LMFDB - Embedded newform 201.4.a.e.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:	$0$
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			1.3
Root			$-3.89104$ 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)

$f(q)$	$=$	$q-3.89104 q^{2} +3.00000 q^{3} +7.14021 q^{4} +11.5975 q^{5} -11.6731 q^{6} +32.2920 q^{7} +3.34547 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.89104 q^{2} +3.00000 q^{3} +7.14021 q^{4} +11.5975 q^{5} -11.6731 q^{6} +32.2920 q^{7} +3.34547 q^{8} +9.00000 q^{9} -45.1263 q^{10} -13.3270 q^{11} +21.4206 q^{12} +50.5234 q^{13} -125.650 q^{14} +34.7925 q^{15} -70.1391 q^{16} -13.3656 q^{17} -35.0194 q^{18} -18.8977 q^{19} +82.8085 q^{20} +96.8760 q^{21} +51.8559 q^{22} -38.3572 q^{23} +10.0364 q^{24} +9.50166 q^{25} -196.589 q^{26} +27.0000 q^{27} +230.572 q^{28} -132.057 q^{29} -135.379 q^{30} +50.6070 q^{31} +246.150 q^{32} -39.9810 q^{33} +52.0060 q^{34} +374.506 q^{35} +64.2619 q^{36} +385.568 q^{37} +73.5316 q^{38} +151.570 q^{39} +38.7991 q^{40} -470.692 q^{41} -376.949 q^{42} +406.932 q^{43} -95.1575 q^{44} +104.377 q^{45} +149.249 q^{46} +26.6782 q^{47} -210.417 q^{48} +699.773 q^{49} -36.9714 q^{50} -40.0967 q^{51} +360.747 q^{52} +203.594 q^{53} -105.058 q^{54} -154.560 q^{55} +108.032 q^{56} -56.6930 q^{57} +513.840 q^{58} +86.0839 q^{59} +248.425 q^{60} -310.426 q^{61} -196.914 q^{62} +290.628 q^{63} -396.669 q^{64} +585.944 q^{65} +155.568 q^{66} +67.0000 q^{67} -95.4331 q^{68} -115.071 q^{69} -1457.22 q^{70} -692.245 q^{71} +30.1093 q^{72} +172.160 q^{73} -1500.26 q^{74} +28.5050 q^{75} -134.933 q^{76} -430.355 q^{77} -589.766 q^{78} -1375.70 q^{79} -813.437 q^{80} +81.0000 q^{81} +1831.48 q^{82} -827.777 q^{83} +691.715 q^{84} -155.007 q^{85} -1583.39 q^{86} -396.172 q^{87} -44.5851 q^{88} +630.402 q^{89} -406.137 q^{90} +1631.50 q^{91} -273.878 q^{92} +151.821 q^{93} -103.806 q^{94} -219.165 q^{95} +738.451 q^{96} -951.415 q^{97} -2722.84 q^{98} -119.943 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.89104	−1.37569	−0.687846	−	0.725857i	$-0.741443\pi$
$2$	−3.89104	−1.37569	−0.687846	+	0.725857i	$0.741443\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	7.14021	0.892526
$5$	11.5975	1.03731	0.518655	−	0.854983i	$-0.326433\pi$
$5$	11.5975	1.03731	0.518655	+	0.854983i	$0.326433\pi$
$6$	−11.6731	−0.794256
$7$	32.2920	1.74360	0.871802	−	0.489859i	$-0.162952\pi$
$7$	32.2920	1.74360	0.871802	+	0.489859i	$0.162952\pi$
$8$	3.34547	0.147850
$9$	9.00000	0.333333
$10$	−45.1263	−1.42702
$11$	−13.3270	−0.365295	−0.182647	−	0.983179i	$-0.558467\pi$
$11$	−13.3270	−0.365295	−0.182647	+	0.983179i	$0.558467\pi$
$12$	21.4206	0.515300
$13$	50.5234	1.07790	0.538948	−	0.842339i	$-0.318822\pi$
$13$	50.5234	1.07790	0.538948	+	0.842339i	$0.318822\pi$
$14$	−125.650	−2.39866
$15$	34.7925	0.598892
$16$	−70.1391	−1.09592
$17$	−13.3656	−0.190684	−0.0953420	−	0.995445i	$-0.530394\pi$
$17$	−13.3656	−0.190684	−0.0953420	+	0.995445i	$0.530394\pi$
$18$	−35.0194	−0.458564
$19$	−18.8977	−0.228180	−0.114090	−	0.993470i	$-0.536395\pi$
$19$	−18.8977	−0.228180	−0.114090	+	0.993470i	$0.536395\pi$
$20$	82.8085	0.925827
$21$	96.8760	1.00667
$22$	51.8559	0.502532
$23$	−38.3572	−0.347740	−0.173870	−	0.984769i	$-0.555627\pi$
$23$	−38.3572	−0.347740	−0.173870	+	0.984769i	$0.555627\pi$
$24$	10.0364	0.0853615
$25$	9.50166	0.0760133
$26$	−196.589	−1.48285
$27$	27.0000	0.192450
$28$	230.572	1.55621
$29$	−132.057	−0.845600	−0.422800	−	0.906223i	$-0.638953\pi$
$29$	−132.057	−0.845600	−0.422800	+	0.906223i	$0.638953\pi$
$30$	−135.379	−0.823890
$31$	50.6070	0.293203	0.146601	−	0.989196i	$-0.453167\pi$
$31$	50.6070	0.293203	0.146601	+	0.989196i	$0.453167\pi$
$32$	246.150	1.35980
$33$	−39.9810	−0.210903
$34$	52.0060	0.262322
$35$	374.506	1.80866
$36$	64.2619	0.297509
$37$	385.568	1.71316	0.856580	−	0.516014i	$-0.172585\pi$
$37$	385.568	1.71316	0.856580	+	0.516014i	$0.172585\pi$
$38$	73.5316	0.313905
$39$	151.570	0.622324
$40$	38.7991	0.153367
$41$	−470.692	−1.79292	−0.896461	−	0.443123i	$-0.853871\pi$
$41$	−470.692	−1.79292	−0.896461	+	0.443123i	$0.853871\pi$
$42$	−376.949	−1.38487
$43$	406.932	1.44318	0.721588	−	0.692323i	$-0.243412\pi$
$43$	406.932	1.44318	0.721588	+	0.692323i	$0.243412\pi$
$44$	−95.1575	−0.326035
$45$	104.377	0.345770
$46$	149.249	0.478383
$47$	26.6782	0.0827959	0.0413980	−	0.999143i	$-0.486819\pi$
$47$	26.6782	0.0827959	0.0413980	+	0.999143i	$0.486819\pi$
$48$	−210.417	−0.632731
$49$	699.773	2.04015
$50$	−36.9714	−0.104571
$51$	−40.0967	−0.110091
$52$	360.747	0.962051
$53$	203.594	0.527656	0.263828	−	0.964570i	$-0.415015\pi$
$53$	203.594	0.527656	0.263828	+	0.964570i	$0.415015\pi$
$54$	−105.058	−0.264752
$55$	−154.560	−0.378924
$56$	108.032	0.257793
$57$	−56.6930	−0.131740
$58$	513.840	1.16328
$59$	86.0839	0.189952	0.0949761	−	0.995480i	$-0.469723\pi$
$59$	86.0839	0.189952	0.0949761	+	0.995480i	$0.469723\pi$
$60$	248.425	0.534527
$61$	−310.426	−0.651574	−0.325787	−	0.945443i	$-0.605629\pi$
$61$	−310.426	−0.651574	−0.325787	+	0.945443i	$0.605629\pi$
$62$	−196.914	−0.403356
$63$	290.628	0.581201
$64$	−396.669	−0.774744
$65$	585.944	1.11811
$66$	155.568	0.290137
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	−95.4331	−0.170191
$69$	−115.071	−0.200768
$70$	−1457.22	−2.48816
$71$	−692.245	−1.15710	−0.578552	−	0.815646i	$-0.696382\pi$
$71$	−692.245	−1.15710	−0.578552	+	0.815646i	$0.696382\pi$
$72$	30.1093	0.0492835
$73$	172.160	0.276025	0.138012	−	0.990431i	$-0.455929\pi$
$73$	172.160	0.276025	0.138012	+	0.990431i	$0.455929\pi$
$74$	−1500.26	−2.35678
$75$	28.5050	0.0438863
$76$	−134.933	−0.203657
$77$	−430.355	−0.636929
$78$	−589.766	−0.856126
$79$	−1375.70	−1.95921	−0.979607	−	0.200921i	$-0.935606\pi$
$79$	−1375.70	−1.95921	−0.979607	+	0.200921i	$0.935606\pi$
$80$	−813.437	−1.13681
$81$	81.0000	0.111111
$82$	1831.48	2.46651
$83$	−827.777	−1.09470	−0.547351	−	0.836903i	$-0.684364\pi$
$83$	−827.777	−1.09470	−0.547351	+	0.836903i	$0.684364\pi$
$84$	691.715	0.898480
$85$	−155.007	−0.197799
$86$	−1583.39	−1.98537
$87$	−396.172	−0.488208
$88$	−44.5851	−0.0540090
$89$	630.402	0.750815	0.375407	−	0.926860i	$-0.377503\pi$
$89$	630.402	0.750815	0.375407	+	0.926860i	$0.377503\pi$
$90$	−406.137	−0.475673
$91$	1631.50	1.87942
$92$	−273.878	−0.310367
$93$	151.821	0.169281
$94$	−103.806	−0.113902
$95$	−219.165	−0.236694
$96$	738.451	0.785082
$97$	−951.415	−0.995892	−0.497946	−	0.867208i	$-0.665912\pi$
$97$	−951.415	−0.995892	−0.497946	+	0.867208i	$0.665912\pi$
$98$	−2722.84	−2.80662
$99$	−119.943	−0.121765
$100$	67.8439	0.0678439
$101$	1214.21	1.19622	0.598111	−	0.801414i	$-0.295918\pi$
$101$	1214.21	1.19622	0.598111	+	0.801414i	$0.295918\pi$
$102$	156.018	0.151452
$103$	184.362	0.176366	0.0881831	−	0.996104i	$-0.471894\pi$
$103$	184.362	0.176366	0.0881831	+	0.996104i	$0.471894\pi$
$104$	169.025	0.159368
$105$	1123.52	1.04423
$106$	−792.192	−0.725892
$107$	1536.64	1.38834	0.694170	−	0.719811i	$-0.255772\pi$
$107$	1536.64	1.38834	0.694170	+	0.719811i	$0.255772\pi$
$108$	192.786	0.171767
$109$	−1032.17	−0.907006	−0.453503	−	0.891255i	$-0.649826\pi$
$109$	−1032.17	−0.907006	−0.453503	+	0.891255i	$0.649826\pi$
$110$	601.398	0.521282
$111$	1156.70	0.989094
$112$	−2264.93	−1.91086
$113$	1073.80	0.893936	0.446968	−	0.894550i	$-0.352504\pi$
$113$	1073.80	0.893936	0.446968	+	0.894550i	$0.352504\pi$
$114$	220.595	0.181233
$115$	−444.847	−0.360714
$116$	−942.916	−0.754721
$117$	454.710	0.359299
$118$	−334.956	−0.261315
$119$	−431.601	−0.332477
$120$	116.397	0.0885464
$121$	−1153.39	−0.866560
$122$	1207.88	0.896365
$123$	−1412.08	−1.03514
$124$	361.344	0.261691
$125$	−1339.49	−0.958461
$126$	−1130.85	−0.799553
$127$	1205.06	0.841981	0.420990	−	0.907065i	$-0.361683\pi$
$127$	1205.06	0.841981	0.420990	+	0.907065i	$0.361683\pi$
$128$	−425.748	−0.293993
$129$	1220.80	0.833218
$130$	−2279.93	−1.53818
$131$	1450.66	0.967520	0.483760	−	0.875201i	$-0.339271\pi$
$131$	1450.66	0.967520	0.483760	+	0.875201i	$0.339271\pi$
$132$	−285.473	−0.188236
$133$	−610.243	−0.397855
$134$	−260.700	−0.168067
$135$	313.132	0.199631
$136$	−44.7142	−0.0281927
$137$	2073.51	1.29308	0.646539	−	0.762881i	$-0.276216\pi$
$137$	2073.51	1.29308	0.646539	+	0.762881i	$0.276216\pi$
$138$	447.748	0.276194
$139$	359.266	0.219227	0.109613	−	0.993974i	$-0.465039\pi$
$139$	359.266	0.219227	0.109613	+	0.993974i	$0.465039\pi$
$140$	2674.05	1.61428
$141$	80.0345	0.0478023
$142$	2693.55	1.59182
$143$	−673.324	−0.393750
$144$	−631.252	−0.365308
$145$	−1531.53	−0.877150
$146$	−669.882	−0.379725
$147$	2099.32	1.17788
$148$	2753.03	1.52904
$149$	769.821	0.423263	0.211632	−	0.977350i	$-0.432122\pi$
$149$	769.821	0.423263	0.211632	+	0.977350i	$0.432122\pi$
$150$	−110.914	−0.0603740
$151$	1858.68	1.00170	0.500851	−	0.865534i	$-0.333021\pi$
$151$	1858.68	1.00170	0.500851	+	0.865534i	$0.333021\pi$
$152$	−63.2216	−0.0337365
$153$	−120.290	−0.0635614
$154$	1674.53	0.876217
$155$	586.914	0.304142
$156$	1082.24	0.555441
$157$	−2590.47	−1.31683	−0.658415	−	0.752655i	$-0.728773\pi$
$157$	−2590.47	−1.31683	−0.658415	+	0.752655i	$0.728773\pi$
$158$	5352.89	2.69527
$159$	610.782	0.304642
$160$	2854.72	1.41054
$161$	−1238.63	−0.606321
$162$	−315.174	−0.152855
$163$	−2572.15	−1.23599	−0.617995	−	0.786182i	$-0.712055\pi$
$163$	−2572.15	−1.23599	−0.617995	+	0.786182i	$0.712055\pi$
$164$	−3360.84	−1.60023
$165$	−463.679	−0.218772
$166$	3220.91	1.50597
$167$	−735.558	−0.340833	−0.170417	−	0.985372i	$-0.554511\pi$
$167$	−735.558	−0.340833	−0.170417	+	0.985372i	$0.554511\pi$
$168$	324.096	0.148837
$169$	355.609	0.161861
$170$	603.139	0.272110
$171$	−170.079	−0.0760600
$172$	2905.58	1.28807
$173$	−2808.88	−1.23442	−0.617211	−	0.786798i	$-0.711737\pi$
$173$	−2808.88	−1.23442	−0.617211	+	0.786798i	$0.711737\pi$
$174$	1541.52	0.671623
$175$	306.827	0.132537
$176$	934.743	0.400335
$177$	258.252	0.109669
$178$	−2452.92	−1.03289
$179$	−2050.23	−0.856097	−0.428048	−	0.903756i	$-0.640799\pi$
$179$	−2050.23	−0.856097	−0.428048	+	0.903756i	$0.640799\pi$
$180$	745.276	0.308609
$181$	2897.30	1.18980	0.594902	−	0.803798i	$-0.297191\pi$
$181$	2897.30	1.18980	0.594902	+	0.803798i	$0.297191\pi$
$182$	−6348.23	−2.58551
$183$	−931.279	−0.376186
$184$	−128.323	−0.0514135
$185$	4471.61	1.77708
$186$	−590.742	−0.232878
$187$	178.123	0.0696558
$188$	190.488	0.0738976
$189$	871.884	0.335557
$190$	852.782	0.325617
$191$	17.5457	0.00664694	0.00332347	−	0.999994i	$-0.498942\pi$
$191$	17.5457	0.00664694	0.00332347	+	0.999994i	$0.498942\pi$
$192$	−1190.01	−0.447298
$193$	599.209	0.223482	0.111741	−	0.993737i	$-0.464357\pi$
$193$	599.209	0.223482	0.111741	+	0.993737i	$0.464357\pi$
$194$	3702.00	1.37004
$195$	1757.83	0.645543
$196$	4996.52	1.82089
$197$	−1580.20	−0.571496	−0.285748	−	0.958305i	$-0.592242\pi$
$197$	−1580.20	−0.571496	−0.285748	+	0.958305i	$0.592242\pi$
$198$	466.703	0.167511
$199$	−2397.94	−0.854199	−0.427100	−	0.904205i	$-0.640465\pi$
$199$	−2397.94	−0.854199	−0.427100	+	0.904205i	$0.640465\pi$
$200$	31.7876	0.0112386
$201$	201.000	0.0705346
$202$	−4724.54	−1.64563
$203$	−4264.39	−1.47439
$204$	−286.299	−0.0982596
$205$	−5458.85	−1.85982
$206$	−717.360	−0.242625
$207$	−345.214	−0.115913
$208$	−3543.66	−1.18129
$209$	251.849	0.0833529
$210$	−4371.65	−1.43654
$211$	5980.43	1.95123	0.975616	−	0.219483i	$-0.0704372\pi$
$211$	5980.43	1.95123	0.975616	+	0.219483i	$0.0704372\pi$
$212$	1453.70	0.470947
$213$	−2076.73	−0.668054
$214$	−5979.12	−1.90993
$215$	4719.39	1.49702
$216$	90.3278	0.0284538
$217$	1634.20	0.511229
$218$	4016.21	1.24776
$219$	516.480	0.159363
$220$	−1103.59	−0.338200
$221$	−675.274	−0.205538
$222$	−4500.78	−1.36069
$223$	−3629.92	−1.09003	−0.545017	−	0.838425i	$-0.683477\pi$
$223$	−3629.92	−1.09003	−0.545017	+	0.838425i	$0.683477\pi$
$224$	7948.68	2.37095
$225$	85.5149	0.0253378
$226$	−4178.21	−1.22978
$227$	−3448.45	−1.00829	−0.504144	−	0.863620i	$-0.668192\pi$
$227$	−3448.45	−1.00829	−0.504144	+	0.863620i	$0.668192\pi$
$228$	−404.800	−0.117581
$229$	−4039.54	−1.16568	−0.582839	−	0.812587i	$-0.698058\pi$
$229$	−4039.54	−1.16568	−0.582839	+	0.812587i	$0.698058\pi$
$230$	1730.92	0.496232
$231$	−1291.07	−0.367731
$232$	−441.794	−0.125022
$233$	−6878.65	−1.93406	−0.967028	−	0.254670i	$-0.918033\pi$
$233$	−6878.65	−1.93406	−0.967028	+	0.254670i	$0.918033\pi$
$234$	−1769.30	−0.494284
$235$	309.400	0.0858851
$236$	614.658	0.169537
$237$	−4127.09	−1.13115
$238$	1679.38	0.457386
$239$	3359.51	0.909241	0.454620	−	0.890685i	$-0.349775\pi$
$239$	3359.51	0.909241	0.454620	+	0.890685i	$0.349775\pi$
$240$	−2440.31	−0.656339
$241$	3647.07	0.974806	0.487403	−	0.873177i	$-0.337944\pi$
$241$	3647.07	0.974806	0.487403	+	0.873177i	$0.337944\pi$
$242$	4487.89	1.19212
$243$	243.000	0.0641500
$244$	−2216.51	−0.581547
$245$	8115.60	2.11627
$246$	5494.45	1.42404
$247$	−954.773	−0.245954
$248$	169.304	0.0433501
$249$	−2483.33	−0.632027
$250$	5212.01	1.31855
$251$	−2401.98	−0.604031	−0.302016	−	0.953303i	$-0.597659\pi$
$251$	−2401.98	−0.604031	−0.302016	+	0.953303i	$0.597659\pi$
$252$	2075.14	0.518737
$253$	511.186	0.127028
$254$	−4688.93	−1.15831
$255$	−465.021	−0.114199
$256$	4829.95	1.17919
$257$	−1332.17	−0.323340	−0.161670	−	0.986845i	$-0.551688\pi$
$257$	−1332.17	−0.323340	−0.161670	+	0.986845i	$0.551688\pi$
$258$	−4750.17	−1.14625
$259$	12450.7	2.98707
$260$	4183.76	0.997946
$261$	−1188.51	−0.281867
$262$	−5644.60	−1.33101
$263$	7926.05	1.85833	0.929165	−	0.369664i	$-0.120527\pi$
$263$	7926.05	1.85833	0.929165	+	0.369664i	$0.120527\pi$
$264$	−133.755	−0.0311821
$265$	2361.18	0.547343
$266$	2374.48	0.547326
$267$	1891.21	0.433483
$268$	478.394	0.109039
$269$	−5067.25	−1.14853	−0.574267	−	0.818668i	$-0.694713\pi$
$269$	−5067.25	−1.14853	−0.574267	+	0.818668i	$0.694713\pi$
$270$	−1218.41	−0.274630
$271$	−3488.23	−0.781900	−0.390950	−	0.920412i	$-0.627853\pi$
$271$	−3488.23	−0.781900	−0.390950	+	0.920412i	$0.627853\pi$
$272$	937.449	0.208975
$273$	4894.50	1.08509
$274$	−8068.11	−1.77888
$275$	−126.629	−0.0277672
$276$	−821.635	−0.179191
$277$	−7835.43	−1.69959	−0.849793	−	0.527117i	$-0.823273\pi$
$277$	−7835.43	−1.69959	−0.849793	+	0.527117i	$0.823273\pi$
$278$	−1397.92	−0.301588
$279$	455.463	0.0977342
$280$	1252.90	0.267411
$281$	−1947.11	−0.413362	−0.206681	−	0.978408i	$-0.566266\pi$
$281$	−1947.11	−0.413362	−0.206681	+	0.978408i	$0.566266\pi$
$282$	−311.418	−0.0657611
$283$	6974.28	1.46494	0.732470	−	0.680799i	$-0.238367\pi$
$283$	6974.28	1.46494	0.732470	+	0.680799i	$0.238367\pi$
$284$	−4942.77	−1.03275
$285$	−657.496	−0.136655
$286$	2619.93	0.541678
$287$	−15199.6	−3.12614
$288$	2215.35	0.453267
$289$	−4734.36	−0.963640
$290$	5959.25	1.20669
$291$	−2854.25	−0.574979
$292$	1229.26	0.246359
$293$	5712.12	1.13893	0.569463	−	0.822017i	$-0.307151\pi$
$293$	5712.12	1.13893	0.569463	+	0.822017i	$0.307151\pi$
$294$	−8168.53	−1.62040
$295$	998.357	0.197039
$296$	1289.91	0.253292
$297$	−359.829	−0.0703010
$298$	−2995.41	−0.582280
$299$	−1937.93	−0.374828
$300$	203.532	0.0391697
$301$	13140.7	2.51633
$302$	−7232.19	−1.37803
$303$	3642.63	0.690639
$304$	1325.46	0.250068
$305$	−3600.16	−0.675885
$306$	468.054	0.0874408
$307$	−2511.57	−0.466915	−0.233457	−	0.972367i	$-0.575004\pi$
$307$	−2511.57	−0.466915	−0.233457	+	0.972367i	$0.575004\pi$
$308$	−3072.83	−0.568476
$309$	553.086	0.101825
$310$	−2283.71	−0.418406
$311$	−3289.09	−0.599702	−0.299851	−	0.953986i	$-0.596937\pi$
$311$	−3289.09	−0.599702	−0.299851	+	0.953986i	$0.596937\pi$
$312$	507.074	0.0920109
$313$	−3759.78	−0.678963	−0.339481	−	0.940613i	$-0.610252\pi$
$313$	−3759.78	−0.678963	−0.339481	+	0.940613i	$0.610252\pi$
$314$	10079.6	1.81155
$315$	3370.55	0.602886
$316$	−9822.76	−1.74865
$317$	−3882.68	−0.687928	−0.343964	−	0.938983i	$-0.611770\pi$
$317$	−3882.68	−0.687928	−0.343964	+	0.938983i	$0.611770\pi$
$318$	−2376.58	−0.419094
$319$	1759.93	0.308893
$320$	−4600.36	−0.803650
$321$	4609.91	0.801558
$322$	4819.56	0.834110
$323$	252.578	0.0435103
$324$	578.357	0.0991696
$325$	480.056	0.0819345
$326$	10008.3	1.70034
$327$	−3096.50	−0.523660
$328$	−1574.69	−0.265084
$329$	861.491	0.144363
$330$	1804.19	0.300962
$331$	757.698	0.125821	0.0629107	−	0.998019i	$-0.479962\pi$
$331$	757.698	0.125821	0.0629107	+	0.998019i	$0.479962\pi$
$332$	−5910.50	−0.977051
$333$	3470.11	0.571053
$334$	2862.09	0.468882
$335$	777.031	0.126728
$336$	−6794.79	−1.10323
$337$	427.944	0.0691738	0.0345869	−	0.999402i	$-0.488988\pi$
$337$	427.944	0.0691738	0.0345869	+	0.999402i	$0.488988\pi$
$338$	−1383.69	−0.222671
$339$	3221.41	0.516114
$340$	−1106.78	−0.176540
$341$	−674.439	−0.107105
$342$	661.784	0.104635
$343$	11520.9	1.81361
$344$	1361.38	0.213374
$345$	−1334.54	−0.208259
$346$	10929.5	1.69818
$347$	7375.83	1.14108	0.570541	−	0.821269i	$-0.306734\pi$
$347$	7375.83	1.14108	0.570541	+	0.821269i	$0.306734\pi$
$348$	−2828.75	−0.435738
$349$	−5620.03	−0.861986	−0.430993	−	0.902355i	$-0.641837\pi$
$349$	−5620.03	−0.861986	−0.430993	+	0.902355i	$0.641837\pi$
$350$	−1193.88	−0.182330
$351$	1364.13	0.207441
$352$	−3280.44	−0.496728
$353$	9809.18	1.47901	0.739504	−	0.673152i	$-0.235060\pi$
$353$	9809.18	1.47901	0.739504	+	0.673152i	$0.235060\pi$
$354$	−1004.87	−0.150871
$355$	−8028.30	−1.20028
$356$	4501.20	0.670122
$357$	−1294.80	−0.191956
$358$	7977.53	1.17772
$359$	−12252.6	−1.80130	−0.900652	−	0.434541i	$-0.856911\pi$
$359$	−12252.6	−1.80130	−0.900652	+	0.434541i	$0.856911\pi$
$360$	349.192	0.0511223
$361$	−6501.88	−0.947934
$362$	−11273.5	−1.63680
$363$	−3460.17	−0.500309
$364$	11649.3	1.67744
$365$	1996.62	0.286323
$366$	3623.65	0.517516
$367$	8097.92	1.15179	0.575897	−	0.817522i	$-0.304653\pi$
$367$	8097.92	1.15179	0.575897	+	0.817522i	$0.304653\pi$
$368$	2690.34	0.381096
$369$	−4236.23	−0.597641
$370$	−17399.2	−2.44471
$371$	6574.45	0.920023
$372$	1084.03	0.151087
$373$	−5011.56	−0.695680	−0.347840	−	0.937554i	$-0.613085\pi$
$373$	−5011.56	−0.695680	−0.347840	+	0.937554i	$0.613085\pi$
$374$	−693.084	−0.0958249
$375$	−4018.47	−0.553368
$376$	89.2511	0.0122414
$377$	−6671.97	−0.911470
$378$	−3392.54	−0.461622
$379$	−10308.6	−1.39714	−0.698568	−	0.715543i	$-0.746179\pi$
$379$	−10308.6	−1.39714	−0.698568	+	0.715543i	$0.746179\pi$
$380$	−1564.89	−0.211255
$381$	3615.17	0.486118
$382$	−68.2712	−0.00914414
$383$	10169.4	1.35675	0.678373	−	0.734717i	$-0.262685\pi$
$383$	10169.4	1.35675	0.678373	+	0.734717i	$0.262685\pi$
$384$	−1277.24	−0.169737
$385$	−4991.04	−0.660693
$386$	−2331.55	−0.307442
$387$	3662.39	0.481059
$388$	−6793.30	−0.888860
$389$	3036.32	0.395752	0.197876	−	0.980227i	$-0.436596\pi$
$389$	3036.32	0.395752	0.197876	+	0.980227i	$0.436596\pi$
$390$	−6839.80	−0.888068
$391$	512.666	0.0663085
$392$	2341.07	0.301638
$393$	4351.99	0.558598
$394$	6148.63	0.786202
$395$	−15954.6	−2.03231
$396$	−856.418	−0.108678
$397$	−5533.99	−0.699605	−0.349803	−	0.936823i	$-0.613751\pi$
$397$	−5533.99	−0.699605	−0.349803	+	0.936823i	$0.613751\pi$
$398$	9330.50	1.17511
$399$	−1830.73	−0.229702
$400$	−666.438	−0.0833047
$401$	−9558.68	−1.19037	−0.595184	−	0.803590i	$-0.702921\pi$
$401$	−9558.68	−1.19037	−0.595184	+	0.803590i	$0.702921\pi$
$402$	−782.100	−0.0970338
$403$	2556.83	0.316042
$404$	8669.71	1.06766
$405$	939.396	0.115257
$406$	16592.9	2.02831
$407$	−5138.46	−0.625808
$408$	−134.143	−0.0162771
$409$	−1808.26	−0.218612	−0.109306	−	0.994008i	$-0.534863\pi$
$409$	−1808.26	−0.218612	−0.109306	+	0.994008i	$0.534863\pi$
$410$	21240.6	2.55853
$411$	6220.52	0.746559
$412$	1316.38	0.157412
$413$	2779.82	0.331201
$414$	1343.24	0.159461
$415$	−9600.13	−1.13555
$416$	12436.3	1.46573
$417$	1077.80	0.126571
$418$	−979.955	−0.114668
$419$	−16990.2	−1.98097	−0.990483	−	0.137635i	$-0.956050\pi$
$419$	−16990.2	−1.98097	−0.990483	+	0.137635i	$0.956050\pi$
$420$	8022.15	0.932002
$421$	−12100.6	−1.40082	−0.700412	−	0.713739i	$-0.747000\pi$
$421$	−12100.6	−1.40082	−0.700412	+	0.713739i	$0.747000\pi$
$422$	−23270.1	−2.68429
$423$	240.103	0.0275986
$424$	681.118	0.0780142
$425$	−126.995	−0.0144945
$426$	8080.66	0.919036
$427$	−10024.3	−1.13609
$428$	10971.9	1.23913
$429$	−2019.97	−0.227332
$430$	−18363.3	−2.05944
$431$	8067.68	0.901639	0.450819	−	0.892615i	$-0.351132\pi$
$431$	8067.68	0.901639	0.450819	+	0.892615i	$0.351132\pi$
$432$	−1893.75	−0.210910
$433$	9176.64	1.01848	0.509239	−	0.860625i	$-0.329927\pi$
$433$	9176.64	1.01848	0.509239	+	0.860625i	$0.329927\pi$
$434$	−6358.74	−0.703293
$435$	−4594.59	−0.506423
$436$	−7369.89	−0.809527
$437$	724.860	0.0793473
$438$	−2009.64	−0.219234
$439$	13636.5	1.48254	0.741268	−	0.671210i	$-0.234225\pi$
$439$	13636.5	1.48254	0.741268	+	0.671210i	$0.234225\pi$
$440$	−517.075	−0.0560241
$441$	6297.95	0.680051
$442$	2627.52	0.282756
$443$	−913.976	−0.0980232	−0.0490116	−	0.998798i	$-0.515607\pi$
$443$	−913.976	−0.0980232	−0.0490116	+	0.998798i	$0.515607\pi$
$444$	8259.10	0.882792
$445$	7311.08	0.778828
$446$	14124.2	1.49955
$447$	2309.46	0.244371
$448$	−12809.2	−1.35085
$449$	12324.6	1.29540	0.647699	−	0.761896i	$-0.275731\pi$
$449$	12324.6	1.29540	0.647699	+	0.761896i	$0.275731\pi$
$450$	−332.742	−0.0348569
$451$	6272.91	0.654945
$452$	7667.17	0.797861
$453$	5576.03	0.578333
$454$	13418.1	1.38709
$455$	18921.3	1.94955
$456$	−189.665	−0.0194778
$457$	−90.9082	−0.00930526	−0.00465263	−	0.999989i	$-0.501481\pi$
$457$	−90.9082	−0.00930526	−0.00465263	+	0.999989i	$0.501481\pi$
$458$	15718.0	1.60361
$459$	−360.871	−0.0366972
$460$	−3176.30	−0.321947
$461$	660.223	0.0667021	0.0333510	−	0.999444i	$-0.489382\pi$
$461$	660.223	0.0667021	0.0333510	+	0.999444i	$0.489382\pi$
$462$	5023.59	0.505884
$463$	−10224.5	−1.02629	−0.513147	−	0.858301i	$-0.671520\pi$
$463$	−10224.5	−1.02629	−0.513147	+	0.858301i	$0.671520\pi$
$464$	9262.37	0.926713
$465$	1760.74	0.175597
$466$	26765.1	2.66066
$467$	17798.2	1.76360	0.881799	−	0.471625i	$-0.156332\pi$
$467$	17798.2	1.76360	0.881799	+	0.471625i	$0.156332\pi$
$468$	3246.73	0.320684
$469$	2163.56	0.213015
$470$	−1203.89	−0.118151
$471$	−7771.42	−0.760273
$472$	287.992	0.0280845
$473$	−5423.18	−0.527184
$474$	16058.7	1.55612
$475$	−179.559	−0.0173447
$476$	−3081.72	−0.296745
$477$	1832.34	0.175885
$478$	−13072.0	−1.25083
$479$	11420.8	1.08941	0.544706	−	0.838627i	$-0.316641\pi$
$479$	11420.8	1.08941	0.544706	+	0.838627i	$0.316641\pi$
$480$	8564.17	0.814373
$481$	19480.2	1.84661
$482$	−14190.9	−1.34103
$483$	−3715.89	−0.350059
$484$	−8235.46	−0.773428
$485$	−11034.0	−1.03305
$486$	−945.523	−0.0882506
$487$	−9358.73	−0.870810	−0.435405	−	0.900235i	$-0.643395\pi$
$487$	−9358.73	−0.870810	−0.435405	+	0.900235i	$0.643395\pi$
$488$	−1038.52	−0.0963355
$489$	−7716.45	−0.713599
$490$	−31578.2	−2.91134
$491$	10985.3	1.00969	0.504846	−	0.863210i	$-0.331549\pi$
$491$	10985.3	1.00969	0.504846	+	0.863210i	$0.331549\pi$
$492$	−10082.5	−0.923893
$493$	1765.02	0.161242
$494$	3715.06	0.338357
$495$	−1391.04	−0.126308
$496$	−3549.53	−0.321327
$497$	−22354.0	−2.01753
$498$	9662.74	0.869474
$499$	3764.77	0.337744	0.168872	−	0.985638i	$-0.445987\pi$
$499$	3764.77	0.337744	0.168872	+	0.985638i	$0.445987\pi$
$500$	−9564.24	−0.855452
$501$	−2206.67	−0.196780
$502$	9346.22	0.830960
$503$	−539.378	−0.0478125	−0.0239063	−	0.999714i	$-0.507610\pi$
$503$	−539.378	−0.0478125	−0.0239063	+	0.999714i	$0.507610\pi$
$504$	972.288	0.0859309
$505$	14081.8	1.24085
$506$	−1989.04	−0.174751
$507$	1066.83	0.0934507
$508$	8604.37	0.751490
$509$	−10038.3	−0.874142	−0.437071	−	0.899427i	$-0.643984\pi$
$509$	−10038.3	−0.874142	−0.437071	+	0.899427i	$0.643984\pi$
$510$	1809.42	0.157103
$511$	5559.39	0.481277
$512$	−15387.6	−1.32820
$513$	−510.237	−0.0439133
$514$	5183.52	0.444816
$515$	2138.13	0.182947
$516$	8716.75	0.743669
$517$	−355.540	−0.0302449
$518$	−48446.4	−4.10929
$519$	−8426.63	−0.712693
$520$	1960.26	0.165314
$521$	−18852.4	−1.58529	−0.792646	−	0.609683i	$-0.791297\pi$
$521$	−18852.4	−1.58529	−0.792646	+	0.609683i	$0.791297\pi$
$522$	4624.56	0.387762
$523$	16211.3	1.35539	0.677696	−	0.735342i	$-0.262978\pi$
$523$	16211.3	1.35539	0.677696	+	0.735342i	$0.262978\pi$
$524$	10358.0	0.863537
$525$	920.482	0.0765203
$526$	−30840.6	−2.55649
$527$	−676.391	−0.0559091
$528$	2804.23	0.231133
$529$	−10695.7	−0.879077
$530$	−9187.44	−0.752975
$531$	774.756	0.0633174
$532$	−4357.26	−0.355097
$533$	−23781.0	−1.93258
$534$	−7358.76	−0.596339
$535$	17821.1	1.44014
$536$	224.147	0.0180628
$537$	−6150.69	−0.494268
$538$	19716.9	1.58003
$539$	−9325.86	−0.745257
$540$	2235.83	0.178176
$541$	19901.2	1.58155	0.790777	−	0.612104i	$-0.209677\pi$
$541$	19901.2	1.58155	0.790777	+	0.612104i	$0.209677\pi$
$542$	13572.8	1.07565
$543$	8691.90	0.686934
$544$	−3289.94	−0.259292
$545$	−11970.5	−0.940847
$546$	−19044.7	−1.49274
$547$	−5532.77	−0.432476	−0.216238	−	0.976341i	$-0.569379\pi$
$547$	−5532.77	−0.432476	−0.216238	+	0.976341i	$0.569379\pi$
$548$	14805.3	1.15411
$549$	−2793.84	−0.217191
$550$	492.717	0.0381991
$551$	2495.57	0.192949
$552$	−384.969	−0.0296836
$553$	−44424.0	−3.41609
$554$	30488.0	2.33810
$555$	13414.8	1.02600
$556$	2565.23	0.195666
$557$	2367.14	0.180070	0.0900351	−	0.995939i	$-0.471302\pi$
$557$	2367.14	0.180070	0.0900351	+	0.995939i	$0.471302\pi$
$558$	−1772.22	−0.134452
$559$	20559.6	1.55560
$560$	−26267.5	−1.98215
$561$	534.369	0.0402158
$562$	7576.28	0.568658
$563$	6467.36	0.484132	0.242066	−	0.970260i	$-0.422175\pi$
$563$	6467.36	0.484132	0.242066	+	0.970260i	$0.422175\pi$
$564$	571.463	0.0426648
$565$	12453.4	0.927289
$566$	−27137.2	−2.01530
$567$	2615.65	0.193734
$568$	−2315.89	−0.171078
$569$	−9481.47	−0.698566	−0.349283	−	0.937017i	$-0.613575\pi$
$569$	−9481.47	−0.698566	−0.349283	+	0.937017i	$0.613575\pi$
$570$	2558.34	0.187995
$571$	8639.89	0.633219	0.316610	−	0.948556i	$-0.397456\pi$
$571$	8639.89	0.633219	0.316610	+	0.948556i	$0.397456\pi$
$572$	−4807.68	−0.351432
$573$	52.6372	0.00383761
$574$	59142.3	4.30061
$575$	−364.457	−0.0264329
$576$	−3570.02	−0.258248
$577$	2199.89	0.158722	0.0793609	−	0.996846i	$-0.474712\pi$
$577$	2199.89	0.158722	0.0793609	+	0.996846i	$0.474712\pi$
$578$	18421.6	1.32567
$579$	1797.63	0.129027
$580$	−10935.5	−0.782880
$581$	−26730.6	−1.90873
$582$	11106.0	0.790993
$583$	−2713.29	−0.192750
$584$	575.957	0.0408104
$585$	5273.49	0.372705
$586$	−22226.1	−1.56681
$587$	838.912	0.0589874	0.0294937	−	0.999565i	$-0.490611\pi$
$587$	838.912	0.0589874	0.0294937	+	0.999565i	$0.490611\pi$
$588$	14989.6	1.05129
$589$	−956.353	−0.0669030
$590$	−3884.65	−0.271065
$591$	−4740.61	−0.329953
$592$	−27043.4	−1.87749
$593$	−13581.9	−0.940541	−0.470271	−	0.882522i	$-0.655844\pi$
$593$	−13581.9	−0.940541	−0.470271	+	0.882522i	$0.655844\pi$
$594$	1400.11	0.0967124
$595$	−5005.49	−0.344882
$596$	5496.69	0.377774
$597$	−7193.83	−0.493172
$598$	7540.58	0.515647
$599$	18496.9	1.26171	0.630854	−	0.775902i	$-0.282705\pi$
$599$	18496.9	1.26171	0.630854	+	0.775902i	$0.282705\pi$
$600$	95.3627	0.00648861
$601$	−12788.1	−0.867947	−0.433973	−	0.900926i	$-0.642889\pi$
$601$	−12788.1	−0.867947	−0.433973	+	0.900926i	$0.642889\pi$
$602$	−51130.8	−3.46169
$603$	603.000	0.0407231
$604$	13271.3	0.894045
$605$	−13376.4	−0.898892
$606$	−14173.6	−0.950106
$607$	−15204.2	−1.01667	−0.508336	−	0.861159i	$-0.669739\pi$
$607$	−15204.2	−1.01667	−0.508336	+	0.861159i	$0.669739\pi$
$608$	−4651.66	−0.310279
$609$	−12793.2	−0.851240
$610$	14008.4	0.929809
$611$	1347.87	0.0892455
$612$	−858.897	−0.0567302
$613$	−23319.3	−1.53647	−0.768235	−	0.640168i	$-0.778865\pi$
$613$	−23319.3	−1.53647	−0.768235	+	0.640168i	$0.778865\pi$
$614$	9772.63	0.642331
$615$	−16376.5	−1.07377
$616$	−1439.74	−0.0941702
$617$	8451.50	0.551450	0.275725	−	0.961237i	$-0.411082\pi$
$617$	8451.50	0.551450	0.275725	+	0.961237i	$0.411082\pi$
$618$	−2152.08	−0.140080
$619$	−402.095	−0.0261091	−0.0130546	−	0.999915i	$-0.504156\pi$
$619$	−402.095	−0.0261091	−0.0130546	+	0.999915i	$0.504156\pi$
$620$	4190.69	0.271455
$621$	−1035.64	−0.0669226
$622$	12798.0	0.825005
$623$	20356.9	1.30912
$624$	−10631.0	−0.682019
$625$	−16722.4	−1.07024
$626$	14629.5	0.934043
$627$	755.547	0.0481238
$628$	−18496.5	−1.17531
$629$	−5153.33	−0.326672
$630$	−13115.0	−0.829385
$631$	−2264.16	−0.142844	−0.0714221	−	0.997446i	$-0.522754\pi$
$631$	−2264.16	−0.142844	−0.0714221	+	0.997446i	$0.522754\pi$
$632$	−4602.36	−0.289671
$633$	17941.3	1.12654
$634$	15107.7	0.946376
$635$	13975.6	0.873396
$636$	4361.11	0.271901
$637$	35354.9	2.19907
$638$	−6847.94	−0.424942
$639$	−6230.20	−0.385701
$640$	−4937.60	−0.304962
$641$	−9274.64	−0.571492	−0.285746	−	0.958305i	$-0.592241\pi$
$641$	−9274.64	−0.571492	−0.285746	+	0.958305i	$0.592241\pi$
$642$	−17937.4	−1.10270
$643$	25005.5	1.53363	0.766813	−	0.641871i	$-0.221841\pi$
$643$	25005.5	1.53363	0.766813	+	0.641871i	$0.221841\pi$
$644$	−8844.07	−0.541157
$645$	14158.2	0.864306
$646$	−982.792	−0.0598567
$647$	−8332.40	−0.506307	−0.253153	−	0.967426i	$-0.581468\pi$
$647$	−8332.40	−0.506307	−0.253153	+	0.967426i	$0.581468\pi$
$648$	270.983	0.0164278
$649$	−1147.24	−0.0693885
$650$	−1867.92	−0.112717
$651$	4902.60	0.295158
$652$	−18365.7	−1.10315
$653$	−12209.7	−0.731701	−0.365851	−	0.930674i	$-0.619222\pi$
$653$	−12209.7	−0.731701	−0.365851	+	0.930674i	$0.619222\pi$
$654$	12048.6	0.720395
$655$	16824.1	1.00362
$656$	33013.9	1.96490
$657$	1549.44	0.0920082
$658$	−3352.10	−0.198599
$659$	−25473.6	−1.50579	−0.752893	−	0.658143i	$-0.771342\pi$
$659$	−25473.6	−1.50579	−0.752893	+	0.658143i	$0.771342\pi$
$660$	−3310.76	−0.195260
$661$	32036.7	1.88515	0.942575	−	0.333995i	$-0.108397\pi$
$661$	32036.7	1.88515	0.942575	+	0.333995i	$0.108397\pi$
$662$	−2948.24	−0.173091
$663$	−2025.82	−0.118667
$664$	−2769.31	−0.161852
$665$	−7077.28	−0.412700
$666$	−13502.3	−0.785593
$667$	5065.34	0.294049
$668$	−5252.04	−0.304203
$669$	−10889.8	−0.629332
$670$	−3023.46	−0.174338
$671$	4137.05	0.238016
$672$	23846.1	1.36887
$673$	17853.1	1.02256	0.511281	−	0.859413i	$-0.329171\pi$
$673$	17853.1	1.02256	0.511281	+	0.859413i	$0.329171\pi$
$674$	−1665.15	−0.0951618
$675$	256.545	0.0146288
$676$	2539.13	0.144466
$677$	−6811.90	−0.386710	−0.193355	−	0.981129i	$-0.561937\pi$
$677$	−6811.90	−0.386710	−0.193355	+	0.981129i	$0.561937\pi$
$678$	−12534.6	−0.710014
$679$	−30723.1	−1.73644
$680$	−518.572	−0.0292446
$681$	−10345.3	−0.582136
$682$	2624.27	0.147344
$683$	16091.0	0.901472	0.450736	−	0.892657i	$-0.351162\pi$
$683$	16091.0	0.901472	0.450736	+	0.892657i	$0.351162\pi$
$684$	−1214.40	−0.0678856
$685$	24047.5	1.34132
$686$	−44828.3	−2.49497
$687$	−12118.6	−0.673005
$688$	−28541.9	−1.58161
$689$	10286.2	0.568759
$690$	5192.75	0.286499
$691$	30137.1	1.65914	0.829572	−	0.558399i	$-0.188584\pi$
$691$	30137.1	1.65914	0.829572	+	0.558399i	$0.188584\pi$
$692$	−20056.0	−1.10175
$693$	−3873.20	−0.212310
$694$	−28699.7	−1.56978
$695$	4166.58	0.227406
$696$	−1325.38	−0.0721817
$697$	6291.08	0.341882
$698$	21867.8	1.18583
$699$	−20635.9	−1.11663
$700$	2190.81	0.118293
$701$	−14269.7	−0.768843	−0.384421	−	0.923158i	$-0.625599\pi$
$701$	−14269.7	−0.768843	−0.384421	+	0.923158i	$0.625599\pi$
$702$	−5307.89	−0.285375
$703$	−7286.33	−0.390909
$704$	5286.40	0.283010
$705$	928.199	0.0495858
$706$	−38167.9	−2.03466
$707$	39209.2	2.08574
$708$	1843.97	0.0978824
$709$	−13850.4	−0.733655	−0.366828	−	0.930289i	$-0.619556\pi$
$709$	−13850.4	−0.733655	−0.366828	+	0.930289i	$0.619556\pi$
$710$	31238.5	1.65121
$711$	−12381.3	−0.653072
$712$	2108.99	0.111008
$713$	−1941.14	−0.101958
$714$	5038.13	0.264072
$715$	−7808.87	−0.408441
$716$	−14639.1	−0.764089
$717$	10078.5	0.524951
$718$	47675.4	2.47804
$719$	10885.2	0.564605	0.282303	−	0.959325i	$-0.408902\pi$
$719$	10885.2	0.564605	0.282303	+	0.959325i	$0.408902\pi$
$720$	−7320.93	−0.378938
$721$	5953.41	0.307513
$722$	25299.1	1.30406
$723$	10941.2	0.562804
$724$	20687.3	1.06193
$725$	−1254.76	−0.0642768
$726$	13463.7	0.688270
$727$	−516.142	−0.0263310	−0.0131655	−	0.999913i	$-0.504191\pi$
$727$	−516.142	−0.0263310	−0.0131655	+	0.999913i	$0.504191\pi$
$728$	5458.14	0.277874
$729$	729.000	0.0370370
$730$	−7768.94	−0.393892
$731$	−5438.88	−0.275191
$732$	−6649.53	−0.335756
$733$	11910.7	0.600181	0.300091	−	0.953911i	$-0.402983\pi$
$733$	11910.7	0.600181	0.300091	+	0.953911i	$0.402983\pi$
$734$	−31509.4	−1.58451
$735$	24346.8	1.22183
$736$	−9441.63	−0.472857
$737$	−892.909	−0.0446278
$738$	16483.4	0.822169
$739$	−17456.3	−0.868933	−0.434466	−	0.900688i	$-0.643063\pi$
$739$	−17456.3	−0.868933	−0.434466	+	0.900688i	$0.643063\pi$
$740$	31928.3	1.58609
$741$	−2864.32	−0.142002
$742$	−25581.5	−1.26567
$743$	33350.4	1.64672	0.823358	−	0.567523i	$-0.192098\pi$
$743$	33350.4	1.64672	0.823358	+	0.567523i	$0.192098\pi$
$744$	507.913	0.0250282
$745$	8927.99	0.439055
$746$	19500.2	0.957041
$747$	−7449.99	−0.364901
$748$	1271.84	0.0621697
$749$	49621.1	2.42071
$750$	15636.0	0.761263
$751$	26305.4	1.27816	0.639080	−	0.769140i	$-0.279315\pi$
$751$	26305.4	1.27816	0.639080	+	0.769140i	$0.279315\pi$
$752$	−1871.18	−0.0907380
$753$	−7205.95	−0.348738
$754$	25960.9	1.25390
$755$	21556.0	1.03908
$756$	6225.43	0.299493
$757$	29245.1	1.40414	0.702069	−	0.712109i	$-0.252260\pi$
$757$	29245.1	1.40414	0.702069	+	0.712109i	$0.252260\pi$
$758$	40111.0	1.92203
$759$	1533.56	0.0733394
$760$	−733.212	−0.0349953
$761$	−14865.9	−0.708131	−0.354066	−	0.935221i	$-0.615201\pi$
$761$	−14865.9	−0.708131	−0.354066	+	0.935221i	$0.615201\pi$
$762$	−14066.8	−0.668748
$763$	−33330.7	−1.58146
$764$	125.280	0.00593257
$765$	−1395.06	−0.0659329
$766$	−39569.7	−1.86646
$767$	4349.25	0.204749
$768$	14489.9	0.680804
$769$	−27383.4	−1.28410	−0.642049	−	0.766664i	$-0.721915\pi$
$769$	−27383.4	−1.28410	−0.642049	+	0.766664i	$0.721915\pi$
$770$	19420.3	0.908910
$771$	−3996.51	−0.186680
$772$	4278.48	0.199464
$773$	26905.8	1.25192	0.625961	−	0.779855i	$-0.284707\pi$
$773$	26905.8	1.25192	0.625961	+	0.779855i	$0.284707\pi$
$774$	−14250.5	−0.661788
$775$	480.850	0.0222873
$776$	−3182.93	−0.147243
$777$	37352.2	1.72459
$778$	−11814.5	−0.544433
$779$	8894.98	0.409109
$780$	12551.3	0.576164
$781$	9225.54	0.422684
$782$	−1994.80	−0.0912200
$783$	−3565.54	−0.162736
$784$	−49081.4	−2.23585
$785$	−30043.0	−1.36596
$786$	−16933.8	−0.768458
$787$	32863.0	1.48849	0.744244	−	0.667908i	$-0.232810\pi$
$787$	32863.0	1.48849	0.744244	+	0.667908i	$0.232810\pi$
$788$	−11283.0	−0.510075
$789$	23778.1	1.07291
$790$	62080.1	2.79584
$791$	34675.2	1.55867
$792$	−401.266	−0.0180030
$793$	−15683.8	−0.702330
$794$	21533.0	0.962440
$795$	7083.53	0.316009
$796$	−17121.8	−0.762396
$797$	−33218.9	−1.47638	−0.738189	−	0.674594i	$-0.764319\pi$
$797$	−33218.9	−1.47638	−0.738189	+	0.674594i	$0.764319\pi$
$798$	7123.44	0.315999
$799$	−356.569	−0.0157879
$800$	2338.84	0.103363
$801$	5673.62	0.250272
$802$	37193.2	1.63758
$803$	−2294.37	−0.100830
$804$	1435.18	0.0629540
$805$	−14365.0	−0.628943
$806$	−9948.75	−0.434776
$807$	−15201.7	−0.663106
$808$	4062.11	0.176862
$809$	13611.0	0.591518	0.295759	−	0.955263i	$-0.404427\pi$
$809$	13611.0	0.591518	0.295759	+	0.955263i	$0.404427\pi$
$810$	−3655.23	−0.158558
$811$	16217.0	0.702166	0.351083	−	0.936344i	$-0.385813\pi$
$811$	16217.0	0.702166	0.351083	+	0.936344i	$0.385813\pi$
$812$	−30448.6	−1.31593
$813$	−10464.7	−0.451430
$814$	19994.0	0.860919
$815$	−29830.5	−1.28211
$816$	2812.35	0.120652
$817$	−7690.07	−0.329304
$818$	7036.00	0.300743
$819$	14683.5	0.626475
$820$	−38977.3	−1.65994
$821$	8645.48	0.367514	0.183757	−	0.982972i	$-0.441174\pi$
$821$	8645.48	0.367514	0.183757	+	0.982972i	$0.441174\pi$
$822$	−24204.3	−1.02703
$823$	−11516.0	−0.487753	−0.243877	−	0.969806i	$-0.578419\pi$
$823$	−11516.0	−0.487753	−0.243877	+	0.969806i	$0.578419\pi$
$824$	616.778	0.0260758
$825$	−379.886	−0.0160314
$826$	−10816.4	−0.455631
$827$	859.073	0.0361220	0.0180610	−	0.999837i	$-0.494251\pi$
$827$	859.073	0.0361220	0.0180610	+	0.999837i	$0.494251\pi$
$828$	−2464.90	−0.103456
$829$	−11247.7	−0.471229	−0.235615	−	0.971847i	$-0.575710\pi$
$829$	−11247.7	−0.471229	−0.235615	+	0.971847i	$0.575710\pi$
$830$	37354.5	1.56216
$831$	−23506.3	−0.981256
$832$	−20041.0	−0.835094
$833$	−9352.87	−0.389025
$834$	−4193.76	−0.174122
$835$	−8530.62	−0.353550
$836$	1798.25	0.0743947
$837$	1366.39	0.0564269
$838$	66109.5	2.72520
$839$	5185.66	0.213384	0.106692	−	0.994292i	$-0.465974\pi$
$839$	5185.66	0.213384	0.106692	+	0.994292i	$0.465974\pi$
$840$	3758.70	0.154390
$841$	−6949.89	−0.284960
$842$	47083.9	1.92710
$843$	−5841.32	−0.238655
$844$	42701.6	1.74153
$845$	4124.17	0.167900
$846$	−934.253	−0.0379672
$847$	−37245.3	−1.51094
$848$	−14279.9	−0.578270
$849$	20922.8	0.845783
$850$	494.144	0.0199400
$851$	−14789.3	−0.595734
$852$	−14828.3	−0.596256
$853$	29967.0	1.20287	0.601437	−	0.798920i	$-0.294595\pi$
$853$	29967.0	1.20287	0.601437	+	0.798920i	$0.294595\pi$
$854$	39004.9	1.56290
$855$	−1972.49	−0.0788978
$856$	5140.78	0.205267
$857$	42235.1	1.68346	0.841729	−	0.539901i	$-0.181538\pi$
$857$	42235.1	1.68346	0.841729	+	0.539901i	$0.181538\pi$
$858$	7859.80	0.312738
$859$	−22996.3	−0.913415	−0.456707	−	0.889617i	$-0.650971\pi$
$859$	−22996.3	−0.913415	−0.456707	+	0.889617i	$0.650971\pi$
$860$	33697.4	1.33613
$861$	−45598.8	−1.80488
$862$	−31391.7	−1.24038
$863$	−38927.0	−1.53545	−0.767723	−	0.640782i	$-0.778610\pi$
$863$	−38927.0	−1.53545	−0.767723	+	0.640782i	$0.778610\pi$
$864$	6646.06	0.261694
$865$	−32575.9	−1.28048
$866$	−35706.7	−1.40111
$867$	−14203.1	−0.556358
$868$	11668.5	0.456285
$869$	18333.9	0.715690
$870$	17877.8	0.696681
$871$	3385.06	0.131686
$872$	−3453.09	−0.134101
$873$	−8562.74	−0.331964
$874$	−2820.46	−0.109157
$875$	−43254.8	−1.67118
$876$	3687.77	0.142236
$877$	33305.3	1.28237	0.641187	−	0.767385i	$-0.278442\pi$
$877$	33305.3	1.28237	0.641187	+	0.767385i	$0.278442\pi$
$878$	−53060.1	−2.03951
$879$	17136.4	0.657560
$880$	10840.7	0.415271
$881$	−10137.8	−0.387685	−0.193843	−	0.981033i	$-0.562095\pi$
$881$	−10137.8	−0.387685	−0.193843	+	0.981033i	$0.562095\pi$
$882$	−24505.6	−0.935540
$883$	−48659.9	−1.85452	−0.927258	−	0.374423i	$-0.877841\pi$
$883$	−48659.9	−1.85452	−0.927258	+	0.374423i	$0.877841\pi$
$884$	−4821.60	−0.183448
$885$	2995.07	0.113761
$886$	3556.32	0.134850
$887$	5616.34	0.212602	0.106301	−	0.994334i	$-0.466099\pi$
$887$	5616.34	0.212602	0.106301	+	0.994334i	$0.466099\pi$
$888$	3869.72	0.146238
$889$	38913.7	1.46808
$890$	−28447.7	−1.07143
$891$	−1079.49	−0.0405883
$892$	−25918.4	−0.972885
$893$	−504.155	−0.0188924
$894$	−8986.22	−0.336179
$895$	−23777.5	−0.888038
$896$	−13748.2	−0.512608
$897$	−5813.80	−0.216407
$898$	−47955.5	−1.78207
$899$	−6683.01	−0.247932
$900$	610.595	0.0226146
$901$	−2721.15	−0.100616
$902$	−24408.2	−0.901001
$903$	39422.0	1.45280
$904$	3592.38	0.132169
$905$	33601.4	1.23420
$906$	−21696.6	−0.795607
$907$	−48952.7	−1.79211	−0.896057	−	0.443938i	$-0.853581\pi$
$907$	−48952.7	−1.79211	−0.896057	+	0.443938i	$0.853581\pi$
$908$	−24622.6	−0.899924
$909$	10927.9	0.398740
$910$	−73623.6	−2.68197
$911$	52095.8	1.89463	0.947316	−	0.320300i	$-0.103784\pi$
$911$	52095.8	1.89463	0.947316	+	0.320300i	$0.103784\pi$
$912$	3976.39	0.144377
$913$	11031.8	0.399889
$914$	353.728	0.0128012
$915$	−10800.5	−0.390222
$916$	−28843.2	−1.04040
$917$	46844.8	1.68697
$918$	1404.16	0.0504840
$919$	25941.1	0.931141	0.465571	−	0.885011i	$-0.345849\pi$
$919$	25941.1	0.931141	0.465571	+	0.885011i	$0.345849\pi$
$920$	−1488.22	−0.0533318
$921$	−7534.71	−0.269573
$922$	−2568.96	−0.0917615
$923$	−34974.5	−1.24724
$924$	−9218.48	−0.328210
$925$	3663.53	0.130223
$926$	39784.1	1.41186
$927$	1659.26	0.0587887
$928$	−32505.9	−1.14985
$929$	−5922.88	−0.209175	−0.104587	−	0.994516i	$-0.533352\pi$
$929$	−5922.88	−0.209175	−0.104587	+	0.994516i	$0.533352\pi$
$930$	−6851.12	−0.241567
$931$	−13224.1	−0.465522
$932$	−49115.0	−1.72620
$933$	−9867.28	−0.346238
$934$	−69253.4	−2.42617
$935$	2065.78	0.0722547
$936$	1521.22	0.0531225
$937$	−27576.1	−0.961444	−0.480722	−	0.876873i	$-0.659625\pi$
$937$	−27576.1	−0.961444	−0.480722	+	0.876873i	$0.659625\pi$
$938$	−8418.52	−0.293043
$939$	−11279.3	−0.391999
$940$	2209.18	0.0766547
$941$	−9762.18	−0.338191	−0.169096	−	0.985600i	$-0.554085\pi$
$941$	−9762.18	−0.338191	−0.169096	+	0.985600i	$0.554085\pi$
$942$	30238.9	1.04590
$943$	18054.4	0.623471
$944$	−6037.85	−0.208173
$945$	10111.7	0.348076
$946$	21101.8	0.725243
$947$	3907.75	0.134092	0.0670458	−	0.997750i	$-0.478643\pi$
$947$	3907.75	0.134092	0.0670458	+	0.997750i	$0.478643\pi$
$948$	−29468.3	−1.00958
$949$	8698.10	0.297526
$950$	698.672	0.0238610
$951$	−11648.0	−0.397175
$952$	−1443.91	−0.0491569
$953$	25076.0	0.852350	0.426175	−	0.904641i	$-0.359861\pi$
$953$	25076.0	0.852350	0.426175	+	0.904641i	$0.359861\pi$
$954$	−7129.73	−0.241964
$955$	203.486	0.00689494
$956$	23987.6	0.811522
$957$	5279.78	0.178340
$958$	−44438.7	−1.49869
$959$	66957.7	2.25462
$960$	−13801.1	−0.463987
$961$	−27229.9	−0.914032
$962$	−75798.2	−2.54036
$963$	13829.7	0.462780
$964$	26040.8	0.870040
$965$	6949.32	0.231820
$966$	14458.7	0.481574
$967$	−5774.45	−0.192031	−0.0960154	−	0.995380i	$-0.530610\pi$
$967$	−5774.45	−0.192031	−0.0960154	+	0.995380i	$0.530610\pi$
$968$	−3858.64	−0.128121
$969$	757.734	0.0251207
$970$	42933.8	1.42116
$971$	4018.88	0.132824	0.0664119	−	0.997792i	$-0.478845\pi$
$971$	4018.88	0.132824	0.0664119	+	0.997792i	$0.478845\pi$
$972$	1735.07	0.0572556
$973$	11601.4	0.382245
$974$	36415.2	1.19797
$975$	1440.17	0.0473049
$976$	21773.0	0.714075
$977$	45877.2	1.50229	0.751147	−	0.660135i	$-0.229501\pi$
$977$	45877.2	1.50229	0.751147	+	0.660135i	$0.229501\pi$
$978$	30025.0	0.981692
$979$	−8401.37	−0.274268
$980$	57947.1	1.88883
$981$	−9289.50	−0.302335
$982$	−42744.2	−1.38902
$983$	6760.86	0.219367	0.109684	−	0.993967i	$-0.465016\pi$
$983$	6760.86	0.219367	0.109684	+	0.993967i	$0.465016\pi$
$984$	−4724.07	−0.153047
$985$	−18326.4	−0.592819
$986$	−6867.77	−0.221820
$987$	2584.47	0.0833482
$988$	−6817.28	−0.219521
$989$	−15608.8	−0.501850
$990$	5412.58	0.173761
$991$	37808.3	1.21193	0.605963	−	0.795492i	$-0.292788\pi$
$991$	37808.3	1.21193	0.605963	+	0.795492i	$0.292788\pi$
$992$	12456.9	0.398697
$993$	2273.09	0.0726430
$994$	86980.2	2.77550
$995$	−27810.1	−0.886070
$996$	−17731.5	−0.564101
$997$	1991.16	0.0632503	0.0316252	−	0.999500i	$-0.489932\pi$
$997$	1991.16	0.0632503	0.0316252	+	0.999500i	$0.489932\pi$
$998$	−14648.9	−0.464632
$999$	10410.3	0.329698

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.e.1.3	✓	11
3.2	odd	2		603.4.a.g.1.9		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.e.1.3	✓	11	1.1	even	1	trivial
603.4.a.g.1.9		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)

\(f(q)\)	\(=\)	\(q-3.89104 q^{2} +3.00000 q^{3} +7.14021 q^{4} +11.5975 q^{5} -11.6731 q^{6} +32.2920 q^{7} +3.34547 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.89104 q^{2} +3.00000 q^{3} +7.14021 q^{4} +11.5975 q^{5} -11.6731 q^{6} +32.2920 q^{7} +3.34547 q^{8} +9.00000 q^{9} -45.1263 q^{10} -13.3270 q^{11} +21.4206 q^{12} +50.5234 q^{13} -125.650 q^{14} +34.7925 q^{15} -70.1391 q^{16} -13.3656 q^{17} -35.0194 q^{18} -18.8977 q^{19} +82.8085 q^{20} +96.8760 q^{21} +51.8559 q^{22} -38.3572 q^{23} +10.0364 q^{24} +9.50166 q^{25} -196.589 q^{26} +27.0000 q^{27} +230.572 q^{28} -132.057 q^{29} -135.379 q^{30} +50.6070 q^{31} +246.150 q^{32} -39.9810 q^{33} +52.0060 q^{34} +374.506 q^{35} +64.2619 q^{36} +385.568 q^{37} +73.5316 q^{38} +151.570 q^{39} +38.7991 q^{40} -470.692 q^{41} -376.949 q^{42} +406.932 q^{43} -95.1575 q^{44} +104.377 q^{45} +149.249 q^{46} +26.6782 q^{47} -210.417 q^{48} +699.773 q^{49} -36.9714 q^{50} -40.0967 q^{51} +360.747 q^{52} +203.594 q^{53} -105.058 q^{54} -154.560 q^{55} +108.032 q^{56} -56.6930 q^{57} +513.840 q^{58} +86.0839 q^{59} +248.425 q^{60} -310.426 q^{61} -196.914 q^{62} +290.628 q^{63} -396.669 q^{64} +585.944 q^{65} +155.568 q^{66} +67.0000 q^{67} -95.4331 q^{68} -115.071 q^{69} -1457.22 q^{70} -692.245 q^{71} +30.1093 q^{72} +172.160 q^{73} -1500.26 q^{74} +28.5050 q^{75} -134.933 q^{76} -430.355 q^{77} -589.766 q^{78} -1375.70 q^{79} -813.437 q^{80} +81.0000 q^{81} +1831.48 q^{82} -827.777 q^{83} +691.715 q^{84} -155.007 q^{85} -1583.39 q^{86} -396.172 q^{87} -44.5851 q^{88} +630.402 q^{89} -406.137 q^{90} +1631.50 q^{91} -273.878 q^{92} +151.821 q^{93} -103.806 q^{94} -219.165 q^{95} +738.451 q^{96} -951.415 q^{97} -2722.84 q^{98} -119.943 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 3 q^{2} + 33 q^{3} + 69 q^{4} + 8 q^{5} + 9 q^{6} + 78 q^{7} + 21 q^{8} + 99 q^{9}+O(q^{10}) \) 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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