LMFDB - Embedded newform 605.2.a.l.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [605,2,Mod(1,605)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(605, 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("605.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 605 = 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	605.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:	$4.83094932229$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	4.4.2525.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 4x^{2} + 5x + 5 $ x^4 - 2x^3 - 4x^2 + 5*x + 5
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 55)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$2.46673$ of defining polynomial
Character	$\chi$	$=$	605.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0935099 q^{2} +1.46673 q^{3} -1.99126 q^{4} +1.00000 q^{5} +0.137154 q^{6} +4.52452 q^{7} -0.373222 q^{8} -0.848698 q^{9} +O(q^{10})$	\(q+0.0935099 q^{2} +1.46673 q^{3} -1.99126 q^{4} +1.00000 q^{5} +0.137154 q^{6} +4.52452 q^{7} -0.373222 q^{8} -0.848698 q^{9} +0.0935099 q^{10} -2.92064 q^{12} -1.14256 q^{13} +0.423088 q^{14} +1.46673 q^{15} +3.94761 q^{16} +3.37322 q^{17} -0.0793616 q^{18} +6.08477 q^{19} -1.99126 q^{20} +6.63626 q^{21} -5.45258 q^{23} -0.547416 q^{24} +1.00000 q^{25} -0.106840 q^{26} -5.64501 q^{27} -9.00949 q^{28} +3.32083 q^{29} +0.137154 q^{30} +1.79091 q^{31} +1.11558 q^{32} +0.315430 q^{34} +4.52452 q^{35} +1.68997 q^{36} +1.48881 q^{37} +0.568986 q^{38} -1.67583 q^{39} -0.373222 q^{40} -1.74726 q^{41} +0.620556 q^{42} -0.263041 q^{43} -0.848698 q^{45} -0.509871 q^{46} +6.92472 q^{47} +5.79009 q^{48} +13.4713 q^{49} +0.0935099 q^{50} +4.94761 q^{51} +2.27513 q^{52} -1.43976 q^{53} -0.527864 q^{54} -1.68865 q^{56} +8.92472 q^{57} +0.310531 q^{58} -7.06810 q^{59} -2.92064 q^{60} +2.50245 q^{61} +0.167467 q^{62} -3.83995 q^{63} -7.79091 q^{64} -1.14256 q^{65} -0.516598 q^{67} -6.71695 q^{68} -7.99748 q^{69} +0.423088 q^{70} -10.7303 q^{71} +0.316753 q^{72} -5.68123 q^{73} +0.139218 q^{74} +1.46673 q^{75} -12.1163 q^{76} -0.156706 q^{78} -11.3033 q^{79} +3.94761 q^{80} -5.73362 q^{81} -0.163386 q^{82} +4.48088 q^{83} -13.2145 q^{84} +3.37322 q^{85} -0.0245970 q^{86} +4.87077 q^{87} +13.2676 q^{89} -0.0793616 q^{90} -5.16953 q^{91} +10.8575 q^{92} +2.62678 q^{93} +0.647530 q^{94} +6.08477 q^{95} +1.63626 q^{96} -3.35655 q^{97} +1.25970 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8}+O(q^{10}) $ 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8	$ 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8} + 3 q^{10} - 14 q^{12} + 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 7 q^{20} - 6 q^{21} - 9 q^{23} - 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} + 7 q^{28} - 8 q^{29} - q^{30} + 3 q^{31} + 6 q^{32} - 10 q^{34} + 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} - 3 q^{39} + 9 q^{40} - 7 q^{41} + 2 q^{42} + 21 q^{43} + 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} + 3 q^{50} + 9 q^{51} + 27 q^{52} - 11 q^{53} - 20 q^{54} + 15 q^{56} + 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} + 4 q^{61} + 11 q^{62} + 3 q^{63} - 27 q^{64} + 7 q^{65} - q^{67} - 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} + 13 q^{72} - 9 q^{73} - 36 q^{74} - 2 q^{75} + 8 q^{76} + 6 q^{78} + 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} + 15 q^{83} - 47 q^{84} + 3 q^{85} - 3 q^{86} + 15 q^{87} + 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} - 11 q^{94} + 12 q^{95} - 26 q^{96} + 6 q^{97} - 42 q^{98}+O(q^{100}) $ 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8 + 3 * q^10 - 14 * q^12 + 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 7 * q^20 - 6 * q^21 - 9 * q^23 - 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 + 7 * q^28 - 8 * q^29 - q^30 + 3 * q^31 + 6 * q^32 - 10 * q^34 + 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 - 3 * q^39 + 9 * q^40 - 7 * q^41 + 2 * q^42 + 21 * q^43 + 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 + 3 * q^50 + 9 * q^51 + 27 * q^52 - 11 * q^53 - 20 * q^54 + 15 * q^56 + 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 + 4 * q^61 + 11 * q^62 + 3 * q^63 - 27 * q^64 + 7 * q^65 - q^67 - 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 + 13 * q^72 - 9 * q^73 - 36 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^78 + 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 + 15 * q^83 - 47 * q^84 + 3 * q^85 - 3 * q^86 + 15 * q^87 + 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 - 11 * q^94 + 12 * q^95 - 26 * q^96 + 6 * q^97 - 42 * 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 $

$2$	0.0935099	0.0661215	0.0330607	−	0.999453i	$-0.489475\pi$
$2$	0.0935099	0.0661215	0.0330607	+	0.999453i	$0.489475\pi$
$3$	1.46673	0.846818	0.423409	−	0.905939i	$-0.360833\pi$
$3$	1.46673	0.846818	0.423409	+	0.905939i	$0.360833\pi$
$4$	−1.99126	−0.995628
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.137154	0.0559929
$7$	4.52452	1.71011	0.855055	−	0.518538i	$-0.173523\pi$
$7$	4.52452	1.71011	0.855055	+	0.518538i	$0.173523\pi$
$8$	−0.373222	−0.131954
$9$	−0.848698	−0.282899
$10$	0.0935099	0.0295704
$11$	0	0
$11$	0	0
$12$	−2.92064	−0.843116
$13$	−1.14256	−0.316889	−0.158444	−	0.987368i	$-0.550648\pi$
$13$	−1.14256	−0.316889	−0.158444	+	0.987368i	$0.550648\pi$
$14$	0.423088	0.113075
$15$	1.46673	0.378709
$16$	3.94761	0.986903
$17$	3.37322	0.818126	0.409063	−	0.912506i	$-0.365856\pi$
$17$	3.37322	0.818126	0.409063	+	0.912506i	$0.365856\pi$
$18$	−0.0793616	−0.0187057
$19$	6.08477	1.39594	0.697971	−	0.716127i	$-0.254087\pi$
$19$	6.08477	1.39594	0.697971	+	0.716127i	$0.254087\pi$
$20$	−1.99126	−0.445258
$21$	6.63626	1.44815
$22$	0	0
$23$	−5.45258	−1.13694	−0.568471	−	0.822703i	$-0.692465\pi$
$23$	−5.45258	−1.13694	−0.568471	+	0.822703i	$0.692465\pi$
$24$	−0.547416	−0.111741
$25$	1.00000	0.200000
$26$	−0.106840	−0.0209531
$27$	−5.64501	−1.08638
$28$	−9.00949	−1.70263
$29$	3.32083	0.616663	0.308332	−	0.951279i	$-0.400229\pi$
$29$	3.32083	0.616663	0.308332	+	0.951279i	$0.400229\pi$
$30$	0.137154	0.0250408
$31$	1.79091	0.321656	0.160828	−	0.986982i	$-0.448584\pi$
$31$	1.79091	0.321656	0.160828	+	0.986982i	$0.448584\pi$
$32$	1.11558	0.197209
$33$	0	0
$34$	0.315430	0.0540957
$35$	4.52452	0.764784
$36$	1.68997	0.281662
$37$	1.48881	0.244758	0.122379	−	0.992483i	$-0.460948\pi$
$37$	1.48881	0.244758	0.122379	+	0.992483i	$0.460948\pi$
$38$	0.568986	0.0923017
$39$	−1.67583	−0.268347
$40$	−0.373222	−0.0590116
$41$	−1.74726	−0.272876	−0.136438	−	0.990649i	$-0.543566\pi$
$41$	−1.74726	−0.272876	−0.136438	+	0.990649i	$0.543566\pi$
$42$	0.620556	0.0957539
$43$	−0.263041	−0.0401134	−0.0200567	−	0.999799i	$-0.506385\pi$
$43$	−0.263041	−0.0401134	−0.0200567	+	0.999799i	$0.506385\pi$
$44$	0	0
$45$	−0.848698	−0.126516
$46$	−0.509871	−0.0751763
$47$	6.92472	1.01007	0.505037	−	0.863098i	$-0.331479\pi$
$47$	6.92472	1.01007	0.505037	+	0.863098i	$0.331479\pi$
$48$	5.79009	0.835727
$49$	13.4713	1.92447
$50$	0.0935099	0.0132243
$51$	4.94761	0.692804
$52$	2.27513	0.315503
$53$	−1.43976	−0.197766	−0.0988830	−	0.995099i	$-0.531527\pi$
$53$	−1.43976	−0.197766	−0.0988830	+	0.995099i	$0.531527\pi$
$54$	−0.527864	−0.0718332
$55$	0	0
$56$	−1.68865	−0.225656
$57$	8.92472	1.18211
$58$	0.310531	0.0407747
$59$	−7.06810	−0.920188	−0.460094	−	0.887870i	$-0.652184\pi$
$59$	−7.06810	−0.920188	−0.460094	+	0.887870i	$0.652184\pi$
$60$	−2.92064	−0.377053
$61$	2.50245	0.320406	0.160203	−	0.987084i	$-0.448785\pi$
$61$	2.50245	0.320406	0.160203	+	0.987084i	$0.448785\pi$
$62$	0.167467	0.0212684
$63$	−3.83995	−0.483789
$64$	−7.79091	−0.973863
$65$	−1.14256	−0.141717
$66$	0	0
$67$	−0.516598	−0.0631124	−0.0315562	−	0.999502i	$-0.510046\pi$
$67$	−0.516598	−0.0631124	−0.0315562	+	0.999502i	$0.510046\pi$
$68$	−6.71695	−0.814550
$69$	−7.99748	−0.962783
$70$	0.423088	0.0505687
$71$	−10.7303	−1.27345	−0.636725	−	0.771091i	$-0.719711\pi$
$71$	−10.7303	−1.27345	−0.636725	+	0.771091i	$0.719711\pi$
$72$	0.316753	0.0373297
$73$	−5.68123	−0.664938	−0.332469	−	0.943114i	$-0.607882\pi$
$73$	−5.68123	−0.664938	−0.332469	+	0.943114i	$0.607882\pi$
$74$	0.139218	0.0161838
$75$	1.46673	0.169364
$76$	−12.1163	−1.38984
$77$	0	0
$78$	−0.156706	−0.0177435
$79$	−11.3033	−1.27173	−0.635863	−	0.771802i	$-0.719356\pi$
$79$	−11.3033	−1.27173	−0.635863	+	0.771802i	$0.719356\pi$
$80$	3.94761	0.441356
$81$	−5.73362	−0.637069
$82$	−0.163386	−0.0180430
$83$	4.48088	0.491840	0.245920	−	0.969290i	$-0.420910\pi$
$83$	4.48088	0.491840	0.245920	+	0.969290i	$0.420910\pi$
$84$	−13.2145	−1.44182
$85$	3.37322	0.365877
$86$	−0.0245970	−0.00265236
$87$	4.87077	0.522202
$88$	0	0
$89$	13.2676	1.40637	0.703183	−	0.711009i	$-0.251762\pi$
$89$	13.2676	1.40637	0.703183	+	0.711009i	$0.251762\pi$
$90$	−0.0793616	−0.00836545
$91$	−5.16953	−0.541914
$92$	10.8575	1.13197
$93$	2.62678	0.272384
$94$	0.647530	0.0667876
$95$	6.08477	0.624284
$96$	1.63626	0.167000
$97$	−3.35655	−0.340806	−0.170403	−	0.985374i	$-0.554507\pi$
$97$	−3.35655	−0.340806	−0.170403	+	0.985374i	$0.554507\pi$
$98$	1.25970	0.127249
$99$	0	0
$100$	−1.99126	−0.199126
$101$	−9.33498	−0.928865	−0.464433	−	0.885608i	$-0.653742\pi$
$101$	−9.33498	−0.928865	−0.464433	+	0.885608i	$0.653742\pi$
$102$	0.462651	0.0458092
$103$	−13.9160	−1.37118	−0.685591	−	0.727987i	$-0.740456\pi$
$103$	−13.9160	−1.37118	−0.685591	+	0.727987i	$0.740456\pi$
$104$	0.426428	0.0418147
$105$	6.63626	0.647633
$106$	−0.134632	−0.0130766
$107$	−16.7883	−1.62299	−0.811493	−	0.584362i	$-0.801345\pi$
$107$	−16.7883	−1.62299	−0.811493	+	0.584362i	$0.801345\pi$
$108$	11.2407	1.08163
$109$	−3.65293	−0.349888	−0.174944	−	0.984578i	$-0.555974\pi$
$109$	−3.65293	−0.349888	−0.174944	+	0.984578i	$0.555974\pi$
$110$	0	0
$111$	2.18368	0.207266
$112$	17.8611	1.68771
$113$	−11.9023	−1.11968	−0.559839	−	0.828602i	$-0.689137\pi$
$113$	−11.9023	−1.11968	−0.559839	+	0.828602i	$0.689137\pi$
$114$	0.834550	0.0781627
$115$	−5.45258	−0.508456
$116$	−6.61263	−0.613967
$117$	0.969687	0.0896476
$118$	−0.660937	−0.0608442
$119$	15.2622	1.39909
$120$	−0.547416	−0.0499721
$121$	0	0
$122$	0.234004	0.0211857
$123$	−2.56276	−0.231077
$124$	−3.56615	−0.320250
$125$	1.00000	0.0894427
$126$	−0.359074	−0.0319888
$127$	19.7627	1.75365	0.876826	−	0.480808i	$-0.159656\pi$
$127$	19.7627	1.75365	0.876826	+	0.480808i	$0.159656\pi$
$128$	−2.95970	−0.261603
$129$	−0.385811	−0.0339688
$130$	−0.106840	−0.00937053
$131$	−1.93479	−0.169043	−0.0845215	−	0.996422i	$-0.526936\pi$
$131$	−1.93479	−0.169043	−0.0845215	+	0.996422i	$0.526936\pi$
$132$	0	0
$133$	27.5307	2.38721
$134$	−0.0483070	−0.00417309
$135$	−5.64501	−0.485845
$136$	−1.25896	−0.107955
$137$	−12.5353	−1.07097	−0.535483	−	0.844546i	$-0.679870\pi$
$137$	−12.5353	−1.07097	−0.535483	+	0.844546i	$0.679870\pi$
$138$	−0.747843	−0.0636606
$139$	−11.2450	−0.953793	−0.476896	−	0.878960i	$-0.658238\pi$
$139$	−11.2450	−0.953793	−0.476896	+	0.878960i	$0.658238\pi$
$140$	−9.00949	−0.761440
$141$	10.1567	0.855349
$142$	−1.00339	−0.0842024
$143$	0	0
$144$	−3.35033	−0.279194
$145$	3.32083	0.275780
$146$	−0.531251	−0.0439667
$147$	19.7588	1.62968
$148$	−2.96459	−0.243688
$149$	−17.3337	−1.42003	−0.710014	−	0.704187i	$-0.751312\pi$
$149$	−17.3337	−1.42003	−0.710014	+	0.704187i	$0.751312\pi$
$150$	0.137154	0.0111986
$151$	−0.00540415	−0.000439784 0	−0.000219892	−	1.00000i	$-0.500070\pi$
$151$	−0.00540415	−0.000439784 0	−0.000219892		1.00000i	$0.500070\pi$
$152$	−2.27097	−0.184200
$153$	−2.86285	−0.231447
$154$	0	0
$155$	1.79091	0.143849
$156$	3.33700	0.267174
$157$	0.554838	0.0442809	0.0221404	−	0.999755i	$-0.492952\pi$
$157$	0.554838	0.0442809	0.0221404	+	0.999755i	$0.492952\pi$
$158$	−1.05697	−0.0840884
$159$	−2.11174	−0.167472
$160$	1.11558	0.0881947
$161$	−24.6703	−1.94430
$162$	−0.536150	−0.0421239
$163$	−7.96428	−0.623811	−0.311905	−	0.950113i	$-0.600967\pi$
$163$	−7.96428	−0.623811	−0.311905	+	0.950113i	$0.600967\pi$
$164$	3.47924	0.271683
$165$	0	0
$166$	0.419007	0.0325212
$167$	3.42643	0.265145	0.132572	−	0.991173i	$-0.457676\pi$
$167$	3.42643	0.265145	0.132572	+	0.991173i	$0.457676\pi$
$168$	−2.47680	−0.191089
$169$	−11.6946	−0.899582
$170$	0.315430	0.0241923
$171$	−5.16413	−0.394911
$172$	0.523783	0.0399381
$173$	20.5669	1.56367	0.781836	−	0.623484i	$-0.214283\pi$
$173$	20.5669	1.56367	0.781836	+	0.623484i	$0.214283\pi$
$174$	0.455465	0.0345287
$175$	4.52452	0.342022
$176$	0	0
$177$	−10.3670	−0.779231
$178$	1.24065	0.0929910
$179$	−2.56432	−0.191666	−0.0958332	−	0.995397i	$-0.530552\pi$
$179$	−2.56432	−0.191666	−0.0958332	+	0.995397i	$0.530552\pi$
$180$	1.68997	0.125963
$181$	13.4169	0.997268	0.498634	−	0.866813i	$-0.333835\pi$
$181$	13.4169	0.997268	0.498634	+	0.866813i	$0.333835\pi$
$182$	−0.483402	−0.0358322
$183$	3.67042	0.271325
$184$	2.03502	0.150024
$185$	1.48881	0.109459
$186$	0.245630	0.0180104
$187$	0	0
$188$	−13.7889	−1.00566
$189$	−25.5410	−1.85783
$190$	0.568986	0.0412786
$191$	18.1898	1.31617	0.658085	−	0.752944i	$-0.271367\pi$
$191$	18.1898	1.31617	0.658085	+	0.752944i	$0.271367\pi$
$192$	−11.4272	−0.824685
$193$	15.6887	1.12929	0.564647	−	0.825333i	$-0.309012\pi$
$193$	15.6887	1.12929	0.564647	+	0.825333i	$0.309012\pi$
$194$	−0.313871	−0.0225346
$195$	−1.67583	−0.120008
$196$	−26.8248	−1.91606
$197$	−21.8486	−1.55665	−0.778325	−	0.627862i	$-0.783930\pi$
$197$	−21.8486	−1.55665	−0.778325	+	0.627862i	$0.783930\pi$
$198$	0	0
$199$	−4.55200	−0.322683	−0.161341	−	0.986899i	$-0.551582\pi$
$199$	−4.55200	−0.322683	−0.161341	+	0.986899i	$0.551582\pi$
$200$	−0.373222	−0.0263908
$201$	−0.757710	−0.0534448
$202$	−0.872913	−0.0614180
$203$	15.0252	1.05456
$204$	−9.85196	−0.689775
$205$	−1.74726	−0.122034
$206$	−1.30128	−0.0906646
$207$	4.62760	0.321640
$208$	−4.51038	−0.312738
$209$	0	0
$210$	0.620556	0.0428225
$211$	18.9604	1.30529	0.652645	−	0.757664i	$-0.273659\pi$
$211$	18.9604	1.30529	0.652645	+	0.757664i	$0.273659\pi$
$212$	2.86693	0.196901
$213$	−15.7384	−1.07838
$214$	−1.56987	−0.107314
$215$	−0.263041	−0.0179393
$216$	2.10684	0.143352
$217$	8.10300	0.550067
$218$	−0.341585	−0.0231351
$219$	−8.33284	−0.563081
$220$	0	0
$221$	−3.85410	−0.259255
$222$	0.204196	0.0137047
$223$	4.87952	0.326757	0.163378	−	0.986563i	$-0.447761\pi$
$223$	4.87952	0.326757	0.163378	+	0.986563i	$0.447761\pi$
$224$	5.04749	0.337250
$225$	−0.848698	−0.0565799
$226$	−1.11299	−0.0740347
$227$	16.3229	1.08339	0.541693	−	0.840577i	$-0.317784\pi$
$227$	16.3229	1.08339	0.541693	+	0.840577i	$0.317784\pi$
$228$	−17.7714	−1.17694
$229$	−4.83167	−0.319286	−0.159643	−	0.987175i	$-0.551034\pi$
$229$	−4.83167	−0.319286	−0.159643	+	0.987175i	$0.551034\pi$
$230$	−0.509871	−0.0336199
$231$	0	0
$232$	−1.23941	−0.0813711
$233$	−8.41975	−0.551596	−0.275798	−	0.961216i	$-0.588942\pi$
$233$	−8.41975	−0.551596	−0.275798	+	0.961216i	$0.588942\pi$
$234$	0.0906753	0.00592763
$235$	6.92472	0.451719
$236$	14.0744	0.916165
$237$	−16.5790	−1.07692
$238$	1.42717	0.0925096
$239$	−22.6928	−1.46787	−0.733937	−	0.679218i	$-0.762319\pi$
$239$	−22.6928	−1.46787	−0.733937	+	0.679218i	$0.762319\pi$
$240$	5.79009	0.373749
$241$	11.6065	0.747638	0.373819	−	0.927502i	$-0.378048\pi$
$241$	11.6065	0.747638	0.373819	+	0.927502i	$0.378048\pi$
$242$	0	0
$243$	8.52534	0.546901
$244$	−4.98302	−0.319005
$245$	13.4713	0.860651
$246$	−0.239644	−0.0152791
$247$	−6.95220	−0.442358
$248$	−0.668405	−0.0424438
$249$	6.57225	0.416499
$250$	0.0935099	0.00591408
$251$	3.31305	0.209118	0.104559	−	0.994519i	$-0.466657\pi$
$251$	3.31305	0.209118	0.104559	+	0.994519i	$0.466657\pi$
$252$	7.64633	0.481674
$253$	0	0
$254$	1.84800	0.115954
$255$	4.94761	0.309831
$256$	15.3051	0.956566
$257$	−26.8466	−1.67465	−0.837323	−	0.546709i	$-0.815880\pi$
$257$	−26.8466	−1.67465	−0.837323	+	0.546709i	$0.815880\pi$
$258$	−0.0360772	−0.00224607
$259$	6.73614	0.418563
$260$	2.27513	0.141097
$261$	−2.81838	−0.174454
$262$	−0.180922	−0.0111774
$263$	12.1682	0.750324	0.375162	−	0.926959i	$-0.377587\pi$
$263$	12.1682	0.750324	0.375162	+	0.926959i	$0.377587\pi$
$264$	0	0
$265$	−1.43976	−0.0884436
$266$	2.57439	0.157846
$267$	19.4601	1.19094
$268$	1.02868	0.0628365
$269$	−2.09351	−0.127644	−0.0638218	−	0.997961i	$-0.520329\pi$
$269$	−2.09351	−0.127644	−0.0638218	+	0.997961i	$0.520329\pi$
$270$	−0.527864	−0.0321248
$271$	15.1428	0.919859	0.459930	−	0.887955i	$-0.347875\pi$
$271$	15.1428	0.919859	0.459930	+	0.887955i	$0.347875\pi$
$272$	13.3162	0.807411
$273$	−7.58232	−0.458903
$274$	−1.17218	−0.0708138
$275$	0	0
$276$	15.9250	0.958574
$277$	8.27066	0.496936	0.248468	−	0.968640i	$-0.420073\pi$
$277$	8.27066	0.496936	0.248468	+	0.968640i	$0.420073\pi$
$278$	−1.05152	−0.0630662
$279$	−1.51994	−0.0909963
$280$	−1.68865	−0.100916
$281$	2.44723	0.145989	0.0729947	−	0.997332i	$-0.476744\pi$
$281$	2.44723	0.145989	0.0729947	+	0.997332i	$0.476744\pi$
$282$	0.949753	0.0565569
$283$	26.0948	1.55117	0.775586	−	0.631242i	$-0.217454\pi$
$283$	26.0948	1.55117	0.775586	+	0.631242i	$0.217454\pi$
$284$	21.3667	1.26788
$285$	8.92472	0.528655
$286$	0	0
$287$	−7.90553	−0.466648
$288$	−0.946794	−0.0557904
$289$	−5.62137	−0.330669
$290$	0.310531	0.0182350
$291$	−4.92316	−0.288601
$292$	11.3128	0.662031
$293$	13.4529	0.785929	0.392965	−	0.919554i	$-0.371449\pi$
$293$	13.4529	0.785929	0.392965	+	0.919554i	$0.371449\pi$
$294$	1.84764	0.107757
$295$	−7.06810	−0.411520
$296$	−0.555655	−0.0322968
$297$	0	0
$298$	−1.62087	−0.0938944
$299$	6.22989	0.360284
$300$	−2.92064	−0.168623
$301$	−1.19014	−0.0685984
$302$	−0.000505342 0	−2.90791e−5 0
$303$	−13.6919	−0.786580
$304$	24.0203	1.37766
$305$	2.50245	0.143290
$306$	−0.267704	−0.0153036
$307$	27.1844	1.55150	0.775748	−	0.631042i	$-0.217373\pi$
$307$	27.1844	1.55150	0.775748	+	0.631042i	$0.217373\pi$
$308$	0	0
$309$	−20.4110	−1.16114
$310$	0.167467	0.00951151
$311$	−13.1990	−0.748448	−0.374224	−	0.927338i	$-0.622091\pi$
$311$	−13.1990	−0.748448	−0.374224	+	0.927338i	$0.622091\pi$
$312$	0.625455	0.0354094
$313$	16.1719	0.914090	0.457045	−	0.889443i	$-0.348908\pi$
$313$	16.1719	0.914090	0.457045	+	0.889443i	$0.348908\pi$
$314$	0.0518828	0.00292792
$315$	−3.83995	−0.216357
$316$	22.5079	1.26617
$317$	−5.38115	−0.302235	−0.151118	−	0.988516i	$-0.548287\pi$
$317$	−5.38115	−0.302235	−0.151118	+	0.988516i	$0.548287\pi$
$318$	−0.197469	−0.0110735
$319$	0	0
$320$	−7.79091	−0.435525
$321$	−24.6239	−1.37437
$322$	−2.30692	−0.128560
$323$	20.5253	1.14206
$324$	11.4171	0.634283
$325$	−1.14256	−0.0633777
$326$	−0.744739	−0.0412473
$327$	−5.35787	−0.296291
$328$	0.652116	0.0360071
$329$	31.3311	1.72734
$330$	0	0
$331$	−18.5702	−1.02071	−0.510356	−	0.859963i	$-0.670486\pi$
$331$	−18.5702	−1.02071	−0.510356	+	0.859963i	$0.670486\pi$
$332$	−8.92258	−0.489690
$333$	−1.26355	−0.0692419
$334$	0.320405	0.0175318
$335$	−0.516598	−0.0282247
$336$	26.1974	1.42918
$337$	9.00615	0.490596	0.245298	−	0.969448i	$-0.421114\pi$
$337$	9.00615	0.490596	0.245298	+	0.969448i	$0.421114\pi$
$338$	−1.09356	−0.0594817
$339$	−17.4575	−0.948163
$340$	−6.71695	−0.364278
$341$	0	0
$342$	−0.482897	−0.0261121
$343$	29.2796	1.58095
$344$	0.0981728	0.00529312
$345$	−7.99748	−0.430570
$346$	1.92321	0.103392
$347$	10.2710	0.551374	0.275687	−	0.961247i	$-0.411095\pi$
$347$	10.2710	0.551374	0.275687	+	0.961247i	$0.411095\pi$
$348$	−9.69895	−0.519919
$349$	17.2613	0.923974	0.461987	−	0.886887i	$-0.347137\pi$
$349$	17.2613	0.923974	0.461987	+	0.886887i	$0.347137\pi$
$350$	0.423088	0.0226150
$351$	6.44975	0.344262
$352$	0	0
$353$	−22.8096	−1.21403	−0.607017	−	0.794689i	$-0.707634\pi$
$353$	−22.8096	−1.21403	−0.607017	+	0.794689i	$0.707634\pi$
$354$	−0.969417	−0.0515239
$355$	−10.7303	−0.569504
$356$	−26.4192	−1.40022
$357$	22.3856	1.18477
$358$	−0.239790	−0.0126733
$359$	−16.0747	−0.848390	−0.424195	−	0.905571i	$-0.639443\pi$
$359$	−16.0747	−0.848390	−0.424195	+	0.905571i	$0.639443\pi$
$360$	0.316753	0.0166943
$361$	18.0244	0.948651
$362$	1.25461	0.0659408
$363$	0	0
$364$	10.2939	0.539545
$365$	−5.68123	−0.297369
$366$	0.343221	0.0179404
$367$	21.9975	1.14826	0.574129	−	0.818765i	$-0.305341\pi$
$367$	21.9975	1.14826	0.574129	+	0.818765i	$0.305341\pi$
$368$	−21.5247	−1.12205
$369$	1.48290	0.0771965
$370$	0.139218	0.00723761
$371$	−6.51422	−0.338202
$372$	−5.23059	−0.271193
$373$	−20.2604	−1.04905	−0.524523	−	0.851396i	$-0.675756\pi$
$373$	−20.2604	−1.04905	−0.524523	+	0.851396i	$0.675756\pi$
$374$	0	0
$375$	1.46673	0.0757417
$376$	−2.58446	−0.133283
$377$	−3.79425	−0.195414
$378$	−2.38833	−0.122843
$379$	−3.72771	−0.191480	−0.0957398	−	0.995406i	$-0.530522\pi$
$379$	−3.72771	−0.191480	−0.0957398	+	0.995406i	$0.530522\pi$
$380$	−12.1163	−0.621554
$381$	28.9865	1.48502
$382$	1.70093	0.0870271
$383$	−10.9974	−0.561941	−0.280970	−	0.959716i	$-0.590656\pi$
$383$	−10.9974	−0.561941	−0.280970	+	0.959716i	$0.590656\pi$
$384$	−4.34108	−0.221530
$385$	0	0
$386$	1.46704	0.0746706
$387$	0.223243	0.0113481
$388$	6.68375	0.339316
$389$	9.38220	0.475697	0.237848	−	0.971302i	$-0.423558\pi$
$389$	9.38220	0.475697	0.237848	+	0.971302i	$0.423558\pi$
$390$	−0.156706	−0.00793513
$391$	−18.3928	−0.930163
$392$	−5.02779	−0.253942
$393$	−2.83781	−0.143149
$394$	−2.04306	−0.102928
$395$	−11.3033	−0.568733
$396$	0	0
$397$	22.3136	1.11989	0.559945	−	0.828530i	$-0.310822\pi$
$397$	22.3136	1.11989	0.559945	+	0.828530i	$0.310822\pi$
$398$	−0.425657	−0.0213363
$399$	40.3801	2.02153
$400$	3.94761	0.197381
$401$	−24.6822	−1.23257	−0.616285	−	0.787523i	$-0.711363\pi$
$401$	−24.6822	−1.23257	−0.616285	+	0.787523i	$0.711363\pi$
$402$	−0.0708534	−0.00353385
$403$	−2.04621	−0.101929
$404$	18.5883	0.924804
$405$	−5.73362	−0.284906
$406$	1.40500	0.0697292
$407$	0	0
$408$	−1.84656	−0.0914182
$409$	29.5056	1.45896	0.729478	−	0.684004i	$-0.239763\pi$
$409$	29.5056	1.45896	0.729478	+	0.684004i	$0.239763\pi$
$410$	−0.163386	−0.00806907
$411$	−18.3860	−0.906913
$412$	27.7103	1.36519
$413$	−31.9798	−1.57362
$414$	0.432726	0.0212673
$415$	4.48088	0.219958
$416$	−1.27462	−0.0624934
$417$	−16.4935	−0.807689
$418$	0	0
$419$	9.03564	0.441420	0.220710	−	0.975339i	$-0.429163\pi$
$419$	9.03564	0.441420	0.220710	+	0.975339i	$0.429163\pi$
$420$	−13.2145	−0.644802
$421$	14.2201	0.693047	0.346524	−	0.938041i	$-0.387362\pi$
$421$	14.2201	0.693047	0.346524	+	0.938041i	$0.387362\pi$
$422$	1.77299	0.0863077
$423$	−5.87699	−0.285749
$424$	0.537349	0.0260960
$425$	3.37322	0.163625
$426$	−1.47170	−0.0713041
$427$	11.3224	0.547929
$428$	33.4298	1.61589
$429$	0	0
$430$	−0.0245970	−0.00118617
$431$	−1.73155	−0.0834060	−0.0417030	−	0.999130i	$-0.513278\pi$
$431$	−1.73155	−0.0834060	−0.0417030	+	0.999130i	$0.513278\pi$
$432$	−22.2843	−1.07215
$433$	18.4476	0.886535	0.443268	−	0.896389i	$-0.353819\pi$
$433$	18.4476	0.886535	0.443268	+	0.896389i	$0.353819\pi$
$434$	0.757710	0.0363713
$435$	4.87077	0.233536
$436$	7.27393	0.348358
$437$	−33.1777	−1.58710
$438$	−0.779203	−0.0372318
$439$	−17.1704	−0.819499	−0.409750	−	0.912198i	$-0.634384\pi$
$439$	−17.1704	−0.819499	−0.409750	+	0.912198i	$0.634384\pi$
$440$	0	0
$441$	−11.4331	−0.544432
$442$	−0.360397	−0.0171423
$443$	36.5992	1.73888	0.869441	−	0.494037i	$-0.164479\pi$
$443$	36.5992	1.73888	0.869441	+	0.494037i	$0.164479\pi$
$444$	−4.34827	−0.206360
$445$	13.2676	0.628946
$446$	0.456283	0.0216056
$447$	−25.4238	−1.20251
$448$	−35.2501	−1.66541
$449$	−16.6029	−0.783540	−0.391770	−	0.920063i	$-0.628137\pi$
$449$	−16.6029	−0.783540	−0.391770	+	0.920063i	$0.628137\pi$
$450$	−0.0793616	−0.00374114
$451$	0	0
$452$	23.7006	1.11478
$453$	−0.00792644	−0.000372417 0
$454$	1.52635	0.0716351
$455$	−5.16953	−0.242351
$456$	−3.33090	−0.155984
$457$	−31.6653	−1.48124	−0.740620	−	0.671924i	$-0.765468\pi$
$457$	−31.6653	−1.48124	−0.740620	+	0.671924i	$0.765468\pi$
$458$	−0.451809	−0.0211116
$459$	−19.0419	−0.888798
$460$	10.8575	0.506233
$461$	−25.4351	−1.18463	−0.592315	−	0.805706i	$-0.701786\pi$
$461$	−25.4351	−1.18463	−0.592315	+	0.805706i	$0.701786\pi$
$462$	0	0
$463$	−16.3319	−0.759007	−0.379503	−	0.925190i	$-0.623905\pi$
$463$	−16.3319	−0.759007	−0.379503	+	0.925190i	$0.623905\pi$
$464$	13.1094	0.608587
$465$	2.62678	0.121814
$466$	−0.787330	−0.0364723
$467$	8.52911	0.394680	0.197340	−	0.980335i	$-0.436770\pi$
$467$	8.52911	0.394680	0.197340	+	0.980335i	$0.436770\pi$
$468$	−1.93089	−0.0892556
$469$	−2.33736	−0.107929
$470$	0.647530	0.0298683
$471$	0.813798	0.0374978
$472$	2.63797	0.121422
$473$	0	0
$474$	−1.55030	−0.0712076
$475$	6.08477	0.279188
$476$	−30.3910	−1.39297
$477$	1.22192	0.0559479
$478$	−2.12200	−0.0970580
$479$	29.9478	1.36835	0.684175	−	0.729318i	$-0.260162\pi$
$479$	29.9478	1.36835	0.684175	+	0.729318i	$0.260162\pi$
$480$	1.63626	0.0746849
$481$	−1.70105	−0.0775611
$482$	1.08532	0.0494349
$483$	−36.1848	−1.64646
$484$	0	0
$485$	−3.35655	−0.152413
$486$	0.797204	0.0361619
$487$	−19.6031	−0.888300	−0.444150	−	0.895952i	$-0.646494\pi$
$487$	−19.6031	−0.888300	−0.444150	+	0.895952i	$0.646494\pi$
$488$	−0.933969	−0.0422788
$489$	−11.6815	−0.528254
$490$	1.25970	0.0569075
$491$	−15.7891	−0.712553	−0.356277	−	0.934381i	$-0.615954\pi$
$491$	−15.7891	−0.712553	−0.356277	+	0.934381i	$0.615954\pi$
$492$	5.10312	0.230066
$493$	11.2019	0.504509
$494$	−0.650099	−0.0292494
$495$	0	0
$496$	7.06980	0.317443
$497$	−48.5494	−2.17774
$498$	0.614570	0.0275396
$499$	11.2081	0.501745	0.250872	−	0.968020i	$-0.419283\pi$
$499$	11.2081	0.501745	0.250872	+	0.968020i	$0.419283\pi$
$500$	−1.99126	−0.0890517
$501$	5.02565	0.224530
$502$	0.309803	0.0138272
$503$	−0.342908	−0.0152895	−0.00764477	−	0.999971i	$-0.502433\pi$
$503$	−0.342908	−0.0152895	−0.00764477	+	0.999971i	$0.502433\pi$
$504$	1.43315	0.0638378
$505$	−9.33498	−0.415401
$506$	0	0
$507$	−17.1528	−0.761782
$508$	−39.3525	−1.74599
$509$	−19.5626	−0.867098	−0.433549	−	0.901130i	$-0.642739\pi$
$509$	−19.5626	−0.867098	−0.433549	+	0.901130i	$0.642739\pi$
$510$	0.462651	0.0204865
$511$	−25.7049	−1.13712
$512$	7.35057	0.324852
$513$	−34.3485	−1.51653
$514$	−2.51042	−0.110730
$515$	−13.9160	−0.613211
$516$	0.768249	0.0338203
$517$	0	0
$518$	0.629896	0.0276760
$519$	30.1661	1.32415
$520$	0.426428	0.0187001
$521$	42.0264	1.84121	0.920606	−	0.390493i	$-0.127695\pi$
$521$	42.0264	1.84121	0.920606	+	0.390493i	$0.127695\pi$
$522$	−0.263547	−0.0115351
$523$	30.0105	1.31227	0.656135	−	0.754644i	$-0.272190\pi$
$523$	30.0105	1.31227	0.656135	+	0.754644i	$0.272190\pi$
$524$	3.85266	0.168304
$525$	6.63626	0.289630
$526$	1.13785	0.0496125
$527$	6.04112	0.263155
$528$	0	0
$529$	6.73067	0.292638
$530$	−0.134632	−0.00584802
$531$	5.99868	0.260320
$532$	−54.8206	−2.37677
$533$	1.99635	0.0864714
$534$	1.81971	0.0787464
$535$	−16.7883	−0.725822
$536$	0.192806	0.00832793
$537$	−3.76117	−0.162307
$538$	−0.195764	−0.00843998
$539$	0	0
$540$	11.2407	0.483721
$541$	−10.3236	−0.443846	−0.221923	−	0.975064i	$-0.571233\pi$
$541$	−10.3236	−0.443846	−0.221923	+	0.975064i	$0.571233\pi$
$542$	1.41600	0.0608225
$543$	19.6789	0.844504
$544$	3.76311	0.161342
$545$	−3.65293	−0.156474
$546$	−0.709022	−0.0303433
$547$	41.8168	1.78796	0.893979	−	0.448108i	$-0.147902\pi$
$547$	41.8168	1.78796	0.893979	+	0.448108i	$0.147902\pi$
$548$	24.9611	1.06628
$549$	−2.12382	−0.0906426
$550$	0	0
$551$	20.2065	0.860826
$552$	2.98483	0.127043
$553$	−51.1423	−2.17479
$554$	0.773388	0.0328581
$555$	2.18368	0.0926920
$556$	22.3918	0.949622
$557$	−38.4828	−1.63057	−0.815285	−	0.579060i	$-0.803420\pi$
$557$	−38.4828	−1.63057	−0.815285	+	0.579060i	$0.803420\pi$
$558$	−0.142129	−0.00601681
$559$	0.300540	0.0127115
$560$	17.8611	0.754768
$561$	0	0
$562$	0.228840	0.00965303
$563$	30.6864	1.29328	0.646639	−	0.762796i	$-0.276174\pi$
$563$	30.6864	1.29328	0.646639	+	0.762796i	$0.276174\pi$
$564$	−20.2246	−0.851609
$565$	−11.9023	−0.500735
$566$	2.44012	0.102566
$567$	−25.9419	−1.08946
$568$	4.00478	0.168037
$569$	13.0485	0.547020	0.273510	−	0.961869i	$-0.411815\pi$
$569$	13.0485	0.547020	0.273510	+	0.961869i	$0.411815\pi$
$570$	0.834550	0.0349554
$571$	16.1300	0.675018	0.337509	−	0.941322i	$-0.390416\pi$
$571$	16.1300	0.675018	0.337509	+	0.941322i	$0.390416\pi$
$572$	0	0
$573$	26.6796	1.11456
$574$	−0.739245	−0.0308555
$575$	−5.45258	−0.227388
$576$	6.61212	0.275505
$577$	−14.5714	−0.606617	−0.303308	−	0.952892i	$-0.598091\pi$
$577$	−14.5714	−0.606617	−0.303308	+	0.952892i	$0.598091\pi$
$578$	−0.525654	−0.0218643
$579$	23.0110	0.956306
$580$	−6.61263	−0.274575
$581$	20.2738	0.841101
$582$	−0.460364	−0.0190827
$583$	0	0
$584$	2.12036	0.0877411
$585$	0.969687	0.0400916
$586$	1.25798	0.0519668
$587$	−27.8742	−1.15049	−0.575246	−	0.817981i	$-0.695094\pi$
$587$	−27.8742	−1.15049	−0.575246	+	0.817981i	$0.695094\pi$
$588$	−39.3448	−1.62255
$589$	10.8972	0.449013
$590$	−0.660937	−0.0272103
$591$	−32.0461	−1.31820
$592$	5.87723	0.241553
$593$	15.1037	0.620236	0.310118	−	0.950698i	$-0.399631\pi$
$593$	15.1037	0.620236	0.310118	+	0.950698i	$0.399631\pi$
$594$	0	0
$595$	15.2622	0.625690
$596$	34.5158	1.41382
$597$	−6.67657	−0.273254
$598$	0.582557	0.0238225
$599$	−25.8757	−1.05725	−0.528626	−	0.848855i	$-0.677292\pi$
$599$	−25.8757	−1.05725	−0.528626	+	0.848855i	$0.677292\pi$
$600$	−0.547416	−0.0223482
$601$	−47.0268	−1.91826	−0.959132	−	0.282959i	$-0.908684\pi$
$601$	−47.0268	−1.91826	−0.959132	+	0.282959i	$0.908684\pi$
$602$	−0.111290	−0.00453583
$603$	0.438435	0.0178545
$604$	0.0107610	0.000437861 0
$605$	0	0
$606$	−1.28033	−0.0520098
$607$	−35.2239	−1.42969	−0.714847	−	0.699281i	$-0.753504\pi$
$607$	−35.2239	−1.42969	−0.714847	+	0.699281i	$0.753504\pi$
$608$	6.78807	0.275293
$609$	22.0379	0.893022
$610$	0.234004	0.00947454
$611$	−7.91189	−0.320081
$612$	5.70066	0.230435
$613$	−23.4117	−0.945590	−0.472795	−	0.881173i	$-0.656755\pi$
$613$	−23.4117	−0.945590	−0.472795	+	0.881173i	$0.656755\pi$
$614$	2.54201	0.102587
$615$	−2.56276	−0.103341
$616$	0	0
$617$	22.8910	0.921557	0.460778	−	0.887515i	$-0.347570\pi$
$617$	22.8910	0.921557	0.460778	+	0.887515i	$0.347570\pi$
$618$	−1.90863	−0.0767764
$619$	2.12752	0.0855124	0.0427562	−	0.999086i	$-0.486386\pi$
$619$	2.12752	0.0855124	0.0427562	+	0.999086i	$0.486386\pi$
$620$	−3.56615	−0.143220
$621$	30.7799	1.23515
$622$	−1.23424	−0.0494885
$623$	60.0297	2.40504
$624$	−6.61551	−0.264832
$625$	1.00000	0.0400000
$626$	1.51223	0.0604410
$627$	0	0
$628$	−1.10482	−0.0440873
$629$	5.02207	0.200243
$630$	−0.359074	−0.0143058
$631$	15.4588	0.615404	0.307702	−	0.951483i	$-0.400440\pi$
$631$	15.4588	0.615404	0.307702	+	0.951483i	$0.400440\pi$
$632$	4.21866	0.167809
$633$	27.8099	1.10534
$634$	−0.503191	−0.0199843
$635$	19.7627	0.784257
$636$	4.20501	0.166740
$637$	−15.3918	−0.609844
$638$	0	0
$639$	9.10676	0.360258
$640$	−2.95970	−0.116992
$641$	14.1805	0.560096	0.280048	−	0.959986i	$-0.409650\pi$
$641$	14.1805	0.560096	0.280048	+	0.959986i	$0.409650\pi$
$642$	−2.30258	−0.0908757
$643$	−12.3941	−0.488774	−0.244387	−	0.969678i	$-0.578587\pi$
$643$	−12.3941	−0.488774	−0.244387	+	0.969678i	$0.578587\pi$
$644$	49.1250	1.93580
$645$	−0.385811	−0.0151913
$646$	1.91932	0.0755145
$647$	33.2465	1.30705	0.653527	−	0.756903i	$-0.273289\pi$
$647$	33.2465	1.30705	0.653527	+	0.756903i	$0.273289\pi$
$648$	2.13991	0.0840637
$649$	0	0
$650$	−0.106840	−0.00419063
$651$	11.8849	0.465807
$652$	15.8589	0.621083
$653$	−34.8066	−1.36209	−0.681043	−	0.732243i	$-0.738474\pi$
$653$	−34.8066	−1.36209	−0.681043	+	0.732243i	$0.738474\pi$
$654$	−0.501014	−0.0195912
$655$	−1.93479	−0.0755984
$656$	−6.89751	−0.269303
$657$	4.82165	0.188110
$658$	2.92976	0.114214
$659$	−34.4953	−1.34375	−0.671873	−	0.740666i	$-0.734510\pi$
$659$	−34.4953	−1.34375	−0.671873	+	0.740666i	$0.734510\pi$
$660$	0	0
$661$	1.77827	0.0691668	0.0345834	−	0.999402i	$-0.488990\pi$
$661$	1.77827	0.0691668	0.0345834	+	0.999402i	$0.488990\pi$
$662$	−1.73650	−0.0674910
$663$	−5.65293	−0.219542
$664$	−1.67236	−0.0649003
$665$	27.5307	1.06759
$666$	−0.118154	−0.00457838
$667$	−18.1071	−0.701111
$668$	−6.82289	−0.263986
$669$	7.15694	0.276703
$670$	−0.0483070	−0.00186626
$671$	0	0
$672$	7.40331	0.285589
$673$	19.2964	0.743823	0.371911	−	0.928268i	$-0.378703\pi$
$673$	19.2964	0.743823	0.371911	+	0.928268i	$0.378703\pi$
$674$	0.842164	0.0324389
$675$	−5.64501	−0.217276
$676$	23.2869	0.895649
$677$	−16.9101	−0.649907	−0.324953	−	0.945730i	$-0.605349\pi$
$677$	−16.9101	−0.649907	−0.324953	+	0.945730i	$0.605349\pi$
$678$	−1.63245	−0.0626939
$679$	−15.1868	−0.582816
$680$	−1.25896	−0.0482789
$681$	23.9412	0.917430
$682$	0	0
$683$	4.14018	0.158420	0.0792098	−	0.996858i	$-0.474760\pi$
$683$	4.14018	0.158420	0.0792098	+	0.996858i	$0.474760\pi$
$684$	10.2831	0.393184
$685$	−12.5353	−0.478950
$686$	2.73794	0.104535
$687$	−7.08676	−0.270377
$688$	−1.03839	−0.0395881
$689$	1.64501	0.0626698
$690$	−0.747843	−0.0284699
$691$	−46.3520	−1.76331	−0.881657	−	0.471891i	$-0.843571\pi$
$691$	−46.3520	−1.76331	−0.881657	+	0.471891i	$0.843571\pi$
$692$	−40.9539	−1.55684
$693$	0	0
$694$	0.960437	0.0364577
$695$	−11.2450	−0.426549
$696$	−1.81788	−0.0689065
$697$	−5.89390	−0.223247
$698$	1.61410	0.0610945
$699$	−12.3495	−0.467101
$700$	−9.00949	−0.340527
$701$	−45.4553	−1.71682	−0.858412	−	0.512961i	$-0.828548\pi$
$701$	−45.4553	−1.71682	−0.858412	+	0.512961i	$0.828548\pi$
$702$	0.603115	0.0227631
$703$	9.05904	0.341668
$704$	0	0
$705$	10.1567	0.382524
$706$	−2.13293	−0.0802738
$707$	−42.2364	−1.58846
$708$	20.6434	0.775825
$709$	−14.0241	−0.526688	−0.263344	−	0.964702i	$-0.584825\pi$
$709$	−14.0241	−0.526688	−0.263344	+	0.964702i	$0.584825\pi$
$710$	−1.00339	−0.0376565
$711$	9.59312	0.359770
$712$	−4.95177	−0.185575
$713$	−9.76506	−0.365704
$714$	2.09327	0.0783388
$715$	0	0
$716$	5.10622	0.190829
$717$	−33.2842	−1.24302
$718$	−1.50314	−0.0560968
$719$	13.1384	0.489980	0.244990	−	0.969526i	$-0.421215\pi$
$719$	13.1384	0.489980	0.244990	+	0.969526i	$0.421215\pi$
$720$	−3.35033	−0.124859
$721$	−62.9632	−2.34487
$722$	1.68546	0.0627262
$723$	17.0236	0.633113
$724$	−26.7164	−0.992908
$725$	3.32083	0.123333
$726$	0	0
$727$	−18.3635	−0.681063	−0.340532	−	0.940233i	$-0.610607\pi$
$727$	−18.3635	−0.681063	−0.340532	+	0.940233i	$0.610607\pi$
$728$	1.92938	0.0715077
$729$	29.7052	1.10019
$730$	−0.531251	−0.0196625
$731$	−0.887297	−0.0328179
$732$	−7.30875	−0.270139
$733$	−36.9977	−1.36654	−0.683270	−	0.730166i	$-0.739443\pi$
$733$	−36.9977	−1.36654	−0.683270	+	0.730166i	$0.739443\pi$
$734$	2.05698	0.0759246
$735$	19.7588	0.728815
$736$	−6.08282	−0.224216
$737$	0	0
$738$	0.138666	0.00510435
$739$	9.85033	0.362350	0.181175	−	0.983451i	$-0.442010\pi$
$739$	9.85033	0.362350	0.181175	+	0.983451i	$0.442010\pi$
$740$	−2.96459	−0.108981
$741$	−10.1970	−0.374597
$742$	−0.609144	−0.0223624
$743$	27.4471	1.00694	0.503468	−	0.864014i	$-0.332057\pi$
$743$	27.4471	1.00694	0.503468	+	0.864014i	$0.332057\pi$
$744$	−0.980371	−0.0359421
$745$	−17.3337	−0.635056
$746$	−1.89455	−0.0693645
$747$	−3.80291	−0.139141
$748$	0	0
$749$	−75.9591	−2.77549
$750$	0.137154	0.00500815
$751$	13.7284	0.500957	0.250479	−	0.968122i	$-0.419412\pi$
$751$	13.7284	0.500957	0.250479	+	0.968122i	$0.419412\pi$
$752$	27.3361	0.996845
$753$	4.85936	0.177085
$754$	−0.354799	−0.0129210
$755$	−0.00540415	−0.000196677 0
$756$	50.8586	1.84971
$757$	−22.9299	−0.833401	−0.416701	−	0.909044i	$-0.636814\pi$
$757$	−22.9299	−0.833401	−0.416701	+	0.909044i	$0.636814\pi$
$758$	−0.348578	−0.0126609
$759$	0	0
$760$	−2.27097	−0.0823767
$761$	−20.6818	−0.749716	−0.374858	−	0.927082i	$-0.622308\pi$
$761$	−20.6818	−0.749716	−0.374858	+	0.927082i	$0.622308\pi$
$762$	2.71053	0.0981920
$763$	−16.5278	−0.598346
$764$	−36.2206	−1.31042
$765$	−2.86285	−0.103506
$766$	−1.02837	−0.0371564
$767$	8.07571	0.291597
$768$	22.4484	0.810037
$769$	38.4306	1.38584	0.692922	−	0.721013i	$-0.256323\pi$
$769$	38.4306	1.38584	0.692922	+	0.721013i	$0.256323\pi$
$770$	0	0
$771$	−39.3768	−1.41812
$772$	−31.2401	−1.12436
$773$	49.9406	1.79624	0.898120	−	0.439751i	$-0.144933\pi$
$773$	49.9406	1.79624	0.898120	+	0.439751i	$0.144933\pi$
$774$	0.0208754	0.000750351 0
$775$	1.79091	0.0643312
$776$	1.25274	0.0449707
$777$	9.88011	0.354447
$778$	0.877329	0.0314538
$779$	−10.6317	−0.380919
$780$	3.33700	0.119484
$781$	0	0
$782$	−1.71991	−0.0615037
$783$	−18.7461	−0.669932
$784$	53.1795	1.89927
$785$	0.554838	0.0198030
$786$	−0.265364	−0.00946521
$787$	−15.5540	−0.554440	−0.277220	−	0.960806i	$-0.589413\pi$
$787$	−15.5540	−0.554440	−0.277220	+	0.960806i	$0.589413\pi$
$788$	43.5062	1.54984
$789$	17.8475	0.635388
$790$	−1.05697	−0.0376055
$791$	−53.8524	−1.91477
$792$	0	0
$793$	−2.85919	−0.101533
$794$	2.08655	0.0740488
$795$	−2.11174	−0.0748957
$796$	9.06420	0.321272
$797$	46.1068	1.63319	0.816593	−	0.577214i	$-0.195860\pi$
$797$	46.1068	1.63319	0.816593	+	0.577214i	$0.195860\pi$
$798$	3.77594	0.133667
$799$	23.3586	0.826368
$800$	1.11558	0.0394419
$801$	−11.2602	−0.397860
$802$	−2.30803	−0.0814994
$803$	0	0
$804$	1.50879	0.0532111
$805$	−24.6703	−0.869515
$806$	−0.191341	−0.00673971
$807$	−3.07062	−0.108091
$808$	3.48402	0.122567
$809$	−37.5394	−1.31981	−0.659907	−	0.751347i	$-0.729404\pi$
$809$	−37.5394	−1.31981	−0.659907	+	0.751347i	$0.729404\pi$
$810$	−0.536150	−0.0188384
$811$	7.20547	0.253018	0.126509	−	0.991965i	$-0.459623\pi$
$811$	7.20547	0.253018	0.126509	+	0.991965i	$0.459623\pi$
$812$	−29.9190	−1.04995
$813$	22.2104	0.778953
$814$	0	0
$815$	−7.96428	−0.278977
$816$	19.5313	0.683731
$817$	−1.60055	−0.0559960
$818$	2.75906	0.0964684
$819$	4.38737	0.153307
$820$	3.47924	0.121500
$821$	−8.63405	−0.301331	−0.150665	−	0.988585i	$-0.548142\pi$
$821$	−8.63405	−0.301331	−0.150665	+	0.988585i	$0.548142\pi$
$822$	−1.71927	−0.0599664
$823$	−25.0121	−0.871865	−0.435933	−	0.899979i	$-0.643581\pi$
$823$	−25.0121	−0.871865	−0.435933	+	0.899979i	$0.643581\pi$
$824$	5.19375	0.180933
$825$	0	0
$826$	−2.99042	−0.104050
$827$	48.8725	1.69946	0.849732	−	0.527216i	$-0.176764\pi$
$827$	48.8725	1.69946	0.849732	+	0.527216i	$0.176764\pi$
$828$	−9.21473	−0.320234
$829$	5.29170	0.183788	0.0918941	−	0.995769i	$-0.470708\pi$
$829$	5.29170	0.183788	0.0918941	+	0.995769i	$0.470708\pi$
$830$	0.419007	0.0145439
$831$	12.1308	0.420814
$832$	8.90156	0.308606
$833$	45.4417	1.57446
$834$	−1.54230	−0.0534056
$835$	3.42643	0.118576
$836$	0	0
$837$	−10.1097	−0.349441
$838$	0.844922	0.0291873
$839$	−13.2419	−0.457160	−0.228580	−	0.973525i	$-0.573408\pi$
$839$	−13.2419	−0.457160	−0.228580	+	0.973525i	$0.573408\pi$
$840$	−2.47680	−0.0854577
$841$	−17.9721	−0.619726
$842$	1.32972	0.0458253
$843$	3.58943	0.123626
$844$	−37.7551	−1.29958
$845$	−11.6946	−0.402305
$846$	−0.549557	−0.0188942
$847$	0	0
$848$	−5.68361	−0.195176
$849$	38.2740	1.31356
$850$	0.315430	0.0108191
$851$	−8.11784	−0.278276
$852$	31.3393	1.07367
$853$	2.21885	0.0759720	0.0379860	−	0.999278i	$-0.487906\pi$
$853$	2.21885	0.0759720	0.0379860	+	0.999278i	$0.487906\pi$
$854$	1.05876	0.0362299
$855$	−5.16413	−0.176609
$856$	6.26576	0.214159
$857$	31.4625	1.07474	0.537368	−	0.843348i	$-0.319418\pi$
$857$	31.4625	1.07474	0.537368	+	0.843348i	$0.319418\pi$
$858$	0	0
$859$	9.07676	0.309695	0.154848	−	0.987938i	$-0.450511\pi$
$859$	9.07676	0.309695	0.154848	+	0.987938i	$0.450511\pi$
$860$	0.523783	0.0178608
$861$	−11.5953	−0.395166
$862$	−0.161917	−0.00551493
$863$	42.4842	1.44618	0.723089	−	0.690755i	$-0.242721\pi$
$863$	42.4842	1.44618	0.723089	+	0.690755i	$0.242721\pi$
$864$	−6.29748	−0.214245
$865$	20.5669	0.699295
$866$	1.72503	0.0586190
$867$	−8.24505	−0.280017
$868$	−16.1351	−0.547662
$869$	0	0
$870$	0.455465	0.0154417
$871$	0.590243	0.0199996
$872$	1.36335	0.0461690
$873$	2.84870	0.0964138
$874$	−3.10244	−0.104942
$875$	4.52452	0.152957
$876$	16.5928	0.560619
$877$	−31.3101	−1.05727	−0.528634	−	0.848850i	$-0.677296\pi$
$877$	−31.3101	−1.05727	−0.528634	+	0.848850i	$0.677296\pi$
$878$	−1.60560	−0.0541865
$879$	19.7319	0.665539
$880$	0	0
$881$	21.5189	0.724990	0.362495	−	0.931986i	$-0.381925\pi$
$881$	21.5189	0.724990	0.362495	+	0.931986i	$0.381925\pi$
$882$	−1.06911	−0.0359987
$883$	−0.652552	−0.0219601	−0.0109801	−	0.999940i	$-0.503495\pi$
$883$	−0.652552	−0.0219601	−0.0109801	+	0.999940i	$0.503495\pi$
$884$	7.67450	0.258121
$885$	−10.3670	−0.348483
$886$	3.42239	0.114977
$887$	−14.6462	−0.491771	−0.245886	−	0.969299i	$-0.579079\pi$
$887$	−14.6462	−0.491771	−0.245886	+	0.969299i	$0.579079\pi$
$888$	−0.814997	−0.0273495
$889$	89.4166	2.99894
$890$	1.24065	0.0415868
$891$	0	0
$892$	−9.71637	−0.325328
$893$	42.1353	1.41000
$894$	−2.37738	−0.0795115
$895$	−2.56432	−0.0857159
$896$	−13.3912	−0.447369
$897$	9.13758	0.305095
$898$	−1.55254	−0.0518088
$899$	5.94730	0.198354
$900$	1.68997	0.0563325
$901$	−4.85662	−0.161798
$902$	0	0
$903$	−1.74561	−0.0580903
$904$	4.44221	0.147746
$905$	13.4169	0.445992
$906$	−0.000741201 0	−2.46247e−5 0
$907$	28.7450	0.954461	0.477231	−	0.878778i	$-0.341641\pi$
$907$	28.7450	0.954461	0.477231	+	0.878778i	$0.341641\pi$
$908$	−32.5030	−1.07865
$909$	7.92258	0.262775
$910$	−0.483402	−0.0160246
$911$	17.2819	0.572573	0.286287	−	0.958144i	$-0.407579\pi$
$911$	17.2819	0.572573	0.286287	+	0.958144i	$0.407579\pi$
$912$	35.2313	1.16663
$913$	0	0
$914$	−2.96102	−0.0979418
$915$	3.67042	0.121340
$916$	9.62109	0.317890
$917$	−8.75399	−0.289082
$918$	−1.78060	−0.0587686
$919$	−2.19845	−0.0725203	−0.0362601	−	0.999342i	$-0.511544\pi$
$919$	−2.19845	−0.0725203	−0.0362601	+	0.999342i	$0.511544\pi$
$920$	2.03502	0.0670927
$921$	39.8723	1.31384
$922$	−2.37843	−0.0783295
$923$	12.2600	0.403542
$924$	0	0
$925$	1.48881	0.0489517
$926$	−1.52719	−0.0501866
$927$	11.8105	0.387906
$928$	3.70467	0.121612
$929$	24.2104	0.794317	0.397158	−	0.917750i	$-0.369996\pi$
$929$	24.2104	0.794317	0.397158	+	0.917750i	$0.369996\pi$
$930$	0.245630	0.00805452
$931$	81.9698	2.68645
$932$	16.7659	0.549184
$933$	−19.3594	−0.633799
$934$	0.797556	0.0260968
$935$	0	0
$936$	−0.361908	−0.0118293
$937$	−20.8227	−0.680249	−0.340125	−	0.940380i	$-0.610469\pi$
$937$	−20.8227	−0.680249	−0.340125	+	0.940380i	$0.610469\pi$
$938$	−0.218566	−0.00713644
$939$	23.7199	0.774068
$940$	−13.7889	−0.449744
$941$	34.2128	1.11530	0.557652	−	0.830075i	$-0.311702\pi$
$941$	34.2128	1.11530	0.557652	+	0.830075i	$0.311702\pi$
$942$	0.0760982	0.00247941
$943$	9.52709	0.310245
$944$	−27.9021	−0.908136
$945$	−25.5410	−0.830848
$946$	0	0
$947$	33.8128	1.09877	0.549383	−	0.835570i	$-0.314863\pi$
$947$	33.8128	1.09877	0.549383	+	0.835570i	$0.314863\pi$
$948$	33.0130	1.07221
$949$	6.49114	0.210711
$950$	0.568986	0.0184603
$951$	−7.89270	−0.255938
$952$	−5.69620	−0.184615
$953$	25.5982	0.829206	0.414603	−	0.910002i	$-0.363920\pi$
$953$	25.5982	0.829206	0.414603	+	0.910002i	$0.363920\pi$
$954$	0.114262	0.00369936
$955$	18.1898	0.588609
$956$	45.1871	1.46146
$957$	0	0
$958$	2.80042	0.0904774
$959$	−56.7164	−1.83147
$960$	−11.4272	−0.368810
$961$	−27.7927	−0.896537
$962$	−0.159065	−0.00512846
$963$	14.2482	0.459142
$964$	−23.1114	−0.744369
$965$	15.6887	0.505036
$966$	−3.38363	−0.108867
$967$	43.8942	1.41154	0.705772	−	0.708439i	$-0.250600\pi$
$967$	43.8942	1.41154	0.705772	+	0.708439i	$0.250600\pi$
$968$	0	0
$969$	30.1051	0.967114
$970$	−0.313871	−0.0100778
$971$	36.3707	1.16719	0.583596	−	0.812044i	$-0.301645\pi$
$971$	36.3707	1.16719	0.583596	+	0.812044i	$0.301645\pi$
$972$	−16.9761	−0.544510
$973$	−50.8785	−1.63109
$974$	−1.83308	−0.0587357
$975$	−1.67583	−0.0536694
$976$	9.87870	0.316209
$977$	10.3516	0.331177	0.165589	−	0.986195i	$-0.447048\pi$
$977$	10.3516	0.331177	0.165589	+	0.986195i	$0.447048\pi$
$978$	−1.09233	−0.0349289
$979$	0	0
$980$	−26.8248	−0.856888
$981$	3.10024	0.0989830
$982$	−1.47644	−0.0471151
$983$	−22.1158	−0.705385	−0.352693	−	0.935739i	$-0.614734\pi$
$983$	−22.1158	−0.705385	−0.352693	+	0.935739i	$0.614734\pi$
$984$	0.956480	0.0304915
$985$	−21.8486	−0.696155
$986$	1.04749	0.0333589
$987$	45.9543	1.46274
$988$	13.8436	0.440424
$989$	1.43426	0.0456067
$990$	0	0
$991$	−55.5911	−1.76591	−0.882955	−	0.469457i	$-0.844450\pi$
$991$	−55.5911	−1.76591	−0.882955	+	0.469457i	$0.844450\pi$
$992$	1.99791	0.0634336
$993$	−27.2376	−0.864358
$994$	−4.53985	−0.143995
$995$	−4.55200	−0.144308
$996$	−13.0870	−0.414678
$997$	10.7911	0.341759	0.170879	−	0.985292i	$-0.445339\pi$
$997$	10.7911	0.341759	0.170879	+	0.985292i	$0.445339\pi$
$998$	1.04807	0.0331761
$999$	−8.40432	−0.265901

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	605.2.a.l.1.2		4
3.2	odd	2		5445.2.a.bg.1.3		4
4.3	odd	2		9680.2.a.cs.1.1		4
5.4	even	2		3025.2.a.v.1.3		4
11.2	odd	10		605.2.g.n.81.1		8
11.3	even	5		605.2.g.j.251.1		8
11.4	even	5		605.2.g.j.511.1		8
11.5	even	5		55.2.g.a.36.2	yes	8
11.6	odd	10		605.2.g.n.366.1		8
11.7	odd	10		605.2.g.g.511.2		8
11.8	odd	10		605.2.g.g.251.2		8
11.9	even	5		55.2.g.a.26.2	✓	8
11.10	odd	2		605.2.a.i.1.3		4
33.5	odd	10		495.2.n.f.91.1		8
33.20	odd	10		495.2.n.f.136.1		8
33.32	even	2		5445.2.a.bu.1.2		4
44.27	odd	10		880.2.bo.e.641.1		8
44.31	odd	10		880.2.bo.e.81.1		8
44.43	even	2		9680.2.a.cv.1.1		4
55.9	even	10		275.2.h.b.26.1		8
55.27	odd	20		275.2.z.b.124.2		16
55.38	odd	20		275.2.z.b.124.3		16
55.42	odd	20		275.2.z.b.224.3		16
55.49	even	10		275.2.h.b.201.1		8
55.53	odd	20		275.2.z.b.224.2		16
55.54	odd	2		3025.2.a.be.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	11.9	even	5
55.2.g.a.36.2	yes	8	11.5	even	5
275.2.h.b.26.1		8	55.9	even	10
275.2.h.b.201.1		8	55.49	even	10
275.2.z.b.124.2		16	55.27	odd	20
275.2.z.b.124.3		16	55.38	odd	20
275.2.z.b.224.2		16	55.53	odd	20
275.2.z.b.224.3		16	55.42	odd	20
495.2.n.f.91.1		8	33.5	odd	10
495.2.n.f.136.1		8	33.20	odd	10
605.2.a.i.1.3		4	11.10	odd	2
605.2.a.l.1.2		4	1.1	even	1	trivial
605.2.g.g.251.2		8	11.8	odd	10
605.2.g.g.511.2		8	11.7	odd	10
605.2.g.j.251.1		8	11.3	even	5
605.2.g.j.511.1		8	11.4	even	5
605.2.g.n.81.1		8	11.2	odd	10
605.2.g.n.366.1		8	11.6	odd	10
880.2.bo.e.81.1		8	44.31	odd	10
880.2.bo.e.641.1		8	44.27	odd	10
3025.2.a.v.1.3		4	5.4	even	2
3025.2.a.be.1.2		4	55.54	odd	2
5445.2.a.bg.1.3		4	3.2	odd	2
5445.2.a.bu.1.2		4	33.32	even	2
9680.2.a.cs.1.1		4	4.3	odd	2
9680.2.a.cv.1.1		4	44.43	even	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	605.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0935099 q^{2} +1.46673 q^{3} -1.99126 q^{4} +1.00000 q^{5} +0.137154 q^{6} +4.52452 q^{7} -0.373222 q^{8} -0.848698 q^{9} +O(q^{10})\)	\(q+0.0935099 q^{2} +1.46673 q^{3} -1.99126 q^{4} +1.00000 q^{5} +0.137154 q^{6} +4.52452 q^{7} -0.373222 q^{8} -0.848698 q^{9} +0.0935099 q^{10} -2.92064 q^{12} -1.14256 q^{13} +0.423088 q^{14} +1.46673 q^{15} +3.94761 q^{16} +3.37322 q^{17} -0.0793616 q^{18} +6.08477 q^{19} -1.99126 q^{20} +6.63626 q^{21} -5.45258 q^{23} -0.547416 q^{24} +1.00000 q^{25} -0.106840 q^{26} -5.64501 q^{27} -9.00949 q^{28} +3.32083 q^{29} +0.137154 q^{30} +1.79091 q^{31} +1.11558 q^{32} +0.315430 q^{34} +4.52452 q^{35} +1.68997 q^{36} +1.48881 q^{37} +0.568986 q^{38} -1.67583 q^{39} -0.373222 q^{40} -1.74726 q^{41} +0.620556 q^{42} -0.263041 q^{43} -0.848698 q^{45} -0.509871 q^{46} +6.92472 q^{47} +5.79009 q^{48} +13.4713 q^{49} +0.0935099 q^{50} +4.94761 q^{51} +2.27513 q^{52} -1.43976 q^{53} -0.527864 q^{54} -1.68865 q^{56} +8.92472 q^{57} +0.310531 q^{58} -7.06810 q^{59} -2.92064 q^{60} +2.50245 q^{61} +0.167467 q^{62} -3.83995 q^{63} -7.79091 q^{64} -1.14256 q^{65} -0.516598 q^{67} -6.71695 q^{68} -7.99748 q^{69} +0.423088 q^{70} -10.7303 q^{71} +0.316753 q^{72} -5.68123 q^{73} +0.139218 q^{74} +1.46673 q^{75} -12.1163 q^{76} -0.156706 q^{78} -11.3033 q^{79} +3.94761 q^{80} -5.73362 q^{81} -0.163386 q^{82} +4.48088 q^{83} -13.2145 q^{84} +3.37322 q^{85} -0.0245970 q^{86} +4.87077 q^{87} +13.2676 q^{89} -0.0793616 q^{90} -5.16953 q^{91} +10.8575 q^{92} +2.62678 q^{93} +0.647530 q^{94} +6.08477 q^{95} +1.63626 q^{96} -3.35655 q^{97} +1.25970 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8}+O(q^{10}) \) 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8	\( 4 q + 3 q^{2} - 2 q^{3} + 7 q^{4} + 4 q^{5} - q^{6} + 11 q^{7} + 9 q^{8} + 3 q^{10} - 14 q^{12} + 7 q^{13} - 2 q^{14} - 2 q^{15} + 5 q^{16} + 3 q^{17} + 2 q^{18} + 12 q^{19} + 7 q^{20} - 6 q^{21} - 9 q^{23} - 15 q^{24} + 4 q^{25} + 13 q^{26} - 5 q^{27} + 7 q^{28} - 8 q^{29} - q^{30} + 3 q^{31} + 6 q^{32} - 10 q^{34} + 11 q^{35} + 8 q^{36} - 3 q^{37} + 12 q^{38} - 3 q^{39} + 9 q^{40} - 7 q^{41} + 2 q^{42} + 21 q^{43} + 12 q^{46} - 3 q^{47} - 2 q^{48} + 15 q^{49} + 3 q^{50} + 9 q^{51} + 27 q^{52} - 11 q^{53} - 20 q^{54} + 15 q^{56} + 5 q^{57} + 2 q^{58} - 7 q^{59} - 14 q^{60} + 4 q^{61} + 11 q^{62} + 3 q^{63} - 27 q^{64} + 7 q^{65} - q^{67} - 15 q^{68} - 28 q^{69} - 2 q^{70} - 15 q^{71} + 13 q^{72} - 9 q^{73} - 36 q^{74} - 2 q^{75} + 8 q^{76} + 6 q^{78} + 6 q^{79} + 5 q^{80} - 20 q^{81} - 44 q^{82} + 15 q^{83} - 47 q^{84} + 3 q^{85} - 3 q^{86} + 15 q^{87} + 2 q^{90} + 4 q^{91} + 18 q^{92} + 21 q^{93} - 11 q^{94} + 12 q^{95} - 26 q^{96} + 6 q^{97} - 42 q^{98}+O(q^{100}) \) 4 * q + 3 * q^2 - 2 * q^3 + 7 * q^4 + 4 * q^5 - q^6 + 11 * q^7 + 9 * q^8 + 3 * q^10 - 14 * q^12 + 7 * q^13 - 2 * q^14 - 2 * q^15 + 5 * q^16 + 3 * q^17 + 2 * q^18 + 12 * q^19 + 7 * q^20 - 6 * q^21 - 9 * q^23 - 15 * q^24 + 4 * q^25 + 13 * q^26 - 5 * q^27 + 7 * q^28 - 8 * q^29 - q^30 + 3 * q^31 + 6 * q^32 - 10 * q^34 + 11 * q^35 + 8 * q^36 - 3 * q^37 + 12 * q^38 - 3 * q^39 + 9 * q^40 - 7 * q^41 + 2 * q^42 + 21 * q^43 + 12 * q^46 - 3 * q^47 - 2 * q^48 + 15 * q^49 + 3 * q^50 + 9 * q^51 + 27 * q^52 - 11 * q^53 - 20 * q^54 + 15 * q^56 + 5 * q^57 + 2 * q^58 - 7 * q^59 - 14 * q^60 + 4 * q^61 + 11 * q^62 + 3 * q^63 - 27 * q^64 + 7 * q^65 - q^67 - 15 * q^68 - 28 * q^69 - 2 * q^70 - 15 * q^71 + 13 * q^72 - 9 * q^73 - 36 * q^74 - 2 * q^75 + 8 * q^76 + 6 * q^78 + 6 * q^79 + 5 * q^80 - 20 * q^81 - 44 * q^82 + 15 * q^83 - 47 * q^84 + 3 * q^85 - 3 * q^86 + 15 * q^87 + 2 * q^90 + 4 * q^91 + 18 * q^92 + 21 * q^93 - 11 * q^94 + 12 * q^95 - 26 * q^96 + 6 * q^97 - 42 * q^98

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