
$294$	0	0
$295$	−11.0134	−0.641222
$296$	28.5617	1.66012
$297$	−0.235000	−0.0136361
$298$	−32.0195	−1.85484
$299$	−0.583656	−0.0337537
$300$	−0.000201166 0	−1.16143e−5 0
$301$	0	0
$302$	−14.4660	−0.832422
$303$	0.0258997	0.00148790
$304$	−17.6298	−1.01114
$305$	−14.5853	−0.835151
$306$	−9.26484	−0.529636
$307$	0.0629963	0.00359539	0.00179769	−	0.999998i	$-0.499428\pi$
$307$	0.0629963	0.00359539	0.00179769	+	0.999998i	$0.499428\pi$
$308$	0	0
$309$	0.107440	0.00611203
$310$	−1.42068	−0.0806892
$311$	−11.2279	−0.636676	−0.318338	−	0.947977i	$-0.603125\pi$
$311$	−11.2279	−0.636676	−0.318338	+	0.947977i	$0.603125\pi$
$312$	0.152767	0.00864872
$313$	23.0425	1.30244	0.651220	−	0.758889i	$-0.274258\pi$
$313$	23.0425	1.30244	0.651220	+	0.758889i	$0.274258\pi$
$314$	−18.2534	−1.03010
$315$	0	0
$316$	0.0234258	0.00131781
$317$	22.5595	1.26707	0.633535	−	0.773714i	$-0.281603\pi$
$317$	22.5595	1.26707	0.633535	+	0.773714i	$0.281603\pi$
$318$	0.0739397	0.00414633
$319$	−18.7281	−1.04857
$320$	7.92534	0.443040
$321$	0.0947818	0.00529020
$322$	0	0
$323$	9.49511	0.528322
$324$	0.164945	0.00916360
$325$	4.94419	0.274254
$326$	−5.36316	−0.297038
$327$	0.169836	0.00939197
$328$	28.2382	1.55919
$329$	0	0
$330$	0.0556445	0.00306313
$331$	29.7856	1.63716	0.818582	−	0.574389i	$-0.194760\pi$
$331$	29.7856	1.63716	0.818582	+	0.574389i	$0.194760\pi$
$332$	−0.132469	−0.00727019
$333$	30.4341	1.66778
$334$	20.4979	1.12159
$335$	−4.07482	−0.222631
$336$	0	0
$337$	−0.678553	−0.0369631	−0.0184816	−	0.999829i	$-0.505883\pi$
$337$	−0.678553	−0.0369631	−0.0184816	+	0.999829i	$0.505883\pi$
$338$	16.2597	0.884409
$339$	−0.0119102	−0.000646872 0
$340$	0.0398462	0.00216096
$341$	3.56878	0.193260
$342$	−18.6149	−1.00658
$343$	0	0
$344$	−5.37071	−0.289570
$345$	0.00129559	6.97524e−5 0
$346$	−31.9771	−1.71910
$347$	−17.0480	−0.915186	−0.457593	−	0.889162i	$-0.651288\pi$
$347$	−17.0480	−0.915186	−0.457593	+	0.889162i	$0.651288\pi$
$348$	−0.00105567	−5.65901e−5 0
$349$	−19.8944	−1.06492	−0.532461	−	0.846454i	$-0.678733\pi$
$349$	−19.8944	−1.06492	−0.532461	+	0.846454i	$0.678733\pi$
$350$	0	0
$351$	0.325570	0.0173776
$352$	0.370024	0.0197223
$353$	19.4983	1.03779	0.518894	−	0.854838i	$-0.326344\pi$
$353$	19.4983	1.03779	0.518894	+	0.854838i	$0.326344\pi$
$354$	0.171721	0.00912684
$355$	6.59972	0.350277
$356$	0.0199730	0.00105857
$357$	0	0
$358$	−30.2814	−1.60042
$359$	30.7915	1.62511	0.812557	−	0.582881i	$-0.198075\pi$
$359$	30.7915	1.62511	0.812557	+	0.582881i	$0.198075\pi$
$360$	8.44562	0.445123
$361$	0.0775842	0.00408338
$362$	12.3822	0.650794
$363$	−0.0190546	−0.00100011
$364$	0	0
$365$	5.32426	0.278685
$366$	0.227414	0.0118871
$367$	−0.229983	−0.0120050	−0.00600252	−	0.999982i	$-0.501911\pi$
$367$	−0.229983	−0.0120050	−0.00600252	+	0.999982i	$0.501911\pi$
$368$	0.476484	0.0248384
$369$	30.0894	1.56639
$370$	−14.4129	−0.749293
$371$	0	0
$372$	0.000201166 0	1.04300e−5 0
$373$	−27.2154	−1.40916	−0.704581	−	0.709624i	$-0.748865\pi$
$373$	−27.2154	−1.40916	−0.704581	+	0.709624i	$0.748865\pi$
$374$	−11.0218	−0.569925
$375$	−0.0109751	−0.000566749 0
$376$	−21.1001	−1.08816
$377$	25.9460	1.33628
$378$	0	0
$379$	−31.4830	−1.61718	−0.808588	−	0.588376i	$-0.799768\pi$
$379$	−31.4830	−1.61718	−0.808588	+	0.588376i	$0.799768\pi$
$380$	0.0800590	0.00410694
$381$	0.139636	0.00715379
$382$	27.3121	1.39741
$383$	−9.74133	−0.497759	−0.248879	−	0.968535i	$-0.580062\pi$
$383$	−9.74133	−0.497759	−0.248879	+	0.968535i	$0.580062\pi$
$384$	−0.125848	−0.00642216
$385$	0	0
$386$	1.93249	0.0983609
$387$	−5.72280	−0.290906
$388$	0.313134	0.0158970
$389$	−16.4808	−0.835611	−0.417805	−	0.908537i	$-0.637201\pi$
$389$	−16.4808	−0.835611	−0.417805	+	0.908537i	$0.637201\pi$
$390$	−0.0770899	−0.00390360
$391$	−0.256626	−0.0129781
$392$	0	0
$393$	0.0640814	0.00323248
$394$	15.0528	0.758348
$395$	1.27805	0.0643055
$396$	0.196233	0.00986108
$397$	−34.4209	−1.72754	−0.863768	−	0.503889i	$-0.831902\pi$
$397$	−34.4209	−1.72754	−0.863768	+	0.503889i	$0.831902\pi$
$398$	−16.2344	−0.813758
$399$	0	0
$400$	−4.03632	−0.201816
$401$	9.74506	0.486645	0.243323	−	0.969945i	$-0.421763\pi$
$401$	9.74506	0.486645	0.243323	+	0.969945i	$0.421763\pi$
$402$	0.0635346	0.00316882
$403$	−4.94419	−0.246288
$404$	−0.0432551	−0.00215202
$405$	8.99892	0.447160
$406$	0	0
$407$	36.2056	1.79465
$408$	0.0671695	0.00332539
$409$	−32.7742	−1.62058	−0.810289	−	0.586031i	$-0.800690\pi$
$409$	−32.7742	−1.62058	−0.810289	+	0.586031i	$0.800690\pi$
$410$	−14.2497	−0.703742
$411$	0.0796287	0.00392779
$412$	−0.179435	−0.00884011
$413$	0	0
$414$	0.503109	0.0247264
$415$	−7.22714	−0.354766
$416$	−0.512631	−0.0251338
$417$	0.188375	0.00922474
$418$	−22.1451	−1.08315
$419$	−9.06849	−0.443025	−0.221512	−	0.975158i	$-0.571099\pi$
$419$	−9.06849	−0.443025	−0.221512	+	0.975158i	$0.571099\pi$
$420$	0	0
$421$	−7.16778	−0.349336	−0.174668	−	0.984627i	$-0.555885\pi$
$421$	−7.16778	−0.349336	−0.174668	+	0.984627i	$0.555885\pi$
$422$	−21.4977	−1.04649
$423$	−22.4834	−1.09318
$424$	13.3506	0.648365
$425$	2.17389	0.105449
$426$	−0.102903	−0.00498567
$427$	0	0
$428$	−0.158295	−0.00765147
$429$	0.193652	0.00934959
$430$	2.71020	0.130697
$431$	−22.8714	−1.10168	−0.550839	−	0.834611i	$-0.685692\pi$
$431$	−22.8714	−1.10168	−0.550839	+	0.834611i	$0.685692\pi$
$432$	−0.265788	−0.0127877
$433$	−4.01819	−0.193102	−0.0965509	−	0.995328i	$-0.530781\pi$
$433$	−4.01819	−0.193102	−0.0965509	+	0.995328i	$0.530781\pi$
$434$	0	0
$435$	−0.0575945	−0.00276145
$436$	−0.283643	−0.0135841
$437$	−0.515613	−0.0246651
$438$	−0.0830160	−0.00396666
$439$	−30.8576	−1.47275	−0.736377	−	0.676572i	$-0.763465\pi$
$439$	−30.8576	−1.47275	−0.736377	+	0.676572i	$0.763465\pi$
$440$	10.0472	0.478984
$441$	0	0
$442$	15.2697	0.726303
$443$	28.8748	1.37188	0.685941	−	0.727657i	$-0.259391\pi$
$443$	28.8748	1.37188	0.685941	+	0.727657i	$0.259391\pi$
$444$	0.00204085	9.68546e−5 0
$445$	1.08967	0.0516554
$446$	32.1142	1.52065
$447$	0.247357	0.0116996
$448$	0	0
$449$	−14.7275	−0.695035	−0.347517	−	0.937674i	$-0.612975\pi$
$449$	−14.7275	−0.695035	−0.347517	+	0.937674i	$0.612975\pi$
$450$	−4.26187	−0.200906
$451$	35.7955	1.68555
$452$	0.0198912	0.000935602 0
$453$	0.111753	0.00525060
$454$	3.08801	0.144928
$455$	0	0
$456$	0.134957	0.00631995
$457$	−10.8669	−0.508332	−0.254166	−	0.967161i	$-0.581801\pi$
$457$	−10.8669	−0.508332	−0.254166	+	0.967161i	$0.581801\pi$
$458$	1.00880	0.0471381
$459$	0.143149	0.00668161
$460$	−0.00216377	−0.000100886 0
$461$	1.93846	0.0902832	0.0451416	−	0.998981i	$-0.485626\pi$
$461$	1.93846	0.0902832	0.0451416	+	0.998981i	$0.485626\pi$
$462$	0	0
$463$	35.6763	1.65802	0.829008	−	0.559236i	$-0.188906\pi$
$463$	35.6763	1.65802	0.829008	+	0.559236i	$0.188906\pi$
$464$	−21.1817	−0.983335
$465$	0.0109751	0.000508956 0
$466$	5.03123	0.233067
$467$	7.51004	0.347523	0.173762	−	0.984788i	$-0.444408\pi$
$467$	7.51004	0.347523	0.173762	+	0.984788i	$0.444408\pi$
$468$	−0.271861	−0.0125668
$469$	0	0
$470$	10.6476	0.491139
$471$	0.141012	0.00649748
$472$	31.0061	1.42717
$473$	−6.80807	−0.313035
$474$	−0.0199273	−0.000915292 0
$475$	4.36779	0.200408
$476$	0	0
$477$	14.2259	0.651358
$478$	−36.6214	−1.67502
$479$	18.5434	0.847269	0.423635	−	0.905833i	$-0.360754\pi$
$479$	18.5434	0.847269	0.423635	+	0.905833i	$0.360754\pi$
$480$	0.00113793	5.19393e−5 0
$481$	−50.1593	−2.28707
$482$	−28.6481	−1.30488
$483$	0	0
$484$	0.0318231	0.00144650
$485$	17.0837	0.775731
$486$	−0.420962	−0.0190952
$487$	4.14108	0.187650	0.0938250	−	0.995589i	$-0.470091\pi$
$487$	4.14108	0.187650	0.0938250	+	0.995589i	$0.470091\pi$
$488$	41.0622	1.85880
$489$	0.0414316	0.00187360
$490$	0	0
$491$	18.9067	0.853248	0.426624	−	0.904429i	$-0.359703\pi$
$491$	18.9067	0.853248	0.426624	+	0.904429i	$0.359703\pi$
$492$	0.00201774	9.09666e−5 0
$493$	11.4081	0.513794
$494$	30.6798	1.38035
$495$	10.7059	0.481195
$496$	4.03632	0.181236
$497$	0	0
$498$	0.112686	0.00504957
$499$	43.5904	1.95137	0.975687	−	0.219169i	$-0.0703345\pi$
$499$	43.5904	1.95137	0.975687	+	0.219169i	$0.0703345\pi$
$500$	0.0183294	0.000819716 0
$501$	−0.158350	−0.00707458
$502$	19.6560	0.877291
$503$	26.4381	1.17882	0.589408	−	0.807836i	$-0.299361\pi$
$503$	26.4381	1.17882	0.589408	+	0.807836i	$0.299361\pi$
$504$	0	0
$505$	−2.35987	−0.105013
$506$	0.598519	0.0266074
$507$	−0.125609	−0.00557851
$508$	−0.233206	−0.0103469
$509$	−14.8955	−0.660233	−0.330116	−	0.943940i	$-0.607088\pi$
$509$	−14.8955	−0.660233	−0.330116	+	0.943940i	$0.607088\pi$
$510$	−0.0338954	−0.00150091
$511$	0	0
$512$	−22.3086	−0.985909
$513$	0.287615	0.0126985
$514$	29.0639	1.28195
$515$	−9.78944	−0.431374
$516$	−0.000383760 0	−1.68941e−5 0
$517$	−26.7471	−1.17634
$518$	0	0
$519$	0.247030	0.0108434
$520$	−13.9195	−0.610409
$521$	−11.7951	−0.516753	−0.258377	−	0.966044i	$-0.583188\pi$
$521$	−11.7951	−0.516753	−0.258377	+	0.966044i	$0.583188\pi$
$522$	−22.3653	−0.978902
$523$	−26.2909	−1.14962	−0.574811	−	0.818286i	$-0.694924\pi$
$523$	−26.2909	−1.14962	−0.574811	+	0.818286i	$0.694924\pi$
$524$	−0.107022	−0.00467529
$525$	0	0
$526$	28.3808	1.23746
$527$	−2.17389	−0.0946963
$528$	−0.158093	−0.00688010
$529$	−22.9861	−0.999394
$530$	−6.73707	−0.292639
$531$	33.0387	1.43376
$532$	0	0
$533$	−49.5912	−2.14803
$534$	−0.0169902	−0.000735238 0
$535$	−8.63611	−0.373372
$536$	11.4719	0.495511
$537$	0.233930	0.0100948
$538$	5.59705	0.241306
$539$	0	0
$540$	0.00120697	5.19399e−5 0
$541$	−26.0601	−1.12041	−0.560206	−	0.828353i	$-0.689278\pi$
$541$	−26.0601	−1.12041	−0.560206	+	0.828353i	$0.689278\pi$
$542$	31.0774	1.33489
$543$	−0.0956551	−0.00410495
$544$	−0.225397	−0.00966381
$545$	−15.4748	−0.662866
$546$	0	0
$547$	28.7705	1.23014	0.615068	−	0.788474i	$-0.289129\pi$
$547$	28.7705	1.23014	0.615068	+	0.788474i	$0.289129\pi$
$548$	−0.132988	−0.00568095
$549$	43.7541	1.86738
$550$	−5.07009	−0.216189
$551$	22.9211	0.976474
$552$	−0.00364751	−0.000155248 0
$553$	0	0
$554$	26.3951	1.12142
$555$	0.111343	0.00472625
$556$	−0.314604	−0.0133422
$557$	−36.0079	−1.52570	−0.762852	−	0.646573i	$-0.776201\pi$
$557$	−36.0079	−1.52570	−0.762852	+	0.646573i	$0.776201\pi$
$558$	4.26187	0.180419
$559$	9.43191	0.398927
$560$	0	0
$561$	0.0851460	0.00359487
$562$	35.6827	1.50519
$563$	7.37072	0.310639	0.155319	−	0.987864i	$-0.450359\pi$
$563$	7.37072	0.310639	0.155319	+	0.987864i	$0.450359\pi$
$564$	−0.00150769	−6.34853e−5 0
$565$	1.08520	0.0456549
$566$	15.1055	0.634932
$567$	0	0
$568$	−18.5803	−0.779613
$569$	−0.888905	−0.0372648	−0.0186324	−	0.999826i	$-0.505931\pi$
$569$	−0.888905	−0.0372648	−0.0186324	+	0.999826i	$0.505931\pi$
$570$	−0.0681027	−0.00285251
$571$	36.8871	1.54368	0.771839	−	0.635818i	$-0.219337\pi$
$571$	36.8871	1.54368	0.771839	+	0.635818i	$0.219337\pi$
$572$	−0.323417	−0.0135228
$573$	−0.210992	−0.00881432
$574$	0	0
$575$	−0.118049	−0.00492298
$576$	−23.7751	−0.990628
$577$	15.8622	0.660352	0.330176	−	0.943919i	$-0.392892\pi$
$577$	15.8622	0.660352	0.330176	+	0.943919i	$0.392892\pi$
$578$	−17.4377	−0.725312
$579$	−0.0149289	−0.000620422 0
$580$	0.0961885	0.00399401
$581$	0	0
$582$	−0.266370	−0.0110414
$583$	16.9237	0.700907
$584$	−14.9895	−0.620270
$585$	−14.8320	−0.613226
$586$	−18.9021	−0.780839
$587$	−28.4383	−1.17377	−0.586887	−	0.809669i	$-0.699647\pi$
$587$	−28.4383	−1.17377	−0.586887	+	0.809669i	$0.699647\pi$
$588$	0	0
$589$	−4.36779	−0.179972
$590$	−15.6464	−0.644154
$591$	−0.116286	−0.00478337
$592$	40.9489	1.68299
$593$	15.3036	0.628444	0.314222	−	0.949350i	$-0.398256\pi$
$593$	15.3036	0.628444	0.314222	+	0.949350i	$0.398256\pi$
$594$	−0.333860	−0.0136985
$595$	0	0
$596$	−0.413111	−0.0169217
$597$	0.125414	0.00513287
$598$	−0.829188	−0.0339080
$599$	25.5656	1.04458	0.522290	−	0.852768i	$-0.325078\pi$
$599$	25.5656	1.04458	0.522290	+	0.852768i	$0.325078\pi$
$600$	0.0308983	0.00126142
$601$	−10.7858	−0.439963	−0.219982	−	0.975504i	$-0.570600\pi$
$601$	−10.7858	−0.439963	−0.219982	+	0.975504i	$0.570600\pi$
$602$	0	0
$603$	12.2240	0.497798
$604$	−0.186638	−0.00759419
$605$	1.73618	0.0705856
$606$	0.0367952	0.00149470
$607$	−18.7306	−0.760253	−0.380126	−	0.924935i	$-0.624119\pi$
$607$	−18.7306	−0.760253	−0.380126	+	0.924935i	$0.624119\pi$
$608$	−0.452868	−0.0183662
$609$	0	0
$610$	−20.7210	−0.838969
$611$	37.0555	1.49910
$612$	−0.119534	−0.00483187
$613$	−20.9835	−0.847515	−0.423757	−	0.905776i	$-0.639289\pi$
$613$	−20.9835	−0.847515	−0.423757	+	0.905776i	$0.639289\pi$
$614$	0.0894975	0.00361183
$615$	0.110082	0.00443893
$616$	0	0
$617$	−8.29480	−0.333936	−0.166968	−	0.985962i	$-0.553398\pi$
$617$	−8.29480	−0.333936	−0.166968	+	0.985962i	$0.553398\pi$
$618$	0.152637	0.00613997
$619$	−14.3327	−0.576080	−0.288040	−	0.957618i	$-0.593004\pi$
$619$	−14.3327	−0.576080	−0.288040	+	0.957618i	$0.593004\pi$
$620$	−0.0183294	−0.000736127 0
$621$	−0.00777340	−0.000311936 0
$622$	−15.9513	−0.639587
$623$	0	0
$624$	0.219022	0.00876789
$625$	1.00000	0.0400000
$626$	32.7360	1.30839
$627$	0.171075	0.00683210
$628$	−0.235504	−0.00939762
$629$	−22.0544	−0.879366
$630$	0	0
$631$	−31.0515	−1.23614	−0.618070	−	0.786123i	$-0.712085\pi$
$631$	−31.0515	−1.23614	−0.618070	+	0.786123i	$0.712085\pi$
$632$	−3.59811	−0.143125
$633$	0.166074	0.00660087
$634$	32.0499	1.27286
$635$	−12.7231	−0.504900
$636$	0.000953960 0	3.78270e−5 0
$637$	0	0
$638$	−26.6066	−1.05337
$639$	−19.7984	−0.783211
$640$	11.4667	0.453263
$641$	33.4114	1.31967	0.659836	−	0.751410i	$-0.270626\pi$
$641$	33.4114	1.31967	0.659836	+	0.751410i	$0.270626\pi$
$642$	0.134654	0.00531439
$643$	−35.0011	−1.38031	−0.690154	−	0.723663i	$-0.742457\pi$
$643$	−35.0011	−1.38031	−0.690154	+	0.723663i	$0.742457\pi$
$644$	0	0
$645$	−0.0209368	−0.000824387 0
$646$	13.4895	0.530737
$647$	−8.45893	−0.332555	−0.166277	−	0.986079i	$-0.553175\pi$
$647$	−8.45893	−0.332555	−0.166277	+	0.986079i	$0.553175\pi$
$648$	−25.3348	−0.995245
$649$	39.3042	1.54283
$650$	7.02411	0.275508
$651$	0	0
$652$	−0.0691948	−0.00270988
$653$	38.7888	1.51792	0.758961	−	0.651137i	$-0.225707\pi$
$653$	38.7888	1.51792	0.758961	+	0.651137i	$0.225707\pi$
$654$	0.241283	0.00943491
$655$	−5.83883	−0.228142
$656$	40.4851	1.58068
$657$	−15.9721	−0.623133
$658$	0	0
$659$	−2.46399	−0.0959833	−0.0479917	−	0.998848i	$-0.515282\pi$
$659$	−2.46399	−0.0959833	−0.0479917	+	0.998848i	$0.515282\pi$
$660$	0.000717918 0	2.79449e−5 0
$661$	−5.44222	−0.211678	−0.105839	−	0.994383i	$-0.533753\pi$
$661$	−5.44222	−0.211678	−0.105839	+	0.994383i	$0.533753\pi$
$662$	42.3158	1.64465
$663$	−0.117961	−0.00458124
$664$	20.3467	0.789605
$665$	0	0
$666$	43.2371	1.67540
$667$	−0.619493	−0.0239869
$668$	0.264461	0.0102323
$669$	−0.248089	−0.00959168
$670$	−5.78901	−0.223649
$671$	52.0516	2.00943
$672$	0	0
$673$	5.84208	0.225196	0.112598	−	0.993641i	$-0.464083\pi$
$673$	5.84208	0.225196	0.112598	+	0.993641i	$0.464083\pi$
$674$	−0.964006	−0.0371321
$675$	0.0658490	0.00253453
$676$	0.209780	0.00806846
$677$	12.6145	0.484813	0.242406	−	0.970175i	$-0.422063\pi$
$677$	12.6145	0.484813	0.242406	+	0.970175i	$0.422063\pi$
$678$	−0.0169205	−0.000649829 0
$679$	0	0
$680$	−6.12020	−0.234699
$681$	−0.0238555	−0.000914147 0
$682$	5.07009	0.194144
$683$	4.57741	0.175150	0.0875748	−	0.996158i	$-0.472088\pi$
$683$	4.57741	0.175150	0.0875748	+	0.996158i	$0.472088\pi$
$684$	−0.240167	−0.00918303
$685$	−7.25543	−0.277216
$686$	0	0
$687$	−0.00779319	−0.000297329 0
$688$	−7.70000	−0.293560
$689$	−23.4461	−0.893224
$690$	0.00184062	7.00713e−5 0
$691$	−0.500516	−0.0190405	−0.00952026	−	0.999955i	$-0.503030\pi$
$691$	−0.500516	−0.0190405	−0.00952026	+	0.999955i	$0.503030\pi$
$692$	−0.412564	−0.0156833
$693$	0	0
$694$	−24.2198	−0.919370
$695$	−17.1639	−0.651063
$696$	0.162147	0.00614616
$697$	−21.8046	−0.825907
$698$	−28.2635	−1.06979
$699$	−0.0388673	−0.00147010
$700$	0	0
$701$	34.6262	1.30781	0.653906	−	0.756576i	$-0.273129\pi$
$701$	34.6262	1.30781	0.653906	+	0.756576i	$0.273129\pi$
$702$	0.462530	0.0174571
$703$	−44.3117	−1.67125
$704$	−28.2838	−1.06599
$705$	−0.0822553	−0.00309791
$706$	27.7008	1.04253
$707$	0	0
$708$	0.00221552	8.32642e−5 0
$709$	21.9334	0.823725	0.411862	−	0.911246i	$-0.364878\pi$
$709$	21.9334	0.823725	0.411862	+	0.911246i	$0.364878\pi$
$710$	9.37609	0.351878
$711$	−3.83398	−0.143786
$712$	−3.06777	−0.114970
$713$	0.118049	0.00442097
$714$	0	0
$715$	−17.6447	−0.659875
$716$	−0.390687	−0.0146006
$717$	0.282908	0.0105654
$718$	43.7449	1.63254
$719$	22.7174	0.847215	0.423608	−	0.905846i	$-0.360764\pi$
$719$	22.7174	0.847215	0.423608	+	0.905846i	$0.360764\pi$
$720$	12.1085	0.451256
$721$	0	0
$722$	0.110222	0.00410205
$723$	0.221313	0.00823070
$724$	0.159753	0.00593719
$725$	5.24777	0.194897
$726$	−0.0270705	−0.00100468
$727$	−24.8583	−0.921942	−0.460971	−	0.887415i	$-0.652499\pi$
$727$	−24.8583	−0.921942	−0.460971	+	0.887415i	$0.652499\pi$
$728$	0	0
$729$	−26.9935	−0.999759
$730$	7.56407	0.279959
$731$	4.14708	0.153385
$732$	0.00293407	0.000108446 0
$733$	−7.48337	−0.276404	−0.138202	−	0.990404i	$-0.544132\pi$
$733$	−7.48337	−0.276404	−0.138202	+	0.990404i	$0.544132\pi$
$734$	−0.326733	−0.0120599
$735$	0	0
$736$	0.0122397	0.000451163 0
$737$	14.5421	0.535666
$738$	42.7474	1.57355
$739$	−6.07719	−0.223553	−0.111777	−	0.993733i	$-0.535654\pi$
$739$	−6.07719	−0.223553	−0.111777	+	0.993733i	$0.535654\pi$
$740$	−0.185954	−0.00683580
$741$	−0.237008	−0.00870671
$742$	0	0
$743$	−10.8148	−0.396756	−0.198378	−	0.980126i	$-0.563567\pi$
$743$	−10.8148	−0.396756	−0.198378	+	0.980126i	$0.563567\pi$
$744$	−0.0308983	−0.00113279
$745$	−22.5381	−0.825733
$746$	−38.6644	−1.41560
$747$	21.6805	0.793250
$748$	−0.142202	−0.00519943
$749$	0	0
$750$	−0.0155920	−0.000569340 0
$751$	39.5655	1.44377	0.721883	−	0.692015i	$-0.243277\pi$
$751$	39.5655	1.44377	0.721883	+	0.692015i	$0.243277\pi$
$752$	−30.2512	−1.10315
$753$	−0.151847	−0.00553361
$754$	36.8609	1.34239
$755$	−10.1824	−0.370576
$756$	0	0
$757$	20.4741	0.744142	0.372071	−	0.928204i	$-0.378648\pi$
$757$	20.4741	0.744142	0.372071	+	0.928204i	$0.378648\pi$
$758$	−44.7273	−1.62457
$759$	−0.00462368	−0.000167829 0
$760$	−12.2967	−0.446049
$761$	10.2978	0.373293	0.186647	−	0.982427i	$-0.440238\pi$
$761$	10.2978	0.373293	0.186647	+	0.982427i	$0.440238\pi$
$762$	0.198378	0.00718649
$763$	0	0
$764$	0.352377	0.0127486
$765$	−6.52142	−0.235782
$766$	−13.8393	−0.500034
$767$	−54.4521	−1.96615
$768$	−0.00482759	−0.000174201 0
$769$	0.0385955	0.00139179	0.000695895	−	1.00000i	$-0.499778\pi$
$769$	0.0385955	0.00139179	0.000695895		1.00000i	$0.499778\pi$
$770$	0	0
$771$	−0.224525	−0.00808607
$772$	0.0249327	0.000897346 0
$773$	14.4057	0.518138	0.259069	−	0.965859i	$-0.416584\pi$
$773$	14.4057	0.518138	0.259069	+	0.965859i	$0.416584\pi$
$774$	−8.13026	−0.292236
$775$	−1.00000	−0.0359211
$776$	−48.0961	−1.72655
$777$	0	0
$778$	−23.4140	−0.839431
$779$	−43.8098	−1.56965
$780$	−0.000994604 0	−3.56125e−5 0
$781$	−23.5529	−0.842790
$782$	−0.364583	−0.0130375
$783$	0.345560	0.0123493
$784$	0	0
$785$	−12.8484	−0.458579
$786$	0.0910392	0.00324726
$787$	−25.4017	−0.905473	−0.452736	−	0.891644i	$-0.649552\pi$
$787$	−25.4017	−0.905473	−0.452736	+	0.891644i	$0.649552\pi$
$788$	0.194209	0.00691841
$789$	−0.219248	−0.00780544
$790$	1.81569	0.0645995
$791$	0	0
$792$	−30.1405	−1.07100
$793$	−72.1124	−2.56079
$794$	−48.9011	−1.73543
$795$	0.0520453	0.00184586
$796$	−0.209454	−0.00742392
$797$	21.0971	0.747298	0.373649	−	0.927570i	$-0.378106\pi$
$797$	21.0971	0.747298	0.373649	+	0.927570i	$0.378106\pi$
$798$	0	0
$799$	16.2928	0.576397
$800$	−0.103684	−0.00366577
$801$	−3.26888	−0.115500
$802$	13.8446	0.488870
$803$	−19.0011	−0.670535
$804$	0.000819715 0	2.89091e−5 0
$805$	0	0
$806$	−7.02411	−0.247414
$807$	−0.0432384	−0.00152206
$808$	6.64380	0.233728
$809$	−7.22050	−0.253859	−0.126930	−	0.991912i	$-0.540512\pi$
$809$	−7.22050	−0.253859	−0.126930	+	0.991912i	$0.540512\pi$
$810$	12.7846	0.449204
$811$	20.4614	0.718496	0.359248	−	0.933242i	$-0.383033\pi$
$811$	20.4614	0.718496	0.359248	+	0.933242i	$0.383033\pi$
$812$	0	0
$813$	−0.240080	−0.00841996
$814$	51.4366	1.80285
$815$	−3.77507	−0.132235
$816$	0.0963010	0.00337121
$817$	8.33233	0.291511
$818$	−46.5616	−1.62799
$819$	0	0
$820$	−0.183848	−0.00642024
$821$	−3.43814	−0.119992	−0.0599960	−	0.998199i	$-0.519109\pi$
$821$	−3.43814	−0.119992	−0.0599960	+	0.998199i	$0.519109\pi$
$822$	0.113127	0.00394575
$823$	23.5196	0.819842	0.409921	−	0.912121i	$-0.365556\pi$
$823$	23.5196	0.819842	0.409921	+	0.912121i	$0.365556\pi$
$824$	27.5604	0.960112
$825$	0.0391675	0.00136364
$826$	0	0
$827$	8.57598	0.298216	0.149108	−	0.988821i	$-0.452360\pi$
$827$	8.57598	0.298216	0.149108	+	0.988821i	$0.452360\pi$
$828$	0.00649104	0.000225579 0
$829$	−32.0349	−1.11262	−0.556309	−	0.830975i	$-0.687783\pi$
$829$	−32.0349	−1.11262	−0.556309	+	0.830975i	$0.687783\pi$
$830$	−10.2674	−0.356388
$831$	−0.203908	−0.00707349
$832$	39.1844	1.35847
$833$	0	0
$834$	0.267620	0.00926691
$835$	14.4282	0.499309
$836$	−0.285713	−0.00988159
$837$	−0.0658490	−0.00227607
$838$	−12.8834	−0.445050
$839$	39.5240	1.36452	0.682260	−	0.731110i	$-0.260997\pi$
$839$	39.5240	1.36452	0.682260	+	0.731110i	$0.260997\pi$
$840$	0	0
$841$	−1.46093	−0.0503769
$842$	−10.1831	−0.350933
$843$	−0.275657	−0.00949412
$844$	−0.277361	−0.00954715
$845$	11.4450	0.393720
$846$	−31.9416	−1.09818
$847$	0	0
$848$	19.1408	0.657299
$849$	−0.116693	−0.00400491
$850$	3.08840	0.105931
$851$	1.19762	0.0410539
$852$	−0.00132764	−4.54842e−5 0
$853$	−12.4277	−0.425517	−0.212758	−	0.977105i	$-0.568245\pi$
$853$	−12.4277	−0.425517	−0.212758	+	0.977105i	$0.568245\pi$
$854$	0	0
$855$	−13.1028	−0.448108
$856$	24.3134	0.831015
$857$	−46.5596	−1.59045	−0.795224	−	0.606316i	$-0.792647\pi$
$857$	−46.5596	−1.59045	−0.795224	+	0.606316i	$0.792647\pi$
$858$	0.275117	0.00939233
$859$	−25.0232	−0.853781	−0.426890	−	0.904303i	$-0.640391\pi$
$859$	−25.0232	−0.853781	−0.426890	+	0.904303i	$0.640391\pi$
$860$	0.0349666	0.00119235
$861$	0	0
$862$	−32.4930	−1.10672
$863$	−10.1881	−0.346807	−0.173404	−	0.984851i	$-0.555477\pi$
$863$	−10.1881	−0.346807	−0.173404	+	0.984851i	$0.555477\pi$
$864$	−0.00682746	−0.000232275 0
$865$	−22.5083	−0.765305
$866$	−5.70856	−0.193985
$867$	0.134710	0.00457499
$868$	0	0
$869$	−4.56106	−0.154723
$870$	−0.0818233	−0.00277407
$871$	−20.1467	−0.682643
$872$	43.5664	1.47534
$873$	−51.2491	−1.73452
$874$	−0.732520	−0.0247779
$875$	0	0
$876$	−0.00107106	−3.61878e−5 0
$877$	−20.8139	−0.702835	−0.351417	−	0.936219i	$-0.614300\pi$
$877$	−20.8139	−0.702835	−0.351417	+	0.936219i	$0.614300\pi$
$878$	−43.8388	−1.47949
$879$	0.146023	0.00492523
$880$	14.4047	0.485584
$881$	−49.8726	−1.68025	−0.840126	−	0.542392i	$-0.817519\pi$
$881$	−49.8726	−1.68025	−0.840126	+	0.542392i	$0.817519\pi$
$882$	0	0
$883$	2.80052	0.0942449	0.0471225	−	0.998889i	$-0.484995\pi$
$883$	2.80052	0.0942449	0.0471225	+	0.998889i	$0.484995\pi$
$884$	0.197007	0.00662606
$885$	0.120872	0.00406307
$886$	41.0218	1.37815
$887$	23.8104	0.799476	0.399738	−	0.916629i	$-0.369101\pi$
$887$	23.8104	0.799476	0.399738	+	0.916629i	$0.369101\pi$
$888$	−0.313466	−0.0105192
$889$	0	0
$890$	1.54807	0.0518916
$891$	−32.1151	−1.07590
$892$	0.414333	0.0138729
$893$	32.7355	1.09545
$894$	0.351415	0.0117531
$895$	−21.3147	−0.712473
$896$	0	0
$897$	0.00640566	0.000213879 0
$898$	−20.9231	−0.698212
$899$	−5.24777	−0.175023
$900$	−0.0549860	−0.00183287
$901$	−10.3089	−0.343440
$902$	50.8540	1.69325
$903$	0	0
$904$	−3.05520	−0.101614
$905$	8.71569	0.289719
$906$	0.158765	0.00527460
$907$	47.5177	1.57780	0.788899	−	0.614523i	$-0.210651\pi$
$907$	47.5177	1.57780	0.788899	+	0.614523i	$0.210651\pi$
$908$	0.0398411	0.00132217
$909$	7.07934	0.234807
$910$	0	0
$911$	−25.3259	−0.839085	−0.419542	−	0.907736i	$-0.637809\pi$
$911$	−25.3259	−0.839085	−0.419542	+	0.907736i	$0.637809\pi$
$912$	0.193488	0.00640703
$913$	25.7920	0.853592
$914$	−15.4384	−0.510656
$915$	0.160074	0.00529189
$916$	0.0130154	0.000430041 0
$917$	0	0
$918$	0.203368	0.00671215
$919$	10.9320	0.360613	0.180306	−	0.983610i	$-0.442291\pi$
$919$	10.9320	0.360613	0.180306	+	0.983610i	$0.442291\pi$
$920$	0.332345	0.0109571
$921$	−0.000691388 0	−2.27820e−5 0
$922$	2.75393	0.0906960
$923$	32.6303	1.07404
$924$	0	0
$925$	−10.1451	−0.333569
$926$	50.6845	1.66560
$927$	29.3671	0.964544
$928$	−0.544107	−0.0178612
$929$	−45.1717	−1.48203	−0.741017	−	0.671486i	$-0.765656\pi$
$929$	−45.1717	−1.48203	−0.741017	+	0.671486i	$0.765656\pi$
$930$	0.0155920	0.000511283 0
$931$	0	0
$932$	0.0649122	0.00212627
$933$	0.123227	0.00403427
$934$	10.6694	0.349112
$935$	−7.75814	−0.253718
$936$	41.7567	1.36486
$937$	−14.8997	−0.486752	−0.243376	−	0.969932i	$-0.578255\pi$
$937$	−14.8997	−0.486752	−0.243376	+	0.969932i	$0.578255\pi$
$938$	0	0
$939$	−0.252893	−0.00825284
$940$	0.137374	0.00448066
$941$	36.4014	1.18665	0.593327	−	0.804962i	$-0.297814\pi$
$941$	36.4014	1.18665	0.593327	+	0.804962i	$0.297814\pi$
$942$	0.200333	0.00652719
$943$	1.18405	0.0385581
$944$	44.4534	1.44684
$945$	0	0
$946$	−9.67209	−0.314467
$947$	45.1785	1.46810	0.734051	−	0.679094i	$-0.237627\pi$
$947$	45.1785	1.46810	0.734051	+	0.679094i	$0.237627\pi$
$948$	−0.000257100 0	−8.35021e−6 0
$949$	26.3241	0.854518
$950$	6.20523	0.201324
$951$	−0.247592	−0.00802873
$952$	0	0
$953$	−26.4199	−0.855824	−0.427912	−	0.903821i	$-0.640751\pi$
$953$	−26.4199	−0.855824	−0.427912	+	0.903821i	$0.640751\pi$
$954$	20.2104	0.654336
$955$	19.2247	0.622096
$956$	−0.472485	−0.0152812
$957$	0.205542	0.00664423
$958$	26.3442	0.851143
$959$	0	0
$960$	−0.0869811	−0.00280730
$961$	1.00000	0.0322581
$962$	−71.2603	−2.29752
$963$	25.9073	0.834851
$964$	−0.369614	−0.0119045
$965$	1.36025	0.0437881
$966$	0	0
$967$	−4.55160	−0.146369	−0.0731847	−	0.997318i	$-0.523316\pi$
$967$	−4.55160	−0.146369	−0.0731847	+	0.997318i	$0.523316\pi$
$968$	−4.88789	−0.157103
$969$	−0.104209	−0.00334768
$970$	24.2705	0.779278
$971$	27.3354	0.877236	0.438618	−	0.898674i	$-0.355468\pi$
$971$	27.3354	0.877236	0.438618	+	0.898674i	$0.355468\pi$
$972$	−0.00543120	−0.000174206 0
$973$	0	0
$974$	5.88314	0.188508
$975$	−0.0542627	−0.00173780
$976$	58.8709	1.88441
$977$	−42.0008	−1.34372	−0.671862	−	0.740676i	$-0.734505\pi$
$977$	−42.0008	−1.34372	−0.671862	+	0.740676i	$0.734505\pi$
$978$	0.0588610	0.00188217
$979$	−3.88880	−0.124286
$980$	0	0
$981$	46.4224	1.48215
$982$	26.8604	0.857149
$983$	47.9997	1.53095	0.765476	−	0.643464i	$-0.222503\pi$
$983$	47.9997	1.53095	0.765476	+	0.643464i	$0.222503\pi$
$984$	−0.309916	−0.00987975
$985$	10.5955	0.337600
$986$	16.2072	0.516143
$987$	0	0
$988$	0.395827	0.0125929
$989$	−0.225199	−0.00716091
$990$	15.2097	0.483395
$991$	20.9272	0.664776	0.332388	−	0.943143i	$-0.392146\pi$
$991$	20.9272	0.664776	0.332388	+	0.943143i	$0.392146\pi$
$992$	0.103684	0.00329196
$993$	−0.326898	−0.0103738
$994$	0	0
$995$	−11.4272	−0.362268
$996$	0.00145386	4.60672e−5 0
$997$	31.9618	1.01224	0.506120	−	0.862463i	$-0.331079\pi$
$997$	31.9618	1.01224	0.506120	+	0.862463i	$0.331079\pi$
$998$	61.9280	1.96030
$999$	−0.668045	−0.0211360

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	7595.2.a.bf.1.16		21
7.3	odd	6		1085.2.j.d.156.6	✓	42
7.5	odd	6		1085.2.j.d.466.6	yes	42
7.6	odd	2		7595.2.a.bg.1.16		21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1085.2.j.d.156.6	✓	42	7.3	odd	6
1085.2.j.d.466.6	yes	42	7.5	odd	6
7595.2.a.bf.1.16		21	1.1	even	1	trivial
7595.2.a.bg.1.16		21	7.6	odd	2

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:	\( N \)	\(=\)	\( 7595 = 5 \cdot 7^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	7595.a (trivial)

\(f(q)\)	\(=\)	\(q+1.42068 q^{2} -0.0109751 q^{3} +0.0183294 q^{4} +1.00000 q^{5} -0.0155920 q^{6} -2.81532 q^{8} -2.99988 q^{9} +O(q^{10})\)	\(q+1.42068 q^{2} -0.0109751 q^{3} +0.0183294 q^{4} +1.00000 q^{5} -0.0155920 q^{6} -2.81532 q^{8} -2.99988 q^{9} +1.42068 q^{10} -3.56878 q^{11} -0.000201166 q^{12} +4.94419 q^{13} -0.0109751 q^{15} -4.03632 q^{16} +2.17389 q^{17} -4.26187 q^{18} +4.36779 q^{19} +0.0183294 q^{20} -5.07009 q^{22} -0.118049 q^{23} +0.0308983 q^{24} +1.00000 q^{25} +7.02411 q^{26} +0.0658490 q^{27} +5.24777 q^{29} -0.0155920 q^{30} -1.00000 q^{31} -0.103684 q^{32} +0.0391675 q^{33} +3.08840 q^{34} -0.0549860 q^{36} -10.1451 q^{37} +6.20523 q^{38} -0.0542627 q^{39} -2.81532 q^{40} -10.0302 q^{41} +1.90768 q^{43} -0.0654136 q^{44} -2.99988 q^{45} -0.167710 q^{46} +7.49475 q^{47} +0.0442989 q^{48} +1.42068 q^{50} -0.0238586 q^{51} +0.0906241 q^{52} -4.74215 q^{53} +0.0935503 q^{54} -3.56878 q^{55} -0.0479367 q^{57} +7.45540 q^{58} -11.0134 q^{59} -0.000201166 q^{60} -14.5853 q^{61} -1.42068 q^{62} +7.92534 q^{64} +4.94419 q^{65} +0.0556445 q^{66} -4.07482 q^{67} +0.0398462 q^{68} +0.00129559 q^{69} +6.59972 q^{71} +8.44562 q^{72} +5.32426 q^{73} -14.4129 q^{74} -0.0109751 q^{75} +0.0800590 q^{76} -0.0770899 q^{78} +1.27805 q^{79} -4.03632 q^{80} +8.99892 q^{81} -14.2497 q^{82} -7.22714 q^{83} +2.17389 q^{85} +2.71020 q^{86} -0.0575945 q^{87} +10.0472 q^{88} +1.08967 q^{89} -4.26187 q^{90} -0.00216377 q^{92} +0.0109751 q^{93} +10.6476 q^{94} +4.36779 q^{95} +0.00113793 q^{96} +17.0837 q^{97} +10.7059 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9}+O(q^{10}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9	\( 21 q - 4 q^{2} - 5 q^{3} + 22 q^{4} + 21 q^{5} - 6 q^{6} - 12 q^{8} + 20 q^{9} - 4 q^{10} - 4 q^{11} - 21 q^{12} - 24 q^{13} - 5 q^{15} + 20 q^{16} - 18 q^{17} - 16 q^{18} - 17 q^{19} + 22 q^{20} + 9 q^{22} - 19 q^{23} - 21 q^{24} + 21 q^{25} - 16 q^{26} - 17 q^{27} - 4 q^{29} - 6 q^{30} - 21 q^{31} - 18 q^{32} - 27 q^{33} + 2 q^{34} + 52 q^{36} - 19 q^{37} + 10 q^{38} + 21 q^{39} - 12 q^{40} - 5 q^{41} - 15 q^{43} - 11 q^{44} + 20 q^{45} + 6 q^{46} - 4 q^{47} - 19 q^{48} - 4 q^{50} + 35 q^{51} - 66 q^{52} - 19 q^{53} - 11 q^{54} - 4 q^{55} - 27 q^{57} - q^{58} + q^{59} - 21 q^{60} - 60 q^{61} + 4 q^{62} - 10 q^{64} - 24 q^{65} - 64 q^{66} + 2 q^{67} - 11 q^{68} - 18 q^{69} - q^{71} - 37 q^{72} - 51 q^{73} + 11 q^{74} - 5 q^{75} - 13 q^{76} - 40 q^{78} + q^{79} + 20 q^{80} + 21 q^{81} + 2 q^{82} - 38 q^{83} - 18 q^{85} + 26 q^{86} - 32 q^{87} + 5 q^{88} - 2 q^{89} - 16 q^{90} - 86 q^{92} + 5 q^{93} - 67 q^{94} - 17 q^{95} + 56 q^{96} - 42 q^{97} - 35 q^{99}+O(q^{100}) \) 21 * q - 4 * q^2 - 5 * q^3 + 22 * q^4 + 21 * q^5 - 6 * q^6 - 12 * q^8 + 20 * q^9 - 4 * q^10 - 4 * q^11 - 21 * q^12 - 24 * q^13 - 5 * q^15 + 20 * q^16 - 18 * q^17 - 16 * q^18 - 17 * q^19 + 22 * q^20 + 9 * q^22 - 19 * q^23 - 21 * q^24 + 21 * q^25 - 16 * q^26 - 17 * q^27 - 4 * q^29 - 6 * q^30 - 21 * q^31 - 18 * q^32 - 27 * q^33 + 2 * q^34 + 52 * q^36 - 19 * q^37 + 10 * q^38 + 21 * q^39 - 12 * q^40 - 5 * q^41 - 15 * q^43 - 11 * q^44 + 20 * q^45 + 6 * q^46 - 4 * q^47 - 19 * q^48 - 4 * q^50 + 35 * q^51 - 66 * q^52 - 19 * q^53 - 11 * q^54 - 4 * q^55 - 27 * q^57 - q^58 + q^59 - 21 * q^60 - 60 * q^61 + 4 * q^62 - 10 * q^64 - 24 * q^65 - 64 * q^66 + 2 * q^67 - 11 * q^68 - 18 * q^69 - q^71 - 37 * q^72 - 51 * q^73 + 11 * q^74 - 5 * q^75 - 13 * q^76 - 40 * q^78 + q^79 + 20 * q^80 + 21 * q^81 + 2 * q^82 - 38 * q^83 - 18 * q^85 + 26 * q^86 - 32 * q^87 + 5 * q^88 - 2 * q^89 - 16 * q^90 - 86 * q^92 + 5 * q^93 - 67 * q^94 - 17 * q^95 + 56 * q^96 - 42 * q^97 - 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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