LMFDB - Embedded newform 6041.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$83$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.27758 q^{2} -1.23058 q^{3} +3.18737 q^{4} +1.22240 q^{5} +2.80274 q^{6} +1.00000 q^{7} -2.70432 q^{8} -1.48568 q^{9} +O(q^{10})$	\(q-2.27758 q^{2} -1.23058 q^{3} +3.18737 q^{4} +1.22240 q^{5} +2.80274 q^{6} +1.00000 q^{7} -2.70432 q^{8} -1.48568 q^{9} -2.78412 q^{10} +0.873356 q^{11} -3.92231 q^{12} -5.86324 q^{13} -2.27758 q^{14} -1.50426 q^{15} -0.215427 q^{16} -3.91368 q^{17} +3.38374 q^{18} +4.09759 q^{19} +3.89625 q^{20} -1.23058 q^{21} -1.98914 q^{22} -2.51197 q^{23} +3.32788 q^{24} -3.50573 q^{25} +13.3540 q^{26} +5.51998 q^{27} +3.18737 q^{28} -1.59718 q^{29} +3.42608 q^{30} +1.39230 q^{31} +5.89929 q^{32} -1.07473 q^{33} +8.91372 q^{34} +1.22240 q^{35} -4.73539 q^{36} +6.33954 q^{37} -9.33259 q^{38} +7.21518 q^{39} -3.30577 q^{40} -2.27577 q^{41} +2.80274 q^{42} +4.31941 q^{43} +2.78371 q^{44} -1.81609 q^{45} +5.72120 q^{46} +10.6673 q^{47} +0.265099 q^{48} +1.00000 q^{49} +7.98458 q^{50} +4.81610 q^{51} -18.6883 q^{52} +2.43009 q^{53} -12.5722 q^{54} +1.06759 q^{55} -2.70432 q^{56} -5.04241 q^{57} +3.63770 q^{58} +4.81405 q^{59} -4.79464 q^{60} -2.55191 q^{61} -3.17107 q^{62} -1.48568 q^{63} -13.0053 q^{64} -7.16725 q^{65} +2.44779 q^{66} +6.66805 q^{67} -12.4743 q^{68} +3.09117 q^{69} -2.78412 q^{70} +9.16045 q^{71} +4.01774 q^{72} +5.28564 q^{73} -14.4388 q^{74} +4.31408 q^{75} +13.0605 q^{76} +0.873356 q^{77} -16.4332 q^{78} -2.00154 q^{79} -0.263338 q^{80} -2.33574 q^{81} +5.18324 q^{82} +6.51767 q^{83} -3.92231 q^{84} -4.78410 q^{85} -9.83780 q^{86} +1.96546 q^{87} -2.36183 q^{88} -18.4036 q^{89} +4.13630 q^{90} -5.86324 q^{91} -8.00656 q^{92} -1.71333 q^{93} -24.2957 q^{94} +5.00891 q^{95} -7.25955 q^{96} +7.92583 q^{97} -2.27758 q^{98} -1.29752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) $ 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.27758	−1.61049	−0.805246	−	0.592941i	$-0.797967\pi$
$2$	−2.27758	−1.61049	−0.805246	+	0.592941i	$0.797967\pi$
$3$	−1.23058	−0.710475	−0.355238	−	0.934776i	$-0.615600\pi$
$3$	−1.23058	−0.710475	−0.355238	+	0.934776i	$0.615600\pi$
$4$	3.18737	1.59368
$5$	1.22240	0.546675	0.273338	−	0.961918i	$-0.411872\pi$
$5$	1.22240	0.546675	0.273338	+	0.961918i	$0.411872\pi$
$6$	2.80274	1.14421
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−2.70432	−0.956122
$9$	−1.48568	−0.495225
$10$	−2.78412	−0.880416
$11$	0.873356	0.263327	0.131663	−	0.991294i	$-0.457968\pi$
$11$	0.873356	0.263327	0.131663	+	0.991294i	$0.457968\pi$
$12$	−3.92231	−1.13227
$13$	−5.86324	−1.62617	−0.813086	−	0.582144i	$-0.802214\pi$
$13$	−5.86324	−1.62617	−0.813086	+	0.582144i	$0.802214\pi$
$14$	−2.27758	−0.608709
$15$	−1.50426	−0.388399
$16$	−0.215427	−0.0538566
$17$	−3.91368	−0.949208	−0.474604	−	0.880200i	$-0.657409\pi$
$17$	−3.91368	−0.949208	−0.474604	+	0.880200i	$0.657409\pi$
$18$	3.38374	0.797556
$19$	4.09759	0.940052	0.470026	−	0.882653i	$-0.344245\pi$
$19$	4.09759	0.940052	0.470026	+	0.882653i	$0.344245\pi$
$20$	3.89625	0.871227
$21$	−1.23058	−0.268534
$22$	−1.98914	−0.424085
$23$	−2.51197	−0.523781	−0.261891	−	0.965098i	$-0.584346\pi$
$23$	−2.51197	−0.523781	−0.261891	+	0.965098i	$0.584346\pi$
$24$	3.32788	0.679301
$25$	−3.50573	−0.701146
$26$	13.3540	2.61894
$27$	5.51998	1.06232
$28$	3.18737	0.602356
$29$	−1.59718	−0.296589	−0.148294	−	0.988943i	$-0.547378\pi$
$29$	−1.59718	−0.296589	−0.148294	+	0.988943i	$0.547378\pi$
$30$	3.42608	0.625514
$31$	1.39230	0.250064	0.125032	−	0.992153i	$-0.460097\pi$
$31$	1.39230	0.250064	0.125032	+	0.992153i	$0.460097\pi$
$32$	5.89929	1.04286
$33$	−1.07473	−0.187087
$34$	8.91372	1.52869
$35$	1.22240	0.206624
$36$	−4.73539	−0.789232
$37$	6.33954	1.04221	0.521107	−	0.853491i	$-0.325519\pi$
$37$	6.33954	1.04221	0.521107	+	0.853491i	$0.325519\pi$
$38$	−9.33259	−1.51395
$39$	7.21518	1.15535
$40$	−3.30577	−0.522688
$41$	−2.27577	−0.355415	−0.177708	−	0.984083i	$-0.556868\pi$
$41$	−2.27577	−0.355415	−0.177708	+	0.984083i	$0.556868\pi$
$42$	2.80274	0.432472
$43$	4.31941	0.658704	0.329352	−	0.944207i	$-0.393170\pi$
$43$	4.31941	0.658704	0.329352	+	0.944207i	$0.393170\pi$
$44$	2.78371	0.419659
$45$	−1.81609	−0.270727
$46$	5.72120	0.843546
$47$	10.6673	1.55599	0.777994	−	0.628272i	$-0.216237\pi$
$47$	10.6673	1.55599	0.777994	+	0.628272i	$0.216237\pi$
$48$	0.265099	0.0382638
$49$	1.00000	0.142857
$50$	7.98458	1.12919
$51$	4.81610	0.674388
$52$	−18.6883	−2.59160
$53$	2.43009	0.333798	0.166899	−	0.985974i	$-0.446625\pi$
$53$	2.43009	0.333798	0.166899	+	0.985974i	$0.446625\pi$
$54$	−12.5722	−1.71086
$55$	1.06759	0.143954
$56$	−2.70432	−0.361380
$57$	−5.04241	−0.667884
$58$	3.63770	0.477654
$59$	4.81405	0.626736	0.313368	−	0.949632i	$-0.398543\pi$
$59$	4.81405	0.626736	0.313368	+	0.949632i	$0.398543\pi$
$60$	−4.79464	−0.618985
$61$	−2.55191	−0.326739	−0.163369	−	0.986565i	$-0.552236\pi$
$61$	−2.55191	−0.326739	−0.163369	+	0.986565i	$0.552236\pi$
$62$	−3.17107	−0.402726
$63$	−1.48568	−0.187177
$64$	−13.0053	−1.62566
$65$	−7.16725	−0.888988
$66$	2.44779	0.301302
$67$	6.66805	0.814632	0.407316	−	0.913287i	$-0.366465\pi$
$67$	6.66805	0.814632	0.407316	+	0.913287i	$0.366465\pi$
$68$	−12.4743	−1.51274
$69$	3.09117	0.372134
$70$	−2.78412	−0.332766
$71$	9.16045	1.08715	0.543573	−	0.839362i	$-0.317071\pi$
$71$	9.16045	1.08715	0.543573	+	0.839362i	$0.317071\pi$
$72$	4.01774	0.473496
$73$	5.28564	0.618637	0.309319	−	0.950958i	$-0.399899\pi$
$73$	5.28564	0.618637	0.309319	+	0.950958i	$0.399899\pi$
$74$	−14.4388	−1.67848
$75$	4.31408	0.498147
$76$	13.0605	1.49815
$77$	0.873356	0.0995281
$78$	−16.4332	−1.86069
$79$	−2.00154	−0.225191	−0.112595	−	0.993641i	$-0.535916\pi$
$79$	−2.00154	−0.225191	−0.112595	+	0.993641i	$0.535916\pi$
$80$	−0.263338	−0.0294421
$81$	−2.33574	−0.259527
$82$	5.18324	0.572393
$83$	6.51767	0.715407	0.357703	−	0.933835i	$-0.383560\pi$
$83$	6.51767	0.715407	0.357703	+	0.933835i	$0.383560\pi$
$84$	−3.92231	−0.427959
$85$	−4.78410	−0.518908
$86$	−9.83780	−1.06084
$87$	1.96546	0.210719
$88$	−2.36183	−0.251772
$89$	−18.4036	−1.95077	−0.975386	−	0.220503i	$-0.929230\pi$
$89$	−18.4036	−1.95077	−0.975386	+	0.220503i	$0.929230\pi$
$90$	4.13630	0.436004
$91$	−5.86324	−0.614635
$92$	−8.00656	−0.834742
$93$	−1.71333	−0.177664
$94$	−24.2957	−2.50591
$95$	5.00891	0.513903
$96$	−7.25955	−0.740925
$97$	7.92583	0.804746	0.402373	−	0.915476i	$-0.368186\pi$
$97$	7.92583	0.804746	0.402373	+	0.915476i	$0.368186\pi$
$98$	−2.27758	−0.230070
$99$	−1.29752	−0.130406
$100$	−11.1740	−1.11740
$101$	−3.73127	−0.371275	−0.185638	−	0.982618i	$-0.559435\pi$
$101$	−3.73127	−0.371275	−0.185638	+	0.982618i	$0.559435\pi$
$102$	−10.9690	−1.08610
$103$	−6.61857	−0.652147	−0.326073	−	0.945344i	$-0.605726\pi$
$103$	−6.61857	−0.652147	−0.326073	+	0.945344i	$0.605726\pi$
$104$	15.8561	1.55482
$105$	−1.50426	−0.146801
$106$	−5.53472	−0.537580
$107$	15.7755	1.52507	0.762536	−	0.646946i	$-0.223954\pi$
$107$	15.7755	1.52507	0.762536	+	0.646946i	$0.223954\pi$
$108$	17.5942	1.69300
$109$	−15.8178	−1.51507	−0.757537	−	0.652792i	$-0.773598\pi$
$109$	−15.8178	−1.51507	−0.757537	+	0.652792i	$0.773598\pi$
$110$	−2.43153	−0.231837
$111$	−7.80130	−0.740467
$112$	−0.215427	−0.0203559
$113$	−15.1420	−1.42444	−0.712219	−	0.701958i	$-0.752310\pi$
$113$	−15.1420	−1.42444	−0.712219	+	0.701958i	$0.752310\pi$
$114$	11.4845	1.07562
$115$	−3.07064	−0.286338
$116$	−5.09080	−0.472669
$117$	8.71088	0.805321
$118$	−10.9644	−1.00935
$119$	−3.91368	−0.358767
$120$	4.06801	0.371357
$121$	−10.2372	−0.930659
$122$	5.81218	0.526210
$123$	2.80051	0.252514
$124$	4.43776	0.398523
$125$	−10.3974	−0.929975
$126$	3.38374	0.301448
$127$	−7.29394	−0.647233	−0.323616	−	0.946188i	$-0.604899\pi$
$127$	−7.29394	−0.647233	−0.323616	+	0.946188i	$0.604899\pi$
$128$	17.8219	1.57525
$129$	−5.31538	−0.467993
$130$	16.3240	1.43171
$131$	11.0772	0.967817	0.483909	−	0.875119i	$-0.339217\pi$
$131$	11.0772	0.967817	0.483909	+	0.875119i	$0.339217\pi$
$132$	−3.42557	−0.298158
$133$	4.09759	0.355306
$134$	−15.1870	−1.31196
$135$	6.74764	0.580744
$136$	10.5839	0.907558
$137$	11.3720	0.971572	0.485786	−	0.874078i	$-0.338533\pi$
$137$	11.3720	0.971572	0.485786	+	0.874078i	$0.338533\pi$
$138$	−7.04039	−0.599318
$139$	−4.09187	−0.347068	−0.173534	−	0.984828i	$-0.555519\pi$
$139$	−4.09187	−0.347068	−0.173534	+	0.984828i	$0.555519\pi$
$140$	3.89625	0.329293
$141$	−13.1270	−1.10549
$142$	−20.8636	−1.75084
$143$	−5.12070	−0.428214
$144$	0.320054	0.0266712
$145$	−1.95240	−0.162138
$146$	−12.0385	−0.996310
$147$	−1.23058	−0.101496
$148$	20.2064	1.66096
$149$	−16.4171	−1.34494	−0.672471	−	0.740124i	$-0.734767\pi$
$149$	−16.4171	−1.34494	−0.672471	+	0.740124i	$0.734767\pi$
$150$	−9.82566	−0.802261
$151$	10.7178	0.872202	0.436101	−	0.899898i	$-0.356359\pi$
$151$	10.7178	0.872202	0.436101	+	0.899898i	$0.356359\pi$
$152$	−11.0812	−0.898805
$153$	5.81446	0.470071
$154$	−1.98914	−0.160289
$155$	1.70195	0.136704
$156$	22.9974	1.84127
$157$	−9.32763	−0.744426	−0.372213	−	0.928147i	$-0.621401\pi$
$157$	−9.32763	−0.744426	−0.372213	+	0.928147i	$0.621401\pi$
$158$	4.55867	0.362668
$159$	−2.99042	−0.237156
$160$	7.21132	0.570105
$161$	−2.51197	−0.197971
$162$	5.31984	0.417966
$163$	−15.1500	−1.18664	−0.593319	−	0.804968i	$-0.702183\pi$
$163$	−15.1500	−1.18664	−0.593319	+	0.804968i	$0.702183\pi$
$164$	−7.25371	−0.566419
$165$	−1.31376	−0.102276
$166$	−14.8445	−1.15216
$167$	23.3969	1.81051	0.905255	−	0.424869i	$-0.139680\pi$
$167$	23.3969	1.81051	0.905255	+	0.424869i	$0.139680\pi$
$168$	3.32788	0.256752
$169$	21.3776	1.64443
$170$	10.8962	0.835698
$171$	−6.08769	−0.465537
$172$	13.7676	1.04977
$173$	−12.7194	−0.967041	−0.483520	−	0.875333i	$-0.660642\pi$
$173$	−12.7194	−0.967041	−0.483520	+	0.875333i	$0.660642\pi$
$174$	−4.47648	−0.339361
$175$	−3.50573	−0.265008
$176$	−0.188144	−0.0141819
$177$	−5.92407	−0.445280
$178$	41.9155	3.14170
$179$	−4.19852	−0.313812	−0.156906	−	0.987614i	$-0.550152\pi$
$179$	−4.19852	−0.313812	−0.156906	+	0.987614i	$0.550152\pi$
$180$	−5.78856	−0.431454
$181$	7.65556	0.569033	0.284517	−	0.958671i	$-0.408167\pi$
$181$	7.65556	0.569033	0.284517	+	0.958671i	$0.408167\pi$
$182$	13.3540	0.989864
$183$	3.14033	0.232140
$184$	6.79317	0.500799
$185$	7.74947	0.569752
$186$	3.90225	0.286127
$187$	−3.41804	−0.249952
$188$	34.0006	2.47975
$189$	5.51998	0.401519
$190$	−11.4082	−0.827637
$191$	−6.37198	−0.461061	−0.230530	−	0.973065i	$-0.574046\pi$
$191$	−6.37198	−0.461061	−0.230530	+	0.973065i	$0.574046\pi$
$192$	16.0040	1.15499
$193$	22.7225	1.63560	0.817800	−	0.575502i	$-0.195193\pi$
$193$	22.7225	1.63560	0.817800	+	0.575502i	$0.195193\pi$
$194$	−18.0517	−1.29604
$195$	8.81986	0.631604
$196$	3.18737	0.227669
$197$	−9.86067	−0.702544	−0.351272	−	0.936274i	$-0.614251\pi$
$197$	−9.86067	−0.702544	−0.351272	+	0.936274i	$0.614251\pi$
$198$	2.95521	0.210018
$199$	2.50281	0.177419	0.0887096	−	0.996058i	$-0.471726\pi$
$199$	2.50281	0.177419	0.0887096	+	0.996058i	$0.471726\pi$
$200$	9.48062	0.670381
$201$	−8.20556	−0.578776
$202$	8.49826	0.597936
$203$	−1.59718	−0.112100
$204$	15.3507	1.07476
$205$	−2.78191	−0.194297
$206$	15.0743	1.05028
$207$	3.73197	0.259390
$208$	1.26310	0.0875801
$209$	3.57866	0.247541
$210$	3.42608	0.236422
$211$	−23.6463	−1.62788	−0.813941	−	0.580948i	$-0.802682\pi$
$211$	−23.6463	−1.62788	−0.813941	+	0.580948i	$0.802682\pi$
$212$	7.74559	0.531969
$213$	−11.2727	−0.772390
$214$	−35.9299	−2.45611
$215$	5.28006	0.360097
$216$	−14.9278	−1.01571
$217$	1.39230	0.0945154
$218$	36.0264	2.44002
$219$	−6.50440	−0.439526
$220$	3.40281	0.229417
$221$	22.9469	1.54357
$222$	17.7681	1.19252
$223$	−25.4462	−1.70400	−0.852002	−	0.523539i	$-0.824611\pi$
$223$	−25.4462	−1.70400	−0.852002	+	0.523539i	$0.824611\pi$
$224$	5.89929	0.394163
$225$	5.20838	0.347225
$226$	34.4870	2.29404
$227$	−18.0467	−1.19780	−0.598902	−	0.800823i	$-0.704396\pi$
$227$	−18.0467	−1.19780	−0.598902	+	0.800823i	$0.704396\pi$
$228$	−16.0720	−1.06440
$229$	−7.75880	−0.512716	−0.256358	−	0.966582i	$-0.582523\pi$
$229$	−7.75880	−0.512716	−0.256358	+	0.966582i	$0.582523\pi$
$230$	6.99362	0.461146
$231$	−1.07473	−0.0707123
$232$	4.31929	0.283575
$233$	20.1460	1.31981	0.659906	−	0.751348i	$-0.270596\pi$
$233$	20.1460	1.31981	0.659906	+	0.751348i	$0.270596\pi$
$234$	−19.8397	−1.29696
$235$	13.0398	0.850620
$236$	15.3441	0.998818
$237$	2.46305	0.159993
$238$	8.91372	0.577791
$239$	6.71703	0.434488	0.217244	−	0.976117i	$-0.430293\pi$
$239$	6.71703	0.434488	0.217244	+	0.976117i	$0.430293\pi$
$240$	0.324058	0.0209179
$241$	−8.14488	−0.524658	−0.262329	−	0.964979i	$-0.584491\pi$
$241$	−8.14488	−0.524658	−0.262329	+	0.964979i	$0.584491\pi$
$242$	23.3161	1.49882
$243$	−13.6856	−0.877933
$244$	−8.13388	−0.520718
$245$	1.22240	0.0780965
$246$	−6.37839	−0.406671
$247$	−24.0252	−1.52869
$248$	−3.76522	−0.239092
$249$	−8.02050	−0.508279
$250$	23.6810	1.49772
$251$	−27.9863	−1.76648	−0.883241	−	0.468919i	$-0.844644\pi$
$251$	−27.9863	−1.76648	−0.883241	+	0.468919i	$0.844644\pi$
$252$	−4.73539	−0.298302
$253$	−2.19384	−0.137926
$254$	16.6125	1.04236
$255$	5.88721	0.368672
$256$	−14.5803	−0.911269
$257$	−1.09731	−0.0684482	−0.0342241	−	0.999414i	$-0.510896\pi$
$257$	−1.09731	−0.0684482	−0.0342241	+	0.999414i	$0.510896\pi$
$258$	12.1062	0.753699
$259$	6.33954	0.393920
$260$	−22.8446	−1.41676
$261$	2.37289	0.146878
$262$	−25.2291	−1.55866
$263$	14.8877	0.918014	0.459007	−	0.888433i	$-0.348205\pi$
$263$	14.8877	0.918014	0.459007	+	0.888433i	$0.348205\pi$
$264$	2.90642	0.178878
$265$	2.97055	0.182479
$266$	−9.33259	−0.572218
$267$	22.6470	1.38598
$268$	21.2535	1.29827
$269$	18.2023	1.10981	0.554907	−	0.831912i	$-0.312754\pi$
$269$	18.2023	1.10981	0.554907	+	0.831912i	$0.312754\pi$
$270$	−15.3683	−0.935284
$271$	6.14398	0.373220	0.186610	−	0.982434i	$-0.440250\pi$
$271$	6.14398	0.373220	0.186610	+	0.982434i	$0.440250\pi$
$272$	0.843111	0.0511211
$273$	7.21518	0.436683
$274$	−25.9005	−1.56471
$275$	−3.06175	−0.184630
$276$	9.85271	0.593063
$277$	11.9041	0.715246	0.357623	−	0.933866i	$-0.383587\pi$
$277$	11.9041	0.715246	0.357623	+	0.933866i	$0.383587\pi$
$278$	9.31956	0.558950
$279$	−2.06850	−0.123838
$280$	−3.30577	−0.197558
$281$	10.4422	0.622927	0.311463	−	0.950258i	$-0.399181\pi$
$281$	10.4422	0.622927	0.311463	+	0.950258i	$0.399181\pi$
$282$	29.8977	1.78038
$283$	7.32961	0.435700	0.217850	−	0.975982i	$-0.430096\pi$
$283$	7.32961	0.435700	0.217850	+	0.975982i	$0.430096\pi$
$284$	29.1977	1.73257
$285$	−6.16386	−0.365116
$286$	11.6628	0.689635
$287$	−2.27577	−0.134334
$288$	−8.76444	−0.516449
$289$	−1.68308	−0.0990048
$290$	4.44674	0.261122
$291$	−9.75336	−0.571752
$292$	16.8473	0.985912
$293$	−13.5024	−0.788818	−0.394409	−	0.918935i	$-0.629051\pi$
$293$	−13.5024	−0.788818	−0.394409	+	0.918935i	$0.629051\pi$
$294$	2.80274	0.163459
$295$	5.88471	0.342621
$296$	−17.1442	−0.996484
$297$	4.82090	0.279737
$298$	37.3913	2.16602
$299$	14.7283	0.851758
$300$	13.7506	0.793888
$301$	4.31941	0.248967
$302$	−24.4106	−1.40467
$303$	4.59162	0.263782
$304$	−0.882730	−0.0506281
$305$	−3.11947	−0.178620
$306$	−13.2429	−0.757046
$307$	−1.71580	−0.0979256	−0.0489628	−	0.998801i	$-0.515592\pi$
$307$	−1.71580	−0.0979256	−0.0489628	+	0.998801i	$0.515592\pi$
$308$	2.78371	0.158616
$309$	8.14467	0.463334
$310$	−3.87632	−0.220160
$311$	13.6193	0.772277	0.386138	−	0.922441i	$-0.373809\pi$
$311$	13.6193	0.772277	0.386138	+	0.922441i	$0.373809\pi$
$312$	−19.5122	−1.10466
$313$	30.5099	1.72452	0.862262	−	0.506462i	$-0.169047\pi$
$313$	30.5099	1.72452	0.862262	+	0.506462i	$0.169047\pi$
$314$	21.2444	1.19889
$315$	−1.81609	−0.102325
$316$	−6.37964	−0.358883
$317$	−13.1235	−0.737087	−0.368543	−	0.929611i	$-0.620143\pi$
$317$	−13.1235	−0.737087	−0.368543	+	0.929611i	$0.620143\pi$
$318$	6.81091	0.381937
$319$	−1.39491	−0.0780997
$320$	−15.8977	−0.888707
$321$	−19.4130	−1.08353
$322$	5.72120	0.318830
$323$	−16.0367	−0.892305
$324$	−7.44487	−0.413604
$325$	20.5550	1.14018
$326$	34.5053	1.91107
$327$	19.4651	1.07642
$328$	6.15441	0.339820
$329$	10.6673	0.588108
$330$	2.99219	0.164714
$331$	−25.8432	−1.42047	−0.710234	−	0.703966i	$-0.751411\pi$
$331$	−25.8432	−1.42047	−0.710234	+	0.703966i	$0.751411\pi$
$332$	20.7742	1.14013
$333$	−9.41850	−0.516130
$334$	−53.2884	−2.91581
$335$	8.15105	0.445339
$336$	0.265099	0.0144624
$337$	−14.6557	−0.798345	−0.399173	−	0.916876i	$-0.630703\pi$
$337$	−14.6557	−0.798345	−0.399173	+	0.916876i	$0.630703\pi$
$338$	−48.6892	−2.64835
$339$	18.6334	1.01203
$340$	−15.2487	−0.826976
$341$	1.21597	0.0658485
$342$	13.8652	0.749744
$343$	1.00000	0.0539949
$344$	−11.6811	−0.629802
$345$	3.77866	0.203436
$346$	28.9695	1.55741
$347$	36.6795	1.96906	0.984529	−	0.175221i	$-0.0560639\pi$
$347$	36.6795	1.96906	0.984529	+	0.175221i	$0.0560639\pi$
$348$	6.26463	0.335819
$349$	−21.9469	−1.17479	−0.587394	−	0.809301i	$-0.699846\pi$
$349$	−21.9469	−1.17479	−0.587394	+	0.809301i	$0.699846\pi$
$350$	7.98458	0.426794
$351$	−32.3650	−1.72751
$352$	5.15218	0.274612
$353$	−12.9843	−0.691084	−0.345542	−	0.938403i	$-0.612305\pi$
$353$	−12.9843	−0.691084	−0.345542	+	0.938403i	$0.612305\pi$
$354$	13.4925	0.717120
$355$	11.1978	0.594315
$356$	−58.6589	−3.10891
$357$	4.81610	0.254895
$358$	9.56246	0.505392
$359$	−5.60117	−0.295618	−0.147809	−	0.989016i	$-0.547222\pi$
$359$	−5.60117	−0.295618	−0.147809	+	0.989016i	$0.547222\pi$
$360$	4.91130	0.258848
$361$	−2.20974	−0.116302
$362$	−17.4361	−0.916424
$363$	12.5977	0.661210
$364$	−18.6883	−0.979534
$365$	6.46118	0.338194
$366$	−7.15235	−0.373859
$367$	0.882609	0.0460718	0.0230359	−	0.999735i	$-0.492667\pi$
$367$	0.882609	0.0460718	0.0230359	+	0.999735i	$0.492667\pi$
$368$	0.541145	0.0282091
$369$	3.38105	0.176011
$370$	−17.6500	−0.917582
$371$	2.43009	0.126164
$372$	−5.46102	−0.283141
$373$	−26.3717	−1.36547	−0.682737	−	0.730664i	$-0.739210\pi$
$373$	−26.3717	−1.36547	−0.682737	+	0.730664i	$0.739210\pi$
$374$	7.78485	0.402545
$375$	12.7949	0.660724
$376$	−28.8478	−1.48771
$377$	9.36465	0.482304
$378$	−12.5722	−0.646643
$379$	−34.4904	−1.77165	−0.885826	−	0.464017i	$-0.846407\pi$
$379$	−34.4904	−1.77165	−0.885826	+	0.464017i	$0.846407\pi$
$380$	15.9652	0.818999
$381$	8.97577	0.459843
$382$	14.5127	0.742534
$383$	−13.2158	−0.675295	−0.337648	−	0.941273i	$-0.609631\pi$
$383$	−13.2158	−0.675295	−0.337648	+	0.941273i	$0.609631\pi$
$384$	−21.9313	−1.11918
$385$	1.06759	0.0544096
$386$	−51.7523	−2.63412
$387$	−6.41724	−0.326207
$388$	25.2625	1.28251
$389$	−33.1726	−1.68192	−0.840958	−	0.541100i	$-0.818008\pi$
$389$	−33.1726	−1.68192	−0.840958	+	0.541100i	$0.818008\pi$
$390$	−20.0879	−1.01719
$391$	9.83104	0.497177
$392$	−2.70432	−0.136589
$393$	−13.6313	−0.687610
$394$	22.4585	1.13144
$395$	−2.44669	−0.123106
$396$	−4.13568	−0.207826
$397$	−17.1249	−0.859475	−0.429738	−	0.902954i	$-0.641394\pi$
$397$	−17.1249	−0.859475	−0.429738	+	0.902954i	$0.641394\pi$
$398$	−5.70034	−0.285732
$399$	−5.04241	−0.252436
$400$	0.755228	0.0377614
$401$	−20.7179	−1.03460	−0.517302	−	0.855803i	$-0.673064\pi$
$401$	−20.7179	−1.03460	−0.517302	+	0.855803i	$0.673064\pi$
$402$	18.6888	0.932114
$403$	−8.16338	−0.406647
$404$	−11.8929	−0.591695
$405$	−2.85522	−0.141877
$406$	3.63770	0.180536
$407$	5.53667	0.274443
$408$	−13.0243	−0.644798
$409$	−7.17157	−0.354611	−0.177306	−	0.984156i	$-0.556738\pi$
$409$	−7.17157	−0.354611	−0.177306	+	0.984156i	$0.556738\pi$
$410$	6.33601	0.312913
$411$	−13.9941	−0.690278
$412$	−21.0958	−1.03932
$413$	4.81405	0.236884
$414$	−8.49985	−0.417745
$415$	7.96722	0.391095
$416$	−34.5890	−1.69587
$417$	5.03537	0.246583
$418$	−8.15067	−0.398662
$419$	16.3210	0.797333	0.398667	−	0.917096i	$-0.369473\pi$
$419$	16.3210	0.797333	0.398667	+	0.917096i	$0.369473\pi$
$420$	−4.79464	−0.233954
$421$	13.6856	0.666995	0.333497	−	0.942751i	$-0.391771\pi$
$421$	13.6856	0.666995	0.333497	+	0.942751i	$0.391771\pi$
$422$	53.8564	2.62169
$423$	−15.8482	−0.770564
$424$	−6.57174	−0.319152
$425$	13.7203	0.665533
$426$	25.6744	1.24393
$427$	−2.55191	−0.123496
$428$	50.2822	2.43048
$429$	6.30142	0.304236
$430$	−12.0258	−0.579934
$431$	26.5638	1.27953	0.639767	−	0.768569i	$-0.279031\pi$
$431$	26.5638	1.27953	0.639767	+	0.768569i	$0.279031\pi$
$432$	−1.18915	−0.0572130
$433$	15.3684	0.738560	0.369280	−	0.929318i	$-0.379604\pi$
$433$	15.3684	0.738560	0.369280	+	0.929318i	$0.379604\pi$
$434$	−3.17107	−0.152216
$435$	2.40258	0.115195
$436$	−50.4173	−2.41455
$437$	−10.2930	−0.492382
$438$	14.8143	0.707854
$439$	−0.172889	−0.00825154	−0.00412577	−	0.999991i	$-0.501313\pi$
$439$	−0.172889	−0.00825154	−0.00412577	+	0.999991i	$0.501313\pi$
$440$	−2.88711	−0.137638
$441$	−1.48568	−0.0707464
$442$	−52.2633	−2.48591
$443$	16.2404	0.771602	0.385801	−	0.922582i	$-0.373925\pi$
$443$	16.2404	0.771602	0.385801	+	0.922582i	$0.373925\pi$
$444$	−24.8656	−1.18007
$445$	−22.4966	−1.06644
$446$	57.9557	2.74428
$447$	20.2025	0.955548
$448$	−13.0053	−0.614441
$449$	−36.2804	−1.71218	−0.856090	−	0.516827i	$-0.827113\pi$
$449$	−36.2804	−1.71218	−0.856090	+	0.516827i	$0.827113\pi$
$450$	−11.8625	−0.559203
$451$	−1.98755	−0.0935903
$452$	−48.2630	−2.27010
$453$	−13.1891	−0.619677
$454$	41.1028	1.92905
$455$	−7.16725	−0.336006
$456$	13.6363	0.638578
$457$	−23.4629	−1.09755	−0.548775	−	0.835970i	$-0.684906\pi$
$457$	−23.4629	−1.09755	−0.548775	+	0.835970i	$0.684906\pi$
$458$	17.6713	0.825725
$459$	−21.6034	−1.00836
$460$	−9.78725	−0.456333
$461$	6.52661	0.303975	0.151987	−	0.988382i	$-0.451433\pi$
$461$	6.52661	0.303975	0.151987	+	0.988382i	$0.451433\pi$
$462$	2.44779	0.113881
$463$	−37.5036	−1.74294	−0.871469	−	0.490450i	$-0.836832\pi$
$463$	−37.5036	−1.74294	−0.871469	+	0.490450i	$0.836832\pi$
$464$	0.344075	0.0159733
$465$	−2.09438	−0.0971247
$466$	−45.8842	−2.12555
$467$	−8.00175	−0.370277	−0.185138	−	0.982712i	$-0.559273\pi$
$467$	−8.00175	−0.370277	−0.185138	+	0.982712i	$0.559273\pi$
$468$	27.7648	1.28343
$469$	6.66805	0.307902
$470$	−29.6991	−1.36992
$471$	11.4784	0.528896
$472$	−13.0187	−0.599236
$473$	3.77238	0.173454
$474$	−5.60980	−0.257667
$475$	−14.3651	−0.659114
$476$	−12.4743	−0.571761
$477$	−3.61032	−0.165305
$478$	−15.2986	−0.699740
$479$	17.0818	0.780486	0.390243	−	0.920712i	$-0.372391\pi$
$479$	17.0818	0.780486	0.390243	+	0.920712i	$0.372391\pi$
$480$	−8.87409	−0.405045
$481$	−37.1703	−1.69482
$482$	18.5506	0.844957
$483$	3.09117	0.140653
$484$	−32.6299	−1.48318
$485$	9.68856	0.439935
$486$	31.1701	1.41390
$487$	−15.2090	−0.689185	−0.344592	−	0.938752i	$-0.611983\pi$
$487$	−15.2090	−0.689185	−0.344592	+	0.938752i	$0.611983\pi$
$488$	6.90119	0.312402
$489$	18.6432	0.843076
$490$	−2.78412	−0.125774
$491$	−23.9629	−1.08143	−0.540716	−	0.841205i	$-0.681847\pi$
$491$	−23.9629	−1.08143	−0.540716	+	0.841205i	$0.681847\pi$
$492$	8.92626	0.402427
$493$	6.25086	0.281524
$494$	54.7193	2.46194
$495$	−1.58610	−0.0712897
$496$	−0.299938	−0.0134676
$497$	9.16045	0.410902
$498$	18.2673	0.818579
$499$	−3.29501	−0.147505	−0.0737524	−	0.997277i	$-0.523497\pi$
$499$	−3.29501	−0.147505	−0.0737524	+	0.997277i	$0.523497\pi$
$500$	−33.1404	−1.48209
$501$	−28.7918	−1.28632
$502$	63.7411	2.84491
$503$	28.1042	1.25310	0.626551	−	0.779380i	$-0.284466\pi$
$503$	28.1042	1.25310	0.626551	+	0.779380i	$0.284466\pi$
$504$	4.01774	0.178965
$505$	−4.56112	−0.202967
$506$	4.99665	0.222128
$507$	−26.3069	−1.16833
$508$	−23.2485	−1.03148
$509$	33.0759	1.46606	0.733032	−	0.680195i	$-0.238105\pi$
$509$	33.0759	1.46606	0.733032	+	0.680195i	$0.238105\pi$
$510$	−13.4086	−0.593742
$511$	5.28564	0.233823
$512$	−2.43603	−0.107658
$513$	22.6186	0.998636
$514$	2.49921	0.110235
$515$	−8.09056	−0.356513
$516$	−16.9421	−0.745833
$517$	9.31636	0.409733
$518$	−14.4388	−0.634404
$519$	15.6523	0.687059
$520$	19.3825	0.849981
$521$	23.5202	1.03044	0.515219	−	0.857059i	$-0.327711\pi$
$521$	23.5202	1.03044	0.515219	+	0.857059i	$0.327711\pi$
$522$	−5.40445	−0.236546
$523$	−11.5646	−0.505687	−0.252843	−	0.967507i	$-0.581366\pi$
$523$	−11.5646	−0.505687	−0.252843	+	0.967507i	$0.581366\pi$
$524$	35.3070	1.54239
$525$	4.31408	0.188282
$526$	−33.9079	−1.47845
$527$	−5.44901	−0.237363
$528$	0.231526	0.0100759
$529$	−16.6900	−0.725653
$530$	−6.76566	−0.293882
$531$	−7.15211	−0.310375
$532$	13.0605	0.566246
$533$	13.3434	0.577966
$534$	−51.5804	−2.23210
$535$	19.2840	0.833719
$536$	−18.0326	−0.778888
$537$	5.16661	0.222956
$538$	−41.4572	−1.78735
$539$	0.873356	0.0376181
$540$	21.5072	0.925522
$541$	21.1165	0.907868	0.453934	−	0.891035i	$-0.350020\pi$
$541$	21.1165	0.907868	0.453934	+	0.891035i	$0.350020\pi$
$542$	−13.9934	−0.601068
$543$	−9.42077	−0.404284
$544$	−23.0880	−0.989889
$545$	−19.3358	−0.828254
$546$	−16.4332	−0.703274
$547$	−4.42444	−0.189175	−0.0945877	−	0.995517i	$-0.530153\pi$
$547$	−4.42444	−0.189175	−0.0945877	+	0.995517i	$0.530153\pi$
$548$	36.2466	1.54838
$549$	3.79131	0.161809
$550$	6.97338	0.297346
$551$	−6.54459	−0.278809
$552$	−8.35953	−0.355805
$553$	−2.00154	−0.0851142
$554$	−27.1125	−1.15190
$555$	−9.53634	−0.404795
$556$	−13.0423	−0.553116
$557$	26.9260	1.14089	0.570445	−	0.821335i	$-0.306771\pi$
$557$	26.9260	1.14089	0.570445	+	0.821335i	$0.306771\pi$
$558$	4.71118	0.199440
$559$	−25.3258	−1.07117
$560$	−0.263338	−0.0111281
$561$	4.20617	0.177584
$562$	−23.7828	−1.00322
$563$	−33.4076	−1.40796	−0.703981	−	0.710219i	$-0.748596\pi$
$563$	−33.4076	−1.40796	−0.703981	+	0.710219i	$0.748596\pi$
$564$	−41.8405	−1.76180
$565$	−18.5096	−0.778705
$566$	−16.6938	−0.701692
$567$	−2.33574	−0.0980920
$568$	−24.7728	−1.03944
$569$	−14.1673	−0.593925	−0.296962	−	0.954889i	$-0.595974\pi$
$569$	−14.1673	−0.593925	−0.296962	+	0.954889i	$0.595974\pi$
$570$	14.0387	0.588016
$571$	−20.6276	−0.863237	−0.431619	−	0.902056i	$-0.642057\pi$
$571$	−20.6276	−0.863237	−0.431619	+	0.902056i	$0.642057\pi$
$572$	−16.3215	−0.682438
$573$	7.84123	0.327572
$574$	5.18324	0.216344
$575$	8.80628	0.367247
$576$	19.3216	0.805066
$577$	4.02426	0.167532	0.0837661	−	0.996485i	$-0.473305\pi$
$577$	4.02426	0.167532	0.0837661	+	0.996485i	$0.473305\pi$
$578$	3.83335	0.159446
$579$	−27.9618	−1.16205
$580$	−6.22301	−0.258396
$581$	6.51767	0.270398
$582$	22.2140	0.920802
$583$	2.12233	0.0878980
$584$	−14.2941	−0.591493
$585$	10.6482	0.440249
$586$	30.7528	1.27038
$587$	45.2377	1.86716	0.933580	−	0.358369i	$-0.116667\pi$
$587$	45.2377	1.86716	0.933580	+	0.358369i	$0.116667\pi$
$588$	−3.92231	−0.161753
$589$	5.70507	0.235073
$590$	−13.4029	−0.551788
$591$	12.1343	0.499140
$592$	−1.36571	−0.0561301
$593$	−6.40521	−0.263031	−0.131515	−	0.991314i	$-0.541984\pi$
$593$	−6.40521	−0.263031	−0.131515	+	0.991314i	$0.541984\pi$
$594$	−10.9800	−0.450514
$595$	−4.78410	−0.196129
$596$	−52.3273	−2.14341
$597$	−3.07990	−0.126052
$598$	−33.5448	−1.37175
$599$	−6.66604	−0.272367	−0.136184	−	0.990684i	$-0.543484\pi$
$599$	−6.66604	−0.272367	−0.136184	+	0.990684i	$0.543484\pi$
$600$	−11.6667	−0.476289
$601$	6.53677	0.266640	0.133320	−	0.991073i	$-0.457436\pi$
$601$	6.53677	0.266640	0.133320	+	0.991073i	$0.457436\pi$
$602$	−9.83780	−0.400959
$603$	−9.90656	−0.403426
$604$	34.1615	1.39001
$605$	−12.5140	−0.508768
$606$	−10.4578	−0.424818
$607$	−47.2905	−1.91946	−0.959732	−	0.280918i	$-0.909361\pi$
$607$	−47.2905	−1.91946	−0.959732	+	0.280918i	$0.909361\pi$
$608$	24.1729	0.980341
$609$	1.96546	0.0796443
$610$	7.10483	0.287666
$611$	−62.5451	−2.53030
$612$	18.5328	0.749145
$613$	−38.0562	−1.53708	−0.768538	−	0.639804i	$-0.779015\pi$
$613$	−38.0562	−1.53708	−0.768538	+	0.639804i	$0.779015\pi$
$614$	3.90786	0.157708
$615$	3.42336	0.138043
$616$	−2.36183	−0.0951610
$617$	−24.2195	−0.975038	−0.487519	−	0.873112i	$-0.662098\pi$
$617$	−24.2195	−0.975038	−0.487519	+	0.873112i	$0.662098\pi$
$618$	−18.5501	−0.746196
$619$	11.6227	0.467154	0.233577	−	0.972338i	$-0.424957\pi$
$619$	11.6227	0.467154	0.233577	+	0.972338i	$0.424957\pi$
$620$	5.42474	0.217863
$621$	−13.8660	−0.556424
$622$	−31.0189	−1.24375
$623$	−18.4036	−0.737323
$624$	−1.55434	−0.0622235
$625$	4.81880	0.192752
$626$	−69.4888	−2.77733
$627$	−4.40382	−0.175872
$628$	−29.7306	−1.18638
$629$	−24.8109	−0.989277
$630$	4.13630	0.164794
$631$	21.0775	0.839083	0.419541	−	0.907736i	$-0.362191\pi$
$631$	21.0775	0.839083	0.419541	+	0.907736i	$0.362191\pi$
$632$	5.41281	0.215310
$633$	29.0987	1.15657
$634$	29.8897	1.18707
$635$	−8.91614	−0.353826
$636$	−9.53156	−0.377951
$637$	−5.86324	−0.232310
$638$	3.17701	0.125779
$639$	−13.6095	−0.538382
$640$	21.7856	0.861150
$641$	41.7302	1.64824	0.824122	−	0.566413i	$-0.191669\pi$
$641$	41.7302	1.64824	0.824122	+	0.566413i	$0.191669\pi$
$642$	44.2145	1.74501
$643$	−34.7739	−1.37135	−0.685675	−	0.727908i	$-0.740493\pi$
$643$	−34.7739	−1.37135	−0.685675	+	0.727908i	$0.740493\pi$
$644$	−8.00656	−0.315503
$645$	−6.49754	−0.255840
$646$	36.5248	1.43705
$647$	−10.4783	−0.411946	−0.205973	−	0.978558i	$-0.566036\pi$
$647$	−10.4783	−0.411946	−0.205973	+	0.978558i	$0.566036\pi$
$648$	6.31660	0.248140
$649$	4.20438	0.165036
$650$	−46.8155	−1.83626
$651$	−1.71333	−0.0671508
$652$	−48.2885	−1.89112
$653$	2.32130	0.0908395	0.0454198	−	0.998968i	$-0.485537\pi$
$653$	2.32130	0.0908395	0.0454198	+	0.998968i	$0.485537\pi$
$654$	−44.3333	−1.73357
$655$	13.5408	0.529082
$656$	0.490261	0.0191415
$657$	−7.85274	−0.306365
$658$	−24.2957	−0.947143
$659$	29.9176	1.16542	0.582712	−	0.812679i	$-0.301992\pi$
$659$	29.9176	1.16542	0.582712	+	0.812679i	$0.301992\pi$
$660$	−4.18743	−0.162995
$661$	−28.6045	−1.11258	−0.556292	−	0.830987i	$-0.687777\pi$
$661$	−28.6045	−1.11258	−0.556292	+	0.830987i	$0.687777\pi$
$662$	58.8598	2.28765
$663$	−28.2379	−1.09667
$664$	−17.6259	−0.684016
$665$	5.00891	0.194237
$666$	21.4514	0.831224
$667$	4.01206	0.155348
$668$	74.5746	2.88538
$669$	31.3136	1.21065
$670$	−18.5647	−0.717215
$671$	−2.22873	−0.0860391
$672$	−7.25955	−0.280043
$673$	4.99322	0.192474	0.0962372	−	0.995358i	$-0.469319\pi$
$673$	4.99322	0.192474	0.0962372	+	0.995358i	$0.469319\pi$
$674$	33.3795	1.28573
$675$	−19.3516	−0.744842
$676$	68.1383	2.62071
$677$	−38.3678	−1.47460	−0.737298	−	0.675568i	$-0.763898\pi$
$677$	−38.3678	−1.47460	−0.737298	+	0.675568i	$0.763898\pi$
$678$	−42.4390	−1.62986
$679$	7.92583	0.304165
$680$	12.9377	0.496140
$681$	22.2079	0.851009
$682$	−2.76947	−0.106049
$683$	25.3057	0.968297	0.484149	−	0.874986i	$-0.339129\pi$
$683$	25.3057	0.968297	0.484149	+	0.874986i	$0.339129\pi$
$684$	−19.4037	−0.741919
$685$	13.9011	0.531135
$686$	−2.27758	−0.0869584
$687$	9.54782	0.364272
$688$	−0.930516	−0.0354756
$689$	−14.2482	−0.542814
$690$	−8.60620	−0.327632
$691$	3.47151	0.132063	0.0660313	−	0.997818i	$-0.478966\pi$
$691$	3.47151	0.132063	0.0660313	+	0.997818i	$0.478966\pi$
$692$	−40.5415	−1.54116
$693$	−1.29752	−0.0492888
$694$	−83.5405	−3.17115
$695$	−5.00192	−0.189733
$696$	−5.31522	−0.201473
$697$	8.90664	0.337363
$698$	49.9857	1.89199
$699$	−24.7913	−0.937693
$700$	−11.1740	−0.422339
$701$	−34.1432	−1.28957	−0.644786	−	0.764364i	$-0.723053\pi$
$701$	−34.1432	−1.28957	−0.644786	+	0.764364i	$0.723053\pi$
$702$	73.7138	2.78215
$703$	25.9768	0.979735
$704$	−11.3582	−0.428079
$705$	−16.0465	−0.604344
$706$	29.5728	1.11299
$707$	−3.73127	−0.140329
$708$	−18.8822	−0.709636
$709$	−21.5316	−0.808636	−0.404318	−	0.914618i	$-0.632491\pi$
$709$	−21.5316	−0.808636	−0.404318	+	0.914618i	$0.632491\pi$
$710$	−25.5038	−0.957140
$711$	2.97364	0.111520
$712$	49.7691	1.86518
$713$	−3.49741	−0.130979
$714$	−10.9690	−0.410506
$715$	−6.25956	−0.234094
$716$	−13.3822	−0.500117
$717$	−8.26583	−0.308693
$718$	12.7571	0.476091
$719$	21.3027	0.794455	0.397228	−	0.917720i	$-0.369972\pi$
$719$	21.3027	0.794455	0.397228	+	0.917720i	$0.369972\pi$
$720$	0.391235	0.0145805
$721$	−6.61857	−0.246488
$722$	5.03285	0.187303
$723$	10.0229	0.372756
$724$	24.4011	0.906859
$725$	5.59928	0.207952
$726$	−28.6924	−1.06487
$727$	−27.2747	−1.01156	−0.505781	−	0.862662i	$-0.668796\pi$
$727$	−27.2747	−1.01156	−0.505781	+	0.862662i	$0.668796\pi$
$728$	15.8561	0.587666
$729$	23.8485	0.883276
$730$	−14.7159	−0.544658
$731$	−16.9048	−0.625247
$732$	10.0094	0.369957
$733$	6.36311	0.235027	0.117514	−	0.993071i	$-0.462508\pi$
$733$	6.36311	0.235027	0.117514	+	0.993071i	$0.462508\pi$
$734$	−2.01021	−0.0741982
$735$	−1.50426	−0.0554856
$736$	−14.8188	−0.546229
$737$	5.82358	0.214514
$738$	−7.70061	−0.283464
$739$	22.3943	0.823788	0.411894	−	0.911232i	$-0.364867\pi$
$739$	22.3943	0.823788	0.411894	+	0.911232i	$0.364867\pi$
$740$	24.7004	0.908005
$741$	29.5649	1.08609
$742$	−5.53472	−0.203186
$743$	18.3496	0.673180	0.336590	−	0.941651i	$-0.390726\pi$
$743$	18.3496	0.673180	0.336590	+	0.941651i	$0.390726\pi$
$744$	4.63340	0.169869
$745$	−20.0683	−0.735246
$746$	60.0636	2.19908
$747$	−9.68314	−0.354287
$748$	−10.8945	−0.398344
$749$	15.7755	0.576423
$750$	−29.1413	−1.06409
$751$	−13.9604	−0.509422	−0.254711	−	0.967017i	$-0.581980\pi$
$751$	−13.9604	−0.509422	−0.254711	+	0.967017i	$0.581980\pi$
$752$	−2.29802	−0.0838003
$753$	34.4394	1.25504
$754$	−21.3287	−0.776747
$755$	13.1015	0.476811
$756$	17.5942	0.639895
$757$	−18.1452	−0.659499	−0.329749	−	0.944069i	$-0.606964\pi$
$757$	−18.1452	−0.659499	−0.329749	+	0.944069i	$0.606964\pi$
$758$	78.5546	2.85323
$759$	2.69969	0.0979927
$760$	−13.5457	−0.491354
$761$	1.71772	0.0622674	0.0311337	−	0.999515i	$-0.490088\pi$
$761$	1.71772	0.0622674	0.0311337	+	0.999515i	$0.490088\pi$
$762$	−20.4430	−0.740573
$763$	−15.8178	−0.572644
$764$	−20.3099	−0.734785
$765$	7.10762	0.256976
$766$	30.1000	1.08756
$767$	−28.2259	−1.01918
$768$	17.9422	0.647434
$769$	−26.4076	−0.952282	−0.476141	−	0.879369i	$-0.657965\pi$
$769$	−26.4076	−0.952282	−0.476141	+	0.879369i	$0.657965\pi$
$770$	−2.43153	−0.0876262
$771$	1.35032	0.0486307
$772$	72.4249	2.60663
$773$	−54.5128	−1.96069	−0.980344	−	0.197296i	$-0.936784\pi$
$773$	−54.5128	−1.96069	−0.980344	+	0.197296i	$0.936784\pi$
$774$	14.6158	0.525353
$775$	−4.88102	−0.175331
$776$	−21.4340	−0.769435
$777$	−7.80130	−0.279870
$778$	75.5532	2.70871
$779$	−9.32517	−0.334109
$780$	28.1121	1.00658
$781$	8.00033	0.286274
$782$	−22.3910	−0.800700
$783$	−8.81640	−0.315072
$784$	−0.215427	−0.00769381
$785$	−11.4021	−0.406959
$786$	31.0464	1.10739
$787$	22.7244	0.810037	0.405019	−	0.914308i	$-0.367265\pi$
$787$	22.7244	0.810037	0.405019	+	0.914308i	$0.367265\pi$
$788$	−31.4296	−1.11963
$789$	−18.3205	−0.652226
$790$	5.57253	0.198262
$791$	−15.1420	−0.538387
$792$	3.50892	0.124684
$793$	14.9625	0.531333
$794$	39.0034	1.38418
$795$	−3.65550	−0.129647
$796$	7.97736	0.282750
$797$	12.6870	0.449398	0.224699	−	0.974428i	$-0.427860\pi$
$797$	12.6870	0.449398	0.224699	+	0.974428i	$0.427860\pi$
$798$	11.4845	0.406547
$799$	−41.7485	−1.47696
$800$	−20.6813	−0.731196
$801$	27.3417	0.966071
$802$	47.1867	1.66622
$803$	4.61624	0.162904
$804$	−26.1541	−0.922385
$805$	−3.07064	−0.108226
$806$	18.5928	0.654902
$807$	−22.3994	−0.788496
$808$	10.0906	0.354984
$809$	−1.21272	−0.0426371	−0.0213186	−	0.999773i	$-0.506786\pi$
$809$	−1.21272	−0.0426371	−0.0213186	+	0.999773i	$0.506786\pi$
$810$	6.50299	0.228492
$811$	−29.2589	−1.02742	−0.513709	−	0.857965i	$-0.671729\pi$
$811$	−29.2589	−1.02742	−0.513709	+	0.857965i	$0.671729\pi$
$812$	−5.09080	−0.178652
$813$	−7.56066	−0.265164
$814$	−12.6102	−0.441988
$815$	−18.5194	−0.648705
$816$	−1.03752	−0.0363203
$817$	17.6992	0.619216
$818$	16.3338	0.571099
$819$	8.71088	0.304383
$820$	−8.86695	−0.309647
$821$	−41.8041	−1.45897	−0.729487	−	0.683995i	$-0.760241\pi$
$821$	−41.8041	−1.45897	−0.729487	+	0.683995i	$0.760241\pi$
$822$	31.8727	1.11169
$823$	−38.7226	−1.34978	−0.674892	−	0.737917i	$-0.735810\pi$
$823$	−38.7226	−1.34978	−0.674892	+	0.737917i	$0.735810\pi$
$824$	17.8987	0.623532
$825$	3.76773	0.131175
$826$	−10.9644	−0.381499
$827$	53.9784	1.87701	0.938506	−	0.345262i	$-0.112210\pi$
$827$	53.9784	1.87701	0.938506	+	0.345262i	$0.112210\pi$
$828$	11.8951	0.413385
$829$	21.5119	0.747140	0.373570	−	0.927602i	$-0.378134\pi$
$829$	21.5119	0.747140	0.373570	+	0.927602i	$0.378134\pi$
$830$	−18.1460	−0.629856
$831$	−14.6489	−0.508165
$832$	76.2530	2.64360
$833$	−3.91368	−0.135601
$834$	−11.4685	−0.397120
$835$	28.6005	0.989761
$836$	11.4065	0.394502
$837$	7.68545	0.265648
$838$	−37.1724	−1.28410
$839$	−15.2227	−0.525546	−0.262773	−	0.964858i	$-0.584637\pi$
$839$	−15.2227	−0.525546	−0.262773	+	0.964858i	$0.584637\pi$
$840$	4.06801	0.140360
$841$	−26.4490	−0.912035
$842$	−31.1700	−1.07419
$843$	−12.8499	−0.442574
$844$	−75.3696	−2.59433
$845$	26.1321	0.898971
$846$	36.0954	1.24099
$847$	−10.2372	−0.351756
$848$	−0.523506	−0.0179773
$849$	−9.01967	−0.309554
$850$	−31.2491	−1.07184
$851$	−15.9247	−0.545892
$852$	−35.9301	−1.23094
$853$	42.4481	1.45339	0.726697	−	0.686958i	$-0.241054\pi$
$853$	42.4481	1.45339	0.726697	+	0.686958i	$0.241054\pi$
$854$	5.81218	0.198889
$855$	−7.44161	−0.254498
$856$	−42.6619	−1.45815
$857$	17.0720	0.583170	0.291585	−	0.956545i	$-0.405817\pi$
$857$	17.0720	0.583170	0.291585	+	0.956545i	$0.405817\pi$
$858$	−14.3520	−0.489969
$859$	5.45560	0.186143	0.0930713	−	0.995659i	$-0.470332\pi$
$859$	5.45560	0.186143	0.0930713	+	0.995659i	$0.470332\pi$
$860$	16.8295	0.573881
$861$	2.80051	0.0954412
$862$	−60.5012	−2.06068
$863$	1.00000	0.0340404
$863$	1.00000	0.0340404
$864$	32.5640	1.10785
$865$	−15.5483	−0.528657
$866$	−35.0028	−1.18944
$867$	2.07117	0.0703405
$868$	4.43776	0.150628
$869$	−1.74806	−0.0592988
$870$	−5.47206	−0.185520
$871$	−39.0964	−1.32473
$872$	42.7765	1.44860
$873$	−11.7752	−0.398530
$874$	23.4432	0.792977
$875$	−10.3974	−0.351497
$876$	−20.7319	−0.700466
$877$	43.9955	1.48562	0.742811	−	0.669501i	$-0.233492\pi$
$877$	43.9955	1.48562	0.742811	+	0.669501i	$0.233492\pi$
$878$	0.393768	0.0132890
$879$	16.6158	0.560436
$880$	−0.229988	−0.00775289
$881$	−16.0176	−0.539647	−0.269823	−	0.962910i	$-0.586965\pi$
$881$	−16.0176	−0.539647	−0.269823	+	0.962910i	$0.586965\pi$
$882$	3.38374	0.113937
$883$	40.6968	1.36956	0.684779	−	0.728751i	$-0.259899\pi$
$883$	40.6968	1.36956	0.684779	+	0.728751i	$0.259899\pi$
$884$	73.1401	2.45997
$885$	−7.24160	−0.243424
$886$	−36.9887	−1.24266
$887$	−34.7864	−1.16801	−0.584007	−	0.811748i	$-0.698516\pi$
$887$	−34.7864	−1.16801	−0.584007	+	0.811748i	$0.698516\pi$
$888$	21.0972	0.707977
$889$	−7.29394	−0.244631
$890$	51.2377	1.71749
$891$	−2.03993	−0.0683404
$892$	−81.1064	−2.71564
$893$	43.7103	1.46271
$894$	−46.0129	−1.53890
$895$	−5.13228	−0.171553
$896$	17.8219	0.595388
$897$	−18.1243	−0.605153
$898$	82.6316	2.75745
$899$	−2.22375	−0.0741662
$900$	16.6010	0.553367
$901$	−9.51060	−0.316844
$902$	4.52681	0.150726
$903$	−5.31538	−0.176885
$904$	40.9488	1.36194
$905$	9.35818	0.311077
$906$	30.0392	0.997985
$907$	21.7688	0.722822	0.361411	−	0.932407i	$-0.382295\pi$
$907$	21.7688	0.722822	0.361411	+	0.932407i	$0.382295\pi$
$908$	−57.5215	−1.90892
$909$	5.54346	0.183865
$910$	16.3240	0.541134
$911$	14.3093	0.474089	0.237044	−	0.971499i	$-0.423821\pi$
$911$	14.3093	0.474089	0.237044	+	0.971499i	$0.423821\pi$
$912$	1.08627	0.0359700
$913$	5.69224	0.188386
$914$	53.4387	1.76759
$915$	3.83875	0.126905
$916$	−24.7302	−0.817107
$917$	11.0772	0.365801
$918$	49.2036	1.62396
$919$	−38.2480	−1.26169	−0.630843	−	0.775910i	$-0.717291\pi$
$919$	−38.2480	−1.26169	−0.630843	+	0.775910i	$0.717291\pi$
$920$	8.30399	0.273774
$921$	2.11142	0.0695737
$922$	−14.8649	−0.489549
$923$	−53.7099	−1.76788
$924$	−3.42557	−0.112693
$925$	−22.2247	−0.730744
$926$	85.4173	2.80699
$927$	9.83304	0.322960
$928$	−9.42223	−0.309300
$929$	−3.73477	−0.122534	−0.0612669	−	0.998121i	$-0.519514\pi$
$929$	−3.73477	−0.122534	−0.0612669	+	0.998121i	$0.519514\pi$
$930$	4.77012	0.156419
$931$	4.09759	0.134293
$932$	64.2128	2.10336
$933$	−16.7596	−0.548684
$934$	18.2246	0.596328
$935$	−4.17822	−0.136642
$936$	−23.5570	−0.769985
$937$	−48.7537	−1.59271	−0.796356	−	0.604828i	$-0.793242\pi$
$937$	−48.7537	−1.59271	−0.796356	+	0.604828i	$0.793242\pi$
$938$	−15.1870	−0.495874
$939$	−37.5449	−1.22523
$940$	41.5625	1.35562
$941$	36.5943	1.19294	0.596470	−	0.802635i	$-0.296569\pi$
$941$	36.5943	1.19294	0.596470	+	0.802635i	$0.296569\pi$
$942$	−26.1429	−0.851783
$943$	5.71665	0.186160
$944$	−1.03707	−0.0337539
$945$	6.74764	0.219501
$946$	−8.59190	−0.279347
$947$	−17.3635	−0.564237	−0.282119	−	0.959380i	$-0.591037\pi$
$947$	−17.3635	−0.564237	−0.282119	+	0.959380i	$0.591037\pi$
$948$	7.85066	0.254977
$949$	−30.9910	−1.00601
$950$	32.7175	1.06150
$951$	16.1494	0.523682
$952$	10.5839	0.343025
$953$	−48.2743	−1.56376	−0.781878	−	0.623431i	$-0.785738\pi$
$953$	−48.2743	−1.56376	−0.781878	+	0.623431i	$0.785738\pi$
$954$	8.22280	0.266223
$955$	−7.78913	−0.252050
$956$	21.4096	0.692437
$957$	1.71654	0.0554879
$958$	−38.9051	−1.25697
$959$	11.3720	0.367220
$960$	19.5633	0.631404
$961$	−29.0615	−0.937468
$962$	84.6582	2.72949
$963$	−23.4372	−0.755254
$964$	−25.9607	−0.836138
$965$	27.7760	0.894142
$966$	−7.04039	−0.226521
$967$	−4.39063	−0.141193	−0.0705965	−	0.997505i	$-0.522490\pi$
$967$	−4.39063	−0.141193	−0.0705965	+	0.997505i	$0.522490\pi$
$968$	27.6848	0.889824
$969$	19.7344	0.633960
$970$	−22.0665	−0.708511
$971$	55.8998	1.79391	0.896955	−	0.442121i	$-0.145774\pi$
$971$	55.8998	1.79391	0.896955	+	0.442121i	$0.145774\pi$
$972$	−43.6211	−1.39915
$973$	−4.09187	−0.131179
$974$	34.6397	1.10993
$975$	−25.2945	−0.810072
$976$	0.549750	0.0175971
$977$	15.3012	0.489530	0.244765	−	0.969582i	$-0.421289\pi$
$977$	15.3012	0.489530	0.244765	+	0.969582i	$0.421289\pi$
$978$	−42.4615	−1.35777
$979$	−16.0728	−0.513690
$980$	3.89625	0.124461
$981$	23.5002	0.750303
$982$	54.5775	1.74164
$983$	−27.0490	−0.862728	−0.431364	−	0.902178i	$-0.641968\pi$
$983$	−27.0490	−0.862728	−0.431364	+	0.902178i	$0.641968\pi$
$984$	−7.57349	−0.241434
$985$	−12.0537	−0.384063
$986$	−14.2368	−0.453393
$987$	−13.1270	−0.417836
$988$	−76.5771	−2.43624
$989$	−10.8502	−0.345017
$990$	3.61246	0.114812
$991$	−34.1000	−1.08322	−0.541610	−	0.840630i	$-0.682185\pi$
$991$	−34.1000	−1.08322	−0.541610	+	0.840630i	$0.682185\pi$
$992$	8.21358	0.260781
$993$	31.8020	1.00921
$994$	−20.8636	−0.661755
$995$	3.05944	0.0969907
$996$	−25.5643	−0.810036
$997$	20.7275	0.656447	0.328223	−	0.944600i	$-0.393550\pi$
$997$	20.7275	0.656447	0.328223	+	0.944600i	$0.393550\pi$
$998$	7.50465	0.237555
$999$	34.9941	1.10716

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.c.1.8	✓	83

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.c.1.8	✓	83	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.27758 q^{2} -1.23058 q^{3} +3.18737 q^{4} +1.22240 q^{5} +2.80274 q^{6} +1.00000 q^{7} -2.70432 q^{8} -1.48568 q^{9} +O(q^{10})\)	\(q-2.27758 q^{2} -1.23058 q^{3} +3.18737 q^{4} +1.22240 q^{5} +2.80274 q^{6} +1.00000 q^{7} -2.70432 q^{8} -1.48568 q^{9} -2.78412 q^{10} +0.873356 q^{11} -3.92231 q^{12} -5.86324 q^{13} -2.27758 q^{14} -1.50426 q^{15} -0.215427 q^{16} -3.91368 q^{17} +3.38374 q^{18} +4.09759 q^{19} +3.89625 q^{20} -1.23058 q^{21} -1.98914 q^{22} -2.51197 q^{23} +3.32788 q^{24} -3.50573 q^{25} +13.3540 q^{26} +5.51998 q^{27} +3.18737 q^{28} -1.59718 q^{29} +3.42608 q^{30} +1.39230 q^{31} +5.89929 q^{32} -1.07473 q^{33} +8.91372 q^{34} +1.22240 q^{35} -4.73539 q^{36} +6.33954 q^{37} -9.33259 q^{38} +7.21518 q^{39} -3.30577 q^{40} -2.27577 q^{41} +2.80274 q^{42} +4.31941 q^{43} +2.78371 q^{44} -1.81609 q^{45} +5.72120 q^{46} +10.6673 q^{47} +0.265099 q^{48} +1.00000 q^{49} +7.98458 q^{50} +4.81610 q^{51} -18.6883 q^{52} +2.43009 q^{53} -12.5722 q^{54} +1.06759 q^{55} -2.70432 q^{56} -5.04241 q^{57} +3.63770 q^{58} +4.81405 q^{59} -4.79464 q^{60} -2.55191 q^{61} -3.17107 q^{62} -1.48568 q^{63} -13.0053 q^{64} -7.16725 q^{65} +2.44779 q^{66} +6.66805 q^{67} -12.4743 q^{68} +3.09117 q^{69} -2.78412 q^{70} +9.16045 q^{71} +4.01774 q^{72} +5.28564 q^{73} -14.4388 q^{74} +4.31408 q^{75} +13.0605 q^{76} +0.873356 q^{77} -16.4332 q^{78} -2.00154 q^{79} -0.263338 q^{80} -2.33574 q^{81} +5.18324 q^{82} +6.51767 q^{83} -3.92231 q^{84} -4.78410 q^{85} -9.83780 q^{86} +1.96546 q^{87} -2.36183 q^{88} -18.4036 q^{89} +4.13630 q^{90} -5.86324 q^{91} -8.00656 q^{92} -1.71333 q^{93} -24.2957 q^{94} +5.00891 q^{95} -7.25955 q^{96} +7.92583 q^{97} -2.27758 q^{98} -1.29752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9}+O(q^{10}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9	\( 83 q - 8 q^{2} - 12 q^{3} + 48 q^{4} - 11 q^{5} - 8 q^{6} + 83 q^{7} - 18 q^{8} + 39 q^{9} - 20 q^{10} - 26 q^{11} - 14 q^{12} - 22 q^{13} - 8 q^{14} - 37 q^{15} - 10 q^{16} - 9 q^{17} - 27 q^{18} - 42 q^{19} - 22 q^{20} - 12 q^{21} - 44 q^{22} - 46 q^{23} - 24 q^{24} - 20 q^{25} - 9 q^{26} - 39 q^{27} + 48 q^{28} - 36 q^{29} - 11 q^{30} - 107 q^{31} - 19 q^{32} - 25 q^{33} - 24 q^{34} - 11 q^{35} - 32 q^{36} - 75 q^{37} - 16 q^{38} - 78 q^{39} - 34 q^{40} - 17 q^{41} - 8 q^{42} - 87 q^{43} - 32 q^{44} - 17 q^{45} - 56 q^{46} - 39 q^{47} - 16 q^{48} + 83 q^{49} - 26 q^{50} - 71 q^{51} - 53 q^{52} - 28 q^{53} - 25 q^{54} - 94 q^{55} - 18 q^{56} - 79 q^{57} - 69 q^{58} - 26 q^{59} - 43 q^{60} - 56 q^{61} - 6 q^{62} + 39 q^{63} - 108 q^{64} - 26 q^{65} + 10 q^{66} - 123 q^{67} - 11 q^{68} + 2 q^{69} - 20 q^{70} - 96 q^{71} - 11 q^{72} - 53 q^{73} - 26 q^{74} - 27 q^{75} - 65 q^{76} - 26 q^{77} - 43 q^{78} - 160 q^{79} + 12 q^{80} - 53 q^{81} - 20 q^{82} - 2 q^{83} - 14 q^{84} - 110 q^{85} + 24 q^{86} - 52 q^{87} - 79 q^{88} - 5 q^{89} - 4 q^{90} - 22 q^{91} - 51 q^{92} - 30 q^{93} - 9 q^{94} - 76 q^{95} - 3 q^{96} - 44 q^{97} - 8 q^{98} - 82 q^{99}+O(q^{100}) \) 83 * q - 8 * q^2 - 12 * q^3 + 48 * q^4 - 11 * q^5 - 8 * q^6 + 83 * q^7 - 18 * q^8 + 39 * q^9 - 20 * q^10 - 26 * q^11 - 14 * q^12 - 22 * q^13 - 8 * q^14 - 37 * q^15 - 10 * q^16 - 9 * q^17 - 27 * q^18 - 42 * q^19 - 22 * q^20 - 12 * q^21 - 44 * q^22 - 46 * q^23 - 24 * q^24 - 20 * q^25 - 9 * q^26 - 39 * q^27 + 48 * q^28 - 36 * q^29 - 11 * q^30 - 107 * q^31 - 19 * q^32 - 25 * q^33 - 24 * q^34 - 11 * q^35 - 32 * q^36 - 75 * q^37 - 16 * q^38 - 78 * q^39 - 34 * q^40 - 17 * q^41 - 8 * q^42 - 87 * q^43 - 32 * q^44 - 17 * q^45 - 56 * q^46 - 39 * q^47 - 16 * q^48 + 83 * q^49 - 26 * q^50 - 71 * q^51 - 53 * q^52 - 28 * q^53 - 25 * q^54 - 94 * q^55 - 18 * q^56 - 79 * q^57 - 69 * q^58 - 26 * q^59 - 43 * q^60 - 56 * q^61 - 6 * q^62 + 39 * q^63 - 108 * q^64 - 26 * q^65 + 10 * q^66 - 123 * q^67 - 11 * q^68 + 2 * q^69 - 20 * q^70 - 96 * q^71 - 11 * q^72 - 53 * q^73 - 26 * q^74 - 27 * q^75 - 65 * q^76 - 26 * q^77 - 43 * q^78 - 160 * q^79 + 12 * q^80 - 53 * q^81 - 20 * q^82 - 2 * q^83 - 14 * q^84 - 110 * q^85 + 24 * q^86 - 52 * q^87 - 79 * q^88 - 5 * q^89 - 4 * q^90 - 22 * q^91 - 51 * q^92 - 30 * q^93 - 9 * q^94 - 76 * q^95 - 3 * q^96 - 44 * q^97 - 8 * q^98 - 82 * q^99

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