LMFDB - Embedded newform 201.4.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("201.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$11.8593839112$
Analytic rank:	$1$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 28x^{4} + 22x^{3} + 202x^{2} - 96x - 384 $ x^6 - x^5 - 28x^4 + 22x^3 + 202x^2 - 96x - 384
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$2.81400$ 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)

$f(q)$	$=$	$q+1.81400 q^{2} +3.00000 q^{3} -4.70941 q^{4} +5.30362 q^{5} +5.44200 q^{6} -31.2342 q^{7} -23.0548 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+1.81400 q^{2} +3.00000 q^{3} -4.70941 q^{4} +5.30362 q^{5} +5.44200 q^{6} -31.2342 q^{7} -23.0548 q^{8} +9.00000 q^{9} +9.62075 q^{10} -38.7569 q^{11} -14.1282 q^{12} -22.3746 q^{13} -56.6587 q^{14} +15.9109 q^{15} -4.14618 q^{16} -74.5616 q^{17} +16.3260 q^{18} +142.955 q^{19} -24.9769 q^{20} -93.7025 q^{21} -70.3050 q^{22} -8.58950 q^{23} -69.1645 q^{24} -96.8716 q^{25} -40.5874 q^{26} +27.0000 q^{27} +147.094 q^{28} -17.4559 q^{29} +28.8623 q^{30} +19.9929 q^{31} +176.918 q^{32} -116.271 q^{33} -135.255 q^{34} -165.654 q^{35} -42.3847 q^{36} +55.1371 q^{37} +259.320 q^{38} -67.1237 q^{39} -122.274 q^{40} -231.812 q^{41} -169.976 q^{42} -499.703 q^{43} +182.522 q^{44} +47.7326 q^{45} -15.5813 q^{46} +105.180 q^{47} -12.4385 q^{48} +632.573 q^{49} -175.725 q^{50} -223.685 q^{51} +105.371 q^{52} +586.084 q^{53} +48.9780 q^{54} -205.552 q^{55} +720.099 q^{56} +428.865 q^{57} -31.6650 q^{58} -284.290 q^{59} -74.9307 q^{60} -319.031 q^{61} +36.2670 q^{62} -281.107 q^{63} +354.098 q^{64} -118.666 q^{65} -210.915 q^{66} -67.0000 q^{67} +351.141 q^{68} -25.7685 q^{69} -300.496 q^{70} -123.780 q^{71} -207.494 q^{72} +673.523 q^{73} +100.019 q^{74} -290.615 q^{75} -673.233 q^{76} +1210.54 q^{77} -121.762 q^{78} -897.265 q^{79} -21.9898 q^{80} +81.0000 q^{81} -420.507 q^{82} -345.013 q^{83} +441.283 q^{84} -395.446 q^{85} -906.461 q^{86} -52.3678 q^{87} +893.535 q^{88} -926.003 q^{89} +86.5868 q^{90} +698.851 q^{91} +40.4515 q^{92} +59.9786 q^{93} +190.797 q^{94} +758.178 q^{95} +530.753 q^{96} +1483.14 q^{97} +1147.49 q^{98} -348.812 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) $ 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * q^98 - 648 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.81400	0.641345	0.320673	−	0.947190i	$-0.396091\pi$
$2$	1.81400	0.641345	0.320673	+	0.947190i	$0.396091\pi$
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	−4.70941	−0.588676
$5$	5.30362	0.474370	0.237185	−	0.971465i	$-0.423775\pi$
$5$	5.30362	0.474370	0.237185	+	0.971465i	$0.423775\pi$
$6$	5.44200	0.370281
$7$	−31.2342	−1.68649	−0.843243	−	0.537532i	$-0.819357\pi$
$7$	−31.2342	−1.68649	−0.843243	+	0.537532i	$0.819357\pi$
$8$	−23.0548	−1.01889
$9$	9.00000	0.333333
$10$	9.62075	0.304235
$11$	−38.7569	−1.06233	−0.531166	−	0.847268i	$-0.678246\pi$
$11$	−38.7569	−1.06233	−0.531166	+	0.847268i	$0.678246\pi$
$12$	−14.1282	−0.339872
$13$	−22.3746	−0.477353	−0.238676	−	0.971099i	$-0.576714\pi$
$13$	−22.3746	−0.477353	−0.238676	+	0.971099i	$0.576714\pi$
$14$	−56.6587	−1.08162
$15$	15.9109	0.273878
$16$	−4.14618	−0.0647841
$17$	−74.5616	−1.06376	−0.531878	−	0.846821i	$-0.678513\pi$
$17$	−74.5616	−1.06376	−0.531878	+	0.846821i	$0.678513\pi$
$18$	16.3260	0.213782
$19$	142.955	1.72611	0.863055	−	0.505110i	$-0.168548\pi$
$19$	142.955	1.72611	0.863055	+	0.505110i	$0.168548\pi$
$20$	−24.9769	−0.279250
$21$	−93.7025	−0.973693
$22$	−70.3050	−0.681321
$23$	−8.58950	−0.0778711	−0.0389355	−	0.999242i	$-0.512397\pi$
$23$	−8.58950	−0.0778711	−0.0389355	+	0.999242i	$0.512397\pi$
$24$	−69.1645	−0.588256
$25$	−96.8716	−0.774973
$26$	−40.5874	−0.306148
$27$	27.0000	0.192450
$28$	147.094	0.992794
$29$	−17.4559	−0.111775	−0.0558876	−	0.998437i	$-0.517799\pi$
$29$	−17.4559	−0.111775	−0.0558876	+	0.998437i	$0.517799\pi$
$30$	28.8623	0.175650
$31$	19.9929	0.115833	0.0579165	−	0.998321i	$-0.481554\pi$
$31$	19.9929	0.115833	0.0579165	+	0.998321i	$0.481554\pi$
$32$	176.918	0.977341
$33$	−116.271	−0.613337
$34$	−135.255	−0.682234
$35$	−165.654	−0.800019
$36$	−42.3847	−0.196225
$37$	55.1371	0.244986	0.122493	−	0.992469i	$-0.460911\pi$
$37$	55.1371	0.244986	0.122493	+	0.992469i	$0.460911\pi$
$38$	259.320	1.10703
$39$	−67.1237	−0.275600
$40$	−122.274	−0.483331
$41$	−231.812	−0.883000	−0.441500	−	0.897261i	$-0.645553\pi$
$41$	−231.812	−0.883000	−0.441500	+	0.897261i	$0.645553\pi$
$42$	−169.976	−0.624474
$43$	−499.703	−1.77219	−0.886093	−	0.463507i	$-0.846591\pi$
$43$	−499.703	−1.77219	−0.886093	+	0.463507i	$0.846591\pi$
$44$	182.522	0.625369
$45$	47.7326	0.158123
$46$	−15.5813	−0.0499422
$47$	105.180	0.326428	0.163214	−	0.986591i	$-0.447814\pi$
$47$	105.180	0.326428	0.163214	+	0.986591i	$0.447814\pi$
$48$	−12.4385	−0.0374031
$49$	632.573	1.84424
$50$	−175.725	−0.497025
$51$	−223.685	−0.614159
$52$	105.371	0.281006
$53$	586.084	1.51896	0.759479	−	0.650532i	$-0.225454\pi$
$53$	586.084	1.51896	0.759479	+	0.650532i	$0.225454\pi$
$54$	48.9780	0.123427
$55$	−205.552	−0.503938
$56$	720.099	1.71834
$57$	428.865	0.996570
$58$	−31.6650	−0.0716865
$59$	−284.290	−0.627312	−0.313656	−	0.949537i	$-0.601554\pi$
$59$	−284.290	−0.627312	−0.313656	+	0.949537i	$0.601554\pi$
$60$	−74.9307	−0.161225
$61$	−319.031	−0.669635	−0.334817	−	0.942283i	$-0.608675\pi$
$61$	−319.031	−0.669635	−0.334817	+	0.942283i	$0.608675\pi$
$62$	36.2670	0.0742890
$63$	−281.107	−0.562162
$64$	354.098	0.691597
$65$	−118.666	−0.226442
$66$	−210.915	−0.393361
$67$	−67.0000	−0.122169
$67$	−67.0000	−0.122169
$68$	351.141	0.626207
$69$	−25.7685	−0.0449589
$70$	−300.496	−0.513088
$71$	−123.780	−0.206901	−0.103450	−	0.994635i	$-0.532988\pi$
$71$	−123.780	−0.206901	−0.103450	+	0.994635i	$0.532988\pi$
$72$	−207.494	−0.339630
$73$	673.523	1.07986	0.539931	−	0.841709i	$-0.318450\pi$
$73$	673.523	1.07986	0.539931	+	0.841709i	$0.318450\pi$
$74$	100.019	0.157121
$75$	−290.615	−0.447431
$76$	−673.233	−1.01612
$77$	1210.54	1.79161
$78$	−121.762	−0.176755
$79$	−897.265	−1.27785	−0.638925	−	0.769269i	$-0.720621\pi$
$79$	−897.265	−1.27785	−0.638925	+	0.769269i	$0.720621\pi$
$80$	−21.9898	−0.0307316
$81$	81.0000	0.111111
$82$	−420.507	−0.566308
$83$	−345.013	−0.456266	−0.228133	−	0.973630i	$-0.573262\pi$
$83$	−345.013	−0.456266	−0.228133	+	0.973630i	$0.573262\pi$
$84$	441.283	0.573190
$85$	−395.446	−0.504614
$86$	−906.461	−1.13658
$87$	−52.3678	−0.0645335
$88$	893.535	1.08240
$89$	−926.003	−1.10288	−0.551439	−	0.834215i	$-0.685921\pi$
$89$	−926.003	−1.10288	−0.551439	+	0.834215i	$0.685921\pi$
$90$	86.5868	0.101412
$91$	698.851	0.805049
$92$	40.4515	0.0458408
$93$	59.9786	0.0668762
$94$	190.797	0.209353
$95$	758.178	0.818815
$96$	530.753	0.564268
$97$	1483.14	1.55247	0.776237	−	0.630441i	$-0.217126\pi$
$97$	1483.14	1.55247	0.776237	+	0.630441i	$0.217126\pi$
$98$	1147.49	1.18279
$99$	−348.812	−0.354110
$100$	456.208	0.456208
$101$	556.880	0.548630	0.274315	−	0.961640i	$-0.411549\pi$
$101$	556.880	0.548630	0.274315	+	0.961640i	$0.411549\pi$
$102$	−405.764	−0.393888
$103$	−747.489	−0.715071	−0.357535	−	0.933900i	$-0.616383\pi$
$103$	−747.489	−0.715071	−0.357535	+	0.933900i	$0.616383\pi$
$104$	515.842	0.486370
$105$	−496.962	−0.461891
$106$	1063.15	0.974177
$107$	1774.60	1.60334	0.801669	−	0.597769i	$-0.203946\pi$
$107$	1774.60	1.60334	0.801669	+	0.597769i	$0.203946\pi$
$108$	−127.154	−0.113291
$109$	−416.620	−0.366100	−0.183050	−	0.983104i	$-0.558597\pi$
$109$	−416.620	−0.366100	−0.183050	+	0.983104i	$0.558597\pi$
$110$	−372.871	−0.323198
$111$	165.411	0.141443
$112$	129.502	0.109257
$113$	1701.82	1.41676	0.708378	−	0.705833i	$-0.249427\pi$
$113$	1701.82	1.41676	0.708378	+	0.705833i	$0.249427\pi$
$114$	777.960	0.639146
$115$	−45.5554	−0.0369397
$116$	82.2071	0.0657994
$117$	−201.371	−0.159118
$118$	−515.701	−0.402323
$119$	2328.87	1.79401
$120$	−366.822	−0.279051
$121$	171.097	0.128548
$122$	−578.721	−0.429467
$123$	−695.437	−0.509800
$124$	−94.1546	−0.0681881
$125$	−1176.72	−0.841994
$126$	−509.929	−0.360540
$127$	−1015.55	−0.709571	−0.354785	−	0.934948i	$-0.615446\pi$
$127$	−1015.55	−0.709571	−0.354785	+	0.934948i	$0.615446\pi$
$128$	−773.008	−0.533788
$129$	−1499.11	−1.02317
$130$	−215.260	−0.145227
$131$	−976.624	−0.651359	−0.325679	−	0.945480i	$-0.605593\pi$
$131$	−976.624	−0.651359	−0.325679	+	0.945480i	$0.605593\pi$
$132$	547.566	0.361057
$133$	−4465.08	−2.91106
$134$	−121.538	−0.0783528
$135$	143.198	0.0912925
$136$	1719.01	1.08385
$137$	2326.91	1.45111	0.725553	−	0.688167i	$-0.241584\pi$
$137$	2326.91	1.45111	0.725553	+	0.688167i	$0.241584\pi$
$138$	−46.7440	−0.0288342
$139$	−2421.93	−1.47788	−0.738939	−	0.673772i	$-0.764673\pi$
$139$	−2421.93	−1.47788	−0.738939	+	0.673772i	$0.764673\pi$
$140$	780.133	0.470952
$141$	315.541	0.188463
$142$	−224.536	−0.132695
$143$	867.169	0.507107
$144$	−37.3156	−0.0215947
$145$	−92.5795	−0.0530228
$146$	1221.77	0.692564
$147$	1897.72	1.06477
$148$	−259.663	−0.144218
$149$	−1961.26	−1.07834	−0.539169	−	0.842197i	$-0.681262\pi$
$149$	−1961.26	−1.07834	−0.539169	+	0.842197i	$0.681262\pi$
$150$	−527.175	−0.286958
$151$	−939.207	−0.506169	−0.253085	−	0.967444i	$-0.581445\pi$
$151$	−939.207	−0.506169	−0.253085	+	0.967444i	$0.581445\pi$
$152$	−3295.80	−1.75872
$153$	−671.054	−0.354585
$154$	2195.92	1.14904
$155$	106.034	0.0549477
$156$	316.113	0.162239
$157$	−736.838	−0.374561	−0.187280	−	0.982306i	$-0.559967\pi$
$157$	−736.838	−0.374561	−0.187280	+	0.982306i	$0.559967\pi$
$158$	−1627.64	−0.819543
$159$	1758.25	0.876971
$160$	938.303	0.463621
$161$	268.286	0.131328
$162$	146.934	0.0712606
$163$	−318.095	−0.152854	−0.0764268	−	0.997075i	$-0.524351\pi$
$163$	−318.095	−0.152854	−0.0764268	+	0.997075i	$0.524351\pi$
$164$	1091.70	0.519801
$165$	−616.655	−0.290949
$166$	−625.853	−0.292624
$167$	−3611.03	−1.67323	−0.836617	−	0.547788i	$-0.815470\pi$
$167$	−3611.03	−1.67323	−0.836617	+	0.547788i	$0.815470\pi$
$168$	2160.30	0.992086
$169$	−1696.38	−0.772134
$170$	−717.339	−0.323631
$171$	1286.59	0.575370
$172$	2353.31	1.04324
$173$	−185.364	−0.0814621	−0.0407310	−	0.999170i	$-0.512969\pi$
$173$	−185.364	−0.0814621	−0.0407310	+	0.999170i	$0.512969\pi$
$174$	−94.9950	−0.0413882
$175$	3025.70	1.30698
$176$	160.693	0.0688221
$177$	−852.870	−0.362179
$178$	−1679.77	−0.707326
$179$	−234.571	−0.0979477	−0.0489738	−	0.998800i	$-0.515595\pi$
$179$	−234.571	−0.0979477	−0.0489738	+	0.998800i	$0.515595\pi$
$180$	−224.792	−0.0930834
$181$	−2575.47	−1.05764	−0.528821	−	0.848733i	$-0.677366\pi$
$181$	−2575.47	−1.05764	−0.528821	+	0.848733i	$0.677366\pi$
$182$	1267.71	0.516314
$183$	−957.092	−0.386614
$184$	198.030	0.0793420
$185$	292.426	0.116214
$186$	108.801	0.0428907
$187$	2889.78	1.13006
$188$	−495.337	−0.192161
$189$	−843.322	−0.324564
$190$	1375.33	0.525143
$191$	−3140.05	−1.18956	−0.594781	−	0.803888i	$-0.702761\pi$
$191$	−3140.05	−1.18956	−0.594781	+	0.803888i	$0.702761\pi$
$192$	1062.29	0.399294
$193$	−3256.79	−1.21466	−0.607329	−	0.794450i	$-0.707759\pi$
$193$	−3256.79	−1.21466	−0.607329	+	0.794450i	$0.707759\pi$
$194$	2690.41	0.995672
$195$	−355.998	−0.130736
$196$	−2979.05	−1.08566
$197$	1748.23	0.632266	0.316133	−	0.948715i	$-0.397615\pi$
$197$	1748.23	0.632266	0.316133	+	0.948715i	$0.397615\pi$
$198$	−632.745	−0.227107
$199$	−3353.89	−1.19473	−0.597365	−	0.801970i	$-0.703785\pi$
$199$	−3353.89	−1.19473	−0.597365	+	0.801970i	$0.703785\pi$
$200$	2233.36	0.789612
$201$	−201.000	−0.0705346
$202$	1010.18	0.351861
$203$	545.221	0.188507
$204$	1053.42	0.361541
$205$	−1229.44	−0.418869
$206$	−1355.94	−0.458607
$207$	−77.3055	−0.0259570
$208$	92.7690	0.0309249
$209$	−5540.49	−1.83370
$210$	−901.489	−0.296232
$211$	1371.21	0.447383	0.223691	−	0.974660i	$-0.428189\pi$
$211$	1371.21	0.447383	0.223691	+	0.974660i	$0.428189\pi$
$212$	−2760.11	−0.894175
$213$	−371.339	−0.119454
$214$	3219.12	1.02829
$215$	−2650.24	−0.840672
$216$	−622.481	−0.196085
$217$	−624.460	−0.195351
$218$	−755.748	−0.234797
$219$	2020.57	0.623459
$220$	968.028	0.296656
$221$	1668.28	0.507787
$222$	300.056	0.0907137
$223$	−2331.41	−0.700102	−0.350051	−	0.936731i	$-0.613836\pi$
$223$	−2331.41	−0.700102	−0.350051	+	0.936731i	$0.613836\pi$
$224$	−5525.87	−1.64827
$225$	−871.845	−0.258324
$226$	3087.09	0.908630
$227$	−3441.58	−1.00628	−0.503141	−	0.864205i	$-0.667822\pi$
$227$	−3441.58	−1.00628	−0.503141	+	0.864205i	$0.667822\pi$
$228$	−2019.70	−0.586657
$229$	4118.61	1.18850	0.594248	−	0.804282i	$-0.297450\pi$
$229$	4118.61	1.18850	0.594248	+	0.804282i	$0.297450\pi$
$230$	−82.6375	−0.0236911
$231$	3631.62	1.03439
$232$	402.444	0.113887
$233$	6151.27	1.72954	0.864771	−	0.502167i	$-0.167464\pi$
$233$	6151.27	1.72954	0.864771	+	0.502167i	$0.167464\pi$
$234$	−365.287	−0.102049
$235$	557.836	0.154848
$236$	1338.84	0.369283
$237$	−2691.79	−0.737767
$238$	4224.56	1.15058
$239$	4304.95	1.16512	0.582560	−	0.812788i	$-0.302051\pi$
$239$	4304.95	1.16512	0.582560	+	0.812788i	$0.302051\pi$
$240$	−65.9693	−0.0177429
$241$	960.434	0.256710	0.128355	−	0.991728i	$-0.459030\pi$
$241$	960.434	0.256710	0.128355	+	0.991728i	$0.459030\pi$
$242$	310.370	0.0824437
$243$	243.000	0.0641500
$244$	1502.45	0.394198
$245$	3354.93	0.874850
$246$	−1261.52	−0.326958
$247$	−3198.55	−0.823964
$248$	−460.932	−0.118021
$249$	−1035.04	−0.263425
$250$	−2134.57	−0.540009
$251$	−6234.75	−1.56787	−0.783933	−	0.620846i	$-0.786789\pi$
$251$	−6234.75	−1.56787	−0.783933	+	0.620846i	$0.786789\pi$
$252$	1323.85	0.330931
$253$	332.902	0.0827249
$254$	−1842.21	−0.455080
$255$	−1186.34	−0.291339
$256$	−4235.02	−1.03394
$257$	6212.61	1.50791	0.753954	−	0.656928i	$-0.228144\pi$
$257$	6212.61	1.50791	0.753954	+	0.656928i	$0.228144\pi$
$258$	−2719.38	−0.656207
$259$	−1722.16	−0.413166
$260$	558.847	0.133301
$261$	−157.103	−0.0372584
$262$	−1771.59	−0.417746
$263$	−3551.35	−0.832644	−0.416322	−	0.909217i	$-0.636681\pi$
$263$	−3551.35	−0.832644	−0.416322	+	0.909217i	$0.636681\pi$
$264$	2680.60	0.624923
$265$	3108.36	0.720548
$266$	−8099.64	−1.86700
$267$	−2778.01	−0.636747
$268$	315.530	0.0719182
$269$	−1994.09	−0.451977	−0.225989	−	0.974130i	$-0.572561\pi$
$269$	−1994.09	−0.451977	−0.225989	+	0.974130i	$0.572561\pi$
$270$	259.760	0.0585500
$271$	6247.58	1.40042	0.700209	−	0.713938i	$-0.253090\pi$
$271$	6247.58	1.40042	0.700209	+	0.713938i	$0.253090\pi$
$272$	309.146	0.0689144
$273$	2096.55	0.464795
$274$	4221.01	0.930660
$275$	3754.44	0.823278
$276$	121.354	0.0264662
$277$	4364.93	0.946799	0.473400	−	0.880848i	$-0.343027\pi$
$277$	4364.93	0.946799	0.473400	+	0.880848i	$0.343027\pi$
$278$	−4393.37	−0.947830
$279$	179.936	0.0386110
$280$	3819.13	0.815131
$281$	7349.37	1.56024	0.780118	−	0.625632i	$-0.215159\pi$
$281$	7349.37	1.56024	0.780118	+	0.625632i	$0.215159\pi$
$282$	572.391	0.120870
$283$	3297.61	0.692660	0.346330	−	0.938113i	$-0.387428\pi$
$283$	3297.61	0.692660	0.346330	+	0.938113i	$0.387428\pi$
$284$	582.930	0.121798
$285$	2274.53	0.472743
$286$	1573.04	0.325231
$287$	7240.46	1.48917
$288$	1592.26	0.325780
$289$	646.428	0.131575
$290$	−167.939	−0.0340059
$291$	4449.42	0.896321
$292$	−3171.90	−0.635689
$293$	−994.414	−0.198274	−0.0991370	−	0.995074i	$-0.531608\pi$
$293$	−994.414	−0.198274	−0.0991370	+	0.995074i	$0.531608\pi$
$294$	3442.46	0.682885
$295$	−1507.76	−0.297578
$296$	−1271.18	−0.249614
$297$	−1046.44	−0.204446
$298$	−3557.72	−0.691588
$299$	192.186	0.0371720
$300$	1368.62	0.263392
$301$	15607.8	2.98877
$302$	−1703.72	−0.324629
$303$	1670.64	0.316751
$304$	−592.717	−0.111824
$305$	−1692.02	−0.317655
$306$	−1217.29	−0.227411
$307$	1105.89	0.205592	0.102796	−	0.994702i	$-0.467221\pi$
$307$	1105.89	0.205592	0.102796	+	0.994702i	$0.467221\pi$
$308$	−5700.93	−1.05468
$309$	−2242.47	−0.412846
$310$	192.346	0.0352405
$311$	7061.27	1.28749	0.643743	−	0.765242i	$-0.277381\pi$
$311$	7061.27	1.28749	0.643743	+	0.765242i	$0.277381\pi$
$312$	1547.53	0.280806
$313$	−8008.86	−1.44629	−0.723143	−	0.690699i	$-0.757303\pi$
$313$	−8008.86	−1.44629	−0.723143	+	0.690699i	$0.757303\pi$
$314$	−1336.62	−0.240223
$315$	−1490.89	−0.266673
$316$	4225.59	0.752240
$317$	−6388.55	−1.13191	−0.565957	−	0.824435i	$-0.691493\pi$
$317$	−6388.55	−1.13191	−0.565957	+	0.824435i	$0.691493\pi$
$318$	3189.46	0.562441
$319$	676.537	0.118742
$320$	1878.00	0.328073
$321$	5323.80	0.925687
$322$	486.670	0.0842269
$323$	−10658.9	−1.83616
$324$	−381.462	−0.0654085
$325$	2167.46	0.369936
$326$	−577.024	−0.0980319
$327$	−1249.86	−0.211368
$328$	5344.40	0.899680
$329$	−3285.22	−0.550517
$330$	−1118.61	−0.186599
$331$	7770.09	1.29028	0.645140	−	0.764064i	$-0.276799\pi$
$331$	7770.09	1.29028	0.645140	+	0.764064i	$0.276799\pi$
$332$	1624.81	0.268593
$333$	496.234	0.0816621
$334$	−6550.41	−1.07312
$335$	−355.342	−0.0579535
$336$	388.507	0.0630798
$337$	11550.2	1.86700	0.933501	−	0.358575i	$-0.116737\pi$
$337$	11550.2	1.86700	0.933501	+	0.358575i	$0.116737\pi$
$338$	−3077.23	−0.495205
$339$	5105.45	0.817965
$340$	1862.32	0.297054
$341$	−774.861	−0.123053
$342$	2333.88	0.369011
$343$	−9044.57	−1.42379
$344$	11520.6	1.80566
$345$	−136.666	−0.0213271
$346$	−336.249	−0.0522453
$347$	−4434.31	−0.686012	−0.343006	−	0.939333i	$-0.611445\pi$
$347$	−4434.31	−0.686012	−0.343006	+	0.939333i	$0.611445\pi$
$348$	246.621	0.0379893
$349$	−9190.00	−1.40954	−0.704770	−	0.709436i	$-0.748950\pi$
$349$	−9190.00	−1.40954	−0.704770	+	0.709436i	$0.748950\pi$
$350$	5488.62	0.838226
$351$	−604.113	−0.0918666
$352$	−6856.78	−1.03826
$353$	−1154.49	−0.174071	−0.0870356	−	0.996205i	$-0.527739\pi$
$353$	−1154.49	−0.174071	−0.0870356	+	0.996205i	$0.527739\pi$
$354$	−1547.10	−0.232281
$355$	−656.480	−0.0981475
$356$	4360.93	0.649238
$357$	6986.61	1.03577
$358$	−425.511	−0.0628183
$359$	−4037.95	−0.593634	−0.296817	−	0.954934i	$-0.595925\pi$
$359$	−4037.95	−0.593634	−0.296817	+	0.954934i	$0.595925\pi$
$360$	−1100.47	−0.161110
$361$	13577.1	1.97946
$362$	−4671.90	−0.678314
$363$	513.292	0.0742172
$364$	−3291.17	−0.473913
$365$	3572.11	0.512254
$366$	−1736.16	−0.247953
$367$	−1679.68	−0.238907	−0.119453	−	0.992840i	$-0.538114\pi$
$367$	−1679.68	−0.238907	−0.119453	+	0.992840i	$0.538114\pi$
$368$	35.6136	0.00504480
$369$	−2086.31	−0.294333
$370$	530.461	0.0745334
$371$	−18305.8	−2.56170
$372$	−282.464	−0.0393684
$373$	−8943.09	−1.24144	−0.620718	−	0.784034i	$-0.713159\pi$
$373$	−8943.09	−1.24144	−0.620718	+	0.784034i	$0.713159\pi$
$374$	5242.05	0.724759
$375$	−3530.17	−0.486125
$376$	−2424.92	−0.332595
$377$	390.569	0.0533562
$378$	−1529.79	−0.208158
$379$	−7866.06	−1.06610	−0.533051	−	0.846083i	$-0.678955\pi$
$379$	−7866.06	−1.06610	−0.533051	+	0.846083i	$0.678955\pi$
$380$	−3570.57	−0.482017
$381$	−3046.65	−0.409671
$382$	−5696.05	−0.762920
$383$	12017.5	1.60331	0.801655	−	0.597787i	$-0.203953\pi$
$383$	12017.5	1.60331	0.801655	+	0.597787i	$0.203953\pi$
$384$	−2319.02	−0.308183
$385$	6420.24	0.849885
$386$	−5907.82	−0.779016
$387$	−4497.33	−0.590729
$388$	−6984.71	−0.913904
$389$	13036.2	1.69913	0.849563	−	0.527487i	$-0.176866\pi$
$389$	13036.2	1.69913	0.849563	+	0.527487i	$0.176866\pi$
$390$	−645.780	−0.0838471
$391$	640.447	0.0828357
$392$	−14583.9	−1.87907
$393$	−2929.87	−0.376062
$394$	3171.29	0.405501
$395$	−4758.75	−0.606174
$396$	1642.70	0.208456
$397$	−12985.5	−1.64162	−0.820812	−	0.571198i	$-0.806479\pi$
$397$	−12985.5	−1.64162	−0.820812	+	0.571198i	$0.806479\pi$
$398$	−6083.96	−0.766234
$399$	−13395.2	−1.68070
$400$	401.647	0.0502059
$401$	5784.74	0.720390	0.360195	−	0.932877i	$-0.382710\pi$
$401$	5784.74	0.720390	0.360195	+	0.932877i	$0.382710\pi$
$402$	−364.614	−0.0452370
$403$	−447.331	−0.0552932
$404$	−2622.57	−0.322965
$405$	429.593	0.0527078
$406$	989.030	0.120898
$407$	−2136.95	−0.260257
$408$	5157.02	0.625761
$409$	−3029.29	−0.366232	−0.183116	−	0.983091i	$-0.558618\pi$
$409$	−3029.29	−0.366232	−0.183116	+	0.983091i	$0.558618\pi$
$410$	−2230.21	−0.268639
$411$	6980.73	0.837796
$412$	3520.23	0.420945
$413$	8879.56	1.05795
$414$	−140.232	−0.0166474
$415$	−1829.82	−0.216439
$416$	−3958.45	−0.466537
$417$	−7265.78	−0.853253
$418$	−10050.4	−1.17604
$419$	6871.02	0.801125	0.400562	−	0.916270i	$-0.368815\pi$
$419$	6871.02	0.801125	0.400562	+	0.916270i	$0.368815\pi$
$420$	2340.40	0.271904
$421$	−9358.27	−1.08336	−0.541679	−	0.840585i	$-0.682211\pi$
$421$	−9358.27	−1.08336	−0.541679	+	0.840585i	$0.682211\pi$
$422$	2487.37	0.286927
$423$	946.623	0.108809
$424$	−13512.1	−1.54765
$425$	7222.90	0.824382
$426$	−673.609	−0.0766114
$427$	9964.66	1.12933
$428$	−8357.32	−0.943847
$429$	2601.51	0.292778
$430$	−4807.52	−0.539161
$431$	11451.8	1.27984	0.639921	−	0.768440i	$-0.278967\pi$
$431$	11451.8	1.27984	0.639921	+	0.768440i	$0.278967\pi$
$432$	−111.947	−0.0124677
$433$	11432.3	1.26882	0.634412	−	0.772995i	$-0.281242\pi$
$433$	11432.3	1.26882	0.634412	+	0.772995i	$0.281242\pi$
$434$	−1132.77	−0.125287
$435$	−277.739	−0.0306127
$436$	1962.03	0.215515
$437$	−1227.91	−0.134414
$438$	3665.31	0.399852
$439$	−12814.6	−1.39318	−0.696589	−	0.717470i	$-0.745300\pi$
$439$	−12814.6	−1.39318	−0.696589	+	0.717470i	$0.745300\pi$
$440$	4738.97	0.513458
$441$	5693.16	0.614745
$442$	3026.26	0.325667
$443$	11549.2	1.23864	0.619320	−	0.785139i	$-0.287409\pi$
$443$	11549.2	1.23864	0.619320	+	0.785139i	$0.287409\pi$
$444$	−778.990	−0.0832641
$445$	−4911.17	−0.523172
$446$	−4229.17	−0.449007
$447$	−5883.77	−0.622579
$448$	−11059.9	−1.16637
$449$	12301.1	1.29293	0.646466	−	0.762942i	$-0.276246\pi$
$449$	12301.1	1.29293	0.646466	+	0.762942i	$0.276246\pi$
$450$	−1581.52	−0.165675
$451$	8984.32	0.938038
$452$	−8014.55	−0.834011
$453$	−2817.62	−0.292237
$454$	−6243.02	−0.645374
$455$	3706.44	0.381891
$456$	−9887.41	−1.01540
$457$	6718.60	0.687708	0.343854	−	0.939023i	$-0.388267\pi$
$457$	6718.60	0.687708	0.343854	+	0.939023i	$0.388267\pi$
$458$	7471.15	0.762236
$459$	−2013.16	−0.204720
$460$	214.539	0.0217455
$461$	−9693.92	−0.979373	−0.489686	−	0.871899i	$-0.662889\pi$
$461$	−9693.92	−0.979373	−0.489686	+	0.871899i	$0.662889\pi$
$462$	6587.75	0.663398
$463$	−3002.02	−0.301330	−0.150665	−	0.988585i	$-0.548141\pi$
$463$	−3002.02	−0.301330	−0.150665	+	0.988585i	$0.548141\pi$
$464$	72.3754	0.00724126
$465$	318.103	0.0317241
$466$	11158.4	1.10923
$467$	−214.537	−0.0212582	−0.0106291	−	0.999944i	$-0.503383\pi$
$467$	−214.537	−0.0212582	−0.0106291	+	0.999944i	$0.503383\pi$
$468$	948.339	0.0936688
$469$	2092.69	0.206037
$470$	1011.91	0.0993109
$471$	−2210.51	−0.216253
$472$	6554.26	0.639162
$473$	19367.0	1.88265
$474$	−4882.91	−0.473164
$475$	−13848.3	−1.33769
$476$	−10967.6	−1.05609
$477$	5274.75	0.506319
$478$	7809.16	0.747244
$479$	3944.43	0.376253	0.188127	−	0.982145i	$-0.439758\pi$
$479$	3944.43	0.376253	0.188127	+	0.982145i	$0.439758\pi$
$480$	2814.91	0.267672
$481$	−1233.67	−0.116945
$482$	1742.23	0.164639
$483$	804.858	0.0758225
$484$	−805.768	−0.0756732
$485$	7866.00	0.736447
$486$	440.802	0.0411423
$487$	189.077	0.0175932	0.00879661	−	0.999961i	$-0.497200\pi$
$487$	189.077	0.0175932	0.00879661	+	0.999961i	$0.497200\pi$
$488$	7355.21	0.682284
$489$	−954.286	−0.0882501
$490$	6085.83	0.561081
$491$	−9001.33	−0.827341	−0.413670	−	0.910427i	$-0.635753\pi$
$491$	−9001.33	−0.827341	−0.413670	+	0.910427i	$0.635753\pi$
$492$	3275.10	0.300107
$493$	1301.54	0.118902
$494$	−5802.17	−0.528445
$495$	−1849.97	−0.167979
$496$	−82.8940	−0.00750413
$497$	3866.16	0.348935
$498$	−1877.56	−0.168947
$499$	−16359.6	−1.46765	−0.733825	−	0.679338i	$-0.762267\pi$
$499$	−16359.6	−1.46765	−0.733825	+	0.679338i	$0.762267\pi$
$500$	5541.67	0.495662
$501$	−10833.1	−0.966043
$502$	−11309.8	−1.00554
$503$	−3807.74	−0.337532	−0.168766	−	0.985656i	$-0.553978\pi$
$503$	−3807.74	−0.337532	−0.168766	+	0.985656i	$0.553978\pi$
$504$	6480.89	0.572781
$505$	2953.48	0.260253
$506$	603.884	0.0530552
$507$	−5089.14	−0.445792
$508$	4782.64	0.417707
$509$	16599.5	1.44550	0.722750	−	0.691109i	$-0.242878\pi$
$509$	16599.5	1.44550	0.722750	+	0.691109i	$0.242878\pi$
$510$	−2152.02	−0.186849
$511$	−21036.9	−1.82117
$512$	−1498.25	−0.129324
$513$	3859.78	0.332190
$514$	11269.7	0.967089
$515$	−3964.40	−0.339208
$516$	7059.92	0.602317
$517$	−4076.46	−0.346775
$518$	−3124.00	−0.264982
$519$	−556.091	−0.0470322
$520$	2735.83	0.230719
$521$	11080.6	0.931765	0.465882	−	0.884847i	$-0.345737\pi$
$521$	11080.6	0.931765	0.465882	+	0.884847i	$0.345737\pi$
$522$	−284.985	−0.0238955
$523$	2636.17	0.220405	0.110202	−	0.993909i	$-0.464850\pi$
$523$	2636.17	0.220405	0.110202	+	0.993909i	$0.464850\pi$
$524$	4599.32	0.383439
$525$	9077.11	0.754586
$526$	−6442.14	−0.534012
$527$	−1490.70	−0.123218
$528$	482.079	0.0397345
$529$	−12093.2	−0.993936
$530$	5638.57	0.462120
$531$	−2558.61	−0.209104
$532$	21027.9	1.71367
$533$	5186.70	0.421502
$534$	−5039.31	−0.408375
$535$	9411.80	0.760575
$536$	1544.67	0.124477
$537$	−703.712	−0.0565501
$538$	−3617.28	−0.289873
$539$	−24516.6	−1.95919
$540$	−674.377	−0.0537418
$541$	−15666.0	−1.24498	−0.622491	−	0.782627i	$-0.713879\pi$
$541$	−15666.0	−1.24498	−0.622491	+	0.782627i	$0.713879\pi$
$542$	11333.1	0.898151
$543$	−7726.41	−0.610630
$544$	−13191.3	−1.03965
$545$	−2209.59	−0.173667
$546$	3803.14	0.298094
$547$	16240.7	1.26948	0.634738	−	0.772727i	$-0.281108\pi$
$547$	16240.7	1.26948	0.634738	+	0.772727i	$0.281108\pi$
$548$	−10958.4	−0.854231
$549$	−2871.28	−0.223212
$550$	6810.56	0.528006
$551$	−2495.41	−0.192936
$552$	594.089	0.0458082
$553$	28025.3	2.15508
$554$	7917.98	0.607225
$555$	877.279	0.0670963
$556$	11405.8	0.869992
$557$	−21490.8	−1.63482	−0.817408	−	0.576059i	$-0.804590\pi$
$557$	−21490.8	−1.63482	−0.817408	+	0.576059i	$0.804590\pi$
$558$	326.403	0.0247630
$559$	11180.6	0.845958
$560$	686.832	0.0518284
$561$	8669.33	0.652441
$562$	13331.7	1.00065
$563$	8719.88	0.652752	0.326376	−	0.945240i	$-0.394173\pi$
$563$	8719.88	0.652752	0.326376	+	0.945240i	$0.394173\pi$
$564$	−1486.01	−0.110944
$565$	9025.79	0.672067
$566$	5981.87	0.444234
$567$	−2529.97	−0.187387
$568$	2853.72	0.210809
$569$	−9965.36	−0.734217	−0.367109	−	0.930178i	$-0.619652\pi$
$569$	−9965.36	−0.734217	−0.367109	+	0.930178i	$0.619652\pi$
$570$	4126.00	0.303192
$571$	−6574.08	−0.481816	−0.240908	−	0.970548i	$-0.577445\pi$
$571$	−6574.08	−0.481816	−0.240908	+	0.970548i	$0.577445\pi$
$572$	−4083.85	−0.298522
$573$	−9420.16	−0.686794
$574$	13134.2	0.955070
$575$	832.079	0.0603480
$576$	3186.88	0.230532
$577$	2937.68	0.211953	0.105977	−	0.994369i	$-0.466203\pi$
$577$	2937.68	0.211953	0.105977	+	0.994369i	$0.466203\pi$
$578$	1172.62	0.0843850
$579$	−9770.38	−0.701284
$580$	435.995	0.0312133
$581$	10776.2	0.769486
$582$	8071.24	0.574851
$583$	−22714.8	−1.61364
$584$	−15528.0	−1.10026
$585$	−1068.00	−0.0754806
$586$	−1803.87	−0.127162
$587$	23963.8	1.68499	0.842496	−	0.538702i	$-0.181085\pi$
$587$	23963.8	1.68499	0.842496	+	0.538702i	$0.181085\pi$
$588$	−8937.14	−0.626805
$589$	2858.08	0.199941
$590$	−2735.08	−0.190850
$591$	5244.69	0.365039
$592$	−228.609	−0.0158712
$593$	−3194.41	−0.221212	−0.110606	−	0.993864i	$-0.535279\pi$
$593$	−3194.41	−0.221212	−0.110606	+	0.993864i	$0.535279\pi$
$594$	−1898.23	−0.131120
$595$	12351.4	0.851024
$596$	9236.37	0.634792
$597$	−10061.7	−0.689777
$598$	348.626	0.0238401
$599$	−25318.4	−1.72702	−0.863509	−	0.504334i	$-0.831738\pi$
$599$	−25318.4	−1.72702	−0.863509	+	0.504334i	$0.831738\pi$
$600$	6700.08	0.455883
$601$	−16367.3	−1.11087	−0.555437	−	0.831559i	$-0.687449\pi$
$601$	−16367.3	−1.11087	−0.555437	+	0.831559i	$0.687449\pi$
$602$	28312.6	1.91683
$603$	−603.000	−0.0407231
$604$	4423.11	0.297970
$605$	907.435	0.0609793
$606$	3030.54	0.203147
$607$	−5258.94	−0.351654	−0.175827	−	0.984421i	$-0.556260\pi$
$607$	−5258.94	−0.351654	−0.175827	+	0.984421i	$0.556260\pi$
$608$	25291.2	1.68700
$609$	1635.66	0.108835
$610$	−3069.32	−0.203726
$611$	−2353.36	−0.155821
$612$	3160.27	0.208736
$613$	14382.3	0.947625	0.473813	−	0.880626i	$-0.342877\pi$
$613$	14382.3	0.947625	0.473813	+	0.880626i	$0.342877\pi$
$614$	2006.09	0.131855
$615$	−3688.33	−0.241834
$616$	−27908.8	−1.82545
$617$	−3484.62	−0.227367	−0.113684	−	0.993517i	$-0.536265\pi$
$617$	−3484.62	−0.227367	−0.113684	+	0.993517i	$0.536265\pi$
$618$	−4067.83	−0.264777
$619$	2275.74	0.147770	0.0738851	−	0.997267i	$-0.476460\pi$
$619$	2275.74	0.147770	0.0738851	+	0.997267i	$0.476460\pi$
$620$	−499.360	−0.0323464
$621$	−231.916	−0.0149863
$622$	12809.1	0.825723
$623$	28922.9	1.85999
$624$	278.307	0.0178545
$625$	5868.07	0.375556
$626$	−14528.1	−0.927568
$627$	−16621.5	−1.05869
$628$	3470.07	0.220495
$629$	−4111.11	−0.260605
$630$	−2704.47	−0.171029
$631$	5721.78	0.360984	0.180492	−	0.983576i	$-0.442231\pi$
$631$	5721.78	0.360984	0.180492	+	0.983576i	$0.442231\pi$
$632$	20686.3	1.30199
$633$	4113.62	0.258297
$634$	−11588.8	−0.725947
$635$	−5386.09	−0.336599
$636$	−8280.32	−0.516252
$637$	−14153.5	−0.880351
$638$	1227.24	0.0761549
$639$	−1114.02	−0.0689669
$640$	−4099.74	−0.253213
$641$	−30325.1	−1.86859	−0.934297	−	0.356496i	$-0.883971\pi$
$641$	−30325.1	−1.86859	−0.934297	+	0.356496i	$0.883971\pi$
$642$	9657.37	0.593685
$643$	−14276.0	−0.875571	−0.437786	−	0.899079i	$-0.644237\pi$
$643$	−14276.0	−0.875571	−0.437786	+	0.899079i	$0.644237\pi$
$644$	−1263.47	−0.0773100
$645$	−7950.71	−0.485362
$646$	−19335.3	−1.17761
$647$	14241.8	0.865380	0.432690	−	0.901543i	$-0.357564\pi$
$647$	14241.8	0.865380	0.432690	+	0.901543i	$0.357564\pi$
$648$	−1867.44	−0.113210
$649$	11018.2	0.666413
$650$	3931.77	0.237256
$651$	−1873.38	−0.112786
$652$	1498.04	0.0899813
$653$	4782.61	0.286612	0.143306	−	0.989678i	$-0.454227\pi$
$653$	4782.61	0.286612	0.143306	+	0.989678i	$0.454227\pi$
$654$	−2267.24	−0.135560
$655$	−5179.64	−0.308985
$656$	961.135	0.0572043
$657$	6061.71	0.359954
$658$	−5959.38	−0.353071
$659$	−9229.12	−0.545547	−0.272773	−	0.962078i	$-0.587941\pi$
$659$	−9229.12	−0.545547	−0.272773	+	0.962078i	$0.587941\pi$
$660$	2904.08	0.171275
$661$	2058.47	0.121127	0.0605637	−	0.998164i	$-0.480710\pi$
$661$	2058.47	0.121127	0.0605637	+	0.998164i	$0.480710\pi$
$662$	14094.9	0.827516
$663$	5004.85	0.293171
$664$	7954.22	0.464885
$665$	−23681.1	−1.38092
$666$	900.168	0.0523736
$667$	149.938	0.00870406
$668$	17005.8	0.984994
$669$	−6994.23	−0.404204
$670$	−644.591	−0.0371682
$671$	12364.6	0.711374
$672$	−16577.6	−0.951631
$673$	2356.37	0.134965	0.0674824	−	0.997720i	$-0.478503\pi$
$673$	2356.37	0.134965	0.0674824	+	0.997720i	$0.478503\pi$
$674$	20952.0	1.19739
$675$	−2615.53	−0.149144
$676$	7988.94	0.454537
$677$	33786.2	1.91804	0.959018	−	0.283346i	$-0.0914444\pi$
$677$	33786.2	1.91804	0.959018	+	0.283346i	$0.0914444\pi$
$678$	9261.28	0.524598
$679$	−46324.6	−2.61823
$680$	9116.95	0.514146
$681$	−10324.7	−0.580977
$682$	−1405.60	−0.0789195
$683$	−31534.1	−1.76665	−0.883323	−	0.468764i	$-0.844699\pi$
$683$	−31534.1	−1.76665	−0.883323	+	0.468764i	$0.844699\pi$
$684$	−6059.10	−0.338707
$685$	12341.0	0.688361
$686$	−16406.8	−0.913143
$687$	12355.8	0.686178
$688$	2071.86	0.114809
$689$	−13113.4	−0.725079
$690$	−247.912	−0.0136781
$691$	18453.2	1.01591	0.507953	−	0.861385i	$-0.330402\pi$
$691$	18453.2	1.01591	0.507953	+	0.861385i	$0.330402\pi$
$692$	872.954	0.0479548
$693$	10894.9	0.597202
$694$	−8043.83	−0.439970
$695$	−12845.0	−0.701061
$696$	1207.33	0.0657525
$697$	17284.3	0.939296
$698$	−16670.6	−0.904002
$699$	18453.8	0.998551
$700$	−14249.3	−0.769389
$701$	−10434.5	−0.562203	−0.281102	−	0.959678i	$-0.590700\pi$
$701$	−10434.5	−0.562203	−0.281102	+	0.959678i	$0.590700\pi$
$702$	−1095.86	−0.0589182
$703$	7882.12	0.422873
$704$	−13723.7	−0.734705
$705$	1673.51	0.0894014
$706$	−2094.24	−0.111640
$707$	−17393.7	−0.925256
$708$	4016.51	0.213206
$709$	−20821.6	−1.10292	−0.551460	−	0.834201i	$-0.685929\pi$
$709$	−20821.6	−1.10292	−0.551460	+	0.834201i	$0.685929\pi$
$710$	−1190.85	−0.0629464
$711$	−8075.38	−0.425950
$712$	21348.9	1.12371
$713$	−171.729	−0.00902004
$714$	12673.7	0.664287
$715$	4599.13	0.240556
$716$	1104.69	0.0576595
$717$	12914.8	0.672683
$718$	−7324.83	−0.380725
$719$	10187.2	0.528400	0.264200	−	0.964468i	$-0.414892\pi$
$719$	10187.2	0.528400	0.264200	+	0.964468i	$0.414892\pi$
$720$	−197.908	−0.0102439
$721$	23347.2	1.20596
$722$	24628.8	1.26952
$723$	2881.30	0.148211
$724$	12128.9	0.622609
$725$	1690.98	0.0866228
$726$	931.111	0.0475989
$727$	28924.3	1.47558	0.737788	−	0.675033i	$-0.235870\pi$
$727$	28924.3	1.47558	0.737788	+	0.675033i	$0.235870\pi$
$728$	−16111.9	−0.820256
$729$	729.000	0.0370370
$730$	6479.80	0.328532
$731$	37258.7	1.88517
$732$	4507.34	0.227590
$733$	−9509.56	−0.479186	−0.239593	−	0.970873i	$-0.577014\pi$
$733$	−9509.56	−0.479186	−0.239593	+	0.970873i	$0.577014\pi$
$734$	−3046.94	−0.153222
$735$	10064.8	0.505095
$736$	−1519.63	−0.0761066
$737$	2596.71	0.129784
$738$	−3784.56	−0.188769
$739$	11786.7	0.586711	0.293356	−	0.956003i	$-0.405228\pi$
$739$	11786.7	0.586711	0.293356	+	0.956003i	$0.405228\pi$
$740$	−1377.16	−0.0684125
$741$	−9595.66	−0.475716
$742$	−33206.8	−1.64294
$743$	−19402.1	−0.958002	−0.479001	−	0.877814i	$-0.659001\pi$
$743$	−19402.1	−0.958002	−0.479001	+	0.877814i	$0.659001\pi$
$744$	−1382.80	−0.0681395
$745$	−10401.8	−0.511532
$746$	−16222.8	−0.796189
$747$	−3105.12	−0.152089
$748$	−13609.1	−0.665240
$749$	−55428.2	−2.70401
$750$	−6403.72	−0.311774
$751$	24692.4	1.19979	0.599893	−	0.800080i	$-0.295210\pi$
$751$	24692.4	1.19979	0.599893	+	0.800080i	$0.295210\pi$
$752$	−436.097	−0.0211473
$753$	−18704.3	−0.905207
$754$	708.491	0.0342198
$755$	−4981.20	−0.240112
$756$	3971.55	0.191063
$757$	28751.0	1.38041	0.690206	−	0.723613i	$-0.257520\pi$
$757$	28751.0	1.38041	0.690206	+	0.723613i	$0.257520\pi$
$758$	−14269.0	−0.683739
$759$	998.707	0.0477612
$760$	−17479.7	−0.834282
$761$	38775.5	1.84706	0.923529	−	0.383528i	$-0.125291\pi$
$761$	38775.5	1.84706	0.923529	+	0.383528i	$0.125291\pi$
$762$	−5526.62	−0.262740
$763$	13012.8	0.617423
$764$	14787.8	0.700266
$765$	−3559.01	−0.168205
$766$	21799.8	1.02827
$767$	6360.86	0.299449
$768$	−12705.1	−0.596945
$769$	−4569.31	−0.214270	−0.107135	−	0.994244i	$-0.534168\pi$
$769$	−4569.31	−0.214270	−0.107135	+	0.994244i	$0.534168\pi$
$770$	11646.3	0.545070
$771$	18637.8	0.870591
$772$	15337.6	0.715041
$773$	−13934.2	−0.648353	−0.324176	−	0.945997i	$-0.605087\pi$
$773$	−13934.2	−0.648353	−0.324176	+	0.945997i	$0.605087\pi$
$774$	−8158.15	−0.378861
$775$	−1936.74	−0.0897675
$776$	−34193.5	−1.58180
$777$	−5166.49	−0.238541
$778$	23647.6	1.08973
$779$	−33138.7	−1.52416
$780$	1676.54	0.0769613
$781$	4797.32	0.219797
$782$	1161.77	0.0531263
$783$	−471.310	−0.0215112
$784$	−2622.76	−0.119477
$785$	−3907.91	−0.177680
$786$	−5314.78	−0.241186
$787$	−7599.58	−0.344213	−0.172107	−	0.985078i	$-0.555057\pi$
$787$	−7599.58	−0.344213	−0.172107	+	0.985078i	$0.555057\pi$
$788$	−8233.14	−0.372200
$789$	−10654.0	−0.480727
$790$	−8632.36	−0.388767
$791$	−53154.8	−2.38934
$792$	8041.81	0.360800
$793$	7138.18	0.319652
$794$	−23555.7	−1.05285
$795$	9325.09	0.416009
$796$	15794.9	0.703309
$797$	43338.6	1.92614	0.963068	−	0.269258i	$-0.0867785\pi$
$797$	43338.6	1.92614	0.963068	+	0.269258i	$0.0867785\pi$
$798$	−24298.9	−1.07791
$799$	−7842.41	−0.347240
$800$	−17138.3	−0.757413
$801$	−8334.03	−0.367626
$802$	10493.5	0.462019
$803$	−26103.7	−1.14717
$804$	946.591	0.0415220
$805$	1422.89	0.0622983
$806$	−811.459	−0.0354620
$807$	−5982.27	−0.260949
$808$	−12838.8	−0.558993
$809$	25859.9	1.12384	0.561919	−	0.827193i	$-0.310063\pi$
$809$	25859.9	1.12384	0.561919	+	0.827193i	$0.310063\pi$
$810$	779.281	0.0338039
$811$	−36953.2	−1.60000	−0.800002	−	0.599997i	$-0.795168\pi$
$811$	−36953.2	−1.60000	−0.800002	+	0.599997i	$0.795168\pi$
$812$	−2567.67	−0.110970
$813$	18742.7	0.808532
$814$	−3876.41	−0.166914
$815$	−1687.06	−0.0725092
$816$	927.437	0.0397877
$817$	−71435.0	−3.05899
$818$	−5495.13	−0.234881
$819$	6289.66	0.268350
$820$	5789.95	0.246578
$821$	14444.1	0.614009	0.307005	−	0.951708i	$-0.400673\pi$
$821$	14444.1	0.614009	0.307005	+	0.951708i	$0.400673\pi$
$822$	12663.0	0.537317
$823$	−28771.0	−1.21858	−0.609291	−	0.792947i	$-0.708546\pi$
$823$	−28771.0	−1.21858	−0.609291	+	0.792947i	$0.708546\pi$
$824$	17233.2	0.728578
$825$	11263.3	0.475320
$826$	16107.5	0.678513
$827$	21282.5	0.894878	0.447439	−	0.894315i	$-0.352336\pi$
$827$	21282.5	0.894878	0.447439	+	0.894315i	$0.352336\pi$
$828$	364.063	0.0152803
$829$	23024.6	0.964629	0.482314	−	0.875998i	$-0.339796\pi$
$829$	23024.6	0.964629	0.482314	+	0.875998i	$0.339796\pi$
$830$	−3319.28	−0.138812
$831$	13094.8	0.546635
$832$	−7922.78	−0.330136
$833$	−47165.6	−1.96182
$834$	−13180.1	−0.547230
$835$	−19151.5	−0.793732
$836$	26092.4	1.07946
$837$	539.807	0.0222921
$838$	12464.0	0.513798
$839$	−39759.0	−1.63604	−0.818018	−	0.575193i	$-0.804927\pi$
$839$	−39759.0	−1.63604	−0.818018	+	0.575193i	$0.804927\pi$
$840$	11457.4	0.470616
$841$	−24084.3	−0.987506
$842$	−16975.9	−0.694807
$843$	22048.1	0.900803
$844$	−6457.58	−0.263364
$845$	−8996.95	−0.366277
$846$	1717.17	0.0697844
$847$	−5344.09	−0.216795
$848$	−2430.01	−0.0984043
$849$	9892.84	0.399907
$850$	13102.3	0.528713
$851$	−473.600	−0.0190773
$852$	1748.79	0.0703198
$853$	−46255.8	−1.85671	−0.928353	−	0.371700i	$-0.878775\pi$
$853$	−46255.8	−1.85671	−0.928353	+	0.371700i	$0.878775\pi$
$854$	18075.9	0.724290
$855$	6823.60	0.272938
$856$	−40913.1	−1.63362
$857$	−38583.2	−1.53790	−0.768948	−	0.639312i	$-0.779219\pi$
$857$	−38583.2	−1.53790	−0.768948	+	0.639312i	$0.779219\pi$
$858$	4719.13	0.187772
$859$	39823.7	1.58180	0.790901	−	0.611943i	$-0.209612\pi$
$859$	39823.7	1.58180	0.790901	+	0.611943i	$0.209612\pi$
$860$	12481.0	0.494884
$861$	21721.4	0.859771
$862$	20773.5	0.820821
$863$	−20165.9	−0.795431	−0.397715	−	0.917509i	$-0.630197\pi$
$863$	−20165.9	−0.795431	−0.397715	+	0.917509i	$0.630197\pi$
$864$	4776.78	0.188089
$865$	−983.098	−0.0386432
$866$	20738.2	0.813755
$867$	1939.28	0.0759648
$868$	2940.84	0.114998
$869$	34775.2	1.35750
$870$	−503.817	−0.0196333
$871$	1499.10	0.0583179
$872$	9605.11	0.373016
$873$	13348.3	0.517491
$874$	−2227.43	−0.0862058
$875$	36753.9	1.42001
$876$	−9515.69	−0.367015
$877$	7854.53	0.302427	0.151214	−	0.988501i	$-0.451682\pi$
$877$	7854.53	0.302427	0.151214	+	0.988501i	$0.451682\pi$
$878$	−23245.6	−0.893509
$879$	−2983.24	−0.114474
$880$	852.255	0.0326472
$881$	−22756.8	−0.870258	−0.435129	−	0.900368i	$-0.643297\pi$
$881$	−22756.8	−0.870258	−0.435129	+	0.900368i	$0.643297\pi$
$882$	10327.4	0.394264
$883$	−21896.8	−0.834526	−0.417263	−	0.908786i	$-0.637011\pi$
$883$	−21896.8	−0.834526	−0.417263	+	0.908786i	$0.637011\pi$
$884$	−7856.63	−0.298922
$885$	−4523.29	−0.171807
$886$	20950.2	0.794395
$887$	34054.9	1.28912	0.644561	−	0.764553i	$-0.277040\pi$
$887$	34054.9	1.28912	0.644561	+	0.764553i	$0.277040\pi$
$888$	−3813.54	−0.144115
$889$	31719.9	1.19668
$890$	−8908.85	−0.335534
$891$	−3139.31	−0.118037
$892$	10979.6	0.412133
$893$	15036.0	0.563451
$894$	−10673.2	−0.399288
$895$	−1244.07	−0.0464634
$896$	24144.3	0.900227
$897$	576.559	0.0214612
$898$	22314.3	0.829216
$899$	−348.994	−0.0129473
$900$	4105.87	0.152069
$901$	−43699.3	−1.61580
$902$	16297.6	0.601607
$903$	46823.4	1.72557
$904$	−39235.1	−1.44352
$905$	−13659.3	−0.501714
$906$	−5111.16	−0.187425
$907$	−4510.11	−0.165111	−0.0825556	−	0.996586i	$-0.526308\pi$
$907$	−4510.11	−0.165111	−0.0825556	+	0.996586i	$0.526308\pi$
$908$	16207.8	0.592374
$909$	5011.92	0.182877
$910$	6723.47	0.244924
$911$	3053.87	0.111064	0.0555320	−	0.998457i	$-0.482315\pi$
$911$	3053.87	0.111064	0.0555320	+	0.998457i	$0.482315\pi$
$912$	−1778.15	−0.0645619
$913$	13371.6	0.484706
$914$	12187.5	0.441058
$915$	−5076.05	−0.183398
$916$	−19396.2	−0.699639
$917$	30504.0	1.09851
$918$	−3651.87	−0.131296
$919$	1926.09	0.0691357	0.0345678	−	0.999402i	$-0.488995\pi$
$919$	1926.09	0.0691357	0.0345678	+	0.999402i	$0.488995\pi$
$920$	1050.27	0.0376375
$921$	3317.68	0.118698
$922$	−17584.8	−0.628116
$923$	2769.52	0.0987647
$924$	−17102.8	−0.608918
$925$	−5341.23	−0.189858
$926$	−5445.65	−0.193256
$927$	−6727.40	−0.238357
$928$	−3088.26	−0.109243
$929$	−1968.84	−0.0695325	−0.0347662	−	0.999395i	$-0.511069\pi$
$929$	−1968.84	−0.0695325	−0.0347662	+	0.999395i	$0.511069\pi$
$930$	577.039	0.0203461
$931$	90429.4	3.18336
$932$	−28968.9	−1.01814
$933$	21183.8	0.743330
$934$	−389.169	−0.0136338
$935$	15326.3	0.536067
$936$	4642.58	0.162123
$937$	−23773.8	−0.828876	−0.414438	−	0.910077i	$-0.636022\pi$
$937$	−23773.8	−0.828876	−0.414438	+	0.910077i	$0.636022\pi$
$938$	3796.13	0.132141
$939$	−24026.6	−0.835013
$940$	−2627.08	−0.0911552
$941$	−3474.57	−0.120370	−0.0601849	−	0.998187i	$-0.519169\pi$
$941$	−3474.57	−0.120370	−0.0601849	+	0.998187i	$0.519169\pi$
$942$	−4009.87	−0.138693
$943$	1991.15	0.0687601
$944$	1178.72	0.0406398
$945$	−4472.66	−0.153964
$946$	35131.6	1.20743
$947$	−7722.55	−0.264994	−0.132497	−	0.991183i	$-0.542299\pi$
$947$	−7722.55	−0.264994	−0.132497	+	0.991183i	$0.542299\pi$
$948$	12676.8	0.434306
$949$	−15069.8	−0.515475
$950$	−25120.7	−0.857921
$951$	−19165.6	−0.653510
$952$	−53691.7	−1.82790
$953$	53364.0	1.81388	0.906940	−	0.421259i	$-0.138412\pi$
$953$	53364.0	1.81388	0.906940	+	0.421259i	$0.138412\pi$
$954$	9568.39	0.324726
$955$	−16653.6	−0.564292
$956$	−20273.8	−0.685879
$957$	2029.61	0.0685559
$958$	7155.18	0.241308
$959$	−72679.1	−2.44727
$960$	5634.00	0.189413
$961$	−29391.3	−0.986583
$962$	−2237.87	−0.0750020
$963$	15971.4	0.534446
$964$	−4523.08	−0.151119
$965$	−17272.8	−0.576198
$966$	1460.01	0.0486284
$967$	7367.58	0.245011	0.122505	−	0.992468i	$-0.460907\pi$
$967$	7367.58	0.245011	0.122505	+	0.992468i	$0.460907\pi$
$968$	−3944.63	−0.130976
$969$	−31976.8	−1.06011
$970$	14268.9	0.472317
$971$	18204.4	0.601656	0.300828	−	0.953678i	$-0.402737\pi$
$971$	18204.4	0.601656	0.300828	+	0.953678i	$0.402737\pi$
$972$	−1144.39	−0.0377636
$973$	75646.8	2.49242
$974$	342.985	0.0112833
$975$	6502.38	0.213582
$976$	1322.76	0.0433816
$977$	4532.16	0.148410	0.0742050	−	0.997243i	$-0.476358\pi$
$977$	4532.16	0.148410	0.0742050	+	0.997243i	$0.476358\pi$
$978$	−1731.07	−0.0565988
$979$	35889.0	1.17162
$980$	−15799.7	−0.515004
$981$	−3749.58	−0.122033
$982$	−16328.4	−0.530611
$983$	−12613.2	−0.409255	−0.204627	−	0.978840i	$-0.565598\pi$
$983$	−12613.2	−0.409255	−0.204627	+	0.978840i	$0.565598\pi$
$984$	16033.2	0.519430
$985$	9271.95	0.299928
$986$	2360.99	0.0762569
$987$	−9855.66	−0.317841
$988$	15063.3	0.485048
$989$	4292.20	0.138002
$990$	−3355.84	−0.107733
$991$	8438.56	0.270494	0.135247	−	0.990812i	$-0.456817\pi$
$991$	8438.56	0.270494	0.135247	+	0.990812i	$0.456817\pi$
$992$	3537.09	0.113208
$993$	23310.3	0.744944
$994$	7013.20	0.223788
$995$	−17787.8	−0.566744
$996$	4874.42	0.155072
$997$	48594.8	1.54364	0.771821	−	0.635840i	$-0.219346\pi$
$997$	48594.8	1.54364	0.771821	+	0.635840i	$0.219346\pi$
$998$	−29676.3	−0.941271
$999$	1488.70	0.0471476

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.a.b.1.5	✓	6
3.2	odd	2		603.4.a.b.1.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.a.b.1.5	✓	6	1.1	even	1	trivial
603.4.a.b.1.2		6	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+1.81400 q^{2} +3.00000 q^{3} -4.70941 q^{4} +5.30362 q^{5} +5.44200 q^{6} -31.2342 q^{7} -23.0548 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+1.81400 q^{2} +3.00000 q^{3} -4.70941 q^{4} +5.30362 q^{5} +5.44200 q^{6} -31.2342 q^{7} -23.0548 q^{8} +9.00000 q^{9} +9.62075 q^{10} -38.7569 q^{11} -14.1282 q^{12} -22.3746 q^{13} -56.6587 q^{14} +15.9109 q^{15} -4.14618 q^{16} -74.5616 q^{17} +16.3260 q^{18} +142.955 q^{19} -24.9769 q^{20} -93.7025 q^{21} -70.3050 q^{22} -8.58950 q^{23} -69.1645 q^{24} -96.8716 q^{25} -40.5874 q^{26} +27.0000 q^{27} +147.094 q^{28} -17.4559 q^{29} +28.8623 q^{30} +19.9929 q^{31} +176.918 q^{32} -116.271 q^{33} -135.255 q^{34} -165.654 q^{35} -42.3847 q^{36} +55.1371 q^{37} +259.320 q^{38} -67.1237 q^{39} -122.274 q^{40} -231.812 q^{41} -169.976 q^{42} -499.703 q^{43} +182.522 q^{44} +47.7326 q^{45} -15.5813 q^{46} +105.180 q^{47} -12.4385 q^{48} +632.573 q^{49} -175.725 q^{50} -223.685 q^{51} +105.371 q^{52} +586.084 q^{53} +48.9780 q^{54} -205.552 q^{55} +720.099 q^{56} +428.865 q^{57} -31.6650 q^{58} -284.290 q^{59} -74.9307 q^{60} -319.031 q^{61} +36.2670 q^{62} -281.107 q^{63} +354.098 q^{64} -118.666 q^{65} -210.915 q^{66} -67.0000 q^{67} +351.141 q^{68} -25.7685 q^{69} -300.496 q^{70} -123.780 q^{71} -207.494 q^{72} +673.523 q^{73} +100.019 q^{74} -290.615 q^{75} -673.233 q^{76} +1210.54 q^{77} -121.762 q^{78} -897.265 q^{79} -21.9898 q^{80} +81.0000 q^{81} -420.507 q^{82} -345.013 q^{83} +441.283 q^{84} -395.446 q^{85} -906.461 q^{86} -52.3678 q^{87} +893.535 q^{88} -926.003 q^{89} +86.5868 q^{90} +698.851 q^{91} +40.4515 q^{92} +59.9786 q^{93} +190.797 q^{94} +758.178 q^{95} +530.753 q^{96} +1483.14 q^{97} +1147.49 q^{98} -348.812 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9}+O(q^{10}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9	\( 6 q - 5 q^{2} + 18 q^{3} + 13 q^{4} - 12 q^{5} - 15 q^{6} - 62 q^{7} - 75 q^{8} + 54 q^{9} - 111 q^{10} - 72 q^{11} + 39 q^{12} - 192 q^{13} + 3 q^{14} - 36 q^{15} - 27 q^{16} - 100 q^{17} - 45 q^{18} - 266 q^{19} + 255 q^{20} - 186 q^{21} + 44 q^{22} + 50 q^{23} - 225 q^{24} - 6 q^{25} + 472 q^{26} + 162 q^{27} - 333 q^{28} - 242 q^{29} - 333 q^{30} - 438 q^{31} + 35 q^{32} - 216 q^{33} - 150 q^{34} - 258 q^{35} + 117 q^{36} - 596 q^{37} + 664 q^{38} - 576 q^{39} - 831 q^{40} + 54 q^{41} + 9 q^{42} - 360 q^{43} - 714 q^{44} - 108 q^{45} - 871 q^{46} - 720 q^{47} - 81 q^{48} - 302 q^{49} + 4 q^{50} - 300 q^{51} - 1118 q^{52} + 694 q^{53} - 135 q^{54} - 990 q^{55} + 1917 q^{56} - 798 q^{57} + 1354 q^{58} - 378 q^{59} + 765 q^{60} - 1396 q^{61} + 1475 q^{62} - 558 q^{63} + 1225 q^{64} - 348 q^{65} + 132 q^{66} - 402 q^{67} + 2032 q^{68} + 150 q^{69} + 2415 q^{70} - 964 q^{71} - 675 q^{72} - 192 q^{73} + 2751 q^{74} - 18 q^{75} - 2306 q^{76} + 2724 q^{77} + 1416 q^{78} - 802 q^{79} + 4221 q^{80} + 486 q^{81} + 1735 q^{82} + 2126 q^{83} - 999 q^{84} - 1206 q^{85} - 609 q^{86} - 726 q^{87} + 3656 q^{88} + 432 q^{89} - 999 q^{90} + 1258 q^{91} + 3163 q^{92} - 1314 q^{93} + 1742 q^{94} + 936 q^{95} + 105 q^{96} + 1290 q^{97} + 2492 q^{98} - 648 q^{99}+O(q^{100}) \) 6 * q - 5 * q^2 + 18 * q^3 + 13 * q^4 - 12 * q^5 - 15 * q^6 - 62 * q^7 - 75 * q^8 + 54 * q^9 - 111 * q^10 - 72 * q^11 + 39 * q^12 - 192 * q^13 + 3 * q^14 - 36 * q^15 - 27 * q^16 - 100 * q^17 - 45 * q^18 - 266 * q^19 + 255 * q^20 - 186 * q^21 + 44 * q^22 + 50 * q^23 - 225 * q^24 - 6 * q^25 + 472 * q^26 + 162 * q^27 - 333 * q^28 - 242 * q^29 - 333 * q^30 - 438 * q^31 + 35 * q^32 - 216 * q^33 - 150 * q^34 - 258 * q^35 + 117 * q^36 - 596 * q^37 + 664 * q^38 - 576 * q^39 - 831 * q^40 + 54 * q^41 + 9 * q^42 - 360 * q^43 - 714 * q^44 - 108 * q^45 - 871 * q^46 - 720 * q^47 - 81 * q^48 - 302 * q^49 + 4 * q^50 - 300 * q^51 - 1118 * q^52 + 694 * q^53 - 135 * q^54 - 990 * q^55 + 1917 * q^56 - 798 * q^57 + 1354 * q^58 - 378 * q^59 + 765 * q^60 - 1396 * q^61 + 1475 * q^62 - 558 * q^63 + 1225 * q^64 - 348 * q^65 + 132 * q^66 - 402 * q^67 + 2032 * q^68 + 150 * q^69 + 2415 * q^70 - 964 * q^71 - 675 * q^72 - 192 * q^73 + 2751 * q^74 - 18 * q^75 - 2306 * q^76 + 2724 * q^77 + 1416 * q^78 - 802 * q^79 + 4221 * q^80 + 486 * q^81 + 1735 * q^82 + 2126 * q^83 - 999 * q^84 - 1206 * q^85 - 609 * q^86 - 726 * q^87 + 3656 * q^88 + 432 * q^89 - 999 * q^90 + 1258 * q^91 + 3163 * q^92 - 1314 * q^93 + 1742 * q^94 + 936 * q^95 + 105 * q^96 + 1290 * q^97 + 2492 * q^98 - 648 * q^99

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