LMFDB - Embedded newform 8002.2.a.g.1.9

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			1.9
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.73826 q^{3} +1.00000 q^{4} -2.29649 q^{5} -2.73826 q^{6} -2.81204 q^{7} +1.00000 q^{8} +4.49807 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.73826 q^{3} +1.00000 q^{4} -2.29649 q^{5} -2.73826 q^{6} -2.81204 q^{7} +1.00000 q^{8} +4.49807 q^{9} -2.29649 q^{10} -0.427274 q^{11} -2.73826 q^{12} +4.79158 q^{13} -2.81204 q^{14} +6.28839 q^{15} +1.00000 q^{16} -4.02173 q^{17} +4.49807 q^{18} -6.99260 q^{19} -2.29649 q^{20} +7.70008 q^{21} -0.427274 q^{22} -4.95038 q^{23} -2.73826 q^{24} +0.273868 q^{25} +4.79158 q^{26} -4.10210 q^{27} -2.81204 q^{28} +0.520862 q^{29} +6.28839 q^{30} +1.50321 q^{31} +1.00000 q^{32} +1.16999 q^{33} -4.02173 q^{34} +6.45781 q^{35} +4.49807 q^{36} +2.51234 q^{37} -6.99260 q^{38} -13.1206 q^{39} -2.29649 q^{40} +1.66234 q^{41} +7.70008 q^{42} -2.51878 q^{43} -0.427274 q^{44} -10.3298 q^{45} -4.95038 q^{46} -2.65278 q^{47} -2.73826 q^{48} +0.907543 q^{49} +0.273868 q^{50} +11.0125 q^{51} +4.79158 q^{52} -7.47105 q^{53} -4.10210 q^{54} +0.981230 q^{55} -2.81204 q^{56} +19.1476 q^{57} +0.520862 q^{58} -6.47039 q^{59} +6.28839 q^{60} -6.52520 q^{61} +1.50321 q^{62} -12.6487 q^{63} +1.00000 q^{64} -11.0038 q^{65} +1.16999 q^{66} -10.5772 q^{67} -4.02173 q^{68} +13.5554 q^{69} +6.45781 q^{70} -5.27424 q^{71} +4.49807 q^{72} +13.4674 q^{73} +2.51234 q^{74} -0.749921 q^{75} -6.99260 q^{76} +1.20151 q^{77} -13.1206 q^{78} -2.81869 q^{79} -2.29649 q^{80} -2.26159 q^{81} +1.66234 q^{82} +9.64904 q^{83} +7.70008 q^{84} +9.23587 q^{85} -2.51878 q^{86} -1.42626 q^{87} -0.427274 q^{88} -2.70197 q^{89} -10.3298 q^{90} -13.4741 q^{91} -4.95038 q^{92} -4.11619 q^{93} -2.65278 q^{94} +16.0584 q^{95} -2.73826 q^{96} -16.0367 q^{97} +0.907543 q^{98} -1.92191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.73826	−1.58094	−0.790468	−	0.612504i	$-0.790162\pi$
$3$	−2.73826	−1.58094	−0.790468	+	0.612504i	$0.790162\pi$
$4$	1.00000	0.500000
$5$	−2.29649	−1.02702	−0.513511	−	0.858083i	$-0.671655\pi$
$5$	−2.29649	−1.02702	−0.513511	+	0.858083i	$0.671655\pi$
$6$	−2.73826	−1.11789
$7$	−2.81204	−1.06285	−0.531425	−	0.847106i	$-0.678343\pi$
$7$	−2.81204	−1.06285	−0.531425	+	0.847106i	$0.678343\pi$
$8$	1.00000	0.353553
$9$	4.49807	1.49936
$10$	−2.29649	−0.726214
$11$	−0.427274	−0.128828	−0.0644139	−	0.997923i	$-0.520518\pi$
$11$	−0.427274	−0.128828	−0.0644139	+	0.997923i	$0.520518\pi$
$12$	−2.73826	−0.790468
$13$	4.79158	1.32895	0.664473	−	0.747312i	$-0.268656\pi$
$13$	4.79158	1.32895	0.664473	+	0.747312i	$0.268656\pi$
$14$	−2.81204	−0.751548
$15$	6.28839	1.62365
$16$	1.00000	0.250000
$17$	−4.02173	−0.975413	−0.487706	−	0.873008i	$-0.662166\pi$
$17$	−4.02173	−0.975413	−0.487706	+	0.873008i	$0.662166\pi$
$18$	4.49807	1.06020
$19$	−6.99260	−1.60421	−0.802106	−	0.597182i	$-0.796287\pi$
$19$	−6.99260	−1.60421	−0.802106	+	0.597182i	$0.796287\pi$
$20$	−2.29649	−0.513511
$21$	7.70008	1.68030
$22$	−0.427274	−0.0910950
$23$	−4.95038	−1.03222	−0.516112	−	0.856521i	$-0.672621\pi$
$23$	−4.95038	−1.03222	−0.516112	+	0.856521i	$0.672621\pi$
$24$	−2.73826	−0.558945
$25$	0.273868	0.0547736
$26$	4.79158	0.939707
$27$	−4.10210	−0.789450
$28$	−2.81204	−0.531425
$29$	0.520862	0.0967217	0.0483609	−	0.998830i	$-0.484600\pi$
$29$	0.520862	0.0967217	0.0483609	+	0.998830i	$0.484600\pi$
$30$	6.28839	1.14810
$31$	1.50321	0.269985	0.134993	−	0.990847i	$-0.456899\pi$
$31$	1.50321	0.269985	0.134993	+	0.990847i	$0.456899\pi$
$32$	1.00000	0.176777
$33$	1.16999	0.203668
$34$	−4.02173	−0.689721
$35$	6.45781	1.09157
$36$	4.49807	0.749678
$37$	2.51234	0.413027	0.206513	−	0.978444i	$-0.433788\pi$
$37$	2.51234	0.413027	0.206513	+	0.978444i	$0.433788\pi$
$38$	−6.99260	−1.13435
$39$	−13.1206	−2.10098
$40$	−2.29649	−0.363107
$41$	1.66234	0.259613	0.129807	−	0.991539i	$-0.458564\pi$
$41$	1.66234	0.259613	0.129807	+	0.991539i	$0.458564\pi$
$42$	7.70008	1.18815
$43$	−2.51878	−0.384110	−0.192055	−	0.981384i	$-0.561515\pi$
$43$	−2.51878	−0.384110	−0.192055	+	0.981384i	$0.561515\pi$
$44$	−0.427274	−0.0644139
$45$	−10.3298	−1.53987
$46$	−4.95038	−0.729893
$47$	−2.65278	−0.386947	−0.193474	−	0.981105i	$-0.561975\pi$
$47$	−2.65278	−0.386947	−0.193474	+	0.981105i	$0.561975\pi$
$48$	−2.73826	−0.395234
$49$	0.907543	0.129649
$50$	0.273868	0.0387308
$51$	11.0125	1.54206
$52$	4.79158	0.664473
$53$	−7.47105	−1.02623	−0.513114	−	0.858320i	$-0.671508\pi$
$53$	−7.47105	−1.02623	−0.513114	+	0.858320i	$0.671508\pi$
$54$	−4.10210	−0.558225
$55$	0.981230	0.132309
$56$	−2.81204	−0.375774
$57$	19.1476	2.53616
$58$	0.520862	0.0683926
$59$	−6.47039	−0.842373	−0.421187	−	0.906974i	$-0.638386\pi$
$59$	−6.47039	−0.842373	−0.421187	+	0.906974i	$0.638386\pi$
$60$	6.28839	0.811827
$61$	−6.52520	−0.835466	−0.417733	−	0.908570i	$-0.637175\pi$
$61$	−6.52520	−0.835466	−0.417733	+	0.908570i	$0.637175\pi$
$62$	1.50321	0.190908
$63$	−12.6487	−1.59359
$64$	1.00000	0.125000
$65$	−11.0038	−1.36486
$66$	1.16999	0.144015
$67$	−10.5772	−1.29221	−0.646106	−	0.763248i	$-0.723604\pi$
$67$	−10.5772	−1.29221	−0.646106	+	0.763248i	$0.723604\pi$
$68$	−4.02173	−0.487706
$69$	13.5554	1.63188
$70$	6.45781	0.771856
$71$	−5.27424	−0.625937	−0.312969	−	0.949763i	$-0.601323\pi$
$71$	−5.27424	−0.625937	−0.312969	+	0.949763i	$0.601323\pi$
$72$	4.49807	0.530102
$73$	13.4674	1.57623	0.788117	−	0.615525i	$-0.211056\pi$
$73$	13.4674	1.57623	0.788117	+	0.615525i	$0.211056\pi$
$74$	2.51234	0.292054
$75$	−0.749921	−0.0865934
$76$	−6.99260	−0.802106
$77$	1.20151	0.136925
$78$	−13.1206	−1.48562
$79$	−2.81869	−0.317127	−0.158564	−	0.987349i	$-0.550686\pi$
$79$	−2.81869	−0.317127	−0.158564	+	0.987349i	$0.550686\pi$
$80$	−2.29649	−0.256755
$81$	−2.26159	−0.251287
$82$	1.66234	0.183574
$83$	9.64904	1.05912	0.529560	−	0.848272i	$-0.322357\pi$
$83$	9.64904	1.05912	0.529560	+	0.848272i	$0.322357\pi$
$84$	7.70008	0.840148
$85$	9.23587	1.00177
$86$	−2.51878	−0.271607
$87$	−1.42626	−0.152911
$88$	−0.427274	−0.0455475
$89$	−2.70197	−0.286408	−0.143204	−	0.989693i	$-0.545741\pi$
$89$	−2.70197	−0.286408	−0.143204	+	0.989693i	$0.545741\pi$
$90$	−10.3298	−1.08885
$91$	−13.4741	−1.41247
$92$	−4.95038	−0.516112
$93$	−4.11619	−0.426829
$94$	−2.65278	−0.273613
$95$	16.0584	1.64756
$96$	−2.73826	−0.279472
$97$	−16.0367	−1.62828	−0.814138	−	0.580671i	$-0.802790\pi$
$97$	−16.0367	−1.62828	−0.814138	+	0.580671i	$0.802790\pi$
$98$	0.907543	0.0916757
$99$	−1.92191	−0.193159
$100$	0.273868	0.0273868
$101$	3.79258	0.377376	0.188688	−	0.982037i	$-0.439577\pi$
$101$	3.79258	0.377376	0.188688	+	0.982037i	$0.439577\pi$
$102$	11.0125	1.09040
$103$	7.66155	0.754915	0.377457	−	0.926027i	$-0.376798\pi$
$103$	7.66155	0.754915	0.377457	+	0.926027i	$0.376798\pi$
$104$	4.79158	0.469853
$105$	−17.6832	−1.72570
$106$	−7.47105	−0.725653
$107$	−17.7783	−1.71870	−0.859348	−	0.511391i	$-0.829130\pi$
$107$	−17.7783	−1.71870	−0.859348	+	0.511391i	$0.829130\pi$
$108$	−4.10210	−0.394725
$109$	−5.00873	−0.479749	−0.239875	−	0.970804i	$-0.577106\pi$
$109$	−5.00873	−0.479749	−0.239875	+	0.970804i	$0.577106\pi$
$110$	0.981230	0.0935566
$111$	−6.87945	−0.652969
$112$	−2.81204	−0.265712
$113$	10.6892	1.00556	0.502778	−	0.864416i	$-0.332311\pi$
$113$	10.6892	1.00556	0.502778	+	0.864416i	$0.332311\pi$
$114$	19.1476	1.79333
$115$	11.3685	1.06012
$116$	0.520862	0.0483609
$117$	21.5529	1.99256
$118$	−6.47039	−0.595648
$119$	11.3092	1.03672
$120$	6.28839	0.574049
$121$	−10.8174	−0.983403
$122$	−6.52520	−0.590763
$123$	−4.55191	−0.410432
$124$	1.50321	0.134993
$125$	10.8535	0.970768
$126$	−12.6487	−1.12684
$127$	−16.9029	−1.49989	−0.749944	−	0.661502i	$-0.769919\pi$
$127$	−16.9029	−1.49989	−0.749944	+	0.661502i	$0.769919\pi$
$128$	1.00000	0.0883883
$129$	6.89707	0.607253
$130$	−11.0038	−0.965099
$131$	14.6477	1.27978	0.639888	−	0.768469i	$-0.278981\pi$
$131$	14.6477	1.27978	0.639888	+	0.768469i	$0.278981\pi$
$132$	1.16999	0.101834
$133$	19.6634	1.70504
$134$	−10.5772	−0.913732
$135$	9.42043	0.810782
$136$	−4.02173	−0.344861
$137$	−1.51747	−0.129646	−0.0648232	−	0.997897i	$-0.520648\pi$
$137$	−1.51747	−0.129646	−0.0648232	+	0.997897i	$0.520648\pi$
$138$	13.5554	1.15391
$139$	−20.4722	−1.73643	−0.868213	−	0.496192i	$-0.834731\pi$
$139$	−20.4722	−1.73643	−0.868213	+	0.496192i	$0.834731\pi$
$140$	6.45781	0.545785
$141$	7.26399	0.611738
$142$	−5.27424	−0.442604
$143$	−2.04732	−0.171205
$144$	4.49807	0.374839
$145$	−1.19616	−0.0993353
$146$	13.4674	1.11457
$147$	−2.48509	−0.204967
$148$	2.51234	0.206513
$149$	−13.5145	−1.10715	−0.553575	−	0.832800i	$-0.686737\pi$
$149$	−13.5145	−1.10715	−0.553575	+	0.832800i	$0.686737\pi$
$150$	−0.749921	−0.0612308
$151$	−7.25782	−0.590633	−0.295316	−	0.955400i	$-0.595425\pi$
$151$	−7.25782	−0.590633	−0.295316	+	0.955400i	$0.595425\pi$
$152$	−6.99260	−0.567175
$153$	−18.0900	−1.46249
$154$	1.20151	0.0968203
$155$	−3.45212	−0.277281
$156$	−13.1206	−1.05049
$157$	−6.36292	−0.507816	−0.253908	−	0.967228i	$-0.581716\pi$
$157$	−6.36292	−0.507816	−0.253908	+	0.967228i	$0.581716\pi$
$158$	−2.81869	−0.224243
$159$	20.4577	1.62240
$160$	−2.29649	−0.181554
$161$	13.9206	1.09710
$162$	−2.26159	−0.177687
$163$	−11.4701	−0.898408	−0.449204	−	0.893429i	$-0.648292\pi$
$163$	−11.4701	−0.898408	−0.449204	+	0.893429i	$0.648292\pi$
$164$	1.66234	0.129807
$165$	−2.68686	−0.209172
$166$	9.64904	0.748911
$167$	9.53698	0.737994	0.368997	−	0.929431i	$-0.379701\pi$
$167$	9.53698	0.737994	0.368997	+	0.929431i	$0.379701\pi$
$168$	7.70008	0.594074
$169$	9.95927	0.766098
$170$	9.23587	0.708359
$171$	−31.4532	−2.40529
$172$	−2.51878	−0.192055
$173$	13.4379	1.02167	0.510833	−	0.859680i	$-0.329337\pi$
$173$	13.4379	1.02167	0.510833	+	0.859680i	$0.329337\pi$
$174$	−1.42626	−0.108124
$175$	−0.770126	−0.0582160
$176$	−0.427274	−0.0322070
$177$	17.7176	1.33174
$178$	−2.70197	−0.202521
$179$	−1.83243	−0.136962	−0.0684810	−	0.997652i	$-0.521815\pi$
$179$	−1.83243	−0.136962	−0.0684810	+	0.997652i	$0.521815\pi$
$180$	−10.3298	−0.769936
$181$	11.4663	0.852286	0.426143	−	0.904656i	$-0.359872\pi$
$181$	11.4663	0.852286	0.426143	+	0.904656i	$0.359872\pi$
$182$	−13.4741	−0.998767
$183$	17.8677	1.32082
$184$	−4.95038	−0.364947
$185$	−5.76958	−0.424188
$186$	−4.11619	−0.301814
$187$	1.71838	0.125660
$188$	−2.65278	−0.193474
$189$	11.5353	0.839066
$190$	16.0584	1.16500
$191$	4.90106	0.354628	0.177314	−	0.984154i	$-0.443259\pi$
$191$	4.90106	0.354628	0.177314	+	0.984154i	$0.443259\pi$
$192$	−2.73826	−0.197617
$193$	19.6228	1.41248	0.706241	−	0.707971i	$-0.250389\pi$
$193$	19.6228	1.41248	0.706241	+	0.707971i	$0.250389\pi$
$194$	−16.0367	−1.15137
$195$	30.1313	2.15775
$196$	0.907543	0.0648245
$197$	20.1468	1.43540	0.717702	−	0.696351i	$-0.245194\pi$
$197$	20.1468	1.43540	0.717702	+	0.696351i	$0.245194\pi$
$198$	−1.92191	−0.136584
$199$	18.2000	1.29016	0.645082	−	0.764114i	$-0.276823\pi$
$199$	18.2000	1.29016	0.645082	+	0.764114i	$0.276823\pi$
$200$	0.273868	0.0193654
$201$	28.9631	2.04290
$202$	3.79258	0.266845
$203$	−1.46468	−0.102801
$204$	11.0125	0.771032
$205$	−3.81754	−0.266628
$206$	7.66155	0.533805
$207$	−22.2671	−1.54767
$208$	4.79158	0.332237
$209$	2.98775	0.206667
$210$	−17.6832	−1.22025
$211$	2.75059	0.189359	0.0946793	−	0.995508i	$-0.469817\pi$
$211$	2.75059	0.189359	0.0946793	+	0.995508i	$0.469817\pi$
$212$	−7.47105	−0.513114
$213$	14.4422	0.989566
$214$	−17.7783	−1.21530
$215$	5.78435	0.394490
$216$	−4.10210	−0.279113
$217$	−4.22709	−0.286954
$218$	−5.00873	−0.339234
$219$	−36.8771	−2.49193
$220$	0.981230	0.0661545
$221$	−19.2705	−1.29627
$222$	−6.87945	−0.461719
$223$	1.72999	0.115849	0.0579244	−	0.998321i	$-0.481552\pi$
$223$	1.72999	0.115849	0.0579244	+	0.998321i	$0.481552\pi$
$224$	−2.81204	−0.187887
$225$	1.23188	0.0821251
$226$	10.6892	0.711035
$227$	9.83096	0.652504	0.326252	−	0.945283i	$-0.394214\pi$
$227$	9.83096	0.652504	0.326252	+	0.945283i	$0.394214\pi$
$228$	19.1476	1.26808
$229$	15.0789	0.996440	0.498220	−	0.867051i	$-0.333987\pi$
$229$	15.0789	0.996440	0.498220	+	0.867051i	$0.333987\pi$
$230$	11.3685	0.749616
$231$	−3.29004	−0.216469
$232$	0.520862	0.0341963
$233$	−3.74198	−0.245145	−0.122573	−	0.992460i	$-0.539114\pi$
$233$	−3.74198	−0.245145	−0.122573	+	0.992460i	$0.539114\pi$
$234$	21.5529	1.40896
$235$	6.09208	0.397403
$236$	−6.47039	−0.421187
$237$	7.71831	0.501358
$238$	11.3092	0.733070
$239$	19.2501	1.24518	0.622591	−	0.782547i	$-0.286080\pi$
$239$	19.2501	1.24518	0.622591	+	0.782547i	$0.286080\pi$
$240$	6.28839	0.405914
$241$	−6.51546	−0.419698	−0.209849	−	0.977734i	$-0.567297\pi$
$241$	−6.51546	−0.419698	−0.209849	+	0.977734i	$0.567297\pi$
$242$	−10.8174	−0.695371
$243$	18.4991	1.18672
$244$	−6.52520	−0.417733
$245$	−2.08416	−0.133152
$246$	−4.55191	−0.290219
$247$	−33.5056	−2.13191
$248$	1.50321	0.0954542
$249$	−26.4216	−1.67440
$250$	10.8535	0.686437
$251$	10.7692	0.679744	0.339872	−	0.940472i	$-0.389616\pi$
$251$	10.7692	0.679744	0.339872	+	0.940472i	$0.389616\pi$
$252$	−12.6487	−0.796795
$253$	2.11516	0.132979
$254$	−16.9029	−1.06058
$255$	−25.2902	−1.58373
$256$	1.00000	0.0625000
$257$	−18.6084	−1.16076	−0.580380	−	0.814346i	$-0.697096\pi$
$257$	−18.6084	−1.16076	−0.580380	+	0.814346i	$0.697096\pi$
$258$	6.89707	0.429393
$259$	−7.06480	−0.438985
$260$	−11.0038	−0.682428
$261$	2.34287	0.145020
$262$	14.6477	0.904938
$263$	−1.79143	−0.110464	−0.0552322	−	0.998474i	$-0.517590\pi$
$263$	−1.79143	−0.110464	−0.0552322	+	0.998474i	$0.517590\pi$
$264$	1.16999	0.0720077
$265$	17.1572	1.05396
$266$	19.6634	1.20564
$267$	7.39869	0.452793
$268$	−10.5772	−0.646106
$269$	9.01714	0.549785	0.274892	−	0.961475i	$-0.411358\pi$
$269$	9.01714	0.549785	0.274892	+	0.961475i	$0.411358\pi$
$270$	9.42043	0.573309
$271$	−13.8650	−0.842237	−0.421119	−	0.907006i	$-0.638362\pi$
$271$	−13.8650	−0.842237	−0.421119	+	0.907006i	$0.638362\pi$
$272$	−4.02173	−0.243853
$273$	36.8956	2.23302
$274$	−1.51747	−0.0916738
$275$	−0.117016	−0.00705636
$276$	13.5554	0.815940
$277$	6.79484	0.408262	0.204131	−	0.978944i	$-0.434563\pi$
$277$	6.79484	0.408262	0.204131	+	0.978944i	$0.434563\pi$
$278$	−20.4722	−1.22784
$279$	6.76156	0.404804
$280$	6.45781	0.385928
$281$	13.6181	0.812390	0.406195	−	0.913786i	$-0.366855\pi$
$281$	13.6181	0.812390	0.406195	+	0.913786i	$0.366855\pi$
$282$	7.26399	0.432564
$283$	23.0842	1.37221	0.686106	−	0.727501i	$-0.259318\pi$
$283$	23.0842	1.37221	0.686106	+	0.727501i	$0.259318\pi$
$284$	−5.27424	−0.312969
$285$	−43.9722	−2.60469
$286$	−2.04732	−0.121060
$287$	−4.67455	−0.275930
$288$	4.49807	0.265051
$289$	−0.825682	−0.0485696
$290$	−1.19616	−0.0702407
$291$	43.9126	2.57420
$292$	13.4674	0.788117
$293$	17.2106	1.00546	0.502728	−	0.864445i	$-0.332330\pi$
$293$	17.2106	1.00546	0.502728	+	0.864445i	$0.332330\pi$
$294$	−2.48509	−0.144933
$295$	14.8592	0.865136
$296$	2.51234	0.146027
$297$	1.75272	0.101703
$298$	−13.5145	−0.782873
$299$	−23.7201	−1.37177
$300$	−0.749921	−0.0432967
$301$	7.08290	0.408251
$302$	−7.25782	−0.417640
$303$	−10.3851	−0.596607
$304$	−6.99260	−0.401053
$305$	14.9850	0.858041
$306$	−18.0900	−1.03414
$307$	23.6421	1.34933	0.674663	−	0.738126i	$-0.264289\pi$
$307$	23.6421	1.34933	0.674663	+	0.738126i	$0.264289\pi$
$308$	1.20151	0.0684623
$309$	−20.9793	−1.19347
$310$	−3.45212	−0.196067
$311$	23.5626	1.33611	0.668057	−	0.744110i	$-0.267126\pi$
$311$	23.5626	1.33611	0.668057	+	0.744110i	$0.267126\pi$
$312$	−13.1206	−0.742808
$313$	30.1533	1.70437	0.852183	−	0.523244i	$-0.175278\pi$
$313$	30.1533	1.70437	0.852183	+	0.523244i	$0.175278\pi$
$314$	−6.36292	−0.359080
$315$	29.0477	1.63665
$316$	−2.81869	−0.158564
$317$	−11.5951	−0.651247	−0.325623	−	0.945500i	$-0.605574\pi$
$317$	−11.5951	−0.651247	−0.325623	+	0.945500i	$0.605574\pi$
$318$	20.4577	1.14721
$319$	−0.222551	−0.0124604
$320$	−2.29649	−0.128378
$321$	48.6817	2.71715
$322$	13.9206	0.775766
$323$	28.1223	1.56477
$324$	−2.26159	−0.125644
$325$	1.31226	0.0727911
$326$	−11.4701	−0.635270
$327$	13.7152	0.758452
$328$	1.66234	0.0917871
$329$	7.45970	0.411267
$330$	−2.68686	−0.147907
$331$	−22.1610	−1.21808	−0.609039	−	0.793140i	$-0.708445\pi$
$331$	−22.1610	−1.21808	−0.609039	+	0.793140i	$0.708445\pi$
$332$	9.64904	0.529560
$333$	11.3007	0.619274
$334$	9.53698	0.521841
$335$	24.2905	1.32713
$336$	7.70008	0.420074
$337$	27.9141	1.52058	0.760290	−	0.649584i	$-0.225057\pi$
$337$	27.9141	1.52058	0.760290	+	0.649584i	$0.225057\pi$
$338$	9.95927	0.541713
$339$	−29.2698	−1.58972
$340$	9.23587	0.500885
$341$	−0.642284	−0.0347816
$342$	−31.4532	−1.70079
$343$	17.1322	0.925052
$344$	−2.51878	−0.135803
$345$	−31.1299	−1.67598
$346$	13.4379	0.722427
$347$	−2.24571	−0.120556	−0.0602780	−	0.998182i	$-0.519199\pi$
$347$	−2.24571	−0.120556	−0.0602780	+	0.998182i	$0.519199\pi$
$348$	−1.42626	−0.0764554
$349$	30.7895	1.64813	0.824063	−	0.566499i	$-0.191702\pi$
$349$	30.7895	1.64813	0.824063	+	0.566499i	$0.191702\pi$
$350$	−0.770126	−0.0411650
$351$	−19.6556	−1.04914
$352$	−0.427274	−0.0227738
$353$	8.38228	0.446144	0.223072	−	0.974802i	$-0.428392\pi$
$353$	8.38228	0.446144	0.223072	+	0.974802i	$0.428392\pi$
$354$	17.7176	0.941681
$355$	12.1122	0.642851
$356$	−2.70197	−0.143204
$357$	−30.9677	−1.63898
$358$	−1.83243	−0.0968468
$359$	0.823875	0.0434824	0.0217412	−	0.999764i	$-0.493079\pi$
$359$	0.823875	0.0434824	0.0217412	+	0.999764i	$0.493079\pi$
$360$	−10.3298	−0.544427
$361$	29.8964	1.57350
$362$	11.4663	0.602657
$363$	29.6210	1.55470
$364$	−13.4741	−0.706235
$365$	−30.9277	−1.61883
$366$	17.8677	0.933959
$367$	−0.973907	−0.0508375	−0.0254188	−	0.999677i	$-0.508092\pi$
$367$	−0.973907	−0.0508375	−0.0254188	+	0.999677i	$0.508092\pi$
$368$	−4.95038	−0.258056
$369$	7.47730	0.389253
$370$	−5.76958	−0.299946
$371$	21.0089	1.09073
$372$	−4.11619	−0.213415
$373$	−38.2234	−1.97913	−0.989567	−	0.144070i	$-0.953981\pi$
$373$	−38.2234	−1.97913	−0.989567	+	0.144070i	$0.953981\pi$
$374$	1.71838	0.0888553
$375$	−29.7198	−1.53472
$376$	−2.65278	−0.136807
$377$	2.49576	0.128538
$378$	11.5353	0.593309
$379$	−15.8445	−0.813877	−0.406938	−	0.913456i	$-0.633404\pi$
$379$	−15.8445	−0.813877	−0.406938	+	0.913456i	$0.633404\pi$
$380$	16.0584	0.823780
$381$	46.2845	2.37122
$382$	4.90106	0.250760
$383$	−29.9524	−1.53050	−0.765248	−	0.643736i	$-0.777384\pi$
$383$	−29.9524	−1.53050	−0.765248	+	0.643736i	$0.777384\pi$
$384$	−2.73826	−0.139736
$385$	−2.75925	−0.140625
$386$	19.6228	0.998776
$387$	−11.3296	−0.575918
$388$	−16.0367	−0.814138
$389$	21.3220	1.08107	0.540533	−	0.841323i	$-0.318223\pi$
$389$	21.3220	1.08107	0.540533	+	0.841323i	$0.318223\pi$
$390$	30.1313	1.52576
$391$	19.9091	1.00685
$392$	0.907543	0.0458378
$393$	−40.1092	−2.02324
$394$	20.1468	1.01498
$395$	6.47310	0.325697
$396$	−1.92191	−0.0965794
$397$	8.43545	0.423363	0.211681	−	0.977339i	$-0.432106\pi$
$397$	8.43545	0.423363	0.211681	+	0.977339i	$0.432106\pi$
$398$	18.2000	0.912283
$399$	−53.8436	−2.69555
$400$	0.273868	0.0136934
$401$	18.7078	0.934221	0.467110	−	0.884199i	$-0.345295\pi$
$401$	18.7078	0.934221	0.467110	+	0.884199i	$0.345295\pi$
$402$	28.9631	1.44455
$403$	7.20278	0.358796
$404$	3.79258	0.188688
$405$	5.19371	0.258078
$406$	−1.46468	−0.0726910
$407$	−1.07346	−0.0532094
$408$	11.0125	0.545202
$409$	−24.0170	−1.18756	−0.593782	−	0.804626i	$-0.702366\pi$
$409$	−24.0170	−1.18756	−0.593782	+	0.804626i	$0.702366\pi$
$410$	−3.81754	−0.188535
$411$	4.15523	0.204962
$412$	7.66155	0.377457
$413$	18.1950	0.895316
$414$	−22.2671	−1.09437
$415$	−22.1589	−1.08774
$416$	4.79158	0.234927
$417$	56.0581	2.74518
$418$	2.98775	0.146136
$419$	28.3569	1.38532	0.692661	−	0.721263i	$-0.256438\pi$
$419$	28.3569	1.38532	0.692661	+	0.721263i	$0.256438\pi$
$420$	−17.6832	−0.862850
$421$	−15.1712	−0.739397	−0.369698	−	0.929152i	$-0.620539\pi$
$421$	−15.1712	−0.739397	−0.369698	+	0.929152i	$0.620539\pi$
$422$	2.75059	0.133897
$423$	−11.9324	−0.580172
$424$	−7.47105	−0.362826
$425$	−1.10142	−0.0534268
$426$	14.4422	0.699729
$427$	18.3491	0.887974
$428$	−17.7783	−0.859348
$429$	5.60609	0.270664
$430$	5.78435	0.278946
$431$	−3.20133	−0.154202	−0.0771012	−	0.997023i	$-0.524566\pi$
$431$	−3.20133	−0.154202	−0.0771012	+	0.997023i	$0.524566\pi$
$432$	−4.10210	−0.197362
$433$	−28.1116	−1.35096	−0.675479	−	0.737379i	$-0.736063\pi$
$433$	−28.1116	−1.35096	−0.675479	+	0.737379i	$0.736063\pi$
$434$	−4.22709	−0.202907
$435$	3.27538	0.157043
$436$	−5.00873	−0.239875
$437$	34.6160	1.65591
$438$	−36.8771	−1.76206
$439$	−16.6502	−0.794671	−0.397335	−	0.917673i	$-0.630065\pi$
$439$	−16.6502	−0.794671	−0.397335	+	0.917673i	$0.630065\pi$
$440$	0.981230	0.0467783
$441$	4.08219	0.194390
$442$	−19.2705	−0.916602
$443$	21.9266	1.04176	0.520881	−	0.853629i	$-0.325603\pi$
$443$	21.9266	1.04176	0.520881	+	0.853629i	$0.325603\pi$
$444$	−6.87945	−0.326484
$445$	6.20504	0.294147
$446$	1.72999	0.0819174
$447$	37.0062	1.75033
$448$	−2.81204	−0.132856
$449$	−28.5889	−1.34920	−0.674598	−	0.738185i	$-0.735683\pi$
$449$	−28.5889	−1.34920	−0.674598	+	0.738185i	$0.735683\pi$
$450$	1.23188	0.0580712
$451$	−0.710272	−0.0334454
$452$	10.6892	0.502778
$453$	19.8738	0.933752
$454$	9.83096	0.461390
$455$	30.9431	1.45064
$456$	19.1476	0.896666
$457$	2.51043	0.117433	0.0587166	−	0.998275i	$-0.481299\pi$
$457$	2.51043	0.117433	0.0587166	+	0.998275i	$0.481299\pi$
$458$	15.0789	0.704589
$459$	16.4975	0.770039
$460$	11.3685	0.530059
$461$	−19.9572	−0.929498	−0.464749	−	0.885443i	$-0.653855\pi$
$461$	−19.9572	−0.929498	−0.464749	+	0.885443i	$0.653855\pi$
$462$	−3.29004	−0.153067
$463$	−2.56038	−0.118991	−0.0594954	−	0.998229i	$-0.518949\pi$
$463$	−2.56038	−0.118991	−0.0594954	+	0.998229i	$0.518949\pi$
$464$	0.520862	0.0241804
$465$	9.45279	0.438363
$466$	−3.74198	−0.173344
$467$	−36.2215	−1.67613	−0.838067	−	0.545568i	$-0.816314\pi$
$467$	−36.2215	−1.67613	−0.838067	+	0.545568i	$0.816314\pi$
$468$	21.5529	0.996282
$469$	29.7435	1.37343
$470$	6.09208	0.281006
$471$	17.4233	0.802824
$472$	−6.47039	−0.297824
$473$	1.07621	0.0494841
$474$	7.71831	0.354514
$475$	−1.91505	−0.0878684
$476$	11.3092	0.518359
$477$	−33.6053	−1.53868
$478$	19.2501	0.880477
$479$	−13.7867	−0.629932	−0.314966	−	0.949103i	$-0.601993\pi$
$479$	−13.7867	−0.629932	−0.314966	+	0.949103i	$0.601993\pi$
$480$	6.28839	0.287024
$481$	12.0381	0.548891
$482$	−6.51546	−0.296771
$483$	−38.1183	−1.73444
$484$	−10.8174	−0.491702
$485$	36.8280	1.67228
$486$	18.4991	0.839137
$487$	18.3854	0.833121	0.416561	−	0.909108i	$-0.363235\pi$
$487$	18.3854	0.833121	0.416561	+	0.909108i	$0.363235\pi$
$488$	−6.52520	−0.295382
$489$	31.4081	1.42032
$490$	−2.08416	−0.0941529
$491$	20.7396	0.935964	0.467982	−	0.883738i	$-0.344981\pi$
$491$	20.7396	0.935964	0.467982	+	0.883738i	$0.344981\pi$
$492$	−4.55191	−0.205216
$493$	−2.09477	−0.0943436
$494$	−33.5056	−1.50749
$495$	4.41364	0.198378
$496$	1.50321	0.0674963
$497$	14.8314	0.665277
$498$	−26.4216	−1.18398
$499$	5.74597	0.257225	0.128612	−	0.991695i	$-0.458948\pi$
$499$	5.74597	0.257225	0.128612	+	0.991695i	$0.458948\pi$
$500$	10.8535	0.485384
$501$	−26.1147	−1.16672
$502$	10.7692	0.480651
$503$	15.6108	0.696051	0.348025	−	0.937485i	$-0.386852\pi$
$503$	15.6108	0.696051	0.348025	+	0.937485i	$0.386852\pi$
$504$	−12.6487	−0.563419
$505$	−8.70962	−0.387573
$506$	2.11516	0.0940305
$507$	−27.2711	−1.21115
$508$	−16.9029	−0.749944
$509$	−12.1760	−0.539693	−0.269846	−	0.962903i	$-0.586973\pi$
$509$	−12.1760	−0.539693	−0.269846	+	0.962903i	$0.586973\pi$
$510$	−25.2902	−1.11987
$511$	−37.8707	−1.67530
$512$	1.00000	0.0441942
$513$	28.6843	1.26644
$514$	−18.6084	−0.820781
$515$	−17.5947	−0.775314
$516$	6.89707	0.303627
$517$	1.13346	0.0498496
$518$	−7.06480	−0.310410
$519$	−36.7965	−1.61519
$520$	−11.0038	−0.482550
$521$	−21.4730	−0.940749	−0.470375	−	0.882467i	$-0.655881\pi$
$521$	−21.4730	−0.940749	−0.470375	+	0.882467i	$0.655881\pi$
$522$	2.34287	0.102545
$523$	−23.4154	−1.02388	−0.511942	−	0.859020i	$-0.671074\pi$
$523$	−23.4154	−1.02388	−0.511942	+	0.859020i	$0.671074\pi$
$524$	14.6477	0.639888
$525$	2.10880	0.0920358
$526$	−1.79143	−0.0781101
$527$	−6.04552	−0.263347
$528$	1.16999	0.0509171
$529$	1.50622	0.0654877
$530$	17.1572	0.745261
$531$	−29.1043	−1.26302
$532$	19.6634	0.852518
$533$	7.96522	0.345012
$534$	7.39869	0.320173
$535$	40.8278	1.76514
$536$	−10.5772	−0.456866
$537$	5.01766	0.216528
$538$	9.01714	0.388756
$539$	−0.387769	−0.0167024
$540$	9.42043	0.405391
$541$	−4.68712	−0.201515	−0.100758	−	0.994911i	$-0.532127\pi$
$541$	−4.68712	−0.201515	−0.100758	+	0.994911i	$0.532127\pi$
$542$	−13.8650	−0.595552
$543$	−31.3978	−1.34741
$544$	−4.02173	−0.172430
$545$	11.5025	0.492713
$546$	36.8956	1.57899
$547$	23.7208	1.01423	0.507115	−	0.861878i	$-0.330712\pi$
$547$	23.7208	1.01423	0.507115	+	0.861878i	$0.330712\pi$
$548$	−1.51747	−0.0648232
$549$	−29.3508	−1.25266
$550$	−0.117016	−0.00498960
$551$	−3.64218	−0.155162
$552$	13.5554	0.576957
$553$	7.92626	0.337059
$554$	6.79484	0.288685
$555$	15.7986	0.670613
$556$	−20.4722	−0.868213
$557$	12.2236	0.517929	0.258964	−	0.965887i	$-0.416619\pi$
$557$	12.2236	0.517929	0.258964	+	0.965887i	$0.416619\pi$
$558$	6.76156	0.286240
$559$	−12.0689	−0.510462
$560$	6.45781	0.272892
$561$	−4.70537	−0.198661
$562$	13.6181	0.574446
$563$	12.0417	0.507497	0.253749	−	0.967270i	$-0.418336\pi$
$563$	12.0417	0.507497	0.253749	+	0.967270i	$0.418336\pi$
$564$	7.26399	0.305869
$565$	−24.5476	−1.03273
$566$	23.0842	0.970301
$567$	6.35966	0.267081
$568$	−5.27424	−0.221302
$569$	2.00469	0.0840409	0.0420204	−	0.999117i	$-0.486621\pi$
$569$	2.00469	0.0840409	0.0420204	+	0.999117i	$0.486621\pi$
$570$	−43.9722	−1.84179
$571$	−3.62023	−0.151502	−0.0757510	−	0.997127i	$-0.524135\pi$
$571$	−3.62023	−0.151502	−0.0757510	+	0.997127i	$0.524135\pi$
$572$	−2.04732	−0.0856026
$573$	−13.4204	−0.560644
$574$	−4.67455	−0.195112
$575$	−1.35575	−0.0565386
$576$	4.49807	0.187420
$577$	33.0256	1.37487	0.687437	−	0.726244i	$-0.258736\pi$
$577$	33.0256	1.37487	0.687437	+	0.726244i	$0.258736\pi$
$578$	−0.825682	−0.0343439
$579$	−53.7324	−2.23304
$580$	−1.19616	−0.0496676
$581$	−27.1335	−1.12569
$582$	43.9126	1.82023
$583$	3.19218	0.132207
$584$	13.4674	0.557283
$585$	−49.4960	−2.04641
$586$	17.2106	0.710964
$587$	−8.84989	−0.365274	−0.182637	−	0.983180i	$-0.558463\pi$
$587$	−8.84989	−0.365274	−0.182637	+	0.983180i	$0.558463\pi$
$588$	−2.48509	−0.102483
$589$	−10.5114	−0.433114
$590$	14.8592	0.611743
$591$	−55.1673	−2.26928
$592$	2.51234	0.103257
$593$	28.9815	1.19013	0.595064	−	0.803678i	$-0.297127\pi$
$593$	28.9815	1.19013	0.595064	+	0.803678i	$0.297127\pi$
$594$	1.75272	0.0719149
$595$	−25.9716	−1.06473
$596$	−13.5145	−0.553575
$597$	−49.8363	−2.03966
$598$	−23.7201	−0.969989
$599$	20.2565	0.827657	0.413829	−	0.910355i	$-0.364191\pi$
$599$	20.2565	0.827657	0.413829	+	0.910355i	$0.364191\pi$
$600$	−0.749921	−0.0306154
$601$	−9.46468	−0.386073	−0.193036	−	0.981192i	$-0.561834\pi$
$601$	−9.46468	−0.386073	−0.193036	+	0.981192i	$0.561834\pi$
$602$	7.08290	0.288677
$603$	−47.5770	−1.93749
$604$	−7.25782	−0.295316
$605$	24.8421	1.00998
$606$	−10.3851	−0.421865
$607$	−16.4135	−0.666204	−0.333102	−	0.942891i	$-0.608095\pi$
$607$	−16.4135	−0.666204	−0.333102	+	0.942891i	$0.608095\pi$
$608$	−6.99260	−0.283587
$609$	4.01068	0.162521
$610$	14.9850	0.606727
$611$	−12.7110	−0.514232
$612$	−18.0900	−0.731246
$613$	20.3491	0.821892	0.410946	−	0.911660i	$-0.365198\pi$
$613$	20.3491	0.821892	0.410946	+	0.911660i	$0.365198\pi$
$614$	23.6421	0.954118
$615$	10.4534	0.421522
$616$	1.20151	0.0484102
$617$	−21.8999	−0.881657	−0.440828	−	0.897591i	$-0.645315\pi$
$617$	−21.8999	−0.881657	−0.440828	+	0.897591i	$0.645315\pi$
$618$	−20.9793	−0.843912
$619$	−1.02262	−0.0411027	−0.0205513	−	0.999789i	$-0.506542\pi$
$619$	−1.02262	−0.0411027	−0.0205513	+	0.999789i	$0.506542\pi$
$620$	−3.45212	−0.138640
$621$	20.3069	0.814889
$622$	23.5626	0.944776
$623$	7.59803	0.304409
$624$	−13.1206	−0.525244
$625$	−26.2943	−1.05177
$626$	30.1533	1.20517
$627$	−8.18124	−0.326727
$628$	−6.36292	−0.253908
$629$	−10.1040	−0.402872
$630$	29.0477	1.15729
$631$	−49.8670	−1.98517	−0.992586	−	0.121544i	$-0.961216\pi$
$631$	−49.8670	−1.98517	−0.992586	+	0.121544i	$0.961216\pi$
$632$	−2.81869	−0.112121
$633$	−7.53184	−0.299364
$634$	−11.5951	−0.460501
$635$	38.8173	1.54042
$636$	20.4577	0.811200
$637$	4.34857	0.172297
$638$	−0.222551	−0.00881087
$639$	−23.7239	−0.938503
$640$	−2.29649	−0.0907768
$641$	−22.5653	−0.891276	−0.445638	−	0.895213i	$-0.647023\pi$
$641$	−22.5653	−0.891276	−0.445638	+	0.895213i	$0.647023\pi$
$642$	48.6817	1.92131
$643$	−16.9492	−0.668412	−0.334206	−	0.942500i	$-0.608468\pi$
$643$	−16.9492	−0.668412	−0.334206	+	0.942500i	$0.608468\pi$
$644$	13.9206	0.548550
$645$	−15.8391	−0.623662
$646$	28.1223	1.10646
$647$	−22.0196	−0.865681	−0.432840	−	0.901471i	$-0.642489\pi$
$647$	−22.0196	−0.865681	−0.432840	+	0.901471i	$0.642489\pi$
$648$	−2.26159	−0.0888435
$649$	2.76463	0.108521
$650$	1.31226	0.0514711
$651$	11.5749	0.453655
$652$	−11.4701	−0.449204
$653$	32.6009	1.27577	0.637886	−	0.770131i	$-0.279809\pi$
$653$	32.6009	1.27577	0.637886	+	0.770131i	$0.279809\pi$
$654$	13.7152	0.536307
$655$	−33.6383	−1.31436
$656$	1.66234	0.0649033
$657$	60.5771	2.36334
$658$	7.45970	0.290809
$659$	16.6907	0.650177	0.325089	−	0.945684i	$-0.394606\pi$
$659$	16.6907	0.650177	0.325089	+	0.945684i	$0.394606\pi$
$660$	−2.68686	−0.104586
$661$	−17.1049	−0.665302	−0.332651	−	0.943050i	$-0.607943\pi$
$661$	−17.1049	−0.665302	−0.332651	+	0.943050i	$0.607943\pi$
$662$	−22.1610	−0.861311
$663$	52.7675	2.04932
$664$	9.64904	0.374456
$665$	−45.1569	−1.75111
$666$	11.3007	0.437893
$667$	−2.57846	−0.0998385
$668$	9.53698	0.368997
$669$	−4.73716	−0.183149
$670$	24.2905	0.938422
$671$	2.78804	0.107631
$672$	7.70008	0.297037
$673$	−38.9294	−1.50062	−0.750309	−	0.661087i	$-0.770095\pi$
$673$	−38.9294	−1.50062	−0.750309	+	0.661087i	$0.770095\pi$
$674$	27.9141	1.07521
$675$	−1.12343	−0.0432410
$676$	9.95927	0.383049
$677$	−16.8779	−0.648669	−0.324335	−	0.945942i	$-0.605140\pi$
$677$	−16.8779	−0.648669	−0.324335	+	0.945942i	$0.605140\pi$
$678$	−29.2698	−1.12410
$679$	45.0957	1.73061
$680$	9.23587	0.354179
$681$	−26.9197	−1.03157
$682$	−0.642284	−0.0245943
$683$	−5.01896	−0.192045	−0.0960227	−	0.995379i	$-0.530612\pi$
$683$	−5.01896	−0.192045	−0.0960227	+	0.995379i	$0.530612\pi$
$684$	−31.4532	−1.20264
$685$	3.48486	0.133150
$686$	17.1322	0.654111
$687$	−41.2899	−1.57531
$688$	−2.51878	−0.0960276
$689$	−35.7982	−1.36380
$690$	−31.1299	−1.18509
$691$	6.16610	0.234570	0.117285	−	0.993098i	$-0.462581\pi$
$691$	6.16610	0.234570	0.117285	+	0.993098i	$0.462581\pi$
$692$	13.4379	0.510833
$693$	5.40447	0.205299
$694$	−2.24571	−0.0852460
$695$	47.0141	1.78335
$696$	−1.42626	−0.0540621
$697$	−6.68547	−0.253230
$698$	30.7895	1.16540
$699$	10.2465	0.387559
$700$	−0.770126	−0.0291080
$701$	13.7341	0.518729	0.259364	−	0.965780i	$-0.416487\pi$
$701$	13.7341	0.518729	0.259364	+	0.965780i	$0.416487\pi$
$702$	−19.6556	−0.741851
$703$	−17.5678	−0.662583
$704$	−0.427274	−0.0161035
$705$	−16.6817	−0.628269
$706$	8.38228	0.315471
$707$	−10.6649	−0.401094
$708$	17.7176	0.665869
$709$	32.8028	1.23194	0.615968	−	0.787771i	$-0.288765\pi$
$709$	32.8028	1.23194	0.615968	+	0.787771i	$0.288765\pi$
$710$	12.1122	0.454564
$711$	−12.6787	−0.475487
$712$	−2.70197	−0.101261
$713$	−7.44147	−0.278685
$714$	−30.9677	−1.15894
$715$	4.70164	0.175832
$716$	−1.83243	−0.0684810
$717$	−52.7117	−1.96855
$718$	0.823875	0.0307467
$719$	20.6102	0.768631	0.384316	−	0.923202i	$-0.374437\pi$
$719$	20.6102	0.768631	0.384316	+	0.923202i	$0.374437\pi$
$720$	−10.3298	−0.384968
$721$	−21.5445	−0.802361
$722$	29.8964	1.11263
$723$	17.8410	0.663515
$724$	11.4663	0.426143
$725$	0.142647	0.00529779
$726$	29.6210	1.09934
$727$	−21.4733	−0.796402	−0.398201	−	0.917298i	$-0.630365\pi$
$727$	−21.4733	−0.796402	−0.398201	+	0.917298i	$0.630365\pi$
$728$	−13.4741	−0.499383
$729$	−43.8706	−1.62484
$730$	−30.9277	−1.14468
$731$	10.1299	0.374666
$732$	17.8677	0.660409
$733$	24.6245	0.909525	0.454763	−	0.890613i	$-0.349724\pi$
$733$	24.6245	0.909525	0.454763	+	0.890613i	$0.349724\pi$
$734$	−0.973907	−0.0359476
$735$	5.70698	0.210505
$736$	−4.95038	−0.182473
$737$	4.51936	0.166473
$738$	7.47730	0.275243
$739$	−29.0178	−1.06744	−0.533718	−	0.845662i	$-0.679206\pi$
$739$	−29.0178	−1.06744	−0.533718	+	0.845662i	$0.679206\pi$
$740$	−5.76958	−0.212094
$741$	91.7471	3.37041
$742$	21.0089	0.771260
$743$	−28.0273	−1.02822	−0.514111	−	0.857724i	$-0.671878\pi$
$743$	−28.0273	−1.02822	−0.514111	+	0.857724i	$0.671878\pi$
$744$	−4.11619	−0.150907
$745$	31.0359	1.13707
$746$	−38.2234	−1.39946
$747$	43.4021	1.58800
$748$	1.71838	0.0628302
$749$	49.9933	1.82672
$750$	−29.7198	−1.08521
$751$	48.1278	1.75621	0.878104	−	0.478470i	$-0.158808\pi$
$751$	48.1278	1.75621	0.878104	+	0.478470i	$0.158808\pi$
$752$	−2.65278	−0.0967368
$753$	−29.4888	−1.07463
$754$	2.49576	0.0908901
$755$	16.6675	0.606593
$756$	11.5353	0.419533
$757$	52.6737	1.91446	0.957229	−	0.289332i	$-0.0934331\pi$
$757$	52.6737	1.91446	0.957229	+	0.289332i	$0.0934331\pi$
$758$	−15.8445	−0.575498
$759$	−5.79187	−0.210232
$760$	16.0584	0.582501
$761$	−34.1680	−1.23859	−0.619295	−	0.785158i	$-0.712582\pi$
$761$	−34.1680	−1.23859	−0.619295	+	0.785158i	$0.712582\pi$
$762$	46.2845	1.67671
$763$	14.0847	0.509901
$764$	4.90106	0.177314
$765$	41.5436	1.50201
$766$	−29.9524	−1.08222
$767$	−31.0034	−1.11947
$768$	−2.73826	−0.0988084
$769$	−39.6349	−1.42927	−0.714635	−	0.699497i	$-0.753407\pi$
$769$	−39.6349	−1.42927	−0.714635	+	0.699497i	$0.753407\pi$
$770$	−2.75925	−0.0994366
$771$	50.9546	1.83509
$772$	19.6228	0.706241
$773$	31.6240	1.13744	0.568719	−	0.822532i	$-0.307439\pi$
$773$	31.6240	1.13744	0.568719	+	0.822532i	$0.307439\pi$
$774$	−11.3296	−0.407236
$775$	0.411682	0.0147881
$776$	−16.0367	−0.575683
$777$	19.3453	0.694008
$778$	21.3220	0.764429
$779$	−11.6240	−0.416475
$780$	30.1313	1.07887
$781$	2.25354	0.0806381
$782$	19.9091	0.711947
$783$	−2.13663	−0.0763569
$784$	0.907543	0.0324122
$785$	14.6124	0.521538
$786$	−40.1092	−1.43065
$787$	20.1543	0.718423	0.359212	−	0.933256i	$-0.383046\pi$
$787$	20.1543	0.718423	0.359212	+	0.933256i	$0.383046\pi$
$788$	20.1468	0.717702
$789$	4.90540	0.174637
$790$	6.47310	0.230302
$791$	−30.0584	−1.06875
$792$	−1.92191	−0.0682919
$793$	−31.2660	−1.11029
$794$	8.43545	0.299363
$795$	−46.9809	−1.66624
$796$	18.2000	0.645082
$797$	6.15375	0.217977	0.108989	−	0.994043i	$-0.465239\pi$
$797$	6.15375	0.217977	0.108989	+	0.994043i	$0.465239\pi$
$798$	−53.8436	−1.90604
$799$	10.6688	0.377433
$800$	0.273868	0.00968269
$801$	−12.1536	−0.429428
$802$	18.7078	0.660594
$803$	−5.75425	−0.203063
$804$	28.9631	1.02145
$805$	−31.9686	−1.12674
$806$	7.20278	0.253707
$807$	−24.6913	−0.869174
$808$	3.79258	0.133423
$809$	−12.1210	−0.426153	−0.213076	−	0.977036i	$-0.568348\pi$
$809$	−12.1210	−0.426153	−0.213076	+	0.977036i	$0.568348\pi$
$810$	5.19371	0.182488
$811$	−20.6703	−0.725832	−0.362916	−	0.931822i	$-0.618219\pi$
$811$	−20.6703	−0.725832	−0.362916	+	0.931822i	$0.618219\pi$
$812$	−1.46468	−0.0514003
$813$	37.9659	1.33152
$814$	−1.07346	−0.0376247
$815$	26.3410	0.922685
$816$	11.0125	0.385516
$817$	17.6128	0.616194
$818$	−24.0170	−0.839734
$819$	−60.6074	−2.11780
$820$	−3.81754	−0.133314
$821$	−34.2048	−1.19376	−0.596878	−	0.802332i	$-0.703592\pi$
$821$	−34.2048	−1.19376	−0.596878	+	0.802332i	$0.703592\pi$
$822$	4.15523	0.144930
$823$	16.2887	0.567788	0.283894	−	0.958856i	$-0.408374\pi$
$823$	16.2887	0.567788	0.283894	+	0.958856i	$0.408374\pi$
$824$	7.66155	0.266903
$825$	0.320422	0.0111556
$826$	18.1950	0.633084
$827$	−0.662816	−0.0230484	−0.0115242	−	0.999934i	$-0.503668\pi$
$827$	−0.662816	−0.0230484	−0.0115242	+	0.999934i	$0.503668\pi$
$828$	−22.2671	−0.773836
$829$	−34.0203	−1.18157	−0.590787	−	0.806827i	$-0.701183\pi$
$829$	−34.0203	−1.18157	−0.590787	+	0.806827i	$0.701183\pi$
$830$	−22.1589	−0.769148
$831$	−18.6060	−0.645436
$832$	4.79158	0.166118
$833$	−3.64989	−0.126461
$834$	56.0581	1.94113
$835$	−21.9016	−0.757936
$836$	2.98775	0.103334
$837$	−6.16634	−0.213140
$838$	28.3569	0.979571
$839$	−24.8117	−0.856594	−0.428297	−	0.903638i	$-0.640886\pi$
$839$	−24.8117	−0.856594	−0.428297	+	0.903638i	$0.640886\pi$
$840$	−17.6832	−0.610127
$841$	−28.7287	−0.990645
$842$	−15.1712	−0.522832
$843$	−37.2900	−1.28434
$844$	2.75059	0.0946793
$845$	−22.8714	−0.786799
$846$	−11.9324	−0.410243
$847$	30.4190	1.04521
$848$	−7.47105	−0.256557
$849$	−63.2105	−2.16938
$850$	−1.10142	−0.0377785
$851$	−12.4370	−0.426337
$852$	14.4422	0.494783
$853$	−5.18922	−0.177676	−0.0888378	−	0.996046i	$-0.528315\pi$
$853$	−5.18922	−0.177676	−0.0888378	+	0.996046i	$0.528315\pi$
$854$	18.3491	0.627893
$855$	72.2319	2.47028
$856$	−17.7783	−0.607651
$857$	12.0466	0.411505	0.205752	−	0.978604i	$-0.434036\pi$
$857$	12.0466	0.411505	0.205752	+	0.978604i	$0.434036\pi$
$858$	5.60609	0.191389
$859$	10.8137	0.368957	0.184478	−	0.982837i	$-0.440940\pi$
$859$	10.8137	0.368957	0.184478	+	0.982837i	$0.440940\pi$
$860$	5.78435	0.197245
$861$	12.8001	0.436227
$862$	−3.20133	−0.109038
$863$	33.9411	1.15537	0.577684	−	0.816260i	$-0.303957\pi$
$863$	33.9411	1.15537	0.577684	+	0.816260i	$0.303957\pi$
$864$	−4.10210	−0.139556
$865$	−30.8601	−1.04927
$866$	−28.1116	−0.955272
$867$	2.26093	0.0767853
$868$	−4.22709	−0.143477
$869$	1.20435	0.0408548
$870$	3.27538	0.111046
$871$	−50.6816	−1.71728
$872$	−5.00873	−0.169617
$873$	−72.1340	−2.44137
$874$	34.6160	1.17090
$875$	−30.5205	−1.03178
$876$	−36.8771	−1.24596
$877$	24.3094	0.820869	0.410434	−	0.911890i	$-0.365377\pi$
$877$	24.3094	0.820869	0.410434	+	0.911890i	$0.365377\pi$
$878$	−16.6502	−0.561917
$879$	−47.1271	−1.58956
$880$	0.981230	0.0330772
$881$	−39.5293	−1.33177	−0.665887	−	0.746052i	$-0.731947\pi$
$881$	−39.5293	−1.33177	−0.665887	+	0.746052i	$0.731947\pi$
$882$	4.08219	0.137454
$883$	−27.0953	−0.911831	−0.455915	−	0.890023i	$-0.650688\pi$
$883$	−27.0953	−0.911831	−0.455915	+	0.890023i	$0.650688\pi$
$884$	−19.2705	−0.648136
$885$	−40.6883	−1.36772
$886$	21.9266	0.736637
$887$	−43.5394	−1.46191	−0.730956	−	0.682425i	$-0.760925\pi$
$887$	−43.5394	−1.46191	−0.730956	+	0.682425i	$0.760925\pi$
$888$	−6.87945	−0.230859
$889$	47.5315	1.59415
$890$	6.20504	0.207994
$891$	0.966316	0.0323728
$892$	1.72999	0.0579244
$893$	18.5498	0.620745
$894$	37.0062	1.23767
$895$	4.20815	0.140663
$896$	−2.81204	−0.0939435
$897$	64.9519	2.16868
$898$	−28.5889	−0.954025
$899$	0.782968	0.0261134
$900$	1.23188	0.0410625
$901$	30.0466	1.00100
$902$	−0.710272	−0.0236495
$903$	−19.3948	−0.645419
$904$	10.6892	0.355518
$905$	−26.3323	−0.875316
$906$	19.8738	0.660262
$907$	46.7651	1.55281	0.776405	−	0.630234i	$-0.217041\pi$
$907$	46.7651	1.55281	0.776405	+	0.630234i	$0.217041\pi$
$908$	9.83096	0.326252
$909$	17.0593	0.565821
$910$	30.9431	1.02576
$911$	46.4637	1.53941	0.769706	−	0.638398i	$-0.220403\pi$
$911$	46.4637	1.53941	0.769706	+	0.638398i	$0.220403\pi$
$912$	19.1476	0.634039
$913$	−4.12278	−0.136444
$914$	2.51043	0.0830378
$915$	−41.0330	−1.35651
$916$	15.0789	0.498220
$917$	−41.1898	−1.36021
$918$	16.4975	0.544500
$919$	−11.7683	−0.388202	−0.194101	−	0.980982i	$-0.562179\pi$
$919$	−11.7683	−0.388202	−0.194101	+	0.980982i	$0.562179\pi$
$920$	11.3685	0.374808
$921$	−64.7382	−2.13320
$922$	−19.9572	−0.657254
$923$	−25.2720	−0.831837
$924$	−3.29004	−0.108234
$925$	0.688050	0.0226230
$926$	−2.56038	−0.0841393
$927$	34.4622	1.13189
$928$	0.520862	0.0170981
$929$	45.2365	1.48416	0.742080	−	0.670311i	$-0.233839\pi$
$929$	45.2365	1.48416	0.742080	+	0.670311i	$0.233839\pi$
$930$	9.45279	0.309969
$931$	−6.34608	−0.207984
$932$	−3.74198	−0.122573
$933$	−64.5206	−2.11231
$934$	−36.2215	−1.18521
$935$	−3.94624	−0.129056
$936$	21.5529	0.704478
$937$	29.4937	0.963519	0.481759	−	0.876304i	$-0.339998\pi$
$937$	29.4937	0.963519	0.481759	+	0.876304i	$0.339998\pi$
$938$	29.7435	0.971159
$939$	−82.5676	−2.69449
$940$	6.09208	0.198702
$941$	−40.4685	−1.31924	−0.659618	−	0.751601i	$-0.729282\pi$
$941$	−40.4685	−1.31924	−0.659618	+	0.751601i	$0.729282\pi$
$942$	17.4233	0.567682
$943$	−8.22919	−0.267979
$944$	−6.47039	−0.210593
$945$	−26.4906	−0.861739
$946$	1.07621	0.0349905
$947$	5.69227	0.184974	0.0924869	−	0.995714i	$-0.470518\pi$
$947$	5.69227	0.184974	0.0924869	+	0.995714i	$0.470518\pi$
$948$	7.71831	0.250679
$949$	64.5300	2.09473
$950$	−1.91505	−0.0621323
$951$	31.7504	1.02958
$952$	11.3092	0.366535
$953$	5.11826	0.165797	0.0828983	−	0.996558i	$-0.473582\pi$
$953$	5.11826	0.165797	0.0828983	+	0.996558i	$0.473582\pi$
$954$	−33.6053	−1.08801
$955$	−11.2552	−0.364211
$956$	19.2501	0.622591
$957$	0.609402	0.0196992
$958$	−13.7867	−0.445430
$959$	4.26718	0.137795
$960$	6.28839	0.202957
$961$	−28.7403	−0.927108
$962$	12.0381	0.388124
$963$	−79.9682	−2.57694
$964$	−6.51546	−0.209849
$965$	−45.0636	−1.45065
$966$	−38.1183	−1.22644
$967$	13.1886	0.424118	0.212059	−	0.977257i	$-0.431983\pi$
$967$	13.1886	0.424118	0.212059	+	0.977257i	$0.431983\pi$
$968$	−10.8174	−0.347686
$969$	−77.0063	−2.47380
$970$	36.8280	1.18248
$971$	44.1539	1.41697	0.708483	−	0.705728i	$-0.249380\pi$
$971$	44.1539	1.41697	0.708483	+	0.705728i	$0.249380\pi$
$972$	18.4991	0.593359
$973$	57.5684	1.84556
$974$	18.3854	0.589106
$975$	−3.59331	−0.115078
$976$	−6.52520	−0.208866
$977$	16.0792	0.514419	0.257210	−	0.966356i	$-0.417197\pi$
$977$	16.0792	0.514419	0.257210	+	0.966356i	$0.417197\pi$
$978$	31.4081	1.00432
$979$	1.15448	0.0368973
$980$	−2.08416	−0.0665762
$981$	−22.5296	−0.719315
$982$	20.7396	0.661827
$983$	−9.63034	−0.307160	−0.153580	−	0.988136i	$-0.549080\pi$
$983$	−9.63034	−0.307160	−0.153580	+	0.988136i	$0.549080\pi$
$984$	−4.55191	−0.145110
$985$	−46.2670	−1.47419
$986$	−2.09477	−0.0667110
$987$	−20.4266	−0.650186
$988$	−33.5056	−1.06596
$989$	12.4689	0.396488
$990$	4.41364	0.140275
$991$	22.3741	0.710737	0.355368	−	0.934726i	$-0.384355\pi$
$991$	22.3741	0.710737	0.355368	+	0.934726i	$0.384355\pi$
$992$	1.50321	0.0477271
$993$	60.6825	1.92570
$994$	14.8314	0.470422
$995$	−41.7961	−1.32503
$996$	−26.4216	−0.837200
$997$	40.8368	1.29331	0.646657	−	0.762781i	$-0.276166\pi$
$997$	40.8368	1.29331	0.646657	+	0.762781i	$0.276166\pi$
$998$	5.74597	0.181885
$999$	−10.3059	−0.326064

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.g.1.9	✓	95

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.9	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.73826 q^{3} +1.00000 q^{4} -2.29649 q^{5} -2.73826 q^{6} -2.81204 q^{7} +1.00000 q^{8} +4.49807 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.73826 q^{3} +1.00000 q^{4} -2.29649 q^{5} -2.73826 q^{6} -2.81204 q^{7} +1.00000 q^{8} +4.49807 q^{9} -2.29649 q^{10} -0.427274 q^{11} -2.73826 q^{12} +4.79158 q^{13} -2.81204 q^{14} +6.28839 q^{15} +1.00000 q^{16} -4.02173 q^{17} +4.49807 q^{18} -6.99260 q^{19} -2.29649 q^{20} +7.70008 q^{21} -0.427274 q^{22} -4.95038 q^{23} -2.73826 q^{24} +0.273868 q^{25} +4.79158 q^{26} -4.10210 q^{27} -2.81204 q^{28} +0.520862 q^{29} +6.28839 q^{30} +1.50321 q^{31} +1.00000 q^{32} +1.16999 q^{33} -4.02173 q^{34} +6.45781 q^{35} +4.49807 q^{36} +2.51234 q^{37} -6.99260 q^{38} -13.1206 q^{39} -2.29649 q^{40} +1.66234 q^{41} +7.70008 q^{42} -2.51878 q^{43} -0.427274 q^{44} -10.3298 q^{45} -4.95038 q^{46} -2.65278 q^{47} -2.73826 q^{48} +0.907543 q^{49} +0.273868 q^{50} +11.0125 q^{51} +4.79158 q^{52} -7.47105 q^{53} -4.10210 q^{54} +0.981230 q^{55} -2.81204 q^{56} +19.1476 q^{57} +0.520862 q^{58} -6.47039 q^{59} +6.28839 q^{60} -6.52520 q^{61} +1.50321 q^{62} -12.6487 q^{63} +1.00000 q^{64} -11.0038 q^{65} +1.16999 q^{66} -10.5772 q^{67} -4.02173 q^{68} +13.5554 q^{69} +6.45781 q^{70} -5.27424 q^{71} +4.49807 q^{72} +13.4674 q^{73} +2.51234 q^{74} -0.749921 q^{75} -6.99260 q^{76} +1.20151 q^{77} -13.1206 q^{78} -2.81869 q^{79} -2.29649 q^{80} -2.26159 q^{81} +1.66234 q^{82} +9.64904 q^{83} +7.70008 q^{84} +9.23587 q^{85} -2.51878 q^{86} -1.42626 q^{87} -0.427274 q^{88} -2.70197 q^{89} -10.3298 q^{90} -13.4741 q^{91} -4.95038 q^{92} -4.11619 q^{93} -2.65278 q^{94} +16.0584 q^{95} -2.73826 q^{96} -16.0367 q^{97} +0.907543 q^{98} -1.92191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 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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