LMFDB - Embedded newform 8002.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, 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("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.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:	$63.8962916974$
Analytic rank:	$1$
Dimension:	$69$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.09800 q^{3} +1.00000 q^{4} -2.64538 q^{5} -3.09800 q^{6} +3.07801 q^{7} +1.00000 q^{8} +6.59762 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.09800 q^{3} +1.00000 q^{4} -2.64538 q^{5} -3.09800 q^{6} +3.07801 q^{7} +1.00000 q^{8} +6.59762 q^{9} -2.64538 q^{10} -2.21532 q^{11} -3.09800 q^{12} +3.83880 q^{13} +3.07801 q^{14} +8.19540 q^{15} +1.00000 q^{16} +3.02764 q^{17} +6.59762 q^{18} -1.43150 q^{19} -2.64538 q^{20} -9.53568 q^{21} -2.21532 q^{22} -1.68937 q^{23} -3.09800 q^{24} +1.99804 q^{25} +3.83880 q^{26} -11.1454 q^{27} +3.07801 q^{28} -10.1345 q^{29} +8.19540 q^{30} -6.75644 q^{31} +1.00000 q^{32} +6.86307 q^{33} +3.02764 q^{34} -8.14251 q^{35} +6.59762 q^{36} +1.29634 q^{37} -1.43150 q^{38} -11.8926 q^{39} -2.64538 q^{40} -0.898028 q^{41} -9.53568 q^{42} -1.79099 q^{43} -2.21532 q^{44} -17.4532 q^{45} -1.68937 q^{46} +6.29459 q^{47} -3.09800 q^{48} +2.47415 q^{49} +1.99804 q^{50} -9.37962 q^{51} +3.83880 q^{52} +1.20789 q^{53} -11.1454 q^{54} +5.86037 q^{55} +3.07801 q^{56} +4.43478 q^{57} -10.1345 q^{58} +5.14420 q^{59} +8.19540 q^{60} -3.71458 q^{61} -6.75644 q^{62} +20.3075 q^{63} +1.00000 q^{64} -10.1551 q^{65} +6.86307 q^{66} +12.9871 q^{67} +3.02764 q^{68} +5.23367 q^{69} -8.14251 q^{70} +4.67918 q^{71} +6.59762 q^{72} +0.143405 q^{73} +1.29634 q^{74} -6.18994 q^{75} -1.43150 q^{76} -6.81878 q^{77} -11.8926 q^{78} +9.02266 q^{79} -2.64538 q^{80} +14.7357 q^{81} -0.898028 q^{82} +1.16562 q^{83} -9.53568 q^{84} -8.00925 q^{85} -1.79099 q^{86} +31.3967 q^{87} -2.21532 q^{88} -15.4087 q^{89} -17.4532 q^{90} +11.8159 q^{91} -1.68937 q^{92} +20.9315 q^{93} +6.29459 q^{94} +3.78685 q^{95} -3.09800 q^{96} +8.67297 q^{97} +2.47415 q^{98} -14.6158 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) $ 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−3.09800	−1.78863	−0.894316	−	0.447435i	$-0.852337\pi$
$3$	−3.09800	−1.78863	−0.894316	+	0.447435i	$0.852337\pi$
$4$	1.00000	0.500000
$5$	−2.64538	−1.18305	−0.591525	−	0.806286i	$-0.701474\pi$
$5$	−2.64538	−1.18305	−0.591525	+	0.806286i	$0.701474\pi$
$6$	−3.09800	−1.26475
$7$	3.07801	1.16338	0.581689	−	0.813411i	$-0.302392\pi$
$7$	3.07801	1.16338	0.581689	+	0.813411i	$0.302392\pi$
$8$	1.00000	0.353553
$9$	6.59762	2.19921
$10$	−2.64538	−0.836543
$11$	−2.21532	−0.667944	−0.333972	−	0.942583i	$-0.608389\pi$
$11$	−2.21532	−0.667944	−0.333972	+	0.942583i	$0.608389\pi$
$12$	−3.09800	−0.894316
$13$	3.83880	1.06469	0.532346	−	0.846527i	$-0.321311\pi$
$13$	3.83880	1.06469	0.532346	+	0.846527i	$0.321311\pi$
$14$	3.07801	0.822633
$15$	8.19540	2.11604
$16$	1.00000	0.250000
$17$	3.02764	0.734310	0.367155	−	0.930160i	$-0.380332\pi$
$17$	3.02764	0.734310	0.367155	+	0.930160i	$0.380332\pi$
$18$	6.59762	1.55507
$19$	−1.43150	−0.328408	−0.164204	−	0.986426i	$-0.552505\pi$
$19$	−1.43150	−0.328408	−0.164204	+	0.986426i	$0.552505\pi$
$20$	−2.64538	−0.591525
$21$	−9.53568	−2.08086
$22$	−2.21532	−0.472308
$23$	−1.68937	−0.352258	−0.176129	−	0.984367i	$-0.556358\pi$
$23$	−1.68937	−0.352258	−0.176129	+	0.984367i	$0.556358\pi$
$24$	−3.09800	−0.632377
$25$	1.99804	0.399609
$26$	3.83880	0.752851
$27$	−11.1454	−2.14494
$28$	3.07801	0.581689
$29$	−10.1345	−1.88193	−0.940963	−	0.338508i	$-0.890078\pi$
$29$	−10.1345	−1.88193	−0.940963	+	0.338508i	$0.890078\pi$
$30$	8.19540	1.49627
$31$	−6.75644	−1.21349	−0.606746	−	0.794895i	$-0.707526\pi$
$31$	−6.75644	−1.21349	−0.606746	+	0.794895i	$0.707526\pi$
$32$	1.00000	0.176777
$33$	6.86307	1.19471
$34$	3.02764	0.519235
$35$	−8.14251	−1.37634
$36$	6.59762	1.09960
$37$	1.29634	0.213118	0.106559	−	0.994306i	$-0.466017\pi$
$37$	1.29634	0.213118	0.106559	+	0.994306i	$0.466017\pi$
$38$	−1.43150	−0.232219
$39$	−11.8926	−1.90434
$40$	−2.64538	−0.418272
$41$	−0.898028	−0.140248	−0.0701242	−	0.997538i	$-0.522340\pi$
$41$	−0.898028	−0.140248	−0.0701242	+	0.997538i	$0.522340\pi$
$42$	−9.53568	−1.47139
$43$	−1.79099	−0.273124	−0.136562	−	0.990632i	$-0.543605\pi$
$43$	−1.79099	−0.273124	−0.136562	+	0.990632i	$0.543605\pi$
$44$	−2.21532	−0.333972
$45$	−17.4532	−2.60177
$46$	−1.68937	−0.249084
$47$	6.29459	0.918160	0.459080	−	0.888395i	$-0.348179\pi$
$47$	6.29459	0.918160	0.459080	+	0.888395i	$0.348179\pi$
$48$	−3.09800	−0.447158
$49$	2.47415	0.353450
$50$	1.99804	0.282566
$51$	−9.37962	−1.31341
$52$	3.83880	0.532346
$53$	1.20789	0.165916	0.0829582	−	0.996553i	$-0.473563\pi$
$53$	1.20789	0.165916	0.0829582	+	0.996553i	$0.473563\pi$
$54$	−11.1454	−1.51670
$55$	5.86037	0.790212
$56$	3.07801	0.411316
$57$	4.43478	0.587401
$58$	−10.1345	−1.33072
$59$	5.14420	0.669717	0.334859	−	0.942268i	$-0.391311\pi$
$59$	5.14420	0.669717	0.334859	+	0.942268i	$0.391311\pi$
$60$	8.19540	1.05802
$61$	−3.71458	−0.475603	−0.237802	−	0.971314i	$-0.576427\pi$
$61$	−3.71458	−0.475603	−0.237802	+	0.971314i	$0.576427\pi$
$62$	−6.75644	−0.858069
$63$	20.3075	2.55851
$64$	1.00000	0.125000
$65$	−10.1551	−1.25958
$66$	6.86307	0.844785
$67$	12.9871	1.58663	0.793314	−	0.608812i	$-0.208354\pi$
$67$	12.9871	1.58663	0.793314	+	0.608812i	$0.208354\pi$
$68$	3.02764	0.367155
$69$	5.23367	0.630059
$70$	−8.14251	−0.973216
$71$	4.67918	0.555317	0.277658	−	0.960680i	$-0.410442\pi$
$71$	4.67918	0.555317	0.277658	+	0.960680i	$0.410442\pi$
$72$	6.59762	0.777537
$73$	0.143405	0.0167842	0.00839212	−	0.999965i	$-0.497329\pi$
$73$	0.143405	0.0167842	0.00839212	+	0.999965i	$0.497329\pi$
$74$	1.29634	0.150697
$75$	−6.18994	−0.714753
$76$	−1.43150	−0.164204
$77$	−6.81878	−0.777072
$78$	−11.8926	−1.34657
$79$	9.02266	1.01513	0.507564	−	0.861614i	$-0.330546\pi$
$79$	9.02266	1.01513	0.507564	+	0.861614i	$0.330546\pi$
$80$	−2.64538	−0.295763
$81$	14.7357	1.63730
$82$	−0.898028	−0.0991706
$83$	1.16562	0.127944	0.0639719	−	0.997952i	$-0.479623\pi$
$83$	1.16562	0.127944	0.0639719	+	0.997952i	$0.479623\pi$
$84$	−9.53568	−1.04043
$85$	−8.00925	−0.868725
$86$	−1.79099	−0.193128
$87$	31.3967	3.36608
$88$	−2.21532	−0.236154
$89$	−15.4087	−1.63332	−0.816658	−	0.577122i	$-0.804176\pi$
$89$	−15.4087	−1.63332	−0.816658	+	0.577122i	$0.804176\pi$
$90$	−17.4532	−1.83973
$91$	11.8159	1.23864
$92$	−1.68937	−0.176129
$93$	20.9315	2.17049
$94$	6.29459	0.649237
$95$	3.78685	0.388523
$96$	−3.09800	−0.316189
$97$	8.67297	0.880607	0.440303	−	0.897849i	$-0.354871\pi$
$97$	8.67297	0.880607	0.440303	+	0.897849i	$0.354871\pi$
$98$	2.47415	0.249927
$99$	−14.6158	−1.46895
$100$	1.99804	0.199804
$101$	−9.91404	−0.986484	−0.493242	−	0.869892i	$-0.664188\pi$
$101$	−9.91404	−0.986484	−0.493242	+	0.869892i	$0.664188\pi$
$102$	−9.37962	−0.928721
$103$	9.76468	0.962142	0.481071	−	0.876682i	$-0.340248\pi$
$103$	9.76468	0.962142	0.481071	+	0.876682i	$0.340248\pi$
$104$	3.83880	0.376425
$105$	25.2255	2.46176
$106$	1.20789	0.117321
$107$	−3.26718	−0.315850	−0.157925	−	0.987451i	$-0.550480\pi$
$107$	−3.26718	−0.315850	−0.157925	+	0.987451i	$0.550480\pi$
$108$	−11.1454	−1.07247
$109$	−1.78608	−0.171076	−0.0855379	−	0.996335i	$-0.527261\pi$
$109$	−1.78608	−0.171076	−0.0855379	+	0.996335i	$0.527261\pi$
$110$	5.86037	0.558764
$111$	−4.01608	−0.381189
$112$	3.07801	0.290845
$113$	3.16696	0.297923	0.148961	−	0.988843i	$-0.452407\pi$
$113$	3.16696	0.297923	0.148961	+	0.988843i	$0.452407\pi$
$114$	4.43478	0.415355
$115$	4.46902	0.416739
$116$	−10.1345	−0.940963
$117$	25.3269	2.34148
$118$	5.14420	0.473562
$119$	9.31910	0.854280
$120$	8.19540	0.748134
$121$	−6.09236	−0.553851
$122$	−3.71458	−0.336302
$123$	2.78209	0.250853
$124$	−6.75644	−0.606746
$125$	7.94132	0.710293
$126$	20.3075	1.80914
$127$	−6.81761	−0.604965	−0.302482	−	0.953155i	$-0.597815\pi$
$127$	−6.81761	−0.604965	−0.302482	+	0.953155i	$0.597815\pi$
$128$	1.00000	0.0883883
$129$	5.54849	0.488518
$130$	−10.1551	−0.890661
$131$	−8.77340	−0.766536	−0.383268	−	0.923637i	$-0.625201\pi$
$131$	−8.77340	−0.766536	−0.383268	+	0.923637i	$0.625201\pi$
$132$	6.86307	0.597353
$133$	−4.40616	−0.382062
$134$	12.9871	1.12192
$135$	29.4839	2.53757
$136$	3.02764	0.259618
$137$	3.48026	0.297339	0.148669	−	0.988887i	$-0.452501\pi$
$137$	3.48026	0.297339	0.148669	+	0.988887i	$0.452501\pi$
$138$	5.23367	0.445519
$139$	−8.89572	−0.754525	−0.377262	−	0.926106i	$-0.623135\pi$
$139$	−8.89572	−0.754525	−0.377262	+	0.926106i	$0.623135\pi$
$140$	−8.14251	−0.688168
$141$	−19.5006	−1.64225
$142$	4.67918	0.392668
$143$	−8.50417	−0.711155
$144$	6.59762	0.549802
$145$	26.8096	2.22641
$146$	0.143405	0.0118683
$147$	−7.66491	−0.632191
$148$	1.29634	0.106559
$149$	−0.764322	−0.0626157	−0.0313078	−	0.999510i	$-0.509967\pi$
$149$	−0.764322	−0.0626157	−0.0313078	+	0.999510i	$0.509967\pi$
$150$	−6.18994	−0.505407
$151$	17.3450	1.41152	0.705758	−	0.708453i	$-0.250606\pi$
$151$	17.3450	1.41152	0.705758	+	0.708453i	$0.250606\pi$
$152$	−1.43150	−0.116110
$153$	19.9752	1.61490
$154$	−6.81878	−0.549473
$155$	17.8734	1.43562
$156$	−11.8926	−0.952171
$157$	−15.4446	−1.23262	−0.616308	−	0.787505i	$-0.711372\pi$
$157$	−15.4446	−1.23262	−0.616308	+	0.787505i	$0.711372\pi$
$158$	9.02266	0.717804
$159$	−3.74205	−0.296764
$160$	−2.64538	−0.209136
$161$	−5.19989	−0.409809
$162$	14.7357	1.15775
$163$	−14.3399	−1.12319	−0.561595	−	0.827412i	$-0.689812\pi$
$163$	−14.3399	−1.12319	−0.561595	+	0.827412i	$0.689812\pi$
$164$	−0.898028	−0.0701242
$165$	−18.1554	−1.41340
$166$	1.16562	0.0904700
$167$	−3.33399	−0.257992	−0.128996	−	0.991645i	$-0.541175\pi$
$167$	−3.33399	−0.257992	−0.128996	+	0.991645i	$0.541175\pi$
$168$	−9.53568	−0.735694
$169$	1.73639	0.133569
$170$	−8.00925	−0.614282
$171$	−9.44446	−0.722236
$172$	−1.79099	−0.136562
$173$	−18.9082	−1.43756	−0.718781	−	0.695237i	$-0.755300\pi$
$173$	−18.9082	−1.43756	−0.718781	+	0.695237i	$0.755300\pi$
$174$	31.3967	2.38017
$175$	6.15000	0.464896
$176$	−2.21532	−0.166986
$177$	−15.9367	−1.19788
$178$	−15.4087	−1.15493
$179$	−4.73487	−0.353901	−0.176950	−	0.984220i	$-0.556623\pi$
$179$	−4.73487	−0.353901	−0.176950	+	0.984220i	$0.556623\pi$
$180$	−17.4532	−1.30089
$181$	−14.5692	−1.08292	−0.541462	−	0.840725i	$-0.682129\pi$
$181$	−14.5692	−1.08292	−0.541462	+	0.840725i	$0.682129\pi$
$182$	11.8159	0.875850
$183$	11.5078	0.850679
$184$	−1.68937	−0.124542
$185$	−3.42932	−0.252129
$186$	20.9315	1.53477
$187$	−6.70718	−0.490478
$188$	6.29459	0.459080
$189$	−34.3057	−2.49538
$190$	3.78685	0.274727
$191$	−12.7519	−0.922693	−0.461347	−	0.887220i	$-0.652634\pi$
$191$	−12.7519	−0.922693	−0.461347	+	0.887220i	$0.652634\pi$
$192$	−3.09800	−0.223579
$193$	19.8366	1.42787	0.713936	−	0.700211i	$-0.246911\pi$
$193$	19.8366	1.42787	0.713936	+	0.700211i	$0.246911\pi$
$194$	8.67297	0.622683
$195$	31.4605	2.25293
$196$	2.47415	0.176725
$197$	13.0385	0.928952	0.464476	−	0.885586i	$-0.346243\pi$
$197$	13.0385	0.928952	0.464476	+	0.885586i	$0.346243\pi$
$198$	−14.6158	−1.03870
$199$	−15.4703	−1.09666	−0.548331	−	0.836262i	$-0.684737\pi$
$199$	−15.4703	−1.09666	−0.548331	+	0.836262i	$0.684737\pi$
$200$	1.99804	0.141283
$201$	−40.2341	−2.83790
$202$	−9.91404	−0.697549
$203$	−31.1940	−2.18939
$204$	−9.37962	−0.656705
$205$	2.37563	0.165921
$206$	9.76468	0.680337
$207$	−11.1458	−0.774687
$208$	3.83880	0.266173
$209$	3.17122	0.219358
$210$	25.2255	1.74073
$211$	19.2436	1.32478	0.662391	−	0.749158i	$-0.269542\pi$
$211$	19.2436	1.32478	0.662391	+	0.749158i	$0.269542\pi$
$212$	1.20789	0.0829582
$213$	−14.4961	−0.993258
$214$	−3.26718	−0.223340
$215$	4.73785	0.323119
$216$	−11.1454	−0.758350
$217$	−20.7964	−1.41175
$218$	−1.78608	−0.120969
$219$	−0.444268	−0.0300208
$220$	5.86037	0.395106
$221$	11.6225	0.781814
$222$	−4.01608	−0.269541
$223$	5.47567	0.366678	0.183339	−	0.983050i	$-0.441309\pi$
$223$	5.47567	0.366678	0.183339	+	0.983050i	$0.441309\pi$
$224$	3.07801	0.205658
$225$	13.1823	0.878822
$226$	3.16696	0.210663
$227$	−4.52193	−0.300131	−0.150066	−	0.988676i	$-0.547949\pi$
$227$	−4.52193	−0.300131	−0.150066	+	0.988676i	$0.547949\pi$
$228$	4.43478	0.293700
$229$	−0.880741	−0.0582010	−0.0291005	−	0.999576i	$-0.509264\pi$
$229$	−0.880741	−0.0582010	−0.0291005	+	0.999576i	$0.509264\pi$
$230$	4.46902	0.294679
$231$	21.1246	1.38990
$232$	−10.1345	−0.665362
$233$	23.6779	1.55119	0.775596	−	0.631229i	$-0.217449\pi$
$233$	23.6779	1.55119	0.775596	+	0.631229i	$0.217449\pi$
$234$	25.3269	1.65567
$235$	−16.6516	−1.08623
$236$	5.14420	0.334859
$237$	−27.9522	−1.81569
$238$	9.31910	0.604067
$239$	−6.06478	−0.392298	−0.196149	−	0.980574i	$-0.562844\pi$
$239$	−6.06478	−0.392298	−0.196149	+	0.980574i	$0.562844\pi$
$240$	8.19540	0.529011
$241$	−18.2169	−1.17346	−0.586728	−	0.809784i	$-0.699584\pi$
$241$	−18.2169	−1.17346	−0.586728	+	0.809784i	$0.699584\pi$
$242$	−6.09236	−0.391631
$243$	−12.2150	−0.783591
$244$	−3.71458	−0.237802
$245$	−6.54506	−0.418149
$246$	2.78209	0.177380
$247$	−5.49523	−0.349653
$248$	−6.75644	−0.429034
$249$	−3.61111	−0.228845
$250$	7.94132	0.502253
$251$	−16.1799	−1.02126	−0.510632	−	0.859800i	$-0.670588\pi$
$251$	−16.1799	−1.02126	−0.510632	+	0.859800i	$0.670588\pi$
$252$	20.3075	1.27925
$253$	3.74249	0.235288
$254$	−6.81761	−0.427775
$255$	24.8127	1.55383
$256$	1.00000	0.0625000
$257$	−20.5296	−1.28060	−0.640301	−	0.768124i	$-0.721191\pi$
$257$	−20.5296	−1.28060	−0.640301	+	0.768124i	$0.721191\pi$
$258$	5.54849	0.345434
$259$	3.99016	0.247936
$260$	−10.1551	−0.629792
$261$	−66.8635	−4.13874
$262$	−8.77340	−0.542023
$263$	14.9555	0.922193	0.461096	−	0.887350i	$-0.347456\pi$
$263$	14.9555	0.922193	0.461096	+	0.887350i	$0.347456\pi$
$264$	6.86307	0.422393
$265$	−3.19533	−0.196288
$266$	−4.40616	−0.270159
$267$	47.7361	2.92140
$268$	12.9871	0.793314
$269$	−19.7665	−1.20519	−0.602593	−	0.798049i	$-0.705866\pi$
$269$	−19.7665	−1.20519	−0.602593	+	0.798049i	$0.705866\pi$
$270$	29.4839	1.79433
$271$	6.34465	0.385410	0.192705	−	0.981257i	$-0.438274\pi$
$271$	6.34465	0.385410	0.192705	+	0.981257i	$0.438274\pi$
$272$	3.02764	0.183577
$273$	−36.6056	−2.21547
$274$	3.48026	0.210250
$275$	−4.42631	−0.266916
$276$	5.23367	0.315030
$277$	2.95981	0.177838	0.0889189	−	0.996039i	$-0.471659\pi$
$277$	2.95981	0.177838	0.0889189	+	0.996039i	$0.471659\pi$
$278$	−8.89572	−0.533530
$279$	−44.5764	−2.66872
$280$	−8.14251	−0.486608
$281$	−3.84944	−0.229638	−0.114819	−	0.993386i	$-0.536629\pi$
$281$	−3.84944	−0.229638	−0.114819	+	0.993386i	$0.536629\pi$
$282$	−19.5006	−1.16125
$283$	5.16757	0.307180	0.153590	−	0.988135i	$-0.450916\pi$
$283$	5.16757	0.307180	0.153590	+	0.988135i	$0.450916\pi$
$284$	4.67918	0.277658
$285$	−11.7317	−0.694925
$286$	−8.50417	−0.502862
$287$	−2.76414	−0.163162
$288$	6.59762	0.388768
$289$	−7.83342	−0.460789
$290$	26.8096	1.57431
$291$	−26.8689	−1.57508
$292$	0.143405	0.00839212
$293$	−17.0851	−0.998121	−0.499060	−	0.866567i	$-0.666321\pi$
$293$	−17.0851	−0.998121	−0.499060	+	0.866567i	$0.666321\pi$
$294$	−7.66491	−0.447027
$295$	−13.6084	−0.792309
$296$	1.29634	0.0753484
$297$	24.6907	1.43270
$298$	−0.764322	−0.0442760
$299$	−6.48515	−0.375046
$300$	−6.18994	−0.357377
$301$	−5.51269	−0.317746
$302$	17.3450	0.998093
$303$	30.7137	1.76446
$304$	−1.43150	−0.0821019
$305$	9.82648	0.562662
$306$	19.9752	1.14191
$307$	0.190275	0.0108596	0.00542978	−	0.999985i	$-0.498272\pi$
$307$	0.190275	0.0108596	0.00542978	+	0.999985i	$0.498272\pi$
$308$	−6.81878	−0.388536
$309$	−30.2510	−1.72092
$310$	17.8734	1.01514
$311$	−17.7303	−1.00539	−0.502695	−	0.864464i	$-0.667658\pi$
$311$	−17.7303	−1.00539	−0.502695	+	0.864464i	$0.667658\pi$
$312$	−11.8926	−0.673287
$313$	30.6130	1.73035	0.865175	−	0.501470i	$-0.167207\pi$
$313$	30.6130	1.73035	0.865175	+	0.501470i	$0.167207\pi$
$314$	−15.4446	−0.871591
$315$	−53.7212	−3.02685
$316$	9.02266	0.507564
$317$	−31.6948	−1.78016	−0.890080	−	0.455804i	$-0.849352\pi$
$317$	−31.6948	−1.78016	−0.890080	+	0.455804i	$0.849352\pi$
$318$	−3.74205	−0.209843
$319$	22.4511	1.25702
$320$	−2.64538	−0.147881
$321$	10.1217	0.564940
$322$	−5.19989	−0.289779
$323$	−4.33405	−0.241153
$324$	14.7357	0.818651
$325$	7.67009	0.425460
$326$	−14.3399	−0.794215
$327$	5.53329	0.305992
$328$	−0.898028	−0.0495853
$329$	19.3748	1.06817
$330$	−18.1554	−0.999424
$331$	25.3499	1.39336	0.696678	−	0.717384i	$-0.254661\pi$
$331$	25.3499	1.39336	0.696678	+	0.717384i	$0.254661\pi$
$332$	1.16562	0.0639719
$333$	8.55278	0.468689
$334$	−3.33399	−0.182428
$335$	−34.3559	−1.87706
$336$	−9.53568	−0.520214
$337$	−29.2304	−1.59228	−0.796140	−	0.605113i	$-0.793128\pi$
$337$	−29.2304	−1.59228	−0.796140	+	0.605113i	$0.793128\pi$
$338$	1.73639	0.0944474
$339$	−9.81126	−0.532874
$340$	−8.00925	−0.434363
$341$	14.9677	0.810545
$342$	−9.44446	−0.510698
$343$	−13.9306	−0.752183
$344$	−1.79099	−0.0965638
$345$	−13.8450	−0.745392
$346$	−18.9082	−1.01651
$347$	−7.35068	−0.394605	−0.197303	−	0.980343i	$-0.563218\pi$
$347$	−7.35068	−0.394605	−0.197303	+	0.980343i	$0.563218\pi$
$348$	31.3967	1.68304
$349$	−2.43187	−0.130175	−0.0650876	−	0.997880i	$-0.520733\pi$
$349$	−2.43187	−0.130175	−0.0650876	+	0.997880i	$0.520733\pi$
$350$	6.15000	0.328731
$351$	−42.7851	−2.28370
$352$	−2.21532	−0.118077
$353$	−1.05006	−0.0558890	−0.0279445	−	0.999609i	$-0.508896\pi$
$353$	−1.05006	−0.0558890	−0.0279445	+	0.999609i	$0.508896\pi$
$354$	−15.9367	−0.847028
$355$	−12.3782	−0.656968
$356$	−15.4087	−0.816658
$357$	−28.8706	−1.52799
$358$	−4.73487	−0.250246
$359$	−8.54944	−0.451222	−0.225611	−	0.974217i	$-0.572438\pi$
$359$	−8.54944	−0.451222	−0.225611	+	0.974217i	$0.572438\pi$
$360$	−17.4532	−0.919865
$361$	−16.9508	−0.892148
$362$	−14.5692	−0.765742
$363$	18.8741	0.990635
$364$	11.8159	0.619320
$365$	−0.379360	−0.0198566
$366$	11.5078	0.601521
$367$	−10.4636	−0.546197	−0.273099	−	0.961986i	$-0.588049\pi$
$367$	−10.4636	−0.546197	−0.273099	+	0.961986i	$0.588049\pi$
$368$	−1.68937	−0.0880644
$369$	−5.92484	−0.308435
$370$	−3.42932	−0.178282
$371$	3.71790	0.193024
$372$	20.9315	1.08525
$373$	14.8133	0.767002	0.383501	−	0.923540i	$-0.374718\pi$
$373$	14.8133	0.767002	0.383501	+	0.923540i	$0.374718\pi$
$374$	−6.70718	−0.346820
$375$	−24.6022	−1.27045
$376$	6.29459	0.324618
$377$	−38.9043	−2.00367
$378$	−34.3057	−1.76450
$379$	−14.6830	−0.754215	−0.377108	−	0.926169i	$-0.623081\pi$
$379$	−14.6830	−0.754215	−0.377108	+	0.926169i	$0.623081\pi$
$380$	3.78685	0.194261
$381$	21.1210	1.08206
$382$	−12.7519	−0.652443
$383$	−6.26003	−0.319872	−0.159936	−	0.987127i	$-0.551129\pi$
$383$	−6.26003	−0.319872	−0.159936	+	0.987127i	$0.551129\pi$
$384$	−3.09800	−0.158094
$385$	18.0383	0.919315
$386$	19.8366	1.00966
$387$	−11.8163	−0.600655
$388$	8.67297	0.440303
$389$	−3.62073	−0.183578	−0.0917892	−	0.995778i	$-0.529259\pi$
$389$	−3.62073	−0.183578	−0.0917892	+	0.995778i	$0.529259\pi$
$390$	31.4605	1.59306
$391$	−5.11479	−0.258666
$392$	2.47415	0.124963
$393$	27.1800	1.37105
$394$	13.0385	0.656869
$395$	−23.8684	−1.20095
$396$	−14.6158	−0.734473
$397$	22.6882	1.13869	0.569343	−	0.822100i	$-0.307198\pi$
$397$	22.6882	1.13869	0.569343	+	0.822100i	$0.307198\pi$
$398$	−15.4703	−0.775457
$399$	13.6503	0.683369
$400$	1.99804	0.0999022
$401$	9.17077	0.457966	0.228983	−	0.973430i	$-0.426460\pi$
$401$	9.17077	0.457966	0.228983	+	0.973430i	$0.426460\pi$
$402$	−40.2341	−2.00669
$403$	−25.9366	−1.29200
$404$	−9.91404	−0.493242
$405$	−38.9816	−1.93701
$406$	−31.1940	−1.54813
$407$	−2.87182	−0.142351
$408$	−9.37962	−0.464361
$409$	−10.1575	−0.502257	−0.251129	−	0.967954i	$-0.580802\pi$
$409$	−10.1575	−0.502257	−0.251129	+	0.967954i	$0.580802\pi$
$410$	2.37563	0.117324
$411$	−10.7819	−0.531830
$412$	9.76468	0.481071
$413$	15.8339	0.779135
$414$	−11.1458	−0.547786
$415$	−3.08352	−0.151364
$416$	3.83880	0.188213
$417$	27.5590	1.34957
$418$	3.17122	0.155110
$419$	−18.3235	−0.895160	−0.447580	−	0.894244i	$-0.647714\pi$
$419$	−18.3235	−0.895160	−0.447580	+	0.894244i	$0.647714\pi$
$420$	25.2255	1.23088
$421$	4.48495	0.218583	0.109291	−	0.994010i	$-0.465142\pi$
$421$	4.48495	0.218583	0.109291	+	0.994010i	$0.465142\pi$
$422$	19.2436	0.936763
$423$	41.5293	2.01922
$424$	1.20789	0.0586603
$425$	6.04935	0.293437
$426$	−14.4961	−0.702339
$427$	−11.4335	−0.553306
$428$	−3.26718	−0.157925
$429$	26.3459	1.27199
$430$	4.73785	0.228480
$431$	17.7456	0.854774	0.427387	−	0.904069i	$-0.359434\pi$
$431$	17.7456	0.854774	0.427387	+	0.904069i	$0.359434\pi$
$432$	−11.1454	−0.536235
$433$	−22.9322	−1.10205	−0.551026	−	0.834488i	$-0.685764\pi$
$433$	−22.9322	−1.10205	−0.551026	+	0.834488i	$0.685764\pi$
$434$	−20.7964	−0.998259
$435$	−83.0561	−3.98224
$436$	−1.78608	−0.0855379
$437$	2.41832	0.115684
$438$	−0.444268	−0.0212279
$439$	4.53752	0.216564	0.108282	−	0.994120i	$-0.465465\pi$
$439$	4.53752	0.216564	0.108282	+	0.994120i	$0.465465\pi$
$440$	5.86037	0.279382
$441$	16.3235	0.777308
$442$	11.6225	0.552826
$443$	8.15917	0.387654	0.193827	−	0.981036i	$-0.437910\pi$
$443$	8.15917	0.387654	0.193827	+	0.981036i	$0.437910\pi$
$444$	−4.01608	−0.190595
$445$	40.7618	1.93230
$446$	5.47567	0.259281
$447$	2.36787	0.111996
$448$	3.07801	0.145422
$449$	−15.4823	−0.730653	−0.365327	−	0.930879i	$-0.619043\pi$
$449$	−15.4823	−0.730653	−0.365327	+	0.930879i	$0.619043\pi$
$450$	13.1823	0.621421
$451$	1.98942	0.0936781
$452$	3.16696	0.148961
$453$	−53.7349	−2.52468
$454$	−4.52193	−0.212225
$455$	−31.2575	−1.46537
$456$	4.43478	0.207678
$457$	3.48455	0.163000	0.0815002	−	0.996673i	$-0.474029\pi$
$457$	3.48455	0.163000	0.0815002	+	0.996673i	$0.474029\pi$
$458$	−0.880741	−0.0411543
$459$	−33.7443	−1.57505
$460$	4.46902	0.208369
$461$	23.8020	1.10857	0.554284	−	0.832327i	$-0.312992\pi$
$461$	23.8020	1.10857	0.554284	+	0.832327i	$0.312992\pi$
$462$	21.1246	0.982805
$463$	30.6752	1.42560	0.712798	−	0.701369i	$-0.247428\pi$
$463$	30.6752	1.42560	0.712798	+	0.701369i	$0.247428\pi$
$464$	−10.1345	−0.470482
$465$	−55.3717	−2.56780
$466$	23.6779	1.09686
$467$	10.9114	0.504921	0.252461	−	0.967607i	$-0.418760\pi$
$467$	10.9114	0.504921	0.252461	+	0.967607i	$0.418760\pi$
$468$	25.3269	1.17074
$469$	39.9745	1.84585
$470$	−16.6516	−0.768080
$471$	47.8475	2.20470
$472$	5.14420	0.236781
$473$	3.96762	0.182431
$474$	−27.9522	−1.28389
$475$	−2.86019	−0.131235
$476$	9.31910	0.427140
$477$	7.96920	0.364884
$478$	−6.06478	−0.277397
$479$	16.6553	0.760999	0.380500	−	0.924781i	$-0.375752\pi$
$479$	16.6553	0.760999	0.380500	+	0.924781i	$0.375752\pi$
$480$	8.19540	0.374067
$481$	4.97641	0.226905
$482$	−18.2169	−0.829759
$483$	16.1093	0.732997
$484$	−6.09236	−0.276925
$485$	−22.9433	−1.04180
$486$	−12.2150	−0.554083
$487$	−6.46773	−0.293081	−0.146540	−	0.989205i	$-0.546814\pi$
$487$	−6.46773	−0.293081	−0.146540	+	0.989205i	$0.546814\pi$
$488$	−3.71458	−0.168151
$489$	44.4251	2.00897
$490$	−6.54506	−0.295676
$491$	−19.4399	−0.877312	−0.438656	−	0.898655i	$-0.644545\pi$
$491$	−19.4399	−0.877312	−0.438656	+	0.898655i	$0.644545\pi$
$492$	2.78209	0.125426
$493$	−30.6835	−1.38192
$494$	−5.49523	−0.247242
$495$	38.6645	1.73784
$496$	−6.75644	−0.303373
$497$	14.4026	0.646044
$498$	−3.61111	−0.161818
$499$	1.83225	0.0820226	0.0410113	−	0.999159i	$-0.486942\pi$
$499$	1.83225	0.0820226	0.0410113	+	0.999159i	$0.486942\pi$
$500$	7.94132	0.355147
$501$	10.3287	0.461452
$502$	−16.1799	−0.722142
$503$	20.7889	0.926932	0.463466	−	0.886115i	$-0.346606\pi$
$503$	20.7889	0.926932	0.463466	+	0.886115i	$0.346606\pi$
$504$	20.3075	0.904570
$505$	26.2264	1.16706
$506$	3.74249	0.166374
$507$	−5.37935	−0.238905
$508$	−6.81761	−0.302482
$509$	8.26477	0.366330	0.183165	−	0.983082i	$-0.441366\pi$
$509$	8.26477	0.366330	0.183165	+	0.983082i	$0.441366\pi$
$510$	24.8127	1.09872
$511$	0.441401	0.0195264
$512$	1.00000	0.0441942
$513$	15.9546	0.704414
$514$	−20.5296	−0.905523
$515$	−25.8313	−1.13826
$516$	5.54849	0.244259
$517$	−13.9445	−0.613279
$518$	3.99016	0.175318
$519$	58.5776	2.57127
$520$	−10.1551	−0.445330
$521$	18.5716	0.813635	0.406818	−	0.913509i	$-0.366638\pi$
$521$	18.5716	0.813635	0.406818	+	0.913509i	$0.366638\pi$
$522$	−66.8635	−2.92653
$523$	34.7737	1.52055	0.760275	−	0.649601i	$-0.225064\pi$
$523$	34.7737	1.52055	0.760275	+	0.649601i	$0.225064\pi$
$524$	−8.77340	−0.383268
$525$	−19.0527	−0.831528
$526$	14.9555	0.652089
$527$	−20.4560	−0.891079
$528$	6.86307	0.298677
$529$	−20.1460	−0.875915
$530$	−3.19533	−0.138796
$531$	33.9394	1.47285
$532$	−4.40616	−0.191031
$533$	−3.44735	−0.149321
$534$	47.7361	2.06574
$535$	8.64294	0.373667
$536$	12.9871	0.560958
$537$	14.6686	0.632998
$538$	−19.7665	−0.852196
$539$	−5.48103	−0.236085
$540$	29.4839	1.26879
$541$	30.7539	1.32221	0.661107	−	0.750292i	$-0.270087\pi$
$541$	30.7539	1.32221	0.661107	+	0.750292i	$0.270087\pi$
$542$	6.34465	0.272526
$543$	45.1356	1.93695
$544$	3.02764	0.129809
$545$	4.72488	0.202391
$546$	−36.6056	−1.56657
$547$	1.70461	0.0728840	0.0364420	−	0.999336i	$-0.488398\pi$
$547$	1.70461	0.0728840	0.0364420	+	0.999336i	$0.488398\pi$
$548$	3.48026	0.148669
$549$	−24.5074	−1.04595
$550$	−4.42631	−0.188738
$551$	14.5075	0.618039
$552$	5.23367	0.222760
$553$	27.7718	1.18098
$554$	2.95981	0.125750
$555$	10.6241	0.450966
$556$	−8.89572	−0.377262
$557$	−10.6522	−0.451349	−0.225675	−	0.974203i	$-0.572459\pi$
$557$	−10.6522	−0.451349	−0.225675	+	0.974203i	$0.572459\pi$
$558$	−44.5764	−1.88707
$559$	−6.87526	−0.290792
$560$	−8.14251	−0.344084
$561$	20.7789	0.877285
$562$	−3.84944	−0.162379
$563$	−43.3181	−1.82564	−0.912820	−	0.408362i	$-0.866100\pi$
$563$	−43.3181	−1.82564	−0.912820	+	0.408362i	$0.866100\pi$
$564$	−19.5006	−0.821125
$565$	−8.37783	−0.352458
$566$	5.16757	0.217209
$567$	45.3567	1.90480
$568$	4.67918	0.196334
$569$	13.8179	0.579277	0.289639	−	0.957136i	$-0.406465\pi$
$569$	13.8179	0.579277	0.289639	+	0.957136i	$0.406465\pi$
$570$	−11.7317	−0.491386
$571$	−8.70415	−0.364257	−0.182129	−	0.983275i	$-0.558299\pi$
$571$	−8.70415	−0.364257	−0.182129	+	0.983275i	$0.558299\pi$
$572$	−8.50417	−0.355577
$573$	39.5053	1.65036
$574$	−2.76414	−0.115373
$575$	−3.37543	−0.140765
$576$	6.59762	0.274901
$577$	−34.0580	−1.41785	−0.708926	−	0.705283i	$-0.750820\pi$
$577$	−34.0580	−1.41785	−0.708926	+	0.705283i	$0.750820\pi$
$578$	−7.83342	−0.325827
$579$	−61.4540	−2.55394
$580$	26.8096	1.11321
$581$	3.58780	0.148847
$582$	−26.8689	−1.11375
$583$	−2.67586	−0.110823
$584$	0.143405	0.00593413
$585$	−66.9994	−2.77009
$586$	−17.0851	−0.705778
$587$	−18.7402	−0.773492	−0.386746	−	0.922186i	$-0.626401\pi$
$587$	−18.7402	−0.773492	−0.386746	+	0.922186i	$0.626401\pi$
$588$	−7.66491	−0.316096
$589$	9.67182	0.398520
$590$	−13.6084	−0.560247
$591$	−40.3932	−1.66155
$592$	1.29634	0.0532794
$593$	27.5562	1.13160	0.565798	−	0.824544i	$-0.308568\pi$
$593$	27.5562	1.13160	0.565798	+	0.824544i	$0.308568\pi$
$594$	24.6907	1.01307
$595$	−24.6526	−1.01066
$596$	−0.764322	−0.0313078
$597$	47.9271	1.96152
$598$	−6.48515	−0.265197
$599$	−8.96083	−0.366130	−0.183065	−	0.983101i	$-0.558602\pi$
$599$	−8.96083	−0.366130	−0.183065	+	0.983101i	$0.558602\pi$
$600$	−6.18994	−0.252703
$601$	−29.3653	−1.19783	−0.598917	−	0.800811i	$-0.704402\pi$
$601$	−29.3653	−1.19783	−0.598917	+	0.800811i	$0.704402\pi$
$602$	−5.51269	−0.224680
$603$	85.6840	3.48932
$604$	17.3450	0.705758
$605$	16.1166	0.655233
$606$	30.7137	1.24766
$607$	−9.28330	−0.376797	−0.188399	−	0.982093i	$-0.560330\pi$
$607$	−9.28330	−0.376797	−0.188399	+	0.982093i	$0.560330\pi$
$608$	−1.43150	−0.0580548
$609$	96.6392	3.91602
$610$	9.82648	0.397862
$611$	24.1637	0.977557
$612$	19.9752	0.807449
$613$	4.85967	0.196280	0.0981402	−	0.995173i	$-0.468711\pi$
$613$	4.85967	0.196280	0.0981402	+	0.995173i	$0.468711\pi$
$614$	0.190275	0.00767886
$615$	−7.35970	−0.296772
$616$	−6.81878	−0.274736
$617$	−24.5197	−0.987128	−0.493564	−	0.869710i	$-0.664306\pi$
$617$	−24.5197	−0.987128	−0.493564	+	0.869710i	$0.664306\pi$
$618$	−30.2510	−1.21687
$619$	−47.8048	−1.92144	−0.960718	−	0.277528i	$-0.910485\pi$
$619$	−47.8048	−1.92144	−0.960718	+	0.277528i	$0.910485\pi$
$620$	17.8734	0.717812
$621$	18.8287	0.755571
$622$	−17.7303	−0.710919
$623$	−47.4281	−1.90017
$624$	−11.8926	−0.476086
$625$	−30.9980	−1.23992
$626$	30.6130	1.22354
$627$	−9.82445	−0.392351
$628$	−15.4446	−0.616308
$629$	3.92486	0.156494
$630$	−53.7212	−2.14030
$631$	−40.4150	−1.60890	−0.804449	−	0.594022i	$-0.797539\pi$
$631$	−40.4150	−1.60890	−0.804449	+	0.594022i	$0.797539\pi$
$632$	9.02266	0.358902
$633$	−59.6166	−2.36955
$634$	−31.6948	−1.25876
$635$	18.0352	0.715704
$636$	−3.74205	−0.148382
$637$	9.49776	0.376315
$638$	22.4511	0.888849
$639$	30.8715	1.22126
$640$	−2.64538	−0.104568
$641$	−46.6431	−1.84229	−0.921146	−	0.389217i	$-0.872746\pi$
$641$	−46.6431	−1.84229	−0.921146	+	0.389217i	$0.872746\pi$
$642$	10.1217	0.399473
$643$	33.0587	1.30371	0.651855	−	0.758344i	$-0.273991\pi$
$643$	33.0587	1.30371	0.651855	+	0.758344i	$0.273991\pi$
$644$	−5.19989	−0.204904
$645$	−14.6779	−0.577941
$646$	−4.33405	−0.170521
$647$	−20.8734	−0.820618	−0.410309	−	0.911947i	$-0.634579\pi$
$647$	−20.8734	−0.820618	−0.410309	+	0.911947i	$0.634579\pi$
$648$	14.7357	0.578873
$649$	−11.3960	−0.447334
$650$	7.67009	0.300846
$651$	64.4273	2.52510
$652$	−14.3399	−0.561595
$653$	11.1065	0.434632	0.217316	−	0.976101i	$-0.430270\pi$
$653$	11.1065	0.434632	0.217316	+	0.976101i	$0.430270\pi$
$654$	5.53329	0.216369
$655$	23.2090	0.906850
$656$	−0.898028	−0.0350621
$657$	0.946129	0.0369120
$658$	19.3748	0.755308
$659$	−27.0585	−1.05405	−0.527026	−	0.849849i	$-0.676693\pi$
$659$	−27.0585	−1.05405	−0.527026	+	0.849849i	$0.676693\pi$
$660$	−18.1554	−0.706699
$661$	9.69117	0.376943	0.188471	−	0.982079i	$-0.439647\pi$
$661$	9.69117	0.376943	0.188471	+	0.982079i	$0.439647\pi$
$662$	25.3499	0.985252
$663$	−36.0065	−1.39838
$664$	1.16562	0.0452350
$665$	11.6560	0.451999
$666$	8.55278	0.331414
$667$	17.1209	0.662923
$668$	−3.33399	−0.128996
$669$	−16.9636	−0.655852
$670$	−34.3559	−1.32728
$671$	8.22898	0.317676
$672$	−9.53568	−0.367847
$673$	−30.9230	−1.19199	−0.595996	−	0.802987i	$-0.703243\pi$
$673$	−30.9230	−1.19199	−0.595996	+	0.802987i	$0.703243\pi$
$674$	−29.2304	−1.12591
$675$	−22.2691	−0.857136
$676$	1.73639	0.0667844
$677$	−39.9586	−1.53573	−0.767867	−	0.640610i	$-0.778682\pi$
$677$	−39.9586	−1.53573	−0.767867	+	0.640610i	$0.778682\pi$
$678$	−9.81126	−0.376799
$679$	26.6955	1.02448
$680$	−8.00925	−0.307141
$681$	14.0090	0.536825
$682$	14.9677	0.573142
$683$	−27.0331	−1.03439	−0.517197	−	0.855867i	$-0.673024\pi$
$683$	−27.0331	−1.03439	−0.517197	+	0.855867i	$0.673024\pi$
$684$	−9.44446	−0.361118
$685$	−9.20662	−0.351767
$686$	−13.9306	−0.531874
$687$	2.72854	0.104100
$688$	−1.79099	−0.0682809
$689$	4.63685	0.176650
$690$	−13.8450	−0.527072
$691$	21.2382	0.807941	0.403970	−	0.914772i	$-0.367630\pi$
$691$	21.2382	0.807941	0.403970	+	0.914772i	$0.367630\pi$
$692$	−18.9082	−0.718781
$693$	−44.9877	−1.70894
$694$	−7.35068	−0.279028
$695$	23.5326	0.892641
$696$	31.3967	1.19009
$697$	−2.71890	−0.102986
$698$	−2.43187	−0.0920478
$699$	−73.3543	−2.77451
$700$	6.15000	0.232448
$701$	1.88429	0.0711687	0.0355844	−	0.999367i	$-0.488671\pi$
$701$	1.88429	0.0711687	0.0355844	+	0.999367i	$0.488671\pi$
$702$	−42.7851	−1.61482
$703$	−1.85571	−0.0699895
$704$	−2.21532	−0.0834930
$705$	51.5866	1.94286
$706$	−1.05006	−0.0395195
$707$	−30.5155	−1.14765
$708$	−15.9367	−0.598939
$709$	5.99391	0.225106	0.112553	−	0.993646i	$-0.464097\pi$
$709$	5.99391	0.225106	0.112553	+	0.993646i	$0.464097\pi$
$710$	−12.3782	−0.464546
$711$	59.5280	2.23248
$712$	−15.4087	−0.577465
$713$	11.4141	0.427462
$714$	−28.8706	−1.08045
$715$	22.4968	0.841332
$716$	−4.73487	−0.176950
$717$	18.7887	0.701677
$718$	−8.54944	−0.319062
$719$	−35.1656	−1.31146	−0.655729	−	0.754997i	$-0.727638\pi$
$719$	−35.1656	−1.31146	−0.655729	+	0.754997i	$0.727638\pi$
$720$	−17.4532	−0.650443
$721$	30.0558	1.11934
$722$	−16.9508	−0.630844
$723$	56.4361	2.09888
$724$	−14.5692	−0.541462
$725$	−20.2491	−0.752034
$726$	18.8741	0.700485
$727$	36.5475	1.35547	0.677736	−	0.735306i	$-0.262961\pi$
$727$	36.5475	1.35547	0.677736	+	0.735306i	$0.262961\pi$
$728$	11.8159	0.437925
$729$	−6.36511	−0.235745
$730$	−0.379360	−0.0140407
$731$	−5.42247	−0.200557
$732$	11.5078	0.425339
$733$	−10.3520	−0.382359	−0.191179	−	0.981555i	$-0.561231\pi$
$733$	−10.3520	−0.382359	−0.191179	+	0.981555i	$0.561231\pi$
$734$	−10.4636	−0.386220
$735$	20.2766	0.747914
$736$	−1.68937	−0.0622709
$737$	−28.7706	−1.05978
$738$	−5.92484	−0.218097
$739$	4.25377	0.156477	0.0782387	−	0.996935i	$-0.475070\pi$
$739$	4.25377	0.156477	0.0782387	+	0.996935i	$0.475070\pi$
$740$	−3.42932	−0.126064
$741$	17.0242	0.625401
$742$	3.71790	0.136488
$743$	−10.4303	−0.382649	−0.191325	−	0.981527i	$-0.561278\pi$
$743$	−10.4303	−0.382649	−0.191325	+	0.981527i	$0.561278\pi$
$744$	20.9315	0.767385
$745$	2.02192	0.0740775
$746$	14.8133	0.542352
$747$	7.69034	0.281375
$748$	−6.70718	−0.245239
$749$	−10.0564	−0.367454
$750$	−24.6022	−0.898346
$751$	−24.0984	−0.879362	−0.439681	−	0.898154i	$-0.644908\pi$
$751$	−24.0984	−0.879362	−0.439681	+	0.898154i	$0.644908\pi$
$752$	6.29459	0.229540
$753$	50.1252	1.82666
$754$	−38.9043	−1.41681
$755$	−45.8842	−1.66990
$756$	−34.3057	−1.24769
$757$	−42.6798	−1.55123	−0.775613	−	0.631209i	$-0.782559\pi$
$757$	−42.6798	−1.55123	−0.775613	+	0.631209i	$0.782559\pi$
$758$	−14.6830	−0.533311
$759$	−11.5942	−0.420844
$760$	3.78685	0.137364
$761$	2.50128	0.0906712	0.0453356	−	0.998972i	$-0.485564\pi$
$761$	2.50128	0.0906712	0.0453356	+	0.998972i	$0.485564\pi$
$762$	21.1210	0.765132
$763$	−5.49759	−0.199026
$764$	−12.7519	−0.461347
$765$	−52.8420	−1.91051
$766$	−6.26003	−0.226184
$767$	19.7475	0.713043
$768$	−3.09800	−0.111790
$769$	21.7036	0.782651	0.391326	−	0.920252i	$-0.372017\pi$
$769$	21.7036	0.782651	0.391326	+	0.920252i	$0.372017\pi$
$770$	18.0383	0.650054
$771$	63.6008	2.29053
$772$	19.8366	0.713936
$773$	−29.8572	−1.07389	−0.536944	−	0.843618i	$-0.680421\pi$
$773$	−29.8572	−1.07389	−0.536944	+	0.843618i	$0.680421\pi$
$774$	−11.8163	−0.424727
$775$	−13.4997	−0.484922
$776$	8.67297	0.311342
$777$	−12.3615	−0.443467
$778$	−3.62073	−0.129810
$779$	1.28552	0.0460587
$780$	31.4605	1.12647
$781$	−10.3659	−0.370921
$782$	−5.11479	−0.182905
$783$	112.953	4.03662
$784$	2.47415	0.0883624
$785$	40.8569	1.45825
$786$	27.1800	0.969479
$787$	−13.7826	−0.491295	−0.245648	−	0.969359i	$-0.579001\pi$
$787$	−13.7826	−0.491295	−0.245648	+	0.969359i	$0.579001\pi$
$788$	13.0385	0.464476
$789$	−46.3320	−1.64946
$790$	−23.8684	−0.849198
$791$	9.74794	0.346597
$792$	−14.6158	−0.519351
$793$	−14.2595	−0.506371
$794$	22.6882	0.805173
$795$	9.89914	0.351086
$796$	−15.4703	−0.548331
$797$	−26.9481	−0.954551	−0.477276	−	0.878754i	$-0.658376\pi$
$797$	−26.9481	−0.954551	−0.477276	+	0.878754i	$0.658376\pi$
$798$	13.6503	0.483215
$799$	19.0577	0.674213
$800$	1.99804	0.0706415
$801$	−101.661	−3.59200
$802$	9.17077	0.323831
$803$	−0.317687	−0.0112109
$804$	−40.2341	−1.41895
$805$	13.7557	0.484825
$806$	−25.9366	−0.913579
$807$	61.2367	2.15564
$808$	−9.91404	−0.348775
$809$	−11.2677	−0.396152	−0.198076	−	0.980187i	$-0.563469\pi$
$809$	−11.2677	−0.396152	−0.198076	+	0.980187i	$0.563469\pi$
$810$	−38.9816	−1.36967
$811$	−50.8623	−1.78602	−0.893008	−	0.450041i	$-0.851409\pi$
$811$	−50.8623	−1.78602	−0.893008	+	0.450041i	$0.851409\pi$
$812$	−31.1940	−1.09470
$813$	−19.6558	−0.689357
$814$	−2.87182	−0.100657
$815$	37.9346	1.32879
$816$	−9.37962	−0.328353
$817$	2.56380	0.0896959
$818$	−10.1575	−0.355150
$819$	77.9566	2.72402
$820$	2.37563	0.0829605
$821$	−10.9553	−0.382342	−0.191171	−	0.981557i	$-0.561229\pi$
$821$	−10.9553	−0.382342	−0.191171	+	0.981557i	$0.561229\pi$
$822$	−10.7819	−0.376061
$823$	12.0717	0.420793	0.210396	−	0.977616i	$-0.432525\pi$
$823$	12.0717	0.420793	0.210396	+	0.977616i	$0.432525\pi$
$824$	9.76468	0.340169
$825$	13.7127	0.477415
$826$	15.8339	0.550931
$827$	17.0181	0.591778	0.295889	−	0.955222i	$-0.404384\pi$
$827$	17.0181	0.591778	0.295889	+	0.955222i	$0.404384\pi$
$828$	−11.1458	−0.387343
$829$	−8.16156	−0.283463	−0.141731	−	0.989905i	$-0.545267\pi$
$829$	−8.16156	−0.283463	−0.141731	+	0.989905i	$0.545267\pi$
$830$	−3.08352	−0.107031
$831$	−9.16950	−0.318086
$832$	3.83880	0.133086
$833$	7.49082	0.259541
$834$	27.5590	0.954288
$835$	8.81967	0.305217
$836$	3.17122	0.109679
$837$	75.3034	2.60287
$838$	−18.3235	−0.632974
$839$	−42.1621	−1.45560	−0.727799	−	0.685791i	$-0.759457\pi$
$839$	−42.1621	−1.45560	−0.727799	+	0.685791i	$0.759457\pi$
$840$	25.2255	0.870363
$841$	73.7078	2.54165
$842$	4.48495	0.154561
$843$	11.9256	0.410738
$844$	19.2436	0.662391
$845$	−4.59342	−0.158019
$846$	41.5293	1.42781
$847$	−18.7523	−0.644338
$848$	1.20789	0.0414791
$849$	−16.0091	−0.549432
$850$	6.04935	0.207491
$851$	−2.19000	−0.0750723
$852$	−14.4961	−0.496629
$853$	−55.9138	−1.91445	−0.957225	−	0.289343i	$-0.906563\pi$
$853$	−55.9138	−1.91445	−0.957225	+	0.289343i	$0.906563\pi$
$854$	−11.4335	−0.391247
$855$	24.9842	0.854442
$856$	−3.26718	−0.111670
$857$	−5.65385	−0.193132	−0.0965659	−	0.995327i	$-0.530786\pi$
$857$	−5.65385	−0.193132	−0.0965659	+	0.995327i	$0.530786\pi$
$858$	26.3459	0.899436
$859$	−26.3075	−0.897601	−0.448800	−	0.893632i	$-0.648149\pi$
$859$	−26.3075	−0.897601	−0.448800	+	0.893632i	$0.648149\pi$
$860$	4.73785	0.161559
$861$	8.56331	0.291837
$862$	17.7456	0.604416
$863$	57.3154	1.95104	0.975519	−	0.219916i	$-0.0705783\pi$
$863$	57.3154	1.95104	0.975519	+	0.219916i	$0.0705783\pi$
$864$	−11.1454	−0.379175
$865$	50.0193	1.70071
$866$	−22.9322	−0.779269
$867$	24.2679	0.824183
$868$	−20.7964	−0.705876
$869$	−19.9881	−0.678049
$870$	−83.0561	−2.81587
$871$	49.8549	1.68927
$872$	−1.78608	−0.0604845
$873$	57.2210	1.93664
$874$	2.41832	0.0818010
$875$	24.4435	0.826340
$876$	−0.444268	−0.0150104
$877$	−52.0205	−1.75661	−0.878303	−	0.478104i	$-0.841324\pi$
$877$	−52.0205	−1.75661	−0.878303	+	0.478104i	$0.841324\pi$
$878$	4.53752	0.153134
$879$	52.9296	1.78527
$880$	5.86037	0.197553
$881$	−22.0343	−0.742354	−0.371177	−	0.928562i	$-0.621046\pi$
$881$	−22.0343	−0.742354	−0.371177	+	0.928562i	$0.621046\pi$
$882$	16.3235	0.549640
$883$	−2.90552	−0.0977785	−0.0488892	−	0.998804i	$-0.515568\pi$
$883$	−2.90552	−0.0977785	−0.0488892	+	0.998804i	$0.515568\pi$
$884$	11.6225	0.390907
$885$	42.1587	1.41715
$886$	8.15917	0.274113
$887$	−23.4956	−0.788904	−0.394452	−	0.918917i	$-0.629066\pi$
$887$	−23.4956	−0.788904	−0.394452	+	0.918917i	$0.629066\pi$
$888$	−4.01608	−0.134771
$889$	−20.9847	−0.703803
$890$	40.7618	1.36634
$891$	−32.6443	−1.09363
$892$	5.47567	0.183339
$893$	−9.01067	−0.301531
$894$	2.36787	0.0791934
$895$	12.5255	0.418682
$896$	3.07801	0.102829
$897$	20.0910	0.670819
$898$	−15.4823	−0.516650
$899$	68.4731	2.28370
$900$	13.1823	0.439411
$901$	3.65705	0.121834
$902$	1.98942	0.0662404
$903$	17.0783	0.568331
$904$	3.16696	0.105332
$905$	38.5412	1.28115
$906$	−53.7349	−1.78522
$907$	−6.20579	−0.206060	−0.103030	−	0.994678i	$-0.532854\pi$
$907$	−6.20579	−0.206060	−0.103030	+	0.994678i	$0.532854\pi$
$908$	−4.52193	−0.150066
$909$	−65.4090	−2.16948
$910$	−31.2575	−1.03618
$911$	−39.2928	−1.30183	−0.650914	−	0.759152i	$-0.725614\pi$
$911$	−39.2928	−1.30183	−0.650914	+	0.759152i	$0.725614\pi$
$912$	4.43478	0.146850
$913$	−2.58223	−0.0854594
$914$	3.48455	0.115259
$915$	−30.4424	−1.00640
$916$	−0.880741	−0.0291005
$917$	−27.0046	−0.891771
$918$	−33.7443	−1.11373
$919$	55.1648	1.81972	0.909859	−	0.414918i	$-0.136190\pi$
$919$	55.1648	1.81972	0.909859	+	0.414918i	$0.136190\pi$
$920$	4.46902	0.147339
$921$	−0.589472	−0.0194237
$922$	23.8020	0.783877
$923$	17.9624	0.591241
$924$	21.1246	0.694948
$925$	2.59015	0.0851636
$926$	30.6752	1.00805
$927$	64.4236	2.11595
$928$	−10.1345	−0.332681
$929$	5.13054	0.168328	0.0841638	−	0.996452i	$-0.473178\pi$
$929$	5.13054	0.168328	0.0841638	+	0.996452i	$0.473178\pi$
$930$	−55.3717	−1.81571
$931$	−3.54173	−0.116076
$932$	23.6779	0.775596
$933$	54.9284	1.79827
$934$	10.9114	0.357033
$935$	17.7431	0.580260
$936$	25.3269	0.827837
$937$	−17.4365	−0.569625	−0.284813	−	0.958583i	$-0.591931\pi$
$937$	−17.4365	−0.569625	−0.284813	+	0.958583i	$0.591931\pi$
$938$	39.9745	1.30521
$939$	−94.8392	−3.09496
$940$	−16.6516	−0.543115
$941$	−17.8110	−0.580621	−0.290310	−	0.956933i	$-0.593759\pi$
$941$	−17.8110	−0.580621	−0.290310	+	0.956933i	$0.593759\pi$
$942$	47.8475	1.55896
$943$	1.51710	0.0494036
$944$	5.14420	0.167429
$945$	90.7518	2.95216
$946$	3.96762	0.128998
$947$	15.2834	0.496642	0.248321	−	0.968678i	$-0.420121\pi$
$947$	15.2834	0.496642	0.248321	+	0.968678i	$0.420121\pi$
$948$	−27.9522	−0.907846
$949$	0.550502	0.0178700
$950$	−2.86019	−0.0927969
$951$	98.1907	3.18405
$952$	9.31910	0.302034
$953$	−7.31737	−0.237033	−0.118516	−	0.992952i	$-0.537814\pi$
$953$	−7.31737	−0.237033	−0.118516	+	0.992952i	$0.537814\pi$
$954$	7.96920	0.258012
$955$	33.7336	1.09159
$956$	−6.06478	−0.196149
$957$	−69.5537	−2.24835
$958$	16.6553	0.538108
$959$	10.7123	0.345918
$960$	8.19540	0.264505
$961$	14.6495	0.472565
$962$	4.97641	0.160446
$963$	−21.5556	−0.694620
$964$	−18.2169	−0.586728
$965$	−52.4755	−1.68925
$966$	16.1093	0.518307
$967$	14.8093	0.476236	0.238118	−	0.971236i	$-0.423469\pi$
$967$	14.8093	0.476236	0.238118	+	0.971236i	$0.423469\pi$
$968$	−6.09236	−0.195816
$969$	13.4269	0.431334
$970$	−22.9433	−0.736666
$971$	38.0877	1.22229	0.611147	−	0.791517i	$-0.290709\pi$
$971$	38.0877	1.22229	0.611147	+	0.791517i	$0.290709\pi$
$972$	−12.2150	−0.391796
$973$	−27.3811	−0.877798
$974$	−6.46773	−0.207239
$975$	−23.7620	−0.760992
$976$	−3.71458	−0.118901
$977$	27.3417	0.874738	0.437369	−	0.899282i	$-0.355910\pi$
$977$	27.3417	0.874738	0.437369	+	0.899282i	$0.355910\pi$
$978$	44.4251	1.42056
$979$	34.1352	1.09096
$980$	−6.54506	−0.209074
$981$	−11.7839	−0.376231
$982$	−19.4399	−0.620353
$983$	−36.3702	−1.16003	−0.580015	−	0.814606i	$-0.696953\pi$
$983$	−36.3702	−1.16003	−0.580015	+	0.814606i	$0.696953\pi$
$984$	2.78209	0.0886899
$985$	−34.4917	−1.09900
$986$	−30.6835	−0.977163
$987$	−60.0232	−1.91056
$988$	−5.49523	−0.174827
$989$	3.02564	0.0962098
$990$	38.6645	1.22884
$991$	10.9382	0.347464	0.173732	−	0.984793i	$-0.444417\pi$
$991$	10.9382	0.347464	0.173732	+	0.984793i	$0.444417\pi$
$992$	−6.75644	−0.214517
$993$	−78.5340	−2.49220
$994$	14.4026	0.456822
$995$	40.9249	1.29741
$996$	−3.61111	−0.114422
$997$	−19.0585	−0.603589	−0.301795	−	0.953373i	$-0.597586\pi$
$997$	−19.0585	−0.603589	−0.301795	+	0.953373i	$0.597586\pi$
$998$	1.83225	0.0579987
$999$	−14.4483	−0.457124

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.d.1.4	✓	69

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.d.1.4	✓	69	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:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.09800 q^{3} +1.00000 q^{4} -2.64538 q^{5} -3.09800 q^{6} +3.07801 q^{7} +1.00000 q^{8} +6.59762 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.09800 q^{3} +1.00000 q^{4} -2.64538 q^{5} -3.09800 q^{6} +3.07801 q^{7} +1.00000 q^{8} +6.59762 q^{9} -2.64538 q^{10} -2.21532 q^{11} -3.09800 q^{12} +3.83880 q^{13} +3.07801 q^{14} +8.19540 q^{15} +1.00000 q^{16} +3.02764 q^{17} +6.59762 q^{18} -1.43150 q^{19} -2.64538 q^{20} -9.53568 q^{21} -2.21532 q^{22} -1.68937 q^{23} -3.09800 q^{24} +1.99804 q^{25} +3.83880 q^{26} -11.1454 q^{27} +3.07801 q^{28} -10.1345 q^{29} +8.19540 q^{30} -6.75644 q^{31} +1.00000 q^{32} +6.86307 q^{33} +3.02764 q^{34} -8.14251 q^{35} +6.59762 q^{36} +1.29634 q^{37} -1.43150 q^{38} -11.8926 q^{39} -2.64538 q^{40} -0.898028 q^{41} -9.53568 q^{42} -1.79099 q^{43} -2.21532 q^{44} -17.4532 q^{45} -1.68937 q^{46} +6.29459 q^{47} -3.09800 q^{48} +2.47415 q^{49} +1.99804 q^{50} -9.37962 q^{51} +3.83880 q^{52} +1.20789 q^{53} -11.1454 q^{54} +5.86037 q^{55} +3.07801 q^{56} +4.43478 q^{57} -10.1345 q^{58} +5.14420 q^{59} +8.19540 q^{60} -3.71458 q^{61} -6.75644 q^{62} +20.3075 q^{63} +1.00000 q^{64} -10.1551 q^{65} +6.86307 q^{66} +12.9871 q^{67} +3.02764 q^{68} +5.23367 q^{69} -8.14251 q^{70} +4.67918 q^{71} +6.59762 q^{72} +0.143405 q^{73} +1.29634 q^{74} -6.18994 q^{75} -1.43150 q^{76} -6.81878 q^{77} -11.8926 q^{78} +9.02266 q^{79} -2.64538 q^{80} +14.7357 q^{81} -0.898028 q^{82} +1.16562 q^{83} -9.53568 q^{84} -8.00925 q^{85} -1.79099 q^{86} +31.3967 q^{87} -2.21532 q^{88} -15.4087 q^{89} -17.4532 q^{90} +11.8159 q^{91} -1.68937 q^{92} +20.9315 q^{93} +6.29459 q^{94} +3.78685 q^{95} -3.09800 q^{96} +8.67297 q^{97} +2.47415 q^{98} -14.6158 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9}+O(q^{10}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9	\( 69 q + 69 q^{2} - 25 q^{3} + 69 q^{4} - 33 q^{5} - 25 q^{6} - 19 q^{7} + 69 q^{8} + 54 q^{9} - 33 q^{10} - 30 q^{11} - 25 q^{12} - 58 q^{13} - 19 q^{14} + 2 q^{15} + 69 q^{16} - 80 q^{17} + 54 q^{18} - 40 q^{19} - 33 q^{20} - 32 q^{21} - 30 q^{22} - 45 q^{23} - 25 q^{24} + 42 q^{25} - 58 q^{26} - 76 q^{27} - 19 q^{28} - 44 q^{29} + 2 q^{30} - 12 q^{31} + 69 q^{32} - 41 q^{33} - 80 q^{34} - 49 q^{35} + 54 q^{36} - 47 q^{37} - 40 q^{38} - 14 q^{39} - 33 q^{40} - 94 q^{41} - 32 q^{42} - 10 q^{43} - 30 q^{44} - 89 q^{45} - 45 q^{46} - 85 q^{47} - 25 q^{48} + 32 q^{49} + 42 q^{50} - 10 q^{51} - 58 q^{52} - 41 q^{53} - 76 q^{54} - 27 q^{55} - 19 q^{56} - 72 q^{57} - 44 q^{58} - 75 q^{59} + 2 q^{60} - 98 q^{61} - 12 q^{62} - 61 q^{63} + 69 q^{64} - 47 q^{65} - 41 q^{66} - 22 q^{67} - 80 q^{68} - 74 q^{69} - 49 q^{70} - 22 q^{71} + 54 q^{72} - 129 q^{73} - 47 q^{74} - 106 q^{75} - 40 q^{76} - 108 q^{77} - 14 q^{78} + 21 q^{79} - 33 q^{80} + 13 q^{81} - 94 q^{82} - 111 q^{83} - 32 q^{84} - 67 q^{85} - 10 q^{86} - 38 q^{87} - 30 q^{88} - 112 q^{89} - 89 q^{90} - 55 q^{91} - 45 q^{92} - 90 q^{93} - 85 q^{94} - 38 q^{95} - 25 q^{96} - 98 q^{97} + 32 q^{98} - 51 q^{99}+O(q^{100}) \) 69 * q + 69 * q^2 - 25 * q^3 + 69 * q^4 - 33 * q^5 - 25 * q^6 - 19 * q^7 + 69 * q^8 + 54 * q^9 - 33 * q^10 - 30 * q^11 - 25 * q^12 - 58 * q^13 - 19 * q^14 + 2 * q^15 + 69 * q^16 - 80 * q^17 + 54 * q^18 - 40 * q^19 - 33 * q^20 - 32 * q^21 - 30 * q^22 - 45 * q^23 - 25 * q^24 + 42 * q^25 - 58 * q^26 - 76 * q^27 - 19 * q^28 - 44 * q^29 + 2 * q^30 - 12 * q^31 + 69 * q^32 - 41 * q^33 - 80 * q^34 - 49 * q^35 + 54 * q^36 - 47 * q^37 - 40 * q^38 - 14 * q^39 - 33 * q^40 - 94 * q^41 - 32 * q^42 - 10 * q^43 - 30 * q^44 - 89 * q^45 - 45 * q^46 - 85 * q^47 - 25 * q^48 + 32 * q^49 + 42 * q^50 - 10 * q^51 - 58 * q^52 - 41 * q^53 - 76 * q^54 - 27 * q^55 - 19 * q^56 - 72 * q^57 - 44 * q^58 - 75 * q^59 + 2 * q^60 - 98 * q^61 - 12 * q^62 - 61 * q^63 + 69 * q^64 - 47 * q^65 - 41 * q^66 - 22 * q^67 - 80 * q^68 - 74 * q^69 - 49 * q^70 - 22 * q^71 + 54 * q^72 - 129 * q^73 - 47 * q^74 - 106 * q^75 - 40 * q^76 - 108 * q^77 - 14 * q^78 + 21 * q^79 - 33 * q^80 + 13 * q^81 - 94 * q^82 - 111 * q^83 - 32 * q^84 - 67 * q^85 - 10 * q^86 - 38 * q^87 - 30 * q^88 - 112 * q^89 - 89 * q^90 - 55 * q^91 - 45 * q^92 - 90 * q^93 - 85 * q^94 - 38 * q^95 - 25 * q^96 - 98 * q^97 + 32 * q^98 - 51 * q^99

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