LMFDB - Embedded newform 4235.2.a.bp.1.9

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			1.9
Root			$-0.371973$ 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)

$f(q)$	$=$	$q-0.371973 q^{2} -1.74007 q^{3} -1.86164 q^{4} +1.00000 q^{5} +0.647257 q^{6} +1.00000 q^{7} +1.43642 q^{8} +0.0278278 q^{9} +O(q^{10})$	\(q-0.371973 q^{2} -1.74007 q^{3} -1.86164 q^{4} +1.00000 q^{5} +0.647257 q^{6} +1.00000 q^{7} +1.43642 q^{8} +0.0278278 q^{9} -0.371973 q^{10} +3.23937 q^{12} -5.54402 q^{13} -0.371973 q^{14} -1.74007 q^{15} +3.18896 q^{16} -6.07505 q^{17} -0.0103512 q^{18} +0.160034 q^{19} -1.86164 q^{20} -1.74007 q^{21} -5.95365 q^{23} -2.49947 q^{24} +1.00000 q^{25} +2.06222 q^{26} +5.17177 q^{27} -1.86164 q^{28} +5.59350 q^{29} +0.647257 q^{30} -3.38371 q^{31} -4.05905 q^{32} +2.25975 q^{34} +1.00000 q^{35} -0.0518053 q^{36} -5.98416 q^{37} -0.0595283 q^{38} +9.64695 q^{39} +1.43642 q^{40} +7.71367 q^{41} +0.647257 q^{42} +2.74955 q^{43} +0.0278278 q^{45} +2.21460 q^{46} +0.838557 q^{47} -5.54900 q^{48} +1.00000 q^{49} -0.371973 q^{50} +10.5710 q^{51} +10.3209 q^{52} -9.90375 q^{53} -1.92376 q^{54} +1.43642 q^{56} -0.278470 q^{57} -2.08063 q^{58} +5.27721 q^{59} +3.23937 q^{60} -5.19668 q^{61} +1.25865 q^{62} +0.0278278 q^{63} -4.86807 q^{64} -5.54402 q^{65} +5.66407 q^{67} +11.3095 q^{68} +10.3597 q^{69} -0.371973 q^{70} -11.4282 q^{71} +0.0399725 q^{72} -13.4715 q^{73} +2.22594 q^{74} -1.74007 q^{75} -0.297925 q^{76} -3.58840 q^{78} -9.17391 q^{79} +3.18896 q^{80} -9.08271 q^{81} -2.86927 q^{82} +5.09464 q^{83} +3.23937 q^{84} -6.07505 q^{85} -1.02276 q^{86} -9.73305 q^{87} +2.46349 q^{89} -0.0103512 q^{90} -5.54402 q^{91} +11.0835 q^{92} +5.88788 q^{93} -0.311920 q^{94} +0.160034 q^{95} +7.06302 q^{96} +11.9820 q^{97} -0.371973 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.371973	−0.263024	−0.131512	−	0.991315i	$-0.541983\pi$
$2$	−0.371973	−0.263024	−0.131512	+	0.991315i	$0.541983\pi$
$3$	−1.74007	−1.00463	−0.502314	−	0.864686i	$-0.667518\pi$
$3$	−1.74007	−1.00463	−0.502314	+	0.864686i	$0.667518\pi$
$4$	−1.86164	−0.930818
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.647257	0.264241
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.43642	0.507852
$9$	0.0278278	0.00927593
$10$	−0.371973	−0.117628
$11$	0	0
$11$	0	0
$12$	3.23937	0.935125
$13$	−5.54402	−1.53763	−0.768817	−	0.639469i	$-0.779154\pi$
$13$	−5.54402	−1.53763	−0.768817	+	0.639469i	$0.779154\pi$
$14$	−0.371973	−0.0994139
$15$	−1.74007	−0.449283
$16$	3.18896	0.797241
$17$	−6.07505	−1.47342	−0.736708	−	0.676211i	$-0.763621\pi$
$17$	−6.07505	−1.47342	−0.736708	+	0.676211i	$0.763621\pi$
$18$	−0.0103512	−0.00243980
$19$	0.160034	0.0367144	0.0183572	−	0.999831i	$-0.494156\pi$
$19$	0.160034	0.0367144	0.0183572	+	0.999831i	$0.494156\pi$
$20$	−1.86164	−0.416275
$21$	−1.74007	−0.379713
$22$	0	0
$23$	−5.95365	−1.24142	−0.620711	−	0.784039i	$-0.713156\pi$
$23$	−5.95365	−1.24142	−0.620711	+	0.784039i	$0.713156\pi$
$24$	−2.49947	−0.510202
$25$	1.00000	0.200000
$26$	2.06222	0.404435
$27$	5.17177	0.995308
$28$	−1.86164	−0.351816
$29$	5.59350	1.03869	0.519343	−	0.854566i	$-0.326177\pi$
$29$	5.59350	1.03869	0.519343	+	0.854566i	$0.326177\pi$
$30$	0.647257	0.118172
$31$	−3.38371	−0.607732	−0.303866	−	0.952715i	$-0.598278\pi$
$31$	−3.38371	−0.607732	−0.303866	+	0.952715i	$0.598278\pi$
$32$	−4.05905	−0.717546
$33$	0	0
$34$	2.25975	0.387544
$35$	1.00000	0.169031
$36$	−0.0518053	−0.00863421
$37$	−5.98416	−0.983790	−0.491895	−	0.870654i	$-0.663696\pi$
$37$	−5.98416	−0.983790	−0.491895	+	0.870654i	$0.663696\pi$
$38$	−0.0595283	−0.00965677
$39$	9.64695	1.54475
$40$	1.43642	0.227118
$41$	7.71367	1.20467	0.602337	−	0.798242i	$-0.294237\pi$
$41$	7.71367	1.20467	0.602337	+	0.798242i	$0.294237\pi$
$42$	0.647257	0.0998739
$43$	2.74955	0.419303	0.209652	−	0.977776i	$-0.432767\pi$
$43$	2.74955	0.419303	0.209652	+	0.977776i	$0.432767\pi$
$44$	0	0
$45$	0.0278278	0.00414832
$46$	2.21460	0.326524
$47$	0.838557	0.122316	0.0611581	−	0.998128i	$-0.480521\pi$
$47$	0.838557	0.122316	0.0611581	+	0.998128i	$0.480521\pi$
$48$	−5.54900	−0.800930
$49$	1.00000	0.142857
$50$	−0.371973	−0.0526049
$51$	10.5710	1.48023
$52$	10.3209	1.43126
$53$	−9.90375	−1.36039	−0.680193	−	0.733033i	$-0.738104\pi$
$53$	−9.90375	−1.36039	−0.680193	+	0.733033i	$0.738104\pi$
$54$	−1.92376	−0.261790
$55$	0	0
$56$	1.43642	0.191950
$57$	−0.278470	−0.0368843
$58$	−2.08063	−0.273200
$59$	5.27721	0.687035	0.343517	−	0.939146i	$-0.388382\pi$
$59$	5.27721	0.687035	0.343517	+	0.939146i	$0.388382\pi$
$60$	3.23937	0.418201
$61$	−5.19668	−0.665367	−0.332684	−	0.943039i	$-0.607954\pi$
$61$	−5.19668	−0.665367	−0.332684	+	0.943039i	$0.607954\pi$
$62$	1.25865	0.159848
$63$	0.0278278	0.00350597
$64$	−4.86807	−0.608509
$65$	−5.54402	−0.687651
$66$	0	0
$67$	5.66407	0.691976	0.345988	−	0.938239i	$-0.387544\pi$
$67$	5.66407	0.691976	0.345988	+	0.938239i	$0.387544\pi$
$68$	11.3095	1.37148
$69$	10.3597	1.24717
$70$	−0.371973	−0.0444592
$71$	−11.4282	−1.35628	−0.678141	−	0.734931i	$-0.737214\pi$
$71$	−11.4282	−1.35628	−0.678141	+	0.734931i	$0.737214\pi$
$72$	0.0399725	0.00471080
$73$	−13.4715	−1.57672	−0.788360	−	0.615214i	$-0.789070\pi$
$73$	−13.4715	−1.57672	−0.788360	+	0.615214i	$0.789070\pi$
$74$	2.22594	0.258761
$75$	−1.74007	−0.200925
$76$	−0.297925	−0.0341744
$77$	0	0
$78$	−3.58840	−0.406306
$79$	−9.17391	−1.03215	−0.516073	−	0.856545i	$-0.672607\pi$
$79$	−9.17391	−1.03215	−0.516073	+	0.856545i	$0.672607\pi$
$80$	3.18896	0.356537
$81$	−9.08271	−1.00919
$82$	−2.86927	−0.316858
$83$	5.09464	0.559210	0.279605	−	0.960115i	$-0.409797\pi$
$83$	5.09464	0.559210	0.279605	+	0.960115i	$0.409797\pi$
$84$	3.23937	0.353444
$85$	−6.07505	−0.658931
$86$	−1.02276	−0.110287
$87$	−9.73305	−1.04349
$88$	0	0
$89$	2.46349	0.261129	0.130565	−	0.991440i	$-0.458321\pi$
$89$	2.46349	0.261129	0.130565	+	0.991440i	$0.458321\pi$
$90$	−0.0103512	−0.00109111
$91$	−5.54402	−0.581171
$92$	11.0835	1.15554
$93$	5.88788	0.610544
$94$	−0.311920	−0.0321721
$95$	0.160034	0.0164192
$96$	7.06302	0.720866
$97$	11.9820	1.21659	0.608295	−	0.793711i	$-0.291854\pi$
$97$	11.9820	1.21659	0.608295	+	0.793711i	$0.291854\pi$
$98$	−0.371973	−0.0375749
$99$	0	0
$100$	−1.86164	−0.186164
$101$	−13.1652	−1.30999	−0.654995	−	0.755633i	$-0.727329\pi$
$101$	−13.1652	−1.30999	−0.654995	+	0.755633i	$0.727329\pi$
$102$	−3.93212	−0.389337
$103$	10.2577	1.01072	0.505362	−	0.862907i	$-0.331359\pi$
$103$	10.2577	1.01072	0.505362	+	0.862907i	$0.331359\pi$
$104$	−7.96355	−0.780891
$105$	−1.74007	−0.169813
$106$	3.68392	0.357814
$107$	−13.4501	−1.30027	−0.650135	−	0.759819i	$-0.725288\pi$
$107$	−13.4501	−1.30027	−0.650135	+	0.759819i	$0.725288\pi$
$108$	−9.62796	−0.926451
$109$	−8.72033	−0.835256	−0.417628	−	0.908618i	$-0.637139\pi$
$109$	−8.72033	−0.835256	−0.417628	+	0.908618i	$0.637139\pi$
$110$	0	0
$111$	10.4128	0.988343
$112$	3.18896	0.301329
$113$	−4.22980	−0.397906	−0.198953	−	0.980009i	$-0.563754\pi$
$113$	−4.22980	−0.397906	−0.198953	+	0.980009i	$0.563754\pi$
$114$	0.103583	0.00970146
$115$	−5.95365	−0.555181
$116$	−10.4131	−0.966828
$117$	−0.154278	−0.0142630
$118$	−1.96298	−0.180707
$119$	−6.07505	−0.556899
$120$	−2.49947	−0.228169
$121$	0	0
$122$	1.93302	0.175008
$123$	−13.4223	−1.21025
$124$	6.29924	0.565688
$125$	1.00000	0.0894427
$126$	−0.0103512	−0.000922156 0
$127$	10.7755	0.956173	0.478086	−	0.878313i	$-0.341331\pi$
$127$	10.7755	0.956173	0.478086	+	0.878313i	$0.341331\pi$
$128$	9.92889	0.877599
$129$	−4.78441	−0.421243
$130$	2.06222	0.180869
$131$	−6.90226	−0.603053	−0.301526	−	0.953458i	$-0.597496\pi$
$131$	−6.90226	−0.603053	−0.301526	+	0.953458i	$0.597496\pi$
$132$	0	0
$133$	0.160034	0.0138767
$134$	−2.10688	−0.182007
$135$	5.17177	0.445115
$136$	−8.72634	−0.748277
$137$	22.2250	1.89881	0.949406	−	0.314052i	$-0.101687\pi$
$137$	22.2250	1.89881	0.949406	+	0.314052i	$0.101687\pi$
$138$	−3.85354	−0.328035
$139$	17.7185	1.50286	0.751432	−	0.659810i	$-0.229363\pi$
$139$	17.7185	1.50286	0.751432	+	0.659810i	$0.229363\pi$
$140$	−1.86164	−0.157337
$141$	−1.45914	−0.122882
$142$	4.25099	0.356735
$143$	0	0
$144$	0.0887418	0.00739515
$145$	5.59350	0.464515
$146$	5.01103	0.414716
$147$	−1.74007	−0.143518
$148$	11.1403	0.915730
$149$	1.67399	0.137139	0.0685695	−	0.997646i	$-0.478157\pi$
$149$	1.67399	0.137139	0.0685695	+	0.997646i	$0.478157\pi$
$150$	0.647257	0.0528483
$151$	6.34876	0.516655	0.258327	−	0.966057i	$-0.416829\pi$
$151$	6.34876	0.516655	0.258327	+	0.966057i	$0.416829\pi$
$152$	0.229877	0.0186455
$153$	−0.169055	−0.0136673
$154$	0	0
$155$	−3.38371	−0.271786
$156$	−17.9591	−1.43788
$157$	−2.42643	−0.193650	−0.0968252	−	0.995301i	$-0.530869\pi$
$157$	−2.42643	−0.193650	−0.0968252	+	0.995301i	$0.530869\pi$
$158$	3.41244	0.271479
$159$	17.2332	1.36668
$160$	−4.05905	−0.320896
$161$	−5.95365	−0.469214
$162$	3.37852	0.265442
$163$	−12.0847	−0.946543	−0.473272	−	0.880917i	$-0.656927\pi$
$163$	−12.0847	−0.946543	−0.473272	+	0.880917i	$0.656927\pi$
$164$	−14.3601	−1.12133
$165$	0	0
$166$	−1.89507	−0.147086
$167$	−0.238238	−0.0184354	−0.00921771	−	0.999958i	$-0.502934\pi$
$167$	−0.238238	−0.0184354	−0.00921771	+	0.999958i	$0.502934\pi$
$168$	−2.49947	−0.192838
$169$	17.7361	1.36432
$170$	2.25975	0.173315
$171$	0.00445340	0.000340560 0
$172$	−5.11867	−0.390295
$173$	−1.32418	−0.100675	−0.0503377	−	0.998732i	$-0.516030\pi$
$173$	−1.32418	−0.100675	−0.0503377	+	0.998732i	$0.516030\pi$
$174$	3.62043	0.274464
$175$	1.00000	0.0755929
$176$	0	0
$177$	−9.18270	−0.690214
$178$	−0.916350	−0.0686833
$179$	−5.94889	−0.444641	−0.222320	−	0.974974i	$-0.571363\pi$
$179$	−5.94889	−0.444641	−0.222320	+	0.974974i	$0.571363\pi$
$180$	−0.0518053	−0.00386134
$181$	22.7031	1.68751	0.843756	−	0.536728i	$-0.180340\pi$
$181$	22.7031	1.68751	0.843756	+	0.536728i	$0.180340\pi$
$182$	2.06222	0.152862
$183$	9.04257	0.668446
$184$	−8.55196	−0.630459
$185$	−5.98416	−0.439964
$186$	−2.19013	−0.160588
$187$	0	0
$188$	−1.56109	−0.113854
$189$	5.17177	0.376191
$190$	−0.0595283	−0.00431864
$191$	23.4256	1.69502	0.847510	−	0.530779i	$-0.178101\pi$
$191$	23.4256	1.69502	0.847510	+	0.530779i	$0.178101\pi$
$192$	8.47076	0.611324
$193$	−14.2797	−1.02787	−0.513937	−	0.857828i	$-0.671813\pi$
$193$	−14.2797	−1.02787	−0.513937	+	0.857828i	$0.671813\pi$
$194$	−4.45698	−0.319993
$195$	9.64695	0.690833
$196$	−1.86164	−0.132974
$197$	13.5748	0.967165	0.483583	−	0.875299i	$-0.339335\pi$
$197$	13.5748	0.967165	0.483583	+	0.875299i	$0.339335\pi$
$198$	0	0
$199$	17.4908	1.23989	0.619946	−	0.784645i	$-0.287155\pi$
$199$	17.4908	1.23989	0.619946	+	0.784645i	$0.287155\pi$
$200$	1.43642	0.101570
$201$	−9.85585	−0.695178
$202$	4.89711	0.344559
$203$	5.59350	0.392587
$204$	−19.6793	−1.37783
$205$	7.71367	0.538746
$206$	−3.81559	−0.265845
$207$	−0.165677	−0.0115154
$208$	−17.6797	−1.22586
$209$	0	0
$210$	0.647257	0.0446650
$211$	−14.8428	−1.02182	−0.510911	−	0.859633i	$-0.670692\pi$
$211$	−14.8428	−1.02182	−0.510911	+	0.859633i	$0.670692\pi$
$212$	18.4372	1.26627
$213$	19.8859	1.36256
$214$	5.00307	0.342003
$215$	2.74955	0.187518
$216$	7.42886	0.505470
$217$	−3.38371	−0.229701
$218$	3.24373	0.219693
$219$	23.4413	1.58402
$220$	0	0
$221$	33.6802	2.26557
$222$	−3.87329	−0.259958
$223$	−19.3712	−1.29719	−0.648597	−	0.761132i	$-0.724644\pi$
$223$	−19.3712	−1.29719	−0.648597	+	0.761132i	$0.724644\pi$
$224$	−4.05905	−0.271207
$225$	0.0278278	0.00185519
$226$	1.57337	0.104659
$227$	2.77503	0.184185	0.0920926	−	0.995750i	$-0.470644\pi$
$227$	2.77503	0.184185	0.0920926	+	0.995750i	$0.470644\pi$
$228$	0.518410	0.0343325
$229$	27.5502	1.82057	0.910283	−	0.413987i	$-0.135864\pi$
$229$	27.5502	1.82057	0.910283	+	0.413987i	$0.135864\pi$
$230$	2.21460	0.146026
$231$	0	0
$232$	8.03463	0.527499
$233$	14.6855	0.962080	0.481040	−	0.876699i	$-0.340259\pi$
$233$	14.6855	0.962080	0.481040	+	0.876699i	$0.340259\pi$
$234$	0.0573871	0.00375151
$235$	0.838557	0.0547015
$236$	−9.82425	−0.639504
$237$	15.9632	1.03692
$238$	2.25975	0.146478
$239$	8.78223	0.568075	0.284038	−	0.958813i	$-0.408326\pi$
$239$	8.78223	0.568075	0.284038	+	0.958813i	$0.408326\pi$
$240$	−5.54900	−0.358187
$241$	14.6871	0.946081	0.473041	−	0.881041i	$-0.343156\pi$
$241$	14.6871	0.946081	0.473041	+	0.881041i	$0.343156\pi$
$242$	0	0
$243$	0.289186	0.0185513
$244$	9.67434	0.619336
$245$	1.00000	0.0638877
$246$	4.99273	0.318325
$247$	−0.887232	−0.0564532
$248$	−4.86044	−0.308638
$249$	−8.86501	−0.561797
$250$	−0.371973	−0.0235256
$251$	−12.8531	−0.811281	−0.405640	−	0.914033i	$-0.632952\pi$
$251$	−12.8531	−0.811281	−0.405640	+	0.914033i	$0.632952\pi$
$252$	−0.0518053	−0.00326342
$253$	0	0
$254$	−4.00820	−0.251497
$255$	10.5710	0.661980
$256$	6.04286	0.377679
$257$	3.47735	0.216911	0.108455	−	0.994101i	$-0.465410\pi$
$257$	3.47735	0.216911	0.108455	+	0.994101i	$0.465410\pi$
$258$	1.77967	0.110797
$259$	−5.98416	−0.371838
$260$	10.3209	0.640078
$261$	0.155655	0.00963479
$262$	2.56745	0.158618
$263$	21.8799	1.34917	0.674586	−	0.738196i	$-0.264322\pi$
$263$	21.8799	1.34917	0.674586	+	0.738196i	$0.264322\pi$
$264$	0	0
$265$	−9.90375	−0.608383
$266$	−0.0595283	−0.00364992
$267$	−4.28663	−0.262337
$268$	−10.5444	−0.644104
$269$	19.9755	1.21792	0.608962	−	0.793199i	$-0.291586\pi$
$269$	19.9755	1.21792	0.608962	+	0.793199i	$0.291586\pi$
$270$	−1.92376	−0.117076
$271$	−8.39340	−0.509863	−0.254931	−	0.966959i	$-0.582053\pi$
$271$	−8.39340	−0.509863	−0.254931	+	0.966959i	$0.582053\pi$
$272$	−19.3731	−1.17467
$273$	9.64695	0.583860
$274$	−8.26710	−0.499434
$275$	0	0
$276$	−19.2861	−1.16089
$277$	−16.6608	−1.00105	−0.500525	−	0.865722i	$-0.666860\pi$
$277$	−16.6608	−1.00105	−0.500525	+	0.865722i	$0.666860\pi$
$278$	−6.59080	−0.395290
$279$	−0.0941612	−0.00563728
$280$	1.43642	0.0858427
$281$	16.8248	1.00368	0.501842	−	0.864959i	$-0.332656\pi$
$281$	16.8248	1.00368	0.501842	+	0.864959i	$0.332656\pi$
$282$	0.542762	0.0323210
$283$	−23.0027	−1.36737	−0.683684	−	0.729778i	$-0.739623\pi$
$283$	−23.0027	−1.36737	−0.683684	+	0.729778i	$0.739623\pi$
$284$	21.2752	1.26245
$285$	−0.278470	−0.0164951
$286$	0	0
$287$	7.71367	0.455324
$288$	−0.112955	−0.00665591
$289$	19.9062	1.17095
$290$	−2.08063	−0.122179
$291$	−20.8495	−1.22222
$292$	25.0791	1.46764
$293$	9.46294	0.552831	0.276415	−	0.961038i	$-0.410853\pi$
$293$	9.46294	0.552831	0.276415	+	0.961038i	$0.410853\pi$
$294$	0.647257	0.0377488
$295$	5.27721	0.307251
$296$	−8.59579	−0.499620
$297$	0	0
$298$	−0.622680	−0.0360709
$299$	33.0071	1.90885
$300$	3.23937	0.187025
$301$	2.74955	0.158482
$302$	−2.36157	−0.135893
$303$	22.9084	1.31605
$304$	0.510343	0.0292702
$305$	−5.19668	−0.297561
$306$	0.0628839	0.00359483
$307$	6.64993	0.379532	0.189766	−	0.981829i	$-0.439227\pi$
$307$	6.64993	0.379532	0.189766	+	0.981829i	$0.439227\pi$
$308$	0	0
$309$	−17.8491	−1.01540
$310$	1.25865	0.0714864
$311$	16.3682	0.928157	0.464079	−	0.885794i	$-0.346386\pi$
$311$	16.3682	0.928157	0.464079	+	0.885794i	$0.346386\pi$
$312$	13.8571	0.784504
$313$	−18.8717	−1.06669	−0.533347	−	0.845896i	$-0.679066\pi$
$313$	−18.8717	−1.06669	−0.533347	+	0.845896i	$0.679066\pi$
$314$	0.902567	0.0509348
$315$	0.0278278	0.00156792
$316$	17.0785	0.960740
$317$	4.88868	0.274576	0.137288	−	0.990531i	$-0.456161\pi$
$317$	4.88868	0.274576	0.137288	+	0.990531i	$0.456161\pi$
$318$	−6.41027	−0.359470
$319$	0	0
$320$	−4.86807	−0.272133
$321$	23.4040	1.30629
$322$	2.21460	0.123415
$323$	−0.972215	−0.0540955
$324$	16.9087	0.939372
$325$	−5.54402	−0.307527
$326$	4.49516	0.248964
$327$	15.1740	0.839121
$328$	11.0801	0.611796
$329$	0.838557	0.0462312
$330$	0	0
$331$	20.2362	1.11228	0.556142	−	0.831087i	$-0.312281\pi$
$331$	20.2362	1.11228	0.556142	+	0.831087i	$0.312281\pi$
$332$	−9.48437	−0.520522
$333$	−0.166526	−0.00912557
$334$	0.0886181	0.00484897
$335$	5.66407	0.309461
$336$	−5.54900	−0.302723
$337$	−32.4758	−1.76907	−0.884534	−	0.466475i	$-0.845524\pi$
$337$	−32.4758	−1.76907	−0.884534	+	0.466475i	$0.845524\pi$
$338$	−6.59735	−0.358848
$339$	7.36012	0.399747
$340$	11.3095	0.613345
$341$	0	0
$342$	−0.00165654	−8.95756e−5 0
$343$	1.00000	0.0539949
$344$	3.94952	0.212944
$345$	10.3597	0.557750
$346$	0.492558	0.0264801
$347$	−1.85387	−0.0995207	−0.0497604	−	0.998761i	$-0.515846\pi$
$347$	−1.85387	−0.0995207	−0.0497604	+	0.998761i	$0.515846\pi$
$348$	18.1194	0.971302
$349$	26.4688	1.41684	0.708420	−	0.705791i	$-0.249408\pi$
$349$	26.4688	1.41684	0.708420	+	0.705791i	$0.249408\pi$
$350$	−0.371973	−0.0198828
$351$	−28.6724	−1.53042
$352$	0	0
$353$	23.7745	1.26539	0.632693	−	0.774403i	$-0.281949\pi$
$353$	23.7745	1.26539	0.632693	+	0.774403i	$0.281949\pi$
$354$	3.41571	0.181543
$355$	−11.4282	−0.606548
$356$	−4.58612	−0.243064
$357$	10.5710	0.559476
$358$	2.21282	0.116951
$359$	−18.7639	−0.990323	−0.495161	−	0.868801i	$-0.664891\pi$
$359$	−18.7639	−0.990323	−0.495161	+	0.868801i	$0.664891\pi$
$360$	0.0399725	0.00210674
$361$	−18.9744	−0.998652
$362$	−8.44495	−0.443856
$363$	0	0
$364$	10.3209	0.540964
$365$	−13.4715	−0.705131
$366$	−3.36359	−0.175818
$367$	6.10777	0.318823	0.159411	−	0.987212i	$-0.449040\pi$
$367$	6.10777	0.318823	0.159411	+	0.987212i	$0.449040\pi$
$368$	−18.9860	−0.989713
$369$	0.214655	0.0111745
$370$	2.22594	0.115721
$371$	−9.90375	−0.514177
$372$	−10.9611	−0.568306
$373$	1.65909	0.0859045	0.0429523	−	0.999077i	$-0.486324\pi$
$373$	1.65909	0.0859045	0.0429523	+	0.999077i	$0.486324\pi$
$374$	0	0
$375$	−1.74007	−0.0898566
$376$	1.20452	0.0621185
$377$	−31.0104	−1.59712
$378$	−1.92376	−0.0989475
$379$	−22.3267	−1.14684	−0.573422	−	0.819260i	$-0.694384\pi$
$379$	−22.3267	−1.14684	−0.573422	+	0.819260i	$0.694384\pi$
$380$	−0.297925	−0.0152833
$381$	−18.7501	−0.960597
$382$	−8.71370	−0.445832
$383$	10.8733	0.555600	0.277800	−	0.960639i	$-0.410395\pi$
$383$	10.8733	0.555600	0.277800	+	0.960639i	$0.410395\pi$
$384$	−17.2769	−0.881659
$385$	0	0
$386$	5.31165	0.270356
$387$	0.0765141	0.00388943
$388$	−22.3062	−1.13242
$389$	23.3031	1.18151	0.590756	−	0.806850i	$-0.298830\pi$
$389$	23.3031	1.18151	0.590756	+	0.806850i	$0.298830\pi$
$390$	−3.58840	−0.181706
$391$	36.1687	1.82913
$392$	1.43642	0.0725503
$393$	12.0104	0.605843
$394$	−5.04946	−0.254388
$395$	−9.17391	−0.461589
$396$	0	0
$397$	11.8213	0.593292	0.296646	−	0.954987i	$-0.404132\pi$
$397$	11.8213	0.593292	0.296646	+	0.954987i	$0.404132\pi$
$398$	−6.50611	−0.326122
$399$	−0.278470	−0.0139409
$400$	3.18896	0.159448
$401$	33.5277	1.67429	0.837147	−	0.546978i	$-0.184222\pi$
$401$	33.5277	1.67429	0.837147	+	0.546978i	$0.184222\pi$
$402$	3.66611	0.182849
$403$	18.7593	0.934469
$404$	24.5089	1.21936
$405$	−9.08271	−0.451323
$406$	−2.08063	−0.103260
$407$	0	0
$408$	15.1844	0.751740
$409$	−17.3737	−0.859076	−0.429538	−	0.903049i	$-0.641324\pi$
$409$	−17.3737	−0.859076	−0.429538	+	0.903049i	$0.641324\pi$
$410$	−2.86927	−0.141703
$411$	−38.6730	−1.90760
$412$	−19.0962	−0.940800
$413$	5.27721	0.259675
$414$	0.0616273	0.00302882
$415$	5.09464	0.250086
$416$	22.5035	1.10332
$417$	−30.8314	−1.50982
$418$	0	0
$419$	−22.6553	−1.10678	−0.553391	−	0.832922i	$-0.686666\pi$
$419$	−22.6553	−1.10678	−0.553391	+	0.832922i	$0.686666\pi$
$420$	3.23937	0.158065
$421$	31.8993	1.55468	0.777339	−	0.629082i	$-0.216569\pi$
$421$	31.8993	1.55468	0.777339	+	0.629082i	$0.216569\pi$
$422$	5.52113	0.268764
$423$	0.0233352	0.00113460
$424$	−14.2260	−0.690875
$425$	−6.07505	−0.294683
$426$	−7.39701	−0.358386
$427$	−5.19668	−0.251485
$428$	25.0392	1.21031
$429$	0	0
$430$	−1.02276	−0.0493218
$431$	−15.5891	−0.750901	−0.375450	−	0.926843i	$-0.622512\pi$
$431$	−15.5891	−0.750901	−0.375450	+	0.926843i	$0.622512\pi$
$432$	16.4926	0.793500
$433$	27.1741	1.30591	0.652953	−	0.757399i	$-0.273530\pi$
$433$	27.1741	1.30591	0.652953	+	0.757399i	$0.273530\pi$
$434$	1.25865	0.0604170
$435$	−9.73305	−0.466664
$436$	16.2341	0.777472
$437$	−0.952788	−0.0455780
$438$	−8.71952	−0.416635
$439$	13.5671	0.647524	0.323762	−	0.946139i	$-0.395052\pi$
$439$	13.5671	0.647524	0.323762	+	0.946139i	$0.395052\pi$
$440$	0	0
$441$	0.0278278	0.00132513
$442$	−12.5281	−0.595901
$443$	−27.3562	−1.29973	−0.649865	−	0.760050i	$-0.725175\pi$
$443$	−27.3562	−1.29973	−0.649865	+	0.760050i	$0.725175\pi$
$444$	−19.3849	−0.919967
$445$	2.46349	0.116780
$446$	7.20557	0.341194
$447$	−2.91286	−0.137774
$448$	−4.86807	−0.229995
$449$	36.7789	1.73570	0.867852	−	0.496823i	$-0.165500\pi$
$449$	36.7789	1.73570	0.867852	+	0.496823i	$0.165500\pi$
$450$	−0.0103512	−0.000487959 0
$451$	0	0
$452$	7.87434	0.370378
$453$	−11.0473	−0.519046
$454$	−1.03224	−0.0484452
$455$	−5.54402	−0.259907
$456$	−0.400001	−0.0187317
$457$	26.7581	1.25169	0.625845	−	0.779947i	$-0.284754\pi$
$457$	26.7581	1.25169	0.625845	+	0.779947i	$0.284754\pi$
$458$	−10.2479	−0.478853
$459$	−31.4188	−1.46650
$460$	11.0835	0.516773
$461$	−4.24466	−0.197694	−0.0988468	−	0.995103i	$-0.531515\pi$
$461$	−4.24466	−0.197694	−0.0988468	+	0.995103i	$0.531515\pi$
$462$	0	0
$463$	−9.41964	−0.437768	−0.218884	−	0.975751i	$-0.570242\pi$
$463$	−9.41964	−0.437768	−0.218884	+	0.975751i	$0.570242\pi$
$464$	17.8375	0.828083
$465$	5.88788	0.273044
$466$	−5.46261	−0.253050
$467$	33.4815	1.54934	0.774669	−	0.632366i	$-0.217916\pi$
$467$	33.4815	1.54934	0.774669	+	0.632366i	$0.217916\pi$
$468$	0.287209	0.0132762
$469$	5.66407	0.261542
$470$	−0.311920	−0.0143878
$471$	4.22215	0.194546
$472$	7.58031	0.348912
$473$	0	0
$474$	−5.93787	−0.272736
$475$	0.160034	0.00734287
$476$	11.3095	0.518371
$477$	−0.275600	−0.0126188
$478$	−3.26675	−0.149418
$479$	−40.6065	−1.85536	−0.927680	−	0.373377i	$-0.878200\pi$
$479$	−40.6065	−1.85536	−0.927680	+	0.373377i	$0.878200\pi$
$480$	7.06302	0.322381
$481$	33.1763	1.51271
$482$	−5.46321	−0.248842
$483$	10.3597	0.471385
$484$	0	0
$485$	11.9820	0.544075
$486$	−0.107569	−0.00487944
$487$	24.6034	1.11489	0.557444	−	0.830214i	$-0.311782\pi$
$487$	24.6034	1.11489	0.557444	+	0.830214i	$0.311782\pi$
$488$	−7.46464	−0.337908
$489$	21.0281	0.950923
$490$	−0.371973	−0.0168040
$491$	−19.1334	−0.863480	−0.431740	−	0.901998i	$-0.642100\pi$
$491$	−19.1334	−0.863480	−0.431740	+	0.901998i	$0.642100\pi$
$492$	24.9874	1.12652
$493$	−33.9808	−1.53042
$494$	0.330026	0.0148486
$495$	0	0
$496$	−10.7905	−0.484509
$497$	−11.4282	−0.512627
$498$	3.29754	0.147766
$499$	3.77670	0.169068	0.0845342	−	0.996421i	$-0.473060\pi$
$499$	3.77670	0.169068	0.0845342	+	0.996421i	$0.473060\pi$
$500$	−1.86164	−0.0832549
$501$	0.414550	0.0185207
$502$	4.78100	0.213387
$503$	−20.4166	−0.910329	−0.455165	−	0.890407i	$-0.650420\pi$
$503$	−20.4166	−0.910329	−0.455165	+	0.890407i	$0.650420\pi$
$504$	0.0399725	0.00178052
$505$	−13.1652	−0.585845
$506$	0	0
$507$	−30.8620	−1.37063
$508$	−20.0601	−0.890023
$509$	23.0272	1.02066	0.510330	−	0.859978i	$-0.329523\pi$
$509$	23.0272	1.02066	0.510330	+	0.859978i	$0.329523\pi$
$510$	−3.93212	−0.174117
$511$	−13.4715	−0.595945
$512$	−22.1056	−0.976937
$513$	0.827661	0.0365421
$514$	−1.29348	−0.0570529
$515$	10.2577	0.452009
$516$	8.90682	0.392101
$517$	0	0
$518$	2.22594	0.0978024
$519$	2.30416	0.101141
$520$	−7.96355	−0.349225
$521$	−25.8562	−1.13278	−0.566390	−	0.824137i	$-0.691661\pi$
$521$	−25.8562	−1.13278	−0.566390	+	0.824137i	$0.691661\pi$
$522$	−0.0578993	−0.00253418
$523$	38.8242	1.69766	0.848831	−	0.528664i	$-0.177307\pi$
$523$	38.8242	1.69766	0.848831	+	0.528664i	$0.177307\pi$
$524$	12.8495	0.561333
$525$	−1.74007	−0.0759427
$526$	−8.13872	−0.354865
$527$	20.5562	0.895442
$528$	0	0
$529$	12.4460	0.541130
$530$	3.68392	0.160019
$531$	0.146853	0.00637289
$532$	−0.297925	−0.0129167
$533$	−42.7647	−1.85235
$534$	1.59451	0.0690011
$535$	−13.4501	−0.581498
$536$	8.13600	0.351422
$537$	10.3515	0.446698
$538$	−7.43032	−0.320344
$539$	0	0
$540$	−9.62796	−0.414322
$541$	−29.6794	−1.27602	−0.638008	−	0.770030i	$-0.720241\pi$
$541$	−29.6794	−1.27602	−0.638008	+	0.770030i	$0.720241\pi$
$542$	3.12212	0.134106
$543$	−39.5049	−1.69532
$544$	24.6589	1.05724
$545$	−8.72033	−0.373538
$546$	−3.58840	−0.153569
$547$	10.6915	0.457134	0.228567	−	0.973528i	$-0.426596\pi$
$547$	10.6915	0.457134	0.228567	+	0.973528i	$0.426596\pi$
$548$	−41.3749	−1.76745
$549$	−0.144612	−0.00617190
$550$	0	0
$551$	0.895151	0.0381347
$552$	14.8810	0.633376
$553$	−9.17391	−0.390114
$554$	6.19736	0.263301
$555$	10.4128	0.442000
$556$	−32.9854	−1.39889
$557$	−21.4026	−0.906857	−0.453428	−	0.891293i	$-0.649799\pi$
$557$	−21.4026	−0.906857	−0.453428	+	0.891293i	$0.649799\pi$
$558$	0.0350254	0.00148274
$559$	−15.2436	−0.644735
$560$	3.18896	0.134758
$561$	0	0
$562$	−6.25837	−0.263993
$563$	21.2457	0.895401	0.447701	−	0.894183i	$-0.352243\pi$
$563$	21.2457	0.895401	0.447701	+	0.894183i	$0.352243\pi$
$564$	2.71640	0.114381
$565$	−4.22980	−0.177949
$566$	8.55637	0.359651
$567$	−9.08271	−0.381438
$568$	−16.4158	−0.688791
$569$	−3.45497	−0.144840	−0.0724199	−	0.997374i	$-0.523072\pi$
$569$	−3.45497	−0.144840	−0.0724199	+	0.997374i	$0.523072\pi$
$570$	0.103583	0.00433862
$571$	40.3679	1.68935	0.844673	−	0.535283i	$-0.179795\pi$
$571$	40.3679	1.68935	0.844673	+	0.535283i	$0.179795\pi$
$572$	0	0
$573$	−40.7622	−1.70286
$574$	−2.86927	−0.119761
$575$	−5.95365	−0.248285
$576$	−0.135468	−0.00564449
$577$	−12.9910	−0.540821	−0.270411	−	0.962745i	$-0.587159\pi$
$577$	−12.9910	−0.540821	−0.270411	+	0.962745i	$0.587159\pi$
$578$	−7.40456	−0.307989
$579$	24.8476	1.03263
$580$	−10.4131	−0.432379
$581$	5.09464	0.211361
$582$	7.75544	0.321473
$583$	0	0
$584$	−19.3508	−0.800741
$585$	−0.154278	−0.00637860
$586$	−3.51996	−0.145408
$587$	−21.9867	−0.907488	−0.453744	−	0.891132i	$-0.649912\pi$
$587$	−21.9867	−0.907488	−0.453744	+	0.891132i	$0.649912\pi$
$588$	3.23937	0.133589
$589$	−0.541509	−0.0223125
$590$	−1.96298	−0.0808145
$591$	−23.6211	−0.971641
$592$	−19.0833	−0.784318
$593$	−21.2529	−0.872750	−0.436375	−	0.899765i	$-0.643738\pi$
$593$	−21.2529	−0.872750	−0.436375	+	0.899765i	$0.643738\pi$
$594$	0	0
$595$	−6.07505	−0.249053
$596$	−3.11637	−0.127651
$597$	−30.4352	−1.24563
$598$	−12.2778	−0.502075
$599$	33.1370	1.35394	0.676970	−	0.736011i	$-0.263293\pi$
$599$	33.1370	1.35394	0.676970	+	0.736011i	$0.263293\pi$
$600$	−2.49947	−0.102040
$601$	−26.5611	−1.08345	−0.541724	−	0.840556i	$-0.682228\pi$
$601$	−26.5611	−1.08345	−0.541724	+	0.840556i	$0.682228\pi$
$602$	−1.02276	−0.0416845
$603$	0.157619	0.00641873
$604$	−11.8191	−0.480912
$605$	0	0
$606$	−8.52128	−0.346154
$607$	23.4280	0.950913	0.475456	−	0.879739i	$-0.342283\pi$
$607$	23.4280	0.950913	0.475456	+	0.879739i	$0.342283\pi$
$608$	−0.649587	−0.0263442
$609$	−9.73305	−0.394403
$610$	1.93302	0.0782659
$611$	−4.64898	−0.188077
$612$	0.314719	0.0127218
$613$	21.5142	0.868951	0.434476	−	0.900684i	$-0.356934\pi$
$613$	21.5142	0.868951	0.434476	+	0.900684i	$0.356934\pi$
$614$	−2.47359	−0.0998260
$615$	−13.4223	−0.541239
$616$	0	0
$617$	−8.52192	−0.343080	−0.171540	−	0.985177i	$-0.554874\pi$
$617$	−8.52192	−0.343080	−0.171540	+	0.985177i	$0.554874\pi$
$618$	6.63938	0.267075
$619$	2.60382	0.104656	0.0523282	−	0.998630i	$-0.483336\pi$
$619$	2.60382	0.104656	0.0523282	+	0.998630i	$0.483336\pi$
$620$	6.29924	0.252983
$621$	−30.7909	−1.23560
$622$	−6.08853	−0.244128
$623$	2.46349	0.0986975
$624$	30.7638	1.23154
$625$	1.00000	0.0400000
$626$	7.01977	0.280567
$627$	0	0
$628$	4.51714	0.180253
$629$	36.3541	1.44953
$630$	−0.0103512	−0.000412401 0
$631$	37.6868	1.50029	0.750145	−	0.661274i	$-0.229984\pi$
$631$	37.6868	1.50029	0.750145	+	0.661274i	$0.229984\pi$
$632$	−13.1776	−0.524177
$633$	25.8275	1.02655
$634$	−1.81846	−0.0722201
$635$	10.7755	0.427613
$636$	−32.0819	−1.27213
$637$	−5.54402	−0.219662
$638$	0	0
$639$	−0.318023	−0.0125808
$640$	9.92889	0.392474
$641$	−41.1792	−1.62648	−0.813241	−	0.581927i	$-0.802299\pi$
$641$	−41.1792	−1.62648	−0.813241	+	0.581927i	$0.802299\pi$
$642$	−8.70566	−0.343585
$643$	−30.5489	−1.20473	−0.602365	−	0.798220i	$-0.705775\pi$
$643$	−30.5489	−1.20473	−0.602365	+	0.798220i	$0.705775\pi$
$644$	11.0835	0.436753
$645$	−4.78441	−0.188386
$646$	0.361637	0.0142284
$647$	43.8646	1.72450	0.862248	−	0.506486i	$-0.169056\pi$
$647$	43.8646	1.72450	0.862248	+	0.506486i	$0.169056\pi$
$648$	−13.0466	−0.512519
$649$	0	0
$650$	2.06222	0.0808870
$651$	5.88788	0.230764
$652$	22.4972	0.881060
$653$	7.88498	0.308563	0.154282	−	0.988027i	$-0.450694\pi$
$653$	7.88498	0.308563	0.154282	+	0.988027i	$0.450694\pi$
$654$	−5.64429	−0.220709
$655$	−6.90226	−0.269693
$656$	24.5986	0.960414
$657$	−0.374883	−0.0146256
$658$	−0.311920	−0.0121599
$659$	−35.5665	−1.38547	−0.692737	−	0.721190i	$-0.743595\pi$
$659$	−35.5665	−1.38547	−0.692737	+	0.721190i	$0.743595\pi$
$660$	0	0
$661$	−7.48510	−0.291136	−0.145568	−	0.989348i	$-0.546501\pi$
$661$	−7.48510	−0.291136	−0.145568	+	0.989348i	$0.546501\pi$
$662$	−7.52732	−0.292558
$663$	−58.6057	−2.27606
$664$	7.31806	0.283996
$665$	0.160034	0.00620586
$666$	0.0619431	0.00240025
$667$	−33.3017	−1.28945
$668$	0.443513	0.0171600
$669$	33.7072	1.30320
$670$	−2.10688	−0.0813958
$671$	0	0
$672$	7.06302	0.272462
$673$	−44.0438	−1.69776	−0.848882	−	0.528583i	$-0.822724\pi$
$673$	−44.0438	−1.69776	−0.848882	+	0.528583i	$0.822724\pi$
$674$	12.0801	0.465308
$675$	5.17177	0.199062
$676$	−33.0182	−1.26993
$677$	−24.0138	−0.922927	−0.461463	−	0.887159i	$-0.652675\pi$
$677$	−24.0138	−0.922927	−0.461463	+	0.887159i	$0.652675\pi$
$678$	−2.73776	−0.105143
$679$	11.9820	0.459828
$680$	−8.72634	−0.334640
$681$	−4.82873	−0.185037
$682$	0	0
$683$	−39.6080	−1.51556	−0.757779	−	0.652511i	$-0.773715\pi$
$683$	−39.6080	−1.51556	−0.757779	+	0.652511i	$0.773715\pi$
$684$	−0.00829061	−0.000316999 0
$685$	22.2250	0.849174
$686$	−0.371973	−0.0142020
$687$	−47.9391	−1.82899
$688$	8.76823	0.334286
$689$	54.9066	2.09177
$690$	−3.85354	−0.146702
$691$	38.7466	1.47399	0.736995	−	0.675898i	$-0.236244\pi$
$691$	38.7466	1.47399	0.736995	+	0.675898i	$0.236244\pi$
$692$	2.46514	0.0937105
$693$	0	0
$694$	0.689587	0.0261764
$695$	17.7185	0.672101
$696$	−13.9808	−0.529940
$697$	−46.8609	−1.77498
$698$	−9.84566	−0.372664
$699$	−25.5537	−0.966531
$700$	−1.86164	−0.0703632
$701$	18.2488	0.689246	0.344623	−	0.938741i	$-0.388007\pi$
$701$	18.2488	0.689246	0.344623	+	0.938741i	$0.388007\pi$
$702$	10.6653	0.402538
$703$	−0.957671	−0.0361192
$704$	0	0
$705$	−1.45914	−0.0549546
$706$	−8.84344	−0.332827
$707$	−13.1652	−0.495130
$708$	17.0948	0.642463
$709$	−7.78867	−0.292510	−0.146255	−	0.989247i	$-0.546722\pi$
$709$	−7.78867	−0.292510	−0.146255	+	0.989247i	$0.546722\pi$
$710$	4.25099	0.159537
$711$	−0.255290	−0.00957411
$712$	3.53861	0.132615
$713$	20.1454	0.754452
$714$	−3.93212	−0.147156
$715$	0	0
$716$	11.0747	0.413880
$717$	−15.2817	−0.570704
$718$	6.97967	0.260479
$719$	−21.8425	−0.814587	−0.407293	−	0.913297i	$-0.633527\pi$
$719$	−21.8425	−0.814587	−0.407293	+	0.913297i	$0.633527\pi$
$720$	0.0887418	0.00330721
$721$	10.2577	0.382018
$722$	7.05795	0.262670
$723$	−25.5566	−0.950459
$724$	−42.2650	−1.57077
$725$	5.59350	0.207737
$726$	0	0
$727$	21.4001	0.793685	0.396843	−	0.917887i	$-0.370106\pi$
$727$	21.4001	0.793685	0.396843	+	0.917887i	$0.370106\pi$
$728$	−7.96355	−0.295149
$729$	26.7449	0.990553
$730$	5.01103	0.185467
$731$	−16.7037	−0.617808
$732$	−16.8340	−0.622202
$733$	−13.2443	−0.489189	−0.244595	−	0.969625i	$-0.578655\pi$
$733$	−13.2443	−0.489189	−0.244595	+	0.969625i	$0.578655\pi$
$734$	−2.27192	−0.0838582
$735$	−1.74007	−0.0641833
$736$	24.1662	0.890778
$737$	0	0
$738$	−0.0798456	−0.00293916
$739$	8.93266	0.328593	0.164297	−	0.986411i	$-0.447465\pi$
$739$	8.93266	0.328593	0.164297	+	0.986411i	$0.447465\pi$
$740$	11.1403	0.409527
$741$	1.54384	0.0567145
$742$	3.68392	0.135241
$743$	−5.69723	−0.209011	−0.104506	−	0.994524i	$-0.533326\pi$
$743$	−5.69723	−0.209011	−0.104506	+	0.994524i	$0.533326\pi$
$744$	8.45748	0.310066
$745$	1.67399	0.0613304
$746$	−0.617137	−0.0225950
$747$	0.141773	0.00518719
$748$	0	0
$749$	−13.4501	−0.491456
$750$	0.647257	0.0236345
$751$	−13.0098	−0.474735	−0.237367	−	0.971420i	$-0.576285\pi$
$751$	−13.0098	−0.474735	−0.237367	+	0.971420i	$0.576285\pi$
$752$	2.67413	0.0975154
$753$	22.3652	0.815035
$754$	11.5350	0.420081
$755$	6.34876	0.231055
$756$	−9.62796	−0.350166
$757$	−6.27726	−0.228151	−0.114075	−	0.993472i	$-0.536391\pi$
$757$	−6.27726	−0.228151	−0.114075	+	0.993472i	$0.536391\pi$
$758$	8.30491	0.301648
$759$	0	0
$760$	0.229877	0.00833851
$761$	21.9208	0.794629	0.397315	−	0.917682i	$-0.369942\pi$
$761$	21.9208	0.794629	0.397315	+	0.917682i	$0.369942\pi$
$762$	6.97453	0.252660
$763$	−8.72033	−0.315697
$764$	−43.6100	−1.57776
$765$	−0.169055	−0.00611220
$766$	−4.04458	−0.146136
$767$	−29.2570	−1.05641
$768$	−10.5150	−0.379426
$769$	32.3147	1.16530	0.582649	−	0.812724i	$-0.302016\pi$
$769$	32.3147	1.16530	0.582649	+	0.812724i	$0.302016\pi$
$770$	0	0
$771$	−6.05081	−0.217915
$772$	26.5836	0.956763
$773$	29.8086	1.07214	0.536071	−	0.844173i	$-0.319908\pi$
$773$	29.8086	1.07214	0.536071	+	0.844173i	$0.319908\pi$
$774$	−0.0284611	−0.00102301
$775$	−3.38371	−0.121546
$776$	17.2112	0.617848
$777$	10.4128	0.373558
$778$	−8.66810	−0.310766
$779$	1.23445	0.0442288
$780$	−17.9591	−0.643039
$781$	0	0
$782$	−13.4538	−0.481106
$783$	28.9283	1.03381
$784$	3.18896	0.113892
$785$	−2.42643	−0.0866031
$786$	−4.46753	−0.159352
$787$	20.6450	0.735916	0.367958	−	0.929842i	$-0.380057\pi$
$787$	20.6450	0.735916	0.367958	+	0.929842i	$0.380057\pi$
$788$	−25.2714	−0.900255
$789$	−38.0724	−1.35541
$790$	3.41244	0.121409
$791$	−4.22980	−0.150394
$792$	0	0
$793$	28.8105	1.02309
$794$	−4.39719	−0.156050
$795$	17.2332	0.611198
$796$	−32.5616	−1.15411
$797$	−6.17497	−0.218729	−0.109364	−	0.994002i	$-0.534882\pi$
$797$	−6.17497	−0.218729	−0.109364	+	0.994002i	$0.534882\pi$
$798$	0.103583	0.00366681
$799$	−5.09428	−0.180223
$800$	−4.05905	−0.143509
$801$	0.0685534	0.00242222
$802$	−12.4714	−0.440380
$803$	0	0
$804$	18.3480	0.647085
$805$	−5.95365	−0.209839
$806$	−6.97796	−0.245788
$807$	−34.7586	−1.22356
$808$	−18.9108	−0.665281
$809$	6.69756	0.235474	0.117737	−	0.993045i	$-0.462436\pi$
$809$	6.69756	0.235474	0.117737	+	0.993045i	$0.462436\pi$
$810$	3.37852	0.118709
$811$	10.8349	0.380466	0.190233	−	0.981739i	$-0.439076\pi$
$811$	10.8349	0.380466	0.190233	+	0.981739i	$0.439076\pi$
$812$	−10.4131	−0.365427
$813$	14.6051	0.512222
$814$	0	0
$815$	−12.0847	−0.423307
$816$	33.7105	1.18010
$817$	0.440023	0.0153944
$818$	6.46256	0.225958
$819$	−0.154278	−0.00539090
$820$	−14.3601	−0.501475
$821$	23.3622	0.815345	0.407673	−	0.913128i	$-0.366340\pi$
$821$	23.3622	0.815345	0.407673	+	0.913128i	$0.366340\pi$
$822$	14.3853	0.501745
$823$	−1.57909	−0.0550435	−0.0275217	−	0.999621i	$-0.508762\pi$
$823$	−1.57909	−0.0550435	−0.0275217	+	0.999621i	$0.508762\pi$
$824$	14.7344	0.513298
$825$	0	0
$826$	−1.96298	−0.0683008
$827$	0.0284286	0.000988558 0	0.000494279	−	1.00000i	$-0.499843\pi$
$827$	0.0284286	0.000988558 0	0.000494279		1.00000i	$0.499843\pi$
$828$	0.308430	0.0107187
$829$	7.19463	0.249880	0.124940	−	0.992164i	$-0.460126\pi$
$829$	7.19463	0.249880	0.124940	+	0.992164i	$0.460126\pi$
$830$	−1.89507	−0.0657787
$831$	28.9909	1.00568
$832$	26.9887	0.935663
$833$	−6.07505	−0.210488
$834$	11.4684	0.397119
$835$	−0.238238	−0.00824457
$836$	0	0
$837$	−17.4998	−0.604881
$838$	8.42713	0.291111
$839$	−8.28716	−0.286105	−0.143052	−	0.989715i	$-0.545692\pi$
$839$	−8.28716	−0.286105	−0.143052	+	0.989715i	$0.545692\pi$
$840$	−2.49947	−0.0862399
$841$	2.28722	0.0788697
$842$	−11.8657	−0.408918
$843$	−29.2763	−1.00833
$844$	27.6320	0.951131
$845$	17.7361	0.610141
$846$	−0.00868006	−0.000298427 0
$847$	0	0
$848$	−31.5827	−1.08455
$849$	40.0262	1.37369
$850$	2.25975	0.0775088
$851$	35.6276	1.22130
$852$	−37.0203	−1.26829
$853$	6.27212	0.214753	0.107377	−	0.994218i	$-0.465755\pi$
$853$	6.27212	0.214753	0.107377	+	0.994218i	$0.465755\pi$
$854$	1.93302	0.0661467
$855$	0.00445340	0.000152303 0
$856$	−19.3200	−0.660345
$857$	1.51105	0.0516164	0.0258082	−	0.999667i	$-0.491784\pi$
$857$	1.51105	0.0516164	0.0258082	+	0.999667i	$0.491784\pi$
$858$	0	0
$859$	26.0521	0.888886	0.444443	−	0.895807i	$-0.353402\pi$
$859$	26.0521	0.888886	0.444443	+	0.895807i	$0.353402\pi$
$860$	−5.11867	−0.174545
$861$	−13.4223	−0.457431
$862$	5.79872	0.197505
$863$	−5.22907	−0.178000	−0.0889998	−	0.996032i	$-0.528367\pi$
$863$	−5.22907	−0.178000	−0.0889998	+	0.996032i	$0.528367\pi$
$864$	−20.9925	−0.714179
$865$	−1.32418	−0.0450234
$866$	−10.1080	−0.343485
$867$	−34.6381	−1.17637
$868$	6.29924	0.213810
$869$	0	0
$870$	3.62043	0.122744
$871$	−31.4017	−1.06401
$872$	−12.5261	−0.424187
$873$	0.333433	0.0112850
$874$	0.354411	0.0119881
$875$	1.00000	0.0338062
$876$	−43.6392	−1.47443
$877$	−2.92869	−0.0988948	−0.0494474	−	0.998777i	$-0.515746\pi$
$877$	−2.92869	−0.0988948	−0.0494474	+	0.998777i	$0.515746\pi$
$878$	−5.04660	−0.170315
$879$	−16.4661	−0.555389
$880$	0	0
$881$	11.6890	0.393812	0.196906	−	0.980422i	$-0.436911\pi$
$881$	11.6890	0.393812	0.196906	+	0.980422i	$0.436911\pi$
$882$	−0.0103512	−0.000348542 0
$883$	−2.10102	−0.0707051	−0.0353525	−	0.999375i	$-0.511255\pi$
$883$	−2.10102	−0.0707051	−0.0353525	+	0.999375i	$0.511255\pi$
$884$	−62.7002	−2.10884
$885$	−9.18270	−0.308673
$886$	10.1757	0.341861
$887$	−18.5520	−0.622916	−0.311458	−	0.950260i	$-0.600817\pi$
$887$	−18.5520	−0.622916	−0.311458	+	0.950260i	$0.600817\pi$
$888$	14.9572	0.501932
$889$	10.7755	0.361399
$890$	−0.916350	−0.0307161
$891$	0	0
$892$	36.0622	1.20745
$893$	0.134198	0.00449076
$894$	1.08350	0.0362378
$895$	−5.94889	−0.198849
$896$	9.92889	0.331701
$897$	−57.4346	−1.91769
$898$	−13.6807	−0.456532
$899$	−18.9268	−0.631243
$900$	−0.0518053	−0.00172684
$901$	60.1658	2.00441
$902$	0	0
$903$	−4.78441	−0.159215
$904$	−6.07578	−0.202077
$905$	22.7031	0.754678
$906$	4.10928	0.136522
$907$	−4.89164	−0.162424	−0.0812122	−	0.996697i	$-0.525879\pi$
$907$	−4.89164	−0.162424	−0.0812122	+	0.996697i	$0.525879\pi$
$908$	−5.16610	−0.171443
$909$	−0.366359	−0.0121514
$910$	2.06222	0.0683620
$911$	−39.9751	−1.32443	−0.662217	−	0.749312i	$-0.730384\pi$
$911$	−39.9751	−1.32443	−0.662217	+	0.749312i	$0.730384\pi$
$912$	−0.888030	−0.0294056
$913$	0	0
$914$	−9.95328	−0.329225
$915$	9.04257	0.298938
$916$	−51.2884	−1.69462
$917$	−6.90226	−0.227933
$918$	11.6869	0.385726
$919$	−14.7866	−0.487765	−0.243883	−	0.969805i	$-0.578421\pi$
$919$	−14.7866	−0.487765	−0.243883	+	0.969805i	$0.578421\pi$
$920$	−8.55196	−0.281950
$921$	−11.5713	−0.381288
$922$	1.57890	0.0519982
$923$	63.3584	2.08547
$924$	0	0
$925$	−5.98416	−0.196758
$926$	3.50385	0.115144
$927$	0.285450	0.00937541
$928$	−22.7043	−0.745305
$929$	−28.0386	−0.919915	−0.459958	−	0.887941i	$-0.652135\pi$
$929$	−28.0386	−0.919915	−0.459958	+	0.887941i	$0.652135\pi$
$930$	−2.19013	−0.0718171
$931$	0.160034	0.00524491
$932$	−27.3391	−0.895521
$933$	−28.4818	−0.932452
$934$	−12.4542	−0.407514
$935$	0	0
$936$	−0.221608	−0.00724349
$937$	35.4722	1.15883	0.579414	−	0.815034i	$-0.303282\pi$
$937$	35.4722	1.15883	0.579414	+	0.815034i	$0.303282\pi$
$938$	−2.10688	−0.0687920
$939$	32.8381	1.07163
$940$	−1.56109	−0.0509171
$941$	−8.77512	−0.286061	−0.143030	−	0.989718i	$-0.545685\pi$
$941$	−8.77512	−0.286061	−0.143030	+	0.989718i	$0.545685\pi$
$942$	−1.57052	−0.0511705
$943$	−45.9245	−1.49551
$944$	16.8288	0.547732
$945$	5.17177	0.168238
$946$	0	0
$947$	−52.3836	−1.70224	−0.851119	−	0.524972i	$-0.824076\pi$
$947$	−52.3836	−1.70224	−0.851119	+	0.524972i	$0.824076\pi$
$948$	−29.7177	−0.965185
$949$	74.6863	2.42442
$950$	−0.0595283	−0.00193135
$951$	−8.50662	−0.275846
$952$	−8.72634	−0.282822
$953$	2.94539	0.0954106	0.0477053	−	0.998861i	$-0.484809\pi$
$953$	2.94539	0.0954106	0.0477053	+	0.998861i	$0.484809\pi$
$954$	0.102516	0.00331906
$955$	23.4256	0.758036
$956$	−16.3493	−0.528775
$957$	0	0
$958$	15.1045	0.488005
$959$	22.2250	0.717683
$960$	8.47076	0.273393
$961$	−19.5505	−0.630662
$962$	−12.3407	−0.397879
$963$	−0.374286	−0.0120612
$964$	−27.3421	−0.880630
$965$	−14.2797	−0.459679
$966$	−3.85354	−0.123986
$967$	−20.2786	−0.652116	−0.326058	−	0.945350i	$-0.605721\pi$
$967$	−20.2786	−0.652116	−0.326058	+	0.945350i	$0.605721\pi$
$968$	0	0
$969$	1.69172	0.0543458
$970$	−4.45698	−0.143105
$971$	2.89351	0.0928571	0.0464285	−	0.998922i	$-0.485216\pi$
$971$	2.89351	0.0928571	0.0464285	+	0.998922i	$0.485216\pi$
$972$	−0.538359	−0.0172679
$973$	17.7185	0.568029
$974$	−9.15181	−0.293243
$975$	9.64695	0.308950
$976$	−16.5720	−0.530458
$977$	−56.6846	−1.81350	−0.906750	−	0.421668i	$-0.861445\pi$
$977$	−56.6846	−1.81350	−0.906750	+	0.421668i	$0.861445\pi$
$978$	−7.82187	−0.250116
$979$	0	0
$980$	−1.86164	−0.0594678
$981$	−0.242668	−0.00774778
$982$	7.11712	0.227116
$983$	10.6310	0.339076	0.169538	−	0.985524i	$-0.445772\pi$
$983$	10.6310	0.339076	0.169538	+	0.985524i	$0.445772\pi$
$984$	−19.2801	−0.614627
$985$	13.5748	0.432529
$986$	12.6399	0.402537
$987$	−1.45914	−0.0464451
$988$	1.65170	0.0525477
$989$	−16.3699	−0.520532
$990$	0	0
$991$	36.2838	1.15259	0.576296	−	0.817241i	$-0.304497\pi$
$991$	36.2838	1.15259	0.576296	+	0.817241i	$0.304497\pi$
$992$	13.7347	0.436076
$993$	−35.2124	−1.11743
$994$	4.25099	0.134833
$995$	17.4908	0.554497
$996$	16.5034	0.522931
$997$	57.2412	1.81285	0.906424	−	0.422369i	$-0.138801\pi$
$997$	57.2412	1.81285	0.906424	+	0.422369i	$0.138801\pi$
$998$	−1.40483	−0.0444691
$999$	−30.9487	−0.979175

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.9		18
11.2	odd	10		385.2.n.f.246.5	yes	36
11.6	odd	10		385.2.n.f.36.5	✓	36
11.10	odd	2		4235.2.a.bo.1.10		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.5	✓	36	11.6	odd	10
385.2.n.f.246.5	yes	36	11.2	odd	10
4235.2.a.bo.1.10		18	11.10	odd	2
4235.2.a.bp.1.9		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-0.371973 q^{2} -1.74007 q^{3} -1.86164 q^{4} +1.00000 q^{5} +0.647257 q^{6} +1.00000 q^{7} +1.43642 q^{8} +0.0278278 q^{9} +O(q^{10})\)	\(q-0.371973 q^{2} -1.74007 q^{3} -1.86164 q^{4} +1.00000 q^{5} +0.647257 q^{6} +1.00000 q^{7} +1.43642 q^{8} +0.0278278 q^{9} -0.371973 q^{10} +3.23937 q^{12} -5.54402 q^{13} -0.371973 q^{14} -1.74007 q^{15} +3.18896 q^{16} -6.07505 q^{17} -0.0103512 q^{18} +0.160034 q^{19} -1.86164 q^{20} -1.74007 q^{21} -5.95365 q^{23} -2.49947 q^{24} +1.00000 q^{25} +2.06222 q^{26} +5.17177 q^{27} -1.86164 q^{28} +5.59350 q^{29} +0.647257 q^{30} -3.38371 q^{31} -4.05905 q^{32} +2.25975 q^{34} +1.00000 q^{35} -0.0518053 q^{36} -5.98416 q^{37} -0.0595283 q^{38} +9.64695 q^{39} +1.43642 q^{40} +7.71367 q^{41} +0.647257 q^{42} +2.74955 q^{43} +0.0278278 q^{45} +2.21460 q^{46} +0.838557 q^{47} -5.54900 q^{48} +1.00000 q^{49} -0.371973 q^{50} +10.5710 q^{51} +10.3209 q^{52} -9.90375 q^{53} -1.92376 q^{54} +1.43642 q^{56} -0.278470 q^{57} -2.08063 q^{58} +5.27721 q^{59} +3.23937 q^{60} -5.19668 q^{61} +1.25865 q^{62} +0.0278278 q^{63} -4.86807 q^{64} -5.54402 q^{65} +5.66407 q^{67} +11.3095 q^{68} +10.3597 q^{69} -0.371973 q^{70} -11.4282 q^{71} +0.0399725 q^{72} -13.4715 q^{73} +2.22594 q^{74} -1.74007 q^{75} -0.297925 q^{76} -3.58840 q^{78} -9.17391 q^{79} +3.18896 q^{80} -9.08271 q^{81} -2.86927 q^{82} +5.09464 q^{83} +3.23937 q^{84} -6.07505 q^{85} -1.02276 q^{86} -9.73305 q^{87} +2.46349 q^{89} -0.0103512 q^{90} -5.54402 q^{91} +11.0835 q^{92} +5.88788 q^{93} -0.311920 q^{94} +0.160034 q^{95} +7.06302 q^{96} +11.9820 q^{97} -0.371973 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 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

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