LMFDB - Embedded newform 6019.2.a.d.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0619569766$
Analytic rank:	$0$
Dimension:	$123$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65517 q^{2} -0.380089 q^{3} +5.04992 q^{4} +1.30385 q^{5} +1.00920 q^{6} +0.922271 q^{7} -8.09806 q^{8} -2.85553 q^{9} +O(q^{10})$	\(q-2.65517 q^{2} -0.380089 q^{3} +5.04992 q^{4} +1.30385 q^{5} +1.00920 q^{6} +0.922271 q^{7} -8.09806 q^{8} -2.85553 q^{9} -3.46193 q^{10} -1.28702 q^{11} -1.91942 q^{12} -1.00000 q^{13} -2.44878 q^{14} -0.495578 q^{15} +11.4019 q^{16} +2.11051 q^{17} +7.58192 q^{18} -6.07297 q^{19} +6.58432 q^{20} -0.350545 q^{21} +3.41724 q^{22} -9.24820 q^{23} +3.07799 q^{24} -3.29999 q^{25} +2.65517 q^{26} +2.22563 q^{27} +4.65739 q^{28} +4.75137 q^{29} +1.31584 q^{30} +2.38071 q^{31} -14.0778 q^{32} +0.489181 q^{33} -5.60375 q^{34} +1.20250 q^{35} -14.4202 q^{36} -3.02721 q^{37} +16.1248 q^{38} +0.380089 q^{39} -10.5586 q^{40} +6.93140 q^{41} +0.930757 q^{42} -2.23711 q^{43} -6.49933 q^{44} -3.72317 q^{45} +24.5555 q^{46} -10.9251 q^{47} -4.33373 q^{48} -6.14942 q^{49} +8.76202 q^{50} -0.802181 q^{51} -5.04992 q^{52} +12.1268 q^{53} -5.90941 q^{54} -1.67807 q^{55} -7.46860 q^{56} +2.30827 q^{57} -12.6157 q^{58} +2.47927 q^{59} -2.50263 q^{60} -12.7459 q^{61} -6.32117 q^{62} -2.63357 q^{63} +14.5751 q^{64} -1.30385 q^{65} -1.29886 q^{66} -7.26745 q^{67} +10.6579 q^{68} +3.51514 q^{69} -3.19284 q^{70} -3.48741 q^{71} +23.1243 q^{72} +15.1979 q^{73} +8.03775 q^{74} +1.25429 q^{75} -30.6680 q^{76} -1.18698 q^{77} -1.00920 q^{78} -2.15722 q^{79} +14.8663 q^{80} +7.72066 q^{81} -18.4040 q^{82} -16.6317 q^{83} -1.77023 q^{84} +2.75178 q^{85} +5.93990 q^{86} -1.80595 q^{87} +10.4223 q^{88} +9.80780 q^{89} +9.88565 q^{90} -0.922271 q^{91} -46.7027 q^{92} -0.904881 q^{93} +29.0080 q^{94} -7.91822 q^{95} +5.35081 q^{96} +8.03325 q^{97} +16.3277 q^{98} +3.67511 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) $ 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * 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 $

$2$	−2.65517	−1.87749	−0.938744	−	0.344615i	$-0.888009\pi$
$2$	−2.65517	−1.87749	−0.938744	+	0.344615i	$0.888009\pi$
$3$	−0.380089	−0.219445	−0.109722	−	0.993962i	$-0.534996\pi$
$3$	−0.380089	−0.219445	−0.109722	+	0.993962i	$0.534996\pi$
$4$	5.04992	2.52496
$5$	1.30385	0.583098	0.291549	−	0.956556i	$-0.405829\pi$
$5$	1.30385	0.583098	0.291549	+	0.956556i	$0.405829\pi$
$6$	1.00920	0.412005
$7$	0.922271	0.348586	0.174293	−	0.984694i	$-0.444236\pi$
$7$	0.922271	0.348586	0.174293	+	0.984694i	$0.444236\pi$
$8$	−8.09806	−2.86310
$9$	−2.85553	−0.951844
$10$	−3.46193	−1.09476
$11$	−1.28702	−0.388050	−0.194025	−	0.980997i	$-0.562154\pi$
$11$	−1.28702	−0.388050	−0.194025	+	0.980997i	$0.562154\pi$
$12$	−1.91942	−0.554089
$13$	−1.00000	−0.277350
$13$	−1.00000	−0.277350
$14$	−2.44878	−0.654465
$15$	−0.495578	−0.127958
$16$	11.4019	2.85047
$17$	2.11051	0.511873	0.255937	−	0.966694i	$-0.417616\pi$
$17$	2.11051	0.511873	0.255937	+	0.966694i	$0.417616\pi$
$18$	7.58192	1.78708
$19$	−6.07297	−1.39324	−0.696618	−	0.717442i	$-0.745313\pi$
$19$	−6.07297	−1.39324	−0.696618	+	0.717442i	$0.745313\pi$
$20$	6.58432	1.47230
$21$	−0.350545	−0.0764952
$22$	3.41724	0.728559
$23$	−9.24820	−1.92838	−0.964192	−	0.265207i	$-0.914560\pi$
$23$	−9.24820	−1.92838	−0.964192	+	0.265207i	$0.914560\pi$
$24$	3.07799	0.628291
$25$	−3.29999	−0.659997
$26$	2.65517	0.520721
$27$	2.22563	0.428322
$28$	4.65739	0.880165
$29$	4.75137	0.882308	0.441154	−	0.897431i	$-0.354569\pi$
$29$	4.75137	0.882308	0.441154	+	0.897431i	$0.354569\pi$
$30$	1.31584	0.240239
$31$	2.38071	0.427587	0.213794	−	0.976879i	$-0.431418\pi$
$31$	2.38071	0.427587	0.213794	+	0.976879i	$0.431418\pi$
$32$	−14.0778	−2.48862
$33$	0.489181	0.0851554
$34$	−5.60375	−0.961036
$35$	1.20250	0.203259
$36$	−14.4202	−2.40337
$37$	−3.02721	−0.497670	−0.248835	−	0.968546i	$-0.580048\pi$
$37$	−3.02721	−0.497670	−0.248835	+	0.968546i	$0.580048\pi$
$38$	16.1248	2.61578
$39$	0.380089	0.0608630
$40$	−10.5586	−1.66946
$41$	6.93140	1.08250	0.541252	−	0.840861i	$-0.317951\pi$
$41$	6.93140	1.08250	0.541252	+	0.840861i	$0.317951\pi$
$42$	0.930757	0.143619
$43$	−2.23711	−0.341156	−0.170578	−	0.985344i	$-0.554563\pi$
$43$	−2.23711	−0.341156	−0.170578	+	0.985344i	$0.554563\pi$
$44$	−6.49933	−0.979810
$45$	−3.72317	−0.555018
$46$	24.5555	3.62052
$47$	−10.9251	−1.59359	−0.796796	−	0.604249i	$-0.793473\pi$
$47$	−10.9251	−1.59359	−0.796796	+	0.604249i	$0.793473\pi$
$48$	−4.33373	−0.625520
$49$	−6.14942	−0.878488
$50$	8.76202	1.23914
$51$	−0.802181	−0.112328
$52$	−5.04992	−0.700298
$53$	12.1268	1.66575	0.832873	−	0.553464i	$-0.186694\pi$
$53$	12.1268	1.66575	0.832873	+	0.553464i	$0.186694\pi$
$54$	−5.90941	−0.804169
$55$	−1.67807	−0.226271
$56$	−7.46860	−0.998034
$57$	2.30827	0.305738
$58$	−12.6157	−1.65652
$59$	2.47927	0.322774	0.161387	−	0.986891i	$-0.448403\pi$
$59$	2.47927	0.322774	0.161387	+	0.986891i	$0.448403\pi$
$60$	−2.50263	−0.323088
$61$	−12.7459	−1.63195	−0.815974	−	0.578088i	$-0.803799\pi$
$61$	−12.7459	−1.63195	−0.815974	+	0.578088i	$0.803799\pi$
$62$	−6.32117	−0.802790
$63$	−2.63357	−0.331799
$64$	14.5751	1.82189
$65$	−1.30385	−0.161722
$66$	−1.29886	−0.159878
$67$	−7.26745	−0.887860	−0.443930	−	0.896061i	$-0.646416\pi$
$67$	−7.26745	−0.887860	−0.443930	+	0.896061i	$0.646416\pi$
$68$	10.6579	1.29246
$69$	3.51514	0.423173
$70$	−3.19284	−0.381617
$71$	−3.48741	−0.413879	−0.206940	−	0.978354i	$-0.566350\pi$
$71$	−3.48741	−0.413879	−0.206940	+	0.978354i	$0.566350\pi$
$72$	23.1243	2.72522
$73$	15.1979	1.77878	0.889389	−	0.457152i	$-0.151130\pi$
$73$	15.1979	1.77878	0.889389	+	0.457152i	$0.151130\pi$
$74$	8.03775	0.934369
$75$	1.25429	0.144833
$76$	−30.6680	−3.51787
$77$	−1.18698	−0.135269
$78$	−1.00920	−0.114270
$79$	−2.15722	−0.242706	−0.121353	−	0.992609i	$-0.538723\pi$
$79$	−2.15722	−0.242706	−0.121353	+	0.992609i	$0.538723\pi$
$80$	14.8663	1.66210
$81$	7.72066	0.857851
$82$	−18.4040	−2.03239
$83$	−16.6317	−1.82557	−0.912784	−	0.408442i	$-0.866072\pi$
$83$	−16.6317	−1.82557	−0.912784	+	0.408442i	$0.866072\pi$
$84$	−1.77023	−0.193148
$85$	2.75178	0.298472
$86$	5.93990	0.640516
$87$	−1.80595	−0.193618
$88$	10.4223	1.11102
$89$	9.80780	1.03962	0.519812	−	0.854281i	$-0.326002\pi$
$89$	9.80780	1.03962	0.519812	+	0.854281i	$0.326002\pi$
$90$	9.88565	1.04204
$91$	−0.922271	−0.0966802
$92$	−46.7027	−4.86909
$93$	−0.904881	−0.0938318
$94$	29.0080	2.99195
$95$	−7.91822	−0.812392
$96$	5.35081	0.546115
$97$	8.03325	0.815653	0.407826	−	0.913060i	$-0.366287\pi$
$97$	8.03325	0.815653	0.407826	+	0.913060i	$0.366287\pi$
$98$	16.3277	1.64935
$99$	3.67511	0.369363
$100$	−16.6647	−1.66647
$101$	−0.505800	−0.0503290	−0.0251645	−	0.999683i	$-0.508011\pi$
$101$	−0.505800	−0.0503290	−0.0251645	+	0.999683i	$0.508011\pi$
$102$	2.12993	0.210894
$103$	−6.10859	−0.601897	−0.300949	−	0.953640i	$-0.597303\pi$
$103$	−6.10859	−0.601897	−0.300949	+	0.953640i	$0.597303\pi$
$104$	8.09806	0.794080
$105$	−0.457057	−0.0446042
$106$	−32.1987	−3.12742
$107$	14.6548	1.41673	0.708365	−	0.705847i	$-0.249433\pi$
$107$	14.6548	1.41673	0.708365	+	0.705847i	$0.249433\pi$
$108$	11.2392	1.08150
$109$	13.8886	1.33029	0.665143	−	0.746716i	$-0.268370\pi$
$109$	13.8886	1.33029	0.665143	+	0.746716i	$0.268370\pi$
$110$	4.45556	0.424821
$111$	1.15061	0.109211
$112$	10.5156	0.993632
$113$	6.79429	0.639153	0.319576	−	0.947561i	$-0.396459\pi$
$113$	6.79429	0.639153	0.319576	+	0.947561i	$0.396459\pi$
$114$	−6.12885	−0.574020
$115$	−12.0582	−1.12444
$116$	23.9941	2.22779
$117$	2.85553	0.263994
$118$	−6.58289	−0.606004
$119$	1.94646	0.178432
$120$	4.01322	0.366355
$121$	−9.34359	−0.849417
$122$	33.8426	3.06396
$123$	−2.63455	−0.237550
$124$	12.0224	1.07964
$125$	−10.8219	−0.967940
$126$	6.99258	0.622949
$127$	−1.74552	−0.154889	−0.0774447	−	0.996997i	$-0.524676\pi$
$127$	−1.74552	−0.154889	−0.0774447	+	0.996997i	$0.524676\pi$
$128$	−10.5439	−0.931956
$129$	0.850301	0.0748649
$130$	3.46193	0.303631
$131$	10.0934	0.881869	0.440934	−	0.897539i	$-0.354647\pi$
$131$	10.0934	0.881869	0.440934	+	0.897539i	$0.354647\pi$
$132$	2.47032	0.215014
$133$	−5.60093	−0.485662
$134$	19.2963	1.66695
$135$	2.90187	0.249753
$136$	−17.0910	−1.46554
$137$	13.9517	1.19198	0.595988	−	0.802993i	$-0.296761\pi$
$137$	13.9517	1.19198	0.595988	+	0.802993i	$0.296761\pi$
$138$	−9.33330	−0.794503
$139$	0.547011	0.0463969	0.0231984	−	0.999731i	$-0.492615\pi$
$139$	0.547011	0.0463969	0.0231984	+	0.999731i	$0.492615\pi$
$140$	6.07253	0.513222
$141$	4.15252	0.349705
$142$	9.25966	0.777054
$143$	1.28702	0.107626
$144$	−32.5584	−2.71320
$145$	6.19506	0.514472
$146$	−40.3529	−3.33963
$147$	2.33733	0.192780
$148$	−15.2872	−1.25660
$149$	22.8019	1.86801	0.934004	−	0.357263i	$-0.116290\pi$
$149$	22.8019	1.86801	0.934004	+	0.357263i	$0.116290\pi$
$150$	−3.33035	−0.271922
$151$	17.6035	1.43255	0.716276	−	0.697817i	$-0.245845\pi$
$151$	17.6035	1.43255	0.716276	+	0.697817i	$0.245845\pi$
$152$	49.1793	3.98897
$153$	−6.02662	−0.487223
$154$	3.15162	0.253965
$155$	3.10407	0.249325
$156$	1.91942	0.153677
$157$	15.1467	1.20884	0.604421	−	0.796665i	$-0.293405\pi$
$157$	15.1467	1.20884	0.604421	+	0.796665i	$0.293405\pi$
$158$	5.72778	0.455678
$159$	−4.60927	−0.365539
$160$	−18.3552	−1.45111
$161$	−8.52934	−0.672206
$162$	−20.4997	−1.61061
$163$	7.10558	0.556552	0.278276	−	0.960501i	$-0.410237\pi$
$163$	7.10558	0.556552	0.278276	+	0.960501i	$0.410237\pi$
$164$	35.0030	2.73328
$165$	0.637816	0.0496539
$166$	44.1600	3.42748
$167$	4.49224	0.347620	0.173810	−	0.984779i	$-0.444392\pi$
$167$	4.49224	0.347620	0.173810	+	0.984779i	$0.444392\pi$
$168$	2.83874	0.219013
$169$	1.00000	0.0769231
$170$	−7.30643	−0.560378
$171$	17.3416	1.32614
$172$	−11.2972	−0.861405
$173$	25.1758	1.91408	0.957042	−	0.289950i	$-0.0936386\pi$
$173$	25.1758	1.91408	0.957042	+	0.289950i	$0.0936386\pi$
$174$	4.79509	0.363515
$175$	−3.04348	−0.230065
$176$	−14.6744	−1.10612
$177$	−0.942346	−0.0708311
$178$	−26.0414	−1.95188
$179$	−3.85828	−0.288382	−0.144191	−	0.989550i	$-0.546058\pi$
$179$	−3.85828	−0.288382	−0.144191	+	0.989550i	$0.546058\pi$
$180$	−18.8017	−1.40140
$181$	−13.7984	−1.02562	−0.512812	−	0.858501i	$-0.671396\pi$
$181$	−13.7984	−1.02562	−0.512812	+	0.858501i	$0.671396\pi$
$182$	2.44878	0.181516
$183$	4.84459	0.358122
$184$	74.8925	5.52115
$185$	−3.94701	−0.290190
$186$	2.40261	0.176168
$187$	−2.71626	−0.198632
$188$	−55.1710	−4.02376
$189$	2.05263	0.149307
$190$	21.0242	1.52526
$191$	17.9655	1.29994	0.649970	−	0.759960i	$-0.274781\pi$
$191$	17.9655	1.29994	0.649970	+	0.759960i	$0.274781\pi$
$192$	−5.53985	−0.399804
$193$	−26.0545	−1.87544	−0.937722	−	0.347386i	$-0.887069\pi$
$193$	−26.0545	−1.87544	−0.937722	+	0.347386i	$0.887069\pi$
$194$	−21.3296	−1.53138
$195$	0.495578	0.0354891
$196$	−31.0541	−2.21815
$197$	−16.6491	−1.18620	−0.593100	−	0.805129i	$-0.702096\pi$
$197$	−16.6491	−1.18620	−0.593100	+	0.805129i	$0.702096\pi$
$198$	−9.75805	−0.693474
$199$	−4.54570	−0.322236	−0.161118	−	0.986935i	$-0.551510\pi$
$199$	−4.54570	−0.322236	−0.161118	+	0.986935i	$0.551510\pi$
$200$	26.7235	1.88964
$201$	2.76228	0.194836
$202$	1.34298	0.0944921
$203$	4.38205	0.307560
$204$	−4.05095	−0.283623
$205$	9.03748	0.631205
$206$	16.2193	1.13005
$207$	26.4085	1.83552
$208$	−11.4019	−0.790577
$209$	7.81601	0.540645
$210$	1.21356	0.0837438
$211$	1.87077	0.128789	0.0643944	−	0.997925i	$-0.479488\pi$
$211$	1.87077	0.128789	0.0643944	+	0.997925i	$0.479488\pi$
$212$	61.2395	4.20594
$213$	1.32553	0.0908236
$214$	−38.9109	−2.65989
$215$	−2.91685	−0.198927
$216$	−18.0232	−1.22633
$217$	2.19565	0.149051
$218$	−36.8766	−2.49760
$219$	−5.77655	−0.390343
$220$	−8.47412	−0.571325
$221$	−2.11051	−0.141968
$222$	−3.05506	−0.205042
$223$	15.2258	1.01960	0.509799	−	0.860294i	$-0.329720\pi$
$223$	15.2258	1.01960	0.509799	+	0.860294i	$0.329720\pi$
$224$	−12.9835	−0.867498
$225$	9.42322	0.628214
$226$	−18.0400	−1.20000
$227$	−1.67924	−0.111455	−0.0557276	−	0.998446i	$-0.517748\pi$
$227$	−1.67924	−0.111455	−0.0557276	+	0.998446i	$0.517748\pi$
$228$	11.6566	0.771977
$229$	11.2052	0.740461	0.370230	−	0.928940i	$-0.379279\pi$
$229$	11.2052	0.740461	0.370230	+	0.928940i	$0.379279\pi$
$230$	32.0166	2.11111
$231$	0.451157	0.0296840
$232$	−38.4769	−2.52613
$233$	−11.5383	−0.755899	−0.377949	−	0.925826i	$-0.623371\pi$
$233$	−11.5383	−0.755899	−0.377949	+	0.925826i	$0.623371\pi$
$234$	−7.58192	−0.495646
$235$	−14.2447	−0.929219
$236$	12.5201	0.814992
$237$	0.819936	0.0532606
$238$	−5.16818	−0.335003
$239$	24.6846	1.59671	0.798356	−	0.602185i	$-0.205703\pi$
$239$	24.6846	1.59671	0.798356	+	0.602185i	$0.205703\pi$
$240$	−5.65051	−0.364739
$241$	−8.25615	−0.531826	−0.265913	−	0.963997i	$-0.585673\pi$
$241$	−8.25615	−0.531826	−0.265913	+	0.963997i	$0.585673\pi$
$242$	24.8088	1.59477
$243$	−9.61142	−0.616573
$244$	−64.3659	−4.12061
$245$	−8.01789	−0.512244
$246$	6.99518	0.445996
$247$	6.07297	0.386414
$248$	−19.2791	−1.22422
$249$	6.32154	0.400611
$250$	28.7340	1.81730
$251$	1.51851	0.0958478	0.0479239	−	0.998851i	$-0.484740\pi$
$251$	1.51851	0.0958478	0.0479239	+	0.998851i	$0.484740\pi$
$252$	−13.2993	−0.837780
$253$	11.9026	0.748308
$254$	4.63464	0.290803
$255$	−1.04592	−0.0654981
$256$	−1.15448	−0.0721549
$257$	−12.8053	−0.798770	−0.399385	−	0.916783i	$-0.630776\pi$
$257$	−12.8053	−0.798770	−0.399385	+	0.916783i	$0.630776\pi$
$258$	−2.25769	−0.140558
$259$	−2.79191	−0.173481
$260$	−6.58432	−0.408342
$261$	−13.5677	−0.839820
$262$	−26.7998	−1.65570
$263$	−14.6048	−0.900572	−0.450286	−	0.892884i	$-0.648678\pi$
$263$	−14.6048	−0.900572	−0.450286	+	0.892884i	$0.648678\pi$
$264$	−3.96141	−0.243808
$265$	15.8115	0.971293
$266$	14.8714	0.911824
$267$	−3.72784	−0.228140
$268$	−36.7001	−2.24181
$269$	−1.98921	−0.121284	−0.0606422	−	0.998160i	$-0.519315\pi$
$269$	−1.98921	−0.121284	−0.0606422	+	0.998160i	$0.519315\pi$
$270$	−7.70496	−0.468909
$271$	5.11429	0.310671	0.155335	−	0.987862i	$-0.450354\pi$
$271$	5.11429	0.310671	0.155335	+	0.987862i	$0.450354\pi$
$272$	24.0637	1.45908
$273$	0.350545	0.0212160
$274$	−37.0442	−2.23792
$275$	4.24713	0.256112
$276$	17.7512	1.06850
$277$	0.221822	0.0133280	0.00666400	−	0.999978i	$-0.497879\pi$
$277$	0.221822	0.0133280	0.00666400	+	0.999978i	$0.497879\pi$
$278$	−1.45241	−0.0871096
$279$	−6.79818	−0.406996
$280$	−9.73791	−0.581951
$281$	6.15571	0.367219	0.183609	−	0.982999i	$-0.441222\pi$
$281$	6.15571	0.367219	0.183609	+	0.982999i	$0.441222\pi$
$282$	−11.0256	−0.656567
$283$	−11.8878	−0.706654	−0.353327	−	0.935500i	$-0.614950\pi$
$283$	−11.8878	−0.706654	−0.353327	+	0.935500i	$0.614950\pi$
$284$	−17.6111	−1.04503
$285$	3.00963	0.178275
$286$	−3.41724	−0.202066
$287$	6.39263	0.377345
$288$	40.1995	2.36878
$289$	−12.5458	−0.737986
$290$	−16.4489	−0.965914
$291$	−3.05335	−0.178991
$292$	76.7481	4.49134
$293$	−15.8167	−0.924020	−0.462010	−	0.886875i	$-0.652872\pi$
$293$	−15.8167	−0.924020	−0.462010	+	0.886875i	$0.652872\pi$
$294$	−6.20600	−0.361941
$295$	3.23259	0.188209
$296$	24.5145	1.42488
$297$	−2.86441	−0.166210
$298$	−60.5430	−3.50716
$299$	9.24820	0.534837
$300$	6.33406	0.365697
$301$	−2.06322	−0.118922
$302$	−46.7402	−2.68960
$303$	0.192249	0.0110444
$304$	−69.2433	−3.97137
$305$	−16.6187	−0.951585
$306$	16.0017	0.914756
$307$	1.09390	0.0624323	0.0312161	−	0.999513i	$-0.490062\pi$
$307$	1.09390	0.0624323	0.0312161	+	0.999513i	$0.490062\pi$
$308$	−5.99414	−0.341548
$309$	2.32181	0.132083
$310$	−8.24184	−0.468105
$311$	−3.00630	−0.170472	−0.0852358	−	0.996361i	$-0.527164\pi$
$311$	−3.00630	−0.170472	−0.0852358	+	0.996361i	$0.527164\pi$
$312$	−3.07799	−0.174257
$313$	−0.275763	−0.0155870	−0.00779352	−	0.999970i	$-0.502481\pi$
$313$	−0.275763	−0.0155870	−0.00779352	+	0.999970i	$0.502481\pi$
$314$	−40.2172	−2.26959
$315$	−3.43377	−0.193471
$316$	−10.8938	−0.612824
$317$	−18.3427	−1.03023	−0.515115	−	0.857121i	$-0.672251\pi$
$317$	−18.3427	−1.03023	−0.515115	+	0.857121i	$0.672251\pi$
$318$	12.2384	0.686295
$319$	−6.11509	−0.342379
$320$	19.0037	1.06234
$321$	−5.57012	−0.310894
$322$	22.6468	1.26206
$323$	−12.8171	−0.713160
$324$	38.9887	2.16604
$325$	3.29999	0.183050
$326$	−18.8665	−1.04492
$327$	−5.27891	−0.291924
$328$	−56.1309	−3.09931
$329$	−10.0759	−0.555503
$330$	−1.69351	−0.0932247
$331$	3.62836	0.199433	0.0997164	−	0.995016i	$-0.468206\pi$
$331$	3.62836	0.199433	0.0997164	+	0.995016i	$0.468206\pi$
$332$	−83.9889	−4.60949
$333$	8.64429	0.473704
$334$	−11.9277	−0.652652
$335$	−9.47563	−0.517709
$336$	−3.99687	−0.218047
$337$	−11.7520	−0.640170	−0.320085	−	0.947389i	$-0.603711\pi$
$337$	−11.7520	−0.640170	−0.320085	+	0.947389i	$0.603711\pi$
$338$	−2.65517	−0.144422
$339$	−2.58244	−0.140259
$340$	13.8963	0.753630
$341$	−3.06400	−0.165925
$342$	−46.0448	−2.48982
$343$	−12.1273	−0.654814
$344$	18.1162	0.976762
$345$	4.58320	0.246751
$346$	−66.8461	−3.59367
$347$	14.3043	0.767896	0.383948	−	0.923355i	$-0.374564\pi$
$347$	14.3043	0.767896	0.383948	+	0.923355i	$0.374564\pi$
$348$	−9.11989	−0.488877
$349$	12.2692	0.656754	0.328377	−	0.944547i	$-0.393498\pi$
$349$	12.2692	0.656754	0.328377	+	0.944547i	$0.393498\pi$
$350$	8.08095	0.431945
$351$	−2.22563	−0.118795
$352$	18.1183	0.965709
$353$	−2.60012	−0.138390	−0.0691952	−	0.997603i	$-0.522043\pi$
$353$	−2.60012	−0.138390	−0.0691952	+	0.997603i	$0.522043\pi$
$354$	2.50209	0.132984
$355$	−4.54704	−0.241332
$356$	49.5286	2.62501
$357$	−0.739828	−0.0391559
$358$	10.2444	0.541433
$359$	35.3336	1.86484	0.932419	−	0.361380i	$-0.117694\pi$
$359$	35.3336	1.86484	0.932419	+	0.361380i	$0.117694\pi$
$360$	30.1505	1.58907
$361$	17.8810	0.941106
$362$	36.6370	1.92560
$363$	3.55140	0.186400
$364$	−4.65739	−0.244114
$365$	19.8157	1.03720
$366$	−12.8632	−0.672370
$367$	−5.89908	−0.307929	−0.153965	−	0.988076i	$-0.549204\pi$
$367$	−5.89908	−0.307929	−0.153965	+	0.988076i	$0.549204\pi$
$368$	−105.447	−5.49679
$369$	−19.7928	−1.03037
$370$	10.4800	0.544828
$371$	11.1842	0.580655
$372$	−4.56958	−0.236922
$373$	−18.6978	−0.968136	−0.484068	−	0.875030i	$-0.660841\pi$
$373$	−18.6978	−0.968136	−0.484068	+	0.875030i	$0.660841\pi$
$374$	7.21212	0.372930
$375$	4.11329	0.212409
$376$	88.4722	4.56261
$377$	−4.75137	−0.244708
$378$	−5.45008	−0.280322
$379$	−8.56820	−0.440119	−0.220059	−	0.975486i	$-0.570625\pi$
$379$	−8.56820	−0.440119	−0.220059	+	0.975486i	$0.570625\pi$
$380$	−39.9864	−2.05126
$381$	0.663452	0.0339897
$382$	−47.7015	−2.44062
$383$	22.0785	1.12816	0.564078	−	0.825721i	$-0.309232\pi$
$383$	22.0785	1.12816	0.564078	+	0.825721i	$0.309232\pi$
$384$	4.00762	0.204513
$385$	−1.54763	−0.0788747
$386$	69.1791	3.52112
$387$	6.38814	0.324727
$388$	40.5673	2.05949
$389$	34.7206	1.76040	0.880202	−	0.474600i	$-0.157407\pi$
$389$	34.7206	1.76040	0.880202	+	0.474600i	$0.157407\pi$
$390$	−1.31584	−0.0666303
$391$	−19.5184	−0.987088
$392$	49.7983	2.51520
$393$	−3.83641	−0.193521
$394$	44.2062	2.22708
$395$	−2.81268	−0.141521
$396$	18.5590	0.932627
$397$	5.23827	0.262901	0.131451	−	0.991323i	$-0.458037\pi$
$397$	5.23827	0.262901	0.131451	+	0.991323i	$0.458037\pi$
$398$	12.0696	0.604995
$399$	2.12885	0.106576
$400$	−37.6260	−1.88130
$401$	−26.9752	−1.34708	−0.673539	−	0.739151i	$-0.735227\pi$
$401$	−26.9752	−1.34708	−0.673539	+	0.739151i	$0.735227\pi$
$402$	−7.33432	−0.365803
$403$	−2.38071	−0.118591
$404$	−2.55425	−0.127079
$405$	10.0665	0.500211
$406$	−11.6351	−0.577440
$407$	3.89606	0.193121
$408$	6.49611	0.321605
$409$	31.8719	1.57597	0.787983	−	0.615697i	$-0.211125\pi$
$409$	31.8719	1.57597	0.787983	+	0.615697i	$0.211125\pi$
$410$	−23.9960	−1.18508
$411$	−5.30290	−0.261573
$412$	−30.8479	−1.51977
$413$	2.28656	0.112514
$414$	−70.1191	−3.44617
$415$	−21.6852	−1.06448
$416$	14.0778	0.690220
$417$	−0.207913	−0.0101815
$418$	−20.7528	−1.01505
$419$	−25.6372	−1.25246	−0.626228	−	0.779640i	$-0.715402\pi$
$419$	−25.6372	−1.25246	−0.626228	+	0.779640i	$0.715402\pi$
$420$	−2.30810	−0.112624
$421$	26.6556	1.29911	0.649556	−	0.760314i	$-0.274955\pi$
$421$	26.6556	1.29911	0.649556	+	0.760314i	$0.274955\pi$
$422$	−4.96720	−0.241800
$423$	31.1970	1.51685
$424$	−98.2037	−4.76919
$425$	−6.96464	−0.337835
$426$	−3.51950	−0.170520
$427$	−11.7552	−0.568874
$428$	74.0054	3.57719
$429$	−0.489181	−0.0236179
$430$	7.74472	0.373483
$431$	22.4611	1.08191	0.540957	−	0.841050i	$-0.318062\pi$
$431$	22.4611	1.08191	0.540957	+	0.841050i	$0.318062\pi$
$432$	25.3763	1.22092
$433$	25.4326	1.22221	0.611105	−	0.791549i	$-0.290725\pi$
$433$	25.4326	1.22221	0.611105	+	0.791549i	$0.290725\pi$
$434$	−5.82983	−0.279841
$435$	−2.35468	−0.112898
$436$	70.1364	3.35892
$437$	56.1641	2.68669
$438$	15.3377	0.732865
$439$	−19.3724	−0.924596	−0.462298	−	0.886725i	$-0.652975\pi$
$439$	−19.3724	−0.924596	−0.462298	+	0.886725i	$0.652975\pi$
$440$	13.5891	0.647835
$441$	17.5599	0.836184
$442$	5.60375	0.266543
$443$	11.3078	0.537251	0.268625	−	0.963245i	$-0.413431\pi$
$443$	11.3078	0.537251	0.268625	+	0.963245i	$0.413431\pi$
$444$	5.81049	0.275754
$445$	12.7879	0.606203
$446$	−40.4272	−1.91428
$447$	−8.66677	−0.409924
$448$	13.4422	0.635085
$449$	−6.75329	−0.318708	−0.159354	−	0.987222i	$-0.550941\pi$
$449$	−6.75329	−0.318708	−0.159354	+	0.987222i	$0.550941\pi$
$450$	−25.0202	−1.17946
$451$	−8.92082	−0.420065
$452$	34.3106	1.61384
$453$	−6.69090	−0.314366
$454$	4.45867	0.209256
$455$	−1.20250	−0.0563740
$456$	−18.6925	−0.875358
$457$	−36.1098	−1.68914	−0.844572	−	0.535442i	$-0.820145\pi$
$457$	−36.1098	−1.68914	−0.844572	+	0.535442i	$0.820145\pi$
$458$	−29.7517	−1.39021
$459$	4.69720	0.219246
$460$	−60.8931	−2.83916
$461$	−14.5113	−0.675858	−0.337929	−	0.941172i	$-0.609726\pi$
$461$	−14.5113	−0.675858	−0.337929	+	0.941172i	$0.609726\pi$
$462$	−1.19790	−0.0557313
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	54.1745	2.51499
$465$	−1.17982	−0.0547131
$466$	30.6361	1.41919
$467$	31.2765	1.44730	0.723651	−	0.690166i	$-0.242463\pi$
$467$	31.2765	1.44730	0.723651	+	0.690166i	$0.242463\pi$
$468$	14.4202	0.666575
$469$	−6.70256	−0.309495
$470$	37.8220	1.74460
$471$	−5.75712	−0.265274
$472$	−20.0773	−0.924133
$473$	2.87919	0.132385
$474$	−2.17707	−0.0999961
$475$	20.0407	0.919532
$476$	9.82947	0.450533
$477$	−34.6285	−1.58553
$478$	−65.5417	−2.99781
$479$	−18.8357	−0.860626	−0.430313	−	0.902680i	$-0.641597\pi$
$479$	−18.8357	−0.860626	−0.430313	+	0.902680i	$0.641597\pi$
$480$	6.97663	0.318438
$481$	3.02721	0.138029
$482$	21.9215	0.998496
$483$	3.24191	0.147512
$484$	−47.1844	−2.14475
$485$	10.4741	0.475605
$486$	25.5199	1.15761
$487$	16.4907	0.747263	0.373632	−	0.927577i	$-0.378112\pi$
$487$	16.4907	0.747263	0.373632	+	0.927577i	$0.378112\pi$
$488$	103.217	4.67242
$489$	−2.70076	−0.122132
$490$	21.2889	0.961733
$491$	4.27674	0.193007	0.0965034	−	0.995333i	$-0.469234\pi$
$491$	4.27674	0.193007	0.0965034	+	0.995333i	$0.469234\pi$
$492$	−13.3043	−0.599803
$493$	10.0278	0.451630
$494$	−16.1248	−0.725488
$495$	4.79178	0.215375
$496$	27.1445	1.21882
$497$	−3.21634	−0.144272
$498$	−16.7848	−0.752143
$499$	41.1603	1.84259	0.921295	−	0.388864i	$-0.127132\pi$
$499$	41.1603	1.84259	0.921295	+	0.388864i	$0.127132\pi$
$500$	−54.6498	−2.44401
$501$	−1.70745	−0.0762833
$502$	−4.03191	−0.179953
$503$	−16.2499	−0.724547	−0.362274	−	0.932072i	$-0.617999\pi$
$503$	−16.2499	−0.724547	−0.362274	+	0.932072i	$0.617999\pi$
$504$	21.3268	0.949973
$505$	−0.659485	−0.0293467
$506$	−31.6033	−1.40494
$507$	−0.380089	−0.0168804
$508$	−8.81472	−0.391090
$509$	−15.7379	−0.697572	−0.348786	−	0.937202i	$-0.613406\pi$
$509$	−15.7379	−0.697572	−0.348786	+	0.937202i	$0.613406\pi$
$510$	2.77710	0.122972
$511$	14.0166	0.620056
$512$	24.1531	1.06743
$513$	−13.5162	−0.596753
$514$	34.0001	1.49968
$515$	−7.96466	−0.350965
$516$	4.29396	0.189031
$517$	14.0608	0.618393
$518$	7.41298	0.325708
$519$	−9.56907	−0.420036
$520$	10.5586	0.463026
$521$	45.5271	1.99458	0.997290	−	0.0735712i	$-0.0234396\pi$
$521$	45.5271	1.99458	0.997290	+	0.0735712i	$0.0234396\pi$
$522$	36.0245	1.57675
$523$	−42.6160	−1.86347	−0.931735	−	0.363139i	$-0.881705\pi$
$523$	−42.6160	−1.86347	−0.931735	+	0.363139i	$0.881705\pi$
$524$	50.9711	2.22668
$525$	1.15679	0.0504866
$526$	38.7783	1.69081
$527$	5.02450	0.218870
$528$	5.57758	0.242733
$529$	62.5292	2.71866
$530$	−41.9822	−1.82359
$531$	−7.07965	−0.307231
$532$	−28.2842	−1.22628
$533$	−6.93140	−0.300232
$534$	9.89804	0.428330
$535$	19.1076	0.826092
$536$	58.8522	2.54203
$537$	1.46649	0.0632838
$538$	5.28170	0.227710
$539$	7.91439	0.340897
$540$	14.6542	0.630618
$541$	−22.3450	−0.960685	−0.480342	−	0.877081i	$-0.659488\pi$
$541$	−22.3450	−0.960685	−0.480342	+	0.877081i	$0.659488\pi$
$542$	−13.5793	−0.583281
$543$	5.24461	0.225068
$544$	−29.7112	−1.27386
$545$	18.1086	0.775687
$546$	−0.930757	−0.0398327
$547$	−16.2470	−0.694674	−0.347337	−	0.937740i	$-0.612914\pi$
$547$	−16.2470	−0.694674	−0.347337	+	0.937740i	$0.612914\pi$
$548$	70.4551	3.00969
$549$	36.3964	1.55336
$550$	−11.2769	−0.480847
$551$	−28.8550	−1.22926
$552$	−28.4658	−1.21159
$553$	−1.98954	−0.0846039
$554$	−0.588975	−0.0250231
$555$	1.50022	0.0636807
$556$	2.76236	0.117150
$557$	−17.9311	−0.759767	−0.379883	−	0.925034i	$-0.624036\pi$
$557$	−17.9311	−0.759767	−0.379883	+	0.925034i	$0.624036\pi$
$558$	18.0503	0.764131
$559$	2.23711	0.0946196
$560$	13.7107	0.579384
$561$	1.03242	0.0435888
$562$	−16.3444	−0.689449
$563$	−36.5984	−1.54244	−0.771219	−	0.636570i	$-0.780353\pi$
$563$	−36.5984	−1.54244	−0.771219	+	0.636570i	$0.780353\pi$
$564$	20.9699	0.882992
$565$	8.85870	0.372688
$566$	31.5640	1.32674
$567$	7.12054	0.299034
$568$	28.2412	1.18498
$569$	9.35601	0.392224	0.196112	−	0.980581i	$-0.437168\pi$
$569$	9.35601	0.392224	0.196112	+	0.980581i	$0.437168\pi$
$570$	−7.99108	−0.334710
$571$	−5.18834	−0.217125	−0.108563	−	0.994090i	$-0.534625\pi$
$571$	−5.18834	−0.217125	−0.108563	+	0.994090i	$0.534625\pi$
$572$	6.49933	0.271750
$573$	−6.82851	−0.285265
$574$	−16.9735	−0.708461
$575$	30.5189	1.27273
$576$	−41.6197	−1.73416
$577$	19.1887	0.798838	0.399419	−	0.916769i	$-0.369212\pi$
$577$	19.1887	0.798838	0.399419	+	0.916769i	$0.369212\pi$
$578$	33.3111	1.38556
$579$	9.90304	0.411556
$580$	31.2846	1.29902
$581$	−15.3389	−0.636367
$582$	8.10716	0.336053
$583$	−15.6074	−0.646392
$584$	−123.073	−5.09281
$585$	3.72317	0.153934
$586$	41.9959	1.73484
$587$	−5.09131	−0.210141	−0.105070	−	0.994465i	$-0.533507\pi$
$587$	−5.09131	−0.210141	−0.105070	+	0.994465i	$0.533507\pi$
$588$	11.8033	0.486761
$589$	−14.4580	−0.595730
$590$	−8.58308	−0.353360
$591$	6.32815	0.260305
$592$	−34.5158	−1.41859
$593$	17.4550	0.716789	0.358395	−	0.933570i	$-0.383324\pi$
$593$	17.4550	0.716789	0.358395	+	0.933570i	$0.383324\pi$
$594$	7.60550	0.312058
$595$	2.53788	0.104043
$596$	115.148	4.71665
$597$	1.72777	0.0707130
$598$	−24.5555	−1.00415
$599$	−17.6718	−0.722050	−0.361025	−	0.932556i	$-0.617573\pi$
$599$	−17.6718	−0.722050	−0.361025	+	0.932556i	$0.617573\pi$
$600$	−10.1573	−0.414670
$601$	25.6575	1.04659	0.523296	−	0.852151i	$-0.324702\pi$
$601$	25.6575	1.04659	0.523296	+	0.852151i	$0.324702\pi$
$602$	5.47820	0.223275
$603$	20.7524	0.845104
$604$	88.8962	3.61714
$605$	−12.1826	−0.495293
$606$	−0.510454	−0.0207358
$607$	−13.4468	−0.545787	−0.272893	−	0.962044i	$-0.587981\pi$
$607$	−13.4468	−0.545787	−0.272893	+	0.962044i	$0.587981\pi$
$608$	85.4940	3.46724
$609$	−1.66557	−0.0674924
$610$	44.1255	1.78659
$611$	10.9251	0.441983
$612$	−30.4340	−1.23022
$613$	47.4892	1.91807	0.959036	−	0.283283i	$-0.0914237\pi$
$613$	47.4892	1.91807	0.959036	+	0.283283i	$0.0914237\pi$
$614$	−2.90449	−0.117216
$615$	−3.43505	−0.138515
$616$	9.61220	0.387287
$617$	38.5316	1.55122	0.775611	−	0.631211i	$-0.217442\pi$
$617$	38.5316	1.55122	0.775611	+	0.631211i	$0.217442\pi$
$618$	−6.16480	−0.247985
$619$	2.93756	0.118071	0.0590353	−	0.998256i	$-0.481198\pi$
$619$	2.93756	0.118071	0.0590353	+	0.998256i	$0.481198\pi$
$620$	15.6753	0.629536
$621$	−20.5830	−0.825969
$622$	7.98224	0.320058
$623$	9.04544	0.362398
$624$	4.33373	0.173488
$625$	2.38984	0.0955935
$626$	0.732197	0.0292645
$627$	−2.97078	−0.118642
$628$	76.4899	3.05228
$629$	−6.38894	−0.254744
$630$	9.11725	0.363240
$631$	19.2499	0.766325	0.383163	−	0.923681i	$-0.374835\pi$
$631$	19.2499	0.766325	0.383163	+	0.923681i	$0.374835\pi$
$632$	17.4693	0.694891
$633$	−0.711058	−0.0282620
$634$	48.7030	1.93424
$635$	−2.27588	−0.0903157
$636$	−23.2765	−0.922972
$637$	6.14942	0.243649
$638$	16.2366	0.642813
$639$	9.95841	0.393949
$640$	−13.7476	−0.543421
$641$	2.89108	0.114191	0.0570953	−	0.998369i	$-0.481816\pi$
$641$	2.89108	0.114191	0.0570953	+	0.998369i	$0.481816\pi$
$642$	14.7896	0.583699
$643$	−29.8263	−1.17623	−0.588116	−	0.808776i	$-0.700130\pi$
$643$	−29.8263	−1.17623	−0.588116	+	0.808776i	$0.700130\pi$
$644$	−43.0725	−1.69730
$645$	1.10866	0.0436535
$646$	34.0315	1.33895
$647$	−5.88828	−0.231492	−0.115746	−	0.993279i	$-0.536926\pi$
$647$	−5.88828	−0.231492	−0.115746	+	0.993279i	$0.536926\pi$
$648$	−62.5224	−2.45611
$649$	−3.19086	−0.125252
$650$	−8.76202	−0.343675
$651$	−0.834545	−0.0327084
$652$	35.8826	1.40527
$653$	−26.2735	−1.02816	−0.514081	−	0.857742i	$-0.671867\pi$
$653$	−26.2735	−1.02816	−0.514081	+	0.857742i	$0.671867\pi$
$654$	14.0164	0.548085
$655$	13.1603	0.514216
$656$	79.0309	3.08564
$657$	−43.3980	−1.69312
$658$	26.7532	1.04295
$659$	3.47293	0.135286	0.0676430	−	0.997710i	$-0.478452\pi$
$659$	3.47293	0.135286	0.0676430	+	0.997710i	$0.478452\pi$
$660$	3.22092	0.125374
$661$	20.2546	0.787813	0.393907	−	0.919150i	$-0.371123\pi$
$661$	20.2546	0.787813	0.393907	+	0.919150i	$0.371123\pi$
$662$	−9.63392	−0.374433
$663$	0.802181	0.0311541
$664$	134.685	5.22678
$665$	−7.30274	−0.283188
$666$	−22.9520	−0.889374
$667$	−43.9417	−1.70143
$668$	22.6855	0.877727
$669$	−5.78718	−0.223745
$670$	25.1594	0.971993
$671$	16.4042	0.633277
$672$	4.93490	0.190368
$673$	17.6292	0.679554	0.339777	−	0.940506i	$-0.389648\pi$
$673$	17.6292	0.679554	0.339777	+	0.940506i	$0.389648\pi$
$674$	31.2034	1.20191
$675$	−7.34453	−0.282691
$676$	5.04992	0.194228
$677$	−5.61882	−0.215949	−0.107974	−	0.994154i	$-0.534436\pi$
$677$	−5.61882	−0.215949	−0.107974	+	0.994154i	$0.534436\pi$
$678$	6.85681	0.263334
$679$	7.40883	0.284325
$680$	−22.2840	−0.854554
$681$	0.638262	0.0244582
$682$	8.13545	0.311522
$683$	20.6240	0.789157	0.394579	−	0.918862i	$-0.370891\pi$
$683$	20.6240	0.789157	0.394579	+	0.918862i	$0.370891\pi$
$684$	87.5736	3.34846
$685$	18.1909	0.695038
$686$	32.2001	1.22941
$687$	−4.25898	−0.162490
$688$	−25.5072	−0.972454
$689$	−12.1268	−0.461995
$690$	−12.1692	−0.463273
$691$	35.0795	1.33449	0.667243	−	0.744840i	$-0.267474\pi$
$691$	35.0795	1.33449	0.667243	+	0.744840i	$0.267474\pi$
$692$	127.136	4.83299
$693$	3.38945	0.128755
$694$	−37.9804	−1.44172
$695$	0.713218	0.0270539
$696$	14.6247	0.554346
$697$	14.6288	0.554104
$698$	−32.5768	−1.23305
$699$	4.38558	0.165878
$700$	−15.3693	−0.580906
$701$	−5.52604	−0.208716	−0.104358	−	0.994540i	$-0.533279\pi$
$701$	−5.52604	−0.208716	−0.104358	+	0.994540i	$0.533279\pi$
$702$	5.90941	0.223036
$703$	18.3842	0.693372
$704$	−18.7584	−0.706984
$705$	5.41424	0.203912
$706$	6.90376	0.259826
$707$	−0.466485	−0.0175440
$708$	−4.75877	−0.178846
$709$	−12.7382	−0.478393	−0.239197	−	0.970971i	$-0.576884\pi$
$709$	−12.7382	−0.478393	−0.239197	+	0.970971i	$0.576884\pi$
$710$	12.0732	0.453098
$711$	6.16001	0.231018
$712$	−79.4241	−2.97654
$713$	−22.0172	−0.824552
$714$	1.96437	0.0735147
$715$	1.67807	0.0627562
$716$	−19.4840	−0.728152
$717$	−9.38235	−0.350390
$718$	−93.8168	−3.50121
$719$	22.3178	0.832315	0.416157	−	0.909293i	$-0.363377\pi$
$719$	22.3178	0.832315	0.416157	+	0.909293i	$0.363377\pi$
$720$	−42.4511	−1.58206
$721$	−5.63377	−0.209813
$722$	−47.4771	−1.76692
$723$	3.13808	0.116706
$724$	−69.6807	−2.58966
$725$	−15.6795	−0.582321
$726$	−9.42957	−0.349964
$727$	−21.1744	−0.785314	−0.392657	−	0.919685i	$-0.628444\pi$
$727$	−21.1744	−0.785314	−0.392657	+	0.919685i	$0.628444\pi$
$728$	7.46860	0.276805
$729$	−19.5088	−0.722547
$730$	−52.6140	−1.94733
$731$	−4.72143	−0.174629
$732$	24.4648	0.904245
$733$	−21.3604	−0.788964	−0.394482	−	0.918904i	$-0.629076\pi$
$733$	−21.3604	−0.788964	−0.394482	+	0.918904i	$0.629076\pi$
$734$	15.6630	0.578133
$735$	3.04752	0.112409
$736$	130.194	4.79902
$737$	9.35332	0.344534
$738$	52.5533	1.93452
$739$	30.7169	1.12994	0.564970	−	0.825111i	$-0.308888\pi$
$739$	30.7169	1.12994	0.564970	+	0.825111i	$0.308888\pi$
$740$	−19.9321	−0.732719
$741$	−2.30827	−0.0847965
$742$	−29.6960	−1.09017
$743$	−43.3354	−1.58982	−0.794911	−	0.606726i	$-0.792483\pi$
$743$	−43.3354	−1.58982	−0.794911	+	0.606726i	$0.792483\pi$
$744$	7.32778	0.268649
$745$	29.7302	1.08923
$746$	49.6458	1.81766
$747$	47.4924	1.73766
$748$	−13.7169	−0.501539
$749$	13.5157	0.493851
$750$	−10.9215	−0.398796
$751$	−43.2500	−1.57821	−0.789107	−	0.614256i	$-0.789456\pi$
$751$	−43.2500	−1.57821	−0.789107	+	0.614256i	$0.789456\pi$
$752$	−124.567	−4.54248
$753$	−0.577171	−0.0210333
$754$	12.6157	0.459437
$755$	22.9522	0.835317
$756$	10.3656	0.376994
$757$	30.3811	1.10422	0.552110	−	0.833771i	$-0.313823\pi$
$757$	30.3811	1.10422	0.552110	+	0.833771i	$0.313823\pi$
$758$	22.7500	0.826318
$759$	−4.52404	−0.164212
$760$	64.1222	2.32596
$761$	5.49665	0.199253	0.0996266	−	0.995025i	$-0.468235\pi$
$761$	5.49665	0.199253	0.0996266	+	0.995025i	$0.468235\pi$
$762$	−1.76158	−0.0638152
$763$	12.8091	0.463719
$764$	90.7246	3.28230
$765$	−7.85779	−0.284099
$766$	−58.6221	−2.11810
$767$	−2.47927	−0.0895214
$768$	0.438805	0.0158340
$769$	30.1979	1.08896	0.544482	−	0.838773i	$-0.316726\pi$
$769$	30.1979	1.08896	0.544482	+	0.838773i	$0.316726\pi$
$770$	4.10923	0.148086
$771$	4.86714	0.175286
$772$	−131.573	−4.73542
$773$	34.1545	1.22845	0.614227	−	0.789130i	$-0.289468\pi$
$773$	34.1545	1.22845	0.614227	+	0.789130i	$0.289468\pi$
$774$	−16.9616	−0.609671
$775$	−7.85629	−0.282206
$776$	−65.0537	−2.33529
$777$	1.06117	0.0380694
$778$	−92.1890	−3.30514
$779$	−42.0942	−1.50818
$780$	2.50263	0.0896085
$781$	4.48835	0.160606
$782$	51.8246	1.85325
$783$	10.5748	0.377912
$784$	−70.1148	−2.50410
$785$	19.7490	0.704873
$786$	10.1863	0.363334
$787$	13.6550	0.486748	0.243374	−	0.969933i	$-0.421746\pi$
$787$	13.6550	0.486748	0.243374	+	0.969933i	$0.421746\pi$
$788$	−84.0767	−2.99511
$789$	5.55114	0.197626
$790$	7.46815	0.265705
$791$	6.26617	0.222799
$792$	−29.7613	−1.05752
$793$	12.7459	0.452621
$794$	−13.9085	−0.493594
$795$	−6.00978	−0.213145
$796$	−22.9554	−0.813634
$797$	−27.4340	−0.971761	−0.485880	−	0.874025i	$-0.661501\pi$
$797$	−27.4340	−0.971761	−0.485880	+	0.874025i	$0.661501\pi$
$798$	−5.65246	−0.200095
$799$	−23.0575	−0.815717
$800$	46.4565	1.64248
$801$	−28.0065	−0.989560
$802$	71.6238	2.52912
$803$	−19.5599	−0.690254
$804$	13.9493	0.491954
$805$	−11.1209	−0.391962
$806$	6.32117	0.222654
$807$	0.756078	0.0266152
$808$	4.09600	0.144097
$809$	−33.3434	−1.17229	−0.586146	−	0.810206i	$-0.699355\pi$
$809$	−33.3434	−1.17229	−0.586146	+	0.810206i	$0.699355\pi$
$810$	−26.7284	−0.939140
$811$	6.57835	0.230997	0.115499	−	0.993308i	$-0.463153\pi$
$811$	6.57835	0.230997	0.115499	+	0.993308i	$0.463153\pi$
$812$	22.1290	0.776577
$813$	−1.94389	−0.0681751
$814$	−10.3447	−0.362582
$815$	9.26458	0.324524
$816$	−9.14637	−0.320187
$817$	13.5859	0.475311
$818$	−84.6254	−2.95886
$819$	2.63357	0.0920245
$820$	45.6386	1.59377
$821$	−5.16066	−0.180108	−0.0900542	−	0.995937i	$-0.528704\pi$
$821$	−5.16066	−0.180108	−0.0900542	+	0.995937i	$0.528704\pi$
$822$	14.0801	0.491100
$823$	−49.9309	−1.74048	−0.870242	−	0.492625i	$-0.836037\pi$
$823$	−49.9309	−1.74048	−0.870242	+	0.492625i	$0.836037\pi$
$824$	49.4677	1.72329
$825$	−1.61429	−0.0562024
$826$	−6.07121	−0.211244
$827$	28.4391	0.988924	0.494462	−	0.869199i	$-0.335365\pi$
$827$	28.4391	0.988924	0.494462	+	0.869199i	$0.335365\pi$
$828$	133.361	4.63462
$829$	9.43196	0.327585	0.163793	−	0.986495i	$-0.447627\pi$
$829$	9.43196	0.327585	0.163793	+	0.986495i	$0.447627\pi$
$830$	57.5779	1.99856
$831$	−0.0843122	−0.00292476
$832$	−14.5751	−0.505302
$833$	−12.9784	−0.449675
$834$	0.552044	0.0191157
$835$	5.85719	0.202696
$836$	39.4702	1.36511
$837$	5.29856	0.183145
$838$	68.0710	2.35147
$839$	26.8331	0.926383	0.463191	−	0.886258i	$-0.346704\pi$
$839$	26.8331	0.926383	0.463191	+	0.886258i	$0.346704\pi$
$840$	3.70127	0.127706
$841$	−6.42444	−0.221533
$842$	−70.7750	−2.43907
$843$	−2.33972	−0.0805842
$844$	9.44722	0.325187
$845$	1.30385	0.0448537
$846$	−82.8333	−2.84787
$847$	−8.61732	−0.296095
$848$	138.268	4.74816
$849$	4.51841	0.155072
$850$	18.4923	0.634281
$851$	27.9962	0.959698
$852$	6.69381	0.229326
$853$	−26.9711	−0.923474	−0.461737	−	0.887017i	$-0.652774\pi$
$853$	−26.9711	−0.923474	−0.461737	+	0.887017i	$0.652774\pi$
$854$	31.2120	1.06805
$855$	22.6107	0.773271
$856$	−118.675	−4.05623
$857$	27.3150	0.933064	0.466532	−	0.884504i	$-0.345503\pi$
$857$	27.3150	0.933064	0.466532	+	0.884504i	$0.345503\pi$
$858$	1.29886	0.0443423
$859$	−32.7373	−1.11698	−0.558492	−	0.829510i	$-0.688620\pi$
$859$	−32.7373	−1.11698	−0.558492	+	0.829510i	$0.688620\pi$
$860$	−14.7298	−0.502283
$861$	−2.42977	−0.0828063
$862$	−59.6380	−2.03128
$863$	−20.7443	−0.706144	−0.353072	−	0.935596i	$-0.614863\pi$
$863$	−20.7443	−0.706144	−0.353072	+	0.935596i	$0.614863\pi$
$864$	−31.3318	−1.06593
$865$	32.8254	1.11610
$866$	−67.5277	−2.29469
$867$	4.76851	0.161947
$868$	11.0879	0.376347
$869$	2.77637	0.0941821
$870$	6.25206	0.211965
$871$	7.26745	0.246248
$872$	−112.471	−3.80874
$873$	−22.9392	−0.776374
$874$	−149.125	−5.04423
$875$	−9.98072	−0.337410
$876$	−29.1711	−0.985601
$877$	4.01195	0.135474	0.0677369	−	0.997703i	$-0.478422\pi$
$877$	4.01195	0.135474	0.0677369	+	0.997703i	$0.478422\pi$
$878$	51.4371	1.73592
$879$	6.01175	0.202771
$880$	−19.1331	−0.644978
$881$	−54.8030	−1.84636	−0.923179	−	0.384369i	$-0.874419\pi$
$881$	−54.8030	−1.84636	−0.923179	+	0.384369i	$0.874419\pi$
$882$	−46.6244	−1.56992
$883$	13.0709	0.439870	0.219935	−	0.975515i	$-0.429415\pi$
$883$	13.0709	0.439870	0.219935	+	0.975515i	$0.429415\pi$
$884$	−10.6579	−0.358464
$885$	−1.22867	−0.0413014
$886$	−30.0242	−1.00868
$887$	33.8288	1.13586	0.567929	−	0.823077i	$-0.307745\pi$
$887$	33.8288	1.13586	0.567929	+	0.823077i	$0.307745\pi$
$888$	−9.31770	−0.312682
$889$	−1.60984	−0.0539922
$890$	−33.9539	−1.13814
$891$	−9.93661	−0.332889
$892$	76.8893	2.57445
$893$	66.3479	2.22025
$894$	23.0117	0.769628
$895$	−5.03061	−0.168155
$896$	−9.72431	−0.324866
$897$	−3.51514	−0.117367
$898$	17.9311	0.598370
$899$	11.3116	0.377264
$900$	47.5865	1.58622
$901$	25.5937	0.852651
$902$	23.6863	0.788667
$903$	0.784208	0.0260968
$904$	−55.0205	−1.82996
$905$	−17.9909	−0.598039
$906$	17.7655	0.590218
$907$	−26.7668	−0.888777	−0.444388	−	0.895834i	$-0.646579\pi$
$907$	−26.7668	−0.888777	−0.444388	+	0.895834i	$0.646579\pi$
$908$	−8.48004	−0.281420
$909$	1.44433	0.0479053
$910$	3.19284	0.105842
$911$	1.86027	0.0616334	0.0308167	−	0.999525i	$-0.490189\pi$
$911$	1.86027	0.0616334	0.0308167	+	0.999525i	$0.490189\pi$
$912$	26.3186	0.871497
$913$	21.4053	0.708411
$914$	95.8776	3.17135
$915$	6.31660	0.208820
$916$	56.5854	1.86963
$917$	9.30889	0.307407
$918$	−12.4719	−0.411633
$919$	5.03275	0.166015	0.0830076	−	0.996549i	$-0.473547\pi$
$919$	5.03275	0.166015	0.0830076	+	0.996549i	$0.473547\pi$
$920$	97.6482	3.21937
$921$	−0.415780	−0.0137004
$922$	38.5299	1.26892
$923$	3.48741	0.114789
$924$	2.27831	0.0749508
$925$	9.98974	0.328461
$926$	−2.65517	−0.0872543
$927$	17.4433	0.572912
$928$	−66.8888	−2.19573
$929$	35.6464	1.16952	0.584760	−	0.811206i	$-0.301189\pi$
$929$	35.6464	1.16952	0.584760	+	0.811206i	$0.301189\pi$
$930$	3.13263	0.102723
$931$	37.3453	1.22394
$932$	−58.2675	−1.90862
$933$	1.14266	0.0374091
$934$	−83.0443	−2.71729
$935$	−3.54158	−0.115822
$936$	−23.1243	−0.755840
$937$	−22.1606	−0.723954	−0.361977	−	0.932187i	$-0.617898\pi$
$937$	−22.1606	−0.723954	−0.361977	+	0.932187i	$0.617898\pi$
$938$	17.7964	0.581074
$939$	0.104815	0.00342049
$940$	−71.9344	−2.34624
$941$	−46.6716	−1.52145	−0.760725	−	0.649075i	$-0.775156\pi$
$941$	−46.6716	−1.52145	−0.760725	+	0.649075i	$0.775156\pi$
$942$	15.2861	0.498049
$943$	−64.1030	−2.08748
$944$	28.2684	0.920057
$945$	2.67631	0.0870604
$946$	−7.64474	−0.248552
$947$	53.4882	1.73813	0.869067	−	0.494694i	$-0.164720\pi$
$947$	53.4882	1.73813	0.869067	+	0.494694i	$0.164720\pi$
$948$	4.14061	0.134481
$949$	−15.1979	−0.493344
$950$	−53.2115	−1.72641
$951$	6.97187	0.226078
$952$	−15.7625	−0.510867
$953$	−0.435255	−0.0140993	−0.00704965	−	0.999975i	$-0.502244\pi$
$953$	−0.435255	−0.0140993	−0.00704965	+	0.999975i	$0.502244\pi$
$954$	91.9446	2.97681
$955$	23.4243	0.757992
$956$	124.655	4.03164
$957$	2.32428	0.0751333
$958$	50.0120	1.61581
$959$	12.8673	0.415506
$960$	−7.22311	−0.233125
$961$	−25.3322	−0.817169
$962$	−8.03775	−0.259147
$963$	−41.8472	−1.34851
$964$	−41.6929	−1.34284
$965$	−33.9711	−1.09357
$966$	−8.60783	−0.276952
$967$	32.1901	1.03516	0.517582	−	0.855634i	$-0.326832\pi$
$967$	32.1901	1.03516	0.517582	+	0.855634i	$0.326832\pi$
$968$	75.6650	2.43196
$969$	4.87163	0.156499
$970$	−27.8105	−0.892943
$971$	38.5220	1.23623	0.618115	−	0.786088i	$-0.287897\pi$
$971$	38.5220	1.23623	0.618115	+	0.786088i	$0.287897\pi$
$972$	−48.5369	−1.55682
$973$	0.504492	0.0161733
$974$	−43.7855	−1.40298
$975$	−1.25429	−0.0401694
$976$	−145.327	−4.65182
$977$	53.4164	1.70894	0.854470	−	0.519500i	$-0.173882\pi$
$977$	53.4164	1.70894	0.854470	+	0.519500i	$0.173882\pi$
$978$	7.17096	0.229302
$979$	−12.6228	−0.403426
$980$	−40.4897	−1.29340
$981$	−39.6594	−1.26623
$982$	−11.3555	−0.362368
$983$	−8.27733	−0.264006	−0.132003	−	0.991249i	$-0.542141\pi$
$983$	−8.27733	−0.264006	−0.132003	+	0.991249i	$0.542141\pi$
$984$	21.3348	0.680127
$985$	−21.7079	−0.691671
$986$	−26.6255	−0.847930
$987$	3.82975	0.121902
$988$	30.6680	0.975681
$989$	20.6892	0.657879
$990$	−12.7230	−0.404363
$991$	−5.47799	−0.174014	−0.0870071	−	0.996208i	$-0.527730\pi$
$991$	−5.47799	−0.174014	−0.0870071	+	0.996208i	$0.527730\pi$
$992$	−33.5150	−1.06410
$993$	−1.37910	−0.0437645
$994$	8.53991	0.270870
$995$	−5.92689	−0.187895
$996$	31.9233	1.01153
$997$	−47.9951	−1.52002	−0.760010	−	0.649912i	$-0.774806\pi$
$997$	−47.9951	−1.52002	−0.760010	+	0.649912i	$0.774806\pi$
$998$	−109.288	−3.45944
$999$	−6.73743	−0.213163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.d.1.6	✓	123

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.d.1.6	✓	123	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65517 q^{2} -0.380089 q^{3} +5.04992 q^{4} +1.30385 q^{5} +1.00920 q^{6} +0.922271 q^{7} -8.09806 q^{8} -2.85553 q^{9} +O(q^{10})\)	\(q-2.65517 q^{2} -0.380089 q^{3} +5.04992 q^{4} +1.30385 q^{5} +1.00920 q^{6} +0.922271 q^{7} -8.09806 q^{8} -2.85553 q^{9} -3.46193 q^{10} -1.28702 q^{11} -1.91942 q^{12} -1.00000 q^{13} -2.44878 q^{14} -0.495578 q^{15} +11.4019 q^{16} +2.11051 q^{17} +7.58192 q^{18} -6.07297 q^{19} +6.58432 q^{20} -0.350545 q^{21} +3.41724 q^{22} -9.24820 q^{23} +3.07799 q^{24} -3.29999 q^{25} +2.65517 q^{26} +2.22563 q^{27} +4.65739 q^{28} +4.75137 q^{29} +1.31584 q^{30} +2.38071 q^{31} -14.0778 q^{32} +0.489181 q^{33} -5.60375 q^{34} +1.20250 q^{35} -14.4202 q^{36} -3.02721 q^{37} +16.1248 q^{38} +0.380089 q^{39} -10.5586 q^{40} +6.93140 q^{41} +0.930757 q^{42} -2.23711 q^{43} -6.49933 q^{44} -3.72317 q^{45} +24.5555 q^{46} -10.9251 q^{47} -4.33373 q^{48} -6.14942 q^{49} +8.76202 q^{50} -0.802181 q^{51} -5.04992 q^{52} +12.1268 q^{53} -5.90941 q^{54} -1.67807 q^{55} -7.46860 q^{56} +2.30827 q^{57} -12.6157 q^{58} +2.47927 q^{59} -2.50263 q^{60} -12.7459 q^{61} -6.32117 q^{62} -2.63357 q^{63} +14.5751 q^{64} -1.30385 q^{65} -1.29886 q^{66} -7.26745 q^{67} +10.6579 q^{68} +3.51514 q^{69} -3.19284 q^{70} -3.48741 q^{71} +23.1243 q^{72} +15.1979 q^{73} +8.03775 q^{74} +1.25429 q^{75} -30.6680 q^{76} -1.18698 q^{77} -1.00920 q^{78} -2.15722 q^{79} +14.8663 q^{80} +7.72066 q^{81} -18.4040 q^{82} -16.6317 q^{83} -1.77023 q^{84} +2.75178 q^{85} +5.93990 q^{86} -1.80595 q^{87} +10.4223 q^{88} +9.80780 q^{89} +9.88565 q^{90} -0.922271 q^{91} -46.7027 q^{92} -0.904881 q^{93} +29.0080 q^{94} -7.91822 q^{95} +5.35081 q^{96} +8.03325 q^{97} +16.3277 q^{98} +3.67511 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9}+O(q^{10}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9	\( 123 q + 10 q^{2} + q^{3} + 136 q^{4} + 46 q^{5} + 16 q^{6} + 12 q^{7} + 30 q^{8} + 154 q^{9} + 5 q^{10} + 53 q^{11} - 6 q^{12} - 123 q^{13} + 21 q^{14} + 29 q^{15} + 166 q^{16} - 35 q^{17} + 28 q^{18} + 23 q^{19} + 93 q^{20} + 72 q^{21} + 8 q^{22} + 42 q^{23} + 55 q^{24} + 153 q^{25} - 10 q^{26} + 7 q^{27} + 39 q^{28} + 86 q^{29} + 44 q^{30} + 16 q^{31} + 70 q^{32} + 40 q^{33} + 10 q^{34} + 6 q^{35} + 222 q^{36} + 52 q^{37} + 12 q^{38} - q^{39} + 14 q^{40} + 80 q^{41} + 29 q^{42} + 2 q^{43} + 143 q^{44} + 137 q^{45} + 39 q^{46} + 45 q^{47} - 27 q^{48} + 163 q^{49} + 102 q^{50} + 48 q^{51} - 136 q^{52} + 117 q^{53} + 75 q^{54} + 20 q^{55} + 88 q^{56} + 67 q^{57} + 56 q^{58} + 88 q^{59} + 96 q^{60} + 57 q^{61} - 13 q^{62} + 48 q^{63} + 228 q^{64} - 46 q^{65} + 28 q^{66} + 43 q^{67} - 56 q^{68} + 92 q^{69} + 14 q^{70} + 90 q^{71} + 98 q^{72} + 25 q^{73} + 80 q^{74} + 21 q^{75} + 75 q^{76} + 112 q^{77} - 16 q^{78} + 36 q^{79} + 208 q^{80} + 231 q^{81} - 27 q^{82} + 93 q^{83} + 175 q^{84} + 77 q^{85} + 199 q^{86} + 15 q^{87} + 43 q^{88} + 140 q^{89} + 11 q^{90} - 12 q^{91} + 93 q^{92} + 140 q^{93} + 4 q^{94} + 23 q^{95} + 105 q^{96} + 43 q^{97} + 67 q^{98} + 140 q^{99}+O(q^{100}) \) 123 * q + 10 * q^2 + q^3 + 136 * q^4 + 46 * q^5 + 16 * q^6 + 12 * q^7 + 30 * q^8 + 154 * q^9 + 5 * q^10 + 53 * q^11 - 6 * q^12 - 123 * q^13 + 21 * q^14 + 29 * q^15 + 166 * q^16 - 35 * q^17 + 28 * q^18 + 23 * q^19 + 93 * q^20 + 72 * q^21 + 8 * q^22 + 42 * q^23 + 55 * q^24 + 153 * q^25 - 10 * q^26 + 7 * q^27 + 39 * q^28 + 86 * q^29 + 44 * q^30 + 16 * q^31 + 70 * q^32 + 40 * q^33 + 10 * q^34 + 6 * q^35 + 222 * q^36 + 52 * q^37 + 12 * q^38 - q^39 + 14 * q^40 + 80 * q^41 + 29 * q^42 + 2 * q^43 + 143 * q^44 + 137 * q^45 + 39 * q^46 + 45 * q^47 - 27 * q^48 + 163 * q^49 + 102 * q^50 + 48 * q^51 - 136 * q^52 + 117 * q^53 + 75 * q^54 + 20 * q^55 + 88 * q^56 + 67 * q^57 + 56 * q^58 + 88 * q^59 + 96 * q^60 + 57 * q^61 - 13 * q^62 + 48 * q^63 + 228 * q^64 - 46 * q^65 + 28 * q^66 + 43 * q^67 - 56 * q^68 + 92 * q^69 + 14 * q^70 + 90 * q^71 + 98 * q^72 + 25 * q^73 + 80 * q^74 + 21 * q^75 + 75 * q^76 + 112 * q^77 - 16 * q^78 + 36 * q^79 + 208 * q^80 + 231 * q^81 - 27 * q^82 + 93 * q^83 + 175 * q^84 + 77 * q^85 + 199 * q^86 + 15 * q^87 + 43 * q^88 + 140 * q^89 + 11 * q^90 - 12 * q^91 + 93 * q^92 + 140 * q^93 + 4 * q^94 + 23 * q^95 + 105 * q^96 + 43 * q^97 + 67 * q^98 + 140 * q^99

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