LMFDB - Embedded newform 201.4.a.e.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.7
Root			$1.96751$ 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)

$f(q)$	$=$	$q+1.96751 q^{2} +3.00000 q^{3} -4.12891 q^{4} +17.2496 q^{5} +5.90252 q^{6} +22.3999 q^{7} -23.8637 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.96751 q^{2} +3.00000 q^{3} -4.12891 q^{4} +17.2496 q^{5} +5.90252 q^{6} +22.3999 q^{7} -23.8637 q^{8} +9.00000 q^{9} +33.9387 q^{10} +7.57943 q^{11} -12.3867 q^{12} -38.6691 q^{13} +44.0719 q^{14} +51.7488 q^{15} -13.9208 q^{16} +18.3866 q^{17} +17.7076 q^{18} -21.0611 q^{19} -71.2221 q^{20} +67.1996 q^{21} +14.9126 q^{22} +178.672 q^{23} -71.5912 q^{24} +172.549 q^{25} -76.0817 q^{26} +27.0000 q^{27} -92.4871 q^{28} +141.708 q^{29} +101.816 q^{30} -205.310 q^{31} +163.521 q^{32} +22.7383 q^{33} +36.1757 q^{34} +386.389 q^{35} -37.1602 q^{36} +138.126 q^{37} -41.4378 q^{38} -116.007 q^{39} -411.640 q^{40} -110.100 q^{41} +132.216 q^{42} -193.600 q^{43} -31.2948 q^{44} +155.246 q^{45} +351.538 q^{46} -626.504 q^{47} -41.7623 q^{48} +158.754 q^{49} +339.491 q^{50} +55.1597 q^{51} +159.661 q^{52} -413.359 q^{53} +53.1227 q^{54} +130.742 q^{55} -534.544 q^{56} -63.1832 q^{57} +278.812 q^{58} -459.763 q^{59} -213.666 q^{60} -237.637 q^{61} -403.949 q^{62} +201.599 q^{63} +433.094 q^{64} -667.026 q^{65} +44.7378 q^{66} +67.0000 q^{67} -75.9165 q^{68} +536.016 q^{69} +760.223 q^{70} +419.094 q^{71} -214.774 q^{72} -268.179 q^{73} +271.764 q^{74} +517.646 q^{75} +86.9592 q^{76} +169.778 q^{77} -228.245 q^{78} +886.326 q^{79} -240.128 q^{80} +81.0000 q^{81} -216.623 q^{82} -423.700 q^{83} -277.461 q^{84} +317.161 q^{85} -380.910 q^{86} +425.125 q^{87} -180.873 q^{88} +229.322 q^{89} +305.449 q^{90} -866.183 q^{91} -737.720 q^{92} -615.930 q^{93} -1232.65 q^{94} -363.295 q^{95} +490.562 q^{96} -462.938 q^{97} +312.350 q^{98} +68.2149 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) $ 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9 + 29 * q^10 + 104 * q^11 + 207 * q^12 + 172 * q^13 + 143 * q^14 + 24 * q^15 + 485 * q^16 - 48 * q^17 + 27 * q^18 + 180 * q^19 - 539 * q^20 + 234 * q^21 - 144 * q^22 + 156 * q^23 + 63 * q^24 + 383 * q^25 - 252 * q^26 + 297 * q^27 + 1011 * q^28 - 4 * q^29 + 87 * q^30 + 514 * q^31 - 119 * q^32 + 312 * q^33 + 72 * q^34 - 338 * q^35 + 621 * q^36 + 854 * q^37 - 308 * q^38 + 516 * q^39 - 15 * q^40 + 674 * q^41 + 429 * q^42 + 738 * q^43 + 356 * q^44 + 72 * q^45 + 507 * q^46 + 54 * q^47 + 1455 * q^48 + 1465 * q^49 + 656 * q^50 - 144 * q^51 - 12 * q^52 - 190 * q^53 + 81 * q^54 + 262 * q^55 + 239 * q^56 + 540 * q^57 - 1466 * q^58 + 18 * q^59 - 1617 * q^60 + 328 * q^61 - 915 * q^62 + 702 * q^63 + 2253 * q^64 - 732 * q^65 - 432 * q^66 + 737 * q^67 - 5746 * q^68 + 468 * q^69 - 4451 * q^70 + 264 * q^71 + 189 * q^72 + 330 * q^73 - 5975 * q^74 + 1149 * q^75 - 178 * q^76 - 368 * q^77 - 756 * q^78 + 456 * q^79 - 8515 * q^80 + 891 * q^81 - 3629 * q^82 - 2432 * q^83 + 3033 * q^84 + 2882 * q^85 - 6225 * q^86 - 12 * q^87 - 5492 * q^88 - 2340 * q^89 + 261 * q^90 - 994 * q^91 - 2939 * q^92 + 1542 * q^93 - 3506 * q^94 - 2568 * q^95 - 357 * q^96 + 1892 * q^97 - 1078 * q^98 + 936 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.96751	0.695619	0.347810	−	0.937565i	$-0.386926\pi$
$2$	1.96751	0.695619	0.347810	+	0.937565i	$0.386926\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−4.12891	−0.516114
$5$	17.2496	1.54285	0.771426	−	0.636319i	$-0.219544\pi$
$5$	17.2496	1.54285	0.771426	+	0.636319i	$0.219544\pi$
$6$	5.90252	0.401616
$7$	22.3999	1.20948	0.604740	−	0.796423i	$-0.293277\pi$
$7$	22.3999	1.20948	0.604740	+	0.796423i	$0.293277\pi$
$8$	−23.8637	−1.05464
$9$	9.00000	0.333333
$10$	33.9387	1.07324
$11$	7.57943	0.207753	0.103877	−	0.994590i	$-0.466875\pi$
$11$	7.57943	0.207753	0.103877	+	0.994590i	$0.466875\pi$
$12$	−12.3867	−0.297979
$13$	−38.6691	−0.824990	−0.412495	−	0.910960i	$-0.635343\pi$
$13$	−38.6691	−0.824990	−0.412495	+	0.910960i	$0.635343\pi$
$14$	44.0719	0.841337
$15$	51.7488	0.890766
$16$	−13.9208	−0.217512
$17$	18.3866	0.262317	0.131159	−	0.991361i	$-0.458130\pi$
$17$	18.3866	0.262317	0.131159	+	0.991361i	$0.458130\pi$
$18$	17.7076	0.231873
$19$	−21.0611	−0.254302	−0.127151	−	0.991883i	$-0.540583\pi$
$19$	−21.0611	−0.254302	−0.127151	+	0.991883i	$0.540583\pi$
$20$	−71.2221	−0.796287
$21$	67.1996	0.698293
$22$	14.9126	0.144517
$23$	178.672	1.61981	0.809906	−	0.586560i	$-0.199518\pi$
$23$	178.672	1.61981	0.809906	+	0.586560i	$0.199518\pi$
$24$	−71.5912	−0.608895
$25$	172.549	1.38039
$26$	−76.0817	−0.573879
$27$	27.0000	0.192450
$28$	−92.4871	−0.624229
$29$	141.708	0.907398	0.453699	−	0.891155i	$-0.350104\pi$
$29$	141.708	0.907398	0.453699	+	0.891155i	$0.350104\pi$
$30$	101.816	0.619634
$31$	−205.310	−1.18951	−0.594755	−	0.803907i	$-0.702751\pi$
$31$	−205.310	−1.18951	−0.594755	+	0.803907i	$0.702751\pi$
$32$	163.521	0.903332
$33$	22.7383	0.119946
$34$	36.1757	0.182473
$35$	386.389	1.86605
$36$	−37.1602	−0.172038
$37$	138.126	0.613724	0.306862	−	0.951754i	$-0.400721\pi$
$37$	138.126	0.613724	0.306862	+	0.951754i	$0.400721\pi$
$38$	−41.4378	−0.176897
$39$	−116.007	−0.476308
$40$	−411.640	−1.62715
$41$	−110.100	−0.419385	−0.209692	−	0.977767i	$-0.567246\pi$
$41$	−110.100	−0.419385	−0.209692	+	0.977767i	$0.567246\pi$
$42$	132.216	0.485746
$43$	−193.600	−0.686599	−0.343299	−	0.939226i	$-0.611545\pi$
$43$	−193.600	−0.686599	−0.343299	+	0.939226i	$0.611545\pi$
$44$	−31.2948	−0.107224
$45$	155.246	0.514284
$46$	351.538	1.12677
$47$	−626.504	−1.94436	−0.972181	−	0.234233i	$-0.924742\pi$
$47$	−626.504	−1.94436	−0.972181	+	0.234233i	$0.924742\pi$
$48$	−41.7623	−0.125581
$49$	158.754	0.462840
$50$	339.491	0.960226
$51$	55.1597	0.151449
$52$	159.661	0.425789
$53$	−413.359	−1.07131	−0.535653	−	0.844438i	$-0.679934\pi$
$53$	−413.359	−1.07131	−0.535653	+	0.844438i	$0.679934\pi$
$54$	53.1227	0.133872
$55$	130.742	0.320532
$56$	−534.544	−1.27556
$57$	−63.1832	−0.146821
$58$	278.812	0.631204
$59$	−459.763	−1.01451	−0.507254	−	0.861797i	$-0.669339\pi$
$59$	−459.763	−1.01451	−0.507254	+	0.861797i	$0.669339\pi$
$60$	−213.666	−0.459737
$61$	−237.637	−0.498791	−0.249396	−	0.968402i	$-0.580232\pi$
$61$	−237.637	−0.498791	−0.249396	+	0.968402i	$0.580232\pi$
$62$	−403.949	−0.827445
$63$	201.599	0.403160
$64$	433.094	0.845887
$65$	−667.026	−1.27284
$66$	44.7378	0.0834369
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	−75.9165	−0.135386
$69$	536.016	0.935198
$70$	760.223	1.29806
$71$	419.094	0.700525	0.350262	−	0.936652i	$-0.386092\pi$
$71$	419.094	0.700525	0.350262	+	0.936652i	$0.386092\pi$
$72$	−214.774	−0.351546
$73$	−268.179	−0.429973	−0.214986	−	0.976617i	$-0.568971\pi$
$73$	−268.179	−0.429973	−0.214986	+	0.976617i	$0.568971\pi$
$74$	271.764	0.426918
$75$	517.646	0.796969
$76$	86.9592	0.131249
$77$	169.778	0.251273
$78$	−228.245	−0.331329
$79$	886.326	1.26227	0.631136	−	0.775673i	$-0.282589\pi$
$79$	886.326	1.26227	0.631136	+	0.775673i	$0.282589\pi$
$80$	−240.128	−0.335589
$81$	81.0000	0.111111
$82$	−216.623	−0.291732
$83$	−423.700	−0.560326	−0.280163	−	0.959952i	$-0.590389\pi$
$83$	−423.700	−0.560326	−0.280163	+	0.959952i	$0.590389\pi$
$84$	−277.461	−0.360399
$85$	317.161	0.404717
$86$	−380.910	−0.477611
$87$	425.125	0.523887
$88$	−180.873	−0.219104
$89$	229.322	0.273124	0.136562	−	0.990632i	$-0.456395\pi$
$89$	229.322	0.273124	0.136562	+	0.990632i	$0.456395\pi$
$90$	305.449	0.357746
$91$	−866.183	−0.997809
$92$	−737.720	−0.836007
$93$	−615.930	−0.686764
$94$	−1232.65	−1.35253
$95$	−363.295	−0.392350
$96$	490.562	0.521539
$97$	−462.938	−0.484580	−0.242290	−	0.970204i	$-0.577899\pi$
$97$	−462.938	−0.484580	−0.242290	+	0.970204i	$0.577899\pi$
$98$	312.350	0.321960
$99$	68.2149	0.0692510
$100$	−712.439	−0.712439
$101$	−2017.85	−1.98796	−0.993979	−	0.109574i	$-0.965051\pi$
$101$	−2017.85	−1.98796	−0.993979	+	0.109574i	$0.965051\pi$
$102$	108.527	0.105351
$103$	−922.325	−0.882324	−0.441162	−	0.897428i	$-0.645434\pi$
$103$	−922.325	−0.882324	−0.441162	+	0.897428i	$0.645434\pi$
$104$	922.789	0.870066
$105$	1159.17	1.07736
$106$	−813.287	−0.745221
$107$	−984.383	−0.889382	−0.444691	−	0.895684i	$-0.646686\pi$
$107$	−984.383	−0.889382	−0.444691	+	0.895684i	$0.646686\pi$
$108$	−111.481	−0.0993262
$109$	−256.389	−0.225300	−0.112650	−	0.993635i	$-0.535934\pi$
$109$	−256.389	−0.225300	−0.112650	+	0.993635i	$0.535934\pi$
$110$	257.236	0.222968
$111$	414.378	0.354334
$112$	−311.824	−0.263076
$113$	1405.45	1.17003	0.585015	−	0.811022i	$-0.301089\pi$
$113$	1405.45	1.17003	0.585015	+	0.811022i	$0.301089\pi$
$114$	−124.313	−0.102132
$115$	3082.02	2.49913
$116$	−585.101	−0.468321
$117$	−348.022	−0.274997
$118$	−904.586	−0.705711
$119$	411.857	0.317268
$120$	−1234.92	−0.939435
$121$	−1273.55	−0.956839
$122$	−467.552	−0.346969
$123$	−330.301	−0.242132
$124$	847.708	0.613923
$125$	820.198	0.586886
$126$	396.647	0.280446
$127$	2192.61	1.53199	0.765995	−	0.642846i	$-0.222247\pi$
$127$	2192.61	1.53199	0.765995	+	0.642846i	$0.222247\pi$
$128$	−456.048	−0.314917
$129$	−580.800	−0.396408
$130$	−1312.38	−0.885410
$131$	−777.738	−0.518712	−0.259356	−	0.965782i	$-0.583510\pi$
$131$	−777.738	−0.518712	−0.259356	+	0.965782i	$0.583510\pi$
$132$	−93.8844	−0.0619060
$133$	−471.765	−0.307573
$134$	131.823	0.0849834
$135$	465.739	0.296922
$136$	−438.772	−0.276650
$137$	1521.28	0.948696	0.474348	−	0.880337i	$-0.342684\pi$
$137$	1521.28	0.948696	0.474348	+	0.880337i	$0.342684\pi$
$138$	1054.61	0.650542
$139$	2997.08	1.82884	0.914420	−	0.404766i	$-0.132647\pi$
$139$	2997.08	1.82884	0.914420	+	0.404766i	$0.132647\pi$
$140$	−1595.37	−0.963093
$141$	−1879.51	−1.12258
$142$	824.570	0.487298
$143$	−293.090	−0.171394
$144$	−125.287	−0.0725041
$145$	2444.41	1.39998
$146$	−527.645	−0.299097
$147$	476.262	0.267221
$148$	−570.310	−0.316751
$149$	−3094.88	−1.70163	−0.850813	−	0.525468i	$-0.823890\pi$
$149$	−3094.88	−1.70163	−0.850813	+	0.525468i	$0.823890\pi$
$150$	1018.47	0.554387
$151$	−1359.32	−0.732583	−0.366291	−	0.930500i	$-0.619373\pi$
$151$	−1359.32	−0.732583	−0.366291	+	0.930500i	$0.619373\pi$
$152$	502.595	0.268196
$153$	165.479	0.0874392
$154$	334.040	0.174790
$155$	−3541.52	−1.83524
$156$	478.984	0.245830
$157$	−1610.83	−0.818843	−0.409421	−	0.912345i	$-0.634269\pi$
$157$	−1610.83	−0.818843	−0.409421	+	0.912345i	$0.634269\pi$
$158$	1743.85	0.878060
$159$	−1240.08	−0.618518
$160$	2820.67	1.39371
$161$	4002.23	1.95913
$162$	159.368	0.0772910
$163$	3969.36	1.90739	0.953695	−	0.300775i	$-0.0972454\pi$
$163$	3969.36	1.90739	0.953695	+	0.300775i	$0.0972454\pi$
$164$	454.594	0.216450
$165$	392.226	0.185059
$166$	−833.633	−0.389774
$167$	2803.08	1.29886	0.649429	−	0.760422i	$-0.275008\pi$
$167$	2803.08	1.29886	0.649429	+	0.760422i	$0.275008\pi$
$168$	−1603.63	−0.736446
$169$	−701.701	−0.319391
$170$	624.017	0.281529
$171$	−189.549	−0.0847673
$172$	799.358	0.354363
$173$	1975.80	0.868306	0.434153	−	0.900839i	$-0.357048\pi$
$173$	1975.80	0.868306	0.434153	+	0.900839i	$0.357048\pi$
$174$	836.436	0.364426
$175$	3865.07	1.66955
$176$	−105.512	−0.0451888
$177$	−1379.29	−0.585727
$178$	451.192	0.189990
$179$	−891.067	−0.372075	−0.186038	−	0.982543i	$-0.559565\pi$
$179$	−891.067	−0.372075	−0.186038	+	0.982543i	$0.559565\pi$
$180$	−640.999	−0.265429
$181$	2478.32	1.01775	0.508874	−	0.860841i	$-0.330062\pi$
$181$	2478.32	1.01775	0.508874	+	0.860841i	$0.330062\pi$
$182$	−1704.22	−0.694095
$183$	−712.910	−0.287977
$184$	−4263.78	−1.70831
$185$	2382.62	0.946884
$186$	−1211.85	−0.477726
$187$	139.360	0.0544973
$188$	2586.78	1.00351
$189$	604.796	0.232764
$190$	−714.785	−0.272926
$191$	−3804.61	−1.44132	−0.720660	−	0.693289i	$-0.756161\pi$
$191$	−3804.61	−1.44132	−0.720660	+	0.693289i	$0.756161\pi$
$192$	1299.28	0.488373
$193$	4271.41	1.59307	0.796536	−	0.604590i	$-0.206663\pi$
$193$	4271.41	1.59307	0.796536	+	0.604590i	$0.206663\pi$
$194$	−910.835	−0.337083
$195$	−2001.08	−0.734873
$196$	−655.482	−0.238878
$197$	−1594.92	−0.576819	−0.288410	−	0.957507i	$-0.593126\pi$
$197$	−1594.92	−0.576819	−0.288410	+	0.957507i	$0.593126\pi$
$198$	134.213	0.0481723
$199$	811.220	0.288974	0.144487	−	0.989507i	$-0.453847\pi$
$199$	811.220	0.288974	0.144487	+	0.989507i	$0.453847\pi$
$200$	−4117.66	−1.45581
$201$	201.000	0.0705346
$202$	−3970.14	−1.38286
$203$	3174.25	1.09748
$204$	−227.750	−0.0781650
$205$	−1899.19	−0.647048
$206$	−1814.68	−0.613761
$207$	1608.05	0.539937
$208$	538.304	0.179445
$209$	−159.631	−0.0528320
$210$	2280.67	0.749434
$211$	3489.60	1.13855	0.569274	−	0.822148i	$-0.307224\pi$
$211$	3489.60	1.13855	0.569274	+	0.822148i	$0.307224\pi$
$212$	1706.72	0.552916
$213$	1257.28	0.404448
$214$	−1936.78	−0.618671
$215$	−3339.52	−1.05932
$216$	−644.321	−0.202965
$217$	−4598.92	−1.43869
$218$	−504.448	−0.156723
$219$	−804.538	−0.248245
$220$	−539.823	−0.165431
$221$	−710.992	−0.216409
$222$	815.292	0.246481
$223$	548.375	0.164672	0.0823361	−	0.996605i	$-0.473762\pi$
$223$	548.375	0.164672	0.0823361	+	0.996605i	$0.473762\pi$
$224$	3662.84	1.09256
$225$	1552.94	0.460130
$226$	2765.23	0.813896
$227$	4343.28	1.26993	0.634964	−	0.772541i	$-0.281015\pi$
$227$	4343.28	1.26993	0.634964	+	0.772541i	$0.281015\pi$
$228$	260.878	0.0757765
$229$	2050.85	0.591808	0.295904	−	0.955218i	$-0.404379\pi$
$229$	2050.85	0.591808	0.295904	+	0.955218i	$0.404379\pi$
$230$	6063.90	1.73844
$231$	509.335	0.145073
$232$	−3381.69	−0.956977
$233$	2995.56	0.842256	0.421128	−	0.907001i	$-0.361634\pi$
$233$	2995.56	0.842256	0.421128	+	0.907001i	$0.361634\pi$
$234$	−684.736	−0.191293
$235$	−10806.9	−2.99986
$236$	1898.32	0.523602
$237$	2658.98	0.728773
$238$	810.331	0.220697
$239$	1295.11	0.350517	0.175258	−	0.984522i	$-0.443924\pi$
$239$	1295.11	0.350517	0.175258	+	0.984522i	$0.443924\pi$
$240$	−720.384	−0.193752
$241$	−3353.31	−0.896290	−0.448145	−	0.893961i	$-0.647915\pi$
$241$	−3353.31	−0.896290	−0.448145	+	0.893961i	$0.647915\pi$
$242$	−2505.72	−0.665595
$243$	243.000	0.0641500
$244$	981.182	0.257433
$245$	2738.45	0.714093
$246$	−649.869	−0.168432
$247$	814.412	0.209797
$248$	4899.47	1.25450
$249$	−1271.10	−0.323505
$250$	1613.75	0.408249
$251$	3831.35	0.963476	0.481738	−	0.876315i	$-0.340006\pi$
$251$	3831.35	0.963476	0.481738	+	0.876315i	$0.340006\pi$
$252$	−832.384	−0.208076
$253$	1354.23	0.336521
$254$	4313.98	1.06568
$255$	951.483	0.233663
$256$	−4362.03	−1.06495
$257$	−4902.51	−1.18992	−0.594961	−	0.803755i	$-0.702832\pi$
$257$	−4902.51	−1.18992	−0.594961	+	0.803755i	$0.702832\pi$
$258$	−1142.73	−0.275749
$259$	3094.00	0.742286
$260$	2754.09	0.656929
$261$	1275.37	0.302466
$262$	−1530.21	−0.360826
$263$	−1751.25	−0.410596	−0.205298	−	0.978700i	$-0.565816\pi$
$263$	−1751.25	−0.410596	−0.205298	+	0.978700i	$0.565816\pi$
$264$	−542.620	−0.126500
$265$	−7130.27	−1.65287
$266$	−928.201	−0.213954
$267$	687.965	0.157688
$268$	−276.637	−0.0630534
$269$	−6157.50	−1.39565	−0.697824	−	0.716269i	$-0.745848\pi$
$269$	−6157.50	−1.39565	−0.697824	+	0.716269i	$0.745848\pi$
$270$	916.346	0.206545
$271$	5210.52	1.16796	0.583979	−	0.811769i	$-0.301495\pi$
$271$	5210.52	1.16796	0.583979	+	0.811769i	$0.301495\pi$
$272$	−255.955	−0.0570573
$273$	−2598.55	−0.576085
$274$	2993.12	0.659931
$275$	1307.82	0.286780
$276$	−2213.16	−0.482669
$277$	532.214	0.115443	0.0577214	−	0.998333i	$-0.481617\pi$
$277$	532.214	0.115443	0.0577214	+	0.998333i	$0.481617\pi$
$278$	5896.78	1.27218
$279$	−1847.79	−0.396503
$280$	−9220.68	−1.96800
$281$	3372.07	0.715875	0.357937	−	0.933746i	$-0.383480\pi$
$281$	3372.07	0.715875	0.357937	+	0.933746i	$0.383480\pi$
$282$	−3697.95	−0.780886
$283$	−4135.01	−0.868553	−0.434277	−	0.900780i	$-0.642996\pi$
$283$	−4135.01	−0.868553	−0.434277	+	0.900780i	$0.642996\pi$
$284$	−1730.40	−0.361551
$285$	−1089.88	−0.226523
$286$	−576.656	−0.119225
$287$	−2466.23	−0.507237
$288$	1471.69	0.301111
$289$	−4574.93	−0.931190
$290$	4809.40	0.973854
$291$	−1388.81	−0.279772
$292$	1107.29	0.221915
$293$	678.967	0.135378	0.0676889	−	0.997706i	$-0.478437\pi$
$293$	678.967	0.135378	0.0676889	+	0.997706i	$0.478437\pi$
$294$	937.050	0.185884
$295$	−7930.72	−1.56524
$296$	−3296.20	−0.647256
$297$	204.645	0.0399821
$298$	−6089.20	−1.18368
$299$	−6909.08	−1.33633
$300$	−2137.32	−0.411327
$301$	−4336.62	−0.830427
$302$	−2674.48	−0.509599
$303$	−6053.55	−1.14775
$304$	293.186	0.0553138
$305$	−4099.14	−0.769561
$306$	325.581	0.0608244
$307$	−1851.82	−0.344264	−0.172132	−	0.985074i	$-0.555066\pi$
$307$	−1851.82	−0.344264	−0.172132	+	0.985074i	$0.555066\pi$
$308$	−700.999	−0.129686
$309$	−2766.97	−0.509410
$310$	−6967.97	−1.27663
$311$	−7762.49	−1.41534	−0.707670	−	0.706544i	$-0.750253\pi$
$311$	−7762.49	−1.41534	−0.707670	+	0.706544i	$0.750253\pi$
$312$	2768.37	0.502333
$313$	3324.73	0.600399	0.300200	−	0.953876i	$-0.402947\pi$
$313$	3324.73	0.600399	0.300200	+	0.953876i	$0.402947\pi$
$314$	−3169.32	−0.569603
$315$	3477.50	0.622016
$316$	−3659.56	−0.651476
$317$	5065.13	0.897433	0.448716	−	0.893674i	$-0.351881\pi$
$317$	5065.13	0.897433	0.448716	+	0.893674i	$0.351881\pi$
$318$	−2439.86	−0.430253
$319$	1074.07	0.188515
$320$	7470.71	1.30508
$321$	−2953.15	−0.513485
$322$	7874.41	1.36281
$323$	−387.240	−0.0667078
$324$	−334.442	−0.0573460
$325$	−6672.30	−1.13881
$326$	7809.76	1.32682
$327$	−769.168	−0.130077
$328$	2627.40	0.442299
$329$	−14033.6	−2.35166
$330$	771.708	0.128731
$331$	9378.35	1.55734	0.778672	−	0.627432i	$-0.215894\pi$
$331$	9378.35	1.55734	0.778672	+	0.627432i	$0.215894\pi$
$332$	1749.42	0.289192
$333$	1243.13	0.204575
$334$	5515.09	0.903510
$335$	1155.72	0.188489
$336$	−935.471	−0.151887
$337$	4156.66	0.671892	0.335946	−	0.941881i	$-0.390944\pi$
$337$	4156.66	0.671892	0.335946	+	0.941881i	$0.390944\pi$
$338$	−1380.60	−0.222174
$339$	4216.34	0.675517
$340$	−1309.53	−0.208880
$341$	−1556.13	−0.247124
$342$	−372.940	−0.0589658
$343$	−4127.08	−0.649684
$344$	4620.02	0.724113
$345$	9246.06	1.44287
$346$	3887.39	0.604011
$347$	−318.633	−0.0492943	−0.0246472	−	0.999696i	$-0.507846\pi$
$347$	−318.633	−0.0492943	−0.0246472	+	0.999696i	$0.507846\pi$
$348$	−1755.30	−0.270385
$349$	9180.20	1.40804	0.704019	−	0.710182i	$-0.251387\pi$
$349$	9180.20	1.40804	0.704019	+	0.710182i	$0.251387\pi$
$350$	7604.56	1.16137
$351$	−1044.07	−0.158769
$352$	1239.39	0.187670
$353$	2725.99	0.411019	0.205510	−	0.978655i	$-0.434115\pi$
$353$	2725.99	0.411019	0.205510	+	0.978655i	$0.434115\pi$
$354$	−2713.76	−0.407443
$355$	7229.20	1.08081
$356$	−946.849	−0.140963
$357$	1235.57	0.183175
$358$	−1753.18	−0.258823
$359$	7890.70	1.16004	0.580021	−	0.814601i	$-0.303044\pi$
$359$	7890.70	1.16004	0.580021	+	0.814601i	$0.303044\pi$
$360$	−3704.76	−0.542383
$361$	−6415.43	−0.935331
$362$	4876.12	0.707964
$363$	−3820.66	−0.552431
$364$	3576.39	0.514983
$365$	−4625.99	−0.663384
$366$	−1402.66	−0.200323
$367$	−6109.73	−0.869006	−0.434503	−	0.900670i	$-0.643076\pi$
$367$	−6109.73	−0.869006	−0.434503	+	0.900670i	$0.643076\pi$
$368$	−2487.25	−0.352329
$369$	−990.902	−0.139795
$370$	4687.82	0.658671
$371$	−9259.18	−1.29572
$372$	2543.12	0.354448
$373$	10742.4	1.49121	0.745606	−	0.666387i	$-0.232160\pi$
$373$	10742.4	1.49121	0.745606	+	0.666387i	$0.232160\pi$
$374$	274.191	0.0379093
$375$	2460.59	0.338839
$376$	14950.7	2.05060
$377$	−5479.73	−0.748595
$378$	1189.94	0.161915
$379$	6812.40	0.923297	0.461648	−	0.887063i	$-0.347258\pi$
$379$	6812.40	0.923297	0.461648	+	0.887063i	$0.347258\pi$
$380$	1500.01	0.202497
$381$	6577.83	0.884495
$382$	−7485.60	−1.00261
$383$	−8183.80	−1.09183	−0.545917	−	0.837839i	$-0.683819\pi$
$383$	−8183.80	−1.09183	−0.545917	+	0.837839i	$0.683819\pi$
$384$	−1368.14	−0.181817
$385$	2928.61	0.387677
$386$	8404.04	1.10817
$387$	−1742.40	−0.228866
$388$	1911.43	0.250099
$389$	−3210.28	−0.418426	−0.209213	−	0.977870i	$-0.567090\pi$
$389$	−3210.28	−0.418426	−0.209213	+	0.977870i	$0.567090\pi$
$390$	−3937.14	−0.511192
$391$	3285.16	0.424905
$392$	−3788.47	−0.488129
$393$	−2333.21	−0.299479
$394$	−3138.02	−0.401246
$395$	15288.8	1.94750
$396$	−281.653	−0.0357414
$397$	−9058.09	−1.14512	−0.572560	−	0.819863i	$-0.694050\pi$
$397$	−9058.09	−1.14512	−0.572560	+	0.819863i	$0.694050\pi$
$398$	1596.08	0.201016
$399$	−1415.29	−0.177577
$400$	−2402.01	−0.300252
$401$	2209.82	0.275195	0.137598	−	0.990488i	$-0.456062\pi$
$401$	2209.82	0.275195	0.137598	+	0.990488i	$0.456062\pi$
$402$	395.469	0.0490652
$403$	7939.16	0.981334
$404$	8331.53	1.02601
$405$	1397.22	0.171428
$406$	6245.35	0.763428
$407$	1046.92	0.127503
$408$	−1316.32	−0.159724
$409$	−15322.1	−1.85239	−0.926195	−	0.377046i	$-0.876940\pi$
$409$	−15322.1	−1.85239	−0.926195	+	0.377046i	$0.876940\pi$
$410$	−3736.66	−0.450099
$411$	4563.83	0.547730
$412$	3808.20	0.455380
$413$	−10298.6	−1.22703
$414$	3163.84	0.375591
$415$	−7308.65	−0.864500
$416$	−6323.19	−0.745241
$417$	8991.24	1.05588
$418$	−314.075	−0.0367509
$419$	14406.9	1.67977	0.839885	−	0.542765i	$-0.182623\pi$
$419$	14406.9	1.67977	0.839885	+	0.542765i	$0.182623\pi$
$420$	−4786.10	−0.556042
$421$	−9499.21	−1.09967	−0.549837	−	0.835272i	$-0.685310\pi$
$421$	−9499.21	−1.09967	−0.549837	+	0.835272i	$0.685310\pi$
$422$	6865.81	0.791996
$423$	−5638.53	−0.648120
$424$	9864.28	1.12984
$425$	3172.58	0.362101
$426$	2473.71	0.281342
$427$	−5323.03	−0.603278
$428$	4064.43	0.459023
$429$	−879.269	−0.0989545
$430$	−6570.54	−0.736883
$431$	11561.0	1.29205	0.646023	−	0.763318i	$-0.276431\pi$
$431$	11561.0	1.29205	0.646023	+	0.763318i	$0.276431\pi$
$432$	−375.861	−0.0418602
$433$	1832.57	0.203389	0.101695	−	0.994816i	$-0.467574\pi$
$433$	1832.57	0.203389	0.101695	+	0.994816i	$0.467574\pi$
$434$	−9048.41	−1.00078
$435$	7333.23	0.808279
$436$	1058.61	0.116280
$437$	−3763.02	−0.411921
$438$	−1582.93	−0.172684
$439$	15171.8	1.64946	0.824728	−	0.565530i	$-0.191328\pi$
$439$	15171.8	1.64946	0.824728	+	0.565530i	$0.191328\pi$
$440$	−3119.99	−0.338045
$441$	1428.79	0.154280
$442$	−1398.88	−0.150539
$443$	8772.59	0.940854	0.470427	−	0.882439i	$-0.344100\pi$
$443$	8772.59	0.940854	0.470427	+	0.882439i	$0.344100\pi$
$444$	−1710.93	−0.182877
$445$	3955.71	0.421390
$446$	1078.93	0.114549
$447$	−9284.64	−0.982435
$448$	9701.26	1.02308
$449$	5051.70	0.530968	0.265484	−	0.964115i	$-0.414468\pi$
$449$	5051.70	0.530968	0.265484	+	0.964115i	$0.414468\pi$
$450$	3055.42	0.320075
$451$	−834.497	−0.0871284
$452$	−5802.97	−0.603869
$453$	−4077.96	−0.422957
$454$	8545.44	0.883387
$455$	−14941.3	−1.53947
$456$	1507.79	0.154843
$457$	925.103	0.0946925	0.0473463	−	0.998879i	$-0.484924\pi$
$457$	925.103	0.0946925	0.0473463	+	0.998879i	$0.484924\pi$
$458$	4035.06	0.411673
$459$	496.437	0.0504830
$460$	−12725.4	−1.28984
$461$	−1268.20	−0.128126	−0.0640629	−	0.997946i	$-0.520406\pi$
$461$	−1268.20	−0.128126	−0.0640629	+	0.997946i	$0.520406\pi$
$462$	1002.12	0.100915
$463$	15838.8	1.58983	0.794917	−	0.606718i	$-0.207514\pi$
$463$	15838.8	1.58983	0.794917	+	0.606718i	$0.207514\pi$
$464$	−1972.69	−0.197370
$465$	−10624.6	−1.05957
$466$	5893.78	0.585889
$467$	−7532.29	−0.746366	−0.373183	−	0.927758i	$-0.621734\pi$
$467$	−7532.29	−0.746366	−0.373183	+	0.927758i	$0.621734\pi$
$468$	1436.95	0.141930
$469$	1500.79	0.147761
$470$	−21262.7	−2.08676
$471$	−4832.49	−0.472759
$472$	10971.6	1.06994
$473$	−1467.38	−0.142643
$474$	5231.56	0.506948
$475$	−3634.06	−0.351036
$476$	−1700.52	−0.163746
$477$	−3720.23	−0.357102
$478$	2548.13	0.243826
$479$	6617.04	0.631190	0.315595	−	0.948894i	$-0.397796\pi$
$479$	6617.04	0.631190	0.315595	+	0.948894i	$0.397796\pi$
$480$	8462.00	0.804657
$481$	−5341.21	−0.506316
$482$	−6597.67	−0.623476
$483$	12006.7	1.13110
$484$	5258.39	0.493838
$485$	−7985.50	−0.747635
$486$	478.104	0.0446240
$487$	4977.09	0.463107	0.231554	−	0.972822i	$-0.425619\pi$
$487$	4977.09	0.463107	0.231554	+	0.972822i	$0.425619\pi$
$488$	5670.90	0.526044
$489$	11908.1	1.10123
$490$	5387.91	0.496737
$491$	−17992.5	−1.65374	−0.826872	−	0.562390i	$-0.809882\pi$
$491$	−17992.5	−1.65374	−0.826872	+	0.562390i	$0.809882\pi$
$492$	1363.78	0.124968
$493$	2605.53	0.238026
$494$	1602.36	0.145939
$495$	1176.68	0.106844
$496$	2858.08	0.258733
$497$	9387.64	0.847270
$498$	−2500.90	−0.225036
$499$	−15767.1	−1.41449	−0.707246	−	0.706968i	$-0.750063\pi$
$499$	−15767.1	−1.41449	−0.707246	+	0.706968i	$0.750063\pi$
$500$	−3386.52	−0.302900
$501$	8409.25	0.749896
$502$	7538.20	0.670212
$503$	13675.1	1.21221	0.606105	−	0.795385i	$-0.292731\pi$
$503$	13675.1	1.21221	0.606105	+	0.795385i	$0.292731\pi$
$504$	−4810.90	−0.425188
$505$	−34807.1	−3.06712
$506$	2664.46	0.234090
$507$	−2105.10	−0.184400
$508$	−9053.10	−0.790682
$509$	−19963.3	−1.73842	−0.869211	−	0.494441i	$-0.835373\pi$
$509$	−19963.3	−1.73842	−0.869211	+	0.494441i	$0.835373\pi$
$510$	1872.05	0.162541
$511$	−6007.18	−0.520043
$512$	−4933.95	−0.425882
$513$	−568.648	−0.0489404
$514$	−9645.72	−0.827732
$515$	−15909.7	−1.36129
$516$	2398.07	0.204592
$517$	−4748.54	−0.403947
$518$	6087.48	0.516348
$519$	5927.39	0.501317
$520$	15917.7	1.34238
$521$	−7404.05	−0.622605	−0.311303	−	0.950311i	$-0.600765\pi$
$521$	−7404.05	−0.622605	−0.311303	+	0.950311i	$0.600765\pi$
$522$	2509.31	0.210401
$523$	3990.01	0.333596	0.166798	−	0.985991i	$-0.446657\pi$
$523$	3990.01	0.333596	0.166798	+	0.985991i	$0.446657\pi$
$524$	3211.21	0.267715
$525$	11595.2	0.963917
$526$	−3445.60	−0.285618
$527$	−3774.95	−0.312029
$528$	−316.535	−0.0260898
$529$	19756.6	1.62379
$530$	−14028.9	−1.14976
$531$	−4137.86	−0.338169
$532$	1947.88	0.158743
$533$	4257.48	0.345988
$534$	1353.58	0.109691
$535$	−16980.2	−1.37218
$536$	−1598.87	−0.128845
$537$	−2673.20	−0.214818
$538$	−12114.9	−0.970839
$539$	1203.27	0.0961564
$540$	−1923.00	−0.153246
$541$	−16100.3	−1.27950	−0.639748	−	0.768585i	$-0.720961\pi$
$541$	−16100.3	−1.27950	−0.639748	+	0.768585i	$0.720961\pi$
$542$	10251.7	0.812454
$543$	7434.97	0.587597
$544$	3006.58	0.236960
$545$	−4422.62	−0.347604
$546$	−5112.66	−0.400736
$547$	−8054.35	−0.629578	−0.314789	−	0.949162i	$-0.601934\pi$
$547$	−8054.35	−0.629578	−0.314789	+	0.949162i	$0.601934\pi$
$548$	−6281.21	−0.489635
$549$	−2138.73	−0.166264
$550$	2573.15	0.199490
$551$	−2984.52	−0.230753
$552$	−12791.3	−0.986296
$553$	19853.6	1.52669
$554$	1047.14	0.0803042
$555$	7147.86	0.546684
$556$	−12374.7	−0.943890
$557$	−6136.57	−0.466813	−0.233407	−	0.972379i	$-0.574987\pi$
$557$	−6136.57	−0.466813	−0.233407	+	0.972379i	$0.574987\pi$
$558$	−3635.54	−0.275815
$559$	7486.34	0.566437
$560$	−5378.83	−0.405888
$561$	418.079	0.0314640
$562$	6634.57	0.497976
$563$	−12767.6	−0.955758	−0.477879	−	0.878426i	$-0.658594\pi$
$563$	−12767.6	−0.955758	−0.477879	+	0.878426i	$0.658594\pi$
$564$	7760.34	0.579378
$565$	24243.4	1.80518
$566$	−8135.66	−0.604182
$567$	1814.39	0.134387
$568$	−10001.1	−0.738800
$569$	−2720.86	−0.200464	−0.100232	−	0.994964i	$-0.531959\pi$
$569$	−2720.86	−0.200464	−0.100232	+	0.994964i	$0.531959\pi$
$570$	−2144.36	−0.157574
$571$	14067.8	1.03103	0.515515	−	0.856881i	$-0.327601\pi$
$571$	14067.8	1.03103	0.515515	+	0.856881i	$0.327601\pi$
$572$	1210.14	0.0884590
$573$	−11413.8	−0.832146
$574$	−4852.33	−0.352844
$575$	30829.6	2.23597
$576$	3897.85	0.281962
$577$	11972.8	0.863836	0.431918	−	0.901913i	$-0.357837\pi$
$577$	11972.8	0.863836	0.431918	+	0.901913i	$0.357837\pi$
$578$	−9001.22	−0.647753
$579$	12814.2	0.919761
$580$	−10092.8	−0.722550
$581$	−9490.82	−0.677703
$582$	−2732.50	−0.194615
$583$	−3133.02	−0.222567
$584$	6399.76	0.453466
$585$	−6003.24	−0.424279
$586$	1335.87	0.0941713
$587$	21594.7	1.51841	0.759207	−	0.650849i	$-0.225587\pi$
$587$	21594.7	1.51841	0.759207	+	0.650849i	$0.225587\pi$
$588$	−1966.45	−0.137916
$589$	4324.05	0.302494
$590$	−15603.8	−1.08881
$591$	−4784.76	−0.333027
$592$	−1922.82	−0.133492
$593$	−19707.9	−1.36477	−0.682384	−	0.730994i	$-0.739057\pi$
$593$	−19707.9	−1.36477	−0.682384	+	0.730994i	$0.739057\pi$
$594$	402.640	0.0278123
$595$	7104.36	0.489497
$596$	12778.5	0.878234
$597$	2433.66	0.166839
$598$	−13593.7	−0.929576
$599$	12686.6	0.865377	0.432688	−	0.901544i	$-0.357565\pi$
$599$	12686.6	0.865377	0.432688	+	0.901544i	$0.357565\pi$
$600$	−12353.0	−0.840513
$601$	−15771.6	−1.07045	−0.535223	−	0.844711i	$-0.679772\pi$
$601$	−15771.6	−1.07045	−0.535223	+	0.844711i	$0.679772\pi$
$602$	−8532.33	−0.577661
$603$	603.000	0.0407231
$604$	5612.52	0.378096
$605$	−21968.3	−1.47626
$606$	−11910.4	−0.798395
$607$	24940.8	1.66774	0.833868	−	0.551964i	$-0.186122\pi$
$607$	24940.8	1.66774	0.833868	+	0.551964i	$0.186122\pi$
$608$	−3443.92	−0.229719
$609$	9522.74	0.633630
$610$	−8065.09	−0.535321
$611$	24226.3	1.60408
$612$	−683.249	−0.0451286
$613$	1934.72	0.127476	0.0637378	−	0.997967i	$-0.479698\pi$
$613$	1934.72	0.127476	0.0637378	+	0.997967i	$0.479698\pi$
$614$	−3643.48	−0.239477
$615$	−5697.56	−0.373573
$616$	−4051.54	−0.265002
$617$	−20874.6	−1.36204	−0.681021	−	0.732264i	$-0.738464\pi$
$617$	−20874.6	−1.36204	−0.681021	+	0.732264i	$0.738464\pi$
$618$	−5444.04	−0.354355
$619$	21934.4	1.42426	0.712131	−	0.702047i	$-0.247730\pi$
$619$	21934.4	1.42426	0.712131	+	0.702047i	$0.247730\pi$
$620$	14622.6	0.947191
$621$	4824.14	0.311733
$622$	−15272.8	−0.984537
$623$	5136.78	0.330338
$624$	1614.91	0.103603
$625$	−7420.52	−0.474913
$626$	6541.44	0.417649
$627$	−478.892	−0.0305026
$628$	6650.98	0.422616
$629$	2539.66	0.160990
$630$	6842.01	0.432686
$631$	−12365.0	−0.780103	−0.390051	−	0.920793i	$-0.627543\pi$
$631$	−12365.0	−0.780103	−0.390051	+	0.920793i	$0.627543\pi$
$632$	−21151.0	−1.33124
$633$	10468.8	0.657341
$634$	9965.69	0.624271
$635$	37821.7	2.36363
$636$	5120.17	0.319226
$637$	−6138.88	−0.381839
$638$	2113.24	0.131134
$639$	3771.84	0.233508
$640$	−7866.65	−0.485870
$641$	18679.2	1.15099	0.575494	−	0.817806i	$-0.304810\pi$
$641$	18679.2	1.15099	0.575494	+	0.817806i	$0.304810\pi$
$642$	−5810.34	−0.357190
$643$	10473.1	0.642331	0.321166	−	0.947023i	$-0.395925\pi$
$643$	10473.1	0.642331	0.321166	+	0.947023i	$0.395925\pi$
$644$	−16524.8	−1.01113
$645$	−10018.6	−0.611598
$646$	−761.899	−0.0464032
$647$	−10674.1	−0.648599	−0.324300	−	0.945954i	$-0.605129\pi$
$647$	−10674.1	−0.648599	−0.324300	+	0.945954i	$0.605129\pi$
$648$	−1932.96	−0.117182
$649$	−3484.74	−0.210767
$650$	−13127.8	−0.792177
$651$	−13796.8	−0.830626
$652$	−16389.2	−0.984431
$653$	1899.26	0.113819	0.0569094	−	0.998379i	$-0.481875\pi$
$653$	1899.26	0.113819	0.0569094	+	0.998379i	$0.481875\pi$
$654$	−1513.34	−0.0904839
$655$	−13415.7	−0.800296
$656$	1532.68	0.0912213
$657$	−2413.61	−0.143324
$658$	−27611.2	−1.63586
$659$	28028.3	1.65680	0.828398	−	0.560139i	$-0.189252\pi$
$659$	28028.3	1.65680	0.828398	+	0.560139i	$0.189252\pi$
$660$	−1619.47	−0.0955117
$661$	−19098.7	−1.12383	−0.561917	−	0.827194i	$-0.689936\pi$
$661$	−19098.7	−1.12383	−0.561917	+	0.827194i	$0.689936\pi$
$662$	18452.0	1.08332
$663$	−2132.98	−0.124944
$664$	10111.1	0.590942
$665$	−8137.75	−0.474539
$666$	2445.88	0.142306
$667$	25319.3	1.46981
$668$	−11573.7	−0.670359
$669$	1645.13	0.0950736
$670$	2273.89	0.131117
$671$	−1801.15	−0.103625
$672$	10988.5	0.630791
$673$	−8398.14	−0.481017	−0.240509	−	0.970647i	$-0.577314\pi$
$673$	−8398.14	−0.481017	−0.240509	+	0.970647i	$0.577314\pi$
$674$	8178.25	0.467381
$675$	4658.82	0.265656
$676$	2897.26	0.164842
$677$	3327.79	0.188918	0.0944589	−	0.995529i	$-0.469888\pi$
$677$	3327.79	0.188918	0.0944589	+	0.995529i	$0.469888\pi$
$678$	8295.69	0.469903
$679$	−10369.8	−0.586089
$680$	−7568.64	−0.426830
$681$	13029.9	0.733194
$682$	−3061.70	−0.171904
$683$	−17844.1	−0.999687	−0.499844	−	0.866116i	$-0.666609\pi$
$683$	−17844.1	−0.999687	−0.499844	+	0.866116i	$0.666609\pi$
$684$	782.633	0.0437496
$685$	26241.4	1.46370
$686$	−8120.07	−0.451933
$687$	6152.55	0.341680
$688$	2695.06	0.149344
$689$	15984.2	0.883817
$690$	18191.7	1.00369
$691$	19392.8	1.06763	0.533817	−	0.845600i	$-0.320757\pi$
$691$	19392.8	1.06763	0.533817	+	0.845600i	$0.320757\pi$
$692$	−8157.89	−0.448145
$693$	1528.00	0.0837577
$694$	−626.913	−0.0342901
$695$	51698.4	2.82163
$696$	−10145.1	−0.552511
$697$	−2024.37	−0.110012
$698$	18062.1	0.979457
$699$	8986.67	0.486276
$700$	−15958.5	−0.861680
$701$	−5759.41	−0.310314	−0.155157	−	0.987890i	$-0.549588\pi$
$701$	−5759.41	−0.310314	−0.155157	+	0.987890i	$0.549588\pi$
$702$	−2054.21	−0.110443
$703$	−2909.08	−0.156071
$704$	3282.61	0.175736
$705$	−32420.8	−1.73197
$706$	5363.40	0.285913
$707$	−45199.6	−2.40439
$708$	5694.96	0.302302
$709$	2884.97	0.152817	0.0764085	−	0.997077i	$-0.475655\pi$
$709$	2884.97	0.152817	0.0764085	+	0.997077i	$0.475655\pi$
$710$	14223.5	0.751829
$711$	7976.93	0.420757
$712$	−5472.47	−0.288047
$713$	−36683.1	−1.92678
$714$	2430.99	0.127420
$715$	−5055.68	−0.264436
$716$	3679.14	0.192033
$717$	3885.32	0.202371
$718$	15525.0	0.806948
$719$	−13283.5	−0.689002	−0.344501	−	0.938786i	$-0.611952\pi$
$719$	−13283.5	−0.689002	−0.344501	+	0.938786i	$0.611952\pi$
$720$	−2161.15	−0.111863
$721$	−20659.9	−1.06715
$722$	−12622.4	−0.650634
$723$	−10059.9	−0.517473
$724$	−10232.8	−0.525274
$725$	24451.6	1.25256
$726$	−7517.17	−0.384282
$727$	20744.7	1.05829	0.529147	−	0.848530i	$-0.322512\pi$
$727$	20744.7	1.05829	0.529147	+	0.848530i	$0.322512\pi$
$728$	20670.3	1.05233
$729$	729.000	0.0370370
$730$	−9101.67	−0.461463
$731$	−3559.64	−0.180107
$732$	2943.54	0.148629
$733$	−8681.60	−0.437466	−0.218733	−	0.975785i	$-0.570192\pi$
$733$	−8681.60	−0.437466	−0.218733	+	0.975785i	$0.570192\pi$
$734$	−12020.9	−0.604497
$735$	8215.34	0.412282
$736$	29216.5	1.46323
$737$	507.822	0.0253811
$738$	−1949.61	−0.0972440
$739$	14980.7	0.745701	0.372851	−	0.927891i	$-0.378380\pi$
$739$	14980.7	0.745701	0.372851	+	0.927891i	$0.378380\pi$
$740$	−9837.63	−0.488700
$741$	2443.23	0.121126
$742$	−18217.5	−0.901329
$743$	−3656.39	−0.180538	−0.0902692	−	0.995917i	$-0.528773\pi$
$743$	−3656.39	−0.180538	−0.0902692	+	0.995917i	$0.528773\pi$
$744$	14698.4	0.724287
$745$	−53385.4	−2.62536
$746$	21135.8	1.03732
$747$	−3813.30	−0.186775
$748$	−575.404	−0.0281268
$749$	−22050.0	−1.07569
$750$	4841.24	0.235703
$751$	−9721.36	−0.472354	−0.236177	−	0.971710i	$-0.575894\pi$
$751$	−9721.36	−0.472354	−0.236177	+	0.971710i	$0.575894\pi$
$752$	8721.42	0.422922
$753$	11494.0	0.556263
$754$	−10781.4	−0.520737
$755$	−23447.8	−1.13027
$756$	−2497.15	−0.120133
$757$	26927.4	1.29286	0.646429	−	0.762974i	$-0.276262\pi$
$757$	26927.4	1.29286	0.646429	+	0.762974i	$0.276262\pi$
$758$	13403.5	0.642263
$759$	4062.69	0.194290
$760$	8669.57	0.413787
$761$	−32275.9	−1.53745	−0.768725	−	0.639579i	$-0.779109\pi$
$761$	−32275.9	−1.53745	−0.768725	+	0.639579i	$0.779109\pi$
$762$	12941.9	0.615272
$763$	−5743.09	−0.272495
$764$	15708.9	0.743885
$765$	2854.45	0.134906
$766$	−16101.7	−0.759501
$767$	17778.6	0.836960
$768$	−13086.1	−0.614849
$769$	39192.5	1.83787	0.918933	−	0.394414i	$-0.129052\pi$
$769$	39192.5	1.83787	0.918933	+	0.394414i	$0.129052\pi$
$770$	5762.06	0.269675
$771$	−14707.5	−0.687002
$772$	−17636.3	−0.822207
$773$	24987.3	1.16265	0.581326	−	0.813671i	$-0.302534\pi$
$773$	24987.3	1.16265	0.581326	+	0.813671i	$0.302534\pi$
$774$	−3428.19	−0.159204
$775$	−35426.0	−1.64199
$776$	11047.4	0.511056
$777$	9282.01	0.428559
$778$	−6316.26	−0.291065
$779$	2318.83	0.106650
$780$	8262.28	0.379278
$781$	3176.49	0.145536
$782$	6463.58	0.295572
$783$	3826.12	0.174629
$784$	−2209.98	−0.100673
$785$	−27786.2	−1.26335
$786$	−4590.62	−0.208323
$787$	−31307.8	−1.41805	−0.709023	−	0.705185i	$-0.750864\pi$
$787$	−31307.8	−1.41805	−0.709023	+	0.705185i	$0.750864\pi$
$788$	6585.29	0.297704
$789$	−5253.75	−0.237057
$790$	30080.8	1.35472
$791$	31481.9	1.41513
$792$	−1627.86	−0.0730347
$793$	9189.20	0.411498
$794$	−17821.9	−0.796567
$795$	−21390.8	−0.954282
$796$	−3349.46	−0.149144
$797$	515.007	0.0228889	0.0114445	−	0.999935i	$-0.496357\pi$
$797$	515.007	0.0228889	0.0114445	+	0.999935i	$0.496357\pi$
$798$	−2784.60	−0.123526
$799$	−11519.3	−0.510040
$800$	28215.3	1.24695
$801$	2063.90	0.0910414
$802$	4347.85	0.191431
$803$	−2032.65	−0.0893282
$804$	−829.911	−0.0364039
$805$	69036.8	3.02264
$806$	15620.4	0.682635
$807$	−18472.5	−0.805778
$808$	48153.5	2.09658
$809$	38476.7	1.67215	0.836075	−	0.548615i	$-0.184845\pi$
$809$	38476.7	1.67215	0.836075	+	0.548615i	$0.184845\pi$
$810$	2749.04	0.119249
$811$	−17887.3	−0.774487	−0.387243	−	0.921978i	$-0.626573\pi$
$811$	−17887.3	−0.774487	−0.387243	+	0.921978i	$0.626573\pi$
$812$	−13106.2	−0.566425
$813$	15631.6	0.674321
$814$	2059.82	0.0886935
$815$	68470.0	2.94282
$816$	−767.866	−0.0329420
$817$	4077.42	0.174603
$818$	−30146.3	−1.28856
$819$	−7795.64	−0.332603
$820$	7841.57	0.333951
$821$	22773.3	0.968081	0.484041	−	0.875046i	$-0.339169\pi$
$821$	22773.3	0.968081	0.484041	+	0.875046i	$0.339169\pi$
$822$	8979.36	0.381011
$823$	−13554.5	−0.574096	−0.287048	−	0.957916i	$-0.592674\pi$
$823$	−13554.5	−0.574096	−0.287048	+	0.957916i	$0.592674\pi$
$824$	22010.1	0.930532
$825$	3923.46	0.165573
$826$	−20262.6	−0.853543
$827$	−23391.2	−0.983546	−0.491773	−	0.870724i	$-0.663651\pi$
$827$	−23391.2	−0.983546	−0.491773	+	0.870724i	$0.663651\pi$
$828$	−6639.48	−0.278669
$829$	19257.3	0.806797	0.403399	−	0.915024i	$-0.367829\pi$
$829$	19257.3	0.806797	0.403399	+	0.915024i	$0.367829\pi$
$830$	−14379.8	−0.601363
$831$	1596.64	0.0666509
$832$	−16747.4	−0.697849
$833$	2918.94	0.121411
$834$	17690.3	0.734491
$835$	48352.1	2.00394
$836$	659.101	0.0272673
$837$	−5543.37	−0.228921
$838$	28345.7	1.16848
$839$	33309.4	1.37064	0.685321	−	0.728241i	$-0.259662\pi$
$839$	33309.4	1.37064	0.685321	+	0.728241i	$0.259662\pi$
$840$	−27662.0	−1.13623
$841$	−4307.78	−0.176628
$842$	−18689.8	−0.764955
$843$	10116.2	0.413310
$844$	−14408.2	−0.587621
$845$	−12104.1	−0.492772
$846$	−11093.9	−0.450845
$847$	−28527.4	−1.15728
$848$	5754.28	0.233022
$849$	−12405.0	−0.501460
$850$	6242.08	0.251884
$851$	24679.2	0.994117
$852$	−5191.20	−0.208741
$853$	13876.3	0.556993	0.278497	−	0.960437i	$-0.410164\pi$
$853$	13876.3	0.556993	0.278497	+	0.960437i	$0.410164\pi$
$854$	−10473.1	−0.419652
$855$	−3269.65	−0.130783
$856$	23491.0	0.937976
$857$	2542.62	0.101347	0.0506734	−	0.998715i	$-0.483863\pi$
$857$	2542.62	0.101347	0.0506734	+	0.998715i	$0.483863\pi$
$858$	−1729.97	−0.0688347
$859$	−47743.7	−1.89638	−0.948192	−	0.317699i	$-0.897090\pi$
$859$	−47743.7	−1.89638	−0.948192	+	0.317699i	$0.897090\pi$
$860$	13788.6	0.546730
$861$	−7398.69	−0.292853
$862$	22746.3	0.898772
$863$	−25394.5	−1.00167	−0.500833	−	0.865544i	$-0.666973\pi$
$863$	−25394.5	−1.00167	−0.500833	+	0.865544i	$0.666973\pi$
$864$	4415.06	0.173846
$865$	34081.7	1.33967
$866$	3605.59	0.141482
$867$	−13724.8	−0.537623
$868$	18988.5	0.742527
$869$	6717.84	0.262241
$870$	14428.2	0.562255
$871$	−2590.83	−0.100789
$872$	6118.41	0.237609
$873$	−4166.44	−0.161527
$874$	−7403.77	−0.286540
$875$	18372.3	0.709826
$876$	3321.87	0.128123
$877$	−35430.3	−1.36419	−0.682096	−	0.731263i	$-0.738931\pi$
$877$	−35430.3	−1.36419	−0.682096	+	0.731263i	$0.738931\pi$
$878$	29850.7	1.14739
$879$	2036.90	0.0781604
$880$	−1820.03	−0.0697196
$881$	−15296.7	−0.584972	−0.292486	−	0.956270i	$-0.594482\pi$
$881$	−15296.7	−0.584972	−0.292486	+	0.956270i	$0.594482\pi$
$882$	2811.15	0.107320
$883$	−20026.0	−0.763226	−0.381613	−	0.924322i	$-0.624631\pi$
$883$	−20026.0	−0.763226	−0.381613	+	0.924322i	$0.624631\pi$
$884$	2935.62	0.111692
$885$	−23792.2	−0.903689
$886$	17260.1	0.654476
$887$	−30997.6	−1.17339	−0.586696	−	0.809808i	$-0.699572\pi$
$887$	−30997.6	−1.17339	−0.586696	+	0.809808i	$0.699572\pi$
$888$	−9888.61	−0.373694
$889$	49114.2	1.85291
$890$	7782.89	0.293127
$891$	613.934	0.0230837
$892$	−2264.19	−0.0849897
$893$	13194.8	0.494455
$894$	−18267.6	−0.683400
$895$	−15370.6	−0.574057
$896$	−10215.4	−0.380885
$897$	−20727.2	−0.771530
$898$	9939.27	0.369352
$899$	−29094.1	−1.07936
$900$	−6411.95	−0.237480
$901$	−7600.25	−0.281022
$902$	−1641.88	−0.0606082
$903$	−13009.8	−0.479447
$904$	−33539.2	−1.23396
$905$	42750.1	1.57023
$906$	−8023.43	−0.294217
$907$	−36577.6	−1.33907	−0.669536	−	0.742780i	$-0.733507\pi$
$907$	−36577.6	−1.33907	−0.669536	+	0.742780i	$0.733507\pi$
$908$	−17933.0	−0.655428
$909$	−18160.7	−0.662652
$910$	−29397.1	−1.07089
$911$	22947.0	0.834541	0.417271	−	0.908782i	$-0.362987\pi$
$911$	22947.0	0.834541	0.417271	+	0.908782i	$0.362987\pi$
$912$	879.559	0.0319354
$913$	−3211.40	−0.116410
$914$	1820.15	0.0658699
$915$	−12297.4	−0.444306
$916$	−8467.78	−0.305440
$917$	−17421.2	−0.627372
$918$	976.744	0.0351170
$919$	26079.4	0.936104	0.468052	−	0.883701i	$-0.344956\pi$
$919$	26079.4	0.936104	0.468052	+	0.883701i	$0.344956\pi$
$920$	−73548.5	−2.63567
$921$	−5555.47	−0.198761
$922$	−2495.19	−0.0891267
$923$	−16206.0	−0.577926
$924$	−2103.00	−0.0748740
$925$	23833.5	0.847178
$926$	31163.0	1.10592
$927$	−8300.92	−0.294108
$928$	23172.2	0.819682
$929$	−52677.5	−1.86038	−0.930189	−	0.367081i	$-0.880357\pi$
$929$	−52677.5	−1.86038	−0.930189	+	0.367081i	$0.880357\pi$
$930$	−20903.9	−0.737060
$931$	−3343.53	−0.117701
$932$	−12368.4	−0.434700
$933$	−23287.5	−0.817146
$934$	−14819.8	−0.519186
$935$	2403.90	0.0840812
$936$	8305.10	0.290022
$937$	−22175.7	−0.773156	−0.386578	−	0.922257i	$-0.626343\pi$
$937$	−22175.7	−0.773156	−0.386578	+	0.922257i	$0.626343\pi$
$938$	2952.82	0.102786
$939$	9974.20	0.346641
$940$	44620.9	1.54827
$941$	49964.6	1.73092	0.865461	−	0.500976i	$-0.167025\pi$
$941$	49964.6	1.73092	0.865461	+	0.500976i	$0.167025\pi$
$942$	−9507.97	−0.328860
$943$	−19671.8	−0.679324
$944$	6400.25	0.220668
$945$	10432.5	0.359121
$946$	−2887.08	−0.0992251
$947$	−25531.1	−0.876081	−0.438041	−	0.898955i	$-0.644327\pi$
$947$	−25531.1	−0.876081	−0.438041	+	0.898955i	$0.644327\pi$
$948$	−10978.7	−0.376130
$949$	10370.3	0.354723
$950$	−7150.04	−0.244187
$951$	15195.4	0.518133
$952$	−9828.44	−0.334602
$953$	−27036.4	−0.918987	−0.459493	−	0.888181i	$-0.651969\pi$
$953$	−27036.4	−0.918987	−0.459493	+	0.888181i	$0.651969\pi$
$954$	−7319.58	−0.248407
$955$	−65628.0	−2.22374
$956$	−5347.38	−0.180907
$957$	3222.20	0.108839
$958$	13019.1	0.439068
$959$	34076.4	1.14743
$960$	22412.1	0.753487
$961$	12361.3	0.414932
$962$	−10508.9	−0.352203
$963$	−8859.44	−0.296461
$964$	13845.5	0.462588
$965$	73680.2	2.45787
$966$	23623.2	0.786817
$967$	−14044.2	−0.467043	−0.233522	−	0.972352i	$-0.575025\pi$
$967$	−14044.2	−0.467043	−0.233522	+	0.972352i	$0.575025\pi$
$968$	30391.7	1.00912
$969$	−1161.72	−0.0385138
$970$	−15711.5	−0.520069
$971$	−14551.3	−0.480920	−0.240460	−	0.970659i	$-0.577298\pi$
$971$	−14551.3	−0.480920	−0.240460	+	0.970659i	$0.577298\pi$
$972$	−1003.33	−0.0331087
$973$	67134.2	2.21194
$974$	9792.46	0.322146
$975$	−20016.9	−0.657492
$976$	3308.09	0.108493
$977$	36134.6	1.18326	0.591631	−	0.806209i	$-0.298484\pi$
$977$	36134.6	1.18326	0.591631	+	0.806209i	$0.298484\pi$
$978$	23429.3	0.766038
$979$	1738.13	0.0567424
$980$	−11306.8	−0.368554
$981$	−2307.50	−0.0750999
$982$	−35400.3	−1.15038
$983$	39590.1	1.28457	0.642283	−	0.766467i	$-0.277987\pi$
$983$	39590.1	1.28457	0.642283	+	0.766467i	$0.277987\pi$
$984$	7882.21	0.255361
$985$	−27511.7	−0.889946
$986$	5126.40	0.165576
$987$	−42100.8	−1.35773
$988$	−3362.63	−0.108279
$989$	−34590.9	−1.11216
$990$	2315.13	0.0743227
$991$	−48713.6	−1.56149	−0.780746	−	0.624848i	$-0.785161\pi$
$991$	−48713.6	−1.56149	−0.780746	+	0.624848i	$0.785161\pi$
$992$	−33572.4	−1.07452
$993$	28135.0	0.899132
$994$	18470.3	0.589377
$995$	13993.2	0.445844
$996$	5248.26	0.166965
$997$	42322.9	1.34441	0.672207	−	0.740364i	$-0.265347\pi$
$997$	42322.9	1.34441	0.672207	+	0.740364i	$0.265347\pi$
$998$	−31021.8	−0.983947
$999$	3729.40	0.118111

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.e.1.7	✓	11
3.2	odd	2		603.4.a.g.1.5		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.e.1.7	✓	11	1.1	even	1	trivial
603.4.a.g.1.5		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+1.96751 q^{2} +3.00000 q^{3} -4.12891 q^{4} +17.2496 q^{5} +5.90252 q^{6} +22.3999 q^{7} -23.8637 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.96751 q^{2} +3.00000 q^{3} -4.12891 q^{4} +17.2496 q^{5} +5.90252 q^{6} +22.3999 q^{7} -23.8637 q^{8} +9.00000 q^{9} +33.9387 q^{10} +7.57943 q^{11} -12.3867 q^{12} -38.6691 q^{13} +44.0719 q^{14} +51.7488 q^{15} -13.9208 q^{16} +18.3866 q^{17} +17.7076 q^{18} -21.0611 q^{19} -71.2221 q^{20} +67.1996 q^{21} +14.9126 q^{22} +178.672 q^{23} -71.5912 q^{24} +172.549 q^{25} -76.0817 q^{26} +27.0000 q^{27} -92.4871 q^{28} +141.708 q^{29} +101.816 q^{30} -205.310 q^{31} +163.521 q^{32} +22.7383 q^{33} +36.1757 q^{34} +386.389 q^{35} -37.1602 q^{36} +138.126 q^{37} -41.4378 q^{38} -116.007 q^{39} -411.640 q^{40} -110.100 q^{41} +132.216 q^{42} -193.600 q^{43} -31.2948 q^{44} +155.246 q^{45} +351.538 q^{46} -626.504 q^{47} -41.7623 q^{48} +158.754 q^{49} +339.491 q^{50} +55.1597 q^{51} +159.661 q^{52} -413.359 q^{53} +53.1227 q^{54} +130.742 q^{55} -534.544 q^{56} -63.1832 q^{57} +278.812 q^{58} -459.763 q^{59} -213.666 q^{60} -237.637 q^{61} -403.949 q^{62} +201.599 q^{63} +433.094 q^{64} -667.026 q^{65} +44.7378 q^{66} +67.0000 q^{67} -75.9165 q^{68} +536.016 q^{69} +760.223 q^{70} +419.094 q^{71} -214.774 q^{72} -268.179 q^{73} +271.764 q^{74} +517.646 q^{75} +86.9592 q^{76} +169.778 q^{77} -228.245 q^{78} +886.326 q^{79} -240.128 q^{80} +81.0000 q^{81} -216.623 q^{82} -423.700 q^{83} -277.461 q^{84} +317.161 q^{85} -380.910 q^{86} +425.125 q^{87} -180.873 q^{88} +229.322 q^{89} +305.449 q^{90} -866.183 q^{91} -737.720 q^{92} -615.930 q^{93} -1232.65 q^{94} -363.295 q^{95} +490.562 q^{96} -462.938 q^{97} +312.350 q^{98} +68.2149 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9} + 29 q^{10} + 104 q^{11} + 207 q^{12} + 172 q^{13} + 143 q^{14} + 24 q^{15} + 485 q^{16} - 48 q^{17} + 27 q^{18} + 180 q^{19} - 539 q^{20} + 234 q^{21} - 144 q^{22} + 156 q^{23} + 63 q^{24} + 383 q^{25} - 252 q^{26} + 297 q^{27} + 1011 q^{28} - 4 q^{29} + 87 q^{30} + 514 q^{31} - 119 q^{32} + 312 q^{33} + 72 q^{34} - 338 q^{35} + 621 q^{36} + 854 q^{37} - 308 q^{38} + 516 q^{39} - 15 q^{40} + 674 q^{41} + 429 q^{42} + 738 q^{43} + 356 q^{44} + 72 q^{45} + 507 q^{46} + 54 q^{47} + 1455 q^{48} + 1465 q^{49} + 656 q^{50} - 144 q^{51} - 12 q^{52} - 190 q^{53} + 81 q^{54} + 262 q^{55} + 239 q^{56} + 540 q^{57} - 1466 q^{58} + 18 q^{59} - 1617 q^{60} + 328 q^{61} - 915 q^{62} + 702 q^{63} + 2253 q^{64} - 732 q^{65} - 432 q^{66} + 737 q^{67} - 5746 q^{68} + 468 q^{69} - 4451 q^{70} + 264 q^{71} + 189 q^{72} + 330 q^{73} - 5975 q^{74} + 1149 q^{75} - 178 q^{76} - 368 q^{77} - 756 q^{78} + 456 q^{79} - 8515 q^{80} + 891 q^{81} - 3629 q^{82} - 2432 q^{83} + 3033 q^{84} + 2882 q^{85} - 6225 q^{86} - 12 q^{87} - 5492 q^{88} - 2340 q^{89} + 261 q^{90} - 994 q^{91} - 2939 q^{92} + 1542 q^{93} - 3506 q^{94} - 2568 q^{95} - 357 q^{96} + 1892 q^{97} - 1078 q^{98} + 936 q^{99}+O(q^{100}) \) 11 * q + 3 * q^2 + 33 * q^3 + 69 * q^4 + 8 * q^5 + 9 * q^6 + 78 * q^7 + 21 * q^8 + 99 * q^9 + 29 * q^10 + 104 * q^11 + 207 * q^12 + 172 * q^13 + 143 * q^14 + 24 * q^15 + 485 * q^16 - 48 * q^17 + 27 * q^18 + 180 * q^19 - 539 * q^20 + 234 * q^21 - 144 * q^22 + 156 * q^23 + 63 * q^24 + 383 * q^25 - 252 * q^26 + 297 * q^27 + 1011 * q^28 - 4 * q^29 + 87 * q^30 + 514 * q^31 - 119 * q^32 + 312 * q^33 + 72 * q^34 - 338 * q^35 + 621 * q^36 + 854 * q^37 - 308 * q^38 + 516 * q^39 - 15 * q^40 + 674 * q^41 + 429 * q^42 + 738 * q^43 + 356 * q^44 + 72 * q^45 + 507 * q^46 + 54 * q^47 + 1455 * q^48 + 1465 * q^49 + 656 * q^50 - 144 * q^51 - 12 * q^52 - 190 * q^53 + 81 * q^54 + 262 * q^55 + 239 * q^56 + 540 * q^57 - 1466 * q^58 + 18 * q^59 - 1617 * q^60 + 328 * q^61 - 915 * q^62 + 702 * q^63 + 2253 * q^64 - 732 * q^65 - 432 * q^66 + 737 * q^67 - 5746 * q^68 + 468 * q^69 - 4451 * q^70 + 264 * q^71 + 189 * q^72 + 330 * q^73 - 5975 * q^74 + 1149 * q^75 - 178 * q^76 - 368 * q^77 - 756 * q^78 + 456 * q^79 - 8515 * q^80 + 891 * q^81 - 3629 * q^82 - 2432 * q^83 + 3033 * q^84 + 2882 * q^85 - 6225 * q^86 - 12 * q^87 - 5492 * q^88 - 2340 * q^89 + 261 * q^90 - 994 * q^91 - 2939 * q^92 + 1542 * q^93 - 3506 * q^94 - 2568 * q^95 - 357 * q^96 + 1892 * q^97 - 1078 * q^98 + 936 * q^99

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