LMFDB - Embedded newform 8002.2.a.e.1.70

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			1.70
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)

$f(q)$	$=$	$q-1.00000 q^{2} +2.89065 q^{3} +1.00000 q^{4} +2.26974 q^{5} -2.89065 q^{6} -2.55487 q^{7} -1.00000 q^{8} +5.35584 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +2.89065 q^{3} +1.00000 q^{4} +2.26974 q^{5} -2.89065 q^{6} -2.55487 q^{7} -1.00000 q^{8} +5.35584 q^{9} -2.26974 q^{10} +1.81298 q^{11} +2.89065 q^{12} -0.873885 q^{13} +2.55487 q^{14} +6.56101 q^{15} +1.00000 q^{16} +6.28864 q^{17} -5.35584 q^{18} +0.484560 q^{19} +2.26974 q^{20} -7.38522 q^{21} -1.81298 q^{22} -3.10952 q^{23} -2.89065 q^{24} +0.151712 q^{25} +0.873885 q^{26} +6.80990 q^{27} -2.55487 q^{28} +0.844764 q^{29} -6.56101 q^{30} +3.14187 q^{31} -1.00000 q^{32} +5.24068 q^{33} -6.28864 q^{34} -5.79888 q^{35} +5.35584 q^{36} -2.93867 q^{37} -0.484560 q^{38} -2.52609 q^{39} -2.26974 q^{40} -6.90942 q^{41} +7.38522 q^{42} +4.91935 q^{43} +1.81298 q^{44} +12.1564 q^{45} +3.10952 q^{46} +12.1971 q^{47} +2.89065 q^{48} -0.472644 q^{49} -0.151712 q^{50} +18.1782 q^{51} -0.873885 q^{52} +1.04539 q^{53} -6.80990 q^{54} +4.11499 q^{55} +2.55487 q^{56} +1.40069 q^{57} -0.844764 q^{58} -9.06837 q^{59} +6.56101 q^{60} +11.7969 q^{61} -3.14187 q^{62} -13.6835 q^{63} +1.00000 q^{64} -1.98349 q^{65} -5.24068 q^{66} -4.63621 q^{67} +6.28864 q^{68} -8.98852 q^{69} +5.79888 q^{70} +1.63277 q^{71} -5.35584 q^{72} +2.89812 q^{73} +2.93867 q^{74} +0.438547 q^{75} +0.484560 q^{76} -4.63192 q^{77} +2.52609 q^{78} +16.2810 q^{79} +2.26974 q^{80} +3.61749 q^{81} +6.90942 q^{82} +17.6596 q^{83} -7.38522 q^{84} +14.2736 q^{85} -4.91935 q^{86} +2.44191 q^{87} -1.81298 q^{88} +15.0109 q^{89} -12.1564 q^{90} +2.23266 q^{91} -3.10952 q^{92} +9.08204 q^{93} -12.1971 q^{94} +1.09982 q^{95} -2.89065 q^{96} +16.1468 q^{97} +0.472644 q^{98} +9.71002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.89065	1.66892	0.834458	−	0.551072i	$-0.185781\pi$
$3$	2.89065	1.66892	0.834458	+	0.551072i	$0.185781\pi$
$4$	1.00000	0.500000
$5$	2.26974	1.01506	0.507529	−	0.861635i	$-0.330559\pi$
$5$	2.26974	1.01506	0.507529	+	0.861635i	$0.330559\pi$
$6$	−2.89065	−1.18010
$7$	−2.55487	−0.965650	−0.482825	−	0.875717i	$-0.660389\pi$
$7$	−2.55487	−0.965650	−0.482825	+	0.875717i	$0.660389\pi$
$8$	−1.00000	−0.353553
$9$	5.35584	1.78528
$10$	−2.26974	−0.717754
$11$	1.81298	0.546634	0.273317	−	0.961924i	$-0.411879\pi$
$11$	1.81298	0.546634	0.273317	+	0.961924i	$0.411879\pi$
$12$	2.89065	0.834458
$13$	−0.873885	−0.242372	−0.121186	−	0.992630i	$-0.538670\pi$
$13$	−0.873885	−0.242372	−0.121186	+	0.992630i	$0.538670\pi$
$14$	2.55487	0.682817
$15$	6.56101	1.69405
$16$	1.00000	0.250000
$17$	6.28864	1.52522	0.762609	−	0.646859i	$-0.223918\pi$
$17$	6.28864	1.52522	0.762609	+	0.646859i	$0.223918\pi$
$18$	−5.35584	−1.26238
$19$	0.484560	0.111166	0.0555828	−	0.998454i	$-0.482298\pi$
$19$	0.484560	0.111166	0.0555828	+	0.998454i	$0.482298\pi$
$20$	2.26974	0.507529
$21$	−7.38522	−1.61159
$22$	−1.81298	−0.386528
$23$	−3.10952	−0.648380	−0.324190	−	0.945992i	$-0.605092\pi$
$23$	−3.10952	−0.648380	−0.324190	+	0.945992i	$0.605092\pi$
$24$	−2.89065	−0.590051
$25$	0.151712	0.0303425
$26$	0.873885	0.171383
$27$	6.80990	1.31057
$28$	−2.55487	−0.482825
$29$	0.844764	0.156869	0.0784343	−	0.996919i	$-0.475008\pi$
$29$	0.844764	0.156869	0.0784343	+	0.996919i	$0.475008\pi$
$30$	−6.56101	−1.19787
$31$	3.14187	0.564297	0.282148	−	0.959371i	$-0.408953\pi$
$31$	3.14187	0.564297	0.282148	+	0.959371i	$0.408953\pi$
$32$	−1.00000	−0.176777
$33$	5.24068	0.912286
$34$	−6.28864	−1.07849
$35$	−5.79888	−0.980190
$36$	5.35584	0.892640
$37$	−2.93867	−0.483114	−0.241557	−	0.970387i	$-0.577658\pi$
$37$	−2.93867	−0.483114	−0.241557	+	0.970387i	$0.577658\pi$
$38$	−0.484560	−0.0786060
$39$	−2.52609	−0.404499
$40$	−2.26974	−0.358877
$41$	−6.90942	−1.07907	−0.539535	−	0.841963i	$-0.681400\pi$
$41$	−6.90942	−1.07907	−0.539535	+	0.841963i	$0.681400\pi$
$42$	7.38522	1.13956
$43$	4.91935	0.750194	0.375097	−	0.926985i	$-0.377609\pi$
$43$	4.91935	0.750194	0.375097	+	0.926985i	$0.377609\pi$
$44$	1.81298	0.273317
$45$	12.1564	1.81216
$46$	3.10952	0.458474
$47$	12.1971	1.77913	0.889567	−	0.456805i	$-0.151006\pi$
$47$	12.1971	1.77913	0.889567	+	0.456805i	$0.151006\pi$
$48$	2.89065	0.417229
$49$	−0.472644	−0.0675206
$50$	−0.151712	−0.0214554
$51$	18.1782	2.54546
$52$	−0.873885	−0.121186
$53$	1.04539	0.143596	0.0717979	−	0.997419i	$-0.477126\pi$
$53$	1.04539	0.143596	0.0717979	+	0.997419i	$0.477126\pi$
$54$	−6.80990	−0.926710
$55$	4.11499	0.554865
$56$	2.55487	0.341409
$57$	1.40069	0.185526
$58$	−0.844764	−0.110923
$59$	−9.06837	−1.18060	−0.590300	−	0.807184i	$-0.700991\pi$
$59$	−9.06837	−1.18060	−0.590300	+	0.807184i	$0.700991\pi$
$60$	6.56101	0.847023
$61$	11.7969	1.51044	0.755218	−	0.655474i	$-0.227531\pi$
$61$	11.7969	1.51044	0.755218	+	0.655474i	$0.227531\pi$
$62$	−3.14187	−0.399018
$63$	−13.6835	−1.72395
$64$	1.00000	0.125000
$65$	−1.98349	−0.246022
$66$	−5.24068	−0.645083
$67$	−4.63621	−0.566403	−0.283202	−	0.959060i	$-0.591397\pi$
$67$	−4.63621	−0.566403	−0.283202	+	0.959060i	$0.591397\pi$
$68$	6.28864	0.762609
$69$	−8.98852	−1.08209
$70$	5.79888	0.693099
$71$	1.63277	0.193775	0.0968874	−	0.995295i	$-0.469111\pi$
$71$	1.63277	0.193775	0.0968874	+	0.995295i	$0.469111\pi$
$72$	−5.35584	−0.631192
$73$	2.89812	0.339199	0.169600	−	0.985513i	$-0.445753\pi$
$73$	2.89812	0.339199	0.169600	+	0.985513i	$0.445753\pi$
$74$	2.93867	0.341613
$75$	0.438547	0.0506390
$76$	0.484560	0.0555828
$77$	−4.63192	−0.527857
$78$	2.52609	0.286024
$79$	16.2810	1.83176	0.915880	−	0.401452i	$-0.131494\pi$
$79$	16.2810	1.83176	0.915880	+	0.401452i	$0.131494\pi$
$80$	2.26974	0.253764
$81$	3.61749	0.401943
$82$	6.90942	0.763018
$83$	17.6596	1.93840	0.969198	−	0.246283i	$-0.0792092\pi$
$83$	17.6596	1.93840	0.969198	+	0.246283i	$0.0792092\pi$
$84$	−7.38522	−0.805794
$85$	14.2736	1.54818
$86$	−4.91935	−0.530468
$87$	2.44191	0.261801
$88$	−1.81298	−0.193264
$89$	15.0109	1.59116	0.795578	−	0.605851i	$-0.207167\pi$
$89$	15.0109	1.59116	0.795578	+	0.605851i	$0.207167\pi$
$90$	−12.1564	−1.28139
$91$	2.23266	0.234047
$92$	−3.10952	−0.324190
$93$	9.08204	0.941764
$94$	−12.1971	−1.25804
$95$	1.09982	0.112840
$96$	−2.89065	−0.295025
$97$	16.1468	1.63946	0.819729	−	0.572752i	$-0.194124\pi$
$97$	16.1468	1.63946	0.819729	+	0.572752i	$0.194124\pi$
$98$	0.472644	0.0477443
$99$	9.71002	0.975894
$100$	0.151712	0.0151712
$101$	9.63512	0.958730	0.479365	−	0.877616i	$-0.340867\pi$
$101$	9.63512	0.958730	0.479365	+	0.877616i	$0.340867\pi$
$102$	−18.1782	−1.79991
$103$	−1.73927	−0.171376	−0.0856879	−	0.996322i	$-0.527309\pi$
$103$	−1.73927	−0.171376	−0.0856879	+	0.996322i	$0.527309\pi$
$104$	0.873885	0.0856915
$105$	−16.7625	−1.63586
$106$	−1.04539	−0.101538
$107$	−9.48327	−0.916782	−0.458391	−	0.888751i	$-0.651574\pi$
$107$	−9.48327	−0.916782	−0.458391	+	0.888751i	$0.651574\pi$
$108$	6.80990	0.655283
$109$	3.53757	0.338838	0.169419	−	0.985544i	$-0.445811\pi$
$109$	3.53757	0.338838	0.169419	+	0.985544i	$0.445811\pi$
$110$	−4.11499	−0.392349
$111$	−8.49464	−0.806276
$112$	−2.55487	−0.241412
$113$	1.27867	0.120287	0.0601437	−	0.998190i	$-0.480844\pi$
$113$	1.27867	0.120287	0.0601437	+	0.998190i	$0.480844\pi$
$114$	−1.40069	−0.131187
$115$	−7.05780	−0.658143
$116$	0.844764	0.0784343
$117$	−4.68039	−0.432702
$118$	9.06837	0.834811
$119$	−16.0666	−1.47283
$120$	−6.56101	−0.598936
$121$	−7.71311	−0.701191
$122$	−11.7969	−1.06804
$123$	−19.9727	−1.80088
$124$	3.14187	0.282148
$125$	−11.0043	−0.984259
$126$	13.6835	1.21902
$127$	6.49545	0.576378	0.288189	−	0.957573i	$-0.406947\pi$
$127$	6.49545	0.576378	0.288189	+	0.957573i	$0.406947\pi$
$128$	−1.00000	−0.0883883
$129$	14.2201	1.25201
$130$	1.98349	0.173964
$131$	−13.0619	−1.14122	−0.570612	−	0.821220i	$-0.693294\pi$
$131$	−13.0619	−1.14122	−0.570612	+	0.821220i	$0.693294\pi$
$132$	5.24068	0.456143
$133$	−1.23799	−0.107347
$134$	4.63621	0.400508
$135$	15.4567	1.33030
$136$	−6.28864	−0.539246
$137$	−12.9071	−1.10273	−0.551363	−	0.834265i	$-0.685892\pi$
$137$	−12.9071	−1.10273	−0.551363	+	0.834265i	$0.685892\pi$
$138$	8.98852	0.765154
$139$	−7.57641	−0.642622	−0.321311	−	0.946974i	$-0.604124\pi$
$139$	−7.57641	−0.642622	−0.321311	+	0.946974i	$0.604124\pi$
$140$	−5.79888	−0.490095
$141$	35.2576	2.96922
$142$	−1.63277	−0.137019
$143$	−1.58434	−0.132489
$144$	5.35584	0.446320
$145$	1.91739	0.159231
$146$	−2.89812	−0.239850
$147$	−1.36625	−0.112686
$148$	−2.93867	−0.241557
$149$	−19.8225	−1.62392	−0.811961	−	0.583712i	$-0.801600\pi$
$149$	−19.8225	−1.62392	−0.811961	+	0.583712i	$0.801600\pi$
$150$	−0.438547	−0.0358072
$151$	20.1711	1.64150	0.820752	−	0.571285i	$-0.193555\pi$
$151$	20.1711	1.64150	0.820752	+	0.571285i	$0.193555\pi$
$152$	−0.484560	−0.0393030
$153$	33.6809	2.72294
$154$	4.63192	0.373251
$155$	7.13123	0.572794
$156$	−2.52609	−0.202249
$157$	5.47888	0.437263	0.218631	−	0.975808i	$-0.429841\pi$
$157$	5.47888	0.437263	0.218631	+	0.975808i	$0.429841\pi$
$158$	−16.2810	−1.29525
$159$	3.02186	0.239649
$160$	−2.26974	−0.179439
$161$	7.94442	0.626108
$162$	−3.61749	−0.284217
$163$	4.15414	0.325377	0.162689	−	0.986677i	$-0.447983\pi$
$163$	4.15414	0.325377	0.162689	+	0.986677i	$0.447983\pi$
$164$	−6.90942	−0.539535
$165$	11.8950	0.926023
$166$	−17.6596	−1.37065
$167$	3.84717	0.297703	0.148851	−	0.988860i	$-0.452442\pi$
$167$	3.84717	0.297703	0.148851	+	0.988860i	$0.452442\pi$
$168$	7.38522	0.569782
$169$	−12.2363	−0.941256
$170$	−14.2736	−1.09473
$171$	2.59522	0.198462
$172$	4.91935	0.375097
$173$	−9.30518	−0.707459	−0.353730	−	0.935348i	$-0.615087\pi$
$173$	−9.30518	−0.707459	−0.353730	+	0.935348i	$0.615087\pi$
$174$	−2.44191	−0.185121
$175$	−0.387605	−0.0293002
$176$	1.81298	0.136658
$177$	−26.2134	−1.97032
$178$	−15.0109	−1.12512
$179$	−8.76303	−0.654980	−0.327490	−	0.944855i	$-0.606203\pi$
$179$	−8.76303	−0.654980	−0.327490	+	0.944855i	$0.606203\pi$
$180$	12.1564	0.906081
$181$	−2.59161	−0.192633	−0.0963165	−	0.995351i	$-0.530706\pi$
$181$	−2.59161	−0.192633	−0.0963165	+	0.995351i	$0.530706\pi$
$182$	−2.23266	−0.165496
$183$	34.1006	2.52079
$184$	3.10952	0.229237
$185$	−6.67000	−0.490388
$186$	−9.08204	−0.665927
$187$	11.4012	0.833736
$188$	12.1971	0.889567
$189$	−17.3984	−1.26555
$190$	−1.09982	−0.0797896
$191$	19.6001	1.41822	0.709108	−	0.705100i	$-0.249098\pi$
$191$	19.6001	1.41822	0.709108	+	0.705100i	$0.249098\pi$
$192$	2.89065	0.208614
$193$	−8.47458	−0.610013	−0.305007	−	0.952350i	$-0.598659\pi$
$193$	−8.47458	−0.610013	−0.305007	+	0.952350i	$0.598659\pi$
$194$	−16.1468	−1.15927
$195$	−5.73357	−0.410589
$196$	−0.472644	−0.0337603
$197$	9.61119	0.684769	0.342384	−	0.939560i	$-0.388766\pi$
$197$	9.61119	0.684769	0.342384	+	0.939560i	$0.388766\pi$
$198$	−9.71002	−0.690061
$199$	−26.4717	−1.87653	−0.938266	−	0.345914i	$-0.887569\pi$
$199$	−26.4717	−1.87653	−0.938266	+	0.345914i	$0.887569\pi$
$200$	−0.151712	−0.0107277
$201$	−13.4016	−0.945279
$202$	−9.63512	−0.677925
$203$	−2.15826	−0.151480
$204$	18.1782	1.27273
$205$	−15.6826	−1.09532
$206$	1.73927	0.121181
$207$	−16.6541	−1.15754
$208$	−0.873885	−0.0605930
$209$	0.878497	0.0607669
$210$	16.7625	1.15672
$211$	5.20511	0.358334	0.179167	−	0.983819i	$-0.442660\pi$
$211$	5.20511	0.358334	0.179167	+	0.983819i	$0.442660\pi$
$212$	1.04539	0.0717979
$213$	4.71977	0.323394
$214$	9.48327	0.648263
$215$	11.1656	0.761491
$216$	−6.80990	−0.463355
$217$	−8.02707	−0.544913
$218$	−3.53757	−0.239594
$219$	8.37743	0.566095
$220$	4.11499	0.277432
$221$	−5.49554	−0.369670
$222$	8.49464	0.570123
$223$	−27.1025	−1.81491	−0.907457	−	0.420145i	$-0.861979\pi$
$223$	−27.1025	−1.81491	−0.907457	+	0.420145i	$0.861979\pi$
$224$	2.55487	0.170704
$225$	0.812547	0.0541698
$226$	−1.27867	−0.0850560
$227$	−22.1702	−1.47149	−0.735743	−	0.677261i	$-0.763167\pi$
$227$	−22.1702	−1.47149	−0.735743	+	0.677261i	$0.763167\pi$
$228$	1.40069	0.0927630
$229$	22.9110	1.51400	0.757001	−	0.653413i	$-0.226664\pi$
$229$	22.9110	1.51400	0.757001	+	0.653413i	$0.226664\pi$
$230$	7.05780	0.465377
$231$	−13.3893	−0.880948
$232$	−0.844764	−0.0554615
$233$	−10.9821	−0.719464	−0.359732	−	0.933056i	$-0.617132\pi$
$233$	−10.9821	−0.719464	−0.359732	+	0.933056i	$0.617132\pi$
$234$	4.68039	0.305966
$235$	27.6843	1.80592
$236$	−9.06837	−0.590300
$237$	47.0627	3.05705
$238$	16.0666	1.04145
$239$	19.9767	1.29218	0.646092	−	0.763260i	$-0.276402\pi$
$239$	19.9767	1.29218	0.646092	+	0.763260i	$0.276402\pi$
$240$	6.56101	0.423511
$241$	12.4053	0.799096	0.399548	−	0.916712i	$-0.369167\pi$
$241$	12.4053	0.799096	0.399548	+	0.916712i	$0.369167\pi$
$242$	7.71311	0.495817
$243$	−9.97280	−0.639756
$244$	11.7969	0.755218
$245$	−1.07278	−0.0685373
$246$	19.9727	1.27341
$247$	−0.423449	−0.0269434
$248$	−3.14187	−0.199509
$249$	51.0477	3.23502
$250$	11.0043	0.695976
$251$	6.36715	0.401891	0.200945	−	0.979602i	$-0.435599\pi$
$251$	6.36715	0.401891	0.200945	+	0.979602i	$0.435599\pi$
$252$	−13.6835	−0.861977
$253$	−5.63750	−0.354426
$254$	−6.49545	−0.407561
$255$	41.2598	2.58379
$256$	1.00000	0.0625000
$257$	24.7563	1.54426	0.772129	−	0.635466i	$-0.219192\pi$
$257$	24.7563	1.54426	0.772129	+	0.635466i	$0.219192\pi$
$258$	−14.2201	−0.885306
$259$	7.50790	0.466518
$260$	−1.98349	−0.123011
$261$	4.52442	0.280054
$262$	13.0619	0.806967
$263$	−19.7295	−1.21657	−0.608287	−	0.793717i	$-0.708143\pi$
$263$	−19.7295	−1.21657	−0.608287	+	0.793717i	$0.708143\pi$
$264$	−5.24068	−0.322542
$265$	2.37277	0.145758
$266$	1.23799	0.0759058
$267$	43.3913	2.65551
$268$	−4.63621	−0.283202
$269$	−20.1023	−1.22566	−0.612829	−	0.790215i	$-0.709969\pi$
$269$	−20.1023	−1.22566	−0.612829	+	0.790215i	$0.709969\pi$
$270$	−15.4567	−0.940664
$271$	22.2613	1.35228	0.676139	−	0.736774i	$-0.263652\pi$
$271$	22.2613	1.35228	0.676139	+	0.736774i	$0.263652\pi$
$272$	6.28864	0.381305
$273$	6.45384	0.390604
$274$	12.9071	0.779746
$275$	0.275051	0.0165862
$276$	−8.98852	−0.541046
$277$	−7.78638	−0.467839	−0.233919	−	0.972256i	$-0.575155\pi$
$277$	−7.78638	−0.467839	−0.233919	+	0.972256i	$0.575155\pi$
$278$	7.57641	0.454403
$279$	16.8274	1.00743
$280$	5.79888	0.346550
$281$	−14.2853	−0.852189	−0.426095	−	0.904679i	$-0.640111\pi$
$281$	−14.2853	−0.852189	−0.426095	+	0.904679i	$0.640111\pi$
$282$	−35.2576	−2.09956
$283$	18.7537	1.11479	0.557395	−	0.830248i	$-0.311801\pi$
$283$	18.7537	1.11479	0.557395	+	0.830248i	$0.311801\pi$
$284$	1.63277	0.0968874
$285$	3.17920	0.188320
$286$	1.58434	0.0936837
$287$	17.6527	1.04200
$288$	−5.35584	−0.315596
$289$	22.5470	1.32629
$290$	−1.91739	−0.112593
$291$	46.6747	2.73612
$292$	2.89812	0.169600
$293$	17.5586	1.02578	0.512891	−	0.858454i	$-0.328574\pi$
$293$	17.5586	1.02578	0.512891	+	0.858454i	$0.328574\pi$
$294$	1.36625	0.0796812
$295$	−20.5828	−1.19838
$296$	2.93867	0.170806
$297$	12.3462	0.716399
$298$	19.8225	1.14829
$299$	2.71736	0.157149
$300$	0.438547	0.0253195
$301$	−12.5683	−0.724425
$302$	−20.1711	−1.16072
$303$	27.8517	1.60004
$304$	0.484560	0.0277914
$305$	26.7758	1.53318
$306$	−33.6809	−1.92541
$307$	12.1515	0.693524	0.346762	−	0.937953i	$-0.387281\pi$
$307$	12.1515	0.693524	0.346762	+	0.937953i	$0.387281\pi$
$308$	−4.63192	−0.263928
$309$	−5.02763	−0.286012
$310$	−7.13123	−0.405026
$311$	−12.1912	−0.691300	−0.345650	−	0.938363i	$-0.612342\pi$
$311$	−12.1912	−0.691300	−0.345650	+	0.938363i	$0.612342\pi$
$312$	2.52609	0.143012
$313$	21.9404	1.24015	0.620074	−	0.784544i	$-0.287103\pi$
$313$	21.9404	1.24015	0.620074	+	0.784544i	$0.287103\pi$
$314$	−5.47888	−0.309191
$315$	−31.0579	−1.74991
$316$	16.2810	0.915880
$317$	−12.6321	−0.709489	−0.354744	−	0.934963i	$-0.615432\pi$
$317$	−12.6321	−0.709489	−0.354744	+	0.934963i	$0.615432\pi$
$318$	−3.02186	−0.169458
$319$	1.53154	0.0857497
$320$	2.26974	0.126882
$321$	−27.4128	−1.53003
$322$	−7.94442	−0.442725
$323$	3.04722	0.169552
$324$	3.61749	0.200972
$325$	−0.132579	−0.00735416
$326$	−4.15414	−0.230076
$327$	10.2259	0.565491
$328$	6.90942	0.381509
$329$	−31.1621	−1.71802
$330$	−11.8950	−0.654797
$331$	−30.6360	−1.68391	−0.841954	−	0.539550i	$-0.818595\pi$
$331$	−30.6360	−1.68391	−0.841954	+	0.539550i	$0.818595\pi$
$332$	17.6596	0.969198
$333$	−15.7390	−0.862493
$334$	−3.84717	−0.210508
$335$	−10.5230	−0.574932
$336$	−7.38522	−0.402897
$337$	−18.6891	−1.01806	−0.509031	−	0.860748i	$-0.669996\pi$
$337$	−18.6891	−1.01806	−0.509031	+	0.860748i	$0.669996\pi$
$338$	12.2363	0.665568
$339$	3.69619	0.200749
$340$	14.2736	0.774092
$341$	5.69615	0.308464
$342$	−2.59522	−0.140334
$343$	19.0916	1.03085
$344$	−4.91935	−0.265234
$345$	−20.4016	−1.09839
$346$	9.30518	0.500249
$347$	7.50829	0.403066	0.201533	−	0.979482i	$-0.435408\pi$
$347$	7.50829	0.403066	0.201533	+	0.979482i	$0.435408\pi$
$348$	2.44191	0.130900
$349$	25.8610	1.38431	0.692153	−	0.721751i	$-0.256662\pi$
$349$	25.8610	1.38431	0.692153	+	0.721751i	$0.256662\pi$
$350$	0.387605	0.0207184
$351$	−5.95107	−0.317644
$352$	−1.81298	−0.0966321
$353$	−5.71616	−0.304240	−0.152120	−	0.988362i	$-0.548610\pi$
$353$	−5.71616	−0.304240	−0.152120	+	0.988362i	$0.548610\pi$
$354$	26.2134	1.39323
$355$	3.70597	0.196693
$356$	15.0109	0.795578
$357$	−46.4430	−2.45802
$358$	8.76303	0.463141
$359$	23.2179	1.22539	0.612696	−	0.790318i	$-0.290085\pi$
$359$	23.2179	1.22539	0.612696	+	0.790318i	$0.290085\pi$
$360$	−12.1564	−0.640696
$361$	−18.7652	−0.987642
$362$	2.59161	0.136212
$363$	−22.2959	−1.17023
$364$	2.23266	0.117023
$365$	6.57797	0.344307
$366$	−34.1006	−1.78247
$367$	−31.2320	−1.63029	−0.815147	−	0.579253i	$-0.803344\pi$
$367$	−31.2320	−1.63029	−0.815147	+	0.579253i	$0.803344\pi$
$368$	−3.10952	−0.162095
$369$	−37.0057	−1.92644
$370$	6.67000	0.346757
$371$	−2.67084	−0.138663
$372$	9.08204	0.470882
$373$	−26.9797	−1.39696	−0.698478	−	0.715631i	$-0.746139\pi$
$373$	−26.9797	−1.39696	−0.698478	+	0.715631i	$0.746139\pi$
$374$	−11.4012	−0.589540
$375$	−31.8097	−1.64264
$376$	−12.1971	−0.629019
$377$	−0.738226	−0.0380206
$378$	17.3984	0.894877
$379$	−2.36203	−0.121329	−0.0606646	−	0.998158i	$-0.519322\pi$
$379$	−2.36203	−0.121329	−0.0606646	+	0.998158i	$0.519322\pi$
$380$	1.09982	0.0564198
$381$	18.7761	0.961927
$382$	−19.6001	−1.00283
$383$	17.7539	0.907183	0.453592	−	0.891210i	$-0.350142\pi$
$383$	17.7539	0.907183	0.453592	+	0.891210i	$0.350142\pi$
$384$	−2.89065	−0.147513
$385$	−10.5133	−0.535805
$386$	8.47458	0.431345
$387$	26.3473	1.33931
$388$	16.1468	0.819729
$389$	36.1880	1.83481	0.917403	−	0.397960i	$-0.130282\pi$
$389$	36.1880	1.83481	0.917403	+	0.397960i	$0.130282\pi$
$390$	5.73357	0.290331
$391$	−19.5546	−0.988921
$392$	0.472644	0.0238721
$393$	−37.7573	−1.90461
$394$	−9.61119	−0.484205
$395$	36.9537	1.85934
$396$	9.71002	0.487947
$397$	−26.0214	−1.30598	−0.652988	−	0.757368i	$-0.726485\pi$
$397$	−26.0214	−1.30598	−0.652988	+	0.757368i	$0.726485\pi$
$398$	26.4717	1.32691
$399$	−3.57858	−0.179153
$400$	0.151712	0.00758561
$401$	−18.5183	−0.924758	−0.462379	−	0.886682i	$-0.653004\pi$
$401$	−18.5183	−0.924758	−0.462379	+	0.886682i	$0.653004\pi$
$402$	13.4016	0.668413
$403$	−2.74563	−0.136770
$404$	9.63512	0.479365
$405$	8.21076	0.407996
$406$	2.15826	0.107113
$407$	−5.32774	−0.264086
$408$	−18.1782	−0.899956
$409$	−11.6561	−0.576359	−0.288180	−	0.957576i	$-0.593050\pi$
$409$	−11.6561	−0.576359	−0.288180	+	0.957576i	$0.593050\pi$
$410$	15.6826	0.774507
$411$	−37.3098	−1.84036
$412$	−1.73927	−0.0856879
$413$	23.1685	1.14005
$414$	16.6541	0.818504
$415$	40.0827	1.96758
$416$	0.873885	0.0428457
$417$	−21.9007	−1.07248
$418$	−0.878497	−0.0429687
$419$	−23.8529	−1.16529	−0.582644	−	0.812727i	$-0.697982\pi$
$419$	−23.8529	−1.16529	−0.582644	+	0.812727i	$0.697982\pi$
$420$	−16.7625	−0.817928
$421$	−10.8301	−0.527827	−0.263914	−	0.964546i	$-0.585013\pi$
$421$	−10.8301	−0.527827	−0.263914	+	0.964546i	$0.585013\pi$
$422$	−5.20511	−0.253381
$423$	65.3259	3.17625
$424$	−1.04539	−0.0507688
$425$	0.954064	0.0462789
$426$	−4.71977	−0.228674
$427$	−30.1395	−1.45855
$428$	−9.48327	−0.458391
$429$	−4.57975	−0.221113
$430$	−11.1656	−0.538455
$431$	12.6296	0.608346	0.304173	−	0.952617i	$-0.401620\pi$
$431$	12.6296	0.608346	0.304173	+	0.952617i	$0.401620\pi$
$432$	6.80990	0.327641
$433$	−36.0140	−1.73072	−0.865362	−	0.501147i	$-0.832912\pi$
$433$	−36.0140	−1.73072	−0.865362	+	0.501147i	$0.832912\pi$
$434$	8.02707	0.385312
$435$	5.54251	0.265743
$436$	3.53757	0.169419
$437$	−1.50675	−0.0720775
$438$	−8.37743	−0.400289
$439$	31.5254	1.50462	0.752312	−	0.658807i	$-0.228939\pi$
$439$	31.5254	1.50462	0.752312	+	0.658807i	$0.228939\pi$
$440$	−4.11499	−0.196174
$441$	−2.53141	−0.120543
$442$	5.49554	0.261396
$443$	−14.3662	−0.682558	−0.341279	−	0.939962i	$-0.610860\pi$
$443$	−14.3662	−0.682558	−0.341279	+	0.939962i	$0.610860\pi$
$444$	−8.49464	−0.403138
$445$	34.0709	1.61512
$446$	27.1025	1.28334
$447$	−57.2998	−2.71019
$448$	−2.55487	−0.120706
$449$	24.6451	1.16307	0.581537	−	0.813520i	$-0.302451\pi$
$449$	24.6451	1.16307	0.581537	+	0.813520i	$0.302451\pi$
$450$	−0.812547	−0.0383038
$451$	−12.5266	−0.589856
$452$	1.27867	0.0601437
$453$	58.3076	2.73953
$454$	22.1702	1.04050
$455$	5.06756	0.237571
$456$	−1.40069	−0.0655934
$457$	9.09873	0.425621	0.212810	−	0.977094i	$-0.431738\pi$
$457$	9.09873	0.425621	0.212810	+	0.977094i	$0.431738\pi$
$458$	−22.9110	−1.07056
$459$	42.8250	1.99890
$460$	−7.05780	−0.329071
$461$	−23.6082	−1.09954	−0.549772	−	0.835315i	$-0.685285\pi$
$461$	−23.6082	−1.09954	−0.549772	+	0.835315i	$0.685285\pi$
$462$	13.3893	0.622925
$463$	31.4125	1.45986	0.729932	−	0.683520i	$-0.239552\pi$
$463$	31.4125	1.45986	0.729932	+	0.683520i	$0.239552\pi$
$464$	0.844764	0.0392172
$465$	20.6139	0.955945
$466$	10.9821	0.508738
$467$	−29.0429	−1.34395	−0.671974	−	0.740575i	$-0.734553\pi$
$467$	−29.0429	−1.34395	−0.671974	+	0.740575i	$0.734553\pi$
$468$	−4.68039	−0.216351
$469$	11.8449	0.546947
$470$	−27.6843	−1.27698
$471$	15.8375	0.729754
$472$	9.06837	0.417405
$473$	8.91869	0.410082
$474$	−47.0627	−2.16166
$475$	0.0735137	0.00337304
$476$	−16.0666	−0.736413
$477$	5.59896	0.256359
$478$	−19.9767	−0.913712
$479$	−14.2706	−0.652041	−0.326021	−	0.945363i	$-0.605708\pi$
$479$	−14.2706	−0.652041	−0.326021	+	0.945363i	$0.605708\pi$
$480$	−6.56101	−0.299468
$481$	2.56806	0.117093
$482$	−12.4053	−0.565046
$483$	22.9645	1.04492
$484$	−7.71311	−0.350596
$485$	36.6490	1.66414
$486$	9.97280	0.452376
$487$	28.3344	1.28396	0.641978	−	0.766723i	$-0.278114\pi$
$487$	28.3344	1.28396	0.641978	+	0.766723i	$0.278114\pi$
$488$	−11.7969	−0.534020
$489$	12.0081	0.543027
$490$	1.07278	0.0484632
$491$	−28.9352	−1.30583	−0.652913	−	0.757433i	$-0.726453\pi$
$491$	−28.9352	−1.30583	−0.652913	+	0.757433i	$0.726453\pi$
$492$	−19.9727	−0.900438
$493$	5.31241	0.239259
$494$	0.423449	0.0190519
$495$	22.0392	0.990589
$496$	3.14187	0.141074
$497$	−4.17153	−0.187118
$498$	−51.0477	−2.28750
$499$	21.1371	0.946226	0.473113	−	0.881002i	$-0.343130\pi$
$499$	21.1371	0.946226	0.473113	+	0.881002i	$0.343130\pi$
$500$	−11.0043	−0.492129
$501$	11.1208	0.496841
$502$	−6.36715	−0.284180
$503$	24.8173	1.10655	0.553275	−	0.832999i	$-0.313378\pi$
$503$	24.8173	1.10655	0.553275	+	0.832999i	$0.313378\pi$
$504$	13.6835	0.609510
$505$	21.8692	0.973167
$506$	5.63750	0.250617
$507$	−35.3709	−1.57088
$508$	6.49545	0.288189
$509$	−18.9236	−0.838773	−0.419387	−	0.907808i	$-0.637755\pi$
$509$	−18.9236	−0.838773	−0.419387	+	0.907808i	$0.637755\pi$
$510$	−41.2598	−1.82702
$511$	−7.40431	−0.327547
$512$	−1.00000	−0.0441942
$513$	3.29980	0.145690
$514$	−24.7563	−1.09195
$515$	−3.94770	−0.173956
$516$	14.2201	0.626006
$517$	22.1131	0.972535
$518$	−7.50790	−0.329878
$519$	−26.8980	−1.18069
$520$	1.98349	0.0869818
$521$	−34.6970	−1.52010	−0.760052	−	0.649862i	$-0.774827\pi$
$521$	−34.6970	−1.52010	−0.760052	+	0.649862i	$0.774827\pi$
$522$	−4.52442	−0.198028
$523$	−13.7557	−0.601496	−0.300748	−	0.953704i	$-0.597236\pi$
$523$	−13.7557	−0.601496	−0.300748	+	0.953704i	$0.597236\pi$
$524$	−13.0619	−0.570612
$525$	−1.12043	−0.0488995
$526$	19.7295	0.860248
$527$	19.7581	0.860676
$528$	5.24068	0.228071
$529$	−13.3309	−0.579604
$530$	−2.37277	−0.103067
$531$	−48.5687	−2.10770
$532$	−1.23799	−0.0536735
$533$	6.03804	0.261536
$534$	−43.3913	−1.87773
$535$	−21.5245	−0.930587
$536$	4.63621	0.200254
$537$	−25.3308	−1.09311
$538$	20.1023	0.866672
$539$	−0.856894	−0.0369091
$540$	15.4567	0.665150
$541$	−10.2511	−0.440729	−0.220365	−	0.975418i	$-0.570725\pi$
$541$	−10.2511	−0.440729	−0.220365	+	0.975418i	$0.570725\pi$
$542$	−22.2613	−0.956205
$543$	−7.49144	−0.321488
$544$	−6.28864	−0.269623
$545$	8.02935	0.343940
$546$	−6.45384	−0.276199
$547$	5.76289	0.246403	0.123202	−	0.992382i	$-0.460684\pi$
$547$	5.76289	0.246403	0.123202	+	0.992382i	$0.460684\pi$
$548$	−12.9071	−0.551363
$549$	63.1822	2.69655
$550$	−0.275051	−0.0117282
$551$	0.409339	0.0174384
$552$	8.98852	0.382577
$553$	−41.5959	−1.76884
$554$	7.78638	0.330812
$555$	−19.2806	−0.818417
$556$	−7.57641	−0.321311
$557$	−35.1316	−1.48858	−0.744288	−	0.667859i	$-0.767211\pi$
$557$	−35.1316	−1.48858	−0.744288	+	0.667859i	$0.767211\pi$
$558$	−16.8274	−0.712359
$559$	−4.29895	−0.181826
$560$	−5.79888	−0.245048
$561$	32.9568	1.39144
$562$	14.2853	0.602589
$563$	43.7597	1.84425	0.922126	−	0.386891i	$-0.126451\pi$
$563$	43.7597	1.84425	0.922126	+	0.386891i	$0.126451\pi$
$564$	35.2576	1.48461
$565$	2.90225	0.122099
$566$	−18.7537	−0.788275
$567$	−9.24221	−0.388136
$568$	−1.63277	−0.0685097
$569$	26.3951	1.10654	0.553269	−	0.833002i	$-0.313380\pi$
$569$	26.3951	1.10654	0.553269	+	0.833002i	$0.313380\pi$
$570$	−3.17920	−0.133162
$571$	22.4102	0.937836	0.468918	−	0.883242i	$-0.344644\pi$
$571$	22.4102	0.937836	0.468918	+	0.883242i	$0.344644\pi$
$572$	−1.58434	−0.0662444
$573$	56.6570	2.36688
$574$	−17.6527	−0.736808
$575$	−0.471752	−0.0196734
$576$	5.35584	0.223160
$577$	31.9104	1.32845	0.664224	−	0.747533i	$-0.268762\pi$
$577$	31.9104	1.32845	0.664224	+	0.747533i	$0.268762\pi$
$578$	−22.5470	−0.937830
$579$	−24.4970	−1.01806
$580$	1.91739	0.0796154
$581$	−45.1180	−1.87181
$582$	−46.6747	−1.93473
$583$	1.89528	0.0784944
$584$	−2.89812	−0.119925
$585$	−10.6233	−0.439217
$586$	−17.5586	−0.725338
$587$	18.3718	0.758287	0.379143	−	0.925338i	$-0.376219\pi$
$587$	18.3718	0.758287	0.379143	+	0.925338i	$0.376219\pi$
$588$	−1.36625	−0.0563431
$589$	1.52242	0.0627304
$590$	20.5828	0.847381
$591$	27.7825	1.14282
$592$	−2.93867	−0.120778
$593$	−12.7768	−0.524682	−0.262341	−	0.964975i	$-0.584495\pi$
$593$	−12.7768	−0.524682	−0.262341	+	0.964975i	$0.584495\pi$
$594$	−12.3462	−0.506571
$595$	−36.4671	−1.49500
$596$	−19.8225	−0.811961
$597$	−76.5205	−3.13177
$598$	−2.71736	−0.111121
$599$	7.58976	0.310109	0.155055	−	0.987906i	$-0.450445\pi$
$599$	7.58976	0.310109	0.155055	+	0.987906i	$0.450445\pi$
$600$	−0.438547	−0.0179036
$601$	−20.2063	−0.824234	−0.412117	−	0.911131i	$-0.635211\pi$
$601$	−20.2063	−0.824234	−0.412117	+	0.911131i	$0.635211\pi$
$602$	12.5683	0.512246
$603$	−24.8308	−1.01119
$604$	20.1711	0.820752
$605$	−17.5067	−0.711750
$606$	−27.8517	−1.13140
$607$	22.5585	0.915623	0.457811	−	0.889049i	$-0.348633\pi$
$607$	22.5585	0.915623	0.457811	+	0.889049i	$0.348633\pi$
$608$	−0.484560	−0.0196515
$609$	−6.23877	−0.252808
$610$	−26.7758	−1.08412
$611$	−10.6589	−0.431212
$612$	33.6809	1.36147
$613$	7.64057	0.308600	0.154300	−	0.988024i	$-0.450688\pi$
$613$	7.64057	0.308600	0.154300	+	0.988024i	$0.450688\pi$
$614$	−12.1515	−0.490396
$615$	−45.3328	−1.82799
$616$	4.63192	0.186626
$617$	4.77453	0.192215	0.0961076	−	0.995371i	$-0.469361\pi$
$617$	4.77453	0.192215	0.0961076	+	0.995371i	$0.469361\pi$
$618$	5.02763	0.202241
$619$	9.52925	0.383013	0.191506	−	0.981491i	$-0.438663\pi$
$619$	9.52925	0.383013	0.191506	+	0.981491i	$0.438663\pi$
$620$	7.13123	0.286397
$621$	−21.1755	−0.849744
$622$	12.1912	0.488823
$623$	−38.3510	−1.53650
$624$	−2.52609	−0.101125
$625$	−25.7355	−1.02942
$626$	−21.9404	−0.876917
$627$	2.53942	0.101415
$628$	5.47888	0.218631
$629$	−18.4802	−0.736854
$630$	31.0579	1.23738
$631$	−11.5350	−0.459203	−0.229601	−	0.973285i	$-0.573742\pi$
$631$	−11.5350	−0.459203	−0.229601	+	0.973285i	$0.573742\pi$
$632$	−16.2810	−0.647625
$633$	15.0461	0.598030
$634$	12.6321	0.501684
$635$	14.7430	0.585057
$636$	3.02186	0.119825
$637$	0.413037	0.0163651
$638$	−1.53154	−0.0606342
$639$	8.74488	0.345942
$640$	−2.26974	−0.0897193
$641$	28.6096	1.13001	0.565007	−	0.825086i	$-0.308874\pi$
$641$	28.6096	1.13001	0.565007	+	0.825086i	$0.308874\pi$
$642$	27.4128	1.08190
$643$	−40.5293	−1.59832	−0.799160	−	0.601119i	$-0.794722\pi$
$643$	−40.5293	−1.59832	−0.799160	+	0.601119i	$0.794722\pi$
$644$	7.94442	0.313054
$645$	32.2759	1.27086
$646$	−3.04722	−0.119891
$647$	42.1971	1.65894	0.829470	−	0.558551i	$-0.188643\pi$
$647$	42.1971	1.65894	0.829470	+	0.558551i	$0.188643\pi$
$648$	−3.61749	−0.142108
$649$	−16.4408	−0.645356
$650$	0.132579	0.00520018
$651$	−23.2034	−0.909414
$652$	4.15414	0.162689
$653$	−26.8150	−1.04935	−0.524676	−	0.851302i	$-0.675814\pi$
$653$	−26.8150	−1.04935	−0.524676	+	0.851302i	$0.675814\pi$
$654$	−10.2259	−0.399863
$655$	−29.6471	−1.15841
$656$	−6.90942	−0.269768
$657$	15.5219	0.605565
$658$	31.1621	1.21482
$659$	−18.1178	−0.705771	−0.352885	−	0.935667i	$-0.614799\pi$
$659$	−18.1178	−0.705771	−0.352885	+	0.935667i	$0.614799\pi$
$660$	11.8950	0.463011
$661$	−21.1135	−0.821218	−0.410609	−	0.911811i	$-0.634684\pi$
$661$	−21.1135	−0.821218	−0.410609	+	0.911811i	$0.634684\pi$
$662$	30.6360	1.19070
$663$	−15.8857	−0.616949
$664$	−17.6596	−0.685327
$665$	−2.80991	−0.108963
$666$	15.7390	0.609874
$667$	−2.62681	−0.101710
$668$	3.84717	0.148851
$669$	−78.3436	−3.02894
$670$	10.5230	0.406538
$671$	21.3875	0.825655
$672$	7.38522	0.284891
$673$	−10.3305	−0.398212	−0.199106	−	0.979978i	$-0.563804\pi$
$673$	−10.3305	−0.398212	−0.199106	+	0.979978i	$0.563804\pi$
$674$	18.6891	0.719878
$675$	1.03315	0.0397658
$676$	−12.2363	−0.470628
$677$	33.3187	1.28054	0.640272	−	0.768149i	$-0.278822\pi$
$677$	33.3187	1.28054	0.640272	+	0.768149i	$0.278822\pi$
$678$	−3.69619	−0.141951
$679$	−41.2529	−1.58314
$680$	−14.2736	−0.547366
$681$	−64.0861	−2.45579
$682$	−5.69615	−0.218117
$683$	−50.7033	−1.94011	−0.970054	−	0.242891i	$-0.921904\pi$
$683$	−50.7033	−1.94011	−0.970054	+	0.242891i	$0.921904\pi$
$684$	2.59522	0.0992309
$685$	−29.2957	−1.11933
$686$	−19.0916	−0.728922
$687$	66.2277	2.52674
$688$	4.91935	0.187549
$689$	−0.913554	−0.0348036
$690$	20.4016	0.776676
$691$	−43.2619	−1.64576	−0.822880	−	0.568215i	$-0.807634\pi$
$691$	−43.2619	−1.64576	−0.822880	+	0.568215i	$0.807634\pi$
$692$	−9.30518	−0.353730
$693$	−24.8078	−0.942372
$694$	−7.50829	−0.285011
$695$	−17.1965	−0.652299
$696$	−2.44191	−0.0925605
$697$	−43.4508	−1.64582
$698$	−25.8610	−0.978852
$699$	−31.7455	−1.20073
$700$	−0.387605	−0.0146501
$701$	−5.58030	−0.210765	−0.105383	−	0.994432i	$-0.533607\pi$
$701$	−5.58030	−0.210765	−0.105383	+	0.994432i	$0.533607\pi$
$702$	5.95107	0.224609
$703$	−1.42396	−0.0537056
$704$	1.81298	0.0683292
$705$	80.0255	3.01393
$706$	5.71616	0.215130
$707$	−24.6165	−0.925798
$708$	−26.2134	−0.985162
$709$	42.4605	1.59464	0.797318	−	0.603559i	$-0.206251\pi$
$709$	42.4605	1.59464	0.797318	+	0.603559i	$0.206251\pi$
$710$	−3.70597	−0.139083
$711$	87.1986	3.27020
$712$	−15.0109	−0.562559
$713$	−9.76971	−0.365879
$714$	46.4430	1.73809
$715$	−3.59603	−0.134484
$716$	−8.76303	−0.327490
$717$	57.7455	2.15655
$718$	−23.2179	−0.866484
$719$	38.0936	1.42065	0.710326	−	0.703873i	$-0.248548\pi$
$719$	38.0936	1.42065	0.710326	+	0.703873i	$0.248548\pi$
$720$	12.1564	0.453040
$721$	4.44362	0.165489
$722$	18.7652	0.698368
$723$	35.8594	1.33362
$724$	−2.59161	−0.0963165
$725$	0.128161	0.00475978
$726$	22.2959	0.827477
$727$	−25.0520	−0.929128	−0.464564	−	0.885540i	$-0.653789\pi$
$727$	−25.0520	−0.929128	−0.464564	+	0.885540i	$0.653789\pi$
$728$	−2.23266	−0.0827479
$729$	−39.6803	−1.46964
$730$	−6.57797	−0.243462
$731$	30.9360	1.14421
$732$	34.1006	1.26040
$733$	−27.1094	−1.00131	−0.500655	−	0.865647i	$-0.666908\pi$
$733$	−27.1094	−1.00131	−0.500655	+	0.865647i	$0.666908\pi$
$734$	31.2320	1.15279
$735$	−3.10102	−0.114383
$736$	3.10952	0.114618
$737$	−8.40535	−0.309615
$738$	37.0057	1.36220
$739$	−35.3253	−1.29946	−0.649731	−	0.760165i	$-0.725118\pi$
$739$	−35.3253	−1.29946	−0.649731	+	0.760165i	$0.725118\pi$
$740$	−6.67000	−0.245194
$741$	−1.22404	−0.0449663
$742$	2.67084	0.0980498
$743$	30.1482	1.10603	0.553015	−	0.833171i	$-0.313477\pi$
$743$	30.1482	1.10603	0.553015	+	0.833171i	$0.313477\pi$
$744$	−9.08204	−0.332964
$745$	−44.9919	−1.64837
$746$	26.9797	0.987798
$747$	94.5821	3.46058
$748$	11.4012	0.416868
$749$	24.2285	0.885290
$750$	31.8097	1.16153
$751$	37.7058	1.37590	0.687951	−	0.725757i	$-0.258510\pi$
$751$	37.7058	1.37590	0.687951	+	0.725757i	$0.258510\pi$
$752$	12.1971	0.444784
$753$	18.4052	0.670722
$754$	0.738226	0.0268846
$755$	45.7832	1.66622
$756$	−17.3984	−0.632773
$757$	−28.0545	−1.01966	−0.509828	−	0.860276i	$-0.670291\pi$
$757$	−28.0545	−1.01966	−0.509828	+	0.860276i	$0.670291\pi$
$758$	2.36203	0.0857928
$759$	−16.2960	−0.591508
$760$	−1.09982	−0.0398948
$761$	−32.9619	−1.19487	−0.597434	−	0.801918i	$-0.703813\pi$
$761$	−32.9619	−1.19487	−0.597434	+	0.801918i	$0.703813\pi$
$762$	−18.7761	−0.680185
$763$	−9.03802	−0.327198
$764$	19.6001	0.709108
$765$	76.4469	2.76394
$766$	−17.7539	−0.641475
$767$	7.92471	0.286145
$768$	2.89065	0.104307
$769$	35.4126	1.27701	0.638505	−	0.769617i	$-0.279553\pi$
$769$	35.4126	1.27701	0.638505	+	0.769617i	$0.279553\pi$
$770$	10.5133	0.378871
$771$	71.5618	2.57724
$772$	−8.47458	−0.305007
$773$	−18.7805	−0.675488	−0.337744	−	0.941238i	$-0.609664\pi$
$773$	−18.7805	−0.675488	−0.337744	+	0.941238i	$0.609664\pi$
$774$	−26.3473	−0.947033
$775$	0.476660	0.0171221
$776$	−16.1468	−0.579636
$777$	21.7027	0.778580
$778$	−36.1880	−1.29740
$779$	−3.34803	−0.119956
$780$	−5.73357	−0.205295
$781$	2.96019	0.105924
$782$	19.5546	0.699273
$783$	5.75275	0.205587
$784$	−0.472644	−0.0168802
$785$	12.4356	0.443847
$786$	37.7573	1.34676
$787$	−37.0735	−1.32153	−0.660764	−	0.750594i	$-0.729767\pi$
$787$	−37.0735	−1.32153	−0.660764	+	0.750594i	$0.729767\pi$
$788$	9.61119	0.342384
$789$	−57.0311	−2.03036
$790$	−36.9537	−1.31475
$791$	−3.26684	−0.116155
$792$	−9.71002	−0.345031
$793$	−10.3091	−0.366088
$794$	26.0214	0.923464
$795$	6.85884	0.243258
$796$	−26.4717	−0.938266
$797$	−2.44971	−0.0867730	−0.0433865	−	0.999058i	$-0.513815\pi$
$797$	−2.44971	−0.0867730	−0.0433865	+	0.999058i	$0.513815\pi$
$798$	3.57858	0.126680
$799$	76.7033	2.71357
$800$	−0.151712	−0.00536384
$801$	80.3962	2.84066
$802$	18.5183	0.653903
$803$	5.25423	0.185418
$804$	−13.4016	−0.472640
$805$	18.0317	0.635536
$806$	2.74563	0.0967108
$807$	−58.1086	−2.04552
$808$	−9.63512	−0.338962
$809$	−2.08315	−0.0732397	−0.0366198	−	0.999329i	$-0.511659\pi$
$809$	−2.08315	−0.0732397	−0.0366198	+	0.999329i	$0.511659\pi$
$810$	−8.21076	−0.288497
$811$	−24.7974	−0.870756	−0.435378	−	0.900248i	$-0.643385\pi$
$811$	−24.7974	−0.870756	−0.435378	+	0.900248i	$0.643385\pi$
$812$	−2.15826	−0.0757401
$813$	64.3496	2.25684
$814$	5.32774	0.186737
$815$	9.42881	0.330277
$816$	18.1782	0.636365
$817$	2.38372	0.0833958
$818$	11.6561	0.407548
$819$	11.9578	0.417838
$820$	−15.6826	−0.547659
$821$	−32.0937	−1.12008	−0.560039	−	0.828466i	$-0.689214\pi$
$821$	−32.0937	−1.12008	−0.560039	+	0.828466i	$0.689214\pi$
$822$	37.3098	1.30133
$823$	−2.62317	−0.0914378	−0.0457189	−	0.998954i	$-0.514558\pi$
$823$	−2.62317	−0.0914378	−0.0457189	+	0.998954i	$0.514558\pi$
$824$	1.73927	0.0605905
$825$	0.795076	0.0276810
$826$	−23.1685	−0.806135
$827$	36.2426	1.26028	0.630139	−	0.776482i	$-0.282998\pi$
$827$	36.2426	1.26028	0.630139	+	0.776482i	$0.282998\pi$
$828$	−16.6541	−0.578769
$829$	−36.5575	−1.26969	−0.634847	−	0.772638i	$-0.718937\pi$
$829$	−36.5575	−1.26969	−0.634847	+	0.772638i	$0.718937\pi$
$830$	−40.0827	−1.39129
$831$	−22.5077	−0.780783
$832$	−0.873885	−0.0302965
$833$	−2.97229	−0.102984
$834$	21.9007	0.758360
$835$	8.73207	0.302186
$836$	0.878497	0.0303835
$837$	21.3958	0.739548
$838$	23.8529	0.823983
$839$	−1.60849	−0.0555313	−0.0277657	−	0.999614i	$-0.508839\pi$
$839$	−1.60849	−0.0555313	−0.0277657	+	0.999614i	$0.508839\pi$
$840$	16.7625	0.578362
$841$	−28.2864	−0.975392
$842$	10.8301	0.373230
$843$	−41.2937	−1.42223
$844$	5.20511	0.179167
$845$	−27.7733	−0.955429
$846$	−65.3259	−2.24595
$847$	19.7060	0.677105
$848$	1.04539	0.0358990
$849$	54.2102	1.86049
$850$	−0.954064	−0.0327241
$851$	9.13784	0.313241
$852$	4.71977	0.161697
$853$	−19.8211	−0.678662	−0.339331	−	0.940667i	$-0.610201\pi$
$853$	−19.8211	−0.678662	−0.339331	+	0.940667i	$0.610201\pi$
$854$	30.1395	1.03135
$855$	5.89048	0.201450
$856$	9.48327	0.324131
$857$	−25.5383	−0.872371	−0.436186	−	0.899857i	$-0.643671\pi$
$857$	−25.5383	−0.872371	−0.436186	+	0.899857i	$0.643671\pi$
$858$	4.57975	0.156350
$859$	−32.3699	−1.10445	−0.552224	−	0.833696i	$-0.686221\pi$
$859$	−32.3699	−1.10445	−0.552224	+	0.833696i	$0.686221\pi$
$860$	11.1656	0.380745
$861$	51.0276	1.73902
$862$	−12.6296	−0.430166
$863$	52.5873	1.79009	0.895047	−	0.445973i	$-0.147142\pi$
$863$	52.5873	1.79009	0.895047	+	0.445973i	$0.147142\pi$
$864$	−6.80990	−0.231677
$865$	−21.1203	−0.718112
$866$	36.0140	1.22381
$867$	65.1753	2.21347
$868$	−8.02707	−0.272456
$869$	29.5172	1.00130
$870$	−5.54251	−0.187909
$871$	4.05151	0.137280
$872$	−3.53757	−0.119797
$873$	86.4796	2.92689
$874$	1.50675	0.0509665
$875$	28.1147	0.950449
$876$	8.37743	0.283047
$877$	12.0567	0.407126	0.203563	−	0.979062i	$-0.434748\pi$
$877$	12.0567	0.407126	0.203563	+	0.979062i	$0.434748\pi$
$878$	−31.5254	−1.06393
$879$	50.7556	1.71194
$880$	4.11499	0.138716
$881$	8.94408	0.301334	0.150667	−	0.988585i	$-0.451858\pi$
$881$	8.94408	0.301334	0.150667	+	0.988585i	$0.451858\pi$
$882$	2.53141	0.0852369
$883$	6.90885	0.232501	0.116251	−	0.993220i	$-0.462912\pi$
$883$	6.90885	0.232501	0.116251	+	0.993220i	$0.462912\pi$
$884$	−5.49554	−0.184835
$885$	−59.4977	−1.99999
$886$	14.3662	0.482642
$887$	−30.4602	−1.02275	−0.511377	−	0.859357i	$-0.670864\pi$
$887$	−30.4602	−1.02275	−0.511377	+	0.859357i	$0.670864\pi$
$888$	8.49464	0.285062
$889$	−16.5950	−0.556580
$890$	−34.0709	−1.14206
$891$	6.55843	0.219716
$892$	−27.1025	−0.907457
$893$	5.91024	0.197779
$894$	57.2998	1.91639
$895$	−19.8898	−0.664842
$896$	2.55487	0.0853522
$897$	7.85494	0.262269
$898$	−24.6451	−0.822418
$899$	2.65414	0.0885205
$900$	0.812547	0.0270849
$901$	6.57410	0.219015
$902$	12.5266	0.417091
$903$	−36.3305	−1.20900
$904$	−1.27867	−0.0425280
$905$	−5.88228	−0.195534
$906$	−58.3076	−1.93714
$907$	46.6236	1.54811	0.774055	−	0.633118i	$-0.218225\pi$
$907$	46.6236	1.54811	0.774055	+	0.633118i	$0.218225\pi$
$908$	−22.1702	−0.735743
$909$	51.6042	1.71160
$910$	−5.06756	−0.167988
$911$	−29.9043	−0.990774	−0.495387	−	0.868672i	$-0.664974\pi$
$911$	−29.9043	−0.990774	−0.495387	+	0.868672i	$0.664974\pi$
$912$	1.40069	0.0463815
$913$	32.0165	1.05959
$914$	−9.09873	−0.300959
$915$	77.3995	2.55875
$916$	22.9110	0.757001
$917$	33.3714	1.10202
$918$	−42.8250	−1.41343
$919$	−34.9535	−1.15301	−0.576504	−	0.817094i	$-0.695584\pi$
$919$	−34.9535	−1.15301	−0.576504	+	0.817094i	$0.695584\pi$
$920$	7.05780	0.232689
$921$	35.1258	1.15743
$922$	23.6082	0.777495
$923$	−1.42686	−0.0469656
$924$	−13.3893	−0.440474
$925$	−0.445832	−0.0146589
$926$	−31.4125	−1.03228
$927$	−9.31527	−0.305954
$928$	−0.844764	−0.0277307
$929$	−18.0818	−0.593245	−0.296622	−	0.954995i	$-0.595860\pi$
$929$	−18.0818	−0.593245	−0.296622	+	0.954995i	$0.595860\pi$
$930$	−20.6139	−0.675955
$931$	−0.229024	−0.00750597
$932$	−10.9821	−0.359732
$933$	−35.2405	−1.15372
$934$	29.0429	0.950314
$935$	25.8777	0.846290
$936$	4.68039	0.152983
$937$	53.6261	1.75189	0.875945	−	0.482412i	$-0.160239\pi$
$937$	53.6261	1.75189	0.875945	+	0.482412i	$0.160239\pi$
$938$	−11.8449	−0.386750
$939$	63.4221	2.06970
$940$	27.6843	0.902962
$941$	−29.4855	−0.961200	−0.480600	−	0.876940i	$-0.659581\pi$
$941$	−29.4855	−0.961200	−0.480600	+	0.876940i	$0.659581\pi$
$942$	−15.8375	−0.516014
$943$	21.4850	0.699647
$944$	−9.06837	−0.295150
$945$	−39.4898	−1.28460
$946$	−8.91869	−0.289971
$947$	28.1360	0.914297	0.457148	−	0.889390i	$-0.348871\pi$
$947$	28.1360	0.914297	0.457148	+	0.889390i	$0.348871\pi$
$948$	47.0627	1.52853
$949$	−2.53262	−0.0822124
$950$	−0.0735137	−0.00238510
$951$	−36.5149	−1.18408
$952$	16.0666	0.520723
$953$	−31.1965	−1.01056	−0.505278	−	0.862957i	$-0.668610\pi$
$953$	−31.1965	−1.01056	−0.505278	+	0.862957i	$0.668610\pi$
$954$	−5.59896	−0.181273
$955$	44.4872	1.43957
$956$	19.9767	0.646092
$957$	4.42714	0.143109
$958$	14.2706	0.461063
$959$	32.9759	1.06485
$960$	6.56101	0.211756
$961$	−21.1286	−0.681569
$962$	−2.56806	−0.0827974
$963$	−50.7908	−1.63671
$964$	12.4053	0.399548
$965$	−19.2351	−0.619199
$966$	−22.9645	−0.738871
$967$	15.6163	0.502186	0.251093	−	0.967963i	$-0.419210\pi$
$967$	15.6163	0.502186	0.251093	+	0.967963i	$0.419210\pi$
$968$	7.71311	0.247909
$969$	8.80844	0.282968
$970$	−36.6490	−1.17673
$971$	3.58758	0.115131	0.0575655	−	0.998342i	$-0.481666\pi$
$971$	3.58758	0.115131	0.0575655	+	0.998342i	$0.481666\pi$
$972$	−9.97280	−0.319878
$973$	19.3567	0.620548
$974$	−28.3344	−0.907894
$975$	−0.383239	−0.0122735
$976$	11.7969	0.377609
$977$	24.0758	0.770252	0.385126	−	0.922864i	$-0.374158\pi$
$977$	24.0758	0.770252	0.385126	+	0.922864i	$0.374158\pi$
$978$	−12.0081	−0.383978
$979$	27.2145	0.869780
$980$	−1.07278	−0.0342687
$981$	18.9466	0.604920
$982$	28.9352	0.923358
$983$	13.9756	0.445751	0.222876	−	0.974847i	$-0.428456\pi$
$983$	13.9756	0.445751	0.222876	+	0.974847i	$0.428456\pi$
$984$	19.9727	0.636706
$985$	21.8149	0.695080
$986$	−5.31241	−0.169182
$987$	−90.0785	−2.86723
$988$	−0.423449	−0.0134717
$989$	−15.2968	−0.486411
$990$	−22.0392	−0.700452
$991$	−60.7625	−1.93018	−0.965092	−	0.261910i	$-0.915648\pi$
$991$	−60.7625	−1.93018	−0.965092	+	0.261910i	$0.915648\pi$
$992$	−3.14187	−0.0997545
$993$	−88.5579	−2.81030
$994$	4.17153	0.132313
$995$	−60.0839	−1.90479
$996$	51.0477	1.61751
$997$	−32.4119	−1.02650	−0.513248	−	0.858240i	$-0.671558\pi$
$997$	−32.4119	−1.02650	−0.513248	+	0.858240i	$0.671558\pi$
$998$	−21.1371	−0.669083
$999$	−20.0120	−0.633152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.70	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.70	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +2.89065 q^{3} +1.00000 q^{4} +2.26974 q^{5} -2.89065 q^{6} -2.55487 q^{7} -1.00000 q^{8} +5.35584 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +2.89065 q^{3} +1.00000 q^{4} +2.26974 q^{5} -2.89065 q^{6} -2.55487 q^{7} -1.00000 q^{8} +5.35584 q^{9} -2.26974 q^{10} +1.81298 q^{11} +2.89065 q^{12} -0.873885 q^{13} +2.55487 q^{14} +6.56101 q^{15} +1.00000 q^{16} +6.28864 q^{17} -5.35584 q^{18} +0.484560 q^{19} +2.26974 q^{20} -7.38522 q^{21} -1.81298 q^{22} -3.10952 q^{23} -2.89065 q^{24} +0.151712 q^{25} +0.873885 q^{26} +6.80990 q^{27} -2.55487 q^{28} +0.844764 q^{29} -6.56101 q^{30} +3.14187 q^{31} -1.00000 q^{32} +5.24068 q^{33} -6.28864 q^{34} -5.79888 q^{35} +5.35584 q^{36} -2.93867 q^{37} -0.484560 q^{38} -2.52609 q^{39} -2.26974 q^{40} -6.90942 q^{41} +7.38522 q^{42} +4.91935 q^{43} +1.81298 q^{44} +12.1564 q^{45} +3.10952 q^{46} +12.1971 q^{47} +2.89065 q^{48} -0.472644 q^{49} -0.151712 q^{50} +18.1782 q^{51} -0.873885 q^{52} +1.04539 q^{53} -6.80990 q^{54} +4.11499 q^{55} +2.55487 q^{56} +1.40069 q^{57} -0.844764 q^{58} -9.06837 q^{59} +6.56101 q^{60} +11.7969 q^{61} -3.14187 q^{62} -13.6835 q^{63} +1.00000 q^{64} -1.98349 q^{65} -5.24068 q^{66} -4.63621 q^{67} +6.28864 q^{68} -8.98852 q^{69} +5.79888 q^{70} +1.63277 q^{71} -5.35584 q^{72} +2.89812 q^{73} +2.93867 q^{74} +0.438547 q^{75} +0.484560 q^{76} -4.63192 q^{77} +2.52609 q^{78} +16.2810 q^{79} +2.26974 q^{80} +3.61749 q^{81} +6.90942 q^{82} +17.6596 q^{83} -7.38522 q^{84} +14.2736 q^{85} -4.91935 q^{86} +2.44191 q^{87} -1.81298 q^{88} +15.0109 q^{89} -12.1564 q^{90} +2.23266 q^{91} -3.10952 q^{92} +9.08204 q^{93} -12.1971 q^{94} +1.09982 q^{95} -2.89065 q^{96} +16.1468 q^{97} +0.472644 q^{98} +9.71002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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