LMFDB - Embedded newform 4235.2.a.bp.1.15

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:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$2.05277$ 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)

$f(q)$	$=$	$q+2.05277 q^{2} -3.41466 q^{3} +2.21386 q^{4} +1.00000 q^{5} -7.00951 q^{6} +1.00000 q^{7} +0.439000 q^{8} +8.65991 q^{9} +O(q^{10})$	\(q+2.05277 q^{2} -3.41466 q^{3} +2.21386 q^{4} +1.00000 q^{5} -7.00951 q^{6} +1.00000 q^{7} +0.439000 q^{8} +8.65991 q^{9} +2.05277 q^{10} -7.55957 q^{12} +3.62061 q^{13} +2.05277 q^{14} -3.41466 q^{15} -3.52655 q^{16} +2.88712 q^{17} +17.7768 q^{18} +7.34843 q^{19} +2.21386 q^{20} -3.41466 q^{21} -2.63683 q^{23} -1.49904 q^{24} +1.00000 q^{25} +7.43228 q^{26} -19.3267 q^{27} +2.21386 q^{28} -1.64376 q^{29} -7.00951 q^{30} +2.23557 q^{31} -8.11719 q^{32} +5.92659 q^{34} +1.00000 q^{35} +19.1718 q^{36} -5.10065 q^{37} +15.0846 q^{38} -12.3632 q^{39} +0.439000 q^{40} +1.33869 q^{41} -7.00951 q^{42} -3.53651 q^{43} +8.65991 q^{45} -5.41280 q^{46} -8.23070 q^{47} +12.0420 q^{48} +1.00000 q^{49} +2.05277 q^{50} -9.85854 q^{51} +8.01552 q^{52} +3.63678 q^{53} -39.6731 q^{54} +0.439000 q^{56} -25.0924 q^{57} -3.37425 q^{58} +3.29779 q^{59} -7.55957 q^{60} +5.24101 q^{61} +4.58911 q^{62} +8.65991 q^{63} -9.60961 q^{64} +3.62061 q^{65} +11.3899 q^{67} +6.39167 q^{68} +9.00388 q^{69} +2.05277 q^{70} -7.06381 q^{71} +3.80170 q^{72} +14.2471 q^{73} -10.4705 q^{74} -3.41466 q^{75} +16.2684 q^{76} -25.3787 q^{78} +11.6679 q^{79} -3.52655 q^{80} +40.0142 q^{81} +2.74802 q^{82} +2.48577 q^{83} -7.55957 q^{84} +2.88712 q^{85} -7.25964 q^{86} +5.61288 q^{87} +12.2946 q^{89} +17.7768 q^{90} +3.62061 q^{91} -5.83757 q^{92} -7.63372 q^{93} -16.8957 q^{94} +7.34843 q^{95} +27.7174 q^{96} -4.09831 q^{97} +2.05277 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * 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 $

$2$	2.05277	1.45153	0.725763	−	0.687945i	$-0.241487\pi$
$2$	2.05277	1.45153	0.725763	+	0.687945i	$0.241487\pi$
$3$	−3.41466	−1.97146	−0.985728	−	0.168349i	$-0.946157\pi$
$3$	−3.41466	−1.97146	−0.985728	+	0.168349i	$0.946157\pi$
$4$	2.21386	1.10693
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−7.00951	−2.86162
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	0.439000	0.155210
$9$	8.65991	2.88664
$10$	2.05277	0.649142
$11$	0	0
$11$	0	0
$12$	−7.55957	−2.18226
$13$	3.62061	1.00418	0.502089	−	0.864816i	$-0.332565\pi$
$13$	3.62061	1.00418	0.502089	+	0.864816i	$0.332565\pi$
$14$	2.05277	0.548625
$15$	−3.41466	−0.881662
$16$	−3.52655	−0.881637
$17$	2.88712	0.700230	0.350115	−	0.936707i	$-0.386143\pi$
$17$	2.88712	0.700230	0.350115	+	0.936707i	$0.386143\pi$
$18$	17.7768	4.19003
$19$	7.34843	1.68585	0.842923	−	0.538034i	$-0.180833\pi$
$19$	7.34843	1.68585	0.842923	+	0.538034i	$0.180833\pi$
$20$	2.21386	0.495034
$21$	−3.41466	−0.745140
$22$	0	0
$23$	−2.63683	−0.549817	−0.274909	−	0.961470i	$-0.588648\pi$
$23$	−2.63683	−0.549817	−0.274909	+	0.961470i	$0.588648\pi$
$24$	−1.49904	−0.305989
$25$	1.00000	0.200000
$26$	7.43228	1.45759
$27$	−19.3267	−3.71942
$28$	2.21386	0.418380
$29$	−1.64376	−0.305238	−0.152619	−	0.988285i	$-0.548771\pi$
$29$	−1.64376	−0.305238	−0.152619	+	0.988285i	$0.548771\pi$
$30$	−7.00951	−1.27975
$31$	2.23557	0.401521	0.200760	−	0.979640i	$-0.435659\pi$
$31$	2.23557	0.401521	0.200760	+	0.979640i	$0.435659\pi$
$32$	−8.11719	−1.43493
$33$	0	0
$34$	5.92659	1.01640
$35$	1.00000	0.169031
$36$	19.1718	3.19530
$37$	−5.10065	−0.838542	−0.419271	−	0.907861i	$-0.637714\pi$
$37$	−5.10065	−0.838542	−0.419271	+	0.907861i	$0.637714\pi$
$38$	15.0846	2.44705
$39$	−12.3632	−1.97969
$40$	0.439000	0.0694120
$41$	1.33869	0.209068	0.104534	−	0.994521i	$-0.466665\pi$
$41$	1.33869	0.209068	0.104534	+	0.994521i	$0.466665\pi$
$42$	−7.00951	−1.08159
$43$	−3.53651	−0.539313	−0.269657	−	0.962957i	$-0.586910\pi$
$43$	−3.53651	−0.539313	−0.269657	+	0.962957i	$0.586910\pi$
$44$	0	0
$45$	8.65991	1.29094
$46$	−5.41280	−0.798074
$47$	−8.23070	−1.20057	−0.600285	−	0.799786i	$-0.704946\pi$
$47$	−8.23070	−1.20057	−0.600285	+	0.799786i	$0.704946\pi$
$48$	12.0420	1.73811
$49$	1.00000	0.142857
$50$	2.05277	0.290305
$51$	−9.85854	−1.38047
$52$	8.01552	1.11155
$53$	3.63678	0.499550	0.249775	−	0.968304i	$-0.419643\pi$
$53$	3.63678	0.499550	0.249775	+	0.968304i	$0.419643\pi$
$54$	−39.6731	−5.39883
$55$	0	0
$56$	0.439000	0.0586638
$57$	−25.0924	−3.32357
$58$	−3.37425	−0.443061
$59$	3.29779	0.429336	0.214668	−	0.976687i	$-0.431133\pi$
$59$	3.29779	0.429336	0.214668	+	0.976687i	$0.431133\pi$
$60$	−7.55957	−0.975937
$61$	5.24101	0.671042	0.335521	−	0.942033i	$-0.391088\pi$
$61$	5.24101	0.671042	0.335521	+	0.942033i	$0.391088\pi$
$62$	4.58911	0.582818
$63$	8.65991	1.09105
$64$	−9.60961	−1.20120
$65$	3.62061	0.449082
$66$	0	0
$67$	11.3899	1.39150	0.695748	−	0.718286i	$-0.255073\pi$
$67$	11.3899	1.39150	0.695748	+	0.718286i	$0.255073\pi$
$68$	6.39167	0.775104
$69$	9.00388	1.08394
$70$	2.05277	0.245353
$71$	−7.06381	−0.838320	−0.419160	−	0.907912i	$-0.637675\pi$
$71$	−7.06381	−0.838320	−0.419160	+	0.907912i	$0.637675\pi$
$72$	3.80170	0.448034
$73$	14.2471	1.66749	0.833746	−	0.552148i	$-0.186192\pi$
$73$	14.2471	1.66749	0.833746	+	0.552148i	$0.186192\pi$
$74$	−10.4705	−1.21717
$75$	−3.41466	−0.394291
$76$	16.2684	1.86611
$77$	0	0
$78$	−25.3787	−2.87357
$79$	11.6679	1.31274	0.656371	−	0.754438i	$-0.272091\pi$
$79$	11.6679	1.31274	0.656371	+	0.754438i	$0.272091\pi$
$80$	−3.52655	−0.394280
$81$	40.0142	4.44603
$82$	2.74802	0.303468
$83$	2.48577	0.272849	0.136424	−	0.990650i	$-0.456439\pi$
$83$	2.48577	0.272849	0.136424	+	0.990650i	$0.456439\pi$
$84$	−7.55957	−0.824817
$85$	2.88712	0.313152
$86$	−7.25964	−0.782827
$87$	5.61288	0.601763
$88$	0	0
$89$	12.2946	1.30323	0.651613	−	0.758552i	$-0.274093\pi$
$89$	12.2946	1.30323	0.651613	+	0.758552i	$0.274093\pi$
$90$	17.7768	1.87384
$91$	3.62061	0.379543
$92$	−5.83757	−0.608609
$93$	−7.63372	−0.791580
$94$	−16.8957	−1.74266
$95$	7.34843	0.753933
$96$	27.7174	2.82890
$97$	−4.09831	−0.416121	−0.208060	−	0.978116i	$-0.566715\pi$
$97$	−4.09831	−0.416121	−0.208060	+	0.978116i	$0.566715\pi$
$98$	2.05277	0.207361
$99$	0	0
$100$	2.21386	0.221386
$101$	−3.09592	−0.308056	−0.154028	−	0.988067i	$-0.549225\pi$
$101$	−3.09592	−0.308056	−0.154028	+	0.988067i	$0.549225\pi$
$102$	−20.2373	−2.00379
$103$	−12.6695	−1.24836	−0.624180	−	0.781281i	$-0.714567\pi$
$103$	−12.6695	−1.24836	−0.624180	+	0.781281i	$0.714567\pi$
$104$	1.58945	0.155858
$105$	−3.41466	−0.333237
$106$	7.46546	0.725110
$107$	−0.972927	−0.0940564	−0.0470282	−	0.998894i	$-0.514975\pi$
$107$	−0.972927	−0.0940564	−0.0470282	+	0.998894i	$0.514975\pi$
$108$	−42.7865	−4.11713
$109$	−0.510002	−0.0488493	−0.0244247	−	0.999702i	$-0.507775\pi$
$109$	−0.510002	−0.0488493	−0.0244247	+	0.999702i	$0.507775\pi$
$110$	0	0
$111$	17.4170	1.65315
$112$	−3.52655	−0.333228
$113$	−6.53128	−0.614411	−0.307206	−	0.951643i	$-0.599394\pi$
$113$	−6.53128	−0.614411	−0.307206	+	0.951643i	$0.599394\pi$
$114$	−51.5089	−4.82425
$115$	−2.63683	−0.245886
$116$	−3.63905	−0.337877
$117$	31.3542	2.89869
$118$	6.76960	0.623192
$119$	2.88712	0.264662
$120$	−1.49904	−0.136843
$121$	0	0
$122$	10.7586	0.974036
$123$	−4.57117	−0.412169
$124$	4.94924	0.444455
$125$	1.00000	0.0894427
$126$	17.7768	1.58368
$127$	14.3950	1.27735	0.638676	−	0.769476i	$-0.279482\pi$
$127$	14.3950	1.27735	0.638676	+	0.769476i	$0.279482\pi$
$128$	−3.49192	−0.308645
$129$	12.0760	1.06323
$130$	7.43228	0.651854
$131$	20.1281	1.75860	0.879301	−	0.476266i	$-0.158010\pi$
$131$	20.1281	1.75860	0.879301	+	0.476266i	$0.158010\pi$
$132$	0	0
$133$	7.34843	0.637190
$134$	23.3808	2.01979
$135$	−19.3267	−1.66337
$136$	1.26745	0.108683
$137$	2.95272	0.252268	0.126134	−	0.992013i	$-0.459743\pi$
$137$	2.95272	0.252268	0.126134	+	0.992013i	$0.459743\pi$
$138$	18.4829	1.57337
$139$	−3.08649	−0.261793	−0.130896	−	0.991396i	$-0.541785\pi$
$139$	−3.08649	−0.261793	−0.130896	+	0.991396i	$0.541785\pi$
$140$	2.21386	0.187105
$141$	28.1050	2.36687
$142$	−14.5004	−1.21684
$143$	0	0
$144$	−30.5396	−2.54497
$145$	−1.64376	−0.136507
$146$	29.2459	2.42041
$147$	−3.41466	−0.281636
$148$	−11.2921	−0.928206
$149$	−1.09409	−0.0896314	−0.0448157	−	0.998995i	$-0.514270\pi$
$149$	−1.09409	−0.0896314	−0.0448157	+	0.998995i	$0.514270\pi$
$150$	−7.00951	−0.572324
$151$	−16.0282	−1.30435	−0.652176	−	0.758067i	$-0.726144\pi$
$151$	−16.0282	−1.30435	−0.652176	+	0.758067i	$0.726144\pi$
$152$	3.22596	0.261660
$153$	25.0022	2.02131
$154$	0	0
$155$	2.23557	0.179565
$156$	−27.3703	−2.19138
$157$	19.8727	1.58602	0.793009	−	0.609210i	$-0.208514\pi$
$157$	19.8727	1.58602	0.793009	+	0.609210i	$0.208514\pi$
$158$	23.9515	1.90548
$159$	−12.4184	−0.984840
$160$	−8.11719	−0.641720
$161$	−2.63683	−0.207811
$162$	82.1400	6.45353
$163$	0.984290	0.0770955	0.0385478	−	0.999257i	$-0.487727\pi$
$163$	0.984290	0.0770955	0.0385478	+	0.999257i	$0.487727\pi$
$164$	2.96367	0.231424
$165$	0	0
$166$	5.10271	0.396047
$167$	−0.454829	−0.0351958	−0.0175979	−	0.999845i	$-0.505602\pi$
$167$	−0.454829	−0.0351958	−0.0175979	+	0.999845i	$0.505602\pi$
$168$	−1.49904	−0.115653
$169$	0.108845	0.00837266
$170$	5.92659	0.454549
$171$	63.6367	4.86642
$172$	−7.82934	−0.596981
$173$	6.05026	0.459993	0.229996	−	0.973191i	$-0.426129\pi$
$173$	6.05026	0.459993	0.229996	+	0.973191i	$0.426129\pi$
$174$	11.5219	0.873475
$175$	1.00000	0.0755929
$176$	0	0
$177$	−11.2608	−0.846416
$178$	25.2380	1.89167
$179$	−9.09077	−0.679476	−0.339738	−	0.940520i	$-0.610338\pi$
$179$	−9.09077	−0.679476	−0.339738	+	0.940520i	$0.610338\pi$
$180$	19.1718	1.42898
$181$	18.1280	1.34744	0.673722	−	0.738985i	$-0.264695\pi$
$181$	18.1280	1.34744	0.673722	+	0.738985i	$0.264695\pi$
$182$	7.43228	0.550917
$183$	−17.8963	−1.32293
$184$	−1.15757	−0.0853371
$185$	−5.10065	−0.375007
$186$	−15.6703	−1.14900
$187$	0	0
$188$	−18.2216	−1.32895
$189$	−19.3267	−1.40581
$190$	15.0846	1.09435
$191$	−19.0963	−1.38176	−0.690879	−	0.722970i	$-0.742776\pi$
$191$	−19.0963	−1.38176	−0.690879	+	0.722970i	$0.742776\pi$
$192$	32.8136	2.36811
$193$	3.83708	0.276199	0.138100	−	0.990418i	$-0.455901\pi$
$193$	3.83708	0.276199	0.138100	+	0.990418i	$0.455901\pi$
$194$	−8.41289	−0.604010
$195$	−12.3632	−0.885345
$196$	2.21386	0.158133
$197$	0.975042	0.0694688	0.0347344	−	0.999397i	$-0.488941\pi$
$197$	0.975042	0.0694688	0.0347344	+	0.999397i	$0.488941\pi$
$198$	0	0
$199$	−14.5484	−1.03131	−0.515653	−	0.856798i	$-0.672451\pi$
$199$	−14.5484	−1.03131	−0.515653	+	0.856798i	$0.672451\pi$
$200$	0.439000	0.0310420
$201$	−38.8926	−2.74327
$202$	−6.35521	−0.447151
$203$	−1.64376	−0.115369
$204$	−21.8254	−1.52808
$205$	1.33869	0.0934982
$206$	−26.0075	−1.81203
$207$	−22.8347	−1.58712
$208$	−12.7683	−0.885321
$209$	0	0
$210$	−7.00951	−0.483702
$211$	8.10145	0.557727	0.278864	−	0.960331i	$-0.410042\pi$
$211$	8.10145	0.557727	0.278864	+	0.960331i	$0.410042\pi$
$212$	8.05131	0.552966
$213$	24.1205	1.65271
$214$	−1.99719	−0.136525
$215$	−3.53651	−0.241188
$216$	−8.48440	−0.577290
$217$	2.23557	0.151760
$218$	−1.04692	−0.0709061
$219$	−48.6489	−3.28739
$220$	0	0
$221$	10.4531	0.703155
$222$	35.7530	2.39959
$223$	29.1237	1.95027	0.975133	−	0.221620i	$-0.0711344\pi$
$223$	29.1237	1.95027	0.975133	+	0.221620i	$0.0711344\pi$
$224$	−8.11719	−0.542353
$225$	8.65991	0.577327
$226$	−13.4072	−0.891834
$227$	−9.65935	−0.641114	−0.320557	−	0.947229i	$-0.603870\pi$
$227$	−9.65935	−0.641114	−0.320557	+	0.947229i	$0.603870\pi$
$228$	−55.5510	−3.67896
$229$	12.6572	0.836409	0.418204	−	0.908353i	$-0.362660\pi$
$229$	12.6572	0.836409	0.418204	+	0.908353i	$0.362660\pi$
$230$	−5.41280	−0.356910
$231$	0	0
$232$	−0.721610	−0.0473760
$233$	−12.3843	−0.811324	−0.405662	−	0.914023i	$-0.632959\pi$
$233$	−12.3843	−0.811324	−0.405662	+	0.914023i	$0.632959\pi$
$234$	64.3629	4.20753
$235$	−8.23070	−0.536911
$236$	7.30084	0.475244
$237$	−39.8419	−2.58801
$238$	5.92659	0.384164
$239$	13.6120	0.880487	0.440244	−	0.897878i	$-0.354892\pi$
$239$	13.6120	0.880487	0.440244	+	0.897878i	$0.354892\pi$
$240$	12.0420	0.777306
$241$	29.9636	1.93012	0.965062	−	0.262021i	$-0.0843888\pi$
$241$	29.9636	1.93012	0.965062	+	0.262021i	$0.0843888\pi$
$242$	0	0
$243$	−78.6551	−5.04573
$244$	11.6028	0.742796
$245$	1.00000	0.0638877
$246$	−9.38356	−0.598274
$247$	26.6058	1.69289
$248$	0.981416	0.0623200
$249$	−8.48807	−0.537909
$250$	2.05277	0.129828
$251$	−7.64817	−0.482748	−0.241374	−	0.970432i	$-0.577598\pi$
$251$	−7.64817	−0.482748	−0.241374	+	0.970432i	$0.577598\pi$
$252$	19.1718	1.20771
$253$	0	0
$254$	29.5496	1.85411
$255$	−9.85854	−0.617366
$256$	12.0511	0.753194
$257$	11.9266	0.743961	0.371980	−	0.928241i	$-0.378679\pi$
$257$	11.9266	0.743961	0.371980	+	0.928241i	$0.378679\pi$
$258$	24.7892	1.54331
$259$	−5.10065	−0.316939
$260$	8.01552	0.497102
$261$	−14.2348	−0.881111
$262$	41.3184	2.55266
$263$	6.21516	0.383243	0.191621	−	0.981469i	$-0.438625\pi$
$263$	6.21516	0.383243	0.191621	+	0.981469i	$0.438625\pi$
$264$	0	0
$265$	3.63678	0.223405
$266$	15.0846	0.924898
$267$	−41.9819	−2.56925
$268$	25.2156	1.54029
$269$	4.81784	0.293749	0.146874	−	0.989155i	$-0.453079\pi$
$269$	4.81784	0.293749	0.146874	+	0.989155i	$0.453079\pi$
$270$	−39.6731	−2.41443
$271$	12.8003	0.777564	0.388782	−	0.921330i	$-0.372896\pi$
$271$	12.8003	0.777564	0.388782	+	0.921330i	$0.372896\pi$
$272$	−10.1816	−0.617349
$273$	−12.3632	−0.748253
$274$	6.06124	0.366173
$275$	0	0
$276$	19.9333	1.19984
$277$	−12.4528	−0.748218	−0.374109	−	0.927385i	$-0.622051\pi$
$277$	−12.4528	−0.748218	−0.374109	+	0.927385i	$0.622051\pi$
$278$	−6.33585	−0.379999
$279$	19.3598	1.15904
$280$	0.439000	0.0262353
$281$	23.7586	1.41732	0.708659	−	0.705551i	$-0.249300\pi$
$281$	23.7586	1.41732	0.708659	+	0.705551i	$0.249300\pi$
$282$	57.6931	3.43558
$283$	−6.52778	−0.388036	−0.194018	−	0.980998i	$-0.562152\pi$
$283$	−6.52778	−0.388036	−0.194018	+	0.980998i	$0.562152\pi$
$284$	−15.6383	−0.927960
$285$	−25.0924	−1.48635
$286$	0	0
$287$	1.33869	0.0790204
$288$	−70.2941	−4.14212
$289$	−8.66453	−0.509678
$290$	−3.37425	−0.198143
$291$	13.9943	0.820363
$292$	31.5410	1.84580
$293$	6.16199	0.359987	0.179994	−	0.983668i	$-0.442392\pi$
$293$	6.16199	0.359987	0.179994	+	0.983668i	$0.442392\pi$
$294$	−7.00951	−0.408803
$295$	3.29779	0.192005
$296$	−2.23919	−0.130150
$297$	0	0
$298$	−2.24591	−0.130102
$299$	−9.54695	−0.552114
$300$	−7.55957	−0.436452
$301$	−3.53651	−0.203841
$302$	−32.9021	−1.89330
$303$	10.5715	0.607318
$304$	−25.9146	−1.48631
$305$	5.24101	0.300099
$306$	51.3237	2.93398
$307$	−2.86349	−0.163428	−0.0817140	−	0.996656i	$-0.526039\pi$
$307$	−2.86349	−0.163428	−0.0817140	+	0.996656i	$0.526039\pi$
$308$	0	0
$309$	43.2619	2.46108
$310$	4.58911	0.260644
$311$	−28.8173	−1.63408	−0.817039	−	0.576582i	$-0.804386\pi$
$311$	−28.8173	−1.63408	−0.817039	+	0.576582i	$0.804386\pi$
$312$	−5.42743	−0.307268
$313$	−8.30975	−0.469695	−0.234847	−	0.972032i	$-0.575459\pi$
$313$	−8.30975	−0.469695	−0.234847	+	0.972032i	$0.575459\pi$
$314$	40.7941	2.30215
$315$	8.65991	0.487930
$316$	25.8311	1.45311
$317$	0.121826	0.00684246	0.00342123	−	0.999994i	$-0.498911\pi$
$317$	0.121826	0.00684246	0.00342123	+	0.999994i	$0.498911\pi$
$318$	−25.4920	−1.42952
$319$	0	0
$320$	−9.60961	−0.537194
$321$	3.32222	0.185428
$322$	−5.41280	−0.301644
$323$	21.2158	1.18048
$324$	88.5858	4.92144
$325$	3.62061	0.200836
$326$	2.02052	0.111906
$327$	1.74148	0.0963042
$328$	0.587685	0.0324495
$329$	−8.23070	−0.453773
$330$	0	0
$331$	10.0982	0.555049	0.277524	−	0.960719i	$-0.410486\pi$
$331$	10.0982	0.555049	0.277524	+	0.960719i	$0.410486\pi$
$332$	5.50315	0.302024
$333$	−44.1711	−2.42056
$334$	−0.933660	−0.0510876
$335$	11.3899	0.622296
$336$	12.0420	0.656943
$337$	5.64375	0.307435	0.153717	−	0.988115i	$-0.450875\pi$
$337$	5.64375	0.307435	0.153717	+	0.988115i	$0.450875\pi$
$338$	0.223433	0.0121531
$339$	22.3021	1.21128
$340$	6.39167	0.346637
$341$	0	0
$342$	130.631	7.06374
$343$	1.00000	0.0539949
$344$	−1.55253	−0.0837068
$345$	9.00388	0.484753
$346$	12.4198	0.667691
$347$	5.92282	0.317954	0.158977	−	0.987282i	$-0.449181\pi$
$347$	5.92282	0.317954	0.158977	+	0.987282i	$0.449181\pi$
$348$	12.4261	0.666109
$349$	−7.91529	−0.423696	−0.211848	−	0.977303i	$-0.567948\pi$
$349$	−7.91529	−0.423696	−0.211848	+	0.977303i	$0.567948\pi$
$350$	2.05277	0.109725
$351$	−69.9744	−3.73495
$352$	0	0
$353$	2.72978	0.145291	0.0726457	−	0.997358i	$-0.476856\pi$
$353$	2.72978	0.145291	0.0726457	+	0.997358i	$0.476856\pi$
$354$	−23.1159	−1.22860
$355$	−7.06381	−0.374908
$356$	27.2185	1.44258
$357$	−9.85854	−0.521769
$358$	−18.6613	−0.986278
$359$	18.6375	0.983651	0.491825	−	0.870694i	$-0.336330\pi$
$359$	18.6375	0.983651	0.491825	+	0.870694i	$0.336330\pi$
$360$	3.80170	0.200367
$361$	34.9995	1.84208
$362$	37.2126	1.95585
$363$	0	0
$364$	8.01552	0.420128
$365$	14.2471	0.745725
$366$	−36.7369	−1.92027
$367$	−23.2090	−1.21150	−0.605751	−	0.795654i	$-0.707127\pi$
$367$	−23.2090	−1.21150	−0.605751	+	0.795654i	$0.707127\pi$
$368$	9.29892	0.484740
$369$	11.5929	0.603504
$370$	−10.4705	−0.544333
$371$	3.63678	0.188812
$372$	−16.9000	−0.876222
$373$	−16.1484	−0.836131	−0.418066	−	0.908417i	$-0.637292\pi$
$373$	−16.1484	−0.836131	−0.418066	+	0.908417i	$0.637292\pi$
$374$	0	0
$375$	−3.41466	−0.176332
$376$	−3.61328	−0.186340
$377$	−5.95141	−0.306513
$378$	−39.6731	−2.04057
$379$	32.2523	1.65669	0.828345	−	0.560218i	$-0.189283\pi$
$379$	32.2523	1.65669	0.828345	+	0.560218i	$0.189283\pi$
$380$	16.2684	0.834551
$381$	−49.1541	−2.51824
$382$	−39.2002	−2.00566
$383$	−19.4115	−0.991881	−0.495941	−	0.868356i	$-0.665177\pi$
$383$	−19.4115	−0.991881	−0.495941	+	0.868356i	$0.665177\pi$
$384$	11.9237	0.608480
$385$	0	0
$386$	7.87664	0.400910
$387$	−30.6259	−1.55680
$388$	−9.07308	−0.460616
$389$	27.5708	1.39789	0.698946	−	0.715174i	$-0.253653\pi$
$389$	27.5708	1.39789	0.698946	+	0.715174i	$0.253653\pi$
$390$	−25.3787	−1.28510
$391$	−7.61285	−0.384998
$392$	0.439000	0.0221728
$393$	−68.7307	−3.46701
$394$	2.00153	0.100836
$395$	11.6679	0.587076
$396$	0	0
$397$	0.919494	0.0461481	0.0230740	−	0.999734i	$-0.492655\pi$
$397$	0.919494	0.0461481	0.0230740	+	0.999734i	$0.492655\pi$
$398$	−29.8644	−1.49697
$399$	−25.0924	−1.25619
$400$	−3.52655	−0.176327
$401$	−18.2169	−0.909707	−0.454854	−	0.890566i	$-0.650308\pi$
$401$	−18.2169	−0.909707	−0.454854	+	0.890566i	$0.650308\pi$
$402$	−79.8375	−3.98193
$403$	8.09414	0.403198
$404$	−6.85393	−0.340996
$405$	40.0142	1.98832
$406$	−3.37425	−0.167461
$407$	0	0
$408$	−4.32790	−0.214263
$409$	−13.3251	−0.658885	−0.329443	−	0.944176i	$-0.606861\pi$
$409$	−13.3251	−0.658885	−0.329443	+	0.944176i	$0.606861\pi$
$410$	2.74802	0.135715
$411$	−10.0825	−0.497334
$412$	−28.0484	−1.38185
$413$	3.29779	0.162274
$414$	−46.8744	−2.30375
$415$	2.48577	0.122022
$416$	−29.3892	−1.44092
$417$	10.5393	0.516112
$418$	0	0
$419$	−11.9359	−0.583109	−0.291554	−	0.956554i	$-0.594172\pi$
$419$	−11.9359	−0.583109	−0.291554	+	0.956554i	$0.594172\pi$
$420$	−7.55957	−0.368869
$421$	9.93600	0.484251	0.242126	−	0.970245i	$-0.422155\pi$
$421$	9.93600	0.484251	0.242126	+	0.970245i	$0.422155\pi$
$422$	16.6304	0.809556
$423$	−71.2771	−3.46561
$424$	1.59655	0.0775351
$425$	2.88712	0.140046
$426$	49.5138	2.39895
$427$	5.24101	0.253630
$428$	−2.15392	−0.104114
$429$	0	0
$430$	−7.25964	−0.350091
$431$	22.7547	1.09606	0.548028	−	0.836460i	$-0.315379\pi$
$431$	22.7547	1.09606	0.548028	+	0.836460i	$0.315379\pi$
$432$	68.1564	3.27918
$433$	7.53474	0.362097	0.181048	−	0.983474i	$-0.442051\pi$
$433$	7.53474	0.362097	0.181048	+	0.983474i	$0.442051\pi$
$434$	4.58911	0.220284
$435$	5.61288	0.269117
$436$	−1.12907	−0.0540727
$437$	−19.3766	−0.926907
$438$	−99.8649	−4.77173
$439$	−28.9992	−1.38406	−0.692028	−	0.721870i	$-0.743283\pi$
$439$	−28.9992	−1.38406	−0.692028	+	0.721870i	$0.743283\pi$
$440$	0	0
$441$	8.65991	0.412376
$442$	21.4579	1.02065
$443$	−21.5567	−1.02419	−0.512096	−	0.858928i	$-0.671131\pi$
$443$	−21.5567	−1.02419	−0.512096	+	0.858928i	$0.671131\pi$
$444$	38.5587	1.82992
$445$	12.2946	0.582820
$446$	59.7842	2.83086
$447$	3.73595	0.176704
$448$	−9.60961	−0.454011
$449$	−16.5843	−0.782662	−0.391331	−	0.920250i	$-0.627985\pi$
$449$	−16.5843	−0.782662	−0.391331	+	0.920250i	$0.627985\pi$
$450$	17.7768	0.838005
$451$	0	0
$452$	−14.4593	−0.680110
$453$	54.7307	2.57147
$454$	−19.8284	−0.930594
$455$	3.62061	0.169737
$456$	−11.0156	−0.515851
$457$	−39.2195	−1.83461	−0.917306	−	0.398183i	$-0.869641\pi$
$457$	−39.2195	−1.83461	−0.917306	+	0.398183i	$0.869641\pi$
$458$	25.9822	1.21407
$459$	−55.7984	−2.60445
$460$	−5.83757	−0.272178
$461$	−9.20598	−0.428765	−0.214383	−	0.976750i	$-0.568774\pi$
$461$	−9.20598	−0.428765	−0.214383	+	0.976750i	$0.568774\pi$
$462$	0	0
$463$	29.4609	1.36917	0.684583	−	0.728935i	$-0.259984\pi$
$463$	29.4609	1.36917	0.684583	+	0.728935i	$0.259984\pi$
$464$	5.79679	0.269109
$465$	−7.63372	−0.354005
$466$	−25.4221	−1.17766
$467$	−15.7904	−0.730691	−0.365345	−	0.930872i	$-0.619049\pi$
$467$	−15.7904	−0.730691	−0.365345	+	0.930872i	$0.619049\pi$
$468$	69.4137	3.20865
$469$	11.3899	0.525936
$470$	−16.8957	−0.779341
$471$	−67.8586	−3.12676
$472$	1.44773	0.0666372
$473$	0	0
$474$	−81.7862	−3.75657
$475$	7.34843	0.337169
$476$	6.39167	0.292962
$477$	31.4941	1.44202
$478$	27.9423	1.27805
$479$	−27.3140	−1.24801	−0.624003	−	0.781422i	$-0.714495\pi$
$479$	−27.3140	−1.24801	−0.624003	+	0.781422i	$0.714495\pi$
$480$	27.7174	1.26512
$481$	−18.4675	−0.842045
$482$	61.5083	2.80163
$483$	9.00388	0.409691
$484$	0	0
$485$	−4.09831	−0.186095
$486$	−161.461	−7.32401
$487$	−22.8135	−1.03378	−0.516889	−	0.856053i	$-0.672910\pi$
$487$	−22.8135	−1.03378	−0.516889	+	0.856053i	$0.672910\pi$
$488$	2.30080	0.104152
$489$	−3.36102	−0.151990
$490$	2.05277	0.0927346
$491$	−17.9376	−0.809512	−0.404756	−	0.914425i	$-0.632644\pi$
$491$	−17.9376	−0.809512	−0.404756	+	0.914425i	$0.632644\pi$
$492$	−10.1199	−0.456242
$493$	−4.74573	−0.213737
$494$	54.6156	2.45727
$495$	0	0
$496$	−7.88386	−0.353996
$497$	−7.06381	−0.316855
$498$	−17.4240	−0.780790
$499$	18.0016	0.805860	0.402930	−	0.915231i	$-0.367992\pi$
$499$	18.0016	0.805860	0.402930	+	0.915231i	$0.367992\pi$
$500$	2.21386	0.0990067
$501$	1.55309	0.0693869
$502$	−15.6999	−0.700721
$503$	−24.6493	−1.09906	−0.549529	−	0.835475i	$-0.685193\pi$
$503$	−24.6493	−1.09906	−0.549529	+	0.835475i	$0.685193\pi$
$504$	3.80170	0.169341
$505$	−3.09592	−0.137767
$506$	0	0
$507$	−0.371667	−0.0165063
$508$	31.8685	1.41394
$509$	−0.192470	−0.00853107	−0.00426554	−	0.999991i	$-0.501358\pi$
$509$	−0.192470	−0.00853107	−0.00426554	+	0.999991i	$0.501358\pi$
$510$	−20.2373	−0.896122
$511$	14.2471	0.630253
$512$	31.7220	1.40193
$513$	−142.021	−6.27036
$514$	24.4825	1.07988
$515$	−12.6695	−0.558283
$516$	26.7345	1.17692
$517$	0	0
$518$	−10.4705	−0.460045
$519$	−20.6596	−0.906855
$520$	1.58945	0.0697020
$521$	−14.0294	−0.614639	−0.307319	−	0.951606i	$-0.599432\pi$
$521$	−14.0294	−0.614639	−0.307319	+	0.951606i	$0.599432\pi$
$522$	−29.2207	−1.27896
$523$	−33.5273	−1.46605	−0.733023	−	0.680203i	$-0.761891\pi$
$523$	−33.5273	−1.46605	−0.733023	+	0.680203i	$0.761891\pi$
$524$	44.5608	1.94665
$525$	−3.41466	−0.149028
$526$	12.7583	0.556287
$527$	6.45437	0.281157
$528$	0	0
$529$	−16.0471	−0.697701
$530$	7.46546	0.324279
$531$	28.5586	1.23934
$532$	16.2684	0.705324
$533$	4.84688	0.209942
$534$	−86.1792	−3.72934
$535$	−0.972927	−0.0420633
$536$	5.00016	0.215974
$537$	31.0419	1.33956
$538$	9.88990	0.426384
$539$	0	0
$540$	−42.7865	−1.84124
$541$	−6.53930	−0.281147	−0.140573	−	0.990070i	$-0.544895\pi$
$541$	−6.53930	−0.281147	−0.140573	+	0.990070i	$0.544895\pi$
$542$	26.2761	1.12865
$543$	−61.9010	−2.65642
$544$	−23.4353	−1.00478
$545$	−0.510002	−0.0218461
$546$	−25.3787	−1.08611
$547$	−37.1563	−1.58869	−0.794344	−	0.607469i	$-0.792185\pi$
$547$	−37.1563	−1.58869	−0.794344	+	0.607469i	$0.792185\pi$
$548$	6.53689	0.279242
$549$	45.3866	1.93705
$550$	0	0
$551$	−12.0790	−0.514585
$552$	3.95270	0.168238
$553$	11.6679	0.496170
$554$	−25.5628	−1.08606
$555$	17.4170	0.739310
$556$	−6.83305	−0.289786
$557$	−12.5828	−0.533151	−0.266576	−	0.963814i	$-0.585892\pi$
$557$	−12.5828	−0.533151	−0.266576	+	0.963814i	$0.585892\pi$
$558$	39.7413	1.68238
$559$	−12.8044	−0.541566
$560$	−3.52655	−0.149024
$561$	0	0
$562$	48.7709	2.05727
$563$	−10.6867	−0.450389	−0.225194	−	0.974314i	$-0.572302\pi$
$563$	−10.6867	−0.450389	−0.225194	+	0.974314i	$0.572302\pi$
$564$	62.2205	2.61996
$565$	−6.53128	−0.274773
$566$	−13.4000	−0.563245
$567$	40.0142	1.68044
$568$	−3.10101	−0.130116
$569$	−37.5773	−1.57532	−0.787662	−	0.616108i	$-0.788708\pi$
$569$	−37.5773	−1.57532	−0.787662	+	0.616108i	$0.788708\pi$
$570$	−51.5089	−2.15747
$571$	39.5308	1.65431	0.827156	−	0.561972i	$-0.189957\pi$
$571$	39.5308	1.65431	0.827156	+	0.561972i	$0.189957\pi$
$572$	0	0
$573$	65.2073	2.72407
$574$	2.74802	0.114700
$575$	−2.63683	−0.109963
$576$	−83.2183	−3.46743
$577$	−23.1192	−0.962466	−0.481233	−	0.876593i	$-0.659811\pi$
$577$	−23.1192	−0.962466	−0.481233	+	0.876593i	$0.659811\pi$
$578$	−17.7863	−0.739812
$579$	−13.1023	−0.544514
$580$	−3.63905	−0.151103
$581$	2.48577	0.103127
$582$	28.7271	1.19078
$583$	0	0
$584$	6.25446	0.258811
$585$	31.3542	1.29634
$586$	12.6491	0.522531
$587$	11.1583	0.460552	0.230276	−	0.973125i	$-0.426037\pi$
$587$	11.1583	0.460552	0.230276	+	0.973125i	$0.426037\pi$
$588$	−7.55957	−0.311751
$589$	16.4280	0.676902
$590$	6.76960	0.278700
$591$	−3.32944	−0.136955
$592$	17.9877	0.739290
$593$	3.78090	0.155263	0.0776315	−	0.996982i	$-0.475264\pi$
$593$	3.78090	0.155263	0.0776315	+	0.996982i	$0.475264\pi$
$594$	0	0
$595$	2.88712	0.118360
$596$	−2.42216	−0.0992155
$597$	49.6777	2.03317
$598$	−19.5977	−0.801408
$599$	35.5144	1.45108	0.725539	−	0.688181i	$-0.241591\pi$
$599$	35.5144	1.45108	0.725539	+	0.688181i	$0.241591\pi$
$600$	−1.49904	−0.0611979
$601$	−41.6580	−1.69927	−0.849633	−	0.527375i	$-0.823176\pi$
$601$	−41.6580	−1.69927	−0.849633	+	0.527375i	$0.823176\pi$
$602$	−7.25964	−0.295881
$603$	98.6353	4.01674
$604$	−35.4841	−1.44383
$605$	0	0
$606$	21.7009	0.881538
$607$	−7.06885	−0.286916	−0.143458	−	0.989656i	$-0.545822\pi$
$607$	−7.06885	−0.286916	−0.143458	+	0.989656i	$0.545822\pi$
$608$	−59.6486	−2.41907
$609$	5.61288	0.227445
$610$	10.7586	0.435602
$611$	−29.8002	−1.20559
$612$	55.3513	2.23744
$613$	7.89034	0.318688	0.159344	−	0.987223i	$-0.449062\pi$
$613$	7.89034	0.318688	0.159344	+	0.987223i	$0.449062\pi$
$614$	−5.87808	−0.237220
$615$	−4.57117	−0.184328
$616$	0	0
$617$	−35.3032	−1.42125	−0.710626	−	0.703570i	$-0.751588\pi$
$617$	−35.3032	−1.42125	−0.710626	+	0.703570i	$0.751588\pi$
$618$	88.8067	3.57233
$619$	40.9495	1.64590	0.822949	−	0.568115i	$-0.192327\pi$
$619$	40.9495	1.64590	0.822949	+	0.568115i	$0.192327\pi$
$620$	4.94924	0.198766
$621$	50.9611	2.04500
$622$	−59.1552	−2.37191
$623$	12.2946	0.492573
$624$	43.5993	1.74537
$625$	1.00000	0.0400000
$626$	−17.0580	−0.681774
$627$	0	0
$628$	43.9954	1.75561
$629$	−14.7262	−0.587172
$630$	17.7768	0.708244
$631$	23.3912	0.931187	0.465594	−	0.884999i	$-0.345841\pi$
$631$	23.3912	0.931187	0.465594	+	0.884999i	$0.345841\pi$
$632$	5.12221	0.203751
$633$	−27.6637	−1.09953
$634$	0.250082	0.00993201
$635$	14.3950	0.571249
$636$	−27.4925	−1.09015
$637$	3.62061	0.143454
$638$	0	0
$639$	−61.1719	−2.41992
$640$	−3.49192	−0.138030
$641$	21.4775	0.848308	0.424154	−	0.905590i	$-0.360571\pi$
$641$	21.4775	0.848308	0.424154	+	0.905590i	$0.360571\pi$
$642$	6.81974	0.269154
$643$	33.9943	1.34061	0.670303	−	0.742088i	$-0.266164\pi$
$643$	33.9943	1.34061	0.670303	+	0.742088i	$0.266164\pi$
$644$	−5.83757	−0.230032
$645$	12.0760	0.475492
$646$	43.5512	1.71350
$647$	12.3600	0.485921	0.242961	−	0.970036i	$-0.421881\pi$
$647$	12.3600	0.485921	0.242961	+	0.970036i	$0.421881\pi$
$648$	17.5663	0.690068
$649$	0	0
$650$	7.43228	0.291518
$651$	−7.63372	−0.299189
$652$	2.17908	0.0853393
$653$	−6.63157	−0.259513	−0.129757	−	0.991546i	$-0.541420\pi$
$653$	−6.63157	−0.259513	−0.129757	+	0.991546i	$0.541420\pi$
$654$	3.57486	0.139788
$655$	20.1281	0.786471
$656$	−4.72096	−0.184323
$657$	123.378	4.81344
$658$	−16.8957	−0.658663
$659$	27.6637	1.07763	0.538813	−	0.842425i	$-0.318873\pi$
$659$	27.6637	1.07763	0.538813	+	0.842425i	$0.318873\pi$
$660$	0	0
$661$	9.69875	0.377238	0.188619	−	0.982050i	$-0.439599\pi$
$661$	9.69875	0.377238	0.188619	+	0.982050i	$0.439599\pi$
$662$	20.7293	0.805668
$663$	−35.6940	−1.38624
$664$	1.09125	0.0423489
$665$	7.34843	0.284960
$666$	−90.6731	−3.51351
$667$	4.33431	0.167825
$668$	−1.00693	−0.0389592
$669$	−99.4475	−3.84486
$670$	23.3808	0.903279
$671$	0	0
$672$	27.7174	1.06922
$673$	5.05941	0.195026	0.0975130	−	0.995234i	$-0.468911\pi$
$673$	5.05941	0.195026	0.0975130	+	0.995234i	$0.468911\pi$
$674$	11.5853	0.446249
$675$	−19.3267	−0.743883
$676$	0.240966	0.00926794
$677$	5.91376	0.227284	0.113642	−	0.993522i	$-0.463748\pi$
$677$	5.91376	0.227284	0.113642	+	0.993522i	$0.463748\pi$
$678$	45.7811	1.75821
$679$	−4.09831	−0.157279
$680$	1.26745	0.0486043
$681$	32.9834	1.26393
$682$	0	0
$683$	−35.8274	−1.37090	−0.685449	−	0.728121i	$-0.740394\pi$
$683$	−35.8274	−1.37090	−0.685449	+	0.728121i	$0.740394\pi$
$684$	140.883	5.38678
$685$	2.95272	0.112817
$686$	2.05277	0.0783751
$687$	−43.2199	−1.64894
$688$	12.4717	0.475479
$689$	13.1674	0.501637
$690$	18.4829	0.703631
$691$	−39.4988	−1.50261	−0.751303	−	0.659957i	$-0.770574\pi$
$691$	−39.4988	−1.50261	−0.751303	+	0.659957i	$0.770574\pi$
$692$	13.3944	0.509179
$693$	0	0
$694$	12.1582	0.461518
$695$	−3.08649	−0.117077
$696$	2.46405	0.0933997
$697$	3.86496	0.146396
$698$	−16.2483	−0.615005
$699$	42.2883	1.59949
$700$	2.21386	0.0836760
$701$	46.6876	1.76337	0.881683	−	0.471843i	$-0.156411\pi$
$701$	46.6876	1.76337	0.881683	+	0.471843i	$0.156411\pi$
$702$	−143.641	−5.42139
$703$	−37.4818	−1.41365
$704$	0	0
$705$	28.1050	1.05850
$706$	5.60360	0.210894
$707$	−3.09592	−0.116434
$708$	−24.9299	−0.936923
$709$	−29.7335	−1.11667	−0.558333	−	0.829617i	$-0.688559\pi$
$709$	−29.7335	−1.11667	−0.558333	+	0.829617i	$0.688559\pi$
$710$	−14.5004	−0.544189
$711$	101.043	3.78941
$712$	5.39733	0.202274
$713$	−5.89482	−0.220763
$714$	−20.2373	−0.757362
$715$	0	0
$716$	−20.1257	−0.752132
$717$	−46.4804	−1.73584
$718$	38.2585	1.42779
$719$	44.7035	1.66716	0.833579	−	0.552400i	$-0.186288\pi$
$719$	44.7035	1.66716	0.833579	+	0.552400i	$0.186288\pi$
$720$	−30.5396	−1.13814
$721$	−12.6695	−0.471836
$722$	71.8458	2.67382
$723$	−102.315	−3.80515
$724$	40.1328	1.49152
$725$	−1.64376	−0.0610476
$726$	0	0
$727$	−4.00410	−0.148504	−0.0742519	−	0.997240i	$-0.523657\pi$
$727$	−4.00410	−0.148504	−0.0742519	+	0.997240i	$0.523657\pi$
$728$	1.58945	0.0589089
$729$	148.538	5.50140
$730$	29.2459	1.08244
$731$	−10.2103	−0.377643
$732$	−39.6198	−1.46439
$733$	30.3850	1.12230	0.561148	−	0.827715i	$-0.310360\pi$
$733$	30.3850	1.12230	0.561148	+	0.827715i	$0.310360\pi$
$734$	−47.6428	−1.75853
$735$	−3.41466	−0.125952
$736$	21.4037	0.788949
$737$	0	0
$738$	23.7976	0.876002
$739$	14.0155	0.515568	0.257784	−	0.966203i	$-0.417008\pi$
$739$	14.0155	0.515568	0.257784	+	0.966203i	$0.417008\pi$
$740$	−11.2921	−0.415106
$741$	−90.8499	−3.33745
$742$	7.46546	0.274066
$743$	−30.7334	−1.12750	−0.563750	−	0.825945i	$-0.690642\pi$
$743$	−30.7334	−1.12750	−0.563750	+	0.825945i	$0.690642\pi$
$744$	−3.35120	−0.122861
$745$	−1.09409	−0.0400844
$746$	−33.1489	−1.21367
$747$	21.5266	0.787615
$748$	0	0
$749$	−0.972927	−0.0355500
$750$	−7.00951	−0.255951
$751$	−8.07310	−0.294591	−0.147296	−	0.989092i	$-0.547057\pi$
$751$	−8.07310	−0.294591	−0.147296	+	0.989092i	$0.547057\pi$
$752$	29.0260	1.05847
$753$	26.1159	0.951716
$754$	−12.2169	−0.444912
$755$	−16.0282	−0.583324
$756$	−42.7865	−1.55613
$757$	−16.8540	−0.612568	−0.306284	−	0.951940i	$-0.599086\pi$
$757$	−16.8540	−0.612568	−0.306284	+	0.951940i	$0.599086\pi$
$758$	66.2065	2.40473
$759$	0	0
$760$	3.22596	0.117018
$761$	21.4483	0.777500	0.388750	−	0.921343i	$-0.372907\pi$
$761$	21.4483	0.777500	0.388750	+	0.921343i	$0.372907\pi$
$762$	−100.902	−3.65529
$763$	−0.510002	−0.0184633
$764$	−42.2765	−1.52951
$765$	25.0022	0.903956
$766$	−39.8473	−1.43974
$767$	11.9400	0.431129
$768$	−41.1505	−1.48489
$769$	0.783202	0.0282430	0.0141215	−	0.999900i	$-0.495505\pi$
$769$	0.783202	0.0282430	0.0141215	+	0.999900i	$0.495505\pi$
$770$	0	0
$771$	−40.7253	−1.46669
$772$	8.49475	0.305733
$773$	38.0824	1.36973	0.684864	−	0.728671i	$-0.259861\pi$
$773$	38.0824	1.36973	0.684864	+	0.728671i	$0.259861\pi$
$774$	−62.8678	−2.25974
$775$	2.23557	0.0803041
$776$	−1.79916	−0.0645860
$777$	17.4170	0.624831
$778$	56.5964	2.02908
$779$	9.83728	0.352457
$780$	−27.3703	−0.980014
$781$	0	0
$782$	−15.6274	−0.558835
$783$	31.7683	1.13531
$784$	−3.52655	−0.125948
$785$	19.8727	0.709288
$786$	−141.088	−5.03245
$787$	3.94183	0.140511	0.0702556	−	0.997529i	$-0.477619\pi$
$787$	3.94183	0.140511	0.0702556	+	0.997529i	$0.477619\pi$
$788$	2.15860	0.0768970
$789$	−21.2226	−0.755546
$790$	23.9515	0.852156
$791$	−6.53128	−0.232226
$792$	0	0
$793$	18.9757	0.673846
$794$	1.88751	0.0669852
$795$	−12.4184	−0.440434
$796$	−32.2080	−1.14158
$797$	30.4634	1.07907	0.539535	−	0.841963i	$-0.318600\pi$
$797$	30.4634	1.07907	0.539535	+	0.841963i	$0.318600\pi$
$798$	−51.5089	−1.82340
$799$	−23.7630	−0.840675
$800$	−8.11719	−0.286986
$801$	106.470	3.76194
$802$	−37.3950	−1.32046
$803$	0	0
$804$	−86.1026	−3.03661
$805$	−2.63683	−0.0929361
$806$	16.6154	0.585252
$807$	−16.4513	−0.579112
$808$	−1.35911	−0.0478133
$809$	−14.5471	−0.511449	−0.255725	−	0.966750i	$-0.582314\pi$
$809$	−14.5471	−0.511449	−0.255725	+	0.966750i	$0.582314\pi$
$810$	82.1400	2.88610
$811$	−11.3095	−0.397131	−0.198566	−	0.980088i	$-0.563628\pi$
$811$	−11.3095	−0.397131	−0.198566	+	0.980088i	$0.563628\pi$
$812$	−3.63905	−0.127705
$813$	−43.7087	−1.53293
$814$	0	0
$815$	0.984290	0.0344782
$816$	34.7666	1.21708
$817$	−25.9878	−0.909199
$818$	−27.3534	−0.956390
$819$	31.3542	1.09560
$820$	2.96367	0.103496
$821$	34.1303	1.19116	0.595578	−	0.803298i	$-0.296923\pi$
$821$	34.1303	1.19116	0.595578	+	0.803298i	$0.296923\pi$
$822$	−20.6971	−0.721894
$823$	−1.39105	−0.0484890	−0.0242445	−	0.999706i	$-0.507718\pi$
$823$	−1.39105	−0.0484890	−0.0242445	+	0.999706i	$0.507718\pi$
$824$	−5.56190	−0.193758
$825$	0	0
$826$	6.76960	0.235545
$827$	−50.2410	−1.74705	−0.873525	−	0.486780i	$-0.838171\pi$
$827$	−50.2410	−1.74705	−0.873525	+	0.486780i	$0.838171\pi$
$828$	−50.5528	−1.75683
$829$	−27.6620	−0.960741	−0.480370	−	0.877066i	$-0.659498\pi$
$829$	−27.6620	−0.960741	−0.480370	+	0.877066i	$0.659498\pi$
$830$	5.10271	0.177118
$831$	42.5222	1.47508
$832$	−34.7927	−1.20622
$833$	2.88712	0.100033
$834$	21.6348	0.749151
$835$	−0.454829	−0.0157400
$836$	0	0
$837$	−43.2061	−1.49342
$838$	−24.5017	−0.846398
$839$	32.8681	1.13473	0.567366	−	0.823466i	$-0.307963\pi$
$839$	32.8681	1.13473	0.567366	+	0.823466i	$0.307963\pi$
$840$	−1.49904	−0.0517217
$841$	−26.2981	−0.906830
$842$	20.3963	0.702903
$843$	−81.1275	−2.79418
$844$	17.9355	0.617364
$845$	0.108845	0.00374437
$846$	−146.315	−5.03042
$847$	0	0
$848$	−12.8253	−0.440422
$849$	22.2901	0.764996
$850$	5.92659	0.203280
$851$	13.4496	0.461045
$852$	53.3994	1.82943
$853$	27.8075	0.952112	0.476056	−	0.879415i	$-0.342066\pi$
$853$	27.8075	0.952112	0.476056	+	0.879415i	$0.342066\pi$
$854$	10.7586	0.368151
$855$	63.6367	2.17633
$856$	−0.427115	−0.0145985
$857$	−23.8428	−0.814454	−0.407227	−	0.913327i	$-0.633504\pi$
$857$	−23.8428	−0.814454	−0.407227	+	0.913327i	$0.633504\pi$
$858$	0	0
$859$	49.1450	1.67681	0.838403	−	0.545051i	$-0.183490\pi$
$859$	49.1450	1.67681	0.838403	+	0.545051i	$0.183490\pi$
$860$	−7.82934	−0.266978
$861$	−4.57117	−0.155785
$862$	46.7102	1.59095
$863$	27.5492	0.937786	0.468893	−	0.883255i	$-0.344653\pi$
$863$	27.5492	0.937786	0.468893	+	0.883255i	$0.344653\pi$
$864$	156.878	5.33710
$865$	6.05026	0.205715
$866$	15.4671	0.525593
$867$	29.5864	1.00481
$868$	4.94924	0.167988
$869$	0	0
$870$	11.5219	0.390630
$871$	41.2384	1.39731
$872$	−0.223891	−0.00758190
$873$	−35.4910	−1.20119
$874$	−39.7756	−1.34543
$875$	1.00000	0.0338062
$876$	−107.702	−3.63890
$877$	−10.4989	−0.354522	−0.177261	−	0.984164i	$-0.556724\pi$
$877$	−10.4989	−0.354522	−0.177261	+	0.984164i	$0.556724\pi$
$878$	−59.5287	−2.00900
$879$	−21.0411	−0.709699
$880$	0	0
$881$	−43.3016	−1.45887	−0.729434	−	0.684051i	$-0.760216\pi$
$881$	−43.3016	−1.45887	−0.729434	+	0.684051i	$0.760216\pi$
$882$	17.7768	0.598575
$883$	−52.5979	−1.77006	−0.885031	−	0.465532i	$-0.845863\pi$
$883$	−52.5979	−1.77006	−0.885031	+	0.465532i	$0.845863\pi$
$884$	23.1418	0.778342
$885$	−11.2608	−0.378529
$886$	−44.2510	−1.48664
$887$	−46.2964	−1.55448	−0.777240	−	0.629204i	$-0.783381\pi$
$887$	−46.2964	−1.55448	−0.777240	+	0.629204i	$0.783381\pi$
$888$	7.64606	0.256585
$889$	14.3950	0.482794
$890$	25.2380	0.845979
$891$	0	0
$892$	64.4757	2.15881
$893$	−60.4827	−2.02398
$894$	7.66903	0.256491
$895$	−9.09077	−0.303871
$896$	−3.49192	−0.116657
$897$	32.5996	1.08847
$898$	−34.0437	−1.13605
$899$	−3.67474	−0.122559
$900$	19.1718	0.639060
$901$	10.4998	0.349800
$902$	0	0
$903$	12.0760	0.401864
$904$	−2.86723	−0.0953627
$905$	18.1280	0.602595
$906$	112.349	3.73256
$907$	6.10483	0.202707	0.101354	−	0.994850i	$-0.467683\pi$
$907$	6.10483	0.202707	0.101354	+	0.994850i	$0.467683\pi$
$908$	−21.3844	−0.709667
$909$	−26.8104	−0.889244
$910$	7.43228	0.246378
$911$	−53.7679	−1.78141	−0.890706	−	0.454580i	$-0.849789\pi$
$911$	−53.7679	−1.78141	−0.890706	+	0.454580i	$0.849789\pi$
$912$	88.4896	2.93018
$913$	0	0
$914$	−80.5086	−2.66299
$915$	−17.8963	−0.591632
$916$	28.0211	0.925845
$917$	20.1281	0.664689
$918$	−114.541	−3.78042
$919$	11.1366	0.367362	0.183681	−	0.982986i	$-0.441199\pi$
$919$	11.1366	0.367362	0.183681	+	0.982986i	$0.441199\pi$
$920$	−1.15757	−0.0381639
$921$	9.77784	0.322191
$922$	−18.8977	−0.622364
$923$	−25.5753	−0.841822
$924$	0	0
$925$	−5.10065	−0.167708
$926$	60.4765	1.98738
$927$	−109.716	−3.60356
$928$	13.3427	0.437995
$929$	17.3169	0.568149	0.284074	−	0.958802i	$-0.408314\pi$
$929$	17.3169	0.568149	0.284074	+	0.958802i	$0.408314\pi$
$930$	−15.6703	−0.513848
$931$	7.34843	0.240835
$932$	−27.4171	−0.898078
$933$	98.4012	3.22151
$934$	−32.4140	−1.06062
$935$	0	0
$936$	13.7645	0.449906
$937$	34.3205	1.12120	0.560600	−	0.828086i	$-0.310570\pi$
$937$	34.3205	1.12120	0.560600	+	0.828086i	$0.310570\pi$
$938$	23.3808	0.763410
$939$	28.3750	0.925982
$940$	−18.2216	−0.594323
$941$	32.0426	1.04456	0.522280	−	0.852774i	$-0.325082\pi$
$941$	32.0426	1.04456	0.522280	+	0.852774i	$0.325082\pi$
$942$	−139.298	−4.53858
$943$	−3.52990	−0.114949
$944$	−11.6298	−0.378519
$945$	−19.3267	−0.628696
$946$	0	0
$947$	−41.8639	−1.36039	−0.680197	−	0.733029i	$-0.738106\pi$
$947$	−41.8639	−1.36039	−0.680197	+	0.733029i	$0.738106\pi$
$948$	−88.2043	−2.86474
$949$	51.5831	1.67446
$950$	15.0846	0.489410
$951$	−0.415996	−0.0134896
$952$	1.26745	0.0410782
$953$	41.0583	1.33001	0.665004	−	0.746840i	$-0.268430\pi$
$953$	41.0583	1.33001	0.665004	+	0.746840i	$0.268430\pi$
$954$	64.6502	2.09313
$955$	−19.0963	−0.617941
$956$	30.1350	0.974636
$957$	0	0
$958$	−56.0692	−1.81151
$959$	2.95272	0.0953482
$960$	32.8136	1.05905
$961$	−26.0022	−0.838781
$962$	−37.9095	−1.22225
$963$	−8.42546	−0.271507
$964$	66.3351	2.13651
$965$	3.83708	0.123520
$966$	18.4829	0.594677
$967$	3.02655	0.0973273	0.0486637	−	0.998815i	$-0.484504\pi$
$967$	3.02655	0.0973273	0.0486637	+	0.998815i	$0.484504\pi$
$968$	0	0
$969$	−72.4448	−2.32726
$970$	−8.41289	−0.270121
$971$	−8.81486	−0.282882	−0.141441	−	0.989947i	$-0.545174\pi$
$971$	−8.81486	−0.282882	−0.141441	+	0.989947i	$0.545174\pi$
$972$	−174.131	−5.58526
$973$	−3.08649	−0.0989483
$974$	−46.8308	−1.50055
$975$	−12.3632	−0.395938
$976$	−18.4827	−0.591616
$977$	−9.76858	−0.312525	−0.156262	−	0.987716i	$-0.549945\pi$
$977$	−9.76858	−0.312525	−0.156262	+	0.987716i	$0.549945\pi$
$978$	−6.89939	−0.220618
$979$	0	0
$980$	2.21386	0.0707191
$981$	−4.41657	−0.141010
$982$	−36.8217	−1.17503
$983$	−9.54910	−0.304569	−0.152285	−	0.988337i	$-0.548663\pi$
$983$	−9.54910	−0.304569	−0.152285	+	0.988337i	$0.548663\pi$
$984$	−2.00675	−0.0639727
$985$	0.975042	0.0310674
$986$	−9.74188	−0.310245
$987$	28.1050	0.894593
$988$	58.9015	1.87391
$989$	9.32519	0.296524
$990$	0	0
$991$	44.8692	1.42532	0.712659	−	0.701511i	$-0.247491\pi$
$991$	44.8692	1.42532	0.712659	+	0.701511i	$0.247491\pi$
$992$	−18.1466	−0.576154
$993$	−34.4820	−1.09425
$994$	−14.5004	−0.459924
$995$	−14.5484	−0.461214
$996$	−18.7914	−0.595427
$997$	20.5748	0.651612	0.325806	−	0.945437i	$-0.394364\pi$
$997$	20.5748	0.651612	0.325806	+	0.945437i	$0.394364\pi$
$998$	36.9530	1.16973
$999$	98.5785	3.11889

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.15		18
11.2	odd	10		385.2.n.f.246.8	yes	36
11.6	odd	10		385.2.n.f.36.8	✓	36
11.10	odd	2		4235.2.a.bo.1.4		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.8	✓	36	11.6	odd	10
385.2.n.f.246.8	yes	36	11.2	odd	10
4235.2.a.bo.1.4		18	11.10	odd	2
4235.2.a.bp.1.15		18	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)

\(f(q)\)	\(=\)	\(q+2.05277 q^{2} -3.41466 q^{3} +2.21386 q^{4} +1.00000 q^{5} -7.00951 q^{6} +1.00000 q^{7} +0.439000 q^{8} +8.65991 q^{9} +O(q^{10})\)	\(q+2.05277 q^{2} -3.41466 q^{3} +2.21386 q^{4} +1.00000 q^{5} -7.00951 q^{6} +1.00000 q^{7} +0.439000 q^{8} +8.65991 q^{9} +2.05277 q^{10} -7.55957 q^{12} +3.62061 q^{13} +2.05277 q^{14} -3.41466 q^{15} -3.52655 q^{16} +2.88712 q^{17} +17.7768 q^{18} +7.34843 q^{19} +2.21386 q^{20} -3.41466 q^{21} -2.63683 q^{23} -1.49904 q^{24} +1.00000 q^{25} +7.43228 q^{26} -19.3267 q^{27} +2.21386 q^{28} -1.64376 q^{29} -7.00951 q^{30} +2.23557 q^{31} -8.11719 q^{32} +5.92659 q^{34} +1.00000 q^{35} +19.1718 q^{36} -5.10065 q^{37} +15.0846 q^{38} -12.3632 q^{39} +0.439000 q^{40} +1.33869 q^{41} -7.00951 q^{42} -3.53651 q^{43} +8.65991 q^{45} -5.41280 q^{46} -8.23070 q^{47} +12.0420 q^{48} +1.00000 q^{49} +2.05277 q^{50} -9.85854 q^{51} +8.01552 q^{52} +3.63678 q^{53} -39.6731 q^{54} +0.439000 q^{56} -25.0924 q^{57} -3.37425 q^{58} +3.29779 q^{59} -7.55957 q^{60} +5.24101 q^{61} +4.58911 q^{62} +8.65991 q^{63} -9.60961 q^{64} +3.62061 q^{65} +11.3899 q^{67} +6.39167 q^{68} +9.00388 q^{69} +2.05277 q^{70} -7.06381 q^{71} +3.80170 q^{72} +14.2471 q^{73} -10.4705 q^{74} -3.41466 q^{75} +16.2684 q^{76} -25.3787 q^{78} +11.6679 q^{79} -3.52655 q^{80} +40.0142 q^{81} +2.74802 q^{82} +2.48577 q^{83} -7.55957 q^{84} +2.88712 q^{85} -7.25964 q^{86} +5.61288 q^{87} +12.2946 q^{89} +17.7768 q^{90} +3.62061 q^{91} -5.83757 q^{92} -7.63372 q^{93} -16.8957 q^{94} +7.34843 q^{95} +27.7174 q^{96} -4.09831 q^{97} +2.05277 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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