LMFDB - Embedded newform 201.4.a.d.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:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 3x^{8} - 54x^{7} + 138x^{6} + 949x^{5} - 2039x^{4} - 5472x^{3} + 10352x^{2} + 3808x - 6656 $ x^9 - 3x^8 - 54x^7 + 138x^6 + 949x^5 - 2039x^4 - 5472x^3 + 10352x^2 + 3808x - 6656
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$4.92710$ 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)

$f(q)$	$=$	$q+4.92710 q^{2} -3.00000 q^{3} +16.2764 q^{4} -2.16819 q^{5} -14.7813 q^{6} +13.4538 q^{7} +40.7785 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+4.92710 q^{2} -3.00000 q^{3} +16.2764 q^{4} -2.16819 q^{5} -14.7813 q^{6} +13.4538 q^{7} +40.7785 q^{8} +9.00000 q^{9} -10.6829 q^{10} +25.8484 q^{11} -48.8291 q^{12} +69.4523 q^{13} +66.2881 q^{14} +6.50457 q^{15} +70.7090 q^{16} +14.3988 q^{17} +44.3439 q^{18} -48.5758 q^{19} -35.2902 q^{20} -40.3613 q^{21} +127.358 q^{22} +96.6605 q^{23} -122.335 q^{24} -120.299 q^{25} +342.199 q^{26} -27.0000 q^{27} +218.978 q^{28} -10.3638 q^{29} +32.0487 q^{30} -265.623 q^{31} +22.1628 q^{32} -77.5453 q^{33} +70.9442 q^{34} -29.1703 q^{35} +146.487 q^{36} -149.655 q^{37} -239.338 q^{38} -208.357 q^{39} -88.4155 q^{40} -50.5289 q^{41} -198.864 q^{42} +432.003 q^{43} +420.718 q^{44} -19.5137 q^{45} +476.256 q^{46} +15.2569 q^{47} -212.127 q^{48} -161.996 q^{49} -592.726 q^{50} -43.1963 q^{51} +1130.43 q^{52} +102.313 q^{53} -133.032 q^{54} -56.0443 q^{55} +548.624 q^{56} +145.727 q^{57} -51.0633 q^{58} -658.761 q^{59} +105.871 q^{60} -220.014 q^{61} -1308.75 q^{62} +121.084 q^{63} -456.474 q^{64} -150.586 q^{65} -382.074 q^{66} -67.0000 q^{67} +234.359 q^{68} -289.982 q^{69} -143.725 q^{70} -244.129 q^{71} +367.006 q^{72} -350.449 q^{73} -737.366 q^{74} +360.897 q^{75} -790.637 q^{76} +347.759 q^{77} -1026.60 q^{78} +491.279 q^{79} -153.311 q^{80} +81.0000 q^{81} -248.961 q^{82} -639.684 q^{83} -656.935 q^{84} -31.2192 q^{85} +2128.52 q^{86} +31.0913 q^{87} +1054.06 q^{88} +813.187 q^{89} -96.1461 q^{90} +934.394 q^{91} +1573.28 q^{92} +796.868 q^{93} +75.1723 q^{94} +105.322 q^{95} -66.4883 q^{96} +265.995 q^{97} -798.173 q^{98} +232.636 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9}+O(q^{10}) $ 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9	\( 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9} + 45 q^{10} + 72 q^{11} - 135 q^{12} - 166 q^{13} + 93 q^{14} - 36 q^{15} + 173 q^{16} + 146 q^{17} + 27 q^{18} + 154 q^{19} + 763 q^{20} - 24 q^{21} + 244 q^{22} + 476 q^{23} - 153 q^{24} + 465 q^{25} + 502 q^{26} - 243 q^{27} - 141 q^{28} + 432 q^{29} - 135 q^{30} + 248 q^{31} + 1171 q^{32} - 216 q^{33} + 146 q^{34} + 178 q^{35} + 405 q^{36} - 240 q^{37} + 1182 q^{38} + 498 q^{39} + 1409 q^{40} + 406 q^{41} - 279 q^{42} + 154 q^{43} + 892 q^{44} + 108 q^{45} + 273 q^{46} + 494 q^{47} - 519 q^{48} + 431 q^{49} + 1658 q^{50} - 438 q^{51} - 1258 q^{52} - 450 q^{53} - 81 q^{54} - 346 q^{55} - 659 q^{56} - 462 q^{57} - 2114 q^{58} + 732 q^{59} - 2289 q^{60} - 914 q^{61} - 1265 q^{62} + 72 q^{63} - 467 q^{64} - 536 q^{65} - 732 q^{66} - 603 q^{67} - 3314 q^{68} - 1428 q^{69} - 4805 q^{70} + 2990 q^{71} + 459 q^{72} - 1384 q^{73} - 2043 q^{74} - 1395 q^{75} + 450 q^{76} + 1660 q^{77} - 1506 q^{78} + 2438 q^{79} + 995 q^{80} + 729 q^{81} - 3561 q^{82} + 972 q^{83} + 423 q^{84} - 2706 q^{85} - 21 q^{86} - 1296 q^{87} - 3796 q^{88} + 1034 q^{89} + 405 q^{90} + 1898 q^{91} + 1827 q^{92} - 744 q^{93} - 3502 q^{94} + 6040 q^{95} - 3513 q^{96} - 1516 q^{97} - 3996 q^{98} + 648 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9 + 45 * q^10 + 72 * q^11 - 135 * q^12 - 166 * q^13 + 93 * q^14 - 36 * q^15 + 173 * q^16 + 146 * q^17 + 27 * q^18 + 154 * q^19 + 763 * q^20 - 24 * q^21 + 244 * q^22 + 476 * q^23 - 153 * q^24 + 465 * q^25 + 502 * q^26 - 243 * q^27 - 141 * q^28 + 432 * q^29 - 135 * q^30 + 248 * q^31 + 1171 * q^32 - 216 * q^33 + 146 * q^34 + 178 * q^35 + 405 * q^36 - 240 * q^37 + 1182 * q^38 + 498 * q^39 + 1409 * q^40 + 406 * q^41 - 279 * q^42 + 154 * q^43 + 892 * q^44 + 108 * q^45 + 273 * q^46 + 494 * q^47 - 519 * q^48 + 431 * q^49 + 1658 * q^50 - 438 * q^51 - 1258 * q^52 - 450 * q^53 - 81 * q^54 - 346 * q^55 - 659 * q^56 - 462 * q^57 - 2114 * q^58 + 732 * q^59 - 2289 * q^60 - 914 * q^61 - 1265 * q^62 + 72 * q^63 - 467 * q^64 - 536 * q^65 - 732 * q^66 - 603 * q^67 - 3314 * q^68 - 1428 * q^69 - 4805 * q^70 + 2990 * q^71 + 459 * q^72 - 1384 * q^73 - 2043 * q^74 - 1395 * q^75 + 450 * q^76 + 1660 * q^77 - 1506 * q^78 + 2438 * q^79 + 995 * q^80 + 729 * q^81 - 3561 * q^82 + 972 * q^83 + 423 * q^84 - 2706 * q^85 - 21 * q^86 - 1296 * q^87 - 3796 * q^88 + 1034 * q^89 + 405 * q^90 + 1898 * q^91 + 1827 * q^92 - 744 * q^93 - 3502 * q^94 + 6040 * q^95 - 3513 * q^96 - 1516 * q^97 - 3996 * q^98 + 648 * 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 $

$2$	4.92710	1.74199	0.870997	−	0.491288i	$-0.163474\pi$
$2$	4.92710	1.74199	0.870997	+	0.491288i	$0.163474\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	16.2764	2.03454
$5$	−2.16819	−0.193929	−0.0969644	−	0.995288i	$-0.530913\pi$
$5$	−2.16819	−0.193929	−0.0969644	+	0.995288i	$0.530913\pi$
$6$	−14.7813	−1.00574
$7$	13.4538	0.726435	0.363217	−	0.931704i	$-0.381678\pi$
$7$	13.4538	0.726435	0.363217	+	0.931704i	$0.381678\pi$
$8$	40.7785	1.80217
$9$	9.00000	0.333333
$10$	−10.6829	−0.337823
$11$	25.8484	0.708509	0.354254	−	0.935149i	$-0.384735\pi$
$11$	25.8484	0.708509	0.354254	+	0.935149i	$0.384735\pi$
$12$	−48.8291	−1.17465
$13$	69.4523	1.48174	0.740869	−	0.671650i	$-0.234414\pi$
$13$	69.4523	1.48174	0.740869	+	0.671650i	$0.234414\pi$
$14$	66.2881	1.26545
$15$	6.50457	0.111965
$16$	70.7090	1.10483
$17$	14.3988	0.205424	0.102712	−	0.994711i	$-0.467248\pi$
$17$	14.3988	0.205424	0.102712	+	0.994711i	$0.467248\pi$
$18$	44.3439	0.580665
$19$	−48.5758	−0.586529	−0.293264	−	0.956031i	$-0.594742\pi$
$19$	−48.5758	−0.586529	−0.293264	+	0.956031i	$0.594742\pi$
$20$	−35.2902	−0.394557
$21$	−40.3613	−0.419407
$22$	127.358	1.23422
$23$	96.6605	0.876309	0.438155	−	0.898900i	$-0.355632\pi$
$23$	96.6605	0.876309	0.438155	+	0.898900i	$0.355632\pi$
$24$	−122.335	−1.04048
$25$	−120.299	−0.962392
$26$	342.199	2.58118
$27$	−27.0000	−0.192450
$28$	218.978	1.47796
$29$	−10.3638	−0.0663621	−0.0331810	−	0.999449i	$-0.510564\pi$
$29$	−10.3638	−0.0663621	−0.0331810	+	0.999449i	$0.510564\pi$
$30$	32.0487	0.195042
$31$	−265.623	−1.53894	−0.769472	−	0.638681i	$-0.779480\pi$
$31$	−265.623	−1.53894	−0.769472	+	0.638681i	$0.779480\pi$
$32$	22.1628	0.122433
$33$	−77.5453	−0.409058
$34$	70.9442	0.357848
$35$	−29.1703	−0.140877
$36$	146.487	0.678182
$37$	−149.655	−0.664950	−0.332475	−	0.943112i	$-0.607884\pi$
$37$	−149.655	−0.664950	−0.332475	+	0.943112i	$0.607884\pi$
$38$	−239.338	−1.02173
$39$	−208.357	−0.855482
$40$	−88.4155	−0.349493
$41$	−50.5289	−0.192470	−0.0962352	−	0.995359i	$-0.530680\pi$
$41$	−50.5289	−0.192470	−0.0962352	+	0.995359i	$0.530680\pi$
$42$	−198.864	−0.730605
$43$	432.003	1.53209	0.766045	−	0.642787i	$-0.222222\pi$
$43$	432.003	1.53209	0.766045	+	0.642787i	$0.222222\pi$
$44$	420.718	1.44149
$45$	−19.5137	−0.0646429
$46$	476.256	1.52653
$47$	15.2569	0.0473499	0.0236750	−	0.999720i	$-0.492463\pi$
$47$	15.2569	0.0473499	0.0236750	+	0.999720i	$0.492463\pi$
$48$	−212.127	−0.637873
$49$	−161.996	−0.472292
$50$	−592.726	−1.67648
$51$	−43.1963	−0.118602
$52$	1130.43	3.01466
$53$	102.313	0.265165	0.132582	−	0.991172i	$-0.457673\pi$
$53$	102.313	0.265165	0.132582	+	0.991172i	$0.457673\pi$
$54$	−133.032	−0.335247
$55$	−56.0443	−0.137400
$56$	548.624	1.30916
$57$	145.727	0.338633
$58$	−51.0633	−0.115602
$59$	−658.761	−1.45362	−0.726808	−	0.686840i	$-0.758997\pi$
$59$	−658.761	−1.45362	−0.726808	+	0.686840i	$0.758997\pi$
$60$	105.871	0.227797
$61$	−220.014	−0.461801	−0.230900	−	0.972977i	$-0.574167\pi$
$61$	−220.014	−0.461801	−0.230900	+	0.972977i	$0.574167\pi$
$62$	−1308.75	−2.68083
$63$	121.084	0.242145
$64$	−456.474	−0.891550
$65$	−150.586	−0.287352
$66$	−382.074	−0.712576
$67$	−67.0000	−0.122169
$67$	−67.0000	−0.122169
$68$	234.359	0.417945
$69$	−289.982	−0.505937
$70$	−143.725	−0.245406
$71$	−244.129	−0.408067	−0.204033	−	0.978964i	$-0.565405\pi$
$71$	−244.129	−0.408067	−0.204033	+	0.978964i	$0.565405\pi$
$72$	367.006	0.600724
$73$	−350.449	−0.561875	−0.280938	−	0.959726i	$-0.590645\pi$
$73$	−350.449	−0.561875	−0.280938	+	0.959726i	$0.590645\pi$
$74$	−737.366	−1.15834
$75$	360.897	0.555637
$76$	−790.637	−1.19332
$77$	347.759	0.514685
$78$	−1026.60	−1.49024
$79$	491.279	0.699661	0.349831	−	0.936813i	$-0.386239\pi$
$79$	491.279	0.699661	0.349831	+	0.936813i	$0.386239\pi$
$80$	−153.311	−0.214258
$81$	81.0000	0.111111
$82$	−248.961	−0.335282
$83$	−639.684	−0.845957	−0.422979	−	0.906140i	$-0.639015\pi$
$83$	−639.684	−0.845957	−0.422979	+	0.906140i	$0.639015\pi$
$84$	−656.935	−0.853303
$85$	−31.2192	−0.0398377
$86$	2128.52	2.66889
$87$	31.0913	0.0383142
$88$	1054.06	1.27685
$89$	813.187	0.968513	0.484257	−	0.874926i	$-0.339090\pi$
$89$	813.187	0.968513	0.484257	+	0.874926i	$0.339090\pi$
$90$	−96.1461	−0.112608
$91$	934.394	1.07639
$92$	1573.28	1.78289
$93$	796.868	0.888509
$94$	75.1723	0.0824833
$95$	105.322	0.113745
$96$	−66.4883	−0.0706868
$97$	265.995	0.278430	0.139215	−	0.990262i	$-0.455542\pi$
$97$	265.995	0.278430	0.139215	+	0.990262i	$0.455542\pi$
$98$	−798.173	−0.822731
$99$	232.636	0.236170
$100$	−1958.03	−1.95803
$101$	−15.7402	−0.0155070	−0.00775349	−	0.999970i	$-0.502468\pi$
$101$	−15.7402	−0.0155070	−0.00775349	+	0.999970i	$0.502468\pi$
$102$	−212.833	−0.206604
$103$	−1309.07	−1.25230	−0.626149	−	0.779704i	$-0.715370\pi$
$103$	−1309.07	−1.25230	−0.626149	+	0.779704i	$0.715370\pi$
$104$	2832.16	2.67035
$105$	87.5109	0.0813352
$106$	504.106	0.461916
$107$	2151.36	1.94374	0.971870	−	0.235519i	$-0.0756790\pi$
$107$	2151.36	1.94374	0.971870	+	0.235519i	$0.0756790\pi$
$108$	−439.462	−0.391548
$109$	−433.319	−0.380775	−0.190387	−	0.981709i	$-0.560974\pi$
$109$	−433.319	−0.380775	−0.190387	+	0.981709i	$0.560974\pi$
$110$	−276.136	−0.239350
$111$	448.965	0.383909
$112$	951.302	0.802586
$113$	982.896	0.818257	0.409128	−	0.912477i	$-0.365833\pi$
$113$	982.896	0.818257	0.409128	+	0.912477i	$0.365833\pi$
$114$	718.014	0.589896
$115$	−209.578	−0.169942
$116$	−168.684	−0.135017
$117$	625.070	0.493913
$118$	−3245.78	−2.53219
$119$	193.718	0.149227
$120$	265.247	0.201780
$121$	−662.859	−0.498015
$122$	−1084.03	−0.804455
$123$	151.587	0.111123
$124$	−4323.37	−3.13105
$125$	531.855	0.380564
$126$	596.593	0.421815
$127$	78.3863	0.0547690	0.0273845	−	0.999625i	$-0.491282\pi$
$127$	78.3863	0.0547690	0.0273845	+	0.999625i	$0.491282\pi$
$128$	−2426.40	−1.67551
$129$	−1296.01	−0.884553
$130$	−741.951	−0.500565
$131$	−626.767	−0.418022	−0.209011	−	0.977913i	$-0.567024\pi$
$131$	−626.767	−0.418022	−0.209011	+	0.977913i	$0.567024\pi$
$132$	−1262.16	−0.832246
$133$	−653.527	−0.426075
$134$	−330.116	−0.212819
$135$	58.5411	0.0373216
$136$	587.160	0.370210
$137$	2278.81	1.42111	0.710555	−	0.703642i	$-0.248444\pi$
$137$	2278.81	1.42111	0.710555	+	0.703642i	$0.248444\pi$
$138$	−1428.77	−0.881340
$139$	−115.209	−0.0703014	−0.0351507	−	0.999382i	$-0.511191\pi$
$139$	−115.209	−0.0703014	−0.0351507	+	0.999382i	$0.511191\pi$
$140$	−474.786	−0.286620
$141$	−45.7707	−0.0273375
$142$	−1202.85	−0.710850
$143$	1795.23	1.04982
$144$	636.381	0.368276
$145$	22.4706	0.0128695
$146$	−1726.70	−0.978784
$147$	485.989	0.272678
$148$	−2435.84	−1.35287
$149$	−729.711	−0.401210	−0.200605	−	0.979672i	$-0.564291\pi$
$149$	−729.711	−0.401210	−0.200605	+	0.979672i	$0.564291\pi$
$150$	1778.18	0.967917
$151$	−794.460	−0.428161	−0.214080	−	0.976816i	$-0.568675\pi$
$151$	−794.460	−0.428161	−0.214080	+	0.976816i	$0.568675\pi$
$152$	−1980.85	−1.05703
$153$	129.589	0.0684747
$154$	1713.44	0.896579
$155$	575.920	0.298445
$156$	−3391.29	−1.74052
$157$	−1334.22	−0.678233	−0.339117	−	0.940744i	$-0.610128\pi$
$157$	−1334.22	−0.678233	−0.339117	+	0.940744i	$0.610128\pi$
$158$	2420.58	1.21881
$159$	−306.938	−0.153093
$160$	−48.0531	−0.0237433
$161$	1300.45	0.636582
$162$	399.095	0.193555
$163$	861.445	0.413948	0.206974	−	0.978346i	$-0.433638\pi$
$163$	861.445	0.413948	0.206974	+	0.978346i	$0.433638\pi$
$164$	−822.426	−0.391590
$165$	168.133	0.0793281
$166$	−3151.79	−1.47365
$167$	3317.82	1.53737	0.768684	−	0.639629i	$-0.220912\pi$
$167$	3317.82	1.53737	0.768684	+	0.639629i	$0.220912\pi$
$168$	−1645.87	−0.755844
$169$	2626.62	1.19555
$170$	−153.820	−0.0693970
$171$	−437.182	−0.195510
$172$	7031.44	3.11711
$173$	−1690.96	−0.743128	−0.371564	−	0.928407i	$-0.621178\pi$
$173$	−1690.96	−0.743128	−0.371564	+	0.928407i	$0.621178\pi$
$174$	153.190	0.0667431
$175$	−1618.47	−0.699115
$176$	1827.72	0.782780
$177$	1976.28	0.839246
$178$	4006.66	1.68714
$179$	1077.97	0.450120	0.225060	−	0.974345i	$-0.427742\pi$
$179$	1077.97	0.450120	0.225060	+	0.974345i	$0.427742\pi$
$180$	−317.612	−0.131519
$181$	−4059.49	−1.66707	−0.833534	−	0.552468i	$-0.813686\pi$
$181$	−4059.49	−1.66707	−0.833534	+	0.552468i	$0.813686\pi$
$182$	4603.86	1.87506
$183$	660.041	0.266621
$184$	3941.67	1.57926
$185$	324.481	0.128953
$186$	3926.25	1.54778
$187$	372.185	0.145545
$188$	248.327	0.0963355
$189$	−363.252	−0.139802
$190$	518.930	0.198143
$191$	2718.19	1.02974	0.514872	−	0.857267i	$-0.327839\pi$
$191$	2718.19	1.02974	0.514872	+	0.857267i	$0.327839\pi$
$192$	1369.42	0.514737
$193$	−2553.97	−0.952531	−0.476266	−	0.879301i	$-0.658010\pi$
$193$	−2553.97	−0.952531	−0.476266	+	0.879301i	$0.658010\pi$
$194$	1310.59	0.485023
$195$	451.757	0.165903
$196$	−2636.71	−0.960900
$197$	−1623.24	−0.587062	−0.293531	−	0.955950i	$-0.594830\pi$
$197$	−1623.24	−0.587062	−0.293531	+	0.955950i	$0.594830\pi$
$198$	1146.22	0.411406
$199$	4106.52	1.46283	0.731416	−	0.681931i	$-0.238860\pi$
$199$	4106.52	1.46283	0.731416	+	0.681931i	$0.238860\pi$
$200$	−4905.61	−1.73439
$201$	201.000	0.0705346
$202$	−77.5535	−0.0270131
$203$	−139.431	−0.0482077
$204$	−703.078	−0.241301
$205$	109.556	0.0373256
$206$	−6449.93	−2.18150
$207$	869.945	0.292103
$208$	4910.90	1.63707
$209$	−1255.61	−0.415561
$210$	431.176	0.141685
$211$	5460.95	1.78174	0.890871	−	0.454257i	$-0.150095\pi$
$211$	5460.95	1.78174	0.890871	+	0.454257i	$0.150095\pi$
$212$	1665.28	0.539490
$213$	732.386	0.235597
$214$	10600.0	3.38598
$215$	−936.665	−0.297116
$216$	−1101.02	−0.346828
$217$	−3573.62	−1.11794
$218$	−2135.01	−0.663307
$219$	1051.35	0.324399
$220$	−912.197	−0.279547
$221$	1000.03	0.304385
$222$	2212.10	0.668767
$223$	−1108.25	−0.332799	−0.166399	−	0.986058i	$-0.553214\pi$
$223$	−1108.25	−0.332799	−0.166399	+	0.986058i	$0.553214\pi$
$224$	298.173	0.0889397
$225$	−1082.69	−0.320797
$226$	4842.83	1.42540
$227$	6363.37	1.86058	0.930291	−	0.366823i	$-0.119555\pi$
$227$	6363.37	1.86058	0.930291	+	0.366823i	$0.119555\pi$
$228$	2371.91	0.688963
$229$	706.905	0.203990	0.101995	−	0.994785i	$-0.467477\pi$
$229$	706.905	0.203990	0.101995	+	0.994785i	$0.467477\pi$
$230$	−1032.61	−0.296037
$231$	−1043.28	−0.297154
$232$	−422.618	−0.119596
$233$	−4263.20	−1.19868	−0.599338	−	0.800496i	$-0.704569\pi$
$233$	−4263.20	−1.19868	−0.599338	+	0.800496i	$0.704569\pi$
$234$	3079.79	0.860393
$235$	−33.0798	−0.00918251
$236$	−10722.2	−2.95745
$237$	−1473.84	−0.403950
$238$	954.466	0.259953
$239$	5857.11	1.58521	0.792605	−	0.609736i	$-0.208725\pi$
$239$	5857.11	1.58521	0.792605	+	0.609736i	$0.208725\pi$
$240$	459.932	0.123702
$241$	−1742.60	−0.465770	−0.232885	−	0.972504i	$-0.574817\pi$
$241$	−1742.60	−0.465770	−0.232885	+	0.972504i	$0.574817\pi$
$242$	−3265.97	−0.867540
$243$	−243.000	−0.0641500
$244$	−3581.02	−0.939555
$245$	351.239	0.0915911
$246$	746.883	0.193575
$247$	−3373.70	−0.869082
$248$	−10831.7	−2.77344
$249$	1919.05	0.488414
$250$	2620.50	0.662941
$251$	−3385.25	−0.851294	−0.425647	−	0.904889i	$-0.639954\pi$
$251$	−3385.25	−0.851294	−0.425647	+	0.904889i	$0.639954\pi$
$252$	1970.80	0.492655
$253$	2498.52	0.620873
$254$	386.218	0.0954073
$255$	93.6577	0.0230003
$256$	−8303.32	−2.02718
$257$	592.615	0.143838	0.0719189	−	0.997410i	$-0.477088\pi$
$257$	592.615	0.143838	0.0719189	+	0.997410i	$0.477088\pi$
$258$	−6385.57	−1.54089
$259$	−2013.42	−0.483043
$260$	−2450.99	−0.584630
$261$	−93.2738	−0.0221207
$262$	−3088.15	−0.728193
$263$	−5880.88	−1.37882	−0.689411	−	0.724370i	$-0.742131\pi$
$263$	−5880.88	−1.37882	−0.689411	+	0.724370i	$0.742131\pi$
$264$	−3162.18	−0.737192
$265$	−221.834	−0.0514231
$266$	−3220.00	−0.742221
$267$	−2439.56	−0.559171
$268$	−1090.52	−0.248559
$269$	−5448.12	−1.23486	−0.617431	−	0.786625i	$-0.711826\pi$
$269$	−5448.12	−1.23486	−0.617431	+	0.786625i	$0.711826\pi$
$270$	288.438	0.0650140
$271$	7876.11	1.76546	0.882730	−	0.469881i	$-0.155703\pi$
$271$	7876.11	1.76546	0.882730	+	0.469881i	$0.155703\pi$
$272$	1018.12	0.226959
$273$	−2803.18	−0.621452
$274$	11227.9	2.47557
$275$	−3109.54	−0.681863
$276$	−4719.84	−1.02935
$277$	6472.85	1.40403	0.702014	−	0.712163i	$-0.252284\pi$
$277$	6472.85	1.40403	0.702014	+	0.712163i	$0.252284\pi$
$278$	−567.646	−0.122465
$279$	−2390.60	−0.512981
$280$	−1189.52	−0.253884
$281$	3762.20	0.798697	0.399348	−	0.916799i	$-0.369236\pi$
$281$	3762.20	0.798697	0.399348	+	0.916799i	$0.369236\pi$
$282$	−225.517	−0.0476217
$283$	−8812.08	−1.85097	−0.925484	−	0.378786i	$-0.876342\pi$
$283$	−8812.08	−1.85097	−0.925484	+	0.378786i	$0.876342\pi$
$284$	−3973.53	−0.830230
$285$	−315.965	−0.0656706
$286$	8845.30	1.82879
$287$	−679.804	−0.139817
$288$	199.465	0.0408111
$289$	−4705.68	−0.957801
$290$	110.715	0.0224186
$291$	−797.985	−0.160752
$292$	−5704.03	−1.14316
$293$	−4939.43	−0.984862	−0.492431	−	0.870351i	$-0.663892\pi$
$293$	−4939.43	−0.984862	−0.492431	+	0.870351i	$0.663892\pi$
$294$	2394.52	0.475004
$295$	1428.32	0.281898
$296$	−6102.71	−1.19835
$297$	−697.908	−0.136353
$298$	−3595.36	−0.698905
$299$	6713.29	1.29846
$300$	5874.09	1.13047
$301$	5812.07	1.11296
$302$	−3914.39	−0.745854
$303$	47.2205	0.00895296
$304$	−3434.75	−0.648014
$305$	477.031	0.0895565
$306$	638.498	0.119283
$307$	−891.592	−0.165752	−0.0828760	−	0.996560i	$-0.526411\pi$
$307$	−891.592	−0.165752	−0.0828760	+	0.996560i	$0.526411\pi$
$308$	5660.25	1.04715
$309$	3927.21	0.723014
$310$	2837.62	0.519890
$311$	5371.87	0.979455	0.489728	−	0.871875i	$-0.337096\pi$
$311$	5371.87	0.979455	0.489728	+	0.871875i	$0.337096\pi$
$312$	−8496.47	−1.54172
$313$	−1344.97	−0.242883	−0.121441	−	0.992599i	$-0.538752\pi$
$313$	−1344.97	−0.242883	−0.121441	+	0.992599i	$0.538752\pi$
$314$	−6573.86	−1.18148
$315$	−262.533	−0.0469589
$316$	7996.24	1.42349
$317$	8900.76	1.57702	0.788512	−	0.615019i	$-0.210852\pi$
$317$	8900.76	1.57702	0.788512	+	0.615019i	$0.210852\pi$
$318$	−1512.32	−0.266687
$319$	−267.887	−0.0470181
$320$	989.722	0.172897
$321$	−6454.09	−1.12222
$322$	6407.44	1.10892
$323$	−699.431	−0.120487
$324$	1318.39	0.226061
$325$	−8355.03	−1.42601
$326$	4244.43	0.721096
$327$	1299.96	0.219840
$328$	−2060.49	−0.346865
$329$	205.263	0.0343966
$330$	828.408	0.138189
$331$	−9835.49	−1.63326	−0.816628	−	0.577165i	$-0.804159\pi$
$331$	−9835.49	−1.63326	−0.816628	+	0.577165i	$0.804159\pi$
$332$	−10411.7	−1.72114
$333$	−1346.90	−0.221650
$334$	16347.2	2.67809
$335$	145.269	0.0236922
$336$	−2853.91	−0.463373
$337$	−10873.7	−1.75765	−0.878823	−	0.477147i	$-0.841671\pi$
$337$	−10873.7	−1.75765	−0.878823	+	0.477147i	$0.841671\pi$
$338$	12941.6	2.08264
$339$	−2948.69	−0.472421
$340$	−508.136	−0.0810515
$341$	−6865.93	−1.09035
$342$	−2154.04	−0.340577
$343$	−6794.10	−1.06952
$344$	17616.4	2.76109
$345$	628.735	0.0981158
$346$	−8331.52	−1.29452
$347$	3764.03	0.582316	0.291158	−	0.956675i	$-0.405959\pi$
$347$	3764.03	0.582316	0.291158	+	0.956675i	$0.405959\pi$
$348$	506.053	0.0779519
$349$	−11102.9	−1.70294	−0.851470	−	0.524403i	$-0.824289\pi$
$349$	−11102.9	−1.70294	−0.851470	+	0.524403i	$0.824289\pi$
$350$	−7974.39	−1.21785
$351$	−1875.21	−0.285161
$352$	572.873	0.0867450
$353$	9848.48	1.48493	0.742467	−	0.669883i	$-0.233656\pi$
$353$	9848.48	1.48493	0.742467	+	0.669883i	$0.233656\pi$
$354$	9737.35	1.46196
$355$	529.317	0.0791359
$356$	13235.7	1.97048
$357$	−581.153	−0.0861565
$358$	5311.29	0.784107
$359$	−9329.14	−1.37151	−0.685756	−	0.727831i	$-0.740528\pi$
$359$	−9329.14	−1.37151	−0.685756	+	0.727831i	$0.740528\pi$
$360$	−795.740	−0.116498
$361$	−4499.39	−0.655984
$362$	−20001.5	−2.90402
$363$	1988.58	0.287529
$364$	15208.5	2.18996
$365$	759.839	0.108964
$366$	3252.09	0.464452
$367$	4303.62	0.612117	0.306059	−	0.952013i	$-0.400990\pi$
$367$	4303.62	0.612117	0.306059	+	0.952013i	$0.400990\pi$
$368$	6834.77	0.968171
$369$	−454.760	−0.0641568
$370$	1598.75	0.224635
$371$	1376.49	0.192625
$372$	12970.1	1.80771
$373$	−7096.79	−0.985141	−0.492571	−	0.870272i	$-0.663943\pi$
$373$	−7096.79	−0.985141	−0.492571	+	0.870272i	$0.663943\pi$
$374$	1833.80	0.253538
$375$	−1595.56	−0.219719
$376$	622.153	0.0853327
$377$	−719.786	−0.0983312
$378$	−1789.78	−0.243535
$379$	11682.4	1.58334	0.791669	−	0.610950i	$-0.209212\pi$
$379$	11682.4	1.58334	0.791669	+	0.610950i	$0.209212\pi$
$380$	1714.25	0.231419
$381$	−235.159	−0.0316209
$382$	13392.8	1.79381
$383$	5167.87	0.689467	0.344733	−	0.938701i	$-0.387969\pi$
$383$	5167.87	0.689467	0.344733	+	0.938701i	$0.387969\pi$
$384$	7279.19	0.967356
$385$	−754.007	−0.0998123
$386$	−12583.7	−1.65930
$387$	3888.03	0.510697
$388$	4329.43	0.566478
$389$	−8880.32	−1.15746	−0.578728	−	0.815521i	$-0.696451\pi$
$389$	−8880.32	−1.15746	−0.578728	+	0.815521i	$0.696451\pi$
$390$	2225.85	0.289001
$391$	1391.79	0.180015
$392$	−6605.96	−0.851152
$393$	1880.30	0.241345
$394$	−7997.88	−1.02266
$395$	−1065.19	−0.135684
$396$	3786.47	0.480498
$397$	−287.840	−0.0363886	−0.0181943	−	0.999834i	$-0.505792\pi$
$397$	−287.840	−0.0363886	−0.0181943	+	0.999834i	$0.505792\pi$
$398$	20233.3	2.54825
$399$	1960.58	0.245995
$400$	−8506.22	−1.06328
$401$	−901.039	−0.112209	−0.0561044	−	0.998425i	$-0.517868\pi$
$401$	−901.039	−0.112209	−0.0561044	+	0.998425i	$0.517868\pi$
$402$	990.348	0.122871
$403$	−18448.1	−2.28031
$404$	−256.193	−0.0315497
$405$	−175.623	−0.0215476
$406$	−686.994	−0.0839776
$407$	−3868.35	−0.471123
$408$	−1761.48	−0.213741
$409$	10529.2	1.27295	0.636475	−	0.771298i	$-0.280392\pi$
$409$	10529.2	1.27295	0.636475	+	0.771298i	$0.280392\pi$
$410$	539.795	0.0650209
$411$	−6836.44	−0.820478
$412$	−21306.9	−2.54786
$413$	−8862.81	−1.05596
$414$	4286.31	0.508842
$415$	1386.96	0.164055
$416$	1539.25	0.181414
$417$	345.627	0.0405885
$418$	−6186.51	−0.723905
$419$	7344.73	0.856357	0.428179	−	0.903694i	$-0.359155\pi$
$419$	7344.73	0.856357	0.428179	+	0.903694i	$0.359155\pi$
$420$	1424.36	0.165480
$421$	7862.82	0.910239	0.455119	−	0.890430i	$-0.349597\pi$
$421$	7862.82	0.910239	0.455119	+	0.890430i	$0.349597\pi$
$422$	26906.7	3.10378
$423$	137.312	0.0157833
$424$	4172.16	0.477873
$425$	−1732.16	−0.197699
$426$	3608.54	0.410410
$427$	−2960.01	−0.335468
$428$	35016.4	3.95463
$429$	−5385.70	−0.606116
$430$	−4615.05	−0.517575
$431$	13683.1	1.52922	0.764608	−	0.644496i	$-0.222933\pi$
$431$	13683.1	1.52922	0.764608	+	0.644496i	$0.222933\pi$
$432$	−1909.14	−0.212624
$433$	9826.55	1.09061	0.545305	−	0.838238i	$-0.316414\pi$
$433$	9826.55	1.09061	0.545305	+	0.838238i	$0.316414\pi$
$434$	−17607.6	−1.94745
$435$	−67.4118	−0.00743022
$436$	−7052.86	−0.774703
$437$	−4695.36	−0.513981
$438$	5180.09	0.565101
$439$	11739.1	1.27626	0.638131	−	0.769928i	$-0.279708\pi$
$439$	11739.1	1.27626	0.638131	+	0.769928i	$0.279708\pi$
$440$	−2285.40	−0.247619
$441$	−1457.97	−0.157431
$442$	4927.23	0.530237
$443$	3480.03	0.373231	0.186615	−	0.982433i	$-0.440248\pi$
$443$	3480.03	0.373231	0.186615	+	0.982433i	$0.440248\pi$
$444$	7307.52	0.781080
$445$	−1763.14	−0.187823
$446$	−5460.48	−0.579734
$447$	2189.13	0.231639
$448$	−6141.29	−0.647653
$449$	−2666.11	−0.280226	−0.140113	−	0.990135i	$-0.544747\pi$
$449$	−2666.11	−0.280226	−0.140113	+	0.990135i	$0.544747\pi$
$450$	−5334.53	−0.558827
$451$	−1306.09	−0.136367
$452$	15998.0	1.66478
$453$	2383.38	0.247199
$454$	31353.0	3.24112
$455$	−2025.94	−0.208742
$456$	5942.54	0.610274
$457$	9850.64	1.00830	0.504150	−	0.863616i	$-0.331806\pi$
$457$	9850.64	1.00830	0.504150	+	0.863616i	$0.331806\pi$
$458$	3483.00	0.355349
$459$	−388.767	−0.0395339
$460$	−3411.17	−0.345754
$461$	−7971.04	−0.805311	−0.402655	−	0.915352i	$-0.631913\pi$
$461$	−7971.04	−0.805311	−0.402655	+	0.915352i	$0.631913\pi$
$462$	−5140.33	−0.517640
$463$	9503.21	0.953891	0.476946	−	0.878933i	$-0.341744\pi$
$463$	9503.21	0.953891	0.476946	+	0.878933i	$0.341744\pi$
$464$	−732.811	−0.0733187
$465$	−1727.76	−0.172308
$466$	−21005.2	−2.08809
$467$	−15486.1	−1.53450	−0.767249	−	0.641349i	$-0.778375\pi$
$467$	−15486.1	−1.53450	−0.767249	+	0.641349i	$0.778375\pi$
$468$	10173.9	1.00489
$469$	−901.402	−0.0887482
$470$	−162.988	−0.0159959
$471$	4002.67	0.391578
$472$	−26863.3	−2.61967
$473$	11166.6	1.08550
$474$	−7261.75	−0.703678
$475$	5843.62	0.564471
$476$	3153.02	0.303610
$477$	920.815	0.0883883
$478$	28858.6	2.76143
$479$	−17908.0	−1.70822	−0.854109	−	0.520094i	$-0.825897\pi$
$479$	−17908.0	−1.70822	−0.854109	+	0.520094i	$0.825897\pi$
$480$	144.159	0.0137082
$481$	−10393.9	−0.985281
$482$	−8585.96	−0.811368
$483$	−3901.34	−0.367531
$484$	−10788.9	−1.01323
$485$	−576.728	−0.0539956
$486$	−1197.29	−0.111749
$487$	1806.48	0.168089	0.0840446	−	0.996462i	$-0.473216\pi$
$487$	1806.48	0.168089	0.0840446	+	0.996462i	$0.473216\pi$
$488$	−8971.82	−0.832245
$489$	−2584.34	−0.238993
$490$	1730.59	0.159551
$491$	8601.40	0.790582	0.395291	−	0.918556i	$-0.370644\pi$
$491$	8601.40	0.790582	0.395291	+	0.918556i	$0.370644\pi$
$492$	2467.28	0.226084
$493$	−149.225	−0.0136324
$494$	−16622.6	−1.51394
$495$	−504.399	−0.0458001
$496$	−18781.9	−1.70027
$497$	−3284.45	−0.296434
$498$	9455.37	0.850814
$499$	650.629	0.0583691	0.0291845	−	0.999574i	$-0.490709\pi$
$499$	650.629	0.0583691	0.0291845	+	0.999574i	$0.490709\pi$
$500$	8656.66	0.774275
$501$	−9953.45	−0.887600
$502$	−16679.5	−1.48295
$503$	831.782	0.0737323	0.0368661	−	0.999320i	$-0.488262\pi$
$503$	831.782	0.0737323	0.0368661	+	0.999320i	$0.488262\pi$
$504$	4937.62	0.436387
$505$	34.1277	0.00300725
$506$	12310.5	1.08156
$507$	−7879.85	−0.690249
$508$	1275.84	0.111430
$509$	29.9027	0.00260396	0.00130198	−	0.999999i	$-0.499586\pi$
$509$	29.9027	0.00260396	0.00130198	+	0.999999i	$0.499586\pi$
$510$	461.461	0.0400664
$511$	−4714.85	−0.408166
$512$	−21500.1	−1.85582
$513$	1311.55	0.112878
$514$	2919.88	0.250565
$515$	2838.31	0.242856
$516$	−21094.3	−1.79966
$517$	394.367	0.0335478
$518$	−9920.35	−0.841458
$519$	5072.87	0.429045
$520$	−6140.66	−0.517857
$521$	15327.8	1.28891	0.644456	−	0.764642i	$-0.277084\pi$
$521$	15327.8	1.28891	0.644456	+	0.764642i	$0.277084\pi$
$522$	−459.570	−0.0385341
$523$	3794.24	0.317228	0.158614	−	0.987341i	$-0.449297\pi$
$523$	3794.24	0.317228	0.158614	+	0.987341i	$0.449297\pi$
$524$	−10201.5	−0.850485
$525$	4855.42	0.403634
$526$	−28975.7	−2.40190
$527$	−3824.64	−0.316136
$528$	−5483.15	−0.451939
$529$	−2823.74	−0.232082
$530$	−1093.00	−0.0895788
$531$	−5928.85	−0.484539
$532$	−10637.0	−0.866869
$533$	−3509.35	−0.285191
$534$	−12020.0	−0.974073
$535$	−4664.56	−0.376947
$536$	−2732.16	−0.220170
$537$	−3233.92	−0.259877
$538$	−26843.5	−2.15112
$539$	−4187.35	−0.334623
$540$	952.836	0.0759325
$541$	−9618.98	−0.764422	−0.382211	−	0.924075i	$-0.624837\pi$
$541$	−9618.98	−0.764422	−0.382211	+	0.924075i	$0.624837\pi$
$542$	38806.4	3.07542
$543$	12178.5	0.962482
$544$	319.116	0.0251507
$545$	939.518	0.0738432
$546$	−13811.6	−1.08257
$547$	10639.6	0.831659	0.415829	−	0.909443i	$-0.363491\pi$
$547$	10639.6	0.831659	0.415829	+	0.909443i	$0.363491\pi$
$548$	37090.8	2.89131
$549$	−1980.12	−0.153934
$550$	−15321.0	−1.18780
$551$	503.428	0.0389233
$552$	−11825.0	−0.911786
$553$	6609.55	0.508258
$554$	31892.4	2.44581
$555$	−973.442	−0.0744510
$556$	−1875.18	−0.143031
$557$	16284.0	1.23873	0.619366	−	0.785102i	$-0.287390\pi$
$557$	16284.0	1.23873	0.619366	+	0.785102i	$0.287390\pi$
$558$	−11778.8	−0.893610
$559$	30003.6	2.27016
$560$	−2062.60	−0.155644
$561$	−1116.56	−0.0840304
$562$	18536.7	1.39133
$563$	10180.6	0.762098	0.381049	−	0.924555i	$-0.375563\pi$
$563$	10180.6	0.762098	0.381049	+	0.924555i	$0.375563\pi$
$564$	−744.980	−0.0556193
$565$	−2131.10	−0.158684
$566$	−43418.1	−3.22438
$567$	1089.75	0.0807150
$568$	−9955.20	−0.735407
$569$	22745.2	1.67579	0.837897	−	0.545829i	$-0.183785\pi$
$569$	22745.2	1.67579	0.837897	+	0.545829i	$0.183785\pi$
$570$	−1556.79	−0.114398
$571$	−10642.6	−0.779996	−0.389998	−	0.920816i	$-0.627524\pi$
$571$	−10642.6	−0.779996	−0.389998	+	0.920816i	$0.627524\pi$
$572$	29219.8	2.13591
$573$	−8154.57	−0.594523
$574$	−3349.46	−0.243561
$575$	−11628.2	−0.843353
$576$	−4108.26	−0.297183
$577$	−8295.59	−0.598527	−0.299264	−	0.954171i	$-0.596741\pi$
$577$	−8295.59	−0.598527	−0.299264	+	0.954171i	$0.596741\pi$
$578$	−23185.4	−1.66848
$579$	7661.90	0.549944
$580$	365.739	0.0261836
$581$	−8606.16	−0.614533
$582$	−3931.76	−0.280028
$583$	2644.62	0.187872
$584$	−14290.8	−1.01260
$585$	−1355.27	−0.0957839
$586$	−24337.1	−1.71562
$587$	6192.98	0.435454	0.217727	−	0.976010i	$-0.430136\pi$
$587$	6192.98	0.435454	0.217727	+	0.976010i	$0.430136\pi$
$588$	7910.13	0.554776
$589$	12902.8	0.902635
$590$	7037.48	0.491065
$591$	4869.72	0.338940
$592$	−10582.0	−0.734655
$593$	18772.6	1.30000	0.650000	−	0.759934i	$-0.274769\pi$
$593$	18772.6	1.30000	0.650000	+	0.759934i	$0.274769\pi$
$594$	−3438.66	−0.237525
$595$	−420.016	−0.0289395
$596$	−11877.0	−0.816279
$597$	−12319.6	−0.844567
$598$	33077.1	2.26191
$599$	−11082.1	−0.755930	−0.377965	−	0.925820i	$-0.623376\pi$
$599$	−11082.1	−0.755930	−0.377965	+	0.925820i	$0.623376\pi$
$600$	14716.8	1.00135
$601$	25555.2	1.73447	0.867237	−	0.497895i	$-0.165894\pi$
$601$	25555.2	1.73447	0.867237	+	0.497895i	$0.165894\pi$
$602$	28636.7	1.93878
$603$	−603.000	−0.0407231
$604$	−12930.9	−0.871112
$605$	1437.20	0.0965795
$606$	232.660	0.0155960
$607$	22750.8	1.52130	0.760648	−	0.649165i	$-0.224881\pi$
$607$	22750.8	1.52130	0.760648	+	0.649165i	$0.224881\pi$
$608$	−1076.57	−0.0718106
$609$	418.294	0.0278328
$610$	2350.38	0.156007
$611$	1059.63	0.0701602
$612$	2109.23	0.139315
$613$	−18916.8	−1.24640	−0.623199	−	0.782063i	$-0.714167\pi$
$613$	−18916.8	−1.24640	−0.623199	+	0.782063i	$0.714167\pi$
$614$	−4392.97	−0.288739
$615$	−328.669	−0.0215499
$616$	14181.1	0.927552
$617$	3643.22	0.237715	0.118858	−	0.992911i	$-0.462077\pi$
$617$	3643.22	0.237715	0.118858	+	0.992911i	$0.462077\pi$
$618$	19349.8	1.25949
$619$	−8207.02	−0.532905	−0.266452	−	0.963848i	$-0.585852\pi$
$619$	−8207.02	−0.532905	−0.266452	+	0.963848i	$0.585852\pi$
$620$	9373.89	0.607201
$621$	−2609.83	−0.168646
$622$	26467.7	1.70621
$623$	10940.4	0.703562
$624$	−14732.7	−0.945160
$625$	13884.2	0.888589
$626$	−6626.81	−0.423100
$627$	3766.82	0.239924
$628$	−21716.3	−1.37990
$629$	−2154.85	−0.136597
$630$	−1293.53	−0.0818021
$631$	10067.6	0.635156	0.317578	−	0.948232i	$-0.397130\pi$
$631$	10067.6	0.635156	0.317578	+	0.948232i	$0.397130\pi$
$632$	20033.6	1.26091
$633$	−16382.9	−1.02869
$634$	43855.0	2.74717
$635$	−169.956	−0.0106213
$636$	−4995.84	−0.311475
$637$	−11251.0	−0.699813
$638$	−1319.91	−0.0819053
$639$	−2197.16	−0.136022
$640$	5260.89	0.324929
$641$	−15670.5	−0.965598	−0.482799	−	0.875731i	$-0.660380\pi$
$641$	−15670.5	−0.965598	−0.482799	+	0.875731i	$0.660380\pi$
$642$	−31800.0	−1.95490
$643$	30506.6	1.87101	0.935507	−	0.353308i	$-0.114943\pi$
$643$	30506.6	1.87101	0.935507	+	0.353308i	$0.114943\pi$
$644$	21166.6	1.29515
$645$	2809.99	0.171540
$646$	−3446.17	−0.209888
$647$	3059.36	0.185898	0.0929489	−	0.995671i	$-0.470371\pi$
$647$	3059.36	0.185898	0.0929489	+	0.995671i	$0.470371\pi$
$648$	3303.06	0.200241
$649$	−17027.9	−1.02990
$650$	−41166.1	−2.48411
$651$	10720.9	0.645444
$652$	14021.2	0.842197
$653$	22904.0	1.37259	0.686295	−	0.727323i	$-0.259236\pi$
$653$	22904.0	1.37259	0.686295	+	0.727323i	$0.259236\pi$
$654$	6405.03	0.382961
$655$	1358.95	0.0810666
$656$	−3572.85	−0.212647
$657$	−3154.04	−0.187292
$658$	1011.35	0.0599187
$659$	−30398.5	−1.79690	−0.898450	−	0.439075i	$-0.855306\pi$
$659$	−30398.5	−1.79690	−0.898450	+	0.439075i	$0.855306\pi$
$660$	2736.59	0.161397
$661$	18459.0	1.08619	0.543096	−	0.839671i	$-0.317252\pi$
$661$	18459.0	1.08619	0.543096	+	0.839671i	$0.317252\pi$
$662$	−48460.5	−2.84512
$663$	−3000.08	−0.175737
$664$	−26085.3	−1.52456
$665$	1416.97	0.0826282
$666$	−6636.30	−0.386113
$667$	−1001.77	−0.0581537
$668$	54002.0	3.12784
$669$	3324.76	0.192141
$670$	715.754	0.0412716
$671$	−5687.01	−0.327190
$672$	−894.518	−0.0513494
$673$	−9640.56	−0.552179	−0.276089	−	0.961132i	$-0.589039\pi$
$673$	−9640.56	−0.552179	−0.276089	+	0.961132i	$0.589039\pi$
$674$	−53575.7	−3.06181
$675$	3248.07	0.185212
$676$	42751.7	2.43239
$677$	−24684.0	−1.40130	−0.700652	−	0.713503i	$-0.747107\pi$
$677$	−24684.0	−1.40130	−0.700652	+	0.713503i	$0.747107\pi$
$678$	−14528.5	−0.822955
$679$	3578.63	0.202261
$680$	−1273.07	−0.0717943
$681$	−19090.1	−1.07421
$682$	−33829.2	−1.89939
$683$	−3477.63	−0.194828	−0.0974142	−	0.995244i	$-0.531057\pi$
$683$	−3477.63	−0.194828	−0.0974142	+	0.995244i	$0.531057\pi$
$684$	−7115.73	−0.397773
$685$	−4940.90	−0.275594
$686$	−33475.2	−1.86311
$687$	−2120.72	−0.117773
$688$	30546.5	1.69270
$689$	7105.85	0.392905
$690$	3097.84	0.170917
$691$	14461.9	0.796175	0.398088	−	0.917347i	$-0.369674\pi$
$691$	14461.9	0.796175	0.398088	+	0.917347i	$0.369674\pi$
$692$	−27522.6	−1.51193
$693$	3129.83	0.171562
$694$	18545.8	1.01439
$695$	249.795	0.0136335
$696$	1267.85	0.0690487
$697$	−727.553	−0.0395381
$698$	−54705.3	−2.96651
$699$	12789.6	0.692056
$700$	−26342.9	−1.42238
$701$	19005.9	1.02403	0.512013	−	0.858977i	$-0.328900\pi$
$701$	19005.9	1.02403	0.512013	+	0.858977i	$0.328900\pi$
$702$	−9239.36	−0.496748
$703$	7269.61	0.390012
$704$	−11799.1	−0.631671
$705$	99.2395	0.00530153
$706$	48524.5	2.58675
$707$	−211.764	−0.0112648
$708$	32166.7	1.70748
$709$	21118.2	1.11863	0.559316	−	0.828954i	$-0.311064\pi$
$709$	21118.2	1.11863	0.559316	+	0.828954i	$0.311064\pi$
$710$	2608.00	0.137854
$711$	4421.51	0.233220
$712$	33160.5	1.74543
$713$	−25675.2	−1.34859
$714$	−2863.40	−0.150084
$715$	−3892.40	−0.203591
$716$	17545.5	0.915790
$717$	−17571.3	−0.915221
$718$	−45965.6	−2.38917
$719$	5875.24	0.304742	0.152371	−	0.988323i	$-0.451309\pi$
$719$	5875.24	0.304742	0.152371	+	0.988323i	$0.451309\pi$
$720$	−1379.79	−0.0714193
$721$	−17611.9	−0.909712
$722$	−22169.0	−1.14272
$723$	5227.79	0.268912
$724$	−66073.7	−3.39173
$725$	1246.75	0.0638663
$726$	9797.92	0.500875
$727$	245.067	0.0125021	0.00625106	−	0.999980i	$-0.498010\pi$
$727$	245.067	0.0125021	0.00625106	+	0.999980i	$0.498010\pi$
$728$	38103.2	1.93983
$729$	729.000	0.0370370
$730$	3743.81	0.189814
$731$	6220.31	0.314728
$732$	10743.1	0.542452
$733$	−6539.21	−0.329510	−0.164755	−	0.986334i	$-0.552683\pi$
$733$	−6539.21	−0.329510	−0.164755	+	0.986334i	$0.552683\pi$
$734$	21204.4	1.06631
$735$	−1053.72	−0.0528801
$736$	2142.26	0.107289
$737$	−1731.84	−0.0865581
$738$	−2240.65	−0.111761
$739$	−35865.7	−1.78530	−0.892652	−	0.450747i	$-0.851158\pi$
$739$	−35865.7	−1.78530	−0.892652	+	0.450747i	$0.851158\pi$
$740$	5281.36	0.262361
$741$	10121.1	0.501765
$742$	6782.12	0.335552
$743$	17914.2	0.884535	0.442268	−	0.896883i	$-0.354174\pi$
$743$	17914.2	0.884535	0.442268	+	0.896883i	$0.354174\pi$
$744$	32495.1	1.60125
$745$	1582.15	0.0778061
$746$	−34966.6	−1.71611
$747$	−5757.16	−0.281986
$748$	6057.82	0.296118
$749$	28943.9	1.41200
$750$	−7861.51	−0.382749
$751$	18908.1	0.918730	0.459365	−	0.888248i	$-0.348077\pi$
$751$	18908.1	0.918730	0.459365	+	0.888248i	$0.348077\pi$
$752$	1078.80	0.0523135
$753$	10155.7	0.491495
$754$	−3546.46	−0.171292
$755$	1722.54	0.0830327
$756$	−5912.41	−0.284434
$757$	−8642.97	−0.414972	−0.207486	−	0.978238i	$-0.566528\pi$
$757$	−8642.97	−0.414972	−0.207486	+	0.978238i	$0.566528\pi$
$758$	57560.5	2.75817
$759$	−7495.57	−0.358461
$760$	4294.85	0.204988
$761$	−2421.33	−0.115339	−0.0576697	−	0.998336i	$-0.518367\pi$
$761$	−2421.33	−0.115339	−0.0576697	+	0.998336i	$0.518367\pi$
$762$	−1158.65	−0.0550834
$763$	−5829.77	−0.276608
$764$	44242.2	2.09506
$765$	−280.973	−0.0132792
$766$	25462.6	1.20105
$767$	−45752.4	−2.15388
$768$	24910.0	1.17039
$769$	20006.9	0.938187	0.469093	−	0.883149i	$-0.344581\pi$
$769$	20006.9	0.938187	0.469093	+	0.883149i	$0.344581\pi$
$770$	−3715.07	−0.173873
$771$	−1777.85	−0.0830448
$772$	−41569.3	−1.93797
$773$	−7953.32	−0.370066	−0.185033	−	0.982732i	$-0.559239\pi$
$773$	−7953.32	−0.370066	−0.185033	+	0.982732i	$0.559239\pi$
$774$	19156.7	0.889631
$775$	31954.1	1.48107
$776$	10846.9	0.501779
$777$	6040.27	0.278885
$778$	−43754.3	−2.01628
$779$	2454.48	0.112889
$780$	7352.96	0.337536
$781$	−6310.34	−0.289119
$782$	6857.50	0.313585
$783$	279.821	0.0127714
$784$	−11454.6	−0.521802
$785$	2892.85	0.131529
$786$	9264.45	0.420422
$787$	1198.68	0.0542925	0.0271462	−	0.999631i	$-0.491358\pi$
$787$	1198.68	0.0542925	0.0271462	+	0.999631i	$0.491358\pi$
$788$	−26420.5	−1.19440
$789$	17642.6	0.796064
$790$	−5248.29	−0.236362
$791$	13223.6	0.594410
$792$	9486.54	0.425618
$793$	−15280.4	−0.684268
$794$	−1418.22	−0.0633887
$795$	665.501	0.0296891
$796$	66839.2	2.97620
$797$	25747.3	1.14431	0.572155	−	0.820145i	$-0.306107\pi$
$797$	25747.3	1.14431	0.572155	+	0.820145i	$0.306107\pi$
$798$	9659.99	0.428521
$799$	219.680	0.00972682
$800$	−2666.16	−0.117829
$801$	7318.69	0.322838
$802$	−4439.51	−0.195467
$803$	−9058.55	−0.398094
$804$	3271.55	0.143506
$805$	−2819.62	−0.123451
$806$	−90895.7	−3.97229
$807$	16344.4	0.712948
$808$	−641.860	−0.0279462
$809$	13182.7	0.572903	0.286451	−	0.958095i	$-0.407524\pi$
$809$	13182.7	0.572903	0.286451	+	0.958095i	$0.407524\pi$
$810$	−865.315	−0.0375359
$811$	36224.7	1.56846	0.784230	−	0.620470i	$-0.213058\pi$
$811$	36224.7	1.56846	0.784230	+	0.620470i	$0.213058\pi$
$812$	−2269.44	−0.0980808
$813$	−23628.3	−1.01929
$814$	−19059.8	−0.820693
$815$	−1867.78	−0.0802765
$816$	−3054.37	−0.131035
$817$	−20984.9	−0.898615
$818$	51878.6	2.21747
$819$	8409.55	0.358795
$820$	1783.18	0.0759405
$821$	−9781.27	−0.415796	−0.207898	−	0.978151i	$-0.566662\pi$
$821$	−9781.27	−0.415796	−0.207898	+	0.978151i	$0.566662\pi$
$822$	−33683.8	−1.42927
$823$	−1200.42	−0.0508431	−0.0254215	−	0.999677i	$-0.508093\pi$
$823$	−1200.42	−0.0508431	−0.0254215	+	0.999677i	$0.508093\pi$
$824$	−53381.9	−2.25685
$825$	9328.62	0.393674
$826$	−43668.0	−1.83947
$827$	1716.41	0.0721709	0.0360854	−	0.999349i	$-0.488511\pi$
$827$	1716.41	0.0721709	0.0360854	+	0.999349i	$0.488511\pi$
$828$	14159.5	0.594297
$829$	−12275.4	−0.514283	−0.257142	−	0.966374i	$-0.582781\pi$
$829$	−12275.4	−0.514283	−0.257142	+	0.966374i	$0.582781\pi$
$830$	6833.68	0.285784
$831$	−19418.5	−0.810616
$832$	−31703.1	−1.32104
$833$	−2332.55	−0.0970203
$834$	1702.94	0.0707050
$835$	−7193.66	−0.298140
$836$	−20436.7	−0.845477
$837$	7171.81	0.296170
$838$	36188.3	1.49177
$839$	−15864.0	−0.652785	−0.326392	−	0.945234i	$-0.605833\pi$
$839$	−15864.0	−0.652785	−0.326392	+	0.945234i	$0.605833\pi$
$840$	3568.56	0.146580
$841$	−24281.6	−0.995596
$842$	38740.9	1.58563
$843$	−11286.6	−0.461128
$844$	88884.4	3.62503
$845$	−5695.00	−0.231851
$846$	676.551	0.0274944
$847$	−8917.94	−0.361776
$848$	7234.44	0.292962
$849$	26436.3	1.06866
$850$	−8534.51	−0.344390
$851$	−14465.7	−0.582702
$852$	11920.6	0.479334
$853$	−16609.2	−0.666693	−0.333346	−	0.942804i	$-0.608178\pi$
$853$	−16609.2	−0.666693	−0.333346	+	0.942804i	$0.608178\pi$
$854$	−14584.3	−0.584384
$855$	947.894	0.0379149
$856$	87729.3	3.50295
$857$	1689.27	0.0673330	0.0336665	−	0.999433i	$-0.489282\pi$
$857$	1689.27	0.0673330	0.0336665	+	0.999433i	$0.489282\pi$
$858$	−26535.9	−1.05585
$859$	−18344.1	−0.728630	−0.364315	−	0.931276i	$-0.618697\pi$
$859$	−18344.1	−0.728630	−0.364315	+	0.931276i	$0.618697\pi$
$860$	−15245.5	−0.604497
$861$	2039.41	0.0807235
$862$	67418.1	2.66389
$863$	−10652.5	−0.420181	−0.210091	−	0.977682i	$-0.567376\pi$
$863$	−10652.5	−0.420181	−0.210091	+	0.977682i	$0.567376\pi$
$864$	−598.395	−0.0235623
$865$	3666.32	0.144114
$866$	48416.4	1.89984
$867$	14117.0	0.552987
$868$	−58165.6	−2.27450
$869$	12698.8	0.495716
$870$	−332.145	−0.0129434
$871$	−4653.30	−0.181023
$872$	−17670.1	−0.686221
$873$	2393.96	0.0928100
$874$	−23134.5	−0.895352
$875$	7155.45	0.276455
$876$	17112.1	0.660004
$877$	10743.4	0.413660	0.206830	−	0.978377i	$-0.433685\pi$
$877$	10743.4	0.413660	0.206830	+	0.978377i	$0.433685\pi$
$878$	57840.0	2.22324
$879$	14818.3	0.568610
$880$	−3962.84	−0.151804
$881$	−33049.4	−1.26386	−0.631930	−	0.775025i	$-0.717737\pi$
$881$	−33049.4	−1.26386	−0.631930	+	0.775025i	$0.717737\pi$
$882$	−7183.55	−0.274244
$883$	−29316.2	−1.11729	−0.558646	−	0.829406i	$-0.688679\pi$
$883$	−29316.2	−1.11729	−0.558646	+	0.829406i	$0.688679\pi$
$884$	16276.8	0.619285
$885$	−4284.96	−0.162754
$886$	17146.5	0.650166
$887$	39170.7	1.48278	0.741389	−	0.671076i	$-0.234168\pi$
$887$	39170.7	1.48278	0.741389	+	0.671076i	$0.234168\pi$
$888$	18308.1	0.691870
$889$	1054.59	0.0397861
$890$	−8687.20	−0.327186
$891$	2093.72	0.0787232
$892$	−18038.3	−0.677094
$893$	−741.115	−0.0277721
$894$	10786.1	0.403513
$895$	−2337.25	−0.0872913
$896$	−32644.2	−1.21715
$897$	−20139.9	−0.749666
$898$	−13136.2	−0.488153
$899$	2752.85	0.102127
$900$	−17622.3	−0.652676
$901$	1473.18	0.0544713
$902$	−6435.26	−0.237551
$903$	−17436.2	−0.642570
$904$	40081.0	1.47464
$905$	8801.74	0.323293
$906$	11743.2	0.430619
$907$	41972.0	1.53656	0.768279	−	0.640115i	$-0.221113\pi$
$907$	41972.0	1.53656	0.768279	+	0.640115i	$0.221113\pi$
$908$	103573.	3.78544
$909$	−141.662	−0.00516899
$910$	−9982.04	−0.363628
$911$	16532.2	0.601249	0.300625	−	0.953743i	$-0.402805\pi$
$911$	16532.2	0.601249	0.300625	+	0.953743i	$0.402805\pi$
$912$	10304.2	0.374131
$913$	−16534.8	−0.599368
$914$	48535.1	1.75645
$915$	−1431.09	−0.0517055
$916$	11505.8	0.415026
$917$	−8432.38	−0.303666
$918$	−1915.49	−0.0688679
$919$	−20246.0	−0.726717	−0.363358	−	0.931649i	$-0.618370\pi$
$919$	−20246.0	−0.726717	−0.363358	+	0.931649i	$0.618370\pi$
$920$	−8546.29	−0.306264
$921$	2674.78	0.0956970
$922$	−39274.2	−1.40285
$923$	−16955.3	−0.604648
$924$	−16980.7	−0.604573
$925$	18003.4	0.639942
$926$	46823.3	1.66167
$927$	−11781.6	−0.417432
$928$	−229.689	−0.00812492
$929$	1183.31	0.0417901	0.0208950	−	0.999782i	$-0.493348\pi$
$929$	1183.31	0.0417901	0.0208950	+	0.999782i	$0.493348\pi$
$930$	−8512.86	−0.300159
$931$	7869.10	0.277013
$932$	−69389.3	−2.43876
$933$	−16115.6	−0.565489
$934$	−76301.6	−2.67309
$935$	−806.968	−0.0282253
$936$	25489.4	0.890115
$937$	−10573.3	−0.368640	−0.184320	−	0.982866i	$-0.559008\pi$
$937$	−10573.3	−0.368640	−0.184320	+	0.982866i	$0.559008\pi$
$938$	−4441.30	−0.154599
$939$	4034.91	0.140228
$940$	−538.419	−0.0186822
$941$	−51465.4	−1.78292	−0.891458	−	0.453103i	$-0.850317\pi$
$941$	−51465.4	−1.78292	−0.891458	+	0.453103i	$0.850317\pi$
$942$	19721.6	0.682127
$943$	−4884.15	−0.168664
$944$	−46580.3	−1.60600
$945$	787.598	0.0271117
$946$	55019.0	1.89093
$947$	−10503.9	−0.360433	−0.180217	−	0.983627i	$-0.557680\pi$
$947$	−10503.9	−0.360433	−0.180217	+	0.983627i	$0.557680\pi$
$948$	−23988.7	−0.821854
$949$	−24339.4	−0.832552
$950$	28792.1	0.983305
$951$	−26702.3	−0.910495
$952$	7899.51	0.268933
$953$	−51448.1	−1.74876	−0.874380	−	0.485242i	$-0.838731\pi$
$953$	−51448.1	−1.74876	−0.874380	+	0.485242i	$0.838731\pi$
$954$	4536.95	0.153972
$955$	−5893.55	−0.199697
$956$	95332.4	3.22518
$957$	803.660	0.0271459
$958$	−88234.5	−2.97571
$959$	30658.6	1.03234
$960$	−2969.17	−0.0998223
$961$	40764.4	1.36835
$962$	−51211.8	−1.71635
$963$	19362.3	0.647913
$964$	−28363.1	−0.947630
$965$	5537.48	0.184723
$966$	−19222.3	−0.640236
$967$	−43383.1	−1.44272	−0.721359	−	0.692562i	$-0.756482\pi$
$967$	−43383.1	−1.44272	−0.721359	+	0.692562i	$0.756482\pi$
$968$	−27030.4	−0.897509
$969$	2098.29	0.0695634
$970$	−2841.60	−0.0940600
$971$	448.452	0.0148213	0.00741066	−	0.999973i	$-0.497641\pi$
$971$	448.452	0.0148213	0.00741066	+	0.999973i	$0.497641\pi$
$972$	−3955.16	−0.130516
$973$	−1549.99	−0.0510694
$974$	8900.71	0.292810
$975$	25065.1	0.823308
$976$	−15556.9	−0.510211
$977$	−50517.5	−1.65424	−0.827122	−	0.562022i	$-0.810024\pi$
$977$	−50517.5	−1.65424	−0.827122	+	0.562022i	$0.810024\pi$
$978$	−12733.3	−0.416325
$979$	21019.6	0.686200
$980$	5716.89	0.186346
$981$	−3899.87	−0.126925
$982$	42380.0	1.37719
$983$	−47421.9	−1.53868	−0.769341	−	0.638838i	$-0.779415\pi$
$983$	−47421.9	−1.53868	−0.769341	+	0.638838i	$0.779415\pi$
$984$	6181.48	0.200262
$985$	3519.50	0.113848
$986$	−735.248	−0.0237475
$987$	−615.788	−0.0198589
$988$	−54911.5	−1.76819
$989$	41757.7	1.34258
$990$	−2485.23	−0.0797835
$991$	28937.3	0.927572	0.463786	−	0.885947i	$-0.346491\pi$
$991$	28937.3	0.927572	0.463786	+	0.885947i	$0.346491\pi$
$992$	−5886.93	−0.188418
$993$	29506.5	0.942961
$994$	−16182.8	−0.516386
$995$	−8903.72	−0.283685
$996$	31235.2	0.993699
$997$	−43478.2	−1.38111	−0.690555	−	0.723280i	$-0.742634\pi$
$997$	−43478.2	−1.38111	−0.690555	+	0.723280i	$0.742634\pi$
$998$	3205.72	0.101679
$999$	4040.69	0.127970

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.d.1.8	✓	9
3.2	odd	2		603.4.a.f.1.2		9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.d.1.8	✓	9	1.1	even	1	trivial
603.4.a.f.1.2		9	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)

\(f(q)\)	\(=\)	\(q+4.92710 q^{2} -3.00000 q^{3} +16.2764 q^{4} -2.16819 q^{5} -14.7813 q^{6} +13.4538 q^{7} +40.7785 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+4.92710 q^{2} -3.00000 q^{3} +16.2764 q^{4} -2.16819 q^{5} -14.7813 q^{6} +13.4538 q^{7} +40.7785 q^{8} +9.00000 q^{9} -10.6829 q^{10} +25.8484 q^{11} -48.8291 q^{12} +69.4523 q^{13} +66.2881 q^{14} +6.50457 q^{15} +70.7090 q^{16} +14.3988 q^{17} +44.3439 q^{18} -48.5758 q^{19} -35.2902 q^{20} -40.3613 q^{21} +127.358 q^{22} +96.6605 q^{23} -122.335 q^{24} -120.299 q^{25} +342.199 q^{26} -27.0000 q^{27} +218.978 q^{28} -10.3638 q^{29} +32.0487 q^{30} -265.623 q^{31} +22.1628 q^{32} -77.5453 q^{33} +70.9442 q^{34} -29.1703 q^{35} +146.487 q^{36} -149.655 q^{37} -239.338 q^{38} -208.357 q^{39} -88.4155 q^{40} -50.5289 q^{41} -198.864 q^{42} +432.003 q^{43} +420.718 q^{44} -19.5137 q^{45} +476.256 q^{46} +15.2569 q^{47} -212.127 q^{48} -161.996 q^{49} -592.726 q^{50} -43.1963 q^{51} +1130.43 q^{52} +102.313 q^{53} -133.032 q^{54} -56.0443 q^{55} +548.624 q^{56} +145.727 q^{57} -51.0633 q^{58} -658.761 q^{59} +105.871 q^{60} -220.014 q^{61} -1308.75 q^{62} +121.084 q^{63} -456.474 q^{64} -150.586 q^{65} -382.074 q^{66} -67.0000 q^{67} +234.359 q^{68} -289.982 q^{69} -143.725 q^{70} -244.129 q^{71} +367.006 q^{72} -350.449 q^{73} -737.366 q^{74} +360.897 q^{75} -790.637 q^{76} +347.759 q^{77} -1026.60 q^{78} +491.279 q^{79} -153.311 q^{80} +81.0000 q^{81} -248.961 q^{82} -639.684 q^{83} -656.935 q^{84} -31.2192 q^{85} +2128.52 q^{86} +31.0913 q^{87} +1054.06 q^{88} +813.187 q^{89} -96.1461 q^{90} +934.394 q^{91} +1573.28 q^{92} +796.868 q^{93} +75.1723 q^{94} +105.322 q^{95} -66.4883 q^{96} +265.995 q^{97} -798.173 q^{98} +232.636 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9}+O(q^{10}) \) 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9	\( 9 q + 3 q^{2} - 27 q^{3} + 45 q^{4} + 12 q^{5} - 9 q^{6} + 8 q^{7} + 51 q^{8} + 81 q^{9} + 45 q^{10} + 72 q^{11} - 135 q^{12} - 166 q^{13} + 93 q^{14} - 36 q^{15} + 173 q^{16} + 146 q^{17} + 27 q^{18} + 154 q^{19} + 763 q^{20} - 24 q^{21} + 244 q^{22} + 476 q^{23} - 153 q^{24} + 465 q^{25} + 502 q^{26} - 243 q^{27} - 141 q^{28} + 432 q^{29} - 135 q^{30} + 248 q^{31} + 1171 q^{32} - 216 q^{33} + 146 q^{34} + 178 q^{35} + 405 q^{36} - 240 q^{37} + 1182 q^{38} + 498 q^{39} + 1409 q^{40} + 406 q^{41} - 279 q^{42} + 154 q^{43} + 892 q^{44} + 108 q^{45} + 273 q^{46} + 494 q^{47} - 519 q^{48} + 431 q^{49} + 1658 q^{50} - 438 q^{51} - 1258 q^{52} - 450 q^{53} - 81 q^{54} - 346 q^{55} - 659 q^{56} - 462 q^{57} - 2114 q^{58} + 732 q^{59} - 2289 q^{60} - 914 q^{61} - 1265 q^{62} + 72 q^{63} - 467 q^{64} - 536 q^{65} - 732 q^{66} - 603 q^{67} - 3314 q^{68} - 1428 q^{69} - 4805 q^{70} + 2990 q^{71} + 459 q^{72} - 1384 q^{73} - 2043 q^{74} - 1395 q^{75} + 450 q^{76} + 1660 q^{77} - 1506 q^{78} + 2438 q^{79} + 995 q^{80} + 729 q^{81} - 3561 q^{82} + 972 q^{83} + 423 q^{84} - 2706 q^{85} - 21 q^{86} - 1296 q^{87} - 3796 q^{88} + 1034 q^{89} + 405 q^{90} + 1898 q^{91} + 1827 q^{92} - 744 q^{93} - 3502 q^{94} + 6040 q^{95} - 3513 q^{96} - 1516 q^{97} - 3996 q^{98} + 648 q^{99}+O(q^{100}) \) 9 * q + 3 * q^2 - 27 * q^3 + 45 * q^4 + 12 * q^5 - 9 * q^6 + 8 * q^7 + 51 * q^8 + 81 * q^9 + 45 * q^10 + 72 * q^11 - 135 * q^12 - 166 * q^13 + 93 * q^14 - 36 * q^15 + 173 * q^16 + 146 * q^17 + 27 * q^18 + 154 * q^19 + 763 * q^20 - 24 * q^21 + 244 * q^22 + 476 * q^23 - 153 * q^24 + 465 * q^25 + 502 * q^26 - 243 * q^27 - 141 * q^28 + 432 * q^29 - 135 * q^30 + 248 * q^31 + 1171 * q^32 - 216 * q^33 + 146 * q^34 + 178 * q^35 + 405 * q^36 - 240 * q^37 + 1182 * q^38 + 498 * q^39 + 1409 * q^40 + 406 * q^41 - 279 * q^42 + 154 * q^43 + 892 * q^44 + 108 * q^45 + 273 * q^46 + 494 * q^47 - 519 * q^48 + 431 * q^49 + 1658 * q^50 - 438 * q^51 - 1258 * q^52 - 450 * q^53 - 81 * q^54 - 346 * q^55 - 659 * q^56 - 462 * q^57 - 2114 * q^58 + 732 * q^59 - 2289 * q^60 - 914 * q^61 - 1265 * q^62 + 72 * q^63 - 467 * q^64 - 536 * q^65 - 732 * q^66 - 603 * q^67 - 3314 * q^68 - 1428 * q^69 - 4805 * q^70 + 2990 * q^71 + 459 * q^72 - 1384 * q^73 - 2043 * q^74 - 1395 * q^75 + 450 * q^76 + 1660 * q^77 - 1506 * q^78 + 2438 * q^79 + 995 * q^80 + 729 * q^81 - 3561 * q^82 + 972 * q^83 + 423 * q^84 - 2706 * q^85 - 21 * q^86 - 1296 * q^87 - 3796 * q^88 + 1034 * q^89 + 405 * q^90 + 1898 * q^91 + 1827 * q^92 - 744 * q^93 - 3502 * q^94 + 6040 * q^95 - 3513 * q^96 - 1516 * q^97 - 3996 * q^98 + 648 * q^99

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