LMFDB - Embedded newform 6010.2.a.g.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6010,2,Mod(1,6010)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6010, 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("6010.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6010 = 2 \cdot 5 \cdot 601 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6010.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:	$47.9900916148$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6010.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.114121 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.114121 q^{6} -3.33992 q^{7} -1.00000 q^{8} -2.98698 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.114121 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.114121 q^{6} -3.33992 q^{7} -1.00000 q^{8} -2.98698 q^{9} -1.00000 q^{10} -5.24130 q^{11} -0.114121 q^{12} -3.09873 q^{13} +3.33992 q^{14} -0.114121 q^{15} +1.00000 q^{16} -4.18652 q^{17} +2.98698 q^{18} -6.74923 q^{19} +1.00000 q^{20} +0.381156 q^{21} +5.24130 q^{22} +1.60407 q^{23} +0.114121 q^{24} +1.00000 q^{25} +3.09873 q^{26} +0.683240 q^{27} -3.33992 q^{28} -3.36492 q^{29} +0.114121 q^{30} -0.441736 q^{31} -1.00000 q^{32} +0.598143 q^{33} +4.18652 q^{34} -3.33992 q^{35} -2.98698 q^{36} -10.6166 q^{37} +6.74923 q^{38} +0.353631 q^{39} -1.00000 q^{40} -6.06742 q^{41} -0.381156 q^{42} +9.37370 q^{43} -5.24130 q^{44} -2.98698 q^{45} -1.60407 q^{46} +6.71286 q^{47} -0.114121 q^{48} +4.15510 q^{49} -1.00000 q^{50} +0.477771 q^{51} -3.09873 q^{52} -4.83315 q^{53} -0.683240 q^{54} -5.24130 q^{55} +3.33992 q^{56} +0.770230 q^{57} +3.36492 q^{58} -4.56623 q^{59} -0.114121 q^{60} -0.516042 q^{61} +0.441736 q^{62} +9.97628 q^{63} +1.00000 q^{64} -3.09873 q^{65} -0.598143 q^{66} -10.7608 q^{67} -4.18652 q^{68} -0.183059 q^{69} +3.33992 q^{70} -10.7000 q^{71} +2.98698 q^{72} -0.485754 q^{73} +10.6166 q^{74} -0.114121 q^{75} -6.74923 q^{76} +17.5055 q^{77} -0.353631 q^{78} +1.69451 q^{79} +1.00000 q^{80} +8.88296 q^{81} +6.06742 q^{82} -3.83558 q^{83} +0.381156 q^{84} -4.18652 q^{85} -9.37370 q^{86} +0.384009 q^{87} +5.24130 q^{88} +14.4093 q^{89} +2.98698 q^{90} +10.3495 q^{91} +1.60407 q^{92} +0.0504114 q^{93} -6.71286 q^{94} -6.74923 q^{95} +0.114121 q^{96} -3.50366 q^{97} -4.15510 q^{98} +15.6556 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.114121	−0.0658879	−0.0329439	−	0.999457i	$-0.510488\pi$
$3$	−0.114121	−0.0658879	−0.0329439	+	0.999457i	$0.510488\pi$
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.114121	0.0465898
$7$	−3.33992	−1.26237	−0.631186	−	0.775631i	$-0.717432\pi$
$7$	−3.33992	−1.26237	−0.631186	+	0.775631i	$0.717432\pi$
$8$	−1.00000	−0.353553
$9$	−2.98698	−0.995659
$10$	−1.00000	−0.316228
$11$	−5.24130	−1.58031	−0.790155	−	0.612907i	$-0.790000\pi$
$11$	−5.24130	−1.58031	−0.790155	+	0.612907i	$0.790000\pi$
$12$	−0.114121	−0.0329439
$13$	−3.09873	−0.859433	−0.429717	−	0.902964i	$-0.641387\pi$
$13$	−3.09873	−0.859433	−0.429717	+	0.902964i	$0.641387\pi$
$14$	3.33992	0.892632
$15$	−0.114121	−0.0294659
$16$	1.00000	0.250000
$17$	−4.18652	−1.01538	−0.507691	−	0.861539i	$-0.669501\pi$
$17$	−4.18652	−1.01538	−0.507691	+	0.861539i	$0.669501\pi$
$18$	2.98698	0.704037
$19$	−6.74923	−1.54838	−0.774190	−	0.632954i	$-0.781842\pi$
$19$	−6.74923	−1.54838	−0.774190	+	0.632954i	$0.781842\pi$
$20$	1.00000	0.223607
$21$	0.381156	0.0831751
$22$	5.24130	1.11745
$23$	1.60407	0.334472	0.167236	−	0.985917i	$-0.446516\pi$
$23$	1.60407	0.334472	0.167236	+	0.985917i	$0.446516\pi$
$24$	0.114121	0.0232949
$25$	1.00000	0.200000
$26$	3.09873	0.607711
$27$	0.683240	0.131490
$28$	−3.33992	−0.631186
$29$	−3.36492	−0.624850	−0.312425	−	0.949942i	$-0.601141\pi$
$29$	−3.36492	−0.624850	−0.312425	+	0.949942i	$0.601141\pi$
$30$	0.114121	0.0208356
$31$	−0.441736	−0.0793381	−0.0396690	−	0.999213i	$-0.512630\pi$
$31$	−0.441736	−0.0793381	−0.0396690	+	0.999213i	$0.512630\pi$
$32$	−1.00000	−0.176777
$33$	0.598143	0.104123
$34$	4.18652	0.717983
$35$	−3.33992	−0.564550
$36$	−2.98698	−0.497829
$37$	−10.6166	−1.74536	−0.872680	−	0.488292i	$-0.837620\pi$
$37$	−10.6166	−1.74536	−0.872680	+	0.488292i	$0.837620\pi$
$38$	6.74923	1.09487
$39$	0.353631	0.0566262
$40$	−1.00000	−0.158114
$41$	−6.06742	−0.947572	−0.473786	−	0.880640i	$-0.657113\pi$
$41$	−6.06742	−0.947572	−0.473786	+	0.880640i	$0.657113\pi$
$42$	−0.381156	−0.0588136
$43$	9.37370	1.42948	0.714738	−	0.699393i	$-0.246546\pi$
$43$	9.37370	1.42948	0.714738	+	0.699393i	$0.246546\pi$
$44$	−5.24130	−0.790155
$45$	−2.98698	−0.445272
$46$	−1.60407	−0.236508
$47$	6.71286	0.979171	0.489586	−	0.871955i	$-0.337148\pi$
$47$	6.71286	0.979171	0.489586	+	0.871955i	$0.337148\pi$
$48$	−0.114121	−0.0164720
$49$	4.15510	0.593585
$50$	−1.00000	−0.141421
$51$	0.477771	0.0669013
$52$	−3.09873	−0.429717
$53$	−4.83315	−0.663885	−0.331942	−	0.943300i	$-0.607704\pi$
$53$	−4.83315	−0.663885	−0.331942	+	0.943300i	$0.607704\pi$
$54$	−0.683240	−0.0929773
$55$	−5.24130	−0.706736
$56$	3.33992	0.446316
$57$	0.770230	0.102019
$58$	3.36492	0.441836
$59$	−4.56623	−0.594472	−0.297236	−	0.954804i	$-0.596065\pi$
$59$	−4.56623	−0.594472	−0.297236	+	0.954804i	$0.596065\pi$
$60$	−0.114121	−0.0147330
$61$	−0.516042	−0.0660724	−0.0330362	−	0.999454i	$-0.510518\pi$
$61$	−0.516042	−0.0660724	−0.0330362	+	0.999454i	$0.510518\pi$
$62$	0.441736	0.0561005
$63$	9.97628	1.25689
$64$	1.00000	0.125000
$65$	−3.09873	−0.384350
$66$	−0.598143	−0.0736263
$67$	−10.7608	−1.31464	−0.657322	−	0.753610i	$-0.728311\pi$
$67$	−10.7608	−1.31464	−0.657322	+	0.753610i	$0.728311\pi$
$68$	−4.18652	−0.507691
$69$	−0.183059	−0.0220377
$70$	3.33992	0.399197
$71$	−10.7000	−1.26986	−0.634930	−	0.772569i	$-0.718971\pi$
$71$	−10.7000	−1.26986	−0.634930	+	0.772569i	$0.718971\pi$
$72$	2.98698	0.352019
$73$	−0.485754	−0.0568532	−0.0284266	−	0.999596i	$-0.509050\pi$
$73$	−0.485754	−0.0568532	−0.0284266	+	0.999596i	$0.509050\pi$
$74$	10.6166	1.23416
$75$	−0.114121	−0.0131776
$76$	−6.74923	−0.774190
$77$	17.5055	1.99494
$78$	−0.353631	−0.0400408
$79$	1.69451	0.190647	0.0953234	−	0.995446i	$-0.469611\pi$
$79$	1.69451	0.190647	0.0953234	+	0.995446i	$0.469611\pi$
$80$	1.00000	0.111803
$81$	8.88296	0.986995
$82$	6.06742	0.670034
$83$	−3.83558	−0.421009	−0.210505	−	0.977593i	$-0.567511\pi$
$83$	−3.83558	−0.421009	−0.210505	+	0.977593i	$0.567511\pi$
$84$	0.381156	0.0415875
$85$	−4.18652	−0.454092
$86$	−9.37370	−1.01079
$87$	0.384009	0.0411700
$88$	5.24130	0.558724
$89$	14.4093	1.52738	0.763692	−	0.645581i	$-0.223385\pi$
$89$	14.4093	1.52738	0.763692	+	0.645581i	$0.223385\pi$
$90$	2.98698	0.314855
$91$	10.3495	1.08493
$92$	1.60407	0.167236
$93$	0.0504114	0.00522742
$94$	−6.71286	−0.692379
$95$	−6.74923	−0.692456
$96$	0.114121	0.0116474
$97$	−3.50366	−0.355742	−0.177871	−	0.984054i	$-0.556921\pi$
$97$	−3.50366	−0.355742	−0.177871	+	0.984054i	$0.556921\pi$
$98$	−4.15510	−0.419728
$99$	15.6556	1.57345
$100$	1.00000	0.100000
$101$	4.52744	0.450497	0.225248	−	0.974301i	$-0.427681\pi$
$101$	4.52744	0.450497	0.225248	+	0.974301i	$0.427681\pi$
$102$	−0.477771	−0.0473064
$103$	−10.2740	−1.01233	−0.506164	−	0.862437i	$-0.668937\pi$
$103$	−10.2740	−1.01233	−0.506164	+	0.862437i	$0.668937\pi$
$104$	3.09873	0.303855
$105$	0.381156	0.0371970
$106$	4.83315	0.469438
$107$	−11.5974	−1.12116	−0.560580	−	0.828101i	$-0.689422\pi$
$107$	−11.5974	−1.12116	−0.560580	+	0.828101i	$0.689422\pi$
$108$	0.683240	0.0657448
$109$	18.3547	1.75806	0.879029	−	0.476769i	$-0.158192\pi$
$109$	18.3547	1.75806	0.879029	+	0.476769i	$0.158192\pi$
$110$	5.24130	0.499738
$111$	1.21158	0.114998
$112$	−3.33992	−0.315593
$113$	−14.6136	−1.37473	−0.687367	−	0.726310i	$-0.741234\pi$
$113$	−14.6136	−1.37473	−0.687367	+	0.726310i	$0.741234\pi$
$114$	−0.770230	−0.0721386
$115$	1.60407	0.149581
$116$	−3.36492	−0.312425
$117$	9.25583	0.855702
$118$	4.56623	0.420355
$119$	13.9827	1.28179
$120$	0.114121	0.0104178
$121$	16.4712	1.49738
$122$	0.516042	0.0467203
$123$	0.692421	0.0624335
$124$	−0.441736	−0.0396690
$125$	1.00000	0.0894427
$126$	−9.97628	−0.888757
$127$	1.49355	0.132531	0.0662657	−	0.997802i	$-0.478891\pi$
$127$	1.49355	0.132531	0.0662657	+	0.997802i	$0.478891\pi$
$128$	−1.00000	−0.0883883
$129$	−1.06974	−0.0941851
$130$	3.09873	0.271777
$131$	19.4658	1.70073	0.850367	−	0.526190i	$-0.176380\pi$
$131$	19.4658	1.70073	0.850367	+	0.526190i	$0.176380\pi$
$132$	0.598143	0.0520616
$133$	22.5419	1.95463
$134$	10.7608	0.929594
$135$	0.683240	0.0588040
$136$	4.18652	0.358992
$137$	−13.4060	−1.14535	−0.572677	−	0.819781i	$-0.694095\pi$
$137$	−13.4060	−1.14535	−0.572677	+	0.819781i	$0.694095\pi$
$138$	0.183059	0.0155830
$139$	−15.9170	−1.35006	−0.675031	−	0.737790i	$-0.735870\pi$
$139$	−15.9170	−1.35006	−0.675031	+	0.737790i	$0.735870\pi$
$140$	−3.33992	−0.282275
$141$	−0.766079	−0.0645155
$142$	10.7000	0.897927
$143$	16.2414	1.35817
$144$	−2.98698	−0.248915
$145$	−3.36492	−0.279442
$146$	0.485754	0.0402013
$147$	−0.474184	−0.0391101
$148$	−10.6166	−0.872680
$149$	15.0650	1.23417	0.617085	−	0.786897i	$-0.288314\pi$
$149$	15.0650	1.23417	0.617085	+	0.786897i	$0.288314\pi$
$150$	0.114121	0.00931795
$151$	19.7353	1.60604	0.803020	−	0.595952i	$-0.203225\pi$
$151$	19.7353	1.60604	0.803020	+	0.595952i	$0.203225\pi$
$152$	6.74923	0.547435
$153$	12.5050	1.01097
$154$	−17.5055	−1.41064
$155$	−0.441736	−0.0354811
$156$	0.353631	0.0283131
$157$	−7.47915	−0.596901	−0.298451	−	0.954425i	$-0.596470\pi$
$157$	−7.47915	−0.596901	−0.298451	+	0.954425i	$0.596470\pi$
$158$	−1.69451	−0.134808
$159$	0.551565	0.0437420
$160$	−1.00000	−0.0790569
$161$	−5.35749	−0.422229
$162$	−8.88296	−0.697911
$163$	6.10593	0.478253	0.239127	−	0.970988i	$-0.423139\pi$
$163$	6.10593	0.478253	0.239127	+	0.970988i	$0.423139\pi$
$164$	−6.06742	−0.473786
$165$	0.598143	0.0465653
$166$	3.83558	0.297698
$167$	0.0294861	0.00228171	0.00114085	−	0.999999i	$-0.499637\pi$
$167$	0.0294861	0.00228171	0.00114085	+	0.999999i	$0.499637\pi$
$168$	−0.381156	−0.0294068
$169$	−3.39787	−0.261375
$170$	4.18652	0.321092
$171$	20.1598	1.54166
$172$	9.37370	0.714738
$173$	−3.86185	−0.293611	−0.146805	−	0.989165i	$-0.546899\pi$
$173$	−3.86185	−0.293611	−0.146805	+	0.989165i	$0.546899\pi$
$174$	−0.384009	−0.0291116
$175$	−3.33992	−0.252475
$176$	−5.24130	−0.395078
$177$	0.521103	0.0391685
$178$	−14.4093	−1.08002
$179$	16.9854	1.26955	0.634773	−	0.772698i	$-0.281093\pi$
$179$	16.9854	1.26955	0.634773	+	0.772698i	$0.281093\pi$
$180$	−2.98698	−0.222636
$181$	1.66851	0.124019	0.0620097	−	0.998076i	$-0.480249\pi$
$181$	1.66851	0.124019	0.0620097	+	0.998076i	$0.480249\pi$
$182$	−10.3495	−0.767158
$183$	0.0588913	0.00435337
$184$	−1.60407	−0.118254
$185$	−10.6166	−0.780549
$186$	−0.0504114	−0.00369634
$187$	21.9428	1.60462
$188$	6.71286	0.489586
$189$	−2.28197	−0.165989
$190$	6.74923	0.489640
$191$	−0.177226	−0.0128236	−0.00641181	−	0.999979i	$-0.502041\pi$
$191$	−0.177226	−0.0128236	−0.00641181	+	0.999979i	$0.502041\pi$
$192$	−0.114121	−0.00823598
$193$	−15.6013	−1.12300	−0.561502	−	0.827476i	$-0.689776\pi$
$193$	−15.6013	−1.12300	−0.561502	+	0.827476i	$0.689776\pi$
$194$	3.50366	0.251548
$195$	0.353631	0.0253240
$196$	4.15510	0.296793
$197$	−1.93090	−0.137571	−0.0687855	−	0.997631i	$-0.521912\pi$
$197$	−1.93090	−0.137571	−0.0687855	+	0.997631i	$0.521912\pi$
$198$	−15.6556	−1.11260
$199$	−18.2112	−1.29096	−0.645478	−	0.763779i	$-0.723342\pi$
$199$	−18.2112	−1.29096	−0.645478	+	0.763779i	$0.723342\pi$
$200$	−1.00000	−0.0707107
$201$	1.22804	0.0866191
$202$	−4.52744	−0.318549
$203$	11.2386	0.788794
$204$	0.477771	0.0334507
$205$	−6.06742	−0.423767
$206$	10.2740	0.715824
$207$	−4.79133	−0.333020
$208$	−3.09873	−0.214858
$209$	35.3747	2.44692
$210$	−0.381156	−0.0263023
$211$	19.1514	1.31844	0.659218	−	0.751952i	$-0.270888\pi$
$211$	19.1514	1.31844	0.659218	+	0.751952i	$0.270888\pi$
$212$	−4.83315	−0.331942
$213$	1.22110	0.0836684
$214$	11.5974	0.792779
$215$	9.37370	0.639281
$216$	−0.683240	−0.0464886
$217$	1.47536	0.100154
$218$	−18.3547	−1.24313
$219$	0.0554348	0.00374594
$220$	−5.24130	−0.353368
$221$	12.9729	0.872652
$222$	−1.21158	−0.0813159
$223$	15.7550	1.05503	0.527516	−	0.849545i	$-0.323124\pi$
$223$	15.7550	1.05503	0.527516	+	0.849545i	$0.323124\pi$
$224$	3.33992	0.223158
$225$	−2.98698	−0.199132
$226$	14.6136	0.972084
$227$	−7.01265	−0.465446	−0.232723	−	0.972543i	$-0.574764\pi$
$227$	−7.01265	−0.465446	−0.232723	+	0.972543i	$0.574764\pi$
$228$	0.770230	0.0510097
$229$	−21.6731	−1.43220	−0.716101	−	0.697997i	$-0.754075\pi$
$229$	−21.6731	−1.43220	−0.716101	+	0.697997i	$0.754075\pi$
$230$	−1.60407	−0.105769
$231$	−1.99775	−0.131442
$232$	3.36492	0.220918
$233$	−6.60748	−0.432870	−0.216435	−	0.976297i	$-0.569443\pi$
$233$	−6.60748	−0.432870	−0.216435	+	0.976297i	$0.569443\pi$
$234$	−9.25583	−0.605073
$235$	6.71286	0.437899
$236$	−4.56623	−0.297236
$237$	−0.193379	−0.0125613
$238$	−13.9827	−0.906362
$239$	−16.8448	−1.08960	−0.544801	−	0.838565i	$-0.683395\pi$
$239$	−16.8448	−1.08960	−0.544801	+	0.838565i	$0.683395\pi$
$240$	−0.114121	−0.00736649
$241$	−5.03185	−0.324130	−0.162065	−	0.986780i	$-0.551815\pi$
$241$	−5.03185	−0.324130	−0.162065	+	0.986780i	$0.551815\pi$
$242$	−16.4712	−1.05881
$243$	−3.06345	−0.196521
$244$	−0.516042	−0.0330362
$245$	4.15510	0.265459
$246$	−0.692421	−0.0441471
$247$	20.9140	1.33073
$248$	0.441736	0.0280503
$249$	0.437720	0.0277394
$250$	−1.00000	−0.0632456
$251$	−28.3676	−1.79055	−0.895273	−	0.445518i	$-0.853019\pi$
$251$	−28.3676	−1.79055	−0.895273	+	0.445518i	$0.853019\pi$
$252$	9.97628	0.628446
$253$	−8.40742	−0.528570
$254$	−1.49355	−0.0937139
$255$	0.477771	0.0299192
$256$	1.00000	0.0625000
$257$	−15.7106	−0.980002	−0.490001	−	0.871722i	$-0.663004\pi$
$257$	−15.7106	−0.980002	−0.490001	+	0.871722i	$0.663004\pi$
$258$	1.06974	0.0665989
$259$	35.4587	2.20330
$260$	−3.09873	−0.192175
$261$	10.0509	0.622138
$262$	−19.4658	−1.20260
$263$	20.2353	1.24776	0.623881	−	0.781519i	$-0.285555\pi$
$263$	20.2353	1.24776	0.623881	+	0.781519i	$0.285555\pi$
$264$	−0.598143	−0.0368131
$265$	−4.83315	−0.296898
$266$	−22.5419	−1.38213
$267$	−1.64441	−0.100636
$268$	−10.7608	−0.657322
$269$	−15.6949	−0.956932	−0.478466	−	0.878106i	$-0.658807\pi$
$269$	−15.6949	−0.956932	−0.478466	+	0.878106i	$0.658807\pi$
$270$	−0.683240	−0.0415807
$271$	−19.4379	−1.18077	−0.590383	−	0.807123i	$-0.701023\pi$
$271$	−19.4379	−1.18077	−0.590383	+	0.807123i	$0.701023\pi$
$272$	−4.18652	−0.253845
$273$	−1.18110	−0.0714834
$274$	13.4060	0.809888
$275$	−5.24130	−0.316062
$276$	−0.183059	−0.0110188
$277$	−12.5610	−0.754717	−0.377358	−	0.926067i	$-0.623167\pi$
$277$	−12.5610	−0.754717	−0.377358	+	0.926067i	$0.623167\pi$
$278$	15.9170	0.954637
$279$	1.31945	0.0789937
$280$	3.33992	0.199599
$281$	−25.1508	−1.50037	−0.750185	−	0.661228i	$-0.770036\pi$
$281$	−25.1508	−1.50037	−0.750185	+	0.661228i	$0.770036\pi$
$282$	0.766079	0.0456194
$283$	4.95731	0.294682	0.147341	−	0.989086i	$-0.452929\pi$
$283$	4.95731	0.294682	0.147341	+	0.989086i	$0.452929\pi$
$284$	−10.7000	−0.634930
$285$	0.770230	0.0456245
$286$	−16.2414	−0.960372
$287$	20.2647	1.19619
$288$	2.98698	0.176009
$289$	0.526987	0.0309992
$290$	3.36492	0.197595
$291$	0.399841	0.0234391
$292$	−0.485754	−0.0284266
$293$	26.6514	1.55699	0.778496	−	0.627650i	$-0.215983\pi$
$293$	26.6514	1.55699	0.778496	+	0.627650i	$0.215983\pi$
$294$	0.474184	0.0276550
$295$	−4.56623	−0.265856
$296$	10.6166	0.617078
$297$	−3.58107	−0.207794
$298$	−15.0650	−0.872689
$299$	−4.97059	−0.287457
$300$	−0.114121	−0.00658879
$301$	−31.3074	−1.80453
$302$	−19.7353	−1.13564
$303$	−0.516676	−0.0296823
$304$	−6.74923	−0.387095
$305$	−0.516042	−0.0295485
$306$	−12.5050	−0.714866
$307$	1.15501	0.0659201	0.0329600	−	0.999457i	$-0.489507\pi$
$307$	1.15501	0.0659201	0.0329600	+	0.999457i	$0.489507\pi$
$308$	17.5055	0.997470
$309$	1.17248	0.0667001
$310$	0.441736	0.0250889
$311$	30.2781	1.71691	0.858457	−	0.512886i	$-0.171424\pi$
$311$	30.2781	1.71691	0.858457	+	0.512886i	$0.171424\pi$
$312$	−0.353631	−0.0200204
$313$	−30.5559	−1.72712	−0.863561	−	0.504244i	$-0.831771\pi$
$313$	−30.5559	−1.72712	−0.863561	+	0.504244i	$0.831771\pi$
$314$	7.47915	0.422073
$315$	9.97628	0.562099
$316$	1.69451	0.0953234
$317$	−25.6290	−1.43947	−0.719734	−	0.694250i	$-0.755736\pi$
$317$	−25.6290	−1.43947	−0.719734	+	0.694250i	$0.755736\pi$
$318$	−0.551565	−0.0309302
$319$	17.6365	0.987457
$320$	1.00000	0.0559017
$321$	1.32350	0.0738708
$322$	5.35749	0.298561
$323$	28.2558	1.57220
$324$	8.88296	0.493498
$325$	−3.09873	−0.171887
$326$	−6.10593	−0.338176
$327$	−2.09465	−0.115835
$328$	6.06742	0.335017
$329$	−22.4204	−1.23608
$330$	−0.598143	−0.0329267
$331$	−9.62489	−0.529032	−0.264516	−	0.964381i	$-0.585212\pi$
$331$	−9.62489	−0.529032	−0.264516	+	0.964381i	$0.585212\pi$
$332$	−3.83558	−0.210505
$333$	31.7116	1.73778
$334$	−0.0294861	−0.00161341
$335$	−10.7608	−0.587927
$336$	0.381156	0.0207938
$337$	−27.8738	−1.51838	−0.759192	−	0.650866i	$-0.774406\pi$
$337$	−27.8738	−1.51838	−0.759192	+	0.650866i	$0.774406\pi$
$338$	3.39787	0.184820
$339$	1.66772	0.0905783
$340$	−4.18652	−0.227046
$341$	2.31527	0.125379
$342$	−20.1598	−1.09012
$343$	9.50176	0.513047
$344$	−9.37370	−0.505396
$345$	−0.183059	−0.00985555
$346$	3.86185	0.207614
$347$	35.7370	1.91846	0.959231	−	0.282625i	$-0.0912051\pi$
$347$	35.7370	1.91846	0.959231	+	0.282625i	$0.0912051\pi$
$348$	0.384009	0.0205850
$349$	28.4741	1.52419	0.762093	−	0.647468i	$-0.224172\pi$
$349$	28.4741	1.52419	0.762093	+	0.647468i	$0.224172\pi$
$350$	3.33992	0.178526
$351$	−2.11718	−0.113007
$352$	5.24130	0.279362
$353$	−3.64303	−0.193899	−0.0969494	−	0.995289i	$-0.530908\pi$
$353$	−3.64303	−0.193899	−0.0969494	+	0.995289i	$0.530908\pi$
$354$	−0.521103	−0.0276963
$355$	−10.7000	−0.567899
$356$	14.4093	0.763692
$357$	−1.59572	−0.0844544
$358$	−16.9854	−0.897705
$359$	−7.76941	−0.410054	−0.205027	−	0.978756i	$-0.565728\pi$
$359$	−7.76941	−0.410054	−0.205027	+	0.978756i	$0.565728\pi$
$360$	2.98698	0.157427
$361$	26.5521	1.39748
$362$	−1.66851	−0.0876950
$363$	−1.87971	−0.0986592
$364$	10.3495	0.542463
$365$	−0.485754	−0.0254255
$366$	−0.0588913	−0.00307830
$367$	−18.6049	−0.971168	−0.485584	−	0.874190i	$-0.661393\pi$
$367$	−18.6049	−0.971168	−0.485584	+	0.874190i	$0.661393\pi$
$368$	1.60407	0.0836181
$369$	18.1232	0.943458
$370$	10.6166	0.551931
$371$	16.1424	0.838070
$372$	0.0504114	0.00261371
$373$	−23.9607	−1.24064	−0.620318	−	0.784350i	$-0.712996\pi$
$373$	−23.9607	−1.24064	−0.620318	+	0.784350i	$0.712996\pi$
$374$	−21.9428	−1.13464
$375$	−0.114121	−0.00589319
$376$	−6.71286	−0.346189
$377$	10.4270	0.537017
$378$	2.28197	0.117372
$379$	38.1452	1.95939	0.979694	−	0.200497i	$-0.0642558\pi$
$379$	38.1452	1.95939	0.979694	+	0.200497i	$0.0642558\pi$
$380$	−6.74923	−0.346228
$381$	−0.170446	−0.00873222
$382$	0.177226	0.00906766
$383$	−12.7531	−0.651651	−0.325826	−	0.945430i	$-0.605642\pi$
$383$	−12.7531	−0.651651	−0.325826	+	0.945430i	$0.605642\pi$
$384$	0.114121	0.00582372
$385$	17.5055	0.892165
$386$	15.6013	0.794083
$387$	−27.9990	−1.42327
$388$	−3.50366	−0.177871
$389$	12.9134	0.654736	0.327368	−	0.944897i	$-0.393838\pi$
$389$	12.9134	0.654736	0.327368	+	0.944897i	$0.393838\pi$
$390$	−0.353631	−0.0179068
$391$	−6.71549	−0.339617
$392$	−4.15510	−0.209864
$393$	−2.22146	−0.112058
$394$	1.93090	0.0972774
$395$	1.69451	0.0852598
$396$	15.6556	0.786725
$397$	−24.9881	−1.25412	−0.627058	−	0.778973i	$-0.715741\pi$
$397$	−24.9881	−1.25412	−0.627058	+	0.778973i	$0.715741\pi$
$398$	18.2112	0.912843
$399$	−2.57251	−0.128787
$400$	1.00000	0.0500000
$401$	−18.3131	−0.914511	−0.457256	−	0.889335i	$-0.651168\pi$
$401$	−18.3131	−0.914511	−0.457256	+	0.889335i	$0.651168\pi$
$402$	−1.22804	−0.0612489
$403$	1.36882	0.0681858
$404$	4.52744	0.225248
$405$	8.88296	0.441398
$406$	−11.2386	−0.557762
$407$	55.6448	2.75821
$408$	−0.477771	−0.0236532
$409$	22.5235	1.11371	0.556857	−	0.830609i	$-0.312007\pi$
$409$	22.5235	1.11371	0.556857	+	0.830609i	$0.312007\pi$
$410$	6.06742	0.299648
$411$	1.52991	0.0754650
$412$	−10.2740	−0.506164
$413$	15.2508	0.750445
$414$	4.79133	0.235481
$415$	−3.83558	−0.188281
$416$	3.09873	0.151928
$417$	1.81646	0.0889526
$418$	−35.3747	−1.73023
$419$	0.779377	0.0380751	0.0190375	−	0.999819i	$-0.493940\pi$
$419$	0.779377	0.0380751	0.0190375	+	0.999819i	$0.493940\pi$
$420$	0.381156	0.0185985
$421$	9.33481	0.454951	0.227475	−	0.973784i	$-0.426953\pi$
$421$	9.33481	0.454951	0.227475	+	0.973784i	$0.426953\pi$
$422$	−19.1514	−0.932275
$423$	−20.0512	−0.974921
$424$	4.83315	0.234719
$425$	−4.18652	−0.203076
$426$	−1.22110	−0.0591625
$427$	1.72354	0.0834081
$428$	−11.5974	−0.560580
$429$	−1.85348	−0.0894870
$430$	−9.37370	−0.452040
$431$	−19.8753	−0.957359	−0.478679	−	0.877990i	$-0.658884\pi$
$431$	−19.8753	−0.957359	−0.478679	+	0.877990i	$0.658884\pi$
$432$	0.683240	0.0328724
$433$	9.71413	0.466831	0.233416	−	0.972377i	$-0.425010\pi$
$433$	9.71413	0.466831	0.233416	+	0.972377i	$0.425010\pi$
$434$	−1.47536	−0.0708198
$435$	0.384009	0.0184118
$436$	18.3547	0.879029
$437$	−10.8263	−0.517890
$438$	−0.0554348	−0.00264878
$439$	3.48523	0.166341	0.0831705	−	0.996535i	$-0.473495\pi$
$439$	3.48523	0.166341	0.0831705	+	0.996535i	$0.473495\pi$
$440$	5.24130	0.249869
$441$	−12.4112	−0.591008
$442$	−12.9729	−0.617058
$443$	−29.6965	−1.41092	−0.705461	−	0.708749i	$-0.749260\pi$
$443$	−29.6965	−1.41092	−0.705461	+	0.708749i	$0.749260\pi$
$444$	1.21158	0.0574990
$445$	14.4093	0.683066
$446$	−15.7550	−0.746020
$447$	−1.71923	−0.0813168
$448$	−3.33992	−0.157797
$449$	0.199613	0.00942031	0.00471016	−	0.999989i	$-0.498501\pi$
$449$	0.199613	0.00942031	0.00471016	+	0.999989i	$0.498501\pi$
$450$	2.98698	0.140807
$451$	31.8011	1.49746
$452$	−14.6136	−0.687367
$453$	−2.25222	−0.105819
$454$	7.01265	0.329120
$455$	10.3495	0.485193
$456$	−0.770230	−0.0360693
$457$	−22.7704	−1.06516	−0.532578	−	0.846381i	$-0.678777\pi$
$457$	−22.7704	−1.06516	−0.532578	+	0.846381i	$0.678777\pi$
$458$	21.6731	1.01272
$459$	−2.86040	−0.133512
$460$	1.60407	0.0747903
$461$	1.61692	0.0753076	0.0376538	−	0.999291i	$-0.488012\pi$
$461$	1.61692	0.0753076	0.0376538	+	0.999291i	$0.488012\pi$
$462$	1.99775	0.0929438
$463$	−11.0006	−0.511241	−0.255620	−	0.966777i	$-0.582280\pi$
$463$	−11.0006	−0.511241	−0.255620	+	0.966777i	$0.582280\pi$
$464$	−3.36492	−0.156213
$465$	0.0504114	0.00233777
$466$	6.60748	0.306086
$467$	−5.43687	−0.251588	−0.125794	−	0.992056i	$-0.540148\pi$
$467$	−5.43687	−0.251588	−0.125794	+	0.992056i	$0.540148\pi$
$468$	9.25583	0.427851
$469$	35.9403	1.65957
$470$	−6.71286	−0.309641
$471$	0.853529	0.0393285
$472$	4.56623	0.210178
$473$	−49.1303	−2.25901
$474$	0.193379	0.00888218
$475$	−6.74923	−0.309676
$476$	13.9827	0.640895
$477$	14.4365	0.661003
$478$	16.8448	0.770465
$479$	−13.8636	−0.633444	−0.316722	−	0.948518i	$-0.602582\pi$
$479$	−13.8636	−0.633444	−0.316722	+	0.948518i	$0.602582\pi$
$480$	0.114121	0.00520889
$481$	32.8980	1.50002
$482$	5.03185	0.229194
$483$	0.611402	0.0278198
$484$	16.4712	0.748690
$485$	−3.50366	−0.159093
$486$	3.06345	0.138961
$487$	−39.7045	−1.79918	−0.899592	−	0.436731i	$-0.856136\pi$
$487$	−39.7045	−1.79918	−0.899592	+	0.436731i	$0.856136\pi$
$488$	0.516042	0.0233601
$489$	−0.696815	−0.0315111
$490$	−4.15510	−0.187708
$491$	−18.4431	−0.832327	−0.416164	−	0.909290i	$-0.636626\pi$
$491$	−18.4431	−0.832327	−0.416164	+	0.909290i	$0.636626\pi$
$492$	0.692421	0.0312167
$493$	14.0873	0.634461
$494$	−20.9140	−0.940967
$495$	15.6556	0.703668
$496$	−0.441736	−0.0198345
$497$	35.7373	1.60304
$498$	−0.437720	−0.0196147
$499$	4.50989	0.201890	0.100945	−	0.994892i	$-0.467813\pi$
$499$	4.50989	0.201890	0.100945	+	0.994892i	$0.467813\pi$
$500$	1.00000	0.0447214
$501$	−0.00336499	−0.000150337 0
$502$	28.3676	1.26611
$503$	21.0830	0.940044	0.470022	−	0.882655i	$-0.344246\pi$
$503$	21.0830	0.940044	0.470022	+	0.882655i	$0.344246\pi$
$504$	−9.97628	−0.444379
$505$	4.52744	0.201468
$506$	8.40742	0.373756
$507$	0.387769	0.0172214
$508$	1.49355	0.0662657
$509$	15.0920	0.668942	0.334471	−	0.942406i	$-0.391442\pi$
$509$	15.0920	0.668942	0.334471	+	0.942406i	$0.391442\pi$
$510$	−0.477771	−0.0211561
$511$	1.62238	0.0717699
$512$	−1.00000	−0.0441942
$513$	−4.61135	−0.203596
$514$	15.7106	0.692966
$515$	−10.2740	−0.452727
$516$	−1.06974	−0.0470925
$517$	−35.1841	−1.54739
$518$	−35.4587	−1.55797
$519$	0.440718	0.0193454
$520$	3.09873	0.135888
$521$	15.7760	0.691161	0.345580	−	0.938389i	$-0.387682\pi$
$521$	15.7760	0.691161	0.345580	+	0.938389i	$0.387682\pi$
$522$	−10.0509	−0.439918
$523$	14.0073	0.612494	0.306247	−	0.951952i	$-0.400927\pi$
$523$	14.0073	0.612494	0.306247	+	0.951952i	$0.400927\pi$
$524$	19.4658	0.850367
$525$	0.381156	0.0166350
$526$	−20.2353	−0.882301
$527$	1.84934	0.0805584
$528$	0.598143	0.0260308
$529$	−20.4269	−0.888128
$530$	4.83315	0.209939
$531$	13.6392	0.591891
$532$	22.5419	0.977316
$533$	18.8013	0.814374
$534$	1.64441	0.0711604
$535$	−11.5974	−0.501398
$536$	10.7608	0.464797
$537$	−1.93839	−0.0836477
$538$	15.6949	0.676653
$539$	−21.7781	−0.938049
$540$	0.683240	0.0294020
$541$	−14.8587	−0.638825	−0.319413	−	0.947616i	$-0.603486\pi$
$541$	−14.8587	−0.638825	−0.319413	+	0.947616i	$0.603486\pi$
$542$	19.4379	0.834927
$543$	−0.190412	−0.00817138
$544$	4.18652	0.179496
$545$	18.3547	0.786227
$546$	1.18110	0.0505464
$547$	34.3629	1.46925	0.734627	−	0.678472i	$-0.237357\pi$
$547$	34.3629	1.46925	0.734627	+	0.678472i	$0.237357\pi$
$548$	−13.4060	−0.572677
$549$	1.54141	0.0657856
$550$	5.24130	0.223490
$551$	22.7106	0.967505
$552$	0.183059	0.00779150
$553$	−5.65952	−0.240667
$554$	12.5610	0.533665
$555$	1.21158	0.0514287
$556$	−15.9170	−0.675031
$557$	0.351202	0.0148809	0.00744046	−	0.999972i	$-0.497632\pi$
$557$	0.351202	0.0148809	0.00744046	+	0.999972i	$0.497632\pi$
$558$	−1.31945	−0.0558570
$559$	−29.0466	−1.22854
$560$	−3.33992	−0.141138
$561$	−2.50414	−0.105725
$562$	25.1508	1.06092
$563$	−15.2989	−0.644772	−0.322386	−	0.946608i	$-0.604485\pi$
$563$	−15.2989	−0.644772	−0.322386	+	0.946608i	$0.604485\pi$
$564$	−0.766079	−0.0322578
$565$	−14.6136	−0.614800
$566$	−4.95731	−0.208371
$567$	−29.6684	−1.24596
$568$	10.7000	0.448963
$569$	10.8820	0.456196	0.228098	−	0.973638i	$-0.426749\pi$
$569$	10.8820	0.456196	0.228098	+	0.973638i	$0.426749\pi$
$570$	−0.770230	−0.0322614
$571$	−46.2000	−1.93341	−0.966705	−	0.255894i	$-0.917630\pi$
$571$	−46.2000	−1.93341	−0.966705	+	0.255894i	$0.917630\pi$
$572$	16.2414	0.679085
$573$	0.0202252	0.000844920 0
$574$	−20.2647	−0.845833
$575$	1.60407	0.0668945
$576$	−2.98698	−0.124457
$577$	−20.9955	−0.874056	−0.437028	−	0.899448i	$-0.643969\pi$
$577$	−20.9955	−0.874056	−0.437028	+	0.899448i	$0.643969\pi$
$578$	−0.526987	−0.0219198
$579$	1.78043	0.0739923
$580$	−3.36492	−0.139721
$581$	12.8105	0.531470
$582$	−0.399841	−0.0165740
$583$	25.3320	1.04914
$584$	0.485754	0.0201006
$585$	9.25583	0.382682
$586$	−26.6514	−1.10096
$587$	37.6900	1.55563	0.777816	−	0.628492i	$-0.216328\pi$
$587$	37.6900	1.55563	0.777816	+	0.628492i	$0.216328\pi$
$588$	−0.474184	−0.0195550
$589$	2.98138	0.122845
$590$	4.56623	0.187989
$591$	0.220357	0.00906426
$592$	−10.6166	−0.436340
$593$	24.5975	1.01010	0.505048	−	0.863091i	$-0.331475\pi$
$593$	24.5975	1.01010	0.505048	+	0.863091i	$0.331475\pi$
$594$	3.58107	0.146933
$595$	13.9827	0.573234
$596$	15.0650	0.617085
$597$	2.07828	0.0850583
$598$	4.97059	0.203263
$599$	38.3262	1.56597	0.782983	−	0.622043i	$-0.213697\pi$
$599$	38.3262	1.56597	0.782983	+	0.622043i	$0.213697\pi$
$600$	0.114121	0.00465898
$601$	−1.00000	−0.0407909
$601$	−1.00000	−0.0407909
$602$	31.3074	1.27600
$603$	32.1423	1.30894
$604$	19.7353	0.803020
$605$	16.4712	0.669649
$606$	0.516676	0.0209885
$607$	28.1729	1.14350	0.571752	−	0.820426i	$-0.306264\pi$
$607$	28.1729	1.14350	0.571752	+	0.820426i	$0.306264\pi$
$608$	6.74923	0.273717
$609$	−1.28256	−0.0519720
$610$	0.516042	0.0208939
$611$	−20.8013	−0.841532
$612$	12.5050	0.505487
$613$	−15.0292	−0.607022	−0.303511	−	0.952828i	$-0.598159\pi$
$613$	−15.0292	−0.607022	−0.303511	+	0.952828i	$0.598159\pi$
$614$	−1.15501	−0.0466125
$615$	0.692421	0.0279211
$616$	−17.5055	−0.705318
$617$	−24.9867	−1.00593	−0.502963	−	0.864308i	$-0.667757\pi$
$617$	−24.9867	−1.00593	−0.502963	+	0.864308i	$0.667757\pi$
$618$	−1.17248	−0.0471641
$619$	−33.9400	−1.36416	−0.682081	−	0.731276i	$-0.738925\pi$
$619$	−33.9400	−1.36416	−0.682081	+	0.731276i	$0.738925\pi$
$620$	−0.441736	−0.0177405
$621$	1.09597	0.0439797
$622$	−30.2781	−1.21404
$623$	−48.1260	−1.92813
$624$	0.353631	0.0141566
$625$	1.00000	0.0400000
$626$	30.5559	1.22126
$627$	−4.03700	−0.161222
$628$	−7.47915	−0.298451
$629$	44.4467	1.77221
$630$	−9.97628	−0.397464
$631$	33.3254	1.32666	0.663331	−	0.748326i	$-0.269142\pi$
$631$	33.3254	1.32666	0.663331	+	0.748326i	$0.269142\pi$
$632$	−1.69451	−0.0674038
$633$	−2.18558	−0.0868689
$634$	25.6290	1.01786
$635$	1.49355	0.0592699
$636$	0.551565	0.0218710
$637$	−12.8755	−0.510147
$638$	−17.6365	−0.698238
$639$	31.9607	1.26435
$640$	−1.00000	−0.0395285
$641$	−2.09244	−0.0826463	−0.0413232	−	0.999146i	$-0.513157\pi$
$641$	−2.09244	−0.0826463	−0.0413232	+	0.999146i	$0.513157\pi$
$642$	−1.32350	−0.0522345
$643$	−27.9015	−1.10033	−0.550164	−	0.835057i	$-0.685435\pi$
$643$	−27.9015	−1.10033	−0.550164	+	0.835057i	$0.685435\pi$
$644$	−5.35749	−0.211114
$645$	−1.06974	−0.0421208
$646$	−28.2558	−1.11171
$647$	45.6440	1.79445	0.897225	−	0.441574i	$-0.145580\pi$
$647$	45.6440	1.79445	0.897225	+	0.441574i	$0.145580\pi$
$648$	−8.88296	−0.348956
$649$	23.9329	0.939450
$650$	3.09873	0.121542
$651$	−0.168370	−0.00659895
$652$	6.10593	0.239127
$653$	−2.91517	−0.114080	−0.0570398	−	0.998372i	$-0.518166\pi$
$653$	−2.91517	−0.114080	−0.0570398	+	0.998372i	$0.518166\pi$
$654$	2.09465	0.0819075
$655$	19.4658	0.760591
$656$	−6.06742	−0.236893
$657$	1.45094	0.0566064
$658$	22.4204	0.874040
$659$	34.1301	1.32952	0.664761	−	0.747056i	$-0.268533\pi$
$659$	34.1301	1.32952	0.664761	+	0.747056i	$0.268533\pi$
$660$	0.598143	0.0232827
$661$	−10.2264	−0.397759	−0.198880	−	0.980024i	$-0.563730\pi$
$661$	−10.2264	−0.397759	−0.198880	+	0.980024i	$0.563730\pi$
$662$	9.62489	0.374082
$663$	−1.48048	−0.0574972
$664$	3.83558	0.148849
$665$	22.5419	0.874138
$666$	−31.7116	−1.22880
$667$	−5.39758	−0.208995
$668$	0.0294861	0.00114085
$669$	−1.79798	−0.0695138
$670$	10.7608	0.415727
$671$	2.70473	0.104415
$672$	−0.381156	−0.0147034
$673$	16.1206	0.621402	0.310701	−	0.950508i	$-0.399436\pi$
$673$	16.1206	0.621402	0.310701	+	0.950508i	$0.399436\pi$
$674$	27.8738	1.07366
$675$	0.683240	0.0262979
$676$	−3.39787	−0.130687
$677$	7.86236	0.302175	0.151087	−	0.988520i	$-0.451722\pi$
$677$	7.86236	0.302175	0.151087	+	0.988520i	$0.451722\pi$
$678$	−1.66772	−0.0640485
$679$	11.7019	0.449080
$680$	4.18652	0.160546
$681$	0.800292	0.0306672
$682$	−2.31527	−0.0886562
$683$	3.86788	0.148000	0.0740002	−	0.997258i	$-0.476423\pi$
$683$	3.86788	0.148000	0.0740002	+	0.997258i	$0.476423\pi$
$684$	20.1598	0.770829
$685$	−13.4060	−0.512218
$686$	−9.50176	−0.362779
$687$	2.47336	0.0943647
$688$	9.37370	0.357369
$689$	14.9766	0.570565
$690$	0.183059	0.00696893
$691$	−17.0893	−0.650107	−0.325053	−	0.945696i	$-0.605382\pi$
$691$	−17.0893	−0.650107	−0.325053	+	0.945696i	$0.605382\pi$
$692$	−3.86185	−0.146805
$693$	−52.2886	−1.98628
$694$	−35.7370	−1.35656
$695$	−15.9170	−0.603766
$696$	−0.384009	−0.0145558
$697$	25.4014	0.962147
$698$	−28.4741	−1.07776
$699$	0.754053	0.0285209
$700$	−3.33992	−0.126237
$701$	13.3418	0.503913	0.251956	−	0.967739i	$-0.418926\pi$
$701$	13.3418	0.503913	0.251956	+	0.967739i	$0.418926\pi$
$702$	2.11718	0.0799077
$703$	71.6539	2.70248
$704$	−5.24130	−0.197539
$705$	−0.766079	−0.0288522
$706$	3.64303	0.137107
$707$	−15.1213	−0.568695
$708$	0.521103	0.0195842
$709$	−24.9339	−0.936411	−0.468206	−	0.883620i	$-0.655099\pi$
$709$	−24.9339	−0.936411	−0.468206	+	0.883620i	$0.655099\pi$
$710$	10.7000	0.401565
$711$	−5.06145	−0.189819
$712$	−14.4093	−0.540011
$713$	−0.708577	−0.0265364
$714$	1.59572	0.0597183
$715$	16.2414	0.607392
$716$	16.9854	0.634773
$717$	1.92235	0.0717915
$718$	7.76941	0.289952
$719$	−9.41545	−0.351137	−0.175569	−	0.984467i	$-0.556176\pi$
$719$	−9.41545	−0.351137	−0.175569	+	0.984467i	$0.556176\pi$
$720$	−2.98698	−0.111318
$721$	34.3144	1.27793
$722$	−26.5521	−0.988166
$723$	0.574240	0.0213562
$724$	1.66851	0.0620097
$725$	−3.36492	−0.124970
$726$	1.87971	0.0697626
$727$	−28.9829	−1.07492	−0.537458	−	0.843291i	$-0.680615\pi$
$727$	−28.9829	−1.07492	−0.537458	+	0.843291i	$0.680615\pi$
$728$	−10.3495	−0.383579
$729$	−26.2993	−0.974047
$730$	0.485754	0.0179786
$731$	−39.2432	−1.45146
$732$	0.0588913	0.00217669
$733$	10.0242	0.370254	0.185127	−	0.982715i	$-0.440730\pi$
$733$	10.0242	0.370254	0.185127	+	0.982715i	$0.440730\pi$
$734$	18.6049	0.686720
$735$	−0.474184	−0.0174906
$736$	−1.60407	−0.0591269
$737$	56.4007	2.07755
$738$	−18.1232	−0.667126
$739$	51.2762	1.88623	0.943113	−	0.332473i	$-0.107883\pi$
$739$	51.2762	1.88623	0.943113	+	0.332473i	$0.107883\pi$
$740$	−10.6166	−0.390274
$741$	−2.38673	−0.0876788
$742$	−16.1424	−0.592605
$743$	31.5196	1.15634	0.578170	−	0.815916i	$-0.303767\pi$
$743$	31.5196	1.15634	0.578170	+	0.815916i	$0.303767\pi$
$744$	−0.0504114	−0.00184817
$745$	15.0650	0.551937
$746$	23.9607	0.877262
$747$	11.4568	0.419181
$748$	21.9428	0.802309
$749$	38.7343	1.41532
$750$	0.114121	0.00416711
$751$	−8.43372	−0.307751	−0.153875	−	0.988090i	$-0.549175\pi$
$751$	−8.43372	−0.307751	−0.153875	+	0.988090i	$0.549175\pi$
$752$	6.71286	0.244793
$753$	3.23734	0.117975
$754$	−10.4270	−0.379728
$755$	19.7353	0.718243
$756$	−2.28197	−0.0829945
$757$	40.0196	1.45454	0.727269	−	0.686353i	$-0.240789\pi$
$757$	40.0196	1.45454	0.727269	+	0.686353i	$0.240789\pi$
$758$	−38.1452	−1.38550
$759$	0.959465	0.0348264
$760$	6.74923	0.244820
$761$	−22.4436	−0.813579	−0.406789	−	0.913522i	$-0.633352\pi$
$761$	−22.4436	−0.813579	−0.406789	+	0.913522i	$0.633352\pi$
$762$	0.170446	0.00617461
$763$	−61.3032	−2.21932
$764$	−0.177226	−0.00641181
$765$	12.5050	0.452121
$766$	12.7531	0.460787
$767$	14.1495	0.510909
$768$	−0.114121	−0.00411799
$769$	−18.6723	−0.673340	−0.336670	−	0.941623i	$-0.609301\pi$
$769$	−18.6723	−0.673340	−0.336670	+	0.941623i	$0.609301\pi$
$770$	−17.5055	−0.630856
$771$	1.79291	0.0645702
$772$	−15.6013	−0.561502
$773$	18.8841	0.679214	0.339607	−	0.940568i	$-0.389706\pi$
$773$	18.8841	0.679214	0.339607	+	0.940568i	$0.389706\pi$
$774$	27.9990	1.00640
$775$	−0.441736	−0.0158676
$776$	3.50366	0.125774
$777$	−4.04659	−0.145170
$778$	−12.9134	−0.462968
$779$	40.9504	1.46720
$780$	0.353631	0.0126620
$781$	56.0820	2.00677
$782$	6.71549	0.240146
$783$	−2.29905	−0.0821614
$784$	4.15510	0.148396
$785$	−7.47915	−0.266942
$786$	2.22146	0.0792368
$787$	4.23439	0.150940	0.0754698	−	0.997148i	$-0.475954\pi$
$787$	4.23439	0.150940	0.0754698	+	0.997148i	$0.475954\pi$
$788$	−1.93090	−0.0687855
$789$	−2.30928	−0.0822124
$790$	−1.69451	−0.0602878
$791$	48.8084	1.73543
$792$	−15.6556	−0.556298
$793$	1.59908	0.0567848
$794$	24.9881	0.886794
$795$	0.551565	0.0195620
$796$	−18.2112	−0.645478
$797$	13.3380	0.472456	0.236228	−	0.971698i	$-0.424089\pi$
$797$	13.3380	0.472456	0.236228	+	0.971698i	$0.424089\pi$
$798$	2.57251	0.0910658
$799$	−28.1036	−0.994232
$800$	−1.00000	−0.0353553
$801$	−43.0402	−1.52075
$802$	18.3131	0.646657
$803$	2.54598	0.0898457
$804$	1.22804	0.0433095
$805$	−5.35749	−0.188827
$806$	−1.36882	−0.0482146
$807$	1.79112	0.0630502
$808$	−4.52744	−0.159275
$809$	6.96257	0.244791	0.122395	−	0.992481i	$-0.460942\pi$
$809$	6.96257	0.244791	0.122395	+	0.992481i	$0.460942\pi$
$810$	−8.88296	−0.312115
$811$	−7.31299	−0.256794	−0.128397	−	0.991723i	$-0.540983\pi$
$811$	−7.31299	−0.256794	−0.128397	+	0.991723i	$0.540983\pi$
$812$	11.2386	0.394397
$813$	2.21827	0.0777981
$814$	−55.6448	−1.95035
$815$	6.10593	0.213881
$816$	0.477771	0.0167253
$817$	−63.2652	−2.21337
$818$	−22.5235	−0.787514
$819$	−30.9138	−1.08022
$820$	−6.06742	−0.211883
$821$	0.738510	0.0257742	0.0128871	−	0.999917i	$-0.495898\pi$
$821$	0.738510	0.0257742	0.0128871	+	0.999917i	$0.495898\pi$
$822$	−1.52991	−0.0533618
$823$	−2.62706	−0.0915736	−0.0457868	−	0.998951i	$-0.514579\pi$
$823$	−2.62706	−0.0915736	−0.0457868	+	0.998951i	$0.514579\pi$
$824$	10.2740	0.357912
$825$	0.598143	0.0208247
$826$	−15.2508	−0.530645
$827$	−17.4289	−0.606063	−0.303032	−	0.952980i	$-0.597999\pi$
$827$	−17.4289	−0.606063	−0.303032	+	0.952980i	$0.597999\pi$
$828$	−4.79133	−0.166510
$829$	−10.9568	−0.380545	−0.190272	−	0.981731i	$-0.560937\pi$
$829$	−10.9568	−0.380545	−0.190272	+	0.981731i	$0.560937\pi$
$830$	3.83558	0.133135
$831$	1.43347	0.0497267
$832$	−3.09873	−0.107429
$833$	−17.3954	−0.602715
$834$	−1.81646	−0.0628990
$835$	0.0294861	0.00102041
$836$	35.3747	1.22346
$837$	−0.301812	−0.0104321
$838$	−0.779377	−0.0269231
$839$	4.88152	0.168529	0.0842644	−	0.996443i	$-0.473146\pi$
$839$	4.88152	0.168529	0.0842644	+	0.996443i	$0.473146\pi$
$840$	−0.381156	−0.0131511
$841$	−17.6773	−0.609562
$842$	−9.33481	−0.321699
$843$	2.87024	0.0988562
$844$	19.1514	0.659218
$845$	−3.39787	−0.116890
$846$	20.0512	0.689373
$847$	−55.0125	−1.89025
$848$	−4.83315	−0.165971
$849$	−0.565734	−0.0194159
$850$	4.18652	0.143597
$851$	−17.0298	−0.583775
$852$	1.22110	0.0418342
$853$	−4.52653	−0.154985	−0.0774927	−	0.996993i	$-0.524691\pi$
$853$	−4.52653	−0.154985	−0.0774927	+	0.996993i	$0.524691\pi$
$854$	−1.72354	−0.0589784
$855$	20.1598	0.689450
$856$	11.5974	0.396390
$857$	44.9424	1.53520	0.767601	−	0.640928i	$-0.221450\pi$
$857$	44.9424	1.53520	0.767601	+	0.640928i	$0.221450\pi$
$858$	1.85348	0.0632768
$859$	4.72350	0.161164	0.0805818	−	0.996748i	$-0.474322\pi$
$859$	4.72350	0.161164	0.0805818	+	0.996748i	$0.474322\pi$
$860$	9.37370	0.319640
$861$	−2.31263	−0.0788143
$862$	19.8753	0.676955
$863$	−25.1850	−0.857309	−0.428654	−	0.903469i	$-0.641012\pi$
$863$	−25.1850	−0.857309	−0.428654	+	0.903469i	$0.641012\pi$
$864$	−0.683240	−0.0232443
$865$	−3.86185	−0.131307
$866$	−9.71413	−0.330100
$867$	−0.0601404	−0.00204247
$868$	1.47536	0.0500771
$869$	−8.88140	−0.301281
$870$	−0.384009	−0.0130191
$871$	33.3449	1.12985
$872$	−18.3547	−0.621567
$873$	10.4653	0.354198
$874$	10.8263	0.366204
$875$	−3.33992	−0.112910
$876$	0.0554348	0.00187297
$877$	3.68367	0.124389	0.0621943	−	0.998064i	$-0.480190\pi$
$877$	3.68367	0.124389	0.0621943	+	0.998064i	$0.480190\pi$
$878$	−3.48523	−0.117621
$879$	−3.04149	−0.102587
$880$	−5.24130	−0.176684
$881$	−56.1306	−1.89109	−0.945545	−	0.325493i	$-0.894470\pi$
$881$	−56.1306	−1.89109	−0.945545	+	0.325493i	$0.894470\pi$
$882$	12.4112	0.417906
$883$	−53.4082	−1.79733	−0.898664	−	0.438637i	$-0.855461\pi$
$883$	−53.4082	−1.79733	−0.898664	+	0.438637i	$0.855461\pi$
$884$	12.9729	0.436326
$885$	0.521103	0.0175167
$886$	29.6965	0.997672
$887$	4.95925	0.166515	0.0832576	−	0.996528i	$-0.473468\pi$
$887$	4.95925	0.166515	0.0832576	+	0.996528i	$0.473468\pi$
$888$	−1.21158	−0.0406580
$889$	−4.98836	−0.167304
$890$	−14.4093	−0.483001
$891$	−46.5582	−1.55976
$892$	15.7550	0.527516
$893$	−45.3066	−1.51613
$894$	1.71923	0.0574996
$895$	16.9854	0.567758
$896$	3.33992	0.111579
$897$	0.567250	0.0189399
$898$	−0.199613	−0.00666117
$899$	1.48641	0.0495744
$900$	−2.98698	−0.0995659
$901$	20.2341	0.674096
$902$	−31.8011	−1.05886
$903$	3.57284	0.118897
$904$	14.6136	0.486042
$905$	1.66851	0.0554632
$906$	2.25222	0.0748250
$907$	6.17315	0.204976	0.102488	−	0.994734i	$-0.467320\pi$
$907$	6.17315	0.204976	0.102488	+	0.994734i	$0.467320\pi$
$908$	−7.01265	−0.232723
$909$	−13.5233	−0.448541
$910$	−10.3495	−0.343083
$911$	−22.1554	−0.734043	−0.367021	−	0.930213i	$-0.619622\pi$
$911$	−22.1554	−0.734043	−0.367021	+	0.930213i	$0.619622\pi$
$912$	0.770230	0.0255048
$913$	20.1034	0.665325
$914$	22.7704	0.753179
$915$	0.0588913	0.00194689
$916$	−21.6731	−0.716101
$917$	−65.0143	−2.14696
$918$	2.86040	0.0944074
$919$	30.1164	0.993449	0.496725	−	0.867908i	$-0.334536\pi$
$919$	30.1164	0.993449	0.496725	+	0.867908i	$0.334536\pi$
$920$	−1.60407	−0.0528847
$921$	−0.131811	−0.00434333
$922$	−1.61692	−0.0532505
$923$	33.1565	1.09136
$924$	−1.99775	−0.0657212
$925$	−10.6166	−0.349072
$926$	11.0006	0.361502
$927$	30.6882	1.00793
$928$	3.36492	0.110459
$929$	−1.75026	−0.0574243	−0.0287121	−	0.999588i	$-0.509141\pi$
$929$	−1.75026	−0.0574243	−0.0287121	+	0.999588i	$0.509141\pi$
$930$	−0.0504114	−0.00165305
$931$	−28.0437	−0.919095
$932$	−6.60748	−0.216435
$933$	−3.45537	−0.113124
$934$	5.43687	0.177900
$935$	21.9428	0.717607
$936$	−9.25583	−0.302536
$937$	−9.80089	−0.320181	−0.160091	−	0.987102i	$-0.551179\pi$
$937$	−9.80089	−0.320181	−0.160091	+	0.987102i	$0.551179\pi$
$938$	−35.9403	−1.17349
$939$	3.48708	0.113796
$940$	6.71286	0.218949
$941$	−52.7958	−1.72109	−0.860547	−	0.509371i	$-0.829878\pi$
$941$	−52.7958	−1.72109	−0.860547	+	0.509371i	$0.829878\pi$
$942$	−0.853529	−0.0278095
$943$	−9.73259	−0.316937
$944$	−4.56623	−0.148618
$945$	−2.28197	−0.0742325
$946$	49.1303	1.59736
$947$	24.0076	0.780141	0.390070	−	0.920785i	$-0.372451\pi$
$947$	24.0076	0.780141	0.390070	+	0.920785i	$0.372451\pi$
$948$	−0.193379	−0.00628065
$949$	1.50522	0.0488615
$950$	6.74923	0.218974
$951$	2.92481	0.0948435
$952$	−13.9827	−0.453181
$953$	−27.8344	−0.901644	−0.450822	−	0.892614i	$-0.648869\pi$
$953$	−27.8344	−0.901644	−0.450822	+	0.892614i	$0.648869\pi$
$954$	−14.4365	−0.467400
$955$	−0.177226	−0.00573489
$956$	−16.8448	−0.544801
$957$	−2.01270	−0.0650614
$958$	13.8636	0.447912
$959$	44.7751	1.44586
$960$	−0.114121	−0.00368324
$961$	−30.8049	−0.993705
$962$	−32.8980	−1.06067
$963$	34.6410	1.11629
$964$	−5.03185	−0.162065
$965$	−15.6013	−0.502222
$966$	−0.611402	−0.0196715
$967$	−22.2759	−0.716346	−0.358173	−	0.933655i	$-0.616600\pi$
$967$	−22.2759	−0.716346	−0.358173	+	0.933655i	$0.616600\pi$
$968$	−16.4712	−0.529404
$969$	−3.22458	−0.103589
$970$	3.50366	0.112496
$971$	25.4970	0.818238	0.409119	−	0.912481i	$-0.365836\pi$
$971$	25.4970	0.818238	0.409119	+	0.912481i	$0.365836\pi$
$972$	−3.06345	−0.0982604
$973$	53.1615	1.70428
$974$	39.7045	1.27222
$975$	0.353631	0.0113252
$976$	−0.516042	−0.0165181
$977$	31.5418	1.00911	0.504556	−	0.863379i	$-0.331656\pi$
$977$	31.5418	1.00911	0.504556	+	0.863379i	$0.331656\pi$
$978$	0.696815	0.0222817
$979$	−75.5234	−2.41374
$980$	4.15510	0.132730
$981$	−54.8249	−1.75043
$982$	18.4431	0.588544
$983$	−38.4491	−1.22634	−0.613168	−	0.789953i	$-0.710105\pi$
$983$	−38.4491	−1.22634	−0.613168	+	0.789953i	$0.710105\pi$
$984$	−0.692421	−0.0220736
$985$	−1.93090	−0.0615237
$986$	−14.0873	−0.448632
$987$	2.55865	0.0814426
$988$	20.9140	0.665364
$989$	15.0361	0.478120
$990$	−15.6556	−0.497568
$991$	−32.3357	−1.02718	−0.513589	−	0.858036i	$-0.671684\pi$
$991$	−32.3357	−1.02718	−0.513589	+	0.858036i	$0.671684\pi$
$992$	0.441736	0.0140251
$993$	1.09840	0.0348568
$994$	−35.7373	−1.13352
$995$	−18.2112	−0.577333
$996$	0.437720	0.0138697
$997$	−57.0232	−1.80594	−0.902971	−	0.429701i	$-0.858619\pi$
$997$	−57.0232	−1.80594	−0.902971	+	0.429701i	$0.858619\pi$
$998$	−4.50989	−0.142758
$999$	−7.25370	−0.229497

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6010.2.a.g.1.13	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6010.2.a.g.1.13	✓	27	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:	\( N \)	\(=\)	\( 6010 = 2 \cdot 5 \cdot 601 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6010.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.114121 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.114121 q^{6} -3.33992 q^{7} -1.00000 q^{8} -2.98698 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.114121 q^{3} +1.00000 q^{4} +1.00000 q^{5} +0.114121 q^{6} -3.33992 q^{7} -1.00000 q^{8} -2.98698 q^{9} -1.00000 q^{10} -5.24130 q^{11} -0.114121 q^{12} -3.09873 q^{13} +3.33992 q^{14} -0.114121 q^{15} +1.00000 q^{16} -4.18652 q^{17} +2.98698 q^{18} -6.74923 q^{19} +1.00000 q^{20} +0.381156 q^{21} +5.24130 q^{22} +1.60407 q^{23} +0.114121 q^{24} +1.00000 q^{25} +3.09873 q^{26} +0.683240 q^{27} -3.33992 q^{28} -3.36492 q^{29} +0.114121 q^{30} -0.441736 q^{31} -1.00000 q^{32} +0.598143 q^{33} +4.18652 q^{34} -3.33992 q^{35} -2.98698 q^{36} -10.6166 q^{37} +6.74923 q^{38} +0.353631 q^{39} -1.00000 q^{40} -6.06742 q^{41} -0.381156 q^{42} +9.37370 q^{43} -5.24130 q^{44} -2.98698 q^{45} -1.60407 q^{46} +6.71286 q^{47} -0.114121 q^{48} +4.15510 q^{49} -1.00000 q^{50} +0.477771 q^{51} -3.09873 q^{52} -4.83315 q^{53} -0.683240 q^{54} -5.24130 q^{55} +3.33992 q^{56} +0.770230 q^{57} +3.36492 q^{58} -4.56623 q^{59} -0.114121 q^{60} -0.516042 q^{61} +0.441736 q^{62} +9.97628 q^{63} +1.00000 q^{64} -3.09873 q^{65} -0.598143 q^{66} -10.7608 q^{67} -4.18652 q^{68} -0.183059 q^{69} +3.33992 q^{70} -10.7000 q^{71} +2.98698 q^{72} -0.485754 q^{73} +10.6166 q^{74} -0.114121 q^{75} -6.74923 q^{76} +17.5055 q^{77} -0.353631 q^{78} +1.69451 q^{79} +1.00000 q^{80} +8.88296 q^{81} +6.06742 q^{82} -3.83558 q^{83} +0.381156 q^{84} -4.18652 q^{85} -9.37370 q^{86} +0.384009 q^{87} +5.24130 q^{88} +14.4093 q^{89} +2.98698 q^{90} +10.3495 q^{91} +1.60407 q^{92} +0.0504114 q^{93} -6.71286 q^{94} -6.74923 q^{95} +0.114121 q^{96} -3.50366 q^{97} -4.15510 q^{98} +15.6556 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9	\( 27 q - 27 q^{2} + 6 q^{3} + 27 q^{4} + 27 q^{5} - 6 q^{6} - 27 q^{8} + 37 q^{9} - 27 q^{10} + 18 q^{11} + 6 q^{12} - 6 q^{13} + 6 q^{15} + 27 q^{16} + 3 q^{17} - 37 q^{18} + 27 q^{19} + 27 q^{20} + 16 q^{21} - 18 q^{22} + 15 q^{23} - 6 q^{24} + 27 q^{25} + 6 q^{26} + 27 q^{27} + 25 q^{29} - 6 q^{30} + 9 q^{31} - 27 q^{32} + 11 q^{33} - 3 q^{34} + 37 q^{36} - 16 q^{37} - 27 q^{38} + 20 q^{39} - 27 q^{40} + 39 q^{41} - 16 q^{42} + 9 q^{43} + 18 q^{44} + 37 q^{45} - 15 q^{46} + 31 q^{47} + 6 q^{48} + 27 q^{49} - 27 q^{50} + 39 q^{51} - 6 q^{52} - 5 q^{53} - 27 q^{54} + 18 q^{55} - 10 q^{57} - 25 q^{58} + 46 q^{59} + 6 q^{60} + 18 q^{61} - 9 q^{62} + 23 q^{63} + 27 q^{64} - 6 q^{65} - 11 q^{66} + 11 q^{67} + 3 q^{68} + 17 q^{69} + 50 q^{71} - 37 q^{72} - 29 q^{73} + 16 q^{74} + 6 q^{75} + 27 q^{76} - 6 q^{77} - 20 q^{78} + 56 q^{79} + 27 q^{80} + 51 q^{81} - 39 q^{82} + 44 q^{83} + 16 q^{84} + 3 q^{85} - 9 q^{86} + 42 q^{87} - 18 q^{88} + 34 q^{89} - 37 q^{90} + 43 q^{91} + 15 q^{92} - 20 q^{93} - 31 q^{94} + 27 q^{95} - 6 q^{96} - 37 q^{97} - 27 q^{98} + 67 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 6 * q^3 + 27 * q^4 + 27 * q^5 - 6 * q^6 - 27 * q^8 + 37 * q^9 - 27 * q^10 + 18 * q^11 + 6 * q^12 - 6 * q^13 + 6 * q^15 + 27 * q^16 + 3 * q^17 - 37 * q^18 + 27 * q^19 + 27 * q^20 + 16 * q^21 - 18 * q^22 + 15 * q^23 - 6 * q^24 + 27 * q^25 + 6 * q^26 + 27 * q^27 + 25 * q^29 - 6 * q^30 + 9 * q^31 - 27 * q^32 + 11 * q^33 - 3 * q^34 + 37 * q^36 - 16 * q^37 - 27 * q^38 + 20 * q^39 - 27 * q^40 + 39 * q^41 - 16 * q^42 + 9 * q^43 + 18 * q^44 + 37 * q^45 - 15 * q^46 + 31 * q^47 + 6 * q^48 + 27 * q^49 - 27 * q^50 + 39 * q^51 - 6 * q^52 - 5 * q^53 - 27 * q^54 + 18 * q^55 - 10 * q^57 - 25 * q^58 + 46 * q^59 + 6 * q^60 + 18 * q^61 - 9 * q^62 + 23 * q^63 + 27 * q^64 - 6 * q^65 - 11 * q^66 + 11 * q^67 + 3 * q^68 + 17 * q^69 + 50 * q^71 - 37 * q^72 - 29 * q^73 + 16 * q^74 + 6 * q^75 + 27 * q^76 - 6 * q^77 - 20 * q^78 + 56 * q^79 + 27 * q^80 + 51 * q^81 - 39 * q^82 + 44 * q^83 + 16 * q^84 + 3 * q^85 - 9 * q^86 + 42 * q^87 - 18 * q^88 + 34 * q^89 - 37 * q^90 + 43 * q^91 + 15 * q^92 - 20 * q^93 - 31 * q^94 + 27 * q^95 - 6 * q^96 - 37 * q^97 - 27 * q^98 + 67 * q^99

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