LMFDB - Embedded newform 4034.2.a.c.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.62176 q^{3} +1.00000 q^{4} +1.44534 q^{5} +2.62176 q^{6} -4.09354 q^{7} -1.00000 q^{8} +3.87363 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.62176 q^{3} +1.00000 q^{4} +1.44534 q^{5} +2.62176 q^{6} -4.09354 q^{7} -1.00000 q^{8} +3.87363 q^{9} -1.44534 q^{10} +1.36002 q^{11} -2.62176 q^{12} -5.47069 q^{13} +4.09354 q^{14} -3.78933 q^{15} +1.00000 q^{16} -6.54138 q^{17} -3.87363 q^{18} -7.18152 q^{19} +1.44534 q^{20} +10.7323 q^{21} -1.36002 q^{22} +0.364985 q^{23} +2.62176 q^{24} -2.91100 q^{25} +5.47069 q^{26} -2.29046 q^{27} -4.09354 q^{28} -8.13182 q^{29} +3.78933 q^{30} +5.99102 q^{31} -1.00000 q^{32} -3.56566 q^{33} +6.54138 q^{34} -5.91655 q^{35} +3.87363 q^{36} -10.8895 q^{37} +7.18152 q^{38} +14.3429 q^{39} -1.44534 q^{40} -0.609989 q^{41} -10.7323 q^{42} -3.38869 q^{43} +1.36002 q^{44} +5.59871 q^{45} -0.364985 q^{46} +6.02904 q^{47} -2.62176 q^{48} +9.75706 q^{49} +2.91100 q^{50} +17.1499 q^{51} -5.47069 q^{52} -3.46241 q^{53} +2.29046 q^{54} +1.96570 q^{55} +4.09354 q^{56} +18.8282 q^{57} +8.13182 q^{58} +1.05886 q^{59} -3.78933 q^{60} +3.80729 q^{61} -5.99102 q^{62} -15.8569 q^{63} +1.00000 q^{64} -7.90700 q^{65} +3.56566 q^{66} -13.4770 q^{67} -6.54138 q^{68} -0.956904 q^{69} +5.91655 q^{70} +4.01685 q^{71} -3.87363 q^{72} -16.8267 q^{73} +10.8895 q^{74} +7.63194 q^{75} -7.18152 q^{76} -5.56731 q^{77} -14.3429 q^{78} -7.89704 q^{79} +1.44534 q^{80} -5.61587 q^{81} +0.609989 q^{82} -1.45700 q^{83} +10.7323 q^{84} -9.45450 q^{85} +3.38869 q^{86} +21.3197 q^{87} -1.36002 q^{88} +12.9834 q^{89} -5.59871 q^{90} +22.3945 q^{91} +0.364985 q^{92} -15.7070 q^{93} -6.02904 q^{94} -10.3797 q^{95} +2.62176 q^{96} -1.54670 q^{97} -9.75706 q^{98} +5.26824 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.62176	−1.51367	−0.756837	−	0.653603i	$-0.773257\pi$
$3$	−2.62176	−1.51367	−0.756837	+	0.653603i	$0.773257\pi$
$4$	1.00000	0.500000
$5$	1.44534	0.646375	0.323187	−	0.946335i	$-0.395246\pi$
$5$	1.44534	0.646375	0.323187	+	0.946335i	$0.395246\pi$
$6$	2.62176	1.07033
$7$	−4.09354	−1.54721	−0.773606	−	0.633667i	$-0.781549\pi$
$7$	−4.09354	−1.54721	−0.773606	+	0.633667i	$0.781549\pi$
$8$	−1.00000	−0.353553
$9$	3.87363	1.29121
$10$	−1.44534	−0.457056
$11$	1.36002	0.410063	0.205031	−	0.978755i	$-0.434270\pi$
$11$	1.36002	0.410063	0.205031	+	0.978755i	$0.434270\pi$
$12$	−2.62176	−0.756837
$13$	−5.47069	−1.51730	−0.758649	−	0.651500i	$-0.774140\pi$
$13$	−5.47069	−1.51730	−0.758649	+	0.651500i	$0.774140\pi$
$14$	4.09354	1.09404
$15$	−3.78933	−0.978401
$16$	1.00000	0.250000
$17$	−6.54138	−1.58652	−0.793258	−	0.608885i	$-0.791617\pi$
$17$	−6.54138	−1.58652	−0.793258	+	0.608885i	$0.791617\pi$
$18$	−3.87363	−0.913024
$19$	−7.18152	−1.64755	−0.823777	−	0.566914i	$-0.808137\pi$
$19$	−7.18152	−1.64755	−0.823777	+	0.566914i	$0.808137\pi$
$20$	1.44534	0.323187
$21$	10.7323	2.34198
$22$	−1.36002	−0.289958
$23$	0.364985	0.0761046	0.0380523	−	0.999276i	$-0.487885\pi$
$23$	0.364985	0.0761046	0.0380523	+	0.999276i	$0.487885\pi$
$24$	2.62176	0.535165
$25$	−2.91100	−0.582200
$26$	5.47069	1.07289
$27$	−2.29046	−0.440799
$28$	−4.09354	−0.773606
$29$	−8.13182	−1.51004	−0.755021	−	0.655701i	$-0.772373\pi$
$29$	−8.13182	−1.51004	−0.755021	+	0.655701i	$0.772373\pi$
$30$	3.78933	0.691834
$31$	5.99102	1.07602	0.538009	−	0.842939i	$-0.319176\pi$
$31$	5.99102	1.07602	0.538009	+	0.842939i	$0.319176\pi$
$32$	−1.00000	−0.176777
$33$	−3.56566	−0.620702
$34$	6.54138	1.12184
$35$	−5.91655	−1.00008
$36$	3.87363	0.645605
$37$	−10.8895	−1.79023	−0.895115	−	0.445836i	$-0.852906\pi$
$37$	−10.8895	−1.79023	−0.895115	+	0.445836i	$0.852906\pi$
$38$	7.18152	1.16500
$39$	14.3429	2.29670
$40$	−1.44534	−0.228528
$41$	−0.609989	−0.0952643	−0.0476322	−	0.998865i	$-0.515168\pi$
$41$	−0.609989	−0.0952643	−0.0476322	+	0.998865i	$0.515168\pi$
$42$	−10.7323	−1.65603
$43$	−3.38869	−0.516771	−0.258385	−	0.966042i	$-0.583190\pi$
$43$	−3.38869	−0.516771	−0.258385	+	0.966042i	$0.583190\pi$
$44$	1.36002	0.205031
$45$	5.59871	0.834606
$46$	−0.364985	−0.0538141
$47$	6.02904	0.879425	0.439713	−	0.898138i	$-0.355080\pi$
$47$	6.02904	0.879425	0.439713	+	0.898138i	$0.355080\pi$
$48$	−2.62176	−0.378419
$49$	9.75706	1.39387
$50$	2.91100	0.411677
$51$	17.1499	2.40147
$52$	−5.47069	−0.758649
$53$	−3.46241	−0.475599	−0.237800	−	0.971314i	$-0.576426\pi$
$53$	−3.46241	−0.475599	−0.237800	+	0.971314i	$0.576426\pi$
$54$	2.29046	0.311692
$55$	1.96570	0.265054
$56$	4.09354	0.547022
$57$	18.8282	2.49386
$58$	8.13182	1.06776
$59$	1.05886	0.137852	0.0689260	−	0.997622i	$-0.478043\pi$
$59$	1.05886	0.137852	0.0689260	+	0.997622i	$0.478043\pi$
$60$	−3.78933	−0.489201
$61$	3.80729	0.487473	0.243737	−	0.969841i	$-0.421627\pi$
$61$	3.80729	0.487473	0.243737	+	0.969841i	$0.421627\pi$
$62$	−5.99102	−0.760860
$63$	−15.8569	−1.99778
$64$	1.00000	0.125000
$65$	−7.90700	−0.980743
$66$	3.56566	0.438902
$67$	−13.4770	−1.64648	−0.823239	−	0.567694i	$-0.807836\pi$
$67$	−13.4770	−1.64648	−0.823239	+	0.567694i	$0.807836\pi$
$68$	−6.54138	−0.793258
$69$	−0.956904	−0.115198
$70$	5.91655	0.707163
$71$	4.01685	0.476712	0.238356	−	0.971178i	$-0.423391\pi$
$71$	4.01685	0.476712	0.238356	+	0.971178i	$0.423391\pi$
$72$	−3.87363	−0.456512
$73$	−16.8267	−1.96942	−0.984710	−	0.174204i	$-0.944265\pi$
$73$	−16.8267	−1.96942	−0.984710	+	0.174204i	$0.944265\pi$
$74$	10.8895	1.26588
$75$	7.63194	0.881261
$76$	−7.18152	−0.823777
$77$	−5.56731	−0.634454
$78$	−14.3429	−1.62401
$79$	−7.89704	−0.888486	−0.444243	−	0.895906i	$-0.646527\pi$
$79$	−7.89704	−0.888486	−0.444243	+	0.895906i	$0.646527\pi$
$80$	1.44534	0.161594
$81$	−5.61587	−0.623985
$82$	0.609989	0.0673621
$83$	−1.45700	−0.159926	−0.0799630	−	0.996798i	$-0.525480\pi$
$83$	−1.45700	−0.159926	−0.0799630	+	0.996798i	$0.525480\pi$
$84$	10.7323	1.17099
$85$	−9.45450	−1.02548
$86$	3.38869	0.365412
$87$	21.3197	2.28571
$88$	−1.36002	−0.144979
$89$	12.9834	1.37624	0.688118	−	0.725599i	$-0.258437\pi$
$89$	12.9834	1.37624	0.688118	+	0.725599i	$0.258437\pi$
$90$	−5.59871	−0.590156
$91$	22.3945	2.34758
$92$	0.364985	0.0380523
$93$	−15.7070	−1.62874
$94$	−6.02904	−0.621848
$95$	−10.3797	−1.06494
$96$	2.62176	0.267582
$97$	−1.54670	−0.157044	−0.0785218	−	0.996912i	$-0.525020\pi$
$97$	−1.54670	−0.157044	−0.0785218	+	0.996912i	$0.525020\pi$
$98$	−9.75706	−0.985612
$99$	5.26824	0.529478
$100$	−2.91100	−0.291100
$101$	4.12010	0.409965	0.204983	−	0.978766i	$-0.434286\pi$
$101$	4.12010	0.409965	0.204983	+	0.978766i	$0.434286\pi$
$102$	−17.1499	−1.69810
$103$	−5.24149	−0.516459	−0.258230	−	0.966084i	$-0.583139\pi$
$103$	−5.24149	−0.516459	−0.258230	+	0.966084i	$0.583139\pi$
$104$	5.47069	0.536446
$105$	15.5118	1.51379
$106$	3.46241	0.336299
$107$	15.2504	1.47431	0.737156	−	0.675722i	$-0.236168\pi$
$107$	15.2504	1.47431	0.737156	+	0.675722i	$0.236168\pi$
$108$	−2.29046	−0.220399
$109$	−4.96261	−0.475332	−0.237666	−	0.971347i	$-0.576382\pi$
$109$	−4.96261	−0.475332	−0.237666	+	0.971347i	$0.576382\pi$
$110$	−1.96570	−0.187422
$111$	28.5498	2.70982
$112$	−4.09354	−0.386803
$113$	−13.4851	−1.26857	−0.634287	−	0.773097i	$-0.718706\pi$
$113$	−13.4851	−1.26857	−0.634287	+	0.773097i	$0.718706\pi$
$114$	−18.8282	−1.76343
$115$	0.527527	0.0491921
$116$	−8.13182	−0.755021
$117$	−21.1915	−1.95915
$118$	−1.05886	−0.0974760
$119$	26.7774	2.45468
$120$	3.78933	0.345917
$121$	−9.15033	−0.831848
$122$	−3.80729	−0.344696
$123$	1.59925	0.144199
$124$	5.99102	0.538009
$125$	−11.4341	−1.02269
$126$	15.8569	1.41264
$127$	8.13770	0.722104	0.361052	−	0.932546i	$-0.382418\pi$
$127$	8.13770	0.722104	0.361052	+	0.932546i	$0.382418\pi$
$128$	−1.00000	−0.0883883
$129$	8.88434	0.782223
$130$	7.90700	0.693490
$131$	−15.0648	−1.31621	−0.658107	−	0.752925i	$-0.728642\pi$
$131$	−15.0648	−1.31621	−0.658107	+	0.752925i	$0.728642\pi$
$132$	−3.56566	−0.310351
$133$	29.3978	2.54912
$134$	13.4770	1.16424
$135$	−3.31048	−0.284921
$136$	6.54138	0.560918
$137$	18.0039	1.53817	0.769087	−	0.639144i	$-0.220711\pi$
$137$	18.0039	1.53817	0.769087	+	0.639144i	$0.220711\pi$
$138$	0.956904	0.0814570
$139$	−21.2018	−1.79832	−0.899158	−	0.437624i	$-0.855820\pi$
$139$	−21.2018	−1.79832	−0.899158	+	0.437624i	$0.855820\pi$
$140$	−5.91655	−0.500039
$141$	−15.8067	−1.33116
$142$	−4.01685	−0.337086
$143$	−7.44028	−0.622187
$144$	3.87363	0.322803
$145$	−11.7532	−0.976053
$146$	16.8267	1.39259
$147$	−25.5807	−2.10986
$148$	−10.8895	−0.895115
$149$	−7.49989	−0.614415	−0.307208	−	0.951643i	$-0.599395\pi$
$149$	−7.49989	−0.614415	−0.307208	+	0.951643i	$0.599395\pi$
$150$	−7.63194	−0.623146
$151$	−16.9662	−1.38069	−0.690347	−	0.723479i	$-0.742542\pi$
$151$	−16.9662	−1.38069	−0.690347	+	0.723479i	$0.742542\pi$
$152$	7.18152	0.582498
$153$	−25.3389	−2.04853
$154$	5.56731	0.448627
$155$	8.65905	0.695511
$156$	14.3429	1.14835
$157$	−9.19808	−0.734086	−0.367043	−	0.930204i	$-0.619630\pi$
$157$	−9.19808	−0.734086	−0.367043	+	0.930204i	$0.619630\pi$
$158$	7.89704	0.628254
$159$	9.07762	0.719902
$160$	−1.44534	−0.114264
$161$	−1.49408	−0.117750
$162$	5.61587	0.441224
$163$	13.3398	1.04485	0.522425	−	0.852685i	$-0.325027\pi$
$163$	13.3398	1.04485	0.522425	+	0.852685i	$0.325027\pi$
$164$	−0.609989	−0.0476322
$165$	−5.15358	−0.401206
$166$	1.45700	0.113085
$167$	13.9074	1.07619	0.538095	−	0.842884i	$-0.319144\pi$
$167$	13.9074	1.07619	0.538095	+	0.842884i	$0.319144\pi$
$168$	−10.7323	−0.828013
$169$	16.9285	1.30219
$170$	9.45450	0.725127
$171$	−27.8186	−2.12734
$172$	−3.38869	−0.258385
$173$	−14.7694	−1.12290	−0.561448	−	0.827512i	$-0.689756\pi$
$173$	−14.7694	−1.12290	−0.561448	+	0.827512i	$0.689756\pi$
$174$	−21.3197	−1.61624
$175$	11.9163	0.900786
$176$	1.36002	0.102516
$177$	−2.77608	−0.208663
$178$	−12.9834	−0.973145
$179$	−13.4258	−1.00349	−0.501746	−	0.865015i	$-0.667309\pi$
$179$	−13.4258	−1.00349	−0.501746	+	0.865015i	$0.667309\pi$
$180$	5.59871	0.417303
$181$	1.06095	0.0788597	0.0394299	−	0.999222i	$-0.487446\pi$
$181$	1.06095	0.0788597	0.0394299	+	0.999222i	$0.487446\pi$
$182$	−22.3945	−1.65999
$183$	−9.98180	−0.737876
$184$	−0.364985	−0.0269071
$185$	−15.7391	−1.15716
$186$	15.7070	1.15169
$187$	−8.89643	−0.650572
$188$	6.02904	0.439713
$189$	9.37607	0.682009
$190$	10.3797	0.753025
$191$	−24.7184	−1.78856	−0.894281	−	0.447505i	$-0.852313\pi$
$191$	−24.7184	−1.78856	−0.894281	+	0.447505i	$0.852313\pi$
$192$	−2.62176	−0.189209
$193$	−3.02058	−0.217426	−0.108713	−	0.994073i	$-0.534673\pi$
$193$	−3.02058	−0.217426	−0.108713	+	0.994073i	$0.534673\pi$
$194$	1.54670	0.111047
$195$	20.7303	1.48453
$196$	9.75706	0.696933
$197$	18.7157	1.33344	0.666720	−	0.745308i	$-0.267698\pi$
$197$	18.7157	1.33344	0.666720	+	0.745308i	$0.267698\pi$
$198$	−5.26824	−0.374397
$199$	7.74076	0.548728	0.274364	−	0.961626i	$-0.411533\pi$
$199$	7.74076	0.548728	0.274364	+	0.961626i	$0.411533\pi$
$200$	2.91100	0.205839
$201$	35.3335	2.49223
$202$	−4.12010	−0.289889
$203$	33.2879	2.33635
$204$	17.1499	1.20074
$205$	−0.881641	−0.0615765
$206$	5.24149	0.365192
$207$	1.41382	0.0982671
$208$	−5.47069	−0.379324
$209$	−9.76705	−0.675601
$210$	−15.5118	−1.07041
$211$	5.83190	0.401484	0.200742	−	0.979644i	$-0.435665\pi$
$211$	5.83190	0.401484	0.200742	+	0.979644i	$0.435665\pi$
$212$	−3.46241	−0.237800
$213$	−10.5312	−0.721587
$214$	−15.2504	−1.04250
$215$	−4.89780	−0.334027
$216$	2.29046	0.155846
$217$	−24.5245	−1.66483
$218$	4.96261	0.336111
$219$	44.1157	2.98106
$220$	1.96570	0.132527
$221$	35.7859	2.40722
$222$	−28.5498	−1.91614
$223$	1.68068	0.112547	0.0562734	−	0.998415i	$-0.482078\pi$
$223$	1.68068	0.112547	0.0562734	+	0.998415i	$0.482078\pi$
$224$	4.09354	0.273511
$225$	−11.2761	−0.751743
$226$	13.4851	0.897018
$227$	19.5353	1.29661	0.648303	−	0.761382i	$-0.275479\pi$
$227$	19.5353	1.29661	0.648303	+	0.761382i	$0.275479\pi$
$228$	18.8282	1.24693
$229$	−5.15115	−0.340398	−0.170199	−	0.985410i	$-0.554441\pi$
$229$	−5.15115	−0.340398	−0.170199	+	0.985410i	$0.554441\pi$
$230$	−0.527527	−0.0347841
$231$	14.5962	0.960357
$232$	8.13182	0.533880
$233$	−8.24409	−0.540088	−0.270044	−	0.962848i	$-0.587038\pi$
$233$	−8.24409	−0.540088	−0.270044	+	0.962848i	$0.587038\pi$
$234$	21.1915	1.38533
$235$	8.71400	0.568438
$236$	1.05886	0.0689260
$237$	20.7041	1.34488
$238$	−26.7774	−1.73572
$239$	11.2771	0.729453	0.364726	−	0.931115i	$-0.381163\pi$
$239$	11.2771	0.729453	0.364726	+	0.931115i	$0.381163\pi$
$240$	−3.78933	−0.244600
$241$	5.90314	0.380254	0.190127	−	0.981759i	$-0.439110\pi$
$241$	5.90314	0.380254	0.190127	+	0.981759i	$0.439110\pi$
$242$	9.15033	0.588206
$243$	21.5948	1.38531
$244$	3.80729	0.243737
$245$	14.1022	0.900959
$246$	−1.59925	−0.101964
$247$	39.2879	2.49983
$248$	−5.99102	−0.380430
$249$	3.81989	0.242076
$250$	11.4341	0.723154
$251$	8.33837	0.526313	0.263157	−	0.964753i	$-0.415236\pi$
$251$	8.33837	0.526313	0.263157	+	0.964753i	$0.415236\pi$
$252$	−15.8569	−0.998889
$253$	0.496389	0.0312077
$254$	−8.13770	−0.510605
$255$	24.7874	1.55225
$256$	1.00000	0.0625000
$257$	31.9857	1.99521	0.997607	−	0.0691432i	$-0.0220265\pi$
$257$	31.9857	1.99521	0.997607	+	0.0691432i	$0.0220265\pi$
$258$	−8.88434	−0.553115
$259$	44.5767	2.76986
$260$	−7.90700	−0.490371
$261$	−31.4997	−1.94978
$262$	15.0648	0.930704
$263$	7.92671	0.488782	0.244391	−	0.969677i	$-0.421412\pi$
$263$	7.92671	0.488782	0.244391	+	0.969677i	$0.421412\pi$
$264$	3.56566	0.219451
$265$	−5.00436	−0.307415
$266$	−29.3978	−1.80250
$267$	−34.0393	−2.08317
$268$	−13.4770	−0.823239
$269$	−27.5788	−1.68151	−0.840754	−	0.541418i	$-0.817888\pi$
$269$	−27.5788	−1.68151	−0.840754	+	0.541418i	$0.817888\pi$
$270$	3.31048	0.201470
$271$	−23.1705	−1.40751	−0.703755	−	0.710443i	$-0.748495\pi$
$271$	−23.1705	−1.40751	−0.703755	+	0.710443i	$0.748495\pi$
$272$	−6.54138	−0.396629
$273$	−58.7130	−3.55347
$274$	−18.0039	−1.08765
$275$	−3.95903	−0.238738
$276$	−0.956904	−0.0575988
$277$	−14.1382	−0.849480	−0.424740	−	0.905315i	$-0.639634\pi$
$277$	−14.1382	−0.849480	−0.424740	+	0.905315i	$0.639634\pi$
$278$	21.2018	1.27160
$279$	23.2070	1.38937
$280$	5.91655	0.353581
$281$	−4.87885	−0.291048	−0.145524	−	0.989355i	$-0.546487\pi$
$281$	−4.87885	−0.291048	−0.145524	+	0.989355i	$0.546487\pi$
$282$	15.8067	0.941275
$283$	−12.8107	−0.761516	−0.380758	−	0.924675i	$-0.624337\pi$
$283$	−12.8107	−0.761516	−0.380758	+	0.924675i	$0.624337\pi$
$284$	4.01685	0.238356
$285$	27.2132	1.61197
$286$	7.44028	0.439953
$287$	2.49701	0.147394
$288$	−3.87363	−0.228256
$289$	25.7896	1.51704
$290$	11.7532	0.690173
$291$	4.05508	0.237713
$292$	−16.8267	−0.984710
$293$	−22.7712	−1.33031	−0.665154	−	0.746706i	$-0.731634\pi$
$293$	−22.7712	−1.33031	−0.665154	+	0.746706i	$0.731634\pi$
$294$	25.5807	1.49190
$295$	1.53041	0.0891040
$296$	10.8895	0.632942
$297$	−3.11508	−0.180755
$298$	7.49989	0.434457
$299$	−1.99672	−0.115473
$300$	7.63194	0.440630
$301$	13.8717	0.799554
$302$	16.9662	0.976298
$303$	−10.8019	−0.620554
$304$	−7.18152	−0.411889
$305$	5.50282	0.315090
$306$	25.3389	1.44853
$307$	26.5484	1.51520	0.757599	−	0.652721i	$-0.226372\pi$
$307$	26.5484	1.51520	0.757599	+	0.652721i	$0.226372\pi$
$308$	−5.56731	−0.317227
$309$	13.7419	0.781751
$310$	−8.65905	−0.491801
$311$	−18.3052	−1.03799	−0.518995	−	0.854777i	$-0.673694\pi$
$311$	−18.3052	−1.03799	−0.518995	+	0.854777i	$0.673694\pi$
$312$	−14.3429	−0.812004
$313$	−1.74796	−0.0988004	−0.0494002	−	0.998779i	$-0.515731\pi$
$313$	−1.74796	−0.0988004	−0.0494002	+	0.998779i	$0.515731\pi$
$314$	9.19808	0.519078
$315$	−22.9185	−1.29131
$316$	−7.89704	−0.444243
$317$	4.85941	0.272931	0.136466	−	0.990645i	$-0.456426\pi$
$317$	4.85941	0.272931	0.136466	+	0.990645i	$0.456426\pi$
$318$	−9.07762	−0.509048
$319$	−11.0595	−0.619212
$320$	1.44534	0.0807968
$321$	−39.9829	−2.23163
$322$	1.49408	0.0832618
$323$	46.9770	2.61387
$324$	−5.61587	−0.311993
$325$	15.9252	0.883370
$326$	−13.3398	−0.738821
$327$	13.0108	0.719498
$328$	0.609989	0.0336810
$329$	−24.6801	−1.36066
$330$	5.15358	0.283695
$331$	14.5539	0.799953	0.399977	−	0.916525i	$-0.369018\pi$
$331$	14.5539	0.799953	0.399977	+	0.916525i	$0.369018\pi$
$332$	−1.45700	−0.0799630
$333$	−42.1821	−2.31156
$334$	−13.9074	−0.760981
$335$	−19.4788	−1.06424
$336$	10.7323	0.585494
$337$	23.1858	1.26301	0.631505	−	0.775372i	$-0.282438\pi$
$337$	23.1858	1.26301	0.631505	+	0.775372i	$0.282438\pi$
$338$	−16.9285	−0.920789
$339$	35.3548	1.92021
$340$	−9.45450	−0.512742
$341$	8.14793	0.441235
$342$	27.8186	1.50426
$343$	−11.2861	−0.609393
$344$	3.38869	0.182706
$345$	−1.38305	−0.0744609
$346$	14.7694	0.794008
$347$	27.3960	1.47069	0.735346	−	0.677692i	$-0.237020\pi$
$347$	27.3960	1.47069	0.735346	+	0.677692i	$0.237020\pi$
$348$	21.3197	1.14286
$349$	26.3999	1.41315	0.706577	−	0.707636i	$-0.250238\pi$
$349$	26.3999	1.41315	0.706577	+	0.707636i	$0.250238\pi$
$350$	−11.9163	−0.636952
$351$	12.5304	0.668823
$352$	−1.36002	−0.0724896
$353$	−13.7470	−0.731681	−0.365840	−	0.930678i	$-0.619218\pi$
$353$	−13.7470	−0.731681	−0.365840	+	0.930678i	$0.619218\pi$
$354$	2.77608	0.147547
$355$	5.80570	0.308135
$356$	12.9834	0.688118
$357$	−70.2039	−3.71558
$358$	13.4258	0.709575
$359$	−3.82307	−0.201774	−0.100887	−	0.994898i	$-0.532168\pi$
$359$	−3.82307	−0.201774	−0.100887	+	0.994898i	$0.532168\pi$
$360$	−5.59871	−0.295078
$361$	32.5743	1.71444
$362$	−1.06095	−0.0557622
$363$	23.9900	1.25915
$364$	22.3945	1.17379
$365$	−24.3203	−1.27298
$366$	9.98180	0.521757
$367$	23.1945	1.21074	0.605372	−	0.795943i	$-0.293024\pi$
$367$	23.1945	1.21074	0.605372	+	0.795943i	$0.293024\pi$
$368$	0.364985	0.0190262
$369$	−2.36287	−0.123006
$370$	15.7391	0.818235
$371$	14.1735	0.735853
$372$	−15.7070	−0.814371
$373$	13.4254	0.695138	0.347569	−	0.937654i	$-0.387007\pi$
$373$	13.4254	0.695138	0.347569	+	0.937654i	$0.387007\pi$
$374$	8.89643	0.460024
$375$	29.9774	1.54803
$376$	−6.02904	−0.310924
$377$	44.4867	2.29118
$378$	−9.37607	−0.482253
$379$	14.3281	0.735985	0.367993	−	0.929829i	$-0.380045\pi$
$379$	14.3281	0.735985	0.367993	+	0.929829i	$0.380045\pi$
$380$	−10.3797	−0.532469
$381$	−21.3351	−1.09303
$382$	24.7184	1.26470
$383$	−4.47181	−0.228499	−0.114249	−	0.993452i	$-0.536446\pi$
$383$	−4.47181	−0.228499	−0.114249	+	0.993452i	$0.536446\pi$
$384$	2.62176	0.133791
$385$	−8.04665	−0.410095
$386$	3.02058	0.153743
$387$	−13.1265	−0.667260
$388$	−1.54670	−0.0785218
$389$	−15.9884	−0.810643	−0.405322	−	0.914174i	$-0.632840\pi$
$389$	−15.9884	−0.810643	−0.405322	+	0.914174i	$0.632840\pi$
$390$	−20.7303	−1.04972
$391$	−2.38750	−0.120741
$392$	−9.75706	−0.492806
$393$	39.4962	1.99232
$394$	−18.7157	−0.942884
$395$	−11.4139	−0.574295
$396$	5.26824	0.264739
$397$	−8.14136	−0.408603	−0.204302	−	0.978908i	$-0.565492\pi$
$397$	−8.14136	−0.408603	−0.204302	+	0.978908i	$0.565492\pi$
$398$	−7.74076	−0.388009
$399$	−77.0741	−3.85853
$400$	−2.91100	−0.145550
$401$	−28.3772	−1.41709	−0.708545	−	0.705665i	$-0.750648\pi$
$401$	−28.3772	−1.41709	−0.708545	+	0.705665i	$0.750648\pi$
$402$	−35.3335	−1.76228
$403$	−32.7750	−1.63264
$404$	4.12010	0.204983
$405$	−8.11683	−0.403328
$406$	−33.2879	−1.65205
$407$	−14.8100	−0.734106
$408$	−17.1499	−0.849048
$409$	29.1329	1.44053	0.720264	−	0.693700i	$-0.244021\pi$
$409$	29.1329	1.44053	0.720264	+	0.693700i	$0.244021\pi$
$410$	0.881641	0.0435411
$411$	−47.2018	−2.32829
$412$	−5.24149	−0.258230
$413$	−4.33449	−0.213286
$414$	−1.41382	−0.0694854
$415$	−2.10585	−0.103372
$416$	5.47069	0.268223
$417$	55.5861	2.72207
$418$	9.76705	0.477722
$419$	10.9845	0.536628	0.268314	−	0.963331i	$-0.413533\pi$
$419$	10.9845	0.536628	0.268314	+	0.963331i	$0.413533\pi$
$420$	15.5118	0.756897
$421$	11.3632	0.553807	0.276903	−	0.960898i	$-0.410692\pi$
$421$	11.3632	0.553807	0.276903	+	0.960898i	$0.410692\pi$
$422$	−5.83190	−0.283892
$423$	23.3543	1.13552
$424$	3.46241	0.168150
$425$	19.0419	0.923670
$426$	10.5312	0.510239
$427$	−15.5853	−0.754225
$428$	15.2504	0.737156
$429$	19.5066	0.941789
$430$	4.89780	0.236193
$431$	37.3716	1.80012	0.900062	−	0.435761i	$-0.143521\pi$
$431$	37.3716	1.80012	0.900062	+	0.435761i	$0.143521\pi$
$432$	−2.29046	−0.110200
$433$	14.2547	0.685038	0.342519	−	0.939511i	$-0.388720\pi$
$433$	14.2547	0.685038	0.342519	+	0.939511i	$0.388720\pi$
$434$	24.5245	1.17721
$435$	30.8142	1.47743
$436$	−4.96261	−0.237666
$437$	−2.62115	−0.125387
$438$	−44.1157	−2.10793
$439$	−2.48473	−0.118590	−0.0592948	−	0.998241i	$-0.518885\pi$
$439$	−2.48473	−0.118590	−0.0592948	+	0.998241i	$0.518885\pi$
$440$	−1.96570	−0.0937108
$441$	37.7953	1.79977
$442$	−35.7859	−1.70216
$443$	−27.4112	−1.30235	−0.651173	−	0.758930i	$-0.725723\pi$
$443$	−27.4112	−1.30235	−0.651173	+	0.758930i	$0.725723\pi$
$444$	28.5498	1.35491
$445$	18.7654	0.889564
$446$	−1.68068	−0.0795827
$447$	19.6629	0.930025
$448$	−4.09354	−0.193402
$449$	−18.5159	−0.873822	−0.436911	−	0.899505i	$-0.643927\pi$
$449$	−18.5159	−0.873822	−0.436911	+	0.899505i	$0.643927\pi$
$450$	11.2761	0.531562
$451$	−0.829601	−0.0390644
$452$	−13.4851	−0.634287
$453$	44.4814	2.08992
$454$	−19.5353	−0.916839
$455$	32.3676	1.51742
$456$	−18.8282	−0.881713
$457$	−19.1505	−0.895821	−0.447911	−	0.894078i	$-0.647832\pi$
$457$	−19.1505	−0.895821	−0.447911	+	0.894078i	$0.647832\pi$
$458$	5.15115	0.240698
$459$	14.9827	0.699334
$460$	0.527527	0.0245961
$461$	−14.9860	−0.697968	−0.348984	−	0.937129i	$-0.613473\pi$
$461$	−14.9860	−0.697968	−0.348984	+	0.937129i	$0.613473\pi$
$462$	−14.5962	−0.679075
$463$	−34.3496	−1.59636	−0.798180	−	0.602419i	$-0.794204\pi$
$463$	−34.3496	−1.59636	−0.798180	+	0.602419i	$0.794204\pi$
$464$	−8.13182	−0.377510
$465$	−22.7020	−1.05278
$466$	8.24409	0.381900
$467$	6.33991	0.293376	0.146688	−	0.989183i	$-0.453139\pi$
$467$	6.33991	0.293376	0.146688	+	0.989183i	$0.453139\pi$
$468$	−21.1915	−0.979576
$469$	55.1687	2.54745
$470$	−8.71400	−0.401947
$471$	24.1152	1.11117
$472$	−1.05886	−0.0487380
$473$	−4.60870	−0.211908
$474$	−20.7041	−0.950973
$475$	20.9054	0.959206
$476$	26.7774	1.22734
$477$	−13.4121	−0.614099
$478$	−11.2771	−0.515801
$479$	−32.6955	−1.49389	−0.746947	−	0.664883i	$-0.768481\pi$
$479$	−32.6955	−1.49389	−0.746947	+	0.664883i	$0.768481\pi$
$480$	3.78933	0.172958
$481$	59.5733	2.71631
$482$	−5.90314	−0.268880
$483$	3.91712	0.178235
$484$	−9.15033	−0.415924
$485$	−2.23550	−0.101509
$486$	−21.5948	−0.979562
$487$	−2.28521	−0.103553	−0.0517764	−	0.998659i	$-0.516488\pi$
$487$	−2.28521	−0.103553	−0.0517764	+	0.998659i	$0.516488\pi$
$488$	−3.80729	−0.172348
$489$	−34.9737	−1.58156
$490$	−14.1022	−0.637074
$491$	−32.2680	−1.45623	−0.728117	−	0.685453i	$-0.759604\pi$
$491$	−32.2680	−1.45623	−0.728117	+	0.685453i	$0.759604\pi$
$492$	1.59925	0.0720996
$493$	53.1933	2.39571
$494$	−39.2879	−1.76765
$495$	7.61438	0.342241
$496$	5.99102	0.269005
$497$	−16.4431	−0.737575
$498$	−3.81989	−0.171174
$499$	−17.9334	−0.802808	−0.401404	−	0.915901i	$-0.631478\pi$
$499$	−17.9334	−0.802808	−0.401404	+	0.915901i	$0.631478\pi$
$500$	−11.4341	−0.511347
$501$	−36.4620	−1.62900
$502$	−8.33837	−0.372160
$503$	35.0425	1.56247	0.781235	−	0.624238i	$-0.214590\pi$
$503$	35.0425	1.56247	0.781235	+	0.624238i	$0.214590\pi$
$504$	15.8569	0.706321
$505$	5.95494	0.264991
$506$	−0.496389	−0.0220672
$507$	−44.3825	−1.97110
$508$	8.13770	0.361052
$509$	30.9489	1.37178	0.685892	−	0.727703i	$-0.259412\pi$
$509$	30.9489	1.37178	0.685892	+	0.727703i	$0.259412\pi$
$510$	−24.7874	−1.09761
$511$	68.8808	3.04711
$512$	−1.00000	−0.0441942
$513$	16.4490	0.726240
$514$	−31.9857	−1.41083
$515$	−7.57572	−0.333826
$516$	8.88434	0.391111
$517$	8.19964	0.360620
$518$	−44.5767	−1.95859
$519$	38.7219	1.69970
$520$	7.90700	0.346745
$521$	16.1727	0.708539	0.354270	−	0.935143i	$-0.384730\pi$
$521$	16.1727	0.708539	0.354270	+	0.935143i	$0.384730\pi$
$522$	31.4997	1.37870
$523$	41.9849	1.83587	0.917936	−	0.396729i	$-0.129855\pi$
$523$	41.9849	1.83587	0.917936	+	0.396729i	$0.129855\pi$
$524$	−15.0648	−0.658107
$525$	−31.2417	−1.36350
$526$	−7.92671	−0.345621
$527$	−39.1895	−1.70712
$528$	−3.56566	−0.155175
$529$	−22.8668	−0.994208
$530$	5.00436	0.217375
$531$	4.10164	0.177996
$532$	29.3978	1.27456
$533$	3.33707	0.144544
$534$	34.0393	1.47303
$535$	22.0420	0.952959
$536$	13.4770	0.582118
$537$	35.1992	1.51896
$538$	27.5788	1.18901
$539$	13.2698	0.571572
$540$	−3.31048	−0.142461
$541$	3.66219	0.157450	0.0787248	−	0.996896i	$-0.474915\pi$
$541$	3.66219	0.157450	0.0787248	+	0.996896i	$0.474915\pi$
$542$	23.1705	0.995259
$543$	−2.78155	−0.119368
$544$	6.54138	0.280459
$545$	−7.17265	−0.307243
$546$	58.7130	2.51269
$547$	−37.4615	−1.60174	−0.800869	−	0.598839i	$-0.795629\pi$
$547$	−37.4615	−1.60174	−0.800869	+	0.598839i	$0.795629\pi$
$548$	18.0039	0.769087
$549$	14.7480	0.629431
$550$	3.95903	0.168814
$551$	58.3989	2.48788
$552$	0.956904	0.0407285
$553$	32.3268	1.37468
$554$	14.1382	0.600673
$555$	41.2641	1.75156
$556$	−21.2018	−0.899158
$557$	−31.2437	−1.32384	−0.661919	−	0.749576i	$-0.730258\pi$
$557$	−31.2437	−1.32384	−0.661919	+	0.749576i	$0.730258\pi$
$558$	−23.2070	−0.982431
$559$	18.5385	0.784095
$560$	−5.91655	−0.250020
$561$	23.3243	0.984754
$562$	4.87885	0.205802
$563$	−40.1601	−1.69254	−0.846272	−	0.532750i	$-0.821158\pi$
$563$	−40.1601	−1.69254	−0.846272	+	0.532750i	$0.821158\pi$
$564$	−15.8067	−0.665582
$565$	−19.4906	−0.819975
$566$	12.8107	0.538473
$567$	22.9888	0.965438
$568$	−4.01685	−0.168543
$569$	29.1994	1.22410	0.612052	−	0.790817i	$-0.290344\pi$
$569$	29.1994	1.22410	0.612052	+	0.790817i	$0.290344\pi$
$570$	−27.2132	−1.13983
$571$	5.97277	0.249953	0.124976	−	0.992160i	$-0.460114\pi$
$571$	5.97277	0.249953	0.124976	+	0.992160i	$0.460114\pi$
$572$	−7.44028	−0.311094
$573$	64.8058	2.70730
$574$	−2.49701	−0.104223
$575$	−1.06247	−0.0443081
$576$	3.87363	0.161401
$577$	−28.5601	−1.18897	−0.594486	−	0.804106i	$-0.702644\pi$
$577$	−28.5601	−1.18897	−0.594486	+	0.804106i	$0.702644\pi$
$578$	−25.7896	−1.07271
$579$	7.91923	0.329112
$580$	−11.7532	−0.488026
$581$	5.96427	0.247440
$582$	−4.05508	−0.168088
$583$	−4.70897	−0.195026
$584$	16.8267	0.696295
$585$	−30.6288	−1.26635
$586$	22.7712	0.940670
$587$	10.9831	0.453322	0.226661	−	0.973974i	$-0.427219\pi$
$587$	10.9831	0.453322	0.226661	+	0.973974i	$0.427219\pi$
$588$	−25.5807	−1.05493
$589$	−43.0246	−1.77280
$590$	−1.53041	−0.0630060
$591$	−49.0681	−2.01839
$592$	−10.8895	−0.447557
$593$	−34.2296	−1.40564	−0.702822	−	0.711366i	$-0.748077\pi$
$593$	−34.2296	−1.40564	−0.702822	+	0.711366i	$0.748077\pi$
$594$	3.11508	0.127813
$595$	38.7024	1.58664
$596$	−7.49989	−0.307208
$597$	−20.2944	−0.830595
$598$	1.99672	0.0816520
$599$	0.488672	0.0199666	0.00998330	−	0.999950i	$-0.496822\pi$
$599$	0.488672	0.0199666	0.00998330	+	0.999950i	$0.496822\pi$
$600$	−7.63194	−0.311573
$601$	−11.1034	−0.452918	−0.226459	−	0.974021i	$-0.572715\pi$
$601$	−11.1034	−0.452918	−0.226459	+	0.974021i	$0.572715\pi$
$602$	−13.8717	−0.565370
$603$	−52.2050	−2.12595
$604$	−16.9662	−0.690347
$605$	−13.2253	−0.537686
$606$	10.8019	0.438798
$607$	30.3342	1.23123	0.615614	−	0.788048i	$-0.288908\pi$
$607$	30.3342	1.23123	0.615614	+	0.788048i	$0.288908\pi$
$608$	7.18152	0.291249
$609$	−87.2730	−3.53648
$610$	−5.50282	−0.222803
$611$	−32.9830	−1.33435
$612$	−25.3389	−1.02426
$613$	16.0652	0.648869	0.324434	−	0.945908i	$-0.394826\pi$
$613$	16.0652	0.648869	0.324434	+	0.945908i	$0.394826\pi$
$614$	−26.5484	−1.07141
$615$	2.31145	0.0932067
$616$	5.56731	0.224313
$617$	−27.7335	−1.11651	−0.558255	−	0.829669i	$-0.688529\pi$
$617$	−27.7335	−1.11651	−0.558255	+	0.829669i	$0.688529\pi$
$618$	−13.7419	−0.552782
$619$	21.0334	0.845405	0.422703	−	0.906268i	$-0.361081\pi$
$619$	21.0334	0.845405	0.422703	+	0.906268i	$0.361081\pi$
$620$	8.65905	0.347756
$621$	−0.835982	−0.0335468
$622$	18.3052	0.733970
$623$	−53.1480	−2.12933
$624$	14.3429	0.574174
$625$	−1.97109	−0.0788438
$626$	1.74796	0.0698624
$627$	25.6069	1.02264
$628$	−9.19808	−0.367043
$629$	71.2326	2.84023
$630$	22.9185	0.913096
$631$	−4.31983	−0.171970	−0.0859849	−	0.996296i	$-0.527404\pi$
$631$	−4.31983	−0.171970	−0.0859849	+	0.996296i	$0.527404\pi$
$632$	7.89704	0.314127
$633$	−15.2898	−0.607717
$634$	−4.85941	−0.192992
$635$	11.7617	0.466750
$636$	9.07762	0.359951
$637$	−53.3779	−2.11491
$638$	11.0595	0.437849
$639$	15.5598	0.615536
$640$	−1.44534	−0.0571320
$641$	3.77164	0.148971	0.0744855	−	0.997222i	$-0.476269\pi$
$641$	3.77164	0.148971	0.0744855	+	0.997222i	$0.476269\pi$
$642$	39.9829	1.57800
$643$	−12.1021	−0.477261	−0.238630	−	0.971110i	$-0.576698\pi$
$643$	−12.1021	−0.477261	−0.238630	+	0.971110i	$0.576698\pi$
$644$	−1.49408	−0.0588750
$645$	12.8409	0.505609
$646$	−46.9770	−1.84829
$647$	−35.5611	−1.39805	−0.699026	−	0.715096i	$-0.746383\pi$
$647$	−35.5611	−1.39805	−0.699026	+	0.715096i	$0.746383\pi$
$648$	5.61587	0.220612
$649$	1.44008	0.0565280
$650$	−15.9252	−0.624637
$651$	64.2973	2.52001
$652$	13.3398	0.522425
$653$	27.2904	1.06796	0.533978	−	0.845499i	$-0.320697\pi$
$653$	27.2904	1.06796	0.533978	+	0.845499i	$0.320697\pi$
$654$	−13.0108	−0.508762
$655$	−21.7737	−0.850767
$656$	−0.609989	−0.0238161
$657$	−65.1806	−2.54294
$658$	24.6801	0.962130
$659$	−31.5019	−1.22714	−0.613570	−	0.789640i	$-0.710267\pi$
$659$	−31.5019	−1.22714	−0.613570	+	0.789640i	$0.710267\pi$
$660$	−5.15358	−0.200603
$661$	3.66417	0.142520	0.0712599	−	0.997458i	$-0.477298\pi$
$661$	3.66417	0.142520	0.0712599	+	0.997458i	$0.477298\pi$
$662$	−14.5539	−0.565652
$663$	−93.8220	−3.64375
$664$	1.45700	0.0565424
$665$	42.4898	1.64768
$666$	42.1821	1.63452
$667$	−2.96799	−0.114921
$668$	13.9074	0.538095
$669$	−4.40635	−0.170359
$670$	19.4788	0.752533
$671$	5.17801	0.199895
$672$	−10.7323	−0.414007
$673$	−22.7724	−0.877810	−0.438905	−	0.898533i	$-0.644634\pi$
$673$	−22.7724	−0.877810	−0.438905	+	0.898533i	$0.644634\pi$
$674$	−23.1858	−0.893082
$675$	6.66751	0.256633
$676$	16.9285	0.651096
$677$	−1.62301	−0.0623773	−0.0311887	−	0.999514i	$-0.509929\pi$
$677$	−1.62301	−0.0623773	−0.0311887	+	0.999514i	$0.509929\pi$
$678$	−35.3548	−1.35779
$679$	6.33148	0.242980
$680$	9.45450	0.362563
$681$	−51.2170	−1.96264
$682$	−8.14793	−0.312001
$683$	−21.3377	−0.816464	−0.408232	−	0.912878i	$-0.633855\pi$
$683$	−21.3377	−0.816464	−0.408232	+	0.912878i	$0.633855\pi$
$684$	−27.8186	−1.06367
$685$	26.0217	0.994237
$686$	11.2861	0.430906
$687$	13.5051	0.515252
$688$	−3.38869	−0.129193
$689$	18.9418	0.721625
$690$	1.38305	0.0526518
$691$	−14.3975	−0.547707	−0.273853	−	0.961771i	$-0.588298\pi$
$691$	−14.3975	−0.547707	−0.273853	+	0.961771i	$0.588298\pi$
$692$	−14.7694	−0.561448
$693$	−21.5657	−0.819214
$694$	−27.3960	−1.03994
$695$	−30.6438	−1.16239
$696$	−21.3197	−0.808121
$697$	3.99017	0.151138
$698$	−26.3999	−0.999251
$699$	21.6140	0.817518
$700$	11.9163	0.450393
$701$	−5.04224	−0.190443	−0.0952213	−	0.995456i	$-0.530356\pi$
$701$	−5.04224	−0.190443	−0.0952213	+	0.995456i	$0.530356\pi$
$702$	−12.5304	−0.472929
$703$	78.2035	2.94950
$704$	1.36002	0.0512579
$705$	−22.8460	−0.860431
$706$	13.7470	0.517376
$707$	−16.8658	−0.634304
$708$	−2.77608	−0.104331
$709$	−36.7624	−1.38064	−0.690320	−	0.723504i	$-0.742530\pi$
$709$	−36.7624	−1.38064	−0.690320	+	0.723504i	$0.742530\pi$
$710$	−5.80570	−0.217884
$711$	−30.5902	−1.14722
$712$	−12.9834	−0.486573
$713$	2.18663	0.0818900
$714$	70.2039	2.62731
$715$	−10.7537	−0.402166
$716$	−13.4258	−0.501746
$717$	−29.5658	−1.10415
$718$	3.82307	0.142676
$719$	41.7979	1.55880	0.779400	−	0.626527i	$-0.215524\pi$
$719$	41.7979	1.55880	0.779400	+	0.626527i	$0.215524\pi$
$720$	5.59871	0.208652
$721$	21.4562	0.799072
$722$	−32.5743	−1.21229
$723$	−15.4766	−0.575582
$724$	1.06095	0.0394299
$725$	23.6717	0.879146
$726$	−23.9900	−0.890352
$727$	−40.7724	−1.51216	−0.756082	−	0.654477i	$-0.772889\pi$
$727$	−40.7724	−1.51216	−0.756082	+	0.654477i	$0.772889\pi$
$728$	−22.3945	−0.829995
$729$	−39.7689	−1.47292
$730$	24.3203	0.900135
$731$	22.1667	0.819865
$732$	−9.98180	−0.368938
$733$	34.8986	1.28901	0.644505	−	0.764600i	$-0.277064\pi$
$733$	34.8986	1.28901	0.644505	+	0.764600i	$0.277064\pi$
$734$	−23.1945	−0.856126
$735$	−36.9727	−1.36376
$736$	−0.364985	−0.0134535
$737$	−18.3291	−0.675160
$738$	2.36287	0.0869786
$739$	35.4057	1.30242	0.651210	−	0.758897i	$-0.274262\pi$
$739$	35.4057	1.30242	0.651210	+	0.758897i	$0.274262\pi$
$740$	−15.7391	−0.578579
$741$	−103.004	−3.78393
$742$	−14.1735	−0.520326
$743$	18.3569	0.673450	0.336725	−	0.941603i	$-0.390681\pi$
$743$	18.3569	0.673450	0.336725	+	0.941603i	$0.390681\pi$
$744$	15.7070	0.575847
$745$	−10.8399	−0.397142
$746$	−13.4254	−0.491537
$747$	−5.64387	−0.206498
$748$	−8.89643	−0.325286
$749$	−62.4281	−2.28107
$750$	−29.9774	−1.09462
$751$	−14.6150	−0.533308	−0.266654	−	0.963792i	$-0.585918\pi$
$751$	−14.6150	−0.533308	−0.266654	+	0.963792i	$0.585918\pi$
$752$	6.02904	0.219856
$753$	−21.8612	−0.796667
$754$	−44.4867	−1.62011
$755$	−24.5220	−0.892445
$756$	9.37607	0.341004
$757$	12.2314	0.444558	0.222279	−	0.974983i	$-0.428650\pi$
$757$	12.2314	0.444558	0.222279	+	0.974983i	$0.428650\pi$
$758$	−14.3281	−0.520420
$759$	−1.30141	−0.0472383
$760$	10.3797	0.376512
$761$	19.6543	0.712468	0.356234	−	0.934397i	$-0.384061\pi$
$761$	19.6543	0.712468	0.356234	+	0.934397i	$0.384061\pi$
$762$	21.3351	0.772890
$763$	20.3146	0.735440
$764$	−24.7184	−0.894281
$765$	−36.6233	−1.32412
$766$	4.47181	0.161573
$767$	−5.79270	−0.209162
$768$	−2.62176	−0.0946047
$769$	−15.1372	−0.545862	−0.272931	−	0.962034i	$-0.587993\pi$
$769$	−15.1372	−0.545862	−0.272931	+	0.962034i	$0.587993\pi$
$770$	8.04665	0.289981
$771$	−83.8589	−3.02010
$772$	−3.02058	−0.108713
$773$	−31.6582	−1.13867	−0.569333	−	0.822107i	$-0.692799\pi$
$773$	−31.6582	−1.13867	−0.569333	+	0.822107i	$0.692799\pi$
$774$	13.1265	0.471824
$775$	−17.4398	−0.626458
$776$	1.54670	0.0555233
$777$	−116.870	−4.19267
$778$	15.9884	0.573211
$779$	4.38065	0.156953
$780$	20.7303	0.742263
$781$	5.46301	0.195482
$782$	2.38750	0.0853770
$783$	18.6256	0.665624
$784$	9.75706	0.348466
$785$	−13.2943	−0.474495
$786$	−39.4962	−1.40878
$787$	8.55072	0.304800	0.152400	−	0.988319i	$-0.451300\pi$
$787$	8.55072	0.304800	0.152400	+	0.988319i	$0.451300\pi$
$788$	18.7157	0.666720
$789$	−20.7819	−0.739856
$790$	11.4139	0.406088
$791$	55.2019	1.96275
$792$	−5.26824	−0.187199
$793$	−20.8285	−0.739642
$794$	8.14136	0.288926
$795$	13.1202	0.465327
$796$	7.74076	0.274364
$797$	13.7192	0.485960	0.242980	−	0.970031i	$-0.421875\pi$
$797$	13.7192	0.485960	0.242980	+	0.970031i	$0.421875\pi$
$798$	77.0741	2.72839
$799$	−39.4382	−1.39522
$800$	2.91100	0.102919
$801$	50.2928	1.77701
$802$	28.3772	1.00203
$803$	−22.8848	−0.807586
$804$	35.3335	1.24612
$805$	−2.15945	−0.0761106
$806$	32.7750	1.15445
$807$	72.3049	2.54525
$808$	−4.12010	−0.144945
$809$	−23.6652	−0.832024	−0.416012	−	0.909359i	$-0.636573\pi$
$809$	−23.6652	−0.832024	−0.416012	+	0.909359i	$0.636573\pi$
$810$	8.11683	0.285196
$811$	9.23019	0.324116	0.162058	−	0.986781i	$-0.448187\pi$
$811$	9.23019	0.324116	0.162058	+	0.986781i	$0.448187\pi$
$812$	33.2879	1.16818
$813$	60.7476	2.13051
$814$	14.8100	0.519092
$815$	19.2805	0.675365
$816$	17.1499	0.600368
$817$	24.3360	0.851408
$818$	−29.1329	−1.01861
$819$	86.7481	3.03122
$820$	−0.881641	−0.0307882
$821$	−2.22857	−0.0777776	−0.0388888	−	0.999244i	$-0.512382\pi$
$821$	−2.22857	−0.0777776	−0.0388888	+	0.999244i	$0.512382\pi$
$822$	47.2018	1.64635
$823$	−29.0424	−1.01235	−0.506177	−	0.862430i	$-0.668942\pi$
$823$	−29.0424	−1.01235	−0.506177	+	0.862430i	$0.668942\pi$
$824$	5.24149	0.182596
$825$	10.3796	0.361372
$826$	4.33449	0.150816
$827$	−40.1550	−1.39633	−0.698163	−	0.715939i	$-0.745999\pi$
$827$	−40.1550	−1.39633	−0.698163	+	0.715939i	$0.745999\pi$
$828$	1.41382	0.0491336
$829$	−34.3636	−1.19350	−0.596749	−	0.802428i	$-0.703541\pi$
$829$	−34.3636	−1.19350	−0.596749	+	0.802428i	$0.703541\pi$
$830$	2.10585	0.0730952
$831$	37.0669	1.28584
$832$	−5.47069	−0.189662
$833$	−63.8246	−2.21139
$834$	−55.5861	−1.92479
$835$	20.1009	0.695621
$836$	−9.76705	−0.337800
$837$	−13.7222	−0.474308
$838$	−10.9845	−0.379454
$839$	−19.2038	−0.662988	−0.331494	−	0.943457i	$-0.607553\pi$
$839$	−19.2038	−0.662988	−0.331494	+	0.943457i	$0.607553\pi$
$840$	−15.5118	−0.535207
$841$	37.1265	1.28022
$842$	−11.3632	−0.391600
$843$	12.7912	0.440552
$844$	5.83190	0.200742
$845$	24.4674	0.841704
$846$	−23.3543	−0.802937
$847$	37.4572	1.28705
$848$	−3.46241	−0.118900
$849$	33.5865	1.15269
$850$	−19.0419	−0.653133
$851$	−3.97452	−0.136245
$852$	−10.5312	−0.360794
$853$	−24.0892	−0.824798	−0.412399	−	0.911003i	$-0.635309\pi$
$853$	−24.0892	−0.824798	−0.412399	+	0.911003i	$0.635309\pi$
$854$	15.5853	0.533317
$855$	−40.2073	−1.37506
$856$	−15.2504	−0.521248
$857$	−38.7433	−1.32345	−0.661724	−	0.749748i	$-0.730175\pi$
$857$	−38.7433	−1.32345	−0.661724	+	0.749748i	$0.730175\pi$
$858$	−19.5066	−0.665946
$859$	−6.26889	−0.213892	−0.106946	−	0.994265i	$-0.534107\pi$
$859$	−6.26889	−0.213892	−0.106946	+	0.994265i	$0.534107\pi$
$860$	−4.89780	−0.167014
$861$	−6.54658	−0.223107
$862$	−37.3716	−1.27288
$863$	5.49493	0.187050	0.0935248	−	0.995617i	$-0.470187\pi$
$863$	5.49493	0.187050	0.0935248	+	0.995617i	$0.470187\pi$
$864$	2.29046	0.0779229
$865$	−21.3468	−0.725812
$866$	−14.2547	−0.484395
$867$	−67.6142	−2.29630
$868$	−24.5245	−0.832415
$869$	−10.7402	−0.364335
$870$	−30.8142	−1.04470
$871$	73.7286	2.49820
$872$	4.96261	0.168055
$873$	−5.99135	−0.202776
$874$	2.62115	0.0886617
$875$	46.8058	1.58232
$876$	44.1157	1.49053
$877$	−49.7005	−1.67827	−0.839134	−	0.543925i	$-0.816938\pi$
$877$	−49.7005	−1.67827	−0.839134	+	0.543925i	$0.816938\pi$
$878$	2.48473	0.0838555
$879$	59.7007	2.01365
$880$	1.96570	0.0662636
$881$	−37.4577	−1.26198	−0.630992	−	0.775790i	$-0.717352\pi$
$881$	−37.4577	−1.26198	−0.630992	+	0.775790i	$0.717352\pi$
$882$	−37.7953	−1.27263
$883$	1.97579	0.0664905	0.0332453	−	0.999447i	$-0.489416\pi$
$883$	1.97579	0.0664905	0.0332453	+	0.999447i	$0.489416\pi$
$884$	35.7859	1.20361
$885$	−4.01237	−0.134874
$886$	27.4112	0.920897
$887$	6.98812	0.234638	0.117319	−	0.993094i	$-0.462570\pi$
$887$	6.98812	0.234638	0.117319	+	0.993094i	$0.462570\pi$
$888$	−28.5498	−0.958068
$889$	−33.3120	−1.11725
$890$	−18.7654	−0.629017
$891$	−7.63772	−0.255873
$892$	1.68068	0.0562734
$893$	−43.2977	−1.44890
$894$	−19.6629	−0.657627
$895$	−19.4048	−0.648631
$896$	4.09354	0.136756
$897$	5.23493	0.174789
$898$	18.5159	0.617885
$899$	−48.7179	−1.62483
$900$	−11.2761	−0.375871
$901$	22.6490	0.754546
$902$	0.829601	0.0276227
$903$	−36.3684	−1.21026
$904$	13.4851	0.448509
$905$	1.53343	0.0509729
$906$	−44.4814	−1.47780
$907$	−24.5916	−0.816550	−0.408275	−	0.912859i	$-0.633870\pi$
$907$	−24.5916	−0.816550	−0.408275	+	0.912859i	$0.633870\pi$
$908$	19.5353	0.648303
$909$	15.9598	0.529352
$910$	−32.3676	−1.07298
$911$	−4.08295	−0.135274	−0.0676370	−	0.997710i	$-0.521546\pi$
$911$	−4.08295	−0.135274	−0.0676370	+	0.997710i	$0.521546\pi$
$912$	18.8282	0.623465
$913$	−1.98155	−0.0655797
$914$	19.1505	0.633441
$915$	−14.4271	−0.476944
$916$	−5.15115	−0.170199
$917$	61.6681	2.03646
$918$	−14.9827	−0.494504
$919$	−44.3861	−1.46416	−0.732081	−	0.681217i	$-0.761451\pi$
$919$	−44.3861	−1.46416	−0.732081	+	0.681217i	$0.761451\pi$
$920$	−0.527527	−0.0173920
$921$	−69.6036	−2.29352
$922$	14.9860	0.493538
$923$	−21.9749	−0.723314
$924$	14.5962	0.480179
$925$	31.6994	1.04227
$926$	34.3496	1.12880
$927$	−20.3036	−0.666858
$928$	8.13182	0.266940
$929$	−11.6401	−0.381899	−0.190950	−	0.981600i	$-0.561157\pi$
$929$	−11.6401	−0.381899	−0.190950	+	0.981600i	$0.561157\pi$
$930$	22.7020	0.744426
$931$	−70.0705	−2.29647
$932$	−8.24409	−0.270044
$933$	47.9918	1.57118
$934$	−6.33991	−0.207448
$935$	−12.8584	−0.420513
$936$	21.1915	0.692665
$937$	33.4034	1.09124	0.545621	−	0.838032i	$-0.316294\pi$
$937$	33.4034	1.09124	0.545621	+	0.838032i	$0.316294\pi$
$938$	−55.1687	−1.80132
$939$	4.58273	0.149552
$940$	8.71400	0.284219
$941$	2.77334	0.0904084	0.0452042	−	0.998978i	$-0.485606\pi$
$941$	2.77334	0.0904084	0.0452042	+	0.998978i	$0.485606\pi$
$942$	−24.1152	−0.785714
$943$	−0.222637	−0.00725006
$944$	1.05886	0.0344630
$945$	13.5516	0.440833
$946$	4.60870	0.149842
$947$	29.1477	0.947174	0.473587	−	0.880747i	$-0.342959\pi$
$947$	29.1477	0.947174	0.473587	+	0.880747i	$0.342959\pi$
$948$	20.7041	0.672439
$949$	92.0539	2.98820
$950$	−20.9054	−0.678261
$951$	−12.7402	−0.413129
$952$	−26.7774	−0.867860
$953$	−25.4242	−0.823570	−0.411785	−	0.911281i	$-0.635095\pi$
$953$	−25.4242	−0.823570	−0.411785	+	0.911281i	$0.635095\pi$
$954$	13.4121	0.434233
$955$	−35.7265	−1.15608
$956$	11.2771	0.364726
$957$	28.9953	0.937285
$958$	32.6955	1.05634
$959$	−73.6995	−2.37988
$960$	−3.78933	−0.122300
$961$	4.89232	0.157817
$962$	−59.5733	−1.92072
$963$	59.0745	1.90365
$964$	5.90314	0.190127
$965$	−4.36575	−0.140539
$966$	−3.91712	−0.126031
$967$	−55.4611	−1.78351	−0.891755	−	0.452519i	$-0.850525\pi$
$967$	−55.4611	−1.78351	−0.891755	+	0.452519i	$0.850525\pi$
$968$	9.15033	0.294103
$969$	−123.163	−3.95655
$970$	2.23550	0.0717777
$971$	−21.4603	−0.688693	−0.344347	−	0.938843i	$-0.611900\pi$
$971$	−21.4603	−0.688693	−0.344347	+	0.938843i	$0.611900\pi$
$972$	21.5948	0.692655
$973$	86.7905	2.78238
$974$	2.28521	0.0732229
$975$	−41.7520	−1.33714
$976$	3.80729	0.121868
$977$	−57.1863	−1.82955	−0.914775	−	0.403963i	$-0.867632\pi$
$977$	−57.1863	−1.82955	−0.914775	+	0.403963i	$0.867632\pi$
$978$	34.9737	1.11833
$979$	17.6577	0.564343
$980$	14.1022	0.450480
$981$	−19.2233	−0.613754
$982$	32.2680	1.02971
$983$	32.3333	1.03127	0.515637	−	0.856807i	$-0.327555\pi$
$983$	32.3333	1.03127	0.515637	+	0.856807i	$0.327555\pi$
$984$	−1.59925	−0.0509821
$985$	27.0505	0.861902
$986$	−53.1933	−1.69402
$987$	64.7053	2.05959
$988$	39.2879	1.24992
$989$	−1.23682	−0.0393286
$990$	−7.61438	−0.242001
$991$	−14.6307	−0.464760	−0.232380	−	0.972625i	$-0.574651\pi$
$991$	−14.6307	−0.464760	−0.232380	+	0.972625i	$0.574651\pi$
$992$	−5.99102	−0.190215
$993$	−38.1568	−1.21087
$994$	16.4431	0.521544
$995$	11.1880	0.354684
$996$	3.81989	0.121038
$997$	5.52588	0.175006	0.0875032	−	0.996164i	$-0.472111\pi$
$997$	5.52588	0.175006	0.0875032	+	0.996164i	$0.472111\pi$
$998$	17.9334	0.567671
$999$	24.9420	0.789130

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.8	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.8	✓	49	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.62176 q^{3} +1.00000 q^{4} +1.44534 q^{5} +2.62176 q^{6} -4.09354 q^{7} -1.00000 q^{8} +3.87363 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.62176 q^{3} +1.00000 q^{4} +1.44534 q^{5} +2.62176 q^{6} -4.09354 q^{7} -1.00000 q^{8} +3.87363 q^{9} -1.44534 q^{10} +1.36002 q^{11} -2.62176 q^{12} -5.47069 q^{13} +4.09354 q^{14} -3.78933 q^{15} +1.00000 q^{16} -6.54138 q^{17} -3.87363 q^{18} -7.18152 q^{19} +1.44534 q^{20} +10.7323 q^{21} -1.36002 q^{22} +0.364985 q^{23} +2.62176 q^{24} -2.91100 q^{25} +5.47069 q^{26} -2.29046 q^{27} -4.09354 q^{28} -8.13182 q^{29} +3.78933 q^{30} +5.99102 q^{31} -1.00000 q^{32} -3.56566 q^{33} +6.54138 q^{34} -5.91655 q^{35} +3.87363 q^{36} -10.8895 q^{37} +7.18152 q^{38} +14.3429 q^{39} -1.44534 q^{40} -0.609989 q^{41} -10.7323 q^{42} -3.38869 q^{43} +1.36002 q^{44} +5.59871 q^{45} -0.364985 q^{46} +6.02904 q^{47} -2.62176 q^{48} +9.75706 q^{49} +2.91100 q^{50} +17.1499 q^{51} -5.47069 q^{52} -3.46241 q^{53} +2.29046 q^{54} +1.96570 q^{55} +4.09354 q^{56} +18.8282 q^{57} +8.13182 q^{58} +1.05886 q^{59} -3.78933 q^{60} +3.80729 q^{61} -5.99102 q^{62} -15.8569 q^{63} +1.00000 q^{64} -7.90700 q^{65} +3.56566 q^{66} -13.4770 q^{67} -6.54138 q^{68} -0.956904 q^{69} +5.91655 q^{70} +4.01685 q^{71} -3.87363 q^{72} -16.8267 q^{73} +10.8895 q^{74} +7.63194 q^{75} -7.18152 q^{76} -5.56731 q^{77} -14.3429 q^{78} -7.89704 q^{79} +1.44534 q^{80} -5.61587 q^{81} +0.609989 q^{82} -1.45700 q^{83} +10.7323 q^{84} -9.45450 q^{85} +3.38869 q^{86} +21.3197 q^{87} -1.36002 q^{88} +12.9834 q^{89} -5.59871 q^{90} +22.3945 q^{91} +0.364985 q^{92} -15.7070 q^{93} -6.02904 q^{94} -10.3797 q^{95} +2.62176 q^{96} -1.54670 q^{97} -9.75706 q^{98} +5.26824 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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