LMFDB - Embedded newform 201.4.a.e.1.8

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			1.8
Root			$2.85564$ 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)

$f(q)$	$=$	$q+2.85564 q^{2} +3.00000 q^{3} +0.154694 q^{4} -2.88345 q^{5} +8.56693 q^{6} +19.3750 q^{7} -22.4034 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.85564 q^{2} +3.00000 q^{3} +0.154694 q^{4} -2.88345 q^{5} +8.56693 q^{6} +19.3750 q^{7} -22.4034 q^{8} +9.00000 q^{9} -8.23409 q^{10} +45.0399 q^{11} +0.464082 q^{12} +92.2911 q^{13} +55.3281 q^{14} -8.65034 q^{15} -65.2136 q^{16} +4.16966 q^{17} +25.7008 q^{18} +92.2723 q^{19} -0.446052 q^{20} +58.1251 q^{21} +128.618 q^{22} -178.357 q^{23} -67.2102 q^{24} -116.686 q^{25} +263.551 q^{26} +27.0000 q^{27} +2.99720 q^{28} +63.5469 q^{29} -24.7023 q^{30} +104.013 q^{31} -6.99967 q^{32} +135.120 q^{33} +11.9071 q^{34} -55.8668 q^{35} +1.39225 q^{36} -368.679 q^{37} +263.497 q^{38} +276.873 q^{39} +64.5990 q^{40} -133.286 q^{41} +165.984 q^{42} -318.081 q^{43} +6.96739 q^{44} -25.9510 q^{45} -509.324 q^{46} -140.687 q^{47} -195.641 q^{48} +32.3913 q^{49} -333.213 q^{50} +12.5090 q^{51} +14.2769 q^{52} +176.594 q^{53} +77.1023 q^{54} -129.870 q^{55} -434.066 q^{56} +276.817 q^{57} +181.467 q^{58} +399.814 q^{59} -1.33816 q^{60} +900.873 q^{61} +297.024 q^{62} +174.375 q^{63} +501.720 q^{64} -266.117 q^{65} +385.853 q^{66} +67.0000 q^{67} +0.645021 q^{68} -535.071 q^{69} -159.536 q^{70} -991.092 q^{71} -201.631 q^{72} +178.009 q^{73} -1052.81 q^{74} -350.057 q^{75} +14.2740 q^{76} +872.648 q^{77} +790.652 q^{78} -437.517 q^{79} +188.040 q^{80} +81.0000 q^{81} -380.616 q^{82} -1096.56 q^{83} +8.99159 q^{84} -12.0230 q^{85} -908.327 q^{86} +190.641 q^{87} -1009.05 q^{88} +899.401 q^{89} -74.1068 q^{90} +1788.14 q^{91} -27.5907 q^{92} +312.039 q^{93} -401.751 q^{94} -266.062 q^{95} -20.9990 q^{96} -534.803 q^{97} +92.4980 q^{98} +405.359 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.85564	1.00962	0.504811	−	0.863230i	$-0.331562\pi$
$2$	2.85564	1.00962	0.504811	+	0.863230i	$0.331562\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	0.154694	0.0193367
$5$	−2.88345	−0.257903	−0.128952	−	0.991651i	$-0.541161\pi$
$5$	−2.88345	−0.257903	−0.128952	+	0.991651i	$0.541161\pi$
$6$	8.56693	0.582906
$7$	19.3750	1.04615	0.523076	−	0.852286i	$-0.324784\pi$
$7$	19.3750	1.04615	0.523076	+	0.852286i	$0.324784\pi$
$8$	−22.4034	−0.990099
$9$	9.00000	0.333333
$10$	−8.23409	−0.260385
$11$	45.0399	1.23455	0.617274	−	0.786748i	$-0.288237\pi$
$11$	45.0399	1.23455	0.617274	+	0.786748i	$0.288237\pi$
$12$	0.464082	0.0111641
$13$	92.2911	1.96900	0.984498	−	0.175393i	$-0.0561197\pi$
$13$	92.2911	1.96900	0.984498	+	0.175393i	$0.0561197\pi$
$14$	55.3281	1.05622
$15$	−8.65034	−0.148901
$16$	−65.2136	−1.01896
$17$	4.16966	0.0594878	0.0297439	−	0.999558i	$-0.490531\pi$
$17$	4.16966	0.0594878	0.0297439	+	0.999558i	$0.490531\pi$
$18$	25.7008	0.336541
$19$	92.2723	1.11414	0.557071	−	0.830465i	$-0.311925\pi$
$19$	92.2723	1.11414	0.557071	+	0.830465i	$0.311925\pi$
$20$	−0.446052	−0.00498701
$21$	58.1251	0.603996
$22$	128.618	1.24643
$23$	−178.357	−1.61696	−0.808479	−	0.588526i	$-0.799709\pi$
$23$	−178.357	−1.61696	−0.808479	+	0.588526i	$0.799709\pi$
$24$	−67.2102	−0.571634
$25$	−116.686	−0.933486
$26$	263.551	1.98794
$27$	27.0000	0.192450
$28$	2.99720	0.0202292
$29$	63.5469	0.406909	0.203455	−	0.979084i	$-0.434783\pi$
$29$	63.5469	0.406909	0.203455	+	0.979084i	$0.434783\pi$
$30$	−24.7023	−0.150333
$31$	104.013	0.602621	0.301311	−	0.953526i	$-0.402576\pi$
$31$	104.013	0.602621	0.301311	+	0.953526i	$0.402576\pi$
$32$	−6.99967	−0.0386681
$33$	135.120	0.712767
$34$	11.9071	0.0600602
$35$	−55.8668	−0.269806
$36$	1.39225	0.00644558
$37$	−368.679	−1.63812	−0.819060	−	0.573708i	$-0.805504\pi$
$37$	−368.679	−1.63812	−0.819060	+	0.573708i	$0.805504\pi$
$38$	263.497	1.12486
$39$	276.873	1.13680
$40$	64.5990	0.255350
$41$	−133.286	−0.507701	−0.253850	−	0.967244i	$-0.581697\pi$
$41$	−133.286	−0.507701	−0.253850	+	0.967244i	$0.581697\pi$
$42$	165.984	0.609808
$43$	−318.081	−1.12807	−0.564034	−	0.825751i	$-0.690752\pi$
$43$	−318.081	−1.12807	−0.564034	+	0.825751i	$0.690752\pi$
$44$	6.96739	0.0238721
$45$	−25.9510	−0.0859678
$46$	−509.324	−1.63252
$47$	−140.687	−0.436623	−0.218312	−	0.975879i	$-0.570055\pi$
$47$	−140.687	−0.436623	−0.218312	+	0.975879i	$0.570055\pi$
$48$	−195.641	−0.588298
$49$	32.3913	0.0944353
$50$	−333.213	−0.942468
$51$	12.5090	0.0343453
$52$	14.2769	0.0380740
$53$	176.594	0.457681	0.228840	−	0.973464i	$-0.426507\pi$
$53$	176.594	0.457681	0.228840	+	0.973464i	$0.426507\pi$
$54$	77.1023	0.194302
$55$	−129.870	−0.318394
$56$	−434.066	−1.03579
$57$	276.817	0.643251
$58$	181.467	0.410825
$59$	399.814	0.882227	0.441114	−	0.897451i	$-0.354584\pi$
$59$	399.814	0.882227	0.441114	+	0.897451i	$0.354584\pi$
$60$	−1.33816	−0.00287925
$61$	900.873	1.89090	0.945450	−	0.325766i	$-0.105622\pi$
$61$	900.873	1.89090	0.945450	+	0.325766i	$0.105622\pi$
$62$	297.024	0.608420
$63$	174.375	0.348718
$64$	501.720	0.979923
$65$	−266.117	−0.507811
$66$	385.853	0.719625
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	0.645021	0.00115030
$69$	−535.071	−0.933551
$70$	−159.536	−0.272402
$71$	−991.092	−1.65663	−0.828317	−	0.560260i	$-0.810701\pi$
$71$	−991.092	−1.65663	−0.828317	+	0.560260i	$0.810701\pi$
$72$	−201.631	−0.330033
$73$	178.009	0.285403	0.142701	−	0.989766i	$-0.454421\pi$
$73$	178.009	0.285403	0.142701	+	0.989766i	$0.454421\pi$
$74$	−1052.81	−1.65388
$75$	−350.057	−0.538948
$76$	14.2740	0.0215439
$77$	872.648	1.29153
$78$	790.652	1.14774
$79$	−437.517	−0.623095	−0.311547	−	0.950231i	$-0.600847\pi$
$79$	−437.517	−0.623095	−0.311547	+	0.950231i	$0.600847\pi$
$80$	188.040	0.262794
$81$	81.0000	0.111111
$82$	−380.616	−0.512586
$83$	−1096.56	−1.45016	−0.725079	−	0.688666i	$-0.758197\pi$
$83$	−1096.56	−1.45016	−0.725079	+	0.688666i	$0.758197\pi$
$84$	8.99159	0.0116793
$85$	−12.0230	−0.0153421
$86$	−908.327	−1.13892
$87$	190.641	0.234929
$88$	−1009.05	−1.22233
$89$	899.401	1.07120	0.535598	−	0.844473i	$-0.320086\pi$
$89$	899.401	1.07120	0.535598	+	0.844473i	$0.320086\pi$
$90$	−74.1068	−0.0867950
$91$	1788.14	2.05987
$92$	−27.5907	−0.0312667
$93$	312.039	0.347924
$94$	−401.751	−0.440824
$95$	−266.062	−0.287341
$96$	−20.9990	−0.0223250
$97$	−534.803	−0.559804	−0.279902	−	0.960029i	$-0.590302\pi$
$97$	−534.803	−0.559804	−0.279902	+	0.960029i	$0.590302\pi$
$98$	92.4980	0.0953440
$99$	405.359	0.411516
$100$	−18.0506	−0.0180506
$101$	−1317.37	−1.29785	−0.648925	−	0.760852i	$-0.724781\pi$
$101$	−1317.37	−1.29785	−0.648925	+	0.760852i	$0.724781\pi$
$102$	35.7212	0.0346757
$103$	−281.166	−0.268972	−0.134486	−	0.990915i	$-0.542938\pi$
$103$	−281.166	−0.268972	−0.134486	+	0.990915i	$0.542938\pi$
$104$	−2067.63	−1.94950
$105$	−167.601	−0.155773
$106$	504.290	0.462085
$107$	274.432	0.247947	0.123974	−	0.992286i	$-0.460436\pi$
$107$	274.432	0.247947	0.123974	+	0.992286i	$0.460436\pi$
$108$	4.17674	0.00372136
$109$	1931.42	1.69722	0.848608	−	0.529023i	$-0.177441\pi$
$109$	1931.42	1.69722	0.848608	+	0.529023i	$0.177441\pi$
$110$	−370.863	−0.321458
$111$	−1106.04	−0.945769
$112$	−1263.52	−1.06599
$113$	−1929.80	−1.60655	−0.803277	−	0.595606i	$-0.796912\pi$
$113$	−1929.80	−1.60655	−0.803277	+	0.595606i	$0.796912\pi$
$114$	790.490	0.649440
$115$	514.283	0.417019
$116$	9.83033	0.00786830
$117$	830.620	0.656332
$118$	1141.73	0.890716
$119$	80.7873	0.0622333
$120$	193.797	0.147426
$121$	697.591	0.524110
$122$	2572.57	1.90910
$123$	−399.857	−0.293121
$124$	16.0902	0.0116527
$125$	696.888	0.498652
$126$	497.953	0.352073
$127$	−1779.41	−1.24328	−0.621640	−	0.783303i	$-0.713533\pi$
$127$	−1779.41	−1.24328	−0.621640	+	0.783303i	$0.713533\pi$
$128$	1488.73	1.02802
$129$	−954.244	−0.651291
$130$	−759.934	−0.512697
$131$	−1257.32	−0.838569	−0.419285	−	0.907855i	$-0.637719\pi$
$131$	−1257.32	−0.838569	−0.419285	+	0.907855i	$0.637719\pi$
$132$	20.9022	0.0137826
$133$	1787.78	1.16556
$134$	191.328	0.123345
$135$	−77.8531	−0.0496335
$136$	−93.4146	−0.0588988
$137$	−2333.90	−1.45546	−0.727731	−	0.685863i	$-0.759425\pi$
$137$	−2333.90	−1.45546	−0.727731	+	0.685863i	$0.759425\pi$
$138$	−1527.97	−0.942533
$139$	1071.72	0.653969	0.326985	−	0.945030i	$-0.393967\pi$
$139$	1071.72	0.653969	0.326985	+	0.945030i	$0.393967\pi$
$140$	−8.64226	−0.00521717
$141$	−422.061	−0.252085
$142$	−2830.20	−1.67257
$143$	4156.78	2.43082
$144$	−586.923	−0.339654
$145$	−183.234	−0.104943
$146$	508.331	0.288149
$147$	97.1739	0.0545222
$148$	−57.0323	−0.0316759
$149$	215.006	0.118215	0.0591074	−	0.998252i	$-0.481175\pi$
$149$	215.006	0.118215	0.0591074	+	0.998252i	$0.481175\pi$
$150$	−999.638	−0.544134
$151$	−738.048	−0.397759	−0.198879	−	0.980024i	$-0.563730\pi$
$151$	−738.048	−0.397759	−0.198879	+	0.980024i	$0.563730\pi$
$152$	−2067.21	−1.10311
$153$	37.5270	0.0198293
$154$	2491.97	1.30395
$155$	−299.916	−0.155418
$156$	42.8306	0.0219820
$157$	1416.50	0.720057	0.360029	−	0.932941i	$-0.382767\pi$
$157$	1416.50	0.720057	0.360029	+	0.932941i	$0.382767\pi$
$158$	−1249.39	−0.629090
$159$	529.783	0.264242
$160$	20.1832	0.00997263
$161$	−3455.67	−1.69158
$162$	231.307	0.112180
$163$	3702.77	1.77928	0.889642	−	0.456658i	$-0.150954\pi$
$163$	3702.77	1.77928	0.889642	+	0.456658i	$0.150954\pi$
$164$	−20.6185	−0.00981728
$165$	−389.610	−0.183825
$166$	−3131.38	−1.46411
$167$	316.346	0.146585	0.0732923	−	0.997311i	$-0.476649\pi$
$167$	316.346	0.146585	0.0732923	+	0.997311i	$0.476649\pi$
$168$	−1302.20	−0.598016
$169$	6320.66	2.87695
$170$	−34.3334	−0.0154897
$171$	830.451	0.371381
$172$	−49.2053	−0.0218132
$173$	−2375.11	−1.04379	−0.521896	−	0.853009i	$-0.674775\pi$
$173$	−2375.11	−1.04379	−0.521896	+	0.853009i	$0.674775\pi$
$174$	544.402	0.237190
$175$	−2260.79	−0.976569
$176$	−2937.21	−1.25796
$177$	1199.44	0.509354
$178$	2568.37	1.08150
$179$	1426.28	0.595559	0.297780	−	0.954635i	$-0.403754\pi$
$179$	1426.28	0.595559	0.297780	+	0.954635i	$0.403754\pi$
$180$	−4.01447	−0.00166234
$181$	2862.13	1.17536	0.587681	−	0.809092i	$-0.300041\pi$
$181$	2862.13	1.17536	0.587681	+	0.809092i	$0.300041\pi$
$182$	5106.30	2.07969
$183$	2702.62	1.09171
$184$	3995.80	1.60095
$185$	1063.07	0.422476
$186$	891.071	0.351271
$187$	187.801	0.0734405
$188$	−21.7634	−0.00844287
$189$	523.125	0.201332
$190$	−759.779	−0.290106
$191$	−43.7588	−0.0165774	−0.00828868	−	0.999966i	$-0.502638\pi$
$191$	−43.7588	−0.0165774	−0.00828868	+	0.999966i	$0.502638\pi$
$192$	1505.16	0.565759
$193$	−4163.32	−1.55276	−0.776378	−	0.630267i	$-0.782945\pi$
$193$	−4163.32	−1.55276	−0.776378	+	0.630267i	$0.782945\pi$
$194$	−1527.21	−0.565190
$195$	−798.350	−0.293185
$196$	5.01074	0.00182607
$197$	1498.89	0.542090	0.271045	−	0.962567i	$-0.412631\pi$
$197$	1498.89	0.542090	0.271045	+	0.962567i	$0.412631\pi$
$198$	1157.56	0.415476
$199$	−3135.45	−1.11692	−0.558458	−	0.829533i	$-0.688607\pi$
$199$	−3135.45	−1.11692	−0.558458	+	0.829533i	$0.688607\pi$
$200$	2614.16	0.924244
$201$	201.000	0.0705346
$202$	−3761.93	−1.31034
$203$	1231.22	0.425689
$204$	1.93506	0.000664126 0
$205$	384.322	0.130938
$206$	−802.911	−0.271560
$207$	−1605.21	−0.538986
$208$	−6018.64	−2.00633
$209$	4155.93	1.37546
$210$	−478.607	−0.157272
$211$	1740.76	0.567955	0.283978	−	0.958831i	$-0.408346\pi$
$211$	1740.76	0.567955	0.283978	+	0.958831i	$0.408346\pi$
$212$	27.3181	0.00885005
$213$	−2973.28	−0.956458
$214$	783.680	0.250333
$215$	917.171	0.290933
$216$	−604.892	−0.190545
$217$	2015.25	0.630434
$218$	5515.45	1.71355
$219$	534.028	0.164777
$220$	−20.0901	−0.00615671
$221$	384.823	0.117131
$222$	−3158.44	−0.954869
$223$	4876.69	1.46443	0.732213	−	0.681076i	$-0.238488\pi$
$223$	4876.69	1.46443	0.732213	+	0.681076i	$0.238488\pi$
$224$	−135.619	−0.0404527
$225$	−1050.17	−0.311162
$226$	−5510.83	−1.62201
$227$	6637.07	1.94061	0.970303	−	0.241892i	$-0.0777680\pi$
$227$	6637.07	1.94061	0.970303	+	0.241892i	$0.0777680\pi$
$228$	42.8219	0.0124384
$229$	−2805.74	−0.809644	−0.404822	−	0.914395i	$-0.632667\pi$
$229$	−2805.74	−0.809644	−0.404822	+	0.914395i	$0.632667\pi$
$230$	1468.61	0.421031
$231$	2617.95	0.745663
$232$	−1423.67	−0.402881
$233$	122.879	0.0345497	0.0172749	−	0.999851i	$-0.494501\pi$
$233$	122.879	0.0345497	0.0172749	+	0.999851i	$0.494501\pi$
$234$	2371.95	0.662648
$235$	405.663	0.112607
$236$	61.8489	0.0170594
$237$	−1312.55	−0.359744
$238$	230.700	0.0628321
$239$	−2320.28	−0.627978	−0.313989	−	0.949427i	$-0.601665\pi$
$239$	−2320.28	−0.627978	−0.313989	+	0.949427i	$0.601665\pi$
$240$	564.120	0.151724
$241$	−5407.95	−1.44546	−0.722732	−	0.691129i	$-0.757114\pi$
$241$	−5407.95	−1.44546	−0.722732	+	0.691129i	$0.757114\pi$
$242$	1992.07	0.529153
$243$	243.000	0.0641500
$244$	139.360	0.0365639
$245$	−93.3986	−0.0243552
$246$	−1141.85	−0.295942
$247$	8515.92	2.19374
$248$	−2330.24	−0.596655
$249$	−3289.68	−0.837249
$250$	1990.06	0.503451
$251$	−987.019	−0.248208	−0.124104	−	0.992269i	$-0.539606\pi$
$251$	−987.019	−0.248208	−0.124104	+	0.992269i	$0.539606\pi$
$252$	26.9748	0.00674306
$253$	−8033.18	−1.99621
$254$	−5081.34	−1.25524
$255$	−36.0690	−0.00885776
$256$	237.522	0.0579887
$257$	5901.83	1.43247	0.716237	−	0.697857i	$-0.245863\pi$
$257$	5901.83	1.43247	0.716237	+	0.697857i	$0.245863\pi$
$258$	−2724.98	−0.657558
$259$	−7143.16	−1.71372
$260$	−41.1666	−0.00981941
$261$	571.923	0.135636
$262$	−3590.46	−0.846638
$263$	3470.98	0.813803	0.406901	−	0.913472i	$-0.366609\pi$
$263$	3470.98	0.813803	0.406901	+	0.913472i	$0.366609\pi$
$264$	−3027.14	−0.705710
$265$	−509.200	−0.118037
$266$	5105.25	1.17678
$267$	2698.20	0.618455
$268$	10.3645	0.00236236
$269$	2065.91	0.468255	0.234128	−	0.972206i	$-0.424777\pi$
$269$	2065.91	0.468255	0.234128	+	0.972206i	$0.424777\pi$
$270$	−222.321	−0.0501111
$271$	18.2711	0.00409554	0.00204777	−	0.999998i	$-0.499348\pi$
$271$	18.2711	0.00409554	0.00204777	+	0.999998i	$0.499348\pi$
$272$	−271.919	−0.0606158
$273$	5364.43	1.18927
$274$	−6664.77	−1.46947
$275$	−5255.51	−1.15243
$276$	−82.7722	−0.0180518
$277$	−1394.44	−0.302469	−0.151234	−	0.988498i	$-0.548325\pi$
$277$	−1394.44	−0.302469	−0.151234	+	0.988498i	$0.548325\pi$
$278$	3060.44	0.660262
$279$	936.116	0.200874
$280$	1251.61	0.267135
$281$	−5926.55	−1.25818	−0.629090	−	0.777333i	$-0.716572\pi$
$281$	−5926.55	−1.25818	−0.629090	+	0.777333i	$0.716572\pi$
$282$	−1205.25	−0.254510
$283$	1133.72	0.238137	0.119069	−	0.992886i	$-0.462009\pi$
$283$	1133.72	0.238137	0.119069	+	0.992886i	$0.462009\pi$
$284$	−153.316	−0.0320339
$285$	−798.187	−0.165897
$286$	11870.3	2.45421
$287$	−2582.41	−0.531132
$288$	−62.9970	−0.0128894
$289$	−4895.61	−0.996461
$290$	−523.252	−0.105953
$291$	−1604.41	−0.323203
$292$	27.5370	0.00551876
$293$	−5098.00	−1.01648	−0.508240	−	0.861216i	$-0.669704\pi$
$293$	−5098.00	−1.01648	−0.508240	+	0.861216i	$0.669704\pi$
$294$	277.494	0.0550469
$295$	−1152.84	−0.227529
$296$	8259.65	1.62190
$297$	1216.08	0.237589
$298$	613.981	0.119352
$299$	−16460.8	−3.18378
$300$	−54.1517	−0.0104215
$301$	−6162.83	−1.18013
$302$	−2107.60	−0.401586
$303$	−3952.10	−0.749314
$304$	−6017.41	−1.13527
$305$	−2597.62	−0.487670
$306$	107.164	0.0200201
$307$	−3861.20	−0.717818	−0.358909	−	0.933373i	$-0.616851\pi$
$307$	−3861.20	−0.717818	−0.358909	+	0.933373i	$0.616851\pi$
$308$	134.993	0.0249739
$309$	−843.499	−0.155291
$310$	−856.452	−0.156913
$311$	2763.73	0.503913	0.251957	−	0.967739i	$-0.418926\pi$
$311$	2763.73	0.503913	0.251957	+	0.967739i	$0.418926\pi$
$312$	−6202.90	−1.12555
$313$	8917.45	1.61036	0.805182	−	0.593028i	$-0.202068\pi$
$313$	8917.45	1.61036	0.805182	+	0.593028i	$0.202068\pi$
$314$	4045.02	0.726986
$315$	−502.802	−0.0899354
$316$	−67.6812	−0.0120486
$317$	−6728.20	−1.19209	−0.596046	−	0.802950i	$-0.703262\pi$
$317$	−6728.20	−1.19209	−0.596046	+	0.802950i	$0.703262\pi$
$318$	1512.87	0.266785
$319$	2862.15	0.502349
$320$	−1446.68	−0.252725
$321$	823.297	0.143152
$322$	−9868.16	−1.70786
$323$	384.744	0.0662779
$324$	12.5302	0.00214853
$325$	−10769.1	−1.83803
$326$	10573.8	1.79640
$327$	5794.26	0.979888
$328$	2986.05	0.502674
$329$	−2725.81	−0.456775
$330$	−1112.59	−0.185594
$331$	−1355.48	−0.225088	−0.112544	−	0.993647i	$-0.535900\pi$
$331$	−1355.48	−0.225088	−0.112544	+	0.993647i	$0.535900\pi$
$332$	−169.631	−0.0280413
$333$	−3318.11	−0.546040
$334$	903.372	0.147995
$335$	−193.191	−0.0315079
$336$	−3790.55	−0.615450
$337$	9201.72	1.48739	0.743694	−	0.668521i	$-0.233072\pi$
$337$	9201.72	1.48739	0.743694	+	0.668521i	$0.233072\pi$
$338$	18049.5	2.90463
$339$	−5789.41	−0.927544
$340$	−1.85989	−0.000296666 0
$341$	4684.73	0.743965
$342$	2371.47	0.374954
$343$	−6018.05	−0.947359
$344$	7126.10	1.11690
$345$	1542.85	0.240766
$346$	−6782.46	−1.05384
$347$	−9981.81	−1.54424	−0.772121	−	0.635476i	$-0.780804\pi$
$347$	−9981.81	−1.54424	−0.772121	+	0.635476i	$0.780804\pi$
$348$	29.4910	0.00454277
$349$	−4493.48	−0.689200	−0.344600	−	0.938750i	$-0.611985\pi$
$349$	−4493.48	−0.689200	−0.344600	+	0.938750i	$0.611985\pi$
$350$	−6456.00	−0.985965
$351$	2491.86	0.378934
$352$	−315.264	−0.0477376
$353$	−8938.27	−1.34769	−0.673847	−	0.738871i	$-0.735359\pi$
$353$	−8938.27	−1.34769	−0.673847	+	0.738871i	$0.735359\pi$
$354$	3425.18	0.514255
$355$	2857.76	0.427251
$356$	139.132	0.0207134
$357$	242.362	0.0359304
$358$	4072.94	0.601290
$359$	2335.44	0.343342	0.171671	−	0.985154i	$-0.445083\pi$
$359$	2335.44	0.343342	0.171671	+	0.985154i	$0.445083\pi$
$360$	581.391	0.0851166
$361$	1655.18	0.241314
$362$	8173.23	1.18667
$363$	2092.77	0.302595
$364$	276.615	0.0398312
$365$	−513.280	−0.0736064
$366$	7717.71	1.10222
$367$	1998.63	0.284271	0.142135	−	0.989847i	$-0.454603\pi$
$367$	1998.63	0.284271	0.142135	+	0.989847i	$0.454603\pi$
$368$	11631.3	1.64762
$369$	−1199.57	−0.169234
$370$	3035.74	0.426542
$371$	3421.52	0.478804
$372$	48.2705	0.00672771
$373$	−900.185	−0.124959	−0.0624797	−	0.998046i	$-0.519901\pi$
$373$	−900.185	−0.124959	−0.0624797	+	0.998046i	$0.519901\pi$
$374$	536.293	0.0741472
$375$	2090.66	0.287897
$376$	3151.86	0.432300
$377$	5864.82	0.801203
$378$	1493.86	0.203269
$379$	8390.80	1.13722	0.568610	−	0.822607i	$-0.307481\pi$
$379$	8390.80	1.13722	0.568610	+	0.822607i	$0.307481\pi$
$380$	−41.1582	−0.00555624
$381$	−5338.22	−0.717809
$382$	−124.959	−0.0167369
$383$	7259.49	0.968519	0.484260	−	0.874924i	$-0.339089\pi$
$383$	7259.49	0.968519	0.484260	+	0.874924i	$0.339089\pi$
$384$	4466.19	0.593527
$385$	−2516.24	−0.333089
$386$	−11888.9	−1.56770
$387$	−2862.73	−0.376023
$388$	−82.7307	−0.0108248
$389$	11054.5	1.44084	0.720421	−	0.693537i	$-0.243949\pi$
$389$	11054.5	1.44084	0.720421	+	0.693537i	$0.243949\pi$
$390$	−2279.80	−0.296006
$391$	−743.689	−0.0961892
$392$	−725.675	−0.0935003
$393$	−3771.96	−0.484148
$394$	4280.30	0.547306
$395$	1261.56	0.160698
$396$	62.7066	0.00795738
$397$	−2476.55	−0.313085	−0.156542	−	0.987671i	$-0.550035\pi$
$397$	−2476.55	−0.313085	−0.156542	+	0.987671i	$0.550035\pi$
$398$	−8953.72	−1.12766
$399$	5363.33	0.672938
$400$	7609.50	0.951187
$401$	−11192.1	−1.39379	−0.696894	−	0.717174i	$-0.745435\pi$
$401$	−11192.1	−1.39379	−0.696894	+	0.717174i	$0.745435\pi$
$402$	573.984	0.0712133
$403$	9599.47	1.18656
$404$	−203.789	−0.0250962
$405$	−233.559	−0.0286559
$406$	3515.93	0.429785
$407$	−16605.2	−2.02234
$408$	−280.244	−0.0340052
$409$	6019.64	0.727755	0.363878	−	0.931447i	$-0.381453\pi$
$409$	6019.64	0.727755	0.363878	+	0.931447i	$0.381453\pi$
$410$	1097.49	0.132198
$411$	−7001.69	−0.840311
$412$	−43.4947	−0.00520105
$413$	7746.41	0.922944
$414$	−4583.92	−0.544172
$415$	3161.87	0.374001
$416$	−646.008	−0.0761373
$417$	3215.15	0.377569
$418$	11867.9	1.38870
$419$	−1786.58	−0.208306	−0.104153	−	0.994561i	$-0.533213\pi$
$419$	−1786.58	−0.208306	−0.104153	+	0.994561i	$0.533213\pi$
$420$	−25.9268	−0.00301214
$421$	385.579	0.0446365	0.0223182	−	0.999751i	$-0.492895\pi$
$421$	385.579	0.0446365	0.0223182	+	0.999751i	$0.492895\pi$
$422$	4970.98	0.573420
$423$	−1266.18	−0.145541
$424$	−3956.31	−0.453149
$425$	−486.540	−0.0555310
$426$	−8490.61	−0.965661
$427$	17454.4	1.97817
$428$	42.4530	0.00479449
$429$	12470.3	1.40344
$430$	2619.11	0.293732
$431$	−2110.38	−0.235855	−0.117927	−	0.993022i	$-0.537625\pi$
$431$	−2110.38	−0.235855	−0.117927	+	0.993022i	$0.537625\pi$
$432$	−1760.77	−0.196099
$433$	1578.93	0.175239	0.0876196	−	0.996154i	$-0.472074\pi$
$433$	1578.93	0.175239	0.0876196	+	0.996154i	$0.472074\pi$
$434$	5754.84	0.636500
$435$	−549.703	−0.0605890
$436$	298.779	0.0328186
$437$	−16457.4	−1.80152
$438$	1524.99	0.166363
$439$	14565.6	1.58355	0.791774	−	0.610814i	$-0.209158\pi$
$439$	14565.6	1.58355	0.791774	+	0.610814i	$0.209158\pi$
$440$	2909.53	0.315242
$441$	291.522	0.0314784
$442$	1098.92	0.118258
$443$	8571.12	0.919247	0.459623	−	0.888114i	$-0.347984\pi$
$443$	8571.12	0.919247	0.459623	+	0.888114i	$0.347984\pi$
$444$	−171.097	−0.0182881
$445$	−2593.38	−0.276265
$446$	13926.1	1.47852
$447$	645.019	0.0682514
$448$	9720.84	1.02515
$449$	−4014.34	−0.421934	−0.210967	−	0.977493i	$-0.567661\pi$
$449$	−4014.34	−0.421934	−0.210967	+	0.977493i	$0.567661\pi$
$450$	−2998.91	−0.314156
$451$	−6003.17	−0.626781
$452$	−298.529	−0.0310655
$453$	−2214.15	−0.229646
$454$	18953.1	1.95928
$455$	−5156.01	−0.531248
$456$	−6201.64	−0.636882
$457$	−6516.20	−0.666991	−0.333496	−	0.942752i	$-0.608228\pi$
$457$	−6516.20	−0.666991	−0.333496	+	0.942752i	$0.608228\pi$
$458$	−8012.19	−0.817435
$459$	112.581	0.0114484
$460$	79.5565	0.00806378
$461$	17261.6	1.74393	0.871967	−	0.489564i	$-0.162844\pi$
$461$	17261.6	1.74393	0.871967	+	0.489564i	$0.162844\pi$
$462$	7475.92	0.752838
$463$	4250.34	0.426630	0.213315	−	0.976983i	$-0.431574\pi$
$463$	4250.34	0.426630	0.213315	+	0.976983i	$0.431574\pi$
$464$	−4144.13	−0.414626
$465$	−899.747	−0.0897306
$466$	350.899	0.0348822
$467$	6173.48	0.611723	0.305861	−	0.952076i	$-0.401056\pi$
$467$	6173.48	0.611723	0.305861	+	0.952076i	$0.401056\pi$
$468$	128.492	0.0126913
$469$	1298.13	0.127808
$470$	1158.43	0.113690
$471$	4249.50	0.415725
$472$	−8957.20	−0.873493
$473$	−14326.4	−1.39266
$474$	−3748.17	−0.363205
$475$	−10766.9	−1.04004
$476$	12.4973	0.00120339
$477$	1589.35	0.152560
$478$	−6625.90	−0.634020
$479$	15274.9	1.45705	0.728525	−	0.685019i	$-0.240206\pi$
$479$	15274.9	1.45705	0.728525	+	0.685019i	$0.240206\pi$
$480$	60.5495	0.00575770
$481$	−34025.8	−3.22545
$482$	−15443.2	−1.45937
$483$	−10367.0	−0.976636
$484$	107.913	0.0101346
$485$	1542.08	0.144375
$486$	693.921	0.0647673
$487$	−6949.45	−0.646632	−0.323316	−	0.946291i	$-0.604798\pi$
$487$	−6949.45	−0.646632	−0.323316	+	0.946291i	$0.604798\pi$
$488$	−20182.6	−1.87218
$489$	11108.3	1.02727
$490$	−266.713	−0.0245895
$491$	−7844.96	−0.721055	−0.360528	−	0.932749i	$-0.617403\pi$
$491$	−7844.96	−0.721055	−0.360528	+	0.932749i	$0.617403\pi$
$492$	−61.8555	−0.00566801
$493$	264.969	0.0242061
$494$	24318.4	2.21485
$495$	−1168.83	−0.106131
$496$	−6783.05	−0.614049
$497$	−19202.4	−1.73309
$498$	−9394.15	−0.845305
$499$	−2547.25	−0.228518	−0.114259	−	0.993451i	$-0.536449\pi$
$499$	−2547.25	−0.228518	−0.114259	+	0.993451i	$0.536449\pi$
$500$	107.804	0.00964231
$501$	949.039	0.0846306
$502$	−2818.57	−0.250596
$503$	10844.0	0.961253	0.480627	−	0.876925i	$-0.340409\pi$
$503$	10844.0	0.961253	0.480627	+	0.876925i	$0.340409\pi$
$504$	−3906.59	−0.345265
$505$	3798.56	0.334720
$506$	−22939.9	−2.01542
$507$	18962.0	1.66101
$508$	−275.263	−0.0240410
$509$	−11069.2	−0.963918	−0.481959	−	0.876194i	$-0.660075\pi$
$509$	−11069.2	−0.963918	−0.481959	+	0.876194i	$0.660075\pi$
$510$	−103.000	−0.00894299
$511$	3448.93	0.298575
$512$	−11231.6	−0.969473
$513$	2491.35	0.214417
$514$	16853.5	1.44626
$515$	810.729	0.0693689
$516$	−147.616	−0.0125938
$517$	−6336.52	−0.539033
$518$	−20398.3	−1.73021
$519$	−7125.33	−0.602634
$520$	5961.91	0.502783
$521$	−20638.3	−1.73547	−0.867734	−	0.497030i	$-0.834424\pi$
$521$	−20638.3	−1.73547	−0.867734	+	0.497030i	$0.834424\pi$
$522$	1633.21	0.136942
$523$	−1640.95	−0.137196	−0.0685981	−	0.997644i	$-0.521853\pi$
$523$	−1640.95	−0.137196	−0.0685981	+	0.997644i	$0.521853\pi$
$524$	−194.500	−0.0162152
$525$	−6782.36	−0.563822
$526$	9911.89	0.821633
$527$	433.699	0.0358486
$528$	−8811.64	−0.726283
$529$	19644.2	1.61455
$530$	−1454.09	−0.119173
$531$	3598.33	0.294076
$532$	276.558	0.0225382
$533$	−12301.1	−0.999661
$534$	7705.11	0.624406
$535$	−791.311	−0.0639464
$536$	−1501.03	−0.120960
$537$	4278.84	0.343846
$538$	5899.49	0.472761
$539$	1458.90	0.116585
$540$	−12.0434	−0.000959750 0
$541$	11094.3	0.881667	0.440834	−	0.897589i	$-0.354683\pi$
$541$	11094.3	0.881667	0.440834	+	0.897589i	$0.354683\pi$
$542$	52.1757	0.00413495
$543$	8586.40	0.678596
$544$	−29.1863	−0.00230028
$545$	−5569.15	−0.437718
$546$	15318.9	1.20071
$547$	3901.21	0.304943	0.152471	−	0.988308i	$-0.451277\pi$
$547$	3901.21	0.304943	0.152471	+	0.988308i	$0.451277\pi$
$548$	−361.039	−0.0281439
$549$	8107.86	0.630300
$550$	−15007.9	−1.16352
$551$	5863.62	0.453355
$552$	11987.4	0.924308
$553$	−8476.89	−0.651852
$554$	−3982.03	−0.305379
$555$	3189.20	0.243917
$556$	165.788	0.0126456
$557$	15230.2	1.15857	0.579287	−	0.815124i	$-0.303331\pi$
$557$	15230.2	1.15857	0.579287	+	0.815124i	$0.303331\pi$
$558$	2673.21	0.202807
$559$	−29356.1	−2.22116
$560$	3643.28	0.274923
$561$	563.403	0.0424009
$562$	−16924.1	−1.27029
$563$	19781.4	1.48079	0.740395	−	0.672172i	$-0.234638\pi$
$563$	19781.4	1.48079	0.740395	+	0.672172i	$0.234638\pi$
$564$	−65.2902	−0.00487449
$565$	5564.48	0.414336
$566$	3237.51	0.240429
$567$	1569.38	0.116239
$568$	22203.8	1.64023
$569$	1955.57	0.144081	0.0720403	−	0.997402i	$-0.477049\pi$
$569$	1955.57	0.144081	0.0720403	+	0.997402i	$0.477049\pi$
$570$	−2279.34	−0.167493
$571$	6498.47	0.476274	0.238137	−	0.971232i	$-0.423463\pi$
$571$	6498.47	0.476274	0.238137	+	0.971232i	$0.423463\pi$
$572$	643.029	0.0470042
$573$	−131.276	−0.00957094
$574$	−7374.45	−0.536243
$575$	20811.7	1.50941
$576$	4515.48	0.326641
$577$	2645.05	0.190841	0.0954203	−	0.995437i	$-0.469581\pi$
$577$	2645.05	0.190841	0.0954203	+	0.995437i	$0.469581\pi$
$578$	−13980.1	−1.00605
$579$	−12489.9	−0.896484
$580$	−28.3452	−0.00202926
$581$	−21245.9	−1.51709
$582$	−4581.62	−0.326313
$583$	7953.78	0.565029
$584$	−3988.01	−0.282577
$585$	−2395.05	−0.169270
$586$	−14558.1	−1.02626
$587$	1959.98	0.137814	0.0689072	−	0.997623i	$-0.478049\pi$
$587$	1959.98	0.137814	0.0689072	+	0.997623i	$0.478049\pi$
$588$	15.0322	0.00105428
$589$	9597.50	0.671406
$590$	−3292.11	−0.229719
$591$	4496.68	0.312976
$592$	24042.9	1.66918
$593$	14573.7	1.00922	0.504611	−	0.863347i	$-0.331636\pi$
$593$	14573.7	1.00922	0.504611	+	0.863347i	$0.331636\pi$
$594$	3472.68	0.239875
$595$	−232.946	−0.0160502
$596$	33.2602	0.00228589
$597$	−9406.35	−0.644851
$598$	−47006.1	−3.21442
$599$	21048.7	1.43577	0.717885	−	0.696162i	$-0.245110\pi$
$599$	21048.7	1.43577	0.717885	+	0.696162i	$0.245110\pi$
$600$	7842.47	0.533612
$601$	−8938.01	−0.606637	−0.303319	−	0.952889i	$-0.598095\pi$
$601$	−8938.01	−0.606637	−0.303319	+	0.952889i	$0.598095\pi$
$602$	−17598.8	−1.19149
$603$	603.000	0.0407231
$604$	−114.172	−0.00769135
$605$	−2011.47	−0.135170
$606$	−11285.8	−0.756524
$607$	707.291	0.0472950	0.0236475	−	0.999720i	$-0.492472\pi$
$607$	707.291	0.0472950	0.0236475	+	0.999720i	$0.492472\pi$
$608$	−645.876	−0.0430818
$609$	3693.67	0.245772
$610$	−7417.87	−0.492362
$611$	−12984.2	−0.859710
$612$	5.80519	0.000383433 0
$613$	−1979.69	−0.130439	−0.0652193	−	0.997871i	$-0.520775\pi$
$613$	−1979.69	−0.130439	−0.0652193	+	0.997871i	$0.520775\pi$
$614$	−11026.2	−0.724725
$615$	1152.97	0.0755969
$616$	−19550.3	−1.27874
$617$	−13959.3	−0.910827	−0.455413	−	0.890280i	$-0.650509\pi$
$617$	−13959.3	−0.910827	−0.455413	+	0.890280i	$0.650509\pi$
$618$	−2408.73	−0.156786
$619$	3711.35	0.240988	0.120494	−	0.992714i	$-0.461552\pi$
$619$	3711.35	0.240988	0.120494	+	0.992714i	$0.461552\pi$
$620$	−46.3951	−0.00300528
$621$	−4815.64	−0.311184
$622$	7892.24	0.508762
$623$	17425.9	1.12063
$624$	−18055.9	−1.15836
$625$	12576.3	0.804882
$626$	25465.0	1.62586
$627$	12467.8	0.794124
$628$	219.124	0.0139236
$629$	−1537.27	−0.0974480
$630$	−1435.82	−0.0908008
$631$	4107.44	0.259135	0.129568	−	0.991571i	$-0.458641\pi$
$631$	4107.44	0.259135	0.129568	+	0.991571i	$0.458641\pi$
$632$	9801.86	0.616926
$633$	5222.27	0.327909
$634$	−19213.3	−1.20356
$635$	5130.82	0.320646
$636$	81.9542	0.00510958
$637$	2989.43	0.185943
$638$	8173.27	0.507183
$639$	−8919.83	−0.552211
$640$	−4292.68	−0.265130
$641$	−21824.4	−1.34479	−0.672397	−	0.740191i	$-0.734735\pi$
$641$	−21824.4	−1.34479	−0.672397	+	0.740191i	$0.734735\pi$
$642$	2351.04	0.144530
$643$	−3780.27	−0.231850	−0.115925	−	0.993258i	$-0.536983\pi$
$643$	−3780.27	−0.231850	−0.115925	+	0.993258i	$0.536983\pi$
$644$	−534.571	−0.0327097
$645$	2751.51	0.167970
$646$	1098.69	0.0669156
$647$	−6160.46	−0.374332	−0.187166	−	0.982328i	$-0.559930\pi$
$647$	−6160.46	−0.374332	−0.187166	+	0.982328i	$0.559930\pi$
$648$	−1814.67	−0.110011
$649$	18007.6	1.08915
$650$	−30752.6	−1.85572
$651$	6045.75	0.363981
$652$	572.796	0.0344056
$653$	13649.8	0.818004	0.409002	−	0.912533i	$-0.365877\pi$
$653$	13649.8	0.818004	0.409002	+	0.912533i	$0.365877\pi$
$654$	16546.3	0.989316
$655$	3625.42	0.216270
$656$	8692.04	0.517328
$657$	1602.08	0.0951343
$658$	−7783.94	−0.461170
$659$	10692.3	0.632036	0.316018	−	0.948753i	$-0.397654\pi$
$659$	10692.3	0.632036	0.316018	+	0.948753i	$0.397654\pi$
$660$	−60.2703	−0.00355458
$661$	−14748.7	−0.867866	−0.433933	−	0.900945i	$-0.642875\pi$
$661$	−14748.7	−0.867866	−0.433933	+	0.900945i	$0.642875\pi$
$662$	−3870.78	−0.227254
$663$	1154.47	0.0676257
$664$	24566.7	1.43580
$665$	−5154.96	−0.300603
$666$	−9475.33	−0.551294
$667$	−11334.0	−0.657955
$668$	48.9368	0.00283447
$669$	14630.1	0.845487
$670$	−551.684	−0.0318111
$671$	40575.2	2.33441
$672$	−406.856	−0.0233554
$673$	−9225.76	−0.528420	−0.264210	−	0.964465i	$-0.585111\pi$
$673$	−9225.76	−0.528420	−0.264210	+	0.964465i	$0.585111\pi$
$674$	26276.8	1.50170
$675$	−3150.51	−0.179649
$676$	977.767	0.0556308
$677$	−8627.93	−0.489806	−0.244903	−	0.969548i	$-0.578756\pi$
$677$	−8627.93	−0.489806	−0.244903	+	0.969548i	$0.578756\pi$
$678$	−16532.5	−0.936469
$679$	−10361.8	−0.585640
$680$	269.356	0.0151902
$681$	19911.2	1.12041
$682$	13377.9	0.751124
$683$	−1728.08	−0.0968128	−0.0484064	−	0.998828i	$-0.515414\pi$
$683$	−1728.08	−0.0968128	−0.0484064	+	0.998828i	$0.515414\pi$
$684$	128.466	0.00718130
$685$	6729.67	0.375368
$686$	−17185.4	−0.956474
$687$	−8417.22	−0.467448
$688$	20743.2	1.14946
$689$	16298.1	0.901172
$690$	4405.83	0.243083
$691$	−359.579	−0.0197960	−0.00989801	−	0.999951i	$-0.503151\pi$
$691$	−359.579	−0.0197960	−0.00989801	+	0.999951i	$0.503151\pi$
$692$	−367.415	−0.0201835
$693$	7853.84	0.430509
$694$	−28504.5	−1.55910
$695$	−3090.24	−0.168661
$696$	−4271.00	−0.232603
$697$	−555.756	−0.0302020
$698$	−12831.8	−0.695831
$699$	368.638	0.0199473
$700$	−349.730	−0.0188837
$701$	9877.77	0.532209	0.266104	−	0.963944i	$-0.414263\pi$
$701$	9877.77	0.532209	0.266104	+	0.963944i	$0.414263\pi$
$702$	7115.86	0.382580
$703$	−34018.8	−1.82510
$704$	22597.4	1.20976
$705$	1216.99	0.0650135
$706$	−25524.5	−1.36066
$707$	−25524.0	−1.35775
$708$	185.547	0.00984925
$709$	31194.3	1.65236	0.826182	−	0.563403i	$-0.190508\pi$
$709$	31194.3	1.65236	0.826182	+	0.563403i	$0.190508\pi$
$710$	8160.74	0.431362
$711$	−3937.65	−0.207698
$712$	−20149.6	−1.06059
$713$	−18551.4	−0.974413
$714$	692.099	0.0362761
$715$	−11985.9	−0.626917
$716$	220.637	0.0115162
$717$	−6960.85	−0.362563
$718$	6669.17	0.346645
$719$	−3746.55	−0.194329	−0.0971645	−	0.995268i	$-0.530977\pi$
$719$	−3746.55	−0.194329	−0.0971645	+	0.995268i	$0.530977\pi$
$720$	1692.36	0.0875980
$721$	−5447.61	−0.281386
$722$	4726.59	0.243636
$723$	−16223.9	−0.834539
$724$	442.755	0.0227277
$725$	−7415.02	−0.379844
$726$	5976.21	0.305507
$727$	5051.16	0.257685	0.128843	−	0.991665i	$-0.458874\pi$
$727$	5051.16	0.257685	0.128843	+	0.991665i	$0.458874\pi$
$728$	−40060.5	−2.03948
$729$	729.000	0.0370370
$730$	−1465.75	−0.0743146
$731$	−1326.29	−0.0671063
$732$	418.079	0.0211101
$733$	20612.0	1.03864	0.519319	−	0.854580i	$-0.326185\pi$
$733$	20612.0	1.03864	0.519319	+	0.854580i	$0.326185\pi$
$734$	5707.36	0.287006
$735$	−280.196	−0.0140615
$736$	1248.44	0.0625246
$737$	3017.67	0.150824
$738$	−3425.55	−0.170862
$739$	1811.36	0.0901652	0.0450826	−	0.998983i	$-0.485645\pi$
$739$	1811.36	0.0901652	0.0450826	+	0.998983i	$0.485645\pi$
$740$	164.450	0.00816932
$741$	25547.7	1.26656
$742$	9770.63	0.483411
$743$	26474.9	1.30723	0.653613	−	0.756829i	$-0.273253\pi$
$743$	26474.9	1.30723	0.653613	+	0.756829i	$0.273253\pi$
$744$	−6990.72	−0.344479
$745$	−619.959	−0.0304880
$746$	−2570.61	−0.126162
$747$	−9869.04	−0.483386
$748$	29.0517	0.00142010
$749$	5317.13	0.259391
$750$	5970.19	0.290667
$751$	15216.2	0.739344	0.369672	−	0.929162i	$-0.379470\pi$
$751$	15216.2	0.739344	0.369672	+	0.929162i	$0.379470\pi$
$752$	9174.70	0.444903
$753$	−2961.06	−0.143303
$754$	16747.8	0.808913
$755$	2128.12	0.102583
$756$	80.9243	0.00389311
$757$	−11683.3	−0.560948	−0.280474	−	0.959862i	$-0.590492\pi$
$757$	−11683.3	−0.560948	−0.280474	+	0.959862i	$0.590492\pi$
$758$	23961.1	1.14816
$759$	−24099.5	−1.15251
$760$	5960.70	0.284496
$761$	−1691.41	−0.0805695	−0.0402848	−	0.999188i	$-0.512827\pi$
$761$	−1691.41	−0.0805695	−0.0402848	+	0.999188i	$0.512827\pi$
$762$	−15244.0	−0.724715
$763$	37421.3	1.77555
$764$	−6.76922	−0.000320552 0
$765$	−108.207	−0.00511403
$766$	20730.5	0.977838
$767$	36899.3	1.73710
$768$	712.565	0.0334798
$769$	−9599.42	−0.450148	−0.225074	−	0.974342i	$-0.572262\pi$
$769$	−9599.42	−0.450148	−0.225074	+	0.974342i	$0.572262\pi$
$770$	−7185.47	−0.336294
$771$	17705.5	0.827040
$772$	−644.040	−0.0300252
$773$	−42467.3	−1.97599	−0.987997	−	0.154476i	$-0.950631\pi$
$773$	−42467.3	−1.97599	−0.987997	+	0.154476i	$0.950631\pi$
$774$	−8174.94	−0.379641
$775$	−12136.8	−0.562538
$776$	11981.4	0.554261
$777$	−21429.5	−0.989418
$778$	31567.8	1.45471
$779$	−12298.6	−0.565651
$780$	−123.500	−0.00566924
$781$	−44638.7	−2.04519
$782$	−2123.71	−0.0971147
$783$	1715.77	0.0783097
$784$	−2112.35	−0.0962260
$785$	−4084.40	−0.185705
$786$	−10771.4	−0.488807
$787$	−21037.0	−0.952844	−0.476422	−	0.879217i	$-0.658066\pi$
$787$	−21037.0	−0.952844	−0.476422	+	0.879217i	$0.658066\pi$
$788$	231.870	0.0104823
$789$	10413.0	0.469849
$790$	3602.55	0.162244
$791$	−37390.0	−1.68070
$792$	−9081.41	−0.407442
$793$	83142.6	3.72318
$794$	−7072.16	−0.316097
$795$	−1527.60	−0.0681489
$796$	−485.035	−0.0215975
$797$	11420.8	0.507587	0.253794	−	0.967258i	$-0.418322\pi$
$797$	11420.8	0.507587	0.253794	+	0.967258i	$0.418322\pi$
$798$	15315.8	0.679413
$799$	−586.617	−0.0259737
$800$	816.762	0.0360961
$801$	8094.61	0.357065
$802$	−31960.8	−1.40720
$803$	8017.52	0.352344
$804$	31.0935	0.00136391
$805$	9964.24	0.436265
$806$	27412.6	1.19798
$807$	6197.72	0.270347
$808$	29513.5	1.28500
$809$	4938.59	0.214625	0.107312	−	0.994225i	$-0.465775\pi$
$809$	4938.59	0.214625	0.107312	+	0.994225i	$0.465775\pi$
$810$	−666.962	−0.0289317
$811$	−31700.8	−1.37258	−0.686292	−	0.727327i	$-0.740763\pi$
$811$	−31700.8	−1.37258	−0.686292	+	0.727327i	$0.740763\pi$
$812$	190.463	0.00823144
$813$	54.8133	0.00236456
$814$	−47418.6	−2.04180
$815$	−10676.7	−0.458883
$816$	−815.757	−0.0349966
$817$	−29350.1	−1.25683
$818$	17189.9	0.734758
$819$	16093.3	0.686624
$820$	59.4523	0.00253191
$821$	37843.6	1.60871	0.804355	−	0.594148i	$-0.202511\pi$
$821$	37843.6	1.60871	0.804355	+	0.594148i	$0.202511\pi$
$822$	−19994.3	−0.848396
$823$	12567.9	0.532306	0.266153	−	0.963931i	$-0.414247\pi$
$823$	12567.9	0.532306	0.266153	+	0.963931i	$0.414247\pi$
$824$	6299.08	0.266309
$825$	−15766.5	−0.665358
$826$	22121.0	0.931825
$827$	16203.3	0.681312	0.340656	−	0.940188i	$-0.389351\pi$
$827$	16203.3	0.681312	0.340656	+	0.940188i	$0.389351\pi$
$828$	−248.317	−0.0104222
$829$	14912.2	0.624753	0.312377	−	0.949958i	$-0.398875\pi$
$829$	14912.2	0.624753	0.312377	+	0.949958i	$0.398875\pi$
$830$	9029.18	0.377599
$831$	−4183.32	−0.174630
$832$	46304.4	1.92946
$833$	135.061	0.00561774
$834$	9181.31	0.381202
$835$	−912.168	−0.0378046
$836$	642.898	0.0265970
$837$	2808.35	0.115975
$838$	−5101.84	−0.210310
$839$	45633.7	1.87777	0.938887	−	0.344226i	$-0.111859\pi$
$839$	45633.7	1.87777	0.938887	+	0.344226i	$0.111859\pi$
$840$	3754.82	0.154230
$841$	−20350.8	−0.834425
$842$	1101.07	0.0450660
$843$	−17779.7	−0.726410
$844$	269.284	0.0109824
$845$	−18225.3	−0.741975
$846$	−3615.76	−0.146941
$847$	13515.8	0.548299
$848$	−11516.3	−0.466360
$849$	3401.17	0.137489
$850$	−1389.38	−0.0560653
$851$	65756.4	2.64877
$852$	−459.948	−0.0184948
$853$	−29479.2	−1.18329	−0.591646	−	0.806198i	$-0.701522\pi$
$853$	−29479.2	−1.18329	−0.591646	+	0.806198i	$0.701522\pi$
$854$	49843.6	1.99720
$855$	−2394.56	−0.0957804
$856$	−6148.21	−0.245492
$857$	−46085.4	−1.83693	−0.918464	−	0.395506i	$-0.870569\pi$
$857$	−46085.4	−1.83693	−0.918464	+	0.395506i	$0.870569\pi$
$858$	35610.9	1.41694
$859$	34707.5	1.37859	0.689293	−	0.724483i	$-0.257921\pi$
$859$	34707.5	1.37859	0.689293	+	0.724483i	$0.257921\pi$
$860$	141.881	0.00562569
$861$	−7747.24	−0.306649
$862$	−6026.49	−0.238124
$863$	30479.0	1.20222	0.601111	−	0.799166i	$-0.294725\pi$
$863$	30479.0	1.20222	0.601111	+	0.799166i	$0.294725\pi$
$864$	−188.991	−0.00744168
$865$	6848.50	0.269198
$866$	4508.86	0.176925
$867$	−14686.8	−0.575307
$868$	311.747	0.0121905
$869$	−19705.7	−0.769241
$870$	−1569.75	−0.0611720
$871$	6183.51	0.240551
$872$	−43270.4	−1.68041
$873$	−4813.22	−0.186601
$874$	−46996.5	−1.81886
$875$	13502.2	0.521667
$876$	82.6109	0.00318626
$877$	6971.29	0.268419	0.134210	−	0.990953i	$-0.457150\pi$
$877$	6971.29	0.268419	0.134210	+	0.990953i	$0.457150\pi$
$878$	41594.1	1.59879
$879$	−15294.0	−0.586865
$880$	8469.30	0.324432
$881$	36242.6	1.38598	0.692988	−	0.720949i	$-0.256294\pi$
$881$	36242.6	1.38598	0.692988	+	0.720949i	$0.256294\pi$
$882$	832.482	0.0317813
$883$	−8162.05	−0.311070	−0.155535	−	0.987830i	$-0.549710\pi$
$883$	−8162.05	−0.311070	−0.155535	+	0.987830i	$0.549710\pi$
$884$	59.5298	0.00226494
$885$	−3458.53	−0.131364
$886$	24476.1	0.928092
$887$	−6232.58	−0.235930	−0.117965	−	0.993018i	$-0.537637\pi$
$887$	−6232.58	−0.235930	−0.117965	+	0.993018i	$0.537637\pi$
$888$	24779.0	0.936405
$889$	−34476.0	−1.30066
$890$	−7405.76	−0.278923
$891$	3648.23	0.137172
$892$	754.393	0.0283172
$893$	−12981.5	−0.486461
$894$	1841.94	0.0689081
$895$	−4112.60	−0.153597
$896$	28844.2	1.07547
$897$	−49382.3	−1.83816
$898$	−11463.5	−0.425994
$899$	6609.70	0.245212
$900$	−162.455	−0.00601686
$901$	736.338	0.0272264
$902$	−17142.9	−0.632812
$903$	−18488.5	−0.681350
$904$	43234.1	1.59065
$905$	−8252.81	−0.303130
$906$	−6322.81	−0.231856
$907$	−29919.6	−1.09533	−0.547665	−	0.836698i	$-0.684483\pi$
$907$	−29919.6	−1.09533	−0.547665	+	0.836698i	$0.684483\pi$
$908$	1026.71	0.0375250
$909$	−11856.3	−0.432617
$910$	−14723.7	−0.536359
$911$	37995.5	1.38183	0.690915	−	0.722936i	$-0.257208\pi$
$911$	37995.5	1.38183	0.690915	+	0.722936i	$0.257208\pi$
$912$	−18052.2	−0.655449
$913$	−49388.9	−1.79029
$914$	−18607.9	−0.673409
$915$	−7792.86	−0.281556
$916$	−434.031	−0.0156559
$917$	−24360.6	−0.877272
$918$	321.491	0.0115586
$919$	2734.85	0.0981657	0.0490828	−	0.998795i	$-0.484370\pi$
$919$	2734.85	0.0981657	0.0490828	+	0.998795i	$0.484370\pi$
$920$	−11521.7	−0.412890
$921$	−11583.6	−0.414433
$922$	49293.0	1.76072
$923$	−91469.0	−3.26191
$924$	404.980	0.0144187
$925$	43019.5	1.52916
$926$	12137.4	0.430735
$927$	−2530.50	−0.0896575
$928$	−444.808	−0.0157344
$929$	12858.9	0.454131	0.227065	−	0.973880i	$-0.427087\pi$
$929$	12858.9	0.454131	0.227065	+	0.973880i	$0.427087\pi$
$930$	−2569.35	−0.0905940
$931$	2988.82	0.105214
$932$	19.0087	0.000668079 0
$933$	8291.20	0.290934
$934$	17629.3	0.617609
$935$	−541.515	−0.0189406
$936$	−18608.7	−0.649834
$937$	3957.90	0.137993	0.0689963	−	0.997617i	$-0.478020\pi$
$937$	3957.90	0.137993	0.0689963	+	0.997617i	$0.478020\pi$
$938$	3706.98	0.129038
$939$	26752.3	0.929744
$940$	62.7536	0.00217744
$941$	9696.68	0.335922	0.167961	−	0.985794i	$-0.446282\pi$
$941$	9696.68	0.335922	0.167961	+	0.985794i	$0.446282\pi$
$942$	12135.1	0.419726
$943$	23772.4	0.820930
$944$	−26073.3	−0.898957
$945$	−1508.40	−0.0519242
$946$	−40910.9	−1.40606
$947$	10296.4	0.353312	0.176656	−	0.984273i	$-0.443472\pi$
$947$	10296.4	0.353312	0.176656	+	0.984273i	$0.443472\pi$
$948$	−203.044	−0.00695627
$949$	16428.7	0.561957
$950$	−30746.3	−1.05004
$951$	−20184.6	−0.688255
$952$	−1809.91	−0.0616171
$953$	21714.9	0.738106	0.369053	−	0.929408i	$-0.379682\pi$
$953$	21714.9	0.738106	0.369053	+	0.929408i	$0.379682\pi$
$954$	4538.61	0.154028
$955$	126.176	0.00427535
$956$	−358.934	−0.0121430
$957$	8586.44	0.290032
$958$	43619.6	1.47107
$959$	−45219.3	−1.52263
$960$	−4340.05	−0.145911
$961$	−18972.3	−0.636848
$962$	−97165.5	−3.25649
$963$	2469.89	0.0826491
$964$	−836.577	−0.0279506
$965$	12004.7	0.400461
$966$	−29604.5	−0.986034
$967$	−48265.4	−1.60508	−0.802539	−	0.596599i	$-0.796518\pi$
$967$	−48265.4	−1.60508	−0.802539	+	0.596599i	$0.796518\pi$
$968$	−15628.4	−0.518921
$969$	1154.23	0.0382655
$970$	4403.62	0.145765
$971$	−23322.2	−0.770797	−0.385398	−	0.922750i	$-0.625936\pi$
$971$	−23322.2	−0.770797	−0.385398	+	0.922750i	$0.625936\pi$
$972$	37.5906	0.00124045
$973$	20764.5	0.684152
$974$	−19845.2	−0.652854
$975$	−32307.2	−1.06119
$976$	−58749.2	−1.92676
$977$	27047.8	0.885708	0.442854	−	0.896594i	$-0.353966\pi$
$977$	27047.8	0.885708	0.442854	+	0.896594i	$0.353966\pi$
$978$	31721.4	1.03715
$979$	40508.9	1.32244
$980$	−14.4482	−0.000470950 0
$981$	17382.8	0.565739
$982$	−22402.4	−0.727993
$983$	−33448.2	−1.08528	−0.542640	−	0.839965i	$-0.682575\pi$
$983$	−33448.2	−1.08528	−0.542640	+	0.839965i	$0.682575\pi$
$984$	8958.15	0.290219
$985$	−4321.98	−0.139807
$986$	756.658	0.0244390
$987$	−8177.43	−0.263719
$988$	1317.36	0.0424199
$989$	56732.1	1.82404
$990$	−3337.76	−0.107153
$991$	13835.4	0.443489	0.221744	−	0.975105i	$-0.428825\pi$
$991$	13835.4	0.443489	0.221744	+	0.975105i	$0.428825\pi$
$992$	−728.056	−0.0233022
$993$	−4066.45	−0.129955
$994$	−54835.2	−1.74977
$995$	9040.90	0.288056
$996$	−508.893	−0.0161897
$997$	10107.6	0.321074	0.160537	−	0.987030i	$-0.448677\pi$
$997$	10107.6	0.321074	0.160537	+	0.987030i	$0.448677\pi$
$998$	−7274.04	−0.230717
$999$	−9954.33	−0.315256

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.e.1.8	✓	11
3.2	odd	2		603.4.a.g.1.4		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.e.1.8	✓	11	1.1	even	1	trivial
603.4.a.g.1.4		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)

\(f(q)\)	\(=\)	\(q+2.85564 q^{2} +3.00000 q^{3} +0.154694 q^{4} -2.88345 q^{5} +8.56693 q^{6} +19.3750 q^{7} -22.4034 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.85564 q^{2} +3.00000 q^{3} +0.154694 q^{4} -2.88345 q^{5} +8.56693 q^{6} +19.3750 q^{7} -22.4034 q^{8} +9.00000 q^{9} -8.23409 q^{10} +45.0399 q^{11} +0.464082 q^{12} +92.2911 q^{13} +55.3281 q^{14} -8.65034 q^{15} -65.2136 q^{16} +4.16966 q^{17} +25.7008 q^{18} +92.2723 q^{19} -0.446052 q^{20} +58.1251 q^{21} +128.618 q^{22} -178.357 q^{23} -67.2102 q^{24} -116.686 q^{25} +263.551 q^{26} +27.0000 q^{27} +2.99720 q^{28} +63.5469 q^{29} -24.7023 q^{30} +104.013 q^{31} -6.99967 q^{32} +135.120 q^{33} +11.9071 q^{34} -55.8668 q^{35} +1.39225 q^{36} -368.679 q^{37} +263.497 q^{38} +276.873 q^{39} +64.5990 q^{40} -133.286 q^{41} +165.984 q^{42} -318.081 q^{43} +6.96739 q^{44} -25.9510 q^{45} -509.324 q^{46} -140.687 q^{47} -195.641 q^{48} +32.3913 q^{49} -333.213 q^{50} +12.5090 q^{51} +14.2769 q^{52} +176.594 q^{53} +77.1023 q^{54} -129.870 q^{55} -434.066 q^{56} +276.817 q^{57} +181.467 q^{58} +399.814 q^{59} -1.33816 q^{60} +900.873 q^{61} +297.024 q^{62} +174.375 q^{63} +501.720 q^{64} -266.117 q^{65} +385.853 q^{66} +67.0000 q^{67} +0.645021 q^{68} -535.071 q^{69} -159.536 q^{70} -991.092 q^{71} -201.631 q^{72} +178.009 q^{73} -1052.81 q^{74} -350.057 q^{75} +14.2740 q^{76} +872.648 q^{77} +790.652 q^{78} -437.517 q^{79} +188.040 q^{80} +81.0000 q^{81} -380.616 q^{82} -1096.56 q^{83} +8.99159 q^{84} -12.0230 q^{85} -908.327 q^{86} +190.641 q^{87} -1009.05 q^{88} +899.401 q^{89} -74.1068 q^{90} +1788.14 q^{91} -27.5907 q^{92} +312.039 q^{93} -401.751 q^{94} -266.062 q^{95} -20.9990 q^{96} -534.803 q^{97} +92.4980 q^{98} +405.359 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) \) 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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