LMFDB - Embedded newform 8035.2.a.e.1.6

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:	$0$
Dimension:	$153$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-2.62009 q^{2} -2.60275 q^{3} +4.86488 q^{4} +1.00000 q^{5} +6.81943 q^{6} +0.626563 q^{7} -7.50624 q^{8} +3.77428 q^{9} +O(q^{10})$	\(q-2.62009 q^{2} -2.60275 q^{3} +4.86488 q^{4} +1.00000 q^{5} +6.81943 q^{6} +0.626563 q^{7} -7.50624 q^{8} +3.77428 q^{9} -2.62009 q^{10} +6.10091 q^{11} -12.6620 q^{12} +4.02402 q^{13} -1.64165 q^{14} -2.60275 q^{15} +9.93729 q^{16} -3.04556 q^{17} -9.88896 q^{18} +5.64003 q^{19} +4.86488 q^{20} -1.63079 q^{21} -15.9849 q^{22} -1.49392 q^{23} +19.5368 q^{24} +1.00000 q^{25} -10.5433 q^{26} -2.01526 q^{27} +3.04816 q^{28} -1.31972 q^{29} +6.81943 q^{30} -7.69551 q^{31} -11.0241 q^{32} -15.8791 q^{33} +7.97965 q^{34} +0.626563 q^{35} +18.3614 q^{36} -0.882299 q^{37} -14.7774 q^{38} -10.4735 q^{39} -7.50624 q^{40} +9.53432 q^{41} +4.27281 q^{42} -1.33708 q^{43} +29.6802 q^{44} +3.77428 q^{45} +3.91421 q^{46} +2.24303 q^{47} -25.8642 q^{48} -6.60742 q^{49} -2.62009 q^{50} +7.92682 q^{51} +19.5763 q^{52} +8.07900 q^{53} +5.28016 q^{54} +6.10091 q^{55} -4.70314 q^{56} -14.6796 q^{57} +3.45778 q^{58} +5.16401 q^{59} -12.6620 q^{60} -2.24592 q^{61} +20.1629 q^{62} +2.36483 q^{63} +9.00961 q^{64} +4.02402 q^{65} +41.6047 q^{66} -10.6801 q^{67} -14.8163 q^{68} +3.88829 q^{69} -1.64165 q^{70} +6.13281 q^{71} -28.3307 q^{72} -2.65449 q^{73} +2.31170 q^{74} -2.60275 q^{75} +27.4381 q^{76} +3.82261 q^{77} +27.4415 q^{78} +5.36540 q^{79} +9.93729 q^{80} -6.07764 q^{81} -24.9808 q^{82} +1.34079 q^{83} -7.93357 q^{84} -3.04556 q^{85} +3.50328 q^{86} +3.43489 q^{87} -45.7949 q^{88} +7.31454 q^{89} -9.88896 q^{90} +2.52130 q^{91} -7.26774 q^{92} +20.0295 q^{93} -5.87695 q^{94} +5.64003 q^{95} +28.6930 q^{96} +1.91629 q^{97} +17.3120 q^{98} +23.0265 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) $ 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * 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 $

$2$	−2.62009	−1.85268	−0.926342	−	0.376683i	$-0.877065\pi$
$2$	−2.62009	−1.85268	−0.926342	+	0.376683i	$0.877065\pi$
$3$	−2.60275	−1.50270	−0.751348	−	0.659906i	$-0.770596\pi$
$3$	−2.60275	−1.50270	−0.751348	+	0.659906i	$0.770596\pi$
$4$	4.86488	2.43244
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	6.81943	2.78402
$7$	0.626563	0.236819	0.118409	−	0.992965i	$-0.462220\pi$
$7$	0.626563	0.236819	0.118409	+	0.992965i	$0.462220\pi$
$8$	−7.50624	−2.65386
$9$	3.77428	1.25809
$10$	−2.62009	−0.828546
$11$	6.10091	1.83949	0.919747	−	0.392513i	$-0.128394\pi$
$11$	6.10091	1.83949	0.919747	+	0.392513i	$0.128394\pi$
$12$	−12.6620	−3.65522
$13$	4.02402	1.11606	0.558031	−	0.829820i	$-0.311557\pi$
$13$	4.02402	1.11606	0.558031	+	0.829820i	$0.311557\pi$
$14$	−1.64165	−0.438750
$15$	−2.60275	−0.672026
$16$	9.93729	2.48432
$17$	−3.04556	−0.738658	−0.369329	−	0.929299i	$-0.620412\pi$
$17$	−3.04556	−0.738658	−0.369329	+	0.929299i	$0.620412\pi$
$18$	−9.88896	−2.33085
$19$	5.64003	1.29391	0.646956	−	0.762527i	$-0.276042\pi$
$19$	5.64003	1.29391	0.646956	+	0.762527i	$0.276042\pi$
$20$	4.86488	1.08782
$21$	−1.63079	−0.355866
$22$	−15.9849	−3.40800
$23$	−1.49392	−0.311504	−0.155752	−	0.987796i	$-0.549780\pi$
$23$	−1.49392	−0.311504	−0.155752	+	0.987796i	$0.549780\pi$
$24$	19.5368	3.98794
$25$	1.00000	0.200000
$26$	−10.5433	−2.06771
$27$	−2.01526	−0.387837
$28$	3.04816	0.576047
$29$	−1.31972	−0.245065	−0.122533	−	0.992464i	$-0.539102\pi$
$29$	−1.31972	−0.245065	−0.122533	+	0.992464i	$0.539102\pi$
$30$	6.81943	1.24505
$31$	−7.69551	−1.38215	−0.691077	−	0.722781i	$-0.742864\pi$
$31$	−7.69551	−1.38215	−0.691077	+	0.722781i	$0.742864\pi$
$32$	−11.0241	−1.94881
$33$	−15.8791	−2.76420
$34$	7.97965	1.36850
$35$	0.626563	0.105909
$36$	18.3614	3.06024
$37$	−0.882299	−0.145049	−0.0725245	−	0.997367i	$-0.523106\pi$
$37$	−0.882299	−0.145049	−0.0725245	+	0.997367i	$0.523106\pi$
$38$	−14.7774	−2.39721
$39$	−10.4735	−1.67710
$40$	−7.50624	−1.18684
$41$	9.53432	1.48901	0.744505	−	0.667617i	$-0.232686\pi$
$41$	9.53432	1.48901	0.744505	+	0.667617i	$0.232686\pi$
$42$	4.27281	0.659308
$43$	−1.33708	−0.203903	−0.101952	−	0.994789i	$-0.532509\pi$
$43$	−1.33708	−0.203903	−0.101952	+	0.994789i	$0.532509\pi$
$44$	29.6802	4.47446
$45$	3.77428	0.562637
$46$	3.91421	0.577118
$47$	2.24303	0.327180	0.163590	−	0.986528i	$-0.447693\pi$
$47$	2.24303	0.327180	0.163590	+	0.986528i	$0.447693\pi$
$48$	−25.8642	−3.73318
$49$	−6.60742	−0.943917
$50$	−2.62009	−0.370537
$51$	7.92682	1.10998
$52$	19.5763	2.71475
$53$	8.07900	1.10974	0.554868	−	0.831939i	$-0.312769\pi$
$53$	8.07900	1.10974	0.554868	+	0.831939i	$0.312769\pi$
$54$	5.28016	0.718539
$55$	6.10091	0.822646
$56$	−4.70314	−0.628483
$57$	−14.6796	−1.94436
$58$	3.45778	0.454028
$59$	5.16401	0.672297	0.336149	−	0.941809i	$-0.390876\pi$
$59$	5.16401	0.672297	0.336149	+	0.941809i	$0.390876\pi$
$60$	−12.6620	−1.63466
$61$	−2.24592	−0.287560	−0.143780	−	0.989610i	$-0.545926\pi$
$61$	−2.24592	−0.287560	−0.143780	+	0.989610i	$0.545926\pi$
$62$	20.1629	2.56070
$63$	2.36483	0.297940
$64$	9.00961	1.12620
$65$	4.02402	0.499118
$66$	41.6047	5.12119
$67$	−10.6801	−1.30478	−0.652391	−	0.757883i	$-0.726234\pi$
$67$	−10.6801	−1.30478	−0.652391	+	0.757883i	$0.726234\pi$
$68$	−14.8163	−1.79674
$69$	3.88829	0.468096
$70$	−1.64165	−0.196215
$71$	6.13281	0.727831	0.363915	−	0.931432i	$-0.381440\pi$
$71$	6.13281	0.727831	0.363915	+	0.931432i	$0.381440\pi$
$72$	−28.3307	−3.33880
$73$	−2.65449	−0.310685	−0.155343	−	0.987861i	$-0.549648\pi$
$73$	−2.65449	−0.310685	−0.155343	+	0.987861i	$0.549648\pi$
$74$	2.31170	0.268730
$75$	−2.60275	−0.300539
$76$	27.4381	3.14736
$77$	3.82261	0.435626
$78$	27.4415	3.10714
$79$	5.36540	0.603654	0.301827	−	0.953363i	$-0.402403\pi$
$79$	5.36540	0.603654	0.301827	+	0.953363i	$0.402403\pi$
$80$	9.93729	1.11102
$81$	−6.07764	−0.675294
$82$	−24.9808	−2.75867
$83$	1.34079	0.147171	0.0735854	−	0.997289i	$-0.476556\pi$
$83$	1.34079	0.147171	0.0735854	+	0.997289i	$0.476556\pi$
$84$	−7.93357	−0.865624
$85$	−3.04556	−0.330338
$86$	3.50328	0.377768
$87$	3.43489	0.368258
$88$	−45.7949	−4.88175
$89$	7.31454	0.775340	0.387670	−	0.921798i	$-0.373280\pi$
$89$	7.31454	0.775340	0.387670	+	0.921798i	$0.373280\pi$
$90$	−9.88896	−1.04239
$91$	2.52130	0.264304
$92$	−7.26774	−0.757714
$93$	20.0295	2.07696
$94$	−5.87695	−0.606161
$95$	5.64003	0.578655
$96$	28.6930	2.92846
$97$	1.91629	0.194570	0.0972848	−	0.995257i	$-0.468984\pi$
$97$	1.91629	0.194570	0.0972848	+	0.995257i	$0.468984\pi$
$98$	17.3120	1.74878
$99$	23.0265	2.31426
$100$	4.86488	0.486488
$101$	0.192878	0.0191921	0.00959606	−	0.999954i	$-0.496945\pi$
$101$	0.192878	0.0191921	0.00959606	+	0.999954i	$0.496945\pi$
$102$	−20.7690	−2.05644
$103$	8.23560	0.811478	0.405739	−	0.913989i	$-0.367014\pi$
$103$	8.23560	0.811478	0.405739	+	0.913989i	$0.367014\pi$
$104$	−30.2052	−2.96187
$105$	−1.63079	−0.159148
$106$	−21.1677	−2.05599
$107$	3.98327	0.385077	0.192539	−	0.981289i	$-0.438328\pi$
$107$	3.98327	0.385077	0.192539	+	0.981289i	$0.438328\pi$
$108$	−9.80399	−0.943389
$109$	−8.39078	−0.803691	−0.401845	−	0.915708i	$-0.631631\pi$
$109$	−8.39078	−0.803691	−0.401845	+	0.915708i	$0.631631\pi$
$110$	−15.9849	−1.52410
$111$	2.29640	0.217965
$112$	6.22634	0.588334
$113$	4.04417	0.380443	0.190222	−	0.981741i	$-0.439079\pi$
$113$	4.04417	0.380443	0.190222	+	0.981741i	$0.439079\pi$
$114$	38.4618	3.60228
$115$	−1.49392	−0.139309
$116$	−6.42026	−0.596106
$117$	15.1878	1.40411
$118$	−13.5302	−1.24555
$119$	−1.90824	−0.174928
$120$	19.5368	1.78346
$121$	26.2211	2.38374
$122$	5.88451	0.532759
$123$	−24.8154	−2.23753
$124$	−37.4377	−3.36201
$125$	1.00000	0.0894427
$126$	−6.19606	−0.551989
$127$	−3.96917	−0.352206	−0.176103	−	0.984372i	$-0.556349\pi$
$127$	−3.96917	−0.352206	−0.176103	+	0.984372i	$0.556349\pi$
$128$	−1.55777	−0.137689
$129$	3.48008	0.306404
$130$	−10.5433	−0.924708
$131$	3.12270	0.272832	0.136416	−	0.990652i	$-0.456442\pi$
$131$	3.12270	0.272832	0.136416	+	0.990652i	$0.456442\pi$
$132$	−77.2499	−6.72374
$133$	3.53384	0.306423
$134$	27.9828	2.41735
$135$	−2.01526	−0.173446
$136$	22.8607	1.96029
$137$	1.86729	0.159533	0.0797666	−	0.996814i	$-0.474583\pi$
$137$	1.86729	0.159533	0.0797666	+	0.996814i	$0.474583\pi$
$138$	−10.1877	−0.867233
$139$	16.5352	1.40250	0.701248	−	0.712917i	$-0.252626\pi$
$139$	16.5352	1.40250	0.701248	+	0.712917i	$0.252626\pi$
$140$	3.04816	0.257616
$141$	−5.83804	−0.491652
$142$	−16.0685	−1.34844
$143$	24.5502	2.05299
$144$	37.5061	3.12551
$145$	−1.31972	−0.109596
$146$	6.95502	0.575601
$147$	17.1974	1.41842
$148$	−4.29228	−0.352823
$149$	−6.30510	−0.516534	−0.258267	−	0.966074i	$-0.583151\pi$
$149$	−6.30510	−0.516534	−0.258267	+	0.966074i	$0.583151\pi$
$150$	6.81943	0.556804
$151$	8.06380	0.656223	0.328111	−	0.944639i	$-0.393588\pi$
$151$	8.06380	0.656223	0.328111	+	0.944639i	$0.393588\pi$
$152$	−42.3354	−3.43386
$153$	−11.4948	−0.929301
$154$	−10.0156	−0.807078
$155$	−7.69551	−0.618118
$156$	−50.9522	−4.07944
$157$	1.51693	0.121064	0.0605321	−	0.998166i	$-0.480720\pi$
$157$	1.51693	0.121064	0.0605321	+	0.998166i	$0.480720\pi$
$158$	−14.0578	−1.11838
$159$	−21.0276	−1.66759
$160$	−11.0241	−0.871533
$161$	−0.936036	−0.0737700
$162$	15.9240	1.25111
$163$	6.94383	0.543883	0.271941	−	0.962314i	$-0.412334\pi$
$163$	6.94383	0.543883	0.271941	+	0.962314i	$0.412334\pi$
$164$	46.3833	3.62193
$165$	−15.8791	−1.23619
$166$	−3.51299	−0.272661
$167$	18.1414	1.40382	0.701910	−	0.712266i	$-0.252331\pi$
$167$	18.1414	1.40382	0.701910	+	0.712266i	$0.252331\pi$
$168$	12.2411	0.944419
$169$	3.19270	0.245593
$170$	7.97965	0.612011
$171$	21.2871	1.62786
$172$	−6.50474	−0.495982
$173$	3.99571	0.303788	0.151894	−	0.988397i	$-0.451463\pi$
$173$	3.99571	0.303788	0.151894	+	0.988397i	$0.451463\pi$
$174$	−8.99971	−0.682267
$175$	0.626563	0.0473637
$176$	60.6265	4.56989
$177$	−13.4406	−1.01026
$178$	−19.1648	−1.43646
$179$	5.19318	0.388156	0.194078	−	0.980986i	$-0.437828\pi$
$179$	5.19318	0.388156	0.194078	+	0.980986i	$0.437828\pi$
$180$	18.3614	1.36858
$181$	−9.05641	−0.673157	−0.336579	−	0.941655i	$-0.609270\pi$
$181$	−9.05641	−0.673157	−0.336579	+	0.941655i	$0.609270\pi$
$182$	−6.60604	−0.489672
$183$	5.84555	0.432116
$184$	11.2137	0.826687
$185$	−0.882299	−0.0648679
$186$	−52.4790	−3.84795
$187$	−18.5807	−1.35876
$188$	10.9121	0.795845
$189$	−1.26269	−0.0918470
$190$	−14.7774	−1.07206
$191$	5.36571	0.388249	0.194125	−	0.980977i	$-0.437813\pi$
$191$	5.36571	0.388249	0.194125	+	0.980977i	$0.437813\pi$
$192$	−23.4497	−1.69234
$193$	21.3624	1.53770	0.768849	−	0.639431i	$-0.220830\pi$
$193$	21.3624	1.53770	0.768849	+	0.639431i	$0.220830\pi$
$194$	−5.02085	−0.360476
$195$	−10.4735	−0.750022
$196$	−32.1443	−2.29602
$197$	20.9798	1.49475	0.747375	−	0.664402i	$-0.231314\pi$
$197$	20.9798	1.49475	0.747375	+	0.664402i	$0.231314\pi$
$198$	−60.3317	−4.28758
$199$	5.96625	0.422936	0.211468	−	0.977385i	$-0.432176\pi$
$199$	5.96625	0.422936	0.211468	+	0.977385i	$0.432176\pi$
$200$	−7.50624	−0.530772
$201$	27.7976	1.96069
$202$	−0.505359	−0.0355569
$203$	−0.826886	−0.0580360
$204$	38.5630	2.69995
$205$	9.53432	0.665906
$206$	−21.5780	−1.50341
$207$	−5.63848	−0.391901
$208$	39.9878	2.77266
$209$	34.4093	2.38014
$210$	4.27281	0.294852
$211$	−24.5387	−1.68931	−0.844655	−	0.535311i	$-0.820195\pi$
$211$	−24.5387	−1.68931	−0.844655	+	0.535311i	$0.820195\pi$
$212$	39.3033	2.69936
$213$	−15.9621	−1.09371
$214$	−10.4365	−0.713427
$215$	−1.33708	−0.0911883
$216$	15.1270	1.02926
$217$	−4.82173	−0.327320
$218$	21.9846	1.48899
$219$	6.90897	0.466865
$220$	29.6802	2.00104
$221$	−12.2554	−0.824387
$222$	−6.01677	−0.403819
$223$	−2.86233	−0.191676	−0.0958380	−	0.995397i	$-0.530553\pi$
$223$	−2.86233	−0.191676	−0.0958380	+	0.995397i	$0.530553\pi$
$224$	−6.90731	−0.461514
$225$	3.77428	0.251619
$226$	−10.5961	−0.704841
$227$	−18.0424	−1.19752	−0.598759	−	0.800929i	$-0.704339\pi$
$227$	−18.0424	−1.19752	−0.598759	+	0.800929i	$0.704339\pi$
$228$	−71.4143	−4.72953
$229$	28.8321	1.90528	0.952640	−	0.304102i	$-0.0983563\pi$
$229$	28.8321	1.90528	0.952640	+	0.304102i	$0.0983563\pi$
$230$	3.91421	0.258095
$231$	−9.94927	−0.654614
$232$	9.90611	0.650368
$233$	−20.5707	−1.34763	−0.673815	−	0.738901i	$-0.735345\pi$
$233$	−20.5707	−1.34763	−0.673815	+	0.738901i	$0.735345\pi$
$234$	−39.7933	−2.60137
$235$	2.24303	0.146319
$236$	25.1223	1.63532
$237$	−13.9648	−0.907109
$238$	4.99976	0.324086
$239$	−5.97529	−0.386509	−0.193255	−	0.981149i	$-0.561904\pi$
$239$	−5.97529	−0.386509	−0.193255	+	0.981149i	$0.561904\pi$
$240$	−25.8642	−1.66953
$241$	12.3264	0.794014	0.397007	−	0.917816i	$-0.370049\pi$
$241$	12.3264	0.794014	0.397007	+	0.917816i	$0.370049\pi$
$242$	−68.7016	−4.41631
$243$	21.8643	1.40260
$244$	−10.9261	−0.699473
$245$	−6.60742	−0.422132
$246$	65.0186	4.14544
$247$	22.6956	1.44408
$248$	57.7644	3.66804
$249$	−3.48974	−0.221153
$250$	−2.62009	−0.165709
$251$	−29.1954	−1.84280	−0.921398	−	0.388619i	$-0.872952\pi$
$251$	−29.1954	−1.84280	−0.921398	+	0.388619i	$0.872952\pi$
$252$	11.5046	0.724722
$253$	−9.11427	−0.573009
$254$	10.3996	0.652527
$255$	7.92682	0.496397
$256$	−13.9377	−0.871107
$257$	25.1420	1.56831	0.784157	−	0.620562i	$-0.213096\pi$
$257$	25.1420	1.56831	0.784157	+	0.620562i	$0.213096\pi$
$258$	−9.11814	−0.567671
$259$	−0.552816	−0.0343503
$260$	19.5763	1.21407
$261$	−4.98098	−0.308315
$262$	−8.18177	−0.505471
$263$	−1.20312	−0.0741873	−0.0370937	−	0.999312i	$-0.511810\pi$
$263$	−1.20312	−0.0741873	−0.0370937	+	0.999312i	$0.511810\pi$
$264$	119.192	7.33579
$265$	8.07900	0.496289
$266$	−9.25898	−0.567704
$267$	−19.0379	−1.16510
$268$	−51.9574	−3.17380
$269$	19.0257	1.16002	0.580008	−	0.814611i	$-0.303049\pi$
$269$	19.0257	1.16002	0.580008	+	0.814611i	$0.303049\pi$
$270$	5.28016	0.321340
$271$	−27.5900	−1.67597	−0.837987	−	0.545690i	$-0.816267\pi$
$271$	−27.5900	−1.67597	−0.837987	+	0.545690i	$0.816267\pi$
$272$	−30.2646	−1.83506
$273$	−6.56231	−0.397169
$274$	−4.89247	−0.295565
$275$	6.10091	0.367899
$276$	18.9161	1.13861
$277$	−19.5689	−1.17578	−0.587891	−	0.808940i	$-0.700041\pi$
$277$	−19.5689	−1.17578	−0.587891	+	0.808940i	$0.700041\pi$
$278$	−43.3237	−2.59838
$279$	−29.0450	−1.73888
$280$	−4.70314	−0.281066
$281$	−14.5771	−0.869597	−0.434799	−	0.900528i	$-0.643180\pi$
$281$	−14.5771	−0.869597	−0.434799	+	0.900528i	$0.643180\pi$
$282$	15.2962	0.910876
$283$	−31.3656	−1.86449	−0.932247	−	0.361823i	$-0.882155\pi$
$283$	−31.3656	−1.86449	−0.932247	+	0.361823i	$0.882155\pi$
$284$	29.8354	1.77040
$285$	−14.6796	−0.869542
$286$	−64.3236	−3.80354
$287$	5.97386	0.352626
$288$	−41.6081	−2.45178
$289$	−7.72455	−0.454385
$290$	3.45778	0.203048
$291$	−4.98761	−0.292379
$292$	−12.9138	−0.755723
$293$	−5.04237	−0.294578	−0.147289	−	0.989093i	$-0.547055\pi$
$293$	−5.04237	−0.294578	−0.147289	+	0.989093i	$0.547055\pi$
$294$	−45.0588	−2.62788
$295$	5.16401	0.300661
$296$	6.62275	0.384940
$297$	−12.2949	−0.713423
$298$	16.5199	0.956974
$299$	−6.01156	−0.347657
$300$	−12.6620	−0.731043
$301$	−0.837767	−0.0482881
$302$	−21.1279	−1.21577
$303$	−0.502013	−0.0288399
$304$	56.0466	3.21449
$305$	−2.24592	−0.128601
$306$	30.1175	1.72170
$307$	−2.70768	−0.154535	−0.0772677	−	0.997010i	$-0.524620\pi$
$307$	−2.70768	−0.154535	−0.0772677	+	0.997010i	$0.524620\pi$
$308$	18.5965	1.05963
$309$	−21.4352	−1.21940
$310$	20.1629	1.14518
$311$	−16.1879	−0.917932	−0.458966	−	0.888454i	$-0.651780\pi$
$311$	−16.1879	−0.917932	−0.458966	+	0.888454i	$0.651780\pi$
$312$	78.6166	4.45079
$313$	1.97419	0.111588	0.0557938	−	0.998442i	$-0.482231\pi$
$313$	1.97419	0.111588	0.0557938	+	0.998442i	$0.482231\pi$
$314$	−3.97450	−0.224294
$315$	2.36483	0.133243
$316$	26.1020	1.46835
$317$	−8.70355	−0.488840	−0.244420	−	0.969669i	$-0.578598\pi$
$317$	−8.70355	−0.488840	−0.244420	+	0.969669i	$0.578598\pi$
$318$	55.0942	3.08953
$319$	−8.05147	−0.450796
$320$	9.00961	0.503652
$321$	−10.3674	−0.578654
$322$	2.45250	0.136672
$323$	−17.1771	−0.955758
$324$	−29.5670	−1.64261
$325$	4.02402	0.223212
$326$	−18.1935	−1.00764
$327$	21.8391	1.20770
$328$	−71.5669	−3.95162
$329$	1.40540	0.0774823
$330$	41.6047	2.29026
$331$	26.5724	1.46055	0.730277	−	0.683151i	$-0.239391\pi$
$331$	26.5724	1.46055	0.730277	+	0.683151i	$0.239391\pi$
$332$	6.52278	0.357984
$333$	−3.33004	−0.182485
$334$	−47.5320	−2.60084
$335$	−10.6801	−0.583516
$336$	−16.2056	−0.884087
$337$	25.7612	1.40330	0.701650	−	0.712522i	$-0.252447\pi$
$337$	25.7612	1.40330	0.701650	+	0.712522i	$0.252447\pi$
$338$	−8.36518	−0.455006
$339$	−10.5259	−0.571691
$340$	−14.8163	−0.803526
$341$	−46.9496	−2.54246
$342$	−55.7741	−3.01592
$343$	−8.52591	−0.460356
$344$	10.0365	0.541130
$345$	3.88829	0.209339
$346$	−10.4691	−0.562824
$347$	−23.7742	−1.27627	−0.638134	−	0.769926i	$-0.720293\pi$
$347$	−23.7742	−1.27627	−0.638134	+	0.769926i	$0.720293\pi$
$348$	16.7103	0.895766
$349$	−7.33975	−0.392888	−0.196444	−	0.980515i	$-0.562939\pi$
$349$	−7.33975	−0.392888	−0.196444	+	0.980515i	$0.562939\pi$
$350$	−1.64165	−0.0877501
$351$	−8.10943	−0.432849
$352$	−67.2571	−3.58482
$353$	26.7665	1.42464	0.712320	−	0.701855i	$-0.247645\pi$
$353$	26.7665	1.42464	0.712320	+	0.701855i	$0.247645\pi$
$354$	35.2156	1.87169
$355$	6.13281	0.325496
$356$	35.5844	1.88597
$357$	4.96666	0.262863
$358$	−13.6066	−0.719131
$359$	−32.7230	−1.72706	−0.863528	−	0.504301i	$-0.831750\pi$
$359$	−32.7230	−1.72706	−0.863528	+	0.504301i	$0.831750\pi$
$360$	−28.3307	−1.49316
$361$	12.8099	0.674208
$362$	23.7286	1.24715
$363$	−68.2468	−3.58203
$364$	12.2658	0.642904
$365$	−2.65449	−0.138943
$366$	−15.3159	−0.800574
$367$	−8.97600	−0.468543	−0.234272	−	0.972171i	$-0.575271\pi$
$367$	−8.97600	−0.468543	−0.234272	+	0.972171i	$0.575271\pi$
$368$	−14.8455	−0.773876
$369$	35.9852	1.87331
$370$	2.31170	0.120180
$371$	5.06200	0.262806
$372$	97.4409	5.05207
$373$	−18.5307	−0.959482	−0.479741	−	0.877410i	$-0.659269\pi$
$373$	−18.5307	−0.959482	−0.479741	+	0.877410i	$0.659269\pi$
$374$	48.6831	2.51735
$375$	−2.60275	−0.134405
$376$	−16.8367	−0.868289
$377$	−5.31056	−0.273508
$378$	3.30836	0.170163
$379$	18.2303	0.936426	0.468213	−	0.883616i	$-0.344898\pi$
$379$	18.2303	0.936426	0.468213	+	0.883616i	$0.344898\pi$
$380$	27.4381	1.40754
$381$	10.3307	0.529259
$382$	−14.0586	−0.719303
$383$	12.5082	0.639137	0.319568	−	0.947563i	$-0.396462\pi$
$383$	12.5082	0.639137	0.319568	+	0.947563i	$0.396462\pi$
$384$	4.05448	0.206904
$385$	3.82261	0.194818
$386$	−55.9714	−2.84887
$387$	−5.04653	−0.256529
$388$	9.32251	0.473279
$389$	22.6690	1.14936	0.574681	−	0.818377i	$-0.305126\pi$
$389$	22.6690	1.14936	0.574681	+	0.818377i	$0.305126\pi$
$390$	27.4415	1.38955
$391$	4.54983	0.230095
$392$	49.5969	2.50502
$393$	−8.12760	−0.409983
$394$	−54.9690	−2.76930
$395$	5.36540	0.269962
$396$	112.021	5.62929
$397$	−33.3210	−1.67233	−0.836167	−	0.548475i	$-0.815209\pi$
$397$	−33.3210	−1.67233	−0.836167	+	0.548475i	$0.815209\pi$
$398$	−15.6321	−0.783568
$399$	−9.19768	−0.460460
$400$	9.93729	0.496864
$401$	30.3939	1.51780	0.758898	−	0.651209i	$-0.225738\pi$
$401$	30.3939	1.51780	0.758898	+	0.651209i	$0.225738\pi$
$402$	−72.8322	−3.63254
$403$	−30.9669	−1.54257
$404$	0.938330	0.0466837
$405$	−6.07764	−0.302000
$406$	2.16652	0.107522
$407$	−5.38282	−0.266817
$408$	−59.5007	−2.94572
$409$	−31.4797	−1.55657	−0.778285	−	0.627911i	$-0.783910\pi$
$409$	−31.4797	−1.55657	−0.778285	+	0.627911i	$0.783910\pi$
$410$	−24.9808	−1.23371
$411$	−4.86007	−0.239730
$412$	40.0652	1.97387
$413$	3.23558	0.159213
$414$	14.7733	0.726069
$415$	1.34079	0.0658168
$416$	−44.3612	−2.17499
$417$	−43.0369	−2.10753
$418$	−90.1555	−4.40965
$419$	15.0905	0.737220	0.368610	−	0.929584i	$-0.379834\pi$
$419$	15.0905	0.737220	0.368610	+	0.929584i	$0.379834\pi$
$420$	−7.93357	−0.387119
$421$	−0.655818	−0.0319626	−0.0159813	−	0.999872i	$-0.505087\pi$
$421$	−0.655818	−0.0319626	−0.0159813	+	0.999872i	$0.505087\pi$
$422$	64.2935	3.12976
$423$	8.46584	0.411623
$424$	−60.6429	−2.94508
$425$	−3.04556	−0.147732
$426$	41.8223	2.02630
$427$	−1.40721	−0.0680997
$428$	19.3781	0.936677
$429$	−63.8978	−3.08501
$430$	3.50328	0.168943
$431$	15.9369	0.767655	0.383828	−	0.923405i	$-0.374606\pi$
$431$	15.9369	0.767655	0.383828	+	0.923405i	$0.374606\pi$
$432$	−20.0262	−0.963511
$433$	23.7279	1.14029	0.570146	−	0.821544i	$-0.306887\pi$
$433$	23.7279	1.14029	0.570146	+	0.821544i	$0.306887\pi$
$434$	12.6334	0.606421
$435$	3.43489	0.164690
$436$	−40.8201	−1.95493
$437$	−8.42576	−0.403059
$438$	−18.1021	−0.864954
$439$	−13.5348	−0.645979	−0.322989	−	0.946403i	$-0.604688\pi$
$439$	−13.5348	−0.645979	−0.322989	+	0.946403i	$0.604688\pi$
$440$	−45.7949	−2.18319
$441$	−24.9383	−1.18754
$442$	32.1103	1.52733
$443$	37.8143	1.79661	0.898306	−	0.439371i	$-0.144799\pi$
$443$	37.8143	1.79661	0.898306	+	0.439371i	$0.144799\pi$
$444$	11.1717	0.530186
$445$	7.31454	0.346743
$446$	7.49958	0.355115
$447$	16.4106	0.776193
$448$	5.64509	0.266705
$449$	−26.5442	−1.25270	−0.626349	−	0.779542i	$-0.715452\pi$
$449$	−26.5442	−1.25270	−0.626349	+	0.779542i	$0.715452\pi$
$450$	−9.88896	−0.466170
$451$	58.1680	2.73902
$452$	19.6744	0.925405
$453$	−20.9880	−0.986103
$454$	47.2728	2.21862
$455$	2.52130	0.118200
$456$	110.188	5.16004
$457$	37.8726	1.77161	0.885804	−	0.464060i	$-0.153608\pi$
$457$	37.8726	1.77161	0.885804	+	0.464060i	$0.153608\pi$
$458$	−75.5427	−3.52988
$459$	6.13760	0.286478
$460$	−7.26774	−0.338860
$461$	−15.8036	−0.736049	−0.368024	−	0.929816i	$-0.619966\pi$
$461$	−15.8036	−0.736049	−0.368024	+	0.929816i	$0.619966\pi$
$462$	26.0680	1.21279
$463$	−12.7170	−0.591008	−0.295504	−	0.955342i	$-0.595488\pi$
$463$	−12.7170	−0.591008	−0.295504	+	0.955342i	$0.595488\pi$
$464$	−13.1144	−0.608821
$465$	20.0295	0.928844
$466$	53.8970	2.49673
$467$	−30.2718	−1.40081	−0.700407	−	0.713744i	$-0.746998\pi$
$467$	−30.2718	−1.40081	−0.700407	+	0.713744i	$0.746998\pi$
$468$	73.8867	3.41541
$469$	−6.69176	−0.308997
$470$	−5.87695	−0.271083
$471$	−3.94818	−0.181923
$472$	−38.7624	−1.78418
$473$	−8.15742	−0.375078
$474$	36.5889	1.68059
$475$	5.64003	0.258782
$476$	−9.28335	−0.425502
$477$	30.4924	1.39615
$478$	15.6558	0.716079
$479$	27.4045	1.25214	0.626072	−	0.779766i	$-0.284662\pi$
$479$	27.4045	1.25214	0.626072	+	0.779766i	$0.284662\pi$
$480$	28.6930	1.30965
$481$	−3.55038	−0.161884
$482$	−32.2963	−1.47106
$483$	2.43626	0.110854
$484$	127.562	5.79829
$485$	1.91629	0.0870142
$486$	−57.2865	−2.59857
$487$	−13.9645	−0.632792	−0.316396	−	0.948627i	$-0.602473\pi$
$487$	−13.9645	−0.632792	−0.316396	+	0.948627i	$0.602473\pi$
$488$	16.8584	0.763144
$489$	−18.0730	−0.817290
$490$	17.3120	0.782078
$491$	−6.99845	−0.315836	−0.157918	−	0.987452i	$-0.550478\pi$
$491$	−6.99845	−0.315836	−0.157918	+	0.987452i	$0.550478\pi$
$492$	−120.724	−5.44265
$493$	4.01928	0.181019
$494$	−59.4645	−2.67543
$495$	23.0265	1.03497
$496$	−76.4725	−3.43372
$497$	3.84259	0.172364
$498$	9.14343	0.409727
$499$	−31.3138	−1.40180	−0.700900	−	0.713259i	$-0.747218\pi$
$499$	−31.3138	−1.40180	−0.700900	+	0.713259i	$0.747218\pi$
$500$	4.86488	0.217564
$501$	−47.2173	−2.10951
$502$	76.4946	3.41412
$503$	1.68753	0.0752434	0.0376217	−	0.999292i	$-0.488022\pi$
$503$	1.68753	0.0752434	0.0376217	+	0.999292i	$0.488022\pi$
$504$	−17.7510	−0.790691
$505$	0.192878	0.00858298
$506$	23.8802	1.06161
$507$	−8.30980	−0.369051
$508$	−19.3095	−0.856721
$509$	44.6396	1.97862	0.989309	−	0.145838i	$-0.0465877\pi$
$509$	44.6396	1.97862	0.989309	+	0.145838i	$0.0465877\pi$
$510$	−20.7690	−0.919667
$511$	−1.66321	−0.0735761
$512$	39.6336	1.75158
$513$	−11.3661	−0.501826
$514$	−65.8743	−2.90559
$515$	8.23560	0.362904
$516$	16.9302	0.745310
$517$	13.6845	0.601845
$518$	1.44843	0.0636403
$519$	−10.3998	−0.456501
$520$	−30.2052	−1.32459
$521$	0.358264	0.0156958	0.00784791	−	0.999969i	$-0.497502\pi$
$521$	0.358264	0.0156958	0.00784791	+	0.999969i	$0.497502\pi$
$522$	13.0506	0.571210
$523$	−10.6545	−0.465890	−0.232945	−	0.972490i	$-0.574836\pi$
$523$	−10.6545	−0.465890	−0.232945	+	0.972490i	$0.574836\pi$
$524$	15.1916	0.663647
$525$	−1.63079	−0.0711733
$526$	3.15227	0.137446
$527$	23.4372	1.02094
$528$	−157.795	−6.86716
$529$	−20.7682	−0.902965
$530$	−21.1677	−0.919467
$531$	19.4904	0.845813
$532$	17.1917	0.745354
$533$	38.3662	1.66183
$534$	49.8810	2.15856
$535$	3.98327	0.172212
$536$	80.1674	3.46270
$537$	−13.5165	−0.583281
$538$	−49.8490	−2.14914
$539$	−40.3113	−1.73633
$540$	−9.80399	−0.421896
$541$	12.0066	0.516204	0.258102	−	0.966118i	$-0.416903\pi$
$541$	12.0066	0.516204	0.258102	+	0.966118i	$0.416903\pi$
$542$	72.2883	3.10505
$543$	23.5715	1.01155
$544$	33.5746	1.43950
$545$	−8.39078	−0.359421
$546$	17.1938	0.735828
$547$	6.88138	0.294227	0.147113	−	0.989120i	$-0.453002\pi$
$547$	6.88138	0.294227	0.147113	+	0.989120i	$0.453002\pi$
$548$	9.08413	0.388055
$549$	−8.47673	−0.361778
$550$	−15.9849	−0.681600
$551$	−7.44324	−0.317093
$552$	−29.1865	−1.24226
$553$	3.36176	0.142957
$554$	51.2723	2.17835
$555$	2.29640	0.0974767
$556$	80.4417	3.41149
$557$	30.4904	1.29192	0.645961	−	0.763371i	$-0.276457\pi$
$557$	30.4904	1.29192	0.645961	+	0.763371i	$0.276457\pi$
$558$	76.1006	3.22160
$559$	−5.38044	−0.227568
$560$	6.22634	0.263111
$561$	48.3608	2.04180
$562$	38.1933	1.61109
$563$	−35.7166	−1.50527	−0.752637	−	0.658435i	$-0.771219\pi$
$563$	−35.7166	−1.50527	−0.752637	+	0.658435i	$0.771219\pi$
$564$	−28.4014	−1.19591
$565$	4.04417	0.170139
$566$	82.1808	3.45432
$567$	−3.80803	−0.159922
$568$	−46.0344	−1.93156
$569$	10.0744	0.422341	0.211171	−	0.977449i	$-0.432272\pi$
$569$	10.0744	0.422341	0.211171	+	0.977449i	$0.432272\pi$
$570$	38.4618	1.61099
$571$	14.5338	0.608221	0.304111	−	0.952637i	$-0.401641\pi$
$571$	14.5338	0.608221	0.304111	+	0.952637i	$0.401641\pi$
$572$	119.434	4.99377
$573$	−13.9656	−0.583420
$574$	−15.6520	−0.653304
$575$	−1.49392	−0.0623008
$576$	34.0048	1.41687
$577$	34.7707	1.44752	0.723761	−	0.690051i	$-0.242412\pi$
$577$	34.7707	1.44752	0.723761	+	0.690051i	$0.242412\pi$
$578$	20.2390	0.841832
$579$	−55.6008	−2.31069
$580$	−6.42026	−0.266587
$581$	0.840090	0.0348528
$582$	13.0680	0.541686
$583$	49.2892	2.04135
$584$	19.9253	0.824514
$585$	15.1878	0.627937
$586$	13.2115	0.545760
$587$	−39.2003	−1.61797	−0.808985	−	0.587830i	$-0.799983\pi$
$587$	−39.2003	−1.61797	−0.808985	+	0.587830i	$0.799983\pi$
$588$	83.6634	3.45022
$589$	−43.4029	−1.78839
$590$	−13.5302	−0.557029
$591$	−54.6051	−2.24615
$592$	−8.76766	−0.360348
$593$	5.61098	0.230415	0.115208	−	0.993341i	$-0.463247\pi$
$593$	5.61098	0.230415	0.115208	+	0.993341i	$0.463247\pi$
$594$	32.2138	1.32175
$595$	−1.90824	−0.0782302
$596$	−30.6735	−1.25644
$597$	−15.5286	−0.635545
$598$	15.7508	0.644099
$599$	−19.4745	−0.795705	−0.397853	−	0.917449i	$-0.630244\pi$
$599$	−19.4745	−0.795705	−0.397853	+	0.917449i	$0.630244\pi$
$600$	19.5368	0.797588
$601$	−34.4715	−1.40612	−0.703061	−	0.711129i	$-0.748184\pi$
$601$	−34.4715	−1.40612	−0.703061	+	0.711129i	$0.748184\pi$
$602$	2.19503	0.0894626
$603$	−40.3097	−1.64154
$604$	39.2294	1.59622
$605$	26.2211	1.06604
$606$	1.31532	0.0534313
$607$	21.8789	0.888038	0.444019	−	0.896017i	$-0.353552\pi$
$607$	21.8789	0.888038	0.444019	+	0.896017i	$0.353552\pi$
$608$	−62.1763	−2.52158
$609$	2.15217	0.0872105
$610$	5.88451	0.238257
$611$	9.02600	0.365153
$612$	−55.9209	−2.26047
$613$	30.5389	1.23346	0.616728	−	0.787177i	$-0.288458\pi$
$613$	30.5389	1.23346	0.616728	+	0.787177i	$0.288458\pi$
$614$	7.09437	0.286305
$615$	−24.8154	−1.00065
$616$	−28.6934	−1.15609
$617$	−0.480408	−0.0193405	−0.00967024	−	0.999953i	$-0.503078\pi$
$617$	−0.480408	−0.0193405	−0.00967024	+	0.999953i	$0.503078\pi$
$618$	56.1621	2.25917
$619$	23.0096	0.924835	0.462417	−	0.886662i	$-0.346982\pi$
$619$	23.0096	0.924835	0.462417	+	0.886662i	$0.346982\pi$
$620$	−37.4377	−1.50354
$621$	3.01064	0.120813
$622$	42.4138	1.70064
$623$	4.58303	0.183615
$624$	−104.078	−4.16646
$625$	1.00000	0.0400000
$626$	−5.17255	−0.206737
$627$	−89.5587	−3.57663
$628$	7.37968	0.294481
$629$	2.68710	0.107142
$630$	−6.19606	−0.246857
$631$	7.04647	0.280516	0.140258	−	0.990115i	$-0.455207\pi$
$631$	7.04647	0.280516	0.140258	+	0.990115i	$0.455207\pi$
$632$	−40.2740	−1.60201
$633$	63.8679	2.53852
$634$	22.8041	0.905667
$635$	−3.96917	−0.157512
$636$	−102.297	−4.05632
$637$	−26.5884	−1.05347
$638$	21.0956	0.835182
$639$	23.1470	0.915679
$640$	−1.55777	−0.0615763
$641$	−10.3928	−0.410490	−0.205245	−	0.978711i	$-0.565799\pi$
$641$	−10.3928	−0.410490	−0.205245	+	0.978711i	$0.565799\pi$
$642$	27.1636	1.07206
$643$	12.3653	0.487642	0.243821	−	0.969820i	$-0.421599\pi$
$643$	12.3653	0.487642	0.243821	+	0.969820i	$0.421599\pi$
$644$	−4.55370	−0.179441
$645$	3.48008	0.137028
$646$	45.0055	1.77072
$647$	36.1866	1.42264	0.711321	−	0.702868i	$-0.248097\pi$
$647$	36.1866	1.42264	0.711321	+	0.702868i	$0.248097\pi$
$648$	45.6203	1.79213
$649$	31.5052	1.23669
$650$	−10.5433	−0.413542
$651$	12.5497	0.491862
$652$	33.7809	1.32296
$653$	−33.8840	−1.32599	−0.662993	−	0.748626i	$-0.730714\pi$
$653$	−33.8840	−1.32599	−0.662993	+	0.748626i	$0.730714\pi$
$654$	−57.2203	−2.23749
$655$	3.12270	0.122014
$656$	94.7453	3.69918
$657$	−10.0188	−0.390871
$658$	−3.68228	−0.143550
$659$	5.04584	0.196558	0.0982790	−	0.995159i	$-0.468666\pi$
$659$	5.04584	0.196558	0.0982790	+	0.995159i	$0.468666\pi$
$660$	−77.2499	−3.00695
$661$	−4.91246	−0.191073	−0.0955363	−	0.995426i	$-0.530457\pi$
$661$	−4.91246	−0.191073	−0.0955363	+	0.995426i	$0.530457\pi$
$662$	−69.6222	−2.70594
$663$	31.8977	1.23880
$664$	−10.0643	−0.390571
$665$	3.53384	0.137036
$666$	8.72502	0.338088
$667$	1.97155	0.0763388
$668$	88.2555	3.41471
$669$	7.44993	0.288031
$670$	27.9828	1.08107
$671$	−13.7021	−0.528965
$672$	17.9780	0.693515
$673$	28.6388	1.10394	0.551972	−	0.833863i	$-0.313876\pi$
$673$	28.6388	1.10394	0.551972	+	0.833863i	$0.313876\pi$
$674$	−67.4966	−2.59987
$675$	−2.01526	−0.0775673
$676$	15.5321	0.597389
$677$	7.64880	0.293967	0.146984	−	0.989139i	$-0.453044\pi$
$677$	7.64880	0.293967	0.146984	+	0.989139i	$0.453044\pi$
$678$	27.5789	1.05916
$679$	1.20068	0.0460777
$680$	22.8607	0.876669
$681$	46.9599	1.79951
$682$	123.012	4.71038
$683$	−13.1156	−0.501854	−0.250927	−	0.968006i	$-0.580735\pi$
$683$	−13.1156	−0.501854	−0.250927	+	0.968006i	$0.580735\pi$
$684$	103.559	3.95968
$685$	1.86729	0.0713454
$686$	22.3387	0.852894
$687$	−75.0426	−2.86305
$688$	−13.2870	−0.506561
$689$	32.5100	1.23853
$690$	−10.1877	−0.387839
$691$	−21.0883	−0.802237	−0.401119	−	0.916026i	$-0.631378\pi$
$691$	−21.0883	−0.802237	−0.401119	+	0.916026i	$0.631378\pi$
$692$	19.4387	0.738947
$693$	14.4276	0.548059
$694$	62.2906	2.36452
$695$	16.5352	0.627215
$696$	−25.7831	−0.977305
$697$	−29.0374	−1.09987
$698$	19.2308	0.727897
$699$	53.5402	2.02508
$700$	3.04816	0.115209
$701$	1.04672	0.0395339	0.0197669	−	0.999805i	$-0.493708\pi$
$701$	1.04672	0.0395339	0.0197669	+	0.999805i	$0.493708\pi$
$702$	21.2475	0.801933
$703$	−4.97619	−0.187681
$704$	54.9668	2.07164
$705$	−5.83804	−0.219873
$706$	−70.1308	−2.63941
$707$	0.120851	0.00454505
$708$	−65.3870	−2.45739
$709$	−25.4130	−0.954404	−0.477202	−	0.878794i	$-0.658349\pi$
$709$	−25.4130	−0.954404	−0.477202	+	0.878794i	$0.658349\pi$
$710$	−16.0685	−0.603041
$711$	20.2505	0.759454
$712$	−54.9047	−2.05764
$713$	11.4965	0.430547
$714$	−13.0131	−0.487003
$715$	24.5502	0.918124
$716$	25.2642	0.944167
$717$	15.5521	0.580806
$718$	85.7374	3.19969
$719$	4.14597	0.154619	0.0773093	−	0.997007i	$-0.475367\pi$
$719$	4.14597	0.154619	0.0773093	+	0.997007i	$0.475367\pi$
$720$	37.5061	1.39777
$721$	5.16013	0.192173
$722$	−33.5632	−1.24909
$723$	−32.0825	−1.19316
$724$	−44.0583	−1.63741
$725$	−1.31972	−0.0490130
$726$	178.813	6.63637
$727$	−31.6888	−1.17527	−0.587637	−	0.809125i	$-0.699942\pi$
$727$	−31.6888	−1.17527	−0.587637	+	0.809125i	$0.699942\pi$
$728$	−18.9255	−0.701426
$729$	−38.6743	−1.43238
$730$	6.95502	0.257417
$731$	4.07217	0.150615
$732$	28.4379	1.05110
$733$	−16.8920	−0.623921	−0.311961	−	0.950095i	$-0.600986\pi$
$733$	−16.8920	−0.623921	−0.311961	+	0.950095i	$0.600986\pi$
$734$	23.5179	0.868063
$735$	17.1974	0.634337
$736$	16.4691	0.607061
$737$	−65.1583	−2.40014
$738$	−94.2845	−3.47066
$739$	21.7263	0.799216	0.399608	−	0.916686i	$-0.369146\pi$
$739$	21.7263	0.799216	0.399608	+	0.916686i	$0.369146\pi$
$740$	−4.29228	−0.157787
$741$	−59.0708	−2.17002
$742$	−13.2629	−0.486897
$743$	−10.1453	−0.372194	−0.186097	−	0.982531i	$-0.559584\pi$
$743$	−10.1453	−0.372194	−0.186097	+	0.982531i	$0.559584\pi$
$744$	−150.346	−5.51195
$745$	−6.30510	−0.231001
$746$	48.5521	1.77762
$747$	5.06052	0.185155
$748$	−90.3929	−3.30509
$749$	2.49577	0.0911936
$750$	6.81943	0.249010
$751$	−24.5494	−0.895821	−0.447910	−	0.894078i	$-0.647832\pi$
$751$	−24.5494	−0.895821	−0.447910	+	0.894078i	$0.647832\pi$
$752$	22.2897	0.812820
$753$	75.9882	2.76916
$754$	13.9142	0.506724
$755$	8.06380	0.293472
$756$	−6.14282	−0.223412
$757$	2.88109	0.104715	0.0523576	−	0.998628i	$-0.483326\pi$
$757$	2.88109	0.104715	0.0523576	+	0.998628i	$0.483326\pi$
$758$	−47.7650	−1.73490
$759$	23.7221	0.861059
$760$	−42.3354	−1.53567
$761$	−2.74630	−0.0995532	−0.0497766	−	0.998760i	$-0.515851\pi$
$761$	−2.74630	−0.0995532	−0.0497766	+	0.998760i	$0.515851\pi$
$762$	−27.0674	−0.980550
$763$	−5.25735	−0.190329
$764$	26.1035	0.944392
$765$	−11.4948	−0.415596
$766$	−32.7725	−1.18412
$767$	20.7801	0.750325
$768$	36.2763	1.30901
$769$	11.1330	0.401465	0.200733	−	0.979646i	$-0.435668\pi$
$769$	11.1330	0.401465	0.200733	+	0.979646i	$0.435668\pi$
$770$	−10.0156	−0.360936
$771$	−65.4382	−2.35670
$772$	103.925	3.74036
$773$	−4.90884	−0.176559	−0.0882793	−	0.996096i	$-0.528137\pi$
$773$	−4.90884	−0.176559	−0.0882793	+	0.996096i	$0.528137\pi$
$774$	13.2224	0.475268
$775$	−7.69551	−0.276431
$776$	−14.3841	−0.516360
$777$	1.43884	0.0516181
$778$	−59.3948	−2.12941
$779$	53.7738	1.92665
$780$	−50.9522	−1.82438
$781$	37.4157	1.33884
$782$	−11.9210	−0.426293
$783$	2.65957	0.0950453
$784$	−65.6598	−2.34499
$785$	1.51693	0.0541416
$786$	21.2951	0.759570
$787$	−12.5494	−0.447337	−0.223669	−	0.974665i	$-0.571803\pi$
$787$	−12.5494	−0.447337	−0.223669	+	0.974665i	$0.571803\pi$
$788$	102.064	3.63589
$789$	3.13140	0.111481
$790$	−14.0578	−0.500155
$791$	2.53393	0.0900961
$792$	−172.843	−6.14170
$793$	−9.03761	−0.320935
$794$	87.3041	3.09831
$795$	−21.0276	−0.745771
$796$	29.0251	1.02877
$797$	10.4149	0.368914	0.184457	−	0.982841i	$-0.440947\pi$
$797$	10.4149	0.368914	0.184457	+	0.982841i	$0.440947\pi$
$798$	24.0988	0.853087
$799$	−6.83130	−0.241674
$800$	−11.0241	−0.389761
$801$	27.6071	0.975451
$802$	−79.6347	−2.81200
$803$	−16.1948	−0.571503
$804$	135.232	4.76926
$805$	−0.936036	−0.0329909
$806$	81.1360	2.85789
$807$	−49.5190	−1.74315
$808$	−1.44779	−0.0509332
$809$	51.0084	1.79336	0.896680	−	0.442680i	$-0.145972\pi$
$809$	51.0084	1.79336	0.896680	+	0.442680i	$0.145972\pi$
$810$	15.9240	0.559511
$811$	9.86857	0.346532	0.173266	−	0.984875i	$-0.444568\pi$
$811$	9.86857	0.346532	0.173266	+	0.984875i	$0.444568\pi$
$812$	−4.02270	−0.141169
$813$	71.8098	2.51848
$814$	14.1035	0.494327
$815$	6.94383	0.243232
$816$	78.7711	2.75754
$817$	−7.54119	−0.263833
$818$	82.4796	2.88383
$819$	9.51610	0.332520
$820$	46.3833	1.61977
$821$	12.5308	0.437327	0.218664	−	0.975800i	$-0.429830\pi$
$821$	12.5308	0.437327	0.218664	+	0.975800i	$0.429830\pi$
$822$	12.7338	0.444144
$823$	25.6924	0.895580	0.447790	−	0.894139i	$-0.352211\pi$
$823$	25.6924	0.895580	0.447790	+	0.894139i	$0.352211\pi$
$824$	−61.8184	−2.15355
$825$	−15.8791	−0.552840
$826$	−8.47752	−0.294971
$827$	21.0995	0.733701	0.366851	−	0.930280i	$-0.380436\pi$
$827$	21.0995	0.733701	0.366851	+	0.930280i	$0.380436\pi$
$828$	−27.4305	−0.953276
$829$	34.3049	1.19146	0.595729	−	0.803185i	$-0.296863\pi$
$829$	34.3049	1.19146	0.595729	+	0.803185i	$0.296863\pi$
$830$	−3.51299	−0.121938
$831$	50.9329	1.76684
$832$	36.2548	1.25691
$833$	20.1233	0.697231
$834$	112.761	3.90458
$835$	18.1414	0.627807
$836$	167.397	5.78955
$837$	15.5084	0.536050
$838$	−39.5385	−1.36584
$839$	−0.996633	−0.0344076	−0.0172038	−	0.999852i	$-0.505476\pi$
$839$	−0.996633	−0.0344076	−0.0172038	+	0.999852i	$0.505476\pi$
$840$	12.2411	0.422357
$841$	−27.2583	−0.939943
$842$	1.71830	0.0592167
$843$	37.9405	1.30674
$844$	−119.378	−4.10915
$845$	3.19270	0.109832
$846$	−22.1813	−0.762608
$847$	16.4292	0.564513
$848$	80.2833	2.75694
$849$	81.6368	2.80177
$850$	7.97965	0.273700
$851$	1.31808	0.0451833
$852$	−77.6539	−2.66038
$853$	57.0630	1.95380	0.976900	−	0.213696i	$-0.0685502\pi$
$853$	57.0630	1.95380	0.976900	+	0.213696i	$0.0685502\pi$
$854$	3.68702	0.126167
$855$	21.2871	0.728002
$856$	−29.8994	−1.02194
$857$	−35.4405	−1.21062	−0.605312	−	0.795988i	$-0.706952\pi$
$857$	−35.4405	−1.21062	−0.605312	+	0.795988i	$0.706952\pi$
$858$	167.418	5.71556
$859$	−0.230402	−0.00786120	−0.00393060	−	0.999992i	$-0.501251\pi$
$859$	−0.230402	−0.00786120	−0.00393060	+	0.999992i	$0.501251\pi$
$860$	−6.50474	−0.221810
$861$	−15.5484	−0.529889
$862$	−41.7562	−1.42222
$863$	48.4731	1.65004	0.825021	−	0.565102i	$-0.191163\pi$
$863$	48.4731	1.65004	0.825021	+	0.565102i	$0.191163\pi$
$864$	22.2164	0.755819
$865$	3.99571	0.135858
$866$	−62.1693	−2.11260
$867$	20.1050	0.682802
$868$	−23.4571	−0.796186
$869$	32.7338	1.11042
$870$	−8.99971	−0.305119
$871$	−42.9769	−1.45622
$872$	62.9832	2.13288
$873$	7.23261	0.244787
$874$	22.0762	0.746740
$875$	0.626563	0.0211817
$876$	33.6113	1.13562
$877$	22.3829	0.755818	0.377909	−	0.925843i	$-0.376643\pi$
$877$	22.3829	0.755818	0.377909	+	0.925843i	$0.376643\pi$
$878$	35.4623	1.19680
$879$	13.1240	0.442661
$880$	60.6265	2.04372
$881$	−23.8491	−0.803496	−0.401748	−	0.915750i	$-0.631597\pi$
$881$	−23.8491	−0.803496	−0.401748	+	0.915750i	$0.631597\pi$
$882$	65.3405	2.20013
$883$	14.8684	0.500363	0.250181	−	0.968199i	$-0.419510\pi$
$883$	14.8684	0.500363	0.250181	+	0.968199i	$0.419510\pi$
$884$	−59.6210	−2.00527
$885$	−13.4406	−0.451801
$886$	−99.0769	−3.32855
$887$	16.3149	0.547802	0.273901	−	0.961758i	$-0.411686\pi$
$887$	16.3149	0.547802	0.273901	+	0.961758i	$0.411686\pi$
$888$	−17.2373	−0.578447
$889$	−2.48693	−0.0834091
$890$	−19.1648	−0.642405
$891$	−37.0791	−1.24220
$892$	−13.9249	−0.466240
$893$	12.6508	0.423342
$894$	−42.9972	−1.43804
$895$	5.19318	0.173589
$896$	−0.976042	−0.0326073
$897$	15.6466	0.522423
$898$	69.5483	2.32086
$899$	10.1559	0.338718
$900$	18.3614	0.612047
$901$	−24.6051	−0.819715
$902$	−152.405	−5.07455
$903$	2.18049	0.0725623
$904$	−30.3565	−1.00964
$905$	−9.05641	−0.301045
$906$	54.9905	1.82694
$907$	23.8246	0.791083	0.395542	−	0.918448i	$-0.370557\pi$
$907$	23.8246	0.791083	0.395542	+	0.918448i	$0.370557\pi$
$908$	−87.7743	−2.91289
$909$	0.727978	0.0241455
$910$	−6.60604	−0.218988
$911$	45.6863	1.51365	0.756827	−	0.653615i	$-0.226748\pi$
$911$	45.6863	1.51365	0.756827	+	0.653615i	$0.226748\pi$
$912$	−145.875	−4.83040
$913$	8.18004	0.270720
$914$	−99.2298	−3.28223
$915$	5.84555	0.193248
$916$	140.265	4.63448
$917$	1.95657	0.0646117
$918$	−16.0811	−0.530754
$919$	−47.1923	−1.55673	−0.778366	−	0.627811i	$-0.783951\pi$
$919$	−47.1923	−1.55673	−0.778366	+	0.627811i	$0.783951\pi$
$920$	11.2137	0.369706
$921$	7.04740	0.232220
$922$	41.4070	1.36367
$923$	24.6785	0.812303
$924$	−48.4020	−1.59231
$925$	−0.882299	−0.0290098
$926$	33.3196	1.09495
$927$	31.0835	1.02092
$928$	14.5487	0.477585
$929$	16.3712	0.537120	0.268560	−	0.963263i	$-0.413452\pi$
$929$	16.3712	0.537120	0.268560	+	0.963263i	$0.413452\pi$
$930$	−52.4790	−1.72085
$931$	−37.2660	−1.22135
$932$	−100.074	−3.27803
$933$	42.1330	1.37937
$934$	79.3150	2.59526
$935$	−18.5807	−0.607654
$936$	−114.003	−3.72631
$937$	−36.4723	−1.19150	−0.595749	−	0.803170i	$-0.703145\pi$
$937$	−36.4723	−1.19150	−0.595749	+	0.803170i	$0.703145\pi$
$938$	17.5330	0.572473
$939$	−5.13830	−0.167682
$940$	10.9121	0.355913
$941$	37.5503	1.22411	0.612053	−	0.790817i	$-0.290344\pi$
$941$	37.5503	1.22411	0.612053	+	0.790817i	$0.290344\pi$
$942$	10.3446	0.337045
$943$	−14.2435	−0.463832
$944$	51.3163	1.67020
$945$	−1.26269	−0.0410752
$946$	21.3732	0.694902
$947$	0.875581	0.0284526	0.0142263	−	0.999899i	$-0.495471\pi$
$947$	0.875581	0.0284526	0.0142263	+	0.999899i	$0.495471\pi$
$948$	−67.9369	−2.20649
$949$	−10.6817	−0.346744
$950$	−14.7774	−0.479442
$951$	22.6531	0.734578
$952$	14.3237	0.464234
$953$	10.0550	0.325713	0.162857	−	0.986650i	$-0.447929\pi$
$953$	10.0550	0.325713	0.162857	+	0.986650i	$0.447929\pi$
$954$	−79.8929	−2.58663
$955$	5.36571	0.173630
$956$	−29.0690	−0.940160
$957$	20.9559	0.677409
$958$	−71.8023	−2.31983
$959$	1.16997	0.0377804
$960$	−23.4497	−0.756836
$961$	28.2209	0.910351
$962$	9.30233	0.299919
$963$	15.0340	0.484464
$964$	59.9665	1.93139
$965$	21.3624	0.687679
$966$	−6.38323	−0.205377
$967$	43.4751	1.39806	0.699032	−	0.715091i	$-0.253615\pi$
$967$	43.4751	1.39806	0.699032	+	0.715091i	$0.253615\pi$
$968$	−196.822	−6.32609
$969$	44.7075	1.43621
$970$	−5.02085	−0.161210
$971$	−14.8491	−0.476531	−0.238266	−	0.971200i	$-0.576579\pi$
$971$	−14.8491	−0.476531	−0.238266	+	0.971200i	$0.576579\pi$
$972$	106.367	3.41173
$973$	10.3603	0.332137
$974$	36.5883	1.17236
$975$	−10.4735	−0.335420
$976$	−22.3183	−0.714392
$977$	−58.5320	−1.87260	−0.936302	−	0.351196i	$-0.885775\pi$
$977$	−58.5320	−1.87260	−0.936302	+	0.351196i	$0.885775\pi$
$978$	47.3530	1.51418
$979$	44.6254	1.42623
$980$	−32.1443	−1.02681
$981$	−31.6692	−1.01112
$982$	18.3366	0.585144
$983$	4.66524	0.148798	0.0743991	−	0.997229i	$-0.476296\pi$
$983$	4.66524	0.148798	0.0743991	+	0.997229i	$0.476296\pi$
$984$	186.270	5.93808
$985$	20.9798	0.668473
$986$	−10.5309	−0.335372
$987$	−3.65790	−0.116432
$988$	110.411	3.51265
$989$	1.99749	0.0635166
$990$	−60.3317	−1.91747
$991$	−0.589351	−0.0187214	−0.00936068	−	0.999956i	$-0.502980\pi$
$991$	−0.589351	−0.0187214	−0.00936068	+	0.999956i	$0.502980\pi$
$992$	84.8362	2.69355
$993$	−69.1613	−2.19477
$994$	−10.0679	−0.319336
$995$	5.96625	0.189143
$996$	−16.9771	−0.537941
$997$	38.7294	1.22657	0.613287	−	0.789860i	$-0.289847\pi$
$997$	38.7294	1.22657	0.613287	+	0.789860i	$0.289847\pi$
$998$	82.0451	2.59709
$999$	1.77806	0.0562553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.e.1.6	✓	153

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.e.1.6	✓	153	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)

\(f(q)\)	\(=\)	\(q-2.62009 q^{2} -2.60275 q^{3} +4.86488 q^{4} +1.00000 q^{5} +6.81943 q^{6} +0.626563 q^{7} -7.50624 q^{8} +3.77428 q^{9} +O(q^{10})\)	\(q-2.62009 q^{2} -2.60275 q^{3} +4.86488 q^{4} +1.00000 q^{5} +6.81943 q^{6} +0.626563 q^{7} -7.50624 q^{8} +3.77428 q^{9} -2.62009 q^{10} +6.10091 q^{11} -12.6620 q^{12} +4.02402 q^{13} -1.64165 q^{14} -2.60275 q^{15} +9.93729 q^{16} -3.04556 q^{17} -9.88896 q^{18} +5.64003 q^{19} +4.86488 q^{20} -1.63079 q^{21} -15.9849 q^{22} -1.49392 q^{23} +19.5368 q^{24} +1.00000 q^{25} -10.5433 q^{26} -2.01526 q^{27} +3.04816 q^{28} -1.31972 q^{29} +6.81943 q^{30} -7.69551 q^{31} -11.0241 q^{32} -15.8791 q^{33} +7.97965 q^{34} +0.626563 q^{35} +18.3614 q^{36} -0.882299 q^{37} -14.7774 q^{38} -10.4735 q^{39} -7.50624 q^{40} +9.53432 q^{41} +4.27281 q^{42} -1.33708 q^{43} +29.6802 q^{44} +3.77428 q^{45} +3.91421 q^{46} +2.24303 q^{47} -25.8642 q^{48} -6.60742 q^{49} -2.62009 q^{50} +7.92682 q^{51} +19.5763 q^{52} +8.07900 q^{53} +5.28016 q^{54} +6.10091 q^{55} -4.70314 q^{56} -14.6796 q^{57} +3.45778 q^{58} +5.16401 q^{59} -12.6620 q^{60} -2.24592 q^{61} +20.1629 q^{62} +2.36483 q^{63} +9.00961 q^{64} +4.02402 q^{65} +41.6047 q^{66} -10.6801 q^{67} -14.8163 q^{68} +3.88829 q^{69} -1.64165 q^{70} +6.13281 q^{71} -28.3307 q^{72} -2.65449 q^{73} +2.31170 q^{74} -2.60275 q^{75} +27.4381 q^{76} +3.82261 q^{77} +27.4415 q^{78} +5.36540 q^{79} +9.93729 q^{80} -6.07764 q^{81} -24.9808 q^{82} +1.34079 q^{83} -7.93357 q^{84} -3.04556 q^{85} +3.50328 q^{86} +3.43489 q^{87} -45.7949 q^{88} +7.31454 q^{89} -9.88896 q^{90} +2.52130 q^{91} -7.26774 q^{92} +20.0295 q^{93} -5.87695 q^{94} +5.64003 q^{95} +28.6930 q^{96} +1.91629 q^{97} +17.3120 q^{98} +23.0265 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9}+O(q^{10}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9	\( 153 q + 18 q^{2} + 7 q^{3} + 176 q^{4} + 153 q^{5} + 19 q^{6} + 5 q^{7} + 57 q^{8} + 206 q^{9} + 18 q^{10} + 38 q^{11} + 14 q^{12} + 28 q^{13} + 53 q^{14} + 7 q^{15} + 214 q^{16} + 50 q^{17} + 47 q^{18} + 65 q^{19} + 176 q^{20} + 109 q^{21} + 13 q^{22} + 52 q^{23} + 66 q^{24} + 153 q^{25} + 36 q^{26} + 19 q^{27} + 26 q^{28} + 172 q^{29} + 19 q^{30} + 60 q^{31} + 107 q^{32} + 4 q^{33} + 40 q^{34} + 5 q^{35} + 241 q^{36} + 65 q^{37} + 29 q^{38} + 56 q^{39} + 57 q^{40} + 152 q^{41} - 19 q^{42} + 22 q^{43} + 97 q^{44} + 206 q^{45} + 86 q^{46} + 37 q^{47} - 4 q^{48} + 260 q^{49} + 18 q^{50} + 102 q^{51} - 6 q^{52} + 169 q^{53} + 64 q^{54} + 38 q^{55} + 146 q^{56} + 40 q^{57} - 9 q^{58} + 64 q^{59} + 14 q^{60} + 164 q^{61} + 12 q^{62} + 19 q^{63} + 259 q^{64} + 28 q^{65} + 6 q^{66} + 5 q^{67} + 112 q^{68} + 119 q^{69} + 53 q^{70} + 100 q^{71} + 77 q^{72} + 10 q^{73} + 98 q^{74} + 7 q^{75} + 126 q^{76} + 80 q^{77} - 4 q^{78} + 110 q^{79} + 214 q^{80} + 305 q^{81} - 27 q^{82} + 36 q^{83} + 172 q^{84} + 50 q^{85} + 44 q^{86} + 23 q^{87} + 47 q^{88} + 143 q^{89} + 47 q^{90} + 82 q^{91} + 130 q^{92} + 31 q^{93} + 77 q^{94} + 65 q^{95} + 57 q^{96} + 11 q^{97} + 29 q^{98} + 99 q^{99}+O(q^{100}) \) 153 * q + 18 * q^2 + 7 * q^3 + 176 * q^4 + 153 * q^5 + 19 * q^6 + 5 * q^7 + 57 * q^8 + 206 * q^9 + 18 * q^10 + 38 * q^11 + 14 * q^12 + 28 * q^13 + 53 * q^14 + 7 * q^15 + 214 * q^16 + 50 * q^17 + 47 * q^18 + 65 * q^19 + 176 * q^20 + 109 * q^21 + 13 * q^22 + 52 * q^23 + 66 * q^24 + 153 * q^25 + 36 * q^26 + 19 * q^27 + 26 * q^28 + 172 * q^29 + 19 * q^30 + 60 * q^31 + 107 * q^32 + 4 * q^33 + 40 * q^34 + 5 * q^35 + 241 * q^36 + 65 * q^37 + 29 * q^38 + 56 * q^39 + 57 * q^40 + 152 * q^41 - 19 * q^42 + 22 * q^43 + 97 * q^44 + 206 * q^45 + 86 * q^46 + 37 * q^47 - 4 * q^48 + 260 * q^49 + 18 * q^50 + 102 * q^51 - 6 * q^52 + 169 * q^53 + 64 * q^54 + 38 * q^55 + 146 * q^56 + 40 * q^57 - 9 * q^58 + 64 * q^59 + 14 * q^60 + 164 * q^61 + 12 * q^62 + 19 * q^63 + 259 * q^64 + 28 * q^65 + 6 * q^66 + 5 * q^67 + 112 * q^68 + 119 * q^69 + 53 * q^70 + 100 * q^71 + 77 * q^72 + 10 * q^73 + 98 * q^74 + 7 * q^75 + 126 * q^76 + 80 * q^77 - 4 * q^78 + 110 * q^79 + 214 * q^80 + 305 * q^81 - 27 * q^82 + 36 * q^83 + 172 * q^84 + 50 * q^85 + 44 * q^86 + 23 * q^87 + 47 * q^88 + 143 * q^89 + 47 * q^90 + 82 * q^91 + 130 * q^92 + 31 * q^93 + 77 * q^94 + 65 * q^95 + 57 * q^96 + 11 * q^97 + 29 * q^98 + 99 * q^99

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