LMFDB - Embedded newform 6001.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.20655 q^{2} +2.67875 q^{3} +2.86888 q^{4} -1.00223 q^{5} -5.91080 q^{6} -0.364832 q^{7} -1.91723 q^{8} +4.17568 q^{9} +O(q^{10})$	\(q-2.20655 q^{2} +2.67875 q^{3} +2.86888 q^{4} -1.00223 q^{5} -5.91080 q^{6} -0.364832 q^{7} -1.91723 q^{8} +4.17568 q^{9} +2.21147 q^{10} -5.35352 q^{11} +7.68500 q^{12} -6.46098 q^{13} +0.805020 q^{14} -2.68472 q^{15} -1.50730 q^{16} +1.00000 q^{17} -9.21387 q^{18} -3.06045 q^{19} -2.87528 q^{20} -0.977291 q^{21} +11.8128 q^{22} +2.95741 q^{23} -5.13576 q^{24} -3.99553 q^{25} +14.2565 q^{26} +3.14936 q^{27} -1.04666 q^{28} -1.30975 q^{29} +5.92398 q^{30} +5.98569 q^{31} +7.16038 q^{32} -14.3407 q^{33} -2.20655 q^{34} +0.365645 q^{35} +11.9795 q^{36} +9.20893 q^{37} +6.75304 q^{38} -17.3073 q^{39} +1.92150 q^{40} -8.01650 q^{41} +2.15645 q^{42} +11.1833 q^{43} -15.3586 q^{44} -4.18500 q^{45} -6.52568 q^{46} -4.68029 q^{47} -4.03766 q^{48} -6.86690 q^{49} +8.81636 q^{50} +2.67875 q^{51} -18.5358 q^{52} +9.58340 q^{53} -6.94923 q^{54} +5.36546 q^{55} +0.699464 q^{56} -8.19816 q^{57} +2.89004 q^{58} +2.51485 q^{59} -7.70214 q^{60} -14.6376 q^{61} -13.2077 q^{62} -1.52342 q^{63} -12.7852 q^{64} +6.47539 q^{65} +31.6436 q^{66} +7.72822 q^{67} +2.86888 q^{68} +7.92215 q^{69} -0.806816 q^{70} +3.97963 q^{71} -8.00573 q^{72} +8.66686 q^{73} -20.3200 q^{74} -10.7030 q^{75} -8.78004 q^{76} +1.95313 q^{77} +38.1895 q^{78} -13.7229 q^{79} +1.51066 q^{80} -4.09072 q^{81} +17.6888 q^{82} +10.1605 q^{83} -2.80373 q^{84} -1.00223 q^{85} -24.6764 q^{86} -3.50850 q^{87} +10.2639 q^{88} +17.1622 q^{89} +9.23442 q^{90} +2.35717 q^{91} +8.48445 q^{92} +16.0341 q^{93} +10.3273 q^{94} +3.06727 q^{95} +19.1808 q^{96} +7.72048 q^{97} +15.1522 q^{98} -22.3546 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.20655	−1.56027	−0.780134	−	0.625612i	$-0.784849\pi$
$2$	−2.20655	−1.56027	−0.780134	+	0.625612i	$0.784849\pi$
$3$	2.67875	1.54658	0.773288	−	0.634056i	$-0.218611\pi$
$3$	2.67875	1.54658	0.773288	+	0.634056i	$0.218611\pi$
$4$	2.86888	1.43444
$5$	−1.00223	−0.448211	−0.224105	−	0.974565i	$-0.571946\pi$
$5$	−1.00223	−0.448211	−0.224105	+	0.974565i	$0.571946\pi$
$6$	−5.91080	−2.41307
$7$	−0.364832	−0.137893	−0.0689467	−	0.997620i	$-0.521964\pi$
$7$	−0.364832	−0.137893	−0.0689467	+	0.997620i	$0.521964\pi$
$8$	−1.91723	−0.677841
$9$	4.17568	1.39189
$10$	2.21147	0.699330
$11$	−5.35352	−1.61415	−0.807074	−	0.590451i	$-0.798950\pi$
$11$	−5.35352	−1.61415	−0.807074	+	0.590451i	$0.798950\pi$
$12$	7.68500	2.21847
$13$	−6.46098	−1.79195	−0.895977	−	0.444101i	$-0.853523\pi$
$13$	−6.46098	−1.79195	−0.895977	+	0.444101i	$0.853523\pi$
$14$	0.805020	0.215151
$15$	−2.68472	−0.693192
$16$	−1.50730	−0.376824
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−9.21387	−2.17173
$19$	−3.06045	−0.702114	−0.351057	−	0.936354i	$-0.614178\pi$
$19$	−3.06045	−0.702114	−0.351057	+	0.936354i	$0.614178\pi$
$20$	−2.87528	−0.642931
$21$	−0.977291	−0.213262
$22$	11.8128	2.51850
$23$	2.95741	0.616663	0.308331	−	0.951279i	$-0.400229\pi$
$23$	2.95741	0.616663	0.308331	+	0.951279i	$0.400229\pi$
$24$	−5.13576	−1.04833
$25$	−3.99553	−0.799107
$26$	14.2565	2.79593
$27$	3.14936	0.606094
$28$	−1.04666	−0.197800
$29$	−1.30975	−0.243215	−0.121608	−	0.992578i	$-0.538805\pi$
$29$	−1.30975	−0.243215	−0.121608	+	0.992578i	$0.538805\pi$
$30$	5.92398	1.08157
$31$	5.98569	1.07506	0.537531	−	0.843244i	$-0.319357\pi$
$31$	5.98569	1.07506	0.537531	+	0.843244i	$0.319357\pi$
$32$	7.16038	1.26579
$33$	−14.3407	−2.49640
$34$	−2.20655	−0.378421
$35$	0.365645	0.0618053
$36$	11.9795	1.99659
$37$	9.20893	1.51394	0.756969	−	0.653450i	$-0.226679\pi$
$37$	9.20893	1.51394	0.756969	+	0.653450i	$0.226679\pi$
$38$	6.75304	1.09549
$39$	−17.3073	−2.77139
$40$	1.92150	0.303816
$41$	−8.01650	−1.25197	−0.625983	−	0.779836i	$-0.715302\pi$
$41$	−8.01650	−1.25197	−0.625983	+	0.779836i	$0.715302\pi$
$42$	2.15645	0.332747
$43$	11.1833	1.70543	0.852715	−	0.522377i	$-0.174954\pi$
$43$	11.1833	1.70543	0.852715	+	0.522377i	$0.174954\pi$
$44$	−15.3586	−2.31540
$45$	−4.18500	−0.623862
$46$	−6.52568	−0.962160
$47$	−4.68029	−0.682691	−0.341345	−	0.939938i	$-0.610883\pi$
$47$	−4.68029	−0.682691	−0.341345	+	0.939938i	$0.610883\pi$
$48$	−4.03766	−0.582786
$49$	−6.86690	−0.980985
$50$	8.81636	1.24682
$51$	2.67875	0.375100
$52$	−18.5358	−2.57045
$53$	9.58340	1.31638	0.658191	−	0.752851i	$-0.271322\pi$
$53$	9.58340	1.31638	0.658191	+	0.752851i	$0.271322\pi$
$54$	−6.94923	−0.945670
$55$	5.36546	0.723479
$56$	0.699464	0.0934699
$57$	−8.19816	−1.08587
$58$	2.89004	0.379481
$59$	2.51485	0.327406	0.163703	−	0.986510i	$-0.447656\pi$
$59$	2.51485	0.327406	0.163703	+	0.986510i	$0.447656\pi$
$60$	−7.70214	−0.994341
$61$	−14.6376	−1.87415	−0.937077	−	0.349122i	$-0.886480\pi$
$61$	−14.6376	−1.87415	−0.937077	+	0.349122i	$0.886480\pi$
$62$	−13.2077	−1.67738
$63$	−1.52342	−0.191933
$64$	−12.7852	−1.59815
$65$	6.47539	0.803173
$66$	31.6436	3.89506
$67$	7.72822	0.944152	0.472076	−	0.881558i	$-0.343505\pi$
$67$	7.72822	0.944152	0.472076	+	0.881558i	$0.343505\pi$
$68$	2.86888	0.347903
$69$	7.92215	0.953715
$70$	−0.806816	−0.0964329
$71$	3.97963	0.472295	0.236147	−	0.971717i	$-0.424115\pi$
$71$	3.97963	0.472295	0.236147	+	0.971717i	$0.424115\pi$
$72$	−8.00573	−0.943484
$73$	8.66686	1.01438	0.507190	−	0.861835i	$-0.330684\pi$
$73$	8.66686	1.01438	0.507190	+	0.861835i	$0.330684\pi$
$74$	−20.3200	−2.36215
$75$	−10.7030	−1.23588
$76$	−8.78004	−1.00714
$77$	1.95313	0.222580
$78$	38.1895	4.32411
$79$	−13.7229	−1.54395	−0.771975	−	0.635653i	$-0.780731\pi$
$79$	−13.7229	−1.54395	−0.771975	+	0.635653i	$0.780731\pi$
$80$	1.51066	0.168897
$81$	−4.09072	−0.454524
$82$	17.6888	1.95340
$83$	10.1605	1.11526	0.557629	−	0.830090i	$-0.311711\pi$
$83$	10.1605	1.11526	0.557629	+	0.830090i	$0.311711\pi$
$84$	−2.80373	−0.305912
$85$	−1.00223	−0.108707
$86$	−24.6764	−2.66093
$87$	−3.50850	−0.376150
$88$	10.2639	1.09414
$89$	17.1622	1.81919	0.909593	−	0.415501i	$-0.136394\pi$
$89$	17.1622	1.81919	0.909593	+	0.415501i	$0.136394\pi$
$90$	9.23442	0.973393
$91$	2.35717	0.247099
$92$	8.48445	0.884565
$93$	16.0341	1.66266
$94$	10.3273	1.06518
$95$	3.06727	0.314695
$96$	19.1808	1.95764
$97$	7.72048	0.783896	0.391948	−	0.919987i	$-0.371801\pi$
$97$	7.72048	0.783896	0.391948	+	0.919987i	$0.371801\pi$
$98$	15.1522	1.53060
$99$	−22.3546	−2.24672
$100$	−11.4627	−1.14627
$101$	−3.67843	−0.366017	−0.183009	−	0.983111i	$-0.558584\pi$
$101$	−3.67843	−0.366017	−0.183009	+	0.983111i	$0.558584\pi$
$102$	−5.91080	−0.585256
$103$	12.9573	1.27672	0.638359	−	0.769739i	$-0.279614\pi$
$103$	12.9573	1.27672	0.638359	+	0.769739i	$0.279614\pi$
$104$	12.3872	1.21466
$105$	0.979471	0.0955866
$106$	−21.1463	−2.05391
$107$	−3.45899	−0.334393	−0.167197	−	0.985924i	$-0.553471\pi$
$107$	−3.45899	−0.334393	−0.167197	+	0.985924i	$0.553471\pi$
$108$	9.03512	0.869405
$109$	13.4647	1.28968	0.644842	−	0.764316i	$-0.276923\pi$
$109$	13.4647	1.28968	0.644842	+	0.764316i	$0.276923\pi$
$110$	−11.8392	−1.12882
$111$	24.6684	2.34142
$112$	0.549909	0.0519615
$113$	12.7565	1.20003	0.600013	−	0.799990i	$-0.295162\pi$
$113$	12.7565	1.20003	0.600013	+	0.799990i	$0.295162\pi$
$114$	18.0897	1.69425
$115$	−2.96401	−0.276395
$116$	−3.75752	−0.348877
$117$	−26.9790	−2.49421
$118$	−5.54916	−0.510842
$119$	−0.364832	−0.0334441
$120$	5.14721	0.469874
$121$	17.6602	1.60547
$122$	32.2987	2.92418
$123$	−21.4742	−1.93626
$124$	17.1722	1.54211
$125$	9.01560	0.806379
$126$	3.36151	0.299467
$127$	−2.62811	−0.233207	−0.116604	−	0.993179i	$-0.537201\pi$
$127$	−2.62811	−0.233207	−0.116604	+	0.993179i	$0.537201\pi$
$128$	13.8904	1.22775
$129$	29.9571	2.63758
$130$	−14.2883	−1.25317
$131$	−7.06183	−0.616995	−0.308498	−	0.951225i	$-0.599826\pi$
$131$	−7.06183	−0.616995	−0.308498	+	0.951225i	$0.599826\pi$
$132$	−41.1418	−3.58093
$133$	1.11655	0.0968169
$134$	−17.0527	−1.47313
$135$	−3.15638	−0.271658
$136$	−1.91723	−0.164401
$137$	−1.88915	−0.161401	−0.0807006	−	0.996738i	$-0.525716\pi$
$137$	−1.88915	−0.161401	−0.0807006	+	0.996738i	$0.525716\pi$
$138$	−17.4807	−1.48805
$139$	−1.90208	−0.161332	−0.0806659	−	0.996741i	$-0.525705\pi$
$139$	−1.90208	−0.161332	−0.0806659	+	0.996741i	$0.525705\pi$
$140$	1.04899	0.0886560
$141$	−12.5373	−1.05583
$142$	−8.78126	−0.736907
$143$	34.5890	2.89248
$144$	−6.29399	−0.524499
$145$	1.31267	0.109012
$146$	−19.1239	−1.58270
$147$	−18.3947	−1.51717
$148$	26.4193	2.17165
$149$	−9.12890	−0.747868	−0.373934	−	0.927455i	$-0.621991\pi$
$149$	−9.12890	−0.747868	−0.373934	+	0.927455i	$0.621991\pi$
$150$	23.6168	1.92830
$151$	−9.42179	−0.766735	−0.383367	−	0.923596i	$-0.625236\pi$
$151$	−9.42179	−0.766735	−0.383367	+	0.923596i	$0.625236\pi$
$152$	5.86756	0.475922
$153$	4.17568	0.337584
$154$	−4.30969	−0.347285
$155$	−5.99904	−0.481854
$156$	−49.6526	−3.97539
$157$	−6.91088	−0.551548	−0.275774	−	0.961222i	$-0.588934\pi$
$157$	−6.91088	−0.551548	−0.275774	+	0.961222i	$0.588934\pi$
$158$	30.2804	2.40898
$159$	25.6715	2.03588
$160$	−7.17635	−0.567340
$161$	−1.07896	−0.0850337
$162$	9.02639	0.709180
$163$	6.50288	0.509345	0.254672	−	0.967027i	$-0.418032\pi$
$163$	6.50288	0.509345	0.254672	+	0.967027i	$0.418032\pi$
$164$	−22.9984	−1.79587
$165$	14.3727	1.11891
$166$	−22.4197	−1.74010
$167$	8.02301	0.620839	0.310420	−	0.950600i	$-0.399530\pi$
$167$	8.02301	0.620839	0.310420	+	0.950600i	$0.399530\pi$
$168$	1.87369	0.144558
$169$	28.7443	2.21110
$170$	2.21147	0.169612
$171$	−12.7795	−0.977269
$172$	32.0834	2.44633
$173$	20.7954	1.58105	0.790524	−	0.612431i	$-0.209808\pi$
$173$	20.7954	1.58105	0.790524	+	0.612431i	$0.209808\pi$
$174$	7.74169	0.586896
$175$	1.45770	0.110192
$176$	8.06934	0.608249
$177$	6.73666	0.506358
$178$	−37.8692	−2.83842
$179$	−1.24144	−0.0927897	−0.0463949	−	0.998923i	$-0.514773\pi$
$179$	−1.24144	−0.0927897	−0.0463949	+	0.998923i	$0.514773\pi$
$180$	−12.0062	−0.894892
$181$	−10.4979	−0.780301	−0.390150	−	0.920751i	$-0.627577\pi$
$181$	−10.4979	−0.780301	−0.390150	+	0.920751i	$0.627577\pi$
$182$	−5.20122	−0.385540
$183$	−39.2105	−2.89852
$184$	−5.67002	−0.418000
$185$	−9.22947	−0.678564
$186$	−35.3802	−2.59420
$187$	−5.35352	−0.391488
$188$	−13.4272	−0.979278
$189$	−1.14899	−0.0835764
$190$	−6.76810	−0.491009
$191$	15.3851	1.11323	0.556614	−	0.830771i	$-0.312100\pi$
$191$	15.3851	1.11323	0.556614	+	0.830771i	$0.312100\pi$
$192$	−34.2482	−2.47165
$193$	−20.0503	−1.44325	−0.721627	−	0.692282i	$-0.756606\pi$
$193$	−20.0503	−1.44325	−0.721627	+	0.692282i	$0.756606\pi$
$194$	−17.0357	−1.22309
$195$	17.3459	1.24217
$196$	−19.7003	−1.40716
$197$	15.8318	1.12797	0.563985	−	0.825785i	$-0.309268\pi$
$197$	15.8318	1.12797	0.563985	+	0.825785i	$0.309268\pi$
$198$	49.3266	3.50549
$199$	−12.1082	−0.858326	−0.429163	−	0.903227i	$-0.641191\pi$
$199$	−12.1082	−0.858326	−0.429163	+	0.903227i	$0.641191\pi$
$200$	7.66034	0.541668
$201$	20.7019	1.46020
$202$	8.11665	0.571086
$203$	0.477840	0.0335378
$204$	7.68500	0.538057
$205$	8.03438	0.561145
$206$	−28.5909	−1.99202
$207$	12.3492	0.858329
$208$	9.73861	0.675251
$209$	16.3842	1.13332
$210$	−2.16126	−0.149141
$211$	16.2270	1.11711	0.558555	−	0.829467i	$-0.311356\pi$
$211$	16.2270	1.11711	0.558555	+	0.829467i	$0.311356\pi$
$212$	27.4936	1.88827
$213$	10.6604	0.730440
$214$	7.63245	0.521743
$215$	−11.2082	−0.764392
$216$	−6.03803	−0.410836
$217$	−2.18377	−0.148244
$218$	−29.7106	−2.01225
$219$	23.2163	1.56881
$220$	15.3929	1.03779
$221$	−6.46098	−0.434613
$222$	−54.4321	−3.65324
$223$	−20.6750	−1.38450	−0.692249	−	0.721659i	$-0.743380\pi$
$223$	−20.6750	−1.38450	−0.692249	+	0.721659i	$0.743380\pi$
$224$	−2.61233	−0.174544
$225$	−16.6841	−1.11227
$226$	−28.1478	−1.87236
$227$	16.8533	1.11859	0.559297	−	0.828967i	$-0.311071\pi$
$227$	16.8533	1.11859	0.559297	+	0.828967i	$0.311071\pi$
$228$	−23.5195	−1.55762
$229$	24.7810	1.63758	0.818788	−	0.574096i	$-0.194646\pi$
$229$	24.7810	1.63758	0.818788	+	0.574096i	$0.194646\pi$
$230$	6.54024	0.431250
$231$	5.23195	0.344237
$232$	2.51109	0.164861
$233$	24.2943	1.59158	0.795788	−	0.605576i	$-0.207057\pi$
$233$	24.2943	1.59158	0.795788	+	0.605576i	$0.207057\pi$
$234$	59.5306	3.89164
$235$	4.69073	0.305989
$236$	7.21481	0.469644
$237$	−36.7602	−2.38783
$238$	0.805020	0.0521817
$239$	19.7513	1.27760	0.638801	−	0.769372i	$-0.279431\pi$
$239$	19.7513	1.27760	0.638801	+	0.769372i	$0.279431\pi$
$240$	4.04667	0.261211
$241$	10.2343	0.659249	0.329624	−	0.944112i	$-0.393078\pi$
$241$	10.2343	0.659249	0.329624	+	0.944112i	$0.393078\pi$
$242$	−38.9682	−2.50497
$243$	−20.4061	−1.30905
$244$	−41.9935	−2.68836
$245$	6.88221	0.439688
$246$	47.3839	3.02109
$247$	19.7735	1.25816
$248$	−11.4759	−0.728721
$249$	27.2174	1.72483
$250$	−19.8934	−1.25817
$251$	−12.6414	−0.797915	−0.398958	−	0.916969i	$-0.630628\pi$
$251$	−12.6414	−0.797915	−0.398958	+	0.916969i	$0.630628\pi$
$252$	−4.37051	−0.275316
$253$	−15.8326	−0.995385
$254$	5.79907	0.363866
$255$	−2.68472	−0.168124
$256$	−5.07957	−0.317473
$257$	−8.45527	−0.527425	−0.263713	−	0.964601i	$-0.584947\pi$
$257$	−8.45527	−0.527425	−0.263713	+	0.964601i	$0.584947\pi$
$258$	−66.1019	−4.11533
$259$	−3.35971	−0.208762
$260$	18.5771	1.15210
$261$	−5.46912	−0.338530
$262$	15.5823	0.962678
$263$	−13.9383	−0.859475	−0.429737	−	0.902954i	$-0.641394\pi$
$263$	−13.9383	−0.859475	−0.429737	+	0.902954i	$0.641394\pi$
$264$	27.4944	1.69216
$265$	−9.60477	−0.590017
$266$	−2.46372	−0.151060
$267$	45.9731	2.81351
$268$	22.1713	1.35433
$269$	6.04699	0.368691	0.184346	−	0.982861i	$-0.440983\pi$
$269$	6.04699	0.368691	0.184346	+	0.982861i	$0.440983\pi$
$270$	6.96472	0.423860
$271$	9.55516	0.580434	0.290217	−	0.956961i	$-0.406272\pi$
$271$	9.55516	0.580434	0.290217	+	0.956961i	$0.406272\pi$
$272$	−1.50730	−0.0913932
$273$	6.31426	0.382156
$274$	4.16852	0.251829
$275$	21.3902	1.28988
$276$	22.7277	1.36805
$277$	11.2902	0.678360	0.339180	−	0.940721i	$-0.389850\pi$
$277$	11.2902	0.678360	0.339180	+	0.940721i	$0.389850\pi$
$278$	4.19703	0.251721
$279$	24.9943	1.49637
$280$	−0.701024	−0.0418942
$281$	7.11027	0.424163	0.212082	−	0.977252i	$-0.431976\pi$
$281$	7.11027	0.424163	0.212082	+	0.977252i	$0.431976\pi$
$282$	27.6643	1.64738
$283$	−4.47172	−0.265816	−0.132908	−	0.991128i	$-0.542431\pi$
$283$	−4.47172	−0.265816	−0.132908	+	0.991128i	$0.542431\pi$
$284$	11.4171	0.677478
$285$	8.21644	0.486700
$286$	−76.3225	−4.51304
$287$	2.92467	0.172638
$288$	29.8995	1.76184
$289$	1.00000	0.0588235
$290$	−2.89649	−0.170088
$291$	20.6812	1.21235
$292$	24.8642	1.45506
$293$	14.5046	0.847367	0.423684	−	0.905810i	$-0.360737\pi$
$293$	14.5046	0.847367	0.423684	+	0.905810i	$0.360737\pi$
$294$	40.5888	2.36719
$295$	−2.52046	−0.146747
$296$	−17.6556	−1.02621
$297$	−16.8602	−0.978325
$298$	20.1434	1.16688
$299$	−19.1078	−1.10503
$300$	−30.7057	−1.77279
$301$	−4.08000	−0.235167
$302$	20.7897	1.19631
$303$	−9.85358	−0.566073
$304$	4.61300	0.264574
$305$	14.6703	0.840017
$306$	−9.21387	−0.526722
$307$	−26.4410	−1.50907	−0.754534	−	0.656260i	$-0.772137\pi$
$307$	−26.4410	−1.50907	−0.754534	+	0.656260i	$0.772137\pi$
$308$	5.60330	0.319278
$309$	34.7093	1.97454
$310$	13.2372	0.751822
$311$	−8.45421	−0.479394	−0.239697	−	0.970848i	$-0.577048\pi$
$311$	−8.45421	−0.479394	−0.239697	+	0.970848i	$0.577048\pi$
$312$	33.1820	1.87856
$313$	−34.5948	−1.95542	−0.977708	−	0.209969i	$-0.932664\pi$
$313$	−34.5948	−1.95542	−0.977708	+	0.209969i	$0.932664\pi$
$314$	15.2492	0.860564
$315$	1.52682	0.0860265
$316$	−39.3694	−2.21470
$317$	20.7456	1.16519	0.582595	−	0.812763i	$-0.302038\pi$
$317$	20.7456	1.16519	0.582595	+	0.812763i	$0.302038\pi$
$318$	−56.6455	−3.17652
$319$	7.01179	0.392585
$320$	12.8137	0.716307
$321$	−9.26576	−0.517164
$322$	2.38078	0.132675
$323$	−3.06045	−0.170288
$324$	−11.7358	−0.651987
$325$	25.8151	1.43196
$326$	−14.3489	−0.794715
$327$	36.0685	1.99459
$328$	15.3694	0.848635
$329$	1.70752	0.0941385
$330$	−31.7142	−1.74581
$331$	−3.86761	−0.212583	−0.106292	−	0.994335i	$-0.533898\pi$
$331$	−3.86761	−0.212583	−0.106292	+	0.994335i	$0.533898\pi$
$332$	29.1492	1.59977
$333$	38.4536	2.10724
$334$	−17.7032	−0.968676
$335$	−7.74545	−0.423179
$336$	1.47307	0.0803624
$337$	−4.21452	−0.229580	−0.114790	−	0.993390i	$-0.536619\pi$
$337$	−4.21452	−0.229580	−0.114790	+	0.993390i	$0.536619\pi$
$338$	−63.4258	−3.44991
$339$	34.1713	1.85593
$340$	−2.87528	−0.155934
$341$	−32.0445	−1.73531
$342$	28.1985	1.52480
$343$	5.05908	0.273165
$344$	−21.4408	−1.15601
$345$	−7.93982	−0.427466
$346$	−45.8862	−2.46686
$347$	−31.7491	−1.70438	−0.852191	−	0.523231i	$-0.824726\pi$
$347$	−31.7491	−1.70438	−0.852191	+	0.523231i	$0.824726\pi$
$348$	−10.0655	−0.539565
$349$	−31.0184	−1.66038	−0.830188	−	0.557483i	$-0.811767\pi$
$349$	−31.0184	−1.66038	−0.830188	+	0.557483i	$0.811767\pi$
$350$	−3.21649	−0.171928
$351$	−20.3479	−1.08609
$352$	−38.3332	−2.04317
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−14.8648	−0.790055
$355$	−3.98850	−0.211688
$356$	49.2362	2.60951
$357$	−0.977291	−0.0517237
$358$	2.73931	0.144777
$359$	18.0104	0.950552	0.475276	−	0.879837i	$-0.342348\pi$
$359$	18.0104	0.950552	0.475276	+	0.879837i	$0.342348\pi$
$360$	8.02358	0.422880
$361$	−9.63367	−0.507035
$362$	23.1641	1.21748
$363$	47.3072	2.48298
$364$	6.76243	0.354448
$365$	−8.68619	−0.454656
$366$	86.5200	4.52247
$367$	12.5247	0.653783	0.326892	−	0.945062i	$-0.393999\pi$
$367$	12.5247	0.653783	0.326892	+	0.945062i	$0.393999\pi$
$368$	−4.45769	−0.232373
$369$	−33.4744	−1.74261
$370$	20.3653	1.05874
$371$	−3.49633	−0.181520
$372$	46.0000	2.38499
$373$	−19.7418	−1.02219	−0.511097	−	0.859523i	$-0.670761\pi$
$373$	−19.7418	−1.02219	−0.511097	+	0.859523i	$0.670761\pi$
$374$	11.8128	0.610827
$375$	24.1505	1.24713
$376$	8.97317	0.462756
$377$	8.46229	0.435830
$378$	2.53530	0.130402
$379$	−26.9722	−1.38547	−0.692734	−	0.721193i	$-0.743594\pi$
$379$	−26.9722	−1.38547	−0.692734	+	0.721193i	$0.743594\pi$
$380$	8.79963	0.451411
$381$	−7.04005	−0.360673
$382$	−33.9481	−1.73694
$383$	25.9535	1.32616	0.663081	−	0.748548i	$-0.269249\pi$
$383$	25.9535	1.32616	0.663081	+	0.748548i	$0.269249\pi$
$384$	37.2088	1.89881
$385$	−1.95749	−0.0997629
$386$	44.2421	2.25187
$387$	46.6977	2.37378
$388$	22.1491	1.12445
$389$	−4.40090	−0.223134	−0.111567	−	0.993757i	$-0.535587\pi$
$389$	−4.40090	−0.223134	−0.111567	+	0.993757i	$0.535587\pi$
$390$	−38.2747	−1.93812
$391$	2.95741	0.149563
$392$	13.1654	0.664953
$393$	−18.9169	−0.954229
$394$	−34.9337	−1.75994
$395$	13.7535	0.692015
$396$	−64.1327	−3.22279
$397$	7.74064	0.388492	0.194246	−	0.980953i	$-0.437774\pi$
$397$	7.74064	0.388492	0.194246	+	0.980953i	$0.437774\pi$
$398$	26.7173	1.33922
$399$	2.99095	0.149735
$400$	6.02245	0.301123
$401$	4.01483	0.200491	0.100246	−	0.994963i	$-0.468037\pi$
$401$	4.01483	0.200491	0.100246	+	0.994963i	$0.468037\pi$
$402$	−45.6799	−2.27831
$403$	−38.6734	−1.92646
$404$	−10.5530	−0.525030
$405$	4.09984	0.203723
$406$	−1.05438	−0.0523279
$407$	−49.3002	−2.44372
$408$	−5.13576	−0.254258
$409$	−0.412311	−0.0203875	−0.0101937	−	0.999948i	$-0.503245\pi$
$409$	−0.412311	−0.0203875	−0.0101937	+	0.999948i	$0.503245\pi$
$410$	−17.7283	−0.875537
$411$	−5.06056	−0.249619
$412$	37.1728	1.83137
$413$	−0.917498	−0.0451471
$414$	−27.2492	−1.33922
$415$	−10.1832	−0.499871
$416$	−46.2631	−2.26823
$417$	−5.09518	−0.249512
$418$	−36.1525	−1.76828
$419$	39.4329	1.92642	0.963211	−	0.268747i	$-0.0866097\pi$
$419$	39.4329	1.92642	0.963211	+	0.268747i	$0.0866097\pi$
$420$	2.80998	0.137113
$421$	−14.9102	−0.726676	−0.363338	−	0.931657i	$-0.618363\pi$
$421$	−14.9102	−0.726676	−0.363338	+	0.931657i	$0.618363\pi$
$422$	−35.8057	−1.74299
$423$	−19.5434	−0.950233
$424$	−18.3735	−0.892298
$425$	−3.99553	−0.193812
$426$	−23.5228	−1.13968
$427$	5.34026	0.258434
$428$	−9.92342	−0.479667
$429$	92.6552	4.47343
$430$	24.7315	1.19266
$431$	−13.1199	−0.631965	−0.315983	−	0.948765i	$-0.602334\pi$
$431$	−13.1199	−0.631965	−0.315983	+	0.948765i	$0.602334\pi$
$432$	−4.74701	−0.228391
$433$	−16.1179	−0.774578	−0.387289	−	0.921958i	$-0.626588\pi$
$433$	−16.1179	−0.774578	−0.387289	+	0.921958i	$0.626588\pi$
$434$	4.81860	0.231300
$435$	3.51632	0.168595
$436$	38.6286	1.84997
$437$	−9.05099	−0.432968
$438$	−51.2280	−2.44777
$439$	−17.3083	−0.826079	−0.413039	−	0.910713i	$-0.635533\pi$
$439$	−17.3083	−0.826079	−0.413039	+	0.910713i	$0.635533\pi$
$440$	−10.2868	−0.490404
$441$	−28.6740	−1.36543
$442$	14.2565	0.678112
$443$	−24.6542	−1.17136	−0.585679	−	0.810543i	$-0.699172\pi$
$443$	−24.6542	−1.17136	−0.585679	+	0.810543i	$0.699172\pi$
$444$	70.7706	3.35862
$445$	−17.2004	−0.815379
$446$	45.6204	2.16019
$447$	−24.4540	−1.15663
$448$	4.66443	0.220374
$449$	16.0799	0.758858	0.379429	−	0.925221i	$-0.376120\pi$
$449$	16.0799	0.758858	0.379429	+	0.925221i	$0.376120\pi$
$450$	36.8143	1.73544
$451$	42.9165	2.02086
$452$	36.5967	1.72137
$453$	−25.2386	−1.18581
$454$	−37.1878	−1.74531
$455$	−2.36243	−0.110752
$456$	15.7177	0.736050
$457$	7.43558	0.347822	0.173911	−	0.984761i	$-0.444360\pi$
$457$	7.43558	0.347822	0.173911	+	0.984761i	$0.444360\pi$
$458$	−54.6807	−2.55506
$459$	3.14936	0.146999
$460$	−8.50337	−0.396472
$461$	−4.30875	−0.200678	−0.100339	−	0.994953i	$-0.531993\pi$
$461$	−4.30875	−0.200678	−0.100339	+	0.994953i	$0.531993\pi$
$462$	−11.5446	−0.537102
$463$	−13.8400	−0.643199	−0.321600	−	0.946876i	$-0.604221\pi$
$463$	−13.8400	−0.643199	−0.321600	+	0.946876i	$0.604221\pi$
$464$	1.97419	0.0916493
$465$	−16.0699	−0.745224
$466$	−53.6068	−2.48329
$467$	16.2476	0.751850	0.375925	−	0.926650i	$-0.377325\pi$
$467$	16.2476	0.751850	0.375925	+	0.926650i	$0.377325\pi$
$468$	−77.3995	−3.57779
$469$	−2.81950	−0.130192
$470$	−10.3503	−0.477426
$471$	−18.5125	−0.853011
$472$	−4.82154	−0.221929
$473$	−59.8698	−2.75282
$474$	81.1134	3.72566
$475$	12.2281	0.561064
$476$	−1.04666	−0.0479735
$477$	40.0172	1.83226
$478$	−43.5822	−1.99340
$479$	−3.08733	−0.141064	−0.0705318	−	0.997510i	$-0.522470\pi$
$479$	−3.08733	−0.141064	−0.0705318	+	0.997510i	$0.522470\pi$
$480$	−19.2236	−0.877434
$481$	−59.4987	−2.71291
$482$	−22.5825	−1.02861
$483$	−2.89025	−0.131511
$484$	50.6649	2.30295
$485$	−7.73770	−0.351351
$486$	45.0271	2.04247
$487$	−3.27789	−0.148535	−0.0742677	−	0.997238i	$-0.523662\pi$
$487$	−3.27789	−0.148535	−0.0742677	+	0.997238i	$0.523662\pi$
$488$	28.0636	1.27038
$489$	17.4196	0.787740
$490$	−15.1860	−0.686032
$491$	−19.3627	−0.873826	−0.436913	−	0.899504i	$-0.643928\pi$
$491$	−19.3627	−0.873826	−0.436913	+	0.899504i	$0.643928\pi$
$492$	−61.6068	−2.77745
$493$	−1.30975	−0.0589883
$494$	−43.6312	−1.96306
$495$	22.4045	1.00701
$496$	−9.02220	−0.405109
$497$	−1.45189	−0.0651264
$498$	−60.0566	−2.69120
$499$	3.10846	0.139154	0.0695768	−	0.997577i	$-0.477835\pi$
$499$	3.10846	0.139154	0.0695768	+	0.997577i	$0.477835\pi$
$500$	25.8646	1.15670
$501$	21.4916	0.960174
$502$	27.8938	1.24496
$503$	1.36245	0.0607487	0.0303744	−	0.999539i	$-0.490330\pi$
$503$	1.36245	0.0607487	0.0303744	+	0.999539i	$0.490330\pi$
$504$	2.92074	0.130100
$505$	3.68663	0.164053
$506$	34.9354	1.55307
$507$	76.9986	3.41963
$508$	−7.53974	−0.334522
$509$	−9.07044	−0.402040	−0.201020	−	0.979587i	$-0.564426\pi$
$509$	−9.07044	−0.402040	−0.201020	+	0.979587i	$0.564426\pi$
$510$	5.92398	0.262318
$511$	−3.16194	−0.139876
$512$	−16.5725	−0.732406
$513$	−9.63844	−0.425547
$514$	18.6570	0.822925
$515$	−12.9862	−0.572239
$516$	85.9432	3.78344
$517$	25.0560	1.10196
$518$	7.41338	0.325725
$519$	55.7057	2.44521
$520$	−12.4148	−0.544424
$521$	6.46075	0.283051	0.141525	−	0.989935i	$-0.454799\pi$
$521$	6.46075	0.283051	0.141525	+	0.989935i	$0.454799\pi$
$522$	12.0679	0.528198
$523$	33.8134	1.47856	0.739278	−	0.673401i	$-0.235167\pi$
$523$	33.8134	1.47856	0.739278	+	0.673401i	$0.235167\pi$
$524$	−20.2595	−0.885042
$525$	3.90480	0.170420
$526$	30.7557	1.34101
$527$	5.98569	0.260741
$528$	21.6157	0.940703
$529$	−14.2537	−0.619727
$530$	21.1934	0.920584
$531$	10.5012	0.455715
$532$	3.20324	0.138878
$533$	51.7944	2.24347
$534$	−101.442	−4.38983
$535$	3.46670	0.149879
$536$	−14.8167	−0.639985
$537$	−3.32551	−0.143506
$538$	−13.3430	−0.575258
$539$	36.7621	1.58346
$540$	−9.05527	−0.389677
$541$	−18.9401	−0.814300	−0.407150	−	0.913361i	$-0.633477\pi$
$541$	−18.9401	−0.814300	−0.407150	+	0.913361i	$0.633477\pi$
$542$	−21.0840	−0.905634
$543$	−28.1211	−1.20679
$544$	7.16038	0.306999
$545$	−13.4947	−0.578050
$546$	−13.9328	−0.596267
$547$	−4.22249	−0.180541	−0.0902704	−	0.995917i	$-0.528773\pi$
$547$	−4.22249	−0.180541	−0.0902704	+	0.995917i	$0.528773\pi$
$548$	−5.41975	−0.231520
$549$	−61.1220	−2.60863
$550$	−47.1986	−2.01255
$551$	4.00843	0.170765
$552$	−15.1886	−0.646468
$553$	5.00656	0.212900
$554$	−24.9124	−1.05842
$555$	−24.7234	−1.04945
$556$	−5.45682	−0.231421
$557$	29.3593	1.24400	0.621998	−	0.783019i	$-0.286321\pi$
$557$	29.3593	1.24400	0.621998	+	0.783019i	$0.286321\pi$
$558$	−55.1513	−2.33474
$559$	−72.2548	−3.05605
$560$	−0.551136	−0.0232897
$561$	−14.3407	−0.605466
$562$	−15.6892	−0.661809
$563$	17.1308	0.721978	0.360989	−	0.932570i	$-0.382439\pi$
$563$	17.1308	0.721978	0.360989	+	0.932570i	$0.382439\pi$
$564$	−35.9680	−1.51453
$565$	−12.7849	−0.537865
$566$	9.86709	0.414745
$567$	1.49242	0.0626759
$568$	−7.62984	−0.320141
$569$	12.8054	0.536830	0.268415	−	0.963303i	$-0.413500\pi$
$569$	12.8054	0.536830	0.268415	+	0.963303i	$0.413500\pi$
$570$	−18.1300	−0.759383
$571$	4.06469	0.170102	0.0850510	−	0.996377i	$-0.472895\pi$
$571$	4.06469	0.170102	0.0850510	+	0.996377i	$0.472895\pi$
$572$	99.2316	4.14908
$573$	41.2128	1.72169
$574$	−6.45344	−0.269362
$575$	−11.8164	−0.492779
$576$	−53.3868	−2.22445
$577$	4.95060	0.206096	0.103048	−	0.994676i	$-0.467140\pi$
$577$	4.95060	0.206096	0.103048	+	0.994676i	$0.467140\pi$
$578$	−2.20655	−0.0917805
$579$	−53.7098	−2.23210
$580$	3.76590	0.156371
$581$	−3.70687	−0.153787
$582$	−45.6342	−1.89160
$583$	−51.3049	−2.12483
$584$	−16.6163	−0.687588
$585$	27.0392	1.11793
$586$	−32.0051	−1.32212
$587$	26.3385	1.08711	0.543553	−	0.839375i	$-0.317079\pi$
$587$	26.3385	1.08711	0.543553	+	0.839375i	$0.317079\pi$
$588$	−52.7721	−2.17628
$589$	−18.3189	−0.754816
$590$	5.56154	0.228965
$591$	42.4094	1.74449
$592$	−13.8806	−0.570488
$593$	18.3334	0.752861	0.376431	−	0.926445i	$-0.377151\pi$
$593$	18.3334	0.752861	0.376431	+	0.926445i	$0.377151\pi$
$594$	37.2028	1.52645
$595$	0.365645	0.0149900
$596$	−26.1897	−1.07277
$597$	−32.4347	−1.32747
$598$	42.1623	1.72415
$599$	−22.2629	−0.909639	−0.454819	−	0.890584i	$-0.650296\pi$
$599$	−22.2629	−0.909639	−0.454819	+	0.890584i	$0.650296\pi$
$600$	20.5201	0.837730
$601$	−10.1811	−0.415298	−0.207649	−	0.978203i	$-0.566581\pi$
$601$	−10.1811	−0.415298	−0.207649	+	0.978203i	$0.566581\pi$
$602$	9.00275	0.366925
$603$	32.2706	1.31416
$604$	−27.0300	−1.09983
$605$	−17.6996	−0.719590
$606$	21.7425	0.883227
$607$	41.0924	1.66789	0.833945	−	0.551847i	$-0.186077\pi$
$607$	41.0924	1.66789	0.833945	+	0.551847i	$0.186077\pi$
$608$	−21.9140	−0.888728
$609$	1.28001	0.0518687
$610$	−32.3707	−1.31065
$611$	30.2393	1.22335
$612$	11.9795	0.484244
$613$	−2.86237	−0.115610	−0.0578050	−	0.998328i	$-0.518410\pi$
$613$	−2.86237	−0.115610	−0.0578050	+	0.998328i	$0.518410\pi$
$614$	58.3435	2.35455
$615$	21.5221	0.867853
$616$	−3.74460	−0.150874
$617$	−22.9869	−0.925416	−0.462708	−	0.886511i	$-0.653122\pi$
$617$	−22.9869	−0.925416	−0.462708	+	0.886511i	$0.653122\pi$
$618$	−76.5878	−3.08081
$619$	11.3139	0.454744	0.227372	−	0.973808i	$-0.426987\pi$
$619$	11.3139	0.454744	0.227372	+	0.973808i	$0.426987\pi$
$620$	−17.2105	−0.691191
$621$	9.31394	0.373756
$622$	18.6547	0.747984
$623$	−6.26130	−0.250854
$624$	26.0873	1.04433
$625$	10.9420	0.437679
$626$	76.3354	3.05097
$627$	43.8890	1.75276
$628$	−19.8265	−0.791162
$629$	9.20893	0.367184
$630$	−3.36901	−0.134224
$631$	43.5588	1.73405	0.867025	−	0.498265i	$-0.166029\pi$
$631$	43.5588	1.73405	0.867025	+	0.498265i	$0.166029\pi$
$632$	26.3099	1.04655
$633$	43.4679	1.72769
$634$	−45.7763	−1.81801
$635$	2.63398	0.104526
$636$	73.6484	2.92035
$637$	44.3669	1.75788
$638$	−15.4719	−0.612538
$639$	16.6177	0.657385
$640$	−13.9214	−0.550291
$641$	−30.1508	−1.19088	−0.595442	−	0.803398i	$-0.703023\pi$
$641$	−30.1508	−1.19088	−0.595442	+	0.803398i	$0.703023\pi$
$642$	20.4454	0.806915
$643$	20.5613	0.810858	0.405429	−	0.914127i	$-0.367122\pi$
$643$	20.5613	0.810858	0.405429	+	0.914127i	$0.367122\pi$
$644$	−3.09540	−0.121976
$645$	−30.0239	−1.18219
$646$	6.75304	0.265695
$647$	−48.2995	−1.89885	−0.949424	−	0.313995i	$-0.898332\pi$
$647$	−48.2995	−1.89885	−0.949424	+	0.313995i	$0.898332\pi$
$648$	7.84283	0.308095
$649$	−13.4633	−0.528482
$650$	−56.9623	−2.23425
$651$	−5.84976	−0.229270
$652$	18.6560	0.730624
$653$	36.1484	1.41460	0.707298	−	0.706916i	$-0.249914\pi$
$653$	36.1484	1.41460	0.707298	+	0.706916i	$0.249914\pi$
$654$	−79.5871	−3.11210
$655$	7.07758	0.276544
$656$	12.0832	0.471771
$657$	36.1901	1.41191
$658$	−3.76773	−0.146881
$659$	4.07344	0.158679	0.0793393	−	0.996848i	$-0.474719\pi$
$659$	4.07344	0.158679	0.0793393	+	0.996848i	$0.474719\pi$
$660$	41.2336	1.60501
$661$	−26.9726	−1.04911	−0.524556	−	0.851376i	$-0.675769\pi$
$661$	−26.9726	−1.04911	−0.524556	+	0.851376i	$0.675769\pi$
$662$	8.53409	0.331687
$663$	−17.3073	−0.672161
$664$	−19.4800	−0.755969
$665$	−1.11904	−0.0433944
$666$	−84.8499	−3.28787
$667$	−3.87348	−0.149982
$668$	23.0170	0.890556
$669$	−55.3830	−2.14123
$670$	17.0908	0.660273
$671$	78.3628	3.02516
$672$	−6.99778	−0.269945
$673$	30.3496	1.16989	0.584946	−	0.811072i	$-0.301116\pi$
$673$	30.3496	1.16989	0.584946	+	0.811072i	$0.301116\pi$
$674$	9.29957	0.358206
$675$	−12.5834	−0.484334
$676$	82.4638	3.17168
$677$	36.2744	1.39414	0.697069	−	0.717004i	$-0.254487\pi$
$677$	36.2744	1.39414	0.697069	+	0.717004i	$0.254487\pi$
$678$	−75.4009	−2.89575
$679$	−2.81668	−0.108094
$680$	1.92150	0.0736862
$681$	45.1458	1.72999
$682$	70.7079	2.70755
$683$	−38.6725	−1.47976	−0.739882	−	0.672737i	$-0.765119\pi$
$683$	−38.6725	−1.47976	−0.739882	+	0.672737i	$0.765119\pi$
$684$	−36.6627	−1.40183
$685$	1.89337	0.0723418
$686$	−11.1631	−0.426211
$687$	66.3821	2.53263
$688$	−16.8565	−0.642647
$689$	−61.9182	−2.35889
$690$	17.5196	0.666961
$691$	−19.2295	−0.731524	−0.365762	−	0.930708i	$-0.619192\pi$
$691$	−19.2295	−0.731524	−0.365762	+	0.930708i	$0.619192\pi$
$692$	59.6596	2.26792
$693$	8.15567	0.309808
$694$	70.0561	2.65929
$695$	1.90632	0.0723107
$696$	6.72658	0.254970
$697$	−8.01650	−0.303646
$698$	68.4438	2.59063
$699$	65.0784	2.46149
$700$	4.18196	0.158063
$701$	0.581284	0.0219548	0.0109774	−	0.999940i	$-0.496506\pi$
$701$	0.581284	0.0219548	0.0109774	+	0.999940i	$0.496506\pi$
$702$	44.8988	1.69460
$703$	−28.1834	−1.06296
$704$	68.4457	2.57964
$705$	12.5653	0.473236
$706$	2.20655	0.0830447
$707$	1.34201	0.0504714
$708$	19.3266	0.726340
$709$	17.7329	0.665972	0.332986	−	0.942932i	$-0.391944\pi$
$709$	17.7329	0.665972	0.332986	+	0.942932i	$0.391944\pi$
$710$	8.80085	0.330290
$711$	−57.3026	−2.14901
$712$	−32.9037	−1.23312
$713$	17.7021	0.662950
$714$	2.15645	0.0807030
$715$	−34.6661	−1.29644
$716$	−3.56154	−0.133101
$717$	52.9086	1.97591
$718$	−39.7409	−1.48312
$719$	11.9942	0.447310	0.223655	−	0.974668i	$-0.428201\pi$
$719$	11.9942	0.447310	0.223655	+	0.974668i	$0.428201\pi$
$720$	6.30803	0.235086
$721$	−4.72722	−0.176051
$722$	21.2572	0.791112
$723$	27.4151	1.01958
$724$	−30.1171	−1.11929
$725$	5.23317	0.194355
$726$	−104.386	−3.87412
$727$	51.4386	1.90775	0.953877	−	0.300198i	$-0.0970527\pi$
$727$	51.4386	1.90775	0.953877	+	0.300198i	$0.0970527\pi$
$728$	−4.51923	−0.167494
$729$	−42.3905	−1.57002
$730$	19.1665	0.709385
$731$	11.1833	0.413627
$732$	−112.490	−4.15775
$733$	23.4499	0.866143	0.433072	−	0.901359i	$-0.357430\pi$
$733$	23.4499	0.866143	0.433072	+	0.901359i	$0.357430\pi$
$734$	−27.6364	−1.02008
$735$	18.4357	0.680011
$736$	21.1762	0.780564
$737$	−41.3732	−1.52400
$738$	73.8629	2.71893
$739$	40.9071	1.50479	0.752396	−	0.658711i	$-0.228898\pi$
$739$	40.9071	1.50479	0.752396	+	0.658711i	$0.228898\pi$
$740$	−26.4782	−0.973358
$741$	52.9681	1.94583
$742$	7.71483	0.283220
$743$	−3.33787	−0.122455	−0.0612274	−	0.998124i	$-0.519501\pi$
$743$	−3.33787	−0.122455	−0.0612274	+	0.998124i	$0.519501\pi$
$744$	−30.7411	−1.12702
$745$	9.14926	0.335203
$746$	43.5614	1.59490
$747$	42.4270	1.55232
$748$	−15.3586	−0.561566
$749$	1.26195	0.0461106
$750$	−53.2894	−1.94585
$751$	20.8746	0.761725	0.380863	−	0.924632i	$-0.375627\pi$
$751$	20.8746	0.761725	0.380863	+	0.924632i	$0.375627\pi$
$752$	7.05458	0.257254
$753$	−33.8630	−1.23404
$754$	−18.6725	−0.680012
$755$	9.44281	0.343659
$756$	−3.29630	−0.119885
$757$	−11.6708	−0.424183	−0.212092	−	0.977250i	$-0.568028\pi$
$757$	−11.6708	−0.424183	−0.212092	+	0.977250i	$0.568028\pi$
$758$	59.5156	2.16170
$759$	−42.4114	−1.53944
$760$	−5.88065	−0.213314
$761$	−20.3438	−0.737461	−0.368731	−	0.929536i	$-0.620208\pi$
$761$	−20.3438	−0.737461	−0.368731	+	0.929536i	$0.620208\pi$
$762$	15.5342	0.562746
$763$	−4.91235	−0.177839
$764$	44.1380	1.59686
$765$	−4.18500	−0.151309
$766$	−57.2678	−2.06917
$767$	−16.2484	−0.586696
$768$	−13.6069	−0.490996
$769$	42.9865	1.55013	0.775066	−	0.631881i	$-0.217717\pi$
$769$	42.9865	1.55013	0.775066	+	0.631881i	$0.217717\pi$
$770$	4.31931	0.155657
$771$	−22.6495	−0.815702
$772$	−57.5220	−2.07026
$773$	37.1504	1.33621	0.668103	−	0.744068i	$-0.267106\pi$
$773$	37.1504	1.33621	0.668103	+	0.744068i	$0.267106\pi$
$774$	−103.041	−3.70373
$775$	−23.9160	−0.859089
$776$	−14.8019	−0.531357
$777$	−8.99981	−0.322866
$778$	9.71082	0.348150
$779$	24.5341	0.879024
$780$	49.7633	1.78181
$781$	−21.3050	−0.762354
$782$	−6.52568	−0.233358
$783$	−4.12488	−0.147411
$784$	10.3504	0.369659
$785$	6.92629	0.247210
$786$	41.7411	1.48885
$787$	−13.8032	−0.492031	−0.246016	−	0.969266i	$-0.579121\pi$
$787$	−13.8032	−0.492031	−0.246016	+	0.969266i	$0.579121\pi$
$788$	45.4195	1.61800
$789$	−37.3373	−1.32924
$790$	−30.3479	−1.07973
$791$	−4.65396	−0.165476
$792$	42.8588	1.52292
$793$	94.5733	3.35840
$794$	−17.0801	−0.606151
$795$	−25.7288	−0.912505
$796$	−34.7369	−1.23122
$797$	26.6957	0.945609	0.472805	−	0.881167i	$-0.343242\pi$
$797$	26.6957	0.945609	0.472805	+	0.881167i	$0.343242\pi$
$798$	−6.59969	−0.233626
$799$	−4.68029	−0.165577
$800$	−28.6095	−1.01150
$801$	71.6638	2.53211
$802$	−8.85894	−0.312820
$803$	−46.3982	−1.63736
$804$	59.3913	2.09457
$805$	1.08136	0.0381130
$806$	85.3350	3.00580
$807$	16.1983	0.570209
$808$	7.05238	0.248102
$809$	41.4694	1.45799	0.728994	−	0.684520i	$-0.239988\pi$
$809$	41.4694	1.45799	0.728994	+	0.684520i	$0.239988\pi$
$810$	−9.04652	−0.317862
$811$	−23.9139	−0.839729	−0.419865	−	0.907587i	$-0.637922\pi$
$811$	−23.9139	−0.839729	−0.419865	+	0.907587i	$0.637922\pi$
$812$	1.37086	0.0481079
$813$	25.5958	0.897685
$814$	108.784	3.81286
$815$	−6.51738	−0.228294
$816$	−4.03766	−0.141346
$817$	−34.2257	−1.19741
$818$	0.909786	0.0318099
$819$	9.84279	0.343935
$820$	23.0496	0.804928
$821$	10.1483	0.354179	0.177089	−	0.984195i	$-0.443332\pi$
$821$	10.1483	0.354179	0.177089	+	0.984195i	$0.443332\pi$
$822$	11.1664	0.389473
$823$	9.66925	0.337049	0.168524	−	0.985697i	$-0.446100\pi$
$823$	9.66925	0.337049	0.168524	+	0.985697i	$0.446100\pi$
$824$	−24.8420	−0.865412
$825$	57.2989	1.99489
$826$	2.02451	0.0704417
$827$	−2.78436	−0.0968217	−0.0484108	−	0.998828i	$-0.515416\pi$
$827$	−2.78436	−0.0968217	−0.0484108	+	0.998828i	$0.515416\pi$
$828$	35.4284	1.23122
$829$	14.9185	0.518141	0.259070	−	0.965858i	$-0.416584\pi$
$829$	14.9185	0.518141	0.259070	+	0.965858i	$0.416584\pi$
$830$	22.4697	0.779934
$831$	30.2435	1.04914
$832$	82.6047	2.86380
$833$	−6.86690	−0.237924
$834$	11.2428	0.389306
$835$	−8.04090	−0.278267
$836$	47.0042	1.62567
$837$	18.8511	0.651588
$838$	−87.0107	−3.00574
$839$	47.3596	1.63503	0.817517	−	0.575904i	$-0.195350\pi$
$839$	47.3596	1.63503	0.817517	+	0.575904i	$0.195350\pi$
$840$	−1.87787	−0.0647926
$841$	−27.2845	−0.940846
$842$	32.9001	1.13381
$843$	19.0466	0.656000
$844$	46.5532	1.60243
$845$	−28.8084	−0.991038
$846$	43.1236	1.48262
$847$	−6.44300	−0.221384
$848$	−14.4450	−0.496044
$849$	−11.9786	−0.411105
$850$	8.81636	0.302399
$851$	27.2346	0.933589
$852$	30.5834	1.04777
$853$	−20.7632	−0.710920	−0.355460	−	0.934692i	$-0.615676\pi$
$853$	−20.7632	−0.710920	−0.355460	+	0.934692i	$0.615676\pi$
$854$	−11.7836	−0.403226
$855$	12.8080	0.438023
$856$	6.63166	0.226666
$857$	−41.3602	−1.41284	−0.706419	−	0.707794i	$-0.749690\pi$
$857$	−41.3602	−1.41284	−0.706419	+	0.707794i	$0.749690\pi$
$858$	−204.449	−6.97976
$859$	−27.0147	−0.921729	−0.460864	−	0.887471i	$-0.652461\pi$
$859$	−27.0147	−0.921729	−0.460864	+	0.887471i	$0.652461\pi$
$860$	−32.1549	−1.09647
$861$	7.83445	0.266997
$862$	28.9499	0.986036
$863$	−31.6353	−1.07688	−0.538439	−	0.842665i	$-0.680986\pi$
$863$	−31.6353	−1.07688	−0.538439	+	0.842665i	$0.680986\pi$
$864$	22.5506	0.767187
$865$	−20.8418	−0.708643
$866$	35.5650	1.20855
$867$	2.67875	0.0909750
$868$	−6.26497	−0.212647
$869$	73.4660	2.49216
$870$	−7.75895	−0.263053
$871$	−49.9319	−1.69188
$872$	−25.8149	−0.874201
$873$	32.2383	1.09110
$874$	19.9715	0.675546
$875$	−3.28917	−0.111194
$876$	66.6048	2.25037
$877$	−49.7257	−1.67912	−0.839558	−	0.543269i	$-0.817186\pi$
$877$	−49.7257	−1.67912	−0.839558	+	0.543269i	$0.817186\pi$
$878$	38.1916	1.28891
$879$	38.8541	1.31052
$880$	−8.08734	−0.272624
$881$	35.9991	1.21284	0.606421	−	0.795144i	$-0.292605\pi$
$881$	35.9991	1.21284	0.606421	+	0.795144i	$0.292605\pi$
$882$	63.2707	2.13043
$883$	−5.02946	−0.169255	−0.0846273	−	0.996413i	$-0.526970\pi$
$883$	−5.02946	−0.169255	−0.0846273	+	0.996413i	$0.526970\pi$
$884$	−18.5358	−0.623425
$885$	−6.75168	−0.226955
$886$	54.4009	1.82763
$887$	−24.0362	−0.807056	−0.403528	−	0.914967i	$-0.632216\pi$
$887$	−24.0362	−0.807056	−0.403528	+	0.914967i	$0.632216\pi$
$888$	−47.2949	−1.58711
$889$	0.958819	0.0321578
$890$	37.9537	1.27221
$891$	21.8998	0.733669
$892$	−59.3140	−1.98598
$893$	14.3238	0.479327
$894$	53.9591	1.80466
$895$	1.24421	0.0415894
$896$	−5.06766	−0.169298
$897$	−51.1849	−1.70901
$898$	−35.4812	−1.18402
$899$	−7.83978	−0.261471
$900$	−47.8646	−1.59549
$901$	9.58340	0.319269
$902$	−94.6975	−3.15308
$903$	−10.9293	−0.363704
$904$	−24.4570	−0.813428
$905$	10.5213	0.349739
$906$	55.6903	1.85019
$907$	−18.6119	−0.618000	−0.309000	−	0.951062i	$-0.599994\pi$
$907$	−18.6119	−0.618000	−0.309000	+	0.951062i	$0.599994\pi$
$908$	48.3501	1.60456
$909$	−15.3600	−0.509458
$910$	5.21282	0.172803
$911$	47.0728	1.55959	0.779796	−	0.626034i	$-0.215323\pi$
$911$	47.0728	1.55959	0.779796	+	0.626034i	$0.215323\pi$
$912$	12.3570	0.409183
$913$	−54.3944	−1.80019
$914$	−16.4070	−0.542696
$915$	39.2979	1.29915
$916$	71.0937	2.34900
$917$	2.57638	0.0850795
$918$	−6.94923	−0.229359
$919$	46.4676	1.53283	0.766413	−	0.642348i	$-0.222040\pi$
$919$	46.4676	1.53283	0.766413	+	0.642348i	$0.222040\pi$
$920$	5.68267	0.187352
$921$	−70.8288	−2.33389
$922$	9.50748	0.313112
$923$	−25.7123	−0.846331
$924$	15.0098	0.493787
$925$	−36.7946	−1.20980
$926$	30.5387	1.00356
$927$	54.1055	1.77706
$928$	−9.37833	−0.307859
$929$	33.7082	1.10593	0.552964	−	0.833205i	$-0.313497\pi$
$929$	33.7082	1.10593	0.552964	+	0.833205i	$0.313497\pi$
$930$	35.4591	1.16275
$931$	21.0158	0.688764
$932$	69.6975	2.28302
$933$	−22.6467	−0.741419
$934$	−35.8512	−1.17309
$935$	5.36546	0.175469
$936$	51.7248	1.69068
$937$	25.4690	0.832035	0.416018	−	0.909357i	$-0.363425\pi$
$937$	25.4690	0.832035	0.416018	+	0.909357i	$0.363425\pi$
$938$	6.22137	0.203135
$939$	−92.6708	−3.02420
$940$	13.4571	0.438923
$941$	−17.0366	−0.555377	−0.277689	−	0.960671i	$-0.589568\pi$
$941$	−17.0366	−0.555377	−0.277689	+	0.960671i	$0.589568\pi$
$942$	40.8488	1.33093
$943$	−23.7081	−0.772041
$944$	−3.79063	−0.123374
$945$	1.15155	0.0374598
$946$	132.106	4.29513
$947$	−22.9865	−0.746962	−0.373481	−	0.927638i	$-0.621836\pi$
$947$	−22.9865	−0.746962	−0.373481	+	0.927638i	$0.621836\pi$
$948$	−105.461	−3.42520
$949$	−55.9964	−1.81772
$950$	−26.9820	−0.875411
$951$	55.5722	1.80205
$952$	0.699464	0.0226698
$953$	−0.453700	−0.0146968	−0.00734839	−	0.999973i	$-0.502339\pi$
$953$	−0.453700	−0.0146968	−0.00734839	+	0.999973i	$0.502339\pi$
$954$	−88.3002	−2.85882
$955$	−15.4194	−0.498961
$956$	56.6639	1.83264
$957$	18.7828	0.607162
$958$	6.81236	0.220097
$959$	0.689223	0.0222562
$960$	34.3246	1.10782
$961$	4.82847	0.155757
$962$	131.287	4.23286
$963$	−14.4436	−0.465440
$964$	29.3609	0.945652
$965$	20.0950	0.646883
$966$	6.37749	0.205193
$967$	32.2257	1.03631	0.518154	−	0.855288i	$-0.326620\pi$
$967$	32.2257	1.03631	0.518154	+	0.855288i	$0.326620\pi$
$968$	−33.8586	−1.08826
$969$	−8.19816	−0.263363
$970$	17.0737	0.548202
$971$	−23.0861	−0.740870	−0.370435	−	0.928858i	$-0.620791\pi$
$971$	−23.0861	−0.740870	−0.370435	+	0.928858i	$0.620791\pi$
$972$	−58.5425	−1.87775
$973$	0.693937	0.0222466
$974$	7.23284	0.231755
$975$	69.1520	2.21464
$976$	22.0632	0.706226
$977$	−2.92628	−0.0936200	−0.0468100	−	0.998904i	$-0.514906\pi$
$977$	−2.92628	−0.0936200	−0.0468100	+	0.998904i	$0.514906\pi$
$978$	−38.4372	−1.22909
$979$	−91.8780	−2.93643
$980$	19.7442	0.630706
$981$	56.2243	1.79510
$982$	42.7248	1.36340
$983$	−11.8520	−0.378021	−0.189011	−	0.981975i	$-0.560528\pi$
$983$	−11.8520	−0.378021	−0.189011	+	0.981975i	$0.560528\pi$
$984$	41.1708	1.31248
$985$	−15.8671	−0.505569
$986$	2.89004	0.0920377
$987$	4.57401	0.145592
$988$	56.7277	1.80475
$989$	33.0735	1.05167
$990$	−49.4367	−1.57120
$991$	−13.0408	−0.414254	−0.207127	−	0.978314i	$-0.566411\pi$
$991$	−13.0408	−0.414254	−0.207127	+	0.978314i	$0.566411\pi$
$992$	42.8598	1.36080
$993$	−10.3604	−0.328776
$994$	3.20368	0.101615
$995$	12.1352	0.384711
$996$	78.0833	2.47417
$997$	6.54335	0.207230	0.103615	−	0.994617i	$-0.466959\pi$
$997$	6.54335	0.207230	0.103615	+	0.994617i	$0.466959\pi$
$998$	−6.85898	−0.217117
$999$	29.0022	0.917589

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.16	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.16	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.20655 q^{2} +2.67875 q^{3} +2.86888 q^{4} -1.00223 q^{5} -5.91080 q^{6} -0.364832 q^{7} -1.91723 q^{8} +4.17568 q^{9} +O(q^{10})\)	\(q-2.20655 q^{2} +2.67875 q^{3} +2.86888 q^{4} -1.00223 q^{5} -5.91080 q^{6} -0.364832 q^{7} -1.91723 q^{8} +4.17568 q^{9} +2.21147 q^{10} -5.35352 q^{11} +7.68500 q^{12} -6.46098 q^{13} +0.805020 q^{14} -2.68472 q^{15} -1.50730 q^{16} +1.00000 q^{17} -9.21387 q^{18} -3.06045 q^{19} -2.87528 q^{20} -0.977291 q^{21} +11.8128 q^{22} +2.95741 q^{23} -5.13576 q^{24} -3.99553 q^{25} +14.2565 q^{26} +3.14936 q^{27} -1.04666 q^{28} -1.30975 q^{29} +5.92398 q^{30} +5.98569 q^{31} +7.16038 q^{32} -14.3407 q^{33} -2.20655 q^{34} +0.365645 q^{35} +11.9795 q^{36} +9.20893 q^{37} +6.75304 q^{38} -17.3073 q^{39} +1.92150 q^{40} -8.01650 q^{41} +2.15645 q^{42} +11.1833 q^{43} -15.3586 q^{44} -4.18500 q^{45} -6.52568 q^{46} -4.68029 q^{47} -4.03766 q^{48} -6.86690 q^{49} +8.81636 q^{50} +2.67875 q^{51} -18.5358 q^{52} +9.58340 q^{53} -6.94923 q^{54} +5.36546 q^{55} +0.699464 q^{56} -8.19816 q^{57} +2.89004 q^{58} +2.51485 q^{59} -7.70214 q^{60} -14.6376 q^{61} -13.2077 q^{62} -1.52342 q^{63} -12.7852 q^{64} +6.47539 q^{65} +31.6436 q^{66} +7.72822 q^{67} +2.86888 q^{68} +7.92215 q^{69} -0.806816 q^{70} +3.97963 q^{71} -8.00573 q^{72} +8.66686 q^{73} -20.3200 q^{74} -10.7030 q^{75} -8.78004 q^{76} +1.95313 q^{77} +38.1895 q^{78} -13.7229 q^{79} +1.51066 q^{80} -4.09072 q^{81} +17.6888 q^{82} +10.1605 q^{83} -2.80373 q^{84} -1.00223 q^{85} -24.6764 q^{86} -3.50850 q^{87} +10.2639 q^{88} +17.1622 q^{89} +9.23442 q^{90} +2.35717 q^{91} +8.48445 q^{92} +16.0341 q^{93} +10.3273 q^{94} +3.06727 q^{95} +19.1808 q^{96} +7.72048 q^{97} +15.1522 q^{98} -22.3546 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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