LMFDB - Embedded newform 6002.2.a.d.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, 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("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$0$
Dimension:	$79$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.35201 q^{3} +1.00000 q^{4} +1.77899 q^{5} -3.35201 q^{6} -4.18423 q^{7} +1.00000 q^{8} +8.23600 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.35201 q^{3} +1.00000 q^{4} +1.77899 q^{5} -3.35201 q^{6} -4.18423 q^{7} +1.00000 q^{8} +8.23600 q^{9} +1.77899 q^{10} +5.11176 q^{11} -3.35201 q^{12} +6.53321 q^{13} -4.18423 q^{14} -5.96320 q^{15} +1.00000 q^{16} +5.03048 q^{17} +8.23600 q^{18} +5.59357 q^{19} +1.77899 q^{20} +14.0256 q^{21} +5.11176 q^{22} +4.85661 q^{23} -3.35201 q^{24} -1.83519 q^{25} +6.53321 q^{26} -17.5512 q^{27} -4.18423 q^{28} -1.53588 q^{29} -5.96320 q^{30} +1.40650 q^{31} +1.00000 q^{32} -17.1347 q^{33} +5.03048 q^{34} -7.44371 q^{35} +8.23600 q^{36} +11.6363 q^{37} +5.59357 q^{38} -21.8994 q^{39} +1.77899 q^{40} -0.495619 q^{41} +14.0256 q^{42} +10.6619 q^{43} +5.11176 q^{44} +14.6518 q^{45} +4.85661 q^{46} -5.91026 q^{47} -3.35201 q^{48} +10.5078 q^{49} -1.83519 q^{50} -16.8623 q^{51} +6.53321 q^{52} -0.430191 q^{53} -17.5512 q^{54} +9.09378 q^{55} -4.18423 q^{56} -18.7497 q^{57} -1.53588 q^{58} -8.87576 q^{59} -5.96320 q^{60} -4.50353 q^{61} +1.40650 q^{62} -34.4614 q^{63} +1.00000 q^{64} +11.6225 q^{65} -17.1347 q^{66} -10.7815 q^{67} +5.03048 q^{68} -16.2794 q^{69} -7.44371 q^{70} -8.73442 q^{71} +8.23600 q^{72} +11.8925 q^{73} +11.6363 q^{74} +6.15159 q^{75} +5.59357 q^{76} -21.3888 q^{77} -21.8994 q^{78} -3.72662 q^{79} +1.77899 q^{80} +34.1238 q^{81} -0.495619 q^{82} -3.05979 q^{83} +14.0256 q^{84} +8.94918 q^{85} +10.6619 q^{86} +5.14829 q^{87} +5.11176 q^{88} -10.7830 q^{89} +14.6518 q^{90} -27.3365 q^{91} +4.85661 q^{92} -4.71462 q^{93} -5.91026 q^{94} +9.95091 q^{95} -3.35201 q^{96} +13.1049 q^{97} +10.5078 q^{98} +42.1005 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) $ 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * 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
$3$	−3.35201	−1.93529	−0.967643	−	0.252322i	$-0.918806\pi$
$3$	−3.35201	−1.93529	−0.967643	+	0.252322i	$0.918806\pi$
$4$	1.00000	0.500000
$5$	1.77899	0.795589	0.397794	−	0.917475i	$-0.369776\pi$
$5$	1.77899	0.795589	0.397794	+	0.917475i	$0.369776\pi$
$6$	−3.35201	−1.36845
$7$	−4.18423	−1.58149	−0.790746	−	0.612145i	$-0.790307\pi$
$7$	−4.18423	−1.58149	−0.790746	+	0.612145i	$0.790307\pi$
$8$	1.00000	0.353553
$9$	8.23600	2.74533
$10$	1.77899	0.562566
$11$	5.11176	1.54125	0.770627	−	0.637286i	$-0.219943\pi$
$11$	5.11176	1.54125	0.770627	+	0.637286i	$0.219943\pi$
$12$	−3.35201	−0.967643
$13$	6.53321	1.81199	0.905993	−	0.423292i	$-0.139125\pi$
$13$	6.53321	1.81199	0.905993	+	0.423292i	$0.139125\pi$
$14$	−4.18423	−1.11828
$15$	−5.96320	−1.53969
$16$	1.00000	0.250000
$17$	5.03048	1.22007	0.610036	−	0.792374i	$-0.291155\pi$
$17$	5.03048	1.22007	0.610036	+	0.792374i	$0.291155\pi$
$18$	8.23600	1.94124
$19$	5.59357	1.28325	0.641627	−	0.767017i	$-0.278260\pi$
$19$	5.59357	1.28325	0.641627	+	0.767017i	$0.278260\pi$
$20$	1.77899	0.397794
$21$	14.0256	3.06064
$22$	5.11176	1.08983
$23$	4.85661	1.01267	0.506337	−	0.862336i	$-0.330999\pi$
$23$	4.85661	1.01267	0.506337	+	0.862336i	$0.330999\pi$
$24$	−3.35201	−0.684227
$25$	−1.83519	−0.367039
$26$	6.53321	1.28127
$27$	−17.5512	−3.37772
$28$	−4.18423	−0.790746
$29$	−1.53588	−0.285205	−0.142603	−	0.989780i	$-0.545547\pi$
$29$	−1.53588	−0.285205	−0.142603	+	0.989780i	$0.545547\pi$
$30$	−5.96320	−1.08873
$31$	1.40650	0.252615	0.126308	−	0.991991i	$-0.459687\pi$
$31$	1.40650	0.252615	0.126308	+	0.991991i	$0.459687\pi$
$32$	1.00000	0.176777
$33$	−17.1347	−2.98277
$34$	5.03048	0.862721
$35$	−7.44371	−1.25822
$36$	8.23600	1.37267
$37$	11.6363	1.91299	0.956495	−	0.291749i	$-0.0942371\pi$
$37$	11.6363	1.91299	0.956495	+	0.291749i	$0.0942371\pi$
$38$	5.59357	0.907397
$39$	−21.8994	−3.50671
$40$	1.77899	0.281283
$41$	−0.495619	−0.0774028	−0.0387014	−	0.999251i	$-0.512322\pi$
$41$	−0.495619	−0.0774028	−0.0387014	+	0.999251i	$0.512322\pi$
$42$	14.0256	2.16420
$43$	10.6619	1.62593	0.812966	−	0.582311i	$-0.197851\pi$
$43$	10.6619	1.62593	0.812966	+	0.582311i	$0.197851\pi$
$44$	5.11176	0.770627
$45$	14.6518	2.18416
$46$	4.85661	0.716068
$47$	−5.91026	−0.862101	−0.431050	−	0.902328i	$-0.641857\pi$
$47$	−5.91026	−0.862101	−0.431050	+	0.902328i	$0.641857\pi$
$48$	−3.35201	−0.483822
$49$	10.5078	1.50112
$50$	−1.83519	−0.259535
$51$	−16.8623	−2.36119
$52$	6.53321	0.905993
$53$	−0.430191	−0.0590913	−0.0295457	−	0.999563i	$-0.509406\pi$
$53$	−0.430191	−0.0590913	−0.0295457	+	0.999563i	$0.509406\pi$
$54$	−17.5512	−2.38841
$55$	9.09378	1.22621
$56$	−4.18423	−0.559142
$57$	−18.7497	−2.48346
$58$	−1.53588	−0.201671
$59$	−8.87576	−1.15553	−0.577763	−	0.816205i	$-0.696074\pi$
$59$	−8.87576	−1.15553	−0.577763	+	0.816205i	$0.696074\pi$
$60$	−5.96320	−0.769846
$61$	−4.50353	−0.576619	−0.288309	−	0.957537i	$-0.593093\pi$
$61$	−4.50353	−0.576619	−0.288309	+	0.957537i	$0.593093\pi$
$62$	1.40650	0.178626
$63$	−34.4614	−4.34172
$64$	1.00000	0.125000
$65$	11.6225	1.44160
$66$	−17.1347	−2.10914
$67$	−10.7815	−1.31717	−0.658585	−	0.752506i	$-0.728845\pi$
$67$	−10.7815	−1.31717	−0.658585	+	0.752506i	$0.728845\pi$
$68$	5.03048	0.610036
$69$	−16.2794	−1.95981
$70$	−7.44371	−0.889694
$71$	−8.73442	−1.03659	−0.518293	−	0.855203i	$-0.673432\pi$
$71$	−8.73442	−1.03659	−0.518293	+	0.855203i	$0.673432\pi$
$72$	8.23600	0.970622
$73$	11.8925	1.39192	0.695959	−	0.718082i	$-0.254980\pi$
$73$	11.8925	1.39192	0.695959	+	0.718082i	$0.254980\pi$
$74$	11.6363	1.35269
$75$	6.15159	0.710325
$76$	5.59357	0.641627
$77$	−21.3888	−2.43748
$78$	−21.8994	−2.47962
$79$	−3.72662	−0.419277	−0.209639	−	0.977779i	$-0.567229\pi$
$79$	−3.72662	−0.419277	−0.209639	+	0.977779i	$0.567229\pi$
$80$	1.77899	0.198897
$81$	34.1238	3.79153
$82$	−0.495619	−0.0547320
$83$	−3.05979	−0.335855	−0.167928	−	0.985799i	$-0.553707\pi$
$83$	−3.05979	−0.335855	−0.167928	+	0.985799i	$0.553707\pi$
$84$	14.0256	1.53032
$85$	8.94918	0.970675
$86$	10.6619	1.14971
$87$	5.14829	0.551954
$88$	5.11176	0.544916
$89$	−10.7830	−1.14300	−0.571500	−	0.820602i	$-0.693638\pi$
$89$	−10.7830	−1.14300	−0.571500	+	0.820602i	$0.693638\pi$
$90$	14.6518	1.54443
$91$	−27.3365	−2.86564
$92$	4.85661	0.506337
$93$	−4.71462	−0.488883
$94$	−5.91026	−0.609597
$95$	9.95091	1.02094
$96$	−3.35201	−0.342114
$97$	13.1049	1.33060	0.665298	−	0.746578i	$-0.268304\pi$
$97$	13.1049	1.33060	0.665298	+	0.746578i	$0.268304\pi$
$98$	10.5078	1.06145
$99$	42.1005	4.23126
$100$	−1.83519	−0.183519
$101$	−6.39419	−0.636246	−0.318123	−	0.948049i	$-0.603052\pi$
$101$	−6.39419	−0.636246	−0.318123	+	0.948049i	$0.603052\pi$
$102$	−16.8623	−1.66961
$103$	13.0304	1.28393	0.641964	−	0.766735i	$-0.278120\pi$
$103$	13.0304	1.28393	0.641964	+	0.766735i	$0.278120\pi$
$104$	6.53321	0.640634
$105$	24.9514	2.43501
$106$	−0.430191	−0.0417839
$107$	−4.22223	−0.408179	−0.204089	−	0.978952i	$-0.565423\pi$
$107$	−4.22223	−0.408179	−0.204089	+	0.978952i	$0.565423\pi$
$108$	−17.5512	−1.68886
$109$	−17.8114	−1.70602	−0.853011	−	0.521893i	$-0.825226\pi$
$109$	−17.8114	−1.70602	−0.853011	+	0.521893i	$0.825226\pi$
$110$	9.09378	0.867058
$111$	−39.0049	−3.70218
$112$	−4.18423	−0.395373
$113$	13.9184	1.30933	0.654667	−	0.755917i	$-0.272809\pi$
$113$	13.9184	1.30933	0.654667	+	0.755917i	$0.272809\pi$
$114$	−18.7497	−1.75607
$115$	8.63987	0.805672
$116$	−1.53588	−0.142603
$117$	53.8076	4.97451
$118$	−8.87576	−0.817080
$119$	−21.0487	−1.92953
$120$	−5.96320	−0.544363
$121$	15.1301	1.37547
$122$	−4.50353	−0.407731
$123$	1.66132	0.149797
$124$	1.40650	0.126308
$125$	−12.1597	−1.08760
$126$	−34.4614	−3.07006
$127$	−1.80015	−0.159738	−0.0798688	−	0.996805i	$-0.525450\pi$
$127$	−1.80015	−0.159738	−0.0798688	+	0.996805i	$0.525450\pi$
$128$	1.00000	0.0883883
$129$	−35.7390	−3.14664
$130$	11.6225	1.01936
$131$	8.72450	0.762263	0.381132	−	0.924521i	$-0.375534\pi$
$131$	8.72450	0.762263	0.381132	+	0.924521i	$0.375534\pi$
$132$	−17.1347	−1.49139
$133$	−23.4048	−2.02945
$134$	−10.7815	−0.931380
$135$	−31.2234	−2.68728
$136$	5.03048	0.431360
$137$	−2.44149	−0.208591	−0.104295	−	0.994546i	$-0.533259\pi$
$137$	−2.44149	−0.208591	−0.104295	+	0.994546i	$0.533259\pi$
$138$	−16.2794	−1.38580
$139$	−9.00821	−0.764066	−0.382033	−	0.924149i	$-0.624776\pi$
$139$	−9.00821	−0.764066	−0.382033	+	0.924149i	$0.624776\pi$
$140$	−7.44371	−0.629108
$141$	19.8113	1.66841
$142$	−8.73442	−0.732976
$143$	33.3962	2.79273
$144$	8.23600	0.686334
$145$	−2.73231	−0.226906
$146$	11.8925	0.984234
$147$	−35.2223	−2.90509
$148$	11.6363	0.956495
$149$	3.20732	0.262754	0.131377	−	0.991332i	$-0.458060\pi$
$149$	3.20732	0.262754	0.131377	+	0.991332i	$0.458060\pi$
$150$	6.15159	0.502275
$151$	12.8076	1.04227	0.521136	−	0.853474i	$-0.325509\pi$
$151$	12.8076	1.04227	0.521136	+	0.853474i	$0.325509\pi$
$152$	5.59357	0.453699
$153$	41.4311	3.34950
$154$	−21.3888	−1.72356
$155$	2.50215	0.200978
$156$	−21.8994	−1.75336
$157$	−14.7406	−1.17643	−0.588214	−	0.808705i	$-0.700169\pi$
$157$	−14.7406	−1.17643	−0.588214	+	0.808705i	$0.700169\pi$
$158$	−3.72662	−0.296474
$159$	1.44201	0.114359
$160$	1.77899	0.140642
$161$	−20.3212	−1.60154
$162$	34.1238	2.68102
$163$	13.1984	1.03378	0.516889	−	0.856053i	$-0.327090\pi$
$163$	13.1984	1.03378	0.516889	+	0.856053i	$0.327090\pi$
$164$	−0.495619	−0.0387014
$165$	−30.4825	−2.37306
$166$	−3.05979	−0.237486
$167$	1.74899	0.135341	0.0676706	−	0.997708i	$-0.478443\pi$
$167$	1.74899	0.135341	0.0676706	+	0.997708i	$0.478443\pi$
$168$	14.0256	1.08210
$169$	29.6828	2.28330
$170$	8.94918	0.686371
$171$	46.0687	3.52296
$172$	10.6619	0.812966
$173$	15.3518	1.16718	0.583589	−	0.812050i	$-0.301648\pi$
$173$	15.3518	1.16718	0.583589	+	0.812050i	$0.301648\pi$
$174$	5.14829	0.390291
$175$	7.67887	0.580468
$176$	5.11176	0.385314
$177$	29.7517	2.23627
$178$	−10.7830	−0.808223
$179$	7.56551	0.565473	0.282736	−	0.959198i	$-0.408758\pi$
$179$	7.56551	0.565473	0.282736	+	0.959198i	$0.408758\pi$
$180$	14.6518	1.09208
$181$	−21.3261	−1.58516	−0.792578	−	0.609771i	$-0.791262\pi$
$181$	−21.3261	−1.58516	−0.792578	+	0.609771i	$0.791262\pi$
$182$	−27.3365	−2.02631
$183$	15.0959	1.11592
$184$	4.85661	0.358034
$185$	20.7008	1.52195
$186$	−4.71462	−0.345692
$187$	25.7146	1.88044
$188$	−5.91026	−0.431050
$189$	73.4382	5.34184
$190$	9.95091	0.721915
$191$	−3.17883	−0.230012	−0.115006	−	0.993365i	$-0.536689\pi$
$191$	−3.17883	−0.230012	−0.115006	+	0.993365i	$0.536689\pi$
$192$	−3.35201	−0.241911
$193$	−19.6462	−1.41417	−0.707083	−	0.707130i	$-0.749989\pi$
$193$	−19.6462	−1.41417	−0.707083	+	0.707130i	$0.749989\pi$
$194$	13.1049	0.940874
$195$	−38.9589	−2.78990
$196$	10.5078	0.750558
$197$	−13.2743	−0.945753	−0.472876	−	0.881129i	$-0.656784\pi$
$197$	−13.2743	−0.945753	−0.472876	+	0.881129i	$0.656784\pi$
$198$	42.1005	2.99195
$199$	−12.0484	−0.854089	−0.427045	−	0.904231i	$-0.640445\pi$
$199$	−12.0484	−0.854089	−0.427045	+	0.904231i	$0.640445\pi$
$200$	−1.83519	−0.129768
$201$	36.1398	2.54910
$202$	−6.39419	−0.449894
$203$	6.42647	0.451050
$204$	−16.8623	−1.18059
$205$	−0.881702	−0.0615808
$206$	13.0304	0.907874
$207$	39.9991	2.78013
$208$	6.53321	0.452997
$209$	28.5930	1.97782
$210$	24.9514	1.72181
$211$	6.60622	0.454791	0.227395	−	0.973803i	$-0.426979\pi$
$211$	6.60622	0.454791	0.227395	+	0.973803i	$0.426979\pi$
$212$	−0.430191	−0.0295457
$213$	29.2779	2.00609
$214$	−4.22223	−0.288626
$215$	18.9675	1.29357
$216$	−17.5512	−1.19421
$217$	−5.88513	−0.399509
$218$	−17.8114	−1.20634
$219$	−39.8640	−2.69376
$220$	9.09378	0.613103
$221$	32.8652	2.21075
$222$	−39.0049	−2.61784
$223$	8.38724	0.561651	0.280826	−	0.959759i	$-0.409392\pi$
$223$	8.38724	0.561651	0.280826	+	0.959759i	$0.409392\pi$
$224$	−4.18423	−0.279571
$225$	−15.1147	−1.00764
$226$	13.9184	0.925839
$227$	−5.13320	−0.340702	−0.170351	−	0.985383i	$-0.554490\pi$
$227$	−5.13320	−0.340702	−0.170351	+	0.985383i	$0.554490\pi$
$228$	−18.7497	−1.24173
$229$	−19.5767	−1.29367	−0.646833	−	0.762631i	$-0.723907\pi$
$229$	−19.5767	−1.29367	−0.646833	+	0.762631i	$0.723907\pi$
$230$	8.63987	0.569696
$231$	71.6956	4.71723
$232$	−1.53588	−0.100835
$233$	−6.60944	−0.432999	−0.216499	−	0.976283i	$-0.569464\pi$
$233$	−6.60944	−0.432999	−0.216499	+	0.976283i	$0.569464\pi$
$234$	53.8076	3.51751
$235$	−10.5143	−0.685877
$236$	−8.87576	−0.577763
$237$	12.4917	0.811422
$238$	−21.0487	−1.36439
$239$	−14.7202	−0.952174	−0.476087	−	0.879398i	$-0.657945\pi$
$239$	−14.7202	−0.952174	−0.476087	+	0.879398i	$0.657945\pi$
$240$	−5.96320	−0.384923
$241$	−18.7593	−1.20839	−0.604197	−	0.796835i	$-0.706506\pi$
$241$	−18.7593	−1.20839	−0.604197	+	0.796835i	$0.706506\pi$
$242$	15.1301	0.972602
$243$	−61.7298	−3.95997
$244$	−4.50353	−0.288309
$245$	18.6933	1.19427
$246$	1.66132	0.105922
$247$	36.5440	2.32524
$248$	1.40650	0.0893130
$249$	10.2565	0.649976
$250$	−12.1597	−0.769050
$251$	3.80240	0.240005	0.120003	−	0.992774i	$-0.461710\pi$
$251$	3.80240	0.240005	0.120003	+	0.992774i	$0.461710\pi$
$252$	−34.4614	−2.17086
$253$	24.8259	1.56079
$254$	−1.80015	−0.112952
$255$	−29.9978	−1.87853
$256$	1.00000	0.0625000
$257$	25.2265	1.57358	0.786792	−	0.617219i	$-0.211741\pi$
$257$	25.2265	1.57358	0.786792	+	0.617219i	$0.211741\pi$
$258$	−35.7390	−2.22501
$259$	−48.6888	−3.02538
$260$	11.6225	0.720798
$261$	−12.6495	−0.782985
$262$	8.72450	0.539001
$263$	5.40143	0.333066	0.166533	−	0.986036i	$-0.446743\pi$
$263$	5.40143	0.333066	0.166533	+	0.986036i	$0.446743\pi$
$264$	−17.1347	−1.05457
$265$	−0.765306	−0.0470124
$266$	−23.4048	−1.43504
$267$	36.1449	2.21203
$268$	−10.7815	−0.658585
$269$	−22.1747	−1.35202	−0.676008	−	0.736894i	$-0.736291\pi$
$269$	−22.1747	−1.35202	−0.676008	+	0.736894i	$0.736291\pi$
$270$	−31.2234	−1.90019
$271$	0.861686	0.0523437	0.0261719	−	0.999657i	$-0.491668\pi$
$271$	0.861686	0.0523437	0.0261719	+	0.999657i	$0.491668\pi$
$272$	5.03048	0.305018
$273$	91.6323	5.54584
$274$	−2.44149	−0.147496
$275$	−9.38107	−0.565700
$276$	−16.2794	−0.979907
$277$	−10.5685	−0.634998	−0.317499	−	0.948259i	$-0.602843\pi$
$277$	−10.5685	−0.634998	−0.317499	+	0.948259i	$0.602843\pi$
$278$	−9.00821	−0.540277
$279$	11.5840	0.693513
$280$	−7.44371	−0.444847
$281$	6.61124	0.394393	0.197197	−	0.980364i	$-0.436816\pi$
$281$	6.61124	0.394393	0.197197	+	0.980364i	$0.436816\pi$
$282$	19.8113	1.17975
$283$	−32.2616	−1.91775	−0.958876	−	0.283825i	$-0.908396\pi$
$283$	−32.2616	−1.91775	−0.958876	+	0.283825i	$0.908396\pi$
$284$	−8.73442	−0.518293
$285$	−33.3556	−1.97582
$286$	33.3962	1.97476
$287$	2.07379	0.122412
$288$	8.23600	0.485311
$289$	8.30577	0.488575
$290$	−2.73231	−0.160447
$291$	−43.9277	−2.57509
$292$	11.8925	0.695959
$293$	32.6082	1.90499	0.952497	−	0.304549i	$-0.0985057\pi$
$293$	32.6082	1.90499	0.952497	+	0.304549i	$0.0985057\pi$
$294$	−35.2223	−2.05421
$295$	−15.7899	−0.919323
$296$	11.6363	0.676344
$297$	−89.7174	−5.20593
$298$	3.20732	0.185795
$299$	31.7293	1.83495
$300$	6.15159	0.355162
$301$	−44.6121	−2.57140
$302$	12.8076	0.736997
$303$	21.4334	1.23132
$304$	5.59357	0.320813
$305$	−8.01175	−0.458751
$306$	41.4311	2.36846
$307$	13.5730	0.774651	0.387325	−	0.921943i	$-0.373399\pi$
$307$	13.5730	0.774651	0.387325	+	0.921943i	$0.373399\pi$
$308$	−21.3888	−1.21874
$309$	−43.6782	−2.48477
$310$	2.50215	0.142113
$311$	−10.9266	−0.619591	−0.309796	−	0.950803i	$-0.600261\pi$
$311$	−10.9266	−0.619591	−0.309796	+	0.950803i	$0.600261\pi$
$312$	−21.8994	−1.23981
$313$	−15.1477	−0.856198	−0.428099	−	0.903732i	$-0.640816\pi$
$313$	−15.1477	−0.856198	−0.428099	+	0.903732i	$0.640816\pi$
$314$	−14.7406	−0.831860
$315$	−61.3064	−3.45423
$316$	−3.72662	−0.209639
$317$	−18.7184	−1.05133	−0.525665	−	0.850691i	$-0.676184\pi$
$317$	−18.7184	−1.05133	−0.525665	+	0.850691i	$0.676184\pi$
$318$	1.44201	0.0808638
$319$	−7.85105	−0.439574
$320$	1.77899	0.0994486
$321$	14.1530	0.789943
$322$	−20.3212	−1.13246
$323$	28.1384	1.56566
$324$	34.1238	1.89576
$325$	−11.9897	−0.665069
$326$	13.1984	0.730991
$327$	59.7040	3.30164
$328$	−0.495619	−0.0273660
$329$	24.7299	1.36340
$330$	−30.4825	−1.67801
$331$	15.2669	0.839142	0.419571	−	0.907723i	$-0.362181\pi$
$331$	15.2669	0.839142	0.419571	+	0.907723i	$0.362181\pi$
$332$	−3.05979	−0.167928
$333$	95.8363	5.25180
$334$	1.74899	0.0957006
$335$	−19.1802	−1.04793
$336$	14.0256	0.765160
$337$	−2.96963	−0.161766	−0.0808831	−	0.996724i	$-0.525774\pi$
$337$	−2.96963	−0.161766	−0.0808831	+	0.996724i	$0.525774\pi$
$338$	29.6828	1.61453
$339$	−46.6547	−2.53394
$340$	8.94918	0.485338
$341$	7.18971	0.389344
$342$	46.0687	2.49111
$343$	−14.6775	−0.792510
$344$	10.6619	0.574854
$345$	−28.9610	−1.55921
$346$	15.3518	0.825319
$347$	−0.105288	−0.00565218	−0.00282609	−	0.999996i	$-0.500900\pi$
$347$	−0.105288	−0.00565218	−0.00282609	+	0.999996i	$0.500900\pi$
$348$	5.14829	0.275977
$349$	24.4121	1.30675	0.653375	−	0.757034i	$-0.273352\pi$
$349$	24.4121	1.30675	0.653375	+	0.757034i	$0.273352\pi$
$350$	7.67887	0.410453
$351$	−114.665	−6.12039
$352$	5.11176	0.272458
$353$	−15.5950	−0.830036	−0.415018	−	0.909813i	$-0.636225\pi$
$353$	−15.5950	−0.830036	−0.415018	+	0.909813i	$0.636225\pi$
$354$	29.7517	1.58128
$355$	−15.5385	−0.824695
$356$	−10.7830	−0.571500
$357$	70.5556	3.73420
$358$	7.56551	0.399850
$359$	−14.3136	−0.755441	−0.377721	−	0.925920i	$-0.623292\pi$
$359$	−14.3136	−0.755441	−0.377721	+	0.925920i	$0.623292\pi$
$360$	14.6518	0.772216
$361$	12.2881	0.646740
$362$	−21.3261	−1.12087
$363$	−50.7164	−2.66192
$364$	−27.3365	−1.43282
$365$	21.1567	1.10739
$366$	15.0959	0.789076
$367$	−21.9375	−1.14513	−0.572563	−	0.819860i	$-0.694051\pi$
$367$	−21.9375	−1.14513	−0.572563	+	0.819860i	$0.694051\pi$
$368$	4.85661	0.253168
$369$	−4.08192	−0.212496
$370$	20.7008	1.07618
$371$	1.80002	0.0934524
$372$	−4.71462	−0.244441
$373$	20.7892	1.07642	0.538211	−	0.842810i	$-0.319100\pi$
$373$	20.7892	1.07642	0.538211	+	0.842810i	$0.319100\pi$
$374$	25.7146	1.32967
$375$	40.7596	2.10482
$376$	−5.91026	−0.304799
$377$	−10.0342	−0.516789
$378$	73.4382	3.77725
$379$	18.5634	0.953535	0.476768	−	0.879029i	$-0.341808\pi$
$379$	18.5634	0.953535	0.476768	+	0.879029i	$0.341808\pi$
$380$	9.95091	0.510471
$381$	6.03414	0.309138
$382$	−3.17883	−0.162643
$383$	4.42332	0.226021	0.113010	−	0.993594i	$-0.463951\pi$
$383$	4.42332	0.226021	0.113010	+	0.993594i	$0.463951\pi$
$384$	−3.35201	−0.171057
$385$	−38.0505	−1.93923
$386$	−19.6462	−0.999967
$387$	87.8119	4.46373
$388$	13.1049	0.665298
$389$	−7.49094	−0.379806	−0.189903	−	0.981803i	$-0.560817\pi$
$389$	−7.49094	−0.379806	−0.189903	+	0.981803i	$0.560817\pi$
$390$	−38.9589	−1.97276
$391$	24.4311	1.23553
$392$	10.5078	0.530725
$393$	−29.2447	−1.47520
$394$	−13.2743	−0.668748
$395$	−6.62962	−0.333572
$396$	42.1005	2.11563
$397$	11.4718	0.575751	0.287875	−	0.957668i	$-0.407051\pi$
$397$	11.4718	0.575751	0.287875	+	0.957668i	$0.407051\pi$
$398$	−12.0484	−0.603932
$399$	78.4533	3.92758
$400$	−1.83519	−0.0917596
$401$	−7.36633	−0.367857	−0.183928	−	0.982940i	$-0.558881\pi$
$401$	−7.36633	−0.367857	−0.183928	+	0.982940i	$0.558881\pi$
$402$	36.1398	1.80249
$403$	9.18897	0.457735
$404$	−6.39419	−0.318123
$405$	60.7058	3.01650
$406$	6.42647	0.318941
$407$	59.4818	2.94841
$408$	−16.8623	−0.834806
$409$	23.2559	1.14993	0.574964	−	0.818178i	$-0.305016\pi$
$409$	23.2559	1.14993	0.574964	+	0.818178i	$0.305016\pi$
$410$	−0.881702	−0.0435442
$411$	8.18391	0.403683
$412$	13.0304	0.641964
$413$	37.1382	1.82745
$414$	39.9991	1.96585
$415$	−5.44333	−0.267203
$416$	6.53321	0.320317
$417$	30.1957	1.47869
$418$	28.5930	1.39853
$419$	−22.7073	−1.10932	−0.554661	−	0.832076i	$-0.687152\pi$
$419$	−22.7073	−1.10932	−0.554661	+	0.832076i	$0.687152\pi$
$420$	24.9514	1.21751
$421$	19.9605	0.972814	0.486407	−	0.873732i	$-0.338307\pi$
$421$	19.9605	0.972814	0.486407	+	0.873732i	$0.338307\pi$
$422$	6.60622	0.321586
$423$	−48.6770	−2.36675
$424$	−0.430191	−0.0208919
$425$	−9.23191	−0.447813
$426$	29.2779	1.41852
$427$	18.8438	0.911917
$428$	−4.22223	−0.204089
$429$	−111.945	−5.40474
$430$	18.9675	0.914694
$431$	11.0284	0.531218	0.265609	−	0.964081i	$-0.414427\pi$
$431$	11.0284	0.531218	0.265609	+	0.964081i	$0.414427\pi$
$432$	−17.5512	−0.844431
$433$	−1.66086	−0.0798160	−0.0399080	−	0.999203i	$-0.512706\pi$
$433$	−1.66086	−0.0798160	−0.0399080	+	0.999203i	$0.512706\pi$
$434$	−5.88513	−0.282495
$435$	9.15876	0.439129
$436$	−17.8114	−0.853011
$437$	27.1658	1.29952
$438$	−39.8640	−1.90478
$439$	−30.1473	−1.43885	−0.719425	−	0.694570i	$-0.755595\pi$
$439$	−30.1473	−1.43885	−0.719425	+	0.694570i	$0.755595\pi$
$440$	9.09378	0.433529
$441$	86.5424	4.12107
$442$	32.8652	1.56324
$443$	15.0719	0.716087	0.358044	−	0.933705i	$-0.383444\pi$
$443$	15.0719	0.716087	0.358044	+	0.933705i	$0.383444\pi$
$444$	−39.0049	−1.85109
$445$	−19.1829	−0.909358
$446$	8.38724	0.397148
$447$	−10.7510	−0.508505
$448$	−4.18423	−0.197686
$449$	−7.40845	−0.349627	−0.174813	−	0.984602i	$-0.555932\pi$
$449$	−7.40845	−0.349627	−0.174813	+	0.984602i	$0.555932\pi$
$450$	−15.1147	−0.712512
$451$	−2.53349	−0.119297
$452$	13.9184	0.654667
$453$	−42.9314	−2.01709
$454$	−5.13320	−0.240913
$455$	−48.6313	−2.27987
$456$	−18.7497	−0.878037
$457$	−25.1103	−1.17461	−0.587306	−	0.809365i	$-0.699812\pi$
$457$	−25.1103	−1.17461	−0.587306	+	0.809365i	$0.699812\pi$
$458$	−19.5767	−0.914761
$459$	−88.2909	−4.12106
$460$	8.63987	0.402836
$461$	12.2938	0.572577	0.286289	−	0.958143i	$-0.407578\pi$
$461$	12.2938	0.572577	0.286289	+	0.958143i	$0.407578\pi$
$462$	71.6956	3.33558
$463$	−20.4915	−0.952319	−0.476160	−	0.879359i	$-0.657972\pi$
$463$	−20.4915	−0.952319	−0.476160	+	0.879359i	$0.657972\pi$
$464$	−1.53588	−0.0713014
$465$	−8.38726	−0.388950
$466$	−6.60944	−0.306176
$467$	−23.2492	−1.07584	−0.537922	−	0.842995i	$-0.680790\pi$
$467$	−23.2492	−1.07584	−0.537922	+	0.842995i	$0.680790\pi$
$468$	53.8076	2.48726
$469$	45.1123	2.08309
$470$	−10.5143	−0.484989
$471$	49.4107	2.27672
$472$	−8.87576	−0.408540
$473$	54.5014	2.50598
$474$	12.4917	0.573762
$475$	−10.2653	−0.471003
$476$	−21.0487	−0.964766
$477$	−3.54306	−0.162225
$478$	−14.7202	−0.673289
$479$	−3.31220	−0.151339	−0.0756693	−	0.997133i	$-0.524109\pi$
$479$	−3.31220	−0.151339	−0.0756693	+	0.997133i	$0.524109\pi$
$480$	−5.96320	−0.272182
$481$	76.0222	3.46631
$482$	−18.7593	−0.854464
$483$	68.1170	3.09943
$484$	15.1301	0.687733
$485$	23.3134	1.05861
$486$	−61.7298	−2.80012
$487$	34.8518	1.57929	0.789643	−	0.613567i	$-0.210266\pi$
$487$	34.8518	1.57929	0.789643	+	0.613567i	$0.210266\pi$
$488$	−4.50353	−0.203865
$489$	−44.2412	−2.00066
$490$	18.6933	0.844477
$491$	−21.7199	−0.980206	−0.490103	−	0.871664i	$-0.663041\pi$
$491$	−21.7199	−0.980206	−0.490103	+	0.871664i	$0.663041\pi$
$492$	1.66132	0.0748983
$493$	−7.72621	−0.347971
$494$	36.5440	1.64419
$495$	74.8964	3.36634
$496$	1.40650	0.0631538
$497$	36.5469	1.63935
$498$	10.2565	0.459603
$499$	2.88677	0.129230	0.0646148	−	0.997910i	$-0.479418\pi$
$499$	2.88677	0.129230	0.0646148	+	0.997910i	$0.479418\pi$
$500$	−12.1597	−0.543800
$501$	−5.86265	−0.261924
$502$	3.80240	0.169709
$503$	9.90062	0.441447	0.220724	−	0.975336i	$-0.429158\pi$
$503$	9.90062	0.441447	0.220724	+	0.975336i	$0.429158\pi$
$504$	−34.4614	−1.53503
$505$	−11.3752	−0.506190
$506$	24.8259	1.10364
$507$	−99.4974	−4.41883
$508$	−1.80015	−0.0798688
$509$	−7.74006	−0.343072	−0.171536	−	0.985178i	$-0.554873\pi$
$509$	−7.74006	−0.343072	−0.171536	+	0.985178i	$0.554873\pi$
$510$	−29.9978	−1.32832
$511$	−49.7612	−2.20131
$512$	1.00000	0.0441942
$513$	−98.1737	−4.33448
$514$	25.2265	1.11269
$515$	23.1810	1.02148
$516$	−35.7390	−1.57332
$517$	−30.2119	−1.32872
$518$	−48.6888	−2.13927
$519$	−51.4595	−2.25882
$520$	11.6225	0.509681
$521$	−28.7670	−1.26030	−0.630152	−	0.776472i	$-0.717007\pi$
$521$	−28.7670	−1.26030	−0.630152	+	0.776472i	$0.717007\pi$
$522$	−12.6495	−0.553654
$523$	15.9838	0.698924	0.349462	−	0.936951i	$-0.386364\pi$
$523$	15.9838	0.698924	0.349462	+	0.936951i	$0.386364\pi$
$524$	8.72450	0.381132
$525$	−25.7397	−1.12337
$526$	5.40143	0.235513
$527$	7.07538	0.308209
$528$	−17.1347	−0.745693
$529$	0.586687	0.0255081
$530$	−0.765306	−0.0332428
$531$	−73.1008	−3.17230
$532$	−23.4048	−1.01473
$533$	−3.23799	−0.140253
$534$	36.1449	1.56414
$535$	−7.51132	−0.324743
$536$	−10.7815	−0.465690
$537$	−25.3597	−1.09435
$538$	−22.1747	−0.956019
$539$	53.7134	2.31360
$540$	−31.2234	−1.34364
$541$	35.4177	1.52273	0.761363	−	0.648326i	$-0.224530\pi$
$541$	35.4177	1.52273	0.761363	+	0.648326i	$0.224530\pi$
$542$	0.861686	0.0370126
$543$	71.4854	3.06773
$544$	5.03048	0.215680
$545$	−31.6863	−1.35729
$546$	91.6323	3.92150
$547$	40.1256	1.71565	0.857824	−	0.513943i	$-0.171816\pi$
$547$	40.1256	1.71565	0.857824	+	0.513943i	$0.171816\pi$
$548$	−2.44149	−0.104295
$549$	−37.0911	−1.58301
$550$	−9.38107	−0.400010
$551$	−8.59105	−0.365991
$552$	−16.2794	−0.692899
$553$	15.5930	0.663084
$554$	−10.5685	−0.449011
$555$	−69.3894	−2.94542
$556$	−9.00821	−0.382033
$557$	23.9644	1.01540	0.507701	−	0.861533i	$-0.330495\pi$
$557$	23.9644	1.01540	0.507701	+	0.861533i	$0.330495\pi$
$558$	11.5840	0.490388
$559$	69.6568	2.94617
$560$	−7.44371	−0.314554
$561$	−86.1959	−3.63919
$562$	6.61124	0.278878
$563$	−33.9108	−1.42917	−0.714585	−	0.699548i	$-0.753385\pi$
$563$	−33.9108	−1.42917	−0.714585	+	0.699548i	$0.753385\pi$
$564$	19.8113	0.834206
$565$	24.7607	1.04169
$566$	−32.2616	−1.35606
$567$	−142.782	−5.99627
$568$	−8.73442	−0.366488
$569$	38.8566	1.62895	0.814476	−	0.580198i	$-0.197025\pi$
$569$	38.8566	1.62895	0.814476	+	0.580198i	$0.197025\pi$
$570$	−33.3556	−1.39711
$571$	−9.79439	−0.409883	−0.204941	−	0.978774i	$-0.565700\pi$
$571$	−9.79439	−0.409883	−0.204941	+	0.978774i	$0.565700\pi$
$572$	33.3962	1.39637
$573$	10.6555	0.445140
$574$	2.07379	0.0865582
$575$	−8.91282	−0.371690
$576$	8.23600	0.343167
$577$	−26.3487	−1.09691	−0.548454	−	0.836181i	$-0.684784\pi$
$577$	−26.3487	−1.09691	−0.548454	+	0.836181i	$0.684784\pi$
$578$	8.30577	0.345474
$579$	65.8545	2.73682
$580$	−2.73231	−0.113453
$581$	12.8029	0.531152
$582$	−43.9277	−1.82086
$583$	−2.19904	−0.0910748
$584$	11.8925	0.492117
$585$	95.7231	3.95766
$586$	32.6082	1.34703
$587$	−5.80823	−0.239731	−0.119866	−	0.992790i	$-0.538246\pi$
$587$	−5.80823	−0.239731	−0.119866	+	0.992790i	$0.538246\pi$
$588$	−35.2223	−1.45254
$589$	7.86737	0.324169
$590$	−15.7899	−0.650060
$591$	44.4956	1.83030
$592$	11.6363	0.478248
$593$	−6.25275	−0.256770	−0.128385	−	0.991724i	$-0.540979\pi$
$593$	−6.25275	−0.256770	−0.128385	+	0.991724i	$0.540979\pi$
$594$	−89.7174	−3.68115
$595$	−37.4455	−1.53511
$596$	3.20732	0.131377
$597$	40.3865	1.65291
$598$	31.7293	1.29751
$599$	−26.6766	−1.08998	−0.544988	−	0.838444i	$-0.683466\pi$
$599$	−26.6766	−1.08998	−0.544988	+	0.838444i	$0.683466\pi$
$600$	6.15159	0.251138
$601$	7.36025	0.300231	0.150115	−	0.988668i	$-0.452035\pi$
$601$	7.36025	0.300231	0.150115	+	0.988668i	$0.452035\pi$
$602$	−44.6121	−1.81825
$603$	−88.7966	−3.61608
$604$	12.8076	0.521136
$605$	26.9164	1.09431
$606$	21.4334	0.870673
$607$	−18.7335	−0.760371	−0.380185	−	0.924910i	$-0.624140\pi$
$607$	−18.7335	−0.760371	−0.380185	+	0.924910i	$0.624140\pi$
$608$	5.59357	0.226849
$609$	−21.5416	−0.872911
$610$	−8.01175	−0.324386
$611$	−38.6130	−1.56211
$612$	41.4311	1.67475
$613$	−7.11810	−0.287497	−0.143749	−	0.989614i	$-0.545916\pi$
$613$	−7.11810	−0.287497	−0.143749	+	0.989614i	$0.545916\pi$
$614$	13.5730	0.547761
$615$	2.95548	0.119176
$616$	−21.3888	−0.861780
$617$	23.4810	0.945310	0.472655	−	0.881247i	$-0.343296\pi$
$617$	23.4810	0.945310	0.472655	+	0.881247i	$0.343296\pi$
$618$	−43.6782	−1.75700
$619$	3.88156	0.156013	0.0780065	−	0.996953i	$-0.475145\pi$
$619$	3.88156	0.156013	0.0780065	+	0.996953i	$0.475145\pi$
$620$	2.50215	0.100489
$621$	−85.2392	−3.42053
$622$	−10.9266	−0.438117
$623$	45.1188	1.80765
$624$	−21.8994	−0.876679
$625$	−12.4561	−0.498244
$626$	−15.1477	−0.605423
$627$	−95.8442	−3.82765
$628$	−14.7406	−0.588214
$629$	58.5360	2.33398
$630$	−61.3064	−2.44251
$631$	18.3302	0.729713	0.364857	−	0.931064i	$-0.381118\pi$
$631$	18.3302	0.729713	0.364857	+	0.931064i	$0.381118\pi$
$632$	−3.72662	−0.148237
$633$	−22.1441	−0.880150
$634$	−18.7184	−0.743403
$635$	−3.20245	−0.127085
$636$	1.44201	0.0571793
$637$	68.6497	2.72000
$638$	−7.85105	−0.310826
$639$	−71.9367	−2.84577
$640$	1.77899	0.0703208
$641$	29.0391	1.14697	0.573487	−	0.819214i	$-0.305590\pi$
$641$	29.0391	1.14697	0.573487	+	0.819214i	$0.305590\pi$
$642$	14.1530	0.558574
$643$	−35.7508	−1.40987	−0.704937	−	0.709269i	$-0.749025\pi$
$643$	−35.7508	−1.40987	−0.704937	+	0.709269i	$0.749025\pi$
$644$	−20.3212	−0.800768
$645$	−63.5794	−2.50344
$646$	28.1384	1.10709
$647$	−17.8844	−0.703109	−0.351554	−	0.936167i	$-0.614347\pi$
$647$	−17.8844	−0.703109	−0.351554	+	0.936167i	$0.614347\pi$
$648$	34.1238	1.34051
$649$	−45.3708	−1.78096
$650$	−11.9897	−0.470275
$651$	19.7271	0.773164
$652$	13.1984	0.516889
$653$	−4.95369	−0.193853	−0.0969265	−	0.995292i	$-0.530901\pi$
$653$	−4.95369	−0.193853	−0.0969265	+	0.995292i	$0.530901\pi$
$654$	59.7040	2.33461
$655$	15.5208	0.606448
$656$	−0.495619	−0.0193507
$657$	97.9471	3.82128
$658$	24.7299	0.964073
$659$	35.3943	1.37877	0.689383	−	0.724397i	$-0.257882\pi$
$659$	35.3943	1.37877	0.689383	+	0.724397i	$0.257882\pi$
$660$	−30.4825	−1.18653
$661$	−33.3097	−1.29560	−0.647799	−	0.761811i	$-0.724310\pi$
$661$	−33.3097	−1.29560	−0.647799	+	0.761811i	$0.724310\pi$
$662$	15.2669	0.593363
$663$	−110.165	−4.27844
$664$	−3.05979	−0.118743
$665$	−41.6369	−1.61461
$666$	95.8363	3.71358
$667$	−7.45917	−0.288820
$668$	1.74899	0.0676706
$669$	−28.1142	−1.08696
$670$	−19.1802	−0.740996
$671$	−23.0210	−0.888716
$672$	14.0256	0.541050
$673$	−9.00029	−0.346936	−0.173468	−	0.984840i	$-0.555497\pi$
$673$	−9.00029	−0.346936	−0.173468	+	0.984840i	$0.555497\pi$
$674$	−2.96963	−0.114386
$675$	32.2098	1.23975
$676$	29.6828	1.14165
$677$	6.81921	0.262084	0.131042	−	0.991377i	$-0.458168\pi$
$677$	6.81921	0.262084	0.131042	+	0.991377i	$0.458168\pi$
$678$	−46.6547	−1.79176
$679$	−54.8338	−2.10433
$680$	8.94918	0.343186
$681$	17.2066	0.659357
$682$	7.18971	0.275308
$683$	−47.1307	−1.80340	−0.901702	−	0.432358i	$-0.857682\pi$
$683$	−47.1307	−1.80340	−0.901702	+	0.432358i	$0.857682\pi$
$684$	46.0687	1.76148
$685$	−4.34339	−0.165952
$686$	−14.6775	−0.560389
$687$	65.6215	2.50362
$688$	10.6619	0.406483
$689$	−2.81053	−0.107073
$690$	−28.9610	−1.10253
$691$	29.1722	1.10976	0.554881	−	0.831930i	$-0.312764\pi$
$691$	29.1722	1.10976	0.554881	+	0.831930i	$0.312764\pi$
$692$	15.3518	0.583589
$693$	−176.158	−6.69170
$694$	−0.105288	−0.00399669
$695$	−16.0255	−0.607883
$696$	5.14829	0.195145
$697$	−2.49321	−0.0944369
$698$	24.4121	0.924012
$699$	22.1549	0.837977
$700$	7.67887	0.290234
$701$	−7.13016	−0.269303	−0.134651	−	0.990893i	$-0.542991\pi$
$701$	−7.13016	−0.269303	−0.134651	+	0.990893i	$0.542991\pi$
$702$	−114.665	−4.32777
$703$	65.0883	2.45485
$704$	5.11176	0.192657
$705$	35.2441	1.32737
$706$	−15.5950	−0.586924
$707$	26.7548	1.00622
$708$	29.7517	1.11814
$709$	−13.4544	−0.505289	−0.252644	−	0.967559i	$-0.581300\pi$
$709$	−13.4544	−0.505289	−0.252644	+	0.967559i	$0.581300\pi$
$710$	−15.5385	−0.583148
$711$	−30.6925	−1.15106
$712$	−10.7830	−0.404112
$713$	6.83083	0.255817
$714$	70.5556	2.64048
$715$	59.4116	2.22187
$716$	7.56551	0.282736
$717$	49.3425	1.84273
$718$	−14.3136	−0.534178
$719$	−26.0593	−0.971848	−0.485924	−	0.874001i	$-0.661517\pi$
$719$	−26.0593	−0.971848	−0.485924	+	0.874001i	$0.661517\pi$
$720$	14.6518	0.546039
$721$	−54.5224	−2.03052
$722$	12.2881	0.457314
$723$	62.8815	2.33859
$724$	−21.3261	−0.792578
$725$	2.81863	0.104681
$726$	−50.7164	−1.88226
$727$	19.8127	0.734812	0.367406	−	0.930061i	$-0.380246\pi$
$727$	19.8127	0.734812	0.367406	+	0.930061i	$0.380246\pi$
$728$	−27.3365	−1.01316
$729$	104.548	3.87215
$730$	21.1567	0.783046
$731$	53.6348	1.98375
$732$	15.0959	0.557961
$733$	−5.25716	−0.194178	−0.0970888	−	0.995276i	$-0.530953\pi$
$733$	−5.25716	−0.194178	−0.0970888	+	0.995276i	$0.530953\pi$
$734$	−21.9375	−0.809727
$735$	−62.6602	−2.31126
$736$	4.85661	0.179017
$737$	−55.1125	−2.03010
$738$	−4.08192	−0.150258
$739$	−50.4181	−1.85466	−0.927330	−	0.374244i	$-0.877902\pi$
$739$	−50.4181	−1.85466	−0.927330	+	0.374244i	$0.877902\pi$
$740$	20.7008	0.760977
$741$	−122.496	−4.50000
$742$	1.80002	0.0660809
$743$	41.9494	1.53898	0.769488	−	0.638662i	$-0.220512\pi$
$743$	41.9494	1.53898	0.769488	+	0.638662i	$0.220512\pi$
$744$	−4.71462	−0.172846
$745$	5.70580	0.209044
$746$	20.7892	0.761145
$747$	−25.2004	−0.922035
$748$	25.7146	0.940221
$749$	17.6668	0.645531
$750$	40.7596	1.48833
$751$	30.3050	1.10585	0.552923	−	0.833232i	$-0.313512\pi$
$751$	30.3050	1.10585	0.552923	+	0.833232i	$0.313512\pi$
$752$	−5.91026	−0.215525
$753$	−12.7457	−0.464479
$754$	−10.0342	−0.365425
$755$	22.7847	0.829219
$756$	73.4382	2.67092
$757$	25.4127	0.923640	0.461820	−	0.886974i	$-0.347197\pi$
$757$	25.4127	0.923640	0.461820	+	0.886974i	$0.347197\pi$
$758$	18.5634	0.674251
$759$	−83.2167	−3.02057
$760$	9.95091	0.360958
$761$	−14.5262	−0.526574	−0.263287	−	0.964718i	$-0.584807\pi$
$761$	−14.5262	−0.526574	−0.263287	+	0.964718i	$0.584807\pi$
$762$	6.03414	0.218594
$763$	74.5270	2.69806
$764$	−3.17883	−0.115006
$765$	73.7055	2.66483
$766$	4.42332	0.159821
$767$	−57.9872	−2.09380
$768$	−3.35201	−0.120955
$769$	15.0136	0.541406	0.270703	−	0.962663i	$-0.412744\pi$
$769$	15.0136	0.541406	0.270703	+	0.962663i	$0.412744\pi$
$770$	−38.0505	−1.37124
$771$	−84.5595	−3.04533
$772$	−19.6462	−0.707083
$773$	−51.5103	−1.85270	−0.926349	−	0.376667i	$-0.877070\pi$
$773$	−51.5103	−1.85270	−0.926349	+	0.376667i	$0.877070\pi$
$774$	87.8119	3.15633
$775$	−2.58120	−0.0927195
$776$	13.1049	0.470437
$777$	163.206	5.85497
$778$	−7.49094	−0.268563
$779$	−2.77228	−0.0993274
$780$	−38.9589	−1.39495
$781$	−44.6483	−1.59764
$782$	24.4311	0.873655
$783$	26.9565	0.963345
$784$	10.5078	0.375279
$785$	−26.2234	−0.935953
$786$	−29.2447	−1.04312
$787$	−14.5643	−0.519163	−0.259581	−	0.965721i	$-0.583585\pi$
$787$	−14.5643	−0.519163	−0.259581	+	0.965721i	$0.583585\pi$
$788$	−13.2743	−0.472876
$789$	−18.1057	−0.644579
$790$	−6.62962	−0.235871
$791$	−58.2379	−2.07070
$792$	42.1005	1.49598
$793$	−29.4225	−1.04483
$794$	11.4718	0.407117
$795$	2.56532	0.0909825
$796$	−12.0484	−0.427045
$797$	−48.3315	−1.71199	−0.855994	−	0.516986i	$-0.827054\pi$
$797$	−48.3315	−1.71199	−0.855994	+	0.516986i	$0.827054\pi$
$798$	78.4533	2.77722
$799$	−29.7315	−1.05182
$800$	−1.83519	−0.0648839
$801$	−88.8092	−3.13792
$802$	−7.36633	−0.260114
$803$	60.7919	2.14530
$804$	36.1398	1.27455
$805$	−36.1512	−1.27416
$806$	9.18897	0.323668
$807$	74.3299	2.61654
$808$	−6.39419	−0.224947
$809$	37.1288	1.30538	0.652689	−	0.757626i	$-0.273641\pi$
$809$	37.1288	1.30538	0.652689	+	0.757626i	$0.273641\pi$
$810$	60.7058	2.13299
$811$	31.7925	1.11638	0.558192	−	0.829712i	$-0.311495\pi$
$811$	31.7925	1.11638	0.558192	+	0.829712i	$0.311495\pi$
$812$	6.42647	0.225525
$813$	−2.88839	−0.101300
$814$	59.4818	2.08484
$815$	23.4798	0.822462
$816$	−16.8623	−0.590297
$817$	59.6384	2.08648
$818$	23.2559	0.813122
$819$	−225.143	−7.86715
$820$	−0.881702	−0.0307904
$821$	−52.9375	−1.84753	−0.923765	−	0.382960i	$-0.874905\pi$
$821$	−52.9375	−1.84753	−0.923765	+	0.382960i	$0.874905\pi$
$822$	8.18391	0.285447
$823$	−22.8298	−0.795796	−0.397898	−	0.917430i	$-0.630260\pi$
$823$	−22.8298	−0.795796	−0.397898	+	0.917430i	$0.630260\pi$
$824$	13.0304	0.453937
$825$	31.4455	1.09479
$826$	37.1382	1.29220
$827$	31.5130	1.09582	0.547908	−	0.836539i	$-0.315424\pi$
$827$	31.5130	1.09582	0.547908	+	0.836539i	$0.315424\pi$
$828$	39.9991	1.39006
$829$	−4.14911	−0.144105	−0.0720523	−	0.997401i	$-0.522955\pi$
$829$	−4.14911	−0.144105	−0.0720523	+	0.997401i	$0.522955\pi$
$830$	−5.44333	−0.188941
$831$	35.4257	1.22890
$832$	6.53321	0.226498
$833$	52.8594	1.83147
$834$	30.1957	1.04559
$835$	3.11144	0.107676
$836$	28.5930	0.988910
$837$	−24.6857	−0.853264
$838$	−22.7073	−0.784409
$839$	18.9658	0.654771	0.327385	−	0.944891i	$-0.393832\pi$
$839$	18.9658	0.654771	0.327385	+	0.944891i	$0.393832\pi$
$840$	24.9514	0.860906
$841$	−26.6411	−0.918658
$842$	19.9605	0.687883
$843$	−22.1610	−0.763264
$844$	6.60622	0.227395
$845$	52.8055	1.81656
$846$	−48.6770	−1.67355
$847$	−63.3080	−2.17529
$848$	−0.430191	−0.0147728
$849$	108.141	3.71140
$850$	−9.23191	−0.316652
$851$	56.5128	1.93723
$852$	29.2779	1.00304
$853$	−14.9489	−0.511841	−0.255921	−	0.966698i	$-0.582379\pi$
$853$	−14.9489	−0.511841	−0.255921	+	0.966698i	$0.582379\pi$
$854$	18.8438	0.644823
$855$	81.9558	2.80283
$856$	−4.22223	−0.144313
$857$	−30.1973	−1.03152	−0.515760	−	0.856733i	$-0.672490\pi$
$857$	−30.1973	−1.03152	−0.515760	+	0.856733i	$0.672490\pi$
$858$	−111.945	−3.82173
$859$	26.4720	0.903212	0.451606	−	0.892217i	$-0.350851\pi$
$859$	26.4720	0.903212	0.451606	+	0.892217i	$0.350851\pi$
$860$	18.9675	0.646787
$861$	−6.95137	−0.236902
$862$	11.0284	0.375628
$863$	−9.12359	−0.310571	−0.155285	−	0.987870i	$-0.549630\pi$
$863$	−9.12359	−0.310571	−0.155285	+	0.987870i	$0.549630\pi$
$864$	−17.5512	−0.597103
$865$	27.3107	0.928593
$866$	−1.66086	−0.0564385
$867$	−27.8411	−0.945532
$868$	−5.88513	−0.199754
$869$	−19.0496	−0.646213
$870$	9.15876	0.310511
$871$	−70.4379	−2.38670
$872$	−17.8114	−0.603170
$873$	107.932	3.65293
$874$	27.1658	0.918897
$875$	50.8792	1.72003
$876$	−39.8640	−1.34688
$877$	−42.6680	−1.44080	−0.720398	−	0.693561i	$-0.756041\pi$
$877$	−42.6680	−1.44080	−0.720398	+	0.693561i	$0.756041\pi$
$878$	−30.1473	−1.01742
$879$	−109.303	−3.68671
$880$	9.09378	0.306551
$881$	−30.8988	−1.04101	−0.520504	−	0.853859i	$-0.674256\pi$
$881$	−30.8988	−1.04101	−0.520504	+	0.853859i	$0.674256\pi$
$882$	86.5424	2.91403
$883$	24.4877	0.824077	0.412039	−	0.911166i	$-0.364817\pi$
$883$	24.4877	0.824077	0.412039	+	0.911166i	$0.364817\pi$
$884$	32.8652	1.10538
$885$	52.9280	1.77915
$886$	15.0719	0.506350
$887$	−5.66762	−0.190300	−0.0951500	−	0.995463i	$-0.530333\pi$
$887$	−5.66762	−0.190300	−0.0951500	+	0.995463i	$0.530333\pi$
$888$	−39.0049	−1.30892
$889$	7.53226	0.252624
$890$	−19.1829	−0.643013
$891$	174.433	5.84371
$892$	8.38724	0.280826
$893$	−33.0595	−1.10629
$894$	−10.7510	−0.359567
$895$	13.4590	0.449884
$896$	−4.18423	−0.139785
$897$	−106.357	−3.55116
$898$	−7.40845	−0.247223
$899$	−2.16022	−0.0720472
$900$	−15.1147	−0.503822
$901$	−2.16407	−0.0720957
$902$	−2.53349	−0.0843560
$903$	149.540	4.97639
$904$	13.9184	0.462920
$905$	−37.9389	−1.26113
$906$	−42.9314	−1.42630
$907$	6.61227	0.219557	0.109778	−	0.993956i	$-0.464986\pi$
$907$	6.61227	0.219557	0.109778	+	0.993956i	$0.464986\pi$
$908$	−5.13320	−0.170351
$909$	−52.6626	−1.74671
$910$	−48.6313	−1.61211
$911$	23.6227	0.782656	0.391328	−	0.920251i	$-0.372016\pi$
$911$	23.6227	0.782656	0.391328	+	0.920251i	$0.372016\pi$
$912$	−18.7497	−0.620866
$913$	−15.6409	−0.517639
$914$	−25.1103	−0.830576
$915$	26.8555	0.887815
$916$	−19.5767	−0.646833
$917$	−36.5053	−1.20551
$918$	−88.2909	−2.91403
$919$	24.3636	0.803681	0.401840	−	0.915710i	$-0.368371\pi$
$919$	24.3636	0.803681	0.401840	+	0.915710i	$0.368371\pi$
$920$	8.63987	0.284848
$921$	−45.4968	−1.49917
$922$	12.2938	0.404873
$923$	−57.0638	−1.87828
$924$	71.6956	2.35861
$925$	−21.3548	−0.702141
$926$	−20.4915	−0.673391
$927$	107.319	3.52481
$928$	−1.53588	−0.0504177
$929$	46.8191	1.53608	0.768042	−	0.640399i	$-0.221231\pi$
$929$	46.8191	1.53608	0.768042	+	0.640399i	$0.221231\pi$
$930$	−8.38726	−0.275029
$931$	58.7762	1.92631
$932$	−6.60944	−0.216499
$933$	36.6262	1.19909
$934$	−23.2492	−0.760736
$935$	45.7461	1.49606
$936$	53.8076	1.75876
$937$	−12.0997	−0.395280	−0.197640	−	0.980275i	$-0.563328\pi$
$937$	−12.0997	−0.395280	−0.197640	+	0.980275i	$0.563328\pi$
$938$	45.1123	1.47297
$939$	50.7753	1.65699
$940$	−10.5143	−0.342939
$941$	3.35130	0.109249	0.0546247	−	0.998507i	$-0.482604\pi$
$941$	3.35130	0.109249	0.0546247	+	0.998507i	$0.482604\pi$
$942$	49.4107	1.60989
$943$	−2.40703	−0.0783837
$944$	−8.87576	−0.288881
$945$	130.646	4.24991
$946$	54.5014	1.77199
$947$	15.0396	0.488721	0.244361	−	0.969684i	$-0.421422\pi$
$947$	15.0396	0.488721	0.244361	+	0.969684i	$0.421422\pi$
$948$	12.4917	0.405711
$949$	77.6965	2.52214
$950$	−10.2653	−0.333050
$951$	62.7444	2.03463
$952$	−21.0487	−0.682193
$953$	24.1757	0.783126	0.391563	−	0.920151i	$-0.371934\pi$
$953$	24.1757	0.783126	0.391563	+	0.920151i	$0.371934\pi$
$954$	−3.54306	−0.114711
$955$	−5.65511	−0.182995
$956$	−14.7202	−0.476087
$957$	26.3168	0.850702
$958$	−3.31220	−0.107012
$959$	10.2158	0.329884
$960$	−5.96320	−0.192462
$961$	−29.0218	−0.936186
$962$	76.0222	2.45105
$963$	−34.7743	−1.12059
$964$	−18.7593	−0.604197
$965$	−34.9505	−1.12510
$966$	68.1170	2.19163
$967$	−23.9503	−0.770190	−0.385095	−	0.922877i	$-0.625831\pi$
$967$	−23.9503	−0.770190	−0.385095	+	0.922877i	$0.625831\pi$
$968$	15.1301	0.486301
$969$	−94.3203	−3.03000
$970$	23.3134	0.748549
$971$	19.0338	0.610824	0.305412	−	0.952220i	$-0.401206\pi$
$971$	19.0338	0.610824	0.305412	+	0.952220i	$0.401206\pi$
$972$	−61.7298	−1.97999
$973$	37.6925	1.20836
$974$	34.8518	1.11672
$975$	40.1897	1.28710
$976$	−4.50353	−0.144155
$977$	20.9532	0.670353	0.335176	−	0.942155i	$-0.391204\pi$
$977$	20.9532	0.670353	0.335176	+	0.942155i	$0.391204\pi$
$978$	−44.2412	−1.41468
$979$	−55.1204	−1.76165
$980$	18.6933	0.597135
$981$	−146.695	−4.68360
$982$	−21.7199	−0.693110
$983$	9.40576	0.299997	0.149999	−	0.988686i	$-0.452073\pi$
$983$	9.40576	0.299997	0.149999	+	0.988686i	$0.452073\pi$
$984$	1.66132	0.0529611
$985$	−23.6148	−0.752430
$986$	−7.72621	−0.246053
$987$	−82.8951	−2.63858
$988$	36.5440	1.16262
$989$	51.7810	1.64654
$990$	74.8964	2.38036
$991$	−30.8799	−0.980933	−0.490466	−	0.871460i	$-0.663174\pi$
$991$	−30.8799	−0.980933	−0.490466	+	0.871460i	$0.663174\pi$
$992$	1.40650	0.0446565
$993$	−51.1747	−1.62398
$994$	36.5469	1.15920
$995$	−21.4340	−0.679504
$996$	10.2565	0.324988
$997$	33.7673	1.06942	0.534710	−	0.845036i	$-0.320421\pi$
$997$	33.7673	1.06942	0.534710	+	0.845036i	$0.320421\pi$
$998$	2.88677	0.0913791
$999$	−204.230	−6.46155

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.d.1.1	✓	79

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.d.1.1	✓	79	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.35201 q^{3} +1.00000 q^{4} +1.77899 q^{5} -3.35201 q^{6} -4.18423 q^{7} +1.00000 q^{8} +8.23600 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.35201 q^{3} +1.00000 q^{4} +1.77899 q^{5} -3.35201 q^{6} -4.18423 q^{7} +1.00000 q^{8} +8.23600 q^{9} +1.77899 q^{10} +5.11176 q^{11} -3.35201 q^{12} +6.53321 q^{13} -4.18423 q^{14} -5.96320 q^{15} +1.00000 q^{16} +5.03048 q^{17} +8.23600 q^{18} +5.59357 q^{19} +1.77899 q^{20} +14.0256 q^{21} +5.11176 q^{22} +4.85661 q^{23} -3.35201 q^{24} -1.83519 q^{25} +6.53321 q^{26} -17.5512 q^{27} -4.18423 q^{28} -1.53588 q^{29} -5.96320 q^{30} +1.40650 q^{31} +1.00000 q^{32} -17.1347 q^{33} +5.03048 q^{34} -7.44371 q^{35} +8.23600 q^{36} +11.6363 q^{37} +5.59357 q^{38} -21.8994 q^{39} +1.77899 q^{40} -0.495619 q^{41} +14.0256 q^{42} +10.6619 q^{43} +5.11176 q^{44} +14.6518 q^{45} +4.85661 q^{46} -5.91026 q^{47} -3.35201 q^{48} +10.5078 q^{49} -1.83519 q^{50} -16.8623 q^{51} +6.53321 q^{52} -0.430191 q^{53} -17.5512 q^{54} +9.09378 q^{55} -4.18423 q^{56} -18.7497 q^{57} -1.53588 q^{58} -8.87576 q^{59} -5.96320 q^{60} -4.50353 q^{61} +1.40650 q^{62} -34.4614 q^{63} +1.00000 q^{64} +11.6225 q^{65} -17.1347 q^{66} -10.7815 q^{67} +5.03048 q^{68} -16.2794 q^{69} -7.44371 q^{70} -8.73442 q^{71} +8.23600 q^{72} +11.8925 q^{73} +11.6363 q^{74} +6.15159 q^{75} +5.59357 q^{76} -21.3888 q^{77} -21.8994 q^{78} -3.72662 q^{79} +1.77899 q^{80} +34.1238 q^{81} -0.495619 q^{82} -3.05979 q^{83} +14.0256 q^{84} +8.94918 q^{85} +10.6619 q^{86} +5.14829 q^{87} +5.11176 q^{88} -10.7830 q^{89} +14.6518 q^{90} -27.3365 q^{91} +4.85661 q^{92} -4.71462 q^{93} -5.91026 q^{94} +9.95091 q^{95} -3.35201 q^{96} +13.1049 q^{97} +10.5078 q^{98} +42.1005 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9}+O(q^{10}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9	\( 79 q + 79 q^{2} + 17 q^{3} + 79 q^{4} + 18 q^{5} + 17 q^{6} + 19 q^{7} + 79 q^{8} + 118 q^{9} + 18 q^{10} + 28 q^{11} + 17 q^{12} + 47 q^{13} + 19 q^{14} + 14 q^{15} + 79 q^{16} + 36 q^{17} + 118 q^{18} + 29 q^{19} + 18 q^{20} + 45 q^{21} + 28 q^{22} + 23 q^{23} + 17 q^{24} + 161 q^{25} + 47 q^{26} + 50 q^{27} + 19 q^{28} + 53 q^{29} + 14 q^{30} + 29 q^{31} + 79 q^{32} + 34 q^{33} + 36 q^{34} + 33 q^{35} + 118 q^{36} + 89 q^{37} + 29 q^{38} - 7 q^{39} + 18 q^{40} + 58 q^{41} + 45 q^{42} + 88 q^{43} + 28 q^{44} + 45 q^{45} + 23 q^{46} + 3 q^{47} + 17 q^{48} + 162 q^{49} + 161 q^{50} + 29 q^{51} + 47 q^{52} + 88 q^{53} + 50 q^{54} + 37 q^{55} + 19 q^{56} + 54 q^{57} + 53 q^{58} + 37 q^{59} + 14 q^{60} + 55 q^{61} + 29 q^{62} + 21 q^{63} + 79 q^{64} + 55 q^{65} + 34 q^{66} + 107 q^{67} + 36 q^{68} + 39 q^{69} + 33 q^{70} - 5 q^{71} + 118 q^{72} + 71 q^{73} + 89 q^{74} + 37 q^{75} + 29 q^{76} + 61 q^{77} - 7 q^{78} + 29 q^{79} + 18 q^{80} + 215 q^{81} + 58 q^{82} + 42 q^{83} + 45 q^{84} + 84 q^{85} + 88 q^{86} + 15 q^{87} + 28 q^{88} + 72 q^{89} + 45 q^{90} + 70 q^{91} + 23 q^{92} + 97 q^{93} + 3 q^{94} - 18 q^{95} + 17 q^{96} + 93 q^{97} + 162 q^{98} + 49 q^{99}+O(q^{100}) \) 79 * q + 79 * q^2 + 17 * q^3 + 79 * q^4 + 18 * q^5 + 17 * q^6 + 19 * q^7 + 79 * q^8 + 118 * q^9 + 18 * q^10 + 28 * q^11 + 17 * q^12 + 47 * q^13 + 19 * q^14 + 14 * q^15 + 79 * q^16 + 36 * q^17 + 118 * q^18 + 29 * q^19 + 18 * q^20 + 45 * q^21 + 28 * q^22 + 23 * q^23 + 17 * q^24 + 161 * q^25 + 47 * q^26 + 50 * q^27 + 19 * q^28 + 53 * q^29 + 14 * q^30 + 29 * q^31 + 79 * q^32 + 34 * q^33 + 36 * q^34 + 33 * q^35 + 118 * q^36 + 89 * q^37 + 29 * q^38 - 7 * q^39 + 18 * q^40 + 58 * q^41 + 45 * q^42 + 88 * q^43 + 28 * q^44 + 45 * q^45 + 23 * q^46 + 3 * q^47 + 17 * q^48 + 162 * q^49 + 161 * q^50 + 29 * q^51 + 47 * q^52 + 88 * q^53 + 50 * q^54 + 37 * q^55 + 19 * q^56 + 54 * q^57 + 53 * q^58 + 37 * q^59 + 14 * q^60 + 55 * q^61 + 29 * q^62 + 21 * q^63 + 79 * q^64 + 55 * q^65 + 34 * q^66 + 107 * q^67 + 36 * q^68 + 39 * q^69 + 33 * q^70 - 5 * q^71 + 118 * q^72 + 71 * q^73 + 89 * q^74 + 37 * q^75 + 29 * q^76 + 61 * q^77 - 7 * q^78 + 29 * q^79 + 18 * q^80 + 215 * q^81 + 58 * q^82 + 42 * q^83 + 45 * q^84 + 84 * q^85 + 88 * q^86 + 15 * q^87 + 28 * q^88 + 72 * q^89 + 45 * q^90 + 70 * q^91 + 23 * q^92 + 97 * q^93 + 3 * q^94 - 18 * q^95 + 17 * q^96 + 93 * q^97 + 162 * q^98 + 49 * q^99

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