LMFDB - Embedded newform 365.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [365,2,Mod(1,365)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(365, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("365.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 365 = 5 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	365.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:	$2.91453967378$
Analytic rank:	$1$
Dimension:	$5$
Coefficient field:	5.5.117688.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - x^{4} - 5x^{3} + 4x^{2} + 4x - 1 $ x^5 - x^4 - 5x^3 + 4x^2 + 4*x - 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$1.44272$ of defining polynomial
Character	$\chi$	$=$	365.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.44272 q^{2} -1.08144 q^{3} +0.0814409 q^{4} -1.00000 q^{5} +1.56022 q^{6} +1.76794 q^{7} +2.76794 q^{8} -1.83049 q^{9} +O(q^{10})$	\(q-1.44272 q^{2} -1.08144 q^{3} +0.0814409 q^{4} -1.00000 q^{5} +1.56022 q^{6} +1.76794 q^{7} +2.76794 q^{8} -1.83049 q^{9} +1.44272 q^{10} +6.18567 q^{11} -0.0880735 q^{12} -3.32522 q^{13} -2.55065 q^{14} +1.08144 q^{15} -4.15625 q^{16} -5.85088 q^{17} +2.64088 q^{18} -1.14249 q^{19} -0.0814409 q^{20} -1.91193 q^{21} -8.92419 q^{22} -7.77967 q^{23} -2.99337 q^{24} +1.00000 q^{25} +4.79737 q^{26} +5.22388 q^{27} +0.143983 q^{28} +2.51459 q^{29} -1.56022 q^{30} -4.38167 q^{31} +0.460417 q^{32} -6.68944 q^{33} +8.44118 q^{34} -1.76794 q^{35} -0.149076 q^{36} -9.33989 q^{37} +1.64829 q^{38} +3.59603 q^{39} -2.76794 q^{40} +1.07038 q^{41} +2.75837 q^{42} -11.9286 q^{43} +0.503767 q^{44} +1.83049 q^{45} +11.2239 q^{46} +6.22239 q^{47} +4.49474 q^{48} -3.87438 q^{49} -1.44272 q^{50} +6.32738 q^{51} -0.270809 q^{52} +7.44781 q^{53} -7.53660 q^{54} -6.18567 q^{55} +4.89357 q^{56} +1.23553 q^{57} -3.62785 q^{58} -6.11356 q^{59} +0.0880735 q^{60} -1.55794 q^{61} +6.32153 q^{62} -3.23619 q^{63} +7.64825 q^{64} +3.32522 q^{65} +9.65099 q^{66} -11.0022 q^{67} -0.476501 q^{68} +8.41325 q^{69} +2.55065 q^{70} +4.63059 q^{71} -5.06668 q^{72} -1.00000 q^{73} +13.4748 q^{74} -1.08144 q^{75} -0.0930453 q^{76} +10.9359 q^{77} -5.18807 q^{78} +5.90446 q^{79} +4.15625 q^{80} -0.157866 q^{81} -1.54425 q^{82} -1.43829 q^{83} -0.155709 q^{84} +5.85088 q^{85} +17.2097 q^{86} -2.71938 q^{87} +17.1216 q^{88} -15.2237 q^{89} -2.64088 q^{90} -5.87881 q^{91} -0.633583 q^{92} +4.73852 q^{93} -8.97717 q^{94} +1.14249 q^{95} -0.497914 q^{96} -3.73416 q^{97} +5.58964 q^{98} -11.3228 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q - q^{2} - 6 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} + 7 q^{9}+O(q^{10}) $ 5 * q - q^2 - 6 * q^3 + q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 + 7 * q^9	\( 5 q - q^{2} - 6 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} + 7 q^{9} + q^{10} + 3 q^{11} - 16 q^{12} - 9 q^{13} - 4 q^{14} + 6 q^{15} - 7 q^{16} - 5 q^{17} - 6 q^{18} - 15 q^{19} - q^{20} + 6 q^{21} - 17 q^{22} - 3 q^{23} + 5 q^{25} - 4 q^{26} - 27 q^{27} - q^{28} + 3 q^{29} - 3 q^{30} - 7 q^{31} + 4 q^{32} - 8 q^{33} - 16 q^{34} + 5 q^{35} + 38 q^{36} - 6 q^{37} + 19 q^{38} + 9 q^{39} + 13 q^{41} - 4 q^{42} - 10 q^{43} + 5 q^{44} - 7 q^{45} + 3 q^{46} - 11 q^{47} + 31 q^{48} - 14 q^{49} - q^{50} - 2 q^{51} - 6 q^{53} + 16 q^{54} - 3 q^{55} + 16 q^{56} + 19 q^{57} + 26 q^{58} - q^{59} + 16 q^{60} + q^{61} - 2 q^{62} - 14 q^{63} - 14 q^{64} + 9 q^{65} + 43 q^{66} - 29 q^{67} + 7 q^{68} - 13 q^{69} + 4 q^{70} + 26 q^{71} - 7 q^{72} - 5 q^{73} + 31 q^{74} - 6 q^{75} - 4 q^{76} + 5 q^{77} + 23 q^{78} - 5 q^{79} + 7 q^{80} + 49 q^{81} + 11 q^{82} - 23 q^{83} + 23 q^{84} + 5 q^{85} + 24 q^{86} - 6 q^{87} + 8 q^{88} + 4 q^{89} + 6 q^{90} - 2 q^{91} + 16 q^{92} + 24 q^{93} - 11 q^{94} + 15 q^{95} - 5 q^{96} - 8 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 5 * q - q^2 - 6 * q^3 + q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 + 7 * q^9 + q^10 + 3 * q^11 - 16 * q^12 - 9 * q^13 - 4 * q^14 + 6 * q^15 - 7 * q^16 - 5 * q^17 - 6 * q^18 - 15 * q^19 - q^20 + 6 * q^21 - 17 * q^22 - 3 * q^23 + 5 * q^25 - 4 * q^26 - 27 * q^27 - q^28 + 3 * q^29 - 3 * q^30 - 7 * q^31 + 4 * q^32 - 8 * q^33 - 16 * q^34 + 5 * q^35 + 38 * q^36 - 6 * q^37 + 19 * q^38 + 9 * q^39 + 13 * q^41 - 4 * q^42 - 10 * q^43 + 5 * q^44 - 7 * q^45 + 3 * q^46 - 11 * q^47 + 31 * q^48 - 14 * q^49 - q^50 - 2 * q^51 - 6 * q^53 + 16 * q^54 - 3 * q^55 + 16 * q^56 + 19 * q^57 + 26 * q^58 - q^59 + 16 * q^60 + q^61 - 2 * q^62 - 14 * q^63 - 14 * q^64 + 9 * q^65 + 43 * q^66 - 29 * q^67 + 7 * q^68 - 13 * q^69 + 4 * q^70 + 26 * q^71 - 7 * q^72 - 5 * q^73 + 31 * q^74 - 6 * q^75 - 4 * q^76 + 5 * q^77 + 23 * q^78 - 5 * q^79 + 7 * q^80 + 49 * q^81 + 11 * q^82 - 23 * q^83 + 23 * q^84 + 5 * q^85 + 24 * q^86 - 6 * q^87 + 8 * q^88 + 4 * q^89 + 6 * q^90 - 2 * q^91 + 16 * q^92 + 24 * q^93 - 11 * q^94 + 15 * q^95 - 5 * q^96 - 8 * q^97 + 9 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.44272	−1.02016	−0.510079	−	0.860128i	$-0.670384\pi$
$2$	−1.44272	−1.02016	−0.510079	+	0.860128i	$0.670384\pi$
$3$	−1.08144	−0.624370	−0.312185	−	0.950021i	$-0.601061\pi$
$3$	−1.08144	−0.624370	−0.312185	+	0.950021i	$0.601061\pi$
$4$	0.0814409	0.0407205
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	1.56022	0.636956
$7$	1.76794	0.668220	0.334110	−	0.942534i	$-0.391564\pi$
$7$	1.76794	0.668220	0.334110	+	0.942534i	$0.391564\pi$
$8$	2.76794	0.978616
$9$	−1.83049	−0.610162
$10$	1.44272	0.456228
$11$	6.18567	1.86505	0.932525	−	0.361105i	$-0.117600\pi$
$11$	6.18567	1.86505	0.932525	+	0.361105i	$0.117600\pi$
$12$	−0.0880735	−0.0254246
$13$	−3.32522	−0.922251	−0.461126	−	0.887335i	$-0.652554\pi$
$13$	−3.32522	−0.922251	−0.461126	+	0.887335i	$0.652554\pi$
$14$	−2.55065	−0.681689
$15$	1.08144	0.279227
$16$	−4.15625	−1.03906
$17$	−5.85088	−1.41905	−0.709523	−	0.704682i	$-0.751090\pi$
$17$	−5.85088	−1.41905	−0.709523	+	0.704682i	$0.751090\pi$
$18$	2.64088	0.622461
$19$	−1.14249	−0.262105	−0.131052	−	0.991375i	$-0.541836\pi$
$19$	−1.14249	−0.262105	−0.131052	+	0.991375i	$0.541836\pi$
$20$	−0.0814409	−0.0182107
$21$	−1.91193	−0.417217
$22$	−8.92419	−1.90264
$23$	−7.77967	−1.62217	−0.811087	−	0.584926i	$-0.801124\pi$
$23$	−7.77967	−1.62217	−0.811087	+	0.584926i	$0.801124\pi$
$24$	−2.99337	−0.611019
$25$	1.00000	0.200000
$26$	4.79737	0.940841
$27$	5.22388	1.00534
$28$	0.143983	0.0272102
$29$	2.51459	0.466948	0.233474	−	0.972363i	$-0.424991\pi$
$29$	2.51459	0.466948	0.233474	+	0.972363i	$0.424991\pi$
$30$	−1.56022	−0.284855
$31$	−4.38167	−0.786972	−0.393486	−	0.919331i	$-0.628731\pi$
$31$	−4.38167	−0.786972	−0.393486	+	0.919331i	$0.628731\pi$
$32$	0.460417	0.0813910
$33$	−6.68944	−1.16448
$34$	8.44118	1.44765
$35$	−1.76794	−0.298837
$36$	−0.149076	−0.0248461
$37$	−9.33989	−1.53547	−0.767734	−	0.640769i	$-0.778616\pi$
$37$	−9.33989	−1.53547	−0.767734	+	0.640769i	$0.778616\pi$
$38$	1.64829	0.267388
$39$	3.59603	0.575826
$40$	−2.76794	−0.437650
$41$	1.07038	0.167165	0.0835824	−	0.996501i	$-0.473364\pi$
$41$	1.07038	0.167165	0.0835824	+	0.996501i	$0.473364\pi$
$42$	2.75837	0.425626
$43$	−11.9286	−1.81910	−0.909549	−	0.415597i	$-0.863573\pi$
$43$	−11.9286	−1.81910	−0.909549	+	0.415597i	$0.863573\pi$
$44$	0.503767	0.0759457
$45$	1.83049	0.272873
$46$	11.2239	1.65487
$47$	6.22239	0.907629	0.453814	−	0.891096i	$-0.350063\pi$
$47$	6.22239	0.907629	0.453814	+	0.891096i	$0.350063\pi$
$48$	4.49474	0.648760
$49$	−3.87438	−0.553482
$50$	−1.44272	−0.204031
$51$	6.32738	0.886011
$52$	−0.270809	−0.0375545
$53$	7.44781	1.02304	0.511518	−	0.859273i	$-0.329083\pi$
$53$	7.44781	1.02304	0.511518	+	0.859273i	$0.329083\pi$
$54$	−7.53660	−1.02560
$55$	−6.18567	−0.834076
$56$	4.89357	0.653930
$57$	1.23553	0.163650
$58$	−3.62785	−0.476360
$59$	−6.11356	−0.795918	−0.397959	−	0.917403i	$-0.630281\pi$
$59$	−6.11356	−0.795918	−0.397959	+	0.917403i	$0.630281\pi$
$60$	0.0880735	0.0113702
$61$	−1.55794	−0.199474	−0.0997370	−	0.995014i	$-0.531800\pi$
$61$	−1.55794	−0.199474	−0.0997370	+	0.995014i	$0.531800\pi$
$62$	6.32153	0.802835
$63$	−3.23619	−0.407722
$64$	7.64825	0.956031
$65$	3.32522	0.412443
$66$	9.65099	1.18795
$67$	−11.0022	−1.34413	−0.672064	−	0.740493i	$-0.734592\pi$
$67$	−11.0022	−1.34413	−0.672064	+	0.740493i	$0.734592\pi$
$68$	−0.476501	−0.0577842
$69$	8.41325	1.01284
$70$	2.55065	0.304861
$71$	4.63059	0.549550	0.274775	−	0.961509i	$-0.411397\pi$
$71$	4.63059	0.549550	0.274775	+	0.961509i	$0.411397\pi$
$72$	−5.06668	−0.597114
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	13.4748	1.56642
$75$	−1.08144	−0.124874
$76$	−0.0930453	−0.0106730
$77$	10.9359	1.24626
$78$	−5.18807	−0.587433
$79$	5.90446	0.664304	0.332152	−	0.943226i	$-0.392225\pi$
$79$	5.90446	0.664304	0.332152	+	0.943226i	$0.392225\pi$
$80$	4.15625	0.464683
$81$	−0.157866	−0.0175407
$82$	−1.54425	−0.170534
$83$	−1.43829	−0.157873	−0.0789363	−	0.996880i	$-0.525152\pi$
$83$	−1.43829	−0.157873	−0.0789363	+	0.996880i	$0.525152\pi$
$84$	−0.155709	−0.0169893
$85$	5.85088	0.634617
$86$	17.2097	1.85577
$87$	−2.71938	−0.291548
$88$	17.1216	1.82517
$89$	−15.2237	−1.61371	−0.806853	−	0.590753i	$-0.798831\pi$
$89$	−15.2237	−1.61371	−0.806853	+	0.590753i	$0.798831\pi$
$90$	−2.64088	−0.278373
$91$	−5.87881	−0.616266
$92$	−0.633583	−0.0660556
$93$	4.73852	0.491362
$94$	−8.97717	−0.925924
$95$	1.14249	0.117217
$96$	−0.497914	−0.0508181
$97$	−3.73416	−0.379147	−0.189573	−	0.981867i	$-0.560710\pi$
$97$	−3.73416	−0.379147	−0.189573	+	0.981867i	$0.560710\pi$
$98$	5.58964	0.564639
$99$	−11.3228	−1.13798
$100$	0.0814409	0.00814409
$101$	8.23888	0.819800	0.409900	−	0.912131i	$-0.365564\pi$
$101$	8.23888	0.819800	0.409900	+	0.912131i	$0.365564\pi$
$102$	−9.12864	−0.903870
$103$	−4.93386	−0.486148	−0.243074	−	0.970008i	$-0.578156\pi$
$103$	−4.93386	−0.486148	−0.243074	+	0.970008i	$0.578156\pi$
$104$	−9.20403	−0.902529
$105$	1.91193	0.186585
$106$	−10.7451	−1.04366
$107$	4.47634	0.432744	0.216372	−	0.976311i	$-0.430578\pi$
$107$	4.47634	0.432744	0.216372	+	0.976311i	$0.430578\pi$
$108$	0.425438	0.0409378
$109$	5.56022	0.532572	0.266286	−	0.963894i	$-0.414203\pi$
$109$	5.56022	0.532572	0.266286	+	0.963894i	$0.414203\pi$
$110$	8.92419	0.850888
$111$	10.1005	0.958700
$112$	−7.34801	−0.694322
$113$	16.1390	1.51823	0.759117	−	0.650954i	$-0.225631\pi$
$113$	16.1390	1.51823	0.759117	+	0.650954i	$0.225631\pi$
$114$	−1.78253	−0.166949
$115$	7.77967	0.725458
$116$	0.204791	0.0190143
$117$	6.08677	0.562722
$118$	8.82016	0.811961
$119$	−10.3440	−0.948235
$120$	2.99337	0.273256
$121$	27.2625	2.47841
$122$	2.24767	0.203495
$123$	−1.15755	−0.104373
$124$	−0.356848	−0.0320459
$125$	−1.00000	−0.0894427
$126$	4.66892	0.415941
$127$	1.54605	0.137190	0.0685949	−	0.997645i	$-0.478148\pi$
$127$	1.54605	0.137190	0.0685949	+	0.997645i	$0.478148\pi$
$128$	−11.9551	−1.05669
$129$	12.9001	1.13579
$130$	−4.79737	−0.420757
$131$	−15.8123	−1.38153	−0.690765	−	0.723079i	$-0.742726\pi$
$131$	−15.8123	−1.38153	−0.690765	+	0.723079i	$0.742726\pi$
$132$	−0.544794	−0.0474182
$133$	−2.01985	−0.175144
$134$	15.8730	1.37122
$135$	−5.22388	−0.449600
$136$	−16.1949	−1.38870
$137$	10.2864	0.878824	0.439412	−	0.898286i	$-0.355187\pi$
$137$	10.2864	0.878824	0.439412	+	0.898286i	$0.355187\pi$
$138$	−12.1380	−1.03325
$139$	−20.7012	−1.75585	−0.877925	−	0.478798i	$-0.841073\pi$
$139$	−20.7012	−1.75585	−0.877925	+	0.478798i	$0.841073\pi$
$140$	−0.143983	−0.0121688
$141$	−6.72915	−0.566696
$142$	−6.68065	−0.560628
$143$	−20.5687	−1.72004
$144$	7.60795	0.633996
$145$	−2.51459	−0.208825
$146$	1.44272	0.119400
$147$	4.18991	0.345578
$148$	−0.760649	−0.0625250
$149$	−14.6016	−1.19621	−0.598104	−	0.801419i	$-0.704079\pi$
$149$	−14.6016	−1.19621	−0.598104	+	0.801419i	$0.704079\pi$
$150$	1.56022	0.127391
$151$	−16.9485	−1.37925	−0.689627	−	0.724165i	$-0.742225\pi$
$151$	−16.9485	−1.37925	−0.689627	+	0.724165i	$0.742225\pi$
$152$	−3.16234	−0.256500
$153$	10.7100	0.865848
$154$	−15.7775	−1.27138
$155$	4.38167	0.351944
$156$	0.292864	0.0234479
$157$	12.1992	0.973602	0.486801	−	0.873513i	$-0.338164\pi$
$157$	12.1992	0.973602	0.486801	+	0.873513i	$0.338164\pi$
$158$	−8.51848	−0.677694
$159$	−8.05437	−0.638753
$160$	−0.460417	−0.0363991
$161$	−13.7540	−1.08397
$162$	0.227757	0.0178943
$163$	14.2288	1.11448	0.557241	−	0.830351i	$-0.311860\pi$
$163$	14.2288	1.11448	0.557241	+	0.830351i	$0.311860\pi$
$164$	0.0871725	0.00680703
$165$	6.68944	0.520772
$166$	2.07505	0.161055
$167$	−2.34118	−0.181166	−0.0905829	−	0.995889i	$-0.528873\pi$
$167$	−2.34118	−0.181166	−0.0905829	+	0.995889i	$0.528873\pi$
$168$	−5.29210	−0.408295
$169$	−1.94289	−0.149453
$170$	−8.44118	−0.647409
$171$	2.09131	0.159926
$172$	−0.971478	−0.0740745
$173$	−19.3478	−1.47099	−0.735495	−	0.677530i	$-0.763050\pi$
$173$	−19.3478	−1.47099	−0.735495	+	0.677530i	$0.763050\pi$
$174$	3.92331	0.297425
$175$	1.76794	0.133644
$176$	−25.7092	−1.93790
$177$	6.61146	0.496947
$178$	21.9635	1.64623
$179$	18.2057	1.36076	0.680380	−	0.732859i	$-0.261815\pi$
$179$	18.2057	1.36076	0.680380	+	0.732859i	$0.261815\pi$
$180$	0.149076	0.0111115
$181$	−15.6877	−1.16606	−0.583029	−	0.812451i	$-0.698133\pi$
$181$	−15.6877	−1.16606	−0.583029	+	0.812451i	$0.698133\pi$
$182$	8.48147	0.628689
$183$	1.68482	0.124546
$184$	−21.5337	−1.58748
$185$	9.33989	0.686682
$186$	−6.83636	−0.501266
$187$	−36.1916	−2.64659
$188$	0.506757	0.0369591
$189$	9.23553	0.671786
$190$	−1.64829	−0.119580
$191$	−4.51305	−0.326553	−0.163277	−	0.986580i	$-0.552206\pi$
$191$	−4.51305	−0.326553	−0.163277	+	0.986580i	$0.552206\pi$
$192$	−8.27113	−0.596917
$193$	1.03207	0.0742898	0.0371449	−	0.999310i	$-0.488174\pi$
$193$	1.03207	0.0742898	0.0371449	+	0.999310i	$0.488174\pi$
$194$	5.38735	0.386789
$195$	−3.59603	−0.257517
$196$	−0.315533	−0.0225381
$197$	−18.9082	−1.34715	−0.673577	−	0.739117i	$-0.735243\pi$
$197$	−18.9082	−1.34715	−0.673577	+	0.739117i	$0.735243\pi$
$198$	16.3356	1.16092
$199$	6.04754	0.428699	0.214349	−	0.976757i	$-0.431237\pi$
$199$	6.04754	0.428699	0.214349	+	0.976757i	$0.431237\pi$
$200$	2.76794	0.195723
$201$	11.8982	0.839233
$202$	−11.8864	−0.836324
$203$	4.44566	0.312024
$204$	0.515308	0.0360788
$205$	−1.07038	−0.0747584
$206$	7.11818	0.495947
$207$	14.2406	0.989788
$208$	13.8205	0.958276
$209$	−7.06705	−0.488838
$210$	−2.75837	−0.190346
$211$	9.25948	0.637449	0.318724	−	0.947847i	$-0.396746\pi$
$211$	9.25948	0.637449	0.318724	+	0.947847i	$0.396746\pi$
$212$	0.606557	0.0416585
$213$	−5.00771	−0.343123
$214$	−6.45810	−0.441467
$215$	11.9286	0.813525
$216$	14.4594	0.983839
$217$	−7.74655	−0.525870
$218$	−8.02184	−0.543307
$219$	1.08144	0.0730770
$220$	−0.503767	−0.0339640
$221$	19.4555	1.30872
$222$	−14.5722	−0.978025
$223$	27.9269	1.87012	0.935061	−	0.354488i	$-0.115345\pi$
$223$	27.9269	1.87012	0.935061	+	0.354488i	$0.115345\pi$
$224$	0.813991	0.0543871
$225$	−1.83049	−0.122032
$226$	−23.2841	−1.54884
$227$	1.52732	0.101372	0.0506858	−	0.998715i	$-0.483859\pi$
$227$	1.52732	0.101372	0.0506858	+	0.998715i	$0.483859\pi$
$228$	0.100623	0.00666392
$229$	28.5853	1.88897	0.944485	−	0.328554i	$-0.106561\pi$
$229$	28.5853	1.88897	0.944485	+	0.328554i	$0.106561\pi$
$230$	−11.2239	−0.740081
$231$	−11.8266	−0.778130
$232$	6.96025	0.456963
$233$	6.34252	0.415512	0.207756	−	0.978181i	$-0.433384\pi$
$233$	6.34252	0.415512	0.207756	+	0.978181i	$0.433384\pi$
$234$	−8.78151	−0.574065
$235$	−6.22239	−0.405904
$236$	−0.497894	−0.0324101
$237$	−6.38533	−0.414771
$238$	14.9235	0.967349
$239$	19.5959	1.26755	0.633776	−	0.773517i	$-0.281504\pi$
$239$	19.5959	1.26755	0.633776	+	0.773517i	$0.281504\pi$
$240$	−4.49474	−0.290134
$241$	10.5663	0.680633	0.340316	−	0.940311i	$-0.389466\pi$
$241$	10.5663	0.680633	0.340316	+	0.940311i	$0.389466\pi$
$242$	−39.3322	−2.52837
$243$	−15.5009	−0.994385
$244$	−0.126880	−0.00812267
$245$	3.87438	0.247525
$246$	1.67002	0.106477
$247$	3.79903	0.241726
$248$	−12.1282	−0.770143
$249$	1.55542	0.0985710
$250$	1.44272	0.0912456
$251$	−16.5573	−1.04508	−0.522542	−	0.852613i	$-0.675016\pi$
$251$	−16.5573	−1.04508	−0.522542	+	0.852613i	$0.675016\pi$
$252$	−0.263559	−0.0166026
$253$	−48.1225	−3.02543
$254$	−2.23052	−0.139955
$255$	−6.32738	−0.396236
$256$	1.95139	0.121962
$257$	−1.30040	−0.0811166	−0.0405583	−	0.999177i	$-0.512914\pi$
$257$	−1.30040	−0.0811166	−0.0405583	+	0.999177i	$0.512914\pi$
$258$	−18.6112	−1.15868
$259$	−16.5124	−1.02603
$260$	0.270809	0.0167949
$261$	−4.60292	−0.284914
$262$	22.8128	1.40938
$263$	26.7467	1.64927	0.824637	−	0.565662i	$-0.191379\pi$
$263$	26.7467	1.64927	0.824637	+	0.565662i	$0.191379\pi$
$264$	−18.5160	−1.13958
$265$	−7.44781	−0.457516
$266$	2.91408	0.178674
$267$	16.4635	1.00755
$268$	−0.896026	−0.0547335
$269$	27.9492	1.70409	0.852047	−	0.523466i	$-0.175361\pi$
$269$	27.9492	1.70409	0.852047	+	0.523466i	$0.175361\pi$
$270$	7.53660	0.458663
$271$	9.29326	0.564525	0.282263	−	0.959337i	$-0.408915\pi$
$271$	9.29326	0.564525	0.282263	+	0.959337i	$0.408915\pi$
$272$	24.3177	1.47448
$273$	6.35758	0.384778
$274$	−14.8404	−0.896539
$275$	6.18567	0.373010
$276$	0.685183	0.0412432
$277$	−12.7694	−0.767240	−0.383620	−	0.923491i	$-0.625323\pi$
$277$	−12.7694	−0.767240	−0.383620	+	0.923491i	$0.625323\pi$
$278$	29.8660	1.79124
$279$	8.02059	0.480180
$280$	−4.89357	−0.292447
$281$	0.259818	0.0154995	0.00774974	−	0.999970i	$-0.497533\pi$
$281$	0.259818	0.0154995	0.00774974	+	0.999970i	$0.497533\pi$
$282$	9.70827	0.578119
$283$	−21.7549	−1.29320	−0.646598	−	0.762831i	$-0.723809\pi$
$283$	−21.7549	−1.29320	−0.646598	+	0.762831i	$0.723809\pi$
$284$	0.377120	0.0223779
$285$	−1.23553	−0.0731867
$286$	29.6749	1.75472
$287$	1.89237	0.111703
$288$	−0.842786	−0.0496617
$289$	17.2328	1.01369
$290$	3.62785	0.213035
$291$	4.03828	0.236728
$292$	−0.0814409	−0.00476597
$293$	2.65355	0.155022	0.0775110	−	0.996991i	$-0.475303\pi$
$293$	2.65355	0.155022	0.0775110	+	0.996991i	$0.475303\pi$
$294$	−6.04486	−0.352544
$295$	6.11356	0.355945
$296$	−25.8523	−1.50263
$297$	32.3132	1.87500
$298$	21.0660	1.22032
$299$	25.8691	1.49605
$300$	−0.0880735	−0.00508493
$301$	−21.0891	−1.21556
$302$	24.4520	1.40705
$303$	−8.90987	−0.511858
$304$	4.74846	0.272343
$305$	1.55794	0.0892075
$306$	−15.4515	−0.883301
$307$	−11.6603	−0.665489	−0.332744	−	0.943017i	$-0.607975\pi$
$307$	−11.6603	−0.665489	−0.332744	+	0.943017i	$0.607975\pi$
$308$	0.890631	0.0507484
$309$	5.33568	0.303536
$310$	−6.32153	−0.359039
$311$	−7.83989	−0.444559	−0.222280	−	0.974983i	$-0.571350\pi$
$311$	−7.83989	−0.444559	−0.222280	+	0.974983i	$0.571350\pi$
$312$	9.95362	0.563513
$313$	21.7420	1.22893	0.614466	−	0.788943i	$-0.289371\pi$
$313$	21.7420	1.22893	0.614466	+	0.788943i	$0.289371\pi$
$314$	−17.6000	−0.993227
$315$	3.23619	0.182339
$316$	0.480865	0.0270508
$317$	−6.35779	−0.357089	−0.178544	−	0.983932i	$-0.557139\pi$
$317$	−6.35779	−0.357089	−0.178544	+	0.983932i	$0.557139\pi$
$318$	11.6202	0.651629
$319$	15.5544	0.870881
$320$	−7.64825	−0.427550
$321$	−4.84089	−0.270192
$322$	19.8432	1.10582
$323$	6.68456	0.371939
$324$	−0.0128568	−0.000714265 0
$325$	−3.32522	−0.184450
$326$	−20.5281	−1.13695
$327$	−6.01305	−0.332522
$328$	2.96274	0.163590
$329$	11.0008	0.606496
$330$	−9.65099	−0.531269
$331$	−1.72124	−0.0946080	−0.0473040	−	0.998881i	$-0.515063\pi$
$331$	−1.72124	−0.0946080	−0.0473040	+	0.998881i	$0.515063\pi$
$332$	−0.117136	−0.00642865
$333$	17.0965	0.936884
$334$	3.37766	0.184818
$335$	11.0022	0.601112
$336$	7.94644	0.433514
$337$	18.4421	1.00460	0.502302	−	0.864692i	$-0.332487\pi$
$337$	18.4421	1.00460	0.502302	+	0.864692i	$0.332487\pi$
$338$	2.80304	0.152465
$339$	−17.4534	−0.947940
$340$	0.476501	0.0258419
$341$	−27.1036	−1.46774
$342$	−3.01717	−0.163150
$343$	−19.2253	−1.03807
$344$	−33.0178	−1.78020
$345$	−8.41325	−0.452954
$346$	27.9135	1.50064
$347$	11.0245	0.591824	0.295912	−	0.955215i	$-0.404376\pi$
$347$	11.0245	0.591824	0.295912	+	0.955215i	$0.404376\pi$
$348$	−0.221469	−0.0118720
$349$	2.79467	0.149595	0.0747976	−	0.997199i	$-0.476169\pi$
$349$	2.79467	0.149595	0.0747976	+	0.997199i	$0.476169\pi$
$350$	−2.55065	−0.136338
$351$	−17.3706	−0.927173
$352$	2.84799	0.151798
$353$	−4.67595	−0.248876	−0.124438	−	0.992227i	$-0.539713\pi$
$353$	−4.67595	−0.248876	−0.124438	+	0.992227i	$0.539713\pi$
$354$	−9.53848	−0.506964
$355$	−4.63059	−0.245766
$356$	−1.23983	−0.0657108
$357$	11.1865	0.592050
$358$	−26.2658	−1.38819
$359$	5.21262	0.275111	0.137556	−	0.990494i	$-0.456075\pi$
$359$	5.21262	0.275111	0.137556	+	0.990494i	$0.456075\pi$
$360$	5.06668	0.267038
$361$	−17.6947	−0.931301
$362$	22.6330	1.18956
$363$	−29.4828	−1.54745
$364$	−0.478775	−0.0250947
$365$	1.00000	0.0523424
$366$	−2.43073	−0.127056
$367$	18.7611	0.979324	0.489662	−	0.871912i	$-0.337120\pi$
$367$	18.7611	0.979324	0.489662	+	0.871912i	$0.337120\pi$
$368$	32.3342	1.68554
$369$	−1.95931	−0.101998
$370$	−13.4748	−0.700524
$371$	13.1673	0.683613
$372$	0.385909	0.0200085
$373$	17.8075	0.922037	0.461018	−	0.887391i	$-0.347484\pi$
$373$	17.8075	0.922037	0.461018	+	0.887391i	$0.347484\pi$
$374$	52.2144	2.69994
$375$	1.08144	0.0558454
$376$	17.2232	0.888220
$377$	−8.36158	−0.430643
$378$	−13.3243	−0.685327
$379$	−20.4550	−1.05070	−0.525351	−	0.850885i	$-0.676066\pi$
$379$	−20.4550	−1.05070	−0.525351	+	0.850885i	$0.676066\pi$
$380$	0.0930453	0.00477312
$381$	−1.67196	−0.0856572
$382$	6.51107	0.333135
$383$	−13.3219	−0.680719	−0.340360	−	0.940295i	$-0.610549\pi$
$383$	−13.3219	−0.680719	−0.340360	+	0.940295i	$0.610549\pi$
$384$	12.9287	0.659767
$385$	−10.9359	−0.557346
$386$	−1.48898	−0.0757872
$387$	21.8352	1.10994
$388$	−0.304114	−0.0154390
$389$	8.65316	0.438733	0.219366	−	0.975643i	$-0.429601\pi$
$389$	8.65316	0.438733	0.219366	+	0.975643i	$0.429601\pi$
$390$	5.18807	0.262708
$391$	45.5179	2.30194
$392$	−10.7241	−0.541646
$393$	17.1001	0.862586
$394$	27.2792	1.37431
$395$	−5.90446	−0.297086
$396$	−0.922138	−0.0463392
$397$	4.57096	0.229410	0.114705	−	0.993400i	$-0.463408\pi$
$397$	4.57096	0.229410	0.114705	+	0.993400i	$0.463408\pi$
$398$	−8.72491	−0.437340
$399$	2.18435	0.109354
$400$	−4.15625	−0.207812
$401$	−26.8989	−1.34327	−0.671634	−	0.740883i	$-0.734407\pi$
$401$	−26.8989	−1.34327	−0.671634	+	0.740883i	$0.734407\pi$
$402$	−17.1657	−0.856150
$403$	14.5700	0.725786
$404$	0.670982	0.0333826
$405$	0.157866	0.00784443
$406$	−6.41384	−0.318313
$407$	−57.7735	−2.86372
$408$	17.5138	0.867064
$409$	16.8074	0.831070	0.415535	−	0.909577i	$-0.363594\pi$
$409$	16.8074	0.831070	0.415535	+	0.909577i	$0.363594\pi$
$410$	1.54425	0.0762653
$411$	−11.1241	−0.548712
$412$	−0.401818	−0.0197962
$413$	−10.8084	−0.531848
$414$	−20.5452	−1.00974
$415$	1.43829	0.0706028
$416$	−1.53099	−0.0750629
$417$	22.3871	1.09630
$418$	10.1958	0.498692
$419$	−0.774703	−0.0378467	−0.0189234	−	0.999821i	$-0.506024\pi$
$419$	−0.774703	−0.0378467	−0.0189234	+	0.999821i	$0.506024\pi$
$420$	0.155709	0.00759782
$421$	−26.6364	−1.29818	−0.649088	−	0.760713i	$-0.724849\pi$
$421$	−26.6364	−1.29818	−0.649088	+	0.760713i	$0.724849\pi$
$422$	−13.3588	−0.650298
$423$	−11.3900	−0.553800
$424$	20.6151	1.00116
$425$	−5.85088	−0.283809
$426$	7.22473	0.350039
$427$	−2.75435	−0.133293
$428$	0.364557	0.0176215
$429$	22.2439	1.07394
$430$	−17.2097	−0.829924
$431$	17.2696	0.831847	0.415923	−	0.909400i	$-0.363458\pi$
$431$	17.2696	0.831847	0.415923	+	0.909400i	$0.363458\pi$
$432$	−21.7118	−1.04461
$433$	4.38933	0.210938	0.105469	−	0.994423i	$-0.466366\pi$
$433$	4.38933	0.210938	0.105469	+	0.994423i	$0.466366\pi$
$434$	11.1761	0.536470
$435$	2.71938	0.130384
$436$	0.452829	0.0216866
$437$	8.88818	0.425179
$438$	−1.56022	−0.0745500
$439$	−31.8599	−1.52059	−0.760294	−	0.649579i	$-0.774945\pi$
$439$	−31.8599	−1.52059	−0.760294	+	0.649579i	$0.774945\pi$
$440$	−17.1216	−0.816240
$441$	7.09199	0.337714
$442$	−28.0688	−1.33510
$443$	−35.8291	−1.70229	−0.851146	−	0.524930i	$-0.824092\pi$
$443$	−35.8291	−1.70229	−0.851146	+	0.524930i	$0.824092\pi$
$444$	0.822597	0.0390387
$445$	15.2237	0.721671
$446$	−40.2906	−1.90782
$447$	15.7907	0.746876
$448$	13.5217	0.638839
$449$	9.50360	0.448502	0.224251	−	0.974531i	$-0.428006\pi$
$449$	9.50360	0.448502	0.224251	+	0.974531i	$0.428006\pi$
$450$	2.64088	0.124492
$451$	6.62100	0.311771
$452$	1.31438	0.0618232
$453$	18.3289	0.861165
$454$	−2.20349	−0.103415
$455$	5.87881	0.275603
$456$	3.41989	0.160151
$457$	5.44941	0.254912	0.127456	−	0.991844i	$-0.459319\pi$
$457$	5.44941	0.254912	0.127456	+	0.991844i	$0.459319\pi$
$458$	−41.2406	−1.92705
$459$	−30.5643	−1.42662
$460$	0.633583	0.0295410
$461$	−13.0738	−0.608910	−0.304455	−	0.952527i	$-0.598474\pi$
$461$	−13.0738	−0.608910	−0.304455	+	0.952527i	$0.598474\pi$
$462$	17.0624	0.793815
$463$	18.7618	0.871937	0.435968	−	0.899962i	$-0.356406\pi$
$463$	18.7618	0.871937	0.435968	+	0.899962i	$0.356406\pi$
$464$	−10.4513	−0.485188
$465$	−4.73852	−0.219744
$466$	−9.15047	−0.423888
$467$	26.0602	1.20592	0.602961	−	0.797770i	$-0.293987\pi$
$467$	26.0602	1.20592	0.602961	+	0.797770i	$0.293987\pi$
$468$	0.495712	0.0229143
$469$	−19.4512	−0.898173
$470$	8.97717	0.414086
$471$	−13.1927	−0.607888
$472$	−16.9220	−0.778898
$473$	−73.7866	−3.39271
$474$	9.21224	0.423132
$475$	−1.14249	−0.0524209
$476$	−0.842427	−0.0386126
$477$	−13.6331	−0.624217
$478$	−28.2713	−1.29310
$479$	−8.47263	−0.387125	−0.193562	−	0.981088i	$-0.562004\pi$
$479$	−8.47263	−0.387125	−0.193562	+	0.981088i	$0.562004\pi$
$480$	0.497914	0.0227265
$481$	31.0572	1.41609
$482$	−15.2442	−0.694353
$483$	14.8742	0.676798
$484$	2.22029	0.100922
$485$	3.73416	0.169560
$486$	22.3635	1.01443
$487$	−34.3070	−1.55460	−0.777299	−	0.629132i	$-0.783411\pi$
$487$	−34.3070	−1.55460	−0.777299	+	0.629132i	$0.783411\pi$
$488$	−4.31230	−0.195208
$489$	−15.3876	−0.695850
$490$	−5.58964	−0.252514
$491$	15.7230	0.709567	0.354784	−	0.934948i	$-0.384555\pi$
$491$	15.7230	0.709567	0.354784	+	0.934948i	$0.384555\pi$
$492$	−0.0942719	−0.00425010
$493$	−14.7126	−0.662621
$494$	−5.48093	−0.246599
$495$	11.3228	0.508921
$496$	18.2113	0.817713
$497$	8.18663	0.367220
$498$	−2.24404	−0.100558
$499$	4.86698	0.217876	0.108938	−	0.994049i	$-0.465255\pi$
$499$	4.86698	0.217876	0.108938	+	0.994049i	$0.465255\pi$
$500$	−0.0814409	−0.00364215
$501$	2.53185	0.113115
$502$	23.8875	1.06615
$503$	6.00362	0.267688	0.133844	−	0.991002i	$-0.457268\pi$
$503$	6.00362	0.267688	0.133844	+	0.991002i	$0.457268\pi$
$504$	−8.95760	−0.399003
$505$	−8.23888	−0.366626
$506$	69.4273	3.08642
$507$	2.10112	0.0933140
$508$	0.125912	0.00558643
$509$	−27.6686	−1.22639	−0.613195	−	0.789931i	$-0.710116\pi$
$509$	−27.6686	−1.22639	−0.613195	+	0.789931i	$0.710116\pi$
$510$	9.12864	0.404223
$511$	−1.76794	−0.0782092
$512$	21.0949	0.932273
$513$	−5.96822	−0.263504
$514$	1.87611	0.0827517
$515$	4.93386	0.217412
$516$	1.05060	0.0462499
$517$	38.4897	1.69277
$518$	23.8228	1.04671
$519$	20.9236	0.918442
$520$	9.20403	0.403623
$521$	−41.7998	−1.83128	−0.915640	−	0.401999i	$-0.868316\pi$
$521$	−41.7998	−1.83128	−0.915640	+	0.401999i	$0.868316\pi$
$522$	6.64073	0.290657
$523$	−18.8864	−0.825845	−0.412923	−	0.910766i	$-0.635492\pi$
$523$	−18.8864	−0.825845	−0.412923	+	0.910766i	$0.635492\pi$
$524$	−1.28777	−0.0562565
$525$	−1.91193	−0.0834433
$526$	−38.5881	−1.68252
$527$	25.6366	1.11675
$528$	27.8030	1.20997
$529$	37.5233	1.63145
$530$	10.7451	0.466738
$531$	11.1908	0.485639
$532$	−0.164499	−0.00713193
$533$	−3.55924	−0.154168
$534$	−23.7522	−1.02786
$535$	−4.47634	−0.193529
$536$	−30.4533	−1.31538
$537$	−19.6884	−0.849618
$538$	−40.3229	−1.73844
$539$	−23.9656	−1.03227
$540$	−0.425438	−0.0183079
$541$	11.5388	0.496091	0.248046	−	0.968748i	$-0.420212\pi$
$541$	11.5388	0.496091	0.248046	+	0.968748i	$0.420212\pi$
$542$	−13.4076	−0.575905
$543$	16.9653	0.728052
$544$	−2.69384	−0.115498
$545$	−5.56022	−0.238174
$546$	−9.17221	−0.392534
$547$	−17.8233	−0.762071	−0.381036	−	0.924560i	$-0.624432\pi$
$547$	−17.8233	−0.762071	−0.381036	+	0.924560i	$0.624432\pi$
$548$	0.837732	0.0357861
$549$	2.85179	0.121711
$550$	−8.92419	−0.380529
$551$	−2.87289	−0.122389
$552$	23.2874	0.991178
$553$	10.4388	0.443901
$554$	18.4227	0.782706
$555$	−10.1005	−0.428744
$556$	−1.68592	−0.0714990
$557$	7.83840	0.332124	0.166062	−	0.986115i	$-0.446895\pi$
$557$	7.83840	0.332124	0.166062	+	0.986115i	$0.446895\pi$
$558$	−11.5715	−0.489859
$559$	39.6653	1.67767
$560$	7.34801	0.310510
$561$	39.1391	1.65245
$562$	−0.374845	−0.0158119
$563$	−43.1970	−1.82054	−0.910268	−	0.414019i	$-0.864125\pi$
$563$	−43.1970	−1.82054	−0.910268	+	0.414019i	$0.864125\pi$
$564$	−0.548028	−0.0230761
$565$	−16.1390	−0.678975
$566$	31.3863	1.31926
$567$	−0.279098	−0.0117210
$568$	12.8172	0.537799
$569$	−2.22442	−0.0932527	−0.0466264	−	0.998912i	$-0.514847\pi$
$569$	−2.22442	−0.0932527	−0.0466264	+	0.998912i	$0.514847\pi$
$570$	1.78253	0.0746619
$571$	27.5650	1.15356	0.576781	−	0.816899i	$-0.304309\pi$
$571$	27.5650	1.15356	0.576781	+	0.816899i	$0.304309\pi$
$572$	−1.67514	−0.0700410
$573$	4.88060	0.203890
$574$	−2.73015	−0.113954
$575$	−7.77967	−0.324435
$576$	−14.0000	−0.583333
$577$	−11.1017	−0.462169	−0.231085	−	0.972934i	$-0.574227\pi$
$577$	−11.1017	−0.462169	−0.231085	+	0.972934i	$0.574227\pi$
$578$	−24.8621	−1.03413
$579$	−1.11612	−0.0463843
$580$	−0.204791	−0.00850347
$581$	−2.54281	−0.105494
$582$	−5.82610	−0.241500
$583$	46.0697	1.90801
$584$	−2.76794	−0.114538
$585$	−6.08677	−0.251657
$586$	−3.82833	−0.158147
$587$	−27.5459	−1.13694	−0.568470	−	0.822704i	$-0.692465\pi$
$587$	−27.5459	−1.13694	−0.568470	+	0.822704i	$0.692465\pi$
$588$	0.341230	0.0140721
$589$	5.00601	0.206269
$590$	−8.82016	−0.363120
$591$	20.4481	0.841122
$592$	38.8189	1.59545
$593$	21.9562	0.901633	0.450817	−	0.892617i	$-0.351133\pi$
$593$	21.9562	0.901633	0.450817	+	0.892617i	$0.351133\pi$
$594$	−46.6190	−1.91280
$595$	10.3440	0.424064
$596$	−1.18917	−0.0487101
$597$	−6.54006	−0.267667
$598$	−37.3219	−1.52621
$599$	29.0162	1.18557	0.592785	−	0.805361i	$-0.298028\pi$
$599$	29.0162	1.18557	0.592785	+	0.805361i	$0.298028\pi$
$600$	−2.99337	−0.122204
$601$	−42.1033	−1.71743	−0.858715	−	0.512454i	$-0.828737\pi$
$601$	−42.1033	−1.71743	−0.858715	+	0.512454i	$0.828737\pi$
$602$	30.4257	1.24006
$603$	20.1393	0.820135
$604$	−1.38031	−0.0561638
$605$	−27.2625	−1.10838
$606$	12.8544	0.522176
$607$	−3.38541	−0.137410	−0.0687048	−	0.997637i	$-0.521887\pi$
$607$	−3.38541	−0.137410	−0.0687048	+	0.997637i	$0.521887\pi$
$608$	−0.526021	−0.0213329
$609$	−4.80771	−0.194818
$610$	−2.24767	−0.0910057
$611$	−20.6908	−0.837062
$612$	0.872228	0.0352577
$613$	5.73190	0.231509	0.115755	−	0.993278i	$-0.463071\pi$
$613$	5.73190	0.231509	0.115755	+	0.993278i	$0.463071\pi$
$614$	16.8226	0.678903
$615$	1.15755	0.0466769
$616$	30.2700	1.21961
$617$	27.7054	1.11538	0.557689	−	0.830050i	$-0.311688\pi$
$617$	27.7054	1.11538	0.557689	+	0.830050i	$0.311688\pi$
$618$	−7.69789	−0.309655
$619$	−19.6308	−0.789029	−0.394515	−	0.918890i	$-0.629087\pi$
$619$	−19.6308	−0.789029	−0.394515	+	0.918890i	$0.629087\pi$
$620$	0.356848	0.0143313
$621$	−40.6401	−1.63083
$622$	11.3108	0.453520
$623$	−26.9146	−1.07831
$624$	−14.9460	−0.598319
$625$	1.00000	0.0400000
$626$	−31.3677	−1.25370
$627$	7.64260	0.305216
$628$	0.993514	0.0396455
$629$	54.6465	2.17890
$630$	−4.66892	−0.186014
$631$	−21.2194	−0.844732	−0.422366	−	0.906425i	$-0.638800\pi$
$631$	−21.2194	−0.844732	−0.422366	+	0.906425i	$0.638800\pi$
$632$	16.3432	0.650098
$633$	−10.0136	−0.398004
$634$	9.17250	0.364287
$635$	−1.54605	−0.0613531
$636$	−0.655955	−0.0260103
$637$	12.8832	0.510450
$638$	−22.4407	−0.888436
$639$	−8.47623	−0.335315
$640$	11.9551	0.472567
$641$	−17.2821	−0.682603	−0.341301	−	0.939954i	$-0.610868\pi$
$641$	−17.2821	−0.682603	−0.341301	+	0.939954i	$0.610868\pi$
$642$	6.98405	0.275639
$643$	27.2120	1.07314	0.536569	−	0.843857i	$-0.319720\pi$
$643$	27.2120	1.07314	0.536569	+	0.843857i	$0.319720\pi$
$644$	−1.12014	−0.0441397
$645$	−12.9001	−0.507941
$646$	−9.64395	−0.379436
$647$	−19.3447	−0.760517	−0.380259	−	0.924880i	$-0.624165\pi$
$647$	−19.3447	−0.760517	−0.380259	+	0.924880i	$0.624165\pi$
$648$	−0.436965	−0.0171656
$649$	−37.8165	−1.48443
$650$	4.79737	0.188168
$651$	8.37744	0.328338
$652$	1.15880	0.0453822
$653$	27.7471	1.08583	0.542915	−	0.839788i	$-0.317321\pi$
$653$	27.7471	1.08583	0.542915	+	0.839788i	$0.317321\pi$
$654$	8.67514	0.339225
$655$	15.8123	0.617839
$656$	−4.44875	−0.173695
$657$	1.83049	0.0714140
$658$	−15.8711	−0.618721
$659$	−13.7539	−0.535777	−0.267888	−	0.963450i	$-0.586326\pi$
$659$	−13.7539	−0.535777	−0.267888	+	0.963450i	$0.586326\pi$
$660$	0.544794	0.0212061
$661$	−4.99027	−0.194099	−0.0970494	−	0.995280i	$-0.530940\pi$
$661$	−4.99027	−0.194099	−0.0970494	+	0.995280i	$0.530940\pi$
$662$	2.48327	0.0965150
$663$	−21.0400	−0.817124
$664$	−3.98110	−0.154497
$665$	2.01985	0.0783266
$666$	−24.6655	−0.955769
$667$	−19.5627	−0.757471
$668$	−0.190668	−0.00737715
$669$	−30.2013	−1.16765
$670$	−15.8730	−0.613229
$671$	−9.63692	−0.372029
$672$	−0.880283	−0.0339577
$673$	38.3916	1.47989	0.739944	−	0.672669i	$-0.234852\pi$
$673$	38.3916	1.47989	0.739944	+	0.672669i	$0.234852\pi$
$674$	−26.6068	−1.02485
$675$	5.22388	0.201067
$676$	−0.158231	−0.00608579
$677$	0.762557	0.0293074	0.0146537	−	0.999893i	$-0.495335\pi$
$677$	0.762557	0.0293074	0.0146537	+	0.999893i	$0.495335\pi$
$678$	25.1804	0.967048
$679$	−6.60179	−0.253353
$680$	16.1949	0.621046
$681$	−1.65170	−0.0632934
$682$	39.1029	1.49733
$683$	−34.8350	−1.33293	−0.666463	−	0.745539i	$-0.732192\pi$
$683$	−34.8350	−1.33293	−0.666463	+	0.745539i	$0.732192\pi$
$684$	0.170318	0.00651227
$685$	−10.2864	−0.393022
$686$	27.7367	1.05899
$687$	−30.9133	−1.17942
$688$	49.5783	1.89016
$689$	−24.7656	−0.943496
$690$	12.1380	0.462085
$691$	−38.7293	−1.47333	−0.736666	−	0.676256i	$-0.763601\pi$
$691$	−38.7293	−1.47333	−0.736666	+	0.676256i	$0.763601\pi$
$692$	−1.57571	−0.0598994
$693$	−20.0180	−0.760423
$694$	−15.9052	−0.603754
$695$	20.7012	0.785240
$696$	−7.52710	−0.285314
$697$	−6.26265	−0.237215
$698$	−4.03193	−0.152611
$699$	−6.85906	−0.259433
$700$	0.143983	0.00544204
$701$	43.0932	1.62761	0.813804	−	0.581139i	$-0.197393\pi$
$701$	43.0932	1.62761	0.813804	+	0.581139i	$0.197393\pi$
$702$	25.0609	0.945862
$703$	10.6707	0.402453
$704$	47.3095	1.78305
$705$	6.72915	0.253434
$706$	6.74609	0.253893
$707$	14.5659	0.547806
$708$	0.538443	0.0202359
$709$	15.5199	0.582863	0.291431	−	0.956592i	$-0.405868\pi$
$709$	15.5199	0.582863	0.291431	+	0.956592i	$0.405868\pi$
$710$	6.68065	0.250720
$711$	−10.8080	−0.405333
$712$	−42.1382	−1.57920
$713$	34.0880	1.27660
$714$	−16.1389	−0.603984
$715$	20.5687	0.769227
$716$	1.48269	0.0554108
$717$	−21.1918	−0.791421
$718$	−7.52035	−0.280657
$719$	−24.1893	−0.902108	−0.451054	−	0.892497i	$-0.648952\pi$
$719$	−24.1893	−0.902108	−0.451054	+	0.892497i	$0.648952\pi$
$720$	−7.60795	−0.283532
$721$	−8.72279	−0.324853
$722$	25.5285	0.950073
$723$	−11.4268	−0.424967
$724$	−1.27762	−0.0474824
$725$	2.51459	0.0933896
$726$	42.5355	1.57864
$727$	−0.933425	−0.0346188	−0.0173094	−	0.999850i	$-0.505510\pi$
$727$	−0.933425	−0.0346188	−0.0173094	+	0.999850i	$0.505510\pi$
$728$	−16.2722	−0.603088
$729$	17.2369	0.638405
$730$	−1.44272	−0.0533975
$731$	69.7929	2.58139
$732$	0.137213	0.00507156
$733$	−24.7749	−0.915084	−0.457542	−	0.889188i	$-0.651270\pi$
$733$	−24.7749	−0.915084	−0.457542	+	0.889188i	$0.651270\pi$
$734$	−27.0671	−0.999064
$735$	−4.18991	−0.154547
$736$	−3.58189	−0.132030
$737$	−68.0557	−2.50687
$738$	2.82673	0.104054
$739$	7.42137	0.273000	0.136500	−	0.990640i	$-0.456415\pi$
$739$	7.42137	0.273000	0.136500	+	0.990640i	$0.456415\pi$
$740$	0.760649	0.0279620
$741$	−4.10842	−0.150927
$742$	−18.9967	−0.697392
$743$	31.5797	1.15855	0.579274	−	0.815133i	$-0.303336\pi$
$743$	31.5797	1.15855	0.579274	+	0.815133i	$0.303336\pi$
$744$	13.1160	0.480854
$745$	14.6016	0.534960
$746$	−25.6912	−0.940622
$747$	2.63277	0.0963279
$748$	−2.94748	−0.107771
$749$	7.91391	0.289168
$750$	−1.56022	−0.0569710
$751$	−37.5961	−1.37190	−0.685951	−	0.727648i	$-0.740614\pi$
$751$	−37.5961	−1.37190	−0.685951	+	0.727648i	$0.740614\pi$
$752$	−25.8618	−0.943083
$753$	17.9057	0.652520
$754$	12.0634	0.439324
$755$	16.9485	0.616821
$756$	0.752150	0.0273554
$757$	−17.3635	−0.631088	−0.315544	−	0.948911i	$-0.602187\pi$
$757$	−17.3635	−0.631088	−0.315544	+	0.948911i	$0.602187\pi$
$758$	29.5108	1.07188
$759$	52.0416	1.88899
$760$	3.16234	0.114710
$761$	−15.3066	−0.554862	−0.277431	−	0.960746i	$-0.589483\pi$
$761$	−15.3066	−0.554862	−0.277431	+	0.960746i	$0.589483\pi$
$762$	2.41217	0.0873838
$763$	9.83015	0.355875
$764$	−0.367547	−0.0132974
$765$	−10.7100	−0.387219
$766$	19.2198	0.694441
$767$	20.3290	0.734036
$768$	−2.11031	−0.0761492
$769$	37.6172	1.35651	0.678255	−	0.734827i	$-0.262737\pi$
$769$	37.6172	1.35651	0.678255	+	0.734827i	$0.262737\pi$
$770$	15.7775	0.568580
$771$	1.40630	0.0506468
$772$	0.0840524	0.00302511
$773$	21.4494	0.771482	0.385741	−	0.922607i	$-0.373946\pi$
$773$	21.4494	0.771482	0.385741	+	0.922607i	$0.373946\pi$
$774$	−31.5020	−1.13232
$775$	−4.38167	−0.157394
$776$	−10.3360	−0.371039
$777$	17.8572	0.640623
$778$	−12.4841	−0.447576
$779$	−1.22289	−0.0438147
$780$	−0.292864	−0.0104862
$781$	28.6433	1.02494
$782$	−65.6696	−2.34834
$783$	13.1359	0.469440
$784$	16.1029	0.575103
$785$	−12.1992	−0.435408
$786$	−24.6707	−0.879973
$787$	−9.04484	−0.322414	−0.161207	−	0.986921i	$-0.551539\pi$
$787$	−9.04484	−0.322414	−0.161207	+	0.986921i	$0.551539\pi$
$788$	−1.53990	−0.0548567
$789$	−28.9250	−1.02976
$790$	8.51848	0.303074
$791$	28.5329	1.01451
$792$	−31.3408	−1.11365
$793$	5.18051	0.183965
$794$	−6.59462	−0.234034
$795$	8.05437	0.285659
$796$	0.492517	0.0174568
$797$	−12.0563	−0.427054	−0.213527	−	0.976937i	$-0.568495\pi$
$797$	−12.0563	−0.427054	−0.213527	+	0.976937i	$0.568495\pi$
$798$	−3.15141	−0.111559
$799$	−36.4065	−1.28797
$800$	0.460417	0.0162782
$801$	27.8667	0.984621
$802$	38.8076	1.37034
$803$	−6.18567	−0.218288
$804$	0.968999	0.0341740
$805$	13.7540	0.484765
$806$	−21.0205	−0.740415
$807$	−30.2254	−1.06399
$808$	22.8048	0.802269
$809$	−39.1832	−1.37761	−0.688804	−	0.724947i	$-0.741864\pi$
$809$	−39.1832	−1.37761	−0.688804	+	0.724947i	$0.741864\pi$
$810$	−0.227757	−0.00800255
$811$	−5.26247	−0.184790	−0.0923952	−	0.995722i	$-0.529452\pi$
$811$	−5.26247	−0.184790	−0.0923952	+	0.995722i	$0.529452\pi$
$812$	0.362058	0.0127058
$813$	−10.0501	−0.352473
$814$	83.3509	2.92145
$815$	−14.2288	−0.498412
$816$	−26.2982	−0.920620
$817$	13.6283	0.476794
$818$	−24.2483	−0.847822
$819$	10.7611	0.376022
$820$	−0.0871725	−0.00304419
$821$	45.1997	1.57748	0.788741	−	0.614726i	$-0.210733\pi$
$821$	45.1997	1.57748	0.788741	+	0.614726i	$0.210733\pi$
$822$	16.0490	0.559772
$823$	8.90299	0.310339	0.155169	−	0.987888i	$-0.450408\pi$
$823$	8.90299	0.310339	0.155169	+	0.987888i	$0.450408\pi$
$824$	−13.6566	−0.475752
$825$	−6.68944	−0.232896
$826$	15.5935	0.542569
$827$	−23.3644	−0.812461	−0.406231	−	0.913771i	$-0.633157\pi$
$827$	−23.3644	−0.812461	−0.406231	+	0.913771i	$0.633157\pi$
$828$	1.15977	0.0403046
$829$	7.24543	0.251644	0.125822	−	0.992053i	$-0.459843\pi$
$829$	7.24543	0.251644	0.125822	+	0.992053i	$0.459843\pi$
$830$	−2.07505	−0.0720259
$831$	13.8094	0.479042
$832$	−25.4321	−0.881700
$833$	22.6685	0.785417
$834$	−32.2983	−1.11840
$835$	2.34118	0.0810198
$836$	−0.575547	−0.0199057
$837$	−22.8894	−0.791172
$838$	1.11768	0.0386096
$839$	44.2354	1.52718	0.763588	−	0.645704i	$-0.223436\pi$
$839$	44.2354	1.52718	0.763588	+	0.645704i	$0.223436\pi$
$840$	5.29210	0.182595
$841$	−22.6768	−0.781960
$842$	38.4288	1.32434
$843$	−0.280978	−0.00967741
$844$	0.754101	0.0259572
$845$	1.94289	0.0668374
$846$	16.4326	0.564963
$847$	48.1986	1.65612
$848$	−30.9550	−1.06300
$849$	23.5267	0.807433
$850$	8.44118	0.289530
$851$	72.6612	2.49079
$852$	−0.407833	−0.0139721
$853$	10.8180	0.370403	0.185201	−	0.982701i	$-0.440706\pi$
$853$	10.8180	0.370403	0.185201	+	0.982701i	$0.440706\pi$
$854$	3.97376	0.135979
$855$	−2.09131	−0.0715212
$856$	12.3902	0.423490
$857$	31.3009	1.06922	0.534610	−	0.845099i	$-0.320459\pi$
$857$	31.3009	1.06922	0.534610	+	0.845099i	$0.320459\pi$
$858$	−32.0917	−1.09559
$859$	−9.84695	−0.335974	−0.167987	−	0.985789i	$-0.553727\pi$
$859$	−9.84695	−0.335974	−0.167987	+	0.985789i	$0.553727\pi$
$860$	0.971478	0.0331271
$861$	−2.04648	−0.0697439
$862$	−24.9152	−0.848615
$863$	−10.4649	−0.356230	−0.178115	−	0.984010i	$-0.557000\pi$
$863$	−10.4649	−0.356230	−0.178115	+	0.984010i	$0.557000\pi$
$864$	2.40516	0.0818253
$865$	19.3478	0.657847
$866$	−6.33257	−0.215190
$867$	−18.6362	−0.632920
$868$	−0.630886	−0.0214137
$869$	36.5231	1.23896
$870$	−3.92331	−0.133013
$871$	36.5846	1.23962
$872$	15.3904	0.521184
$873$	6.83533	0.231341
$874$	−12.8232	−0.433750
$875$	−1.76794	−0.0597674
$876$	0.0880735	0.00297573
$877$	−49.5345	−1.67266	−0.836330	−	0.548226i	$-0.815303\pi$
$877$	−49.5345	−1.67266	−0.836330	+	0.548226i	$0.815303\pi$
$878$	45.9649	1.55124
$879$	−2.86966	−0.0967911
$880$	25.7092	0.866657
$881$	25.2185	0.849633	0.424817	−	0.905279i	$-0.360339\pi$
$881$	25.2185	0.849633	0.424817	+	0.905279i	$0.360339\pi$
$882$	−10.2318	−0.344521
$883$	13.9049	0.467936	0.233968	−	0.972244i	$-0.424829\pi$
$883$	13.9049	0.467936	0.233968	+	0.972244i	$0.424829\pi$
$884$	1.58447	0.0532916
$885$	−6.61146	−0.222242
$886$	51.6913	1.73660
$887$	7.30408	0.245247	0.122624	−	0.992453i	$-0.460869\pi$
$887$	7.30408	0.245247	0.122624	+	0.992453i	$0.460869\pi$
$888$	27.9577	0.938199
$889$	2.73333	0.0916729
$890$	−21.9635	−0.736218
$891$	−0.976508	−0.0327143
$892$	2.27439	0.0761522
$893$	−7.10900	−0.237894
$894$	−22.7816	−0.761931
$895$	−18.2057	−0.608550
$896$	−21.1360	−0.706103
$897$	−27.9759	−0.934090
$898$	−13.7110	−0.457543
$899$	−11.0181	−0.367475
$900$	−0.149076	−0.00496921
$901$	−43.5763	−1.45174
$902$	−9.55225	−0.318055
$903$	22.8067	0.758958
$904$	44.6720	1.48577
$905$	15.6877	0.521477
$906$	−26.4434	−0.878523
$907$	−35.5665	−1.18097	−0.590483	−	0.807050i	$-0.701063\pi$
$907$	−35.5665	−1.18097	−0.590483	+	0.807050i	$0.701063\pi$
$908$	0.124386	0.00412790
$909$	−15.0812	−0.500210
$910$	−8.48147	−0.281158
$911$	4.93762	0.163591	0.0817954	−	0.996649i	$-0.473935\pi$
$911$	4.93762	0.163591	0.0817954	+	0.996649i	$0.473935\pi$
$912$	−5.13518	−0.170043
$913$	−8.89678	−0.294440
$914$	−7.86197	−0.260051
$915$	−1.68482	−0.0556985
$916$	2.32801	0.0769198
$917$	−27.9553	−0.923166
$918$	44.0958	1.45538
$919$	18.0885	0.596683	0.298342	−	0.954459i	$-0.403566\pi$
$919$	18.0885	0.596683	0.298342	+	0.954459i	$0.403566\pi$
$920$	21.5337	0.709945
$921$	12.6099	0.415512
$922$	18.8619	0.621184
$923$	−15.3978	−0.506823
$924$	−0.963165	−0.0316858
$925$	−9.33989	−0.307094
$926$	−27.0681	−0.889512
$927$	9.03136	0.296629
$928$	1.15776	0.0380053
$929$	−24.4012	−0.800577	−0.400289	−	0.916389i	$-0.631090\pi$
$929$	−24.4012	−0.800577	−0.400289	+	0.916389i	$0.631090\pi$
$930$	6.83636	0.224173
$931$	4.42643	0.145070
$932$	0.516540	0.0169198
$933$	8.47838	0.277570
$934$	−37.5976	−1.23023
$935$	36.1916	1.18359
$936$	16.8478	0.550689
$937$	13.2865	0.434051	0.217026	−	0.976166i	$-0.430364\pi$
$937$	13.2865	0.434051	0.217026	+	0.976166i	$0.430364\pi$
$938$	28.0626	0.916277
$939$	−23.5127	−0.767309
$940$	−0.506757	−0.0165286
$941$	−41.4096	−1.34991	−0.674957	−	0.737857i	$-0.735838\pi$
$941$	−41.4096	−1.34991	−0.674957	+	0.737857i	$0.735838\pi$
$942$	19.0334	0.620141
$943$	−8.32718	−0.271170
$944$	25.4095	0.827008
$945$	−9.23553	−0.300432
$946$	106.453	3.46110
$947$	−13.6826	−0.444626	−0.222313	−	0.974975i	$-0.571361\pi$
$947$	−13.6826	−0.444626	−0.222313	+	0.974975i	$0.571361\pi$
$948$	−0.520027	−0.0168897
$949$	3.32522	0.107941
$950$	1.64829	0.0534776
$951$	6.87557	0.222956
$952$	−28.6317	−0.927958
$953$	0.531545	0.0172184	0.00860922	−	0.999963i	$-0.497260\pi$
$953$	0.531545	0.0172184	0.00860922	+	0.999963i	$0.497260\pi$
$954$	19.6688	0.636800
$955$	4.51305	0.146039
$956$	1.59591	0.0516153
$957$	−16.8212	−0.543752
$958$	12.2236	0.394928
$959$	18.1857	0.587248
$960$	8.27113	0.266949
$961$	−11.8009	−0.380676
$962$	−44.8069	−1.44463
$963$	−8.19387	−0.264044
$964$	0.860526	0.0277157
$965$	−1.03207	−0.0332234
$966$	−21.4592	−0.690440
$967$	−5.32702	−0.171305	−0.0856527	−	0.996325i	$-0.527298\pi$
$967$	−5.32702	−0.171305	−0.0856527	+	0.996325i	$0.527298\pi$
$968$	75.4612	2.42541
$969$	−7.22896	−0.232227
$970$	−5.38735	−0.172977
$971$	−33.9898	−1.09078	−0.545392	−	0.838181i	$-0.683619\pi$
$971$	−33.9898	−1.09078	−0.545392	+	0.838181i	$0.683619\pi$
$972$	−1.26241	−0.0404918
$973$	−36.5985	−1.17329
$974$	49.4954	1.58593
$975$	3.59603	0.115165
$976$	6.47520	0.207266
$977$	28.0686	0.897995	0.448997	−	0.893533i	$-0.351781\pi$
$977$	28.0686	0.897995	0.448997	+	0.893533i	$0.351781\pi$
$978$	22.1999	0.709876
$979$	−94.1686	−3.00964
$980$	0.315533	0.0100793
$981$	−10.1779	−0.324955
$982$	−22.6838	−0.723870
$983$	−9.53374	−0.304079	−0.152040	−	0.988374i	$-0.548584\pi$
$983$	−9.53374	−0.304079	−0.152040	+	0.988374i	$0.548584\pi$
$984$	−3.20403	−0.102141
$985$	18.9082	0.602465
$986$	21.2261	0.675978
$987$	−11.8968	−0.378678
$988$	0.309396	0.00984321
$989$	92.8008	2.95089
$990$	−16.3356	−0.519180
$991$	−2.52542	−0.0802227	−0.0401114	−	0.999195i	$-0.512771\pi$
$991$	−2.52542	−0.0802227	−0.0401114	+	0.999195i	$0.512771\pi$
$992$	−2.01740	−0.0640524
$993$	1.86142	0.0590704
$994$	−11.8110	−0.374623
$995$	−6.04754	−0.191720
$996$	0.126675	0.00401386
$997$	−19.1640	−0.606931	−0.303466	−	0.952842i	$-0.598144\pi$
$997$	−19.1640	−0.606931	−0.303466	+	0.952842i	$0.598144\pi$
$998$	−7.02169	−0.222268
$999$	−48.7905	−1.54366

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	365.2.a.c.1.2	✓	5
3.2	odd	2		3285.2.a.l.1.4		5
4.3	odd	2		5840.2.a.ba.1.3		5
5.4	even	2		1825.2.a.f.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
365.2.a.c.1.2	✓	5	1.1	even	1	trivial
1825.2.a.f.1.4		5	5.4	even	2
3285.2.a.l.1.4		5	3.2	odd	2
5840.2.a.ba.1.3		5	4.3	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:	\( N \)	\(=\)	\( 365 = 5 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	365.a (trivial)

\(f(q)\)	\(=\)	\(q-1.44272 q^{2} -1.08144 q^{3} +0.0814409 q^{4} -1.00000 q^{5} +1.56022 q^{6} +1.76794 q^{7} +2.76794 q^{8} -1.83049 q^{9} +O(q^{10})\)	\(q-1.44272 q^{2} -1.08144 q^{3} +0.0814409 q^{4} -1.00000 q^{5} +1.56022 q^{6} +1.76794 q^{7} +2.76794 q^{8} -1.83049 q^{9} +1.44272 q^{10} +6.18567 q^{11} -0.0880735 q^{12} -3.32522 q^{13} -2.55065 q^{14} +1.08144 q^{15} -4.15625 q^{16} -5.85088 q^{17} +2.64088 q^{18} -1.14249 q^{19} -0.0814409 q^{20} -1.91193 q^{21} -8.92419 q^{22} -7.77967 q^{23} -2.99337 q^{24} +1.00000 q^{25} +4.79737 q^{26} +5.22388 q^{27} +0.143983 q^{28} +2.51459 q^{29} -1.56022 q^{30} -4.38167 q^{31} +0.460417 q^{32} -6.68944 q^{33} +8.44118 q^{34} -1.76794 q^{35} -0.149076 q^{36} -9.33989 q^{37} +1.64829 q^{38} +3.59603 q^{39} -2.76794 q^{40} +1.07038 q^{41} +2.75837 q^{42} -11.9286 q^{43} +0.503767 q^{44} +1.83049 q^{45} +11.2239 q^{46} +6.22239 q^{47} +4.49474 q^{48} -3.87438 q^{49} -1.44272 q^{50} +6.32738 q^{51} -0.270809 q^{52} +7.44781 q^{53} -7.53660 q^{54} -6.18567 q^{55} +4.89357 q^{56} +1.23553 q^{57} -3.62785 q^{58} -6.11356 q^{59} +0.0880735 q^{60} -1.55794 q^{61} +6.32153 q^{62} -3.23619 q^{63} +7.64825 q^{64} +3.32522 q^{65} +9.65099 q^{66} -11.0022 q^{67} -0.476501 q^{68} +8.41325 q^{69} +2.55065 q^{70} +4.63059 q^{71} -5.06668 q^{72} -1.00000 q^{73} +13.4748 q^{74} -1.08144 q^{75} -0.0930453 q^{76} +10.9359 q^{77} -5.18807 q^{78} +5.90446 q^{79} +4.15625 q^{80} -0.157866 q^{81} -1.54425 q^{82} -1.43829 q^{83} -0.155709 q^{84} +5.85088 q^{85} +17.2097 q^{86} -2.71938 q^{87} +17.1216 q^{88} -15.2237 q^{89} -2.64088 q^{90} -5.87881 q^{91} -0.633583 q^{92} +4.73852 q^{93} -8.97717 q^{94} +1.14249 q^{95} -0.497914 q^{96} -3.73416 q^{97} +5.58964 q^{98} -11.3228 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q - q^{2} - 6 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} + 7 q^{9}+O(q^{10}) \) 5 * q - q^2 - 6 * q^3 + q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 + 7 * q^9	\( 5 q - q^{2} - 6 q^{3} + q^{4} - 5 q^{5} + 3 q^{6} - 5 q^{7} + 7 q^{9} + q^{10} + 3 q^{11} - 16 q^{12} - 9 q^{13} - 4 q^{14} + 6 q^{15} - 7 q^{16} - 5 q^{17} - 6 q^{18} - 15 q^{19} - q^{20} + 6 q^{21} - 17 q^{22} - 3 q^{23} + 5 q^{25} - 4 q^{26} - 27 q^{27} - q^{28} + 3 q^{29} - 3 q^{30} - 7 q^{31} + 4 q^{32} - 8 q^{33} - 16 q^{34} + 5 q^{35} + 38 q^{36} - 6 q^{37} + 19 q^{38} + 9 q^{39} + 13 q^{41} - 4 q^{42} - 10 q^{43} + 5 q^{44} - 7 q^{45} + 3 q^{46} - 11 q^{47} + 31 q^{48} - 14 q^{49} - q^{50} - 2 q^{51} - 6 q^{53} + 16 q^{54} - 3 q^{55} + 16 q^{56} + 19 q^{57} + 26 q^{58} - q^{59} + 16 q^{60} + q^{61} - 2 q^{62} - 14 q^{63} - 14 q^{64} + 9 q^{65} + 43 q^{66} - 29 q^{67} + 7 q^{68} - 13 q^{69} + 4 q^{70} + 26 q^{71} - 7 q^{72} - 5 q^{73} + 31 q^{74} - 6 q^{75} - 4 q^{76} + 5 q^{77} + 23 q^{78} - 5 q^{79} + 7 q^{80} + 49 q^{81} + 11 q^{82} - 23 q^{83} + 23 q^{84} + 5 q^{85} + 24 q^{86} - 6 q^{87} + 8 q^{88} + 4 q^{89} + 6 q^{90} - 2 q^{91} + 16 q^{92} + 24 q^{93} - 11 q^{94} + 15 q^{95} - 5 q^{96} - 8 q^{97} + 9 q^{98} - 7 q^{99}+O(q^{100}) \) 5 * q - q^2 - 6 * q^3 + q^4 - 5 * q^5 + 3 * q^6 - 5 * q^7 + 7 * q^9 + q^10 + 3 * q^11 - 16 * q^12 - 9 * q^13 - 4 * q^14 + 6 * q^15 - 7 * q^16 - 5 * q^17 - 6 * q^18 - 15 * q^19 - q^20 + 6 * q^21 - 17 * q^22 - 3 * q^23 + 5 * q^25 - 4 * q^26 - 27 * q^27 - q^28 + 3 * q^29 - 3 * q^30 - 7 * q^31 + 4 * q^32 - 8 * q^33 - 16 * q^34 + 5 * q^35 + 38 * q^36 - 6 * q^37 + 19 * q^38 + 9 * q^39 + 13 * q^41 - 4 * q^42 - 10 * q^43 + 5 * q^44 - 7 * q^45 + 3 * q^46 - 11 * q^47 + 31 * q^48 - 14 * q^49 - q^50 - 2 * q^51 - 6 * q^53 + 16 * q^54 - 3 * q^55 + 16 * q^56 + 19 * q^57 + 26 * q^58 - q^59 + 16 * q^60 + q^61 - 2 * q^62 - 14 * q^63 - 14 * q^64 + 9 * q^65 + 43 * q^66 - 29 * q^67 + 7 * q^68 - 13 * q^69 + 4 * q^70 + 26 * q^71 - 7 * q^72 - 5 * q^73 + 31 * q^74 - 6 * q^75 - 4 * q^76 + 5 * q^77 + 23 * q^78 - 5 * q^79 + 7 * q^80 + 49 * q^81 + 11 * q^82 - 23 * q^83 + 23 * q^84 + 5 * q^85 + 24 * q^86 - 6 * q^87 + 8 * q^88 + 4 * q^89 + 6 * q^90 - 2 * q^91 + 16 * q^92 + 24 * q^93 - 11 * q^94 + 15 * q^95 - 5 * q^96 - 8 * q^97 + 9 * q^98 - 7 * q^99

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