LMFDB - Embedded newform 1849.4.a.k.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1849,4,Mod(1,1849)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1849, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("1849.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 1849 = 43^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	1849.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:	$109.094531601$
Analytic rank:	$1$
Dimension:	$60$
Twist minimal:	no (minimal twist has level 43)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	1849.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.40283 q^{2} +5.79667 q^{3} +3.57928 q^{4} +10.2155 q^{5} -19.7251 q^{6} +9.81633 q^{7} +15.0430 q^{8} +6.60143 q^{9} +O(q^{10})$	\(q-3.40283 q^{2} +5.79667 q^{3} +3.57928 q^{4} +10.2155 q^{5} -19.7251 q^{6} +9.81633 q^{7} +15.0430 q^{8} +6.60143 q^{9} -34.7615 q^{10} +28.2886 q^{11} +20.7479 q^{12} -7.62305 q^{13} -33.4033 q^{14} +59.2157 q^{15} -79.8230 q^{16} -51.5372 q^{17} -22.4636 q^{18} +84.9503 q^{19} +36.5640 q^{20} +56.9021 q^{21} -96.2616 q^{22} -129.288 q^{23} +87.1992 q^{24} -20.6443 q^{25} +25.9400 q^{26} -118.244 q^{27} +35.1354 q^{28} +108.621 q^{29} -201.501 q^{30} -311.688 q^{31} +151.281 q^{32} +163.980 q^{33} +175.372 q^{34} +100.278 q^{35} +23.6284 q^{36} -28.5795 q^{37} -289.072 q^{38} -44.1883 q^{39} +153.671 q^{40} -318.296 q^{41} -193.628 q^{42} +101.253 q^{44} +67.4367 q^{45} +439.946 q^{46} -407.003 q^{47} -462.708 q^{48} -246.640 q^{49} +70.2492 q^{50} -298.744 q^{51} -27.2851 q^{52} -420.939 q^{53} +402.364 q^{54} +288.982 q^{55} +147.667 q^{56} +492.429 q^{57} -369.619 q^{58} +406.948 q^{59} +211.950 q^{60} -410.905 q^{61} +1060.62 q^{62} +64.8018 q^{63} +123.801 q^{64} -77.8730 q^{65} -557.997 q^{66} -326.028 q^{67} -184.466 q^{68} -749.441 q^{69} -341.231 q^{70} -777.772 q^{71} +99.3051 q^{72} -587.238 q^{73} +97.2512 q^{74} -119.668 q^{75} +304.061 q^{76} +277.691 q^{77} +150.366 q^{78} -538.553 q^{79} -815.429 q^{80} -863.660 q^{81} +1083.11 q^{82} +1263.46 q^{83} +203.669 q^{84} -526.476 q^{85} +629.640 q^{87} +425.545 q^{88} +42.2417 q^{89} -229.476 q^{90} -74.8304 q^{91} -462.759 q^{92} -1806.76 q^{93} +1384.96 q^{94} +867.807 q^{95} +876.925 q^{96} +1321.55 q^{97} +839.274 q^{98} +186.746 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) $ 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 - 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 - 625 * q^18 - 610 * q^19 - 345 * q^20 + 611 * q^21 - 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 - 1071 * q^26 - 1609 * q^27 - 46 * q^28 - 773 * q^29 - 375 * q^30 - 97 * q^31 - 1967 * q^32 - 500 * q^33 - 217 * q^34 + 247 * q^35 + 175 * q^36 - 228 * q^37 + 1253 * q^38 - 1493 * q^39 + 2220 * q^40 - 951 * q^41 - 2643 * q^42 - 1378 * q^44 - 1086 * q^45 + 565 * q^46 - 2 * q^47 - 2303 * q^48 + 1264 * q^49 - 3273 * q^50 - 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 - 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 - 2999 * q^61 - 5569 * q^62 - 2377 * q^63 + 2082 * q^64 - 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 - 1817 * q^69 - 2738 * q^70 - 8003 * q^71 - 1412 * q^72 + 1011 * q^73 - 1413 * q^74 - 7457 * q^75 - 5516 * q^76 - 4052 * q^77 + 1091 * q^78 - 4422 * q^79 - 1610 * q^80 + 2108 * q^81 - 4676 * q^82 - 297 * q^83 - 54 * q^84 - 4333 * q^85 + 1377 * q^87 - 3652 * q^88 - 2480 * q^89 - 1414 * q^90 - 4551 * q^91 - 3286 * q^92 - 4 * q^93 - 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 - 753 * q^98 + 5072 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−3.40283	−1.20308	−0.601542	−	0.798841i	$-0.705447\pi$
$2$	−3.40283	−1.20308	−0.601542	+	0.798841i	$0.705447\pi$
$3$	5.79667	1.11557	0.557785	−	0.829985i	$-0.311651\pi$
$3$	5.79667	1.11557	0.557785	+	0.829985i	$0.311651\pi$
$4$	3.57928	0.447410
$5$	10.2155	0.913699	0.456849	−	0.889544i	$-0.348978\pi$
$5$	10.2155	0.913699	0.456849	+	0.889544i	$0.348978\pi$
$6$	−19.7251	−1.34212
$7$	9.81633	0.530032	0.265016	−	0.964244i	$-0.414623\pi$
$7$	9.81633	0.530032	0.265016	+	0.964244i	$0.414623\pi$
$8$	15.0430	0.664812
$9$	6.60143	0.244497
$10$	−34.7615	−1.09926
$11$	28.2886	0.775395	0.387698	−	0.921787i	$-0.373270\pi$
$11$	28.2886	0.775395	0.387698	+	0.921787i	$0.373270\pi$
$12$	20.7479	0.499118
$13$	−7.62305	−0.162635	−0.0813175	−	0.996688i	$-0.525913\pi$
$13$	−7.62305	−0.162635	−0.0813175	+	0.996688i	$0.525913\pi$
$14$	−33.4033	−0.637673
$15$	59.2157	1.01930
$16$	−79.8230	−1.24723
$17$	−51.5372	−0.735271	−0.367635	−	0.929970i	$-0.619833\pi$
$17$	−51.5372	−0.735271	−0.367635	+	0.929970i	$0.619833\pi$
$18$	−22.4636	−0.294151
$19$	84.9503	1.02573	0.512867	−	0.858468i	$-0.328583\pi$
$19$	84.9503	1.02573	0.512867	+	0.858468i	$0.328583\pi$
$20$	36.5640	0.408798
$21$	56.9021	0.591288
$22$	−96.2616	−0.932865
$23$	−129.288	−1.17211	−0.586053	−	0.810273i	$-0.699319\pi$
$23$	−129.288	−1.17211	−0.586053	+	0.810273i	$0.699319\pi$
$24$	87.1992	0.741644
$25$	−20.6443	−0.165155
$26$	25.9400	0.195663
$27$	−118.244	−0.842816
$28$	35.1354	0.237142
$29$	108.621	0.695531	0.347766	−	0.937582i	$-0.386941\pi$
$29$	108.621	0.695531	0.347766	+	0.937582i	$0.386941\pi$
$30$	−201.501	−1.22630
$31$	−311.688	−1.80583	−0.902917	−	0.429814i	$-0.858579\pi$
$31$	−311.688	−1.80583	−0.902917	+	0.429814i	$0.858579\pi$
$32$	151.281	0.835716
$33$	163.980	0.865008
$34$	175.372	0.884592
$35$	100.278	0.484290
$36$	23.6284	0.109391
$37$	−28.5795	−0.126985	−0.0634923	−	0.997982i	$-0.520224\pi$
$37$	−28.5795	−0.126985	−0.0634923	+	0.997982i	$0.520224\pi$
$38$	−289.072	−1.23404
$39$	−44.1883	−0.181431
$40$	153.671	0.607438
$41$	−318.296	−1.21243	−0.606213	−	0.795302i	$-0.707312\pi$
$41$	−318.296	−1.21243	−0.606213	+	0.795302i	$0.707312\pi$
$42$	−193.628	−0.711369
$43$	0	0
$43$	0	0
$44$	101.253	0.346920
$45$	67.4367	0.223397
$46$	439.946	1.41014
$47$	−407.003	−1.26314	−0.631569	−	0.775320i	$-0.717589\pi$
$47$	−407.003	−1.26314	−0.631569	+	0.775320i	$0.717589\pi$
$48$	−462.708	−1.39138
$49$	−246.640	−0.719066
$50$	70.2492	0.198695
$51$	−298.744	−0.820246
$52$	−27.2851	−0.0727645
$53$	−420.939	−1.09095	−0.545476	−	0.838127i	$-0.683651\pi$
$53$	−420.939	−1.09095	−0.545476	+	0.838127i	$0.683651\pi$
$54$	402.364	1.01398
$55$	288.982	0.708478
$56$	147.667	0.352371
$57$	492.429	1.14428
$58$	−369.619	−0.836782
$59$	406.948	0.897968	0.448984	−	0.893540i	$-0.351786\pi$
$59$	406.948	0.897968	0.448984	+	0.893540i	$0.351786\pi$
$60$	211.950	0.456043
$61$	−410.905	−0.862474	−0.431237	−	0.902239i	$-0.641923\pi$
$61$	−410.905	−0.862474	−0.431237	+	0.902239i	$0.641923\pi$
$62$	1060.62	2.17257
$63$	64.8018	0.129591
$64$	123.801	0.241799
$65$	−77.8730	−0.148599
$66$	−557.997	−1.04068
$67$	−326.028	−0.594488	−0.297244	−	0.954802i	$-0.596067\pi$
$67$	−326.028	−0.594488	−0.297244	+	0.954802i	$0.596067\pi$
$68$	−184.466	−0.328968
$69$	−749.441	−1.30757
$70$	−341.231	−0.582641
$71$	−777.772	−1.30006	−0.650032	−	0.759906i	$-0.725245\pi$
$71$	−777.772	−1.30006	−0.650032	+	0.759906i	$0.725245\pi$
$72$	99.3051	0.162545
$73$	−587.238	−0.941521	−0.470761	−	0.882261i	$-0.656020\pi$
$73$	−587.238	−0.941521	−0.470761	+	0.882261i	$0.656020\pi$
$74$	97.2512	0.152773
$75$	−119.668	−0.184242
$76$	304.061	0.458924
$77$	277.691	0.410984
$78$	150.366	0.218276
$79$	−538.553	−0.766987	−0.383494	−	0.923544i	$-0.625279\pi$
$79$	−538.553	−0.766987	−0.383494	+	0.923544i	$0.625279\pi$
$80$	−815.429	−1.13960
$81$	−863.660	−1.18472
$82$	1083.11	1.45865
$83$	1263.46	1.67088	0.835439	−	0.549582i	$-0.185213\pi$
$83$	1263.46	1.67088	0.835439	+	0.549582i	$0.185213\pi$
$84$	203.669	0.264548
$85$	−526.476	−0.671816
$86$	0	0
$87$	629.640	0.775914
$88$	425.545	0.515492
$89$	42.2417	0.0503103	0.0251551	−	0.999684i	$-0.491992\pi$
$89$	42.2417	0.0503103	0.0251551	+	0.999684i	$0.491992\pi$
$90$	−229.476	−0.268765
$91$	−74.8304	−0.0862017
$92$	−462.759	−0.524412
$93$	−1806.76	−2.01454
$94$	1384.96	1.51966
$95$	867.807	0.937212
$96$	876.925	0.932300
$97$	1321.55	1.38333	0.691665	−	0.722218i	$-0.256877\pi$
$97$	1321.55	1.38333	0.691665	+	0.722218i	$0.256877\pi$
$98$	839.274	0.865097
$99$	186.746	0.189582
$100$	−73.8918	−0.0738918
$101$	−359.904	−0.354572	−0.177286	−	0.984159i	$-0.556732\pi$
$101$	−359.904	−0.354572	−0.177286	+	0.984159i	$0.556732\pi$
$102$	1016.58	0.986825
$103$	−1822.00	−1.74298	−0.871489	−	0.490415i	$-0.836845\pi$
$103$	−1822.00	−1.74298	−0.871489	+	0.490415i	$0.836845\pi$
$104$	−114.673	−0.108122
$105$	581.281	0.540259
$106$	1432.39	1.31251
$107$	−516.947	−0.467058	−0.233529	−	0.972350i	$-0.575027\pi$
$107$	−516.947	−0.467058	−0.233529	+	0.972350i	$0.575027\pi$
$108$	−423.228	−0.377085
$109$	698.726	0.613999	0.306999	−	0.951710i	$-0.400675\pi$
$109$	698.726	0.613999	0.306999	+	0.951710i	$0.400675\pi$
$110$	−983.357	−0.852358
$111$	−165.666	−0.141660
$112$	−783.569	−0.661074
$113$	−942.882	−0.784946	−0.392473	−	0.919764i	$-0.628380\pi$
$113$	−942.882	−0.784946	−0.392473	+	0.919764i	$0.628380\pi$
$114$	−1675.66	−1.37666
$115$	−1320.74	−1.07095
$116$	388.785	0.311188
$117$	−50.3231	−0.0397638
$118$	−1384.78	−1.08033
$119$	−505.906	−0.389717
$120$	890.780	0.677639
$121$	−530.753	−0.398762
$122$	1398.24	1.03763
$123$	−1845.06	−1.35255
$124$	−1115.62	−0.807949
$125$	−1487.82	−1.06460
$126$	−220.510	−0.155909
$127$	−1215.10	−0.848997	−0.424499	−	0.905429i	$-0.639550\pi$
$127$	−1215.10	−0.848997	−0.424499	+	0.905429i	$0.639550\pi$
$128$	−1631.52	−1.12662
$129$	0	0
$130$	264.989	0.178777
$131$	2230.48	1.48762	0.743810	−	0.668392i	$-0.233017\pi$
$131$	2230.48	1.48762	0.743810	+	0.668392i	$0.233017\pi$
$132$	586.931	0.387014
$133$	833.900	0.543672
$134$	1109.42	0.715219
$135$	−1207.92	−0.770080
$136$	−775.272	−0.488817
$137$	2855.10	1.78050	0.890248	−	0.455477i	$-0.150531\pi$
$137$	2855.10	1.78050	0.890248	+	0.455477i	$0.150531\pi$
$138$	2550.22	1.57311
$139$	2733.36	1.66792	0.833958	−	0.551828i	$-0.186069\pi$
$139$	2733.36	1.66792	0.833958	+	0.551828i	$0.186069\pi$
$140$	358.925	0.216676
$141$	−2359.26	−1.40912
$142$	2646.63	1.56409
$143$	−215.646	−0.126106
$144$	−526.946	−0.304946
$145$	1109.61	0.635506
$146$	1998.27	1.13273
$147$	−1429.69	−0.802169
$148$	−102.294	−0.0568143
$149$	1398.51	0.768927	0.384463	−	0.923140i	$-0.374386\pi$
$149$	1398.51	0.768927	0.384463	+	0.923140i	$0.374386\pi$
$150$	407.212	0.221658
$151$	−1258.91	−0.678469	−0.339234	−	0.940702i	$-0.610168\pi$
$151$	−1258.91	−0.678469	−0.339234	+	0.940702i	$0.610168\pi$
$152$	1277.91	0.681920
$153$	−340.219	−0.179772
$154$	−944.935	−0.494448
$155$	−3184.04	−1.64999
$156$	−158.163	−0.0811740
$157$	−894.821	−0.454869	−0.227435	−	0.973793i	$-0.573034\pi$
$157$	−894.821	−0.454869	−0.227435	+	0.973793i	$0.573034\pi$
$158$	1832.61	0.922750
$159$	−2440.05	−1.21703
$160$	1545.40	0.763592
$161$	−1269.13	−0.621254
$162$	2938.89	1.42532
$163$	2191.13	1.05290	0.526449	−	0.850207i	$-0.323523\pi$
$163$	2191.13	1.05290	0.526449	+	0.850207i	$0.323523\pi$
$164$	−1139.27	−0.542452
$165$	1675.13	0.790357
$166$	−4299.35	−2.01021
$167$	−427.211	−0.197955	−0.0989777	−	0.995090i	$-0.531557\pi$
$167$	−427.211	−0.197955	−0.0989777	+	0.995090i	$0.531557\pi$
$168$	855.976	0.393095
$169$	−2138.89	−0.973550
$170$	1791.51	0.808251
$171$	560.794	0.250789
$172$	0	0
$173$	3203.58	1.40788	0.703941	−	0.710259i	$-0.251422\pi$
$173$	3203.58	1.40788	0.703941	+	0.710259i	$0.251422\pi$
$174$	−2142.56	−0.933489
$175$	−202.651	−0.0875372
$176$	−2258.08	−0.967100
$177$	2358.95	1.00175
$178$	−143.742	−0.0605275
$179$	−2062.69	−0.861298	−0.430649	−	0.902519i	$-0.641715\pi$
$179$	−2062.69	−0.861298	−0.430649	+	0.902519i	$0.641715\pi$
$180$	241.375	0.0999501
$181$	2007.97	0.824594	0.412297	−	0.911049i	$-0.364727\pi$
$181$	2007.97	0.824594	0.412297	+	0.911049i	$0.364727\pi$
$182$	254.635	0.103708
$183$	−2381.88	−0.962151
$184$	−1944.88	−0.779230
$185$	−291.952	−0.116026
$186$	6148.09	2.42366
$187$	−1457.92	−0.570125
$188$	−1456.78	−0.565141
$189$	−1160.72	−0.446720
$190$	−2953.00	−1.12754
$191$	−446.056	−0.168982	−0.0844908	−	0.996424i	$-0.526926\pi$
$191$	−446.056	−0.168982	−0.0844908	+	0.996424i	$0.526926\pi$
$192$	717.633	0.269743
$193$	2664.37	0.993708	0.496854	−	0.867834i	$-0.334488\pi$
$193$	2664.37	0.993708	0.496854	+	0.867834i	$0.334488\pi$
$194$	−4497.02	−1.66426
$195$	−451.404	−0.165773
$196$	−882.793	−0.321718
$197$	390.340	0.141170	0.0705852	−	0.997506i	$-0.477513\pi$
$197$	390.340	0.141170	0.0705852	+	0.997506i	$0.477513\pi$
$198$	−635.464	−0.228083
$199$	1900.87	0.677132	0.338566	−	0.940943i	$-0.390058\pi$
$199$	1900.87	0.677132	0.338566	+	0.940943i	$0.390058\pi$
$200$	−310.552	−0.109797
$201$	−1889.88	−0.663193
$202$	1224.69	0.426580
$203$	1066.26	0.368654
$204$	−1069.29	−0.366987
$205$	−3251.54	−1.10779
$206$	6199.96	2.09695
$207$	−853.487	−0.286577
$208$	608.495	0.202844
$209$	2403.13	0.795349
$210$	−1978.00	−0.649977
$211$	−1999.32	−0.652318	−0.326159	−	0.945315i	$-0.605754\pi$
$211$	−1999.32	−0.652318	−0.326159	+	0.945315i	$0.605754\pi$
$212$	−1506.66	−0.488103
$213$	−4508.49	−1.45031
$214$	1759.09	0.561910
$215$	0	0
$216$	−1778.74	−0.560314
$217$	−3059.63	−0.957150
$218$	−2377.65	−0.738692
$219$	−3404.03	−1.05033
$220$	1034.35	0.316980
$221$	392.871	0.119581
$222$	563.733	0.170429
$223$	5343.46	1.60460	0.802298	−	0.596924i	$-0.203611\pi$
$223$	5343.46	1.60460	0.802298	+	0.596924i	$0.203611\pi$
$224$	1485.02	0.442956
$225$	−136.282	−0.0403799
$226$	3208.47	0.944355
$227$	6363.16	1.86052	0.930260	−	0.366901i	$-0.119581\pi$
$227$	6363.16	1.86052	0.930260	+	0.366901i	$0.119581\pi$
$228$	1762.54	0.511962
$229$	−2194.25	−0.633187	−0.316594	−	0.948561i	$-0.602539\pi$
$229$	−2194.25	−0.633187	−0.316594	+	0.948561i	$0.602539\pi$
$230$	4494.25	1.28844
$231$	1609.68	0.458482
$232$	1633.98	0.462397
$233$	4961.22	1.39494	0.697469	−	0.716615i	$-0.254309\pi$
$233$	4961.22	1.39494	0.697469	+	0.716615i	$0.254309\pi$
$234$	171.241	0.0478392
$235$	−4157.72	−1.15413
$236$	1456.58	0.401760
$237$	−3121.82	−0.855628
$238$	1721.51	0.468862
$239$	3408.00	0.922364	0.461182	−	0.887306i	$-0.347426\pi$
$239$	3408.00	0.922364	0.461182	+	0.887306i	$0.347426\pi$
$240$	−4726.78	−1.27130
$241$	3212.06	0.858535	0.429268	−	0.903177i	$-0.358772\pi$
$241$	3212.06	0.858535	0.429268	+	0.903177i	$0.358772\pi$
$242$	1806.06	0.479744
$243$	−1813.77	−0.478821
$244$	−1470.74	−0.385880
$245$	−2519.54	−0.657010
$246$	6278.42	1.62723
$247$	−647.581	−0.166820
$248$	−4688.72	−1.20054
$249$	7323.88	1.86398
$250$	5062.82	1.28080
$251$	−21.1938	−0.00532965	−0.00266482	−	0.999996i	$-0.500848\pi$
$251$	−21.1938	−0.00532965	−0.00266482	+	0.999996i	$0.500848\pi$
$252$	231.944	0.0579806
$253$	−3657.39	−0.908845
$254$	4134.78	1.02141
$255$	−3051.81	−0.749458
$256$	4561.38	1.11362
$257$	829.318	0.201290	0.100645	−	0.994922i	$-0.467909\pi$
$257$	829.318	0.201290	0.100645	+	0.994922i	$0.467909\pi$
$258$	0	0
$259$	−280.545	−0.0673059
$260$	−278.729	−0.0664849
$261$	717.054	0.170056
$262$	−7589.96	−1.78973
$263$	−905.493	−0.212301	−0.106150	−	0.994350i	$-0.533852\pi$
$263$	−905.493	−0.212301	−0.106150	+	0.994350i	$0.533852\pi$
$264$	2466.75	0.575067
$265$	−4300.09	−0.996801
$266$	−2837.62	−0.654082
$267$	244.862	0.0561247
$268$	−1166.95	−0.265980
$269$	−1097.60	−0.248779	−0.124390	−	0.992233i	$-0.539697\pi$
$269$	−1097.60	−0.248779	−0.124390	+	0.992233i	$0.539697\pi$
$270$	4110.34	0.926471
$271$	581.095	0.130255	0.0651274	−	0.997877i	$-0.479255\pi$
$271$	581.095	0.130255	0.0651274	+	0.997877i	$0.479255\pi$
$272$	4113.85	0.917055
$273$	−433.767	−0.0961641
$274$	−9715.44	−2.14208
$275$	−584.000	−0.128060
$276$	−2682.46	−0.585019
$277$	−3879.22	−0.841443	−0.420721	−	0.907190i	$-0.638223\pi$
$277$	−3879.22	−0.841443	−0.420721	+	0.907190i	$0.638223\pi$
$278$	−9301.16	−2.00664
$279$	−2057.59	−0.441522
$280$	1508.48	0.321961
$281$	−5472.94	−1.16188	−0.580940	−	0.813947i	$-0.697315\pi$
$281$	−5472.94	−1.16188	−0.580940	+	0.813947i	$0.697315\pi$
$282$	8028.18	1.69529
$283$	2546.01	0.534786	0.267393	−	0.963588i	$-0.413838\pi$
$283$	2546.01	0.534786	0.267393	+	0.963588i	$0.413838\pi$
$284$	−2783.87	−0.581662
$285$	5030.39	1.04553
$286$	733.807	0.151716
$287$	−3124.50	−0.642624
$288$	998.669	0.204330
$289$	−2256.92	−0.459377
$290$	−3775.83	−0.764567
$291$	7660.60	1.54320
$292$	−2101.89	−0.421246
$293$	4747.22	0.946538	0.473269	−	0.880918i	$-0.343074\pi$
$293$	4747.22	0.946538	0.473269	+	0.880918i	$0.343074\pi$
$294$	4865.00	0.965076
$295$	4157.16	0.820473
$296$	−429.920	−0.0844209
$297$	−3344.96	−0.653516
$298$	−4758.89	−0.925083
$299$	985.570	0.190625
$300$	−428.327	−0.0824316
$301$	0	0
$302$	4283.87	0.816255
$303$	−2086.24	−0.395550
$304$	−6780.99	−1.27933
$305$	−4197.58	−0.788042
$306$	1157.71	0.216281
$307$	1920.84	0.357094	0.178547	−	0.983931i	$-0.442860\pi$
$307$	1920.84	0.357094	0.178547	+	0.983931i	$0.442860\pi$
$308$	993.933	0.183879
$309$	−10561.5	−1.94442
$310$	10834.8	1.98507
$311$	3184.89	0.580703	0.290352	−	0.956920i	$-0.406228\pi$
$311$	3184.89	0.580703	0.290352	+	0.956920i	$0.406228\pi$
$312$	−664.724	−0.120617
$313$	4212.60	0.760735	0.380367	−	0.924835i	$-0.375798\pi$
$313$	4212.60	0.760735	0.380367	+	0.924835i	$0.375798\pi$
$314$	3044.93	0.547246
$315$	661.981	0.118408
$316$	−1927.63	−0.343158
$317$	−8534.17	−1.51207	−0.756036	−	0.654530i	$-0.772866\pi$
$317$	−8534.17	−1.51207	−0.756036	+	0.654530i	$0.772866\pi$
$318$	8303.07	1.46419
$319$	3072.74	0.539312
$320$	1264.68	0.220931
$321$	−2996.58	−0.521036
$322$	4318.65	0.747420
$323$	−4378.10	−0.754192
$324$	−3091.28	−0.530055
$325$	157.373	0.0268599
$326$	−7456.04	−1.26672
$327$	4050.29	0.684959
$328$	−4788.11	−0.806035
$329$	−3995.27	−0.669503
$330$	−5700.20	−0.950865
$331$	5139.20	0.853401	0.426701	−	0.904393i	$-0.359676\pi$
$331$	5139.20	0.853401	0.426701	+	0.904393i	$0.359676\pi$
$332$	4522.29	0.747568
$333$	−188.665	−0.0310474
$334$	1453.73	0.238157
$335$	−3330.53	−0.543183
$336$	−4542.09	−0.737475
$337$	67.5867	0.0109249	0.00546244	−	0.999985i	$-0.498261\pi$
$337$	67.5867	0.0109249	0.00546244	+	0.999985i	$0.498261\pi$
$338$	7278.29	1.17126
$339$	−5465.58	−0.875662
$340$	−1884.41	−0.300577
$341$	−8817.24	−1.40024
$342$	−1908.29	−0.301721
$343$	−5788.10	−0.911160
$344$	0	0
$345$	−7655.89	−1.19472
$346$	−10901.2	−1.69380
$347$	8870.46	1.37231	0.686155	−	0.727456i	$-0.259297\pi$
$347$	8870.46	1.37231	0.686155	+	0.727456i	$0.259297\pi$
$348$	2253.66	0.347152
$349$	10421.6	1.59844	0.799222	−	0.601036i	$-0.205245\pi$
$349$	10421.6	1.59844	0.799222	+	0.601036i	$0.205245\pi$
$350$	689.589	0.105315
$351$	901.379	0.137071
$352$	4279.53	0.648010
$353$	−6561.40	−0.989315	−0.494657	−	0.869088i	$-0.664706\pi$
$353$	−6561.40	−0.989315	−0.494657	+	0.869088i	$0.664706\pi$
$354$	−8027.10	−1.20519
$355$	−7945.31	−1.18787
$356$	151.195	0.0225093
$357$	−2932.57	−0.434757
$358$	7018.98	1.03621
$359$	−9658.66	−1.41996	−0.709978	−	0.704223i	$-0.751295\pi$
$359$	−9658.66	−1.41996	−0.709978	+	0.704223i	$0.751295\pi$
$360$	1014.45	0.148517
$361$	357.558	0.0521298
$362$	−6832.81	−0.992056
$363$	−3076.60	−0.444847
$364$	−267.839	−0.0385675
$365$	−5998.91	−0.860267
$366$	8105.14	1.15755
$367$	6046.19	0.859969	0.429985	−	0.902836i	$-0.358519\pi$
$367$	6046.19	0.859969	0.429985	+	0.902836i	$0.358519\pi$
$368$	10320.2	1.46189
$369$	−2101.21	−0.296435
$370$	993.466	0.139589
$371$	−4132.08	−0.578239
$372$	−6466.89	−0.901324
$373$	−7157.35	−0.993548	−0.496774	−	0.867880i	$-0.665482\pi$
$373$	−7157.35	−0.993548	−0.496774	+	0.867880i	$0.665482\pi$
$374$	4961.05	0.685909
$375$	−8624.43	−1.18764
$376$	−6122.53	−0.839748
$377$	−828.023	−0.113118
$378$	3949.74	0.537441
$379$	−6251.07	−0.847218	−0.423609	−	0.905845i	$-0.639237\pi$
$379$	−6251.07	−0.847218	−0.423609	+	0.905845i	$0.639237\pi$
$380$	3106.13	0.419318
$381$	−7043.54	−0.947116
$382$	1517.86	0.203299
$383$	−7398.99	−0.987130	−0.493565	−	0.869709i	$-0.664306\pi$
$383$	−7398.99	−0.987130	−0.493565	+	0.869709i	$0.664306\pi$
$384$	−9457.39	−1.25682
$385$	2836.74	0.375516
$386$	−9066.42	−1.19551
$387$	0	0
$388$	4730.20	0.618916
$389$	−2470.01	−0.321940	−0.160970	−	0.986959i	$-0.551462\pi$
$389$	−2470.01	−0.321940	−0.160970	+	0.986959i	$0.551462\pi$
$390$	1536.05	0.199439
$391$	6663.14	0.861815
$392$	−3710.19	−0.478044
$393$	12929.4	1.65954
$394$	−1328.26	−0.169840
$395$	−5501.57	−0.700795
$396$	668.415	0.0848210
$397$	−2437.26	−0.308118	−0.154059	−	0.988062i	$-0.549235\pi$
$397$	−2437.26	−0.308118	−0.154059	+	0.988062i	$0.549235\pi$
$398$	−6468.35	−0.814646
$399$	4833.85	0.606504
$400$	1647.89	0.205986
$401$	−13524.1	−1.68420	−0.842098	−	0.539324i	$-0.818680\pi$
$401$	−13524.1	−1.68420	−0.842098	+	0.539324i	$0.818680\pi$
$402$	6430.95	0.797877
$403$	2376.02	0.293692
$404$	−1288.20	−0.158639
$405$	−8822.68	−1.08248
$406$	−3628.30	−0.443521
$407$	−808.474	−0.0984633
$408$	−4494.00	−0.545309
$409$	−10404.5	−1.25787	−0.628937	−	0.777457i	$-0.716509\pi$
$409$	−10404.5	−1.25787	−0.628937	+	0.777457i	$0.716509\pi$
$410$	11064.5	1.33277
$411$	16550.1	1.98627
$412$	−6521.44	−0.779826
$413$	3994.74	0.475952
$414$	2904.27	0.344776
$415$	12906.8	1.52668
$416$	−1153.22	−0.135917
$417$	15844.4	1.86068
$418$	−8177.45	−0.956871
$419$	−1023.16	−0.119296	−0.0596478	−	0.998219i	$-0.518998\pi$
$419$	−1023.16	−0.119296	−0.0596478	+	0.998219i	$0.518998\pi$
$420$	2080.57	0.241717
$421$	−10457.1	−1.21057	−0.605284	−	0.796009i	$-0.706941\pi$
$421$	−10457.1	−1.21057	−0.605284	+	0.796009i	$0.706941\pi$
$422$	6803.36	0.784793
$423$	−2686.80	−0.308834
$424$	−6332.17	−0.725277
$425$	1063.95	0.121433
$426$	15341.7	1.74485
$427$	−4033.57	−0.457139
$428$	−1850.30	−0.208967
$429$	−1250.03	−0.140681
$430$	0	0
$431$	−7764.33	−0.867737	−0.433869	−	0.900976i	$-0.642852\pi$
$431$	−7764.33	−0.867737	−0.433869	+	0.900976i	$0.642852\pi$
$432$	9438.58	1.05119
$433$	−3288.59	−0.364987	−0.182494	−	0.983207i	$-0.558417\pi$
$433$	−3288.59	−0.364987	−0.182494	+	0.983207i	$0.558417\pi$
$434$	10411.4	1.15153
$435$	6432.07	0.708952
$436$	2500.94	0.274709
$437$	−10983.1	−1.20227
$438$	11583.3	1.26364
$439$	8325.24	0.905107	0.452553	−	0.891737i	$-0.350513\pi$
$439$	8325.24	0.905107	0.452553	+	0.891737i	$0.350513\pi$
$440$	4347.14	0.471004
$441$	−1628.17	−0.175810
$442$	−1336.87	−0.143866
$443$	−1578.25	−0.169266	−0.0846331	−	0.996412i	$-0.526972\pi$
$443$	−1578.25	−0.169266	−0.0846331	+	0.996412i	$0.526972\pi$
$444$	−592.965	−0.0633803
$445$	431.519	0.0459684
$446$	−18182.9	−1.93046
$447$	8106.69	0.857792
$448$	1215.27	0.128161
$449$	−10797.9	−1.13493	−0.567464	−	0.823398i	$-0.692076\pi$
$449$	−10797.9	−1.13493	−0.567464	+	0.823398i	$0.692076\pi$
$450$	463.745	0.0485804
$451$	−9004.16	−0.940109
$452$	−3374.84	−0.351193
$453$	−7297.50	−0.756880
$454$	−21652.8	−2.23836
$455$	−764.427	−0.0787624
$456$	7407.60	0.760730
$457$	−10995.8	−1.12552	−0.562758	−	0.826622i	$-0.690260\pi$
$457$	−10995.8	−1.12552	−0.562758	+	0.826622i	$0.690260\pi$
$458$	7466.66	0.761777
$459$	6093.95	0.619698
$460$	−4727.29	−0.479155
$461$	16048.9	1.62141	0.810706	−	0.585454i	$-0.199084\pi$
$461$	16048.9	1.62141	0.810706	+	0.585454i	$0.199084\pi$
$462$	−5477.48	−0.551592
$463$	−4939.72	−0.495827	−0.247914	−	0.968782i	$-0.579745\pi$
$463$	−4939.72	−0.495827	−0.247914	+	0.968782i	$0.579745\pi$
$464$	−8670.45	−0.867490
$465$	−18456.8	−1.84068
$466$	−16882.2	−1.67823
$467$	−18954.5	−1.87818	−0.939088	−	0.343678i	$-0.888327\pi$
$467$	−18954.5	−1.87818	−0.939088	+	0.343678i	$0.888327\pi$
$468$	−180.120	−0.0177907
$469$	−3200.40	−0.315097
$470$	14148.0	1.38851
$471$	−5186.99	−0.507439
$472$	6121.71	0.596980
$473$	0	0
$474$	10623.0	1.02939
$475$	−1753.74	−0.169405
$476$	−1810.78	−0.174363
$477$	−2778.80	−0.266735
$478$	−11596.8	−1.10968
$479$	−883.498	−0.0842757	−0.0421379	−	0.999112i	$-0.513417\pi$
$479$	−883.498	−0.0842757	−0.0421379	+	0.999112i	$0.513417\pi$
$480$	8958.19	0.851841
$481$	217.863	0.0206521
$482$	−10930.1	−1.03289
$483$	−7356.76	−0.693052
$484$	−1899.71	−0.178410
$485$	13500.2	1.26395
$486$	6171.96	0.576061
$487$	−16551.1	−1.54005	−0.770024	−	0.638014i	$-0.779756\pi$
$487$	−16551.1	−1.54005	−0.770024	+	0.638014i	$0.779756\pi$
$488$	−6181.23	−0.573383
$489$	12701.2	1.17458
$490$	8573.57	0.790438
$491$	8570.89	0.787778	0.393889	−	0.919158i	$-0.371129\pi$
$491$	8570.89	0.787778	0.393889	+	0.919158i	$0.371129\pi$
$492$	−6603.98	−0.605143
$493$	−5598.02	−0.511404
$494$	2203.61	0.200699
$495$	1907.69	0.173221
$496$	24879.9	2.25230
$497$	−7634.87	−0.689076
$498$	−24921.9	−2.24253
$499$	1749.79	0.156977	0.0784884	−	0.996915i	$-0.474991\pi$
$499$	1749.79	0.156977	0.0784884	+	0.996915i	$0.474991\pi$
$500$	−5325.34	−0.476313
$501$	−2476.40	−0.220833
$502$	72.1190	0.00641201
$503$	−12263.4	−1.08707	−0.543535	−	0.839387i	$-0.682914\pi$
$503$	−12263.4	−1.08707	−0.543535	+	0.839387i	$0.682914\pi$
$504$	974.812	0.0861539
$505$	−3676.58	−0.323972
$506$	12445.5	1.09342
$507$	−12398.4	−1.08606
$508$	−4349.19	−0.379850
$509$	−6076.70	−0.529165	−0.264582	−	0.964363i	$-0.585234\pi$
$509$	−6076.70	−0.529165	−0.264582	+	0.964363i	$0.585234\pi$
$510$	10384.8	0.901661
$511$	−5764.52	−0.499036
$512$	−2469.48	−0.213157
$513$	−10044.9	−0.864505
$514$	−2822.03	−0.242168
$515$	−18612.5	−1.59256
$516$	0	0
$517$	−11513.6	−0.979431
$518$	954.649	0.0809747
$519$	18570.1	1.57059
$520$	−1171.44	−0.0987906
$521$	499.594	0.0420108	0.0210054	−	0.999779i	$-0.493313\pi$
$521$	499.594	0.0420108	0.0210054	+	0.999779i	$0.493313\pi$
$522$	−2440.01	−0.204591
$523$	10780.9	0.901369	0.450685	−	0.892683i	$-0.351180\pi$
$523$	10780.9	0.901369	0.450685	+	0.892683i	$0.351180\pi$
$524$	7983.52	0.665576
$525$	−1174.70	−0.0976539
$526$	3081.24	0.255416
$527$	16063.5	1.32778
$528$	−13089.4	−1.07887
$529$	4548.42	0.373832
$530$	14632.5	1.19923
$531$	2686.44	0.219551
$532$	2984.76	0.243244
$533$	2426.39	0.197183
$534$	−833.223	−0.0675227
$535$	−5280.86	−0.426750
$536$	−4904.43	−0.395222
$537$	−11956.7	−0.960839
$538$	3734.94	0.299302
$539$	−6977.10	−0.557560
$540$	−4323.47	−0.344542
$541$	13009.0	1.03383	0.516913	−	0.856038i	$-0.327081\pi$
$541$	13009.0	1.03383	0.516913	+	0.856038i	$0.327081\pi$
$542$	−1977.37	−0.156707
$543$	11639.6	0.919893
$544$	−7796.58	−0.614477
$545$	7137.81	0.561010
$546$	1476.04	0.115693
$547$	−6072.16	−0.474638	−0.237319	−	0.971432i	$-0.576269\pi$
$547$	−6072.16	−0.474638	−0.237319	+	0.971432i	$0.576269\pi$
$548$	10219.2	0.796612
$549$	−2712.56	−0.210873
$550$	1987.25	0.154067
$551$	9227.38	0.713430
$552$	−11273.8	−0.869286
$553$	−5286.62	−0.406528
$554$	13200.3	1.01233
$555$	−1692.35	−0.129435
$556$	9783.46	0.746243
$557$	559.821	0.0425859	0.0212930	−	0.999773i	$-0.493222\pi$
$557$	559.821	0.0425859	0.0212930	+	0.999773i	$0.493222\pi$
$558$	7001.63	0.531188
$559$	0	0
$560$	−8004.52	−0.604023
$561$	−8451.07	−0.636015
$562$	18623.5	1.39784
$563$	3939.23	0.294883	0.147441	−	0.989071i	$-0.452896\pi$
$563$	3939.23	0.294883	0.147441	+	0.989071i	$0.452896\pi$
$564$	−8444.47	−0.630454
$565$	−9631.97	−0.717204
$566$	−8663.64	−0.643392
$567$	−8477.97	−0.627939
$568$	−11700.0	−0.864298
$569$	6624.73	0.488090	0.244045	−	0.969764i	$-0.421526\pi$
$569$	6624.73	0.488090	0.244045	+	0.969764i	$0.421526\pi$
$570$	−17117.6	−1.25785
$571$	2837.72	0.207977	0.103989	−	0.994578i	$-0.466839\pi$
$571$	2837.72	0.207977	0.103989	+	0.994578i	$0.466839\pi$
$572$	−771.857	−0.0564213
$573$	−2585.64	−0.188511
$574$	10632.1	0.773131
$575$	2669.06	0.193579
$576$	817.263	0.0591191
$577$	16764.3	1.20954	0.604772	−	0.796399i	$-0.293264\pi$
$577$	16764.3	1.20954	0.604772	+	0.796399i	$0.293264\pi$
$578$	7679.92	0.552669
$579$	15444.5	1.10855
$580$	3971.62	0.284332
$581$	12402.6	0.885619
$582$	−26067.7	−1.85660
$583$	−11907.8	−0.845918
$584$	−8833.81	−0.625934
$585$	−514.073	−0.0363322
$586$	−16154.0	−1.13876
$587$	4528.39	0.318410	0.159205	−	0.987246i	$-0.449107\pi$
$587$	4528.39	0.318410	0.159205	+	0.987246i	$0.449107\pi$
$588$	−5117.26	−0.358899
$589$	−26478.0	−1.85231
$590$	−14146.1	−0.987097
$591$	2262.67	0.157486
$592$	2281.30	0.158380
$593$	11498.0	0.796235	0.398117	−	0.917334i	$-0.369664\pi$
$593$	11498.0	0.796235	0.398117	+	0.917334i	$0.369664\pi$
$594$	11382.3	0.786234
$595$	−5168.06	−0.356084
$596$	5005.65	0.344026
$597$	11018.7	0.755388
$598$	−3353.73	−0.229338
$599$	21198.2	1.44597	0.722986	−	0.690863i	$-0.242769\pi$
$599$	21198.2	1.44597	0.722986	+	0.690863i	$0.242769\pi$
$600$	−1800.17	−0.122486
$601$	25502.1	1.73087	0.865435	−	0.501021i	$-0.167042\pi$
$601$	25502.1	1.73087	0.865435	+	0.501021i	$0.167042\pi$
$602$	0	0
$603$	−2152.25	−0.145351
$604$	−4506.00	−0.303554
$605$	−5421.88	−0.364349
$606$	7099.14	0.475880
$607$	19290.1	1.28989	0.644943	−	0.764231i	$-0.276881\pi$
$607$	19290.1	1.28989	0.644943	+	0.764231i	$0.276881\pi$
$608$	12851.3	0.857222
$609$	6180.76	0.411259
$610$	14283.7	0.948080
$611$	3102.60	0.205430
$612$	−1217.74	−0.0804318
$613$	−18738.7	−1.23467	−0.617333	−	0.786702i	$-0.711787\pi$
$613$	−18738.7	−1.23467	−0.617333	+	0.786702i	$0.711787\pi$
$614$	−6536.29	−0.429614
$615$	−18848.1	−1.23582
$616$	4177.29	0.273227
$617$	−15477.2	−1.00987	−0.504933	−	0.863158i	$-0.668483\pi$
$617$	−15477.2	−1.00987	−0.504933	+	0.863158i	$0.668483\pi$
$618$	35939.1	2.33929
$619$	16940.7	1.10001	0.550003	−	0.835163i	$-0.314626\pi$
$619$	16940.7	1.10001	0.550003	+	0.835163i	$0.314626\pi$
$620$	−11396.6	−0.738222
$621$	15287.5	0.987870
$622$	−10837.7	−0.698634
$623$	414.659	0.0266661
$624$	3527.25	0.226287
$625$	−12618.3	−0.807569
$626$	−14334.8	−0.915228
$627$	13930.2	0.887268
$628$	−3202.82	−0.203513
$629$	1472.90	0.0933681
$630$	−2252.61	−0.142454
$631$	16474.8	1.03938	0.519691	−	0.854354i	$-0.326047\pi$
$631$	16474.8	1.03938	0.519691	+	0.854354i	$0.326047\pi$
$632$	−8101.44	−0.509902
$633$	−11589.4	−0.727706
$634$	29040.4	1.81915
$635$	−12412.8	−0.775728
$636$	−8733.61	−0.544513
$637$	1880.15	0.116945
$638$	−10456.0	−0.648837
$639$	−5134.41	−0.317863
$640$	−16666.7	−1.02939
$641$	14626.9	0.901291	0.450646	−	0.892703i	$-0.351194\pi$
$641$	14626.9	0.901291	0.450646	+	0.892703i	$0.351194\pi$
$642$	10196.9	0.626850
$643$	−26858.1	−1.64725	−0.823623	−	0.567138i	$-0.808051\pi$
$643$	−26858.1	−1.64725	−0.823623	+	0.567138i	$0.808051\pi$
$644$	−4542.59	−0.277955
$645$	0	0
$646$	14898.0	0.907356
$647$	1736.10	0.105492	0.0527459	−	0.998608i	$-0.483203\pi$
$647$	1736.10	0.105492	0.0527459	+	0.998608i	$0.483203\pi$
$648$	−12992.0	−0.787615
$649$	11512.0	0.696280
$650$	−535.513	−0.0323147
$651$	−17735.7	−1.06777
$652$	7842.66	0.471077
$653$	−29716.2	−1.78084	−0.890418	−	0.455143i	$-0.849588\pi$
$653$	−29716.2	−1.78084	−0.890418	+	0.455143i	$0.849588\pi$
$654$	−13782.5	−0.824063
$655$	22785.4	1.35924
$656$	25407.3	1.51218
$657$	−3876.61	−0.230200
$658$	13595.3	0.805468
$659$	−21289.5	−1.25846	−0.629228	−	0.777220i	$-0.716629\pi$
$659$	−21289.5	−1.25846	−0.629228	+	0.777220i	$0.716629\pi$
$660$	5995.77	0.353614
$661$	−24511.8	−1.44236	−0.721179	−	0.692748i	$-0.756400\pi$
$661$	−24511.8	−1.44236	−0.721179	+	0.692748i	$0.756400\pi$
$662$	−17487.8	−1.02671
$663$	2277.34	0.133401
$664$	19006.2	1.11082
$665$	8518.68	0.496752
$666$	641.997	0.0373527
$667$	−14043.4	−0.815236
$668$	−1529.11	−0.0885673
$669$	30974.3	1.79004
$670$	11333.2	0.653494
$671$	−11623.9	−0.668759
$672$	8608.18	0.494149
$673$	15488.4	0.887126	0.443563	−	0.896243i	$-0.353714\pi$
$673$	15488.4	0.887126	0.443563	+	0.896243i	$0.353714\pi$
$674$	−229.986	−0.0131435
$675$	2441.06	0.139195
$676$	−7655.69	−0.435576
$677$	10103.5	0.573575	0.286787	−	0.957994i	$-0.407413\pi$
$677$	10103.5	0.573575	0.286787	+	0.957994i	$0.407413\pi$
$678$	18598.5	1.05349
$679$	12972.8	0.733209
$680$	−7919.77	−0.446631
$681$	36885.2	2.07554
$682$	30003.6	1.68460
$683$	−16097.1	−0.901815	−0.450908	−	0.892571i	$-0.648900\pi$
$683$	−16097.1	−0.901815	−0.450908	+	0.892571i	$0.648900\pi$
$684$	2007.24	0.112206
$685$	29166.2	1.62684
$686$	19695.9	1.09620
$687$	−12719.3	−0.706365
$688$	0	0
$689$	3208.84	0.177427
$690$	26051.7	1.43735
$691$	−5437.66	−0.299361	−0.149680	−	0.988734i	$-0.547824\pi$
$691$	−5437.66	−0.299361	−0.149680	+	0.988734i	$0.547824\pi$
$692$	11466.5	0.629901
$693$	1833.16	0.100485
$694$	−30184.7	−1.65100
$695$	27922.5	1.52397
$696$	9471.66	0.515837
$697$	16404.1	0.891461
$698$	−35463.1	−1.92306
$699$	28758.6	1.55615
$700$	−725.347	−0.0391650
$701$	−15106.3	−0.813917	−0.406959	−	0.913447i	$-0.633411\pi$
$701$	−15106.3	−0.813917	−0.406959	+	0.913447i	$0.633411\pi$
$702$	−3067.24	−0.164908
$703$	−2427.83	−0.130252
$704$	3502.16	0.187489
$705$	−24101.0	−1.28751
$706$	22327.4	1.19023
$707$	−3532.93	−0.187934
$708$	8443.33	0.448192
$709$	34192.9	1.81120	0.905601	−	0.424130i	$-0.139420\pi$
$709$	34192.9	1.81120	0.905601	+	0.424130i	$0.139420\pi$
$710$	27036.6	1.42910
$711$	−3555.22	−0.187526
$712$	635.441	0.0334469
$713$	40297.6	2.11663
$714$	9979.06	0.523049
$715$	−2202.92	−0.115223
$716$	−7382.94	−0.385354
$717$	19755.0	1.02896
$718$	32866.8	1.70833
$719$	3683.18	0.191042	0.0955212	−	0.995427i	$-0.469548\pi$
$719$	3683.18	0.191042	0.0955212	+	0.995427i	$0.469548\pi$
$720$	−5383.00	−0.278628
$721$	−17885.3	−0.923834
$722$	−1216.71	−0.0627165
$723$	18619.3	0.957757
$724$	7187.11	0.368932
$725$	−2242.41	−0.114870
$726$	10469.2	0.535189
$727$	4535.82	0.231395	0.115698	−	0.993284i	$-0.463090\pi$
$727$	4535.82	0.231395	0.115698	+	0.993284i	$0.463090\pi$
$728$	−1125.67	−0.0573079
$729$	12805.0	0.650560
$730$	20413.3	1.03497
$731$	0	0
$732$	−8525.42	−0.430476
$733$	3566.62	0.179722	0.0898609	−	0.995954i	$-0.471358\pi$
$733$	3566.62	0.179722	0.0898609	+	0.995954i	$0.471358\pi$
$734$	−20574.2	−1.03462
$735$	−14604.9	−0.732941
$736$	−19558.8	−0.979547
$737$	−9222.90	−0.460963
$738$	7150.06	0.356636
$739$	10852.7	0.540223	0.270111	−	0.962829i	$-0.412939\pi$
$739$	10852.7	0.540223	0.270111	+	0.962829i	$0.412939\pi$
$740$	−1044.98	−0.0519111
$741$	−3753.81	−0.186100
$742$	14060.8	0.695670
$743$	−10757.2	−0.531148	−0.265574	−	0.964090i	$-0.585561\pi$
$743$	−10757.2	−0.531148	−0.265574	+	0.964090i	$0.585561\pi$
$744$	−27179.0	−1.33929
$745$	14286.4	0.702568
$746$	24355.3	1.19532
$747$	8340.66	0.408526
$748$	−5218.30	−0.255080
$749$	−5074.53	−0.247556
$750$	29347.5	1.42883
$751$	37615.8	1.82772	0.913862	−	0.406025i	$-0.133086\pi$
$751$	37615.8	1.82772	0.913862	+	0.406025i	$0.133086\pi$
$752$	32488.2	1.57543
$753$	−122.854	−0.00594560
$754$	2817.63	0.136090
$755$	−12860.4	−0.619916
$756$	−4154.55	−0.199867
$757$	82.3414	0.00395343	0.00197672	−	0.999998i	$-0.499371\pi$
$757$	82.3414	0.00395343	0.00197672	+	0.999998i	$0.499371\pi$
$758$	21271.4	1.01927
$759$	−21200.7	−1.01388
$760$	13054.4	0.623069
$761$	−11883.8	−0.566081	−0.283041	−	0.959108i	$-0.591343\pi$
$761$	−11883.8	−0.566081	−0.283041	+	0.959108i	$0.591343\pi$
$762$	23968.0	1.13946
$763$	6858.93	0.325439
$764$	−1596.56	−0.0756041
$765$	−3475.50	−0.164257
$766$	25177.5	1.18760
$767$	−3102.19	−0.146041
$768$	26440.9	1.24232
$769$	33767.0	1.58344	0.791722	−	0.610881i	$-0.209185\pi$
$769$	33767.0	1.58344	0.791722	+	0.610881i	$0.209185\pi$
$770$	−9652.95	−0.451777
$771$	4807.29	0.224553
$772$	9536.54	0.444595
$773$	−13668.1	−0.635976	−0.317988	−	0.948095i	$-0.603007\pi$
$773$	−13668.1	−0.635976	−0.317988	+	0.948095i	$0.603007\pi$
$774$	0	0
$775$	6434.59	0.298242
$776$	19880.0	0.919654
$777$	−1626.23	−0.0750845
$778$	8405.05	0.387321
$779$	−27039.3	−1.24363
$780$	−1615.70	−0.0741686
$781$	−22002.1	−1.00806
$782$	−22673.6	−1.03684
$783$	−12843.8	−0.586205
$784$	19687.5	0.896844
$785$	−9141.01	−0.415614
$786$	−43996.5	−1.99657
$787$	21140.3	0.957521	0.478760	−	0.877946i	$-0.341086\pi$
$787$	21140.3	0.957521	0.478760	+	0.877946i	$0.341086\pi$
$788$	1397.14	0.0631611
$789$	−5248.85	−0.236836
$790$	18720.9	0.843115
$791$	−9255.64	−0.416046
$792$	2809.21	0.126036
$793$	3132.35	0.140268
$794$	8293.60	0.370691
$795$	−24926.2	−1.11200
$796$	6803.76	0.302956
$797$	−5253.82	−0.233500	−0.116750	−	0.993161i	$-0.537248\pi$
$797$	−5253.82	−0.233500	−0.116750	+	0.993161i	$0.537248\pi$
$798$	−16448.8	−0.729675
$799$	20975.8	0.928748
$800$	−3123.09	−0.138022
$801$	278.856	0.0123007
$802$	46020.4	2.02623
$803$	−16612.2	−0.730051
$804$	−6764.41	−0.296719
$805$	−12964.8	−0.567639
$806$	−8085.19	−0.353336
$807$	−6362.41	−0.277531
$808$	−5414.02	−0.235723
$809$	−20082.2	−0.872747	−0.436373	−	0.899766i	$-0.643737\pi$
$809$	−20082.2	−0.872747	−0.436373	+	0.899766i	$0.643737\pi$
$810$	30022.1	1.30231
$811$	−8541.65	−0.369837	−0.184918	−	0.982754i	$-0.559202\pi$
$811$	−8541.65	−0.369837	−0.184918	+	0.982754i	$0.559202\pi$
$812$	3816.44	0.164939
$813$	3368.42	0.145308
$814$	2751.10	0.118460
$815$	22383.4	0.962031
$816$	23846.7	1.02304
$817$	0	0
$818$	35404.8	1.51333
$819$	−493.988	−0.0210761
$820$	−11638.2	−0.495638
$821$	−28778.2	−1.22334	−0.611671	−	0.791112i	$-0.709503\pi$
$821$	−28778.2	−1.22334	−0.611671	+	0.791112i	$0.709503\pi$
$822$	−56317.2	−2.38965
$823$	16760.9	0.709902	0.354951	−	0.934885i	$-0.384498\pi$
$823$	16760.9	0.709902	0.354951	+	0.934885i	$0.384498\pi$
$824$	−27408.3	−1.15875
$825$	−3385.26	−0.142860
$826$	−13593.4	−0.572610
$827$	−4293.62	−0.180537	−0.0902683	−	0.995917i	$-0.528772\pi$
$827$	−4293.62	−0.180537	−0.0902683	+	0.995917i	$0.528772\pi$
$828$	−3054.87	−0.128217
$829$	−18065.0	−0.756842	−0.378421	−	0.925634i	$-0.623533\pi$
$829$	−18065.0	−0.756842	−0.378421	+	0.925634i	$0.623533\pi$
$830$	−43919.9	−1.83672
$831$	−22486.6	−0.938689
$832$	−943.740	−0.0393249
$833$	12711.1	0.528708
$834$	−53915.8	−2.23855
$835$	−4364.15	−0.180872
$836$	8601.48	0.355847
$837$	36855.2	1.52199
$838$	3481.66	0.143523
$839$	32031.9	1.31807	0.659037	−	0.752111i	$-0.270964\pi$
$839$	32031.9	1.31807	0.659037	+	0.752111i	$0.270964\pi$
$840$	8744.19	0.359171
$841$	−12590.5	−0.516236
$842$	35583.9	1.45642
$843$	−31724.8	−1.29616
$844$	−7156.14	−0.291854
$845$	−21849.7	−0.889531
$846$	9142.74	0.371553
$847$	−5210.04	−0.211357
$848$	33600.6	1.36067
$849$	14758.4	0.596591
$850$	−3620.45	−0.146094
$851$	3694.98	0.148839
$852$	−16137.2	−0.648885
$853$	16554.1	0.664480	0.332240	−	0.943195i	$-0.392196\pi$
$853$	16554.1	0.664480	0.332240	+	0.943195i	$0.392196\pi$
$854$	13725.6	0.549976
$855$	5728.77	0.229146
$856$	−7776.42	−0.310506
$857$	−33956.3	−1.35347	−0.676735	−	0.736226i	$-0.736606\pi$
$857$	−33956.3	−1.35347	−0.676735	+	0.736226i	$0.736606\pi$
$858$	4253.64	0.169250
$859$	27129.3	1.07758	0.538789	−	0.842441i	$-0.318882\pi$
$859$	27129.3	1.07758	0.538789	+	0.842441i	$0.318882\pi$
$860$	0	0
$861$	−18111.7	−0.716893
$862$	26420.7	1.04396
$863$	−35639.0	−1.40575	−0.702877	−	0.711311i	$-0.748102\pi$
$863$	−35639.0	−1.40575	−0.702877	+	0.711311i	$0.748102\pi$
$864$	−17888.0	−0.704355
$865$	32726.0	1.28638
$866$	11190.5	0.439110
$867$	−13082.6	−0.512467
$868$	−10951.3	−0.428239
$869$	−15234.9	−0.594718
$870$	−21887.3	−0.852928
$871$	2485.33	0.0966845
$872$	10510.9	0.408193
$873$	8724.12	0.338221
$874$	37373.6	1.44643
$875$	−14605.0	−0.564272
$876$	−12184.0	−0.469930
$877$	−50359.2	−1.93901	−0.969503	−	0.245077i	$-0.921187\pi$
$877$	−50359.2	−1.93901	−0.969503	+	0.245077i	$0.921187\pi$
$878$	−28329.4	−1.08892
$879$	27518.1	1.05593
$880$	−23067.4	−0.883638
$881$	−7692.34	−0.294167	−0.147084	−	0.989124i	$-0.546989\pi$
$881$	−7692.34	−0.294167	−0.147084	+	0.989124i	$0.546989\pi$
$882$	5540.41	0.211514
$883$	33633.6	1.28184	0.640918	−	0.767610i	$-0.278554\pi$
$883$	33633.6	1.28184	0.640918	+	0.767610i	$0.278554\pi$
$884$	1406.19	0.0535016
$885$	24097.7	0.915295
$886$	5370.52	0.203641
$887$	7996.52	0.302702	0.151351	−	0.988480i	$-0.451638\pi$
$887$	7996.52	0.302702	0.151351	+	0.988480i	$0.451638\pi$
$888$	−2492.11	−0.0941775
$889$	−11927.8	−0.449996
$890$	−1468.39	−0.0553039
$891$	−24431.8	−0.918625
$892$	19125.8	0.717913
$893$	−34575.0	−1.29564
$894$	−27585.7	−1.03200
$895$	−21071.3	−0.786967
$896$	−16015.5	−0.597144
$897$	5713.03	0.212656
$898$	36743.4	1.36541
$899$	−33855.9	−1.25601
$900$	−487.792	−0.0180664
$901$	21694.0	0.802144
$902$	30639.7	1.13103
$903$	0	0
$904$	−14183.7	−0.521841
$905$	20512.4	0.753431
$906$	24832.2	0.910590
$907$	33.0507	0.00120996	0.000604979	−	1.00000i	$-0.499807\pi$
$907$	33.0507	0.00120996	0.000604979		1.00000i	$0.499807\pi$
$908$	22775.6	0.832416
$909$	−2375.88	−0.0866919
$910$	2601.22	0.0947578
$911$	−38258.1	−1.39138	−0.695690	−	0.718342i	$-0.744901\pi$
$911$	−38258.1	−1.39138	−0.695690	+	0.718342i	$0.744901\pi$
$912$	−39307.2	−1.42718
$913$	35741.6	1.29559
$914$	37416.8	1.35409
$915$	−24332.0	−0.879116
$916$	−7853.83	−0.283294
$917$	21895.1	0.788486
$918$	−20736.7	−0.745549
$919$	35847.6	1.28673	0.643364	−	0.765560i	$-0.277538\pi$
$919$	35847.6	1.28673	0.643364	+	0.765560i	$0.277538\pi$
$920$	−19867.8	−0.711981
$921$	11134.5	0.398364
$922$	−54611.7	−1.95069
$923$	5929.00	0.211436
$924$	5761.51	0.205130
$925$	590.003	0.0209721
$926$	16809.0	0.596522
$927$	−12027.8	−0.426154
$928$	16432.3	0.581266
$929$	−15077.8	−0.532493	−0.266247	−	0.963905i	$-0.585784\pi$
$929$	−15077.8	−0.532493	−0.266247	+	0.963905i	$0.585784\pi$
$930$	62805.6	2.21449
$931$	−20952.1	−0.737570
$932$	17757.6	0.624110
$933$	18461.8	0.647815
$934$	64498.9	2.25960
$935$	−14893.3	−0.520923
$936$	−757.008	−0.0264355
$937$	37719.4	1.31509	0.657546	−	0.753415i	$-0.271595\pi$
$937$	37719.4	1.31509	0.657546	+	0.753415i	$0.271595\pi$
$938$	10890.4	0.379089
$939$	24419.0	0.848653
$940$	−14881.7	−0.516368
$941$	54768.8	1.89736	0.948678	−	0.316244i	$-0.102422\pi$
$941$	54768.8	1.89736	0.948678	+	0.316244i	$0.102422\pi$
$942$	17650.5	0.610491
$943$	41151.9	1.42109
$944$	−32483.8	−1.11998
$945$	−11857.3	−0.408167
$946$	0	0
$947$	17166.1	0.589043	0.294521	−	0.955645i	$-0.404840\pi$
$947$	17166.1	0.589043	0.294521	+	0.955645i	$0.404840\pi$
$948$	−11173.9	−0.382817
$949$	4476.55	0.153124
$950$	5967.69	0.203808
$951$	−49469.8	−1.68682
$952$	−7610.33	−0.259088
$953$	54233.3	1.84343	0.921714	−	0.387869i	$-0.126789\pi$
$953$	54233.3	1.84343	0.921714	+	0.387869i	$0.126789\pi$
$954$	9455.80	0.320904
$955$	−4556.67	−0.154398
$956$	12198.2	0.412675
$957$	17811.7	0.601640
$958$	3006.40	0.101391
$959$	28026.6	0.943719
$960$	7330.95	0.246464
$961$	67358.6	2.26104
$962$	−741.351	−0.0248463
$963$	−3412.59	−0.114194
$964$	11496.9	0.384118
$965$	27217.8	0.907950
$966$	25033.8	0.833800
$967$	−43616.5	−1.45048	−0.725239	−	0.688497i	$-0.758271\pi$
$967$	−43616.5	−1.45048	−0.725239	+	0.688497i	$0.758271\pi$
$968$	−7984.09	−0.265102
$969$	−25378.4	−0.841354
$970$	−45939.1	−1.52063
$971$	−496.832	−0.0164203	−0.00821015	−	0.999966i	$-0.502613\pi$
$971$	−496.832	−0.0164203	−0.00821015	+	0.999966i	$0.502613\pi$
$972$	−6492.00	−0.214229
$973$	26831.5	0.884049
$974$	56320.8	1.85281
$975$	912.238	0.0299641
$976$	32799.6	1.07571
$977$	−34433.2	−1.12755	−0.563775	−	0.825928i	$-0.690652\pi$
$977$	−34433.2	−1.12755	−0.563775	+	0.825928i	$0.690652\pi$
$978$	−43220.2	−1.41312
$979$	1194.96	0.0390103
$980$	−9018.14	−0.293953
$981$	4612.59	0.150121
$982$	−29165.3	−0.947763
$983$	−14959.5	−0.485386	−0.242693	−	0.970103i	$-0.578031\pi$
$983$	−14959.5	−0.485386	−0.242693	+	0.970103i	$0.578031\pi$
$984$	−27755.1	−0.899189
$985$	3987.50	0.128987
$986$	19049.1	0.615261
$987$	−23159.3	−0.746878
$988$	−2317.87	−0.0746371
$989$	0	0
$990$	−6491.56	−0.208399
$991$	8889.71	0.284955	0.142478	−	0.989798i	$-0.454493\pi$
$991$	8889.71	0.284955	0.142478	+	0.989798i	$0.454493\pi$
$992$	−47152.4	−1.50916
$993$	29790.3	0.952029
$994$	25980.2	0.829016
$995$	19418.3	0.618695
$996$	26214.2	0.833965
$997$	33159.9	1.05334	0.526672	−	0.850069i	$-0.323440\pi$
$997$	33159.9	1.05334	0.526672	+	0.850069i	$0.323440\pi$
$998$	−5954.25	−0.188856
$999$	3379.34	0.107025

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1849.4.a.k.1.16		60
43.20	odd	42		43.4.g.a.13.3	yes	120
43.28	odd	42		43.4.g.a.10.3	✓	120
43.42	odd	2		1849.4.a.l.1.45		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.g.a.10.3	✓	120	43.28	odd	42
43.4.g.a.13.3	yes	120	43.20	odd	42
1849.4.a.k.1.16		60	1.1	even	1	trivial
1849.4.a.l.1.45		60	43.42	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:	\( N \)	\(=\)	\( 1849 = 43^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1849.a (trivial)

\(f(q)\)	\(=\)	\(q-3.40283 q^{2} +5.79667 q^{3} +3.57928 q^{4} +10.2155 q^{5} -19.7251 q^{6} +9.81633 q^{7} +15.0430 q^{8} +6.60143 q^{9} +O(q^{10})\)	\(q-3.40283 q^{2} +5.79667 q^{3} +3.57928 q^{4} +10.2155 q^{5} -19.7251 q^{6} +9.81633 q^{7} +15.0430 q^{8} +6.60143 q^{9} -34.7615 q^{10} +28.2886 q^{11} +20.7479 q^{12} -7.62305 q^{13} -33.4033 q^{14} +59.2157 q^{15} -79.8230 q^{16} -51.5372 q^{17} -22.4636 q^{18} +84.9503 q^{19} +36.5640 q^{20} +56.9021 q^{21} -96.2616 q^{22} -129.288 q^{23} +87.1992 q^{24} -20.6443 q^{25} +25.9400 q^{26} -118.244 q^{27} +35.1354 q^{28} +108.621 q^{29} -201.501 q^{30} -311.688 q^{31} +151.281 q^{32} +163.980 q^{33} +175.372 q^{34} +100.278 q^{35} +23.6284 q^{36} -28.5795 q^{37} -289.072 q^{38} -44.1883 q^{39} +153.671 q^{40} -318.296 q^{41} -193.628 q^{42} +101.253 q^{44} +67.4367 q^{45} +439.946 q^{46} -407.003 q^{47} -462.708 q^{48} -246.640 q^{49} +70.2492 q^{50} -298.744 q^{51} -27.2851 q^{52} -420.939 q^{53} +402.364 q^{54} +288.982 q^{55} +147.667 q^{56} +492.429 q^{57} -369.619 q^{58} +406.948 q^{59} +211.950 q^{60} -410.905 q^{61} +1060.62 q^{62} +64.8018 q^{63} +123.801 q^{64} -77.8730 q^{65} -557.997 q^{66} -326.028 q^{67} -184.466 q^{68} -749.441 q^{69} -341.231 q^{70} -777.772 q^{71} +99.3051 q^{72} -587.238 q^{73} +97.2512 q^{74} -119.668 q^{75} +304.061 q^{76} +277.691 q^{77} +150.366 q^{78} -538.553 q^{79} -815.429 q^{80} -863.660 q^{81} +1083.11 q^{82} +1263.46 q^{83} +203.669 q^{84} -526.476 q^{85} +629.640 q^{87} +425.545 q^{88} +42.2417 q^{89} -229.476 q^{90} -74.8304 q^{91} -462.759 q^{92} -1806.76 q^{93} +1384.96 q^{94} +867.807 q^{95} +876.925 q^{96} +1321.55 q^{97} +839.274 q^{98} +186.746 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9}+O(q^{10}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9	\( 60 q - 15 q^{2} - 37 q^{3} + 213 q^{4} - 51 q^{5} + 22 q^{6} - 54 q^{7} - 204 q^{8} + 387 q^{9} + 27 q^{10} + 43 q^{11} - 432 q^{12} + 13 q^{13} + 96 q^{14} + 65 q^{15} + 717 q^{16} - 138 q^{17} - 625 q^{18} - 610 q^{19} - 345 q^{20} + 611 q^{21} - 118 q^{22} - 243 q^{23} + 258 q^{24} + 899 q^{25} - 1071 q^{26} - 1609 q^{27} - 46 q^{28} - 773 q^{29} - 375 q^{30} - 97 q^{31} - 1967 q^{32} - 500 q^{33} - 217 q^{34} + 247 q^{35} + 175 q^{36} - 228 q^{37} + 1253 q^{38} - 1493 q^{39} + 2220 q^{40} - 951 q^{41} - 2643 q^{42} - 1378 q^{44} - 1086 q^{45} + 565 q^{46} - 2 q^{47} - 2303 q^{48} + 1264 q^{49} - 3273 q^{50} - 3076 q^{51} - 2825 q^{52} - 39 q^{53} + 5201 q^{54} - 1306 q^{55} + 3683 q^{56} + 1342 q^{57} + 2588 q^{58} - 1065 q^{59} + 2803 q^{60} - 2999 q^{61} - 5569 q^{62} - 2377 q^{63} + 2082 q^{64} - 5578 q^{65} + 3338 q^{66} + 961 q^{67} - 3754 q^{68} - 1817 q^{69} - 2738 q^{70} - 8003 q^{71} - 1412 q^{72} + 1011 q^{73} - 1413 q^{74} - 7457 q^{75} - 5516 q^{76} - 4052 q^{77} + 1091 q^{78} - 4422 q^{79} - 1610 q^{80} + 2108 q^{81} - 4676 q^{82} - 297 q^{83} - 54 q^{84} - 4333 q^{85} + 1377 q^{87} - 3652 q^{88} - 2480 q^{89} - 1414 q^{90} - 4551 q^{91} - 3286 q^{92} - 4 q^{93} - 4609 q^{94} - 835 q^{95} + 5864 q^{96} + 3785 q^{97} - 753 q^{98} + 5072 q^{99}+O(q^{100}) \) 60 * q - 15 * q^2 - 37 * q^3 + 213 * q^4 - 51 * q^5 + 22 * q^6 - 54 * q^7 - 204 * q^8 + 387 * q^9 + 27 * q^10 + 43 * q^11 - 432 * q^12 + 13 * q^13 + 96 * q^14 + 65 * q^15 + 717 * q^16 - 138 * q^17 - 625 * q^18 - 610 * q^19 - 345 * q^20 + 611 * q^21 - 118 * q^22 - 243 * q^23 + 258 * q^24 + 899 * q^25 - 1071 * q^26 - 1609 * q^27 - 46 * q^28 - 773 * q^29 - 375 * q^30 - 97 * q^31 - 1967 * q^32 - 500 * q^33 - 217 * q^34 + 247 * q^35 + 175 * q^36 - 228 * q^37 + 1253 * q^38 - 1493 * q^39 + 2220 * q^40 - 951 * q^41 - 2643 * q^42 - 1378 * q^44 - 1086 * q^45 + 565 * q^46 - 2 * q^47 - 2303 * q^48 + 1264 * q^49 - 3273 * q^50 - 3076 * q^51 - 2825 * q^52 - 39 * q^53 + 5201 * q^54 - 1306 * q^55 + 3683 * q^56 + 1342 * q^57 + 2588 * q^58 - 1065 * q^59 + 2803 * q^60 - 2999 * q^61 - 5569 * q^62 - 2377 * q^63 + 2082 * q^64 - 5578 * q^65 + 3338 * q^66 + 961 * q^67 - 3754 * q^68 - 1817 * q^69 - 2738 * q^70 - 8003 * q^71 - 1412 * q^72 + 1011 * q^73 - 1413 * q^74 - 7457 * q^75 - 5516 * q^76 - 4052 * q^77 + 1091 * q^78 - 4422 * q^79 - 1610 * q^80 + 2108 * q^81 - 4676 * q^82 - 297 * q^83 - 54 * q^84 - 4333 * q^85 + 1377 * q^87 - 3652 * q^88 - 2480 * q^89 - 1414 * q^90 - 4551 * q^91 - 3286 * q^92 - 4 * q^93 - 4609 * q^94 - 835 * q^95 + 5864 * q^96 + 3785 * q^97 - 753 * q^98 + 5072 * q^99

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