LMFDB - Embedded newform 4007.2.a.b.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.80768 q^{2} +0.834495 q^{3} +5.88309 q^{4} +4.09159 q^{5} -2.34300 q^{6} +3.13441 q^{7} -10.9025 q^{8} -2.30362 q^{9} +O(q^{10})$	\(q-2.80768 q^{2} +0.834495 q^{3} +5.88309 q^{4} +4.09159 q^{5} -2.34300 q^{6} +3.13441 q^{7} -10.9025 q^{8} -2.30362 q^{9} -11.4879 q^{10} -5.77637 q^{11} +4.90941 q^{12} +4.00064 q^{13} -8.80042 q^{14} +3.41441 q^{15} +18.8446 q^{16} +4.74929 q^{17} +6.46783 q^{18} +6.25479 q^{19} +24.0712 q^{20} +2.61565 q^{21} +16.2182 q^{22} -2.59720 q^{23} -9.09807 q^{24} +11.7411 q^{25} -11.2325 q^{26} -4.42584 q^{27} +18.4400 q^{28} +2.07901 q^{29} -9.58658 q^{30} +8.97510 q^{31} -31.1046 q^{32} -4.82035 q^{33} -13.3345 q^{34} +12.8247 q^{35} -13.5524 q^{36} +6.43016 q^{37} -17.5615 q^{38} +3.33851 q^{39} -44.6085 q^{40} +5.73521 q^{41} -7.34391 q^{42} -6.20242 q^{43} -33.9829 q^{44} -9.42546 q^{45} +7.29213 q^{46} +3.91052 q^{47} +15.7257 q^{48} +2.82451 q^{49} -32.9653 q^{50} +3.96326 q^{51} +23.5361 q^{52} -3.24514 q^{53} +12.4264 q^{54} -23.6345 q^{55} -34.1728 q^{56} +5.21959 q^{57} -5.83719 q^{58} -4.62160 q^{59} +20.0873 q^{60} -3.14915 q^{61} -25.1993 q^{62} -7.22048 q^{63} +49.6428 q^{64} +16.3690 q^{65} +13.5340 q^{66} +0.550502 q^{67} +27.9405 q^{68} -2.16735 q^{69} -36.0077 q^{70} -6.90811 q^{71} +25.1152 q^{72} -6.43810 q^{73} -18.0539 q^{74} +9.79787 q^{75} +36.7975 q^{76} -18.1055 q^{77} -9.37349 q^{78} -10.1371 q^{79} +77.1042 q^{80} +3.21752 q^{81} -16.1026 q^{82} +3.16507 q^{83} +15.3881 q^{84} +19.4321 q^{85} +17.4144 q^{86} +1.73492 q^{87} +62.9768 q^{88} +6.19090 q^{89} +26.4637 q^{90} +12.5396 q^{91} -15.2796 q^{92} +7.48967 q^{93} -10.9795 q^{94} +25.5920 q^{95} -25.9566 q^{96} +3.57153 q^{97} -7.93032 q^{98} +13.3065 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.80768	−1.98533	−0.992666	−	0.120887i	$-0.961426\pi$
$2$	−2.80768	−1.98533	−0.992666	+	0.120887i	$0.961426\pi$
$3$	0.834495	0.481796	0.240898	−	0.970550i	$-0.422558\pi$
$3$	0.834495	0.481796	0.240898	+	0.970550i	$0.422558\pi$
$4$	5.88309	2.94155
$5$	4.09159	1.82981	0.914907	−	0.403665i	$-0.132264\pi$
$5$	4.09159	1.82981	0.914907	+	0.403665i	$0.132264\pi$
$6$	−2.34300	−0.956525
$7$	3.13441	1.18469	0.592347	−	0.805683i	$-0.298201\pi$
$7$	3.13441	1.18469	0.592347	+	0.805683i	$0.298201\pi$
$8$	−10.9025	−3.85461
$9$	−2.30362	−0.767873
$10$	−11.4879	−3.63279
$11$	−5.77637	−1.74164	−0.870820	−	0.491602i	$-0.836411\pi$
$11$	−5.77637	−1.74164	−0.870820	+	0.491602i	$0.836411\pi$
$12$	4.90941	1.41722
$13$	4.00064	1.10958	0.554789	−	0.831991i	$-0.312799\pi$
$13$	4.00064	1.10958	0.554789	+	0.831991i	$0.312799\pi$
$14$	−8.80042	−2.35201
$15$	3.41441	0.881596
$16$	18.8446	4.71114
$17$	4.74929	1.15187	0.575936	−	0.817495i	$-0.304638\pi$
$17$	4.74929	1.15187	0.575936	+	0.817495i	$0.304638\pi$
$18$	6.46783	1.52448
$19$	6.25479	1.43495	0.717474	−	0.696586i	$-0.245298\pi$
$19$	6.25479	1.43495	0.717474	+	0.696586i	$0.245298\pi$
$20$	24.0712	5.38248
$21$	2.61565	0.570781
$22$	16.2182	3.45773
$23$	−2.59720	−0.541554	−0.270777	−	0.962642i	$-0.587281\pi$
$23$	−2.59720	−0.541554	−0.270777	+	0.962642i	$0.587281\pi$
$24$	−9.09807	−1.85714
$25$	11.7411	2.34822
$26$	−11.2325	−2.20288
$27$	−4.42584	−0.851753
$28$	18.4400	3.48483
$29$	2.07901	0.386062	0.193031	−	0.981193i	$-0.438168\pi$
$29$	2.07901	0.386062	0.193031	+	0.981193i	$0.438168\pi$
$30$	−9.58658	−1.75026
$31$	8.97510	1.61198	0.805988	−	0.591932i	$-0.201635\pi$
$31$	8.97510	1.61198	0.805988	+	0.591932i	$0.201635\pi$
$32$	−31.1046	−5.49857
$33$	−4.82035	−0.839114
$34$	−13.3345	−2.28685
$35$	12.8247	2.16777
$36$	−13.5524	−2.25873
$37$	6.43016	1.05711	0.528556	−	0.848899i	$-0.322734\pi$
$37$	6.43016	1.05711	0.528556	+	0.848899i	$0.322734\pi$
$38$	−17.5615	−2.84885
$39$	3.33851	0.534590
$40$	−44.6085	−7.05322
$41$	5.73521	0.895689	0.447844	−	0.894112i	$-0.352192\pi$
$41$	5.73521	0.895689	0.447844	+	0.894112i	$0.352192\pi$
$42$	−7.34391	−1.13319
$43$	−6.20242	−0.945860	−0.472930	−	0.881100i	$-0.656804\pi$
$43$	−6.20242	−0.945860	−0.472930	+	0.881100i	$0.656804\pi$
$44$	−33.9829	−5.12311
$45$	−9.42546	−1.40506
$46$	7.29213	1.07517
$47$	3.91052	0.570407	0.285204	−	0.958467i	$-0.407939\pi$
$47$	3.91052	0.570407	0.285204	+	0.958467i	$0.407939\pi$
$48$	15.7257	2.26981
$49$	2.82451	0.403501
$50$	−32.9653	−4.66199
$51$	3.96326	0.554967
$52$	23.5361	3.26388
$53$	−3.24514	−0.445755	−0.222877	−	0.974846i	$-0.571545\pi$
$53$	−3.24514	−0.445755	−0.222877	+	0.974846i	$0.571545\pi$
$54$	12.4264	1.69101
$55$	−23.6345	−3.18688
$56$	−34.1728	−4.56654
$57$	5.21959	0.691351
$58$	−5.83719	−0.766461
$59$	−4.62160	−0.601681	−0.300840	−	0.953675i	$-0.597267\pi$
$59$	−4.62160	−0.601681	−0.300840	+	0.953675i	$0.597267\pi$
$60$	20.0873	2.59325
$61$	−3.14915	−0.403208	−0.201604	−	0.979467i	$-0.564615\pi$
$61$	−3.14915	−0.403208	−0.201604	+	0.979467i	$0.564615\pi$
$62$	−25.1993	−3.20031
$63$	−7.22048	−0.909695
$64$	49.6428	6.20535
$65$	16.3690	2.03032
$66$	13.5340	1.66592
$67$	0.550502	0.0672545	0.0336273	−	0.999434i	$-0.489294\pi$
$67$	0.550502	0.0672545	0.0336273	+	0.999434i	$0.489294\pi$
$68$	27.9405	3.38828
$69$	−2.16735	−0.260919
$70$	−36.0077	−4.30374
$71$	−6.90811	−0.819842	−0.409921	−	0.912121i	$-0.634444\pi$
$71$	−6.90811	−0.819842	−0.409921	+	0.912121i	$0.634444\pi$
$72$	25.1152	2.95985
$73$	−6.43810	−0.753522	−0.376761	−	0.926310i	$-0.622962\pi$
$73$	−6.43810	−0.753522	−0.376761	+	0.926310i	$0.622962\pi$
$74$	−18.0539	−2.09872
$75$	9.79787	1.13136
$76$	36.7975	4.22096
$77$	−18.1055	−2.06331
$78$	−9.37349	−1.06134
$79$	−10.1371	−1.14051	−0.570254	−	0.821468i	$-0.693155\pi$
$79$	−10.1371	−1.14051	−0.570254	+	0.821468i	$0.693155\pi$
$80$	77.1042	8.62051
$81$	3.21752	0.357502
$82$	−16.1026	−1.77824
$83$	3.16507	0.347411	0.173706	−	0.984798i	$-0.444426\pi$
$83$	3.16507	0.347411	0.173706	+	0.984798i	$0.444426\pi$
$84$	15.3881	1.67898
$85$	19.4321	2.10771
$86$	17.4144	1.87785
$87$	1.73492	0.186003
$88$	62.9768	6.71335
$89$	6.19090	0.656234	0.328117	−	0.944637i	$-0.393586\pi$
$89$	6.19090	0.656234	0.328117	+	0.944637i	$0.393586\pi$
$90$	26.4637	2.78952
$91$	12.5396	1.31451
$92$	−15.2796	−1.59301
$93$	7.48967	0.776643
$94$	−10.9795	−1.13245
$95$	25.5920	2.62569
$96$	−25.9566	−2.64919
$97$	3.57153	0.362634	0.181317	−	0.983425i	$-0.441964\pi$
$97$	3.57153	0.362634	0.181317	+	0.983425i	$0.441964\pi$
$98$	−7.93032	−0.801083
$99$	13.3065	1.33736
$100$	69.0739	6.90739
$101$	−6.01237	−0.598253	−0.299126	−	0.954214i	$-0.596695\pi$
$101$	−6.01237	−0.598253	−0.299126	+	0.954214i	$0.596695\pi$
$102$	−11.1276	−1.10179
$103$	−18.7572	−1.84820	−0.924101	−	0.382149i	$-0.875184\pi$
$103$	−18.7572	−1.84820	−0.924101	+	0.382149i	$0.875184\pi$
$104$	−43.6170	−4.27700
$105$	10.7021	1.04442
$106$	9.11134	0.884972
$107$	−8.19251	−0.792000	−0.396000	−	0.918251i	$-0.629602\pi$
$107$	−8.19251	−0.792000	−0.396000	+	0.918251i	$0.629602\pi$
$108$	−26.0376	−2.50547
$109$	−5.48783	−0.525639	−0.262819	−	0.964845i	$-0.584652\pi$
$109$	−5.48783	−0.525639	−0.262819	+	0.964845i	$0.584652\pi$
$110$	66.3582	6.32701
$111$	5.36593	0.509312
$112$	59.0666	5.58126
$113$	−8.08338	−0.760421	−0.380210	−	0.924900i	$-0.624148\pi$
$113$	−8.08338	−0.760421	−0.380210	+	0.924900i	$0.624148\pi$
$114$	−14.6550	−1.37256
$115$	−10.6267	−0.990943
$116$	12.2310	1.13562
$117$	−9.21596	−0.852016
$118$	12.9760	1.19454
$119$	14.8862	1.36462
$120$	−37.2255	−3.39821
$121$	22.3664	2.03331
$122$	8.84183	0.800502
$123$	4.78600	0.431539
$124$	52.8013	4.74170
$125$	27.5817	2.46699
$126$	20.2728	1.80605
$127$	−1.73642	−0.154082	−0.0770411	−	0.997028i	$-0.524547\pi$
$127$	−1.73642	−0.154082	−0.0770411	+	0.997028i	$0.524547\pi$
$128$	−77.1721	−6.82111
$129$	−5.17588	−0.455711
$130$	−45.9589	−4.03086
$131$	12.6007	1.10093	0.550464	−	0.834859i	$-0.314451\pi$
$131$	12.6007	1.10093	0.550464	+	0.834859i	$0.314451\pi$
$132$	−28.3585	−2.46829
$133$	19.6051	1.69997
$134$	−1.54564	−0.133523
$135$	−18.1087	−1.55855
$136$	−51.7791	−4.44002
$137$	4.33929	0.370730	0.185365	−	0.982670i	$-0.440653\pi$
$137$	4.33929	0.370730	0.185365	+	0.982670i	$0.440653\pi$
$138$	6.08524	0.518010
$139$	−10.8274	−0.918369	−0.459185	−	0.888341i	$-0.651858\pi$
$139$	−10.8274	−0.918369	−0.459185	+	0.888341i	$0.651858\pi$
$140$	75.4489	6.37659
$141$	3.26330	0.274820
$142$	19.3958	1.62766
$143$	−23.1092	−1.93249
$144$	−43.4107	−3.61756
$145$	8.50643	0.706421
$146$	18.0761	1.49599
$147$	2.35703	0.194405
$148$	37.8292	3.10954
$149$	2.75397	0.225614	0.112807	−	0.993617i	$-0.464016\pi$
$149$	2.75397	0.225614	0.112807	+	0.993617i	$0.464016\pi$
$150$	−27.5093	−2.24613
$151$	−2.74395	−0.223300	−0.111650	−	0.993748i	$-0.535614\pi$
$151$	−2.74395	−0.223300	−0.111650	+	0.993748i	$0.535614\pi$
$152$	−68.1928	−5.53117
$153$	−10.9406	−0.884492
$154$	50.8345	4.09636
$155$	36.7224	2.94961
$156$	19.6408	1.57252
$157$	−15.4454	−1.23268	−0.616340	−	0.787480i	$-0.711385\pi$
$157$	−15.4454	−1.23268	−0.616340	+	0.787480i	$0.711385\pi$
$158$	28.4617	2.26429
$159$	−2.70806	−0.214763
$160$	−127.267	−10.0614
$161$	−8.14069	−0.641576
$162$	−9.03377	−0.709760
$163$	−15.2916	−1.19773	−0.598865	−	0.800850i	$-0.704381\pi$
$163$	−15.2916	−1.19773	−0.598865	+	0.800850i	$0.704381\pi$
$164$	33.7407	2.63471
$165$	−19.7229	−1.53542
$166$	−8.88651	−0.689727
$167$	18.8356	1.45754	0.728770	−	0.684758i	$-0.240092\pi$
$167$	18.8356	1.45754	0.728770	+	0.684758i	$0.240092\pi$
$168$	−28.5170	−2.20014
$169$	3.00514	0.231165
$170$	−54.5593	−4.18451
$171$	−14.4087	−1.10186
$172$	−36.4894	−2.78229
$173$	0.532755	0.0405046	0.0202523	−	0.999795i	$-0.493553\pi$
$173$	0.532755	0.0405046	0.0202523	+	0.999795i	$0.493553\pi$
$174$	−4.87110	−0.369277
$175$	36.8013	2.78192
$176$	−108.853	−8.20511
$177$	−3.85670	−0.289887
$178$	−17.3821	−1.30284
$179$	15.8612	1.18552	0.592762	−	0.805378i	$-0.298038\pi$
$179$	15.8612	1.18552	0.592762	+	0.805378i	$0.298038\pi$
$180$	−55.4508	−4.13306
$181$	5.66783	0.421286	0.210643	−	0.977563i	$-0.432444\pi$
$181$	5.66783	0.421286	0.210643	+	0.977563i	$0.432444\pi$
$182$	−35.2074	−2.60974
$183$	−2.62795	−0.194264
$184$	28.3160	2.08748
$185$	26.3096	1.93432
$186$	−21.0286	−1.54189
$187$	−27.4336	−2.00615
$188$	23.0059	1.67788
$189$	−13.8724	−1.00907
$190$	−71.8543	−5.21286
$191$	6.82522	0.493856	0.246928	−	0.969034i	$-0.420579\pi$
$191$	6.82522	0.493856	0.246928	+	0.969034i	$0.420579\pi$
$192$	41.4267	2.98971
$193$	1.54353	0.111105	0.0555527	−	0.998456i	$-0.482308\pi$
$193$	1.54353	0.111105	0.0555527	+	0.998456i	$0.482308\pi$
$194$	−10.0277	−0.719948
$195$	13.6598	0.978200
$196$	16.6168	1.18692
$197$	11.3546	0.808983	0.404491	−	0.914542i	$-0.367449\pi$
$197$	11.3546	0.808983	0.404491	+	0.914542i	$0.367449\pi$
$198$	−37.3606	−2.65510
$199$	−24.3876	−1.72879	−0.864394	−	0.502815i	$-0.832298\pi$
$199$	−24.3876	−1.72879	−0.864394	+	0.502815i	$0.832298\pi$
$200$	−128.007	−9.05147
$201$	0.459391	0.0324029
$202$	16.8808	1.18773
$203$	6.51645	0.457365
$204$	23.3162	1.63246
$205$	23.4661	1.63894
$206$	52.6643	3.66929
$207$	5.98297	0.415845
$208$	75.3904	5.22738
$209$	−36.1300	−2.49916
$210$	−30.0482	−2.07352
$211$	0.546328	0.0376108	0.0188054	−	0.999823i	$-0.494014\pi$
$211$	0.546328	0.0376108	0.0188054	+	0.999823i	$0.494014\pi$
$212$	−19.0915	−1.31121
$213$	−5.76478	−0.394996
$214$	23.0020	1.57238
$215$	−25.3777	−1.73075
$216$	48.2527	3.28318
$217$	28.1316	1.90970
$218$	15.4081	1.04357
$219$	−5.37256	−0.363044
$220$	−139.044	−9.37434
$221$	19.0002	1.27809
$222$	−15.0658	−1.01115
$223$	28.2529	1.89195	0.945977	−	0.324234i	$-0.105107\pi$
$223$	28.2529	1.89195	0.945977	+	0.324234i	$0.105107\pi$
$224$	−97.4945	−6.51413
$225$	−27.0470	−1.80313
$226$	22.6956	1.50969
$227$	10.4495	0.693560	0.346780	−	0.937947i	$-0.387275\pi$
$227$	10.4495	0.693560	0.346780	+	0.937947i	$0.387275\pi$
$228$	30.7073	2.03364
$229$	−28.1192	−1.85817	−0.929085	−	0.369867i	$-0.879403\pi$
$229$	−28.1192	−1.85817	−0.929085	+	0.369867i	$0.879403\pi$
$230$	29.8364	1.96735
$231$	−15.1089	−0.994094
$232$	−22.6663	−1.48812
$233$	8.31136	0.544495	0.272248	−	0.962227i	$-0.412233\pi$
$233$	8.31136	0.544495	0.272248	+	0.962227i	$0.412233\pi$
$234$	25.8755	1.69153
$235$	16.0002	1.04374
$236$	−27.1893	−1.76987
$237$	−8.45932	−0.549492
$238$	−41.7958	−2.70922
$239$	−5.15219	−0.333268	−0.166634	−	0.986019i	$-0.553290\pi$
$239$	−5.15219	−0.333268	−0.166634	+	0.986019i	$0.553290\pi$
$240$	64.3430	4.15333
$241$	17.0054	1.09541	0.547707	−	0.836670i	$-0.315501\pi$
$241$	17.0054	1.09541	0.547707	+	0.836670i	$0.315501\pi$
$242$	−62.7978	−4.03679
$243$	15.9625	1.02400
$244$	−18.5268	−1.18605
$245$	11.5567	0.738331
$246$	−13.4376	−0.856748
$247$	25.0232	1.59219
$248$	−97.8510	−6.21354
$249$	2.64123	0.167381
$250$	−77.4408	−4.89779
$251$	−14.5626	−0.919182	−0.459591	−	0.888131i	$-0.652004\pi$
$251$	−14.5626	−0.919182	−0.459591	+	0.888131i	$0.652004\pi$
$252$	−42.4787	−2.67591
$253$	15.0024	0.943193
$254$	4.87531	0.305904
$255$	16.2160	1.01549
$256$	117.389	7.33683
$257$	1.82339	0.113740	0.0568701	−	0.998382i	$-0.481888\pi$
$257$	1.82339	0.113740	0.0568701	+	0.998382i	$0.481888\pi$
$258$	14.5322	0.904738
$259$	20.1547	1.25235
$260$	96.3002	5.97228
$261$	−4.78924	−0.296446
$262$	−35.3788	−2.18571
$263$	17.5796	1.08400	0.542002	−	0.840377i	$-0.317667\pi$
$263$	17.5796	1.08400	0.542002	+	0.840377i	$0.317667\pi$
$264$	52.5538	3.23446
$265$	−13.2778	−0.815648
$266$	−55.0448	−3.37501
$267$	5.16627	0.316170
$268$	3.23865	0.197832
$269$	3.98966	0.243254	0.121627	−	0.992576i	$-0.461189\pi$
$269$	3.98966	0.243254	0.121627	+	0.992576i	$0.461189\pi$
$270$	50.8435	3.09424
$271$	−1.69431	−0.102922	−0.0514609	−	0.998675i	$-0.516388\pi$
$271$	−1.69431	−0.102922	−0.0514609	+	0.998675i	$0.516388\pi$
$272$	89.4984	5.42664
$273$	10.4643	0.633326
$274$	−12.1834	−0.736023
$275$	−67.8208	−4.08975
$276$	−12.7507	−0.767504
$277$	31.5510	1.89572	0.947859	−	0.318689i	$-0.103243\pi$
$277$	31.5510	1.89572	0.947859	+	0.318689i	$0.103243\pi$
$278$	30.4000	1.82327
$279$	−20.6752	−1.23779
$280$	−139.821	−8.35591
$281$	19.0226	1.13479	0.567397	−	0.823444i	$-0.307951\pi$
$281$	19.0226	1.13479	0.567397	+	0.823444i	$0.307951\pi$
$282$	−9.16233	−0.545609
$283$	16.5125	0.981565	0.490782	−	0.871282i	$-0.336711\pi$
$283$	16.5125	0.981565	0.490782	+	0.871282i	$0.336711\pi$
$284$	−40.6410	−2.41160
$285$	21.3564	1.26504
$286$	64.8833	3.83663
$287$	17.9765	1.06112
$288$	71.6532	4.22221
$289$	5.55577	0.326810
$290$	−23.8834	−1.40248
$291$	2.98042	0.174715
$292$	−37.8759	−2.21652
$293$	3.47377	0.202940	0.101470	−	0.994839i	$-0.467645\pi$
$293$	3.47377	0.202940	0.101470	+	0.994839i	$0.467645\pi$
$294$	−6.61781	−0.385958
$295$	−18.9097	−1.10096
$296$	−70.1048	−4.07476
$297$	25.5653	1.48345
$298$	−7.73229	−0.447919
$299$	−10.3905	−0.600897
$300$	57.6418	3.32795
$301$	−19.4409	−1.12055
$302$	7.70416	0.443324
$303$	−5.01729	−0.288236
$304$	117.869	6.76024
$305$	−12.8850	−0.737795
$306$	30.7176	1.75601
$307$	−13.7949	−0.787318	−0.393659	−	0.919257i	$-0.628791\pi$
$307$	−13.7949	−0.787318	−0.393659	+	0.919257i	$0.628791\pi$
$308$	−106.516	−6.06932
$309$	−15.6528	−0.890455
$310$	−103.105	−5.85597
$311$	−10.3168	−0.585013	−0.292507	−	0.956263i	$-0.594489\pi$
$311$	−10.3168	−0.585013	−0.292507	+	0.956263i	$0.594489\pi$
$312$	−36.3981	−2.06064
$313$	29.8510	1.68728	0.843640	−	0.536909i	$-0.180408\pi$
$313$	29.8510	1.68728	0.843640	+	0.536909i	$0.180408\pi$
$314$	43.3659	2.44728
$315$	−29.5432	−1.66457
$316$	−59.6372	−3.35486
$317$	−19.2345	−1.08032	−0.540159	−	0.841563i	$-0.681636\pi$
$317$	−19.2345	−1.08032	−0.540159	+	0.841563i	$0.681636\pi$
$318$	7.60336	0.426376
$319$	−12.0091	−0.672380
$320$	203.118	11.3546
$321$	−6.83660	−0.381582
$322$	22.8565	1.27374
$323$	29.7058	1.65288
$324$	18.9289	1.05161
$325$	46.9719	2.60553
$326$	42.9340	2.37789
$327$	−4.57956	−0.253250
$328$	−62.5280	−3.45253
$329$	12.2571	0.675758
$330$	55.3756	3.04832
$331$	−14.6048	−0.802754	−0.401377	−	0.915913i	$-0.631468\pi$
$331$	−14.6048	−0.802754	−0.401377	+	0.915913i	$0.631468\pi$
$332$	18.6204	1.02193
$333$	−14.8126	−0.811728
$334$	−52.8843	−2.89370
$335$	2.25243	0.123063
$336$	49.2907	2.68903
$337$	12.5431	0.683266	0.341633	−	0.939833i	$-0.389020\pi$
$337$	12.5431	0.683266	0.341633	+	0.939833i	$0.389020\pi$
$338$	−8.43750	−0.458939
$339$	−6.74554	−0.366367
$340$	114.321	6.19993
$341$	−51.8435	−2.80748
$342$	40.4549	2.18755
$343$	−13.0877	−0.706669
$344$	67.6218	3.64592
$345$	−8.86791	−0.477432
$346$	−1.49581	−0.0804151
$347$	36.6328	1.96655	0.983277	−	0.182118i	$-0.0582954\pi$
$347$	36.6328	1.96655	0.983277	+	0.182118i	$0.0582954\pi$
$348$	10.2067	0.547136
$349$	−4.09960	−0.219446	−0.109723	−	0.993962i	$-0.534996\pi$
$349$	−4.09960	−0.219446	−0.109723	+	0.993962i	$0.534996\pi$
$350$	−103.327	−5.52303
$351$	−17.7062	−0.945088
$352$	179.672	9.57653
$353$	7.00886	0.373044	0.186522	−	0.982451i	$-0.440278\pi$
$353$	7.00886	0.373044	0.186522	+	0.982451i	$0.440278\pi$
$354$	10.8284	0.575522
$355$	−28.2651	−1.50016
$356$	36.4216	1.93034
$357$	12.4225	0.657466
$358$	−44.5333	−2.35366
$359$	29.9469	1.58054	0.790270	−	0.612759i	$-0.209940\pi$
$359$	29.9469	1.58054	0.790270	+	0.612759i	$0.209940\pi$
$360$	102.761	5.41598
$361$	20.1224	1.05907
$362$	−15.9135	−0.836394
$363$	18.6646	0.979639
$364$	73.7718	3.86670
$365$	−26.3420	−1.37881
$366$	7.37846	0.385678
$367$	−22.2140	−1.15956	−0.579782	−	0.814772i	$-0.696862\pi$
$367$	−22.2140	−1.15956	−0.579782	+	0.814772i	$0.696862\pi$
$368$	−48.9432	−2.55134
$369$	−13.2117	−0.687775
$370$	−73.8689	−3.84026
$371$	−10.1716	−0.528083
$372$	44.0624	2.28453
$373$	14.7650	0.764504	0.382252	−	0.924058i	$-0.375149\pi$
$373$	14.7650	0.764504	0.382252	+	0.924058i	$0.375149\pi$
$374$	77.0250	3.98287
$375$	23.0168	1.18858
$376$	−42.6344	−2.19870
$377$	8.31736	0.428366
$378$	38.9493	2.00333
$379$	−23.4305	−1.20354	−0.601772	−	0.798668i	$-0.705538\pi$
$379$	−23.4305	−1.20354	−0.601772	+	0.798668i	$0.705538\pi$
$380$	150.560	7.72357
$381$	−1.44903	−0.0742361
$382$	−19.1631	−0.980468
$383$	8.29218	0.423710	0.211855	−	0.977301i	$-0.432049\pi$
$383$	8.29218	0.423710	0.211855	+	0.977301i	$0.432049\pi$
$384$	−64.3997	−3.28638
$385$	−74.0801	−3.77547
$386$	−4.33373	−0.220581
$387$	14.2880	0.726300
$388$	21.0116	1.06670
$389$	−9.51967	−0.482666	−0.241333	−	0.970442i	$-0.577585\pi$
$389$	−9.51967	−0.482666	−0.241333	+	0.970442i	$0.577585\pi$
$390$	−38.3525	−1.94205
$391$	−12.3349	−0.623802
$392$	−30.7941	−1.55534
$393$	10.5152	0.530422
$394$	−31.8802	−1.60610
$395$	−41.4767	−2.08692
$396$	78.2836	3.93390
$397$	−8.39829	−0.421498	−0.210749	−	0.977540i	$-0.567590\pi$
$397$	−8.39829	−0.421498	−0.210749	+	0.977540i	$0.567590\pi$
$398$	68.4725	3.43222
$399$	16.3603	0.819040
$400$	221.256	11.0628
$401$	16.3228	0.815123	0.407561	−	0.913178i	$-0.366379\pi$
$401$	16.3228	0.815123	0.407561	+	0.913178i	$0.366379\pi$
$402$	−1.28983	−0.0643306
$403$	35.9062	1.78861
$404$	−35.3713	−1.75979
$405$	13.1647	0.654162
$406$	−18.2961	−0.908022
$407$	−37.1430	−1.84111
$408$	−43.2094	−2.13918
$409$	−15.9049	−0.786449	−0.393225	−	0.919442i	$-0.628640\pi$
$409$	−15.9049	−0.786449	−0.393225	+	0.919442i	$0.628640\pi$
$410$	−65.8854	−3.25385
$411$	3.62111	0.178616
$412$	−110.350	−5.43657
$413$	−14.4860	−0.712808
$414$	−16.7983	−0.825591
$415$	12.9501	0.635698
$416$	−124.438	−6.10110
$417$	−9.03542	−0.442466
$418$	101.441	4.96167
$419$	5.60353	0.273750	0.136875	−	0.990588i	$-0.456294\pi$
$419$	5.60353	0.273750	0.136875	+	0.990588i	$0.456294\pi$
$420$	62.9617	3.07221
$421$	7.49757	0.365409	0.182705	−	0.983168i	$-0.441515\pi$
$421$	7.49757	0.365409	0.182705	+	0.983168i	$0.441515\pi$
$422$	−1.53392	−0.0746699
$423$	−9.00834	−0.438000
$424$	35.3802	1.71821
$425$	55.7618	2.70485
$426$	16.1857	0.784199
$427$	−9.87073	−0.477678
$428$	−48.1973	−2.32970
$429$	−19.2845	−0.931063
$430$	71.2527	3.43611
$431$	−0.261255	−0.0125842	−0.00629211	−	0.999980i	$-0.502003\pi$
$431$	−0.261255	−0.0125842	−0.00629211	+	0.999980i	$0.502003\pi$
$432$	−83.4031	−4.01273
$433$	−1.00412	−0.0482548	−0.0241274	−	0.999709i	$-0.507681\pi$
$433$	−1.00412	−0.0482548	−0.0241274	+	0.999709i	$0.507681\pi$
$434$	−78.9847	−3.79139
$435$	7.09857	0.340350
$436$	−32.2854	−1.54619
$437$	−16.2450	−0.777102
$438$	15.0844	0.720763
$439$	16.8764	0.805466	0.402733	−	0.915317i	$-0.368060\pi$
$439$	16.8764	0.805466	0.402733	+	0.915317i	$0.368060\pi$
$440$	257.675	12.2842
$441$	−6.50658	−0.309837
$442$	−53.3466	−2.53744
$443$	4.54228	0.215810	0.107905	−	0.994161i	$-0.465586\pi$
$443$	4.54228	0.215810	0.107905	+	0.994161i	$0.465586\pi$
$444$	31.5683	1.49816
$445$	25.3306	1.20078
$446$	−79.3252	−3.75616
$447$	2.29818	0.108700
$448$	155.601	7.35145
$449$	−28.9226	−1.36494	−0.682472	−	0.730912i	$-0.739095\pi$
$449$	−28.9226	−1.36494	−0.682472	+	0.730912i	$0.739095\pi$
$450$	75.9394	3.57982
$451$	−33.1286	−1.55997
$452$	−47.5553	−2.23681
$453$	−2.28981	−0.107585
$454$	−29.3390	−1.37695
$455$	51.3070	2.40531
$456$	−56.9065	−2.66489
$457$	−23.3755	−1.09346	−0.546731	−	0.837308i	$-0.684128\pi$
$457$	−23.3755	−1.09346	−0.546731	+	0.837308i	$0.684128\pi$
$458$	78.9498	3.68908
$459$	−21.0196	−0.981111
$460$	−62.5177	−2.91491
$461$	22.8228	1.06296	0.531482	−	0.847069i	$-0.321635\pi$
$461$	22.8228	1.06296	0.531482	+	0.847069i	$0.321635\pi$
$462$	42.4211	1.97361
$463$	−24.6483	−1.14551	−0.572753	−	0.819728i	$-0.694124\pi$
$463$	−24.6483	−1.14551	−0.572753	+	0.819728i	$0.694124\pi$
$464$	39.1780	1.81879
$465$	30.6447	1.42111
$466$	−23.3357	−1.08100
$467$	−38.8980	−1.79999	−0.899993	−	0.435904i	$-0.856429\pi$
$467$	−38.8980	−1.79999	−0.899993	+	0.435904i	$0.856429\pi$
$468$	−54.2183	−2.50624
$469$	1.72550	0.0796761
$470$	−44.9236	−2.07217
$471$	−12.8891	−0.593900
$472$	50.3869	2.31925
$473$	35.8274	1.64735
$474$	23.7511	1.09092
$475$	73.4380	3.36957
$476$	87.5769	4.01408
$477$	7.47558	0.342283
$478$	14.4657	0.661647
$479$	−30.4946	−1.39333	−0.696667	−	0.717395i	$-0.745334\pi$
$479$	−30.4946	−1.39333	−0.696667	+	0.717395i	$0.745334\pi$
$480$	−106.204	−4.84752
$481$	25.7248	1.17295
$482$	−47.7458	−2.17476
$483$	−6.79336	−0.309109
$484$	131.584	5.98107
$485$	14.6132	0.663552
$486$	−44.8177	−2.03297
$487$	32.2268	1.46034	0.730169	−	0.683267i	$-0.239441\pi$
$487$	32.2268	1.46034	0.730169	+	0.683267i	$0.239441\pi$
$488$	34.3336	1.55421
$489$	−12.7608	−0.577061
$490$	−32.4476	−1.46583
$491$	−38.5544	−1.73994	−0.869968	−	0.493109i	$-0.835861\pi$
$491$	−38.5544	−1.73994	−0.869968	+	0.493109i	$0.835861\pi$
$492$	28.1565	1.26939
$493$	9.87380	0.444694
$494$	−70.2572	−3.16102
$495$	54.4449	2.44712
$496$	169.132	7.59425
$497$	−21.6528	−0.971262
$498$	−7.41574	−0.332307
$499$	−8.69088	−0.389057	−0.194529	−	0.980897i	$-0.562318\pi$
$499$	−8.69088	−0.389057	−0.194529	+	0.980897i	$0.562318\pi$
$500$	162.266	7.25675
$501$	15.7182	0.702237
$502$	40.8871	1.82488
$503$	16.0695	0.716502	0.358251	−	0.933625i	$-0.383373\pi$
$503$	16.0695	0.716502	0.358251	+	0.933625i	$0.383373\pi$
$504$	78.7212	3.50652
$505$	−24.6001	−1.09469
$506$	−42.1220	−1.87255
$507$	2.50778	0.111374
$508$	−10.2155	−0.453240
$509$	−37.5233	−1.66319	−0.831595	−	0.555383i	$-0.812572\pi$
$509$	−37.5233	−1.66319	−0.831595	+	0.555383i	$0.812572\pi$
$510$	−45.5294	−2.01608
$511$	−20.1796	−0.892694
$512$	−175.248	−7.74493
$513$	−27.6827	−1.22222
$514$	−5.11951	−0.225812
$515$	−76.7467	−3.38186
$516$	−30.4502	−1.34049
$517$	−22.5886	−0.993444
$518$	−56.5881	−2.48634
$519$	0.444581	0.0195149
$520$	−178.463	−7.82611
$521$	−3.71952	−0.162955	−0.0814776	−	0.996675i	$-0.525964\pi$
$521$	−3.71952	−0.162955	−0.0814776	+	0.996675i	$0.525964\pi$
$522$	13.4467	0.588544
$523$	24.0494	1.05161	0.525803	−	0.850606i	$-0.323765\pi$
$523$	24.0494	1.05161	0.525803	+	0.850606i	$0.323765\pi$
$524$	74.1311	3.23843
$525$	30.7105	1.34032
$526$	−49.3579	−2.15211
$527$	42.6254	1.85679
$528$	−90.8373	−3.95319
$529$	−16.2545	−0.706719
$530$	37.2798	1.61933
$531$	10.6464	0.462014
$532$	115.338	5.00055
$533$	22.9445	0.993837
$534$	−14.5052	−0.627704
$535$	−33.5204	−1.44921
$536$	−6.00185	−0.259240
$537$	13.2361	0.571180
$538$	−11.2017	−0.482939
$539$	−16.3154	−0.702753
$540$	−106.535	−4.58454
$541$	5.07185	0.218056	0.109028	−	0.994039i	$-0.465226\pi$
$541$	5.07185	0.218056	0.109028	+	0.994039i	$0.465226\pi$
$542$	4.75708	0.204334
$543$	4.72977	0.202974
$544$	−147.725	−6.33365
$545$	−22.4539	−0.961820
$546$	−29.3803	−1.25736
$547$	45.1285	1.92955	0.964777	−	0.263068i	$-0.0847342\pi$
$547$	45.1285	1.92955	0.964777	+	0.263068i	$0.0847342\pi$
$548$	25.5284	1.09052
$549$	7.25445	0.309612
$550$	190.419	8.11951
$551$	13.0037	0.553978
$552$	23.6295	1.00574
$553$	−31.7737	−1.35115
$554$	−88.5854	−3.76363
$555$	21.9552	0.931946
$556$	−63.6987	−2.70143
$557$	−26.9212	−1.14069	−0.570343	−	0.821407i	$-0.693190\pi$
$557$	−26.9212	−1.14069	−0.570343	+	0.821407i	$0.693190\pi$
$558$	58.0495	2.45743
$559$	−24.8137	−1.04951
$560$	241.676	10.2127
$561$	−22.8932	−0.966553
$562$	−53.4095	−2.25294
$563$	−24.1983	−1.01984	−0.509918	−	0.860223i	$-0.670324\pi$
$563$	−24.1983	−1.01984	−0.509918	+	0.860223i	$0.670324\pi$
$564$	19.1983	0.808395
$565$	−33.0739	−1.39143
$566$	−46.3618	−1.94873
$567$	10.0850	0.423530
$568$	75.3156	3.16017
$569$	24.8047	1.03987	0.519933	−	0.854207i	$-0.325957\pi$
$569$	24.8047	1.03987	0.519933	+	0.854207i	$0.325957\pi$
$570$	−59.9620	−2.51153
$571$	−12.8810	−0.539054	−0.269527	−	0.962993i	$-0.586867\pi$
$571$	−12.8810	−0.539054	−0.269527	+	0.962993i	$0.586867\pi$
$572$	−135.953	−5.68450
$573$	5.69561	0.237937
$574$	−50.4722	−2.10667
$575$	−30.4940	−1.27169
$576$	−114.358	−4.76492
$577$	23.7549	0.988928	0.494464	−	0.869198i	$-0.335364\pi$
$577$	23.7549	0.988928	0.494464	+	0.869198i	$0.335364\pi$
$578$	−15.5989	−0.648827
$579$	1.28806	0.0535301
$580$	50.0441	2.07797
$581$	9.92060	0.411576
$582$	−8.36808	−0.346868
$583$	18.7451	0.776344
$584$	70.1913	2.90454
$585$	−37.7079	−1.55903
$586$	−9.75325	−0.402903
$587$	5.36912	0.221607	0.110804	−	0.993842i	$-0.464658\pi$
$587$	5.36912	0.221607	0.110804	+	0.993842i	$0.464658\pi$
$588$	13.8666	0.571851
$589$	56.1374	2.31310
$590$	53.0924	2.18578
$591$	9.47536	0.389764
$592$	121.174	4.98020
$593$	−15.1833	−0.623504	−0.311752	−	0.950163i	$-0.600916\pi$
$593$	−15.1833	−0.623504	−0.311752	+	0.950163i	$0.600916\pi$
$594$	−71.7792	−2.94514
$595$	60.9082	2.49699
$596$	16.2019	0.663655
$597$	−20.3513	−0.832922
$598$	29.1732	1.19298
$599$	19.5143	0.797331	0.398666	−	0.917096i	$-0.369473\pi$
$599$	19.5143	0.797331	0.398666	+	0.917096i	$0.369473\pi$
$600$	−106.821	−4.36096
$601$	31.1759	1.27169	0.635846	−	0.771816i	$-0.280651\pi$
$601$	31.1759	1.27169	0.635846	+	0.771816i	$0.280651\pi$
$602$	54.5839	2.22467
$603$	−1.26815	−0.0516430
$604$	−16.1429	−0.656846
$605$	91.5141	3.72058
$606$	14.0870	0.572243
$607$	−27.2452	−1.10585	−0.552924	−	0.833232i	$-0.686488\pi$
$607$	−27.2452	−1.10585	−0.552924	+	0.833232i	$0.686488\pi$
$608$	−194.553	−7.89016
$609$	5.43794	0.220356
$610$	36.1771	1.46477
$611$	15.6446	0.632912
$612$	−64.3643	−2.60177
$613$	14.9259	0.602852	0.301426	−	0.953490i	$-0.402537\pi$
$613$	14.9259	0.602852	0.301426	+	0.953490i	$0.402537\pi$
$614$	38.7318	1.56309
$615$	19.5823	0.789636
$616$	197.395	7.95326
$617$	−1.12630	−0.0453432	−0.0226716	−	0.999743i	$-0.507217\pi$
$617$	−1.12630	−0.0453432	−0.0226716	+	0.999743i	$0.507217\pi$
$618$	43.9480	1.76785
$619$	21.5622	0.866660	0.433330	−	0.901235i	$-0.357338\pi$
$619$	21.5622	0.866660	0.433330	+	0.901235i	$0.357338\pi$
$620$	216.041	8.67643
$621$	11.4948	0.461271
$622$	28.9664	1.16145
$623$	19.4048	0.777436
$624$	62.9129	2.51853
$625$	54.1476	2.16591
$626$	−83.8123	−3.34981
$627$	−30.1502	−1.20408
$628$	−90.8670	−3.62599
$629$	30.5387	1.21766
$630$	82.9480	3.30473
$631$	8.25596	0.328665	0.164332	−	0.986405i	$-0.447453\pi$
$631$	8.25596	0.328665	0.164332	+	0.986405i	$0.447453\pi$
$632$	110.519	4.39622
$633$	0.455908	0.0181207
$634$	54.0045	2.14479
$635$	−7.10471	−0.281942
$636$	−15.9317	−0.631734
$637$	11.2998	0.447716
$638$	33.7177	1.33490
$639$	15.9137	0.629534
$640$	−315.756	−12.4814
$641$	−25.8375	−1.02052	−0.510261	−	0.860020i	$-0.670451\pi$
$641$	−25.8375	−1.02052	−0.510261	+	0.860020i	$0.670451\pi$
$642$	19.1950	0.757567
$643$	−45.3482	−1.78836	−0.894180	−	0.447708i	$-0.852241\pi$
$643$	−45.3482	−1.78836	−0.894180	+	0.447708i	$0.852241\pi$
$644$	−47.8924	−1.88723
$645$	−21.1776	−0.833866
$646$	−83.4046	−3.28151
$647$	35.2363	1.38528	0.692640	−	0.721283i	$-0.256447\pi$
$647$	35.2363	1.38528	0.692640	+	0.721283i	$0.256447\pi$
$648$	−35.0789	−1.37803
$649$	26.6960	1.04791
$650$	−131.882	−5.17285
$651$	23.4757	0.920085
$652$	−89.9618	−3.52318
$653$	−14.5447	−0.569176	−0.284588	−	0.958650i	$-0.591857\pi$
$653$	−14.5447	−0.569176	−0.284588	+	0.958650i	$0.591857\pi$
$654$	12.8580	0.502786
$655$	51.5569	2.01449
$656$	108.078	4.21972
$657$	14.8309	0.578609
$658$	−34.4142	−1.34161
$659$	−11.7527	−0.457821	−0.228910	−	0.973448i	$-0.573516\pi$
$659$	−11.7527	−0.457821	−0.228910	+	0.973448i	$0.573516\pi$
$660$	−116.031	−4.51652
$661$	23.7591	0.924123	0.462061	−	0.886848i	$-0.347110\pi$
$661$	23.7591	0.924123	0.462061	+	0.886848i	$0.347110\pi$
$662$	41.0058	1.59373
$663$	15.8556	0.615780
$664$	−34.5071	−1.33914
$665$	80.2158	3.11063
$666$	41.5892	1.61155
$667$	−5.39960	−0.209073
$668$	110.811	4.28742
$669$	23.5769	0.911535
$670$	−6.32411	−0.244322
$671$	18.1907	0.702243
$672$	−81.3587	−3.13848
$673$	12.0863	0.465892	0.232946	−	0.972490i	$-0.425163\pi$
$673$	12.0863	0.465892	0.232946	+	0.972490i	$0.425163\pi$
$674$	−35.2170	−1.35651
$675$	−51.9642	−2.00010
$676$	17.6795	0.679982
$677$	10.3654	0.398373	0.199186	−	0.979962i	$-0.436170\pi$
$677$	10.3654	0.398373	0.199186	+	0.979962i	$0.436170\pi$
$678$	18.9393	0.727361
$679$	11.1946	0.429610
$680$	−211.859	−8.12441
$681$	8.72008	0.334154
$682$	145.560	5.57378
$683$	19.1128	0.731330	0.365665	−	0.930747i	$-0.380842\pi$
$683$	19.1128	0.731330	0.365665	+	0.930747i	$0.380842\pi$
$684$	−84.7674	−3.24116
$685$	17.7546	0.678367
$686$	36.7461	1.40297
$687$	−23.4653	−0.895258
$688$	−116.882	−4.45608
$689$	−12.9827	−0.494600
$690$	24.8983	0.947862
$691$	24.4368	0.929621	0.464810	−	0.885410i	$-0.346122\pi$
$691$	24.4368	0.929621	0.464810	+	0.885410i	$0.346122\pi$
$692$	3.13425	0.119146
$693$	41.7081	1.58436
$694$	−102.853	−3.90426
$695$	−44.3013	−1.68044
$696$	−18.9149	−0.716969
$697$	27.2382	1.03172
$698$	11.5104	0.435674
$699$	6.93578	0.262335
$700$	216.506	8.18314
$701$	−16.3321	−0.616853	−0.308427	−	0.951248i	$-0.599802\pi$
$701$	−16.3321	−0.616853	−0.308427	+	0.951248i	$0.599802\pi$
$702$	49.7134	1.87631
$703$	40.2193	1.51690
$704$	−286.755	−10.8075
$705$	13.3521	0.502869
$706$	−19.6787	−0.740616
$707$	−18.8452	−0.708747
$708$	−22.6893	−0.852716
$709$	19.4866	0.731836	0.365918	−	0.930647i	$-0.380755\pi$
$709$	19.4866	0.731836	0.365918	+	0.930647i	$0.380755\pi$
$710$	79.3596	2.97831
$711$	23.3519	0.875765
$712$	−67.4962	−2.52953
$713$	−23.3102	−0.872973
$714$	−34.8783	−1.30529
$715$	−94.5532	−3.53609
$716$	93.3130	3.48727
$717$	−4.29948	−0.160567
$718$	−84.0816	−3.13790
$719$	−34.5844	−1.28978	−0.644891	−	0.764275i	$-0.723097\pi$
$719$	−34.5844	−1.28978	−0.644891	+	0.764275i	$0.723097\pi$
$720$	−177.619	−6.61946
$721$	−58.7927	−2.18955
$722$	−56.4973	−2.10261
$723$	14.1909	0.527765
$724$	33.3444	1.23923
$725$	24.4098	0.906556
$726$	−52.4044	−1.94491
$727$	−39.1541	−1.45215	−0.726073	−	0.687618i	$-0.758656\pi$
$727$	−39.1541	−1.45215	−0.726073	+	0.687618i	$0.758656\pi$
$728$	−136.713	−5.06693
$729$	3.66809	0.135855
$730$	73.9601	2.73739
$731$	−29.4571	−1.08951
$732$	−15.4605	−0.571436
$733$	−41.8050	−1.54410	−0.772052	−	0.635560i	$-0.780769\pi$
$733$	−41.8050	−1.54410	−0.772052	+	0.635560i	$0.780769\pi$
$734$	62.3700	2.30212
$735$	9.64401	0.355725
$736$	80.7850	2.97778
$737$	−3.17990	−0.117133
$738$	37.0944	1.36546
$739$	−33.1772	−1.22044	−0.610222	−	0.792230i	$-0.708920\pi$
$739$	−33.1772	−1.22044	−0.610222	+	0.792230i	$0.708920\pi$
$740$	154.782	5.68988
$741$	20.8817	0.767109
$742$	28.5587	1.04842
$743$	−6.80717	−0.249731	−0.124865	−	0.992174i	$-0.539850\pi$
$743$	−6.80717	−0.249731	−0.124865	+	0.992174i	$0.539850\pi$
$744$	−81.6561	−2.99366
$745$	11.2681	0.412832
$746$	−41.4555	−1.51779
$747$	−7.29111	−0.266768
$748$	−161.395	−5.90117
$749$	−25.6787	−0.938278
$750$	−64.6239	−2.35973
$751$	23.9409	0.873617	0.436808	−	0.899555i	$-0.356109\pi$
$751$	23.9409	0.873617	0.436808	+	0.899555i	$0.356109\pi$
$752$	73.6920	2.68727
$753$	−12.1524	−0.442858
$754$	−23.3525	−0.850448
$755$	−11.2271	−0.408597
$756$	−81.6125	−2.96822
$757$	33.9872	1.23529	0.617643	−	0.786459i	$-0.288088\pi$
$757$	33.9872	1.23529	0.617643	+	0.786459i	$0.288088\pi$
$758$	65.7854	2.38943
$759$	12.5194	0.454426
$760$	−279.017	−10.1210
$761$	−6.98048	−0.253042	−0.126521	−	0.991964i	$-0.540381\pi$
$761$	−6.98048	−0.253042	−0.126521	+	0.991964i	$0.540381\pi$
$762$	4.06842	0.147383
$763$	−17.2011	−0.622721
$764$	40.1534	1.45270
$765$	−44.7642	−1.61845
$766$	−23.2818	−0.841206
$767$	−18.4894	−0.667612
$768$	97.9607	3.53485
$769$	−32.7852	−1.18227	−0.591133	−	0.806574i	$-0.701319\pi$
$769$	−32.7852	−1.18227	−0.591133	+	0.806574i	$0.701319\pi$
$770$	207.994	7.49557
$771$	1.52161	0.0547995
$772$	9.08070	0.326822
$773$	−10.8491	−0.390216	−0.195108	−	0.980782i	$-0.562506\pi$
$773$	−10.8491	−0.390216	−0.195108	+	0.980782i	$0.562506\pi$
$774$	−40.1162	−1.44195
$775$	105.377	3.78527
$776$	−38.9385	−1.39781
$777$	16.8190	0.603379
$778$	26.7282	0.958253
$779$	35.8725	1.28527
$780$	80.3620	2.87742
$781$	39.9038	1.42787
$782$	34.6324	1.23845
$783$	−9.20135	−0.328829
$784$	53.2266	1.90095
$785$	−63.1964	−2.25558
$786$	−29.5234	−1.05306
$787$	2.04659	0.0729531	0.0364765	−	0.999335i	$-0.488387\pi$
$787$	2.04659	0.0729531	0.0364765	+	0.999335i	$0.488387\pi$
$788$	66.8002	2.37966
$789$	14.6701	0.522268
$790$	116.453	4.14322
$791$	−25.3366	−0.900866
$792$	−145.074	−5.15500
$793$	−12.5986	−0.447391
$794$	23.5797	0.836814
$795$	−11.0802	−0.392976
$796$	−143.474	−5.08531
$797$	−16.4814	−0.583801	−0.291900	−	0.956449i	$-0.594288\pi$
$797$	−16.4814	−0.583801	−0.291900	+	0.956449i	$0.594288\pi$
$798$	−45.9346	−1.62607
$799$	18.5722	0.657037
$800$	−365.202	−12.9118
$801$	−14.2615	−0.503904
$802$	−45.8293	−1.61829
$803$	37.1888	1.31236
$804$	2.70264	0.0953147
$805$	−33.3084	−1.17397
$806$	−100.813	−3.55099
$807$	3.32935	0.117199
$808$	65.5498	2.30603
$809$	29.1940	1.02641	0.513204	−	0.858267i	$-0.328459\pi$
$809$	29.1940	1.02641	0.513204	+	0.858267i	$0.328459\pi$
$810$	−36.9625	−1.29873
$811$	−48.2858	−1.69554	−0.847771	−	0.530362i	$-0.822056\pi$
$811$	−48.2858	−1.69554	−0.847771	+	0.530362i	$0.822056\pi$
$812$	38.3369	1.34536
$813$	−1.41389	−0.0495873
$814$	104.286	3.65521
$815$	−62.5669	−2.19162
$816$	74.6859	2.61453
$817$	−38.7948	−1.35726
$818$	44.6561	1.56136
$819$	−28.8866	−1.00938
$820$	138.053	4.82103
$821$	−18.9551	−0.661536	−0.330768	−	0.943712i	$-0.607308\pi$
$821$	−18.9551	−0.661536	−0.330768	+	0.943712i	$0.607308\pi$
$822$	−10.1669	−0.354613
$823$	−41.1211	−1.43339	−0.716696	−	0.697386i	$-0.754346\pi$
$823$	−41.1211	−1.43339	−0.716696	+	0.697386i	$0.754346\pi$
$824$	204.500	7.12410
$825$	−56.5961	−1.97042
$826$	40.6720	1.41516
$827$	13.9496	0.485074	0.242537	−	0.970142i	$-0.422020\pi$
$827$	13.9496	0.485074	0.242537	+	0.970142i	$0.422020\pi$
$828$	35.1983	1.22323
$829$	15.1796	0.527210	0.263605	−	0.964631i	$-0.415089\pi$
$829$	15.1796	0.527210	0.263605	+	0.964631i	$0.415089\pi$
$830$	−36.3599	−1.26207
$831$	26.3292	0.913349
$832$	198.603	6.88533
$833$	13.4144	0.464781
$834$	25.3686	0.878443
$835$	77.0674	2.66703
$836$	−212.556	−7.35139
$837$	−39.7224	−1.37301
$838$	−15.7329	−0.543486
$839$	−7.41854	−0.256116	−0.128058	−	0.991767i	$-0.540874\pi$
$839$	−7.41854	−0.256116	−0.128058	+	0.991767i	$0.540874\pi$
$840$	−116.680	−4.02584
$841$	−24.6777	−0.850956
$842$	−21.0508	−0.725459
$843$	15.8743	0.546739
$844$	3.21410	0.110634
$845$	12.2958	0.422989
$846$	25.2926	0.869576
$847$	70.1054	2.40885
$848$	−61.1534	−2.10002
$849$	13.7796	0.472914
$850$	−156.562	−5.37002
$851$	−16.7004	−0.572484
$852$	−33.9147	−1.16190
$853$	32.4664	1.11163	0.555814	−	0.831307i	$-0.312407\pi$
$853$	32.4664	1.11163	0.555814	+	0.831307i	$0.312407\pi$
$854$	27.7139	0.948350
$855$	−58.9543	−2.01619
$856$	89.3188	3.05285
$857$	−40.3433	−1.37810	−0.689051	−	0.724713i	$-0.741972\pi$
$857$	−40.3433	−1.37810	−0.689051	+	0.724713i	$0.741972\pi$
$858$	54.1447	1.84847
$859$	41.4202	1.41324	0.706619	−	0.707594i	$-0.250220\pi$
$859$	41.4202	1.41324	0.706619	+	0.707594i	$0.250220\pi$
$860$	−149.299	−5.09107
$861$	15.0013	0.511242
$862$	0.733522	0.0249838
$863$	45.2818	1.54141	0.770705	−	0.637192i	$-0.219904\pi$
$863$	45.2818	1.54141	0.770705	+	0.637192i	$0.219904\pi$
$864$	137.664	4.68343
$865$	2.17981	0.0741159
$866$	2.81924	0.0958018
$867$	4.63626	0.157456
$868$	165.501	5.61747
$869$	58.5553	1.98635
$870$	−19.9305	−0.675709
$871$	2.20236	0.0746242
$872$	59.8310	2.02613
$873$	−8.22744	−0.278457
$874$	45.6107	1.54281
$875$	86.4524	2.92262
$876$	−31.6072	−1.06791
$877$	27.3836	0.924679	0.462339	−	0.886703i	$-0.347010\pi$
$877$	27.3836	0.924679	0.462339	+	0.886703i	$0.347010\pi$
$878$	−47.3836	−1.59912
$879$	2.89884	0.0977755
$880$	−445.382	−15.0138
$881$	−52.3359	−1.76324	−0.881620	−	0.471960i	$-0.843547\pi$
$881$	−52.3359	−1.76324	−0.881620	+	0.471960i	$0.843547\pi$
$882$	18.2684	0.615130
$883$	−30.8223	−1.03725	−0.518627	−	0.855001i	$-0.673557\pi$
$883$	−30.8223	−1.03725	−0.518627	+	0.855001i	$0.673557\pi$
$884$	111.780	3.75957
$885$	−15.7800	−0.530439
$886$	−12.7533	−0.428455
$887$	45.4884	1.52735	0.763675	−	0.645601i	$-0.223393\pi$
$887$	45.4884	1.52735	0.763675	+	0.645601i	$0.223393\pi$
$888$	−58.5020	−1.96320
$889$	−5.44264	−0.182540
$890$	−71.1203	−2.38396
$891$	−18.5856	−0.622639
$892$	166.214	5.56527
$893$	24.4595	0.818504
$894$	−6.45255	−0.215806
$895$	64.8976	2.16929
$896$	−241.889	−8.08094
$897$	−8.67080	−0.289510
$898$	81.2056	2.70987
$899$	18.6593	0.622322
$900$	−159.120	−5.30399
$901$	−15.4121	−0.513453
$902$	93.0148	3.09705
$903$	−16.2233	−0.539878
$904$	88.1290	2.93113
$905$	23.1904	0.770876
$906$	6.42908	0.213592
$907$	−19.0432	−0.632320	−0.316160	−	0.948706i	$-0.602394\pi$
$907$	−19.0432	−0.632320	−0.316160	+	0.948706i	$0.602394\pi$
$908$	61.4755	2.04014
$909$	13.8502	0.459382
$910$	−144.054	−4.77534
$911$	−37.6711	−1.24810	−0.624049	−	0.781385i	$-0.714513\pi$
$911$	−37.6711	−1.24810	−0.624049	+	0.781385i	$0.714513\pi$
$912$	98.3609	3.25705
$913$	−18.2826	−0.605065
$914$	65.6312	2.17089
$915$	−10.7525	−0.355467
$916$	−165.428	−5.46589
$917$	39.4957	1.30426
$918$	59.0164	1.94783
$919$	38.5207	1.27068	0.635341	−	0.772232i	$-0.280860\pi$
$919$	38.5207	1.27068	0.635341	+	0.772232i	$0.280860\pi$
$920$	115.857	3.81970
$921$	−11.5118	−0.379326
$922$	−64.0793	−2.11034
$923$	−27.6369	−0.909679
$924$	−88.8872	−2.92417
$925$	75.4970	2.48233
$926$	69.2048	2.27421
$927$	43.2094	1.41918
$928$	−64.6667	−2.12279
$929$	−32.0627	−1.05194	−0.525972	−	0.850502i	$-0.676298\pi$
$929$	−32.0627	−1.05194	−0.525972	+	0.850502i	$0.676298\pi$
$930$	−86.0405	−2.82138
$931$	17.6667	0.579002
$932$	48.8965	1.60166
$933$	−8.60933	−0.281857
$934$	109.213	3.57357
$935$	−112.247	−3.67087
$936$	100.477	3.28419
$937$	4.19209	0.136950	0.0684748	−	0.997653i	$-0.478187\pi$
$937$	4.19209	0.136950	0.0684748	+	0.997653i	$0.478187\pi$
$938$	−4.84465	−0.158184
$939$	24.9105	0.812924
$940$	94.1307	3.07021
$941$	−7.13601	−0.232627	−0.116314	−	0.993213i	$-0.537108\pi$
$941$	−7.13601	−0.232627	−0.116314	+	0.993213i	$0.537108\pi$
$942$	36.1886	1.17909
$943$	−14.8955	−0.485064
$944$	−87.0920	−2.83460
$945$	−56.7601	−1.84641
$946$	−100.592	−3.27053
$947$	−54.3172	−1.76507	−0.882537	−	0.470243i	$-0.844166\pi$
$947$	−54.3172	−1.76507	−0.882537	+	0.470243i	$0.844166\pi$
$948$	−49.7669	−1.61636
$949$	−25.7565	−0.836092
$950$	−206.191	−6.68971
$951$	−16.0511	−0.520493
$952$	−162.297	−5.26007
$953$	−0.935982	−0.0303194	−0.0151597	−	0.999885i	$-0.504826\pi$
$953$	−0.935982	−0.0303194	−0.0151597	+	0.999885i	$0.504826\pi$
$954$	−20.9891	−0.679546
$955$	27.9260	0.903664
$956$	−30.3108	−0.980322
$957$	−10.0215	−0.323950
$958$	85.6192	2.76623
$959$	13.6011	0.439202
$960$	169.501	5.47061
$961$	49.5525	1.59847
$962$	−72.2270	−2.32869
$963$	18.8724	0.608155
$964$	100.044	3.22221
$965$	6.31547	0.203302
$966$	19.0736	0.613684
$967$	24.7600	0.796228	0.398114	−	0.917336i	$-0.369665\pi$
$967$	24.7600	0.796228	0.398114	+	0.917336i	$0.369665\pi$
$968$	−243.849	−7.83762
$969$	24.7893	0.796348
$970$	−41.0293	−1.31737
$971$	−5.87794	−0.188632	−0.0943161	−	0.995542i	$-0.530066\pi$
$971$	−5.87794	−0.188632	−0.0943161	+	0.995542i	$0.530066\pi$
$972$	93.9090	3.01213
$973$	−33.9375	−1.08799
$974$	−90.4828	−2.89926
$975$	39.1978	1.25533
$976$	−59.3445	−1.89957
$977$	6.30777	0.201803	0.100902	−	0.994896i	$-0.467827\pi$
$977$	6.30777	0.201803	0.100902	+	0.994896i	$0.467827\pi$
$978$	35.8282	1.14566
$979$	−35.7609	−1.14292
$980$	67.9892	2.17183
$981$	12.6419	0.403624
$982$	108.249	3.45435
$983$	24.9187	0.794784	0.397392	−	0.917649i	$-0.369915\pi$
$983$	24.9187	0.794784	0.397392	+	0.917649i	$0.369915\pi$
$984$	−52.1793	−1.66342
$985$	46.4584	1.48029
$986$	−27.7225	−0.882865
$987$	10.2285	0.325577
$988$	147.214	4.68349
$989$	16.1089	0.512235
$990$	−152.864	−4.85834
$991$	15.7689	0.500916	0.250458	−	0.968127i	$-0.419419\pi$
$991$	15.7689	0.500916	0.250458	+	0.968127i	$0.419419\pi$
$992$	−279.167	−8.86357
$993$	−12.1877	−0.386764
$994$	60.7943	1.92828
$995$	−99.7838	−3.16336
$996$	15.5386	0.492359
$997$	−41.1787	−1.30414	−0.652071	−	0.758158i	$-0.726100\pi$
$997$	−41.1787	−1.30414	−0.652071	+	0.758158i	$0.726100\pi$
$998$	24.4012	0.772408
$999$	−28.4589	−0.900399

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.80768 q^{2} +0.834495 q^{3} +5.88309 q^{4} +4.09159 q^{5} -2.34300 q^{6} +3.13441 q^{7} -10.9025 q^{8} -2.30362 q^{9} +O(q^{10})\)	\(q-2.80768 q^{2} +0.834495 q^{3} +5.88309 q^{4} +4.09159 q^{5} -2.34300 q^{6} +3.13441 q^{7} -10.9025 q^{8} -2.30362 q^{9} -11.4879 q^{10} -5.77637 q^{11} +4.90941 q^{12} +4.00064 q^{13} -8.80042 q^{14} +3.41441 q^{15} +18.8446 q^{16} +4.74929 q^{17} +6.46783 q^{18} +6.25479 q^{19} +24.0712 q^{20} +2.61565 q^{21} +16.2182 q^{22} -2.59720 q^{23} -9.09807 q^{24} +11.7411 q^{25} -11.2325 q^{26} -4.42584 q^{27} +18.4400 q^{28} +2.07901 q^{29} -9.58658 q^{30} +8.97510 q^{31} -31.1046 q^{32} -4.82035 q^{33} -13.3345 q^{34} +12.8247 q^{35} -13.5524 q^{36} +6.43016 q^{37} -17.5615 q^{38} +3.33851 q^{39} -44.6085 q^{40} +5.73521 q^{41} -7.34391 q^{42} -6.20242 q^{43} -33.9829 q^{44} -9.42546 q^{45} +7.29213 q^{46} +3.91052 q^{47} +15.7257 q^{48} +2.82451 q^{49} -32.9653 q^{50} +3.96326 q^{51} +23.5361 q^{52} -3.24514 q^{53} +12.4264 q^{54} -23.6345 q^{55} -34.1728 q^{56} +5.21959 q^{57} -5.83719 q^{58} -4.62160 q^{59} +20.0873 q^{60} -3.14915 q^{61} -25.1993 q^{62} -7.22048 q^{63} +49.6428 q^{64} +16.3690 q^{65} +13.5340 q^{66} +0.550502 q^{67} +27.9405 q^{68} -2.16735 q^{69} -36.0077 q^{70} -6.90811 q^{71} +25.1152 q^{72} -6.43810 q^{73} -18.0539 q^{74} +9.79787 q^{75} +36.7975 q^{76} -18.1055 q^{77} -9.37349 q^{78} -10.1371 q^{79} +77.1042 q^{80} +3.21752 q^{81} -16.1026 q^{82} +3.16507 q^{83} +15.3881 q^{84} +19.4321 q^{85} +17.4144 q^{86} +1.73492 q^{87} +62.9768 q^{88} +6.19090 q^{89} +26.4637 q^{90} +12.5396 q^{91} -15.2796 q^{92} +7.48967 q^{93} -10.9795 q^{94} +25.5920 q^{95} -25.9566 q^{96} +3.57153 q^{97} -7.93032 q^{98} +13.3065 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 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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