LMFDB - Embedded newform 4235.2.a.bo.1.18

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			1.18
Root			$-2.67006$ 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)

$f(q)$	$=$	$q+2.67006 q^{2} -3.09834 q^{3} +5.12921 q^{4} +1.00000 q^{5} -8.27276 q^{6} -1.00000 q^{7} +8.35518 q^{8} +6.59974 q^{9} +O(q^{10})$	\(q+2.67006 q^{2} -3.09834 q^{3} +5.12921 q^{4} +1.00000 q^{5} -8.27276 q^{6} -1.00000 q^{7} +8.35518 q^{8} +6.59974 q^{9} +2.67006 q^{10} -15.8921 q^{12} -2.75125 q^{13} -2.67006 q^{14} -3.09834 q^{15} +12.0504 q^{16} +5.39845 q^{17} +17.6217 q^{18} +0.181499 q^{19} +5.12921 q^{20} +3.09834 q^{21} -3.93235 q^{23} -25.8872 q^{24} +1.00000 q^{25} -7.34599 q^{26} -11.1532 q^{27} -5.12921 q^{28} +8.00932 q^{29} -8.27276 q^{30} -3.02596 q^{31} +15.4649 q^{32} +14.4142 q^{34} -1.00000 q^{35} +33.8515 q^{36} +6.80944 q^{37} +0.484613 q^{38} +8.52431 q^{39} +8.35518 q^{40} +1.17738 q^{41} +8.27276 q^{42} +7.58022 q^{43} +6.59974 q^{45} -10.4996 q^{46} -5.56162 q^{47} -37.3363 q^{48} +1.00000 q^{49} +2.67006 q^{50} -16.7263 q^{51} -14.1117 q^{52} +6.23222 q^{53} -29.7798 q^{54} -8.35518 q^{56} -0.562346 q^{57} +21.3854 q^{58} +9.44947 q^{59} -15.8921 q^{60} -6.09558 q^{61} -8.07950 q^{62} -6.59974 q^{63} +17.1914 q^{64} -2.75125 q^{65} -15.5238 q^{67} +27.6898 q^{68} +12.1838 q^{69} -2.67006 q^{70} +8.88216 q^{71} +55.1420 q^{72} -2.58692 q^{73} +18.1816 q^{74} -3.09834 q^{75} +0.930946 q^{76} +22.7604 q^{78} -0.967879 q^{79} +12.0504 q^{80} +14.7573 q^{81} +3.14367 q^{82} +6.34917 q^{83} +15.8921 q^{84} +5.39845 q^{85} +20.2396 q^{86} -24.8156 q^{87} +8.87631 q^{89} +17.6217 q^{90} +2.75125 q^{91} -20.1699 q^{92} +9.37548 q^{93} -14.8498 q^{94} +0.181499 q^{95} -47.9155 q^{96} +12.6197 q^{97} +2.67006 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.67006	1.88802	0.944008	−	0.329922i	$-0.107022\pi$
$2$	2.67006	1.88802	0.944008	+	0.329922i	$0.107022\pi$
$3$	−3.09834	−1.78883	−0.894415	−	0.447238i	$-0.852408\pi$
$3$	−3.09834	−1.78883	−0.894415	+	0.447238i	$0.852408\pi$
$4$	5.12921	2.56461
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−8.27276	−3.37734
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	8.35518	2.95400
$9$	6.59974	2.19991
$10$	2.67006	0.844347
$11$	0	0
$11$	0	0
$12$	−15.8921	−4.58764
$13$	−2.75125	−0.763058	−0.381529	−	0.924357i	$-0.624602\pi$
$13$	−2.75125	−0.763058	−0.381529	+	0.924357i	$0.624602\pi$
$14$	−2.67006	−0.713603
$15$	−3.09834	−0.799989
$16$	12.0504	3.01260
$17$	5.39845	1.30932	0.654658	−	0.755925i	$-0.272813\pi$
$17$	5.39845	1.30932	0.654658	+	0.755925i	$0.272813\pi$
$18$	17.6217	4.15347
$19$	0.181499	0.0416387	0.0208193	−	0.999783i	$-0.493373\pi$
$19$	0.181499	0.0416387	0.0208193	+	0.999783i	$0.493373\pi$
$20$	5.12921	1.14693
$21$	3.09834	0.676114
$22$	0	0
$23$	−3.93235	−0.819952	−0.409976	−	0.912096i	$-0.634463\pi$
$23$	−3.93235	−0.819952	−0.409976	+	0.912096i	$0.634463\pi$
$24$	−25.8872	−5.28421
$25$	1.00000	0.200000
$26$	−7.34599	−1.44067
$27$	−11.1532	−2.14644
$28$	−5.12921	−0.969330
$29$	8.00932	1.48729	0.743647	−	0.668572i	$-0.233094\pi$
$29$	8.00932	1.48729	0.743647	+	0.668572i	$0.233094\pi$
$30$	−8.27276	−1.51039
$31$	−3.02596	−0.543479	−0.271740	−	0.962371i	$-0.587599\pi$
$31$	−3.02596	−0.543479	−0.271740	+	0.962371i	$0.587599\pi$
$32$	15.4649	2.73383
$33$	0	0
$34$	14.4142	2.47201
$35$	−1.00000	−0.169031
$36$	33.8515	5.64191
$37$	6.80944	1.11946	0.559732	−	0.828673i	$-0.310904\pi$
$37$	6.80944	1.11946	0.559732	+	0.828673i	$0.310904\pi$
$38$	0.484613	0.0786145
$39$	8.52431	1.36498
$40$	8.35518	1.32107
$41$	1.17738	0.183876	0.0919379	−	0.995765i	$-0.470694\pi$
$41$	1.17738	0.183876	0.0919379	+	0.995765i	$0.470694\pi$
$42$	8.27276	1.27651
$43$	7.58022	1.15597	0.577986	−	0.816046i	$-0.303839\pi$
$43$	7.58022	1.15597	0.577986	+	0.816046i	$0.303839\pi$
$44$	0	0
$45$	6.59974	0.983831
$46$	−10.4996	−1.54808
$47$	−5.56162	−0.811245	−0.405623	−	0.914041i	$-0.632945\pi$
$47$	−5.56162	−0.811245	−0.405623	+	0.914041i	$0.632945\pi$
$48$	−37.3363	−5.38902
$49$	1.00000	0.142857
$50$	2.67006	0.377603
$51$	−16.7263	−2.34214
$52$	−14.1117	−1.95694
$53$	6.23222	0.856061	0.428031	−	0.903764i	$-0.359208\pi$
$53$	6.23222	0.856061	0.428031	+	0.903764i	$0.359208\pi$
$54$	−29.7798	−4.05252
$55$	0	0
$56$	−8.35518	−1.11651
$57$	−0.562346	−0.0744846
$58$	21.3854	2.80804
$59$	9.44947	1.23022	0.615108	−	0.788443i	$-0.289112\pi$
$59$	9.44947	1.23022	0.615108	+	0.788443i	$0.289112\pi$
$60$	−15.8921	−2.05166
$61$	−6.09558	−0.780459	−0.390230	−	0.920718i	$-0.627604\pi$
$61$	−6.09558	−0.780459	−0.390230	+	0.920718i	$0.627604\pi$
$62$	−8.07950	−1.02610
$63$	−6.59974	−0.831489
$64$	17.1914	2.14892
$65$	−2.75125	−0.341250
$66$	0	0
$67$	−15.5238	−1.89653	−0.948267	−	0.317473i	$-0.897166\pi$
$67$	−15.5238	−1.89653	−0.948267	+	0.317473i	$0.897166\pi$
$68$	27.6898	3.35788
$69$	12.1838	1.46676
$70$	−2.67006	−0.319133
$71$	8.88216	1.05412	0.527059	−	0.849829i	$-0.323295\pi$
$71$	8.88216	1.05412	0.527059	+	0.849829i	$0.323295\pi$
$72$	55.1420	6.49855
$73$	−2.58692	−0.302776	−0.151388	−	0.988474i	$-0.548374\pi$
$73$	−2.58692	−0.302776	−0.151388	+	0.988474i	$0.548374\pi$
$74$	18.1816	2.11357
$75$	−3.09834	−0.357766
$76$	0.930946	0.106787
$77$	0	0
$78$	22.7604	2.57711
$79$	−0.967879	−0.108895	−0.0544474	−	0.998517i	$-0.517340\pi$
$79$	−0.967879	−0.108895	−0.0544474	+	0.998517i	$0.517340\pi$
$80$	12.0504	1.34727
$81$	14.7573	1.63971
$82$	3.14367	0.347160
$83$	6.34917	0.696912	0.348456	−	0.937325i	$-0.386706\pi$
$83$	6.34917	0.696912	0.348456	+	0.937325i	$0.386706\pi$
$84$	15.8921	1.73397
$85$	5.39845	0.585544
$86$	20.2396	2.18250
$87$	−24.8156	−2.66052
$88$	0	0
$89$	8.87631	0.940887	0.470443	−	0.882430i	$-0.344094\pi$
$89$	8.87631	0.940887	0.470443	+	0.882430i	$0.344094\pi$
$90$	17.6217	1.85749
$91$	2.75125	0.288409
$92$	−20.1699	−2.10285
$93$	9.37548	0.972192
$94$	−14.8498	−1.53164
$95$	0.181499	0.0186214
$96$	−47.9155	−4.89036
$97$	12.6197	1.28134	0.640669	−	0.767817i	$-0.278657\pi$
$97$	12.6197	1.28134	0.640669	+	0.767817i	$0.278657\pi$
$98$	2.67006	0.269717
$99$	0	0
$100$	5.12921	0.512921
$101$	−0.490544	−0.0488110	−0.0244055	−	0.999702i	$-0.507769\pi$
$101$	−0.490544	−0.0488110	−0.0244055	+	0.999702i	$0.507769\pi$
$102$	−44.6601	−4.42201
$103$	18.0612	1.77962	0.889810	−	0.456332i	$-0.150837\pi$
$103$	18.0612	1.77962	0.889810	+	0.456332i	$0.150837\pi$
$104$	−22.9871	−2.25408
$105$	3.09834	0.302367
$106$	16.6404	1.61626
$107$	−7.93973	−0.767563	−0.383781	−	0.923424i	$-0.625378\pi$
$107$	−7.93973	−0.767563	−0.383781	+	0.923424i	$0.625378\pi$
$108$	−57.2073	−5.50477
$109$	1.31837	0.126277	0.0631385	−	0.998005i	$-0.479889\pi$
$109$	1.31837	0.126277	0.0631385	+	0.998005i	$0.479889\pi$
$110$	0	0
$111$	−21.0980	−2.00253
$112$	−12.0504	−1.13865
$113$	−15.6864	−1.47565	−0.737827	−	0.674990i	$-0.764148\pi$
$113$	−15.6864	−1.47565	−0.737827	+	0.674990i	$0.764148\pi$
$114$	−1.50150	−0.140628
$115$	−3.93235	−0.366694
$116$	41.0815	3.81432
$117$	−18.1575	−1.67866
$118$	25.2306	2.32267
$119$	−5.39845	−0.494875
$120$	−25.8872	−2.36317
$121$	0	0
$122$	−16.2756	−1.47352
$123$	−3.64793	−0.328922
$124$	−15.5208	−1.39381
$125$	1.00000	0.0894427
$126$	−17.6217	−1.56986
$127$	−6.14787	−0.545535	−0.272768	−	0.962080i	$-0.587939\pi$
$127$	−6.14787	−0.545535	−0.272768	+	0.962080i	$0.587939\pi$
$128$	14.9722	1.32337
$129$	−23.4861	−2.06784
$130$	−7.34599	−0.644286
$131$	15.4723	1.35182	0.675911	−	0.736983i	$-0.263750\pi$
$131$	15.4723	1.35182	0.675911	+	0.736983i	$0.263750\pi$
$132$	0	0
$133$	−0.181499	−0.0157379
$134$	−41.4495	−3.58069
$135$	−11.1532	−0.959918
$136$	45.1050	3.86772
$137$	11.8290	1.01062	0.505311	−	0.862937i	$-0.331378\pi$
$137$	11.8290	1.01062	0.505311	+	0.862937i	$0.331378\pi$
$138$	32.5314	2.76926
$139$	−6.08494	−0.516118	−0.258059	−	0.966129i	$-0.583083\pi$
$139$	−6.08494	−0.516118	−0.258059	+	0.966129i	$0.583083\pi$
$140$	−5.12921	−0.433497
$141$	17.2318	1.45118
$142$	23.7159	1.99019
$143$	0	0
$144$	79.5294	6.62745
$145$	8.00932	0.665138
$146$	−6.90722	−0.571646
$147$	−3.09834	−0.255547
$148$	34.9271	2.87099
$149$	21.9841	1.80101	0.900503	−	0.434849i	$-0.143198\pi$
$149$	21.9841	1.80101	0.900503	+	0.434849i	$0.143198\pi$
$150$	−8.27276	−0.675468
$151$	13.6268	1.10893	0.554466	−	0.832206i	$-0.312923\pi$
$151$	13.6268	1.10893	0.554466	+	0.832206i	$0.312923\pi$
$152$	1.51646	0.123001
$153$	35.6284	2.88038
$154$	0	0
$155$	−3.02596	−0.243051
$156$	43.7230	3.50064
$157$	2.91441	0.232595	0.116298	−	0.993214i	$-0.462897\pi$
$157$	2.91441	0.232595	0.116298	+	0.993214i	$0.462897\pi$
$158$	−2.58429	−0.205595
$159$	−19.3096	−1.53135
$160$	15.4649	1.22261
$161$	3.93235	0.309913
$162$	39.4030	3.09579
$163$	−6.42124	−0.502950	−0.251475	−	0.967864i	$-0.580916\pi$
$163$	−6.42124	−0.502950	−0.251475	+	0.967864i	$0.580916\pi$
$164$	6.03903	0.471569
$165$	0	0
$166$	16.9526	1.31578
$167$	10.4008	0.804840	0.402420	−	0.915455i	$-0.368169\pi$
$167$	10.4008	0.804840	0.402420	+	0.915455i	$0.368169\pi$
$168$	25.8872	1.99724
$169$	−5.43065	−0.417742
$170$	14.4142	1.10552
$171$	1.19785	0.0916015
$172$	38.8806	2.96461
$173$	−6.03379	−0.458741	−0.229370	−	0.973339i	$-0.573667\pi$
$173$	−6.03379	−0.458741	−0.229370	+	0.973339i	$0.573667\pi$
$174$	−66.2592	−5.02310
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−29.2777	−2.20065
$178$	23.7003	1.77641
$179$	13.2402	0.989621	0.494811	−	0.869001i	$-0.335237\pi$
$179$	13.2402	0.989621	0.494811	+	0.869001i	$0.335237\pi$
$180$	33.8515	2.52314
$181$	−5.44909	−0.405028	−0.202514	−	0.979279i	$-0.564911\pi$
$181$	−5.44909	−0.405028	−0.202514	+	0.979279i	$0.564911\pi$
$182$	7.34599	0.544521
$183$	18.8862	1.39611
$184$	−32.8555	−2.42214
$185$	6.80944	0.500640
$186$	25.0331	1.83551
$187$	0	0
$188$	−28.5267	−2.08052
$189$	11.1532	0.811278
$190$	0.484613	0.0351575
$191$	4.67717	0.338428	0.169214	−	0.985579i	$-0.445877\pi$
$191$	4.67717	0.338428	0.169214	+	0.985579i	$0.445877\pi$
$192$	−53.2648	−3.84405
$193$	−2.26026	−0.162697	−0.0813484	−	0.996686i	$-0.525923\pi$
$193$	−2.26026	−0.162697	−0.0813484	+	0.996686i	$0.525923\pi$
$194$	33.6954	2.41919
$195$	8.52431	0.610438
$196$	5.12921	0.366372
$197$	−3.25787	−0.232114	−0.116057	−	0.993243i	$-0.537025\pi$
$197$	−3.25787	−0.232114	−0.116057	+	0.993243i	$0.537025\pi$
$198$	0	0
$199$	−0.180575	−0.0128006	−0.00640030	−	0.999980i	$-0.502037\pi$
$199$	−0.180575	−0.0128006	−0.00640030	+	0.999980i	$0.502037\pi$
$200$	8.35518	0.590800
$201$	48.0981	3.39258
$202$	−1.30978	−0.0921560
$203$	−8.00932	−0.562144
$204$	−85.7925	−6.00668
$205$	1.17738	0.0822317
$206$	48.2244	3.35995
$207$	−25.9525	−1.80382
$208$	−33.1536	−2.29879
$209$	0	0
$210$	8.27276	0.570875
$211$	7.72279	0.531659	0.265829	−	0.964020i	$-0.414354\pi$
$211$	7.72279	0.531659	0.265829	+	0.964020i	$0.414354\pi$
$212$	31.9664	2.19546
$213$	−27.5200	−1.88564
$214$	−21.1995	−1.44917
$215$	7.58022	0.516967
$216$	−93.1872	−6.34059
$217$	3.02596	0.205416
$218$	3.52013	0.238413
$219$	8.01517	0.541615
$220$	0	0
$221$	−14.8525	−0.999085
$222$	−56.3329	−3.78081
$223$	−20.5205	−1.37415	−0.687077	−	0.726584i	$-0.741107\pi$
$223$	−20.5205	−1.37415	−0.687077	+	0.726584i	$0.741107\pi$
$224$	−15.4649	−1.03329
$225$	6.59974	0.439983
$226$	−41.8836	−2.78606
$227$	−28.5136	−1.89252	−0.946258	−	0.323414i	$-0.895169\pi$
$227$	−28.5136	−1.89252	−0.946258	+	0.323414i	$0.895169\pi$
$228$	−2.88439	−0.191024
$229$	1.84664	0.122029	0.0610146	−	0.998137i	$-0.480566\pi$
$229$	1.84664	0.122029	0.0610146	+	0.998137i	$0.480566\pi$
$230$	−10.4996	−0.692324
$231$	0	0
$232$	66.9193	4.39347
$233$	3.29842	0.216087	0.108043	−	0.994146i	$-0.465541\pi$
$233$	3.29842	0.216087	0.108043	+	0.994146i	$0.465541\pi$
$234$	−48.4816	−3.16934
$235$	−5.56162	−0.362800
$236$	48.4683	3.15502
$237$	2.99882	0.194794
$238$	−14.4142	−0.934332
$239$	8.52671	0.551547	0.275774	−	0.961223i	$-0.411066\pi$
$239$	8.52671	0.551547	0.275774	+	0.961223i	$0.411066\pi$
$240$	−37.3363	−2.41004
$241$	−15.1782	−0.977714	−0.488857	−	0.872364i	$-0.662586\pi$
$241$	−15.1782	−0.977714	−0.488857	+	0.872364i	$0.662586\pi$
$242$	0	0
$243$	−12.2636	−0.786713
$244$	−31.2655	−2.00157
$245$	1.00000	0.0638877
$246$	−9.74017	−0.621011
$247$	−0.499348	−0.0317728
$248$	−25.2825	−1.60544
$249$	−19.6719	−1.24666
$250$	2.67006	0.168869
$251$	4.27519	0.269847	0.134924	−	0.990856i	$-0.456921\pi$
$251$	4.27519	0.269847	0.134924	+	0.990856i	$0.456921\pi$
$252$	−33.8515	−2.13244
$253$	0	0
$254$	−16.4152	−1.02998
$255$	−16.7263	−1.04744
$256$	5.59386	0.349616
$257$	5.99342	0.373859	0.186930	−	0.982373i	$-0.440146\pi$
$257$	5.99342	0.373859	0.186930	+	0.982373i	$0.440146\pi$
$258$	−62.7094	−3.90411
$259$	−6.80944	−0.423118
$260$	−14.1117	−0.875172
$261$	52.8595	3.27192
$262$	41.3120	2.55226
$263$	−13.6076	−0.839083	−0.419542	−	0.907736i	$-0.637809\pi$
$263$	−13.6076	−0.839083	−0.419542	+	0.907736i	$0.637809\pi$
$264$	0	0
$265$	6.23222	0.382842
$266$	−0.484613	−0.0297135
$267$	−27.5019	−1.68309
$268$	−79.6249	−4.86386
$269$	−6.46928	−0.394439	−0.197219	−	0.980359i	$-0.563191\pi$
$269$	−6.46928	−0.394439	−0.197219	+	0.980359i	$0.563191\pi$
$270$	−29.7798	−1.81234
$271$	9.25668	0.562303	0.281152	−	0.959663i	$-0.409284\pi$
$271$	9.25668	0.562303	0.281152	+	0.959663i	$0.409284\pi$
$272$	65.0534	3.94444
$273$	−8.52431	−0.515915
$274$	31.5842	1.90807
$275$	0	0
$276$	62.4932	3.76165
$277$	−22.0781	−1.32655	−0.663273	−	0.748377i	$-0.730833\pi$
$277$	−22.0781	−1.32655	−0.663273	+	0.748377i	$0.730833\pi$
$278$	−16.2471	−0.974439
$279$	−19.9706	−1.19561
$280$	−8.35518	−0.499317
$281$	5.87855	0.350685	0.175342	−	0.984508i	$-0.443897\pi$
$281$	5.87855	0.350685	0.175342	+	0.984508i	$0.443897\pi$
$282$	46.0099	2.73985
$283$	6.37564	0.378993	0.189496	−	0.981881i	$-0.439314\pi$
$283$	6.37564	0.378993	0.189496	+	0.981881i	$0.439314\pi$
$284$	45.5585	2.70340
$285$	−0.562346	−0.0333105
$286$	0	0
$287$	−1.17738	−0.0694985
$288$	102.064	6.01419
$289$	12.1433	0.714309
$290$	21.3854	1.25579
$291$	−39.1002	−2.29210
$292$	−13.2689	−0.776501
$293$	−30.7144	−1.79435	−0.897177	−	0.441670i	$-0.854386\pi$
$293$	−30.7144	−1.79435	−0.897177	+	0.441670i	$0.854386\pi$
$294$	−8.27276	−0.482477
$295$	9.44947	0.550169
$296$	56.8941	3.30690
$297$	0	0
$298$	58.6988	3.40033
$299$	10.8189	0.625671
$300$	−15.8921	−0.917529
$301$	−7.58022	−0.436917
$302$	36.3843	2.09368
$303$	1.51988	0.0873146
$304$	2.18713	0.125441
$305$	−6.09558	−0.349032
$306$	95.1298	5.43821
$307$	−16.5393	−0.943947	−0.471974	−	0.881613i	$-0.656458\pi$
$307$	−16.5393	−0.943947	−0.471974	+	0.881613i	$0.656458\pi$
$308$	0	0
$309$	−55.9597	−3.18344
$310$	−8.07950	−0.458885
$311$	−9.53057	−0.540429	−0.270215	−	0.962800i	$-0.587095\pi$
$311$	−9.53057	−0.540429	−0.270215	+	0.962800i	$0.587095\pi$
$312$	71.2221	4.03216
$313$	7.13450	0.403266	0.201633	−	0.979461i	$-0.435375\pi$
$313$	7.13450	0.403266	0.201633	+	0.979461i	$0.435375\pi$
$314$	7.78165	0.439144
$315$	−6.59974	−0.371853
$316$	−4.96446	−0.279272
$317$	9.08448	0.510235	0.255118	−	0.966910i	$-0.417886\pi$
$317$	9.08448	0.510235	0.255118	+	0.966910i	$0.417886\pi$
$318$	−51.5577	−2.89121
$319$	0	0
$320$	17.1914	0.961026
$321$	24.6000	1.37304
$322$	10.4996	0.585121
$323$	0.979812	0.0545182
$324$	75.6935	4.20520
$325$	−2.75125	−0.152612
$326$	−17.1451	−0.949578
$327$	−4.08476	−0.225888
$328$	9.83721	0.543169
$329$	5.56162	0.306622
$330$	0	0
$331$	16.2392	0.892588	0.446294	−	0.894886i	$-0.352744\pi$
$331$	16.2392	0.892588	0.446294	+	0.894886i	$0.352744\pi$
$332$	32.5662	1.78730
$333$	44.9405	2.46273
$334$	27.7708	1.51955
$335$	−15.5238	−0.848156
$336$	37.3363	2.03686
$337$	11.5916	0.631433	0.315716	−	0.948854i	$-0.397755\pi$
$337$	11.5916	0.631433	0.315716	+	0.948854i	$0.397755\pi$
$338$	−14.5001	−0.788704
$339$	48.6019	2.63969
$340$	27.6898	1.50169
$341$	0	0
$342$	3.19832	0.172945
$343$	−1.00000	−0.0539949
$344$	63.3341	3.41474
$345$	12.1838	0.655953
$346$	−16.1106	−0.866110
$347$	−24.4825	−1.31429	−0.657143	−	0.753766i	$-0.728235\pi$
$347$	−24.4825	−1.31429	−0.657143	+	0.753766i	$0.728235\pi$
$348$	−127.285	−6.82318
$349$	−4.43683	−0.237498	−0.118749	−	0.992924i	$-0.537888\pi$
$349$	−4.43683	−0.237498	−0.118749	+	0.992924i	$0.537888\pi$
$350$	−2.67006	−0.142721
$351$	30.6853	1.63786
$352$	0	0
$353$	24.7805	1.31894	0.659468	−	0.751733i	$-0.270782\pi$
$353$	24.7805	1.31894	0.659468	+	0.751733i	$0.270782\pi$
$354$	−78.1732	−4.15486
$355$	8.88216	0.471416
$356$	45.5285	2.41300
$357$	16.7263	0.885247
$358$	35.3522	1.86842
$359$	−20.4310	−1.07831	−0.539153	−	0.842208i	$-0.681256\pi$
$359$	−20.4310	−1.07831	−0.539153	+	0.842208i	$0.681256\pi$
$360$	55.1420	2.90624
$361$	−18.9671	−0.998266
$362$	−14.5494	−0.764699
$363$	0	0
$364$	14.1117	0.739655
$365$	−2.58692	−0.135406
$366$	50.4273	2.63588
$367$	−19.2061	−1.00255	−0.501276	−	0.865288i	$-0.667136\pi$
$367$	−19.2061	−1.00255	−0.501276	+	0.865288i	$0.667136\pi$
$368$	−47.3864	−2.47019
$369$	7.77039	0.404511
$370$	18.1816	0.945216
$371$	−6.23222	−0.323561
$372$	48.0888	2.49329
$373$	−21.6133	−1.11909	−0.559547	−	0.828799i	$-0.689025\pi$
$373$	−21.6133	−1.11909	−0.559547	+	0.828799i	$0.689025\pi$
$374$	0	0
$375$	−3.09834	−0.159998
$376$	−46.4683	−2.39642
$377$	−22.0356	−1.13489
$378$	29.7798	1.53171
$379$	−25.1002	−1.28931	−0.644655	−	0.764474i	$-0.722999\pi$
$379$	−25.1002	−1.28931	−0.644655	+	0.764474i	$0.722999\pi$
$380$	0.930946	0.0477565
$381$	19.0482	0.975870
$382$	12.4883	0.638958
$383$	27.6960	1.41520	0.707599	−	0.706614i	$-0.249778\pi$
$383$	27.6960	1.41520	0.707599	+	0.706614i	$0.249778\pi$
$384$	−46.3890	−2.36728
$385$	0	0
$386$	−6.03501	−0.307174
$387$	50.0275	2.54304
$388$	64.7292	3.28613
$389$	−4.02073	−0.203859	−0.101930	−	0.994792i	$-0.532502\pi$
$389$	−4.02073	−0.203859	−0.101930	+	0.994792i	$0.532502\pi$
$390$	22.7604	1.15252
$391$	−21.2286	−1.07358
$392$	8.35518	0.422000
$393$	−47.9385	−2.41818
$394$	−8.69871	−0.438235
$395$	−0.967879	−0.0486993
$396$	0	0
$397$	9.36585	0.470058	0.235029	−	0.971988i	$-0.424481\pi$
$397$	9.36585	0.470058	0.235029	+	0.971988i	$0.424481\pi$
$398$	−0.482145	−0.0241678
$399$	0.562346	0.0281525
$400$	12.0504	0.602519
$401$	−5.66696	−0.282994	−0.141497	−	0.989939i	$-0.545192\pi$
$401$	−5.66696	−0.282994	−0.141497	+	0.989939i	$0.545192\pi$
$402$	128.425	6.40524
$403$	8.32517	0.414706
$404$	−2.51611	−0.125181
$405$	14.7573	0.733298
$406$	−21.3854	−1.06134
$407$	0	0
$408$	−139.751	−6.91870
$409$	−34.9057	−1.72598	−0.862988	−	0.505225i	$-0.831410\pi$
$409$	−34.9057	−1.72598	−0.862988	+	0.505225i	$0.831410\pi$
$410$	3.14367	0.155255
$411$	−36.6504	−1.80783
$412$	92.6395	4.56402
$413$	−9.44947	−0.464978
$414$	−69.2947	−3.40565
$415$	6.34917	0.311668
$416$	−42.5477	−2.08607
$417$	18.8532	0.923247
$418$	0	0
$419$	−7.38969	−0.361010	−0.180505	−	0.983574i	$-0.557773\pi$
$419$	−7.38969	−0.361010	−0.180505	+	0.983574i	$0.557773\pi$
$420$	15.8921	0.775453
$421$	−5.12435	−0.249745	−0.124873	−	0.992173i	$-0.539852\pi$
$421$	−5.12435	−0.249745	−0.124873	+	0.992173i	$0.539852\pi$
$422$	20.6203	1.00378
$423$	−36.7052	−1.78467
$424$	52.0713	2.52881
$425$	5.39845	0.261863
$426$	−73.4800	−3.56012
$427$	6.09558	0.294986
$428$	−40.7246	−1.96850
$429$	0	0
$430$	20.2396	0.976042
$431$	−18.5049	−0.891348	−0.445674	−	0.895195i	$-0.647036\pi$
$431$	−18.5049	−0.891348	−0.445674	+	0.895195i	$0.647036\pi$
$432$	−134.401	−6.46636
$433$	5.12847	0.246459	0.123229	−	0.992378i	$-0.460675\pi$
$433$	5.12847	0.246459	0.123229	+	0.992378i	$0.460675\pi$
$434$	8.07950	0.387828
$435$	−24.8156	−1.18982
$436$	6.76220	0.323851
$437$	−0.713718	−0.0341417
$438$	21.4010	1.02258
$439$	−31.3865	−1.49800	−0.748999	−	0.662571i	$-0.769465\pi$
$439$	−31.3865	−1.49800	−0.748999	+	0.662571i	$0.769465\pi$
$440$	0	0
$441$	6.59974	0.314273
$442$	−39.6569	−1.88629
$443$	1.30106	0.0618151	0.0309075	−	0.999522i	$-0.490160\pi$
$443$	1.30106	0.0618151	0.0309075	+	0.999522i	$0.490160\pi$
$444$	−108.216	−5.13571
$445$	8.87631	0.420777
$446$	−54.7909	−2.59443
$447$	−68.1143	−3.22170
$448$	−17.1914	−0.812216
$449$	−22.6327	−1.06810	−0.534050	−	0.845453i	$-0.679331\pi$
$449$	−22.6327	−1.06810	−0.534050	+	0.845453i	$0.679331\pi$
$450$	17.6217	0.830694
$451$	0	0
$452$	−80.4589	−3.78447
$453$	−42.2205	−1.98369
$454$	−76.1330	−3.57310
$455$	2.75125	0.128980
$456$	−4.69850	−0.220027
$457$	−28.3612	−1.32668	−0.663341	−	0.748318i	$-0.730862\pi$
$457$	−28.3612	−1.32668	−0.663341	+	0.748318i	$0.730862\pi$
$458$	4.93063	0.230393
$459$	−60.2102	−2.81037
$460$	−20.1699	−0.940425
$461$	19.7306	0.918944	0.459472	−	0.888192i	$-0.348039\pi$
$461$	19.7306	0.918944	0.459472	+	0.888192i	$0.348039\pi$
$462$	0	0
$463$	−5.34273	−0.248298	−0.124149	−	0.992264i	$-0.539620\pi$
$463$	−5.34273	−0.248298	−0.124149	+	0.992264i	$0.539620\pi$
$464$	96.5155	4.48062
$465$	9.37548	0.434777
$466$	8.80699	0.407976
$467$	−36.0616	−1.66873	−0.834366	−	0.551211i	$-0.814166\pi$
$467$	−36.0616	−1.66873	−0.834366	+	0.551211i	$0.814166\pi$
$468$	−93.1337	−4.30511
$469$	15.5238	0.716823
$470$	−14.8498	−0.684972
$471$	−9.02985	−0.416074
$472$	78.9520	3.63406
$473$	0	0
$474$	8.00703	0.367775
$475$	0.181499	0.00832774
$476$	−27.6898	−1.26916
$477$	41.1310	1.88326
$478$	22.7668	1.04133
$479$	−7.17013	−0.327611	−0.163806	−	0.986493i	$-0.552377\pi$
$479$	−7.17013	−0.327611	−0.163806	+	0.986493i	$0.552377\pi$
$480$	−47.9155	−2.18703
$481$	−18.7344	−0.854217
$482$	−40.5267	−1.84594
$483$	−12.1838	−0.554381
$484$	0	0
$485$	12.6197	0.573032
$486$	−32.7446	−1.48533
$487$	−18.5647	−0.841246	−0.420623	−	0.907236i	$-0.638188\pi$
$487$	−18.5647	−0.841246	−0.420623	+	0.907236i	$0.638188\pi$
$488$	−50.9297	−2.30548
$489$	19.8952	0.899692
$490$	2.67006	0.120621
$491$	29.9039	1.34954	0.674771	−	0.738027i	$-0.264242\pi$
$491$	29.9039	1.34954	0.674771	+	0.738027i	$0.264242\pi$
$492$	−18.7110	−0.843556
$493$	43.2379	1.94734
$494$	−1.33329	−0.0599875
$495$	0	0
$496$	−36.4640	−1.63728
$497$	−8.88216	−0.398419
$498$	−52.5251	−2.35371
$499$	22.2239	0.994878	0.497439	−	0.867499i	$-0.334274\pi$
$499$	22.2239	0.994878	0.497439	+	0.867499i	$0.334274\pi$
$500$	5.12921	0.229385
$501$	−32.2253	−1.43972
$502$	11.4150	0.509476
$503$	32.6405	1.45537	0.727684	−	0.685912i	$-0.240597\pi$
$503$	32.6405	1.45537	0.727684	+	0.685912i	$0.240597\pi$
$504$	−55.1420	−2.45622
$505$	−0.490544	−0.0218289
$506$	0	0
$507$	16.8260	0.747270
$508$	−31.5337	−1.39908
$509$	32.6072	1.44529	0.722643	−	0.691221i	$-0.242927\pi$
$509$	32.6072	1.44529	0.722643	+	0.691221i	$0.242927\pi$
$510$	−44.6601	−1.97758
$511$	2.58692	0.114439
$512$	−15.0084	−0.663285
$513$	−2.02430	−0.0893750
$514$	16.0028	0.705853
$515$	18.0612	0.795870
$516$	−120.465	−5.30319
$517$	0	0
$518$	−18.1816	−0.798854
$519$	18.6948	0.820609
$520$	−22.9871	−1.00805
$521$	−12.8515	−0.563035	−0.281518	−	0.959556i	$-0.590838\pi$
$521$	−12.8515	−0.563035	−0.281518	+	0.959556i	$0.590838\pi$
$522$	141.138	6.17743
$523$	−30.3941	−1.32904	−0.664521	−	0.747269i	$-0.731364\pi$
$523$	−30.3941	−1.32904	−0.664521	+	0.747269i	$0.731364\pi$
$524$	79.3607	3.46689
$525$	3.09834	0.135223
$526$	−36.3332	−1.58420
$527$	−16.3355	−0.711586
$528$	0	0
$529$	−7.53660	−0.327678
$530$	16.6404	0.722812
$531$	62.3640	2.70637
$532$	−0.930946	−0.0403616
$533$	−3.23926	−0.140308
$534$	−73.4316	−3.17769
$535$	−7.93973	−0.343265
$536$	−129.704	−5.60237
$537$	−41.0228	−1.77026
$538$	−17.2733	−0.744707
$539$	0	0
$540$	−57.2073	−2.46181
$541$	−7.54565	−0.324413	−0.162207	−	0.986757i	$-0.551861\pi$
$541$	−7.54565	−0.324413	−0.162207	+	0.986757i	$0.551861\pi$
$542$	24.7159	1.06164
$543$	16.8832	0.724525
$544$	83.4864	3.57945
$545$	1.31837	0.0564728
$546$	−22.7604	−0.974055
$547$	10.5651	0.451731	0.225866	−	0.974158i	$-0.427479\pi$
$547$	10.5651	0.451731	0.225866	+	0.974158i	$0.427479\pi$
$548$	60.6736	2.59185
$549$	−40.2292	−1.71694
$550$	0	0
$551$	1.45368	0.0619290
$552$	101.798	4.33280
$553$	0.967879	0.0411584
$554$	−58.9499	−2.50454
$555$	−21.0980	−0.895560
$556$	−31.2109	−1.32364
$557$	4.51395	0.191262	0.0956312	−	0.995417i	$-0.469513\pi$
$557$	4.51395	0.191262	0.0956312	+	0.995417i	$0.469513\pi$
$558$	−53.3226	−2.25732
$559$	−20.8550	−0.882075
$560$	−12.0504	−0.509222
$561$	0	0
$562$	15.6961	0.662099
$563$	32.8369	1.38391	0.691954	−	0.721941i	$-0.256750\pi$
$563$	32.8369	1.38391	0.691954	+	0.721941i	$0.256750\pi$
$564$	88.3856	3.72170
$565$	−15.6864	−0.659932
$566$	17.0233	0.715544
$567$	−14.7573	−0.619750
$568$	74.2120	3.11387
$569$	0.298385	0.0125089	0.00625447	−	0.999980i	$-0.498009\pi$
$569$	0.298385	0.0125089	0.00625447	+	0.999980i	$0.498009\pi$
$570$	−1.50150	−0.0628908
$571$	−15.2808	−0.639480	−0.319740	−	0.947505i	$-0.603596\pi$
$571$	−15.2808	−0.639480	−0.319740	+	0.947505i	$0.603596\pi$
$572$	0	0
$573$	−14.4915	−0.605391
$574$	−3.14367	−0.131214
$575$	−3.93235	−0.163990
$576$	113.459	4.72744
$577$	−22.6320	−0.942182	−0.471091	−	0.882085i	$-0.656140\pi$
$577$	−22.6320	−0.942182	−0.471091	+	0.882085i	$0.656140\pi$
$578$	32.4232	1.34863
$579$	7.00305	0.291037
$580$	41.0815	1.70582
$581$	−6.34917	−0.263408
$582$	−104.400	−4.32752
$583$	0	0
$584$	−21.6142	−0.894400
$585$	−18.1575	−0.750720
$586$	−82.0093	−3.38777
$587$	1.30253	0.0537611	0.0268806	−	0.999639i	$-0.491443\pi$
$587$	1.30253	0.0537611	0.0268806	+	0.999639i	$0.491443\pi$
$588$	−15.8921	−0.655378
$589$	−0.549209	−0.0226298
$590$	25.2306	1.03873
$591$	10.0940	0.415212
$592$	82.0564	3.37250
$593$	9.63367	0.395607	0.197804	−	0.980242i	$-0.436619\pi$
$593$	9.63367	0.395607	0.197804	+	0.980242i	$0.436619\pi$
$594$	0	0
$595$	−5.39845	−0.221315
$596$	112.761	4.61887
$597$	0.559483	0.0228981
$598$	28.8870	1.18128
$599$	40.1227	1.63937	0.819685	−	0.572815i	$-0.194148\pi$
$599$	40.1227	1.63937	0.819685	+	0.572815i	$0.194148\pi$
$600$	−25.8872	−1.05684
$601$	−13.6675	−0.557511	−0.278755	−	0.960362i	$-0.589922\pi$
$601$	−13.6675	−0.557511	−0.278755	+	0.960362i	$0.589922\pi$
$602$	−20.2396	−0.824906
$603$	−102.453	−4.17221
$604$	69.8947	2.84397
$605$	0	0
$606$	4.05816	0.164851
$607$	13.4691	0.546695	0.273348	−	0.961915i	$-0.411869\pi$
$607$	13.4691	0.546695	0.273348	+	0.961915i	$0.411869\pi$
$608$	2.80686	0.113833
$609$	24.8156	1.00558
$610$	−16.2756	−0.658978
$611$	15.3014	0.619027
$612$	182.745	7.38704
$613$	−45.3567	−1.83194	−0.915970	−	0.401248i	$-0.868577\pi$
$613$	−45.3567	−1.83194	−0.915970	+	0.401248i	$0.868577\pi$
$614$	−44.1609	−1.78219
$615$	−3.64793	−0.147099
$616$	0	0
$617$	13.2211	0.532263	0.266132	−	0.963937i	$-0.414254\pi$
$617$	13.2211	0.532263	0.266132	+	0.963937i	$0.414254\pi$
$618$	−149.416	−6.01038
$619$	48.2634	1.93987	0.969935	−	0.243364i	$-0.0782509\pi$
$619$	48.2634	1.93987	0.969935	+	0.243364i	$0.0782509\pi$
$620$	−15.5208	−0.623330
$621$	43.8585	1.75998
$622$	−25.4472	−1.02034
$623$	−8.87631	−0.355622
$624$	102.721	4.11214
$625$	1.00000	0.0400000
$626$	19.0495	0.761373
$627$	0	0
$628$	14.9486	0.596515
$629$	36.7604	1.46573
$630$	−17.6217	−0.702065
$631$	−35.4558	−1.41147	−0.705736	−	0.708475i	$-0.749383\pi$
$631$	−35.4558	−1.41147	−0.705736	+	0.708475i	$0.749383\pi$
$632$	−8.08680	−0.321676
$633$	−23.9279	−0.951047
$634$	24.2561	0.963332
$635$	−6.14787	−0.243971
$636$	−99.0428	−3.92730
$637$	−2.75125	−0.109008
$638$	0	0
$639$	58.6199	2.31897
$640$	14.9722	0.591827
$641$	−32.4938	−1.28343	−0.641713	−	0.766945i	$-0.721776\pi$
$641$	−32.4938	−1.28343	−0.641713	+	0.766945i	$0.721776\pi$
$642$	65.6835	2.59232
$643$	−6.43358	−0.253716	−0.126858	−	0.991921i	$-0.540489\pi$
$643$	−6.43358	−0.253716	−0.126858	+	0.991921i	$0.540489\pi$
$644$	20.1699	0.794804
$645$	−23.4861	−0.924766
$646$	2.61616	0.102931
$647$	−24.1915	−0.951067	−0.475533	−	0.879698i	$-0.657745\pi$
$647$	−24.1915	−0.951067	−0.475533	+	0.879698i	$0.657745\pi$
$648$	123.300	4.84369
$649$	0	0
$650$	−7.34599	−0.288133
$651$	−9.37548	−0.367454
$652$	−32.9359	−1.28987
$653$	−9.93321	−0.388717	−0.194358	−	0.980931i	$-0.562262\pi$
$653$	−9.93321	−0.388717	−0.194358	+	0.980931i	$0.562262\pi$
$654$	−10.9066	−0.426480
$655$	15.4723	0.604553
$656$	14.1879	0.553943
$657$	−17.0730	−0.666081
$658$	14.8498	0.578907
$659$	−18.1033	−0.705205	−0.352602	−	0.935773i	$-0.614703\pi$
$659$	−18.1033	−0.705205	−0.352602	+	0.935773i	$0.614703\pi$
$660$	0	0
$661$	13.9796	0.543743	0.271872	−	0.962334i	$-0.412357\pi$
$661$	13.9796	0.543743	0.271872	+	0.962334i	$0.412357\pi$
$662$	43.3597	1.68522
$663$	46.0180	1.78719
$664$	53.0484	2.05868
$665$	−0.181499	−0.00703822
$666$	119.994	4.64967
$667$	−31.4955	−1.21951
$668$	53.3480	2.06410
$669$	63.5796	2.45813
$670$	−41.4495	−1.60133
$671$	0	0
$672$	47.9155	1.84838
$673$	−19.1895	−0.739702	−0.369851	−	0.929091i	$-0.620591\pi$
$673$	−19.1895	−0.739702	−0.369851	+	0.929091i	$0.620591\pi$
$674$	30.9502	1.19216
$675$	−11.1532	−0.429288
$676$	−27.8549	−1.07134
$677$	23.0275	0.885017	0.442508	−	0.896764i	$-0.354089\pi$
$677$	23.0275	0.885017	0.442508	+	0.896764i	$0.354089\pi$
$678$	129.770	4.98379
$679$	−12.6197	−0.484300
$680$	45.1050	1.72970
$681$	88.3450	3.38539
$682$	0	0
$683$	−36.0805	−1.38058	−0.690291	−	0.723532i	$-0.742517\pi$
$683$	−36.0805	−1.38058	−0.690291	+	0.723532i	$0.742517\pi$
$684$	6.14400	0.234922
$685$	11.8290	0.451964
$686$	−2.67006	−0.101943
$687$	−5.72152	−0.218290
$688$	91.3446	3.48248
$689$	−17.1464	−0.653225
$690$	32.5314	1.23845
$691$	37.2835	1.41833	0.709165	−	0.705042i	$-0.249072\pi$
$691$	37.2835	1.41833	0.709165	+	0.705042i	$0.249072\pi$
$692$	−30.9486	−1.17649
$693$	0	0
$694$	−65.3696	−2.48140
$695$	−6.08494	−0.230815
$696$	−207.339	−7.85917
$697$	6.35602	0.240751
$698$	−11.8466	−0.448400
$699$	−10.2197	−0.386543
$700$	−5.12921	−0.193866
$701$	−0.284456	−0.0107438	−0.00537188	−	0.999986i	$-0.501710\pi$
$701$	−0.284456	−0.0107438	−0.00537188	+	0.999986i	$0.501710\pi$
$702$	81.9315	3.09231
$703$	1.23591	0.0466131
$704$	0	0
$705$	17.2318	0.648987
$706$	66.1655	2.49017
$707$	0.490544	0.0184488
$708$	−150.172	−5.64379
$709$	52.5541	1.97371	0.986855	−	0.161611i	$-0.0516689\pi$
$709$	52.5541	1.97371	0.986855	+	0.161611i	$0.0516689\pi$
$710$	23.7159	0.890041
$711$	−6.38775	−0.239559
$712$	74.1631	2.77938
$713$	11.8992	0.445627
$714$	44.6601	1.67136
$715$	0	0
$716$	67.9119	2.53799
$717$	−26.4187	−0.986624
$718$	−54.5520	−2.03586
$719$	−37.0098	−1.38023	−0.690117	−	0.723698i	$-0.742441\pi$
$719$	−37.0098	−1.38023	−0.690117	+	0.723698i	$0.742441\pi$
$720$	79.5294	2.96389
$721$	−18.0612	−0.672633
$722$	−50.6432	−1.88474
$723$	47.0273	1.74896
$724$	−27.9495	−1.03874
$725$	8.00932	0.297459
$726$	0	0
$727$	−29.9652	−1.11135	−0.555674	−	0.831400i	$-0.687540\pi$
$727$	−29.9652	−1.11135	−0.555674	+	0.831400i	$0.687540\pi$
$728$	22.9871	0.851960
$729$	−6.27505	−0.232409
$730$	−6.90722	−0.255648
$731$	40.9214	1.51353
$732$	96.8714	3.58047
$733$	0.982351	0.0362840	0.0181420	−	0.999835i	$-0.494225\pi$
$733$	0.982351	0.0362840	0.0181420	+	0.999835i	$0.494225\pi$
$734$	−51.2815	−1.89283
$735$	−3.09834	−0.114284
$736$	−60.8134	−2.24161
$737$	0	0
$738$	20.7474	0.763723
$739$	13.2021	0.485648	0.242824	−	0.970070i	$-0.421926\pi$
$739$	13.2021	0.485648	0.242824	+	0.970070i	$0.421926\pi$
$740$	34.9271	1.28394
$741$	1.54715	0.0568361
$742$	−16.6404	−0.610888
$743$	−32.2028	−1.18141	−0.590703	−	0.806889i	$-0.701149\pi$
$743$	−32.2028	−1.18141	−0.590703	+	0.806889i	$0.701149\pi$
$744$	78.3338	2.87186
$745$	21.9841	0.805435
$746$	−57.7088	−2.11287
$747$	41.9028	1.53314
$748$	0	0
$749$	7.93973	0.290111
$750$	−8.27276	−0.302079
$751$	−4.49705	−0.164100	−0.0820498	−	0.996628i	$-0.526147\pi$
$751$	−4.49705	−0.164100	−0.0820498	+	0.996628i	$0.526147\pi$
$752$	−67.0196	−2.44395
$753$	−13.2460	−0.482711
$754$	−58.8364	−2.14269
$755$	13.6268	0.495930
$756$	57.2073	2.08061
$757$	−7.44776	−0.270693	−0.135347	−	0.990798i	$-0.543215\pi$
$757$	−7.44776	−0.270693	−0.135347	+	0.990798i	$0.543215\pi$
$758$	−67.0190	−2.43424
$759$	0	0
$760$	1.51646	0.0550076
$761$	−26.7775	−0.970685	−0.485342	−	0.874324i	$-0.661305\pi$
$761$	−26.7775	−0.970685	−0.485342	+	0.874324i	$0.661305\pi$
$762$	50.8599	1.84246
$763$	−1.31837	−0.0477282
$764$	23.9902	0.867936
$765$	35.6284	1.28815
$766$	73.9499	2.67192
$767$	−25.9978	−0.938726
$768$	−17.3317	−0.625404
$769$	−36.8125	−1.32749	−0.663747	−	0.747957i	$-0.731035\pi$
$769$	−36.8125	−1.32749	−0.663747	+	0.747957i	$0.731035\pi$
$770$	0	0
$771$	−18.5697	−0.668771
$772$	−11.5933	−0.417253
$773$	15.1755	0.545825	0.272913	−	0.962039i	$-0.412013\pi$
$773$	15.1755	0.545825	0.272913	+	0.962039i	$0.412013\pi$
$774$	133.576	4.80130
$775$	−3.02596	−0.108696
$776$	105.440	3.78507
$777$	21.0980	0.756886
$778$	−10.7356	−0.384889
$779$	0.213693	0.00765635
$780$	43.7230	1.56553
$781$	0	0
$782$	−56.6816	−2.02693
$783$	−89.3299	−3.19239
$784$	12.0504	0.430371
$785$	2.91441	0.104020
$786$	−127.999	−4.56556
$787$	38.6530	1.37783	0.688915	−	0.724842i	$-0.258087\pi$
$787$	38.6530	1.37783	0.688915	+	0.724842i	$0.258087\pi$
$788$	−16.7103	−0.595280
$789$	42.1612	1.50098
$790$	−2.58429	−0.0919450
$791$	15.6864	0.557745
$792$	0	0
$793$	16.7704	0.595536
$794$	25.0074	0.887478
$795$	−19.3096	−0.684840
$796$	−0.926206	−0.0328285
$797$	14.0967	0.499332	0.249666	−	0.968332i	$-0.419679\pi$
$797$	14.0967	0.499332	0.249666	+	0.968332i	$0.419679\pi$
$798$	1.50150	0.0531524
$799$	−30.0241	−1.06218
$800$	15.4649	0.546766
$801$	58.5813	2.06987
$802$	−15.1311	−0.534298
$803$	0	0
$804$	246.705	8.70063
$805$	3.93235	0.138597
$806$	22.2287	0.782972
$807$	20.0440	0.705584
$808$	−4.09859	−0.144188
$809$	−32.3836	−1.13855	−0.569274	−	0.822148i	$-0.692776\pi$
$809$	−32.3836	−1.13855	−0.569274	+	0.822148i	$0.692776\pi$
$810$	39.4030	1.38448
$811$	18.8406	0.661584	0.330792	−	0.943704i	$-0.392684\pi$
$811$	18.8406	0.661584	0.330792	+	0.943704i	$0.392684\pi$
$812$	−41.0815	−1.44168
$813$	−28.6804	−1.00586
$814$	0	0
$815$	−6.42124	−0.224926
$816$	−201.558	−7.05594
$817$	1.37580	0.0481332
$818$	−93.2002	−3.25867
$819$	18.1575	0.634475
$820$	6.03903	0.210892
$821$	−21.2378	−0.741203	−0.370601	−	0.928792i	$-0.620848\pi$
$821$	−21.2378	−0.741203	−0.370601	+	0.928792i	$0.620848\pi$
$822$	−97.8587	−3.41321
$823$	−28.1074	−0.979764	−0.489882	−	0.871789i	$-0.662960\pi$
$823$	−28.1074	−0.979764	−0.489882	+	0.871789i	$0.662960\pi$
$824$	150.904	5.25700
$825$	0	0
$826$	−25.2306	−0.877886
$827$	40.7995	1.41874	0.709369	−	0.704837i	$-0.248980\pi$
$827$	40.7995	1.41874	0.709369	+	0.704837i	$0.248980\pi$
$828$	−133.116	−4.62610
$829$	−13.3943	−0.465202	−0.232601	−	0.972572i	$-0.574724\pi$
$829$	−13.3943	−0.465202	−0.232601	+	0.972572i	$0.574724\pi$
$830$	16.9526	0.588435
$831$	68.4057	2.37297
$832$	−47.2977	−1.63975
$833$	5.39845	0.187045
$834$	50.3392	1.74311
$835$	10.4008	0.359935
$836$	0	0
$837$	33.7493	1.16655
$838$	−19.7309	−0.681593
$839$	34.6351	1.19574	0.597868	−	0.801595i	$-0.296015\pi$
$839$	34.6351	1.19574	0.597868	+	0.801595i	$0.296015\pi$
$840$	25.8872	0.893194
$841$	35.1493	1.21204
$842$	−13.6823	−0.471523
$843$	−18.2138	−0.627316
$844$	39.6118	1.36350
$845$	−5.43065	−0.186820
$846$	−98.0051	−3.36948
$847$	0	0
$848$	75.1007	2.57897
$849$	−19.7539	−0.677953
$850$	14.4142	0.494402
$851$	−26.7771	−0.917908
$852$	−141.156	−4.83592
$853$	−31.2320	−1.06936	−0.534681	−	0.845054i	$-0.679568\pi$
$853$	−31.2320	−1.06936	−0.534681	+	0.845054i	$0.679568\pi$
$854$	16.2756	0.556938
$855$	1.19785	0.0409654
$856$	−66.3379	−2.26738
$857$	38.5277	1.31608	0.658040	−	0.752983i	$-0.271386\pi$
$857$	38.5277	1.31608	0.658040	+	0.752983i	$0.271386\pi$
$858$	0	0
$859$	35.4568	1.20977	0.604886	−	0.796312i	$-0.293219\pi$
$859$	35.4568	1.20977	0.604886	+	0.796312i	$0.293219\pi$
$860$	38.8806	1.32582
$861$	3.64793	0.124321
$862$	−49.4091	−1.68288
$863$	−32.9706	−1.12233	−0.561166	−	0.827703i	$-0.689647\pi$
$863$	−32.9706	−1.12233	−0.561166	+	0.827703i	$0.689647\pi$
$864$	−172.483	−5.86801
$865$	−6.03379	−0.205155
$866$	13.6933	0.465318
$867$	−37.6240	−1.27778
$868$	15.5208	0.526810
$869$	0	0
$870$	−66.2592	−2.24640
$871$	42.7098	1.44717
$872$	11.0152	0.373022
$873$	83.2868	2.81883
$874$	−1.90567	−0.0644602
$875$	−1.00000	−0.0338062
$876$	41.1115	1.38903
$877$	15.8062	0.533739	0.266869	−	0.963733i	$-0.414011\pi$
$877$	15.8062	0.533739	0.266869	+	0.963733i	$0.414011\pi$
$878$	−83.8039	−2.82824
$879$	95.1638	3.20980
$880$	0	0
$881$	−12.4859	−0.420661	−0.210331	−	0.977630i	$-0.567454\pi$
$881$	−12.4859	−0.420661	−0.210331	+	0.977630i	$0.567454\pi$
$882$	17.6217	0.593353
$883$	37.7322	1.26979	0.634895	−	0.772599i	$-0.281044\pi$
$883$	37.7322	1.26979	0.634895	+	0.772599i	$0.281044\pi$
$884$	−76.1814	−2.56226
$885$	−29.2777	−0.984159
$886$	3.47390	0.116708
$887$	−37.8650	−1.27138	−0.635690	−	0.771944i	$-0.719284\pi$
$887$	−37.8650	−1.27138	−0.635690	+	0.771944i	$0.719284\pi$
$888$	−176.277	−5.91548
$889$	6.14787	0.206193
$890$	23.7003	0.794434
$891$	0	0
$892$	−105.254	−3.52416
$893$	−1.00943	−0.0337792
$894$	−181.869	−6.08261
$895$	13.2402	0.442572
$896$	−14.9722	−0.500185
$897$	−33.5206	−1.11922
$898$	−60.4305	−2.01659
$899$	−24.2359	−0.808313
$900$	33.8515	1.12838
$901$	33.6443	1.12085
$902$	0	0
$903$	23.4861	0.781570
$904$	−131.063	−4.35908
$905$	−5.44909	−0.181134
$906$	−112.731	−3.74524
$907$	0.318786	0.0105851	0.00529255	−	0.999986i	$-0.498315\pi$
$907$	0.318786	0.0105851	0.00529255	+	0.999986i	$0.498315\pi$
$908$	−146.252	−4.85356
$909$	−3.23747	−0.107380
$910$	7.34599	0.243517
$911$	28.4188	0.941556	0.470778	−	0.882252i	$-0.343973\pi$
$911$	28.4188	0.941556	0.470778	+	0.882252i	$0.343973\pi$
$912$	−6.77649	−0.224392
$913$	0	0
$914$	−75.7261	−2.50480
$915$	18.8862	0.624359
$916$	9.47179	0.312957
$917$	−15.4723	−0.510941
$918$	−160.765	−5.30602
$919$	−1.06616	−0.0351694	−0.0175847	−	0.999845i	$-0.505598\pi$
$919$	−1.06616	−0.0351694	−0.0175847	+	0.999845i	$0.505598\pi$
$920$	−32.8555	−1.08321
$921$	51.2444	1.68856
$922$	52.6818	1.73498
$923$	−24.4370	−0.804354
$924$	0	0
$925$	6.80944	0.223893
$926$	−14.2654	−0.468790
$927$	119.199	3.91501
$928$	123.863	4.06601
$929$	57.1562	1.87523	0.937616	−	0.347672i	$-0.113028\pi$
$929$	57.1562	1.87523	0.937616	+	0.347672i	$0.113028\pi$
$930$	25.0331	0.820867
$931$	0.181499	0.00594839
$932$	16.9183	0.554178
$933$	29.5290	0.966736
$934$	−96.2866	−3.15059
$935$	0	0
$936$	−151.709	−4.95877
$937$	−31.6625	−1.03437	−0.517184	−	0.855874i	$-0.673020\pi$
$937$	−31.6625	−1.03437	−0.517184	+	0.855874i	$0.673020\pi$
$938$	41.4495	1.35337
$939$	−22.1051	−0.721374
$940$	−28.5267	−0.930439
$941$	9.98407	0.325471	0.162736	−	0.986670i	$-0.447968\pi$
$941$	9.98407	0.325471	0.162736	+	0.986670i	$0.447968\pi$
$942$	−24.1102	−0.785554
$943$	−4.62987	−0.150769
$944$	113.870	3.70614
$945$	11.1532	0.362815
$946$	0	0
$947$	9.13010	0.296688	0.148344	−	0.988936i	$-0.452606\pi$
$947$	9.13010	0.296688	0.148344	+	0.988936i	$0.452606\pi$
$948$	15.3816	0.499571
$949$	7.11725	0.231036
$950$	0.484613	0.0157229
$951$	−28.1468	−0.912724
$952$	−45.1050	−1.46186
$953$	−42.3250	−1.37104	−0.685521	−	0.728053i	$-0.740426\pi$
$953$	−42.3250	−1.37104	−0.685521	+	0.728053i	$0.740426\pi$
$954$	109.822	3.55563
$955$	4.67717	0.151350
$956$	43.7353	1.41450
$957$	0	0
$958$	−19.1447	−0.618536
$959$	−11.8290	−0.381979
$960$	−53.2648	−1.71911
$961$	−21.8435	−0.704631
$962$	−50.0220	−1.61278
$963$	−52.4002	−1.68857
$964$	−77.8522	−2.50745
$965$	−2.26026	−0.0727602
$966$	−32.5314	−1.04668
$967$	60.7721	1.95430	0.977150	−	0.212550i	$-0.0681768\pi$
$967$	60.7721	1.95430	0.977150	+	0.212550i	$0.0681768\pi$
$968$	0	0
$969$	−3.03580	−0.0975238
$970$	33.6954	1.08189
$971$	−28.5720	−0.916921	−0.458460	−	0.888715i	$-0.651599\pi$
$971$	−28.5720	−0.916921	−0.458460	+	0.888715i	$0.651599\pi$
$972$	−62.9028	−2.01761
$973$	6.08494	0.195074
$974$	−49.5688	−1.58829
$975$	8.52431	0.272996
$976$	−73.4541	−2.35121
$977$	−30.1254	−0.963796	−0.481898	−	0.876227i	$-0.660052\pi$
$977$	−30.1254	−0.963796	−0.481898	+	0.876227i	$0.660052\pi$
$978$	53.1213	1.69863
$979$	0	0
$980$	5.12921	0.163847
$981$	8.70090	0.277798
$982$	79.8450	2.54796
$983$	26.6632	0.850425	0.425213	−	0.905094i	$-0.360199\pi$
$983$	26.6632	0.850425	0.425213	+	0.905094i	$0.360199\pi$
$984$	−30.4791	−0.971637
$985$	−3.25787	−0.103804
$986$	115.448	3.67661
$987$	−17.2318	−0.548494
$988$	−2.56126	−0.0814846
$989$	−29.8081	−0.947843
$990$	0	0
$991$	−27.4560	−0.872170	−0.436085	−	0.899906i	$-0.643635\pi$
$991$	−27.4560	−0.872170	−0.436085	+	0.899906i	$0.643635\pi$
$992$	−46.7962	−1.48578
$993$	−50.3147	−1.59669
$994$	−23.7159	−0.752222
$995$	−0.180575	−0.00572461
$996$	−100.901	−3.19718
$997$	−1.98320	−0.0628087	−0.0314044	−	0.999507i	$-0.509998\pi$
$997$	−1.98320	−0.0628087	−0.0314044	+	0.999507i	$0.509998\pi$
$998$	59.3391	1.87835
$999$	−75.9473	−2.40287

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bo.1.18		18
11.3	even	5		385.2.n.f.141.9	yes	36
11.4	even	5		385.2.n.f.71.9	✓	36
11.10	odd	2		4235.2.a.bp.1.1		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.71.9	✓	36	11.4	even	5
385.2.n.f.141.9	yes	36	11.3	even	5
4235.2.a.bo.1.18		18	1.1	even	1	trivial
4235.2.a.bp.1.1		18	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)

\(f(q)\)	\(=\)	\(q+2.67006 q^{2} -3.09834 q^{3} +5.12921 q^{4} +1.00000 q^{5} -8.27276 q^{6} -1.00000 q^{7} +8.35518 q^{8} +6.59974 q^{9} +O(q^{10})\)	\(q+2.67006 q^{2} -3.09834 q^{3} +5.12921 q^{4} +1.00000 q^{5} -8.27276 q^{6} -1.00000 q^{7} +8.35518 q^{8} +6.59974 q^{9} +2.67006 q^{10} -15.8921 q^{12} -2.75125 q^{13} -2.67006 q^{14} -3.09834 q^{15} +12.0504 q^{16} +5.39845 q^{17} +17.6217 q^{18} +0.181499 q^{19} +5.12921 q^{20} +3.09834 q^{21} -3.93235 q^{23} -25.8872 q^{24} +1.00000 q^{25} -7.34599 q^{26} -11.1532 q^{27} -5.12921 q^{28} +8.00932 q^{29} -8.27276 q^{30} -3.02596 q^{31} +15.4649 q^{32} +14.4142 q^{34} -1.00000 q^{35} +33.8515 q^{36} +6.80944 q^{37} +0.484613 q^{38} +8.52431 q^{39} +8.35518 q^{40} +1.17738 q^{41} +8.27276 q^{42} +7.58022 q^{43} +6.59974 q^{45} -10.4996 q^{46} -5.56162 q^{47} -37.3363 q^{48} +1.00000 q^{49} +2.67006 q^{50} -16.7263 q^{51} -14.1117 q^{52} +6.23222 q^{53} -29.7798 q^{54} -8.35518 q^{56} -0.562346 q^{57} +21.3854 q^{58} +9.44947 q^{59} -15.8921 q^{60} -6.09558 q^{61} -8.07950 q^{62} -6.59974 q^{63} +17.1914 q^{64} -2.75125 q^{65} -15.5238 q^{67} +27.6898 q^{68} +12.1838 q^{69} -2.67006 q^{70} +8.88216 q^{71} +55.1420 q^{72} -2.58692 q^{73} +18.1816 q^{74} -3.09834 q^{75} +0.930946 q^{76} +22.7604 q^{78} -0.967879 q^{79} +12.0504 q^{80} +14.7573 q^{81} +3.14367 q^{82} +6.34917 q^{83} +15.8921 q^{84} +5.39845 q^{85} +20.2396 q^{86} -24.8156 q^{87} +8.87631 q^{89} +17.6217 q^{90} +2.75125 q^{91} -20.1699 q^{92} +9.37548 q^{93} -14.8498 q^{94} +0.181499 q^{95} -47.9155 q^{96} +12.6197 q^{97} +2.67006 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} + q^{6} - 18 q^{7} - 6 q^{8} + 37 q^{9}+O(q^{10}) \) 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

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Representations

Groups

Database

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