LMFDB - Embedded newform 6019.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$130$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65690 q^{2} -1.17656 q^{3} +5.05912 q^{4} -3.97344 q^{5} +3.12601 q^{6} -1.98444 q^{7} -8.12779 q^{8} -1.61571 q^{9} +O(q^{10})$	\(q-2.65690 q^{2} -1.17656 q^{3} +5.05912 q^{4} -3.97344 q^{5} +3.12601 q^{6} -1.98444 q^{7} -8.12779 q^{8} -1.61571 q^{9} +10.5570 q^{10} +3.06486 q^{11} -5.95237 q^{12} +1.00000 q^{13} +5.27247 q^{14} +4.67499 q^{15} +11.4765 q^{16} +4.82877 q^{17} +4.29277 q^{18} -1.87946 q^{19} -20.1021 q^{20} +2.33482 q^{21} -8.14303 q^{22} +3.96518 q^{23} +9.56284 q^{24} +10.7882 q^{25} -2.65690 q^{26} +5.43066 q^{27} -10.0395 q^{28} +10.1973 q^{29} -12.4210 q^{30} +1.96081 q^{31} -14.2363 q^{32} -3.60599 q^{33} -12.8296 q^{34} +7.88506 q^{35} -8.17405 q^{36} -10.4081 q^{37} +4.99355 q^{38} -1.17656 q^{39} +32.2953 q^{40} +10.2820 q^{41} -6.20338 q^{42} +9.66829 q^{43} +15.5055 q^{44} +6.41990 q^{45} -10.5351 q^{46} +1.09660 q^{47} -13.5028 q^{48} -3.06198 q^{49} -28.6632 q^{50} -5.68133 q^{51} +5.05912 q^{52} +0.613431 q^{53} -14.4287 q^{54} -12.1780 q^{55} +16.1291 q^{56} +2.21130 q^{57} -27.0932 q^{58} +8.78784 q^{59} +23.6513 q^{60} +3.09399 q^{61} -5.20967 q^{62} +3.20628 q^{63} +14.8715 q^{64} -3.97344 q^{65} +9.58077 q^{66} -5.68402 q^{67} +24.4293 q^{68} -4.66527 q^{69} -20.9498 q^{70} +1.46209 q^{71} +13.1321 q^{72} -12.1577 q^{73} +27.6534 q^{74} -12.6930 q^{75} -9.50844 q^{76} -6.08204 q^{77} +3.12601 q^{78} +5.94489 q^{79} -45.6011 q^{80} -1.54238 q^{81} -27.3182 q^{82} +8.26160 q^{83} +11.8121 q^{84} -19.1868 q^{85} -25.6877 q^{86} -11.9977 q^{87} -24.9106 q^{88} -0.0123574 q^{89} -17.0570 q^{90} -1.98444 q^{91} +20.0603 q^{92} -2.30701 q^{93} -2.91355 q^{94} +7.46793 q^{95} +16.7499 q^{96} +9.42141 q^{97} +8.13539 q^{98} -4.95191 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) $ 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * 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 $

$2$	−2.65690	−1.87871	−0.939356	−	0.342942i	$-0.888576\pi$
$2$	−2.65690	−1.87871	−0.939356	+	0.342942i	$0.888576\pi$
$3$	−1.17656	−0.679288	−0.339644	−	0.940554i	$-0.610307\pi$
$3$	−1.17656	−0.679288	−0.339644	+	0.940554i	$0.610307\pi$
$4$	5.05912	2.52956
$5$	−3.97344	−1.77697	−0.888487	−	0.458901i	$-0.848243\pi$
$5$	−3.97344	−1.77697	−0.888487	+	0.458901i	$0.848243\pi$
$6$	3.12601	1.27619
$7$	−1.98444	−0.750049	−0.375025	−	0.927015i	$-0.622366\pi$
$7$	−1.98444	−0.750049	−0.375025	+	0.927015i	$0.622366\pi$
$8$	−8.12779	−2.87361
$9$	−1.61571	−0.538568
$10$	10.5570	3.33843
$11$	3.06486	0.924090	0.462045	−	0.886856i	$-0.347116\pi$
$11$	3.06486	0.924090	0.462045	+	0.886856i	$0.347116\pi$
$12$	−5.95237	−1.71830
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	5.27247	1.40913
$15$	4.67499	1.20708
$16$	11.4765	2.86912
$17$	4.82877	1.17115	0.585574	−	0.810619i	$-0.300869\pi$
$17$	4.82877	1.17115	0.585574	+	0.810619i	$0.300869\pi$
$18$	4.29277	1.01182
$19$	−1.87946	−0.431178	−0.215589	−	0.976484i	$-0.569167\pi$
$19$	−1.87946	−0.431178	−0.215589	+	0.976484i	$0.569167\pi$
$20$	−20.1021	−4.49497
$21$	2.33482	0.509499
$22$	−8.14303	−1.73610
$23$	3.96518	0.826797	0.413398	−	0.910550i	$-0.364342\pi$
$23$	3.96518	0.826797	0.413398	+	0.910550i	$0.364342\pi$
$24$	9.56284	1.95201
$25$	10.7882	2.15764
$26$	−2.65690	−0.521061
$27$	5.43066	1.04513
$28$	−10.0395	−1.89730
$29$	10.1973	1.89359	0.946795	−	0.321837i	$-0.104300\pi$
$29$	10.1973	1.89359	0.946795	+	0.321837i	$0.104300\pi$
$30$	−12.4210	−2.26775
$31$	1.96081	0.352172	0.176086	−	0.984375i	$-0.443656\pi$
$31$	1.96081	0.352172	0.176086	+	0.984375i	$0.443656\pi$
$32$	−14.2363	−2.51665
$33$	−3.60599	−0.627723
$34$	−12.8296	−2.20025
$35$	7.88506	1.33282
$36$	−8.17405	−1.36234
$37$	−10.4081	−1.71109	−0.855543	−	0.517732i	$-0.826776\pi$
$37$	−10.4081	−1.71109	−0.855543	+	0.517732i	$0.826776\pi$
$38$	4.99355	0.810061
$39$	−1.17656	−0.188400
$40$	32.2953	5.10633
$41$	10.2820	1.60578	0.802889	−	0.596129i	$-0.203295\pi$
$41$	10.2820	1.60578	0.802889	+	0.596129i	$0.203295\pi$
$42$	−6.20338	−0.957202
$43$	9.66829	1.47440	0.737201	−	0.675674i	$-0.236147\pi$
$43$	9.66829	1.47440	0.737201	+	0.675674i	$0.236147\pi$
$44$	15.5055	2.33754
$45$	6.41990	0.957023
$46$	−10.5351	−1.55331
$47$	1.09660	0.159955	0.0799776	−	0.996797i	$-0.474515\pi$
$47$	1.09660	0.159955	0.0799776	+	0.996797i	$0.474515\pi$
$48$	−13.5028	−1.94896
$49$	−3.06198	−0.437426
$50$	−28.6632	−4.05358
$51$	−5.68133	−0.795546
$52$	5.05912	0.701574
$53$	0.613431	0.0842613	0.0421306	−	0.999112i	$-0.486585\pi$
$53$	0.613431	0.0842613	0.0421306	+	0.999112i	$0.486585\pi$
$54$	−14.4287	−1.96350
$55$	−12.1780	−1.64209
$56$	16.1291	2.15535
$57$	2.21130	0.292894
$58$	−27.0932	−3.55751
$59$	8.78784	1.14408	0.572040	−	0.820226i	$-0.306152\pi$
$59$	8.78784	1.14408	0.572040	+	0.820226i	$0.306152\pi$
$60$	23.6513	3.05338
$61$	3.09399	0.396145	0.198072	−	0.980187i	$-0.436532\pi$
$61$	3.09399	0.396145	0.198072	+	0.980187i	$0.436532\pi$
$62$	−5.20967	−0.661629
$63$	3.20628	0.403953
$64$	14.8715	1.85894
$65$	−3.97344	−0.492844
$66$	9.58077	1.17931
$67$	−5.68402	−0.694414	−0.347207	−	0.937789i	$-0.612870\pi$
$67$	−5.68402	−0.694414	−0.347207	+	0.937789i	$0.612870\pi$
$68$	24.4293	2.96249
$69$	−4.66527	−0.561633
$70$	−20.9498	−2.50398
$71$	1.46209	0.173518	0.0867590	−	0.996229i	$-0.472349\pi$
$71$	1.46209	0.173518	0.0867590	+	0.996229i	$0.472349\pi$
$72$	13.1321	1.54763
$73$	−12.1577	−1.42295	−0.711474	−	0.702712i	$-0.751972\pi$
$73$	−12.1577	−1.42295	−0.711474	+	0.702712i	$0.751972\pi$
$74$	27.6534	3.21464
$75$	−12.6930	−1.46566
$76$	−9.50844	−1.09069
$77$	−6.08204	−0.693113
$78$	3.12601	0.353950
$79$	5.94489	0.668852	0.334426	−	0.942422i	$-0.391458\pi$
$79$	5.94489	0.668852	0.334426	+	0.942422i	$0.391458\pi$
$80$	−45.6011	−5.09836
$81$	−1.54238	−0.171376
$82$	−27.3182	−3.01679
$83$	8.26160	0.906829	0.453414	−	0.891300i	$-0.350206\pi$
$83$	8.26160	0.906829	0.453414	+	0.891300i	$0.350206\pi$
$84$	11.8121	1.28881
$85$	−19.1868	−2.08110
$86$	−25.6877	−2.76998
$87$	−11.9977	−1.28629
$88$	−24.9106	−2.65547
$89$	−0.0123574	−0.00130988	−0.000654940	−	1.00000i	$-0.500208\pi$
$89$	−0.0123574	−0.00130988	−0.000654940		1.00000i	$0.500208\pi$
$90$	−17.0570	−1.79797
$91$	−1.98444	−0.208026
$92$	20.0603	2.09143
$93$	−2.30701	−0.239226
$94$	−2.91355	−0.300510
$95$	7.46793	0.766193
$96$	16.7499	1.70953
$97$	9.42141	0.956600	0.478300	−	0.878197i	$-0.341253\pi$
$97$	9.42141	0.956600	0.478300	+	0.878197i	$0.341253\pi$
$98$	8.13539	0.821798
$99$	−4.95191	−0.497686
$100$	54.5788	5.45788
$101$	−10.8874	−1.08334	−0.541671	−	0.840591i	$-0.682208\pi$
$101$	−10.8874	−1.08334	−0.541671	+	0.840591i	$0.682208\pi$
$102$	15.0947	1.49460
$103$	2.12250	0.209136	0.104568	−	0.994518i	$-0.466654\pi$
$103$	2.12250	0.209136	0.104568	+	0.994518i	$0.466654\pi$
$104$	−8.12779	−0.796995
$105$	−9.27725	−0.905367
$106$	−1.62983	−0.158303
$107$	−17.3367	−1.67600	−0.838002	−	0.545667i	$-0.816276\pi$
$107$	−17.3367	−1.67600	−0.838002	+	0.545667i	$0.816276\pi$
$108$	27.4744	2.64372
$109$	16.6563	1.59538	0.797691	−	0.603067i	$-0.206055\pi$
$109$	16.6563	1.59538	0.797691	+	0.603067i	$0.206055\pi$
$110$	32.3558	3.08501
$111$	12.2458	1.16232
$112$	−22.7744	−2.15198
$113$	−0.437226	−0.0411308	−0.0205654	−	0.999789i	$-0.506547\pi$
$113$	−0.437226	−0.0411308	−0.0205654	+	0.999789i	$0.506547\pi$
$114$	−5.87521	−0.550264
$115$	−15.7554	−1.46920
$116$	51.5894	4.78995
$117$	−1.61571	−0.149372
$118$	−23.3484	−2.14940
$119$	−9.58241	−0.878418
$120$	−37.9973	−3.46867
$121$	−1.60663	−0.146057
$122$	−8.22042	−0.744242
$123$	−12.0974	−1.09078
$124$	9.91997	0.890840
$125$	−22.9990	−2.05710
$126$	−8.51876	−0.758911
$127$	−11.0495	−0.980485	−0.490242	−	0.871586i	$-0.663092\pi$
$127$	−11.0495	−0.980485	−0.490242	+	0.871586i	$0.663092\pi$
$128$	−11.0395	−0.975763
$129$	−11.3753	−1.00154
$130$	10.5570	0.925913
$131$	−9.01334	−0.787499	−0.393750	−	0.919218i	$-0.628822\pi$
$131$	−9.01334	−0.787499	−0.393750	+	0.919218i	$0.628822\pi$
$132$	−18.2432	−1.58786
$133$	3.72969	0.323405
$134$	15.1019	1.30460
$135$	−21.5784	−1.85717
$136$	−39.2472	−3.36542
$137$	−16.9279	−1.44625	−0.723126	−	0.690716i	$-0.757295\pi$
$137$	−16.9279	−1.44625	−0.723126	+	0.690716i	$0.757295\pi$
$138$	12.3952	1.05515
$139$	−7.03091	−0.596354	−0.298177	−	0.954511i	$-0.596379\pi$
$139$	−7.03091	−0.596354	−0.298177	+	0.954511i	$0.596379\pi$
$140$	39.8915	3.37145
$141$	−1.29021	−0.108656
$142$	−3.88462	−0.325990
$143$	3.06486	0.256297
$144$	−18.5426	−1.54522
$145$	−40.5183	−3.36486
$146$	32.3018	2.67331
$147$	3.60261	0.297138
$148$	−52.6560	−4.32830
$149$	12.2129	1.00052	0.500262	−	0.865874i	$-0.333237\pi$
$149$	12.2129	1.00052	0.500262	+	0.865874i	$0.333237\pi$
$150$	33.7240	2.75355
$151$	3.66650	0.298376	0.149188	−	0.988809i	$-0.452334\pi$
$151$	3.66650	0.298376	0.149188	+	0.988809i	$0.452334\pi$
$152$	15.2759	1.23904
$153$	−7.80186	−0.630743
$154$	16.1594	1.30216
$155$	−7.79115	−0.625800
$156$	−5.95237	−0.476571
$157$	11.4086	0.910502	0.455251	−	0.890363i	$-0.349550\pi$
$157$	11.4086	0.910502	0.455251	+	0.890363i	$0.349550\pi$
$158$	−15.7950	−1.25658
$159$	−0.721739	−0.0572376
$160$	56.5671	4.47202
$161$	−7.86867	−0.620138
$162$	4.09795	0.321965
$163$	−4.35309	−0.340961	−0.170480	−	0.985361i	$-0.554532\pi$
$163$	−4.35309	−0.340961	−0.170480	+	0.985361i	$0.554532\pi$
$164$	52.0179	4.06191
$165$	14.3282	1.11545
$166$	−21.9503	−1.70367
$167$	17.7186	1.37111	0.685554	−	0.728022i	$-0.259560\pi$
$167$	17.7186	1.37111	0.685554	+	0.728022i	$0.259560\pi$
$168$	−18.9769	−1.46410
$169$	1.00000	0.0769231
$170$	50.9774	3.90979
$171$	3.03666	0.232219
$172$	48.9131	3.72959
$173$	26.0485	1.98043	0.990214	−	0.139558i	$-0.0445682\pi$
$173$	26.0485	1.98043	0.990214	+	0.139558i	$0.0445682\pi$
$174$	31.8768	2.41657
$175$	−21.4086	−1.61834
$176$	35.1738	2.65133
$177$	−10.3394	−0.777159
$178$	0.0328324	0.00246089
$179$	15.8317	1.18332	0.591658	−	0.806189i	$-0.298474\pi$
$179$	15.8317	1.18332	0.591658	+	0.806189i	$0.298474\pi$
$180$	32.4791	2.42085
$181$	0.966140	0.0718126	0.0359063	−	0.999355i	$-0.488568\pi$
$181$	0.966140	0.0718126	0.0359063	+	0.999355i	$0.488568\pi$
$182$	5.27247	0.390822
$183$	−3.64026	−0.269096
$184$	−32.2281	−2.37589
$185$	41.3560	3.04056
$186$	6.12950	0.449436
$187$	14.7995	1.08225
$188$	5.54782	0.404617
$189$	−10.7768	−0.783899
$190$	−19.8415	−1.43946
$191$	24.0959	1.74351	0.871757	−	0.489938i	$-0.162981\pi$
$191$	24.0959	1.74351	0.871757	+	0.489938i	$0.162981\pi$
$192$	−17.4972	−1.26275
$193$	21.3639	1.53781	0.768904	−	0.639365i	$-0.220803\pi$
$193$	21.3639	1.53781	0.768904	+	0.639365i	$0.220803\pi$
$194$	−25.0318	−1.79718
$195$	4.67499	0.334783
$196$	−15.4910	−1.10650
$197$	11.0926	0.790313	0.395157	−	0.918614i	$-0.370690\pi$
$197$	11.0926	0.790313	0.395157	+	0.918614i	$0.370690\pi$
$198$	13.1567	0.935009
$199$	7.03091	0.498408	0.249204	−	0.968451i	$-0.419831\pi$
$199$	7.03091	0.498408	0.249204	+	0.968451i	$0.419831\pi$
$200$	−87.6842	−6.20021
$201$	6.68760	0.471707
$202$	28.9269	2.03529
$203$	−20.2360	−1.42029
$204$	−28.7426	−2.01238
$205$	−40.8548	−2.85343
$206$	−5.63928	−0.392907
$207$	−6.40656	−0.445287
$208$	11.4765	0.795751
$209$	−5.76029	−0.398448
$210$	24.6487	1.70092
$211$	6.33567	0.436166	0.218083	−	0.975930i	$-0.430020\pi$
$211$	6.33567	0.436166	0.218083	+	0.975930i	$0.430020\pi$
$212$	3.10343	0.213144
$213$	−1.72024	−0.117869
$214$	46.0620	3.14873
$215$	−38.4164	−2.61997
$216$	−44.1392	−3.00330
$217$	−3.89111	−0.264146
$218$	−44.2541	−2.99726
$219$	14.3042	0.966591
$220$	−61.6102	−4.15376
$221$	4.82877	0.324818
$222$	−32.5359	−2.18366
$223$	−17.3622	−1.16266	−0.581331	−	0.813667i	$-0.697468\pi$
$223$	−17.3622	−1.16266	−0.581331	+	0.813667i	$0.697468\pi$
$224$	28.2512	1.88761
$225$	−17.4305	−1.16204
$226$	1.16167	0.0772730
$227$	−0.475918	−0.0315878	−0.0157939	−	0.999875i	$-0.505028\pi$
$227$	−0.475918	−0.0315878	−0.0157939	+	0.999875i	$0.505028\pi$
$228$	11.1873	0.740894
$229$	−24.1579	−1.59640	−0.798199	−	0.602394i	$-0.794214\pi$
$229$	−24.1579	−1.59640	−0.798199	+	0.602394i	$0.794214\pi$
$230$	41.8605	2.76020
$231$	7.15589	0.470823
$232$	−82.8815	−5.44144
$233$	−7.25831	−0.475508	−0.237754	−	0.971325i	$-0.576411\pi$
$233$	−7.25831	−0.475508	−0.237754	+	0.971325i	$0.576411\pi$
$234$	4.29277	0.280627
$235$	−4.35726	−0.284236
$236$	44.4588	2.89402
$237$	−6.99452	−0.454343
$238$	25.4595	1.65030
$239$	18.2769	1.18223	0.591117	−	0.806586i	$-0.298687\pi$
$239$	18.2769	1.18223	0.591117	+	0.806586i	$0.298687\pi$
$240$	53.6525	3.46325
$241$	24.6535	1.58807	0.794036	−	0.607871i	$-0.207976\pi$
$241$	24.6535	1.58807	0.794036	+	0.607871i	$0.207976\pi$
$242$	4.26865	0.274399
$243$	−14.4773	−0.928717
$244$	15.6529	1.00207
$245$	12.1666	0.777295
$246$	32.1416	2.04927
$247$	−1.87946	−0.119587
$248$	−15.9370	−1.01200
$249$	−9.72028	−0.615998
$250$	61.1061	3.86469
$251$	−15.0931	−0.952666	−0.476333	−	0.879265i	$-0.658034\pi$
$251$	−15.0931	−0.952666	−0.476333	+	0.879265i	$0.658034\pi$
$252$	16.2210	1.02182
$253$	12.1527	0.764035
$254$	29.3574	1.84205
$255$	22.5744	1.41367
$256$	−0.412156	−0.0257598
$257$	−9.89505	−0.617236	−0.308618	−	0.951186i	$-0.599867\pi$
$257$	−9.89505	−0.617236	−0.308618	+	0.951186i	$0.599867\pi$
$258$	30.2231	1.88161
$259$	20.6543	1.28340
$260$	−20.1021	−1.24668
$261$	−16.4758	−1.01983
$262$	23.9476	1.47949
$263$	−15.1484	−0.934092	−0.467046	−	0.884233i	$-0.654682\pi$
$263$	−15.1484	−0.934092	−0.467046	+	0.884233i	$0.654682\pi$
$264$	29.3088	1.80383
$265$	−2.43743	−0.149730
$266$	−9.90942	−0.607585
$267$	0.0145392	0.000889785 0
$268$	−28.7562	−1.75656
$269$	3.11677	0.190033	0.0950164	−	0.995476i	$-0.469710\pi$
$269$	3.11677	0.190033	0.0950164	+	0.995476i	$0.469710\pi$
$270$	57.3316	3.48909
$271$	−12.4574	−0.756735	−0.378368	−	0.925655i	$-0.623514\pi$
$271$	−12.4574	−0.756735	−0.378368	+	0.925655i	$0.623514\pi$
$272$	55.4173	3.36017
$273$	2.33482	0.141310
$274$	44.9759	2.71709
$275$	33.0643	1.99385
$276$	−23.6022	−1.42069
$277$	−13.9653	−0.839092	−0.419546	−	0.907734i	$-0.637811\pi$
$277$	−13.9653	−0.839092	−0.419546	+	0.907734i	$0.637811\pi$
$278$	18.6804	1.12038
$279$	−3.16809	−0.189668
$280$	−64.0881	−3.83000
$281$	−13.8823	−0.828150	−0.414075	−	0.910243i	$-0.635895\pi$
$281$	−13.8823	−0.828150	−0.414075	+	0.910243i	$0.635895\pi$
$282$	3.42797	0.204133
$283$	20.4315	1.21453	0.607263	−	0.794501i	$-0.292267\pi$
$283$	20.4315	1.21453	0.607263	+	0.794501i	$0.292267\pi$
$284$	7.39689	0.438924
$285$	−8.78647	−0.520465
$286$	−8.14303	−0.481508
$287$	−20.4040	−1.20441
$288$	23.0017	1.35539
$289$	6.31697	0.371587
$290$	107.653	6.32161
$291$	−11.0849	−0.649806
$292$	−61.5072	−3.59944
$293$	−33.9016	−1.98055	−0.990277	−	0.139113i	$-0.955575\pi$
$293$	−33.9016	−1.98055	−0.990277	+	0.139113i	$0.955575\pi$
$294$	−9.57177	−0.558237
$295$	−34.9179	−2.03300
$296$	84.5951	4.91699
$297$	16.6442	0.965795
$298$	−32.4486	−1.87970
$299$	3.96518	0.229312
$300$	−64.2153	−3.70747
$301$	−19.1862	−1.10587
$302$	−9.74153	−0.560562
$303$	12.8097	0.735900
$304$	−21.5696	−1.23710
$305$	−12.2938	−0.703939
$306$	20.7288	1.18499
$307$	−9.32207	−0.532039	−0.266019	−	0.963968i	$-0.585709\pi$
$307$	−9.32207	−0.532039	−0.266019	+	0.963968i	$0.585709\pi$
$308$	−30.7698	−1.75327
$309$	−2.49725	−0.142064
$310$	20.7003	1.17570
$311$	−27.6274	−1.56661	−0.783304	−	0.621639i	$-0.786467\pi$
$311$	−27.6274	−1.56661	−0.783304	+	0.621639i	$0.786467\pi$
$312$	9.56284	0.541389
$313$	−7.43171	−0.420065	−0.210032	−	0.977694i	$-0.567357\pi$
$313$	−7.43171	−0.420065	−0.210032	+	0.977694i	$0.567357\pi$
$314$	−30.3114	−1.71057
$315$	−12.7399	−0.717814
$316$	30.0759	1.69190
$317$	12.9504	0.727365	0.363682	−	0.931523i	$-0.381519\pi$
$317$	12.9504	0.727365	0.363682	+	0.931523i	$0.381519\pi$
$318$	1.91759	0.107533
$319$	31.2533	1.74985
$320$	−59.0910	−3.30329
$321$	20.3977	1.13849
$322$	20.9063	1.16506
$323$	−9.07549	−0.504974
$324$	−7.80309	−0.433505
$325$	10.7882	0.598421
$326$	11.5657	0.640567
$327$	−19.5971	−1.08372
$328$	−83.5699	−4.61437
$329$	−2.17614	−0.119974
$330$	−38.0686	−2.09561
$331$	8.48585	0.466424	0.233212	−	0.972426i	$-0.425076\pi$
$331$	8.48585	0.466424	0.233212	+	0.972426i	$0.425076\pi$
$332$	41.7965	2.29388
$333$	16.8165	0.921537
$334$	−47.0766	−2.57592
$335$	22.5851	1.23396
$336$	26.7955	1.46182
$337$	9.07019	0.494085	0.247042	−	0.969005i	$-0.420541\pi$
$337$	9.07019	0.494085	0.247042	+	0.969005i	$0.420541\pi$
$338$	−2.65690	−0.144516
$339$	0.514423	0.0279396
$340$	−97.0684	−5.26427
$341$	6.00960	0.325438
$342$	−8.06810	−0.436273
$343$	19.9674	1.07814
$344$	−78.5819	−4.23685
$345$	18.5372	0.998007
$346$	−69.2082	−3.72066
$347$	−10.3017	−0.553022	−0.276511	−	0.961011i	$-0.589178\pi$
$347$	−10.3017	−0.553022	−0.276511	+	0.961011i	$0.589178\pi$
$348$	−60.6980	−3.25376
$349$	12.8012	0.685234	0.342617	−	0.939475i	$-0.388687\pi$
$349$	12.8012	0.685234	0.342617	+	0.939475i	$0.388687\pi$
$350$	56.8804	3.04039
$351$	5.43066	0.289867
$352$	−43.6323	−2.32561
$353$	−3.02271	−0.160882	−0.0804412	−	0.996759i	$-0.525633\pi$
$353$	−3.02271	−0.160882	−0.0804412	+	0.996759i	$0.525633\pi$
$354$	27.4708	1.46006
$355$	−5.80951	−0.308337
$356$	−0.0625176	−0.00331342
$357$	11.2743	0.596699
$358$	−42.0632	−2.22311
$359$	35.4670	1.87188	0.935938	−	0.352163i	$-0.114554\pi$
$359$	35.4670	1.87188	0.935938	+	0.352163i	$0.114554\pi$
$360$	−52.1796	−2.75011
$361$	−15.4676	−0.814085
$362$	−2.56694	−0.134915
$363$	1.89029	0.0992146
$364$	−10.0395	−0.526215
$365$	48.3078	2.52854
$366$	9.67182	0.505554
$367$	−13.3714	−0.697983	−0.348992	−	0.937126i	$-0.613476\pi$
$367$	−13.3714	−0.697983	−0.348992	+	0.937126i	$0.613476\pi$
$368$	45.5063	2.37218
$369$	−16.6127	−0.864821
$370$	−109.879	−5.71233
$371$	−1.21732	−0.0632001
$372$	−11.6714	−0.605136
$373$	16.1585	0.836657	0.418328	−	0.908296i	$-0.362616\pi$
$373$	16.1585	0.836657	0.418328	+	0.908296i	$0.362616\pi$
$374$	−39.3208	−2.03323
$375$	27.0597	1.39736
$376$	−8.91291	−0.459648
$377$	10.1973	0.525188
$378$	28.6330	1.47272
$379$	−5.71821	−0.293725	−0.146862	−	0.989157i	$-0.546917\pi$
$379$	−5.71821	−0.293725	−0.146862	+	0.989157i	$0.546917\pi$
$380$	37.7812	1.93813
$381$	13.0004	0.666031
$382$	−64.0203	−3.27556
$383$	−26.2662	−1.34214	−0.671069	−	0.741394i	$-0.734165\pi$
$383$	−26.2662	−1.34214	−0.671069	+	0.741394i	$0.734165\pi$
$384$	12.9886	0.662824
$385$	24.1666	1.23164
$386$	−56.7618	−2.88910
$387$	−15.6211	−0.794066
$388$	47.6641	2.41978
$389$	30.3037	1.53646	0.768230	−	0.640174i	$-0.221138\pi$
$389$	30.3037	1.53646	0.768230	+	0.640174i	$0.221138\pi$
$390$	−12.4210	−0.628961
$391$	19.1469	0.968301
$392$	24.8872	1.25699
$393$	10.6047	0.534938
$394$	−29.4719	−1.48477
$395$	−23.6216	−1.18853
$396$	−25.0523	−1.25893
$397$	8.20491	0.411793	0.205896	−	0.978574i	$-0.433989\pi$
$397$	8.20491	0.411793	0.205896	+	0.978574i	$0.433989\pi$
$398$	−18.6804	−0.936365
$399$	−4.38820	−0.219685
$400$	123.811	6.19053
$401$	−26.7591	−1.33628	−0.668142	−	0.744034i	$-0.732910\pi$
$401$	−26.7591	−1.33628	−0.668142	+	0.744034i	$0.732910\pi$
$402$	−17.7683	−0.886201
$403$	1.96081	0.0976748
$404$	−55.0809	−2.74038
$405$	6.12855	0.304530
$406$	53.7650	2.66831
$407$	−31.8995	−1.58120
$408$	46.1767	2.28609
$409$	−32.1955	−1.59197	−0.795983	−	0.605320i	$-0.793045\pi$
$409$	−32.1955	−1.59197	−0.795983	+	0.605320i	$0.793045\pi$
$410$	108.547	5.36077
$411$	19.9167	0.982420
$412$	10.7380	0.529024
$413$	−17.4390	−0.858116
$414$	17.0216	0.836566
$415$	−32.8270	−1.61141
$416$	−14.2363	−0.697993
$417$	8.27229	0.405096
$418$	15.3045	0.748569
$419$	−20.5499	−1.00393	−0.501963	−	0.864889i	$-0.667389\pi$
$419$	−20.5499	−1.00393	−0.501963	+	0.864889i	$0.667389\pi$
$420$	−46.9348	−2.29018
$421$	−5.75164	−0.280318	−0.140159	−	0.990129i	$-0.544761\pi$
$421$	−5.75164	−0.280318	−0.140159	+	0.990129i	$0.544761\pi$
$422$	−16.8333	−0.819430
$423$	−1.77178	−0.0861468
$424$	−4.98584	−0.242134
$425$	52.0937	2.52691
$426$	4.57050	0.221441
$427$	−6.13984	−0.297128
$428$	−87.7086	−4.23956
$429$	−3.60599	−0.174099
$430$	102.068	4.92218
$431$	26.1633	1.26024	0.630122	−	0.776496i	$-0.283005\pi$
$431$	26.1633	1.26024	0.630122	+	0.776496i	$0.283005\pi$
$432$	62.3249	2.99861
$433$	−0.476113	−0.0228805	−0.0114403	−	0.999935i	$-0.503642\pi$
$433$	−0.476113	−0.0228805	−0.0114403	+	0.999935i	$0.503642\pi$
$434$	10.3383	0.496254
$435$	47.6722	2.28571
$436$	84.2661	4.03562
$437$	−7.45241	−0.356497
$438$	−38.0050	−1.81595
$439$	15.3683	0.733489	0.366744	−	0.930322i	$-0.380472\pi$
$439$	15.3683	0.733489	0.366744	+	0.930322i	$0.380472\pi$
$440$	98.9805	4.71871
$441$	4.94726	0.235584
$442$	−12.8296	−0.610240
$443$	−6.57632	−0.312451	−0.156225	−	0.987721i	$-0.549933\pi$
$443$	−6.57632	−0.312451	−0.156225	+	0.987721i	$0.549933\pi$
$444$	61.9530	2.94016
$445$	0.0491013	0.00232762
$446$	46.1298	2.18431
$447$	−14.3693	−0.679643
$448$	−29.5117	−1.39430
$449$	−14.9077	−0.703537	−0.351768	−	0.936087i	$-0.614420\pi$
$449$	−14.9077	−0.703537	−0.351768	+	0.936087i	$0.614420\pi$
$450$	46.3112	2.18313
$451$	31.5129	1.48388
$452$	−2.21198	−0.104043
$453$	−4.31386	−0.202683
$454$	1.26447	0.0593444
$455$	7.88506	0.369657
$456$	−17.9730	−0.841663
$457$	−15.8093	−0.739530	−0.369765	−	0.929125i	$-0.620562\pi$
$457$	−15.8093	−0.739530	−0.369765	+	0.929125i	$0.620562\pi$
$458$	64.1851	2.99917
$459$	26.2234	1.22400
$460$	−79.7084	−3.71643
$461$	−12.1802	−0.567288	−0.283644	−	0.958930i	$-0.591543\pi$
$461$	−12.1802	−0.567288	−0.283644	+	0.958930i	$0.591543\pi$
$462$	−19.0125	−0.884542
$463$	−1.00000	−0.0464739
$463$	−1.00000	−0.0464739
$464$	117.029	5.43294
$465$	9.16675	0.425098
$466$	19.2846	0.893342
$467$	12.0447	0.557362	0.278681	−	0.960384i	$-0.410103\pi$
$467$	12.0447	0.557362	0.278681	+	0.960384i	$0.410103\pi$
$468$	−8.17405	−0.377846
$469$	11.2796	0.520845
$470$	11.5768	0.533998
$471$	−13.4229	−0.618493
$472$	−71.4257	−3.28764
$473$	29.6320	1.36248
$474$	18.5837	0.853580
$475$	−20.2760	−0.930327
$476$	−48.4786	−2.22201
$477$	−0.991124	−0.0453805
$478$	−48.5599	−2.22108
$479$	27.4121	1.25249	0.626245	−	0.779626i	$-0.284591\pi$
$479$	27.4121	1.25249	0.626245	+	0.779626i	$0.284591\pi$
$480$	−66.5546	−3.03779
$481$	−10.4081	−0.474570
$482$	−65.5019	−2.98353
$483$	9.25797	0.421252
$484$	−8.12812	−0.369460
$485$	−37.4354	−1.69985
$486$	38.4647	1.74479
$487$	25.6063	1.16033	0.580166	−	0.814498i	$-0.302988\pi$
$487$	25.6063	1.16033	0.580166	+	0.814498i	$0.302988\pi$
$488$	−25.1473	−1.13836
$489$	5.12168	0.231610
$490$	−32.3254	−1.46031
$491$	27.1838	1.22679	0.613393	−	0.789778i	$-0.289804\pi$
$491$	27.1838	1.22679	0.613393	+	0.789778i	$0.289804\pi$
$492$	−61.2022	−2.75921
$493$	49.2404	2.21767
$494$	4.99355	0.224670
$495$	19.6761	0.884375
$496$	22.5032	1.01042
$497$	−2.90143	−0.130147
$498$	25.8258	1.15728
$499$	24.7709	1.10890	0.554449	−	0.832218i	$-0.312929\pi$
$499$	24.7709	1.10890	0.554449	+	0.832218i	$0.312929\pi$
$500$	−116.355	−5.20355
$501$	−20.8470	−0.931376
$502$	40.1008	1.78979
$503$	2.17207	0.0968480	0.0484240	−	0.998827i	$-0.484580\pi$
$503$	2.17207	0.0968480	0.0484240	+	0.998827i	$0.484580\pi$
$504$	−26.0599	−1.16080
$505$	43.2606	1.92507
$506$	−32.2886	−1.43540
$507$	−1.17656	−0.0522529
$508$	−55.9008	−2.48020
$509$	20.5415	0.910485	0.455243	−	0.890367i	$-0.349552\pi$
$509$	20.5415	0.910485	0.455243	+	0.890367i	$0.349552\pi$
$510$	−59.9780	−2.65587
$511$	24.1262	1.06728
$512$	23.1741	1.02416
$513$	−10.2067	−0.450638
$514$	26.2902	1.15961
$515$	−8.43363	−0.371630
$516$	−57.5492	−2.53346
$517$	3.36092	0.147813
$518$	−54.8766	−2.41114
$519$	−30.6476	−1.34528
$520$	32.2953	1.41624
$521$	−32.8503	−1.43920	−0.719598	−	0.694391i	$-0.755674\pi$
$521$	−32.8503	−1.43920	−0.719598	+	0.694391i	$0.755674\pi$
$522$	43.7746	1.91596
$523$	36.4545	1.59404	0.797022	−	0.603950i	$-0.206407\pi$
$523$	36.4545	1.59404	0.797022	+	0.603950i	$0.206407\pi$
$524$	−45.5996	−1.99203
$525$	25.1885	1.09932
$526$	40.2479	1.75489
$527$	9.46828	0.412445
$528$	−41.3842	−1.80101
$529$	−7.27736	−0.316407
$530$	6.47601	0.281300
$531$	−14.1986	−0.616165
$532$	18.8690	0.818073
$533$	10.2820	0.445362
$534$	−0.0386293	−0.00167165
$535$	68.8864	2.97822
$536$	46.1985	1.99547
$537$	−18.6269	−0.803812
$538$	−8.28095	−0.357017
$539$	−9.38455	−0.404221
$540$	−109.168	−4.69783
$541$	45.1577	1.94148	0.970740	−	0.240132i	$-0.0771906\pi$
$541$	45.1577	1.94148	0.970740	+	0.240132i	$0.0771906\pi$
$542$	33.0982	1.42169
$543$	−1.13672	−0.0487814
$544$	−68.7438	−2.94737
$545$	−66.1826	−2.83495
$546$	−6.20338	−0.265480
$547$	−41.7375	−1.78456	−0.892282	−	0.451478i	$-0.850897\pi$
$547$	−41.7375	−1.78456	−0.892282	+	0.451478i	$0.850897\pi$
$548$	−85.6405	−3.65838
$549$	−4.99897	−0.213351
$550$	−87.8486	−3.74588
$551$	−19.1654	−0.816475
$552$	37.9184	1.61391
$553$	−11.7973	−0.501672
$554$	37.1044	1.57641
$555$	−48.6579	−2.06541
$556$	−35.5702	−1.50851
$557$	28.1938	1.19461	0.597306	−	0.802014i	$-0.296238\pi$
$557$	28.1938	1.19461	0.597306	+	0.802014i	$0.296238\pi$
$558$	8.41730	0.356333
$559$	9.66829	0.408925
$560$	90.4928	3.82402
$561$	−17.4125	−0.735156
$562$	36.8840	1.55586
$563$	10.5047	0.442722	0.221361	−	0.975192i	$-0.428950\pi$
$563$	10.5047	0.442722	0.221361	+	0.975192i	$0.428950\pi$
$564$	−6.52735	−0.274851
$565$	1.73729	0.0730884
$566$	−54.2845	−2.28175
$567$	3.06077	0.128540
$568$	−11.8835	−0.498623
$569$	−34.5144	−1.44692	−0.723459	−	0.690367i	$-0.757449\pi$
$569$	−34.5144	−1.44692	−0.723459	+	0.690367i	$0.757449\pi$
$570$	23.3448	0.977805
$571$	−17.5453	−0.734247	−0.367123	−	0.930172i	$-0.619657\pi$
$571$	−17.5453	−0.734247	−0.367123	+	0.930172i	$0.619657\pi$
$572$	15.5055	0.648318
$573$	−28.3502	−1.18435
$574$	54.2115	2.26274
$575$	42.7771	1.78393
$576$	−24.0280	−1.00117
$577$	−15.2246	−0.633810	−0.316905	−	0.948457i	$-0.602644\pi$
$577$	−15.2246	−0.633810	−0.316905	+	0.948457i	$0.602644\pi$
$578$	−16.7836	−0.698105
$579$	−25.1359	−1.04461
$580$	−204.987	−8.51163
$581$	−16.3947	−0.680166
$582$	29.4514	1.22080
$583$	1.88008	0.0778650
$584$	98.8151	4.08900
$585$	6.41990	0.265430
$586$	90.0732	3.72089
$587$	−10.8413	−0.447468	−0.223734	−	0.974650i	$-0.571825\pi$
$587$	−10.8413	−0.447468	−0.223734	+	0.974650i	$0.571825\pi$
$588$	18.2260	0.751629
$589$	−3.68527	−0.151849
$590$	92.7735	3.81942
$591$	−13.0511	−0.536850
$592$	−119.449	−4.90931
$593$	8.07669	0.331670	0.165835	−	0.986154i	$-0.446968\pi$
$593$	8.07669	0.331670	0.165835	+	0.986154i	$0.446968\pi$
$594$	−44.2220	−1.81445
$595$	38.0751	1.56093
$596$	61.7868	2.53089
$597$	−8.27229	−0.338562
$598$	−10.5351	−0.430812
$599$	−8.26183	−0.337569	−0.168785	−	0.985653i	$-0.553984\pi$
$599$	−8.26183	−0.337569	−0.168785	+	0.985653i	$0.553984\pi$
$600$	103.166	4.21172
$601$	7.32359	0.298736	0.149368	−	0.988782i	$-0.452276\pi$
$601$	7.32359	0.298736	0.149368	+	0.988782i	$0.452276\pi$
$602$	50.9758	2.07762
$603$	9.18371	0.373989
$604$	18.5493	0.754760
$605$	6.38382	0.259539
$606$	−34.0342	−1.38255
$607$	25.9269	1.05234	0.526170	−	0.850380i	$-0.323628\pi$
$607$	25.9269	1.05234	0.526170	+	0.850380i	$0.323628\pi$
$608$	26.7566	1.08512
$609$	23.8088	0.964783
$610$	32.6633	1.32250
$611$	1.09660	0.0443636
$612$	−39.4706	−1.59550
$613$	−5.12832	−0.207131	−0.103565	−	0.994623i	$-0.533025\pi$
$613$	−5.12832	−0.207131	−0.103565	+	0.994623i	$0.533025\pi$
$614$	24.7678	0.999548
$615$	48.0682	1.93830
$616$	49.4336	1.99174
$617$	22.5852	0.909246	0.454623	−	0.890684i	$-0.349774\pi$
$617$	22.5852	0.909246	0.454623	+	0.890684i	$0.349774\pi$
$618$	6.63496	0.266897
$619$	44.6843	1.79601	0.898007	−	0.439982i	$-0.145015\pi$
$619$	44.6843	1.79601	0.898007	+	0.439982i	$0.145015\pi$
$620$	−39.4164	−1.58300
$621$	21.5335	0.864110
$622$	73.4034	2.94321
$623$	0.0245225	0.000982475 0
$624$	−13.5028	−0.540544
$625$	37.4442	1.49777
$626$	19.7453	0.789181
$627$	6.77733	0.270661
$628$	57.7173	2.30317
$629$	−50.2584	−2.00393
$630$	33.8487	1.34857
$631$	1.04529	0.0416123	0.0208062	−	0.999784i	$-0.493377\pi$
$631$	1.04529	0.0416123	0.0208062	+	0.999784i	$0.493377\pi$
$632$	−48.3188	−1.92202
$633$	−7.45430	−0.296282
$634$	−34.4078	−1.36651
$635$	43.9045	1.74230
$636$	−3.65137	−0.144786
$637$	−3.06198	−0.121320
$638$	−83.0369	−3.28746
$639$	−2.36230	−0.0934513
$640$	43.8648	1.73391
$641$	24.0903	0.951512	0.475756	−	0.879577i	$-0.342175\pi$
$641$	24.0903	0.951512	0.475756	+	0.879577i	$0.342175\pi$
$642$	−54.1947	−2.13889
$643$	−11.5578	−0.455797	−0.227899	−	0.973685i	$-0.573185\pi$
$643$	−11.5578	−0.455797	−0.227899	+	0.973685i	$0.573185\pi$
$644$	−39.8086	−1.56868
$645$	45.1992	1.77972
$646$	24.1127	0.948700
$647$	39.6724	1.55968	0.779841	−	0.625978i	$-0.215300\pi$
$647$	39.6724	1.55968	0.779841	+	0.625978i	$0.215300\pi$
$648$	12.5361	0.492466
$649$	26.9335	1.05723
$650$	−28.6632	−1.12426
$651$	4.57813	0.179431
$652$	−22.0228	−0.862481
$653$	7.02959	0.275089	0.137545	−	0.990496i	$-0.456079\pi$
$653$	7.02959	0.275089	0.137545	+	0.990496i	$0.456079\pi$
$654$	52.0676	2.03600
$655$	35.8139	1.39937
$656$	118.001	4.60717
$657$	19.6432	0.766355
$658$	5.78178	0.225397
$659$	9.20097	0.358419	0.179210	−	0.983811i	$-0.442646\pi$
$659$	9.20097	0.358419	0.179210	+	0.983811i	$0.442646\pi$
$660$	72.4881	2.82160
$661$	40.8089	1.58728	0.793642	−	0.608385i	$-0.208182\pi$
$661$	40.8089	1.58728	0.793642	+	0.608385i	$0.208182\pi$
$662$	−22.5461	−0.876277
$663$	−5.68133	−0.220645
$664$	−67.1486	−2.60587
$665$	−14.8197	−0.574683
$666$	−44.6797	−1.73130
$667$	40.4341	1.56561
$668$	89.6407	3.46830
$669$	20.4277	0.789781
$670$	−60.0064	−2.31825
$671$	9.48264	0.366073
$672$	−33.2392	−1.28223
$673$	−40.7545	−1.57097	−0.785486	−	0.618880i	$-0.787587\pi$
$673$	−40.7545	−1.57097	−0.785486	+	0.618880i	$0.787587\pi$
$674$	−24.0986	−0.928244
$675$	58.5870	2.25501
$676$	5.05912	0.194582
$677$	25.4388	0.977693	0.488847	−	0.872370i	$-0.337418\pi$
$677$	25.4388	0.977693	0.488847	+	0.872370i	$0.337418\pi$
$678$	−1.36677	−0.0524906
$679$	−18.6963	−0.717497
$680$	155.946	5.98026
$681$	0.559946	0.0214572
$682$	−15.9669	−0.611405
$683$	−43.6830	−1.67148	−0.835742	−	0.549123i	$-0.814962\pi$
$683$	−43.6830	−1.67148	−0.835742	+	0.549123i	$0.814962\pi$
$684$	15.3628	0.587413
$685$	67.2621	2.56995
$686$	−53.0515	−2.02552
$687$	28.4232	1.08441
$688$	110.958	4.23024
$689$	0.613431	0.0233699
$690$	−49.2514	−1.87497
$691$	−21.0404	−0.800416	−0.400208	−	0.916424i	$-0.631062\pi$
$691$	−21.0404	−0.800416	−0.400208	+	0.916424i	$0.631062\pi$
$692$	131.782	5.00962
$693$	9.82679	0.373289
$694$	27.3705	1.03897
$695$	27.9369	1.05971
$696$	97.5151	3.69630
$697$	49.6493	1.88060
$698$	−34.0116	−1.28736
$699$	8.53984	0.323006
$700$	−108.309	−4.09368
$701$	9.87176	0.372851	0.186426	−	0.982469i	$-0.440310\pi$
$701$	9.87176	0.372851	0.186426	+	0.982469i	$0.440310\pi$
$702$	−14.4287	−0.544577
$703$	19.5617	0.737783
$704$	45.5791	1.71783
$705$	5.12658	0.193078
$706$	8.03103	0.302252
$707$	21.6055	0.812559
$708$	−52.3084	−1.96587
$709$	−37.2705	−1.39972	−0.699862	−	0.714278i	$-0.746755\pi$
$709$	−37.2705	−1.39972	−0.699862	+	0.714278i	$0.746755\pi$
$710$	15.4353	0.579277
$711$	−9.60518	−0.360223
$712$	0.100438	0.00376408
$713$	7.77495	0.291174
$714$	−29.9547	−1.12103
$715$	−12.1780	−0.455433
$716$	80.0945	2.99327
$717$	−21.5039	−0.803077
$718$	−94.2323	−3.51672
$719$	−34.9981	−1.30521	−0.652604	−	0.757699i	$-0.726324\pi$
$719$	−34.9981	−1.30521	−0.652604	+	0.757699i	$0.726324\pi$
$720$	73.6779	2.74581
$721$	−4.21199	−0.156863
$722$	41.0959	1.52943
$723$	−29.0063	−1.07876
$724$	4.88782	0.181654
$725$	110.010	4.08568
$726$	−5.02232	−0.186396
$727$	17.3768	0.644468	0.322234	−	0.946660i	$-0.395566\pi$
$727$	17.3768	0.644468	0.322234	+	0.946660i	$0.395566\pi$
$728$	16.1291	0.597786
$729$	21.6605	0.802241
$730$	−128.349	−4.75041
$731$	46.6859	1.72674
$732$	−18.4165	−0.680695
$733$	−30.5994	−1.13021	−0.565107	−	0.825017i	$-0.691165\pi$
$733$	−30.5994	−1.13021	−0.565107	+	0.825017i	$0.691165\pi$
$734$	35.5266	1.31131
$735$	−14.3147	−0.528007
$736$	−56.4495	−2.08076
$737$	−17.4207	−0.641701
$738$	44.1382	1.62475
$739$	28.2850	1.04048	0.520241	−	0.854020i	$-0.325842\pi$
$739$	28.2850	1.04048	0.520241	+	0.854020i	$0.325842\pi$
$740$	209.225	7.69128
$741$	2.21130	0.0812342
$742$	3.23430	0.118735
$743$	−23.3959	−0.858311	−0.429155	−	0.903231i	$-0.641189\pi$
$743$	−23.3959	−0.858311	−0.429155	+	0.903231i	$0.641189\pi$
$744$	18.7509	0.687441
$745$	−48.5274	−1.77790
$746$	−42.9316	−1.57184
$747$	−13.3483	−0.488389
$748$	74.8725	2.73761
$749$	34.4037	1.25709
$750$	−71.8951	−2.62524
$751$	49.0605	1.79024	0.895122	−	0.445822i	$-0.147088\pi$
$751$	49.0605	1.79024	0.895122	+	0.445822i	$0.147088\pi$
$752$	12.5851	0.458931
$753$	17.7579	0.647134
$754$	−27.0932	−0.986677
$755$	−14.5686	−0.530206
$756$	−54.5213	−1.98292
$757$	−11.0993	−0.403412	−0.201706	−	0.979446i	$-0.564649\pi$
$757$	−11.0993	−0.403412	−0.201706	+	0.979446i	$0.564649\pi$
$758$	15.1927	0.551825
$759$	−14.2984	−0.518999
$760$	−60.6978	−2.20174
$761$	−6.43818	−0.233384	−0.116692	−	0.993168i	$-0.537229\pi$
$761$	−6.43818	−0.233384	−0.116692	+	0.993168i	$0.537229\pi$
$762$	−34.5408	−1.25128
$763$	−33.0534	−1.19661
$764$	121.904	4.41033
$765$	31.0002	1.12081
$766$	69.7866	2.52149
$767$	8.78784	0.317310
$768$	0.484927	0.0174983
$769$	13.2246	0.476892	0.238446	−	0.971156i	$-0.423362\pi$
$769$	13.2246	0.476892	0.238446	+	0.971156i	$0.423362\pi$
$770$	−64.2083	−2.31391
$771$	11.6421	0.419281
$772$	108.083	3.88998
$773$	−17.4756	−0.628553	−0.314276	−	0.949332i	$-0.601762\pi$
$773$	−17.4756	−0.628553	−0.314276	+	0.949332i	$0.601762\pi$
$774$	41.5038	1.49182
$775$	21.1536	0.759859
$776$	−76.5753	−2.74889
$777$	−24.3011	−0.871797
$778$	−80.5140	−2.88657
$779$	−19.3246	−0.692376
$780$	23.6513	0.846854
$781$	4.48110	0.160346
$782$	−50.8715	−1.81916
$783$	55.3780	1.97905
$784$	−35.1408	−1.25503
$785$	−45.3312	−1.61794
$786$	−28.1757	−1.00500
$787$	−17.5036	−0.623936	−0.311968	−	0.950093i	$-0.600988\pi$
$787$	−17.5036	−0.623936	−0.311968	+	0.950093i	$0.600988\pi$
$788$	56.1187	1.99915
$789$	17.8230	0.634517
$790$	62.7603	2.23291
$791$	0.867651	0.0308501
$792$	40.2481	1.43015
$793$	3.09399	0.109871
$794$	−21.7996	−0.773640
$795$	2.86778	0.101710
$796$	35.5702	1.26075
$797$	22.3330	0.791075	0.395538	−	0.918450i	$-0.370558\pi$
$797$	22.3330	0.791075	0.395538	+	0.918450i	$0.370558\pi$
$798$	11.6590	0.412725
$799$	5.29521	0.187331
$800$	−153.584	−5.43002
$801$	0.0199659	0.000705460 0
$802$	71.0962	2.51050
$803$	−37.2616	−1.31493
$804$	33.8334	1.19321
$805$	31.2657	1.10197
$806$	−5.20967	−0.183503
$807$	−3.66707	−0.129087
$808$	88.4909	3.11310
$809$	25.0649	0.881235	0.440618	−	0.897695i	$-0.354759\pi$
$809$	25.0649	0.881235	0.440618	+	0.897695i	$0.354759\pi$
$810$	−16.2829	−0.572124
$811$	16.3762	0.575046	0.287523	−	0.957774i	$-0.407168\pi$
$811$	16.3762	0.575046	0.287523	+	0.957774i	$0.407168\pi$
$812$	−102.376	−3.59270
$813$	14.6569	0.514041
$814$	84.7537	2.97062
$815$	17.2967	0.605878
$816$	−65.2018	−2.28252
$817$	−18.1712	−0.635730
$818$	85.5403	2.99085
$819$	3.20628	0.112036
$820$	−206.690	−7.21792
$821$	12.2886	0.428875	0.214437	−	0.976738i	$-0.431208\pi$
$821$	12.2886	0.428875	0.214437	+	0.976738i	$0.431208\pi$
$822$	−52.9168	−1.84569
$823$	−53.6582	−1.87041	−0.935203	−	0.354111i	$-0.884783\pi$
$823$	−53.6582	−1.87041	−0.935203	+	0.354111i	$0.884783\pi$
$824$	−17.2513	−0.600976
$825$	−38.9022	−1.35440
$826$	46.3336	1.61215
$827$	−38.3316	−1.33292	−0.666461	−	0.745540i	$-0.732192\pi$
$827$	−38.3316	−1.33292	−0.666461	+	0.745540i	$0.732192\pi$
$828$	−32.4116	−1.12638
$829$	−38.0853	−1.32276	−0.661378	−	0.750053i	$-0.730028\pi$
$829$	−38.0853	−1.32276	−0.661378	+	0.750053i	$0.730028\pi$
$830$	87.2180	3.02738
$831$	16.4310	0.569985
$832$	14.8715	0.515577
$833$	−14.7856	−0.512291
$834$	−21.9787	−0.761059
$835$	−70.4038	−2.43642
$836$	−29.1420	−1.00790
$837$	10.6485	0.368065
$838$	54.5989	1.88609
$839$	25.7616	0.889391	0.444695	−	0.895682i	$-0.353312\pi$
$839$	25.7616	0.889391	0.444695	+	0.895682i	$0.353312\pi$
$840$	75.4036	2.60167
$841$	74.9849	2.58568
$842$	15.2815	0.526637
$843$	16.3334	0.562552
$844$	32.0530	1.10331
$845$	−3.97344	−0.136690
$846$	4.70744	0.161845
$847$	3.18826	0.109550
$848$	7.04004	0.241756
$849$	−24.0389	−0.825013
$850$	−138.408	−4.74735
$851$	−41.2701	−1.41472
$852$	−8.70288	−0.298156
$853$	−39.4292	−1.35003	−0.675015	−	0.737804i	$-0.735863\pi$
$853$	−39.4292	−1.35003	−0.675015	+	0.737804i	$0.735863\pi$
$854$	16.3130	0.558218
$855$	−12.0660	−0.412647
$856$	140.909	4.81618
$857$	24.0158	0.820363	0.410182	−	0.912004i	$-0.365465\pi$
$857$	24.0158	0.820363	0.410182	+	0.912004i	$0.365465\pi$
$858$	9.58077	0.327082
$859$	19.7622	0.674277	0.337139	−	0.941455i	$-0.390541\pi$
$859$	19.7622	0.674277	0.337139	+	0.941455i	$0.390541\pi$
$860$	−194.353	−6.62739
$861$	24.0066	0.818142
$862$	−69.5134	−2.36764
$863$	−27.9906	−0.952812	−0.476406	−	0.879225i	$-0.658061\pi$
$863$	−27.9906	−0.952812	−0.476406	+	0.879225i	$0.658061\pi$
$864$	−77.3126	−2.63023
$865$	−103.502	−3.51917
$866$	1.26499	0.0429859
$867$	−7.43230	−0.252414
$868$	−19.6856	−0.668174
$869$	18.2203	0.618080
$870$	−126.660	−4.29419
$871$	−5.68402	−0.192596
$872$	−135.379	−4.58450
$873$	−15.2222	−0.515194
$874$	19.8003	0.669755
$875$	45.6403	1.54292
$876$	72.3670	2.44505
$877$	−24.4648	−0.826118	−0.413059	−	0.910704i	$-0.635540\pi$
$877$	−24.4648	−0.826118	−0.413059	+	0.910704i	$0.635540\pi$
$878$	−40.8320	−1.37801
$879$	39.8873	1.34537
$880$	−139.761	−4.71134
$881$	10.8885	0.366841	0.183421	−	0.983035i	$-0.441283\pi$
$881$	10.8885	0.366841	0.183421	+	0.983035i	$0.441283\pi$
$882$	−13.1444	−0.442595
$883$	58.4943	1.96849	0.984245	−	0.176813i	$-0.0565787\pi$
$883$	58.4943	1.96849	0.984245	+	0.176813i	$0.0565787\pi$
$884$	24.4293	0.821647
$885$	41.0830	1.38099
$886$	17.4726	0.587005
$887$	46.6267	1.56557	0.782786	−	0.622290i	$-0.213798\pi$
$887$	46.6267	1.56557	0.782786	+	0.622290i	$0.213798\pi$
$888$	−99.5313	−3.34005
$889$	21.9271	0.735412
$890$	−0.130457	−0.00437294
$891$	−4.72718	−0.158367
$892$	−87.8377	−2.94102
$893$	−2.06101	−0.0689692
$894$	38.1777	1.27685
$895$	−62.9062	−2.10272
$896$	21.9073	0.731871
$897$	−4.66527	−0.155769
$898$	39.6082	1.32174
$899$	19.9949	0.666869
$900$	−88.1833	−2.93944
$901$	2.96212	0.0986824
$902$	−83.7266	−2.78779
$903$	22.5737	0.751206
$904$	3.55368	0.118194
$905$	−3.83889	−0.127609
$906$	11.4615	0.380783
$907$	−26.7541	−0.888354	−0.444177	−	0.895939i	$-0.646504\pi$
$907$	−26.7541	−0.888354	−0.444177	+	0.895939i	$0.646504\pi$
$908$	−2.40773	−0.0799033
$909$	17.5909	0.583453
$910$	−20.9498	−0.694480
$911$	−46.4151	−1.53780	−0.768900	−	0.639369i	$-0.779196\pi$
$911$	−46.4151	−1.53780	−0.768900	+	0.639369i	$0.779196\pi$
$912$	25.3780	0.840349
$913$	25.3207	0.837992
$914$	42.0039	1.38936
$915$	14.4644	0.478177
$916$	−122.218	−4.03819
$917$	17.8865	0.590663
$918$	−69.6729	−2.29955
$919$	23.2605	0.767293	0.383646	−	0.923480i	$-0.374668\pi$
$919$	23.2605	0.767293	0.383646	+	0.923480i	$0.374668\pi$
$920$	128.056	4.22190
$921$	10.9680	0.361407
$922$	32.3615	1.06577
$923$	1.46209	0.0481252
$924$	36.2026	1.19098
$925$	−112.285	−3.69191
$926$	2.65690	0.0873112
$927$	−3.42934	−0.112634
$928$	−145.172	−4.76550
$929$	−2.51259	−0.0824355	−0.0412178	−	0.999150i	$-0.513124\pi$
$929$	−2.51259	−0.0824355	−0.0412178	+	0.999150i	$0.513124\pi$
$930$	−24.3552	−0.798637
$931$	5.75488	0.188609
$932$	−36.7207	−1.20283
$933$	32.5053	1.06418
$934$	−32.0016	−1.04712
$935$	−58.8049	−1.92312
$936$	13.1321	0.429237
$937$	−21.5271	−0.703259	−0.351630	−	0.936139i	$-0.614372\pi$
$937$	−21.5271	−0.703259	−0.351630	+	0.936139i	$0.614372\pi$
$938$	−29.9688	−0.978517
$939$	8.74385	0.285345
$940$	−22.0439	−0.718993
$941$	−8.25916	−0.269241	−0.134620	−	0.990897i	$-0.542982\pi$
$941$	−8.25916	−0.269241	−0.134620	+	0.990897i	$0.542982\pi$
$942$	35.6632	1.16197
$943$	40.7699	1.32765
$944$	100.854	3.28250
$945$	42.8211	1.39297
$946$	−78.7293	−2.55971
$947$	−10.2538	−0.333203	−0.166602	−	0.986024i	$-0.553279\pi$
$947$	−10.2538	−0.333203	−0.166602	+	0.986024i	$0.553279\pi$
$948$	−35.3861	−1.14929
$949$	−12.1577	−0.394655
$950$	53.8714	1.74782
$951$	−15.2369	−0.494090
$952$	77.8839	2.52423
$953$	27.0557	0.876420	0.438210	−	0.898873i	$-0.355613\pi$
$953$	27.0557	0.876420	0.438210	+	0.898873i	$0.355613\pi$
$954$	2.63332	0.0852569
$955$	−95.7433	−3.09818
$956$	92.4651	2.99054
$957$	−36.7714	−1.18865
$958$	−72.8312	−2.35307
$959$	33.5925	1.08476
$960$	69.5241	2.24388
$961$	−27.1552	−0.875975
$962$	27.6534	0.891580
$963$	28.0110	0.902643
$964$	124.725	4.01713
$965$	−84.8881	−2.73264
$966$	−24.5975	−0.791412
$967$	−13.6939	−0.440367	−0.220183	−	0.975459i	$-0.570666\pi$
$967$	−13.6939	−0.440367	−0.220183	+	0.975459i	$0.570666\pi$
$968$	13.0583	0.419710
$969$	10.6779	0.343022
$970$	99.4621	3.19354
$971$	−14.4397	−0.463394	−0.231697	−	0.972788i	$-0.574428\pi$
$971$	−14.4397	−0.463394	−0.231697	+	0.972788i	$0.574428\pi$
$972$	−73.2423	−2.34925
$973$	13.9524	0.447295
$974$	−68.0334	−2.17993
$975$	−12.6930	−0.406500
$976$	35.5081	1.13659
$977$	28.1840	0.901685	0.450842	−	0.892604i	$-0.351124\pi$
$977$	28.1840	0.901685	0.450842	+	0.892604i	$0.351124\pi$
$978$	−13.6078	−0.435129
$979$	−0.0378737	−0.00121045
$980$	61.5523	1.96622
$981$	−26.9116	−0.859222
$982$	−72.2246	−2.30478
$983$	24.5555	0.783197	0.391599	−	0.920136i	$-0.371922\pi$
$983$	24.5555	0.783197	0.391599	+	0.920136i	$0.371922\pi$
$984$	98.3250	3.13449
$985$	−44.0756	−1.40437
$986$	−130.827	−4.16637
$987$	2.56036	0.0814970
$988$	−9.50844	−0.302504
$989$	38.3365	1.21903
$990$	−52.2775	−1.66149
$991$	−11.6704	−0.370724	−0.185362	−	0.982670i	$-0.559346\pi$
$991$	−11.6704	−0.370724	−0.185362	+	0.982670i	$0.559346\pi$
$992$	−27.9147	−0.886292
$993$	−9.98411	−0.316836
$994$	7.70882	0.244509
$995$	−27.9369	−0.885658
$996$	−49.1761	−1.55820
$997$	−0.0786553	−0.00249104	−0.00124552	−	0.999999i	$-0.500396\pi$
$997$	−0.0786553	−0.00249104	−0.00124552	+	0.999999i	$0.500396\pi$
$998$	−65.8138	−2.08330
$999$	−56.5230	−1.78831

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.e.1.4	✓	130

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.e.1.4	✓	130	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65690 q^{2} -1.17656 q^{3} +5.05912 q^{4} -3.97344 q^{5} +3.12601 q^{6} -1.98444 q^{7} -8.12779 q^{8} -1.61571 q^{9} +O(q^{10})\)	\(q-2.65690 q^{2} -1.17656 q^{3} +5.05912 q^{4} -3.97344 q^{5} +3.12601 q^{6} -1.98444 q^{7} -8.12779 q^{8} -1.61571 q^{9} +10.5570 q^{10} +3.06486 q^{11} -5.95237 q^{12} +1.00000 q^{13} +5.27247 q^{14} +4.67499 q^{15} +11.4765 q^{16} +4.82877 q^{17} +4.29277 q^{18} -1.87946 q^{19} -20.1021 q^{20} +2.33482 q^{21} -8.14303 q^{22} +3.96518 q^{23} +9.56284 q^{24} +10.7882 q^{25} -2.65690 q^{26} +5.43066 q^{27} -10.0395 q^{28} +10.1973 q^{29} -12.4210 q^{30} +1.96081 q^{31} -14.2363 q^{32} -3.60599 q^{33} -12.8296 q^{34} +7.88506 q^{35} -8.17405 q^{36} -10.4081 q^{37} +4.99355 q^{38} -1.17656 q^{39} +32.2953 q^{40} +10.2820 q^{41} -6.20338 q^{42} +9.66829 q^{43} +15.5055 q^{44} +6.41990 q^{45} -10.5351 q^{46} +1.09660 q^{47} -13.5028 q^{48} -3.06198 q^{49} -28.6632 q^{50} -5.68133 q^{51} +5.05912 q^{52} +0.613431 q^{53} -14.4287 q^{54} -12.1780 q^{55} +16.1291 q^{56} +2.21130 q^{57} -27.0932 q^{58} +8.78784 q^{59} +23.6513 q^{60} +3.09399 q^{61} -5.20967 q^{62} +3.20628 q^{63} +14.8715 q^{64} -3.97344 q^{65} +9.58077 q^{66} -5.68402 q^{67} +24.4293 q^{68} -4.66527 q^{69} -20.9498 q^{70} +1.46209 q^{71} +13.1321 q^{72} -12.1577 q^{73} +27.6534 q^{74} -12.6930 q^{75} -9.50844 q^{76} -6.08204 q^{77} +3.12601 q^{78} +5.94489 q^{79} -45.6011 q^{80} -1.54238 q^{81} -27.3182 q^{82} +8.26160 q^{83} +11.8121 q^{84} -19.1868 q^{85} -25.6877 q^{86} -11.9977 q^{87} -24.9106 q^{88} -0.0123574 q^{89} -17.0570 q^{90} -1.98444 q^{91} +20.0603 q^{92} -2.30701 q^{93} -2.91355 q^{94} +7.46793 q^{95} +16.7499 q^{96} +9.42141 q^{97} +8.13539 q^{98} -4.95191 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9}+O(q^{10}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9	\( 130 q + 10 q^{2} + 11 q^{3} + 146 q^{4} + 40 q^{5} + 4 q^{6} + 8 q^{7} + 24 q^{8} + 181 q^{9} + 5 q^{10} + 43 q^{11} + 28 q^{12} + 130 q^{13} + 47 q^{14} + 29 q^{15} + 170 q^{16} + 85 q^{17} + 20 q^{18} + 3 q^{19} + 73 q^{20} + 62 q^{21} + 12 q^{22} + 62 q^{23} - 5 q^{24} + 178 q^{25} + 10 q^{26} + 35 q^{27} - q^{28} + 134 q^{29} + 24 q^{30} + 14 q^{31} + 48 q^{32} + 4 q^{33} + 4 q^{34} + 50 q^{35} + 244 q^{36} + 32 q^{37} + 76 q^{38} + 11 q^{39} - 6 q^{40} + 48 q^{41} + 9 q^{42} + 34 q^{43} + 123 q^{44} + 115 q^{45} + 5 q^{46} + 25 q^{47} + 35 q^{48} + 210 q^{49} + 24 q^{50} + 20 q^{51} + 146 q^{52} + 193 q^{53} - 39 q^{54} + 32 q^{55} + 122 q^{56} + 7 q^{57} - 4 q^{58} + 50 q^{59} + 42 q^{60} + 57 q^{61} + 51 q^{62} + 8 q^{63} + 172 q^{64} + 40 q^{65} - 4 q^{66} + 21 q^{67} + 132 q^{68} + 92 q^{69} - 46 q^{70} + 58 q^{71} - 26 q^{72} + 15 q^{73} + 120 q^{74} + 23 q^{75} - 65 q^{76} + 192 q^{77} + 4 q^{78} + 32 q^{79} + 66 q^{80} + 326 q^{81} + 11 q^{82} + 33 q^{83} + 5 q^{84} + 43 q^{85} + 105 q^{86} + 31 q^{87} - 17 q^{88} + 84 q^{89} - 73 q^{90} + 8 q^{91} + 161 q^{92} + 52 q^{93} + 4 q^{94} + 59 q^{95} - 77 q^{96} + 9 q^{97} - 61 q^{98} + 100 q^{99}+O(q^{100}) \) 130 * q + 10 * q^2 + 11 * q^3 + 146 * q^4 + 40 * q^5 + 4 * q^6 + 8 * q^7 + 24 * q^8 + 181 * q^9 + 5 * q^10 + 43 * q^11 + 28 * q^12 + 130 * q^13 + 47 * q^14 + 29 * q^15 + 170 * q^16 + 85 * q^17 + 20 * q^18 + 3 * q^19 + 73 * q^20 + 62 * q^21 + 12 * q^22 + 62 * q^23 - 5 * q^24 + 178 * q^25 + 10 * q^26 + 35 * q^27 - q^28 + 134 * q^29 + 24 * q^30 + 14 * q^31 + 48 * q^32 + 4 * q^33 + 4 * q^34 + 50 * q^35 + 244 * q^36 + 32 * q^37 + 76 * q^38 + 11 * q^39 - 6 * q^40 + 48 * q^41 + 9 * q^42 + 34 * q^43 + 123 * q^44 + 115 * q^45 + 5 * q^46 + 25 * q^47 + 35 * q^48 + 210 * q^49 + 24 * q^50 + 20 * q^51 + 146 * q^52 + 193 * q^53 - 39 * q^54 + 32 * q^55 + 122 * q^56 + 7 * q^57 - 4 * q^58 + 50 * q^59 + 42 * q^60 + 57 * q^61 + 51 * q^62 + 8 * q^63 + 172 * q^64 + 40 * q^65 - 4 * q^66 + 21 * q^67 + 132 * q^68 + 92 * q^69 - 46 * q^70 + 58 * q^71 - 26 * q^72 + 15 * q^73 + 120 * q^74 + 23 * q^75 - 65 * q^76 + 192 * q^77 + 4 * q^78 + 32 * q^79 + 66 * q^80 + 326 * q^81 + 11 * q^82 + 33 * q^83 + 5 * q^84 + 43 * q^85 + 105 * q^86 + 31 * q^87 - 17 * q^88 + 84 * q^89 - 73 * q^90 + 8 * q^91 + 161 * q^92 + 52 * q^93 + 4 * q^94 + 59 * q^95 - 77 * q^96 + 9 * q^97 - 61 * q^98 + 100 * q^99

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