LMFDB - Embedded newform 6015.2.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$0$
Dimension:	$31$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.16128 q^{2} -1.00000 q^{3} +2.67112 q^{4} -1.00000 q^{5} +2.16128 q^{6} +1.73409 q^{7} -1.45047 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.16128 q^{2} -1.00000 q^{3} +2.67112 q^{4} -1.00000 q^{5} +2.16128 q^{6} +1.73409 q^{7} -1.45047 q^{8} +1.00000 q^{9} +2.16128 q^{10} +1.46726 q^{11} -2.67112 q^{12} -3.78453 q^{13} -3.74784 q^{14} +1.00000 q^{15} -2.20737 q^{16} +1.43835 q^{17} -2.16128 q^{18} +4.88932 q^{19} -2.67112 q^{20} -1.73409 q^{21} -3.17115 q^{22} +9.37705 q^{23} +1.45047 q^{24} +1.00000 q^{25} +8.17942 q^{26} -1.00000 q^{27} +4.63195 q^{28} -3.85468 q^{29} -2.16128 q^{30} -2.26495 q^{31} +7.67167 q^{32} -1.46726 q^{33} -3.10868 q^{34} -1.73409 q^{35} +2.67112 q^{36} +9.68494 q^{37} -10.5672 q^{38} +3.78453 q^{39} +1.45047 q^{40} +2.12847 q^{41} +3.74784 q^{42} -6.66770 q^{43} +3.91921 q^{44} -1.00000 q^{45} -20.2664 q^{46} +6.36209 q^{47} +2.20737 q^{48} -3.99294 q^{49} -2.16128 q^{50} -1.43835 q^{51} -10.1089 q^{52} -4.69219 q^{53} +2.16128 q^{54} -1.46726 q^{55} -2.51524 q^{56} -4.88932 q^{57} +8.33102 q^{58} +4.27963 q^{59} +2.67112 q^{60} -6.46259 q^{61} +4.89517 q^{62} +1.73409 q^{63} -12.1659 q^{64} +3.78453 q^{65} +3.17115 q^{66} +3.94579 q^{67} +3.84201 q^{68} -9.37705 q^{69} +3.74784 q^{70} +5.41881 q^{71} -1.45047 q^{72} +6.88669 q^{73} -20.9318 q^{74} -1.00000 q^{75} +13.0599 q^{76} +2.54435 q^{77} -8.17942 q^{78} +2.38280 q^{79} +2.20737 q^{80} +1.00000 q^{81} -4.60020 q^{82} +10.8433 q^{83} -4.63195 q^{84} -1.43835 q^{85} +14.4108 q^{86} +3.85468 q^{87} -2.12821 q^{88} +5.53179 q^{89} +2.16128 q^{90} -6.56271 q^{91} +25.0472 q^{92} +2.26495 q^{93} -13.7502 q^{94} -4.88932 q^{95} -7.67167 q^{96} -7.80584 q^{97} +8.62984 q^{98} +1.46726 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) $ 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - 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 $

$2$	−2.16128	−1.52825	−0.764127	−	0.645066i	$-0.776830\pi$
$2$	−2.16128	−1.52825	−0.764127	+	0.645066i	$0.776830\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	2.67112	1.33556
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	2.16128	0.882337
$7$	1.73409	0.655424	0.327712	−	0.944778i	$-0.393722\pi$
$7$	1.73409	0.655424	0.327712	+	0.944778i	$0.393722\pi$
$8$	−1.45047	−0.512818
$9$	1.00000	0.333333
$10$	2.16128	0.683456
$11$	1.46726	0.442394	0.221197	−	0.975229i	$-0.429004\pi$
$11$	1.46726	0.442394	0.221197	+	0.975229i	$0.429004\pi$
$12$	−2.67112	−0.771085
$13$	−3.78453	−1.04964	−0.524820	−	0.851213i	$-0.675867\pi$
$13$	−3.78453	−1.04964	−0.524820	+	0.851213i	$0.675867\pi$
$14$	−3.74784	−1.00165
$15$	1.00000	0.258199
$16$	−2.20737	−0.551842
$17$	1.43835	0.348852	0.174426	−	0.984670i	$-0.444193\pi$
$17$	1.43835	0.348852	0.174426	+	0.984670i	$0.444193\pi$
$18$	−2.16128	−0.509418
$19$	4.88932	1.12169	0.560843	−	0.827922i	$-0.310477\pi$
$19$	4.88932	1.12169	0.560843	+	0.827922i	$0.310477\pi$
$20$	−2.67112	−0.597280
$21$	−1.73409	−0.378409
$22$	−3.17115	−0.676091
$23$	9.37705	1.95525	0.977625	−	0.210353i	$-0.0674614\pi$
$23$	9.37705	1.95525	0.977625	+	0.210353i	$0.0674614\pi$
$24$	1.45047	0.296076
$25$	1.00000	0.200000
$26$	8.17942	1.60412
$27$	−1.00000	−0.192450
$28$	4.63195	0.875357
$29$	−3.85468	−0.715795	−0.357898	−	0.933761i	$-0.616506\pi$
$29$	−3.85468	−0.715795	−0.357898	+	0.933761i	$0.616506\pi$
$30$	−2.16128	−0.394593
$31$	−2.26495	−0.406796	−0.203398	−	0.979096i	$-0.565199\pi$
$31$	−2.26495	−0.406796	−0.203398	+	0.979096i	$0.565199\pi$
$32$	7.67167	1.35617
$33$	−1.46726	−0.255416
$34$	−3.10868	−0.533135
$35$	−1.73409	−0.293114
$36$	2.67112	0.445186
$37$	9.68494	1.59219	0.796097	−	0.605169i	$-0.206895\pi$
$37$	9.68494	1.59219	0.796097	+	0.605169i	$0.206895\pi$
$38$	−10.5672	−1.71422
$39$	3.78453	0.606010
$40$	1.45047	0.229339
$41$	2.12847	0.332411	0.166205	−	0.986091i	$-0.446849\pi$
$41$	2.12847	0.332411	0.166205	+	0.986091i	$0.446849\pi$
$42$	3.74784	0.578305
$43$	−6.66770	−1.01682	−0.508408	−	0.861117i	$-0.669766\pi$
$43$	−6.66770	−1.01682	−0.508408	+	0.861117i	$0.669766\pi$
$44$	3.91921	0.590843
$45$	−1.00000	−0.149071
$46$	−20.2664	−2.98812
$47$	6.36209	0.928006	0.464003	−	0.885833i	$-0.346413\pi$
$47$	6.36209	0.928006	0.464003	+	0.885833i	$0.346413\pi$
$48$	2.20737	0.318606
$49$	−3.99294	−0.570420
$50$	−2.16128	−0.305651
$51$	−1.43835	−0.201410
$52$	−10.1089	−1.40186
$53$	−4.69219	−0.644522	−0.322261	−	0.946651i	$-0.604443\pi$
$53$	−4.69219	−0.644522	−0.322261	+	0.946651i	$0.604443\pi$
$54$	2.16128	0.294112
$55$	−1.46726	−0.197845
$56$	−2.51524	−0.336113
$57$	−4.88932	−0.647606
$58$	8.33102	1.09392
$59$	4.27963	0.557160	0.278580	−	0.960413i	$-0.410136\pi$
$59$	4.27963	0.557160	0.278580	+	0.960413i	$0.410136\pi$
$60$	2.67112	0.344840
$61$	−6.46259	−0.827450	−0.413725	−	0.910402i	$-0.635772\pi$
$61$	−6.46259	−0.827450	−0.413725	+	0.910402i	$0.635772\pi$
$62$	4.89517	0.621688
$63$	1.73409	0.218475
$64$	−12.1659	−1.52073
$65$	3.78453	0.469413
$66$	3.17115	0.390341
$67$	3.94579	0.482055	0.241027	−	0.970518i	$-0.422516\pi$
$67$	3.94579	0.482055	0.241027	+	0.970518i	$0.422516\pi$
$68$	3.84201	0.465913
$69$	−9.37705	−1.12886
$70$	3.74784	0.447953
$71$	5.41881	0.643094	0.321547	−	0.946894i	$-0.395797\pi$
$71$	5.41881	0.643094	0.321547	+	0.946894i	$0.395797\pi$
$72$	−1.45047	−0.170939
$73$	6.88669	0.806026	0.403013	−	0.915194i	$-0.367963\pi$
$73$	6.88669	0.806026	0.403013	+	0.915194i	$0.367963\pi$
$74$	−20.9318	−2.43328
$75$	−1.00000	−0.115470
$76$	13.0599	1.49808
$77$	2.54435	0.289956
$78$	−8.17942	−0.926137
$79$	2.38280	0.268086	0.134043	−	0.990976i	$-0.457204\pi$
$79$	2.38280	0.268086	0.134043	+	0.990976i	$0.457204\pi$
$80$	2.20737	0.246791
$81$	1.00000	0.111111
$82$	−4.60020	−0.508008
$83$	10.8433	1.19021	0.595103	−	0.803650i	$-0.297111\pi$
$83$	10.8433	1.19021	0.595103	+	0.803650i	$0.297111\pi$
$84$	−4.63195	−0.505387
$85$	−1.43835	−0.156011
$86$	14.4108	1.55395
$87$	3.85468	0.413265
$88$	−2.12821	−0.226868
$89$	5.53179	0.586368	0.293184	−	0.956056i	$-0.405285\pi$
$89$	5.53179	0.586368	0.293184	+	0.956056i	$0.405285\pi$
$90$	2.16128	0.227819
$91$	−6.56271	−0.687959
$92$	25.0472	2.61135
$93$	2.26495	0.234864
$94$	−13.7502	−1.41823
$95$	−4.88932	−0.501633
$96$	−7.67167	−0.782987
$97$	−7.80584	−0.792563	−0.396282	−	0.918129i	$-0.629700\pi$
$97$	−7.80584	−0.792563	−0.396282	+	0.918129i	$0.629700\pi$
$98$	8.62984	0.871746
$99$	1.46726	0.147465
$100$	2.67112	0.267112
$101$	−15.2977	−1.52217	−0.761087	−	0.648650i	$-0.775334\pi$
$101$	−15.2977	−1.52217	−0.761087	+	0.648650i	$0.775334\pi$
$102$	3.10868	0.307805
$103$	10.2147	1.00648	0.503242	−	0.864145i	$-0.332140\pi$
$103$	10.2147	1.00648	0.503242	+	0.864145i	$0.332140\pi$
$104$	5.48934	0.538274
$105$	1.73409	0.169230
$106$	10.1411	0.984993
$107$	10.9395	1.05756	0.528780	−	0.848759i	$-0.322650\pi$
$107$	10.9395	1.05756	0.528780	+	0.848759i	$0.322650\pi$
$108$	−2.67112	−0.257028
$109$	9.57301	0.916928	0.458464	−	0.888713i	$-0.348400\pi$
$109$	9.57301	0.916928	0.458464	+	0.888713i	$0.348400\pi$
$110$	3.17115	0.302357
$111$	−9.68494	−0.919254
$112$	−3.82777	−0.361691
$113$	14.7317	1.38584	0.692922	−	0.721013i	$-0.256323\pi$
$113$	14.7317	1.38584	0.692922	+	0.721013i	$0.256323\pi$
$114$	10.5672	0.989706
$115$	−9.37705	−0.874415
$116$	−10.2963	−0.955987
$117$	−3.78453	−0.349880
$118$	−9.24946	−0.851482
$119$	2.49423	0.228646
$120$	−1.45047	−0.132409
$121$	−8.84716	−0.804287
$122$	13.9674	1.26455
$123$	−2.12847	−0.191917
$124$	−6.04993	−0.543300
$125$	−1.00000	−0.0894427
$126$	−3.74784	−0.333884
$127$	1.25177	0.111077	0.0555384	−	0.998457i	$-0.482312\pi$
$127$	1.25177	0.111077	0.0555384	+	0.998457i	$0.482312\pi$
$128$	10.9505	0.967893
$129$	6.66770	0.587059
$130$	−8.17942	−0.717382
$131$	21.2019	1.85242	0.926209	−	0.377010i	$-0.123048\pi$
$131$	21.2019	1.85242	0.926209	+	0.377010i	$0.123048\pi$
$132$	−3.91921	−0.341124
$133$	8.47851	0.735180
$134$	−8.52794	−0.736702
$135$	1.00000	0.0860663
$136$	−2.08629	−0.178898
$137$	−3.47971	−0.297292	−0.148646	−	0.988891i	$-0.547491\pi$
$137$	−3.47971	−0.297292	−0.148646	+	0.988891i	$0.547491\pi$
$138$	20.2664	1.72519
$139$	4.29329	0.364152	0.182076	−	0.983284i	$-0.441718\pi$
$139$	4.29329	0.364152	0.182076	+	0.983284i	$0.441718\pi$
$140$	−4.63195	−0.391471
$141$	−6.36209	−0.535785
$142$	−11.7115	−0.982811
$143$	−5.55287	−0.464355
$144$	−2.20737	−0.183947
$145$	3.85468	0.320113
$146$	−14.8840	−1.23181
$147$	3.99294	0.329332
$148$	25.8696	2.12647
$149$	−5.45364	−0.446779	−0.223390	−	0.974729i	$-0.571712\pi$
$149$	−5.45364	−0.446779	−0.223390	+	0.974729i	$0.571712\pi$
$150$	2.16128	0.176467
$151$	−15.1934	−1.23642	−0.618210	−	0.786013i	$-0.712142\pi$
$151$	−15.1934	−1.23642	−0.618210	+	0.786013i	$0.712142\pi$
$152$	−7.09180	−0.575221
$153$	1.43835	0.116284
$154$	−5.49905	−0.443126
$155$	2.26495	0.181925
$156$	10.1089	0.809362
$157$	−11.7719	−0.939500	−0.469750	−	0.882800i	$-0.655656\pi$
$157$	−11.7719	−0.939500	−0.469750	+	0.882800i	$0.655656\pi$
$158$	−5.14989	−0.409703
$159$	4.69219	0.372115
$160$	−7.67167	−0.606499
$161$	16.2606	1.28152
$162$	−2.16128	−0.169806
$163$	−16.7493	−1.31191	−0.655954	−	0.754800i	$-0.727734\pi$
$163$	−16.7493	−1.31191	−0.655954	+	0.754800i	$0.727734\pi$
$164$	5.68538	0.443954
$165$	1.46726	0.114226
$166$	−23.4353	−1.81894
$167$	2.45463	0.189945	0.0949723	−	0.995480i	$-0.469724\pi$
$167$	2.45463	0.189945	0.0949723	+	0.995480i	$0.469724\pi$
$168$	2.51524	0.194055
$169$	1.32267	0.101744
$170$	3.10868	0.238425
$171$	4.88932	0.373895
$172$	−17.8102	−1.35802
$173$	−21.6863	−1.64878	−0.824391	−	0.566021i	$-0.808482\pi$
$173$	−21.6863	−1.64878	−0.824391	+	0.566021i	$0.808482\pi$
$174$	−8.33102	−0.631573
$175$	1.73409	0.131085
$176$	−3.23878	−0.244132
$177$	−4.27963	−0.321677
$178$	−11.9557	−0.896119
$179$	−8.30344	−0.620628	−0.310314	−	0.950634i	$-0.600434\pi$
$179$	−8.30344	−0.620628	−0.310314	+	0.950634i	$0.600434\pi$
$180$	−2.67112	−0.199093
$181$	−21.7053	−1.61335	−0.806673	−	0.590999i	$-0.798734\pi$
$181$	−21.7053	−1.61335	−0.806673	+	0.590999i	$0.798734\pi$
$182$	14.1838	1.05138
$183$	6.46259	0.477728
$184$	−13.6011	−1.00269
$185$	−9.68494	−0.712051
$186$	−4.89517	−0.358932
$187$	2.11043	0.154330
$188$	16.9939	1.23941
$189$	−1.73409	−0.126136
$190$	10.5672	0.766623
$191$	1.82914	0.132352	0.0661761	−	0.997808i	$-0.478920\pi$
$191$	1.82914	0.132352	0.0661761	+	0.997808i	$0.478920\pi$
$192$	12.1659	0.877996
$193$	−5.62783	−0.405100	−0.202550	−	0.979272i	$-0.564923\pi$
$193$	−5.62783	−0.405100	−0.202550	+	0.979272i	$0.564923\pi$
$194$	16.8706	1.21124
$195$	−3.78453	−0.271016
$196$	−10.6656	−0.761829
$197$	0.670297	0.0477567	0.0238783	−	0.999715i	$-0.492399\pi$
$197$	0.670297	0.0477567	0.0238783	+	0.999715i	$0.492399\pi$
$198$	−3.17115	−0.225364
$199$	−19.6246	−1.39115	−0.695574	−	0.718455i	$-0.744850\pi$
$199$	−19.6246	−1.39115	−0.695574	+	0.718455i	$0.744850\pi$
$200$	−1.45047	−0.102564
$201$	−3.94579	−0.278315
$202$	33.0625	2.32627
$203$	−6.68435	−0.469149
$204$	−3.84201	−0.268995
$205$	−2.12847	−0.148659
$206$	−22.0768	−1.53816
$207$	9.37705	0.651750
$208$	8.35386	0.579236
$209$	7.17388	0.496228
$210$	−3.74784	−0.258626
$211$	−3.87576	−0.266818	−0.133409	−	0.991061i	$-0.542592\pi$
$211$	−3.87576	−0.266818	−0.133409	+	0.991061i	$0.542592\pi$
$212$	−12.5334	−0.860797
$213$	−5.41881	−0.371290
$214$	−23.6433	−1.61622
$215$	6.66770	0.454734
$216$	1.45047	0.0986919
$217$	−3.92762	−0.266624
$218$	−20.6899	−1.40130
$219$	−6.88669	−0.465359
$220$	−3.91921	−0.264233
$221$	−5.44350	−0.366169
$222$	20.9318	1.40485
$223$	2.78451	0.186465	0.0932323	−	0.995644i	$-0.470280\pi$
$223$	2.78451	0.186465	0.0932323	+	0.995644i	$0.470280\pi$
$224$	13.3034	0.888868
$225$	1.00000	0.0666667
$226$	−31.8393	−2.11792
$227$	−4.17814	−0.277313	−0.138656	−	0.990341i	$-0.544278\pi$
$227$	−4.17814	−0.277313	−0.138656	+	0.990341i	$0.544278\pi$
$228$	−13.0599	−0.864915
$229$	2.69921	0.178369	0.0891843	−	0.996015i	$-0.471574\pi$
$229$	2.69921	0.178369	0.0891843	+	0.996015i	$0.471574\pi$
$230$	20.2664	1.33633
$231$	−2.54435	−0.167406
$232$	5.59109	0.367073
$233$	−14.2719	−0.934986	−0.467493	−	0.883997i	$-0.654843\pi$
$233$	−14.2719	−0.934986	−0.467493	+	0.883997i	$0.654843\pi$
$234$	8.17942	0.534705
$235$	−6.36209	−0.415017
$236$	11.4314	0.744120
$237$	−2.38280	−0.154779
$238$	−5.39073	−0.349429
$239$	8.39634	0.543114	0.271557	−	0.962422i	$-0.412461\pi$
$239$	8.39634	0.543114	0.271557	+	0.962422i	$0.412461\pi$
$240$	−2.20737	−0.142485
$241$	26.1048	1.68156	0.840779	−	0.541378i	$-0.182097\pi$
$241$	26.1048	1.68156	0.840779	+	0.541378i	$0.182097\pi$
$242$	19.1212	1.22915
$243$	−1.00000	−0.0641500
$244$	−17.2623	−1.10511
$245$	3.99294	0.255099
$246$	4.60020	0.293298
$247$	−18.5038	−1.17737
$248$	3.28523	0.208612
$249$	−10.8433	−0.687165
$250$	2.16128	0.136691
$251$	−1.24994	−0.0788956	−0.0394478	−	0.999222i	$-0.512560\pi$
$251$	−1.24994	−0.0788956	−0.0394478	+	0.999222i	$0.512560\pi$
$252$	4.63195	0.291786
$253$	13.7585	0.864992
$254$	−2.70542	−0.169753
$255$	1.43835	0.0900733
$256$	0.664761	0.0415476
$257$	11.6070	0.724024	0.362012	−	0.932173i	$-0.382090\pi$
$257$	11.6070	0.724024	0.362012	+	0.932173i	$0.382090\pi$
$258$	−14.4108	−0.897174
$259$	16.7945	1.04356
$260$	10.1089	0.626929
$261$	−3.85468	−0.238598
$262$	−45.8232	−2.83096
$263$	12.1310	0.748028	0.374014	−	0.927423i	$-0.377981\pi$
$263$	12.1310	0.748028	0.374014	+	0.927423i	$0.377981\pi$
$264$	2.12821	0.130982
$265$	4.69219	0.288239
$266$	−18.3244	−1.12354
$267$	−5.53179	−0.338540
$268$	10.5397	0.643812
$269$	−16.5817	−1.01100	−0.505501	−	0.862826i	$-0.668692\pi$
$269$	−16.5817	−1.01100	−0.505501	+	0.862826i	$0.668692\pi$
$270$	−2.16128	−0.131531
$271$	3.32316	0.201868	0.100934	−	0.994893i	$-0.467817\pi$
$271$	3.32316	0.201868	0.100934	+	0.994893i	$0.467817\pi$
$272$	−3.17498	−0.192511
$273$	6.56271	0.397193
$274$	7.52061	0.454337
$275$	1.46726	0.0884789
$276$	−25.0472	−1.50766
$277$	−7.22662	−0.434205	−0.217103	−	0.976149i	$-0.569661\pi$
$277$	−7.22662	−0.434205	−0.217103	+	0.976149i	$0.569661\pi$
$278$	−9.27898	−0.556516
$279$	−2.26495	−0.135599
$280$	2.51524	0.150314
$281$	−15.4179	−0.919757	−0.459878	−	0.887982i	$-0.652107\pi$
$281$	−15.4179	−0.919757	−0.459878	+	0.887982i	$0.652107\pi$
$282$	13.7502	0.818815
$283$	24.7772	1.47285	0.736426	−	0.676518i	$-0.236512\pi$
$283$	24.7772	1.47285	0.736426	+	0.676518i	$0.236512\pi$
$284$	14.4743	0.858890
$285$	4.88932	0.289618
$286$	12.0013	0.709652
$287$	3.69095	0.217870
$288$	7.67167	0.452058
$289$	−14.9311	−0.878302
$290$	−8.33102	−0.489214
$291$	7.80584	0.457587
$292$	18.3951	1.07649
$293$	28.3158	1.65423	0.827115	−	0.562033i	$-0.189981\pi$
$293$	28.3158	1.65423	0.827115	+	0.562033i	$0.189981\pi$
$294$	−8.62984	−0.503303
$295$	−4.27963	−0.249170
$296$	−14.0477	−0.816506
$297$	−1.46726	−0.0851388
$298$	11.7868	0.682792
$299$	−35.4877	−2.05231
$300$	−2.67112	−0.154217
$301$	−11.5624	−0.666445
$302$	32.8371	1.88956
$303$	15.2977	0.878827
$304$	−10.7925	−0.618994
$305$	6.46259	0.370047
$306$	−3.10868	−0.177712
$307$	24.7001	1.40971	0.704856	−	0.709351i	$-0.251012\pi$
$307$	24.7001	1.40971	0.704856	+	0.709351i	$0.251012\pi$
$308$	6.79626	0.387253
$309$	−10.2147	−0.581094
$310$	−4.89517	−0.278027
$311$	13.3910	0.759331	0.379666	−	0.925124i	$-0.376039\pi$
$311$	13.3910	0.759331	0.379666	+	0.925124i	$0.376039\pi$
$312$	−5.48934	−0.310773
$313$	22.4249	1.26753	0.633766	−	0.773525i	$-0.281508\pi$
$313$	22.4249	1.26753	0.633766	+	0.773525i	$0.281508\pi$
$314$	25.4423	1.43579
$315$	−1.73409	−0.0977048
$316$	6.36474	0.358044
$317$	6.14926	0.345377	0.172688	−	0.984977i	$-0.444755\pi$
$317$	6.14926	0.345377	0.172688	+	0.984977i	$0.444755\pi$
$318$	−10.1411	−0.568686
$319$	−5.65580	−0.316664
$320$	12.1659	0.680093
$321$	−10.9395	−0.610582
$322$	−35.1437	−1.95848
$323$	7.03257	0.391303
$324$	2.67112	0.148395
$325$	−3.78453	−0.209928
$326$	36.1999	2.00493
$327$	−9.57301	−0.529388
$328$	−3.08727	−0.170466
$329$	11.0324	0.608237
$330$	−3.17115	−0.174566
$331$	−13.5035	−0.742222	−0.371111	−	0.928589i	$-0.621023\pi$
$331$	−13.5035	−0.742222	−0.371111	+	0.928589i	$0.621023\pi$
$332$	28.9637	1.58959
$333$	9.68494	0.530731
$334$	−5.30513	−0.290284
$335$	−3.94579	−0.215582
$336$	3.82777	0.208822
$337$	−30.6719	−1.67081	−0.835403	−	0.549638i	$-0.814766\pi$
$337$	−30.6719	−1.67081	−0.835403	+	0.549638i	$0.814766\pi$
$338$	−2.85866	−0.155491
$339$	−14.7317	−0.800117
$340$	−3.84201	−0.208362
$341$	−3.32326	−0.179964
$342$	−10.5672	−0.571407
$343$	−19.0627	−1.02929
$344$	9.67130	0.521441
$345$	9.37705	0.504844
$346$	46.8702	2.51976
$347$	−5.03964	−0.270542	−0.135271	−	0.990809i	$-0.543191\pi$
$347$	−5.03964	−0.270542	−0.135271	+	0.990809i	$0.543191\pi$
$348$	10.2963	0.551939
$349$	3.39438	0.181697	0.0908486	−	0.995865i	$-0.471042\pi$
$349$	3.39438	0.181697	0.0908486	+	0.995865i	$0.471042\pi$
$350$	−3.74784	−0.200331
$351$	3.78453	0.202003
$352$	11.2563	0.599963
$353$	0.261961	0.0139428	0.00697139	−	0.999976i	$-0.497781\pi$
$353$	0.261961	0.0139428	0.00697139	+	0.999976i	$0.497781\pi$
$354$	9.24946	0.491603
$355$	−5.41881	−0.287600
$356$	14.7760	0.783129
$357$	−2.49423	−0.132009
$358$	17.9460	0.948477
$359$	12.3418	0.651373	0.325686	−	0.945478i	$-0.394405\pi$
$359$	12.3418	0.651373	0.325686	+	0.945478i	$0.394405\pi$
$360$	1.45047	0.0764464
$361$	4.90542	0.258180
$362$	46.9112	2.46560
$363$	8.84716	0.464355
$364$	−17.5298	−0.918809
$365$	−6.88669	−0.360466
$366$	−13.9674	−0.730090
$367$	−14.7838	−0.771707	−0.385854	−	0.922560i	$-0.626093\pi$
$367$	−14.7838	−0.771707	−0.385854	+	0.922560i	$0.626093\pi$
$368$	−20.6986	−1.07899
$369$	2.12847	0.110804
$370$	20.9318	1.08819
$371$	−8.13668	−0.422435
$372$	6.04993	0.313675
$373$	−12.2676	−0.635194	−0.317597	−	0.948226i	$-0.602876\pi$
$373$	−12.2676	−0.635194	−0.317597	+	0.948226i	$0.602876\pi$
$374$	−4.56123	−0.235856
$375$	1.00000	0.0516398
$376$	−9.22801	−0.475899
$377$	14.5881	0.751327
$378$	3.74784	0.192768
$379$	13.1139	0.673615	0.336807	−	0.941574i	$-0.390653\pi$
$379$	13.1139	0.673615	0.336807	+	0.941574i	$0.390653\pi$
$380$	−13.0599	−0.669961
$381$	−1.25177	−0.0641302
$382$	−3.95328	−0.202268
$383$	33.1942	1.69614	0.848071	−	0.529882i	$-0.177764\pi$
$383$	33.1942	1.69614	0.848071	+	0.529882i	$0.177764\pi$
$384$	−10.9505	−0.558813
$385$	−2.54435	−0.129672
$386$	12.1633	0.619096
$387$	−6.66770	−0.338938
$388$	−20.8503	−1.05851
$389$	−26.6819	−1.35283	−0.676414	−	0.736522i	$-0.736467\pi$
$389$	−26.6819	−1.35283	−0.676414	+	0.736522i	$0.736467\pi$
$390$	8.17942	0.414181
$391$	13.4875	0.682094
$392$	5.79163	0.292522
$393$	−21.2019	−1.06949
$394$	−1.44870	−0.0729843
$395$	−2.38280	−0.119892
$396$	3.91921	0.196948
$397$	7.40781	0.371787	0.185894	−	0.982570i	$-0.440482\pi$
$397$	7.40781	0.371787	0.185894	+	0.982570i	$0.440482\pi$
$398$	42.4141	2.12603
$399$	−8.47851	−0.424456
$400$	−2.20737	−0.110368
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	8.52794	0.425335
$403$	8.57176	0.426990
$404$	−40.8618	−2.03295
$405$	−1.00000	−0.0496904
$406$	14.4467	0.716979
$407$	14.2103	0.704378
$408$	2.08629	0.103287
$409$	25.0870	1.24047	0.620236	−	0.784415i	$-0.287037\pi$
$409$	25.0870	1.24047	0.620236	+	0.784415i	$0.287037\pi$
$410$	4.60020	0.227188
$411$	3.47971	0.171641
$412$	27.2847	1.34422
$413$	7.42126	0.365176
$414$	−20.2664	−0.996040
$415$	−10.8433	−0.532276
$416$	−29.0337	−1.42349
$417$	−4.29329	−0.210243
$418$	−15.5047	−0.758361
$419$	−8.51772	−0.416118	−0.208059	−	0.978116i	$-0.566715\pi$
$419$	−8.51772	−0.416118	−0.208059	+	0.978116i	$0.566715\pi$
$420$	4.63195	0.226016
$421$	29.5362	1.43951	0.719753	−	0.694230i	$-0.244255\pi$
$421$	29.5362	1.43951	0.719753	+	0.694230i	$0.244255\pi$
$422$	8.37658	0.407766
$423$	6.36209	0.309335
$424$	6.80588	0.330523
$425$	1.43835	0.0697705
$426$	11.7115	0.567426
$427$	−11.2067	−0.542330
$428$	29.2206	1.41243
$429$	5.55287	0.268095
$430$	−14.4108	−0.694948
$431$	25.0438	1.20632	0.603158	−	0.797621i	$-0.293909\pi$
$431$	25.0438	1.20632	0.603158	+	0.797621i	$0.293909\pi$
$432$	2.20737	0.106202
$433$	−9.83298	−0.472543	−0.236271	−	0.971687i	$-0.575925\pi$
$433$	−9.83298	−0.472543	−0.236271	+	0.971687i	$0.575925\pi$
$434$	8.48866	0.407469
$435$	−3.85468	−0.184818
$436$	25.5706	1.22461
$437$	45.8474	2.19318
$438$	14.8840	0.711187
$439$	10.0707	0.480650	0.240325	−	0.970693i	$-0.422746\pi$
$439$	10.0707	0.480650	0.240325	+	0.970693i	$0.422746\pi$
$440$	2.12821	0.101458
$441$	−3.99294	−0.190140
$442$	11.7649	0.559599
$443$	10.1325	0.481409	0.240705	−	0.970598i	$-0.422621\pi$
$443$	10.1325	0.481409	0.240705	+	0.970598i	$0.422621\pi$
$444$	−25.8696	−1.22772
$445$	−5.53179	−0.262232
$446$	−6.01810	−0.284965
$447$	5.45364	0.257948
$448$	−21.0967	−0.996725
$449$	−1.36431	−0.0643856	−0.0321928	−	0.999482i	$-0.510249\pi$
$449$	−1.36431	−0.0643856	−0.0321928	+	0.999482i	$0.510249\pi$
$450$	−2.16128	−0.101884
$451$	3.12300	0.147057
$452$	39.3501	1.85088
$453$	15.1934	0.713847
$454$	9.03012	0.423804
$455$	6.56271	0.307665
$456$	7.09180	0.332104
$457$	32.0728	1.50030	0.750151	−	0.661266i	$-0.229981\pi$
$457$	32.0728	1.50030	0.750151	+	0.661266i	$0.229981\pi$
$458$	−5.83373	−0.272592
$459$	−1.43835	−0.0671367
$460$	−25.0472	−1.16783
$461$	1.15322	0.0537110	0.0268555	−	0.999639i	$-0.491451\pi$
$461$	1.15322	0.0537110	0.0268555	+	0.999639i	$0.491451\pi$
$462$	5.49905	0.255839
$463$	30.6892	1.42625	0.713125	−	0.701037i	$-0.247279\pi$
$463$	30.6892	1.42625	0.713125	+	0.701037i	$0.247279\pi$
$464$	8.50869	0.395006
$465$	−2.26495	−0.105034
$466$	30.8456	1.42890
$467$	7.56028	0.349848	0.174924	−	0.984582i	$-0.444032\pi$
$467$	7.56028	0.349848	0.174924	+	0.984582i	$0.444032\pi$
$468$	−10.1089	−0.467285
$469$	6.84235	0.315950
$470$	13.7502	0.634251
$471$	11.7719	0.542420
$472$	−6.20747	−0.285722
$473$	−9.78323	−0.449833
$474$	5.14989	0.236542
$475$	4.88932	0.224337
$476$	6.66239	0.305370
$477$	−4.69219	−0.214841
$478$	−18.1468	−0.830016
$479$	−3.16556	−0.144638	−0.0723190	−	0.997382i	$-0.523040\pi$
$479$	−3.16556	−0.144638	−0.0723190	+	0.997382i	$0.523040\pi$
$480$	7.67167	0.350162
$481$	−36.6529	−1.67123
$482$	−56.4197	−2.56985
$483$	−16.2606	−0.739885
$484$	−23.6318	−1.07417
$485$	7.80584	0.354445
$486$	2.16128	0.0980375
$487$	−3.69689	−0.167522	−0.0837610	−	0.996486i	$-0.526693\pi$
$487$	−3.69689	−0.167522	−0.0837610	+	0.996486i	$0.526693\pi$
$488$	9.37378	0.424331
$489$	16.7493	0.757431
$490$	−8.62984	−0.389857
$491$	−36.9143	−1.66592	−0.832959	−	0.553334i	$-0.813355\pi$
$491$	−36.9143	−1.66592	−0.832959	+	0.553334i	$0.813355\pi$
$492$	−5.68538	−0.256317
$493$	−5.54439	−0.249707
$494$	39.9918	1.79931
$495$	−1.46726	−0.0659482
$496$	4.99957	0.224487
$497$	9.39669	0.421499
$498$	23.4353	1.05016
$499$	22.5138	1.00786	0.503928	−	0.863746i	$-0.331888\pi$
$499$	22.5138	1.00786	0.503928	+	0.863746i	$0.331888\pi$
$500$	−2.67112	−0.119456
$501$	−2.45463	−0.109665
$502$	2.70147	0.120573
$503$	−0.289489	−0.0129077	−0.00645383	−	0.999979i	$-0.502054\pi$
$503$	−0.289489	−0.0129077	−0.00645383	+	0.999979i	$0.502054\pi$
$504$	−2.51524	−0.112038
$505$	15.2977	0.680737
$506$	−29.7360	−1.32193
$507$	−1.32267	−0.0587419
$508$	3.34363	0.148349
$509$	−3.08467	−0.136726	−0.0683628	−	0.997661i	$-0.521778\pi$
$509$	−3.08467	−0.136726	−0.0683628	+	0.997661i	$0.521778\pi$
$510$	−3.10868	−0.137655
$511$	11.9421	0.528288
$512$	−23.3377	−1.03139
$513$	−4.88932	−0.215869
$514$	−25.0859	−1.10649
$515$	−10.2147	−0.450114
$516$	17.8102	0.784051
$517$	9.33482	0.410545
$518$	−36.2976	−1.59483
$519$	21.6863	0.951924
$520$	−5.48934	−0.240724
$521$	−10.6663	−0.467298	−0.233649	−	0.972321i	$-0.575067\pi$
$521$	−10.6663	−0.467298	−0.233649	+	0.972321i	$0.575067\pi$
$522$	8.33102	0.364639
$523$	−1.67295	−0.0731528	−0.0365764	−	0.999331i	$-0.511645\pi$
$523$	−1.67295	−0.0731528	−0.0365764	+	0.999331i	$0.511645\pi$
$524$	56.6327	2.47401
$525$	−1.73409	−0.0756818
$526$	−26.2184	−1.14318
$527$	−3.25780	−0.141912
$528$	3.23878	0.140950
$529$	64.9291	2.82301
$530$	−10.1411	−0.440502
$531$	4.27963	0.185720
$532$	22.6471	0.981875
$533$	−8.05525	−0.348911
$534$	11.9557	0.517375
$535$	−10.9395	−0.472955
$536$	−5.72324	−0.247206
$537$	8.30344	0.358320
$538$	35.8376	1.54507
$539$	−5.85866	−0.252350
$540$	2.67112	0.114947
$541$	−2.74992	−0.118228	−0.0591142	−	0.998251i	$-0.518828\pi$
$541$	−2.74992	−0.118228	−0.0591142	+	0.998251i	$0.518828\pi$
$542$	−7.18227	−0.308505
$543$	21.7053	0.931465
$544$	11.0346	0.473104
$545$	−9.57301	−0.410063
$546$	−14.1838	−0.607012
$547$	−7.01498	−0.299939	−0.149970	−	0.988691i	$-0.547918\pi$
$547$	−7.01498	−0.299939	−0.149970	+	0.988691i	$0.547918\pi$
$548$	−9.29471	−0.397050
$549$	−6.46259	−0.275817
$550$	−3.17115	−0.135218
$551$	−18.8467	−0.802898
$552$	13.6011	0.578902
$553$	4.13199	0.175710
$554$	15.6187	0.663576
$555$	9.68494	0.411103
$556$	11.4679	0.486346
$557$	−20.5557	−0.870973	−0.435487	−	0.900195i	$-0.643424\pi$
$557$	−20.5557	−0.870973	−0.435487	+	0.900195i	$0.643424\pi$
$558$	4.89517	0.207229
$559$	25.2341	1.06729
$560$	3.82777	0.161753
$561$	−2.11043	−0.0891026
$562$	33.3224	1.40562
$563$	13.2380	0.557917	0.278959	−	0.960303i	$-0.410011\pi$
$563$	13.2380	0.557917	0.278959	+	0.960303i	$0.410011\pi$
$564$	−16.9939	−0.715572
$565$	−14.7317	−0.619768
$566$	−53.5504	−2.25089
$567$	1.73409	0.0728249
$568$	−7.85981	−0.329790
$569$	17.7682	0.744882	0.372441	−	0.928056i	$-0.378521\pi$
$569$	17.7682	0.744882	0.372441	+	0.928056i	$0.378521\pi$
$570$	−10.5672	−0.442610
$571$	12.0849	0.505738	0.252869	−	0.967500i	$-0.418626\pi$
$571$	12.0849	0.505738	0.252869	+	0.967500i	$0.418626\pi$
$572$	−14.8324	−0.620173
$573$	−1.82914	−0.0764135
$574$	−7.97716	−0.332960
$575$	9.37705	0.391050
$576$	−12.1659	−0.506911
$577$	−17.9924	−0.749032	−0.374516	−	0.927220i	$-0.622191\pi$
$577$	−17.9924	−0.749032	−0.374516	+	0.927220i	$0.622191\pi$
$578$	32.2703	1.34227
$579$	5.62783	0.233885
$580$	10.2963	0.427530
$581$	18.8032	0.780089
$582$	−16.8706	−0.699308
$583$	−6.88465	−0.285133
$584$	−9.98892	−0.413345
$585$	3.78453	0.156471
$586$	−61.1984	−2.52808
$587$	−13.8033	−0.569725	−0.284862	−	0.958568i	$-0.591948\pi$
$587$	−13.8033	−0.569725	−0.284862	+	0.958568i	$0.591948\pi$
$588$	10.6656	0.439842
$589$	−11.0740	−0.456298
$590$	9.24946	0.380794
$591$	−0.670297	−0.0275723
$592$	−21.3782	−0.878640
$593$	−8.66374	−0.355777	−0.177889	−	0.984051i	$-0.556927\pi$
$593$	−8.66374	−0.355777	−0.177889	+	0.984051i	$0.556927\pi$
$594$	3.17115	0.130114
$595$	−2.49423	−0.102254
$596$	−14.5673	−0.596700
$597$	19.6246	0.803180
$598$	76.6988	3.13645
$599$	1.18985	0.0486161	0.0243081	−	0.999705i	$-0.492262\pi$
$599$	1.18985	0.0486161	0.0243081	+	0.999705i	$0.492262\pi$
$600$	1.45047	0.0592151
$601$	−6.17245	−0.251780	−0.125890	−	0.992044i	$-0.540179\pi$
$601$	−6.17245	−0.251780	−0.125890	+	0.992044i	$0.540179\pi$
$602$	24.9895	1.01850
$603$	3.94579	0.160685
$604$	−40.5833	−1.65131
$605$	8.84716	0.359688
$606$	−33.0625	−1.34307
$607$	29.8469	1.21145	0.605725	−	0.795674i	$-0.292883\pi$
$607$	29.8469	1.21145	0.605725	+	0.795674i	$0.292883\pi$
$608$	37.5092	1.52120
$609$	6.68435	0.270863
$610$	−13.9674	−0.565525
$611$	−24.0775	−0.974073
$612$	3.84201	0.155304
$613$	−17.4093	−0.703154	−0.351577	−	0.936159i	$-0.614354\pi$
$613$	−17.4093	−0.703154	−0.351577	+	0.936159i	$0.614354\pi$
$614$	−53.3838	−2.15440
$615$	2.12847	0.0858280
$616$	−3.69050	−0.148695
$617$	−25.0324	−1.00777	−0.503883	−	0.863772i	$-0.668096\pi$
$617$	−25.0324	−1.00777	−0.503883	+	0.863772i	$0.668096\pi$
$618$	22.0768	0.888059
$619$	38.8436	1.56125	0.780627	−	0.624997i	$-0.214900\pi$
$619$	38.8436	1.56125	0.780627	+	0.624997i	$0.214900\pi$
$620$	6.04993	0.242971
$621$	−9.37705	−0.376288
$622$	−28.9416	−1.16045
$623$	9.59261	0.384320
$624$	−8.35386	−0.334422
$625$	1.00000	0.0400000
$626$	−48.4665	−1.93711
$627$	−7.17388	−0.286497
$628$	−31.4441	−1.25476
$629$	13.9304	0.555440
$630$	3.74784	0.149318
$631$	−31.0277	−1.23519	−0.617597	−	0.786494i	$-0.711894\pi$
$631$	−31.0277	−1.23519	−0.617597	+	0.786494i	$0.711894\pi$
$632$	−3.45618	−0.137479
$633$	3.87576	0.154047
$634$	−13.2903	−0.527823
$635$	−1.25177	−0.0496750
$636$	12.5334	0.496981
$637$	15.1114	0.598735
$638$	12.2237	0.483943
$639$	5.41881	0.214365
$640$	−10.9505	−0.432855
$641$	−27.1423	−1.07206	−0.536029	−	0.844200i	$-0.680076\pi$
$641$	−27.1423	−1.07206	−0.536029	+	0.844200i	$0.680076\pi$
$642$	23.6433	0.933125
$643$	−5.51909	−0.217652	−0.108826	−	0.994061i	$-0.534709\pi$
$643$	−5.51909	−0.217652	−0.108826	+	0.994061i	$0.534709\pi$
$644$	43.4341	1.71154
$645$	−6.66770	−0.262541
$646$	−15.1993	−0.598010
$647$	33.5986	1.32090	0.660449	−	0.750871i	$-0.270366\pi$
$647$	33.5986	1.32090	0.660449	+	0.750871i	$0.270366\pi$
$648$	−1.45047	−0.0569798
$649$	6.27931	0.246485
$650$	8.17942	0.320823
$651$	3.92762	0.153935
$652$	−44.7394	−1.75213
$653$	7.44032	0.291162	0.145581	−	0.989346i	$-0.453495\pi$
$653$	7.44032	0.291162	0.145581	+	0.989346i	$0.453495\pi$
$654$	20.6899	0.809040
$655$	−21.2019	−0.828427
$656$	−4.69831	−0.183438
$657$	6.88669	0.268675
$658$	−23.8441	−0.929541
$659$	17.5457	0.683482	0.341741	−	0.939794i	$-0.388983\pi$
$659$	17.5457	0.683482	0.341741	+	0.939794i	$0.388983\pi$
$660$	3.91921	0.152555
$661$	14.2527	0.554368	0.277184	−	0.960817i	$-0.410599\pi$
$661$	14.2527	0.554368	0.277184	+	0.960817i	$0.410599\pi$
$662$	29.1849	1.13430
$663$	5.44350	0.211408
$664$	−15.7278	−0.610359
$665$	−8.47851	−0.328782
$666$	−20.9318	−0.811092
$667$	−36.1455	−1.39956
$668$	6.55659	0.253682
$669$	−2.78451	−0.107655
$670$	8.52794	0.329463
$671$	−9.48227	−0.366059
$672$	−13.3034	−0.513188
$673$	42.0222	1.61984	0.809918	−	0.586544i	$-0.199512\pi$
$673$	42.0222	1.61984	0.809918	+	0.586544i	$0.199512\pi$
$674$	66.2905	2.55341
$675$	−1.00000	−0.0384900
$676$	3.53301	0.135885
$677$	32.6685	1.25555	0.627777	−	0.778393i	$-0.283965\pi$
$677$	32.6685	1.25555	0.627777	+	0.778393i	$0.283965\pi$
$678$	31.8393	1.22278
$679$	−13.5360	−0.519465
$680$	2.08629	0.0800055
$681$	4.17814	0.160107
$682$	7.18247	0.275031
$683$	37.7010	1.44259	0.721294	−	0.692629i	$-0.243548\pi$
$683$	37.7010	1.44259	0.721294	+	0.692629i	$0.243548\pi$
$684$	13.0599	0.499359
$685$	3.47971	0.132953
$686$	41.1998	1.57302
$687$	−2.69921	−0.102981
$688$	14.7181	0.561122
$689$	17.7577	0.676516
$690$	−20.2664	−0.771529
$691$	−2.55332	−0.0971327	−0.0485663	−	0.998820i	$-0.515465\pi$
$691$	−2.55332	−0.0971327	−0.0485663	+	0.998820i	$0.515465\pi$
$692$	−57.9267	−2.20204
$693$	2.54435	0.0966519
$694$	10.8921	0.413457
$695$	−4.29329	−0.162854
$696$	−5.59109	−0.211930
$697$	3.06149	0.115962
$698$	−7.33620	−0.277679
$699$	14.2719	0.539814
$700$	4.63195	0.175071
$701$	15.0691	0.569151	0.284575	−	0.958654i	$-0.408147\pi$
$701$	15.0691	0.569151	0.284575	+	0.958654i	$0.408147\pi$
$702$	−8.17942	−0.308712
$703$	47.3527	1.78594
$704$	−17.8504	−0.672764
$705$	6.36209	0.239610
$706$	−0.566171	−0.0213081
$707$	−26.5275	−0.997669
$708$	−11.4314	−0.429618
$709$	24.8341	0.932663	0.466331	−	0.884610i	$-0.345575\pi$
$709$	24.8341	0.932663	0.466331	+	0.884610i	$0.345575\pi$
$710$	11.7115	0.439526
$711$	2.38280	0.0893620
$712$	−8.02368	−0.300700
$713$	−21.2385	−0.795389
$714$	5.39073	0.201743
$715$	5.55287	0.207666
$716$	−22.1794	−0.828885
$717$	−8.39634	−0.313567
$718$	−26.6739	−0.995463
$719$	16.2615	0.606451	0.303226	−	0.952919i	$-0.401936\pi$
$719$	16.2615	0.606451	0.303226	+	0.952919i	$0.401936\pi$
$720$	2.20737	0.0822638
$721$	17.7132	0.659674
$722$	−10.6020	−0.394564
$723$	−26.1048	−0.970848
$724$	−57.9775	−2.15472
$725$	−3.85468	−0.143159
$726$	−19.1212	−0.709653
$727$	−15.1582	−0.562187	−0.281094	−	0.959680i	$-0.590697\pi$
$727$	−15.1582	−0.562187	−0.281094	+	0.959680i	$0.590697\pi$
$728$	9.51900	0.352798
$729$	1.00000	0.0370370
$730$	14.8840	0.550883
$731$	−9.59052	−0.354718
$732$	17.2623	0.638034
$733$	−23.3407	−0.862110	−0.431055	−	0.902326i	$-0.641859\pi$
$733$	−23.3407	−0.862110	−0.431055	+	0.902326i	$0.641859\pi$
$734$	31.9519	1.17936
$735$	−3.99294	−0.147282
$736$	71.9377	2.65166
$737$	5.78948	0.213258
$738$	−4.60020	−0.169336
$739$	22.8102	0.839087	0.419543	−	0.907735i	$-0.362190\pi$
$739$	22.8102	0.839087	0.419543	+	0.907735i	$0.362190\pi$
$740$	−25.8696	−0.950985
$741$	18.5038	0.679753
$742$	17.5856	0.645588
$743$	43.0465	1.57922	0.789612	−	0.613607i	$-0.210282\pi$
$743$	43.0465	1.57922	0.789612	+	0.613607i	$0.210282\pi$
$744$	−3.28523	−0.120442
$745$	5.45364	0.199806
$746$	26.5137	0.970737
$747$	10.8433	0.396735
$748$	5.63722	0.206117
$749$	18.9700	0.693150
$750$	−2.16128	−0.0789187
$751$	−12.5165	−0.456735	−0.228368	−	0.973575i	$-0.573339\pi$
$751$	−12.5165	−0.456735	−0.228368	+	0.973575i	$0.573339\pi$
$752$	−14.0435	−0.512113
$753$	1.24994	0.0455504
$754$	−31.5290	−1.14822
$755$	15.1934	0.552944
$756$	−4.63195	−0.168462
$757$	−11.6737	−0.424287	−0.212144	−	0.977238i	$-0.568044\pi$
$757$	−11.6737	−0.424287	−0.212144	+	0.977238i	$0.568044\pi$
$758$	−28.3427	−1.02945
$759$	−13.7585	−0.499403
$760$	7.09180	0.257247
$761$	45.9686	1.66636	0.833180	−	0.553001i	$-0.186518\pi$
$761$	45.9686	1.66636	0.833180	+	0.553001i	$0.186518\pi$
$762$	2.70542	0.0980072
$763$	16.6004	0.600976
$764$	4.88585	0.176764
$765$	−1.43835	−0.0520038
$766$	−71.7418	−2.59214
$767$	−16.1964	−0.584818
$768$	−0.664761	−0.0239875
$769$	43.0128	1.55108	0.775541	−	0.631297i	$-0.217477\pi$
$769$	43.0128	1.55108	0.775541	+	0.631297i	$0.217477\pi$
$770$	5.49905	0.198172
$771$	−11.6070	−0.418016
$772$	−15.0326	−0.541035
$773$	19.9909	0.719022	0.359511	−	0.933141i	$-0.382944\pi$
$773$	19.9909	0.719022	0.359511	+	0.933141i	$0.382944\pi$
$774$	14.4108	0.517984
$775$	−2.26495	−0.0813593
$776$	11.3221	0.406441
$777$	−16.7945	−0.602501
$778$	57.6670	2.06746
$779$	10.4067	0.372860
$780$	−10.1089	−0.361957
$781$	7.95078	0.284501
$782$	−29.1503	−1.04241
$783$	3.85468	0.137755
$784$	8.81389	0.314782
$785$	11.7719	0.420157
$786$	45.8232	1.63446
$787$	11.3822	0.405731	0.202866	−	0.979207i	$-0.434975\pi$
$787$	11.3822	0.405731	0.202866	+	0.979207i	$0.434975\pi$
$788$	1.79044	0.0637818
$789$	−12.1310	−0.431874
$790$	5.14989	0.183225
$791$	25.5461	0.908315
$792$	−2.12821	−0.0756226
$793$	24.4579	0.868524
$794$	−16.0103	−0.568185
$795$	−4.69219	−0.166415
$796$	−52.4195	−1.85796
$797$	−8.56035	−0.303223	−0.151612	−	0.988440i	$-0.548446\pi$
$797$	−8.56035	−0.303223	−0.151612	+	0.988440i	$0.548446\pi$
$798$	18.3244	0.648677
$799$	9.15095	0.323737
$800$	7.67167	0.271235
$801$	5.53179	0.195456
$802$	−2.16128	−0.0763173
$803$	10.1045	0.356581
$804$	−10.5397	−0.371705
$805$	−16.2606	−0.573112
$806$	−18.5259	−0.652548
$807$	16.5817	0.583703
$808$	22.1888	0.780598
$809$	−25.9126	−0.911038	−0.455519	−	0.890226i	$-0.650546\pi$
$809$	−25.9126	−0.911038	−0.455519	+	0.890226i	$0.650546\pi$
$810$	2.16128	0.0759395
$811$	20.8674	0.732752	0.366376	−	0.930467i	$-0.380598\pi$
$811$	20.8674	0.732752	0.366376	+	0.930467i	$0.380598\pi$
$812$	−17.8547	−0.626576
$813$	−3.32316	−0.116548
$814$	−30.7123	−1.07647
$815$	16.7493	0.586704
$816$	3.17498	0.111147
$817$	−32.6005	−1.14055
$818$	−54.2199	−1.89576
$819$	−6.56271	−0.229320
$820$	−5.68538	−0.198542
$821$	29.9143	1.04402	0.522008	−	0.852940i	$-0.325183\pi$
$821$	29.9143	1.04402	0.522008	+	0.852940i	$0.325183\pi$
$822$	−7.52061	−0.262311
$823$	51.0480	1.77942	0.889710	−	0.456526i	$-0.150907\pi$
$823$	51.0480	1.77942	0.889710	+	0.456526i	$0.150907\pi$
$824$	−14.8161	−0.516143
$825$	−1.46726	−0.0510833
$826$	−16.0394	−0.558082
$827$	−0.686837	−0.0238837	−0.0119418	−	0.999929i	$-0.503801\pi$
$827$	−0.686837	−0.0238837	−0.0119418	+	0.999929i	$0.503801\pi$
$828$	25.0472	0.870450
$829$	−6.96882	−0.242037	−0.121019	−	0.992650i	$-0.538616\pi$
$829$	−6.96882	−0.242037	−0.121019	+	0.992650i	$0.538616\pi$
$830$	23.4353	0.813453
$831$	7.22662	0.250689
$832$	46.0421	1.59622
$833$	−5.74326	−0.198992
$834$	9.27898	0.321305
$835$	−2.45463	−0.0849458
$836$	19.1623	0.662741
$837$	2.26495	0.0782880
$838$	18.4091	0.635933
$839$	0.812748	0.0280592	0.0140296	−	0.999902i	$-0.495534\pi$
$839$	0.812748	0.0280592	0.0140296	+	0.999902i	$0.495534\pi$
$840$	−2.51524	−0.0867840
$841$	−14.1415	−0.487637
$842$	−63.8359	−2.19993
$843$	15.4179	0.531022
$844$	−10.3526	−0.356351
$845$	−1.32267	−0.0455013
$846$	−13.7502	−0.472743
$847$	−15.3418	−0.527149
$848$	10.3574	0.355675
$849$	−24.7772	−0.850351
$850$	−3.10868	−0.106627
$851$	90.8162	3.11314
$852$	−14.4743	−0.495880
$853$	18.3498	0.628286	0.314143	−	0.949376i	$-0.398283\pi$
$853$	18.3498	0.628286	0.314143	+	0.949376i	$0.398283\pi$
$854$	24.2208	0.828818
$855$	−4.88932	−0.167211
$856$	−15.8674	−0.542336
$857$	40.7743	1.39282	0.696412	−	0.717642i	$-0.254778\pi$
$857$	40.7743	1.39282	0.696412	+	0.717642i	$0.254778\pi$
$858$	−12.0013	−0.409718
$859$	−49.0395	−1.67321	−0.836604	−	0.547809i	$-0.815462\pi$
$859$	−49.0395	−1.67321	−0.836604	+	0.547809i	$0.815462\pi$
$860$	17.8102	0.607323
$861$	−3.69095	−0.125787
$862$	−54.1266	−1.84356
$863$	26.7340	0.910038	0.455019	−	0.890482i	$-0.349633\pi$
$863$	26.7340	0.910038	0.455019	+	0.890482i	$0.349633\pi$
$864$	−7.67167	−0.260996
$865$	21.6863	0.737357
$866$	21.2518	0.722165
$867$	14.9311	0.507088
$868$	−10.4911	−0.356092
$869$	3.49618	0.118600
$870$	8.33102	0.282448
$871$	−14.9330	−0.505984
$872$	−13.8853	−0.470217
$873$	−7.80584	−0.264188
$874$	−99.0889	−3.35173
$875$	−1.73409	−0.0586229
$876$	−18.3951	−0.621514
$877$	−4.89786	−0.165389	−0.0826945	−	0.996575i	$-0.526353\pi$
$877$	−4.89786	−0.165389	−0.0826945	+	0.996575i	$0.526353\pi$
$878$	−21.7656	−0.734554
$879$	−28.3158	−0.955070
$880$	3.23878	0.109179
$881$	−33.7299	−1.13639	−0.568195	−	0.822894i	$-0.692358\pi$
$881$	−33.7299	−1.13639	−0.568195	+	0.822894i	$0.692358\pi$
$882$	8.62984	0.290582
$883$	−8.48746	−0.285626	−0.142813	−	0.989750i	$-0.545615\pi$
$883$	−8.48746	−0.285626	−0.142813	+	0.989750i	$0.545615\pi$
$884$	−14.5402	−0.489040
$885$	4.27963	0.143858
$886$	−21.8991	−0.735715
$887$	−44.7803	−1.50357	−0.751787	−	0.659405i	$-0.770808\pi$
$887$	−44.7803	−1.50357	−0.751787	+	0.659405i	$0.770808\pi$
$888$	14.0477	0.471410
$889$	2.17068	0.0728023
$890$	11.9557	0.400757
$891$	1.46726	0.0491549
$892$	7.43775	0.249034
$893$	31.1063	1.04093
$894$	−11.7868	−0.394210
$895$	8.30344	0.277553
$896$	18.9891	0.634380
$897$	35.4877	1.18490
$898$	2.94864	0.0983974
$899$	8.73063	0.291183
$900$	2.67112	0.0890372
$901$	−6.74904	−0.224843
$902$	−6.74968	−0.224740
$903$	11.5624	0.384772
$904$	−21.3679	−0.710686
$905$	21.7053	0.721510
$906$	−32.8371	−1.09094
$907$	27.7694	0.922068	0.461034	−	0.887382i	$-0.347479\pi$
$907$	27.7694	0.922068	0.461034	+	0.887382i	$0.347479\pi$
$908$	−11.1603	−0.370368
$909$	−15.2977	−0.507391
$910$	−14.1838	−0.470189
$911$	−33.9436	−1.12460	−0.562301	−	0.826932i	$-0.690084\pi$
$911$	−33.9436	−1.12460	−0.562301	+	0.826932i	$0.690084\pi$
$912$	10.7925	0.357376
$913$	15.9099	0.526540
$914$	−69.3182	−2.29284
$915$	−6.46259	−0.213647
$916$	7.20989	0.238222
$917$	36.7660	1.21412
$918$	3.10868	0.102602
$919$	38.3288	1.26435	0.632175	−	0.774826i	$-0.282162\pi$
$919$	38.3288	1.26435	0.632175	+	0.774826i	$0.282162\pi$
$920$	13.6011	0.448416
$921$	−24.7001	−0.813897
$922$	−2.49244	−0.0820840
$923$	−20.5076	−0.675017
$924$	−6.79626	−0.223580
$925$	9.68494	0.318439
$926$	−66.3280	−2.17967
$927$	10.2147	0.335495
$928$	−29.5718	−0.970742
$929$	49.6371	1.62854	0.814269	−	0.580487i	$-0.197138\pi$
$929$	49.6371	1.62854	0.814269	+	0.580487i	$0.197138\pi$
$930$	4.89517	0.160519
$931$	−19.5227	−0.639832
$932$	−38.1220	−1.24873
$933$	−13.3910	−0.438400
$934$	−16.3398	−0.534656
$935$	−2.11043	−0.0690186
$936$	5.48934	0.179425
$937$	18.9461	0.618944	0.309472	−	0.950909i	$-0.399848\pi$
$937$	18.9461	0.618944	0.309472	+	0.950909i	$0.399848\pi$
$938$	−14.7882	−0.482852
$939$	−22.4249	−0.731810
$940$	−16.9939	−0.554280
$941$	−23.4046	−0.762969	−0.381485	−	0.924375i	$-0.624587\pi$
$941$	−23.4046	−0.762969	−0.381485	+	0.924375i	$0.624587\pi$
$942$	−25.4423	−0.828956
$943$	19.9587	0.649946
$944$	−9.44672	−0.307465
$945$	1.73409	0.0564099
$946$	21.1443	0.687459
$947$	−42.8402	−1.39212	−0.696059	−	0.717984i	$-0.745065\pi$
$947$	−42.8402	−1.39212	−0.696059	+	0.717984i	$0.745065\pi$
$948$	−6.36474	−0.206717
$949$	−26.0629	−0.846037
$950$	−10.5672	−0.342844
$951$	−6.14926	−0.199403
$952$	−3.61781	−0.117254
$953$	22.4896	0.728508	0.364254	−	0.931300i	$-0.381324\pi$
$953$	22.4896	0.728508	0.364254	+	0.931300i	$0.381324\pi$
$954$	10.1411	0.328331
$955$	−1.82914	−0.0591897
$956$	22.4276	0.725361
$957$	5.65580	0.182826
$958$	6.84164	0.221043
$959$	−6.03412	−0.194852
$960$	−12.1659	−0.392652
$961$	−25.8700	−0.834517
$962$	79.2171	2.55406
$963$	10.9395	0.352520
$964$	69.7290	2.24582
$965$	5.62783	0.181166
$966$	35.1437	1.13073
$967$	−29.8180	−0.958883	−0.479442	−	0.877574i	$-0.659161\pi$
$967$	−29.8180	−0.958883	−0.479442	+	0.877574i	$0.659161\pi$
$968$	12.8325	0.412453
$969$	−7.03257	−0.225919
$970$	−16.8706	−0.541682
$971$	−35.6668	−1.14460	−0.572301	−	0.820044i	$-0.693949\pi$
$971$	−35.6668	−1.14460	−0.572301	+	0.820044i	$0.693949\pi$
$972$	−2.67112	−0.0856761
$973$	7.44494	0.238674
$974$	7.99000	0.256016
$975$	3.78453	0.121202
$976$	14.2653	0.456622
$977$	5.77143	0.184644	0.0923222	−	0.995729i	$-0.470571\pi$
$977$	5.77143	0.184644	0.0923222	+	0.995729i	$0.470571\pi$
$978$	−36.1999	−1.15755
$979$	8.11655	0.259406
$980$	10.6656	0.340700
$981$	9.57301	0.305643
$982$	79.7820	2.54595
$983$	47.6623	1.52019	0.760096	−	0.649811i	$-0.225152\pi$
$983$	47.6623	1.52019	0.760096	+	0.649811i	$0.225152\pi$
$984$	3.08727	0.0984187
$985$	−0.670297	−0.0213574
$986$	11.9830	0.381615
$987$	−11.0324	−0.351166
$988$	−49.4257	−1.57244
$989$	−62.5234	−1.98813
$990$	3.17115	0.100786
$991$	23.4541	0.745044	0.372522	−	0.928023i	$-0.378493\pi$
$991$	23.4541	0.745044	0.372522	+	0.928023i	$0.378493\pi$
$992$	−17.3759	−0.551686
$993$	13.5035	0.428522
$994$	−20.3088	−0.644157
$995$	19.6246	0.622140
$996$	−28.9637	−0.917750
$997$	27.4484	0.869299	0.434650	−	0.900600i	$-0.356872\pi$
$997$	27.4484	0.869299	0.434650	+	0.900600i	$0.356872\pi$
$998$	−48.6585	−1.54026
$999$	−9.68494	−0.306418

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.e.1.4	✓	31

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.e.1.4	✓	31	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.16128 q^{2} -1.00000 q^{3} +2.67112 q^{4} -1.00000 q^{5} +2.16128 q^{6} +1.73409 q^{7} -1.45047 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.16128 q^{2} -1.00000 q^{3} +2.67112 q^{4} -1.00000 q^{5} +2.16128 q^{6} +1.73409 q^{7} -1.45047 q^{8} +1.00000 q^{9} +2.16128 q^{10} +1.46726 q^{11} -2.67112 q^{12} -3.78453 q^{13} -3.74784 q^{14} +1.00000 q^{15} -2.20737 q^{16} +1.43835 q^{17} -2.16128 q^{18} +4.88932 q^{19} -2.67112 q^{20} -1.73409 q^{21} -3.17115 q^{22} +9.37705 q^{23} +1.45047 q^{24} +1.00000 q^{25} +8.17942 q^{26} -1.00000 q^{27} +4.63195 q^{28} -3.85468 q^{29} -2.16128 q^{30} -2.26495 q^{31} +7.67167 q^{32} -1.46726 q^{33} -3.10868 q^{34} -1.73409 q^{35} +2.67112 q^{36} +9.68494 q^{37} -10.5672 q^{38} +3.78453 q^{39} +1.45047 q^{40} +2.12847 q^{41} +3.74784 q^{42} -6.66770 q^{43} +3.91921 q^{44} -1.00000 q^{45} -20.2664 q^{46} +6.36209 q^{47} +2.20737 q^{48} -3.99294 q^{49} -2.16128 q^{50} -1.43835 q^{51} -10.1089 q^{52} -4.69219 q^{53} +2.16128 q^{54} -1.46726 q^{55} -2.51524 q^{56} -4.88932 q^{57} +8.33102 q^{58} +4.27963 q^{59} +2.67112 q^{60} -6.46259 q^{61} +4.89517 q^{62} +1.73409 q^{63} -12.1659 q^{64} +3.78453 q^{65} +3.17115 q^{66} +3.94579 q^{67} +3.84201 q^{68} -9.37705 q^{69} +3.74784 q^{70} +5.41881 q^{71} -1.45047 q^{72} +6.88669 q^{73} -20.9318 q^{74} -1.00000 q^{75} +13.0599 q^{76} +2.54435 q^{77} -8.17942 q^{78} +2.38280 q^{79} +2.20737 q^{80} +1.00000 q^{81} -4.60020 q^{82} +10.8433 q^{83} -4.63195 q^{84} -1.43835 q^{85} +14.4108 q^{86} +3.85468 q^{87} -2.12821 q^{88} +5.53179 q^{89} +2.16128 q^{90} -6.56271 q^{91} +25.0472 q^{92} +2.26495 q^{93} -13.7502 q^{94} -4.88932 q^{95} -7.67167 q^{96} -7.80584 q^{97} +8.62984 q^{98} +1.46726 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9}+O(q^{10}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9	\( 31 q + 6 q^{2} - 31 q^{3} + 24 q^{4} - 31 q^{5} - 6 q^{6} - 4 q^{7} + 15 q^{8} + 31 q^{9} - 6 q^{10} - q^{11} - 24 q^{12} + 8 q^{13} + 8 q^{14} + 31 q^{15} + 10 q^{16} + 42 q^{17} + 6 q^{18} - 19 q^{19} - 24 q^{20} + 4 q^{21} + 17 q^{22} + 26 q^{23} - 15 q^{24} + 31 q^{25} + 4 q^{26} - 31 q^{27} - 16 q^{28} - 11 q^{29} + 6 q^{30} - 3 q^{31} + 41 q^{32} + q^{33} + 6 q^{34} + 4 q^{35} + 24 q^{36} + 10 q^{37} + 12 q^{38} - 8 q^{39} - 15 q^{40} + 27 q^{41} - 8 q^{42} - 37 q^{43} - 9 q^{44} - 31 q^{45} - 23 q^{46} + 48 q^{47} - 10 q^{48} + 31 q^{49} + 6 q^{50} - 42 q^{51} + 18 q^{52} + 35 q^{53} - 6 q^{54} + q^{55} + 7 q^{56} + 19 q^{57} - 26 q^{58} - 3 q^{59} + 24 q^{60} + 11 q^{61} + 49 q^{62} - 4 q^{63} - 27 q^{64} - 8 q^{65} - 17 q^{66} - 44 q^{67} + 72 q^{68} - 26 q^{69} - 8 q^{70} + 6 q^{71} + 15 q^{72} + 49 q^{73} - 6 q^{74} - 31 q^{75} - 36 q^{76} + 66 q^{77} - 4 q^{78} - 41 q^{79} - 10 q^{80} + 31 q^{81} + 9 q^{82} + 53 q^{83} + 16 q^{84} - 42 q^{85} + 3 q^{86} + 11 q^{87} + 21 q^{88} + 31 q^{89} - 6 q^{90} - 45 q^{91} + 45 q^{92} + 3 q^{93} - 4 q^{94} + 19 q^{95} - 41 q^{96} + 37 q^{97} + 41 q^{98} - q^{99}+O(q^{100}) \) 31 * q + 6 * q^2 - 31 * q^3 + 24 * q^4 - 31 * q^5 - 6 * q^6 - 4 * q^7 + 15 * q^8 + 31 * q^9 - 6 * q^10 - q^11 - 24 * q^12 + 8 * q^13 + 8 * q^14 + 31 * q^15 + 10 * q^16 + 42 * q^17 + 6 * q^18 - 19 * q^19 - 24 * q^20 + 4 * q^21 + 17 * q^22 + 26 * q^23 - 15 * q^24 + 31 * q^25 + 4 * q^26 - 31 * q^27 - 16 * q^28 - 11 * q^29 + 6 * q^30 - 3 * q^31 + 41 * q^32 + q^33 + 6 * q^34 + 4 * q^35 + 24 * q^36 + 10 * q^37 + 12 * q^38 - 8 * q^39 - 15 * q^40 + 27 * q^41 - 8 * q^42 - 37 * q^43 - 9 * q^44 - 31 * q^45 - 23 * q^46 + 48 * q^47 - 10 * q^48 + 31 * q^49 + 6 * q^50 - 42 * q^51 + 18 * q^52 + 35 * q^53 - 6 * q^54 + q^55 + 7 * q^56 + 19 * q^57 - 26 * q^58 - 3 * q^59 + 24 * q^60 + 11 * q^61 + 49 * q^62 - 4 * q^63 - 27 * q^64 - 8 * q^65 - 17 * q^66 - 44 * q^67 + 72 * q^68 - 26 * q^69 - 8 * q^70 + 6 * q^71 + 15 * q^72 + 49 * q^73 - 6 * q^74 - 31 * q^75 - 36 * q^76 + 66 * q^77 - 4 * q^78 - 41 * q^79 - 10 * q^80 + 31 * q^81 + 9 * q^82 + 53 * q^83 + 16 * q^84 - 42 * q^85 + 3 * q^86 + 11 * q^87 + 21 * q^88 + 31 * q^89 - 6 * q^90 - 45 * q^91 + 45 * q^92 + 3 * q^93 - 4 * q^94 + 19 * q^95 - 41 * q^96 + 37 * q^97 + 41 * q^98 - q^99

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