LMFDB - Embedded newform 6001.2.a.b.1.13

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:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-2.31496 q^{2} -0.975130 q^{3} +3.35906 q^{4} -3.23089 q^{5} +2.25739 q^{6} +5.09566 q^{7} -3.14618 q^{8} -2.04912 q^{9} +O(q^{10})$	\(q-2.31496 q^{2} -0.975130 q^{3} +3.35906 q^{4} -3.23089 q^{5} +2.25739 q^{6} +5.09566 q^{7} -3.14618 q^{8} -2.04912 q^{9} +7.47940 q^{10} +3.94926 q^{11} -3.27552 q^{12} +1.47706 q^{13} -11.7963 q^{14} +3.15054 q^{15} +0.565168 q^{16} +1.00000 q^{17} +4.74365 q^{18} +0.961810 q^{19} -10.8528 q^{20} -4.96893 q^{21} -9.14240 q^{22} +0.0822184 q^{23} +3.06793 q^{24} +5.43865 q^{25} -3.41933 q^{26} +4.92355 q^{27} +17.1166 q^{28} +1.83070 q^{29} -7.29338 q^{30} -1.55664 q^{31} +4.98401 q^{32} -3.85104 q^{33} -2.31496 q^{34} -16.4635 q^{35} -6.88313 q^{36} -2.94351 q^{37} -2.22656 q^{38} -1.44032 q^{39} +10.1650 q^{40} -5.60727 q^{41} +11.5029 q^{42} -4.26746 q^{43} +13.2658 q^{44} +6.62049 q^{45} -0.190333 q^{46} -2.32412 q^{47} -0.551112 q^{48} +18.9658 q^{49} -12.5903 q^{50} -0.975130 q^{51} +4.96152 q^{52} -12.8541 q^{53} -11.3978 q^{54} -12.7596 q^{55} -16.0319 q^{56} -0.937889 q^{57} -4.23801 q^{58} -3.51340 q^{59} +10.5828 q^{60} +11.7464 q^{61} +3.60356 q^{62} -10.4416 q^{63} -12.6681 q^{64} -4.77221 q^{65} +8.91502 q^{66} -7.16350 q^{67} +3.35906 q^{68} -0.0801736 q^{69} +38.1125 q^{70} -3.49907 q^{71} +6.44690 q^{72} +3.92593 q^{73} +6.81412 q^{74} -5.30339 q^{75} +3.23078 q^{76} +20.1241 q^{77} +3.33429 q^{78} -15.0133 q^{79} -1.82600 q^{80} +1.34627 q^{81} +12.9806 q^{82} -12.0942 q^{83} -16.6909 q^{84} -3.23089 q^{85} +9.87901 q^{86} -1.78517 q^{87} -12.4251 q^{88} -9.02816 q^{89} -15.3262 q^{90} +7.52658 q^{91} +0.276176 q^{92} +1.51792 q^{93} +5.38026 q^{94} -3.10750 q^{95} -4.86006 q^{96} -15.5578 q^{97} -43.9051 q^{98} -8.09252 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.31496	−1.63693	−0.818464	−	0.574558i	$-0.805174\pi$
$2$	−2.31496	−1.63693	−0.818464	+	0.574558i	$0.805174\pi$
$3$	−0.975130	−0.562991	−0.281496	−	0.959563i	$-0.590831\pi$
$3$	−0.975130	−0.562991	−0.281496	+	0.959563i	$0.590831\pi$
$4$	3.35906	1.67953
$5$	−3.23089	−1.44490	−0.722449	−	0.691424i	$-0.756984\pi$
$5$	−3.23089	−1.44490	−0.722449	+	0.691424i	$0.756984\pi$
$6$	2.25739	0.921576
$7$	5.09566	1.92598	0.962989	−	0.269539i	$-0.0868713\pi$
$7$	5.09566	1.92598	0.962989	+	0.269539i	$0.0868713\pi$
$8$	−3.14618	−1.11234
$9$	−2.04912	−0.683041
$10$	7.47940	2.36519
$11$	3.94926	1.19075	0.595374	−	0.803449i	$-0.297004\pi$
$11$	3.94926	1.19075	0.595374	+	0.803449i	$0.297004\pi$
$12$	−3.27552	−0.945561
$13$	1.47706	0.409662	0.204831	−	0.978797i	$-0.434336\pi$
$13$	1.47706	0.409662	0.204831	+	0.978797i	$0.434336\pi$
$14$	−11.7963	−3.15269
$15$	3.15054	0.813465
$16$	0.565168	0.141292
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	4.74365	1.11809
$19$	0.961810	0.220654	0.110327	−	0.993895i	$-0.464810\pi$
$19$	0.961810	0.220654	0.110327	+	0.993895i	$0.464810\pi$
$20$	−10.8528	−2.42675
$21$	−4.96893	−1.08431
$22$	−9.14240	−1.94917
$23$	0.0822184	0.0171437	0.00857186	−	0.999963i	$-0.497271\pi$
$23$	0.0822184	0.0171437	0.00857186	+	0.999963i	$0.497271\pi$
$24$	3.06793	0.626239
$25$	5.43865	1.08773
$26$	−3.41933	−0.670586
$27$	4.92355	0.947537
$28$	17.1166	3.23474
$29$	1.83070	0.339953	0.169976	−	0.985448i	$-0.445631\pi$
$29$	1.83070	0.339953	0.169976	+	0.985448i	$0.445631\pi$
$30$	−7.29338	−1.33158
$31$	−1.55664	−0.279580	−0.139790	−	0.990181i	$-0.544643\pi$
$31$	−1.55664	−0.279580	−0.139790	+	0.990181i	$0.544643\pi$
$32$	4.98401	0.881057
$33$	−3.85104	−0.670380
$34$	−2.31496	−0.397013
$35$	−16.4635	−2.78284
$36$	−6.88313	−1.14719
$37$	−2.94351	−0.483910	−0.241955	−	0.970287i	$-0.577789\pi$
$37$	−2.94351	−0.483910	−0.241955	+	0.970287i	$0.577789\pi$
$38$	−2.22656	−0.361195
$39$	−1.44032	−0.230636
$40$	10.1650	1.60722
$41$	−5.60727	−0.875709	−0.437855	−	0.899046i	$-0.644262\pi$
$41$	−5.60727	−0.875709	−0.437855	+	0.899046i	$0.644262\pi$
$42$	11.5029	1.77494
$43$	−4.26746	−0.650781	−0.325390	−	0.945580i	$-0.605496\pi$
$43$	−4.26746	−0.650781	−0.325390	+	0.945580i	$0.605496\pi$
$44$	13.2658	1.99990
$45$	6.62049	0.986924
$46$	−0.190333	−0.0280630
$47$	−2.32412	−0.339008	−0.169504	−	0.985529i	$-0.554217\pi$
$47$	−2.32412	−0.339008	−0.169504	+	0.985529i	$0.554217\pi$
$48$	−0.551112	−0.0795462
$49$	18.9658	2.70939
$50$	−12.5903	−1.78053
$51$	−0.975130	−0.136545
$52$	4.96152	0.688039
$53$	−12.8541	−1.76565	−0.882825	−	0.469702i	$-0.844361\pi$
$53$	−12.8541	−1.76565	−0.882825	+	0.469702i	$0.844361\pi$
$54$	−11.3978	−1.55105
$55$	−12.7596	−1.72051
$56$	−16.0319	−2.14235
$57$	−0.937889	−0.124226
$58$	−4.23801	−0.556478
$59$	−3.51340	−0.457406	−0.228703	−	0.973496i	$-0.573448\pi$
$59$	−3.51340	−0.457406	−0.228703	+	0.973496i	$0.573448\pi$
$60$	10.5828	1.36624
$61$	11.7464	1.50397	0.751987	−	0.659178i	$-0.229096\pi$
$61$	11.7464	1.50397	0.751987	+	0.659178i	$0.229096\pi$
$62$	3.60356	0.457653
$63$	−10.4416	−1.31552
$64$	−12.6681	−1.58352
$65$	−4.77221	−0.591919
$66$	8.91502	1.09736
$67$	−7.16350	−0.875161	−0.437580	−	0.899179i	$-0.644164\pi$
$67$	−7.16350	−0.875161	−0.437580	+	0.899179i	$0.644164\pi$
$68$	3.35906	0.407346
$69$	−0.0801736	−0.00965176
$70$	38.1125	4.55531
$71$	−3.49907	−0.415263	−0.207631	−	0.978207i	$-0.566575\pi$
$71$	−3.49907	−0.415263	−0.207631	+	0.978207i	$0.566575\pi$
$72$	6.44690	0.759775
$73$	3.92593	0.459496	0.229748	−	0.973250i	$-0.426210\pi$
$73$	3.92593	0.459496	0.229748	+	0.973250i	$0.426210\pi$
$74$	6.81412	0.792125
$75$	−5.30339	−0.612383
$76$	3.23078	0.370596
$77$	20.1241	2.29335
$78$	3.33429	0.377534
$79$	−15.0133	−1.68912	−0.844562	−	0.535458i	$-0.820139\pi$
$79$	−15.0133	−1.68912	−0.844562	+	0.535458i	$0.820139\pi$
$80$	−1.82600	−0.204153
$81$	1.34627	0.149585
$82$	12.9806	1.43347
$83$	−12.0942	−1.32751	−0.663753	−	0.747952i	$-0.731037\pi$
$83$	−12.0942	−1.32751	−0.663753	+	0.747952i	$0.731037\pi$
$84$	−16.6909	−1.82113
$85$	−3.23089	−0.350439
$86$	9.87901	1.06528
$87$	−1.78517	−0.191390
$88$	−12.4251	−1.32452
$89$	−9.02816	−0.956983	−0.478491	−	0.878092i	$-0.658816\pi$
$89$	−9.02816	−0.956983	−0.478491	+	0.878092i	$0.658816\pi$
$90$	−15.3262	−1.61552
$91$	7.52658	0.789000
$92$	0.276176	0.0287934
$93$	1.51792	0.157401
$94$	5.38026	0.554932
$95$	−3.10750	−0.318823
$96$	−4.86006	−0.496027
$97$	−15.5578	−1.57966	−0.789830	−	0.613326i	$-0.789831\pi$
$97$	−15.5578	−1.57966	−0.789830	+	0.613326i	$0.789831\pi$
$98$	−43.9051	−4.43508
$99$	−8.09252	−0.813329
$100$	18.2688	1.82688
$101$	−17.1315	−1.70465	−0.852325	−	0.523013i	$-0.824808\pi$
$101$	−17.1315	−1.70465	−0.852325	+	0.523013i	$0.824808\pi$
$102$	2.25739	0.223515
$103$	11.3524	1.11858	0.559291	−	0.828972i	$-0.311074\pi$
$103$	11.3524	1.11858	0.559291	+	0.828972i	$0.311074\pi$
$104$	−4.64708	−0.455684
$105$	16.0541	1.56672
$106$	29.7569	2.89024
$107$	6.89544	0.666608	0.333304	−	0.942819i	$-0.391837\pi$
$107$	6.89544	0.666608	0.333304	+	0.942819i	$0.391837\pi$
$108$	16.5385	1.59142
$109$	4.21954	0.404159	0.202079	−	0.979369i	$-0.435230\pi$
$109$	4.21954	0.404159	0.202079	+	0.979369i	$0.435230\pi$
$110$	29.5381	2.81635
$111$	2.87030	0.272437
$112$	2.87991	0.272126
$113$	−15.1434	−1.42457	−0.712285	−	0.701890i	$-0.752340\pi$
$113$	−15.1434	−1.42457	−0.712285	+	0.701890i	$0.752340\pi$
$114$	2.17118	0.203350
$115$	−0.265638	−0.0247709
$116$	6.14944	0.570961
$117$	−3.02667	−0.279816
$118$	8.13340	0.748740
$119$	5.09566	0.467119
$120$	−9.91215	−0.904851
$121$	4.59666	0.417879
$122$	−27.1925	−2.46190
$123$	5.46782	0.493017
$124$	−5.22884	−0.469564
$125$	−1.41723	−0.126761
$126$	24.1720	2.15341
$127$	11.7883	1.04604	0.523022	−	0.852319i	$-0.324804\pi$
$127$	11.7883	1.04604	0.523022	+	0.852319i	$0.324804\pi$
$128$	19.3583	1.71105
$129$	4.16132	0.366384
$130$	11.0475	0.968929
$131$	14.2259	1.24292	0.621461	−	0.783445i	$-0.286540\pi$
$131$	14.2259	1.24292	0.621461	+	0.783445i	$0.286540\pi$
$132$	−12.9359	−1.12592
$133$	4.90106	0.424976
$134$	16.5833	1.43257
$135$	−15.9074	−1.36909
$136$	−3.14618	−0.269783
$137$	−15.3869	−1.31459	−0.657296	−	0.753633i	$-0.728300\pi$
$137$	−15.3869	−1.31459	−0.657296	+	0.753633i	$0.728300\pi$
$138$	0.185599	0.0157992
$139$	8.67144	0.735502	0.367751	−	0.929924i	$-0.380128\pi$
$139$	8.67144	0.735502	0.367751	+	0.929924i	$0.380128\pi$
$140$	−55.3020	−4.67387
$141$	2.26632	0.190859
$142$	8.10022	0.679755
$143$	5.83328	0.487803
$144$	−1.15810	−0.0965083
$145$	−5.91479	−0.491197
$146$	−9.08840	−0.752161
$147$	−18.4941	−1.52537
$148$	−9.88743	−0.812741
$149$	9.16059	0.750465	0.375233	−	0.926931i	$-0.377563\pi$
$149$	9.16059	0.750465	0.375233	+	0.926931i	$0.377563\pi$
$150$	12.2772	1.00243
$151$	19.7017	1.60330	0.801652	−	0.597791i	$-0.203955\pi$
$151$	19.7017	1.60330	0.801652	+	0.597791i	$0.203955\pi$
$152$	−3.02602	−0.245443
$153$	−2.04912	−0.165662
$154$	−46.5866	−3.75405
$155$	5.02933	0.403965
$156$	−4.83813	−0.387360
$157$	9.17987	0.732633	0.366317	−	0.930490i	$-0.380619\pi$
$157$	9.17987	0.732633	0.366317	+	0.930490i	$0.380619\pi$
$158$	34.7552	2.76497
$159$	12.5344	0.994046
$160$	−16.1028	−1.27304
$161$	0.418957	0.0330184
$162$	−3.11657	−0.244861
$163$	12.5729	0.984784	0.492392	−	0.870374i	$-0.336123\pi$
$163$	12.5729	0.984784	0.492392	+	0.870374i	$0.336123\pi$
$164$	−18.8352	−1.47078
$165$	12.4423	0.968631
$166$	27.9975	2.17303
$167$	−12.1075	−0.936905	−0.468452	−	0.883489i	$-0.655188\pi$
$167$	−12.1075	−0.936905	−0.468452	+	0.883489i	$0.655188\pi$
$168$	15.6331	1.20612
$169$	−10.8183	−0.832177
$170$	7.47940	0.573643
$171$	−1.97087	−0.150716
$172$	−14.3346	−1.09301
$173$	−2.70441	−0.205613	−0.102806	−	0.994701i	$-0.532782\pi$
$173$	−2.70441	−0.205613	−0.102806	+	0.994701i	$0.532782\pi$
$174$	4.13261	0.313292
$175$	27.7135	2.09495
$176$	2.23200	0.168243
$177$	3.42602	0.257516
$178$	20.8999	1.56651
$179$	−8.36383	−0.625142	−0.312571	−	0.949894i	$-0.601190\pi$
$179$	−8.36383	−0.625142	−0.312571	+	0.949894i	$0.601190\pi$
$180$	22.2386	1.65757
$181$	−26.4137	−1.96332	−0.981659	−	0.190645i	$-0.938942\pi$
$181$	−26.4137	−1.96332	−0.981659	+	0.190645i	$0.938942\pi$
$182$	−17.4238	−1.29154
$183$	−11.4543	−0.846724
$184$	−0.258674	−0.0190697
$185$	9.51015	0.699200
$186$	−3.51394	−0.257654
$187$	3.94926	0.288799
$188$	−7.80687	−0.569375
$189$	25.0887	1.82494
$190$	7.19376	0.521890
$191$	16.7188	1.20973	0.604863	−	0.796329i	$-0.293228\pi$
$191$	16.7188	1.20973	0.604863	+	0.796329i	$0.293228\pi$
$192$	12.3531	0.891507
$193$	−8.30325	−0.597681	−0.298840	−	0.954303i	$-0.596600\pi$
$193$	−8.30325	−0.597681	−0.298840	+	0.954303i	$0.596600\pi$
$194$	36.0158	2.58579
$195$	4.65352	0.333245
$196$	63.7072	4.55051
$197$	16.4215	1.16999	0.584993	−	0.811038i	$-0.301097\pi$
$197$	16.4215	1.16999	0.584993	+	0.811038i	$0.301097\pi$
$198$	18.7339	1.33136
$199$	3.74110	0.265200	0.132600	−	0.991170i	$-0.457668\pi$
$199$	3.74110	0.265200	0.132600	+	0.991170i	$0.457668\pi$
$200$	−17.1110	−1.20993
$201$	6.98534	0.492708
$202$	39.6588	2.79039
$203$	9.32863	0.654742
$204$	−3.27552	−0.229332
$205$	18.1165	1.26531
$206$	−26.2803	−1.83104
$207$	−0.168475	−0.0117099
$208$	0.834786	0.0578820
$209$	3.79844	0.262743
$210$	−37.1646	−2.56460
$211$	6.58421	0.453276	0.226638	−	0.973979i	$-0.427227\pi$
$211$	6.58421	0.453276	0.226638	+	0.973979i	$0.427227\pi$
$212$	−43.1778	−2.96546
$213$	3.41204	0.233789
$214$	−15.9627	−1.09119
$215$	13.7877	0.940312
$216$	−15.4904	−1.05399
$217$	−7.93210	−0.538466
$218$	−9.76809	−0.661579
$219$	−3.82829	−0.258692
$220$	−42.8604	−2.88965
$221$	1.47706	0.0993576
$222$	−6.64465	−0.445960
$223$	−1.28082	−0.0857699	−0.0428849	−	0.999080i	$-0.513655\pi$
$223$	−1.28082	−0.0857699	−0.0428849	+	0.999080i	$0.513655\pi$
$224$	25.3968	1.69690
$225$	−11.1445	−0.742964
$226$	35.0564	2.33192
$227$	4.99025	0.331215	0.165607	−	0.986192i	$-0.447042\pi$
$227$	4.99025	0.331215	0.165607	+	0.986192i	$0.447042\pi$
$228$	−3.15043	−0.208642
$229$	−21.5807	−1.42609	−0.713046	−	0.701118i	$-0.752685\pi$
$229$	−21.5807	−1.42609	−0.713046	+	0.701118i	$0.752685\pi$
$230$	0.614944	0.0405482
$231$	−19.6236	−1.29114
$232$	−5.75971	−0.378144
$233$	10.1690	0.666196	0.333098	−	0.942892i	$-0.391906\pi$
$233$	10.1690	0.666196	0.333098	+	0.942892i	$0.391906\pi$
$234$	7.00663	0.458038
$235$	7.50899	0.489832
$236$	−11.8017	−0.768227
$237$	14.6399	0.950962
$238$	−11.7963	−0.764639
$239$	5.95173	0.384986	0.192493	−	0.981298i	$-0.438343\pi$
$239$	5.95173	0.384986	0.192493	+	0.981298i	$0.438343\pi$
$240$	1.78058	0.114936
$241$	−9.56344	−0.616036	−0.308018	−	0.951381i	$-0.599666\pi$
$241$	−9.56344	−0.616036	−0.308018	+	0.951381i	$0.599666\pi$
$242$	−10.6411	−0.684037
$243$	−16.0834	−1.03175
$244$	39.4569	2.52597
$245$	−61.2763	−3.91480
$246$	−12.6578	−0.807032
$247$	1.42065	0.0903936
$248$	4.89746	0.310989
$249$	11.7934	0.747375
$250$	3.28084	0.207499
$251$	−19.5596	−1.23459	−0.617296	−	0.786731i	$-0.711772\pi$
$251$	−19.5596	−1.23459	−0.617296	+	0.786731i	$0.711772\pi$
$252$	−35.0741	−2.20946
$253$	0.324702	0.0204138
$254$	−27.2896	−1.71230
$255$	3.15054	0.197294
$256$	−19.4775	−1.21734
$257$	−23.5030	−1.46607	−0.733037	−	0.680189i	$-0.761898\pi$
$257$	−23.5030	−1.46607	−0.733037	+	0.680189i	$0.761898\pi$
$258$	−9.63331	−0.599744
$259$	−14.9991	−0.932000
$260$	−16.0301	−0.994147
$261$	−3.75133	−0.232201
$262$	−32.9324	−2.03457
$263$	8.47884	0.522827	0.261414	−	0.965227i	$-0.415811\pi$
$263$	8.47884	0.522827	0.261414	+	0.965227i	$0.415811\pi$
$264$	12.1161	0.745692
$265$	41.5303	2.55118
$266$	−11.3458	−0.695654
$267$	8.80362	0.538773
$268$	−24.0626	−1.46986
$269$	5.93906	0.362111	0.181056	−	0.983473i	$-0.442049\pi$
$269$	5.93906	0.362111	0.181056	+	0.983473i	$0.442049\pi$
$270$	36.8252	2.24111
$271$	5.79440	0.351985	0.175992	−	0.984392i	$-0.443687\pi$
$271$	5.79440	0.351985	0.175992	+	0.984392i	$0.443687\pi$
$272$	0.565168	0.0342684
$273$	−7.33939	−0.444200
$274$	35.6201	2.15189
$275$	21.4787	1.29521
$276$	−0.269308	−0.0162104
$277$	14.7705	0.887471	0.443736	−	0.896158i	$-0.353653\pi$
$277$	14.7705	0.887471	0.443736	+	0.896158i	$0.353653\pi$
$278$	−20.0741	−1.20396
$279$	3.18974	0.190965
$280$	51.7972	3.09547
$281$	1.52330	0.0908726	0.0454363	−	0.998967i	$-0.485532\pi$
$281$	1.52330	0.0908726	0.0454363	+	0.998967i	$0.485532\pi$
$282$	−5.24645	−0.312422
$283$	4.88616	0.290452	0.145226	−	0.989399i	$-0.453609\pi$
$283$	4.88616	0.290452	0.145226	+	0.989399i	$0.453609\pi$
$284$	−11.7536	−0.697447
$285$	3.03022	0.179495
$286$	−13.5038	−0.798499
$287$	−28.5728	−1.68660
$288$	−10.2128	−0.601798
$289$	1.00000	0.0588235
$290$	13.6925	0.804053
$291$	15.1709	0.889334
$292$	13.1875	0.771737
$293$	−30.0061	−1.75297	−0.876487	−	0.481426i	$-0.840119\pi$
$293$	−30.0061	−1.75297	−0.876487	+	0.481426i	$0.840119\pi$
$294$	42.8131	2.49691
$295$	11.3514	0.660905
$296$	9.26080	0.538273
$297$	19.4444	1.12828
$298$	−21.2064	−1.22846
$299$	0.121441	0.00702312
$300$	−17.8144	−1.02852
$301$	−21.7455	−1.25339
$302$	−45.6088	−2.62449
$303$	16.7054	0.959703
$304$	0.543585	0.0311767
$305$	−37.9514	−2.17309
$306$	4.74365	0.271176
$307$	22.0721	1.25972	0.629862	−	0.776707i	$-0.283112\pi$
$307$	22.0721	1.25972	0.629862	+	0.776707i	$0.283112\pi$
$308$	67.5981	3.85176
$309$	−11.0700	−0.629752
$310$	−11.6427	−0.661261
$311$	8.92023	0.505820	0.252910	−	0.967490i	$-0.418612\pi$
$311$	8.92023	0.505820	0.252910	+	0.967490i	$0.418612\pi$
$312$	4.53151	0.256546
$313$	−3.71894	−0.210207	−0.105103	−	0.994461i	$-0.533517\pi$
$313$	−3.71894	−0.210207	−0.105103	+	0.994461i	$0.533517\pi$
$314$	−21.2511	−1.19927
$315$	33.7358	1.90080
$316$	−50.4305	−2.83694
$317$	16.4600	0.924488	0.462244	−	0.886753i	$-0.347044\pi$
$317$	16.4600	0.924488	0.462244	+	0.886753i	$0.347044\pi$
$318$	−29.0168	−1.62718
$319$	7.22992	0.404798
$320$	40.9294	2.28802
$321$	−6.72395	−0.375294
$322$	−0.969870	−0.0540488
$323$	0.961810	0.0535165
$324$	4.52220	0.251233
$325$	8.03319	0.445601
$326$	−29.1058	−1.61202
$327$	−4.11460	−0.227538
$328$	17.6415	0.974088
$329$	−11.8429	−0.652923
$330$	−28.8035	−1.58558
$331$	13.7072	0.753415	0.376708	−	0.926332i	$-0.377056\pi$
$331$	13.7072	0.753415	0.376708	+	0.926332i	$0.377056\pi$
$332$	−40.6250	−2.22959
$333$	6.03161	0.330530
$334$	28.0284	1.53364
$335$	23.1445	1.26452
$336$	−2.80828	−0.153204
$337$	−3.18886	−0.173709	−0.0868543	−	0.996221i	$-0.527681\pi$
$337$	−3.18886	−0.173709	−0.0868543	+	0.996221i	$0.527681\pi$
$338$	25.0440	1.36221
$339$	14.7668	0.802021
$340$	−10.8528	−0.588573
$341$	−6.14757	−0.332910
$342$	4.56249	0.246711
$343$	60.9735	3.29226
$344$	13.4262	0.723891
$345$	0.259032	0.0139458
$346$	6.26062	0.336573
$347$	−11.3690	−0.610322	−0.305161	−	0.952301i	$-0.598710\pi$
$347$	−11.3690	−0.610322	−0.305161	+	0.952301i	$0.598710\pi$
$348$	−5.99650	−0.321446
$349$	−32.1142	−1.71903	−0.859517	−	0.511107i	$-0.829235\pi$
$349$	−32.1142	−1.71903	−0.859517	+	0.511107i	$0.829235\pi$
$350$	−64.1558	−3.42927
$351$	7.27236	0.388170
$352$	19.6832	1.04912
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−7.93112	−0.421534
$355$	11.3051	0.600013
$356$	−30.3261	−1.60728
$357$	−4.96893	−0.262984
$358$	19.3620	1.02331
$359$	−8.22777	−0.434245	−0.217123	−	0.976144i	$-0.569667\pi$
$359$	−8.22777	−0.434245	−0.217123	+	0.976144i	$0.569667\pi$
$360$	−20.8292	−1.09780
$361$	−18.0749	−0.951312
$362$	61.1469	3.21381
$363$	−4.48234	−0.235262
$364$	25.2822	1.32515
$365$	−12.6843	−0.663925
$366$	26.5162	1.38603
$367$	2.86471	0.149537	0.0747683	−	0.997201i	$-0.476178\pi$
$367$	2.86471	0.149537	0.0747683	+	0.997201i	$0.476178\pi$
$368$	0.0464672	0.00242227
$369$	11.4900	0.598145
$370$	−22.0157	−1.14454
$371$	−65.5003	−3.40061
$372$	5.09880	0.264360
$373$	−11.1652	−0.578113	−0.289056	−	0.957312i	$-0.593342\pi$
$373$	−11.1652	−0.578113	−0.289056	+	0.957312i	$0.593342\pi$
$374$	−9.14240	−0.472742
$375$	1.38198	0.0713654
$376$	7.31211	0.377093
$377$	2.70405	0.139266
$378$	−58.0795	−2.98729
$379$	13.1683	0.676410	0.338205	−	0.941072i	$-0.390180\pi$
$379$	13.1683	0.676410	0.338205	+	0.941072i	$0.390180\pi$
$380$	−10.4383	−0.535473
$381$	−11.4951	−0.588914
$382$	−38.7033	−1.98023
$383$	−3.94285	−0.201470	−0.100735	−	0.994913i	$-0.532119\pi$
$383$	−3.94285	−0.201470	−0.100735	+	0.994913i	$0.532119\pi$
$384$	−18.8768	−0.963305
$385$	−65.0187	−3.31366
$386$	19.2217	0.978360
$387$	8.74454	0.444510
$388$	−52.2597	−2.65309
$389$	−38.1938	−1.93650	−0.968251	−	0.249978i	$-0.919577\pi$
$389$	−38.1938	−1.93650	−0.968251	+	0.249978i	$0.919577\pi$
$390$	−10.7727	−0.545499
$391$	0.0822184	0.00415796
$392$	−59.6697	−3.01377
$393$	−13.8721	−0.699754
$394$	−38.0153	−1.91518
$395$	48.5062	2.44061
$396$	−27.1833	−1.36601
$397$	1.40125	0.0703266	0.0351633	−	0.999382i	$-0.488805\pi$
$397$	1.40125	0.0703266	0.0351633	+	0.999382i	$0.488805\pi$
$398$	−8.66051	−0.434112
$399$	−4.77917	−0.239258
$400$	3.07375	0.153688
$401$	13.4242	0.670372	0.335186	−	0.942152i	$-0.391201\pi$
$401$	13.4242	0.670372	0.335186	+	0.942152i	$0.391201\pi$
$402$	−16.1708	−0.806527
$403$	−2.29924	−0.114533
$404$	−57.5458	−2.86301
$405$	−4.34965	−0.216136
$406$	−21.5955	−1.07176
$407$	−11.6247	−0.576214
$408$	3.06793	0.151885
$409$	−12.4585	−0.616031	−0.308016	−	0.951381i	$-0.599665\pi$
$409$	−12.4585	−0.616031	−0.308016	+	0.951381i	$0.599665\pi$
$410$	−41.9390	−2.07122
$411$	15.0042	0.740103
$412$	38.1333	1.87869
$413$	−17.9031	−0.880954
$414$	0.390015	0.0191682
$415$	39.0749	1.91811
$416$	7.36166	0.360935
$417$	−8.45578	−0.414081
$418$	−8.79325	−0.430092
$419$	34.5718	1.68894	0.844471	−	0.535601i	$-0.179915\pi$
$419$	34.5718	1.68894	0.844471	+	0.535601i	$0.179915\pi$
$420$	53.9266	2.63135
$421$	−34.9102	−1.70142	−0.850709	−	0.525638i	$-0.823827\pi$
$421$	−34.9102	−1.70142	−0.850709	+	0.525638i	$0.823827\pi$
$422$	−15.2422	−0.741980
$423$	4.76241	0.231556
$424$	40.4414	1.96401
$425$	5.43865	0.263813
$426$	−7.89876	−0.382696
$427$	59.8557	2.89662
$428$	23.1622	1.11959
$429$	−5.68820	−0.274629
$430$	−31.9180	−1.53922
$431$	−21.9997	−1.05969	−0.529844	−	0.848095i	$-0.677750\pi$
$431$	−21.9997	−1.05969	−0.529844	+	0.848095i	$0.677750\pi$
$432$	2.78263	0.133880
$433$	−7.96814	−0.382924	−0.191462	−	0.981500i	$-0.561323\pi$
$433$	−7.96814	−0.382924	−0.191462	+	0.981500i	$0.561323\pi$
$434$	18.3625	0.881429
$435$	5.76769	0.276540
$436$	14.1737	0.678797
$437$	0.0790784	0.00378283
$438$	8.86237	0.423460
$439$	−28.1535	−1.34369	−0.671846	−	0.740691i	$-0.734498\pi$
$439$	−28.1535	−1.34369	−0.671846	+	0.740691i	$0.734498\pi$
$440$	40.1441	1.91379
$441$	−38.8632	−1.85063
$442$	−3.41933	−0.162641
$443$	−8.12688	−0.386120	−0.193060	−	0.981187i	$-0.561841\pi$
$443$	−8.12688	−0.386120	−0.193060	+	0.981187i	$0.561841\pi$
$444$	9.64152	0.457566
$445$	29.1690	1.38274
$446$	2.96505	0.140399
$447$	−8.93277	−0.422505
$448$	−64.5526	−3.04982
$449$	21.6675	1.02255	0.511276	−	0.859417i	$-0.329173\pi$
$449$	21.6675	1.02255	0.511276	+	0.859417i	$0.329173\pi$
$450$	25.7990	1.21618
$451$	−22.1446	−1.04275
$452$	−50.8676	−2.39261
$453$	−19.2117	−0.902646
$454$	−11.5523	−0.542174
$455$	−24.3175	−1.14002
$456$	2.95077	0.138182
$457$	15.7052	0.734660	0.367330	−	0.930091i	$-0.380272\pi$
$457$	15.7052	0.734660	0.367330	+	0.930091i	$0.380272\pi$
$458$	49.9585	2.33441
$459$	4.92355	0.229812
$460$	−0.892296	−0.0416035
$461$	23.6910	1.10340	0.551701	−	0.834042i	$-0.313979\pi$
$461$	23.6910	1.10340	0.551701	+	0.834042i	$0.313979\pi$
$462$	45.4279	2.11350
$463$	−13.9742	−0.649436	−0.324718	−	0.945811i	$-0.605269\pi$
$463$	−13.9742	−0.649436	−0.324718	+	0.945811i	$0.605269\pi$
$464$	1.03465	0.0480326
$465$	−4.90424	−0.227429
$466$	−23.5410	−1.09051
$467$	30.2264	1.39871	0.699355	−	0.714774i	$-0.253471\pi$
$467$	30.2264	1.39871	0.699355	+	0.714774i	$0.253471\pi$
$468$	−10.1668	−0.469959
$469$	−36.5028	−1.68554
$470$	−17.3830	−0.801820
$471$	−8.95156	−0.412466
$472$	11.0538	0.508792
$473$	−16.8533	−0.774916
$474$	−33.8908	−1.55666
$475$	5.23095	0.240012
$476$	17.1166	0.784540
$477$	26.3397	1.20601
$478$	−13.7781	−0.630194
$479$	−18.9822	−0.867321	−0.433660	−	0.901076i	$-0.642778\pi$
$479$	−18.9822	−0.867321	−0.433660	+	0.901076i	$0.642778\pi$
$480$	15.7023	0.716709
$481$	−4.34773	−0.198239
$482$	22.1390	1.00841
$483$	−0.408537	−0.0185891
$484$	15.4405	0.701840
$485$	50.2657	2.28245
$486$	37.2326	1.68890
$487$	21.7268	0.984536	0.492268	−	0.870444i	$-0.336168\pi$
$487$	21.7268	0.984536	0.492268	+	0.870444i	$0.336168\pi$
$488$	−36.9563	−1.67293
$489$	−12.2602	−0.554425
$490$	141.852	6.40824
$491$	−28.8138	−1.30035	−0.650175	−	0.759785i	$-0.725304\pi$
$491$	−28.8138	−1.30035	−0.650175	+	0.759785i	$0.725304\pi$
$492$	18.3667	0.828036
$493$	1.83070	0.0824506
$494$	−3.28875	−0.147968
$495$	26.1460	1.17518
$496$	−0.879763	−0.0395025
$497$	−17.8301	−0.799788
$498$	−27.3012	−1.22340
$499$	17.2099	0.770421	0.385211	−	0.922829i	$-0.374129\pi$
$499$	17.2099	0.770421	0.385211	+	0.922829i	$0.374129\pi$
$500$	−4.76057	−0.212899
$501$	11.8064	0.527469
$502$	45.2798	2.02094
$503$	12.1872	0.543401	0.271700	−	0.962382i	$-0.412414\pi$
$503$	12.1872	0.543401	0.271700	+	0.962382i	$0.412414\pi$
$504$	32.8512	1.46331
$505$	55.3500	2.46304
$506$	−0.751673	−0.0334159
$507$	10.5492	0.468509
$508$	39.5977	1.75686
$509$	4.30600	0.190860	0.0954300	−	0.995436i	$-0.469577\pi$
$509$	4.30600	0.190860	0.0954300	+	0.995436i	$0.469577\pi$
$510$	−7.29338	−0.322956
$511$	20.0052	0.884979
$512$	6.37305	0.281652
$513$	4.73552	0.209078
$514$	54.4085	2.39986
$515$	−36.6782	−1.61624
$516$	13.9781	0.615353
$517$	−9.17857	−0.403673
$518$	34.7224	1.52562
$519$	2.63715	0.115758
$520$	15.0142	0.658417
$521$	18.0573	0.791105	0.395552	−	0.918443i	$-0.370553\pi$
$521$	18.0573	0.791105	0.395552	+	0.918443i	$0.370553\pi$
$522$	8.68420	0.380097
$523$	9.01805	0.394332	0.197166	−	0.980370i	$-0.436826\pi$
$523$	9.01805	0.394332	0.197166	+	0.980370i	$0.436826\pi$
$524$	47.7856	2.08752
$525$	−27.0243	−1.17944
$526$	−19.6282	−0.855830
$527$	−1.55664	−0.0678082
$528$	−2.17649	−0.0947194
$529$	−22.9932	−0.999706
$530$	−96.1411	−4.17610
$531$	7.19939	0.312427
$532$	16.4629	0.713759
$533$	−8.28226	−0.358744
$534$	−20.3801	−0.881932
$535$	−22.2784	−0.963180
$536$	22.5376	0.973478
$537$	8.15582	0.351950
$538$	−13.7487	−0.592750
$539$	74.9008	3.22620
$540$	−53.4341	−2.29944
$541$	−18.2680	−0.785403	−0.392701	−	0.919666i	$-0.628459\pi$
$541$	−18.2680	−0.785403	−0.392701	+	0.919666i	$0.628459\pi$
$542$	−13.4138	−0.576173
$543$	25.7568	1.10533
$544$	4.98401	0.213688
$545$	−13.6329	−0.583968
$546$	16.9904	0.727123
$547$	17.9544	0.767675	0.383837	−	0.923401i	$-0.374602\pi$
$547$	17.9544	0.767675	0.383837	+	0.923401i	$0.374602\pi$
$548$	−51.6855	−2.20790
$549$	−24.0698	−1.02728
$550$	−49.7223	−2.12017
$551$	1.76079	0.0750120
$552$	0.252240	0.0107361
$553$	−76.5025	−3.25322
$554$	−34.1931	−1.45273
$555$	−9.27363	−0.393644
$556$	29.1279	1.23530
$557$	−7.03492	−0.298079	−0.149040	−	0.988831i	$-0.547618\pi$
$557$	−7.03492	−0.298079	−0.149040	+	0.988831i	$0.547618\pi$
$558$	−7.38414	−0.312595
$559$	−6.30327	−0.266600
$560$	−9.30466	−0.393194
$561$	−3.85104	−0.162591
$562$	−3.52639	−0.148752
$563$	−6.54504	−0.275841	−0.137920	−	0.990443i	$-0.544042\pi$
$563$	−6.54504	−0.275841	−0.137920	+	0.990443i	$0.544042\pi$
$564$	7.61271	0.320553
$565$	48.9266	2.05836
$566$	−11.3113	−0.475449
$567$	6.86013	0.288099
$568$	11.0087	0.461914
$569$	12.9868	0.544435	0.272217	−	0.962236i	$-0.412243\pi$
$569$	12.9868	0.544435	0.272217	+	0.962236i	$0.412243\pi$
$570$	−7.01484	−0.293820
$571$	−45.1872	−1.89103	−0.945513	−	0.325583i	$-0.894439\pi$
$571$	−45.1872	−1.89103	−0.945513	+	0.325583i	$0.894439\pi$
$572$	19.5943	0.819281
$573$	−16.3030	−0.681066
$574$	66.1450	2.76084
$575$	0.447157	0.0186477
$576$	25.9586	1.08161
$577$	19.8916	0.828099	0.414050	−	0.910254i	$-0.364114\pi$
$577$	19.8916	0.828099	0.414050	+	0.910254i	$0.364114\pi$
$578$	−2.31496	−0.0962898
$579$	8.09674	0.336489
$580$	−19.8682	−0.824980
$581$	−61.6277	−2.55675
$582$	−35.1201	−1.45578
$583$	−50.7643	−2.10244
$584$	−12.3517	−0.511116
$585$	9.77883	0.404305
$586$	69.4630	2.86949
$587$	−0.895011	−0.0369411	−0.0184705	−	0.999829i	$-0.505880\pi$
$587$	−0.895011	−0.0369411	−0.0184705	+	0.999829i	$0.505880\pi$
$588$	−62.1227	−2.56190
$589$	−1.49719	−0.0616906
$590$	−26.2781	−1.08185
$591$	−16.0131	−0.658692
$592$	−1.66358	−0.0683726
$593$	28.0200	1.15064	0.575322	−	0.817927i	$-0.304877\pi$
$593$	28.0200	1.15064	0.575322	+	0.817927i	$0.304877\pi$
$594$	−45.0130	−1.84691
$595$	−16.4635	−0.674939
$596$	30.7710	1.26043
$597$	−3.64806	−0.149305
$598$	−0.281132	−0.0114963
$599$	−31.3412	−1.28057	−0.640284	−	0.768138i	$-0.721183\pi$
$599$	−31.3412	−1.28057	−0.640284	+	0.768138i	$0.721183\pi$
$600$	16.6854	0.681179
$601$	−7.60498	−0.310214	−0.155107	−	0.987898i	$-0.549572\pi$
$601$	−7.60498	−0.310214	−0.155107	+	0.987898i	$0.549572\pi$
$602$	50.3401	2.05171
$603$	14.6789	0.597771
$604$	66.1793	2.69280
$605$	−14.8513	−0.603792
$606$	−38.6725	−1.57096
$607$	−38.9874	−1.58245	−0.791225	−	0.611525i	$-0.790556\pi$
$607$	−38.9874	−1.58245	−0.791225	+	0.611525i	$0.790556\pi$
$608$	4.79367	0.194409
$609$	−9.09662	−0.368614
$610$	87.8561	3.55719
$611$	−3.43286	−0.138879
$612$	−6.88313	−0.278234
$613$	−24.1124	−0.973892	−0.486946	−	0.873432i	$-0.661889\pi$
$613$	−24.1124	−0.973892	−0.486946	+	0.873432i	$0.661889\pi$
$614$	−51.0962	−2.06207
$615$	−17.6659	−0.712359
$616$	−63.3140	−2.55099
$617$	5.91291	0.238045	0.119022	−	0.992892i	$-0.462024\pi$
$617$	5.91291	0.238045	0.119022	+	0.992892i	$0.462024\pi$
$618$	25.6267	1.03086
$619$	−29.2263	−1.17471	−0.587353	−	0.809331i	$-0.699830\pi$
$619$	−29.2263	−1.17471	−0.587353	+	0.809331i	$0.699830\pi$
$620$	16.8938	0.678472
$621$	0.404806	0.0162443
$622$	−20.6500	−0.827990
$623$	−46.0044	−1.84313
$624$	−0.814024	−0.0325870
$625$	−22.6143	−0.904573
$626$	8.60921	0.344093
$627$	−3.70397	−0.147922
$628$	30.8357	1.23048
$629$	−2.94351	−0.117365
$630$	−78.0971	−3.11146
$631$	−31.1366	−1.23953	−0.619764	−	0.784788i	$-0.712772\pi$
$631$	−31.1366	−1.23953	−0.619764	+	0.784788i	$0.712772\pi$
$632$	47.2344	1.87888
$633$	−6.42046	−0.255190
$634$	−38.1044	−1.51332
$635$	−38.0868	−1.51143
$636$	42.1040	1.66953
$637$	28.0135	1.10994
$638$	−16.7370	−0.662624
$639$	7.17002	0.283642
$640$	−62.5445	−2.47229
$641$	−20.8234	−0.822473	−0.411237	−	0.911529i	$-0.634903\pi$
$641$	−20.8234	−0.822473	−0.411237	+	0.911529i	$0.634903\pi$
$642$	15.5657	0.614329
$643$	−44.6488	−1.76078	−0.880388	−	0.474254i	$-0.842718\pi$
$643$	−44.6488	−1.76078	−0.880388	+	0.474254i	$0.842718\pi$
$644$	1.40730	0.0554555
$645$	−13.4448	−0.529388
$646$	−2.22656	−0.0876027
$647$	5.83462	0.229382	0.114691	−	0.993401i	$-0.463412\pi$
$647$	5.83462	0.229382	0.114691	+	0.993401i	$0.463412\pi$
$648$	−4.23560	−0.166390
$649$	−13.8753	−0.544655
$650$	−18.5966	−0.729417
$651$	7.73482	0.303152
$652$	42.2331	1.65397
$653$	7.78089	0.304490	0.152245	−	0.988343i	$-0.451350\pi$
$653$	7.78089	0.304490	0.152245	+	0.988343i	$0.451350\pi$
$654$	9.52515	0.372463
$655$	−45.9623	−1.79589
$656$	−3.16905	−0.123731
$657$	−8.04472	−0.313854
$658$	27.4160	1.06879
$659$	12.2616	0.477644	0.238822	−	0.971063i	$-0.423239\pi$
$659$	12.2616	0.477644	0.238822	+	0.971063i	$0.423239\pi$
$660$	41.7944	1.62685
$661$	12.7416	0.495592	0.247796	−	0.968812i	$-0.420294\pi$
$661$	12.7416	0.495592	0.247796	+	0.968812i	$0.420294\pi$
$662$	−31.7316	−1.23329
$663$	−1.44032	−0.0559374
$664$	38.0504	1.47664
$665$	−15.8348	−0.614046
$666$	−13.9630	−0.541054
$667$	0.150517	0.00582805
$668$	−40.6698	−1.57356
$669$	1.24896	0.0482877
$670$	−53.5787	−2.06992
$671$	46.3897	1.79085
$672$	−24.7652	−0.955338
$673$	−31.2782	−1.20569	−0.602843	−	0.797860i	$-0.705966\pi$
$673$	−31.2782	−1.20569	−0.602843	+	0.797860i	$0.705966\pi$
$674$	7.38211	0.284348
$675$	26.7775	1.03066
$676$	−36.3393	−1.39767
$677$	47.4505	1.82367	0.911835	−	0.410557i	$-0.134666\pi$
$677$	47.4505	1.82367	0.911835	+	0.410557i	$0.134666\pi$
$678$	−34.1846	−1.31285
$679$	−79.2775	−3.04239
$680$	10.1650	0.389808
$681$	−4.86614	−0.186471
$682$	14.2314	0.544949
$683$	7.81016	0.298848	0.149424	−	0.988773i	$-0.452258\pi$
$683$	7.81016	0.298848	0.149424	+	0.988773i	$0.452258\pi$
$684$	−6.62026	−0.253132
$685$	49.7134	1.89945
$686$	−141.151	−5.38919
$687$	21.0440	0.802877
$688$	−2.41183	−0.0919502
$689$	−18.9863	−0.723319
$690$	−0.599650	−0.0228283
$691$	−2.52960	−0.0962306	−0.0481153	−	0.998842i	$-0.515321\pi$
$691$	−2.52960	−0.0962306	−0.0481153	+	0.998842i	$0.515321\pi$
$692$	−9.08428	−0.345333
$693$	−41.2367	−1.56645
$694$	26.3189	0.999053
$695$	−28.0165	−1.06273
$696$	5.61646	0.212892
$697$	−5.60727	−0.212391
$698$	74.3432	2.81393
$699$	−9.91614	−0.375063
$700$	93.0914	3.51852
$701$	−32.2114	−1.21661	−0.608304	−	0.793704i	$-0.708150\pi$
$701$	−32.2114	−1.21661	−0.608304	+	0.793704i	$0.708150\pi$
$702$	−16.8353	−0.635406
$703$	−2.83110	−0.106777
$704$	−50.0298	−1.88557
$705$	−7.32223	−0.275771
$706$	−2.31496	−0.0871248
$707$	−87.2964	−3.28312
$708$	11.5082	0.432505
$709$	19.3867	0.728082	0.364041	−	0.931383i	$-0.381397\pi$
$709$	19.3867	0.728082	0.364041	+	0.931383i	$0.381397\pi$
$710$	−26.1709	−0.982177
$711$	30.7640	1.15374
$712$	28.4042	1.06449
$713$	−0.127984	−0.00479305
$714$	11.5029	0.430485
$715$	−18.8467	−0.704826
$716$	−28.0946	−1.04995
$717$	−5.80371	−0.216744
$718$	19.0470	0.710828
$719$	−38.5136	−1.43632	−0.718158	−	0.695880i	$-0.755015\pi$
$719$	−38.5136	−1.43632	−0.718158	+	0.695880i	$0.755015\pi$
$720$	3.74169	0.139445
$721$	57.8478	2.15436
$722$	41.8428	1.55723
$723$	9.32560	0.346823
$724$	−88.7254	−3.29745
$725$	9.95654	0.369777
$726$	10.3765	0.385107
$727$	20.2795	0.752125	0.376062	−	0.926594i	$-0.377278\pi$
$727$	20.2795	0.752125	0.376062	+	0.926594i	$0.377278\pi$
$728$	−23.6800	−0.877637
$729$	11.6446	0.431282
$730$	29.3636	1.08680
$731$	−4.26746	−0.157838
$732$	−38.4756	−1.42210
$733$	−25.2118	−0.931220	−0.465610	−	0.884990i	$-0.654165\pi$
$733$	−25.2118	−0.931220	−0.465610	+	0.884990i	$0.654165\pi$
$734$	−6.63170	−0.244780
$735$	59.7523	2.20400
$736$	0.409777	0.0151046
$737$	−28.2905	−1.04210
$738$	−26.5989	−0.979120
$739$	44.6719	1.64328	0.821641	−	0.570006i	$-0.193059\pi$
$739$	44.6719	1.64328	0.821641	+	0.570006i	$0.193059\pi$
$740$	31.9452	1.17433
$741$	−1.38532	−0.0508908
$742$	151.631	5.56654
$743$	−44.7104	−1.64026	−0.820132	−	0.572174i	$-0.806100\pi$
$743$	−44.7104	−1.64026	−0.820132	+	0.572174i	$0.806100\pi$
$744$	−4.77566	−0.175084
$745$	−29.5969	−1.08435
$746$	25.8471	0.946329
$747$	24.7824	0.906741
$748$	13.2658	0.485046
$749$	35.1368	1.28387
$750$	−3.19925	−0.116820
$751$	−32.5783	−1.18880	−0.594399	−	0.804170i	$-0.702610\pi$
$751$	−32.5783	−1.18880	−0.594399	+	0.804170i	$0.702610\pi$
$752$	−1.31352	−0.0478992
$753$	19.0732	0.695065
$754$	−6.25978	−0.227968
$755$	−63.6541	−2.31661
$756$	84.2746	3.06504
$757$	−26.4883	−0.962735	−0.481368	−	0.876519i	$-0.659860\pi$
$757$	−26.4883	−0.962735	−0.481368	+	0.876519i	$0.659860\pi$
$758$	−30.4841	−1.10723
$759$	−0.316626	−0.0114928
$760$	9.77675	0.354640
$761$	−4.50312	−0.163238	−0.0816189	−	0.996664i	$-0.526009\pi$
$761$	−4.50312	−0.163238	−0.0816189	+	0.996664i	$0.526009\pi$
$762$	26.6109	0.964010
$763$	21.5014	0.778401
$764$	56.1593	2.03177
$765$	6.62049	0.239364
$766$	9.12757	0.329792
$767$	−5.18949	−0.187382
$768$	18.9930	0.685352
$769$	−38.6285	−1.39298	−0.696489	−	0.717567i	$-0.745256\pi$
$769$	−38.6285	−1.39298	−0.696489	+	0.717567i	$0.745256\pi$
$770$	150.516	5.42422
$771$	22.9184	0.825387
$772$	−27.8911	−1.00382
$773$	2.65589	0.0955257	0.0477629	−	0.998859i	$-0.484791\pi$
$773$	2.65589	0.0955257	0.0477629	+	0.998859i	$0.484791\pi$
$774$	−20.2433	−0.727630
$775$	−8.46601	−0.304108
$776$	48.9477	1.75712
$777$	14.6261	0.524708
$778$	88.4173	3.16991
$779$	−5.39313	−0.193229
$780$	15.6315	0.559696
$781$	−13.8187	−0.494473
$782$	−0.190333	−0.00680628
$783$	9.01354	0.322118
$784$	10.7189	0.382816
$785$	−29.6592	−1.05858
$786$	32.1134	1.14545
$787$	20.3729	0.726214	0.363107	−	0.931747i	$-0.381716\pi$
$787$	20.3729	0.726214	0.363107	+	0.931747i	$0.381716\pi$
$788$	55.1610	1.96503
$789$	−8.26796	−0.294347
$790$	−112.290	−3.99510
$791$	−77.1656	−2.74369
$792$	25.4605	0.904700
$793$	17.3501	0.616121
$794$	−3.24384	−0.115120
$795$	−40.4974	−1.43629
$796$	12.5666	0.445411
$797$	13.5277	0.479177	0.239588	−	0.970875i	$-0.422988\pi$
$797$	13.5277	0.479177	0.239588	+	0.970875i	$0.422988\pi$
$798$	11.0636	0.391647
$799$	−2.32412	−0.0822216
$800$	27.1063	0.958352
$801$	18.4998	0.653658
$802$	−31.0765	−1.09735
$803$	15.5045	0.547143
$804$	23.4642	0.827518
$805$	−1.35360	−0.0477083
$806$	5.32266	0.187483
$807$	−5.79136	−0.203865
$808$	53.8988	1.89615
$809$	−55.1260	−1.93813	−0.969063	−	0.246815i	$-0.920616\pi$
$809$	−55.1260	−1.93813	−0.969063	+	0.246815i	$0.920616\pi$
$810$	10.0693	0.353799
$811$	3.64856	0.128118	0.0640592	−	0.997946i	$-0.479595\pi$
$811$	3.64856	0.128118	0.0640592	+	0.997946i	$0.479595\pi$
$812$	31.3354	1.09966
$813$	−5.65029	−0.198164
$814$	26.9107	0.943221
$815$	−40.6216	−1.42291
$816$	−0.551112	−0.0192928
$817$	−4.10448	−0.143598
$818$	28.8409	1.00840
$819$	−15.4229	−0.538919
$820$	60.8544	2.12513
$821$	8.15487	0.284607	0.142303	−	0.989823i	$-0.454549\pi$
$821$	8.15487	0.284607	0.142303	+	0.989823i	$0.454549\pi$
$822$	−34.7342	−1.21150
$823$	43.5122	1.51674	0.758369	−	0.651825i	$-0.225996\pi$
$823$	43.5122	1.51674	0.758369	+	0.651825i	$0.225996\pi$
$824$	−35.7165	−1.24424
$825$	−20.9445	−0.729193
$826$	41.4450	1.44206
$827$	−34.9566	−1.21556	−0.607780	−	0.794105i	$-0.707940\pi$
$827$	−34.9566	−1.21556	−0.607780	+	0.794105i	$0.707940\pi$
$828$	−0.565919	−0.0196671
$829$	−11.9545	−0.415197	−0.207599	−	0.978214i	$-0.566565\pi$
$829$	−11.9545	−0.415197	−0.207599	+	0.978214i	$0.566565\pi$
$830$	−90.4570	−3.13981
$831$	−14.4031	−0.499639
$832$	−18.7116	−0.648707
$833$	18.9658	0.657125
$834$	19.5748	0.677821
$835$	39.1179	1.35373
$836$	12.7592	0.441286
$837$	−7.66418	−0.264913
$838$	−80.0325	−2.76468
$839$	−31.5780	−1.09019	−0.545096	−	0.838374i	$-0.683507\pi$
$839$	−31.5780	−1.09019	−0.545096	+	0.838374i	$0.683507\pi$
$840$	−50.5089	−1.74272
$841$	−25.6485	−0.884432
$842$	80.8158	2.78510
$843$	−1.48542	−0.0511605
$844$	22.1168	0.761291
$845$	34.9528	1.20241
$846$	−11.0248	−0.379041
$847$	23.4230	0.804825
$848$	−7.26475	−0.249472
$849$	−4.76464	−0.163522
$850$	−12.5903	−0.431843
$851$	−0.242010	−0.00829601
$852$	11.4613	0.392657
$853$	−9.22541	−0.315872	−0.157936	−	0.987449i	$-0.550484\pi$
$853$	−9.22541	−0.315872	−0.157936	+	0.987449i	$0.550484\pi$
$854$	−138.564	−4.74156
$855$	6.36765	0.217769
$856$	−21.6943	−0.741496
$857$	−2.24654	−0.0767402	−0.0383701	−	0.999264i	$-0.512217\pi$
$857$	−2.24654	−0.0767402	−0.0383701	+	0.999264i	$0.512217\pi$
$858$	13.1680	0.449548
$859$	7.79945	0.266114	0.133057	−	0.991108i	$-0.457521\pi$
$859$	7.79945	0.266114	0.133057	+	0.991108i	$0.457521\pi$
$860$	46.3137	1.57928
$861$	27.8622	0.949540
$862$	50.9285	1.73463
$863$	−2.54935	−0.0867810	−0.0433905	−	0.999058i	$-0.513816\pi$
$863$	−2.54935	−0.0867810	−0.0433905	+	0.999058i	$0.513816\pi$
$864$	24.5390	0.834834
$865$	8.73766	0.297089
$866$	18.4460	0.626819
$867$	−0.975130	−0.0331171
$868$	−26.6444	−0.904370
$869$	−59.2913	−2.01132
$870$	−13.3520	−0.452675
$871$	−10.5809	−0.358520
$872$	−13.2754	−0.449563
$873$	31.8799	1.07897
$874$	−0.183064	−0.00619222
$875$	−7.22173	−0.244139
$876$	−12.8595	−0.434481
$877$	17.4325	0.588653	0.294326	−	0.955705i	$-0.404905\pi$
$877$	17.4325	0.588653	0.294326	+	0.955705i	$0.404905\pi$
$878$	65.1743	2.19953
$879$	29.2598	0.986909
$880$	−7.21134	−0.243094
$881$	−11.9016	−0.400977	−0.200488	−	0.979696i	$-0.564253\pi$
$881$	−11.9016	−0.400977	−0.200488	+	0.979696i	$0.564253\pi$
$882$	89.9669	3.02934
$883$	0.299105	0.0100657	0.00503285	−	0.999987i	$-0.498398\pi$
$883$	0.299105	0.0100657	0.00503285	+	0.999987i	$0.498398\pi$
$884$	4.96152	0.166874
$885$	−11.0691	−0.372084
$886$	18.8134	0.632050
$887$	15.6498	0.525468	0.262734	−	0.964868i	$-0.415376\pi$
$887$	15.6498	0.525468	0.262734	+	0.964868i	$0.415376\pi$
$888$	−9.03048	−0.303043
$889$	60.0693	2.01466
$890$	−67.5251	−2.26345
$891$	5.31677	0.178118
$892$	−4.30234	−0.144053
$893$	−2.23536	−0.0748036
$894$	20.6790	0.691610
$895$	27.0226	0.903267
$896$	98.6433	3.29544
$897$	−0.118421	−0.00395396
$898$	−50.1594	−1.67384
$899$	−2.84974	−0.0950441
$900$	−37.4349	−1.24783
$901$	−12.8541	−0.428233
$902$	51.2639	1.70690
$903$	21.2047	0.705648
$904$	47.6438	1.58461
$905$	85.3399	2.83679
$906$	44.4745	1.47757
$907$	29.7957	0.989349	0.494675	−	0.869078i	$-0.335287\pi$
$907$	29.7957	0.989349	0.494675	+	0.869078i	$0.335287\pi$
$908$	16.7626	0.556285
$909$	35.1046	1.16435
$910$	56.2943	1.86614
$911$	48.9586	1.62207	0.811035	−	0.584998i	$-0.198905\pi$
$911$	48.9586	1.62207	0.811035	+	0.584998i	$0.198905\pi$
$912$	−0.530065	−0.0175522
$913$	−47.7630	−1.58072
$914$	−36.3571	−1.20258
$915$	37.0075	1.22343
$916$	−72.4908	−2.39516
$917$	72.4903	2.39384
$918$	−11.3978	−0.376185
$919$	15.9791	0.527102	0.263551	−	0.964645i	$-0.415106\pi$
$919$	15.9791	0.527102	0.263551	+	0.964645i	$0.415106\pi$
$920$	0.835746	0.0275537
$921$	−21.5232	−0.709213
$922$	−54.8439	−1.80619
$923$	−5.16832	−0.170117
$924$	−65.9169	−2.16851
$925$	−16.0087	−0.526363
$926$	32.3498	1.06308
$927$	−23.2624	−0.764037
$928$	9.12423	0.299518
$929$	50.0587	1.64237	0.821186	−	0.570660i	$-0.193313\pi$
$929$	50.0587	1.64237	0.821186	+	0.570660i	$0.193313\pi$
$930$	11.3532	0.372284
$931$	18.2415	0.597840
$932$	34.1584	1.11890
$933$	−8.69838	−0.284772
$934$	−69.9730	−2.28959
$935$	−12.7596	−0.417284
$936$	9.52244	0.311251
$937$	25.4041	0.829917	0.414958	−	0.909840i	$-0.363796\pi$
$937$	25.4041	0.829917	0.414958	+	0.909840i	$0.363796\pi$
$938$	84.5026	2.75911
$939$	3.62645	0.118345
$940$	25.2231	0.822688
$941$	43.9137	1.43155	0.715773	−	0.698333i	$-0.246074\pi$
$941$	43.9137	1.43155	0.715773	+	0.698333i	$0.246074\pi$
$942$	20.7226	0.675177
$943$	−0.461021	−0.0150129
$944$	−1.98566	−0.0646278
$945$	−81.0589	−2.63685
$946$	39.0148	1.26848
$947$	−7.18780	−0.233572	−0.116786	−	0.993157i	$-0.537259\pi$
$947$	−7.18780	−0.233572	−0.116786	+	0.993157i	$0.537259\pi$
$948$	49.1762	1.59717
$949$	5.79883	0.188238
$950$	−12.1095	−0.392883
$951$	−16.0507	−0.520478
$952$	−16.0319	−0.519595
$953$	7.07513	0.229186	0.114593	−	0.993413i	$-0.463444\pi$
$953$	7.07513	0.229186	0.114593	+	0.993413i	$0.463444\pi$
$954$	−60.9754	−1.97415
$955$	−54.0165	−1.74793
$956$	19.9922	0.646595
$957$	−7.05010	−0.227898
$958$	43.9432	1.41974
$959$	−78.4064	−2.53188
$960$	−39.9115	−1.28814
$961$	−28.5769	−0.921835
$962$	10.0648	0.324503
$963$	−14.1296	−0.455320
$964$	−32.1242	−1.03465
$965$	26.8269	0.863588
$966$	0.945749	0.0304290
$967$	−51.2004	−1.64649	−0.823247	−	0.567684i	$-0.807840\pi$
$967$	−51.2004	−1.64649	−0.823247	+	0.567684i	$0.807840\pi$
$968$	−14.4619	−0.464824
$969$	−0.937889	−0.0301293
$970$	−116.363	−3.73620
$971$	55.5540	1.78281	0.891407	−	0.453204i	$-0.149719\pi$
$971$	55.5540	1.78281	0.891407	+	0.453204i	$0.149719\pi$
$972$	−54.0252	−1.73286
$973$	44.1867	1.41656
$974$	−50.2968	−1.61161
$975$	−7.83340	−0.250870
$976$	6.63870	0.212500
$977$	−58.5148	−1.87205	−0.936026	−	0.351930i	$-0.885526\pi$
$977$	−58.5148	−1.87205	−0.936026	+	0.351930i	$0.885526\pi$
$978$	28.3819	0.907553
$979$	−35.6545	−1.13952
$980$	−205.831	−6.57502
$981$	−8.64636	−0.276057
$982$	66.7030	2.12858
$983$	24.1245	0.769453	0.384727	−	0.923031i	$-0.374296\pi$
$983$	24.1245	0.769453	0.384727	+	0.923031i	$0.374296\pi$
$984$	−17.2027	−0.548403
$985$	−53.0562	−1.69051
$986$	−4.23801	−0.134966
$987$	11.5484	0.367590
$988$	4.77204	0.151819
$989$	−0.350863	−0.0111568
$990$	−60.5272	−1.92368
$991$	−42.6626	−1.35522	−0.677611	−	0.735421i	$-0.736985\pi$
$991$	−42.6626	−1.35522	−0.677611	+	0.735421i	$0.736985\pi$
$992$	−7.75830	−0.246326
$993$	−13.3663	−0.424166
$994$	41.2760	1.30919
$995$	−12.0871	−0.383186
$996$	39.6147	1.25524
$997$	7.28060	0.230579	0.115290	−	0.993332i	$-0.463220\pi$
$997$	7.28060	0.230579	0.115290	+	0.993332i	$0.463220\pi$
$998$	−39.8403	−1.26112
$999$	−14.4925	−0.458523

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.13	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.13	✓	114	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)

\(f(q)\)	\(=\)	\(q-2.31496 q^{2} -0.975130 q^{3} +3.35906 q^{4} -3.23089 q^{5} +2.25739 q^{6} +5.09566 q^{7} -3.14618 q^{8} -2.04912 q^{9} +O(q^{10})\)	\(q-2.31496 q^{2} -0.975130 q^{3} +3.35906 q^{4} -3.23089 q^{5} +2.25739 q^{6} +5.09566 q^{7} -3.14618 q^{8} -2.04912 q^{9} +7.47940 q^{10} +3.94926 q^{11} -3.27552 q^{12} +1.47706 q^{13} -11.7963 q^{14} +3.15054 q^{15} +0.565168 q^{16} +1.00000 q^{17} +4.74365 q^{18} +0.961810 q^{19} -10.8528 q^{20} -4.96893 q^{21} -9.14240 q^{22} +0.0822184 q^{23} +3.06793 q^{24} +5.43865 q^{25} -3.41933 q^{26} +4.92355 q^{27} +17.1166 q^{28} +1.83070 q^{29} -7.29338 q^{30} -1.55664 q^{31} +4.98401 q^{32} -3.85104 q^{33} -2.31496 q^{34} -16.4635 q^{35} -6.88313 q^{36} -2.94351 q^{37} -2.22656 q^{38} -1.44032 q^{39} +10.1650 q^{40} -5.60727 q^{41} +11.5029 q^{42} -4.26746 q^{43} +13.2658 q^{44} +6.62049 q^{45} -0.190333 q^{46} -2.32412 q^{47} -0.551112 q^{48} +18.9658 q^{49} -12.5903 q^{50} -0.975130 q^{51} +4.96152 q^{52} -12.8541 q^{53} -11.3978 q^{54} -12.7596 q^{55} -16.0319 q^{56} -0.937889 q^{57} -4.23801 q^{58} -3.51340 q^{59} +10.5828 q^{60} +11.7464 q^{61} +3.60356 q^{62} -10.4416 q^{63} -12.6681 q^{64} -4.77221 q^{65} +8.91502 q^{66} -7.16350 q^{67} +3.35906 q^{68} -0.0801736 q^{69} +38.1125 q^{70} -3.49907 q^{71} +6.44690 q^{72} +3.92593 q^{73} +6.81412 q^{74} -5.30339 q^{75} +3.23078 q^{76} +20.1241 q^{77} +3.33429 q^{78} -15.0133 q^{79} -1.82600 q^{80} +1.34627 q^{81} +12.9806 q^{82} -12.0942 q^{83} -16.6909 q^{84} -3.23089 q^{85} +9.87901 q^{86} -1.78517 q^{87} -12.4251 q^{88} -9.02816 q^{89} -15.3262 q^{90} +7.52658 q^{91} +0.276176 q^{92} +1.51792 q^{93} +5.38026 q^{94} -3.10750 q^{95} -4.86006 q^{96} -15.5578 q^{97} -43.9051 q^{98} -8.09252 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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