LMFDB - Embedded newform 4034.2.a.c.1.20

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			1.20
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +0.124605 q^{5} +0.372757 q^{6} -2.88406 q^{7} -1.00000 q^{8} -2.86105 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +0.124605 q^{5} +0.372757 q^{6} -2.88406 q^{7} -1.00000 q^{8} -2.86105 q^{9} -0.124605 q^{10} -5.02827 q^{11} -0.372757 q^{12} -3.71610 q^{13} +2.88406 q^{14} -0.0464474 q^{15} +1.00000 q^{16} +3.34877 q^{17} +2.86105 q^{18} -3.40830 q^{19} +0.124605 q^{20} +1.07505 q^{21} +5.02827 q^{22} +8.69928 q^{23} +0.372757 q^{24} -4.98447 q^{25} +3.71610 q^{26} +2.18475 q^{27} -2.88406 q^{28} +0.896884 q^{29} +0.0464474 q^{30} -7.38171 q^{31} -1.00000 q^{32} +1.87432 q^{33} -3.34877 q^{34} -0.359368 q^{35} -2.86105 q^{36} -11.3501 q^{37} +3.40830 q^{38} +1.38520 q^{39} -0.124605 q^{40} -8.90979 q^{41} -1.07505 q^{42} +2.03710 q^{43} -5.02827 q^{44} -0.356502 q^{45} -8.69928 q^{46} -4.99491 q^{47} -0.372757 q^{48} +1.31780 q^{49} +4.98447 q^{50} -1.24828 q^{51} -3.71610 q^{52} +6.24290 q^{53} -2.18475 q^{54} -0.626548 q^{55} +2.88406 q^{56} +1.27047 q^{57} -0.896884 q^{58} -0.943907 q^{59} -0.0464474 q^{60} -5.01882 q^{61} +7.38171 q^{62} +8.25145 q^{63} +1.00000 q^{64} -0.463045 q^{65} -1.87432 q^{66} -1.41497 q^{67} +3.34877 q^{68} -3.24272 q^{69} +0.359368 q^{70} -8.28978 q^{71} +2.86105 q^{72} +8.83052 q^{73} +11.3501 q^{74} +1.85800 q^{75} -3.40830 q^{76} +14.5018 q^{77} -1.38520 q^{78} +5.41849 q^{79} +0.124605 q^{80} +7.76877 q^{81} +8.90979 q^{82} +5.92719 q^{83} +1.07505 q^{84} +0.417274 q^{85} -2.03710 q^{86} -0.334320 q^{87} +5.02827 q^{88} +4.98647 q^{89} +0.356502 q^{90} +10.7175 q^{91} +8.69928 q^{92} +2.75159 q^{93} +4.99491 q^{94} -0.424691 q^{95} +0.372757 q^{96} -3.72135 q^{97} -1.31780 q^{98} +14.3861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.372757	−0.215212	−0.107606	−	0.994194i	$-0.534318\pi$
$3$	−0.372757	−0.215212	−0.107606	+	0.994194i	$0.534318\pi$
$4$	1.00000	0.500000
$5$	0.124605	0.0557251	0.0278625	−	0.999612i	$-0.491130\pi$
$5$	0.124605	0.0557251	0.0278625	+	0.999612i	$0.491130\pi$
$6$	0.372757	0.152178
$7$	−2.88406	−1.09007	−0.545036	−	0.838413i	$-0.683484\pi$
$7$	−2.88406	−1.09007	−0.545036	+	0.838413i	$0.683484\pi$
$8$	−1.00000	−0.353553
$9$	−2.86105	−0.953684
$10$	−0.124605	−0.0394036
$11$	−5.02827	−1.51608	−0.758040	−	0.652208i	$-0.773843\pi$
$11$	−5.02827	−1.51608	−0.758040	+	0.652208i	$0.773843\pi$
$12$	−0.372757	−0.107606
$13$	−3.71610	−1.03066	−0.515331	−	0.856991i	$-0.672331\pi$
$13$	−3.71610	−1.03066	−0.515331	+	0.856991i	$0.672331\pi$
$14$	2.88406	0.770798
$15$	−0.0464474	−0.0119927
$16$	1.00000	0.250000
$17$	3.34877	0.812196	0.406098	−	0.913830i	$-0.366889\pi$
$17$	3.34877	0.812196	0.406098	+	0.913830i	$0.366889\pi$
$18$	2.86105	0.674356
$19$	−3.40830	−0.781917	−0.390958	−	0.920408i	$-0.627856\pi$
$19$	−3.40830	−0.781917	−0.390958	+	0.920408i	$0.627856\pi$
$20$	0.124605	0.0278625
$21$	1.07505	0.234596
$22$	5.02827	1.07203
$23$	8.69928	1.81393	0.906963	−	0.421211i	$-0.138395\pi$
$23$	8.69928	1.81393	0.906963	+	0.421211i	$0.138395\pi$
$24$	0.372757	0.0760888
$25$	−4.98447	−0.996895
$26$	3.71610	0.728788
$27$	2.18475	0.420455
$28$	−2.88406	−0.545036
$29$	0.896884	0.166547	0.0832736	−	0.996527i	$-0.473462\pi$
$29$	0.896884	0.166547	0.0832736	+	0.996527i	$0.473462\pi$
$30$	0.0464474	0.00848010
$31$	−7.38171	−1.32579	−0.662897	−	0.748710i	$-0.730673\pi$
$31$	−7.38171	−1.32579	−0.662897	+	0.748710i	$0.730673\pi$
$32$	−1.00000	−0.176777
$33$	1.87432	0.326278
$34$	−3.34877	−0.574309
$35$	−0.359368	−0.0607444
$36$	−2.86105	−0.476842
$37$	−11.3501	−1.86595	−0.932976	−	0.359937i	$-0.882798\pi$
$37$	−11.3501	−1.86595	−0.932976	+	0.359937i	$0.882798\pi$
$38$	3.40830	0.552898
$39$	1.38520	0.221810
$40$	−0.124605	−0.0197018
$41$	−8.90979	−1.39147	−0.695737	−	0.718296i	$-0.744922\pi$
$41$	−8.90979	−1.39147	−0.695737	+	0.718296i	$0.744922\pi$
$42$	−1.07505	−0.165885
$43$	2.03710	0.310654	0.155327	−	0.987863i	$-0.450357\pi$
$43$	2.03710	0.310654	0.155327	+	0.987863i	$0.450357\pi$
$44$	−5.02827	−0.758040
$45$	−0.356502	−0.0531441
$46$	−8.69928	−1.28264
$47$	−4.99491	−0.728582	−0.364291	−	0.931285i	$-0.618689\pi$
$47$	−4.99491	−0.728582	−0.364291	+	0.931285i	$0.618689\pi$
$48$	−0.372757	−0.0538029
$49$	1.31780	0.188258
$50$	4.98447	0.704911
$51$	−1.24828	−0.174794
$52$	−3.71610	−0.515331
$53$	6.24290	0.857528	0.428764	−	0.903416i	$-0.358949\pi$
$53$	6.24290	0.857528	0.428764	+	0.903416i	$0.358949\pi$
$54$	−2.18475	−0.297307
$55$	−0.626548	−0.0844837
$56$	2.88406	0.385399
$57$	1.27047	0.168277
$58$	−0.896884	−0.117767
$59$	−0.943907	−0.122886	−0.0614431	−	0.998111i	$-0.519570\pi$
$59$	−0.943907	−0.122886	−0.0614431	+	0.998111i	$0.519570\pi$
$60$	−0.0464474	−0.00599634
$61$	−5.01882	−0.642594	−0.321297	−	0.946978i	$-0.604119\pi$
$61$	−5.01882	−0.642594	−0.321297	+	0.946978i	$0.604119\pi$
$62$	7.38171	0.937478
$63$	8.25145	1.03958
$64$	1.00000	0.125000
$65$	−0.463045	−0.0574337
$66$	−1.87432	−0.230713
$67$	−1.41497	−0.172866	−0.0864332	−	0.996258i	$-0.527547\pi$
$67$	−1.41497	−0.172866	−0.0864332	+	0.996258i	$0.527547\pi$
$68$	3.34877	0.406098
$69$	−3.24272	−0.390378
$70$	0.359368	0.0429528
$71$	−8.28978	−0.983815	−0.491908	−	0.870647i	$-0.663700\pi$
$71$	−8.28978	−0.983815	−0.491908	+	0.870647i	$0.663700\pi$
$72$	2.86105	0.337178
$73$	8.83052	1.03353	0.516767	−	0.856126i	$-0.327135\pi$
$73$	8.83052	1.03353	0.516767	+	0.856126i	$0.327135\pi$
$74$	11.3501	1.31943
$75$	1.85800	0.214543
$76$	−3.40830	−0.390958
$77$	14.5018	1.65264
$78$	−1.38520	−0.156844
$79$	5.41849	0.609628	0.304814	−	0.952412i	$-0.401406\pi$
$79$	5.41849	0.609628	0.304814	+	0.952412i	$0.401406\pi$
$80$	0.124605	0.0139313
$81$	7.76877	0.863197
$82$	8.90979	0.983921
$83$	5.92719	0.650593	0.325297	−	0.945612i	$-0.394536\pi$
$83$	5.92719	0.650593	0.325297	+	0.945612i	$0.394536\pi$
$84$	1.07505	0.117298
$85$	0.417274	0.0452597
$86$	−2.03710	−0.219666
$87$	−0.334320	−0.0358429
$88$	5.02827	0.536015
$89$	4.98647	0.528565	0.264282	−	0.964445i	$-0.414865\pi$
$89$	4.98647	0.528565	0.264282	+	0.964445i	$0.414865\pi$
$90$	0.356502	0.0375786
$91$	10.7175	1.12350
$92$	8.69928	0.906963
$93$	2.75159	0.285326
$94$	4.99491	0.515186
$95$	−0.424691	−0.0435724
$96$	0.372757	0.0380444
$97$	−3.72135	−0.377846	−0.188923	−	0.981992i	$-0.560500\pi$
$97$	−3.72135	−0.377846	−0.188923	+	0.981992i	$0.560500\pi$
$98$	−1.31780	−0.133118
$99$	14.3861	1.44586
$100$	−4.98447	−0.498447
$101$	8.05056	0.801061	0.400530	−	0.916284i	$-0.368826\pi$
$101$	8.05056	0.801061	0.400530	+	0.916284i	$0.368826\pi$
$102$	1.24828	0.123598
$103$	−4.05277	−0.399331	−0.199666	−	0.979864i	$-0.563986\pi$
$103$	−4.05277	−0.399331	−0.199666	+	0.979864i	$0.563986\pi$
$104$	3.71610	0.364394
$105$	0.133957	0.0130729
$106$	−6.24290	−0.606364
$107$	−0.456381	−0.0441200	−0.0220600	−	0.999757i	$-0.507022\pi$
$107$	−0.456381	−0.0441200	−0.0220600	+	0.999757i	$0.507022\pi$
$108$	2.18475	0.210228
$109$	10.7643	1.03104	0.515518	−	0.856879i	$-0.327600\pi$
$109$	10.7643	1.03104	0.515518	+	0.856879i	$0.327600\pi$
$110$	0.626548	0.0597390
$111$	4.23085	0.401575
$112$	−2.88406	−0.272518
$113$	−9.00893	−0.847488	−0.423744	−	0.905782i	$-0.639284\pi$
$113$	−9.00893	−0.847488	−0.423744	+	0.905782i	$0.639284\pi$
$114$	−1.27047	−0.118990
$115$	1.08397	0.101081
$116$	0.896884	0.0832736
$117$	10.6320	0.982925
$118$	0.943907	0.0868936
$119$	−9.65805	−0.885352
$120$	0.0464474	0.00424005
$121$	14.2835	1.29850
$122$	5.01882	0.454383
$123$	3.32119	0.299461
$124$	−7.38171	−0.662897
$125$	−1.24412	−0.111277
$126$	−8.25145	−0.735097
$127$	8.23696	0.730912	0.365456	−	0.930829i	$-0.380913\pi$
$127$	8.23696	0.730912	0.365456	+	0.930829i	$0.380913\pi$
$128$	−1.00000	−0.0883883
$129$	−0.759342	−0.0668564
$130$	0.463045	0.0406117
$131$	−11.9848	−1.04712	−0.523559	−	0.851990i	$-0.675396\pi$
$131$	−11.9848	−1.04712	−0.523559	+	0.851990i	$0.675396\pi$
$132$	1.87432	0.163139
$133$	9.82973	0.852346
$134$	1.41497	0.122235
$135$	0.272231	0.0234299
$136$	−3.34877	−0.287155
$137$	−10.6754	−0.912065	−0.456032	−	0.889963i	$-0.650730\pi$
$137$	−10.6754	−0.912065	−0.456032	+	0.889963i	$0.650730\pi$
$138$	3.24272	0.276039
$139$	19.5794	1.66070	0.830352	−	0.557239i	$-0.188139\pi$
$139$	19.5794	1.66070	0.830352	+	0.557239i	$0.188139\pi$
$140$	−0.359368	−0.0303722
$141$	1.86189	0.156799
$142$	8.28978	0.695663
$143$	18.6856	1.56256
$144$	−2.86105	−0.238421
$145$	0.111756	0.00928085
$146$	−8.83052	−0.730819
$147$	−0.491221	−0.0405153
$148$	−11.3501	−0.932976
$149$	−12.8626	−1.05375	−0.526874	−	0.849943i	$-0.676636\pi$
$149$	−12.8626	−1.05375	−0.526874	+	0.849943i	$0.676636\pi$
$150$	−1.85800	−0.151705
$151$	−3.88889	−0.316473	−0.158237	−	0.987401i	$-0.550581\pi$
$151$	−3.88889	−0.316473	−0.158237	+	0.987401i	$0.550581\pi$
$152$	3.40830	0.276449
$153$	−9.58100	−0.774578
$154$	−14.5018	−1.16859
$155$	−0.919798	−0.0738800
$156$	1.38520	0.110905
$157$	3.03338	0.242090	0.121045	−	0.992647i	$-0.461375\pi$
$157$	3.03338	0.242090	0.121045	+	0.992647i	$0.461375\pi$
$158$	−5.41849	−0.431072
$159$	−2.32709	−0.184550
$160$	−0.124605	−0.00985089
$161$	−25.0892	−1.97731
$162$	−7.76877	−0.610373
$163$	11.7693	0.921843	0.460921	−	0.887441i	$-0.347519\pi$
$163$	11.7693	0.921843	0.460921	+	0.887441i	$0.347519\pi$
$164$	−8.90979	−0.695737
$165$	0.233550	0.0181819
$166$	−5.92719	−0.460039
$167$	19.2198	1.48727	0.743636	−	0.668585i	$-0.233100\pi$
$167$	19.2198	1.48727	0.743636	+	0.668585i	$0.233100\pi$
$168$	−1.07505	−0.0829423
$169$	0.809419	0.0622630
$170$	−0.417274	−0.0320034
$171$	9.75131	0.745701
$172$	2.03710	0.155327
$173$	−9.71672	−0.738749	−0.369374	−	0.929281i	$-0.620428\pi$
$173$	−9.71672	−0.738749	−0.369374	+	0.929281i	$0.620428\pi$
$174$	0.334320	0.0253447
$175$	14.3755	1.08669
$176$	−5.02827	−0.379020
$177$	0.351848	0.0264465
$178$	−4.98647	−0.373752
$179$	1.83501	0.137155	0.0685776	−	0.997646i	$-0.478154\pi$
$179$	1.83501	0.137155	0.0685776	+	0.997646i	$0.478154\pi$
$180$	−0.356502	−0.0265721
$181$	−6.93504	−0.515478	−0.257739	−	0.966215i	$-0.582977\pi$
$181$	−6.93504	−0.515478	−0.257739	+	0.966215i	$0.582977\pi$
$182$	−10.7175	−0.794431
$183$	1.87080	0.138294
$184$	−8.69928	−0.641319
$185$	−1.41429	−0.103980
$186$	−2.75159	−0.201756
$187$	−16.8385	−1.23135
$188$	−4.99491	−0.364291
$189$	−6.30095	−0.458327
$190$	0.424691	0.0308103
$191$	12.3796	0.895758	0.447879	−	0.894094i	$-0.352180\pi$
$191$	12.3796	0.895758	0.447879	+	0.894094i	$0.352180\pi$
$192$	−0.372757	−0.0269014
$193$	−5.31131	−0.382317	−0.191158	−	0.981559i	$-0.561224\pi$
$193$	−5.31131	−0.382317	−0.191158	+	0.981559i	$0.561224\pi$
$194$	3.72135	0.267178
$195$	0.172603	0.0123604
$196$	1.31780	0.0941289
$197$	−21.6746	−1.54425	−0.772127	−	0.635468i	$-0.780807\pi$
$197$	−21.6746	−1.54425	−0.772127	+	0.635468i	$0.780807\pi$
$198$	−14.3861	−1.02238
$199$	11.4529	0.811873	0.405937	−	0.913901i	$-0.366945\pi$
$199$	11.4529	0.811873	0.405937	+	0.913901i	$0.366945\pi$
$200$	4.98447	0.352456
$201$	0.527441	0.0372028
$202$	−8.05056	−0.566435
$203$	−2.58667	−0.181548
$204$	−1.24828	−0.0873970
$205$	−1.11020	−0.0775400
$206$	4.05277	0.282370
$207$	−24.8891	−1.72991
$208$	−3.71610	−0.257665
$209$	17.1378	1.18545
$210$	−0.133957	−0.00924393
$211$	8.67526	0.597229	0.298615	−	0.954374i	$-0.403475\pi$
$211$	8.67526	0.597229	0.298615	+	0.954374i	$0.403475\pi$
$212$	6.24290	0.428764
$213$	3.09007	0.211728
$214$	0.456381	0.0311975
$215$	0.253832	0.0173112
$216$	−2.18475	−0.148653
$217$	21.2893	1.44521
$218$	−10.7643	−0.729052
$219$	−3.29164	−0.222429
$220$	−0.626548	−0.0422418
$221$	−12.4444	−0.837099
$222$	−4.23085	−0.283956
$223$	18.0146	1.20635	0.603173	−	0.797610i	$-0.293903\pi$
$223$	18.0146	1.20635	0.603173	+	0.797610i	$0.293903\pi$
$224$	2.88406	0.192699
$225$	14.2608	0.950723
$226$	9.00893	0.599265
$227$	2.57357	0.170814	0.0854069	−	0.996346i	$-0.472781\pi$
$227$	2.57357	0.170814	0.0854069	+	0.996346i	$0.472781\pi$
$228$	1.27047	0.0841387
$229$	3.03330	0.200446	0.100223	−	0.994965i	$-0.468044\pi$
$229$	3.03330	0.200446	0.100223	+	0.994965i	$0.468044\pi$
$230$	−1.08397	−0.0714751
$231$	−5.40566	−0.355667
$232$	−0.896884	−0.0588833
$233$	17.0403	1.11634	0.558172	−	0.829725i	$-0.311503\pi$
$233$	17.0403	1.11634	0.558172	+	0.829725i	$0.311503\pi$
$234$	−10.6320	−0.695033
$235$	−0.622391	−0.0406003
$236$	−0.943907	−0.0614431
$237$	−2.01978	−0.131199
$238$	9.65805	0.626039
$239$	4.04838	0.261868	0.130934	−	0.991391i	$-0.458202\pi$
$239$	4.04838	0.261868	0.130934	+	0.991391i	$0.458202\pi$
$240$	−0.0464474	−0.00299817
$241$	23.1452	1.49091	0.745456	−	0.666555i	$-0.232232\pi$
$241$	23.1452	1.49091	0.745456	+	0.666555i	$0.232232\pi$
$242$	−14.2835	−0.918177
$243$	−9.45012	−0.606225
$244$	−5.01882	−0.321297
$245$	0.164205	0.0104907
$246$	−3.32119	−0.211751
$247$	12.6656	0.805891
$248$	7.38171	0.468739
$249$	−2.20940	−0.140015
$250$	1.24412	0.0786848
$251$	−10.4774	−0.661329	−0.330665	−	0.943748i	$-0.607273\pi$
$251$	−10.4774	−0.661329	−0.330665	+	0.943748i	$0.607273\pi$
$252$	8.25145	0.519792
$253$	−43.7423	−2.75006
$254$	−8.23696	−0.516833
$255$	−0.155542	−0.00974040
$256$	1.00000	0.0625000
$257$	9.68634	0.604217	0.302109	−	0.953273i	$-0.402309\pi$
$257$	9.68634	0.604217	0.302109	+	0.953273i	$0.402309\pi$
$258$	0.759342	0.0472746
$259$	32.7345	2.03402
$260$	−0.463045	−0.0287168
$261$	−2.56603	−0.158833
$262$	11.9848	0.740424
$263$	2.87009	0.176977	0.0884887	−	0.996077i	$-0.471796\pi$
$263$	2.87009	0.176977	0.0884887	+	0.996077i	$0.471796\pi$
$264$	−1.87432	−0.115357
$265$	0.777897	0.0477858
$266$	−9.82973	−0.602699
$267$	−1.85874	−0.113753
$268$	−1.41497	−0.0864332
$269$	4.06115	0.247612	0.123806	−	0.992306i	$-0.460490\pi$
$269$	4.06115	0.247612	0.123806	+	0.992306i	$0.460490\pi$
$270$	−0.272231	−0.0165674
$271$	21.0376	1.27794	0.638971	−	0.769231i	$-0.279360\pi$
$271$	21.0376	1.27794	0.638971	+	0.769231i	$0.279360\pi$
$272$	3.34877	0.203049
$273$	−3.99501	−0.241789
$274$	10.6754	0.644927
$275$	25.0633	1.51137
$276$	−3.24272	−0.195189
$277$	−20.4993	−1.23168	−0.615841	−	0.787871i	$-0.711183\pi$
$277$	−20.4993	−1.23168	−0.615841	+	0.787871i	$0.711183\pi$
$278$	−19.5794	−1.17430
$279$	21.1195	1.26439
$280$	0.359368	0.0214764
$281$	−7.50044	−0.447439	−0.223719	−	0.974654i	$-0.571820\pi$
$281$	−7.50044	−0.447439	−0.223719	+	0.974654i	$0.571820\pi$
$282$	−1.86189	−0.110874
$283$	−13.0748	−0.777217	−0.388608	−	0.921403i	$-0.627044\pi$
$283$	−13.0748	−0.777217	−0.388608	+	0.921403i	$0.627044\pi$
$284$	−8.28978	−0.491908
$285$	0.158307	0.00937727
$286$	−18.6856	−1.10490
$287$	25.6964	1.51681
$288$	2.86105	0.168589
$289$	−5.78575	−0.340338
$290$	−0.111756	−0.00656256
$291$	1.38716	0.0813169
$292$	8.83052	0.516767
$293$	−5.69803	−0.332883	−0.166441	−	0.986051i	$-0.553228\pi$
$293$	−5.69803	−0.332883	−0.166441	+	0.986051i	$0.553228\pi$
$294$	0.491221	0.0286486
$295$	−0.117616	−0.00684784
$296$	11.3501	0.659714
$297$	−10.9855	−0.637444
$298$	12.8626	0.745113
$299$	−32.3274	−1.86954
$300$	1.85800	0.107272
$301$	−5.87511	−0.338636
$302$	3.88889	0.223780
$303$	−3.00091	−0.172398
$304$	−3.40830	−0.195479
$305$	−0.625370	−0.0358086
$306$	9.58100	0.547709
$307$	−15.2323	−0.869354	−0.434677	−	0.900586i	$-0.643137\pi$
$307$	−15.2323	−0.869354	−0.434677	+	0.900586i	$0.643137\pi$
$308$	14.5018	0.826318
$309$	1.51070	0.0859407
$310$	0.919798	0.0522410
$311$	6.17297	0.350037	0.175018	−	0.984565i	$-0.444001\pi$
$311$	6.17297	0.350037	0.175018	+	0.984565i	$0.444001\pi$
$312$	−1.38520	−0.0784218
$313$	11.3429	0.641137	0.320569	−	0.947225i	$-0.396126\pi$
$313$	11.3429	0.641137	0.320569	+	0.947225i	$0.396126\pi$
$314$	−3.03338	−0.171184
$315$	1.02817	0.0579309
$316$	5.41849	0.304814
$317$	−2.40581	−0.135124	−0.0675619	−	0.997715i	$-0.521522\pi$
$317$	−2.40581	−0.135124	−0.0675619	+	0.997715i	$0.521522\pi$
$318$	2.32709	0.130497
$319$	−4.50977	−0.252499
$320$	0.124605	0.00696563
$321$	0.170119	0.00949513
$322$	25.0892	1.39817
$323$	−11.4136	−0.635069
$324$	7.76877	0.431599
$325$	18.5228	1.02746
$326$	−11.7693	−0.651841
$327$	−4.01248	−0.221891
$328$	8.90979	0.491961
$329$	14.4056	0.794207
$330$	−0.233550	−0.0128565
$331$	25.7176	1.41357	0.706785	−	0.707429i	$-0.250145\pi$
$331$	25.7176	1.41357	0.706785	+	0.707429i	$0.250145\pi$
$332$	5.92719	0.325297
$333$	32.4734	1.77953
$334$	−19.2198	−1.05166
$335$	−0.176313	−0.00963299
$336$	1.07505	0.0586490
$337$	25.5949	1.39424	0.697121	−	0.716953i	$-0.254464\pi$
$337$	25.5949	1.39424	0.697121	+	0.716953i	$0.254464\pi$
$338$	−0.809419	−0.0440266
$339$	3.35814	0.182389
$340$	0.417274	0.0226298
$341$	37.1172	2.01001
$342$	−9.75131	−0.527290
$343$	16.3878	0.884858
$344$	−2.03710	−0.109833
$345$	−0.404059	−0.0217538
$346$	9.71672	0.522374
$347$	−26.6085	−1.42842	−0.714211	−	0.699931i	$-0.753214\pi$
$347$	−26.6085	−1.42842	−0.714211	+	0.699931i	$0.753214\pi$
$348$	−0.334320	−0.0179214
$349$	1.53089	0.0819468	0.0409734	−	0.999160i	$-0.486954\pi$
$349$	1.53089	0.0819468	0.0409734	+	0.999160i	$0.486954\pi$
$350$	−14.3755	−0.768404
$351$	−8.11876	−0.433347
$352$	5.02827	0.268008
$353$	−33.7275	−1.79513	−0.897566	−	0.440880i	$-0.854666\pi$
$353$	−33.7275	−1.79513	−0.897566	+	0.440880i	$0.854666\pi$
$354$	−0.351848	−0.0187005
$355$	−1.03295	−0.0548232
$356$	4.98647	0.264282
$357$	3.60011	0.190538
$358$	−1.83501	−0.0969834
$359$	−24.6493	−1.30094	−0.650471	−	0.759531i	$-0.725429\pi$
$359$	−24.6493	−1.30094	−0.650471	+	0.759531i	$0.725429\pi$
$360$	0.356502	0.0187893
$361$	−7.38352	−0.388607
$362$	6.93504	0.364498
$363$	−5.32427	−0.279452
$364$	10.7175	0.561748
$365$	1.10033	0.0575938
$366$	−1.87080	−0.0977884
$367$	−15.5019	−0.809195	−0.404597	−	0.914495i	$-0.632588\pi$
$367$	−15.5019	−0.809195	−0.404597	+	0.914495i	$0.632588\pi$
$368$	8.69928	0.453481
$369$	25.4914	1.32703
$370$	1.41429	0.0735252
$371$	−18.0049	−0.934768
$372$	2.75159	0.142663
$373$	−15.1251	−0.783147	−0.391573	−	0.920147i	$-0.628069\pi$
$373$	−15.1251	−0.783147	−0.391573	+	0.920147i	$0.628069\pi$
$374$	16.8385	0.870698
$375$	0.463753	0.0239481
$376$	4.99491	0.257593
$377$	−3.33291	−0.171654
$378$	6.30095	0.324086
$379$	12.1529	0.624250	0.312125	−	0.950041i	$-0.398959\pi$
$379$	12.1529	0.624250	0.312125	+	0.950041i	$0.398959\pi$
$380$	−0.424691	−0.0217862
$381$	−3.07039	−0.157301
$382$	−12.3796	−0.633396
$383$	−18.8238	−0.961852	−0.480926	−	0.876761i	$-0.659700\pi$
$383$	−18.8238	−0.961852	−0.480926	+	0.876761i	$0.659700\pi$
$384$	0.372757	0.0190222
$385$	1.80700	0.0920933
$386$	5.31131	0.270339
$387$	−5.82824	−0.296266
$388$	−3.72135	−0.188923
$389$	−13.6811	−0.693660	−0.346830	−	0.937928i	$-0.612742\pi$
$389$	−13.6811	−0.693660	−0.346830	+	0.937928i	$0.612742\pi$
$390$	−0.172603	−0.00874012
$391$	29.1319	1.47326
$392$	−1.31780	−0.0665592
$393$	4.46743	0.225352
$394$	21.6746	1.09195
$395$	0.675172	0.0339716
$396$	14.3861	0.722931
$397$	32.1542	1.61377	0.806885	−	0.590708i	$-0.201151\pi$
$397$	32.1542	1.61377	0.806885	+	0.590708i	$0.201151\pi$
$398$	−11.4529	−0.574081
$399$	−3.66410	−0.183435
$400$	−4.98447	−0.249224
$401$	23.0481	1.15097	0.575483	−	0.817814i	$-0.304814\pi$
$401$	23.0481	1.15097	0.575483	+	0.817814i	$0.304814\pi$
$402$	−0.527441	−0.0263064
$403$	27.4312	1.36645
$404$	8.05056	0.400530
$405$	0.968028	0.0481017
$406$	2.58667	0.128374
$407$	57.0716	2.82893
$408$	1.24828	0.0617990
$409$	−9.90132	−0.489589	−0.244794	−	0.969575i	$-0.578720\pi$
$409$	−9.90132	−0.489589	−0.244794	+	0.969575i	$0.578720\pi$
$410$	1.11020	0.0548291
$411$	3.97935	0.196287
$412$	−4.05277	−0.199666
$413$	2.72228	0.133955
$414$	24.8891	1.22323
$415$	0.738557	0.0362544
$416$	3.71610	0.182197
$417$	−7.29837	−0.357403
$418$	−17.1378	−0.838238
$419$	−27.2539	−1.33144	−0.665720	−	0.746201i	$-0.731876\pi$
$419$	−27.2539	−1.33144	−0.665720	+	0.746201i	$0.731876\pi$
$420$	0.133957	0.00653644
$421$	−35.7696	−1.74330	−0.871652	−	0.490126i	$-0.836951\pi$
$421$	−35.7696	−1.74330	−0.871652	+	0.490126i	$0.836951\pi$
$422$	−8.67526	−0.422305
$423$	14.2907	0.694837
$424$	−6.24290	−0.303182
$425$	−16.6919	−0.809674
$426$	−3.09007	−0.149715
$427$	14.4746	0.700474
$428$	−0.456381	−0.0220600
$429$	−6.96518	−0.336282
$430$	−0.253832	−0.0122409
$431$	20.0064	0.963672	0.481836	−	0.876261i	$-0.339970\pi$
$431$	20.0064	0.963672	0.481836	+	0.876261i	$0.339970\pi$
$432$	2.18475	0.105114
$433$	−8.59686	−0.413139	−0.206569	−	0.978432i	$-0.566230\pi$
$433$	−8.59686	−0.413139	−0.206569	+	0.978432i	$0.566230\pi$
$434$	−21.2893	−1.02192
$435$	−0.0416580	−0.00199735
$436$	10.7643	0.515518
$437$	−29.6497	−1.41834
$438$	3.29164	0.157281
$439$	−13.1657	−0.628363	−0.314181	−	0.949363i	$-0.601730\pi$
$439$	−13.1657	−0.628363	−0.314181	+	0.949363i	$0.601730\pi$
$440$	0.626548	0.0298695
$441$	−3.77031	−0.179538
$442$	12.4444	0.591918
$443$	19.2164	0.912997	0.456499	−	0.889724i	$-0.349103\pi$
$443$	19.2164	0.912997	0.456499	+	0.889724i	$0.349103\pi$
$444$	4.23085	0.200787
$445$	0.621339	0.0294543
$446$	−18.0146	−0.853015
$447$	4.79464	0.226779
$448$	−2.88406	−0.136259
$449$	4.07182	0.192161	0.0960805	−	0.995374i	$-0.469369\pi$
$449$	4.07182	0.192161	0.0960805	+	0.995374i	$0.469369\pi$
$450$	−14.2608	−0.672262
$451$	44.8008	2.10959
$452$	−9.00893	−0.423744
$453$	1.44961	0.0681087
$454$	−2.57357	−0.120784
$455$	1.33545	0.0626069
$456$	−1.27047	−0.0594951
$457$	−34.3528	−1.60696	−0.803479	−	0.595334i	$-0.797020\pi$
$457$	−34.3528	−1.60696	−0.803479	+	0.595334i	$0.797020\pi$
$458$	−3.03330	−0.141737
$459$	7.31622	0.341492
$460$	1.08397	0.0505406
$461$	−8.23815	−0.383689	−0.191845	−	0.981425i	$-0.561447\pi$
$461$	−8.23815	−0.383689	−0.191845	+	0.981425i	$0.561447\pi$
$462$	5.40566	0.251494
$463$	9.87351	0.458861	0.229431	−	0.973325i	$-0.426314\pi$
$463$	9.87351	0.458861	0.229431	+	0.973325i	$0.426314\pi$
$464$	0.896884	0.0416368
$465$	0.342862	0.0158998
$466$	−17.0403	−0.789375
$467$	17.4222	0.806202	0.403101	−	0.915155i	$-0.367932\pi$
$467$	17.4222	0.806202	0.403101	+	0.915155i	$0.367932\pi$
$468$	10.6320	0.491463
$469$	4.08086	0.188437
$470$	0.622391	0.0287087
$471$	−1.13072	−0.0521006
$472$	0.943907	0.0434468
$473$	−10.2431	−0.470976
$474$	2.01978	0.0927717
$475$	16.9886	0.779488
$476$	−9.65805	−0.442676
$477$	−17.8613	−0.817811
$478$	−4.04838	−0.185169
$479$	−20.4062	−0.932384	−0.466192	−	0.884684i	$-0.654374\pi$
$479$	−20.4062	−0.932384	−0.466192	+	0.884684i	$0.654374\pi$
$480$	0.0464474	0.00212003
$481$	42.1783	1.92317
$482$	−23.1452	−1.05423
$483$	9.35220	0.425540
$484$	14.2835	0.649249
$485$	−0.463699	−0.0210555
$486$	9.45012	0.428666
$487$	−22.4747	−1.01842	−0.509212	−	0.860641i	$-0.670063\pi$
$487$	−22.4747	−1.01842	−0.509212	+	0.860641i	$0.670063\pi$
$488$	5.01882	0.227191
$489$	−4.38709	−0.198391
$490$	−0.164205	−0.00741803
$491$	14.5178	0.655180	0.327590	−	0.944820i	$-0.393764\pi$
$491$	14.5178	0.655180	0.327590	+	0.944820i	$0.393764\pi$
$492$	3.32119	0.149731
$493$	3.00346	0.135269
$494$	−12.6656	−0.569851
$495$	1.79259	0.0805707
$496$	−7.38171	−0.331449
$497$	23.9082	1.07243
$498$	2.20940	0.0990057
$499$	12.7201	0.569428	0.284714	−	0.958612i	$-0.408101\pi$
$499$	12.7201	0.569428	0.284714	+	0.958612i	$0.408101\pi$
$500$	−1.24412	−0.0556386
$501$	−7.16432	−0.320078
$502$	10.4774	0.467631
$503$	−18.9568	−0.845244	−0.422622	−	0.906306i	$-0.638890\pi$
$503$	−18.9568	−0.845244	−0.422622	+	0.906306i	$0.638890\pi$
$504$	−8.25145	−0.367549
$505$	1.00314	0.0446392
$506$	43.7423	1.94458
$507$	−0.301717	−0.0133997
$508$	8.23696	0.365456
$509$	−2.40098	−0.106422	−0.0532108	−	0.998583i	$-0.516946\pi$
$509$	−2.40098	−0.106422	−0.0532108	+	0.998583i	$0.516946\pi$
$510$	0.155542	0.00688751
$511$	−25.4678	−1.12663
$512$	−1.00000	−0.0441942
$513$	−7.44627	−0.328761
$514$	−9.68634	−0.427246
$515$	−0.504995	−0.0222528
$516$	−0.759342	−0.0334282
$517$	25.1157	1.10459
$518$	−32.7345	−1.43827
$519$	3.62198	0.158987
$520$	0.463045	0.0203059
$521$	41.8288	1.83256	0.916278	−	0.400544i	$-0.131179\pi$
$521$	41.8288	1.83256	0.916278	+	0.400544i	$0.131179\pi$
$522$	2.56603	0.112312
$523$	28.8318	1.26072	0.630362	−	0.776301i	$-0.282906\pi$
$523$	28.8318	1.26072	0.630362	+	0.776301i	$0.282906\pi$
$524$	−11.9848	−0.523559
$525$	−5.35858	−0.233868
$526$	−2.87009	−0.125142
$527$	−24.7196	−1.07680
$528$	1.87432	0.0815695
$529$	52.6775	2.29032
$530$	−0.777897	−0.0337897
$531$	2.70057	0.117195
$532$	9.82973	0.426173
$533$	33.1097	1.43414
$534$	1.85874	0.0804357
$535$	−0.0568673	−0.00245859
$536$	1.41497	0.0611175
$537$	−0.684014	−0.0295174
$538$	−4.06115	−0.175088
$539$	−6.62628	−0.285414
$540$	0.272231	0.0117150
$541$	−0.456091	−0.0196089	−0.00980445	−	0.999952i	$-0.503121\pi$
$541$	−0.456091	−0.0196089	−0.00980445	+	0.999952i	$0.503121\pi$
$542$	−21.0376	−0.903642
$543$	2.58509	0.110937
$544$	−3.34877	−0.143577
$545$	1.34129	0.0574545
$546$	3.99501	0.170971
$547$	−39.2563	−1.67848	−0.839239	−	0.543762i	$-0.816999\pi$
$547$	−39.2563	−1.67848	−0.839239	+	0.543762i	$0.816999\pi$
$548$	−10.6754	−0.456032
$549$	14.3591	0.612832
$550$	−25.0633	−1.06870
$551$	−3.05685	−0.130226
$552$	3.24272	0.138019
$553$	−15.6273	−0.664539
$554$	20.4993	0.870930
$555$	0.527185	0.0223778
$556$	19.5794	0.830352
$557$	16.6058	0.703611	0.351805	−	0.936073i	$-0.385568\pi$
$557$	16.6058	0.703611	0.351805	+	0.936073i	$0.385568\pi$
$558$	−21.1195	−0.894058
$559$	−7.57006	−0.320179
$560$	−0.359368	−0.0151861
$561$	6.27668	0.265002
$562$	7.50044	0.316387
$563$	−16.5033	−0.695532	−0.347766	−	0.937581i	$-0.613060\pi$
$563$	−16.5033	−0.695532	−0.347766	+	0.937581i	$0.613060\pi$
$564$	1.86189	0.0783997
$565$	−1.12256	−0.0472264
$566$	13.0748	0.549575
$567$	−22.4056	−0.940947
$568$	8.28978	0.347831
$569$	0.510689	0.0214092	0.0107046	−	0.999943i	$-0.496593\pi$
$569$	0.510689	0.0214092	0.0107046	+	0.999943i	$0.496593\pi$
$570$	−0.158307	−0.00663073
$571$	15.2185	0.636874	0.318437	−	0.947944i	$-0.396842\pi$
$571$	15.2185	0.636874	0.318437	+	0.947944i	$0.396842\pi$
$572$	18.6856	0.781282
$573$	−4.61459	−0.192777
$574$	−25.6964	−1.07255
$575$	−43.3613	−1.80829
$576$	−2.86105	−0.119210
$577$	−19.0464	−0.792911	−0.396455	−	0.918054i	$-0.629760\pi$
$577$	−19.0464	−0.792911	−0.396455	+	0.918054i	$0.629760\pi$
$578$	5.78575	0.240655
$579$	1.97983	0.0822790
$580$	0.111756	0.00464043
$581$	−17.0944	−0.709194
$582$	−1.38716	−0.0574997
$583$	−31.3910	−1.30008
$584$	−8.83052	−0.365410
$585$	1.32480	0.0547736
$586$	5.69803	0.235384
$587$	−5.64466	−0.232980	−0.116490	−	0.993192i	$-0.537164\pi$
$587$	−5.64466	−0.232980	−0.116490	+	0.993192i	$0.537164\pi$
$588$	−0.491221	−0.0202576
$589$	25.1590	1.03666
$590$	0.117616	0.00484215
$591$	8.07938	0.332341
$592$	−11.3501	−0.466488
$593$	−16.1646	−0.663802	−0.331901	−	0.943314i	$-0.607690\pi$
$593$	−16.1646	−0.663802	−0.331901	+	0.943314i	$0.607690\pi$
$594$	10.9855	0.450741
$595$	−1.20344	−0.0493363
$596$	−12.8626	−0.526874
$597$	−4.26915	−0.174725
$598$	32.3274	1.32197
$599$	23.3674	0.954766	0.477383	−	0.878695i	$-0.341585\pi$
$599$	23.3674	0.954766	0.477383	+	0.878695i	$0.341585\pi$
$600$	−1.85800	−0.0758525
$601$	−13.3305	−0.543764	−0.271882	−	0.962331i	$-0.587646\pi$
$601$	−13.3305	−0.543764	−0.271882	+	0.962331i	$0.587646\pi$
$602$	5.87511	0.239451
$603$	4.04831	0.164860
$604$	−3.88889	−0.158237
$605$	1.77979	0.0723589
$606$	3.00091	0.121903
$607$	−39.4125	−1.59970	−0.799851	−	0.600198i	$-0.795088\pi$
$607$	−39.4125	−1.59970	−0.799851	+	0.600198i	$0.795088\pi$
$608$	3.40830	0.138225
$609$	0.964199	0.0390713
$610$	0.625370	0.0253205
$611$	18.5616	0.750922
$612$	−9.58100	−0.387289
$613$	−41.8692	−1.69108	−0.845541	−	0.533910i	$-0.820722\pi$
$613$	−41.8692	−1.69108	−0.845541	+	0.533910i	$0.820722\pi$
$614$	15.2323	0.614726
$615$	0.413837	0.0166875
$616$	−14.5018	−0.584295
$617$	23.2235	0.934941	0.467470	−	0.884009i	$-0.345165\pi$
$617$	23.2235	0.934941	0.467470	+	0.884009i	$0.345165\pi$
$618$	−1.51070	−0.0607692
$619$	−35.8219	−1.43980	−0.719902	−	0.694076i	$-0.755813\pi$
$619$	−35.8219	−1.43980	−0.719902	+	0.694076i	$0.755813\pi$
$620$	−0.919798	−0.0369400
$621$	19.0058	0.762675
$622$	−6.17297	−0.247513
$623$	−14.3813	−0.576174
$624$	1.38520	0.0554526
$625$	24.7673	0.990694
$626$	−11.3429	−0.453352
$627$	−6.38825	−0.255122
$628$	3.03338	0.121045
$629$	−38.0090	−1.51552
$630$	−1.02817	−0.0409634
$631$	−13.6165	−0.542063	−0.271031	−	0.962571i	$-0.587365\pi$
$631$	−13.6165	−0.542063	−0.271031	+	0.962571i	$0.587365\pi$
$632$	−5.41849	−0.215536
$633$	−3.23377	−0.128531
$634$	2.40581	0.0955470
$635$	1.02637	0.0407301
$636$	−2.32709	−0.0922750
$637$	−4.89710	−0.194030
$638$	4.50977	0.178544
$639$	23.7175	0.938249
$640$	−0.124605	−0.00492545
$641$	−2.04105	−0.0806167	−0.0403083	−	0.999187i	$-0.512834\pi$
$641$	−2.04105	−0.0806167	−0.0403083	+	0.999187i	$0.512834\pi$
$642$	−0.170119	−0.00671407
$643$	−6.34173	−0.250093	−0.125047	−	0.992151i	$-0.539908\pi$
$643$	−6.34173	−0.250093	−0.125047	+	0.992151i	$0.539908\pi$
$644$	−25.0892	−0.988655
$645$	−0.0946179	−0.00372558
$646$	11.4136	0.449062
$647$	27.9171	1.09754	0.548768	−	0.835975i	$-0.315097\pi$
$647$	27.9171	1.09754	0.548768	+	0.835975i	$0.315097\pi$
$648$	−7.76877	−0.305186
$649$	4.74621	0.186305
$650$	−18.5228	−0.726525
$651$	−7.93574	−0.311026
$652$	11.7693	0.460921
$653$	35.4087	1.38565	0.692825	−	0.721105i	$-0.256366\pi$
$653$	35.4087	1.38565	0.692825	+	0.721105i	$0.256366\pi$
$654$	4.01248	0.156900
$655$	−1.49337	−0.0583507
$656$	−8.90979	−0.347869
$657$	−25.2646	−0.985666
$658$	−14.4056	−0.561589
$659$	32.8809	1.28086	0.640430	−	0.768017i	$-0.278756\pi$
$659$	32.8809	1.28086	0.640430	+	0.768017i	$0.278756\pi$
$660$	0.233550	0.00909093
$661$	11.4595	0.445722	0.222861	−	0.974850i	$-0.428460\pi$
$661$	11.4595	0.445722	0.222861	+	0.974850i	$0.428460\pi$
$662$	−25.7176	−0.999544
$663$	4.63873	0.180153
$664$	−5.92719	−0.230019
$665$	1.22483	0.0474970
$666$	−32.4734	−1.25832
$667$	7.80225	0.302104
$668$	19.2198	0.743636
$669$	−6.71507	−0.259620
$670$	0.176313	0.00681155
$671$	25.2360	0.974224
$672$	−1.07505	−0.0414711
$673$	−36.1904	−1.39504	−0.697518	−	0.716567i	$-0.745712\pi$
$673$	−36.1904	−1.39504	−0.697518	+	0.716567i	$0.745712\pi$
$674$	−25.5949	−0.985878
$675$	−10.8898	−0.419150
$676$	0.809419	0.0311315
$677$	6.91999	0.265957	0.132978	−	0.991119i	$-0.457546\pi$
$677$	6.91999	0.265957	0.132978	+	0.991119i	$0.457546\pi$
$678$	−3.35814	−0.128969
$679$	10.7326	0.411880
$680$	−0.417274	−0.0160017
$681$	−0.959316	−0.0367611
$682$	−37.1172	−1.42129
$683$	33.0102	1.26310	0.631550	−	0.775335i	$-0.282419\pi$
$683$	33.0102	1.26310	0.631550	+	0.775335i	$0.282419\pi$
$684$	9.75131	0.372851
$685$	−1.33021	−0.0508249
$686$	−16.3878	−0.625689
$687$	−1.13068	−0.0431382
$688$	2.03710	0.0776635
$689$	−23.1993	−0.883821
$690$	0.404059	0.0153823
$691$	−14.3231	−0.544878	−0.272439	−	0.962173i	$-0.587830\pi$
$691$	−14.3231	−0.544878	−0.272439	+	0.962173i	$0.587830\pi$
$692$	−9.71672	−0.369374
$693$	−41.4905	−1.57609
$694$	26.6085	1.01005
$695$	2.43969	0.0925429
$696$	0.334320	0.0126724
$697$	−29.8368	−1.13015
$698$	−1.53089	−0.0579452
$699$	−6.35188	−0.240250
$700$	14.3755	0.543344
$701$	−11.7814	−0.444979	−0.222489	−	0.974935i	$-0.571418\pi$
$701$	−11.7814	−0.444979	−0.222489	+	0.974935i	$0.571418\pi$
$702$	8.11876	0.306423
$703$	38.6847	1.45902
$704$	−5.02827	−0.189510
$705$	0.232001	0.00873765
$706$	33.7275	1.26935
$707$	−23.2183	−0.873214
$708$	0.351848	0.0132233
$709$	−4.73649	−0.177883	−0.0889414	−	0.996037i	$-0.528348\pi$
$709$	−4.73649	−0.177883	−0.0889414	+	0.996037i	$0.528348\pi$
$710$	1.03295	0.0387658
$711$	−15.5026	−0.581393
$712$	−4.98647	−0.186876
$713$	−64.2156	−2.40489
$714$	−3.60011	−0.134731
$715$	2.32832	0.0870740
$716$	1.83501	0.0685776
$717$	−1.50906	−0.0563570
$718$	24.6493	0.919905
$719$	5.23007	0.195049	0.0975243	−	0.995233i	$-0.468908\pi$
$719$	5.23007	0.195049	0.0975243	+	0.995233i	$0.468908\pi$
$720$	−0.356502	−0.0132860
$721$	11.6884	0.435300
$722$	7.38352	0.274786
$723$	−8.62753	−0.320861
$724$	−6.93504	−0.257739
$725$	−4.47050	−0.166030
$726$	5.32427	0.197602
$727$	20.0250	0.742686	0.371343	−	0.928496i	$-0.378897\pi$
$727$	20.0250	0.742686	0.371343	+	0.928496i	$0.378897\pi$
$728$	−10.7175	−0.397216
$729$	−19.7837	−0.732730
$730$	−1.10033	−0.0407250
$731$	6.82176	0.252312
$732$	1.87080	0.0691468
$733$	−35.4356	−1.30884	−0.654422	−	0.756130i	$-0.727088\pi$
$733$	−35.4356	−1.30884	−0.654422	+	0.756130i	$0.727088\pi$
$734$	15.5019	0.572187
$735$	−0.0612087	−0.00225772
$736$	−8.69928	−0.320660
$737$	7.11486	0.262079
$738$	−25.4914	−0.938350
$739$	22.4447	0.825641	0.412821	−	0.910812i	$-0.364544\pi$
$739$	22.4447	0.825641	0.412821	+	0.910812i	$0.364544\pi$
$740$	−1.41429	−0.0519902
$741$	−4.72119	−0.173437
$742$	18.0049	0.660981
$743$	3.58394	0.131482	0.0657410	−	0.997837i	$-0.479059\pi$
$743$	3.58394	0.131482	0.0657410	+	0.997837i	$0.479059\pi$
$744$	−2.75159	−0.100878
$745$	−1.60275	−0.0587202
$746$	15.1251	0.553768
$747$	−16.9580	−0.620460
$748$	−16.8385	−0.615677
$749$	1.31623	0.0480940
$750$	−0.463753	−0.0169339
$751$	−5.10440	−0.186262	−0.0931311	−	0.995654i	$-0.529688\pi$
$751$	−5.10440	−0.186262	−0.0931311	+	0.995654i	$0.529688\pi$
$752$	−4.99491	−0.182146
$753$	3.90554	0.142326
$754$	3.33291	0.121378
$755$	−0.484575	−0.0176355
$756$	−6.30095	−0.229163
$757$	−3.46322	−0.125873	−0.0629364	−	0.998018i	$-0.520047\pi$
$757$	−3.46322	−0.125873	−0.0629364	+	0.998018i	$0.520047\pi$
$758$	−12.1529	−0.441411
$759$	16.3053	0.591844
$760$	0.424691	0.0154052
$761$	−15.8246	−0.573642	−0.286821	−	0.957984i	$-0.592599\pi$
$761$	−15.8246	−0.573642	−0.286821	+	0.957984i	$0.592599\pi$
$762$	3.07039	0.111228
$763$	−31.0450	−1.12390
$764$	12.3796	0.447879
$765$	−1.19384	−0.0431634
$766$	18.8238	0.680132
$767$	3.50765	0.126654
$768$	−0.372757	−0.0134507
$769$	32.4271	1.16935	0.584676	−	0.811267i	$-0.301222\pi$
$769$	32.4271	1.16935	0.584676	+	0.811267i	$0.301222\pi$
$770$	−1.80700	−0.0651198
$771$	−3.61065	−0.130035
$772$	−5.31131	−0.191158
$773$	32.2911	1.16143	0.580715	−	0.814107i	$-0.302773\pi$
$773$	32.2911	1.16143	0.580715	+	0.814107i	$0.302773\pi$
$774$	5.82824	0.209492
$775$	36.7939	1.32168
$776$	3.72135	0.133589
$777$	−12.2020	−0.437745
$778$	13.6811	0.490492
$779$	30.3672	1.08802
$780$	0.172603	0.00618020
$781$	41.6832	1.49154
$782$	−29.1319	−1.04175
$783$	1.95947	0.0700257
$784$	1.31780	0.0470645
$785$	0.377975	0.0134905
$786$	−4.46743	−0.159348
$787$	38.3167	1.36584	0.682921	−	0.730492i	$-0.260709\pi$
$787$	38.3167	1.36584	0.682921	+	0.730492i	$0.260709\pi$
$788$	−21.6746	−0.772127
$789$	−1.06985	−0.0380876
$790$	−0.675172	−0.0240215
$791$	25.9823	0.923824
$792$	−14.3861	−0.511189
$793$	18.6505	0.662297
$794$	−32.1542	−1.14111
$795$	−0.289967	−0.0102841
$796$	11.4529	0.405937
$797$	15.6661	0.554923	0.277461	−	0.960737i	$-0.410507\pi$
$797$	15.6661	0.554923	0.277461	+	0.960737i	$0.410507\pi$
$798$	3.66410	0.129708
$799$	−16.7268	−0.591751
$800$	4.98447	0.176228
$801$	−14.2665	−0.504084
$802$	−23.0481	−0.813855
$803$	−44.4022	−1.56692
$804$	0.527441	0.0186014
$805$	−3.12625	−0.110186
$806$	−27.4312	−0.966223
$807$	−1.51382	−0.0532890
$808$	−8.05056	−0.283218
$809$	22.2396	0.781903	0.390952	−	0.920411i	$-0.372146\pi$
$809$	22.2396	0.781903	0.390952	+	0.920411i	$0.372146\pi$
$810$	−0.968028	−0.0340131
$811$	1.53551	0.0539190	0.0269595	−	0.999637i	$-0.491417\pi$
$811$	1.53551	0.0539190	0.0269595	+	0.999637i	$0.491417\pi$
$812$	−2.58667	−0.0907742
$813$	−7.84192	−0.275028
$814$	−57.0716	−2.00036
$815$	1.46651	0.0513698
$816$	−1.24828	−0.0436985
$817$	−6.94302	−0.242906
$818$	9.90132	0.346192
$819$	−30.6632	−1.07146
$820$	−1.11020	−0.0387700
$821$	−41.3253	−1.44226	−0.721132	−	0.692798i	$-0.756378\pi$
$821$	−41.3253	−1.44226	−0.721132	+	0.692798i	$0.756378\pi$
$822$	−3.97935	−0.138796
$823$	12.9250	0.450539	0.225269	−	0.974297i	$-0.427674\pi$
$823$	12.9250	0.450539	0.225269	+	0.974297i	$0.427674\pi$
$824$	4.05277	0.141185
$825$	−9.34252	−0.325265
$826$	−2.72228	−0.0947204
$827$	33.1134	1.15147	0.575734	−	0.817637i	$-0.304717\pi$
$827$	33.1134	1.15147	0.575734	+	0.817637i	$0.304717\pi$
$828$	−24.8891	−0.864956
$829$	52.9119	1.83771	0.918853	−	0.394600i	$-0.129117\pi$
$829$	52.9119	1.83771	0.918853	+	0.394600i	$0.129117\pi$
$830$	−0.738557	−0.0256357
$831$	7.64125	0.265072
$832$	−3.71610	−0.128833
$833$	4.41302	0.152902
$834$	7.29837	0.252722
$835$	2.39488	0.0828783
$836$	17.1378	0.592724
$837$	−16.1272	−0.557437
$838$	27.2539	0.941471
$839$	36.3143	1.25371	0.626854	−	0.779137i	$-0.284342\pi$
$839$	36.3143	1.25371	0.626854	+	0.779137i	$0.284342\pi$
$840$	−0.133957	−0.00462196
$841$	−28.1956	−0.972262
$842$	35.7696	1.23270
$843$	2.79585	0.0962940
$844$	8.67526	0.298615
$845$	0.100858	0.00346961
$846$	−14.2907	−0.491324
$847$	−41.1944	−1.41546
$848$	6.24290	0.214382
$849$	4.87373	0.167266
$850$	16.6919	0.572526
$851$	−98.7381	−3.38470
$852$	3.09007	0.105864
$853$	−38.6101	−1.32199	−0.660993	−	0.750392i	$-0.729865\pi$
$853$	−38.6101	−1.32199	−0.660993	+	0.750392i	$0.729865\pi$
$854$	−14.4746	−0.495310
$855$	1.21506	0.0415543
$856$	0.456381	0.0155988
$857$	−51.8658	−1.77170	−0.885850	−	0.463971i	$-0.846424\pi$
$857$	−51.8658	−1.77170	−0.885850	+	0.463971i	$0.846424\pi$
$858$	6.96518	0.237787
$859$	−19.3835	−0.661357	−0.330678	−	0.943744i	$-0.607278\pi$
$859$	−19.3835	−0.661357	−0.330678	+	0.943744i	$0.607278\pi$
$860$	0.253832	0.00865561
$861$	−9.57851	−0.326435
$862$	−20.0064	−0.681419
$863$	22.0715	0.751324	0.375662	−	0.926757i	$-0.377415\pi$
$863$	22.0715	0.751324	0.375662	+	0.926757i	$0.377415\pi$
$864$	−2.18475	−0.0743267
$865$	−1.21075	−0.0411668
$866$	8.59686	0.292133
$867$	2.15668	0.0732447
$868$	21.2893	0.722606
$869$	−27.2456	−0.924245
$870$	0.0416580	0.00141234
$871$	5.25818	0.178167
$872$	−10.7643	−0.364526
$873$	10.6470	0.360346
$874$	29.6497	1.00292
$875$	3.58811	0.121300
$876$	−3.29164	−0.111214
$877$	4.92806	0.166409	0.0832044	−	0.996532i	$-0.473485\pi$
$877$	4.92806	0.166409	0.0832044	+	0.996532i	$0.473485\pi$
$878$	13.1657	0.444319
$879$	2.12398	0.0716402
$880$	−0.626548	−0.0211209
$881$	−8.06594	−0.271749	−0.135874	−	0.990726i	$-0.543384\pi$
$881$	−8.06594	−0.271749	−0.135874	+	0.990726i	$0.543384\pi$
$882$	3.77031	0.126953
$883$	−57.1740	−1.92406	−0.962030	−	0.272944i	$-0.912003\pi$
$883$	−57.1740	−1.92406	−0.962030	+	0.272944i	$0.912003\pi$
$884$	−12.4444	−0.418549
$885$	0.0438420	0.00147373
$886$	−19.2164	−0.645587
$887$	−7.24578	−0.243290	−0.121645	−	0.992574i	$-0.538817\pi$
$887$	−7.24578	−0.243290	−0.121645	+	0.992574i	$0.538817\pi$
$888$	−4.23085	−0.141978
$889$	−23.7559	−0.796747
$890$	−0.621339	−0.0208273
$891$	−39.0635	−1.30868
$892$	18.0146	0.603173
$893$	17.0241	0.569691
$894$	−4.79464	−0.160357
$895$	0.228652	0.00764298
$896$	2.88406	0.0963497
$897$	12.0503	0.402347
$898$	−4.07182	−0.135878
$899$	−6.62054	−0.220807
$900$	14.2608	0.475361
$901$	20.9060	0.696481
$902$	−44.8008	−1.49170
$903$	2.18999	0.0728783
$904$	9.00893	0.299632
$905$	−0.864141	−0.0287250
$906$	−1.44961	−0.0481601
$907$	13.3554	0.443457	0.221729	−	0.975108i	$-0.428830\pi$
$907$	13.3554	0.443457	0.221729	+	0.975108i	$0.428830\pi$
$908$	2.57357	0.0854069
$909$	−23.0331	−0.763959
$910$	−1.33545	−0.0442697
$911$	52.5411	1.74076	0.870382	−	0.492376i	$-0.163872\pi$
$911$	52.5411	1.74076	0.870382	+	0.492376i	$0.163872\pi$
$912$	1.27047	0.0420694
$913$	−29.8035	−0.986351
$914$	34.3528	1.13629
$915$	0.233111	0.00770643
$916$	3.03330	0.100223
$917$	34.5649	1.14143
$918$	−7.31622	−0.241471
$919$	−32.5071	−1.07231	−0.536156	−	0.844119i	$-0.680124\pi$
$919$	−32.5071	−1.07231	−0.536156	+	0.844119i	$0.680124\pi$
$920$	−1.08397	−0.0357376
$921$	5.67796	0.187095
$922$	8.23815	0.271309
$923$	30.8057	1.01398
$924$	−5.40566	−0.177833
$925$	56.5745	1.86016
$926$	−9.87351	−0.324464
$927$	11.5952	0.380836
$928$	−0.896884	−0.0294417
$929$	52.2494	1.71425	0.857124	−	0.515111i	$-0.172249\pi$
$929$	52.2494	1.71425	0.857124	+	0.515111i	$0.172249\pi$
$930$	−0.342862	−0.0112429
$931$	−4.49147	−0.147202
$932$	17.0403	0.558172
$933$	−2.30102	−0.0753320
$934$	−17.4222	−0.570071
$935$	−2.09816	−0.0686173
$936$	−10.6320	−0.347517
$937$	22.4004	0.731790	0.365895	−	0.930656i	$-0.380763\pi$
$937$	22.4004	0.731790	0.365895	+	0.930656i	$0.380763\pi$
$938$	−4.08086	−0.133245
$939$	−4.22814	−0.137980
$940$	−0.622391	−0.0203002
$941$	−40.8880	−1.33291	−0.666455	−	0.745546i	$-0.732189\pi$
$941$	−40.8880	−1.33291	−0.666455	+	0.745546i	$0.732189\pi$
$942$	1.13072	0.0368407
$943$	−77.5087	−2.52403
$944$	−0.943907	−0.0307215
$945$	−0.785130	−0.0255403
$946$	10.2431	0.333031
$947$	−20.8532	−0.677638	−0.338819	−	0.940852i	$-0.610027\pi$
$947$	−20.8532	−0.677638	−0.338819	+	0.940852i	$0.610027\pi$
$948$	−2.01978	−0.0655995
$949$	−32.8151	−1.06522
$950$	−16.9886	−0.551182
$951$	0.896784	0.0290802
$952$	9.65805	0.313019
$953$	−57.9437	−1.87698	−0.938491	−	0.345304i	$-0.887776\pi$
$953$	−57.9437	−1.87698	−0.938491	+	0.345304i	$0.887776\pi$
$954$	17.8613	0.578280
$955$	1.54256	0.0499162
$956$	4.04838	0.130934
$957$	1.68105	0.0543407
$958$	20.4062	0.659295
$959$	30.7886	0.994217
$960$	−0.0464474	−0.00149908
$961$	23.4897	0.757731
$962$	−42.1783	−1.35988
$963$	1.30573	0.0420765
$964$	23.1452	0.745456
$965$	−0.661816	−0.0213046
$966$	−9.35220	−0.300902
$967$	58.8908	1.89380	0.946901	−	0.321526i	$-0.104196\pi$
$967$	58.8908	1.89380	0.946901	+	0.321526i	$0.104196\pi$
$968$	−14.2835	−0.459088
$969$	4.25450	0.136674
$970$	0.463699	0.0148885
$971$	7.41010	0.237802	0.118901	−	0.992906i	$-0.462063\pi$
$971$	7.41010	0.237802	0.118901	+	0.992906i	$0.462063\pi$
$972$	−9.45012	−0.303113
$973$	−56.4682	−1.81029
$974$	22.4747	0.720134
$975$	−6.90452	−0.221121
$976$	−5.01882	−0.160649
$977$	−5.26391	−0.168407	−0.0842037	−	0.996449i	$-0.526835\pi$
$977$	−5.26391	−0.168407	−0.0842037	+	0.996449i	$0.526835\pi$
$978$	4.38709	0.140284
$979$	−25.0733	−0.801346
$980$	0.164205	0.00524534
$981$	−30.7973	−0.983282
$982$	−14.5178	−0.463282
$983$	−10.9397	−0.348923	−0.174462	−	0.984664i	$-0.555818\pi$
$983$	−10.9397	−0.348923	−0.174462	+	0.984664i	$0.555818\pi$
$984$	−3.32119	−0.105876
$985$	−2.70077	−0.0860537
$986$	−3.00346	−0.0956496
$987$	−5.36980	−0.170923
$988$	12.6656	0.402946
$989$	17.7213	0.563503
$990$	−1.79259	−0.0569721
$991$	−53.3837	−1.69579	−0.847894	−	0.530166i	$-0.822130\pi$
$991$	−53.3837	−1.69579	−0.847894	+	0.530166i	$0.822130\pi$
$992$	7.38171	0.234370
$993$	−9.58644	−0.304216
$994$	−23.9082	−0.758323
$995$	1.42709	0.0452417
$996$	−2.20940	−0.0700076
$997$	−33.8646	−1.07250	−0.536251	−	0.844059i	$-0.680160\pi$
$997$	−33.8646	−1.07250	−0.536251	+	0.844059i	$0.680160\pi$
$998$	−12.7201	−0.402647
$999$	−24.7972	−0.784550

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.20	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.20	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +0.124605 q^{5} +0.372757 q^{6} -2.88406 q^{7} -1.00000 q^{8} -2.86105 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.372757 q^{3} +1.00000 q^{4} +0.124605 q^{5} +0.372757 q^{6} -2.88406 q^{7} -1.00000 q^{8} -2.86105 q^{9} -0.124605 q^{10} -5.02827 q^{11} -0.372757 q^{12} -3.71610 q^{13} +2.88406 q^{14} -0.0464474 q^{15} +1.00000 q^{16} +3.34877 q^{17} +2.86105 q^{18} -3.40830 q^{19} +0.124605 q^{20} +1.07505 q^{21} +5.02827 q^{22} +8.69928 q^{23} +0.372757 q^{24} -4.98447 q^{25} +3.71610 q^{26} +2.18475 q^{27} -2.88406 q^{28} +0.896884 q^{29} +0.0464474 q^{30} -7.38171 q^{31} -1.00000 q^{32} +1.87432 q^{33} -3.34877 q^{34} -0.359368 q^{35} -2.86105 q^{36} -11.3501 q^{37} +3.40830 q^{38} +1.38520 q^{39} -0.124605 q^{40} -8.90979 q^{41} -1.07505 q^{42} +2.03710 q^{43} -5.02827 q^{44} -0.356502 q^{45} -8.69928 q^{46} -4.99491 q^{47} -0.372757 q^{48} +1.31780 q^{49} +4.98447 q^{50} -1.24828 q^{51} -3.71610 q^{52} +6.24290 q^{53} -2.18475 q^{54} -0.626548 q^{55} +2.88406 q^{56} +1.27047 q^{57} -0.896884 q^{58} -0.943907 q^{59} -0.0464474 q^{60} -5.01882 q^{61} +7.38171 q^{62} +8.25145 q^{63} +1.00000 q^{64} -0.463045 q^{65} -1.87432 q^{66} -1.41497 q^{67} +3.34877 q^{68} -3.24272 q^{69} +0.359368 q^{70} -8.28978 q^{71} +2.86105 q^{72} +8.83052 q^{73} +11.3501 q^{74} +1.85800 q^{75} -3.40830 q^{76} +14.5018 q^{77} -1.38520 q^{78} +5.41849 q^{79} +0.124605 q^{80} +7.76877 q^{81} +8.90979 q^{82} +5.92719 q^{83} +1.07505 q^{84} +0.417274 q^{85} -2.03710 q^{86} -0.334320 q^{87} +5.02827 q^{88} +4.98647 q^{89} +0.356502 q^{90} +10.7175 q^{91} +8.69928 q^{92} +2.75159 q^{93} +4.99491 q^{94} -0.424691 q^{95} +0.372757 q^{96} -3.72135 q^{97} -1.31780 q^{98} +14.3861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 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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