LMFDB - Embedded newform 8026.2.a.c.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8026,2,Mod(1,8026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8026, 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("8026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8026 = 2 \cdot 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8026.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:	$64.0879326623$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	8026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.25486 q^{3} +1.00000 q^{4} +3.01406 q^{5} +3.25486 q^{6} -0.942473 q^{7} -1.00000 q^{8} +7.59411 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.25486 q^{3} +1.00000 q^{4} +3.01406 q^{5} +3.25486 q^{6} -0.942473 q^{7} -1.00000 q^{8} +7.59411 q^{9} -3.01406 q^{10} +2.92999 q^{11} -3.25486 q^{12} -2.11202 q^{13} +0.942473 q^{14} -9.81035 q^{15} +1.00000 q^{16} -7.68861 q^{17} -7.59411 q^{18} +3.51048 q^{19} +3.01406 q^{20} +3.06762 q^{21} -2.92999 q^{22} +3.08551 q^{23} +3.25486 q^{24} +4.08458 q^{25} +2.11202 q^{26} -14.9532 q^{27} -0.942473 q^{28} -4.20193 q^{29} +9.81035 q^{30} -3.23381 q^{31} -1.00000 q^{32} -9.53670 q^{33} +7.68861 q^{34} -2.84067 q^{35} +7.59411 q^{36} -9.00655 q^{37} -3.51048 q^{38} +6.87434 q^{39} -3.01406 q^{40} +1.80546 q^{41} -3.06762 q^{42} +2.32770 q^{43} +2.92999 q^{44} +22.8891 q^{45} -3.08551 q^{46} -7.38970 q^{47} -3.25486 q^{48} -6.11175 q^{49} -4.08458 q^{50} +25.0253 q^{51} -2.11202 q^{52} +2.98167 q^{53} +14.9532 q^{54} +8.83117 q^{55} +0.942473 q^{56} -11.4261 q^{57} +4.20193 q^{58} -1.82712 q^{59} -9.81035 q^{60} +13.7346 q^{61} +3.23381 q^{62} -7.15724 q^{63} +1.00000 q^{64} -6.36578 q^{65} +9.53670 q^{66} -15.7729 q^{67} -7.68861 q^{68} -10.0429 q^{69} +2.84067 q^{70} +1.12608 q^{71} -7.59411 q^{72} +7.54882 q^{73} +9.00655 q^{74} -13.2947 q^{75} +3.51048 q^{76} -2.76143 q^{77} -6.87434 q^{78} +11.8901 q^{79} +3.01406 q^{80} +25.8882 q^{81} -1.80546 q^{82} +13.8456 q^{83} +3.06762 q^{84} -23.1739 q^{85} -2.32770 q^{86} +13.6767 q^{87} -2.92999 q^{88} +2.30618 q^{89} -22.8891 q^{90} +1.99053 q^{91} +3.08551 q^{92} +10.5256 q^{93} +7.38970 q^{94} +10.5808 q^{95} +3.25486 q^{96} -5.26823 q^{97} +6.11175 q^{98} +22.2506 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * 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
$3$	−3.25486	−1.87919	−0.939597	−	0.342283i	$-0.888800\pi$
$3$	−3.25486	−1.87919	−0.939597	+	0.342283i	$0.888800\pi$
$4$	1.00000	0.500000
$5$	3.01406	1.34793	0.673965	−	0.738763i	$-0.264590\pi$
$5$	3.01406	1.34793	0.673965	+	0.738763i	$0.264590\pi$
$6$	3.25486	1.32879
$7$	−0.942473	−0.356221	−0.178111	−	0.984010i	$-0.556998\pi$
$7$	−0.942473	−0.356221	−0.178111	+	0.984010i	$0.556998\pi$
$8$	−1.00000	−0.353553
$9$	7.59411	2.53137
$10$	−3.01406	−0.953130
$11$	2.92999	0.883425	0.441712	−	0.897157i	$-0.354371\pi$
$11$	2.92999	0.883425	0.441712	+	0.897157i	$0.354371\pi$
$12$	−3.25486	−0.939597
$13$	−2.11202	−0.585770	−0.292885	−	0.956148i	$-0.594615\pi$
$13$	−2.11202	−0.585770	−0.292885	+	0.956148i	$0.594615\pi$
$14$	0.942473	0.251886
$15$	−9.81035	−2.53302
$16$	1.00000	0.250000
$17$	−7.68861	−1.86476	−0.932380	−	0.361479i	$-0.882272\pi$
$17$	−7.68861	−1.86476	−0.932380	+	0.361479i	$0.882272\pi$
$18$	−7.59411	−1.78995
$19$	3.51048	0.805359	0.402680	−	0.915341i	$-0.368079\pi$
$19$	3.51048	0.805359	0.402680	+	0.915341i	$0.368079\pi$
$20$	3.01406	0.673965
$21$	3.06762	0.669409
$22$	−2.92999	−0.624676
$23$	3.08551	0.643373	0.321687	−	0.946846i	$-0.395750\pi$
$23$	3.08551	0.643373	0.321687	+	0.946846i	$0.395750\pi$
$24$	3.25486	0.664395
$25$	4.08458	0.816915
$26$	2.11202	0.414202
$27$	−14.9532	−2.87774
$28$	−0.942473	−0.178111
$29$	−4.20193	−0.780280	−0.390140	−	0.920756i	$-0.627573\pi$
$29$	−4.20193	−0.780280	−0.390140	+	0.920756i	$0.627573\pi$
$30$	9.81035	1.79112
$31$	−3.23381	−0.580809	−0.290404	−	0.956904i	$-0.593790\pi$
$31$	−3.23381	−0.580809	−0.290404	+	0.956904i	$0.593790\pi$
$32$	−1.00000	−0.176777
$33$	−9.53670	−1.66013
$34$	7.68861	1.31859
$35$	−2.84067	−0.480161
$36$	7.59411	1.26568
$37$	−9.00655	−1.48067	−0.740334	−	0.672239i	$-0.765333\pi$
$37$	−9.00655	−1.48067	−0.740334	+	0.672239i	$0.765333\pi$
$38$	−3.51048	−0.569475
$39$	6.87434	1.10078
$40$	−3.01406	−0.476565
$41$	1.80546	0.281965	0.140983	−	0.990012i	$-0.454974\pi$
$41$	1.80546	0.281965	0.140983	+	0.990012i	$0.454974\pi$
$42$	−3.06762	−0.473343
$43$	2.32770	0.354971	0.177485	−	0.984123i	$-0.443204\pi$
$43$	2.32770	0.354971	0.177485	+	0.984123i	$0.443204\pi$
$44$	2.92999	0.441712
$45$	22.8891	3.41211
$46$	−3.08551	−0.454934
$47$	−7.38970	−1.07790	−0.538950	−	0.842338i	$-0.681179\pi$
$47$	−7.38970	−1.07790	−0.538950	+	0.842338i	$0.681179\pi$
$48$	−3.25486	−0.469798
$49$	−6.11175	−0.873106
$50$	−4.08458	−0.577646
$51$	25.0253	3.50425
$52$	−2.11202	−0.292885
$53$	2.98167	0.409563	0.204782	−	0.978808i	$-0.434352\pi$
$53$	2.98167	0.409563	0.204782	+	0.978808i	$0.434352\pi$
$54$	14.9532	2.03487
$55$	8.83117	1.19079
$56$	0.942473	0.125943
$57$	−11.4261	−1.51343
$58$	4.20193	0.551741
$59$	−1.82712	−0.237871	−0.118935	−	0.992902i	$-0.537948\pi$
$59$	−1.82712	−0.237871	−0.118935	+	0.992902i	$0.537948\pi$
$60$	−9.81035	−1.26651
$61$	13.7346	1.75854	0.879271	−	0.476323i	$-0.158031\pi$
$61$	13.7346	1.75854	0.879271	+	0.476323i	$0.158031\pi$
$62$	3.23381	0.410694
$63$	−7.15724	−0.901727
$64$	1.00000	0.125000
$65$	−6.36578	−0.789577
$66$	9.53670	1.17389
$67$	−15.7729	−1.92697	−0.963483	−	0.267769i	$-0.913713\pi$
$67$	−15.7729	−1.92697	−0.963483	+	0.267769i	$0.913713\pi$
$68$	−7.68861	−0.932380
$69$	−10.0429	−1.20902
$70$	2.84067	0.339525
$71$	1.12608	0.133641	0.0668203	−	0.997765i	$-0.478715\pi$
$71$	1.12608	0.133641	0.0668203	+	0.997765i	$0.478715\pi$
$72$	−7.59411	−0.894974
$73$	7.54882	0.883522	0.441761	−	0.897133i	$-0.354354\pi$
$73$	7.54882	0.883522	0.441761	+	0.897133i	$0.354354\pi$
$74$	9.00655	1.04699
$75$	−13.2947	−1.53514
$76$	3.51048	0.402680
$77$	−2.76143	−0.314695
$78$	−6.87434	−0.778366
$79$	11.8901	1.33774	0.668872	−	0.743378i	$-0.266777\pi$
$79$	11.8901	1.33774	0.668872	+	0.743378i	$0.266777\pi$
$80$	3.01406	0.336983
$81$	25.8882	2.87646
$82$	−1.80546	−0.199380
$83$	13.8456	1.51975	0.759874	−	0.650070i	$-0.225261\pi$
$83$	13.8456	1.51975	0.759874	+	0.650070i	$0.225261\pi$
$84$	3.06762	0.334704
$85$	−23.1739	−2.51357
$86$	−2.32770	−0.251002
$87$	13.6767	1.46630
$88$	−2.92999	−0.312338
$89$	2.30618	0.244455	0.122227	−	0.992502i	$-0.460996\pi$
$89$	2.30618	0.244455	0.122227	+	0.992502i	$0.460996\pi$
$90$	−22.8891	−2.41273
$91$	1.99053	0.208664
$92$	3.08551	0.321687
$93$	10.5256	1.09145
$94$	7.38970	0.762190
$95$	10.5808	1.08557
$96$	3.25486	0.332198
$97$	−5.26823	−0.534907	−0.267454	−	0.963571i	$-0.586182\pi$
$97$	−5.26823	−0.534907	−0.267454	+	0.963571i	$0.586182\pi$
$98$	6.11175	0.617380
$99$	22.2506	2.23627
$100$	4.08458	0.408458
$101$	−4.30609	−0.428472	−0.214236	−	0.976782i	$-0.568726\pi$
$101$	−4.30609	−0.428472	−0.214236	+	0.976782i	$0.568726\pi$
$102$	−25.0253	−2.47788
$103$	17.6917	1.74322	0.871609	−	0.490201i	$-0.163077\pi$
$103$	17.6917	1.74322	0.871609	+	0.490201i	$0.163077\pi$
$104$	2.11202	0.207101
$105$	9.24599	0.902316
$106$	−2.98167	−0.289605
$107$	14.6587	1.41711	0.708554	−	0.705657i	$-0.249348\pi$
$107$	14.6587	1.41711	0.708554	+	0.705657i	$0.249348\pi$
$108$	−14.9532	−1.43887
$109$	−8.21181	−0.786549	−0.393275	−	0.919421i	$-0.628658\pi$
$109$	−8.21181	−0.786549	−0.393275	+	0.919421i	$0.628658\pi$
$110$	−8.83117	−0.842019
$111$	29.3151	2.78246
$112$	−0.942473	−0.0890553
$113$	15.8692	1.49285	0.746426	−	0.665469i	$-0.231768\pi$
$113$	15.8692	1.49285	0.746426	+	0.665469i	$0.231768\pi$
$114$	11.4261	1.07015
$115$	9.29992	0.867222
$116$	−4.20193	−0.390140
$117$	−16.0389	−1.48280
$118$	1.82712	0.168200
$119$	7.24630	0.664267
$120$	9.81035	0.895558
$121$	−2.41517	−0.219561
$122$	−13.7346	−1.24348
$123$	−5.87652	−0.529868
$124$	−3.23381	−0.290404
$125$	−2.75914	−0.246785
$126$	7.15724	0.637618
$127$	−8.35029	−0.740969	−0.370484	−	0.928839i	$-0.620808\pi$
$127$	−8.35029	−0.740969	−0.370484	+	0.928839i	$0.620808\pi$
$128$	−1.00000	−0.0883883
$129$	−7.57634	−0.667059
$130$	6.36578	0.558315
$131$	3.94848	0.344980	0.172490	−	0.985011i	$-0.444819\pi$
$131$	3.94848	0.344980	0.172490	+	0.985011i	$0.444819\pi$
$132$	−9.53670	−0.830063
$133$	−3.30853	−0.286886
$134$	15.7729	1.36257
$135$	−45.0698	−3.87899
$136$	7.68861	0.659293
$137$	−14.7206	−1.25766	−0.628831	−	0.777542i	$-0.716466\pi$
$137$	−14.7206	−1.25766	−0.628831	+	0.777542i	$0.716466\pi$
$138$	10.0429	0.854908
$139$	11.9993	1.01777	0.508884	−	0.860835i	$-0.330058\pi$
$139$	11.9993	1.01777	0.508884	+	0.860835i	$0.330058\pi$
$140$	−2.84067	−0.240081
$141$	24.0524	2.02558
$142$	−1.12608	−0.0944982
$143$	−6.18821	−0.517484
$144$	7.59411	0.632842
$145$	−12.6649	−1.05176
$146$	−7.54882	−0.624744
$147$	19.8929	1.64074
$148$	−9.00655	−0.740334
$149$	2.49943	0.204762	0.102381	−	0.994745i	$-0.467354\pi$
$149$	2.49943	0.204762	0.102381	+	0.994745i	$0.467354\pi$
$150$	13.2947	1.08551
$151$	15.0123	1.22169	0.610843	−	0.791752i	$-0.290831\pi$
$151$	15.0123	1.22169	0.610843	+	0.791752i	$0.290831\pi$
$152$	−3.51048	−0.284737
$153$	−58.3881	−4.72040
$154$	2.76143	0.222523
$155$	−9.74690	−0.782889
$156$	6.87434	0.550388
$157$	10.8471	0.865694	0.432847	−	0.901467i	$-0.357509\pi$
$157$	10.8471	0.865694	0.432847	+	0.901467i	$0.357509\pi$
$158$	−11.8901	−0.945928
$159$	−9.70490	−0.769649
$160$	−3.01406	−0.238283
$161$	−2.90801	−0.229183
$162$	−25.8882	−2.03397
$163$	18.3818	1.43977	0.719885	−	0.694093i	$-0.244194\pi$
$163$	18.3818	1.43977	0.719885	+	0.694093i	$0.244194\pi$
$164$	1.80546	0.140983
$165$	−28.7442	−2.23773
$166$	−13.8456	−1.07462
$167$	22.1260	1.71216	0.856081	−	0.516842i	$-0.172893\pi$
$167$	22.1260	1.71216	0.856081	+	0.516842i	$0.172893\pi$
$168$	−3.06762	−0.236672
$169$	−8.53935	−0.656873
$170$	23.1739	1.77736
$171$	26.6590	2.03866
$172$	2.32770	0.177485
$173$	−7.84524	−0.596462	−0.298231	−	0.954494i	$-0.596397\pi$
$173$	−7.84524	−0.596462	−0.298231	+	0.954494i	$0.596397\pi$
$174$	−13.6767	−1.03683
$175$	−3.84960	−0.291003
$176$	2.92999	0.220856
$177$	5.94702	0.447005
$178$	−2.30618	−0.172856
$179$	−25.8607	−1.93292	−0.966461	−	0.256813i	$-0.917328\pi$
$179$	−25.8607	−1.93292	−0.966461	+	0.256813i	$0.917328\pi$
$180$	22.8891	1.70605
$181$	−1.78003	−0.132309	−0.0661543	−	0.997809i	$-0.521073\pi$
$181$	−1.78003	−0.132309	−0.0661543	+	0.997809i	$0.521073\pi$
$182$	−1.99053	−0.147548
$183$	−44.7043	−3.30464
$184$	−3.08551	−0.227467
$185$	−27.1463	−1.99584
$186$	−10.5256	−0.771773
$187$	−22.5275	−1.64738
$188$	−7.38970	−0.538950
$189$	14.0930	1.02511
$190$	−10.5808	−0.767612
$191$	25.3495	1.83422	0.917111	−	0.398631i	$-0.130515\pi$
$191$	25.3495	1.83422	0.917111	+	0.398631i	$0.130515\pi$
$192$	−3.25486	−0.234899
$193$	−19.1127	−1.37576	−0.687880	−	0.725825i	$-0.741458\pi$
$193$	−19.1127	−1.37576	−0.687880	+	0.725825i	$0.741458\pi$
$194$	5.26823	0.378237
$195$	20.7197	1.48377
$196$	−6.11175	−0.436553
$197$	−12.7231	−0.906483	−0.453242	−	0.891388i	$-0.649733\pi$
$197$	−12.7231	−0.906483	−0.453242	+	0.891388i	$0.649733\pi$
$198$	−22.2506	−1.58128
$199$	−11.9316	−0.845810	−0.422905	−	0.906174i	$-0.638990\pi$
$199$	−11.9316	−0.845810	−0.422905	+	0.906174i	$0.638990\pi$
$200$	−4.08458	−0.288823
$201$	51.3386	3.62114
$202$	4.30609	0.302976
$203$	3.96021	0.277952
$204$	25.0253	1.75212
$205$	5.44177	0.380070
$206$	−17.6917	−1.23264
$207$	23.4317	1.62862
$208$	−2.11202	−0.146443
$209$	10.2857	0.711474
$210$	−9.24599	−0.638034
$211$	10.0464	0.691622	0.345811	−	0.938304i	$-0.387604\pi$
$211$	10.0464	0.691622	0.345811	+	0.938304i	$0.387604\pi$
$212$	2.98167	0.204782
$213$	−3.66522	−0.251137
$214$	−14.6587	−1.00205
$215$	7.01584	0.478476
$216$	14.9532	1.01743
$217$	3.04777	0.206896
$218$	8.21181	0.556174
$219$	−24.5703	−1.66031
$220$	8.83117	0.595397
$221$	16.2385	1.09232
$222$	−29.3151	−1.96750
$223$	17.3942	1.16480	0.582400	−	0.812902i	$-0.302114\pi$
$223$	17.3942	1.16480	0.582400	+	0.812902i	$0.302114\pi$
$224$	0.942473	0.0629716
$225$	31.0187	2.06792
$226$	−15.8692	−1.05561
$227$	−15.8810	−1.05406	−0.527031	−	0.849846i	$-0.676695\pi$
$227$	−15.8810	−1.05406	−0.527031	+	0.849846i	$0.676695\pi$
$228$	−11.4261	−0.756713
$229$	0.950740	0.0628266	0.0314133	−	0.999506i	$-0.489999\pi$
$229$	0.950740	0.0628266	0.0314133	+	0.999506i	$0.489999\pi$
$230$	−9.29992	−0.613219
$231$	8.98808	0.591372
$232$	4.20193	0.275870
$233$	1.15088	0.0753965	0.0376983	−	0.999289i	$-0.487997\pi$
$233$	1.15088	0.0753965	0.0376983	+	0.999289i	$0.487997\pi$
$234$	16.0389	1.04850
$235$	−22.2730	−1.45293
$236$	−1.82712	−0.118935
$237$	−38.7007	−2.51388
$238$	−7.24630	−0.469708
$239$	−3.34537	−0.216394	−0.108197	−	0.994129i	$-0.534508\pi$
$239$	−3.34537	−0.216394	−0.108197	+	0.994129i	$0.534508\pi$
$240$	−9.81035	−0.633255
$241$	30.7959	1.98374	0.991869	−	0.127261i	$-0.0406185\pi$
$241$	30.7959	1.98374	0.991869	+	0.127261i	$0.0406185\pi$
$242$	2.41517	0.155253
$243$	−39.4028	−2.52769
$244$	13.7346	0.879271
$245$	−18.4212	−1.17689
$246$	5.87652	0.374673
$247$	−7.41422	−0.471755
$248$	3.23381	0.205347
$249$	−45.0654	−2.85590
$250$	2.75914	0.174503
$251$	−28.9647	−1.82823	−0.914117	−	0.405450i	$-0.867115\pi$
$251$	−28.9647	−1.82823	−0.914117	+	0.405450i	$0.867115\pi$
$252$	−7.15724	−0.450864
$253$	9.04051	0.568372
$254$	8.35029	0.523944
$255$	75.4279	4.72348
$256$	1.00000	0.0625000
$257$	−5.09439	−0.317780	−0.158890	−	0.987296i	$-0.550791\pi$
$257$	−5.09439	−0.317780	−0.158890	+	0.987296i	$0.550791\pi$
$258$	7.57634	0.471682
$259$	8.48843	0.527445
$260$	−6.36578	−0.394789
$261$	−31.9099	−1.97518
$262$	−3.94848	−0.243938
$263$	25.7332	1.58678	0.793390	−	0.608714i	$-0.208314\pi$
$263$	25.7332	1.58678	0.793390	+	0.608714i	$0.208314\pi$
$264$	9.53670	0.586943
$265$	8.98693	0.552063
$266$	3.30853	0.202859
$267$	−7.50630	−0.459378
$268$	−15.7729	−0.963483
$269$	16.5561	1.00944	0.504721	−	0.863283i	$-0.331595\pi$
$269$	16.5561	1.00944	0.504721	+	0.863283i	$0.331595\pi$
$270$	45.0698	2.74286
$271$	−26.4780	−1.60842	−0.804212	−	0.594342i	$-0.797412\pi$
$271$	−26.4780	−1.60842	−0.804212	+	0.594342i	$0.797412\pi$
$272$	−7.68861	−0.466190
$273$	−6.47888	−0.392120
$274$	14.7206	0.889301
$275$	11.9678	0.721683
$276$	−10.0429	−0.604512
$277$	6.02251	0.361857	0.180929	−	0.983496i	$-0.442090\pi$
$277$	6.02251	0.361857	0.180929	+	0.983496i	$0.442090\pi$
$278$	−11.9993	−0.719670
$279$	−24.5579	−1.47024
$280$	2.84067	0.169763
$281$	−9.24938	−0.551771	−0.275886	−	0.961190i	$-0.588971\pi$
$281$	−9.24938	−0.551771	−0.275886	+	0.961190i	$0.588971\pi$
$282$	−24.0524	−1.43230
$283$	14.5292	0.863674	0.431837	−	0.901952i	$-0.357866\pi$
$283$	14.5292	0.863674	0.431837	+	0.901952i	$0.357866\pi$
$284$	1.12608	0.0668203
$285$	−34.4390	−2.03999
$286$	6.18821	0.365916
$287$	−1.70160	−0.100442
$288$	−7.59411	−0.447487
$289$	42.1147	2.47733
$290$	12.6649	0.743708
$291$	17.1473	1.00519
$292$	7.54882	0.441761
$293$	−23.4455	−1.36970	−0.684851	−	0.728683i	$-0.740133\pi$
$293$	−23.4455	−1.36970	−0.684851	+	0.728683i	$0.740133\pi$
$294$	−19.8929	−1.16018
$295$	−5.50705	−0.320633
$296$	9.00655	0.523495
$297$	−43.8126	−2.54227
$298$	−2.49943	−0.144788
$299$	−6.51667	−0.376869
$300$	−13.2947	−0.767571
$301$	−2.19379	−0.126448
$302$	−15.0123	−0.863862
$303$	14.0157	0.805182
$304$	3.51048	0.201340
$305$	41.3971	2.37039
$306$	58.3881	3.33783
$307$	9.94741	0.567729	0.283864	−	0.958864i	$-0.408383\pi$
$307$	9.94741	0.567729	0.283864	+	0.958864i	$0.408383\pi$
$308$	−2.76143	−0.157347
$309$	−57.5841	−3.27585
$310$	9.74690	0.553586
$311$	−9.25961	−0.525065	−0.262532	−	0.964923i	$-0.584558\pi$
$311$	−9.25961	−0.525065	−0.262532	+	0.964923i	$0.584558\pi$
$312$	−6.87434	−0.389183
$313$	30.3804	1.71720	0.858600	−	0.512645i	$-0.171334\pi$
$313$	30.3804	1.71720	0.858600	+	0.512645i	$0.171334\pi$
$314$	−10.8471	−0.612138
$315$	−21.5724	−1.21547
$316$	11.8901	0.668872
$317$	12.8925	0.724116	0.362058	−	0.932156i	$-0.382074\pi$
$317$	12.8925	0.724116	0.362058	+	0.932156i	$0.382074\pi$
$318$	9.70490	0.544224
$319$	−12.3116	−0.689318
$320$	3.01406	0.168491
$321$	−47.7119	−2.66302
$322$	2.90801	0.162057
$323$	−26.9907	−1.50180
$324$	25.8882	1.43823
$325$	−8.62673	−0.478525
$326$	−18.3818	−1.01807
$327$	26.7283	1.47808
$328$	−1.80546	−0.0996898
$329$	6.96459	0.383970
$330$	28.7442	1.58232
$331$	−16.7413	−0.920185	−0.460093	−	0.887871i	$-0.652184\pi$
$331$	−16.7413	−0.920185	−0.460093	+	0.887871i	$0.652184\pi$
$332$	13.8456	0.759874
$333$	−68.3967	−3.74812
$334$	−22.1260	−1.21068
$335$	−47.5405	−2.59742
$336$	3.06762	0.167352
$337$	−21.9612	−1.19630	−0.598150	−	0.801384i	$-0.704097\pi$
$337$	−21.9612	−1.19630	−0.598150	+	0.801384i	$0.704097\pi$
$338$	8.53935	0.464480
$339$	−51.6521	−2.80536
$340$	−23.1739	−1.25678
$341$	−9.47501	−0.513101
$342$	−26.6590	−1.44155
$343$	12.3575	0.667240
$344$	−2.32770	−0.125501
$345$	−30.2699	−1.62968
$346$	7.84524	0.421763
$347$	−18.8365	−1.01120	−0.505598	−	0.862769i	$-0.668728\pi$
$347$	−18.8365	−1.01120	−0.505598	+	0.862769i	$0.668728\pi$
$348$	13.6767	0.733148
$349$	−6.58962	−0.352734	−0.176367	−	0.984324i	$-0.556435\pi$
$349$	−6.58962	−0.352734	−0.176367	+	0.984324i	$0.556435\pi$
$350$	3.84960	0.205770
$351$	31.5815	1.68569
$352$	−2.92999	−0.156169
$353$	−2.66073	−0.141616	−0.0708081	−	0.997490i	$-0.522558\pi$
$353$	−2.66073	−0.141616	−0.0708081	+	0.997490i	$0.522558\pi$
$354$	−5.94702	−0.316080
$355$	3.39407	0.180138
$356$	2.30618	0.122227
$357$	−23.5857	−1.24829
$358$	25.8607	1.36678
$359$	−21.4079	−1.12987	−0.564933	−	0.825137i	$-0.691098\pi$
$359$	−21.4079	−1.12987	−0.564933	+	0.825137i	$0.691098\pi$
$360$	−22.8891	−1.20636
$361$	−6.67654	−0.351397
$362$	1.78003	0.0935563
$363$	7.86104	0.412598
$364$	1.99053	0.104332
$365$	22.7526	1.19093
$366$	44.7043	2.33673
$367$	8.31250	0.433909	0.216954	−	0.976182i	$-0.430388\pi$
$367$	8.31250	0.433909	0.216954	+	0.976182i	$0.430388\pi$
$368$	3.08551	0.160843
$369$	13.7109	0.713759
$370$	27.1463	1.41127
$371$	−2.81014	−0.145895
$372$	10.5256	0.545726
$373$	−8.79751	−0.455518	−0.227759	−	0.973718i	$-0.573140\pi$
$373$	−8.79751	−0.455518	−0.227759	+	0.973718i	$0.573140\pi$
$374$	22.5275	1.16487
$375$	8.98062	0.463757
$376$	7.38970	0.381095
$377$	8.87459	0.457065
$378$	−14.0930	−0.724864
$379$	−25.4907	−1.30937	−0.654683	−	0.755903i	$-0.727198\pi$
$379$	−25.4907	−1.30937	−0.654683	+	0.755903i	$0.727198\pi$
$380$	10.5808	0.542784
$381$	27.1790	1.39242
$382$	−25.3495	−1.29699
$383$	29.5457	1.50971	0.754856	−	0.655890i	$-0.227707\pi$
$383$	29.5457	1.50971	0.754856	+	0.655890i	$0.227707\pi$
$384$	3.25486	0.166099
$385$	−8.32313	−0.424186
$386$	19.1127	0.972809
$387$	17.6768	0.898563
$388$	−5.26823	−0.267454
$389$	24.4280	1.23855	0.619275	−	0.785174i	$-0.287427\pi$
$389$	24.4280	1.23855	0.619275	+	0.785174i	$0.287427\pi$
$390$	−20.7197	−1.04918
$391$	−23.7233	−1.19974
$392$	6.11175	0.308690
$393$	−12.8518	−0.648285
$394$	12.7231	0.640980
$395$	35.8376	1.80319
$396$	22.2506	1.11814
$397$	6.15604	0.308963	0.154482	−	0.987996i	$-0.450629\pi$
$397$	6.15604	0.308963	0.154482	+	0.987996i	$0.450629\pi$
$398$	11.9316	0.598078
$399$	10.7688	0.539114
$400$	4.08458	0.204229
$401$	10.2273	0.510728	0.255364	−	0.966845i	$-0.417805\pi$
$401$	10.2273	0.510728	0.255364	+	0.966845i	$0.417805\pi$
$402$	−51.3386	−2.56053
$403$	6.82988	0.340220
$404$	−4.30609	−0.214236
$405$	78.0286	3.87727
$406$	−3.96021	−0.196542
$407$	−26.3891	−1.30806
$408$	−25.0253	−1.23894
$409$	−12.2635	−0.606391	−0.303195	−	0.952928i	$-0.598054\pi$
$409$	−12.2635	−0.606391	−0.303195	+	0.952928i	$0.598054\pi$
$410$	−5.44177	−0.268750
$411$	47.9133	2.36339
$412$	17.6917	0.871609
$413$	1.72201	0.0847345
$414$	−23.4317	−1.15161
$415$	41.7314	2.04851
$416$	2.11202	0.103551
$417$	−39.0560	−1.91258
$418$	−10.2857	−0.503088
$419$	23.0805	1.12756	0.563779	−	0.825926i	$-0.309347\pi$
$419$	23.0805	1.12756	0.563779	+	0.825926i	$0.309347\pi$
$420$	9.24599	0.451158
$421$	30.3758	1.48043	0.740213	−	0.672373i	$-0.234725\pi$
$421$	30.3758	1.48043	0.740213	+	0.672373i	$0.234725\pi$
$422$	−10.0464	−0.489051
$423$	−56.1182	−2.72856
$424$	−2.98167	−0.144802
$425$	−31.4047	−1.52335
$426$	3.66522	0.177581
$427$	−12.9445	−0.626430
$428$	14.6587	0.708554
$429$	20.1417	0.972452
$430$	−7.01584	−0.338334
$431$	−6.87452	−0.331134	−0.165567	−	0.986199i	$-0.552945\pi$
$431$	−6.87452	−0.331134	−0.165567	+	0.986199i	$0.552945\pi$
$432$	−14.9532	−0.719435
$433$	15.8005	0.759324	0.379662	−	0.925125i	$-0.376040\pi$
$433$	15.8005	0.759324	0.379662	+	0.925125i	$0.376040\pi$
$434$	−3.04777	−0.146298
$435$	41.2225	1.97647
$436$	−8.21181	−0.393275
$437$	10.8316	0.518146
$438$	24.5703	1.17402
$439$	34.1070	1.62784	0.813919	−	0.580978i	$-0.197330\pi$
$439$	34.1070	1.62784	0.813919	+	0.580978i	$0.197330\pi$
$440$	−8.83117	−0.421009
$441$	−46.4133	−2.21016
$442$	−16.2385	−0.772388
$443$	21.1696	1.00580	0.502899	−	0.864345i	$-0.332267\pi$
$443$	21.1696	1.00580	0.502899	+	0.864345i	$0.332267\pi$
$444$	29.3151	1.39123
$445$	6.95098	0.329508
$446$	−17.3942	−0.823638
$447$	−8.13530	−0.384787
$448$	−0.942473	−0.0445276
$449$	−13.7417	−0.648511	−0.324256	−	0.945969i	$-0.605114\pi$
$449$	−13.7417	−0.648511	−0.324256	+	0.945969i	$0.605114\pi$
$450$	−31.0187	−1.46224
$451$	5.28997	0.249095
$452$	15.8692	0.746426
$453$	−48.8630	−2.29578
$454$	15.8810	0.745334
$455$	5.99957	0.281264
$456$	11.4261	0.535077
$457$	13.3406	0.624049	0.312024	−	0.950074i	$-0.398993\pi$
$457$	13.3406	0.624049	0.312024	+	0.950074i	$0.398993\pi$
$458$	−0.950740	−0.0444251
$459$	114.969	5.36630
$460$	9.29992	0.433611
$461$	27.8222	1.29581	0.647904	−	0.761722i	$-0.275646\pi$
$461$	27.8222	1.29581	0.647904	+	0.761722i	$0.275646\pi$
$462$	−8.98808	−0.418163
$463$	−4.77261	−0.221802	−0.110901	−	0.993831i	$-0.535374\pi$
$463$	−4.77261	−0.221802	−0.110901	+	0.993831i	$0.535374\pi$
$464$	−4.20193	−0.195070
$465$	31.7248	1.47120
$466$	−1.15088	−0.0533134
$467$	22.8555	1.05762	0.528812	−	0.848739i	$-0.322638\pi$
$467$	22.8555	1.05762	0.528812	+	0.848739i	$0.322638\pi$
$468$	−16.0389	−0.741400
$469$	14.8655	0.686426
$470$	22.2730	1.02738
$471$	−35.3058	−1.62681
$472$	1.82712	0.0841000
$473$	6.82013	0.313590
$474$	38.7007	1.77758
$475$	14.3388	0.657910
$476$	7.24630	0.332134
$477$	22.6431	1.03676
$478$	3.34537	0.153014
$479$	19.4926	0.890638	0.445319	−	0.895372i	$-0.353090\pi$
$479$	19.4926	0.890638	0.445319	+	0.895372i	$0.353090\pi$
$480$	9.81035	0.447779
$481$	19.0221	0.867331
$482$	−30.7959	−1.40272
$483$	9.46516	0.430680
$484$	−2.41517	−0.109781
$485$	−15.8788	−0.721018
$486$	39.4028	1.78735
$487$	30.9919	1.40438	0.702189	−	0.711991i	$-0.252206\pi$
$487$	30.9919	1.40438	0.702189	+	0.711991i	$0.252206\pi$
$488$	−13.7346	−0.621738
$489$	−59.8300	−2.70561
$490$	18.4212	0.832184
$491$	−10.2447	−0.462336	−0.231168	−	0.972914i	$-0.574255\pi$
$491$	−10.2447	−0.462336	−0.231168	+	0.972914i	$0.574255\pi$
$492$	−5.87652	−0.264934
$493$	32.3070	1.45503
$494$	7.41422	0.333581
$495$	67.0649	3.01434
$496$	−3.23381	−0.145202
$497$	−1.06130	−0.0476056
$498$	45.0654	2.01943
$499$	26.8781	1.20323	0.601615	−	0.798786i	$-0.294524\pi$
$499$	26.8781	1.20323	0.601615	+	0.798786i	$0.294524\pi$
$500$	−2.75914	−0.123393
$501$	−72.0170	−3.21748
$502$	28.9647	1.29276
$503$	4.88344	0.217742	0.108871	−	0.994056i	$-0.465277\pi$
$503$	4.88344	0.217742	0.108871	+	0.994056i	$0.465277\pi$
$504$	7.15724	0.318809
$505$	−12.9788	−0.577551
$506$	−9.04051	−0.401900
$507$	27.7944	1.23439
$508$	−8.35029	−0.370484
$509$	34.8754	1.54582	0.772912	−	0.634513i	$-0.218799\pi$
$509$	34.8754	1.54582	0.772912	+	0.634513i	$0.218799\pi$
$510$	−75.4279	−3.34000
$511$	−7.11455	−0.314729
$512$	−1.00000	−0.0441942
$513$	−52.4928	−2.31761
$514$	5.09439	0.224704
$515$	53.3240	2.34974
$516$	−7.57634	−0.333530
$517$	−21.6517	−0.952243
$518$	−8.48843	−0.372960
$519$	25.5351	1.12087
$520$	6.36578	0.279158
$521$	−6.65677	−0.291638	−0.145819	−	0.989311i	$-0.546582\pi$
$521$	−6.65677	−0.291638	−0.145819	+	0.989311i	$0.546582\pi$
$522$	31.9099	1.39666
$523$	28.3170	1.23821	0.619107	−	0.785307i	$-0.287495\pi$
$523$	28.3170	1.23821	0.619107	+	0.785307i	$0.287495\pi$
$524$	3.94848	0.172490
$525$	12.5299	0.546850
$526$	−25.7332	−1.12202
$527$	24.8635	1.08307
$528$	−9.53670	−0.415032
$529$	−13.4796	−0.586071
$530$	−8.98693	−0.390367
$531$	−13.8753	−0.602138
$532$	−3.30853	−0.143443
$533$	−3.81317	−0.165167
$534$	7.50630	0.324829
$535$	44.1822	1.91016
$536$	15.7729	0.681285
$537$	84.1731	3.63234
$538$	−16.5561	−0.713783
$539$	−17.9073	−0.771324
$540$	−45.0698	−1.93950
$541$	36.8592	1.58470	0.792350	−	0.610067i	$-0.208857\pi$
$541$	36.8592	1.58470	0.792350	+	0.610067i	$0.208857\pi$
$542$	26.4780	1.13733
$543$	5.79375	0.248634
$544$	7.68861	0.329646
$545$	−24.7509	−1.06021
$546$	6.47888	0.277270
$547$	−6.87039	−0.293757	−0.146878	−	0.989155i	$-0.546923\pi$
$547$	−6.87039	−0.293757	−0.146878	+	0.989155i	$0.546923\pi$
$548$	−14.7206	−0.628831
$549$	104.302	4.45152
$550$	−11.9678	−0.510307
$551$	−14.7508	−0.628405
$552$	10.0429	0.427454
$553$	−11.2061	−0.476533
$554$	−6.02251	−0.255872
$555$	88.3574	3.75056
$556$	11.9993	0.508884
$557$	−4.88957	−0.207178	−0.103589	−	0.994620i	$-0.533033\pi$
$557$	−4.88957	−0.207178	−0.103589	+	0.994620i	$0.533033\pi$
$558$	24.5579	1.03962
$559$	−4.91616	−0.207931
$560$	−2.84067	−0.120040
$561$	73.3239	3.09574
$562$	9.24938	0.390161
$563$	−29.8475	−1.25792	−0.628961	−	0.777437i	$-0.716519\pi$
$563$	−29.8475	−1.25792	−0.628961	+	0.777437i	$0.716519\pi$
$564$	24.0524	1.01279
$565$	47.8309	2.01226
$566$	−14.5292	−0.610710
$567$	−24.3989	−1.02466
$568$	−1.12608	−0.0472491
$569$	−1.15412	−0.0483831	−0.0241916	−	0.999707i	$-0.507701\pi$
$569$	−1.15412	−0.0483831	−0.0241916	+	0.999707i	$0.507701\pi$
$570$	34.4390	1.44249
$571$	−21.2069	−0.887482	−0.443741	−	0.896155i	$-0.646349\pi$
$571$	−21.2069	−0.887482	−0.443741	+	0.896155i	$0.646349\pi$
$572$	−6.18821	−0.258742
$573$	−82.5089	−3.44686
$574$	1.70160	0.0710232
$575$	12.6030	0.525582
$576$	7.59411	0.316421
$577$	3.67578	0.153025	0.0765124	−	0.997069i	$-0.475622\pi$
$577$	3.67578	0.153025	0.0765124	+	0.997069i	$0.475622\pi$
$578$	−42.1147	−1.75174
$579$	62.2090	2.58532
$580$	−12.6649	−0.525881
$581$	−13.0491	−0.541366
$582$	−17.1473	−0.710780
$583$	8.73624	0.361818
$584$	−7.54882	−0.312372
$585$	−48.3424	−1.99871
$586$	23.4455	0.968526
$587$	45.4715	1.87681	0.938404	−	0.345539i	$-0.112304\pi$
$587$	45.4715	1.87681	0.938404	+	0.345539i	$0.112304\pi$
$588$	19.8929	0.820368
$589$	−11.3522	−0.467760
$590$	5.50705	0.226722
$591$	41.4119	1.70346
$592$	−9.00655	−0.370167
$593$	−17.3155	−0.711061	−0.355530	−	0.934665i	$-0.615700\pi$
$593$	−17.3155	−0.711061	−0.355530	+	0.934665i	$0.615700\pi$
$594$	43.8126	1.79765
$595$	21.8408	0.895386
$596$	2.49943	0.102381
$597$	38.8357	1.58944
$598$	6.51667	0.266487
$599$	−13.2630	−0.541911	−0.270956	−	0.962592i	$-0.587340\pi$
$599$	−13.2630	−0.541911	−0.270956	+	0.962592i	$0.587340\pi$
$600$	13.2947	0.542755
$601$	−11.2067	−0.457132	−0.228566	−	0.973528i	$-0.573404\pi$
$601$	−11.2067	−0.457132	−0.228566	+	0.973528i	$0.573404\pi$
$602$	2.19379	0.0894123
$603$	−119.781	−4.87786
$604$	15.0123	0.610843
$605$	−7.27948	−0.295953
$606$	−14.0157	−0.569350
$607$	−42.5301	−1.72624	−0.863121	−	0.504997i	$-0.831494\pi$
$607$	−42.5301	−1.72624	−0.863121	+	0.504997i	$0.831494\pi$
$608$	−3.51048	−0.142369
$609$	−12.8899	−0.522326
$610$	−41.3971	−1.67612
$611$	15.6072	0.631401
$612$	−58.3881	−2.36020
$613$	−22.6567	−0.915096	−0.457548	−	0.889185i	$-0.651272\pi$
$613$	−22.6567	−0.915096	−0.457548	+	0.889185i	$0.651272\pi$
$614$	−9.94741	−0.401445
$615$	−17.7122	−0.714224
$616$	2.76143	0.111261
$617$	45.5558	1.83401	0.917004	−	0.398878i	$-0.130600\pi$
$617$	45.5558	1.83401	0.917004	+	0.398878i	$0.130600\pi$
$618$	57.5841	2.31637
$619$	14.6612	0.589285	0.294642	−	0.955608i	$-0.404799\pi$
$619$	14.6612	0.589285	0.294642	+	0.955608i	$0.404799\pi$
$620$	−9.74690	−0.391445
$621$	−46.1382	−1.85146
$622$	9.25961	0.371277
$623$	−2.17351	−0.0870799
$624$	6.87434	0.275194
$625$	−28.7391	−1.14956
$626$	−30.3804	−1.21424
$627$	−33.4784	−1.33700
$628$	10.8471	0.432847
$629$	69.2478	2.76109
$630$	21.5724	0.859464
$631$	−46.6007	−1.85514	−0.927571	−	0.373646i	$-0.878108\pi$
$631$	−46.6007	−1.85514	−0.927571	+	0.373646i	$0.878108\pi$
$632$	−11.8901	−0.472964
$633$	−32.6996	−1.29969
$634$	−12.8925	−0.512027
$635$	−25.1683	−0.998774
$636$	−9.70490	−0.384824
$637$	12.9082	0.511440
$638$	12.3116	0.487422
$639$	8.55155	0.338294
$640$	−3.01406	−0.119141
$641$	33.4002	1.31923	0.659613	−	0.751605i	$-0.270720\pi$
$641$	33.4002	1.31923	0.659613	+	0.751605i	$0.270720\pi$
$642$	47.7119	1.88304
$643$	33.7922	1.33263	0.666316	−	0.745669i	$-0.267870\pi$
$643$	33.7922	1.33263	0.666316	+	0.745669i	$0.267870\pi$
$644$	−2.90801	−0.114592
$645$	−22.8356	−0.899149
$646$	26.9907	1.06193
$647$	24.8454	0.976772	0.488386	−	0.872628i	$-0.337586\pi$
$647$	24.8454	0.976772	0.488386	+	0.872628i	$0.337586\pi$
$648$	−25.8882	−1.01698
$649$	−5.35344	−0.210141
$650$	8.62673	0.338368
$651$	−9.92007	−0.388798
$652$	18.3818	0.719885
$653$	16.9508	0.663338	0.331669	−	0.943396i	$-0.392388\pi$
$653$	16.9508	0.663338	0.331669	+	0.943396i	$0.392388\pi$
$654$	−26.7283	−1.04516
$655$	11.9010	0.465010
$656$	1.80546	0.0704913
$657$	57.3265	2.23652
$658$	−6.96459	−0.271508
$659$	−3.49453	−0.136128	−0.0680639	−	0.997681i	$-0.521682\pi$
$659$	−3.49453	−0.136128	−0.0680639	+	0.997681i	$0.521682\pi$
$660$	−28.7442	−1.11887
$661$	−3.99047	−0.155211	−0.0776056	−	0.996984i	$-0.524727\pi$
$661$	−3.99047	−0.155211	−0.0776056	+	0.996984i	$0.524727\pi$
$662$	16.7413	0.650669
$663$	−52.8541	−2.05268
$664$	−13.8456	−0.537312
$665$	−9.97212	−0.386702
$666$	68.3967	2.65032
$667$	−12.9651	−0.502011
$668$	22.1260	0.856081
$669$	−56.6156	−2.18889
$670$	47.5405	1.83665
$671$	40.2423	1.55354
$672$	−3.06762	−0.118336
$673$	−11.4445	−0.441155	−0.220577	−	0.975369i	$-0.570794\pi$
$673$	−11.4445	−0.441155	−0.220577	+	0.975369i	$0.570794\pi$
$674$	21.9612	0.845912
$675$	−61.0774	−2.35087
$676$	−8.53935	−0.328437
$677$	−43.0689	−1.65527	−0.827637	−	0.561264i	$-0.810315\pi$
$677$	−43.0689	−1.65527	−0.827637	+	0.561264i	$0.810315\pi$
$678$	51.6521	1.98369
$679$	4.96516	0.190545
$680$	23.1739	0.888680
$681$	51.6906	1.98079
$682$	9.47501	0.362817
$683$	17.2192	0.658876	0.329438	−	0.944177i	$-0.393141\pi$
$683$	17.2192	0.658876	0.329438	+	0.944177i	$0.393141\pi$
$684$	26.6590	1.01933
$685$	−44.3687	−1.69524
$686$	−12.3575	−0.471810
$687$	−3.09452	−0.118063
$688$	2.32770	0.0887427
$689$	−6.29735	−0.239910
$690$	30.2699	1.15236
$691$	4.33627	0.164960	0.0824798	−	0.996593i	$-0.473716\pi$
$691$	4.33627	0.164960	0.0824798	+	0.996593i	$0.473716\pi$
$692$	−7.84524	−0.298231
$693$	−20.9706	−0.796608
$694$	18.8365	0.715023
$695$	36.1666	1.37188
$696$	−13.6767	−0.518414
$697$	−13.8815	−0.525798
$698$	6.58962	0.249421
$699$	−3.74595	−0.141685
$700$	−3.84960	−0.145501
$701$	24.5188	0.926062	0.463031	−	0.886342i	$-0.346762\pi$
$701$	24.5188	0.926062	0.463031	+	0.886342i	$0.346762\pi$
$702$	−31.5815	−1.19197
$703$	−31.6173	−1.19247
$704$	2.92999	0.110428
$705$	72.4956	2.73034
$706$	2.66073	0.100138
$707$	4.05837	0.152631
$708$	5.94702	0.223503
$709$	−4.25166	−0.159674	−0.0798371	−	0.996808i	$-0.525440\pi$
$709$	−4.25166	−0.159674	−0.0798371	+	0.996808i	$0.525440\pi$
$710$	−3.39407	−0.127377
$711$	90.2949	3.38632
$712$	−2.30618	−0.0864278
$713$	−9.97794	−0.373677
$714$	23.5857	0.882672
$715$	−18.6516	−0.697532
$716$	−25.8607	−0.966461
$717$	10.8887	0.406647
$718$	21.4079	0.798936
$719$	22.5330	0.840339	0.420169	−	0.907446i	$-0.361971\pi$
$719$	22.5330	0.840339	0.420169	+	0.907446i	$0.361971\pi$
$720$	22.8891	0.853027
$721$	−16.6740	−0.620971
$722$	6.67654	0.248475
$723$	−100.236	−3.72783
$724$	−1.78003	−0.0661543
$725$	−17.1631	−0.637422
$726$	−7.86104	−0.291751
$727$	−12.7163	−0.471621	−0.235811	−	0.971799i	$-0.575775\pi$
$727$	−12.7163	−0.471621	−0.235811	+	0.971799i	$0.575775\pi$
$728$	−1.99053	−0.0737738
$729$	50.5861	1.87356
$730$	−22.7526	−0.842112
$731$	−17.8968	−0.661936
$732$	−44.7043	−1.65232
$733$	26.8685	0.992409	0.496205	−	0.868206i	$-0.334727\pi$
$733$	26.8685	0.992409	0.496205	+	0.868206i	$0.334727\pi$
$734$	−8.31250	−0.306820
$735$	59.9584	2.21160
$736$	−3.08551	−0.113733
$737$	−46.2144	−1.70233
$738$	−13.7109	−0.504704
$739$	−52.5076	−1.93152	−0.965761	−	0.259434i	$-0.916464\pi$
$739$	−52.5076	−1.93152	−0.965761	+	0.259434i	$0.916464\pi$
$740$	−27.1463	−0.997919
$741$	24.1322	0.886520
$742$	2.81014	0.103163
$743$	12.3847	0.454351	0.227175	−	0.973854i	$-0.427051\pi$
$743$	12.3847	0.454351	0.227175	+	0.973854i	$0.427051\pi$
$744$	−10.5256	−0.385887
$745$	7.53345	0.276004
$746$	8.79751	0.322100
$747$	105.145	3.84704
$748$	−22.5275	−0.823688
$749$	−13.8154	−0.504804
$750$	−8.98062	−0.327926
$751$	4.19077	0.152923	0.0764617	−	0.997073i	$-0.475638\pi$
$751$	4.19077	0.152923	0.0764617	+	0.997073i	$0.475638\pi$
$752$	−7.38970	−0.269475
$753$	94.2759	3.43561
$754$	−8.87459	−0.323193
$755$	45.2481	1.64675
$756$	14.0930	0.512556
$757$	−7.25152	−0.263561	−0.131781	−	0.991279i	$-0.542069\pi$
$757$	−7.25152	−0.263561	−0.131781	+	0.991279i	$0.542069\pi$
$758$	25.4907	0.925862
$759$	−29.4256	−1.06808
$760$	−10.5808	−0.383806
$761$	−0.353813	−0.0128257	−0.00641285	−	0.999979i	$-0.502041\pi$
$761$	−0.353813	−0.0128257	−0.00641285	+	0.999979i	$0.502041\pi$
$762$	−27.1790	−0.984592
$763$	7.73941	0.280185
$764$	25.3495	0.917111
$765$	−175.985	−6.36277
$766$	−29.5457	−1.06753
$767$	3.85892	0.139338
$768$	−3.25486	−0.117450
$769$	2.15233	0.0776151	0.0388075	−	0.999247i	$-0.487644\pi$
$769$	2.15233	0.0776151	0.0388075	+	0.999247i	$0.487644\pi$
$770$	8.32313	0.299945
$771$	16.5815	0.597170
$772$	−19.1127	−0.687880
$773$	7.44070	0.267623	0.133812	−	0.991007i	$-0.457278\pi$
$773$	7.44070	0.267623	0.133812	+	0.991007i	$0.457278\pi$
$774$	−17.6768	−0.635380
$775$	−13.2087	−0.474472
$776$	5.26823	0.189118
$777$	−27.6286	−0.991172
$778$	−24.4280	−0.875787
$779$	6.33803	0.227083
$780$	20.7197	0.741884
$781$	3.29939	0.118061
$782$	23.7233	0.848342
$783$	62.8323	2.24544
$784$	−6.11175	−0.218277
$785$	32.6939	1.16689
$786$	12.8518	0.458407
$787$	24.6537	0.878808	0.439404	−	0.898289i	$-0.355190\pi$
$787$	24.6537	0.878808	0.439404	+	0.898289i	$0.355190\pi$
$788$	−12.7231	−0.453242
$789$	−83.7581	−2.98187
$790$	−35.8376	−1.27504
$791$	−14.9563	−0.531785
$792$	−22.2506	−0.790642
$793$	−29.0079	−1.03010
$794$	−6.15604	−0.218470
$795$	−29.2512	−1.03743
$796$	−11.9316	−0.422905
$797$	−38.5658	−1.36607	−0.683034	−	0.730386i	$-0.739340\pi$
$797$	−38.5658	−1.36607	−0.683034	+	0.730386i	$0.739340\pi$
$798$	−10.7688	−0.381211
$799$	56.8165	2.01002
$800$	−4.08458	−0.144412
$801$	17.5134	0.618805
$802$	−10.2273	−0.361139
$803$	22.1179	0.780525
$804$	51.3386	1.81057
$805$	−8.76492	−0.308923
$806$	−6.82988	−0.240572
$807$	−53.8877	−1.89694
$808$	4.30609	0.151488
$809$	16.3669	0.575428	0.287714	−	0.957716i	$-0.407105\pi$
$809$	16.3669	0.575428	0.287714	+	0.957716i	$0.407105\pi$
$810$	−78.0286	−2.74164
$811$	22.3575	0.785079	0.392539	−	0.919735i	$-0.371597\pi$
$811$	22.3575	0.785079	0.392539	+	0.919735i	$0.371597\pi$
$812$	3.96021	0.138976
$813$	86.1822	3.02254
$814$	26.3891	0.924937
$815$	55.4038	1.94071
$816$	25.0253	0.876062
$817$	8.17134	0.285879
$818$	12.2635	0.428783
$819$	15.1163	0.528205
$820$	5.44177	0.190035
$821$	37.2327	1.29943	0.649715	−	0.760178i	$-0.274888\pi$
$821$	37.2327	1.29943	0.649715	+	0.760178i	$0.274888\pi$
$822$	−47.9133	−1.67117
$823$	−26.3216	−0.917512	−0.458756	−	0.888562i	$-0.651705\pi$
$823$	−26.3216	−0.917512	−0.458756	+	0.888562i	$0.651705\pi$
$824$	−17.6917	−0.616321
$825$	−38.9534	−1.35618
$826$	−1.72201	−0.0599164
$827$	−27.4533	−0.954646	−0.477323	−	0.878728i	$-0.658393\pi$
$827$	−27.4533	−0.954646	−0.477323	+	0.878728i	$0.658393\pi$
$828$	23.4317	0.814308
$829$	−4.69139	−0.162939	−0.0814694	−	0.996676i	$-0.525961\pi$
$829$	−4.69139	−0.162939	−0.0814694	+	0.996676i	$0.525961\pi$
$830$	−41.7314	−1.44852
$831$	−19.6024	−0.680000
$832$	−2.11202	−0.0732213
$833$	46.9908	1.62813
$834$	39.0560	1.35240
$835$	66.6892	2.30787
$836$	10.2857	0.355737
$837$	48.3557	1.67142
$838$	−23.0805	−0.797304
$839$	−14.6447	−0.505591	−0.252796	−	0.967520i	$-0.581350\pi$
$839$	−14.6447	−0.505591	−0.252796	+	0.967520i	$0.581350\pi$
$840$	−9.24599	−0.319017
$841$	−11.3437	−0.391164
$842$	−30.3758	−1.04682
$843$	30.1054	1.03689
$844$	10.0464	0.345811
$845$	−25.7381	−0.885419
$846$	56.1182	1.92938
$847$	2.27623	0.0782123
$848$	2.98167	0.102391
$849$	−47.2906	−1.62301
$850$	31.4047	1.07717
$851$	−27.7898	−0.952622
$852$	−3.66522	−0.125568
$853$	13.9684	0.478268	0.239134	−	0.970987i	$-0.423136\pi$
$853$	13.9684	0.478268	0.239134	+	0.970987i	$0.423136\pi$
$854$	12.9445	0.442953
$855$	80.3518	2.74797
$856$	−14.6587	−0.501023
$857$	5.49302	0.187638	0.0938190	−	0.995589i	$-0.470092\pi$
$857$	5.49302	0.187638	0.0938190	+	0.995589i	$0.470092\pi$
$858$	−20.1417	−0.687628
$859$	−4.13231	−0.140993	−0.0704964	−	0.997512i	$-0.522458\pi$
$859$	−4.13231	−0.140993	−0.0704964	+	0.997512i	$0.522458\pi$
$860$	7.01584	0.239238
$861$	5.53846	0.188750
$862$	6.87452	0.234147
$863$	−3.73953	−0.127295	−0.0636476	−	0.997972i	$-0.520273\pi$
$863$	−3.73953	−0.127295	−0.0636476	+	0.997972i	$0.520273\pi$
$864$	14.9532	0.508717
$865$	−23.6460	−0.803990
$866$	−15.8005	−0.536923
$867$	−137.077	−4.65539
$868$	3.04777	0.103448
$869$	34.8379	1.18180
$870$	−41.2225	−1.39757
$871$	33.3127	1.12876
$872$	8.21181	0.278087
$873$	−40.0075	−1.35405
$874$	−10.8316	−0.366385
$875$	2.60042	0.0879101
$876$	−24.5703	−0.830155
$877$	−39.1031	−1.32042	−0.660208	−	0.751082i	$-0.729532\pi$
$877$	−39.1031	−1.32042	−0.660208	+	0.751082i	$0.729532\pi$
$878$	−34.1070	−1.15106
$879$	76.3119	2.57394
$880$	8.83117	0.297699
$881$	−16.3068	−0.549389	−0.274694	−	0.961532i	$-0.588577\pi$
$881$	−16.3068	−0.549389	−0.274694	+	0.961532i	$0.588577\pi$
$882$	46.4133	1.56282
$883$	0.910732	0.0306486	0.0153243	−	0.999883i	$-0.495122\pi$
$883$	0.910732	0.0306486	0.0153243	+	0.999883i	$0.495122\pi$
$884$	16.2385	0.546161
$885$	17.9247	0.602532
$886$	−21.1696	−0.711207
$887$	5.89141	0.197814	0.0989070	−	0.995097i	$-0.468465\pi$
$887$	5.89141	0.197814	0.0989070	+	0.995097i	$0.468465\pi$
$888$	−29.3151	−0.983749
$889$	7.86992	0.263949
$890$	−6.95098	−0.232997
$891$	75.8520	2.54114
$892$	17.3942	0.582400
$893$	−25.9414	−0.868096
$894$	8.13530	0.272085
$895$	−77.9459	−2.60544
$896$	0.942473	0.0314858
$897$	21.2109	0.708210
$898$	13.7417	0.458567
$899$	13.5882	0.453193
$900$	31.0187	1.03396
$901$	−22.9249	−0.763738
$902$	−5.28997	−0.176137
$903$	7.14049	0.237621
$904$	−15.8692	−0.527803
$905$	−5.36512	−0.178343
$906$	48.8630	1.62336
$907$	−24.6335	−0.817942	−0.408971	−	0.912547i	$-0.634112\pi$
$907$	−24.6335	−0.817942	−0.408971	+	0.912547i	$0.634112\pi$
$908$	−15.8810	−0.527031
$909$	−32.7009	−1.08462
$910$	−5.99957	−0.198884
$911$	−48.1029	−1.59372	−0.796860	−	0.604164i	$-0.793507\pi$
$911$	−48.1029	−1.59372	−0.796860	+	0.604164i	$0.793507\pi$
$912$	−11.4261	−0.378356
$913$	40.5673	1.34258
$914$	−13.3406	−0.441269
$915$	−134.742	−4.45442
$916$	0.950740	0.0314133
$917$	−3.72134	−0.122889
$918$	−114.969	−3.79455
$919$	−21.7524	−0.717546	−0.358773	−	0.933425i	$-0.616805\pi$
$919$	−21.7524	−0.717546	−0.358773	+	0.933425i	$0.616805\pi$
$920$	−9.29992	−0.306609
$921$	−32.3774	−1.06687
$922$	−27.8222	−0.916274
$923$	−2.37830	−0.0782827
$924$	8.98808	0.295686
$925$	−36.7880	−1.20958
$926$	4.77261	0.156838
$927$	134.353	4.41273
$928$	4.20193	0.137935
$929$	−3.84013	−0.125991	−0.0629953	−	0.998014i	$-0.520065\pi$
$929$	−3.84013	−0.125991	−0.0629953	+	0.998014i	$0.520065\pi$
$930$	−31.7248	−1.04030
$931$	−21.4552	−0.703164
$932$	1.15088	0.0376983
$933$	30.1387	0.986698
$934$	−22.8555	−0.747854
$935$	−67.8994	−2.22055
$936$	16.0389	0.524249
$937$	40.1630	1.31207	0.656034	−	0.754731i	$-0.272233\pi$
$937$	40.1630	1.31207	0.656034	+	0.754731i	$0.272233\pi$
$938$	−14.8655	−0.485377
$939$	−98.8839	−3.22695
$940$	−22.2730	−0.726466
$941$	42.1772	1.37494	0.687468	−	0.726214i	$-0.258722\pi$
$941$	42.1772	1.37494	0.687468	+	0.726214i	$0.258722\pi$
$942$	35.3058	1.15033
$943$	5.57076	0.181409
$944$	−1.82712	−0.0594677
$945$	42.4771	1.38178
$946$	−6.82013	−0.221742
$947$	33.2029	1.07895	0.539474	−	0.842002i	$-0.318623\pi$
$947$	33.2029	1.07895	0.539474	+	0.842002i	$0.318623\pi$
$948$	−38.7007	−1.25694
$949$	−15.9433	−0.517541
$950$	−14.3388	−0.465213
$951$	−41.9633	−1.36075
$952$	−7.24630	−0.234854
$953$	−3.91285	−0.126750	−0.0633748	−	0.997990i	$-0.520186\pi$
$953$	−3.91285	−0.126750	−0.0633748	+	0.997990i	$0.520186\pi$
$954$	−22.6431	−0.733097
$955$	76.4049	2.47240
$956$	−3.34537	−0.108197
$957$	40.0726	1.29536
$958$	−19.4926	−0.629776
$959$	13.8737	0.448006
$960$	−9.81035	−0.316628
$961$	−20.5425	−0.662661
$962$	−19.0221	−0.613296
$963$	111.320	3.58722
$964$	30.7959	0.991869
$965$	−57.6068	−1.85443
$966$	−9.46516	−0.304536
$967$	52.4544	1.68682	0.843410	−	0.537270i	$-0.180545\pi$
$967$	52.4544	1.68682	0.843410	+	0.537270i	$0.180545\pi$
$968$	2.41517	0.0776265
$969$	87.8509	2.82218
$970$	15.8788	0.509837
$971$	24.7262	0.793503	0.396751	−	0.917926i	$-0.370138\pi$
$971$	24.7262	0.793503	0.396751	+	0.917926i	$0.370138\pi$
$972$	−39.4028	−1.26385
$973$	−11.3090	−0.362550
$974$	−30.9919	−0.993045
$975$	28.0788	0.899241
$976$	13.7346	0.439635
$977$	52.7471	1.68753	0.843765	−	0.536713i	$-0.180334\pi$
$977$	52.7471	1.68753	0.843765	+	0.536713i	$0.180334\pi$
$978$	59.8300	1.91315
$979$	6.75708	0.215957
$980$	−18.4212	−0.588443
$981$	−62.3614	−1.99105
$982$	10.2447	0.326921
$983$	24.4020	0.778304	0.389152	−	0.921174i	$-0.372768\pi$
$983$	24.4020	0.778304	0.389152	+	0.921174i	$0.372768\pi$
$984$	5.87652	0.187336
$985$	−38.3482	−1.22188
$986$	−32.3070	−1.02886
$987$	−22.6688	−0.721555
$988$	−7.41422	−0.235878
$989$	7.18214	0.228379
$990$	−67.0649	−2.13146
$991$	−60.1572	−1.91096	−0.955478	−	0.295061i	$-0.904660\pi$
$991$	−60.1572	−1.91096	−0.955478	+	0.295061i	$0.904660\pi$
$992$	3.23381	0.102673
$993$	54.4906	1.72921
$994$	1.06130	0.0336623
$995$	−35.9626	−1.14009
$996$	−45.0654	−1.42795
$997$	−23.4346	−0.742182	−0.371091	−	0.928597i	$-0.621016\pi$
$997$	−23.4346	−0.742182	−0.371091	+	0.928597i	$0.621016\pi$
$998$	−26.8781	−0.850812
$999$	134.677	4.26098

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8026.2.a.c.1.1	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8026.2.a.c.1.1	✓	86	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:	\( N \)	\(=\)	\( 8026 = 2 \cdot 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.25486 q^{3} +1.00000 q^{4} +3.01406 q^{5} +3.25486 q^{6} -0.942473 q^{7} -1.00000 q^{8} +7.59411 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.25486 q^{3} +1.00000 q^{4} +3.01406 q^{5} +3.25486 q^{6} -0.942473 q^{7} -1.00000 q^{8} +7.59411 q^{9} -3.01406 q^{10} +2.92999 q^{11} -3.25486 q^{12} -2.11202 q^{13} +0.942473 q^{14} -9.81035 q^{15} +1.00000 q^{16} -7.68861 q^{17} -7.59411 q^{18} +3.51048 q^{19} +3.01406 q^{20} +3.06762 q^{21} -2.92999 q^{22} +3.08551 q^{23} +3.25486 q^{24} +4.08458 q^{25} +2.11202 q^{26} -14.9532 q^{27} -0.942473 q^{28} -4.20193 q^{29} +9.81035 q^{30} -3.23381 q^{31} -1.00000 q^{32} -9.53670 q^{33} +7.68861 q^{34} -2.84067 q^{35} +7.59411 q^{36} -9.00655 q^{37} -3.51048 q^{38} +6.87434 q^{39} -3.01406 q^{40} +1.80546 q^{41} -3.06762 q^{42} +2.32770 q^{43} +2.92999 q^{44} +22.8891 q^{45} -3.08551 q^{46} -7.38970 q^{47} -3.25486 q^{48} -6.11175 q^{49} -4.08458 q^{50} +25.0253 q^{51} -2.11202 q^{52} +2.98167 q^{53} +14.9532 q^{54} +8.83117 q^{55} +0.942473 q^{56} -11.4261 q^{57} +4.20193 q^{58} -1.82712 q^{59} -9.81035 q^{60} +13.7346 q^{61} +3.23381 q^{62} -7.15724 q^{63} +1.00000 q^{64} -6.36578 q^{65} +9.53670 q^{66} -15.7729 q^{67} -7.68861 q^{68} -10.0429 q^{69} +2.84067 q^{70} +1.12608 q^{71} -7.59411 q^{72} +7.54882 q^{73} +9.00655 q^{74} -13.2947 q^{75} +3.51048 q^{76} -2.76143 q^{77} -6.87434 q^{78} +11.8901 q^{79} +3.01406 q^{80} +25.8882 q^{81} -1.80546 q^{82} +13.8456 q^{83} +3.06762 q^{84} -23.1739 q^{85} -2.32770 q^{86} +13.6767 q^{87} -2.92999 q^{88} +2.30618 q^{89} -22.8891 q^{90} +1.99053 q^{91} +3.08551 q^{92} +10.5256 q^{93} +7.38970 q^{94} +10.5808 q^{95} +3.25486 q^{96} -5.26823 q^{97} +6.11175 q^{98} +22.2506 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9	\( 86 q - 86 q^{2} + 11 q^{3} + 86 q^{4} + 25 q^{5} - 11 q^{6} - 3 q^{7} - 86 q^{8} + 105 q^{9} - 25 q^{10} + 44 q^{11} + 11 q^{12} - 36 q^{13} + 3 q^{14} + 19 q^{15} + 86 q^{16} + 21 q^{17} - 105 q^{18} + 35 q^{19} + 25 q^{20} + 23 q^{21} - 44 q^{22} + 38 q^{23} - 11 q^{24} + 85 q^{25} + 36 q^{26} + 47 q^{27} - 3 q^{28} + 30 q^{29} - 19 q^{30} + 23 q^{31} - 86 q^{32} + 5 q^{33} - 21 q^{34} + 59 q^{35} + 105 q^{36} - 20 q^{37} - 35 q^{38} + 4 q^{39} - 25 q^{40} + 64 q^{41} - 23 q^{42} + 23 q^{43} + 44 q^{44} + 60 q^{45} - 38 q^{46} + 77 q^{47} + 11 q^{48} + 109 q^{49} - 85 q^{50} + 47 q^{51} - 36 q^{52} + 22 q^{53} - 47 q^{54} + 6 q^{55} + 3 q^{56} - 9 q^{57} - 30 q^{58} + 145 q^{59} + 19 q^{60} - 24 q^{61} - 23 q^{62} + 6 q^{63} + 86 q^{64} + 37 q^{65} - 5 q^{66} + 44 q^{67} + 21 q^{68} + 25 q^{69} - 59 q^{70} + 107 q^{71} - 105 q^{72} - 55 q^{73} + 20 q^{74} + 86 q^{75} + 35 q^{76} + 25 q^{77} - 4 q^{78} + 2 q^{79} + 25 q^{80} + 170 q^{81} - 64 q^{82} + 109 q^{83} + 23 q^{84} - 13 q^{85} - 23 q^{86} + 3 q^{87} - 44 q^{88} + 121 q^{89} - 60 q^{90} + 81 q^{91} + 38 q^{92} + 27 q^{93} - 77 q^{94} + 49 q^{95} - 11 q^{96} - 56 q^{97} - 109 q^{98} + 158 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 11 * q^3 + 86 * q^4 + 25 * q^5 - 11 * q^6 - 3 * q^7 - 86 * q^8 + 105 * q^9 - 25 * q^10 + 44 * q^11 + 11 * q^12 - 36 * q^13 + 3 * q^14 + 19 * q^15 + 86 * q^16 + 21 * q^17 - 105 * q^18 + 35 * q^19 + 25 * q^20 + 23 * q^21 - 44 * q^22 + 38 * q^23 - 11 * q^24 + 85 * q^25 + 36 * q^26 + 47 * q^27 - 3 * q^28 + 30 * q^29 - 19 * q^30 + 23 * q^31 - 86 * q^32 + 5 * q^33 - 21 * q^34 + 59 * q^35 + 105 * q^36 - 20 * q^37 - 35 * q^38 + 4 * q^39 - 25 * q^40 + 64 * q^41 - 23 * q^42 + 23 * q^43 + 44 * q^44 + 60 * q^45 - 38 * q^46 + 77 * q^47 + 11 * q^48 + 109 * q^49 - 85 * q^50 + 47 * q^51 - 36 * q^52 + 22 * q^53 - 47 * q^54 + 6 * q^55 + 3 * q^56 - 9 * q^57 - 30 * q^58 + 145 * q^59 + 19 * q^60 - 24 * q^61 - 23 * q^62 + 6 * q^63 + 86 * q^64 + 37 * q^65 - 5 * q^66 + 44 * q^67 + 21 * q^68 + 25 * q^69 - 59 * q^70 + 107 * q^71 - 105 * q^72 - 55 * q^73 + 20 * q^74 + 86 * q^75 + 35 * q^76 + 25 * q^77 - 4 * q^78 + 2 * q^79 + 25 * q^80 + 170 * q^81 - 64 * q^82 + 109 * q^83 + 23 * q^84 - 13 * q^85 - 23 * q^86 + 3 * q^87 - 44 * q^88 + 121 * q^89 - 60 * q^90 + 81 * q^91 + 38 * q^92 + 27 * q^93 - 77 * q^94 + 49 * q^95 - 11 * q^96 - 56 * q^97 - 109 * q^98 + 158 * q^99

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