LMFDB - Embedded newform 119.2.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [119,2,Mod(1,119)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(119, 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("119.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 119 = 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	119.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:	$0.950219784053$
Analytic rank:	$0$
Dimension:	$5$
Coefficient field:	5.5.453749.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 5x^{3} + 10x^{2} + x - 3 $ x^5 - 2x^4 - 5x^3 + 10*x^2 + x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.78972$ of defining polynomial
Character	$\chi$	$=$	119.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.32942 q^{2} -3.21594 q^{3} +3.42621 q^{4} -3.16902 q^{5} +7.49128 q^{6} -1.00000 q^{7} -3.32226 q^{8} +7.34225 q^{9} +7.38200 q^{10} +0.406219 q^{11} -11.0185 q^{12} +3.07940 q^{13} +2.32942 q^{14} +10.1914 q^{15} +0.886514 q^{16} +1.00000 q^{17} -17.1032 q^{18} -1.57945 q^{19} -10.8578 q^{20} +3.21594 q^{21} -0.946255 q^{22} +0.852428 q^{23} +10.6842 q^{24} +5.04271 q^{25} -7.17323 q^{26} -13.9644 q^{27} -3.42621 q^{28} -1.49995 q^{29} -23.7400 q^{30} -0.316596 q^{31} +4.57945 q^{32} -1.30637 q^{33} -2.32942 q^{34} +3.16902 q^{35} +25.1561 q^{36} +10.6445 q^{37} +3.67920 q^{38} -9.90316 q^{39} +10.5283 q^{40} +11.8748 q^{41} -7.49128 q^{42} -4.70156 q^{43} +1.39179 q^{44} -23.2678 q^{45} -1.98567 q^{46} +9.09072 q^{47} -2.85097 q^{48} +1.00000 q^{49} -11.7466 q^{50} -3.21594 q^{51} +10.5507 q^{52} -4.34225 q^{53} +32.5290 q^{54} -1.28732 q^{55} +3.32226 q^{56} +5.07940 q^{57} +3.49403 q^{58} +7.15889 q^{59} +34.9178 q^{60} -3.87478 q^{61} +0.737485 q^{62} -7.34225 q^{63} -12.4405 q^{64} -9.75869 q^{65} +3.04310 q^{66} +5.48982 q^{67} +3.42621 q^{68} -2.74135 q^{69} -7.38200 q^{70} -8.73834 q^{71} -24.3928 q^{72} +6.25535 q^{73} -24.7956 q^{74} -16.2170 q^{75} -5.41152 q^{76} -0.406219 q^{77} +23.0686 q^{78} +3.77303 q^{79} -2.80938 q^{80} +22.8819 q^{81} -27.6614 q^{82} -5.35247 q^{83} +11.0185 q^{84} -3.16902 q^{85} +10.9519 q^{86} +4.82376 q^{87} -1.34956 q^{88} +14.1845 q^{89} +54.2005 q^{90} -3.07940 q^{91} +2.92060 q^{92} +1.01815 q^{93} -21.1761 q^{94} +5.00530 q^{95} -14.7272 q^{96} -0.623061 q^{97} -2.32942 q^{98} +2.98256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) $ 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

Coefficient data

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

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

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

$2$	−2.32942	−1.64715	−0.823576	−	0.567207i	$-0.808024\pi$
$2$	−2.32942	−1.64715	−0.823576	+	0.567207i	$0.808024\pi$
$3$	−3.21594	−1.85672	−0.928361	−	0.371680i	$-0.878782\pi$
$3$	−3.21594	−1.85672	−0.928361	+	0.371680i	$0.878782\pi$
$4$	3.42621	1.71311
$5$	−3.16902	−1.41723	−0.708615	−	0.705595i	$-0.750680\pi$
$5$	−3.16902	−1.41723	−0.708615	+	0.705595i	$0.750680\pi$
$6$	7.49128	3.05830
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.32226	−1.17459
$9$	7.34225	2.44742
$10$	7.38200	2.33439
$11$	0.406219	0.122480	0.0612398	−	0.998123i	$-0.480495\pi$
$11$	0.406219	0.122480	0.0612398	+	0.998123i	$0.480495\pi$
$12$	−11.0185	−3.18076
$13$	3.07940	0.854072	0.427036	−	0.904235i	$-0.359558\pi$
$13$	3.07940	0.854072	0.427036	+	0.904235i	$0.359558\pi$
$14$	2.32942	0.622565
$15$	10.1914	2.63140
$16$	0.886514	0.221628
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−17.1032	−4.03127
$19$	−1.57945	−0.362350	−0.181175	−	0.983451i	$-0.557990\pi$
$19$	−1.57945	−0.362350	−0.181175	+	0.983451i	$0.557990\pi$
$20$	−10.8578	−2.42787
$21$	3.21594	0.701775
$22$	−0.946255	−0.201742
$23$	0.852428	0.177743	0.0888717	−	0.996043i	$-0.471674\pi$
$23$	0.852428	0.177743	0.0888717	+	0.996043i	$0.471674\pi$
$24$	10.6842	2.18090
$25$	5.04271	1.00854
$26$	−7.17323	−1.40679
$27$	−13.9644	−2.68745
$28$	−3.42621	−0.647494
$29$	−1.49995	−0.278534	−0.139267	−	0.990255i	$-0.544475\pi$
$29$	−1.49995	−0.278534	−0.139267	+	0.990255i	$0.544475\pi$
$30$	−23.7400	−4.33432
$31$	−0.316596	−0.0568623	−0.0284311	−	0.999596i	$-0.509051\pi$
$31$	−0.316596	−0.0568623	−0.0284311	+	0.999596i	$0.509051\pi$
$32$	4.57945	0.809539
$33$	−1.30637	−0.227410
$34$	−2.32942	−0.399493
$35$	3.16902	0.535663
$36$	25.1561	4.19269
$37$	10.6445	1.74995	0.874974	−	0.484171i	$-0.160879\pi$
$37$	10.6445	1.74995	0.874974	+	0.484171i	$0.160879\pi$
$38$	3.67920	0.596845
$39$	−9.90316	−1.58577
$40$	10.5283	1.66467
$41$	11.8748	1.85453	0.927265	−	0.374406i	$-0.122153\pi$
$41$	11.8748	1.85453	0.927265	+	0.374406i	$0.122153\pi$
$42$	−7.49128	−1.15593
$43$	−4.70156	−0.716981	−0.358490	−	0.933533i	$-0.616708\pi$
$43$	−4.70156	−0.716981	−0.358490	+	0.933533i	$0.616708\pi$
$44$	1.39179	0.209820
$45$	−23.2678	−3.46855
$46$	−1.98567	−0.292770
$47$	9.09072	1.32602	0.663009	−	0.748611i	$-0.269279\pi$
$47$	9.09072	1.32602	0.663009	+	0.748611i	$0.269279\pi$
$48$	−2.85097	−0.411502
$49$	1.00000	0.142857
$50$	−11.7466	−1.66122
$51$	−3.21594	−0.450321
$52$	10.5507	1.46312
$53$	−4.34225	−0.596454	−0.298227	−	0.954495i	$-0.596395\pi$
$53$	−4.34225	−0.596454	−0.298227	+	0.954495i	$0.596395\pi$
$54$	32.5290	4.42664
$55$	−1.28732	−0.173582
$56$	3.32226	0.443955
$57$	5.07940	0.672783
$58$	3.49403	0.458788
$59$	7.15889	0.932008	0.466004	−	0.884782i	$-0.345693\pi$
$59$	7.15889	0.932008	0.466004	+	0.884782i	$0.345693\pi$
$60$	34.9178	4.50787
$61$	−3.87478	−0.496115	−0.248058	−	0.968745i	$-0.579792\pi$
$61$	−3.87478	−0.496115	−0.248058	+	0.968745i	$0.579792\pi$
$62$	0.737485	0.0936607
$63$	−7.34225	−0.925037
$64$	−12.4405	−1.55506
$65$	−9.75869	−1.21042
$66$	3.04310	0.374579
$67$	5.48982	0.670689	0.335344	−	0.942096i	$-0.391147\pi$
$67$	5.48982	0.670689	0.335344	+	0.942096i	$0.391147\pi$
$68$	3.42621	0.415489
$69$	−2.74135	−0.330020
$70$	−7.38200	−0.882317
$71$	−8.73834	−1.03705	−0.518525	−	0.855062i	$-0.673519\pi$
$71$	−8.73834	−1.03705	−0.518525	+	0.855062i	$0.673519\pi$
$72$	−24.3928	−2.87472
$73$	6.25535	0.732133	0.366066	−	0.930589i	$-0.380704\pi$
$73$	6.25535	0.732133	0.366066	+	0.930589i	$0.380704\pi$
$74$	−24.7956	−2.88243
$75$	−16.2170	−1.87258
$76$	−5.41152	−0.620744
$77$	−0.406219	−0.0462929
$78$	23.0686	2.61201
$79$	3.77303	0.424499	0.212249	−	0.977216i	$-0.431921\pi$
$79$	3.77303	0.424499	0.212249	+	0.977216i	$0.431921\pi$
$80$	−2.80938	−0.314098
$81$	22.8819	2.54243
$82$	−27.6614	−3.05469
$83$	−5.35247	−0.587510	−0.293755	−	0.955881i	$-0.594905\pi$
$83$	−5.35247	−0.587510	−0.293755	+	0.955881i	$0.594905\pi$
$84$	11.0185	1.20222
$85$	−3.16902	−0.343729
$86$	10.9519	1.18098
$87$	4.82376	0.517161
$88$	−1.34956	−0.143864
$89$	14.1845	1.50355	0.751775	−	0.659420i	$-0.229198\pi$
$89$	14.1845	1.50355	0.751775	+	0.659420i	$0.229198\pi$
$90$	54.2005	5.71323
$91$	−3.07940	−0.322809
$92$	2.92060	0.304494
$93$	1.01815	0.105577
$94$	−21.1761	−2.18415
$95$	5.00530	0.513533
$96$	−14.7272	−1.50309
$97$	−0.623061	−0.0632623	−0.0316311	−	0.999500i	$-0.510070\pi$
$97$	−0.623061	−0.0632623	−0.0316311	+	0.999500i	$0.510070\pi$
$98$	−2.32942	−0.235307
$99$	2.98256	0.299758
$100$	17.2774	1.72774
$101$	−16.3494	−1.62682	−0.813411	−	0.581689i	$-0.802392\pi$
$101$	−16.3494	−1.62682	−0.813411	+	0.581689i	$0.802392\pi$
$102$	7.49128	0.741747
$103$	−9.80642	−0.966255	−0.483128	−	0.875550i	$-0.660499\pi$
$103$	−9.80642	−0.966255	−0.483128	+	0.875550i	$0.660499\pi$
$104$	−10.2306	−1.00319
$105$	−10.1914	−0.994577
$106$	10.1149	0.982450
$107$	11.3034	1.09274	0.546368	−	0.837545i	$-0.316010\pi$
$107$	11.3034	1.09274	0.546368	+	0.837545i	$0.316010\pi$
$108$	−47.8450	−4.60389
$109$	5.18756	0.496878	0.248439	−	0.968647i	$-0.420082\pi$
$109$	5.18756	0.496878	0.248439	+	0.968647i	$0.420082\pi$
$110$	2.99870	0.285915
$111$	−34.2321	−3.24917
$112$	−0.886514	−0.0837677
$113$	4.83809	0.455129	0.227565	−	0.973763i	$-0.426924\pi$
$113$	4.83809	0.455129	0.227565	+	0.973763i	$0.426924\pi$
$114$	−11.8321	−1.10818
$115$	−2.70136	−0.251903
$116$	−5.13916	−0.477159
$117$	22.6097	2.09027
$118$	−16.6761	−1.53516
$119$	−1.00000	−0.0916698
$120$	−33.8584	−3.09083
$121$	−10.8350	−0.984999
$122$	9.02601	0.817177
$123$	−38.1886	−3.44335
$124$	−1.08472	−0.0974111
$125$	−0.135346	−0.0121057
$126$	17.1032	1.52368
$127$	0.856632	0.0760138	0.0380069	−	0.999277i	$-0.487899\pi$
$127$	0.856632	0.0760138	0.0380069	+	0.999277i	$0.487899\pi$
$128$	19.8203	1.75188
$129$	15.1199	1.33123
$130$	22.7321	1.99374
$131$	9.31769	0.814091	0.407045	−	0.913408i	$-0.366559\pi$
$131$	9.31769	0.814091	0.407045	+	0.913408i	$0.366559\pi$
$132$	−4.47591	−0.389578
$133$	1.57945	0.136955
$134$	−12.7881	−1.10473
$135$	44.2535	3.80874
$136$	−3.32226	−0.284881
$137$	−2.66224	−0.227450	−0.113725	−	0.993512i	$-0.536278\pi$
$137$	−2.66224	−0.227450	−0.113725	+	0.993512i	$0.536278\pi$
$138$	6.38577	0.543593
$139$	4.13735	0.350925	0.175463	−	0.984486i	$-0.443858\pi$
$139$	4.13735	0.350925	0.175463	+	0.984486i	$0.443858\pi$
$140$	10.8578	0.917648
$141$	−29.2352	−2.46205
$142$	20.3553	1.70818
$143$	1.25091	0.104606
$144$	6.50901	0.542417
$145$	4.75339	0.394748
$146$	−14.5714	−1.20593
$147$	−3.21594	−0.265246
$148$	36.4704	2.99785
$149$	9.54806	0.782207	0.391104	−	0.920347i	$-0.372093\pi$
$149$	9.54806	0.782207	0.391104	+	0.920347i	$0.372093\pi$
$150$	37.7763	3.08443
$151$	12.9746	1.05586	0.527930	−	0.849288i	$-0.322968\pi$
$151$	12.9746	1.05586	0.527930	+	0.849288i	$0.322968\pi$
$152$	5.24733	0.425614
$153$	7.34225	0.593586
$154$	0.946255	0.0762514
$155$	1.00330	0.0805869
$156$	−33.9303	−2.71660
$157$	9.42877	0.752498	0.376249	−	0.926519i	$-0.377214\pi$
$157$	9.42877	0.752498	0.376249	+	0.926519i	$0.377214\pi$
$158$	−8.78898	−0.699214
$159$	13.9644	1.10745
$160$	−14.5124	−1.14730
$161$	−0.852428	−0.0671807
$162$	−53.3016	−4.18777
$163$	11.4259	0.894942	0.447471	−	0.894298i	$-0.352325\pi$
$163$	11.4259	0.894942	0.447471	+	0.894298i	$0.352325\pi$
$164$	40.6855	3.17701
$165$	4.13993	0.322293
$166$	12.4682	0.967718
$167$	16.6190	1.28602	0.643010	−	0.765858i	$-0.277685\pi$
$167$	16.6190	1.28602	0.643010	+	0.765858i	$0.277685\pi$
$168$	−10.6842	−0.824301
$169$	−3.51729	−0.270561
$170$	7.38200	0.566173
$171$	−11.5967	−0.886821
$172$	−16.1085	−1.22826
$173$	−14.3921	−1.09421	−0.547105	−	0.837064i	$-0.684270\pi$
$173$	−14.3921	−1.09421	−0.547105	+	0.837064i	$0.684270\pi$
$174$	−11.2366	−0.851843
$175$	−5.04271	−0.381193
$176$	0.360118	0.0271449
$177$	−23.0225	−1.73048
$178$	−33.0416	−2.47657
$179$	2.35510	0.176028	0.0880142	−	0.996119i	$-0.471948\pi$
$179$	2.35510	0.176028	0.0880142	+	0.996119i	$0.471948\pi$
$180$	−79.7203	−5.94200
$181$	8.97124	0.666827	0.333413	−	0.942781i	$-0.391800\pi$
$181$	8.97124	0.666827	0.333413	+	0.942781i	$0.391800\pi$
$182$	7.17323	0.531715
$183$	12.4611	0.921148
$184$	−2.83198	−0.208777
$185$	−33.7327	−2.48008
$186$	−2.37171	−0.173902
$187$	0.406219	0.0297056
$188$	31.1468	2.27161
$189$	13.9644	1.01576
$190$	−11.6595	−0.845867
$191$	10.3023	0.745445	0.372723	−	0.927943i	$-0.378424\pi$
$191$	10.3023	0.745445	0.372723	+	0.927943i	$0.378424\pi$
$192$	40.0079	2.88732
$193$	−8.39709	−0.604436	−0.302218	−	0.953239i	$-0.597727\pi$
$193$	−8.39709	−0.604436	−0.302218	+	0.953239i	$0.597727\pi$
$194$	1.45137	0.104203
$195$	31.3833	2.24741
$196$	3.42621	0.244730
$197$	−14.7861	−1.05346	−0.526732	−	0.850032i	$-0.676583\pi$
$197$	−14.7861	−1.05346	−0.526732	+	0.850032i	$0.676583\pi$
$198$	−6.94764	−0.493747
$199$	5.46016	0.387060	0.193530	−	0.981094i	$-0.438006\pi$
$199$	5.46016	0.387060	0.193530	+	0.981094i	$0.438006\pi$
$200$	−16.7532	−1.18463
$201$	−17.6549	−1.24528
$202$	38.0846	2.67962
$203$	1.49995	0.105276
$204$	−11.0185	−0.771448
$205$	−37.6315	−2.62830
$206$	22.8433	1.59157
$207$	6.25874	0.435012
$208$	2.72993	0.189287
$209$	−0.641600	−0.0443804
$210$	23.7400	1.63822
$211$	14.2155	0.978639	0.489319	−	0.872105i	$-0.337245\pi$
$211$	14.2155	0.978639	0.489319	+	0.872105i	$0.337245\pi$
$212$	−14.8775	−1.02179
$213$	28.1019	1.92551
$214$	−26.3303	−1.79990
$215$	14.8993	1.01613
$216$	46.3933	3.15667
$217$	0.316596	0.0214919
$218$	−12.0840	−0.818434
$219$	−20.1168	−1.35937
$220$	−4.41062	−0.297364
$221$	3.07940	0.207143
$222$	79.7410	5.35187
$223$	−26.2555	−1.75820	−0.879101	−	0.476636i	$-0.841856\pi$
$223$	−26.2555	−1.75820	−0.879101	+	0.476636i	$0.841856\pi$
$224$	−4.57945	−0.305977
$225$	37.0248	2.46832
$226$	−11.2700	−0.749667
$227$	−5.12903	−0.340426	−0.170213	−	0.985407i	$-0.554446\pi$
$227$	−5.12903	−0.340426	−0.170213	+	0.985407i	$0.554446\pi$
$228$	17.4031	1.15255
$229$	−5.65894	−0.373953	−0.186977	−	0.982364i	$-0.559869\pi$
$229$	−5.65894	−0.373953	−0.186977	+	0.982364i	$0.559869\pi$
$230$	6.29262	0.414923
$231$	1.30637	0.0859531
$232$	4.98323	0.327165
$233$	−27.4144	−1.79598	−0.897990	−	0.440017i	$-0.854973\pi$
$233$	−27.4144	−1.79598	−0.897990	+	0.440017i	$0.854973\pi$
$234$	−52.6676	−3.44299
$235$	−28.8087	−1.87927
$236$	24.5279	1.59663
$237$	−12.1338	−0.788176
$238$	2.32942	0.150994
$239$	−18.4064	−1.19061	−0.595306	−	0.803499i	$-0.702969\pi$
$239$	−18.4064	−1.19061	−0.595306	+	0.803499i	$0.702969\pi$
$240$	9.03480	0.583194
$241$	−7.00401	−0.451168	−0.225584	−	0.974224i	$-0.572429\pi$
$241$	−7.00401	−0.451168	−0.225584	+	0.974224i	$0.572429\pi$
$242$	25.2393	1.62244
$243$	−31.6935	−2.03314
$244$	−13.2758	−0.849898
$245$	−3.16902	−0.202461
$246$	88.9573	5.67171
$247$	−4.86375	−0.309473
$248$	1.05181	0.0667901
$249$	17.2132	1.09084
$250$	0.315279	0.0199400
$251$	23.2556	1.46788	0.733941	−	0.679213i	$-0.237679\pi$
$251$	23.2556	1.46788	0.733941	+	0.679213i	$0.237679\pi$
$252$	−25.1561	−1.58469
$253$	0.346272	0.0217699
$254$	−1.99546	−0.125206
$255$	10.1914	0.638209
$256$	−21.2889	−1.33055
$257$	17.1702	1.07105	0.535524	−	0.844520i	$-0.320114\pi$
$257$	17.1702	1.07105	0.535524	+	0.844520i	$0.320114\pi$
$258$	−35.2207	−2.19274
$259$	−10.6445	−0.661418
$260$	−33.4354	−2.07357
$261$	−11.0130	−0.681690
$262$	−21.7049	−1.34093
$263$	18.1588	1.11972	0.559860	−	0.828587i	$-0.310855\pi$
$263$	18.1588	1.11972	0.559860	+	0.828587i	$0.310855\pi$
$264$	4.34011	0.267115
$265$	13.7607	0.845313
$266$	−3.67920	−0.225586
$267$	−45.6163	−2.79167
$268$	18.8093	1.14896
$269$	−11.5172	−0.702216	−0.351108	−	0.936335i	$-0.614195\pi$
$269$	−11.5172	−0.702216	−0.351108	+	0.936335i	$0.614195\pi$
$270$	−103.085	−6.27357
$271$	15.8750	0.964336	0.482168	−	0.876079i	$-0.339849\pi$
$271$	15.8750	0.964336	0.482168	+	0.876079i	$0.339849\pi$
$272$	0.886514	0.0537528
$273$	9.90316	0.599366
$274$	6.20148	0.374645
$275$	2.04844	0.123526
$276$	−9.39246	−0.565360
$277$	27.2578	1.63776	0.818882	−	0.573962i	$-0.194594\pi$
$277$	27.2578	1.63776	0.818882	+	0.573962i	$0.194594\pi$
$278$	−9.63764	−0.578027
$279$	−2.32453	−0.139166
$280$	−10.5283	−0.629187
$281$	23.6720	1.41215	0.706076	−	0.708136i	$-0.250464\pi$
$281$	23.6720	1.41215	0.706076	+	0.708136i	$0.250464\pi$
$282$	68.1011	4.05536
$283$	20.9808	1.24718	0.623591	−	0.781751i	$-0.285673\pi$
$283$	20.9808	1.24718	0.623591	+	0.781751i	$0.285673\pi$
$284$	−29.9394	−1.77658
$285$	−16.0967	−0.953489
$286$	−2.91390	−0.172302
$287$	−11.8748	−0.700946
$288$	33.6234	1.98128
$289$	1.00000	0.0588235
$290$	−11.0727	−0.650209
$291$	2.00372	0.117460
$292$	21.4322	1.25422
$293$	7.74485	0.452459	0.226229	−	0.974074i	$-0.427360\pi$
$293$	7.74485	0.452459	0.226229	+	0.974074i	$0.427360\pi$
$294$	7.49128	0.436900
$295$	−22.6867	−1.32087
$296$	−35.3638	−2.05548
$297$	−5.67260	−0.329158
$298$	−22.2415	−1.28841
$299$	2.62497	0.151806
$300$	−55.5630	−3.20793
$301$	4.70156	0.270993
$302$	−30.2234	−1.73916
$303$	52.5785	3.02056
$304$	−1.40020	−0.0803070
$305$	12.2793	0.703110
$306$	−17.1032	−0.977726
$307$	16.4689	0.939927	0.469963	−	0.882686i	$-0.344267\pi$
$307$	16.4689	0.939927	0.469963	+	0.882686i	$0.344267\pi$
$308$	−1.39179	−0.0793047
$309$	31.5368	1.79407
$310$	−2.33711	−0.132739
$311$	−24.5185	−1.39032	−0.695158	−	0.718857i	$-0.744666\pi$
$311$	−24.5185	−1.39032	−0.695158	+	0.718857i	$0.744666\pi$
$312$	32.9008	1.86264
$313$	−32.3504	−1.82855	−0.914276	−	0.405093i	$-0.867239\pi$
$313$	−32.3504	−1.82855	−0.914276	+	0.405093i	$0.867239\pi$
$314$	−21.9636	−1.23948
$315$	23.2678	1.31099
$316$	12.9272	0.727212
$317$	−26.0626	−1.46382	−0.731912	−	0.681400i	$-0.761372\pi$
$317$	−26.0626	−1.46382	−0.731912	+	0.681400i	$0.761372\pi$
$318$	−32.5290	−1.82414
$319$	−0.609309	−0.0341148
$320$	39.4242	2.20388
$321$	−36.3509	−2.02891
$322$	1.98567	0.110657
$323$	−1.57945	−0.0878828
$324$	78.3983	4.35546
$325$	15.5285	0.861367
$326$	−26.6157	−1.47410
$327$	−16.6829	−0.922565
$328$	−39.4511	−2.17832
$329$	−9.09072	−0.501188
$330$	−9.64364	−0.530865
$331$	−12.1539	−0.668038	−0.334019	−	0.942566i	$-0.608405\pi$
$331$	−12.1539	−0.668038	−0.334019	+	0.942566i	$0.608405\pi$
$332$	−18.3387	−1.00647
$333$	78.1547	4.28285
$334$	−38.7128	−2.11827
$335$	−17.3974	−0.950520
$336$	2.85097	0.155533
$337$	32.2753	1.75815	0.879073	−	0.476687i	$-0.158163\pi$
$337$	32.2753	1.75815	0.879073	+	0.476687i	$0.158163\pi$
$338$	8.19326	0.445655
$339$	−15.5590	−0.845049
$340$	−10.8578	−0.588844
$341$	−0.128607	−0.00696446
$342$	27.0136	1.46073
$343$	−1.00000	−0.0539949
$344$	15.6198	0.842162
$345$	8.68741	0.467715
$346$	33.5252	1.80233
$347$	16.3828	0.879473	0.439736	−	0.898127i	$-0.355072\pi$
$347$	16.3828	0.879473	0.439736	+	0.898127i	$0.355072\pi$
$348$	16.5272	0.885952
$349$	26.6822	1.42827	0.714133	−	0.700010i	$-0.246821\pi$
$349$	26.6822	1.42827	0.714133	+	0.700010i	$0.246821\pi$
$350$	11.7466	0.627882
$351$	−43.0020	−2.29528
$352$	1.86026	0.0991520
$353$	11.6588	0.620533	0.310266	−	0.950650i	$-0.399582\pi$
$353$	11.6588	0.620533	0.310266	+	0.950650i	$0.399582\pi$
$354$	53.6293	2.85036
$355$	27.6920	1.46974
$356$	48.5990	2.57574
$357$	3.21594	0.170205
$358$	−5.48603	−0.289945
$359$	−32.9090	−1.73687	−0.868435	−	0.495803i	$-0.834874\pi$
$359$	−32.9090	−1.73687	−0.868435	+	0.495803i	$0.834874\pi$
$360$	77.3015	4.07415
$361$	−16.5053	−0.868703
$362$	−20.8978	−1.09836
$363$	34.8446	1.82887
$364$	−10.5507	−0.553006
$365$	−19.8233	−1.03760
$366$	−29.0271	−1.51727
$367$	−2.89834	−0.151292	−0.0756459	−	0.997135i	$-0.524102\pi$
$367$	−2.89834	−0.151292	−0.0756459	+	0.997135i	$0.524102\pi$
$368$	0.755689	0.0393930
$369$	87.1876	4.53881
$370$	78.5778	4.08506
$371$	4.34225	0.225438
$372$	3.48841	0.180865
$373$	9.95108	0.515247	0.257624	−	0.966245i	$-0.417061\pi$
$373$	9.95108	0.515247	0.257624	+	0.966245i	$0.417061\pi$
$374$	−0.946255	−0.0489297
$375$	0.435265	0.0224770
$376$	−30.2017	−1.55753
$377$	−4.61896	−0.237889
$378$	−32.5290	−1.67311
$379$	37.2004	1.91086	0.955428	−	0.295223i	$-0.0953940\pi$
$379$	37.2004	1.91086	0.955428	+	0.295223i	$0.0953940\pi$
$380$	17.1492	0.879737
$381$	−2.75488	−0.141137
$382$	−23.9983	−1.22786
$383$	−7.73595	−0.395288	−0.197644	−	0.980274i	$-0.563329\pi$
$383$	−7.73595	−0.395288	−0.197644	+	0.980274i	$0.563329\pi$
$384$	−63.7408	−3.25276
$385$	1.28732	0.0656077
$386$	19.5604	0.995598
$387$	−34.5200	−1.75475
$388$	−2.13474	−0.108375
$389$	−3.90378	−0.197929	−0.0989647	−	0.995091i	$-0.531553\pi$
$389$	−3.90378	−0.197929	−0.0989647	+	0.995091i	$0.531553\pi$
$390$	−73.1051	−3.70182
$391$	0.852428	0.0431091
$392$	−3.32226	−0.167799
$393$	−29.9651	−1.51154
$394$	34.4430	1.73521
$395$	−11.9568	−0.601612
$396$	10.2189	0.513518
$397$	−25.2992	−1.26973	−0.634864	−	0.772624i	$-0.718944\pi$
$397$	−25.2992	−1.26973	−0.634864	+	0.772624i	$0.718944\pi$
$398$	−12.7190	−0.637547
$399$	−5.07940	−0.254288
$400$	4.47043	0.223522
$401$	−30.5733	−1.52676	−0.763380	−	0.645950i	$-0.776461\pi$
$401$	−30.5733	−1.52676	−0.763380	+	0.645950i	$0.776461\pi$
$402$	41.1258	2.05117
$403$	−0.974925	−0.0485645
$404$	−56.0164	−2.78692
$405$	−72.5133	−3.60321
$406$	−3.49403	−0.173406
$407$	4.32400	0.214333
$408$	10.6842	0.528945
$409$	28.9796	1.43295	0.716476	−	0.697612i	$-0.245754\pi$
$409$	28.9796	1.43295	0.716476	+	0.697612i	$0.245754\pi$
$410$	87.6596	4.32920
$411$	8.56159	0.422312
$412$	−33.5989	−1.65530
$413$	−7.15889	−0.352266
$414$	−14.5793	−0.716531
$415$	16.9621	0.832637
$416$	14.1019	0.691405
$417$	−13.3055	−0.651571
$418$	1.49456	0.0731013
$419$	0.703757	0.0343808	0.0171904	−	0.999852i	$-0.494528\pi$
$419$	0.703757	0.0343808	0.0171904	+	0.999852i	$0.494528\pi$
$420$	−34.9178	−1.70382
$421$	−7.06526	−0.344340	−0.172170	−	0.985067i	$-0.555078\pi$
$421$	−7.06526	−0.344340	−0.172170	+	0.985067i	$0.555078\pi$
$422$	−33.1140	−1.61197
$423$	66.7464	3.24532
$424$	14.4261	0.700592
$425$	5.04271	0.244607
$426$	−65.4613	−3.17161
$427$	3.87478	0.187514
$428$	38.7277	1.87198
$429$	−4.02285	−0.194225
$430$	−34.7069	−1.67371
$431$	18.0528	0.869574	0.434787	−	0.900533i	$-0.356824\pi$
$431$	18.0528	0.869574	0.434787	+	0.900533i	$0.356824\pi$
$432$	−12.3796	−0.595616
$433$	13.3572	0.641906	0.320953	−	0.947095i	$-0.395997\pi$
$433$	13.3572	0.641906	0.320953	+	0.947095i	$0.395997\pi$
$434$	−0.737485	−0.0354004
$435$	−15.2866	−0.732936
$436$	17.7737	0.851206
$437$	−1.34636	−0.0644053
$438$	46.8606	2.23908
$439$	16.0510	0.766073	0.383037	−	0.923733i	$-0.374878\pi$
$439$	16.0510	0.766073	0.383037	+	0.923733i	$0.374878\pi$
$440$	4.27679	0.203888
$441$	7.34225	0.349631
$442$	−7.17323	−0.341196
$443$	25.8638	1.22883	0.614414	−	0.788984i	$-0.289392\pi$
$443$	25.8638	1.22883	0.614414	+	0.788984i	$0.289392\pi$
$444$	−117.286	−5.56617
$445$	−44.9509	−2.13088
$446$	61.1603	2.89602
$447$	−30.7060	−1.45234
$448$	12.4405	0.587758
$449$	−29.9450	−1.41319	−0.706595	−	0.707618i	$-0.749770\pi$
$449$	−29.9450	−1.41319	−0.706595	+	0.707618i	$0.749770\pi$
$450$	−86.2465	−4.06570
$451$	4.82376	0.227142
$452$	16.5763	0.779685
$453$	−41.7256	−1.96044
$454$	11.9477	0.560733
$455$	9.75869	0.457495
$456$	−16.8751	−0.790248
$457$	6.60873	0.309143	0.154572	−	0.987982i	$-0.450600\pi$
$457$	6.60873	0.309143	0.154572	+	0.987982i	$0.450600\pi$
$458$	13.1821	0.615957
$459$	−13.9644	−0.651803
$460$	−9.25545	−0.431537
$461$	−18.6368	−0.868001	−0.434001	−	0.900913i	$-0.642898\pi$
$461$	−18.6368	−0.868001	−0.434001	+	0.900913i	$0.642898\pi$
$462$	−3.04310	−0.141578
$463$	−29.0418	−1.34969	−0.674843	−	0.737961i	$-0.735789\pi$
$463$	−29.0418	−1.34969	−0.674843	+	0.737961i	$0.735789\pi$
$464$	−1.32973	−0.0617311
$465$	−3.22655	−0.149628
$466$	63.8598	2.95825
$467$	−25.3554	−1.17331	−0.586654	−	0.809838i	$-0.699555\pi$
$467$	−25.3554	−1.17331	−0.586654	+	0.809838i	$0.699555\pi$
$468$	77.4658	3.58086
$469$	−5.48982	−0.253497
$470$	67.1077	3.09545
$471$	−30.3223	−1.39718
$472$	−23.7837	−1.09473
$473$	−1.90986	−0.0878154
$474$	28.2648	1.29825
$475$	−7.96469	−0.365445
$476$	−3.42621	−0.157040
$477$	−31.8819	−1.45977
$478$	42.8763	1.96112
$479$	−2.15307	−0.0983762	−0.0491881	−	0.998790i	$-0.515663\pi$
$479$	−2.15307	−0.0983762	−0.0491881	+	0.998790i	$0.515663\pi$
$480$	46.6709	2.13022
$481$	32.7787	1.49458
$482$	16.3153	0.743142
$483$	2.74135	0.124736
$484$	−37.1230	−1.68741
$485$	1.97449	0.0896572
$486$	73.8277	3.34889
$487$	−20.0304	−0.907663	−0.453832	−	0.891088i	$-0.649943\pi$
$487$	−20.0304	−0.907663	−0.453832	+	0.891088i	$0.649943\pi$
$488$	12.8730	0.582734
$489$	−36.7448	−1.66166
$490$	7.38200	0.333485
$491$	−2.07170	−0.0934947	−0.0467473	−	0.998907i	$-0.514886\pi$
$491$	−2.07170	−0.0934947	−0.0467473	+	0.998907i	$0.514886\pi$
$492$	−130.842	−5.89882
$493$	−1.49995	−0.0675545
$494$	11.3297	0.509749
$495$	−9.45180	−0.424827
$496$	−0.280666	−0.0126023
$497$	8.73834	0.391968
$498$	−40.0969	−1.79678
$499$	−17.9861	−0.805166	−0.402583	−	0.915383i	$-0.631888\pi$
$499$	−17.9861	−0.805166	−0.402583	+	0.915383i	$0.631888\pi$
$500$	−0.463725	−0.0207384
$501$	−53.4458	−2.38778
$502$	−54.1722	−2.41782
$503$	−25.6283	−1.14271	−0.571354	−	0.820704i	$-0.693582\pi$
$503$	−25.6283	−1.14271	−0.571354	+	0.820704i	$0.693582\pi$
$504$	24.3928	1.08654
$505$	51.8115	2.30558
$506$	−0.806614	−0.0358584
$507$	11.3114	0.502357
$508$	2.93501	0.130220
$509$	−10.8374	−0.480358	−0.240179	−	0.970729i	$-0.577206\pi$
$509$	−10.8374	−0.480358	−0.240179	+	0.970729i	$0.577206\pi$
$510$	−23.7400	−1.05123
$511$	−6.25535	−0.276720
$512$	9.95019	0.439740
$513$	22.0560	0.973798
$514$	−39.9967	−1.76418
$515$	31.0768	1.36941
$516$	51.8040	2.28055
$517$	3.69282	0.162410
$518$	24.7956	1.08946
$519$	46.2840	2.03164
$520$	32.4209	1.42175
$521$	7.52173	0.329533	0.164766	−	0.986333i	$-0.447313\pi$
$521$	7.52173	0.329533	0.164766	+	0.986333i	$0.447313\pi$
$522$	25.6540	1.12285
$523$	5.85252	0.255913	0.127956	−	0.991780i	$-0.459158\pi$
$523$	5.85252	0.255913	0.127956	+	0.991780i	$0.459158\pi$
$524$	31.9244	1.39462
$525$	16.2170	0.707769
$526$	−42.2995	−1.84435
$527$	−0.316596	−0.0137911
$528$	−1.15812	−0.0504006
$529$	−22.2734	−0.968407
$530$	−32.0545	−1.39236
$531$	52.5624	2.28101
$532$	5.41152	0.234619
$533$	36.5672	1.58390
$534$	106.260	4.59831
$535$	−35.8206	−1.54866
$536$	−18.2386	−0.787788
$537$	−7.57385	−0.326836
$538$	26.8284	1.15666
$539$	0.406219	0.0174971
$540$	151.622	6.52477
$541$	8.18397	0.351856	0.175928	−	0.984403i	$-0.443707\pi$
$541$	8.18397	0.351856	0.175928	+	0.984403i	$0.443707\pi$
$542$	−36.9795	−1.58841
$543$	−28.8509	−1.23811
$544$	4.57945	0.196342
$545$	−16.4395	−0.704191
$546$	−23.0686	−0.987247
$547$	43.3576	1.85384	0.926918	−	0.375264i	$-0.122448\pi$
$547$	43.3576	1.85384	0.926918	+	0.375264i	$0.122448\pi$
$548$	−9.12140	−0.389647
$549$	−28.4496	−1.21420
$550$	−4.77169	−0.203466
$551$	2.36910	0.100927
$552$	9.10748	0.387640
$553$	−3.77303	−0.160445
$554$	−63.4950	−2.69765
$555$	108.482	4.60482
$556$	14.1754	0.601173
$557$	−24.2328	−1.02677	−0.513387	−	0.858157i	$-0.671610\pi$
$557$	−24.2328	−1.02677	−0.513387	+	0.858157i	$0.671610\pi$
$558$	5.41480	0.229227
$559$	−14.4780	−0.612353
$560$	2.80938	0.118718
$561$	−1.30637	−0.0551551
$562$	−55.1421	−2.32603
$563$	−14.1397	−0.595919	−0.297960	−	0.954578i	$-0.596306\pi$
$563$	−14.1397	−0.595919	−0.297960	+	0.954578i	$0.596306\pi$
$564$	−100.166	−4.21775
$565$	−15.3320	−0.645023
$566$	−48.8733	−2.05430
$567$	−22.8819	−0.960949
$568$	29.0310	1.21811
$569$	29.2527	1.22634	0.613169	−	0.789952i	$-0.289894\pi$
$569$	29.2527	1.22634	0.613169	+	0.789952i	$0.289894\pi$
$570$	37.4961	1.57054
$571$	−7.49928	−0.313835	−0.156918	−	0.987612i	$-0.550156\pi$
$571$	−7.49928	−0.313835	−0.156918	+	0.987612i	$0.550156\pi$
$572$	4.28588	0.179202
$573$	−33.1314	−1.38409
$574$	27.6614	1.15456
$575$	4.29854	0.179262
$576$	−91.3413	−3.80589
$577$	−7.26408	−0.302408	−0.151204	−	0.988503i	$-0.548315\pi$
$577$	−7.26408	−0.302408	−0.151204	+	0.988503i	$0.548315\pi$
$578$	−2.32942	−0.0968912
$579$	27.0045	1.12227
$580$	16.2861	0.676245
$581$	5.35247	0.222058
$582$	−4.66752	−0.193475
$583$	−1.76390	−0.0730534
$584$	−20.7819	−0.859960
$585$	−71.6508	−2.96239
$586$	−18.0410	−0.745268
$587$	−16.4734	−0.679930	−0.339965	−	0.940438i	$-0.610415\pi$
$587$	−16.4734	−0.679930	−0.339965	+	0.940438i	$0.610415\pi$
$588$	−11.0185	−0.454395
$589$	0.500046	0.0206040
$590$	52.8469	2.17567
$591$	47.5511	1.95599
$592$	9.43650	0.387838
$593$	23.7078	0.973561	0.486781	−	0.873524i	$-0.338171\pi$
$593$	23.7078	0.973561	0.486781	+	0.873524i	$0.338171\pi$
$594$	13.2139	0.542173
$595$	3.16902	0.129917
$596$	32.7137	1.34000
$597$	−17.5595	−0.718663
$598$	−6.11466	−0.250047
$599$	−39.4069	−1.61012	−0.805061	−	0.593192i	$-0.797867\pi$
$599$	−39.4069	−1.61012	−0.805061	+	0.593192i	$0.797867\pi$
$600$	53.8771	2.19953
$601$	−14.0058	−0.571309	−0.285655	−	0.958333i	$-0.592211\pi$
$601$	−14.0058	−0.571309	−0.285655	+	0.958333i	$0.592211\pi$
$602$	−10.9519	−0.446367
$603$	40.3077	1.64145
$604$	44.4539	1.80880
$605$	34.3363	1.39597
$606$	−122.478	−4.97532
$607$	−30.8936	−1.25393	−0.626966	−	0.779046i	$-0.715704\pi$
$607$	−30.8936	−1.25393	−0.626966	+	0.779046i	$0.715704\pi$
$608$	−7.23299	−0.293337
$609$	−4.82376	−0.195469
$610$	−28.6036	−1.15813
$611$	27.9940	1.13251
$612$	25.1561	1.01688
$613$	−1.71729	−0.0693605	−0.0346802	−	0.999398i	$-0.511041\pi$
$613$	−1.71729	−0.0693605	−0.0346802	+	0.999398i	$0.511041\pi$
$614$	−38.3629	−1.54820
$615$	121.020	4.88001
$616$	1.34956	0.0543754
$617$	−7.40794	−0.298232	−0.149116	−	0.988820i	$-0.547643\pi$
$617$	−7.40794	−0.298232	−0.149116	+	0.988820i	$0.547643\pi$
$618$	−73.4626	−2.95510
$619$	43.3915	1.74405	0.872025	−	0.489461i	$-0.162807\pi$
$619$	43.3915	1.74405	0.872025	+	0.489461i	$0.162807\pi$
$620$	3.43752	0.138054
$621$	−11.9036	−0.477677
$622$	57.1139	2.29006
$623$	−14.1845	−0.568288
$624$	−8.77928	−0.351453
$625$	−24.7846	−0.991385
$626$	75.3577	3.01190
$627$	2.06335	0.0824021
$628$	32.3050	1.28911
$629$	10.6445	0.424424
$630$	−54.2005	−2.15940
$631$	42.5352	1.69330	0.846650	−	0.532151i	$-0.178616\pi$
$631$	42.5352	1.69330	0.846650	+	0.532151i	$0.178616\pi$
$632$	−12.5350	−0.498614
$633$	−45.7163	−1.81706
$634$	60.7109	2.41114
$635$	−2.71469	−0.107729
$636$	47.8450	1.89718
$637$	3.07940	0.122010
$638$	1.41934	0.0561922
$639$	−64.1591	−2.53809
$640$	−62.8110	−2.48282
$641$	23.6927	0.935806	0.467903	−	0.883780i	$-0.345010\pi$
$641$	23.6927	0.935806	0.467903	+	0.883780i	$0.345010\pi$
$642$	84.6766	3.34192
$643$	−33.2424	−1.31095	−0.655476	−	0.755216i	$-0.727532\pi$
$643$	−33.2424	−1.31095	−0.655476	+	0.755216i	$0.727532\pi$
$644$	−2.92060	−0.115088
$645$	−47.9153	−1.88666
$646$	3.67920	0.144756
$647$	3.51380	0.138142	0.0690709	−	0.997612i	$-0.477997\pi$
$647$	3.51380	0.138142	0.0690709	+	0.997612i	$0.477997\pi$
$648$	−76.0195	−2.98633
$649$	2.90808	0.114152
$650$	−36.1725	−1.41880
$651$	−1.01815	−0.0399045
$652$	39.1474	1.53313
$653$	17.8863	0.699945	0.349972	−	0.936760i	$-0.386191\pi$
$653$	17.8863	0.699945	0.349972	+	0.936760i	$0.386191\pi$
$654$	38.8615	1.51960
$655$	−29.5280	−1.15375
$656$	10.5272	0.411016
$657$	45.9283	1.79183
$658$	21.1761	0.825532
$659$	−2.09435	−0.0815841	−0.0407921	−	0.999168i	$-0.512988\pi$
$659$	−2.09435	−0.0815841	−0.0407921	+	0.999168i	$0.512988\pi$
$660$	14.1843	0.552122
$661$	20.6582	0.803510	0.401755	−	0.915747i	$-0.368400\pi$
$661$	20.6582	0.803510	0.401755	+	0.915747i	$0.368400\pi$
$662$	28.3115	1.10036
$663$	−9.90316	−0.384607
$664$	17.7823	0.690087
$665$	−5.00530	−0.194097
$666$	−182.055	−7.05450
$667$	−1.27860	−0.0495077
$668$	56.9404	2.20309
$669$	84.4362	3.26449
$670$	40.5259	1.56565
$671$	−1.57401	−0.0607640
$672$	14.7272	0.568115
$673$	−37.0558	−1.42840	−0.714199	−	0.699943i	$-0.753209\pi$
$673$	−37.0558	−1.42840	−0.714199	+	0.699943i	$0.753209\pi$
$674$	−75.1828	−2.89593
$675$	−70.4184	−2.71041
$676$	−12.0510	−0.463500
$677$	11.7562	0.451826	0.225913	−	0.974147i	$-0.427463\pi$
$677$	11.7562	0.451826	0.225913	+	0.974147i	$0.427463\pi$
$678$	36.2435	1.39192
$679$	0.623061	0.0239109
$680$	10.5283	0.403742
$681$	16.4946	0.632076
$682$	0.299580	0.0114715
$683$	16.5559	0.633494	0.316747	−	0.948510i	$-0.397409\pi$
$683$	16.5559	0.633494	0.316747	+	0.948510i	$0.397409\pi$
$684$	−39.7327	−1.51922
$685$	8.43669	0.322350
$686$	2.32942	0.0889378
$687$	18.1988	0.694327
$688$	−4.16799	−0.158903
$689$	−13.3715	−0.509415
$690$	−20.2367	−0.770397
$691$	−19.6125	−0.746096	−0.373048	−	0.927812i	$-0.621687\pi$
$691$	−19.6125	−0.746096	−0.373048	+	0.927812i	$0.621687\pi$
$692$	−49.3103	−1.87450
$693$	−2.98256	−0.113298
$694$	−38.1624	−1.44862
$695$	−13.1114	−0.497342
$696$	−16.0258	−0.607455
$697$	11.8748	0.449790
$698$	−62.1542	−2.35257
$699$	88.1631	3.33463
$700$	−17.2774	−0.653024
$701$	−18.5688	−0.701333	−0.350667	−	0.936500i	$-0.614045\pi$
$701$	−18.5688	−0.701333	−0.350667	+	0.936500i	$0.614045\pi$
$702$	100.170	3.78067
$703$	−16.8124	−0.634093
$704$	−5.05356	−0.190463
$705$	92.6470	3.48929
$706$	−27.1582	−1.02211
$707$	16.3494	0.614881
$708$	−78.8802	−2.96450
$709$	18.7436	0.703929	0.351964	−	0.936013i	$-0.385514\pi$
$709$	18.7436	0.703929	0.351964	+	0.936013i	$0.385514\pi$
$710$	−64.5064	−2.42088
$711$	27.7025	1.03893
$712$	−47.1244	−1.76606
$713$	−0.269875	−0.0101069
$714$	−7.49128	−0.280354
$715$	−3.96416	−0.148251
$716$	8.06908	0.301556
$717$	59.1939	2.21064
$718$	76.6589	2.86089
$719$	16.7267	0.623802	0.311901	−	0.950115i	$-0.399034\pi$
$719$	16.7267	0.623802	0.311901	+	0.950115i	$0.399034\pi$
$720$	−20.6272	−0.768730
$721$	9.80642	0.365210
$722$	38.4479	1.43088
$723$	22.5245	0.837693
$724$	30.7374	1.14235
$725$	−7.56383	−0.280914
$726$	−81.1679	−3.01242
$727$	−4.78206	−0.177357	−0.0886784	−	0.996060i	$-0.528264\pi$
$727$	−4.78206	−0.177357	−0.0886784	+	0.996060i	$0.528264\pi$
$728$	10.2306	0.379170
$729$	33.2787	1.23254
$730$	46.1770	1.70909
$731$	−4.70156	−0.173893
$732$	42.6943	1.57803
$733$	9.86848	0.364501	0.182250	−	0.983252i	$-0.441662\pi$
$733$	9.86848	0.364501	0.182250	+	0.983252i	$0.441662\pi$
$734$	6.75145	0.249201
$735$	10.1914	0.375915
$736$	3.90365	0.143890
$737$	2.23007	0.0821456
$738$	−203.097	−7.47610
$739$	−0.405842	−0.0149291	−0.00746456	−	0.999972i	$-0.502376\pi$
$739$	−0.405842	−0.0149291	−0.00746456	+	0.999972i	$0.502376\pi$
$740$	−115.575	−4.24864
$741$	15.6415	0.574605
$742$	−10.1149	−0.371331
$743$	19.5639	0.717730	0.358865	−	0.933389i	$-0.383164\pi$
$743$	19.5639	0.717730	0.358865	+	0.933389i	$0.383164\pi$
$744$	−3.38256	−0.124011
$745$	−30.2580	−1.10857
$746$	−23.1803	−0.848690
$747$	−39.2992	−1.43788
$748$	1.39179	0.0508889
$749$	−11.3034	−0.413016
$750$	−1.01392	−0.0370230
$751$	−13.1133	−0.478510	−0.239255	−	0.970957i	$-0.576903\pi$
$751$	−13.1133	−0.478510	−0.239255	+	0.970957i	$0.576903\pi$
$752$	8.05905	0.293883
$753$	−74.7886	−2.72545
$754$	10.7595	0.391838
$755$	−41.1169	−1.49640
$756$	47.8450	1.74011
$757$	32.8555	1.19415	0.597077	−	0.802184i	$-0.296329\pi$
$757$	32.8555	1.19415	0.597077	+	0.802184i	$0.296329\pi$
$758$	−86.6555	−3.14747
$759$	−1.11359	−0.0404207
$760$	−16.6289	−0.603194
$761$	22.1867	0.804267	0.402134	−	0.915581i	$-0.368269\pi$
$761$	22.1867	0.804267	0.402134	+	0.915581i	$0.368269\pi$
$762$	6.41727	0.232473
$763$	−5.18756	−0.187802
$764$	35.2977	1.27703
$765$	−23.2678	−0.841248
$766$	18.0203	0.651100
$767$	22.0451	0.796002
$768$	68.4636	2.47047
$769$	21.8949	0.789551	0.394776	−	0.918778i	$-0.370822\pi$
$769$	21.8949	0.789551	0.394776	+	0.918778i	$0.370822\pi$
$770$	−2.99870	−0.108066
$771$	−55.2183	−1.98864
$772$	−28.7702	−1.03546
$773$	35.2872	1.26919	0.634596	−	0.772844i	$-0.281167\pi$
$773$	35.2872	1.26919	0.634596	+	0.772844i	$0.281167\pi$
$774$	80.4117	2.89034
$775$	−1.59650	−0.0573480
$776$	2.06997	0.0743075
$777$	34.2321	1.22807
$778$	9.09355	0.326020
$779$	−18.7556	−0.671989
$780$	107.526	3.85005
$781$	−3.54968	−0.127017
$782$	−1.98567	−0.0710072
$783$	20.9460	0.748548
$784$	0.886514	0.0316612
$785$	−29.8800	−1.06646
$786$	69.8014	2.48974
$787$	−52.2039	−1.86087	−0.930434	−	0.366459i	$-0.880570\pi$
$787$	−52.2039	−1.86087	−0.930434	+	0.366459i	$0.880570\pi$
$788$	−50.6602	−1.80470
$789$	−58.3976	−2.07901
$790$	27.8525	0.990947
$791$	−4.83809	−0.172023
$792$	−9.90882	−0.352095
$793$	−11.9320	−0.423718
$794$	58.9324	2.09143
$795$	−44.2535	−1.56951
$796$	18.7077	0.663076
$797$	−26.0121	−0.921397	−0.460698	−	0.887557i	$-0.652401\pi$
$797$	−26.0121	−0.921397	−0.460698	+	0.887557i	$0.652401\pi$
$798$	11.8321	0.418851
$799$	9.09072	0.321607
$800$	23.0928	0.816454
$801$	104.146	3.67981
$802$	71.2182	2.51480
$803$	2.54104	0.0896713
$804$	−60.4896	−2.13330
$805$	2.70136	0.0952105
$806$	2.27101	0.0799930
$807$	37.0386	1.30382
$808$	54.3168	1.91086
$809$	8.26515	0.290587	0.145294	−	0.989389i	$-0.453587\pi$
$809$	8.26515	0.290587	0.145294	+	0.989389i	$0.453587\pi$
$810$	168.914	5.93504
$811$	4.12383	0.144807	0.0724036	−	0.997375i	$-0.476933\pi$
$811$	4.12383	0.144807	0.0724036	+	0.997375i	$0.476933\pi$
$812$	5.13916	0.180349
$813$	−51.0529	−1.79050
$814$	−10.0724	−0.353038
$815$	−36.2088	−1.26834
$816$	−2.85097	−0.0998040
$817$	7.42586	0.259798
$818$	−67.5059	−2.36029
$819$	−22.6097	−0.790048
$820$	−128.933	−4.50255
$821$	25.8547	0.902336	0.451168	−	0.892439i	$-0.351008\pi$
$821$	25.8547	0.902336	0.451168	+	0.892439i	$0.351008\pi$
$822$	−19.9436	−0.695612
$823$	15.1792	0.529112	0.264556	−	0.964370i	$-0.414775\pi$
$823$	15.1792	0.529112	0.264556	+	0.964370i	$0.414775\pi$
$824$	32.5794	1.13496
$825$	−6.58766	−0.229353
$826$	16.6761	0.580236
$827$	27.4401	0.954185	0.477093	−	0.878853i	$-0.341691\pi$
$827$	27.4401	0.954185	0.477093	+	0.878853i	$0.341691\pi$
$828$	21.4438	0.745223
$829$	−26.2319	−0.911071	−0.455536	−	0.890218i	$-0.650552\pi$
$829$	−26.2319	−0.911071	−0.455536	+	0.890218i	$0.650552\pi$
$830$	−39.5119	−1.37148
$831$	−87.6595	−3.04087
$832$	−38.3093	−1.32814
$833$	1.00000	0.0346479
$834$	30.9940	1.07324
$835$	−52.6662	−1.82259
$836$	−2.19826	−0.0760284
$837$	4.42107	0.152815
$838$	−1.63935	−0.0566303
$839$	−2.25100	−0.0777132	−0.0388566	−	0.999245i	$-0.512372\pi$
$839$	−2.25100	−0.0777132	−0.0388566	+	0.999245i	$0.512372\pi$
$840$	33.8584	1.16822
$841$	−26.7501	−0.922419
$842$	16.4580	0.567179
$843$	−76.1276	−2.62197
$844$	48.7055	1.67651
$845$	11.1464	0.383447
$846$	−155.481	−5.34553
$847$	10.8350	0.372295
$848$	−3.84946	−0.132191
$849$	−67.4731	−2.31567
$850$	−11.7466	−0.402905
$851$	9.07368	0.311042
$852$	96.2833	3.29861
$853$	8.78493	0.300790	0.150395	−	0.988626i	$-0.451945\pi$
$853$	8.78493	0.300790	0.150395	+	0.988626i	$0.451945\pi$
$854$	−9.02601	−0.308864
$855$	36.7502	1.25683
$856$	−37.5527	−1.28352
$857$	−7.00660	−0.239341	−0.119670	−	0.992814i	$-0.538184\pi$
$857$	−7.00660	−0.239341	−0.119670	+	0.992814i	$0.538184\pi$
$858$	9.37091	0.319918
$859$	12.2783	0.418930	0.209465	−	0.977816i	$-0.432828\pi$
$859$	12.2783	0.418930	0.209465	+	0.977816i	$0.432828\pi$
$860$	51.0483	1.74073
$861$	38.1886	1.30146
$862$	−42.0527	−1.43232
$863$	34.3165	1.16815	0.584074	−	0.811701i	$-0.301458\pi$
$863$	34.3165	1.16815	0.584074	+	0.811701i	$0.301458\pi$
$864$	−63.9493	−2.17560
$865$	45.6088	1.55075
$866$	−31.1146	−1.05732
$867$	−3.21594	−0.109219
$868$	1.08472	0.0368180
$869$	1.53267	0.0519924
$870$	35.6090	1.20726
$871$	16.9054	0.572816
$872$	−17.2344	−0.583631
$873$	−4.57467	−0.154829
$874$	3.13625	0.106085
$875$	0.135346	0.00457554
$876$	−68.9245	−2.32874
$877$	19.9415	0.673377	0.336689	−	0.941616i	$-0.390693\pi$
$877$	19.9415	0.673377	0.336689	+	0.941616i	$0.390693\pi$
$878$	−37.3896	−1.26184
$879$	−24.9069	−0.840090
$880$	−1.14122	−0.0384706
$881$	50.0266	1.68544	0.842719	−	0.538354i	$-0.180954\pi$
$881$	50.0266	1.68544	0.842719	+	0.538354i	$0.180954\pi$
$882$	−17.1032	−0.575895
$883$	−5.26405	−0.177150	−0.0885748	−	0.996070i	$-0.528231\pi$
$883$	−5.26405	−0.177150	−0.0885748	+	0.996070i	$0.528231\pi$
$884$	10.5507	0.354858
$885$	72.9590	2.45249
$886$	−60.2478	−2.02407
$887$	−33.0440	−1.10951	−0.554754	−	0.832014i	$-0.687188\pi$
$887$	−33.0440	−1.10951	−0.554754	+	0.832014i	$0.687188\pi$
$888$	113.728	3.81645
$889$	−0.856632	−0.0287305
$890$	104.710	3.50987
$891$	9.29505	0.311396
$892$	−89.9571	−3.01199
$893$	−14.3583	−0.480482
$894$	71.5272	2.39223
$895$	−7.46337	−0.249473
$896$	−19.8203	−0.662150
$897$	−8.44173	−0.281861
$898$	69.7545	2.32774
$899$	0.474879	0.0158381
$900$	126.855	4.22850
$901$	−4.34225	−0.144661
$902$	−11.2366	−0.374137
$903$	−15.1199	−0.503159
$904$	−16.0734	−0.534593
$905$	−28.4301	−0.945047
$906$	97.1966	3.22914
$907$	16.4750	0.547042	0.273521	−	0.961866i	$-0.411812\pi$
$907$	16.4750	0.547042	0.273521	+	0.961866i	$0.411812\pi$
$908$	−17.5732	−0.583186
$909$	−120.041	−3.98151
$910$	−22.7321	−0.753563
$911$	42.6838	1.41418	0.707088	−	0.707125i	$-0.250008\pi$
$911$	42.6838	1.41418	0.707088	+	0.707125i	$0.250008\pi$
$912$	4.50296	0.149108
$913$	−2.17427	−0.0719580
$914$	−15.3945	−0.509206
$915$	−39.4894	−1.30548
$916$	−19.3887	−0.640622
$917$	−9.31769	−0.307697
$918$	32.5290	1.07362
$919$	1.02519	0.0338178	0.0169089	−	0.999857i	$-0.494617\pi$
$919$	1.02519	0.0338178	0.0169089	+	0.999857i	$0.494617\pi$
$920$	8.97462	0.295884
$921$	−52.9628	−1.74518
$922$	43.4129	1.42973
$923$	−26.9088	−0.885715
$924$	4.47591	0.147247
$925$	53.6772	1.76489
$926$	67.6507	2.22314
$927$	−72.0012	−2.36483
$928$	−6.86896	−0.225485
$929$	23.4712	0.770064	0.385032	−	0.922903i	$-0.374190\pi$
$929$	23.4712	0.770064	0.385032	+	0.922903i	$0.374190\pi$
$930$	7.51599	0.246459
$931$	−1.57945	−0.0517643
$932$	−93.9277	−3.07670
$933$	78.8499	2.58143
$934$	59.0634	1.93261
$935$	−1.28732	−0.0420997
$936$	−75.1153	−2.45522
$937$	38.7136	1.26472	0.632358	−	0.774676i	$-0.282087\pi$
$937$	38.7136	1.26472	0.632358	+	0.774676i	$0.282087\pi$
$938$	12.7881	0.417547
$939$	104.037	3.39511
$940$	−98.7048	−3.21940
$941$	−49.4182	−1.61099	−0.805494	−	0.592603i	$-0.798100\pi$
$941$	−49.4182	−1.61099	−0.805494	+	0.592603i	$0.798100\pi$
$942$	70.6335	2.30136
$943$	10.1224	0.329631
$944$	6.34646	0.206560
$945$	−44.2535	−1.43957
$946$	4.44887	0.144645
$947$	−8.47578	−0.275426	−0.137713	−	0.990472i	$-0.543975\pi$
$947$	−8.47578	−0.275426	−0.137713	+	0.990472i	$0.543975\pi$
$948$	−41.5731	−1.35023
$949$	19.2627	0.625294
$950$	18.5531	0.601943
$951$	83.8158	2.71791
$952$	3.32226	0.107675
$953$	15.9693	0.517297	0.258649	−	0.965971i	$-0.416723\pi$
$953$	15.9693	0.517297	0.258649	+	0.965971i	$0.416723\pi$
$954$	74.2664	2.40447
$955$	−32.6481	−1.05647
$956$	−63.0643	−2.03965
$957$	1.95950	0.0633416
$958$	5.01541	0.162040
$959$	2.66224	0.0859682
$960$	−126.786	−4.09200
$961$	−30.8998	−0.996767
$962$	−76.3555	−2.46180
$963$	82.9921	2.67438
$964$	−23.9972	−0.772899
$965$	26.6106	0.856625
$966$	−6.38577	−0.205459
$967$	−57.1099	−1.83653	−0.918266	−	0.395965i	$-0.870410\pi$
$967$	−57.1099	−1.83653	−0.918266	+	0.395965i	$0.870410\pi$
$968$	35.9966	1.15697
$969$	5.07940	0.163174
$970$	−4.59943	−0.147679
$971$	−11.9809	−0.384487	−0.192243	−	0.981347i	$-0.561576\pi$
$971$	−11.9809	−0.384487	−0.192243	+	0.981347i	$0.561576\pi$
$972$	−108.589	−3.48299
$973$	−4.13735	−0.132637
$974$	46.6592	1.49506
$975$	−49.9387	−1.59932
$976$	−3.43505	−0.109953
$977$	41.2060	1.31830	0.659148	−	0.752013i	$-0.270917\pi$
$977$	41.2060	1.31830	0.659148	+	0.752013i	$0.270917\pi$
$978$	85.5943	2.73700
$979$	5.76199	0.184154
$980$	−10.8578	−0.346838
$981$	38.0884	1.21607
$982$	4.82588	0.154000
$983$	45.1946	1.44148	0.720742	−	0.693204i	$-0.243801\pi$
$983$	45.1946	1.44148	0.720742	+	0.693204i	$0.243801\pi$
$984$	126.872	4.04454
$985$	46.8574	1.49300
$986$	3.49403	0.111273
$987$	29.2352	0.930566
$988$	−16.6642	−0.530160
$989$	−4.00774	−0.127439
$990$	22.0172	0.699754
$991$	−6.05455	−0.192329	−0.0961646	−	0.995365i	$-0.530658\pi$
$991$	−6.05455	−0.192329	−0.0961646	+	0.995365i	$0.530658\pi$
$992$	−1.44983	−0.0460322
$993$	39.0861	1.24036
$994$	−20.3553	−0.645631
$995$	−17.3034	−0.548553
$996$	58.9762	1.86873
$997$	−1.70376	−0.0539587	−0.0269794	−	0.999636i	$-0.508589\pi$
$997$	−1.70376	−0.0539587	−0.0269794	+	0.999636i	$0.508589\pi$
$998$	41.8971	1.32623
$999$	−148.644	−4.70290

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	119.2.a.b.1.1	✓	5
3.2	odd	2		1071.2.a.m.1.5		5
4.3	odd	2		1904.2.a.t.1.5		5
5.4	even	2		2975.2.a.m.1.5		5
7.2	even	3		833.2.e.i.18.5		10
7.3	odd	6		833.2.e.h.324.5		10
7.4	even	3		833.2.e.i.324.5		10
7.5	odd	6		833.2.e.h.18.5		10
7.6	odd	2		833.2.a.g.1.1		5
8.3	odd	2		7616.2.a.bq.1.1		5
8.5	even	2		7616.2.a.bt.1.5		5
17.16	even	2		2023.2.a.j.1.1		5
21.20	even	2		7497.2.a.br.1.5		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
119.2.a.b.1.1	✓	5	1.1	even	1	trivial
833.2.a.g.1.1		5	7.6	odd	2
833.2.e.h.18.5		10	7.5	odd	6
833.2.e.h.324.5		10	7.3	odd	6
833.2.e.i.18.5		10	7.2	even	3
833.2.e.i.324.5		10	7.4	even	3
1071.2.a.m.1.5		5	3.2	odd	2
1904.2.a.t.1.5		5	4.3	odd	2
2023.2.a.j.1.1		5	17.16	even	2
2975.2.a.m.1.5		5	5.4	even	2
7497.2.a.br.1.5		5	21.20	even	2
7616.2.a.bq.1.1		5	8.3	odd	2
7616.2.a.bt.1.5		5	8.5	even	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 119 = 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	119.a (trivial)

\(f(q)\)	\(=\)	\(q-2.32942 q^{2} -3.21594 q^{3} +3.42621 q^{4} -3.16902 q^{5} +7.49128 q^{6} -1.00000 q^{7} -3.32226 q^{8} +7.34225 q^{9} +7.38200 q^{10} +0.406219 q^{11} -11.0185 q^{12} +3.07940 q^{13} +2.32942 q^{14} +10.1914 q^{15} +0.886514 q^{16} +1.00000 q^{17} -17.1032 q^{18} -1.57945 q^{19} -10.8578 q^{20} +3.21594 q^{21} -0.946255 q^{22} +0.852428 q^{23} +10.6842 q^{24} +5.04271 q^{25} -7.17323 q^{26} -13.9644 q^{27} -3.42621 q^{28} -1.49995 q^{29} -23.7400 q^{30} -0.316596 q^{31} +4.57945 q^{32} -1.30637 q^{33} -2.32942 q^{34} +3.16902 q^{35} +25.1561 q^{36} +10.6445 q^{37} +3.67920 q^{38} -9.90316 q^{39} +10.5283 q^{40} +11.8748 q^{41} -7.49128 q^{42} -4.70156 q^{43} +1.39179 q^{44} -23.2678 q^{45} -1.98567 q^{46} +9.09072 q^{47} -2.85097 q^{48} +1.00000 q^{49} -11.7466 q^{50} -3.21594 q^{51} +10.5507 q^{52} -4.34225 q^{53} +32.5290 q^{54} -1.28732 q^{55} +3.32226 q^{56} +5.07940 q^{57} +3.49403 q^{58} +7.15889 q^{59} +34.9178 q^{60} -3.87478 q^{61} +0.737485 q^{62} -7.34225 q^{63} -12.4405 q^{64} -9.75869 q^{65} +3.04310 q^{66} +5.48982 q^{67} +3.42621 q^{68} -2.74135 q^{69} -7.38200 q^{70} -8.73834 q^{71} -24.3928 q^{72} +6.25535 q^{73} -24.7956 q^{74} -16.2170 q^{75} -5.41152 q^{76} -0.406219 q^{77} +23.0686 q^{78} +3.77303 q^{79} -2.80938 q^{80} +22.8819 q^{81} -27.6614 q^{82} -5.35247 q^{83} +11.0185 q^{84} -3.16902 q^{85} +10.9519 q^{86} +4.82376 q^{87} -1.34956 q^{88} +14.1845 q^{89} +54.2005 q^{90} -3.07940 q^{91} +2.92060 q^{92} +1.01815 q^{93} -21.1761 q^{94} +5.00530 q^{95} -14.7272 q^{96} -0.623061 q^{97} -2.32942 q^{98} +2.98256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 2 q^{2} - 2 q^{3} + 10 q^{4} - q^{6} - 5 q^{7} + 6 q^{8} + 11 q^{9} + 4 q^{10} - 2 q^{11} - 22 q^{12} + 2 q^{13} - 2 q^{14} + 8 q^{15} + 4 q^{16} + 5 q^{17} - 18 q^{18} + 6 q^{19} - 19 q^{20} + 2 q^{21}+ \cdots - 62 q^{99}+O(q^{100}) \) 5 * q + 2 * q^2 - 2 * q^3 + 10 * q^4 - q^6 - 5 * q^7 + 6 * q^8 + 11 * q^9 + 4 * q^10 - 2 * q^11 - 22 * q^12 + 2 * q^13 - 2 * q^14 + 8 * q^15 + 4 * q^16 + 5 * q^17 - 18 * q^18 + 6 * q^19 - 19 * q^20 + 2 * q^21 + 6 * q^22 - 10 * q^23 + 2 * q^24 + 21 * q^25 - 26 * q^26 - 26 * q^27 - 10 * q^28 - 8 * q^29 - 51 * q^30 + 9 * q^32 + 6 * q^33 + 2 * q^34 + 39 * q^36 + 8 * q^37 + 14 * q^38 + 14 * q^39 + 5 * q^40 + 18 * q^41 + q^42 + 8 * q^43 - 14 * q^44 + 8 * q^46 - 10 * q^47 - 27 * q^48 + 5 * q^49 + 27 * q^50 - 2 * q^51 + 4 * q^52 + 4 * q^53 + 5 * q^54 - 24 * q^55 - 6 * q^56 + 12 * q^57 + 12 * q^58 + 8 * q^59 - 7 * q^60 + 22 * q^61 + 16 * q^62 - 11 * q^63 - 16 * q^64 - 30 * q^65 + 68 * q^66 + 16 * q^67 + 10 * q^68 - 32 * q^69 - 4 * q^70 - 2 * q^71 + 9 * q^72 + 10 * q^73 - 40 * q^74 - 14 * q^75 + 24 * q^76 + 2 * q^77 + 30 * q^78 + 18 * q^79 - 4 * q^80 + 25 * q^81 - 31 * q^82 - 12 * q^83 + 22 * q^84 + 23 * q^86 - 26 * q^87 - 46 * q^88 + 20 * q^89 + 97 * q^90 - 2 * q^91 + 28 * q^92 - 28 * q^93 - 42 * q^94 - 22 * q^95 - 18 * q^96 + 12 * q^97 + 2 * q^98 - 62 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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