LMFDB - Embedded newform 8002.2.a.g.1.1

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			1.1
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.41089 q^{3} +1.00000 q^{4} +2.42267 q^{5} -3.41089 q^{6} +3.23449 q^{7} +1.00000 q^{8} +8.63416 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.41089 q^{3} +1.00000 q^{4} +2.42267 q^{5} -3.41089 q^{6} +3.23449 q^{7} +1.00000 q^{8} +8.63416 q^{9} +2.42267 q^{10} -0.942159 q^{11} -3.41089 q^{12} +3.74746 q^{13} +3.23449 q^{14} -8.26345 q^{15} +1.00000 q^{16} -5.15941 q^{17} +8.63416 q^{18} -0.0231708 q^{19} +2.42267 q^{20} -11.0325 q^{21} -0.942159 q^{22} -0.417845 q^{23} -3.41089 q^{24} +0.869316 q^{25} +3.74746 q^{26} -19.2175 q^{27} +3.23449 q^{28} +5.71959 q^{29} -8.26345 q^{30} -0.739094 q^{31} +1.00000 q^{32} +3.21360 q^{33} -5.15941 q^{34} +7.83608 q^{35} +8.63416 q^{36} +5.31579 q^{37} -0.0231708 q^{38} -12.7822 q^{39} +2.42267 q^{40} +1.45373 q^{41} -11.0325 q^{42} +0.213976 q^{43} -0.942159 q^{44} +20.9177 q^{45} -0.417845 q^{46} +9.87439 q^{47} -3.41089 q^{48} +3.46189 q^{49} +0.869316 q^{50} +17.5982 q^{51} +3.74746 q^{52} +7.46777 q^{53} -19.2175 q^{54} -2.28254 q^{55} +3.23449 q^{56} +0.0790330 q^{57} +5.71959 q^{58} +6.93556 q^{59} -8.26345 q^{60} +6.48999 q^{61} -0.739094 q^{62} +27.9271 q^{63} +1.00000 q^{64} +9.07885 q^{65} +3.21360 q^{66} -9.57906 q^{67} -5.15941 q^{68} +1.42522 q^{69} +7.83608 q^{70} -11.3966 q^{71} +8.63416 q^{72} +11.7358 q^{73} +5.31579 q^{74} -2.96514 q^{75} -0.0231708 q^{76} -3.04740 q^{77} -12.7822 q^{78} +3.09404 q^{79} +2.42267 q^{80} +39.6463 q^{81} +1.45373 q^{82} -9.17319 q^{83} -11.0325 q^{84} -12.4995 q^{85} +0.213976 q^{86} -19.5089 q^{87} -0.942159 q^{88} +4.96269 q^{89} +20.9177 q^{90} +12.1211 q^{91} -0.417845 q^{92} +2.52097 q^{93} +9.87439 q^{94} -0.0561351 q^{95} -3.41089 q^{96} +9.81298 q^{97} +3.46189 q^{98} -8.13476 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−3.41089	−1.96928	−0.984639	−	0.174603i	$-0.944136\pi$
$3$	−3.41089	−1.96928	−0.984639	+	0.174603i	$0.944136\pi$
$4$	1.00000	0.500000
$5$	2.42267	1.08345	0.541725	−	0.840556i	$-0.317771\pi$
$5$	2.42267	1.08345	0.541725	+	0.840556i	$0.317771\pi$
$6$	−3.41089	−1.39249
$7$	3.23449	1.22252	0.611260	−	0.791430i	$-0.290663\pi$
$7$	3.23449	1.22252	0.611260	+	0.791430i	$0.290663\pi$
$8$	1.00000	0.353553
$9$	8.63416	2.87805
$10$	2.42267	0.766115
$11$	−0.942159	−0.284072	−0.142036	−	0.989862i	$-0.545365\pi$
$11$	−0.942159	−0.284072	−0.142036	+	0.989862i	$0.545365\pi$
$12$	−3.41089	−0.984639
$13$	3.74746	1.03936	0.519679	−	0.854361i	$-0.326051\pi$
$13$	3.74746	1.03936	0.519679	+	0.854361i	$0.326051\pi$
$14$	3.23449	0.864453
$15$	−8.26345	−2.13361
$16$	1.00000	0.250000
$17$	−5.15941	−1.25134	−0.625670	−	0.780088i	$-0.715174\pi$
$17$	−5.15941	−1.25134	−0.625670	+	0.780088i	$0.715174\pi$
$18$	8.63416	2.03509
$19$	−0.0231708	−0.00531574	−0.00265787	−	0.999996i	$-0.500846\pi$
$19$	−0.0231708	−0.00531574	−0.00265787	+	0.999996i	$0.500846\pi$
$20$	2.42267	0.541725
$21$	−11.0325	−2.40748
$22$	−0.942159	−0.200869
$23$	−0.417845	−0.0871267	−0.0435633	−	0.999051i	$-0.513871\pi$
$23$	−0.417845	−0.0871267	−0.0435633	+	0.999051i	$0.513871\pi$
$24$	−3.41089	−0.696245
$25$	0.869316	0.173863
$26$	3.74746	0.734937
$27$	−19.2175	−3.69841
$28$	3.23449	0.611260
$29$	5.71959	1.06210	0.531051	−	0.847340i	$-0.321797\pi$
$29$	5.71959	1.06210	0.531051	+	0.847340i	$0.321797\pi$
$30$	−8.26345	−1.50869
$31$	−0.739094	−0.132745	−0.0663726	−	0.997795i	$-0.521143\pi$
$31$	−0.739094	−0.132745	−0.0663726	+	0.997795i	$0.521143\pi$
$32$	1.00000	0.176777
$33$	3.21360	0.559416
$34$	−5.15941	−0.884831
$35$	7.83608	1.32454
$36$	8.63416	1.43903
$37$	5.31579	0.873911	0.436956	−	0.899483i	$-0.356057\pi$
$37$	5.31579	0.873911	0.436956	+	0.899483i	$0.356057\pi$
$38$	−0.0231708	−0.00375880
$39$	−12.7822	−2.04679
$40$	2.42267	0.383057
$41$	1.45373	0.227034	0.113517	−	0.993536i	$-0.463788\pi$
$41$	1.45373	0.227034	0.113517	+	0.993536i	$0.463788\pi$
$42$	−11.0325	−1.70235
$43$	0.213976	0.0326311	0.0163155	−	0.999867i	$-0.494806\pi$
$43$	0.213976	0.0326311	0.0163155	+	0.999867i	$0.494806\pi$
$44$	−0.942159	−0.142036
$45$	20.9177	3.11823
$46$	−0.417845	−0.0616079
$47$	9.87439	1.44033	0.720164	−	0.693804i	$-0.244066\pi$
$47$	9.87439	1.44033	0.720164	+	0.693804i	$0.244066\pi$
$48$	−3.41089	−0.492319
$49$	3.46189	0.494556
$50$	0.869316	0.122940
$51$	17.5982	2.46424
$52$	3.74746	0.519679
$53$	7.46777	1.02578	0.512889	−	0.858455i	$-0.328575\pi$
$53$	7.46777	1.02578	0.512889	+	0.858455i	$0.328575\pi$
$54$	−19.2175	−2.61517
$55$	−2.28254	−0.307777
$56$	3.23449	0.432226
$57$	0.0790330	0.0104682
$58$	5.71959	0.751019
$59$	6.93556	0.902933	0.451466	−	0.892288i	$-0.350901\pi$
$59$	6.93556	0.902933	0.451466	+	0.892288i	$0.350901\pi$
$60$	−8.26345	−1.06681
$61$	6.48999	0.830958	0.415479	−	0.909603i	$-0.363614\pi$
$61$	6.48999	0.830958	0.415479	+	0.909603i	$0.363614\pi$
$62$	−0.739094	−0.0938651
$63$	27.9271	3.51848
$64$	1.00000	0.125000
$65$	9.07885	1.12609
$66$	3.21360	0.395567
$67$	−9.57906	−1.17027	−0.585134	−	0.810937i	$-0.698958\pi$
$67$	−9.57906	−1.17027	−0.585134	+	0.810937i	$0.698958\pi$
$68$	−5.15941	−0.625670
$69$	1.42522	0.171577
$70$	7.83608	0.936591
$71$	−11.3966	−1.35253	−0.676264	−	0.736660i	$-0.736402\pi$
$71$	−11.3966	−1.35253	−0.676264	+	0.736660i	$0.736402\pi$
$72$	8.63416	1.01755
$73$	11.7358	1.37357	0.686786	−	0.726860i	$-0.259021\pi$
$73$	11.7358	1.37357	0.686786	+	0.726860i	$0.259021\pi$
$74$	5.31579	0.617949
$75$	−2.96514	−0.342385
$76$	−0.0231708	−0.00265787
$77$	−3.04740	−0.347284
$78$	−12.7822	−1.44730
$79$	3.09404	0.348106	0.174053	−	0.984736i	$-0.444314\pi$
$79$	3.09404	0.348106	0.174053	+	0.984736i	$0.444314\pi$
$80$	2.42267	0.270862
$81$	39.6463	4.40515
$82$	1.45373	0.160537
$83$	−9.17319	−1.00689	−0.503444	−	0.864028i	$-0.667934\pi$
$83$	−9.17319	−1.00689	−0.503444	+	0.864028i	$0.667934\pi$
$84$	−11.0325	−1.20374
$85$	−12.4995	−1.35576
$86$	0.213976	0.0230737
$87$	−19.5089	−2.09157
$88$	−0.942159	−0.100435
$89$	4.96269	0.526044	0.263022	−	0.964790i	$-0.415281\pi$
$89$	4.96269	0.526044	0.263022	+	0.964790i	$0.415281\pi$
$90$	20.9177	2.20492
$91$	12.1211	1.27064
$92$	−0.417845	−0.0435633
$93$	2.52097	0.261412
$94$	9.87439	1.01847
$95$	−0.0561351	−0.00575934
$96$	−3.41089	−0.348122
$97$	9.81298	0.996357	0.498179	−	0.867074i	$-0.334002\pi$
$97$	9.81298	0.996357	0.498179	+	0.867074i	$0.334002\pi$
$98$	3.46189	0.349704
$99$	−8.13476	−0.817574
$100$	0.869316	0.0869316
$101$	−4.43052	−0.440854	−0.220427	−	0.975404i	$-0.570745\pi$
$101$	−4.43052	−0.440854	−0.220427	+	0.975404i	$0.570745\pi$
$102$	17.5982	1.74248
$103$	−8.68332	−0.855593	−0.427797	−	0.903875i	$-0.640710\pi$
$103$	−8.68332	−0.855593	−0.427797	+	0.903875i	$0.640710\pi$
$104$	3.74746	0.367469
$105$	−26.7280	−2.60839
$106$	7.46777	0.725334
$107$	−6.84237	−0.661477	−0.330738	−	0.943722i	$-0.607298\pi$
$107$	−6.84237	−0.661477	−0.330738	+	0.943722i	$0.607298\pi$
$108$	−19.2175	−1.84921
$109$	−16.8822	−1.61702	−0.808511	−	0.588481i	$-0.799726\pi$
$109$	−16.8822	−1.61702	−0.808511	+	0.588481i	$0.799726\pi$
$110$	−2.28254	−0.217632
$111$	−18.1316	−1.72097
$112$	3.23449	0.305630
$113$	6.24210	0.587207	0.293604	−	0.955927i	$-0.405145\pi$
$113$	6.24210	0.587207	0.293604	+	0.955927i	$0.405145\pi$
$114$	0.0790330	0.00740212
$115$	−1.01230	−0.0943974
$116$	5.71959	0.531051
$117$	32.3562	2.99133
$118$	6.93556	0.638470
$119$	−16.6880	−1.52979
$120$	−8.26345	−0.754346
$121$	−10.1123	−0.919303
$122$	6.48999	0.587576
$123$	−4.95850	−0.447093
$124$	−0.739094	−0.0663726
$125$	−10.0073	−0.895078
$126$	27.9271	2.48794
$127$	5.24218	0.465169	0.232584	−	0.972576i	$-0.425282\pi$
$127$	5.24218	0.465169	0.232584	+	0.972576i	$0.425282\pi$
$128$	1.00000	0.0883883
$129$	−0.729850	−0.0642597
$130$	9.07885	0.796268
$131$	15.0339	1.31352	0.656758	−	0.754102i	$-0.271927\pi$
$131$	15.0339	1.31352	0.656758	+	0.754102i	$0.271927\pi$
$132$	3.21360	0.279708
$133$	−0.0749456	−0.00649861
$134$	−9.57906	−0.827505
$135$	−46.5576	−4.00704
$136$	−5.15941	−0.442416
$137$	4.54121	0.387981	0.193991	−	0.981003i	$-0.437857\pi$
$137$	4.54121	0.387981	0.193991	+	0.981003i	$0.437857\pi$
$138$	1.42522	0.121323
$139$	−11.4182	−0.968476	−0.484238	−	0.874936i	$-0.660903\pi$
$139$	−11.4182	−0.968476	−0.484238	+	0.874936i	$0.660903\pi$
$140$	7.83608	0.662270
$141$	−33.6805	−2.83641
$142$	−11.3966	−0.956381
$143$	−3.53070	−0.295252
$144$	8.63416	0.719514
$145$	13.8567	1.15073
$146$	11.7358	0.971262
$147$	−11.8081	−0.973919
$148$	5.31579	0.436956
$149$	−3.76547	−0.308480	−0.154240	−	0.988033i	$-0.549293\pi$
$149$	−3.76547	−0.308480	−0.154240	+	0.988033i	$0.549293\pi$
$150$	−2.96514	−0.242103
$151$	10.0271	0.815991	0.407995	−	0.912984i	$-0.366228\pi$
$151$	10.0271	0.815991	0.407995	+	0.912984i	$0.366228\pi$
$152$	−0.0231708	−0.00187940
$153$	−44.5472	−3.60143
$154$	−3.04740	−0.245567
$155$	−1.79058	−0.143823
$156$	−12.7822	−1.02339
$157$	3.44716	0.275113	0.137557	−	0.990494i	$-0.456075\pi$
$157$	3.44716	0.275113	0.137557	+	0.990494i	$0.456075\pi$
$158$	3.09404	0.246148
$159$	−25.4718	−2.02004
$160$	2.42267	0.191529
$161$	−1.35151	−0.106514
$162$	39.6463	3.11491
$163$	4.78890	0.375096	0.187548	−	0.982255i	$-0.439946\pi$
$163$	4.78890	0.375096	0.187548	+	0.982255i	$0.439946\pi$
$164$	1.45373	0.113517
$165$	7.78549	0.606099
$166$	−9.17319	−0.711977
$167$	12.5544	0.971491	0.485746	−	0.874100i	$-0.338548\pi$
$167$	12.5544	0.971491	0.485746	+	0.874100i	$0.338548\pi$
$168$	−11.0325	−0.851174
$169$	1.04346	0.0802658
$170$	−12.4995	−0.958670
$171$	−0.200060	−0.0152990
$172$	0.213976	0.0163155
$173$	−7.20366	−0.547684	−0.273842	−	0.961775i	$-0.588295\pi$
$173$	−7.20366	−0.547684	−0.273842	+	0.961775i	$0.588295\pi$
$174$	−19.5089	−1.47897
$175$	2.81179	0.212551
$176$	−0.942159	−0.0710179
$177$	−23.6564	−1.77813
$178$	4.96269	0.371970
$179$	14.5142	1.08484	0.542422	−	0.840106i	$-0.317507\pi$
$179$	14.5142	1.08484	0.542422	+	0.840106i	$0.317507\pi$
$180$	20.9177	1.55911
$181$	8.33769	0.619735	0.309868	−	0.950780i	$-0.399715\pi$
$181$	8.33769	0.619735	0.309868	+	0.950780i	$0.399715\pi$
$182$	12.1211	0.898476
$183$	−22.1366	−1.63639
$184$	−0.417845	−0.0308039
$185$	12.8784	0.946839
$186$	2.52097	0.184846
$187$	4.86099	0.355471
$188$	9.87439	0.720164
$189$	−62.1588	−4.52138
$190$	−0.0561351	−0.00407247
$191$	−2.29194	−0.165839	−0.0829195	−	0.996556i	$-0.526424\pi$
$191$	−2.29194	−0.165839	−0.0829195	+	0.996556i	$0.526424\pi$
$192$	−3.41089	−0.246160
$193$	−26.6906	−1.92123	−0.960617	−	0.277875i	$-0.910370\pi$
$193$	−26.6906	−1.92123	−0.960617	+	0.277875i	$0.910370\pi$
$194$	9.81298	0.704531
$195$	−30.9669	−2.21759
$196$	3.46189	0.247278
$197$	11.4224	0.813816	0.406908	−	0.913469i	$-0.366607\pi$
$197$	11.4224	0.813816	0.406908	+	0.913469i	$0.366607\pi$
$198$	−8.13476	−0.578112
$199$	17.0652	1.20972	0.604860	−	0.796332i	$-0.293229\pi$
$199$	17.0652	1.20972	0.604860	+	0.796332i	$0.293229\pi$
$200$	0.869316	0.0614699
$201$	32.6731	2.30458
$202$	−4.43052	−0.311731
$203$	18.4999	1.29844
$204$	17.5982	1.23212
$205$	3.52190	0.245980
$206$	−8.68332	−0.604996
$207$	−3.60774	−0.250755
$208$	3.74746	0.259840
$209$	0.0218306	0.00151005
$210$	−26.7280	−1.84441
$211$	10.3824	0.714755	0.357378	−	0.933960i	$-0.383671\pi$
$211$	10.3824	0.714755	0.357378	+	0.933960i	$0.383671\pi$
$212$	7.46777	0.512889
$213$	38.8725	2.66350
$214$	−6.84237	−0.467735
$215$	0.518394	0.0353542
$216$	−19.2175	−1.30759
$217$	−2.39059	−0.162284
$218$	−16.8822	−1.14341
$219$	−40.0295	−2.70494
$220$	−2.28254	−0.153889
$221$	−19.3347	−1.30059
$222$	−18.1316	−1.21691
$223$	−4.70650	−0.315170	−0.157585	−	0.987505i	$-0.550371\pi$
$223$	−4.70650	−0.315170	−0.157585	+	0.987505i	$0.550371\pi$
$224$	3.23449	0.216113
$225$	7.50582	0.500388
$226$	6.24210	0.415218
$227$	19.2649	1.27866	0.639328	−	0.768934i	$-0.279213\pi$
$227$	19.2649	1.27866	0.639328	+	0.768934i	$0.279213\pi$
$228$	0.0790330	0.00523409
$229$	6.25665	0.413451	0.206725	−	0.978399i	$-0.433719\pi$
$229$	6.25665	0.413451	0.206725	+	0.978399i	$0.433719\pi$
$230$	−1.01230	−0.0667490
$231$	10.3943	0.683898
$232$	5.71959	0.375510
$233$	−1.71316	−0.112233	−0.0561163	−	0.998424i	$-0.517872\pi$
$233$	−1.71316	−0.112233	−0.0561163	+	0.998424i	$0.517872\pi$
$234$	32.3562	2.11519
$235$	23.9224	1.56052
$236$	6.93556	0.451466
$237$	−10.5534	−0.685518
$238$	−16.6880	−1.08172
$239$	−24.1257	−1.56056	−0.780281	−	0.625429i	$-0.784924\pi$
$239$	−24.1257	−1.56056	−0.780281	+	0.625429i	$0.784924\pi$
$240$	−8.26345	−0.533403
$241$	−5.44948	−0.351032	−0.175516	−	0.984477i	$-0.556159\pi$
$241$	−5.44948	−0.351032	−0.175516	+	0.984477i	$0.556159\pi$
$242$	−10.1123	−0.650046
$243$	−77.5766	−4.97654
$244$	6.48999	0.415479
$245$	8.38702	0.535827
$246$	−4.95850	−0.316143
$247$	−0.0868316	−0.00552496
$248$	−0.739094	−0.0469325
$249$	31.2887	1.98284
$250$	−10.0073	−0.632915
$251$	16.8612	1.06427	0.532134	−	0.846660i	$-0.321390\pi$
$251$	16.8612	1.06427	0.532134	+	0.846660i	$0.321390\pi$
$252$	27.9271	1.75924
$253$	0.393677	0.0247502
$254$	5.24218	0.328924
$255$	42.6345	2.66988
$256$	1.00000	0.0625000
$257$	24.2944	1.51545	0.757723	−	0.652577i	$-0.226312\pi$
$257$	24.2944	1.51545	0.757723	+	0.652577i	$0.226312\pi$
$258$	−0.729850	−0.0454385
$259$	17.1939	1.06837
$260$	9.07885	0.563046
$261$	49.3839	3.05679
$262$	15.0339	0.928796
$263$	−0.690026	−0.0425488	−0.0212744	−	0.999774i	$-0.506772\pi$
$263$	−0.690026	−0.0425488	−0.0212744	+	0.999774i	$0.506772\pi$
$264$	3.21360	0.197783
$265$	18.0919	1.11138
$266$	−0.0749456	−0.00459521
$267$	−16.9272	−1.03593
$268$	−9.57906	−0.585134
$269$	−8.73530	−0.532601	−0.266300	−	0.963890i	$-0.585801\pi$
$269$	−8.73530	−0.532601	−0.266300	+	0.963890i	$0.585801\pi$
$270$	−46.5576	−2.83341
$271$	−14.2118	−0.863305	−0.431652	−	0.902040i	$-0.642069\pi$
$271$	−14.2118	−0.863305	−0.431652	+	0.902040i	$0.642069\pi$
$272$	−5.15941	−0.312835
$273$	−41.3437	−2.50224
$274$	4.54121	0.274344
$275$	−0.819034	−0.0493896
$276$	1.42522	0.0857883
$277$	22.9888	1.38126	0.690632	−	0.723207i	$-0.257333\pi$
$277$	22.9888	1.38126	0.690632	+	0.723207i	$0.257333\pi$
$278$	−11.4182	−0.684816
$279$	−6.38146	−0.382048
$280$	7.83608	0.468295
$281$	−6.95498	−0.414899	−0.207450	−	0.978246i	$-0.566516\pi$
$281$	−6.95498	−0.414899	−0.207450	+	0.978246i	$0.566516\pi$
$282$	−33.6805	−2.00564
$283$	3.44645	0.204870	0.102435	−	0.994740i	$-0.467337\pi$
$283$	3.44645	0.204870	0.102435	+	0.994740i	$0.467337\pi$
$284$	−11.3966	−0.676264
$285$	0.191471	0.0113417
$286$	−3.53070	−0.208775
$287$	4.70206	0.277554
$288$	8.63416	0.508773
$289$	9.61950	0.565853
$290$	13.8567	0.813692
$291$	−33.4710	−1.96210
$292$	11.7358	0.686786
$293$	5.05769	0.295473	0.147737	−	0.989027i	$-0.452801\pi$
$293$	5.05769	0.295473	0.147737	+	0.989027i	$0.452801\pi$
$294$	−11.8081	−0.688665
$295$	16.8025	0.978282
$296$	5.31579	0.308974
$297$	18.1060	1.05061
$298$	−3.76547	−0.218128
$299$	−1.56586	−0.0905559
$300$	−2.96514	−0.171192
$301$	0.692104	0.0398922
$302$	10.0271	0.576993
$303$	15.1120	0.868163
$304$	−0.0231708	−0.00132894
$305$	15.7231	0.900301
$306$	−44.5472	−2.54659
$307$	−6.94093	−0.396140	−0.198070	−	0.980188i	$-0.563467\pi$
$307$	−6.94093	−0.396140	−0.198070	+	0.980188i	$0.563467\pi$
$308$	−3.04740	−0.173642
$309$	29.6179	1.68490
$310$	−1.79058	−0.101698
$311$	18.8760	1.07036	0.535181	−	0.844737i	$-0.320243\pi$
$311$	18.8760	1.07036	0.535181	+	0.844737i	$0.320243\pi$
$312$	−12.7822	−0.723648
$313$	−22.2089	−1.25532	−0.627661	−	0.778487i	$-0.715988\pi$
$313$	−22.2089	−1.25532	−0.627661	+	0.778487i	$0.715988\pi$
$314$	3.44716	0.194535
$315$	67.6580	3.81210
$316$	3.09404	0.174053
$317$	−15.6538	−0.879206	−0.439603	−	0.898192i	$-0.644881\pi$
$317$	−15.6538	−0.879206	−0.439603	+	0.898192i	$0.644881\pi$
$318$	−25.4718	−1.42838
$319$	−5.38877	−0.301713
$320$	2.42267	0.135431
$321$	23.3386	1.30263
$322$	−1.35151	−0.0753169
$323$	0.119548	0.00665181
$324$	39.6463	2.20257
$325$	3.25773	0.180706
$326$	4.78890	0.265233
$327$	57.5833	3.18436
$328$	1.45373	0.0802686
$329$	31.9386	1.76083
$330$	7.78549	0.428577
$331$	−9.88142	−0.543132	−0.271566	−	0.962420i	$-0.587542\pi$
$331$	−9.88142	−0.543132	−0.271566	+	0.962420i	$0.587542\pi$
$332$	−9.17319	−0.503444
$333$	45.8974	2.51516
$334$	12.5544	0.686948
$335$	−23.2069	−1.26793
$336$	−11.0325	−0.601871
$337$	4.49953	0.245105	0.122552	−	0.992462i	$-0.460892\pi$
$337$	4.49953	0.245105	0.122552	+	0.992462i	$0.460892\pi$
$338$	1.04346	0.0567565
$339$	−21.2911	−1.15637
$340$	−12.4995	−0.677882
$341$	0.696345	0.0377092
$342$	−0.200060	−0.0108180
$343$	−11.4439	−0.617915
$344$	0.213976	0.0115368
$345$	3.45284	0.185895
$346$	−7.20366	−0.387271
$347$	24.8597	1.33454	0.667268	−	0.744817i	$-0.267463\pi$
$347$	24.8597	1.33454	0.667268	+	0.744817i	$0.267463\pi$
$348$	−19.5089	−1.04579
$349$	−9.31999	−0.498888	−0.249444	−	0.968389i	$-0.580248\pi$
$349$	−9.31999	−0.498888	−0.249444	+	0.968389i	$0.580248\pi$
$350$	2.81179	0.150296
$351$	−72.0169	−3.84398
$352$	−0.942159	−0.0502173
$353$	29.2353	1.55604	0.778018	−	0.628241i	$-0.216225\pi$
$353$	29.2353	1.55604	0.778018	+	0.628241i	$0.216225\pi$
$354$	−23.6564	−1.25732
$355$	−27.6102	−1.46539
$356$	4.96269	0.263022
$357$	56.9210	3.01258
$358$	14.5142	0.767100
$359$	27.9706	1.47623	0.738117	−	0.674673i	$-0.235715\pi$
$359$	27.9706	1.47623	0.738117	+	0.674673i	$0.235715\pi$
$360$	20.9177	1.10246
$361$	−18.9995	−0.999972
$362$	8.33769	0.438219
$363$	34.4921	1.81036
$364$	12.1211	0.635318
$365$	28.4319	1.48820
$366$	−22.1366	−1.15710
$367$	−23.6145	−1.23267	−0.616333	−	0.787486i	$-0.711383\pi$
$367$	−23.6145	−1.23267	−0.616333	+	0.787486i	$0.711383\pi$
$368$	−0.417845	−0.0217817
$369$	12.5517	0.653416
$370$	12.8784	0.669516
$371$	24.1544	1.25403
$372$	2.52097	0.130706
$373$	−14.1077	−0.730471	−0.365236	−	0.930915i	$-0.619012\pi$
$373$	−14.1077	−0.730471	−0.365236	+	0.930915i	$0.619012\pi$
$374$	4.86099	0.251356
$375$	34.1337	1.76266
$376$	9.87439	0.509233
$377$	21.4339	1.10390
$378$	−62.1588	−3.19710
$379$	−37.8335	−1.94338	−0.971689	−	0.236263i	$-0.924077\pi$
$379$	−37.8335	−1.94338	−0.971689	+	0.236263i	$0.924077\pi$
$380$	−0.0561351	−0.00287967
$381$	−17.8805	−0.916046
$382$	−2.29194	−0.117266
$383$	−10.9410	−0.559057	−0.279528	−	0.960137i	$-0.590178\pi$
$383$	−10.9410	−0.559057	−0.279528	+	0.960137i	$0.590178\pi$
$384$	−3.41089	−0.174061
$385$	−7.38284	−0.376264
$386$	−26.6906	−1.35852
$387$	1.84751	0.0939141
$388$	9.81298	0.498179
$389$	−28.2466	−1.43216	−0.716081	−	0.698018i	$-0.754066\pi$
$389$	−28.2466	−1.43216	−0.716081	+	0.698018i	$0.754066\pi$
$390$	−30.9669	−1.56807
$391$	2.15583	0.109025
$392$	3.46189	0.174852
$393$	−51.2789	−2.58668
$394$	11.4224	0.575455
$395$	7.49582	0.377156
$396$	−8.13476	−0.408787
$397$	33.3156	1.67206	0.836030	−	0.548683i	$-0.184871\pi$
$397$	33.3156	1.67206	0.836030	+	0.548683i	$0.184871\pi$
$398$	17.0652	0.855401
$399$	0.255631	0.0127976
$400$	0.869316	0.0434658
$401$	−26.6870	−1.33269	−0.666343	−	0.745645i	$-0.732142\pi$
$401$	−26.6870	−1.33269	−0.666343	+	0.745645i	$0.732142\pi$
$402$	32.6731	1.62959
$403$	−2.76973	−0.137970
$404$	−4.43052	−0.220427
$405$	96.0498	4.77275
$406$	18.4999	0.918137
$407$	−5.00833	−0.248254
$408$	17.5982	0.871239
$409$	−15.1054	−0.746915	−0.373458	−	0.927647i	$-0.621828\pi$
$409$	−15.1054	−0.746915	−0.373458	+	0.927647i	$0.621828\pi$
$410$	3.52190	0.173934
$411$	−15.4896	−0.764043
$412$	−8.68332	−0.427797
$413$	22.4330	1.10385
$414$	−3.60774	−0.177311
$415$	−22.2236	−1.09091
$416$	3.74746	0.183734
$417$	38.9461	1.90720
$418$	0.0218306	0.00106777
$419$	−27.8149	−1.35885	−0.679425	−	0.733745i	$-0.737771\pi$
$419$	−27.8149	−1.35885	−0.679425	+	0.733745i	$0.737771\pi$
$420$	−26.7280	−1.30419
$421$	3.88068	0.189133	0.0945663	−	0.995519i	$-0.469854\pi$
$421$	3.88068	0.189133	0.0945663	+	0.995519i	$0.469854\pi$
$422$	10.3824	0.505408
$423$	85.2572	4.14534
$424$	7.46777	0.362667
$425$	−4.48516	−0.217562
$426$	38.8725	1.88338
$427$	20.9918	1.01586
$428$	−6.84237	−0.330738
$429$	12.0428	0.581434
$430$	0.518394	0.0249992
$431$	15.7696	0.759597	0.379798	−	0.925069i	$-0.375993\pi$
$431$	15.7696	0.759597	0.379798	+	0.925069i	$0.375993\pi$
$432$	−19.2175	−0.924603
$433$	31.1225	1.49565	0.747827	−	0.663894i	$-0.231097\pi$
$433$	31.1225	1.49565	0.747827	+	0.663894i	$0.231097\pi$
$434$	−2.39059	−0.114752
$435$	−47.2636	−2.26611
$436$	−16.8822	−0.808511
$437$	0.00968180	0.000463143 0
$438$	−40.0295	−1.91268
$439$	−15.6073	−0.744898	−0.372449	−	0.928053i	$-0.621482\pi$
$439$	−15.6073	−0.744898	−0.372449	+	0.928053i	$0.621482\pi$
$440$	−2.28254	−0.108816
$441$	29.8906	1.42336
$442$	−19.3347	−0.919657
$443$	7.97189	0.378756	0.189378	−	0.981904i	$-0.439353\pi$
$443$	7.97189	0.378756	0.189378	+	0.981904i	$0.439353\pi$
$444$	−18.1316	−0.860487
$445$	12.0230	0.569943
$446$	−4.70650	−0.222859
$447$	12.8436	0.607482
$448$	3.23449	0.152815
$449$	30.3189	1.43084	0.715419	−	0.698695i	$-0.246236\pi$
$449$	30.3189	1.43084	0.715419	+	0.698695i	$0.246236\pi$
$450$	7.50582	0.353828
$451$	−1.36964	−0.0644939
$452$	6.24210	0.293604
$453$	−34.2012	−1.60691
$454$	19.2649	0.904146
$455$	29.3654	1.37667
$456$	0.0790330	0.00370106
$457$	−4.17247	−0.195180	−0.0975898	−	0.995227i	$-0.531113\pi$
$457$	−4.17247	−0.195180	−0.0975898	+	0.995227i	$0.531113\pi$
$458$	6.25665	0.292354
$459$	99.1510	4.62797
$460$	−1.01230	−0.0471987
$461$	28.5839	1.33128	0.665642	−	0.746271i	$-0.268158\pi$
$461$	28.5839	1.33128	0.665642	+	0.746271i	$0.268158\pi$
$462$	10.3943	0.483589
$463$	−12.2111	−0.567496	−0.283748	−	0.958899i	$-0.591578\pi$
$463$	−12.2111	−0.567496	−0.283748	+	0.958899i	$0.591578\pi$
$464$	5.71959	0.265525
$465$	6.10747	0.283227
$466$	−1.71316	−0.0793605
$467$	−9.90904	−0.458536	−0.229268	−	0.973363i	$-0.573633\pi$
$467$	−9.90904	−0.458536	−0.229268	+	0.973363i	$0.573633\pi$
$468$	32.3562	1.49567
$469$	−30.9833	−1.43068
$470$	23.9224	1.10346
$471$	−11.7579	−0.541775
$472$	6.93556	0.319235
$473$	−0.201600	−0.00926957
$474$	−10.5534	−0.484734
$475$	−0.0201427	−0.000924212 0
$476$	−16.6880	−0.764895
$477$	64.4780	2.95224
$478$	−24.1257	−1.10348
$479$	−29.8182	−1.36243	−0.681215	−	0.732083i	$-0.738548\pi$
$479$	−29.8182	−1.36243	−0.681215	+	0.732083i	$0.738548\pi$
$480$	−8.26345	−0.377173
$481$	19.9207	0.908307
$482$	−5.44948	−0.248217
$483$	4.60986	0.209756
$484$	−10.1123	−0.459652
$485$	23.7736	1.07950
$486$	−77.5766	−3.51895
$487$	−7.25358	−0.328691	−0.164345	−	0.986403i	$-0.552551\pi$
$487$	−7.25358	−0.328691	−0.164345	+	0.986403i	$0.552551\pi$
$488$	6.48999	0.293788
$489$	−16.3344	−0.738668
$490$	8.38702	0.378887
$491$	19.1866	0.865878	0.432939	−	0.901423i	$-0.357477\pi$
$491$	19.1866	0.865878	0.432939	+	0.901423i	$0.357477\pi$
$492$	−4.95850	−0.223547
$493$	−29.5097	−1.32905
$494$	−0.0868316	−0.00390674
$495$	−19.7078	−0.885800
$496$	−0.739094	−0.0331863
$497$	−36.8621	−1.65349
$498$	31.2887	1.40208
$499$	−1.41241	−0.0632284	−0.0316142	−	0.999500i	$-0.510065\pi$
$499$	−1.41241	−0.0632284	−0.0316142	+	0.999500i	$0.510065\pi$
$500$	−10.0073	−0.447539
$501$	−42.8218	−1.91314
$502$	16.8612	0.752551
$503$	−21.6016	−0.963166	−0.481583	−	0.876401i	$-0.659938\pi$
$503$	−21.6016	−0.963166	−0.481583	+	0.876401i	$0.659938\pi$
$504$	27.9271	1.24397
$505$	−10.7337	−0.477643
$506$	0.393677	0.0175011
$507$	−3.55911	−0.158066
$508$	5.24218	0.232584
$509$	25.2730	1.12021	0.560103	−	0.828423i	$-0.310762\pi$
$509$	25.2730	1.12021	0.560103	+	0.828423i	$0.310762\pi$
$510$	42.6345	1.88789
$511$	37.9593	1.67922
$512$	1.00000	0.0441942
$513$	0.445285	0.0196598
$514$	24.2944	1.07158
$515$	−21.0368	−0.926992
$516$	−0.729850	−0.0321298
$517$	−9.30325	−0.409157
$518$	17.1939	0.755455
$519$	24.5709	1.07854
$520$	9.07885	0.398134
$521$	28.8259	1.26289	0.631443	−	0.775422i	$-0.282463\pi$
$521$	28.8259	1.26289	0.631443	+	0.775422i	$0.282463\pi$
$522$	49.3839	2.16147
$523$	4.39398	0.192135	0.0960677	−	0.995375i	$-0.469373\pi$
$523$	4.39398	0.192135	0.0960677	+	0.995375i	$0.469373\pi$
$524$	15.0339	0.656758
$525$	−9.59070	−0.418573
$526$	−0.690026	−0.0300865
$527$	3.81329	0.166110
$528$	3.21360	0.139854
$529$	−22.8254	−0.992409
$530$	18.0919	0.785863
$531$	59.8827	2.59869
$532$	−0.0749456	−0.00324930
$533$	5.44778	0.235970
$534$	−16.9272	−0.732511
$535$	−16.5768	−0.716677
$536$	−9.57906	−0.413752
$537$	−49.5064	−2.13636
$538$	−8.73530	−0.376605
$539$	−3.26166	−0.140489
$540$	−46.5576	−2.00352
$541$	25.5355	1.09786	0.548929	−	0.835869i	$-0.315036\pi$
$541$	25.5355	1.09786	0.548929	+	0.835869i	$0.315036\pi$
$542$	−14.2118	−0.610448
$543$	−28.4389	−1.22043
$544$	−5.15941	−0.221208
$545$	−40.9000	−1.75196
$546$	−41.3437	−1.76935
$547$	−38.3112	−1.63807	−0.819034	−	0.573745i	$-0.805490\pi$
$547$	−38.3112	−1.63807	−0.819034	+	0.573745i	$0.805490\pi$
$548$	4.54121	0.193991
$549$	56.0356	2.39154
$550$	−0.819034	−0.0349237
$551$	−0.132527	−0.00564586
$552$	1.42522	0.0606615
$553$	10.0076	0.425567
$554$	22.9888	0.976701
$555$	−43.9268	−1.86459
$556$	−11.4182	−0.484238
$557$	40.1919	1.70298	0.851492	−	0.524367i	$-0.175698\pi$
$557$	40.1919	1.70298	0.851492	+	0.524367i	$0.175698\pi$
$558$	−6.38146	−0.270149
$559$	0.801868	0.0339154
$560$	7.83608	0.331135
$561$	−16.5803	−0.700020
$562$	−6.95498	−0.293378
$563$	6.52767	0.275109	0.137554	−	0.990494i	$-0.456076\pi$
$563$	6.52767	0.275109	0.137554	+	0.990494i	$0.456076\pi$
$564$	−33.6805	−1.41820
$565$	15.1225	0.636210
$566$	3.44645	0.144865
$567$	128.235	5.38538
$568$	−11.3966	−0.478191
$569$	32.3316	1.35541	0.677706	−	0.735333i	$-0.262974\pi$
$569$	32.3316	1.35541	0.677706	+	0.735333i	$0.262974\pi$
$570$	0.191471	0.00801982
$571$	−12.8274	−0.536808	−0.268404	−	0.963306i	$-0.586496\pi$
$571$	−12.8274	−0.536808	−0.268404	+	0.963306i	$0.586496\pi$
$572$	−3.53070	−0.147626
$573$	7.81756	0.326583
$574$	4.70206	0.196260
$575$	−0.363239	−0.0151481
$576$	8.63416	0.359757
$577$	22.4450	0.934396	0.467198	−	0.884153i	$-0.345264\pi$
$577$	22.4450	0.934396	0.467198	+	0.884153i	$0.345264\pi$
$578$	9.61950	0.400119
$579$	91.0388	3.78344
$580$	13.8567	0.575367
$581$	−29.6705	−1.23094
$582$	−33.4710	−1.38742
$583$	−7.03583	−0.291394
$584$	11.7358	0.485631
$585$	78.3883	3.24096
$586$	5.05769	0.208931
$587$	−1.16859	−0.0482329	−0.0241165	−	0.999709i	$-0.507677\pi$
$587$	−1.16859	−0.0482329	−0.0241165	+	0.999709i	$0.507677\pi$
$588$	−11.8081	−0.486959
$589$	0.0171254	0.000705640 0
$590$	16.8025	0.691750
$591$	−38.9607	−1.60263
$592$	5.31579	0.218478
$593$	−43.3842	−1.78157	−0.890787	−	0.454421i	$-0.849846\pi$
$593$	−43.3842	−1.78157	−0.890787	+	0.454421i	$0.849846\pi$
$594$	18.1060	0.742897
$595$	−40.4295	−1.65745
$596$	−3.76547	−0.154240
$597$	−58.2075	−2.38227
$598$	−1.56586	−0.0640327
$599$	17.8327	0.728622	0.364311	−	0.931277i	$-0.381304\pi$
$599$	17.8327	0.728622	0.364311	+	0.931277i	$0.381304\pi$
$600$	−2.96514	−0.121051
$601$	25.4224	1.03700	0.518501	−	0.855077i	$-0.326490\pi$
$601$	25.4224	1.03700	0.518501	+	0.855077i	$0.326490\pi$
$602$	0.692104	0.0282080
$603$	−82.7072	−3.36810
$604$	10.0271	0.407995
$605$	−24.4988	−0.996019
$606$	15.1120	0.613884
$607$	19.8248	0.804664	0.402332	−	0.915494i	$-0.368200\pi$
$607$	19.8248	0.804664	0.402332	+	0.915494i	$0.368200\pi$
$608$	−0.0231708	−0.000939700 0
$609$	−63.1012	−2.55699
$610$	15.7231	0.636609
$611$	37.0039	1.49702
$612$	−44.5472	−1.80071
$613$	44.7269	1.80650	0.903251	−	0.429113i	$-0.141174\pi$
$613$	44.7269	1.80650	0.903251	+	0.429113i	$0.141174\pi$
$614$	−6.94093	−0.280113
$615$	−12.0128	−0.484403
$616$	−3.04740	−0.122783
$617$	−2.23751	−0.0900789	−0.0450395	−	0.998985i	$-0.514341\pi$
$617$	−2.23751	−0.0900789	−0.0450395	+	0.998985i	$0.514341\pi$
$618$	29.6179	1.19140
$619$	14.8850	0.598278	0.299139	−	0.954210i	$-0.403301\pi$
$619$	14.8850	0.598278	0.299139	+	0.954210i	$0.403301\pi$
$620$	−1.79058	−0.0719114
$621$	8.02994	0.322230
$622$	18.8760	0.756860
$623$	16.0518	0.643100
$624$	−12.7822	−0.511696
$625$	−28.5909	−1.14363
$626$	−22.2089	−0.887647
$627$	−0.0744617	−0.00297371
$628$	3.44716	0.137557
$629$	−27.4264	−1.09356
$630$	67.6580	2.69556
$631$	−26.8547	−1.06907	−0.534535	−	0.845146i	$-0.679513\pi$
$631$	−26.8547	−1.06907	−0.534535	+	0.845146i	$0.679513\pi$
$632$	3.09404	0.123074
$633$	−35.4133	−1.40755
$634$	−15.6538	−0.621693
$635$	12.7001	0.503987
$636$	−25.4718	−1.01002
$637$	12.9733	0.514021
$638$	−5.38877	−0.213343
$639$	−98.4001	−3.89265
$640$	2.42267	0.0957643
$641$	15.6776	0.619229	0.309614	−	0.950862i	$-0.399800\pi$
$641$	15.6776	0.619229	0.309614	+	0.950862i	$0.399800\pi$
$642$	23.3386	0.921100
$643$	44.9966	1.77449	0.887245	−	0.461298i	$-0.152616\pi$
$643$	44.9966	1.77449	0.887245	+	0.461298i	$0.152616\pi$
$644$	−1.35151	−0.0532571
$645$	−1.76818	−0.0696221
$646$	0.119548	0.00470354
$647$	−14.9282	−0.586890	−0.293445	−	0.955976i	$-0.594802\pi$
$647$	−14.9282	−0.586890	−0.293445	+	0.955976i	$0.594802\pi$
$648$	39.6463	1.55745
$649$	−6.53440	−0.256498
$650$	3.25773	0.127779
$651$	8.15404	0.319582
$652$	4.78890	0.187548
$653$	16.7505	0.655499	0.327750	−	0.944765i	$-0.393710\pi$
$653$	16.7505	0.655499	0.327750	+	0.944765i	$0.393710\pi$
$654$	57.5833	2.25169
$655$	36.4221	1.42313
$656$	1.45373	0.0567585
$657$	101.329	3.95321
$658$	31.9386	1.24510
$659$	−24.9967	−0.973732	−0.486866	−	0.873477i	$-0.661860\pi$
$659$	−24.9967	−0.973732	−0.486866	+	0.873477i	$0.661860\pi$
$660$	7.78549	0.303050
$661$	22.8510	0.888802	0.444401	−	0.895828i	$-0.353417\pi$
$661$	22.8510	0.888802	0.444401	+	0.895828i	$0.353417\pi$
$662$	−9.88142	−0.384052
$663$	65.9484	2.56123
$664$	−9.17319	−0.355989
$665$	−0.181568	−0.00704091
$666$	45.8974	1.77849
$667$	−2.38990	−0.0925374
$668$	12.5544	0.485746
$669$	16.0533	0.620658
$670$	−23.2069	−0.896560
$671$	−6.11460	−0.236052
$672$	−11.0325	−0.425587
$673$	8.24659	0.317883	0.158941	−	0.987288i	$-0.449192\pi$
$673$	8.24659	0.317883	0.158941	+	0.987288i	$0.449192\pi$
$674$	4.49953	0.173315
$675$	−16.7061	−0.643018
$676$	1.04346	0.0401329
$677$	9.29291	0.357156	0.178578	−	0.983926i	$-0.442850\pi$
$677$	9.29291	0.357156	0.178578	+	0.983926i	$0.442850\pi$
$678$	−21.2911	−0.817680
$679$	31.7399	1.21807
$680$	−12.4995	−0.479335
$681$	−65.7104	−2.51803
$682$	0.696345	0.0266644
$683$	−9.68823	−0.370710	−0.185355	−	0.982672i	$-0.559343\pi$
$683$	−9.68823	−0.370710	−0.185355	+	0.982672i	$0.559343\pi$
$684$	−0.200060	−0.00764950
$685$	11.0018	0.420358
$686$	−11.4439	−0.436932
$687$	−21.3407	−0.814200
$688$	0.213976	0.00815777
$689$	27.9852	1.06615
$690$	3.45284	0.131447
$691$	31.1445	1.18479	0.592397	−	0.805646i	$-0.298182\pi$
$691$	31.1445	1.18479	0.592397	+	0.805646i	$0.298182\pi$
$692$	−7.20366	−0.273842
$693$	−26.3118	−0.999501
$694$	24.8597	0.943660
$695$	−27.6624	−1.04929
$696$	−19.5089	−0.739483
$697$	−7.50037	−0.284097
$698$	−9.31999	−0.352767
$699$	5.84339	0.221017
$700$	2.81179	0.106276
$701$	−15.3861	−0.581126	−0.290563	−	0.956856i	$-0.593843\pi$
$701$	−15.3861	−0.581126	−0.290563	+	0.956856i	$0.593843\pi$
$702$	−72.0169	−2.71810
$703$	−0.123171	−0.00464549
$704$	−0.942159	−0.0355090
$705$	−81.5966	−3.07310
$706$	29.2353	1.10028
$707$	−14.3305	−0.538952
$708$	−23.6564	−0.889063
$709$	−14.5570	−0.546699	−0.273350	−	0.961915i	$-0.588132\pi$
$709$	−14.5570	−0.546699	−0.273350	+	0.961915i	$0.588132\pi$
$710$	−27.6102	−1.03619
$711$	26.7144	1.00187
$712$	4.96269	0.185985
$713$	0.308827	0.0115657
$714$	56.9210	2.13022
$715$	−8.55372	−0.319891
$716$	14.5142	0.542422
$717$	82.2901	3.07318
$718$	27.9706	1.04386
$719$	37.6922	1.40568	0.702841	−	0.711347i	$-0.251915\pi$
$719$	37.6922	1.40568	0.702841	+	0.711347i	$0.251915\pi$
$720$	20.9177	0.779557
$721$	−28.0861	−1.04598
$722$	−18.9995	−0.707087
$723$	18.5876	0.691279
$724$	8.33769	0.309868
$725$	4.97213	0.184660
$726$	34.4921	1.28012
$727$	−20.1487	−0.747275	−0.373638	−	0.927575i	$-0.621890\pi$
$727$	−20.1487	−0.747275	−0.373638	+	0.927575i	$0.621890\pi$
$728$	12.1211	0.449238
$729$	145.666	5.39505
$730$	28.4319	1.05231
$731$	−1.10399	−0.0408326
$732$	−22.1366	−0.818193
$733$	21.5236	0.794994	0.397497	−	0.917604i	$-0.369879\pi$
$733$	21.5236	0.794994	0.397497	+	0.917604i	$0.369879\pi$
$734$	−23.6145	−0.871627
$735$	−28.6072	−1.05519
$736$	−0.417845	−0.0154020
$737$	9.02500	0.332440
$738$	12.5517	0.462035
$739$	−9.27215	−0.341082	−0.170541	−	0.985351i	$-0.554551\pi$
$739$	−9.27215	−0.341082	−0.170541	+	0.985351i	$0.554551\pi$
$740$	12.8784	0.473419
$741$	0.296173	0.0108802
$742$	24.1544	0.886736
$743$	29.2734	1.07394	0.536969	−	0.843602i	$-0.319569\pi$
$743$	29.2734	1.07394	0.536969	+	0.843602i	$0.319569\pi$
$744$	2.52097	0.0924232
$745$	−9.12249	−0.334222
$746$	−14.1077	−0.516521
$747$	−79.2028	−2.89788
$748$	4.86099	0.177735
$749$	−22.1315	−0.808669
$750$	34.1337	1.24639
$751$	−37.7376	−1.37707	−0.688533	−	0.725205i	$-0.741745\pi$
$751$	−37.7376	−1.37707	−0.688533	+	0.725205i	$0.741745\pi$
$752$	9.87439	0.360082
$753$	−57.5116	−2.09584
$754$	21.4339	0.780578
$755$	24.2922	0.884085
$756$	−62.1588	−2.26069
$757$	−16.5647	−0.602055	−0.301027	−	0.953615i	$-0.597330\pi$
$757$	−16.5647	−0.602055	−0.301027	+	0.953615i	$0.597330\pi$
$758$	−37.8335	−1.37418
$759$	−1.34279	−0.0487401
$760$	−0.0561351	−0.00203623
$761$	−8.93978	−0.324067	−0.162033	−	0.986785i	$-0.551805\pi$
$761$	−8.93978	−0.324067	−0.162033	+	0.986785i	$0.551805\pi$
$762$	−17.8805	−0.647742
$763$	−54.6052	−1.97684
$764$	−2.29194	−0.0829195
$765$	−107.923	−3.90196
$766$	−10.9410	−0.395313
$767$	25.9907	0.938470
$768$	−3.41089	−0.123080
$769$	−19.3457	−0.697624	−0.348812	−	0.937193i	$-0.613415\pi$
$769$	−19.3457	−0.697624	−0.348812	+	0.937193i	$0.613415\pi$
$770$	−7.38284	−0.266059
$771$	−82.8656	−2.98433
$772$	−26.6906	−0.960617
$773$	−13.6285	−0.490183	−0.245092	−	0.969500i	$-0.578818\pi$
$773$	−13.6285	−0.490183	−0.245092	+	0.969500i	$0.578818\pi$
$774$	1.84751	0.0664073
$775$	−0.642507	−0.0230795
$776$	9.81298	0.352265
$777$	−58.6463	−2.10393
$778$	−28.2466	−1.01269
$779$	−0.0336840	−0.00120685
$780$	−30.9669	−1.10879
$781$	10.7374	0.384215
$782$	2.15583	0.0770924
$783$	−109.916	−3.92809
$784$	3.46189	0.123639
$785$	8.35132	0.298071
$786$	−51.2789	−1.82906
$787$	−24.1373	−0.860400	−0.430200	−	0.902734i	$-0.641557\pi$
$787$	−24.1373	−0.860400	−0.430200	+	0.902734i	$0.641557\pi$
$788$	11.4224	0.406908
$789$	2.35360	0.0837904
$790$	7.49582	0.266689
$791$	20.1900	0.717873
$792$	−8.13476	−0.289056
$793$	24.3210	0.863663
$794$	33.3156	1.18233
$795$	−61.7096	−2.18861
$796$	17.0652	0.604860
$797$	−10.5605	−0.374073	−0.187037	−	0.982353i	$-0.559888\pi$
$797$	−10.5605	−0.374073	−0.187037	+	0.982353i	$0.559888\pi$
$798$	0.255631	0.00904924
$799$	−50.9460	−1.80234
$800$	0.869316	0.0307350
$801$	42.8487	1.51398
$802$	−26.6870	−0.942352
$803$	−11.0570	−0.390193
$804$	32.6731	1.15229
$805$	−3.27427	−0.115403
$806$	−2.76973	−0.0975595
$807$	29.7951	1.04884
$808$	−4.43052	−0.155865
$809$	18.6799	0.656749	0.328375	−	0.944548i	$-0.393499\pi$
$809$	18.6799	0.656749	0.328375	+	0.944548i	$0.393499\pi$
$810$	96.0498	3.37485
$811$	−48.9156	−1.71766	−0.858829	−	0.512263i	$-0.828807\pi$
$811$	−48.9156	−1.71766	−0.858829	+	0.512263i	$0.828807\pi$
$812$	18.4999	0.649221
$813$	48.4748	1.70009
$814$	−5.00833	−0.175542
$815$	11.6019	0.406397
$816$	17.5982	0.616059
$817$	−0.00495800	−0.000173459 0
$818$	−15.1054	−0.528149
$819$	104.656	3.65696
$820$	3.52190	0.122990
$821$	36.7192	1.28151	0.640754	−	0.767746i	$-0.278622\pi$
$821$	36.7192	1.28151	0.640754	+	0.767746i	$0.278622\pi$
$822$	−15.4896	−0.540260
$823$	−24.2487	−0.845257	−0.422628	−	0.906303i	$-0.638892\pi$
$823$	−24.2487	−0.845257	−0.422628	+	0.906303i	$0.638892\pi$
$824$	−8.68332	−0.302498
$825$	2.79363	0.0972619
$826$	22.4330	0.780542
$827$	25.0763	0.871989	0.435995	−	0.899949i	$-0.356397\pi$
$827$	25.0763	0.871989	0.435995	+	0.899949i	$0.356397\pi$
$828$	−3.60774	−0.125378
$829$	0.424991	0.0147605	0.00738027	−	0.999973i	$-0.497651\pi$
$829$	0.424991	0.0147605	0.00738027	+	0.999973i	$0.497651\pi$
$830$	−22.2236	−0.771392
$831$	−78.4123	−2.72009
$832$	3.74746	0.129920
$833$	−17.8613	−0.618858
$834$	38.9461	1.34859
$835$	30.4152	1.05256
$836$	0.0218306	0.000755026 0
$837$	14.2036	0.490947
$838$	−27.8149	−0.960851
$839$	−4.45799	−0.153907	−0.0769534	−	0.997035i	$-0.524519\pi$
$839$	−4.45799	−0.153907	−0.0769534	+	0.997035i	$0.524519\pi$
$840$	−26.7280	−0.922204
$841$	3.71374	0.128060
$842$	3.88068	0.133737
$843$	23.7227	0.817052
$844$	10.3824	0.357378
$845$	2.52795	0.0869640
$846$	85.2572	2.93120
$847$	−32.7082	−1.12387
$848$	7.46777	0.256444
$849$	−11.7554	−0.403446
$850$	−4.48516	−0.153840
$851$	−2.22118	−0.0761410
$852$	38.8725	1.33175
$853$	6.87139	0.235272	0.117636	−	0.993057i	$-0.462468\pi$
$853$	6.87139	0.235272	0.117636	+	0.993057i	$0.462468\pi$
$854$	20.9918	0.718323
$855$	−0.484680	−0.0165757
$856$	−6.84237	−0.233867
$857$	52.4177	1.79055	0.895277	−	0.445510i	$-0.146977\pi$
$857$	52.4177	1.79055	0.895277	+	0.445510i	$0.146977\pi$
$858$	12.0428	0.411136
$859$	9.72388	0.331774	0.165887	−	0.986145i	$-0.446951\pi$
$859$	9.72388	0.331774	0.165887	+	0.986145i	$0.446951\pi$
$860$	0.518394	0.0176771
$861$	−16.0382	−0.546580
$862$	15.7696	0.537116
$863$	−40.4356	−1.37645	−0.688223	−	0.725499i	$-0.741609\pi$
$863$	−40.4356	−1.37645	−0.688223	+	0.725499i	$0.741609\pi$
$864$	−19.2175	−0.653793
$865$	−17.4521	−0.593388
$866$	31.1225	1.05759
$867$	−32.8111	−1.11432
$868$	−2.39059	−0.0811419
$869$	−2.91508	−0.0988872
$870$	−47.2636	−1.60238
$871$	−35.8971	−1.21633
$872$	−16.8822	−0.571703
$873$	84.7269	2.86757
$874$	0.00968180	0.000327492 0
$875$	−32.3684	−1.09425
$876$	−40.0295	−1.35247
$877$	22.7016	0.766579	0.383290	−	0.923628i	$-0.374791\pi$
$877$	22.7016	0.766579	0.383290	+	0.923628i	$0.374791\pi$
$878$	−15.6073	−0.526722
$879$	−17.2512	−0.581869
$880$	−2.28254	−0.0769444
$881$	−28.9644	−0.975835	−0.487917	−	0.872890i	$-0.662243\pi$
$881$	−28.9644	−0.975835	−0.487917	+	0.872890i	$0.662243\pi$
$882$	29.8906	1.00647
$883$	23.2998	0.784101	0.392050	−	0.919944i	$-0.371766\pi$
$883$	23.2998	0.784101	0.392050	+	0.919944i	$0.371766\pi$
$884$	−19.3347	−0.650296
$885$	−57.3116	−1.92651
$886$	7.97189	0.267821
$887$	−26.6474	−0.894731	−0.447366	−	0.894351i	$-0.647638\pi$
$887$	−26.6474	−0.894731	−0.447366	+	0.894351i	$0.647638\pi$
$888$	−18.1316	−0.608456
$889$	16.9558	0.568678
$890$	12.0230	0.403010
$891$	−37.3531	−1.25138
$892$	−4.70650	−0.157585
$893$	−0.228798	−0.00765642
$894$	12.8436	0.429555
$895$	35.1631	1.17537
$896$	3.23449	0.108057
$897$	5.34097	0.178330
$898$	30.3189	1.01176
$899$	−4.22732	−0.140989
$900$	7.50582	0.250194
$901$	−38.5293	−1.28360
$902$	−1.36964	−0.0456041
$903$	−2.36069	−0.0785588
$904$	6.24210	0.207609
$905$	20.1994	0.671452
$906$	−34.2012	−1.13626
$907$	51.7201	1.71734	0.858669	−	0.512531i	$-0.171292\pi$
$907$	51.7201	1.71734	0.858669	+	0.512531i	$0.171292\pi$
$908$	19.2649	0.639328
$909$	−38.2539	−1.26880
$910$	29.3654	0.973453
$911$	−47.6908	−1.58007	−0.790034	−	0.613064i	$-0.789937\pi$
$911$	−47.6908	−1.58007	−0.790034	+	0.613064i	$0.789937\pi$
$912$	0.0790330	0.00261704
$913$	8.64260	0.286028
$914$	−4.17247	−0.138013
$915$	−53.6297	−1.77294
$916$	6.25665	0.206725
$917$	48.6268	1.60580
$918$	99.1510	3.27247
$919$	7.20431	0.237648	0.118824	−	0.992915i	$-0.462088\pi$
$919$	7.20431	0.237648	0.118824	+	0.992915i	$0.462088\pi$
$920$	−1.01230	−0.0333745
$921$	23.6747	0.780109
$922$	28.5839	0.941360
$923$	−42.7083	−1.40576
$924$	10.3943	0.341949
$925$	4.62110	0.151941
$926$	−12.2111	−0.401281
$927$	−74.9732	−2.46244
$928$	5.71959	0.187755
$929$	16.2848	0.534287	0.267143	−	0.963657i	$-0.413920\pi$
$929$	16.2848	0.534287	0.267143	+	0.963657i	$0.413920\pi$
$930$	6.10747	0.200272
$931$	−0.0802148	−0.00262894
$932$	−1.71316	−0.0561163
$933$	−64.3841	−2.10784
$934$	−9.90904	−0.324234
$935$	11.7766	0.385134
$936$	32.3562	1.05760
$937$	9.90590	0.323612	0.161806	−	0.986823i	$-0.448268\pi$
$937$	9.90590	0.323612	0.161806	+	0.986823i	$0.448268\pi$
$938$	−30.9833	−1.01164
$939$	75.7522	2.47208
$940$	23.9224	0.780262
$941$	−46.9723	−1.53125	−0.765627	−	0.643284i	$-0.777571\pi$
$941$	−46.9723	−1.53125	−0.765627	+	0.643284i	$0.777571\pi$
$942$	−11.7579	−0.383093
$943$	−0.607432	−0.0197807
$944$	6.93556	0.225733
$945$	−150.590	−4.89869
$946$	−0.201600	−0.00655458
$947$	−36.4567	−1.18468	−0.592342	−	0.805687i	$-0.701796\pi$
$947$	−36.4567	−1.18468	−0.592342	+	0.805687i	$0.701796\pi$
$948$	−10.5534	−0.342759
$949$	43.9794	1.42763
$950$	−0.0201427	−0.000653517 0
$951$	53.3934	1.73140
$952$	−16.6880	−0.540862
$953$	−40.6451	−1.31662	−0.658312	−	0.752745i	$-0.728729\pi$
$953$	−40.6451	−1.31662	−0.658312	+	0.752745i	$0.728729\pi$
$954$	64.4780	2.08755
$955$	−5.55261	−0.179678
$956$	−24.1257	−0.780281
$957$	18.3805	0.594157
$958$	−29.8182	−0.963384
$959$	14.6885	0.474315
$960$	−8.26345	−0.266702
$961$	−30.4537	−0.982379
$962$	19.9207	0.642270
$963$	−59.0781	−1.90377
$964$	−5.44948	−0.175516
$965$	−64.6625	−2.08156
$966$	4.60986	0.148320
$967$	25.7869	0.829252	0.414626	−	0.909992i	$-0.363912\pi$
$967$	25.7869	0.829252	0.414626	+	0.909992i	$0.363912\pi$
$968$	−10.1123	−0.325023
$969$	−0.407764	−0.0130993
$970$	23.7736	0.763324
$971$	17.9030	0.574534	0.287267	−	0.957851i	$-0.407253\pi$
$971$	17.9030	0.574534	0.287267	+	0.957851i	$0.407253\pi$
$972$	−77.5766	−2.48827
$973$	−36.9319	−1.18398
$974$	−7.25358	−0.232420
$975$	−11.1117	−0.355861
$976$	6.48999	0.207739
$977$	−56.4508	−1.80602	−0.903011	−	0.429618i	$-0.858648\pi$
$977$	−56.4508	−1.80602	−0.903011	+	0.429618i	$0.858648\pi$
$978$	−16.3344	−0.522317
$979$	−4.67565	−0.149434
$980$	8.38702	0.267913
$981$	−145.764	−4.65388
$982$	19.1866	0.612268
$983$	17.5654	0.560249	0.280125	−	0.959964i	$-0.409624\pi$
$983$	17.5654	0.560249	0.280125	+	0.959964i	$0.409624\pi$
$984$	−4.95850	−0.158071
$985$	27.6728	0.881728
$986$	−29.5097	−0.939781
$987$	−108.939	−3.46757
$988$	−0.0868316	−0.00276248
$989$	−0.0894090	−0.00284304
$990$	−19.7078	−0.626355
$991$	4.57801	0.145425	0.0727126	−	0.997353i	$-0.476834\pi$
$991$	4.57801	0.145425	0.0727126	+	0.997353i	$0.476834\pi$
$992$	−0.739094	−0.0234663
$993$	33.7044	1.06958
$994$	−36.8621	−1.16920
$995$	41.3433	1.31067
$996$	31.2887	0.991421
$997$	20.4381	0.647282	0.323641	−	0.946180i	$-0.395093\pi$
$997$	20.4381	0.647282	0.323641	+	0.946180i	$0.395093\pi$
$998$	−1.41241	−0.0447092
$999$	−102.156	−3.23208

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.g.1.1	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.41089 q^{3} +1.00000 q^{4} +2.42267 q^{5} -3.41089 q^{6} +3.23449 q^{7} +1.00000 q^{8} +8.63416 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.41089 q^{3} +1.00000 q^{4} +2.42267 q^{5} -3.41089 q^{6} +3.23449 q^{7} +1.00000 q^{8} +8.63416 q^{9} +2.42267 q^{10} -0.942159 q^{11} -3.41089 q^{12} +3.74746 q^{13} +3.23449 q^{14} -8.26345 q^{15} +1.00000 q^{16} -5.15941 q^{17} +8.63416 q^{18} -0.0231708 q^{19} +2.42267 q^{20} -11.0325 q^{21} -0.942159 q^{22} -0.417845 q^{23} -3.41089 q^{24} +0.869316 q^{25} +3.74746 q^{26} -19.2175 q^{27} +3.23449 q^{28} +5.71959 q^{29} -8.26345 q^{30} -0.739094 q^{31} +1.00000 q^{32} +3.21360 q^{33} -5.15941 q^{34} +7.83608 q^{35} +8.63416 q^{36} +5.31579 q^{37} -0.0231708 q^{38} -12.7822 q^{39} +2.42267 q^{40} +1.45373 q^{41} -11.0325 q^{42} +0.213976 q^{43} -0.942159 q^{44} +20.9177 q^{45} -0.417845 q^{46} +9.87439 q^{47} -3.41089 q^{48} +3.46189 q^{49} +0.869316 q^{50} +17.5982 q^{51} +3.74746 q^{52} +7.46777 q^{53} -19.2175 q^{54} -2.28254 q^{55} +3.23449 q^{56} +0.0790330 q^{57} +5.71959 q^{58} +6.93556 q^{59} -8.26345 q^{60} +6.48999 q^{61} -0.739094 q^{62} +27.9271 q^{63} +1.00000 q^{64} +9.07885 q^{65} +3.21360 q^{66} -9.57906 q^{67} -5.15941 q^{68} +1.42522 q^{69} +7.83608 q^{70} -11.3966 q^{71} +8.63416 q^{72} +11.7358 q^{73} +5.31579 q^{74} -2.96514 q^{75} -0.0231708 q^{76} -3.04740 q^{77} -12.7822 q^{78} +3.09404 q^{79} +2.42267 q^{80} +39.6463 q^{81} +1.45373 q^{82} -9.17319 q^{83} -11.0325 q^{84} -12.4995 q^{85} +0.213976 q^{86} -19.5089 q^{87} -0.942159 q^{88} +4.96269 q^{89} +20.9177 q^{90} +12.1211 q^{91} -0.417845 q^{92} +2.52097 q^{93} +9.87439 q^{94} -0.0561351 q^{95} -3.41089 q^{96} +9.81298 q^{97} +3.46189 q^{98} -8.13476 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 95 q + 95 q^{2} + 24 q^{3} + 95 q^{4} + 36 q^{5} + 24 q^{6} + 21 q^{7} + 95 q^{8} + 121 q^{9}+O(q^{10}) \) 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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