LMFDB - Embedded newform 6038.2.a.e.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, 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("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.76800 q^{3} +1.00000 q^{4} +1.61299 q^{5} -1.76800 q^{6} +3.26382 q^{7} +1.00000 q^{8} +0.125835 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.76800 q^{3} +1.00000 q^{4} +1.61299 q^{5} -1.76800 q^{6} +3.26382 q^{7} +1.00000 q^{8} +0.125835 q^{9} +1.61299 q^{10} -4.15638 q^{11} -1.76800 q^{12} +5.45303 q^{13} +3.26382 q^{14} -2.85177 q^{15} +1.00000 q^{16} +5.33728 q^{17} +0.125835 q^{18} +8.51564 q^{19} +1.61299 q^{20} -5.77045 q^{21} -4.15638 q^{22} +0.437438 q^{23} -1.76800 q^{24} -2.39826 q^{25} +5.45303 q^{26} +5.08153 q^{27} +3.26382 q^{28} -1.51728 q^{29} -2.85177 q^{30} -1.80771 q^{31} +1.00000 q^{32} +7.34849 q^{33} +5.33728 q^{34} +5.26452 q^{35} +0.125835 q^{36} +2.74058 q^{37} +8.51564 q^{38} -9.64097 q^{39} +1.61299 q^{40} -12.1537 q^{41} -5.77045 q^{42} +8.18919 q^{43} -4.15638 q^{44} +0.202971 q^{45} +0.437438 q^{46} -0.266439 q^{47} -1.76800 q^{48} +3.65254 q^{49} -2.39826 q^{50} -9.43633 q^{51} +5.45303 q^{52} -1.86044 q^{53} +5.08153 q^{54} -6.70420 q^{55} +3.26382 q^{56} -15.0557 q^{57} -1.51728 q^{58} -10.4214 q^{59} -2.85177 q^{60} +12.3996 q^{61} -1.80771 q^{62} +0.410704 q^{63} +1.00000 q^{64} +8.79569 q^{65} +7.34849 q^{66} +2.49612 q^{67} +5.33728 q^{68} -0.773391 q^{69} +5.26452 q^{70} +1.93351 q^{71} +0.125835 q^{72} -12.9183 q^{73} +2.74058 q^{74} +4.24013 q^{75} +8.51564 q^{76} -13.5657 q^{77} -9.64097 q^{78} +8.09092 q^{79} +1.61299 q^{80} -9.36167 q^{81} -12.1537 q^{82} -6.24269 q^{83} -5.77045 q^{84} +8.60899 q^{85} +8.18919 q^{86} +2.68256 q^{87} -4.15638 q^{88} +8.52519 q^{89} +0.202971 q^{90} +17.7977 q^{91} +0.437438 q^{92} +3.19604 q^{93} -0.266439 q^{94} +13.7357 q^{95} -1.76800 q^{96} +7.60095 q^{97} +3.65254 q^{98} -0.523019 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * 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
$3$	−1.76800	−1.02076	−0.510379	−	0.859950i	$-0.670495\pi$
$3$	−1.76800	−1.02076	−0.510379	+	0.859950i	$0.670495\pi$
$4$	1.00000	0.500000
$5$	1.61299	0.721352	0.360676	−	0.932691i	$-0.382546\pi$
$5$	1.61299	0.721352	0.360676	+	0.932691i	$0.382546\pi$
$6$	−1.76800	−0.721784
$7$	3.26382	1.23361	0.616804	−	0.787116i	$-0.288427\pi$
$7$	3.26382	1.23361	0.616804	+	0.787116i	$0.288427\pi$
$8$	1.00000	0.353553
$9$	0.125835	0.0419451
$10$	1.61299	0.510073
$11$	−4.15638	−1.25319	−0.626597	−	0.779343i	$-0.715553\pi$
$11$	−4.15638	−1.25319	−0.626597	+	0.779343i	$0.715553\pi$
$12$	−1.76800	−0.510379
$13$	5.45303	1.51240	0.756199	−	0.654342i	$-0.227054\pi$
$13$	5.45303	1.51240	0.756199	+	0.654342i	$0.227054\pi$
$14$	3.26382	0.872293
$15$	−2.85177	−0.736325
$16$	1.00000	0.250000
$17$	5.33728	1.29448	0.647240	−	0.762286i	$-0.275923\pi$
$17$	5.33728	1.29448	0.647240	+	0.762286i	$0.275923\pi$
$18$	0.125835	0.0296597
$19$	8.51564	1.95362	0.976811	−	0.214104i	$-0.0686832\pi$
$19$	8.51564	1.95362	0.976811	+	0.214104i	$0.0686832\pi$
$20$	1.61299	0.360676
$21$	−5.77045	−1.25922
$22$	−4.15638	−0.886142
$23$	0.437438	0.0912121	0.0456060	−	0.998960i	$-0.485478\pi$
$23$	0.437438	0.0912121	0.0456060	+	0.998960i	$0.485478\pi$
$24$	−1.76800	−0.360892
$25$	−2.39826	−0.479652
$26$	5.45303	1.06943
$27$	5.08153	0.977941
$28$	3.26382	0.616804
$29$	−1.51728	−0.281752	−0.140876	−	0.990027i	$-0.544992\pi$
$29$	−1.51728	−0.281752	−0.140876	+	0.990027i	$0.544992\pi$
$30$	−2.85177	−0.520660
$31$	−1.80771	−0.324674	−0.162337	−	0.986735i	$-0.551903\pi$
$31$	−1.80771	−0.324674	−0.162337	+	0.986735i	$0.551903\pi$
$32$	1.00000	0.176777
$33$	7.34849	1.27921
$34$	5.33728	0.915336
$35$	5.26452	0.889866
$36$	0.125835	0.0209726
$37$	2.74058	0.450549	0.225275	−	0.974295i	$-0.427672\pi$
$37$	2.74058	0.450549	0.225275	+	0.974295i	$0.427672\pi$
$38$	8.51564	1.38142
$39$	−9.64097	−1.54379
$40$	1.61299	0.255036
$41$	−12.1537	−1.89809	−0.949046	−	0.315136i	$-0.897950\pi$
$41$	−12.1537	−1.89809	−0.949046	+	0.315136i	$0.897950\pi$
$42$	−5.77045	−0.890400
$43$	8.18919	1.24884	0.624420	−	0.781089i	$-0.285336\pi$
$43$	8.18919	1.24884	0.624420	+	0.781089i	$0.285336\pi$
$44$	−4.15638	−0.626597
$45$	0.202971	0.0302572
$46$	0.437438	0.0644967
$47$	−0.266439	−0.0388641	−0.0194320	−	0.999811i	$-0.506186\pi$
$47$	−0.266439	−0.0388641	−0.0194320	+	0.999811i	$0.506186\pi$
$48$	−1.76800	−0.255189
$49$	3.65254	0.521791
$50$	−2.39826	−0.339165
$51$	−9.43633	−1.32135
$52$	5.45303	0.756199
$53$	−1.86044	−0.255551	−0.127775	−	0.991803i	$-0.540784\pi$
$53$	−1.86044	−0.255551	−0.127775	+	0.991803i	$0.540784\pi$
$54$	5.08153	0.691509
$55$	−6.70420	−0.903994
$56$	3.26382	0.436147
$57$	−15.0557	−1.99417
$58$	−1.51728	−0.199229
$59$	−10.4214	−1.35675	−0.678373	−	0.734718i	$-0.737315\pi$
$59$	−10.4214	−1.35675	−0.678373	+	0.734718i	$0.737315\pi$
$60$	−2.85177	−0.368162
$61$	12.3996	1.58760	0.793801	−	0.608178i	$-0.208099\pi$
$61$	12.3996	1.58760	0.793801	+	0.608178i	$0.208099\pi$
$62$	−1.80771	−0.229579
$63$	0.410704	0.0517439
$64$	1.00000	0.125000
$65$	8.79569	1.09097
$66$	7.34849	0.904536
$67$	2.49612	0.304949	0.152475	−	0.988307i	$-0.451276\pi$
$67$	2.49612	0.304949	0.152475	+	0.988307i	$0.451276\pi$
$68$	5.33728	0.647240
$69$	−0.773391	−0.0931054
$70$	5.26452	0.629230
$71$	1.93351	0.229466	0.114733	−	0.993396i	$-0.463399\pi$
$71$	1.93351	0.229466	0.114733	+	0.993396i	$0.463399\pi$
$72$	0.125835	0.0148298
$73$	−12.9183	−1.51197	−0.755985	−	0.654589i	$-0.772842\pi$
$73$	−12.9183	−1.51197	−0.755985	+	0.654589i	$0.772842\pi$
$74$	2.74058	0.318586
$75$	4.24013	0.489608
$76$	8.51564	0.976811
$77$	−13.5657	−1.54595
$78$	−9.64097	−1.09163
$79$	8.09092	0.910299	0.455150	−	0.890415i	$-0.349586\pi$
$79$	8.09092	0.910299	0.455150	+	0.890415i	$0.349586\pi$
$80$	1.61299	0.180338
$81$	−9.36167	−1.04019
$82$	−12.1537	−1.34215
$83$	−6.24269	−0.685224	−0.342612	−	0.939477i	$-0.611312\pi$
$83$	−6.24269	−0.685224	−0.342612	+	0.939477i	$0.611312\pi$
$84$	−5.77045	−0.629608
$85$	8.60899	0.933776
$86$	8.18919	0.883063
$87$	2.68256	0.287600
$88$	−4.15638	−0.443071
$89$	8.52519	0.903668	0.451834	−	0.892102i	$-0.350770\pi$
$89$	8.52519	0.903668	0.451834	+	0.892102i	$0.350770\pi$
$90$	0.202971	0.0213951
$91$	17.7977	1.86571
$92$	0.437438	0.0456060
$93$	3.19604	0.331414
$94$	−0.266439	−0.0274810
$95$	13.7357	1.40925
$96$	−1.76800	−0.180446
$97$	7.60095	0.771759	0.385880	−	0.922549i	$-0.373898\pi$
$97$	7.60095	0.771759	0.385880	+	0.922549i	$0.373898\pi$
$98$	3.65254	0.368962
$99$	−0.523019	−0.0525654
$100$	−2.39826	−0.239826
$101$	2.30568	0.229424	0.114712	−	0.993399i	$-0.463406\pi$
$101$	2.30568	0.229424	0.114712	+	0.993399i	$0.463406\pi$
$102$	−9.43633	−0.934336
$103$	−2.88769	−0.284533	−0.142266	−	0.989828i	$-0.545439\pi$
$103$	−2.88769	−0.284533	−0.142266	+	0.989828i	$0.545439\pi$
$104$	5.45303	0.534714
$105$	−9.30768	−0.908337
$106$	−1.86044	−0.180702
$107$	2.33798	0.226021	0.113011	−	0.993594i	$-0.463951\pi$
$107$	2.33798	0.226021	0.113011	+	0.993594i	$0.463951\pi$
$108$	5.08153	0.488971
$109$	0.723134	0.0692637	0.0346318	−	0.999400i	$-0.488974\pi$
$109$	0.723134	0.0692637	0.0346318	+	0.999400i	$0.488974\pi$
$110$	−6.70420	−0.639220
$111$	−4.84536	−0.459901
$112$	3.26382	0.308402
$113$	4.81709	0.453153	0.226577	−	0.973993i	$-0.427247\pi$
$113$	4.81709	0.453153	0.226577	+	0.973993i	$0.427247\pi$
$114$	−15.0557	−1.41009
$115$	0.705583	0.0657960
$116$	−1.51728	−0.140876
$117$	0.686184	0.0634377
$118$	−10.4214	−0.959365
$119$	17.4199	1.59688
$120$	−2.85177	−0.260330
$121$	6.27546	0.570496
$122$	12.3996	1.12260
$123$	21.4878	1.93749
$124$	−1.80771	−0.162337
$125$	−11.9333	−1.06735
$126$	0.410704	0.0365884
$127$	−7.05021	−0.625605	−0.312803	−	0.949818i	$-0.601268\pi$
$127$	−7.05021	−0.625605	−0.312803	+	0.949818i	$0.601268\pi$
$128$	1.00000	0.0883883
$129$	−14.4785	−1.27476
$130$	8.79569	0.771433
$131$	11.2601	0.983800	0.491900	−	0.870652i	$-0.336303\pi$
$131$	11.2601	0.983800	0.491900	+	0.870652i	$0.336303\pi$
$132$	7.34849	0.639604
$133$	27.7935	2.41001
$134$	2.49612	0.215632
$135$	8.19647	0.705440
$136$	5.33728	0.457668
$137$	−11.6966	−0.999308	−0.499654	−	0.866225i	$-0.666539\pi$
$137$	−11.6966	−0.999308	−0.499654	+	0.866225i	$0.666539\pi$
$138$	−0.773391	−0.0658354
$139$	−2.52463	−0.214136	−0.107068	−	0.994252i	$-0.534146\pi$
$139$	−2.52463	−0.214136	−0.107068	+	0.994252i	$0.534146\pi$
$140$	5.26452	0.444933
$141$	0.471064	0.0396708
$142$	1.93351	0.162257
$143$	−22.6648	−1.89533
$144$	0.125835	0.0104863
$145$	−2.44736	−0.203242
$146$	−12.9183	−1.06912
$147$	−6.45770	−0.532622
$148$	2.74058	0.225275
$149$	−4.91289	−0.402480	−0.201240	−	0.979542i	$-0.564497\pi$
$149$	−4.91289	−0.402480	−0.201240	+	0.979542i	$0.564497\pi$
$150$	4.24013	0.346205
$151$	12.0896	0.983834	0.491917	−	0.870642i	$-0.336296\pi$
$151$	12.0896	0.983834	0.491917	+	0.870642i	$0.336296\pi$
$152$	8.51564	0.690710
$153$	0.671618	0.0542971
$154$	−13.5657	−1.09315
$155$	−2.91582	−0.234204
$156$	−9.64097	−0.771896
$157$	−23.0882	−1.84264	−0.921320	−	0.388806i	$-0.872888\pi$
$157$	−23.0882	−1.84264	−0.921320	+	0.388806i	$0.872888\pi$
$158$	8.09092	0.643679
$159$	3.28926	0.260855
$160$	1.61299	0.127518
$161$	1.42772	0.112520
$162$	−9.36167	−0.735522
$163$	22.8730	1.79155	0.895776	−	0.444505i	$-0.146620\pi$
$163$	22.8730	1.79155	0.895776	+	0.444505i	$0.146620\pi$
$164$	−12.1537	−0.949046
$165$	11.8530	0.922758
$166$	−6.24269	−0.484527
$167$	−12.0615	−0.933349	−0.466674	−	0.884429i	$-0.654548\pi$
$167$	−12.0615	−0.933349	−0.466674	+	0.884429i	$0.654548\pi$
$168$	−5.77045	−0.445200
$169$	16.7355	1.28735
$170$	8.60899	0.660279
$171$	1.07157	0.0819449
$172$	8.18919	0.624420
$173$	−20.8986	−1.58889	−0.794446	−	0.607334i	$-0.792239\pi$
$173$	−20.8986	−1.58889	−0.794446	+	0.607334i	$0.792239\pi$
$174$	2.68256	0.203364
$175$	−7.82749	−0.591703
$176$	−4.15638	−0.313299
$177$	18.4250	1.38491
$178$	8.52519	0.638990
$179$	18.4253	1.37717	0.688587	−	0.725154i	$-0.258232\pi$
$179$	18.4253	1.37717	0.688587	+	0.725154i	$0.258232\pi$
$180$	0.202971	0.0151286
$181$	−4.42982	−0.329266	−0.164633	−	0.986355i	$-0.552644\pi$
$181$	−4.42982	−0.329266	−0.164633	+	0.986355i	$0.552644\pi$
$182$	17.7977	1.31925
$183$	−21.9225	−1.62056
$184$	0.437438	0.0322483
$185$	4.42054	0.325004
$186$	3.19604	0.234345
$187$	−22.1837	−1.62224
$188$	−0.266439	−0.0194320
$189$	16.5852	1.20640
$190$	13.7357	0.996489
$191$	1.14639	0.0829500	0.0414750	−	0.999140i	$-0.486794\pi$
$191$	1.14639	0.0829500	0.0414750	+	0.999140i	$0.486794\pi$
$192$	−1.76800	−0.127595
$193$	−0.962669	−0.0692944	−0.0346472	−	0.999400i	$-0.511031\pi$
$193$	−0.962669	−0.0692944	−0.0346472	+	0.999400i	$0.511031\pi$
$194$	7.60095	0.545716
$195$	−15.5508	−1.11362
$196$	3.65254	0.260895
$197$	5.86807	0.418083	0.209041	−	0.977907i	$-0.432966\pi$
$197$	5.86807	0.418083	0.209041	+	0.977907i	$0.432966\pi$
$198$	−0.523019	−0.0371693
$199$	13.8030	0.978472	0.489236	−	0.872151i	$-0.337276\pi$
$199$	13.8030	0.978472	0.489236	+	0.872151i	$0.337276\pi$
$200$	−2.39826	−0.169582
$201$	−4.41315	−0.311279
$202$	2.30568	0.162227
$203$	−4.95213	−0.347572
$204$	−9.43633	−0.660675
$205$	−19.6039	−1.36919
$206$	−2.88769	−0.201195
$207$	0.0550451	0.00382590
$208$	5.45303	0.378100
$209$	−35.3942	−2.44827
$210$	−9.30768	−0.642291
$211$	−5.15874	−0.355142	−0.177571	−	0.984108i	$-0.556824\pi$
$211$	−5.15874	−0.355142	−0.177571	+	0.984108i	$0.556824\pi$
$212$	−1.86044	−0.127775
$213$	−3.41845	−0.234229
$214$	2.33798	0.159821
$215$	13.2091	0.900852
$216$	5.08153	0.345754
$217$	−5.90004	−0.400521
$218$	0.723134	0.0489768
$219$	22.8396	1.54335
$220$	−6.70420	−0.451997
$221$	29.1043	1.95777
$222$	−4.84536	−0.325199
$223$	−1.79459	−0.120174	−0.0600872	−	0.998193i	$-0.519138\pi$
$223$	−1.79459	−0.120174	−0.0600872	+	0.998193i	$0.519138\pi$
$224$	3.26382	0.218073
$225$	−0.301786	−0.0201190
$226$	4.81709	0.320428
$227$	−8.58511	−0.569813	−0.284907	−	0.958555i	$-0.591963\pi$
$227$	−8.58511	−0.569813	−0.284907	+	0.958555i	$0.591963\pi$
$228$	−15.0557	−0.997087
$229$	1.11574	0.0737299	0.0368649	−	0.999320i	$-0.488263\pi$
$229$	1.11574	0.0737299	0.0368649	+	0.999320i	$0.488263\pi$
$230$	0.705583	0.0465248
$231$	23.9842	1.57804
$232$	−1.51728	−0.0996143
$233$	17.3850	1.13893	0.569463	−	0.822017i	$-0.307151\pi$
$233$	17.3850	1.13893	0.569463	+	0.822017i	$0.307151\pi$
$234$	0.686184	0.0448572
$235$	−0.429763	−0.0280347
$236$	−10.4214	−0.678373
$237$	−14.3048	−0.929195
$238$	17.4199	1.12917
$239$	−14.2827	−0.923874	−0.461937	−	0.886913i	$-0.652845\pi$
$239$	−14.2827	−0.923874	−0.461937	+	0.886913i	$0.652845\pi$
$240$	−2.85177	−0.184081
$241$	−3.35221	−0.215935	−0.107967	−	0.994154i	$-0.534434\pi$
$241$	−3.35221	−0.215935	−0.107967	+	0.994154i	$0.534434\pi$
$242$	6.27546	0.403402
$243$	1.30687	0.0838356
$244$	12.3996	0.793801
$245$	5.89151	0.376395
$246$	21.4878	1.37001
$247$	46.4360	2.95465
$248$	−1.80771	−0.114790
$249$	11.0371	0.699448
$250$	−11.9333	−0.754730
$251$	21.7236	1.37118	0.685592	−	0.727986i	$-0.259544\pi$
$251$	21.7236	1.37118	0.685592	+	0.727986i	$0.259544\pi$
$252$	0.410704	0.0258719
$253$	−1.81816	−0.114306
$254$	−7.05021	−0.442370
$255$	−15.2207	−0.953158
$256$	1.00000	0.0625000
$257$	−4.59410	−0.286572	−0.143286	−	0.989681i	$-0.545767\pi$
$257$	−4.59410	−0.286572	−0.143286	+	0.989681i	$0.545767\pi$
$258$	−14.4785	−0.901393
$259$	8.94478	0.555801
$260$	8.79569	0.545486
$261$	−0.190927	−0.0118181
$262$	11.2601	0.695652
$263$	23.6448	1.45800	0.728999	−	0.684515i	$-0.239986\pi$
$263$	23.6448	1.45800	0.728999	+	0.684515i	$0.239986\pi$
$264$	7.34849	0.452268
$265$	−3.00087	−0.184342
$266$	27.7935	1.70413
$267$	−15.0726	−0.922426
$268$	2.49612	0.152475
$269$	21.6632	1.32083	0.660415	−	0.750901i	$-0.270381\pi$
$269$	21.6632	1.32083	0.660415	+	0.750901i	$0.270381\pi$
$270$	8.19647	0.498821
$271$	3.10055	0.188345	0.0941724	−	0.995556i	$-0.469980\pi$
$271$	3.10055	0.188345	0.0941724	+	0.995556i	$0.469980\pi$
$272$	5.33728	0.323620
$273$	−31.4664	−1.90443
$274$	−11.6966	−0.706617
$275$	9.96806	0.601097
$276$	−0.773391	−0.0465527
$277$	−4.08234	−0.245284	−0.122642	−	0.992451i	$-0.539137\pi$
$277$	−4.08234	−0.245284	−0.122642	+	0.992451i	$0.539137\pi$
$278$	−2.52463	−0.151417
$279$	−0.227474	−0.0136185
$280$	5.26452	0.314615
$281$	−5.60338	−0.334270	−0.167135	−	0.985934i	$-0.553452\pi$
$281$	−5.60338	−0.334270	−0.167135	+	0.985934i	$0.553452\pi$
$282$	0.471064	0.0280515
$283$	6.80795	0.404691	0.202345	−	0.979314i	$-0.435144\pi$
$283$	6.80795	0.404691	0.202345	+	0.979314i	$0.435144\pi$
$284$	1.93351	0.114733
$285$	−24.2847	−1.43850
$286$	−22.6648	−1.34020
$287$	−39.6676	−2.34150
$288$	0.125835	0.00741492
$289$	11.4866	0.675680
$290$	−2.44736	−0.143714
$291$	−13.4385	−0.787779
$292$	−12.9183	−0.755985
$293$	27.5133	1.60734	0.803672	−	0.595072i	$-0.202877\pi$
$293$	27.5133	1.60734	0.803672	+	0.595072i	$0.202877\pi$
$294$	−6.45770	−0.376620
$295$	−16.8096	−0.978691
$296$	2.74058	0.159293
$297$	−21.1208	−1.22555
$298$	−4.91289	−0.284596
$299$	2.38536	0.137949
$300$	4.24013	0.244804
$301$	26.7281	1.54058
$302$	12.0896	0.695676
$303$	−4.07645	−0.234186
$304$	8.51564	0.488405
$305$	20.0004	1.14522
$306$	0.671618	0.0383939
$307$	18.4943	1.05552	0.527762	−	0.849392i	$-0.323031\pi$
$307$	18.4943	1.05552	0.527762	+	0.849392i	$0.323031\pi$
$308$	−13.5657	−0.772976
$309$	5.10545	0.290439
$310$	−2.91582	−0.165607
$311$	−2.49947	−0.141732	−0.0708659	−	0.997486i	$-0.522576\pi$
$311$	−2.49947	−0.141732	−0.0708659	+	0.997486i	$0.522576\pi$
$312$	−9.64097	−0.545813
$313$	34.2705	1.93708	0.968541	−	0.248854i	$-0.0800539\pi$
$313$	34.2705	1.93708	0.968541	+	0.248854i	$0.0800539\pi$
$314$	−23.0882	−1.30294
$315$	0.662462	0.0373255
$316$	8.09092	0.455150
$317$	−14.2914	−0.802688	−0.401344	−	0.915927i	$-0.631457\pi$
$317$	−14.2914	−0.802688	−0.401344	+	0.915927i	$0.631457\pi$
$318$	3.28926	0.184453
$319$	6.30639	0.353090
$320$	1.61299	0.0901690
$321$	−4.13356	−0.230713
$322$	1.42772	0.0795637
$323$	45.4504	2.52893
$324$	−9.36167	−0.520093
$325$	−13.0778	−0.725424
$326$	22.8730	1.26682
$327$	−1.27850	−0.0707014
$328$	−12.1537	−0.671077
$329$	−0.869608	−0.0479431
$330$	11.8530	0.652489
$331$	8.64755	0.475312	0.237656	−	0.971349i	$-0.423621\pi$
$331$	8.64755	0.475312	0.237656	+	0.971349i	$0.423621\pi$
$332$	−6.24269	−0.342612
$333$	0.344862	0.0188983
$334$	−12.0615	−0.659977
$335$	4.02622	0.219976
$336$	−5.77045	−0.314804
$337$	3.02466	0.164764	0.0823820	−	0.996601i	$-0.473747\pi$
$337$	3.02466	0.164764	0.0823820	+	0.996601i	$0.473747\pi$
$338$	16.7355	0.910293
$339$	−8.51663	−0.462560
$340$	8.60899	0.466888
$341$	7.51352	0.406880
$342$	1.07157	0.0579438
$343$	−10.9255	−0.589923
$344$	8.18919	0.441531
$345$	−1.24747	−0.0671617
$346$	−20.8986	−1.12352
$347$	−24.1756	−1.29781	−0.648907	−	0.760867i	$-0.724774\pi$
$347$	−24.1756	−1.29781	−0.648907	+	0.760867i	$0.724774\pi$
$348$	2.68256	0.143800
$349$	−31.7853	−1.70143	−0.850714	−	0.525628i	$-0.823830\pi$
$349$	−31.7853	−1.70143	−0.850714	+	0.525628i	$0.823830\pi$
$350$	−7.82749	−0.418397
$351$	27.7097	1.47904
$352$	−4.15638	−0.221536
$353$	−10.6042	−0.564404	−0.282202	−	0.959355i	$-0.591065\pi$
$353$	−10.6042	−0.564404	−0.282202	+	0.959355i	$0.591065\pi$
$354$	18.4250	0.979278
$355$	3.11874	0.165525
$356$	8.52519	0.451834
$357$	−30.7985	−1.63003
$358$	18.4253	0.973809
$359$	−5.00911	−0.264371	−0.132185	−	0.991225i	$-0.542199\pi$
$359$	−5.00911	−0.264371	−0.132185	+	0.991225i	$0.542199\pi$
$360$	0.202971	0.0106975
$361$	53.5161	2.81664
$362$	−4.42982	−0.232826
$363$	−11.0950	−0.582338
$364$	17.7977	0.932854
$365$	−20.8371	−1.09066
$366$	−21.9225	−1.14591
$367$	18.6389	0.972944	0.486472	−	0.873696i	$-0.338284\pi$
$367$	18.6389	0.972944	0.486472	+	0.873696i	$0.338284\pi$
$368$	0.437438	0.0228030
$369$	−1.52937	−0.0796157
$370$	4.42054	0.229813
$371$	−6.07214	−0.315250
$372$	3.19604	0.165707
$373$	−17.1215	−0.886518	−0.443259	−	0.896394i	$-0.646178\pi$
$373$	−17.1215	−0.886518	−0.443259	+	0.896394i	$0.646178\pi$
$374$	−22.1837	−1.14709
$375$	21.0982	1.08950
$376$	−0.266439	−0.0137405
$377$	−8.27377	−0.426121
$378$	16.5852	0.853052
$379$	−23.4305	−1.20354	−0.601771	−	0.798669i	$-0.705538\pi$
$379$	−23.4305	−1.20354	−0.601771	+	0.798669i	$0.705538\pi$
$380$	13.7357	0.704624
$381$	12.4648	0.638591
$382$	1.14639	0.0586545
$383$	−4.21273	−0.215260	−0.107630	−	0.994191i	$-0.534326\pi$
$383$	−4.21273	−0.215260	−0.107630	+	0.994191i	$0.534326\pi$
$384$	−1.76800	−0.0902230
$385$	−21.8813	−1.11517
$386$	−0.962669	−0.0489986
$387$	1.03049	0.0523827
$388$	7.60095	0.385880
$389$	−22.6600	−1.14891	−0.574454	−	0.818537i	$-0.694786\pi$
$389$	−22.6600	−1.14891	−0.574454	+	0.818537i	$0.694786\pi$
$390$	−15.5508	−0.787446
$391$	2.33473	0.118072
$392$	3.65254	0.184481
$393$	−19.9079	−1.00422
$394$	5.86807	0.295629
$395$	13.0506	0.656646
$396$	−0.523019	−0.0262827
$397$	−18.7140	−0.939227	−0.469613	−	0.882872i	$-0.655607\pi$
$397$	−18.7140	−0.939227	−0.469613	+	0.882872i	$0.655607\pi$
$398$	13.8030	0.691884
$399$	−49.1391	−2.46003
$400$	−2.39826	−0.119913
$401$	1.76129	0.0879545	0.0439773	−	0.999033i	$-0.485997\pi$
$401$	1.76129	0.0879545	0.0439773	+	0.999033i	$0.485997\pi$
$402$	−4.41315	−0.220108
$403$	−9.85749	−0.491037
$404$	2.30568	0.114712
$405$	−15.1003	−0.750340
$406$	−4.95213	−0.245770
$407$	−11.3909	−0.564626
$408$	−9.43633	−0.467168
$409$	−31.5194	−1.55853	−0.779266	−	0.626693i	$-0.784408\pi$
$409$	−31.5194	−1.55853	−0.779266	+	0.626693i	$0.784408\pi$
$410$	−19.6039	−0.968165
$411$	20.6796	1.02005
$412$	−2.88769	−0.142266
$413$	−34.0135	−1.67369
$414$	0.0550451	0.00270532
$415$	−10.0694	−0.494288
$416$	5.45303	0.267357
$417$	4.46356	0.218581
$418$	−35.3942	−1.73119
$419$	22.9807	1.12268	0.561339	−	0.827586i	$-0.310286\pi$
$419$	22.9807	1.12268	0.561339	+	0.827586i	$0.310286\pi$
$420$	−9.30768	−0.454168
$421$	21.9878	1.07162	0.535810	−	0.844339i	$-0.320006\pi$
$421$	21.9878	1.07162	0.535810	+	0.844339i	$0.320006\pi$
$422$	−5.15874	−0.251124
$423$	−0.0335274	−0.00163016
$424$	−1.86044	−0.0903509
$425$	−12.8002	−0.620900
$426$	−3.41845	−0.165625
$427$	40.4700	1.95848
$428$	2.33798	0.113011
$429$	40.0715	1.93467
$430$	13.2091	0.636999
$431$	21.8894	1.05437	0.527187	−	0.849749i	$-0.323247\pi$
$431$	21.8894	1.05437	0.527187	+	0.849749i	$0.323247\pi$
$432$	5.08153	0.244485
$433$	29.2422	1.40529	0.702646	−	0.711539i	$-0.252002\pi$
$433$	29.2422	1.40529	0.702646	+	0.711539i	$0.252002\pi$
$434$	−5.90004	−0.283211
$435$	4.32694	0.207461
$436$	0.723134	0.0346318
$437$	3.72506	0.178194
$438$	22.8396	1.09132
$439$	24.8209	1.18464	0.592319	−	0.805704i	$-0.298213\pi$
$439$	24.8209	1.18464	0.592319	+	0.805704i	$0.298213\pi$
$440$	−6.70420	−0.319610
$441$	0.459618	0.0218866
$442$	29.1043	1.38435
$443$	0.378165	0.0179672	0.00898358	−	0.999960i	$-0.497140\pi$
$443$	0.378165	0.0179672	0.00898358	+	0.999960i	$0.497140\pi$
$444$	−4.84536	−0.229951
$445$	13.7511	0.651863
$446$	−1.79459	−0.0849761
$447$	8.68601	0.410834
$448$	3.26382	0.154201
$449$	−32.7368	−1.54495	−0.772473	−	0.635048i	$-0.780980\pi$
$449$	−32.7368	−1.54495	−0.772473	+	0.635048i	$0.780980\pi$
$450$	−0.301786	−0.0142263
$451$	50.5154	2.37868
$452$	4.81709	0.226577
$453$	−21.3744	−1.00426
$454$	−8.58511	−0.402919
$455$	28.7076	1.34583
$456$	−15.0557	−0.705047
$457$	0.123226	0.00576427	0.00288214	−	0.999996i	$-0.499083\pi$
$457$	0.123226	0.00576427	0.00288214	+	0.999996i	$0.499083\pi$
$458$	1.11574	0.0521349
$459$	27.1216	1.26593
$460$	0.705583	0.0328980
$461$	−1.27899	−0.0595683	−0.0297841	−	0.999556i	$-0.509482\pi$
$461$	−1.27899	−0.0595683	−0.0297841	+	0.999556i	$0.509482\pi$
$462$	23.9842	1.11584
$463$	4.64474	0.215859	0.107930	−	0.994159i	$-0.465578\pi$
$463$	4.64474	0.215859	0.107930	+	0.994159i	$0.465578\pi$
$464$	−1.51728	−0.0704380
$465$	5.15518	0.239066
$466$	17.3850	0.805343
$467$	−11.7538	−0.543903	−0.271951	−	0.962311i	$-0.587669\pi$
$467$	−11.7538	−0.543903	−0.271951	+	0.962311i	$0.587669\pi$
$468$	0.686184	0.0317189
$469$	8.14689	0.376188
$470$	−0.429763	−0.0198235
$471$	40.8200	1.88089
$472$	−10.4214	−0.479682
$473$	−34.0373	−1.56504
$474$	−14.3048	−0.657040
$475$	−20.4227	−0.937058
$476$	17.4199	0.798441
$477$	−0.234109	−0.0107191
$478$	−14.2827	−0.653278
$479$	2.92317	0.133563	0.0667816	−	0.997768i	$-0.478727\pi$
$479$	2.92317	0.133563	0.0667816	+	0.997768i	$0.478727\pi$
$480$	−2.85177	−0.130165
$481$	14.9445	0.681410
$482$	−3.35221	−0.152689
$483$	−2.52421	−0.114856
$484$	6.27546	0.285248
$485$	12.2603	0.556710
$486$	1.30687	0.0592807
$487$	35.5507	1.61096	0.805478	−	0.592626i	$-0.201909\pi$
$487$	35.5507	1.61096	0.805478	+	0.592626i	$0.201909\pi$
$488$	12.3996	0.561302
$489$	−40.4396	−1.82874
$490$	5.89151	0.266151
$491$	1.99783	0.0901607	0.0450804	−	0.998983i	$-0.485646\pi$
$491$	1.99783	0.0901607	0.0450804	+	0.998983i	$0.485646\pi$
$492$	21.4878	0.968746
$493$	−8.09815	−0.364722
$494$	46.4360	2.08926
$495$	−0.843625	−0.0379181
$496$	−1.80771	−0.0811686
$497$	6.31064	0.283071
$498$	11.0371	0.494584
$499$	26.6693	1.19388	0.596941	−	0.802285i	$-0.296383\pi$
$499$	26.6693	1.19388	0.596941	+	0.802285i	$0.296383\pi$
$500$	−11.9333	−0.533675
$501$	21.3248	0.952723
$502$	21.7236	0.969573
$503$	−13.7350	−0.612412	−0.306206	−	0.951965i	$-0.599060\pi$
$503$	−13.7350	−0.612412	−0.306206	+	0.951965i	$0.599060\pi$
$504$	0.410704	0.0182942
$505$	3.71904	0.165495
$506$	−1.81816	−0.0808269
$507$	−29.5885	−1.31407
$508$	−7.05021	−0.312803
$509$	25.7517	1.14142	0.570711	−	0.821151i	$-0.306668\pi$
$509$	25.7517	1.14142	0.570711	+	0.821151i	$0.306668\pi$
$510$	−15.2207	−0.673985
$511$	−42.1630	−1.86518
$512$	1.00000	0.0441942
$513$	43.2725	1.91053
$514$	−4.59410	−0.202637
$515$	−4.65782	−0.205248
$516$	−14.4785	−0.637381
$517$	1.10742	0.0487042
$518$	8.94478	0.393011
$519$	36.9488	1.62187
$520$	8.79569	0.385717
$521$	41.9013	1.83573	0.917866	−	0.396891i	$-0.129911\pi$
$521$	41.9013	1.83573	0.917866	+	0.396891i	$0.129911\pi$
$522$	−0.190927	−0.00835667
$523$	−5.46666	−0.239041	−0.119520	−	0.992832i	$-0.538136\pi$
$523$	−5.46666	−0.239041	−0.119520	+	0.992832i	$0.538136\pi$
$524$	11.2601	0.491900
$525$	13.8390	0.603985
$526$	23.6448	1.03096
$527$	−9.64825	−0.420285
$528$	7.34849	0.319802
$529$	−22.8086	−0.991680
$530$	−3.00087	−0.130350
$531$	−1.31138	−0.0569089
$532$	27.7935	1.20500
$533$	−66.2746	−2.87067
$534$	−15.0726	−0.652254
$535$	3.77115	0.163041
$536$	2.49612	0.107816
$537$	−32.5760	−1.40576
$538$	21.6632	0.933967
$539$	−15.1813	−0.653905
$540$	8.19647	0.352720
$541$	7.04951	0.303082	0.151541	−	0.988451i	$-0.451576\pi$
$541$	7.04951	0.303082	0.151541	+	0.988451i	$0.451576\pi$
$542$	3.10055	0.133180
$543$	7.83194	0.336101
$544$	5.33728	0.228834
$545$	1.16641	0.0499635
$546$	−31.4664	−1.34664
$547$	−23.3720	−0.999314	−0.499657	−	0.866223i	$-0.666541\pi$
$547$	−23.3720	−0.999314	−0.499657	+	0.866223i	$0.666541\pi$
$548$	−11.6966	−0.499654
$549$	1.56030	0.0665921
$550$	9.96806	0.425040
$551$	−12.9206	−0.550437
$552$	−0.773391	−0.0329177
$553$	26.4073	1.12295
$554$	−4.08234	−0.173442
$555$	−7.81552	−0.331751
$556$	−2.52463	−0.107068
$557$	−7.96623	−0.337540	−0.168770	−	0.985655i	$-0.553979\pi$
$557$	−7.96623	−0.337540	−0.168770	+	0.985655i	$0.553979\pi$
$558$	−0.227474	−0.00962973
$559$	44.6559	1.88874
$560$	5.26452	0.222466
$561$	39.2209	1.65591
$562$	−5.60338	−0.236365
$563$	10.1189	0.426460	0.213230	−	0.977002i	$-0.431602\pi$
$563$	10.1189	0.426460	0.213230	+	0.977002i	$0.431602\pi$
$564$	0.471064	0.0198354
$565$	7.76992	0.326883
$566$	6.80795	0.286159
$567$	−30.5548	−1.28318
$568$	1.93351	0.0811283
$569$	13.0199	0.545823	0.272912	−	0.962039i	$-0.412013\pi$
$569$	13.0199	0.545823	0.272912	+	0.962039i	$0.412013\pi$
$570$	−24.2847	−1.01717
$571$	−14.8521	−0.621540	−0.310770	−	0.950485i	$-0.600587\pi$
$571$	−14.8521	−0.621540	−0.310770	+	0.950485i	$0.600587\pi$
$572$	−22.6648	−0.947665
$573$	−2.02682	−0.0846718
$574$	−39.6676	−1.65569
$575$	−1.04909	−0.0437500
$576$	0.125835	0.00524314
$577$	−41.7953	−1.73996	−0.869980	−	0.493087i	$-0.835868\pi$
$577$	−41.7953	−1.73996	−0.869980	+	0.493087i	$0.835868\pi$
$578$	11.4866	0.477778
$579$	1.70200	0.0707328
$580$	−2.44736	−0.101621
$581$	−20.3750	−0.845299
$582$	−13.4385	−0.557044
$583$	7.73268	0.320255
$584$	−12.9183	−0.534562
$585$	1.10681	0.0457609
$586$	27.5133	1.13656
$587$	−27.5395	−1.13668	−0.568338	−	0.822795i	$-0.692413\pi$
$587$	−27.5395	−1.13668	−0.568338	+	0.822795i	$0.692413\pi$
$588$	−6.45770	−0.266311
$589$	−15.3938	−0.634291
$590$	−16.8096	−0.692039
$591$	−10.3748	−0.426761
$592$	2.74058	0.112637
$593$	−29.9177	−1.22857	−0.614287	−	0.789083i	$-0.710556\pi$
$593$	−29.9177	−1.22857	−0.614287	+	0.789083i	$0.710556\pi$
$594$	−21.1208	−0.866595
$595$	28.0982	1.15191
$596$	−4.91289	−0.201240
$597$	−24.4038	−0.998782
$598$	2.38536	0.0975447
$599$	7.68233	0.313891	0.156946	−	0.987607i	$-0.449835\pi$
$599$	7.68233	0.313891	0.156946	+	0.987607i	$0.449835\pi$
$600$	4.24013	0.173103
$601$	11.9539	0.487611	0.243806	−	0.969824i	$-0.421604\pi$
$601$	11.9539	0.487611	0.243806	+	0.969824i	$0.421604\pi$
$602$	26.7281	1.08935
$603$	0.314100	0.0127911
$604$	12.0896	0.491917
$605$	10.1223	0.411528
$606$	−4.07645	−0.165594
$607$	15.0927	0.612594	0.306297	−	0.951936i	$-0.400910\pi$
$607$	15.0927	0.612594	0.306297	+	0.951936i	$0.400910\pi$
$608$	8.51564	0.345355
$609$	8.75539	0.354786
$610$	20.0004	0.809792
$611$	−1.45290	−0.0587779
$612$	0.671618	0.0271486
$613$	20.9152	0.844756	0.422378	−	0.906420i	$-0.361195\pi$
$613$	20.9152	0.844756	0.422378	+	0.906420i	$0.361195\pi$
$614$	18.4943	0.746368
$615$	34.6597	1.39761
$616$	−13.5657	−0.546577
$617$	45.0505	1.81366	0.906832	−	0.421492i	$-0.138493\pi$
$617$	45.0505	1.81366	0.906832	+	0.421492i	$0.138493\pi$
$618$	5.10545	0.205371
$619$	−27.0554	−1.08745	−0.543725	−	0.839263i	$-0.682987\pi$
$619$	−27.0554	−1.08745	−0.543725	+	0.839263i	$0.682987\pi$
$620$	−2.91582	−0.117102
$621$	2.22285	0.0892001
$622$	−2.49947	−0.100220
$623$	27.8247	1.11477
$624$	−9.64097	−0.385948
$625$	−7.25706	−0.290283
$626$	34.2705	1.36972
$627$	62.5771	2.49909
$628$	−23.0882	−0.921320
$629$	14.6273	0.583227
$630$	0.662462	0.0263931
$631$	−43.7813	−1.74291	−0.871453	−	0.490479i	$-0.836822\pi$
$631$	−43.7813	−1.74291	−0.871453	+	0.490479i	$0.836822\pi$
$632$	8.09092	0.321839
$633$	9.12067	0.362514
$634$	−14.2914	−0.567586
$635$	−11.3719	−0.451281
$636$	3.28926	0.130428
$637$	19.9174	0.789156
$638$	6.30639	0.249672
$639$	0.243304	0.00962496
$640$	1.61299	0.0637591
$641$	−3.54042	−0.139838	−0.0699190	−	0.997553i	$-0.522274\pi$
$641$	−3.54042	−0.139838	−0.0699190	+	0.997553i	$0.522274\pi$
$642$	−4.13356	−0.163139
$643$	32.9843	1.30077	0.650386	−	0.759604i	$-0.274607\pi$
$643$	32.9843	1.30077	0.650386	+	0.759604i	$0.274607\pi$
$644$	1.42772	0.0562600
$645$	−23.3537	−0.919552
$646$	45.4504	1.78822
$647$	−31.9860	−1.25750	−0.628750	−	0.777608i	$-0.716433\pi$
$647$	−31.9860	−1.25750	−0.628750	+	0.777608i	$0.716433\pi$
$648$	−9.36167	−0.367761
$649$	43.3151	1.70027
$650$	−13.0778	−0.512953
$651$	10.4313	0.408835
$652$	22.8730	0.895776
$653$	−15.6131	−0.610987	−0.305493	−	0.952194i	$-0.598821\pi$
$653$	−15.6131	−0.610987	−0.305493	+	0.952194i	$0.598821\pi$
$654$	−1.27850	−0.0499934
$655$	18.1625	0.709666
$656$	−12.1537	−0.474523
$657$	−1.62558	−0.0634198
$658$	−0.869608	−0.0339009
$659$	1.41846	0.0552553	0.0276276	−	0.999618i	$-0.491205\pi$
$659$	1.41846	0.0552553	0.0276276	+	0.999618i	$0.491205\pi$
$660$	11.8530	0.461379
$661$	14.6648	0.570394	0.285197	−	0.958469i	$-0.407941\pi$
$661$	14.6648	0.570394	0.285197	+	0.958469i	$0.407941\pi$
$662$	8.64755	0.336097
$663$	−51.4566	−1.99841
$664$	−6.24269	−0.242263
$665$	44.8307	1.73846
$666$	0.344862	0.0133631
$667$	−0.663716	−0.0256992
$668$	−12.0615	−0.466674
$669$	3.17284	0.122669
$670$	4.02622	0.155546
$671$	−51.5372	−1.98957
$672$	−5.77045	−0.222600
$673$	−45.5499	−1.75582	−0.877909	−	0.478827i	$-0.841062\pi$
$673$	−45.5499	−1.75582	−0.877909	+	0.478827i	$0.841062\pi$
$674$	3.02466	0.116506
$675$	−12.1868	−0.469071
$676$	16.7355	0.643674
$677$	8.53871	0.328169	0.164085	−	0.986446i	$-0.447533\pi$
$677$	8.53871	0.328169	0.164085	+	0.986446i	$0.447533\pi$
$678$	−8.51663	−0.327079
$679$	24.8081	0.952049
$680$	8.60899	0.330140
$681$	15.1785	0.581641
$682$	7.51352	0.287708
$683$	−32.6260	−1.24840	−0.624199	−	0.781266i	$-0.714574\pi$
$683$	−32.6260	−1.24840	−0.624199	+	0.781266i	$0.714574\pi$
$684$	1.07157	0.0409724
$685$	−18.8665	−0.720852
$686$	−10.9255	−0.417139
$687$	−1.97262	−0.0752603
$688$	8.18919	0.312210
$689$	−10.1450	−0.386495
$690$	−1.24747	−0.0474905
$691$	11.7627	0.447473	0.223737	−	0.974650i	$-0.428174\pi$
$691$	11.7627	0.447473	0.223737	+	0.974650i	$0.428174\pi$
$692$	−20.8986	−0.794446
$693$	−1.70704	−0.0648451
$694$	−24.1756	−0.917694
$695$	−4.07221	−0.154468
$696$	2.68256	0.101682
$697$	−64.8678	−2.45704
$698$	−31.7853	−1.20309
$699$	−30.7367	−1.16257
$700$	−7.82749	−0.295851
$701$	4.49575	0.169802	0.0849011	−	0.996389i	$-0.472943\pi$
$701$	4.49575	0.169802	0.0849011	+	0.996389i	$0.472943\pi$
$702$	27.7097	1.04584
$703$	23.3378	0.880203
$704$	−4.15638	−0.156649
$705$	0.759823	0.0286166
$706$	−10.6042	−0.399094
$707$	7.52533	0.283019
$708$	18.4250	0.692454
$709$	−17.2261	−0.646941	−0.323470	−	0.946238i	$-0.604850\pi$
$709$	−17.2261	−0.646941	−0.323470	+	0.946238i	$0.604850\pi$
$710$	3.11874	0.117044
$711$	1.01812	0.0381826
$712$	8.52519	0.319495
$713$	−0.790760	−0.0296142
$714$	−30.7985	−1.15260
$715$	−36.5582	−1.36720
$716$	18.4253	0.688587
$717$	25.2519	0.943051
$718$	−5.00911	−0.186938
$719$	−0.179777	−0.00670457	−0.00335228	−	0.999994i	$-0.501067\pi$
$719$	−0.179777	−0.00670457	−0.00335228	+	0.999994i	$0.501067\pi$
$720$	0.202971	0.00756429
$721$	−9.42492	−0.351002
$722$	53.5161	1.99166
$723$	5.92671	0.220417
$724$	−4.42982	−0.164633
$725$	3.63883	0.135143
$726$	−11.0950	−0.411775
$727$	17.9507	0.665754	0.332877	−	0.942970i	$-0.391981\pi$
$727$	17.9507	0.665754	0.332877	+	0.942970i	$0.391981\pi$
$728$	17.7977	0.659627
$729$	25.7745	0.954610
$730$	−20.8371	−0.771215
$731$	43.7080	1.61660
$732$	−21.9225	−0.810278
$733$	−13.1729	−0.486551	−0.243275	−	0.969957i	$-0.578222\pi$
$733$	−13.1729	−0.486551	−0.243275	+	0.969957i	$0.578222\pi$
$734$	18.6389	0.687975
$735$	−10.4162	−0.384208
$736$	0.437438	0.0161242
$737$	−10.3748	−0.382161
$738$	−1.52937	−0.0562968
$739$	−2.54851	−0.0937485	−0.0468742	−	0.998901i	$-0.514926\pi$
$739$	−2.54851	−0.0937485	−0.0468742	+	0.998901i	$0.514926\pi$
$740$	4.42054	0.162502
$741$	−82.0991	−3.01598
$742$	−6.07214	−0.222915
$743$	19.6960	0.722575	0.361287	−	0.932455i	$-0.382337\pi$
$743$	19.6960	0.722575	0.361287	+	0.932455i	$0.382337\pi$
$744$	3.19604	0.117172
$745$	−7.92445	−0.290330
$746$	−17.1215	−0.626863
$747$	−0.785551	−0.0287418
$748$	−22.1837	−0.811118
$749$	7.63076	0.278822
$750$	21.0982	0.770396
$751$	−53.5757	−1.95501	−0.977503	−	0.210921i	$-0.932354\pi$
$751$	−53.5757	−1.95501	−0.977503	+	0.210921i	$0.932354\pi$
$752$	−0.266439	−0.00971602
$753$	−38.4075	−1.39965
$754$	−8.27377	−0.301313
$755$	19.5004	0.709691
$756$	16.5852	0.603199
$757$	−50.1685	−1.82341	−0.911703	−	0.410850i	$-0.865232\pi$
$757$	−50.1685	−1.82341	−0.911703	+	0.410850i	$0.865232\pi$
$758$	−23.4305	−0.851033
$759$	3.21451	0.116679
$760$	13.7357	0.498245
$761$	−17.9319	−0.650031	−0.325015	−	0.945709i	$-0.605369\pi$
$761$	−17.9319	−0.650031	−0.325015	+	0.945709i	$0.605369\pi$
$762$	12.4648	0.451552
$763$	2.36018	0.0854443
$764$	1.14639	0.0414750
$765$	1.08331	0.0391673
$766$	−4.21273	−0.152212
$767$	−56.8280	−2.05194
$768$	−1.76800	−0.0637973
$769$	−21.3711	−0.770663	−0.385331	−	0.922778i	$-0.625913\pi$
$769$	−21.3711	−0.770663	−0.385331	+	0.922778i	$0.625913\pi$
$770$	−21.8813	−0.788548
$771$	8.12239	0.292521
$772$	−0.962669	−0.0346472
$773$	13.2242	0.475640	0.237820	−	0.971309i	$-0.423567\pi$
$773$	13.2242	0.475640	0.237820	+	0.971309i	$0.423567\pi$
$774$	1.03049	0.0370402
$775$	4.33536	0.155731
$776$	7.60095	0.272858
$777$	−15.8144	−0.567338
$778$	−22.6600	−0.812401
$779$	−103.497	−3.70816
$780$	−15.5508	−0.556808
$781$	−8.03640	−0.287565
$782$	2.33473	0.0834897
$783$	−7.71011	−0.275537
$784$	3.65254	0.130448
$785$	−37.2411	−1.32919
$786$	−19.9079	−0.710091
$787$	−44.4851	−1.58572	−0.792861	−	0.609403i	$-0.791409\pi$
$787$	−44.4851	−1.58572	−0.792861	+	0.609403i	$0.791409\pi$
$788$	5.86807	0.209041
$789$	−41.8040	−1.48826
$790$	13.0506	0.464319
$791$	15.7221	0.559014
$792$	−0.523019	−0.0185847
$793$	67.6152	2.40109
$794$	−18.7140	−0.664134
$795$	5.30555	0.188168
$796$	13.8030	0.489236
$797$	−41.4126	−1.46691	−0.733455	−	0.679738i	$-0.762094\pi$
$797$	−41.4126	−1.46691	−0.733455	+	0.679738i	$0.762094\pi$
$798$	−49.1391	−1.73950
$799$	−1.42206	−0.0503088
$800$	−2.39826	−0.0847912
$801$	1.07277	0.0379045
$802$	1.76129	0.0621933
$803$	53.6932	1.89479
$804$	−4.41315	−0.155640
$805$	2.30290	0.0811665
$806$	−9.85749	−0.347215
$807$	−38.3006	−1.34825
$808$	2.30568	0.0811136
$809$	29.6953	1.04403	0.522016	−	0.852936i	$-0.325180\pi$
$809$	29.6953	1.04403	0.522016	+	0.852936i	$0.325180\pi$
$810$	−15.1003	−0.530570
$811$	−42.4112	−1.48926	−0.744630	−	0.667478i	$-0.767374\pi$
$811$	−42.4112	−1.48926	−0.744630	+	0.667478i	$0.767374\pi$
$812$	−4.95213	−0.173786
$813$	−5.48177	−0.192254
$814$	−11.3909	−0.399251
$815$	36.8940	1.29234
$816$	−9.43633	−0.330338
$817$	69.7362	2.43976
$818$	−31.5194	−1.10205
$819$	2.23958	0.0782573
$820$	−19.6039	−0.684596
$821$	2.25222	0.0786030	0.0393015	−	0.999227i	$-0.487487\pi$
$821$	2.25222	0.0786030	0.0393015	+	0.999227i	$0.487487\pi$
$822$	20.6796	0.721284
$823$	−21.6875	−0.755978	−0.377989	−	0.925810i	$-0.623384\pi$
$823$	−21.6875	−0.755978	−0.377989	+	0.925810i	$0.623384\pi$
$824$	−2.88769	−0.100598
$825$	−17.6236	−0.613574
$826$	−34.0135	−1.18348
$827$	−9.27580	−0.322551	−0.161276	−	0.986909i	$-0.551561\pi$
$827$	−9.27580	−0.322551	−0.161276	+	0.986909i	$0.551561\pi$
$828$	0.0550451	0.00191295
$829$	−50.5698	−1.75636	−0.878182	−	0.478327i	$-0.841243\pi$
$829$	−50.5698	−1.75636	−0.878182	+	0.478327i	$0.841243\pi$
$830$	−10.0694	−0.349514
$831$	7.21759	0.250375
$832$	5.45303	0.189050
$833$	19.4946	0.675448
$834$	4.46356	0.154560
$835$	−19.4551	−0.673273
$836$	−35.3942	−1.22413
$837$	−9.18594	−0.317512
$838$	22.9807	0.793854
$839$	28.7948	0.994107	0.497053	−	0.867720i	$-0.334415\pi$
$839$	28.7948	0.994107	0.497053	+	0.867720i	$0.334415\pi$
$840$	−9.30768	−0.321146
$841$	−26.6979	−0.920616
$842$	21.9878	0.757749
$843$	9.90680	0.341208
$844$	−5.15874	−0.177571
$845$	26.9943	0.928631
$846$	−0.0335274	−0.00115270
$847$	20.4820	0.703769
$848$	−1.86044	−0.0638877
$849$	−12.0365	−0.413091
$850$	−12.8002	−0.439042
$851$	1.19883	0.0410955
$852$	−3.41845	−0.117114
$853$	16.3400	0.559470	0.279735	−	0.960077i	$-0.409753\pi$
$853$	16.3400	0.559470	0.279735	+	0.960077i	$0.409753\pi$
$854$	40.4700	1.38485
$855$	1.72843	0.0591111
$856$	2.33798	0.0799106
$857$	13.5129	0.461593	0.230796	−	0.973002i	$-0.425867\pi$
$857$	13.5129	0.461593	0.230796	+	0.973002i	$0.425867\pi$
$858$	40.0715	1.36802
$859$	−26.5461	−0.905742	−0.452871	−	0.891576i	$-0.649600\pi$
$859$	−26.5461	−0.905742	−0.452871	+	0.891576i	$0.649600\pi$
$860$	13.2091	0.450426
$861$	70.1324	2.39011
$862$	21.8894	0.745555
$863$	−5.31835	−0.181039	−0.0905194	−	0.995895i	$-0.528853\pi$
$863$	−5.31835	−0.181039	−0.0905194	+	0.995895i	$0.528853\pi$
$864$	5.08153	0.172877
$865$	−33.7093	−1.14615
$866$	29.2422	0.993692
$867$	−20.3083	−0.689705
$868$	−5.90004	−0.200261
$869$	−33.6289	−1.14078
$870$	4.32694	0.146697
$871$	13.6114	0.461205
$872$	0.723134	0.0244884
$873$	0.956468	0.0323715
$874$	3.72506	0.126002
$875$	−38.9483	−1.31669
$876$	22.8396	0.771677
$877$	−5.51518	−0.186234	−0.0931172	−	0.995655i	$-0.529683\pi$
$877$	−5.51518	−0.186234	−0.0931172	+	0.995655i	$0.529683\pi$
$878$	24.8209	0.837665
$879$	−48.6436	−1.64071
$880$	−6.70420	−0.225998
$881$	−20.2059	−0.680753	−0.340376	−	0.940289i	$-0.610554\pi$
$881$	−20.2059	−0.680753	−0.340376	+	0.940289i	$0.610554\pi$
$882$	0.459618	0.0154761
$883$	−11.4933	−0.386780	−0.193390	−	0.981122i	$-0.561948\pi$
$883$	−11.4933	−0.386780	−0.193390	+	0.981122i	$0.561948\pi$
$884$	29.1043	0.978885
$885$	29.7194	0.999006
$886$	0.378165	0.0127047
$887$	−7.56311	−0.253944	−0.126972	−	0.991906i	$-0.540526\pi$
$887$	−7.56311	−0.253944	−0.126972	+	0.991906i	$0.540526\pi$
$888$	−4.84536	−0.162600
$889$	−23.0106	−0.771752
$890$	13.7511	0.460937
$891$	38.9106	1.30355
$892$	−1.79459	−0.0600872
$893$	−2.26890	−0.0759257
$894$	8.68601	0.290504
$895$	29.7199	0.993426
$896$	3.26382	0.109037
$897$	−4.21733	−0.140812
$898$	−32.7368	−1.09244
$899$	2.74280	0.0914776
$900$	−0.301786	−0.0100595
$901$	−9.92968	−0.330806
$902$	50.5154	1.68198
$903$	−47.2553	−1.57256
$904$	4.81709	0.160214
$905$	−7.14526	−0.237517
$906$	−21.3744	−0.710116
$907$	9.36060	0.310814	0.155407	−	0.987851i	$-0.450331\pi$
$907$	9.36060	0.310814	0.155407	+	0.987851i	$0.450331\pi$
$908$	−8.58511	−0.284907
$909$	0.290136	0.00962321
$910$	28.7076	0.951647
$911$	−1.59323	−0.0527862	−0.0263931	−	0.999652i	$-0.508402\pi$
$911$	−1.59323	−0.0527862	−0.0263931	+	0.999652i	$0.508402\pi$
$912$	−15.0557	−0.498543
$913$	25.9470	0.858719
$914$	0.123226	0.00407596
$915$	−35.3608	−1.16899
$916$	1.11574	0.0368649
$917$	36.7510	1.21362
$918$	27.1216	0.895145
$919$	39.2828	1.29582	0.647909	−	0.761718i	$-0.275644\pi$
$919$	39.2828	1.29582	0.647909	+	0.761718i	$0.275644\pi$
$920$	0.705583	0.0232624
$921$	−32.6979	−1.07743
$922$	−1.27899	−0.0421211
$923$	10.5435	0.347043
$924$	23.9842	0.789021
$925$	−6.57263	−0.216107
$926$	4.64474	0.152636
$927$	−0.363374	−0.0119348
$928$	−1.51728	−0.0498072
$929$	44.4591	1.45865	0.729327	−	0.684165i	$-0.239833\pi$
$929$	44.4591	1.45865	0.729327	+	0.684165i	$0.239833\pi$
$930$	5.15518	0.169045
$931$	31.1037	1.01938
$932$	17.3850	0.569463
$933$	4.41907	0.144674
$934$	−11.7538	−0.384597
$935$	−35.7822	−1.17020
$936$	0.686184	0.0224286
$937$	60.1512	1.96505	0.982526	−	0.186124i	$-0.0595925\pi$
$937$	60.1512	1.96505	0.982526	+	0.186124i	$0.0595925\pi$
$938$	8.14689	0.266005
$939$	−60.5903	−1.97729
$940$	−0.429763	−0.0140173
$941$	32.0375	1.04439	0.522196	−	0.852825i	$-0.325113\pi$
$941$	32.0375	1.04439	0.522196	+	0.852825i	$0.325113\pi$
$942$	40.8200	1.32999
$943$	−5.31650	−0.173129
$944$	−10.4214	−0.339187
$945$	26.7518	0.870237
$946$	−34.0373	−1.10665
$947$	17.7065	0.575384	0.287692	−	0.957723i	$-0.407112\pi$
$947$	17.7065	0.575384	0.287692	+	0.957723i	$0.407112\pi$
$948$	−14.3048	−0.464597
$949$	−70.4438	−2.28670
$950$	−20.4227	−0.662600
$951$	25.2673	0.819349
$952$	17.4199	0.564583
$953$	2.32653	0.0753637	0.0376819	−	0.999290i	$-0.488003\pi$
$953$	2.32653	0.0753637	0.0376819	+	0.999290i	$0.488003\pi$
$954$	−0.234109	−0.00757955
$955$	1.84912	0.0598361
$956$	−14.2827	−0.461937
$957$	−11.1497	−0.360419
$958$	2.92317	0.0944434
$959$	−38.1756	−1.23275
$960$	−2.85177	−0.0920406
$961$	−27.7322	−0.894587
$962$	14.9445	0.481829
$963$	0.294201	0.00948049
$964$	−3.35221	−0.107967
$965$	−1.55278	−0.0499857
$966$	−2.52421	−0.0812152
$967$	42.9058	1.37976	0.689878	−	0.723926i	$-0.257664\pi$
$967$	42.9058	1.37976	0.689878	+	0.723926i	$0.257664\pi$
$968$	6.27546	0.201701
$969$	−80.3564	−2.58142
$970$	12.2603	0.393653
$971$	−61.6405	−1.97814	−0.989069	−	0.147455i	$-0.952892\pi$
$971$	−61.6405	−1.97814	−0.989069	+	0.147455i	$0.952892\pi$
$972$	1.30687	0.0419178
$973$	−8.23995	−0.264161
$974$	35.5507	1.13912
$975$	23.1215	0.740482
$976$	12.3996	0.396900
$977$	30.2496	0.967770	0.483885	−	0.875132i	$-0.339225\pi$
$977$	30.2496	0.967770	0.483885	+	0.875132i	$0.339225\pi$
$978$	−40.4396	−1.29311
$979$	−35.4339	−1.13247
$980$	5.89151	0.188197
$981$	0.0909958	0.00290527
$982$	1.99783	0.0637533
$983$	−7.16580	−0.228553	−0.114277	−	0.993449i	$-0.536455\pi$
$983$	−7.16580	−0.228553	−0.114277	+	0.993449i	$0.536455\pi$
$984$	21.4878	0.685007
$985$	9.46515	0.301585
$986$	−8.09815	−0.257898
$987$	1.53747	0.0489382
$988$	46.4360	1.47733
$989$	3.58226	0.113909
$990$	−0.843625	−0.0268122
$991$	−31.5617	−1.00259	−0.501295	−	0.865277i	$-0.667143\pi$
$991$	−31.5617	−1.00259	−0.501295	+	0.865277i	$0.667143\pi$
$992$	−1.80771	−0.0573948
$993$	−15.2889	−0.485178
$994$	6.31064	0.200161
$995$	22.2642	0.705822
$996$	11.0371	0.349724
$997$	6.42963	0.203628	0.101814	−	0.994803i	$-0.467535\pi$
$997$	6.42963	0.203628	0.101814	+	0.994803i	$0.467535\pi$
$998$	26.6693	0.844202
$999$	13.9264	0.440611

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.14	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.14	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.76800 q^{3} +1.00000 q^{4} +1.61299 q^{5} -1.76800 q^{6} +3.26382 q^{7} +1.00000 q^{8} +0.125835 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.76800 q^{3} +1.00000 q^{4} +1.61299 q^{5} -1.76800 q^{6} +3.26382 q^{7} +1.00000 q^{8} +0.125835 q^{9} +1.61299 q^{10} -4.15638 q^{11} -1.76800 q^{12} +5.45303 q^{13} +3.26382 q^{14} -2.85177 q^{15} +1.00000 q^{16} +5.33728 q^{17} +0.125835 q^{18} +8.51564 q^{19} +1.61299 q^{20} -5.77045 q^{21} -4.15638 q^{22} +0.437438 q^{23} -1.76800 q^{24} -2.39826 q^{25} +5.45303 q^{26} +5.08153 q^{27} +3.26382 q^{28} -1.51728 q^{29} -2.85177 q^{30} -1.80771 q^{31} +1.00000 q^{32} +7.34849 q^{33} +5.33728 q^{34} +5.26452 q^{35} +0.125835 q^{36} +2.74058 q^{37} +8.51564 q^{38} -9.64097 q^{39} +1.61299 q^{40} -12.1537 q^{41} -5.77045 q^{42} +8.18919 q^{43} -4.15638 q^{44} +0.202971 q^{45} +0.437438 q^{46} -0.266439 q^{47} -1.76800 q^{48} +3.65254 q^{49} -2.39826 q^{50} -9.43633 q^{51} +5.45303 q^{52} -1.86044 q^{53} +5.08153 q^{54} -6.70420 q^{55} +3.26382 q^{56} -15.0557 q^{57} -1.51728 q^{58} -10.4214 q^{59} -2.85177 q^{60} +12.3996 q^{61} -1.80771 q^{62} +0.410704 q^{63} +1.00000 q^{64} +8.79569 q^{65} +7.34849 q^{66} +2.49612 q^{67} +5.33728 q^{68} -0.773391 q^{69} +5.26452 q^{70} +1.93351 q^{71} +0.125835 q^{72} -12.9183 q^{73} +2.74058 q^{74} +4.24013 q^{75} +8.51564 q^{76} -13.5657 q^{77} -9.64097 q^{78} +8.09092 q^{79} +1.61299 q^{80} -9.36167 q^{81} -12.1537 q^{82} -6.24269 q^{83} -5.77045 q^{84} +8.60899 q^{85} +8.18919 q^{86} +2.68256 q^{87} -4.15638 q^{88} +8.52519 q^{89} +0.202971 q^{90} +17.7977 q^{91} +0.437438 q^{92} +3.19604 q^{93} -0.266439 q^{94} +13.7357 q^{95} -1.76800 q^{96} +7.60095 q^{97} +3.65254 q^{98} -0.523019 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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