LMFDB - Embedded newform 201.4.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$11.8593839112$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 38x^{5} + 18x^{4} + 373x^{3} - 151x^{2} - 956x + 498 $ x^7 - x^6 - 38x^5 + 18x^4 + 373x^3 - 151x^2 - 956*x + 498
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$1.85609$ 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)

$f(q)$	$=$	$q-1.85609 q^{2} -3.00000 q^{3} -4.55494 q^{4} -4.35854 q^{5} +5.56826 q^{6} +17.6123 q^{7} +23.3031 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-1.85609 q^{2} -3.00000 q^{3} -4.55494 q^{4} -4.35854 q^{5} +5.56826 q^{6} +17.6123 q^{7} +23.3031 q^{8} +9.00000 q^{9} +8.08983 q^{10} +1.41625 q^{11} +13.6648 q^{12} +18.8836 q^{13} -32.6899 q^{14} +13.0756 q^{15} -6.81292 q^{16} -10.5730 q^{17} -16.7048 q^{18} -42.7082 q^{19} +19.8529 q^{20} -52.8368 q^{21} -2.62869 q^{22} -171.703 q^{23} -69.9092 q^{24} -106.003 q^{25} -35.0496 q^{26} -27.0000 q^{27} -80.2228 q^{28} +33.2473 q^{29} -24.2695 q^{30} +169.393 q^{31} -173.779 q^{32} -4.24876 q^{33} +19.6245 q^{34} -76.7638 q^{35} -40.9945 q^{36} +67.8964 q^{37} +79.2701 q^{38} -56.6508 q^{39} -101.567 q^{40} -253.695 q^{41} +98.0696 q^{42} +21.7706 q^{43} -6.45095 q^{44} -39.2269 q^{45} +318.695 q^{46} -280.649 q^{47} +20.4388 q^{48} -32.8086 q^{49} +196.751 q^{50} +31.7191 q^{51} -86.0138 q^{52} -455.678 q^{53} +50.1143 q^{54} -6.17280 q^{55} +410.419 q^{56} +128.125 q^{57} -61.7099 q^{58} -589.495 q^{59} -59.5588 q^{60} -142.626 q^{61} -314.408 q^{62} +158.510 q^{63} +377.052 q^{64} -82.3050 q^{65} +7.88606 q^{66} +67.0000 q^{67} +48.1596 q^{68} +515.108 q^{69} +142.480 q^{70} +140.641 q^{71} +209.728 q^{72} -106.392 q^{73} -126.022 q^{74} +318.009 q^{75} +194.533 q^{76} +24.9434 q^{77} +105.149 q^{78} +1124.19 q^{79} +29.6944 q^{80} +81.0000 q^{81} +470.879 q^{82} -173.130 q^{83} +240.669 q^{84} +46.0831 q^{85} -40.4081 q^{86} -99.7419 q^{87} +33.0030 q^{88} -754.583 q^{89} +72.8085 q^{90} +332.583 q^{91} +782.096 q^{92} -508.179 q^{93} +520.908 q^{94} +186.146 q^{95} +521.337 q^{96} +1038.18 q^{97} +60.8955 q^{98} +12.7463 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9} - 51 q^{10} - 130 q^{11} - 63 q^{12} + 16 q^{13} + 5 q^{14} - 33 q^{15} + 77 q^{16} + 90 q^{17} - 9 q^{18} - 132 q^{19} - 359 q^{20} + 99 q^{21} - 192 q^{22} - 399 q^{23} + 135 q^{24} - 132 q^{25} - 638 q^{26} - 189 q^{27} - 245 q^{28} - 302 q^{29} + 153 q^{30} - 555 q^{31} - 1031 q^{32} + 390 q^{33} - 832 q^{34} - 775 q^{35} + 189 q^{36} + 297 q^{37} + 98 q^{38} - 48 q^{39} + 305 q^{40} - 717 q^{41} - 15 q^{42} - 245 q^{43} - 1766 q^{44} + 99 q^{45} - 497 q^{46} - 1072 q^{47} - 231 q^{48} + 314 q^{49} + 454 q^{50} - 270 q^{51} + 1344 q^{52} + 265 q^{53} + 27 q^{54} + 1096 q^{55} - 477 q^{56} + 396 q^{57} + 1610 q^{58} - 255 q^{59} + 1077 q^{60} + 418 q^{61} - 191 q^{62} - 297 q^{63} + 1889 q^{64} + 262 q^{65} + 576 q^{66} + 469 q^{67} + 3720 q^{68} + 1197 q^{69} + 1309 q^{70} - 1194 q^{71} - 405 q^{72} + 995 q^{73} + 259 q^{74} + 396 q^{75} + 1506 q^{76} + 230 q^{77} + 1914 q^{78} - 2640 q^{79} - 1949 q^{80} + 567 q^{81} + 1535 q^{82} - 2579 q^{83} + 735 q^{84} - 562 q^{85} + 1991 q^{86} + 906 q^{87} + 3624 q^{88} - 1604 q^{89} - 459 q^{90} - 2116 q^{91} - 351 q^{92} + 1665 q^{93} + 6178 q^{94} - 3028 q^{95} + 3093 q^{96} - 808 q^{97} + 258 q^{98} - 1170 q^{99}+O(q^{100}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9 - 51 * q^10 - 130 * q^11 - 63 * q^12 + 16 * q^13 + 5 * q^14 - 33 * q^15 + 77 * q^16 + 90 * q^17 - 9 * q^18 - 132 * q^19 - 359 * q^20 + 99 * q^21 - 192 * q^22 - 399 * q^23 + 135 * q^24 - 132 * q^25 - 638 * q^26 - 189 * q^27 - 245 * q^28 - 302 * q^29 + 153 * q^30 - 555 * q^31 - 1031 * q^32 + 390 * q^33 - 832 * q^34 - 775 * q^35 + 189 * q^36 + 297 * q^37 + 98 * q^38 - 48 * q^39 + 305 * q^40 - 717 * q^41 - 15 * q^42 - 245 * q^43 - 1766 * q^44 + 99 * q^45 - 497 * q^46 - 1072 * q^47 - 231 * q^48 + 314 * q^49 + 454 * q^50 - 270 * q^51 + 1344 * q^52 + 265 * q^53 + 27 * q^54 + 1096 * q^55 - 477 * q^56 + 396 * q^57 + 1610 * q^58 - 255 * q^59 + 1077 * q^60 + 418 * q^61 - 191 * q^62 - 297 * q^63 + 1889 * q^64 + 262 * q^65 + 576 * q^66 + 469 * q^67 + 3720 * q^68 + 1197 * q^69 + 1309 * q^70 - 1194 * q^71 - 405 * q^72 + 995 * q^73 + 259 * q^74 + 396 * q^75 + 1506 * q^76 + 230 * q^77 + 1914 * q^78 - 2640 * q^79 - 1949 * q^80 + 567 * q^81 + 1535 * q^82 - 2579 * q^83 + 735 * q^84 - 562 * q^85 + 1991 * q^86 + 906 * q^87 + 3624 * q^88 - 1604 * q^89 - 459 * q^90 - 2116 * q^91 - 351 * q^92 + 1665 * q^93 + 6178 * q^94 - 3028 * q^95 + 3093 * q^96 - 808 * q^97 + 258 * q^98 - 1170 * 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 $

$2$	−1.85609	−0.656225	−0.328113	−	0.944639i	$-0.606413\pi$
$2$	−1.85609	−0.656225	−0.328113	+	0.944639i	$0.606413\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	−4.55494	−0.569368
$5$	−4.35854	−0.389840	−0.194920	−	0.980819i	$-0.562445\pi$
$5$	−4.35854	−0.389840	−0.194920	+	0.980819i	$0.562445\pi$
$6$	5.56826	0.378872
$7$	17.6123	0.950972	0.475486	−	0.879723i	$-0.342272\pi$
$7$	17.6123	0.950972	0.475486	+	0.879723i	$0.342272\pi$
$8$	23.3031	1.02986
$9$	9.00000	0.333333
$10$	8.08983	0.255823
$11$	1.41625	0.0388196	0.0194098	−	0.999812i	$-0.493821\pi$
$11$	1.41625	0.0388196	0.0194098	+	0.999812i	$0.493821\pi$
$12$	13.6648	0.328725
$13$	18.8836	0.402875	0.201437	−	0.979501i	$-0.435439\pi$
$13$	18.8836	0.402875	0.201437	+	0.979501i	$0.435439\pi$
$14$	−32.6899	−0.624052
$15$	13.0756	0.225074
$16$	−6.81292	−0.106452
$17$	−10.5730	−0.150843	−0.0754217	−	0.997152i	$-0.524030\pi$
$17$	−10.5730	−0.150843	−0.0754217	+	0.997152i	$0.524030\pi$
$18$	−16.7048	−0.218742
$19$	−42.7082	−0.515681	−0.257840	−	0.966188i	$-0.583011\pi$
$19$	−42.7082	−0.515681	−0.257840	+	0.966188i	$0.583011\pi$
$20$	19.8529	0.221963
$21$	−52.8368	−0.549044
$22$	−2.62869	−0.0254744
$23$	−171.703	−1.55663	−0.778315	−	0.627874i	$-0.783925\pi$
$23$	−171.703	−1.55663	−0.778315	+	0.627874i	$0.783925\pi$
$24$	−69.9092	−0.594590
$25$	−106.003	−0.848025
$26$	−35.0496	−0.264377
$27$	−27.0000	−0.192450
$28$	−80.2228	−0.541453
$29$	33.2473	0.212892	0.106446	−	0.994318i	$-0.466053\pi$
$29$	33.2473	0.212892	0.106446	+	0.994318i	$0.466053\pi$
$30$	−24.2695	−0.147699
$31$	169.393	0.981415	0.490708	−	0.871324i	$-0.336738\pi$
$31$	169.393	0.981415	0.490708	+	0.871324i	$0.336738\pi$
$32$	−173.779	−0.960003
$33$	−4.24876	−0.0224125
$34$	19.6245	0.0989873
$35$	−76.7638	−0.370727
$36$	−40.9945	−0.189789
$37$	67.8964	0.301679	0.150839	−	0.988558i	$-0.451802\pi$
$37$	67.8964	0.301679	0.150839	+	0.988558i	$0.451802\pi$
$38$	79.2701	0.338403
$39$	−56.6508	−0.232600
$40$	−101.567	−0.401480
$41$	−253.695	−0.966352	−0.483176	−	0.875523i	$-0.660517\pi$
$41$	−253.695	−0.966352	−0.483176	+	0.875523i	$0.660517\pi$
$42$	98.0696	0.360297
$43$	21.7706	0.0772090	0.0386045	−	0.999255i	$-0.487709\pi$
$43$	21.7706	0.0772090	0.0386045	+	0.999255i	$0.487709\pi$
$44$	−6.45095	−0.0221027
$45$	−39.2269	−0.129947
$46$	318.695	1.02150
$47$	−280.649	−0.870996	−0.435498	−	0.900190i	$-0.643428\pi$
$47$	−280.649	−0.870996	−0.435498	+	0.900190i	$0.643428\pi$
$48$	20.4388	0.0614600
$49$	−32.8086	−0.0956518
$50$	196.751	0.556495
$51$	31.7191	0.0870895
$52$	−86.0138	−0.229384
$53$	−455.678	−1.18098	−0.590492	−	0.807043i	$-0.701066\pi$
$53$	−455.678	−1.18098	−0.590492	+	0.807043i	$0.701066\pi$
$54$	50.1143	0.126291
$55$	−6.17280	−0.0151334
$56$	410.419	0.979368
$57$	128.125	0.297728
$58$	−61.7099	−0.139705
$59$	−589.495	−1.30077	−0.650387	−	0.759603i	$-0.725393\pi$
$59$	−589.495	−1.30077	−0.650387	+	0.759603i	$0.725393\pi$
$60$	−59.5588	−0.128150
$61$	−142.626	−0.299367	−0.149683	−	0.988734i	$-0.547825\pi$
$61$	−142.626	−0.299367	−0.149683	+	0.988734i	$0.547825\pi$
$62$	−314.408	−0.644030
$63$	158.510	0.316991
$64$	377.052	0.736430
$65$	−82.3050	−0.157057
$66$	7.88606	0.0147077
$67$	67.0000	0.122169
$67$	67.0000	0.122169
$68$	48.1596	0.0858855
$69$	515.108	0.898721
$70$	142.480	0.243281
$71$	140.641	0.235084	0.117542	−	0.993068i	$-0.462498\pi$
$71$	140.641	0.235084	0.117542	+	0.993068i	$0.462498\pi$
$72$	209.728	0.343286
$73$	−106.392	−0.170578	−0.0852890	−	0.996356i	$-0.527181\pi$
$73$	−106.392	−0.170578	−0.0852890	+	0.996356i	$0.527181\pi$
$74$	−126.022	−0.197969
$75$	318.009	0.489607
$76$	194.533	0.293612
$77$	24.9434	0.0369164
$78$	105.149	0.152638
$79$	1124.19	1.60103	0.800513	−	0.599315i	$-0.204560\pi$
$79$	1124.19	1.60103	0.800513	+	0.599315i	$0.204560\pi$
$80$	29.6944	0.0414992
$81$	81.0000	0.111111
$82$	470.879	0.634145
$83$	−173.130	−0.228958	−0.114479	−	0.993426i	$-0.536520\pi$
$83$	−173.130	−0.228958	−0.114479	+	0.993426i	$0.536520\pi$
$84$	240.669	0.312608
$85$	46.0831	0.0588048
$86$	−40.4081	−0.0506665
$87$	−99.7419	−0.122913
$88$	33.0030	0.0399788
$89$	−754.583	−0.898715	−0.449357	−	0.893352i	$-0.648347\pi$
$89$	−754.583	−0.898715	−0.449357	+	0.893352i	$0.648347\pi$
$90$	72.8085	0.0852743
$91$	332.583	0.383123
$92$	782.096	0.886295
$93$	−508.179	−0.566620
$94$	520.908	0.571570
$95$	186.146	0.201033
$96$	521.337	0.554258
$97$	1038.18	1.08671	0.543356	−	0.839503i	$-0.317153\pi$
$97$	1038.18	1.08671	0.543356	+	0.839503i	$0.317153\pi$
$98$	60.8955	0.0627692
$99$	12.7463	0.0129399
$100$	482.838	0.482838
$101$	−333.698	−0.328755	−0.164377	−	0.986398i	$-0.552561\pi$
$101$	−333.698	−0.328755	−0.164377	+	0.986398i	$0.552561\pi$
$102$	−58.8734	−0.0571504
$103$	−1438.80	−1.37640	−0.688202	−	0.725519i	$-0.741600\pi$
$103$	−1438.80	−1.37640	−0.688202	+	0.725519i	$0.741600\pi$
$104$	440.046	0.414904
$105$	230.291	0.214039
$106$	845.778	0.774992
$107$	−1395.64	−1.26095	−0.630474	−	0.776211i	$-0.717139\pi$
$107$	−1395.64	−1.26095	−0.630474	+	0.776211i	$0.717139\pi$
$108$	122.984	0.109575
$109$	228.631	0.200907	0.100454	−	0.994942i	$-0.467971\pi$
$109$	228.631	0.200907	0.100454	+	0.994942i	$0.467971\pi$
$110$	11.4572	0.00993096
$111$	−203.689	−0.174174
$112$	−119.991	−0.101233
$113$	−106.115	−0.0883405	−0.0441702	−	0.999024i	$-0.514064\pi$
$113$	−106.115	−0.0883405	−0.0441702	+	0.999024i	$0.514064\pi$
$114$	−237.810	−0.195377
$115$	748.374	0.606837
$116$	−151.440	−0.121214
$117$	169.952	0.134292
$118$	1094.15	0.853601
$119$	−186.215	−0.143448
$120$	304.702	0.231795
$121$	−1328.99	−0.998493
$122$	264.726	0.196452
$123$	761.084	0.557924
$124$	−771.575	−0.558786
$125$	1006.84	0.720434
$126$	−294.209	−0.208017
$127$	−1383.20	−0.966448	−0.483224	−	0.875497i	$-0.660534\pi$
$127$	−1383.20	−0.966448	−0.483224	+	0.875497i	$0.660534\pi$
$128$	690.391	0.476739
$129$	−65.3119	−0.0445767
$130$	152.765	0.103065
$131$	299.606	0.199822	0.0999112	−	0.994996i	$-0.468144\pi$
$131$	299.606	0.199822	0.0999112	+	0.994996i	$0.468144\pi$
$132$	19.3528	0.0127610
$133$	−752.187	−0.490398
$134$	−124.358	−0.0801707
$135$	117.681	0.0750248
$136$	−246.384	−0.155348
$137$	1025.05	0.639239	0.319620	−	0.947546i	$-0.396445\pi$
$137$	1025.05	0.639239	0.319620	+	0.947546i	$0.396445\pi$
$138$	−956.085	−0.589763
$139$	−1867.27	−1.13942	−0.569712	−	0.821844i	$-0.692945\pi$
$139$	−1867.27	−1.13942	−0.569712	+	0.821844i	$0.692945\pi$
$140$	349.655	0.211080
$141$	841.946	0.502870
$142$	−261.041	−0.154268
$143$	26.7439	0.0156394
$144$	−61.3163	−0.0354840
$145$	−144.910	−0.0829939
$146$	197.472	0.111938
$147$	98.4257	0.0552246
$148$	−309.265	−0.171766
$149$	−983.361	−0.540672	−0.270336	−	0.962766i	$-0.587135\pi$
$149$	−983.361	−0.540672	−0.270336	+	0.962766i	$0.587135\pi$
$150$	−590.253	−0.321293
$151$	−1658.48	−0.893811	−0.446905	−	0.894581i	$-0.647474\pi$
$151$	−1658.48	−0.893811	−0.446905	+	0.894581i	$0.647474\pi$
$152$	−995.231	−0.531078
$153$	−95.1574	−0.0502812
$154$	−46.2971	−0.0242255
$155$	−738.307	−0.382595
$156$	258.041	0.132435
$157$	1141.20	0.580112	0.290056	−	0.957010i	$-0.406326\pi$
$157$	1141.20	0.580112	0.290056	+	0.957010i	$0.406326\pi$
$158$	−2086.59	−1.05063
$159$	1367.03	0.681842
$160$	757.424	0.374248
$161$	−3024.07	−1.48031
$162$	−150.343	−0.0729139
$163$	−693.646	−0.333316	−0.166658	−	0.986015i	$-0.553298\pi$
$163$	−693.646	−0.333316	−0.166658	+	0.986015i	$0.553298\pi$
$164$	1155.57	0.550210
$165$	18.5184	0.00873730
$166$	321.345	0.150248
$167$	795.749	0.368724	0.184362	−	0.982858i	$-0.440978\pi$
$167$	795.749	0.368724	0.184362	+	0.982858i	$0.440978\pi$
$168$	−1231.26	−0.565438
$169$	−1840.41	−0.837692
$170$	−85.5341	−0.0385892
$171$	−384.374	−0.171894
$172$	−99.1640	−0.0439604
$173$	2009.99	0.883335	0.441668	−	0.897179i	$-0.354387\pi$
$173$	2009.99	0.883335	0.441668	+	0.897179i	$0.354387\pi$
$174$	185.130	0.0806588
$175$	−1866.95	−0.806448
$176$	−9.64881	−0.00413242
$177$	1768.48	0.751003
$178$	1400.57	0.589760
$179$	−1794.36	−0.749257	−0.374628	−	0.927175i	$-0.622230\pi$
$179$	−1794.36	−0.749257	−0.374628	+	0.927175i	$0.622230\pi$
$180$	178.676	0.0739875
$181$	1602.82	0.658213	0.329107	−	0.944293i	$-0.393252\pi$
$181$	1602.82	0.658213	0.329107	+	0.944293i	$0.393252\pi$
$182$	−617.302	−0.251415
$183$	427.878	0.172839
$184$	−4001.20	−1.60311
$185$	−295.930	−0.117606
$186$	943.224	0.371831
$187$	−14.9741	−0.00585569
$188$	1278.34	0.495917
$189$	−475.531	−0.183015
$190$	−345.502	−0.131923
$191$	−2068.39	−0.783579	−0.391790	−	0.920055i	$-0.628144\pi$
$191$	−2068.39	−0.783579	−0.391790	+	0.920055i	$0.628144\pi$
$192$	−1131.16	−0.425178
$193$	−60.3857	−0.0225215	−0.0112608	−	0.999937i	$-0.503584\pi$
$193$	−60.3857	−0.0225215	−0.0112608	+	0.999937i	$0.503584\pi$
$194$	−1926.95	−0.713128
$195$	246.915	0.0906767
$196$	149.441	0.0544611
$197$	3540.83	1.28058	0.640288	−	0.768135i	$-0.278815\pi$
$197$	3540.83	1.28058	0.640288	+	0.768135i	$0.278815\pi$
$198$	−23.6582	−0.00849148
$199$	−5068.82	−1.80562	−0.902812	−	0.430036i	$-0.858501\pi$
$199$	−5068.82	−1.80562	−0.902812	+	0.430036i	$0.858501\pi$
$200$	−2470.20	−0.873346
$201$	−201.000	−0.0705346
$202$	619.372	0.215737
$203$	585.560	0.202454
$204$	−144.479	−0.0495860
$205$	1105.74	0.376723
$206$	2670.54	0.903231
$207$	−1545.32	−0.518877
$208$	−128.652	−0.0428868
$209$	−60.4856	−0.0200185
$210$	−427.441	−0.140458
$211$	3010.51	0.982237	0.491118	−	0.871093i	$-0.336588\pi$
$211$	3010.51	0.982237	0.491118	+	0.871093i	$0.336588\pi$
$212$	2075.59	0.672415
$213$	−421.922	−0.135726
$214$	2590.42	0.827466
$215$	−94.8882	−0.0300992
$216$	−629.183	−0.198197
$217$	2983.39	0.933299
$218$	−424.359	−0.131840
$219$	319.175	0.0984833
$220$	28.1167	0.00861650
$221$	−199.657	−0.0607710
$222$	378.065	0.114298
$223$	−761.130	−0.228561	−0.114280	−	0.993449i	$-0.536456\pi$
$223$	−761.130	−0.228561	−0.114280	+	0.993449i	$0.536456\pi$
$224$	−3060.64	−0.912936
$225$	−954.028	−0.282675
$226$	196.959	0.0579713
$227$	1067.06	0.311998	0.155999	−	0.987757i	$-0.450140\pi$
$227$	1067.06	0.311998	0.155999	+	0.987757i	$0.450140\pi$
$228$	−583.600	−0.169517
$229$	573.276	0.165429	0.0827143	−	0.996573i	$-0.473641\pi$
$229$	573.276	0.165429	0.0827143	+	0.996573i	$0.473641\pi$
$230$	−1389.05	−0.398222
$231$	−74.8302	−0.0213137
$232$	774.764	0.219249
$233$	−935.102	−0.262921	−0.131460	−	0.991321i	$-0.541967\pi$
$233$	−935.102	−0.262921	−0.131460	+	0.991321i	$0.541967\pi$
$234$	−315.446	−0.0881255
$235$	1223.22	0.339549
$236$	2685.12	0.740620
$237$	−3372.57	−0.924353
$238$	345.631	0.0941342
$239$	2582.97	0.699073	0.349537	−	0.936923i	$-0.386339\pi$
$239$	2582.97	0.699073	0.349537	+	0.936923i	$0.386339\pi$
$240$	−89.0832	−0.0239596
$241$	5131.67	1.37162	0.685808	−	0.727782i	$-0.259449\pi$
$241$	5131.67	1.37162	0.685808	+	0.727782i	$0.259449\pi$
$242$	2466.73	0.655237
$243$	−243.000	−0.0641500
$244$	649.653	0.170450
$245$	142.998	0.0372889
$246$	−1412.64	−0.366124
$247$	−806.485	−0.207755
$248$	3947.37	1.01072
$249$	519.391	0.132189
$250$	−1868.78	−0.472767
$251$	−5121.11	−1.28781	−0.643907	−	0.765104i	$-0.722688\pi$
$251$	−5121.11	−1.28781	−0.643907	+	0.765104i	$0.722688\pi$
$252$	−722.006	−0.180484
$253$	−243.174	−0.0604278
$254$	2567.33	0.634208
$255$	−138.249	−0.0339510
$256$	−4297.84	−1.04928
$257$	3184.14	0.772845	0.386422	−	0.922322i	$-0.373711\pi$
$257$	3184.14	0.772845	0.386422	+	0.922322i	$0.373711\pi$
$258$	121.224	0.0292523
$259$	1195.81	0.286888
$260$	374.895	0.0894231
$261$	299.226	0.0709640
$262$	−556.095	−0.131129
$263$	−467.836	−0.109688	−0.0548442	−	0.998495i	$-0.517466\pi$
$263$	−467.836	−0.109688	−0.0548442	+	0.998495i	$0.517466\pi$
$264$	−99.0090	−0.0230818
$265$	1986.09	0.460395
$266$	1396.12	0.321812
$267$	2263.75	0.518873
$268$	−305.181	−0.0695594
$269$	6385.40	1.44730	0.723652	−	0.690165i	$-0.242462\pi$
$269$	6385.40	1.44730	0.723652	+	0.690165i	$0.242462\pi$
$270$	−218.425	−0.0492332
$271$	−1252.49	−0.280749	−0.140375	−	0.990098i	$-0.544831\pi$
$271$	−1252.49	−0.280749	−0.140375	+	0.990098i	$0.544831\pi$
$272$	72.0333	0.0160576
$273$	−997.749	−0.221196
$274$	−1902.58	−0.419485
$275$	−150.127	−0.0329200
$276$	−2346.29	−0.511703
$277$	6690.67	1.45128	0.725638	−	0.688077i	$-0.241545\pi$
$277$	6690.67	1.45128	0.725638	+	0.688077i	$0.241545\pi$
$278$	3465.82	0.747719
$279$	1524.54	0.327138
$280$	−1788.83	−0.381797
$281$	3670.17	0.779161	0.389580	−	0.920992i	$-0.372620\pi$
$281$	3670.17	0.779161	0.389580	+	0.920992i	$0.372620\pi$
$282$	−1562.72	−0.329996
$283$	−1147.67	−0.241066	−0.120533	−	0.992709i	$-0.538460\pi$
$283$	−1147.67	−0.241066	−0.120533	+	0.992709i	$0.538460\pi$
$284$	−640.611	−0.133850
$285$	−558.437	−0.116066
$286$	−49.6391	−0.0102630
$287$	−4468.13	−0.918974
$288$	−1564.01	−0.320001
$289$	−4801.21	−0.977246
$290$	268.965	0.0544627
$291$	−3114.53	−0.627413
$292$	484.608	0.0971217
$293$	8400.16	1.67489	0.837445	−	0.546522i	$-0.184049\pi$
$293$	8400.16	1.67489	0.837445	+	0.546522i	$0.184049\pi$
$294$	−182.687	−0.0362398
$295$	2569.34	0.507094
$296$	1582.19	0.310687
$297$	−38.2388	−0.00747084
$298$	1825.20	0.354803
$299$	−3242.37	−0.627127
$300$	−1448.51	−0.278767
$301$	383.430	0.0734237
$302$	3078.29	0.586541
$303$	1001.09	0.189807
$304$	290.967	0.0548952
$305$	621.641	0.116705
$306$	176.620	0.0329958
$307$	6608.86	1.22862	0.614312	−	0.789063i	$-0.289433\pi$
$307$	6608.86	1.22862	0.614312	+	0.789063i	$0.289433\pi$
$308$	−113.616	−0.0210190
$309$	4316.41	0.794667
$310$	1370.36	0.251069
$311$	−2009.15	−0.366329	−0.183165	−	0.983082i	$-0.558634\pi$
$311$	−2009.15	−0.366329	−0.183165	+	0.983082i	$0.558634\pi$
$312$	−1320.14	−0.239545
$313$	−10409.4	−1.87980	−0.939898	−	0.341455i	$-0.889080\pi$
$313$	−10409.4	−1.87980	−0.939898	+	0.341455i	$0.889080\pi$
$314$	−2118.16	−0.380684
$315$	−690.874	−0.123576
$316$	−5120.62	−0.911574
$317$	1624.76	0.287872	0.143936	−	0.989587i	$-0.454024\pi$
$317$	1624.76	0.287872	0.143936	+	0.989587i	$0.454024\pi$
$318$	−2537.33	−0.447442
$319$	47.0866	0.00826439
$320$	−1643.40	−0.287090
$321$	4186.91	0.728008
$322$	5612.94	0.971418
$323$	451.555	0.0777871
$324$	−368.951	−0.0632631
$325$	−2001.72	−0.341648
$326$	1287.47	0.218731
$327$	−685.893	−0.115994
$328$	−5911.86	−0.995207
$329$	−4942.85	−0.828293
$330$	−34.3717	−0.00573364
$331$	−83.1843	−0.0138134	−0.00690668	−	0.999976i	$-0.502198\pi$
$331$	−83.1843	−0.0138134	−0.00690668	+	0.999976i	$0.502198\pi$
$332$	788.599	0.130361
$333$	611.068	0.100560
$334$	−1476.98	−0.241966
$335$	−292.022	−0.0476265
$336$	359.973	0.0584468
$337$	12114.4	1.95819	0.979097	−	0.203396i	$-0.0651978\pi$
$337$	12114.4	1.95819	0.979097	+	0.203396i	$0.0651978\pi$
$338$	3415.96	0.549715
$339$	318.345	0.0510034
$340$	−209.906	−0.0334816
$341$	239.903	0.0380982
$342$	713.431	0.112801
$343$	−6618.84	−1.04193
$344$	507.322	0.0795145
$345$	−2245.12	−0.350357
$346$	−3730.72	−0.579667
$347$	1424.77	0.220420	0.110210	−	0.993908i	$-0.464848\pi$
$347$	1424.77	0.220420	0.110210	+	0.993908i	$0.464848\pi$
$348$	454.319	0.0699829
$349$	3654.89	0.560579	0.280289	−	0.959916i	$-0.409570\pi$
$349$	3654.89	0.560579	0.280289	+	0.959916i	$0.409570\pi$
$350$	3465.23	0.529212
$351$	−509.857	−0.0775333
$352$	−246.115	−0.0372670
$353$	407.392	0.0614257	0.0307128	−	0.999528i	$-0.490222\pi$
$353$	407.392	0.0614257	0.0307128	+	0.999528i	$0.490222\pi$
$354$	−3282.46	−0.492827
$355$	−612.989	−0.0916453
$356$	3437.08	0.511700
$357$	558.645	0.0828197
$358$	3330.49	0.491681
$359$	3915.10	0.575575	0.287787	−	0.957694i	$-0.407080\pi$
$359$	3915.10	0.575575	0.287787	+	0.957694i	$0.407080\pi$
$360$	−914.107	−0.133827
$361$	−5035.01	−0.734074
$362$	−2974.97	−0.431936
$363$	3986.98	0.576480
$364$	−1514.90	−0.218138
$365$	463.713	0.0664982
$366$	−794.177	−0.113422
$367$	4005.90	0.569772	0.284886	−	0.958561i	$-0.408044\pi$
$367$	4005.90	0.569772	0.284886	+	0.958561i	$0.408044\pi$
$368$	1169.80	0.165706
$369$	−2283.25	−0.322117
$370$	549.271	0.0771763
$371$	−8025.52	−1.12308
$372$	2314.73	0.322616
$373$	6594.45	0.915409	0.457704	−	0.889104i	$-0.348672\pi$
$373$	6594.45	0.915409	0.457704	+	0.889104i	$0.348672\pi$
$374$	27.7932	0.00384265
$375$	−3020.51	−0.415943
$376$	−6539.97	−0.897003
$377$	627.829	0.0857688
$378$	882.626	0.120099
$379$	−3608.21	−0.489027	−0.244514	−	0.969646i	$-0.578628\pi$
$379$	−3608.21	−0.489027	−0.244514	+	0.969646i	$0.578628\pi$
$380$	−847.883	−0.114462
$381$	4149.59	0.557979
$382$	3839.12	0.514205
$383$	2257.75	0.301215	0.150608	−	0.988594i	$-0.451877\pi$
$383$	2257.75	0.301215	0.150608	+	0.988594i	$0.451877\pi$
$384$	−2071.17	−0.275245
$385$	−108.717	−0.0143915
$386$	112.081	0.0147792
$387$	195.936	0.0257363
$388$	−4728.84	−0.618739
$389$	−8098.89	−1.05560	−0.527802	−	0.849367i	$-0.676984\pi$
$389$	−8098.89	−1.05560	−0.527802	+	0.849367i	$0.676984\pi$
$390$	−458.296	−0.0595044
$391$	1815.42	0.234807
$392$	−764.540	−0.0985079
$393$	−898.819	−0.115368
$394$	−6572.08	−0.840347
$395$	−4899.83	−0.624144
$396$	−58.0585	−0.00736755
$397$	457.258	0.0578064	0.0289032	−	0.999582i	$-0.490799\pi$
$397$	457.258	0.0578064	0.0289032	+	0.999582i	$0.490799\pi$
$398$	9408.16	1.18490
$399$	2256.56	0.283131
$400$	722.190	0.0902738
$401$	−7899.98	−0.983806	−0.491903	−	0.870650i	$-0.663699\pi$
$401$	−7899.98	−0.983806	−0.491903	+	0.870650i	$0.663699\pi$
$402$	373.073	0.0462866
$403$	3198.75	0.395387
$404$	1519.98	0.187182
$405$	−353.042	−0.0433156
$406$	−1086.85	−0.132856
$407$	96.1585	0.0117111
$408$	739.153	0.0896900
$409$	2143.20	0.259106	0.129553	−	0.991572i	$-0.458646\pi$
$409$	2143.20	0.259106	0.129553	+	0.991572i	$0.458646\pi$
$410$	−2052.35	−0.247215
$411$	−3075.15	−0.369065
$412$	6553.67	0.783680
$413$	−10382.3	−1.23700
$414$	2868.25	0.340500
$415$	754.596	0.0892570
$416$	−3281.58	−0.386761
$417$	5601.82	0.657847
$418$	112.266	0.0131367
$419$	12166.7	1.41857	0.709286	−	0.704920i	$-0.249017\pi$
$419$	12166.7	1.41857	0.709286	+	0.704920i	$0.249017\pi$
$420$	−1048.96	−0.121867
$421$	−3810.57	−0.441130	−0.220565	−	0.975372i	$-0.570790\pi$
$421$	−3810.57	−0.441130	−0.220565	+	0.975372i	$0.570790\pi$
$422$	−5587.76	−0.644569
$423$	−2525.84	−0.290332
$424$	−10618.7	−1.21625
$425$	1120.78	0.127919
$426$	783.124	0.0890669
$427$	−2511.96	−0.284689
$428$	6357.05	0.717943
$429$	−80.2318	−0.00902944
$430$	176.121	0.0197518
$431$	−2661.67	−0.297466	−0.148733	−	0.988877i	$-0.547520\pi$
$431$	−2661.67	−0.297466	−0.148733	+	0.988877i	$0.547520\pi$
$432$	183.949	0.0204867
$433$	−7410.10	−0.822418	−0.411209	−	0.911541i	$-0.634893\pi$
$433$	−7410.10	−0.822418	−0.411209	+	0.911541i	$0.634893\pi$
$434$	−5537.43	−0.612454
$435$	434.730	0.0479165
$436$	−1041.40	−0.114390
$437$	7333.11	0.802724
$438$	−592.416	−0.0646272
$439$	−905.445	−0.0984386	−0.0492193	−	0.998788i	$-0.515673\pi$
$439$	−905.445	−0.0984386	−0.0492193	+	0.998788i	$0.515673\pi$
$440$	−143.845	−0.0155853
$441$	−295.277	−0.0318839
$442$	370.581	0.0398795
$443$	4559.02	0.488951	0.244476	−	0.969655i	$-0.421384\pi$
$443$	4559.02	0.488951	0.244476	+	0.969655i	$0.421384\pi$
$444$	927.794	0.0991692
$445$	3288.88	0.350355
$446$	1412.72	0.149987
$447$	2950.08	0.312157
$448$	6640.74	0.700325
$449$	−14763.1	−1.55170	−0.775848	−	0.630919i	$-0.782678\pi$
$449$	−14763.1	−1.55170	−0.775848	+	0.630919i	$0.782678\pi$
$450$	1770.76	0.185498
$451$	−359.296	−0.0375135
$452$	483.349	0.0502982
$453$	4975.45	0.516042
$454$	−1980.56	−0.204741
$455$	−1449.58	−0.149357
$456$	2985.69	0.306618
$457$	1745.48	0.178665	0.0893325	−	0.996002i	$-0.471527\pi$
$457$	1745.48	0.178665	0.0893325	+	0.996002i	$0.471527\pi$
$458$	−1064.05	−0.108558
$459$	285.472	0.0290298
$460$	−3408.80	−0.345513
$461$	2315.85	0.233969	0.116985	−	0.993134i	$-0.462677\pi$
$461$	2315.85	0.233969	0.116985	+	0.993134i	$0.462677\pi$
$462$	138.891	0.0139866
$463$	−14730.2	−1.47855	−0.739277	−	0.673402i	$-0.764832\pi$
$463$	−14730.2	−1.47855	−0.739277	+	0.673402i	$0.764832\pi$
$464$	−226.511	−0.0226628
$465$	2214.92	0.220891
$466$	1735.63	0.172535
$467$	−10130.6	−1.00383	−0.501917	−	0.864916i	$-0.667372\pi$
$467$	−10130.6	−1.00383	−0.501917	+	0.864916i	$0.667372\pi$
$468$	−774.124	−0.0764613
$469$	1180.02	0.116180
$470$	−2270.40	−0.222821
$471$	−3423.59	−0.334928
$472$	−13737.0	−1.33961
$473$	30.8327	0.00299723
$474$	6259.77	0.606584
$475$	4527.20	0.437310
$476$	848.199	0.0816747
$477$	−4101.10	−0.393662
$478$	−4794.22	−0.458750
$479$	−4919.17	−0.469233	−0.234617	−	0.972088i	$-0.575383\pi$
$479$	−4919.17	−0.469233	−0.234617	+	0.972088i	$0.575383\pi$
$480$	−2272.27	−0.216072
$481$	1282.13	0.121539
$482$	−9524.81	−0.900090
$483$	9072.21	0.854658
$484$	6053.50	0.568510
$485$	−4524.95	−0.423644
$486$	451.029	0.0420969
$487$	−11040.3	−1.02727	−0.513636	−	0.858008i	$-0.671702\pi$
$487$	−11040.3	−1.02727	−0.513636	+	0.858008i	$0.671702\pi$
$488$	−3323.62	−0.308306
$489$	2080.94	0.192440
$490$	−265.416	−0.0244699
$491$	−4339.19	−0.398829	−0.199415	−	0.979915i	$-0.563904\pi$
$491$	−4339.19	−0.398829	−0.199415	+	0.979915i	$0.563904\pi$
$492$	−3466.70	−0.317664
$493$	−351.525	−0.0321134
$494$	1496.90	0.136334
$495$	−55.5552	−0.00504448
$496$	−1154.06	−0.104473
$497$	2477.00	0.223559
$498$	−964.034	−0.0867458
$499$	14576.8	1.30771	0.653855	−	0.756620i	$-0.273151\pi$
$499$	14576.8	1.30771	0.653855	+	0.756620i	$0.273151\pi$
$500$	−4586.09	−0.410192
$501$	−2387.25	−0.212883
$502$	9505.21	0.845097
$503$	−2517.54	−0.223164	−0.111582	−	0.993755i	$-0.535592\pi$
$503$	−2517.54	−0.223164	−0.111582	+	0.993755i	$0.535592\pi$
$504$	3693.77	0.326456
$505$	1454.44	0.128162
$506$	451.352	0.0396543
$507$	5521.23	0.483642
$508$	6300.38	0.550264
$509$	−4527.42	−0.394252	−0.197126	−	0.980378i	$-0.563161\pi$
$509$	−4527.42	−0.394252	−0.197126	+	0.980378i	$0.563161\pi$
$510$	256.602	0.0222795
$511$	−1873.80	−0.162215
$512$	2454.04	0.211825
$513$	1153.12	0.0992428
$514$	−5910.03	−0.507160
$515$	6271.09	0.536577
$516$	297.492	0.0253805
$517$	−397.469	−0.0338117
$518$	−2219.53	−0.188263
$519$	−6029.98	−0.509994
$520$	−1917.96	−0.161746
$521$	−15789.5	−1.32773	−0.663867	−	0.747851i	$-0.731086\pi$
$521$	−15789.5	−1.32773	−0.663867	+	0.747851i	$0.731086\pi$
$522$	−555.389	−0.0465684
$523$	−10579.8	−0.884552	−0.442276	−	0.896879i	$-0.645829\pi$
$523$	−10579.8	−0.884552	−0.442276	+	0.896879i	$0.645829\pi$
$524$	−1364.69	−0.113773
$525$	5600.86	0.465603
$526$	868.345	0.0719803
$527$	−1791.00	−0.148040
$528$	28.9464	0.00238586
$529$	17314.8	1.42310
$530$	−3686.36	−0.302123
$531$	−5305.45	−0.433592
$532$	3426.17	0.279217
$533$	−4790.67	−0.389319
$534$	−4201.71	−0.340498
$535$	6082.95	0.491568
$536$	1561.30	0.125817
$537$	5383.09	0.432584
$538$	−11851.8	−0.949757
$539$	−46.4652	−0.00371317
$540$	−536.029	−0.0427167
$541$	20499.9	1.62913	0.814563	−	0.580074i	$-0.196977\pi$
$541$	20499.9	1.62913	0.814563	+	0.580074i	$0.196977\pi$
$542$	2324.72	0.184235
$543$	−4808.46	−0.380020
$544$	1837.37	0.144810
$545$	−996.499	−0.0783217
$546$	1851.91	0.145154
$547$	19521.4	1.52591	0.762956	−	0.646450i	$-0.223747\pi$
$547$	19521.4	1.52591	0.762956	+	0.646450i	$0.223747\pi$
$548$	−4669.04	−0.363963
$549$	−1283.63	−0.0997889
$550$	278.649	0.0216030
$551$	−1419.93	−0.109784
$552$	12003.6	0.925556
$553$	19799.5	1.52253
$554$	−12418.5	−0.952364
$555$	887.789	0.0679001
$556$	8505.32	0.648752
$557$	−6308.23	−0.479872	−0.239936	−	0.970789i	$-0.577126\pi$
$557$	−6308.23	−0.479872	−0.239936	+	0.970789i	$0.577126\pi$
$558$	−2829.67	−0.214677
$559$	411.108	0.0311056
$560$	522.985	0.0394646
$561$	44.9223	0.00338078
$562$	−6812.16	−0.511305
$563$	5076.45	0.380012	0.190006	−	0.981783i	$-0.439149\pi$
$563$	5076.45	0.380012	0.190006	+	0.981783i	$0.439149\pi$
$564$	−3835.02	−0.286318
$565$	462.508	0.0344387
$566$	2130.17	0.158194
$567$	1426.59	0.105664
$568$	3277.36	0.242104
$569$	−6064.32	−0.446801	−0.223400	−	0.974727i	$-0.571716\pi$
$569$	−6064.32	−0.446801	−0.223400	+	0.974727i	$0.571716\pi$
$570$	1036.51	0.0761658
$571$	−17140.5	−1.25623	−0.628116	−	0.778120i	$-0.716174\pi$
$571$	−17140.5	−1.25623	−0.628116	+	0.778120i	$0.716174\pi$
$572$	−121.817	−0.00890460
$573$	6205.18	0.452400
$574$	8293.24	0.603054
$575$	18201.0	1.32006
$576$	3393.47	0.245477
$577$	16521.9	1.19205	0.596026	−	0.802965i	$-0.296746\pi$
$577$	16521.9	1.19205	0.596026	+	0.802965i	$0.296746\pi$
$578$	8911.46	0.641294
$579$	181.157	0.0130028
$580$	660.057	0.0472541
$581$	−3049.21	−0.217733
$582$	5780.84	0.411725
$583$	−645.355	−0.0458454
$584$	−2479.25	−0.175671
$585$	−740.745	−0.0523522
$586$	−15591.4	−1.09910
$587$	18579.6	1.30641	0.653206	−	0.757180i	$-0.273424\pi$
$587$	18579.6	1.30641	0.653206	+	0.757180i	$0.273424\pi$
$588$	−448.324	−0.0314431
$589$	−7234.47	−0.506097
$590$	−4768.92	−0.332768
$591$	−10622.5	−0.739341
$592$	−462.573	−0.0321142
$593$	17901.9	1.23970	0.619849	−	0.784721i	$-0.287194\pi$
$593$	17901.9	1.23970	0.619849	+	0.784721i	$0.287194\pi$
$594$	70.9745	0.00490256
$595$	811.627	0.0559218
$596$	4479.16	0.307841
$597$	15206.5	1.04248
$598$	6018.11	0.411536
$599$	12443.4	0.848786	0.424393	−	0.905478i	$-0.360487\pi$
$599$	12443.4	0.848786	0.424393	+	0.905478i	$0.360487\pi$
$600$	7410.59	0.504227
$601$	16794.3	1.13986	0.569929	−	0.821694i	$-0.306971\pi$
$601$	16794.3	1.13986	0.569929	+	0.821694i	$0.306971\pi$
$602$	−711.678	−0.0481825
$603$	603.000	0.0407231
$604$	7554.30	0.508907
$605$	5792.48	0.389253
$606$	−1858.12	−0.124556
$607$	−3170.43	−0.211999	−0.106000	−	0.994366i	$-0.533804\pi$
$607$	−3170.43	−0.211999	−0.106000	+	0.994366i	$0.533804\pi$
$608$	7421.79	0.495055
$609$	−1756.68	−0.116887
$610$	−1153.82	−0.0765849
$611$	−5299.66	−0.350902
$612$	433.437	0.0286285
$613$	9210.72	0.606880	0.303440	−	0.952851i	$-0.401865\pi$
$613$	9210.72	0.606880	0.303440	+	0.952851i	$0.401865\pi$
$614$	−12266.6	−0.806255
$615$	−3317.22	−0.217501
$616$	581.257	0.0380187
$617$	16743.3	1.09248	0.546239	−	0.837629i	$-0.316059\pi$
$617$	16743.3	1.09248	0.546239	+	0.837629i	$0.316059\pi$
$618$	−8011.63	−0.521481
$619$	11544.7	0.749627	0.374813	−	0.927100i	$-0.377707\pi$
$619$	11544.7	0.749627	0.374813	+	0.927100i	$0.377707\pi$
$620$	3362.95	0.217837
$621$	4635.97	0.299574
$622$	3729.15	0.240395
$623$	−13289.9	−0.854653
$624$	385.957	0.0247607
$625$	8862.04	0.567171
$626$	19320.8	1.23357
$627$	181.457	0.0115577
$628$	−5198.09	−0.330297
$629$	−717.872	−0.0455062
$630$	1282.32	0.0810935
$631$	4386.22	0.276724	0.138362	−	0.990382i	$-0.455816\pi$
$631$	4386.22	0.276724	0.138362	+	0.990382i	$0.455816\pi$
$632$	26197.0	1.64883
$633$	−9031.53	−0.567095
$634$	−3015.69	−0.188909
$635$	6028.72	0.376760
$636$	−6226.77	−0.388219
$637$	−619.544	−0.0385357
$638$	−87.3967	−0.00542331
$639$	1265.77	0.0783615
$640$	−3009.10	−0.185852
$641$	−22521.1	−1.38772	−0.693862	−	0.720108i	$-0.744092\pi$
$641$	−22521.1	−1.38772	−0.693862	+	0.720108i	$0.744092\pi$
$642$	−7771.27	−0.477737
$643$	−9339.41	−0.572800	−0.286400	−	0.958110i	$-0.592459\pi$
$643$	−9339.41	−0.572800	−0.286400	+	0.958110i	$0.592459\pi$
$644$	13774.5	0.842842
$645$	284.665	0.0173778
$646$	−838.126	−0.0510458
$647$	−5458.88	−0.331701	−0.165851	−	0.986151i	$-0.553037\pi$
$647$	−5458.88	−0.331701	−0.165851	+	0.986151i	$0.553037\pi$
$648$	1887.55	0.114429
$649$	−834.873	−0.0504956
$650$	3715.37	0.224198
$651$	−8950.17	−0.538840
$652$	3159.52	0.189780
$653$	−4825.40	−0.289177	−0.144588	−	0.989492i	$-0.546186\pi$
$653$	−4825.40	−0.289177	−0.144588	+	0.989492i	$0.546186\pi$
$654$	1273.08	0.0761181
$655$	−1305.85	−0.0778988
$656$	1728.40	0.102870
$657$	−957.525	−0.0568594
$658$	9174.36	0.543547
$659$	−11702.8	−0.691770	−0.345885	−	0.938277i	$-0.612421\pi$
$659$	−11702.8	−0.691770	−0.345885	+	0.938277i	$0.612421\pi$
$660$	−84.3502	−0.00497474
$661$	−1980.14	−0.116518	−0.0582592	−	0.998301i	$-0.518555\pi$
$661$	−1980.14	−0.116518	−0.0582592	+	0.998301i	$0.518555\pi$
$662$	154.397	0.00906468
$663$	598.971	0.0350862
$664$	−4034.47	−0.235795
$665$	3278.44	0.191177
$666$	−1134.19	−0.0659897
$667$	−5708.65	−0.331394
$668$	−3624.59	−0.209940
$669$	2283.39	0.131960
$670$	542.019	0.0312538
$671$	−201.994	−0.0116213
$672$	9181.92	0.527084
$673$	−16453.9	−0.942423	−0.471211	−	0.882020i	$-0.656183\pi$
$673$	−16453.9	−0.942423	−0.471211	+	0.882020i	$0.656183\pi$
$674$	−22485.3	−1.28502
$675$	2862.08	0.163202
$676$	8382.96	0.476955
$677$	−790.873	−0.0448977	−0.0224488	−	0.999748i	$-0.507146\pi$
$677$	−790.873	−0.0448977	−0.0224488	+	0.999748i	$0.507146\pi$
$678$	−590.876	−0.0334697
$679$	18284.7	1.03343
$680$	1073.88	0.0605607
$681$	−3201.19	−0.180132
$682$	−445.281	−0.0250010
$683$	−16820.0	−0.942311	−0.471156	−	0.882050i	$-0.656163\pi$
$683$	−16820.0	−0.942311	−0.471156	+	0.882050i	$0.656163\pi$
$684$	1750.80	0.0978707
$685$	−4467.72	−0.249201
$686$	12285.1	0.683744
$687$	−1719.83	−0.0955102
$688$	−148.321	−0.00821905
$689$	−8604.85	−0.475789
$690$	4167.14	0.229913
$691$	−29841.7	−1.64288	−0.821440	−	0.570295i	$-0.806829\pi$
$691$	−29841.7	−1.64288	−0.821440	+	0.570295i	$0.806829\pi$
$692$	−9155.41	−0.502943
$693$	224.490	0.0123055
$694$	−2644.49	−0.144645
$695$	8138.59	0.444193
$696$	−2324.29	−0.126583
$697$	2682.32	0.145768
$698$	−6783.80	−0.367866
$699$	2805.31	0.151797
$700$	8503.87	0.459166
$701$	−11806.6	−0.636135	−0.318067	−	0.948068i	$-0.603034\pi$
$701$	−11806.6	−0.636135	−0.318067	+	0.948068i	$0.603034\pi$
$702$	946.339	0.0508793
$703$	−2899.73	−0.155570
$704$	534.001	0.0285880
$705$	−3669.66	−0.196039
$706$	−756.154	−0.0403091
$707$	−5877.18	−0.312636
$708$	−8055.35	−0.427597
$709$	22077.3	1.16944	0.584719	−	0.811236i	$-0.301205\pi$
$709$	22077.3	1.16944	0.584719	+	0.811236i	$0.301205\pi$
$710$	1137.76	0.0601400
$711$	10117.7	0.533676
$712$	−17584.1	−0.925550
$713$	−29085.2	−1.52770
$714$	−1036.89	−0.0543484
$715$	−116.565	−0.00609688
$716$	8173.22	0.426603
$717$	−7748.91	−0.403610
$718$	−7266.77	−0.377707
$719$	−29616.5	−1.53617	−0.768086	−	0.640346i	$-0.778791\pi$
$719$	−29616.5	−1.53617	−0.768086	+	0.640346i	$0.778791\pi$
$720$	267.250	0.0138331
$721$	−25340.6	−1.30892
$722$	9345.41	0.481718
$723$	−15395.0	−0.791903
$724$	−7300.75	−0.374766
$725$	−3524.32	−0.180538
$726$	−7400.18	−0.378301
$727$	8833.51	0.450642	0.225321	−	0.974285i	$-0.427657\pi$
$727$	8833.51	0.450642	0.225321	+	0.974285i	$0.427657\pi$
$728$	7750.20	0.394562
$729$	729.000	0.0370370
$730$	−860.691	−0.0436378
$731$	−230.182	−0.0116465
$732$	−1948.96	−0.0984093
$733$	−23783.8	−1.19846	−0.599232	−	0.800575i	$-0.704527\pi$
$733$	−23783.8	−1.19846	−0.599232	+	0.800575i	$0.704527\pi$
$734$	−7435.29	−0.373899
$735$	−428.993	−0.0215288
$736$	29838.3	1.49437
$737$	94.8889	0.00474257
$738$	4237.91	0.211382
$739$	−24461.3	−1.21762	−0.608812	−	0.793314i	$-0.708354\pi$
$739$	−24461.3	−1.21762	−0.608812	+	0.793314i	$0.708354\pi$
$740$	1347.94	0.0669613
$741$	2419.45	0.119947
$742$	14896.0	0.736996
$743$	−38353.4	−1.89374	−0.946870	−	0.321618i	$-0.895773\pi$
$743$	−38353.4	−1.89374	−0.946870	+	0.321618i	$0.895773\pi$
$744$	−11842.1	−0.583539
$745$	4286.02	0.210775
$746$	−12239.9	−0.600715
$747$	−1558.17	−0.0763194
$748$	68.2061	0.00333404
$749$	−24580.3	−1.19913
$750$	5606.33	0.272952
$751$	−26520.7	−1.28862	−0.644310	−	0.764764i	$-0.722855\pi$
$751$	−26520.7	−1.28862	−0.644310	+	0.764764i	$0.722855\pi$
$752$	1912.04	0.0927191
$753$	15363.3	0.743520
$754$	−1165.30	−0.0562837
$755$	7228.57	0.348443
$756$	2166.02	0.104203
$757$	−3584.10	−0.172082	−0.0860411	−	0.996292i	$-0.527422\pi$
$757$	−3584.10	−0.172082	−0.0860411	+	0.996292i	$0.527422\pi$
$758$	6697.15	0.320912
$759$	729.523	0.0348880
$760$	4337.76	0.207036
$761$	30252.4	1.44106	0.720532	−	0.693421i	$-0.243897\pi$
$761$	30252.4	1.44106	0.720532	+	0.693421i	$0.243897\pi$
$762$	−7702.00	−0.366160
$763$	4026.71	0.191057
$764$	9421.42	0.446145
$765$	414.748	0.0196016
$766$	−4190.57	−0.197665
$767$	−11131.8	−0.524049
$768$	12893.5	0.605801
$769$	−18695.0	−0.876670	−0.438335	−	0.898812i	$-0.644432\pi$
$769$	−18695.0	−0.876670	−0.438335	+	0.898812i	$0.644432\pi$
$770$	201.788	0.00944406
$771$	−9552.41	−0.446202
$772$	275.053	0.0128230
$773$	35421.9	1.64817	0.824087	−	0.566463i	$-0.191689\pi$
$773$	35421.9	1.64817	0.824087	+	0.566463i	$0.191689\pi$
$774$	−363.673	−0.0168888
$775$	−17956.2	−0.832264
$776$	24192.7	1.11916
$777$	−3587.43	−0.165635
$778$	15032.2	0.692714
$779$	10834.8	0.498329
$780$	−1124.68	−0.0516284
$781$	199.183	0.00912589
$782$	−3369.57	−0.154087
$783$	−897.677	−0.0409711
$784$	223.522	0.0101823
$785$	−4973.96	−0.226151
$786$	1668.29	0.0757071
$787$	−6884.49	−0.311824	−0.155912	−	0.987771i	$-0.549832\pi$
$787$	−6884.49	−0.311824	−0.155912	+	0.987771i	$0.549832\pi$
$788$	−16128.3	−0.729119
$789$	1403.51	0.0633286
$790$	9094.50	0.409579
$791$	−1868.93	−0.0840093
$792$	297.027	0.0133263
$793$	−2693.29	−0.120607
$794$	−848.711	−0.0379340
$795$	−5958.28	−0.265809
$796$	23088.2	1.02806
$797$	−7356.27	−0.326942	−0.163471	−	0.986548i	$-0.552269\pi$
$797$	−7356.27	−0.326942	−0.163471	+	0.986548i	$0.552269\pi$
$798$	−4188.37	−0.185798
$799$	2967.31	0.131384
$800$	18421.1	0.814106
$801$	−6791.25	−0.299572
$802$	14663.1	0.645599
$803$	−150.677	−0.00662178
$804$	915.544	0.0401601
$805$	13180.5	0.577085
$806$	−5937.15	−0.259463
$807$	−19156.2	−0.835601
$808$	−7776.19	−0.338571
$809$	−13559.8	−0.589294	−0.294647	−	0.955606i	$-0.595202\pi$
$809$	−13559.8	−0.589294	−0.294647	+	0.955606i	$0.595202\pi$
$810$	655.276	0.0284248
$811$	43307.4	1.87513	0.937563	−	0.347815i	$-0.113076\pi$
$811$	43307.4	1.87513	0.937563	+	0.347815i	$0.113076\pi$
$812$	−2667.19	−0.115271
$813$	3757.46	0.162091
$814$	−178.478	−0.00768509
$815$	3023.29	0.129940
$816$	−216.100	−0.00927084
$817$	−929.784	−0.0398152
$818$	−3977.96	−0.170032
$819$	2993.25	0.127708
$820$	−5036.58	−0.214494
$821$	34445.2	1.46424	0.732122	−	0.681173i	$-0.238530\pi$
$821$	34445.2	1.46424	0.732122	+	0.681173i	$0.238530\pi$
$822$	5707.73	0.242190
$823$	−34101.8	−1.44436	−0.722182	−	0.691703i	$-0.756861\pi$
$823$	−34101.8	−1.44436	−0.722182	+	0.691703i	$0.756861\pi$
$824$	−33528.5	−1.41750
$825$	450.381	0.0190064
$826$	19270.5	0.811751
$827$	32575.6	1.36973	0.684863	−	0.728672i	$-0.259862\pi$
$827$	32575.6	1.36973	0.684863	+	0.728672i	$0.259862\pi$
$828$	7038.87	0.295432
$829$	3718.03	0.155769	0.0778845	−	0.996962i	$-0.475183\pi$
$829$	3718.03	0.155769	0.0778845	+	0.996962i	$0.475183\pi$
$830$	−1400.60	−0.0585727
$831$	−20072.0	−0.837895
$832$	7120.11	0.296689
$833$	346.886	0.0144285
$834$	−10397.5	−0.431696
$835$	−3468.31	−0.143743
$836$	275.508	0.0113979
$837$	−4573.61	−0.188873
$838$	−22582.4	−0.930904
$839$	42697.8	1.75696	0.878482	−	0.477775i	$-0.158557\pi$
$839$	42697.8	1.75696	0.878482	+	0.477775i	$0.158557\pi$
$840$	5366.49	0.220430
$841$	−23283.6	−0.954677
$842$	7072.74	0.289481
$843$	−11010.5	−0.449849
$844$	−13712.7	−0.559254
$845$	8021.51	0.326566
$846$	4688.17	0.190523
$847$	−23406.6	−0.949539
$848$	3104.50	0.125718
$849$	3443.00	0.139180
$850$	−2080.25	−0.0839437
$851$	−11658.0	−0.469602
$852$	1921.83	0.0772781
$853$	−11507.4	−0.461906	−0.230953	−	0.972965i	$-0.574184\pi$
$853$	−11507.4	−0.461906	−0.230953	+	0.972965i	$0.574184\pi$
$854$	4662.42	0.186820
$855$	1675.31	0.0670110
$856$	−32522.6	−1.29860
$857$	−12511.4	−0.498696	−0.249348	−	0.968414i	$-0.580216\pi$
$857$	−12511.4	−0.498696	−0.249348	+	0.968414i	$0.580216\pi$
$858$	148.917	0.00592535
$859$	−24574.5	−0.976102	−0.488051	−	0.872815i	$-0.662292\pi$
$859$	−24574.5	−0.976102	−0.488051	+	0.872815i	$0.662292\pi$
$860$	432.211	0.0171375
$861$	13404.4	0.530570
$862$	4940.28	0.195205
$863$	38347.2	1.51258	0.756288	−	0.654239i	$-0.227011\pi$
$863$	38347.2	1.51258	0.756288	+	0.654239i	$0.227011\pi$
$864$	4692.04	0.184753
$865$	−8760.65	−0.344359
$866$	13753.8	0.539692
$867$	14403.6	0.564213
$868$	−13589.2	−0.531390
$869$	1592.13	0.0621513
$870$	−806.896	−0.0314441
$871$	1265.20	0.0492190
$872$	5327.80	0.206906
$873$	9343.60	0.362237
$874$	−13610.9	−0.526768
$875$	17732.7	0.685113
$876$	−1453.82	−0.0560732
$877$	8191.72	0.315410	0.157705	−	0.987486i	$-0.449590\pi$
$877$	8191.72	0.315410	0.157705	+	0.987486i	$0.449590\pi$
$878$	1680.58	0.0645979
$879$	−25200.5	−0.966998
$880$	42.0548	0.00161098
$881$	41793.6	1.59826	0.799128	−	0.601161i	$-0.205295\pi$
$881$	41793.6	1.59826	0.799128	+	0.601161i	$0.205295\pi$
$882$	548.060	0.0209231
$883$	−47118.5	−1.79577	−0.897884	−	0.440232i	$-0.854896\pi$
$883$	−47118.5	−1.79577	−0.897884	+	0.440232i	$0.854896\pi$
$884$	909.427	0.0346011
$885$	−7708.02	−0.292771
$886$	−8461.93	−0.320862
$887$	38218.5	1.44673	0.723366	−	0.690464i	$-0.242594\pi$
$887$	38218.5	1.44673	0.723366	+	0.690464i	$0.242594\pi$
$888$	−4746.58	−0.179375
$889$	−24361.2	−0.919065
$890$	−6104.45	−0.229912
$891$	114.716	0.00431329
$892$	3466.90	0.130135
$893$	11986.0	0.449156
$894$	−5475.61	−0.204845
$895$	7820.81	0.292090
$896$	12159.3	0.453365
$897$	9727.10	0.362072
$898$	27401.5	1.01826
$899$	5631.86	0.208936
$900$	4345.54	0.160946
$901$	4817.90	0.178144
$902$	666.883	0.0246173
$903$	−1150.29	−0.0423912
$904$	−2472.81	−0.0909783
$905$	−6985.96	−0.256598
$906$	−9234.86	−0.338640
$907$	15079.0	0.552029	0.276014	−	0.961153i	$-0.410986\pi$
$907$	15079.0	0.552029	0.276014	+	0.961153i	$0.410986\pi$
$908$	−4860.42	−0.177642
$909$	−3003.28	−0.109585
$910$	2690.54	0.0980116
$911$	−48067.0	−1.74811	−0.874056	−	0.485825i	$-0.838519\pi$
$911$	−48067.0	−1.74811	−0.874056	+	0.485825i	$0.838519\pi$
$912$	−872.902	−0.0316937
$913$	−245.196	−0.00888807
$914$	−3239.75	−0.117245
$915$	−1864.92	−0.0673797
$916$	−2611.24	−0.0941898
$917$	5276.75	0.190026
$918$	−529.861	−0.0190501
$919$	−20454.1	−0.734187	−0.367093	−	0.930184i	$-0.619647\pi$
$919$	−20454.1	−0.734187	−0.367093	+	0.930184i	$0.619647\pi$
$920$	17439.4	0.624956
$921$	−19826.6	−0.709347
$922$	−4298.41	−0.153536
$923$	2655.81	0.0947096
$924$	340.847	0.0121353
$925$	−7197.23	−0.255831
$926$	27340.5	0.970265
$927$	−12949.2	−0.458801
$928$	−5777.69	−0.204377
$929$	−6688.35	−0.236208	−0.118104	−	0.993001i	$-0.537682\pi$
$929$	−6688.35	−0.236208	−0.118104	+	0.993001i	$0.537682\pi$
$930$	−4111.08	−0.144954
$931$	1401.20	0.0493258
$932$	4259.34	0.149699
$933$	6027.45	0.211500
$934$	18803.4	0.658741
$935$	65.2652	0.00228278
$936$	3960.41	0.138301
$937$	29305.7	1.02174	0.510872	−	0.859657i	$-0.329322\pi$
$937$	29305.7	1.02174	0.510872	+	0.859657i	$0.329322\pi$
$938$	−2190.22	−0.0762401
$939$	31228.3	1.08530
$940$	−5571.70	−0.193328
$941$	−1198.39	−0.0415158	−0.0207579	−	0.999785i	$-0.506608\pi$
$941$	−1198.39	−0.0415158	−0.0207579	+	0.999785i	$0.506608\pi$
$942$	6354.49	0.219788
$943$	43560.1	1.50425
$944$	4016.18	0.138470
$945$	2072.62	0.0713465
$946$	−57.2281	−0.00196686
$947$	20700.2	0.710314	0.355157	−	0.934807i	$-0.384427\pi$
$947$	20700.2	0.710314	0.355157	+	0.934807i	$0.384427\pi$
$948$	15361.9	0.526297
$949$	−2009.06	−0.0687216
$950$	−8402.87	−0.286974
$951$	−4874.28	−0.166203
$952$	−4339.38	−0.147731
$953$	34434.1	1.17044	0.585220	−	0.810875i	$-0.301008\pi$
$953$	34434.1	1.17044	0.585220	+	0.810875i	$0.301008\pi$
$954$	7612.00	0.258331
$955$	9015.18	0.305471
$956$	−11765.3	−0.398030
$957$	−141.260	−0.00477145
$958$	9130.40	0.307923
$959$	18053.4	0.607899
$960$	4930.20	0.165751
$961$	−1097.03	−0.0368243
$962$	−2379.74	−0.0797568
$963$	−12560.7	−0.420316
$964$	−23374.5	−0.780955
$965$	263.194	0.00877979
$966$	−16838.8	−0.560849
$967$	40097.0	1.33344	0.666718	−	0.745310i	$-0.267699\pi$
$967$	40097.0	1.33344	0.666718	+	0.745310i	$0.267699\pi$
$968$	−30969.6	−1.02831
$969$	−1354.67	−0.0449104
$970$	8398.69	0.278006
$971$	35575.9	1.17578	0.587891	−	0.808940i	$-0.299959\pi$
$971$	35575.9	1.17578	0.587891	+	0.808940i	$0.299959\pi$
$972$	1106.85	0.0365250
$973$	−32886.9	−1.08356
$974$	20491.7	0.674122
$975$	6005.16	0.197250
$976$	971.698	0.0318681
$977$	24477.9	0.801554	0.400777	−	0.916176i	$-0.368740\pi$
$977$	24477.9	0.801554	0.400777	+	0.916176i	$0.368740\pi$
$978$	−3862.40	−0.126284
$979$	−1068.68	−0.0348878
$980$	−651.346	−0.0212311
$981$	2057.68	0.0669691
$982$	8053.92	0.261722
$983$	48118.6	1.56129	0.780643	−	0.624977i	$-0.214892\pi$
$983$	48118.6	1.56129	0.780643	+	0.624977i	$0.214892\pi$
$984$	17735.6	0.574583
$985$	−15432.9	−0.499220
$986$	652.461	0.0210736
$987$	14828.6	0.478215
$988$	3673.49	0.118289
$989$	−3738.07	−0.120186
$990$	103.115	0.00331032
$991$	−52042.3	−1.66819	−0.834096	−	0.551619i	$-0.814010\pi$
$991$	−52042.3	−1.66819	−0.834096	+	0.551619i	$0.814010\pi$
$992$	−29437.0	−0.942161
$993$	249.553	0.00797515
$994$	−4597.53	−0.146705
$995$	22092.7	0.703904
$996$	−2365.80	−0.0752642
$997$	−16339.8	−0.519042	−0.259521	−	0.965737i	$-0.583565\pi$
$997$	−16339.8	−0.519042	−0.259521	+	0.965737i	$0.583565\pi$
$998$	−27055.8	−0.858152
$999$	−1833.20	−0.0580581

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.c.1.3	✓	7
3.2	odd	2		603.4.a.c.1.5		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.c.1.3	✓	7	1.1	even	1	trivial
603.4.a.c.1.5		7	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)

\(f(q)\)	\(=\)	\(q-1.85609 q^{2} -3.00000 q^{3} -4.55494 q^{4} -4.35854 q^{5} +5.56826 q^{6} +17.6123 q^{7} +23.3031 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-1.85609 q^{2} -3.00000 q^{3} -4.55494 q^{4} -4.35854 q^{5} +5.56826 q^{6} +17.6123 q^{7} +23.3031 q^{8} +9.00000 q^{9} +8.08983 q^{10} +1.41625 q^{11} +13.6648 q^{12} +18.8836 q^{13} -32.6899 q^{14} +13.0756 q^{15} -6.81292 q^{16} -10.5730 q^{17} -16.7048 q^{18} -42.7082 q^{19} +19.8529 q^{20} -52.8368 q^{21} -2.62869 q^{22} -171.703 q^{23} -69.9092 q^{24} -106.003 q^{25} -35.0496 q^{26} -27.0000 q^{27} -80.2228 q^{28} +33.2473 q^{29} -24.2695 q^{30} +169.393 q^{31} -173.779 q^{32} -4.24876 q^{33} +19.6245 q^{34} -76.7638 q^{35} -40.9945 q^{36} +67.8964 q^{37} +79.2701 q^{38} -56.6508 q^{39} -101.567 q^{40} -253.695 q^{41} +98.0696 q^{42} +21.7706 q^{43} -6.45095 q^{44} -39.2269 q^{45} +318.695 q^{46} -280.649 q^{47} +20.4388 q^{48} -32.8086 q^{49} +196.751 q^{50} +31.7191 q^{51} -86.0138 q^{52} -455.678 q^{53} +50.1143 q^{54} -6.17280 q^{55} +410.419 q^{56} +128.125 q^{57} -61.7099 q^{58} -589.495 q^{59} -59.5588 q^{60} -142.626 q^{61} -314.408 q^{62} +158.510 q^{63} +377.052 q^{64} -82.3050 q^{65} +7.88606 q^{66} +67.0000 q^{67} +48.1596 q^{68} +515.108 q^{69} +142.480 q^{70} +140.641 q^{71} +209.728 q^{72} -106.392 q^{73} -126.022 q^{74} +318.009 q^{75} +194.533 q^{76} +24.9434 q^{77} +105.149 q^{78} +1124.19 q^{79} +29.6944 q^{80} +81.0000 q^{81} +470.879 q^{82} -173.130 q^{83} +240.669 q^{84} +46.0831 q^{85} -40.4081 q^{86} -99.7419 q^{87} +33.0030 q^{88} -754.583 q^{89} +72.8085 q^{90} +332.583 q^{91} +782.096 q^{92} -508.179 q^{93} +520.908 q^{94} +186.146 q^{95} +521.337 q^{96} +1038.18 q^{97} +60.8955 q^{98} +12.7463 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9	\( 7 q - q^{2} - 21 q^{3} + 21 q^{4} + 11 q^{5} + 3 q^{6} - 33 q^{7} - 45 q^{8} + 63 q^{9} - 51 q^{10} - 130 q^{11} - 63 q^{12} + 16 q^{13} + 5 q^{14} - 33 q^{15} + 77 q^{16} + 90 q^{17} - 9 q^{18} - 132 q^{19} - 359 q^{20} + 99 q^{21} - 192 q^{22} - 399 q^{23} + 135 q^{24} - 132 q^{25} - 638 q^{26} - 189 q^{27} - 245 q^{28} - 302 q^{29} + 153 q^{30} - 555 q^{31} - 1031 q^{32} + 390 q^{33} - 832 q^{34} - 775 q^{35} + 189 q^{36} + 297 q^{37} + 98 q^{38} - 48 q^{39} + 305 q^{40} - 717 q^{41} - 15 q^{42} - 245 q^{43} - 1766 q^{44} + 99 q^{45} - 497 q^{46} - 1072 q^{47} - 231 q^{48} + 314 q^{49} + 454 q^{50} - 270 q^{51} + 1344 q^{52} + 265 q^{53} + 27 q^{54} + 1096 q^{55} - 477 q^{56} + 396 q^{57} + 1610 q^{58} - 255 q^{59} + 1077 q^{60} + 418 q^{61} - 191 q^{62} - 297 q^{63} + 1889 q^{64} + 262 q^{65} + 576 q^{66} + 469 q^{67} + 3720 q^{68} + 1197 q^{69} + 1309 q^{70} - 1194 q^{71} - 405 q^{72} + 995 q^{73} + 259 q^{74} + 396 q^{75} + 1506 q^{76} + 230 q^{77} + 1914 q^{78} - 2640 q^{79} - 1949 q^{80} + 567 q^{81} + 1535 q^{82} - 2579 q^{83} + 735 q^{84} - 562 q^{85} + 1991 q^{86} + 906 q^{87} + 3624 q^{88} - 1604 q^{89} - 459 q^{90} - 2116 q^{91} - 351 q^{92} + 1665 q^{93} + 6178 q^{94} - 3028 q^{95} + 3093 q^{96} - 808 q^{97} + 258 q^{98} - 1170 q^{99}+O(q^{100}) \) 7 * q - q^2 - 21 * q^3 + 21 * q^4 + 11 * q^5 + 3 * q^6 - 33 * q^7 - 45 * q^8 + 63 * q^9 - 51 * q^10 - 130 * q^11 - 63 * q^12 + 16 * q^13 + 5 * q^14 - 33 * q^15 + 77 * q^16 + 90 * q^17 - 9 * q^18 - 132 * q^19 - 359 * q^20 + 99 * q^21 - 192 * q^22 - 399 * q^23 + 135 * q^24 - 132 * q^25 - 638 * q^26 - 189 * q^27 - 245 * q^28 - 302 * q^29 + 153 * q^30 - 555 * q^31 - 1031 * q^32 + 390 * q^33 - 832 * q^34 - 775 * q^35 + 189 * q^36 + 297 * q^37 + 98 * q^38 - 48 * q^39 + 305 * q^40 - 717 * q^41 - 15 * q^42 - 245 * q^43 - 1766 * q^44 + 99 * q^45 - 497 * q^46 - 1072 * q^47 - 231 * q^48 + 314 * q^49 + 454 * q^50 - 270 * q^51 + 1344 * q^52 + 265 * q^53 + 27 * q^54 + 1096 * q^55 - 477 * q^56 + 396 * q^57 + 1610 * q^58 - 255 * q^59 + 1077 * q^60 + 418 * q^61 - 191 * q^62 - 297 * q^63 + 1889 * q^64 + 262 * q^65 + 576 * q^66 + 469 * q^67 + 3720 * q^68 + 1197 * q^69 + 1309 * q^70 - 1194 * q^71 - 405 * q^72 + 995 * q^73 + 259 * q^74 + 396 * q^75 + 1506 * q^76 + 230 * q^77 + 1914 * q^78 - 2640 * q^79 - 1949 * q^80 + 567 * q^81 + 1535 * q^82 - 2579 * q^83 + 735 * q^84 - 562 * q^85 + 1991 * q^86 + 906 * q^87 + 3624 * q^88 - 1604 * q^89 - 459 * q^90 - 2116 * q^91 - 351 * q^92 + 1665 * q^93 + 6178 * q^94 - 3028 * q^95 + 3093 * q^96 - 808 * q^97 + 258 * q^98 - 1170 * q^99

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