LMFDB - Embedded newform 4235.2.a.bl.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4235,2,Mod(1,4235)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, 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("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4235 = 5 \cdot 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4235.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:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 14x^{8} + 26x^{7} + 63x^{6} - 106x^{5} - 96x^{4} + 140x^{3} + 38x^{2} - 38x - 11 $ x^10 - 2x^9 - 14x^8 + 26x^7 + 63x^6 - 106x^5 - 96x^4 + 140x^3 + 38x^2 - 38*x - 11
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.40864$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.40864 q^{2} +2.97205 q^{3} -0.0157228 q^{4} -1.00000 q^{5} -4.18655 q^{6} +1.00000 q^{7} +2.83944 q^{8} +5.83306 q^{9} +O(q^{10})$	\(q-1.40864 q^{2} +2.97205 q^{3} -0.0157228 q^{4} -1.00000 q^{5} -4.18655 q^{6} +1.00000 q^{7} +2.83944 q^{8} +5.83306 q^{9} +1.40864 q^{10} -0.0467290 q^{12} +6.87188 q^{13} -1.40864 q^{14} -2.97205 q^{15} -3.96831 q^{16} +7.90613 q^{17} -8.21670 q^{18} -3.35365 q^{19} +0.0157228 q^{20} +2.97205 q^{21} +2.29809 q^{23} +8.43893 q^{24} +1.00000 q^{25} -9.68002 q^{26} +8.41997 q^{27} -0.0157228 q^{28} +4.72831 q^{29} +4.18655 q^{30} +0.522381 q^{31} -0.0889397 q^{32} -11.1369 q^{34} -1.00000 q^{35} -0.0917122 q^{36} -6.97730 q^{37} +4.72410 q^{38} +20.4235 q^{39} -2.83944 q^{40} +3.27449 q^{41} -4.18655 q^{42} -7.28742 q^{43} -5.83306 q^{45} -3.23719 q^{46} +3.87392 q^{47} -11.7940 q^{48} +1.00000 q^{49} -1.40864 q^{50} +23.4974 q^{51} -0.108045 q^{52} -7.36031 q^{53} -11.8607 q^{54} +2.83944 q^{56} -9.96720 q^{57} -6.66051 q^{58} +4.29439 q^{59} +0.0467290 q^{60} +6.79532 q^{61} -0.735849 q^{62} +5.83306 q^{63} +8.06190 q^{64} -6.87188 q^{65} -0.907079 q^{67} -0.124307 q^{68} +6.83004 q^{69} +1.40864 q^{70} -10.9701 q^{71} +16.5626 q^{72} -2.36420 q^{73} +9.82853 q^{74} +2.97205 q^{75} +0.0527289 q^{76} -28.7695 q^{78} +14.8341 q^{79} +3.96831 q^{80} +7.52538 q^{81} -4.61259 q^{82} -9.12029 q^{83} -0.0467290 q^{84} -7.90613 q^{85} +10.2654 q^{86} +14.0528 q^{87} -5.32583 q^{89} +8.21670 q^{90} +6.87188 q^{91} -0.0361326 q^{92} +1.55254 q^{93} -5.45698 q^{94} +3.35365 q^{95} -0.264333 q^{96} -4.21302 q^{97} -1.40864 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) $ 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9	$ 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 16 q^{12} + 26 q^{13} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 4 q^{17} + 8 q^{18} + 6 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{23} + 22 q^{24} + 10 q^{25} - 6 q^{26} + 10 q^{27} + 12 q^{28} - 4 q^{29} + 18 q^{31} + 24 q^{32} + 8 q^{34} - 10 q^{35} - 10 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 6 q^{40} - 30 q^{41} + 22 q^{43} - 6 q^{45} + 28 q^{46} + 14 q^{47} - 4 q^{48} + 10 q^{49} + 2 q^{50} + 36 q^{51} + 34 q^{52} - 10 q^{53} + 6 q^{54} + 6 q^{56} - 2 q^{57} - 38 q^{58} + 22 q^{59} - 16 q^{60} + 12 q^{61} - 6 q^{62} + 6 q^{63} + 8 q^{64} - 26 q^{65} - 14 q^{67} + 70 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} + 26 q^{72} + 30 q^{73} - 20 q^{74} + 4 q^{75} + 18 q^{76} - 32 q^{78} + 8 q^{79} - 20 q^{80} + 10 q^{81} - 28 q^{82} - 14 q^{83} + 16 q^{84} - 4 q^{85} - 14 q^{86} - 24 q^{87} - 6 q^{89} - 8 q^{90} + 26 q^{91} - 20 q^{92} + 14 q^{93} + 16 q^{94} - 6 q^{95} + 24 q^{96} + 20 q^{97} + 2 q^{98}+O(q^{100}) $ 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 16 * q^12 + 26 * q^13 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 4 * q^17 + 8 * q^18 + 6 * q^19 - 12 * q^20 + 4 * q^21 - 8 * q^23 + 22 * q^24 + 10 * q^25 - 6 * q^26 + 10 * q^27 + 12 * q^28 - 4 * q^29 + 18 * q^31 + 24 * q^32 + 8 * q^34 - 10 * q^35 - 10 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 6 * q^40 - 30 * q^41 + 22 * q^43 - 6 * q^45 + 28 * q^46 + 14 * q^47 - 4 * q^48 + 10 * q^49 + 2 * q^50 + 36 * q^51 + 34 * q^52 - 10 * q^53 + 6 * q^54 + 6 * q^56 - 2 * q^57 - 38 * q^58 + 22 * q^59 - 16 * q^60 + 12 * q^61 - 6 * q^62 + 6 * q^63 + 8 * q^64 - 26 * q^65 - 14 * q^67 + 70 * q^68 + 8 * q^69 - 2 * q^70 - 8 * q^71 + 26 * q^72 + 30 * q^73 - 20 * q^74 + 4 * q^75 + 18 * q^76 - 32 * q^78 + 8 * q^79 - 20 * q^80 + 10 * q^81 - 28 * q^82 - 14 * q^83 + 16 * q^84 - 4 * q^85 - 14 * q^86 - 24 * q^87 - 6 * q^89 - 8 * q^90 + 26 * q^91 - 20 * q^92 + 14 * q^93 + 16 * q^94 - 6 * q^95 + 24 * q^96 + 20 * q^97 + 2 * q^98

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 $

$2$	−1.40864	−0.996062	−0.498031	−	0.867159i	$-0.665943\pi$
$2$	−1.40864	−0.996062	−0.498031	+	0.867159i	$0.665943\pi$
$3$	2.97205	1.71591	0.857956	−	0.513724i	$-0.171734\pi$
$3$	2.97205	1.71591	0.857956	+	0.513724i	$0.171734\pi$
$4$	−0.0157228	−0.00786142
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−4.18655	−1.70915
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	2.83944	1.00389
$9$	5.83306	1.94435
$10$	1.40864	0.445452
$11$	0	0
$11$	0	0
$12$	−0.0467290	−0.0134895
$13$	6.87188	1.90592	0.952958	−	0.303103i	$-0.0980228\pi$
$13$	6.87188	1.90592	0.952958	+	0.303103i	$0.0980228\pi$
$14$	−1.40864	−0.376476
$15$	−2.97205	−0.767379
$16$	−3.96831	−0.992077
$17$	7.90613	1.91752	0.958759	−	0.284222i	$-0.0917351\pi$
$17$	7.90613	1.91752	0.958759	+	0.284222i	$0.0917351\pi$
$18$	−8.21670	−1.93669
$19$	−3.35365	−0.769380	−0.384690	−	0.923046i	$-0.625692\pi$
$19$	−3.35365	−0.769380	−0.384690	+	0.923046i	$0.625692\pi$
$20$	0.0157228	0.00351573
$21$	2.97205	0.648554
$22$	0	0
$23$	2.29809	0.479186	0.239593	−	0.970873i	$-0.422986\pi$
$23$	2.29809	0.479186	0.239593	+	0.970873i	$0.422986\pi$
$24$	8.43893	1.72259
$25$	1.00000	0.200000
$26$	−9.68002	−1.89841
$27$	8.41997	1.62042
$28$	−0.0157228	−0.00297134
$29$	4.72831	0.878026	0.439013	−	0.898481i	$-0.355328\pi$
$29$	4.72831	0.878026	0.439013	+	0.898481i	$0.355328\pi$
$30$	4.18655	0.764357
$31$	0.522381	0.0938225	0.0469112	−	0.998899i	$-0.485062\pi$
$31$	0.522381	0.0938225	0.0469112	+	0.998899i	$0.485062\pi$
$32$	−0.0889397	−0.0157225
$33$	0	0
$34$	−11.1369	−1.90997
$35$	−1.00000	−0.169031
$36$	−0.0917122	−0.0152854
$37$	−6.97730	−1.14706	−0.573530	−	0.819184i	$-0.694427\pi$
$37$	−6.97730	−1.14706	−0.573530	+	0.819184i	$0.694427\pi$
$38$	4.72410	0.766350
$39$	20.4235	3.27038
$40$	−2.83944	−0.448954
$41$	3.27449	0.511390	0.255695	−	0.966758i	$-0.417696\pi$
$41$	3.27449	0.511390	0.255695	+	0.966758i	$0.417696\pi$
$42$	−4.18655	−0.645999
$43$	−7.28742	−1.11132	−0.555660	−	0.831409i	$-0.687535\pi$
$43$	−7.28742	−1.11132	−0.555660	+	0.831409i	$0.687535\pi$
$44$	0	0
$45$	−5.83306	−0.869541
$46$	−3.23719	−0.477298
$47$	3.87392	0.565070	0.282535	−	0.959257i	$-0.408825\pi$
$47$	3.87392	0.565070	0.282535	+	0.959257i	$0.408825\pi$
$48$	−11.7940	−1.70232
$49$	1.00000	0.142857
$50$	−1.40864	−0.199212
$51$	23.4974	3.29029
$52$	−0.108045	−0.0149832
$53$	−7.36031	−1.01102	−0.505508	−	0.862822i	$-0.668695\pi$
$53$	−7.36031	−1.01102	−0.505508	+	0.862822i	$0.668695\pi$
$54$	−11.8607	−1.61404
$55$	0	0
$56$	2.83944	0.379436
$57$	−9.96720	−1.32019
$58$	−6.66051	−0.874567
$59$	4.29439	0.559082	0.279541	−	0.960134i	$-0.409818\pi$
$59$	4.29439	0.559082	0.279541	+	0.960134i	$0.409818\pi$
$60$	0.0467290	0.00603269
$61$	6.79532	0.870052	0.435026	−	0.900418i	$-0.356739\pi$
$61$	6.79532	0.870052	0.435026	+	0.900418i	$0.356739\pi$
$62$	−0.735849	−0.0934529
$63$	5.83306	0.734896
$64$	8.06190	1.00774
$65$	−6.87188	−0.852351
$66$	0	0
$67$	−0.907079	−0.110817	−0.0554087	−	0.998464i	$-0.517646\pi$
$67$	−0.907079	−0.110817	−0.0554087	+	0.998464i	$0.517646\pi$
$68$	−0.124307	−0.0150744
$69$	6.83004	0.822240
$70$	1.40864	0.168365
$71$	−10.9701	−1.30191	−0.650953	−	0.759118i	$-0.725630\pi$
$71$	−10.9701	−1.30191	−0.650953	+	0.759118i	$0.725630\pi$
$72$	16.5626	1.95192
$73$	−2.36420	−0.276708	−0.138354	−	0.990383i	$-0.544181\pi$
$73$	−2.36420	−0.276708	−0.138354	+	0.990383i	$0.544181\pi$
$74$	9.82853	1.14254
$75$	2.97205	0.343182
$76$	0.0527289	0.00604842
$77$	0	0
$78$	−28.7695	−3.25750
$79$	14.8341	1.66897	0.834483	−	0.551034i	$-0.185767\pi$
$79$	14.8341	1.66897	0.834483	+	0.551034i	$0.185767\pi$
$80$	3.96831	0.443670
$81$	7.52538	0.836153
$82$	−4.61259	−0.509376
$83$	−9.12029	−1.00108	−0.500541	−	0.865713i	$-0.666865\pi$
$83$	−9.12029	−1.00108	−0.500541	+	0.865713i	$0.666865\pi$
$84$	−0.0467290	−0.00509855
$85$	−7.90613	−0.857540
$86$	10.2654	1.10694
$87$	14.0528	1.50661
$88$	0	0
$89$	−5.32583	−0.564537	−0.282269	−	0.959335i	$-0.591087\pi$
$89$	−5.32583	−0.564537	−0.282269	+	0.959335i	$0.591087\pi$
$90$	8.21670	0.866116
$91$	6.87188	0.720368
$92$	−0.0361326	−0.00376708
$93$	1.55254	0.160991
$94$	−5.45698	−0.562845
$95$	3.35365	0.344077
$96$	−0.264333	−0.0269784
$97$	−4.21302	−0.427768	−0.213884	−	0.976859i	$-0.568611\pi$
$97$	−4.21302	−0.427768	−0.213884	+	0.976859i	$0.568611\pi$
$98$	−1.40864	−0.142295
$99$	0	0
$100$	−0.0157228	−0.00157228
$101$	−17.1009	−1.70161	−0.850804	−	0.525483i	$-0.823884\pi$
$101$	−17.1009	−1.70161	−0.850804	+	0.525483i	$0.823884\pi$
$102$	−33.0994	−3.27733
$103$	−14.0643	−1.38580	−0.692898	−	0.721036i	$-0.743666\pi$
$103$	−14.0643	−1.38580	−0.692898	+	0.721036i	$0.743666\pi$
$104$	19.5122	1.91333
$105$	−2.97205	−0.290042
$106$	10.3681	1.00703
$107$	17.2424	1.66688	0.833441	−	0.552608i	$-0.186367\pi$
$107$	17.2424	1.66688	0.833441	+	0.552608i	$0.186367\pi$
$108$	−0.132386	−0.0127388
$109$	6.79417	0.650763	0.325382	−	0.945583i	$-0.394507\pi$
$109$	6.79417	0.650763	0.325382	+	0.945583i	$0.394507\pi$
$110$	0	0
$111$	−20.7369	−1.96825
$112$	−3.96831	−0.374970
$113$	−0.671872	−0.0632044	−0.0316022	−	0.999501i	$-0.510061\pi$
$113$	−0.671872	−0.0632044	−0.0316022	+	0.999501i	$0.510061\pi$
$114$	14.0402	1.31499
$115$	−2.29809	−0.214298
$116$	−0.0743425	−0.00690253
$117$	40.0840	3.70577
$118$	−6.04927	−0.556880
$119$	7.90613	0.724753
$120$	−8.43893	−0.770366
$121$	0	0
$122$	−9.57219	−0.866625
$123$	9.73194	0.877500
$124$	−0.00821332	−0.000737578 0
$125$	−1.00000	−0.0894427
$126$	−8.21670	−0.732002
$127$	−16.4516	−1.45984	−0.729921	−	0.683531i	$-0.760443\pi$
$127$	−16.4516	−1.45984	−0.729921	+	0.683531i	$0.760443\pi$
$128$	−11.1785	−0.988046
$129$	−21.6585	−1.90693
$130$	9.68002	0.848994
$131$	−22.4338	−1.96005	−0.980026	−	0.198867i	$-0.936274\pi$
$131$	−22.4338	−1.96005	−0.980026	+	0.198867i	$0.936274\pi$
$132$	0	0
$133$	−3.35365	−0.290798
$134$	1.27775	0.110381
$135$	−8.41997	−0.724676
$136$	22.4489	1.92498
$137$	14.0013	1.19621	0.598105	−	0.801418i	$-0.295920\pi$
$137$	14.0013	1.19621	0.598105	+	0.801418i	$0.295920\pi$
$138$	−9.62109	−0.819002
$139$	−2.12518	−0.180255	−0.0901276	−	0.995930i	$-0.528727\pi$
$139$	−2.12518	−0.180255	−0.0901276	+	0.995930i	$0.528727\pi$
$140$	0.0157228	0.00132882
$141$	11.5135	0.969610
$142$	15.4529	1.29678
$143$	0	0
$144$	−23.1474	−1.92895
$145$	−4.72831	−0.392665
$146$	3.33031	0.275619
$147$	2.97205	0.245130
$148$	0.109703	0.00901753
$149$	−14.7341	−1.20706	−0.603531	−	0.797340i	$-0.706240\pi$
$149$	−14.7341	−1.20706	−0.603531	+	0.797340i	$0.706240\pi$
$150$	−4.18655	−0.341831
$151$	13.5781	1.10497	0.552487	−	0.833522i	$-0.313679\pi$
$151$	13.5781	1.10497	0.552487	+	0.833522i	$0.313679\pi$
$152$	−9.52247	−0.772374
$153$	46.1169	3.72833
$154$	0	0
$155$	−0.522381	−0.0419587
$156$	−0.321116	−0.0257098
$157$	22.0767	1.76191	0.880956	−	0.473198i	$-0.156900\pi$
$157$	22.0767	1.76191	0.880956	+	0.473198i	$0.156900\pi$
$158$	−20.8960	−1.66239
$159$	−21.8752	−1.73482
$160$	0.0889397	0.00703130
$161$	2.29809	0.181115
$162$	−10.6006	−0.832860
$163$	−2.48408	−0.194568	−0.0972841	−	0.995257i	$-0.531016\pi$
$163$	−2.48408	−0.194568	−0.0972841	+	0.995257i	$0.531016\pi$
$164$	−0.0514843	−0.00402025
$165$	0	0
$166$	12.8472	0.997139
$167$	0.126778	0.00981036	0.00490518	−	0.999988i	$-0.498439\pi$
$167$	0.126778	0.00981036	0.00490518	+	0.999988i	$0.498439\pi$
$168$	8.43893	0.651078
$169$	34.2227	2.63251
$170$	11.1369	0.854162
$171$	−19.5620	−1.49595
$172$	0.114579	0.00873656
$173$	1.63959	0.124656	0.0623280	−	0.998056i	$-0.480148\pi$
$173$	1.63959	0.124656	0.0623280	+	0.998056i	$0.480148\pi$
$174$	−19.7953	−1.50068
$175$	1.00000	0.0755929
$176$	0	0
$177$	12.7631	0.959335
$178$	7.50220	0.562314
$179$	2.21977	0.165914	0.0829568	−	0.996553i	$-0.473564\pi$
$179$	2.21977	0.165914	0.0829568	+	0.996553i	$0.473564\pi$
$180$	0.0917122	0.00683582
$181$	15.4039	1.14496	0.572481	−	0.819918i	$-0.305981\pi$
$181$	15.4039	1.14496	0.572481	+	0.819918i	$0.305981\pi$
$182$	−9.68002	−0.717531
$183$	20.1960	1.49293
$184$	6.52529	0.481051
$185$	6.97730	0.512981
$186$	−2.18698	−0.160357
$187$	0	0
$188$	−0.0609091	−0.00444225
$189$	8.41997	0.612463
$190$	−4.72410	−0.342722
$191$	−14.5232	−1.05086	−0.525430	−	0.850837i	$-0.676095\pi$
$191$	−14.5232	−1.05086	−0.525430	+	0.850837i	$0.676095\pi$
$192$	23.9603	1.72919
$193$	7.02930	0.505980	0.252990	−	0.967469i	$-0.418586\pi$
$193$	7.02930	0.505980	0.252990	+	0.967469i	$0.418586\pi$
$194$	5.93465	0.426083
$195$	−20.4235	−1.46256
$196$	−0.0157228	−0.00112306
$197$	−14.8872	−1.06067	−0.530336	−	0.847788i	$-0.677934\pi$
$197$	−14.8872	−1.06067	−0.530336	+	0.847788i	$0.677934\pi$
$198$	0	0
$199$	15.8909	1.12648	0.563239	−	0.826294i	$-0.309555\pi$
$199$	15.8909	1.12648	0.563239	+	0.826294i	$0.309555\pi$
$200$	2.83944	0.200778
$201$	−2.69588	−0.190153
$202$	24.0891	1.69491
$203$	4.72831	0.331862
$204$	−0.369445	−0.0258664
$205$	−3.27449	−0.228700
$206$	19.8116	1.38034
$207$	13.4049	0.931706
$208$	−27.2697	−1.89081
$209$	0	0
$210$	4.18655	0.288900
$211$	16.4990	1.13584	0.567919	−	0.823084i	$-0.307749\pi$
$211$	16.4990	1.13584	0.567919	+	0.823084i	$0.307749\pi$
$212$	0.115725	0.00794803
$213$	−32.6035	−2.23395
$214$	−24.2883	−1.66032
$215$	7.28742	0.496998
$216$	23.9080	1.62673
$217$	0.522381	0.0354616
$218$	−9.57056	−0.648200
$219$	−7.02650	−0.474807
$220$	0	0
$221$	54.3299	3.65463
$222$	29.2108	1.96050
$223$	−13.7866	−0.923221	−0.461611	−	0.887083i	$-0.652728\pi$
$223$	−13.7866	−0.923221	−0.461611	+	0.887083i	$0.652728\pi$
$224$	−0.0889397	−0.00594254
$225$	5.83306	0.388870
$226$	0.946428	0.0629554
$227$	22.2174	1.47462	0.737309	−	0.675556i	$-0.236096\pi$
$227$	22.2174	1.47462	0.737309	+	0.675556i	$0.236096\pi$
$228$	0.156713	0.0103786
$229$	−0.473196	−0.0312697	−0.0156348	−	0.999878i	$-0.504977\pi$
$229$	−0.473196	−0.0312697	−0.0156348	+	0.999878i	$0.504977\pi$
$230$	3.23719	0.213454
$231$	0	0
$232$	13.4257	0.881443
$233$	−3.55771	−0.233073	−0.116537	−	0.993186i	$-0.537179\pi$
$233$	−3.55771	−0.233073	−0.116537	+	0.993186i	$0.537179\pi$
$234$	−56.4641	−3.69118
$235$	−3.87392	−0.252707
$236$	−0.0675200	−0.00439518
$237$	44.0876	2.86380
$238$	−11.1369	−0.721899
$239$	1.97466	0.127730	0.0638649	−	0.997959i	$-0.479657\pi$
$239$	1.97466	0.127730	0.0638649	+	0.997959i	$0.479657\pi$
$240$	11.7940	0.761299
$241$	−0.753977	−0.0485680	−0.0242840	−	0.999705i	$-0.507731\pi$
$241$	−0.753977	−0.0485680	−0.0242840	+	0.999705i	$0.507731\pi$
$242$	0	0
$243$	−2.89416	−0.185660
$244$	−0.106842	−0.00683984
$245$	−1.00000	−0.0638877
$246$	−13.7088	−0.874044
$247$	−23.0459	−1.46637
$248$	1.48327	0.0941876
$249$	−27.1059	−1.71777
$250$	1.40864	0.0890905
$251$	−10.8191	−0.682898	−0.341449	−	0.939900i	$-0.610918\pi$
$251$	−10.8191	−0.682898	−0.341449	+	0.939900i	$0.610918\pi$
$252$	−0.0917122	−0.00577733
$253$	0	0
$254$	23.1744	1.45409
$255$	−23.4974	−1.47146
$256$	−0.377325	−0.0235828
$257$	−17.2040	−1.07316	−0.536578	−	0.843851i	$-0.680283\pi$
$257$	−17.2040	−1.07316	−0.536578	+	0.843851i	$0.680283\pi$
$258$	30.5092	1.89942
$259$	−6.97730	−0.433548
$260$	0.108045	0.00670069
$261$	27.5805	1.70719
$262$	31.6013	1.95233
$263$	17.0208	1.04955	0.524774	−	0.851242i	$-0.324150\pi$
$263$	17.0208	1.04955	0.524774	+	0.851242i	$0.324150\pi$
$264$	0	0
$265$	7.36031	0.452140
$266$	4.72410	0.289653
$267$	−15.8286	−0.968696
$268$	0.0142619	0.000871181 0
$269$	20.8058	1.26855	0.634277	−	0.773106i	$-0.281298\pi$
$269$	20.8058	1.26855	0.634277	+	0.773106i	$0.281298\pi$
$270$	11.8607	0.721822
$271$	20.4669	1.24327	0.621637	−	0.783305i	$-0.286468\pi$
$271$	20.4669	1.24327	0.621637	+	0.783305i	$0.286468\pi$
$272$	−31.3739	−1.90232
$273$	20.4235	1.23609
$274$	−19.7228	−1.19150
$275$	0	0
$276$	−0.107388	−0.00646397
$277$	30.7603	1.84821	0.924104	−	0.382142i	$-0.124813\pi$
$277$	30.7603	1.84821	0.924104	+	0.382142i	$0.124813\pi$
$278$	2.99362	0.179545
$279$	3.04708	0.182424
$280$	−2.83944	−0.169689
$281$	−3.58750	−0.214012	−0.107006	−	0.994258i	$-0.534126\pi$
$281$	−3.58750	−0.214012	−0.107006	+	0.994258i	$0.534126\pi$
$282$	−16.2184	−0.965791
$283$	6.49908	0.386330	0.193165	−	0.981166i	$-0.438125\pi$
$283$	6.49908	0.386330	0.193165	+	0.981166i	$0.438125\pi$
$284$	0.172480	0.0102348
$285$	9.96720	0.590406
$286$	0	0
$287$	3.27449	0.193287
$288$	−0.518791	−0.0305700
$289$	45.5068	2.67687
$290$	6.66051	0.391118
$291$	−12.5213	−0.734011
$292$	0.0371719	0.00217532
$293$	−0.729456	−0.0426153	−0.0213076	−	0.999773i	$-0.506783\pi$
$293$	−0.729456	−0.0426153	−0.0213076	+	0.999773i	$0.506783\pi$
$294$	−4.18655	−0.244165
$295$	−4.29439	−0.250029
$296$	−19.8116	−1.15153
$297$	0	0
$298$	20.7550	1.20231
$299$	15.7922	0.913287
$300$	−0.0467290	−0.00269790
$301$	−7.28742	−0.420040
$302$	−19.1268	−1.10062
$303$	−50.8248	−2.91981
$304$	13.3083	0.763284
$305$	−6.79532	−0.389099
$306$	−64.9623	−3.71364
$307$	−31.1821	−1.77966	−0.889829	−	0.456294i	$-0.849177\pi$
$307$	−31.1821	−1.77966	−0.889829	+	0.456294i	$0.849177\pi$
$308$	0	0
$309$	−41.7997	−2.37790
$310$	0.735849	0.0417934
$311$	−24.9460	−1.41456	−0.707278	−	0.706935i	$-0.750077\pi$
$311$	−24.9460	−1.41456	−0.707278	+	0.706935i	$0.750077\pi$
$312$	57.9913	3.28311
$313$	17.4097	0.984052	0.492026	−	0.870580i	$-0.336256\pi$
$313$	17.4097	0.984052	0.492026	+	0.870580i	$0.336256\pi$
$314$	−31.0982	−1.75497
$315$	−5.83306	−0.328655
$316$	−0.233234	−0.0131204
$317$	−1.97054	−0.110676	−0.0553382	−	0.998468i	$-0.517624\pi$
$317$	−1.97054	−0.110676	−0.0553382	+	0.998468i	$0.517624\pi$
$318$	30.8143	1.72798
$319$	0	0
$320$	−8.06190	−0.450674
$321$	51.2451	2.86022
$322$	−3.23719	−0.180402
$323$	−26.5144	−1.47530
$324$	−0.118320	−0.00657335
$325$	6.87188	0.381183
$326$	3.49918	0.193802
$327$	20.1926	1.11665
$328$	9.29771	0.513380
$329$	3.87392	0.213576
$330$	0	0
$331$	−17.5657	−0.965498	−0.482749	−	0.875759i	$-0.660362\pi$
$331$	−17.5657	−0.965498	−0.482749	+	0.875759i	$0.660362\pi$
$332$	0.143397	0.00786992
$333$	−40.6990	−2.23029
$334$	−0.178585	−0.00977173
$335$	0.907079	0.0495590
$336$	−11.7940	−0.643415
$337$	11.5389	0.628565	0.314282	−	0.949330i	$-0.398236\pi$
$337$	11.5389	0.628565	0.314282	+	0.949330i	$0.398236\pi$
$338$	−48.2076	−2.62215
$339$	−1.99683	−0.108453
$340$	0.124307	0.00674148
$341$	0	0
$342$	27.5559	1.49005
$343$	1.00000	0.0539949
$344$	−20.6922	−1.11565
$345$	−6.83004	−0.367717
$346$	−2.30960	−0.124165
$347$	−11.6054	−0.623011	−0.311506	−	0.950244i	$-0.600833\pi$
$347$	−11.6054	−0.623011	−0.311506	+	0.950244i	$0.600833\pi$
$348$	−0.220949	−0.0118441
$349$	16.3172	0.873439	0.436719	−	0.899598i	$-0.356140\pi$
$349$	16.3172	0.873439	0.436719	+	0.899598i	$0.356140\pi$
$350$	−1.40864	−0.0752952
$351$	57.8610	3.08839
$352$	0	0
$353$	−30.4498	−1.62068	−0.810339	−	0.585962i	$-0.800717\pi$
$353$	−30.4498	−1.62068	−0.810339	+	0.585962i	$0.800717\pi$
$354$	−17.9787	−0.955557
$355$	10.9701	0.582230
$356$	0.0837372	0.00443806
$357$	23.4974	1.24361
$358$	−3.12687	−0.165260
$359$	−29.9595	−1.58120	−0.790600	−	0.612333i	$-0.790231\pi$
$359$	−29.9595	−1.58120	−0.790600	+	0.612333i	$0.790231\pi$
$360$	−16.5626	−0.872925
$361$	−7.75304	−0.408055
$362$	−21.6986	−1.14045
$363$	0	0
$364$	−0.108045	−0.00566312
$365$	2.36420	0.123748
$366$	−28.4490	−1.48705
$367$	−8.84144	−0.461519	−0.230760	−	0.973011i	$-0.574121\pi$
$367$	−8.84144	−0.461519	−0.230760	+	0.973011i	$0.574121\pi$
$368$	−9.11954	−0.475389
$369$	19.1003	0.994322
$370$	−9.82853	−0.510961
$371$	−7.36031	−0.382128
$372$	−0.0244104	−0.00126562
$373$	0.920466	0.0476599	0.0238300	−	0.999716i	$-0.492414\pi$
$373$	0.920466	0.0476599	0.0238300	+	0.999716i	$0.492414\pi$
$374$	0	0
$375$	−2.97205	−0.153476
$376$	10.9998	0.567269
$377$	32.4924	1.67344
$378$	−11.8607	−0.610051
$379$	−0.701850	−0.0360516	−0.0180258	−	0.999838i	$-0.505738\pi$
$379$	−0.701850	−0.0360516	−0.0180258	+	0.999838i	$0.505738\pi$
$380$	−0.0527289	−0.00270494
$381$	−48.8949	−2.50496
$382$	20.4580	1.04672
$383$	−7.51974	−0.384241	−0.192120	−	0.981371i	$-0.561536\pi$
$383$	−7.51974	−0.384241	−0.192120	+	0.981371i	$0.561536\pi$
$384$	−33.2229	−1.69540
$385$	0	0
$386$	−9.90178	−0.503988
$387$	−42.5079	−2.16080
$388$	0.0662407	0.00336286
$389$	16.5100	0.837092	0.418546	−	0.908196i	$-0.362540\pi$
$389$	16.5100	0.837092	0.418546	+	0.908196i	$0.362540\pi$
$390$	28.7695	1.45680
$391$	18.1690	0.918847
$392$	2.83944	0.143413
$393$	−66.6744	−3.36328
$394$	20.9708	1.05649
$395$	−14.8341	−0.746384
$396$	0	0
$397$	6.58310	0.330396	0.165198	−	0.986260i	$-0.447174\pi$
$397$	6.58310	0.330396	0.165198	+	0.986260i	$0.447174\pi$
$398$	−22.3847	−1.12204
$399$	−9.96720	−0.498984
$400$	−3.96831	−0.198415
$401$	−24.9040	−1.24365	−0.621823	−	0.783158i	$-0.713608\pi$
$401$	−24.9040	−1.24365	−0.621823	+	0.783158i	$0.713608\pi$
$402$	3.79753	0.189404
$403$	3.58974	0.178818
$404$	0.268875	0.0133771
$405$	−7.52538	−0.373939
$406$	−6.66051	−0.330555
$407$	0	0
$408$	66.7193	3.30310
$409$	−9.42392	−0.465983	−0.232992	−	0.972479i	$-0.574851\pi$
$409$	−9.42392	−0.465983	−0.232992	+	0.972479i	$0.574851\pi$
$410$	4.61259	0.227800
$411$	41.6125	2.05259
$412$	0.221131	0.0108943
$413$	4.29439	0.211313
$414$	−18.8827	−0.928036
$415$	9.12029	0.447697
$416$	−0.611183	−0.0299657
$417$	−6.31613	−0.309302
$418$	0	0
$419$	17.4140	0.850731	0.425365	−	0.905022i	$-0.360146\pi$
$419$	17.4140	0.850731	0.425365	+	0.905022i	$0.360146\pi$
$420$	0.0467290	0.00228014
$421$	−20.0241	−0.975914	−0.487957	−	0.872868i	$-0.662258\pi$
$421$	−20.0241	−0.975914	−0.487957	+	0.872868i	$0.662258\pi$
$422$	−23.2412	−1.13136
$423$	22.5968	1.09870
$424$	−20.8991	−1.01495
$425$	7.90613	0.383503
$426$	45.9267	2.22516
$427$	6.79532	0.328849
$428$	−0.271099	−0.0131041
$429$	0	0
$430$	−10.2654	−0.495040
$431$	8.72554	0.420294	0.210147	−	0.977670i	$-0.432606\pi$
$431$	8.72554	0.420294	0.210147	+	0.977670i	$0.432606\pi$
$432$	−33.4130	−1.60759
$433$	−21.1645	−1.01710	−0.508550	−	0.861032i	$-0.669818\pi$
$433$	−21.1645	−1.01710	−0.508550	+	0.861032i	$0.669818\pi$
$434$	−0.735849	−0.0353219
$435$	−14.0528	−0.673778
$436$	−0.106824	−0.00511592
$437$	−7.70700	−0.368676
$438$	9.89784	0.472937
$439$	−32.4862	−1.55048	−0.775240	−	0.631667i	$-0.782371\pi$
$439$	−32.4862	−1.55048	−0.775240	+	0.631667i	$0.782371\pi$
$440$	0	0
$441$	5.83306	0.277765
$442$	−76.5315	−3.64023
$443$	0.131704	0.00625746	0.00312873	−	0.999995i	$-0.499004\pi$
$443$	0.131704	0.00625746	0.00312873	+	0.999995i	$0.499004\pi$
$444$	0.326042	0.0154733
$445$	5.32583	0.252469
$446$	19.4205	0.919585
$447$	−43.7903	−2.07121
$448$	8.06190	0.380889
$449$	11.8096	0.557330	0.278665	−	0.960388i	$-0.410108\pi$
$449$	11.8096	0.557330	0.278665	+	0.960388i	$0.410108\pi$
$450$	−8.21670	−0.387339
$451$	0	0
$452$	0.0105637	0.000496876 0
$453$	40.3549	1.89604
$454$	−31.2963	−1.46881
$455$	−6.87188	−0.322158
$456$	−28.3012	−1.32533
$457$	−23.3179	−1.09077	−0.545384	−	0.838186i	$-0.683616\pi$
$457$	−23.3179	−1.09077	−0.545384	+	0.838186i	$0.683616\pi$
$458$	0.666565	0.0311465
$459$	66.5694	3.10719
$460$	0.0361326	0.00168469
$461$	34.8915	1.62506	0.812531	−	0.582919i	$-0.198089\pi$
$461$	34.8915	1.62506	0.812531	+	0.582919i	$0.198089\pi$
$462$	0	0
$463$	6.22233	0.289176	0.144588	−	0.989492i	$-0.453814\pi$
$463$	6.22233	0.289176	0.144588	+	0.989492i	$0.453814\pi$
$464$	−18.7634	−0.871069
$465$	−1.55254	−0.0719974
$466$	5.01154	0.232155
$467$	9.28754	0.429776	0.214888	−	0.976639i	$-0.431061\pi$
$467$	9.28754	0.429776	0.214888	+	0.976639i	$0.431061\pi$
$468$	−0.630235	−0.0291326
$469$	−0.907079	−0.0418850
$470$	5.45698	0.251712
$471$	65.6130	3.02329
$472$	12.1936	0.561258
$473$	0	0
$474$	−62.1037	−2.85252
$475$	−3.35365	−0.153876
$476$	−0.124307	−0.00569759
$477$	−42.9331	−1.96577
$478$	−2.78159	−0.127227
$479$	−20.6693	−0.944406	−0.472203	−	0.881490i	$-0.656541\pi$
$479$	−20.6693	−0.944406	−0.472203	+	0.881490i	$0.656541\pi$
$480$	0.264333	0.0120651
$481$	−47.9471	−2.18620
$482$	1.06209	0.0483767
$483$	6.83004	0.310778
$484$	0	0
$485$	4.21302	0.191303
$486$	4.07684	0.184929
$487$	3.12444	0.141582	0.0707908	−	0.997491i	$-0.477448\pi$
$487$	3.12444	0.141582	0.0707908	+	0.997491i	$0.477448\pi$
$488$	19.2949	0.873438
$489$	−7.38280	−0.333862
$490$	1.40864	0.0636360
$491$	−9.59454	−0.432996	−0.216498	−	0.976283i	$-0.569463\pi$
$491$	−9.59454	−0.432996	−0.216498	+	0.976283i	$0.569463\pi$
$492$	−0.153014	−0.00689839
$493$	37.3826	1.68363
$494$	32.4634	1.46060
$495$	0	0
$496$	−2.07297	−0.0930791
$497$	−10.9701	−0.492074
$498$	38.1826	1.71100
$499$	29.0722	1.30145	0.650726	−	0.759313i	$-0.274465\pi$
$499$	29.0722	1.30145	0.650726	+	0.759313i	$0.274465\pi$
$500$	0.0157228	0.000703147 0
$501$	0.376790	0.0168337
$502$	15.2403	0.680208
$503$	22.1783	0.988881	0.494441	−	0.869211i	$-0.335373\pi$
$503$	22.1783	0.988881	0.494441	+	0.869211i	$0.335373\pi$
$504$	16.5626	0.737756
$505$	17.1009	0.760982
$506$	0	0
$507$	101.711	4.51716
$508$	0.258666	0.0114764
$509$	−8.70086	−0.385659	−0.192830	−	0.981232i	$-0.561766\pi$
$509$	−8.70086	−0.385659	−0.192830	+	0.981232i	$0.561766\pi$
$510$	33.0994	1.46567
$511$	−2.36420	−0.104586
$512$	22.8884	1.01154
$513$	−28.2376	−1.24672
$514$	24.2343	1.06893
$515$	14.0643	0.619747
$516$	0.340534	0.0149912
$517$	0	0
$518$	9.82853	0.431841
$519$	4.87295	0.213899
$520$	−19.5122	−0.855669
$521$	25.6269	1.12273	0.561366	−	0.827567i	$-0.310276\pi$
$521$	25.6269	1.12273	0.561366	+	0.827567i	$0.310276\pi$
$522$	−38.8511	−1.70047
$523$	5.14596	0.225017	0.112508	−	0.993651i	$-0.464111\pi$
$523$	5.14596	0.225017	0.112508	+	0.993651i	$0.464111\pi$
$524$	0.352724	0.0154088
$525$	2.97205	0.129711
$526$	−23.9763	−1.04541
$527$	4.13001	0.179906
$528$	0	0
$529$	−17.7188	−0.770381
$530$	−10.3681	−0.450360
$531$	25.0494	1.08705
$532$	0.0527289	0.00228609
$533$	22.5019	0.974666
$534$	22.2969	0.964881
$535$	−17.2424	−0.745452
$536$	−2.57559	−0.111249
$537$	6.59727	0.284693
$538$	−29.3080	−1.26356
$539$	0	0
$540$	0.132386	0.00569698
$541$	1.21971	0.0524396	0.0262198	−	0.999656i	$-0.491653\pi$
$541$	1.21971	0.0524396	0.0262198	+	0.999656i	$0.491653\pi$
$542$	−28.8305	−1.23838
$543$	45.7811	1.96465
$544$	−0.703169	−0.0301481
$545$	−6.79417	−0.291030
$546$	−28.7695	−1.23122
$547$	15.0661	0.644182	0.322091	−	0.946709i	$-0.395614\pi$
$547$	15.0661	0.644182	0.322091	+	0.946709i	$0.395614\pi$
$548$	−0.220140	−0.00940391
$549$	39.6375	1.69169
$550$	0	0
$551$	−15.8571	−0.675535
$552$	19.3935	0.825440
$553$	14.8341	0.630810
$554$	−43.3303	−1.84093
$555$	20.7369	0.880230
$556$	0.0334138	0.00141706
$557$	43.0392	1.82363	0.911815	−	0.410602i	$-0.134681\pi$
$557$	43.0392	1.82363	0.911815	+	0.410602i	$0.134681\pi$
$558$	−4.29225	−0.181705
$559$	−50.0782	−2.11808
$560$	3.96831	0.167692
$561$	0	0
$562$	5.05351	0.213169
$563$	−3.71644	−0.156629	−0.0783147	−	0.996929i	$-0.524954\pi$
$563$	−3.71644	−0.156629	−0.0783147	+	0.996929i	$0.524954\pi$
$564$	−0.181025	−0.00762251
$565$	0.671872	0.0282659
$566$	−9.15490	−0.384809
$567$	7.52538	0.316036
$568$	−31.1488	−1.30697
$569$	5.81354	0.243716	0.121858	−	0.992548i	$-0.461115\pi$
$569$	5.81354	0.243716	0.121858	+	0.992548i	$0.461115\pi$
$570$	−14.0402	−0.588081
$571$	16.7223	0.699806	0.349903	−	0.936786i	$-0.386215\pi$
$571$	16.7223	0.699806	0.349903	+	0.936786i	$0.386215\pi$
$572$	0	0
$573$	−43.1635	−1.80318
$574$	−4.61259	−0.192526
$575$	2.29809	0.0958371
$576$	47.0255	1.95940
$577$	−32.0239	−1.33317	−0.666586	−	0.745428i	$-0.732245\pi$
$577$	−32.0239	−1.33317	−0.666586	+	0.745428i	$0.732245\pi$
$578$	−64.1029	−2.66633
$579$	20.8914	0.868217
$580$	0.0743425	0.00308690
$581$	−9.12029	−0.378373
$582$	17.6380	0.731120
$583$	0	0
$584$	−6.71298	−0.277785
$585$	−40.0840	−1.65727
$586$	1.02754	0.0424474
$587$	−11.2506	−0.464361	−0.232181	−	0.972673i	$-0.574586\pi$
$587$	−11.2506	−0.464361	−0.232181	+	0.972673i	$0.574586\pi$
$588$	−0.0467290	−0.00192707
$589$	−1.75188	−0.0721851
$590$	6.04927	0.249044
$591$	−44.2455	−1.82002
$592$	27.6881	1.13797
$593$	33.0191	1.35593	0.677965	−	0.735094i	$-0.262862\pi$
$593$	33.0191	1.35593	0.677965	+	0.735094i	$0.262862\pi$
$594$	0	0
$595$	−7.90613	−0.324120
$596$	0.231661	0.00948922
$597$	47.2286	1.93294
$598$	−22.2456	−0.909690
$599$	−32.0182	−1.30823	−0.654115	−	0.756395i	$-0.726959\pi$
$599$	−32.0182	−1.30823	−0.654115	+	0.756395i	$0.726959\pi$
$600$	8.43893	0.344518
$601$	−4.26008	−0.173772	−0.0868861	−	0.996218i	$-0.527692\pi$
$601$	−4.26008	−0.173772	−0.0868861	+	0.996218i	$0.527692\pi$
$602$	10.2654	0.418386
$603$	−5.29104	−0.215468
$604$	−0.213487	−0.00868666
$605$	0	0
$606$	71.5940	2.90831
$607$	−30.1350	−1.22314	−0.611571	−	0.791190i	$-0.709462\pi$
$607$	−30.1350	−1.22314	−0.611571	+	0.791190i	$0.709462\pi$
$608$	0.298273	0.0120966
$609$	14.0528	0.569447
$610$	9.57219	0.387567
$611$	26.6211	1.07698
$612$	−0.725088	−0.0293100
$613$	26.1892	1.05777	0.528886	−	0.848693i	$-0.322610\pi$
$613$	26.1892	1.05777	0.528886	+	0.848693i	$0.322610\pi$
$614$	43.9245	1.77265
$615$	−9.73194	−0.392430
$616$	0	0
$617$	−34.4517	−1.38697	−0.693486	−	0.720470i	$-0.743926\pi$
$617$	−34.4517	−1.38697	−0.693486	+	0.720470i	$0.743926\pi$
$618$	58.8809	2.36854
$619$	34.3680	1.38137	0.690684	−	0.723157i	$-0.257310\pi$
$619$	34.3680	1.38137	0.690684	+	0.723157i	$0.257310\pi$
$620$	0.00821332	0.000329855 0
$621$	19.3499	0.776484
$622$	35.1400	1.40899
$623$	−5.32583	−0.213375
$624$	−81.0468	−3.24447
$625$	1.00000	0.0400000
$626$	−24.5240	−0.980177
$627$	0	0
$628$	−0.347108	−0.0138511
$629$	−55.1634	−2.19951
$630$	8.21670	0.327361
$631$	8.67134	0.345201	0.172600	−	0.984992i	$-0.444783\pi$
$631$	8.67134	0.345201	0.172600	+	0.984992i	$0.444783\pi$
$632$	42.1204	1.67546
$633$	49.0358	1.94900
$634$	2.77579	0.110241
$635$	16.4516	0.652861
$636$	0.343940	0.0136381
$637$	6.87188	0.272274
$638$	0	0
$639$	−63.9889	−2.53136
$640$	11.1785	0.441868
$641$	7.84629	0.309910	0.154955	−	0.987922i	$-0.450477\pi$
$641$	7.84629	0.309910	0.154955	+	0.987922i	$0.450477\pi$
$642$	−72.1861	−2.84896
$643$	−24.4717	−0.965069	−0.482534	−	0.875877i	$-0.660284\pi$
$643$	−24.4717	−0.965069	−0.482534	+	0.875877i	$0.660284\pi$
$644$	−0.0361326	−0.00142382
$645$	21.6585	0.852804
$646$	37.3493	1.46949
$647$	14.5583	0.572344	0.286172	−	0.958178i	$-0.407617\pi$
$647$	14.5583	0.572344	0.286172	+	0.958178i	$0.407617\pi$
$648$	21.3678	0.839407
$649$	0	0
$650$	−9.68002	−0.379682
$651$	1.55254	0.0608489
$652$	0.0390568	0.00152958
$653$	14.5979	0.571261	0.285631	−	0.958340i	$-0.407797\pi$
$653$	14.5979	0.571261	0.285631	+	0.958340i	$0.407797\pi$
$654$	−28.4442	−1.11225
$655$	22.4338	0.876562
$656$	−12.9942	−0.507338
$657$	−13.7905	−0.538018
$658$	−5.45698	−0.212735
$659$	11.3774	0.443202	0.221601	−	0.975137i	$-0.428872\pi$
$659$	11.3774	0.443202	0.221601	+	0.975137i	$0.428872\pi$
$660$	0	0
$661$	−2.69976	−0.105008	−0.0525042	−	0.998621i	$-0.516720\pi$
$661$	−2.69976	−0.105008	−0.0525042	+	0.998621i	$0.516720\pi$
$662$	24.7438	0.961696
$663$	161.471	6.27101
$664$	−25.8965	−1.00498
$665$	3.35365	0.130049
$666$	57.3304	2.22151
$667$	10.8661	0.420737
$668$	−0.00199331	−7.71234e−5 0
$669$	−40.9745	−1.58417
$670$	−1.27775	−0.0493638
$671$	0	0
$672$	−0.264333	−0.0101969
$673$	21.7564	0.838648	0.419324	−	0.907837i	$-0.362267\pi$
$673$	21.7564	0.838648	0.419324	+	0.907837i	$0.362267\pi$
$674$	−16.2542	−0.626089
$675$	8.41997	0.324085
$676$	−0.538078	−0.0206953
$677$	−45.4448	−1.74658	−0.873292	−	0.487197i	$-0.838019\pi$
$677$	−45.4448	−1.74658	−0.873292	+	0.487197i	$0.838019\pi$
$678$	2.81283	0.108026
$679$	−4.21302	−0.161681
$680$	−22.4489	−0.860877
$681$	66.0310	2.53031
$682$	0	0
$683$	−16.4450	−0.629249	−0.314625	−	0.949216i	$-0.601879\pi$
$683$	−16.4450	−0.629249	−0.314625	+	0.949216i	$0.601879\pi$
$684$	0.307571	0.0117603
$685$	−14.0013	−0.534962
$686$	−1.40864	−0.0537823
$687$	−1.40636	−0.0536560
$688$	28.9187	1.10252
$689$	−50.5792	−1.92691
$690$	9.62109	0.366269
$691$	−28.7792	−1.09481	−0.547405	−	0.836868i	$-0.684384\pi$
$691$	−28.7792	−1.09481	−0.547405	+	0.836868i	$0.684384\pi$
$692$	−0.0257791	−0.000979973 0
$693$	0	0
$694$	16.3479	0.620558
$695$	2.12518	0.0806126
$696$	39.9019	1.51248
$697$	25.8886	0.980599
$698$	−22.9851	−0.869999
$699$	−10.5737	−0.399933
$700$	−0.0157228	−0.000594268 0
$701$	0.390327	0.0147424	0.00737122	−	0.999973i	$-0.497654\pi$
$701$	0.390327	0.0147424	0.00737122	+	0.999973i	$0.497654\pi$
$702$	−81.5055	−3.07623
$703$	23.3994	0.882526
$704$	0	0
$705$	−11.5135	−0.433623
$706$	42.8929	1.61429
$707$	−17.1009	−0.643147
$708$	−0.200673	−0.00754174
$709$	−17.0887	−0.641779	−0.320890	−	0.947117i	$-0.603982\pi$
$709$	−17.0887	−0.641779	−0.320890	+	0.947117i	$0.603982\pi$
$710$	−15.4529	−0.579937
$711$	86.5281	3.24506
$712$	−15.1224	−0.566734
$713$	1.20048	0.0449584
$714$	−33.0994	−1.23871
$715$	0	0
$716$	−0.0349011	−0.00130432
$717$	5.86877	0.219173
$718$	42.2022	1.57497
$719$	36.6954	1.36851	0.684254	−	0.729244i	$-0.260128\pi$
$719$	36.6954	1.36851	0.684254	+	0.729244i	$0.260128\pi$
$720$	23.1474	0.862651
$721$	−14.0643	−0.523781
$722$	10.9213	0.406447
$723$	−2.24086	−0.0833383
$724$	−0.242193	−0.00900103
$725$	4.72831	0.175605
$726$	0	0
$727$	−21.0979	−0.782476	−0.391238	−	0.920289i	$-0.627953\pi$
$727$	−21.0979	−0.782476	−0.391238	+	0.920289i	$0.627953\pi$
$728$	19.5122	0.723172
$729$	−31.1777	−1.15473
$730$	−3.33031	−0.123260
$731$	−57.6153	−2.13098
$732$	−0.317539	−0.0117366
$733$	23.1082	0.853523	0.426761	−	0.904364i	$-0.359654\pi$
$733$	23.1082	0.853523	0.426761	+	0.904364i	$0.359654\pi$
$734$	12.4544	0.459702
$735$	−2.97205	−0.109626
$736$	−0.204392	−0.00753398
$737$	0	0
$738$	−26.9055	−0.990406
$739$	−36.3513	−1.33720	−0.668602	−	0.743620i	$-0.733107\pi$
$739$	−36.3513	−1.33720	−0.668602	+	0.743620i	$0.733107\pi$
$740$	−0.109703	−0.00403276
$741$	−68.4934	−2.51617
$742$	10.3681	0.380623
$743$	−11.9860	−0.439722	−0.219861	−	0.975531i	$-0.570560\pi$
$743$	−11.9860	−0.439722	−0.219861	+	0.975531i	$0.570560\pi$
$744$	4.40834	0.161618
$745$	14.7341	0.539814
$746$	−1.29661	−0.0474722
$747$	−53.1992	−1.94646
$748$	0	0
$749$	17.2424	0.630022
$750$	4.18655	0.152871
$751$	40.6668	1.48395	0.741977	−	0.670426i	$-0.233888\pi$
$751$	40.6668	1.48395	0.741977	+	0.670426i	$0.233888\pi$
$752$	−15.3729	−0.560593
$753$	−32.1550	−1.17179
$754$	−45.7702	−1.66685
$755$	−13.5781	−0.494159
$756$	−0.132386	−0.00481483
$757$	20.1601	0.732732	0.366366	−	0.930471i	$-0.380602\pi$
$757$	20.1601	0.732732	0.366366	+	0.930471i	$0.380602\pi$
$758$	0.988657	0.0359096
$759$	0	0
$760$	9.52247	0.345416
$761$	−50.0878	−1.81568	−0.907840	−	0.419317i	$-0.862270\pi$
$761$	−50.0878	−1.81568	−0.907840	+	0.419317i	$0.862270\pi$
$762$	68.8755	2.49509
$763$	6.79417	0.245965
$764$	0.228345	0.00826125
$765$	−46.1169	−1.66736
$766$	10.5926	0.382728
$767$	29.5105	1.06556
$768$	−1.12143	−0.0404660
$769$	−23.8422	−0.859773	−0.429887	−	0.902883i	$-0.641446\pi$
$769$	−23.8422	−0.859773	−0.429887	+	0.902883i	$0.641446\pi$
$770$	0	0
$771$	−51.1311	−1.84144
$772$	−0.110521	−0.00397772
$773$	45.3103	1.62970	0.814849	−	0.579674i	$-0.196820\pi$
$773$	45.3103	1.62970	0.814849	+	0.579674i	$0.196820\pi$
$774$	59.8785	2.15229
$775$	0.522381	0.0187645
$776$	−11.9626	−0.429432
$777$	−20.7369	−0.743930
$778$	−23.2568	−0.833796
$779$	−10.9815	−0.393453
$780$	0.321116	0.0114978
$781$	0	0
$782$	−25.5937	−0.915228
$783$	39.8123	1.42277
$784$	−3.96831	−0.141725
$785$	−22.0767	−0.787951
$786$	93.9204	3.35003
$787$	10.1684	0.362465	0.181232	−	0.983440i	$-0.441991\pi$
$787$	10.1684	0.362465	0.181232	+	0.983440i	$0.441991\pi$
$788$	0.234070	0.00833838
$789$	50.5866	1.80093
$790$	20.8960	0.743445
$791$	−0.671872	−0.0238890
$792$	0	0
$793$	46.6966	1.65825
$794$	−9.27325	−0.329095
$795$	21.8752	0.775833
$796$	−0.249851	−0.00885572
$797$	13.0793	0.463294	0.231647	−	0.972800i	$-0.425589\pi$
$797$	13.0793	0.463294	0.231647	+	0.972800i	$0.425589\pi$
$798$	14.0402	0.497019
$799$	30.6277	1.08353
$800$	−0.0889397	−0.00314449
$801$	−31.0659	−1.09766
$802$	35.0809	1.23875
$803$	0	0
$804$	0.0423869	0.00149487
$805$	−2.29809	−0.0809972
$806$	−5.05666	−0.178113
$807$	61.8359	2.17673
$808$	−48.5570	−1.70823
$809$	−20.0647	−0.705437	−0.352718	−	0.935730i	$-0.614743\pi$
$809$	−20.0647	−0.705437	−0.352718	+	0.935730i	$0.614743\pi$
$810$	10.6006	0.372466
$811$	31.4766	1.10529	0.552647	−	0.833416i	$-0.313618\pi$
$811$	31.4766	1.10529	0.552647	+	0.833416i	$0.313618\pi$
$812$	−0.0743425	−0.00260891
$813$	60.8285	2.13335
$814$	0	0
$815$	2.48408	0.0870135
$816$	−93.2448	−3.26422
$817$	24.4394	0.855028
$818$	13.2750	0.464148
$819$	40.0840	1.40065
$820$	0.0514843	0.00179791
$821$	5.30792	0.185248	0.0926238	−	0.995701i	$-0.470475\pi$
$821$	5.30792	0.185248	0.0926238	+	0.995701i	$0.470475\pi$
$822$	−58.6171	−2.04451
$823$	−21.1623	−0.737670	−0.368835	−	0.929495i	$-0.620243\pi$
$823$	−21.1623	−0.737670	−0.368835	+	0.929495i	$0.620243\pi$
$824$	−39.9346	−1.39119
$825$	0	0
$826$	−6.04927	−0.210481
$827$	−24.4982	−0.851884	−0.425942	−	0.904750i	$-0.640057\pi$
$827$	−24.4982	−0.851884	−0.425942	+	0.904750i	$0.640057\pi$
$828$	−0.210763	−0.00732453
$829$	−36.3085	−1.26105	−0.630524	−	0.776170i	$-0.717160\pi$
$829$	−36.3085	−1.26105	−0.630524	+	0.776170i	$0.717160\pi$
$830$	−12.8472	−0.445934
$831$	91.4210	3.17136
$832$	55.4004	1.92066
$833$	7.90613	0.273931
$834$	8.89717	0.308084
$835$	−0.126778	−0.00438733
$836$	0	0
$837$	4.39844	0.152032
$838$	−24.5302	−0.847380
$839$	−11.0610	−0.381869	−0.190935	−	0.981603i	$-0.561152\pi$
$839$	−11.0610	−0.381869	−0.190935	+	0.981603i	$0.561152\pi$
$840$	−8.43893	−0.291171
$841$	−6.64306	−0.229071
$842$	28.2068	0.972070
$843$	−10.6622	−0.367226
$844$	−0.259411	−0.00892930
$845$	−34.2227	−1.17730
$846$	−31.8309	−1.09437
$847$	0	0
$848$	29.2080	1.00301
$849$	19.3156	0.662909
$850$	−11.1369	−0.381993
$851$	−16.0345	−0.549655
$852$	0.512620	0.0175621
$853$	−50.6613	−1.73461	−0.867304	−	0.497779i	$-0.834149\pi$
$853$	−50.6613	−1.73461	−0.867304	+	0.497779i	$0.834149\pi$
$854$	−9.57219	−0.327554
$855$	19.5620	0.669007
$856$	48.9586	1.67337
$857$	−3.70108	−0.126426	−0.0632132	−	0.998000i	$-0.520135\pi$
$857$	−3.70108	−0.126426	−0.0632132	+	0.998000i	$0.520135\pi$
$858$	0	0
$859$	11.8995	0.406005	0.203002	−	0.979178i	$-0.434930\pi$
$859$	11.8995	0.406005	0.203002	+	0.979178i	$0.434930\pi$
$860$	−0.114579	−0.00390711
$861$	9.73194	0.331664
$862$	−12.2912	−0.418639
$863$	−4.86475	−0.165598	−0.0827989	−	0.996566i	$-0.526386\pi$
$863$	−4.86475	−0.165598	−0.0827989	+	0.996566i	$0.526386\pi$
$864$	−0.748870	−0.0254771
$865$	−1.63959	−0.0557479
$866$	29.8132	1.01309
$867$	135.248	4.59328
$868$	−0.00821332	−0.000278778 0
$869$	0	0
$870$	19.7953	0.671125
$871$	−6.23333	−0.211208
$872$	19.2916	0.653296
$873$	−24.5748	−0.831731
$874$	10.8564	0.367224
$875$	−1.00000	−0.0338062
$876$	0.110477	0.00373266
$877$	53.6132	1.81039	0.905194	−	0.424998i	$-0.139725\pi$
$877$	53.6132	1.81039	0.905194	+	0.424998i	$0.139725\pi$
$878$	45.7614	1.54437
$879$	−2.16798	−0.0731240
$880$	0	0
$881$	−3.19882	−0.107771	−0.0538855	−	0.998547i	$-0.517161\pi$
$881$	−3.19882	−0.107771	−0.0538855	+	0.998547i	$0.517161\pi$
$882$	−8.21670	−0.276671
$883$	−19.0645	−0.641571	−0.320786	−	0.947152i	$-0.603947\pi$
$883$	−19.0645	−0.641571	−0.320786	+	0.947152i	$0.603947\pi$
$884$	−0.854221	−0.0287305
$885$	−12.7631	−0.429028
$886$	−0.185524	−0.00623281
$887$	−37.6234	−1.26327	−0.631635	−	0.775266i	$-0.717616\pi$
$887$	−37.6234	−1.26327	−0.631635	+	0.775266i	$0.717616\pi$
$888$	−58.8809	−1.97592
$889$	−16.4516	−0.551769
$890$	−7.50220	−0.251474
$891$	0	0
$892$	0.216765	0.00725783
$893$	−12.9918	−0.434754
$894$	61.6849	2.06305
$895$	−2.21977	−0.0741988
$896$	−11.1785	−0.373446
$897$	46.9352	1.56712
$898$	−16.6355	−0.555135
$899$	2.46998	0.0823785
$900$	−0.0917122	−0.00305707
$901$	−58.1916	−1.93864
$902$	0	0
$903$	−21.6585	−0.720751
$904$	−1.90774	−0.0634504
$905$	−15.4039	−0.512043
$906$	−56.8456	−1.88857
$907$	−37.2754	−1.23771	−0.618854	−	0.785506i	$-0.712403\pi$
$907$	−37.2754	−1.23771	−0.618854	+	0.785506i	$0.712403\pi$
$908$	−0.349320	−0.0115926
$909$	−99.7508	−3.30852
$910$	9.68002	0.320890
$911$	−2.10027	−0.0695849	−0.0347925	−	0.999395i	$-0.511077\pi$
$911$	−2.10027	−0.0695849	−0.0347925	+	0.999395i	$0.511077\pi$
$912$	39.5529	1.30973
$913$	0	0
$914$	32.8467	1.08647
$915$	−20.1960	−0.667659
$916$	0.00743999	0.000245824 0
$917$	−22.4338	−0.740830
$918$	−93.7725	−3.09495
$919$	49.6452	1.63764	0.818822	−	0.574047i	$-0.194627\pi$
$919$	49.6452	1.63764	0.818822	+	0.574047i	$0.194627\pi$
$920$	−6.52529	−0.215132
$921$	−92.6747	−3.05374
$922$	−49.1498	−1.61866
$923$	−75.3848	−2.48132
$924$	0	0
$925$	−6.97730	−0.229412
$926$	−8.76504	−0.288037
$927$	−82.0378	−2.69447
$928$	−0.420535	−0.0138047
$929$	25.4532	0.835093	0.417547	−	0.908655i	$-0.362890\pi$
$929$	25.4532	0.835093	0.417547	+	0.908655i	$0.362890\pi$
$930$	2.18698	0.0717138
$931$	−3.35365	−0.109911
$932$	0.0559373	0.00183229
$933$	−74.1406	−2.42725
$934$	−13.0828	−0.428083
$935$	0	0
$936$	113.816	3.72019
$937$	−26.6660	−0.871142	−0.435571	−	0.900154i	$-0.643453\pi$
$937$	−26.6660	−0.871142	−0.435571	+	0.900154i	$0.643453\pi$
$938$	1.27775	0.0417200
$939$	51.7423	1.68855
$940$	0.0609091	0.00198664
$941$	−7.79560	−0.254129	−0.127065	−	0.991894i	$-0.540556\pi$
$941$	−7.79560	−0.254129	−0.127065	+	0.991894i	$0.540556\pi$
$942$	−92.4253	−3.01138
$943$	7.52509	0.245051
$944$	−17.0415	−0.554652
$945$	−8.41997	−0.273902
$946$	0	0
$947$	−3.87187	−0.125819	−0.0629095	−	0.998019i	$-0.520038\pi$
$947$	−3.87187	−0.125819	−0.0629095	+	0.998019i	$0.520038\pi$
$948$	−0.693182	−0.0225135
$949$	−16.2465	−0.527383
$950$	4.72410	0.153270
$951$	−5.85653	−0.189911
$952$	22.4489	0.727574
$953$	−1.07015	−0.0346656	−0.0173328	−	0.999850i	$-0.505517\pi$
$953$	−1.07015	−0.0346656	−0.0173328	+	0.999850i	$0.505517\pi$
$954$	60.4775	1.95803
$955$	14.5232	0.469959
$956$	−0.0310472	−0.00100414
$957$	0	0
$958$	29.1157	0.940687
$959$	14.0013	0.452125
$960$	−23.9603	−0.773316
$961$	−30.7271	−0.991197
$962$	67.5404	2.17759
$963$	100.576	3.24101
$964$	0.0118547	0.000381813 0
$965$	−7.02930	−0.226281
$966$	−9.62109	−0.309554
$967$	−5.03691	−0.161976	−0.0809880	−	0.996715i	$-0.525808\pi$
$967$	−5.03691	−0.161976	−0.0809880	+	0.996715i	$0.525808\pi$
$968$	0	0
$969$	−78.8019	−2.53148
$970$	−5.93465	−0.190550
$971$	−21.5803	−0.692545	−0.346273	−	0.938134i	$-0.612553\pi$
$971$	−21.5803	−0.692545	−0.346273	+	0.938134i	$0.612553\pi$
$972$	0.0455044	0.00145955
$973$	−2.12518	−0.0681301
$974$	−4.40122	−0.141024
$975$	20.4235	0.654076
$976$	−26.9659	−0.863158
$977$	−32.3876	−1.03617	−0.518085	−	0.855329i	$-0.673355\pi$
$977$	−32.3876	−1.03617	−0.518085	+	0.855329i	$0.673355\pi$
$978$	10.3997	0.332547
$979$	0	0
$980$	0.0157228	0.000502248 0
$981$	39.6308	1.26531
$982$	13.5153	0.431290
$983$	3.89854	0.124344	0.0621721	−	0.998065i	$-0.480197\pi$
$983$	3.89854	0.124344	0.0621721	+	0.998065i	$0.480197\pi$
$984$	27.6332	0.880915
$985$	14.8872	0.474347
$986$	−52.6588	−1.67700
$987$	11.5135	0.366478
$988$	0.362346	0.0115278
$989$	−16.7472	−0.532529
$990$	0	0
$991$	16.6805	0.529873	0.264936	−	0.964266i	$-0.414649\pi$
$991$	16.6805	0.529873	0.264936	+	0.964266i	$0.414649\pi$
$992$	−0.0464605	−0.00147512
$993$	−52.2061	−1.65671
$994$	15.4529	0.490136
$995$	−15.8909	−0.503777
$996$	0.426182	0.0135041
$997$	−5.49978	−0.174180	−0.0870898	−	0.996200i	$-0.527757\pi$
$997$	−5.49978	−0.174180	−0.0870898	+	0.996200i	$0.527757\pi$
$998$	−40.9524	−1.29633
$999$	−58.7487	−1.85873

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bl.1.3	yes	10
11.10	odd	2		4235.2.a.bj.1.8	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bj.1.8	✓	10	11.10	odd	2
4235.2.a.bl.1.3	yes	10	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4235 = 5 \cdot 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4235.a (trivial)

\(f(q)\)	\(=\)	\(q-1.40864 q^{2} +2.97205 q^{3} -0.0157228 q^{4} -1.00000 q^{5} -4.18655 q^{6} +1.00000 q^{7} +2.83944 q^{8} +5.83306 q^{9} +O(q^{10})\)	\(q-1.40864 q^{2} +2.97205 q^{3} -0.0157228 q^{4} -1.00000 q^{5} -4.18655 q^{6} +1.00000 q^{7} +2.83944 q^{8} +5.83306 q^{9} +1.40864 q^{10} -0.0467290 q^{12} +6.87188 q^{13} -1.40864 q^{14} -2.97205 q^{15} -3.96831 q^{16} +7.90613 q^{17} -8.21670 q^{18} -3.35365 q^{19} +0.0157228 q^{20} +2.97205 q^{21} +2.29809 q^{23} +8.43893 q^{24} +1.00000 q^{25} -9.68002 q^{26} +8.41997 q^{27} -0.0157228 q^{28} +4.72831 q^{29} +4.18655 q^{30} +0.522381 q^{31} -0.0889397 q^{32} -11.1369 q^{34} -1.00000 q^{35} -0.0917122 q^{36} -6.97730 q^{37} +4.72410 q^{38} +20.4235 q^{39} -2.83944 q^{40} +3.27449 q^{41} -4.18655 q^{42} -7.28742 q^{43} -5.83306 q^{45} -3.23719 q^{46} +3.87392 q^{47} -11.7940 q^{48} +1.00000 q^{49} -1.40864 q^{50} +23.4974 q^{51} -0.108045 q^{52} -7.36031 q^{53} -11.8607 q^{54} +2.83944 q^{56} -9.96720 q^{57} -6.66051 q^{58} +4.29439 q^{59} +0.0467290 q^{60} +6.79532 q^{61} -0.735849 q^{62} +5.83306 q^{63} +8.06190 q^{64} -6.87188 q^{65} -0.907079 q^{67} -0.124307 q^{68} +6.83004 q^{69} +1.40864 q^{70} -10.9701 q^{71} +16.5626 q^{72} -2.36420 q^{73} +9.82853 q^{74} +2.97205 q^{75} +0.0527289 q^{76} -28.7695 q^{78} +14.8341 q^{79} +3.96831 q^{80} +7.52538 q^{81} -4.61259 q^{82} -9.12029 q^{83} -0.0467290 q^{84} -7.90613 q^{85} +10.2654 q^{86} +14.0528 q^{87} -5.32583 q^{89} +8.21670 q^{90} +6.87188 q^{91} -0.0361326 q^{92} +1.55254 q^{93} -5.45698 q^{94} +3.35365 q^{95} -0.264333 q^{96} -4.21302 q^{97} -1.40864 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9}+O(q^{10}) \) 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9	\( 10 q + 2 q^{2} + 4 q^{3} + 12 q^{4} - 10 q^{5} + 10 q^{7} + 6 q^{8} + 6 q^{9} - 2 q^{10} + 16 q^{12} + 26 q^{13} + 2 q^{14} - 4 q^{15} + 20 q^{16} + 4 q^{17} + 8 q^{18} + 6 q^{19} - 12 q^{20} + 4 q^{21} - 8 q^{23} + 22 q^{24} + 10 q^{25} - 6 q^{26} + 10 q^{27} + 12 q^{28} - 4 q^{29} + 18 q^{31} + 24 q^{32} + 8 q^{34} - 10 q^{35} - 10 q^{36} - 16 q^{37} - 2 q^{38} + 16 q^{39} - 6 q^{40} - 30 q^{41} + 22 q^{43} - 6 q^{45} + 28 q^{46} + 14 q^{47} - 4 q^{48} + 10 q^{49} + 2 q^{50} + 36 q^{51} + 34 q^{52} - 10 q^{53} + 6 q^{54} + 6 q^{56} - 2 q^{57} - 38 q^{58} + 22 q^{59} - 16 q^{60} + 12 q^{61} - 6 q^{62} + 6 q^{63} + 8 q^{64} - 26 q^{65} - 14 q^{67} + 70 q^{68} + 8 q^{69} - 2 q^{70} - 8 q^{71} + 26 q^{72} + 30 q^{73} - 20 q^{74} + 4 q^{75} + 18 q^{76} - 32 q^{78} + 8 q^{79} - 20 q^{80} + 10 q^{81} - 28 q^{82} - 14 q^{83} + 16 q^{84} - 4 q^{85} - 14 q^{86} - 24 q^{87} - 6 q^{89} - 8 q^{90} + 26 q^{91} - 20 q^{92} + 14 q^{93} + 16 q^{94} - 6 q^{95} + 24 q^{96} + 20 q^{97} + 2 q^{98}+O(q^{100}) \) 10 * q + 2 * q^2 + 4 * q^3 + 12 * q^4 - 10 * q^5 + 10 * q^7 + 6 * q^8 + 6 * q^9 - 2 * q^10 + 16 * q^12 + 26 * q^13 + 2 * q^14 - 4 * q^15 + 20 * q^16 + 4 * q^17 + 8 * q^18 + 6 * q^19 - 12 * q^20 + 4 * q^21 - 8 * q^23 + 22 * q^24 + 10 * q^25 - 6 * q^26 + 10 * q^27 + 12 * q^28 - 4 * q^29 + 18 * q^31 + 24 * q^32 + 8 * q^34 - 10 * q^35 - 10 * q^36 - 16 * q^37 - 2 * q^38 + 16 * q^39 - 6 * q^40 - 30 * q^41 + 22 * q^43 - 6 * q^45 + 28 * q^46 + 14 * q^47 - 4 * q^48 + 10 * q^49 + 2 * q^50 + 36 * q^51 + 34 * q^52 - 10 * q^53 + 6 * q^54 + 6 * q^56 - 2 * q^57 - 38 * q^58 + 22 * q^59 - 16 * q^60 + 12 * q^61 - 6 * q^62 + 6 * q^63 + 8 * q^64 - 26 * q^65 - 14 * q^67 + 70 * q^68 + 8 * q^69 - 2 * q^70 - 8 * q^71 + 26 * q^72 + 30 * q^73 - 20 * q^74 + 4 * q^75 + 18 * q^76 - 32 * q^78 + 8 * q^79 - 20 * q^80 + 10 * q^81 - 28 * q^82 - 14 * q^83 + 16 * q^84 - 4 * q^85 - 14 * q^86 - 24 * q^87 - 6 * q^89 - 8 * q^90 + 26 * q^91 - 20 * q^92 + 14 * q^93 + 16 * q^94 - 6 * q^95 + 24 * q^96 + 20 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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