LMFDB - Embedded newform 201.4.a.e.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(1,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - 3 x^{10} - 74 x^{9} + 208 x^{8} + 1913 x^{7} - 4831 x^{6} - 20432 x^{5} + 42994 x^{4} + \cdots + 3072 $ x^11 - 3x^10 - 74x^9 + 208x^8 + 1913x^7 - 4831x^6 - 20432x^5 + 42994x^4 + 79648x^3 - 112288x^2 - 85440x + 3072
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$0.0344354$ of defining polynomial
Character	$\chi$	$=$	201.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.0344354 q^{2} +3.00000 q^{3} -7.99881 q^{4} +3.05553 q^{5} +0.103306 q^{6} -26.7198 q^{7} -0.550926 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+0.0344354 q^{2} +3.00000 q^{3} -7.99881 q^{4} +3.05553 q^{5} +0.103306 q^{6} -26.7198 q^{7} -0.550926 q^{8} +9.00000 q^{9} +0.105218 q^{10} +54.5533 q^{11} -23.9964 q^{12} +78.6046 q^{13} -0.920106 q^{14} +9.16658 q^{15} +63.9715 q^{16} +100.128 q^{17} +0.309919 q^{18} -112.719 q^{19} -24.4406 q^{20} -80.1593 q^{21} +1.87857 q^{22} +212.693 q^{23} -1.65278 q^{24} -115.664 q^{25} +2.70678 q^{26} +27.0000 q^{27} +213.727 q^{28} -138.048 q^{29} +0.315655 q^{30} +125.426 q^{31} +6.61029 q^{32} +163.660 q^{33} +3.44795 q^{34} -81.6430 q^{35} -71.9893 q^{36} +29.8713 q^{37} -3.88151 q^{38} +235.814 q^{39} -1.68337 q^{40} -172.963 q^{41} -2.76032 q^{42} +451.462 q^{43} -436.362 q^{44} +27.4997 q^{45} +7.32415 q^{46} +13.7379 q^{47} +191.915 q^{48} +370.946 q^{49} -3.98293 q^{50} +300.385 q^{51} -628.743 q^{52} -191.507 q^{53} +0.929756 q^{54} +166.689 q^{55} +14.7206 q^{56} -338.156 q^{57} -4.75374 q^{58} +83.4618 q^{59} -73.3218 q^{60} -210.259 q^{61} +4.31909 q^{62} -240.478 q^{63} -511.545 q^{64} +240.178 q^{65} +5.63570 q^{66} +67.0000 q^{67} -800.907 q^{68} +638.078 q^{69} -2.81141 q^{70} +852.348 q^{71} -4.95833 q^{72} +812.185 q^{73} +1.02863 q^{74} -346.991 q^{75} +901.614 q^{76} -1457.65 q^{77} +8.12034 q^{78} +347.904 q^{79} +195.467 q^{80} +81.0000 q^{81} -5.95605 q^{82} -203.907 q^{83} +641.180 q^{84} +305.944 q^{85} +15.5463 q^{86} -414.144 q^{87} -30.0548 q^{88} -1399.25 q^{89} +0.946965 q^{90} -2100.30 q^{91} -1701.29 q^{92} +376.278 q^{93} +0.473071 q^{94} -344.415 q^{95} +19.8309 q^{96} +124.143 q^{97} +12.7737 q^{98} +490.980 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) $ 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9 + 29 * q^10 + 104 * q^11 + 207 * q^12 + 172 * q^13 + 143 * q^14 + 24 * q^15 + 485 * q^16 - 48 * q^17 + 27 * q^18 + 180 * q^19 - 539 * q^20 + 234 * q^21 - 144 * q^22 + 156 * q^23 + 63 * q^24 + 383 * q^25 - 252 * q^26 + 297 * q^27 + 1011 * q^28 - 4 * q^29 + 87 * q^30 + 514 * q^31 - 119 * q^32 + 312 * q^33 + 72 * q^34 - 338 * q^35 + 621 * q^36 + 854 * q^37 - 308 * q^38 + 516 * q^39 - 15 * q^40 + 674 * q^41 + 429 * q^42 + 738 * q^43 + 356 * q^44 + 72 * q^45 + 507 * q^46 + 54 * q^47 + 1455 * q^48 + 1465 * q^49 + 656 * q^50 - 144 * q^51 - 12 * q^52 - 190 * q^53 + 81 * q^54 + 262 * q^55 + 239 * q^56 + 540 * q^57 - 1466 * q^58 + 18 * q^59 - 1617 * q^60 + 328 * q^61 - 915 * q^62 + 702 * q^63 + 2253 * q^64 - 732 * q^65 - 432 * q^66 + 737 * q^67 - 5746 * q^68 + 468 * q^69 - 4451 * q^70 + 264 * q^71 + 189 * q^72 + 330 * q^73 - 5975 * q^74 + 1149 * q^75 - 178 * q^76 - 368 * q^77 - 756 * q^78 + 456 * q^79 - 8515 * q^80 + 891 * q^81 - 3629 * q^82 - 2432 * q^83 + 3033 * q^84 + 2882 * q^85 - 6225 * q^86 - 12 * q^87 - 5492 * q^88 - 2340 * q^89 + 261 * q^90 - 994 * q^91 - 2939 * q^92 + 1542 * q^93 - 3506 * q^94 - 2568 * q^95 - 357 * q^96 + 1892 * q^97 - 1078 * q^98 + 936 * 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 $

$2$	0.0344354	0.0121748	0.00608738	−	0.999981i	$-0.498062\pi$
$2$	0.0344354	0.0121748	0.00608738	+	0.999981i	$0.498062\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−7.99881	−0.999852
$5$	3.05553	0.273295	0.136647	−	0.990620i	$-0.456367\pi$
$5$	3.05553	0.273295	0.136647	+	0.990620i	$0.456367\pi$
$6$	0.103306	0.00702910
$7$	−26.7198	−1.44273	−0.721366	−	0.692554i	$-0.756485\pi$
$7$	−26.7198	−1.44273	−0.721366	+	0.692554i	$0.756485\pi$
$8$	−0.550926	−0.0243477
$9$	9.00000	0.333333
$10$	0.105218	0.00332730
$11$	54.5533	1.49531	0.747656	−	0.664086i	$-0.231179\pi$
$11$	54.5533	1.49531	0.747656	+	0.664086i	$0.231179\pi$
$12$	−23.9964	−0.577265
$13$	78.6046	1.67700	0.838499	−	0.544903i	$-0.183433\pi$
$13$	78.6046	1.67700	0.838499	+	0.544903i	$0.183433\pi$
$14$	−0.920106	−0.0175649
$15$	9.16658	0.157787
$16$	63.9715	0.999555
$17$	100.128	1.42851	0.714254	−	0.699886i	$-0.246766\pi$
$17$	100.128	1.42851	0.714254	+	0.699886i	$0.246766\pi$
$18$	0.309919	0.00405825
$19$	−112.719	−1.36102	−0.680511	−	0.732738i	$-0.738242\pi$
$19$	−112.719	−1.36102	−0.680511	+	0.732738i	$0.738242\pi$
$20$	−24.4406	−0.273254
$21$	−80.1593	−0.832962
$22$	1.87857	0.0182051
$23$	212.693	1.92824	0.964119	−	0.265471i	$-0.0855275\pi$
$23$	212.693	1.92824	0.964119	+	0.265471i	$0.0855275\pi$
$24$	−1.65278	−0.0140572
$25$	−115.664	−0.925310
$26$	2.70678	0.0204170
$27$	27.0000	0.192450
$28$	213.727	1.44252
$29$	−138.048	−0.883960	−0.441980	−	0.897025i	$-0.645724\pi$
$29$	−138.048	−0.883960	−0.441980	+	0.897025i	$0.645724\pi$
$30$	0.315655	0.00192101
$31$	125.426	0.726683	0.363341	−	0.931656i	$-0.381636\pi$
$31$	125.426	0.726683	0.363341	+	0.931656i	$0.381636\pi$
$32$	6.61029	0.0365170
$33$	163.660	0.863319
$34$	3.44795	0.0173917
$35$	−81.6430	−0.394291
$36$	−71.9893	−0.333284
$37$	29.8713	0.132725	0.0663624	−	0.997796i	$-0.478861\pi$
$37$	29.8713	0.132725	0.0663624	+	0.997796i	$0.478861\pi$
$38$	−3.88151	−0.0165701
$39$	235.814	0.968216
$40$	−1.68337	−0.00665410
$41$	−172.963	−0.658836	−0.329418	−	0.944184i	$-0.606852\pi$
$41$	−172.963	−0.658836	−0.329418	+	0.944184i	$0.606852\pi$
$42$	−2.76032	−0.0101411
$43$	451.462	1.60110	0.800551	−	0.599265i	$-0.204540\pi$
$43$	451.462	1.60110	0.800551	+	0.599265i	$0.204540\pi$
$44$	−436.362	−1.49509
$45$	27.4997	0.0910982
$46$	7.32415	0.0234758
$47$	13.7379	0.0426358	0.0213179	−	0.999773i	$-0.493214\pi$
$47$	13.7379	0.0426358	0.0213179	+	0.999773i	$0.493214\pi$
$48$	191.915	0.577094
$49$	370.946	1.08148
$50$	−3.98293	−0.0112654
$51$	300.385	0.824750
$52$	−628.743	−1.67675
$53$	−191.507	−0.496331	−0.248166	−	0.968718i	$-0.579828\pi$
$53$	−191.507	−0.496331	−0.248166	+	0.968718i	$0.579828\pi$
$54$	0.929756	0.00234303
$55$	166.689	0.408661
$56$	14.7206	0.0351272
$57$	−338.156	−0.785786
$58$	−4.75374	−0.0107620
$59$	83.4618	0.184166	0.0920831	−	0.995751i	$-0.470647\pi$
$59$	83.4618	0.184166	0.0920831	+	0.995751i	$0.470647\pi$
$60$	−73.3218	−0.157763
$61$	−210.259	−0.441326	−0.220663	−	0.975350i	$-0.570822\pi$
$61$	−210.259	−0.441326	−0.220663	+	0.975350i	$0.570822\pi$
$62$	4.31909	0.00884718
$63$	−240.478	−0.480911
$64$	−511.545	−0.999111
$65$	240.178	0.458315
$66$	5.63570	0.0105107
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	−800.907	−1.42830
$69$	638.078	1.11327
$70$	−2.81141	−0.00480040
$71$	852.348	1.42472	0.712360	−	0.701814i	$-0.247626\pi$
$71$	852.348	1.42472	0.712360	+	0.701814i	$0.247626\pi$
$72$	−4.95833	−0.00811590
$73$	812.185	1.30218	0.651090	−	0.759001i	$-0.274312\pi$
$73$	812.185	1.30218	0.651090	+	0.759001i	$0.274312\pi$
$74$	1.02863	0.00161589
$75$	−346.991	−0.534228
$76$	901.614	1.36082
$77$	−1457.65	−2.15734
$78$	8.12034	0.0117878
$79$	347.904	0.495472	0.247736	−	0.968828i	$-0.420314\pi$
$79$	347.904	0.495472	0.247736	+	0.968828i	$0.420314\pi$
$80$	195.467	0.273173
$81$	81.0000	0.111111
$82$	−5.95605	−0.00802116
$83$	−203.907	−0.269659	−0.134830	−	0.990869i	$-0.543049\pi$
$83$	−203.907	−0.269659	−0.134830	+	0.990869i	$0.543049\pi$
$84$	641.180	0.832838
$85$	305.944	0.390404
$86$	15.5463	0.0194930
$87$	−414.144	−0.510355
$88$	−30.0548	−0.0364074
$89$	−1399.25	−1.66652	−0.833261	−	0.552880i	$-0.813529\pi$
$89$	−1399.25	−1.66652	−0.833261	+	0.552880i	$0.813529\pi$
$90$	0.946965	0.00110910
$91$	−2100.30	−2.41946
$92$	−1701.29	−1.92795
$93$	376.278	0.419550
$94$	0.473071	0.000519080 0
$95$	−344.415	−0.371960
$96$	19.8309	0.0210831
$97$	124.143	0.129947	0.0649734	−	0.997887i	$-0.479304\pi$
$97$	124.143	0.129947	0.0649734	+	0.997887i	$0.479304\pi$
$98$	12.7737	0.0131667
$99$	490.980	0.498438
$100$	925.173	0.925173
$101$	229.010	0.225618	0.112809	−	0.993617i	$-0.464015\pi$
$101$	229.010	0.225618	0.112809	+	0.993617i	$0.464015\pi$
$102$	10.3439	0.0100411
$103$	−1218.99	−1.16613	−0.583064	−	0.812426i	$-0.698146\pi$
$103$	−1218.99	−1.16613	−0.583064	+	0.812426i	$0.698146\pi$
$104$	−43.3053	−0.0408311
$105$	−244.929	−0.227644
$106$	−6.59463	−0.00604271
$107$	823.167	0.743725	0.371862	−	0.928288i	$-0.378719\pi$
$107$	823.167	0.743725	0.371862	+	0.928288i	$0.378719\pi$
$108$	−215.968	−0.192422
$109$	−972.675	−0.854728	−0.427364	−	0.904080i	$-0.640558\pi$
$109$	−972.675	−0.854728	−0.427364	+	0.904080i	$0.640558\pi$
$110$	5.74001	0.00497535
$111$	89.6140	0.0766287
$112$	−1709.31	−1.44209
$113$	−1916.14	−1.59518	−0.797590	−	0.603200i	$-0.793892\pi$
$113$	−1916.14	−1.59518	−0.797590	+	0.603200i	$0.793892\pi$
$114$	−11.6445	−0.00956675
$115$	649.888	0.526977
$116$	1104.22	0.883829
$117$	707.441	0.559000
$118$	2.87404	0.00224218
$119$	−2675.40	−2.06096
$120$	−5.05011	−0.00384175
$121$	1645.06	1.23596
$122$	−7.24035	−0.00537303
$123$	−518.889	−0.380379
$124$	−1003.26	−0.726575
$125$	−735.355	−0.526177
$126$	−8.28096	−0.00585497
$127$	−413.803	−0.289126	−0.144563	−	0.989496i	$-0.546178\pi$
$127$	−413.803	−0.289126	−0.144563	+	0.989496i	$0.546178\pi$
$128$	−70.4976	−0.0486810
$129$	1354.39	0.924396
$130$	8.27064	0.00557987
$131$	1580.06	1.05382	0.526909	−	0.849922i	$-0.323351\pi$
$131$	1580.06	1.05382	0.526909	+	0.849922i	$0.323351\pi$
$132$	−1309.09	−0.863191
$133$	3011.81	1.96359
$134$	2.30717	0.00148738
$135$	82.4992	0.0525956
$136$	−55.1632	−0.0347809
$137$	1963.76	1.22464	0.612320	−	0.790610i	$-0.290236\pi$
$137$	1963.76	1.22464	0.612320	+	0.790610i	$0.290236\pi$
$138$	21.9725	0.0135538
$139$	298.043	0.181868	0.0909341	−	0.995857i	$-0.471015\pi$
$139$	298.043	0.181868	0.0909341	+	0.995857i	$0.471015\pi$
$140$	653.047	0.394233
$141$	41.2138	0.0246158
$142$	29.3510	0.0173456
$143$	4288.14	2.50764
$144$	575.744	0.333185
$145$	−421.809	−0.241582
$146$	27.9679	0.0158537
$147$	1112.84	0.624391
$148$	−238.935	−0.132705
$149$	774.575	0.425877	0.212938	−	0.977066i	$-0.431697\pi$
$149$	774.575	0.425877	0.212938	+	0.977066i	$0.431697\pi$
$150$	−11.9488	−0.00650409
$151$	3625.27	1.95378	0.976888	−	0.213753i	$-0.0685689\pi$
$151$	3625.27	1.95378	0.976888	+	0.213753i	$0.0685689\pi$
$152$	62.0995	0.0331377
$153$	901.154	0.476170
$154$	−50.1948	−0.0262650
$155$	383.242	0.198599
$156$	−1886.23	−0.968072
$157$	−627.850	−0.319158	−0.159579	−	0.987185i	$-0.551014\pi$
$157$	−627.850	−0.319158	−0.159579	+	0.987185i	$0.551014\pi$
$158$	11.9802	0.00603224
$159$	−574.522	−0.286557
$160$	20.1979	0.00997991
$161$	−5683.10	−2.78193
$162$	2.78927	0.00135275
$163$	−909.613	−0.437094	−0.218547	−	0.975826i	$-0.570132\pi$
$163$	−909.613	−0.437094	−0.218547	+	0.975826i	$0.570132\pi$
$164$	1383.50	0.658738
$165$	500.067	0.235941
$166$	−7.02163	−0.00328304
$167$	−902.141	−0.418022	−0.209011	−	0.977913i	$-0.567025\pi$
$167$	−902.141	−0.418022	−0.209011	+	0.977913i	$0.567025\pi$
$168$	44.1618	0.0202807
$169$	3981.68	1.81232
$170$	10.5353	0.00475307
$171$	−1014.47	−0.453674
$172$	−3611.16	−1.60086
$173$	534.966	0.235103	0.117551	−	0.993067i	$-0.462496\pi$
$173$	534.966	0.235103	0.117551	+	0.993067i	$0.462496\pi$
$174$	−14.2612	−0.00621344
$175$	3090.51	1.33497
$176$	3489.86	1.49465
$177$	250.385	0.106328
$178$	−48.1838	−0.0202895
$179$	−1971.74	−0.823322	−0.411661	−	0.911337i	$-0.635051\pi$
$179$	−1971.74	−0.823322	−0.411661	+	0.911337i	$0.635051\pi$
$180$	−219.965	−0.0910847
$181$	−158.420	−0.0650568	−0.0325284	−	0.999471i	$-0.510356\pi$
$181$	−158.420	−0.0650568	−0.0325284	+	0.999471i	$0.510356\pi$
$182$	−72.3245	−0.0294563
$183$	−630.776	−0.254800
$184$	−117.178	−0.0469482
$185$	91.2726	0.0362730
$186$	12.9573	0.00510792
$187$	5462.32	2.13607
$188$	−109.887	−0.0426295
$189$	−721.434	−0.277654
$190$	−11.8601	−0.00452852
$191$	−528.284	−0.200132	−0.100066	−	0.994981i	$-0.531905\pi$
$191$	−528.284	−0.200132	−0.100066	+	0.994981i	$0.531905\pi$
$192$	−1534.63	−0.576837
$193$	−4056.38	−1.51287	−0.756436	−	0.654068i	$-0.773061\pi$
$193$	−4056.38	−1.51287	−0.756436	+	0.654068i	$0.773061\pi$
$194$	4.27492	0.00158207
$195$	720.535	0.264608
$196$	−2967.13	−1.08132
$197$	2931.33	1.06015	0.530073	−	0.847952i	$-0.322164\pi$
$197$	2931.33	1.06015	0.530073	+	0.847952i	$0.322164\pi$
$198$	16.9071	0.00606836
$199$	−3915.03	−1.39462	−0.697310	−	0.716770i	$-0.745620\pi$
$199$	−3915.03	−1.39462	−0.697310	+	0.716770i	$0.745620\pi$
$200$	63.7221	0.0225292
$201$	201.000	0.0705346
$202$	7.88606	0.00274684
$203$	3688.61	1.27532
$204$	−2402.72	−0.824628
$205$	−528.493	−0.180056
$206$	−41.9766	−0.0141973
$207$	1914.23	0.642746
$208$	5028.45	1.67625
$209$	−6149.17	−2.03515
$210$	−8.43423	−0.00277151
$211$	−4860.36	−1.58579	−0.792893	−	0.609361i	$-0.791426\pi$
$211$	−4860.36	−1.58579	−0.792893	+	0.609361i	$0.791426\pi$
$212$	1531.83	0.496258
$213$	2557.05	0.822563
$214$	28.3461	0.00905467
$215$	1379.46	0.437573
$216$	−14.8750	−0.00468572
$217$	−3351.35	−1.04841
$218$	−33.4944	−0.0104061
$219$	2436.56	0.751814
$220$	−1333.32	−0.408600
$221$	7870.53	2.39561
$222$	3.08589	0.000932935 0
$223$	3219.21	0.966701	0.483351	−	0.875427i	$-0.339420\pi$
$223$	3219.21	0.966701	0.483351	+	0.875427i	$0.339420\pi$
$224$	−176.626	−0.0526843
$225$	−1040.97	−0.308437
$226$	−65.9831	−0.0194209
$227$	3979.05	1.16343	0.581716	−	0.813392i	$-0.302382\pi$
$227$	3979.05	1.16343	0.581716	+	0.813392i	$0.302382\pi$
$228$	2704.84	0.785669
$229$	3604.19	1.04005	0.520025	−	0.854151i	$-0.325923\pi$
$229$	3604.19	1.04005	0.520025	+	0.854151i	$0.325923\pi$
$230$	22.3792	0.00641582
$231$	−4372.96	−1.24554
$232$	76.0541	0.0215224
$233$	−4868.41	−1.36884	−0.684421	−	0.729087i	$-0.739945\pi$
$233$	−4868.41	−1.36884	−0.684421	+	0.729087i	$0.739945\pi$
$234$	24.3610	0.00680568
$235$	41.9766	0.0116521
$236$	−667.596	−0.184139
$237$	1043.71	0.286061
$238$	−92.1286	−0.0250916
$239$	−748.985	−0.202711	−0.101355	−	0.994850i	$-0.532318\pi$
$239$	−748.985	−0.202711	−0.101355	+	0.994850i	$0.532318\pi$
$240$	586.400	0.157717
$241$	−3278.01	−0.876162	−0.438081	−	0.898935i	$-0.644342\pi$
$241$	−3278.01	−0.876162	−0.438081	+	0.898935i	$0.644342\pi$
$242$	56.6484	0.0150475
$243$	243.000	0.0641500
$244$	1681.82	0.441261
$245$	1133.44	0.295562
$246$	−17.8681	−0.00463102
$247$	−8860.19	−2.28243
$248$	−69.1004	−0.0176931
$249$	−611.722	−0.155688
$250$	−25.3222	−0.00640608
$251$	−5783.13	−1.45429	−0.727147	−	0.686482i	$-0.759154\pi$
$251$	−5783.13	−1.45429	−0.727147	+	0.686482i	$0.759154\pi$
$252$	1923.54	0.480839
$253$	11603.1	2.88332
$254$	−14.2495	−0.00352004
$255$	917.833	0.225400
$256$	4089.93	0.998518
$257$	−643.689	−0.156234	−0.0781172	−	0.996944i	$-0.524891\pi$
$257$	−643.689	−0.156234	−0.0781172	+	0.996944i	$0.524891\pi$
$258$	46.6389	0.0112543
$259$	−798.155	−0.191486
$260$	−1921.14	−0.458247
$261$	−1242.43	−0.294653
$262$	54.4099	0.0128300
$263$	−5486.53	−1.28636	−0.643182	−	0.765713i	$-0.722386\pi$
$263$	−5486.53	−1.28636	−0.643182	+	0.765713i	$0.722386\pi$
$264$	−90.1645	−0.0210198
$265$	−585.156	−0.135645
$266$	103.713	0.0239062
$267$	−4197.76	−0.962167
$268$	−535.921	−0.122151
$269$	6354.30	1.44025	0.720127	−	0.693842i	$-0.244083\pi$
$269$	6354.30	1.44025	0.720127	+	0.693842i	$0.244083\pi$
$270$	2.84089	0.000640338 0
$271$	−2200.46	−0.493241	−0.246621	−	0.969112i	$-0.579320\pi$
$271$	−2200.46	−0.493241	−0.246621	+	0.969112i	$0.579320\pi$
$272$	6405.35	1.42787
$273$	−6300.89	−1.39688
$274$	67.6230	0.0149097
$275$	−6309.84	−1.38363
$276$	−5103.86	−1.11310
$277$	−1419.81	−0.307972	−0.153986	−	0.988073i	$-0.549211\pi$
$277$	−1419.81	−0.307972	−0.153986	+	0.988073i	$0.549211\pi$
$278$	10.2632	0.00221420
$279$	1128.83	0.242228
$280$	44.9792	0.00960008
$281$	−2929.76	−0.621975	−0.310988	−	0.950414i	$-0.600660\pi$
$281$	−2929.76	−0.621975	−0.310988	+	0.950414i	$0.600660\pi$
$282$	1.41921	0.000299691 0
$283$	−3198.46	−0.671832	−0.335916	−	0.941892i	$-0.609046\pi$
$283$	−3198.46	−0.671832	−0.335916	+	0.941892i	$0.609046\pi$
$284$	−6817.78	−1.42451
$285$	−1033.24	−0.214751
$286$	147.664	0.0305299
$287$	4621.53	0.950523
$288$	59.4926	0.0121723
$289$	5112.65	1.04064
$290$	−14.5252	−0.00294120
$291$	372.430	0.0750248
$292$	−6496.52	−1.30199
$293$	6637.56	1.32345	0.661724	−	0.749747i	$-0.269825\pi$
$293$	6637.56	1.32345	0.661724	+	0.749747i	$0.269825\pi$
$294$	38.3211	0.00760180
$295$	255.020	0.0503316
$296$	−16.4569	−0.00323154
$297$	1472.94	0.287773
$298$	26.6728	0.00518494
$299$	16718.6	3.23365
$300$	2775.52	0.534149
$301$	−12063.0	−2.30996
$302$	124.838	0.0237867
$303$	687.031	0.130260
$304$	−7210.78	−1.36042
$305$	−642.452	−0.120612
$306$	31.0316	0.00579725
$307$	3628.06	0.674476	0.337238	−	0.941419i	$-0.390507\pi$
$307$	3628.06	0.674476	0.337238	+	0.941419i	$0.390507\pi$
$308$	11659.5	2.15702
$309$	−3656.98	−0.673264
$310$	13.1971	0.00241789
$311$	−4379.70	−0.798553	−0.399277	−	0.916831i	$-0.630739\pi$
$311$	−4379.70	−0.798553	−0.399277	+	0.916831i	$0.630739\pi$
$312$	−129.916	−0.0235738
$313$	−1774.04	−0.320366	−0.160183	−	0.987087i	$-0.551208\pi$
$313$	−1774.04	−0.320366	−0.160183	+	0.987087i	$0.551208\pi$
$314$	−21.6203	−0.00388568
$315$	−734.787	−0.131430
$316$	−2782.82	−0.495398
$317$	−3849.29	−0.682012	−0.341006	−	0.940061i	$-0.610768\pi$
$317$	−3849.29	−0.682012	−0.341006	+	0.940061i	$0.610768\pi$
$318$	−19.7839	−0.00348876
$319$	−7530.97	−1.32180
$320$	−1563.04	−0.273052
$321$	2469.50	0.429390
$322$	−195.700	−0.0338693
$323$	−11286.3	−1.94423
$324$	−647.904	−0.111095
$325$	−9091.70	−1.55174
$326$	−31.3229	−0.00532152
$327$	−2918.02	−0.493477
$328$	95.2897	0.0160411
$329$	−367.074	−0.0615120
$330$	17.2200	0.00287252
$331$	6141.58	1.01985	0.509927	−	0.860217i	$-0.329672\pi$
$331$	6141.58	1.01985	0.509927	+	0.860217i	$0.329672\pi$
$332$	1631.02	0.269620
$333$	268.842	0.0442416
$334$	−31.0656	−0.00508932
$335$	204.720	0.0333883
$336$	−5127.92	−0.832592
$337$	−7130.05	−1.15252	−0.576259	−	0.817267i	$-0.695488\pi$
$337$	−7130.05	−1.15252	−0.576259	+	0.817267i	$0.695488\pi$
$338$	137.111	0.0220646
$339$	−5748.42	−0.920978
$340$	−2447.19	−0.390346
$341$	6842.40	1.08662
$342$	−34.9336	−0.00552337
$343$	−746.723	−0.117549
$344$	−248.722	−0.0389831
$345$	1949.66	0.304250
$346$	18.4218	0.00286232
$347$	−5906.73	−0.913803	−0.456902	−	0.889517i	$-0.651041\pi$
$347$	−5906.73	−0.913803	−0.456902	+	0.889517i	$0.651041\pi$
$348$	3312.66	0.510279
$349$	−2020.70	−0.309930	−0.154965	−	0.987920i	$-0.549527\pi$
$349$	−2020.70	−0.309930	−0.154965	+	0.987920i	$0.549527\pi$
$350$	106.423	0.0162530
$351$	2122.32	0.322739
$352$	360.613	0.0546044
$353$	−8111.52	−1.22304	−0.611519	−	0.791230i	$-0.709441\pi$
$353$	−8111.52	−1.22304	−0.611519	+	0.791230i	$0.709441\pi$
$354$	8.62213	0.00129452
$355$	2604.37	0.389369
$356$	11192.4	1.66627
$357$	−8026.21	−1.18989
$358$	−67.8976	−0.0100237
$359$	12533.4	1.84258	0.921289	−	0.388879i	$-0.127138\pi$
$359$	12533.4	1.84258	0.921289	+	0.388879i	$0.127138\pi$
$360$	−15.1503	−0.00221803
$361$	5846.46	0.852379
$362$	−5.45526	−0.000792050 0
$363$	4935.19	0.713582
$364$	16799.9	2.41910
$365$	2481.65	0.355879
$366$	−21.7210	−0.00310212
$367$	6902.64	0.981785	0.490892	−	0.871220i	$-0.336671\pi$
$367$	6902.64	0.981785	0.490892	+	0.871220i	$0.336671\pi$
$368$	13606.3	1.92738
$369$	−1556.67	−0.219612
$370$	3.14301	0.000441614 0
$371$	5117.03	0.716073
$372$	−3009.78	−0.419488
$373$	4795.58	0.665699	0.332849	−	0.942980i	$-0.391990\pi$
$373$	4795.58	0.665699	0.332849	+	0.942980i	$0.391990\pi$
$374$	188.097	0.0260061
$375$	−2206.06	−0.303788
$376$	−7.56857	−0.00103808
$377$	−10851.2	−1.48240
$378$	−24.8429	−0.00338037
$379$	944.105	0.127956	0.0639781	−	0.997951i	$-0.479621\pi$
$379$	944.105	0.127956	0.0639781	+	0.997951i	$0.479621\pi$
$380$	2754.91	0.371905
$381$	−1241.41	−0.166927
$382$	−18.1917	−0.00243656
$383$	9671.62	1.29033	0.645165	−	0.764043i	$-0.276788\pi$
$383$	9671.62	1.29033	0.645165	+	0.764043i	$0.276788\pi$
$384$	−211.493	−0.0281060
$385$	−4453.90	−0.589589
$386$	−139.683	−0.0184188
$387$	4063.16	0.533700
$388$	−992.999	−0.129927
$389$	−11834.5	−1.54250	−0.771251	−	0.636532i	$-0.780368\pi$
$389$	−11834.5	−1.54250	−0.771251	+	0.636532i	$0.780368\pi$
$390$	24.8119	0.00322154
$391$	21296.5	2.75450
$392$	−204.364	−0.0263315
$393$	4740.17	0.608422
$394$	100.942	0.0129070
$395$	1063.03	0.135410
$396$	−3927.26	−0.498364
$397$	−13282.3	−1.67914	−0.839571	−	0.543250i	$-0.817193\pi$
$397$	−13282.3	−1.67914	−0.839571	+	0.543250i	$0.817193\pi$
$398$	−134.816	−0.0169791
$399$	9035.44	1.13368
$400$	−7399.19	−0.924899
$401$	−8655.73	−1.07792	−0.538961	−	0.842331i	$-0.681183\pi$
$401$	−8655.73	−1.07792	−0.538961	+	0.842331i	$0.681183\pi$
$402$	6.92152	0.000858741 0
$403$	9859.05	1.21865
$404$	−1831.81	−0.225584
$405$	247.498	0.0303661
$406$	127.019	0.0155267
$407$	1629.58	0.198465
$408$	−165.490	−0.0200808
$409$	1133.56	0.137044	0.0685219	−	0.997650i	$-0.478172\pi$
$409$	1133.56	0.137044	0.0685219	+	0.997650i	$0.478172\pi$
$410$	−18.1989	−0.00219214
$411$	5891.29	0.707046
$412$	9750.51	1.16595
$413$	−2230.08	−0.265703
$414$	65.9174	0.00782527
$415$	−623.044	−0.0736965
$416$	519.599	0.0612390
$417$	894.129	0.105002
$418$	−211.749	−0.0247775
$419$	−2877.35	−0.335484	−0.167742	−	0.985831i	$-0.553648\pi$
$419$	−2877.35	−0.335484	−0.167742	+	0.985831i	$0.553648\pi$
$420$	1959.14	0.227610
$421$	6419.33	0.743133	0.371567	−	0.928406i	$-0.378821\pi$
$421$	6419.33	0.743133	0.371567	+	0.928406i	$0.378821\pi$
$422$	−167.368	−0.0193066
$423$	123.641	0.0142119
$424$	105.506	0.0120845
$425$	−11581.2	−1.32181
$426$	88.0529	0.0100145
$427$	5618.07	0.636715
$428$	−6584.36	−0.743614
$429$	12864.4	1.44779
$430$	47.5021	0.00532734
$431$	1419.14	0.158603	0.0793014	−	0.996851i	$-0.474731\pi$
$431$	1419.14	0.158603	0.0793014	+	0.996851i	$0.474731\pi$
$432$	1727.23	0.192365
$433$	−10034.2	−1.11365	−0.556826	−	0.830629i	$-0.687981\pi$
$433$	−10034.2	−1.11365	−0.556826	+	0.830629i	$0.687981\pi$
$434$	−115.405	−0.0127641
$435$	−1265.43	−0.139477
$436$	7780.24	0.854601
$437$	−23974.4	−2.62437
$438$	83.9038	0.00915315
$439$	12777.8	1.38918	0.694590	−	0.719406i	$-0.255586\pi$
$439$	12777.8	1.38918	0.694590	+	0.719406i	$0.255586\pi$
$440$	−91.8333	−0.00994996
$441$	3338.52	0.360492
$442$	271.025	0.0291659
$443$	−7832.80	−0.840062	−0.420031	−	0.907510i	$-0.637981\pi$
$443$	−7832.80	−0.840062	−0.420031	+	0.907510i	$0.637981\pi$
$444$	−716.805	−0.0766173
$445$	−4275.45	−0.455451
$446$	110.855	0.0117693
$447$	2323.72	0.245880
$448$	13668.4	1.44145
$449$	−9752.57	−1.02506	−0.512530	−	0.858669i	$-0.671292\pi$
$449$	−9752.57	−1.02506	−0.512530	+	0.858669i	$0.671292\pi$
$450$	−35.8464	−0.00375514
$451$	−9435.70	−0.985165
$452$	15326.9	1.59494
$453$	10875.8	1.12801
$454$	137.020	0.0141645
$455$	−6417.51	−0.661226
$456$	186.299	0.0191321
$457$	−1951.10	−0.199713	−0.0998564	−	0.995002i	$-0.531838\pi$
$457$	−1951.10	−0.199713	−0.0998564	+	0.995002i	$0.531838\pi$
$458$	124.112	0.0126624
$459$	2703.46	0.274917
$460$	−5198.33	−0.526899
$461$	−662.911	−0.0669736	−0.0334868	−	0.999439i	$-0.510661\pi$
$461$	−662.911	−0.0669736	−0.0334868	+	0.999439i	$0.510661\pi$
$462$	−150.585	−0.0151641
$463$	−12445.5	−1.24922	−0.624611	−	0.780936i	$-0.714743\pi$
$463$	−12445.5	−1.24922	−0.624611	+	0.780936i	$0.714743\pi$
$464$	−8831.14	−0.883567
$465$	1149.73	0.114661
$466$	−167.646	−0.0166653
$467$	8737.41	0.865780	0.432890	−	0.901447i	$-0.357494\pi$
$467$	8737.41	0.865780	0.432890	+	0.901447i	$0.357494\pi$
$468$	−5658.69	−0.558917
$469$	−1790.23	−0.176258
$470$	1.44548	0.000141862 0
$471$	−1883.55	−0.184266
$472$	−45.9813	−0.00448402
$473$	24628.8	2.39415
$474$	35.9406	0.00348272
$475$	13037.4	1.25937
$476$	21400.0	2.06065
$477$	−1723.57	−0.165444
$478$	−25.7916	−0.00246795
$479$	−2045.09	−0.195079	−0.0975394	−	0.995232i	$-0.531097\pi$
$479$	−2045.09	−0.195079	−0.0975394	+	0.995232i	$0.531097\pi$
$480$	60.5938	0.00576191
$481$	2348.02	0.222579
$482$	−112.880	−0.0106671
$483$	−17049.3	−1.60615
$484$	−13158.6	−1.23578
$485$	379.323	0.0355138
$486$	8.36780	0.000781011 0
$487$	16650.2	1.54927	0.774635	−	0.632409i	$-0.217934\pi$
$487$	16650.2	1.54927	0.774635	+	0.632409i	$0.217934\pi$
$488$	115.837	0.0107453
$489$	−2728.84	−0.252357
$490$	39.0304	0.00359839
$491$	−12624.9	−1.16039	−0.580196	−	0.814477i	$-0.697024\pi$
$491$	−12624.9	−1.16039	−0.580196	+	0.814477i	$0.697024\pi$
$492$	4150.49	0.380323
$493$	−13822.5	−1.26275
$494$	−305.104	−0.0277880
$495$	1500.20	0.136220
$496$	8023.69	0.726360
$497$	−22774.6	−2.05549
$498$	−21.0649	−0.00189546
$499$	−825.634	−0.0740690	−0.0370345	−	0.999314i	$-0.511791\pi$
$499$	−825.634	−0.0740690	−0.0370345	+	0.999314i	$0.511791\pi$
$500$	5881.97	0.526099
$501$	−2706.42	−0.241345
$502$	−199.144	−0.0177057
$503$	−10853.5	−0.962091	−0.481045	−	0.876696i	$-0.659743\pi$
$503$	−10853.5	−0.962091	−0.481045	+	0.876696i	$0.659743\pi$
$504$	132.485	0.0117091
$505$	699.747	0.0616601
$506$	399.557	0.0351037
$507$	11945.0	1.04635
$508$	3309.93	0.289084
$509$	14872.3	1.29510	0.647549	−	0.762024i	$-0.275794\pi$
$509$	14872.3	1.29510	0.647549	+	0.762024i	$0.275794\pi$
$510$	31.6060	0.00274419
$511$	−21701.4	−1.87870
$512$	704.819	0.0608377
$513$	−3043.40	−0.261929
$514$	−22.1657	−0.00190212
$515$	−3724.67	−0.318696
$516$	−10833.5	−0.924259
$517$	749.449	0.0637539
$518$	−27.4848	−0.00233130
$519$	1604.90	0.135737
$520$	−132.320	−0.0111589
$521$	12831.3	1.07898	0.539492	−	0.841991i	$-0.318616\pi$
$521$	12831.3	1.07898	0.539492	+	0.841991i	$0.318616\pi$
$522$	−42.7836	−0.00358733
$523$	−6946.69	−0.580799	−0.290399	−	0.956906i	$-0.593788\pi$
$523$	−6946.69	−0.580799	−0.290399	+	0.956906i	$0.593788\pi$
$524$	−12638.6	−1.05366
$525$	9271.53	0.770748
$526$	−188.931	−0.0156612
$527$	12558.7	1.03807
$528$	10469.6	0.862935
$529$	33071.1	2.71810
$530$	−20.1501	−0.00165144
$531$	751.156	0.0613887
$532$	−24090.9	−1.96330
$533$	−13595.7	−1.10487
$534$	−144.551	−0.0117141
$535$	2515.21	0.203256
$536$	−36.9120	−0.00297455
$537$	−5915.22	−0.475345
$538$	218.813	0.0175347
$539$	20236.4	1.61715
$540$	−659.896	−0.0525878
$541$	−12311.9	−0.978428	−0.489214	−	0.872164i	$-0.662716\pi$
$541$	−12311.9	−0.978428	−0.489214	+	0.872164i	$0.662716\pi$
$542$	−75.7737	−0.00600509
$543$	−475.261	−0.0375606
$544$	661.876	0.0521649
$545$	−2972.03	−0.233593
$546$	−216.974	−0.0170066
$547$	10696.4	0.836099	0.418049	−	0.908424i	$-0.362714\pi$
$547$	10696.4	0.836099	0.418049	+	0.908424i	$0.362714\pi$
$548$	−15707.8	−1.22446
$549$	−1892.33	−0.147109
$550$	−217.282	−0.0168453
$551$	15560.6	1.20309
$552$	−351.533	−0.0271055
$553$	−9295.92	−0.714833
$554$	−48.8918	−0.00374949
$555$	273.818	0.0209422
$556$	−2383.99	−0.181841
$557$	−15116.9	−1.14995	−0.574977	−	0.818169i	$-0.694989\pi$
$557$	−15116.9	−1.14995	−0.574977	+	0.818169i	$0.694989\pi$
$558$	38.8718	0.00294906
$559$	35487.0	2.68504
$560$	−5222.83	−0.394116
$561$	16387.0	1.23326
$562$	−100.888	−0.00757240
$563$	414.485	0.0310275	0.0155137	−	0.999880i	$-0.495062\pi$
$563$	414.485	0.0310275	0.0155137	+	0.999880i	$0.495062\pi$
$564$	−329.661	−0.0246121
$565$	−5854.82	−0.435954
$566$	−110.140	−0.00817939
$567$	−2164.30	−0.160304
$568$	−469.581	−0.0346887
$569$	16836.2	1.24044	0.620219	−	0.784429i	$-0.287044\pi$
$569$	16836.2	1.24044	0.620219	+	0.784429i	$0.287044\pi$
$570$	−35.5802	−0.00261454
$571$	8985.43	0.658544	0.329272	−	0.944235i	$-0.393197\pi$
$571$	8985.43	0.658544	0.329272	+	0.944235i	$0.393197\pi$
$572$	−34300.0	−2.50727
$573$	−1584.85	−0.115547
$574$	159.144	0.0115724
$575$	−24600.8	−1.78422
$576$	−4603.90	−0.333037
$577$	−1975.29	−0.142517	−0.0712586	−	0.997458i	$-0.522702\pi$
$577$	−1975.29	−0.142517	−0.0712586	+	0.997458i	$0.522702\pi$
$578$	176.056	0.0126695
$579$	−12169.1	−0.873457
$580$	3373.97	0.241546
$581$	5448.36	0.389046
$582$	12.8248	0.000913408 0
$583$	−10447.4	−0.742171
$584$	−447.454	−0.0317051
$585$	2161.61	0.152772
$586$	228.567	0.0161127
$587$	−22645.8	−1.59232	−0.796159	−	0.605088i	$-0.793138\pi$
$587$	−22645.8	−1.59232	−0.796159	+	0.605088i	$0.793138\pi$
$588$	−8901.40	−0.624298
$589$	−14137.8	−0.989031
$590$	8.78171	0.000612775 0
$591$	8794.00	0.612076
$592$	1910.91	0.132666
$593$	−22127.7	−1.53234	−0.766169	−	0.642639i	$-0.777839\pi$
$593$	−22127.7	−1.53234	−0.766169	+	0.642639i	$0.777839\pi$
$594$	50.7213	0.00350357
$595$	−8174.77	−0.563248
$596$	−6195.68	−0.425814
$597$	−11745.1	−0.805184
$598$	575.712	0.0393689
$599$	−17616.1	−1.20163	−0.600815	−	0.799388i	$-0.705157\pi$
$599$	−17616.1	−1.20163	−0.600815	+	0.799388i	$0.705157\pi$
$600$	191.166	0.0130072
$601$	−10268.8	−0.696963	−0.348482	−	0.937316i	$-0.613303\pi$
$601$	−10268.8	−0.696963	−0.348482	+	0.937316i	$0.613303\pi$
$602$	−415.393	−0.0281232
$603$	603.000	0.0407231
$604$	−28997.8	−1.95349
$605$	5026.54	0.337781
$606$	23.6582	0.00158589
$607$	17810.3	1.19093	0.595467	−	0.803380i	$-0.296967\pi$
$607$	17810.3	1.19093	0.595467	+	0.803380i	$0.296967\pi$
$608$	−745.102	−0.0497005
$609$	11065.8	0.736305
$610$	−22.1231	−0.00146842
$611$	1079.86	0.0715002
$612$	−7208.16	−0.476099
$613$	−5929.53	−0.390688	−0.195344	−	0.980735i	$-0.562582\pi$
$613$	−5929.53	−0.390688	−0.195344	+	0.980735i	$0.562582\pi$
$614$	124.934	0.00821158
$615$	−1585.48	−0.103956
$616$	803.058	0.0525262
$617$	−14431.2	−0.941620	−0.470810	−	0.882235i	$-0.656038\pi$
$617$	−14431.2	−0.941620	−0.470810	+	0.882235i	$0.656038\pi$
$618$	−125.930	−0.00819682
$619$	17674.3	1.14764	0.573820	−	0.818982i	$-0.305461\pi$
$619$	17674.3	1.14764	0.573820	+	0.818982i	$0.305461\pi$
$620$	−3065.48	−0.198569
$621$	5742.70	0.371089
$622$	−150.817	−0.00972219
$623$	37387.7	2.40434
$624$	15085.4	0.967785
$625$	12211.1	0.781509
$626$	−61.0896	−0.00390037
$627$	−18447.5	−1.17500
$628$	5022.05	0.319111
$629$	2990.96	0.189598
$630$	−25.3027	−0.00160013
$631$	−16281.6	−1.02720	−0.513598	−	0.858031i	$-0.671688\pi$
$631$	−16281.6	−1.02720	−0.513598	+	0.858031i	$0.671688\pi$
$632$	−191.669	−0.0120636
$633$	−14581.1	−0.915554
$634$	−132.552	−0.00830333
$635$	−1264.39	−0.0790167
$636$	4595.50	0.286515
$637$	29158.1	1.81363
$638$	−259.332	−0.0160926
$639$	7671.14	0.474907
$640$	−215.407	−0.0133043
$641$	8350.85	0.514569	0.257285	−	0.966336i	$-0.417172\pi$
$641$	8350.85	0.514569	0.257285	+	0.966336i	$0.417172\pi$
$642$	85.0382	0.00522771
$643$	−11763.0	−0.721442	−0.360721	−	0.932674i	$-0.617469\pi$
$643$	−11763.0	−0.721442	−0.360721	+	0.932674i	$0.617469\pi$
$644$	45458.0	2.78152
$645$	4138.37	0.252633
$646$	−388.648	−0.0236705
$647$	1678.29	0.101979	0.0509895	−	0.998699i	$-0.483763\pi$
$647$	1678.29	0.101979	0.0509895	+	0.998699i	$0.483763\pi$
$648$	−44.6250	−0.00270530
$649$	4553.12	0.275386
$650$	−313.076	−0.0188921
$651$	−10054.1	−0.605299
$652$	7275.83	0.437030
$653$	−3407.21	−0.204187	−0.102094	−	0.994775i	$-0.532554\pi$
$653$	−3407.21	−0.204187	−0.102094	+	0.994775i	$0.532554\pi$
$654$	−100.483	−0.00600797
$655$	4827.91	0.288003
$656$	−11064.7	−0.658543
$657$	7309.67	0.434060
$658$	−12.6404	−0.000748894 0
$659$	13098.9	0.774296	0.387148	−	0.922018i	$-0.373460\pi$
$659$	13098.9	0.774296	0.387148	+	0.922018i	$0.373460\pi$
$660$	−3999.95	−0.235906
$661$	1070.26	0.0629776	0.0314888	−	0.999504i	$-0.489975\pi$
$661$	1070.26	0.0629776	0.0314888	+	0.999504i	$0.489975\pi$
$662$	211.488	0.0124165
$663$	23611.6	1.38310
$664$	112.338	0.00656559
$665$	9202.68	0.536638
$666$	9.25768	0.000538630 0
$667$	−29361.8	−1.70449
$668$	7216.06	0.417960
$669$	9657.63	0.558125
$670$	7.04963	0.000406494 0
$671$	−11470.3	−0.659920
$672$	−529.877	−0.0304173
$673$	−2119.05	−0.121372	−0.0606862	−	0.998157i	$-0.519329\pi$
$673$	−2119.05	−0.121372	−0.0606862	+	0.998157i	$0.519329\pi$
$674$	−245.526	−0.0140316
$675$	−3122.92	−0.178076
$676$	−31848.7	−1.81206
$677$	−10450.9	−0.593293	−0.296647	−	0.954987i	$-0.595868\pi$
$677$	−10450.9	−0.593293	−0.296647	+	0.954987i	$0.595868\pi$
$678$	−197.949	−0.0112127
$679$	−3317.08	−0.187478
$680$	−168.553	−0.00950544
$681$	11937.2	0.671707
$682$	235.621	0.0132293
$683$	−354.662	−0.0198694	−0.00993468	−	0.999951i	$-0.503162\pi$
$683$	−354.662	−0.0198694	−0.00993468	+	0.999951i	$0.503162\pi$
$684$	8114.53	0.453606
$685$	6000.33	0.334688
$686$	−25.7137	−0.00143113
$687$	10812.6	0.600473
$688$	28880.7	1.60039
$689$	−15053.4	−0.832347
$690$	67.1375	0.00370417
$691$	2615.30	0.143981	0.0719905	−	0.997405i	$-0.477065\pi$
$691$	2615.30	0.143981	0.0719905	+	0.997405i	$0.477065\pi$
$692$	−4279.10	−0.235068
$693$	−13118.9	−0.719112
$694$	−203.401	−0.0111253
$695$	910.679	0.0497036
$696$	228.162	0.0124260
$697$	−17318.5	−0.941153
$698$	−69.5837	−0.00377333
$699$	−14605.2	−0.790301
$700$	−24720.4	−1.33478
$701$	−25711.6	−1.38533	−0.692664	−	0.721261i	$-0.743563\pi$
$701$	−25711.6	−1.38533	−0.692664	+	0.721261i	$0.743563\pi$
$702$	73.0831	0.00392926
$703$	−3367.05	−0.180641
$704$	−27906.5	−1.49398
$705$	125.930	0.00672736
$706$	−279.323	−0.0148902
$707$	−6119.10	−0.325506
$708$	−2002.79	−0.106313
$709$	4553.11	0.241178	0.120589	−	0.992702i	$-0.461522\pi$
$709$	4553.11	0.241178	0.120589	+	0.992702i	$0.461522\pi$
$710$	89.6827	0.00474047
$711$	3131.14	0.165157
$712$	770.884	0.0405760
$713$	26677.2	1.40122
$714$	−276.386	−0.0144867
$715$	13102.5	0.685324
$716$	15771.6	0.823200
$717$	−2246.96	−0.117035
$718$	431.591	0.0224329
$719$	−29110.4	−1.50993	−0.754963	−	0.655768i	$-0.772345\pi$
$719$	−29110.4	−1.50993	−0.754963	+	0.655768i	$0.772345\pi$
$720$	1759.20	0.0910577
$721$	32571.3	1.68241
$722$	201.325	0.0103775
$723$	−9834.03	−0.505853
$724$	1267.17	0.0650471
$725$	15967.1	0.817937
$726$	169.945	0.00868769
$727$	−3227.23	−0.164637	−0.0823187	−	0.996606i	$-0.526233\pi$
$727$	−3227.23	−0.164637	−0.0823187	+	0.996606i	$0.526233\pi$
$728$	1157.11	0.0589083
$729$	729.000	0.0370370
$730$	85.4568	0.00433274
$731$	45204.1	2.28719
$732$	5045.46	0.254762
$733$	27257.6	1.37351	0.686756	−	0.726888i	$-0.259034\pi$
$733$	27257.6	1.37351	0.686756	+	0.726888i	$0.259034\pi$
$734$	237.695	0.0119530
$735$	3400.31	0.170643
$736$	1405.96	0.0704135
$737$	3655.07	0.182682
$738$	−53.6044	−0.00267372
$739$	20335.1	1.01223	0.506115	−	0.862466i	$-0.331081\pi$
$739$	20335.1	1.01223	0.506115	+	0.862466i	$0.331081\pi$
$740$	−730.073	−0.0362676
$741$	−26580.6	−1.31776
$742$	176.207	0.00871802
$743$	3024.30	0.149328	0.0746641	−	0.997209i	$-0.476212\pi$
$743$	3024.30	0.149328	0.0746641	+	0.997209i	$0.476212\pi$
$744$	−207.301	−0.0102151
$745$	2366.73	0.116390
$746$	165.138	0.00810472
$747$	−1835.17	−0.0898865
$748$	−43692.1	−2.13575
$749$	−21994.8	−1.07300
$750$	−75.9667	−0.00369855
$751$	−31945.5	−1.55221	−0.776104	−	0.630605i	$-0.782807\pi$
$751$	−31945.5	−1.55221	−0.776104	+	0.630605i	$0.782807\pi$
$752$	878.836	0.0426168
$753$	−17349.4	−0.839637
$754$	−373.665	−0.0180479
$755$	11077.1	0.533956
$756$	5770.62	0.277613
$757$	19844.1	0.952769	0.476385	−	0.879237i	$-0.341947\pi$
$757$	19844.1	0.952769	0.476385	+	0.879237i	$0.341947\pi$
$758$	32.5106	0.00155784
$759$	34809.2	1.66468
$760$	189.747	0.00905637
$761$	31291.9	1.49058	0.745290	−	0.666740i	$-0.232311\pi$
$761$	31291.9	1.49058	0.745290	+	0.666740i	$0.232311\pi$
$762$	−42.7484	−0.00203230
$763$	25989.7	1.23314
$764$	4225.65	0.200103
$765$	2753.50	0.130135
$766$	333.046	0.0157095
$767$	6560.48	0.308846
$768$	12269.8	0.576495
$769$	7409.30	0.347446	0.173723	−	0.984795i	$-0.444420\pi$
$769$	7409.30	0.347446	0.173723	+	0.984795i	$0.444420\pi$
$770$	−153.372	−0.00717810
$771$	−1931.07	−0.0902020
$772$	32446.2	1.51265
$773$	−12825.0	−0.596743	−0.298372	−	0.954450i	$-0.596443\pi$
$773$	−12825.0	−0.596743	−0.298372	+	0.954450i	$0.596443\pi$
$774$	139.917	0.00649767
$775$	−14507.2	−0.672407
$776$	−68.3937	−0.00316391
$777$	−2394.47	−0.110555
$778$	−407.526	−0.0187796
$779$	19496.1	0.896689
$780$	−5763.43	−0.264569
$781$	46498.4	2.13040
$782$	733.354	0.0335354
$783$	−3727.29	−0.170118
$784$	23730.0	1.08100
$785$	−1918.41	−0.0872243
$786$	163.230	0.00740739
$787$	−13607.9	−0.616353	−0.308176	−	0.951329i	$-0.599719\pi$
$787$	−13607.9	−0.616353	−0.308176	+	0.951329i	$0.599719\pi$
$788$	−23447.2	−1.05999
$789$	−16459.6	−0.742683
$790$	36.6059	0.00164858
$791$	51198.9	2.30142
$792$	−270.493	−0.0121358
$793$	−16527.3	−0.740103
$794$	−457.381	−0.0204431
$795$	−1755.47	−0.0783145
$796$	31315.6	1.39441
$797$	4739.38	0.210637	0.105318	−	0.994439i	$-0.466414\pi$
$797$	4739.38	0.210637	0.105318	+	0.994439i	$0.466414\pi$
$798$	311.139	0.0138023
$799$	1375.55	0.0609056
$800$	−764.571	−0.0337896
$801$	−12593.3	−0.555507
$802$	−298.063	−0.0131234
$803$	44307.4	1.94717
$804$	−1607.76	−0.0705241
$805$	−17364.9	−0.760287
$806$	339.500	0.0148367
$807$	19062.9	0.831531
$808$	−126.168	−0.00549327
$809$	12886.5	0.560029	0.280015	−	0.959996i	$-0.409661\pi$
$809$	12886.5	0.560029	0.280015	+	0.959996i	$0.409661\pi$
$810$	8.52268	0.000369699 0
$811$	−45685.5	−1.97810	−0.989048	−	0.147595i	$-0.952847\pi$
$811$	−45685.5	−1.97810	−0.989048	+	0.147595i	$0.952847\pi$
$812$	−29504.5	−1.27513
$813$	−6601.38	−0.284773
$814$	56.1152	0.00241626
$815$	−2779.35	−0.119456
$816$	19216.1	0.824383
$817$	−50888.2	−2.17913
$818$	39.0346	0.00166848
$819$	−18902.7	−0.806487
$820$	4227.32	0.180030
$821$	14646.2	0.622602	0.311301	−	0.950311i	$-0.399235\pi$
$821$	14646.2	0.622602	0.311301	+	0.950311i	$0.399235\pi$
$822$	202.869	0.00860811
$823$	3022.88	0.128033	0.0640165	−	0.997949i	$-0.479609\pi$
$823$	3022.88	0.128033	0.0640165	+	0.997949i	$0.479609\pi$
$824$	671.576	0.0283925
$825$	−18929.5	−0.798838
$826$	−76.7938	−0.00323486
$827$	−13760.1	−0.578579	−0.289289	−	0.957242i	$-0.593419\pi$
$827$	−13760.1	−0.578579	−0.289289	+	0.957242i	$0.593419\pi$
$828$	−15311.6	−0.642651
$829$	−26623.1	−1.11539	−0.557695	−	0.830046i	$-0.688314\pi$
$829$	−26623.1	−1.11539	−0.557695	+	0.830046i	$0.688314\pi$
$830$	−21.4548	−0.000897237 0
$831$	−4259.44	−0.177808
$832$	−40209.7	−1.67551
$833$	37142.2	1.54490
$834$	30.7897	0.00127837
$835$	−2756.52	−0.114243
$836$	49186.1	2.03485
$837$	3386.50	0.139850
$838$	−99.0828	−0.00408444
$839$	−12413.0	−0.510779	−0.255390	−	0.966838i	$-0.582204\pi$
$839$	−12413.0	−0.510779	−0.255390	+	0.966838i	$0.582204\pi$
$840$	134.938	0.00554261
$841$	−5331.78	−0.218614
$842$	221.052	0.00904747
$843$	−8789.29	−0.359098
$844$	38877.1	1.58555
$845$	12166.1	0.495299
$846$	4.25764	0.000173027 0
$847$	−43955.7	−1.78316
$848$	−12251.0	−0.496111
$849$	−9595.37	−0.387883
$850$	−398.803	−0.0160928
$851$	6353.41	0.255925
$852$	−20453.3	−0.822441
$853$	27189.9	1.09140	0.545701	−	0.837980i	$-0.316263\pi$
$853$	27189.9	1.09140	0.545701	+	0.837980i	$0.316263\pi$
$854$	193.460	0.00775185
$855$	−3099.73	−0.123987
$856$	−453.504	−0.0181080
$857$	7196.01	0.286827	0.143414	−	0.989663i	$-0.454192\pi$
$857$	7196.01	0.286827	0.143414	+	0.989663i	$0.454192\pi$
$858$	442.991	0.0176264
$859$	10608.4	0.421368	0.210684	−	0.977554i	$-0.432431\pi$
$859$	10608.4	0.421368	0.210684	+	0.977554i	$0.432431\pi$
$860$	−11034.0	−0.437508
$861$	13864.6	0.548785
$862$	48.8688	0.00193095
$863$	41229.3	1.62626	0.813130	−	0.582082i	$-0.197762\pi$
$863$	41229.3	1.62626	0.813130	+	0.582082i	$0.197762\pi$
$864$	178.478	0.00702771
$865$	1634.60	0.0642523
$866$	−345.531	−0.0135584
$867$	15338.0	0.600812
$868$	26806.9	1.04825
$869$	18979.3	0.740885
$870$	−43.5755	−0.00169810
$871$	5266.51	0.204878
$872$	535.871	0.0208107
$873$	1117.29	0.0433156
$874$	−825.568	−0.0319511
$875$	19648.5	0.759133
$876$	−19489.6	−0.751702
$877$	47751.2	1.83859	0.919296	−	0.393567i	$-0.128759\pi$
$877$	47751.2	1.83859	0.919296	+	0.393567i	$0.128759\pi$
$878$	440.008	0.0169129
$879$	19912.7	0.764093
$880$	10663.4	0.408479
$881$	−25350.1	−0.969428	−0.484714	−	0.874673i	$-0.661076\pi$
$881$	−25350.1	−0.969428	−0.484714	+	0.874673i	$0.661076\pi$
$882$	114.963	0.00438890
$883$	−45665.2	−1.74038	−0.870191	−	0.492715i	$-0.836004\pi$
$883$	−45665.2	−1.74038	−0.870191	+	0.492715i	$0.836004\pi$
$884$	−62954.9	−2.39525
$885$	765.060	0.0290590
$886$	−269.726	−0.0102275
$887$	−12026.7	−0.455263	−0.227631	−	0.973747i	$-0.573098\pi$
$887$	−12026.7	−0.455263	−0.227631	+	0.973747i	$0.573098\pi$
$888$	−49.3706	−0.00186573
$889$	11056.7	0.417132
$890$	−147.227	−0.00554501
$891$	4418.82	0.166146
$892$	−25749.9	−0.966558
$893$	−1548.52	−0.0580282
$894$	80.0184	0.00299353
$895$	−6024.70	−0.225010
$896$	1883.68	0.0702336
$897$	50155.8	1.86695
$898$	−335.834	−0.0124799
$899$	−17314.8	−0.642359
$900$	8326.56	0.308391
$901$	−19175.3	−0.709014
$902$	−324.922	−0.0119941
$903$	−36188.9	−1.33366
$904$	1055.65	0.0388390
$905$	−484.057	−0.0177797
$906$	374.513	0.0137333
$907$	20757.8	0.759923	0.379962	−	0.925002i	$-0.375937\pi$
$907$	20757.8	0.759923	0.379962	+	0.925002i	$0.375937\pi$
$908$	−31827.7	−1.16326
$909$	2061.09	0.0752059
$910$	−220.990	−0.00805026
$911$	9848.09	0.358158	0.179079	−	0.983835i	$-0.442688\pi$
$911$	9848.09	0.358158	0.179079	+	0.983835i	$0.442688\pi$
$912$	−21632.3	−0.785437
$913$	−11123.8	−0.403225
$914$	−67.1871	−0.00243146
$915$	−1927.35	−0.0696354
$916$	−28829.2	−1.03990
$917$	−42218.8	−1.52038
$918$	93.0948	0.00334704
$919$	17111.9	0.614220	0.307110	−	0.951674i	$-0.400638\pi$
$919$	17111.9	0.614220	0.307110	+	0.951674i	$0.400638\pi$
$920$	−358.040	−0.0128307
$921$	10884.2	0.389409
$922$	−22.8276	−0.000815387 0
$923$	66998.5	2.38925
$924$	34978.5	1.24535
$925$	−3455.03	−0.122812
$926$	−428.565	−0.0152090
$927$	−10971.0	−0.388709
$928$	−912.537	−0.0322796
$929$	−3247.10	−0.114676	−0.0573380	−	0.998355i	$-0.518261\pi$
$929$	−3247.10	−0.114676	−0.0573380	+	0.998355i	$0.518261\pi$
$930$	39.5913	0.00139597
$931$	−41812.5	−1.47191
$932$	38941.5	1.36864
$933$	−13139.1	−0.461045
$934$	300.876	0.0105407
$935$	16690.3	0.583776
$936$	−389.747	−0.0136104
$937$	−32101.3	−1.11922	−0.559608	−	0.828758i	$-0.689048\pi$
$937$	−32101.3	−1.11922	−0.559608	+	0.828758i	$0.689048\pi$
$938$	−61.6471	−0.00214590
$939$	−5322.11	−0.184963
$940$	−335.763	−0.0116504
$941$	−48803.8	−1.69071	−0.845355	−	0.534204i	$-0.820611\pi$
$941$	−48803.8	−1.69071	−0.845355	+	0.534204i	$0.820611\pi$
$942$	−64.8608	−0.00224340
$943$	−36787.9	−1.27039
$944$	5339.18	0.184084
$945$	−2204.36	−0.0758814
$946$	848.102	0.0291482
$947$	−3285.62	−0.112744	−0.0563719	−	0.998410i	$-0.517953\pi$
$947$	−3285.62	−0.112744	−0.0563719	+	0.998410i	$0.517953\pi$
$948$	−8348.46	−0.286018
$949$	63841.5	2.18375
$950$	448.950	0.0153325
$951$	−11547.9	−0.393760
$952$	1473.95	0.0501795
$953$	44841.6	1.52420	0.762099	−	0.647460i	$-0.224169\pi$
$953$	44841.6	1.52420	0.762099	+	0.647460i	$0.224169\pi$
$954$	−59.3517	−0.00201424
$955$	−1614.19	−0.0546951
$956$	5990.99	0.202681
$957$	−22592.9	−0.763140
$958$	−70.4236	−0.00237504
$959$	−52471.3	−1.76683
$960$	−4689.12	−0.157646
$961$	−14059.3	−0.471932
$962$	80.8551	0.00270985
$963$	7408.50	0.247908
$964$	26220.2	0.876032
$965$	−12394.4	−0.413460
$966$	−587.099	−0.0195545
$967$	17813.3	0.592387	0.296194	−	0.955128i	$-0.404283\pi$
$967$	17813.3	0.592387	0.296194	+	0.955128i	$0.404283\pi$
$968$	−906.308	−0.0300928
$969$	−33858.9	−1.12250
$970$	13.0621	0.000432371 0
$971$	−25462.5	−0.841536	−0.420768	−	0.907168i	$-0.638239\pi$
$971$	−25462.5	−0.841536	−0.420768	+	0.907168i	$0.638239\pi$
$972$	−1943.71	−0.0641405
$973$	−7963.64	−0.262387
$974$	573.358	0.0188620
$975$	−27275.1	−0.895900
$976$	−13450.6	−0.441130
$977$	−40269.3	−1.31866	−0.659329	−	0.751854i	$-0.729160\pi$
$977$	−40269.3	−1.31866	−0.659329	+	0.751854i	$0.729160\pi$
$978$	−93.9687	−0.00307238
$979$	−76333.8	−2.49197
$980$	−9066.15	−0.295518
$981$	−8754.07	−0.284909
$982$	−434.742	−0.0141275
$983$	24315.0	0.788941	0.394470	−	0.918909i	$-0.370928\pi$
$983$	24315.0	0.788941	0.394470	+	0.918909i	$0.370928\pi$
$984$	285.869	0.00926135
$985$	8956.77	0.289732
$986$	−475.983	−0.0153736
$987$	−1101.22	−0.0355140
$988$	70871.0	2.28209
$989$	96022.7	3.08730
$990$	51.6601	0.00165845
$991$	49786.6	1.59589	0.797943	−	0.602733i	$-0.205921\pi$
$991$	49786.6	1.59589	0.797943	+	0.602733i	$0.205921\pi$
$992$	829.102	0.0265363
$993$	18424.7	0.588813
$994$	−784.251	−0.0250251
$995$	−11962.5	−0.381142
$996$	4893.05	0.155665
$997$	−25664.5	−0.815248	−0.407624	−	0.913150i	$-0.633643\pi$
$997$	−25664.5	−0.815248	−0.407624	+	0.913150i	$0.633643\pi$
$998$	−28.4310	−0.000901772 0
$999$	806.526	0.0255429

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.e.1.6	✓	11
3.2	odd	2		603.4.a.g.1.6		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.e.1.6	✓	11	1.1	even	1	trivial
603.4.a.g.1.6		11	3.2	odd	2

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.a (trivial)

\(f(q)\)	\(=\)	\(q+0.0344354 q^{2} +3.00000 q^{3} -7.99881 q^{4} +3.05553 q^{5} +0.103306 q^{6} -26.7198 q^{7} -0.550926 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+0.0344354 q^{2} +3.00000 q^{3} -7.99881 q^{4} +3.05553 q^{5} +0.103306 q^{6} -26.7198 q^{7} -0.550926 q^{8} +9.00000 q^{9} +0.105218 q^{10} +54.5533 q^{11} -23.9964 q^{12} +78.6046 q^{13} -0.920106 q^{14} +9.16658 q^{15} +63.9715 q^{16} +100.128 q^{17} +0.309919 q^{18} -112.719 q^{19} -24.4406 q^{20} -80.1593 q^{21} +1.87857 q^{22} +212.693 q^{23} -1.65278 q^{24} -115.664 q^{25} +2.70678 q^{26} +27.0000 q^{27} +213.727 q^{28} -138.048 q^{29} +0.315655 q^{30} +125.426 q^{31} +6.61029 q^{32} +163.660 q^{33} +3.44795 q^{34} -81.6430 q^{35} -71.9893 q^{36} +29.8713 q^{37} -3.88151 q^{38} +235.814 q^{39} -1.68337 q^{40} -172.963 q^{41} -2.76032 q^{42} +451.462 q^{43} -436.362 q^{44} +27.4997 q^{45} +7.32415 q^{46} +13.7379 q^{47} +191.915 q^{48} +370.946 q^{49} -3.98293 q^{50} +300.385 q^{51} -628.743 q^{52} -191.507 q^{53} +0.929756 q^{54} +166.689 q^{55} +14.7206 q^{56} -338.156 q^{57} -4.75374 q^{58} +83.4618 q^{59} -73.3218 q^{60} -210.259 q^{61} +4.31909 q^{62} -240.478 q^{63} -511.545 q^{64} +240.178 q^{65} +5.63570 q^{66} +67.0000 q^{67} -800.907 q^{68} +638.078 q^{69} -2.81141 q^{70} +852.348 q^{71} -4.95833 q^{72} +812.185 q^{73} +1.02863 q^{74} -346.991 q^{75} +901.614 q^{76} -1457.65 q^{77} +8.12034 q^{78} +347.904 q^{79} +195.467 q^{80} +81.0000 q^{81} -5.95605 q^{82} -203.907 q^{83} +641.180 q^{84} +305.944 q^{85} +15.5463 q^{86} -414.144 q^{87} -30.0548 q^{88} -1399.25 q^{89} +0.946965 q^{90} -2100.30 q^{91} -1701.29 q^{92} +376.278 q^{93} +0.473071 q^{94} -344.415 q^{95} +19.8309 q^{96} +124.143 q^{97} +12.7737 q^{98} +490.980 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9 + 29 * q^10 + 104 * q^11 + 207 * q^12 + 172 * q^13 + 143 * q^14 + 24 * q^15 + 485 * q^16 - 48 * q^17 + 27 * q^18 + 180 * q^19 - 539 * q^20 + 234 * q^21 - 144 * q^22 + 156 * q^23 + 63 * q^24 + 383 * q^25 - 252 * q^26 + 297 * q^27 + 1011 * q^28 - 4 * q^29 + 87 * q^30 + 514 * q^31 - 119 * q^32 + 312 * q^33 + 72 * q^34 - 338 * q^35 + 621 * q^36 + 854 * q^37 - 308 * q^38 + 516 * q^39 - 15 * q^40 + 674 * q^41 + 429 * q^42 + 738 * q^43 + 356 * q^44 + 72 * q^45 + 507 * q^46 + 54 * q^47 + 1455 * q^48 + 1465 * q^49 + 656 * q^50 - 144 * q^51 - 12 * q^52 - 190 * q^53 + 81 * q^54 + 262 * q^55 + 239 * q^56 + 540 * q^57 - 1466 * q^58 + 18 * q^59 - 1617 * q^60 + 328 * q^61 - 915 * q^62 + 702 * q^63 + 2253 * q^64 - 732 * q^65 - 432 * q^66 + 737 * q^67 - 5746 * q^68 + 468 * q^69 - 4451 * q^70 + 264 * q^71 + 189 * q^72 + 330 * q^73 - 5975 * q^74 + 1149 * q^75 - 178 * q^76 - 368 * q^77 - 756 * q^78 + 456 * q^79 - 8515 * q^80 + 891 * q^81 - 3629 * q^82 - 2432 * q^83 + 3033 * q^84 + 2882 * q^85 - 6225 * q^86 - 12 * q^87 - 5492 * q^88 - 2340 * q^89 + 261 * q^90 - 994 * q^91 - 2939 * q^92 + 1542 * q^93 - 3506 * q^94 - 2568 * q^95 - 357 * q^96 + 1892 * q^97 - 1078 * q^98 + 936 * q^99

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