LMFDB - Embedded newform 8007.2.a.e.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.943890 q^{2} +1.00000 q^{3} -1.10907 q^{4} +3.50883 q^{5} -0.943890 q^{6} -2.32814 q^{7} +2.93462 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.943890 q^{2} +1.00000 q^{3} -1.10907 q^{4} +3.50883 q^{5} -0.943890 q^{6} -2.32814 q^{7} +2.93462 q^{8} +1.00000 q^{9} -3.31195 q^{10} -5.01861 q^{11} -1.10907 q^{12} +1.00539 q^{13} +2.19751 q^{14} +3.50883 q^{15} -0.551813 q^{16} -1.00000 q^{17} -0.943890 q^{18} +3.26521 q^{19} -3.89155 q^{20} -2.32814 q^{21} +4.73701 q^{22} -3.55015 q^{23} +2.93462 q^{24} +7.31191 q^{25} -0.948979 q^{26} +1.00000 q^{27} +2.58208 q^{28} -4.86661 q^{29} -3.31195 q^{30} +2.30575 q^{31} -5.34839 q^{32} -5.01861 q^{33} +0.943890 q^{34} -8.16906 q^{35} -1.10907 q^{36} -1.16260 q^{37} -3.08200 q^{38} +1.00539 q^{39} +10.2971 q^{40} -10.1573 q^{41} +2.19751 q^{42} +10.0192 q^{43} +5.56600 q^{44} +3.50883 q^{45} +3.35095 q^{46} +9.68937 q^{47} -0.551813 q^{48} -1.57975 q^{49} -6.90163 q^{50} -1.00000 q^{51} -1.11505 q^{52} +10.3774 q^{53} -0.943890 q^{54} -17.6094 q^{55} -6.83222 q^{56} +3.26521 q^{57} +4.59354 q^{58} -5.16679 q^{59} -3.89155 q^{60} -1.49433 q^{61} -2.17637 q^{62} -2.32814 q^{63} +6.15192 q^{64} +3.52775 q^{65} +4.73701 q^{66} -3.48575 q^{67} +1.10907 q^{68} -3.55015 q^{69} +7.71069 q^{70} -6.84335 q^{71} +2.93462 q^{72} -1.60666 q^{73} +1.09736 q^{74} +7.31191 q^{75} -3.62136 q^{76} +11.6840 q^{77} -0.948979 q^{78} -11.4385 q^{79} -1.93622 q^{80} +1.00000 q^{81} +9.58739 q^{82} +8.66231 q^{83} +2.58208 q^{84} -3.50883 q^{85} -9.45697 q^{86} -4.86661 q^{87} -14.7277 q^{88} -16.3560 q^{89} -3.31195 q^{90} -2.34070 q^{91} +3.93738 q^{92} +2.30575 q^{93} -9.14569 q^{94} +11.4571 q^{95} -5.34839 q^{96} -6.59296 q^{97} +1.49111 q^{98} -5.01861 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−0.943890	−0.667431	−0.333715	−	0.942674i	$-0.608302\pi$
$2$	−0.943890	−0.667431	−0.333715	+	0.942674i	$0.608302\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.10907	−0.554536
$5$	3.50883	1.56920	0.784599	−	0.620004i	$-0.212869\pi$
$5$	3.50883	1.56920	0.784599	+	0.620004i	$0.212869\pi$
$6$	−0.943890	−0.385341
$7$	−2.32814	−0.879955	−0.439978	−	0.898009i	$-0.645014\pi$
$7$	−2.32814	−0.879955	−0.439978	+	0.898009i	$0.645014\pi$
$8$	2.93462	1.03755
$9$	1.00000	0.333333
$10$	−3.31195	−1.04733
$11$	−5.01861	−1.51317	−0.756583	−	0.653897i	$-0.773133\pi$
$11$	−5.01861	−1.51317	−0.756583	+	0.653897i	$0.773133\pi$
$12$	−1.10907	−0.320162
$13$	1.00539	0.278846	0.139423	−	0.990233i	$-0.455475\pi$
$13$	1.00539	0.278846	0.139423	+	0.990233i	$0.455475\pi$
$14$	2.19751	0.587309
$15$	3.50883	0.905977
$16$	−0.551813	−0.137953
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−0.943890	−0.222477
$19$	3.26521	0.749091	0.374546	−	0.927209i	$-0.377799\pi$
$19$	3.26521	0.749091	0.374546	+	0.927209i	$0.377799\pi$
$20$	−3.89155	−0.870177
$21$	−2.32814	−0.508042
$22$	4.73701	1.00993
$23$	−3.55015	−0.740258	−0.370129	−	0.928980i	$-0.620686\pi$
$23$	−3.55015	−0.740258	−0.370129	+	0.928980i	$0.620686\pi$
$24$	2.93462	0.599027
$25$	7.31191	1.46238
$26$	−0.948979	−0.186110
$27$	1.00000	0.192450
$28$	2.58208	0.487967
$29$	−4.86661	−0.903706	−0.451853	−	0.892092i	$-0.649237\pi$
$29$	−4.86661	−0.903706	−0.451853	+	0.892092i	$0.649237\pi$
$30$	−3.31195	−0.604677
$31$	2.30575	0.414124	0.207062	−	0.978328i	$-0.433610\pi$
$31$	2.30575	0.414124	0.207062	+	0.978328i	$0.433610\pi$
$32$	−5.34839	−0.945471
$33$	−5.01861	−0.873627
$34$	0.943890	0.161876
$35$	−8.16906	−1.38082
$36$	−1.10907	−0.184845
$37$	−1.16260	−0.191129	−0.0955647	−	0.995423i	$-0.530466\pi$
$37$	−1.16260	−0.191129	−0.0955647	+	0.995423i	$0.530466\pi$
$38$	−3.08200	−0.499966
$39$	1.00539	0.160992
$40$	10.2971	1.62811
$41$	−10.1573	−1.58631	−0.793153	−	0.609022i	$-0.791562\pi$
$41$	−10.1573	−1.58631	−0.793153	+	0.609022i	$0.791562\pi$
$42$	2.19751	0.339083
$43$	10.0192	1.52791	0.763953	−	0.645272i	$-0.223256\pi$
$43$	10.0192	1.52791	0.763953	+	0.645272i	$0.223256\pi$
$44$	5.56600	0.839106
$45$	3.50883	0.523066
$46$	3.35095	0.494071
$47$	9.68937	1.41334	0.706670	−	0.707544i	$-0.250197\pi$
$47$	9.68937	1.41334	0.706670	+	0.707544i	$0.250197\pi$
$48$	−0.551813	−0.0796474
$49$	−1.57975	−0.225679
$50$	−6.90163	−0.976039
$51$	−1.00000	−0.140028
$52$	−1.11505	−0.154630
$53$	10.3774	1.42544	0.712719	−	0.701449i	$-0.247463\pi$
$53$	10.3774	1.42544	0.712719	+	0.701449i	$0.247463\pi$
$54$	−0.943890	−0.128447
$55$	−17.6094	−2.37446
$56$	−6.83222	−0.912993
$57$	3.26521	0.432488
$58$	4.59354	0.603161
$59$	−5.16679	−0.672659	−0.336329	−	0.941744i	$-0.609186\pi$
$59$	−5.16679	−0.672659	−0.336329	+	0.941744i	$0.609186\pi$
$60$	−3.89155	−0.502397
$61$	−1.49433	−0.191329	−0.0956646	−	0.995414i	$-0.530498\pi$
$61$	−1.49433	−0.191329	−0.0956646	+	0.995414i	$0.530498\pi$
$62$	−2.17637	−0.276399
$63$	−2.32814	−0.293318
$64$	6.15192	0.768990
$65$	3.52775	0.437564
$66$	4.73701	0.583086
$67$	−3.48575	−0.425853	−0.212926	−	0.977068i	$-0.568299\pi$
$67$	−3.48575	−0.425853	−0.212926	+	0.977068i	$0.568299\pi$
$68$	1.10907	0.134495
$69$	−3.55015	−0.427388
$70$	7.71069	0.921604
$71$	−6.84335	−0.812156	−0.406078	−	0.913838i	$-0.633104\pi$
$71$	−6.84335	−0.812156	−0.406078	+	0.913838i	$0.633104\pi$
$72$	2.93462	0.345848
$73$	−1.60666	−0.188045	−0.0940226	−	0.995570i	$-0.529973\pi$
$73$	−1.60666	−0.188045	−0.0940226	+	0.995570i	$0.529973\pi$
$74$	1.09736	0.127566
$75$	7.31191	0.844307
$76$	−3.62136	−0.415398
$77$	11.6840	1.33152
$78$	−0.948979	−0.107451
$79$	−11.4385	−1.28693	−0.643467	−	0.765474i	$-0.722505\pi$
$79$	−11.4385	−1.28693	−0.643467	+	0.765474i	$0.722505\pi$
$80$	−1.93622	−0.216476
$81$	1.00000	0.111111
$82$	9.58739	1.05875
$83$	8.66231	0.950812	0.475406	−	0.879767i	$-0.342301\pi$
$83$	8.66231	0.950812	0.475406	+	0.879767i	$0.342301\pi$
$84$	2.58208	0.281728
$85$	−3.50883	−0.380586
$86$	−9.45697	−1.01977
$87$	−4.86661	−0.521755
$88$	−14.7277	−1.56998
$89$	−16.3560	−1.73373	−0.866865	−	0.498543i	$-0.833869\pi$
$89$	−16.3560	−1.73373	−0.866865	+	0.498543i	$0.833869\pi$
$90$	−3.31195	−0.349110
$91$	−2.34070	−0.245372
$92$	3.93738	0.410500
$93$	2.30575	0.239095
$94$	−9.14569	−0.943306
$95$	11.4571	1.17547
$96$	−5.34839	−0.545868
$97$	−6.59296	−0.669414	−0.334707	−	0.942322i	$-0.608637\pi$
$97$	−6.59296	−0.669414	−0.334707	+	0.942322i	$0.608637\pi$
$98$	1.49111	0.150625
$99$	−5.01861	−0.504389
$100$	−8.10944	−0.810944
$101$	3.16781	0.315208	0.157604	−	0.987502i	$-0.449623\pi$
$101$	3.16781	0.315208	0.157604	+	0.987502i	$0.449623\pi$
$102$	0.943890	0.0934590
$103$	3.10167	0.305617	0.152808	−	0.988256i	$-0.451168\pi$
$103$	3.10167	0.305617	0.152808	+	0.988256i	$0.451168\pi$
$104$	2.95045	0.289315
$105$	−8.16906	−0.797219
$106$	−9.79507	−0.951382
$107$	8.91967	0.862297	0.431148	−	0.902281i	$-0.358109\pi$
$107$	8.91967	0.862297	0.431148	+	0.902281i	$0.358109\pi$
$108$	−1.10907	−0.106721
$109$	−7.30757	−0.699938	−0.349969	−	0.936761i	$-0.613808\pi$
$109$	−7.30757	−0.699938	−0.349969	+	0.936761i	$0.613808\pi$
$110$	16.6214	1.58479
$111$	−1.16260	−0.110349
$112$	1.28470	0.121393
$113$	−13.3017	−1.25131	−0.625657	−	0.780098i	$-0.715169\pi$
$113$	−13.3017	−1.25131	−0.625657	+	0.780098i	$0.715169\pi$
$114$	−3.08200	−0.288656
$115$	−12.4569	−1.16161
$116$	5.39742	0.501138
$117$	1.00539	0.0929485
$118$	4.87688	0.448953
$119$	2.32814	0.213420
$120$	10.2971	0.939992
$121$	14.1864	1.28967
$122$	1.41048	0.127699
$123$	−10.1573	−0.915854
$124$	−2.55724	−0.229647
$125$	8.11210	0.725569
$126$	2.19751	0.195770
$127$	10.8779	0.965258	0.482629	−	0.875825i	$-0.339682\pi$
$127$	10.8779	0.965258	0.482629	+	0.875825i	$0.339682\pi$
$128$	4.89005	0.432224
$129$	10.0192	0.882137
$130$	−3.32981	−0.292044
$131$	8.73616	0.763282	0.381641	−	0.924311i	$-0.375359\pi$
$131$	8.73616	0.763282	0.381641	+	0.924311i	$0.375359\pi$
$132$	5.56600	0.484458
$133$	−7.60188	−0.659166
$134$	3.29017	0.284227
$135$	3.50883	0.301992
$136$	−2.93462	−0.251642
$137$	−5.67042	−0.484457	−0.242229	−	0.970219i	$-0.577878\pi$
$137$	−5.67042	−0.484457	−0.242229	+	0.970219i	$0.577878\pi$
$138$	3.35095	0.285252
$139$	−6.45656	−0.547638	−0.273819	−	0.961781i	$-0.588287\pi$
$139$	−6.45656	−0.547638	−0.273819	+	0.961781i	$0.588287\pi$
$140$	9.06008	0.765717
$141$	9.68937	0.815992
$142$	6.45936	0.542058
$143$	−5.04567	−0.421940
$144$	−0.551813	−0.0459844
$145$	−17.0761	−1.41809
$146$	1.51651	0.125507
$147$	−1.57975	−0.130296
$148$	1.28940	0.105988
$149$	−21.6118	−1.77051	−0.885255	−	0.465106i	$-0.846016\pi$
$149$	−21.6118	−1.77051	−0.885255	+	0.465106i	$0.846016\pi$
$150$	−6.90163	−0.563516
$151$	2.51616	0.204762	0.102381	−	0.994745i	$-0.467354\pi$
$151$	2.51616	0.204762	0.102381	+	0.994745i	$0.467354\pi$
$152$	9.58216	0.777216
$153$	−1.00000	−0.0808452
$154$	−11.0284	−0.888696
$155$	8.09048	0.649843
$156$	−1.11505	−0.0892757
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	10.7967	0.858939
$159$	10.3774	0.822977
$160$	−18.7666	−1.48363
$161$	8.26526	0.651394
$162$	−0.943890	−0.0741590
$163$	17.4822	1.36931	0.684657	−	0.728865i	$-0.259952\pi$
$163$	17.4822	1.36931	0.684657	+	0.728865i	$0.259952\pi$
$164$	11.2652	0.879664
$165$	−17.6094	−1.37089
$166$	−8.17626	−0.634601
$167$	−16.1605	−1.25054	−0.625268	−	0.780410i	$-0.715010\pi$
$167$	−16.1605	−1.25054	−0.625268	+	0.780410i	$0.715010\pi$
$168$	−6.83222	−0.527117
$169$	−11.9892	−0.922245
$170$	3.31195	0.254015
$171$	3.26521	0.249697
$172$	−11.1120	−0.847279
$173$	6.75760	0.513771	0.256885	−	0.966442i	$-0.417304\pi$
$173$	6.75760	0.513771	0.256885	+	0.966442i	$0.417304\pi$
$174$	4.59354	0.348235
$175$	−17.0232	−1.28683
$176$	2.76933	0.208746
$177$	−5.16679	−0.388360
$178$	15.4382	1.15714
$179$	−18.5229	−1.38447	−0.692235	−	0.721672i	$-0.743374\pi$
$179$	−18.5229	−1.38447	−0.692235	+	0.721672i	$0.743374\pi$
$180$	−3.89155	−0.290059
$181$	−20.7954	−1.54571	−0.772854	−	0.634584i	$-0.781172\pi$
$181$	−20.7954	−1.54571	−0.772854	+	0.634584i	$0.781172\pi$
$182$	2.20936	0.163769
$183$	−1.49433	−0.110464
$184$	−10.4183	−0.768051
$185$	−4.07935	−0.299920
$186$	−2.17637	−0.159579
$187$	5.01861	0.366997
$188$	−10.7462	−0.783748
$189$	−2.32814	−0.169347
$190$	−10.8142	−0.784546
$191$	13.5891	0.983271	0.491636	−	0.870801i	$-0.336399\pi$
$191$	13.5891	0.983271	0.491636	+	0.870801i	$0.336399\pi$
$192$	6.15192	0.443976
$193$	−13.8923	−0.999991	−0.499996	−	0.866028i	$-0.666665\pi$
$193$	−13.8923	−0.999991	−0.499996	+	0.866028i	$0.666665\pi$
$194$	6.22303	0.446787
$195$	3.52775	0.252628
$196$	1.75206	0.125147
$197$	5.71584	0.407237	0.203618	−	0.979050i	$-0.434730\pi$
$197$	5.71584	0.407237	0.203618	+	0.979050i	$0.434730\pi$
$198$	4.73701	0.336645
$199$	−24.5328	−1.73908	−0.869541	−	0.493861i	$-0.835585\pi$
$199$	−24.5328	−1.73908	−0.869541	+	0.493861i	$0.835585\pi$
$200$	21.4577	1.51729
$201$	−3.48575	−0.245866
$202$	−2.99006	−0.210380
$203$	11.3302	0.795221
$204$	1.10907	0.0776506
$205$	−35.6403	−2.48923
$206$	−2.92764	−0.203978
$207$	−3.55015	−0.246753
$208$	−0.554789	−0.0384677
$209$	−16.3868	−1.13350
$210$	7.71069	0.532088
$211$	−2.65539	−0.182805	−0.0914023	−	0.995814i	$-0.529135\pi$
$211$	−2.65539	−0.182805	−0.0914023	+	0.995814i	$0.529135\pi$
$212$	−11.5092	−0.790457
$213$	−6.84335	−0.468898
$214$	−8.41918	−0.575523
$215$	35.1555	2.39759
$216$	2.93462	0.199676
$217$	−5.36811	−0.364411
$218$	6.89754	0.467160
$219$	−1.60666	−0.108568
$220$	19.5302	1.31672
$221$	−1.00539	−0.0676300
$222$	1.09736	0.0736501
$223$	8.14373	0.545345	0.272672	−	0.962107i	$-0.412093\pi$
$223$	8.14373	0.545345	0.272672	+	0.962107i	$0.412093\pi$
$224$	12.4518	0.831972
$225$	7.31191	0.487461
$226$	12.5553	0.835166
$227$	−25.2961	−1.67896	−0.839479	−	0.543392i	$-0.817140\pi$
$227$	−25.2961	−1.67896	−0.839479	+	0.543392i	$0.817140\pi$
$228$	−3.62136	−0.239830
$229$	−17.9428	−1.18569	−0.592847	−	0.805315i	$-0.701996\pi$
$229$	−17.9428	−1.18569	−0.592847	+	0.805315i	$0.701996\pi$
$230$	11.7579	0.775295
$231$	11.6840	0.768753
$232$	−14.2816	−0.937636
$233$	3.92422	0.257084	0.128542	−	0.991704i	$-0.458970\pi$
$233$	3.92422	0.257084	0.128542	+	0.991704i	$0.458970\pi$
$234$	−0.948979	−0.0620367
$235$	33.9984	2.21781
$236$	5.73034	0.373014
$237$	−11.4385	−0.743012
$238$	−2.19751	−0.142443
$239$	−3.38682	−0.219075	−0.109537	−	0.993983i	$-0.534937\pi$
$239$	−3.38682	−0.219075	−0.109537	+	0.993983i	$0.534937\pi$
$240$	−1.93622	−0.124983
$241$	26.9066	1.73321	0.866604	−	0.498996i	$-0.166298\pi$
$241$	26.9066	1.73321	0.866604	+	0.498996i	$0.166298\pi$
$242$	−13.3904	−0.860767
$243$	1.00000	0.0641500
$244$	1.65732	0.106099
$245$	−5.54309	−0.354135
$246$	9.58739	0.611269
$247$	3.28282	0.208881
$248$	6.76649	0.429673
$249$	8.66231	0.548952
$250$	−7.65693	−0.484267
$251$	−18.0513	−1.13939	−0.569693	−	0.821858i	$-0.692938\pi$
$251$	−18.0513	−1.13939	−0.569693	+	0.821858i	$0.692938\pi$
$252$	2.58208	0.162656
$253$	17.8168	1.12013
$254$	−10.2675	−0.644243
$255$	−3.50883	−0.219732
$256$	−16.9195	−1.05747
$257$	9.84097	0.613863	0.306931	−	0.951732i	$-0.400698\pi$
$257$	9.84097	0.613863	0.306931	+	0.951732i	$0.400698\pi$
$258$	−9.45697	−0.588765
$259$	2.70669	0.168185
$260$	−3.91253	−0.242645
$261$	−4.86661	−0.301235
$262$	−8.24597	−0.509438
$263$	−26.3248	−1.62326	−0.811628	−	0.584175i	$-0.801418\pi$
$263$	−26.3248	−1.62326	−0.811628	+	0.584175i	$0.801418\pi$
$264$	−14.7277	−0.906428
$265$	36.4124	2.23680
$266$	7.17533	0.439948
$267$	−16.3560	−1.00097
$268$	3.86595	0.236151
$269$	−26.8069	−1.63444	−0.817222	−	0.576323i	$-0.804487\pi$
$269$	−26.8069	−1.63444	−0.817222	+	0.576323i	$0.804487\pi$
$270$	−3.31195	−0.201559
$271$	−14.8379	−0.901339	−0.450670	−	0.892691i	$-0.648815\pi$
$271$	−14.8379	−0.901339	−0.450670	+	0.892691i	$0.648815\pi$
$272$	0.551813	0.0334586
$273$	−2.34070	−0.141665
$274$	5.35225	0.323342
$275$	−36.6956	−2.21283
$276$	3.93738	0.237002
$277$	−18.8597	−1.13317	−0.566584	−	0.824004i	$-0.691735\pi$
$277$	−18.8597	−1.13317	−0.566584	+	0.824004i	$0.691735\pi$
$278$	6.09428	0.365511
$279$	2.30575	0.138041
$280$	−23.9731	−1.43267
$281$	24.0689	1.43583	0.717916	−	0.696129i	$-0.245096\pi$
$281$	24.0689	1.43583	0.717916	+	0.696129i	$0.245096\pi$
$282$	−9.14569	−0.544618
$283$	15.7161	0.934228	0.467114	−	0.884197i	$-0.345294\pi$
$283$	15.7161	0.934228	0.467114	+	0.884197i	$0.345294\pi$
$284$	7.58977	0.450370
$285$	11.4571	0.678659
$286$	4.76255	0.281616
$287$	23.6477	1.39588
$288$	−5.34839	−0.315157
$289$	1.00000	0.0588235
$290$	16.1180	0.946479
$291$	−6.59296	−0.386486
$292$	1.78190	0.104278
$293$	−2.79213	−0.163118	−0.0815590	−	0.996669i	$-0.525990\pi$
$293$	−2.79213	−0.163118	−0.0815590	+	0.996669i	$0.525990\pi$
$294$	1.49111	0.0869635
$295$	−18.1294	−1.05553
$296$	−3.41178	−0.198305
$297$	−5.01861	−0.291209
$298$	20.3992	1.18169
$299$	−3.56929	−0.206418
$300$	−8.10944	−0.468199
$301$	−23.3260	−1.34449
$302$	−2.37498	−0.136665
$303$	3.16781	0.181986
$304$	−1.80179	−0.103340
$305$	−5.24335	−0.300233
$306$	0.943890	0.0539586
$307$	27.0903	1.54612	0.773062	−	0.634330i	$-0.218724\pi$
$307$	27.0903	1.54612	0.773062	+	0.634330i	$0.218724\pi$
$308$	−12.9584	−0.738375
$309$	3.10167	0.176448
$310$	−7.63652	−0.433725
$311$	24.4301	1.38530	0.692652	−	0.721272i	$-0.256442\pi$
$311$	24.4301	1.38530	0.692652	+	0.721272i	$0.256442\pi$
$312$	2.95045	0.167036
$313$	28.9536	1.63655	0.818276	−	0.574825i	$-0.194930\pi$
$313$	28.9536	1.63655	0.818276	+	0.574825i	$0.194930\pi$
$314$	−0.943890	−0.0532668
$315$	−8.16906	−0.460275
$316$	12.6861	0.713652
$317$	−5.24581	−0.294634	−0.147317	−	0.989089i	$-0.547064\pi$
$317$	−5.24581	−0.294634	−0.147317	+	0.989089i	$0.547064\pi$
$318$	−9.79507	−0.549280
$319$	24.4236	1.36746
$320$	21.5861	1.20670
$321$	8.91967	0.497847
$322$	−7.80149	−0.434760
$323$	−3.26521	−0.181681
$324$	−1.10907	−0.0616151
$325$	7.35134	0.407779
$326$	−16.5013	−0.913923
$327$	−7.30757	−0.404109
$328$	−29.8079	−1.64586
$329$	−22.5582	−1.24367
$330$	16.6214	0.914977
$331$	−17.9999	−0.989364	−0.494682	−	0.869074i	$-0.664715\pi$
$331$	−17.9999	−0.989364	−0.494682	+	0.869074i	$0.664715\pi$
$332$	−9.60713	−0.527260
$333$	−1.16260	−0.0637098
$334$	15.2537	0.834647
$335$	−12.2309	−0.668247
$336$	1.28470	0.0700861
$337$	−33.1093	−1.80358	−0.901789	−	0.432177i	$-0.857746\pi$
$337$	−33.1093	−1.80358	−0.901789	+	0.432177i	$0.857746\pi$
$338$	11.3165	0.615535
$339$	−13.3017	−0.722447
$340$	3.89155	0.211049
$341$	−11.5716	−0.626639
$342$	−3.08200	−0.166655
$343$	19.9749	1.07854
$344$	29.4024	1.58527
$345$	−12.4569	−0.670656
$346$	−6.37843	−0.342906
$347$	−4.18747	−0.224795	−0.112398	−	0.993663i	$-0.535853\pi$
$347$	−4.18747	−0.224795	−0.112398	+	0.993663i	$0.535853\pi$
$348$	5.39742	0.289332
$349$	23.6159	1.26413	0.632066	−	0.774915i	$-0.282207\pi$
$349$	23.6159	1.26413	0.632066	+	0.774915i	$0.282207\pi$
$350$	16.0680	0.858870
$351$	1.00539	0.0536639
$352$	26.8415	1.43066
$353$	−4.53137	−0.241181	−0.120590	−	0.992702i	$-0.538479\pi$
$353$	−4.53137	−0.241181	−0.120590	+	0.992702i	$0.538479\pi$
$354$	4.87688	0.259203
$355$	−24.0122	−1.27443
$356$	18.1400	0.961416
$357$	2.32814	0.123218
$358$	17.4836	0.924037
$359$	−3.37665	−0.178213	−0.0891065	−	0.996022i	$-0.528401\pi$
$359$	−3.37665	−0.178213	−0.0891065	+	0.996022i	$0.528401\pi$
$360$	10.2971	0.542705
$361$	−8.33839	−0.438863
$362$	19.6285	1.03165
$363$	14.1864	0.744593
$364$	2.59600	0.136067
$365$	−5.63750	−0.295080
$366$	1.41048	0.0737270
$367$	−30.0202	−1.56704	−0.783521	−	0.621365i	$-0.786578\pi$
$367$	−30.0202	−1.56704	−0.783521	+	0.621365i	$0.786578\pi$
$368$	1.95902	0.102121
$369$	−10.1573	−0.528769
$370$	3.85046	0.200176
$371$	−24.1599	−1.25432
$372$	−2.55724	−0.132587
$373$	−4.41263	−0.228477	−0.114239	−	0.993453i	$-0.536443\pi$
$373$	−4.41263	−0.228477	−0.114239	+	0.993453i	$0.536443\pi$
$374$	−4.73701	−0.244945
$375$	8.11210	0.418907
$376$	28.4346	1.46640
$377$	−4.89285	−0.251995
$378$	2.19751	0.113028
$379$	−20.0683	−1.03084	−0.515419	−	0.856938i	$-0.672364\pi$
$379$	−20.0683	−1.03084	−0.515419	+	0.856938i	$0.672364\pi$
$380$	−12.7067	−0.651842
$381$	10.8779	0.557292
$382$	−12.8266	−0.656265
$383$	22.4140	1.14530	0.572651	−	0.819799i	$-0.305915\pi$
$383$	22.4140	1.14530	0.572651	+	0.819799i	$0.305915\pi$
$384$	4.89005	0.249544
$385$	40.9973	2.08942
$386$	13.1128	0.667425
$387$	10.0192	0.509302
$388$	7.31207	0.371214
$389$	3.95429	0.200490	0.100245	−	0.994963i	$-0.468037\pi$
$389$	3.95429	0.200490	0.100245	+	0.994963i	$0.468037\pi$
$390$	−3.32981	−0.168611
$391$	3.55015	0.179539
$392$	−4.63598	−0.234152
$393$	8.73616	0.440681
$394$	−5.39513	−0.271802
$395$	−40.1359	−2.01945
$396$	5.56600	0.279702
$397$	21.5545	1.08179	0.540894	−	0.841091i	$-0.318086\pi$
$397$	21.5545	1.08179	0.540894	+	0.841091i	$0.318086\pi$
$398$	23.1562	1.16072
$399$	−7.60188	−0.380570
$400$	−4.03481	−0.201740
$401$	16.5882	0.828375	0.414187	−	0.910192i	$-0.364066\pi$
$401$	16.5882	0.828375	0.414187	+	0.910192i	$0.364066\pi$
$402$	3.29017	0.164099
$403$	2.31818	0.115477
$404$	−3.51333	−0.174795
$405$	3.50883	0.174355
$406$	−10.6944	−0.530755
$407$	5.83461	0.289211
$408$	−2.93462	−0.145285
$409$	37.6527	1.86181	0.930903	−	0.365267i	$-0.119022\pi$
$409$	37.6527	1.86181	0.930903	+	0.365267i	$0.119022\pi$
$410$	33.6405	1.66139
$411$	−5.67042	−0.279701
$412$	−3.43998	−0.169476
$413$	12.0290	0.591909
$414$	3.35095	0.164690
$415$	30.3946	1.49201
$416$	−5.37723	−0.263640
$417$	−6.45656	−0.316179
$418$	15.4673	0.756532
$419$	−17.8056	−0.869859	−0.434930	−	0.900464i	$-0.643227\pi$
$419$	−17.8056	−0.869859	−0.434930	+	0.900464i	$0.643227\pi$
$420$	9.06008	0.442087
$421$	19.0402	0.927961	0.463981	−	0.885845i	$-0.346421\pi$
$421$	19.0402	0.927961	0.463981	+	0.885845i	$0.346421\pi$
$422$	2.50640	0.122009
$423$	9.68937	0.471113
$424$	30.4536	1.47896
$425$	−7.31191	−0.354680
$426$	6.45936	0.312957
$427$	3.47901	0.168361
$428$	−9.89256	−0.478175
$429$	−5.04567	−0.243607
$430$	−33.1829	−1.60022
$431$	30.5449	1.47130	0.735648	−	0.677364i	$-0.236878\pi$
$431$	30.5449	1.47130	0.735648	+	0.677364i	$0.236878\pi$
$432$	−0.551813	−0.0265491
$433$	4.19960	0.201820	0.100910	−	0.994896i	$-0.467825\pi$
$433$	4.19960	0.201820	0.100910	+	0.994896i	$0.467825\pi$
$434$	5.06690	0.243219
$435$	−17.0761	−0.818737
$436$	8.10462	0.388141
$437$	−11.5920	−0.554520
$438$	1.51651	0.0724616
$439$	29.3668	1.40160	0.700801	−	0.713357i	$-0.252826\pi$
$439$	29.3668	1.40160	0.700801	+	0.713357i	$0.252826\pi$
$440$	−51.6771	−2.46361
$441$	−1.57975	−0.0752264
$442$	0.948979	0.0451383
$443$	24.7954	1.17807	0.589033	−	0.808109i	$-0.299509\pi$
$443$	24.7954	1.17807	0.589033	+	0.808109i	$0.299509\pi$
$444$	1.28940	0.0611923
$445$	−57.3904	−2.72057
$446$	−7.68678	−0.363980
$447$	−21.6118	−1.02220
$448$	−14.3225	−0.676676
$449$	−4.65991	−0.219915	−0.109957	−	0.993936i	$-0.535071\pi$
$449$	−4.65991	−0.219915	−0.109957	+	0.993936i	$0.535071\pi$
$450$	−6.90163	−0.325346
$451$	50.9756	2.40035
$452$	14.7525	0.693899
$453$	2.51616	0.118220
$454$	23.8767	1.12059
$455$	−8.21311	−0.385037
$456$	9.58216	0.448726
$457$	−4.81819	−0.225385	−0.112693	−	0.993630i	$-0.535948\pi$
$457$	−4.81819	−0.225385	−0.112693	+	0.993630i	$0.535948\pi$
$458$	16.9360	0.791368
$459$	−1.00000	−0.0466760
$460$	13.8156	0.644155
$461$	−7.87020	−0.366552	−0.183276	−	0.983062i	$-0.558670\pi$
$461$	−7.87020	−0.366552	−0.183276	+	0.983062i	$0.558670\pi$
$462$	−11.0284	−0.513089
$463$	4.08451	0.189823	0.0949116	−	0.995486i	$-0.469743\pi$
$463$	4.08451	0.189823	0.0949116	+	0.995486i	$0.469743\pi$
$464$	2.68546	0.124669
$465$	8.09048	0.375187
$466$	−3.70403	−0.171586
$467$	−16.2716	−0.752961	−0.376481	−	0.926424i	$-0.622866\pi$
$467$	−16.2716	−0.752961	−0.376481	+	0.926424i	$0.622866\pi$
$468$	−1.11505	−0.0515433
$469$	8.11533	0.374731
$470$	−32.0907	−1.48023
$471$	1.00000	0.0460776
$472$	−15.1626	−0.697914
$473$	−50.2822	−2.31198
$474$	10.7967	0.495909
$475$	23.8749	1.09546
$476$	−2.58208	−0.118349
$477$	10.3774	0.475146
$478$	3.19678	0.146217
$479$	−31.3862	−1.43407	−0.717037	−	0.697035i	$-0.754502\pi$
$479$	−31.3862	−1.43407	−0.717037	+	0.697035i	$0.754502\pi$
$480$	−18.7666	−0.856575
$481$	−1.16886	−0.0532956
$482$	−25.3969	−1.15680
$483$	8.26526	0.376082
$484$	−15.7337	−0.715170
$485$	−23.1336	−1.05044
$486$	−0.943890	−0.0428157
$487$	−14.7583	−0.668762	−0.334381	−	0.942438i	$-0.608527\pi$
$487$	−14.7583	−0.668762	−0.334381	+	0.942438i	$0.608527\pi$
$488$	−4.38529	−0.198513
$489$	17.4822	0.790574
$490$	5.23207	0.236361
$491$	−17.0491	−0.769417	−0.384708	−	0.923038i	$-0.625698\pi$
$491$	−17.0491	−0.769417	−0.384708	+	0.923038i	$0.625698\pi$
$492$	11.2652	0.507874
$493$	4.86661	0.219181
$494$	−3.09862	−0.139413
$495$	−17.6094	−0.791486
$496$	−1.27234	−0.0571298
$497$	15.9323	0.714660
$498$	−8.17626	−0.366387
$499$	−6.81219	−0.304955	−0.152478	−	0.988307i	$-0.548725\pi$
$499$	−6.81219	−0.304955	−0.152478	+	0.988307i	$0.548725\pi$
$500$	−8.99691	−0.402354
$501$	−16.1605	−0.721998
$502$	17.0384	0.760461
$503$	−25.1211	−1.12009	−0.560047	−	0.828461i	$-0.689217\pi$
$503$	−25.1211	−1.12009	−0.560047	+	0.828461i	$0.689217\pi$
$504$	−6.83222	−0.304331
$505$	11.1153	0.494624
$506$	−16.8171	−0.747611
$507$	−11.9892	−0.532458
$508$	−12.0644	−0.535271
$509$	−14.8097	−0.656427	−0.328214	−	0.944604i	$-0.606447\pi$
$509$	−14.8097	−0.656427	−0.328214	+	0.944604i	$0.606447\pi$
$510$	3.31195	0.146656
$511$	3.74053	0.165471
$512$	6.19004	0.273564
$513$	3.26521	0.144163
$514$	−9.28879	−0.409711
$515$	10.8832	0.479573
$516$	−11.1120	−0.489177
$517$	−48.6271	−2.13862
$518$	−2.55481	−0.112252
$519$	6.75760	0.296626
$520$	10.3526	0.453992
$521$	−18.6113	−0.815374	−0.407687	−	0.913122i	$-0.633665\pi$
$521$	−18.6113	−0.815374	−0.407687	+	0.913122i	$0.633665\pi$
$522$	4.59354	0.201054
$523$	12.2074	0.533790	0.266895	−	0.963726i	$-0.414002\pi$
$523$	12.2074	0.533790	0.266895	+	0.963726i	$0.414002\pi$
$524$	−9.68903	−0.423267
$525$	−17.0232	−0.742952
$526$	24.8477	1.08341
$527$	−2.30575	−0.100440
$528$	2.76933	0.120520
$529$	−10.3964	−0.452018
$530$	−34.3693	−1.49291
$531$	−5.16679	−0.224220
$532$	8.43103	0.365532
$533$	−10.2121	−0.442335
$534$	15.4382	0.668078
$535$	31.2976	1.35311
$536$	−10.2294	−0.441841
$537$	−18.5229	−0.799324
$538$	25.3027	1.09088
$539$	7.92816	0.341490
$540$	−3.89155	−0.167466
$541$	2.27708	0.0978993	0.0489497	−	0.998801i	$-0.484413\pi$
$541$	2.27708	0.0978993	0.0489497	+	0.998801i	$0.484413\pi$
$542$	14.0054	0.601582
$543$	−20.7954	−0.892415
$544$	5.34839	0.229310
$545$	−25.6410	−1.09834
$546$	2.20936	0.0945518
$547$	−19.5696	−0.836736	−0.418368	−	0.908278i	$-0.637398\pi$
$547$	−19.5696	−0.836736	−0.418368	+	0.908278i	$0.637398\pi$
$548$	6.28891	0.268649
$549$	−1.49433	−0.0637764
$550$	34.6366	1.47691
$551$	−15.8905	−0.676958
$552$	−10.4183	−0.443434
$553$	26.6305	1.13244
$554$	17.8014	0.756310
$555$	−4.07935	−0.173159
$556$	7.16079	0.303685
$557$	4.77606	0.202368	0.101184	−	0.994868i	$-0.467737\pi$
$557$	4.77606	0.202368	0.101184	+	0.994868i	$0.467737\pi$
$558$	−2.17637	−0.0921331
$559$	10.0732	0.426050
$560$	4.50780	0.190489
$561$	5.01861	0.211886
$562$	−22.7184	−0.958319
$563$	12.6274	0.532181	0.266091	−	0.963948i	$-0.414268\pi$
$563$	12.6274	0.532181	0.266091	+	0.963948i	$0.414268\pi$
$564$	−10.7462	−0.452497
$565$	−46.6733	−1.96356
$566$	−14.8343	−0.623532
$567$	−2.32814	−0.0977728
$568$	−20.0826	−0.842648
$569$	−15.3620	−0.644007	−0.322003	−	0.946739i	$-0.604356\pi$
$569$	−15.3620	−0.644007	−0.322003	+	0.946739i	$0.604356\pi$
$570$	−10.8142	−0.452958
$571$	−11.6263	−0.486544	−0.243272	−	0.969958i	$-0.578221\pi$
$571$	−11.6263	−0.486544	−0.243272	+	0.969958i	$0.578221\pi$
$572$	5.59601	0.233981
$573$	13.5891	0.567692
$574$	−22.3208	−0.931652
$575$	−25.9584	−1.08254
$576$	6.15192	0.256330
$577$	0.662416	0.0275768	0.0137884	−	0.999905i	$-0.495611\pi$
$577$	0.662416	0.0275768	0.0137884	+	0.999905i	$0.495611\pi$
$578$	−0.943890	−0.0392606
$579$	−13.8923	−0.577345
$580$	18.9386	0.786384
$581$	−20.1671	−0.836672
$582$	6.22303	0.257953
$583$	−52.0798	−2.15693
$584$	−4.71494	−0.195106
$585$	3.52775	0.145855
$586$	2.63546	0.108870
$587$	19.5779	0.808067	0.404034	−	0.914744i	$-0.367608\pi$
$587$	19.5779	0.808067	0.404034	+	0.914744i	$0.367608\pi$
$588$	1.75206	0.0722538
$589$	7.52875	0.310217
$590$	17.1121	0.704496
$591$	5.71584	0.235118
$592$	0.641535	0.0263669
$593$	−5.06598	−0.208035	−0.104018	−	0.994575i	$-0.533170\pi$
$593$	−5.06598	−0.208035	−0.104018	+	0.994575i	$0.533170\pi$
$594$	4.73701	0.194362
$595$	8.16906	0.334899
$596$	23.9691	0.981812
$597$	−24.5328	−1.00406
$598$	3.36902	0.137769
$599$	−3.15884	−0.129067	−0.0645333	−	0.997916i	$-0.520556\pi$
$599$	−3.15884	−0.129067	−0.0645333	+	0.997916i	$0.520556\pi$
$600$	21.4577	0.876006
$601$	−28.8749	−1.17783	−0.588916	−	0.808194i	$-0.700445\pi$
$601$	−28.8749	−1.17783	−0.588916	+	0.808194i	$0.700445\pi$
$602$	22.0172	0.897353
$603$	−3.48575	−0.141951
$604$	−2.79060	−0.113548
$605$	49.7777	2.02375
$606$	−2.99006	−0.121463
$607$	−17.2862	−0.701626	−0.350813	−	0.936446i	$-0.614095\pi$
$607$	−17.2862	−0.701626	−0.350813	+	0.936446i	$0.614095\pi$
$608$	−17.4636	−0.708244
$609$	11.3302	0.459121
$610$	4.94914	0.200385
$611$	9.74161	0.394103
$612$	1.10907	0.0448316
$613$	−8.17573	−0.330214	−0.165107	−	0.986276i	$-0.552797\pi$
$613$	−8.17573	−0.330214	−0.165107	+	0.986276i	$0.552797\pi$
$614$	−25.5702	−1.03193
$615$	−35.6403	−1.43716
$616$	34.2882	1.38151
$617$	−7.63160	−0.307237	−0.153618	−	0.988130i	$-0.549093\pi$
$617$	−7.63160	−0.307237	−0.153618	+	0.988130i	$0.549093\pi$
$618$	−2.92764	−0.117767
$619$	19.6432	0.789525	0.394763	−	0.918783i	$-0.370827\pi$
$619$	19.6432	0.789525	0.394763	+	0.918783i	$0.370827\pi$
$620$	−8.97293	−0.360362
$621$	−3.55015	−0.142463
$622$	−23.0593	−0.924594
$623$	38.0790	1.52560
$624$	−0.554789	−0.0222093
$625$	−8.09553	−0.323821
$626$	−27.3290	−1.09229
$627$	−16.3868	−0.654426
$628$	−1.10907	−0.0442568
$629$	1.16260	0.0463557
$630$	7.71069	0.307201
$631$	43.5189	1.73246	0.866229	−	0.499647i	$-0.166537\pi$
$631$	43.5189	1.73246	0.866229	+	0.499647i	$0.166537\pi$
$632$	−33.5677	−1.33525
$633$	−2.65539	−0.105542
$634$	4.95147	0.196648
$635$	38.1688	1.51468
$636$	−11.5092	−0.456371
$637$	−1.58827	−0.0629296
$638$	−23.0532	−0.912683
$639$	−6.84335	−0.270719
$640$	17.1584	0.678244
$641$	−35.6057	−1.40634	−0.703170	−	0.711022i	$-0.748233\pi$
$641$	−35.6057	−1.40634	−0.703170	+	0.711022i	$0.748233\pi$
$642$	−8.41918	−0.332279
$643$	−38.1629	−1.50500	−0.752500	−	0.658593i	$-0.771152\pi$
$643$	−38.1629	−1.50500	−0.752500	+	0.658593i	$0.771152\pi$
$644$	−9.16677	−0.361221
$645$	35.1555	1.38425
$646$	3.08200	0.121260
$647$	29.6505	1.16568	0.582840	−	0.812587i	$-0.301942\pi$
$647$	29.6505	1.16568	0.582840	+	0.812587i	$0.301942\pi$
$648$	2.93462	0.115283
$649$	25.9301	1.01784
$650$	−6.93885	−0.272164
$651$	−5.36811	−0.210393
$652$	−19.3891	−0.759334
$653$	−20.4813	−0.801496	−0.400748	−	0.916188i	$-0.631250\pi$
$653$	−20.4813	−0.801496	−0.400748	+	0.916188i	$0.631250\pi$
$654$	6.89754	0.269715
$655$	30.6537	1.19774
$656$	5.60494	0.218836
$657$	−1.60666	−0.0626818
$658$	21.2925	0.830067
$659$	11.2831	0.439528	0.219764	−	0.975553i	$-0.429471\pi$
$659$	11.2831	0.439528	0.219764	+	0.975553i	$0.429471\pi$
$660$	19.5302	0.760210
$661$	−30.2059	−1.17487	−0.587436	−	0.809271i	$-0.699863\pi$
$661$	−30.2059	−1.17487	−0.587436	+	0.809271i	$0.699863\pi$
$662$	16.9899	0.660332
$663$	−1.00539	−0.0390462
$664$	25.4206	0.986510
$665$	−26.6737	−1.03436
$666$	1.09736	0.0425219
$667$	17.2772	0.668975
$668$	17.9232	0.693468
$669$	8.14373	0.314855
$670$	11.5446	0.446009
$671$	7.49945	0.289513
$672$	12.4518	0.480339
$673$	21.1764	0.816291	0.408145	−	0.912917i	$-0.366176\pi$
$673$	21.1764	0.816291	0.408145	+	0.912917i	$0.366176\pi$
$674$	31.2515	1.20376
$675$	7.31191	0.281436
$676$	13.2969	0.511418
$677$	−2.85289	−0.109645	−0.0548227	−	0.998496i	$-0.517459\pi$
$677$	−2.85289	−0.109645	−0.0548227	+	0.998496i	$0.517459\pi$
$678$	12.5553	0.482183
$679$	15.3494	0.589054
$680$	−10.2971	−0.394876
$681$	−25.2961	−0.969347
$682$	10.9223	0.418238
$683$	25.1103	0.960821	0.480410	−	0.877044i	$-0.340488\pi$
$683$	25.1103	0.960821	0.480410	+	0.877044i	$0.340488\pi$
$684$	−3.62136	−0.138466
$685$	−19.8966	−0.760209
$686$	−18.8541	−0.719852
$687$	−17.9428	−0.684560
$688$	−5.52870	−0.210780
$689$	10.4333	0.397477
$690$	11.7579	0.447617
$691$	32.2779	1.22791	0.613955	−	0.789341i	$-0.289578\pi$
$691$	32.2779	1.22791	0.613955	+	0.789341i	$0.289578\pi$
$692$	−7.49467	−0.284905
$693$	11.6840	0.443840
$694$	3.95251	0.150035
$695$	−22.6550	−0.859353
$696$	−14.2816	−0.541344
$697$	10.1573	0.384736
$698$	−22.2908	−0.843720
$699$	3.92422	0.148427
$700$	18.8799	0.713594
$701$	−4.68951	−0.177120	−0.0885601	−	0.996071i	$-0.528227\pi$
$701$	−4.68951	−0.177120	−0.0885601	+	0.996071i	$0.528227\pi$
$702$	−0.948979	−0.0358169
$703$	−3.79612	−0.143173
$704$	−30.8740	−1.16361
$705$	33.9984	1.28045
$706$	4.27711	0.160971
$707$	−7.37510	−0.277369
$708$	5.73034	0.215359
$709$	−25.6853	−0.964631	−0.482315	−	0.875998i	$-0.660204\pi$
$709$	−25.6853	−0.964631	−0.482315	+	0.875998i	$0.660204\pi$
$710$	22.6648	0.850596
$711$	−11.4385	−0.428978
$712$	−47.9986	−1.79882
$713$	−8.18575	−0.306559
$714$	−2.19751	−0.0822397
$715$	−17.7044	−0.662107
$716$	20.5433	0.767738
$717$	−3.38682	−0.126483
$718$	3.18719	0.118945
$719$	23.9735	0.894062	0.447031	−	0.894518i	$-0.352481\pi$
$719$	23.9735	0.894062	0.447031	+	0.894518i	$0.352481\pi$
$720$	−1.93622	−0.0721587
$721$	−7.22113	−0.268929
$722$	7.87052	0.292910
$723$	26.9066	1.00067
$724$	23.0636	0.857151
$725$	−35.5842	−1.32156
$726$	−13.3904	−0.496964
$727$	11.4994	0.426489	0.213245	−	0.976999i	$-0.431597\pi$
$727$	11.4994	0.426489	0.213245	+	0.976999i	$0.431597\pi$
$728$	−6.86906	−0.254584
$729$	1.00000	0.0370370
$730$	5.32118	0.196946
$731$	−10.0192	−0.370572
$732$	1.65732	0.0612563
$733$	2.16985	0.0801453	0.0400726	−	0.999197i	$-0.487241\pi$
$733$	2.16985	0.0801453	0.0400726	+	0.999197i	$0.487241\pi$
$734$	28.3358	1.04589
$735$	−5.54309	−0.204460
$736$	18.9876	0.699892
$737$	17.4936	0.644386
$738$	9.58739	0.352917
$739$	30.3377	1.11599	0.557995	−	0.829844i	$-0.311571\pi$
$739$	30.3377	1.11599	0.557995	+	0.829844i	$0.311571\pi$
$740$	4.52430	0.166316
$741$	3.28282	0.120597
$742$	22.8043	0.837173
$743$	12.0601	0.442444	0.221222	−	0.975224i	$-0.428996\pi$
$743$	12.0601	0.442444	0.221222	+	0.975224i	$0.428996\pi$
$744$	6.76649	0.248072
$745$	−75.8323	−2.77828
$746$	4.16503	0.152493
$747$	8.66231	0.316937
$748$	−5.56600	−0.203513
$749$	−20.7663	−0.758782
$750$	−7.65693	−0.279592
$751$	−43.1501	−1.57457	−0.787285	−	0.616589i	$-0.788514\pi$
$751$	−43.1501	−1.57457	−0.787285	+	0.616589i	$0.788514\pi$
$752$	−5.34672	−0.194975
$753$	−18.0513	−0.657825
$754$	4.61831	0.168189
$755$	8.82878	0.321312
$756$	2.58208	0.0939093
$757$	−12.5373	−0.455675	−0.227838	−	0.973699i	$-0.573166\pi$
$757$	−12.5373	−0.455675	−0.227838	+	0.973699i	$0.573166\pi$
$758$	18.9422	0.688013
$759$	17.8168	0.646709
$760$	33.6222	1.21961
$761$	16.7430	0.606935	0.303467	−	0.952842i	$-0.401856\pi$
$761$	16.7430	0.606935	0.303467	+	0.952842i	$0.401856\pi$
$762$	−10.2675	−0.371954
$763$	17.0131	0.615914
$764$	−15.0713	−0.545259
$765$	−3.50883	−0.126862
$766$	−21.1563	−0.764409
$767$	−5.19465	−0.187568
$768$	−16.9195	−0.610530
$769$	−41.8387	−1.50874	−0.754372	−	0.656447i	$-0.772058\pi$
$769$	−41.8387	−1.50874	−0.754372	+	0.656447i	$0.772058\pi$
$770$	−38.6969	−1.39454
$771$	9.84097	0.354414
$772$	15.4076	0.554531
$773$	−42.0271	−1.51161	−0.755804	−	0.654798i	$-0.772754\pi$
$773$	−42.0271	−1.51161	−0.755804	+	0.654798i	$0.772754\pi$
$774$	−9.45697	−0.339924
$775$	16.8594	0.605608
$776$	−19.3478	−0.694547
$777$	2.70669	0.0971019
$778$	−3.73241	−0.133813
$779$	−33.1658	−1.18829
$780$	−3.91253	−0.140091
$781$	34.3441	1.22893
$782$	−3.35095	−0.119830
$783$	−4.86661	−0.173918
$784$	0.871729	0.0311332
$785$	3.50883	0.125236
$786$	−8.24597	−0.294124
$787$	2.07376	0.0739214	0.0369607	−	0.999317i	$-0.488232\pi$
$787$	2.07376	0.0739214	0.0369607	+	0.999317i	$0.488232\pi$
$788$	−6.33928	−0.225828
$789$	−26.3248	−0.937187
$790$	37.8838	1.34785
$791$	30.9681	1.10110
$792$	−14.7277	−0.523326
$793$	−1.50239	−0.0533513
$794$	−20.3450	−0.722018
$795$	36.4124	1.29141
$796$	27.2086	0.964384
$797$	27.2290	0.964501	0.482250	−	0.876033i	$-0.339820\pi$
$797$	27.2290	0.964501	0.482250	+	0.876033i	$0.339820\pi$
$798$	7.17533	0.254004
$799$	−9.68937	−0.342785
$800$	−39.1070	−1.38264
$801$	−16.3560	−0.577910
$802$	−15.6574	−0.552883
$803$	8.06319	0.284544
$804$	3.86595	0.136342
$805$	29.0014	1.02217
$806$	−2.18811	−0.0770728
$807$	−26.8069	−0.943647
$808$	9.29631	0.327043
$809$	−41.9532	−1.47500	−0.737498	−	0.675350i	$-0.763993\pi$
$809$	−41.9532	−1.47500	−0.737498	+	0.675350i	$0.763993\pi$
$810$	−3.31195	−0.116370
$811$	−6.55463	−0.230164	−0.115082	−	0.993356i	$-0.536713\pi$
$811$	−6.55463	−0.230164	−0.115082	+	0.993356i	$0.536713\pi$
$812$	−12.5660	−0.440979
$813$	−14.8379	−0.520389
$814$	−5.50722	−0.193028
$815$	61.3422	2.14873
$816$	0.551813	0.0193173
$817$	32.7147	1.14454
$818$	−35.5400	−1.24263
$819$	−2.34070	−0.0817905
$820$	39.5277	1.38037
$821$	23.4737	0.819237	0.409618	−	0.912257i	$-0.365662\pi$
$821$	23.4737	0.819237	0.409618	+	0.912257i	$0.365662\pi$
$822$	5.35225	0.186681
$823$	−16.1427	−0.562700	−0.281350	−	0.959605i	$-0.590782\pi$
$823$	−16.1427	−0.562700	−0.281350	+	0.959605i	$0.590782\pi$
$824$	9.10223	0.317091
$825$	−36.6956	−1.27758
$826$	−11.3541	−0.395058
$827$	6.01408	0.209130	0.104565	−	0.994518i	$-0.466655\pi$
$827$	6.01408	0.209130	0.104565	+	0.994518i	$0.466655\pi$
$828$	3.93738	0.136833
$829$	23.0125	0.799258	0.399629	−	0.916677i	$-0.369139\pi$
$829$	23.0125	0.799258	0.399629	+	0.916677i	$0.369139\pi$
$830$	−28.6891	−0.995815
$831$	−18.8597	−0.654234
$832$	6.18509	0.214429
$833$	1.57975	0.0547352
$834$	6.09428	0.211028
$835$	−56.7045	−1.96234
$836$	18.1742	0.628567
$837$	2.30575	0.0796983
$838$	16.8065	0.580571
$839$	−23.0000	−0.794048	−0.397024	−	0.917808i	$-0.629957\pi$
$839$	−23.0000	−0.794048	−0.397024	+	0.917808i	$0.629957\pi$
$840$	−23.9731	−0.827151
$841$	−5.31614	−0.183315
$842$	−17.9718	−0.619350
$843$	24.0689	0.828978
$844$	2.94502	0.101372
$845$	−42.0681	−1.44719
$846$	−9.14569	−0.314435
$847$	−33.0280	−1.13485
$848$	−5.72636	−0.196644
$849$	15.7161	0.539377
$850$	6.90163	0.236724
$851$	4.12739	0.141485
$852$	7.58977	0.260021
$853$	−56.0393	−1.91875	−0.959374	−	0.282136i	$-0.908957\pi$
$853$	−56.0393	−1.91875	−0.959374	+	0.282136i	$0.908957\pi$
$854$	−3.28380	−0.112369
$855$	11.4571	0.391824
$856$	26.1758	0.894672
$857$	−24.5248	−0.837750	−0.418875	−	0.908044i	$-0.637575\pi$
$857$	−24.5248	−0.837750	−0.418875	+	0.908044i	$0.637575\pi$
$858$	4.76255	0.162591
$859$	−43.5237	−1.48501	−0.742506	−	0.669840i	$-0.766363\pi$
$859$	−43.5237	−1.48501	−0.742506	+	0.669840i	$0.766363\pi$
$860$	−38.9900	−1.32955
$861$	23.6477	0.805911
$862$	−28.8310	−0.981988
$863$	−26.1440	−0.889952	−0.444976	−	0.895543i	$-0.646788\pi$
$863$	−26.1440	−0.889952	−0.444976	+	0.895543i	$0.646788\pi$
$864$	−5.34839	−0.181956
$865$	23.7113	0.806208
$866$	−3.96396	−0.134701
$867$	1.00000	0.0339618
$868$	5.95362	0.202079
$869$	57.4054	1.94735
$870$	16.1180	0.546450
$871$	−3.50455	−0.118747
$872$	−21.4449	−0.726217
$873$	−6.59296	−0.223138
$874$	10.9416	0.370104
$875$	−18.8861	−0.638468
$876$	1.78190	0.0602049
$877$	−13.6800	−0.461941	−0.230970	−	0.972961i	$-0.574190\pi$
$877$	−13.6800	−0.461941	−0.230970	+	0.972961i	$0.574190\pi$
$878$	−27.7190	−0.935472
$879$	−2.79213	−0.0941762
$880$	9.71713	0.327564
$881$	−19.4123	−0.654018	−0.327009	−	0.945021i	$-0.606041\pi$
$881$	−19.4123	−0.654018	−0.327009	+	0.945021i	$0.606041\pi$
$882$	1.49111	0.0502084
$883$	−23.0824	−0.776785	−0.388392	−	0.921494i	$-0.626969\pi$
$883$	−23.0824	−0.776785	−0.388392	+	0.921494i	$0.626969\pi$
$884$	1.11505	0.0375033
$885$	−18.1294	−0.609413
$886$	−23.4042	−0.786278
$887$	−12.6679	−0.425347	−0.212674	−	0.977123i	$-0.568217\pi$
$887$	−12.6679	−0.425347	−0.212674	+	0.977123i	$0.568217\pi$
$888$	−3.41178	−0.114492
$889$	−25.3253	−0.849384
$890$	54.1702	1.81579
$891$	−5.01861	−0.168130
$892$	−9.03199	−0.302413
$893$	31.6378	1.05872
$894$	20.3992	0.682251
$895$	−64.9939	−2.17251
$896$	−11.3847	−0.380337
$897$	−3.56929	−0.119175
$898$	4.39844	0.146778
$899$	−11.2212	−0.374247
$900$	−8.10944	−0.270315
$901$	−10.3774	−0.345720
$902$	−48.1153	−1.60206
$903$	−23.3260	−0.776241
$904$	−39.0353	−1.29830
$905$	−72.9675	−2.42552
$906$	−2.37498	−0.0789033
$907$	31.7150	1.05308	0.526540	−	0.850150i	$-0.323489\pi$
$907$	31.7150	1.05308	0.526540	+	0.850150i	$0.323489\pi$
$908$	28.0552	0.931043
$909$	3.16781	0.105069
$910$	7.75227	0.256985
$911$	9.15482	0.303313	0.151656	−	0.988433i	$-0.451539\pi$
$911$	9.15482	0.303313	0.151656	+	0.988433i	$0.451539\pi$
$912$	−1.80179	−0.0596631
$913$	−43.4727	−1.43874
$914$	4.54784	0.150429
$915$	−5.24335	−0.173340
$916$	19.8999	0.657510
$917$	−20.3390	−0.671653
$918$	0.943890	0.0311530
$919$	−33.2804	−1.09782	−0.548909	−	0.835882i	$-0.684957\pi$
$919$	−33.2804	−1.09782	−0.548909	+	0.835882i	$0.684957\pi$
$920$	−36.5562	−1.20522
$921$	27.0903	0.892655
$922$	7.42860	0.244648
$923$	−6.88025	−0.226466
$924$	−12.9584	−0.426301
$925$	−8.50079	−0.279504
$926$	−3.85533	−0.126694
$927$	3.10167	0.101872
$928$	26.0285	0.854428
$929$	−24.3960	−0.800407	−0.400204	−	0.916426i	$-0.631061\pi$
$929$	−24.3960	−0.800407	−0.400204	+	0.916426i	$0.631061\pi$
$930$	−7.63652	−0.250411
$931$	−5.15823	−0.169054
$932$	−4.35224	−0.142562
$933$	24.4301	0.799805
$934$	15.3586	0.502550
$935$	17.6094	0.575891
$936$	2.95045	0.0964383
$937$	46.8690	1.53114	0.765571	−	0.643351i	$-0.222456\pi$
$937$	46.8690	1.53114	0.765571	+	0.643351i	$0.222456\pi$
$938$	−7.65998	−0.250107
$939$	28.9536	0.944864
$940$	−37.7067	−1.22986
$941$	−57.9973	−1.89066	−0.945328	−	0.326120i	$-0.894259\pi$
$941$	−57.9973	−1.89066	−0.945328	+	0.326120i	$0.894259\pi$
$942$	−0.943890	−0.0307536
$943$	36.0600	1.17428
$944$	2.85110	0.0927955
$945$	−8.16906	−0.265740
$946$	47.4608	1.54308
$947$	26.2220	0.852101	0.426050	−	0.904699i	$-0.359905\pi$
$947$	26.2220	0.852101	0.426050	+	0.904699i	$0.359905\pi$
$948$	12.6861	0.412027
$949$	−1.61532	−0.0524356
$950$	−22.5353	−0.731142
$951$	−5.24581	−0.170107
$952$	6.83222	0.221433
$953$	33.6122	1.08881	0.544404	−	0.838823i	$-0.316756\pi$
$953$	33.6122	1.08881	0.544404	+	0.838823i	$0.316756\pi$
$954$	−9.79507	−0.317127
$955$	47.6818	1.54295
$956$	3.75622	0.121485
$957$	24.4236	0.789502
$958$	29.6251	0.957145
$959$	13.2016	0.426300
$960$	21.5861	0.696687
$961$	−25.6835	−0.828501
$962$	1.10328	0.0355711
$963$	8.91967	0.287432
$964$	−29.8414	−0.961127
$965$	−48.7458	−1.56918
$966$	−7.80149	−0.251009
$967$	−41.2020	−1.32497	−0.662484	−	0.749076i	$-0.730498\pi$
$967$	−41.2020	−1.32497	−0.662484	+	0.749076i	$0.730498\pi$
$968$	41.6317	1.33809
$969$	−3.26521	−0.104894
$970$	21.8356	0.701098
$971$	−4.14084	−0.132886	−0.0664429	−	0.997790i	$-0.521165\pi$
$971$	−4.14084	−0.132886	−0.0664429	+	0.997790i	$0.521165\pi$
$972$	−1.10907	−0.0355735
$973$	15.0318	0.481897
$974$	13.9302	0.446353
$975$	7.35134	0.235431
$976$	0.824590	0.0263945
$977$	−6.84908	−0.219122	−0.109561	−	0.993980i	$-0.534944\pi$
$977$	−6.84908	−0.219122	−0.109561	+	0.993980i	$0.534944\pi$
$978$	−16.5013	−0.527653
$979$	82.0842	2.62342
$980$	6.14769	0.196381
$981$	−7.30757	−0.233313
$982$	16.0925	0.513532
$983$	13.9052	0.443508	0.221754	−	0.975103i	$-0.428822\pi$
$983$	13.9052	0.443508	0.221754	+	0.975103i	$0.428822\pi$
$984$	−29.8079	−0.950240
$985$	20.0559	0.639035
$986$	−4.59354	−0.146288
$987$	−22.5582	−0.718036
$988$	−3.64088	−0.115832
$989$	−35.5695	−1.13104
$990$	16.6214	0.528262
$991$	56.9848	1.81018	0.905091	−	0.425218i	$-0.139802\pi$
$991$	56.9848	1.81018	0.905091	+	0.425218i	$0.139802\pi$
$992$	−12.3320	−0.391543
$993$	−17.9999	−0.571209
$994$	−15.0383	−0.476986
$995$	−86.0814	−2.72896
$996$	−9.60713	−0.304414
$997$	45.0997	1.42832	0.714161	−	0.699982i	$-0.246808\pi$
$997$	45.0997	1.42832	0.714161	+	0.699982i	$0.246808\pi$
$998$	6.42995	0.203537
$999$	−1.16260	−0.0367829

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.17	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.17	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-0.943890 q^{2} +1.00000 q^{3} -1.10907 q^{4} +3.50883 q^{5} -0.943890 q^{6} -2.32814 q^{7} +2.93462 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.943890 q^{2} +1.00000 q^{3} -1.10907 q^{4} +3.50883 q^{5} -0.943890 q^{6} -2.32814 q^{7} +2.93462 q^{8} +1.00000 q^{9} -3.31195 q^{10} -5.01861 q^{11} -1.10907 q^{12} +1.00539 q^{13} +2.19751 q^{14} +3.50883 q^{15} -0.551813 q^{16} -1.00000 q^{17} -0.943890 q^{18} +3.26521 q^{19} -3.89155 q^{20} -2.32814 q^{21} +4.73701 q^{22} -3.55015 q^{23} +2.93462 q^{24} +7.31191 q^{25} -0.948979 q^{26} +1.00000 q^{27} +2.58208 q^{28} -4.86661 q^{29} -3.31195 q^{30} +2.30575 q^{31} -5.34839 q^{32} -5.01861 q^{33} +0.943890 q^{34} -8.16906 q^{35} -1.10907 q^{36} -1.16260 q^{37} -3.08200 q^{38} +1.00539 q^{39} +10.2971 q^{40} -10.1573 q^{41} +2.19751 q^{42} +10.0192 q^{43} +5.56600 q^{44} +3.50883 q^{45} +3.35095 q^{46} +9.68937 q^{47} -0.551813 q^{48} -1.57975 q^{49} -6.90163 q^{50} -1.00000 q^{51} -1.11505 q^{52} +10.3774 q^{53} -0.943890 q^{54} -17.6094 q^{55} -6.83222 q^{56} +3.26521 q^{57} +4.59354 q^{58} -5.16679 q^{59} -3.89155 q^{60} -1.49433 q^{61} -2.17637 q^{62} -2.32814 q^{63} +6.15192 q^{64} +3.52775 q^{65} +4.73701 q^{66} -3.48575 q^{67} +1.10907 q^{68} -3.55015 q^{69} +7.71069 q^{70} -6.84335 q^{71} +2.93462 q^{72} -1.60666 q^{73} +1.09736 q^{74} +7.31191 q^{75} -3.62136 q^{76} +11.6840 q^{77} -0.948979 q^{78} -11.4385 q^{79} -1.93622 q^{80} +1.00000 q^{81} +9.58739 q^{82} +8.66231 q^{83} +2.58208 q^{84} -3.50883 q^{85} -9.45697 q^{86} -4.86661 q^{87} -14.7277 q^{88} -16.3560 q^{89} -3.31195 q^{90} -2.34070 q^{91} +3.93738 q^{92} +2.30575 q^{93} -9.14569 q^{94} +11.4571 q^{95} -5.34839 q^{96} -6.59296 q^{97} +1.49111 q^{98} -5.01861 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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