LMFDB - Embedded newform 8002.2.a.e.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8002,2,Mod(1,8002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8002 = 2 \cdot 4001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8002.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$63.8962916974$
Analytic rank:	$0$
Dimension:	$77$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	8002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.50919 q^{3} +1.00000 q^{4} -3.69214 q^{5} +2.50919 q^{6} -2.32427 q^{7} -1.00000 q^{8} +3.29603 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.50919 q^{3} +1.00000 q^{4} -3.69214 q^{5} +2.50919 q^{6} -2.32427 q^{7} -1.00000 q^{8} +3.29603 q^{9} +3.69214 q^{10} +1.21449 q^{11} -2.50919 q^{12} -1.51284 q^{13} +2.32427 q^{14} +9.26428 q^{15} +1.00000 q^{16} +4.40033 q^{17} -3.29603 q^{18} +1.84008 q^{19} -3.69214 q^{20} +5.83203 q^{21} -1.21449 q^{22} +3.38598 q^{23} +2.50919 q^{24} +8.63189 q^{25} +1.51284 q^{26} -0.742794 q^{27} -2.32427 q^{28} -5.83234 q^{29} -9.26428 q^{30} -3.57673 q^{31} -1.00000 q^{32} -3.04738 q^{33} -4.40033 q^{34} +8.58153 q^{35} +3.29603 q^{36} +1.70011 q^{37} -1.84008 q^{38} +3.79599 q^{39} +3.69214 q^{40} +2.65356 q^{41} -5.83203 q^{42} +7.86167 q^{43} +1.21449 q^{44} -12.1694 q^{45} -3.38598 q^{46} +5.16719 q^{47} -2.50919 q^{48} -1.59777 q^{49} -8.63189 q^{50} -11.0413 q^{51} -1.51284 q^{52} +5.38323 q^{53} +0.742794 q^{54} -4.48406 q^{55} +2.32427 q^{56} -4.61712 q^{57} +5.83234 q^{58} -2.12801 q^{59} +9.26428 q^{60} +10.9496 q^{61} +3.57673 q^{62} -7.66086 q^{63} +1.00000 q^{64} +5.58560 q^{65} +3.04738 q^{66} -11.8691 q^{67} +4.40033 q^{68} -8.49607 q^{69} -8.58153 q^{70} +12.4845 q^{71} -3.29603 q^{72} +13.4429 q^{73} -1.70011 q^{74} -21.6591 q^{75} +1.84008 q^{76} -2.82280 q^{77} -3.79599 q^{78} -7.00049 q^{79} -3.69214 q^{80} -8.02428 q^{81} -2.65356 q^{82} -11.3465 q^{83} +5.83203 q^{84} -16.2466 q^{85} -7.86167 q^{86} +14.6344 q^{87} -1.21449 q^{88} -9.16985 q^{89} +12.1694 q^{90} +3.51624 q^{91} +3.38598 q^{92} +8.97468 q^{93} -5.16719 q^{94} -6.79385 q^{95} +2.50919 q^{96} -2.69458 q^{97} +1.59777 q^{98} +4.00299 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) $ 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.50919	−1.44868	−0.724340	−	0.689442i	$-0.757856\pi$
$3$	−2.50919	−1.44868	−0.724340	+	0.689442i	$0.757856\pi$
$4$	1.00000	0.500000
$5$	−3.69214	−1.65117	−0.825587	−	0.564274i	$-0.809156\pi$
$5$	−3.69214	−1.65117	−0.825587	+	0.564274i	$0.809156\pi$
$6$	2.50919	1.02437
$7$	−2.32427	−0.878491	−0.439246	−	0.898367i	$-0.644754\pi$
$7$	−2.32427	−0.878491	−0.439246	+	0.898367i	$0.644754\pi$
$8$	−1.00000	−0.353553
$9$	3.29603	1.09868
$10$	3.69214	1.16756
$11$	1.21449	0.366182	0.183091	−	0.983096i	$-0.441390\pi$
$11$	1.21449	0.366182	0.183091	+	0.983096i	$0.441390\pi$
$12$	−2.50919	−0.724340
$13$	−1.51284	−0.419585	−0.209793	−	0.977746i	$-0.567279\pi$
$13$	−1.51284	−0.419585	−0.209793	+	0.977746i	$0.567279\pi$
$14$	2.32427	0.621187
$15$	9.26428	2.39203
$16$	1.00000	0.250000
$17$	4.40033	1.06724	0.533618	−	0.845726i	$-0.320832\pi$
$17$	4.40033	1.06724	0.533618	+	0.845726i	$0.320832\pi$
$18$	−3.29603	−0.776882
$19$	1.84008	0.422144	0.211072	−	0.977470i	$-0.432304\pi$
$19$	1.84008	0.422144	0.211072	+	0.977470i	$0.432304\pi$
$20$	−3.69214	−0.825587
$21$	5.83203	1.27265
$22$	−1.21449	−0.258930
$23$	3.38598	0.706026	0.353013	−	0.935618i	$-0.385157\pi$
$23$	3.38598	0.706026	0.353013	+	0.935618i	$0.385157\pi$
$24$	2.50919	0.512186
$25$	8.63189	1.72638
$26$	1.51284	0.296692
$27$	−0.742794	−0.142951
$28$	−2.32427	−0.439246
$29$	−5.83234	−1.08304	−0.541519	−	0.840688i	$-0.682151\pi$
$29$	−5.83234	−1.08304	−0.541519	+	0.840688i	$0.682151\pi$
$30$	−9.26428	−1.69142
$31$	−3.57673	−0.642399	−0.321199	−	0.947012i	$-0.604086\pi$
$31$	−3.57673	−0.642399	−0.321199	+	0.947012i	$0.604086\pi$
$32$	−1.00000	−0.176777
$33$	−3.04738	−0.530481
$34$	−4.40033	−0.754650
$35$	8.58153	1.45054
$36$	3.29603	0.549338
$37$	1.70011	0.279496	0.139748	−	0.990187i	$-0.455371\pi$
$37$	1.70011	0.279496	0.139748	+	0.990187i	$0.455371\pi$
$38$	−1.84008	−0.298501
$39$	3.79599	0.607845
$40$	3.69214	0.583779
$41$	2.65356	0.414416	0.207208	−	0.978297i	$-0.433562\pi$
$41$	2.65356	0.414416	0.207208	+	0.978297i	$0.433562\pi$
$42$	−5.83203	−0.899902
$43$	7.86167	1.19889	0.599447	−	0.800415i	$-0.295387\pi$
$43$	7.86167	1.19889	0.599447	+	0.800415i	$0.295387\pi$
$44$	1.21449	0.183091
$45$	−12.1694	−1.81411
$46$	−3.38598	−0.499236
$47$	5.16719	0.753712	0.376856	−	0.926272i	$-0.377005\pi$
$47$	5.16719	0.753712	0.376856	+	0.926272i	$0.377005\pi$
$48$	−2.50919	−0.362170
$49$	−1.59777	−0.228253
$50$	−8.63189	−1.22073
$51$	−11.0413	−1.54608
$52$	−1.51284	−0.209793
$53$	5.38323	0.739444	0.369722	−	0.929142i	$-0.379453\pi$
$53$	5.38323	0.739444	0.369722	+	0.929142i	$0.379453\pi$
$54$	0.742794	0.101081
$55$	−4.48406	−0.604630
$56$	2.32427	0.310594
$57$	−4.61712	−0.611553
$58$	5.83234	0.765824
$59$	−2.12801	−0.277043	−0.138521	−	0.990359i	$-0.544235\pi$
$59$	−2.12801	−0.277043	−0.138521	+	0.990359i	$0.544235\pi$
$60$	9.26428	1.19601
$61$	10.9496	1.40196	0.700978	−	0.713183i	$-0.252747\pi$
$61$	10.9496	1.40196	0.700978	+	0.713183i	$0.252747\pi$
$62$	3.57673	0.454245
$63$	−7.66086	−0.965178
$64$	1.00000	0.125000
$65$	5.58560	0.692809
$66$	3.04738	0.375106
$67$	−11.8691	−1.45004	−0.725019	−	0.688729i	$-0.758169\pi$
$67$	−11.8691	−1.45004	−0.725019	+	0.688729i	$0.758169\pi$
$68$	4.40033	0.533618
$69$	−8.49607	−1.02281
$70$	−8.58153	−1.02569
$71$	12.4845	1.48164	0.740821	−	0.671702i	$-0.234437\pi$
$71$	12.4845	1.48164	0.740821	+	0.671702i	$0.234437\pi$
$72$	−3.29603	−0.388441
$73$	13.4429	1.57337	0.786684	−	0.617356i	$-0.211796\pi$
$73$	13.4429	1.57337	0.786684	+	0.617356i	$0.211796\pi$
$74$	−1.70011	−0.197633
$75$	−21.6591	−2.50097
$76$	1.84008	0.211072
$77$	−2.82280	−0.321687
$78$	−3.79599	−0.429811
$79$	−7.00049	−0.787617	−0.393808	−	0.919193i	$-0.628843\pi$
$79$	−7.00049	−0.787617	−0.393808	+	0.919193i	$0.628843\pi$
$80$	−3.69214	−0.412794
$81$	−8.02428	−0.891586
$82$	−2.65356	−0.293037
$83$	−11.3465	−1.24544	−0.622722	−	0.782443i	$-0.713973\pi$
$83$	−11.3465	−1.24544	−0.622722	+	0.782443i	$0.713973\pi$
$84$	5.83203	0.636327
$85$	−16.2466	−1.76219
$86$	−7.86167	−0.847746
$87$	14.6344	1.56898
$88$	−1.21449	−0.129465
$89$	−9.16985	−0.972002	−0.486001	−	0.873958i	$-0.661545\pi$
$89$	−9.16985	−0.972002	−0.486001	+	0.873958i	$0.661545\pi$
$90$	12.1694	1.28277
$91$	3.51624	0.368602
$92$	3.38598	0.353013
$93$	8.97468	0.930631
$94$	−5.16719	−0.532955
$95$	−6.79385	−0.697034
$96$	2.50919	0.256093
$97$	−2.69458	−0.273593	−0.136797	−	0.990599i	$-0.543681\pi$
$97$	−2.69458	−0.273593	−0.136797	+	0.990599i	$0.543681\pi$
$98$	1.59777	0.161399
$99$	4.00299	0.402315
$100$	8.63189	0.863189
$101$	13.4685	1.34017	0.670085	−	0.742284i	$-0.266257\pi$
$101$	13.4685	1.34017	0.670085	+	0.742284i	$0.266257\pi$
$102$	11.0413	1.09325
$103$	−0.813326	−0.0801394	−0.0400697	−	0.999197i	$-0.512758\pi$
$103$	−0.813326	−0.0801394	−0.0400697	+	0.999197i	$0.512758\pi$
$104$	1.51284	0.148346
$105$	−21.5327	−2.10137
$106$	−5.38323	−0.522866
$107$	−18.9350	−1.83052	−0.915258	−	0.402869i	$-0.868013\pi$
$107$	−18.9350	−1.83052	−0.915258	+	0.402869i	$0.868013\pi$
$108$	−0.742794	−0.0714754
$109$	−13.0713	−1.25200	−0.626000	−	0.779823i	$-0.715309\pi$
$109$	−13.0713	−1.25200	−0.626000	+	0.779823i	$0.715309\pi$
$110$	4.48406	0.427538
$111$	−4.26589	−0.404900
$112$	−2.32427	−0.219623
$113$	−13.3212	−1.25315	−0.626575	−	0.779361i	$-0.715544\pi$
$113$	−13.3212	−1.25315	−0.626575	+	0.779361i	$0.715544\pi$
$114$	4.61712	0.432433
$115$	−12.5015	−1.16577
$116$	−5.83234	−0.541519
$117$	−4.98635	−0.460988
$118$	2.12801	0.195899
$119$	−10.2275	−0.937557
$120$	−9.26428	−0.845709
$121$	−9.52502	−0.865911
$122$	−10.9496	−0.991332
$123$	−6.65828	−0.600357
$124$	−3.57673	−0.321199
$125$	−13.4095	−1.19938
$126$	7.66086	0.682484
$127$	17.2191	1.52795	0.763974	−	0.645247i	$-0.223245\pi$
$127$	17.2191	1.52795	0.763974	+	0.645247i	$0.223245\pi$
$128$	−1.00000	−0.0883883
$129$	−19.7264	−1.73681
$130$	−5.58560	−0.489890
$131$	−13.0873	−1.14344	−0.571720	−	0.820448i	$-0.693724\pi$
$131$	−13.0873	−1.14344	−0.571720	+	0.820448i	$0.693724\pi$
$132$	−3.04738	−0.265240
$133$	−4.27685	−0.370850
$134$	11.8691	1.02533
$135$	2.74250	0.236037
$136$	−4.40033	−0.377325
$137$	17.1461	1.46489	0.732444	−	0.680827i	$-0.238380\pi$
$137$	17.1461	1.46489	0.732444	+	0.680827i	$0.238380\pi$
$138$	8.49607	0.723233
$139$	−2.52851	−0.214465	−0.107233	−	0.994234i	$-0.534199\pi$
$139$	−2.52851	−0.214465	−0.107233	+	0.994234i	$0.534199\pi$
$140$	8.58153	0.725271
$141$	−12.9655	−1.09189
$142$	−12.4845	−1.04768
$143$	−1.83732	−0.153644
$144$	3.29603	0.274669
$145$	21.5338	1.78829
$146$	−13.4429	−1.11254
$147$	4.00911	0.330666
$148$	1.70011	0.139748
$149$	0.193971	0.0158907	0.00794536	−	0.999968i	$-0.497471\pi$
$149$	0.193971	0.0158907	0.00794536	+	0.999968i	$0.497471\pi$
$150$	21.6591	1.76845
$151$	10.2822	0.836752	0.418376	−	0.908274i	$-0.362599\pi$
$151$	10.2822	0.836752	0.418376	+	0.908274i	$0.362599\pi$
$152$	−1.84008	−0.149251
$153$	14.5036	1.17255
$154$	2.82280	0.227467
$155$	13.2058	1.06071
$156$	3.79599	0.303923
$157$	−21.7896	−1.73900	−0.869499	−	0.493935i	$-0.835558\pi$
$157$	−21.7896	−1.73900	−0.869499	+	0.493935i	$0.835558\pi$
$158$	7.00049	0.556929
$159$	−13.5076	−1.07122
$160$	3.69214	0.291889
$161$	−7.86993	−0.620238
$162$	8.02428	0.630447
$163$	23.9342	1.87467	0.937335	−	0.348429i	$-0.113285\pi$
$163$	23.9342	1.87467	0.937335	+	0.348429i	$0.113285\pi$
$164$	2.65356	0.207208
$165$	11.2513	0.875916
$166$	11.3465	0.880662
$167$	14.6972	1.13731	0.568653	−	0.822578i	$-0.307465\pi$
$167$	14.6972	1.13731	0.568653	+	0.822578i	$0.307465\pi$
$168$	−5.83203	−0.449951
$169$	−10.7113	−0.823948
$170$	16.2466	1.24606
$171$	6.06497	0.463800
$172$	7.86167	0.599447
$173$	10.3244	0.784950	0.392475	−	0.919763i	$-0.371619\pi$
$173$	10.3244	0.784950	0.392475	+	0.919763i	$0.371619\pi$
$174$	−14.6344	−1.10943
$175$	−20.0628	−1.51661
$176$	1.21449	0.0915454
$177$	5.33957	0.401347
$178$	9.16985	0.687309
$179$	−10.2653	−0.767264	−0.383632	−	0.923486i	$-0.625327\pi$
$179$	−10.2653	−0.767264	−0.383632	+	0.923486i	$0.625327\pi$
$180$	−12.1694	−0.907054
$181$	−18.9276	−1.40688	−0.703440	−	0.710755i	$-0.748353\pi$
$181$	−18.9276	−1.40688	−0.703440	+	0.710755i	$0.748353\pi$
$182$	−3.51624	−0.260641
$183$	−27.4747	−2.03099
$184$	−3.38598	−0.249618
$185$	−6.27703	−0.461496
$186$	−8.97468	−0.658056
$187$	5.34414	0.390802
$188$	5.16719	0.376856
$189$	1.72645	0.125581
$190$	6.79385	0.492878
$191$	−10.0968	−0.730575	−0.365288	−	0.930895i	$-0.619029\pi$
$191$	−10.0968	−0.730575	−0.365288	+	0.930895i	$0.619029\pi$
$192$	−2.50919	−0.181085
$193$	−16.9104	−1.21724	−0.608618	−	0.793464i	$-0.708276\pi$
$193$	−16.9104	−1.21724	−0.608618	+	0.793464i	$0.708276\pi$
$194$	2.69458	0.193460
$195$	−14.0153	−1.00366
$196$	−1.59777	−0.114127
$197$	9.98318	0.711272	0.355636	−	0.934625i	$-0.384264\pi$
$197$	9.98318	0.711272	0.355636	+	0.934625i	$0.384264\pi$
$198$	−4.00299	−0.284480
$199$	0.798766	0.0566230	0.0283115	−	0.999599i	$-0.490987\pi$
$199$	0.798766	0.0566230	0.0283115	+	0.999599i	$0.490987\pi$
$200$	−8.63189	−0.610367
$201$	29.7817	2.10064
$202$	−13.4685	−0.947644
$203$	13.5559	0.951440
$204$	−11.0413	−0.773042
$205$	−9.79731	−0.684274
$206$	0.813326	0.0566671
$207$	11.1603	0.775694
$208$	−1.51284	−0.104896
$209$	2.23476	0.154582
$210$	21.5327	1.48590
$211$	−11.4585	−0.788835	−0.394418	−	0.918931i	$-0.629054\pi$
$211$	−11.4585	−0.788835	−0.394418	+	0.918931i	$0.629054\pi$
$212$	5.38323	0.369722
$213$	−31.3261	−2.14643
$214$	18.9350	1.29437
$215$	−29.0264	−1.97958
$216$	0.742794	0.0505407
$217$	8.31328	0.564342
$218$	13.0713	0.885298
$219$	−33.7307	−2.27931
$220$	−4.48406	−0.302315
$221$	−6.65697	−0.447796
$222$	4.26589	0.286308
$223$	−14.8652	−0.995446	−0.497723	−	0.867336i	$-0.665830\pi$
$223$	−14.8652	−0.995446	−0.497723	+	0.867336i	$0.665830\pi$
$224$	2.32427	0.155297
$225$	28.4510	1.89673
$226$	13.3212	0.886111
$227$	16.8836	1.12060	0.560301	−	0.828289i	$-0.310685\pi$
$227$	16.8836	1.12060	0.560301	+	0.828289i	$0.310685\pi$
$228$	−4.61712	−0.305776
$229$	−3.31633	−0.219149	−0.109575	−	0.993979i	$-0.534949\pi$
$229$	−3.31633	−0.219149	−0.109575	+	0.993979i	$0.534949\pi$
$230$	12.5015	0.824325
$231$	7.08293	0.466022
$232$	5.83234	0.382912
$233$	1.41856	0.0929333	0.0464666	−	0.998920i	$-0.485204\pi$
$233$	1.41856	0.0929333	0.0464666	+	0.998920i	$0.485204\pi$
$234$	4.98635	0.325968
$235$	−19.0780	−1.24451
$236$	−2.12801	−0.138521
$237$	17.5656	1.14101
$238$	10.2275	0.662953
$239$	11.5402	0.746472	0.373236	−	0.927736i	$-0.378248\pi$
$239$	11.5402	0.746472	0.373236	+	0.927736i	$0.378248\pi$
$240$	9.26428	0.598006
$241$	28.5779	1.84086	0.920431	−	0.390906i	$-0.127838\pi$
$241$	28.5779	1.84086	0.920431	+	0.390906i	$0.127838\pi$
$242$	9.52502	0.612291
$243$	22.3628	1.43458
$244$	10.9496	0.700978
$245$	5.89920	0.376886
$246$	6.65828	0.424516
$247$	−2.78375	−0.177126
$248$	3.57673	0.227122
$249$	28.4706	1.80425
$250$	13.4095	0.848089
$251$	20.8228	1.31432	0.657161	−	0.753751i	$-0.271757\pi$
$251$	20.8228	1.31432	0.657161	+	0.753751i	$0.271757\pi$
$252$	−7.66086	−0.482589
$253$	4.11223	0.258534
$254$	−17.2191	−1.08042
$255$	40.7658	2.55286
$256$	1.00000	0.0625000
$257$	2.04174	0.127360	0.0636800	−	0.997970i	$-0.479716\pi$
$257$	2.04174	0.127360	0.0636800	+	0.997970i	$0.479716\pi$
$258$	19.7264	1.22811
$259$	−3.95150	−0.245534
$260$	5.58560	0.346404
$261$	−19.2236	−1.18991
$262$	13.0873	0.808535
$263$	−18.5902	−1.14632	−0.573160	−	0.819444i	$-0.694282\pi$
$263$	−18.5902	−1.14632	−0.573160	+	0.819444i	$0.694282\pi$
$264$	3.04738	0.187553
$265$	−19.8756	−1.22095
$266$	4.27685	0.262231
$267$	23.0089	1.40812
$268$	−11.8691	−0.725019
$269$	23.3760	1.42526	0.712630	−	0.701541i	$-0.247504\pi$
$269$	23.3760	1.42526	0.712630	+	0.701541i	$0.247504\pi$
$270$	−2.74250	−0.166903
$271$	10.1022	0.613667	0.306833	−	0.951763i	$-0.400731\pi$
$271$	10.1022	0.613667	0.306833	+	0.951763i	$0.400731\pi$
$272$	4.40033	0.266809
$273$	−8.82291	−0.533987
$274$	−17.1461	−1.03583
$275$	10.4833	0.632168
$276$	−8.49607	−0.511403
$277$	−8.80553	−0.529073	−0.264537	−	0.964376i	$-0.585219\pi$
$277$	−8.80553	−0.529073	−0.264537	+	0.964376i	$0.585219\pi$
$278$	2.52851	0.151650
$279$	−11.7890	−0.705789
$280$	−8.58153	−0.512844
$281$	−18.6722	−1.11389	−0.556946	−	0.830549i	$-0.688027\pi$
$281$	−18.6722	−1.11389	−0.556946	+	0.830549i	$0.688027\pi$
$282$	12.9655	0.772082
$283$	−3.53530	−0.210152	−0.105076	−	0.994464i	$-0.533509\pi$
$283$	−3.53530	−0.210152	−0.105076	+	0.994464i	$0.533509\pi$
$284$	12.4845	0.740821
$285$	17.0471	1.00978
$286$	1.83732	0.108643
$287$	−6.16759	−0.364061
$288$	−3.29603	−0.194220
$289$	2.36287	0.138992
$290$	−21.5338	−1.26451
$291$	6.76121	0.396349
$292$	13.4429	0.786684
$293$	11.0927	0.648045	0.324022	−	0.946049i	$-0.394965\pi$
$293$	11.0927	0.648045	0.324022	+	0.946049i	$0.394965\pi$
$294$	−4.00911	−0.233816
$295$	7.85690	0.457446
$296$	−1.70011	−0.0988166
$297$	−0.902114	−0.0523459
$298$	−0.193971	−0.0112364
$299$	−5.12243	−0.296238
$300$	−21.6591	−1.25049
$301$	−18.2726	−1.05322
$302$	−10.2822	−0.591673
$303$	−33.7951	−1.94148
$304$	1.84008	0.105536
$305$	−40.4275	−2.31487
$306$	−14.5036	−0.829116
$307$	−32.3668	−1.84727	−0.923635	−	0.383272i	$-0.874797\pi$
$307$	−32.3668	−1.84727	−0.923635	+	0.383272i	$0.874797\pi$
$308$	−2.82280	−0.160844
$309$	2.04079	0.116096
$310$	−13.2058	−0.750037
$311$	10.2327	0.580242	0.290121	−	0.956990i	$-0.406304\pi$
$311$	10.2327	0.580242	0.290121	+	0.956990i	$0.406304\pi$
$312$	−3.79599	−0.214906
$313$	32.4146	1.83218	0.916090	−	0.400972i	$-0.131328\pi$
$313$	32.4146	1.83218	0.916090	+	0.400972i	$0.131328\pi$
$314$	21.7896	1.22966
$315$	28.2850	1.59368
$316$	−7.00049	−0.393808
$317$	9.14630	0.513708	0.256854	−	0.966450i	$-0.417314\pi$
$317$	9.14630	0.513708	0.256854	+	0.966450i	$0.417314\pi$
$318$	13.5076	0.757466
$319$	−7.08330	−0.396589
$320$	−3.69214	−0.206397
$321$	47.5115	2.65183
$322$	7.86993	0.438574
$323$	8.09697	0.450528
$324$	−8.02428	−0.445793
$325$	−13.0586	−0.724363
$326$	−23.9342	−1.32559
$327$	32.7983	1.81375
$328$	−2.65356	−0.146518
$329$	−12.0099	−0.662129
$330$	−11.2513	−0.619366
$331$	−4.76609	−0.261968	−0.130984	−	0.991384i	$-0.541814\pi$
$331$	−4.76609	−0.261968	−0.130984	+	0.991384i	$0.541814\pi$
$332$	−11.3465	−0.622722
$333$	5.60360	0.307075
$334$	−14.6972	−0.804197
$335$	43.8223	2.39427
$336$	5.83203	0.318163
$337$	−26.6513	−1.45179	−0.725894	−	0.687807i	$-0.758574\pi$
$337$	−26.6513	−1.45179	−0.725894	+	0.687807i	$0.758574\pi$
$338$	10.7113	0.582619
$339$	33.4253	1.81542
$340$	−16.2466	−0.881097
$341$	−4.34389	−0.235235
$342$	−6.06497	−0.327956
$343$	19.9835	1.07901
$344$	−7.86167	−0.423873
$345$	31.3687	1.68883
$346$	−10.3244	−0.555043
$347$	−30.8312	−1.65511	−0.827553	−	0.561387i	$-0.810268\pi$
$347$	−30.8312	−1.65511	−0.827553	+	0.561387i	$0.810268\pi$
$348$	14.6344	0.784489
$349$	−17.0144	−0.910757	−0.455379	−	0.890298i	$-0.650496\pi$
$349$	−17.0144	−0.910757	−0.455379	+	0.890298i	$0.650496\pi$
$350$	20.0628	1.07240
$351$	1.12373	0.0599800
$352$	−1.21449	−0.0647324
$353$	34.0165	1.81051	0.905257	−	0.424864i	$-0.139678\pi$
$353$	34.0165	1.81051	0.905257	+	0.424864i	$0.139678\pi$
$354$	−5.33957	−0.283795
$355$	−46.0947	−2.44645
$356$	−9.16985	−0.486001
$357$	25.6628	1.35822
$358$	10.2653	0.542537
$359$	−10.9451	−0.577659	−0.288830	−	0.957381i	$-0.593266\pi$
$359$	−10.9451	−0.577659	−0.288830	+	0.957381i	$0.593266\pi$
$360$	12.1694	0.641384
$361$	−15.6141	−0.821794
$362$	18.9276	0.994814
$363$	23.9001	1.25443
$364$	3.51624	0.184301
$365$	−49.6329	−2.59791
$366$	27.4747	1.43612
$367$	23.5268	1.22809	0.614043	−	0.789272i	$-0.289542\pi$
$367$	23.5268	1.22809	0.614043	+	0.789272i	$0.289542\pi$
$368$	3.38598	0.176506
$369$	8.74621	0.455309
$370$	6.27703	0.326327
$371$	−12.5121	−0.649595
$372$	8.97468	0.465316
$373$	−8.38561	−0.434191	−0.217095	−	0.976150i	$-0.569658\pi$
$373$	−8.38561	−0.434191	−0.217095	+	0.976150i	$0.569658\pi$
$374$	−5.34414	−0.276339
$375$	33.6469	1.73752
$376$	−5.16719	−0.266477
$377$	8.82337	0.454427
$378$	−1.72645	−0.0887991
$379$	−29.8928	−1.53549	−0.767746	−	0.640754i	$-0.778622\pi$
$379$	−29.8928	−1.53549	−0.767746	+	0.640754i	$0.778622\pi$
$380$	−6.79385	−0.348517
$381$	−43.2060	−2.21351
$382$	10.0968	0.516595
$383$	13.5443	0.692079	0.346039	−	0.938220i	$-0.387526\pi$
$383$	13.5443	0.692079	0.346039	+	0.938220i	$0.387526\pi$
$384$	2.50919	0.128047
$385$	10.4222	0.531162
$386$	16.9104	0.860716
$387$	25.9123	1.31720
$388$	−2.69458	−0.136797
$389$	15.4684	0.784280	0.392140	−	0.919905i	$-0.371735\pi$
$389$	15.4684	0.784280	0.392140	+	0.919905i	$0.371735\pi$
$390$	14.0153	0.709694
$391$	14.8994	0.753496
$392$	1.59777	0.0806997
$393$	32.8385	1.65648
$394$	−9.98318	−0.502945
$395$	25.8468	1.30049
$396$	4.00299	0.201158
$397$	18.6320	0.935113	0.467557	−	0.883963i	$-0.345134\pi$
$397$	18.6320	0.935113	0.467557	+	0.883963i	$0.345134\pi$
$398$	−0.798766	−0.0400385
$399$	10.7314	0.537244
$400$	8.63189	0.431595
$401$	−26.5409	−1.32539	−0.662694	−	0.748891i	$-0.730587\pi$
$401$	−26.5409	−1.32539	−0.662694	+	0.748891i	$0.730587\pi$
$402$	−29.7817	−1.48538
$403$	5.41100	0.269541
$404$	13.4685	0.670085
$405$	29.6268	1.47217
$406$	−13.5559	−0.672769
$407$	2.06476	0.102346
$408$	11.0413	0.546623
$409$	5.83949	0.288744	0.144372	−	0.989523i	$-0.453884\pi$
$409$	5.83949	0.288744	0.144372	+	0.989523i	$0.453884\pi$
$410$	9.79731	0.483855
$411$	−43.0227	−2.12215
$412$	−0.813326	−0.0400697
$413$	4.94606	0.243380
$414$	−11.1603	−0.548498
$415$	41.8930	2.05645
$416$	1.51284	0.0741729
$417$	6.34450	0.310691
$418$	−2.23476	−0.109306
$419$	5.90643	0.288548	0.144274	−	0.989538i	$-0.453915\pi$
$419$	5.90643	0.288548	0.144274	+	0.989538i	$0.453915\pi$
$420$	−21.5327	−1.05069
$421$	−37.1517	−1.81066	−0.905331	−	0.424706i	$-0.860378\pi$
$421$	−37.1517	−1.81066	−0.905331	+	0.424706i	$0.860378\pi$
$422$	11.4585	0.557791
$423$	17.0312	0.828086
$424$	−5.38323	−0.261433
$425$	37.9831	1.84245
$426$	31.3261	1.51775
$427$	−25.4499	−1.23161
$428$	−18.9350	−0.915258
$429$	4.61018	0.222582
$430$	29.0264	1.39978
$431$	−16.1970	−0.780182	−0.390091	−	0.920776i	$-0.627556\pi$
$431$	−16.1970	−0.780182	−0.390091	+	0.920776i	$0.627556\pi$
$432$	−0.742794	−0.0357377
$433$	−41.1029	−1.97528	−0.987640	−	0.156740i	$-0.949901\pi$
$433$	−41.1029	−1.97528	−0.987640	+	0.156740i	$0.949901\pi$
$434$	−8.31328	−0.399050
$435$	−54.0324	−2.59066
$436$	−13.0713	−0.626000
$437$	6.23049	0.298045
$438$	33.7307	1.61171
$439$	16.0877	0.767824	0.383912	−	0.923370i	$-0.374577\pi$
$439$	16.0877	0.767824	0.383912	+	0.923370i	$0.374577\pi$
$440$	4.48406	0.213769
$441$	−5.26630	−0.250776
$442$	6.65697	0.316640
$443$	40.1459	1.90739	0.953696	−	0.300774i	$-0.0972448\pi$
$443$	40.1459	1.90739	0.953696	+	0.300774i	$0.0972448\pi$
$444$	−4.26589	−0.202450
$445$	33.8564	1.60495
$446$	14.8652	0.703887
$447$	−0.486710	−0.0230206
$448$	−2.32427	−0.109811
$449$	18.0300	0.850891	0.425445	−	0.904984i	$-0.360117\pi$
$449$	18.0300	0.850891	0.425445	+	0.904984i	$0.360117\pi$
$450$	−28.4510	−1.34119
$451$	3.22271	0.151752
$452$	−13.3212	−0.626575
$453$	−25.7999	−1.21219
$454$	−16.8836	−0.792385
$455$	−12.9824	−0.608626
$456$	4.61712	0.216216
$457$	−19.4355	−0.909153	−0.454577	−	0.890708i	$-0.650209\pi$
$457$	−19.4355	−0.909153	−0.454577	+	0.890708i	$0.650209\pi$
$458$	3.31633	0.154962
$459$	−3.26853	−0.152562
$460$	−12.5015	−0.582886
$461$	−1.89912	−0.0884509	−0.0442254	−	0.999022i	$-0.514082\pi$
$461$	−1.89912	−0.0884509	−0.0442254	+	0.999022i	$0.514082\pi$
$462$	−7.08293	−0.329528
$463$	30.4165	1.41357	0.706787	−	0.707426i	$-0.250144\pi$
$463$	30.4165	1.41357	0.706787	+	0.707426i	$0.250144\pi$
$464$	−5.83234	−0.270760
$465$	−33.1358	−1.53663
$466$	−1.41856	−0.0657137
$467$	−7.01036	−0.324401	−0.162200	−	0.986758i	$-0.551859\pi$
$467$	−7.01036	−0.324401	−0.162200	+	0.986758i	$0.551859\pi$
$468$	−4.98635	−0.230494
$469$	27.5869	1.27385
$470$	19.0780	0.880002
$471$	54.6742	2.51925
$472$	2.12801	0.0979495
$473$	9.54790	0.439013
$474$	−17.5656	−0.806813
$475$	15.8834	0.728781
$476$	−10.2275	−0.468779
$477$	17.7433	0.812410
$478$	−11.5402	−0.527836
$479$	17.6789	0.807768	0.403884	−	0.914810i	$-0.367660\pi$
$479$	17.6789	0.807768	0.403884	+	0.914810i	$0.367660\pi$
$480$	−9.26428	−0.422854
$481$	−2.57198	−0.117272
$482$	−28.5779	−1.30169
$483$	19.7471	0.898526
$484$	−9.52502	−0.432955
$485$	9.94877	0.451750
$486$	−22.3628	−1.01440
$487$	36.8933	1.67179	0.835897	−	0.548887i	$-0.184948\pi$
$487$	36.8933	1.67179	0.835897	+	0.548887i	$0.184948\pi$
$488$	−10.9496	−0.495666
$489$	−60.0554	−2.71580
$490$	−5.89920	−0.266499
$491$	37.1460	1.67637	0.838187	−	0.545382i	$-0.183616\pi$
$491$	37.1460	1.67637	0.838187	+	0.545382i	$0.183616\pi$
$492$	−6.65828	−0.300178
$493$	−25.6642	−1.15586
$494$	2.78375	0.125247
$495$	−14.7796	−0.664293
$496$	−3.57673	−0.160600
$497$	−29.0174	−1.30161
$498$	−28.4706	−1.27580
$499$	20.1331	0.901280	0.450640	−	0.892706i	$-0.351196\pi$
$499$	20.1331	0.901280	0.450640	+	0.892706i	$0.351196\pi$
$500$	−13.4095	−0.599689
$501$	−36.8781	−1.64759
$502$	−20.8228	−0.929366
$503$	22.9342	1.02258	0.511292	−	0.859407i	$-0.329167\pi$
$503$	22.9342	1.02258	0.511292	+	0.859407i	$0.329167\pi$
$504$	7.66086	0.341242
$505$	−49.7278	−2.21286
$506$	−4.11223	−0.182811
$507$	26.8767	1.19364
$508$	17.2191	0.763974
$509$	−3.08340	−0.136669	−0.0683347	−	0.997662i	$-0.521769\pi$
$509$	−3.08340	−0.136669	−0.0683347	+	0.997662i	$0.521769\pi$
$510$	−40.7658	−1.80514
$511$	−31.2448	−1.38219
$512$	−1.00000	−0.0441942
$513$	−1.36680	−0.0603458
$514$	−2.04174	−0.0900572
$515$	3.00291	0.132324
$516$	−19.7264	−0.868407
$517$	6.27549	0.275996
$518$	3.95150	0.173619
$519$	−25.9059	−1.13714
$520$	−5.58560	−0.244945
$521$	−24.6477	−1.07983	−0.539917	−	0.841718i	$-0.681544\pi$
$521$	−24.6477	−1.07983	−0.539917	+	0.841718i	$0.681544\pi$
$522$	19.2236	0.841393
$523$	21.9461	0.959634	0.479817	−	0.877369i	$-0.340703\pi$
$523$	21.9461	0.959634	0.479817	+	0.877369i	$0.340703\pi$
$524$	−13.0873	−0.571720
$525$	50.3415	2.19708
$526$	18.5902	0.810570
$527$	−15.7388	−0.685591
$528$	−3.04738	−0.132620
$529$	−11.5351	−0.501527
$530$	19.8756	0.863343
$531$	−7.01397	−0.304381
$532$	−4.27685	−0.185425
$533$	−4.01440	−0.173883
$534$	−23.0089	−0.995692
$535$	69.9107	3.02250
$536$	11.8691	0.512666
$537$	25.7576	1.11152
$538$	−23.3760	−1.00781
$539$	−1.94047	−0.0835821
$540$	2.74250	0.118018
$541$	23.4737	1.00921	0.504607	−	0.863349i	$-0.331637\pi$
$541$	23.4737	1.00921	0.504607	+	0.863349i	$0.331637\pi$
$542$	−10.1022	−0.433928
$543$	47.4930	2.03812
$544$	−4.40033	−0.188662
$545$	48.2610	2.06727
$546$	8.82291	0.377586
$547$	2.91554	0.124659	0.0623297	−	0.998056i	$-0.480147\pi$
$547$	2.91554	0.124659	0.0623297	+	0.998056i	$0.480147\pi$
$548$	17.1461	0.732444
$549$	36.0903	1.54030
$550$	−10.4833	−0.447011
$551$	−10.7320	−0.457199
$552$	8.49607	0.361617
$553$	16.2710	0.691914
$554$	8.80553	0.374111
$555$	15.7502	0.668561
$556$	−2.52851	−0.107233
$557$	−25.0893	−1.06307	−0.531534	−	0.847037i	$-0.678384\pi$
$557$	−25.0893	−1.06307	−0.531534	+	0.847037i	$0.678384\pi$
$558$	11.7890	0.499068
$559$	−11.8934	−0.503038
$560$	8.58153	0.362636
$561$	−13.4095	−0.566148
$562$	18.6722	0.787641
$563$	−3.78344	−0.159453	−0.0797264	−	0.996817i	$-0.525405\pi$
$563$	−3.78344	−0.159453	−0.0797264	+	0.996817i	$0.525405\pi$
$564$	−12.9655	−0.545944
$565$	49.1836	2.06917
$566$	3.53530	0.148600
$567$	18.6506	0.783251
$568$	−12.4845	−0.523840
$569$	−13.5832	−0.569439	−0.284719	−	0.958611i	$-0.591900\pi$
$569$	−13.5832	−0.569439	−0.284719	+	0.958611i	$0.591900\pi$
$570$	−17.0471	−0.714022
$571$	11.9627	0.500625	0.250312	−	0.968165i	$-0.419467\pi$
$571$	11.9627	0.500625	0.250312	+	0.968165i	$0.419467\pi$
$572$	−1.83732	−0.0768222
$573$	25.3347	1.05837
$574$	6.16759	0.257430
$575$	29.2274	1.21887
$576$	3.29603	0.137335
$577$	−17.9893	−0.748903	−0.374451	−	0.927247i	$-0.622169\pi$
$577$	−17.9893	−0.748903	−0.374451	+	0.927247i	$0.622169\pi$
$578$	−2.36287	−0.0982825
$579$	42.4313	1.76339
$580$	21.5338	0.894143
$581$	26.3724	1.09411
$582$	−6.76121	−0.280261
$583$	6.53787	0.270771
$584$	−13.4429	−0.556270
$585$	18.4103	0.761172
$586$	−11.0927	−0.458237
$587$	−20.2323	−0.835076	−0.417538	−	0.908659i	$-0.637107\pi$
$587$	−20.2323	−0.835076	−0.417538	+	0.908659i	$0.637107\pi$
$588$	4.00911	0.165333
$589$	−6.58148	−0.271185
$590$	−7.85690	−0.323463
$591$	−25.0497	−1.03041
$592$	1.70011	0.0698739
$593$	2.05939	0.0845690	0.0422845	−	0.999106i	$-0.486536\pi$
$593$	2.05939	0.0845690	0.0422845	+	0.999106i	$0.486536\pi$
$594$	0.902114	0.0370142
$595$	37.7615	1.54807
$596$	0.193971	0.00794536
$597$	−2.00426	−0.0820287
$598$	5.12243	0.209472
$599$	0.292320	0.0119439	0.00597194	−	0.999982i	$-0.498099\pi$
$599$	0.292320	0.0119439	0.00597194	+	0.999982i	$0.498099\pi$
$600$	21.6591	0.884227
$601$	36.6086	1.49330	0.746648	−	0.665220i	$-0.231662\pi$
$601$	36.6086	1.49330	0.746648	+	0.665220i	$0.231662\pi$
$602$	18.2726	0.744737
$603$	−39.1208	−1.59312
$604$	10.2822	0.418376
$605$	35.1677	1.42977
$606$	33.7951	1.37283
$607$	−10.7173	−0.435003	−0.217501	−	0.976060i	$-0.569791\pi$
$607$	−10.7173	−0.435003	−0.217501	+	0.976060i	$0.569791\pi$
$608$	−1.84008	−0.0746253
$609$	−34.0144	−1.37833
$610$	40.4275	1.63686
$611$	−7.81711	−0.316246
$612$	14.5036	0.586273
$613$	−20.3254	−0.820935	−0.410467	−	0.911875i	$-0.634634\pi$
$613$	−20.3254	−0.820935	−0.410467	+	0.911875i	$0.634634\pi$
$614$	32.3668	1.30622
$615$	24.5833	0.991294
$616$	2.82280	0.113734
$617$	37.4009	1.50570	0.752851	−	0.658191i	$-0.228678\pi$
$617$	37.4009	1.50570	0.752851	+	0.658191i	$0.228678\pi$
$618$	−2.04079	−0.0820926
$619$	−36.2608	−1.45744	−0.728722	−	0.684809i	$-0.759885\pi$
$619$	−36.2608	−1.45744	−0.728722	+	0.684809i	$0.759885\pi$
$620$	13.2058	0.530357
$621$	−2.51509	−0.100927
$622$	−10.2327	−0.410293
$623$	21.3132	0.853895
$624$	3.79599	0.151961
$625$	6.35012	0.254005
$626$	−32.4146	−1.29555
$627$	−5.60744	−0.223939
$628$	−21.7896	−0.869499
$629$	7.48102	0.298288
$630$	−28.2850	−1.12690
$631$	−4.28808	−0.170706	−0.0853529	−	0.996351i	$-0.527202\pi$
$631$	−4.28808	−0.170706	−0.0853529	+	0.996351i	$0.527202\pi$
$632$	7.00049	0.278465
$633$	28.7515	1.14277
$634$	−9.14630	−0.363246
$635$	−63.5753	−2.52291
$636$	−13.5076	−0.535609
$637$	2.41717	0.0957716
$638$	7.08330	0.280431
$639$	41.1494	1.62785
$640$	3.69214	0.145945
$641$	−4.37018	−0.172612	−0.0863059	−	0.996269i	$-0.527506\pi$
$641$	−4.37018	−0.172612	−0.0863059	+	0.996269i	$0.527506\pi$
$642$	−47.5115	−1.87513
$643$	−11.1269	−0.438801	−0.219401	−	0.975635i	$-0.570410\pi$
$643$	−11.1269	−0.438801	−0.219401	+	0.975635i	$0.570410\pi$
$644$	−7.86993	−0.310119
$645$	72.8327	2.86778
$646$	−8.09697	−0.318571
$647$	−3.41131	−0.134112	−0.0670562	−	0.997749i	$-0.521361\pi$
$647$	−3.41131	−0.134112	−0.0670562	+	0.997749i	$0.521361\pi$
$648$	8.02428	0.315223
$649$	−2.58444	−0.101448
$650$	13.0586	0.512202
$651$	−20.8596	−0.817551
$652$	23.9342	0.937335
$653$	34.1849	1.33776	0.668880	−	0.743370i	$-0.266774\pi$
$653$	34.1849	1.33776	0.668880	+	0.743370i	$0.266774\pi$
$654$	−32.7983	−1.28251
$655$	48.3201	1.88802
$656$	2.65356	0.103604
$657$	44.3081	1.72862
$658$	12.0099	0.468196
$659$	38.2622	1.49048	0.745241	−	0.666795i	$-0.232334\pi$
$659$	38.2622	1.49048	0.745241	+	0.666795i	$0.232334\pi$
$660$	11.2513	0.437958
$661$	11.0529	0.429909	0.214954	−	0.976624i	$-0.431040\pi$
$661$	11.0529	0.429909	0.214954	+	0.976624i	$0.431040\pi$
$662$	4.76609	0.185239
$663$	16.7036	0.648714
$664$	11.3465	0.440331
$665$	15.7907	0.612339
$666$	−5.60360	−0.217135
$667$	−19.7482	−0.764653
$668$	14.6972	0.568653
$669$	37.2995	1.44208
$670$	−43.8223	−1.69300
$671$	13.2982	0.513371
$672$	−5.83203	−0.224975
$673$	−29.2303	−1.12675	−0.563373	−	0.826203i	$-0.690497\pi$
$673$	−29.2303	−1.12675	−0.563373	+	0.826203i	$0.690497\pi$
$674$	26.6513	1.02657
$675$	−6.41172	−0.246787
$676$	−10.7113	−0.411974
$677$	−0.910983	−0.0350119	−0.0175060	−	0.999847i	$-0.505573\pi$
$677$	−0.910983	−0.0350119	−0.0175060	+	0.999847i	$0.505573\pi$
$678$	−33.4253	−1.28369
$679$	6.26293	0.240349
$680$	16.2466	0.623029
$681$	−42.3641	−1.62339
$682$	4.34389	0.166336
$683$	34.7309	1.32894	0.664470	−	0.747315i	$-0.268657\pi$
$683$	34.7309	1.32894	0.664470	+	0.747315i	$0.268657\pi$
$684$	6.06497	0.231900
$685$	−63.3057	−2.41879
$686$	−19.9835	−0.762975
$687$	8.32130	0.317477
$688$	7.86167	0.299723
$689$	−8.14395	−0.310260
$690$	−31.3687	−1.19418
$691$	8.83052	0.335929	0.167964	−	0.985793i	$-0.446281\pi$
$691$	8.83052	0.335929	0.167964	+	0.985793i	$0.446281\pi$
$692$	10.3244	0.392475
$693$	−9.30402	−0.353430
$694$	30.8312	1.17034
$695$	9.33559	0.354119
$696$	−14.6344	−0.554717
$697$	11.6765	0.442280
$698$	17.0144	0.644003
$699$	−3.55945	−0.134631
$700$	−20.0628	−0.758304
$701$	17.4132	0.657687	0.328843	−	0.944384i	$-0.393341\pi$
$701$	17.4132	0.657687	0.328843	+	0.944384i	$0.393341\pi$
$702$	−1.12373	−0.0424123
$703$	3.12834	0.117988
$704$	1.21449	0.0457727
$705$	47.8703	1.80290
$706$	−34.0165	−1.28023
$707$	−31.3045	−1.17733
$708$	5.33957	0.200673
$709$	−9.30814	−0.349575	−0.174787	−	0.984606i	$-0.555924\pi$
$709$	−9.30814	−0.349575	−0.174787	+	0.984606i	$0.555924\pi$
$710$	46.0947	1.72990
$711$	−23.0738	−0.865336
$712$	9.16985	0.343655
$713$	−12.1107	−0.453550
$714$	−25.6628	−0.960408
$715$	6.78364	0.253694
$716$	−10.2653	−0.383632
$717$	−28.9565	−1.08140
$718$	10.9451	0.408467
$719$	−41.0909	−1.53243	−0.766217	−	0.642582i	$-0.777863\pi$
$719$	−41.0909	−1.53243	−0.766217	+	0.642582i	$0.777863\pi$
$720$	−12.1694	−0.453527
$721$	1.89039	0.0704017
$722$	15.6141	0.581096
$723$	−71.7072	−2.66682
$724$	−18.9276	−0.703440
$725$	−50.3441	−1.86973
$726$	−23.9001	−0.887015
$727$	41.2270	1.52902	0.764512	−	0.644610i	$-0.222980\pi$
$727$	41.2270	1.52902	0.764512	+	0.644610i	$0.222980\pi$
$728$	−3.51624	−0.130320
$729$	−32.0397	−1.18666
$730$	49.6329	1.83700
$731$	34.5939	1.27950
$732$	−27.4747	−1.01549
$733$	17.8158	0.658043	0.329022	−	0.944322i	$-0.393281\pi$
$733$	17.8158	0.658043	0.329022	+	0.944322i	$0.393281\pi$
$734$	−23.5268	−0.868389
$735$	−14.8022	−0.545987
$736$	−3.38598	−0.124809
$737$	−14.4148	−0.530977
$738$	−8.74621	−0.321952
$739$	−21.0947	−0.775982	−0.387991	−	0.921663i	$-0.626831\pi$
$739$	−21.0947	−0.775982	−0.387991	+	0.921663i	$0.626831\pi$
$740$	−6.27703	−0.230748
$741$	6.98495	0.256598
$742$	12.5121	0.459333
$743$	14.0708	0.516209	0.258105	−	0.966117i	$-0.416902\pi$
$743$	14.0708	0.516209	0.258105	+	0.966117i	$0.416902\pi$
$744$	−8.97468	−0.329028
$745$	−0.716168	−0.0262384
$746$	8.38561	0.307019
$747$	−37.3985	−1.36834
$748$	5.34414	0.195401
$749$	44.0100	1.60809
$750$	−33.6469	−1.22861
$751$	18.4007	0.671450	0.335725	−	0.941960i	$-0.391019\pi$
$751$	18.4007	0.671450	0.335725	+	0.941960i	$0.391019\pi$
$752$	5.16719	0.188428
$753$	−52.2483	−1.90403
$754$	−8.82337	−0.321328
$755$	−37.9633	−1.38162
$756$	1.72645	0.0627905
$757$	−21.7375	−0.790064	−0.395032	−	0.918667i	$-0.629266\pi$
$757$	−21.7375	−0.790064	−0.395032	+	0.918667i	$0.629266\pi$
$758$	29.8928	1.08576
$759$	−10.3184	−0.374533
$760$	6.79385	0.246439
$761$	9.12115	0.330642	0.165321	−	0.986240i	$-0.447134\pi$
$761$	9.12115	0.330642	0.165321	+	0.986240i	$0.447134\pi$
$762$	43.2060	1.56519
$763$	30.3812	1.09987
$764$	−10.0968	−0.365288
$765$	−53.5493	−1.93608
$766$	−13.5443	−0.489374
$767$	3.21933	0.116243
$768$	−2.50919	−0.0905426
$769$	−48.6123	−1.75300	−0.876502	−	0.481397i	$-0.840129\pi$
$769$	−48.6123	−1.75300	−0.876502	+	0.481397i	$0.840129\pi$
$770$	−10.4222	−0.375588
$771$	−5.12311	−0.184504
$772$	−16.9104	−0.608618
$773$	−26.6898	−0.959965	−0.479983	−	0.877278i	$-0.659357\pi$
$773$	−26.6898	−0.959965	−0.479983	+	0.877278i	$0.659357\pi$
$774$	−25.9123	−0.931398
$775$	−30.8739	−1.10902
$776$	2.69458	0.0967298
$777$	9.91507	0.355701
$778$	−15.4684	−0.554570
$779$	4.88277	0.174944
$780$	−14.0153	−0.501829
$781$	15.1623	0.542550
$782$	−14.8994	−0.532802
$783$	4.33223	0.154821
$784$	−1.59777	−0.0570633
$785$	80.4502	2.87139
$786$	−32.8385	−1.17131
$787$	12.5883	0.448726	0.224363	−	0.974506i	$-0.427970\pi$
$787$	12.5883	0.448726	0.224363	+	0.974506i	$0.427970\pi$
$788$	9.98318	0.355636
$789$	46.6463	1.66065
$790$	−25.8468	−0.919587
$791$	30.9620	1.10088
$792$	−4.00299	−0.142240
$793$	−16.5650	−0.588240
$794$	−18.6320	−0.661225
$795$	49.8718	1.76877
$796$	0.798766	0.0283115
$797$	−0.0444540	−0.00157464	−0.000787320	−	1.00000i	$-0.500251\pi$
$797$	−0.0444540	−0.00157464	−0.000787320		1.00000i	$0.500251\pi$
$798$	−10.7314	−0.379889
$799$	22.7373	0.804389
$800$	−8.63189	−0.305184
$801$	−30.2241	−1.06792
$802$	26.5409	0.937190
$803$	16.3262	0.576139
$804$	29.7817	1.05032
$805$	29.0569	1.02412
$806$	−5.41100	−0.190594
$807$	−58.6548	−2.06475
$808$	−13.4685	−0.473822
$809$	−21.0760	−0.740994	−0.370497	−	0.928834i	$-0.620813\pi$
$809$	−21.0760	−0.740994	−0.370497	+	0.928834i	$0.620813\pi$
$810$	−29.6268	−1.04098
$811$	−24.7779	−0.870071	−0.435036	−	0.900413i	$-0.643264\pi$
$811$	−24.7779	−0.870071	−0.435036	+	0.900413i	$0.643264\pi$
$812$	13.5559	0.475720
$813$	−25.3484	−0.889008
$814$	−2.06476	−0.0723697
$815$	−88.3684	−3.09541
$816$	−11.0413	−0.386521
$817$	14.4661	0.506106
$818$	−5.83949	−0.204173
$819$	11.5896	0.404974
$820$	−9.79731	−0.342137
$821$	−39.2963	−1.37145	−0.685726	−	0.727860i	$-0.740515\pi$
$821$	−39.2963	−1.37145	−0.685726	+	0.727860i	$0.740515\pi$
$822$	43.0227	1.50059
$823$	−43.3750	−1.51196	−0.755978	−	0.654597i	$-0.772838\pi$
$823$	−43.3750	−1.51196	−0.755978	+	0.654597i	$0.772838\pi$
$824$	0.813326	0.0283336
$825$	−26.3046	−0.915810
$826$	−4.94606	−0.172096
$827$	−3.65692	−0.127164	−0.0635818	−	0.997977i	$-0.520252\pi$
$827$	−3.65692	−0.127164	−0.0635818	+	0.997977i	$0.520252\pi$
$828$	11.1603	0.387847
$829$	0.411757	0.0143009	0.00715045	−	0.999974i	$-0.497724\pi$
$829$	0.411757	0.0143009	0.00715045	+	0.999974i	$0.497724\pi$
$830$	−41.8930	−1.45413
$831$	22.0947	0.766458
$832$	−1.51284	−0.0524481
$833$	−7.03072	−0.243600
$834$	−6.34450	−0.219692
$835$	−54.2642	−1.87789
$836$	2.23476	0.0772908
$837$	2.65677	0.0918314
$838$	−5.90643	−0.204034
$839$	42.5626	1.46942	0.734711	−	0.678380i	$-0.237318\pi$
$839$	42.5626	1.46942	0.734711	+	0.678380i	$0.237318\pi$
$840$	21.5327	0.742948
$841$	5.01619	0.172972
$842$	37.1517	1.28033
$843$	46.8522	1.61367
$844$	−11.4585	−0.394418
$845$	39.5477	1.36048
$846$	−17.0312	−0.585545
$847$	22.1387	0.760695
$848$	5.38323	0.184861
$849$	8.87073	0.304443
$850$	−37.9831	−1.30281
$851$	5.75652	0.197331
$852$	−31.3261	−1.07321
$853$	−8.22454	−0.281603	−0.140801	−	0.990038i	$-0.544968\pi$
$853$	−8.22454	−0.281603	−0.140801	+	0.990038i	$0.544968\pi$
$854$	25.4499	0.870877
$855$	−22.3927	−0.765815
$856$	18.9350	0.647185
$857$	−6.44021	−0.219993	−0.109997	−	0.993932i	$-0.535084\pi$
$857$	−6.44021	−0.219993	−0.109997	+	0.993932i	$0.535084\pi$
$858$	−4.61018	−0.157389
$859$	42.1664	1.43870	0.719350	−	0.694648i	$-0.244440\pi$
$859$	42.1664	1.43870	0.719350	+	0.694648i	$0.244440\pi$
$860$	−29.0264	−0.989792
$861$	15.4756	0.527408
$862$	16.1970	0.551672
$863$	52.4475	1.78533	0.892667	−	0.450718i	$-0.148832\pi$
$863$	52.4475	1.78533	0.892667	+	0.450718i	$0.148832\pi$
$864$	0.742794	0.0252704
$865$	−38.1191	−1.29609
$866$	41.1029	1.39673
$867$	−5.92889	−0.201356
$868$	8.31328	0.282171
$869$	−8.50201	−0.288411
$870$	54.0324	1.83187
$871$	17.9560	0.608414
$872$	13.0713	0.442649
$873$	−8.88142	−0.300591
$874$	−6.23049	−0.210750
$875$	31.1672	1.05364
$876$	−33.7307	−1.13965
$877$	37.5461	1.26784	0.633922	−	0.773397i	$-0.281444\pi$
$877$	37.5461	1.26784	0.633922	+	0.773397i	$0.281444\pi$
$878$	−16.0877	−0.542934
$879$	−27.8338	−0.938810
$880$	−4.48406	−0.151158
$881$	5.65461	0.190509	0.0952543	−	0.995453i	$-0.469634\pi$
$881$	5.65461	0.190509	0.0952543	+	0.995453i	$0.469634\pi$
$882$	5.26630	0.177326
$883$	−10.4475	−0.351588	−0.175794	−	0.984427i	$-0.556249\pi$
$883$	−10.4475	−0.351588	−0.175794	+	0.984427i	$0.556249\pi$
$884$	−6.65697	−0.223898
$885$	−19.7144	−0.662694
$886$	−40.1459	−1.34873
$887$	40.7281	1.36752	0.683758	−	0.729709i	$-0.260345\pi$
$887$	40.7281	1.36752	0.683758	+	0.729709i	$0.260345\pi$
$888$	4.26589	0.143154
$889$	−40.0218	−1.34229
$890$	−33.8564	−1.13487
$891$	−9.74539	−0.326483
$892$	−14.8652	−0.497723
$893$	9.50807	0.318175
$894$	0.486710	0.0162780
$895$	37.9009	1.26689
$896$	2.32427	0.0776484
$897$	12.8532	0.429154
$898$	−18.0300	−0.601671
$899$	20.8607	0.695743
$900$	28.4510	0.948366
$901$	23.6880	0.789161
$902$	−3.22271	−0.107305
$903$	45.8495	1.52578
$904$	13.3212	0.443056
$905$	69.8834	2.32300
$906$	25.7999	0.857146
$907$	−57.4575	−1.90784	−0.953922	−	0.300053i	$-0.902996\pi$
$907$	−57.4575	−1.90784	−0.953922	+	0.300053i	$0.902996\pi$
$908$	16.8836	0.560301
$909$	44.3927	1.47241
$910$	12.9824	0.430364
$911$	−54.1787	−1.79502	−0.897511	−	0.440992i	$-0.854627\pi$
$911$	−54.1787	−1.79502	−0.897511	+	0.440992i	$0.854627\pi$
$912$	−4.61712	−0.152888
$913$	−13.7802	−0.456059
$914$	19.4355	0.642868
$915$	101.440	3.35351
$916$	−3.31633	−0.109575
$917$	30.4184	1.00450
$918$	3.26853	0.107878
$919$	27.4012	0.903882	0.451941	−	0.892048i	$-0.350732\pi$
$919$	27.4012	0.903882	0.451941	+	0.892048i	$0.350732\pi$
$920$	12.5015	0.412163
$921$	81.2144	2.67611
$922$	1.89912	0.0625442
$923$	−18.8871	−0.621675
$924$	7.08293	0.233011
$925$	14.6751	0.482515
$926$	−30.4165	−0.999548
$927$	−2.68075	−0.0880473
$928$	5.83234	0.191456
$929$	43.3176	1.42121	0.710603	−	0.703593i	$-0.248422\pi$
$929$	43.3176	1.42121	0.710603	+	0.703593i	$0.248422\pi$
$930$	33.1358	1.08656
$931$	−2.94004	−0.0963558
$932$	1.41856	0.0464666
$933$	−25.6757	−0.840586
$934$	7.01036	0.229386
$935$	−19.7313	−0.645283
$936$	4.98635	0.162984
$937$	1.16655	0.0381096	0.0190548	−	0.999818i	$-0.493934\pi$
$937$	1.16655	0.0381096	0.0190548	+	0.999818i	$0.493934\pi$
$938$	−27.5869	−0.900745
$939$	−81.3343	−2.65424
$940$	−19.0780	−0.622255
$941$	−34.9273	−1.13860	−0.569299	−	0.822131i	$-0.692785\pi$
$941$	−34.9273	−1.13860	−0.569299	+	0.822131i	$0.692785\pi$
$942$	−54.6742	−1.78138
$943$	8.98490	0.292589
$944$	−2.12801	−0.0692607
$945$	−6.37430	−0.207356
$946$	−9.54790	−0.310429
$947$	−45.2160	−1.46932	−0.734661	−	0.678434i	$-0.762659\pi$
$947$	−45.2160	−1.46932	−0.734661	+	0.678434i	$0.762659\pi$
$948$	17.5656	0.570503
$949$	−20.3368	−0.660162
$950$	−15.8834	−0.515326
$951$	−22.9498	−0.744198
$952$	10.2275	0.331477
$953$	46.1715	1.49564	0.747821	−	0.663901i	$-0.231100\pi$
$953$	46.1715	1.49564	0.747821	+	0.663901i	$0.231100\pi$
$954$	−17.7433	−0.574460
$955$	37.2786	1.20631
$956$	11.5402	0.373236
$957$	17.7733	0.574531
$958$	−17.6789	−0.571178
$959$	−39.8521	−1.28689
$960$	9.26428	0.299003
$961$	−18.2070	−0.587324
$962$	2.57198	0.0829240
$963$	−62.4103	−2.01114
$964$	28.5779	0.920431
$965$	62.4355	2.00987
$966$	−19.7471	−0.635354
$967$	11.0874	0.356546	0.178273	−	0.983981i	$-0.442949\pi$
$967$	11.0874	0.356546	0.178273	+	0.983981i	$0.442949\pi$
$968$	9.52502	0.306146
$969$	−20.3168	−0.652671
$970$	−9.94877	−0.319436
$971$	−40.7302	−1.30710	−0.653548	−	0.756885i	$-0.726720\pi$
$971$	−40.7302	−1.30710	−0.653548	+	0.756885i	$0.726720\pi$
$972$	22.3628	0.717288
$973$	5.87693	0.188406
$974$	−36.8933	−1.18214
$975$	32.7666	1.04937
$976$	10.9496	0.350489
$977$	−6.07444	−0.194339	−0.0971693	−	0.995268i	$-0.530979\pi$
$977$	−6.07444	−0.194339	−0.0971693	+	0.995268i	$0.530979\pi$
$978$	60.0554	1.92036
$979$	−11.1367	−0.355929
$980$	5.89920	0.188443
$981$	−43.0833	−1.37554
$982$	−37.1460	−1.18538
$983$	6.82114	0.217560	0.108780	−	0.994066i	$-0.465306\pi$
$983$	6.82114	0.217560	0.108780	+	0.994066i	$0.465306\pi$
$984$	6.65828	0.212258
$985$	−36.8593	−1.17443
$986$	25.6642	0.817315
$987$	30.1352	0.959214
$988$	−2.78375	−0.0885628
$989$	26.6195	0.846450
$990$	14.7796	0.469726
$991$	42.4574	1.34870	0.674352	−	0.738410i	$-0.264423\pi$
$991$	42.4574	1.34870	0.674352	+	0.738410i	$0.264423\pi$
$992$	3.57673	0.113561
$993$	11.9590	0.379508
$994$	29.0174	0.920377
$995$	−2.94916	−0.0934945
$996$	28.4706	0.902126
$997$	−44.6702	−1.41472	−0.707359	−	0.706855i	$-0.750114\pi$
$997$	−44.6702	−1.41472	−0.707359	+	0.706855i	$0.750114\pi$
$998$	−20.1331	−0.637301
$999$	−1.26283	−0.0399541

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.9	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.9	✓	77	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8002 = 2 \cdot 4001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.50919 q^{3} +1.00000 q^{4} -3.69214 q^{5} +2.50919 q^{6} -2.32427 q^{7} -1.00000 q^{8} +3.29603 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.50919 q^{3} +1.00000 q^{4} -3.69214 q^{5} +2.50919 q^{6} -2.32427 q^{7} -1.00000 q^{8} +3.29603 q^{9} +3.69214 q^{10} +1.21449 q^{11} -2.50919 q^{12} -1.51284 q^{13} +2.32427 q^{14} +9.26428 q^{15} +1.00000 q^{16} +4.40033 q^{17} -3.29603 q^{18} +1.84008 q^{19} -3.69214 q^{20} +5.83203 q^{21} -1.21449 q^{22} +3.38598 q^{23} +2.50919 q^{24} +8.63189 q^{25} +1.51284 q^{26} -0.742794 q^{27} -2.32427 q^{28} -5.83234 q^{29} -9.26428 q^{30} -3.57673 q^{31} -1.00000 q^{32} -3.04738 q^{33} -4.40033 q^{34} +8.58153 q^{35} +3.29603 q^{36} +1.70011 q^{37} -1.84008 q^{38} +3.79599 q^{39} +3.69214 q^{40} +2.65356 q^{41} -5.83203 q^{42} +7.86167 q^{43} +1.21449 q^{44} -12.1694 q^{45} -3.38598 q^{46} +5.16719 q^{47} -2.50919 q^{48} -1.59777 q^{49} -8.63189 q^{50} -11.0413 q^{51} -1.51284 q^{52} +5.38323 q^{53} +0.742794 q^{54} -4.48406 q^{55} +2.32427 q^{56} -4.61712 q^{57} +5.83234 q^{58} -2.12801 q^{59} +9.26428 q^{60} +10.9496 q^{61} +3.57673 q^{62} -7.66086 q^{63} +1.00000 q^{64} +5.58560 q^{65} +3.04738 q^{66} -11.8691 q^{67} +4.40033 q^{68} -8.49607 q^{69} -8.58153 q^{70} +12.4845 q^{71} -3.29603 q^{72} +13.4429 q^{73} -1.70011 q^{74} -21.6591 q^{75} +1.84008 q^{76} -2.82280 q^{77} -3.79599 q^{78} -7.00049 q^{79} -3.69214 q^{80} -8.02428 q^{81} -2.65356 q^{82} -11.3465 q^{83} +5.83203 q^{84} -16.2466 q^{85} -7.86167 q^{86} +14.6344 q^{87} -1.21449 q^{88} -9.16985 q^{89} +12.1694 q^{90} +3.51624 q^{91} +3.38598 q^{92} +8.97468 q^{93} -5.16719 q^{94} -6.79385 q^{95} +2.50919 q^{96} -2.69458 q^{97} +1.59777 q^{98} +4.00299 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9} - 18 q^{10} + 30 q^{11} + 10 q^{12} - 2 q^{13} - 21 q^{14} + 21 q^{15} + 77 q^{16} + 60 q^{17} - 71 q^{18} - 3 q^{19} + 18 q^{20} + 10 q^{21} - 30 q^{22} + 53 q^{23} - 10 q^{24} + 59 q^{25} + 2 q^{26} + 43 q^{27} + 21 q^{28} + 30 q^{29} - 21 q^{30} + 22 q^{31} - 77 q^{32} + 31 q^{33} - 60 q^{34} + 41 q^{35} + 71 q^{36} - 3 q^{37} + 3 q^{38} + 44 q^{39} - 18 q^{40} + 48 q^{41} - 10 q^{42} + 21 q^{43} + 30 q^{44} + 33 q^{45} - 53 q^{46} + 107 q^{47} + 10 q^{48} + 24 q^{49} - 59 q^{50} + 18 q^{51} - 2 q^{52} + 42 q^{53} - 43 q^{54} + 49 q^{55} - 21 q^{56} + 32 q^{57} - 30 q^{58} + 42 q^{59} + 21 q^{60} - 31 q^{61} - 22 q^{62} + 109 q^{63} + 77 q^{64} + 39 q^{65} - 31 q^{66} - q^{67} + 60 q^{68} - 33 q^{69} - 41 q^{70} + 58 q^{71} - 71 q^{72} + 35 q^{73} + 3 q^{74} + 34 q^{75} - 3 q^{76} + 86 q^{77} - 44 q^{78} + 25 q^{79} + 18 q^{80} + 53 q^{81} - 48 q^{82} + 107 q^{83} + 10 q^{84} + 21 q^{85} - 21 q^{86} + 100 q^{87} - 30 q^{88} + 34 q^{89} - 33 q^{90} - 51 q^{91} + 53 q^{92} + 48 q^{93} - 107 q^{94} + 118 q^{95} - 10 q^{96} - 13 q^{97} - 24 q^{98} + 63 q^{99}+O(q^{100}) \) 77 * q - 77 * q^2 + 10 * q^3 + 77 * q^4 + 18 * q^5 - 10 * q^6 + 21 * q^7 - 77 * q^8 + 71 * q^9 - 18 * q^10 + 30 * q^11 + 10 * q^12 - 2 * q^13 - 21 * q^14 + 21 * q^15 + 77 * q^16 + 60 * q^17 - 71 * q^18 - 3 * q^19 + 18 * q^20 + 10 * q^21 - 30 * q^22 + 53 * q^23 - 10 * q^24 + 59 * q^25 + 2 * q^26 + 43 * q^27 + 21 * q^28 + 30 * q^29 - 21 * q^30 + 22 * q^31 - 77 * q^32 + 31 * q^33 - 60 * q^34 + 41 * q^35 + 71 * q^36 - 3 * q^37 + 3 * q^38 + 44 * q^39 - 18 * q^40 + 48 * q^41 - 10 * q^42 + 21 * q^43 + 30 * q^44 + 33 * q^45 - 53 * q^46 + 107 * q^47 + 10 * q^48 + 24 * q^49 - 59 * q^50 + 18 * q^51 - 2 * q^52 + 42 * q^53 - 43 * q^54 + 49 * q^55 - 21 * q^56 + 32 * q^57 - 30 * q^58 + 42 * q^59 + 21 * q^60 - 31 * q^61 - 22 * q^62 + 109 * q^63 + 77 * q^64 + 39 * q^65 - 31 * q^66 - q^67 + 60 * q^68 - 33 * q^69 - 41 * q^70 + 58 * q^71 - 71 * q^72 + 35 * q^73 + 3 * q^74 + 34 * q^75 - 3 * q^76 + 86 * q^77 - 44 * q^78 + 25 * q^79 + 18 * q^80 + 53 * q^81 - 48 * q^82 + 107 * q^83 + 10 * q^84 + 21 * q^85 - 21 * q^86 + 100 * q^87 - 30 * q^88 + 34 * q^89 - 33 * q^90 - 51 * q^91 + 53 * q^92 + 48 * q^93 - 107 * q^94 + 118 * q^95 - 10 * q^96 - 13 * q^97 - 24 * q^98 + 63 * q^99

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