LMFDB - Embedded newform 6007.2.a.b.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6007,2,Mod(1,6007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6007, 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("6007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6007.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:	$47.9661364942$
Analytic rank:	$1$
Dimension:	$237$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.54016 q^{2} +0.887378 q^{3} +4.45240 q^{4} -3.77266 q^{5} -2.25408 q^{6} -4.31374 q^{7} -6.22948 q^{8} -2.21256 q^{9} +O(q^{10})$	\(q-2.54016 q^{2} +0.887378 q^{3} +4.45240 q^{4} -3.77266 q^{5} -2.25408 q^{6} -4.31374 q^{7} -6.22948 q^{8} -2.21256 q^{9} +9.58314 q^{10} +5.96244 q^{11} +3.95096 q^{12} -5.29547 q^{13} +10.9576 q^{14} -3.34777 q^{15} +6.91905 q^{16} -5.06724 q^{17} +5.62025 q^{18} -3.59246 q^{19} -16.7974 q^{20} -3.82791 q^{21} -15.1455 q^{22} -1.07505 q^{23} -5.52790 q^{24} +9.23295 q^{25} +13.4513 q^{26} -4.62551 q^{27} -19.2065 q^{28} +8.57398 q^{29} +8.50387 q^{30} +9.23222 q^{31} -5.11653 q^{32} +5.29094 q^{33} +12.8716 q^{34} +16.2742 q^{35} -9.85120 q^{36} +2.10182 q^{37} +9.12540 q^{38} -4.69908 q^{39} +23.5017 q^{40} -12.7217 q^{41} +9.72351 q^{42} +4.20772 q^{43} +26.5472 q^{44} +8.34723 q^{45} +2.73081 q^{46} +10.7846 q^{47} +6.13982 q^{48} +11.6083 q^{49} -23.4531 q^{50} -4.49656 q^{51} -23.5775 q^{52} +0.791560 q^{53} +11.7495 q^{54} -22.4942 q^{55} +26.8723 q^{56} -3.18787 q^{57} -21.7793 q^{58} -4.00570 q^{59} -14.9056 q^{60} +9.21897 q^{61} -23.4513 q^{62} +9.54440 q^{63} -0.841320 q^{64} +19.9780 q^{65} -13.4398 q^{66} +5.60928 q^{67} -22.5614 q^{68} -0.953980 q^{69} -41.3391 q^{70} +3.02158 q^{71} +13.7831 q^{72} +4.77519 q^{73} -5.33896 q^{74} +8.19312 q^{75} -15.9950 q^{76} -25.7204 q^{77} +11.9364 q^{78} -9.51812 q^{79} -26.1032 q^{80} +2.53310 q^{81} +32.3150 q^{82} +5.91287 q^{83} -17.0434 q^{84} +19.1170 q^{85} -10.6883 q^{86} +7.60837 q^{87} -37.1429 q^{88} -11.2774 q^{89} -21.2033 q^{90} +22.8433 q^{91} -4.78657 q^{92} +8.19247 q^{93} -27.3945 q^{94} +13.5531 q^{95} -4.54030 q^{96} +7.67581 q^{97} -29.4869 q^{98} -13.1923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) $ 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * 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 $

$2$	−2.54016	−1.79616	−0.898081	−	0.439830i	$-0.855039\pi$
$2$	−2.54016	−1.79616	−0.898081	+	0.439830i	$0.855039\pi$
$3$	0.887378	0.512328	0.256164	−	0.966633i	$-0.417541\pi$
$3$	0.887378	0.512328	0.256164	+	0.966633i	$0.417541\pi$
$4$	4.45240	2.22620
$5$	−3.77266	−1.68718	−0.843592	−	0.536985i	$-0.819563\pi$
$5$	−3.77266	−1.68718	−0.843592	+	0.536985i	$0.819563\pi$
$6$	−2.25408	−0.920224
$7$	−4.31374	−1.63044	−0.815219	−	0.579152i	$-0.803384\pi$
$7$	−4.31374	−1.63044	−0.815219	+	0.579152i	$0.803384\pi$
$8$	−6.22948	−2.20245
$9$	−2.21256	−0.737520
$10$	9.58314	3.03046
$11$	5.96244	1.79774	0.898872	−	0.438212i	$-0.144388\pi$
$11$	5.96244	1.79774	0.898872	+	0.438212i	$0.144388\pi$
$12$	3.95096	1.14054
$13$	−5.29547	−1.46870	−0.734349	−	0.678772i	$-0.762513\pi$
$13$	−5.29547	−1.46870	−0.734349	+	0.678772i	$0.762513\pi$
$14$	10.9576	2.92853
$15$	−3.34777	−0.864392
$16$	6.91905	1.72976
$17$	−5.06724	−1.22899	−0.614493	−	0.788922i	$-0.710640\pi$
$17$	−5.06724	−1.22899	−0.614493	+	0.788922i	$0.710640\pi$
$18$	5.62025	1.32471
$19$	−3.59246	−0.824166	−0.412083	−	0.911146i	$-0.635199\pi$
$19$	−3.59246	−0.824166	−0.412083	+	0.911146i	$0.635199\pi$
$20$	−16.7974	−3.75601
$21$	−3.82791	−0.835320
$22$	−15.1455	−3.22904
$23$	−1.07505	−0.224164	−0.112082	−	0.993699i	$-0.535752\pi$
$23$	−1.07505	−0.224164	−0.112082	+	0.993699i	$0.535752\pi$
$24$	−5.52790	−1.12838
$25$	9.23295	1.84659
$26$	13.4513	2.63802
$27$	−4.62551	−0.890180
$28$	−19.2065	−3.62968
$29$	8.57398	1.59215	0.796074	−	0.605199i	$-0.206906\pi$
$29$	8.57398	1.59215	0.796074	+	0.605199i	$0.206906\pi$
$30$	8.50387	1.55259
$31$	9.23222	1.65816	0.829078	−	0.559133i	$-0.188866\pi$
$31$	9.23222	1.65816	0.829078	+	0.559133i	$0.188866\pi$
$32$	−5.11653	−0.904483
$33$	5.29094	0.921034
$34$	12.8716	2.20746
$35$	16.2742	2.75085
$36$	−9.85120	−1.64187
$37$	2.10182	0.345538	0.172769	−	0.984962i	$-0.444729\pi$
$37$	2.10182	0.345538	0.172769	+	0.984962i	$0.444729\pi$
$38$	9.12540	1.48034
$39$	−4.69908	−0.752456
$40$	23.5017	3.71594
$41$	−12.7217	−1.98679	−0.993395	−	0.114741i	$-0.963396\pi$
$41$	−12.7217	−1.98679	−0.993395	+	0.114741i	$0.963396\pi$
$42$	9.72351	1.50037
$43$	4.20772	0.641672	0.320836	−	0.947135i	$-0.396036\pi$
$43$	4.20772	0.641672	0.320836	+	0.947135i	$0.396036\pi$
$44$	26.5472	4.00213
$45$	8.34723	1.24433
$46$	2.73081	0.402635
$47$	10.7846	1.57309	0.786546	−	0.617532i	$-0.211867\pi$
$47$	10.7846	1.57309	0.786546	+	0.617532i	$0.211867\pi$
$48$	6.13982	0.886206
$49$	11.6083	1.65833
$50$	−23.4531	−3.31677
$51$	−4.49656	−0.629644
$52$	−23.5775	−3.26962
$53$	0.791560	0.108729	0.0543646	−	0.998521i	$-0.482687\pi$
$53$	0.791560	0.108729	0.0543646	+	0.998521i	$0.482687\pi$
$54$	11.7495	1.59891
$55$	−22.4942	−3.03312
$56$	26.8723	3.59096
$57$	−3.18787	−0.422243
$58$	−21.7793	−2.85976
$59$	−4.00570	−0.521498	−0.260749	−	0.965407i	$-0.583970\pi$
$59$	−4.00570	−0.521498	−0.260749	+	0.965407i	$0.583970\pi$
$60$	−14.9056	−1.92431
$61$	9.21897	1.18037	0.590184	−	0.807269i	$-0.299055\pi$
$61$	9.21897	1.18037	0.590184	+	0.807269i	$0.299055\pi$
$62$	−23.4513	−2.97832
$63$	9.54440	1.20248
$64$	−0.841320	−0.105165
$65$	19.9780	2.47796
$66$	−13.4398	−1.65433
$67$	5.60928	0.685282	0.342641	−	0.939466i	$-0.388678\pi$
$67$	5.60928	0.685282	0.342641	+	0.939466i	$0.388678\pi$
$68$	−22.5614	−2.73597
$69$	−0.953980	−0.114846
$70$	−41.3391	−4.94097
$71$	3.02158	0.358596	0.179298	−	0.983795i	$-0.442617\pi$
$71$	3.02158	0.358596	0.179298	+	0.983795i	$0.442617\pi$
$72$	13.7831	1.62435
$73$	4.77519	0.558893	0.279447	−	0.960161i	$-0.409849\pi$
$73$	4.77519	0.558893	0.279447	+	0.960161i	$0.409849\pi$
$74$	−5.33896	−0.620642
$75$	8.19312	0.946059
$76$	−15.9950	−1.83476
$77$	−25.7204	−2.93111
$78$	11.9364	1.35153
$79$	−9.51812	−1.07087	−0.535436	−	0.844576i	$-0.679853\pi$
$79$	−9.51812	−1.07087	−0.535436	+	0.844576i	$0.679853\pi$
$80$	−26.1032	−2.91843
$81$	2.53310	0.281456
$82$	32.3150	3.56860
$83$	5.91287	0.649022	0.324511	−	0.945882i	$-0.394800\pi$
$83$	5.91287	0.649022	0.324511	+	0.945882i	$0.394800\pi$
$84$	−17.0434	−1.85959
$85$	19.1170	2.07353
$86$	−10.6883	−1.15255
$87$	7.60837	0.815703
$88$	−37.1429	−3.95944
$89$	−11.2774	−1.19541	−0.597703	−	0.801718i	$-0.703920\pi$
$89$	−11.2774	−1.19541	−0.597703	+	0.801718i	$0.703920\pi$
$90$	−21.2033	−2.23502
$91$	22.8433	2.39462
$92$	−4.78657	−0.499034
$93$	8.19247	0.849520
$94$	−27.3945	−2.82553
$95$	13.5531	1.39052
$96$	−4.54030	−0.463392
$97$	7.67581	0.779361	0.389680	−	0.920950i	$-0.372585\pi$
$97$	7.67581	0.779361	0.389680	+	0.920950i	$0.372585\pi$
$98$	−29.4869	−2.97863
$99$	−13.1923	−1.32587
$100$	41.1088	4.11088
$101$	−15.1491	−1.50739	−0.753695	−	0.657225i	$-0.771730\pi$
$101$	−15.1491	−1.50739	−0.753695	+	0.657225i	$0.771730\pi$
$102$	11.4220	1.13094
$103$	5.91046	0.582375	0.291188	−	0.956666i	$-0.405950\pi$
$103$	5.91046	0.582375	0.291188	+	0.956666i	$0.405950\pi$
$104$	32.9880	3.23474
$105$	14.4414	1.40934
$106$	−2.01069	−0.195295
$107$	2.77329	0.268104	0.134052	−	0.990974i	$-0.457201\pi$
$107$	2.77329	0.268104	0.134052	+	0.990974i	$0.457201\pi$
$108$	−20.5946	−1.98172
$109$	3.95603	0.378919	0.189459	−	0.981889i	$-0.439327\pi$
$109$	3.95603	0.378919	0.189459	+	0.981889i	$0.439327\pi$
$110$	57.1389	5.44798
$111$	1.86511	0.177029
$112$	−29.8470	−2.82027
$113$	−12.7457	−1.19901	−0.599506	−	0.800370i	$-0.704636\pi$
$113$	−12.7457	−1.19901	−0.599506	+	0.800370i	$0.704636\pi$
$114$	8.09768	0.758417
$115$	4.05581	0.378206
$116$	38.1748	3.54444
$117$	11.7165	1.08319
$118$	10.1751	0.936695
$119$	21.8587	2.00379
$120$	20.8549	1.90378
$121$	24.5507	2.23188
$122$	−23.4176	−2.12013
$123$	−11.2889	−1.01789
$124$	41.1055	3.69139
$125$	−15.9695	−1.42835
$126$	−24.2443	−2.15985
$127$	−9.01888	−0.800296	−0.400148	−	0.916451i	$-0.631041\pi$
$127$	−9.01888	−0.800296	−0.400148	+	0.916451i	$0.631041\pi$
$128$	12.3701	1.09338
$129$	3.73384	0.328746
$130$	−50.7472	−4.45083
$131$	9.12852	0.797563	0.398781	−	0.917046i	$-0.369433\pi$
$131$	9.12852	0.797563	0.398781	+	0.917046i	$0.369433\pi$
$132$	23.5574	2.05041
$133$	15.4969	1.34375
$134$	−14.2484	−1.23088
$135$	17.4505	1.50190
$136$	31.5663	2.70679
$137$	4.73511	0.404547	0.202274	−	0.979329i	$-0.435167\pi$
$137$	4.73511	0.404547	0.202274	+	0.979329i	$0.435167\pi$
$138$	2.42326	0.206281
$139$	−3.48547	−0.295634	−0.147817	−	0.989015i	$-0.547225\pi$
$139$	−3.48547	−0.295634	−0.147817	+	0.989015i	$0.547225\pi$
$140$	72.4594	6.12394
$141$	9.57000	0.805939
$142$	−7.67529	−0.644096
$143$	−31.5739	−2.64034
$144$	−15.3088	−1.27573
$145$	−32.3467	−2.68625
$146$	−12.1297	−1.00386
$147$	10.3010	0.849609
$148$	9.35816	0.769236
$149$	8.75124	0.716930	0.358465	−	0.933543i	$-0.383300\pi$
$149$	8.75124	0.716930	0.358465	+	0.933543i	$0.383300\pi$
$150$	−20.8118	−1.69928
$151$	21.9001	1.78220	0.891102	−	0.453804i	$-0.149933\pi$
$151$	21.9001	1.78220	0.891102	+	0.453804i	$0.149933\pi$
$152$	22.3791	1.81519
$153$	11.2116	0.906402
$154$	65.3338	5.26475
$155$	−34.8300	−2.79761
$156$	−20.9222	−1.67512
$157$	−20.4381	−1.63114	−0.815569	−	0.578660i	$-0.803576\pi$
$157$	−20.4381	−1.63114	−0.815569	+	0.578660i	$0.803576\pi$
$158$	24.1775	1.92346
$159$	0.702413	0.0557050
$160$	19.3029	1.52603
$161$	4.63750	0.365486
$162$	−6.43448	−0.505540
$163$	−6.85017	−0.536547	−0.268273	−	0.963343i	$-0.586453\pi$
$163$	−6.85017	−0.536547	−0.268273	+	0.963343i	$0.586453\pi$
$164$	−56.6419	−4.42299
$165$	−19.9609	−1.55395
$166$	−15.0196	−1.16575
$167$	−14.9455	−1.15651	−0.578257	−	0.815855i	$-0.696267\pi$
$167$	−14.9455	−1.15651	−0.578257	+	0.815855i	$0.696267\pi$
$168$	23.8459	1.83975
$169$	15.0420	1.15708
$170$	−48.5601	−3.72439
$171$	7.94852	0.607839
$172$	18.7345	1.42849
$173$	−7.34746	−0.558617	−0.279308	−	0.960201i	$-0.590105\pi$
$173$	−7.34746	−0.558617	−0.279308	+	0.960201i	$0.590105\pi$
$174$	−19.3264	−1.46513
$175$	−39.8285	−3.01075
$176$	41.2544	3.10967
$177$	−3.55457	−0.267178
$178$	28.6465	2.14714
$179$	−12.4945	−0.933880	−0.466940	−	0.884289i	$-0.654644\pi$
$179$	−12.4945	−0.933880	−0.466940	+	0.884289i	$0.654644\pi$
$180$	37.1652	2.77013
$181$	5.25606	0.390680	0.195340	−	0.980736i	$-0.437419\pi$
$181$	5.25606	0.390680	0.195340	+	0.980736i	$0.437419\pi$
$182$	−58.0255	−4.30113
$183$	8.18071	0.604736
$184$	6.69703	0.493711
$185$	−7.92946	−0.582986
$186$	−20.8102	−1.52588
$187$	−30.2131	−2.20940
$188$	48.0172	3.50202
$189$	19.9532	1.45138
$190$	−34.4270	−2.49760
$191$	5.54934	0.401536	0.200768	−	0.979639i	$-0.435656\pi$
$191$	5.54934	0.401536	0.200768	+	0.979639i	$0.435656\pi$
$192$	−0.746569	−0.0538790
$193$	14.1235	1.01663	0.508314	−	0.861172i	$-0.330269\pi$
$193$	14.1235	1.01663	0.508314	+	0.861172i	$0.330269\pi$
$194$	−19.4978	−1.39986
$195$	17.7280	1.26953
$196$	51.6848	3.69177
$197$	−2.42503	−0.172776	−0.0863880	−	0.996262i	$-0.527532\pi$
$197$	−2.42503	−0.172776	−0.0863880	+	0.996262i	$0.527532\pi$
$198$	33.5104	2.38148
$199$	−0.348515	−0.0247055	−0.0123528	−	0.999924i	$-0.503932\pi$
$199$	−0.348515	−0.0247055	−0.0123528	+	0.999924i	$0.503932\pi$
$200$	−57.5164	−4.06703
$201$	4.97755	0.351089
$202$	38.4810	2.70752
$203$	−36.9859	−2.59590
$204$	−20.0205	−1.40171
$205$	47.9945	3.35208
$206$	−15.0135	−1.04604
$207$	2.37862	0.165326
$208$	−36.6396	−2.54050
$209$	−21.4198	−1.48164
$210$	−36.6835	−2.53140
$211$	−0.254135	−0.0174954	−0.00874768	−	0.999962i	$-0.502785\pi$
$211$	−0.254135	−0.0174954	−0.00874768	+	0.999962i	$0.502785\pi$
$212$	3.52434	0.242053
$213$	2.68128	0.183719
$214$	−7.04459	−0.481558
$215$	−15.8743	−1.08262
$216$	28.8145	1.96058
$217$	−39.8254	−2.70352
$218$	−10.0489	−0.680599
$219$	4.23740	0.286337
$220$	−100.153	−6.75234
$221$	26.8334	1.80501
$222$	−4.73768	−0.317972
$223$	11.0515	0.740061	0.370030	−	0.929020i	$-0.379347\pi$
$223$	11.0515	0.740061	0.370030	+	0.929020i	$0.379347\pi$
$224$	22.0714	1.47470
$225$	−20.4284	−1.36190
$226$	32.3760	2.15362
$227$	−10.7868	−0.715944	−0.357972	−	0.933732i	$-0.616532\pi$
$227$	−10.7868	−0.715944	−0.357972	+	0.933732i	$0.616532\pi$
$228$	−14.1937	−0.939998
$229$	16.3117	1.07791	0.538955	−	0.842334i	$-0.318819\pi$
$229$	16.3117	1.07791	0.538955	+	0.842334i	$0.318819\pi$
$230$	−10.3024	−0.679320
$231$	−22.8237	−1.50169
$232$	−53.4114	−3.50663
$233$	−27.1295	−1.77732	−0.888658	−	0.458571i	$-0.848362\pi$
$233$	−27.1295	−1.77732	−0.888658	+	0.458571i	$0.848362\pi$
$234$	−29.7619	−1.94559
$235$	−40.6865	−2.65410
$236$	−17.8350	−1.16096
$237$	−8.44617	−0.548638
$238$	−55.5247	−3.59913
$239$	−13.2155	−0.854839	−0.427420	−	0.904053i	$-0.640577\pi$
$239$	−13.2155	−0.854839	−0.427420	+	0.904053i	$0.640577\pi$
$240$	−23.1634	−1.49519
$241$	13.6807	0.881251	0.440626	−	0.897691i	$-0.354757\pi$
$241$	13.6807	0.881251	0.440626	+	0.897691i	$0.354757\pi$
$242$	−62.3626	−4.00882
$243$	16.1244	1.03438
$244$	41.0465	2.62773
$245$	−43.7942	−2.79791
$246$	28.6757	1.82829
$247$	19.0237	1.21045
$248$	−57.5119	−3.65201
$249$	5.24695	0.332512
$250$	40.5649	2.56555
$251$	7.81559	0.493316	0.246658	−	0.969103i	$-0.420668\pi$
$251$	7.81559	0.493316	0.246658	+	0.969103i	$0.420668\pi$
$252$	42.4955	2.67696
$253$	−6.40995	−0.402990
$254$	22.9094	1.43746
$255$	16.9640	1.06233
$256$	−29.7395	−1.85872
$257$	−20.2085	−1.26057	−0.630285	−	0.776364i	$-0.717062\pi$
$257$	−20.2085	−1.26057	−0.630285	+	0.776364i	$0.717062\pi$
$258$	−9.48454	−0.590482
$259$	−9.06671	−0.563378
$260$	88.9500	5.51644
$261$	−18.9705	−1.17424
$262$	−23.1879	−1.43255
$263$	5.89748	0.363654	0.181827	−	0.983331i	$-0.441799\pi$
$263$	5.89748	0.363654	0.181827	+	0.983331i	$0.441799\pi$
$264$	−32.9598	−2.02853
$265$	−2.98628	−0.183446
$266$	−39.3646	−2.41360
$267$	−10.0074	−0.612440
$268$	24.9747	1.52558
$269$	13.4679	0.821151	0.410576	−	0.911827i	$-0.365328\pi$
$269$	13.4679	0.821151	0.410576	+	0.911827i	$0.365328\pi$
$270$	−44.3269	−2.69765
$271$	14.2320	0.864531	0.432265	−	0.901746i	$-0.357714\pi$
$271$	14.2320	0.864531	0.432265	+	0.901746i	$0.357714\pi$
$272$	−35.0605	−2.12586
$273$	20.2706	1.22683
$274$	−12.0279	−0.726633
$275$	55.0509	3.31969
$276$	−4.24750	−0.255669
$277$	18.7343	1.12563	0.562817	−	0.826581i	$-0.309717\pi$
$277$	18.7343	1.12563	0.562817	+	0.826581i	$0.309717\pi$
$278$	8.85364	0.531006
$279$	−20.4268	−1.22292
$280$	−101.380	−6.05862
$281$	2.51226	0.149869	0.0749344	−	0.997188i	$-0.476125\pi$
$281$	2.51226	0.149869	0.0749344	+	0.997188i	$0.476125\pi$
$282$	−24.3093	−1.44760
$283$	−30.8326	−1.83281	−0.916405	−	0.400253i	$-0.868922\pi$
$283$	−30.8326	−1.83281	−0.916405	+	0.400253i	$0.868922\pi$
$284$	13.4533	0.798305
$285$	12.0267	0.712402
$286$	80.2027	4.74249
$287$	54.8779	3.23934
$288$	11.3206	0.667074
$289$	8.67695	0.510409
$290$	82.1657	4.82494
$291$	6.81135	0.399288
$292$	21.2610	1.24421
$293$	−14.0698	−0.821968	−0.410984	−	0.911643i	$-0.634815\pi$
$293$	−14.0698	−0.821968	−0.410984	+	0.911643i	$0.634815\pi$
$294$	−26.1661	−1.52604
$295$	15.1121	0.879863
$296$	−13.0933	−0.761031
$297$	−27.5793	−1.60032
$298$	−22.2295	−1.28772
$299$	5.69292	0.329230
$300$	36.4790	2.10612
$301$	−18.1510	−1.04621
$302$	−55.6297	−3.20113
$303$	−13.4430	−0.772278
$304$	−24.8564	−1.42561
$305$	−34.7800	−1.99150
$306$	−28.4792	−1.62805
$307$	−22.9778	−1.31141	−0.655707	−	0.755016i	$-0.727629\pi$
$307$	−22.9778	−1.31141	−0.655707	+	0.755016i	$0.727629\pi$
$308$	−114.517	−6.52524
$309$	5.24482	0.298367
$310$	88.4737	5.02497
$311$	6.08701	0.345162	0.172581	−	0.984995i	$-0.444789\pi$
$311$	6.08701	0.345162	0.172581	+	0.984995i	$0.444789\pi$
$312$	29.2728	1.65725
$313$	−31.2220	−1.76477	−0.882386	−	0.470526i	$-0.844064\pi$
$313$	−31.2220	−1.76477	−0.882386	+	0.470526i	$0.844064\pi$
$314$	51.9160	2.92979
$315$	−36.0077	−2.02881
$316$	−42.3784	−2.38397
$317$	11.9271	0.669890	0.334945	−	0.942238i	$-0.391282\pi$
$317$	11.9271	0.669890	0.334945	+	0.942238i	$0.391282\pi$
$318$	−1.78424	−0.100055
$319$	51.1219	2.86228
$320$	3.17401	0.177433
$321$	2.46096	0.137357
$322$	−11.7800	−0.656473
$323$	18.2038	1.01289
$324$	11.2784	0.626576
$325$	−48.8928	−2.71208
$326$	17.4005	0.963725
$327$	3.51049	0.194131
$328$	79.2493	4.37581
$329$	−46.5218	−2.56483
$330$	50.7038	2.79115
$331$	13.9187	0.765039	0.382520	−	0.923947i	$-0.375056\pi$
$331$	13.9187	0.765039	0.382520	+	0.923947i	$0.375056\pi$
$332$	26.3265	1.44485
$333$	−4.65041	−0.254841
$334$	37.9638	2.07729
$335$	−21.1619	−1.15620
$336$	−26.4855	−1.44490
$337$	6.65242	0.362381	0.181190	−	0.983448i	$-0.442005\pi$
$337$	6.65242	0.362381	0.181190	+	0.983448i	$0.442005\pi$
$338$	−38.2090	−2.07830
$339$	−11.3102	−0.614287
$340$	85.1164	4.61608
$341$	55.0466	2.98094
$342$	−20.1905	−1.09178
$343$	−19.8791	−1.07337
$344$	−26.2119	−1.41325
$345$	3.59904	0.193766
$346$	18.6637	1.00337
$347$	3.00180	0.161145	0.0805725	−	0.996749i	$-0.474325\pi$
$347$	3.00180	0.161145	0.0805725	+	0.996749i	$0.474325\pi$
$348$	33.8755	1.81592
$349$	−5.50964	−0.294924	−0.147462	−	0.989068i	$-0.547110\pi$
$349$	−5.50964	−0.294924	−0.147462	+	0.989068i	$0.547110\pi$
$350$	101.171	5.40780
$351$	24.4943	1.30741
$352$	−30.5070	−1.62603
$353$	33.3162	1.77324	0.886620	−	0.462499i	$-0.153047\pi$
$353$	33.3162	1.77324	0.886620	+	0.462499i	$0.153047\pi$
$354$	9.02918	0.479895
$355$	−11.3994	−0.605017
$356$	−50.2116	−2.66121
$357$	19.3970	1.02660
$358$	31.7379	1.67740
$359$	−29.3046	−1.54664	−0.773319	−	0.634017i	$-0.781405\pi$
$359$	−29.3046	−1.54664	−0.773319	+	0.634017i	$0.781405\pi$
$360$	−51.9989	−2.74058
$361$	−6.09426	−0.320751
$362$	−13.3512	−0.701724
$363$	21.7857	1.14346
$364$	101.707	5.33091
$365$	−18.0151	−0.942956
$366$	−20.7803	−1.08620
$367$	18.0999	0.944808	0.472404	−	0.881382i	$-0.343386\pi$
$367$	18.0999	0.944808	0.472404	+	0.881382i	$0.343386\pi$
$368$	−7.43836	−0.387751
$369$	28.1475	1.46530
$370$	20.1421	1.04714
$371$	−3.41458	−0.177276
$372$	36.4762	1.89120
$373$	24.2397	1.25508	0.627541	−	0.778583i	$-0.284061\pi$
$373$	24.2397	1.25508	0.627541	+	0.778583i	$0.284061\pi$
$374$	76.7461	3.96845
$375$	−14.1709	−0.731785
$376$	−67.1823	−3.46466
$377$	−45.4033	−2.33839
$378$	−50.6844	−2.60692
$379$	5.75291	0.295507	0.147753	−	0.989024i	$-0.452796\pi$
$379$	5.75291	0.295507	0.147753	+	0.989024i	$0.452796\pi$
$380$	60.3438	3.09557
$381$	−8.00315	−0.410014
$382$	−14.0962	−0.721224
$383$	5.45349	0.278660	0.139330	−	0.990246i	$-0.455505\pi$
$383$	5.45349	0.278660	0.139330	+	0.990246i	$0.455505\pi$
$384$	10.9770	0.560167
$385$	97.0342	4.94532
$386$	−35.8758	−1.82603
$387$	−9.30984	−0.473246
$388$	34.1758	1.73501
$389$	20.3208	1.03031	0.515153	−	0.857098i	$-0.327735\pi$
$389$	20.3208	1.03031	0.515153	+	0.857098i	$0.327735\pi$
$390$	−45.0320	−2.28028
$391$	5.44756	0.275495
$392$	−72.3137	−3.65239
$393$	8.10045	0.408614
$394$	6.15995	0.310334
$395$	35.9086	1.80676
$396$	−58.7372	−2.95165
$397$	8.27295	0.415207	0.207604	−	0.978213i	$-0.433434\pi$
$397$	8.27295	0.415207	0.207604	+	0.978213i	$0.433434\pi$
$398$	0.885282	0.0443752
$399$	13.7516	0.688442
$400$	63.8832	3.19416
$401$	14.9795	0.748042	0.374021	−	0.927420i	$-0.377979\pi$
$401$	14.9795	0.748042	0.374021	+	0.927420i	$0.377979\pi$
$402$	−12.6438	−0.630614
$403$	−48.8889	−2.43533
$404$	−67.4497	−3.35575
$405$	−9.55652	−0.474868
$406$	93.9500	4.66266
$407$	12.5320	0.621188
$408$	28.0112	1.38676
$409$	−17.0771	−0.844406	−0.422203	−	0.906501i	$-0.638743\pi$
$409$	−17.0771	−0.844406	−0.422203	+	0.906501i	$0.638743\pi$
$410$	−121.914	−6.02088
$411$	4.20183	0.207261
$412$	26.3157	1.29648
$413$	17.2795	0.850271
$414$	−6.04207	−0.296952
$415$	−22.3072	−1.09502
$416$	27.0944	1.32841
$417$	−3.09293	−0.151461
$418$	54.4097	2.66126
$419$	1.89780	0.0927137	0.0463568	−	0.998925i	$-0.485239\pi$
$419$	1.89780	0.0927137	0.0463568	+	0.998925i	$0.485239\pi$
$420$	64.2989	3.13747
$421$	23.9762	1.16853	0.584263	−	0.811564i	$-0.301384\pi$
$421$	23.9762	1.16853	0.584263	+	0.811564i	$0.301384\pi$
$422$	0.645543	0.0314245
$423$	−23.8615	−1.16019
$424$	−4.93100	−0.239471
$425$	−46.7856	−2.26943
$426$	−6.81088	−0.329988
$427$	−39.7682	−1.92452
$428$	12.3478	0.596853
$429$	−28.0180	−1.35272
$430$	40.3232	1.94456
$431$	−28.3800	−1.36701	−0.683507	−	0.729944i	$-0.739546\pi$
$431$	−28.3800	−1.36701	−0.683507	+	0.729944i	$0.739546\pi$
$432$	−32.0042	−1.53980
$433$	−7.60993	−0.365710	−0.182855	−	0.983140i	$-0.558534\pi$
$433$	−7.60993	−0.365710	−0.182855	+	0.983140i	$0.558534\pi$
$434$	101.163	4.85596
$435$	−28.7038	−1.37624
$436$	17.6138	0.843548
$437$	3.86208	0.184749
$438$	−10.7637	−0.514307
$439$	−10.3904	−0.495908	−0.247954	−	0.968772i	$-0.579758\pi$
$439$	−10.3904	−0.495908	−0.247954	+	0.968772i	$0.579758\pi$
$440$	140.127	6.68031
$441$	−25.6841	−1.22305
$442$	−68.1611	−3.24209
$443$	−37.3662	−1.77532	−0.887661	−	0.460497i	$-0.847671\pi$
$443$	−37.3662	−1.77532	−0.887661	+	0.460497i	$0.847671\pi$
$444$	8.30423	0.394101
$445$	42.5459	2.01687
$446$	−28.0725	−1.32927
$447$	7.76566	0.367303
$448$	3.62923	0.171465
$449$	37.7493	1.78150	0.890750	−	0.454493i	$-0.150180\pi$
$449$	37.7493	1.78150	0.890750	+	0.454493i	$0.150180\pi$
$450$	51.8915	2.44619
$451$	−75.8522	−3.57174
$452$	−56.7488	−2.66924
$453$	19.4337	0.913073
$454$	27.4001	1.28595
$455$	−86.1798	−4.04017
$456$	19.8587	0.929971
$457$	15.6090	0.730160	0.365080	−	0.930976i	$-0.381042\pi$
$457$	15.6090	0.730160	0.365080	+	0.930976i	$0.381042\pi$
$458$	−41.4344	−1.93610
$459$	23.4386	1.09402
$460$	18.0581	0.841963
$461$	17.6371	0.821440	0.410720	−	0.911762i	$-0.365277\pi$
$461$	17.6371	0.821440	0.410720	+	0.911762i	$0.365277\pi$
$462$	57.9758	2.69728
$463$	14.1427	0.657266	0.328633	−	0.944458i	$-0.393412\pi$
$463$	14.1427	0.657266	0.328633	+	0.944458i	$0.393412\pi$
$464$	59.3239	2.75404
$465$	−30.9074	−1.43330
$466$	68.9133	3.19235
$467$	−8.52688	−0.394577	−0.197289	−	0.980345i	$-0.563214\pi$
$467$	−8.52688	−0.394577	−0.197289	+	0.980345i	$0.563214\pi$
$468$	52.1667	2.41141
$469$	−24.1969	−1.11731
$470$	103.350	4.76719
$471$	−18.1363	−0.835677
$472$	24.9534	1.14857
$473$	25.0883	1.15356
$474$	21.4546	0.985442
$475$	−33.1689	−1.52190
$476$	97.3238	4.46083
$477$	−1.75137	−0.0801899
$478$	33.5694	1.53543
$479$	−20.3449	−0.929581	−0.464791	−	0.885421i	$-0.653870\pi$
$479$	−20.3449	−0.929581	−0.464791	+	0.885421i	$0.653870\pi$
$480$	17.1290	0.781827
$481$	−11.1301	−0.507491
$482$	−34.7511	−1.58287
$483$	4.11522	0.187249
$484$	109.309	4.96861
$485$	−28.9582	−1.31492
$486$	−40.9584	−1.85791
$487$	35.1040	1.59071	0.795357	−	0.606142i	$-0.207283\pi$
$487$	35.1040	1.59071	0.795357	+	0.606142i	$0.207283\pi$
$488$	−57.4294	−2.59970
$489$	−6.07869	−0.274888
$490$	111.244	5.02550
$491$	−2.21358	−0.0998973	−0.0499486	−	0.998752i	$-0.515906\pi$
$491$	−2.21358	−0.0998973	−0.0499486	+	0.998752i	$0.515906\pi$
$492$	−50.2628	−2.26602
$493$	−43.4465	−1.95673
$494$	−48.3233	−2.17417
$495$	49.7699	2.23699
$496$	63.8782	2.86822
$497$	−13.0343	−0.584668
$498$	−13.3281	−0.597246
$499$	−26.2448	−1.17488	−0.587440	−	0.809268i	$-0.699864\pi$
$499$	−26.2448	−1.17488	−0.587440	+	0.809268i	$0.699864\pi$
$500$	−71.1024	−3.17980
$501$	−13.2623	−0.592515
$502$	−19.8528	−0.886076
$503$	−5.56407	−0.248090	−0.124045	−	0.992277i	$-0.539587\pi$
$503$	−5.56407	−0.248090	−0.124045	+	0.992277i	$0.539587\pi$
$504$	−59.4566	−2.64841
$505$	57.1523	2.54324
$506$	16.2823	0.723835
$507$	13.3479	0.592803
$508$	−40.1556	−1.78162
$509$	2.88239	0.127760	0.0638799	−	0.997958i	$-0.479653\pi$
$509$	2.88239	0.127760	0.0638799	+	0.997958i	$0.479653\pi$
$510$	−43.0912	−1.90811
$511$	−20.5989	−0.911241
$512$	50.8026	2.24518
$513$	16.6169	0.733656
$514$	51.3327	2.26419
$515$	−22.2982	−0.982574
$516$	16.6245	0.731855
$517$	64.3024	2.82802
$518$	23.0309	1.01192
$519$	−6.51997	−0.286195
$520$	−124.452	−5.45760
$521$	40.8513	1.78973	0.894864	−	0.446339i	$-0.147272\pi$
$521$	40.8513	1.78973	0.894864	+	0.446339i	$0.147272\pi$
$522$	48.1879	2.10913
$523$	−19.5992	−0.857014	−0.428507	−	0.903539i	$-0.640960\pi$
$523$	−19.5992	−0.857014	−0.428507	+	0.903539i	$0.640960\pi$
$524$	40.6438	1.77553
$525$	−35.3429	−1.54249
$526$	−14.9805	−0.653182
$527$	−46.7819	−2.03785
$528$	36.6083	1.59317
$529$	−21.8443	−0.949750
$530$	7.58563	0.329499
$531$	8.86286	0.384615
$532$	68.9984	2.99146
$533$	67.3672	2.91800
$534$	25.4202	1.10004
$535$	−10.4627	−0.452341
$536$	−34.9429	−1.50930
$537$	−11.0873	−0.478453
$538$	−34.2105	−1.47492
$539$	69.2139	2.98125
$540$	77.6965	3.34352
$541$	15.5687	0.669351	0.334676	−	0.942333i	$-0.391373\pi$
$541$	15.5687	0.669351	0.334676	+	0.942333i	$0.391373\pi$
$542$	−36.1515	−1.55284
$543$	4.66411	0.200156
$544$	25.9267	1.11160
$545$	−14.9247	−0.639305
$546$	−51.4905	−2.20359
$547$	−10.2691	−0.439076	−0.219538	−	0.975604i	$-0.570455\pi$
$547$	−10.2691	−0.439076	−0.219538	+	0.975604i	$0.570455\pi$
$548$	21.0826	0.900603
$549$	−20.3975	−0.870545
$550$	−139.838	−5.96271
$551$	−30.8017	−1.31219
$552$	5.94279	0.252942
$553$	41.0586	1.74599
$554$	−47.5880	−2.02182
$555$	−7.03643	−0.298680
$556$	−15.5187	−0.658140
$557$	−0.640289	−0.0271299	−0.0135650	−	0.999908i	$-0.504318\pi$
$557$	−0.640289	−0.0271299	−0.0135650	+	0.999908i	$0.504318\pi$
$558$	51.8874	2.19657
$559$	−22.2819	−0.942422
$560$	112.602	4.75832
$561$	−26.8105	−1.13194
$562$	−6.38153	−0.269189
$563$	−10.9029	−0.459503	−0.229751	−	0.973249i	$-0.573791\pi$
$563$	−10.9029	−0.459503	−0.229751	+	0.973249i	$0.573791\pi$
$564$	42.6094	1.79418
$565$	48.0850	2.02295
$566$	78.3197	3.29202
$567$	−10.9271	−0.458896
$568$	−18.8229	−0.789790
$569$	−43.0406	−1.80435	−0.902177	−	0.431366i	$-0.858032\pi$
$569$	−43.0406	−1.80435	−0.902177	+	0.431366i	$0.858032\pi$
$570$	−30.5498	−1.27959
$571$	3.46187	0.144875	0.0724374	−	0.997373i	$-0.476922\pi$
$571$	3.46187	0.144875	0.0724374	+	0.997373i	$0.476922\pi$
$572$	−140.580	−5.87793
$573$	4.92436	0.205718
$574$	−139.399	−5.81838
$575$	−9.92592	−0.413939
$576$	1.86147	0.0775613
$577$	8.01324	0.333596	0.166798	−	0.985991i	$-0.446657\pi$
$577$	8.01324	0.333596	0.166798	+	0.985991i	$0.446657\pi$
$578$	−22.0408	−0.916777
$579$	12.5328	0.520847
$580$	−144.020	−5.98012
$581$	−25.5066	−1.05819
$582$	−17.3019	−0.717187
$583$	4.71963	0.195467
$584$	−29.7469	−1.23094
$585$	−44.2025	−1.82755
$586$	35.7396	1.47639
$587$	−22.8982	−0.945111	−0.472555	−	0.881301i	$-0.656668\pi$
$587$	−22.8982	−0.945111	−0.472555	+	0.881301i	$0.656668\pi$
$588$	45.8640	1.89140
$589$	−33.1663	−1.36660
$590$	−38.3872	−1.58038
$591$	−2.15192	−0.0885180
$592$	14.5426	0.597699
$593$	5.74445	0.235896	0.117948	−	0.993020i	$-0.462368\pi$
$593$	5.74445	0.235896	0.117948	+	0.993020i	$0.462368\pi$
$594$	70.0559	2.87443
$595$	−82.4656	−3.38076
$596$	38.9640	1.59603
$597$	−0.309264	−0.0126573
$598$	−14.4609	−0.591350
$599$	−25.2426	−1.03138	−0.515692	−	0.856774i	$-0.672465\pi$
$599$	−25.2426	−1.03138	−0.515692	+	0.856774i	$0.672465\pi$
$600$	−51.0388	−2.08365
$601$	39.0960	1.59476	0.797380	−	0.603478i	$-0.206219\pi$
$601$	39.0960	1.59476	0.797380	+	0.603478i	$0.206219\pi$
$602$	46.1064	1.87916
$603$	−12.4109	−0.505409
$604$	97.5079	3.96754
$605$	−92.6214	−3.76559
$606$	34.1472	1.38714
$607$	21.8621	0.887354	0.443677	−	0.896187i	$-0.353674\pi$
$607$	21.8621	0.887354	0.443677	+	0.896187i	$0.353674\pi$
$608$	18.3809	0.745444
$609$	−32.8205	−1.32995
$610$	88.3467	3.57705
$611$	−57.1094	−2.31040
$612$	49.9184	2.01783
$613$	−35.1700	−1.42050	−0.710251	−	0.703948i	$-0.751419\pi$
$613$	−35.1700	−1.42050	−0.710251	+	0.703948i	$0.751419\pi$
$614$	58.3673	2.35551
$615$	42.5893	1.71737
$616$	160.225	6.45563
$617$	−9.25683	−0.372666	−0.186333	−	0.982487i	$-0.559660\pi$
$617$	−9.25683	−0.372666	−0.186333	+	0.982487i	$0.559660\pi$
$618$	−13.3227	−0.535916
$619$	−37.4783	−1.50638	−0.753190	−	0.657803i	$-0.771486\pi$
$619$	−37.4783	−1.50638	−0.753190	+	0.657803i	$0.771486\pi$
$620$	−155.077	−6.22805
$621$	4.97268	0.199547
$622$	−15.4620	−0.619968
$623$	48.6479	1.94904
$624$	−32.5132	−1.30157
$625$	14.0826	0.563303
$626$	79.3088	3.16982
$627$	−19.0075	−0.759085
$628$	−90.9985	−3.63124
$629$	−10.6505	−0.424661
$630$	91.4653	3.64407
$631$	−37.6396	−1.49841	−0.749204	−	0.662339i	$-0.769564\pi$
$631$	−37.6396	−1.49841	−0.749204	+	0.662339i	$0.769564\pi$
$632$	59.2929	2.35854
$633$	−0.225514	−0.00896337
$634$	−30.2966	−1.20323
$635$	34.0251	1.35025
$636$	3.12742	0.124010
$637$	−61.4715	−2.43559
$638$	−129.858	−5.14111
$639$	−6.68543	−0.264471
$640$	−46.6683	−1.84473
$641$	16.9330	0.668812	0.334406	−	0.942429i	$-0.391464\pi$
$641$	16.9330	0.668812	0.334406	+	0.942429i	$0.391464\pi$
$642$	−6.25122	−0.246716
$643$	−40.7908	−1.60863	−0.804316	−	0.594202i	$-0.797468\pi$
$643$	−40.7908	−1.60863	−0.804316	+	0.594202i	$0.797468\pi$
$644$	20.6480	0.813645
$645$	−14.0865	−0.554656
$646$	−46.2406	−1.81931
$647$	48.2749	1.89788	0.948942	−	0.315452i	$-0.102156\pi$
$647$	48.2749	1.89788	0.948942	+	0.315452i	$0.102156\pi$
$648$	−15.7799	−0.619893
$649$	−23.8838	−0.937520
$650$	124.195	4.87134
$651$	−35.3402	−1.38509
$652$	−30.4997	−1.19446
$653$	−9.40144	−0.367907	−0.183953	−	0.982935i	$-0.558890\pi$
$653$	−9.40144	−0.367907	−0.183953	+	0.982935i	$0.558890\pi$
$654$	−8.91720	−0.348690
$655$	−34.4388	−1.34563
$656$	−88.0219	−3.43668
$657$	−10.5654	−0.412195
$658$	118.173	4.60685
$659$	35.9938	1.40212	0.701059	−	0.713104i	$-0.252711\pi$
$659$	35.9938	1.40212	0.701059	+	0.713104i	$0.252711\pi$
$660$	−88.8739	−3.45941
$661$	2.90671	0.113058	0.0565289	−	0.998401i	$-0.481997\pi$
$661$	2.90671	0.113058	0.0565289	+	0.998401i	$0.481997\pi$
$662$	−35.3556	−1.37413
$663$	23.8114	0.924758
$664$	−36.8341	−1.42944
$665$	−58.4645	−2.26716
$666$	11.8128	0.457736
$667$	−9.21750	−0.356903
$668$	−66.5431	−2.57463
$669$	9.80683	0.379154
$670$	53.7545	2.07672
$671$	54.9676	2.12200
$672$	19.5856	0.755532
$673$	−19.1795	−0.739314	−0.369657	−	0.929168i	$-0.620525\pi$
$673$	−19.1795	−0.739314	−0.369657	+	0.929168i	$0.620525\pi$
$674$	−16.8982	−0.650894
$675$	−42.7071	−1.64380
$676$	66.9729	2.57588
$677$	12.2159	0.469494	0.234747	−	0.972057i	$-0.424574\pi$
$677$	12.2159	0.469494	0.234747	+	0.972057i	$0.424574\pi$
$678$	28.7298	1.10336
$679$	−33.1114	−1.27070
$680$	−119.089	−4.56684
$681$	−9.57196	−0.366798
$682$	−139.827	−5.35425
$683$	−23.3257	−0.892532	−0.446266	−	0.894900i	$-0.647246\pi$
$683$	−23.3257	−0.892532	−0.446266	+	0.894900i	$0.647246\pi$
$684$	35.3900	1.35317
$685$	−17.8639	−0.682546
$686$	50.4959	1.92794
$687$	14.4747	0.552244
$688$	29.1135	1.10994
$689$	−4.19168	−0.159690
$690$	−9.14212	−0.348035
$691$	−0.0119278	−0.000453754 0	−0.000226877	−	1.00000i	$-0.500072\pi$
$691$	−0.0119278	−0.000453754 0	−0.000226877		1.00000i	$0.500072\pi$
$692$	−32.7138	−1.24359
$693$	56.9079	2.16175
$694$	−7.62504	−0.289443
$695$	13.1495	0.498789
$696$	−47.3961	−1.79655
$697$	64.4638	2.44174
$698$	13.9954	0.529732
$699$	−24.0742	−0.910569
$700$	−177.332	−6.70253
$701$	−40.4774	−1.52881	−0.764405	−	0.644736i	$-0.776967\pi$
$701$	−40.4774	−1.52881	−0.764405	+	0.644736i	$0.776967\pi$
$702$	−62.2193	−2.34831
$703$	−7.55071	−0.284780
$704$	−5.01632	−0.189060
$705$	−36.1043	−1.35977
$706$	−84.6283	−3.18503
$707$	65.3491	2.45771
$708$	−15.8264	−0.594792
$709$	−47.9235	−1.79980	−0.899902	−	0.436091i	$-0.856362\pi$
$709$	−47.9235	−1.79980	−0.899902	+	0.436091i	$0.856362\pi$
$710$	28.9562	1.08671
$711$	21.0594	0.789789
$712$	70.2525	2.63282
$713$	−9.92514	−0.371699
$714$	−49.2714	−1.84393
$715$	119.118	4.45474
$716$	−55.6303	−2.07900
$717$	−11.7271	−0.437958
$718$	74.4383	2.77801
$719$	29.5928	1.10363	0.551813	−	0.833968i	$-0.313936\pi$
$719$	29.5928	1.10363	0.551813	+	0.833968i	$0.313936\pi$
$720$	57.7549	2.15240
$721$	−25.4962	−0.949527
$722$	15.4804	0.576120
$723$	12.1400	0.451490
$724$	23.4021	0.869731
$725$	79.1631	2.94005
$726$	−55.3392	−2.05383
$727$	17.1704	0.636814	0.318407	−	0.947954i	$-0.396852\pi$
$727$	17.1704	0.636814	0.318407	+	0.947954i	$0.396852\pi$
$728$	−142.302	−5.27404
$729$	6.70910	0.248485
$730$	45.7613	1.69370
$731$	−21.3216	−0.788606
$732$	36.4238	1.34626
$733$	44.0831	1.62825	0.814123	−	0.580692i	$-0.197218\pi$
$733$	44.0831	1.62825	0.814123	+	0.580692i	$0.197218\pi$
$734$	−45.9766	−1.69703
$735$	−38.8620	−1.43345
$736$	5.50055	0.202753
$737$	33.4450	1.23196
$738$	−71.4990	−2.63191
$739$	17.7600	0.653313	0.326656	−	0.945143i	$-0.394078\pi$
$739$	17.7600	0.653313	0.326656	+	0.945143i	$0.394078\pi$
$740$	−35.3051	−1.29784
$741$	16.8812	0.620148
$742$	8.67357	0.318417
$743$	−50.3075	−1.84560	−0.922801	−	0.385277i	$-0.874106\pi$
$743$	−50.3075	−1.84560	−0.922801	+	0.385277i	$0.874106\pi$
$744$	−51.0348	−1.87103
$745$	−33.0154	−1.20959
$746$	−61.5726	−2.25433
$747$	−13.0826	−0.478667
$748$	−134.521	−4.91857
$749$	−11.9632	−0.437127
$750$	35.9964	1.31440
$751$	−13.9241	−0.508098	−0.254049	−	0.967191i	$-0.581762\pi$
$751$	−13.9241	−0.508098	−0.254049	+	0.967191i	$0.581762\pi$
$752$	74.6190	2.72108
$753$	6.93539	0.252740
$754$	115.331	4.20012
$755$	−82.6215	−3.00690
$756$	88.8397	3.23107
$757$	44.5293	1.61845	0.809223	−	0.587501i	$-0.199888\pi$
$757$	44.5293	1.61845	0.809223	+	0.587501i	$0.199888\pi$
$758$	−14.6133	−0.530778
$759$	−5.68805	−0.206463
$760$	−84.4288	−3.06255
$761$	−46.0092	−1.66783	−0.833917	−	0.551890i	$-0.813907\pi$
$761$	−46.0092	−1.66783	−0.833917	+	0.551890i	$0.813907\pi$
$762$	20.3293	0.736452
$763$	−17.0652	−0.617803
$764$	24.7079	0.893899
$765$	−42.2975	−1.52927
$766$	−13.8527	−0.500519
$767$	21.2121	0.765924
$768$	−26.3902	−0.952273
$769$	−28.3081	−1.02081	−0.510407	−	0.859933i	$-0.670505\pi$
$769$	−28.3081	−1.02081	−0.510407	+	0.859933i	$0.670505\pi$
$770$	−246.482	−8.88260
$771$	−17.9326	−0.645826
$772$	62.8833	2.26322
$773$	−1.89256	−0.0680706	−0.0340353	−	0.999421i	$-0.510836\pi$
$773$	−1.89256	−0.0680706	−0.0340353	+	0.999421i	$0.510836\pi$
$774$	23.6485	0.850026
$775$	85.2406	3.06193
$776$	−47.8163	−1.71650
$777$	−8.04560	−0.288634
$778$	−51.6180	−1.85060
$779$	45.7020	1.63745
$780$	78.9323	2.82623
$781$	18.0160	0.644663
$782$	−13.8377	−0.494834
$783$	−39.6591	−1.41730
$784$	80.3185	2.86852
$785$	77.1059	2.75203
$786$	−20.5764	−0.733937
$787$	51.8901	1.84968	0.924841	−	0.380355i	$-0.124198\pi$
$787$	51.8901	1.84968	0.924841	+	0.380355i	$0.124198\pi$
$788$	−10.7972	−0.384634
$789$	5.23329	0.186310
$790$	−91.2135	−3.24523
$791$	54.9814	1.95492
$792$	82.1809	2.92017
$793$	−48.8188	−1.73361
$794$	−21.0146	−0.745780
$795$	−2.64996	−0.0939845
$796$	−1.55173	−0.0549995
$797$	−18.8378	−0.667268	−0.333634	−	0.942703i	$-0.608275\pi$
$797$	−18.8378	−0.667268	−0.333634	+	0.942703i	$0.608275\pi$
$798$	−34.9313	−1.23655
$799$	−54.6481	−1.93331
$800$	−47.2406	−1.67021
$801$	24.9520	0.881636
$802$	−38.0504	−1.34360
$803$	28.4718	1.00475
$804$	22.1620	0.781595
$805$	−17.4957	−0.616642
$806$	124.186	4.37425
$807$	11.9511	0.420699
$808$	94.3708	3.31995
$809$	29.6227	1.04148	0.520740	−	0.853715i	$-0.325656\pi$
$809$	29.6227	1.04148	0.520740	+	0.853715i	$0.325656\pi$
$810$	24.2751	0.852939
$811$	39.6450	1.39212	0.696062	−	0.717982i	$-0.254934\pi$
$811$	39.6450	1.39212	0.696062	+	0.717982i	$0.254934\pi$
$812$	−164.676	−5.77899
$813$	12.6291	0.442923
$814$	−31.8333	−1.11575
$815$	25.8433	0.905253
$816$	−31.1119	−1.08914
$817$	−15.1161	−0.528844
$818$	43.3784	1.51669
$819$	−50.5421	−1.76608
$820$	213.691	7.46240
$821$	−14.9319	−0.521127	−0.260563	−	0.965457i	$-0.583908\pi$
$821$	−14.9319	−0.521127	−0.260563	+	0.965457i	$0.583908\pi$
$822$	−10.6733	−0.372274
$823$	2.30030	0.0801833	0.0400917	−	0.999196i	$-0.487235\pi$
$823$	2.30030	0.0801833	0.0400917	+	0.999196i	$0.487235\pi$
$824$	−36.8191	−1.28265
$825$	48.8510	1.70077
$826$	−43.8928	−1.52722
$827$	0.279186	0.00970826	0.00485413	−	0.999988i	$-0.498455\pi$
$827$	0.279186	0.00970826	0.00485413	+	0.999988i	$0.498455\pi$
$828$	10.5906	0.368048
$829$	−9.83941	−0.341737	−0.170868	−	0.985294i	$-0.554657\pi$
$829$	−9.83941	−0.341737	−0.170868	+	0.985294i	$0.554657\pi$
$830$	56.6639	1.96683
$831$	16.6244	0.576694
$832$	4.45518	0.154456
$833$	−58.8222	−2.03807
$834$	7.85653	0.272049
$835$	56.3841	1.95125
$836$	−95.3695	−3.29842
$837$	−42.7038	−1.47606
$838$	−4.82072	−0.166529
$839$	−26.6637	−0.920533	−0.460267	−	0.887781i	$-0.652246\pi$
$839$	−26.6637	−0.920533	−0.460267	+	0.887781i	$0.652246\pi$
$840$	−89.9624	−3.10400
$841$	44.5132	1.53494
$842$	−60.9032	−2.09886
$843$	2.22932	0.0767819
$844$	−1.13151	−0.0389482
$845$	−56.7483	−1.95220
$846$	60.6120	2.08388
$847$	−105.905	−3.63895
$848$	5.47684	0.188076
$849$	−27.3602	−0.938999
$850$	118.843	4.07627
$851$	−2.25958	−0.0774572
$852$	11.9381	0.408994
$853$	7.69877	0.263601	0.131800	−	0.991276i	$-0.457924\pi$
$853$	7.69877	0.263601	0.131800	+	0.991276i	$0.457924\pi$
$854$	101.017	3.45675
$855$	−29.9871	−1.02554
$856$	−17.2761	−0.590486
$857$	10.2658	0.350673	0.175337	−	0.984509i	$-0.443899\pi$
$857$	10.2658	0.350673	0.175337	+	0.984509i	$0.443899\pi$
$858$	71.1701	2.42971
$859$	3.20447	0.109335	0.0546676	−	0.998505i	$-0.482590\pi$
$859$	3.20447	0.109335	0.0546676	+	0.998505i	$0.482590\pi$
$860$	−70.6787	−2.41012
$861$	48.6975	1.65961
$862$	72.0895	2.45538
$863$	46.2476	1.57429	0.787144	−	0.616770i	$-0.211559\pi$
$863$	46.2476	1.57429	0.787144	+	0.616770i	$0.211559\pi$
$864$	23.6666	0.805153
$865$	27.7194	0.942489
$866$	19.3304	0.656875
$867$	7.69974	0.261497
$868$	−177.318	−6.01858
$869$	−56.7512	−1.92515
$870$	72.9121	2.47195
$871$	−29.7038	−1.00647
$872$	−24.6440	−0.834550
$873$	−16.9832	−0.574794
$874$	−9.81030	−0.331838
$875$	68.8880	2.32884
$876$	18.8666	0.637443
$877$	−15.6093	−0.527090	−0.263545	−	0.964647i	$-0.584892\pi$
$877$	−15.6093	−0.527090	−0.263545	+	0.964647i	$0.584892\pi$
$878$	26.3933	0.890731
$879$	−12.4853	−0.421117
$880$	−155.639	−5.24659
$881$	45.9576	1.54835	0.774176	−	0.632970i	$-0.218164\pi$
$881$	45.9576	1.54835	0.774176	+	0.632970i	$0.218164\pi$
$882$	65.2416	2.19680
$883$	−23.6792	−0.796870	−0.398435	−	0.917197i	$-0.630447\pi$
$883$	−23.6792	−0.796870	−0.398435	+	0.917197i	$0.630447\pi$
$884$	119.473	4.01832
$885$	13.4102	0.450779
$886$	94.9160	3.18877
$887$	−18.1983	−0.611039	−0.305520	−	0.952186i	$-0.598830\pi$
$887$	−18.1983	−0.611039	−0.305520	+	0.952186i	$0.598830\pi$
$888$	−11.6187	−0.389897
$889$	38.9051	1.30483
$890$	−108.073	−3.62263
$891$	15.1035	0.505985
$892$	49.2055	1.64752
$893$	−38.7431	−1.29649
$894$	−19.7260	−0.659736
$895$	47.1373	1.57563
$896$	−53.3615	−1.78268
$897$	5.05177	0.168674
$898$	−95.8892	−3.19986
$899$	79.1569	2.64003
$900$	−90.9556	−3.03185
$901$	−4.01103	−0.133627
$902$	192.676	6.41542
$903$	−16.1068	−0.536001
$904$	79.3988	2.64077
$905$	−19.8293	−0.659149
$906$	−49.3645	−1.64003
$907$	17.0583	0.566413	0.283206	−	0.959059i	$-0.408602\pi$
$907$	17.0583	0.566413	0.283206	+	0.959059i	$0.408602\pi$
$908$	−48.0271	−1.59383
$909$	33.5182	1.11173
$910$	218.910	7.25680
$911$	−29.9204	−0.991306	−0.495653	−	0.868521i	$-0.665071\pi$
$911$	−29.9204	−0.991306	−0.495653	+	0.868521i	$0.665071\pi$
$912$	−22.0570	−0.730381
$913$	35.2551	1.16677
$914$	−39.6494	−1.31149
$915$	−30.8630	−1.02030
$916$	72.6264	2.39964
$917$	−39.3780	−1.30038
$918$	−59.5377	−1.96504
$919$	7.60425	0.250841	0.125421	−	0.992104i	$-0.459972\pi$
$919$	7.60425	0.250841	0.125421	+	0.992104i	$0.459972\pi$
$920$	−25.2656	−0.832982
$921$	−20.3900	−0.671874
$922$	−44.8009	−1.47544
$923$	−16.0007	−0.526669
$924$	−101.620	−3.34306
$925$	19.4060	0.638066
$926$	−35.9246	−1.18056
$927$	−13.0773	−0.429513
$928$	−43.8690	−1.44007
$929$	−3.07010	−0.100727	−0.0503634	−	0.998731i	$-0.516038\pi$
$929$	−3.07010	−0.100727	−0.0503634	+	0.998731i	$0.516038\pi$
$930$	78.5096	2.57443
$931$	−41.7024	−1.36674
$932$	−120.792	−3.95666
$933$	5.40148	0.176836
$934$	21.6596	0.708724
$935$	113.984	3.72767
$936$	−72.9879	−2.38569
$937$	29.0743	0.949815	0.474908	−	0.880036i	$-0.342481\pi$
$937$	29.0743	0.949815	0.474908	+	0.880036i	$0.342481\pi$
$938$	61.4640	2.00687
$939$	−27.7057	−0.904143
$940$	−181.153	−5.90854
$941$	58.4421	1.90516	0.952579	−	0.304292i	$-0.0984198\pi$
$941$	58.4421	1.90516	0.952579	+	0.304292i	$0.0984198\pi$
$942$	46.0691	1.50101
$943$	13.6765	0.445368
$944$	−27.7157	−0.902068
$945$	−75.2767	−2.44875
$946$	−63.7282	−2.07198
$947$	−5.23455	−0.170100	−0.0850500	−	0.996377i	$-0.527105\pi$
$947$	−5.23455	−0.170100	−0.0850500	+	0.996377i	$0.527105\pi$
$948$	−37.6057	−1.22138
$949$	−25.2869	−0.820846
$950$	84.2543	2.73357
$951$	10.5838	0.343204
$952$	−136.169	−4.41325
$953$	−7.98186	−0.258558	−0.129279	−	0.991608i	$-0.541266\pi$
$953$	−7.98186	−0.258558	−0.129279	+	0.991608i	$0.541266\pi$
$954$	4.44876	0.144034
$955$	−20.9358	−0.677465
$956$	−58.8406	−1.90304
$957$	45.3644	1.46642
$958$	51.6792	1.66968
$959$	−20.4260	−0.659590
$960$	2.81655	0.0909037
$961$	54.2339	1.74948
$962$	28.2723	0.911536
$963$	−6.13607	−0.197732
$964$	60.9119	1.96184
$965$	−53.2830	−1.71524
$966$	−10.4533	−0.336329
$967$	52.5832	1.69096	0.845482	−	0.534004i	$-0.179313\pi$
$967$	52.5832	1.69096	0.845482	+	0.534004i	$0.179313\pi$
$968$	−152.938	−4.91561
$969$	16.1537	0.518931
$970$	73.5584	2.36182
$971$	−32.3451	−1.03801	−0.519003	−	0.854773i	$-0.673696\pi$
$971$	−32.3451	−1.03801	−0.519003	+	0.854773i	$0.673696\pi$
$972$	71.7920	2.30273
$973$	15.0354	0.482013
$974$	−89.1697	−2.85718
$975$	−43.3864	−1.38948
$976$	63.7865	2.04176
$977$	−11.5828	−0.370568	−0.185284	−	0.982685i	$-0.559320\pi$
$977$	−11.5828	−0.370568	−0.185284	+	0.982685i	$0.559320\pi$
$978$	15.4408	0.493743
$979$	−67.2410	−2.14903
$980$	−194.989	−6.22870
$981$	−8.75294	−0.279460
$982$	5.62283	0.179432
$983$	1.99400	0.0635986	0.0317993	−	0.999494i	$-0.489876\pi$
$983$	1.99400	0.0635986	0.0317993	+	0.999494i	$0.489876\pi$
$984$	70.3241	2.24185
$985$	9.14880	0.291505
$986$	110.361	3.51461
$987$	−41.2824	−1.31403
$988$	84.7013	2.69471
$989$	−4.52353	−0.143840
$990$	−126.423	−4.01800
$991$	−41.5571	−1.32010	−0.660052	−	0.751220i	$-0.729466\pi$
$991$	−41.5571	−1.32010	−0.660052	+	0.751220i	$0.729466\pi$
$992$	−47.2369	−1.49977
$993$	12.3511	0.391951
$994$	33.1092	1.05016
$995$	1.31483	0.0416828
$996$	23.3615	0.740238
$997$	−31.4493	−0.996009	−0.498005	−	0.867174i	$-0.665934\pi$
$997$	−31.4493	−0.996009	−0.498005	+	0.867174i	$0.665934\pi$
$998$	66.6659	2.11027
$999$	−9.72201	−0.307591

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6007.2.a.b.1.18	✓	237

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6007.2.a.b.1.18	✓	237	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:	\( N \)	\(=\)	\( 6007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.54016 q^{2} +0.887378 q^{3} +4.45240 q^{4} -3.77266 q^{5} -2.25408 q^{6} -4.31374 q^{7} -6.22948 q^{8} -2.21256 q^{9} +O(q^{10})\)	\(q-2.54016 q^{2} +0.887378 q^{3} +4.45240 q^{4} -3.77266 q^{5} -2.25408 q^{6} -4.31374 q^{7} -6.22948 q^{8} -2.21256 q^{9} +9.58314 q^{10} +5.96244 q^{11} +3.95096 q^{12} -5.29547 q^{13} +10.9576 q^{14} -3.34777 q^{15} +6.91905 q^{16} -5.06724 q^{17} +5.62025 q^{18} -3.59246 q^{19} -16.7974 q^{20} -3.82791 q^{21} -15.1455 q^{22} -1.07505 q^{23} -5.52790 q^{24} +9.23295 q^{25} +13.4513 q^{26} -4.62551 q^{27} -19.2065 q^{28} +8.57398 q^{29} +8.50387 q^{30} +9.23222 q^{31} -5.11653 q^{32} +5.29094 q^{33} +12.8716 q^{34} +16.2742 q^{35} -9.85120 q^{36} +2.10182 q^{37} +9.12540 q^{38} -4.69908 q^{39} +23.5017 q^{40} -12.7217 q^{41} +9.72351 q^{42} +4.20772 q^{43} +26.5472 q^{44} +8.34723 q^{45} +2.73081 q^{46} +10.7846 q^{47} +6.13982 q^{48} +11.6083 q^{49} -23.4531 q^{50} -4.49656 q^{51} -23.5775 q^{52} +0.791560 q^{53} +11.7495 q^{54} -22.4942 q^{55} +26.8723 q^{56} -3.18787 q^{57} -21.7793 q^{58} -4.00570 q^{59} -14.9056 q^{60} +9.21897 q^{61} -23.4513 q^{62} +9.54440 q^{63} -0.841320 q^{64} +19.9780 q^{65} -13.4398 q^{66} +5.60928 q^{67} -22.5614 q^{68} -0.953980 q^{69} -41.3391 q^{70} +3.02158 q^{71} +13.7831 q^{72} +4.77519 q^{73} -5.33896 q^{74} +8.19312 q^{75} -15.9950 q^{76} -25.7204 q^{77} +11.9364 q^{78} -9.51812 q^{79} -26.1032 q^{80} +2.53310 q^{81} +32.3150 q^{82} +5.91287 q^{83} -17.0434 q^{84} +19.1170 q^{85} -10.6883 q^{86} +7.60837 q^{87} -37.1429 q^{88} -11.2774 q^{89} -21.2033 q^{90} +22.8433 q^{91} -4.78657 q^{92} +8.19247 q^{93} -27.3945 q^{94} +13.5531 q^{95} -4.54030 q^{96} +7.67581 q^{97} -29.4869 q^{98} -13.1923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9}+O(q^{10}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9	\( 237 q - 26 q^{2} - 24 q^{3} + 226 q^{4} - 67 q^{5} - 30 q^{6} - 37 q^{7} - 75 q^{8} + 189 q^{9} - 39 q^{10} - 38 q^{11} - 67 q^{12} - 52 q^{13} - 54 q^{14} - 24 q^{15} + 208 q^{16} - 255 q^{17} - 71 q^{18} - 24 q^{19} - 154 q^{20} - 60 q^{21} - 39 q^{22} - 118 q^{23} - 85 q^{24} + 170 q^{25} - 61 q^{26} - 87 q^{27} - 99 q^{28} - 87 q^{29} - 30 q^{30} - 28 q^{31} - 156 q^{32} - 173 q^{33} - 4 q^{34} - 113 q^{35} + 152 q^{36} - 49 q^{37} - 145 q^{38} - 49 q^{39} - 91 q^{40} - 197 q^{41} - 61 q^{42} - 63 q^{43} - 106 q^{44} - 181 q^{45} - 2 q^{46} - 119 q^{47} - 142 q^{48} + 150 q^{49} - 89 q^{50} - 40 q^{51} - 97 q^{52} - 190 q^{53} - 97 q^{54} - 55 q^{55} - 154 q^{56} - 202 q^{57} - 27 q^{58} - 86 q^{59} - 48 q^{60} - 96 q^{61} - 239 q^{62} - 149 q^{63} + 183 q^{64} - 259 q^{65} - 72 q^{66} - 28 q^{67} - 482 q^{68} - 83 q^{69} + 20 q^{70} - 63 q^{71} - 193 q^{72} - 206 q^{73} - 132 q^{74} - 89 q^{75} - 11 q^{76} - 179 q^{77} - 58 q^{78} - 32 q^{79} - 320 q^{80} + 57 q^{81} - 77 q^{82} - 245 q^{83} - 133 q^{84} + q^{85} - 39 q^{86} - 179 q^{87} - 104 q^{88} - 227 q^{89} - 146 q^{90} - 36 q^{91} - 315 q^{92} - 87 q^{93} - 48 q^{94} - 111 q^{95} - 134 q^{96} - 221 q^{97} - 161 q^{98} - 68 q^{99}+O(q^{100}) \) 237 * q - 26 * q^2 - 24 * q^3 + 226 * q^4 - 67 * q^5 - 30 * q^6 - 37 * q^7 - 75 * q^8 + 189 * q^9 - 39 * q^10 - 38 * q^11 - 67 * q^12 - 52 * q^13 - 54 * q^14 - 24 * q^15 + 208 * q^16 - 255 * q^17 - 71 * q^18 - 24 * q^19 - 154 * q^20 - 60 * q^21 - 39 * q^22 - 118 * q^23 - 85 * q^24 + 170 * q^25 - 61 * q^26 - 87 * q^27 - 99 * q^28 - 87 * q^29 - 30 * q^30 - 28 * q^31 - 156 * q^32 - 173 * q^33 - 4 * q^34 - 113 * q^35 + 152 * q^36 - 49 * q^37 - 145 * q^38 - 49 * q^39 - 91 * q^40 - 197 * q^41 - 61 * q^42 - 63 * q^43 - 106 * q^44 - 181 * q^45 - 2 * q^46 - 119 * q^47 - 142 * q^48 + 150 * q^49 - 89 * q^50 - 40 * q^51 - 97 * q^52 - 190 * q^53 - 97 * q^54 - 55 * q^55 - 154 * q^56 - 202 * q^57 - 27 * q^58 - 86 * q^59 - 48 * q^60 - 96 * q^61 - 239 * q^62 - 149 * q^63 + 183 * q^64 - 259 * q^65 - 72 * q^66 - 28 * q^67 - 482 * q^68 - 83 * q^69 + 20 * q^70 - 63 * q^71 - 193 * q^72 - 206 * q^73 - 132 * q^74 - 89 * q^75 - 11 * q^76 - 179 * q^77 - 58 * q^78 - 32 * q^79 - 320 * q^80 + 57 * q^81 - 77 * q^82 - 245 * q^83 - 133 * q^84 + q^85 - 39 * q^86 - 179 * q^87 - 104 * q^88 - 227 * q^89 - 146 * q^90 - 36 * q^91 - 315 * q^92 - 87 * q^93 - 48 * q^94 - 111 * q^95 - 134 * q^96 - 221 * q^97 - 161 * q^98 - 68 * q^99

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