LMFDB - Embedded newform 8035.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.72603 q^{2} -2.40516 q^{3} +5.43123 q^{4} -1.00000 q^{5} +6.55652 q^{6} -0.808497 q^{7} -9.35364 q^{8} +2.78477 q^{9} +O(q^{10})$	\(q-2.72603 q^{2} -2.40516 q^{3} +5.43123 q^{4} -1.00000 q^{5} +6.55652 q^{6} -0.808497 q^{7} -9.35364 q^{8} +2.78477 q^{9} +2.72603 q^{10} +2.33214 q^{11} -13.0630 q^{12} +4.71445 q^{13} +2.20399 q^{14} +2.40516 q^{15} +14.6358 q^{16} -1.10632 q^{17} -7.59138 q^{18} -2.41717 q^{19} -5.43123 q^{20} +1.94456 q^{21} -6.35749 q^{22} -6.04819 q^{23} +22.4970 q^{24} +1.00000 q^{25} -12.8517 q^{26} +0.517650 q^{27} -4.39114 q^{28} +6.90691 q^{29} -6.55652 q^{30} +5.13061 q^{31} -21.1904 q^{32} -5.60917 q^{33} +3.01587 q^{34} +0.808497 q^{35} +15.1248 q^{36} +5.36282 q^{37} +6.58929 q^{38} -11.3390 q^{39} +9.35364 q^{40} -5.29981 q^{41} -5.30093 q^{42} +6.87266 q^{43} +12.6664 q^{44} -2.78477 q^{45} +16.4875 q^{46} -6.14544 q^{47} -35.2015 q^{48} -6.34633 q^{49} -2.72603 q^{50} +2.66088 q^{51} +25.6053 q^{52} -11.3876 q^{53} -1.41113 q^{54} -2.33214 q^{55} +7.56239 q^{56} +5.81368 q^{57} -18.8284 q^{58} -2.12195 q^{59} +13.0630 q^{60} +3.73238 q^{61} -13.9862 q^{62} -2.25148 q^{63} +28.4940 q^{64} -4.71445 q^{65} +15.2908 q^{66} -2.93150 q^{67} -6.00870 q^{68} +14.5468 q^{69} -2.20399 q^{70} -8.58294 q^{71} -26.0478 q^{72} -4.70389 q^{73} -14.6192 q^{74} -2.40516 q^{75} -13.1282 q^{76} -1.88553 q^{77} +30.9104 q^{78} +12.8813 q^{79} -14.6358 q^{80} -9.59935 q^{81} +14.4474 q^{82} +14.7601 q^{83} +10.5614 q^{84} +1.10632 q^{85} -18.7351 q^{86} -16.6122 q^{87} -21.8140 q^{88} +9.35140 q^{89} +7.59138 q^{90} -3.81162 q^{91} -32.8491 q^{92} -12.3399 q^{93} +16.7526 q^{94} +2.41717 q^{95} +50.9662 q^{96} -16.8513 q^{97} +17.3003 q^{98} +6.49450 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * 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 $

$2$	−2.72603	−1.92759	−0.963797	−	0.266638i	$-0.914087\pi$
$2$	−2.72603	−1.92759	−0.963797	+	0.266638i	$0.914087\pi$
$3$	−2.40516	−1.38862	−0.694309	−	0.719677i	$-0.744290\pi$
$3$	−2.40516	−1.38862	−0.694309	+	0.719677i	$0.744290\pi$
$4$	5.43123	2.71562
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	6.55652	2.67669
$7$	−0.808497	−0.305583	−0.152792	−	0.988258i	$-0.548826\pi$
$7$	−0.808497	−0.305583	−0.152792	+	0.988258i	$0.548826\pi$
$8$	−9.35364	−3.30701
$9$	2.78477	0.928258
$10$	2.72603	0.862046
$11$	2.33214	0.703168	0.351584	−	0.936156i	$-0.385643\pi$
$11$	2.33214	0.703168	0.351584	+	0.936156i	$0.385643\pi$
$12$	−13.0630	−3.77095
$13$	4.71445	1.30755	0.653777	−	0.756688i	$-0.273184\pi$
$13$	4.71445	1.30755	0.653777	+	0.756688i	$0.273184\pi$
$14$	2.20399	0.589040
$15$	2.40516	0.621009
$16$	14.6358	3.65896
$17$	−1.10632	−0.268323	−0.134161	−	0.990960i	$-0.542834\pi$
$17$	−1.10632	−0.268323	−0.134161	+	0.990960i	$0.542834\pi$
$18$	−7.59138	−1.78930
$19$	−2.41717	−0.554538	−0.277269	−	0.960792i	$-0.589429\pi$
$19$	−2.41717	−0.554538	−0.277269	+	0.960792i	$0.589429\pi$
$20$	−5.43123	−1.21446
$21$	1.94456	0.424338
$22$	−6.35749	−1.35542
$23$	−6.04819	−1.26113	−0.630567	−	0.776134i	$-0.717178\pi$
$23$	−6.04819	−1.26113	−0.630567	+	0.776134i	$0.717178\pi$
$24$	22.4970	4.59217
$25$	1.00000	0.200000
$26$	−12.8517	−2.52043
$27$	0.517650	0.0996218
$28$	−4.39114	−0.829847
$29$	6.90691	1.28258	0.641290	−	0.767298i	$-0.278399\pi$
$29$	6.90691	1.28258	0.641290	+	0.767298i	$0.278399\pi$
$30$	−6.55652	−1.19705
$31$	5.13061	0.921484	0.460742	−	0.887534i	$-0.347583\pi$
$31$	5.13061	0.921484	0.460742	+	0.887534i	$0.347583\pi$
$32$	−21.1904	−3.74597
$33$	−5.60917	−0.976431
$34$	3.01587	0.517217
$35$	0.808497	0.136661
$36$	15.1248	2.52079
$37$	5.36282	0.881643	0.440821	−	0.897595i	$-0.354687\pi$
$37$	5.36282	0.881643	0.440821	+	0.897595i	$0.354687\pi$
$38$	6.58929	1.06892
$39$	−11.3390	−1.81569
$40$	9.35364	1.47894
$41$	−5.29981	−0.827692	−0.413846	−	0.910347i	$-0.635815\pi$
$41$	−5.29981	−0.827692	−0.413846	+	0.910347i	$0.635815\pi$
$42$	−5.30093	−0.817951
$43$	6.87266	1.04807	0.524036	−	0.851696i	$-0.324426\pi$
$43$	6.87266	1.04807	0.524036	+	0.851696i	$0.324426\pi$
$44$	12.6664	1.90953
$45$	−2.78477	−0.415130
$46$	16.4875	2.43096
$47$	−6.14544	−0.896404	−0.448202	−	0.893932i	$-0.647935\pi$
$47$	−6.14544	−0.896404	−0.448202	+	0.893932i	$0.647935\pi$
$48$	−35.2015	−5.08089
$49$	−6.34633	−0.906619
$50$	−2.72603	−0.385519
$51$	2.66088	0.372598
$52$	25.6053	3.55081
$53$	−11.3876	−1.56421	−0.782105	−	0.623146i	$-0.785854\pi$
$53$	−11.3876	−1.56421	−0.782105	+	0.623146i	$0.785854\pi$
$54$	−1.41113	−0.192030
$55$	−2.33214	−0.314466
$56$	7.56239	1.01057
$57$	5.81368	0.770041
$58$	−18.8284	−2.47229
$59$	−2.12195	−0.276255	−0.138128	−	0.990414i	$-0.544108\pi$
$59$	−2.12195	−0.276255	−0.138128	+	0.990414i	$0.544108\pi$
$60$	13.0630	1.68642
$61$	3.73238	0.477883	0.238941	−	0.971034i	$-0.423200\pi$
$61$	3.73238	0.477883	0.238941	+	0.971034i	$0.423200\pi$
$62$	−13.9862	−1.77625
$63$	−2.25148	−0.283660
$64$	28.4940	3.56175
$65$	−4.71445	−0.584756
$66$	15.2908	1.88216
$67$	−2.93150	−0.358139	−0.179070	−	0.983836i	$-0.557309\pi$
$67$	−2.93150	−0.358139	−0.179070	+	0.983836i	$0.557309\pi$
$68$	−6.00870	−0.728661
$69$	14.5468	1.75123
$70$	−2.20399	−0.263427
$71$	−8.58294	−1.01861	−0.509304	−	0.860587i	$-0.670097\pi$
$71$	−8.58294	−1.01861	−0.509304	+	0.860587i	$0.670097\pi$
$72$	−26.0478	−3.06976
$73$	−4.70389	−0.550548	−0.275274	−	0.961366i	$-0.588769\pi$
$73$	−4.70389	−0.550548	−0.275274	+	0.961366i	$0.588769\pi$
$74$	−14.6192	−1.69945
$75$	−2.40516	−0.277723
$76$	−13.1282	−1.50591
$77$	−1.88553	−0.214876
$78$	30.9104	3.49991
$79$	12.8813	1.44926	0.724632	−	0.689136i	$-0.242010\pi$
$79$	12.8813	1.44926	0.724632	+	0.689136i	$0.242010\pi$
$80$	−14.6358	−1.63634
$81$	−9.59935	−1.06659
$82$	14.4474	1.59545
$83$	14.7601	1.62013	0.810067	−	0.586337i	$-0.199430\pi$
$83$	14.7601	1.62013	0.810067	+	0.586337i	$0.199430\pi$
$84$	10.5614	1.15234
$85$	1.10632	0.119998
$86$	−18.7351	−2.02026
$87$	−16.6122	−1.78101
$88$	−21.8140	−2.32538
$89$	9.35140	0.991246	0.495623	−	0.868538i	$-0.334940\pi$
$89$	9.35140	0.991246	0.495623	+	0.868538i	$0.334940\pi$
$90$	7.59138	0.800201
$91$	−3.81162	−0.399566
$92$	−32.8491	−3.42476
$93$	−12.3399	−1.27959
$94$	16.7526	1.72790
$95$	2.41717	0.247997
$96$	50.9662	5.20172
$97$	−16.8513	−1.71099	−0.855493	−	0.517815i	$-0.826746\pi$
$97$	−16.8513	−1.71099	−0.855493	+	0.517815i	$0.826746\pi$
$98$	17.3003	1.74759
$99$	6.49450	0.652722
$100$	5.43123	0.543123
$101$	5.82866	0.579974	0.289987	−	0.957031i	$-0.406349\pi$
$101$	5.82866	0.579974	0.289987	+	0.957031i	$0.406349\pi$
$102$	−7.25363	−0.718217
$103$	−18.8760	−1.85991	−0.929953	−	0.367678i	$-0.880153\pi$
$103$	−18.8760	−1.85991	−0.929953	+	0.367678i	$0.880153\pi$
$104$	−44.0973	−4.32409
$105$	−1.94456	−0.189770
$106$	31.0430	3.01516
$107$	8.84941	0.855504	0.427752	−	0.903896i	$-0.359306\pi$
$107$	8.84941	0.855504	0.427752	+	0.903896i	$0.359306\pi$
$108$	2.81148	0.270534
$109$	1.35922	0.130190	0.0650948	−	0.997879i	$-0.479265\pi$
$109$	1.35922	0.130190	0.0650948	+	0.997879i	$0.479265\pi$
$110$	6.35749	0.606163
$111$	−12.8984	−1.22426
$112$	−11.8330	−1.11812
$113$	5.41738	0.509624	0.254812	−	0.966991i	$-0.417986\pi$
$113$	5.41738	0.509624	0.254812	+	0.966991i	$0.417986\pi$
$114$	−15.8483	−1.48433
$115$	6.04819	0.563997
$116$	37.5130	3.48300
$117$	13.1287	1.21375
$118$	5.78451	0.532507
$119$	0.894458	0.0819949
$120$	−22.4970	−2.05368
$121$	−5.56110	−0.505555
$122$	−10.1746	−0.921163
$123$	12.7469	1.14935
$124$	27.8655	2.50240
$125$	−1.00000	−0.0894427
$126$	6.13760	0.546781
$127$	−3.64880	−0.323779	−0.161890	−	0.986809i	$-0.551759\pi$
$127$	−3.64880	−0.323779	−0.161890	+	0.986809i	$0.551759\pi$
$128$	−35.2947	−3.11964
$129$	−16.5298	−1.45537
$130$	12.8517	1.12717
$131$	14.3168	1.25087	0.625434	−	0.780277i	$-0.284922\pi$
$131$	14.3168	1.25087	0.625434	+	0.780277i	$0.284922\pi$
$132$	−30.4647	−2.65161
$133$	1.95428	0.169457
$134$	7.99135	0.690347
$135$	−0.517650	−0.0445522
$136$	10.3481	0.887346
$137$	−22.3469	−1.90923	−0.954614	−	0.297846i	$-0.903732\pi$
$137$	−22.3469	−1.90923	−0.954614	+	0.297846i	$0.903732\pi$
$138$	−39.6551	−3.37567
$139$	3.06162	0.259683	0.129842	−	0.991535i	$-0.458553\pi$
$139$	3.06162	0.259683	0.129842	+	0.991535i	$0.458553\pi$
$140$	4.39114	0.371119
$141$	14.7807	1.24476
$142$	23.3973	1.96346
$143$	10.9948	0.919430
$144$	40.7575	3.39646
$145$	−6.90691	−0.573587
$146$	12.8229	1.06123
$147$	15.2639	1.25895
$148$	29.1267	2.39420
$149$	−24.1231	−1.97624	−0.988120	−	0.153687i	$-0.950885\pi$
$149$	−24.1231	−1.97624	−0.988120	+	0.153687i	$0.950885\pi$
$150$	6.55652	0.535338
$151$	0.539495	0.0439035	0.0219517	−	0.999759i	$-0.493012\pi$
$151$	0.539495	0.0439035	0.0219517	+	0.999759i	$0.493012\pi$
$152$	22.6094	1.83386
$153$	−3.08086	−0.249073
$154$	5.14001	0.414194
$155$	−5.13061	−0.412100
$156$	−61.5847	−4.93072
$157$	−15.6259	−1.24708	−0.623541	−	0.781791i	$-0.714307\pi$
$157$	−15.6259	−1.24708	−0.623541	+	0.781791i	$0.714307\pi$
$158$	−35.1149	−2.79359
$159$	27.3890	2.17209
$160$	21.1904	1.67525
$161$	4.88994	0.385382
$162$	26.1681	2.05596
$163$	18.7234	1.46653	0.733265	−	0.679943i	$-0.237996\pi$
$163$	18.7234	1.46653	0.733265	+	0.679943i	$0.237996\pi$
$164$	−28.7845	−2.24769
$165$	5.60917	0.436673
$166$	−40.2365	−3.12296
$167$	−3.34078	−0.258517	−0.129259	−	0.991611i	$-0.541260\pi$
$167$	−3.34078	−0.258517	−0.129259	+	0.991611i	$0.541260\pi$
$168$	−18.1887	−1.40329
$169$	9.22604	0.709695
$170$	−3.01587	−0.231306
$171$	−6.73129	−0.514754
$172$	37.3270	2.84616
$173$	−21.1096	−1.60493	−0.802466	−	0.596698i	$-0.796479\pi$
$173$	−21.1096	−1.60493	−0.802466	+	0.596698i	$0.796479\pi$
$174$	45.2853	3.43307
$175$	−0.808497	−0.0611166
$176$	34.1329	2.57286
$177$	5.10363	0.383613
$178$	−25.4922	−1.91072
$179$	3.02603	0.226176	0.113088	−	0.993585i	$-0.463926\pi$
$179$	3.02603	0.226176	0.113088	+	0.993585i	$0.463926\pi$
$180$	−15.1248	−1.12733
$181$	−6.53800	−0.485966	−0.242983	−	0.970031i	$-0.578126\pi$
$181$	−6.53800	−0.485966	−0.242983	+	0.970031i	$0.578126\pi$
$182$	10.3906	0.770201
$183$	−8.97696	−0.663596
$184$	56.5726	4.17059
$185$	−5.36282	−0.394283
$186$	33.6389	2.46653
$187$	−2.58010	−0.188676
$188$	−33.3773	−2.43429
$189$	−0.418518	−0.0304427
$190$	−6.58929	−0.478037
$191$	−23.2044	−1.67901	−0.839506	−	0.543351i	$-0.817155\pi$
$191$	−23.2044	−1.67901	−0.839506	+	0.543351i	$0.817155\pi$
$192$	−68.5325	−4.94591
$193$	13.9883	1.00690	0.503451	−	0.864024i	$-0.332063\pi$
$193$	13.9883	1.00690	0.503451	+	0.864024i	$0.332063\pi$
$194$	45.9370	3.29808
$195$	11.3390	0.812002
$196$	−34.4684	−2.46203
$197$	16.6207	1.18418	0.592088	−	0.805873i	$-0.298304\pi$
$197$	16.6207	1.18418	0.592088	+	0.805873i	$0.298304\pi$
$198$	−17.7042	−1.25818
$199$	−6.86700	−0.486789	−0.243394	−	0.969927i	$-0.578261\pi$
$199$	−6.86700	−0.486789	−0.243394	+	0.969927i	$0.578261\pi$
$200$	−9.35364	−0.661402
$201$	7.05071	0.497319
$202$	−15.8891	−1.11795
$203$	−5.58421	−0.391935
$204$	14.4519	1.01183
$205$	5.29981	0.370155
$206$	51.4565	3.58514
$207$	−16.8428	−1.17066
$208$	68.9999	4.78428
$209$	−5.63720	−0.389933
$210$	5.30093	0.365799
$211$	−4.14333	−0.285239	−0.142619	−	0.989778i	$-0.545552\pi$
$211$	−4.14333	−0.285239	−0.142619	+	0.989778i	$0.545552\pi$
$212$	−61.8489	−4.24780
$213$	20.6433	1.41446
$214$	−24.1237	−1.64906
$215$	−6.87266	−0.468712
$216$	−4.84191	−0.329450
$217$	−4.14808	−0.281590
$218$	−3.70527	−0.250952
$219$	11.3136	0.764501
$220$	−12.6664	−0.853970
$221$	−5.21570	−0.350846
$222$	35.1615	2.35988
$223$	17.5698	1.17656	0.588279	−	0.808658i	$-0.299806\pi$
$223$	17.5698	1.17656	0.588279	+	0.808658i	$0.299806\pi$
$224$	17.1324	1.14471
$225$	2.78477	0.185652
$226$	−14.7679	−0.982349
$227$	17.8611	1.18548	0.592741	−	0.805393i	$-0.298046\pi$
$227$	17.8611	1.18548	0.592741	+	0.805393i	$0.298046\pi$
$228$	31.5755	2.09114
$229$	−1.42490	−0.0941598	−0.0470799	−	0.998891i	$-0.514992\pi$
$229$	−1.42490	−0.0941598	−0.0470799	+	0.998891i	$0.514992\pi$
$230$	−16.4875	−1.08716
$231$	4.53500	0.298381
$232$	−64.6047	−4.24151
$233$	−6.77624	−0.443926	−0.221963	−	0.975055i	$-0.571246\pi$
$233$	−6.77624	−0.443926	−0.221963	+	0.975055i	$0.571246\pi$
$234$	−35.7892	−2.33961
$235$	6.14544	0.400884
$236$	−11.5248	−0.750203
$237$	−30.9816	−2.01247
$238$	−2.43832	−0.158053
$239$	27.5229	1.78031	0.890155	−	0.455659i	$-0.150596\pi$
$239$	27.5229	1.78031	0.890155	+	0.455659i	$0.150596\pi$
$240$	35.2015	2.27224
$241$	−20.6434	−1.32976	−0.664880	−	0.746950i	$-0.731517\pi$
$241$	−20.6434	−1.32976	−0.664880	+	0.746950i	$0.731517\pi$
$242$	15.1597	0.974504
$243$	21.5350	1.38147
$244$	20.2714	1.29775
$245$	6.34633	0.405452
$246$	−34.7484	−2.21547
$247$	−11.3957	−0.725088
$248$	−47.9899	−3.04736
$249$	−35.5004	−2.24975
$250$	2.72603	0.172409
$251$	14.7499	0.931007	0.465504	−	0.885046i	$-0.345873\pi$
$251$	14.7499	0.931007	0.465504	+	0.885046i	$0.345873\pi$
$252$	−12.2283	−0.770312
$253$	−14.1053	−0.886790
$254$	9.94675	0.624114
$255$	−2.66088	−0.166631
$256$	39.2263	2.45164
$257$	18.0277	1.12454	0.562268	−	0.826955i	$-0.309929\pi$
$257$	18.0277	1.12454	0.562268	+	0.826955i	$0.309929\pi$
$258$	45.0608	2.80536
$259$	−4.33583	−0.269415
$260$	−25.6053	−1.58797
$261$	19.2342	1.19057
$262$	−39.0281	−2.41116
$263$	−7.22910	−0.445765	−0.222883	−	0.974845i	$-0.571547\pi$
$263$	−7.22910	−0.445765	−0.222883	+	0.974845i	$0.571547\pi$
$264$	52.4662	3.22907
$265$	11.3876	0.699536
$266$	−5.32742	−0.326645
$267$	−22.4916	−1.37646
$268$	−15.9216	−0.972569
$269$	20.5645	1.25384	0.626920	−	0.779083i	$-0.284315\pi$
$269$	20.5645	1.25384	0.626920	+	0.779083i	$0.284315\pi$
$270$	1.41113	0.0858785
$271$	11.8451	0.719538	0.359769	−	0.933041i	$-0.382856\pi$
$271$	11.8451	0.719538	0.359769	+	0.933041i	$0.382856\pi$
$272$	−16.1919	−0.981781
$273$	9.16754	0.554845
$274$	60.9184	3.68021
$275$	2.33214	0.140634
$276$	79.0073	4.75568
$277$	2.11630	0.127156	0.0635782	−	0.997977i	$-0.479749\pi$
$277$	2.11630	0.127156	0.0635782	+	0.997977i	$0.479749\pi$
$278$	−8.34607	−0.500564
$279$	14.2876	0.855375
$280$	−7.56239	−0.451939
$281$	−2.73816	−0.163345	−0.0816724	−	0.996659i	$-0.526026\pi$
$281$	−2.73816	−0.163345	−0.0816724	+	0.996659i	$0.526026\pi$
$282$	−40.2927	−2.39940
$283$	32.8231	1.95113	0.975564	−	0.219715i	$-0.0705128\pi$
$283$	32.8231	1.95113	0.975564	+	0.219715i	$0.0705128\pi$
$284$	−46.6159	−2.76615
$285$	−5.81368	−0.344373
$286$	−29.9721	−1.77229
$287$	4.28488	0.252929
$288$	−59.0105	−3.47723
$289$	−15.7761	−0.928003
$290$	18.8284	1.10564
$291$	40.5299	2.37590
$292$	−25.5479	−1.49508
$293$	−4.16742	−0.243463	−0.121731	−	0.992563i	$-0.538845\pi$
$293$	−4.16742	−0.243463	−0.121731	+	0.992563i	$0.538845\pi$
$294$	−41.6099	−2.42674
$295$	2.12195	0.123545
$296$	−50.1619	−2.91560
$297$	1.20723	0.0700508
$298$	65.7602	3.80939
$299$	−28.5139	−1.64900
$300$	−13.0630	−0.754191
$301$	−5.55653	−0.320273
$302$	−1.47068	−0.0846280
$303$	−14.0188	−0.805361
$304$	−35.3774	−2.02903
$305$	−3.73238	−0.213716
$306$	8.39851	0.480111
$307$	7.07006	0.403509	0.201755	−	0.979436i	$-0.435336\pi$
$307$	7.07006	0.403509	0.201755	+	0.979436i	$0.435336\pi$
$308$	−10.2408	−0.583522
$309$	45.3997	2.58270
$310$	13.9862	0.794362
$311$	−22.6984	−1.28711	−0.643553	−	0.765402i	$-0.722540\pi$
$311$	−22.6984	−1.28711	−0.643553	+	0.765402i	$0.722540\pi$
$312$	106.061	6.00451
$313$	−0.687466	−0.0388579	−0.0194290	−	0.999811i	$-0.506185\pi$
$313$	−0.687466	−0.0388579	−0.0194290	+	0.999811i	$0.506185\pi$
$314$	42.5966	2.40387
$315$	2.25148	0.126857
$316$	69.9616	3.93565
$317$	−3.41632	−0.191880	−0.0959398	−	0.995387i	$-0.530586\pi$
$317$	−3.41632	−0.191880	−0.0959398	+	0.995387i	$0.530586\pi$
$318$	−74.6632	−4.18691
$319$	16.1079	0.901870
$320$	−28.4940	−1.59286
$321$	−21.2842	−1.18797
$322$	−13.3301	−0.742859
$323$	2.67418	0.148795
$324$	−52.1363	−2.89646
$325$	4.71445	0.261511
$326$	−51.0405	−2.82687
$327$	−3.26913	−0.180783
$328$	49.5726	2.73719
$329$	4.96857	0.273926
$330$	−15.2908	−0.841729
$331$	0.794603	0.0436753	0.0218377	−	0.999762i	$-0.493048\pi$
$331$	0.794603	0.0436753	0.0218377	+	0.999762i	$0.493048\pi$
$332$	80.1657	4.39967
$333$	14.9343	0.818392
$334$	9.10707	0.498316
$335$	2.93150	0.160165
$336$	28.4603	1.55263
$337$	21.7963	1.18732	0.593659	−	0.804717i	$-0.297683\pi$
$337$	21.7963	1.18732	0.593659	+	0.804717i	$0.297683\pi$
$338$	−25.1505	−1.36800
$339$	−13.0296	−0.707673
$340$	6.00870	0.325867
$341$	11.9653	0.647958
$342$	18.3497	0.992237
$343$	10.7905	0.582631
$344$	−64.2844	−3.46598
$345$	−14.5468	−0.783176
$346$	57.5453	3.09365
$347$	19.2735	1.03465	0.517327	−	0.855788i	$-0.326927\pi$
$347$	19.2735	1.03465	0.517327	+	0.855788i	$0.326927\pi$
$348$	−90.2247	−4.83655
$349$	9.23824	0.494512	0.247256	−	0.968950i	$-0.420471\pi$
$349$	9.23824	0.494512	0.247256	+	0.968950i	$0.420471\pi$
$350$	2.20399	0.117808
$351$	2.44043	0.130261
$352$	−49.4191	−2.63405
$353$	0.389624	0.0207376	0.0103688	−	0.999946i	$-0.496699\pi$
$353$	0.389624	0.0207376	0.0103688	+	0.999946i	$0.496699\pi$
$354$	−13.9126	−0.739449
$355$	8.58294	0.455535
$356$	50.7896	2.69184
$357$	−2.15131	−0.113860
$358$	−8.24903	−0.435975
$359$	−2.80897	−0.148252	−0.0741260	−	0.997249i	$-0.523617\pi$
$359$	−2.80897	−0.148252	−0.0741260	+	0.997249i	$0.523617\pi$
$360$	26.0478	1.37284
$361$	−13.1573	−0.692488
$362$	17.8228	0.936744
$363$	13.3753	0.702022
$364$	−20.7018	−1.08507
$365$	4.70389	0.246213
$366$	24.4715	1.27914
$367$	−15.5804	−0.813290	−0.406645	−	0.913586i	$-0.633301\pi$
$367$	−15.5804	−0.813290	−0.406645	+	0.913586i	$0.633301\pi$
$368$	−88.5203	−4.61444
$369$	−14.7588	−0.768312
$370$	14.6192	0.760017
$371$	9.20686	0.477996
$372$	−67.0209	−3.47487
$373$	−11.0196	−0.570571	−0.285285	−	0.958443i	$-0.592088\pi$
$373$	−11.0196	−0.570571	−0.285285	+	0.958443i	$0.592088\pi$
$374$	7.03344	0.363690
$375$	2.40516	0.124202
$376$	57.4822	2.96442
$377$	32.5623	1.67704
$378$	1.14089	0.0586812
$379$	−30.4453	−1.56387	−0.781934	−	0.623361i	$-0.785767\pi$
$379$	−30.4453	−1.56387	−0.781934	+	0.623361i	$0.785767\pi$
$380$	13.1282	0.673465
$381$	8.77594	0.449605
$382$	63.2559	3.23645
$383$	4.83387	0.246999	0.123500	−	0.992345i	$-0.460588\pi$
$383$	4.83387	0.246999	0.123500	+	0.992345i	$0.460588\pi$
$384$	84.8892	4.33198
$385$	1.88553	0.0960956
$386$	−38.1326	−1.94090
$387$	19.1388	0.972881
$388$	−91.5231	−4.64638
$389$	−18.9336	−0.959972	−0.479986	−	0.877276i	$-0.659358\pi$
$389$	−18.9336	−0.959972	−0.479986	+	0.877276i	$0.659358\pi$
$390$	−30.9104	−1.56521
$391$	6.69125	0.338391
$392$	59.3613	2.99820
$393$	−34.4342	−1.73698
$394$	−45.3085	−2.28261
$395$	−12.8813	−0.648131
$396$	35.2731	1.77254
$397$	32.3366	1.62293	0.811463	−	0.584403i	$-0.198671\pi$
$397$	32.3366	1.62293	0.811463	+	0.584403i	$0.198671\pi$
$398$	18.7196	0.938330
$399$	−4.70034	−0.235312
$400$	14.6358	0.731791
$401$	25.7421	1.28550	0.642751	−	0.766075i	$-0.277793\pi$
$401$	25.7421	1.28550	0.642751	+	0.766075i	$0.277793\pi$
$402$	−19.2204	−0.958628
$403$	24.1880	1.20489
$404$	31.6568	1.57499
$405$	9.59935	0.476996
$406$	15.2227	0.755491
$407$	12.5069	0.619943
$408$	−24.8889	−1.23218
$409$	20.9093	1.03390	0.516948	−	0.856017i	$-0.327068\pi$
$409$	20.9093	1.03390	0.516948	+	0.856017i	$0.327068\pi$
$410$	−14.4474	−0.713508
$411$	53.7479	2.65119
$412$	−102.520	−5.05079
$413$	1.71559	0.0844189
$414$	45.9141	2.25655
$415$	−14.7601	−0.724546
$416$	−99.9011	−4.89806
$417$	−7.36368	−0.360601
$418$	15.3672	0.751633
$419$	−30.5641	−1.49315	−0.746576	−	0.665300i	$-0.768304\pi$
$419$	−30.5641	−1.49315	−0.746576	+	0.665300i	$0.768304\pi$
$420$	−10.5614	−0.515342
$421$	36.7949	1.79327	0.896637	−	0.442766i	$-0.146003\pi$
$421$	36.7949	1.79327	0.896637	+	0.442766i	$0.146003\pi$
$422$	11.2948	0.549824
$423$	−17.1137	−0.832094
$424$	106.516	5.17286
$425$	−1.10632	−0.0536645
$426$	−56.2743	−2.72650
$427$	−3.01762	−0.146033
$428$	48.0632	2.32322
$429$	−26.4442	−1.27674
$430$	18.7351	0.903486
$431$	−31.5250	−1.51851	−0.759253	−	0.650796i	$-0.774435\pi$
$431$	−31.5250	−1.51851	−0.759253	+	0.650796i	$0.774435\pi$
$432$	7.57623	0.364512
$433$	30.2868	1.45549	0.727745	−	0.685848i	$-0.240568\pi$
$433$	30.2868	1.45549	0.727745	+	0.685848i	$0.240568\pi$
$434$	11.3078	0.542791
$435$	16.6122	0.796494
$436$	7.38223	0.353545
$437$	14.6195	0.699347
$438$	−30.8411	−1.47365
$439$	−5.80719	−0.277162	−0.138581	−	0.990351i	$-0.544254\pi$
$439$	−5.80719	−0.277162	−0.138581	+	0.990351i	$0.544254\pi$
$440$	21.8140	1.03994
$441$	−17.6731	−0.841577
$442$	14.2182	0.676289
$443$	9.58757	0.455519	0.227760	−	0.973717i	$-0.426860\pi$
$443$	9.58757	0.455519	0.227760	+	0.973717i	$0.426860\pi$
$444$	−70.0544	−3.32463
$445$	−9.35140	−0.443299
$446$	−47.8957	−2.26793
$447$	58.0197	2.74424
$448$	−23.0373	−1.08841
$449$	−8.96575	−0.423120	−0.211560	−	0.977365i	$-0.567854\pi$
$449$	−8.96575	−0.423120	−0.211560	+	0.977365i	$0.567854\pi$
$450$	−7.59138	−0.357861
$451$	−12.3599	−0.582006
$452$	29.4231	1.38394
$453$	−1.29757	−0.0609651
$454$	−48.6898	−2.28513
$455$	3.81162	0.178691
$456$	−54.3791	−2.54653
$457$	2.86309	0.133930	0.0669648	−	0.997755i	$-0.478668\pi$
$457$	2.86309	0.133930	0.0669648	+	0.997755i	$0.478668\pi$
$458$	3.88431	0.181502
$459$	−0.572688	−0.0267308
$460$	32.8491	1.53160
$461$	24.9444	1.16177	0.580887	−	0.813984i	$-0.302706\pi$
$461$	24.9444	1.16177	0.580887	+	0.813984i	$0.302706\pi$
$462$	−12.3625	−0.575157
$463$	12.7239	0.591331	0.295665	−	0.955292i	$-0.404459\pi$
$463$	12.7239	0.591331	0.295665	+	0.955292i	$0.404459\pi$
$464$	101.088	4.69291
$465$	12.3399	0.572250
$466$	18.4722	0.855710
$467$	−6.36688	−0.294624	−0.147312	−	0.989090i	$-0.547062\pi$
$467$	−6.36688	−0.294624	−0.147312	+	0.989090i	$0.547062\pi$
$468$	71.3049	3.29607
$469$	2.37011	0.109441
$470$	−16.7526	−0.772741
$471$	37.5827	1.73172
$472$	19.8480	0.913578
$473$	16.0280	0.736970
$474$	84.4569	3.87923
$475$	−2.41717	−0.110908
$476$	4.85801	0.222667
$477$	−31.7120	−1.45199
$478$	−75.0283	−3.43171
$479$	3.00664	0.137377	0.0686885	−	0.997638i	$-0.478119\pi$
$479$	3.00664	0.137377	0.0686885	+	0.997638i	$0.478119\pi$
$480$	−50.9662	−2.32628
$481$	25.2828	1.15279
$482$	56.2746	2.56324
$483$	−11.7611	−0.535148
$484$	−30.2036	−1.37289
$485$	16.8513	0.765176
$486$	−58.7050	−2.66291
$487$	31.5299	1.42876	0.714378	−	0.699760i	$-0.246710\pi$
$487$	31.5299	1.42876	0.714378	+	0.699760i	$0.246710\pi$
$488$	−34.9114	−1.58036
$489$	−45.0327	−2.03645
$490$	−17.3003	−0.781547
$491$	1.04144	0.0469997	0.0234999	−	0.999724i	$-0.492519\pi$
$491$	1.04144	0.0469997	0.0234999	+	0.999724i	$0.492519\pi$
$492$	69.2313	3.12119
$493$	−7.64127	−0.344145
$494$	31.0649	1.39767
$495$	−6.49450	−0.291906
$496$	75.0907	3.37167
$497$	6.93928	0.311269
$498$	96.7752	4.33660
$499$	13.0998	0.586426	0.293213	−	0.956047i	$-0.405275\pi$
$499$	13.0998	0.586426	0.293213	+	0.956047i	$0.405275\pi$
$500$	−5.43123	−0.242892
$501$	8.03510	0.358982
$502$	−40.2087	−1.79460
$503$	22.1933	0.989552	0.494776	−	0.869020i	$-0.335250\pi$
$503$	22.1933	0.989552	0.494776	+	0.869020i	$0.335250\pi$
$504$	21.0596	0.938067
$505$	−5.82866	−0.259372
$506$	38.4513	1.70937
$507$	−22.1901	−0.985495
$508$	−19.8175	−0.879260
$509$	−7.79453	−0.345487	−0.172743	−	0.984967i	$-0.555263\pi$
$509$	−7.79453	−0.345487	−0.172743	+	0.984967i	$0.555263\pi$
$510$	7.25363	0.321196
$511$	3.80308	0.168238
$512$	−36.3426	−1.60613
$513$	−1.25125	−0.0552440
$514$	−49.1440	−2.16765
$515$	18.8760	0.831775
$516$	−89.7774	−3.95223
$517$	−14.3320	−0.630323
$518$	11.8196	0.519323
$519$	50.7718	2.22864
$520$	44.0973	1.93379
$521$	22.4051	0.981587	0.490794	−	0.871276i	$-0.336707\pi$
$521$	22.4051	0.981587	0.490794	+	0.871276i	$0.336707\pi$
$522$	−52.4329	−2.29493
$523$	11.8832	0.519616	0.259808	−	0.965660i	$-0.416341\pi$
$523$	11.8832	0.519616	0.259808	+	0.965660i	$0.416341\pi$
$524$	77.7580	3.39688
$525$	1.94456	0.0848676
$526$	19.7067	0.859254
$527$	−5.67611	−0.247255
$528$	−82.0949	−3.57272
$529$	13.5806	0.590461
$530$	−31.0430	−1.34842
$531$	−5.90917	−0.256436
$532$	10.6141	0.460181
$533$	−24.9857	−1.08225
$534$	61.3127	2.65326
$535$	−8.84941	−0.382593
$536$	27.4202	1.18437
$537$	−7.27806	−0.314072
$538$	−56.0595	−2.41689
$539$	−14.8006	−0.637505
$540$	−2.81148	−0.120987
$541$	−36.2814	−1.55986	−0.779931	−	0.625866i	$-0.784746\pi$
$541$	−36.2814	−1.55986	−0.779931	+	0.625866i	$0.784746\pi$
$542$	−32.2900	−1.38698
$543$	15.7249	0.674820
$544$	23.4434	1.00513
$545$	−1.35922	−0.0582225
$546$	−24.9910	−1.06951
$547$	24.6833	1.05538	0.527691	−	0.849436i	$-0.323058\pi$
$547$	24.6833	1.05538	0.527691	+	0.849436i	$0.323058\pi$
$548$	−121.371	−5.18473
$549$	10.3938	0.443599
$550$	−6.35749	−0.271084
$551$	−16.6952	−0.711240
$552$	−136.066	−5.79135
$553$	−10.4145	−0.442871
$554$	−5.76910	−0.245106
$555$	12.8984	0.547508
$556$	16.6284	0.705201
$557$	−41.1112	−1.74194	−0.870969	−	0.491338i	$-0.836508\pi$
$557$	−41.1112	−1.74194	−0.870969	+	0.491338i	$0.836508\pi$
$558$	−38.9484	−1.64882
$559$	32.4008	1.37041
$560$	11.8330	0.500036
$561$	6.20555	0.261999
$562$	7.46429	0.314862
$563$	−43.5610	−1.83588	−0.917939	−	0.396722i	$-0.870148\pi$
$563$	−43.5610	−1.83588	−0.917939	+	0.396722i	$0.870148\pi$
$564$	80.2776	3.38030
$565$	−5.41738	−0.227911
$566$	−89.4766	−3.76098
$567$	7.76105	0.325933
$568$	80.2817	3.36855
$569$	−19.1348	−0.802172	−0.401086	−	0.916040i	$-0.631367\pi$
$569$	−19.1348	−0.802172	−0.401086	+	0.916040i	$0.631367\pi$
$570$	15.8483	0.663811
$571$	−25.4406	−1.06466	−0.532329	−	0.846538i	$-0.678683\pi$
$571$	−25.4406	−1.06466	−0.532329	+	0.846538i	$0.678683\pi$
$572$	59.7152	2.49682
$573$	55.8102	2.33150
$574$	−11.6807	−0.487544
$575$	−6.04819	−0.252227
$576$	79.3494	3.30623
$577$	−7.14819	−0.297583	−0.148791	−	0.988869i	$-0.547538\pi$
$577$	−7.14819	−0.297583	−0.148791	+	0.988869i	$0.547538\pi$
$578$	43.0060	1.78881
$579$	−33.6441	−1.39820
$580$	−37.5130	−1.55764
$581$	−11.9335	−0.495086
$582$	−110.486	−4.57978
$583$	−26.5576	−1.09990
$584$	43.9985	1.82067
$585$	−13.1287	−0.542804
$586$	11.3605	0.469298
$587$	10.7419	0.443366	0.221683	−	0.975119i	$-0.428845\pi$
$587$	10.7419	0.443366	0.221683	+	0.975119i	$0.428845\pi$
$588$	82.9019	3.41882
$589$	−12.4016	−0.510998
$590$	−5.78451	−0.238145
$591$	−39.9754	−1.64437
$592$	78.4894	3.22589
$593$	−9.81925	−0.403228	−0.201614	−	0.979465i	$-0.564619\pi$
$593$	−9.81925	−0.403228	−0.201614	+	0.979465i	$0.564619\pi$
$594$	−3.29095	−0.135030
$595$	−0.894458	−0.0366692
$596$	−131.018	−5.36671
$597$	16.5162	0.675963
$598$	77.7297	3.17860
$599$	−14.8596	−0.607147	−0.303574	−	0.952808i	$-0.598180\pi$
$599$	−14.8596	−0.607147	−0.303574	+	0.952808i	$0.598180\pi$
$600$	22.4970	0.918435
$601$	14.9859	0.611286	0.305643	−	0.952146i	$-0.401129\pi$
$601$	14.9859	0.611286	0.305643	+	0.952146i	$0.401129\pi$
$602$	15.1473	0.617356
$603$	−8.16356	−0.332446
$604$	2.93012	0.119225
$605$	5.56110	0.226091
$606$	38.2158	1.55241
$607$	−37.3007	−1.51399	−0.756994	−	0.653422i	$-0.773333\pi$
$607$	−37.3007	−1.51399	−0.756994	+	0.653422i	$0.773333\pi$
$608$	51.2209	2.07728
$609$	13.4309	0.544248
$610$	10.1746	0.411957
$611$	−28.9724	−1.17210
$612$	−16.7329	−0.676386
$613$	45.7820	1.84912	0.924560	−	0.381037i	$-0.124433\pi$
$613$	45.7820	1.84912	0.924560	+	0.381037i	$0.124433\pi$
$614$	−19.2732	−0.777802
$615$	−12.7469	−0.514004
$616$	17.6366	0.710598
$617$	−24.7715	−0.997263	−0.498631	−	0.866814i	$-0.666164\pi$
$617$	−24.7715	−0.997263	−0.498631	+	0.866814i	$0.666164\pi$
$618$	−123.761	−4.97839
$619$	−8.74661	−0.351556	−0.175778	−	0.984430i	$-0.556244\pi$
$619$	−8.74661	−0.351556	−0.175778	+	0.984430i	$0.556244\pi$
$620$	−27.8655	−1.11911
$621$	−3.13084	−0.125636
$622$	61.8764	2.48102
$623$	−7.56057	−0.302908
$624$	−165.955	−6.64354
$625$	1.00000	0.0400000
$626$	1.87405	0.0749022
$627$	13.5583	0.541468
$628$	−84.8679	−3.38660
$629$	−5.93301	−0.236565
$630$	−6.13760	−0.244528
$631$	−15.2845	−0.608465	−0.304233	−	0.952598i	$-0.598400\pi$
$631$	−15.2845	−0.608465	−0.304233	+	0.952598i	$0.598400\pi$
$632$	−120.487	−4.79273
$633$	9.96536	0.396087
$634$	9.31298	0.369866
$635$	3.64880	0.144798
$636$	148.756	5.89856
$637$	−29.9195	−1.18545
$638$	−43.9106	−1.73844
$639$	−23.9016	−0.945531
$640$	35.2947	1.39514
$641$	−31.4062	−1.24047	−0.620235	−	0.784416i	$-0.712963\pi$
$641$	−31.4062	−1.24047	−0.620235	+	0.784416i	$0.712963\pi$
$642$	58.0214	2.28992
$643$	−24.1761	−0.953414	−0.476707	−	0.879062i	$-0.658170\pi$
$643$	−24.1761	−0.953414	−0.476707	+	0.879062i	$0.658170\pi$
$644$	26.5584	1.04655
$645$	16.5298	0.650861
$646$	−7.28988	−0.286816
$647$	27.0237	1.06241	0.531206	−	0.847243i	$-0.321739\pi$
$647$	27.0237	1.06241	0.531206	+	0.847243i	$0.321739\pi$
$648$	89.7889	3.52724
$649$	−4.94871	−0.194254
$650$	−12.8517	−0.504086
$651$	9.97678	0.391021
$652$	101.691	3.98253
$653$	−4.61113	−0.180448	−0.0902238	−	0.995922i	$-0.528758\pi$
$653$	−4.61113	−0.180448	−0.0902238	+	0.995922i	$0.528758\pi$
$654$	8.91175	0.348477
$655$	−14.3168	−0.559405
$656$	−77.5672	−3.02849
$657$	−13.0993	−0.511051
$658$	−13.5445	−0.528018
$659$	12.1942	0.475017	0.237509	−	0.971385i	$-0.423669\pi$
$659$	12.1942	0.475017	0.237509	+	0.971385i	$0.423669\pi$
$660$	30.4647	1.18584
$661$	−5.34955	−0.208073	−0.104037	−	0.994573i	$-0.533176\pi$
$661$	−5.34955	−0.208073	−0.104037	+	0.994573i	$0.533176\pi$
$662$	−2.16611	−0.0841882
$663$	12.5446	0.487191
$664$	−138.061	−5.35780
$665$	−1.95428	−0.0757837
$666$	−40.7112	−1.57753
$667$	−41.7743	−1.61751
$668$	−18.1446	−0.702034
$669$	−42.2580	−1.63379
$670$	−7.99135	−0.308733
$671$	8.70445	0.336032
$672$	−41.2060	−1.58956
$673$	−15.5851	−0.600761	−0.300381	−	0.953819i	$-0.597114\pi$
$673$	−15.5851	−0.600761	−0.300381	+	0.953819i	$0.597114\pi$
$674$	−59.4172	−2.28867
$675$	0.517650	0.0199244
$676$	50.1088	1.92726
$677$	−34.2489	−1.31629	−0.658146	−	0.752891i	$-0.728659\pi$
$677$	−34.2489	−1.31629	−0.658146	+	0.752891i	$0.728659\pi$
$678$	35.5192	1.36411
$679$	13.6242	0.522848
$680$	−10.3481	−0.396833
$681$	−42.9587	−1.64618
$682$	−32.6178	−1.24900
$683$	4.83331	0.184941	0.0924707	−	0.995715i	$-0.470524\pi$
$683$	4.83331	0.184941	0.0924707	+	0.995715i	$0.470524\pi$
$684$	−36.5592	−1.39788
$685$	22.3469	0.853833
$686$	−29.4151	−1.12307
$687$	3.42710	0.130752
$688$	100.587	3.83485
$689$	−53.6864	−2.04529
$690$	39.6551	1.50964
$691$	−4.25906	−0.162022	−0.0810112	−	0.996713i	$-0.525815\pi$
$691$	−4.25906	−0.162022	−0.0810112	+	0.996713i	$0.525815\pi$
$692$	−114.651	−4.35838
$693$	−5.25078	−0.199461
$694$	−52.5401	−1.99439
$695$	−3.06162	−0.116134
$696$	155.384	5.88983
$697$	5.86330	0.222088
$698$	−25.1837	−0.953218
$699$	16.2979	0.616444
$700$	−4.39114	−0.165969
$701$	−9.76870	−0.368959	−0.184479	−	0.982836i	$-0.559060\pi$
$701$	−9.76870	−0.368959	−0.184479	+	0.982836i	$0.559060\pi$
$702$	−6.65269	−0.251090
$703$	−12.9629	−0.488904
$704$	66.4521	2.50451
$705$	−14.7807	−0.556675
$706$	−1.06213	−0.0399737
$707$	−4.71246	−0.177230
$708$	27.7190	1.04174
$709$	15.0909	0.566752	0.283376	−	0.959009i	$-0.408546\pi$
$709$	15.0909	0.566752	0.283376	+	0.959009i	$0.408546\pi$
$710$	−23.3973	−0.878087
$711$	35.8716	1.34529
$712$	−87.4696	−3.27806
$713$	−31.0309	−1.16212
$714$	5.86454	0.219475
$715$	−10.9948	−0.411181
$716$	16.4350	0.614207
$717$	−66.1969	−2.47217
$718$	7.65734	0.285769
$719$	−12.6648	−0.472318	−0.236159	−	0.971714i	$-0.575889\pi$
$719$	−12.6648	−0.472318	−0.236159	+	0.971714i	$0.575889\pi$
$720$	−40.7575	−1.51894
$721$	15.2612	0.568356
$722$	35.8671	1.33483
$723$	49.6507	1.84653
$724$	−35.5094	−1.31970
$725$	6.90691	0.256516
$726$	−36.4615	−1.35321
$727$	24.3449	0.902903	0.451452	−	0.892296i	$-0.350906\pi$
$727$	24.3449	0.902903	0.451452	+	0.892296i	$0.350906\pi$
$728$	35.6525	1.32137
$729$	−22.9970	−0.851739
$730$	−12.8229	−0.474598
$731$	−7.60338	−0.281221
$732$	−48.7560	−1.80207
$733$	15.2789	0.564340	0.282170	−	0.959364i	$-0.408946\pi$
$733$	15.2789	0.564340	0.282170	+	0.959364i	$0.408946\pi$
$734$	42.4726	1.56769
$735$	−15.2639	−0.563018
$736$	128.164	4.72417
$737$	−6.83668	−0.251832
$738$	40.2329	1.48099
$739$	−23.1873	−0.852960	−0.426480	−	0.904497i	$-0.640247\pi$
$739$	−23.1873	−0.852960	−0.426480	+	0.904497i	$0.640247\pi$
$740$	−29.1267	−1.07072
$741$	27.4083	1.00687
$742$	−25.0982	−0.921383
$743$	−13.1723	−0.483245	−0.241623	−	0.970370i	$-0.577680\pi$
$743$	−13.1723	−0.483245	−0.241623	+	0.970370i	$0.577680\pi$
$744$	115.423	4.23162
$745$	24.1231	0.883801
$746$	30.0396	1.09983
$747$	41.1036	1.50390
$748$	−14.0131	−0.512371
$749$	−7.15472	−0.261428
$750$	−6.55652	−0.239410
$751$	−42.4450	−1.54884	−0.774421	−	0.632671i	$-0.781959\pi$
$751$	−42.4450	−1.54884	−0.774421	+	0.632671i	$0.781959\pi$
$752$	−89.9436	−3.27990
$753$	−35.4759	−1.29281
$754$	−88.7657	−3.23266
$755$	−0.539495	−0.0196342
$756$	−2.27307	−0.0826708
$757$	15.7421	0.572155	0.286077	−	0.958207i	$-0.407649\pi$
$757$	15.7421	0.572155	0.286077	+	0.958207i	$0.407649\pi$
$758$	82.9947	3.01450
$759$	33.9253	1.23141
$760$	−22.6094	−0.820129
$761$	−32.5206	−1.17887	−0.589436	−	0.807815i	$-0.700650\pi$
$761$	−32.5206	−1.17887	−0.589436	+	0.807815i	$0.700650\pi$
$762$	−23.9235	−0.866656
$763$	−1.09892	−0.0397837
$764$	−126.029	−4.55955
$765$	3.08086	0.111389
$766$	−13.1773	−0.476114
$767$	−10.0039	−0.361218
$768$	−94.3453	−3.40439
$769$	4.36869	0.157539	0.0787695	−	0.996893i	$-0.474901\pi$
$769$	4.36869	0.157539	0.0787695	+	0.996893i	$0.474901\pi$
$770$	−5.14001	−0.185233
$771$	−43.3594	−1.56155
$772$	75.9739	2.73436
$773$	−24.5807	−0.884105	−0.442053	−	0.896989i	$-0.645750\pi$
$773$	−24.5807	−0.884105	−0.442053	+	0.896989i	$0.645750\pi$
$774$	−52.1730	−1.87532
$775$	5.13061	0.184297
$776$	157.621	5.65825
$777$	10.4283	0.374115
$778$	51.6136	1.85044
$779$	12.8106	0.458987
$780$	61.5847	2.20509
$781$	−20.0167	−0.716252
$782$	−18.2405	−0.652280
$783$	3.57536	0.127773
$784$	−92.8838	−3.31728
$785$	15.6259	0.557712
$786$	93.8686	3.34818
$787$	11.5095	0.410271	0.205135	−	0.978734i	$-0.434237\pi$
$787$	11.5095	0.410271	0.205135	+	0.978734i	$0.434237\pi$
$788$	90.2709	3.21577
$789$	17.3871	0.618997
$790$	35.1149	1.24933
$791$	−4.37994	−0.155733
$792$	−60.7472	−2.15856
$793$	17.5961	0.624857
$794$	−88.1505	−3.12834
$795$	−27.3890	−0.971388
$796$	−37.2963	−1.32193
$797$	−10.8597	−0.384669	−0.192334	−	0.981329i	$-0.561606\pi$
$797$	−10.8597	−0.384669	−0.192334	+	0.981329i	$0.561606\pi$
$798$	12.8133	0.453585
$799$	6.79884	0.240525
$800$	−21.1904	−0.749194
$801$	26.0415	0.920132
$802$	−70.1738	−2.47792
$803$	−10.9701	−0.387128
$804$	38.2940	1.35053
$805$	−4.88994	−0.172348
$806$	−65.9372	−2.32254
$807$	−49.4609	−1.74110
$808$	−54.5192	−1.91798
$809$	−1.37513	−0.0483469	−0.0241735	−	0.999708i	$-0.507695\pi$
$809$	−1.37513	−0.0483469	−0.0241735	+	0.999708i	$0.507695\pi$
$810$	−26.1681	−0.919454
$811$	−4.77273	−0.167593	−0.0837966	−	0.996483i	$-0.526705\pi$
$811$	−4.77273	−0.167593	−0.0837966	+	0.996483i	$0.526705\pi$
$812$	−30.3292	−1.06435
$813$	−28.4893	−0.999162
$814$	−34.0941	−1.19500
$815$	−18.7234	−0.655852
$816$	38.9442	1.36332
$817$	−16.6124	−0.581195
$818$	−56.9993	−1.99293
$819$	−10.6145	−0.370901
$820$	28.7845	1.00520
$821$	31.2267	1.08982	0.544909	−	0.838495i	$-0.316564\pi$
$821$	31.2267	1.08982	0.544909	+	0.838495i	$0.316564\pi$
$822$	−146.518	−5.11041
$823$	−35.2279	−1.22797	−0.613983	−	0.789319i	$-0.710434\pi$
$823$	−35.2279	−1.22797	−0.613983	+	0.789319i	$0.710434\pi$
$824$	176.559	6.15073
$825$	−5.60917	−0.195286
$826$	−4.67676	−0.162725
$827$	−49.1417	−1.70882	−0.854412	−	0.519596i	$-0.826082\pi$
$827$	−49.1417	−1.70882	−0.854412	+	0.519596i	$0.826082\pi$
$828$	−91.4774	−3.17906
$829$	−39.0335	−1.35569	−0.677845	−	0.735205i	$-0.737086\pi$
$829$	−39.0335	−1.35569	−0.677845	+	0.735205i	$0.737086\pi$
$830$	40.2365	1.39663
$831$	−5.09004	−0.176572
$832$	134.334	4.65718
$833$	7.02109	0.243266
$834$	20.0736	0.695092
$835$	3.34078	0.115612
$836$	−30.6170	−1.05891
$837$	2.65586	0.0917999
$838$	83.3185	2.87819
$839$	36.9243	1.27477	0.637385	−	0.770546i	$-0.280016\pi$
$839$	36.9243	1.27477	0.637385	+	0.770546i	$0.280016\pi$
$840$	18.1887	0.627571
$841$	18.7054	0.645013
$842$	−100.304	−3.45670
$843$	6.58569	0.226823
$844$	−22.5034	−0.774599
$845$	−9.22604	−0.317385
$846$	46.6523	1.60394
$847$	4.49613	0.154489
$848$	−166.667	−5.72338
$849$	−78.9446	−2.70937
$850$	3.01587	0.103443
$851$	−32.4354	−1.11187
$852$	112.119	3.84112
$853$	29.0003	0.992951	0.496476	−	0.868051i	$-0.334627\pi$
$853$	29.0003	0.992951	0.496476	+	0.868051i	$0.334627\pi$
$854$	8.22612	0.281492
$855$	6.73129	0.230205
$856$	−82.7742	−2.82916
$857$	−44.7873	−1.52991	−0.764953	−	0.644087i	$-0.777238\pi$
$857$	−44.7873	−1.52991	−0.764953	+	0.644087i	$0.777238\pi$
$858$	72.0875	2.46103
$859$	17.7195	0.604583	0.302292	−	0.953215i	$-0.402248\pi$
$859$	17.7195	0.604583	0.302292	+	0.953215i	$0.402248\pi$
$860$	−37.3270	−1.27284
$861$	−10.3058	−0.351221
$862$	85.9381	2.92706
$863$	35.7448	1.21677	0.608384	−	0.793643i	$-0.291818\pi$
$863$	35.7448	1.21677	0.608384	+	0.793643i	$0.291818\pi$
$864$	−10.9692	−0.373180
$865$	21.1096	0.717747
$866$	−82.5626	−2.80559
$867$	37.9439	1.28864
$868$	−22.5292	−0.764690
$869$	30.0412	1.01908
$870$	−45.2853	−1.53532
$871$	−13.8204	−0.468286
$872$	−12.7136	−0.430538
$873$	−46.9270	−1.58824
$874$	−39.8533	−1.34806
$875$	0.808497	0.0273322
$876$	61.4467	2.07609
$877$	−14.6366	−0.494241	−0.247121	−	0.968985i	$-0.579484\pi$
$877$	−14.6366	−0.494241	−0.247121	+	0.968985i	$0.579484\pi$
$878$	15.8306	0.534255
$879$	10.0233	0.338077
$880$	−34.1329	−1.15062
$881$	−1.63269	−0.0550068	−0.0275034	−	0.999622i	$-0.508756\pi$
$881$	−1.63269	−0.0550068	−0.0275034	+	0.999622i	$0.508756\pi$
$882$	48.1774	1.62222
$883$	34.5322	1.16210	0.581051	−	0.813867i	$-0.302642\pi$
$883$	34.5322	1.16210	0.581051	+	0.813867i	$0.302642\pi$
$884$	−28.3277	−0.952764
$885$	−5.10363	−0.171557
$886$	−26.1360	−0.878056
$887$	−4.00281	−0.134401	−0.0672006	−	0.997739i	$-0.521407\pi$
$887$	−4.00281	−0.134401	−0.0672006	+	0.997739i	$0.521407\pi$
$888$	120.647	4.04866
$889$	2.95005	0.0989414
$890$	25.4922	0.854500
$891$	−22.3871	−0.749995
$892$	95.4255	3.19508
$893$	14.8546	0.497090
$894$	−158.164	−5.28978
$895$	−3.02603	−0.101149
$896$	28.5356	0.953309
$897$	68.5804	2.28983
$898$	24.4409	0.815603
$899$	35.4366	1.18188
$900$	15.1248	0.504159
$901$	12.5984	0.419713
$902$	33.6935	1.12187
$903$	13.3643	0.444737
$904$	−50.6723	−1.68533
$905$	6.53800	0.217330
$906$	3.53721	0.117516
$907$	−29.0168	−0.963485	−0.481743	−	0.876313i	$-0.659996\pi$
$907$	−29.0168	−0.963485	−0.481743	+	0.876313i	$0.659996\pi$
$908$	97.0077	3.21931
$909$	16.2315	0.538365
$910$	−10.3906	−0.344444
$911$	−19.3080	−0.639702	−0.319851	−	0.947468i	$-0.603633\pi$
$911$	−19.3080	−0.639702	−0.319851	+	0.947468i	$0.603633\pi$
$912$	85.0881	2.81755
$913$	34.4228	1.13923
$914$	−7.80486	−0.258162
$915$	8.97696	0.296769
$916$	−7.73894	−0.255702
$917$	−11.5751	−0.382244
$918$	1.56116	0.0515261
$919$	16.8456	0.555686	0.277843	−	0.960626i	$-0.410380\pi$
$919$	16.8456	0.555686	0.277843	+	0.960626i	$0.410380\pi$
$920$	−56.5726	−1.86514
$921$	−17.0046	−0.560320
$922$	−67.9991	−2.23943
$923$	−40.4638	−1.33188
$924$	24.6306	0.810288
$925$	5.36282	0.176329
$926$	−34.6858	−1.13985
$927$	−52.5654	−1.72647
$928$	−146.360	−4.80451
$929$	−8.67530	−0.284627	−0.142314	−	0.989822i	$-0.545454\pi$
$929$	−8.67530	−0.284627	−0.142314	+	0.989822i	$0.545454\pi$
$930$	−33.6389	−1.10306
$931$	15.3402	0.502755
$932$	−36.8033	−1.20553
$933$	54.5931	1.78730
$934$	17.3563	0.567916
$935$	2.58010	0.0843784
$936$	−122.801	−4.01388
$937$	−51.7151	−1.68946	−0.844729	−	0.535194i	$-0.820238\pi$
$937$	−51.7151	−1.68946	−0.844729	+	0.535194i	$0.820238\pi$
$938$	−6.46098	−0.210958
$939$	1.65346	0.0539588
$940$	33.3773	1.08865
$941$	−57.2104	−1.86501	−0.932503	−	0.361161i	$-0.882380\pi$
$941$	−57.2104	−1.86501	−0.932503	+	0.361161i	$0.882380\pi$
$942$	−102.452	−3.33805
$943$	32.0543	1.04383
$944$	−31.0566	−1.01081
$945$	0.418518	0.0136144
$946$	−43.6929	−1.42058
$947$	−35.7540	−1.16185	−0.580925	−	0.813957i	$-0.697309\pi$
$947$	−35.7540	−1.16185	−0.580925	+	0.813957i	$0.697309\pi$
$948$	−168.269	−5.46511
$949$	−22.1762	−0.719871
$950$	6.58929	0.213785
$951$	8.21678	0.266447
$952$	−8.36644	−0.271158
$953$	−16.8288	−0.545138	−0.272569	−	0.962136i	$-0.587873\pi$
$953$	−16.8288	−0.545138	−0.272569	+	0.962136i	$0.587873\pi$
$954$	86.4478	2.79885
$955$	23.2044	0.750877
$956$	149.483	4.83464
$957$	−38.7420	−1.25235
$958$	−8.19620	−0.264807
$959$	18.0674	0.583428
$960$	68.5325	2.21188
$961$	−4.67688	−0.150867
$962$	−68.9215	−2.22212
$963$	24.6436	0.794129
$964$	−112.119	−3.61112
$965$	−13.9883	−0.450300
$966$	32.0610	1.03155
$967$	−38.2698	−1.23067	−0.615337	−	0.788264i	$-0.710980\pi$
$967$	−38.2698	−1.23067	−0.615337	+	0.788264i	$0.710980\pi$
$968$	52.0166	1.67188
$969$	−6.43181	−0.206619
$970$	−45.9370	−1.47495
$971$	6.55446	0.210343	0.105171	−	0.994454i	$-0.466461\pi$
$971$	6.55446	0.210343	0.105171	+	0.994454i	$0.466461\pi$
$972$	116.962	3.75154
$973$	−2.47531	−0.0793549
$974$	−85.9514	−2.75406
$975$	−11.3390	−0.363138
$976$	54.6265	1.74855
$977$	−52.0764	−1.66607	−0.833036	−	0.553218i	$-0.813399\pi$
$977$	−52.0764	−1.66607	−0.833036	+	0.553218i	$0.813399\pi$
$978$	122.760	3.92544
$979$	21.8088	0.697012
$980$	34.4684	1.10105
$981$	3.78512	0.120850
$982$	−2.83901	−0.0905964
$983$	−49.1177	−1.56661	−0.783305	−	0.621638i	$-0.786468\pi$
$983$	−49.1177	−1.56661	−0.783305	+	0.621638i	$0.786468\pi$
$984$	−119.230	−3.80090
$985$	−16.6207	−0.529580
$986$	20.8303	0.663372
$987$	−11.9502	−0.380378
$988$	−61.8924	−1.96906
$989$	−41.5672	−1.32176
$990$	17.7042	0.562676
$991$	−7.65622	−0.243208	−0.121604	−	0.992579i	$-0.538804\pi$
$991$	−7.65622	−0.243208	−0.121604	+	0.992579i	$0.538804\pi$
$992$	−108.720	−3.45185
$993$	−1.91114	−0.0606483
$994$	−18.9167	−0.600001
$995$	6.86700	0.217698
$996$	−192.811	−6.10945
$997$	−7.39451	−0.234187	−0.117093	−	0.993121i	$-0.537358\pi$
$997$	−7.39451	−0.234187	−0.117093	+	0.993121i	$0.537358\pi$
$998$	−35.7104	−1.13039
$999$	2.77606	0.0878308

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.4	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.4	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.72603 q^{2} -2.40516 q^{3} +5.43123 q^{4} -1.00000 q^{5} +6.55652 q^{6} -0.808497 q^{7} -9.35364 q^{8} +2.78477 q^{9} +O(q^{10})\)	\(q-2.72603 q^{2} -2.40516 q^{3} +5.43123 q^{4} -1.00000 q^{5} +6.55652 q^{6} -0.808497 q^{7} -9.35364 q^{8} +2.78477 q^{9} +2.72603 q^{10} +2.33214 q^{11} -13.0630 q^{12} +4.71445 q^{13} +2.20399 q^{14} +2.40516 q^{15} +14.6358 q^{16} -1.10632 q^{17} -7.59138 q^{18} -2.41717 q^{19} -5.43123 q^{20} +1.94456 q^{21} -6.35749 q^{22} -6.04819 q^{23} +22.4970 q^{24} +1.00000 q^{25} -12.8517 q^{26} +0.517650 q^{27} -4.39114 q^{28} +6.90691 q^{29} -6.55652 q^{30} +5.13061 q^{31} -21.1904 q^{32} -5.60917 q^{33} +3.01587 q^{34} +0.808497 q^{35} +15.1248 q^{36} +5.36282 q^{37} +6.58929 q^{38} -11.3390 q^{39} +9.35364 q^{40} -5.29981 q^{41} -5.30093 q^{42} +6.87266 q^{43} +12.6664 q^{44} -2.78477 q^{45} +16.4875 q^{46} -6.14544 q^{47} -35.2015 q^{48} -6.34633 q^{49} -2.72603 q^{50} +2.66088 q^{51} +25.6053 q^{52} -11.3876 q^{53} -1.41113 q^{54} -2.33214 q^{55} +7.56239 q^{56} +5.81368 q^{57} -18.8284 q^{58} -2.12195 q^{59} +13.0630 q^{60} +3.73238 q^{61} -13.9862 q^{62} -2.25148 q^{63} +28.4940 q^{64} -4.71445 q^{65} +15.2908 q^{66} -2.93150 q^{67} -6.00870 q^{68} +14.5468 q^{69} -2.20399 q^{70} -8.58294 q^{71} -26.0478 q^{72} -4.70389 q^{73} -14.6192 q^{74} -2.40516 q^{75} -13.1282 q^{76} -1.88553 q^{77} +30.9104 q^{78} +12.8813 q^{79} -14.6358 q^{80} -9.59935 q^{81} +14.4474 q^{82} +14.7601 q^{83} +10.5614 q^{84} +1.10632 q^{85} -18.7351 q^{86} -16.6122 q^{87} -21.8140 q^{88} +9.35140 q^{89} +7.59138 q^{90} -3.81162 q^{91} -32.8491 q^{92} -12.3399 q^{93} +16.7526 q^{94} +2.41717 q^{95} +50.9662 q^{96} -16.8513 q^{97} +17.3003 q^{98} +6.49450 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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