LMFDB - Embedded newform 8007.2.a.d.1.10

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:	$40$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-1.83549 q^{2} +1.00000 q^{3} +1.36903 q^{4} -0.437870 q^{5} -1.83549 q^{6} +1.24463 q^{7} +1.15814 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.83549 q^{2} +1.00000 q^{3} +1.36903 q^{4} -0.437870 q^{5} -1.83549 q^{6} +1.24463 q^{7} +1.15814 q^{8} +1.00000 q^{9} +0.803707 q^{10} -4.18923 q^{11} +1.36903 q^{12} -0.354810 q^{13} -2.28450 q^{14} -0.437870 q^{15} -4.86382 q^{16} +1.00000 q^{17} -1.83549 q^{18} +3.62100 q^{19} -0.599458 q^{20} +1.24463 q^{21} +7.68930 q^{22} -7.10736 q^{23} +1.15814 q^{24} -4.80827 q^{25} +0.651252 q^{26} +1.00000 q^{27} +1.70393 q^{28} +7.65987 q^{29} +0.803707 q^{30} -4.08390 q^{31} +6.61122 q^{32} -4.18923 q^{33} -1.83549 q^{34} -0.544985 q^{35} +1.36903 q^{36} +7.50660 q^{37} -6.64632 q^{38} -0.354810 q^{39} -0.507114 q^{40} -5.31722 q^{41} -2.28450 q^{42} +8.08609 q^{43} -5.73519 q^{44} -0.437870 q^{45} +13.0455 q^{46} +5.99685 q^{47} -4.86382 q^{48} -5.45090 q^{49} +8.82554 q^{50} +1.00000 q^{51} -0.485747 q^{52} +8.25780 q^{53} -1.83549 q^{54} +1.83434 q^{55} +1.44145 q^{56} +3.62100 q^{57} -14.0596 q^{58} -9.36164 q^{59} -0.599458 q^{60} -10.4794 q^{61} +7.49596 q^{62} +1.24463 q^{63} -2.40721 q^{64} +0.155361 q^{65} +7.68930 q^{66} +5.43697 q^{67} +1.36903 q^{68} -7.10736 q^{69} +1.00032 q^{70} -0.930596 q^{71} +1.15814 q^{72} +10.5188 q^{73} -13.7783 q^{74} -4.80827 q^{75} +4.95727 q^{76} -5.21403 q^{77} +0.651252 q^{78} +4.16125 q^{79} +2.12972 q^{80} +1.00000 q^{81} +9.75972 q^{82} -14.9513 q^{83} +1.70393 q^{84} -0.437870 q^{85} -14.8419 q^{86} +7.65987 q^{87} -4.85171 q^{88} +3.77674 q^{89} +0.803707 q^{90} -0.441607 q^{91} -9.73020 q^{92} -4.08390 q^{93} -11.0072 q^{94} -1.58553 q^{95} +6.61122 q^{96} +12.7136 q^{97} +10.0051 q^{98} -4.18923 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) $ 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * 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 $

$2$	−1.83549	−1.29789	−0.648944	−	0.760836i	$-0.724789\pi$
$2$	−1.83549	−1.29789	−0.648944	+	0.760836i	$0.724789\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.36903	0.684516
$5$	−0.437870	−0.195821	−0.0979107	−	0.995195i	$-0.531216\pi$
$5$	−0.437870	−0.195821	−0.0979107	+	0.995195i	$0.531216\pi$
$6$	−1.83549	−0.749336
$7$	1.24463	0.470425	0.235212	−	0.971944i	$-0.424421\pi$
$7$	1.24463	0.470425	0.235212	+	0.971944i	$0.424421\pi$
$8$	1.15814	0.409464
$9$	1.00000	0.333333
$10$	0.803707	0.254154
$11$	−4.18923	−1.26310	−0.631551	−	0.775335i	$-0.717581\pi$
$11$	−4.18923	−1.26310	−0.631551	+	0.775335i	$0.717581\pi$
$12$	1.36903	0.395205
$13$	−0.354810	−0.0984067	−0.0492034	−	0.998789i	$-0.515668\pi$
$13$	−0.354810	−0.0984067	−0.0492034	+	0.998789i	$0.515668\pi$
$14$	−2.28450	−0.610559
$15$	−0.437870	−0.113058
$16$	−4.86382	−1.21595
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−1.83549	−0.432630
$19$	3.62100	0.830715	0.415358	−	0.909658i	$-0.363656\pi$
$19$	3.62100	0.830715	0.415358	+	0.909658i	$0.363656\pi$
$20$	−0.599458	−0.134043
$21$	1.24463	0.271600
$22$	7.68930	1.63936
$23$	−7.10736	−1.48199	−0.740994	−	0.671512i	$-0.765645\pi$
$23$	−7.10736	−1.48199	−0.740994	+	0.671512i	$0.765645\pi$
$24$	1.15814	0.236404
$25$	−4.80827	−0.961654
$26$	0.651252	0.127721
$27$	1.00000	0.192450
$28$	1.70393	0.322013
$29$	7.65987	1.42240	0.711201	−	0.702989i	$-0.248152\pi$
$29$	7.65987	1.42240	0.711201	+	0.702989i	$0.248152\pi$
$30$	0.803707	0.146736
$31$	−4.08390	−0.733489	−0.366745	−	0.930322i	$-0.619528\pi$
$31$	−4.08390	−0.733489	−0.366745	+	0.930322i	$0.619528\pi$
$32$	6.61122	1.16871
$33$	−4.18923	−0.729252
$34$	−1.83549	−0.314784
$35$	−0.544985	−0.0921193
$36$	1.36903	0.228172
$37$	7.50660	1.23408	0.617038	−	0.786933i	$-0.288332\pi$
$37$	7.50660	1.23408	0.617038	+	0.786933i	$0.288332\pi$
$38$	−6.64632	−1.07818
$39$	−0.354810	−0.0568151
$40$	−0.507114	−0.0801818
$41$	−5.31722	−0.830410	−0.415205	−	0.909728i	$-0.636290\pi$
$41$	−5.31722	−0.830410	−0.415205	+	0.909728i	$0.636290\pi$
$42$	−2.28450	−0.352507
$43$	8.08609	1.23312	0.616558	−	0.787309i	$-0.288527\pi$
$43$	8.08609	1.23312	0.616558	+	0.787309i	$0.288527\pi$
$44$	−5.73519	−0.864612
$45$	−0.437870	−0.0652738
$46$	13.0455	1.92346
$47$	5.99685	0.874730	0.437365	−	0.899284i	$-0.355912\pi$
$47$	5.99685	0.874730	0.437365	+	0.899284i	$0.355912\pi$
$48$	−4.86382	−0.702031
$49$	−5.45090	−0.778700
$50$	8.82554	1.24812
$51$	1.00000	0.140028
$52$	−0.485747	−0.0673609
$53$	8.25780	1.13430	0.567148	−	0.823616i	$-0.308047\pi$
$53$	8.25780	1.13430	0.567148	+	0.823616i	$0.308047\pi$
$54$	−1.83549	−0.249779
$55$	1.83434	0.247342
$56$	1.44145	0.192622
$57$	3.62100	0.479614
$58$	−14.0596	−1.84612
$59$	−9.36164	−1.21878	−0.609391	−	0.792870i	$-0.708586\pi$
$59$	−9.36164	−1.21878	−0.609391	+	0.792870i	$0.708586\pi$
$60$	−0.599458	−0.0773896
$61$	−10.4794	−1.34176	−0.670878	−	0.741568i	$-0.734083\pi$
$61$	−10.4794	−1.34176	−0.670878	+	0.741568i	$0.734083\pi$
$62$	7.49596	0.951988
$63$	1.24463	0.156808
$64$	−2.40721	−0.300901
$65$	0.155361	0.0192701
$66$	7.68930	0.946488
$67$	5.43697	0.664231	0.332116	−	0.943239i	$-0.392238\pi$
$67$	5.43697	0.664231	0.332116	+	0.943239i	$0.392238\pi$
$68$	1.36903	0.166019
$69$	−7.10736	−0.855626
$70$	1.00032	0.119561
$71$	−0.930596	−0.110441	−0.0552207	−	0.998474i	$-0.517586\pi$
$71$	−0.930596	−0.110441	−0.0552207	+	0.998474i	$0.517586\pi$
$72$	1.15814	0.136488
$73$	10.5188	1.23113	0.615566	−	0.788086i	$-0.288928\pi$
$73$	10.5188	1.23113	0.615566	+	0.788086i	$0.288928\pi$
$74$	−13.7783	−1.60169
$75$	−4.80827	−0.555211
$76$	4.95727	0.568638
$77$	−5.21403	−0.594194
$78$	0.651252	0.0737397
$79$	4.16125	0.468177	0.234089	−	0.972215i	$-0.424789\pi$
$79$	4.16125	0.468177	0.234089	+	0.972215i	$0.424789\pi$
$80$	2.12972	0.238110
$81$	1.00000	0.111111
$82$	9.75972	1.07778
$83$	−14.9513	−1.64112	−0.820561	−	0.571559i	$-0.806339\pi$
$83$	−14.9513	−1.64112	−0.820561	+	0.571559i	$0.806339\pi$
$84$	1.70393	0.185914
$85$	−0.437870	−0.0474937
$86$	−14.8419	−1.60045
$87$	7.65987	0.821224
$88$	−4.85171	−0.517194
$89$	3.77674	0.400334	0.200167	−	0.979762i	$-0.435852\pi$
$89$	3.77674	0.400334	0.200167	+	0.979762i	$0.435852\pi$
$90$	0.803707	0.0847181
$91$	−0.441607	−0.0462930
$92$	−9.73020	−1.01444
$93$	−4.08390	−0.423480
$94$	−11.0072	−1.13530
$95$	−1.58553	−0.162672
$96$	6.61122	0.674755
$97$	12.7136	1.29087	0.645437	−	0.763813i	$-0.276675\pi$
$97$	12.7136	1.29087	0.645437	+	0.763813i	$0.276675\pi$
$98$	10.0051	1.01067
$99$	−4.18923	−0.421034
$100$	−6.58267	−0.658267
$101$	−15.1759	−1.51006	−0.755030	−	0.655690i	$-0.772378\pi$
$101$	−15.1759	−1.51006	−0.755030	+	0.655690i	$0.772378\pi$
$102$	−1.83549	−0.181741
$103$	−0.139247	−0.0137204	−0.00686022	−	0.999976i	$-0.502184\pi$
$103$	−0.139247	−0.0137204	−0.00686022	+	0.999976i	$0.502184\pi$
$104$	−0.410920	−0.0402940
$105$	−0.544985	−0.0531851
$106$	−15.1571	−1.47219
$107$	−4.63775	−0.448348	−0.224174	−	0.974549i	$-0.571968\pi$
$107$	−4.63775	−0.448348	−0.224174	+	0.974549i	$0.571968\pi$
$108$	1.36903	0.131735
$109$	−0.154599	−0.0148079	−0.00740394	−	0.999973i	$-0.502357\pi$
$109$	−0.154599	−0.0148079	−0.00740394	+	0.999973i	$0.502357\pi$
$110$	−3.36691	−0.321023
$111$	7.50660	0.712495
$112$	−6.05364	−0.572015
$113$	−14.2453	−1.34009	−0.670044	−	0.742321i	$-0.733725\pi$
$113$	−14.2453	−1.34009	−0.670044	+	0.742321i	$0.733725\pi$
$114$	−6.64632	−0.622485
$115$	3.11210	0.290205
$116$	10.4866	0.973656
$117$	−0.354810	−0.0328022
$118$	17.1832	1.58184
$119$	1.24463	0.114095
$120$	−0.507114	−0.0462930
$121$	6.54967	0.595425
$122$	19.2349	1.74145
$123$	−5.31722	−0.479438
$124$	−5.59098	−0.502085
$125$	4.29475	0.384134
$126$	−2.28450	−0.203520
$127$	8.98515	0.797303	0.398651	−	0.917103i	$-0.369478\pi$
$127$	8.98515	0.797303	0.398651	+	0.917103i	$0.369478\pi$
$128$	−8.80403	−0.778173
$129$	8.08609	0.711940
$130$	−0.285164	−0.0250105
$131$	−8.95445	−0.782354	−0.391177	−	0.920315i	$-0.627932\pi$
$131$	−8.95445	−0.782354	−0.391177	+	0.920315i	$0.627932\pi$
$132$	−5.73519	−0.499184
$133$	4.50680	0.390789
$134$	−9.97951	−0.862099
$135$	−0.437870	−0.0376858
$136$	1.15814	0.0993096
$137$	−6.46051	−0.551958	−0.275979	−	0.961164i	$-0.589002\pi$
$137$	−6.46051	−0.551958	−0.275979	+	0.961164i	$0.589002\pi$
$138$	13.0455	1.11051
$139$	9.16654	0.777496	0.388748	−	0.921344i	$-0.372908\pi$
$139$	9.16654	0.777496	0.388748	+	0.921344i	$0.372908\pi$
$140$	−0.746101	−0.0630571
$141$	5.99685	0.505025
$142$	1.70810	0.143341
$143$	1.48638	0.124298
$144$	−4.86382	−0.405318
$145$	−3.35403	−0.278537
$146$	−19.3072	−1.59787
$147$	−5.45090	−0.449583
$148$	10.2768	0.844745
$149$	−4.52252	−0.370500	−0.185250	−	0.982691i	$-0.559309\pi$
$149$	−4.52252	−0.370500	−0.185250	+	0.982691i	$0.559309\pi$
$150$	8.82554	0.720602
$151$	−10.0572	−0.818445	−0.409223	−	0.912435i	$-0.634200\pi$
$151$	−10.0572	−0.818445	−0.409223	+	0.912435i	$0.634200\pi$
$152$	4.19362	0.340148
$153$	1.00000	0.0808452
$154$	9.57032	0.771198
$155$	1.78822	0.143633
$156$	−0.485747	−0.0388908
$157$	−1.00000	−0.0798087
$157$	−1.00000	−0.0798087
$158$	−7.63794	−0.607642
$159$	8.25780	0.654886
$160$	−2.89485	−0.228858
$161$	−8.84602	−0.697164
$162$	−1.83549	−0.144210
$163$	−14.2353	−1.11499	−0.557497	−	0.830179i	$-0.688238\pi$
$163$	−14.2353	−1.11499	−0.557497	+	0.830179i	$0.688238\pi$
$164$	−7.27944	−0.568429
$165$	1.83434	0.142803
$166$	27.4431	2.12999
$167$	2.36992	0.183390	0.0916949	−	0.995787i	$-0.470772\pi$
$167$	2.36992	0.183390	0.0916949	+	0.995787i	$0.470772\pi$
$168$	1.44145	0.111210
$169$	−12.8741	−0.990316
$170$	0.803707	0.0616415
$171$	3.62100	0.276905
$172$	11.0701	0.844087
$173$	−22.0665	−1.67768	−0.838841	−	0.544376i	$-0.816766\pi$
$173$	−22.0665	−1.67768	−0.838841	+	0.544376i	$0.816766\pi$
$174$	−14.0596	−1.06586
$175$	−5.98451	−0.452386
$176$	20.3757	1.53587
$177$	−9.36164	−0.703664
$178$	−6.93218	−0.519588
$179$	7.51935	0.562023	0.281011	−	0.959704i	$-0.409330\pi$
$179$	7.51935	0.562023	0.281011	+	0.959704i	$0.409330\pi$
$180$	−0.599458	−0.0446809
$181$	−19.5347	−1.45200	−0.726001	−	0.687694i	$-0.758623\pi$
$181$	−19.5347	−1.45200	−0.726001	+	0.687694i	$0.758623\pi$
$182$	0.810566	0.0600831
$183$	−10.4794	−0.774663
$184$	−8.23131	−0.606820
$185$	−3.28691	−0.241659
$186$	7.49596	0.549630
$187$	−4.18923	−0.306347
$188$	8.20987	0.598766
$189$	1.24463	0.0905333
$190$	2.91023	0.211130
$191$	20.1068	1.45487	0.727437	−	0.686174i	$-0.240711\pi$
$191$	20.1068	1.45487	0.727437	+	0.686174i	$0.240711\pi$
$192$	−2.40721	−0.173725
$193$	9.30172	0.669552	0.334776	−	0.942298i	$-0.391339\pi$
$193$	9.30172	0.669552	0.334776	+	0.942298i	$0.391339\pi$
$194$	−23.3358	−1.67541
$195$	0.155361	0.0111256
$196$	−7.46245	−0.533032
$197$	−5.15075	−0.366975	−0.183488	−	0.983022i	$-0.558739\pi$
$197$	−5.15075	−0.366975	−0.183488	+	0.983022i	$0.558739\pi$
$198$	7.68930	0.546455
$199$	−1.84768	−0.130979	−0.0654894	−	0.997853i	$-0.520861\pi$
$199$	−1.84768	−0.130979	−0.0654894	+	0.997853i	$0.520861\pi$
$200$	−5.56864	−0.393762
$201$	5.43697	0.383494
$202$	27.8553	1.95989
$203$	9.53369	0.669134
$204$	1.36903	0.0958513
$205$	2.32825	0.162612
$206$	0.255587	0.0178076
$207$	−7.10736	−0.493996
$208$	1.72573	0.119658
$209$	−15.1692	−1.04928
$210$	1.00032	0.0690283
$211$	−8.13078	−0.559746	−0.279873	−	0.960037i	$-0.590292\pi$
$211$	−8.13078	−0.559746	−0.279873	+	0.960037i	$0.590292\pi$
$212$	11.3052	0.776443
$213$	−0.930596	−0.0637634
$214$	8.51255	0.581906
$215$	−3.54065	−0.241471
$216$	1.15814	0.0788013
$217$	−5.08293	−0.345052
$218$	0.283765	0.0192190
$219$	10.5188	0.710794
$220$	2.51127	0.169310
$221$	−0.354810	−0.0238671
$222$	−13.7783	−0.924739
$223$	−11.8947	−0.796525	−0.398263	−	0.917271i	$-0.630387\pi$
$223$	−11.8947	−0.796525	−0.398263	+	0.917271i	$0.630387\pi$
$224$	8.22851	0.549790
$225$	−4.80827	−0.320551
$226$	26.1472	1.73929
$227$	20.3160	1.34842	0.674211	−	0.738539i	$-0.264484\pi$
$227$	20.3160	1.34842	0.674211	+	0.738539i	$0.264484\pi$
$228$	4.95727	0.328303
$229$	−17.2042	−1.13689	−0.568444	−	0.822722i	$-0.692454\pi$
$229$	−17.2042	−1.13689	−0.568444	+	0.822722i	$0.692454\pi$
$230$	−5.71224	−0.376654
$231$	−5.21403	−0.343058
$232$	8.87119	0.582422
$233$	−8.24640	−0.540240	−0.270120	−	0.962827i	$-0.587063\pi$
$233$	−8.24640	−0.540240	−0.270120	+	0.962827i	$0.587063\pi$
$234$	0.651252	0.0425737
$235$	−2.62584	−0.171291
$236$	−12.8164	−0.834275
$237$	4.16125	0.270302
$238$	−2.28450	−0.148082
$239$	23.0434	1.49056	0.745278	−	0.666754i	$-0.232317\pi$
$239$	23.0434	1.49056	0.745278	+	0.666754i	$0.232317\pi$
$240$	2.12972	0.137473
$241$	2.58894	0.166768	0.0833842	−	0.996517i	$-0.473427\pi$
$241$	2.58894	0.166768	0.0833842	+	0.996517i	$0.473427\pi$
$242$	−12.0219	−0.772795
$243$	1.00000	0.0641500
$244$	−14.3467	−0.918453
$245$	2.38679	0.152486
$246$	9.75972	0.622257
$247$	−1.28477	−0.0817480
$248$	−4.72972	−0.300337
$249$	−14.9513	−0.947502
$250$	−7.88297	−0.498563
$251$	14.4899	0.914596	0.457298	−	0.889313i	$-0.348817\pi$
$251$	14.4899	0.914596	0.457298	+	0.889313i	$0.348817\pi$
$252$	1.70393	0.107338
$253$	29.7744	1.87190
$254$	−16.4922	−1.03481
$255$	−0.437870	−0.0274205
$256$	20.9741	1.31088
$257$	28.4252	1.77312	0.886559	−	0.462616i	$-0.153089\pi$
$257$	28.4252	1.77312	0.886559	+	0.462616i	$0.153089\pi$
$258$	−14.8419	−0.924019
$259$	9.34292	0.580541
$260$	0.212694	0.0131907
$261$	7.65987	0.474134
$262$	16.4358	1.01541
$263$	−15.7413	−0.970649	−0.485325	−	0.874334i	$-0.661299\pi$
$263$	−15.7413	−0.970649	−0.485325	+	0.874334i	$0.661299\pi$
$264$	−4.85171	−0.298602
$265$	−3.61584	−0.222119
$266$	−8.27220	−0.507201
$267$	3.77674	0.231133
$268$	7.44338	0.454677
$269$	14.0486	0.856559	0.428279	−	0.903646i	$-0.359120\pi$
$269$	14.0486	0.856559	0.428279	+	0.903646i	$0.359120\pi$
$270$	0.803707	0.0489120
$271$	−32.5182	−1.97534	−0.987671	−	0.156546i	$-0.949964\pi$
$271$	−32.5182	−1.97534	−0.987671	+	0.156546i	$0.949964\pi$
$272$	−4.86382	−0.294912
$273$	−0.441607	−0.0267273
$274$	11.8582	0.716381
$275$	20.1430	1.21467
$276$	−9.73020	−0.585689
$277$	11.9040	0.715243	0.357622	−	0.933867i	$-0.383588\pi$
$277$	11.9040	0.715243	0.357622	+	0.933867i	$0.383588\pi$
$278$	−16.8251	−1.00910
$279$	−4.08390	−0.244496
$280$	−0.631168	−0.0377195
$281$	−27.1766	−1.62122	−0.810609	−	0.585588i	$-0.800864\pi$
$281$	−27.1766	−1.62122	−0.810609	+	0.585588i	$0.800864\pi$
$282$	−11.0072	−0.655467
$283$	21.6417	1.28647	0.643233	−	0.765670i	$-0.277593\pi$
$283$	21.6417	1.28647	0.643233	+	0.765670i	$0.277593\pi$
$284$	−1.27401	−0.0755989
$285$	−1.58553	−0.0939186
$286$	−2.72825	−0.161325
$287$	−6.61796	−0.390646
$288$	6.61122	0.389570
$289$	1.00000	0.0588235
$290$	6.15629	0.361510
$291$	12.7136	0.745287
$292$	14.4005	0.842728
$293$	−30.3861	−1.77518	−0.887588	−	0.460638i	$-0.847621\pi$
$293$	−30.3861	−1.77518	−0.887588	+	0.460638i	$0.847621\pi$
$294$	10.0051	0.583509
$295$	4.09918	0.238663
$296$	8.69368	0.505310
$297$	−4.18923	−0.243084
$298$	8.30105	0.480867
$299$	2.52177	0.145838
$300$	−6.58267	−0.380051
$301$	10.0642	0.580089
$302$	18.4600	1.06225
$303$	−15.1759	−0.871833
$304$	−17.6119	−1.01011
$305$	4.58863	0.262744
$306$	−1.83549	−0.104928
$307$	2.35307	0.134297	0.0671483	−	0.997743i	$-0.478610\pi$
$307$	2.35307	0.134297	0.0671483	+	0.997743i	$0.478610\pi$
$308$	−7.13817	−0.406735
$309$	−0.139247	−0.00792150
$310$	−3.28225	−0.186420
$311$	−13.5622	−0.769044	−0.384522	−	0.923116i	$-0.625634\pi$
$311$	−13.5622	−0.769044	−0.384522	+	0.923116i	$0.625634\pi$
$312$	−0.410920	−0.0232637
$313$	8.59236	0.485669	0.242834	−	0.970068i	$-0.421923\pi$
$313$	8.59236	0.485669	0.242834	+	0.970068i	$0.421923\pi$
$314$	1.83549	0.103583
$315$	−0.544985	−0.0307064
$316$	5.69688	0.320474
$317$	−22.5225	−1.26499	−0.632494	−	0.774565i	$-0.717969\pi$
$317$	−22.5225	−1.26499	−0.632494	+	0.774565i	$0.717969\pi$
$318$	−15.1571	−0.849969
$319$	−32.0890	−1.79664
$320$	1.05404	0.0589228
$321$	−4.63775	−0.258854
$322$	16.2368	0.904841
$323$	3.62100	0.201478
$324$	1.36903	0.0760573
$325$	1.70602	0.0946332
$326$	26.1288	1.44714
$327$	−0.154599	−0.00854933
$328$	−6.15808	−0.340023
$329$	7.46384	0.411495
$330$	−3.36691	−0.185343
$331$	−23.7706	−1.30655	−0.653275	−	0.757121i	$-0.726606\pi$
$331$	−23.7706	−1.30655	−0.653275	+	0.757121i	$0.726606\pi$
$332$	−20.4688	−1.12337
$333$	7.50660	0.411359
$334$	−4.34997	−0.238020
$335$	−2.38068	−0.130071
$336$	−6.05364	−0.330253
$337$	25.9480	1.41348	0.706740	−	0.707474i	$-0.250165\pi$
$337$	25.9480	1.41348	0.706740	+	0.707474i	$0.250165\pi$
$338$	23.6303	1.28532
$339$	−14.2453	−0.773701
$340$	−0.599458	−0.0325101
$341$	17.1084	0.926471
$342$	−6.64632	−0.359392
$343$	−15.4967	−0.836745
$344$	9.36481	0.504917
$345$	3.11210	0.167550
$346$	40.5028	2.17744
$347$	−19.4257	−1.04282	−0.521412	−	0.853305i	$-0.674594\pi$
$347$	−19.4257	−1.04282	−0.521412	+	0.853305i	$0.674594\pi$
$348$	10.4866	0.562141
$349$	−10.5334	−0.563839	−0.281920	−	0.959438i	$-0.590971\pi$
$349$	−10.5334	−0.563839	−0.281920	+	0.959438i	$0.590971\pi$
$350$	10.9845	0.587147
$351$	−0.354810	−0.0189384
$352$	−27.6959	−1.47620
$353$	9.02418	0.480309	0.240154	−	0.970735i	$-0.422802\pi$
$353$	9.02418	0.480309	0.240154	+	0.970735i	$0.422802\pi$
$354$	17.1832	0.913277
$355$	0.407480	0.0216268
$356$	5.17047	0.274035
$357$	1.24463	0.0658727
$358$	−13.8017	−0.729443
$359$	−22.9725	−1.21244	−0.606220	−	0.795297i	$-0.707315\pi$
$359$	−22.9725	−1.21244	−0.606220	+	0.795297i	$0.707315\pi$
$360$	−0.507114	−0.0267273
$361$	−5.88833	−0.309912
$362$	35.8557	1.88454
$363$	6.54967	0.343769
$364$	−0.604574	−0.0316883
$365$	−4.60586	−0.241082
$366$	19.2349	1.00543
$367$	30.8286	1.60924	0.804620	−	0.593791i	$-0.202369\pi$
$367$	30.8286	1.60924	0.804620	+	0.593791i	$0.202369\pi$
$368$	34.5689	1.80203
$369$	−5.31722	−0.276803
$370$	6.03310	0.313646
$371$	10.2779	0.533601
$372$	−5.59098	−0.289879
$373$	−6.95593	−0.360164	−0.180082	−	0.983652i	$-0.557636\pi$
$373$	−6.95593	−0.360164	−0.180082	+	0.983652i	$0.557636\pi$
$374$	7.68930	0.397604
$375$	4.29475	0.221780
$376$	6.94518	0.358170
$377$	−2.71780	−0.139974
$378$	−2.28450	−0.117502
$379$	17.6545	0.906850	0.453425	−	0.891294i	$-0.350202\pi$
$379$	17.6545	0.906850	0.453425	+	0.891294i	$0.350202\pi$
$380$	−2.17064	−0.111351
$381$	8.98515	0.460323
$382$	−36.9058	−1.88827
$383$	−27.1112	−1.38532	−0.692659	−	0.721266i	$-0.743561\pi$
$383$	−27.1112	−1.38532	−0.692659	+	0.721266i	$0.743561\pi$
$384$	−8.80403	−0.449279
$385$	2.28307	0.116356
$386$	−17.0732	−0.869004
$387$	8.08609	0.411039
$388$	17.4054	0.883624
$389$	−14.2056	−0.720251	−0.360126	−	0.932904i	$-0.617266\pi$
$389$	−14.2056	−0.720251	−0.360126	+	0.932904i	$0.617266\pi$
$390$	−0.285164	−0.0144398
$391$	−7.10736	−0.359435
$392$	−6.31290	−0.318850
$393$	−8.95445	−0.451692
$394$	9.45415	0.476293
$395$	−1.82209	−0.0916791
$396$	−5.73519	−0.288204
$397$	−6.24345	−0.313350	−0.156675	−	0.987650i	$-0.550077\pi$
$397$	−6.24345	−0.313350	−0.156675	+	0.987650i	$0.550077\pi$
$398$	3.39141	0.169996
$399$	4.50680	0.225622
$400$	23.3865	1.16933
$401$	−32.4367	−1.61981	−0.809907	−	0.586559i	$-0.800482\pi$
$401$	−32.4367	−1.61981	−0.809907	+	0.586559i	$0.800482\pi$
$402$	−9.97951	−0.497733
$403$	1.44901	0.0721803
$404$	−20.7763	−1.03366
$405$	−0.437870	−0.0217579
$406$	−17.4990	−0.868461
$407$	−31.4469	−1.55876
$408$	1.15814	0.0573364
$409$	22.8357	1.12915	0.564577	−	0.825380i	$-0.309039\pi$
$409$	22.8357	1.12915	0.564577	+	0.825380i	$0.309039\pi$
$410$	−4.27349	−0.211052
$411$	−6.46051	−0.318673
$412$	−0.190634	−0.00939186
$413$	−11.6518	−0.573345
$414$	13.0455	0.641152
$415$	6.54674	0.321367
$416$	−2.34573	−0.115009
$417$	9.16654	0.448887
$418$	27.8430	1.36185
$419$	−36.1267	−1.76491	−0.882453	−	0.470400i	$-0.844110\pi$
$419$	−36.1267	−1.76491	−0.882453	+	0.470400i	$0.844110\pi$
$420$	−0.746101	−0.0364060
$421$	36.2576	1.76709	0.883543	−	0.468350i	$-0.155151\pi$
$421$	36.2576	1.76709	0.883543	+	0.468350i	$0.155151\pi$
$422$	14.9240	0.726488
$423$	5.99685	0.291577
$424$	9.56367	0.464453
$425$	−4.80827	−0.233235
$426$	1.70810	0.0827578
$427$	−13.0430	−0.631195
$428$	−6.34922	−0.306901
$429$	1.48638	0.0717633
$430$	6.49884	0.313402
$431$	17.8384	0.859244	0.429622	−	0.903009i	$-0.358647\pi$
$431$	17.8384	0.859244	0.429622	+	0.903009i	$0.358647\pi$
$432$	−4.86382	−0.234010
$433$	−1.00954	−0.0485153	−0.0242576	−	0.999706i	$-0.507722\pi$
$433$	−1.00954	−0.0485153	−0.0242576	+	0.999706i	$0.507722\pi$
$434$	9.32968	0.447839
$435$	−3.35403	−0.160813
$436$	−0.211651	−0.0101362
$437$	−25.7358	−1.23111
$438$	−19.3072	−0.922531
$439$	18.9564	0.904739	0.452369	−	0.891831i	$-0.350579\pi$
$439$	18.9564	0.904739	0.452369	+	0.891831i	$0.350579\pi$
$440$	2.12442	0.101278
$441$	−5.45090	−0.259567
$442$	0.651252	0.0309769
$443$	−4.45158	−0.211501	−0.105751	−	0.994393i	$-0.533725\pi$
$443$	−4.45158	−0.211501	−0.105751	+	0.994393i	$0.533725\pi$
$444$	10.2768	0.487714
$445$	−1.65372	−0.0783939
$446$	21.8326	1.03380
$447$	−4.52252	−0.213908
$448$	−2.99608	−0.141551
$449$	−41.6222	−1.96427	−0.982136	−	0.188173i	$-0.939743\pi$
$449$	−41.6222	−1.96427	−0.982136	+	0.188173i	$0.939743\pi$
$450$	8.82554	0.416040
$451$	22.2751	1.04889
$452$	−19.5023	−0.917312
$453$	−10.0572	−0.472530
$454$	−37.2899	−1.75010
$455$	0.193366	0.00906515
$456$	4.19362	0.196384
$457$	2.69085	0.125873	0.0629364	−	0.998018i	$-0.479953\pi$
$457$	2.69085	0.125873	0.0629364	+	0.998018i	$0.479953\pi$
$458$	31.5782	1.47555
$459$	1.00000	0.0466760
$460$	4.26056	0.198650
$461$	−6.65223	−0.309825	−0.154913	−	0.987928i	$-0.549510\pi$
$461$	−6.65223	−0.309825	−0.154913	+	0.987928i	$0.549510\pi$
$462$	9.57032	0.445252
$463$	−16.7956	−0.780560	−0.390280	−	0.920696i	$-0.627622\pi$
$463$	−16.7956	−0.780560	−0.390280	+	0.920696i	$0.627622\pi$
$464$	−37.2562	−1.72958
$465$	1.78822	0.0829265
$466$	15.1362	0.701171
$467$	25.4834	1.17923	0.589616	−	0.807683i	$-0.299279\pi$
$467$	25.4834	1.17923	0.589616	+	0.807683i	$0.299279\pi$
$468$	−0.485747	−0.0224536
$469$	6.76700	0.312471
$470$	4.81970	0.222316
$471$	−1.00000	−0.0460776
$472$	−10.8421	−0.499047
$473$	−33.8745	−1.55755
$474$	−7.63794	−0.350822
$475$	−17.4108	−0.798861
$476$	1.70393	0.0780997
$477$	8.25780	0.378099
$478$	−42.2960	−1.93458
$479$	−13.6757	−0.624859	−0.312430	−	0.949941i	$-0.601143\pi$
$479$	−13.6757	−0.624859	−0.312430	+	0.949941i	$0.601143\pi$
$480$	−2.89485	−0.132131
$481$	−2.66342	−0.121441
$482$	−4.75198	−0.216447
$483$	−8.84602	−0.402508
$484$	8.96670	0.407577
$485$	−5.56692	−0.252781
$486$	−1.83549	−0.0832596
$487$	34.1599	1.54793	0.773966	−	0.633227i	$-0.218270\pi$
$487$	34.1599	1.54793	0.773966	+	0.633227i	$0.218270\pi$
$488$	−12.1367	−0.549400
$489$	−14.2353	−0.643742
$490$	−4.38093	−0.197910
$491$	29.1595	1.31595	0.657975	−	0.753040i	$-0.271413\pi$
$491$	29.1595	1.31595	0.657975	+	0.753040i	$0.271413\pi$
$492$	−7.27944	−0.328183
$493$	7.65987	0.344983
$494$	2.35819	0.106100
$495$	1.83434	0.0824474
$496$	19.8633	0.891889
$497$	−1.15825	−0.0519544
$498$	27.4431	1.22975
$499$	−38.1884	−1.70955	−0.854775	−	0.518999i	$-0.826305\pi$
$499$	−38.1884	−1.70955	−0.854775	+	0.518999i	$0.826305\pi$
$500$	5.87964	0.262946
$501$	2.36992	0.105880
$502$	−26.5961	−1.18704
$503$	24.5332	1.09388	0.546942	−	0.837171i	$-0.315792\pi$
$503$	24.5332	1.09388	0.546942	+	0.837171i	$0.315792\pi$
$504$	1.44145	0.0642073
$505$	6.64508	0.295702
$506$	−54.6507	−2.42952
$507$	−12.8741	−0.571759
$508$	12.3009	0.545766
$509$	−13.8448	−0.613662	−0.306831	−	0.951764i	$-0.599269\pi$
$509$	−13.8448	−0.613662	−0.306831	+	0.951764i	$0.599269\pi$
$510$	0.803707	0.0355887
$511$	13.0920	0.579155
$512$	−20.8898	−0.923208
$513$	3.62100	0.159871
$514$	−52.1743	−2.30131
$515$	0.0609722	0.00268676
$516$	11.0701	0.487334
$517$	−25.1222	−1.10487
$518$	−17.1488	−0.753477
$519$	−22.0665	−0.968610
$520$	0.179929	0.00789042
$521$	−9.32550	−0.408558	−0.204279	−	0.978913i	$-0.565485\pi$
$521$	−9.32550	−0.408558	−0.204279	+	0.978913i	$0.565485\pi$
$522$	−14.0596	−0.615373
$523$	−16.1228	−0.705003	−0.352501	−	0.935811i	$-0.614669\pi$
$523$	−16.1228	−0.705003	−0.352501	+	0.935811i	$0.614669\pi$
$524$	−12.2589	−0.535533
$525$	−5.98451	−0.261185
$526$	28.8930	1.25979
$527$	−4.08390	−0.177897
$528$	20.3757	0.886737
$529$	27.5146	1.19629
$530$	6.63685	0.288286
$531$	−9.36164	−0.406260
$532$	6.16995	0.267501
$533$	1.88661	0.0817180
$534$	−6.93218	−0.299985
$535$	2.03073	0.0877961
$536$	6.29676	0.271979
$537$	7.51935	0.324484
$538$	−25.7861	−1.11172
$539$	22.8351	0.983577
$540$	−0.599458	−0.0257965
$541$	−34.0611	−1.46440	−0.732201	−	0.681089i	$-0.761507\pi$
$541$	−34.0611	−1.46440	−0.732201	+	0.681089i	$0.761507\pi$
$542$	59.6869	2.56377
$543$	−19.5347	−0.838313
$544$	6.61122	0.283454
$545$	0.0676942	0.00289970
$546$	0.810566	0.0346890
$547$	30.0526	1.28496	0.642478	−	0.766304i	$-0.277907\pi$
$547$	30.0526	1.28496	0.642478	+	0.766304i	$0.277907\pi$
$548$	−8.84463	−0.377824
$549$	−10.4794	−0.447252
$550$	−36.9722	−1.57650
$551$	27.7364	1.18161
$552$	−8.23131	−0.350348
$553$	5.17920	0.220242
$554$	−21.8497	−0.928307
$555$	−3.28691	−0.139522
$556$	12.5493	0.532208
$557$	−18.8914	−0.800453	−0.400226	−	0.916416i	$-0.631068\pi$
$557$	−18.8914	−0.800453	−0.400226	+	0.916416i	$0.631068\pi$
$558$	7.49596	0.317329
$559$	−2.86903	−0.121347
$560$	2.65071	0.112013
$561$	−4.18923	−0.176870
$562$	49.8823	2.10416
$563$	−30.7521	−1.29605	−0.648023	−	0.761621i	$-0.724404\pi$
$563$	−30.7521	−1.29605	−0.648023	+	0.761621i	$0.724404\pi$
$564$	8.20987	0.345698
$565$	6.23761	0.262418
$566$	−39.7232	−1.66969
$567$	1.24463	0.0522694
$568$	−1.07776	−0.0452218
$569$	9.27766	0.388940	0.194470	−	0.980908i	$-0.437701\pi$
$569$	9.27766	0.388940	0.194470	+	0.980908i	$0.437701\pi$
$570$	2.91023	0.121896
$571$	−22.7625	−0.952580	−0.476290	−	0.879288i	$-0.658019\pi$
$571$	−22.7625	−0.952580	−0.476290	+	0.879288i	$0.658019\pi$
$572$	2.03491	0.0850837
$573$	20.1068	0.839972
$574$	12.1472	0.507015
$575$	34.1741	1.42516
$576$	−2.40721	−0.100300
$577$	23.9020	0.995052	0.497526	−	0.867449i	$-0.334242\pi$
$577$	23.9020	0.995052	0.497526	+	0.867449i	$0.334242\pi$
$578$	−1.83549	−0.0763464
$579$	9.30172	0.386566
$580$	−4.59177	−0.190663
$581$	−18.6088	−0.772025
$582$	−23.3358	−0.967299
$583$	−34.5938	−1.43273
$584$	12.1822	0.504104
$585$	0.155361	0.00642338
$586$	55.7735	2.30398
$587$	39.6064	1.63473	0.817366	−	0.576119i	$-0.195434\pi$
$587$	39.6064	1.63473	0.817366	+	0.576119i	$0.195434\pi$
$588$	−7.46245	−0.307746
$589$	−14.7878	−0.609321
$590$	−7.52401	−0.309759
$591$	−5.15075	−0.211873
$592$	−36.5107	−1.50058
$593$	−1.79957	−0.0738993	−0.0369497	−	0.999317i	$-0.511764\pi$
$593$	−1.79957	−0.0738993	−0.0369497	+	0.999317i	$0.511764\pi$
$594$	7.68930	0.315496
$595$	−0.544985	−0.0223422
$596$	−6.19147	−0.253613
$597$	−1.84768	−0.0756207
$598$	−4.62868	−0.189281
$599$	25.8173	1.05487	0.527434	−	0.849596i	$-0.323154\pi$
$599$	25.8173	1.05487	0.527434	+	0.849596i	$0.323154\pi$
$600$	−5.56864	−0.227339
$601$	−19.8178	−0.808387	−0.404193	−	0.914674i	$-0.632448\pi$
$601$	−19.8178	−0.808387	−0.404193	+	0.914674i	$0.632448\pi$
$602$	−18.4727	−0.752891
$603$	5.43697	0.221410
$604$	−13.7686	−0.560238
$605$	−2.86790	−0.116597
$606$	27.8553	1.13154
$607$	−48.0135	−1.94881	−0.974404	−	0.224805i	$-0.927825\pi$
$607$	−48.0135	−1.94881	−0.974404	+	0.224805i	$0.927825\pi$
$608$	23.9393	0.970865
$609$	9.53369	0.386324
$610$	−8.42240	−0.341013
$611$	−2.12774	−0.0860793
$612$	1.36903	0.0553398
$613$	−23.4435	−0.946874	−0.473437	−	0.880828i	$-0.656987\pi$
$613$	−23.4435	−0.946874	−0.473437	+	0.880828i	$0.656987\pi$
$614$	−4.31904	−0.174302
$615$	2.32825	0.0938841
$616$	−6.03857	−0.243301
$617$	−34.1431	−1.37455	−0.687275	−	0.726398i	$-0.741193\pi$
$617$	−34.1431	−1.37455	−0.687275	+	0.726398i	$0.741193\pi$
$618$	0.255587	0.0102812
$619$	43.0175	1.72902	0.864510	−	0.502616i	$-0.167629\pi$
$619$	43.0175	1.72902	0.864510	+	0.502616i	$0.167629\pi$
$620$	2.44812	0.0983190
$621$	−7.10736	−0.285209
$622$	24.8934	0.998134
$623$	4.70063	0.188327
$624$	1.72573	0.0690846
$625$	22.1608	0.886432
$626$	−15.7712	−0.630344
$627$	−15.1692	−0.605801
$628$	−1.36903	−0.0546303
$629$	7.50660	0.299308
$630$	1.00032	0.0398535
$631$	15.2313	0.606347	0.303174	−	0.952935i	$-0.401954\pi$
$631$	15.2313	0.606347	0.303174	+	0.952935i	$0.401954\pi$
$632$	4.81930	0.191702
$633$	−8.13078	−0.323169
$634$	41.3398	1.64181
$635$	−3.93433	−0.156129
$636$	11.3052	0.448280
$637$	1.93404	0.0766293
$638$	58.8991	2.33184
$639$	−0.930596	−0.0368138
$640$	3.85502	0.152383
$641$	−32.0969	−1.26775	−0.633877	−	0.773434i	$-0.718537\pi$
$641$	−32.0969	−1.26775	−0.633877	+	0.773434i	$0.718537\pi$
$642$	8.51255	0.335963
$643$	46.8622	1.84806	0.924032	−	0.382315i	$-0.124873\pi$
$643$	46.8622	1.84806	0.924032	+	0.382315i	$0.124873\pi$
$644$	−12.1105	−0.477220
$645$	−3.54065	−0.139413
$646$	−6.64632	−0.261496
$647$	−35.3822	−1.39102	−0.695509	−	0.718517i	$-0.744821\pi$
$647$	−35.3822	−1.39102	−0.695509	+	0.718517i	$0.744821\pi$
$648$	1.15814	0.0454960
$649$	39.2181	1.53944
$650$	−3.13139	−0.122823
$651$	−5.08293	−0.199216
$652$	−19.4886	−0.763231
$653$	0.196095	0.00767379	0.00383690	−	0.999993i	$-0.498779\pi$
$653$	0.196095	0.00767379	0.00383690	+	0.999993i	$0.498779\pi$
$654$	0.283765	0.0110961
$655$	3.92088	0.153202
$656$	25.8620	1.00974
$657$	10.5188	0.410377
$658$	−13.6998	−0.534074
$659$	−22.6253	−0.881357	−0.440678	−	0.897665i	$-0.645262\pi$
$659$	−22.6253	−0.881357	−0.440678	+	0.897665i	$0.645262\pi$
$660$	2.51127	0.0977509
$661$	−25.3924	−0.987649	−0.493824	−	0.869562i	$-0.664401\pi$
$661$	−25.3924	−0.987649	−0.493824	+	0.869562i	$0.664401\pi$
$662$	43.6307	1.69576
$663$	−0.354810	−0.0137797
$664$	−17.3157	−0.671980
$665$	−1.97339	−0.0765249
$666$	−13.7783	−0.533898
$667$	−54.4415	−2.10798
$668$	3.24449	0.125533
$669$	−11.8947	−0.459874
$670$	4.36973	0.168817
$671$	43.9008	1.69477
$672$	8.22851	0.317421
$673$	−31.8576	−1.22802	−0.614011	−	0.789298i	$-0.710445\pi$
$673$	−31.8576	−1.22802	−0.614011	+	0.789298i	$0.710445\pi$
$674$	−47.6274	−1.83454
$675$	−4.80827	−0.185070
$676$	−17.6251	−0.677887
$677$	10.1893	0.391608	0.195804	−	0.980643i	$-0.437268\pi$
$677$	10.1893	0.391608	0.195804	+	0.980643i	$0.437268\pi$
$678$	26.1472	1.00418
$679$	15.8237	0.607260
$680$	−0.507114	−0.0194469
$681$	20.3160	0.778512
$682$	−31.4023	−1.20246
$683$	5.74055	0.219656	0.109828	−	0.993951i	$-0.464970\pi$
$683$	5.74055	0.219656	0.109828	+	0.993951i	$0.464970\pi$
$684$	4.95727	0.189546
$685$	2.82886	0.108085
$686$	28.4441	1.08600
$687$	−17.2042	−0.656382
$688$	−39.3292	−1.49941
$689$	−2.92995	−0.111622
$690$	−5.71224	−0.217461
$691$	28.4987	1.08414	0.542071	−	0.840333i	$-0.317640\pi$
$691$	28.4987	1.08414	0.542071	+	0.840333i	$0.317640\pi$
$692$	−30.2097	−1.14840
$693$	−5.21403	−0.198065
$694$	35.6556	1.35347
$695$	−4.01375	−0.152250
$696$	8.87119	0.336262
$697$	−5.31722	−0.201404
$698$	19.3339	0.731800
$699$	−8.24640	−0.311908
$700$	−8.19297	−0.309665
$701$	13.8697	0.523852	0.261926	−	0.965088i	$-0.415642\pi$
$701$	13.8697	0.523852	0.261926	+	0.965088i	$0.415642\pi$
$702$	0.651252	0.0245799
$703$	27.1814	1.02517
$704$	10.0844	0.380068
$705$	−2.62584	−0.0988948
$706$	−16.5638	−0.623388
$707$	−18.8884	−0.710370
$708$	−12.8164	−0.481669
$709$	−21.9831	−0.825591	−0.412795	−	0.910824i	$-0.635448\pi$
$709$	−21.9831	−0.825591	−0.412795	+	0.910824i	$0.635448\pi$
$710$	−0.747926	−0.0280692
$711$	4.16125	0.156059
$712$	4.37399	0.163922
$713$	29.0257	1.08702
$714$	−2.28450	−0.0854954
$715$	−0.650843	−0.0243401
$716$	10.2942	0.384713
$717$	23.0434	0.860572
$718$	42.1658	1.57361
$719$	−5.24905	−0.195757	−0.0978783	−	0.995198i	$-0.531206\pi$
$719$	−5.24905	−0.195757	−0.0978783	+	0.995198i	$0.531206\pi$
$720$	2.12972	0.0793699
$721$	−0.173311	−0.00645444
$722$	10.8080	0.402231
$723$	2.58894	0.0962838
$724$	−26.7436	−0.993917
$725$	−36.8307	−1.36786
$726$	−12.0219	−0.446173
$727$	−22.9429	−0.850905	−0.425452	−	0.904981i	$-0.639885\pi$
$727$	−22.9429	−0.850905	−0.425452	+	0.904981i	$0.639885\pi$
$728$	−0.511442	−0.0189553
$729$	1.00000	0.0370370
$730$	8.45402	0.312897
$731$	8.08609	0.299075
$732$	−14.3467	−0.530269
$733$	43.1782	1.59482	0.797412	−	0.603436i	$-0.206202\pi$
$733$	43.1782	1.59482	0.797412	+	0.603436i	$0.206202\pi$
$734$	−56.5856	−2.08861
$735$	2.38679	0.0880379
$736$	−46.9883	−1.73201
$737$	−22.7767	−0.838992
$738$	9.75972	0.359260
$739$	−41.6098	−1.53064	−0.765321	−	0.643648i	$-0.777420\pi$
$739$	−41.6098	−1.53064	−0.765321	+	0.643648i	$0.777420\pi$
$740$	−4.49989	−0.165419
$741$	−1.28477	−0.0471972
$742$	−18.8650	−0.692555
$743$	19.2041	0.704532	0.352266	−	0.935900i	$-0.385411\pi$
$743$	19.2041	0.704532	0.352266	+	0.935900i	$0.385411\pi$
$744$	−4.72972	−0.173400
$745$	1.98028	0.0725517
$746$	12.7676	0.467453
$747$	−14.9513	−0.547041
$748$	−5.73519	−0.209699
$749$	−5.77227	−0.210914
$750$	−7.88297	−0.287845
$751$	15.5956	0.569092	0.284546	−	0.958662i	$-0.408157\pi$
$751$	15.5956	0.569092	0.284546	+	0.958662i	$0.408157\pi$
$752$	−29.1676	−1.06363
$753$	14.4899	0.528042
$754$	4.98850	0.181671
$755$	4.40376	0.160269
$756$	1.70393	0.0619715
$757$	−29.0536	−1.05597	−0.527986	−	0.849253i	$-0.677053\pi$
$757$	−29.0536	−1.05597	−0.527986	+	0.849253i	$0.677053\pi$
$758$	−32.4047	−1.17699
$759$	29.7744	1.08074
$760$	−1.83626	−0.0666082
$761$	−27.8123	−1.00819	−0.504097	−	0.863647i	$-0.668175\pi$
$761$	−27.8123	−1.00819	−0.504097	+	0.863647i	$0.668175\pi$
$762$	−16.4922	−0.597448
$763$	−0.192418	−0.00696600
$764$	27.5268	0.995884
$765$	−0.437870	−0.0158312
$766$	49.7624	1.79799
$767$	3.32161	0.119936
$768$	20.9741	0.756839
$769$	−36.0224	−1.29900	−0.649501	−	0.760361i	$-0.725022\pi$
$769$	−36.0224	−1.29900	−0.649501	+	0.760361i	$0.725022\pi$
$770$	−4.19055	−0.151017
$771$	28.4252	1.02371
$772$	12.7343	0.458319
$773$	23.5177	0.845875	0.422937	−	0.906159i	$-0.360999\pi$
$773$	23.5177	0.845875	0.422937	+	0.906159i	$0.360999\pi$
$774$	−14.8419	−0.533483
$775$	19.6365	0.705363
$776$	14.7242	0.528566
$777$	9.34292	0.335175
$778$	26.0742	0.934806
$779$	−19.2537	−0.689835
$780$	0.212694	0.00761566
$781$	3.89848	0.139499
$782$	13.0455	0.466506
$783$	7.65987	0.273741
$784$	26.5122	0.946864
$785$	0.437870	0.0156282
$786$	16.4358	0.586246
$787$	31.8651	1.13587	0.567935	−	0.823074i	$-0.307743\pi$
$787$	31.8651	1.13587	0.567935	+	0.823074i	$0.307743\pi$
$788$	−7.05153	−0.251200
$789$	−15.7413	−0.560405
$790$	3.34442	0.118989
$791$	−17.7301	−0.630411
$792$	−4.85171	−0.172398
$793$	3.71822	0.132038
$794$	11.4598	0.406693
$795$	−3.61584	−0.128241
$796$	−2.52954	−0.0896571
$797$	2.41351	0.0854910	0.0427455	−	0.999086i	$-0.486390\pi$
$797$	2.41351	0.0854910	0.0427455	+	0.999086i	$0.486390\pi$
$798$	−8.27220	−0.292833
$799$	5.99685	0.212153
$800$	−31.7885	−1.12389
$801$	3.77674	0.133445
$802$	59.5374	2.10234
$803$	−44.0657	−1.55504
$804$	7.44338	0.262508
$805$	3.87341	0.136520
$806$	−2.65964	−0.0936820
$807$	14.0486	0.494534
$808$	−17.5758	−0.618315
$809$	2.12540	0.0747250	0.0373625	−	0.999302i	$-0.488104\pi$
$809$	2.12540	0.0747250	0.0373625	+	0.999302i	$0.488104\pi$
$810$	0.803707	0.0282394
$811$	−33.5938	−1.17964	−0.589819	−	0.807536i	$-0.700801\pi$
$811$	−33.5938	−1.17964	−0.589819	+	0.807536i	$0.700801\pi$
$812$	13.0519	0.458032
$813$	−32.5182	−1.14046
$814$	57.7205	2.02310
$815$	6.23320	0.218340
$816$	−4.86382	−0.170268
$817$	29.2798	1.02437
$818$	−41.9148	−1.46552
$819$	−0.441607	−0.0154310
$820$	3.18745	0.111311
$821$	−8.60547	−0.300333	−0.150167	−	0.988661i	$-0.547981\pi$
$821$	−8.60547	−0.300333	−0.150167	+	0.988661i	$0.547981\pi$
$822$	11.8582	0.413603
$823$	6.67419	0.232648	0.116324	−	0.993211i	$-0.462889\pi$
$823$	6.67419	0.232648	0.116324	+	0.993211i	$0.462889\pi$
$824$	−0.161268	−0.00561803
$825$	20.1430	0.701288
$826$	21.3867	0.744138
$827$	−33.3168	−1.15854	−0.579269	−	0.815136i	$-0.696662\pi$
$827$	−33.3168	−1.15854	−0.579269	+	0.815136i	$0.696662\pi$
$828$	−9.73020	−0.338148
$829$	1.18841	0.0412751	0.0206375	−	0.999787i	$-0.493430\pi$
$829$	1.18841	0.0412751	0.0206375	+	0.999787i	$0.493430\pi$
$830$	−12.0165	−0.417098
$831$	11.9040	0.412946
$832$	0.854102	0.0296107
$833$	−5.45090	−0.188863
$834$	−16.8251	−0.582606
$835$	−1.03772	−0.0359116
$836$	−20.7671	−0.718247
$837$	−4.08390	−0.141160
$838$	66.3103	2.29065
$839$	3.84858	0.132868	0.0664339	−	0.997791i	$-0.478838\pi$
$839$	3.84858	0.132868	0.0664339	+	0.997791i	$0.478838\pi$
$840$	−0.631168	−0.0217774
$841$	29.6736	1.02323
$842$	−66.5505	−2.29348
$843$	−27.1766	−0.936010
$844$	−11.1313	−0.383155
$845$	5.63719	0.193925
$846$	−11.0072	−0.378434
$847$	8.15190	0.280103
$848$	−40.1644	−1.37925
$849$	21.6417	0.742742
$850$	8.82554	0.302714
$851$	−53.3521	−1.82889
$852$	−1.27401	−0.0436470
$853$	0.321373	0.0110036	0.00550179	−	0.999985i	$-0.498249\pi$
$853$	0.321373	0.0110036	0.00550179	+	0.999985i	$0.498249\pi$
$854$	23.9403	0.819222
$855$	−1.58553	−0.0542239
$856$	−5.37115	−0.183582
$857$	−31.9145	−1.09018	−0.545089	−	0.838378i	$-0.683504\pi$
$857$	−31.9145	−1.09018	−0.545089	+	0.838378i	$0.683504\pi$
$858$	−2.72825	−0.0931408
$859$	−31.8644	−1.08720	−0.543600	−	0.839345i	$-0.682939\pi$
$859$	−31.8644	−1.08720	−0.543600	+	0.839345i	$0.682939\pi$
$860$	−4.84726	−0.165290
$861$	−6.61796	−0.225539
$862$	−32.7422	−1.11520
$863$	−24.2455	−0.825325	−0.412663	−	0.910884i	$-0.635401\pi$
$863$	−24.2455	−0.825325	−0.412663	+	0.910884i	$0.635401\pi$
$864$	6.61122	0.224918
$865$	9.66224	0.328526
$866$	1.85300	0.0629674
$867$	1.00000	0.0339618
$868$	−6.95869	−0.236193
$869$	−17.4324	−0.591355
$870$	6.15629	0.208718
$871$	−1.92909	−0.0653648
$872$	−0.179047	−0.00606329
$873$	12.7136	0.430292
$874$	47.2378	1.59784
$875$	5.34536	0.180706
$876$	14.4005	0.486549
$877$	−33.8767	−1.14393	−0.571967	−	0.820277i	$-0.693819\pi$
$877$	−33.8767	−1.14393	−0.571967	+	0.820277i	$0.693819\pi$
$878$	−34.7943	−1.17425
$879$	−30.3861	−1.02490
$880$	−8.92189	−0.300757
$881$	7.00714	0.236077	0.118038	−	0.993009i	$-0.462339\pi$
$881$	7.00714	0.236077	0.118038	+	0.993009i	$0.462339\pi$
$882$	10.0051	0.336889
$883$	−42.6014	−1.43365	−0.716825	−	0.697253i	$-0.754406\pi$
$883$	−42.6014	−1.43365	−0.716825	+	0.697253i	$0.754406\pi$
$884$	−0.485747	−0.0163374
$885$	4.09918	0.137792
$886$	8.17085	0.274505
$887$	−17.7231	−0.595085	−0.297542	−	0.954709i	$-0.596167\pi$
$887$	−17.7231	−0.595085	−0.297542	+	0.954709i	$0.596167\pi$
$888$	8.69368	0.291741
$889$	11.1832	0.375071
$890$	3.03539	0.101747
$891$	−4.18923	−0.140345
$892$	−16.2842	−0.545234
$893$	21.7146	0.726652
$894$	8.30105	0.277629
$895$	−3.29250	−0.110056
$896$	−10.9577	−0.366072
$897$	2.52177	0.0841993
$898$	76.3972	2.54941
$899$	−31.2821	−1.04332
$900$	−6.58267	−0.219422
$901$	8.25780	0.275107
$902$	−40.8857	−1.36135
$903$	10.0642	0.334914
$904$	−16.4981	−0.548718
$905$	8.55365	0.284333
$906$	18.4600	0.613291
$907$	21.9276	0.728094	0.364047	−	0.931380i	$-0.381395\pi$
$907$	21.9276	0.728094	0.364047	+	0.931380i	$0.381395\pi$
$908$	27.8133	0.923016
$909$	−15.1759	−0.503353
$910$	−0.354922	−0.0117656
$911$	43.6972	1.44775	0.723876	−	0.689930i	$-0.242359\pi$
$911$	43.6972	1.44775	0.723876	+	0.689930i	$0.242359\pi$
$912$	−17.6119	−0.583188
$913$	62.6346	2.07290
$914$	−4.93904	−0.163369
$915$	4.58863	0.151696
$916$	−23.5531	−0.778217
$917$	−11.1450	−0.368039
$918$	−1.83549	−0.0605803
$919$	−23.4041	−0.772030	−0.386015	−	0.922492i	$-0.626149\pi$
$919$	−23.4041	−0.772030	−0.386015	+	0.922492i	$0.626149\pi$
$920$	3.60424	0.118828
$921$	2.35307	0.0775362
$922$	12.2101	0.402119
$923$	0.330185	0.0108682
$924$	−7.13817	−0.234829
$925$	−36.0937	−1.18675
$926$	30.8283	1.01308
$927$	−0.139247	−0.00457348
$928$	50.6411	1.66237
$929$	−0.626580	−0.0205574	−0.0102787	−	0.999947i	$-0.503272\pi$
$929$	−0.626580	−0.0205574	−0.0102787	+	0.999947i	$0.503272\pi$
$930$	−3.28225	−0.107629
$931$	−19.7377	−0.646878
$932$	−11.2896	−0.369803
$933$	−13.5622	−0.444008
$934$	−46.7746	−1.53051
$935$	1.83434	0.0599893
$936$	−0.410920	−0.0134313
$937$	4.86279	0.158861	0.0794303	−	0.996840i	$-0.474690\pi$
$937$	4.86279	0.158861	0.0794303	+	0.996840i	$0.474690\pi$
$938$	−12.4208	−0.405553
$939$	8.59236	0.280401
$940$	−3.59485	−0.117251
$941$	52.8266	1.72210	0.861049	−	0.508523i	$-0.169808\pi$
$941$	52.8266	1.72210	0.861049	+	0.508523i	$0.169808\pi$
$942$	1.83549	0.0598036
$943$	37.7914	1.23066
$944$	45.5333	1.48198
$945$	−0.544985	−0.0177284
$946$	62.1764	2.02153
$947$	3.75765	0.122107	0.0610537	−	0.998134i	$-0.480554\pi$
$947$	3.75765	0.122107	0.0610537	+	0.998134i	$0.480554\pi$
$948$	5.69688	0.185026
$949$	−3.73218	−0.121152
$950$	31.9573	1.03683
$951$	−22.5225	−0.730341
$952$	1.44145	0.0467177
$953$	−39.5225	−1.28026	−0.640129	−	0.768267i	$-0.721119\pi$
$953$	−39.5225	−1.28026	−0.640129	+	0.768267i	$0.721119\pi$
$954$	−15.1571	−0.490730
$955$	−8.80415	−0.284896
$956$	31.5472	1.02031
$957$	−32.0890	−1.03729
$958$	25.1017	0.810998
$959$	−8.04092	−0.259655
$960$	1.05404	0.0340191
$961$	−14.3218	−0.461993
$962$	4.88868	0.157617
$963$	−4.63775	−0.149449
$964$	3.54434	0.114156
$965$	−4.07294	−0.131113
$966$	16.2368	0.522410
$967$	−4.69900	−0.151110	−0.0755548	−	0.997142i	$-0.524073\pi$
$967$	−4.69900	−0.151110	−0.0755548	+	0.997142i	$0.524073\pi$
$968$	7.58543	0.243805
$969$	3.62100	0.116323
$970$	10.2180	0.328081
$971$	−56.8504	−1.82442	−0.912208	−	0.409728i	$-0.865624\pi$
$971$	−56.8504	−1.82442	−0.912208	+	0.409728i	$0.865624\pi$
$972$	1.36903	0.0439117
$973$	11.4089	0.365753
$974$	−62.7002	−2.00904
$975$	1.70602	0.0546365
$976$	50.9701	1.63151
$977$	5.60351	0.179272	0.0896361	−	0.995975i	$-0.471430\pi$
$977$	5.60351	0.179272	0.0896361	+	0.995975i	$0.471430\pi$
$978$	26.1288	0.835506
$979$	−15.8216	−0.505662
$980$	3.26758	0.104379
$981$	−0.154599	−0.00493596
$982$	−53.5220	−1.70796
$983$	24.9619	0.796162	0.398081	−	0.917350i	$-0.369676\pi$
$983$	24.9619	0.796162	0.398081	+	0.917350i	$0.369676\pi$
$984$	−6.15808	−0.196312
$985$	2.25536	0.0718616
$986$	−14.0596	−0.447750
$987$	7.46384	0.237577
$988$	−1.75889	−0.0559578
$989$	−57.4707	−1.82746
$990$	−3.36691	−0.107008
$991$	−49.6059	−1.57578	−0.787892	−	0.615813i	$-0.788828\pi$
$991$	−49.6059	−1.57578	−0.787892	+	0.615813i	$0.788828\pi$
$992$	−26.9995	−0.857236
$993$	−23.7706	−0.754337
$994$	2.12595	0.0674310
$995$	0.809045	0.0256485
$996$	−20.4688	−0.648580
$997$	59.9800	1.89959	0.949793	−	0.312880i	$-0.101294\pi$
$997$	59.9800	1.89959	0.949793	+	0.312880i	$0.101294\pi$
$998$	70.0946	2.21881
$999$	7.50660	0.237498

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.d.1.10	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.d.1.10	✓	40	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)

\(f(q)\)	\(=\)	\(q-1.83549 q^{2} +1.00000 q^{3} +1.36903 q^{4} -0.437870 q^{5} -1.83549 q^{6} +1.24463 q^{7} +1.15814 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.83549 q^{2} +1.00000 q^{3} +1.36903 q^{4} -0.437870 q^{5} -1.83549 q^{6} +1.24463 q^{7} +1.15814 q^{8} +1.00000 q^{9} +0.803707 q^{10} -4.18923 q^{11} +1.36903 q^{12} -0.354810 q^{13} -2.28450 q^{14} -0.437870 q^{15} -4.86382 q^{16} +1.00000 q^{17} -1.83549 q^{18} +3.62100 q^{19} -0.599458 q^{20} +1.24463 q^{21} +7.68930 q^{22} -7.10736 q^{23} +1.15814 q^{24} -4.80827 q^{25} +0.651252 q^{26} +1.00000 q^{27} +1.70393 q^{28} +7.65987 q^{29} +0.803707 q^{30} -4.08390 q^{31} +6.61122 q^{32} -4.18923 q^{33} -1.83549 q^{34} -0.544985 q^{35} +1.36903 q^{36} +7.50660 q^{37} -6.64632 q^{38} -0.354810 q^{39} -0.507114 q^{40} -5.31722 q^{41} -2.28450 q^{42} +8.08609 q^{43} -5.73519 q^{44} -0.437870 q^{45} +13.0455 q^{46} +5.99685 q^{47} -4.86382 q^{48} -5.45090 q^{49} +8.82554 q^{50} +1.00000 q^{51} -0.485747 q^{52} +8.25780 q^{53} -1.83549 q^{54} +1.83434 q^{55} +1.44145 q^{56} +3.62100 q^{57} -14.0596 q^{58} -9.36164 q^{59} -0.599458 q^{60} -10.4794 q^{61} +7.49596 q^{62} +1.24463 q^{63} -2.40721 q^{64} +0.155361 q^{65} +7.68930 q^{66} +5.43697 q^{67} +1.36903 q^{68} -7.10736 q^{69} +1.00032 q^{70} -0.930596 q^{71} +1.15814 q^{72} +10.5188 q^{73} -13.7783 q^{74} -4.80827 q^{75} +4.95727 q^{76} -5.21403 q^{77} +0.651252 q^{78} +4.16125 q^{79} +2.12972 q^{80} +1.00000 q^{81} +9.75972 q^{82} -14.9513 q^{83} +1.70393 q^{84} -0.437870 q^{85} -14.8419 q^{86} +7.65987 q^{87} -4.85171 q^{88} +3.77674 q^{89} +0.803707 q^{90} -0.441607 q^{91} -9.73020 q^{92} -4.08390 q^{93} -11.0072 q^{94} -1.58553 q^{95} +6.61122 q^{96} +12.7136 q^{97} +10.0051 q^{98} -4.18923 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9}+O(q^{10}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9	\( 40 q - 7 q^{2} + 40 q^{3} + 29 q^{4} - 15 q^{5} - 7 q^{6} - 13 q^{7} - 18 q^{8} + 40 q^{9} - 6 q^{10} - 25 q^{11} + 29 q^{12} - 24 q^{13} - 22 q^{14} - 15 q^{15} + 7 q^{16} + 40 q^{17} - 7 q^{18} - 18 q^{19} - 20 q^{20} - 13 q^{21} - 25 q^{22} - 28 q^{23} - 18 q^{24} - 11 q^{25} - 13 q^{26} + 40 q^{27} - 8 q^{28} - 23 q^{29} - 6 q^{30} - 11 q^{31} - 23 q^{32} - 25 q^{33} - 7 q^{34} - 45 q^{35} + 29 q^{36} - 38 q^{37} - 30 q^{38} - 24 q^{39} - 12 q^{40} - 33 q^{41} - 22 q^{42} - 25 q^{43} - 14 q^{44} - 15 q^{45} + 8 q^{46} - 55 q^{47} + 7 q^{48} - 21 q^{49} + 2 q^{50} + 40 q^{51} - 39 q^{52} - 39 q^{53} - 7 q^{54} - 9 q^{55} - 48 q^{56} - 18 q^{57} - 13 q^{58} - 81 q^{59} - 20 q^{60} - 9 q^{61} - 16 q^{62} - 13 q^{63} - 4 q^{64} - 43 q^{65} - 25 q^{66} - 24 q^{67} + 29 q^{68} - 28 q^{69} + 48 q^{70} - 32 q^{71} - 18 q^{72} - 43 q^{73} - 20 q^{74} - 11 q^{75} - 58 q^{76} - 32 q^{77} - 13 q^{78} - 22 q^{79} - 48 q^{80} + 40 q^{81} - 11 q^{82} - 45 q^{83} - 8 q^{84} - 15 q^{85} - 30 q^{86} - 23 q^{87} - 48 q^{88} - 94 q^{89} - 6 q^{90} - 7 q^{91} - 98 q^{92} - 11 q^{93} + 32 q^{94} - 23 q^{96} - 28 q^{97} - 46 q^{98} - 25 q^{99}+O(q^{100}) \) 40 * q - 7 * q^2 + 40 * q^3 + 29 * q^4 - 15 * q^5 - 7 * q^6 - 13 * q^7 - 18 * q^8 + 40 * q^9 - 6 * q^10 - 25 * q^11 + 29 * q^12 - 24 * q^13 - 22 * q^14 - 15 * q^15 + 7 * q^16 + 40 * q^17 - 7 * q^18 - 18 * q^19 - 20 * q^20 - 13 * q^21 - 25 * q^22 - 28 * q^23 - 18 * q^24 - 11 * q^25 - 13 * q^26 + 40 * q^27 - 8 * q^28 - 23 * q^29 - 6 * q^30 - 11 * q^31 - 23 * q^32 - 25 * q^33 - 7 * q^34 - 45 * q^35 + 29 * q^36 - 38 * q^37 - 30 * q^38 - 24 * q^39 - 12 * q^40 - 33 * q^41 - 22 * q^42 - 25 * q^43 - 14 * q^44 - 15 * q^45 + 8 * q^46 - 55 * q^47 + 7 * q^48 - 21 * q^49 + 2 * q^50 + 40 * q^51 - 39 * q^52 - 39 * q^53 - 7 * q^54 - 9 * q^55 - 48 * q^56 - 18 * q^57 - 13 * q^58 - 81 * q^59 - 20 * q^60 - 9 * q^61 - 16 * q^62 - 13 * q^63 - 4 * q^64 - 43 * q^65 - 25 * q^66 - 24 * q^67 + 29 * q^68 - 28 * q^69 + 48 * q^70 - 32 * q^71 - 18 * q^72 - 43 * q^73 - 20 * q^74 - 11 * q^75 - 58 * q^76 - 32 * q^77 - 13 * q^78 - 22 * q^79 - 48 * q^80 + 40 * q^81 - 11 * q^82 - 45 * q^83 - 8 * q^84 - 15 * q^85 - 30 * q^86 - 23 * q^87 - 48 * q^88 - 94 * q^89 - 6 * q^90 - 7 * q^91 - 98 * q^92 - 11 * q^93 + 32 * q^94 - 23 * q^96 - 28 * q^97 - 46 * q^98 - 25 * q^99

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