LMFDB - Embedded newform 605.2.a.i.1.3

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:	$1$
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			1.3
Root			$-1.46673$ 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	$-0.510525\pi$
$2$	−0.0935099	−0.0661215	−0.0330607	+	0.999453i	$0.510525\pi$
$3$	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	$-0.826477\pi$
$7$	−4.52452	−1.71011	−0.855055	+	0.518538i	$0.826477\pi$
$8$	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	$-0.449352\pi$
$13$	1.14256	0.316889	0.158444	+	0.987368i	$0.449352\pi$
$14$	0.423088	0.113075
$15$	1.46673	0.378709
$16$	3.94761	0.986903
$17$	−3.37322	−0.818126	−0.409063	−	0.912506i	$-0.634144\pi$
$17$	−3.37322	−0.818126	−0.409063	+	0.912506i	$0.634144\pi$
$18$	0.0793616	0.0187057
$19$	−6.08477	−1.39594	−0.697971	−	0.716127i	$-0.745913\pi$
$19$	−6.08477	−1.39594	−0.697971	+	0.716127i	$0.745913\pi$
$20$	−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	$-0.599771\pi$
$29$	−3.32083	−0.616663	−0.308332	+	0.951279i	$0.599771\pi$
$30$	−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	$-0.456434\pi$
$41$	1.74726	0.272876	0.136438	+	0.990649i	$0.456434\pi$
$42$	0.620556	0.0957539
$43$	0.263041	0.0401134	0.0200567	−	0.999799i	$-0.493615\pi$
$43$	0.263041	0.0401134	0.0200567	+	0.999799i	$0.493615\pi$
$44$	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	$-0.551215\pi$
$61$	−2.50245	−0.320406	−0.160203	+	0.987084i	$0.551215\pi$
$62$	−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	$-0.392118\pi$
$73$	5.68123	0.664938	0.332469	+	0.943114i	$0.392118\pi$
$74$	−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	$-0.280644\pi$
$79$	11.3033	1.27173	0.635863	+	0.771802i	$0.280644\pi$
$80$	3.94761	0.441356
$81$	−5.73362	−0.637069
$82$	−0.163386	−0.0180430
$83$	−4.48088	−0.491840	−0.245920	−	0.969290i	$-0.579090\pi$
$83$	−4.48088	−0.491840	−0.245920	+	0.969290i	$0.579090\pi$
$84$	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	$-0.346258\pi$
$101$	9.33498	0.928865	0.464433	+	0.885608i	$0.346258\pi$
$102$	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	$-0.198655\pi$
$107$	16.7883	1.62299	0.811493	+	0.584362i	$0.198655\pi$
$108$	11.2407	1.08163
$109$	3.65293	0.349888	0.174944	−	0.984578i	$-0.444026\pi$
$109$	3.65293	0.349888	0.174944	+	0.984578i	$0.444026\pi$
$110$	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	$-0.840344\pi$
$127$	−19.7627	−1.75365	−0.876826	+	0.480808i	$0.840344\pi$
$128$	2.95970	0.261603
$129$	0.385811	0.0339688
$130$	−0.106840	−0.00937053
$131$	1.93479	0.169043	0.0845215	−	0.996422i	$-0.473064\pi$
$131$	1.93479	0.169043	0.0845215	+	0.996422i	$0.473064\pi$
$132$	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	$-0.341762\pi$
$139$	11.2450	0.953793	0.476896	+	0.878960i	$0.341762\pi$
$140$	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	$-0.248688\pi$
$149$	17.3337	1.42003	0.710014	+	0.704187i	$0.248688\pi$
$150$	−0.137154	−0.0111986
$151$	0.00540415	0.000439784 0	0.000219892	−	1.00000i	$-0.499930\pi$
$151$	0.00540415	0.000439784 0	0.000219892		1.00000i	$0.499930\pi$
$152$	−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	$-0.542324\pi$
$167$	−3.42643	−0.265145	−0.132572	+	0.991173i	$0.542324\pi$
$168$	−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	$-0.785717\pi$
$173$	−20.5669	−1.56367	−0.781836	+	0.623484i	$0.785717\pi$
$174$	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	$-0.690988\pi$
$193$	−15.6887	−1.12929	−0.564647	+	0.825333i	$0.690988\pi$
$194$	0.313871	0.0225346
$195$	1.67583	0.120008
$196$	−26.8248	−1.91606
$197$	21.8486	1.55665	0.778325	−	0.627862i	$-0.216070\pi$
$197$	21.8486	1.55665	0.778325	+	0.627862i	$0.216070\pi$
$198$	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	$-0.726341\pi$
$211$	−18.9604	−1.30529	−0.652645	+	0.757664i	$0.726341\pi$
$212$	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	$-0.682216\pi$
$227$	−16.3229	−1.08339	−0.541693	+	0.840577i	$0.682216\pi$
$228$	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	$-0.411058\pi$
$233$	8.41975	0.551596	0.275798	+	0.961216i	$0.411058\pi$
$234$	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	$-0.237681\pi$
$239$	22.6928	1.46787	0.733937	+	0.679218i	$0.237681\pi$
$240$	5.79009	0.373749
$241$	−11.6065	−0.747638	−0.373819	−	0.927502i	$-0.621952\pi$
$241$	−11.6065	−0.747638	−0.373819	+	0.927502i	$0.621952\pi$
$242$	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	$-0.622413\pi$
$263$	−12.1682	−0.750324	−0.375162	+	0.926959i	$0.622413\pi$
$264$	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	$-0.652125\pi$
$271$	−15.1428	−0.919859	−0.459930	+	0.887955i	$0.652125\pi$
$272$	−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	$-0.579927\pi$
$277$	−8.27066	−0.496936	−0.248468	+	0.968640i	$0.579927\pi$
$278$	−1.05152	−0.0630662
$279$	−1.51994	−0.0909963
$280$	−1.68865	−0.100916
$281$	−2.44723	−0.145989	−0.0729947	−	0.997332i	$-0.523256\pi$
$281$	−2.44723	−0.145989	−0.0729947	+	0.997332i	$0.523256\pi$
$282$	−0.949753	−0.0565569
$283$	−26.0948	−1.55117	−0.775586	−	0.631242i	$-0.782546\pi$
$283$	−26.0948	−1.55117	−0.775586	+	0.631242i	$0.782546\pi$
$284$	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	$-0.628551\pi$
$293$	−13.4529	−0.785929	−0.392965	+	0.919554i	$0.628551\pi$
$294$	−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	$-0.782627\pi$
$307$	−27.1844	−1.55150	−0.775748	+	0.631042i	$0.782627\pi$
$308$	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	$-0.578886\pi$
$337$	−9.00615	−0.490596	−0.245298	+	0.969448i	$0.578886\pi$
$338$	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	$-0.588905\pi$
$347$	−10.2710	−0.551374	−0.275687	+	0.961247i	$0.588905\pi$
$348$	9.69895	0.519919
$349$	−17.2613	−0.923974	−0.461987	−	0.886887i	$-0.652863\pi$
$349$	−17.2613	−0.923974	−0.461987	+	0.886887i	$0.652863\pi$
$350$	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	$-0.360557\pi$
$359$	16.0747	0.848390	0.424195	+	0.905571i	$0.360557\pi$
$360$	−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	$-0.324244\pi$
$373$	20.2604	1.04905	0.524523	+	0.851396i	$0.324244\pi$
$374$	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	$-0.760237\pi$
$409$	−29.5056	−1.45896	−0.729478	+	0.684004i	$0.760237\pi$
$410$	−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	$-0.486722\pi$
$431$	1.73155	0.0834060	0.0417030	+	0.999130i	$0.486722\pi$
$432$	−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	$-0.365616\pi$
$439$	17.1704	0.819499	0.409750	+	0.912198i	$0.365616\pi$
$440$	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	$-0.234532\pi$
$457$	31.6653	1.48124	0.740620	+	0.671924i	$0.234532\pi$
$458$	0.451809	0.0211116
$459$	19.0419	0.888798
$460$	10.8575	0.506233
$461$	25.4351	1.18463	0.592315	−	0.805706i	$-0.298214\pi$
$461$	25.4351	1.18463	0.592315	+	0.805706i	$0.298214\pi$
$462$	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	$-0.739838\pi$
$479$	−29.9478	−1.36835	−0.684175	+	0.729318i	$0.739838\pi$
$480$	−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	$-0.384046\pi$
$491$	15.7891	0.712553	0.356277	+	0.934381i	$0.384046\pi$
$492$	−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	$-0.497567\pi$
$503$	0.342908	0.0152895	0.00764477	+	0.999971i	$0.497567\pi$
$504$	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	$-0.727810\pi$
$523$	−30.0105	−1.31227	−0.656135	+	0.754644i	$0.727810\pi$
$524$	−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	$-0.428767\pi$
$541$	10.3236	0.443846	0.221923	+	0.975064i	$0.428767\pi$
$542$	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	$-0.852098\pi$
$547$	−41.8168	−1.78796	−0.893979	+	0.448108i	$0.852098\pi$
$548$	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	$-0.196580\pi$
$557$	38.4828	1.63057	0.815285	+	0.579060i	$0.196580\pi$
$558$	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	$-0.723826\pi$
$563$	−30.6864	−1.29328	−0.646639	+	0.762796i	$0.723826\pi$
$564$	−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	$-0.588185\pi$
$569$	−13.0485	−0.547020	−0.273510	+	0.961869i	$0.588185\pi$
$570$	0.834550	0.0349554
$571$	−16.1300	−0.675018	−0.337509	−	0.941322i	$-0.609584\pi$
$571$	−16.1300	−0.675018	−0.337509	+	0.941322i	$0.609584\pi$
$572$	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	$-0.600369\pi$
$593$	−15.1037	−0.620236	−0.310118	+	0.950698i	$0.600369\pi$
$594$	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	$-0.0913160\pi$
$601$	47.0268	1.91826	0.959132	+	0.282959i	$0.0913160\pi$
$602$	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	$-0.246496\pi$
$607$	35.2239	1.42969	0.714847	+	0.699281i	$0.246496\pi$
$608$	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	$-0.343245\pi$
$613$	23.4117	0.945590	0.472795	+	0.881173i	$0.343245\pi$
$614$	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	$-0.265490\pi$
$659$	34.4953	1.34375	0.671873	+	0.740666i	$0.265490\pi$
$660$	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	$-0.621297\pi$
$673$	−19.2964	−0.743823	−0.371911	+	0.928268i	$0.621297\pi$
$674$	0.842164	0.0324389
$675$	−5.64501	−0.217276
$676$	23.2869	0.895649
$677$	16.9101	0.649907	0.324953	−	0.945730i	$-0.394651\pi$
$677$	16.9101	0.649907	0.324953	+	0.945730i	$0.394651\pi$
$678$	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	$-0.171452\pi$
$701$	45.4553	1.71682	0.858412	+	0.512961i	$0.171452\pi$
$702$	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	$-0.260557\pi$
$733$	36.9977	1.36654	0.683270	+	0.730166i	$0.260557\pi$
$734$	−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	$-0.557990\pi$
$739$	−9.85033	−0.362350	−0.181175	+	0.983451i	$0.557990\pi$
$740$	−2.96459	−0.108981
$741$	−10.1970	−0.374597
$742$	−0.609144	−0.0223624
$743$	−27.4471	−1.00694	−0.503468	−	0.864014i	$-0.667943\pi$
$743$	−27.4471	−1.00694	−0.503468	+	0.864014i	$0.667943\pi$
$744$	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	$-0.377692\pi$
$761$	20.6818	0.749716	0.374858	+	0.927082i	$0.377692\pi$
$762$	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	$-0.743677\pi$
$769$	−38.4306	−1.38584	−0.692922	+	0.721013i	$0.743677\pi$
$770$	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	$-0.410587\pi$
$787$	15.5540	0.554440	0.277220	+	0.960806i	$0.410587\pi$
$788$	−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	$-0.270596\pi$
$809$	37.5394	1.31981	0.659907	+	0.751347i	$0.270596\pi$
$810$	0.536150	0.0188384
$811$	−7.20547	−0.253018	−0.126509	−	0.991965i	$-0.540377\pi$
$811$	−7.20547	−0.253018	−0.126509	+	0.991965i	$0.540377\pi$
$812$	−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	$-0.451858\pi$
$821$	8.63405	0.301331	0.150665	+	0.988585i	$0.451858\pi$
$822$	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	$-0.823236\pi$
$827$	−48.8725	−1.69946	−0.849732	+	0.527216i	$0.823236\pi$
$828$	−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	$-0.512094\pi$
$853$	−2.21885	−0.0759720	−0.0379860	+	0.999278i	$0.512094\pi$
$854$	−1.05876	−0.0362299
$855$	5.16413	0.176609
$856$	6.26576	0.214159
$857$	−31.4625	−1.07474	−0.537368	−	0.843348i	$-0.680582\pi$
$857$	−31.4625	−1.07474	−0.537368	+	0.843348i	$0.680582\pi$
$858$	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	$-0.322704\pi$
$877$	31.3101	1.05727	0.528634	+	0.848850i	$0.322704\pi$
$878$	−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	$-0.420921\pi$
$887$	14.6462	0.491771	0.245886	+	0.969299i	$0.420921\pi$
$888$	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	$-0.488456\pi$
$919$	2.19845	0.0725203	0.0362601	+	0.999342i	$0.488456\pi$
$920$	−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	$-0.389531\pi$
$937$	20.8227	0.680249	0.340125	+	0.940380i	$0.389531\pi$
$938$	−0.218566	−0.00713644
$939$	23.7199	0.774068
$940$	−13.7889	−0.449744
$941$	−34.2128	−1.11530	−0.557652	−	0.830075i	$-0.688298\pi$
$941$	−34.2128	−1.11530	−0.557652	+	0.830075i	$0.688298\pi$
$942$	−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	$-0.636080\pi$
$953$	−25.5982	−0.829206	−0.414603	+	0.910002i	$0.636080\pi$
$954$	−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	$-0.749400\pi$
$967$	−43.8942	−1.41154	−0.705772	+	0.708439i	$0.749400\pi$
$968$	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	$-0.554661\pi$
$997$	−10.7911	−0.341759	−0.170879	+	0.985292i	$0.554661\pi$
$998$	−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.i.1.3		4
3.2	odd	2		5445.2.a.bu.1.2		4
4.3	odd	2		9680.2.a.cv.1.1		4
5.4	even	2		3025.2.a.be.1.2		4
11.2	odd	10		55.2.g.a.26.2	✓	8
11.3	even	5		605.2.g.g.251.2		8
11.4	even	5		605.2.g.g.511.2		8
11.5	even	5		605.2.g.n.366.1		8
11.6	odd	10		55.2.g.a.36.2	yes	8
11.7	odd	10		605.2.g.j.511.1		8
11.8	odd	10		605.2.g.j.251.1		8
11.9	even	5		605.2.g.n.81.1		8
11.10	odd	2		605.2.a.l.1.2		4
33.2	even	10		495.2.n.f.136.1		8
33.17	even	10		495.2.n.f.91.1		8
33.32	even	2		5445.2.a.bg.1.3		4
44.35	even	10		880.2.bo.e.81.1		8
44.39	even	10		880.2.bo.e.641.1		8
44.43	even	2		9680.2.a.cs.1.1		4
55.2	even	20		275.2.z.b.224.3		16
55.13	even	20		275.2.z.b.224.2		16
55.17	even	20		275.2.z.b.124.2		16
55.24	odd	10		275.2.h.b.26.1		8
55.28	even	20		275.2.z.b.124.3		16
55.39	odd	10		275.2.h.b.201.1		8
55.54	odd	2		3025.2.a.v.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
55.2.g.a.26.2	✓	8	11.2	odd	10
55.2.g.a.36.2	yes	8	11.6	odd	10
275.2.h.b.26.1		8	55.24	odd	10
275.2.h.b.201.1		8	55.39	odd	10
275.2.z.b.124.2		16	55.17	even	20
275.2.z.b.124.3		16	55.28	even	20
275.2.z.b.224.2		16	55.13	even	20
275.2.z.b.224.3		16	55.2	even	20
495.2.n.f.91.1		8	33.17	even	10
495.2.n.f.136.1		8	33.2	even	10
605.2.a.i.1.3		4	1.1	even	1	trivial
605.2.a.l.1.2		4	11.10	odd	2
605.2.g.g.251.2		8	11.3	even	5
605.2.g.g.511.2		8	11.4	even	5
605.2.g.j.251.1		8	11.8	odd	10
605.2.g.j.511.1		8	11.7	odd	10
605.2.g.n.81.1		8	11.9	even	5
605.2.g.n.366.1		8	11.5	even	5
880.2.bo.e.81.1		8	44.35	even	10
880.2.bo.e.641.1		8	44.39	even	10
3025.2.a.v.1.3		4	55.54	odd	2
3025.2.a.be.1.2		4	5.4	even	2
5445.2.a.bg.1.3		4	33.32	even	2
5445.2.a.bu.1.2		4	3.2	odd	2
9680.2.a.cs.1.1		4	44.43	even	2
9680.2.a.cv.1.1		4	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:	\( N \)	\(=\)	\( 605 = 5 \cdot 11^{2} \)
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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