LMFDB - Embedded newform 6001.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78095 q^{2} -2.69588 q^{3} +5.73371 q^{4} +2.30800 q^{5} +7.49712 q^{6} +4.50681 q^{7} -10.3833 q^{8} +4.26777 q^{9} +O(q^{10})$	\(q-2.78095 q^{2} -2.69588 q^{3} +5.73371 q^{4} +2.30800 q^{5} +7.49712 q^{6} +4.50681 q^{7} -10.3833 q^{8} +4.26777 q^{9} -6.41845 q^{10} -3.11576 q^{11} -15.4574 q^{12} +4.45445 q^{13} -12.5332 q^{14} -6.22210 q^{15} +17.4080 q^{16} -1.00000 q^{17} -11.8685 q^{18} -6.76014 q^{19} +13.2334 q^{20} -12.1498 q^{21} +8.66479 q^{22} -5.64786 q^{23} +27.9921 q^{24} +0.326883 q^{25} -12.3876 q^{26} -3.41777 q^{27} +25.8407 q^{28} +7.48266 q^{29} +17.3034 q^{30} +0.427409 q^{31} -27.6443 q^{32} +8.39972 q^{33} +2.78095 q^{34} +10.4017 q^{35} +24.4702 q^{36} -9.70653 q^{37} +18.7996 q^{38} -12.0087 q^{39} -23.9646 q^{40} -0.0130662 q^{41} +33.7881 q^{42} +0.920521 q^{43} -17.8649 q^{44} +9.85004 q^{45} +15.7064 q^{46} +6.38029 q^{47} -46.9299 q^{48} +13.3113 q^{49} -0.909046 q^{50} +2.69588 q^{51} +25.5405 q^{52} +9.00462 q^{53} +9.50465 q^{54} -7.19119 q^{55} -46.7954 q^{56} +18.2245 q^{57} -20.8090 q^{58} -8.25149 q^{59} -35.6757 q^{60} +6.41748 q^{61} -1.18861 q^{62} +19.2340 q^{63} +42.0615 q^{64} +10.2809 q^{65} -23.3592 q^{66} -4.57280 q^{67} -5.73371 q^{68} +15.2260 q^{69} -28.9267 q^{70} -11.1276 q^{71} -44.3135 q^{72} -0.406310 q^{73} +26.9934 q^{74} -0.881237 q^{75} -38.7607 q^{76} -14.0421 q^{77} +33.3956 q^{78} -7.32797 q^{79} +40.1777 q^{80} -3.58943 q^{81} +0.0363364 q^{82} +1.27532 q^{83} -69.6635 q^{84} -2.30800 q^{85} -2.55993 q^{86} -20.1724 q^{87} +32.3518 q^{88} -12.4228 q^{89} -27.3925 q^{90} +20.0754 q^{91} -32.3832 q^{92} -1.15224 q^{93} -17.7433 q^{94} -15.6024 q^{95} +74.5257 q^{96} +14.9415 q^{97} -37.0182 q^{98} -13.2974 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.78095	−1.96643	−0.983216	−	0.182446i	$-0.941599\pi$
$2$	−2.78095	−1.96643	−0.983216	+	0.182446i	$0.941599\pi$
$3$	−2.69588	−1.55647	−0.778234	−	0.627975i	$-0.783884\pi$
$3$	−2.69588	−1.55647	−0.778234	+	0.627975i	$0.783884\pi$
$4$	5.73371	2.86685
$5$	2.30800	1.03217	0.516085	−	0.856537i	$-0.327389\pi$
$5$	2.30800	1.03217	0.516085	+	0.856537i	$0.327389\pi$
$6$	7.49712	3.06069
$7$	4.50681	1.70341	0.851707	−	0.524019i	$-0.175568\pi$
$7$	4.50681	1.70341	0.851707	+	0.524019i	$0.175568\pi$
$8$	−10.3833	−3.67104
$9$	4.26777	1.42259
$10$	−6.41845	−2.02969
$11$	−3.11576	−0.939437	−0.469719	−	0.882816i	$-0.655645\pi$
$11$	−3.11576	−0.939437	−0.469719	+	0.882816i	$0.655645\pi$
$12$	−15.4574	−4.46217
$13$	4.45445	1.23544	0.617721	−	0.786397i	$-0.288056\pi$
$13$	4.45445	1.23544	0.617721	+	0.786397i	$0.288056\pi$
$14$	−12.5332	−3.34965
$15$	−6.22210	−1.60654
$16$	17.4080	4.35200
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−11.8685	−2.79743
$19$	−6.76014	−1.55088	−0.775442	−	0.631419i	$-0.782473\pi$
$19$	−6.76014	−1.55088	−0.775442	+	0.631419i	$0.782473\pi$
$20$	13.2334	2.95908
$21$	−12.1498	−2.65131
$22$	8.66479	1.84734
$23$	−5.64786	−1.17766	−0.588830	−	0.808257i	$-0.700411\pi$
$23$	−5.64786	−1.17766	−0.588830	+	0.808257i	$0.700411\pi$
$24$	27.9921	5.71386
$25$	0.326883	0.0653765
$26$	−12.3876	−2.42941
$27$	−3.41777	−0.657750
$28$	25.8407	4.88344
$29$	7.48266	1.38950	0.694748	−	0.719253i	$-0.255516\pi$
$29$	7.48266	1.38950	0.694748	+	0.719253i	$0.255516\pi$
$30$	17.3034	3.15915
$31$	0.427409	0.0767649	0.0383825	−	0.999263i	$-0.487779\pi$
$31$	0.427409	0.0767649	0.0383825	+	0.999263i	$0.487779\pi$
$32$	−27.6443	−4.88687
$33$	8.39972	1.46220
$34$	2.78095	0.476930
$35$	10.4017	1.75821
$36$	24.4702	4.07836
$37$	−9.70653	−1.59574	−0.797872	−	0.602827i	$-0.794041\pi$
$37$	−9.70653	−1.59574	−0.797872	+	0.602827i	$0.794041\pi$
$38$	18.7996	3.04971
$39$	−12.0087	−1.92293
$40$	−23.9646	−3.78914
$41$	−0.0130662	−0.00204059	−0.00102030	−	0.999999i	$-0.500325\pi$
$41$	−0.0130662	−0.00204059	−0.00102030	+	0.999999i	$0.500325\pi$
$42$	33.7881	5.21361
$43$	0.920521	0.140378	0.0701891	−	0.997534i	$-0.477640\pi$
$43$	0.920521	0.140378	0.0701891	+	0.997534i	$0.477640\pi$
$44$	−17.8649	−2.69323
$45$	9.85004	1.46836
$46$	15.7064	2.31579
$47$	6.38029	0.930660	0.465330	−	0.885137i	$-0.345936\pi$
$47$	6.38029	0.930660	0.465330	+	0.885137i	$0.345936\pi$
$48$	−46.9299	−6.77374
$49$	13.3113	1.90162
$50$	−0.909046	−0.128558
$51$	2.69588	0.377499
$52$	25.5405	3.54183
$53$	9.00462	1.23688	0.618440	−	0.785832i	$-0.287765\pi$
$53$	9.00462	1.23688	0.618440	+	0.785832i	$0.287765\pi$
$54$	9.50465	1.29342
$55$	−7.19119	−0.969660
$56$	−46.7954	−6.25330
$57$	18.2245	2.41390
$58$	−20.8090	−2.73235
$59$	−8.25149	−1.07425	−0.537126	−	0.843502i	$-0.680490\pi$
$59$	−8.25149	−1.07425	−0.537126	+	0.843502i	$0.680490\pi$
$60$	−35.6757	−4.60572
$61$	6.41748	0.821674	0.410837	−	0.911709i	$-0.365237\pi$
$61$	6.41748	0.821674	0.410837	+	0.911709i	$0.365237\pi$
$62$	−1.18861	−0.150953
$63$	19.2340	2.42326
$64$	42.0615	5.25769
$65$	10.2809	1.27519
$66$	−23.3592	−2.87532
$67$	−4.57280	−0.558656	−0.279328	−	0.960196i	$-0.590112\pi$
$67$	−4.57280	−0.558656	−0.279328	+	0.960196i	$0.590112\pi$
$68$	−5.73371	−0.695314
$69$	15.2260	1.83299
$70$	−28.9267	−3.45741
$71$	−11.1276	−1.32060	−0.660299	−	0.751003i	$-0.729570\pi$
$71$	−11.1276	−1.32060	−0.660299	+	0.751003i	$0.729570\pi$
$72$	−44.3135	−5.22239
$73$	−0.406310	−0.0475550	−0.0237775	−	0.999717i	$-0.507569\pi$
$73$	−0.406310	−0.0475550	−0.0237775	+	0.999717i	$0.507569\pi$
$74$	26.9934	3.13792
$75$	−0.881237	−0.101756
$76$	−38.7607	−4.44616
$77$	−14.0421	−1.60025
$78$	33.3956	3.78130
$79$	−7.32797	−0.824461	−0.412230	−	0.911080i	$-0.635250\pi$
$79$	−7.32797	−0.824461	−0.412230	+	0.911080i	$0.635250\pi$
$80$	40.1777	4.49200
$81$	−3.58943	−0.398825
$82$	0.0363364	0.00401268
$83$	1.27532	0.139984	0.0699921	−	0.997548i	$-0.477703\pi$
$83$	1.27532	0.139984	0.0699921	+	0.997548i	$0.477703\pi$
$84$	−69.6635	−7.60091
$85$	−2.30800	−0.250338
$86$	−2.55993	−0.276044
$87$	−20.1724	−2.16271
$88$	32.3518	3.44871
$89$	−12.4228	−1.31681	−0.658407	−	0.752662i	$-0.728770\pi$
$89$	−12.4228	−1.31681	−0.658407	+	0.752662i	$0.728770\pi$
$90$	−27.3925	−2.88742
$91$	20.0754	2.10447
$92$	−32.3832	−3.37618
$93$	−1.15224	−0.119482
$94$	−17.7433	−1.83008
$95$	−15.6024	−1.60078
$96$	74.5257	7.60625
$97$	14.9415	1.51707	0.758537	−	0.651630i	$-0.225914\pi$
$97$	14.9415	1.51707	0.758537	+	0.651630i	$0.225914\pi$
$98$	−37.0182	−3.73940
$99$	−13.2974	−1.33644
$100$	1.87425	0.187425
$101$	−15.0762	−1.50013	−0.750067	−	0.661362i	$-0.769979\pi$
$101$	−15.0762	−1.50013	−0.750067	+	0.661362i	$0.769979\pi$
$102$	−7.49712	−0.742326
$103$	15.1777	1.49550	0.747750	−	0.663980i	$-0.231134\pi$
$103$	15.1777	1.49550	0.747750	+	0.663980i	$0.231134\pi$
$104$	−46.2518	−4.53536
$105$	−28.0418	−2.73660
$106$	−25.0414	−2.43224
$107$	−14.9704	−1.44724	−0.723622	−	0.690197i	$-0.757524\pi$
$107$	−14.9704	−1.44724	−0.723622	+	0.690197i	$0.757524\pi$
$108$	−19.5965	−1.88567
$109$	−3.60827	−0.345610	−0.172805	−	0.984956i	$-0.555283\pi$
$109$	−3.60827	−0.345610	−0.172805	+	0.984956i	$0.555283\pi$
$110$	19.9984	1.90677
$111$	26.1677	2.48372
$112$	78.4545	7.41325
$113$	−8.91771	−0.838907	−0.419454	−	0.907777i	$-0.637778\pi$
$113$	−8.91771	−0.838907	−0.419454	+	0.907777i	$0.637778\pi$
$114$	−50.6816	−4.74677
$115$	−13.0353	−1.21555
$116$	42.9034	3.98348
$117$	19.0106	1.75753
$118$	22.9470	2.11244
$119$	−4.50681	−0.413138
$120$	64.6058	5.89768
$121$	−1.29203	−0.117457
$122$	−17.8467	−1.61577
$123$	0.0352248	0.00317611
$124$	2.45064	0.220074
$125$	−10.7856	−0.964691
$126$	−53.4890	−4.76518
$127$	−1.56414	−0.138795	−0.0693973	−	0.997589i	$-0.522108\pi$
$127$	−1.56414	−0.138795	−0.0693973	+	0.997589i	$0.522108\pi$
$128$	−61.6826	−5.45202
$129$	−2.48162	−0.218494
$130$	−28.5907	−2.50757
$131$	13.7540	1.20169	0.600845	−	0.799366i	$-0.294831\pi$
$131$	13.7540	1.20169	0.600845	+	0.799366i	$0.294831\pi$
$132$	48.1615	4.19192
$133$	−30.4667	−2.64179
$134$	12.7167	1.09856
$135$	−7.88822	−0.678910
$136$	10.3833	0.890358
$137$	−17.8847	−1.52799	−0.763995	−	0.645222i	$-0.776765\pi$
$137$	−17.8847	−1.52799	−0.763995	+	0.645222i	$0.776765\pi$
$138$	−42.3427	−3.60445
$139$	−2.35744	−0.199956	−0.0999778	−	0.994990i	$-0.531877\pi$
$139$	−2.35744	−0.199956	−0.0999778	+	0.994990i	$0.531877\pi$
$140$	59.6405	5.04054
$141$	−17.2005	−1.44854
$142$	30.9452	2.59687
$143$	−13.8790	−1.16062
$144$	74.2934	6.19111
$145$	17.2700	1.43420
$146$	1.12993	0.0935137
$147$	−35.8857	−2.95980
$148$	−55.6544	−4.57477
$149$	13.4792	1.10426	0.552131	−	0.833757i	$-0.313815\pi$
$149$	13.4792	1.10426	0.552131	+	0.833757i	$0.313815\pi$
$150$	2.45068	0.200097
$151$	−18.7016	−1.52192	−0.760959	−	0.648800i	$-0.775271\pi$
$151$	−18.7016	−1.52192	−0.760959	+	0.648800i	$0.775271\pi$
$152$	70.1924	5.69336
$153$	−4.26777	−0.345029
$154$	39.0505	3.14678
$155$	0.986462	0.0792345
$156$	−68.8542	−5.51275
$157$	3.05915	0.244147	0.122073	−	0.992521i	$-0.461046\pi$
$157$	3.05915	0.244147	0.122073	+	0.992521i	$0.461046\pi$
$158$	20.3787	1.62125
$159$	−24.2754	−1.92516
$160$	−63.8031	−5.04408
$161$	−25.4538	−2.00604
$162$	9.98204	0.784263
$163$	14.7914	1.15855	0.579276	−	0.815131i	$-0.303335\pi$
$163$	14.7914	1.15855	0.579276	+	0.815131i	$0.303335\pi$
$164$	−0.0749175	−0.00585008
$165$	19.3866	1.50924
$166$	−3.54660	−0.275269
$167$	−19.6957	−1.52410	−0.762050	−	0.647518i	$-0.775807\pi$
$167$	−19.6957	−1.52410	−0.762050	+	0.647518i	$0.775807\pi$
$168$	126.155	9.73306
$169$	6.84214	0.526318
$170$	6.41845	0.492273
$171$	−28.8508	−2.20627
$172$	5.27800	0.402444
$173$	15.2117	1.15652	0.578262	−	0.815851i	$-0.303731\pi$
$173$	15.2117	1.15652	0.578262	+	0.815851i	$0.303731\pi$
$174$	56.0985	4.25281
$175$	1.47320	0.111363
$176$	−54.2391	−4.08843
$177$	22.2450	1.67204
$178$	34.5473	2.58943
$179$	−16.3231	−1.22004	−0.610022	−	0.792385i	$-0.708839\pi$
$179$	−16.3231	−1.22004	−0.610022	+	0.792385i	$0.708839\pi$
$180$	56.4772	4.20957
$181$	−4.64085	−0.344951	−0.172476	−	0.985014i	$-0.555177\pi$
$181$	−4.64085	−0.344951	−0.172476	+	0.985014i	$0.555177\pi$
$182$	−55.8286	−4.13829
$183$	−17.3008	−1.27891
$184$	58.6433	4.32324
$185$	−22.4027	−1.64708
$186$	3.20434	0.234953
$187$	3.11576	0.227847
$188$	36.5827	2.66807
$189$	−15.4032	−1.12042
$190$	43.3897	3.14782
$191$	1.32772	0.0960705	0.0480353	−	0.998846i	$-0.484704\pi$
$191$	1.32772	0.0960705	0.0480353	+	0.998846i	$0.484704\pi$
$192$	−113.393	−8.18342
$193$	17.5229	1.26133	0.630663	−	0.776057i	$-0.282783\pi$
$193$	17.5229	1.26133	0.630663	+	0.776057i	$0.282783\pi$
$194$	−41.5515	−2.98322
$195$	−27.7161	−1.98479
$196$	76.3232	5.45166
$197$	13.3647	0.952193	0.476097	−	0.879393i	$-0.342051\pi$
$197$	13.3647	0.952193	0.476097	+	0.879393i	$0.342051\pi$
$198$	36.9794	2.62801
$199$	9.99003	0.708175	0.354087	−	0.935212i	$-0.384792\pi$
$199$	9.99003	0.708175	0.354087	+	0.935212i	$0.384792\pi$
$200$	−3.39411	−0.240000
$201$	12.3277	0.869530
$202$	41.9261	2.94991
$203$	33.7229	2.36689
$204$	15.4574	1.08223
$205$	−0.0301567	−0.00210624
$206$	−42.2084	−2.94080
$207$	−24.1038	−1.67533
$208$	77.5430	5.37664
$209$	21.0630	1.45696
$210$	77.9830	5.38134
$211$	−20.0494	−1.38026	−0.690130	−	0.723685i	$-0.742447\pi$
$211$	−20.0494	−1.38026	−0.690130	+	0.723685i	$0.742447\pi$
$212$	51.6299	3.54595
$213$	29.9986	2.05547
$214$	41.6320	2.84591
$215$	2.12457	0.144894
$216$	35.4876	2.41463
$217$	1.92625	0.130762
$218$	10.0344	0.679618
$219$	1.09536	0.0740178
$220$	−41.2322	−2.77987
$221$	−4.45445	−0.299639
$222$	−72.7711	−4.88407
$223$	4.78575	0.320477	0.160239	−	0.987078i	$-0.448774\pi$
$223$	4.78575	0.320477	0.160239	+	0.987078i	$0.448774\pi$
$224$	−124.587	−8.32435
$225$	1.39506	0.0930041
$226$	24.7997	1.64965
$227$	−13.4195	−0.890685	−0.445343	−	0.895360i	$-0.646918\pi$
$227$	−13.4195	−0.890685	−0.445343	+	0.895360i	$0.646918\pi$
$228$	104.494	6.92030
$229$	−1.24258	−0.0821117	−0.0410559	−	0.999157i	$-0.513072\pi$
$229$	−1.24258	−0.0821117	−0.0410559	+	0.999157i	$0.513072\pi$
$230$	36.2505	2.39029
$231$	37.8559	2.49074
$232$	−77.6945	−5.10090
$233$	−0.456950	−0.0299358	−0.0149679	−	0.999888i	$-0.504765\pi$
$233$	−0.456950	−0.0299358	−0.0149679	+	0.999888i	$0.504765\pi$
$234$	−52.8676	−3.45606
$235$	14.7257	0.960601
$236$	−47.3116	−3.07973
$237$	19.7553	1.28325
$238$	12.5332	0.812408
$239$	−12.5744	−0.813371	−0.406685	−	0.913568i	$-0.633315\pi$
$239$	−12.5744	−0.813371	−0.406685	+	0.913568i	$0.633315\pi$
$240$	−108.314	−6.99166
$241$	−28.8773	−1.86015	−0.930074	−	0.367373i	$-0.880257\pi$
$241$	−28.8773	−1.86015	−0.930074	+	0.367373i	$0.880257\pi$
$242$	3.59308	0.230972
$243$	19.9300	1.27851
$244$	36.7959	2.35562
$245$	30.7226	1.96279
$246$	−0.0979586	−0.00624561
$247$	−30.1127	−1.91603
$248$	−4.43790	−0.281807
$249$	−3.43810	−0.217881
$250$	29.9942	1.89700
$251$	21.1560	1.33535	0.667677	−	0.744451i	$-0.267289\pi$
$251$	21.1560	1.33535	0.667677	+	0.744451i	$0.267289\pi$
$252$	110.282	6.94713
$253$	17.5974	1.10634
$254$	4.34979	0.272930
$255$	6.22210	0.389643
$256$	87.4135	5.46334
$257$	22.2450	1.38761	0.693804	−	0.720164i	$-0.255934\pi$
$257$	22.2450	1.38761	0.693804	+	0.720164i	$0.255934\pi$
$258$	6.90126	0.429654
$259$	−43.7455	−2.71821
$260$	58.9476	3.65578
$261$	31.9343	1.97668
$262$	−38.2491	−2.36304
$263$	−23.3104	−1.43738	−0.718691	−	0.695329i	$-0.755259\pi$
$263$	−23.3104	−1.43738	−0.718691	+	0.695329i	$0.755259\pi$
$264$	−87.2166	−5.36781
$265$	20.7827	1.27667
$266$	84.7264	5.19491
$267$	33.4904	2.04958
$268$	−26.2191	−1.60159
$269$	10.7240	0.653857	0.326928	−	0.945049i	$-0.393986\pi$
$269$	10.7240	0.653857	0.326928	+	0.945049i	$0.393986\pi$
$270$	21.9368	1.33503
$271$	−0.0363411	−0.00220757	−0.00110378	−	0.999999i	$-0.500351\pi$
$271$	−0.0363411	−0.00220757	−0.00110378	+	0.999999i	$0.500351\pi$
$272$	−17.4080	−1.05551
$273$	−54.1208	−3.27554
$274$	49.7365	3.00469
$275$	−1.01849	−0.0614171
$276$	87.3012	5.25492
$277$	−18.6456	−1.12031	−0.560153	−	0.828389i	$-0.689258\pi$
$277$	−18.6456	−1.12031	−0.560153	+	0.828389i	$0.689258\pi$
$278$	6.55594	0.393199
$279$	1.82409	0.109205
$280$	−108.004	−6.45447
$281$	−16.2386	−0.968711	−0.484356	−	0.874871i	$-0.660946\pi$
$281$	−16.2386	−0.968711	−0.484356	+	0.874871i	$0.660946\pi$
$282$	47.8338	2.84846
$283$	−5.26218	−0.312804	−0.156402	−	0.987693i	$-0.549990\pi$
$283$	−5.26218	−0.312804	−0.156402	+	0.987693i	$0.549990\pi$
$284$	−63.8022	−3.78596
$285$	42.0623	2.49156
$286$	38.5969	2.28228
$287$	−0.0588866	−0.00347597
$288$	−117.980	−6.95201
$289$	1.00000	0.0588235
$290$	−48.0271	−2.82025
$291$	−40.2804	−2.36128
$292$	−2.32966	−0.136333
$293$	−8.54979	−0.499484	−0.249742	−	0.968312i	$-0.580346\pi$
$293$	−8.54979	−0.499484	−0.249742	+	0.968312i	$0.580346\pi$
$294$	99.7965	5.82025
$295$	−19.0445	−1.10881
$296$	100.786	5.85804
$297$	10.6489	0.617914
$298$	−37.4852	−2.17146
$299$	−25.1581	−1.45493
$300$	−5.05275	−0.291721
$301$	4.14861	0.239122
$302$	52.0084	2.99275
$303$	40.6435	2.33491
$304$	−117.680	−6.74944
$305$	14.8116	0.848108
$306$	11.8685	0.678476
$307$	27.9646	1.59602	0.798011	−	0.602643i	$-0.205886\pi$
$307$	27.9646	1.59602	0.798011	+	0.602643i	$0.205886\pi$
$308$	−80.5135	−4.58768
$309$	−40.9172	−2.32770
$310$	−2.74331	−0.155809
$311$	−12.5750	−0.713064	−0.356532	−	0.934283i	$-0.616041\pi$
$311$	−12.5750	−0.713064	−0.356532	+	0.934283i	$0.616041\pi$
$312$	124.689	7.05914
$313$	22.3829	1.26516	0.632578	−	0.774497i	$-0.281997\pi$
$313$	22.3829	1.26516	0.632578	+	0.774497i	$0.281997\pi$
$314$	−8.50735	−0.480097
$315$	44.3922	2.50122
$316$	−42.0164	−2.36361
$317$	−20.9056	−1.17418	−0.587088	−	0.809523i	$-0.699726\pi$
$317$	−20.9056	−1.17418	−0.587088	+	0.809523i	$0.699726\pi$
$318$	67.5088	3.78570
$319$	−23.3142	−1.30534
$320$	97.0782	5.42683
$321$	40.3584	2.25259
$322$	70.7859	3.94475
$323$	6.76014	0.376144
$324$	−20.5807	−1.14337
$325$	1.45608	0.0807689
$326$	−41.1342	−2.27821
$327$	9.72747	0.537930
$328$	0.135669	0.00749109
$329$	28.7547	1.58530
$330$	−53.9132	−2.96783
$331$	−10.3714	−0.570066	−0.285033	−	0.958518i	$-0.592005\pi$
$331$	−10.3714	−0.570066	−0.285033	+	0.958518i	$0.592005\pi$
$332$	7.31229	0.401314
$333$	−41.4253	−2.27009
$334$	54.7729	2.99704
$335$	−10.5540	−0.576629
$336$	−211.504	−11.5385
$337$	11.7130	0.638046	0.319023	−	0.947747i	$-0.396645\pi$
$337$	11.7130	0.638046	0.319023	+	0.947747i	$0.396645\pi$
$338$	−19.0277	−1.03497
$339$	24.0411	1.30573
$340$	−13.2334	−0.717683
$341$	−1.33170	−0.0721158
$342$	80.2326	4.33848
$343$	28.4439	1.53582
$344$	−9.55802	−0.515334
$345$	35.1416	1.89196
$346$	−42.3030	−2.27423
$347$	19.7035	1.05774	0.528870	−	0.848703i	$-0.322616\pi$
$347$	19.7035	1.05774	0.528870	+	0.848703i	$0.322616\pi$
$348$	−115.662	−6.20016
$349$	−15.3108	−0.819571	−0.409785	−	0.912182i	$-0.634396\pi$
$349$	−15.3108	−0.819571	−0.409785	+	0.912182i	$0.634396\pi$
$350$	−4.09689	−0.218988
$351$	−15.2243	−0.812612
$352$	86.1330	4.59090
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−61.8624	−3.28795
$355$	−25.6824	−1.36308
$356$	−71.2287	−3.77511
$357$	12.1498	0.643036
$358$	45.3937	2.39913
$359$	0.416926	0.0220045	0.0110023	−	0.999939i	$-0.496498\pi$
$359$	0.416926	0.0220045	0.0110023	+	0.999939i	$0.496498\pi$
$360$	−102.276	−5.39040
$361$	26.6995	1.40524
$362$	12.9060	0.678323
$363$	3.48317	0.182819
$364$	115.106	6.03320
$365$	−0.937765	−0.0490849
$366$	48.1126	2.51489
$367$	15.2614	0.796640	0.398320	−	0.917246i	$-0.369593\pi$
$367$	15.2614	0.796640	0.398320	+	0.917246i	$0.369593\pi$
$368$	−98.3179	−5.12518
$369$	−0.0557634	−0.00290293
$370$	62.3009	3.23887
$371$	40.5821	2.10692
$372$	−6.60663	−0.342538
$373$	−27.0198	−1.39903	−0.699516	−	0.714617i	$-0.746601\pi$
$373$	−27.0198	−1.39903	−0.699516	+	0.714617i	$0.746601\pi$
$374$	−8.66479	−0.448046
$375$	29.0766	1.50151
$376$	−66.2482	−3.41649
$377$	33.3312	1.71664
$378$	42.8356	2.20323
$379$	2.01712	0.103612	0.0518062	−	0.998657i	$-0.483502\pi$
$379$	2.01712	0.103612	0.0518062	+	0.998657i	$0.483502\pi$
$380$	−89.4598	−4.58919
$381$	4.21672	0.216029
$382$	−3.69233	−0.188916
$383$	−34.6019	−1.76807	−0.884037	−	0.467417i	$-0.845185\pi$
$383$	−34.6019	−1.76807	−0.884037	+	0.467417i	$0.845185\pi$
$384$	166.289	8.48590
$385$	−32.4093	−1.65173
$386$	−48.7304	−2.48031
$387$	3.92858	0.199701
$388$	85.6699	4.34923
$389$	15.8337	0.802803	0.401401	−	0.915902i	$-0.368523\pi$
$389$	15.8337	0.802803	0.401401	+	0.915902i	$0.368523\pi$
$390$	77.0771	3.90295
$391$	5.64786	0.285625
$392$	−138.215	−6.98091
$393$	−37.0790	−1.87039
$394$	−37.1665	−1.87242
$395$	−16.9130	−0.850984
$396$	−76.2432	−3.83136
$397$	−31.5293	−1.58241	−0.791204	−	0.611552i	$-0.790546\pi$
$397$	−31.5293	−1.58241	−0.791204	+	0.611552i	$0.790546\pi$
$398$	−27.7818	−1.39258
$399$	82.1345	4.11187
$400$	5.69037	0.284518
$401$	−0.733714	−0.0366399	−0.0183200	−	0.999832i	$-0.505832\pi$
$401$	−0.733714	−0.0366399	−0.0183200	+	0.999832i	$0.505832\pi$
$402$	−34.2828	−1.70987
$403$	1.90387	0.0948387
$404$	−86.4423	−4.30066
$405$	−8.28442	−0.411656
$406$	−93.7819	−4.65432
$407$	30.2432	1.49910
$408$	−27.9921	−1.38581
$409$	8.20855	0.405887	0.202943	−	0.979190i	$-0.434949\pi$
$409$	8.20855	0.405887	0.202943	+	0.979190i	$0.434949\pi$
$410$	0.0838645	0.00414177
$411$	48.2149	2.37827
$412$	87.0243	4.28738
$413$	−37.1879	−1.82990
$414$	67.0316	3.29442
$415$	2.94344	0.144488
$416$	−123.140	−6.03744
$417$	6.35538	0.311224
$418$	−58.5752	−2.86501
$419$	20.9003	1.02105	0.510524	−	0.859863i	$-0.329451\pi$
$419$	20.9003	1.02105	0.510524	+	0.859863i	$0.329451\pi$
$420$	−160.784	−7.84544
$421$	−14.0018	−0.682405	−0.341202	−	0.939990i	$-0.610834\pi$
$421$	−14.0018	−0.682405	−0.341202	+	0.939990i	$0.610834\pi$
$422$	55.7566	2.71419
$423$	27.2296	1.32395
$424$	−93.4974	−4.54064
$425$	−0.326883	−0.0158561
$426$	−83.4247	−4.04194
$427$	28.9223	1.39965
$428$	−85.8359	−4.14903
$429$	37.4161	1.80647
$430$	−5.90832	−0.284925
$431$	−3.60952	−0.173864	−0.0869322	−	0.996214i	$-0.527706\pi$
$431$	−3.60952	−0.173864	−0.0869322	+	0.996214i	$0.527706\pi$
$432$	−59.4965	−2.86252
$433$	2.88146	0.138474	0.0692369	−	0.997600i	$-0.477944\pi$
$433$	2.88146	0.138474	0.0692369	+	0.997600i	$0.477944\pi$
$434$	−5.35681	−0.257135
$435$	−46.5579	−2.23228
$436$	−20.6888	−0.990812
$437$	38.1803	1.82641
$438$	−3.04616	−0.145551
$439$	−18.8350	−0.898948	−0.449474	−	0.893294i	$-0.648388\pi$
$439$	−18.8350	−0.898948	−0.449474	+	0.893294i	$0.648388\pi$
$440$	74.6681	3.55966
$441$	56.8097	2.70522
$442$	12.3876	0.589219
$443$	23.2631	1.10526	0.552632	−	0.833426i	$-0.313624\pi$
$443$	23.2631	1.10526	0.552632	+	0.833426i	$0.313624\pi$
$444$	150.038	7.12047
$445$	−28.6719	−1.35918
$446$	−13.3089	−0.630197
$447$	−36.3384	−1.71875
$448$	189.563	8.95602
$449$	−14.1980	−0.670047	−0.335024	−	0.942210i	$-0.608744\pi$
$449$	−14.1980	−0.670047	−0.335024	+	0.942210i	$0.608744\pi$
$450$	−3.87960	−0.182886
$451$	0.0407110	0.00191701
$452$	−51.1315	−2.40502
$453$	50.4174	2.36881
$454$	37.3191	1.75147
$455$	46.3340	2.17217
$456$	−189.230	−8.86152
$457$	−0.0632706	−0.00295968	−0.00147984	−	0.999999i	$-0.500471\pi$
$457$	−0.0632706	−0.00295968	−0.00147984	+	0.999999i	$0.500471\pi$
$458$	3.45555	0.161467
$459$	3.41777	0.159528
$460$	−74.7405	−3.48479
$461$	−4.64472	−0.216326	−0.108163	−	0.994133i	$-0.534497\pi$
$461$	−4.64472	−0.216326	−0.108163	+	0.994133i	$0.534497\pi$
$462$	−105.276	−4.89786
$463$	−18.3269	−0.851725	−0.425862	−	0.904788i	$-0.640029\pi$
$463$	−18.3269	−0.851725	−0.425862	+	0.904788i	$0.640029\pi$
$464$	130.258	6.04708
$465$	−2.65938	−0.123326
$466$	1.27076	0.0588666
$467$	19.3799	0.896793	0.448397	−	0.893835i	$-0.351995\pi$
$467$	19.3799	0.896793	0.448397	+	0.893835i	$0.351995\pi$
$468$	109.001	5.03858
$469$	−20.6087	−0.951622
$470$	−40.9516	−1.88896
$471$	−8.24710	−0.380006
$472$	85.6775	3.94363
$473$	−2.86812	−0.131876
$474$	−54.9387	−2.52342
$475$	−2.20977	−0.101391
$476$	−25.8407	−1.18441
$477$	38.4297	1.75957
$478$	34.9688	1.59944
$479$	−16.3088	−0.745170	−0.372585	−	0.927998i	$-0.621528\pi$
$479$	−16.3088	−0.745170	−0.372585	+	0.927998i	$0.621528\pi$
$480$	172.006	7.85095
$481$	−43.2373	−1.97145
$482$	80.3063	3.65785
$483$	68.6205	3.12234
$484$	−7.40814	−0.336733
$485$	34.4849	1.56588
$486$	−55.4243	−2.51410
$487$	−5.70057	−0.258317	−0.129159	−	0.991624i	$-0.541228\pi$
$487$	−5.70057	−0.258317	−0.129159	+	0.991624i	$0.541228\pi$
$488$	−66.6344	−3.01640
$489$	−39.8759	−1.80325
$490$	−85.4380	−3.85970
$491$	−8.34486	−0.376598	−0.188299	−	0.982112i	$-0.560297\pi$
$491$	−8.34486	−0.376598	−0.188299	+	0.982112i	$0.560297\pi$
$492$	0.201969	0.00910545
$493$	−7.48266	−0.337002
$494$	83.7421	3.76774
$495$	−30.6904	−1.37943
$496$	7.44033	0.334081
$497$	−50.1498	−2.24952
$498$	9.56121	0.428448
$499$	−24.6248	−1.10236	−0.551179	−	0.834387i	$-0.685822\pi$
$499$	−24.6248	−1.10236	−0.551179	+	0.834387i	$0.685822\pi$
$500$	−61.8413	−2.76563
$501$	53.0973	2.37221
$502$	−58.8339	−2.62588
$503$	−11.5553	−0.515225	−0.257613	−	0.966248i	$-0.582936\pi$
$503$	−11.5553	−0.515225	−0.257613	+	0.966248i	$0.582936\pi$
$504$	−199.712	−8.89589
$505$	−34.7958	−1.54839
$506$	−48.9375	−2.17554
$507$	−18.4456	−0.819197
$508$	−8.96830	−0.397904
$509$	−23.3352	−1.03431	−0.517157	−	0.855891i	$-0.673010\pi$
$509$	−23.3352	−1.03431	−0.517157	+	0.855891i	$0.673010\pi$
$510$	−17.3034	−0.766207
$511$	−1.83116	−0.0810058
$512$	−119.728	−5.29126
$513$	23.1046	1.02009
$514$	−61.8624	−2.72864
$515$	35.0301	1.54361
$516$	−14.2289	−0.626390
$517$	−19.8794	−0.874297
$518$	121.654	5.34518
$519$	−41.0089	−1.80009
$520$	−106.749	−4.68127
$521$	−11.1669	−0.489233	−0.244616	−	0.969620i	$-0.578662\pi$
$521$	−11.1669	−0.489233	−0.244616	+	0.969620i	$0.578662\pi$
$522$	−88.8079	−3.88702
$523$	3.28967	0.143847	0.0719236	−	0.997410i	$-0.477086\pi$
$523$	3.28967	0.143847	0.0719236	+	0.997410i	$0.477086\pi$
$524$	78.8612	3.44507
$525$	−3.97156	−0.173333
$526$	64.8253	2.82652
$527$	−0.427409	−0.0186182
$528$	146.222	6.36351
$529$	8.89834	0.386884
$530$	−57.7958	−2.51049
$531$	−35.2155	−1.52822
$532$	−174.687	−7.57364
$533$	−0.0582026	−0.00252103
$534$	−93.1353	−4.03036
$535$	−34.5517	−1.49380
$536$	47.4806	2.05085
$537$	44.0051	1.89896
$538$	−29.8231	−1.28576
$539$	−41.4749	−1.78645
$540$	−45.2287	−1.94634
$541$	14.1591	0.608746	0.304373	−	0.952553i	$-0.401553\pi$
$541$	14.1591	0.608746	0.304373	+	0.952553i	$0.401553\pi$
$542$	0.101063	0.00434103
$543$	12.5112	0.536906
$544$	27.6443	1.18524
$545$	−8.32790	−0.356728
$546$	150.507	6.44112
$547$	−28.3279	−1.21121	−0.605607	−	0.795764i	$-0.707070\pi$
$547$	−28.3279	−1.21121	−0.605607	+	0.795764i	$0.707070\pi$
$548$	−102.545	−4.38053
$549$	27.3883	1.16891
$550$	2.83237	0.120773
$551$	−50.5839	−2.15495
$552$	−158.095	−6.72898
$553$	−33.0257	−1.40440
$554$	51.8526	2.20300
$555$	60.3951	2.56363
$556$	−13.5169	−0.573243
$557$	20.0846	0.851011	0.425505	−	0.904956i	$-0.360096\pi$
$557$	20.0846	0.851011	0.425505	+	0.904956i	$0.360096\pi$
$558$	−5.07270	−0.214744
$559$	4.10042	0.173429
$560$	181.073	7.65174
$561$	−8.39972	−0.354636
$562$	45.1587	1.90490
$563$	28.2777	1.19176	0.595882	−	0.803072i	$-0.296802\pi$
$563$	28.2777	1.19176	0.595882	+	0.803072i	$0.296802\pi$
$564$	−98.6226	−4.15276
$565$	−20.5821	−0.865895
$566$	14.6339	0.615108
$567$	−16.1769	−0.679364
$568$	115.540	4.84797
$569$	43.8560	1.83854	0.919270	−	0.393629i	$-0.128780\pi$
$569$	43.8560	1.83854	0.919270	+	0.393629i	$0.128780\pi$
$570$	−116.973	−4.89948
$571$	36.2544	1.51720	0.758601	−	0.651556i	$-0.225883\pi$
$571$	36.2544	1.51720	0.758601	+	0.651556i	$0.225883\pi$
$572$	−79.5782	−3.32733
$573$	−3.57938	−0.149531
$574$	0.163761	0.00683526
$575$	−1.84619	−0.0769913
$576$	179.509	7.47954
$577$	−20.7822	−0.865174	−0.432587	−	0.901592i	$-0.642399\pi$
$577$	−20.7822	−0.865174	−0.432587	+	0.901592i	$0.642399\pi$
$578$	−2.78095	−0.115672
$579$	−47.2396	−1.96321
$580$	99.0213	4.11163
$581$	5.74761	0.238451
$582$	112.018	4.64329
$583$	−28.0563	−1.16197
$584$	4.21883	0.174576
$585$	43.8765	1.81407
$586$	23.7766	0.982201
$587$	22.1904	0.915895	0.457948	−	0.888979i	$-0.348585\pi$
$587$	22.1904	0.915895	0.457948	+	0.888979i	$0.348585\pi$
$588$	−205.758	−8.48532
$589$	−2.88935	−0.119053
$590$	52.9618	2.18040
$591$	−36.0296	−1.48206
$592$	−168.971	−6.94467
$593$	−23.9600	−0.983918	−0.491959	−	0.870618i	$-0.663719\pi$
$593$	−23.9600	−0.983918	−0.491959	+	0.870618i	$0.663719\pi$
$594$	−29.6142	−1.21509
$595$	−10.4017	−0.426429
$596$	77.2860	3.16576
$597$	−26.9319	−1.10225
$598$	69.9636	2.86102
$599$	2.20992	0.0902947	0.0451474	−	0.998980i	$-0.485624\pi$
$599$	2.20992	0.0902947	0.0451474	+	0.998980i	$0.485624\pi$
$600$	9.15012	0.373552
$601$	−9.54525	−0.389359	−0.194680	−	0.980867i	$-0.562367\pi$
$601$	−9.54525	−0.389359	−0.194680	+	0.980867i	$0.562367\pi$
$602$	−11.5371	−0.470217
$603$	−19.5157	−0.794739
$604$	−107.230	−4.36311
$605$	−2.98202	−0.121236
$606$	−113.028	−4.59144
$607$	−10.6132	−0.430778	−0.215389	−	0.976528i	$-0.569102\pi$
$607$	−10.6132	−0.430778	−0.215389	+	0.976528i	$0.569102\pi$
$608$	186.879	7.57896
$609$	−90.9130	−3.68398
$610$	−41.1903	−1.66775
$611$	28.4207	1.14978
$612$	−24.4702	−0.989148
$613$	8.57297	0.346259	0.173130	−	0.984899i	$-0.444612\pi$
$613$	8.57297	0.346259	0.173130	+	0.984899i	$0.444612\pi$
$614$	−77.7682	−3.13847
$615$	0.0812990	0.00327829
$616$	145.803	5.87458
$617$	8.05618	0.324330	0.162165	−	0.986764i	$-0.448152\pi$
$617$	8.05618	0.324330	0.162165	+	0.986764i	$0.448152\pi$
$618$	113.789	4.57726
$619$	−15.7467	−0.632913	−0.316456	−	0.948607i	$-0.602493\pi$
$619$	−15.7467	−0.632913	−0.316456	+	0.948607i	$0.602493\pi$
$620$	5.65608	0.227154
$621$	19.3031	0.774606
$622$	34.9706	1.40219
$623$	−55.9872	−2.24308
$624$	−209.047	−8.36857
$625$	−26.5276	−1.06110
$626$	−62.2458	−2.48784
$627$	−56.7833	−2.26771
$628$	17.5403	0.699932
$629$	9.70653	0.387025
$630$	−123.453	−4.91848
$631$	−7.96329	−0.317013	−0.158507	−	0.987358i	$-0.550668\pi$
$631$	−7.96329	−0.317013	−0.158507	+	0.987358i	$0.550668\pi$
$632$	76.0883	3.02663
$633$	54.0509	2.14833
$634$	58.1375	2.30894
$635$	−3.61003	−0.143260
$636$	−139.188	−5.51916
$637$	59.2946	2.34934
$638$	64.8357	2.56687
$639$	−47.4899	−1.87867
$640$	−142.364	−5.62742
$641$	10.8880	0.430051	0.215026	−	0.976608i	$-0.431016\pi$
$641$	10.8880	0.430051	0.215026	+	0.976608i	$0.431016\pi$
$642$	−112.235	−4.42956
$643$	−0.640897	−0.0252745	−0.0126373	−	0.999920i	$-0.504023\pi$
$643$	−0.640897	−0.0252745	−0.0126373	+	0.999920i	$0.504023\pi$
$644$	−145.945	−5.75103
$645$	−5.72758	−0.225523
$646$	−18.7996	−0.739662
$647$	42.9759	1.68956	0.844778	−	0.535117i	$-0.179733\pi$
$647$	42.9759	1.68956	0.844778	+	0.535117i	$0.179733\pi$
$648$	37.2700	1.46410
$649$	25.7097	1.00919
$650$	−4.04930	−0.158827
$651$	−5.19294	−0.203527
$652$	84.8096	3.32140
$653$	18.1182	0.709020	0.354510	−	0.935052i	$-0.384648\pi$
$653$	18.1182	0.709020	0.354510	+	0.935052i	$0.384648\pi$
$654$	−27.0516	−1.05780
$655$	31.7442	1.24035
$656$	−0.227455	−0.00888065
$657$	−1.73404	−0.0676513
$658$	−79.9656	−3.11738
$659$	40.7230	1.58634	0.793171	−	0.608999i	$-0.208429\pi$
$659$	40.7230	1.58634	0.793171	+	0.608999i	$0.208429\pi$
$660$	111.157	4.32678
$661$	−28.8235	−1.12110	−0.560551	−	0.828120i	$-0.689411\pi$
$661$	−28.8235	−1.12110	−0.560551	+	0.828120i	$0.689411\pi$
$662$	28.8425	1.12100
$663$	12.0087	0.466378
$664$	−13.2420	−0.513888
$665$	−70.3172	−2.72678
$666$	115.202	4.46398
$667$	−42.2611	−1.63635
$668$	−112.930	−4.36937
$669$	−12.9018	−0.498812
$670$	29.3503	1.13390
$671$	−19.9953	−0.771911
$672$	335.873	12.9566
$673$	−29.9051	−1.15276	−0.576378	−	0.817183i	$-0.695534\pi$
$673$	−29.9051	−1.15276	−0.576378	+	0.817183i	$0.695534\pi$
$674$	−32.5732	−1.25467
$675$	−1.11721	−0.0430014
$676$	39.2308	1.50888
$677$	−21.9407	−0.843249	−0.421625	−	0.906771i	$-0.638540\pi$
$677$	−21.9407	−0.843249	−0.421625	+	0.906771i	$0.638540\pi$
$678$	−66.8571	−2.56763
$679$	67.3382	2.58420
$680$	23.9646	0.919002
$681$	36.1774	1.38632
$682$	3.70341	0.141811
$683$	32.6194	1.24815	0.624073	−	0.781366i	$-0.285477\pi$
$683$	32.6194	1.24815	0.624073	+	0.781366i	$0.285477\pi$
$684$	−165.422	−6.32506
$685$	−41.2779	−1.57715
$686$	−79.1011	−3.02009
$687$	3.34984	0.127804
$688$	16.0244	0.610925
$689$	40.1107	1.52809
$690$	−97.7271	−3.72041
$691$	10.4293	0.396751	0.198375	−	0.980126i	$-0.436433\pi$
$691$	10.4293	0.396751	0.198375	+	0.980126i	$0.436433\pi$
$692$	87.2195	3.31559
$693$	−59.9287	−2.27650
$694$	−54.7945	−2.07997
$695$	−5.44098	−0.206388
$696$	209.455	7.93938
$697$	0.0130662	0.000494916 0
$698$	42.5788	1.61163
$699$	1.23188	0.0465941
$700$	8.44688	0.319262
$701$	−26.4522	−0.999084	−0.499542	−	0.866290i	$-0.666498\pi$
$701$	−26.4522	−0.999084	−0.499542	+	0.866290i	$0.666498\pi$
$702$	42.3380	1.59795
$703$	65.6175	2.47481
$704$	−131.054	−4.93927
$705$	−39.6988	−1.49514
$706$	2.78095	0.104663
$707$	−67.9453	−2.55535
$708$	127.547	4.79349
$709$	−9.02317	−0.338872	−0.169436	−	0.985541i	$-0.554195\pi$
$709$	−9.02317	−0.338872	−0.169436	+	0.985541i	$0.554195\pi$
$710$	71.4217	2.68041
$711$	−31.2741	−1.17287
$712$	128.989	4.83408
$713$	−2.41395	−0.0904030
$714$	−33.7881	−1.26449
$715$	−32.0328	−1.19796
$716$	−93.5917	−3.49769
$717$	33.8991	1.26598
$718$	−1.15945	−0.0432704
$719$	−28.6474	−1.06837	−0.534184	−	0.845368i	$-0.679381\pi$
$719$	−28.6474	−1.06837	−0.534184	+	0.845368i	$0.679381\pi$
$720$	171.469	6.39029
$721$	68.4028	2.54745
$722$	−74.2502	−2.76331
$723$	77.8496	2.89526
$724$	−26.6093	−0.988925
$725$	2.44595	0.0908404
$726$	−9.68653	−0.359501
$727$	−14.4728	−0.536767	−0.268384	−	0.963312i	$-0.586489\pi$
$727$	−14.4728	−0.536767	−0.268384	+	0.963312i	$0.586489\pi$
$728$	−208.448	−7.72559
$729$	−42.9605	−1.59113
$730$	2.60788	0.0965221
$731$	−0.920521	−0.0340467
$732$	−99.1975	−3.66645
$733$	−12.3078	−0.454599	−0.227299	−	0.973825i	$-0.572990\pi$
$733$	−12.3078	−0.454599	−0.227299	+	0.973825i	$0.572990\pi$
$734$	−42.4413	−1.56654
$735$	−82.8244	−3.05502
$736$	156.131	5.75507
$737$	14.2477	0.524823
$738$	0.155075	0.00570841
$739$	−44.3047	−1.62978	−0.814888	−	0.579618i	$-0.803202\pi$
$739$	−44.3047	−1.62978	−0.814888	+	0.579618i	$0.803202\pi$
$740$	−128.451	−4.72194
$741$	81.1803	2.98223
$742$	−112.857	−4.14311
$743$	10.6701	0.391448	0.195724	−	0.980659i	$-0.437294\pi$
$743$	10.6701	0.391448	0.195724	+	0.980659i	$0.437294\pi$
$744$	11.9641	0.438624
$745$	31.1101	1.13979
$746$	75.1408	2.75110
$747$	5.44276	0.199140
$748$	17.8649	0.653204
$749$	−67.4687	−2.46525
$750$	−80.8608	−2.95262
$751$	−23.7311	−0.865960	−0.432980	−	0.901404i	$-0.642538\pi$
$751$	−23.7311	−0.865960	−0.432980	+	0.901404i	$0.642538\pi$
$752$	111.068	4.05023
$753$	−57.0340	−2.07844
$754$	−92.6925	−3.37566
$755$	−43.1634	−1.57088
$756$	−88.3175	−3.21208
$757$	36.4410	1.32447	0.662236	−	0.749295i	$-0.269608\pi$
$757$	36.4410	1.32447	0.662236	+	0.749295i	$0.269608\pi$
$758$	−5.60952	−0.203747
$759$	−47.4405	−1.72198
$760$	162.004	5.87651
$761$	20.5574	0.745205	0.372602	−	0.927991i	$-0.378466\pi$
$761$	20.5574	0.745205	0.372602	+	0.927991i	$0.378466\pi$
$762$	−11.7265	−0.424807
$763$	−16.2618	−0.588716
$764$	7.61277	0.275420
$765$	−9.85004	−0.356129
$766$	96.2263	3.47680
$767$	−36.7559	−1.32718
$768$	−235.656	−8.50351
$769$	−7.15248	−0.257925	−0.128962	−	0.991649i	$-0.541165\pi$
$769$	−7.15248	−0.257925	−0.128962	+	0.991649i	$0.541165\pi$
$770$	90.1288	3.24802
$771$	−59.9700	−2.15977
$772$	100.471	3.61604
$773$	28.9544	1.04142	0.520708	−	0.853735i	$-0.325668\pi$
$773$	28.9544	1.04142	0.520708	+	0.853735i	$0.325668\pi$
$774$	−10.9252	−0.392698
$775$	0.139713	0.00501862
$776$	−155.141	−5.56924
$777$	117.933	4.23081
$778$	−44.0329	−1.57866
$779$	0.0883291	0.00316472
$780$	−158.916	−5.69010
$781$	34.6708	1.24062
$782$	−15.7064	−0.561661
$783$	−25.5740	−0.913940
$784$	231.723	8.27583
$785$	7.06052	0.252001
$786$	103.115	3.67800
$787$	3.29148	0.117329	0.0586643	−	0.998278i	$-0.481316\pi$
$787$	3.29148	0.117329	0.0586643	+	0.998278i	$0.481316\pi$
$788$	76.6291	2.72980
$789$	62.8422	2.23724
$790$	47.0342	1.67340
$791$	−40.1904	−1.42901
$792$	138.070	4.90611
$793$	28.5863	1.01513
$794$	87.6815	3.11170
$795$	−56.0277	−1.98710
$796$	57.2799	2.03023
$797$	−9.15431	−0.324262	−0.162131	−	0.986769i	$-0.551837\pi$
$797$	−9.15431	−0.324262	−0.162131	+	0.986769i	$0.551837\pi$
$798$	−228.412	−8.08571
$799$	−6.38029	−0.225718
$800$	−9.03644	−0.319486
$801$	−53.0177	−1.87329
$802$	2.04042	0.0720499
$803$	1.26597	0.0446749
$804$	70.6835	2.49282
$805$	−58.7475	−2.07058
$806$	−5.29458	−0.186494
$807$	−28.9108	−1.01771
$808$	156.540	5.50705
$809$	−36.3234	−1.27706	−0.638532	−	0.769596i	$-0.720458\pi$
$809$	−36.3234	−1.27706	−0.638532	+	0.769596i	$0.720458\pi$
$810$	23.0386	0.809493
$811$	45.6518	1.60305	0.801526	−	0.597960i	$-0.204022\pi$
$811$	45.6518	1.60305	0.801526	+	0.597960i	$0.204022\pi$
$812$	193.357	6.78552
$813$	0.0979713	0.00343600
$814$	−84.1051	−2.94788
$815$	34.1386	1.19582
$816$	46.9299	1.64287
$817$	−6.22285	−0.217710
$818$	−22.8276	−0.798149
$819$	85.6771	2.99380
$820$	−0.172910	−0.00603828
$821$	5.82784	0.203393	0.101696	−	0.994815i	$-0.467573\pi$
$821$	5.82784	0.203393	0.101696	+	0.994815i	$0.467573\pi$
$822$	−134.084	−4.67670
$823$	−15.0978	−0.526277	−0.263139	−	0.964758i	$-0.584758\pi$
$823$	−15.0978	−0.526277	−0.263139	+	0.964758i	$0.584758\pi$
$824$	−157.594	−5.49004
$825$	2.74572	0.0955938
$826$	103.418	3.59837
$827$	54.0732	1.88031	0.940155	−	0.340747i	$-0.110680\pi$
$827$	54.0732	1.88031	0.940155	+	0.340747i	$0.110680\pi$
$828$	−138.204	−4.80292
$829$	−33.7584	−1.17248	−0.586238	−	0.810139i	$-0.699392\pi$
$829$	−33.7584	−1.17248	−0.586238	+	0.810139i	$0.699392\pi$
$830$	−8.18556	−0.284125
$831$	50.2663	1.74372
$832$	187.361	6.49557
$833$	−13.3113	−0.461210
$834$	−17.6740	−0.612001
$835$	−45.4578	−1.57313
$836$	120.769	4.17688
$837$	−1.46078	−0.0504921
$838$	−58.1229	−2.00782
$839$	13.0331	0.449952	0.224976	−	0.974364i	$-0.427770\pi$
$839$	13.0331	0.449952	0.224976	+	0.974364i	$0.427770\pi$
$840$	291.166	10.0462
$841$	26.9903	0.930699
$842$	38.9383	1.34190
$843$	43.7772	1.50777
$844$	−114.958	−3.95701
$845$	15.7917	0.543250
$846$	−75.7243	−2.60346
$847$	−5.82294	−0.200079
$848$	156.752	5.38290
$849$	14.1862	0.486869
$850$	0.909046	0.0311800
$851$	54.8211	1.87924
$852$	172.003	5.89273
$853$	37.7165	1.29139	0.645694	−	0.763596i	$-0.276568\pi$
$853$	37.7165	1.29139	0.645694	+	0.763596i	$0.276568\pi$
$854$	−80.4317	−2.75232
$855$	−66.5877	−2.27725
$856$	155.442	5.31289
$857$	21.7143	0.741748	0.370874	−	0.928683i	$-0.379058\pi$
$857$	21.7143	0.741748	0.370874	+	0.928683i	$0.379058\pi$
$858$	−104.053	−3.55230
$859$	13.8678	0.473164	0.236582	−	0.971612i	$-0.423973\pi$
$859$	13.8678	0.473164	0.236582	+	0.971612i	$0.423973\pi$
$860$	12.1816	0.415391
$861$	0.158751	0.00541023
$862$	10.0379	0.341892
$863$	−12.3253	−0.419559	−0.209780	−	0.977749i	$-0.567275\pi$
$863$	−12.3253	−0.419559	−0.209780	+	0.977749i	$0.567275\pi$
$864$	94.4817	3.21433
$865$	35.1087	1.19373
$866$	−8.01320	−0.272299
$867$	−2.69588	−0.0915569
$868$	11.0446	0.374877
$869$	22.8322	0.774529
$870$	129.475	4.38963
$871$	−20.3693	−0.690188
$872$	37.4656	1.26875
$873$	63.7667	2.15818
$874$	−106.178	−3.59152
$875$	−48.6085	−1.64327
$876$	6.28049	0.212198
$877$	53.9168	1.82064	0.910321	−	0.413903i	$-0.135835\pi$
$877$	53.9168	1.82064	0.910321	+	0.413903i	$0.135835\pi$
$878$	52.3794	1.76772
$879$	23.0492	0.777431
$880$	−125.184	−4.21996
$881$	45.9996	1.54976	0.774882	−	0.632106i	$-0.217809\pi$
$881$	45.9996	1.54976	0.774882	+	0.632106i	$0.217809\pi$
$882$	−157.985	−5.31964
$883$	−8.00989	−0.269554	−0.134777	−	0.990876i	$-0.543032\pi$
$883$	−8.00989	−0.269554	−0.134777	+	0.990876i	$0.543032\pi$
$884$	−25.5405	−0.859021
$885$	51.3416	1.72583
$886$	−64.6936	−2.17342
$887$	13.4846	0.452769	0.226385	−	0.974038i	$-0.427309\pi$
$887$	13.4846	0.452769	0.226385	+	0.974038i	$0.427309\pi$
$888$	−271.706	−9.11785
$889$	−7.04926	−0.236425
$890$	79.7352	2.67273
$891$	11.1838	0.374671
$892$	27.4401	0.918761
$893$	−43.1316	−1.44335
$894$	101.056	3.37980
$895$	−37.6737	−1.25929
$896$	−277.992	−9.28705
$897$	67.8233	2.26455
$898$	39.4841	1.31760
$899$	3.19816	0.106665
$900$	7.99887	0.266629
$901$	−9.00462	−0.299987
$902$	−0.113215	−0.00376966
$903$	−11.1842	−0.372186
$904$	92.5950	3.07966
$905$	−10.7111	−0.356049
$906$	−140.208	−4.65811
$907$	−14.8631	−0.493520	−0.246760	−	0.969077i	$-0.579366\pi$
$907$	−14.8631	−0.493520	−0.246760	+	0.969077i	$0.579366\pi$
$908$	−76.9436	−2.55346
$909$	−64.3416	−2.13408
$910$	−128.853	−4.27143
$911$	8.31509	0.275491	0.137746	−	0.990468i	$-0.456014\pi$
$911$	8.31509	0.275491	0.137746	+	0.990468i	$0.456014\pi$
$912$	317.253	10.5053
$913$	−3.97358	−0.131506
$914$	0.175953	0.00582000
$915$	−39.9302	−1.32005
$916$	−7.12457	−0.235402
$917$	61.9865	2.04697
$918$	−9.50465	−0.313700
$919$	37.4163	1.23425	0.617125	−	0.786865i	$-0.288297\pi$
$919$	37.4163	1.23425	0.617125	+	0.786865i	$0.288297\pi$
$920$	135.349	4.46232
$921$	−75.3891	−2.48416
$922$	12.9168	0.425391
$923$	−49.5672	−1.63152
$924$	217.055	7.14058
$925$	−3.17290	−0.104324
$926$	50.9664	1.67486
$927$	64.7749	2.12749
$928$	−206.853	−6.79028
$929$	19.8035	0.649731	0.324866	−	0.945760i	$-0.394681\pi$
$929$	19.8035	0.649731	0.324866	+	0.945760i	$0.394681\pi$
$930$	7.39562	0.242512
$931$	−89.9864	−2.94918
$932$	−2.62002	−0.0858215
$933$	33.9008	1.10986
$934$	−53.8945	−1.76348
$935$	7.19119	0.235177
$936$	−197.392	−6.45196
$937$	15.9822	0.522115	0.261057	−	0.965323i	$-0.415929\pi$
$937$	15.9822	0.522115	0.261057	+	0.965323i	$0.415929\pi$
$938$	57.3119	1.87130
$939$	−60.3416	−1.96917
$940$	84.4330	2.75390
$941$	−25.3998	−0.828009	−0.414004	−	0.910275i	$-0.635870\pi$
$941$	−25.3998	−0.828009	−0.414004	+	0.910275i	$0.635870\pi$
$942$	22.9348	0.747256
$943$	0.0737958	0.00240312
$944$	−143.642	−4.67515
$945$	−35.5507	−1.15646
$946$	7.97612	0.259326
$947$	−56.5384	−1.83725	−0.918626	−	0.395129i	$-0.870700\pi$
$947$	−56.5384	−1.83725	−0.918626	+	0.395129i	$0.870700\pi$
$948$	113.271	3.67888
$949$	−1.80989	−0.0587515
$950$	6.14528	0.199379
$951$	56.3590	1.82757
$952$	46.7954	1.51665
$953$	−3.27966	−0.106239	−0.0531193	−	0.998588i	$-0.516916\pi$
$953$	−3.27966	−0.106239	−0.0531193	+	0.998588i	$0.516916\pi$
$954$	−106.871	−3.46008
$955$	3.06439	0.0991612
$956$	−72.0980	−2.33181
$957$	62.8523	2.03173
$958$	45.3541	1.46533
$959$	−80.6028	−2.60280
$960$	−261.711	−8.44669
$961$	−30.8173	−0.994107
$962$	120.241	3.87672
$963$	−63.8903	−2.05884
$964$	−165.574	−5.33277
$965$	40.4429	1.30190
$966$	−190.830	−6.13987
$967$	−25.0689	−0.806161	−0.403080	−	0.915165i	$-0.632060\pi$
$967$	−25.0689	−0.806161	−0.403080	+	0.915165i	$0.632060\pi$
$968$	13.4155	0.431191
$969$	−18.2245	−0.585457
$970$	−95.9010	−3.07920
$971$	48.1784	1.54612	0.773060	−	0.634333i	$-0.218725\pi$
$971$	48.1784	1.54612	0.773060	+	0.634333i	$0.218725\pi$
$972$	114.273	3.66530
$973$	−10.6245	−0.340607
$974$	15.8530	0.507964
$975$	−3.92543	−0.125714
$976$	111.715	3.57592
$977$	31.2572	1.00001	0.500003	−	0.866024i	$-0.333332\pi$
$977$	31.2572	1.00001	0.500003	+	0.866024i	$0.333332\pi$
$978$	110.893	3.54597
$979$	38.7065	1.23706
$980$	176.154	5.62704
$981$	−15.3993	−0.491661
$982$	23.2067	0.740555
$983$	−44.7747	−1.42809	−0.714046	−	0.700099i	$-0.753139\pi$
$983$	−44.7747	−1.42809	−0.714046	+	0.700099i	$0.753139\pi$
$984$	−0.365749	−0.0116596
$985$	30.8457	0.982826
$986$	20.8090	0.662692
$987$	−77.5193	−2.46747
$988$	−172.658	−5.49297
$989$	−5.19898	−0.165318
$990$	85.3485	2.71255
$991$	−3.73066	−0.118508	−0.0592541	−	0.998243i	$-0.518872\pi$
$991$	−3.73066	−0.118508	−0.0592541	+	0.998243i	$0.518872\pi$
$992$	−11.8154	−0.375140
$993$	27.9602	0.887290
$994$	139.464	4.42354
$995$	23.0570	0.730957
$996$	−19.7131	−0.624633
$997$	49.3616	1.56330	0.781649	−	0.623719i	$-0.214379\pi$
$997$	49.3616	1.56330	0.781649	+	0.623719i	$0.214379\pi$
$998$	68.4804	2.16771
$999$	33.1747	1.04960

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.1	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.1	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78095 q^{2} -2.69588 q^{3} +5.73371 q^{4} +2.30800 q^{5} +7.49712 q^{6} +4.50681 q^{7} -10.3833 q^{8} +4.26777 q^{9} +O(q^{10})\)	\(q-2.78095 q^{2} -2.69588 q^{3} +5.73371 q^{4} +2.30800 q^{5} +7.49712 q^{6} +4.50681 q^{7} -10.3833 q^{8} +4.26777 q^{9} -6.41845 q^{10} -3.11576 q^{11} -15.4574 q^{12} +4.45445 q^{13} -12.5332 q^{14} -6.22210 q^{15} +17.4080 q^{16} -1.00000 q^{17} -11.8685 q^{18} -6.76014 q^{19} +13.2334 q^{20} -12.1498 q^{21} +8.66479 q^{22} -5.64786 q^{23} +27.9921 q^{24} +0.326883 q^{25} -12.3876 q^{26} -3.41777 q^{27} +25.8407 q^{28} +7.48266 q^{29} +17.3034 q^{30} +0.427409 q^{31} -27.6443 q^{32} +8.39972 q^{33} +2.78095 q^{34} +10.4017 q^{35} +24.4702 q^{36} -9.70653 q^{37} +18.7996 q^{38} -12.0087 q^{39} -23.9646 q^{40} -0.0130662 q^{41} +33.7881 q^{42} +0.920521 q^{43} -17.8649 q^{44} +9.85004 q^{45} +15.7064 q^{46} +6.38029 q^{47} -46.9299 q^{48} +13.3113 q^{49} -0.909046 q^{50} +2.69588 q^{51} +25.5405 q^{52} +9.00462 q^{53} +9.50465 q^{54} -7.19119 q^{55} -46.7954 q^{56} +18.2245 q^{57} -20.8090 q^{58} -8.25149 q^{59} -35.6757 q^{60} +6.41748 q^{61} -1.18861 q^{62} +19.2340 q^{63} +42.0615 q^{64} +10.2809 q^{65} -23.3592 q^{66} -4.57280 q^{67} -5.73371 q^{68} +15.2260 q^{69} -28.9267 q^{70} -11.1276 q^{71} -44.3135 q^{72} -0.406310 q^{73} +26.9934 q^{74} -0.881237 q^{75} -38.7607 q^{76} -14.0421 q^{77} +33.3956 q^{78} -7.32797 q^{79} +40.1777 q^{80} -3.58943 q^{81} +0.0363364 q^{82} +1.27532 q^{83} -69.6635 q^{84} -2.30800 q^{85} -2.55993 q^{86} -20.1724 q^{87} +32.3518 q^{88} -12.4228 q^{89} -27.3925 q^{90} +20.0754 q^{91} -32.3832 q^{92} -1.15224 q^{93} -17.7433 q^{94} -15.6024 q^{95} +74.5257 q^{96} +14.9415 q^{97} -37.0182 q^{98} -13.2974 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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