LMFDB - Embedded newform 6023.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.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:	$48.0938971374$
Analytic rank:	$0$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.24180 q^{2} -2.80359 q^{3} +3.02567 q^{4} +1.63656 q^{5} +6.28509 q^{6} +0.514582 q^{7} -2.29934 q^{8} +4.86012 q^{9} +O(q^{10})$	\(q-2.24180 q^{2} -2.80359 q^{3} +3.02567 q^{4} +1.63656 q^{5} +6.28509 q^{6} +0.514582 q^{7} -2.29934 q^{8} +4.86012 q^{9} -3.66885 q^{10} +6.29782 q^{11} -8.48273 q^{12} -2.17381 q^{13} -1.15359 q^{14} -4.58825 q^{15} -0.896676 q^{16} +5.80025 q^{17} -10.8954 q^{18} -1.00000 q^{19} +4.95169 q^{20} -1.44268 q^{21} -14.1185 q^{22} +7.15102 q^{23} +6.44640 q^{24} -2.32166 q^{25} +4.87325 q^{26} -5.21501 q^{27} +1.55695 q^{28} +5.80198 q^{29} +10.2859 q^{30} -4.83525 q^{31} +6.60885 q^{32} -17.6565 q^{33} -13.0030 q^{34} +0.842145 q^{35} +14.7051 q^{36} +10.0832 q^{37} +2.24180 q^{38} +6.09448 q^{39} -3.76301 q^{40} -9.05813 q^{41} +3.23419 q^{42} -0.788951 q^{43} +19.0551 q^{44} +7.95389 q^{45} -16.0312 q^{46} -0.189678 q^{47} +2.51391 q^{48} -6.73521 q^{49} +5.20471 q^{50} -16.2615 q^{51} -6.57723 q^{52} +11.5641 q^{53} +11.6910 q^{54} +10.3068 q^{55} -1.18320 q^{56} +2.80359 q^{57} -13.0069 q^{58} +2.10753 q^{59} -13.8825 q^{60} +11.6966 q^{61} +10.8397 q^{62} +2.50093 q^{63} -13.0224 q^{64} -3.55758 q^{65} +39.5824 q^{66} +5.59627 q^{67} +17.5496 q^{68} -20.0485 q^{69} -1.88792 q^{70} +6.46369 q^{71} -11.1751 q^{72} +7.53408 q^{73} -22.6045 q^{74} +6.50899 q^{75} -3.02567 q^{76} +3.24075 q^{77} -13.6626 q^{78} +7.02748 q^{79} -1.46747 q^{80} +0.0404028 q^{81} +20.3065 q^{82} +14.6539 q^{83} -4.36506 q^{84} +9.49247 q^{85} +1.76867 q^{86} -16.2664 q^{87} -14.4808 q^{88} +3.52772 q^{89} -17.8310 q^{90} -1.11860 q^{91} +21.6366 q^{92} +13.5561 q^{93} +0.425220 q^{94} -1.63656 q^{95} -18.5285 q^{96} -10.8046 q^{97} +15.0990 q^{98} +30.6082 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) $ 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * 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 $

$2$	−2.24180	−1.58519	−0.792596	−	0.609747i	$-0.791271\pi$
$2$	−2.24180	−1.58519	−0.792596	+	0.609747i	$0.791271\pi$
$3$	−2.80359	−1.61865	−0.809327	−	0.587359i	$-0.800168\pi$
$3$	−2.80359	−1.61865	−0.809327	+	0.587359i	$0.800168\pi$
$4$	3.02567	1.51283
$5$	1.63656	0.731893	0.365946	−	0.930636i	$-0.380745\pi$
$5$	1.63656	0.731893	0.365946	+	0.930636i	$0.380745\pi$
$6$	6.28509	2.56588
$7$	0.514582	0.194494	0.0972469	−	0.995260i	$-0.468996\pi$
$7$	0.514582	0.194494	0.0972469	+	0.995260i	$0.468996\pi$
$8$	−2.29934	−0.812939
$9$	4.86012	1.62004
$10$	−3.66885	−1.16019
$11$	6.29782	1.89886	0.949432	−	0.313972i	$-0.101660\pi$
$11$	6.29782	1.89886	0.949432	+	0.313972i	$0.101660\pi$
$12$	−8.48273	−2.44875
$13$	−2.17381	−0.602907	−0.301453	−	0.953481i	$-0.597472\pi$
$13$	−2.17381	−0.602907	−0.301453	+	0.953481i	$0.597472\pi$
$14$	−1.15359	−0.308310
$15$	−4.58825	−1.18468
$16$	−0.896676	−0.224169
$17$	5.80025	1.40677	0.703384	−	0.710810i	$-0.251672\pi$
$17$	5.80025	1.40677	0.703384	+	0.710810i	$0.251672\pi$
$18$	−10.8954	−2.56807
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.95169	1.10723
$21$	−1.44268	−0.314818
$22$	−14.1185	−3.01006
$23$	7.15102	1.49109	0.745546	−	0.666455i	$-0.232189\pi$
$23$	7.15102	1.49109	0.745546	+	0.666455i	$0.232189\pi$
$24$	6.44640	1.31587
$25$	−2.32166	−0.464333
$26$	4.87325	0.955723
$27$	−5.21501	−1.00363
$28$	1.55695	0.294237
$29$	5.80198	1.07740	0.538700	−	0.842498i	$-0.318916\pi$
$29$	5.80198	1.07740	0.538700	+	0.842498i	$0.318916\pi$
$30$	10.2859	1.87795
$31$	−4.83525	−0.868437	−0.434218	−	0.900808i	$-0.642975\pi$
$31$	−4.83525	−0.868437	−0.434218	+	0.900808i	$0.642975\pi$
$32$	6.60885	1.16829
$33$	−17.6565	−3.07360
$34$	−13.0030	−2.23000
$35$	0.842145	0.142349
$36$	14.7051	2.45085
$37$	10.0832	1.65766	0.828832	−	0.559497i	$-0.189006\pi$
$37$	10.0832	1.65766	0.828832	+	0.559497i	$0.189006\pi$
$38$	2.24180	0.363668
$39$	6.09448	0.975897
$40$	−3.76301	−0.594984
$41$	−9.05813	−1.41464	−0.707321	−	0.706892i	$-0.750096\pi$
$41$	−9.05813	−1.41464	−0.707321	+	0.706892i	$0.750096\pi$
$42$	3.23419	0.499047
$43$	−0.788951	−0.120314	−0.0601570	−	0.998189i	$-0.519160\pi$
$43$	−0.788951	−0.120314	−0.0601570	+	0.998189i	$0.519160\pi$
$44$	19.0551	2.87267
$45$	7.95389	1.18570
$46$	−16.0312	−2.36367
$47$	−0.189678	−0.0276674	−0.0138337	−	0.999904i	$-0.504404\pi$
$47$	−0.189678	−0.0276674	−0.0138337	+	0.999904i	$0.504404\pi$
$48$	2.51391	0.362852
$49$	−6.73521	−0.962172
$50$	5.20471	0.736056
$51$	−16.2615	−2.27707
$52$	−6.57723	−0.912098
$53$	11.5641	1.58846	0.794228	−	0.607620i	$-0.207876\pi$
$53$	11.5641	1.58846	0.794228	+	0.607620i	$0.207876\pi$
$54$	11.6910	1.59095
$55$	10.3068	1.38977
$56$	−1.18320	−0.158112
$57$	2.80359	0.371345
$58$	−13.0069	−1.70789
$59$	2.10753	0.274377	0.137189	−	0.990545i	$-0.456193\pi$
$59$	2.10753	0.274377	0.137189	+	0.990545i	$0.456193\pi$
$60$	−13.8825	−1.79222
$61$	11.6966	1.49760	0.748799	−	0.662797i	$-0.230631\pi$
$61$	11.6966	1.49760	0.748799	+	0.662797i	$0.230631\pi$
$62$	10.8397	1.37664
$63$	2.50093	0.315088
$64$	−13.0224	−1.62779
$65$	−3.55758	−0.441263
$66$	39.5824	4.87225
$67$	5.59627	0.683693	0.341847	−	0.939756i	$-0.388948\pi$
$67$	5.59627	0.683693	0.341847	+	0.939756i	$0.388948\pi$
$68$	17.5496	2.12820
$69$	−20.0485	−2.41356
$70$	−1.88792	−0.225650
$71$	6.46369	0.767099	0.383549	−	0.923520i	$-0.374702\pi$
$71$	6.46369	0.767099	0.383549	+	0.923520i	$0.374702\pi$
$72$	−11.1751	−1.31699
$73$	7.53408	0.881797	0.440898	−	0.897557i	$-0.354660\pi$
$73$	7.53408	0.881797	0.440898	+	0.897557i	$0.354660\pi$
$74$	−22.6045	−2.62772
$75$	6.50899	0.751594
$76$	−3.02567	−0.347068
$77$	3.24075	0.369317
$78$	−13.6626	−1.54698
$79$	7.02748	0.790653	0.395327	−	0.918541i	$-0.370631\pi$
$79$	7.02748	0.790653	0.395327	+	0.918541i	$0.370631\pi$
$80$	−1.46747	−0.164068
$81$	0.0404028	0.00448920
$82$	20.3065	2.24248
$83$	14.6539	1.60847	0.804235	−	0.594311i	$-0.202575\pi$
$83$	14.6539	1.60847	0.804235	+	0.594311i	$0.202575\pi$
$84$	−4.36506	−0.476267
$85$	9.49247	1.02960
$86$	1.76867	0.190721
$87$	−16.2664	−1.74394
$88$	−14.4808	−1.54366
$89$	3.52772	0.373938	0.186969	−	0.982366i	$-0.440134\pi$
$89$	3.52772	0.373938	0.186969	+	0.982366i	$0.440134\pi$
$90$	−17.8310	−1.87956
$91$	−1.11860	−0.117262
$92$	21.6366	2.25577
$93$	13.5561	1.40570
$94$	0.425220	0.0438581
$95$	−1.63656	−0.167908
$96$	−18.5285	−1.89106
$97$	−10.8046	−1.09704	−0.548522	−	0.836136i	$-0.684809\pi$
$97$	−10.8046	−1.09704	−0.548522	+	0.836136i	$0.684809\pi$
$98$	15.0990	1.52523
$99$	30.6082	3.07624
$100$	−7.02458	−0.702458
$101$	−1.18077	−0.117491	−0.0587454	−	0.998273i	$-0.518710\pi$
$101$	−1.18077	−0.117491	−0.0587454	+	0.998273i	$0.518710\pi$
$102$	36.4551	3.60959
$103$	−1.73242	−0.170701	−0.0853504	−	0.996351i	$-0.527201\pi$
$103$	−1.73242	−0.170701	−0.0853504	+	0.996351i	$0.527201\pi$
$104$	4.99833	0.490126
$105$	−2.36103	−0.230413
$106$	−25.9245	−2.51801
$107$	5.91005	0.571346	0.285673	−	0.958327i	$-0.407783\pi$
$107$	5.91005	0.571346	0.285673	+	0.958327i	$0.407783\pi$
$108$	−15.7789	−1.51832
$109$	6.01026	0.575678	0.287839	−	0.957679i	$-0.407063\pi$
$109$	6.01026	0.575678	0.287839	+	0.957679i	$0.407063\pi$
$110$	−23.1057	−2.20304
$111$	−28.2691	−2.68318
$112$	−0.461413	−0.0435995
$113$	17.6685	1.66212	0.831058	−	0.556186i	$-0.187736\pi$
$113$	17.6685	1.66212	0.831058	+	0.556186i	$0.187736\pi$
$114$	−6.28509	−0.588652
$115$	11.7031	1.09132
$116$	17.5548	1.62993
$117$	−10.5650	−0.976733
$118$	−4.72467	−0.434941
$119$	2.98470	0.273607
$120$	10.5499	0.963073
$121$	28.6625	2.60569
$122$	−26.2215	−2.37398
$123$	25.3953	2.28982
$124$	−14.6299	−1.31380
$125$	−11.9824	−1.07173
$126$	−5.60658	−0.499474
$127$	−18.6831	−1.65785	−0.828927	−	0.559357i	$-0.811048\pi$
$127$	−18.6831	−1.65785	−0.828927	+	0.559357i	$0.811048\pi$
$128$	15.9758	1.41208
$129$	2.21190	0.194747
$130$	7.97538	0.699487
$131$	3.15501	0.275654	0.137827	−	0.990456i	$-0.455988\pi$
$131$	3.15501	0.275654	0.137827	+	0.990456i	$0.455988\pi$
$132$	−53.4227	−4.64985
$133$	−0.514582	−0.0446199
$134$	−12.5457	−1.08379
$135$	−8.53469	−0.734550
$136$	−13.3367	−1.14362
$137$	−0.749799	−0.0640597	−0.0320298	−	0.999487i	$-0.510197\pi$
$137$	−0.749799	−0.0640597	−0.0320298	+	0.999487i	$0.510197\pi$
$138$	44.9448	3.82596
$139$	−2.30395	−0.195418	−0.0977092	−	0.995215i	$-0.531152\pi$
$139$	−2.30395	−0.195418	−0.0977092	+	0.995215i	$0.531152\pi$
$140$	2.54805	0.215350
$141$	0.531779	0.0447839
$142$	−14.4903	−1.21600
$143$	−13.6903	−1.14484
$144$	−4.35795	−0.363163
$145$	9.49530	0.788541
$146$	−16.8899	−1.39782
$147$	18.8828	1.55742
$148$	30.5083	2.50777
$149$	−6.70835	−0.549569	−0.274785	−	0.961506i	$-0.588607\pi$
$149$	−6.70835	−0.549569	−0.274785	+	0.961506i	$0.588607\pi$
$150$	−14.5919	−1.19142
$151$	−7.50528	−0.610771	−0.305385	−	0.952229i	$-0.598785\pi$
$151$	−7.50528	−0.610771	−0.305385	+	0.952229i	$0.598785\pi$
$152$	2.29934	0.186501
$153$	28.1899	2.27902
$154$	−7.26510	−0.585439
$155$	−7.91319	−0.635603
$156$	18.4399	1.47637
$157$	17.6202	1.40625	0.703124	−	0.711067i	$-0.251788\pi$
$157$	17.6202	1.40625	0.703124	+	0.711067i	$0.251788\pi$
$158$	−15.7542	−1.25334
$159$	−32.4211	−2.57116
$160$	10.8158	0.855063
$161$	3.67979	0.290008
$162$	−0.0905750	−0.00711624
$163$	−19.0027	−1.48841	−0.744204	−	0.667952i	$-0.767171\pi$
$163$	−19.0027	−1.48841	−0.744204	+	0.667952i	$0.767171\pi$
$164$	−27.4069	−2.14012
$165$	−28.8960	−2.24955
$166$	−32.8510	−2.54973
$167$	20.1725	1.56099	0.780497	−	0.625160i	$-0.214966\pi$
$167$	20.1725	1.56099	0.780497	+	0.625160i	$0.214966\pi$
$168$	3.31720	0.255928
$169$	−8.27454	−0.636503
$170$	−21.2802	−1.63212
$171$	−4.86012	−0.371663
$172$	−2.38710	−0.182015
$173$	−2.55737	−0.194433	−0.0972166	−	0.995263i	$-0.530994\pi$
$173$	−2.55737	−0.194433	−0.0972166	+	0.995263i	$0.530994\pi$
$174$	36.4659	2.76448
$175$	−1.19469	−0.0903098
$176$	−5.64711	−0.425667
$177$	−5.90866	−0.444122
$178$	−7.90844	−0.592763
$179$	−16.7493	−1.25190	−0.625952	−	0.779862i	$-0.715289\pi$
$179$	−16.7493	−1.25190	−0.625952	+	0.779862i	$0.715289\pi$
$180$	24.0658	1.79376
$181$	−8.81589	−0.655280	−0.327640	−	0.944803i	$-0.606253\pi$
$181$	−8.81589	−0.655280	−0.327640	+	0.944803i	$0.606253\pi$
$182$	2.50769	0.185882
$183$	−32.7925	−2.42409
$184$	−16.4426	−1.21217
$185$	16.5018	1.21323
$186$	−30.3900	−2.22830
$187$	36.5289	2.67126
$188$	−0.573902	−0.0418561
$189$	−2.68355	−0.195200
$190$	3.66885	0.266166
$191$	13.1116	0.948719	0.474359	−	0.880331i	$-0.342680\pi$
$191$	13.1116	0.948719	0.474359	+	0.880331i	$0.342680\pi$
$192$	36.5094	2.63484
$193$	−23.8821	−1.71907	−0.859535	−	0.511076i	$-0.829247\pi$
$193$	−23.8821	−1.71907	−0.859535	+	0.511076i	$0.829247\pi$
$194$	24.2218	1.73903
$195$	9.97399	0.714252
$196$	−20.3785	−1.45561
$197$	9.12082	0.649832	0.324916	−	0.945743i	$-0.394664\pi$
$197$	9.12082	0.649832	0.324916	+	0.945743i	$0.394664\pi$
$198$	−68.6174	−4.87642
$199$	−15.4392	−1.09445	−0.547226	−	0.836985i	$-0.684316\pi$
$199$	−15.4392	−1.09445	−0.547226	+	0.836985i	$0.684316\pi$
$200$	5.33829	0.377474
$201$	−15.6897	−1.10666
$202$	2.64705	0.186245
$203$	2.98559	0.209548
$204$	−49.2020	−3.44483
$205$	−14.8242	−1.03537
$206$	3.88375	0.270594
$207$	34.7548	2.41563
$208$	1.94921	0.135153
$209$	−6.29782	−0.435629
$210$	5.29296	0.365249
$211$	7.92929	0.545875	0.272937	−	0.962032i	$-0.412005\pi$
$211$	7.92929	0.545875	0.272937	+	0.962032i	$0.412005\pi$
$212$	34.9892	2.40307
$213$	−18.1215	−1.24167
$214$	−13.2491	−0.905693
$215$	−1.29117	−0.0880569
$216$	11.9911	0.815890
$217$	−2.48813	−0.168906
$218$	−13.4738	−0.912560
$219$	−21.1225	−1.42732
$220$	31.1849	2.10248
$221$	−12.6087	−0.848150
$222$	63.3737	4.25336
$223$	−23.9724	−1.60531	−0.802654	−	0.596445i	$-0.796579\pi$
$223$	−23.9724	−1.60531	−0.802654	+	0.596445i	$0.796579\pi$
$224$	3.40079	0.227225
$225$	−11.2836	−0.752238
$226$	−39.6093	−2.63477
$227$	−12.4725	−0.827830	−0.413915	−	0.910316i	$-0.635839\pi$
$227$	−12.4725	−0.827830	−0.413915	+	0.910316i	$0.635839\pi$
$228$	8.48273	0.561782
$229$	8.93810	0.590647	0.295323	−	0.955397i	$-0.404573\pi$
$229$	8.93810	0.590647	0.295323	+	0.955397i	$0.404573\pi$
$230$	−26.2360	−1.72995
$231$	−9.08572	−0.597797
$232$	−13.3407	−0.875860
$233$	−10.9836	−0.719558	−0.359779	−	0.933038i	$-0.617148\pi$
$233$	−10.9836	−0.719558	−0.359779	+	0.933038i	$0.617148\pi$
$234$	23.6846	1.54831
$235$	−0.310420	−0.0202495
$236$	6.37669	0.415087
$237$	−19.7022	−1.27979
$238$	−6.69111	−0.433720
$239$	−1.69022	−0.109331	−0.0546656	−	0.998505i	$-0.517409\pi$
$239$	−1.69022	−0.109331	−0.0546656	+	0.998505i	$0.517409\pi$
$240$	4.11417	0.265569
$241$	12.0087	0.773548	0.386774	−	0.922175i	$-0.373589\pi$
$241$	12.0087	0.773548	0.386774	+	0.922175i	$0.373589\pi$
$242$	−64.2557	−4.13051
$243$	15.5318	0.996363
$244$	35.3900	2.26562
$245$	−11.0226	−0.704207
$246$	−56.9311	−3.62980
$247$	2.17381	0.138316
$248$	11.1179	0.705986
$249$	−41.0834	−2.60356
$250$	26.8620	1.69891
$251$	−16.3517	−1.03211	−0.516055	−	0.856556i	$-0.672600\pi$
$251$	−16.3517	−1.03211	−0.516055	+	0.856556i	$0.672600\pi$
$252$	7.56698	0.476675
$253$	45.0359	2.83138
$254$	41.8837	2.62802
$255$	−26.6130	−1.66657
$256$	−9.76989	−0.610618
$257$	10.8585	0.677336	0.338668	−	0.940906i	$-0.390024\pi$
$257$	10.8585	0.677336	0.338668	+	0.940906i	$0.390024\pi$
$258$	−4.95863	−0.308711
$259$	5.18862	0.322405
$260$	−10.7640	−0.667558
$261$	28.1983	1.74543
$262$	−7.07290	−0.436965
$263$	−9.03243	−0.556964	−0.278482	−	0.960442i	$-0.589831\pi$
$263$	−9.03243	−0.556964	−0.278482	+	0.960442i	$0.589831\pi$
$264$	40.5983	2.49865
$265$	18.9254	1.16258
$266$	1.15359	0.0707311
$267$	−9.89028	−0.605276
$268$	16.9324	1.03431
$269$	−15.7636	−0.961124	−0.480562	−	0.876961i	$-0.659567\pi$
$269$	−15.7636	−0.961124	−0.480562	+	0.876961i	$0.659567\pi$
$270$	19.1331	1.16440
$271$	−1.69880	−0.103195	−0.0515973	−	0.998668i	$-0.516431\pi$
$271$	−1.69880	−0.103195	−0.0515973	+	0.998668i	$0.516431\pi$
$272$	−5.20095	−0.315354
$273$	3.13611	0.189806
$274$	1.68090	0.101547
$275$	−14.6214	−0.881705
$276$	−60.6602	−3.65131
$277$	28.0710	1.68662	0.843311	−	0.537426i	$-0.180603\pi$
$277$	28.0710	1.68662	0.843311	+	0.537426i	$0.180603\pi$
$278$	5.16499	0.309776
$279$	−23.4999	−1.40690
$280$	−1.93638	−0.115721
$281$	−32.5196	−1.93996	−0.969979	−	0.243190i	$-0.921806\pi$
$281$	−32.5196	−1.93996	−0.969979	+	0.243190i	$0.921806\pi$
$282$	−1.19214	−0.0709910
$283$	−11.8360	−0.703580	−0.351790	−	0.936079i	$-0.614427\pi$
$283$	−11.8360	−0.703580	−0.351790	+	0.936079i	$0.614427\pi$
$284$	19.5570	1.16049
$285$	4.58825	0.271785
$286$	30.6909	1.81479
$287$	−4.66115	−0.275139
$288$	32.1198	1.89268
$289$	16.6429	0.978994
$290$	−21.2866	−1.24999
$291$	30.2918	1.77573
$292$	22.7956	1.33401
$293$	7.91062	0.462143	0.231072	−	0.972937i	$-0.425777\pi$
$293$	7.91062	0.462143	0.231072	+	0.972937i	$0.425777\pi$
$294$	−42.3314	−2.46882
$295$	3.44911	0.200815
$296$	−23.1846	−1.34758
$297$	−32.8432	−1.90576
$298$	15.0388	0.871173
$299$	−15.5450	−0.898989
$300$	19.6940	1.13704
$301$	−0.405980	−0.0234003
$302$	16.8253	0.968189
$303$	3.31039	0.190177
$304$	0.896676	0.0514279
$305$	19.1422	1.09608
$306$	−63.1961	−3.61268
$307$	12.0130	0.685618	0.342809	−	0.939405i	$-0.388622\pi$
$307$	12.0130	0.685618	0.342809	+	0.939405i	$0.388622\pi$
$308$	9.80541	0.558715
$309$	4.85701	0.276306
$310$	17.7398	1.00755
$311$	−6.09671	−0.345713	−0.172856	−	0.984947i	$-0.555300\pi$
$311$	−6.09671	−0.345713	−0.172856	+	0.984947i	$0.555300\pi$
$312$	−14.0133	−0.793345
$313$	27.3547	1.54618	0.773089	−	0.634298i	$-0.218711\pi$
$313$	27.3547	1.54618	0.773089	+	0.634298i	$0.218711\pi$
$314$	−39.5010	−2.22917
$315$	4.09293	0.230610
$316$	21.2628	1.19613
$317$	1.00000	0.0561656
$317$	1.00000	0.0561656
$318$	72.6816	4.07578
$319$	36.5398	2.04584
$320$	−21.3119	−1.19137
$321$	−16.5694	−0.924811
$322$	−8.24935	−0.459718
$323$	−5.80025	−0.322735
$324$	0.122245	0.00679141
$325$	5.04686	0.279949
$326$	42.6003	2.35941
$327$	−16.8503	−0.931823
$328$	20.8277	1.15002
$329$	−0.0976048	−0.00538113
$330$	64.7790	3.56597
$331$	−33.2294	−1.82645	−0.913226	−	0.407453i	$-0.866417\pi$
$331$	−33.2294	−1.82645	−0.913226	+	0.407453i	$0.866417\pi$
$332$	44.3377	2.43335
$333$	49.0055	2.68548
$334$	−45.2227	−2.47447
$335$	9.15865	0.500390
$336$	1.29361	0.0705724
$337$	9.74106	0.530629	0.265315	−	0.964162i	$-0.414524\pi$
$337$	9.74106	0.530629	0.265315	+	0.964162i	$0.414524\pi$
$338$	18.5499	1.00898
$339$	−49.5353	−2.69039
$340$	28.7210	1.55762
$341$	−30.4516	−1.64904
$342$	10.8954	0.589157
$343$	−7.06789	−0.381630
$344$	1.81407	0.0978079
$345$	−32.8107	−1.76647
$346$	5.73311	0.308214
$347$	0.107695	0.00578139	0.00289070	−	0.999996i	$-0.499080\pi$
$347$	0.107695	0.00578139	0.00289070	+	0.999996i	$0.499080\pi$
$348$	−49.2166	−2.63829
$349$	−16.3213	−0.873657	−0.436829	−	0.899545i	$-0.643898\pi$
$349$	−16.3213	−0.873657	−0.436829	+	0.899545i	$0.643898\pi$
$350$	2.67825	0.143158
$351$	11.3365	0.605095
$352$	41.6213	2.21842
$353$	−23.9094	−1.27257	−0.636284	−	0.771455i	$-0.719529\pi$
$353$	−23.9094	−1.27257	−0.636284	+	0.771455i	$0.719529\pi$
$354$	13.2460	0.704018
$355$	10.5782	0.561434
$356$	10.6737	0.565705
$357$	−8.36789	−0.442876
$358$	37.5486	1.98451
$359$	−15.4825	−0.817133	−0.408567	−	0.912729i	$-0.633971\pi$
$359$	−15.4825	−0.817133	−0.408567	+	0.912729i	$0.633971\pi$
$360$	−18.2887	−0.963898
$361$	1.00000	0.0526316
$362$	19.7635	1.03874
$363$	−80.3580	−4.21770
$364$	−3.38452	−0.177397
$365$	12.3300	0.645381
$366$	73.5142	3.84265
$367$	−12.7921	−0.667742	−0.333871	−	0.942619i	$-0.608355\pi$
$367$	−12.7921	−0.667742	−0.333871	+	0.942619i	$0.608355\pi$
$368$	−6.41215	−0.334256
$369$	−44.0236	−2.29178
$370$	−36.9936	−1.92321
$371$	5.95069	0.308945
$372$	41.0161	2.12659
$373$	7.69041	0.398194	0.199097	−	0.979980i	$-0.436199\pi$
$373$	7.69041	0.398194	0.199097	+	0.979980i	$0.436199\pi$
$374$	−81.8906	−4.23446
$375$	33.5936	1.73477
$376$	0.436134	0.0224919
$377$	−12.6124	−0.649572
$378$	6.01599	0.309429
$379$	−8.37016	−0.429946	−0.214973	−	0.976620i	$-0.568966\pi$
$379$	−8.37016	−0.429946	−0.214973	+	0.976620i	$0.568966\pi$
$380$	−4.95169	−0.254016
$381$	52.3797	2.68349
$382$	−29.3935	−1.50390
$383$	−36.8678	−1.88385	−0.941927	−	0.335818i	$-0.890987\pi$
$383$	−36.8678	−1.88385	−0.941927	+	0.335818i	$0.890987\pi$
$384$	−44.7897	−2.28566
$385$	5.30368	0.270301
$386$	53.5389	2.72506
$387$	−3.83440	−0.194913
$388$	−32.6912	−1.65964
$389$	21.1769	1.07371	0.536855	−	0.843674i	$-0.319612\pi$
$389$	21.1769	1.07371	0.536855	+	0.843674i	$0.319612\pi$
$390$	−22.3597	−1.13223
$391$	41.4777	2.09762
$392$	15.4865	0.782187
$393$	−8.84535	−0.446189
$394$	−20.4471	−1.03011
$395$	11.5009	0.578673
$396$	92.6101	4.65383
$397$	−10.1454	−0.509182	−0.254591	−	0.967049i	$-0.581941\pi$
$397$	−10.1454	−0.509182	−0.254591	+	0.967049i	$0.581941\pi$
$398$	34.6115	1.73492
$399$	1.44268	0.0722242
$400$	2.08178	0.104089
$401$	21.7086	1.08407	0.542037	−	0.840355i	$-0.317653\pi$
$401$	21.7086	1.08407	0.542037	+	0.840355i	$0.317653\pi$
$402$	35.1731	1.75427
$403$	10.5109	0.523587
$404$	−3.57261	−0.177744
$405$	0.0661217	0.00328561
$406$	−6.69310	−0.332173
$407$	63.5021	3.14768
$408$	37.3908	1.85112
$409$	30.7491	1.52044	0.760222	−	0.649663i	$-0.225090\pi$
$409$	30.7491	1.52044	0.760222	+	0.649663i	$0.225090\pi$
$410$	33.2329	1.64125
$411$	2.10213	0.103690
$412$	−5.24174	−0.258242
$413$	1.08450	0.0533647
$414$	−77.9133	−3.82923
$415$	23.9820	1.17723
$416$	−14.3664	−0.704370
$417$	6.45933	0.316315
$418$	14.1185	0.690556
$419$	−9.53823	−0.465973	−0.232987	−	0.972480i	$-0.574850\pi$
$419$	−9.53823	−0.465973	−0.232987	+	0.972480i	$0.574850\pi$
$420$	−7.14369	−0.348576
$421$	15.8567	0.772806	0.386403	−	0.922330i	$-0.373717\pi$
$421$	15.8567	0.772806	0.386403	+	0.922330i	$0.373717\pi$
$422$	−17.7759	−0.865316
$423$	−0.921857	−0.0448222
$424$	−26.5899	−1.29132
$425$	−13.4662	−0.653208
$426$	40.6249	1.96828
$427$	6.01887	0.291273
$428$	17.8818	0.864351
$429$	38.3819	1.85310
$430$	2.89454	0.139587
$431$	31.3669	1.51089	0.755446	−	0.655211i	$-0.227420\pi$
$431$	31.3669	1.51089	0.755446	+	0.655211i	$0.227420\pi$
$432$	4.67618	0.224983
$433$	19.1205	0.918872	0.459436	−	0.888211i	$-0.348052\pi$
$433$	19.1205	0.918872	0.459436	+	0.888211i	$0.348052\pi$
$434$	5.57790	0.267748
$435$	−26.6209	−1.27638
$436$	18.1850	0.870905
$437$	−7.15102	−0.342080
$438$	47.3523	2.26258
$439$	−19.7566	−0.942932	−0.471466	−	0.881884i	$-0.656275\pi$
$439$	−19.7566	−0.942932	−0.471466	+	0.881884i	$0.656275\pi$
$440$	−23.6988	−1.12979
$441$	−32.7339	−1.55876
$442$	28.2661	1.34448
$443$	−5.61829	−0.266933	−0.133467	−	0.991053i	$-0.542611\pi$
$443$	−5.61829	−0.266933	−0.133467	+	0.991053i	$0.542611\pi$
$444$	−85.5329	−4.05921
$445$	5.77333	0.273682
$446$	53.7412	2.54472
$447$	18.8075	0.889562
$448$	−6.70107	−0.316596
$449$	17.6810	0.834419	0.417210	−	0.908810i	$-0.363008\pi$
$449$	17.6810	0.834419	0.417210	+	0.908810i	$0.363008\pi$
$450$	25.2955	1.19244
$451$	−57.0465	−2.68621
$452$	53.4591	2.51450
$453$	21.0417	0.988626
$454$	27.9609	1.31227
$455$	−1.83067	−0.0858229
$456$	−6.44640	−0.301880
$457$	−27.4037	−1.28189	−0.640945	−	0.767587i	$-0.721457\pi$
$457$	−27.4037	−1.28189	−0.640945	+	0.767587i	$0.721457\pi$
$458$	−20.0374	−0.936288
$459$	−30.2484	−1.41187
$460$	35.4097	1.65098
$461$	−33.6814	−1.56870	−0.784349	−	0.620320i	$-0.787003\pi$
$461$	−33.6814	−1.56870	−0.784349	+	0.620320i	$0.787003\pi$
$462$	20.3684	0.947622
$463$	11.2267	0.521748	0.260874	−	0.965373i	$-0.415989\pi$
$463$	11.2267	0.521748	0.260874	+	0.965373i	$0.415989\pi$
$464$	−5.20249	−0.241520
$465$	22.1853	1.02882
$466$	24.6230	1.14064
$467$	8.46555	0.391739	0.195869	−	0.980630i	$-0.437247\pi$
$467$	8.46555	0.391739	0.195869	+	0.980630i	$0.437247\pi$
$468$	−31.9661	−1.47763
$469$	2.87974	0.132974
$470$	0.695899	0.0320994
$471$	−49.3999	−2.27623
$472$	−4.84593	−0.223052
$473$	−4.96867	−0.228460
$474$	44.1683	2.02872
$475$	2.32166	0.106525
$476$	9.03072	0.413922
$477$	56.2031	2.57336
$478$	3.78914	0.173311
$479$	4.42480	0.202174	0.101087	−	0.994878i	$-0.467768\pi$
$479$	4.42480	0.202174	0.101087	+	0.994878i	$0.467768\pi$
$480$	−30.3230	−1.38405
$481$	−21.9189	−0.999417
$482$	−26.9211	−1.22622
$483$	−10.3166	−0.469422
$484$	86.7233	3.94197
$485$	−17.6825	−0.802919
$486$	−34.8191	−1.57943
$487$	19.8378	0.898938	0.449469	−	0.893296i	$-0.351613\pi$
$487$	19.8378	0.898938	0.449469	+	0.893296i	$0.351613\pi$
$488$	−26.8945	−1.21746
$489$	53.2759	2.40922
$490$	24.7104	1.11630
$491$	−22.7341	−1.02597	−0.512987	−	0.858396i	$-0.671461\pi$
$491$	−22.7341	−1.02597	−0.512987	+	0.858396i	$0.671461\pi$
$492$	76.8377	3.46411
$493$	33.6529	1.51565
$494$	−4.87325	−0.219258
$495$	50.0922	2.25148
$496$	4.33565	0.194677
$497$	3.32610	0.149196
$498$	92.1008	4.12714
$499$	34.2774	1.53447	0.767235	−	0.641367i	$-0.221632\pi$
$499$	34.2774	1.53447	0.767235	+	0.641367i	$0.221632\pi$
$500$	−36.2546	−1.62136
$501$	−56.5554	−2.52671
$502$	36.6572	1.63609
$503$	−10.6761	−0.476022	−0.238011	−	0.971263i	$-0.576495\pi$
$503$	−10.6761	−0.476022	−0.238011	+	0.971263i	$0.576495\pi$
$504$	−5.75048	−0.256147
$505$	−1.93240	−0.0859907
$506$	−100.961	−4.48828
$507$	23.1984	1.03028
$508$	−56.5287	−2.50806
$509$	18.9003	0.837742	0.418871	−	0.908046i	$-0.362426\pi$
$509$	18.9003	0.837742	0.418871	+	0.908046i	$0.362426\pi$
$510$	59.6610	2.64183
$511$	3.87690	0.171504
$512$	−10.0495	−0.444130
$513$	5.21501	0.230248
$514$	−24.3426	−1.07371
$515$	−2.83522	−0.124935
$516$	6.69246	0.294619
$517$	−1.19456	−0.0525366
$518$	−11.6319	−0.511074
$519$	7.16982	0.314720
$520$	8.18008	0.358720
$521$	0.0175558	0.000769134 0	0.000384567	−	1.00000i	$-0.499878\pi$
$521$	0.0175558	0.000769134 0	0.000384567		1.00000i	$0.499878\pi$
$522$	−63.2149	−2.76684
$523$	−34.3126	−1.50039	−0.750193	−	0.661219i	$-0.770039\pi$
$523$	−34.3126	−1.50039	−0.750193	+	0.661219i	$0.770039\pi$
$524$	9.54600	0.417019
$525$	3.34941	0.146180
$526$	20.2489	0.882894
$527$	−28.0457	−1.22169
$528$	15.8322	0.689007
$529$	28.1371	1.22335
$530$	−42.4270	−1.84291
$531$	10.2429	0.444502
$532$	−1.55695	−0.0675025
$533$	19.6907	0.852898
$534$	22.1720	0.959478
$535$	9.67216	0.418164
$536$	−12.8677	−0.555801
$537$	46.9583	2.02640
$538$	35.3389	1.52357
$539$	−42.4171	−1.82703
$540$	−25.8231	−1.11125
$541$	−16.0878	−0.691668	−0.345834	−	0.938296i	$-0.612404\pi$
$541$	−16.0878	−0.691668	−0.345834	+	0.938296i	$0.612404\pi$
$542$	3.80837	0.163583
$543$	24.7162	1.06067
$544$	38.3330	1.64351
$545$	9.83616	0.421335
$546$	−7.03053	−0.300879
$547$	−22.4291	−0.958998	−0.479499	−	0.877542i	$-0.659182\pi$
$547$	−22.4291	−0.958998	−0.479499	+	0.877542i	$0.659182\pi$
$548$	−2.26864	−0.0969116
$549$	56.8469	2.42617
$550$	32.7783	1.39767
$551$	−5.80198	−0.247173
$552$	46.0984	1.96208
$553$	3.61621	0.153777
$554$	−62.9295	−2.67362
$555$	−46.2642	−1.96380
$556$	−6.97098	−0.295635
$557$	−9.98368	−0.423022	−0.211511	−	0.977376i	$-0.567838\pi$
$557$	−9.98368	−0.423022	−0.211511	+	0.977376i	$0.567838\pi$
$558$	52.6821	2.23021
$559$	1.71503	0.0725381
$560$	−0.755132	−0.0319101
$561$	−102.412	−4.32385
$562$	72.9025	3.07520
$563$	−8.30017	−0.349811	−0.174905	−	0.984585i	$-0.555962\pi$
$563$	−8.30017	−0.349811	−0.174905	+	0.984585i	$0.555962\pi$
$564$	1.60899	0.0677505
$565$	28.9157	1.21649
$566$	26.5340	1.11531
$567$	0.0207906	0.000873121 0
$568$	−14.8622	−0.623605
$569$	38.1588	1.59970	0.799850	−	0.600200i	$-0.204912\pi$
$569$	38.1588	1.59970	0.799850	+	0.600200i	$0.204912\pi$
$570$	−10.2859	−0.430831
$571$	−27.8653	−1.16613	−0.583064	−	0.812426i	$-0.698146\pi$
$571$	−27.8653	−1.16613	−0.583064	+	0.812426i	$0.698146\pi$
$572$	−41.4222	−1.73195
$573$	−36.7594	−1.53565
$574$	10.4494	0.436148
$575$	−16.6023	−0.692362
$576$	−63.2902	−2.63709
$577$	−39.3972	−1.64013	−0.820064	−	0.572272i	$-0.806062\pi$
$577$	−39.3972	−1.64013	−0.820064	+	0.572272i	$0.806062\pi$
$578$	−37.3101	−1.55189
$579$	66.9556	2.78258
$580$	28.7296	1.19293
$581$	7.54061	0.312837
$582$	−67.9081	−2.81488
$583$	72.8288	3.01626
$584$	−17.3234	−0.716847
$585$	−17.2903	−0.714864
$586$	−17.7340	−0.732586
$587$	−3.88023	−0.160154	−0.0800770	−	0.996789i	$-0.525517\pi$
$587$	−3.88023	−0.160154	−0.0800770	+	0.996789i	$0.525517\pi$
$588$	57.1329	2.35612
$589$	4.83525	0.199233
$590$	−7.73221	−0.318330
$591$	−25.5711	−1.05185
$592$	−9.04135	−0.371597
$593$	22.5870	0.927535	0.463768	−	0.885957i	$-0.346497\pi$
$593$	22.5870	0.927535	0.463768	+	0.885957i	$0.346497\pi$
$594$	73.6279	3.02099
$595$	4.88465	0.200251
$596$	−20.2972	−0.831407
$597$	43.2851	1.77154
$598$	34.8487	1.42507
$599$	35.9999	1.47091	0.735457	−	0.677571i	$-0.236967\pi$
$599$	35.9999	1.47091	0.735457	+	0.677571i	$0.236967\pi$
$600$	−14.9664	−0.611000
$601$	−3.27724	−0.133681	−0.0668407	−	0.997764i	$-0.521292\pi$
$601$	−3.27724	−0.133681	−0.0668407	+	0.997764i	$0.521292\pi$
$602$	0.910126	0.0370940
$603$	27.1985	1.10761
$604$	−22.7085	−0.923994
$605$	46.9080	1.90708
$606$	−7.42123	−0.301467
$607$	32.2980	1.31093	0.655467	−	0.755224i	$-0.272472\pi$
$607$	32.2980	1.31093	0.655467	+	0.755224i	$0.272472\pi$
$608$	−6.60885	−0.268024
$609$	−8.37038	−0.339185
$610$	−42.9131	−1.73750
$611$	0.412324	0.0166808
$612$	85.2933	3.44778
$613$	33.7212	1.36199	0.680994	−	0.732289i	$-0.261548\pi$
$613$	33.7212	1.36199	0.680994	+	0.732289i	$0.261548\pi$
$614$	−26.9307	−1.08684
$615$	41.5610	1.67590
$616$	−7.45157	−0.300232
$617$	−1.79465	−0.0722497	−0.0361248	−	0.999347i	$-0.511501\pi$
$617$	−1.79465	−0.0722497	−0.0361248	+	0.999347i	$0.511501\pi$
$618$	−10.8884	−0.437997
$619$	−34.0912	−1.37024	−0.685120	−	0.728430i	$-0.740250\pi$
$619$	−34.0912	−1.37024	−0.685120	+	0.728430i	$0.740250\pi$
$620$	−23.9427	−0.961561
$621$	−37.2927	−1.49650
$622$	13.6676	0.548021
$623$	1.81530	0.0727285
$624$	−5.46477	−0.218766
$625$	−8.00156	−0.320062
$626$	−61.3237	−2.45099
$627$	17.6565	0.705133
$628$	53.3130	2.12742
$629$	58.4850	2.33195
$630$	−9.17552	−0.365562
$631$	−27.4403	−1.09238	−0.546191	−	0.837661i	$-0.683923\pi$
$631$	−27.4403	−1.09238	−0.546191	+	0.837661i	$0.683923\pi$
$632$	−16.1586	−0.642753
$633$	−22.2305	−0.883582
$634$	−2.24180	−0.0890332
$635$	−30.5760	−1.21337
$636$	−98.0954	−3.88974
$637$	14.6411	0.580100
$638$	−81.9149	−3.24304
$639$	31.4143	1.24273
$640$	26.1454	1.03349
$641$	18.8833	0.745845	0.372922	−	0.927863i	$-0.378356\pi$
$641$	18.8833	0.745845	0.372922	+	0.927863i	$0.378356\pi$
$642$	37.1452	1.46600
$643$	−0.621639	−0.0245150	−0.0122575	−	0.999925i	$-0.503902\pi$
$643$	−0.621639	−0.0245150	−0.0122575	+	0.999925i	$0.503902\pi$
$644$	11.1338	0.438733
$645$	3.61991	0.142534
$646$	13.0030	0.511596
$647$	−6.61235	−0.259958	−0.129979	−	0.991517i	$-0.541491\pi$
$647$	−6.61235	−0.259958	−0.129979	+	0.991517i	$0.541491\pi$
$648$	−0.0928997	−0.00364944
$649$	13.2729	0.521005
$650$	−11.3140	−0.443774
$651$	6.97571	0.273400
$652$	−57.4959	−2.25171
$653$	9.43223	0.369112	0.184556	−	0.982822i	$-0.440915\pi$
$653$	9.43223	0.369112	0.184556	+	0.982822i	$0.440915\pi$
$654$	37.7750	1.47712
$655$	5.16337	0.201749
$656$	8.12221	0.317119
$657$	36.6165	1.42855
$658$	0.218810	0.00853012
$659$	23.3497	0.909574	0.454787	−	0.890600i	$-0.349715\pi$
$659$	23.3497	0.909574	0.454787	+	0.890600i	$0.349715\pi$
$660$	−87.4296	−3.40319
$661$	−21.8530	−0.849983	−0.424991	−	0.905197i	$-0.639723\pi$
$661$	−21.8530	−0.849983	−0.424991	+	0.905197i	$0.639723\pi$
$662$	74.4936	2.89528
$663$	35.3495	1.37286
$664$	−33.6942	−1.30759
$665$	−0.842145	−0.0326570
$666$	−109.860	−4.25700
$667$	41.4901	1.60650
$668$	61.0352	2.36152
$669$	67.2087	2.59844
$670$	−20.5319	−0.793215
$671$	73.6632	2.84374
$672$	−9.53443	−0.367799
$673$	−20.3946	−0.786156	−0.393078	−	0.919505i	$-0.628590\pi$
$673$	−20.3946	−0.786156	−0.393078	+	0.919505i	$0.628590\pi$
$674$	−21.8375	−0.841149
$675$	12.1075	0.466018
$676$	−25.0360	−0.962923
$677$	−23.7370	−0.912286	−0.456143	−	0.889906i	$-0.650769\pi$
$677$	−23.7370	−0.912286	−0.456143	+	0.889906i	$0.650769\pi$
$678$	111.048	4.26479
$679$	−5.55987	−0.213368
$680$	−21.8264	−0.837004
$681$	34.9678	1.33997
$682$	68.2663	2.61405
$683$	7.29988	0.279322	0.139661	−	0.990199i	$-0.455399\pi$
$683$	7.29988	0.279322	0.139661	+	0.990199i	$0.455399\pi$
$684$	−14.7051	−0.562264
$685$	−1.22709	−0.0468848
$686$	15.8448	0.604957
$687$	−25.0588	−0.956052
$688$	0.707434	0.0269707
$689$	−25.1382	−0.957691
$690$	73.5550	2.80019
$691$	−18.6049	−0.707764	−0.353882	−	0.935290i	$-0.615139\pi$
$691$	−18.6049	−0.707764	−0.353882	+	0.935290i	$0.615139\pi$
$692$	−7.73775	−0.294145
$693$	15.7504	0.598309
$694$	−0.241432	−0.00916462
$695$	−3.77056	−0.143025
$696$	37.4019	1.41771
$697$	−52.5394	−1.99007
$698$	36.5890	1.38491
$699$	30.7935	1.16472
$700$	−3.61472	−0.136624
$701$	−0.0351656	−0.00132819	−0.000664093	−	1.00000i	$-0.500211\pi$
$701$	−0.0351656	−0.00132819	−0.000664093		1.00000i	$0.500211\pi$
$702$	−25.4141	−0.959192
$703$	−10.0832	−0.380294
$704$	−82.0125	−3.09096
$705$	0.870290	0.0327770
$706$	53.6000	2.01726
$707$	−0.607602	−0.0228512
$708$	−17.8776	−0.671882
$709$	−18.3283	−0.688334	−0.344167	−	0.938908i	$-0.611839\pi$
$709$	−18.3283	−0.688334	−0.344167	+	0.938908i	$0.611839\pi$
$710$	−23.7143	−0.889981
$711$	34.1544	1.28089
$712$	−8.11142	−0.303988
$713$	−34.5770	−1.29492
$714$	18.7591	0.702043
$715$	−22.4050	−0.837899
$716$	−50.6779	−1.89392
$717$	4.73869	0.176969
$718$	34.7086	1.29531
$719$	47.8807	1.78565	0.892825	−	0.450404i	$-0.148720\pi$
$719$	47.8807	1.78565	0.892825	+	0.450404i	$0.148720\pi$
$720$	−7.13206	−0.265796
$721$	−0.891475	−0.0332002
$722$	−2.24180	−0.0834311
$723$	−33.6674	−1.25211
$724$	−26.6740	−0.991330
$725$	−13.4702	−0.500272
$726$	180.147	6.68587
$727$	13.6010	0.504433	0.252216	−	0.967671i	$-0.418841\pi$
$727$	13.6010	0.504433	0.252216	+	0.967671i	$0.418841\pi$
$728$	2.57205	0.0953265
$729$	−43.6659	−1.61726
$730$	−27.6414	−1.02305
$731$	−4.57611	−0.169254
$732$	−99.2192	−3.66725
$733$	−21.8270	−0.806199	−0.403099	−	0.915156i	$-0.632067\pi$
$733$	−21.8270	−0.806199	−0.403099	+	0.915156i	$0.632067\pi$
$734$	28.6773	1.05850
$735$	30.9028	1.13987
$736$	47.2600	1.74203
$737$	35.2443	1.29824
$738$	98.6921	3.63291
$739$	27.8042	1.02279	0.511397	−	0.859345i	$-0.329128\pi$
$739$	27.8042	1.02279	0.511397	+	0.859345i	$0.329128\pi$
$740$	49.9288	1.83542
$741$	−6.09448	−0.223886
$742$	−13.3403	−0.489736
$743$	41.3632	1.51747	0.758734	−	0.651401i	$-0.225818\pi$
$743$	41.3632	1.51747	0.758734	+	0.651401i	$0.225818\pi$
$744$	−31.1700	−1.14275
$745$	−10.9786	−0.402226
$746$	−17.2404	−0.631214
$747$	71.2195	2.60579
$748$	110.524	4.04117
$749$	3.04120	0.111123
$750$	−75.3102	−2.74994
$751$	−10.0312	−0.366044	−0.183022	−	0.983109i	$-0.558588\pi$
$751$	−10.0312	−0.366044	−0.183022	+	0.983109i	$0.558588\pi$
$752$	0.170080	0.00620217
$753$	45.8434	1.67063
$754$	28.2745	1.02970
$755$	−12.2829	−0.447019
$756$	−8.11953	−0.295305
$757$	23.1831	0.842604	0.421302	−	0.906920i	$-0.361573\pi$
$757$	23.1831	0.842604	0.421302	+	0.906920i	$0.361573\pi$
$758$	18.7642	0.681548
$759$	−126.262	−4.58302
$760$	3.76301	0.136499
$761$	−33.9029	−1.22898	−0.614490	−	0.788924i	$-0.710638\pi$
$761$	−33.9029	−1.22898	−0.614490	+	0.788924i	$0.710638\pi$
$762$	−117.425	−4.25385
$763$	3.09277	0.111966
$764$	39.6712	1.43525
$765$	46.1345	1.66800
$766$	82.6501	2.98627
$767$	−4.58138	−0.165424
$768$	27.3908	0.988379
$769$	36.1167	1.30240	0.651200	−	0.758906i	$-0.274266\pi$
$769$	36.1167	1.30240	0.651200	+	0.758906i	$0.274266\pi$
$770$	−11.8898	−0.428478
$771$	−30.4428	−1.09637
$772$	−72.2592	−2.60067
$773$	−25.4342	−0.914804	−0.457402	−	0.889260i	$-0.651220\pi$
$773$	−25.4342	−0.914804	−0.457402	+	0.889260i	$0.651220\pi$
$774$	8.59595	0.308975
$775$	11.2258	0.403244
$776$	24.8435	0.891830
$777$	−14.5468	−0.521863
$778$	−47.4743	−1.70204
$779$	9.05813	0.324541
$780$	30.1780	1.08054
$781$	40.7072	1.45662
$782$	−92.9847	−3.32513
$783$	−30.2574	−1.08131
$784$	6.03930	0.215689
$785$	28.8366	1.02922
$786$	19.8295	0.707295
$787$	−12.4557	−0.443999	−0.222000	−	0.975047i	$-0.571258\pi$
$787$	−12.4557	−0.443999	−0.222000	+	0.975047i	$0.571258\pi$
$788$	27.5966	0.983087
$789$	25.3232	0.901531
$790$	−25.7827	−0.917308
$791$	9.09191	0.323271
$792$	−70.3785	−2.50079
$793$	−25.4262	−0.902912
$794$	22.7439	0.807150
$795$	−53.0591	−1.88181
$796$	−46.7137	−1.65572
$797$	9.45554	0.334932	0.167466	−	0.985878i	$-0.446442\pi$
$797$	9.45554	0.334932	0.167466	+	0.985878i	$0.446442\pi$
$798$	−3.23419	−0.114489
$799$	−1.10018	−0.0389215
$800$	−15.3435	−0.542475
$801$	17.1451	0.605794
$802$	−48.6663	−1.71847
$803$	47.4483	1.67441
$804$	−47.4717	−1.67420
$805$	6.02220	0.212255
$806$	−23.5634	−0.829985
$807$	44.1947	1.55573
$808$	2.71499	0.0955129
$809$	−24.0185	−0.844446	−0.422223	−	0.906492i	$-0.638750\pi$
$809$	−24.0185	−0.844446	−0.422223	+	0.906492i	$0.638750\pi$
$810$	−0.148232	−0.00520833
$811$	−43.8799	−1.54083	−0.770415	−	0.637543i	$-0.779951\pi$
$811$	−43.8799	−1.54083	−0.770415	+	0.637543i	$0.779951\pi$
$812$	9.03341	0.317010
$813$	4.76273	0.167036
$814$	−142.359	−4.98968
$815$	−31.0991	−1.08936
$816$	14.5813	0.510448
$817$	0.788951	0.0276019
$818$	−68.9333	−2.41020
$819$	−5.43655	−0.189968
$820$	−44.8531	−1.56634
$821$	−24.4250	−0.852438	−0.426219	−	0.904620i	$-0.640155\pi$
$821$	−24.4250	−0.852438	−0.426219	+	0.904620i	$0.640155\pi$
$822$	−4.71256	−0.164369
$823$	22.3929	0.780568	0.390284	−	0.920695i	$-0.372377\pi$
$823$	22.3929	0.780568	0.390284	+	0.920695i	$0.372377\pi$
$824$	3.98343	0.138769
$825$	40.9925	1.42718
$826$	−2.43123	−0.0845932
$827$	−0.691761	−0.0240549	−0.0120274	−	0.999928i	$-0.503829\pi$
$827$	−0.691761	−0.0240549	−0.0120274	+	0.999928i	$0.503829\pi$
$828$	105.156	3.65444
$829$	−1.68440	−0.0585015	−0.0292507	−	0.999572i	$-0.509312\pi$
$829$	−1.68440	−0.0585015	−0.0292507	+	0.999572i	$0.509312\pi$
$830$	−53.7627	−1.86613
$831$	−78.6995	−2.73006
$832$	28.3081	0.981408
$833$	−39.0659	−1.35355
$834$	−14.4805	−0.501420
$835$	33.0135	1.14248
$836$	−19.0551	−0.659035
$837$	25.2159	0.871589
$838$	21.3828	0.738657
$839$	−0.655500	−0.0226304	−0.0113152	−	0.999936i	$-0.503602\pi$
$839$	−0.655500	−0.0226304	−0.0113152	+	0.999936i	$0.503602\pi$
$840$	5.42881	0.187312
$841$	4.66293	0.160791
$842$	−35.5475	−1.22505
$843$	91.1717	3.14012
$844$	23.9914	0.825818
$845$	−13.5418	−0.465852
$846$	2.06662	0.0710518
$847$	14.7492	0.506790
$848$	−10.3693	−0.356083
$849$	33.1834	1.13885
$850$	30.1886	1.03546
$851$	72.1050	2.47173
$852$	−54.8297	−1.87844
$853$	−9.37701	−0.321063	−0.160531	−	0.987031i	$-0.551321\pi$
$853$	−9.37701	−0.321063	−0.160531	+	0.987031i	$0.551321\pi$
$854$	−13.4931	−0.461724
$855$	−7.95389	−0.272017
$856$	−13.5892	−0.464469
$857$	38.7027	1.32206	0.661029	−	0.750361i	$-0.270120\pi$
$857$	38.7027	1.32206	0.661029	+	0.750361i	$0.270120\pi$
$858$	−86.0446	−2.93751
$859$	13.4730	0.459693	0.229846	−	0.973227i	$-0.426178\pi$
$859$	13.4730	0.459693	0.229846	+	0.973227i	$0.426178\pi$
$860$	−3.90664	−0.133215
$861$	13.0680	0.445355
$862$	−70.3184	−2.39505
$863$	52.6275	1.79146	0.895731	−	0.444597i	$-0.146653\pi$
$863$	52.6275	1.79146	0.895731	+	0.444597i	$0.146653\pi$
$864$	−34.4652	−1.17253
$865$	−4.18529	−0.142304
$866$	−42.8643	−1.45659
$867$	−46.6599	−1.58465
$868$	−7.52826	−0.255526
$869$	44.2578	1.50134
$870$	59.6788	2.02330
$871$	−12.1652	−0.412203
$872$	−13.8196	−0.467991
$873$	−52.5118	−1.77726
$874$	16.0312	0.542262
$875$	−6.16591	−0.208446
$876$	−63.9095	−2.15930
$877$	44.8021	1.51286	0.756429	−	0.654075i	$-0.226942\pi$
$877$	44.8021	1.51286	0.756429	+	0.654075i	$0.226942\pi$
$878$	44.2904	1.49473
$879$	−22.1781	−0.748050
$880$	−9.24184	−0.311542
$881$	7.07982	0.238525	0.119263	−	0.992863i	$-0.461947\pi$
$881$	7.07982	0.238525	0.119263	+	0.992863i	$0.461947\pi$
$882$	73.3829	2.47093
$883$	−10.0376	−0.337793	−0.168896	−	0.985634i	$-0.554020\pi$
$883$	−10.0376	−0.337793	−0.168896	+	0.985634i	$0.554020\pi$
$884$	−38.1496	−1.28311
$885$	−9.66989	−0.325050
$886$	12.5951	0.423140
$887$	−15.6688	−0.526106	−0.263053	−	0.964781i	$-0.584729\pi$
$887$	−15.6688	−0.526106	−0.263053	+	0.964781i	$0.584729\pi$
$888$	65.0002	2.18127
$889$	−9.61397	−0.322442
$890$	−12.9427	−0.433839
$891$	0.254450	0.00852438
$892$	−72.5324	−2.42856
$893$	0.189678	0.00634733
$894$	−42.1626	−1.41013
$895$	−27.4113	−0.916259
$896$	8.22087	0.274640
$897$	43.5817	1.45515
$898$	−39.6373	−1.32271
$899$	−28.0540	−0.935654
$900$	−34.1403	−1.13801
$901$	67.0749	2.23459
$902$	127.887	4.25816
$903$	1.13820	0.0378770
$904$	−40.6259	−1.35120
$905$	−14.4278	−0.479595
$906$	−47.1713	−1.56716
$907$	−29.3969	−0.976107	−0.488054	−	0.872814i	$-0.662293\pi$
$907$	−29.3969	−0.976107	−0.488054	+	0.872814i	$0.662293\pi$
$908$	−37.7377	−1.25237
$909$	−5.73867	−0.190340
$910$	4.10399	0.136046
$911$	41.0267	1.35927	0.679637	−	0.733548i	$-0.262137\pi$
$911$	41.0267	1.35927	0.679637	+	0.733548i	$0.262137\pi$
$912$	−2.51391	−0.0832440
$913$	92.2874	3.05427
$914$	61.4335	2.03204
$915$	−53.6670	−1.77418
$916$	27.0437	0.893550
$917$	1.62351	0.0536130
$918$	67.8108	2.23809
$919$	11.8194	0.389884	0.194942	−	0.980815i	$-0.437548\pi$
$919$	11.8194	0.389884	0.194942	+	0.980815i	$0.437548\pi$
$920$	−26.9094	−0.887176
$921$	−33.6795	−1.10978
$922$	75.5069	2.48669
$923$	−14.0508	−0.462489
$924$	−27.4904	−0.904367
$925$	−23.4098	−0.769708
$926$	−25.1680	−0.827070
$927$	−8.41979	−0.276542
$928$	38.3444	1.25872
$929$	15.0514	0.493819	0.246910	−	0.969039i	$-0.420585\pi$
$929$	15.0514	0.493819	0.246910	+	0.969039i	$0.420585\pi$
$930$	−49.7351	−1.63088
$931$	6.73521	0.220737
$932$	−33.2326	−1.08857
$933$	17.0927	0.559589
$934$	−18.9781	−0.620981
$935$	59.7819	1.95508
$936$	24.2925	0.794024
$937$	36.1278	1.18024	0.590121	−	0.807315i	$-0.299080\pi$
$937$	36.1278	1.18024	0.590121	+	0.807315i	$0.299080\pi$
$938$	−6.45580	−0.210789
$939$	−76.6913	−2.50273
$940$	−0.939226	−0.0306342
$941$	27.7674	0.905191	0.452596	−	0.891716i	$-0.350498\pi$
$941$	27.7674	0.905191	0.452596	+	0.891716i	$0.350498\pi$
$942$	110.745	3.60826
$943$	−64.7749	−2.10936
$944$	−1.88977	−0.0615069
$945$	−4.39180	−0.142865
$946$	11.1388	0.362153
$947$	−22.2225	−0.722135	−0.361068	−	0.932540i	$-0.617588\pi$
$947$	−22.2225	−0.722135	−0.361068	+	0.932540i	$0.617588\pi$
$948$	−59.6122	−1.93611
$949$	−16.3777	−0.531641
$950$	−5.20471	−0.168863
$951$	−2.80359	−0.0909126
$952$	−6.86285	−0.222426
$953$	2.06868	0.0670111	0.0335056	−	0.999439i	$-0.489333\pi$
$953$	2.06868	0.0670111	0.0335056	+	0.999439i	$0.489333\pi$
$954$	−125.996	−4.07927
$955$	21.4579	0.694361
$956$	−5.11404	−0.165400
$957$	−102.443	−3.31150
$958$	−9.91951	−0.320485
$959$	−0.385833	−0.0124592
$960$	59.7498	1.92842
$961$	−7.62034	−0.245817
$962$	49.1379	1.58427
$963$	28.7235	0.925603
$964$	36.3343	1.17025
$965$	−39.0845	−1.25818
$966$	23.1278	0.744124
$967$	−35.1793	−1.13129	−0.565644	−	0.824649i	$-0.691373\pi$
$967$	−35.1793	−1.13129	−0.565644	+	0.824649i	$0.691373\pi$
$968$	−65.9049	−2.11826
$969$	16.2615	0.522395
$970$	39.6405	1.27278
$971$	−51.1539	−1.64161	−0.820803	−	0.571212i	$-0.806473\pi$
$971$	−51.1539	−1.64161	−0.820803	+	0.571212i	$0.806473\pi$
$972$	46.9939	1.50733
$973$	−1.18557	−0.0380077
$974$	−44.4724	−1.42499
$975$	−14.1493	−0.453141
$976$	−10.4881	−0.335715
$977$	38.6373	1.23612	0.618058	−	0.786133i	$-0.287920\pi$
$977$	38.6373	1.23612	0.618058	+	0.786133i	$0.287920\pi$
$978$	−119.434	−3.81907
$979$	22.2170	0.710057
$980$	−33.3507	−1.06535
$981$	29.2106	0.932621
$982$	50.9652	1.62636
$983$	−42.9418	−1.36963	−0.684815	−	0.728717i	$-0.740117\pi$
$983$	−42.9418	−1.36963	−0.684815	+	0.728717i	$0.740117\pi$
$984$	−58.3924	−1.86148
$985$	14.9268	0.475607
$986$	−75.4431	−2.40260
$987$	0.273644	0.00871018
$988$	6.57723	0.209250
$989$	−5.64181	−0.179399
$990$	−112.297	−3.56902
$991$	−57.3754	−1.82259	−0.911295	−	0.411753i	$-0.864917\pi$
$991$	−57.3754	−1.82259	−0.911295	+	0.411753i	$0.864917\pi$
$992$	−31.9554	−1.01459
$993$	93.1616	2.95639
$994$	−7.45645	−0.236504
$995$	−25.2671	−0.801022
$996$	−124.305	−3.93875
$997$	−13.8473	−0.438550	−0.219275	−	0.975663i	$-0.570369\pi$
$997$	−13.8473	−0.438550	−0.219275	+	0.975663i	$0.570369\pi$
$998$	−76.8432	−2.43243
$999$	−52.5839	−1.66368

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.d.1.18	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.d.1.18	✓	140	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.24180 q^{2} -2.80359 q^{3} +3.02567 q^{4} +1.63656 q^{5} +6.28509 q^{6} +0.514582 q^{7} -2.29934 q^{8} +4.86012 q^{9} +O(q^{10})\)	\(q-2.24180 q^{2} -2.80359 q^{3} +3.02567 q^{4} +1.63656 q^{5} +6.28509 q^{6} +0.514582 q^{7} -2.29934 q^{8} +4.86012 q^{9} -3.66885 q^{10} +6.29782 q^{11} -8.48273 q^{12} -2.17381 q^{13} -1.15359 q^{14} -4.58825 q^{15} -0.896676 q^{16} +5.80025 q^{17} -10.8954 q^{18} -1.00000 q^{19} +4.95169 q^{20} -1.44268 q^{21} -14.1185 q^{22} +7.15102 q^{23} +6.44640 q^{24} -2.32166 q^{25} +4.87325 q^{26} -5.21501 q^{27} +1.55695 q^{28} +5.80198 q^{29} +10.2859 q^{30} -4.83525 q^{31} +6.60885 q^{32} -17.6565 q^{33} -13.0030 q^{34} +0.842145 q^{35} +14.7051 q^{36} +10.0832 q^{37} +2.24180 q^{38} +6.09448 q^{39} -3.76301 q^{40} -9.05813 q^{41} +3.23419 q^{42} -0.788951 q^{43} +19.0551 q^{44} +7.95389 q^{45} -16.0312 q^{46} -0.189678 q^{47} +2.51391 q^{48} -6.73521 q^{49} +5.20471 q^{50} -16.2615 q^{51} -6.57723 q^{52} +11.5641 q^{53} +11.6910 q^{54} +10.3068 q^{55} -1.18320 q^{56} +2.80359 q^{57} -13.0069 q^{58} +2.10753 q^{59} -13.8825 q^{60} +11.6966 q^{61} +10.8397 q^{62} +2.50093 q^{63} -13.0224 q^{64} -3.55758 q^{65} +39.5824 q^{66} +5.59627 q^{67} +17.5496 q^{68} -20.0485 q^{69} -1.88792 q^{70} +6.46369 q^{71} -11.1751 q^{72} +7.53408 q^{73} -22.6045 q^{74} +6.50899 q^{75} -3.02567 q^{76} +3.24075 q^{77} -13.6626 q^{78} +7.02748 q^{79} -1.46747 q^{80} +0.0404028 q^{81} +20.3065 q^{82} +14.6539 q^{83} -4.36506 q^{84} +9.49247 q^{85} +1.76867 q^{86} -16.2664 q^{87} -14.4808 q^{88} +3.52772 q^{89} -17.8310 q^{90} -1.11860 q^{91} +21.6366 q^{92} +13.5561 q^{93} +0.425220 q^{94} -1.63656 q^{95} -18.5285 q^{96} -10.8046 q^{97} +15.0990 q^{98} +30.6082 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9}+O(q^{10}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9	\( 140 q + 4 q^{2} + 3 q^{3} + 162 q^{4} + 13 q^{5} + 12 q^{6} + 25 q^{7} + 12 q^{8} + 181 q^{9} + 8 q^{10} + 19 q^{11} + 17 q^{12} + 28 q^{13} + 5 q^{14} + 14 q^{15} + 202 q^{16} + 38 q^{17} + 26 q^{18} - 140 q^{19} + 36 q^{20} + 4 q^{21} + 53 q^{22} + 58 q^{23} + 47 q^{24} + 279 q^{25} + 29 q^{26} + 21 q^{27} + 69 q^{28} + 18 q^{29} + 50 q^{30} + 20 q^{31} + 13 q^{32} + 47 q^{33} + 6 q^{34} + 35 q^{35} + 230 q^{36} + 88 q^{37} - 4 q^{38} + 32 q^{39} + 32 q^{40} + 24 q^{41} + 75 q^{42} + 100 q^{43} + 63 q^{44} + 87 q^{45} + 23 q^{46} + 35 q^{47} + 46 q^{48} + 255 q^{49} + 11 q^{50} - 6 q^{51} + 47 q^{52} + 77 q^{53} + 16 q^{54} + 63 q^{55} + 21 q^{56} - 3 q^{57} + 165 q^{58} + 18 q^{59} + 28 q^{60} + 99 q^{61} + 34 q^{62} + 89 q^{63} + 298 q^{64} + 78 q^{65} - 3 q^{66} + 28 q^{67} + 93 q^{68} + 19 q^{69} + 16 q^{70} + q^{71} + 43 q^{72} + 201 q^{73} + 32 q^{74} + 22 q^{75} - 162 q^{76} + 86 q^{77} + 122 q^{78} + 58 q^{79} + 92 q^{80} + 288 q^{81} + 143 q^{82} + 57 q^{83} + q^{84} + 136 q^{85} - 6 q^{86} + 43 q^{87} + 198 q^{88} + 46 q^{89} + 30 q^{90} + 26 q^{91} + 129 q^{92} + 111 q^{93} + 44 q^{94} - 13 q^{95} + 32 q^{96} + 110 q^{97} - 34 q^{98} + 62 q^{99}+O(q^{100}) \) 140 * q + 4 * q^2 + 3 * q^3 + 162 * q^4 + 13 * q^5 + 12 * q^6 + 25 * q^7 + 12 * q^8 + 181 * q^9 + 8 * q^10 + 19 * q^11 + 17 * q^12 + 28 * q^13 + 5 * q^14 + 14 * q^15 + 202 * q^16 + 38 * q^17 + 26 * q^18 - 140 * q^19 + 36 * q^20 + 4 * q^21 + 53 * q^22 + 58 * q^23 + 47 * q^24 + 279 * q^25 + 29 * q^26 + 21 * q^27 + 69 * q^28 + 18 * q^29 + 50 * q^30 + 20 * q^31 + 13 * q^32 + 47 * q^33 + 6 * q^34 + 35 * q^35 + 230 * q^36 + 88 * q^37 - 4 * q^38 + 32 * q^39 + 32 * q^40 + 24 * q^41 + 75 * q^42 + 100 * q^43 + 63 * q^44 + 87 * q^45 + 23 * q^46 + 35 * q^47 + 46 * q^48 + 255 * q^49 + 11 * q^50 - 6 * q^51 + 47 * q^52 + 77 * q^53 + 16 * q^54 + 63 * q^55 + 21 * q^56 - 3 * q^57 + 165 * q^58 + 18 * q^59 + 28 * q^60 + 99 * q^61 + 34 * q^62 + 89 * q^63 + 298 * q^64 + 78 * q^65 - 3 * q^66 + 28 * q^67 + 93 * q^68 + 19 * q^69 + 16 * q^70 + q^71 + 43 * q^72 + 201 * q^73 + 32 * q^74 + 22 * q^75 - 162 * q^76 + 86 * q^77 + 122 * q^78 + 58 * q^79 + 92 * q^80 + 288 * q^81 + 143 * q^82 + 57 * q^83 + q^84 + 136 * q^85 - 6 * q^86 + 43 * q^87 + 198 * q^88 + 46 * q^89 + 30 * q^90 + 26 * q^91 + 129 * q^92 + 111 * q^93 + 44 * q^94 - 13 * q^95 + 32 * q^96 + 110 * q^97 - 34 * q^98 + 62 * q^99

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