LMFDB - Embedded newform 4235.2.a.bo.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4235, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$18$
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			1.10
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	$-0.458017\pi$
$2$	0.371973	0.263024	0.131512	+	0.991315i	$0.458017\pi$
$3$	−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	$-0.220846\pi$
$13$	5.54402	1.53763	0.768817	+	0.639469i	$0.220846\pi$
$14$	−0.371973	−0.0994139
$15$	−1.74007	−0.449283
$16$	3.18896	0.797241
$17$	6.07505	1.47342	0.736708	−	0.676211i	$-0.236379\pi$
$17$	6.07505	1.47342	0.736708	+	0.676211i	$0.236379\pi$
$18$	0.0103512	0.00243980
$19$	−0.160034	−0.0367144	−0.0183572	−	0.999831i	$-0.505844\pi$
$19$	−0.160034	−0.0367144	−0.0183572	+	0.999831i	$0.505844\pi$
$20$	−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	$-0.673823\pi$
$29$	−5.59350	−1.03869	−0.519343	+	0.854566i	$0.673823\pi$
$30$	−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	$-0.705763\pi$
$41$	−7.71367	−1.20467	−0.602337	+	0.798242i	$0.705763\pi$
$42$	0.647257	0.0998739
$43$	−2.74955	−0.419303	−0.209652	−	0.977776i	$-0.567233\pi$
$43$	−2.74955	−0.419303	−0.209652	+	0.977776i	$0.567233\pi$
$44$	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	$-0.392046\pi$
$61$	5.19668	0.665367	0.332684	+	0.943039i	$0.392046\pi$
$62$	−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	$-0.210930\pi$
$73$	13.4715	1.57672	0.788360	+	0.615214i	$0.210930\pi$
$74$	−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	$-0.327393\pi$
$79$	9.17391	1.03215	0.516073	+	0.856545i	$0.327393\pi$
$80$	3.18896	0.356537
$81$	−9.08271	−1.00919
$82$	−2.86927	−0.316858
$83$	−5.09464	−0.559210	−0.279605	−	0.960115i	$-0.590203\pi$
$83$	−5.09464	−0.559210	−0.279605	+	0.960115i	$0.590203\pi$
$84$	−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	$-0.272671\pi$
$101$	13.1652	1.30999	0.654995	+	0.755633i	$0.272671\pi$
$102$	−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	$-0.274712\pi$
$107$	13.4501	1.30027	0.650135	+	0.759819i	$0.274712\pi$
$108$	−9.62796	−0.926451
$109$	8.72033	0.835256	0.417628	−	0.908618i	$-0.362861\pi$
$109$	8.72033	0.835256	0.417628	+	0.908618i	$0.362861\pi$
$110$	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	$-0.658669\pi$
$127$	−10.7755	−0.956173	−0.478086	+	0.878313i	$0.658669\pi$
$128$	−9.92889	−0.877599
$129$	4.78441	0.421243
$130$	2.06222	0.180869
$131$	6.90226	0.603053	0.301526	−	0.953458i	$-0.402504\pi$
$131$	6.90226	0.603053	0.301526	+	0.953458i	$0.402504\pi$
$132$	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	$-0.770637\pi$
$139$	−17.7185	−1.50286	−0.751432	+	0.659810i	$0.770637\pi$
$140$	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	$-0.521843\pi$
$149$	−1.67399	−0.137139	−0.0685695	+	0.997646i	$0.521843\pi$
$150$	−0.647257	−0.0528483
$151$	−6.34876	−0.516655	−0.258327	−	0.966057i	$-0.583171\pi$
$151$	−6.34876	−0.516655	−0.258327	+	0.966057i	$0.583171\pi$
$152$	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	$-0.497066\pi$
$167$	0.238238	0.0184354	0.00921771	+	0.999958i	$0.497066\pi$
$168$	−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	$-0.483970\pi$
$173$	1.32418	0.100675	0.0503377	+	0.998732i	$0.483970\pi$
$174$	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	$-0.328187\pi$
$193$	14.2797	1.02787	0.513937	+	0.857828i	$0.328187\pi$
$194$	4.45698	0.319993
$195$	−9.64695	−0.690833
$196$	−1.86164	−0.132974
$197$	−13.5748	−0.967165	−0.483583	−	0.875299i	$-0.660665\pi$
$197$	−13.5748	−0.967165	−0.483583	+	0.875299i	$0.660665\pi$
$198$	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	$-0.329308\pi$
$211$	14.8428	1.02182	0.510911	+	0.859633i	$0.329308\pi$
$212$	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	$-0.529356\pi$
$227$	−2.77503	−0.184185	−0.0920926	+	0.995750i	$0.529356\pi$
$228$	−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	$-0.659741\pi$
$233$	−14.6855	−0.962080	−0.481040	+	0.876699i	$0.659741\pi$
$234$	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	$-0.591674\pi$
$239$	−8.78223	−0.568075	−0.284038	+	0.958813i	$0.591674\pi$
$240$	−5.54900	−0.358187
$241$	−14.6871	−0.946081	−0.473041	−	0.881041i	$-0.656844\pi$
$241$	−14.6871	−0.946081	−0.473041	+	0.881041i	$0.656844\pi$
$242$	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	$-0.735678\pi$
$263$	−21.8799	−1.34917	−0.674586	+	0.738196i	$0.735678\pi$
$264$	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	$-0.417947\pi$
$271$	8.39340	0.509863	0.254931	+	0.966959i	$0.417947\pi$
$272$	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	$-0.333140\pi$
$277$	16.6608	1.00105	0.500525	+	0.865722i	$0.333140\pi$
$278$	−6.59080	−0.395290
$279$	−0.0941612	−0.00563728
$280$	1.43642	0.0858427
$281$	−16.8248	−1.00368	−0.501842	−	0.864959i	$-0.667344\pi$
$281$	−16.8248	−1.00368	−0.501842	+	0.864959i	$0.667344\pi$
$282$	−0.542762	−0.0323210
$283$	23.0027	1.36737	0.683684	−	0.729778i	$-0.260377\pi$
$283$	23.0027	1.36737	0.683684	+	0.729778i	$0.260377\pi$
$284$	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	$-0.589147\pi$
$293$	−9.46294	−0.552831	−0.276415	+	0.961038i	$0.589147\pi$
$294$	−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	$-0.560773\pi$
$307$	−6.64993	−0.379532	−0.189766	+	0.981829i	$0.560773\pi$
$308$	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	$-0.154476\pi$
$337$	32.4758	1.76907	0.884534	+	0.466475i	$0.154476\pi$
$338$	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	$-0.484154\pi$
$347$	1.85387	0.0995207	0.0497604	+	0.998761i	$0.484154\pi$
$348$	−18.1194	−0.971302
$349$	−26.4688	−1.41684	−0.708420	−	0.705791i	$-0.750592\pi$
$349$	−26.4688	−1.41684	−0.708420	+	0.705791i	$0.750592\pi$
$350$	−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	$-0.335109\pi$
$359$	18.7639	0.990323	0.495161	+	0.868801i	$0.335109\pi$
$360$	−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	$-0.513676\pi$
$373$	−1.65909	−0.0859045	−0.0429523	+	0.999077i	$0.513676\pi$
$374$	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	$-0.358676\pi$
$409$	17.3737	0.859076	0.429538	+	0.903049i	$0.358676\pi$
$410$	−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	$-0.377488\pi$
$431$	15.5891	0.750901	0.375450	+	0.926843i	$0.377488\pi$
$432$	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	$-0.604948\pi$
$439$	−13.5671	−0.647524	−0.323762	+	0.946139i	$0.604948\pi$
$440$	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	$-0.715246\pi$
$457$	−26.7581	−1.25169	−0.625845	+	0.779947i	$0.715246\pi$
$458$	10.2479	0.478853
$459$	31.4188	1.46650
$460$	11.0835	0.516773
$461$	4.24466	0.197694	0.0988468	−	0.995103i	$-0.468485\pi$
$461$	4.24466	0.197694	0.0988468	+	0.995103i	$0.468485\pi$
$462$	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	$-0.121800\pi$
$479$	40.6065	1.85536	0.927680	+	0.373377i	$0.121800\pi$
$480$	−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	$-0.357900\pi$
$491$	19.1334	0.863480	0.431740	+	0.901998i	$0.357900\pi$
$492$	−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	$-0.349580\pi$
$503$	20.4166	0.910329	0.455165	+	0.890407i	$0.349580\pi$
$504$	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	$-0.822693\pi$
$523$	−38.8242	−1.69766	−0.848831	+	0.528664i	$0.822693\pi$
$524$	−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	$-0.279759\pi$
$541$	29.6794	1.27602	0.638008	+	0.770030i	$0.279759\pi$
$542$	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	$-0.573404\pi$
$547$	−10.6915	−0.457134	−0.228567	+	0.973528i	$0.573404\pi$
$548$	−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	$-0.350201\pi$
$557$	21.4026	0.906857	0.453428	+	0.891293i	$0.350201\pi$
$558$	−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	$-0.647757\pi$
$563$	−21.2457	−0.895401	−0.447701	+	0.894183i	$0.647757\pi$
$564$	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	$-0.476928\pi$
$569$	3.45497	0.144840	0.0724199	+	0.997374i	$0.476928\pi$
$570$	0.103583	0.00433862
$571$	−40.3679	−1.68935	−0.844673	−	0.535283i	$-0.820205\pi$
$571$	−40.3679	−1.68935	−0.844673	+	0.535283i	$0.820205\pi$
$572$	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	$-0.356262\pi$
$593$	21.2529	0.872750	0.436375	+	0.899765i	$0.356262\pi$
$594$	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	$-0.317772\pi$
$601$	26.5611	1.08345	0.541724	+	0.840556i	$0.317772\pi$
$602$	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	$-0.657717\pi$
$607$	−23.4280	−0.950913	−0.475456	+	0.879739i	$0.657717\pi$
$608$	−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	$-0.643066\pi$
$613$	−21.5142	−0.868951	−0.434476	+	0.900684i	$0.643066\pi$
$614$	−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	$-0.256405\pi$
$659$	35.5665	1.38547	0.692737	+	0.721190i	$0.256405\pi$
$660$	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	$-0.177276\pi$
$673$	44.0438	1.69776	0.848882	+	0.528583i	$0.177276\pi$
$674$	12.0801	0.465308
$675$	5.17177	0.199062
$676$	−33.0182	−1.26993
$677$	24.0138	0.922927	0.461463	−	0.887159i	$-0.347325\pi$
$677$	24.0138	0.922927	0.461463	+	0.887159i	$0.347325\pi$
$678$	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	$-0.611993\pi$
$701$	−18.2488	−0.689246	−0.344623	+	0.938741i	$0.611993\pi$
$702$	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	$-0.421345\pi$
$733$	13.2443	0.489189	0.244595	+	0.969625i	$0.421345\pi$
$734$	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	$-0.552535\pi$
$739$	−8.93266	−0.328593	−0.164297	+	0.986411i	$0.552535\pi$
$740$	11.1403	0.409527
$741$	1.54384	0.0567145
$742$	3.68392	0.135241
$743$	5.69723	0.209011	0.104506	−	0.994524i	$-0.466674\pi$
$743$	5.69723	0.209011	0.104506	+	0.994524i	$0.466674\pi$
$744$	−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	$-0.630058\pi$
$761$	−21.9208	−0.794629	−0.397315	+	0.917682i	$0.630058\pi$
$762$	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	$-0.697984\pi$
$769$	−32.3147	−1.16530	−0.582649	+	0.812724i	$0.697984\pi$
$770$	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	$-0.619943\pi$
$787$	−20.6450	−0.735916	−0.367958	+	0.929842i	$0.619943\pi$
$788$	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	$-0.537564\pi$
$809$	−6.69756	−0.235474	−0.117737	+	0.993045i	$0.537564\pi$
$810$	−3.37852	−0.118709
$811$	−10.8349	−0.380466	−0.190233	−	0.981739i	$-0.560924\pi$
$811$	−10.8349	−0.380466	−0.190233	+	0.981739i	$0.560924\pi$
$812$	−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	$-0.633660\pi$
$821$	−23.3622	−0.815345	−0.407673	+	0.913128i	$0.633660\pi$
$822$	−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	$-0.500157\pi$
$827$	−0.0284286	−0.000988558 0	−0.000494279		1.00000i	$0.500157\pi$
$828$	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	$-0.534245\pi$
$853$	−6.27212	−0.214753	−0.107377	+	0.994218i	$0.534245\pi$
$854$	−1.93302	−0.0661467
$855$	−0.00445340	−0.000152303 0
$856$	−19.3200	−0.660345
$857$	−1.51105	−0.0516164	−0.0258082	−	0.999667i	$-0.508216\pi$
$857$	−1.51105	−0.0516164	−0.0258082	+	0.999667i	$0.508216\pi$
$858$	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	$-0.484254\pi$
$877$	2.92869	0.0988948	0.0494474	+	0.998777i	$0.484254\pi$
$878$	−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	$-0.399183\pi$
$887$	18.5520	0.622916	0.311458	+	0.950260i	$0.399183\pi$
$888$	−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	$-0.421579\pi$
$919$	14.7866	0.487765	0.243883	+	0.969805i	$0.421579\pi$
$920$	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	$-0.696718\pi$
$937$	−35.4722	−1.15883	−0.579414	+	0.815034i	$0.696718\pi$
$938$	−2.10688	−0.0687920
$939$	32.8381	1.07163
$940$	−1.56109	−0.0509171
$941$	8.77512	0.286061	0.143030	−	0.989718i	$-0.454315\pi$
$941$	8.77512	0.286061	0.143030	+	0.989718i	$0.454315\pi$
$942$	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	$-0.515191\pi$
$953$	−2.94539	−0.0954106	−0.0477053	+	0.998861i	$0.515191\pi$
$954$	−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	$-0.394279\pi$
$967$	20.2786	0.652116	0.326058	+	0.945350i	$0.394279\pi$
$968$	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	$-0.861199\pi$
$997$	−57.2412	−1.81285	−0.906424	+	0.422369i	$0.861199\pi$
$998$	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.bo.1.10		18
11.5	even	5		385.2.n.f.36.5	✓	36
11.9	even	5		385.2.n.f.246.5	yes	36
11.10	odd	2		4235.2.a.bp.1.9		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.36.5	✓	36	11.5	even	5
385.2.n.f.246.5	yes	36	11.9	even	5
4235.2.a.bo.1.10		18	1.1	even	1	trivial
4235.2.a.bp.1.9		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)

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