LMFDB - Embedded newform 8002.2.a.e.1.11

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			1.11
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)

$f(q)$	$=$	$q-1.00000 q^{2} -2.42114 q^{3} +1.00000 q^{4} -1.19106 q^{5} +2.42114 q^{6} -3.77401 q^{7} -1.00000 q^{8} +2.86190 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.42114 q^{3} +1.00000 q^{4} -1.19106 q^{5} +2.42114 q^{6} -3.77401 q^{7} -1.00000 q^{8} +2.86190 q^{9} +1.19106 q^{10} -4.05323 q^{11} -2.42114 q^{12} +4.55675 q^{13} +3.77401 q^{14} +2.88372 q^{15} +1.00000 q^{16} -1.21373 q^{17} -2.86190 q^{18} +3.72235 q^{19} -1.19106 q^{20} +9.13739 q^{21} +4.05323 q^{22} +5.44972 q^{23} +2.42114 q^{24} -3.58137 q^{25} -4.55675 q^{26} +0.334365 q^{27} -3.77401 q^{28} -4.71760 q^{29} -2.88372 q^{30} +4.49242 q^{31} -1.00000 q^{32} +9.81341 q^{33} +1.21373 q^{34} +4.49508 q^{35} +2.86190 q^{36} -3.22114 q^{37} -3.72235 q^{38} -11.0325 q^{39} +1.19106 q^{40} +2.91252 q^{41} -9.13739 q^{42} -0.507770 q^{43} -4.05323 q^{44} -3.40870 q^{45} -5.44972 q^{46} +1.10085 q^{47} -2.42114 q^{48} +7.24314 q^{49} +3.58137 q^{50} +2.93862 q^{51} +4.55675 q^{52} +0.544770 q^{53} -0.334365 q^{54} +4.82764 q^{55} +3.77401 q^{56} -9.01232 q^{57} +4.71760 q^{58} -1.10577 q^{59} +2.88372 q^{60} -14.8634 q^{61} -4.49242 q^{62} -10.8008 q^{63} +1.00000 q^{64} -5.42737 q^{65} -9.81341 q^{66} -3.02571 q^{67} -1.21373 q^{68} -13.1945 q^{69} -4.49508 q^{70} +15.7675 q^{71} -2.86190 q^{72} -6.91652 q^{73} +3.22114 q^{74} +8.67099 q^{75} +3.72235 q^{76} +15.2969 q^{77} +11.0325 q^{78} -9.08476 q^{79} -1.19106 q^{80} -9.39524 q^{81} -2.91252 q^{82} -2.39658 q^{83} +9.13739 q^{84} +1.44563 q^{85} +0.507770 q^{86} +11.4220 q^{87} +4.05323 q^{88} -13.5949 q^{89} +3.40870 q^{90} -17.1972 q^{91} +5.44972 q^{92} -10.8768 q^{93} -1.10085 q^{94} -4.43355 q^{95} +2.42114 q^{96} -6.06191 q^{97} -7.24314 q^{98} -11.5999 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.42114	−1.39784	−0.698922	−	0.715198i	$-0.746336\pi$
$3$	−2.42114	−1.39784	−0.698922	+	0.715198i	$0.746336\pi$
$4$	1.00000	0.500000
$5$	−1.19106	−0.532659	−0.266330	−	0.963882i	$-0.585811\pi$
$5$	−1.19106	−0.532659	−0.266330	+	0.963882i	$0.585811\pi$
$6$	2.42114	0.988424
$7$	−3.77401	−1.42644	−0.713220	−	0.700940i	$-0.752764\pi$
$7$	−3.77401	−1.42644	−0.713220	+	0.700940i	$0.752764\pi$
$8$	−1.00000	−0.353553
$9$	2.86190	0.953966
$10$	1.19106	0.376647
$11$	−4.05323	−1.22209	−0.611047	−	0.791595i	$-0.709251\pi$
$11$	−4.05323	−1.22209	−0.611047	+	0.791595i	$0.709251\pi$
$12$	−2.42114	−0.698922
$13$	4.55675	1.26381	0.631907	−	0.775044i	$-0.282272\pi$
$13$	4.55675	1.26381	0.631907	+	0.775044i	$0.282272\pi$
$14$	3.77401	1.00865
$15$	2.88372	0.744574
$16$	1.00000	0.250000
$17$	−1.21373	−0.294374	−0.147187	−	0.989109i	$-0.547022\pi$
$17$	−1.21373	−0.294374	−0.147187	+	0.989109i	$0.547022\pi$
$18$	−2.86190	−0.674556
$19$	3.72235	0.853966	0.426983	−	0.904260i	$-0.359576\pi$
$19$	3.72235	0.853966	0.426983	+	0.904260i	$0.359576\pi$
$20$	−1.19106	−0.266330
$21$	9.13739	1.99394
$22$	4.05323	0.864150
$23$	5.44972	1.13635	0.568173	−	0.822909i	$-0.307651\pi$
$23$	5.44972	1.13635	0.568173	+	0.822909i	$0.307651\pi$
$24$	2.42114	0.494212
$25$	−3.58137	−0.716274
$26$	−4.55675	−0.893652
$27$	0.334365	0.0643485
$28$	−3.77401	−0.713220
$29$	−4.71760	−0.876036	−0.438018	−	0.898966i	$-0.644319\pi$
$29$	−4.71760	−0.876036	−0.438018	+	0.898966i	$0.644319\pi$
$30$	−2.88372	−0.526493
$31$	4.49242	0.806863	0.403431	−	0.915010i	$-0.367817\pi$
$31$	4.49242	0.806863	0.403431	+	0.915010i	$0.367817\pi$
$32$	−1.00000	−0.176777
$33$	9.81341	1.70829
$34$	1.21373	0.208154
$35$	4.49508	0.759807
$36$	2.86190	0.476983
$37$	−3.22114	−0.529551	−0.264776	−	0.964310i	$-0.585298\pi$
$37$	−3.22114	−0.529551	−0.264776	+	0.964310i	$0.585298\pi$
$38$	−3.72235	−0.603845
$39$	−11.0325	−1.76661
$40$	1.19106	0.188323
$41$	2.91252	0.454859	0.227430	−	0.973794i	$-0.426968\pi$
$41$	2.91252	0.454859	0.227430	+	0.973794i	$0.426968\pi$
$42$	−9.13739	−1.40993
$43$	−0.507770	−0.0774342	−0.0387171	−	0.999250i	$-0.512327\pi$
$43$	−0.507770	−0.0774342	−0.0387171	+	0.999250i	$0.512327\pi$
$44$	−4.05323	−0.611047
$45$	−3.40870	−0.508139
$46$	−5.44972	−0.803517
$47$	1.10085	0.160575	0.0802874	−	0.996772i	$-0.474416\pi$
$47$	1.10085	0.160575	0.0802874	+	0.996772i	$0.474416\pi$
$48$	−2.42114	−0.349461
$49$	7.24314	1.03473
$50$	3.58137	0.506482
$51$	2.93862	0.411488
$52$	4.55675	0.631907
$53$	0.544770	0.0748299	0.0374149	−	0.999300i	$-0.488088\pi$
$53$	0.544770	0.0748299	0.0374149	+	0.999300i	$0.488088\pi$
$54$	−0.334365	−0.0455013
$55$	4.82764	0.650959
$56$	3.77401	0.504323
$57$	−9.01232	−1.19371
$58$	4.71760	0.619451
$59$	−1.10577	−0.143959	−0.0719797	−	0.997406i	$-0.522932\pi$
$59$	−1.10577	−0.143959	−0.0719797	+	0.997406i	$0.522932\pi$
$60$	2.88372	0.372287
$61$	−14.8634	−1.90306	−0.951532	−	0.307549i	$-0.900491\pi$
$61$	−14.8634	−1.90306	−0.951532	+	0.307549i	$0.900491\pi$
$62$	−4.49242	−0.570538
$63$	−10.8008	−1.36078
$64$	1.00000	0.125000
$65$	−5.42737	−0.673182
$66$	−9.81341	−1.20795
$67$	−3.02571	−0.369649	−0.184825	−	0.982772i	$-0.559172\pi$
$67$	−3.02571	−0.369649	−0.184825	+	0.982772i	$0.559172\pi$
$68$	−1.21373	−0.147187
$69$	−13.1945	−1.58843
$70$	−4.49508	−0.537265
$71$	15.7675	1.87126	0.935631	−	0.352979i	$-0.114831\pi$
$71$	15.7675	1.87126	0.935631	+	0.352979i	$0.114831\pi$
$72$	−2.86190	−0.337278
$73$	−6.91652	−0.809517	−0.404759	−	0.914424i	$-0.632644\pi$
$73$	−6.91652	−0.809517	−0.404759	+	0.914424i	$0.632644\pi$
$74$	3.22114	0.374449
$75$	8.67099	1.00124
$76$	3.72235	0.426983
$77$	15.2969	1.74324
$78$	11.0325	1.24919
$79$	−9.08476	−1.02212	−0.511058	−	0.859546i	$-0.670746\pi$
$79$	−9.08476	−1.02212	−0.511058	+	0.859546i	$0.670746\pi$
$80$	−1.19106	−0.133165
$81$	−9.39524	−1.04392
$82$	−2.91252	−0.321634
$83$	−2.39658	−0.263058	−0.131529	−	0.991312i	$-0.541989\pi$
$83$	−2.39658	−0.263058	−0.131529	+	0.991312i	$0.541989\pi$
$84$	9.13739	0.996970
$85$	1.44563	0.156801
$86$	0.507770	0.0547542
$87$	11.4220	1.22456
$88$	4.05323	0.432075
$89$	−13.5949	−1.44106	−0.720530	−	0.693424i	$-0.756101\pi$
$89$	−13.5949	−1.44106	−0.720530	+	0.693424i	$0.756101\pi$
$90$	3.40870	0.359308
$91$	−17.1972	−1.80276
$92$	5.44972	0.568173
$93$	−10.8768	−1.12787
$94$	−1.10085	−0.113544
$95$	−4.43355	−0.454873
$96$	2.42114	0.247106
$97$	−6.06191	−0.615493	−0.307747	−	0.951468i	$-0.599575\pi$
$97$	−6.06191	−0.615493	−0.307747	+	0.951468i	$0.599575\pi$
$98$	−7.24314	−0.731667
$99$	−11.5999	−1.16584
$100$	−3.58137	−0.358137
$101$	−10.1678	−1.01173	−0.505866	−	0.862612i	$-0.668827\pi$
$101$	−10.1678	−1.01173	−0.505866	+	0.862612i	$0.668827\pi$
$102$	−2.93862	−0.290966
$103$	−13.0078	−1.28170	−0.640849	−	0.767667i	$-0.721418\pi$
$103$	−13.0078	−1.28170	−0.640849	+	0.767667i	$0.721418\pi$
$104$	−4.55675	−0.446826
$105$	−10.8832	−1.06209
$106$	−0.544770	−0.0529127
$107$	−4.76857	−0.460995	−0.230498	−	0.973073i	$-0.574035\pi$
$107$	−4.76857	−0.460995	−0.230498	+	0.973073i	$0.574035\pi$
$108$	0.334365	0.0321743
$109$	−8.45849	−0.810176	−0.405088	−	0.914278i	$-0.632759\pi$
$109$	−8.45849	−0.810176	−0.405088	+	0.914278i	$0.632759\pi$
$110$	−4.82764	−0.460298
$111$	7.79881	0.740230
$112$	−3.77401	−0.356610
$113$	18.4306	1.73380	0.866901	−	0.498481i	$-0.166109\pi$
$113$	18.4306	1.73380	0.866901	+	0.498481i	$0.166109\pi$
$114$	9.01232	0.844081
$115$	−6.49096	−0.605285
$116$	−4.71760	−0.438018
$117$	13.0409	1.20564
$118$	1.10577	0.101795
$119$	4.58064	0.419907
$120$	−2.88372	−0.263247
$121$	5.42863	0.493512
$122$	14.8634	1.34567
$123$	−7.05161	−0.635822
$124$	4.49242	0.403431
$125$	10.2209	0.914189
$126$	10.8008	0.962214
$127$	3.20094	0.284037	0.142019	−	0.989864i	$-0.454641\pi$
$127$	3.20094	0.284037	0.142019	+	0.989864i	$0.454641\pi$
$128$	−1.00000	−0.0883883
$129$	1.22938	0.108241
$130$	5.42737	0.476012
$131$	19.0299	1.66265	0.831324	−	0.555789i	$-0.187584\pi$
$131$	19.0299	1.66265	0.831324	+	0.555789i	$0.187584\pi$
$132$	9.81341	0.854147
$133$	−14.0482	−1.21813
$134$	3.02571	0.261382
$135$	−0.398249	−0.0342758
$136$	1.21373	0.104077
$137$	−4.95703	−0.423508	−0.211754	−	0.977323i	$-0.567918\pi$
$137$	−4.95703	−0.423508	−0.211754	+	0.977323i	$0.567918\pi$
$138$	13.1945	1.12319
$139$	−2.34546	−0.198939	−0.0994697	−	0.995041i	$-0.531715\pi$
$139$	−2.34546	−0.198939	−0.0994697	+	0.995041i	$0.531715\pi$
$140$	4.49508	0.379903
$141$	−2.66530	−0.224458
$142$	−15.7675	−1.32318
$143$	−18.4695	−1.54450
$144$	2.86190	0.238491
$145$	5.61895	0.466629
$146$	6.91652	0.572415
$147$	−17.5366	−1.44640
$148$	−3.22114	−0.264776
$149$	−9.26218	−0.758788	−0.379394	−	0.925235i	$-0.623867\pi$
$149$	−9.26218	−0.758788	−0.379394	+	0.925235i	$0.623867\pi$
$150$	−8.67099	−0.707983
$151$	−4.63025	−0.376805	−0.188402	−	0.982092i	$-0.560331\pi$
$151$	−4.63025	−0.376805	−0.188402	+	0.982092i	$0.560331\pi$
$152$	−3.72235	−0.301923
$153$	−3.47358	−0.280823
$154$	−15.2969	−1.23266
$155$	−5.35075	−0.429783
$156$	−11.0325	−0.883307
$157$	−14.6829	−1.17182	−0.585912	−	0.810375i	$-0.699264\pi$
$157$	−14.6829	−1.17182	−0.585912	+	0.810375i	$0.699264\pi$
$158$	9.08476	0.722745
$159$	−1.31896	−0.104600
$160$	1.19106	0.0941617
$161$	−20.5673	−1.62093
$162$	9.39524	0.738159
$163$	−4.37158	−0.342408	−0.171204	−	0.985236i	$-0.554766\pi$
$163$	−4.37158	−0.342408	−0.171204	+	0.985236i	$0.554766\pi$
$164$	2.91252	0.227430
$165$	−11.6884	−0.909939
$166$	2.39658	0.186010
$167$	−5.25233	−0.406438	−0.203219	−	0.979133i	$-0.565140\pi$
$167$	−5.25233	−0.406438	−0.203219	+	0.979133i	$0.565140\pi$
$168$	−9.13739	−0.704965
$169$	7.76396	0.597228
$170$	−1.44563	−0.110875
$171$	10.6530	0.814655
$172$	−0.507770	−0.0387171
$173$	11.0187	0.837740	0.418870	−	0.908046i	$-0.362426\pi$
$173$	11.0187	0.837740	0.418870	+	0.908046i	$0.362426\pi$
$174$	−11.4220	−0.865896
$175$	13.5161	1.02172
$176$	−4.05323	−0.305523
$177$	2.67723	0.201233
$178$	13.5949	1.01898
$179$	−2.29122	−0.171254	−0.0856270	−	0.996327i	$-0.527289\pi$
$179$	−2.29122	−0.171254	−0.0856270	+	0.996327i	$0.527289\pi$
$180$	−3.40870	−0.254069
$181$	8.46887	0.629486	0.314743	−	0.949177i	$-0.398082\pi$
$181$	8.46887	0.629486	0.314743	+	0.949177i	$0.398082\pi$
$182$	17.1972	1.27474
$183$	35.9863	2.66019
$184$	−5.44972	−0.401759
$185$	3.83657	0.282070
$186$	10.8768	0.797523
$187$	4.91954	0.359752
$188$	1.10085	0.0802874
$189$	−1.26190	−0.0917894
$190$	4.43355	0.321644
$191$	18.4418	1.33440	0.667200	−	0.744879i	$-0.267493\pi$
$191$	18.4418	1.33440	0.667200	+	0.744879i	$0.267493\pi$
$192$	−2.42114	−0.174730
$193$	4.83354	0.347926	0.173963	−	0.984752i	$-0.444343\pi$
$193$	4.83354	0.347926	0.173963	+	0.984752i	$0.444343\pi$
$194$	6.06191	0.435220
$195$	13.1404	0.941004
$196$	7.24314	0.517367
$197$	19.4368	1.38482	0.692408	−	0.721506i	$-0.256550\pi$
$197$	19.4368	1.38482	0.692408	+	0.721506i	$0.256550\pi$
$198$	11.5999	0.824370
$199$	0.391267	0.0277362	0.0138681	−	0.999904i	$-0.495586\pi$
$199$	0.391267	0.0277362	0.0138681	+	0.999904i	$0.495586\pi$
$200$	3.58137	0.253241
$201$	7.32566	0.516712
$202$	10.1678	0.715402
$203$	17.8043	1.24961
$204$	2.93862	0.205744
$205$	−3.46899	−0.242285
$206$	13.0078	0.906298
$207$	15.5965	1.08403
$208$	4.55675	0.315954
$209$	−15.0875	−1.04363
$210$	10.8832	0.751012
$211$	−1.44290	−0.0993332	−0.0496666	−	0.998766i	$-0.515816\pi$
$211$	−1.44290	−0.0993332	−0.0496666	+	0.998766i	$0.515816\pi$
$212$	0.544770	0.0374149
$213$	−38.1754	−2.61573
$214$	4.76857	0.325973
$215$	0.604785	0.0412460
$216$	−0.334365	−0.0227506
$217$	−16.9544	−1.15094
$218$	8.45849	0.572881
$219$	16.7458	1.13158
$220$	4.82764	0.325480
$221$	−5.53068	−0.372034
$222$	−7.79881	−0.523422
$223$	0.155125	0.0103879	0.00519397	−	0.999987i	$-0.498347\pi$
$223$	0.155125	0.0103879	0.00519397	+	0.999987i	$0.498347\pi$
$224$	3.77401	0.252162
$225$	−10.2495	−0.683301
$226$	−18.4306	−1.22598
$227$	12.9969	0.862636	0.431318	−	0.902200i	$-0.358049\pi$
$227$	12.9969	0.862636	0.431318	+	0.902200i	$0.358049\pi$
$228$	−9.01232	−0.596856
$229$	−21.8368	−1.44302	−0.721508	−	0.692406i	$-0.756551\pi$
$229$	−21.8368	−1.44302	−0.721508	+	0.692406i	$0.756551\pi$
$230$	6.49096	0.428001
$231$	−37.0359	−2.43678
$232$	4.71760	0.309726
$233$	3.15738	0.206847	0.103423	−	0.994637i	$-0.467020\pi$
$233$	3.15738	0.206847	0.103423	+	0.994637i	$0.467020\pi$
$234$	−13.0409	−0.852513
$235$	−1.31118	−0.0855317
$236$	−1.10577	−0.0719797
$237$	21.9954	1.42876
$238$	−4.58064	−0.296919
$239$	−12.5523	−0.811940	−0.405970	−	0.913886i	$-0.633066\pi$
$239$	−12.5523	−0.811940	−0.405970	+	0.913886i	$0.633066\pi$
$240$	2.88372	0.186144
$241$	−13.2212	−0.851652	−0.425826	−	0.904805i	$-0.640016\pi$
$241$	−13.2212	−0.851652	−0.425826	+	0.904805i	$0.640016\pi$
$242$	−5.42863	−0.348966
$243$	21.7440	1.39488
$244$	−14.8634	−0.951532
$245$	−8.62702	−0.551160
$246$	7.05161	0.449594
$247$	16.9618	1.07926
$248$	−4.49242	−0.285269
$249$	5.80244	0.367715
$250$	−10.2209	−0.646429
$251$	−11.1448	−0.703456	−0.351728	−	0.936102i	$-0.614406\pi$
$251$	−11.1448	−0.703456	−0.351728	+	0.936102i	$0.614406\pi$
$252$	−10.8008	−0.680388
$253$	−22.0889	−1.38872
$254$	−3.20094	−0.200845
$255$	−3.50007	−0.219183
$256$	1.00000	0.0625000
$257$	15.9989	0.997985	0.498993	−	0.866606i	$-0.333703\pi$
$257$	15.9989	0.997985	0.498993	+	0.866606i	$0.333703\pi$
$258$	−1.22938	−0.0765378
$259$	12.1566	0.755374
$260$	−5.42737	−0.336591
$261$	−13.5013	−0.835709
$262$	−19.0299	−1.17567
$263$	5.52745	0.340837	0.170419	−	0.985372i	$-0.445488\pi$
$263$	5.52745	0.340837	0.170419	+	0.985372i	$0.445488\pi$
$264$	−9.81341	−0.603973
$265$	−0.648855	−0.0398588
$266$	14.0482	0.861350
$267$	32.9152	2.01438
$268$	−3.02571	−0.184825
$269$	−21.4404	−1.30724	−0.653622	−	0.756821i	$-0.726751\pi$
$269$	−21.4404	−1.30724	−0.653622	+	0.756821i	$0.726751\pi$
$270$	0.398249	0.0242367
$271$	−2.64571	−0.160715	−0.0803576	−	0.996766i	$-0.525606\pi$
$271$	−2.64571	−0.160715	−0.0803576	+	0.996766i	$0.525606\pi$
$272$	−1.21373	−0.0735935
$273$	41.6368	2.51997
$274$	4.95703	0.299465
$275$	14.5161	0.875354
$276$	−13.1945	−0.794216
$277$	5.11141	0.307115	0.153558	−	0.988140i	$-0.450927\pi$
$277$	5.11141	0.307115	0.153558	+	0.988140i	$0.450927\pi$
$278$	2.34546	0.140671
$279$	12.8568	0.769719
$280$	−4.49508	−0.268632
$281$	−26.1082	−1.55749	−0.778744	−	0.627342i	$-0.784143\pi$
$281$	−26.1082	−1.55749	−0.778744	+	0.627342i	$0.784143\pi$
$282$	2.66530	0.158716
$283$	−13.6087	−0.808952	−0.404476	−	0.914549i	$-0.632546\pi$
$283$	−13.6087	−0.808952	−0.404476	+	0.914549i	$0.632546\pi$
$284$	15.7675	0.935631
$285$	10.7342	0.635841
$286$	18.4695	1.09213
$287$	−10.9919	−0.648830
$288$	−2.86190	−0.168639
$289$	−15.5268	−0.913344
$290$	−5.61895	−0.329956
$291$	14.6767	0.860363
$292$	−6.91652	−0.404759
$293$	−7.31349	−0.427259	−0.213629	−	0.976915i	$-0.568528\pi$
$293$	−7.31349	−0.427259	−0.213629	+	0.976915i	$0.568528\pi$
$294$	17.5366	1.02276
$295$	1.31704	0.0766813
$296$	3.22114	0.187225
$297$	−1.35526	−0.0786399
$298$	9.26218	0.536544
$299$	24.8330	1.43613
$300$	8.67099	0.500620
$301$	1.91633	0.110455
$302$	4.63025	0.266441
$303$	24.6176	1.41424
$304$	3.72235	0.213492
$305$	17.7032	1.01368
$306$	3.47358	0.198572
$307$	5.26143	0.300286	0.150143	−	0.988664i	$-0.452027\pi$
$307$	5.26143	0.300286	0.150143	+	0.988664i	$0.452027\pi$
$308$	15.2969	0.871622
$309$	31.4937	1.79161
$310$	5.35075	0.303902
$311$	−1.31851	−0.0747659	−0.0373829	−	0.999301i	$-0.511902\pi$
$311$	−1.31851	−0.0747659	−0.0373829	+	0.999301i	$0.511902\pi$
$312$	11.0325	0.624593
$313$	−29.2825	−1.65514	−0.827572	−	0.561359i	$-0.810279\pi$
$313$	−29.2825	−1.65514	−0.827572	+	0.561359i	$0.810279\pi$
$314$	14.6829	0.828605
$315$	12.8645	0.724830
$316$	−9.08476	−0.511058
$317$	12.9282	0.726121	0.363061	−	0.931766i	$-0.381732\pi$
$317$	12.9282	0.726121	0.363061	+	0.931766i	$0.381732\pi$
$318$	1.31896	0.0739637
$319$	19.1215	1.07060
$320$	−1.19106	−0.0665824
$321$	11.5454	0.644399
$322$	20.5673	1.14617
$323$	−4.51795	−0.251385
$324$	−9.39524	−0.521958
$325$	−16.3194	−0.905238
$326$	4.37158	0.242119
$327$	20.4791	1.13250
$328$	−2.91252	−0.160817
$329$	−4.15460	−0.229051
$330$	11.6884	0.643424
$331$	14.7764	0.812185	0.406092	−	0.913832i	$-0.366891\pi$
$331$	14.7764	0.812185	0.406092	+	0.913832i	$0.366891\pi$
$332$	−2.39658	−0.131529
$333$	−9.21856	−0.505174
$334$	5.25233	0.287395
$335$	3.60381	0.196897
$336$	9.13739	0.498485
$337$	20.2729	1.10434	0.552169	−	0.833732i	$-0.313800\pi$
$337$	20.2729	1.10434	0.552169	+	0.833732i	$0.313800\pi$
$338$	−7.76396	−0.422304
$339$	−44.6229	−2.42358
$340$	1.44563	0.0784005
$341$	−18.2088	−0.986061
$342$	−10.6530	−0.576048
$343$	−0.917599	−0.0495457
$344$	0.507770	0.0273771
$345$	15.7155	0.846093
$346$	−11.0187	−0.592371
$347$	12.0865	0.648838	0.324419	−	0.945914i	$-0.394831\pi$
$347$	12.0865	0.648838	0.324419	+	0.945914i	$0.394831\pi$
$348$	11.4220	0.612281
$349$	−3.16619	−0.169482	−0.0847411	−	0.996403i	$-0.527006\pi$
$349$	−3.16619	−0.169482	−0.0847411	+	0.996403i	$0.527006\pi$
$350$	−13.5161	−0.722467
$351$	1.52362	0.0813246
$352$	4.05323	0.216038
$353$	4.79538	0.255232	0.127616	−	0.991824i	$-0.459267\pi$
$353$	4.79538	0.255232	0.127616	+	0.991824i	$0.459267\pi$
$354$	−2.67723	−0.142293
$355$	−18.7801	−0.996745
$356$	−13.5949	−0.720530
$357$	−11.0904	−0.586964
$358$	2.29122	0.121095
$359$	−17.5257	−0.924973	−0.462486	−	0.886626i	$-0.653043\pi$
$359$	−17.5257	−0.924973	−0.462486	+	0.886626i	$0.653043\pi$
$360$	3.40870	0.179654
$361$	−5.14409	−0.270741
$362$	−8.46887	−0.445114
$363$	−13.1435	−0.689853
$364$	−17.1972	−0.901379
$365$	8.23800	0.431197
$366$	−35.9863	−1.88104
$367$	28.0392	1.46364	0.731818	−	0.681500i	$-0.238672\pi$
$367$	28.0392	1.46364	0.731818	+	0.681500i	$0.238672\pi$
$368$	5.44972	0.284086
$369$	8.33534	0.433920
$370$	−3.83657	−0.199454
$371$	−2.05597	−0.106740
$372$	−10.8768	−0.563934
$373$	−7.72894	−0.400189	−0.200095	−	0.979777i	$-0.564125\pi$
$373$	−7.72894	−0.400189	−0.200095	+	0.979777i	$0.564125\pi$
$374$	−4.91954	−0.254383
$375$	−24.7463	−1.27789
$376$	−1.10085	−0.0567718
$377$	−21.4969	−1.10715
$378$	1.26190	0.0649049
$379$	7.67069	0.394017	0.197008	−	0.980402i	$-0.436877\pi$
$379$	7.67069	0.394017	0.197008	+	0.980402i	$0.436877\pi$
$380$	−4.43355	−0.227437
$381$	−7.74990	−0.397040
$382$	−18.4418	−0.943563
$383$	−27.5071	−1.40555	−0.702774	−	0.711413i	$-0.748056\pi$
$383$	−27.5071	−1.40555	−0.702774	+	0.711413i	$0.748056\pi$
$384$	2.42114	0.123553
$385$	−18.2196	−0.928555
$386$	−4.83354	−0.246021
$387$	−1.45318	−0.0738695
$388$	−6.06191	−0.307747
$389$	−10.8598	−0.550612	−0.275306	−	0.961357i	$-0.588779\pi$
$389$	−10.8598	−0.550612	−0.275306	+	0.961357i	$0.588779\pi$
$390$	−13.1404	−0.665390
$391$	−6.61451	−0.334510
$392$	−7.24314	−0.365834
$393$	−46.0739	−2.32412
$394$	−19.4368	−0.979213
$395$	10.8205	0.544439
$396$	−11.5999	−0.582918
$397$	−14.0850	−0.706905	−0.353453	−	0.935452i	$-0.614992\pi$
$397$	−14.0850	−0.706905	−0.353453	+	0.935452i	$0.614992\pi$
$398$	−0.391267	−0.0196124
$399$	34.0126	1.70276
$400$	−3.58137	−0.179069
$401$	13.3483	0.666580	0.333290	−	0.942824i	$-0.391841\pi$
$401$	13.3483	0.666580	0.333290	+	0.942824i	$0.391841\pi$
$402$	−7.32566	−0.365371
$403$	20.4708	1.01972
$404$	−10.1678	−0.505866
$405$	11.1903	0.556051
$406$	−17.8043	−0.883611
$407$	13.0560	0.647161
$408$	−2.93862	−0.145483
$409$	14.6977	0.726757	0.363378	−	0.931642i	$-0.381623\pi$
$409$	14.6977	0.726757	0.363378	+	0.931642i	$0.381623\pi$
$410$	3.46899	0.171321
$411$	12.0016	0.591997
$412$	−13.0078	−0.640849
$413$	4.17320	0.205350
$414$	−15.5965	−0.766528
$415$	2.85447	0.140121
$416$	−4.55675	−0.223413
$417$	5.67868	0.278086
$418$	15.0875	0.737955
$419$	−21.4892	−1.04981	−0.524907	−	0.851160i	$-0.675900\pi$
$419$	−21.4892	−1.04981	−0.524907	+	0.851160i	$0.675900\pi$
$420$	−10.8832	−0.531045
$421$	29.0308	1.41488	0.707438	−	0.706775i	$-0.249851\pi$
$421$	29.0308	1.41488	0.707438	+	0.706775i	$0.249851\pi$
$422$	1.44290	0.0702392
$423$	3.15051	0.153183
$424$	−0.544770	−0.0264564
$425$	4.34683	0.210852
$426$	38.1754	1.84960
$427$	56.0946	2.71461
$428$	−4.76857	−0.230498
$429$	44.7172	2.15897
$430$	−0.604785	−0.0291653
$431$	−24.4782	−1.17907	−0.589537	−	0.807741i	$-0.700690\pi$
$431$	−24.4782	−1.17907	−0.589537	+	0.807741i	$0.700690\pi$
$432$	0.334365	0.0160871
$433$	−21.3135	−1.02426	−0.512131	−	0.858907i	$-0.671144\pi$
$433$	−21.3135	−1.02426	−0.512131	+	0.858907i	$0.671144\pi$
$434$	16.9544	0.813839
$435$	−13.6043	−0.652274
$436$	−8.45849	−0.405088
$437$	20.2858	0.970401
$438$	−16.7458	−0.800147
$439$	29.8915	1.42664	0.713321	−	0.700837i	$-0.247190\pi$
$439$	29.8915	1.42664	0.713321	+	0.700837i	$0.247190\pi$
$440$	−4.82764	−0.230149
$441$	20.7291	0.987101
$442$	5.53068	0.263068
$443$	−35.0460	−1.66508	−0.832542	−	0.553962i	$-0.813115\pi$
$443$	−35.0460	−1.66508	−0.832542	+	0.553962i	$0.813115\pi$
$444$	7.79881	0.370115
$445$	16.1924	0.767594
$446$	−0.155125	−0.00734539
$447$	22.4250	1.06067
$448$	−3.77401	−0.178305
$449$	0.835529	0.0394310	0.0197155	−	0.999806i	$-0.493724\pi$
$449$	0.835529	0.0394310	0.0197155	+	0.999806i	$0.493724\pi$
$450$	10.2495	0.483167
$451$	−11.8051	−0.555881
$452$	18.4306	0.866901
$453$	11.2105	0.526714
$454$	−12.9969	−0.609975
$455$	20.4829	0.960255
$456$	9.01232	0.422041
$457$	0.895256	0.0418783	0.0209392	−	0.999781i	$-0.493334\pi$
$457$	0.895256	0.0418783	0.0209392	+	0.999781i	$0.493334\pi$
$458$	21.8368	1.02037
$459$	−0.405830	−0.0189425
$460$	−6.49096	−0.302642
$461$	25.1774	1.17263	0.586314	−	0.810084i	$-0.300579\pi$
$461$	25.1774	1.17263	0.586314	+	0.810084i	$0.300579\pi$
$462$	37.0359	1.72306
$463$	3.24013	0.150582	0.0752908	−	0.997162i	$-0.476012\pi$
$463$	3.24013	0.150582	0.0752908	+	0.997162i	$0.476012\pi$
$464$	−4.71760	−0.219009
$465$	12.9549	0.600769
$466$	−3.15738	−0.146263
$467$	−2.58485	−0.119612	−0.0598062	−	0.998210i	$-0.519048\pi$
$467$	−2.58485	−0.119612	−0.0598062	+	0.998210i	$0.519048\pi$
$468$	13.0409	0.602818
$469$	11.4191	0.527283
$470$	1.31118	0.0604800
$471$	35.5493	1.63803
$472$	1.10577	0.0508973
$473$	2.05810	0.0946318
$474$	−21.9954	−1.01028
$475$	−13.3311	−0.611674
$476$	4.58064	0.209953
$477$	1.55908	0.0713852
$478$	12.5523	0.574128
$479$	1.56801	0.0716442	0.0358221	−	0.999358i	$-0.488595\pi$
$479$	1.56801	0.0716442	0.0358221	+	0.999358i	$0.488595\pi$
$480$	−2.88372	−0.131623
$481$	−14.6779	−0.669255
$482$	13.2212	0.602209
$483$	49.7962	2.26581
$484$	5.42863	0.246756
$485$	7.22011	0.327848
$486$	−21.7440	−0.986330
$487$	1.10775	0.0501969	0.0250985	−	0.999685i	$-0.492010\pi$
$487$	1.10775	0.0501969	0.0250985	+	0.999685i	$0.492010\pi$
$488$	14.8634	0.672835
$489$	10.5842	0.478633
$490$	8.62702	0.389729
$491$	11.7817	0.531700	0.265850	−	0.964014i	$-0.414347\pi$
$491$	11.7817	0.531700	0.265850	+	0.964014i	$0.414347\pi$
$492$	−7.05161	−0.317911
$493$	5.72591	0.257882
$494$	−16.9618	−0.763149
$495$	13.8162	0.620993
$496$	4.49242	0.201716
$497$	−59.5068	−2.66925
$498$	−5.80244	−0.260013
$499$	−30.6724	−1.37308	−0.686542	−	0.727090i	$-0.740872\pi$
$499$	−30.6724	−1.37308	−0.686542	+	0.727090i	$0.740872\pi$
$500$	10.2209	0.457095
$501$	12.7166	0.568136
$502$	11.1448	0.497418
$503$	4.79178	0.213655	0.106828	−	0.994278i	$-0.465931\pi$
$503$	4.79178	0.213655	0.106828	+	0.994278i	$0.465931\pi$
$504$	10.8008	0.481107
$505$	12.1104	0.538908
$506$	22.0889	0.981973
$507$	−18.7976	−0.834831
$508$	3.20094	0.142019
$509$	30.4590	1.35007	0.675036	−	0.737785i	$-0.264128\pi$
$509$	30.4590	1.35007	0.675036	+	0.737785i	$0.264128\pi$
$510$	3.50007	0.154986
$511$	26.1030	1.15473
$512$	−1.00000	−0.0441942
$513$	1.24462	0.0549515
$514$	−15.9989	−0.705682
$515$	15.4931	0.682709
$516$	1.22938	0.0541204
$517$	−4.46198	−0.196237
$518$	−12.1566	−0.534130
$519$	−26.6779	−1.17103
$520$	5.42737	0.238006
$521$	3.59477	0.157490	0.0787450	−	0.996895i	$-0.474909\pi$
$521$	3.59477	0.157490	0.0787450	+	0.996895i	$0.474909\pi$
$522$	13.5013	0.590935
$523$	−16.6484	−0.727984	−0.363992	−	0.931402i	$-0.618586\pi$
$523$	−16.6484	−0.727984	−0.363992	+	0.931402i	$0.618586\pi$
$524$	19.0299	0.831324
$525$	−32.7244	−1.42821
$526$	−5.52745	−0.241008
$527$	−5.45261	−0.237519
$528$	9.81341	0.427074
$529$	6.69946	0.291281
$530$	0.648855	0.0281844
$531$	−3.16461	−0.137332
$532$	−14.0482	−0.609066
$533$	13.2716	0.574858
$534$	−32.9152	−1.42438
$535$	5.67967	0.245553
$536$	3.02571	0.130691
$537$	5.54736	0.239386
$538$	21.4404	0.924361
$539$	−29.3581	−1.26454
$540$	−0.398249	−0.0171379
$541$	9.29547	0.399643	0.199822	−	0.979832i	$-0.435964\pi$
$541$	9.29547	0.399643	0.199822	+	0.979832i	$0.435964\pi$
$542$	2.64571	0.113643
$543$	−20.5043	−0.879923
$544$	1.21373	0.0520384
$545$	10.0746	0.431548
$546$	−41.6368	−1.78189
$547$	20.1077	0.859743	0.429872	−	0.902890i	$-0.358559\pi$
$547$	20.1077	0.859743	0.429872	+	0.902890i	$0.358559\pi$
$548$	−4.95703	−0.211754
$549$	−42.5375	−1.81546
$550$	−14.5161	−0.618969
$551$	−17.5606	−0.748106
$552$	13.1945	0.561596
$553$	34.2860	1.45799
$554$	−5.11141	−0.217163
$555$	−9.28886	−0.394290
$556$	−2.34546	−0.0994697
$557$	24.4631	1.03653	0.518267	−	0.855219i	$-0.326577\pi$
$557$	24.4631	1.03653	0.518267	+	0.855219i	$0.326577\pi$
$558$	−12.8568	−0.544274
$559$	−2.31378	−0.0978624
$560$	4.49508	0.189952
$561$	−11.9109	−0.502877
$562$	26.1082	1.10131
$563$	34.1214	1.43805	0.719023	−	0.694986i	$-0.244589\pi$
$563$	34.1214	1.43805	0.719023	+	0.694986i	$0.244589\pi$
$564$	−2.66530	−0.112229
$565$	−21.9519	−0.923525
$566$	13.6087	0.572015
$567$	35.4577	1.48908
$568$	−15.7675	−0.661591
$569$	−5.33566	−0.223682	−0.111841	−	0.993726i	$-0.535675\pi$
$569$	−5.33566	−0.223682	−0.111841	+	0.993726i	$0.535675\pi$
$570$	−10.7342	−0.449608
$571$	20.3701	0.852464	0.426232	−	0.904614i	$-0.359841\pi$
$571$	20.3701	0.852464	0.426232	+	0.904614i	$0.359841\pi$
$572$	−18.4695	−0.772250
$573$	−44.6500	−1.86528
$574$	10.9919	0.458792
$575$	−19.5175	−0.813935
$576$	2.86190	0.119246
$577$	−10.0639	−0.418965	−0.209483	−	0.977812i	$-0.567178\pi$
$577$	−10.0639	−0.418965	−0.209483	+	0.977812i	$0.567178\pi$
$578$	15.5268	0.645832
$579$	−11.7027	−0.486346
$580$	5.61895	0.233314
$581$	9.04470	0.375237
$582$	−14.6767	−0.608369
$583$	−2.20807	−0.0914491
$584$	6.91652	0.286208
$585$	−15.5326	−0.642193
$586$	7.31349	0.302118
$587$	30.7251	1.26816	0.634081	−	0.773267i	$-0.281379\pi$
$587$	30.7251	1.26816	0.634081	+	0.773267i	$0.281379\pi$
$588$	−17.5366	−0.723198
$589$	16.7224	0.689034
$590$	−1.31704	−0.0542219
$591$	−47.0592	−1.93576
$592$	−3.22114	−0.132388
$593$	6.18075	0.253813	0.126906	−	0.991915i	$-0.459495\pi$
$593$	6.18075	0.253813	0.126906	+	0.991915i	$0.459495\pi$
$594$	1.35526	0.0556068
$595$	−5.45583	−0.223667
$596$	−9.26218	−0.379394
$597$	−0.947310	−0.0387708
$598$	−24.8330	−1.01550
$599$	22.9386	0.937246	0.468623	−	0.883398i	$-0.344750\pi$
$599$	22.9386	0.937246	0.468623	+	0.883398i	$0.344750\pi$
$600$	−8.67099	−0.353991
$601$	21.2860	0.868275	0.434137	−	0.900847i	$-0.357053\pi$
$601$	21.2860	0.868275	0.434137	+	0.900847i	$0.357053\pi$
$602$	−1.91633	−0.0781037
$603$	−8.65927	−0.352633
$604$	−4.63025	−0.188402
$605$	−6.46584	−0.262874
$606$	−24.6176	−1.00002
$607$	25.6169	1.03976	0.519878	−	0.854240i	$-0.325977\pi$
$607$	25.6169	1.03976	0.519878	+	0.854240i	$0.325977\pi$
$608$	−3.72235	−0.150961
$609$	−43.1065	−1.74676
$610$	−17.7032	−0.716783
$611$	5.01628	0.202937
$612$	−3.47358	−0.140411
$613$	3.44936	0.139318	0.0696591	−	0.997571i	$-0.477809\pi$
$613$	3.44936	0.139318	0.0696591	+	0.997571i	$0.477809\pi$
$614$	−5.26143	−0.212334
$615$	8.39890	0.338677
$616$	−15.2969	−0.616330
$617$	13.5406	0.545125	0.272562	−	0.962138i	$-0.412129\pi$
$617$	13.5406	0.545125	0.272562	+	0.962138i	$0.412129\pi$
$618$	−31.4937	−1.26686
$619$	−6.48815	−0.260781	−0.130390	−	0.991463i	$-0.541623\pi$
$619$	−6.48815	−0.260781	−0.130390	+	0.991463i	$0.541623\pi$
$620$	−5.35075	−0.214891
$621$	1.82220	0.0731222
$622$	1.31851	0.0528675
$623$	51.3074	2.05559
$624$	−11.0325	−0.441654
$625$	5.73308	0.229323
$626$	29.2825	1.17036
$627$	36.5290	1.45883
$628$	−14.6829	−0.585912
$629$	3.90960	0.155886
$630$	−12.8645	−0.512532
$631$	12.2932	0.489386	0.244693	−	0.969601i	$-0.421313\pi$
$631$	12.2932	0.489386	0.244693	+	0.969601i	$0.421313\pi$
$632$	9.08476	0.361372
$633$	3.49345	0.138852
$634$	−12.9282	−0.513445
$635$	−3.81252	−0.151295
$636$	−1.31896	−0.0523002
$637$	33.0052	1.30771
$638$	−19.1215	−0.757027
$639$	45.1251	1.78512
$640$	1.19106	0.0470809
$641$	15.3514	0.606345	0.303172	−	0.952936i	$-0.401954\pi$
$641$	15.3514	0.606345	0.303172	+	0.952936i	$0.401954\pi$
$642$	−11.5454	−0.455659
$643$	23.4730	0.925685	0.462843	−	0.886440i	$-0.346829\pi$
$643$	23.4730	0.925685	0.462843	+	0.886440i	$0.346829\pi$
$644$	−20.5673	−0.810465
$645$	−1.46427	−0.0576555
$646$	4.51795	0.177756
$647$	1.79563	0.0705934	0.0352967	−	0.999377i	$-0.488762\pi$
$647$	1.79563	0.0705934	0.0352967	+	0.999377i	$0.488762\pi$
$648$	9.39524	0.369080
$649$	4.48195	0.175932
$650$	16.3194	0.640100
$651$	41.0490	1.60884
$652$	−4.37158	−0.171204
$653$	−18.8023	−0.735790	−0.367895	−	0.929867i	$-0.619921\pi$
$653$	−18.8023	−0.735790	−0.367895	+	0.929867i	$0.619921\pi$
$654$	−20.4791	−0.800798
$655$	−22.6658	−0.885624
$656$	2.91252	0.113715
$657$	−19.7944	−0.772252
$658$	4.15460	0.161963
$659$	−11.5759	−0.450932	−0.225466	−	0.974251i	$-0.572390\pi$
$659$	−11.5759	−0.450932	−0.225466	+	0.974251i	$0.572390\pi$
$660$	−11.6884	−0.454969
$661$	−31.2107	−1.21396	−0.606978	−	0.794719i	$-0.707618\pi$
$661$	−31.2107	−1.21396	−0.606978	+	0.794719i	$0.707618\pi$
$662$	−14.7764	−0.574301
$663$	13.3905	0.520045
$664$	2.39658	0.0930052
$665$	16.7323	0.648850
$666$	9.21856	0.357212
$667$	−25.7096	−0.995480
$668$	−5.25233	−0.203219
$669$	−0.375579	−0.0145207
$670$	−3.60381	−0.139227
$671$	60.2447	2.32572
$672$	−9.13739	−0.352482
$673$	5.66703	0.218448	0.109224	−	0.994017i	$-0.465163\pi$
$673$	5.66703	0.218448	0.109224	+	0.994017i	$0.465163\pi$
$674$	−20.2729	−0.780884
$675$	−1.19748	−0.0460912
$676$	7.76396	0.298614
$677$	27.1326	1.04279	0.521394	−	0.853316i	$-0.325412\pi$
$677$	27.1326	1.04279	0.521394	+	0.853316i	$0.325412\pi$
$678$	44.6229	1.71373
$679$	22.8777	0.877965
$680$	−1.44563	−0.0554375
$681$	−31.4673	−1.20583
$682$	18.2088	0.697251
$683$	36.2859	1.38844	0.694220	−	0.719763i	$-0.255749\pi$
$683$	36.2859	1.38844	0.694220	+	0.719763i	$0.255749\pi$
$684$	10.6530	0.407327
$685$	5.90413	0.225585
$686$	0.917599	0.0350341
$687$	52.8699	2.01711
$688$	−0.507770	−0.0193585
$689$	2.48238	0.0945711
$690$	−15.7155	−0.598278
$691$	4.91245	0.186878	0.0934391	−	0.995625i	$-0.470214\pi$
$691$	4.91245	0.186878	0.0934391	+	0.995625i	$0.470214\pi$
$692$	11.0187	0.418870
$693$	43.7782	1.66300
$694$	−12.0865	−0.458797
$695$	2.79359	0.105967
$696$	−11.4220	−0.432948
$697$	−3.53503	−0.133899
$698$	3.16619	0.119842
$699$	−7.64445	−0.289140
$700$	13.5161	0.510861
$701$	−32.2635	−1.21858	−0.609288	−	0.792949i	$-0.708545\pi$
$701$	−32.2635	−1.21858	−0.609288	+	0.792949i	$0.708545\pi$
$702$	−1.52362	−0.0575052
$703$	−11.9902	−0.452219
$704$	−4.05323	−0.152762
$705$	3.17453	0.119560
$706$	−4.79538	−0.180476
$707$	38.3733	1.44317
$708$	2.67723	0.100616
$709$	−6.54439	−0.245780	−0.122890	−	0.992420i	$-0.539216\pi$
$709$	−6.54439	−0.245780	−0.122890	+	0.992420i	$0.539216\pi$
$710$	18.7801	0.704805
$711$	−25.9997	−0.975063
$712$	13.5949	0.509492
$713$	24.4824	0.916875
$714$	11.0904	0.415046
$715$	21.9984	0.822692
$716$	−2.29122	−0.0856270
$717$	30.3908	1.13497
$718$	17.5257	0.654055
$719$	−12.3867	−0.461947	−0.230974	−	0.972960i	$-0.574191\pi$
$719$	−12.3867	−0.461947	−0.230974	+	0.972960i	$0.574191\pi$
$720$	−3.40870	−0.127035
$721$	49.0916	1.82827
$722$	5.14409	0.191443
$723$	32.0103	1.19048
$724$	8.46887	0.314743
$725$	16.8955	0.627482
$726$	13.1435	0.487799
$727$	25.9484	0.962373	0.481187	−	0.876618i	$-0.340206\pi$
$727$	25.9484	0.962373	0.481187	+	0.876618i	$0.340206\pi$
$728$	17.1972	0.637371
$729$	−24.4596	−0.905910
$730$	−8.23800	−0.304902
$731$	0.616298	0.0227946
$732$	35.9863	1.33009
$733$	15.1379	0.559132	0.279566	−	0.960126i	$-0.409809\pi$
$733$	15.1379	0.559132	0.279566	+	0.960126i	$0.409809\pi$
$734$	−28.0392	−1.03495
$735$	20.8872	0.770436
$736$	−5.44972	−0.200879
$737$	12.2639	0.451746
$738$	−8.33534	−0.306828
$739$	−48.8716	−1.79777	−0.898885	−	0.438185i	$-0.855622\pi$
$739$	−48.8716	−1.79777	−0.898885	+	0.438185i	$0.855622\pi$
$740$	3.83657	0.141035
$741$	−41.0669	−1.50863
$742$	2.05597	0.0754769
$743$	−1.38032	−0.0506390	−0.0253195	−	0.999679i	$-0.508060\pi$
$743$	−1.38032	−0.0506390	−0.0253195	+	0.999679i	$0.508060\pi$
$744$	10.8768	0.398761
$745$	11.0318	0.404175
$746$	7.72894	0.282977
$747$	−6.85876	−0.250949
$748$	4.91954	0.179876
$749$	17.9966	0.657583
$750$	24.7463	0.903607
$751$	−45.0002	−1.64208	−0.821041	−	0.570869i	$-0.806606\pi$
$751$	−45.0002	−1.64208	−0.821041	+	0.570869i	$0.806606\pi$
$752$	1.10085	0.0401437
$753$	26.9832	0.983321
$754$	21.4969	0.782872
$755$	5.51492	0.200708
$756$	−1.26190	−0.0458947
$757$	−12.6466	−0.459647	−0.229824	−	0.973232i	$-0.573815\pi$
$757$	−12.6466	−0.459647	−0.229824	+	0.973232i	$0.573815\pi$
$758$	−7.67069	−0.278612
$759$	53.4803	1.94121
$760$	4.43355	0.160822
$761$	−21.2754	−0.771234	−0.385617	−	0.922659i	$-0.626011\pi$
$761$	−21.2754	−0.771234	−0.385617	+	0.922659i	$0.626011\pi$
$762$	7.74990	0.280749
$763$	31.9224	1.15567
$764$	18.4418	0.667200
$765$	4.13725	0.149583
$766$	27.5071	0.993873
$767$	−5.03873	−0.181938
$768$	−2.42114	−0.0873652
$769$	44.2214	1.59466	0.797332	−	0.603541i	$-0.206244\pi$
$769$	44.2214	1.59466	0.797332	+	0.603541i	$0.206244\pi$
$770$	18.2196	0.656587
$771$	−38.7356	−1.39503
$772$	4.83354	0.173963
$773$	−29.4341	−1.05867	−0.529335	−	0.848413i	$-0.677559\pi$
$773$	−29.4341	−1.05867	−0.529335	+	0.848413i	$0.677559\pi$
$774$	1.45318	0.0522337
$775$	−16.0890	−0.577935
$776$	6.06191	0.217610
$777$	−29.4328	−1.05589
$778$	10.8598	0.389342
$779$	10.8414	0.388435
$780$	13.1404	0.470502
$781$	−63.9094	−2.28686
$782$	6.61451	0.236535
$783$	−1.57740	−0.0563717
$784$	7.24314	0.258683
$785$	17.4883	0.624183
$786$	46.0739	1.64340
$787$	24.6186	0.877560	0.438780	−	0.898595i	$-0.355411\pi$
$787$	24.6186	0.877560	0.438780	+	0.898595i	$0.355411\pi$
$788$	19.4368	0.692408
$789$	−13.3827	−0.476437
$790$	−10.8205	−0.384977
$791$	−69.5571	−2.47317
$792$	11.5999	0.412185
$793$	−67.7288	−2.40512
$794$	14.0850	0.499857
$795$	1.57097	0.0557164
$796$	0.391267	0.0138681
$797$	−42.1421	−1.49275	−0.746375	−	0.665525i	$-0.768208\pi$
$797$	−42.1421	−1.49275	−0.746375	+	0.665525i	$0.768208\pi$
$798$	−34.0126	−1.20403
$799$	−1.33613	−0.0472690
$800$	3.58137	0.126621
$801$	−38.9073	−1.37472
$802$	−13.3483	−0.471344
$803$	28.0342	0.989306
$804$	7.32566	0.258356
$805$	24.4969	0.863403
$806$	−20.4708	−0.721054
$807$	51.9101	1.82732
$808$	10.1678	0.357701
$809$	26.6330	0.936366	0.468183	−	0.883632i	$-0.344909\pi$
$809$	26.6330	0.936366	0.468183	+	0.883632i	$0.344909\pi$
$810$	−11.1903	−0.393187
$811$	27.0936	0.951384	0.475692	−	0.879612i	$-0.342198\pi$
$811$	27.0936	0.951384	0.475692	+	0.879612i	$0.342198\pi$
$812$	17.8043	0.624807
$813$	6.40561	0.224655
$814$	−13.0560	−0.457612
$815$	5.20682	0.182387
$816$	2.93862	0.102872
$817$	−1.89010	−0.0661262
$818$	−14.6977	−0.513895
$819$	−49.2166	−1.71977
$820$	−3.46899	−0.121143
$821$	−45.7306	−1.59601	−0.798004	−	0.602652i	$-0.794111\pi$
$821$	−45.7306	−1.59601	−0.798004	+	0.602652i	$0.794111\pi$
$822$	−12.0016	−0.418605
$823$	6.76446	0.235794	0.117897	−	0.993026i	$-0.462385\pi$
$823$	6.76446	0.235794	0.117897	+	0.993026i	$0.462385\pi$
$824$	13.0078	0.453149
$825$	−35.1455	−1.22361
$826$	−4.17320	−0.145204
$827$	41.3750	1.43875	0.719375	−	0.694622i	$-0.244428\pi$
$827$	41.3750	1.43875	0.719375	+	0.694622i	$0.244428\pi$
$828$	15.5965	0.542017
$829$	32.6071	1.13249	0.566246	−	0.824236i	$-0.308395\pi$
$829$	32.6071	1.13249	0.566246	+	0.824236i	$0.308395\pi$
$830$	−2.85447	−0.0990802
$831$	−12.3754	−0.429299
$832$	4.55675	0.157977
$833$	−8.79124	−0.304599
$834$	−5.67868	−0.196636
$835$	6.25585	0.216493
$836$	−15.0875	−0.521813
$837$	1.50211	0.0519204
$838$	21.4892	0.742331
$839$	−8.47783	−0.292687	−0.146344	−	0.989234i	$-0.546750\pi$
$839$	−8.47783	−0.292687	−0.146344	+	0.989234i	$0.546750\pi$
$840$	10.8832	0.375506
$841$	−6.74425	−0.232560
$842$	−29.0308	−1.00047
$843$	63.2116	2.17712
$844$	−1.44290	−0.0496666
$845$	−9.24736	−0.318119
$846$	−3.15051	−0.108317
$847$	−20.4877	−0.703966
$848$	0.544770	0.0187075
$849$	32.9484	1.13079
$850$	−4.34683	−0.149095
$851$	−17.5543	−0.601753
$852$	−38.1754	−1.30787
$853$	−47.4072	−1.62319	−0.811596	−	0.584219i	$-0.801401\pi$
$853$	−47.4072	−1.62319	−0.811596	+	0.584219i	$0.801401\pi$
$854$	−56.0946	−1.91952
$855$	−12.6884	−0.433933
$856$	4.76857	0.162986
$857$	52.4303	1.79098	0.895492	−	0.445077i	$-0.146824\pi$
$857$	52.4303	1.79098	0.895492	+	0.445077i	$0.146824\pi$
$858$	−44.7172	−1.52662
$859$	−38.5493	−1.31529	−0.657643	−	0.753330i	$-0.728446\pi$
$859$	−38.5493	−1.31529	−0.657643	+	0.753330i	$0.728446\pi$
$860$	0.604785	0.0206230
$861$	26.6128	0.906963
$862$	24.4782	0.833731
$863$	23.7400	0.808120	0.404060	−	0.914732i	$-0.367599\pi$
$863$	23.7400	0.808120	0.404060	+	0.914732i	$0.367599\pi$
$864$	−0.334365	−0.0113753
$865$	−13.1240	−0.446230
$866$	21.3135	0.724263
$867$	37.5926	1.27671
$868$	−16.9544	−0.575471
$869$	36.8226	1.24912
$870$	13.6043	0.461227
$871$	−13.7874	−0.467168
$872$	8.45849	0.286440
$873$	−17.3486	−0.587160
$874$	−20.2858	−0.686177
$875$	−38.5739	−1.30404
$876$	16.7458	0.565789
$877$	30.9822	1.04619	0.523097	−	0.852273i	$-0.324777\pi$
$877$	30.9822	1.04619	0.523097	+	0.852273i	$0.324777\pi$
$878$	−29.8915	−1.00879
$879$	17.7070	0.597241
$880$	4.82764	0.162740
$881$	52.6496	1.77381	0.886906	−	0.461951i	$-0.152850\pi$
$881$	52.6496	1.77381	0.886906	+	0.461951i	$0.152850\pi$
$882$	−20.7291	−0.697986
$883$	−24.9835	−0.840761	−0.420381	−	0.907348i	$-0.638103\pi$
$883$	−24.9835	−0.840761	−0.420381	+	0.907348i	$0.638103\pi$
$884$	−5.53068	−0.186017
$885$	−3.18874	−0.107188
$886$	35.0460	1.17739
$887$	−17.5402	−0.588942	−0.294471	−	0.955660i	$-0.595143\pi$
$887$	−17.5402	−0.588942	−0.294471	+	0.955660i	$0.595143\pi$
$888$	−7.79881	−0.261711
$889$	−12.0804	−0.405162
$890$	−16.1924	−0.542771
$891$	38.0810	1.27576
$892$	0.155125	0.00519397
$893$	4.09774	0.137126
$894$	−22.4250	−0.750004
$895$	2.72899	0.0912201
$896$	3.77401	0.126081
$897$	−60.1241	−2.00748
$898$	−0.835529	−0.0278820
$899$	−21.1934	−0.706841
$900$	−10.2495	−0.341651
$901$	−0.661206	−0.0220280
$902$	11.8051	0.393067
$903$	−4.63969	−0.154399
$904$	−18.4306	−0.612991
$905$	−10.0870	−0.335302
$906$	−11.2105	−0.372443
$907$	−32.7170	−1.08635	−0.543175	−	0.839620i	$-0.682778\pi$
$907$	−32.7170	−1.08635	−0.543175	+	0.839620i	$0.682778\pi$
$908$	12.9969	0.431318
$909$	−29.0991	−0.965157
$910$	−20.4829	−0.679003
$911$	−4.25563	−0.140995	−0.0704977	−	0.997512i	$-0.522459\pi$
$911$	−4.25563	−0.140995	−0.0704977	+	0.997512i	$0.522459\pi$
$912$	−9.01232	−0.298428
$913$	9.71387	0.321482
$914$	−0.895256	−0.0296125
$915$	−42.8619	−1.41697
$916$	−21.8368	−0.721508
$917$	−71.8189	−2.37167
$918$	0.405830	0.0133944
$919$	19.6378	0.647792	0.323896	−	0.946093i	$-0.395007\pi$
$919$	19.6378	0.647792	0.323896	+	0.946093i	$0.395007\pi$
$920$	6.49096	0.214000
$921$	−12.7386	−0.419753
$922$	−25.1774	−0.829173
$923$	71.8487	2.36493
$924$	−37.0359	−1.21839
$925$	11.5361	0.379304
$926$	−3.24013	−0.106477
$927$	−37.2271	−1.22270
$928$	4.71760	0.154863
$929$	−33.9022	−1.11229	−0.556147	−	0.831084i	$-0.687721\pi$
$929$	−33.9022	−1.11229	−0.556147	+	0.831084i	$0.687721\pi$
$930$	−12.9549	−0.424808
$931$	26.9615	0.883628
$932$	3.15738	0.103423
$933$	3.19229	0.104511
$934$	2.58485	0.0845788
$935$	−5.85948	−0.191625
$936$	−13.0409	−0.426257
$937$	43.3772	1.41707	0.708536	−	0.705674i	$-0.249356\pi$
$937$	43.3772	1.41707	0.708536	+	0.705674i	$0.249356\pi$
$938$	−11.4191	−0.372845
$939$	70.8969	2.31363
$940$	−1.31118	−0.0427658
$941$	−12.3451	−0.402437	−0.201219	−	0.979546i	$-0.564490\pi$
$941$	−12.3451	−0.402437	−0.201219	+	0.979546i	$0.564490\pi$
$942$	−35.5493	−1.15826
$943$	15.8724	0.516877
$944$	−1.10577	−0.0359899
$945$	1.50300	0.0488925
$946$	−2.05810	−0.0669148
$947$	22.0054	0.715080	0.357540	−	0.933898i	$-0.383616\pi$
$947$	22.0054	0.715080	0.357540	+	0.933898i	$0.383616\pi$
$948$	21.9954	0.714379
$949$	−31.5168	−1.02308
$950$	13.3311	0.432519
$951$	−31.3010	−1.01500
$952$	−4.58064	−0.148459
$953$	24.7244	0.800902	0.400451	−	0.916318i	$-0.368853\pi$
$953$	24.7244	0.800902	0.400451	+	0.916318i	$0.368853\pi$
$954$	−1.55908	−0.0504769
$955$	−21.9653	−0.710780
$956$	−12.5523	−0.405970
$957$	−46.2957	−1.49653
$958$	−1.56801	−0.0506601
$959$	18.7079	0.604109
$960$	2.88372	0.0930718
$961$	−10.8182	−0.348973
$962$	14.6779	0.473235
$963$	−13.6472	−0.439774
$964$	−13.2212	−0.425826
$965$	−5.75705	−0.185326
$966$	−49.7962	−1.60217
$967$	15.5679	0.500629	0.250314	−	0.968165i	$-0.419466\pi$
$967$	15.5679	0.500629	0.250314	+	0.968165i	$0.419466\pi$
$968$	−5.42863	−0.174483
$969$	10.9386	0.351397
$970$	−7.22011	−0.231824
$971$	2.49356	0.0800222	0.0400111	−	0.999199i	$-0.487261\pi$
$971$	2.49356	0.0800222	0.0400111	+	0.999199i	$0.487261\pi$
$972$	21.7440	0.697441
$973$	8.85178	0.283775
$974$	−1.10775	−0.0354946
$975$	39.5115	1.26538
$976$	−14.8634	−0.475766
$977$	44.1235	1.41164	0.705818	−	0.708393i	$-0.250579\pi$
$977$	44.1235	1.41164	0.705818	+	0.708393i	$0.250579\pi$
$978$	−10.5842	−0.338445
$979$	55.1033	1.76111
$980$	−8.62702	−0.275580
$981$	−24.2073	−0.772880
$982$	−11.7817	−0.375968
$983$	−26.0986	−0.832416	−0.416208	−	0.909269i	$-0.636641\pi$
$983$	−26.0986	−0.832416	−0.416208	+	0.909269i	$0.636641\pi$
$984$	7.05161	0.224797
$985$	−23.1505	−0.737635
$986$	−5.72591	−0.182350
$987$	10.0589	0.320177
$988$	16.9618	0.539628
$989$	−2.76720	−0.0879919
$990$	−13.8162	−0.439108
$991$	−46.5745	−1.47949	−0.739743	−	0.672889i	$-0.765053\pi$
$991$	−46.5745	−1.47949	−0.739743	+	0.672889i	$0.765053\pi$
$992$	−4.49242	−0.142634
$993$	−35.7757	−1.13531
$994$	59.5068	1.88744
$995$	−0.466023	−0.0147739
$996$	5.80244	0.183857
$997$	17.2731	0.547046	0.273523	−	0.961865i	$-0.411811\pi$
$997$	17.2731	0.547046	0.273523	+	0.961865i	$0.411811\pi$
$998$	30.6724	0.970918
$999$	−1.07703	−0.0340759

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8002.2.a.e.1.11	✓	77

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8002.2.a.e.1.11	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.42114 q^{3} +1.00000 q^{4} -1.19106 q^{5} +2.42114 q^{6} -3.77401 q^{7} -1.00000 q^{8} +2.86190 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.42114 q^{3} +1.00000 q^{4} -1.19106 q^{5} +2.42114 q^{6} -3.77401 q^{7} -1.00000 q^{8} +2.86190 q^{9} +1.19106 q^{10} -4.05323 q^{11} -2.42114 q^{12} +4.55675 q^{13} +3.77401 q^{14} +2.88372 q^{15} +1.00000 q^{16} -1.21373 q^{17} -2.86190 q^{18} +3.72235 q^{19} -1.19106 q^{20} +9.13739 q^{21} +4.05323 q^{22} +5.44972 q^{23} +2.42114 q^{24} -3.58137 q^{25} -4.55675 q^{26} +0.334365 q^{27} -3.77401 q^{28} -4.71760 q^{29} -2.88372 q^{30} +4.49242 q^{31} -1.00000 q^{32} +9.81341 q^{33} +1.21373 q^{34} +4.49508 q^{35} +2.86190 q^{36} -3.22114 q^{37} -3.72235 q^{38} -11.0325 q^{39} +1.19106 q^{40} +2.91252 q^{41} -9.13739 q^{42} -0.507770 q^{43} -4.05323 q^{44} -3.40870 q^{45} -5.44972 q^{46} +1.10085 q^{47} -2.42114 q^{48} +7.24314 q^{49} +3.58137 q^{50} +2.93862 q^{51} +4.55675 q^{52} +0.544770 q^{53} -0.334365 q^{54} +4.82764 q^{55} +3.77401 q^{56} -9.01232 q^{57} +4.71760 q^{58} -1.10577 q^{59} +2.88372 q^{60} -14.8634 q^{61} -4.49242 q^{62} -10.8008 q^{63} +1.00000 q^{64} -5.42737 q^{65} -9.81341 q^{66} -3.02571 q^{67} -1.21373 q^{68} -13.1945 q^{69} -4.49508 q^{70} +15.7675 q^{71} -2.86190 q^{72} -6.91652 q^{73} +3.22114 q^{74} +8.67099 q^{75} +3.72235 q^{76} +15.2969 q^{77} +11.0325 q^{78} -9.08476 q^{79} -1.19106 q^{80} -9.39524 q^{81} -2.91252 q^{82} -2.39658 q^{83} +9.13739 q^{84} +1.44563 q^{85} +0.507770 q^{86} +11.4220 q^{87} +4.05323 q^{88} -13.5949 q^{89} +3.40870 q^{90} -17.1972 q^{91} +5.44972 q^{92} -10.8768 q^{93} -1.10085 q^{94} -4.43355 q^{95} +2.42114 q^{96} -6.06191 q^{97} -7.24314 q^{98} -11.5999 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 77 q - 77 q^{2} + 10 q^{3} + 77 q^{4} + 18 q^{5} - 10 q^{6} + 21 q^{7} - 77 q^{8} + 71 q^{9}+O(q^{10}) \) 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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