LMFDB - Embedded newform 201.4.a.b.1.3

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:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 28x^{4} + 22x^{3} + 202x^{2} - 96x - 384 $ x^6 - x^5 - 28x^4 + 22x^3 + 202x^2 - 96x - 384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-1.43201$ 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)

$f(q)$	$=$	$q-2.43201 q^{2} +3.00000 q^{3} -2.08534 q^{4} -2.10555 q^{5} -7.29602 q^{6} -2.84912 q^{7} +24.5276 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.43201 q^{2} +3.00000 q^{3} -2.08534 q^{4} -2.10555 q^{5} -7.29602 q^{6} -2.84912 q^{7} +24.5276 q^{8} +9.00000 q^{9} +5.12071 q^{10} -13.8200 q^{11} -6.25603 q^{12} +25.3149 q^{13} +6.92907 q^{14} -6.31665 q^{15} -42.9686 q^{16} -81.8257 q^{17} -21.8881 q^{18} -49.3856 q^{19} +4.39079 q^{20} -8.54735 q^{21} +33.6103 q^{22} +30.0404 q^{23} +73.5829 q^{24} -120.567 q^{25} -61.5660 q^{26} +27.0000 q^{27} +5.94139 q^{28} +188.759 q^{29} +15.3621 q^{30} -334.716 q^{31} -91.7211 q^{32} -41.4599 q^{33} +199.001 q^{34} +5.99896 q^{35} -18.7681 q^{36} -346.705 q^{37} +120.106 q^{38} +75.9447 q^{39} -51.6441 q^{40} +86.7408 q^{41} +20.7872 q^{42} -219.367 q^{43} +28.8194 q^{44} -18.9499 q^{45} -73.0583 q^{46} -167.649 q^{47} -128.906 q^{48} -334.883 q^{49} +293.219 q^{50} -245.477 q^{51} -52.7902 q^{52} -193.047 q^{53} -65.6642 q^{54} +29.0986 q^{55} -69.8821 q^{56} -148.157 q^{57} -459.062 q^{58} -336.509 q^{59} +13.1724 q^{60} -258.855 q^{61} +814.031 q^{62} -25.6421 q^{63} +566.815 q^{64} -53.3017 q^{65} +100.831 q^{66} -67.0000 q^{67} +170.635 q^{68} +90.1211 q^{69} -14.5895 q^{70} +760.383 q^{71} +220.749 q^{72} +860.956 q^{73} +843.189 q^{74} -361.700 q^{75} +102.986 q^{76} +39.3747 q^{77} -184.698 q^{78} +349.866 q^{79} +90.4725 q^{80} +81.0000 q^{81} -210.954 q^{82} -840.864 q^{83} +17.8242 q^{84} +172.288 q^{85} +533.501 q^{86} +566.276 q^{87} -338.971 q^{88} +1293.17 q^{89} +46.0864 q^{90} -72.1251 q^{91} -62.6444 q^{92} -1004.15 q^{93} +407.724 q^{94} +103.984 q^{95} -275.163 q^{96} -100.654 q^{97} +814.437 q^{98} -124.380 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * 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 $

$2$	−2.43201	−0.859844	−0.429922	−	0.902866i	$-0.641459\pi$
$2$	−2.43201	−0.859844	−0.429922	+	0.902866i	$0.641459\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−2.08534	−0.260668
$5$	−2.10555	−0.188326	−0.0941630	−	0.995557i	$-0.530017\pi$
$5$	−2.10555	−0.188326	−0.0941630	+	0.995557i	$0.530017\pi$
$6$	−7.29602	−0.496431
$7$	−2.84912	−0.153838	−0.0769189	−	0.997037i	$-0.524508\pi$
$7$	−2.84912	−0.153838	−0.0769189	+	0.997037i	$0.524508\pi$
$8$	24.5276	1.08398
$9$	9.00000	0.333333
$10$	5.12071	0.161931
$11$	−13.8200	−0.378807	−0.189403	−	0.981899i	$-0.560655\pi$
$11$	−13.8200	−0.378807	−0.189403	+	0.981899i	$0.560655\pi$
$12$	−6.25603	−0.150497
$13$	25.3149	0.540084	0.270042	−	0.962849i	$-0.412962\pi$
$13$	25.3149	0.540084	0.270042	+	0.962849i	$0.412962\pi$
$14$	6.92907	0.132277
$15$	−6.31665	−0.108730
$16$	−42.9686	−0.671384
$17$	−81.8257	−1.16739	−0.583695	−	0.811973i	$-0.698394\pi$
$17$	−81.8257	−1.16739	−0.583695	+	0.811973i	$0.698394\pi$
$18$	−21.8881	−0.286615
$19$	−49.3856	−0.596307	−0.298153	−	0.954518i	$-0.596371\pi$
$19$	−49.3856	−0.596307	−0.298153	+	0.954518i	$0.596371\pi$
$20$	4.39079	0.0490905
$21$	−8.54735	−0.0888183
$22$	33.6103	0.325715
$23$	30.0404	0.272341	0.136171	−	0.990685i	$-0.456520\pi$
$23$	30.0404	0.272341	0.136171	+	0.990685i	$0.456520\pi$
$24$	73.5829	0.625835
$25$	−120.567	−0.964533
$26$	−61.5660	−0.464388
$27$	27.0000	0.192450
$28$	5.94139	0.0401006
$29$	188.759	1.20868	0.604338	−	0.796728i	$-0.293438\pi$
$29$	188.759	1.20868	0.604338	+	0.796728i	$0.293438\pi$
$30$	15.3621	0.0934909
$31$	−334.716	−1.93925	−0.969625	−	0.244597i	$-0.921344\pi$
$31$	−334.716	−1.93925	−0.969625	+	0.244597i	$0.921344\pi$
$32$	−91.7211	−0.506692
$33$	−41.4599	−0.218704
$34$	199.001	1.00377
$35$	5.99896	0.0289717
$36$	−18.7681	−0.0868893
$37$	−346.705	−1.54048	−0.770242	−	0.637751i	$-0.779865\pi$
$37$	−346.705	−1.54048	−0.770242	+	0.637751i	$0.779865\pi$
$38$	120.106	0.512731
$39$	75.9447	0.311817
$40$	−51.6441	−0.204141
$41$	86.7408	0.330406	0.165203	−	0.986260i	$-0.447172\pi$
$41$	86.7408	0.330406	0.165203	+	0.986260i	$0.447172\pi$
$42$	20.7872	0.0763699
$43$	−219.367	−0.777979	−0.388989	−	0.921242i	$-0.627176\pi$
$43$	−219.367	−0.777979	−0.388989	+	0.921242i	$0.627176\pi$
$44$	28.8194	0.0987428
$45$	−18.9499	−0.0627753
$46$	−73.0583	−0.234171
$47$	−167.649	−0.520301	−0.260151	−	0.965568i	$-0.583772\pi$
$47$	−167.649	−0.520301	−0.260151	+	0.965568i	$0.583772\pi$
$48$	−128.906	−0.387624
$49$	−334.883	−0.976334
$50$	293.219	0.829348
$51$	−245.477	−0.673993
$52$	−52.7902	−0.140782
$53$	−193.047	−0.500323	−0.250161	−	0.968204i	$-0.580484\pi$
$53$	−193.047	−0.500323	−0.250161	+	0.968204i	$0.580484\pi$
$54$	−65.6642	−0.165477
$55$	29.0986	0.0713392
$56$	−69.8821	−0.166757
$57$	−148.157	−0.344278
$58$	−459.062	−1.03927
$59$	−336.509	−0.742537	−0.371269	−	0.928526i	$-0.621077\pi$
$59$	−336.509	−0.742537	−0.371269	+	0.928526i	$0.621077\pi$
$60$	13.1724	0.0283424
$61$	−258.855	−0.543328	−0.271664	−	0.962392i	$-0.587574\pi$
$61$	−258.855	−0.543328	−0.271664	+	0.962392i	$0.587574\pi$
$62$	814.031	1.66745
$63$	−25.6421	−0.0512793
$64$	566.815	1.10706
$65$	−53.3017	−0.101712
$66$	100.831	0.188052
$67$	−67.0000	−0.122169
$67$	−67.0000	−0.122169
$68$	170.635	0.304301
$69$	90.1211	0.157236
$70$	−14.5895	−0.0249111
$71$	760.383	1.27100	0.635499	−	0.772102i	$-0.280795\pi$
$71$	760.383	1.27100	0.635499	+	0.772102i	$0.280795\pi$
$72$	220.749	0.361326
$73$	860.956	1.38037	0.690186	−	0.723632i	$-0.257528\pi$
$73$	860.956	1.38037	0.690186	+	0.723632i	$0.257528\pi$
$74$	843.189	1.32458
$75$	−361.700	−0.556874
$76$	102.986	0.155438
$77$	39.3747	0.0582749
$78$	−184.698	−0.268114
$79$	349.866	0.498266	0.249133	−	0.968469i	$-0.419854\pi$
$79$	349.866	0.498266	0.249133	+	0.968469i	$0.419854\pi$
$80$	90.4725	0.126439
$81$	81.0000	0.111111
$82$	−210.954	−0.284097
$83$	−840.864	−1.11201	−0.556005	−	0.831179i	$-0.687666\pi$
$83$	−840.864	−1.11201	−0.556005	+	0.831179i	$0.687666\pi$
$84$	17.8242	0.0231521
$85$	172.288	0.219850
$86$	533.501	0.668940
$87$	566.276	0.697829
$88$	−338.971	−0.410618
$89$	1293.17	1.54018	0.770091	−	0.637934i	$-0.220211\pi$
$89$	1293.17	1.54018	0.770091	+	0.637934i	$0.220211\pi$
$90$	46.0864	0.0539770
$91$	−72.1251	−0.0830853
$92$	−62.6444	−0.0709906
$93$	−1004.15	−1.11963
$94$	407.724	0.447378
$95$	103.984	0.112300
$96$	−275.163	−0.292539
$97$	−100.654	−0.105359	−0.0526797	−	0.998611i	$-0.516776\pi$
$97$	−100.654	−0.105359	−0.0526797	+	0.998611i	$0.516776\pi$
$98$	814.437	0.839495
$99$	−124.380	−0.126269
$100$	251.423	0.251423
$101$	984.519	0.969933	0.484967	−	0.874533i	$-0.338832\pi$
$101$	984.519	0.969933	0.484967	+	0.874533i	$0.338832\pi$
$102$	597.002	0.579529
$103$	854.261	0.817212	0.408606	−	0.912711i	$-0.366015\pi$
$103$	854.261	0.817212	0.408606	+	0.912711i	$0.366015\pi$
$104$	620.914	0.585439
$105$	17.9969	0.0167268
$106$	469.492	0.430199
$107$	1154.64	1.04321	0.521603	−	0.853188i	$-0.325334\pi$
$107$	1154.64	1.04321	0.521603	+	0.853188i	$0.325334\pi$
$108$	−56.3043	−0.0501656
$109$	−1383.07	−1.21536	−0.607681	−	0.794181i	$-0.707900\pi$
$109$	−1383.07	−1.21536	−0.607681	+	0.794181i	$0.707900\pi$
$110$	−70.7680	−0.0613406
$111$	−1040.11	−0.889399
$112$	122.423	0.103284
$113$	−180.062	−0.149901	−0.0749506	−	0.997187i	$-0.523880\pi$
$113$	−180.062	−0.149901	−0.0749506	+	0.997187i	$0.523880\pi$
$114$	360.318	0.296025
$115$	−63.2514	−0.0512889
$116$	−393.626	−0.315063
$117$	227.834	0.180028
$118$	818.391	0.638466
$119$	233.131	0.179589
$120$	−154.932	−0.117861
$121$	−1140.01	−0.856505
$122$	629.537	0.467177
$123$	260.222	0.190760
$124$	697.997	0.505500
$125$	517.053	0.369973
$126$	62.3617	0.0440922
$127$	214.992	0.150216	0.0751081	−	0.997175i	$-0.476070\pi$
$127$	214.992	0.150216	0.0751081	+	0.997175i	$0.476070\pi$
$128$	−644.730	−0.445208
$129$	−658.100	−0.449166
$130$	129.630	0.0874563
$131$	−1505.49	−1.00409	−0.502044	−	0.864842i	$-0.667418\pi$
$131$	−1505.49	−1.00409	−0.502044	+	0.864842i	$0.667418\pi$
$132$	86.4581	0.0570092
$133$	140.705	0.0917346
$134$	162.944	0.105047
$135$	−56.8498	−0.0362434
$136$	−2006.99	−1.26543
$137$	−2808.71	−1.75157	−0.875783	−	0.482706i	$-0.839654\pi$
$137$	−2808.71	−1.75157	−0.875783	+	0.482706i	$0.839654\pi$
$138$	−219.175	−0.135199
$139$	1348.90	0.823111	0.411555	−	0.911385i	$-0.364986\pi$
$139$	1348.90	0.823111	0.411555	+	0.911385i	$0.364986\pi$
$140$	−12.5099	−0.00755198
$141$	−502.948	−0.300396
$142$	−1849.26	−1.09286
$143$	−349.851	−0.204587
$144$	−386.717	−0.223795
$145$	−397.440	−0.227625
$146$	−2093.85	−1.18691
$147$	−1004.65	−0.563687
$148$	722.998	0.401555
$149$	1097.86	0.603626	0.301813	−	0.953367i	$-0.402408\pi$
$149$	1097.86	0.603626	0.301813	+	0.953367i	$0.402408\pi$
$150$	879.657	0.478825
$151$	−904.692	−0.487568	−0.243784	−	0.969830i	$-0.578389\pi$
$151$	−904.692	−0.487568	−0.243784	+	0.969830i	$0.578389\pi$
$152$	−1211.31	−0.646383
$153$	−736.431	−0.389130
$154$	−95.7595	−0.0501073
$155$	704.761	0.365211
$156$	−158.371	−0.0812808
$157$	247.709	0.125919	0.0629596	−	0.998016i	$-0.479946\pi$
$157$	247.709	0.125919	0.0629596	+	0.998016i	$0.479946\pi$
$158$	−850.876	−0.428431
$159$	−579.142	−0.288861
$160$	193.123	0.0954233
$161$	−85.5885	−0.0418964
$162$	−196.993	−0.0955382
$163$	931.526	0.447624	0.223812	−	0.974632i	$-0.428150\pi$
$163$	931.526	0.447624	0.223812	+	0.974632i	$0.428150\pi$
$164$	−180.884	−0.0861261
$165$	87.2958	0.0411877
$166$	2044.99	0.956156
$167$	−365.827	−0.169512	−0.0847560	−	0.996402i	$-0.527011\pi$
$167$	−365.827	−0.169512	−0.0847560	+	0.996402i	$0.527011\pi$
$168$	−209.646	−0.0962771
$169$	−1556.16	−0.708310
$170$	−419.006	−0.189037
$171$	−444.470	−0.198769
$172$	457.454	0.202794
$173$	−3767.28	−1.65561	−0.827806	−	0.561015i	$-0.810411\pi$
$173$	−3767.28	−1.65561	−0.827806	+	0.561015i	$0.810411\pi$
$174$	−1377.19	−0.600024
$175$	343.509	0.148382
$176$	593.825	0.254325
$177$	−1009.53	−0.428704
$178$	−3145.01	−1.32432
$179$	−1316.63	−0.549773	−0.274887	−	0.961477i	$-0.588640\pi$
$179$	−1316.63	−0.549773	−0.274887	+	0.961477i	$0.588640\pi$
$180$	39.5171	0.0163635
$181$	2073.14	0.851357	0.425678	−	0.904875i	$-0.360036\pi$
$181$	2073.14	0.851357	0.425678	+	0.904875i	$0.360036\pi$
$182$	175.409	0.0714404
$183$	−776.565	−0.313690
$184$	736.818	0.295212
$185$	730.004	0.290113
$186$	2442.09	0.962704
$187$	1130.83	0.442216
$188$	349.606	0.135626
$189$	−76.9262	−0.0296061
$190$	−252.889	−0.0965606
$191$	3176.40	1.20333	0.601665	−	0.798748i	$-0.294504\pi$
$191$	3176.40	1.20333	0.601665	+	0.798748i	$0.294504\pi$
$192$	1700.45	0.639162
$193$	2751.20	1.02609	0.513047	−	0.858361i	$-0.328517\pi$
$193$	2751.20	1.02609	0.513047	+	0.858361i	$0.328517\pi$
$194$	244.791	0.0905927
$195$	−159.905	−0.0587233
$196$	698.345	0.254499
$197$	2748.71	0.994099	0.497049	−	0.867722i	$-0.334417\pi$
$197$	2748.71	0.994099	0.497049	+	0.867722i	$0.334417\pi$
$198$	302.492	0.108572
$199$	1397.02	0.497647	0.248824	−	0.968549i	$-0.419956\pi$
$199$	1397.02	0.497647	0.248824	+	0.968549i	$0.419956\pi$
$200$	−2957.21	−1.04553
$201$	−201.000	−0.0705346
$202$	−2394.36	−0.833992
$203$	−537.795	−0.185940
$204$	511.904	0.175688
$205$	−182.637	−0.0622240
$206$	−2077.57	−0.702675
$207$	270.363	0.0907804
$208$	−1087.75	−0.362604
$209$	682.507	0.225885
$210$	−43.7685	−0.0143824
$211$	−4602.21	−1.50156	−0.750781	−	0.660552i	$-0.770322\pi$
$211$	−4602.21	−1.50156	−0.750781	+	0.660552i	$0.770322\pi$
$212$	402.570	0.130418
$213$	2281.15	0.733811
$214$	−2808.09	−0.896995
$215$	461.887	0.146514
$216$	662.246	0.208612
$217$	953.645	0.298330
$218$	3363.65	1.04502
$219$	2582.87	0.796959
$220$	−60.6806	−0.0185958
$221$	−2071.41	−0.630489
$222$	2529.57	0.764745
$223$	−4664.86	−1.40082	−0.700409	−	0.713742i	$-0.746999\pi$
$223$	−4664.86	−1.40082	−0.700409	+	0.713742i	$0.746999\pi$
$224$	261.324	0.0779484
$225$	−1085.10	−0.321511
$226$	437.913	0.128892
$227$	1849.95	0.540906	0.270453	−	0.962733i	$-0.412827\pi$
$227$	1849.95	0.540906	0.270453	+	0.962733i	$0.412827\pi$
$228$	308.958	0.0897422
$229$	19.5862	0.00565194	0.00282597	−	0.999996i	$-0.499100\pi$
$229$	19.5862	0.00565194	0.00282597	+	0.999996i	$0.499100\pi$
$230$	153.828	0.0441005
$231$	118.124	0.0336450
$232$	4629.80	1.31018
$233$	1210.48	0.340347	0.170174	−	0.985414i	$-0.445567\pi$
$233$	1210.48	0.340347	0.170174	+	0.985414i	$0.445567\pi$
$234$	−554.094	−0.154796
$235$	352.994	0.0979863
$236$	701.736	0.193556
$237$	1049.60	0.287674
$238$	−566.976	−0.154419
$239$	−6857.89	−1.85607	−0.928033	−	0.372498i	$-0.878501\pi$
$239$	−6857.89	−1.85607	−0.928033	+	0.372498i	$0.878501\pi$
$240$	271.417	0.0729997
$241$	5864.97	1.56762	0.783809	−	0.621002i	$-0.213274\pi$
$241$	5864.97	1.56762	0.783809	+	0.621002i	$0.213274\pi$
$242$	2772.51	0.736461
$243$	243.000	0.0641500
$244$	539.802	0.141628
$245$	705.112	0.183869
$246$	−632.862	−0.164024
$247$	−1250.19	−0.322056
$248$	−8209.78	−2.10210
$249$	−2522.59	−0.642019
$250$	−1257.48	−0.318119
$251$	−3390.63	−0.852648	−0.426324	−	0.904570i	$-0.640192\pi$
$251$	−3390.63	−0.852648	−0.426324	+	0.904570i	$0.640192\pi$
$252$	53.4725	0.0133669
$253$	−415.157	−0.103165
$254$	−522.862	−0.129163
$255$	516.864	0.126930
$256$	−2966.53	−0.724251
$257$	4417.30	1.07215	0.536077	−	0.844169i	$-0.319905\pi$
$257$	4417.30	1.07215	0.536077	+	0.844169i	$0.319905\pi$
$258$	1600.50	0.386213
$259$	987.803	0.236985
$260$	111.152	0.0265130
$261$	1698.83	0.402892
$262$	3661.37	0.863359
$263$	653.244	0.153159	0.0765794	−	0.997063i	$-0.475600\pi$
$263$	653.244	0.153159	0.0765794	+	0.997063i	$0.475600\pi$
$264$	−1016.91	−0.237071
$265$	406.471	0.0942238
$266$	−342.196	−0.0788774
$267$	3879.52	0.889224
$268$	139.718	0.0318456
$269$	4101.11	0.929551	0.464775	−	0.885429i	$-0.346135\pi$
$269$	4101.11	0.929551	0.464775	+	0.885429i	$0.346135\pi$
$270$	138.259	0.0311636
$271$	−3515.84	−0.788089	−0.394044	−	0.919091i	$-0.628924\pi$
$271$	−3515.84	−0.788089	−0.394044	+	0.919091i	$0.628924\pi$
$272$	3515.94	0.783768
$273$	−216.375	−0.0479693
$274$	6830.81	1.50607
$275$	1666.23	0.365372
$276$	−187.933	−0.0409864
$277$	−5068.18	−1.09934	−0.549671	−	0.835381i	$-0.685247\pi$
$277$	−5068.18	−1.09934	−0.549671	+	0.835381i	$0.685247\pi$
$278$	−3280.54	−0.707747
$279$	−3012.44	−0.646417
$280$	147.140	0.0314047
$281$	−1083.01	−0.229917	−0.114959	−	0.993370i	$-0.536674\pi$
$281$	−1083.01	−0.229917	−0.114959	+	0.993370i	$0.536674\pi$
$282$	1223.17	0.258294
$283$	1071.09	0.224981	0.112490	−	0.993653i	$-0.464117\pi$
$283$	1071.09	0.224981	0.112490	+	0.993653i	$0.464117\pi$
$284$	−1585.66	−0.331308
$285$	311.951	0.0648365
$286$	850.840	0.175913
$287$	−247.135	−0.0508289
$288$	−825.489	−0.168897
$289$	1782.44	0.362801
$290$	966.578	0.195722
$291$	−301.962	−0.0608293
$292$	−1795.39	−0.359819
$293$	−855.519	−0.170580	−0.0852900	−	0.996356i	$-0.527182\pi$
$293$	−855.519	−0.170580	−0.0852900	+	0.996356i	$0.527182\pi$
$294$	2443.31	0.484683
$295$	708.535	0.139839
$296$	−8503.85	−1.66985
$297$	−373.139	−0.0729014
$298$	−2670.01	−0.519025
$299$	760.468	0.147087
$300$	754.269	0.145159
$301$	625.001	0.119683
$302$	2200.22	0.419233
$303$	2953.56	0.559991
$304$	2122.03	0.400351
$305$	545.032	0.102323
$306$	1791.01	0.334591
$307$	7566.90	1.40673	0.703364	−	0.710830i	$-0.251680\pi$
$307$	7566.90	1.40673	0.703364	+	0.710830i	$0.251680\pi$
$308$	−82.1098	−0.0151904
$309$	2562.78	0.471817
$310$	−1713.98	−0.314025
$311$	−6355.53	−1.15881	−0.579404	−	0.815041i	$-0.696715\pi$
$311$	−6355.53	−1.15881	−0.579404	+	0.815041i	$0.696715\pi$
$312$	1862.74	0.338003
$313$	4665.59	0.842539	0.421270	−	0.906935i	$-0.361585\pi$
$313$	4665.59	0.842539	0.421270	+	0.906935i	$0.361585\pi$
$314$	−602.430	−0.108271
$315$	53.9906	0.00965722
$316$	−729.590	−0.129882
$317$	−1879.63	−0.333029	−0.166515	−	0.986039i	$-0.553251\pi$
$317$	−1879.63	−0.333029	−0.166515	+	0.986039i	$0.553251\pi$
$318$	1408.48	0.248376
$319$	−2608.64	−0.457855
$320$	−1193.46	−0.208488
$321$	3463.91	0.602295
$322$	208.152	0.0360244
$323$	4041.01	0.696123
$324$	−168.913	−0.0289631
$325$	−3052.13	−0.520929
$326$	−2265.48	−0.384887
$327$	−4149.22	−0.701690
$328$	2127.55	0.358153
$329$	477.652	0.0800420
$330$	−212.304	−0.0354150
$331$	−4333.88	−0.719673	−0.359837	−	0.933015i	$-0.617168\pi$
$331$	−4333.88	−0.719673	−0.359837	+	0.933015i	$0.617168\pi$
$332$	1753.49	0.289865
$333$	−3120.34	−0.513495
$334$	889.693	0.145754
$335$	141.072	0.0230077
$336$	367.268	0.0596312
$337$	5261.38	0.850463	0.425231	−	0.905085i	$-0.360193\pi$
$337$	5261.38	0.850463	0.425231	+	0.905085i	$0.360193\pi$
$338$	3784.58	0.609036
$339$	−540.187	−0.0865456
$340$	−359.280	−0.0573078
$341$	4625.76	0.734601
$342$	1080.95	0.170910
$343$	1931.37	0.304035
$344$	−5380.54	−0.843312
$345$	−189.754	−0.0296117
$346$	9162.04	1.42357
$347$	4051.14	0.626734	0.313367	−	0.949632i	$-0.398543\pi$
$347$	4051.14	0.626734	0.313367	+	0.949632i	$0.398543\pi$
$348$	−1180.88	−0.181902
$349$	−4526.85	−0.694318	−0.347159	−	0.937806i	$-0.612854\pi$
$349$	−4526.85	−0.694318	−0.347159	+	0.937806i	$0.612854\pi$
$350$	−835.415	−0.127585
$351$	683.502	0.103939
$352$	1267.58	0.191938
$353$	5946.12	0.896544	0.448272	−	0.893897i	$-0.352040\pi$
$353$	5946.12	0.896544	0.448272	+	0.893897i	$0.352040\pi$
$354$	2455.17	0.368619
$355$	−1601.02	−0.239362
$356$	−2696.71	−0.401476
$357$	699.393	0.103686
$358$	3202.05	0.472719
$359$	3165.15	0.465320	0.232660	−	0.972558i	$-0.425257\pi$
$359$	3165.15	0.465320	0.232660	+	0.972558i	$0.425257\pi$
$360$	−464.797	−0.0680471
$361$	−4420.06	−0.644418
$362$	−5041.90	−0.732034
$363$	−3420.03	−0.494504
$364$	150.406	0.0216577
$365$	−1812.78	−0.259960
$366$	1888.61	0.269725
$367$	−4705.81	−0.669322	−0.334661	−	0.942339i	$-0.608622\pi$
$367$	−4705.81	−0.669322	−0.334661	+	0.942339i	$0.608622\pi$
$368$	−1290.79	−0.182846
$369$	780.667	0.110135
$370$	−1775.37	−0.249452
$371$	550.015	0.0769686
$372$	2093.99	0.291851
$373$	7259.50	1.00773	0.503864	−	0.863783i	$-0.331911\pi$
$373$	7259.50	1.00773	0.503864	+	0.863783i	$0.331911\pi$
$374$	−2750.18	−0.380237
$375$	1551.16	0.213604
$376$	−4112.04	−0.563995
$377$	4778.40	0.652786
$378$	187.085	0.0254566
$379$	6590.72	0.893252	0.446626	−	0.894721i	$-0.352626\pi$
$379$	6590.72	0.893252	0.446626	+	0.894721i	$0.352626\pi$
$380$	−216.842	−0.0292730
$381$	644.976	0.0867274
$382$	−7725.03	−1.03468
$383$	−5874.94	−0.783801	−0.391900	−	0.920008i	$-0.628182\pi$
$383$	−5874.94	−0.783801	−0.391900	+	0.920008i	$0.628182\pi$
$384$	−1934.19	−0.257041
$385$	−82.9054	−0.0109747
$386$	−6690.95	−0.882280
$387$	−1974.30	−0.259326
$388$	209.898	0.0274638
$389$	2578.42	0.336069	0.168035	−	0.985781i	$-0.446258\pi$
$389$	2578.42	0.336069	0.168035	+	0.985781i	$0.446258\pi$
$390$	388.891	0.0504929
$391$	−2458.07	−0.317929
$392$	−8213.87	−1.05832
$393$	−4516.48	−0.579711
$394$	−6684.88	−0.854770
$395$	−736.660	−0.0938364
$396$	259.374	0.0329143
$397$	8393.97	1.06116	0.530581	−	0.847634i	$-0.321974\pi$
$397$	8393.97	1.06116	0.530581	+	0.847634i	$0.321974\pi$
$398$	−3397.55	−0.427899
$399$	422.116	0.0529630
$400$	5180.58	0.647573
$401$	4721.44	0.587974	0.293987	−	0.955809i	$-0.405018\pi$
$401$	4721.44	0.587974	0.293987	+	0.955809i	$0.405018\pi$
$402$	488.833	0.0606487
$403$	−8473.30	−1.04736
$404$	−2053.06	−0.252830
$405$	−170.549	−0.0209251
$406$	1307.92	0.159879
$407$	4791.45	0.583546
$408$	−6020.97	−0.730594
$409$	6954.83	0.840817	0.420409	−	0.907335i	$-0.361887\pi$
$409$	6954.83	0.840817	0.420409	+	0.907335i	$0.361887\pi$
$410$	444.174	0.0535029
$411$	−8426.13	−1.01127
$412$	−1781.43	−0.213021
$413$	958.753	0.114230
$414$	−657.525	−0.0780570
$415$	1770.48	0.209420
$416$	−2321.91	−0.273656
$417$	4046.71	0.475223
$418$	−1659.86	−0.194226
$419$	−10378.5	−1.21007	−0.605037	−	0.796197i	$-0.706842\pi$
$419$	−10378.5	−1.21007	−0.605037	+	0.796197i	$0.706842\pi$
$420$	−37.5296	−0.00436014
$421$	−4401.61	−0.509552	−0.254776	−	0.967000i	$-0.582002\pi$
$421$	−4401.61	−0.509552	−0.254776	+	0.967000i	$0.582002\pi$
$422$	11192.6	1.29111
$423$	−1508.84	−0.173434
$424$	−4734.99	−0.542339
$425$	9865.45	1.12599
$426$	−5547.77	−0.630963
$427$	737.508	0.0835844
$428$	−2407.82	−0.271930
$429$	−1049.55	−0.118119
$430$	−1123.31	−0.125979
$431$	−4859.24	−0.543066	−0.271533	−	0.962429i	$-0.587531\pi$
$431$	−4859.24	−0.543066	−0.271533	+	0.962429i	$0.587531\pi$
$432$	−1160.15	−0.129208
$433$	535.903	0.0594777	0.0297389	−	0.999558i	$-0.490532\pi$
$433$	535.903	0.0594777	0.0297389	+	0.999558i	$0.490532\pi$
$434$	−2319.27	−0.256517
$435$	−1192.32	−0.131419
$436$	2884.18	0.316806
$437$	−1483.56	−0.162399
$438$	−6281.55	−0.685260
$439$	−5126.15	−0.557307	−0.278654	−	0.960392i	$-0.589888\pi$
$439$	−5126.15	−0.557307	−0.278654	+	0.960392i	$0.589888\pi$
$440$	713.720	0.0773301
$441$	−3013.94	−0.325445
$442$	5037.68	0.542122
$443$	2784.23	0.298606	0.149303	−	0.988791i	$-0.452297\pi$
$443$	2784.23	0.298606	0.149303	+	0.988791i	$0.452297\pi$
$444$	2169.00	0.231838
$445$	−2722.84	−0.290056
$446$	11345.0	1.20449
$447$	3293.58	0.348504
$448$	−1614.92	−0.170308
$449$	6749.31	0.709397	0.354699	−	0.934981i	$-0.384583\pi$
$449$	6749.31	0.709397	0.354699	+	0.934981i	$0.384583\pi$
$450$	2638.97	0.276449
$451$	−1198.75	−0.125160
$452$	375.492	0.0390744
$453$	−2714.08	−0.281498
$454$	−4499.10	−0.465095
$455$	151.863	0.0156471
$456$	−3633.93	−0.373190
$457$	5432.45	0.556060	0.278030	−	0.960572i	$-0.410319\pi$
$457$	5432.45	0.556060	0.278030	+	0.960572i	$0.410319\pi$
$458$	−47.6338	−0.00485979
$459$	−2209.29	−0.224664
$460$	131.901	0.0133694
$461$	−2899.81	−0.292967	−0.146484	−	0.989213i	$-0.546796\pi$
$461$	−2899.81	−0.292967	−0.146484	+	0.989213i	$0.546796\pi$
$462$	−287.279	−0.0289295
$463$	−13589.3	−1.36404	−0.682018	−	0.731336i	$-0.738897\pi$
$463$	−13589.3	−1.36404	−0.682018	+	0.731336i	$0.738897\pi$
$464$	−8110.69	−0.811486
$465$	2114.28	0.210855
$466$	−2943.89	−0.292646
$467$	8272.71	0.819733	0.409867	−	0.912145i	$-0.365575\pi$
$467$	8272.71	0.819733	0.409867	+	0.912145i	$0.365575\pi$
$468$	−475.112	−0.0469275
$469$	190.891	0.0187943
$470$	−858.483	−0.0842529
$471$	743.127	0.0726995
$472$	−8253.76	−0.804894
$473$	3031.64	0.294704
$474$	−2552.63	−0.247355
$475$	5954.25	0.575158
$476$	−486.158	−0.0468131
$477$	−1737.43	−0.166774
$478$	16678.4	1.59593
$479$	−16933.7	−1.61528	−0.807642	−	0.589673i	$-0.799257\pi$
$479$	−16933.7	−1.61528	−0.807642	+	0.589673i	$0.799257\pi$
$480$	579.369	0.0550927
$481$	−8776.79	−0.831990
$482$	−14263.6	−1.34791
$483$	−256.765	−0.0241889
$484$	2377.31	0.223263
$485$	211.932	0.0198419
$486$	−590.978	−0.0551590
$487$	14256.9	1.32658	0.663288	−	0.748364i	$-0.269160\pi$
$487$	14256.9	1.32658	0.663288	+	0.748364i	$0.269160\pi$
$488$	−6349.10	−0.588955
$489$	2794.58	0.258436
$490$	−1714.84	−0.158099
$491$	−15222.4	−1.39914	−0.699570	−	0.714564i	$-0.746625\pi$
$491$	−15222.4	−1.39914	−0.699570	+	0.714564i	$0.746625\pi$
$492$	−542.653	−0.0497250
$493$	−15445.3	−1.41100
$494$	3040.47	0.276918
$495$	261.888	0.0237797
$496$	14382.3	1.30198
$497$	−2166.42	−0.195528
$498$	6134.96	0.552037
$499$	3844.98	0.344940	0.172470	−	0.985015i	$-0.444825\pi$
$499$	3844.98	0.344940	0.172470	+	0.985015i	$0.444825\pi$
$500$	−1078.23	−0.0964400
$501$	−1097.48	−0.0978678
$502$	8246.04	0.733145
$503$	8313.96	0.736980	0.368490	−	0.929632i	$-0.379875\pi$
$503$	8313.96	0.736980	0.368490	+	0.929632i	$0.379875\pi$
$504$	−628.939	−0.0555856
$505$	−2072.95	−0.182664
$506$	1009.66	0.0887056
$507$	−4668.47	−0.408943
$508$	−448.332	−0.0391565
$509$	9265.13	0.806817	0.403408	−	0.915020i	$-0.367825\pi$
$509$	9265.13	0.806817	0.403408	+	0.915020i	$0.367825\pi$
$510$	−1257.02	−0.109140
$511$	−2452.96	−0.212354
$512$	12372.5	1.06795
$513$	−1333.41	−0.114759
$514$	−10742.9	−0.921886
$515$	−1798.69	−0.153902
$516$	1372.36	0.117083
$517$	2316.91	0.197094
$518$	−2402.34	−0.203770
$519$	−11301.8	−0.955867
$520$	−1307.36	−0.110253
$521$	20086.1	1.68903	0.844516	−	0.535530i	$-0.179888\pi$
$521$	20086.1	1.68903	0.844516	+	0.535530i	$0.179888\pi$
$522$	−4131.56	−0.346424
$523$	−1546.65	−0.129313	−0.0646563	−	0.997908i	$-0.520595\pi$
$523$	−1546.65	−0.129313	−0.0646563	+	0.997908i	$0.520595\pi$
$524$	3139.47	0.261733
$525$	1030.53	0.0856682
$526$	−1588.69	−0.131693
$527$	27388.4	2.26386
$528$	1781.47	0.146835
$529$	−11264.6	−0.925830
$530$	−988.539	−0.0810178
$531$	−3028.58	−0.247512
$532$	−293.419	−0.0239123
$533$	2195.83	0.178447
$534$	−9435.02	−0.764594
$535$	−2431.15	−0.196463
$536$	−1643.35	−0.132429
$537$	−3949.88	−0.317412
$538$	−9973.93	−0.799269
$539$	4628.07	0.369842
$540$	118.551	0.00944748
$541$	−9773.42	−0.776695	−0.388348	−	0.921513i	$-0.626954\pi$
$541$	−9773.42	−0.776695	−0.388348	+	0.921513i	$0.626954\pi$
$542$	8550.54	0.677633
$543$	6219.43	0.491531
$544$	7505.14	0.591508
$545$	2912.13	0.228884
$546$	526.226	0.0412462
$547$	5096.50	0.398374	0.199187	−	0.979961i	$-0.436170\pi$
$547$	5096.50	0.398374	0.199187	+	0.979961i	$0.436170\pi$
$548$	5857.13	0.456577
$549$	−2329.70	−0.181109
$550$	−4052.28	−0.314163
$551$	−9321.95	−0.720741
$552$	2210.46	0.170441
$553$	−996.809	−0.0766521
$554$	12325.9	0.945262
$555$	2190.01	0.167497
$556$	−2812.92	−0.214558
$557$	23231.5	1.76724	0.883619	−	0.468207i	$-0.155100\pi$
$557$	23231.5	1.76724	0.883619	+	0.468207i	$0.155100\pi$
$558$	7326.28	0.555818
$559$	−5553.24	−0.420174
$560$	−257.767	−0.0194511
$561$	3392.48	0.255313
$562$	2633.88	0.197693
$563$	−12586.7	−0.942212	−0.471106	−	0.882077i	$-0.656145\pi$
$563$	−12586.7	−0.942212	−0.471106	+	0.882077i	$0.656145\pi$
$564$	1048.82	0.0783036
$565$	379.130	0.0282303
$566$	−2604.89	−0.193448
$567$	−230.779	−0.0170931
$568$	18650.4	1.37773
$569$	11410.6	0.840698	0.420349	−	0.907363i	$-0.361908\pi$
$569$	11410.6	0.840698	0.420349	+	0.907363i	$0.361908\pi$
$570$	−758.668	−0.0557493
$571$	−10566.7	−0.774438	−0.387219	−	0.921988i	$-0.626564\pi$
$571$	−10566.7	−0.774438	−0.387219	+	0.921988i	$0.626564\pi$
$572$	729.559	0.0533294
$573$	9529.20	0.694743
$574$	601.033	0.0437049
$575$	−3621.87	−0.262682
$576$	5101.34	0.369020
$577$	−27135.0	−1.95779	−0.978896	−	0.204358i	$-0.934489\pi$
$577$	−27135.0	−1.95779	−0.978896	+	0.204358i	$0.934489\pi$
$578$	−4334.91	−0.311953
$579$	8253.61	0.592415
$580$	828.800	0.0593345
$581$	2395.72	0.171069
$582$	734.373	0.0523037
$583$	2667.91	0.189526
$584$	21117.2	1.49629
$585$	−479.716	−0.0339039
$586$	2080.63	0.146672
$587$	18740.9	1.31775	0.658877	−	0.752251i	$-0.271032\pi$
$587$	18740.9	1.31775	0.658877	+	0.752251i	$0.271032\pi$
$588$	2095.03	0.146935
$589$	16530.1	1.15639
$590$	−1723.16	−0.120240
$591$	8246.13	0.573943
$592$	14897.4	1.03426
$593$	−22396.7	−1.55097	−0.775483	−	0.631368i	$-0.782494\pi$
$593$	−22396.7	−1.55097	−0.775483	+	0.631368i	$0.782494\pi$
$594$	907.477	0.0626839
$595$	−490.869	−0.0338213
$596$	−2289.42	−0.157346
$597$	4191.05	0.287317
$598$	−1849.46	−0.126472
$599$	−11477.8	−0.782920	−0.391460	−	0.920195i	$-0.628030\pi$
$599$	−11477.8	−0.782920	−0.391460	+	0.920195i	$0.628030\pi$
$600$	−8871.64	−0.603639
$601$	14883.4	1.01016	0.505080	−	0.863073i	$-0.331463\pi$
$601$	14883.4	1.01016	0.505080	+	0.863073i	$0.331463\pi$
$602$	−1520.01	−0.102908
$603$	−603.000	−0.0407231
$604$	1886.59	0.127093
$605$	2400.34	0.161302
$606$	−7183.07	−0.481505
$607$	−5155.69	−0.344750	−0.172375	−	0.985031i	$-0.555144\pi$
$607$	−5155.69	−0.344750	−0.172375	+	0.985031i	$0.555144\pi$
$608$	4529.70	0.302144
$609$	−1613.39	−0.107353
$610$	−1325.52	−0.0879816
$611$	−4244.02	−0.281006
$612$	1535.71	0.101434
$613$	17546.5	1.15611	0.578054	−	0.815998i	$-0.303812\pi$
$613$	17546.5	1.15611	0.578054	+	0.815998i	$0.303812\pi$
$614$	−18402.7	−1.20957
$615$	−547.911	−0.0359250
$616$	965.768	0.0631687
$617$	22890.4	1.49357	0.746784	−	0.665067i	$-0.231597\pi$
$617$	22890.4	1.49357	0.746784	+	0.665067i	$0.231597\pi$
$618$	−6232.70	−0.405690
$619$	−27500.9	−1.78571	−0.892854	−	0.450346i	$-0.851301\pi$
$619$	−27500.9	−1.78571	−0.892854	+	0.450346i	$0.851301\pi$
$620$	−1469.67	−0.0951988
$621$	811.090	0.0524121
$622$	15456.7	0.996394
$623$	−3684.40	−0.236938
$624$	−3263.24	−0.209349
$625$	13982.2	0.894858
$626$	−11346.8	−0.724453
$627$	2047.52	0.130415
$628$	−516.558	−0.0328231
$629$	28369.4	1.79835
$630$	−131.306	−0.00830371
$631$	−28437.9	−1.79413	−0.897064	−	0.441900i	$-0.854305\pi$
$631$	−28437.9	−1.79413	−0.897064	+	0.441900i	$0.854305\pi$
$632$	8581.38	0.540109
$633$	−13806.6	−0.866927
$634$	4571.26	0.286353
$635$	−452.676	−0.0282896
$636$	1207.71	0.0752969
$637$	−8477.51	−0.527302
$638$	6344.22	0.393684
$639$	6843.44	0.423666
$640$	1357.51	0.0838442
$641$	19284.9	1.18831	0.594157	−	0.804349i	$-0.297486\pi$
$641$	19284.9	1.18831	0.594157	+	0.804349i	$0.297486\pi$
$642$	−8424.26	−0.517880
$643$	17966.1	1.10188	0.550942	−	0.834543i	$-0.314268\pi$
$643$	17966.1	1.10188	0.550942	+	0.834543i	$0.314268\pi$
$644$	178.481	0.0109210
$645$	1385.66	0.0845897
$646$	−9827.76	−0.598557
$647$	−18972.5	−1.15284	−0.576420	−	0.817153i	$-0.695551\pi$
$647$	−18972.5	−1.15284	−0.576420	+	0.817153i	$0.695551\pi$
$648$	1986.74	0.120442
$649$	4650.54	0.281278
$650$	7422.81	0.447918
$651$	2860.93	0.172241
$652$	−1942.55	−0.116681
$653$	12144.5	0.727794	0.363897	−	0.931439i	$-0.381446\pi$
$653$	12144.5	0.727794	0.363897	+	0.931439i	$0.381446\pi$
$654$	10090.9	0.603344
$655$	3169.89	0.189096
$656$	−3727.13	−0.221829
$657$	7748.60	0.460124
$658$	−1161.65	−0.0688237
$659$	12581.5	0.743712	0.371856	−	0.928290i	$-0.378721\pi$
$659$	12581.5	0.743712	0.371856	+	0.928290i	$0.378721\pi$
$660$	−182.042	−0.0107363
$661$	17013.1	1.00111	0.500554	−	0.865705i	$-0.333130\pi$
$661$	17013.1	1.00111	0.500554	+	0.865705i	$0.333130\pi$
$662$	10540.0	0.618807
$663$	−6214.23	−0.364013
$664$	−20624.4	−1.20539
$665$	−296.262	−0.0172760
$666$	7588.70	0.441526
$667$	5670.37	0.329172
$668$	762.874	0.0441863
$669$	−13994.6	−0.808762
$670$	−343.088	−0.0197830
$671$	3577.37	0.205816
$672$	783.972	0.0450035
$673$	10588.6	0.606478	0.303239	−	0.952914i	$-0.401932\pi$
$673$	10588.6	0.606478	0.303239	+	0.952914i	$0.401932\pi$
$674$	−12795.7	−0.731265
$675$	−3255.30	−0.185625
$676$	3245.12	0.184634
$677$	−24950.5	−1.41644	−0.708218	−	0.705994i	$-0.750501\pi$
$677$	−24950.5	−1.41644	−0.708218	+	0.705994i	$0.750501\pi$
$678$	1313.74	0.0744157
$679$	286.775	0.0162083
$680$	4225.81	0.238313
$681$	5549.86	0.312292
$682$	−11249.9	−0.631643
$683$	−8896.36	−0.498404	−0.249202	−	0.968452i	$-0.580168\pi$
$683$	−8896.36	−0.498404	−0.249202	+	0.968452i	$0.580168\pi$
$684$	926.873	0.0518127
$685$	5913.88	0.329865
$686$	−4697.10	−0.261423
$687$	58.7586	0.00326315
$688$	9425.87	0.522323
$689$	−4886.97	−0.270216
$690$	461.484	0.0254614
$691$	−23204.2	−1.27747	−0.638733	−	0.769428i	$-0.720541\pi$
$691$	−23204.2	−1.27747	−0.638733	+	0.769428i	$0.720541\pi$
$692$	7856.06	0.431565
$693$	354.372	0.0194250
$694$	−9852.40	−0.538893
$695$	−2840.18	−0.155013
$696$	13889.4	0.756431
$697$	−7097.62	−0.385713
$698$	11009.3	0.597005
$699$	3631.43	0.196500
$700$	−716.333	−0.0386784
$701$	178.940	0.00964116	0.00482058	−	0.999988i	$-0.498466\pi$
$701$	178.940	0.00964116	0.00482058	+	0.999988i	$0.498466\pi$
$702$	−1662.28	−0.0893715
$703$	17122.2	0.918601
$704$	−7833.36	−0.419362
$705$	1058.98	0.0565724
$706$	−14461.0	−0.770888
$707$	−2805.01	−0.149212
$708$	2105.21	0.111749
$709$	−28438.9	−1.50641	−0.753206	−	0.657784i	$-0.771494\pi$
$709$	−28438.9	−1.50641	−0.753206	+	0.657784i	$0.771494\pi$
$710$	3893.70	0.205814
$711$	3148.79	0.166089
$712$	31718.5	1.66952
$713$	−10055.0	−0.528138
$714$	−1700.93	−0.0891536
$715$	736.628	0.0385291
$716$	2745.62	0.143308
$717$	−20573.7	−1.07160
$718$	−7697.66	−0.400103
$719$	−15649.3	−0.811713	−0.405857	−	0.913937i	$-0.633027\pi$
$719$	−15649.3	−0.811713	−0.405857	+	0.913937i	$0.633027\pi$
$720$	814.252	0.0421464
$721$	−2433.89	−0.125718
$722$	10749.6	0.554099
$723$	17594.9	0.905065
$724$	−4323.22	−0.221921
$725$	−22758.0	−1.16581
$726$	8317.53	0.425196
$727$	−29007.5	−1.47982	−0.739909	−	0.672707i	$-0.765132\pi$
$727$	−29007.5	−1.47982	−0.739909	+	0.672707i	$0.765132\pi$
$728$	−1769.06	−0.0900627
$729$	729.000	0.0370370
$730$	4408.70	0.223525
$731$	17949.8	0.908205
$732$	1619.40	0.0817690
$733$	−23566.8	−1.18753	−0.593765	−	0.804638i	$-0.702359\pi$
$733$	−23566.8	−1.18753	−0.593765	+	0.804638i	$0.702359\pi$
$734$	11444.6	0.575512
$735$	2115.33	0.106157
$736$	−2755.33	−0.137993
$737$	925.938	0.0462786
$738$	−1898.59	−0.0946991
$739$	−13583.7	−0.676165	−0.338082	−	0.941117i	$-0.609778\pi$
$739$	−13583.7	−0.676165	−0.338082	+	0.941117i	$0.609778\pi$
$740$	−1522.31	−0.0756232
$741$	−3750.57	−0.185939
$742$	−1337.64	−0.0661810
$743$	−32667.8	−1.61301	−0.806504	−	0.591229i	$-0.798643\pi$
$743$	−32667.8	−1.61301	−0.806504	+	0.591229i	$0.798643\pi$
$744$	−24629.4	−1.21365
$745$	−2311.60	−0.113679
$746$	−17655.1	−0.866489
$747$	−7567.78	−0.370670
$748$	−2358.16	−0.115271
$749$	−3289.70	−0.160485
$750$	−3772.43	−0.183666
$751$	−10002.8	−0.486030	−0.243015	−	0.970023i	$-0.578136\pi$
$751$	−10002.8	−0.486030	−0.243015	+	0.970023i	$0.578136\pi$
$752$	7203.65	0.349322
$753$	−10171.9	−0.492277
$754$	−11621.1	−0.561294
$755$	1904.87	0.0918217
$756$	160.417	0.00771736
$757$	21376.4	1.02634	0.513171	−	0.858287i	$-0.328471\pi$
$757$	21376.4	1.02634	0.513171	+	0.858287i	$0.328471\pi$
$758$	−16028.7	−0.768057
$759$	−1245.47	−0.0595622
$760$	2550.47	0.121731
$761$	−32623.0	−1.55399	−0.776993	−	0.629509i	$-0.783256\pi$
$761$	−32623.0	−1.55399	−0.776993	+	0.629509i	$0.783256\pi$
$762$	−1568.59	−0.0745720
$763$	3940.54	0.186969
$764$	−6623.88	−0.313670
$765$	1550.59	0.0732834
$766$	14287.9	0.673946
$767$	−8518.68	−0.401032
$768$	−8899.60	−0.418147
$769$	−33104.7	−1.55239	−0.776193	−	0.630495i	$-0.782852\pi$
$769$	−33104.7	−1.55239	−0.776193	+	0.630495i	$0.782852\pi$
$770$	201.626	0.00943651
$771$	13251.9	0.619009
$772$	−5737.20	−0.267469
$773$	−4986.94	−0.232041	−0.116020	−	0.993247i	$-0.537014\pi$
$773$	−4986.94	−0.232041	−0.116020	+	0.993247i	$0.537014\pi$
$774$	4801.51	0.222980
$775$	40355.6	1.87047
$776$	−2468.80	−0.114207
$777$	2963.41	0.136823
$778$	−6270.72	−0.288967
$779$	−4283.74	−0.197023
$780$	333.457	0.0153073
$781$	−10508.5	−0.481463
$782$	5978.05	0.273369
$783$	5096.48	0.232610
$784$	14389.4	0.655495
$785$	−521.563	−0.0237139
$786$	10984.1	0.498461
$787$	14870.1	0.673523	0.336762	−	0.941590i	$-0.390668\pi$
$787$	14870.1	0.673523	0.336762	+	0.941590i	$0.390668\pi$
$788$	−5732.00	−0.259130
$789$	1959.73	0.0884262
$790$	1791.56	0.0806847
$791$	513.019	0.0230605
$792$	−3050.74	−0.136873
$793$	−6552.89	−0.293442
$794$	−20414.2	−0.912434
$795$	1219.41	0.0544001
$796$	−2913.26	−0.129721
$797$	−30940.0	−1.37510	−0.687549	−	0.726138i	$-0.741313\pi$
$797$	−30940.0	−1.37510	−0.687549	+	0.726138i	$0.741313\pi$
$798$	−1026.59	−0.0455399
$799$	13718.0	0.607395
$800$	11058.5	0.488721
$801$	11638.6	0.513394
$802$	−11482.6	−0.505566
$803$	−11898.4	−0.522895
$804$	419.154	0.0183861
$805$	180.211	0.00789018
$806$	20607.1	0.900564
$807$	12303.3	0.536676
$808$	24147.9	1.05139
$809$	−28896.9	−1.25582	−0.627912	−	0.778284i	$-0.716090\pi$
$809$	−28896.9	−1.25582	−0.627912	+	0.778284i	$0.716090\pi$
$810$	414.777	0.0179923
$811$	−10438.7	−0.451977	−0.225988	−	0.974130i	$-0.572561\pi$
$811$	−10438.7	−0.451977	−0.225988	+	0.974130i	$0.572561\pi$
$812$	1121.49	0.0484686
$813$	−10547.5	−0.455003
$814$	−11652.8	−0.501759
$815$	−1961.37	−0.0842992
$816$	10547.8	0.452509
$817$	10833.5	0.463914
$818$	−16914.2	−0.722972
$819$	−649.126	−0.0276951
$820$	380.861	0.0162198
$821$	−30590.1	−1.30037	−0.650184	−	0.759777i	$-0.725308\pi$
$821$	−30590.1	−1.30037	−0.650184	+	0.759777i	$0.725308\pi$
$822$	20492.4	0.869532
$823$	−18522.4	−0.784508	−0.392254	−	0.919857i	$-0.628305\pi$
$823$	−18522.4	−0.784508	−0.392254	+	0.919857i	$0.628305\pi$
$824$	20953.0	0.885840
$825$	4998.68	0.210948
$826$	−2331.69	−0.0982203
$827$	−7517.74	−0.316103	−0.158052	−	0.987431i	$-0.550521\pi$
$827$	−7517.74	−0.316103	−0.158052	+	0.987431i	$0.550521\pi$
$828$	−563.800	−0.0236635
$829$	−17951.4	−0.752085	−0.376043	−	0.926602i	$-0.622715\pi$
$829$	−17951.4	−0.752085	−0.376043	+	0.926602i	$0.622715\pi$
$830$	−4305.82	−0.180069
$831$	−15204.5	−0.634705
$832$	14348.9	0.597905
$833$	27402.0	1.13976
$834$	−9841.62	−0.408618
$835$	770.266	0.0319235
$836$	−1423.26	−0.0588810
$837$	−9037.33	−0.373209
$838$	25240.5	1.04047
$839$	12119.4	0.498699	0.249349	−	0.968414i	$-0.419783\pi$
$839$	12119.4	0.498699	0.249349	+	0.968414i	$0.419783\pi$
$840$	441.420	0.0181315
$841$	11240.8	0.460896
$842$	10704.7	0.438135
$843$	−3249.02	−0.132743
$844$	9597.19	0.391409
$845$	3276.56	0.133393
$846$	3669.52	0.149126
$847$	3248.02	0.131763
$848$	8294.98	0.335909
$849$	3213.26	0.129893
$850$	−23992.8	−0.968174
$851$	−10415.1	−0.419537
$852$	−4756.98	−0.191281
$853$	1851.39	0.0743146	0.0371573	−	0.999309i	$-0.488170\pi$
$853$	1851.39	0.0743146	0.0371573	+	0.999309i	$0.488170\pi$
$854$	−1793.63	−0.0718696
$855$	935.854	0.0374334
$856$	28320.5	1.13081
$857$	36115.1	1.43952	0.719760	−	0.694223i	$-0.244252\pi$
$857$	36115.1	1.43952	0.719760	+	0.694223i	$0.244252\pi$
$858$	2552.52	0.101564
$859$	24606.8	0.977384	0.488692	−	0.872456i	$-0.337474\pi$
$859$	24606.8	0.977384	0.488692	+	0.872456i	$0.337474\pi$
$860$	−963.193	−0.0381914
$861$	−741.404	−0.0293461
$862$	11817.7	0.466952
$863$	−20266.6	−0.799400	−0.399700	−	0.916646i	$-0.630886\pi$
$863$	−20266.6	−0.799400	−0.399700	+	0.916646i	$0.630886\pi$
$864$	−2476.47	−0.0975129
$865$	7932.18	0.311795
$866$	−1303.32	−0.0511416
$867$	5347.33	0.209464
$868$	−1988.68	−0.0777651
$869$	−4835.13	−0.188747
$870$	2899.73	0.113000
$871$	−1696.10	−0.0659817
$872$	−33923.5	−1.31743
$873$	−905.886	−0.0351198
$874$	3608.03	0.139638
$875$	−1473.14	−0.0569158
$876$	−5386.16	−0.207742
$877$	37608.7	1.44807	0.724033	−	0.689765i	$-0.242286\pi$
$877$	37608.7	1.44807	0.724033	+	0.689765i	$0.242286\pi$
$878$	12466.8	0.479197
$879$	−2566.56	−0.0984844
$880$	−1250.33	−0.0478960
$881$	−1203.30	−0.0460162	−0.0230081	−	0.999735i	$-0.507324\pi$
$881$	−1203.30	−0.0460162	−0.0230081	+	0.999735i	$0.507324\pi$
$882$	7329.93	0.279832
$883$	33506.8	1.27700	0.638501	−	0.769621i	$-0.279555\pi$
$883$	33506.8	1.27700	0.638501	+	0.769621i	$0.279555\pi$
$884$	4319.60	0.164348
$885$	2125.61	0.0807361
$886$	−6771.26	−0.256755
$887$	−34490.4	−1.30561	−0.652803	−	0.757527i	$-0.726407\pi$
$887$	−34490.4	−1.30561	−0.652803	+	0.757527i	$0.726407\pi$
$888$	−25511.5	−0.964089
$889$	−612.537	−0.0231089
$890$	6621.97	0.249403
$891$	−1119.42	−0.0420897
$892$	9727.84	0.365148
$893$	8279.46	0.310259
$894$	−8010.02	−0.299659
$895$	2772.22	0.103537
$896$	1836.91	0.0684898
$897$	2281.40	0.0849207
$898$	−16414.4	−0.609971
$899$	−63180.5	−2.34392
$900$	2262.81	0.0838076
$901$	15796.2	0.584072
$902$	2915.38	0.107618
$903$	1875.00	0.0690988
$904$	−4416.50	−0.162490
$905$	−4365.10	−0.160333
$906$	6600.65	0.242044
$907$	−21858.3	−0.800212	−0.400106	−	0.916469i	$-0.631027\pi$
$907$	−21858.3	−0.800212	−0.400106	+	0.916469i	$0.631027\pi$
$908$	−3857.79	−0.140997
$909$	8860.67	0.323311
$910$	−369.332	−0.0134541
$911$	36936.9	1.34333	0.671666	−	0.740854i	$-0.265579\pi$
$911$	36936.9	1.34333	0.671666	+	0.740854i	$0.265579\pi$
$912$	6366.09	0.231143
$913$	11620.7	0.421237
$914$	−13211.8	−0.478125
$915$	1635.10	0.0590761
$916$	−40.8440	−0.00147328
$917$	4289.33	0.154467
$918$	5373.02	0.193176
$919$	22758.8	0.816915	0.408457	−	0.912777i	$-0.366067\pi$
$919$	22758.8	0.816915	0.408457	+	0.912777i	$0.366067\pi$
$920$	−1551.41	−0.0555961
$921$	22700.7	0.812175
$922$	7052.37	0.251906
$923$	19249.0	0.686445
$924$	−246.329	−0.00877017
$925$	41801.0	1.48585
$926$	33049.3	1.17286
$927$	7688.35	0.272404
$928$	−17313.1	−0.612426
$929$	−35511.5	−1.25414	−0.627070	−	0.778963i	$-0.715746\pi$
$929$	−35511.5	−1.25414	−0.627070	+	0.778963i	$0.715746\pi$
$930$	−5141.95	−0.181302
$931$	16538.4	0.582195
$932$	−2524.26	−0.0887176
$933$	−19066.6	−0.669038
$934$	−20119.3	−0.704843
$935$	−2381.01	−0.0832807
$936$	5588.23	0.195146
$937$	13473.1	0.469742	0.234871	−	0.972027i	$-0.424533\pi$
$937$	13473.1	0.469742	0.234871	+	0.972027i	$0.424533\pi$
$938$	−464.248	−0.0161602
$939$	13996.8	0.486440
$940$	−736.113	−0.0255419
$941$	−6827.90	−0.236539	−0.118269	−	0.992982i	$-0.537735\pi$
$941$	−6827.90	−0.236539	−0.118269	+	0.992982i	$0.537735\pi$
$942$	−1807.29	−0.0625103
$943$	2605.72	0.0899831
$944$	14459.3	0.498528
$945$	161.972	0.00557560
$946$	−7372.96	−0.253399
$947$	−22816.9	−0.782944	−0.391472	−	0.920190i	$-0.628034\pi$
$947$	−22816.9	−0.782944	−0.391472	+	0.920190i	$0.628034\pi$
$948$	−2188.77	−0.0749873
$949$	21795.0	0.745517
$950$	−14480.8	−0.494546
$951$	−5638.88	−0.192275
$952$	5718.15	0.194670
$953$	31393.2	1.06708	0.533539	−	0.845775i	$-0.320862\pi$
$953$	31393.2	1.06708	0.533539	+	0.845775i	$0.320862\pi$
$954$	4225.43	0.143400
$955$	−6688.06	−0.226619
$956$	14301.0	0.483817
$957$	−7825.91	−0.264343
$958$	41182.9	1.38889
$959$	8002.35	0.269457
$960$	−3580.37	−0.120371
$961$	82243.7	2.76069
$962$	21345.2	0.715382
$963$	10391.7	0.347735
$964$	−12230.5	−0.408628
$965$	−5792.79	−0.193240
$966$	624.455	0.0207987
$967$	−13951.7	−0.463966	−0.231983	−	0.972720i	$-0.574521\pi$
$967$	−13951.7	−0.463966	−0.231983	+	0.972720i	$0.574521\pi$
$968$	−27961.7	−0.928433
$969$	12123.0	0.401907
$970$	−515.420	−0.0170610
$971$	16788.7	0.554867	0.277434	−	0.960745i	$-0.410516\pi$
$971$	16788.7	0.554867	0.277434	+	0.960745i	$0.410516\pi$
$972$	−506.738	−0.0167219
$973$	−3843.18	−0.126626
$974$	−34672.9	−1.14065
$975$	−9156.40	−0.300758
$976$	11122.6	0.364782
$977$	−18457.3	−0.604403	−0.302201	−	0.953244i	$-0.597721\pi$
$977$	−18457.3	−0.604403	−0.302201	+	0.953244i	$0.597721\pi$
$978$	−6796.43	−0.222215
$979$	−17871.6	−0.583431
$980$	−1470.40	−0.0479288
$981$	−12447.7	−0.405121
$982$	37021.0	1.20304
$983$	14586.4	0.473279	0.236639	−	0.971598i	$-0.423954\pi$
$983$	14586.4	0.473279	0.236639	+	0.971598i	$0.423954\pi$
$984$	6382.64	0.206779
$985$	−5787.54	−0.187215
$986$	37563.1	1.21324
$987$	1432.96	0.0462123
$988$	2607.08	0.0839495
$989$	−6589.85	−0.211876
$990$	−636.912	−0.0204469
$991$	−3447.30	−0.110502	−0.0552508	−	0.998473i	$-0.517596\pi$
$991$	−3447.30	−0.110502	−0.0552508	+	0.998473i	$0.517596\pi$
$992$	30700.5	0.982602
$993$	−13001.7	−0.415504
$994$	5268.75	0.168123
$995$	−2941.48	−0.0937199
$996$	5260.47	0.167354
$997$	−27198.2	−0.863968	−0.431984	−	0.901881i	$-0.642186\pi$
$997$	−27198.2	−0.863968	−0.431984	+	0.901881i	$0.642186\pi$
$998$	−9351.02	−0.296594
$999$	−9361.03	−0.296466

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.b.1.3	✓	6
3.2	odd	2		603.4.a.b.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.b.1.3	✓	6	1.1	even	1	trivial
603.4.a.b.1.4		6	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)

\(f(q)\)	\(=\)	\(q-2.43201 q^{2} +3.00000 q^{3} -2.08534 q^{4} -2.10555 q^{5} -7.29602 q^{6} -2.84912 q^{7} +24.5276 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.43201 q^{2} +3.00000 q^{3} -2.08534 q^{4} -2.10555 q^{5} -7.29602 q^{6} -2.84912 q^{7} +24.5276 q^{8} +9.00000 q^{9} +5.12071 q^{10} -13.8200 q^{11} -6.25603 q^{12} +25.3149 q^{13} +6.92907 q^{14} -6.31665 q^{15} -42.9686 q^{16} -81.8257 q^{17} -21.8881 q^{18} -49.3856 q^{19} +4.39079 q^{20} -8.54735 q^{21} +33.6103 q^{22} +30.0404 q^{23} +73.5829 q^{24} -120.567 q^{25} -61.5660 q^{26} +27.0000 q^{27} +5.94139 q^{28} +188.759 q^{29} +15.3621 q^{30} -334.716 q^{31} -91.7211 q^{32} -41.4599 q^{33} +199.001 q^{34} +5.99896 q^{35} -18.7681 q^{36} -346.705 q^{37} +120.106 q^{38} +75.9447 q^{39} -51.6441 q^{40} +86.7408 q^{41} +20.7872 q^{42} -219.367 q^{43} +28.8194 q^{44} -18.9499 q^{45} -73.0583 q^{46} -167.649 q^{47} -128.906 q^{48} -334.883 q^{49} +293.219 q^{50} -245.477 q^{51} -52.7902 q^{52} -193.047 q^{53} -65.6642 q^{54} +29.0986 q^{55} -69.8821 q^{56} -148.157 q^{57} -459.062 q^{58} -336.509 q^{59} +13.1724 q^{60} -258.855 q^{61} +814.031 q^{62} -25.6421 q^{63} +566.815 q^{64} -53.3017 q^{65} +100.831 q^{66} -67.0000 q^{67} +170.635 q^{68} +90.1211 q^{69} -14.5895 q^{70} +760.383 q^{71} +220.749 q^{72} +860.956 q^{73} +843.189 q^{74} -361.700 q^{75} +102.986 q^{76} +39.3747 q^{77} -184.698 q^{78} +349.866 q^{79} +90.4725 q^{80} +81.0000 q^{81} -210.954 q^{82} -840.864 q^{83} +17.8242 q^{84} +172.288 q^{85} +533.501 q^{86} +566.276 q^{87} -338.971 q^{88} +1293.17 q^{89} +46.0864 q^{90} -72.1251 q^{91} -62.6444 q^{92} -1004.15 q^{93} +407.724 q^{94} +103.984 q^{95} -275.163 q^{96} -100.654 q^{97} +814.437 q^{98} -124.380 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * q^98 - 648 * q^99

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