LMFDB - Embedded newform 8014.2.a.d.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, 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("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.96788 q^{3} +1.00000 q^{4} -0.993306 q^{5} -1.96788 q^{6} -1.68889 q^{7} +1.00000 q^{8} +0.872539 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.96788 q^{3} +1.00000 q^{4} -0.993306 q^{5} -1.96788 q^{6} -1.68889 q^{7} +1.00000 q^{8} +0.872539 q^{9} -0.993306 q^{10} -3.54585 q^{11} -1.96788 q^{12} -1.21810 q^{13} -1.68889 q^{14} +1.95470 q^{15} +1.00000 q^{16} +4.69264 q^{17} +0.872539 q^{18} +0.606930 q^{19} -0.993306 q^{20} +3.32353 q^{21} -3.54585 q^{22} +2.16601 q^{23} -1.96788 q^{24} -4.01334 q^{25} -1.21810 q^{26} +4.18658 q^{27} -1.68889 q^{28} -5.65319 q^{29} +1.95470 q^{30} -3.76380 q^{31} +1.00000 q^{32} +6.97780 q^{33} +4.69264 q^{34} +1.67759 q^{35} +0.872539 q^{36} +4.79543 q^{37} +0.606930 q^{38} +2.39708 q^{39} -0.993306 q^{40} -8.14780 q^{41} +3.32353 q^{42} +2.45285 q^{43} -3.54585 q^{44} -0.866697 q^{45} +2.16601 q^{46} -4.87844 q^{47} -1.96788 q^{48} -4.14764 q^{49} -4.01334 q^{50} -9.23454 q^{51} -1.21810 q^{52} -6.91221 q^{53} +4.18658 q^{54} +3.52212 q^{55} -1.68889 q^{56} -1.19436 q^{57} -5.65319 q^{58} +3.70141 q^{59} +1.95470 q^{60} -11.9084 q^{61} -3.76380 q^{62} -1.47362 q^{63} +1.00000 q^{64} +1.20995 q^{65} +6.97780 q^{66} -4.57983 q^{67} +4.69264 q^{68} -4.26243 q^{69} +1.67759 q^{70} -8.13730 q^{71} +0.872539 q^{72} +9.62333 q^{73} +4.79543 q^{74} +7.89777 q^{75} +0.606930 q^{76} +5.98857 q^{77} +2.39708 q^{78} -5.35065 q^{79} -0.993306 q^{80} -10.8563 q^{81} -8.14780 q^{82} +6.02278 q^{83} +3.32353 q^{84} -4.66123 q^{85} +2.45285 q^{86} +11.1248 q^{87} -3.54585 q^{88} +2.29777 q^{89} -0.866697 q^{90} +2.05725 q^{91} +2.16601 q^{92} +7.40669 q^{93} -4.87844 q^{94} -0.602867 q^{95} -1.96788 q^{96} +1.71084 q^{97} -4.14764 q^{98} -3.09389 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) $ 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * 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
$3$	−1.96788	−1.13615	−0.568077	−	0.822975i	$-0.692312\pi$
$3$	−1.96788	−1.13615	−0.568077	+	0.822975i	$0.692312\pi$
$4$	1.00000	0.500000
$5$	−0.993306	−0.444220	−0.222110	−	0.975022i	$-0.571294\pi$
$5$	−0.993306	−0.444220	−0.222110	+	0.975022i	$0.571294\pi$
$6$	−1.96788	−0.803382
$7$	−1.68889	−0.638341	−0.319171	−	0.947697i	$-0.603404\pi$
$7$	−1.68889	−0.638341	−0.319171	+	0.947697i	$0.603404\pi$
$8$	1.00000	0.353553
$9$	0.872539	0.290846
$10$	−0.993306	−0.314111
$11$	−3.54585	−1.06912	−0.534558	−	0.845132i	$-0.679522\pi$
$11$	−3.54585	−1.06912	−0.534558	+	0.845132i	$0.679522\pi$
$12$	−1.96788	−0.568077
$13$	−1.21810	−0.337841	−0.168921	−	0.985630i	$-0.554028\pi$
$13$	−1.21810	−0.337841	−0.168921	+	0.985630i	$0.554028\pi$
$14$	−1.68889	−0.451375
$15$	1.95470	0.504702
$16$	1.00000	0.250000
$17$	4.69264	1.13813	0.569066	−	0.822292i	$-0.307305\pi$
$17$	4.69264	1.13813	0.569066	+	0.822292i	$0.307305\pi$
$18$	0.872539	0.205659
$19$	0.606930	0.139239	0.0696197	−	0.997574i	$-0.477821\pi$
$19$	0.606930	0.139239	0.0696197	+	0.997574i	$0.477821\pi$
$20$	−0.993306	−0.222110
$21$	3.32353	0.725254
$22$	−3.54585	−0.755979
$23$	2.16601	0.451643	0.225822	−	0.974169i	$-0.427493\pi$
$23$	2.16601	0.451643	0.225822	+	0.974169i	$0.427493\pi$
$24$	−1.96788	−0.401691
$25$	−4.01334	−0.802669
$26$	−1.21810	−0.238890
$27$	4.18658	0.805708
$28$	−1.68889	−0.319171
$29$	−5.65319	−1.04977	−0.524886	−	0.851173i	$-0.675892\pi$
$29$	−5.65319	−1.04977	−0.524886	+	0.851173i	$0.675892\pi$
$30$	1.95470	0.356878
$31$	−3.76380	−0.675998	−0.337999	−	0.941146i	$-0.609750\pi$
$31$	−3.76380	−0.675998	−0.337999	+	0.941146i	$0.609750\pi$
$32$	1.00000	0.176777
$33$	6.97780	1.21468
$34$	4.69264	0.804781
$35$	1.67759	0.283564
$36$	0.872539	0.145423
$37$	4.79543	0.788364	0.394182	−	0.919032i	$-0.371028\pi$
$37$	4.79543	0.788364	0.394182	+	0.919032i	$0.371028\pi$
$38$	0.606930	0.0984571
$39$	2.39708	0.383840
$40$	−0.993306	−0.157055
$41$	−8.14780	−1.27247	−0.636237	−	0.771494i	$-0.719510\pi$
$41$	−8.14780	−1.27247	−0.636237	+	0.771494i	$0.719510\pi$
$42$	3.32353	0.512832
$43$	2.45285	0.374056	0.187028	−	0.982355i	$-0.440114\pi$
$43$	2.45285	0.374056	0.187028	+	0.982355i	$0.440114\pi$
$44$	−3.54585	−0.534558
$45$	−0.866697	−0.129200
$46$	2.16601	0.319360
$47$	−4.87844	−0.711594	−0.355797	−	0.934563i	$-0.615791\pi$
$47$	−4.87844	−0.711594	−0.355797	+	0.934563i	$0.615791\pi$
$48$	−1.96788	−0.284039
$49$	−4.14764	−0.592520
$50$	−4.01334	−0.567573
$51$	−9.23454	−1.29309
$52$	−1.21810	−0.168921
$53$	−6.91221	−0.949464	−0.474732	−	0.880130i	$-0.657455\pi$
$53$	−6.91221	−0.949464	−0.474732	+	0.880130i	$0.657455\pi$
$54$	4.18658	0.569722
$55$	3.52212	0.474922
$56$	−1.68889	−0.225688
$57$	−1.19436	−0.158197
$58$	−5.65319	−0.742300
$59$	3.70141	0.481883	0.240942	−	0.970540i	$-0.422544\pi$
$59$	3.70141	0.481883	0.240942	+	0.970540i	$0.422544\pi$
$60$	1.95470	0.252351
$61$	−11.9084	−1.52471	−0.762356	−	0.647158i	$-0.775957\pi$
$61$	−11.9084	−1.52471	−0.762356	+	0.647158i	$0.775957\pi$
$62$	−3.76380	−0.478003
$63$	−1.47362	−0.185659
$64$	1.00000	0.125000
$65$	1.20995	0.150076
$66$	6.97780	0.858908
$67$	−4.57983	−0.559515	−0.279757	−	0.960071i	$-0.590254\pi$
$67$	−4.57983	−0.559515	−0.279757	+	0.960071i	$0.590254\pi$
$68$	4.69264	0.569066
$69$	−4.26243	−0.513137
$70$	1.67759	0.200510
$71$	−8.13730	−0.965720	−0.482860	−	0.875697i	$-0.660402\pi$
$71$	−8.13730	−0.965720	−0.482860	+	0.875697i	$0.660402\pi$
$72$	0.872539	0.102830
$73$	9.62333	1.12633	0.563163	−	0.826346i	$-0.309584\pi$
$73$	9.62333	1.12633	0.563163	+	0.826346i	$0.309584\pi$
$74$	4.79543	0.557457
$75$	7.89777	0.911955
$76$	0.606930	0.0696197
$77$	5.98857	0.682460
$78$	2.39708	0.271416
$79$	−5.35065	−0.601995	−0.300998	−	0.953625i	$-0.597320\pi$
$79$	−5.35065	−0.601995	−0.300998	+	0.953625i	$0.597320\pi$
$80$	−0.993306	−0.111055
$81$	−10.8563	−1.20625
$82$	−8.14780	−0.899774
$83$	6.02278	0.661086	0.330543	−	0.943791i	$-0.392768\pi$
$83$	6.02278	0.661086	0.330543	+	0.943791i	$0.392768\pi$
$84$	3.32353	0.362627
$85$	−4.66123	−0.505581
$86$	2.45285	0.264497
$87$	11.1248	1.19270
$88$	−3.54585	−0.377989
$89$	2.29777	0.243563	0.121781	−	0.992557i	$-0.461139\pi$
$89$	2.29777	0.243563	0.121781	+	0.992557i	$0.461139\pi$
$90$	−0.866697	−0.0913579
$91$	2.05725	0.215658
$92$	2.16601	0.225822
$93$	7.40669	0.768038
$94$	−4.87844	−0.503173
$95$	−0.602867	−0.0618529
$96$	−1.96788	−0.200846
$97$	1.71084	0.173709	0.0868546	−	0.996221i	$-0.472318\pi$
$97$	1.71084	0.173709	0.0868546	+	0.996221i	$0.472318\pi$
$98$	−4.14764	−0.418975
$99$	−3.09389	−0.310948
$100$	−4.01334	−0.401334
$101$	−3.03132	−0.301628	−0.150814	−	0.988562i	$-0.548189\pi$
$101$	−3.03132	−0.301628	−0.150814	+	0.988562i	$0.548189\pi$
$102$	−9.23454	−0.914356
$103$	−4.14228	−0.408151	−0.204075	−	0.978955i	$-0.565419\pi$
$103$	−4.14228	−0.408151	−0.204075	+	0.978955i	$0.565419\pi$
$104$	−1.21810	−0.119445
$105$	−3.30128	−0.322172
$106$	−6.91221	−0.671373
$107$	4.69397	0.453783	0.226892	−	0.973920i	$-0.427144\pi$
$107$	4.69397	0.453783	0.226892	+	0.973920i	$0.427144\pi$
$108$	4.18658	0.402854
$109$	13.0906	1.25385	0.626924	−	0.779080i	$-0.284314\pi$
$109$	13.0906	1.25385	0.626924	+	0.779080i	$0.284314\pi$
$110$	3.52212	0.335821
$111$	−9.43681	−0.895703
$112$	−1.68889	−0.159585
$113$	15.1250	1.42284	0.711419	−	0.702768i	$-0.248053\pi$
$113$	15.1250	1.42284	0.711419	+	0.702768i	$0.248053\pi$
$114$	−1.19436	−0.111862
$115$	−2.15151	−0.200629
$116$	−5.65319	−0.524886
$117$	−1.06284	−0.0982599
$118$	3.70141	0.340743
$119$	−7.92537	−0.726517
$120$	1.95470	0.178439
$121$	1.57308	0.143007
$122$	−11.9084	−1.07813
$123$	16.0339	1.44573
$124$	−3.76380	−0.337999
$125$	8.95301	0.800781
$126$	−1.47362	−0.131281
$127$	17.6384	1.56515	0.782577	−	0.622554i	$-0.213905\pi$
$127$	17.6384	1.56515	0.782577	+	0.622554i	$0.213905\pi$
$128$	1.00000	0.0883883
$129$	−4.82690	−0.424985
$130$	1.20995	0.106120
$131$	2.13681	0.186694	0.0933469	−	0.995634i	$-0.470243\pi$
$131$	2.13681	0.186694	0.0933469	+	0.995634i	$0.470243\pi$
$132$	6.97780	0.607340
$133$	−1.02504	−0.0888823
$134$	−4.57983	−0.395637
$135$	−4.15856	−0.357911
$136$	4.69264	0.402391
$137$	0.401501	0.0343026	0.0171513	−	0.999853i	$-0.494540\pi$
$137$	0.401501	0.0343026	0.0171513	+	0.999853i	$0.494540\pi$
$138$	−4.26243	−0.362842
$139$	7.63691	0.647755	0.323877	−	0.946099i	$-0.395014\pi$
$139$	7.63691	0.647755	0.323877	+	0.946099i	$0.395014\pi$
$140$	1.67759	0.141782
$141$	9.60018	0.808481
$142$	−8.13730	−0.682867
$143$	4.31922	0.361191
$144$	0.872539	0.0727115
$145$	5.61535	0.466329
$146$	9.62333	0.796432
$147$	8.16205	0.673194
$148$	4.79543	0.394182
$149$	12.8866	1.05571	0.527856	−	0.849334i	$-0.322996\pi$
$149$	12.8866	1.05571	0.527856	+	0.849334i	$0.322996\pi$
$150$	7.89777	0.644850
$151$	−8.64428	−0.703461	−0.351731	−	0.936101i	$-0.614407\pi$
$151$	−8.64428	−0.703461	−0.351731	+	0.936101i	$0.614407\pi$
$152$	0.606930	0.0492286
$153$	4.09451	0.331021
$154$	5.98857	0.482572
$155$	3.73860	0.300292
$156$	2.39708	0.191920
$157$	22.1029	1.76401	0.882003	−	0.471244i	$-0.156195\pi$
$157$	22.1029	1.76401	0.882003	+	0.471244i	$0.156195\pi$
$158$	−5.35065	−0.425675
$159$	13.6024	1.07874
$160$	−0.993306	−0.0785277
$161$	−3.65815	−0.288303
$162$	−10.8563	−0.852951
$163$	7.71039	0.603924	0.301962	−	0.953320i	$-0.402358\pi$
$163$	7.71039	0.603924	0.301962	+	0.953320i	$0.402358\pi$
$164$	−8.14780	−0.636237
$165$	−6.93109	−0.539585
$166$	6.02278	0.467459
$167$	15.6409	1.21033	0.605166	−	0.796100i	$-0.293107\pi$
$167$	15.6409	1.21033	0.605166	+	0.796100i	$0.293107\pi$
$168$	3.32353	0.256416
$169$	−11.5162	−0.885863
$170$	−4.66123	−0.357500
$171$	0.529570	0.0404972
$172$	2.45285	0.187028
$173$	10.7759	0.819277	0.409639	−	0.912248i	$-0.365655\pi$
$173$	10.7759	0.819277	0.409639	+	0.912248i	$0.365655\pi$
$174$	11.1248	0.843368
$175$	6.77811	0.512377
$176$	−3.54585	−0.267279
$177$	−7.28393	−0.547493
$178$	2.29777	0.172225
$179$	−14.9034	−1.11393	−0.556965	−	0.830536i	$-0.688034\pi$
$179$	−14.9034	−1.11393	−0.556965	+	0.830536i	$0.688034\pi$
$180$	−0.866697	−0.0645998
$181$	−14.5777	−1.08355	−0.541775	−	0.840523i	$-0.682248\pi$
$181$	−14.5777	−1.08355	−0.541775	+	0.840523i	$0.682248\pi$
$182$	2.05725	0.152493
$183$	23.4342	1.73231
$184$	2.16601	0.159680
$185$	−4.76333	−0.350207
$186$	7.40669	0.543085
$187$	−16.6394	−1.21679
$188$	−4.87844	−0.355797
$189$	−7.07069	−0.514317
$190$	−0.602867	−0.0437366
$191$	14.3894	1.04118	0.520591	−	0.853806i	$-0.325712\pi$
$191$	14.3894	1.04118	0.520591	+	0.853806i	$0.325712\pi$
$192$	−1.96788	−0.142019
$193$	−1.54516	−0.111223	−0.0556115	−	0.998452i	$-0.517711\pi$
$193$	−1.54516	−0.111223	−0.0556115	+	0.998452i	$0.517711\pi$
$194$	1.71084	0.122831
$195$	−2.38103	−0.170509
$196$	−4.14764	−0.296260
$197$	2.59426	0.184834	0.0924168	−	0.995720i	$-0.470541\pi$
$197$	2.59426	0.184834	0.0924168	+	0.995720i	$0.470541\pi$
$198$	−3.09389	−0.219874
$199$	26.4120	1.87230	0.936150	−	0.351600i	$-0.114362\pi$
$199$	26.4120	1.87230	0.936150	+	0.351600i	$0.114362\pi$
$200$	−4.01334	−0.283786
$201$	9.01253	0.635695
$202$	−3.03132	−0.213283
$203$	9.54763	0.670112
$204$	−9.23454	−0.646547
$205$	8.09326	0.565258
$206$	−4.14228	−0.288606
$207$	1.88992	0.131359
$208$	−1.21810	−0.0844603
$209$	−2.15209	−0.148863
$210$	−3.30128	−0.227810
$211$	4.31589	0.297118	0.148559	−	0.988904i	$-0.452537\pi$
$211$	4.31589	0.297118	0.148559	+	0.988904i	$0.452537\pi$
$212$	−6.91221	−0.474732
$213$	16.0132	1.09721
$214$	4.69397	0.320873
$215$	−2.43643	−0.166163
$216$	4.18658	0.284861
$217$	6.35665	0.431518
$218$	13.0906	0.886605
$219$	−18.9375	−1.27968
$220$	3.52212	0.237461
$221$	−5.71613	−0.384508
$222$	−9.43681	−0.633357
$223$	−16.2869	−1.09065	−0.545325	−	0.838225i	$-0.683594\pi$
$223$	−16.2869	−1.09065	−0.545325	+	0.838225i	$0.683594\pi$
$224$	−1.68889	−0.112844
$225$	−3.50180	−0.233453
$226$	15.1250	1.00610
$227$	−7.91135	−0.525095	−0.262547	−	0.964919i	$-0.584563\pi$
$227$	−7.91135	−0.525095	−0.262547	+	0.964919i	$0.584563\pi$
$228$	−1.19436	−0.0790987
$229$	−27.0144	−1.78516	−0.892582	−	0.450885i	$-0.851109\pi$
$229$	−27.0144	−1.78516	−0.892582	+	0.450885i	$0.851109\pi$
$230$	−2.15151	−0.141866
$231$	−11.7848	−0.775380
$232$	−5.65319	−0.371150
$233$	−4.86561	−0.318757	−0.159378	−	0.987218i	$-0.550949\pi$
$233$	−4.86561	−0.318757	−0.159378	+	0.987218i	$0.550949\pi$
$234$	−1.06284	−0.0694802
$235$	4.84579	0.316104
$236$	3.70141	0.240942
$237$	10.5294	0.683959
$238$	−7.92537	−0.513725
$239$	25.6824	1.66126	0.830628	−	0.556828i	$-0.187982\pi$
$239$	25.6824	1.66126	0.830628	+	0.556828i	$0.187982\pi$
$240$	1.95470	0.126176
$241$	−7.20409	−0.464056	−0.232028	−	0.972709i	$-0.574536\pi$
$241$	−7.20409	−0.464056	−0.232028	+	0.972709i	$0.574536\pi$
$242$	1.57308	0.101122
$243$	8.80410	0.564783
$244$	−11.9084	−0.762356
$245$	4.11988	0.263209
$246$	16.0339	1.02228
$247$	−0.739305	−0.0470408
$248$	−3.76380	−0.239001
$249$	−11.8521	−0.751096
$250$	8.95301	0.566238
$251$	−6.11365	−0.385890	−0.192945	−	0.981210i	$-0.561804\pi$
$251$	−6.11365	−0.385890	−0.192945	+	0.981210i	$0.561804\pi$
$252$	−1.47362	−0.0928296
$253$	−7.68034	−0.482859
$254$	17.6384	1.10673
$255$	9.17272	0.574418
$256$	1.00000	0.0625000
$257$	−9.26809	−0.578128	−0.289064	−	0.957310i	$-0.593344\pi$
$257$	−9.26809	−0.578128	−0.289064	+	0.957310i	$0.593344\pi$
$258$	−4.82690	−0.300510
$259$	−8.09896	−0.503245
$260$	1.20995	0.0750379
$261$	−4.93263	−0.305322
$262$	2.13681	0.132012
$263$	30.0809	1.85487	0.927433	−	0.373989i	$-0.122010\pi$
$263$	30.0809	1.85487	0.927433	+	0.373989i	$0.122010\pi$
$264$	6.97780	0.429454
$265$	6.86593	0.421771
$266$	−1.02504	−0.0628492
$267$	−4.52172	−0.276725
$268$	−4.57983	−0.279757
$269$	11.2991	0.688921	0.344460	−	0.938801i	$-0.388062\pi$
$269$	11.2991	0.688921	0.344460	+	0.938801i	$0.388062\pi$
$270$	−4.15856	−0.253082
$271$	30.4727	1.85109	0.925544	−	0.378641i	$-0.123608\pi$
$271$	30.4727	1.85109	0.925544	+	0.378641i	$0.123608\pi$
$272$	4.69264	0.284533
$273$	−4.04841	−0.245021
$274$	0.401501	0.0242556
$275$	14.2307	0.858145
$276$	−4.26243	−0.256568
$277$	4.83630	0.290585	0.145293	−	0.989389i	$-0.453588\pi$
$277$	4.83630	0.290585	0.145293	+	0.989389i	$0.453588\pi$
$278$	7.63691	0.458032
$279$	−3.28406	−0.196611
$280$	1.67759	0.100255
$281$	3.33725	0.199084	0.0995418	−	0.995033i	$-0.468262\pi$
$281$	3.33725	0.199084	0.0995418	+	0.995033i	$0.468262\pi$
$282$	9.60018	0.571682
$283$	8.10209	0.481619	0.240810	−	0.970572i	$-0.422587\pi$
$283$	8.10209	0.481619	0.240810	+	0.970572i	$0.422587\pi$
$284$	−8.13730	−0.482860
$285$	1.18637	0.0702744
$286$	4.31922	0.255401
$287$	13.7608	0.812272
$288$	0.872539	0.0514148
$289$	5.02088	0.295346
$290$	5.61535	0.329745
$291$	−3.36672	−0.197361
$292$	9.62333	0.563163
$293$	−32.1263	−1.87684	−0.938420	−	0.345498i	$-0.887710\pi$
$293$	−32.1263	−1.87684	−0.938420	+	0.345498i	$0.887710\pi$
$294$	8.16205	0.476020
$295$	−3.67664	−0.214062
$296$	4.79543	0.278729
$297$	−14.8450	−0.861395
$298$	12.8866	0.746501
$299$	−2.63842	−0.152584
$300$	7.89777	0.455978
$301$	−4.14260	−0.238775
$302$	−8.64428	−0.497422
$303$	5.96527	0.342696
$304$	0.606930	0.0348098
$305$	11.8287	0.677307
$306$	4.09451	0.234068
$307$	13.3308	0.760831	0.380415	−	0.924816i	$-0.375781\pi$
$307$	13.3308	0.760831	0.380415	+	0.924816i	$0.375781\pi$
$308$	5.98857	0.341230
$309$	8.15149	0.463722
$310$	3.73860	0.212338
$311$	13.0884	0.742176	0.371088	−	0.928598i	$-0.378985\pi$
$311$	13.0884	0.742176	0.371088	+	0.928598i	$0.378985\pi$
$312$	2.39708	0.135708
$313$	27.1218	1.53301	0.766506	−	0.642237i	$-0.221993\pi$
$313$	27.1218	1.53301	0.766506	+	0.642237i	$0.221993\pi$
$314$	22.1029	1.24734
$315$	1.46376	0.0824735
$316$	−5.35065	−0.300998
$317$	−9.63065	−0.540911	−0.270456	−	0.962732i	$-0.587174\pi$
$317$	−9.63065	−0.540911	−0.270456	+	0.962732i	$0.587174\pi$
$318$	13.6024	0.762783
$319$	20.0454	1.12233
$320$	−0.993306	−0.0555275
$321$	−9.23715	−0.515568
$322$	−3.65815	−0.203861
$323$	2.84811	0.158473
$324$	−10.8563	−0.603127
$325$	4.88867	0.271175
$326$	7.71039	0.427039
$327$	−25.7606	−1.42456
$328$	−8.14780	−0.449887
$329$	8.23917	0.454240
$330$	−6.93109	−0.381544
$331$	6.07784	0.334068	0.167034	−	0.985951i	$-0.446581\pi$
$331$	6.07784	0.334068	0.167034	+	0.985951i	$0.446581\pi$
$332$	6.02278	0.330543
$333$	4.18420	0.229293
$334$	15.6409	0.855833
$335$	4.54917	0.248548
$336$	3.32353	0.181314
$337$	−17.6827	−0.963240	−0.481620	−	0.876380i	$-0.659951\pi$
$337$	−17.6827	−0.963240	−0.481620	+	0.876380i	$0.659951\pi$
$338$	−11.5162	−0.626400
$339$	−29.7641	−1.61656
$340$	−4.66123	−0.252791
$341$	13.3459	0.722720
$342$	0.529570	0.0286359
$343$	18.8272	1.01657
$344$	2.45285	0.132249
$345$	4.23390	0.227945
$346$	10.7759	0.579317
$347$	−0.0776439	−0.00416814	−0.00208407	−	0.999998i	$-0.500663\pi$
$347$	−0.0776439	−0.00416814	−0.00208407	+	0.999998i	$0.500663\pi$
$348$	11.1248	0.596351
$349$	7.30161	0.390846	0.195423	−	0.980719i	$-0.437392\pi$
$349$	7.30161	0.390846	0.195423	+	0.980719i	$0.437392\pi$
$350$	6.77811	0.362305
$351$	−5.09969	−0.272202
$352$	−3.54585	−0.188995
$353$	−3.77807	−0.201086	−0.100543	−	0.994933i	$-0.532058\pi$
$353$	−3.77807	−0.201086	−0.100543	+	0.994933i	$0.532058\pi$
$354$	−7.28393	−0.387136
$355$	8.08283	0.428992
$356$	2.29777	0.121781
$357$	15.5961	0.825435
$358$	−14.9034	−0.787668
$359$	15.0929	0.796573	0.398286	−	0.917261i	$-0.369605\pi$
$359$	15.0929	0.796573	0.398286	+	0.917261i	$0.369605\pi$
$360$	−0.866697	−0.0456790
$361$	−18.6316	−0.980612
$362$	−14.5777	−0.766186
$363$	−3.09563	−0.162479
$364$	2.05725	0.107829
$365$	−9.55891	−0.500336
$366$	23.4342	1.22493
$367$	4.72482	0.246633	0.123317	−	0.992367i	$-0.460647\pi$
$367$	4.72482	0.246633	0.123317	+	0.992367i	$0.460647\pi$
$368$	2.16601	0.112911
$369$	−7.10927	−0.370094
$370$	−4.76333	−0.247634
$371$	11.6740	0.606082
$372$	7.40669	0.384019
$373$	17.5822	0.910373	0.455187	−	0.890396i	$-0.349573\pi$
$373$	17.5822	0.910373	0.455187	+	0.890396i	$0.349573\pi$
$374$	−16.6394	−0.860404
$375$	−17.6184	−0.909811
$376$	−4.87844	−0.251587
$377$	6.88618	0.354656
$378$	−7.07069	−0.363677
$379$	28.5126	1.46460	0.732298	−	0.680984i	$-0.238448\pi$
$379$	28.5126	1.46460	0.732298	+	0.680984i	$0.238448\pi$
$380$	−0.602867	−0.0309264
$381$	−34.7102	−1.77826
$382$	14.3894	0.736227
$383$	−27.9762	−1.42952	−0.714759	−	0.699371i	$-0.753464\pi$
$383$	−27.9762	−1.42952	−0.714759	+	0.699371i	$0.753464\pi$
$384$	−1.96788	−0.100423
$385$	−5.94848	−0.303162
$386$	−1.54516	−0.0786466
$387$	2.14021	0.108793
$388$	1.71084	0.0868546
$389$	−14.4478	−0.732530	−0.366265	−	0.930511i	$-0.619364\pi$
$389$	−14.4478	−0.732530	−0.366265	+	0.930511i	$0.619364\pi$
$390$	−2.38103	−0.120568
$391$	10.1643	0.514030
$392$	−4.14764	−0.209488
$393$	−4.20497	−0.212113
$394$	2.59426	0.130697
$395$	5.31483	0.267418
$396$	−3.09389	−0.155474
$397$	21.4338	1.07573	0.537865	−	0.843031i	$-0.319231\pi$
$397$	21.4338	1.07573	0.537865	+	0.843031i	$0.319231\pi$
$398$	26.4120	1.32392
$399$	2.01715	0.100984
$400$	−4.01334	−0.200667
$401$	−26.2582	−1.31127	−0.655635	−	0.755078i	$-0.727599\pi$
$401$	−26.2582	−1.31127	−0.655635	+	0.755078i	$0.727599\pi$
$402$	9.01253	0.449504
$403$	4.58470	0.228380
$404$	−3.03132	−0.150814
$405$	10.7836	0.535842
$406$	9.54763	0.473841
$407$	−17.0039	−0.842852
$408$	−9.23454	−0.457178
$409$	4.20000	0.207676	0.103838	−	0.994594i	$-0.466888\pi$
$409$	4.20000	0.207676	0.103838	+	0.994594i	$0.466888\pi$
$410$	8.09326	0.399698
$411$	−0.790105	−0.0389730
$412$	−4.14228	−0.204075
$413$	−6.25129	−0.307606
$414$	1.88992	0.0928847
$415$	−5.98246	−0.293668
$416$	−1.21810	−0.0597225
$417$	−15.0285	−0.735949
$418$	−2.15209	−0.105262
$419$	25.5391	1.24767	0.623834	−	0.781557i	$-0.285574\pi$
$419$	25.5391	1.24767	0.623834	+	0.781557i	$0.285574\pi$
$420$	−3.30128	−0.161086
$421$	23.9694	1.16820	0.584098	−	0.811683i	$-0.301448\pi$
$421$	23.9694	1.16820	0.584098	+	0.811683i	$0.301448\pi$
$422$	4.31589	0.210094
$423$	−4.25663	−0.206964
$424$	−6.91221	−0.335686
$425$	−18.8332	−0.913543
$426$	16.0132	0.775843
$427$	20.1120	0.973287
$428$	4.69397	0.226892
$429$	−8.49969	−0.410369
$430$	−2.43643	−0.117495
$431$	10.1946	0.491055	0.245527	−	0.969390i	$-0.421039\pi$
$431$	10.1946	0.491055	0.245527	+	0.969390i	$0.421039\pi$
$432$	4.18658	0.201427
$433$	−36.1016	−1.73493	−0.867466	−	0.497496i	$-0.834253\pi$
$433$	−36.1016	−1.73493	−0.867466	+	0.497496i	$0.834253\pi$
$434$	6.35665	0.305129
$435$	−11.0503	−0.529822
$436$	13.0906	0.626924
$437$	1.31461	0.0628866
$438$	−18.9375	−0.904870
$439$	−18.3502	−0.875809	−0.437904	−	0.899021i	$-0.644279\pi$
$439$	−18.3502	−0.875809	−0.437904	+	0.899021i	$0.644279\pi$
$440$	3.52212	0.167910
$441$	−3.61898	−0.172332
$442$	−5.71613	−0.271888
$443$	−29.5151	−1.40231	−0.701153	−	0.713011i	$-0.747331\pi$
$443$	−29.5151	−1.40231	−0.701153	+	0.713011i	$0.747331\pi$
$444$	−9.43681	−0.447851
$445$	−2.28239	−0.108195
$446$	−16.2869	−0.771206
$447$	−25.3592	−1.19945
$448$	−1.68889	−0.0797927
$449$	−20.1318	−0.950077	−0.475039	−	0.879965i	$-0.657566\pi$
$449$	−20.1318	−0.950077	−0.475039	+	0.879965i	$0.657566\pi$
$450$	−3.50180	−0.165076
$451$	28.8909	1.36042
$452$	15.1250	0.711419
$453$	17.0109	0.799240
$454$	−7.91135	−0.371298
$455$	−2.04348	−0.0957996
$456$	−1.19436	−0.0559312
$457$	21.2865	0.995741	0.497870	−	0.867251i	$-0.334116\pi$
$457$	21.2865	0.995741	0.497870	+	0.867251i	$0.334116\pi$
$458$	−27.0144	−1.26230
$459$	19.6461	0.917003
$460$	−2.15151	−0.100314
$461$	−4.04525	−0.188406	−0.0942031	−	0.995553i	$-0.530030\pi$
$461$	−4.04525	−0.188406	−0.0942031	+	0.995553i	$0.530030\pi$
$462$	−11.7848	−0.548277
$463$	16.0637	0.746543	0.373271	−	0.927722i	$-0.378236\pi$
$463$	16.0637	0.746543	0.373271	+	0.927722i	$0.378236\pi$
$464$	−5.65319	−0.262443
$465$	−7.35711	−0.341178
$466$	−4.86561	−0.225395
$467$	−2.26706	−0.104907	−0.0524535	−	0.998623i	$-0.516704\pi$
$467$	−2.26706	−0.104907	−0.0524535	+	0.998623i	$0.516704\pi$
$468$	−1.06284	−0.0491299
$469$	7.73483	0.357161
$470$	4.84579	0.223519
$471$	−43.4958	−2.00418
$472$	3.70141	0.170371
$473$	−8.69744	−0.399909
$474$	10.5294	0.483632
$475$	−2.43582	−0.111763
$476$	−7.92537	−0.363259
$477$	−6.03117	−0.276148
$478$	25.6824	1.17469
$479$	17.7442	0.810751	0.405376	−	0.914150i	$-0.367141\pi$
$479$	17.7442	0.810751	0.405376	+	0.914150i	$0.367141\pi$
$480$	1.95470	0.0892196
$481$	−5.84133	−0.266342
$482$	−7.20409	−0.328137
$483$	7.19879	0.327556
$484$	1.57308	0.0715037
$485$	−1.69939	−0.0771651
$486$	8.80410	0.399362
$487$	−17.7908	−0.806179	−0.403090	−	0.915160i	$-0.632064\pi$
$487$	−17.7908	−0.806179	−0.403090	+	0.915160i	$0.632064\pi$
$488$	−11.9084	−0.539067
$489$	−15.1731	−0.686151
$490$	4.11988	0.186117
$491$	19.2959	0.870812	0.435406	−	0.900234i	$-0.356605\pi$
$491$	19.2959	0.870812	0.435406	+	0.900234i	$0.356605\pi$
$492$	16.0339	0.722863
$493$	−26.5284	−1.19478
$494$	−0.739305	−0.0332629
$495$	3.07318	0.138129
$496$	−3.76380	−0.169000
$497$	13.7430	0.616459
$498$	−11.8521	−0.531105
$499$	−21.7938	−0.975624	−0.487812	−	0.872949i	$-0.662205\pi$
$499$	−21.7938	−0.975624	−0.487812	+	0.872949i	$0.662205\pi$
$500$	8.95301	0.400391
$501$	−30.7794	−1.37512
$502$	−6.11365	−0.272866
$503$	−37.6338	−1.67801	−0.839004	−	0.544125i	$-0.816862\pi$
$503$	−37.6338	−1.67801	−0.839004	+	0.544125i	$0.816862\pi$
$504$	−1.47362	−0.0656404
$505$	3.01103	0.133989
$506$	−7.68034	−0.341433
$507$	22.6625	1.00648
$508$	17.6384	0.782577
$509$	42.6934	1.89235	0.946176	−	0.323651i	$-0.104910\pi$
$509$	42.6934	1.89235	0.946176	+	0.323651i	$0.104910\pi$
$510$	9.17272	0.406175
$511$	−16.2528	−0.718980
$512$	1.00000	0.0441942
$513$	2.54096	0.112186
$514$	−9.26809	−0.408798
$515$	4.11455	0.181309
$516$	−4.82690	−0.212493
$517$	17.2983	0.760776
$518$	−8.09896	−0.355848
$519$	−21.2057	−0.930825
$520$	1.20995	0.0530598
$521$	27.3830	1.19967	0.599836	−	0.800123i	$-0.295233\pi$
$521$	27.3830	1.19967	0.599836	+	0.800123i	$0.295233\pi$
$522$	−4.93263	−0.215895
$523$	−22.7550	−0.995006	−0.497503	−	0.867462i	$-0.665750\pi$
$523$	−22.7550	−0.995006	−0.497503	+	0.867462i	$0.665750\pi$
$524$	2.13681	0.0933469
$525$	−13.3385	−0.582139
$526$	30.0809	1.31159
$527$	−17.6622	−0.769376
$528$	6.97780	0.303670
$529$	−18.3084	−0.796018
$530$	6.86593	0.298237
$531$	3.22963	0.140154
$532$	−1.02504	−0.0444411
$533$	9.92487	0.429894
$534$	−4.52172	−0.195674
$535$	−4.66255	−0.201579
$536$	−4.57983	−0.197818
$537$	29.3280	1.26560
$538$	11.2991	0.487141
$539$	14.7069	0.633473
$540$	−4.15856	−0.178956
$541$	−12.4836	−0.536713	−0.268356	−	0.963320i	$-0.586480\pi$
$541$	−12.4836	−0.536713	−0.268356	+	0.963320i	$0.586480\pi$
$542$	30.4727	1.30892
$543$	28.6871	1.23108
$544$	4.69264	0.201195
$545$	−13.0029	−0.556984
$546$	−4.04841	−0.173256
$547$	−5.28303	−0.225886	−0.112943	−	0.993601i	$-0.536028\pi$
$547$	−5.28303	−0.225886	−0.112943	+	0.993601i	$0.536028\pi$
$548$	0.401501	0.0171513
$549$	−10.3905	−0.443457
$550$	14.2307	0.606800
$551$	−3.43109	−0.146170
$552$	−4.26243	−0.181421
$553$	9.03667	0.384278
$554$	4.83630	0.205475
$555$	9.37364	0.397889
$556$	7.63691	0.323877
$557$	22.6579	0.960045	0.480022	−	0.877256i	$-0.340629\pi$
$557$	22.6579	0.960045	0.480022	+	0.877256i	$0.340629\pi$
$558$	−3.28406	−0.139025
$559$	−2.98783	−0.126372
$560$	1.67759	0.0708910
$561$	32.7443	1.38247
$562$	3.33725	0.140773
$563$	42.3030	1.78286	0.891430	−	0.453158i	$-0.149703\pi$
$563$	42.3030	1.78286	0.891430	+	0.453158i	$0.149703\pi$
$564$	9.60018	0.404240
$565$	−15.0237	−0.632053
$566$	8.10209	0.340556
$567$	18.3351	0.770002
$568$	−8.13730	−0.341434
$569$	−4.49694	−0.188521	−0.0942607	−	0.995548i	$-0.530049\pi$
$569$	−4.49694	−0.188521	−0.0942607	+	0.995548i	$0.530049\pi$
$570$	1.18637	0.0496915
$571$	21.5242	0.900759	0.450380	−	0.892837i	$-0.351289\pi$
$571$	21.5242	0.900759	0.450380	+	0.892837i	$0.351289\pi$
$572$	4.31922	0.180596
$573$	−28.3166	−1.18294
$574$	13.7608	0.574363
$575$	−8.69293	−0.362520
$576$	0.872539	0.0363558
$577$	−19.0100	−0.791395	−0.395697	−	0.918381i	$-0.629497\pi$
$577$	−19.0100	−0.791395	−0.395697	+	0.918381i	$0.629497\pi$
$578$	5.02088	0.208841
$579$	3.04069	0.126367
$580$	5.61535	0.233165
$581$	−10.1718	−0.421999
$582$	−3.36672	−0.139555
$583$	24.5097	1.01509
$584$	9.62333	0.398216
$585$	1.05573	0.0436490
$586$	−32.1263	−1.32713
$587$	13.5477	0.559175	0.279587	−	0.960120i	$-0.409802\pi$
$587$	13.5477	0.559175	0.279587	+	0.960120i	$0.409802\pi$
$588$	8.16205	0.336597
$589$	−2.28436	−0.0941256
$590$	−3.67664	−0.151365
$591$	−5.10519	−0.209999
$592$	4.79543	0.197091
$593$	−23.7860	−0.976774	−0.488387	−	0.872627i	$-0.662414\pi$
$593$	−23.7860	−0.976774	−0.488387	+	0.872627i	$0.662414\pi$
$594$	−14.8450	−0.609098
$595$	7.87231	0.322733
$596$	12.8866	0.527856
$597$	−51.9756	−2.12722
$598$	−2.63842	−0.107893
$599$	−26.2560	−1.07279	−0.536396	−	0.843966i	$-0.680215\pi$
$599$	−26.2560	−1.07279	−0.536396	+	0.843966i	$0.680215\pi$
$600$	7.89777	0.322425
$601$	5.68308	0.231818	0.115909	−	0.993260i	$-0.463022\pi$
$601$	5.68308	0.231818	0.115909	+	0.993260i	$0.463022\pi$
$602$	−4.14260	−0.168840
$603$	−3.99607	−0.162733
$604$	−8.64428	−0.351731
$605$	−1.56255	−0.0635268
$606$	5.96527	0.242323
$607$	0.355091	0.0144127	0.00720634	−	0.999974i	$-0.497706\pi$
$607$	0.355091	0.0144127	0.00720634	+	0.999974i	$0.497706\pi$
$608$	0.606930	0.0246143
$609$	−18.7886	−0.761351
$610$	11.8287	0.478929
$611$	5.94245	0.240406
$612$	4.09451	0.165511
$613$	33.6004	1.35711	0.678554	−	0.734551i	$-0.262607\pi$
$613$	33.6004	1.35711	0.678554	+	0.734551i	$0.262607\pi$
$614$	13.3308	0.537988
$615$	−15.9265	−0.642220
$616$	5.98857	0.241286
$617$	−4.53451	−0.182553	−0.0912763	−	0.995826i	$-0.529095\pi$
$617$	−4.53451	−0.182553	−0.0912763	+	0.995826i	$0.529095\pi$
$618$	8.15149	0.327901
$619$	3.64461	0.146489	0.0732447	−	0.997314i	$-0.476665\pi$
$619$	3.64461	0.146489	0.0732447	+	0.997314i	$0.476665\pi$
$620$	3.73860	0.150146
$621$	9.06816	0.363893
$622$	13.0884	0.524798
$623$	−3.88068	−0.155476
$624$	2.39708	0.0959600
$625$	11.1736	0.446946
$626$	27.1218	1.08400
$627$	4.23504	0.169131
$628$	22.1029	0.882003
$629$	22.5032	0.897262
$630$	1.46376	0.0583175
$631$	−27.1341	−1.08019	−0.540096	−	0.841603i	$-0.681612\pi$
$631$	−27.1341	−1.08019	−0.540096	+	0.841603i	$0.681612\pi$
$632$	−5.35065	−0.212837
$633$	−8.49314	−0.337572
$634$	−9.63065	−0.382482
$635$	−17.5203	−0.695272
$636$	13.6024	0.539369
$637$	5.05226	0.200178
$638$	20.0454	0.793605
$639$	−7.10011	−0.280876
$640$	−0.993306	−0.0392639
$641$	10.0570	0.397228	0.198614	−	0.980078i	$-0.436356\pi$
$641$	10.0570	0.397228	0.198614	+	0.980078i	$0.436356\pi$
$642$	−9.23715	−0.364561
$643$	4.23725	0.167101	0.0835503	−	0.996504i	$-0.473374\pi$
$643$	4.23725	0.167101	0.0835503	+	0.996504i	$0.473374\pi$
$644$	−3.65815	−0.144151
$645$	4.79459	0.188787
$646$	2.84811	0.112057
$647$	0.0543706	0.00213753	0.00106876	−	0.999999i	$-0.499660\pi$
$647$	0.0543706	0.00213753	0.00106876	+	0.999999i	$0.499660\pi$
$648$	−10.8563	−0.426475
$649$	−13.1247	−0.515188
$650$	4.88867	0.191749
$651$	−12.5091	−0.490270
$652$	7.71039	0.301962
$653$	21.9656	0.859581	0.429791	−	0.902929i	$-0.358587\pi$
$653$	21.9656	0.859581	0.429791	+	0.902929i	$0.358587\pi$
$654$	−25.7606	−1.00732
$655$	−2.12250	−0.0829331
$656$	−8.14780	−0.318118
$657$	8.39673	0.327587
$658$	8.23917	0.321196
$659$	29.1785	1.13663	0.568317	−	0.822809i	$-0.307595\pi$
$659$	29.1785	1.13663	0.568317	+	0.822809i	$0.307595\pi$
$660$	−6.93109	−0.269792
$661$	−4.00352	−0.155719	−0.0778595	−	0.996964i	$-0.524809\pi$
$661$	−4.00352	−0.155719	−0.0778595	+	0.996964i	$0.524809\pi$
$662$	6.07784	0.236222
$663$	11.2486	0.436861
$664$	6.02278	0.233729
$665$	1.01818	0.0394833
$666$	4.18420	0.162134
$667$	−12.2448	−0.474122
$668$	15.6409	0.605166
$669$	32.0506	1.23915
$670$	4.54917	0.175750
$671$	42.2254	1.63009
$672$	3.32353	0.128208
$673$	−3.69395	−0.142391	−0.0711957	−	0.997462i	$-0.522681\pi$
$673$	−3.69395	−0.142391	−0.0711957	+	0.997462i	$0.522681\pi$
$674$	−17.6827	−0.681114
$675$	−16.8022	−0.646717
$676$	−11.5162	−0.442932
$677$	−8.02182	−0.308304	−0.154152	−	0.988047i	$-0.549264\pi$
$677$	−8.02182	−0.308304	−0.154152	+	0.988047i	$0.549264\pi$
$678$	−29.7641	−1.14308
$679$	−2.88942	−0.110886
$680$	−4.66123	−0.178750
$681$	15.5686	0.596589
$682$	13.3459	0.511040
$683$	19.9992	0.765247	0.382623	−	0.923904i	$-0.375021\pi$
$683$	19.9992	0.765247	0.382623	+	0.923904i	$0.375021\pi$
$684$	0.529570	0.0202486
$685$	−0.398814	−0.0152379
$686$	18.8272	0.718825
$687$	53.1611	2.02822
$688$	2.45285	0.0935140
$689$	8.41979	0.320768
$690$	4.23390	0.161182
$691$	6.56077	0.249584	0.124792	−	0.992183i	$-0.460174\pi$
$691$	6.56077	0.249584	0.124792	+	0.992183i	$0.460174\pi$
$692$	10.7759	0.409639
$693$	5.22525	0.198491
$694$	−0.0776439	−0.00294732
$695$	−7.58579	−0.287745
$696$	11.1248	0.421684
$697$	−38.2347	−1.44824
$698$	7.30161	0.276370
$699$	9.57492	0.362157
$700$	6.77811	0.256188
$701$	45.0174	1.70028	0.850142	−	0.526554i	$-0.176516\pi$
$701$	45.0174	1.70028	0.850142	+	0.526554i	$0.176516\pi$
$702$	−5.09969	−0.192476
$703$	2.91049	0.109771
$704$	−3.54585	−0.133639
$705$	−9.53591	−0.359143
$706$	−3.77807	−0.142190
$707$	5.11958	0.192542
$708$	−7.28393	−0.273747
$709$	−1.05379	−0.0395759	−0.0197879	−	0.999804i	$-0.506299\pi$
$709$	−1.05379	−0.0395759	−0.0197879	+	0.999804i	$0.506299\pi$
$710$	8.08283	0.303343
$711$	−4.66865	−0.175088
$712$	2.29777	0.0861125
$713$	−8.15241	−0.305310
$714$	15.5961	0.583671
$715$	−4.29031	−0.160448
$716$	−14.9034	−0.556965
$717$	−50.5398	−1.88744
$718$	15.0929	0.563262
$719$	−36.1890	−1.34962	−0.674810	−	0.737991i	$-0.735775\pi$
$719$	−36.1890	−1.34962	−0.674810	+	0.737991i	$0.735775\pi$
$720$	−0.866697	−0.0322999
$721$	6.99586	0.260540
$722$	−18.6316	−0.693398
$723$	14.1768	0.527239
$724$	−14.5777	−0.541775
$725$	22.6882	0.842619
$726$	−3.09563	−0.114890
$727$	−2.34262	−0.0868831	−0.0434415	−	0.999056i	$-0.513832\pi$
$727$	−2.34262	−0.0868831	−0.0434415	+	0.999056i	$0.513832\pi$
$728$	2.05725	0.0762467
$729$	15.2435	0.564574
$730$	−9.55891	−0.353791
$731$	11.5103	0.425725
$732$	23.4342	0.866154
$733$	16.6331	0.614357	0.307179	−	0.951652i	$-0.400615\pi$
$733$	16.6331	0.614357	0.307179	+	0.951652i	$0.400615\pi$
$734$	4.72482	0.174396
$735$	−8.10741	−0.299046
$736$	2.16601	0.0798400
$737$	16.2394	0.598186
$738$	−7.10927	−0.261696
$739$	30.8282	1.13404	0.567018	−	0.823706i	$-0.308097\pi$
$739$	30.8282	1.13404	0.567018	+	0.823706i	$0.308097\pi$
$740$	−4.76333	−0.175103
$741$	1.45486	0.0534456
$742$	11.6740	0.428565
$743$	20.8917	0.766441	0.383221	−	0.923657i	$-0.374815\pi$
$743$	20.8917	0.766441	0.383221	+	0.923657i	$0.374815\pi$
$744$	7.40669	0.271542
$745$	−12.8003	−0.468968
$746$	17.5822	0.643731
$747$	5.25511	0.192274
$748$	−16.6394	−0.608397
$749$	−7.92761	−0.289668
$750$	−17.6184	−0.643333
$751$	8.12013	0.296308	0.148154	−	0.988964i	$-0.452667\pi$
$751$	8.12013	0.296308	0.148154	+	0.988964i	$0.452667\pi$
$752$	−4.87844	−0.177899
$753$	12.0309	0.438431
$754$	6.88618	0.250780
$755$	8.58641	0.312491
$756$	−7.07069	−0.257158
$757$	−37.9713	−1.38009	−0.690045	−	0.723766i	$-0.742409\pi$
$757$	−37.9713	−1.38009	−0.690045	+	0.723766i	$0.742409\pi$
$758$	28.5126	1.03563
$759$	15.1140	0.548602
$760$	−0.602867	−0.0218683
$761$	−10.6189	−0.384935	−0.192467	−	0.981303i	$-0.561649\pi$
$761$	−10.6189	−0.384935	−0.192467	+	0.981303i	$0.561649\pi$
$762$	−34.7102	−1.25742
$763$	−22.1085	−0.800383
$764$	14.3894	0.520591
$765$	−4.06710	−0.147046
$766$	−27.9762	−1.01082
$767$	−4.50871	−0.162800
$768$	−1.96788	−0.0710096
$769$	−26.3741	−0.951075	−0.475538	−	0.879695i	$-0.657746\pi$
$769$	−26.3741	−0.951075	−0.475538	+	0.879695i	$0.657746\pi$
$770$	−5.94848	−0.214368
$771$	18.2385	0.656842
$772$	−1.54516	−0.0556115
$773$	2.41925	0.0870144	0.0435072	−	0.999053i	$-0.486147\pi$
$773$	2.41925	0.0870144	0.0435072	+	0.999053i	$0.486147\pi$
$774$	2.14021	0.0769281
$775$	15.1054	0.542603
$776$	1.71084	0.0614155
$777$	15.9378	0.571764
$778$	−14.4478	−0.517977
$779$	−4.94515	−0.177178
$780$	−2.38103	−0.0852546
$781$	28.8537	1.03247
$782$	10.1643	0.363474
$783$	−23.6676	−0.845809
$784$	−4.14764	−0.148130
$785$	−21.9550	−0.783606
$786$	−4.20497	−0.149986
$787$	24.5589	0.875430	0.437715	−	0.899114i	$-0.355788\pi$
$787$	24.5589	0.875430	0.437715	+	0.899114i	$0.355788\pi$
$788$	2.59426	0.0924168
$789$	−59.1955	−2.10741
$790$	5.31483	0.189093
$791$	−25.5445	−0.908257
$792$	−3.09389	−0.109937
$793$	14.5057	0.515111
$794$	21.4338	0.760656
$795$	−13.5113	−0.479197
$796$	26.4120	0.936150
$797$	−2.20953	−0.0782656	−0.0391328	−	0.999234i	$-0.512460\pi$
$797$	−2.20953	−0.0782656	−0.0391328	+	0.999234i	$0.512460\pi$
$798$	2.01715	0.0714064
$799$	−22.8928	−0.809888
$800$	−4.01334	−0.141893
$801$	2.00489	0.0708394
$802$	−26.2582	−0.927208
$803$	−34.1229	−1.20417
$804$	9.01253	0.317847
$805$	3.63366	0.128070
$806$	4.58470	0.161489
$807$	−22.2353	−0.782720
$808$	−3.03132	−0.106642
$809$	35.9289	1.26319	0.631597	−	0.775297i	$-0.282400\pi$
$809$	35.9289	1.26319	0.631597	+	0.775297i	$0.282400\pi$
$810$	10.7836	0.378898
$811$	−46.7612	−1.64201	−0.821004	−	0.570923i	$-0.806585\pi$
$811$	−46.7612	−1.64201	−0.821004	+	0.570923i	$0.806585\pi$
$812$	9.54763	0.335056
$813$	−59.9666	−2.10312
$814$	−17.0039	−0.595986
$815$	−7.65877	−0.268275
$816$	−9.23454	−0.323273
$817$	1.48871	0.0520833
$818$	4.20000	0.146849
$819$	1.79503	0.0627233
$820$	8.09326	0.282629
$821$	0.583956	0.0203802	0.0101901	−	0.999948i	$-0.496756\pi$
$821$	0.583956	0.0203802	0.0101901	+	0.999948i	$0.496756\pi$
$822$	−0.790105	−0.0275581
$823$	−51.5209	−1.79591	−0.897953	−	0.440091i	$-0.854946\pi$
$823$	−51.5209	−1.79591	−0.897953	+	0.440091i	$0.854946\pi$
$824$	−4.14228	−0.144303
$825$	−28.0043	−0.974985
$826$	−6.25129	−0.217510
$827$	21.9167	0.762120	0.381060	−	0.924550i	$-0.375559\pi$
$827$	21.9167	0.762120	0.381060	+	0.924550i	$0.375559\pi$
$828$	1.88992	0.0656794
$829$	26.3670	0.915763	0.457881	−	0.889013i	$-0.348608\pi$
$829$	26.3670	0.915763	0.457881	+	0.889013i	$0.348608\pi$
$830$	−5.98246	−0.207654
$831$	−9.51725	−0.330150
$832$	−1.21810	−0.0422302
$833$	−19.4634	−0.674367
$834$	−15.0285	−0.520395
$835$	−15.5362	−0.537653
$836$	−2.15209	−0.0744315
$837$	−15.7575	−0.544657
$838$	25.5391	0.882235
$839$	33.0608	1.14138	0.570692	−	0.821164i	$-0.306675\pi$
$839$	33.0608	1.14138	0.570692	+	0.821164i	$0.306675\pi$
$840$	−3.30128	−0.113905
$841$	2.95858	0.102020
$842$	23.9694	0.826039
$843$	−6.56729	−0.226190
$844$	4.31589	0.148559
$845$	11.4391	0.393518
$846$	−4.25663	−0.146346
$847$	−2.65677	−0.0912876
$848$	−6.91221	−0.237366
$849$	−15.9439	−0.547194
$850$	−18.8332	−0.645973
$851$	10.3869	0.356059
$852$	16.0132	0.548604
$853$	1.33778	0.0458047	0.0229023	−	0.999738i	$-0.492709\pi$
$853$	1.33778	0.0458047	0.0229023	+	0.999738i	$0.492709\pi$
$854$	20.1120	0.688218
$855$	−0.526025	−0.0179897
$856$	4.69397	0.160437
$857$	−47.6222	−1.62674	−0.813372	−	0.581745i	$-0.802370\pi$
$857$	−47.6222	−1.62674	−0.813372	+	0.581745i	$0.802370\pi$
$858$	−8.49969	−0.290175
$859$	6.56130	0.223869	0.111934	−	0.993716i	$-0.464295\pi$
$859$	6.56130	0.223869	0.111934	+	0.993716i	$0.464295\pi$
$860$	−2.43643	−0.0830815
$861$	−27.0795	−0.922866
$862$	10.1946	0.347228
$863$	15.2500	0.519115	0.259557	−	0.965728i	$-0.416423\pi$
$863$	15.2500	0.519115	0.259557	+	0.965728i	$0.416423\pi$
$864$	4.18658	0.142430
$865$	−10.7038	−0.363939
$866$	−36.1016	−1.22678
$867$	−9.88047	−0.335558
$868$	6.35665	0.215759
$869$	18.9726	0.643602
$870$	−11.0503	−0.374641
$871$	5.57871	0.189027
$872$	13.0906	0.443302
$873$	1.49277	0.0505227
$874$	1.31461	0.0444675
$875$	−15.1207	−0.511172
$876$	−18.9375	−0.639840
$877$	34.5283	1.16594	0.582968	−	0.812495i	$-0.301891\pi$
$877$	34.5283	1.16594	0.582968	+	0.812495i	$0.301891\pi$
$878$	−18.3502	−0.619290
$879$	63.2206	2.13238
$880$	3.52212	0.118731
$881$	−15.0410	−0.506745	−0.253373	−	0.967369i	$-0.581540\pi$
$881$	−15.0410	−0.506745	−0.253373	+	0.967369i	$0.581540\pi$
$882$	−3.61898	−0.121857
$883$	38.7460	1.30391	0.651953	−	0.758259i	$-0.273950\pi$
$883$	38.7460	1.30391	0.651953	+	0.758259i	$0.273950\pi$
$884$	−5.71613	−0.192254
$885$	7.23516	0.243207
$886$	−29.5151	−0.991580
$887$	3.71298	0.124670	0.0623348	−	0.998055i	$-0.480145\pi$
$887$	3.71298	0.124670	0.0623348	+	0.998055i	$0.480145\pi$
$888$	−9.43681	−0.316679
$889$	−29.7893	−0.999102
$890$	−2.28239	−0.0765058
$891$	38.4948	1.28963
$892$	−16.2869	−0.545325
$893$	−2.96088	−0.0990819
$894$	−25.3592	−0.848140
$895$	14.8036	0.494830
$896$	−1.68889	−0.0564219
$897$	5.19209	0.173359
$898$	−20.1318	−0.671806
$899$	21.2775	0.709644
$900$	−3.50180	−0.116727
$901$	−32.4365	−1.08062
$902$	28.8909	0.961962
$903$	8.15212	0.271286
$904$	15.1250	0.503050
$905$	14.4801	0.481335
$906$	17.0109	0.565148
$907$	−33.4164	−1.10957	−0.554786	−	0.831993i	$-0.687200\pi$
$907$	−33.4164	−1.10957	−0.554786	+	0.831993i	$0.687200\pi$
$908$	−7.91135	−0.262547
$909$	−2.64495	−0.0877273
$910$	−2.04348	−0.0677406
$911$	−5.90849	−0.195757	−0.0978785	−	0.995198i	$-0.531206\pi$
$911$	−5.90849	−0.195757	−0.0978785	+	0.995198i	$0.531206\pi$
$912$	−1.19436	−0.0395493
$913$	−21.3559	−0.706777
$914$	21.2865	0.704095
$915$	−23.2774	−0.769525
$916$	−27.0144	−0.892582
$917$	−3.60884	−0.119174
$918$	19.6461	0.648419
$919$	−45.2539	−1.49279	−0.746395	−	0.665503i	$-0.768217\pi$
$919$	−45.2539	−1.49279	−0.746395	+	0.665503i	$0.768217\pi$
$920$	−2.15151	−0.0709331
$921$	−26.2334	−0.864421
$922$	−4.04525	−0.133223
$923$	9.91209	0.326260
$924$	−11.7848	−0.387690
$925$	−19.2457	−0.632795
$926$	16.0637	0.527886
$927$	−3.61430	−0.118709
$928$	−5.65319	−0.185575
$929$	−51.5223	−1.69039	−0.845196	−	0.534456i	$-0.820516\pi$
$929$	−51.5223	−1.69039	−0.845196	+	0.534456i	$0.820516\pi$
$930$	−7.35711	−0.241249
$931$	−2.51733	−0.0825022
$932$	−4.86561	−0.159378
$933$	−25.7564	−0.843227
$934$	−2.26706	−0.0741805
$935$	16.5280	0.540524
$936$	−1.06284	−0.0347401
$937$	19.9653	0.652237	0.326119	−	0.945329i	$-0.394259\pi$
$937$	19.9653	0.652237	0.326119	+	0.945329i	$0.394259\pi$
$938$	7.73483	0.252551
$939$	−53.3723	−1.74174
$940$	4.84579	0.158052
$941$	−5.65286	−0.184278	−0.0921390	−	0.995746i	$-0.529370\pi$
$941$	−5.65286	−0.184278	−0.0921390	+	0.995746i	$0.529370\pi$
$942$	−43.4958	−1.41717
$943$	−17.6482	−0.574704
$944$	3.70141	0.120471
$945$	7.02335	0.228470
$946$	−8.69744	−0.282778
$947$	1.71251	0.0556492	0.0278246	−	0.999613i	$-0.491142\pi$
$947$	1.71251	0.0556492	0.0278246	+	0.999613i	$0.491142\pi$
$948$	10.5294	0.341980
$949$	−11.7222	−0.380519
$950$	−2.43582	−0.0790284
$951$	18.9519	0.614558
$952$	−7.92537	−0.256863
$953$	40.0927	1.29873	0.649365	−	0.760477i	$-0.275035\pi$
$953$	40.0927	1.29873	0.649365	+	0.760477i	$0.275035\pi$
$954$	−6.03117	−0.195266
$955$	−14.2931	−0.462514
$956$	25.6824	0.830628
$957$	−39.4469	−1.27514
$958$	17.7442	0.573288
$959$	−0.678093	−0.0218968
$960$	1.95470	0.0630878
$961$	−16.8338	−0.543026
$962$	−5.84133	−0.188332
$963$	4.09567	0.131981
$964$	−7.20409	−0.232028
$965$	1.53482	0.0494075
$966$	7.19879	0.231617
$967$	48.1530	1.54850	0.774249	−	0.632881i	$-0.218128\pi$
$967$	48.1530	1.54850	0.774249	+	0.632881i	$0.218128\pi$
$968$	1.57308	0.0505608
$969$	−5.60472	−0.180050
$970$	−1.69939	−0.0545640
$971$	3.21630	0.103216	0.0516080	−	0.998667i	$-0.483565\pi$
$971$	3.21630	0.103216	0.0516080	+	0.998667i	$0.483565\pi$
$972$	8.80410	0.282392
$973$	−12.8979	−0.413488
$974$	−17.7908	−0.570055
$975$	−9.62030	−0.308096
$976$	−11.9084	−0.381178
$977$	57.0437	1.82499	0.912494	−	0.409089i	$-0.134154\pi$
$977$	57.0437	1.82499	0.912494	+	0.409089i	$0.134154\pi$
$978$	−15.1731	−0.485182
$979$	−8.14755	−0.260397
$980$	4.11988	0.131605
$981$	11.4220	0.364677
$982$	19.2959	0.615757
$983$	−30.3654	−0.968507	−0.484253	−	0.874928i	$-0.660909\pi$
$983$	−30.3654	−0.968507	−0.484253	+	0.874928i	$0.660909\pi$
$984$	16.0339	0.511141
$985$	−2.57690	−0.0821068
$986$	−26.5284	−0.844836
$987$	−16.2137	−0.516087
$988$	−0.739305	−0.0235204
$989$	5.31288	0.168940
$990$	3.07318	0.0976722
$991$	35.6623	1.13285	0.566425	−	0.824113i	$-0.308326\pi$
$991$	35.6623	1.13285	0.566425	+	0.824113i	$0.308326\pi$
$992$	−3.76380	−0.119501
$993$	−11.9604	−0.379553
$994$	13.7430	0.435902
$995$	−26.2352	−0.831713
$996$	−11.8521	−0.375548
$997$	−43.7329	−1.38503	−0.692517	−	0.721402i	$-0.743498\pi$
$997$	−43.7329	−1.38503	−0.692517	+	0.721402i	$0.743498\pi$
$998$	−21.7938	−0.689871
$999$	20.0765	0.635191

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.d.1.17	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.d.1.17	✓	88	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.96788 q^{3} +1.00000 q^{4} -0.993306 q^{5} -1.96788 q^{6} -1.68889 q^{7} +1.00000 q^{8} +0.872539 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.96788 q^{3} +1.00000 q^{4} -0.993306 q^{5} -1.96788 q^{6} -1.68889 q^{7} +1.00000 q^{8} +0.872539 q^{9} -0.993306 q^{10} -3.54585 q^{11} -1.96788 q^{12} -1.21810 q^{13} -1.68889 q^{14} +1.95470 q^{15} +1.00000 q^{16} +4.69264 q^{17} +0.872539 q^{18} +0.606930 q^{19} -0.993306 q^{20} +3.32353 q^{21} -3.54585 q^{22} +2.16601 q^{23} -1.96788 q^{24} -4.01334 q^{25} -1.21810 q^{26} +4.18658 q^{27} -1.68889 q^{28} -5.65319 q^{29} +1.95470 q^{30} -3.76380 q^{31} +1.00000 q^{32} +6.97780 q^{33} +4.69264 q^{34} +1.67759 q^{35} +0.872539 q^{36} +4.79543 q^{37} +0.606930 q^{38} +2.39708 q^{39} -0.993306 q^{40} -8.14780 q^{41} +3.32353 q^{42} +2.45285 q^{43} -3.54585 q^{44} -0.866697 q^{45} +2.16601 q^{46} -4.87844 q^{47} -1.96788 q^{48} -4.14764 q^{49} -4.01334 q^{50} -9.23454 q^{51} -1.21810 q^{52} -6.91221 q^{53} +4.18658 q^{54} +3.52212 q^{55} -1.68889 q^{56} -1.19436 q^{57} -5.65319 q^{58} +3.70141 q^{59} +1.95470 q^{60} -11.9084 q^{61} -3.76380 q^{62} -1.47362 q^{63} +1.00000 q^{64} +1.20995 q^{65} +6.97780 q^{66} -4.57983 q^{67} +4.69264 q^{68} -4.26243 q^{69} +1.67759 q^{70} -8.13730 q^{71} +0.872539 q^{72} +9.62333 q^{73} +4.79543 q^{74} +7.89777 q^{75} +0.606930 q^{76} +5.98857 q^{77} +2.39708 q^{78} -5.35065 q^{79} -0.993306 q^{80} -10.8563 q^{81} -8.14780 q^{82} +6.02278 q^{83} +3.32353 q^{84} -4.66123 q^{85} +2.45285 q^{86} +11.1248 q^{87} -3.54585 q^{88} +2.29777 q^{89} -0.866697 q^{90} +2.05725 q^{91} +2.16601 q^{92} +7.40669 q^{93} -4.87844 q^{94} -0.602867 q^{95} -1.96788 q^{96} +1.71084 q^{97} -4.14764 q^{98} -3.09389 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

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