LMFDB - Embedded newform 8002.2.a.g.1.11

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:	$0$
Dimension:	$95$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.68330 q^{3} +1.00000 q^{4} -1.68032 q^{5} -2.68330 q^{6} +0.225636 q^{7} +1.00000 q^{8} +4.20011 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.68330 q^{3} +1.00000 q^{4} -1.68032 q^{5} -2.68330 q^{6} +0.225636 q^{7} +1.00000 q^{8} +4.20011 q^{9} -1.68032 q^{10} +3.84702 q^{11} -2.68330 q^{12} -2.95410 q^{13} +0.225636 q^{14} +4.50880 q^{15} +1.00000 q^{16} +4.77287 q^{17} +4.20011 q^{18} -1.36548 q^{19} -1.68032 q^{20} -0.605449 q^{21} +3.84702 q^{22} -8.06646 q^{23} -2.68330 q^{24} -2.17654 q^{25} -2.95410 q^{26} -3.22025 q^{27} +0.225636 q^{28} +5.05096 q^{29} +4.50880 q^{30} +6.01553 q^{31} +1.00000 q^{32} -10.3227 q^{33} +4.77287 q^{34} -0.379140 q^{35} +4.20011 q^{36} +11.6724 q^{37} -1.36548 q^{38} +7.92675 q^{39} -1.68032 q^{40} +5.20726 q^{41} -0.605449 q^{42} -10.7804 q^{43} +3.84702 q^{44} -7.05751 q^{45} -8.06646 q^{46} +6.78382 q^{47} -2.68330 q^{48} -6.94909 q^{49} -2.17654 q^{50} -12.8070 q^{51} -2.95410 q^{52} +0.601041 q^{53} -3.22025 q^{54} -6.46421 q^{55} +0.225636 q^{56} +3.66399 q^{57} +5.05096 q^{58} -3.91123 q^{59} +4.50880 q^{60} -10.8515 q^{61} +6.01553 q^{62} +0.947695 q^{63} +1.00000 q^{64} +4.96383 q^{65} -10.3227 q^{66} +10.2729 q^{67} +4.77287 q^{68} +21.6447 q^{69} -0.379140 q^{70} -15.4875 q^{71} +4.20011 q^{72} +2.03264 q^{73} +11.6724 q^{74} +5.84030 q^{75} -1.36548 q^{76} +0.868026 q^{77} +7.92675 q^{78} -4.20596 q^{79} -1.68032 q^{80} -3.95942 q^{81} +5.20726 q^{82} -0.353279 q^{83} -0.605449 q^{84} -8.01993 q^{85} -10.7804 q^{86} -13.5533 q^{87} +3.84702 q^{88} +4.55562 q^{89} -7.05751 q^{90} -0.666552 q^{91} -8.06646 q^{92} -16.1415 q^{93} +6.78382 q^{94} +2.29443 q^{95} -2.68330 q^{96} +15.7585 q^{97} -6.94909 q^{98} +16.1579 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) $ 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * 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
$3$	−2.68330	−1.54920	−0.774602	−	0.632448i	$-0.782050\pi$
$3$	−2.68330	−1.54920	−0.774602	+	0.632448i	$0.782050\pi$
$4$	1.00000	0.500000
$5$	−1.68032	−0.751461	−0.375730	−	0.926729i	$-0.622608\pi$
$5$	−1.68032	−0.751461	−0.375730	+	0.926729i	$0.622608\pi$
$6$	−2.68330	−1.09545
$7$	0.225636	0.0852824	0.0426412	−	0.999090i	$-0.486423\pi$
$7$	0.225636	0.0852824	0.0426412	+	0.999090i	$0.486423\pi$
$8$	1.00000	0.353553
$9$	4.20011	1.40004
$10$	−1.68032	−0.531363
$11$	3.84702	1.15992	0.579960	−	0.814645i	$-0.303068\pi$
$11$	3.84702	1.15992	0.579960	+	0.814645i	$0.303068\pi$
$12$	−2.68330	−0.774602
$13$	−2.95410	−0.819320	−0.409660	−	0.912238i	$-0.634353\pi$
$13$	−2.95410	−0.819320	−0.409660	+	0.912238i	$0.634353\pi$
$14$	0.225636	0.0603037
$15$	4.50880	1.16417
$16$	1.00000	0.250000
$17$	4.77287	1.15759	0.578795	−	0.815473i	$-0.303523\pi$
$17$	4.77287	1.15759	0.578795	+	0.815473i	$0.303523\pi$
$18$	4.20011	0.989975
$19$	−1.36548	−0.313262	−0.156631	−	0.987657i	$-0.550063\pi$
$19$	−1.36548	−0.313262	−0.156631	+	0.987657i	$0.550063\pi$
$20$	−1.68032	−0.375730
$21$	−0.605449	−0.132120
$22$	3.84702	0.820187
$23$	−8.06646	−1.68197	−0.840986	−	0.541056i	$-0.818025\pi$
$23$	−8.06646	−1.68197	−0.840986	+	0.541056i	$0.818025\pi$
$24$	−2.68330	−0.547727
$25$	−2.17654	−0.435307
$26$	−2.95410	−0.579347
$27$	−3.22025	−0.619737
$28$	0.225636	0.0426412
$29$	5.05096	0.937940	0.468970	−	0.883214i	$-0.344625\pi$
$29$	5.05096	0.937940	0.468970	+	0.883214i	$0.344625\pi$
$30$	4.50880	0.823190
$31$	6.01553	1.08042	0.540210	−	0.841530i	$-0.318345\pi$
$31$	6.01553	1.08042	0.540210	+	0.841530i	$0.318345\pi$
$32$	1.00000	0.176777
$33$	−10.3227	−1.79695
$34$	4.77287	0.818540
$35$	−0.379140	−0.0640863
$36$	4.20011	0.700018
$37$	11.6724	1.91893	0.959463	−	0.281835i	$-0.0909432\pi$
$37$	11.6724	1.91893	0.959463	+	0.281835i	$0.0909432\pi$
$38$	−1.36548	−0.221510
$39$	7.92675	1.26930
$40$	−1.68032	−0.265681
$41$	5.20726	0.813237	0.406619	−	0.913598i	$-0.366708\pi$
$41$	5.20726	0.813237	0.406619	+	0.913598i	$0.366708\pi$
$42$	−0.605449	−0.0934229
$43$	−10.7804	−1.64399	−0.821997	−	0.569492i	$-0.807140\pi$
$43$	−10.7804	−1.64399	−0.821997	+	0.569492i	$0.807140\pi$
$44$	3.84702	0.579960
$45$	−7.05751	−1.05207
$46$	−8.06646	−1.18933
$47$	6.78382	0.989522	0.494761	−	0.869029i	$-0.335256\pi$
$47$	6.78382	0.989522	0.494761	+	0.869029i	$0.335256\pi$
$48$	−2.68330	−0.387301
$49$	−6.94909	−0.992727
$50$	−2.17654	−0.307809
$51$	−12.8070	−1.79334
$52$	−2.95410	−0.409660
$53$	0.601041	0.0825594	0.0412797	−	0.999148i	$-0.486857\pi$
$53$	0.601041	0.0825594	0.0412797	+	0.999148i	$0.486857\pi$
$54$	−3.22025	−0.438220
$55$	−6.46421	−0.871634
$56$	0.225636	0.0301519
$57$	3.66399	0.485307
$58$	5.05096	0.663224
$59$	−3.91123	−0.509199	−0.254600	−	0.967047i	$-0.581944\pi$
$59$	−3.91123	−0.509199	−0.254600	+	0.967047i	$0.581944\pi$
$60$	4.50880	0.582083
$61$	−10.8515	−1.38939	−0.694694	−	0.719306i	$-0.744460\pi$
$61$	−10.8515	−1.38939	−0.694694	+	0.719306i	$0.744460\pi$
$62$	6.01553	0.763973
$63$	0.947695	0.119398
$64$	1.00000	0.125000
$65$	4.96383	0.615687
$66$	−10.3227	−1.27064
$67$	10.2729	1.25503	0.627514	−	0.778605i	$-0.284072\pi$
$67$	10.2729	1.25503	0.627514	+	0.778605i	$0.284072\pi$
$68$	4.77287	0.578795
$69$	21.6447	2.60572
$70$	−0.379140	−0.0453159
$71$	−15.4875	−1.83803	−0.919014	−	0.394225i	$-0.871013\pi$
$71$	−15.4875	−1.83803	−0.919014	+	0.394225i	$0.871013\pi$
$72$	4.20011	0.494987
$73$	2.03264	0.237902	0.118951	−	0.992900i	$-0.462047\pi$
$73$	2.03264	0.237902	0.118951	+	0.992900i	$0.462047\pi$
$74$	11.6724	1.35689
$75$	5.84030	0.674380
$76$	−1.36548	−0.156631
$77$	0.868026	0.0989207
$78$	7.92675	0.897527
$79$	−4.20596	−0.473208	−0.236604	−	0.971606i	$-0.576034\pi$
$79$	−4.20596	−0.473208	−0.236604	+	0.971606i	$0.576034\pi$
$80$	−1.68032	−0.187865
$81$	−3.95942	−0.439936
$82$	5.20726	0.575045
$83$	−0.353279	−0.0387774	−0.0193887	−	0.999812i	$-0.506172\pi$
$83$	−0.353279	−0.0387774	−0.0193887	+	0.999812i	$0.506172\pi$
$84$	−0.605449	−0.0660599
$85$	−8.01993	−0.869883
$86$	−10.7804	−1.16248
$87$	−13.5533	−1.45306
$88$	3.84702	0.410094
$89$	4.55562	0.482895	0.241447	−	0.970414i	$-0.422378\pi$
$89$	4.55562	0.482895	0.241447	+	0.970414i	$0.422378\pi$
$90$	−7.05751	−0.743927
$91$	−0.666552	−0.0698736
$92$	−8.06646	−0.840986
$93$	−16.1415	−1.67379
$94$	6.78382	0.699697
$95$	2.29443	0.235404
$96$	−2.68330	−0.273863
$97$	15.7585	1.60004	0.800018	−	0.599976i	$-0.204823\pi$
$97$	15.7585	1.60004	0.800018	+	0.599976i	$0.204823\pi$
$98$	−6.94909	−0.701964
$99$	16.1579	1.62393
$100$	−2.17654	−0.217654
$101$	7.95815	0.791866	0.395933	−	0.918279i	$-0.370421\pi$
$101$	7.95815	0.791866	0.395933	+	0.918279i	$0.370421\pi$
$102$	−12.8070	−1.26809
$103$	14.9934	1.47734	0.738671	−	0.674066i	$-0.235454\pi$
$103$	14.9934	1.47734	0.738671	+	0.674066i	$0.235454\pi$
$104$	−2.95410	−0.289673
$105$	1.01735	0.0992829
$106$	0.601041	0.0583783
$107$	−12.5165	−1.21001	−0.605007	−	0.796220i	$-0.706830\pi$
$107$	−12.5165	−1.21001	−0.605007	+	0.796220i	$0.706830\pi$
$108$	−3.22025	−0.309869
$109$	−10.6058	−1.01585	−0.507924	−	0.861402i	$-0.669587\pi$
$109$	−10.6058	−1.01585	−0.507924	+	0.861402i	$0.669587\pi$
$110$	−6.46421	−0.616338
$111$	−31.3205	−2.97281
$112$	0.225636	0.0213206
$113$	−19.5772	−1.84167	−0.920834	−	0.389955i	$-0.872491\pi$
$113$	−19.5772	−1.84167	−0.920834	+	0.389955i	$0.872491\pi$
$114$	3.66399	0.343164
$115$	13.5542	1.26394
$116$	5.05096	0.468970
$117$	−12.4075	−1.14708
$118$	−3.91123	−0.360058
$119$	1.07693	0.0987221
$120$	4.50880	0.411595
$121$	3.79956	0.345415
$122$	−10.8515	−0.982445
$123$	−13.9726	−1.25987
$124$	6.01553	0.540210
$125$	12.0589	1.07858
$126$	0.947695	0.0844274
$127$	16.5915	1.47225	0.736127	−	0.676844i	$-0.236653\pi$
$127$	16.5915	1.47225	0.736127	+	0.676844i	$0.236653\pi$
$128$	1.00000	0.0883883
$129$	28.9270	2.54688
$130$	4.96383	0.435356
$131$	−16.5521	−1.44617	−0.723083	−	0.690762i	$-0.757275\pi$
$131$	−16.5521	−1.44617	−0.723083	+	0.690762i	$0.757275\pi$
$132$	−10.3227	−0.898477
$133$	−0.308101	−0.0267157
$134$	10.2729	0.887439
$135$	5.41104	0.465708
$136$	4.77287	0.409270
$137$	−21.3183	−1.82134	−0.910672	−	0.413131i	$-0.864435\pi$
$137$	−21.3183	−1.82134	−0.910672	+	0.413131i	$0.864435\pi$
$138$	21.6447	1.84252
$139$	9.91975	0.841382	0.420691	−	0.907204i	$-0.361788\pi$
$139$	9.91975	0.841382	0.420691	+	0.907204i	$0.361788\pi$
$140$	−0.379140	−0.0320432
$141$	−18.2030	−1.53297
$142$	−15.4875	−1.29968
$143$	−11.3645	−0.950346
$144$	4.20011	0.350009
$145$	−8.48722	−0.704825
$146$	2.03264	0.168222
$147$	18.6465	1.53794
$148$	11.6724	0.959463
$149$	17.4631	1.43063	0.715317	−	0.698800i	$-0.246282\pi$
$149$	17.4631	1.43063	0.715317	+	0.698800i	$0.246282\pi$
$150$	5.84030	0.476859
$151$	0.506723	0.0412365	0.0206183	−	0.999787i	$-0.493437\pi$
$151$	0.506723	0.0412365	0.0206183	+	0.999787i	$0.493437\pi$
$152$	−1.36548	−0.110755
$153$	20.0466	1.62067
$154$	0.868026	0.0699475
$155$	−10.1080	−0.811893
$156$	7.92675	0.634648
$157$	7.32806	0.584843	0.292422	−	0.956290i	$-0.405539\pi$
$157$	7.32806	0.584843	0.292422	+	0.956290i	$0.405539\pi$
$158$	−4.20596	−0.334608
$159$	−1.61278	−0.127901
$160$	−1.68032	−0.132841
$161$	−1.82008	−0.143443
$162$	−3.95942	−0.311081
$163$	22.7737	1.78377	0.891886	−	0.452261i	$-0.149382\pi$
$163$	22.7737	1.78377	0.891886	+	0.452261i	$0.149382\pi$
$164$	5.20726	0.406619
$165$	17.3454	1.35034
$166$	−0.353279	−0.0274197
$167$	2.42920	0.187977	0.0939885	−	0.995573i	$-0.470038\pi$
$167$	2.42920	0.187977	0.0939885	+	0.995573i	$0.470038\pi$
$168$	−0.605449	−0.0467114
$169$	−4.27328	−0.328714
$170$	−8.01993	−0.615101
$171$	−5.73515	−0.438578
$172$	−10.7804	−0.821997
$173$	3.84593	0.292401	0.146200	−	0.989255i	$-0.453296\pi$
$173$	3.84593	0.292401	0.146200	+	0.989255i	$0.453296\pi$
$174$	−13.5533	−1.02747
$175$	−0.491105	−0.0371240
$176$	3.84702	0.289980
$177$	10.4950	0.788854
$178$	4.55562	0.341458
$179$	17.5869	1.31451	0.657254	−	0.753670i	$-0.271718\pi$
$179$	17.5869	1.31451	0.657254	+	0.753670i	$0.271718\pi$
$180$	−7.05751	−0.526036
$181$	−6.37852	−0.474112	−0.237056	−	0.971496i	$-0.576182\pi$
$181$	−6.37852	−0.474112	−0.237056	+	0.971496i	$0.576182\pi$
$182$	−0.666552	−0.0494081
$183$	29.1178	2.15245
$184$	−8.06646	−0.594667
$185$	−19.6133	−1.44200
$186$	−16.1415	−1.18355
$187$	18.3613	1.34271
$188$	6.78382	0.494761
$189$	−0.726604	−0.0528527
$190$	2.29443	0.166456
$191$	−6.42409	−0.464831	−0.232415	−	0.972617i	$-0.574663\pi$
$191$	−6.42409	−0.464831	−0.232415	+	0.972617i	$0.574663\pi$
$192$	−2.68330	−0.193651
$193$	3.71798	0.267626	0.133813	−	0.991007i	$-0.457278\pi$
$193$	3.71798	0.267626	0.133813	+	0.991007i	$0.457278\pi$
$194$	15.7585	1.13140
$195$	−13.3194	−0.953825
$196$	−6.94909	−0.496363
$197$	−0.678498	−0.0483410	−0.0241705	−	0.999708i	$-0.507694\pi$
$197$	−0.678498	−0.0483410	−0.0241705	+	0.999708i	$0.507694\pi$
$198$	16.1579	1.14829
$199$	−20.9925	−1.48812	−0.744059	−	0.668114i	$-0.767102\pi$
$199$	−20.9925	−1.48812	−0.744059	+	0.668114i	$0.767102\pi$
$200$	−2.17654	−0.153904
$201$	−27.5652	−1.94430
$202$	7.95815	0.559934
$203$	1.13968	0.0799898
$204$	−12.8070	−0.896672
$205$	−8.74984	−0.611116
$206$	14.9934	1.04464
$207$	−33.8800	−2.35482
$208$	−2.95410	−0.204830
$209$	−5.25302	−0.363359
$210$	1.01735	0.0702036
$211$	21.8374	1.50335	0.751674	−	0.659535i	$-0.229247\pi$
$211$	21.8374	1.50335	0.751674	+	0.659535i	$0.229247\pi$
$212$	0.601041	0.0412797
$213$	41.5576	2.84748
$214$	−12.5165	−0.855609
$215$	18.1145	1.23540
$216$	−3.22025	−0.219110
$217$	1.35732	0.0921408
$218$	−10.6058	−0.718313
$219$	−5.45417	−0.368559
$220$	−6.46421	−0.435817
$221$	−14.0995	−0.948437
$222$	−31.3205	−2.10209
$223$	7.19054	0.481514	0.240757	−	0.970585i	$-0.422604\pi$
$223$	7.19054	0.481514	0.240757	+	0.970585i	$0.422604\pi$
$224$	0.225636	0.0150759
$225$	−9.14168	−0.609445
$226$	−19.5772	−1.30226
$227$	−10.6488	−0.706784	−0.353392	−	0.935475i	$-0.614972\pi$
$227$	−10.6488	−0.706784	−0.353392	+	0.935475i	$0.614972\pi$
$228$	3.66399	0.242653
$229$	8.32483	0.550120	0.275060	−	0.961427i	$-0.411302\pi$
$229$	8.32483	0.550120	0.275060	+	0.961427i	$0.411302\pi$
$230$	13.5542	0.893738
$231$	−2.32918	−0.153248
$232$	5.05096	0.331612
$233$	8.86125	0.580520	0.290260	−	0.956948i	$-0.406258\pi$
$233$	8.86125	0.580520	0.290260	+	0.956948i	$0.406258\pi$
$234$	−12.4075	−0.811107
$235$	−11.3990	−0.743586
$236$	−3.91123	−0.254600
$237$	11.2859	0.733096
$238$	1.07693	0.0698070
$239$	−9.42805	−0.609850	−0.304925	−	0.952376i	$-0.598631\pi$
$239$	−9.42805	−0.609850	−0.304925	+	0.952376i	$0.598631\pi$
$240$	4.50880	0.291042
$241$	−17.5918	−1.13319	−0.566593	−	0.823998i	$-0.691739\pi$
$241$	−17.5918	−1.13319	−0.566593	+	0.823998i	$0.691739\pi$
$242$	3.79956	0.244245
$243$	20.2851	1.30129
$244$	−10.8515	−0.694694
$245$	11.6767	0.745995
$246$	−13.9726	−0.890863
$247$	4.03376	0.256662
$248$	6.01553	0.381986
$249$	0.947953	0.0600741
$250$	12.0589	0.762669
$251$	10.8159	0.682692	0.341346	−	0.939938i	$-0.389117\pi$
$251$	10.8159	0.682692	0.341346	+	0.939938i	$0.389117\pi$
$252$	0.947695	0.0596992
$253$	−31.0318	−1.95095
$254$	16.5915	1.04104
$255$	21.5199	1.34763
$256$	1.00000	0.0625000
$257$	17.0486	1.06346	0.531730	−	0.846914i	$-0.321542\pi$
$257$	17.0486	1.06346	0.531730	+	0.846914i	$0.321542\pi$
$258$	28.9270	1.80092
$259$	2.63371	0.163651
$260$	4.96383	0.307843
$261$	21.2146	1.31315
$262$	−16.5521	−1.02259
$263$	−7.59101	−0.468082	−0.234041	−	0.972227i	$-0.575195\pi$
$263$	−7.59101	−0.468082	−0.234041	+	0.972227i	$0.575195\pi$
$264$	−10.3227	−0.635319
$265$	−1.00994	−0.0620401
$266$	−0.308101	−0.0188909
$267$	−12.2241	−0.748103
$268$	10.2729	0.627514
$269$	19.8977	1.21318	0.606592	−	0.795013i	$-0.292536\pi$
$269$	19.8977	1.21318	0.606592	+	0.795013i	$0.292536\pi$
$270$	5.41104	0.329305
$271$	7.67959	0.466502	0.233251	−	0.972417i	$-0.425064\pi$
$271$	7.67959	0.466502	0.233251	+	0.972417i	$0.425064\pi$
$272$	4.77287	0.289398
$273$	1.78856	0.108249
$274$	−21.3183	−1.28788
$275$	−8.37318	−0.504921
$276$	21.6447	1.30286
$277$	−4.56678	−0.274392	−0.137196	−	0.990544i	$-0.543809\pi$
$277$	−4.56678	−0.274392	−0.137196	+	0.990544i	$0.543809\pi$
$278$	9.91975	0.594947
$279$	25.2659	1.51263
$280$	−0.379140	−0.0226579
$281$	0.119233	0.00711283	0.00355641	−	0.999994i	$-0.498868\pi$
$281$	0.119233	0.00711283	0.00355641	+	0.999994i	$0.498868\pi$
$282$	−18.2030	−1.08397
$283$	0.672403	0.0399702	0.0199851	−	0.999800i	$-0.493638\pi$
$283$	0.672403	0.0399702	0.0199851	+	0.999800i	$0.493638\pi$
$284$	−15.4875	−0.919014
$285$	−6.15666	−0.364689
$286$	−11.3645	−0.671996
$287$	1.17494	0.0693548
$288$	4.20011	0.247494
$289$	5.78026	0.340016
$290$	−8.48722	−0.498387
$291$	−42.2849	−2.47878
$292$	2.03264	0.118951
$293$	29.1055	1.70036	0.850181	−	0.526490i	$-0.176492\pi$
$293$	29.1055	1.70036	0.850181	+	0.526490i	$0.176492\pi$
$294$	18.6465	1.08749
$295$	6.57211	0.382643
$296$	11.6724	0.678443
$297$	−12.3884	−0.718846
$298$	17.4631	1.01161
$299$	23.8291	1.37807
$300$	5.84030	0.337190
$301$	−2.43244	−0.140204
$302$	0.506723	0.0291586
$303$	−21.3541	−1.22676
$304$	−1.36548	−0.0783155
$305$	18.2339	1.04407
$306$	20.0466	1.14599
$307$	23.7691	1.35657	0.678287	−	0.734797i	$-0.262723\pi$
$307$	23.7691	1.35657	0.678287	+	0.734797i	$0.262723\pi$
$308$	0.868026	0.0494604
$309$	−40.2318	−2.28871
$310$	−10.1080	−0.574095
$311$	9.28733	0.526636	0.263318	−	0.964709i	$-0.415183\pi$
$311$	9.28733	0.526636	0.263318	+	0.964709i	$0.415183\pi$
$312$	7.92675	0.448764
$313$	21.5581	1.21854	0.609269	−	0.792964i	$-0.291463\pi$
$313$	21.5581	1.21854	0.609269	+	0.792964i	$0.291463\pi$
$314$	7.32806	0.413547
$315$	−1.59243	−0.0897232
$316$	−4.20596	−0.236604
$317$	24.7069	1.38768	0.693840	−	0.720129i	$-0.255918\pi$
$317$	24.7069	1.38768	0.693840	+	0.720129i	$0.255918\pi$
$318$	−1.61278	−0.0904399
$319$	19.4312	1.08794
$320$	−1.68032	−0.0939326
$321$	33.5855	1.87456
$322$	−1.82008	−0.101429
$323$	−6.51724	−0.362629
$324$	−3.95942	−0.219968
$325$	6.42971	0.356656
$326$	22.7737	1.26132
$327$	28.4585	1.57376
$328$	5.20726	0.287523
$329$	1.53067	0.0843888
$330$	17.3454	0.954835
$331$	20.0324	1.10108	0.550541	−	0.834808i	$-0.314422\pi$
$331$	20.0324	1.10108	0.550541	+	0.834808i	$0.314422\pi$
$332$	−0.353279	−0.0193887
$333$	49.0252	2.68656
$334$	2.42920	0.132920
$335$	−17.2616	−0.943104
$336$	−0.605449	−0.0330300
$337$	12.1012	0.659193	0.329597	−	0.944122i	$-0.393087\pi$
$337$	12.1012	0.659193	0.329597	+	0.944122i	$0.393087\pi$
$338$	−4.27328	−0.232436
$339$	52.5315	2.85312
$340$	−8.01993	−0.434942
$341$	23.1419	1.25320
$342$	−5.73515	−0.310121
$343$	−3.14742	−0.169944
$344$	−10.7804	−0.581240
$345$	−36.3700	−1.95810
$346$	3.84593	0.206758
$347$	12.1759	0.653634	0.326817	−	0.945088i	$-0.394024\pi$
$347$	12.1759	0.653634	0.326817	+	0.945088i	$0.394024\pi$
$348$	−13.5533	−0.726531
$349$	6.28232	0.336285	0.168142	−	0.985763i	$-0.446223\pi$
$349$	6.28232	0.336285	0.168142	+	0.985763i	$0.446223\pi$
$350$	−0.491105	−0.0262506
$351$	9.51294	0.507763
$352$	3.84702	0.205047
$353$	16.3024	0.867690	0.433845	−	0.900987i	$-0.357156\pi$
$353$	16.3024	0.867690	0.433845	+	0.900987i	$0.357156\pi$
$354$	10.4950	0.557804
$355$	26.0239	1.38121
$356$	4.55562	0.241447
$357$	−2.88973	−0.152941
$358$	17.5869	0.929497
$359$	26.2461	1.38522	0.692609	−	0.721313i	$-0.256461\pi$
$359$	26.2461	1.38522	0.692609	+	0.721313i	$0.256461\pi$
$360$	−7.05751	−0.371963
$361$	−17.1355	−0.901867
$362$	−6.37852	−0.335248
$363$	−10.1954	−0.535118
$364$	−0.666552	−0.0349368
$365$	−3.41547	−0.178774
$366$	29.1178	1.52201
$367$	26.2518	1.37033	0.685166	−	0.728387i	$-0.259730\pi$
$367$	26.2518	1.37033	0.685166	+	0.728387i	$0.259730\pi$
$368$	−8.06646	−0.420493
$369$	21.8710	1.13856
$370$	−19.6133	−1.01965
$371$	0.135617	0.00704086
$372$	−16.1415	−0.836896
$373$	36.8164	1.90628	0.953141	−	0.302525i	$-0.0978297\pi$
$373$	36.8164	1.90628	0.953141	+	0.302525i	$0.0978297\pi$
$374$	18.3613	0.949441
$375$	−32.3575	−1.67094
$376$	6.78382	0.349849
$377$	−14.9211	−0.768474
$378$	−0.726604	−0.0373725
$379$	−33.7663	−1.73446	−0.867230	−	0.497908i	$-0.834102\pi$
$379$	−33.7663	−1.73446	−0.867230	+	0.497908i	$0.834102\pi$
$380$	2.29443	0.117702
$381$	−44.5199	−2.28082
$382$	−6.42409	−0.328685
$383$	22.2087	1.13481	0.567407	−	0.823438i	$-0.307947\pi$
$383$	22.2087	1.13481	0.567407	+	0.823438i	$0.307947\pi$
$384$	−2.68330	−0.136932
$385$	−1.45856	−0.0743350
$386$	3.71798	0.189240
$387$	−45.2788	−2.30165
$388$	15.7585	0.800018
$389$	14.1829	0.719103	0.359552	−	0.933125i	$-0.382930\pi$
$389$	14.1829	0.719103	0.359552	+	0.933125i	$0.382930\pi$
$390$	−13.3194	−0.674456
$391$	−38.5001	−1.94704
$392$	−6.94909	−0.350982
$393$	44.4143	2.24041
$394$	−0.678498	−0.0341822
$395$	7.06735	0.355597
$396$	16.1579	0.811965
$397$	17.4555	0.876067	0.438034	−	0.898959i	$-0.355675\pi$
$397$	17.4555	0.876067	0.438034	+	0.898959i	$0.355675\pi$
$398$	−20.9925	−1.05226
$399$	0.826727	0.0413881
$400$	−2.17654	−0.108827
$401$	4.63869	0.231645	0.115823	−	0.993270i	$-0.463050\pi$
$401$	4.63869	0.231645	0.115823	+	0.993270i	$0.463050\pi$
$402$	−27.5652	−1.37483
$403$	−17.7705	−0.885211
$404$	7.95815	0.395933
$405$	6.65308	0.330594
$406$	1.13968	0.0565613
$407$	44.9038	2.22580
$408$	−12.8070	−0.634043
$409$	−13.1906	−0.652231	−0.326116	−	0.945330i	$-0.605740\pi$
$409$	−13.1906	−0.652231	−0.326116	+	0.945330i	$0.605740\pi$
$410$	−8.74984	−0.432124
$411$	57.2034	2.82163
$412$	14.9934	0.738671
$413$	−0.882515	−0.0434257
$414$	−33.8800	−1.66511
$415$	0.593620	0.0291397
$416$	−2.95410	−0.144837
$417$	−26.6177	−1.30347
$418$	−5.25302	−0.256933
$419$	10.9101	0.532995	0.266498	−	0.963836i	$-0.414134\pi$
$419$	10.9101	0.532995	0.266498	+	0.963836i	$0.414134\pi$
$420$	1.01735	0.0496414
$421$	20.0882	0.979038	0.489519	−	0.871993i	$-0.337172\pi$
$421$	20.0882	0.979038	0.489519	+	0.871993i	$0.337172\pi$
$422$	21.8374	1.06303
$423$	28.4928	1.38537
$424$	0.601041	0.0291891
$425$	−10.3883	−0.503907
$426$	41.5576	2.01347
$427$	−2.44848	−0.118490
$428$	−12.5165	−0.605007
$429$	30.4943	1.47228
$430$	18.1145	0.873557
$431$	−16.7089	−0.804837	−0.402419	−	0.915456i	$-0.631830\pi$
$431$	−16.7089	−0.804837	−0.402419	+	0.915456i	$0.631830\pi$
$432$	−3.22025	−0.154934
$433$	19.2394	0.924588	0.462294	−	0.886727i	$-0.347027\pi$
$433$	19.2394	0.924588	0.462294	+	0.886727i	$0.347027\pi$
$434$	1.35732	0.0651534
$435$	22.7738	1.09192
$436$	−10.6058	−0.507924
$437$	11.0146	0.526898
$438$	−5.45417	−0.260610
$439$	−30.8022	−1.47011	−0.735055	−	0.678008i	$-0.762844\pi$
$439$	−30.8022	−1.47011	−0.735055	+	0.678008i	$0.762844\pi$
$440$	−6.46421	−0.308169
$441$	−29.1869	−1.38985
$442$	−14.0995	−0.670647
$443$	−23.3912	−1.11135	−0.555675	−	0.831400i	$-0.687540\pi$
$443$	−23.3912	−1.11135	−0.555675	+	0.831400i	$0.687540\pi$
$444$	−31.3205	−1.48640
$445$	−7.65489	−0.362876
$446$	7.19054	0.340482
$447$	−46.8588	−2.21635
$448$	0.225636	0.0106603
$449$	38.3699	1.81079	0.905393	−	0.424575i	$-0.139576\pi$
$449$	38.3699	1.81079	0.905393	+	0.424575i	$0.139576\pi$
$450$	−9.14168	−0.430943
$451$	20.0324	0.943290
$452$	−19.5772	−0.920834
$453$	−1.35969	−0.0638839
$454$	−10.6488	−0.499772
$455$	1.12002	0.0525072
$456$	3.66399	0.171582
$457$	−6.02517	−0.281846	−0.140923	−	0.990021i	$-0.545007\pi$
$457$	−6.02517	−0.281846	−0.140923	+	0.990021i	$0.545007\pi$
$458$	8.32483	0.388994
$459$	−15.3698	−0.717402
$460$	13.5542	0.631968
$461$	10.2411	0.476974	0.238487	−	0.971146i	$-0.423349\pi$
$461$	10.2411	0.476974	0.238487	+	0.971146i	$0.423349\pi$
$462$	−2.32918	−0.108363
$463$	−21.3465	−0.992054	−0.496027	−	0.868307i	$-0.665208\pi$
$463$	−21.3465	−0.992054	−0.496027	+	0.868307i	$0.665208\pi$
$464$	5.05096	0.234485
$465$	27.1228	1.25779
$466$	8.86125	0.410490
$467$	−19.0455	−0.881321	−0.440661	−	0.897674i	$-0.645256\pi$
$467$	−19.0455	−0.881321	−0.440661	+	0.897674i	$0.645256\pi$
$468$	−12.4075	−0.573539
$469$	2.31792	0.107032
$470$	−11.3990	−0.525795
$471$	−19.6634	−0.906042
$472$	−3.91123	−0.180029
$473$	−41.4724	−1.90690
$474$	11.2859	0.518377
$475$	2.97201	0.136365
$476$	1.07693	0.0493610
$477$	2.52444	0.115586
$478$	−9.42805	−0.431229
$479$	−30.5336	−1.39512	−0.697559	−	0.716528i	$-0.745730\pi$
$479$	−30.5336	−1.39512	−0.697559	+	0.716528i	$0.745730\pi$
$480$	4.50880	0.205797
$481$	−34.4814	−1.57221
$482$	−17.5918	−0.801284
$483$	4.88383	0.222222
$484$	3.79956	0.172707
$485$	−26.4793	−1.20236
$486$	20.2851	0.920149
$487$	−13.0500	−0.591353	−0.295677	−	0.955288i	$-0.595545\pi$
$487$	−13.0500	−0.591353	−0.295677	+	0.955288i	$0.595545\pi$
$488$	−10.8515	−0.491223
$489$	−61.1086	−2.76343
$490$	11.6767	0.527498
$491$	−15.2680	−0.689034	−0.344517	−	0.938780i	$-0.611957\pi$
$491$	−15.2680	−0.689034	−0.344517	+	0.938780i	$0.611957\pi$
$492$	−13.9726	−0.629935
$493$	24.1076	1.08575
$494$	4.03376	0.181487
$495$	−27.1504	−1.22032
$496$	6.01553	0.270105
$497$	−3.49454	−0.156751
$498$	0.947953	0.0424788
$499$	14.3339	0.641674	0.320837	−	0.947134i	$-0.396036\pi$
$499$	14.3339	0.641674	0.320837	+	0.947134i	$0.396036\pi$
$500$	12.0589	0.539288
$501$	−6.51827	−0.291215
$502$	10.8159	0.482736
$503$	4.41655	0.196924	0.0984622	−	0.995141i	$-0.468608\pi$
$503$	4.41655	0.196924	0.0984622	+	0.995141i	$0.468608\pi$
$504$	0.947695	0.0422137
$505$	−13.3722	−0.595056
$506$	−31.0318	−1.37953
$507$	11.4665	0.509246
$508$	16.5915	0.736127
$509$	−14.0675	−0.623531	−0.311766	−	0.950159i	$-0.600920\pi$
$509$	−14.0675	−0.623531	−0.311766	+	0.950159i	$0.600920\pi$
$510$	21.5199	0.952917
$511$	0.458636	0.0202888
$512$	1.00000	0.0441942
$513$	4.39718	0.194140
$514$	17.0486	0.751980
$515$	−25.1936	−1.11016
$516$	28.9270	1.27344
$517$	26.0975	1.14777
$518$	2.63371	0.115718
$519$	−10.3198	−0.452988
$520$	4.96383	0.217678
$521$	31.8288	1.39445	0.697223	−	0.716854i	$-0.254419\pi$
$521$	31.8288	1.39445	0.697223	+	0.716854i	$0.254419\pi$
$522$	21.2146	0.928537
$523$	−6.34236	−0.277332	−0.138666	−	0.990339i	$-0.544281\pi$
$523$	−6.34236	−0.277332	−0.138666	+	0.990339i	$0.544281\pi$
$524$	−16.5521	−0.723083
$525$	1.31778	0.0575127
$526$	−7.59101	−0.330984
$527$	28.7113	1.25068
$528$	−10.3227	−0.449238
$529$	42.0677	1.82903
$530$	−1.00994	−0.0438690
$531$	−16.4276	−0.712897
$532$	−0.308101	−0.0133579
$533$	−15.3828	−0.666302
$534$	−12.2241	−0.528989
$535$	21.0317	0.909278
$536$	10.2729	0.443720
$537$	−47.1910	−2.03644
$538$	19.8977	0.857851
$539$	−26.7333	−1.15148
$540$	5.41104	0.232854
$541$	34.2015	1.47044	0.735220	−	0.677829i	$-0.237079\pi$
$541$	34.2015	1.47044	0.735220	+	0.677829i	$0.237079\pi$
$542$	7.67959	0.329867
$543$	17.1155	0.734496
$544$	4.77287	0.204635
$545$	17.8211	0.763370
$546$	1.78856	0.0765432
$547$	−42.1308	−1.80138	−0.900692	−	0.434458i	$-0.856940\pi$
$547$	−42.1308	−1.80138	−0.900692	+	0.434458i	$0.856940\pi$
$548$	−21.3183	−0.910672
$549$	−45.5773	−1.94519
$550$	−8.37318	−0.357033
$551$	−6.89697	−0.293821
$552$	21.6447	0.921261
$553$	−0.949016	−0.0403563
$554$	−4.56678	−0.194024
$555$	52.6283	2.23395
$556$	9.91975	0.420691
$557$	−27.1023	−1.14836	−0.574181	−	0.818728i	$-0.694679\pi$
$557$	−27.1023	−1.14836	−0.574181	+	0.818728i	$0.694679\pi$
$558$	25.2659	1.06959
$559$	31.8464	1.34696
$560$	−0.379140	−0.0160216
$561$	−49.2689	−2.08014
$562$	0.119233	0.00502953
$563$	7.97741	0.336208	0.168104	−	0.985769i	$-0.446236\pi$
$563$	7.97741	0.336208	0.168104	+	0.985769i	$0.446236\pi$
$564$	−18.2030	−0.766486
$565$	32.8959	1.38394
$566$	0.672403	0.0282632
$567$	−0.893388	−0.0375188
$568$	−15.4875	−0.649841
$569$	5.05963	0.212111	0.106055	−	0.994360i	$-0.466178\pi$
$569$	5.05963	0.212111	0.106055	+	0.994360i	$0.466178\pi$
$570$	−6.15666	−0.257874
$571$	9.67371	0.404832	0.202416	−	0.979300i	$-0.435121\pi$
$571$	9.67371	0.404832	0.202416	+	0.979300i	$0.435121\pi$
$572$	−11.3645	−0.475173
$573$	17.2378	0.720118
$574$	1.17494	0.0490412
$575$	17.5569	0.732175
$576$	4.20011	0.175004
$577$	11.5695	0.481645	0.240823	−	0.970569i	$-0.422583\pi$
$577$	11.5695	0.481645	0.240823	+	0.970569i	$0.422583\pi$
$578$	5.78026	0.240427
$579$	−9.97646	−0.414607
$580$	−8.48722	−0.352413
$581$	−0.0797124	−0.00330703
$582$	−42.2849	−1.75276
$583$	2.31222	0.0957623
$584$	2.03264	0.0841110
$585$	20.8486	0.861984
$586$	29.1055	1.20234
$587$	10.5560	0.435694	0.217847	−	0.975983i	$-0.430097\pi$
$587$	10.5560	0.435694	0.217847	+	0.975983i	$0.430097\pi$
$588$	18.6465	0.768969
$589$	−8.21406	−0.338455
$590$	6.57211	0.270569
$591$	1.82062	0.0748901
$592$	11.6724	0.479731
$593$	−8.82954	−0.362586	−0.181293	−	0.983429i	$-0.558028\pi$
$593$	−8.82954	−0.362586	−0.181293	+	0.983429i	$0.558028\pi$
$594$	−12.3884	−0.508301
$595$	−1.80958	−0.0741857
$596$	17.4631	0.715317
$597$	56.3292	2.30540
$598$	23.8291	0.974446
$599$	−1.97107	−0.0805355	−0.0402678	−	0.999189i	$-0.512821\pi$
$599$	−1.97107	−0.0805355	−0.0402678	+	0.999189i	$0.512821\pi$
$600$	5.84030	0.238429
$601$	25.5369	1.04167	0.520837	−	0.853656i	$-0.325620\pi$
$601$	25.5369	1.04167	0.520837	+	0.853656i	$0.325620\pi$
$602$	−2.43244	−0.0991390
$603$	43.1471	1.75708
$604$	0.506723	0.0206183
$605$	−6.38447	−0.259566
$606$	−21.3541	−0.867452
$607$	12.1428	0.492860	0.246430	−	0.969161i	$-0.420742\pi$
$607$	12.1428	0.492860	0.246430	+	0.969161i	$0.420742\pi$
$608$	−1.36548	−0.0553774
$609$	−3.05810	−0.123921
$610$	18.2339	0.738269
$611$	−20.0401	−0.810735
$612$	20.0466	0.810334
$613$	−18.0253	−0.728033	−0.364017	−	0.931392i	$-0.618595\pi$
$613$	−18.0253	−0.728033	−0.364017	+	0.931392i	$0.618595\pi$
$614$	23.7691	0.959243
$615$	23.4785	0.946743
$616$	0.868026	0.0349738
$617$	16.1230	0.649086	0.324543	−	0.945871i	$-0.394790\pi$
$617$	16.1230	0.649086	0.324543	+	0.945871i	$0.394790\pi$
$618$	−40.2318	−1.61836
$619$	−25.3181	−1.01762	−0.508811	−	0.860879i	$-0.669915\pi$
$619$	−25.3181	−1.01762	−0.508811	+	0.860879i	$0.669915\pi$
$620$	−10.1080	−0.405947
$621$	25.9760	1.04238
$622$	9.28733	0.372388
$623$	1.02791	0.0411824
$624$	7.92675	0.317324
$625$	−9.38002	−0.375201
$626$	21.5581	0.861636
$627$	14.0954	0.562917
$628$	7.32806	0.292422
$629$	55.7107	2.22133
$630$	−1.59243	−0.0634439
$631$	−21.7155	−0.864479	−0.432239	−	0.901759i	$-0.642276\pi$
$631$	−21.7155	−0.864479	−0.432239	+	0.901759i	$0.642276\pi$
$632$	−4.20596	−0.167304
$633$	−58.5963	−2.32899
$634$	24.7069	0.981238
$635$	−27.8789	−1.10634
$636$	−1.61278	−0.0639507
$637$	20.5283	0.813361
$638$	19.4312	0.769287
$639$	−65.0492	−2.57330
$640$	−1.68032	−0.0664204
$641$	13.4720	0.532112	0.266056	−	0.963958i	$-0.414279\pi$
$641$	13.4720	0.532112	0.266056	+	0.963958i	$0.414279\pi$
$642$	33.5855	1.32551
$643$	−2.58080	−0.101777	−0.0508884	−	0.998704i	$-0.516205\pi$
$643$	−2.58080	−0.101777	−0.0508884	+	0.998704i	$0.516205\pi$
$644$	−1.82008	−0.0717213
$645$	−48.6066	−1.91388
$646$	−6.51724	−0.256417
$647$	21.5142	0.845811	0.422905	−	0.906174i	$-0.361010\pi$
$647$	21.5142	0.845811	0.422905	+	0.906174i	$0.361010\pi$
$648$	−3.95942	−0.155541
$649$	−15.0466	−0.590630
$650$	6.42971	0.252194
$651$	−3.64210	−0.142745
$652$	22.7737	0.891886
$653$	11.5442	0.451758	0.225879	−	0.974155i	$-0.427475\pi$
$653$	11.5442	0.451758	0.225879	+	0.974155i	$0.427475\pi$
$654$	28.4585	1.11281
$655$	27.8128	1.08674
$656$	5.20726	0.203309
$657$	8.53729	0.333071
$658$	1.53067	0.0596719
$659$	−2.96362	−0.115446	−0.0577231	−	0.998333i	$-0.518384\pi$
$659$	−2.96362	−0.115446	−0.0577231	+	0.998333i	$0.518384\pi$
$660$	17.3454	0.675170
$661$	−43.1303	−1.67757	−0.838787	−	0.544459i	$-0.816735\pi$
$661$	−43.1303	−1.67757	−0.838787	+	0.544459i	$0.816735\pi$
$662$	20.0324	0.778582
$663$	37.8333	1.46932
$664$	−0.353279	−0.0137099
$665$	0.517707	0.0200758
$666$	49.0252	1.89969
$667$	−40.7434	−1.57759
$668$	2.42920	0.0939885
$669$	−19.2944	−0.745964
$670$	−17.2616	−0.666875
$671$	−41.7458	−1.61158
$672$	−0.605449	−0.0233557
$673$	−9.68284	−0.373246	−0.186623	−	0.982432i	$-0.559754\pi$
$673$	−9.68284	−0.373246	−0.186623	+	0.982432i	$0.559754\pi$
$674$	12.1012	0.466120
$675$	7.00899	0.269776
$676$	−4.27328	−0.164357
$677$	20.7483	0.797424	0.398712	−	0.917076i	$-0.369457\pi$
$677$	20.7483	0.797424	0.398712	+	0.917076i	$0.369457\pi$
$678$	52.5315	2.01746
$679$	3.55569	0.136455
$680$	−8.01993	−0.307550
$681$	28.5739	1.09495
$682$	23.1419	0.886147
$683$	−1.94790	−0.0745344	−0.0372672	−	0.999305i	$-0.511865\pi$
$683$	−1.94790	−0.0745344	−0.0372672	+	0.999305i	$0.511865\pi$
$684$	−5.73515	−0.219289
$685$	35.8215	1.36867
$686$	−3.14742	−0.120169
$687$	−22.3380	−0.852249
$688$	−10.7804	−0.410999
$689$	−1.77554	−0.0676426
$690$	−36.3700	−1.38458
$691$	−33.2622	−1.26535	−0.632677	−	0.774416i	$-0.718044\pi$
$691$	−33.2622	−1.26535	−0.632677	+	0.774416i	$0.718044\pi$
$692$	3.84593	0.146200
$693$	3.64580	0.138493
$694$	12.1759	0.462189
$695$	−16.6683	−0.632266
$696$	−13.5533	−0.513735
$697$	24.8536	0.941395
$698$	6.28232	0.237789
$699$	−23.7774	−0.899344
$700$	−0.491105	−0.0185620
$701$	12.6612	0.478209	0.239104	−	0.970994i	$-0.423146\pi$
$701$	12.6612	0.478209	0.239104	+	0.970994i	$0.423146\pi$
$702$	9.51294	0.359043
$703$	−15.9383	−0.601126
$704$	3.84702	0.144990
$705$	30.5869	1.15197
$706$	16.3024	0.613550
$707$	1.79565	0.0675322
$708$	10.4950	0.394427
$709$	−35.6941	−1.34052	−0.670260	−	0.742126i	$-0.733818\pi$
$709$	−35.6941	−1.34052	−0.670260	+	0.742126i	$0.733818\pi$
$710$	26.0239	0.976660
$711$	−17.6655	−0.662508
$712$	4.55562	0.170729
$713$	−48.5240	−1.81724
$714$	−2.88973	−0.108145
$715$	19.0959	0.714148
$716$	17.5869	0.657254
$717$	25.2983	0.944783
$718$	26.2461	0.979497
$719$	−46.8750	−1.74814	−0.874071	−	0.485798i	$-0.838529\pi$
$719$	−46.8750	−1.74814	−0.874071	+	0.485798i	$0.838529\pi$
$720$	−7.05751	−0.263018
$721$	3.38305	0.125991
$722$	−17.1355	−0.637716
$723$	47.2041	1.75554
$724$	−6.37852	−0.237056
$725$	−10.9936	−0.408292
$726$	−10.1954	−0.378386
$727$	−46.0093	−1.70639	−0.853195	−	0.521591i	$-0.825339\pi$
$727$	−46.0093	−1.70639	−0.853195	+	0.521591i	$0.825339\pi$
$728$	−0.666552	−0.0247040
$729$	−42.5527	−1.57603
$730$	−3.41547	−0.126412
$731$	−51.4534	−1.90307
$732$	29.1178	1.07622
$733$	30.8570	1.13973	0.569866	−	0.821738i	$-0.306995\pi$
$733$	30.8570	1.13973	0.569866	+	0.821738i	$0.306995\pi$
$734$	26.2518	0.968972
$735$	−31.3320	−1.15570
$736$	−8.06646	−0.297334
$737$	39.5199	1.45573
$738$	21.8710	0.805084
$739$	5.59810	0.205929	0.102965	−	0.994685i	$-0.467167\pi$
$739$	5.59810	0.205929	0.102965	+	0.994685i	$0.467167\pi$
$740$	−19.6133	−0.720998
$741$	−10.8238	−0.397622
$742$	0.135617	0.00497864
$743$	33.9157	1.24425	0.622123	−	0.782920i	$-0.286270\pi$
$743$	33.9157	1.24425	0.622123	+	0.782920i	$0.286270\pi$
$744$	−16.1415	−0.591775
$745$	−29.3436	−1.07507
$746$	36.8164	1.34795
$747$	−1.48381	−0.0542897
$748$	18.3613	0.671356
$749$	−2.82417	−0.103193
$750$	−32.3575	−1.18153
$751$	−44.6549	−1.62948	−0.814741	−	0.579825i	$-0.803121\pi$
$751$	−44.6549	−1.62948	−0.814741	+	0.579825i	$0.803121\pi$
$752$	6.78382	0.247380
$753$	−29.0222	−1.05763
$754$	−14.9211	−0.543393
$755$	−0.851455	−0.0309876
$756$	−0.726604	−0.0264263
$757$	23.6763	0.860528	0.430264	−	0.902703i	$-0.358420\pi$
$757$	23.6763	0.860528	0.430264	+	0.902703i	$0.358420\pi$
$758$	−33.7663	−1.22645
$759$	83.2677	3.02243
$760$	2.29443	0.0832279
$761$	0.431496	0.0156417	0.00782086	−	0.999969i	$-0.497511\pi$
$761$	0.431496	0.0156417	0.00782086	+	0.999969i	$0.497511\pi$
$762$	−44.5199	−1.61278
$763$	−2.39304	−0.0866340
$764$	−6.42409	−0.232415
$765$	−33.6846	−1.21787
$766$	22.2087	0.802434
$767$	11.5542	0.417197
$768$	−2.68330	−0.0968253
$769$	1.91917	0.0692069	0.0346035	−	0.999401i	$-0.488983\pi$
$769$	1.91917	0.0692069	0.0346035	+	0.999401i	$0.488983\pi$
$770$	−1.45856	−0.0525628
$771$	−45.7464	−1.64752
$772$	3.71798	0.133813
$773$	−52.3153	−1.88165	−0.940825	−	0.338893i	$-0.889948\pi$
$773$	−52.3153	−1.88165	−0.940825	+	0.338893i	$0.889948\pi$
$774$	−45.2788	−1.62751
$775$	−13.0930	−0.470315
$776$	15.7585	0.565698
$777$	−7.06703	−0.253528
$778$	14.1829	0.508483
$779$	−7.11039	−0.254756
$780$	−13.3194	−0.476913
$781$	−59.5807	−2.13197
$782$	−38.5001	−1.37676
$783$	−16.2654	−0.581277
$784$	−6.94909	−0.248182
$785$	−12.3135	−0.439487
$786$	44.4143	1.58421
$787$	−4.64276	−0.165496	−0.0827482	−	0.996570i	$-0.526370\pi$
$787$	−4.64276	−0.165496	−0.0827482	+	0.996570i	$0.526370\pi$
$788$	−0.678498	−0.0241705
$789$	20.3690	0.725155
$790$	7.06735	0.251445
$791$	−4.41732	−0.157062
$792$	16.1579	0.574146
$793$	32.0563	1.13835
$794$	17.4555	0.619473
$795$	2.70997	0.0961128
$796$	−20.9925	−0.744059
$797$	17.0240	0.603022	0.301511	−	0.953463i	$-0.402509\pi$
$797$	17.0240	0.603022	0.301511	+	0.953463i	$0.402509\pi$
$798$	0.826727	0.0292658
$799$	32.3783	1.14546
$800$	−2.17654	−0.0769521
$801$	19.1341	0.676070
$802$	4.63869	0.163798
$803$	7.81959	0.275947
$804$	−27.5652	−0.972148
$805$	3.05832	0.107791
$806$	−17.7705	−0.625938
$807$	−53.3916	−1.87947
$808$	7.95815	0.279967
$809$	36.0486	1.26740	0.633701	−	0.773578i	$-0.281535\pi$
$809$	36.0486	1.26740	0.633701	+	0.773578i	$0.281535\pi$
$810$	6.65308	0.233765
$811$	54.7598	1.92288	0.961438	−	0.275023i	$-0.0886855\pi$
$811$	54.7598	1.92288	0.961438	+	0.275023i	$0.0886855\pi$
$812$	1.13968	0.0399949
$813$	−20.6067	−0.722707
$814$	44.9038	1.57388
$815$	−38.2670	−1.34043
$816$	−12.8070	−0.448336
$817$	14.7204	0.515001
$818$	−13.1906	−0.461197
$819$	−2.79959	−0.0978255
$820$	−8.74984	−0.305558
$821$	−42.5798	−1.48605	−0.743023	−	0.669266i	$-0.766609\pi$
$821$	−42.5798	−1.48605	−0.743023	+	0.669266i	$0.766609\pi$
$822$	57.2034	1.99520
$823$	10.9712	0.382431	0.191215	−	0.981548i	$-0.438757\pi$
$823$	10.9712	0.382431	0.191215	+	0.981548i	$0.438757\pi$
$824$	14.9934	0.522319
$825$	22.4678	0.782227
$826$	−0.882515	−0.0307066
$827$	28.0809	0.976469	0.488235	−	0.872712i	$-0.337641\pi$
$827$	28.0809	0.976469	0.488235	+	0.872712i	$0.337641\pi$
$828$	−33.8800	−1.17741
$829$	−38.7257	−1.34500	−0.672500	−	0.740097i	$-0.734779\pi$
$829$	−38.7257	−1.34500	−0.672500	+	0.740097i	$0.734779\pi$
$830$	0.593620	0.0206048
$831$	12.2541	0.425089
$832$	−2.95410	−0.102415
$833$	−33.1671	−1.14917
$834$	−26.6177	−0.921695
$835$	−4.08182	−0.141257
$836$	−5.25302	−0.181679
$837$	−19.3715	−0.669577
$838$	10.9101	0.376885
$839$	11.2050	0.386839	0.193419	−	0.981116i	$-0.438042\pi$
$839$	11.2050	0.386839	0.193419	+	0.981116i	$0.438042\pi$
$840$	1.01735	0.0351018
$841$	−3.48777	−0.120268
$842$	20.0882	0.692285
$843$	−0.319937	−0.0110192
$844$	21.8374	0.751674
$845$	7.18047	0.247016
$846$	28.4928	0.979602
$847$	0.857318	0.0294578
$848$	0.601041	0.0206398
$849$	−1.80426	−0.0619220
$850$	−10.3883	−0.356316
$851$	−94.1547	−3.22758
$852$	41.5576	1.42374
$853$	32.1920	1.10223	0.551116	−	0.834428i	$-0.314202\pi$
$853$	32.1920	1.10223	0.551116	+	0.834428i	$0.314202\pi$
$854$	−2.44848	−0.0837853
$855$	9.63687	0.329574
$856$	−12.5165	−0.427805
$857$	−5.88904	−0.201166	−0.100583	−	0.994929i	$-0.532071\pi$
$857$	−5.88904	−0.201166	−0.100583	+	0.994929i	$0.532071\pi$
$858$	30.4943	1.04106
$859$	−24.1026	−0.822371	−0.411185	−	0.911552i	$-0.634885\pi$
$859$	−24.1026	−0.822371	−0.411185	+	0.911552i	$0.634885\pi$
$860$	18.1145	0.617698
$861$	−3.15273	−0.107445
$862$	−16.7089	−0.569106
$863$	44.4893	1.51443	0.757217	−	0.653163i	$-0.226558\pi$
$863$	44.4893	1.51443	0.757217	+	0.653163i	$0.226558\pi$
$864$	−3.22025	−0.109555
$865$	−6.46238	−0.219728
$866$	19.2394	0.653782
$867$	−15.5102	−0.526754
$868$	1.35732	0.0460704
$869$	−16.1804	−0.548883
$870$	22.7738	0.772103
$871$	−30.3470	−1.02827
$872$	−10.6058	−0.359157
$873$	66.1875	2.24011
$874$	11.0146	0.372573
$875$	2.72091	0.0919836
$876$	−5.45417	−0.184279
$877$	18.1579	0.613147	0.306574	−	0.951847i	$-0.400817\pi$
$877$	18.1579	0.613147	0.306574	+	0.951847i	$0.400817\pi$
$878$	−30.8022	−1.03952
$879$	−78.0989	−2.63421
$880$	−6.46421	−0.217909
$881$	3.90672	0.131621	0.0658103	−	0.997832i	$-0.479037\pi$
$881$	3.90672	0.131621	0.0658103	+	0.997832i	$0.479037\pi$
$882$	−29.1869	−0.982775
$883$	46.5102	1.56519	0.782596	−	0.622530i	$-0.213895\pi$
$883$	46.5102	1.56519	0.782596	+	0.622530i	$0.213895\pi$
$884$	−14.0995	−0.474219
$885$	−17.6350	−0.592792
$886$	−23.3912	−0.785843
$887$	43.7691	1.46962	0.734811	−	0.678271i	$-0.237271\pi$
$887$	43.7691	1.46962	0.734811	+	0.678271i	$0.237271\pi$
$888$	−31.3205	−1.05105
$889$	3.74363	0.125557
$890$	−7.65489	−0.256592
$891$	−15.2320	−0.510290
$892$	7.19054	0.240757
$893$	−9.26315	−0.309979
$894$	−46.8588	−1.56719
$895$	−29.5516	−0.987800
$896$	0.225636	0.00753797
$897$	−63.9408	−2.13492
$898$	38.3699	1.28042
$899$	30.3842	1.01337
$900$	−9.14168	−0.304723
$901$	2.86869	0.0955699
$902$	20.0324	0.667007
$903$	6.52698	0.217204
$904$	−19.5772	−0.651128
$905$	10.7179	0.356276
$906$	−1.35969	−0.0451727
$907$	36.4271	1.20954	0.604771	−	0.796399i	$-0.293265\pi$
$907$	36.4271	1.20954	0.604771	+	0.796399i	$0.293265\pi$
$908$	−10.6488	−0.353392
$909$	33.4251	1.10864
$910$	1.12002	0.0371282
$911$	53.6734	1.77828	0.889139	−	0.457637i	$-0.151304\pi$
$911$	53.6734	1.77828	0.889139	+	0.457637i	$0.151304\pi$
$912$	3.66399	0.121327
$913$	−1.35907	−0.0449786
$914$	−6.02517	−0.199295
$915$	−48.9270	−1.61748
$916$	8.32483	0.275060
$917$	−3.73475	−0.123332
$918$	−15.3698	−0.507280
$919$	−49.3526	−1.62799	−0.813996	−	0.580870i	$-0.802712\pi$
$919$	−49.3526	−1.62799	−0.813996	+	0.580870i	$0.802712\pi$
$920$	13.5542	0.446869
$921$	−63.7797	−2.10161
$922$	10.2411	0.337272
$923$	45.7516	1.50593
$924$	−2.32918	−0.0766242
$925$	−25.4053	−0.835322
$926$	−21.3465	−0.701488
$927$	62.9738	2.06833
$928$	5.05096	0.165806
$929$	10.9159	0.358140	0.179070	−	0.983836i	$-0.442691\pi$
$929$	10.9159	0.358140	0.179070	+	0.983836i	$0.442691\pi$
$930$	27.1228	0.889391
$931$	9.48882	0.310984
$932$	8.86125	0.290260
$933$	−24.9207	−0.815868
$934$	−19.0455	−0.623188
$935$	−30.8528	−1.00900
$936$	−12.4075	−0.405553
$937$	13.4346	0.438890	0.219445	−	0.975625i	$-0.429575\pi$
$937$	13.4346	0.438890	0.219445	+	0.975625i	$0.429575\pi$
$938$	2.31792	0.0756829
$939$	−57.8470	−1.88776
$940$	−11.3990	−0.371793
$941$	−1.16986	−0.0381363	−0.0190682	−	0.999818i	$-0.506070\pi$
$941$	−1.16986	−0.0381363	−0.0190682	+	0.999818i	$0.506070\pi$
$942$	−19.6634	−0.640668
$943$	−42.0041	−1.36784
$944$	−3.91123	−0.127300
$945$	1.22093	0.0397167
$946$	−41.4724	−1.34838
$947$	28.3277	0.920526	0.460263	−	0.887783i	$-0.347755\pi$
$947$	28.3277	0.920526	0.460263	+	0.887783i	$0.347755\pi$
$948$	11.2859	0.366548
$949$	−6.00461	−0.194918
$950$	2.97201	0.0964247
$951$	−66.2962	−2.14980
$952$	1.07693	0.0349035
$953$	−0.229724	−0.00744150	−0.00372075	−	0.999993i	$-0.501184\pi$
$953$	−0.229724	−0.00744150	−0.00372075	+	0.999993i	$0.501184\pi$
$954$	2.52444	0.0817317
$955$	10.7945	0.349302
$956$	−9.42805	−0.304925
$957$	−52.1396	−1.68544
$958$	−30.5336	−0.986497
$959$	−4.81017	−0.155328
$960$	4.50880	0.145521
$961$	5.18656	0.167308
$962$	−34.4814	−1.11172
$963$	−52.5706	−1.69406
$964$	−17.5918	−0.566593
$965$	−6.24738	−0.201110
$966$	4.88383	0.157135
$967$	−49.2093	−1.58247	−0.791233	−	0.611515i	$-0.790560\pi$
$967$	−49.2093	−1.58247	−0.791233	+	0.611515i	$0.790560\pi$
$968$	3.79956	0.122123
$969$	17.4877	0.561787
$970$	−26.4793	−0.850199
$971$	18.0725	0.579974	0.289987	−	0.957031i	$-0.406349\pi$
$971$	18.0725	0.579974	0.289987	+	0.957031i	$0.406349\pi$
$972$	20.2851	0.650644
$973$	2.23825	0.0717551
$974$	−13.0500	−0.418150
$975$	−17.2528	−0.552533
$976$	−10.8515	−0.347347
$977$	−1.98541	−0.0635189	−0.0317595	−	0.999496i	$-0.510111\pi$
$977$	−1.98541	−0.0635189	−0.0317595	+	0.999496i	$0.510111\pi$
$978$	−61.1086	−1.95404
$979$	17.5256	0.560119
$980$	11.6767	0.372998
$981$	−44.5454	−1.42222
$982$	−15.2680	−0.487220
$983$	34.3541	1.09573	0.547863	−	0.836568i	$-0.315442\pi$
$983$	34.3541	1.09573	0.547863	+	0.836568i	$0.315442\pi$
$984$	−13.9726	−0.445432
$985$	1.14009	0.0363263
$986$	24.1076	0.767742
$987$	−4.10726	−0.130735
$988$	4.03376	0.128331
$989$	86.9596	2.76515
$990$	−27.1504	−0.862896
$991$	−3.79368	−0.120510	−0.0602551	−	0.998183i	$-0.519191\pi$
$991$	−3.79368	−0.120510	−0.0602551	+	0.998183i	$0.519191\pi$
$992$	6.01553	0.190993
$993$	−53.7530	−1.70580
$994$	−3.49454	−0.110840
$995$	35.2740	1.11826
$996$	0.947953	0.0300370
$997$	−29.5813	−0.936850	−0.468425	−	0.883503i	$-0.655178\pi$
$997$	−29.5813	−0.936850	−0.468425	+	0.883503i	$0.655178\pi$
$998$	14.3339	0.453732
$999$	−37.5879	−1.18923

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.11	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.11	✓	95	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.68330 q^{3} +1.00000 q^{4} -1.68032 q^{5} -2.68330 q^{6} +0.225636 q^{7} +1.00000 q^{8} +4.20011 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.68330 q^{3} +1.00000 q^{4} -1.68032 q^{5} -2.68330 q^{6} +0.225636 q^{7} +1.00000 q^{8} +4.20011 q^{9} -1.68032 q^{10} +3.84702 q^{11} -2.68330 q^{12} -2.95410 q^{13} +0.225636 q^{14} +4.50880 q^{15} +1.00000 q^{16} +4.77287 q^{17} +4.20011 q^{18} -1.36548 q^{19} -1.68032 q^{20} -0.605449 q^{21} +3.84702 q^{22} -8.06646 q^{23} -2.68330 q^{24} -2.17654 q^{25} -2.95410 q^{26} -3.22025 q^{27} +0.225636 q^{28} +5.05096 q^{29} +4.50880 q^{30} +6.01553 q^{31} +1.00000 q^{32} -10.3227 q^{33} +4.77287 q^{34} -0.379140 q^{35} +4.20011 q^{36} +11.6724 q^{37} -1.36548 q^{38} +7.92675 q^{39} -1.68032 q^{40} +5.20726 q^{41} -0.605449 q^{42} -10.7804 q^{43} +3.84702 q^{44} -7.05751 q^{45} -8.06646 q^{46} +6.78382 q^{47} -2.68330 q^{48} -6.94909 q^{49} -2.17654 q^{50} -12.8070 q^{51} -2.95410 q^{52} +0.601041 q^{53} -3.22025 q^{54} -6.46421 q^{55} +0.225636 q^{56} +3.66399 q^{57} +5.05096 q^{58} -3.91123 q^{59} +4.50880 q^{60} -10.8515 q^{61} +6.01553 q^{62} +0.947695 q^{63} +1.00000 q^{64} +4.96383 q^{65} -10.3227 q^{66} +10.2729 q^{67} +4.77287 q^{68} +21.6447 q^{69} -0.379140 q^{70} -15.4875 q^{71} +4.20011 q^{72} +2.03264 q^{73} +11.6724 q^{74} +5.84030 q^{75} -1.36548 q^{76} +0.868026 q^{77} +7.92675 q^{78} -4.20596 q^{79} -1.68032 q^{80} -3.95942 q^{81} +5.20726 q^{82} -0.353279 q^{83} -0.605449 q^{84} -8.01993 q^{85} -10.7804 q^{86} -13.5533 q^{87} +3.84702 q^{88} +4.55562 q^{89} -7.05751 q^{90} -0.666552 q^{91} -8.06646 q^{92} -16.1415 q^{93} +6.78382 q^{94} +2.29443 q^{95} -2.68330 q^{96} +15.7585 q^{97} -6.94909 q^{98} +16.1579 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9} + 36 q^{10} + 40 q^{11} + 24 q^{12} + 52 q^{13} + 21 q^{14} + 15 q^{15} + 95 q^{16} + 84 q^{17} + 121 q^{18} + 37 q^{19} + 36 q^{20} + 36 q^{21} + 40 q^{22} + 37 q^{23} + 24 q^{24} + 133 q^{25} + 52 q^{26} + 93 q^{27} + 21 q^{28} + 66 q^{29} + 15 q^{30} + 10 q^{31} + 95 q^{32} + 63 q^{33} + 84 q^{34} + 55 q^{35} + 121 q^{36} + 49 q^{37} + 37 q^{38} + 14 q^{39} + 36 q^{40} + 98 q^{41} + 36 q^{42} + 37 q^{43} + 40 q^{44} + 97 q^{45} + 37 q^{46} + 91 q^{47} + 24 q^{48} + 170 q^{49} + 133 q^{50} + 22 q^{51} + 52 q^{52} + 70 q^{53} + 93 q^{54} - q^{55} + 21 q^{56} + 50 q^{57} + 66 q^{58} + 72 q^{59} + 15 q^{60} + 97 q^{61} + 10 q^{62} + 75 q^{63} + 95 q^{64} + 75 q^{65} + 63 q^{66} + 39 q^{67} + 84 q^{68} + 65 q^{69} + 55 q^{70} + 28 q^{71} + 121 q^{72} + 117 q^{73} + 49 q^{74} + 62 q^{75} + 37 q^{76} + 92 q^{77} + 14 q^{78} + q^{79} + 36 q^{80} + 155 q^{81} + 98 q^{82} + 117 q^{83} + 36 q^{84} + 81 q^{85} + 37 q^{86} + 46 q^{87} + 40 q^{88} + 90 q^{89} + 97 q^{90} + 65 q^{91} + 37 q^{92} + 36 q^{93} + 91 q^{94} + 38 q^{95} + 24 q^{96} + 111 q^{97} + 170 q^{98} + 97 q^{99}+O(q^{100}) \) 95 * q + 95 * q^2 + 24 * q^3 + 95 * q^4 + 36 * q^5 + 24 * q^6 + 21 * q^7 + 95 * q^8 + 121 * q^9 + 36 * q^10 + 40 * q^11 + 24 * q^12 + 52 * q^13 + 21 * q^14 + 15 * q^15 + 95 * q^16 + 84 * q^17 + 121 * q^18 + 37 * q^19 + 36 * q^20 + 36 * q^21 + 40 * q^22 + 37 * q^23 + 24 * q^24 + 133 * q^25 + 52 * q^26 + 93 * q^27 + 21 * q^28 + 66 * q^29 + 15 * q^30 + 10 * q^31 + 95 * q^32 + 63 * q^33 + 84 * q^34 + 55 * q^35 + 121 * q^36 + 49 * q^37 + 37 * q^38 + 14 * q^39 + 36 * q^40 + 98 * q^41 + 36 * q^42 + 37 * q^43 + 40 * q^44 + 97 * q^45 + 37 * q^46 + 91 * q^47 + 24 * q^48 + 170 * q^49 + 133 * q^50 + 22 * q^51 + 52 * q^52 + 70 * q^53 + 93 * q^54 - q^55 + 21 * q^56 + 50 * q^57 + 66 * q^58 + 72 * q^59 + 15 * q^60 + 97 * q^61 + 10 * q^62 + 75 * q^63 + 95 * q^64 + 75 * q^65 + 63 * q^66 + 39 * q^67 + 84 * q^68 + 65 * q^69 + 55 * q^70 + 28 * q^71 + 121 * q^72 + 117 * q^73 + 49 * q^74 + 62 * q^75 + 37 * q^76 + 92 * q^77 + 14 * q^78 + q^79 + 36 * q^80 + 155 * q^81 + 98 * q^82 + 117 * q^83 + 36 * q^84 + 81 * q^85 + 37 * q^86 + 46 * q^87 + 40 * q^88 + 90 * q^89 + 97 * q^90 + 65 * q^91 + 37 * q^92 + 36 * q^93 + 91 * q^94 + 38 * q^95 + 24 * q^96 + 111 * q^97 + 170 * q^98 + 97 * q^99

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