LMFDB - Embedded newform 4235.2.a.bm.1.10

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:	$14$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - x^{13} - 24 x^{12} + 22 x^{11} + 223 x^{10} - 190 x^{9} - 1003 x^{8} + 814 x^{7} + 2214 x^{6} + \cdots + 80 $ x^14 - x^13 - 24x^12 + 22x^11 + 223x^10 - 190x^9 - 1003x^8 + 814x^7 + 2214x^6 - 1775x^5 - 2075x^4 + 1750x^3 + 400x^2 - 480x + 80
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			1.10
Root			$-1.49190$ 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)

$f(q)$	$=$	$q+1.49190 q^{2} +1.35098 q^{3} +0.225752 q^{4} -1.00000 q^{5} +2.01553 q^{6} +1.00000 q^{7} -2.64699 q^{8} -1.17484 q^{9} +O(q^{10})$	\(q+1.49190 q^{2} +1.35098 q^{3} +0.225752 q^{4} -1.00000 q^{5} +2.01553 q^{6} +1.00000 q^{7} -2.64699 q^{8} -1.17484 q^{9} -1.49190 q^{10} +0.304987 q^{12} +6.34422 q^{13} +1.49190 q^{14} -1.35098 q^{15} -4.40054 q^{16} +0.0757830 q^{17} -1.75274 q^{18} -0.311743 q^{19} -0.225752 q^{20} +1.35098 q^{21} +5.00434 q^{23} -3.57605 q^{24} +1.00000 q^{25} +9.46492 q^{26} -5.64015 q^{27} +0.225752 q^{28} +0.785663 q^{29} -2.01553 q^{30} -2.58497 q^{31} -1.27116 q^{32} +0.113060 q^{34} -1.00000 q^{35} -0.265223 q^{36} +5.71928 q^{37} -0.465087 q^{38} +8.57095 q^{39} +2.64699 q^{40} +4.84467 q^{41} +2.01553 q^{42} +11.0475 q^{43} +1.17484 q^{45} +7.46595 q^{46} +8.48737 q^{47} -5.94506 q^{48} +1.00000 q^{49} +1.49190 q^{50} +0.102382 q^{51} +1.43222 q^{52} -9.49354 q^{53} -8.41451 q^{54} -2.64699 q^{56} -0.421159 q^{57} +1.17213 q^{58} +1.60647 q^{59} -0.304987 q^{60} +5.73302 q^{61} -3.85650 q^{62} -1.17484 q^{63} +6.90464 q^{64} -6.34422 q^{65} +2.21029 q^{67} +0.0171082 q^{68} +6.76078 q^{69} -1.49190 q^{70} +15.7149 q^{71} +3.10980 q^{72} +0.0283248 q^{73} +8.53257 q^{74} +1.35098 q^{75} -0.0703765 q^{76} +12.7870 q^{78} -1.51955 q^{79} +4.40054 q^{80} -4.09523 q^{81} +7.22774 q^{82} -6.52652 q^{83} +0.304987 q^{84} -0.0757830 q^{85} +16.4817 q^{86} +1.06142 q^{87} +0.774912 q^{89} +1.75274 q^{90} +6.34422 q^{91} +1.12974 q^{92} -3.49225 q^{93} +12.6623 q^{94} +0.311743 q^{95} -1.71732 q^{96} +4.09128 q^{97} +1.49190 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} + q^{6} + 14 q^{7} - 3 q^{8} + 17 q^{9}+O(q^{10}) $ 14 * q - q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 + q^6 + 14 * q^7 - 3 * q^8 + 17 * q^9	$ 14 q - q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} + q^{6} + 14 q^{7} - 3 q^{8} + 17 q^{9} + q^{10} + 15 q^{12} + 10 q^{13} - q^{14} - 5 q^{15} + 31 q^{16} + 11 q^{17} - 21 q^{18} + 21 q^{19} - 21 q^{20} + 5 q^{21} + 8 q^{23} + 22 q^{24} + 14 q^{25} - 18 q^{26} + 26 q^{27} + 21 q^{28} - 4 q^{29} - q^{30} + 6 q^{31} - 42 q^{32} + 16 q^{34} - 14 q^{35} + 28 q^{36} + 48 q^{37} + 35 q^{38} + 6 q^{39} + 3 q^{40} + 13 q^{41} + q^{42} - 17 q^{45} - 31 q^{46} + 11 q^{47} + 59 q^{48} + 14 q^{49} - q^{50} - 33 q^{51} + 52 q^{52} + 31 q^{53} - 57 q^{54} - 3 q^{56} - 4 q^{57} + 52 q^{58} - 4 q^{59} - 15 q^{60} + 17 q^{61} - 27 q^{62} + 17 q^{63} + 43 q^{64} - 10 q^{65} + 45 q^{67} + 14 q^{68} + 20 q^{69} + q^{70} - 6 q^{71} - 14 q^{72} + 11 q^{73} - 33 q^{74} + 5 q^{75} - 5 q^{76} + 52 q^{78} + 30 q^{79} - 31 q^{80} - 6 q^{81} + 26 q^{82} + 23 q^{83} + 15 q^{84} - 11 q^{85} - 23 q^{86} + 23 q^{87} - 15 q^{89} + 21 q^{90} + 10 q^{91} + 44 q^{92} + 29 q^{93} + 49 q^{94} - 21 q^{95} - 52 q^{96} + 44 q^{97} - q^{98}+O(q^{100}) $ 14 * q - q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 + q^6 + 14 * q^7 - 3 * q^8 + 17 * q^9 + q^10 + 15 * q^12 + 10 * q^13 - q^14 - 5 * q^15 + 31 * q^16 + 11 * q^17 - 21 * q^18 + 21 * q^19 - 21 * q^20 + 5 * q^21 + 8 * q^23 + 22 * q^24 + 14 * q^25 - 18 * q^26 + 26 * q^27 + 21 * q^28 - 4 * q^29 - q^30 + 6 * q^31 - 42 * q^32 + 16 * q^34 - 14 * q^35 + 28 * q^36 + 48 * q^37 + 35 * q^38 + 6 * q^39 + 3 * q^40 + 13 * q^41 + q^42 - 17 * q^45 - 31 * q^46 + 11 * q^47 + 59 * q^48 + 14 * q^49 - q^50 - 33 * q^51 + 52 * q^52 + 31 * q^53 - 57 * q^54 - 3 * q^56 - 4 * q^57 + 52 * q^58 - 4 * q^59 - 15 * q^60 + 17 * q^61 - 27 * q^62 + 17 * q^63 + 43 * q^64 - 10 * q^65 + 45 * q^67 + 14 * q^68 + 20 * q^69 + q^70 - 6 * q^71 - 14 * q^72 + 11 * q^73 - 33 * q^74 + 5 * q^75 - 5 * q^76 + 52 * q^78 + 30 * q^79 - 31 * q^80 - 6 * q^81 + 26 * q^82 + 23 * q^83 + 15 * q^84 - 11 * q^85 - 23 * q^86 + 23 * q^87 - 15 * q^89 + 21 * q^90 + 10 * q^91 + 44 * q^92 + 29 * q^93 + 49 * q^94 - 21 * q^95 - 52 * q^96 + 44 * q^97 - 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 $

$2$	1.49190	1.05493	0.527465	−	0.849577i	$-0.323143\pi$
$2$	1.49190	1.05493	0.527465	+	0.849577i	$0.323143\pi$
$3$	1.35098	0.779991	0.389996	−	0.920817i	$-0.372477\pi$
$3$	1.35098	0.779991	0.389996	+	0.920817i	$0.372477\pi$
$4$	0.225752	0.112876
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.01553	0.822836
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.64699	−0.935853
$9$	−1.17484	−0.391614
$10$	−1.49190	−0.471779
$11$	0	0
$11$	0	0
$12$	0.304987	0.0880423
$13$	6.34422	1.75957	0.879785	−	0.475371i	$-0.157686\pi$
$13$	6.34422	1.75957	0.879785	+	0.475371i	$0.157686\pi$
$14$	1.49190	0.398726
$15$	−1.35098	−0.348823
$16$	−4.40054	−1.10014
$17$	0.0757830	0.0183801	0.00919004	−	0.999958i	$-0.497075\pi$
$17$	0.0757830	0.0183801	0.00919004	+	0.999958i	$0.497075\pi$
$18$	−1.75274	−0.413125
$19$	−0.311743	−0.0715186	−0.0357593	−	0.999360i	$-0.511385\pi$
$19$	−0.311743	−0.0715186	−0.0357593	+	0.999360i	$0.511385\pi$
$20$	−0.225752	−0.0504797
$21$	1.35098	0.294809
$22$	0	0
$23$	5.00434	1.04348	0.521738	−	0.853106i	$-0.325284\pi$
$23$	5.00434	1.04348	0.521738	+	0.853106i	$0.325284\pi$
$24$	−3.57605	−0.729957
$25$	1.00000	0.200000
$26$	9.46492	1.85622
$27$	−5.64015	−1.08545
$28$	0.225752	0.0426631
$29$	0.785663	0.145894	0.0729470	−	0.997336i	$-0.476760\pi$
$29$	0.785663	0.145894	0.0729470	+	0.997336i	$0.476760\pi$
$30$	−2.01553	−0.367983
$31$	−2.58497	−0.464273	−0.232137	−	0.972683i	$-0.574572\pi$
$31$	−2.58497	−0.464273	−0.232137	+	0.972683i	$0.574572\pi$
$32$	−1.27116	−0.224712
$33$	0	0
$34$	0.113060	0.0193897
$35$	−1.00000	−0.169031
$36$	−0.265223	−0.0442038
$37$	5.71928	0.940244	0.470122	−	0.882602i	$-0.344210\pi$
$37$	5.71928	0.940244	0.470122	+	0.882602i	$0.344210\pi$
$38$	−0.465087	−0.0754471
$39$	8.57095	1.37245
$40$	2.64699	0.418526
$41$	4.84467	0.756610	0.378305	−	0.925681i	$-0.376507\pi$
$41$	4.84467	0.756610	0.378305	+	0.925681i	$0.376507\pi$
$42$	2.01553	0.311003
$43$	11.0475	1.68472	0.842361	−	0.538914i	$-0.181165\pi$
$43$	11.0475	1.68472	0.842361	+	0.538914i	$0.181165\pi$
$44$	0	0
$45$	1.17484	0.175135
$46$	7.46595	1.10079
$47$	8.48737	1.23801	0.619005	−	0.785387i	$-0.287536\pi$
$47$	8.48737	1.23801	0.619005	+	0.785387i	$0.287536\pi$
$48$	−5.94506	−0.858096
$49$	1.00000	0.142857
$50$	1.49190	0.210986
$51$	0.102382	0.0143363
$52$	1.43222	0.198613
$53$	−9.49354	−1.30404	−0.652019	−	0.758203i	$-0.726078\pi$
$53$	−9.49354	−1.30404	−0.652019	+	0.758203i	$0.726078\pi$
$54$	−8.41451	−1.14507
$55$	0	0
$56$	−2.64699	−0.353719
$57$	−0.421159	−0.0557839
$58$	1.17213	0.153908
$59$	1.60647	0.209145	0.104572	−	0.994517i	$-0.466653\pi$
$59$	1.60647	0.209145	0.104572	+	0.994517i	$0.466653\pi$
$60$	−0.304987	−0.0393737
$61$	5.73302	0.734038	0.367019	−	0.930213i	$-0.380378\pi$
$61$	5.73302	0.734038	0.367019	+	0.930213i	$0.380378\pi$
$62$	−3.85650	−0.489776
$63$	−1.17484	−0.148016
$64$	6.90464	0.863080
$65$	−6.34422	−0.786904
$66$	0	0
$67$	2.21029	0.270030	0.135015	−	0.990844i	$-0.456892\pi$
$67$	2.21029	0.270030	0.135015	+	0.990844i	$0.456892\pi$
$68$	0.0171082	0.00207467
$69$	6.76078	0.813902
$70$	−1.49190	−0.178316
$71$	15.7149	1.86502	0.932508	−	0.361149i	$-0.117616\pi$
$71$	15.7149	1.86502	0.932508	+	0.361149i	$0.117616\pi$
$72$	3.10980	0.366493
$73$	0.0283248	0.00331517	0.00165758	−	0.999999i	$-0.499472\pi$
$73$	0.0283248	0.00331517	0.00165758	+	0.999999i	$0.499472\pi$
$74$	8.53257	0.991891
$75$	1.35098	0.155998
$76$	−0.0703765	−0.00807274
$77$	0	0
$78$	12.7870	1.44784
$79$	−1.51955	−0.170963	−0.0854814	−	0.996340i	$-0.527243\pi$
$79$	−1.51955	−0.170963	−0.0854814	+	0.996340i	$0.527243\pi$
$80$	4.40054	0.491995
$81$	−4.09523	−0.455025
$82$	7.22774	0.798170
$83$	−6.52652	−0.716379	−0.358189	−	0.933649i	$-0.616606\pi$
$83$	−6.52652	−0.716379	−0.358189	+	0.933649i	$0.616606\pi$
$84$	0.304987	0.0332769
$85$	−0.0757830	−0.00821983
$86$	16.4817	1.77726
$87$	1.06142	0.113796
$88$	0	0
$89$	0.774912	0.0821406	0.0410703	−	0.999156i	$-0.486923\pi$
$89$	0.774912	0.0821406	0.0410703	+	0.999156i	$0.486923\pi$
$90$	1.75274	0.184755
$91$	6.34422	0.665055
$92$	1.12974	0.117783
$93$	−3.49225	−0.362129
$94$	12.6623	1.30601
$95$	0.311743	0.0319841
$96$	−1.71732	−0.175273
$97$	4.09128	0.415407	0.207703	−	0.978192i	$-0.433401\pi$
$97$	4.09128	0.415407	0.207703	+	0.978192i	$0.433401\pi$
$98$	1.49190	0.150704
$99$	0	0
$100$	0.225752	0.0225752
$101$	−6.14042	−0.610994	−0.305497	−	0.952193i	$-0.598823\pi$
$101$	−6.14042	−0.610994	−0.305497	+	0.952193i	$0.598823\pi$
$102$	0.152743	0.0151238
$103$	−10.7559	−1.05981	−0.529904	−	0.848058i	$-0.677772\pi$
$103$	−10.7559	−1.05981	−0.529904	+	0.848058i	$0.677772\pi$
$104$	−16.7931	−1.64670
$105$	−1.35098	−0.131843
$106$	−14.1634	−1.37567
$107$	−7.70577	−0.744945	−0.372473	−	0.928043i	$-0.621490\pi$
$107$	−7.70577	−0.744945	−0.372473	+	0.928043i	$0.621490\pi$
$108$	−1.27327	−0.122521
$109$	−5.70098	−0.546055	−0.273027	−	0.962006i	$-0.588025\pi$
$109$	−5.70098	−0.546055	−0.273027	+	0.962006i	$0.588025\pi$
$110$	0	0
$111$	7.72666	0.733382
$112$	−4.40054	−0.415812
$113$	14.2657	1.34201	0.671003	−	0.741455i	$-0.265864\pi$
$113$	14.2657	1.34201	0.671003	+	0.741455i	$0.265864\pi$
$114$	−0.628326	−0.0588481
$115$	−5.00434	−0.466657
$116$	0.177365	0.0164679
$117$	−7.45345	−0.689072
$118$	2.39669	0.220633
$119$	0.0757830	0.00694702
$120$	3.57605	0.326447
$121$	0	0
$122$	8.55307	0.774359
$123$	6.54507	0.590149
$124$	−0.583561	−0.0524053
$125$	−1.00000	−0.0894427
$126$	−1.75274	−0.156146
$127$	−7.89458	−0.700531	−0.350265	−	0.936651i	$-0.613909\pi$
$127$	−7.89458	−0.700531	−0.350265	+	0.936651i	$0.613909\pi$
$128$	12.8433	1.13520
$129$	14.9249	1.31407
$130$	−9.46492	−0.830128
$131$	11.8881	1.03867	0.519333	−	0.854572i	$-0.326181\pi$
$131$	11.8881	1.03867	0.519333	+	0.854572i	$0.326181\pi$
$132$	0	0
$133$	−0.311743	−0.0270315
$134$	3.29752	0.284863
$135$	5.64015	0.485426
$136$	−0.200597	−0.0172011
$137$	−12.8740	−1.09990	−0.549951	−	0.835197i	$-0.685353\pi$
$137$	−12.8740	−1.09990	−0.549951	+	0.835197i	$0.685353\pi$
$138$	10.0864	0.858609
$139$	−6.80005	−0.576773	−0.288386	−	0.957514i	$-0.593119\pi$
$139$	−6.80005	−0.576773	−0.288386	+	0.957514i	$0.593119\pi$
$140$	−0.225752	−0.0190795
$141$	11.4663	0.965637
$142$	23.4450	1.96746
$143$	0	0
$144$	5.16993	0.430828
$145$	−0.785663	−0.0652458
$146$	0.0422576	0.00349727
$147$	1.35098	0.111427
$148$	1.29114	0.106131
$149$	12.3723	1.01358	0.506788	−	0.862071i	$-0.330833\pi$
$149$	12.3723	1.01358	0.506788	+	0.862071i	$0.330833\pi$
$150$	2.01553	0.164567
$151$	11.5321	0.938473	0.469236	−	0.883073i	$-0.344529\pi$
$151$	11.5321	0.938473	0.469236	+	0.883073i	$0.344529\pi$
$152$	0.825180	0.0669309
$153$	−0.0890330	−0.00719789
$154$	0	0
$155$	2.58497	0.207629
$156$	1.93491	0.154917
$157$	13.0364	1.04042	0.520210	−	0.854039i	$-0.325854\pi$
$157$	13.0364	1.04042	0.520210	+	0.854039i	$0.325854\pi$
$158$	−2.26701	−0.180354
$159$	−12.8256	−1.01714
$160$	1.27116	0.100494
$161$	5.00434	0.394397
$162$	−6.10965	−0.480019
$163$	20.0259	1.56855	0.784276	−	0.620412i	$-0.213035\pi$
$163$	20.0259	1.56855	0.784276	+	0.620412i	$0.213035\pi$
$164$	1.09369	0.0854031
$165$	0	0
$166$	−9.73689	−0.755729
$167$	−17.8818	−1.38373	−0.691866	−	0.722026i	$-0.743211\pi$
$167$	−17.8818	−1.38373	−0.691866	+	0.722026i	$0.743211\pi$
$168$	−3.57605	−0.275898
$169$	27.2492	2.09609
$170$	−0.113060	−0.00867134
$171$	0.366248	0.0280077
$172$	2.49399	0.190165
$173$	22.6352	1.72092	0.860461	−	0.509517i	$-0.170176\pi$
$173$	22.6352	1.72092	0.860461	+	0.509517i	$0.170176\pi$
$174$	1.58353	0.120047
$175$	1.00000	0.0755929
$176$	0	0
$177$	2.17032	0.163131
$178$	1.15609	0.0866525
$179$	15.0254	1.12305	0.561526	−	0.827459i	$-0.310214\pi$
$179$	15.0254	1.12305	0.561526	+	0.827459i	$0.310214\pi$
$180$	0.265223	0.0197685
$181$	−13.1748	−0.979276	−0.489638	−	0.871926i	$-0.662871\pi$
$181$	−13.1748	−0.979276	−0.489638	+	0.871926i	$0.662871\pi$
$182$	9.46492	0.701586
$183$	7.74522	0.572543
$184$	−13.2464	−0.976540
$185$	−5.71928	−0.420490
$186$	−5.21007	−0.382021
$187$	0	0
$188$	1.91604	0.139742
$189$	−5.64015	−0.410260
$190$	0.465087	0.0337410
$191$	−6.32997	−0.458020	−0.229010	−	0.973424i	$-0.573549\pi$
$191$	−6.32997	−0.458020	−0.229010	+	0.973424i	$0.573549\pi$
$192$	9.32806	0.673195
$193$	1.50138	0.108072	0.0540360	−	0.998539i	$-0.482791\pi$
$193$	1.50138	0.108072	0.0540360	+	0.998539i	$0.482791\pi$
$194$	6.10377	0.438225
$195$	−8.57095	−0.613778
$196$	0.225752	0.0161251
$197$	−22.7297	−1.61942	−0.809712	−	0.586828i	$-0.800377\pi$
$197$	−22.7297	−1.61942	−0.809712	+	0.586828i	$0.800377\pi$
$198$	0	0
$199$	−5.83977	−0.413970	−0.206985	−	0.978344i	$-0.566365\pi$
$199$	−5.83977	−0.413970	−0.206985	+	0.978344i	$0.566365\pi$
$200$	−2.64699	−0.187171
$201$	2.98607	0.210621
$202$	−9.16086	−0.644556
$203$	0.785663	0.0551427
$204$	0.0231129	0.00161823
$205$	−4.84467	−0.338366
$206$	−16.0466	−1.11802
$207$	−5.87930	−0.408639
$208$	−27.9180	−1.93577
$209$	0	0
$210$	−2.01553	−0.139085
$211$	−23.7558	−1.63542	−0.817708	−	0.575634i	$-0.804755\pi$
$211$	−23.7558	−1.63542	−0.817708	+	0.575634i	$0.804755\pi$
$212$	−2.14318	−0.147195
$213$	21.2306	1.45470
$214$	−11.4962	−0.785864
$215$	−11.0475	−0.753430
$216$	14.9294	1.01582
$217$	−2.58497	−0.175479
$218$	−8.50526	−0.576049
$219$	0.0382664	0.00258580
$220$	0	0
$221$	0.480784	0.0323411
$222$	11.5274	0.773666
$223$	−18.5516	−1.24231	−0.621155	−	0.783688i	$-0.713336\pi$
$223$	−18.5516	−1.24231	−0.621155	+	0.783688i	$0.713336\pi$
$224$	−1.27116	−0.0849330
$225$	−1.17484	−0.0783227
$226$	21.2830	1.41572
$227$	−22.6107	−1.50072	−0.750362	−	0.661028i	$-0.770121\pi$
$227$	−22.6107	−1.50072	−0.750362	+	0.661028i	$0.770121\pi$
$228$	−0.0950776	−0.00629666
$229$	24.7774	1.63734	0.818670	−	0.574265i	$-0.194712\pi$
$229$	24.7774	1.63734	0.818670	+	0.574265i	$0.194712\pi$
$230$	−7.46595	−0.492290
$231$	0	0
$232$	−2.07964	−0.136535
$233$	20.6370	1.35197	0.675987	−	0.736914i	$-0.263718\pi$
$233$	20.6370	1.35197	0.675987	+	0.736914i	$0.263718\pi$
$234$	−11.1198	−0.726922
$235$	−8.48737	−0.553655
$236$	0.362665	0.0236075
$237$	−2.05289	−0.133350
$238$	0.113060	0.00732862
$239$	−17.1220	−1.10753	−0.553765	−	0.832673i	$-0.686809\pi$
$239$	−17.1220	−1.10753	−0.553765	+	0.832673i	$0.686809\pi$
$240$	5.94506	0.383752
$241$	17.6558	1.13731	0.568656	−	0.822576i	$-0.307464\pi$
$241$	17.6558	1.13731	0.568656	+	0.822576i	$0.307464\pi$
$242$	0	0
$243$	11.3878	0.730531
$244$	1.29424	0.0828553
$245$	−1.00000	−0.0638877
$246$	9.76456	0.622566
$247$	−1.97776	−0.125842
$248$	6.84238	0.434492
$249$	−8.81723	−0.558769
$250$	−1.49190	−0.0943558
$251$	22.5827	1.42541	0.712703	−	0.701466i	$-0.247471\pi$
$251$	22.5827	1.42541	0.712703	+	0.701466i	$0.247471\pi$
$252$	−0.265223	−0.0167075
$253$	0	0
$254$	−11.7779	−0.739010
$255$	−0.102382	−0.00641139
$256$	5.35161	0.334476
$257$	−22.8806	−1.42725	−0.713625	−	0.700528i	$-0.752948\pi$
$257$	−22.8806	−1.42725	−0.713625	+	0.700528i	$0.752948\pi$
$258$	22.2665	1.38625
$259$	5.71928	0.355379
$260$	−1.43222	−0.0888226
$261$	−0.923029	−0.0571341
$262$	17.7358	1.09572
$263$	−8.13304	−0.501504	−0.250752	−	0.968051i	$-0.580678\pi$
$263$	−8.13304	−0.501504	−0.250752	+	0.968051i	$0.580678\pi$
$264$	0	0
$265$	9.49354	0.583183
$266$	−0.465087	−0.0285163
$267$	1.04689	0.0640689
$268$	0.498978	0.0304799
$269$	3.51755	0.214469	0.107234	−	0.994234i	$-0.465800\pi$
$269$	3.51755	0.214469	0.107234	+	0.994234i	$0.465800\pi$
$270$	8.41451	0.512091
$271$	−17.7055	−1.07553	−0.537766	−	0.843094i	$-0.680732\pi$
$271$	−17.7055	−1.07553	−0.537766	+	0.843094i	$0.680732\pi$
$272$	−0.333486	−0.0202206
$273$	8.57095	0.518737
$274$	−19.2067	−1.16032
$275$	0	0
$276$	1.52626	0.0918700
$277$	−17.2636	−1.03727	−0.518635	−	0.854996i	$-0.673560\pi$
$277$	−17.2636	−1.03727	−0.518635	+	0.854996i	$0.673560\pi$
$278$	−10.1450	−0.608455
$279$	3.03692	0.181816
$280$	2.64699	0.158188
$281$	−11.2009	−0.668187	−0.334093	−	0.942540i	$-0.608430\pi$
$281$	−11.2009	−0.668187	−0.334093	+	0.942540i	$0.608430\pi$
$282$	17.1065	1.01868
$283$	17.2953	1.02810	0.514051	−	0.857760i	$-0.328144\pi$
$283$	17.2953	1.02810	0.514051	+	0.857760i	$0.328144\pi$
$284$	3.54767	0.210516
$285$	0.421159	0.0249473
$286$	0	0
$287$	4.84467	0.285972
$288$	1.49341	0.0880001
$289$	−16.9943	−0.999662
$290$	−1.17213	−0.0688297
$291$	5.52726	0.324014
$292$	0.00639438	0.000374203 0
$293$	−29.9970	−1.75244	−0.876221	−	0.481909i	$-0.839944\pi$
$293$	−29.9970	−1.75244	−0.876221	+	0.481909i	$0.839944\pi$
$294$	2.01553	0.117548
$295$	−1.60647	−0.0935325
$296$	−15.1389	−0.879930
$297$	0	0
$298$	18.4581	1.06925
$299$	31.7486	1.83607
$300$	0.304987	0.0176085
$301$	11.0475	0.636765
$302$	17.2048	0.990023
$303$	−8.29561	−0.476570
$304$	1.37184	0.0786802
$305$	−5.73302	−0.328272
$306$	−0.132828	−0.00759327
$307$	14.1114	0.805382	0.402691	−	0.915336i	$-0.368075\pi$
$307$	14.1114	0.805382	0.402691	+	0.915336i	$0.368075\pi$
$308$	0	0
$309$	−14.5310	−0.826641
$310$	3.85650	0.219034
$311$	−18.3028	−1.03786	−0.518929	−	0.854818i	$-0.673669\pi$
$311$	−18.3028	−1.03786	−0.518929	+	0.854818i	$0.673669\pi$
$312$	−22.6872	−1.28441
$313$	28.9496	1.63633	0.818164	−	0.574985i	$-0.194992\pi$
$313$	28.9496	1.63633	0.818164	+	0.574985i	$0.194992\pi$
$314$	19.4490	1.09757
$315$	1.17484	0.0661948
$316$	−0.343042	−0.0192976
$317$	−25.4705	−1.43057	−0.715283	−	0.698835i	$-0.753702\pi$
$317$	−25.4705	−1.43057	−0.715283	+	0.698835i	$0.753702\pi$
$318$	−19.1345	−1.07301
$319$	0	0
$320$	−6.90464	−0.385981
$321$	−10.4104	−0.581051
$322$	7.46595	0.416061
$323$	−0.0236248	−0.00131452
$324$	−0.924505	−0.0513614
$325$	6.34422	0.351914
$326$	29.8766	1.65471
$327$	−7.70193	−0.425918
$328$	−12.8238	−0.708076
$329$	8.48737	0.467924
$330$	0	0
$331$	25.0208	1.37527	0.687633	−	0.726059i	$-0.258650\pi$
$331$	25.0208	1.37527	0.687633	+	0.726059i	$0.258650\pi$
$332$	−1.47337	−0.0808620
$333$	−6.71924	−0.368212
$334$	−26.6777	−1.45974
$335$	−2.21029	−0.120761
$336$	−5.94506	−0.324330
$337$	8.10721	0.441628	0.220814	−	0.975316i	$-0.429129\pi$
$337$	8.10721	0.441628	0.220814	+	0.975316i	$0.429129\pi$
$338$	40.6529	2.21123
$339$	19.2728	1.04675
$340$	−0.0171082	−0.000927821 0
$341$	0	0
$342$	0.546404	0.0295461
$343$	1.00000	0.0539949
$344$	−29.2425	−1.57665
$345$	−6.76078	−0.363988
$346$	33.7693	1.81545
$347$	−29.0019	−1.55690	−0.778452	−	0.627704i	$-0.783995\pi$
$347$	−29.0019	−1.55690	−0.778452	+	0.627704i	$0.783995\pi$
$348$	0.239617	0.0128448
$349$	−5.42802	−0.290555	−0.145278	−	0.989391i	$-0.546408\pi$
$349$	−5.42802	−0.290555	−0.145278	+	0.989391i	$0.546408\pi$
$350$	1.49190	0.0797452
$351$	−35.7823	−1.90992
$352$	0	0
$353$	−30.4032	−1.61820	−0.809098	−	0.587673i	$-0.800044\pi$
$353$	−30.4032	−1.61820	−0.809098	+	0.587673i	$0.800044\pi$
$354$	3.23789	0.172092
$355$	−15.7149	−0.834061
$356$	0.174938	0.00927170
$357$	0.102382	0.00541862
$358$	22.4164	1.18474
$359$	−5.70813	−0.301264	−0.150632	−	0.988590i	$-0.548131\pi$
$359$	−5.70813	−0.301264	−0.150632	+	0.988590i	$0.548131\pi$
$360$	−3.10980	−0.163901
$361$	−18.9028	−0.994885
$362$	−19.6554	−1.03307
$363$	0	0
$364$	1.43222	0.0750688
$365$	−0.0283248	−0.00148259
$366$	11.5551	0.603993
$367$	29.9827	1.56508	0.782541	−	0.622598i	$-0.213923\pi$
$367$	29.9827	1.56508	0.782541	+	0.622598i	$0.213923\pi$
$368$	−22.0218	−1.14796
$369$	−5.69172	−0.296299
$370$	−8.53257	−0.443587
$371$	−9.49354	−0.492880
$372$	−0.788382	−0.0408757
$373$	−12.5049	−0.647479	−0.323740	−	0.946146i	$-0.604940\pi$
$373$	−12.5049	−0.647479	−0.323740	+	0.946146i	$0.604940\pi$
$374$	0	0
$375$	−1.35098	−0.0697645
$376$	−22.4660	−1.15860
$377$	4.98442	0.256711
$378$	−8.41451	−0.432796
$379$	4.15404	0.213379	0.106689	−	0.994292i	$-0.465975\pi$
$379$	4.15404	0.213379	0.106689	+	0.994292i	$0.465975\pi$
$380$	0.0703765	0.00361024
$381$	−10.6655	−0.546408
$382$	−9.44365	−0.483179
$383$	−7.00894	−0.358140	−0.179070	−	0.983836i	$-0.557309\pi$
$383$	−7.00894	−0.358140	−0.179070	+	0.983836i	$0.557309\pi$
$384$	17.3511	0.885446
$385$	0	0
$386$	2.23991	0.114008
$387$	−12.9790	−0.659760
$388$	0.923616	0.0468895
$389$	−23.3173	−1.18224	−0.591118	−	0.806585i	$-0.701313\pi$
$389$	−23.3173	−1.18224	−0.591118	+	0.806585i	$0.701313\pi$
$390$	−12.7870	−0.647493
$391$	0.379244	0.0191792
$392$	−2.64699	−0.133693
$393$	16.0606	0.810150
$394$	−33.9103	−1.70838
$395$	1.51955	0.0764569
$396$	0	0
$397$	27.5828	1.38434	0.692170	−	0.721735i	$-0.256655\pi$
$397$	27.5828	1.38434	0.692170	+	0.721735i	$0.256655\pi$
$398$	−8.71232	−0.436709
$399$	−0.421159	−0.0210843
$400$	−4.40054	−0.220027
$401$	8.09399	0.404195	0.202097	−	0.979365i	$-0.435224\pi$
$401$	8.09399	0.404195	0.202097	+	0.979365i	$0.435224\pi$
$402$	4.45490	0.222190
$403$	−16.3996	−0.816922
$404$	−1.38621	−0.0689666
$405$	4.09523	0.203493
$406$	1.17213	0.0581717
$407$	0	0
$408$	−0.271004	−0.0134167
$409$	1.93013	0.0954388	0.0477194	−	0.998861i	$-0.484805\pi$
$409$	1.93013	0.0954388	0.0477194	+	0.998861i	$0.484805\pi$
$410$	−7.22774	−0.356953
$411$	−17.3926	−0.857913
$412$	−2.42816	−0.119627
$413$	1.60647	0.0790494
$414$	−8.77130	−0.431086
$415$	6.52652	0.320374
$416$	−8.06452	−0.395396
$417$	−9.18676	−0.449878
$418$	0	0
$419$	−26.0415	−1.27221	−0.636104	−	0.771603i	$-0.719455\pi$
$419$	−26.0415	−1.27221	−0.636104	+	0.771603i	$0.719455\pi$
$420$	−0.304987	−0.0148819
$421$	1.59858	0.0779102	0.0389551	−	0.999241i	$-0.487597\pi$
$421$	1.59858	0.0779102	0.0389551	+	0.999241i	$0.487597\pi$
$422$	−35.4411	−1.72525
$423$	−9.97131	−0.484821
$424$	25.1293	1.22039
$425$	0.0757830	0.00367602
$426$	31.6738	1.53460
$427$	5.73302	0.277440
$428$	−1.73959	−0.0840864
$429$	0	0
$430$	−16.4817	−0.794816
$431$	23.6385	1.13862	0.569312	−	0.822121i	$-0.307210\pi$
$431$	23.6385	1.13862	0.569312	+	0.822121i	$0.307210\pi$
$432$	24.8197	1.19414
$433$	32.3769	1.55593	0.777967	−	0.628306i	$-0.216251\pi$
$433$	32.3769	1.55593	0.777967	+	0.628306i	$0.216251\pi$
$434$	−3.85650	−0.185118
$435$	−1.06142	−0.0508911
$436$	−1.28701	−0.0616365
$437$	−1.56006	−0.0746280
$438$	0.0570894	0.00272784
$439$	−12.0262	−0.573980	−0.286990	−	0.957934i	$-0.592655\pi$
$439$	−12.0262	−0.573980	−0.286990	+	0.957934i	$0.592655\pi$
$440$	0	0
$441$	−1.17484	−0.0559448
$442$	0.717280	0.0341175
$443$	30.8124	1.46394	0.731970	−	0.681337i	$-0.238601\pi$
$443$	30.8124	1.46394	0.731970	+	0.681337i	$0.238601\pi$
$444$	1.74431	0.0827812
$445$	−0.774912	−0.0367344
$446$	−27.6771	−1.31055
$447$	16.7147	0.790580
$448$	6.90464	0.326214
$449$	−21.6425	−1.02137	−0.510686	−	0.859767i	$-0.670608\pi$
$449$	−21.6425	−1.02137	−0.510686	+	0.859767i	$0.670608\pi$
$450$	−1.75274	−0.0826249
$451$	0	0
$452$	3.22051	0.151480
$453$	15.5798	0.732001
$454$	−33.7328	−1.58316
$455$	−6.34422	−0.297422
$456$	1.11481	0.0522056
$457$	−39.8194	−1.86267	−0.931337	−	0.364158i	$-0.881357\pi$
$457$	−39.8194	−1.86267	−0.931337	+	0.364158i	$0.881357\pi$
$458$	36.9653	1.72728
$459$	−0.427427	−0.0199506
$460$	−1.12974	−0.0526743
$461$	28.3415	1.31999	0.659997	−	0.751268i	$-0.270558\pi$
$461$	28.3415	1.31999	0.659997	+	0.751268i	$0.270558\pi$
$462$	0	0
$463$	4.78425	0.222343	0.111172	−	0.993801i	$-0.464540\pi$
$463$	4.78425	0.222343	0.111172	+	0.993801i	$0.464540\pi$
$464$	−3.45734	−0.160503
$465$	3.49225	0.161949
$466$	30.7882	1.42624
$467$	11.6167	0.537558	0.268779	−	0.963202i	$-0.413380\pi$
$467$	11.6167	0.537558	0.268779	+	0.963202i	$0.413380\pi$
$468$	−1.68263	−0.0777797
$469$	2.21029	0.102062
$470$	−12.6623	−0.584067
$471$	17.6120	0.811518
$472$	−4.25232	−0.195729
$473$	0	0
$474$	−3.06270	−0.140674
$475$	−0.311743	−0.0143037
$476$	0.0171082	0.000784152 0
$477$	11.1534	0.510679
$478$	−25.5442	−1.16837
$479$	29.0571	1.32765	0.663826	−	0.747887i	$-0.268931\pi$
$479$	29.0571	1.32765	0.663826	+	0.747887i	$0.268931\pi$
$480$	1.71732	0.0783845
$481$	36.2844	1.65443
$482$	26.3406	1.19978
$483$	6.76078	0.307626
$484$	0	0
$485$	−4.09128	−0.185776
$486$	16.9895	0.770658
$487$	31.3877	1.42231	0.711157	−	0.703033i	$-0.248172\pi$
$487$	31.3877	1.42231	0.711157	+	0.703033i	$0.248172\pi$
$488$	−15.1753	−0.686952
$489$	27.0547	1.22346
$490$	−1.49190	−0.0673970
$491$	−20.6025	−0.929779	−0.464890	−	0.885369i	$-0.653906\pi$
$491$	−20.6025	−0.929779	−0.464890	+	0.885369i	$0.653906\pi$
$492$	1.47756	0.0666137
$493$	0.0595399	0.00268154
$494$	−2.95062	−0.132755
$495$	0	0
$496$	11.3752	0.510764
$497$	15.7149	0.704910
$498$	−13.1544	−0.589462
$499$	−0.244897	−0.0109631	−0.00548154	−	0.999985i	$-0.501745\pi$
$499$	−0.244897	−0.0109631	−0.00548154	+	0.999985i	$0.501745\pi$
$500$	−0.225752	−0.0100959
$501$	−24.1580	−1.07930
$502$	33.6910	1.50370
$503$	5.16623	0.230351	0.115176	−	0.993345i	$-0.463257\pi$
$503$	5.16623	0.230351	0.115176	+	0.993345i	$0.463257\pi$
$504$	3.10980	0.138521
$505$	6.14042	0.273245
$506$	0	0
$507$	36.8132	1.63493
$508$	−1.78222	−0.0790731
$509$	−20.3719	−0.902967	−0.451484	−	0.892279i	$-0.649105\pi$
$509$	−20.3719	−0.902967	−0.451484	+	0.892279i	$0.649105\pi$
$510$	−0.152743	−0.00676357
$511$	0.0283248	0.00125302
$512$	−17.7026	−0.782352
$513$	1.75827	0.0776297
$514$	−34.1354	−1.50565
$515$	10.7559	0.473961
$516$	3.36934	0.148327
$517$	0	0
$518$	8.53257	0.374899
$519$	30.5798	1.34230
$520$	16.7931	0.736427
$521$	5.05704	0.221553	0.110777	−	0.993845i	$-0.464666\pi$
$521$	5.05704	0.221553	0.110777	+	0.993845i	$0.464666\pi$
$522$	−1.37706	−0.0602724
$523$	−24.2301	−1.05951	−0.529753	−	0.848152i	$-0.677715\pi$
$523$	−24.2301	−1.05951	−0.529753	+	0.848152i	$0.677715\pi$
$524$	2.68376	0.117240
$525$	1.35098	0.0589618
$526$	−12.1336	−0.529052
$527$	−0.195897	−0.00853339
$528$	0	0
$529$	2.04337	0.0888423
$530$	14.1634	0.615217
$531$	−1.88735	−0.0819040
$532$	−0.0703765	−0.00305121
$533$	30.7357	1.33131
$534$	1.56186	0.0675882
$535$	7.70577	0.333150
$536$	−5.85063	−0.252709
$537$	20.2991	0.875971
$538$	5.24782	0.226249
$539$	0	0
$540$	1.27327	0.0547930
$541$	−9.84353	−0.423206	−0.211603	−	0.977356i	$-0.567868\pi$
$541$	−9.84353	−0.423206	−0.211603	+	0.977356i	$0.567868\pi$
$542$	−26.4147	−1.13461
$543$	−17.7990	−0.763827
$544$	−0.0963324	−0.00413022
$545$	5.70098	0.244203
$546$	12.7870	0.547231
$547$	−41.4100	−1.77056	−0.885281	−	0.465056i	$-0.846034\pi$
$547$	−41.4100	−1.77056	−0.885281	+	0.465056i	$0.846034\pi$
$548$	−2.90633	−0.124152
$549$	−6.73539	−0.287459
$550$	0	0
$551$	−0.244925	−0.0104341
$552$	−17.8957	−0.761693
$553$	−1.51955	−0.0646179
$554$	−25.7555	−1.09425
$555$	−7.72666	−0.327978
$556$	−1.53513	−0.0651038
$557$	−21.7967	−0.923557	−0.461779	−	0.886995i	$-0.652789\pi$
$557$	−21.7967	−0.923557	−0.461779	+	0.886995i	$0.652789\pi$
$558$	4.53077	0.191803
$559$	70.0875	2.96439
$560$	4.40054	0.185957
$561$	0	0
$562$	−16.7105	−0.704890
$563$	−27.1411	−1.14386	−0.571930	−	0.820302i	$-0.693805\pi$
$563$	−27.1411	−1.14386	−0.571930	+	0.820302i	$0.693805\pi$
$564$	2.58854	0.108997
$565$	−14.2657	−0.600163
$566$	25.8028	1.08457
$567$	−4.09523	−0.171983
$568$	−41.5972	−1.74538
$569$	17.8884	0.749919	0.374959	−	0.927041i	$-0.377657\pi$
$569$	17.8884	0.749919	0.374959	+	0.927041i	$0.377657\pi$
$570$	0.628326	0.0263177
$571$	−7.57881	−0.317163	−0.158582	−	0.987346i	$-0.550692\pi$
$571$	−7.57881	−0.317163	−0.158582	+	0.987346i	$0.550692\pi$
$572$	0	0
$573$	−8.55169	−0.357252
$574$	7.22774	0.301680
$575$	5.00434	0.208695
$576$	−8.11186	−0.337994
$577$	−31.5743	−1.31445	−0.657227	−	0.753693i	$-0.728271\pi$
$577$	−31.5743	−1.31445	−0.657227	+	0.753693i	$0.728271\pi$
$578$	−25.3537	−1.05457
$579$	2.02835	0.0842952
$580$	−0.177365	−0.00736468
$581$	−6.52652	−0.270766
$582$	8.24610	0.341812
$583$	0	0
$584$	−0.0749755	−0.00310251
$585$	7.45345	0.308162
$586$	−44.7524	−1.84870
$587$	18.7579	0.774221	0.387111	−	0.922033i	$-0.373473\pi$
$587$	18.7579	0.774221	0.387111	+	0.922033i	$0.373473\pi$
$588$	0.304987	0.0125775
$589$	0.805844	0.0332042
$590$	−2.39669	−0.0986702
$591$	−30.7075	−1.26314
$592$	−25.1679	−1.03439
$593$	−19.6140	−0.805449	−0.402725	−	0.915321i	$-0.631937\pi$
$593$	−19.6140	−0.805449	−0.402725	+	0.915321i	$0.631937\pi$
$594$	0	0
$595$	−0.0757830	−0.00310680
$596$	2.79306	0.114408
$597$	−7.88944	−0.322893
$598$	47.3656	1.93692
$599$	−18.4420	−0.753520	−0.376760	−	0.926311i	$-0.622962\pi$
$599$	−18.4420	−0.753520	−0.376760	+	0.926311i	$0.622962\pi$
$600$	−3.57605	−0.145991
$601$	36.0937	1.47229	0.736147	−	0.676822i	$-0.236643\pi$
$601$	36.0937	1.47229	0.736147	+	0.676822i	$0.236643\pi$
$602$	16.4817	0.671742
$603$	−2.59674	−0.105747
$604$	2.60341	0.105931
$605$	0	0
$606$	−12.3762	−0.502748
$607$	−20.9753	−0.851360	−0.425680	−	0.904874i	$-0.639965\pi$
$607$	−20.9753	−0.851360	−0.425680	+	0.904874i	$0.639965\pi$
$608$	0.396275	0.0160711
$609$	1.06142	0.0430108
$610$	−8.55307	−0.346304
$611$	53.8457	2.17837
$612$	−0.0200994	−0.000812469 0
$613$	−7.11619	−0.287420	−0.143710	−	0.989620i	$-0.545903\pi$
$613$	−7.11619	−0.287420	−0.143710	+	0.989620i	$0.545903\pi$
$614$	21.0528	0.849622
$615$	−6.54507	−0.263923
$616$	0	0
$617$	−20.7586	−0.835711	−0.417855	−	0.908514i	$-0.637218\pi$
$617$	−20.7586	−0.835711	−0.417855	+	0.908514i	$0.637218\pi$
$618$	−21.6788	−0.872048
$619$	11.1393	0.447727	0.223864	−	0.974620i	$-0.428133\pi$
$619$	11.1393	0.447727	0.223864	+	0.974620i	$0.428133\pi$
$620$	0.583561	0.0234364
$621$	−28.2252	−1.13264
$622$	−27.3059	−1.09487
$623$	0.774912	0.0310462
$624$	−37.7168	−1.50988
$625$	1.00000	0.0400000
$626$	43.1898	1.72621
$627$	0	0
$628$	2.94300	0.117438
$629$	0.433424	0.0172818
$630$	1.75274	0.0698308
$631$	30.3126	1.20673	0.603363	−	0.797466i	$-0.293827\pi$
$631$	30.3126	1.20673	0.603363	+	0.797466i	$0.293827\pi$
$632$	4.02224	0.159996
$633$	−32.0937	−1.27561
$634$	−37.9993	−1.50915
$635$	7.89458	0.313287
$636$	−2.89541	−0.114810
$637$	6.34422	0.251367
$638$	0	0
$639$	−18.4625	−0.730366
$640$	−12.8433	−0.507677
$641$	−15.7061	−0.620354	−0.310177	−	0.950679i	$-0.600388\pi$
$641$	−15.7061	−0.620354	−0.310177	+	0.950679i	$0.600388\pi$
$642$	−15.5312	−0.612967
$643$	17.9577	0.708182	0.354091	−	0.935211i	$-0.384790\pi$
$643$	17.9577	0.708182	0.354091	+	0.935211i	$0.384790\pi$
$644$	1.12974	0.0445179
$645$	−14.9249	−0.587669
$646$	−0.0352457	−0.00138672
$647$	3.32734	0.130811	0.0654055	−	0.997859i	$-0.479166\pi$
$647$	3.32734	0.130811	0.0654055	+	0.997859i	$0.479166\pi$
$648$	10.8400	0.425837
$649$	0	0
$650$	9.46492	0.371245
$651$	−3.49225	−0.136872
$652$	4.52089	0.177052
$653$	14.4010	0.563554	0.281777	−	0.959480i	$-0.409076\pi$
$653$	14.4010	0.563554	0.281777	+	0.959480i	$0.409076\pi$
$654$	−11.4905	−0.449313
$655$	−11.8881	−0.464505
$656$	−21.3192	−0.832373
$657$	−0.0332771	−0.00129826
$658$	12.6623	0.493626
$659$	17.3046	0.674090	0.337045	−	0.941489i	$-0.390573\pi$
$659$	17.3046	0.674090	0.337045	+	0.941489i	$0.390573\pi$
$660$	0	0
$661$	30.5400	1.18787	0.593933	−	0.804514i	$-0.297574\pi$
$661$	30.5400	1.18787	0.593933	+	0.804514i	$0.297574\pi$
$662$	37.3284	1.45081
$663$	0.649532	0.0252257
$664$	17.2756	0.670425
$665$	0.311743	0.0120889
$666$	−10.0244	−0.388438
$667$	3.93172	0.152237
$668$	−4.03684	−0.156190
$669$	−25.0630	−0.968990
$670$	−3.29752	−0.127394
$671$	0	0
$672$	−1.71732	−0.0662470
$673$	−4.74062	−0.182737	−0.0913687	−	0.995817i	$-0.529124\pi$
$673$	−4.74062	−0.182737	−0.0913687	+	0.995817i	$0.529124\pi$
$674$	12.0951	0.465886
$675$	−5.64015	−0.217089
$676$	6.15155	0.236598
$677$	−39.6939	−1.52556	−0.762780	−	0.646659i	$-0.776166\pi$
$677$	−39.6939	−1.52556	−0.762780	+	0.646659i	$0.776166\pi$
$678$	28.7529	1.10425
$679$	4.09128	0.157009
$680$	0.200597	0.00769255
$681$	−30.5467	−1.17055
$682$	0	0
$683$	−22.5125	−0.861417	−0.430708	−	0.902491i	$-0.641736\pi$
$683$	−22.5125	−0.861417	−0.430708	+	0.902491i	$0.641736\pi$
$684$	0.0826812	0.00316139
$685$	12.8740	0.491891
$686$	1.49190	0.0569608
$687$	33.4739	1.27711
$688$	−48.6148	−1.85342
$689$	−60.2291	−2.29455
$690$	−10.0864	−0.383982
$691$	−27.8363	−1.05894	−0.529472	−	0.848327i	$-0.677610\pi$
$691$	−27.8363	−1.05894	−0.529472	+	0.848327i	$0.677610\pi$
$692$	5.10994	0.194251
$693$	0	0
$694$	−43.2678	−1.64242
$695$	6.80005	0.257941
$696$	−2.80957	−0.106496
$697$	0.367144	0.0139066
$698$	−8.09804	−0.306515
$699$	27.8803	1.05453
$700$	0.225752	0.00853262
$701$	−3.00182	−0.113377	−0.0566886	−	0.998392i	$-0.518054\pi$
$701$	−3.00182	−0.113377	−0.0566886	+	0.998392i	$0.518054\pi$
$702$	−53.3835	−2.01483
$703$	−1.78294	−0.0672450
$704$	0	0
$705$	−11.4663	−0.431846
$706$	−45.3583	−1.70708
$707$	−6.14042	−0.230934
$708$	0.489954	0.0184136
$709$	−11.7612	−0.441703	−0.220852	−	0.975307i	$-0.570884\pi$
$709$	−11.7612	−0.441703	−0.220852	+	0.975307i	$0.570884\pi$
$710$	−23.4450	−0.879875
$711$	1.78523	0.0669514
$712$	−2.05119	−0.0768715
$713$	−12.9360	−0.484458
$714$	0.152743	0.00571626
$715$	0	0
$716$	3.39202	0.126766
$717$	−23.1316	−0.863864
$718$	−8.51594	−0.317812
$719$	33.8582	1.26270	0.631349	−	0.775499i	$-0.282502\pi$
$719$	33.8582	1.26270	0.631349	+	0.775499i	$0.282502\pi$
$720$	−5.16993	−0.192672
$721$	−10.7559	−0.400570
$722$	−28.2010	−1.04953
$723$	23.8527	0.887093
$724$	−2.97424	−0.110537
$725$	0.785663	0.0291788
$726$	0	0
$727$	−23.9238	−0.887285	−0.443643	−	0.896204i	$-0.646314\pi$
$727$	−23.9238	−0.887285	−0.443643	+	0.896204i	$0.646314\pi$
$728$	−16.7931	−0.622394
$729$	27.6705	1.02483
$730$	−0.0422576	−0.00156403
$731$	0.837210	0.0309653
$732$	1.74850	0.0646264
$733$	39.2996	1.45156	0.725781	−	0.687926i	$-0.241479\pi$
$733$	39.2996	1.45156	0.725781	+	0.687926i	$0.241479\pi$
$734$	44.7310	1.65105
$735$	−1.35098	−0.0498318
$736$	−6.36131	−0.234481
$737$	0	0
$738$	−8.49144	−0.312574
$739$	44.1926	1.62565	0.812825	−	0.582508i	$-0.197929\pi$
$739$	44.1926	1.62565	0.812825	+	0.582508i	$0.197929\pi$
$740$	−1.29114	−0.0474632
$741$	−2.67193	−0.0981557
$742$	−14.1634	−0.519953
$743$	13.8306	0.507394	0.253697	−	0.967284i	$-0.418353\pi$
$743$	13.8306	0.507394	0.253697	+	0.967284i	$0.418353\pi$
$744$	9.24395	0.338900
$745$	−12.3723	−0.453285
$746$	−18.6560	−0.683045
$747$	7.66762	0.280544
$748$	0	0
$749$	−7.70577	−0.281563
$750$	−2.01553	−0.0735967
$751$	19.7349	0.720135	0.360068	−	0.932926i	$-0.382754\pi$
$751$	19.7349	0.720135	0.360068	+	0.932926i	$0.382754\pi$
$752$	−37.3490	−1.36198
$753$	30.5088	1.11180
$754$	7.43623	0.270812
$755$	−11.5321	−0.419698
$756$	−1.27327	−0.0463085
$757$	−13.2416	−0.481275	−0.240638	−	0.970615i	$-0.577357\pi$
$757$	−13.2416	−0.481275	−0.240638	+	0.970615i	$0.577357\pi$
$758$	6.19739	0.225099
$759$	0	0
$760$	−0.825180	−0.0299324
$761$	42.2650	1.53210	0.766052	−	0.642779i	$-0.222219\pi$
$761$	42.2650	1.53210	0.766052	+	0.642779i	$0.222219\pi$
$762$	−15.9117	−0.576422
$763$	−5.70098	−0.206389
$764$	−1.42900	−0.0516995
$765$	0.0890330	0.00321900
$766$	−10.4566	−0.377813
$767$	10.1918	0.368005
$768$	7.22995	0.260888
$769$	−14.3054	−0.515867	−0.257934	−	0.966163i	$-0.583042\pi$
$769$	−14.3054	−0.515867	−0.257934	+	0.966163i	$0.583042\pi$
$770$	0	0
$771$	−30.9113	−1.11324
$772$	0.338940	0.0121987
$773$	−14.0653	−0.505894	−0.252947	−	0.967480i	$-0.581400\pi$
$773$	−14.0653	−0.505894	−0.252947	+	0.967480i	$0.581400\pi$
$774$	−19.3633	−0.696000
$775$	−2.58497	−0.0928547
$776$	−10.8296	−0.388760
$777$	7.72666	0.277192
$778$	−34.7870	−1.24717
$779$	−1.51029	−0.0541117
$780$	−1.93491	−0.0692808
$781$	0	0
$782$	0.565792	0.0202327
$783$	−4.43125	−0.158360
$784$	−4.40054	−0.157162
$785$	−13.0364	−0.465290
$786$	23.9607	0.854651
$787$	48.4622	1.72749	0.863746	−	0.503928i	$-0.168112\pi$
$787$	48.4622	1.72749	0.863746	+	0.503928i	$0.168112\pi$
$788$	−5.13127	−0.182794
$789$	−10.9876	−0.391169
$790$	2.26701	0.0806567
$791$	14.2657	0.507231
$792$	0	0
$793$	36.3716	1.29159
$794$	41.1506	1.46038
$795$	12.8256	0.454878
$796$	−1.31834	−0.0467273
$797$	33.3889	1.18270	0.591348	−	0.806417i	$-0.298596\pi$
$797$	33.3889	1.18270	0.591348	+	0.806417i	$0.298596\pi$
$798$	−0.628326	−0.0222425
$799$	0.643198	0.0227547
$800$	−1.27116	−0.0449423
$801$	−0.910399	−0.0321674
$802$	12.0754	0.426397
$803$	0	0
$804$	0.674111	0.0237741
$805$	−5.00434	−0.176380
$806$	−24.4665	−0.861795
$807$	4.75216	0.167284
$808$	16.2536	0.571801
$809$	3.24062	0.113934	0.0569670	−	0.998376i	$-0.481857\pi$
$809$	3.24062	0.113934	0.0569670	+	0.998376i	$0.481857\pi$
$810$	6.10965	0.214671
$811$	−24.2686	−0.852185	−0.426092	−	0.904680i	$-0.640110\pi$
$811$	−24.2686	−0.852185	−0.426092	+	0.904680i	$0.640110\pi$
$812$	0.177365	0.00622429
$813$	−23.9198	−0.838906
$814$	0	0
$815$	−20.0259	−0.701478
$816$	−0.450535	−0.0157719
$817$	−3.44396	−0.120489
$818$	2.87955	0.100681
$819$	−7.45345	−0.260445
$820$	−1.09369	−0.0381934
$821$	31.5739	1.10194	0.550968	−	0.834526i	$-0.314258\pi$
$821$	31.5739	1.10194	0.550968	+	0.834526i	$0.314258\pi$
$822$	−25.9479	−0.905038
$823$	−22.2420	−0.775309	−0.387655	−	0.921805i	$-0.626715\pi$
$823$	−22.2420	−0.775309	−0.387655	+	0.921805i	$0.626715\pi$
$824$	28.4707	0.991825
$825$	0	0
$826$	2.39669	0.0833915
$827$	−7.14896	−0.248594	−0.124297	−	0.992245i	$-0.539668\pi$
$827$	−7.14896	−0.248594	−0.124297	+	0.992245i	$0.539668\pi$
$828$	−1.32726	−0.0461256
$829$	34.7140	1.20567	0.602834	−	0.797866i	$-0.294038\pi$
$829$	34.7140	1.20567	0.602834	+	0.797866i	$0.294038\pi$
$830$	9.73689	0.337972
$831$	−23.3229	−0.809062
$832$	43.8046	1.51865
$833$	0.0757830	0.00262573
$834$	−13.7057	−0.474589
$835$	17.8818	0.618824
$836$	0	0
$837$	14.5796	0.503944
$838$	−38.8511	−1.34209
$839$	44.5054	1.53650	0.768249	−	0.640151i	$-0.221128\pi$
$839$	44.5054	1.53650	0.768249	+	0.640151i	$0.221128\pi$
$840$	3.57605	0.123385
$841$	−28.3827	−0.978715
$842$	2.38492	0.0821897
$843$	−15.1322	−0.521180
$844$	−5.36291	−0.184599
$845$	−27.2492	−0.937399
$846$	−14.8761	−0.511452
$847$	0	0
$848$	41.7767	1.43462
$849$	23.3657	0.801910
$850$	0.113060	0.00387794
$851$	28.6212	0.981122
$852$	4.79285	0.164200
$853$	−34.4171	−1.17842	−0.589209	−	0.807980i	$-0.700561\pi$
$853$	−34.4171	−1.17842	−0.589209	+	0.807980i	$0.700561\pi$
$854$	8.55307	0.292680
$855$	−0.366248	−0.0125254
$856$	20.3971	0.697159
$857$	46.5242	1.58924	0.794618	−	0.607109i	$-0.207671\pi$
$857$	46.5242	1.58924	0.794618	+	0.607109i	$0.207671\pi$
$858$	0	0
$859$	−46.5008	−1.58659	−0.793293	−	0.608840i	$-0.791635\pi$
$859$	−46.5008	−1.58659	−0.793293	+	0.608840i	$0.791635\pi$
$860$	−2.49399	−0.0850442
$861$	6.54507	0.223055
$862$	35.2661	1.20117
$863$	−2.48059	−0.0844403	−0.0422201	−	0.999108i	$-0.513443\pi$
$863$	−2.48059	−0.0844403	−0.0422201	+	0.999108i	$0.513443\pi$
$864$	7.16953	0.243912
$865$	−22.6352	−0.769619
$866$	48.3029	1.64140
$867$	−22.9590	−0.779728
$868$	−0.583561	−0.0198074
$869$	0	0
$870$	−1.58353	−0.0536865
$871$	14.0226	0.475137
$872$	15.0904	0.511027
$873$	−4.80661	−0.162679
$874$	−2.32745	−0.0787273
$875$	−1.00000	−0.0338062
$876$	0.00863871	0.000291875 0
$877$	−0.305749	−0.0103244	−0.00516220	−	0.999987i	$-0.501643\pi$
$877$	−0.305749	−0.0103244	−0.00516220	+	0.999987i	$0.501643\pi$
$878$	−17.9418	−0.605508
$879$	−40.5255	−1.36689
$880$	0	0
$881$	7.28125	0.245312	0.122656	−	0.992449i	$-0.460859\pi$
$881$	7.28125	0.245312	0.122656	+	0.992449i	$0.460859\pi$
$882$	−1.75274	−0.0590178
$883$	−43.6079	−1.46752	−0.733761	−	0.679408i	$-0.762237\pi$
$883$	−43.6079	−1.46752	−0.733761	+	0.679408i	$0.762237\pi$
$884$	0.108538	0.00365053
$885$	−2.17032	−0.0729545
$886$	45.9688	1.54435
$887$	−35.0886	−1.17816	−0.589081	−	0.808074i	$-0.700510\pi$
$887$	−35.0886	−1.17816	−0.589081	+	0.808074i	$0.700510\pi$
$888$	−20.4524	−0.686338
$889$	−7.89458	−0.264776
$890$	−1.15609	−0.0387522
$891$	0	0
$892$	−4.18807	−0.140227
$893$	−2.64587	−0.0885408
$894$	24.9366	0.834006
$895$	−15.0254	−0.502244
$896$	12.8433	0.429065
$897$	42.8919	1.43212
$898$	−32.2883	−1.07747
$899$	−2.03091	−0.0677347
$900$	−0.265223	−0.00884076
$901$	−0.719449	−0.0239683
$902$	0	0
$903$	14.9249	0.496671
$904$	−37.7613	−1.25592
$905$	13.1748	0.437946
$906$	23.2434	0.772209
$907$	−58.3903	−1.93882	−0.969409	−	0.245452i	$-0.921064\pi$
$907$	−58.3903	−1.93882	−0.969409	+	0.245452i	$0.921064\pi$
$908$	−5.10440	−0.169396
$909$	7.21402	0.239274
$910$	−9.46492	−0.313759
$911$	−37.8273	−1.25328	−0.626638	−	0.779310i	$-0.715570\pi$
$911$	−37.8273	−1.25328	−0.626638	+	0.779310i	$0.715570\pi$
$912$	1.85333	0.0613698
$913$	0	0
$914$	−59.4064	−1.96499
$915$	−7.74522	−0.256049
$916$	5.59356	0.184816
$917$	11.8881	0.392579
$918$	−0.637677	−0.0210465
$919$	−6.18399	−0.203991	−0.101996	−	0.994785i	$-0.532523\pi$
$919$	−6.18399	−0.203991	−0.101996	+	0.994785i	$0.532523\pi$
$920$	13.2464	0.436722
$921$	19.0643	0.628191
$922$	42.2825	1.39250
$923$	99.6988	3.28163
$924$	0	0
$925$	5.71928	0.188049
$926$	7.13760	0.234556
$927$	12.6364	0.415035
$928$	−0.998704	−0.0327841
$929$	−3.35897	−0.110204	−0.0551021	−	0.998481i	$-0.517548\pi$
$929$	−3.35897	−0.110204	−0.0551021	+	0.998481i	$0.517548\pi$
$930$	5.21007	0.170845
$931$	−0.311743	−0.0102169
$932$	4.65884	0.152605
$933$	−24.7268	−0.809519
$934$	17.3310	0.567086
$935$	0	0
$936$	19.7292	0.644870
$937$	−7.48058	−0.244380	−0.122190	−	0.992507i	$-0.538992\pi$
$937$	−7.48058	−0.244380	−0.122190	+	0.992507i	$0.538992\pi$
$938$	3.29752	0.107668
$939$	39.1105	1.27632
$940$	−1.91604	−0.0624943
$941$	−31.9681	−1.04213	−0.521065	−	0.853517i	$-0.674465\pi$
$941$	−31.9681	−1.04213	−0.521065	+	0.853517i	$0.674465\pi$
$942$	26.2753	0.856094
$943$	24.2443	0.789505
$944$	−7.06935	−0.230088
$945$	5.64015	0.183474
$946$	0	0
$947$	14.0660	0.457083	0.228541	−	0.973534i	$-0.426604\pi$
$947$	14.0660	0.457083	0.228541	+	0.973534i	$0.426604\pi$
$948$	−0.463444	−0.0150520
$949$	0.179699	0.00583327
$950$	−0.465087	−0.0150894
$951$	−34.4103	−1.11583
$952$	−0.200597	−0.00650139
$953$	−8.86691	−0.287227	−0.143614	−	0.989634i	$-0.545872\pi$
$953$	−8.86691	−0.287227	−0.143614	+	0.989634i	$0.545872\pi$
$954$	16.6397	0.538730
$955$	6.32997	0.204833
$956$	−3.86533	−0.125014
$957$	0	0
$958$	43.3501	1.40058
$959$	−12.8740	−0.415724
$960$	−9.32806	−0.301062
$961$	−24.3180	−0.784450
$962$	54.1325	1.74530
$963$	9.05306	0.291731
$964$	3.98584	0.128375
$965$	−1.50138	−0.0483312
$966$	10.0864	0.324524
$967$	45.8049	1.47299	0.736494	−	0.676445i	$-0.236480\pi$
$967$	45.8049	1.47299	0.736494	+	0.676445i	$0.236480\pi$
$968$	0	0
$969$	−0.0319167	−0.00102531
$970$	−6.10377	−0.195980
$971$	−9.14234	−0.293392	−0.146696	−	0.989182i	$-0.546864\pi$
$971$	−9.14234	−0.293392	−0.146696	+	0.989182i	$0.546864\pi$
$972$	2.57083	0.0824594
$973$	−6.80005	−0.218000
$974$	46.8272	1.50044
$975$	8.57095	0.274490
$976$	−25.2284	−0.807541
$977$	−24.5682	−0.786008	−0.393004	−	0.919537i	$-0.628564\pi$
$977$	−24.5682	−0.786008	−0.393004	+	0.919537i	$0.628564\pi$
$978$	40.3628	1.29066
$979$	0	0
$980$	−0.225752	−0.00721138
$981$	6.69774	0.213842
$982$	−30.7368	−0.980851
$983$	−13.9590	−0.445224	−0.222612	−	0.974907i	$-0.571458\pi$
$983$	−13.9590	−0.445224	−0.222612	+	0.974907i	$0.571458\pi$
$984$	−17.3248	−0.552293
$985$	22.7297	0.724228
$986$	0.0888274	0.00282884
$987$	11.4663	0.364976
$988$	−0.446484	−0.0142046
$989$	55.2852	1.75797
$990$	0	0
$991$	−15.1429	−0.481031	−0.240515	−	0.970645i	$-0.577316\pi$
$991$	−15.1429	−0.481031	−0.240515	+	0.970645i	$0.577316\pi$
$992$	3.28591	0.104328
$993$	33.8027	1.07269
$994$	23.4450	0.743630
$995$	5.83977	0.185133
$996$	−1.99051	−0.0630716
$997$	20.4780	0.648545	0.324273	−	0.945964i	$-0.394881\pi$
$997$	20.4780	0.648545	0.324273	+	0.945964i	$0.394881\pi$
$998$	−0.365360	−0.0115653
$999$	−32.2576	−1.02058

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bm.1.10		14
11.3	even	5		385.2.n.e.141.5	yes	28
11.4	even	5		385.2.n.e.71.5	✓	28
11.10	odd	2		4235.2.a.bn.1.5		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.e.71.5	✓	28	11.4	even	5
385.2.n.e.141.5	yes	28	11.3	even	5
4235.2.a.bm.1.10		14	1.1	even	1	trivial
4235.2.a.bn.1.5		14	11.10	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.49190 q^{2} +1.35098 q^{3} +0.225752 q^{4} -1.00000 q^{5} +2.01553 q^{6} +1.00000 q^{7} -2.64699 q^{8} -1.17484 q^{9} +O(q^{10})\)	\(q+1.49190 q^{2} +1.35098 q^{3} +0.225752 q^{4} -1.00000 q^{5} +2.01553 q^{6} +1.00000 q^{7} -2.64699 q^{8} -1.17484 q^{9} -1.49190 q^{10} +0.304987 q^{12} +6.34422 q^{13} +1.49190 q^{14} -1.35098 q^{15} -4.40054 q^{16} +0.0757830 q^{17} -1.75274 q^{18} -0.311743 q^{19} -0.225752 q^{20} +1.35098 q^{21} +5.00434 q^{23} -3.57605 q^{24} +1.00000 q^{25} +9.46492 q^{26} -5.64015 q^{27} +0.225752 q^{28} +0.785663 q^{29} -2.01553 q^{30} -2.58497 q^{31} -1.27116 q^{32} +0.113060 q^{34} -1.00000 q^{35} -0.265223 q^{36} +5.71928 q^{37} -0.465087 q^{38} +8.57095 q^{39} +2.64699 q^{40} +4.84467 q^{41} +2.01553 q^{42} +11.0475 q^{43} +1.17484 q^{45} +7.46595 q^{46} +8.48737 q^{47} -5.94506 q^{48} +1.00000 q^{49} +1.49190 q^{50} +0.102382 q^{51} +1.43222 q^{52} -9.49354 q^{53} -8.41451 q^{54} -2.64699 q^{56} -0.421159 q^{57} +1.17213 q^{58} +1.60647 q^{59} -0.304987 q^{60} +5.73302 q^{61} -3.85650 q^{62} -1.17484 q^{63} +6.90464 q^{64} -6.34422 q^{65} +2.21029 q^{67} +0.0171082 q^{68} +6.76078 q^{69} -1.49190 q^{70} +15.7149 q^{71} +3.10980 q^{72} +0.0283248 q^{73} +8.53257 q^{74} +1.35098 q^{75} -0.0703765 q^{76} +12.7870 q^{78} -1.51955 q^{79} +4.40054 q^{80} -4.09523 q^{81} +7.22774 q^{82} -6.52652 q^{83} +0.304987 q^{84} -0.0757830 q^{85} +16.4817 q^{86} +1.06142 q^{87} +0.774912 q^{89} +1.75274 q^{90} +6.34422 q^{91} +1.12974 q^{92} -3.49225 q^{93} +12.6623 q^{94} +0.311743 q^{95} -1.71732 q^{96} +4.09128 q^{97} +1.49190 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} + q^{6} + 14 q^{7} - 3 q^{8} + 17 q^{9}+O(q^{10}) \) 14 * q - q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 + q^6 + 14 * q^7 - 3 * q^8 + 17 * q^9	\( 14 q - q^{2} + 5 q^{3} + 21 q^{4} - 14 q^{5} + q^{6} + 14 q^{7} - 3 q^{8} + 17 q^{9} + q^{10} + 15 q^{12} + 10 q^{13} - q^{14} - 5 q^{15} + 31 q^{16} + 11 q^{17} - 21 q^{18} + 21 q^{19} - 21 q^{20} + 5 q^{21} + 8 q^{23} + 22 q^{24} + 14 q^{25} - 18 q^{26} + 26 q^{27} + 21 q^{28} - 4 q^{29} - q^{30} + 6 q^{31} - 42 q^{32} + 16 q^{34} - 14 q^{35} + 28 q^{36} + 48 q^{37} + 35 q^{38} + 6 q^{39} + 3 q^{40} + 13 q^{41} + q^{42} - 17 q^{45} - 31 q^{46} + 11 q^{47} + 59 q^{48} + 14 q^{49} - q^{50} - 33 q^{51} + 52 q^{52} + 31 q^{53} - 57 q^{54} - 3 q^{56} - 4 q^{57} + 52 q^{58} - 4 q^{59} - 15 q^{60} + 17 q^{61} - 27 q^{62} + 17 q^{63} + 43 q^{64} - 10 q^{65} + 45 q^{67} + 14 q^{68} + 20 q^{69} + q^{70} - 6 q^{71} - 14 q^{72} + 11 q^{73} - 33 q^{74} + 5 q^{75} - 5 q^{76} + 52 q^{78} + 30 q^{79} - 31 q^{80} - 6 q^{81} + 26 q^{82} + 23 q^{83} + 15 q^{84} - 11 q^{85} - 23 q^{86} + 23 q^{87} - 15 q^{89} + 21 q^{90} + 10 q^{91} + 44 q^{92} + 29 q^{93} + 49 q^{94} - 21 q^{95} - 52 q^{96} + 44 q^{97} - q^{98}+O(q^{100}) \) 14 * q - q^2 + 5 * q^3 + 21 * q^4 - 14 * q^5 + q^6 + 14 * q^7 - 3 * q^8 + 17 * q^9 + q^10 + 15 * q^12 + 10 * q^13 - q^14 - 5 * q^15 + 31 * q^16 + 11 * q^17 - 21 * q^18 + 21 * q^19 - 21 * q^20 + 5 * q^21 + 8 * q^23 + 22 * q^24 + 14 * q^25 - 18 * q^26 + 26 * q^27 + 21 * q^28 - 4 * q^29 - q^30 + 6 * q^31 - 42 * q^32 + 16 * q^34 - 14 * q^35 + 28 * q^36 + 48 * q^37 + 35 * q^38 + 6 * q^39 + 3 * q^40 + 13 * q^41 + q^42 - 17 * q^45 - 31 * q^46 + 11 * q^47 + 59 * q^48 + 14 * q^49 - q^50 - 33 * q^51 + 52 * q^52 + 31 * q^53 - 57 * q^54 - 3 * q^56 - 4 * q^57 + 52 * q^58 - 4 * q^59 - 15 * q^60 + 17 * q^61 - 27 * q^62 + 17 * q^63 + 43 * q^64 - 10 * q^65 + 45 * q^67 + 14 * q^68 + 20 * q^69 + q^70 - 6 * q^71 - 14 * q^72 + 11 * q^73 - 33 * q^74 + 5 * q^75 - 5 * q^76 + 52 * q^78 + 30 * q^79 - 31 * q^80 - 6 * q^81 + 26 * q^82 + 23 * q^83 + 15 * q^84 - 11 * q^85 - 23 * q^86 + 23 * q^87 - 15 * q^89 + 21 * q^90 + 10 * q^91 + 44 * q^92 + 29 * q^93 + 49 * q^94 - 21 * q^95 - 52 * q^96 + 44 * q^97 - q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more