LMFDB - Embedded newform 4007.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.42566 q^{2} +0.883893 q^{3} +3.88381 q^{4} -3.90163 q^{5} -2.14402 q^{6} +3.11093 q^{7} -4.56949 q^{8} -2.21873 q^{9} +O(q^{10})$	\(q-2.42566 q^{2} +0.883893 q^{3} +3.88381 q^{4} -3.90163 q^{5} -2.14402 q^{6} +3.11093 q^{7} -4.56949 q^{8} -2.21873 q^{9} +9.46401 q^{10} -4.04677 q^{11} +3.43288 q^{12} -0.946888 q^{13} -7.54604 q^{14} -3.44862 q^{15} +3.31639 q^{16} +5.88549 q^{17} +5.38189 q^{18} +2.85900 q^{19} -15.1532 q^{20} +2.74973 q^{21} +9.81608 q^{22} +2.29889 q^{23} -4.03894 q^{24} +10.2227 q^{25} +2.29683 q^{26} -4.61280 q^{27} +12.0823 q^{28} +0.00945516 q^{29} +8.36517 q^{30} +5.58748 q^{31} +1.09456 q^{32} -3.57691 q^{33} -14.2762 q^{34} -12.1377 q^{35} -8.61715 q^{36} -6.12901 q^{37} -6.93495 q^{38} -0.836948 q^{39} +17.8284 q^{40} -12.3441 q^{41} -6.66989 q^{42} -3.12777 q^{43} -15.7169 q^{44} +8.65667 q^{45} -5.57632 q^{46} -6.03246 q^{47} +2.93133 q^{48} +2.67786 q^{49} -24.7967 q^{50} +5.20214 q^{51} -3.67754 q^{52} -12.3487 q^{53} +11.1891 q^{54} +15.7890 q^{55} -14.2153 q^{56} +2.52705 q^{57} -0.0229350 q^{58} +14.1608 q^{59} -13.3938 q^{60} +15.1240 q^{61} -13.5533 q^{62} -6.90232 q^{63} -9.28780 q^{64} +3.69440 q^{65} +8.67636 q^{66} -9.98172 q^{67} +22.8581 q^{68} +2.03197 q^{69} +29.4418 q^{70} -6.92927 q^{71} +10.1385 q^{72} +1.49674 q^{73} +14.8669 q^{74} +9.03576 q^{75} +11.1038 q^{76} -12.5892 q^{77} +2.03015 q^{78} -7.63328 q^{79} -12.9393 q^{80} +2.57898 q^{81} +29.9427 q^{82} -4.79115 q^{83} +10.6794 q^{84} -22.9630 q^{85} +7.58689 q^{86} +0.00835735 q^{87} +18.4917 q^{88} -2.65473 q^{89} -20.9981 q^{90} -2.94570 q^{91} +8.92846 q^{92} +4.93874 q^{93} +14.6327 q^{94} -11.1547 q^{95} +0.967476 q^{96} +3.16063 q^{97} -6.49558 q^{98} +8.97870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.42566	−1.71520	−0.857599	−	0.514318i	$-0.828045\pi$
$2$	−2.42566	−1.71520	−0.857599	+	0.514318i	$0.828045\pi$
$3$	0.883893	0.510316	0.255158	−	0.966899i	$-0.417873\pi$
$3$	0.883893	0.510316	0.255158	+	0.966899i	$0.417873\pi$
$4$	3.88381	1.94191
$5$	−3.90163	−1.74486	−0.872430	−	0.488739i	$-0.837457\pi$
$5$	−3.90163	−1.74486	−0.872430	+	0.488739i	$0.837457\pi$
$6$	−2.14402	−0.875293
$7$	3.11093	1.17582	0.587910	−	0.808926i	$-0.299951\pi$
$7$	3.11093	1.17582	0.587910	+	0.808926i	$0.299951\pi$
$8$	−4.56949	−1.61556
$9$	−2.21873	−0.739578
$10$	9.46401	2.99278
$11$	−4.04677	−1.22015	−0.610074	−	0.792345i	$-0.708860\pi$
$11$	−4.04677	−1.22015	−0.610074	+	0.792345i	$0.708860\pi$
$12$	3.43288	0.990986
$13$	−0.946888	−0.262619	−0.131310	−	0.991341i	$-0.541918\pi$
$13$	−0.946888	−0.262619	−0.131310	+	0.991341i	$0.541918\pi$
$14$	−7.54604	−2.01676
$15$	−3.44862	−0.890430
$16$	3.31639	0.829096
$17$	5.88549	1.42744	0.713720	−	0.700431i	$-0.247009\pi$
$17$	5.88549	1.42744	0.713720	+	0.700431i	$0.247009\pi$
$18$	5.38189	1.26852
$19$	2.85900	0.655899	0.327950	−	0.944695i	$-0.393642\pi$
$19$	2.85900	0.655899	0.327950	+	0.944695i	$0.393642\pi$
$20$	−15.1532	−3.38836
$21$	2.74973	0.600039
$22$	9.81608	2.09280
$23$	2.29889	0.479351	0.239676	−	0.970853i	$-0.422959\pi$
$23$	2.29889	0.479351	0.239676	+	0.970853i	$0.422959\pi$
$24$	−4.03894	−0.824445
$25$	10.2227	2.04454
$26$	2.29683	0.450445
$27$	−4.61280	−0.887734
$28$	12.0823	2.28333
$29$	0.00945516	0.00175578	0.000877890	−	1.00000i	$-0.499721\pi$
$29$	0.00945516	0.00175578	0.000877890		1.00000i	$0.499721\pi$
$30$	8.36517	1.52726
$31$	5.58748	1.00354	0.501771	−	0.865001i	$-0.332682\pi$
$31$	5.58748	1.00354	0.501771	+	0.865001i	$0.332682\pi$
$32$	1.09456	0.193493
$33$	−3.57691	−0.622660
$34$	−14.2762	−2.44834
$35$	−12.1377	−2.05164
$36$	−8.61715	−1.43619
$37$	−6.12901	−1.00760	−0.503801	−	0.863820i	$-0.668066\pi$
$37$	−6.12901	−1.00760	−0.503801	+	0.863820i	$0.668066\pi$
$38$	−6.93495	−1.12500
$39$	−0.836948	−0.134019
$40$	17.8284	2.81892
$41$	−12.3441	−1.92783	−0.963916	−	0.266207i	$-0.914230\pi$
$41$	−12.3441	−1.92783	−0.963916	+	0.266207i	$0.914230\pi$
$42$	−6.66989	−1.02919
$43$	−3.12777	−0.476980	−0.238490	−	0.971145i	$-0.576652\pi$
$43$	−3.12777	−0.476980	−0.238490	+	0.971145i	$0.576652\pi$
$44$	−15.7169	−2.36941
$45$	8.65667	1.29046
$46$	−5.57632	−0.822183
$47$	−6.03246	−0.879924	−0.439962	−	0.898016i	$-0.645008\pi$
$47$	−6.03246	−0.879924	−0.439962	+	0.898016i	$0.645008\pi$
$48$	2.93133	0.423101
$49$	2.67786	0.382552
$50$	−24.7967	−3.50679
$51$	5.20214	0.728445
$52$	−3.67754	−0.509983
$53$	−12.3487	−1.69623	−0.848113	−	0.529815i	$-0.822261\pi$
$53$	−12.3487	−1.69623	−0.848113	+	0.529815i	$0.822261\pi$
$54$	11.1891	1.52264
$55$	15.7890	2.12899
$56$	−14.2153	−1.89960
$57$	2.52705	0.334716
$58$	−0.0229350	−0.00301151
$59$	14.1608	1.84358	0.921789	−	0.387692i	$-0.126728\pi$
$59$	14.1608	1.84358	0.921789	+	0.387692i	$0.126728\pi$
$60$	−13.3938	−1.72913
$61$	15.1240	1.93643	0.968214	−	0.250122i	$-0.0804709\pi$
$61$	15.1240	1.93643	0.968214	+	0.250122i	$0.0804709\pi$
$62$	−13.5533	−1.72127
$63$	−6.90232	−0.869610
$64$	−9.28780	−1.16098
$65$	3.69440	0.458234
$66$	8.67636	1.06799
$67$	−9.98172	−1.21946	−0.609731	−	0.792609i	$-0.708722\pi$
$67$	−9.98172	−1.21946	−0.609731	+	0.792609i	$0.708722\pi$
$68$	22.8581	2.77196
$69$	2.03197	0.244621
$70$	29.4418	3.51897
$71$	−6.92927	−0.822353	−0.411176	−	0.911556i	$-0.634882\pi$
$71$	−6.92927	−0.822353	−0.411176	+	0.911556i	$0.634882\pi$
$72$	10.1385	1.19483
$73$	1.49674	0.175180	0.0875901	−	0.996157i	$-0.472083\pi$
$73$	1.49674	0.175180	0.0875901	+	0.996157i	$0.472083\pi$
$74$	14.8669	1.72824
$75$	9.03576	1.04336
$76$	11.1038	1.27370
$77$	−12.5892	−1.43467
$78$	2.03015	0.229869
$79$	−7.63328	−0.858811	−0.429406	−	0.903112i	$-0.641277\pi$
$79$	−7.63328	−0.858811	−0.429406	+	0.903112i	$0.641277\pi$
$80$	−12.9393	−1.44666
$81$	2.57898	0.286553
$82$	29.9427	3.30662
$83$	−4.79115	−0.525897	−0.262949	−	0.964810i	$-0.584695\pi$
$83$	−4.79115	−0.525897	−0.262949	+	0.964810i	$0.584695\pi$
$84$	10.6794	1.16522
$85$	−22.9630	−2.49068
$86$	7.58689	0.818115
$87$	0.00835735	0.000896002 0
$88$	18.4917	1.97122
$89$	−2.65473	−0.281401	−0.140700	−	0.990052i	$-0.544935\pi$
$89$	−2.65473	−0.281401	−0.140700	+	0.990052i	$0.544935\pi$
$90$	−20.9981	−2.21340
$91$	−2.94570	−0.308793
$92$	8.92846	0.930856
$93$	4.93874	0.512123
$94$	14.6327	1.50925
$95$	−11.1547	−1.14445
$96$	0.967476	0.0987426
$97$	3.16063	0.320913	0.160457	−	0.987043i	$-0.448703\pi$
$97$	3.16063	0.320913	0.160457	+	0.987043i	$0.448703\pi$
$98$	−6.49558	−0.656153
$99$	8.97870	0.902394
$100$	39.7030	3.97030
$101$	18.4609	1.83693	0.918464	−	0.395504i	$-0.129430\pi$
$101$	18.4609	1.83693	0.918464	+	0.395504i	$0.129430\pi$
$102$	−12.6186	−1.24943
$103$	1.25958	0.124110	0.0620549	−	0.998073i	$-0.480235\pi$
$103$	1.25958	0.124110	0.0620549	+	0.998073i	$0.480235\pi$
$104$	4.32679	0.424277
$105$	−10.7284	−1.04699
$106$	29.9538	2.90937
$107$	7.23269	0.699211	0.349605	−	0.936897i	$-0.386316\pi$
$107$	7.23269	0.699211	0.349605	+	0.936897i	$0.386316\pi$
$108$	−17.9153	−1.72390
$109$	−14.8454	−1.42193	−0.710965	−	0.703228i	$-0.751741\pi$
$109$	−14.8454	−1.42193	−0.710965	+	0.703228i	$0.751741\pi$
$110$	−38.2987	−3.65164
$111$	−5.41739	−0.514196
$112$	10.3170	0.974868
$113$	15.6805	1.47509	0.737547	−	0.675295i	$-0.235984\pi$
$113$	15.6805	1.47509	0.737547	+	0.675295i	$0.235984\pi$
$114$	−6.12975	−0.574104
$115$	−8.96941	−0.836401
$116$	0.0367221	0.00340956
$117$	2.10089	0.194227
$118$	−34.3492	−3.16210
$119$	18.3093	1.67841
$120$	15.7584	1.43854
$121$	5.37635	0.488759
$122$	−36.6856	−3.32136
$123$	−10.9109	−0.983803
$124$	21.7007	1.94878
$125$	−20.3770	−1.82257
$126$	16.7427	1.49155
$127$	5.38145	0.477526	0.238763	−	0.971078i	$-0.423258\pi$
$127$	5.38145	0.477526	0.238763	+	0.971078i	$0.423258\pi$
$128$	20.3399	1.79781
$129$	−2.76461	−0.243410
$130$	−8.96136	−0.785963
$131$	−8.21114	−0.717411	−0.358706	−	0.933451i	$-0.616782\pi$
$131$	−8.21114	−0.717411	−0.358706	+	0.933451i	$0.616782\pi$
$132$	−13.8921	−1.20915
$133$	8.89413	0.771219
$134$	24.2122	2.09162
$135$	17.9974	1.54897
$136$	−26.8937	−2.30611
$137$	5.81231	0.496579	0.248290	−	0.968686i	$-0.420132\pi$
$137$	5.81231	0.496579	0.248290	+	0.968686i	$0.420132\pi$
$138$	−4.92887	−0.419573
$139$	−9.42614	−0.799515	−0.399757	−	0.916621i	$-0.630906\pi$
$139$	−9.42614	−0.799515	−0.399757	+	0.916621i	$0.630906\pi$
$140$	−47.1405	−3.98410
$141$	−5.33205	−0.449039
$142$	16.8080	1.41050
$143$	3.83184	0.320434
$144$	−7.35817	−0.613181
$145$	−0.0368905	−0.00306359
$146$	−3.63058	−0.300469
$147$	2.36694	0.195222
$148$	−23.8039	−1.95667
$149$	9.85339	0.807221	0.403611	−	0.914931i	$-0.367755\pi$
$149$	9.85339	0.807221	0.403611	+	0.914931i	$0.367755\pi$
$150$	−21.9177	−1.78957
$151$	0.429968	0.0349903	0.0174951	−	0.999847i	$-0.494431\pi$
$151$	0.429968	0.0349903	0.0174951	+	0.999847i	$0.494431\pi$
$152$	−13.0642	−1.05964
$153$	−13.0583	−1.05570
$154$	30.5371	2.46075
$155$	−21.8003	−1.75104
$156$	−3.25055	−0.260252
$157$	15.0776	1.20333	0.601663	−	0.798750i	$-0.294505\pi$
$157$	15.0776	1.20333	0.601663	+	0.798750i	$0.294505\pi$
$158$	18.5157	1.47303
$159$	−10.9149	−0.865611
$160$	−4.27057	−0.337619
$161$	7.15167	0.563631
$162$	−6.25571	−0.491495
$163$	−4.01817	−0.314727	−0.157364	−	0.987541i	$-0.550299\pi$
$163$	−4.01817	−0.314727	−0.157364	+	0.987541i	$0.550299\pi$
$164$	−47.9424	−3.74367
$165$	13.9558	1.08646
$166$	11.6217	0.902018
$167$	11.2395	0.869741	0.434871	−	0.900493i	$-0.356794\pi$
$167$	11.2395	0.869741	0.434871	+	0.900493i	$0.356794\pi$
$168$	−12.5648	−0.969399
$169$	−12.1034	−0.931031
$170$	55.7003	4.27202
$171$	−6.34335	−0.485088
$172$	−12.1477	−0.926250
$173$	−2.34529	−0.178309	−0.0891546	−	0.996018i	$-0.528417\pi$
$173$	−2.34529	−0.178309	−0.0891546	+	0.996018i	$0.528417\pi$
$174$	−0.0202721	−0.00153682
$175$	31.8020	2.40401
$176$	−13.4206	−1.01162
$177$	12.5166	0.940807
$178$	6.43947	0.482658
$179$	4.26830	0.319028	0.159514	−	0.987196i	$-0.449007\pi$
$179$	4.26830	0.319028	0.159514	+	0.987196i	$0.449007\pi$
$180$	33.6209	2.50595
$181$	15.5371	1.15486	0.577432	−	0.816439i	$-0.304055\pi$
$181$	15.5371	1.15486	0.577432	+	0.816439i	$0.304055\pi$
$182$	7.14526	0.529642
$183$	13.3680	0.988190
$184$	−10.5047	−0.774420
$185$	23.9131	1.75813
$186$	−11.9797	−0.878393
$187$	−23.8172	−1.74169
$188$	−23.4289	−1.70873
$189$	−14.3501	−1.04382
$190$	27.0576	1.96296
$191$	21.4607	1.55284	0.776421	−	0.630214i	$-0.217033\pi$
$191$	21.4607	1.55284	0.776421	+	0.630214i	$0.217033\pi$
$192$	−8.20942	−0.592464
$193$	23.2972	1.67697	0.838486	−	0.544924i	$-0.183441\pi$
$193$	23.2972	1.67697	0.838486	+	0.544924i	$0.183441\pi$
$194$	−7.66661	−0.550430
$195$	3.26546	0.233844
$196$	10.4003	0.742880
$197$	−23.3973	−1.66699	−0.833494	−	0.552528i	$-0.813663\pi$
$197$	−23.3973	−1.66699	−0.833494	+	0.552528i	$0.813663\pi$
$198$	−21.7793	−1.54778
$199$	4.65562	0.330028	0.165014	−	0.986291i	$-0.447233\pi$
$199$	4.65562	0.330028	0.165014	+	0.986291i	$0.447233\pi$
$200$	−46.7125	−3.30307
$201$	−8.82277	−0.622310
$202$	−44.7798	−3.15070
$203$	0.0294143	0.00206448
$204$	20.2041	1.41457
$205$	48.1623	3.36380
$206$	−3.05530	−0.212873
$207$	−5.10062	−0.354518
$208$	−3.14024	−0.217737
$209$	−11.5697	−0.800293
$210$	26.0234	1.79579
$211$	9.97191	0.686495	0.343247	−	0.939245i	$-0.388473\pi$
$211$	9.97191	0.686495	0.343247	+	0.939245i	$0.388473\pi$
$212$	−47.9601	−3.29391
$213$	−6.12473	−0.419660
$214$	−17.5440	−1.19929
$215$	12.2034	0.832263
$216$	21.0781	1.43419
$217$	17.3822	1.17998
$218$	36.0098	2.43889
$219$	1.32296	0.0893972
$220$	61.3215	4.13429
$221$	−5.57290	−0.374873
$222$	13.1407	0.881948
$223$	−1.17397	−0.0786148	−0.0393074	−	0.999227i	$-0.512515\pi$
$223$	−1.17397	−0.0786148	−0.0393074	+	0.999227i	$0.512515\pi$
$224$	3.40510	0.227513
$225$	−22.6814	−1.51209
$226$	−38.0355	−2.53008
$227$	13.0429	0.865690	0.432845	−	0.901468i	$-0.357510\pi$
$227$	13.0429	0.865690	0.432845	+	0.901468i	$0.357510\pi$
$228$	9.81459	0.649987
$229$	6.64751	0.439280	0.219640	−	0.975581i	$-0.429512\pi$
$229$	6.64751	0.439280	0.219640	+	0.975581i	$0.429512\pi$
$230$	21.7567	1.43459
$231$	−11.1275	−0.732136
$232$	−0.0432053	−0.00283656
$233$	−10.9099	−0.714732	−0.357366	−	0.933964i	$-0.616325\pi$
$233$	−10.9099	−0.714732	−0.357366	+	0.933964i	$0.616325\pi$
$234$	−5.09604	−0.333139
$235$	23.5364	1.53535
$236$	54.9979	3.58006
$237$	−6.74701	−0.438265
$238$	−44.4121	−2.87881
$239$	6.51719	0.421562	0.210781	−	0.977533i	$-0.432399\pi$
$239$	6.51719	0.421562	0.210781	+	0.977533i	$0.432399\pi$
$240$	−11.4370	−0.738252
$241$	−5.96773	−0.384415	−0.192208	−	0.981354i	$-0.561565\pi$
$241$	−5.96773	−0.384415	−0.192208	+	0.981354i	$0.561565\pi$
$242$	−13.0412	−0.838319
$243$	16.1179	1.03397
$244$	58.7388	3.76036
$245$	−10.4480	−0.667500
$246$	26.4661	1.68742
$247$	−2.70715	−0.172252
$248$	−25.5319	−1.62128
$249$	−4.23486	−0.268374
$250$	49.4276	3.12608
$251$	11.7067	0.738919	0.369460	−	0.929247i	$-0.379543\pi$
$251$	11.7067	0.738919	0.369460	+	0.929247i	$0.379543\pi$
$252$	−26.8073	−1.68870
$253$	−9.30307	−0.584879
$254$	−13.0536	−0.819053
$255$	−20.2968	−1.27104
$256$	−30.7620	−1.92263
$257$	−13.0168	−0.811964	−0.405982	−	0.913881i	$-0.633070\pi$
$257$	−13.0168	−0.811964	−0.405982	+	0.913881i	$0.633070\pi$
$258$	6.70600	0.417497
$259$	−19.0669	−1.18476
$260$	14.3484	0.889848
$261$	−0.0209785	−0.00129854
$262$	19.9174	1.23050
$263$	−7.23593	−0.446186	−0.223093	−	0.974797i	$-0.571615\pi$
$263$	−7.23593	−0.446186	−0.223093	+	0.974797i	$0.571615\pi$
$264$	16.3447	1.00594
$265$	48.1801	2.95968
$266$	−21.5741	−1.32279
$267$	−2.34650	−0.143603
$268$	−38.7671	−2.36808
$269$	16.6165	1.01313	0.506564	−	0.862202i	$-0.330915\pi$
$269$	16.6165	1.01313	0.506564	+	0.862202i	$0.330915\pi$
$270$	−43.6556	−2.65680
$271$	28.9520	1.75871	0.879355	−	0.476167i	$-0.157974\pi$
$271$	28.9520	1.75871	0.879355	+	0.476167i	$0.157974\pi$
$272$	19.5185	1.18349
$273$	−2.60368	−0.157582
$274$	−14.0987	−0.851732
$275$	−41.3689	−2.49464
$276$	7.89180	0.475031
$277$	−19.6366	−1.17985	−0.589925	−	0.807458i	$-0.700843\pi$
$277$	−19.6366	−1.17985	−0.589925	+	0.807458i	$0.700843\pi$
$278$	22.8646	1.37133
$279$	−12.3971	−0.742197
$280$	55.4630	3.31455
$281$	8.17625	0.487754	0.243877	−	0.969806i	$-0.421581\pi$
$281$	8.17625	0.487754	0.243877	+	0.969806i	$0.421581\pi$
$282$	12.9337	0.770192
$283$	8.62086	0.512457	0.256228	−	0.966616i	$-0.417520\pi$
$283$	8.62086	0.512457	0.256228	+	0.966616i	$0.417520\pi$
$284$	−26.9120	−1.59693
$285$	−9.85960	−0.584032
$286$	−9.29473	−0.549609
$287$	−38.4017	−2.26678
$288$	−2.42854	−0.143103
$289$	17.6389	1.03759
$290$	0.0894838	0.00525467
$291$	2.79366	0.163767
$292$	5.81306	0.340184
$293$	12.9161	0.754564	0.377282	−	0.926098i	$-0.376859\pi$
$293$	12.9161	0.754564	0.377282	+	0.926098i	$0.376859\pi$
$294$	−5.74140	−0.334845
$295$	−55.2501	−3.21679
$296$	28.0064	1.62784
$297$	18.6669	1.08317
$298$	−23.9009	−1.38454
$299$	−2.17679	−0.125887
$300$	35.0932	2.02611
$301$	−9.73025	−0.560842
$302$	−1.04295	−0.0600153
$303$	16.3175	0.937414
$304$	9.48154	0.543804
$305$	−59.0082	−3.37880
$306$	31.6750	1.81074
$307$	24.3540	1.38996	0.694978	−	0.719031i	$-0.255414\pi$
$307$	24.3540	1.38996	0.694978	+	0.719031i	$0.255414\pi$
$308$	−48.8941	−2.78600
$309$	1.11333	0.0633352
$310$	52.8800	3.00338
$311$	−18.8675	−1.06988	−0.534940	−	0.844890i	$-0.679666\pi$
$311$	−18.8675	−1.06988	−0.534940	+	0.844890i	$0.679666\pi$
$312$	3.82442	0.216515
$313$	9.09787	0.514242	0.257121	−	0.966379i	$-0.417226\pi$
$313$	9.09787	0.514242	0.257121	+	0.966379i	$0.417226\pi$
$314$	−36.5732	−2.06394
$315$	26.9303	1.51735
$316$	−29.6463	−1.66773
$317$	−20.8411	−1.17056	−0.585278	−	0.810833i	$-0.699014\pi$
$317$	−20.8411	−1.17056	−0.585278	+	0.810833i	$0.699014\pi$
$318$	26.4759	1.48470
$319$	−0.0382629	−0.00214231
$320$	36.2375	2.02574
$321$	6.39293	0.356818
$322$	−17.3475	−0.966739
$323$	16.8266	0.936257
$324$	10.0163	0.556459
$325$	−9.67974	−0.536935
$326$	9.74670	0.539820
$327$	−13.1217	−0.725633
$328$	56.4064	3.11452
$329$	−18.7665	−1.03463
$330$	−33.8519	−1.86349
$331$	−10.1695	−0.558968	−0.279484	−	0.960150i	$-0.590163\pi$
$331$	−10.1695	−0.558968	−0.279484	+	0.960150i	$0.590163\pi$
$332$	−18.6079	−1.02124
$333$	13.5986	0.745201
$334$	−27.2633	−1.49178
$335$	38.9449	2.12779
$336$	9.11915	0.497490
$337$	−7.75213	−0.422285	−0.211143	−	0.977455i	$-0.567718\pi$
$337$	−7.75213	−0.422285	−0.211143	+	0.977455i	$0.567718\pi$
$338$	29.3587	1.59690
$339$	13.8599	0.752764
$340$	−89.1839	−4.83668
$341$	−22.6113	−1.22447
$342$	15.3868	0.832023
$343$	−13.4459	−0.726008
$344$	14.2923	0.770589
$345$	−7.92799	−0.426829
$346$	5.68887	0.305836
$347$	3.41398	0.183272	0.0916360	−	0.995793i	$-0.470790\pi$
$347$	3.41398	0.183272	0.0916360	+	0.995793i	$0.470790\pi$
$348$	0.0324584	0.00173995
$349$	−20.0888	−1.07533	−0.537664	−	0.843159i	$-0.680693\pi$
$349$	−20.0888	−1.07533	−0.537664	+	0.843159i	$0.680693\pi$
$350$	−77.1408	−4.12335
$351$	4.36781	0.233136
$352$	−4.42944	−0.236090
$353$	6.75227	0.359387	0.179694	−	0.983723i	$-0.442489\pi$
$353$	6.75227	0.359387	0.179694	+	0.983723i	$0.442489\pi$
$354$	−30.3610	−1.61367
$355$	27.0354	1.43489
$356$	−10.3105	−0.546454
$357$	16.1835	0.856520
$358$	−10.3534	−0.547196
$359$	20.6256	1.08858	0.544288	−	0.838899i	$-0.316800\pi$
$359$	20.6256	1.08858	0.544288	+	0.838899i	$0.316800\pi$
$360$	−39.5565	−2.08481
$361$	−10.8261	−0.569796
$362$	−37.6877	−1.98082
$363$	4.75212	0.249422
$364$	−11.4405	−0.599647
$365$	−5.83972	−0.305665
$366$	−32.4262	−1.69494
$367$	17.6641	0.922061	0.461030	−	0.887384i	$-0.347480\pi$
$367$	17.6641	0.922061	0.461030	+	0.887384i	$0.347480\pi$
$368$	7.62400	0.397428
$369$	27.3884	1.42578
$370$	−58.0050	−3.01554
$371$	−38.4159	−1.99446
$372$	19.1811	0.994496
$373$	−30.1479	−1.56100	−0.780500	−	0.625156i	$-0.785035\pi$
$373$	−30.1479	−1.56100	−0.780500	+	0.625156i	$0.785035\pi$
$374$	57.7724	2.98734
$375$	−18.0111	−0.930088
$376$	27.5652	1.42157
$377$	−0.00895298	−0.000461102 0
$378$	34.8084	1.79035
$379$	29.1566	1.49767	0.748837	−	0.662754i	$-0.230612\pi$
$379$	29.1566	1.49767	0.748837	+	0.662754i	$0.230612\pi$
$380$	−43.3229	−2.22242
$381$	4.75663	0.243689
$382$	−52.0563	−2.66343
$383$	4.99716	0.255343	0.127672	−	0.991817i	$-0.459250\pi$
$383$	4.99716	0.255343	0.127672	+	0.991817i	$0.459250\pi$
$384$	17.9783	0.917451
$385$	49.1184	2.50330
$386$	−56.5111	−2.87634
$387$	6.93968	0.352764
$388$	12.2753	0.623184
$389$	14.2149	0.720726	0.360363	−	0.932812i	$-0.382653\pi$
$389$	14.2149	0.720726	0.360363	+	0.932812i	$0.382653\pi$
$390$	−7.92088	−0.401089
$391$	13.5301	0.684245
$392$	−12.2365	−0.618035
$393$	−7.25777	−0.366106
$394$	56.7538	2.85922
$395$	29.7822	1.49851
$396$	34.8716	1.75236
$397$	−4.74227	−0.238007	−0.119004	−	0.992894i	$-0.537970\pi$
$397$	−4.74227	−0.238007	−0.119004	+	0.992894i	$0.537970\pi$
$398$	−11.2929	−0.566064
$399$	7.86146	0.393565
$400$	33.9024	1.69512
$401$	31.9566	1.59584	0.797918	−	0.602767i	$-0.205935\pi$
$401$	31.9566	1.59584	0.797918	+	0.602767i	$0.205935\pi$
$402$	21.4010	1.06739
$403$	−5.29072	−0.263550
$404$	71.6987	3.56715
$405$	−10.0622	−0.499995
$406$	−0.0713491	−0.00354099
$407$	24.8027	1.22942
$408$	−23.7711	−1.17685
$409$	17.6517	0.872820	0.436410	−	0.899748i	$-0.356250\pi$
$409$	17.6517	0.872820	0.436410	+	0.899748i	$0.356250\pi$
$410$	−116.825	−5.76958
$411$	5.13746	0.253412
$412$	4.89196	0.241010
$413$	44.0532	2.16772
$414$	12.3724	0.608068
$415$	18.6933	0.917617
$416$	−1.03643	−0.0508151
$417$	−8.33170	−0.408005
$418$	28.0641	1.37266
$419$	19.2842	0.942097	0.471048	−	0.882107i	$-0.343876\pi$
$419$	19.2842	0.942097	0.471048	+	0.882107i	$0.343876\pi$
$420$	−41.6671	−2.03315
$421$	17.9521	0.874933	0.437466	−	0.899235i	$-0.355876\pi$
$421$	17.9521	0.874933	0.437466	+	0.899235i	$0.355876\pi$
$422$	−24.1884	−1.17748
$423$	13.3844	0.650772
$424$	56.4273	2.74035
$425$	60.1655	2.91846
$426$	14.8565	0.719800
$427$	47.0496	2.27689
$428$	28.0904	1.35780
$429$	3.38693	0.163523
$430$	−29.6012	−1.42750
$431$	−15.6238	−0.752574	−0.376287	−	0.926503i	$-0.622799\pi$
$431$	−15.6238	−0.752574	−0.376287	+	0.926503i	$0.622799\pi$
$432$	−15.2978	−0.736017
$433$	29.3853	1.41217	0.706085	−	0.708128i	$-0.250460\pi$
$433$	29.3853	1.41217	0.706085	+	0.708128i	$0.250460\pi$
$434$	−42.1634	−2.02391
$435$	−0.0326073	−0.00156340
$436$	−57.6567	−2.76125
$437$	6.57252	0.314406
$438$	−3.20904	−0.153334
$439$	22.5148	1.07457	0.537285	−	0.843401i	$-0.319450\pi$
$439$	22.5148	1.07457	0.537285	+	0.843401i	$0.319450\pi$
$440$	−72.1476	−3.43950
$441$	−5.94146	−0.282927
$442$	13.5179	0.642983
$443$	−8.73009	−0.414779	−0.207389	−	0.978258i	$-0.566497\pi$
$443$	−8.73009	−0.414779	−0.207389	+	0.978258i	$0.566497\pi$
$444$	−21.0401	−0.998520
$445$	10.3578	0.491005
$446$	2.84765	0.134840
$447$	8.70934	0.411938
$448$	−28.8937	−1.36510
$449$	28.6173	1.35053	0.675267	−	0.737574i	$-0.264029\pi$
$449$	28.6173	1.35053	0.675267	+	0.737574i	$0.264029\pi$
$450$	55.0174	2.59354
$451$	49.9539	2.35224
$452$	60.9000	2.86450
$453$	0.380045	0.0178561
$454$	−31.6377	−1.48483
$455$	11.4930	0.538801
$456$	−11.5473	−0.540753
$457$	−12.1756	−0.569549	−0.284775	−	0.958594i	$-0.591919\pi$
$457$	−12.1756	−0.569549	−0.284775	+	0.958594i	$0.591919\pi$
$458$	−16.1246	−0.753452
$459$	−27.1486	−1.26719
$460$	−34.8355	−1.62421
$461$	−32.9683	−1.53549	−0.767743	−	0.640758i	$-0.778620\pi$
$461$	−32.9683	−1.53549	−0.767743	+	0.640758i	$0.778620\pi$
$462$	26.9915	1.25576
$463$	26.7143	1.24152	0.620760	−	0.784001i	$-0.286824\pi$
$463$	26.7143	1.24152	0.620760	+	0.784001i	$0.286824\pi$
$464$	0.0313570	0.00145571
$465$	−19.2691	−0.893584
$466$	26.4637	1.22591
$467$	30.0414	1.39015	0.695075	−	0.718937i	$-0.255371\pi$
$467$	30.0414	1.39015	0.695075	+	0.718937i	$0.255371\pi$
$468$	8.15947	0.377172
$469$	−31.0524	−1.43387
$470$	−57.0912	−2.63342
$471$	13.3270	0.614076
$472$	−64.7076	−2.97841
$473$	12.6573	0.581986
$474$	16.3659	0.751712
$475$	29.2266	1.34101
$476$	71.1100	3.25932
$477$	27.3985	1.25449
$478$	−15.8085	−0.723062
$479$	−42.4129	−1.93790	−0.968948	−	0.247263i	$-0.920469\pi$
$479$	−42.4129	−1.93790	−0.968948	+	0.247263i	$0.920469\pi$
$480$	−3.77473	−0.172292
$481$	5.80348	0.264616
$482$	14.4757	0.659349
$483$	6.32131	0.287630
$484$	20.8807	0.949125
$485$	−12.3316	−0.559949
$486$	−39.0966	−1.77346
$487$	37.5946	1.70357	0.851787	−	0.523888i	$-0.175519\pi$
$487$	37.5946	1.70357	0.851787	+	0.523888i	$0.175519\pi$
$488$	−69.1089	−3.12841
$489$	−3.55163	−0.160610
$490$	25.3433	1.14489
$491$	28.8246	1.30084	0.650418	−	0.759576i	$-0.274594\pi$
$491$	28.8246	1.30084	0.650418	+	0.759576i	$0.274594\pi$
$492$	−42.3759	−1.91045
$493$	0.0556482	0.00250627
$494$	6.56662	0.295446
$495$	−35.0315	−1.57455
$496$	18.5302	0.832033
$497$	−21.5564	−0.966939
$498$	10.2723	0.460314
$499$	7.11177	0.318367	0.159183	−	0.987249i	$-0.449114\pi$
$499$	7.11177	0.318367	0.159183	+	0.987249i	$0.449114\pi$
$500$	−79.1404	−3.53927
$501$	9.93454	0.443843
$502$	−28.3964	−1.26739
$503$	37.3522	1.66545	0.832726	−	0.553685i	$-0.186779\pi$
$503$	37.3522	1.66545	0.832726	+	0.553685i	$0.186779\pi$
$504$	31.5400	1.40491
$505$	−72.0276	−3.20518
$506$	22.5661	1.00318
$507$	−10.6981	−0.475120
$508$	20.9006	0.927312
$509$	6.92505	0.306947	0.153474	−	0.988153i	$-0.450954\pi$
$509$	6.92505	0.306947	0.153474	+	0.988153i	$0.450954\pi$
$510$	49.2331	2.18008
$511$	4.65625	0.205980
$512$	33.9384	1.49988
$513$	−13.1880	−0.582264
$514$	31.5742	1.39268
$515$	−4.91440	−0.216554
$516$	−10.7372	−0.472680
$517$	24.4120	1.07364
$518$	46.2498	2.03210
$519$	−2.07299	−0.0909940
$520$	−16.8815	−0.740304
$521$	14.0097	0.613776	0.306888	−	0.951746i	$-0.400712\pi$
$521$	14.0097	0.613776	0.306888	+	0.951746i	$0.400712\pi$
$522$	0.0508866	0.00222725
$523$	−28.1650	−1.23157	−0.615784	−	0.787915i	$-0.711161\pi$
$523$	−28.1650	−1.23157	−0.615784	+	0.787915i	$0.711161\pi$
$524$	−31.8906	−1.39315
$525$	28.1096	1.22680
$526$	17.5519	0.765298
$527$	32.8851	1.43250
$528$	−11.8624	−0.516245
$529$	−17.7151	−0.770222
$530$	−116.868	−5.07644
$531$	−31.4190	−1.36347
$532$	34.5432	1.49764
$533$	11.6885	0.506286
$534$	5.69180	0.246308
$535$	−28.2193	−1.22003
$536$	45.6114	1.97011
$537$	3.77272	0.162805
$538$	−40.3060	−1.73772
$539$	−10.8367	−0.466770
$540$	69.8987	3.00796
$541$	−4.72267	−0.203043	−0.101522	−	0.994833i	$-0.532371\pi$
$541$	−4.72267	−0.203043	−0.101522	+	0.994833i	$0.532371\pi$
$542$	−70.2277	−3.01654
$543$	13.7331	0.589345
$544$	6.44203	0.276200
$545$	57.9211	2.48107
$546$	6.31564	0.270284
$547$	−1.66563	−0.0712173	−0.0356086	−	0.999366i	$-0.511337\pi$
$547$	−1.66563	−0.0712173	−0.0356086	+	0.999366i	$0.511337\pi$
$548$	22.5739	0.964311
$549$	−33.5561	−1.43214
$550$	100.347	4.27880
$551$	0.0270323	0.00115161
$552$	−9.28507	−0.395199
$553$	−23.7466	−1.00981
$554$	47.6317	2.02368
$555$	21.1366	0.897200
$556$	−36.6094	−1.55258
$557$	14.6966	0.622713	0.311356	−	0.950293i	$-0.399217\pi$
$557$	14.6966	0.622713	0.311356	+	0.950293i	$0.399217\pi$
$558$	30.0712	1.27302
$559$	2.96164	0.125264
$560$	−40.2532	−1.70101
$561$	−21.0519	−0.888811
$562$	−19.8328	−0.836595
$563$	27.5442	1.16085	0.580426	−	0.814313i	$-0.302886\pi$
$563$	27.5442	1.16085	0.580426	+	0.814313i	$0.302886\pi$
$564$	−20.7087	−0.871993
$565$	−61.1793	−2.57383
$566$	−20.9113	−0.878965
$567$	8.02300	0.336935
$568$	31.6632	1.32856
$569$	−31.1795	−1.30711	−0.653556	−	0.756878i	$-0.726724\pi$
$569$	−31.1795	−1.30711	−0.653556	+	0.756878i	$0.726724\pi$
$570$	23.9160	1.00173
$571$	−30.6349	−1.28203	−0.641015	−	0.767529i	$-0.721486\pi$
$571$	−30.6349	−1.28203	−0.641015	+	0.767529i	$0.721486\pi$
$572$	14.8821	0.622254
$573$	18.9690	0.792440
$574$	93.1495	3.88798
$575$	23.5008	0.980052
$576$	20.6072	0.858632
$577$	11.1179	0.462846	0.231423	−	0.972853i	$-0.425662\pi$
$577$	11.1179	0.462846	0.231423	+	0.972853i	$0.425662\pi$
$578$	−42.7860	−1.77966
$579$	20.5923	0.855785
$580$	−0.143276	−0.00594921
$581$	−14.9049	−0.618360
$582$	−6.77646	−0.280893
$583$	49.9724	2.06965
$584$	−6.83934	−0.283014
$585$	−8.19689	−0.338900
$586$	−31.3299	−1.29423
$587$	−10.6454	−0.439384	−0.219692	−	0.975569i	$-0.570505\pi$
$587$	−10.6454	−0.439384	−0.219692	+	0.975569i	$0.570505\pi$
$588$	9.19277	0.379104
$589$	15.9746	0.658222
$590$	134.018	5.51743
$591$	−20.6807	−0.850691
$592$	−20.3262	−0.835400
$593$	35.5784	1.46103	0.730515	−	0.682896i	$-0.239280\pi$
$593$	35.5784	1.46103	0.730515	+	0.682896i	$0.239280\pi$
$594$	−45.2796	−1.85785
$595$	−71.4361	−2.92859
$596$	38.2687	1.56755
$597$	4.11507	0.168419
$598$	5.28015	0.215921
$599$	−26.9808	−1.10240	−0.551202	−	0.834372i	$-0.685831\pi$
$599$	−26.9808	−1.10240	−0.551202	+	0.834372i	$0.685831\pi$
$600$	−41.2888	−1.68561
$601$	−4.45306	−0.181644	−0.0908221	−	0.995867i	$-0.528949\pi$
$601$	−4.45306	−0.181644	−0.0908221	+	0.995867i	$0.528949\pi$
$602$	23.6022	0.961956
$603$	22.1468	0.901886
$604$	1.66991	0.0679478
$605$	−20.9765	−0.852816
$606$	−39.5806	−1.60785
$607$	47.5453	1.92980	0.964902	−	0.262611i	$-0.0845836\pi$
$607$	47.5453	1.92980	0.964902	+	0.262611i	$0.0845836\pi$
$608$	3.12935	0.126912
$609$	0.0259991	0.00105354
$610$	143.134	5.79531
$611$	5.71206	0.231085
$612$	−50.7161	−2.05008
$613$	−9.04020	−0.365130	−0.182565	−	0.983194i	$-0.558440\pi$
$613$	−9.04020	−0.365130	−0.182565	+	0.983194i	$0.558440\pi$
$614$	−59.0744	−2.38405
$615$	42.5703	1.71660
$616$	57.5262	2.31780
$617$	−30.5482	−1.22982	−0.614911	−	0.788596i	$-0.710808\pi$
$617$	−30.5482	−1.22982	−0.614911	+	0.788596i	$0.710808\pi$
$618$	−2.70056	−0.108632
$619$	−21.5445	−0.865948	−0.432974	−	0.901406i	$-0.642536\pi$
$619$	−21.5445	−0.865948	−0.432974	+	0.901406i	$0.642536\pi$
$620$	−84.6682	−3.40036
$621$	−10.6043	−0.425537
$622$	45.7662	1.83506
$623$	−8.25867	−0.330877
$624$	−2.77564	−0.111115
$625$	28.3899	1.13560
$626$	−22.0683	−0.882028
$627$	−10.2264	−0.408402
$628$	58.5587	2.33675
$629$	−36.0722	−1.43829
$630$	−65.3236	−2.60255
$631$	−5.38228	−0.214265	−0.107133	−	0.994245i	$-0.534167\pi$
$631$	−5.38228	−0.214265	−0.107133	+	0.994245i	$0.534167\pi$
$632$	34.8802	1.38746
$633$	8.81410	0.350329
$634$	50.5535	2.00774
$635$	−20.9964	−0.833217
$636$	−42.3916	−1.68094
$637$	−2.53564	−0.100466
$638$	0.0928126	0.00367449
$639$	15.3742	0.608194
$640$	−79.3587	−3.13693
$641$	37.0044	1.46158	0.730792	−	0.682600i	$-0.239151\pi$
$641$	37.0044	1.46158	0.730792	+	0.682600i	$0.239151\pi$
$642$	−15.5070	−0.612014
$643$	34.8339	1.37371	0.686857	−	0.726793i	$-0.258990\pi$
$643$	34.8339	1.37371	0.686857	+	0.726793i	$0.258990\pi$
$644$	27.7758	1.09452
$645$	10.7865	0.424717
$646$	−40.8156	−1.60587
$647$	−3.33463	−0.131098	−0.0655488	−	0.997849i	$-0.520880\pi$
$647$	−3.33463	−0.131098	−0.0655488	+	0.997849i	$0.520880\pi$
$648$	−11.7846	−0.462943
$649$	−57.3055	−2.24944
$650$	23.4797	0.920951
$651$	15.3640	0.602165
$652$	−15.6058	−0.611171
$653$	27.7472	1.08583	0.542916	−	0.839787i	$-0.317320\pi$
$653$	27.7472	1.08583	0.542916	+	0.839787i	$0.317320\pi$
$654$	31.8288	1.24461
$655$	32.0368	1.25178
$656$	−40.9379	−1.59836
$657$	−3.32087	−0.129559
$658$	45.5212	1.77460
$659$	−32.9934	−1.28524	−0.642620	−	0.766185i	$-0.722153\pi$
$659$	−32.9934	−1.28524	−0.642620	+	0.766185i	$0.722153\pi$
$660$	54.2016	2.10980
$661$	22.5514	0.877149	0.438575	−	0.898695i	$-0.355484\pi$
$661$	22.5514	0.877149	0.438575	+	0.898695i	$0.355484\pi$
$662$	24.6678	0.958741
$663$	−4.92584	−0.191304
$664$	21.8931	0.849617
$665$	−34.7016	−1.34567
$666$	−32.9856	−1.27817
$667$	0.0217364	0.000841636 0
$668$	43.6523	1.68896
$669$	−1.03766	−0.0401184
$670$	−94.4671	−3.64958
$671$	−61.2033	−2.36273
$672$	3.00975	0.116104
$673$	2.18819	0.0843485	0.0421743	−	0.999110i	$-0.486572\pi$
$673$	2.18819	0.0843485	0.0421743	+	0.999110i	$0.486572\pi$
$674$	18.8040	0.724303
$675$	−47.1552	−1.81501
$676$	−47.0074	−1.80798
$677$	19.0576	0.732445	0.366222	−	0.930527i	$-0.380651\pi$
$677$	19.0576	0.732445	0.366222	+	0.930527i	$0.380651\pi$
$678$	−33.6193	−1.29114
$679$	9.83249	0.377336
$680$	104.929	4.02384
$681$	11.5286	0.441775
$682$	54.8472	2.10021
$683$	28.2352	1.08039	0.540194	−	0.841540i	$-0.318351\pi$
$683$	28.2352	1.08039	0.540194	+	0.841540i	$0.318351\pi$
$684$	−24.6364	−0.941997
$685$	−22.6775	−0.866462
$686$	32.6150	1.24525
$687$	5.87569	0.224171
$688$	−10.3729	−0.395462
$689$	11.6928	0.445462
$690$	19.2306	0.732096
$691$	−20.9880	−0.798419	−0.399210	−	0.916860i	$-0.630715\pi$
$691$	−20.9880	−0.798419	−0.399210	+	0.916860i	$0.630715\pi$
$692$	−9.10867	−0.346260
$693$	27.9321	1.06105
$694$	−8.28114	−0.314348
$695$	36.7773	1.39504
$696$	−0.0381888	−0.00144754
$697$	−72.6513	−2.75186
$698$	48.7285	1.84440
$699$	−9.64320	−0.364739
$700$	123.513	4.66836
$701$	−30.2574	−1.14281	−0.571403	−	0.820670i	$-0.693601\pi$
$701$	−30.2574	−1.14281	−0.571403	+	0.820670i	$0.693601\pi$
$702$	−10.5948	−0.399875
$703$	−17.5228	−0.660886
$704$	37.5856	1.41656
$705$	20.8037	0.783511
$706$	−16.3787	−0.616420
$707$	57.4305	2.15990
$708$	48.6122	1.82696
$709$	−29.4684	−1.10671	−0.553354	−	0.832946i	$-0.686652\pi$
$709$	−29.4684	−1.10671	−0.553354	+	0.832946i	$0.686652\pi$
$710$	−65.5787	−2.46112
$711$	16.9362	0.635158
$712$	12.1308	0.454619
$713$	12.8450	0.481049
$714$	−39.2556	−1.46910
$715$	−14.9504	−0.559113
$716$	16.5773	0.619522
$717$	5.76050	0.215130
$718$	−50.0306	−1.86712
$719$	39.2031	1.46203	0.731014	−	0.682362i	$-0.239047\pi$
$719$	39.2031	1.46203	0.731014	+	0.682362i	$0.239047\pi$
$720$	28.7088	1.06992
$721$	3.91845	0.145931
$722$	26.2605	0.977314
$723$	−5.27484	−0.196173
$724$	60.3432	2.24264
$725$	0.0966572	0.00358976
$726$	−11.5270	−0.427808
$727$	26.0858	0.967470	0.483735	−	0.875215i	$-0.339280\pi$
$727$	26.0858	0.967470	0.483735	+	0.875215i	$0.339280\pi$
$728$	13.4603	0.498873
$729$	6.50961	0.241097
$730$	14.1652	0.524276
$731$	−18.4084	−0.680860
$732$	51.9188	1.91897
$733$	4.19431	0.154921	0.0774603	−	0.996995i	$-0.475319\pi$
$733$	4.19431	0.154921	0.0774603	+	0.996995i	$0.475319\pi$
$734$	−42.8472	−1.58152
$735$	−9.23493	−0.340636
$736$	2.51628	0.0927512
$737$	40.3937	1.48792
$738$	−66.4348	−2.44550
$739$	−30.8014	−1.13305	−0.566525	−	0.824045i	$-0.691712\pi$
$739$	−30.8014	−1.13305	−0.566525	+	0.824045i	$0.691712\pi$
$740$	92.8740	3.41412
$741$	−2.39283	−0.0879029
$742$	93.1839	3.42089
$743$	17.8003	0.653031	0.326516	−	0.945192i	$-0.394125\pi$
$743$	17.8003	0.653031	0.326516	+	0.945192i	$0.394125\pi$
$744$	−22.5675	−0.827365
$745$	−38.4442	−1.40849
$746$	73.1285	2.67743
$747$	10.6303	0.388942
$748$	−92.5016	−3.38219
$749$	22.5004	0.822146
$750$	43.6887	1.59529
$751$	−38.3122	−1.39803	−0.699016	−	0.715106i	$-0.746378\pi$
$751$	−38.3122	−1.39803	−0.699016	+	0.715106i	$0.746378\pi$
$752$	−20.0060	−0.729542
$753$	10.3475	0.377082
$754$	0.0217169	0.000790881 0
$755$	−1.67757	−0.0610531
$756$	−55.7331	−2.02699
$757$	−47.6636	−1.73236	−0.866182	−	0.499728i	$-0.833433\pi$
$757$	−47.6636	−1.73236	−0.866182	+	0.499728i	$0.833433\pi$
$758$	−70.7240	−2.56881
$759$	−8.22292	−0.298473
$760$	50.9715	1.84893
$761$	28.8267	1.04497	0.522484	−	0.852649i	$-0.325005\pi$
$761$	28.8267	1.04497	0.522484	+	0.852649i	$0.325005\pi$
$762$	−11.5379	−0.417976
$763$	−46.1829	−1.67193
$764$	83.3494	3.01548
$765$	50.9487	1.84205
$766$	−12.1214	−0.437964
$767$	−13.4087	−0.484159
$768$	−27.1904	−0.981147
$769$	−9.54578	−0.344230	−0.172115	−	0.985077i	$-0.555060\pi$
$769$	−9.54578	−0.344230	−0.172115	+	0.985077i	$0.555060\pi$
$770$	−119.144	−4.29366
$771$	−11.5054	−0.414358
$772$	90.4821	3.25652
$773$	−33.0754	−1.18964	−0.594821	−	0.803858i	$-0.702777\pi$
$773$	−33.0754	−1.18964	−0.594821	+	0.803858i	$0.702777\pi$
$774$	−16.8333	−0.605060
$775$	57.1191	2.05178
$776$	−14.4425	−0.518454
$777$	−16.8531	−0.604601
$778$	−34.4806	−1.23619
$779$	−35.2919	−1.26446
$780$	12.6824	0.454104
$781$	28.0412	1.00339
$782$	−32.8193	−1.17362
$783$	−0.0436148	−0.00155867
$784$	8.88082	0.317172
$785$	−58.8273	−2.09964
$786$	17.6049	0.627945
$787$	19.9927	0.712662	0.356331	−	0.934360i	$-0.384028\pi$
$787$	19.9927	0.712662	0.356331	+	0.934360i	$0.384028\pi$
$788$	−90.8708	−3.23714
$789$	−6.39579	−0.227696
$790$	−72.2415	−2.57024
$791$	48.7808	1.73445
$792$	−41.0281	−1.45787
$793$	−14.3207	−0.508544
$794$	11.5031	0.408230
$795$	42.5860	1.51037
$796$	18.0816	0.640884
$797$	−26.8830	−0.952244	−0.476122	−	0.879379i	$-0.657958\pi$
$797$	−26.8830	−0.952244	−0.476122	+	0.879379i	$0.657958\pi$
$798$	−19.0692	−0.675043
$799$	−35.5039	−1.25604
$800$	11.1894	0.395604
$801$	5.89014	0.208118
$802$	−77.5157	−2.73717
$803$	−6.05696	−0.213746
$804$	−34.2660	−1.20847
$805$	−27.9032	−0.983457
$806$	12.8335	0.452040
$807$	14.6872	0.517015
$808$	−84.3569	−2.96767
$809$	−10.5239	−0.370001	−0.185001	−	0.982738i	$-0.559229\pi$
$809$	−10.5239	−0.370001	−0.185001	+	0.982738i	$0.559229\pi$
$810$	24.4075	0.857591
$811$	−26.3575	−0.925535	−0.462768	−	0.886480i	$-0.653144\pi$
$811$	−26.3575	−0.925535	−0.462768	+	0.886480i	$0.653144\pi$
$812$	0.114240	0.00400903
$813$	25.5905	0.897497
$814$	−60.1628	−2.10871
$815$	15.6774	0.549155
$816$	17.2523	0.603951
$817$	−8.94228	−0.312851
$818$	−42.8170	−1.49706
$819$	6.53572	0.228376
$820$	187.053	6.53218
$821$	17.3354	0.605008	0.302504	−	0.953148i	$-0.402177\pi$
$821$	17.3354	0.605008	0.302504	+	0.953148i	$0.402177\pi$
$822$	−12.4617	−0.434653
$823$	49.6355	1.73019	0.865093	−	0.501612i	$-0.167260\pi$
$823$	49.6355	1.73019	0.865093	+	0.501612i	$0.167260\pi$
$824$	−5.75562	−0.200507
$825$	−36.5657	−1.27305
$826$	−106.858	−3.71806
$827$	21.3746	0.743269	0.371635	−	0.928379i	$-0.378797\pi$
$827$	21.3746	0.743269	0.371635	+	0.928379i	$0.378797\pi$
$828$	−19.8099	−0.688440
$829$	3.63824	0.126361	0.0631806	−	0.998002i	$-0.479876\pi$
$829$	3.63824	0.126361	0.0631806	+	0.998002i	$0.479876\pi$
$830$	−45.3435	−1.57390
$831$	−17.3567	−0.602096
$832$	8.79451	0.304895
$833$	15.7605	0.546070
$834$	20.2099	0.699810
$835$	−43.8525	−1.51758
$836$	−44.9346	−1.55410
$837$	−25.7740	−0.890878
$838$	−46.7770	−1.61588
$839$	54.8337	1.89307	0.946535	−	0.322602i	$-0.104557\pi$
$839$	54.8337	1.89307	0.946535	+	0.322602i	$0.104557\pi$
$840$	49.0233	1.69147
$841$	−28.9999	−0.999997
$842$	−43.5457	−1.50068
$843$	7.22693	0.248909
$844$	38.7291	1.33311
$845$	47.2230	1.62452
$846$	−32.4660	−1.11620
$847$	16.7254	0.574693
$848$	−40.9531	−1.40634
$849$	7.61992	0.261515
$850$	−145.941	−5.00573
$851$	−14.0899	−0.482996
$852$	−23.7873	−0.814940
$853$	−42.2586	−1.44691	−0.723453	−	0.690374i	$-0.757446\pi$
$853$	−42.2586	−1.44691	−0.723453	+	0.690374i	$0.757446\pi$
$854$	−114.126	−3.90532
$855$	24.7494	0.846412
$856$	−33.0497	−1.12962
$857$	51.7846	1.76893	0.884464	−	0.466609i	$-0.154524\pi$
$857$	51.7846	1.76893	0.884464	+	0.466609i	$0.154524\pi$
$858$	−8.21554	−0.280474
$859$	46.6205	1.59067	0.795336	−	0.606169i	$-0.207295\pi$
$859$	46.6205	1.59067	0.795336	+	0.606169i	$0.207295\pi$
$860$	47.3956	1.61618
$861$	−33.9430	−1.15678
$862$	37.8981	1.29081
$863$	−54.4874	−1.85477	−0.927387	−	0.374104i	$-0.877950\pi$
$863$	−54.4874	−1.85477	−0.927387	+	0.374104i	$0.877950\pi$
$864$	−5.04900	−0.171770
$865$	9.15045	0.311125
$866$	−71.2788	−2.42215
$867$	15.5909	0.529496
$868$	67.5094	2.29142
$869$	30.8901	1.04788
$870$	0.0790941	0.00268154
$871$	9.45157	0.320254
$872$	67.8358	2.29721
$873$	−7.01259	−0.237340
$874$	−15.9427	−0.539269
$875$	−63.3913	−2.14302
$876$	5.13812	0.173601
$877$	−8.69795	−0.293709	−0.146854	−	0.989158i	$-0.546915\pi$
$877$	−8.69795	−0.293709	−0.146854	+	0.989158i	$0.546915\pi$
$878$	−54.6131	−1.84310
$879$	11.4164	0.385066
$880$	52.3624	1.76513
$881$	−53.1014	−1.78903	−0.894515	−	0.447038i	$-0.852479\pi$
$881$	−53.1014	−1.78903	−0.894515	+	0.447038i	$0.852479\pi$
$882$	14.4120	0.485276
$883$	−25.8248	−0.869074	−0.434537	−	0.900654i	$-0.643088\pi$
$883$	−25.8248	−0.869074	−0.434537	+	0.900654i	$0.643088\pi$
$884$	−21.6441	−0.727970
$885$	−48.8352	−1.64158
$886$	21.1762	0.711428
$887$	39.5207	1.32698	0.663488	−	0.748187i	$-0.269075\pi$
$887$	39.5207	1.32698	0.663488	+	0.748187i	$0.269075\pi$
$888$	24.7547	0.830713
$889$	16.7413	0.561485
$890$	−25.1244	−0.842172
$891$	−10.4365	−0.349637
$892$	−4.55948	−0.152663
$893$	−17.2468	−0.577142
$894$	−21.1259	−0.706555
$895$	−16.6533	−0.556659
$896$	63.2759	2.11390
$897$	−1.92405	−0.0642421
$898$	−69.4157	−2.31643
$899$	0.0528306	0.00176200
$900$	−88.0904	−2.93635
$901$	−72.6782	−2.42126
$902$	−121.171	−4.03456
$903$	−8.60050	−0.286207
$904$	−71.6517	−2.38310
$905$	−60.6200	−2.01508
$906$	−0.921860	−0.0306267
$907$	−2.91718	−0.0968633	−0.0484317	−	0.998826i	$-0.515422\pi$
$907$	−2.91718	−0.0968633	−0.0484317	+	0.998826i	$0.515422\pi$
$908$	50.6563	1.68109
$909$	−40.9598	−1.35855
$910$	−27.8781	−0.924151
$911$	−30.6229	−1.01458	−0.507290	−	0.861775i	$-0.669353\pi$
$911$	−30.6229	−1.01458	−0.507290	+	0.861775i	$0.669353\pi$
$912$	8.38067	0.277512
$913$	19.3887	0.641672
$914$	29.5338	0.976890
$915$	−52.1569	−1.72425
$916$	25.8177	0.853040
$917$	−25.5443	−0.843546
$918$	65.8532	2.17348
$919$	−24.0520	−0.793403	−0.396702	−	0.917948i	$-0.629845\pi$
$919$	−24.0520	−0.793403	−0.396702	+	0.917948i	$0.629845\pi$
$920$	40.9856	1.35125
$921$	21.5263	0.709316
$922$	79.9697	2.63366
$923$	6.56124	0.215966
$924$	−43.2172	−1.42174
$925$	−62.6549	−2.06008
$926$	−64.7998	−2.12945
$927$	−2.79466	−0.0917888
$928$	0.0103493	0.000339731 0
$929$	−23.2196	−0.761810	−0.380905	−	0.924614i	$-0.624388\pi$
$929$	−23.2196	−0.761810	−0.380905	+	0.924614i	$0.624388\pi$
$930$	46.7403	1.53267
$931$	7.65600	0.250915
$932$	−42.3721	−1.38794
$933$	−16.6769	−0.545977
$934$	−72.8701	−2.38438
$935$	92.9259	3.03900
$936$	−9.60000	−0.313786
$937$	45.5877	1.48928	0.744642	−	0.667464i	$-0.232620\pi$
$937$	45.5877	1.48928	0.744642	+	0.667464i	$0.232620\pi$
$938$	75.3225	2.45937
$939$	8.04155	0.262426
$940$	91.4110	2.98150
$941$	−44.0343	−1.43548	−0.717738	−	0.696313i	$-0.754822\pi$
$941$	−44.0343	−1.43548	−0.717738	+	0.696313i	$0.754822\pi$
$942$	−32.3268	−1.05326
$943$	−28.3778	−0.924109
$944$	46.9626	1.52850
$945$	55.9887	1.82131
$946$	−30.7024	−0.998221
$947$	−30.4291	−0.988814	−0.494407	−	0.869230i	$-0.664615\pi$
$947$	−30.4291	−0.988814	−0.494407	+	0.869230i	$0.664615\pi$
$948$	−26.2041	−0.851070
$949$	−1.41725	−0.0460057
$950$	−70.8938	−2.30010
$951$	−18.4213	−0.597353
$952$	−83.6642	−2.71157
$953$	−29.9776	−0.971070	−0.485535	−	0.874217i	$-0.661375\pi$
$953$	−29.9776	−0.971070	−0.485535	+	0.874217i	$0.661375\pi$
$954$	−66.4594	−2.15170
$955$	−83.7317	−2.70949
$956$	25.3115	0.818634
$957$	−0.0338203	−0.00109325
$958$	102.879	3.32388
$959$	18.0817	0.583888
$960$	32.0301	1.03377
$961$	0.219966	0.00709569
$962$	−14.0773	−0.453869
$963$	−16.0474	−0.517121
$964$	−23.1776	−0.746499
$965$	−90.8971	−2.92608
$966$	−15.3333	−0.493342
$967$	−5.76588	−0.185418	−0.0927091	−	0.995693i	$-0.529553\pi$
$967$	−5.76588	−0.185418	−0.0927091	+	0.995693i	$0.529553\pi$
$968$	−24.5672	−0.789619
$969$	14.8729	0.477787
$970$	29.9122	0.960424
$971$	36.9145	1.18464	0.592321	−	0.805702i	$-0.298212\pi$
$971$	36.9145	1.18464	0.592321	+	0.805702i	$0.298212\pi$
$972$	62.5991	2.00787
$973$	−29.3240	−0.940085
$974$	−91.1916	−2.92197
$975$	−8.55586	−0.274007
$976$	50.1570	1.60549
$977$	44.8482	1.43482	0.717411	−	0.696650i	$-0.245327\pi$
$977$	44.8482	1.43482	0.717411	+	0.696650i	$0.245327\pi$
$978$	8.61504	0.275479
$979$	10.7431	0.343350
$980$	−40.5782	−1.29622
$981$	32.9379	1.05163
$982$	−69.9186	−2.23119
$983$	25.3840	0.809623	0.404811	−	0.914400i	$-0.367337\pi$
$983$	25.3840	0.809623	0.404811	+	0.914400i	$0.367337\pi$
$984$	49.8573	1.58939
$985$	91.2875	2.90866
$986$	−0.134984	−0.00429875
$987$	−16.5876	−0.527989
$988$	−10.5141	−0.334497
$989$	−7.19038	−0.228641
$990$	84.9745	2.70067
$991$	53.6456	1.70411	0.852054	−	0.523454i	$-0.175357\pi$
$991$	53.6456	1.70411	0.852054	+	0.523454i	$0.175357\pi$
$992$	6.11585	0.194178
$993$	−8.98877	−0.285250
$994$	52.2886	1.65849
$995$	−18.1645	−0.575853
$996$	−16.4474	−0.521157
$997$	−17.1353	−0.542681	−0.271340	−	0.962483i	$-0.587467\pi$
$997$	−17.1353	−0.542681	−0.271340	+	0.962483i	$0.587467\pi$
$998$	−17.2507	−0.546062
$999$	28.2719	0.894483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.18	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.18	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.42566 q^{2} +0.883893 q^{3} +3.88381 q^{4} -3.90163 q^{5} -2.14402 q^{6} +3.11093 q^{7} -4.56949 q^{8} -2.21873 q^{9} +O(q^{10})\)	\(q-2.42566 q^{2} +0.883893 q^{3} +3.88381 q^{4} -3.90163 q^{5} -2.14402 q^{6} +3.11093 q^{7} -4.56949 q^{8} -2.21873 q^{9} +9.46401 q^{10} -4.04677 q^{11} +3.43288 q^{12} -0.946888 q^{13} -7.54604 q^{14} -3.44862 q^{15} +3.31639 q^{16} +5.88549 q^{17} +5.38189 q^{18} +2.85900 q^{19} -15.1532 q^{20} +2.74973 q^{21} +9.81608 q^{22} +2.29889 q^{23} -4.03894 q^{24} +10.2227 q^{25} +2.29683 q^{26} -4.61280 q^{27} +12.0823 q^{28} +0.00945516 q^{29} +8.36517 q^{30} +5.58748 q^{31} +1.09456 q^{32} -3.57691 q^{33} -14.2762 q^{34} -12.1377 q^{35} -8.61715 q^{36} -6.12901 q^{37} -6.93495 q^{38} -0.836948 q^{39} +17.8284 q^{40} -12.3441 q^{41} -6.66989 q^{42} -3.12777 q^{43} -15.7169 q^{44} +8.65667 q^{45} -5.57632 q^{46} -6.03246 q^{47} +2.93133 q^{48} +2.67786 q^{49} -24.7967 q^{50} +5.20214 q^{51} -3.67754 q^{52} -12.3487 q^{53} +11.1891 q^{54} +15.7890 q^{55} -14.2153 q^{56} +2.52705 q^{57} -0.0229350 q^{58} +14.1608 q^{59} -13.3938 q^{60} +15.1240 q^{61} -13.5533 q^{62} -6.90232 q^{63} -9.28780 q^{64} +3.69440 q^{65} +8.67636 q^{66} -9.98172 q^{67} +22.8581 q^{68} +2.03197 q^{69} +29.4418 q^{70} -6.92927 q^{71} +10.1385 q^{72} +1.49674 q^{73} +14.8669 q^{74} +9.03576 q^{75} +11.1038 q^{76} -12.5892 q^{77} +2.03015 q^{78} -7.63328 q^{79} -12.9393 q^{80} +2.57898 q^{81} +29.9427 q^{82} -4.79115 q^{83} +10.6794 q^{84} -22.9630 q^{85} +7.58689 q^{86} +0.00835735 q^{87} +18.4917 q^{88} -2.65473 q^{89} -20.9981 q^{90} -2.94570 q^{91} +8.92846 q^{92} +4.93874 q^{93} +14.6327 q^{94} -11.1547 q^{95} +0.967476 q^{96} +3.16063 q^{97} -6.49558 q^{98} +8.97870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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